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Cantata No.48, 'Ich elender Mensch': movement I-IV by Sebastian Bach Cantata Music Analysis

2013-05-10T10:06:00.000+01:00

Below is a complete analysis of the A2 Music baroque piece, Cantata No.48, 'Ich elender Mensch': movement I-IV which consists of Ich elender Mensch, Recitativo, Bach Chorale and Aria. Feel free to skip to the parts most relevant to you.

Be sure to check out the other A2 musical pieces and AS musical pieces I have analysed on Ask Will Online.

Ich elender Mensch

Introduction

The cantata was a piece of music written for a quiet orchestra or soloists for church services.
It is music for a biblical story based in protestant Germany.
It is like an oratorio. However, a cantata is a shorter version of an oratorio.

Texture

The texture has three layers: trumpet and two oboes, 1st violin melody choral parts with chordal string accompaniment and choral parts.
The piece is dominated by a contrapuntal texture - a texture Bach was good at composing in.
The entries of the Soprano and Tenor parts are imitative. The Tenor and Bass parts enter just over a bar later at the end of bar 14 with the notes a fourth lower than the Soprano and Alto parts.
At bars 31-44, the four part choir has imitative entries.
A contrapuntal texture appears at the end from the Trumpet part adding an additional part in bars 127-130.

Harmony

There is the use of diminished chords. This helps to modulate the piece intensifying the musical expression.
The ritornello moves to an expected cadence from the four falling bars of 9-12.
The of Section A features a tierce de picardie from adding a sharp to the F of the final chord of D major. A tierce de picardie is a technique used to finish a minor piece on a major chord.
There is the preparation for a final plagal cadence in G minor through the C minor chord appearing at bar 131. This is supported by a dominant pedal of C minor being a G (tonic pedal in G minor) during bars 131-138 in the Oboe part.
The piece finishes on another tierce de picardie naturalising the B in the G minor chord to make it a G major. The C minor chord before the tierce de picardie makes the end harmonisation a plagal cadence.

Tonality

The piece starts in G minor. This is clear from the key signature of B flat and E flat with F sharp accents appearing at bar 2.
Bar 41 modulates to the key of D minor.
The key changes back to G minor at bar 45.
The tonality at the start of Section 3 (bar 88 beat 3) features the tonality descending every 5th. It starts in D minor first, then modulates to G minor (bar 90), then C minor (bar 92) and finally F minor at bar 95.

Melody

Bars 1-12 is an orchestral ritornello (a short instrumental refrain).
There is a repeating two bar melody being bars 1-2. Each time repeated, it ascends in pitch until it descends back down to a cadence.
There is the use of appoggiaturas throughout the piece (mainly in the main Violin melody such as at bar 2 beat 1-2, bar 4, bar 6 and bar 8. An appoggiatura is an unprepared suspension.
The quaver moment of bar 2 Violin I/II features a rise of a 6th. This is similar to the choral motif.
The first time we hear the choral motif is at bars 13-14 being the G to Eb flat. This is a minor 6th leap.
The choral motif at bars 13-14 extends to a 7 bar melody which is when the opening melody of the quaver movement appears again. The two melodies are never played together.
The choral melody features in the Trumpet at bars 14-16. This is followed by a canon of the choral melody by the Oboe at bars 16-20 which plays at a perfect 4th lower.
The melody at bar 16 in the Soprano part is melismatic.
There are descending intervals in the soprano part in bars 18-19.
The translation of the german vocals is ‘Unhappy man that I am: who will deliver me from this deathly body?’.
The canon of bar 12 beat 3 reappears in the Trumpet at bars 56 beat 3 - 59.
The gap between melodies of the Soprano and Alto at bar 113 is an octave. The same octave gap re-appears too in the Tenor and Bass parts at bars 115-116.
The melody of the SATB at bars 114-120 is a continuation of a melody moving down in steps.

Rhythm and Metre

At bar 2 in the Violin I/II part, there is a rising quaver figure which is repeated three times.

The Viola Continuo features an chordal accompaniment at the start to accompany the Violin I/II melody. The chords are on the 3rd beat of bar 1 and 1st beat of bar 2. This helps to link other parts together.

The rhythm of a crochet at the end of a bar and start of the next bar is broken by the continuous crochet movement in the Viola Continuo part at bars 9-12.
At bars 42-43, the hemiola rhythms creates the impression of a change of meter from 3/4 to 3/2.

Structure

Section 1 is from bar 1-44 and is in G minor.
Bars 20-31 features another orchestral ritornello.
Section B starts at bar 45 and is back into the key of G minor. It is the near the same as Section A. However, this time, instead of the soprano and alto singing, it is tenor and bass.
Section 3 starts on the last beat of bar 88. This section features imitative choral entries which are a 5th lower than previous ones.
Section 4 starts at bar 114. The string ritornello in bars 108-113 creates a bridge between Section 3 finishing and Section 4 starting.

Recitativo

Introduction

This piece is a recitativo stromentato. This means it was not composed for music to words. Instead, it is words to music.
A recitativo stromento is an accompanied recitativo. The violins add to the accompaniment.
A recitativo is usually followed by an Aria.

Texture

The texture of the piece is homophonic with the melody being in the alto. The four part string is used as the accompaniment and harmony.

Harmony

The slow moving sustained chords makes the accompaniment from the strings very sparse.
There is a dominant 7th chord of A flat at bar 5 (A flat is the leading note of B flat minor).
A perfect cadence of V-I appears at bar 8 in B flat minor. The cadence is only in the strings. The next bar moves to a diminished 7th chord.
There is a dominant 7th chord of E major at bar 10 including the alto. The next bar’s chord is E major.
There is a diminished 7th chord on A sharp at bar 12 with the alto singing a G natural.
The third beat of bar 14 features a dominant 7th chord of E flat. Again, we cannot tell if it is major or minor.
The perfect cadence at the end fo the piece is only in the strings with a preparation chord of E natural before the cadence at the start of bar 15. The cadence is in B flat major. Therefore, there is a tierce de picardie.

Tonality

The piece starts in E flat major.
At bar 2, the piece moves to F minor.
At bar 3, the piece moves to C minor from the naturalised B and flattened A. (every bar brings a modulation. The tonality changes reflect the uneasy mood of the piece).
The D natural in the Violin I/II at bar 9 suggests a move back to E flat (major or minor: the third is not present).
AT bar 13, the key moves to G minor.

Melody

The melody is dictated by the recitative style.
The melody is fragmented due to the rhythm being dictated by the natural speech rhythm of the text. This means the instruments have to wait for the voice.
The melody has the use of tortuous intervals such as in the alto at bar 1 B flat - D flat.

Rhythm and Meter

With the piece being a recitativo stromento with words to music, it helps to create rhythms that reflect natural speak.
The rhythms are dictated by the recitative style.

Dynamics

There are no dynamics in the piece.

Structure

Section 1 starts the piece in E flat major.
There is not a specific structure.

Timbre

The piece features a four part homophonic accompaniment of two Violins, a Viola and Continuo bass as well as the alto with the melody.

Bach Chorale

Harmony

At the end of the piece, there is an extended plagal cadence of 1b (beat 1, bar 9), IV (beat 3, beat 9) and I (beat 1, bar 10). This can be seen clearly through the falling leading note at the end of bar 9 in the alto part.

Tonality

This chorale of Bach’s is chromatic.
The key suggests the piece is in in B flat major. However we are unsure due to its chromaticism.

Melody

The unexpected D flat at bar 2 in the bass part part makes the G in the soprano part a passing note.
The melody is conjunct motion moving in step.

Rhythm and Meter

The chorale is in simple quadruple time which uses mainly crotchets and quavers.

Structure

There are symbols above notes to end to mark the end of a phrase such as during beat three bar 4. However, this symbol (which usually means to lengthen a note) has no impact on the rhythmic flow of the music.

Timbre

Bach’s Chorale uses a thick texture with multiple instruments for the soprano, alto, tenor and bass parts such as Trumpets, Violins, Viola and Continuo bass.

Aria

The Aria is a solo song found in operas, oratorios and cantatas.

Texture

The Aria is in a three part texture.
The texture is thin and would have been filled by an organ producing harmonies from the figured bass notation.

Harmony

There is an imperfect cadence at bar 7.
There is an imperfect cadence at bar 16.
There is a cadence at bar 28 in B flat major.
At bars 78-79, there is a perfect cadence in E flat major (V-I).

Tonality

The piece starts in E flat major which is made clear from the key signature.
The first and second beat of bar 10 is in B flat major.
The third beat of bar 10 to second beat of bar 12 is in C minor.
Bars 13 - 14 are in B flat major.
Bars 20-21 are in F minor.
Bars 27-28 are in B flat major.
Bars 30 - 30.2 (second beat of bar 30) are in F minor.
Bars 34-37 are in B flat minor.
At the start of Section B, bars 49-50 are in C minor. The next two bars (bars 51-52) are in E flat major and the next four bars (bars 53-56) are in A flat major.
The piece at bar 60 is now in F minor. At bar 63, the key modulates to E flat major.
At bar 68, the key is F minor. It then modulates to A flat major at bar 72, B flat major at bar 74 and finally E flat major at bar 76. The rate of change of keys increases towards the end creating anticipation.

Melody

There is a Oboe ritornello from the start to bar 16 modulating to A flat major.
The melody of the alto at bars 20-21 features unexpected notes and intervals.
The melody is shared between the voice and Oboe (they are in counterpoint with each other).
There is an unexpected G flat in the alto part at the start of bar 27.
There is an Oboe ritornello during bars 39-48.
At the end of bar 60, the alto enters with the theme from the beginning of Section B.
At bar 65, the Oboe begins the restatement of its ritornello theme using the melody from the opening ritornello. The ritornello is adapted to fit with the alto and continuo parts.

Rhythm and Meter

The piece in in 3/8 (three quaver beats per bar).
The continuo has an uninterrupted succession of quavers in 3/8 time.
There is a variety of rhythmic patterns such as at bar 11 in the Oboe part.
The rhythmic patters of Section B are similar to Section A.

Structure

The piece starts with an introduction up to bar 16.
Section A starts at bar 16 which is an alto solo with Oboe obbligato and finishes at ar 48.
Section B starts at bar 48 and features an alto solo and Oboe obbligato.
The last bar of the piece features writing above it ‘D.C. al fine’. This means to go back to the beginning and finish when reached the ‘Fine’. The Fine is at bar 16.

Timbre

The piece uses an Alto voice, Oboe and bass continuo. The bass works on harmonising the piece while the Alto and Oboe are in counterpoint with each other.

Be sure to check out the other musical pieces I have analysed on Ask Will Online.

Johann Sebastian Bach Musical Biography

2013-05-10T09:38:00.000+01:00

Born: March 1685
Died: July 1750

Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist of the Baroque Period. Bach was more widely known for his ability as an organist. He was not widely known for being a great composer up until a revival of interest in his music in the early stages of the 19th century. Bach is now considered to be one of the greatest composers of all time.

Bach performed a cantata each Sunday. His cantatas varied greatly with some being for solo singers while others were for whole choruses. In total, he wrote over 300 sacred cantatas with 200 of them surviving. Many of his cantatas, at the end, featured an Aria (for soloists or duets) along with a concluding chorale. An example of such a cantata is ‘Ich elender Mensch’.

Bach produced a musical style from his skill of using a contrapuntal texture which is displayed clearly in ‘Ich elender Mensch’.

April 2013 - Ask Will Online's Stats From Google Analytics

2013-05-06T14:02:00.003+01:00

This month is going to be the last month before I start my exams. Therefore, you might not find that I analyse Ask Will Online's stats next month. Without further due, let's get right into analysing April's traffic!

Ask Will Online Stats (From Google Analytics) April 1st - May 1st

Visits - 16,583

This is an improvement of 1,500 which is great news. Pageviews can change every month. The number of visits does not normally. An improvement is a good start to this article!

Unfortunately, my bounce rate is 83.42% this month which means the bounce rate has increased nor decreased. The bounce rate is relatively high for Ask Will Online. Hopefully, it will naturally decrease next month when it is exam time for students.

Pageviews 22,927 therefore average pages per visit is 1.33

This is an increase in pageviews of 2,000 which is good and an increase of 0.08 fr average pages per visit. Is does annoy me though as I look at Blogger stats and they show this many pageviews:

That's nearly double what Analytics says! Ask Will Online has over 40,000 pageviews a month!

Search Engine Traffic - 78.4%

Interestingly enough, search engine traffic has decreased this month compared to last month by 3% and direct traffic has increased by 3%. More and more people must be bookmarking Ask Will Online which is great news! An audience is being built!

Charity

To sum up how well Ask Will Online has been making money in April:

January had a CTR of 0.46%.
February had a CTR of 0.59%.
March has a CTR of 0.79%.
April has a CTR of 0.74%.

It has always been a scare of mine that this increase, month by month, will stop and start to go down. However, it stayed pretty consistent which is really good news. Hopefully, it will increase next month.

Like every month, £15 will be donated equally to Teenage Cancer Trust, Help For Heroes and Dementia Research.

Key Gothic Themes & Elements From Frankenstein, Dr Faustus and The Bloody Chamber

2013-04-13T17:25:00.000+01:00

Below are the main Gothic themes and elements that are likely to be involved in English A2 LITB exam. To structure this article, I will highlight the main Gothic themes/elements at the start and then apply each theme or element to each individual literature text with quotes and evidence towards why that is a key theme or element in the text. Feel free to skip to the parts of the article most relevant to you.

Gothic Themes and Elements

The presence of a castle.
Dark settings such as dungeons, crypts, labyrinths and winding stairs.
Low lighting such as the candle being the only source of light, shadows, the moonlight against the dark sky etc.
Extreme landscapes such as rugged mountains, large forests or cold icy wastes with the addition of extreme weathers.
Magic and the supernatural.
Death, decay, darkness and madness.
A passion-driven, wilful villain-hero or villain.
A heroine with a tendency to faint and a need to be rescued, or a femme fatale.
A hero whose true identity is revealed by the end of the text.
Evil deeds leading to the downfall of a character.
Horrifying events or the threat of such happenings.
Gloom, mystery, suspense, the dramatic, macabre and sensational.

A Gothic novel is designed to be pleasurable terrifying - to thrill the reader with the fantastic and frightening events.

Frankenstein

Now, I will try to relate each theme/element of Gothic texts with the contents of Frankenstein.

A Castle - There is no castle in Frankenstein. The reason for Shelley leaving this out is most likely due to the plot of the story which features alot of chasing around and movement. Gothic texts that have castles in them, such as the first story of The Bloody Chamber, have the whole story set in the castle or based around the castle. A castle is used in Gothic texts when the setting is going to still the same throughout the text: unlike the setting in Frankenstein.

P97 'Ruined castles hanging over precipices of piny mountains'. Nature is strong enough to overpower man.

Dark Settings - There are lots of dark settings in Frankenstein. When the monster is created, Frankenstein describes how it was a, 'P58 on a dreary night of November'. This pathetic fallacy sets the scene for the start of chapter five which features the birth of the monster. It is a foreshadows the darkness to come further on in the novel.

P60 'black and comfortless sky' Massive pathetic fallacy is used here to make clear that what Frankenstein has done is wrong.
P170 'I sat one evening in my laboratory; the sun had set, and the moon was just rising from the sea'. This creates an echo/parallel construction to that of Chapter 5 (P58) with the dark setting of when the monster was originally created. This also creates the impression that if the setting is worst than a P58 'dreary night of November', the new creation might be even more evil than the first creation.
P71 'I saw, by the light of the moon, the daemon at the casement'. The moon is associated with the monster as being evil. Therefore, dark is evil.

The Effect of Low Lighting - This is used lots especially, again, on P58, 'my candle was nearly burnt out'. At this moment, light represents life and with the candle that is just about to be burnt out, it juxtaposes to what is about to happen (being the birth of the monster). This creates a negativity over the monster before he is even born. The low lighting of Frankenstein is made more apparent with the moon, 'P59 dim and yellow light of the moon'. The moon does not normally shine yellow but white or blue. Therefore, Shelley is making the connection between the moon and the monster seeing that the monster had 'P58 yellow skin'. This makes clear that the reader is meant to associate the monster with being something of darkness. If light represents life and heaven, then darkness represents death and hell. The moon is trying to be light, but it is tinted with the colour of death. The monster is alive, but it is tinted with death from the body parts used to make it and foreshadowing evilness.

P39 'The saintly soul of Elizabeth shone like a shrine dedicated lamp in our peaceful home'. Elizabeth is seen as a light in darkness.

Extreme Landscapes and Weather

The start of the novel has the setting as the North Pole: a strange unknown and weird area that is a place God could potentially be.
The remote setting of the North Pole creates a isolated and mysterious mood, (P25) 'surrounded by ice, which closed in the ship on all sides', 'thick fog', 'vast and irregular plains of ice', 'lost among the distant inequalities of the ice' and 'many hundred miles from any land'.
P42 'the thunder burst at once with frightful loudness from various quarters of the heavens'. The use of lightning will continually link to how Frankenstein created the monster: it was lightning that gave life to the monster. An AO4 point would be about Luigi Galvani who could have possibly been the motivation to include lightening as a way of creating life since Luigi used electricity to cause dead frog's legs to move.
P76 'Dear mountains! My own beautiful lake!' Frankenstein's negative emotions at this time cannot link with the landscape. This makes the landscape sublime as it makes the reader and Victor feel insignificant.
P97 'The immense mountains and precipices that overhung me on every side - the sound of the river raging among the rocks, and the dashing of the waterfalls around, spoke a power might of Omnipotence'. Omnipotence means 'all powerful' and is a word used to describe God. Victor is making the landscape sound immensely strong and powerful making it sublime. Shelley makes the setting seem sublime to Frankenstein to make it seem like the watchful eye of God is looking down on him. However, Victor goes to the mountains to cleanse his guilt P100 'It had then filled me with a sublime ecstasy, that gave wings to the soul, and allowed it to soar from the obscure world to light and joy'.
P140 'a fierce wind'. This represents the vengeance of the monster.
P168 'With this resolution I traversed the northern highlands, and fixed one of the remotest of the Orkneys as the scene of my labours. It was a place fitted for such a word, being hardly more than a rock, whose high sides were continually beaten upon by the waves'. This is the epitome of a Gothic setting. The setting is like this because Victor is ashamed of creating another creature like the monster. At first, he was doing it for the greater good of science. Now, he is doing it for the monster.
At Chapter 7 Volume 3 (P205), Victory moves further North away from humanity alienating him further.
P208 '[monster] Follow me; I seek the everlasting ices of the north, where you will feel the misery of cold and frost, to which I am impassive. As well as recognising that the monster can write and now has mastered the last form of language, it is luring Frankenstein further North. Frankenstein follows on the vengeance of Elizabeth's death.

Death, Decay, Darkness and Madness

(P27) 'I never saw a more interesting creature; his eyes have generally an expression of wildness, and even madness'. The reader's first description of Frankenstein is of him being mad - this is a punishment for evil deeds.
P52 'To examine the causes of life, we must first have recourse to death'. Frankenstein is meddling with death and the anatomy of humans.
P94 'I was tempted to plunge into the silent lake, that the waters might close over me and my calamities forever'. Frankenstein is thinking about committing suicide here which, in essence, is an easy escape from his misery: a cowardly move to make.
P144 'I grasped his throat to silence him and in a moment he lay dead at my feet'. The description of William's death is not as graphical as it could have been - does Shelley want us to feel slightly sorry for the monster?
The monster cannot be loved because of his ugly appearance which is Victor's fault. Therefore, the monster destroys the people that love Victor so that Victor feels the same as the monster: loneliness (some sense of justice here maybe?).
P220 'his eyes closed forever'. Frankenstein's ultimate punishment is death. It is a pathetic death which goes with him possessing feminine qualities.
P224 'I shall quit your vessel on the ice-raft which brought me thither, and shall seek the most northern extremity of the globe; I shall collect my funeral pile, and consume to ashes this miserable frame'. The monster is going to destroy himself: completely and utterly negative.

Passion-Drive, Wilful Villain-Hero or Villain

Walton, at the start of the novel, is pursuing a scientific truth just like Frankenstein is.
P102 'do not you fear the fierce vengeance of my arm wreaked on your miserable head?' Victor wants to kill the monster for killing his family. Frankenstein + monster = doppelgänger.
P102 'Life, although it may only be accumulation of anguish, is dear to me, and I will defend it'. The monster's survival instincts means he will not be killed easily.

Heroine with the Tendency to Faint and Need to be Rescued
Although the women are stereotyped in the novel as powerless, it is Frankenstein that it closest to being that of Heroine.

P181 'passed like a dream from my memory'. Victor faints at the sight of Clerval's dead body. This should have been the typical reaction for a women - Victor is feminised. This creates the juxtaposition from the doppelgänger that Victor is feminist and the monster is masculine (an example binary opposition too).

Hero whose True Identity is Revealed at the End

P54 'how dangerous is the acquirement of knowledge'. After Frankenstein's past experience, he is warnings Walton about transgression. He has learnt from his mistakes.
(kind of revealed true identity) P190 'A thousand times would I have shed my own blood, drop by drop, to have saved their lives'. This is ironic from Victor seeing that he had the opportunity to save many of his family's lives many times.

Evil Deeds Leading to the Downfall of a Character

P38 'thirst for knowledge'. This can be seen to be Frankenstein's main downfall: his obsession for transgression was what made him make the monster.
P51 'I read with ardour those works, so full of genius and discrimination'. Frankenstein has a passion for knowledge which makes science, to him, seem obsessive and unrestrained.
P81 'My tale was not one to announce publicly; its astounding horror would be looked upon as madness by the vulgar'. This is Victor's excuse not to reveal the monster as the murderer to William. This makes clear that Shelley is being ironic as Victor could have done something but chose not to (he could have saved Justine and everyone else who was murdered.
P93 'Sleep fled from my eyes'. Guilt leads to sleeplessness.
P132 'but I was wretched, helpless, and alone. Many times I considered Satan as the fitter emblem of my condition; for often, like him, when I was viewed the bliss of my protectors, the bitter gall of envy rose within me'.The monster's story makes him more like Satin and less like Adam (evil which is not good).

Horrifying Events or the Threat of Such Happenings

P35 'He strove to shelter her, as a fair exotic is sheltered by the gardener, from every rougher wing'. Botanical imagery is used on Caroline to illustrate tat Caroline is just like an exotic plant which needs to be cared for more than normal. This represents the general vulnerability of women in the novel.
P58 'How can I describe my emotions at this catastrophe?'
'I shall be with you on your wedding-night'.

Gloom, Mystery, Suspense, the Dramatic, Macabre and Sensational

(P25) 'the shape of a man, but apparently of gigantic stature'. This is the first sight of the monster which is a dramatic moment to the plot of the novel. Already, the reader can tell this 'thing' is not normal and possesses abnormal qualities.
(P27) 'But he is generally melancholy and despairing . Frankenstein is depressed which helps to build tension and drama because it is a foreshadow: why is he depressed?
P43 'Destiny was too potent, and her immutable laws had decreed my utter and terrible destruction'.
P55 'I dabbled among the unhallowed damps of the grave or tortured the living animal to animate the lifeless clay?' Here, it is clear Frankenstein is obsessed with death with him knowing that what he is about to do is cruel.
P73 'William is dead! - that sweet child'. The short happiness Victor had after creating and forgetting about the monster is shattered by the letter which states his brother is dead. What makes it worst is that William was young and at the epitome of innocence: there was no reason for him to die as he had done nothing wrong.
P90 'graves of William and Justine, the first hapless victims to my unhallowed arts'. This sets the reader up for Volume 2 because it foreshadows the monster as something that is likely to kill again.
P133 'Why did you form a monster so hideous that even you turned from me in disgust?' This mimics when Adam complained to God in Paradise Lost.
P138 'my feelings were those of rage and revenge'. The monster was born innocent. However, with his bad experiences with humanity, he has turned vengeful towards them.
P199 'I heard a shrill and dreadful scream'. The scream is Elizabeth who has been attacked by the monster. But, because the attack was only heard by sound but not directly seen by Victor, suspense is created to if Elizabeth is dead or alive.
P222 'I [monster] abhorred myself'. From everyone hating the monster has led the monster to hating himself.

Pleasurably Terrifying?

P55 'A new species would bless me as its creator'. Frankenstein is playing the role of God which can be seen to be his tragic flaw. By putting himself in the position of God, he is making the audience, especially to the audience the novel was written in, worried. What will the consequences be of playing God? As the audience, we are sacred but curious was is to follow in Frankenstein's journey through transgression.
P77 'it was the wretch, the filthy daemon'. When Frankenstein sees the monster for the second time, he knows it was it who killed William. Evil destroyed goodness (symbolic moment of good vs evil). Monster is described worst as he has done an evil deed.
P101 'and then close with him in mortal combat'. Victor wants to kill the monster as he killed William and Justine. This creates anticipation and excitement because we are unsure whether Victor can defeat something that is of 'gigantic stature' and extremely strong.
P146 'My companion must be of the same species, and have the same defects. This being you must create'. The monster finishes his narration demanding Victor to create him a partner or 'Eve' so that the monster is not lonely. This creates suspense about what Victor chooses to do: creating one like the monster is maybe double the trouble - has Victor not learnt from his mistake?
P173 'I shall be with you on your wedding-night'. From the monster saying this creates tension to when Victor marries Elizabeth. He thinks he is in danger, P195 'I had prepared only my own death'. However the monster wants Victor to suffer; Elizabeth is in danger.
P199 'Great God!' Victor also says this during the creation of the monster. Therefore, the death of Justine is linked to the creation of the monster.

Dr Faustus

Below are some of the key Gothic quotes from Dr Faustus. Ultimately, Dr Faustus transgressed and had a thirst for knowledge which led him to perform magic of the dark arts. He sold his soul to Lucifer for 24 years of power. After 24 years, he was sent to hell.

A Castle - There is no castle present in Dr Faustus because he has come from 'base of stock'. He has not got the wealth to live a castle.

Dark Settings

P17 'gloomy shadow of the earth' - Darkness is associated with evil (Gothical pathetic fallacy).
P17 'Orion's drizzling look' - The stars have gone out because they are associated with heaven: the presence of evil and hell has made them disappear.
P47 'When I behold the heavens, then I repent And curse thee' - Faustus is looking up at the starts (heavens) and wants to be close to the person that made the stars (God).

The Effect of Low Lighting - Faustus' study is often only lit by a single flickering candle. This creates a dark setting for the devil and hell to enter.

Extreme Landscapes and Weather

P111 'Thunder and lightning' appears when the clock strikes twelve signifying the presence of hell and damnation that is coming to Faustus.

Magic and the Supernatural

P7 'necromantic books are heavenly . These are the types of books that can bring spirits back to life: Faustus is transgressing death. At the time this play was created, people believed in witchcraft and hell.
Faustus begins his magical chant or 'incantations' on P17.
The appearance of Lucifer and the seven deadly sins furing Act 2 Scene 5 is extremely Gothic (sinning is Gothic).

Death, Decay, Darkness and Madness

The Old Man is killed by Mephistopheles on P105, 'Hence, hell! For hence I fly unto my God'. He goes to heaven because he keeps his faith with God.

Passion-Drive, Wilful Villain-Hero or Villain

P5 'Settle thy studies, Faustus' - Straight away, the audience (because this is a play) will view Faustus as an arrogant man from the way he talks to himself.
On P9, Faustus lists all what he desires from transgressing - he thinks his list of desires are all worth eternal damnation.

Hero whose True Identity is Revealed at the End - Although Faustus did transgress, the audience will learn that deep down, he still doesn't deserve this because he is far too clever to die and become dammed in the way in which he was.

Evil Deeds Leading to the Downfall of a Character

P7 'The reward of sin is death...Why then belike we must sin, And so consequently die'. Faustus is arguing with himself that if we have all sinned we will all die and go to hell. Therefore, he might as well transgress seeing that his fate is already settled.
Faustus, when he summons the devil for the first time, should have learned not to transgress. He appears arrogant as it is evident he feels he is greater than hell.
On P103, Helen is brought forward (which is the devil disguised). Faustus kisses her making clear he is focusing on the moment and not eternity, 'Here will I dwell, for heaven be in these lips'. Faustus doesn't know she is the devil and is so damming himself.

Horrifying Events or the Threat of Such Happenings
The few hours Faustus has left to live creates a sense of panic and fear that he is close to going to hell soon.

Gloom, Mystery, Suspense, the Dramatic, Macabre and Sensational

P89 - Faustus' leg coming off.
P35 - Faustus cutting his arm.
P105 - The Old Man getting murdered.
Wife as devil appears to Faustus.
P113 - The whole ending how Faustus is dragged to hell.

Pleasurably Terrifying

P19 'Thou [Mephistopheles[ art too ugly to attend on me' - The audience is suspended with disbelief that Faustus has managed to summon the devil. As much as the audience are terrified, they are enticed by this magic.
P113 'Ah, Mephistopheles ' - This is not pleasurable in any way but complete and utterly terrifying. The audience will learn that nothing is worth the same fate Faustus received damnation and being dragged into hell.

The Bloody Chamber

In The Bloody Chamber which is split up into ten short stories, I will pick key quotes from different stories that relate to the Gothic themes and elements.

A Castle

The Bloody Chamber - The setting of the first story is set in a castle. This helps to isolate the girl from society making her seem in more trouble from the Marquis.
In The Courtship Of Mr Lyon, Carter creates the idea of claustrophobia around the Beast's castle, 'it might have been the reflection of a star, if any stars could have penetrated the snow that whirled yet more thickly'. The idea of shielding the castle of the Beast from the outside world.

Dark Settings

The Company Of Wolves - 'the forest closed upon her like a pair of jaws' - This demonstrates the entrapment of the setting: especially how it creates isolation and a Gothic atmosphere.
The Courtship Of Mr Lyon - 'When the sky darkened towards evening'. The transition of light foreshadows the transitions of Beauty and the Beast.

The Effect of Low Lighting

[Not so much low lighting] The Erl King - 'vertical bars of a brass coloured distillation of light coming down'. This shows her desire to be caught, light is a positive image yet it is creating cage-like patterns. This links to the Gothic idea of confinement.

Extreme Landscapes and Weather

The Erl King - 'the wood swallows you up'. The wood is personified here creating the sense of isolation too.
The Erl King - The Erl-king can 'tie up the winds in his handkerchief'. The use of the Erl-king controlling the weather illustrates his immense power.

Magic and the Supernatural

The Courtship Of Mr Lyon - 'white rose' [in winter]. To have a perfect white rose blossom in winter suggests the presence of magic.
The Erl King - 'magic lasses of inhuman music'.

Death, Decay, Darkness and Madness

The Bloody Chamber - 'She was pierced, not by one but a hundred spikes'. From the contents of the Chamber, we can see the Marquis is mad which can be linked (AO4) to the Maquis de Sade who wrote a novel '120 days in Sodom'. If the Marquis is going to do this to previous lovers of his, the reader will fear for the young girl's life.
The Courtship Of Mr Lyon - 'Since you left me, I have been sick. I could not go hunting, I found I had not the stomach to kill the gentle beasts, I could not eat. I am sick and I must die; but I shall die happy because you have come to say goodbye to me'. This is the moment where Beast prepares to die making clear the juxtaposition of fortunes. At the start, Beast was the powerful one. Now, it is Beauty who has the power.
The Erl King - 'eyes as green as apples. Green as dead sea fruit' - Green is the colour of life yet, in this sense, it is 'dead'. This shows that he controls death as he controls the greenery in the forest.

Hero whose True Identity is Revealed at the End

The Courtship Of Mr Lyon - 'Mr and Mrs Lyon walk in the garden'. The identity of Beauty and Beasts have been revealed showing Beauty's masculine submission caused by Beast.

Gloom, Mystery, Suspense, the Dramatic, Macabre and Sensational

The Company Of Wolves - 'carnivore incarnate'. This is repeated numerous times when describing the wolves. It creates a sense of dread and fear.
The Courtship Of Mr Lyon - 'a mighty, furious roaring' - The beast is a powerful and dangerous creature creating suspense of what he is going to do.

Pleasurably Terrifying?

The Courtship Of Mr Lyon - 'Indescribable shock...on all fours'. Beauty's nativity is shown here as it is obvious that he will run on all fours from being a lion. Although this is pleasurably terrifying for Beauty, it isn't to the reader as we expected the Beast to have animalistic features.
The Erl King - 'I knew from the first moment I saw him, how Erl-King would do me grievous harm'. This is foreboding and terrifying: the reader fears for her. However, she still continues to see him, part of her own endangerment?

This is only a quick Gothic summary to Frankenstein, Dr Faustus and The Bloody Chamber. More analysis will be on Ask Will Online soon.

March 2013 - Ask Will Online's Stats From Google Analytics - Progression

2013-04-04T15:28:00.000+01:00

Things have been improving at Ask Will Online which is always great news. I can see a steady increase in pageviews per month (and even day!) which I guess is good in helping to sell site and good for making money. For March's states, I will compare with February's.

Ask Will Online Stats (From Google Analytics) March 1st - April 1st

Visits - 15,178

This is a 3,000 visits increase from last month which is great news. Using percentages, that is roughly a 25% increase in visits! The best part of this is that I know it is all natural growth. If you look at the recent month's post, I have posted once in March (with their being three guest posts). Ask Will Online is naturally growing!

The bounce rate, this month, has increased to 84% which is not good news at all (that is a 4% increase upon last month. I have tried alot of things to reduce the bounce rate and it seems they work for a little while then don't. I honestly can't think what else I can do to reduce my website's bounce rate - hopefully, it will naturally decrease in April.

Pageviews 20,229 therefore average pages per visit is 1.33

When comparing my pageviews to last month, I think I have had an increase because last month's pageviews was around 22,500 with 6,000 of them being 'robots.txt'. So, it is still good news, I guess? Hopefully, they will continue to increase consistantly in April. One thing I have noticed is that my Blogger stats say I have had 35,000 pageviews a month with roughly 1,200 a day. I think there are alot of people on the internet that use ad blockers...

Search Engine Traffic - 81.06%

The fact the search engine traffic has stayed pretty much the same while there being an increase in traffic is great news. It means more people are visiting Ask Will Online organically. People are finding my website and not the other way round - that is the best way for website's to gain the best traffic.

All the percentages for traffic have stayed quite constant this month compared to last month. Again, consistency in statistics is a good thing (exception being the bounce rate!).

Charity

To sum up how well Ask Will Online has been making money in March:

January had a CTR of 0.46%.
February had a CTR of 0.59%.
March has a CTR of 0.79%.

From January to February saw a 28% increase in CTR. From February to March saw a 34% increase which is quite staggering! The only thing I changed about March was the ad categories in Google Adsense. I had some that were blocked so I ended up unblocking all the categories and it has helped massively. Let's hope this positive correlation occurs!

This month, I have had a friend that kindly suggested Ask Will Online should donate to Help for Heroes charity which is a charity which helps those who have thought in war and recover from the most shocking and worse of injuries - it is a great choice. Therefore, to make things fair, £5 will go to Help for Heroes, Teenage Cancer Trust and Dementia Research.

Social Media Tools to Look Forward to in 2013

2013-03-23T16:58:00.000Z

Social media has long emerged as the main focus of marketing strategies of businesses around the world. Businesses need to regularly monitor their activity on social media platforms in order to check the performance of their social media strategy and make appropriate changes to it. One simple way of monitoring are internal methods like Facebook likes and retweets. The other way is to use proper social media tools which have far better monitoring and analytics capacity. Just like the new apps and websites, 2013 will also see the emergence of some new social media tools. Some of the top social media to forward to in 2013 are:

Pinster

Pinster is the equivalent of Google Analytics for Pinterest. Pinster allows you to know the right time you can add pins to your account. After this you can schedule the time for posting the pins or post them on your own right away from pinster. The sophisticated pin automation technology makes scheduling and posting of the pins very simple. A unique analytics tool also lets you to measure interactions and website referrals which can give a good idea about the benefits (ROI to be specific) of using Pinterest for your blog.

Splash

Splash is like a local or personal version of Twitter. Splash allows you to follow the topics that are of interest to you, instead of following other users and celebrities. Splash shows content from users who are in your close proximity through Bluetooth and Wi-Fi. Simply put, Splash is a great way of meeting new people and connecting locally.

Ping.it

Ping.it is new social media tool for content recommendations. This tool allows you to receive personal recommendations regarding the content from people you want. You can both send and receive commendations without the need for using any social network sites or URLs. The recommendations are delivered directly into your personal Web Inbox. This tool also allows you to send your own recommendations to your friends, email contacts, other Ping.it users, and related private or public groups.

Tagtivate

Tagtivate belongs to a new breed of search engines which can collate information from both traditional search engines and social networks and allow to view social content curated from across the world wide web. Tagtivate promises to take the utility of the ubiquitous hashtags to an all new level. This innovative social media tool enables to use hashtags as a means to share and pull together the content from the internet. After collating the content TAGtivate dissects the content and analyses all posts made on the various social networks. The tool then assigns a set of hash-tags to them. It also uses some social metrics to rank the contents depending upon their value. Using this social media tool, you will be able to keep yourself up to date with the content that is important to you.

ParaBlu

ParaBlu is the social media tool for the new generation computing which increasingly works from the cloud. ParaBlu is like a personal cloud that allows you to sync your files across multiple devices and platforms. You can select whether the data kept in your personal cloud is publicly visible or kept private. There is one more option which enables you to choose the people you want to see your data stored on the cloud. The data that is stored on the cloud or the linked devices can also be searched from anywhere. You can store as much data as you want on the private cloud without any restrictions.

Tweet Deck

Tweet Deck is a highly effective tool that can arrange feeds from all your social networks in one single place through the Tweet Deck dashboard. Using this tool, you can schedule the time of the tweets and set-up feeds depending upon your social search needs. Lists of people whom you follow can be createdwhich will facilitate the managing of different target groups with whom you want to interact and keep an eye on what's tweeted about.

Sysomos

Sysomos is an excellent social media analysis tool for businesses. This social media tool collects information from blogs, social networks, wikis, major news sources, etc. and gives valuable intelligence and insights to businesses regarding what's is working and what is not working. The tool also gives you the ability to notice the tone of conversations and identify opinions on the basis of gender, age and location. Sysomos has another component called Heartbeat. Heartbeat gives updated snapshots of social media conversations through different kinds of user-friendly and intuitive graphics.

A new year brings a new set of social media tools into this dynamic field. You can select some of these new tools depending upon your need.

Alia is a writer/blogger. She loves writing, travelling and reading books. She contributes to Social Cloud.

6 Fabulous Tips For Multiplying The Number Of Followers On Twitter

2013-03-23T16:34:00.000Z

No doubt, Twitter plays a very consequential part in increasing your reach to potential customers. However, many business owners fail to gain maximum benefits from this highly popular platform because the number of their followers does not increase in leaps and bounds.

Read on to discover 6 Tips to Get More Followers on Twitter and spread your brand name boundlessly:

1. Recognize the social flavour of Twitter and act accordingly

You can win more followers on this networking site by acknowledging the fact that it is a social platform. Other Twitter users will be attracted towards you only when you come across as communicative and responsive.

Do not be shy about posting your responses to other users' tweets, liking what others have posted, and retweeting profusely. It will show that you are interested in going through what other people have to say, and that is a big motivation for them to follow you. The more connected you are with your followers, the more popular you will become.

However, do not follow just about anyone. Keep your target market in mind and focus on those users who are related and interested in your field.

2. Do not go overboard with brand promotion in your posts

Undoubtedly, Twitter is an effective medium for popularizing the existing products and announcing the new arrivals. However, too much talk about your products will annoy your present followers and discourage the potential ones from following you.

You will maintain and in fact, increase your following if you promote your brand sensibly. That does not mean you should not provide links to your company page. Surely, do so but do not forget to appear interesting and creative in your promotional posts.

3. Show your face to the Twitter users and gain followers

Being a social medium, Twitter will bring you great commercial returns if you let the users see your face clearly.

When you keep the photo box empty, it portrays a negative image about you. The informative and entertaining tweets that you post will not get optimum results to you, as you will be known only as a faceless user.

You will be considered either as a newbie to the site, who is still trying to figure out the relevance of tweeting or as a spammer. In both cases, you will lose a large number of followers, as users will not be convinced of your integrity.

Hence, place your picture and gain more followers.

4. Make your posts loaded with value

You will attract more followers if you succeed in making your posts informative and valuable. When the Twitter users are able making the quality of their lives better and more positive because of your posts, they will appreciate what you write. They will look forward to your posts and follow you for the same reason.

Write in simple language and in a thought-provoking manner. Choose topics that are relevant and have potential of starting discussions.

As you keep impressing your followers, your posts will be shared and it will, in turn, bring you more followers.

5. Tweet often and follow a schedule

Make it a habit to post your tweets at regular intervals without fail. Remain active in interacting and communicating with your followers. It will project you as someone, who takes sharing of his views and experiences seriously.

It does not mean that you should not be funny and light-spirited in your posts. However, you should speak with honesty and from your heart. Genuine posts always manage to strike a chord and that will win you more followers for sure.

Do not be lax in posting your tweets because it may annoy your followers, who must be looking forward to reading your posts.

Make sure to tweet around 4-5 times per day.

6. Use your other social media accounts for popularizing your Twitter account

You can use your accounts on other social networking sites like a springboard for promoting your Twitter presence. For instance, if you have a blog, do not forget to introduce your Twitter account in one of the posts and that too, encouragingly.

Moreover, place buttons for Twitter sharing on your home page and on the posts.

Similarly, on other networking sites, utilize the apps and tools that allow you to republish your tweets. Additionally, mention your Twitter account details in your e-mail signature and business card.

By combining the potential of your accounts on multiple platforms and Twitter, you will gain the maximum in terms of followers.

Jason Smith is an online manager for Superior Notary Services. He is an expert on SEO & PPC tactics and in his free times likes to read and understand about notary signing services.

Don't Block Any Ad Categories In Google Adsense

2013-03-12T16:50:00.000Z

This might seem hypocritical at first since I did create an article explaining that changing ad categories will improve your Adsense CTR. This is true. However, from increasing your CTR, you may in fact be significantly decreasing your CPC which ultimately means you will be losing money from changing ad categories.

The way I came to this conclusion was from looking at what makes a CPC high being competition. Take an example such as the PPC program Ad Dynamo. There are near to no advertisers out there which means there will not be many advertisers bidding for keywords and ad spots. This will relate to a low CPC for publishers of Ad Dynamo.

Take this logic of 'supply and demand' and then apply it to Adsense. Although the ad categories that you are blocking have low CTRs (if any clicks at all), you are blocking thousands if not millions of advertisers from bidding for your advertising space from blocking the ad category. Therefore, there will be thousands/millions of advertisers that will not be able to bid for your ad space and raise the CPC. Let's create an example.

I (metaphorically) have a website about football. Before blocking any ad categories, I had a CTR of 1% and a CPC of £0.40. If I was to get 10,000 impressions, I would make £40.

I then decide to remove the ad categories that are gaining impressions but not producing high earnings output. My CTR rises dramatically to 1.6%. However, my CPC decreases to £0.22. If I was to get 10,000 impressions with there new statistics, you will find I would have only made £35.20: £4.80 less than without blocking ad categories.

The point of this article is that lots of advertisers think the main and only variable they can control in PPC is the click through rate. However, I believe you can change your CPC just as if not easier than the CTR. For example, I have already created an article highlighting 14 ways you can increase your Adsense CPC. Next time you block an ad category, just think about what you might be doing to your CPC: although you are trying to make more money from blocking the category, you may in fact be preventing yourself from making any more money.

February 2013 - Ask Will Online's Stats From Google Analytics - Reality

2013-03-04T19:06:00.000Z

After a great month being January, February, for Ask Will Online, has high expectations which will hopefully bring in just as much traffic (if not more). However, after carefully looking at the traffic from last month, it is clear the huge fluctuation in traffic came from a robot crawler (which is used to gather data of articles to put on search engines). This is a bit disappointing. For this reason, I will compare February's stats to a month that will have more accurate statistics than January: December.

Ask Will Online Stats (From Google Analytics) February 1st - March 1st

Visits - 12,334

From December, this is around a 2,000 increase which is great news. However, I am starting to realise that the visits statistic is not as important as pageviews statistic. If you can make each visitor visit an extra page (from my perspective), that is a 12,334 increase in traffic! It makes sense to prioritise pageviews over visitors although with visitors, there are no pageviews.

Again, you will see that the top page on Ask Will Online is '/robots.txt?m=1'. The number is much smaller than January though with January being 17,000. The bounce rate has increased back up to 80.93% which unfortunately makes sense seeing that the only real page keeping it down is the 'robot' page which has decreased dramatically from last month.

Pageviews 22,523 therefore average pages per visit is 1.83

Again, this has decreased due to the 'robot' page decreasing. However, 22,500 pageviews is not a bad number at all baring in mind Google Analytics only records traffic that do not use ad blockers. From December, there is an increase in pageviews but a larger decrease in pages/visits. Therefore, I will need to look to increase the number of pages visitors view on Ask Will Online.

Search Engine Traffic - 80.91%

At least one statistic has stayed relatively consistent and I am really glad it is the organic traffic. Most of my traffic comes from search engines. Therefore, if any changes happen to this traffic, the problems will be much worse. However, Ask Will Online has always been good with search engines with a current page rank of 2. Therefore, there is nothing to worry about.

I have noticed that my direct traffic to Ask Will Online has increased by over 1%. This makes clear that more people are bookmarking and visiting Ask Will Online directly which is always good news!

Charity

To sum up how well Ask Will Online has been making money in February:

January had a CTR of 0.46%.
February has a CTR of 0.59%.

To the untrained eye, this might not seem like a huge increase. However, from 0.46 to 0.59 is a 28% increase in the number of clicks Ask Will Online received in February! This is great news which I hope continues through to March. Again, Ask Will Online will be donating £10 to Teenage Cancer Trust and £5 to Dementia/Alzheimer Research.

Under The Waterfall By Thomas Hardy Poem Analysis

2013-02-14T20:40:00.000Z

Here is a complete analysis of Thomas Hardy's poem Under The Waterfall which retells the romantic event of a picnic by a waterfall. The poem will be retold by myself bringing out the key features and analytically comments from it. At the end of the article, there is the historical context to this poem. Feel free to skip to the parts most relevant to you.

When reading this analysis, please remember much of this is an interpretation from me. As long as it is backed with evidence from the poem, it is a valid point.

What is the Poem about?

In short form, we can understand that a voice is evoked by a memory of having a picnic near a waterfall with their romantic partner every time s/he places their hands into a pool of water or 'basin of water'. I say 's/he' because the poem does not specifically tell the reader if it is the woman or man speaking. However, if you skip to near the bottom of this article, you will understand that it is the woman who is the first voice.

Breakdown Analysis of Under The Waterfall

The poem starts with the following lines:

Whenever I plunge my arm, like this,
In a basin of water, I never miss
The sweet sharp sense of a fugitive day.

Already, we can gather the poem is being told by a woman in hindsight of a moment in time. From this, it brings to light straight away that she is talking about something from the past that cannot be regained or repeated. In essence, the 'fugitive' day has escaped.

Hardy also uses an oxymoron here with 'sweet sharp' to describe the day making clear that it was a nice delicate memory but is also a spiteful memory. The word 'fugitive' means criminal which suggests that this memory of lovers was possibly against the law or was an affair where the couple was rebellious. This supports the reason why one of the couple remembers the memory vividly: from remembering the memory enables them to relive the emotions and excitement of being rebellious. However, the point is brought forward that we cannot live in the past like the start of this poem does.

Fetched back from its thickening shroud of gray.

Grey, in this context, is a symbolism for death. This is because a 'shroud' is a lengthening piece of cloth which a dead person is wrapped in before a burial. The fact that this 'shroud of gray' is thickening makes clear that the memory is disappearing/becoming forgotten which will result in permanent loss like the cycle of life and death is. It could also mean that this memory has not been thought about for a long time too representing the lack of romance.

Hence the only prime

And real love-rhyme

That I know by heart

And that leaves no smart

This part of the poem has a fluent and natural flow to it due to the rhyming being in pairs that progress as A A / B B. This makes it feel fluent which is all used to represent the flow of the waterfall from the memory. Note the lack of use of sharp sounding letters - the 's' on 'leaves' and 'smart' adds to the symbolised motion of the waterfall from the way is continues the soft and flowing sound of this extract.

Is a purl of a little valley fall

About three spans wide and two spans tall

Over a table of solid rock,

And into a scoop of the self-same block;

In these four stanzas, there is a slight theme of sublime here from the way that human affairs (such as the one between the woman and man) have such little impact to the environment of mother nature's landscape. The use of 'purl' makes the scenery of the waterfall feel like it is a treasure to see. More than anything though, human's affairs come and go with time. The scenery does not. The scenery lives through time unlike humans do.

The purl of a runlet that never ceases

In stir of kingdoms, in wars, in peaces;

With a hollow boiling voice it speaks

And has spoken since hills were turfless peaks'.

The use of 'kingdom' provides an archaic form to this poem at this moment. We associate kingdoms and castles with the middle ages where there were 'wars, in peaces'. Again, Hardy uses 'purl' again to add similarities between the runlet (small stream) and valley. However, this can bring up a different interpretation that he uses purl again as a form of juxtaposition: the power of a valley is far greater than that of a stream.

This concludes the end of the first stanza. From this stanza, the following themes are arose:

Love
Beauty
Time
Power
Nature

The first stanza basically is about a women having an event in the present time (being dipping her arm in water) which evokes a memory from the past which has strong feelings tied to it. Can we live in the past with memories?

Stanza Two

The second stanza starts with the following four lines:

'And why gives this only prime

Idea to you of a real love-rhyme?

And why does plunging your arm in a bowl

Full of spring water, bring throbs to your soul?'

From the start of the second stanza, is clear that the second voice (being the man) is now talking from the use of speech marks. The man is questioning the woman. He is asking her why she is getting strong emotions from just plunging her arm into a bowl of water. From my point of view, this contrasts against the above stanza which was very dreamy. This stanza starts sharply back into reality with the man asking exactly why she is being dreamy.

A great point which I think reappears throughout the poem is the words used by Hardy associated with falling such as 'plunged' and 'slipped'. As well as representing the water falling down the waterfall, it could also represent the ups and downs of the lover's relationship.

'Well, under the fall, in a crease of the stone,

Though where precisely none ever has known,

Jammed darkly, nothing to show how prized,

And by now with its smoothness opalized,

The woman answers the questions at lines 17-20. She found an object under the waterfall of much beauty. We can gather its precious and beautiful from the words that describe it such as 'prized', 'smoothness opalized'. The word 'opalized' makes clear that the object is showing varying colours (like an opal does). An opal is a gem stone. Therefore, whatever she is describing is very naturally beautiful and divine.

Is a drinking glass:

For, down that pass

My lover and I

Walked under a sky

This passage of the poem replicates the structure at lines 5-8. Just like at lines 5-8, there is the used of the 's' (glass, pass and sky) to make this section flow much like the waterfall. The voice describes their partner as 'my lover'. Therefore, we can deem the couple to be very affectionate for each other.

Of blue with a leaf-wove awning of green,

In the burn of August, to paint the scene,

And we placed our basket of fruit and wine

By the runlet's rim, where we sat to dine

The woman is expanding on her memory going into more detail. The shock of a question to the poem slowly resorts its way back to being dreamy again from the woman answering with a detailed explanation of their memory. We can gather the memory was by the edge of a stream where the lovers sat down to fruit and wine in a basket to have a picnic. There is alot of imagery used in this poem to help encapsulate the reader into the thought process of the first voice so that the reader relives the beautiful memory like the voice is. The vivid colours creates a scenery of perfection: the sky is blue, the grass is green and the weather is hot, 'In the burn of August'. From describing this memory in such detail makes apparent to the reader that this is not just any memory - it must be a special memory for the first voice to remember it in such detail even though it was 'Fetched back from its thickening shroud of gray'.

And when we had drunk from the glass together,

Arched by the oak-copse from the weather,

I held the vessel to rinse in the fall,

Where it slipped, and sank, and was past recall

The woman is now describing how they both drank from the same wine bottle (with the bottle representing their love for each other) and she went to rinse the bottle but it slipped and fell into the stream. Again, 'sank' is another word associated with falling.

Though we stooped and plumbed the little abyss

With long bared arms. There the glass still is.

And, as said, if I thrust my arm below

Cold water in basin or bowl, a throe

Here, the lovers are attempting to recover the glass by plunging their arms into the water to retrieve the bottle. This is most likely why the first voice recalls the memory 'Whenever I plunge my arm, like this / In a basin of water'. Thomas Hardy uses imagery lovely imagery here 'stooped and plumbed' and 'little abyss'. With an abyss being a seemingly bottomless chasm, it is clear by describing it as 'little' contrasts against the true meaning of what an abyss is. The actions of the lovers being 'stooped and plumbed' help make the poem flow. They are not aggressive words - instead, they are being delicate when trying to retrieve the bottle. The fact that the bottle has fallen could represent how the love of the couple has deteriorated: the bottle will stay there forever contrasting against the lover's love which will not.

From the past awakens a sense of that time,

And the glass we used, and the cascade's rhyme.

The basin seems the pool, and its edge

The hard smooth face of the brook-side ledge

This is the part of the poem which answers why she 'awakens a sense of that time' from dipping her arm into water. The bottle she had dropped into the stream had obviously not been retrieved by the lovers. Therefore, that is why she was able to see the bottle 'under the fall, in a crease of the stone'. The word 'cascade' is a small waterfall. Hardy gives the waterfall a poetic feature such that the waterfall is rhyming when the water cascades down, 'cascade's rhyme'.

And the leafy pattern of china-ware

The hanging pants that were bathing there

The attention to detail from the first voice makes clear how beautiful a memory it was to her because she has not forgotten any of the detail. The reader is also able to know now that the memory was a very distant memory because there are now plants growing around the bottle. This links in with the question, 'Can we live in the past with memories?' It is clear the woman is doing exactly this: if it was a memory that only just happened, then it is clear that one of the reasons they are recalling it is because it is still fresh in their memory. However, the fact its distant makes clear she is living in the past. This begs the question why? Is the relationship with the lover not as good as what is use to be? Is the relationship going downhill like Hardy hints at with the constant use of words associated with falling? This poem's message can be based much on interpretation.

'By night, by day, when it shines or lours...

...And its presence adds to the rhyme of love...

...In turns therefrom sipped lover' wine.'

We finish the poem with a final stanza in short form above. This stanza does not follow the structure of the poem of having moderately long stanzas with four short indented lines in the middle representing the flow of a waterfall (and also looking like one too visually). Instead, it is a six line stanza with the first voice still speaking. Just to confirm, the women is the one speaking, 'No lip has touched it since his and mine', bringing a sense of virginity to the bottle that the last time it has been in contact properly was with the two lovers while having their picnic. She describes the bottle as a 'chalice' giving the bottle a sense of religious important. This makes the reader feel that there was more to the couple's love than we first thought - their love was spiritually angelic. The waterfall is personified here:

And its presence adds to the rhyme of love

Persistently sung by the fall above

As long as the waterfall keeps having water fall down it, the lover's love will continue. Hardy makes a link between nature and love using the waterfall as a symbol for the couple's love. This gives the waterfall great importance because it can be deemed one of the main features of the woman's memory.

Thomas Hardy Writing About Emma

To give this poem a bit of historical context, the poem was wrote about a woman named Emma Lavina Gifford who married Thomas Hardy back in 1874. However, they no longer become affectionate to each other and Emma Lavina Gifford died in 1912. Even though Hardy had been alienated away from Emma for so long, he took the death of Emma extremely badly, often finding that the only way to manage his traumatic feelings was to write poetry about her. Under the Waterfall is one of many poems that Thomas Hardy created for Emma after she died.

Although it is unsure whether this actual memory ever happened (and somewhere by a waterfall, there is a bottle down the crease of a rock), one thing is for sure that his love for Emma never disappeared - when he died, his heart was buried with Emma and his body at the Abbey's Poet Corner. Therefore, when Hardy uses imagery that the waterfall 'Persistently sung by the fall above', Emma and Hardy's affection for each other may have died (or deteriorated). However, their love for one another was more than just a slight affection. The waterfall is a powerful symbol. Hardy describes that the stream is a 'runlet that never ceases'. Just like the waterfall will never cease too, Hardy's love for Emma will continue for eternity.

I asked why is the women living in the past earlier on in this article. It isn't the woman living in the past but Thomas Hardy himself. The only way he can manage his feelings towards the passed-away Emma is through reliving their best memories together through poems. Thomas Hardy is using the art of poetry to let himself feel again the emotions he felt while with Emma.

Hardy has been really clever here. He knows like everyone, we will all be born and die. Our love for one another will only last as long as we live. If you represent your love for someone as a symbol from nature, such as a waterfall, it will last forever because a waterfall will never stop flowing. Time is the limiting factor of love. But, for Hardy's love to Emma, there is no limiting factor. His love for Emma is truly eternal.

January 2013 - Ask Will Online's Stats From Google Analytics

2013-02-06T23:08:00.001Z

After, what I deem as, a disappointing month of December, I was hoping that everything on Ask Will Online will improve in January for the main reason that many students will be undertaking exams in January and will therefore be looking at websites to try and review for (hopefully, one of them was mine!). As it turns out, they did!

Ask Will Online Stats (From Google Analytics) January 1st - February 1st

Visits - 14,090

This is an improvement of 4,000 visits from last month. However, compared to November, this is a 3,000 decrease. I am quite satisfied with 14,000 for the meantime. I am nearly up to the magic number 15,000 which will be displayed on my BuySellAds marketplace that may help to get some of my adverts sold quicker.

Interestingly, the top page on Ask Will Online has changed to robot.txt....? This is the homepage (I think) for the mobile version of my website. So, I am guessing that people have been using their smartphones more to access AskWillOnline.com to help them revise. The bounce rate for this is a low 44% which has brought the whole of Ask Will Online's bounce rate down to 76.28% - 1% lower than last month (every little helps!).

Pageviews 37,347 therefore average pages per visit is 2.65

WOAH! What has happened here? My pageviews has increased by a staggering 16,000 views in one month with page/visit increasing by 0.6 too! This means that Ask Will Online is displaying great relevant content to web users which are encouraging them to click on further articles to read! A great achievement - this is the highest amount of pageviews Ask Will Online has ever had in one month.

Search Engine Traffic - 81.45%

What made me just worry was that this new record of pageviews and pages/visit might have been affected by the source of traffic (direct traffic is more likely to view more than one page). However, search engine traffic has pretty much stayed constant give or take half a percent. This is great news. I just hope it is not a one month fluke!

What I did find interesting about my sources of traffic is that my direct traffic has increased. This is most likely due to people bookmarking webpages on Ask Will Online that they will continually refer back to for help with revising for exams.

Charity

To sum up how well Ask Will Online has been making money:

November had a CTR of 0.42%.
December had a CTR of 0.68%
January has a CTR of 0.46%.
My priority for February is to have a play with the adverts to try and increase the CTR.

Your first impressions are most likely that Ask Will Online has done bad that it's CTR has decreased. However, taking into account the extra pageviews of 16,000(!), this means the overall earnings have been much higher. Like always, Ask Will Online will donate £10 to Teenage Cancer Trust and £5 to Dementia Research.

Promote Your Blog on Google Communities: 6 Ways

2013-02-04T16:42:00.000Z

Google Plus has been striving hard to compete with Facebook. But it seems that most people are less informed about the features of Google Plus, much less about the newly rolled-out Google Communities. Google communities to some extent are similar to the Facebook Groups in terms of its features. With Google Communities, you can have discussions, share photos and videos. It is also believed that photos shared on Google Plus are of high quality. The main advantage of going into Google Communities is that the Google search engine feature will also extend to Google communities. This feature helps you find what you need and also help others find you. Here are the ways that help you promote your blog on Google Communities.

1. Produce Unique and Quality Content

Once you have posted your content onto your blog, you need to recommend it to the Google community. But make sure that the content you produce is always unique and fresh so that people would find it interesting to read. You need to put great efforts in proofreading and checking your text for spelling and grammar and graphics before bringing them to the public. Also, you need to write all your posts in a conversational tone as this helps in building an emotional bond with your readers. Thus it makes your readers to stay long on your blogs and explore them further.

2. Identify Your Niche

You must write on topics of your interest for your blog. You need to focus on what you are writing. Is it related with some sort of professional work? Has it got something to do with personal journal or diary? Is it related to a certain hobby or school? You need to carry a lot of research. You need not focus on just one theme or topic, but don’t try to cover unimportant things which make you to end up with nothing.

3. Find Who, Join the Right Group

In Google Communities, one needs to be grouped with people of same niche. To do this, you can search for the discussion groups by entering keywords into the search tab. By doing so, you are taken to the list of groups along with their particular descriptions. Here, you have to read the descriptions carefully and join the right group. Don’t just join a group because it has more members. You need to join a group that has more active members. Also, you should consider the group that has similar interest or aim as that of your blogs. Next, you have to tag your post for your blog with the right tags so that it makes easy for people to find you. Thus Google Communities are designed to establish relationship among the members of the community where you can join the groups and as well invite others to join your group.

4. Make Your Profile Interesting

Your profile conveys a lot which is most important in promoting your blog. This should include your name and the blogs, where you contribute your content. If users like the posts you share in the public Google+ community, they will be tempted to visit your profile to gather more information about you. In this process, they will click on the links of your blogs and find out if there are any informative posts that are helpful to their area of knowledge. So you need to be careful in creating your profile and make sure that it is updated. Your profile also helps in adding more users to your circle. You can make use of these contacts to see how they are active in Google Communities and share tips on usage with them.

5. Be Active and Post Regularly

Many times, people don’t like to comment on and share our posts just because we don’t do so on theirs. So to keep things going, you need to take the initiative to react to other’s postings. This is called reciprocity. All you need to do is hit the +1 button when you like their posts truly. Also, you can gain leverage from some existing discussion groups on Google Communities. For instance, you can find out from them how to expand your circles and get more groups to your blog.

6. Organize Online Contests

Many social media networks organize online contests with freebies and coupons to grab the attention of people. Likewise, Google Communities also help to organize such contest in a more fascinating way than you think. You can simply create a blog post with mechanics and rewards of the competition and share this with your Google community. Also add a note in your post description that names of winners will be announced on your blog so they have to visit your blogs regularly. Also, encourage them to subscribe to your RSS feeds to keep informed about your latest.

Alia is a writer/blogger. She loves writing travelling and reading books. She contributes on Hotline America Reviews

PPC Challenge: Ad Dynamo vs Adsense

2013-01-30T19:39:00.000Z

I have always been sceptical whether Google Adsense is actually the best PPC program out there for publishers to monetize their website. The problem is that there will be reviews on the internet recommending how good or bad a PPC program is: take me with my review on Ad Dynamo. However, there are no real statistics that compare PPC programs alongside each other. This is where my new series, 'The PPC Challenge' comes into place. I will implement different PPC adverts onto AskWillOnline.com to see which will make me the most money.

The first contender to go against Adsense (seeing as they are the top dog at the moment) is Ad Dynamo who entered the PPC market back in 2008. I have followed their progression since the start and, to be honest, they say they have grown the fastest out of every PPC program out there...I cannot see this 'growth' of there's because there publisher side has not changed at all in the last few years.

Adsense Stats

To compare statistically Adsense and Ad Dynamo, I will show you what I earned on the 29th January 2013 from Adsense being £1.76:

Blogger claimed I had around 1,200 pageviews overall which goes to show how much of my traffic that uses ad blockers (roughly 46% of traffic saw my ads if ad pageviews was 589).
I gained a CTR of 1.02% which is quite good I think.
I gained 6 clicks worth on average £0.29 each.
My page RPM was £2.99.

Click to enlarge

Ad Dynamo Stats

Blogger received exactly 900 pageviews on the 30th January 2013 with my adverts gaining 617 ad impressions. This means Ad Dynamo adverts are viewed by 69% of my traffic (although this may be due to external reasons).

I gained a CTR of 0.16% which is quite poor.
I gained 3 clicks work on average £0.00 each.
The RPM is £0.00.
Just for the sake of it, I made £0.01.

Now, I hope this makes clear the difference between Ad Dynamo and Adsense. One will make you money. One will not. What annoyed me most about Ad Dynamo is that around 70% of the adverts being displayed by Ad Dynamo adverts are Ad Dynamo themselves trying to advertise themselves! So, I blocked them from my adverts and then I found that all the advertising units were then completely blank (suggesting there are no advertisers). When there are adverts in the units, they have extremely low CPCs of lower than a penny.

What's your experience with Ad Dynamo and Adsense? Have you ever found it to be a more profitable PPC program than Adsense?

4 Great Tips To Make Money With BuySellAds

2013-01-25T20:11:00.003Z

BuySellAds is unlike the other forms of online monetization such as Adsense in the sense that you have much more control over the ad sizes, pricing and more. What sets BuySellAds apart from competitors for for PPC and in-text advertising is that you have complete control over monetizing your website without spending huge amounts of time on it. However, you will need to spend a bit of time setting up your BuySellAds profile so that you can then leave it and watch the advertisers buy your advertising spaces.

I did create an article explaining a few of the reasons why you may not have been selling your ad units on BuySellAds. However, I made that article ages ago and I think it's only sensible to do an in-depth update to the topic. Below are four tips you can use with BuySellAds to help you make money with them and banner advertising.

#1 Don't Price Your Adverts Too High

This is the number one problem with advertisers. They feel that their website is of the highest quality and therefore deserves a premium price. Unfortunately, BuySellAds does not work like this. When you are first using BuySellAds, make sure you get advertisers before you adopt high prices. Take Ask Will Online for example (I will refer to my website as an example because many of the tips below are because of my experience!). At the moment of writing this article, I have around 30,000 monthly impressions. This is a good number which could probably get around $20 asking price for a 125x125 sidebar advert. However, it will take ages for them to sell. Therefore, instead, I made them as cheap as possible at $10. I now have three advertisers renewing their ad spots.

Lots of advertisers at a cheap price makes more money than few advertisers at expensive price (that is if you get any advertisers at all).

Therefore, the first tip is to make sure you are underpricing your adverts. If you have too much demand for your adverts then, you can then look to increase their prices to match the demand.

#2 Include As Many Statistics As Possible For Advertisers To See

Transparency is a great trait to have with a website. I have it with Ask Will Online because I publish my stats every month for the online world to see. If you don't publish your stats on BuySellAds, the advertisers get suspicious why you haven't let them see them (they must be bad if they can't see them). In the past, BuySellAds was able to let you show your Compete rank, Alexa rank and more. Now, the only stats you can show alongside the amount of impressions you get is your total number of RSS subscribers, Twitter followers and Facebook likes. I highly recommend you include all three statistics even if they are not good - you want the advertiser to know as much about your website as possible because from doing this, they will gain a more transparent and trustworthy view of your website.

#3 Use Only BuySellAds To Monetize Your Website

I know it will be difficult for publishers to do this but, from recent experiments with Ask Will Online, I have found that a website with just BuySellAds on it (and not anything else like Adsense) will gain more advertisers. This is advertiser know that if they buy an advertising unit on that site, they will have absolute priority and won't have to be worrying about competing against other adverts on other advertising platforms. The only problem is that if you don't have any advertisers with BuySellAds, your website won't be making any money at all. Therefore, I recommend that you carrying on using Adsense or Infolinks or whatever platform you use to monetize your site. But, promise your advertisers in the description that if they buy your advert, all other advertising units from other platforms will be removed maximising the performance of their advert.

#4 Write A Compelling Description

The description of your website in BuySellAds can be deemed the 'make or break' part of gaining an advertiser or not. Basically, you have to try and show off your website without boasting too much. To look in more detail about how to create a good advert, click here. Below is the advert I have used for Ask Will Online on BuySellAds:

Ask Will Online is primarily a website full of topics to help students with their studies. As well as this, Ask Will Online has help for bloggers on Adsense, increasing traffic, PPC programs, Twitter and more. We gain the majority of our traffic from England and America with search engine traffic totalling 88% of all traffic. This consequently means that a lot of new visitors will see your advert. As well as all this, Ask Will Online donates a proportion of its earnings to Teenage Cancer Trust and Dementia research. Therefore, your money will also be going to great causes.

The first sentence states exactly what Ask Will Online is about with the next sentence going into a bit more detail. I explain a benefit to the advertiser of advertising on Ask Will Online that the website gets alot of new visitors. As well as this, another benefit to advertise with Ask Will Online is that it donates a portion of its earnings to charity. Try and give the advertiser as many reasons to advertise on your site in the description as possible.

If you have any more tips to getting advertisers to be your units, feel free to comment below and share.

How Conservations Laws Led To The Discovery Of The Neutrino

2013-01-21T11:35:00.002Z

The conservation law in fundamental particles of matter is the idea that which every decay of a nucleus, the charge, energy, lepton number and nucleon number is always conserved (a bit like momentum). With alpha decay, the energy, lepton number and charge stays the same before the decay and after because scientists were able to measure the properties of the alpha particle and calculate that everything was conserved. This led scientists to believe that the same must apply to beta decay.

The problem with beta decay is that if you take the same approach to beta decay you did for alpha decay,it simply would not work. If after the decay, one beta particle is released, scientists saw that the energy before the decay was in fact more than the energy after the decay. There must therefore be another fundamental particle that is emitted from beta decay.

In 1930 Austrian theoretical physicist Wolfgang Pauli came up with a brilliant solution. He suggested that a third, unseen and almost undetectable particle is emitted in beta decay. The particle is called an anti neutrino (v) (neutrino in beta-plus decay). Energy is conserved for all beta decays because the 0.546 MeV is shared between the electron and the anti neutrino.

Pauli's idea also solved other problems with beta decay. The creation of the anti neutrino balances the creation of an electron, in the same way that an anti-electron balances an electron in pair creation. Neutrinos and electrons are assigned to the same particle family, called leptons, and all interactions (as far as is known) conserve lepton number. This works by giving electrons and neutrinos lepton number 1 and the antiparticles (positrons and anti neutrinos) lepton number -1. Perhaps you begin to see more clearly why anti matter is a theoretical necessity. There is more to conserve than just electric charge.

Consideration like these define the properties of an anti neutrino:

It must be neutral (to conserve electric charge).
It must be an anti lepton with lepton number -1.
It must carry away energy.
It must carry away linear momentum to conserve momentum.
It must interact extremely weakly with matter (otherwise it would be detected).

The best initial guess was that its mass - that is, its rest energy - is zero. If so, it ravels at the speed of light, as a photon does, with momentum E/c. It was twenty six years before the neutrino was detected. You may be surprised to learn that billions of neutrinos have passed through you as you read this sentence. But don't worry, they are so weakly interacting that most of them would pass through a lighlt year of lead without hitting anything.

Unmatched Ad Request In Google Adsense Explained

2013-01-14T23:06:00.000Z

Lately, while I was looking through some of the statistics of Ask Will Online on Adsense, I came across that nearly 9% of my traffic is getting 'unmatched ad requests' instead of a CPC or CPM bid. What is this unmatched ad request Google Adsense displays in reports. How can a publisher and blogger reduce this?

The way you can view your unmatched ad requests if through clicking on the 'Bid types' column under reports. This will show you the amount of impressions you gain through unmatched ad impressions:

Notice how the coverage of unmatched ad requests is 0% meaning you will not gain or even have the opportunity to gain a click from it. Unmatched ad requests are not good.

Unmatched Ad Requests Explained

Every time a web user visits your website, your Google Adsense adverts will send an ad request to Google to display an advert for that web user. If you have three adverts per page, every view, your adverts will send three advert requests and so on...

An unmatched ad request is when you send off for an ad request. However, you do not display an advert for the request. This means the advert will be displayed as blank to the web user preventing any clicks on any adverts from happening.

From what I have seen, most publishers of Adsense will get unmatched ad requests every day. The trouble is that some publishers will have more unmatched ad requests than others. For example, mine is 9% whereas I have seen people with up to 20%. Even so, that is 9% or 20% of earnings publishers are missing out on!

This is where 'backup ads' come into place. When creating your ad unit in Adsense, there is an option of what to display as backup ads:

As default, backup ads (which are basically unmatched ad requests) display blank space which is no good for us publishers and I can strongly guess that most publishers forget about even looking at 'backup ads' when creating their own adverts. There are two other options in the scroll down:

Show ads from another URL.
Fill space with a solid colour.

Both options are not exactly the best solutions...

Reasons For Unmatched Ad Requests

Below are some of the reasons why you may find yourself having a few too many unmatched ad requests:

You have blocked to many categories and websites in the 'Allow & block ads' column.
Your content is not being bid for by advertisers. This may be because your content is poor or the topic the content is about is negligible to advertisers.
You have too many adverts on one page (supply and demand).
The advert type. Limiting yourself to juts text or image stops advertisers using the other type of advert from bidding on your advertising space.
The advert size - I have found that the linked units such as the 468x15 unit has a much higher unmatched ad requests than the normal squarer adverts.

From this, you can look to reduce your unmatched ad requests through:

Limiting the amount of websites and categories you block from advertising on your website.
Write high quality content advertisers will want to bid for.
Keep your articles to one topic to make it easy for advertisers to pick out keywords to bid for.
Limit the amount of adverts you have on your page.
The bigger and squarer the advert, the less chance of an unmatched ad request.

Unmatched ad requests is quite a new and unexplored feature from Adsense which they have only just introduced. Therefore, if you have any information on unmatched ad requests, be sure to comment below.

December 2012 - Ask Will Online's Stats From Google Analytics

2013-01-08T22:35:00.002Z

To sum up December it has been an average month. The traffic has decreased due to Christmas (however, this is on the rise again). Saying this, I gained a few extra advertisers on BuySellAds. I'm sorry to say that this will be an extremely short post because I simply do not have the time to write in these past few weeks due to revising for upcoming January exams. Nevertheless, below is a image from the homepage of Google Analytics which contains all the information and statistics a web user may want! As well as this, like always, £15 will be donated to charity from the earnings of Ask Will Online. £10 to Teenage Cancer Trust and £5 to Dementia Research. I hope everyone had a great Christmas and happy new year!

Click on Google Analytics Image to Enlarge

Movement Of Heat In Physics

2013-01-04T10:04:00.000Z

Heat flow occurs from a hotter substance to a cooler substance. For example, a metal at 400°C is placed into water of temperature 60°C. The heat will flow from 400°C-60°C.

The greater the temperature difference between hot and cold, the greater rate of heat flow.

The First Law Of Thermodynamics

Change in internal energy (J) = work done on the substance (J) + heat supplied to the system (J)

The 'Zeroth' Law Of Thermodynamics

If body A is in thermal equilibrium with body B and body B is in thermal equilibrium with body C, then bodies A and C are also in thermal equilibrium.

These bodies have a common property called temperature.

Specific Heat Capacity and Latent Heat Experiments In Physics

2013-01-03T14:06:00.003Z

The following experiment measures the specific heat capacity of a block of metal.

Method

Before you start the experiment, you will need the equipment for the experiment. You will need:

12V battery pack.
5 wires (two black and three red preferably).
Ammeter.
Voltmeter.
Metal block (copper in our case).
Immersion heater.
Insulation to surround the metal block.
Stop clock.

The first step to the experiment is to set up a series circuit connecting the battery pack to ammeter and inversion heater and then back to the battery pack. You need to make sure that the battery pack is accurate and will need to use a Voltmeter to get the voltage coming out at exactly 12 volts. You need to also check all cables to make sure they work. Measure the mass of the metal block and record this.

The immersion heater needs to be placed into the metal block with the help of a bit of oil. Once you have done this, connect the Voltmeter in parallel to the series circuit so it is connecting only to the immersion heater.

It is important to fully cover your chosen metal block in insulation so that it doesn't lose heat to the surroundings. You can now place the thermometer into the other whole in the metal block. The set up for the experiment is complete.

You need to record the first temperature reading of the metal block before the experiment. Once you have done this, you can turn the battery back on and start the stop clock. When recording the volts and amps, take an average for the duration of the experiment.

After 5 minutes (300 seconds), turn the battery pack off but leave the circuit as it is for another minute. This is because the immersion heater after the battery pack is turned off will still be providing heat to the metal block. After a minute, record the temperature and find the temperature change (measuring temperature in degrees Celsius or kelvin).

You now have all the information needed to work out the metal's specific heat capacity. You have the voltage (V) and current (I) of the circuit and time (300s). Therefore, we can work out the power provided being E = VIT. Now we know E, the mass of the metal block and temperature change, we can work out the metal's specific heat capacity through using the equation C = E / (m x △T). The answer will be in J/kg/K.

For our experiment, we gained the following information:

Mass of our copper block = 1.011kg
Voltage = 11.6V
Current = 4.9A
Power = VIT = 16, 824.6 J
Temperature change = 41K.

The specific heat capacity (C) = E / (m x △T) = 16,824.6 / (1.011 x 41). This equals to 405.9 J/kg/K which is not far off the upper limit true value of 380-400 J/kg/K.

Specific Heat Capacity of Water

For the experiment to explore the specific heat capacity of water, we need:

Distilled water (250ml).
Aluminium calorimeter, lid and stirrer.
Thermometer.
3-4V immersion heater.
2 multimeters.
Electronic mass balance, 0.1g.
Stop clock.
Power supply.

Method

Set up the apparatus as shown in the diagram above but without the water.
Check the heating element draws a current when 3-4V d.c. approximately is across the terminals. Use multimeters to measure this (Ammeter set to 10A d.c.)
Measure the mass of the empty inner calorimeter and record this.
Add enough water to bring the level to 1cm below the bayonet locking points on the lid.
Measure the mass of the water and calorimeter and water and record this.
Check that the bare wire element does not touch the thermometer when it is inserted.
Carefully place the filled inner calorimeter inside the outer container so that it is supported by the 'rim'.
Measure the initial temperature of the water and record this.
Ensure the 3-4V d.c. supply is connected and the ammeter is connected in series and the voltmeter in parallel (like the first experiment in this article).
Prepare the stop clock.
Begin the experiment by switching the power supply on and start the stop clock.
Run the experiment until the temperature has risen by roughly 20 degrees Celsius (or kelvin: does not matter).
Record the voltage and current readings every minute.
Switch the power supply off and record the time.
Continue to watch the temperature rise until it peaks and then record this temperature.
Leave the equipment to coll and consider your data - how will you use it to find a reliable and accurate answer for the specific heat capacity of water? Aluminium (which is what the calorimeter is made from) has a specific heat capacity of 880-937 J/kg/k at a temperature of 273-373K (0-100 degrees Celsius).

From doing the above experiment, we obtained the following data:

Mass of aluminium with water = 0.1477 kg.
Mass of aluminium without water = 0.0323 kg.
Therefore, mass of water = 0.1154 kg.
Starting temperature = 23 degrees Celsius.
Time taken to cause an rise in temperature of 8 degrees Celsius = 381s.
Voltage = 3.23V.
Current = 4A.

Below are the step by step equations that will result in us calculating the SHC of water:

If C = E / (m x △T), E = mC△T.
E = (m_water x C_water x △T) + (m_aluminum x C_aluminium x △T)
E / △T = (m_water x C_water) + (m_aluminum x C_aluminium)
(E/△T) - (m_aluminum x C_aluminium) = (m_water x C_water)
C_water = ((E/△T) - (m_aluminum x C_aluminium)) / m_water
But, E = VIT.
C_water = ((VIT/△T) - (m_aluminum x C_aluminium)) / m_water

This time, temperature has to be in kelvin and by using the SHC of aluminium and the temperature we were working at as 900, we produced a specific heat capacity, for water, of 5080 J/kg/K. The real answer is roughly 4200 so we are a bit out.

The electrical energy supplied will heat both the inner aluminium calorimeter and the water. This is why E = (m_water x C_water x △T) + (m_aluminum x C_aluminium x △T).

Specific Latent Heat

The specific latent heat is the energy that is absorbed by a chemical substance during a change of state. In this case, we are looking at how water obsorbs the energy from a kettle to enable it to vaporize.
T start = 21 degrees Celsius (294K). T finish = 100 degrees Celsius (373K).
Time to rolling boil = 155s.
Power = 2200W (kettle).
M (water and kettle) = 1.409kg. Mass of kettle = 0.596kg. At boiling temperature of water, mass = 1.385kg. After a rolling boil of 68 seconds, mass decreases by 0.050kg to 1.335kg.
Power = energy / time. therefore, energy = power x time.
The specific latent heat (L) = E / m. This produces the energy per unit mass.
We know that C (SHC) of water = 4200 J/kg/K.
L = (Pxt) / m = (2200x60) / 0.050 = 2.992x10^6 J/kg.
△E = mC△T = (1.409-0.596) x 4200 x 68 = 232.2x10^3J.
E = P x t = 2200 x 155 = 341,000J.
230,000 / 341,000 = 67%. Only 67% of the energy produced from the kettle goes into the water to vaporize it.
2.992x10^6 x 0.67 = 2005 KJ/kg.
For 1kg, E for vapourisation - 2.260x10^6J.
Molar mass of water = 0.018kg.
0.018 x 2.260x10^6 = 40,680J/mol.
For one particle, 40,680/Na (6.02x10^23) = 6.76x10^-20J.
At 373K, KT is the average energy of the water molecules. 1.38x10^-23 x 373 = 5.15x10^-21 J. This roughly 12 times smaller than 6.76x10^-20J.

Summary

E = VIT.
To work out the specific heat capacity, C = E / m △T.
The specific latent heat (L) = E / m.

Chapter 13 and 14 Physics A2 OCR Revision

2013-01-02T20:01:00.001Z

When looking at the macroscopic world and gases, we need to have macroscopic properties to measure the gases with. This can be:

Volume, V.
Mass, m.
Density, p (rho).
Temperature, T.
Pressure, p.

Pressure vs Volume

To perform an experiment of pressure vs volume, we need to make sure the mass and temperature of the gas stays constant. By changing the pressure, we can see how the volume changes. How are they proportional?

From this table and graph, it is clear it follows a typical y = mx graph where the y is 1/V and x is pressure. This is Boyle's law of pressure vs volume. If pressure is inversely proportional to volume, them the equation for pressure vs volume is:

p = k/V where k is a constant.

There is no '+ c' in the equation because the graph passes through the origins. This also means that pressure x volume will find the constant. This brings us onto Boyle's law:

For a fixed mass of has at constant temperature, pressure is inversely portion all to volume.

The next equation we will look at for gases is the pressure/temperature law which is also known as Charles' Law.

The above experiment produced the following table of results. This proves that volume is proportional to temperature.

The Gas Laws

From producing a graph of pressure x volume = constant, while having temperature and mass constant, it will produce a straight line graph passing through the origin.

From producing a graph of volume / temperature will also produce a straight line graph passing through the origin. At this time, both pressure and mass are constants.

From producing a graph of pressure / temperature will produce a straight line graph passes through the origin. Volume and mass are constants.

From these three graphs, we can gather that pV/T will equal a constant. We can then add the number of moles of the gas to the equation to produce pV/nT = R (constant). From this, the following equation is produced:

pV = nRT

P - pressure in Pa or N/m²
n - number of moles of gas.
V - volume in meters cubed.
T - temperature in kelvin.
R - molar gas constant = 8.3

The Molar Gas Constant, R

pV = nRT.
If n = 1 mole, pV = 1 x RT = RT.
R = PV /T = 8.31 J/K

As a reminder, the molar gas constant is the energy needs to change one mole of gas by one kelvin through changing pressure and volume.

R / Na (number of particles in a mole) = 8.31 / 6.023x10^23 = 1.38x10^-23 J/K per particle.

1.38x10^-23 is also known as the Boltzmann constant. It is also important to make clear that it doesn't matter what type of atom it is, it is universal. This is because of the equation KE = 1/2 mv². The atom's mass will vary causing velocity to change. However, the kinetic energy of the particle will not differ.

The Kinetic Theory Of Gases

pV = nRT

The consequence of the above relationship is that there is a lower limit to when T = absolute 0. This implies that the volume will be 0 and pressure will be 0. Gases are made of tiny particles. The particles have kinetic energy which falls as temperature moves towards 0 kelvin. When the particles collide, this involves the transfer of momentum.

Newton's third law describes equal but opposite forces on particles and the walls of a container. The collisions are elastic which creates the pressure.

From observable measurements and chemistry:

pV = nRT from gas laws where R = 8.31 J/mol/K
K = R /Na which is the Boltzmann constant which is 1.38x10^-23 J/K

But, what does this mean? From kinetic theory, we can produce this equation:

pV = 1/3 N m v_rms

m = mass of the gas particle.
N = number of particles in sample.
v_rms= average of the square of the speeds of the particles.

p = 1/3 ρ (rho) v_rms as density = ρ = Nm / V

Therefore, v_rms = 3p / ρ (rho) = (3 x pressure) / density. Root mean square or 'v_rms' is a microscopic quantity and pressure (p) and density (ρ) are macroscopic properties. v_rms is appropriate as it is taken from a range of speeds and if we averaged only v, as it is a vector, it would equal zero.

The Boltzmann Constant and Average Kinetic Energy

pV = nRT and k = R / Na

N = number of particles, n = number of moles and Na = number of particles in one mole, we can come to an equation involving all three:

N = nNa

nRT = 1/3 N m v_rms (N = number of particles, m = mass of one particle and v_rms = average speed squared).
But, K = R / Na and
Therefore, we can change nRT = 1/3 N m v_rms to n K Na T = 1/3 N m v_rms .
If we divide through by 'n', we get K Na T = 1/3 (N/n) m v_rms. But, N/n = Na.
Therefore, K Na T = 1/3 Na m v_rms. However, both 'Na's cancel each other out.
Now, we will try to put the equation for kinetic energy into the equation (1/2mv²).
1/2 KT = 1/3 x 1/2 m v_rms.

This produces the final equation:

3/2 KT = 1/2 m v_rms = average kinetic energy of one particle

Where K = Boltzmann constant at 1.38x10^-23, T = temperature in kelvin (+273 to any temperature in degrees Celsius), m = mass of the particle and v_rms = average speed of the particle squared.

For gases, the average KE is proportional to Temperatre for one molecule or particle.

Brownian Motion

This can be observed in crushed pollen grains in water, carbon particles in oil, small polystyrene beads in water and smoke particles in air. The motion is that particles adopt a random walk. This is because they are continually being bombarded by other particles colliding with them. For this reason, they are constantly changing direction randomly. Particles such as air are actually moving at extremely high velocities (around 300 m/s). However, because they have such a low mass compared to, let's say, a smoke particle, they don't cause the smoke particle a huge change in direction: enough to make it randomly move.

From the above extremely inaccurate diagram, it gives you an idea about the size difference between a smoke particle and air particle. Even with such high velocities, the air particle only slightly moves the smoke particle.

Average Thermal Energy

For gases, we know that the average thermal energy is 3/2 KT for each particle. For all other situations, more generally, KT is the average energy of a particle.

How do we express these energies?

In Joules per particle.
In electron-volts where 1eV - 1.6x10^-19 J (W = QV = 1.6x10^-19 x 1V).

For groups of particles, we use the mole (6.023x10^23 particles). If we multiply KT by Na, we get NaKT which is the energy per mole at temperature T (in kelvin).

What Do We Really Mean By Average Energy, KT?

If a real gas particle were observed:

KT = 1/2 m v_rms = Average Kinetic Energy.

For a mixture of gases, at temperature T, the value of KT gives us the average KE per particle but for less massive molecules, their average speed will be greater. For example, a hydrogen atom will have a lighter mass and therefore a faster velocity. A oxygen molecule is heavier than hydrogen. Therefore, it will have a slower velocity to maintain the same KT as the hydrogen.

But, what do we really mean by average? What is the distribution of speeds that make up the average? From an experiment, we found the average energy per particle of warm water to be 5.15x10^-20 J. The energy needed to vaporize one molecule of water (ε) is 6.76x10^-20 J. We can make a ratio:

ε / kt = 6.76x10^-20 / 5.15x10^-21 ≈ 13

The graph makes clear that when measuring the average energy of particles, we measure the highest probability density of the particles. You will find, though, that although KT is not enough energy to vaporise the particles (such as in a liquid), there will be some particles that will 'get lucky' with the collisions and gain enough energy to vaporize. This is at the point ε on the graph. ε is usually 15-30 times the value of KT. Therefore, ε/KT should produce a ratio of 15-30. Basically, a small proportion of the particles have the energy to vaporize.

ε/KT is a rule of thumb because we begin to observe the effect when the ratio lies between 10-30. For example, when boiling a kettle, steam starts appearing way before the average heat of the water is 100 degrees Celsius. It is statistical in its function and should be more precisely modeled.

The Magic Ratio and the Boltzmann Factor

We already know that 'Magic Ratio' to be ε/KT. This coincides with the Boltzmann factor which is e^-ε/kt. The ratio of numbers of particles in states differing by energy ε is temperature T.

Let's say ε1 - ε2 = ε. If difference between ε1 and ε2 does not change (difference being ε), the ratio of the number of particles from ε1 to ε2 is always the same.

Summary

Boyle's Law states pressure is inversely proportional to volume.
Charles' law states volume is proportional to temperature.
pV = nRT with R being the molar gas constant of 8.31 J/K.
The Boltzmann Constant can be worked out through R / Na which equals to 1.38x10^-23 J/K per particle.
pV = 1/3 N m v_rms.
v_rms= 3 p / ρ (rho).
N = nNa
For gases only, 3/2 KT = 1/2 m v_rms= average thermal energy per particle.
The average energy per particle is KT.
We can express average energy of a particle in electron-volts. 1eV = 1.6x10^-19 J.
ε / KT is the 'Magic Ratio' which is usually 15-30 times larger than KT. If it is not (roughly) 15-30 times larger than KT, it is likely there are not any particles that have been 'lucky' enough to collide with other particles to gain extra momentum and energy to vaporize.
The Boltzmann factor is e^-ε/KT.
It is important to remember when putting temperature into any of the above formulas, it needs to be in kelvin. Physics and most other subjects only measure temperature in kelvin. To change your temperature from degrees Celsius to kelvin, add 277 to your current degrees Celsius temperature (0 degrees Celsius = 277 kelvin).

3 Sources Of Evidence Towards The Big Bang

2013-01-02T14:30:00.001Z

The Big Bang theory suggests the the Universe originated in a very hot and very dense state from which it has expanded and cooled.

Red Shift

Red shift of light from distance galaxies is evidence that the universe is expanding because:

Light from all galaxies is red shifted suggesting that all galaxies are moving away from us (and from each other).
If all galaxies are moving apart it suggests that they started from some common point and expanding outwards.

Cosmological Microwave Background Radiation

The cosmological microwave background radiation (CMBR) is evidence that the universe used to be very hot because:

If the universe used to be much hotter, nuclear fusion of hydrogen would have taken place producing helium and EM radiation.
This radiation would still be around today, but red shifted because of the expansion of the universe.
This is CMBR.

Cosmological Red Shift

For light from objects that are very far away the red shift is due to the expansion of space itself as the waves travel through it (rather than due to an object moving through fixed space).
This is called cosmological red shift, Z.
From the cosmological red shift we can calculate how much the universe has expanded since the light set off.

From this, we can produce the equation:

R observed / R emitted = λ observed / λ emitted

But, the observed λ wavelength will be equal to λ emitted + △λ.

R observed / R emitted = (λ emitted + △λ) / λ emitted.
R observed / R emitted = 1 + △λ / λ emitted.

The cosmological red shift is given as △λ / λ emitted = Z. Therefore...

△λ / λ emitted = 1 + Z

Summary

We can provide evidence towards the big bang theory:

Red shift of light from distance galaxies (wavelength increases therefore moves towards the red spectrum).
Cosmological Microwave Background Radiation (CMBR). The radiation from the nuclear fusion of hydrogen atoms can still be picked up which is present in every direction. However, the radiation has red shift due to the expansion of the universe (we on Earth know the wavelength of radiation from Hydrogen fusion by performing fusion of Hydrogen atoms on Earth). This gives evidence towards the universe being extremely hot.
Cosmological red shift. The expansion of space itself has stretched waves that were emitted at the time of the big bang. We can tell from this how much the universe expanded since the light set off.

Hubble's Law, Constant and the Expanding Universe

2013-01-02T13:41:00.001Z

The Hubble Constant is the ratio of speed of recession of a galaxy due to the expansion of the universe. The problem with measuring the Hubble Constant is that it is extremely difficult to get an accurate number (there are lots of variables we cannot control that will affect the value). However, over the years, due to scientific instruments that are more accurate, we are gaining a more accurate value for the Hubble Constant. Over the years, the Hubble constant keeps decreasing in value. At the moment, the value of Hubble's Constant is roughly 70 km/s/Mpc.

This can be quite difficult to understand. Therefore, if you want a implied and shorter version of this article, scroll down to the bottom and look for 'Hubble's Law and the Age of the Universe'.

A galaxy of distance d from us takes a time d/v to reach us in a reversed universe. From Hubble's law, we know that v = H₀d. Therefore:

t = d / H₀d which equals 1 / H₀.

This time is the age of the universe. If that was a bit difficult to explain, here is it in simple terms:

We can use the equation speed = distance / time to find how long it will take a galaxy at the speed it is travelling away from us to get to us (at that speed). For example, if a galaxy is travelling away from us at 100km/s, the time it takes for the galaxy to reach us is the the time it takes the galaxy to reach us at the 100km/s.

Using time = distance / speed, we know that the distance (from the graph above) is 'd'. We also know that the speed or velocity of the galaxy travelling away from us is H₀d. Therefore:

Time for the galaxy to reach us at the speed it's travelling away from us = d / H₀d.
t = 1 / H₀. This is the age of the universe.

Time is an upper limit because we have assumed a constant velocity where the average velocity of the galaxy would have been faster because in a reversed universe where everything is falling together, gravity would accelerate their velocities.

A bigger H₀ --> faster expansion --> less time to get to present size --> younger universe.

Taking the value of H₀ nowadays of 70 km/s/Mpc...

1 Mpc - 3.10x10^19 km.
H₀ = 70 km/s / 3.10x10^19 km (km cancel each other out).
H₀ = 2.26 x10^-18
1 / H₀ = t _universe= 4.43x10^17 seconds which is 14 billion years.

However, studies have now showed that there are still some galaxies in the universe that are older than 14 billion years. Therefore, we must still not have the true value of the Hubble's Constant. But, we are getting more accurate over the years!

Summary

The graph with Hubble's Constant as the gradient makes clear that the further away a galaxy is from us, the faster it will be moving away from us. This supports the big bang theory because the graph proves everything is expanding outwards from each other.
v = H₀d where v is the velocity of the galaxy and d is the distance the galaxy is from Earth.
We can measure the age of the universe with 1/ H₀. This is an upper limit because we are implying that the velocity of the galaxies are staying constant.
The age, at the moment, of the universe is 14 billion years although there are galaxies still older than this.

Hubble's Law and the Age of the Universe

Hubble found that the further away a galaxy is, the larger its red shift.
He interpreted this to mean that distant galaxies are receding from us.
For a galaxy a distance 'd' from us, Hubble wrote v = H₀d where v is the speed of a galaxy away from us and H₀is a constant called the Hubble constant.

Run the Universe back in time...distance galaxies are further away but are moving faster...

...in the past galaxies must have been closer together...

....even further back, all the matter and space in the Universe was concentrated to a single point.

A galaxy of distance 'd' from us takes a time t = d/v to reach us in a reversed Universe. From Hubble's law:

t = d/v = d / H₀d = 1 / H₀

This time is independent of d and v and tells us how long ago the Universe was a single point - this is the age of the Universe.

Strictly, in a reversed Universe, the galaxies accelerates as they fall together so that the 'Hubble time', 1 / H₀, gives an upper limit for the age of the universe.

Relativistic Doppler Shift With Equations

2013-01-02T13:03:00.002Z

I have already looked at the non-relativistic Doppler effect on Ask Will Online. This lead us onto the equation △λ / λ = v / c when v << c (velocity of the object is very much less than the speed of light) with the maximum velocity being around 0.1c. This is because after 0.1c, due to time dilation time starts to significantly slow down.

As we already know, t = γτ. At low speeds, γ will equal extremely close to 1. This means at low speeds, the time of the observed time with the moving object will be the same as a wristwatch time of someone stationary. The equation △λ / λ = v / c works up to around 0.1c because it is an exponential graph. This means that towards 0 to around 0.1c, the time dialtion factor will still be roughly 1. However, after roughly 0.1c, the gradient starts to increase and increase until the graph gets to an isotope. Therefore, we need a new equation for when the speed of which we are trying to measure Doppler shift is more than 0.1c.

Equations

We will take 'k' to be the relativistic Doppler shift.

k = △λ / λ...
This also equals √1+v/c / 1-v/c...
Which is γ (1+v/c) where γ = 1 / √1-v²/c².

If v = 0, k will equal 1 which means the change in wavelength will 0. But, because γ is roughly 1..

1 + △λ / λ = 1 + v/c
△λ / λ = 1 + v/c which is the non-relativistic Doppler shift equation.

Summary

Time dilation is only a theory. If you wanted to include this theory when calculating the Doppler shift factor, you can use √1+v/c / 1-v/c or γ (1+v/c) where γ = 1 / √1-v²/c².
Not taking time dilation into account, △λ / λ = v / c.
The time dilation, from the graph, does not move significantly above 1 until speeds very close to the speed of light.

Light Clocks And Time Dilation

2013-01-02T12:15:00.000Z

The explanation of how we get to the equation γ = 1 / √1-v²/c² is through a diagram where light bounces back and forth between two mirrors. While the light is bouncing back and forth, a clock is ticking.

The distance can be worked out through distance = speed x time. The speed is the speed of light (c) and the time taken is t' (tau) or τ which is a symbol for the wristwatch time. One tick of the wristwatch clock = 2τ.

Now, let's create the same scenario However, this time, you are stationary and a clock with light bouncing against mirrors are moving past you with a speed of v.

You can see from the diagram that the distance between the two mirrors has stayed the same at cτ (tau) with τ being wristwatch (observer's) clock time. However, due to the clock pasting you at speed of v with the light and mirrors, the distance the light has to travel has become longer. However, the speed has not increased, it is still c. Therefore, t (normal t) is longer to accommodate the longer distance the light has to travel. From this, the moving clock travelling past you at speed v ticks more slowly than the observer's wristwatch clock.

The motion of the light clock (travelling at the same speed as the light and mirrors) does not affect the speed of light.The speed of light is a constant.
The horizontal distance moved due to speed v is x = vt.

We can use Pythagoras's theorem to come up with the equation:

c²t² = c²τ² = v²t²

We can arrange that to center the equation around τ.

τ² = t²(c² - v²) / c²

Where τ is the wristwatch time and t is the observed time. We can use the above equation to show that t = γτ where γ = 1 / √1-v²/c²:

τ² = t²(c² - v²) / c²
τ² = (t²c² - t²v²) / c²
τ² = t²- t²v² / c²
τ² = t²(1- v²/c²)
τ = t √ (1- v²/c²)
If t = γτ, the γ = 1 / √1-v²/c².
As v = 0, γ =1. As v = c, γ = infinity

Therefore, if τ = 1 nano second and v = 0.75c, what will t be? Well, after using the above equation in bold, the answer would be 1.5 nano seconds. Therefore, at wristwatch time, it will be at 1 nano second. However, the observed time, due to speed of v, will tick 1.5 nano seconds.

Summary

The speed of light is the constant in the universe. Time slows down as you approach the speed of light.
We can use the equation τ = t √ (1- v²/c²) to work out how time dilates. The wristwatch time measure the time of the moving object relative to wristwatch. The observed time is the time observed by a clock of the same speed as the moving object.
As v = 0, γ =1. As v = c, γ = infinity

Parallax, Standard Candles and Measuring Astronomical Distances

2013-01-01T15:30:00.000Z

A standard candle is an astronomical object of which the intrinsic brightness and distance from the Earth are known. By comparing the apparent brightness of a star with the apparent brightness of the standard candle, it is possible to work out the distance of the star from Earth. To do this, you need to know the intrinsic brightness of the star.

Two examples of standard candles are:

Cepheid Variables - intrinsic brightness related to time period of pulsation.
Type Ia supernovae - all have the same intrinsic brightness because stars explode after reaching the same critical mass.

How does comparing the brightness tell us the distance?

As you move further away from a light source, the apparent intensity of the light drops following the inverse square law. This is because the light travels out in every direction to cover the surface of the imaginary sphere. Here is a bullet point guide to the relation between distance and apparent brightness:

At distance r, apparent brightness is B.
At distance 2r, apparent brightness is B/4.
At distance 3r, apparent brightness is B/9.
At distance 4r, apparent brightness is B/16.
At distance 5r, apparent brightness is B/25.
At distance 6r, apparent brightness is B/36.

For any star, the apparent brightness α intrinsic brightness / distance from Earth ²

B α I / d²

We can consider two starts A + B of equal intrinsic brightness to relate both to the above equation:

B(A) α I / d(A)² and B(B) α I / d(B)²

Therefore, B(A)d(A)² = B(B)d(B)². This then produces the equation:

B(A) / B(B) = d(B)² / d(A)²

Using Parallax and Standard Candles to Measure Astronomical Distances

Parallax

Imagine observing an object against a fixed background. If you move the position of the object relative to the fixed background changes. The further away the object, the smaller the apparent change in position. This is the basis of stellar parallax.

The Parsec

A unit of distance in common use amongst astronomers is the parsec. As the Earth moves in its orbit around the sun, the position of nearby stars against the background of very distant stars seem to change.

The parallax angle of a star is the angle labelled Ø on the diagram. These angles are very small because nearby stars are very distant compared with the Earth's orbital diameter. Small angles can be expressed in minutes and seconds; one minute of arc is 1/60 of a degree; one second of arc is 1/60 of a minute (1/3600 of a degree).

If the radius of the Earth's orbit is R then the distance to a star with parallax angle Ø is:

d = R / tanØ

A star at a distance of 1 parsec (a pc) from us has a stellar parallax angle of 1 second.

If R = 150x10^6 km, find the value of 1 parsec in meters.

To work this out, we can put the above information into the above formula:

d = 150x10^9 (m) / tan 1/3600 (one second)
d = 3.09x10^13 km

The length of one parsec is 3.09x10^13 km.

Summary

We can measure the distance of a distance star if it is a standard candle. We can use the equation B α I / d² and B(A) / B(B) = d(B)² / d(A)² where B is the apparent brightness, I is the intrinsic brightness and d is the distance from Earth.
The apparent intensity of the light from the distance star drops following the inversely square law.
From using distance stars as a background, we can work out the distance of nearby stars through the equation d = R / tanØ where R is the distance of Earth's orbit from the sun, Ø is the parallax angle and d is the distance of the nearby star to the sun.
A star of distance one parsec (3.09x10^16m) away from Earth will have a parallax angle of 1 second or 1/3600 of a degree.