1879.] in the anatomy of Peripatus Gapensis. 269 



cords in a lateral compartment of the body-cavity, and extends, 

 backwards for a varying distance. 



This organ may perhaps be best compared with the simple 

 salivary-gland of Julus. It is not to be confused with the slime- 

 glands of Mr Moseley which have their opening in the oral papillse. 

 If I am correct in regarding it as homologous with the salivary 

 glands so widely distributed amongst the Tracheata, its presence 

 indicates a hitherto unnoticed arthropodan affinity in Peripatus. 



(5) Mr J. W. L. Glatsher, M.A., F.E.S., On a symbolic 

 theorem involving repeated differentiations. 



The theorem is 



(e-«H = (->-2".»!g^)^ (1). 



It can be established by direct expansion, for it is not difficult to 

 verify that each side of the equation is equal to 



(-)-f^-{i- 



2 ax 

 n + 2 . w + 1 . 7?, . ?i — 1 1 I e" 



+ 27i -^-^"- 



but it may also be proved by means of the integral 



'dx = '^ e 

 2a 



as follows : 





2ab 



Let u denote this integral ; then 



dii r°° , *^ 



da 



so that 



and therefore 



Again 



dSi 

 dd' 



= -2ax'e~'''''^^'dx, 

 Jo 



/•CO 52 



= {-2af + 4aV) e-«'^'-i"= dx, 

 Jo 



