306 



Dr. Hagen on Malic Acid, and the Changes 



in biaxal crystals. Sir J. Herschel has given a solution in 

 Art. 1072 of his ' Treatise on Light,' but which, in my opinion, 

 is unnecessarily tedious and prolix. 



Problem. — Required a curve P A, such that a line drawn 

 from A bisecting the < between lines A P, A P' drawn to two 

 given points P, P', shall always be J_ ar to a given line x O. 



Solution.— Let O P = O F= «, OM=.r, M A = */, 

 PAD = FAD = 0, DOM = «. 

 By Euclid, 



A F _ F D 

 AP "" PD 



a cos a + x 

 a cos a — x' 



(1.) 



cos a 



Also, K A = A F cos = K M + M A = a sin « + y 

 AB=APcos0 = AM-MB=#-ftsin«; 



AF 

 AP 



a sin a + y _ a cos a + x 



y — asm a 

 y _ a cos a 



a cos a — x 



',by(i.) 



(r 



, or x y = a 2 sin a cos a ss — sm 2 a. 

 a smu x J 2 



Trinity College, Cambridge, Sept. 16, 1841. J. E. 



XLV. On Malic Acid, and the Changes undergone by its Salts 

 at High Temperatures. By Robert Hagen, Ph. Z).* 



\ FTER the publication of Mr. Graham's observation, that 

 ■^*- phosphoric acid, in its different states, possesses the pro- 

 perty of combining with one, with two, and with three atoms 

 of base respectively, it was discovered by Liebig that the same 



* Read before the Chemical Society, June 1, 1841, having been trans- 

 lated and communicated by T. G. Tilley, Esq., now communicated by the 

 Society. 



