1891.] of the Oviduct in the Frog. 151 



ment, because there is, especially in front, some lymphoid tissue 

 at the outer border of the kidney — in fact the whole pointed end 

 of the mesonephros degenerates to a string of such tissue. 



The lumen of the duct appears first in front and then behind 

 in the region of the kidney. In the latter position it appears here 

 and there in patches. It is formed by the rearrangement of some 

 of the cells in the rod in a stellate manner, sometimes one cell 

 and sometimes two cells deep beneath the surface. 



The conclusion which seems to be suggested by these investi- 

 gations is the complete independence of the oviduct from the 

 Wolffian duct in the Anura. 



I have, in conclusion, to express my warmest thanks to Mr 

 Sedgwick for his advice and assistance to me in this work. 



February 23, 1891. 



Prof. G. H. Darwin, President, in the Chair. 



The following Communications were made to the Society : 



(1) Tidal Prediction— a general account of the theory and 

 ■methods in use and the accuracy attained. By Prof. G. H. Darwin. 



Published in Nature, Vol. 43, p. 609. 



(2) On Quaternion Functions, with especial Reference to the 

 Discussion of Laplace s Equation. By J. Brill, M.A., St John's 

 College. 



1. The following communication is intended as a sequel to 

 the one that I made to the Society at the end of last term. In 

 that paper I showed how we might obtain analogues to the 

 theorems connected with conjugate functions with the aid of 

 four related solutions of Laplace's Equation obtainable from the 

 solution of a quaternion differential equation of the first order. 

 I now propose to obtain a form for the general integral of the said 

 equation. 



2. On account of the non-commutative character of the 

 symbols involved, quaternion functions are of a more complicated 

 character than ordinary scalar functions, and for their full dis- 

 cussion would require a notation and nomenclature of their own. 

 We may, however, in the case of functions of a single quaternion, 

 as was done by Hamilton in the case of the exponential, extend 

 the definitions of some of the ordinary scalar functions so as to 

 apply to quaternions, by defining the quaternion function as the 

 sum of a quaternion series exactly similar in form to the scalar 

 series which defines the corresponding scalar function. It is to be 

 remarked, however, that this method cannot be consistently carried 



