1887.] 



On certain Definite Integrals. 



477 



post mortem, this, winch has always been denied by Virchow and 

 others, is negatived by the occurrence in the stools here examined of 

 an abundance of epithelial cells, often very slightly differing in 

 appearance from the normal. Occasionally fchey are coherent as 

 groups of four and five ; there are, however, no finger-shaped casts of 

 complete villi. 



The cases of a doubtful nature from Yenetia have not disclosed 

 any comma-bacilli under microscopical examination. In one of them 

 the ulcers present in the ileum, which to the naked eye resembled 

 those of enteric fever, pass deeply into the thickness of the muscular 

 coat of the intestine, a condition to which I have only once seen any 

 close approach in Asiatic cholera. 



XXXII. " On certain Definite Integrals. No. 15." By W. H. L. 

 Russell, F.R.S. Received June 16, 1887. 



Mr. Fox Talbot's researches on the comparison of transcendents 

 are well known. The following are founded on the same principle, 

 applied in a different manner : — 



Let— 



a 2 a? 3 + % 3 + c 2 z 3 = %, 



be two equations connecting the variables x, y, and z. Then we can 

 find x and y in terms of z, x and z in terms of y, y and z in terms of 

 (x). Or if — 



^i c 2~" c A = Al> c i a 2~ a i c 2 — Bi» a^ — b^z = C x ; 

 and also 



e l a 2~ e 2 a l == A 2 , e A~ e 2^1 = ^2' e l c 2~ e 2 C l = ^2 5 



we shall have x = 3//r , ^ y(B 2 + A 1 ^ 3 ), 



1^ 



y = -"^cj ^( a 2-b^ 3 ), 



