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Document number: 01607
Date: 29 Oct 1827
Recipient: HERSCHEL John Frederick William
Author: TALBOT William Henry Fox
Collection: Royal Society, London
Collection number: HS 17:267
Last updated: 28th January 2012

Ansd <1>

Lacock Abbey, Wiltshire
October 29th 1827

Dear Sir

My old college friend Professor Key writes me word that he is a candidate for the Professorship of Pure Mathematics at the London University <2> and that he understands you will be consulted regarding the choice of a Professor. He therefore wishes me to mention to you my opinion of his abilities, which I do with pleasure, as I consider them of a high order & such as would have procured him a high situation in the Tripos of his year, if he had continued to read with the same diligence as at first.

Having since been Professor some years at the University of Virginia I have no doubt that his mathematical attainments are very superior.

You were so good as to promise me a copy of your Treatise on Optics. <3> It will give me much pleasure to possess it, especially as I intend when I have any leisure to resume my optical researches. Faraday <4> shewed me a very singular phenomenon last summer. A glass rod strongly heated (not to redness) is held in a dark room over a vessel containing ether; the glass rod appears immediately surrounded with a lambent light of a greyish blue tint. We also analysed the light of burning Potassium, which was very curious in its phenomena.

I recollect sending you some time ago, a little theorem concerning the Ellipse in which nothing was given except three Radii Sectors & the angles between them. I have since extended this Theorem to any number of Radii Vectors that may be given (provided of course that they can belong to the same ellipse) and I sent to Gergonne <5> (the editor of the very excellent Annales de Mathematiques) the Theorem which I obtained in the case of Five Radii Vectors being given. This he has published (Vol 17 page 366 &c) as the invention of a colleague of his M. Lenth¨¦rie <6> which is a singular want of good faith, unless it originated in a mistake. It is as follows. Given a,b,c,d,e five Radii Vectors of an Ellipse, and the angle between them being likewise given,

viz. (a,b) the angle between a and b
(b,c) the angle between b and c, and so on
Then if we make
(b,c) + (d,e) = Á
(c,d) + (e,a) = Â
(d,e) + (a,b) = Ã
(e, Á) + (b,c) = Ä
(a,b) + (c,d) = Å
The semiparameter or latus rectum will be equal to this symmetrical quantity, viz.
[mathematical formula]

I hope Utzschneider's <7> prisms have answered your purpose

& am Dear Sir Yours most truly
H.F. Talbot

J.F.W. Herschel Esqr
near Windsor


1. Written in Herschel's hand. [See Doc. No: 01657].

2. Thomas Hewitt Key (1799-1875), philologist. [See Doc. No: 01606]. Key’s history is an interesting one. After graduating 19th Wrangler at Cambridge in 1821, he was the founding Professor of Pure Mathematics in the University of Virginia from 1821-1825. Although this position was financially sound, he found it devoid of intellectual challenge, and returning to England was appointed in 1829 Professor of Latin in the newly founded University of London. In 1842, he became headmaster of their affiliated institution, the University College School, a position he held for the rest of his life. Key was also one of the founders of the London Library, a member of the Society for the Diffusion of Useful Knowledge, and President of the Philological Society of London.

3. Possibly he means Herschel's 'On Certain Remarkable Instances of Deviation from Newton's Scale in the Tints Developed by Crystals with One Axis of Double Refraction on Exposure to Polarized Light', Edinburgh Philosophical Journal v. 4, 1820-1821, pp. 334-341.

4. Prof Michael Faraday (1791-1867), scientist.

5. Joseph Diez Gergonne (1771-1859), French mathematician, editor of Annales de Mathématiques Pures et Appliquées.

6. M. Lentherie, 'Demonstration du premier des deux theorems de Geometrie enonces a la page 283 du present volume', Annales de Mathematiques pures et appliquees, v.17 no. 12, 1 June 1827, pp. 366-377. It was in response to 'Questions Proposees', v. 17 no. 9, 1 March 1827, p. 283.

7. Joseph von Utzschneider (1763-1840), German instrument maker.