On the Integration of Partial Differential Equations. 283 



It Las been concluded from histological and physiological evidence 

 that the suprarenal bodies of Teleostean fishes consist solely of 

 cortex.* The physiologically active material is wanting, as in cor- 

 tical substance elsewhere, and it would be interesting to determine 

 the presence or absence of the chromogen. Unfortunately we have 

 been unable so far to obtain sufficient material for chemical examina- 

 tion. The same remarks apply to the suprarenal bodies of the 

 Ganoids. 



For the purpose of comparison, we have chemically tested an 

 extract made from the suprarenal glands of the frog. Six good- 

 sized animals were killed and the suprarenals snipped off from the 

 kidney with scissors. Although there was a considerable admixture 

 of kidney substance with the material thus obtained, the weight in a 

 moist state only amounted to 0"13 gram. This was treated in the 

 way described above for the Elasmobranch material, and gave the 

 chromogen reactions in a perfectly definite manner. 



" Memoir on the Integration of Partial Differential Equations 

 of the Second Order in Three Independent Variables, 

 when an Intermediary Integral does not exist in general." 

 By A. R. FORSYTH, F.R.S., Sadlerian Professor in the 

 University of Cambridge. Received November 23, — 

 Read December 16, 1897. 



(Abstract.) 



The general feature of most of the methods of integration of any 

 partial differential equation is the construction of an appropriate 

 subsidiary system and the establishment of the proper relations 

 between integrals of this system and the solution of the original 

 equation. Methods, which in this sense may be called complete, are 

 possessed for partial differential equations of the first order in one 

 dependent variable and any number of independent variables; for 

 certain classes of equations of the first order in two independent 

 variables and a number of dependent variables ; and for equations of 

 the second (and higher) orders in one dependent and two independent 

 variables. The present memoir discusses the theory of partial dif- 

 ferential equations of the second order in one dependent and three 

 independent variables ; and the. method adopted is seen, without 

 difficulty, to be applicable to equations which involve more than 

 three independent variables and which can be of order higher than 

 the second. The reason why equations of the type considered are 

 taken to be such as do not possess an intermediary integral, that is, a 



* "Vincent, loc. tit. 



