MR, R. T. GLAZEBROOK OR PLANE WAVES IN A BIAXAL CRYSTAL. 
373 
Hence from the triangle POP' we get 
PCP'^O 0 58 
But from the triangle A C P 
ACP =57° 42' 30" [Section II.] 
ACP'=58° 40' 30" 
but 
whence 
ACM = 58° 7' 30" [Section II. (7)] 
. MCP= 0° 33' 
cos MP'= cos MCP sin CP' 
MP'=54° 58' 50" 
The original value of M P' was as given by the mean of a large number of 
observations 
MP' = 54° 17' 6" [Section II. (3)]. 
The difference, amounting as it does to over 40', is far beyond any possible error of 
experiment. 
Let us find further the change in M' P, 
cos M'P = sin CP' cos M'CP' 
M'CP'=63° 47' —33' 
whence 
The observed value was 
= 6 3° 14' 
M'P'= 74° 39' 40" 
M / P=75° 16' 20" [Section III. (4)]. 
The difference is 0° 36' 40". This, again, is far beyond any possible experimental 
error. Thus, so long as we assume the position of the axes of elasticity to be 
definitely fixed in the crystal so that O C is parallel to the intersection of m m while O B 
bisects the angle between them, the displacement of the plane P IP necessary to bring 
the results of experiment and theory into agreement is far too great to be possible. 
But there remains the supposition that the axes of elasticity have not exactly the 
same position in all crystals of arragonite. So that the displacement of P R relatively 
to the axes might be effected by changing slightly their position with reference to the 
faces of the crystal, P R retaining their position, relatively to those faces, unchanged. 
The possibility of this is a cjuestion for the mineralogist. I have been as yet unable to 
find data for a satisfactory answer. It seems, however, plausible to suppose that in a 
substance like arragonite which is not chemically pure, but contains foreign substances 
to a variable degree in different specimens, some slight variation such as that indicated 
might occur. 
