— 102 — 



lied in the Transactions will do myself the pleasure of sending 

 you a copy of it. I show how Foifisofs ellipsoid by a slight 

 addition may be made to express the timeto the senses and how 

 the motion of any rigid body may by reduced to depend in the 

 most simple manner upon that of an indefinitely flattened disc. 



I also prove that Poinsot's ellipsoid rolling on a rough 

 plane moves precisely in time with the free body of which it 

 is the Kinematical Exponent. This is very elementary Mathe- 

 matic ; but I think the results are somewhat interesting and our 

 great and bearned mutual friend Mr. C. considers them 

 original. 



I hope your health is good and that yon will pay yom- 

 promised visit to England and become my guest here in 

 Woolwich. 



With assm-ances most sincere of unfailing attachment and 

 high esteem I remain, my dear Sir, yours very sincerely. 



Cayley an Schläfli. 



Dear Sir 

 I must not any longer delay writing to thank you for your 

 two letters of nov. 10 "^ & 26**», which I have now at last found 

 leisure to study — the simplification of the second letter, in 



/ R — R \ 



effect substituting for D" - M ^ + ^ ) its expansion as a 



hypergeometric Series is most satisf actory ; and the final result a 

 very beautiful one.*^) I am afraid we must defer it until the number 

 next after the forthcoming one of the mathematical Journal, for 

 which it is a most acceptable contribution. Prof. Sylvester^ is 

 quite well — occupied just now with a theory of Symbols of Ope- 

 ration such as (x, y • • • •) ^ ((5 x, <5 y • • • •) " viz. functions of 



=»^) Solution of a Partial Differential Equation. By Professor Schlaefli, 

 Quarterly Journal, Vol. VIII, p. 252—256. 



