40 



and 



or 



Mr. Connel's Analysis of Levyne. 

 0=P 1 /(y-«)-P 2 /(9) 



1= fir r+f (JZtj< 



(3.) 



The second equation is identical. 



Now any form of # /(0) which fully satisfies the equations 

 (2.) (3.) must satisfy the conditions of the problem; and there 



can be but one form which does satisfy the equations, for -p 1 - 



must have a definite numerical value for every value of 5, and 

 •'• f (0) can contain no arbitrary quantities. 



Now / (0) = cos 



fully satisfies equations (2.) (3.), .\ this is the only, and .\ the 

 true, value off(8). 



Hence by equations (1.) 



R = P cos0 + Q cos (a — 0) 



= Psin0-Qsin (*-0) (4.) 



adding the squares 



R* = P 3 + Q 2 + 2PQcos * (5.) 



Take AB, AC proportional to P and 

 Q ; draw BD parallel to AC, cutting 

 AD in D ; and join DC : 



BD = 



sin 



AB 



g.AB 



sin (a — 0) 

 by (4.) = AC. 



.*. AD is in the direction of the dia- 

 gonal. 



Also AD 2 = AB 2 + AC 2 + 2.AB. 

 AC . cos a. 



Comparing this with equation (5.), 

 we see that AD represents R in mag- 

 nitude as well as direction. 

 Caius College, Dec. 6, 1833. 



J. H. Pratt. 



VI. Analysis of Levyne. By ArthurConnel,^^. F.R.S.Ed.* 



A FEW years ago Sir David Brewster described this mi- 

 ■**■ neral as a new species, founding his discrimination of it on 

 an examination of its optical properties by himself, and on a 

 determination of its crystallographical characters by Mr.' Hai- 



* Communicated by the Author. 



