272 Mr Orr, Theorems on the contacts of spheres. [Feb. 22, 



5. In the same case any three pairs of conjugates are touched 

 by four spheres besides the original four. This follows from 

 theorem (3). 



6. In the same case if the original four spheres be A, B, G, D, 

 the four pairs of conjugates which belong to the same doubly 

 infinite family touching any two of the given four as A, B are 

 touched by two other spheres besides the original four, namely, the 

 inverses of G, D with respect to one of the spheres of similitude 

 of A and B. This is obvious as the eight spheres mentioned, 

 touching G and D and cutting the sphere of similitude orthogo- 

 nally, must touch the inverses of G, D with respect to that sphere 

 of similitude. In this theorem as in the last we have a group of 

 eight spheres touched by a group of six. 



(4) Change of the independent variable in a differential 

 coefficient. By E. G. Gallop, M.A., Gonville and Caius College. 



[This paper will appear in the Transactions, Vol. xvi. 

 Part II.] 



Monday, 8 March, 1897. 

 The President, Mr F. Darwin, in the Chair. 



The following Communications were made : 



(1) On the injection of the intercellular spaces occurring in 

 the leaves of Elodea during recovery from plasmolysis. By the 

 President, Mr F. Darwin, and Miss D. F. M. Pertz. 



Elodea continues to assimilate in salt solutions strong enough 

 to plasmolyse the cells. On replacing the plant in water assimila- 

 tion ceases, the gas disappears from the intercellular spaces, and 

 the leaf is injected with water. The disappearance takes place 

 partly by the escape of bubbles at the open ends of the inter- 

 cellular spaces, but chiefly by solution. The first of these 

 phenomena depends on the surface tension of salt solutions being 

 greater than that of water. The authors are not able to explain 

 the solution of the air in the intercellular spaces. 



