Llandaff
Thursday evening, Decr. 15th
My dear Father,
I did not mean to say that 2 straight lines was were the limit of a protracted cycloid but of a contracted one. On consideration however it turns out to be a mistake. The limit is a circle of infinite radius.
[illustration]
If when generating for if the [symbol] is at the extremity, E of the cycloid, a pt is indefinitely distant, in the direction A being alluded to centre of [illegible] [symbol]. Then when the generating w pt is at the vector of the cycloid this [illegible deletion] second point is indefinitely distant in the direction B. and since again when the generating pt reaches the end of the cycloid, it is indefinitely distant in the direction C. Therefore the limit of the contracted cycloid is a [symbol] of infinite radius. Since the base of the cycloid is indefinitely small compared with it the distance of the moving point.
There is going to be a ball at Bridgend on the 29th, and a dance of some kind I believe at Margam on the 27th. Champneys and I were to go to Merthyr Mawr on the 26th but Mrs Nicholl <1> has just written to say she will be there on the Xmas day and asks us g to go on the 24th. I think I shall, but Champneys I am afraid is engag engaged for Xmas day and so will have to follow on Monday. I am going to Lacock on Monday next to shoot some pheasants and have asked Mr F. Awdry <2> to come over on Tuesday and shoot. I have not had his answer yet. Bagwell an has I am sorry to say been summoned away to a ball at Clonwell so I shant have the pleasure of his company.
I have sent an extract of your letter about the photoglyphic engraving to Mr Nesbitt. <3> I will send you the photographic paper tomorrow. I have to read the account of Your photographic process in it which sounds promising. Trevelyan <4> has promised to propose me for the New University Club and has I expect done so. Champneys is going to second me. I am reading the times of James II in Macaulay <5> and find his account interesting.
As you have been to the British Museum did you see and duly admire the Assyrian sculptures in the basement story with the lions lions coming out of cages? Our weather here [illegible deletion] has today turned cold. I do not know whether a front is coming. I do It did not I believe freeze last night though it felt like it.
Please thank Ela <6> for her last letter. I am going to write soon to somebody. I hope you have pretty fine weather at Edinburgh and that everybody is able to enjoy it.
Your affect son
Charles
[envelope]
H Fox Talbot Esq
13 Gt Stuart St
Edinburgh
Notes:
1. Christiana Judy Nicholl, of Merthyr Mawr.
2. Frederick Awdry (1817–1884), solicitor, Chippenham.
3. Alexander Nesbitt (1817–1886), archaeologist & ancient glass collector.
4. Walter Calverley Trevelyan, 6th Baronet (1797–1879), naturalist & antiquary.
5. Thomas Babington Macaulay (1800–1859), MP & historian.
6. Ela Theresa Talbot (1835–1893), WHFT’s 1st daughter.