Edinb.
Jany 8th
My Dear Charles
I return Mr Nesbitt’s <1> letter. I hope you received mine of yesterday, containing a reply to Mr N’s questions.
The problem about the Centre of gravity of a Trapezium is a proof of great geometrical sagacity, but I think if you construct the figure with a Ruler you may perhaps perceive the demonstration of it.
I told you I think that I had found a very neat solution of a theorem which Professor Kelland <2> had obtained by means of Sir W. Hamilton’s <3> doctrine of Quaternions <4> – viz. in any triangle the centre of circumscribed circle centre of gravity, and concourse of perpendiculars from angles on sides lie in a straight line, and so that the centre of gravity always trisects the distance between the 2 others.
To which I added the following, for which Professor Kelland gave me Κυδος <5>
The centre of the six-point circle lies in the same straight line and always bisects it.
N.B. The six-point circle is that which passes thro’ the middle points of the sides, and which always passes thro’ the feet of the 3 perpendiculars from angles on sides.
Professor Tait <6> says that Quaternions ought not to be employed for solving such simple matters, but kept in reserve for the higher geometry.
Your mother <7> has sent you today an old Courant containing an account of the models for the Prince Consort’s <8> Memorial – They are now on exhibition here but we have not yet seen them. We think of going there tomorrow.
Your affte
Father
Envelope:
C. H. Talbot EsqMr Prichard’s <9>
Architect
Llandaff
Notes:
1. Alexander Nesbitt (1817–1886), archaeologist & ancient glass collector.
2. Prof Philip Kelland (1808–1879), Scottish mathematician.
3. Sir William Rowan Hamilton (1805–1865), Irish mathematician.
4. A calculus invented by Sir William Rowan Hamilton, concerning the operation of changing one vector into another, or the quotient of two vectors, depending on four geometrical elements and expressible by an algebraical quadrinomial.
5. Kudos, credit.
6. Prof Peter Guthrie Tait (1831–1901), Scottish mathematician.
7. Constance Talbot, née Mundy (1811–1880), WHFT’s wife.
8. Albert Saxe-Coburg (Prince Albert) (1819–1861). The Albert Memorial was completed in 1875.
9. John Prichard, Welsh architect; Charles Henry Talbot apprenticed to.