186 Mr Glaisher, On a method of [Feb. 6, 



(2) Mr R. Irwin Lyxch exhibited to the Society a plant of 

 Duboisia myoporoides, from the Botanic Garden, and also some 

 dried specimens to shew the inflorescence. 



This plant, quite recently introduced by seeds from the Baron 

 von Mueller, is of interest as the souree of a new alkaloid, probably 

 of considerable medicinal value. It is called Duboisin, ami at 

 Sydney and Brisbane is now used in ophthalmic cases instead of 

 atropine. It is said to be superior and is much more powerful 

 and rapid, is less irritating, and is useful when the patient does 

 not respond properly to atropine. 



This Duboisia rnyojwroides forms a small tree about 20 ft. 

 high, and is native of Australia, near Sydney and at Cape York ; 

 it is also native of New Guinea and New Caledonia. It has small, 

 ]3ale lilac or white flowers, and belongs to the Solaneae. 



(3) On a method of deriving formula} in Elliptic Functions. 

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



[Read November 28, 1881.] 



If sn u, when the modulus is put equal to unity, be denoted by 

 sn 1 u, we have 



. . sn. u — sn. v 

 sn. (u - v) = ^ , 



and also, the modulus being k, 



j / ox i , o\ fcsn 2 g-fcsn 2 /3 



k sn (a — a) sn (a + p) = , u — § 2io 



v ^' K ^ 1 - k sn 2 a sir ft 



if therefore we put 



sn x u = k sn 2 a, sn t v = k sn 2 /3, 



we convert 



sUj (u — v) into k sn (a - /3) sn (a + /3). 



It follows therefore that if we have any formula involving only 

 the sn's of differences of quantities, if we first put k=l, we may 

 replace the sn of each difference by k times the product of the sn's 

 of the sums and differences of the quantities, i.e. 



snj (u - v) by k sn(u- v) sn (u + v), 



sn x {u — ?/>) by k sn {u — w) sn (u + w), &c. 



thus obtaining a new formulae which will be true for modulus k. 



