Jany 22nd 1822 -
Dear Talbot -
Thank God we have got over this business at last - You will find me somewhat lower in the Tripos than you expected - but considering that I have not been able to read much for the last 4 or 5 months - & considg also the style of our Examiners - I thank my stars that I have got off so well - Imagine the luxury of being examined by Hind (solus) on Friday "Now Gentlemen wull [sic] begin with a vary pratty [sic] prob. from Mr Vince's fluxions" <1> - The necessity of working all that day at the commonest book-work - in o[rder] <2> to maintain one's place was truly disgusting -
Old Hamilton <3> was completely floored till the Friday when he was examined by Gwatkin & beat all his brackett <4> in no time - Our sixth man did about as much & as well as Atkinson <5> did last year - By the bye Atkinson is married - Bird is to marry in the summer
There are no Fellowships yet vacant at Trinity <6> - but hopes are entertained that that [sic] there will be 2 or 3 before September - Thank you for your Problems wch were very good - but did not come into play Indeed we had none at all set throughout the examination - except indeed the followg - "find the no of changes that can be rung on 5 bells - no one ever being rung in its proper place" - the no you will find to be 44<7> My brother is at home<8> - where he will remain till Midsummer I shall return shortly to Cambridge -
Your very sincere friend
W. L. Arnold
W. H. Talbot Esqre
1. Rev. Samuel Vince, A Treatise on Fluxions (Cambridge: J. Smith); this textbook was widely used to introduce Newton's calculus to university students - Arnold was perhaps using the 5th edition, corrected and enlarged throughout, published in 1818.
2. Text torn away under seal.
3. Edward Michael Hamilton (1802-1860), of Brown Hall, Ballinfra, Ireland.
4. That is, bracket, or group of similar people.
5. Solomon Atkinson (1797-1865), the Senior Wrangler at Trinity in 1821. His marriage ruled out a fellowship. In 1824 Francis Gilmore offered him the founding chair of maths at Virginia but it seems he never got the letter. In 1825 he fled his creditors, sailing to New York. When he returned he went in for laws and ended up as an author of legal textbooks.
6. Trinity College, Cambridge.
7. The number of bell changes possible with five bells. The total possible number is 120 (factorial 5) and the number with no bell in its proper position is correctly calculated as 44. This is a vivid demonstration of the mathematical prowess of William, who was a Wrangler.
8. His older brother, Rev Thomas Kerchever Arnold (1800-1853), editor & author. In contrast to his brother William, he was a Junior Optime who never showed the confidence in mathematics which he had in classics.