1882.] of protoplasm in the motile organs of leaves. 271 



than these and are widely distributed, although I am not at pre- 

 sent in a position to support this statement by facts. 



I think then it may now be urged with fair certainty that 

 the propagation of the stimulus is effected by means of these 

 protoplasmic threads, and the whole pulvinus may well be com- 

 pared to an ordinary animal muscle. As I understand, it matters 

 not how fine the connections are as long as they are there. With 

 regard to the cause of the escape of water I cannot but think 

 that there is no doubt that it is caused by contraction. There 

 are two principal views on the subject, those of Pfeffer and 

 those of Vines. The former supposes that by the action of the 

 stimulus the protoplasm undergoes some change by which it 

 becomes suddenly permeable to the cell sap. The water simply 

 runs out. The latter relying, as it seems to me, on the true 

 analogy between animals and plants, suggests that there is a 

 definite contraction and in fact a filtration of water under pres- 

 sure. According to Pfeffer Ave have the already omnipotent 

 protoplasm laden with a fresh and certainly unknown power for 

 which we have no grounds for support. We require to simplify 

 matters and diminish the load, not to increase it by fresh unte- 

 nable hypotheses. The wide bearing of this subject cannot fail 

 to be apparent. We are now in a position if not to explain, at 

 least to get a somewhat clearer insight into such phenomena as the 

 wonderful action of a germinating embryo on the endosperm cells 

 which are practically outside of it, of the various phenomena 

 attending the whole process of germination, of the action of a 

 tendril towards its support, of the action of the root tip with 

 regard to the medium which it traverses and the movements it 

 makes. 



Nov. 27, 1882. 

 Mr Glaisher, President, in the chair. 

 The following communications were made to the Society : 



(1) On the Complex Multiplication of Elliptic Functions. By 

 A. G. Greenhill, M.A. 



Jacobi, in a posthumous paper, " De multiplicatione functionum 

 ellipticarum per quantitatem imaginariam pro certo quodam modu- 

 lorum systemate " {Gesammelte Werke,Vol. I. p. 491) has shown how, 



when = = Jn and n is an odd integer, to express sn (a + ib \/n) u 

 A 



20—2 



