184 Mr Glaisher, On the developments of [Nov. 24, 



(5) On the secretory hairs on the stem of Thunbergia laurifolia. 

 By Messrs. W. Gardiner and R. I. Lynch. 



In this investigation Mr Lynch made the observations as to 

 the external morphology of the hairs, and Mr Gardiner examined 

 their microscopic structure and development. The authors stated 

 that the hairs exhibited many points of interest. They occurred 

 on the stem only at the base of each leaf insertion, and were thus 

 localised in a very exceptional manner. They were of a most 

 perfect cup form, and the watery and slightly acid secretion ap- 

 peared on the free surface and did not cause the raising of the 

 cuticle as so usually occurs in most secretory structures. They are 

 apparently unique as to their distribution, since they neither occur 

 in Thunbergia alata nor in such closely related genera as Meyenia 

 and Hexacentris. They are essentially transitory in nature and 

 are developed from a single epidermal cell. 



November 24, 1884. 



Prof. Foster, President, in the Chair. 



The following communications were made to the Society : 



(1) On the developments ofK', E', J' , G' in powers of the modulus. 

 By J. W. L. Glaisher, M.A. 



The quantities E, J, G, § 1. 



§ 1. Besides the quantities K and E of Legendre and Jacobi 

 and the quantity J=K — E of Weierstrass I have found it de- 

 sirable to treat also E — k' 2 K as a fundamental quantity, form- 

 ing one of a triad of which E and J are the other two members*. 

 Denoting E - k'*K by G it is found that not only E, J, G but also 

 J— G, E + G, E — J enter into the formulae of Elliptic Functions 

 in such a manner that these six functions form a special group by 

 themselves. 



Using accented letters to denote the same functions of k' that 

 the unaccented letters are of k we are thus concerned with the 

 following fourteen functions : 



* See a paper "On the Quantities K, E, J, G, K', E', J', G' in Elliptic 

 Functions," Quarterly Journal of Mathematics, Vol. xx., pp. 313 — 361. 



