268 Proceedings ami List oj Papers read. 



^ logV ^{^dz 

 Jo 



can be expressed in terms of double gamma functions of equal para- 

 meters, and the two integrals 



r\ogV.2{z)dz, [\ogV2{z)dz 

 Jo Jo 



can be substantially expressed in terms of the double Stirling function 

 of ooj and a>2. 



It is shown in Part V that it is possible to obtain an asymptotic 

 approximation when \ z\ is very large, for 



log V.2 {z + a), 



which is valid over that part of the region at infinity in which there 

 are no zeros of T2~'^{z). The coefficients in this expansion are double 

 Bernoullian functions of a. 



Finally it is proved that the double gamma function does not satisfy 

 any differential equation whose coefficients are not substantially that 

 function or its derivatives. 



There exist 7i-ple gamma functions whose properties can be obtained 

 by an easy generalisation of the previous theory. 



March 22, 1900. 



The LORD LISTER, F.R.C.S., D.C.L., President, in the Chair. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The Croonian Lecture — " On Immunity, with Special Reference to 

 Cell Life " — was delivered by Professor Paul Ehrlich, of Frankfort- 

 on-the-Main. 



March 29, 1900. 



The LORD LISTER, F.R.C.S., D.C.L., President, in the Chair. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The following Papers were read : — 



