296 
MR. R. T. GLAZEBROOK ON PLANE WAYES*IN A BIAXAL CRYSTAL. 
Again, from triangle P M B, 
cos PM= cos BP cos BM+ sin BP sin BM cos PBM 
or 
and from P If M, 
cos 6= cos (3 sin /x+ sin (3 cos fx cos B 
cos 6'= cos ft sin [x — sin (3 cos jx cos B 
cos 0 + cos 0' 
.*. cos (3= 
2 sin ix 
0 + 0 ' 0'-0 
cos —— cos —— 
sm jx 
Now the angles 6 9' were determined by observation. 
Each angle was observed six times on two different days. 
The mean of the results was, 
6 = 77° 18' 44" 
0'=lOO o 43' 30" 
Some difficulty was experienced about the angle /a. 
Professor Miller gives it as 58° 5'; but this, when substituted in the above formulae, 
gives a value for P P / the supplement of the angle of the crystal, which differs con¬ 
siderably from the measured angle. 
I therefore measured the angle /x and found it to be 58° 30' nearly. 
Mr. Garnett (the Demonstrator at the Cavendish Laboratory) kindly communicated 
this result to the Pev. H. P. Gijrney, of Clare College, who was then lecturing for 
Professor Miller, and he measured the angle with very nearly the same result as I 
had already arrived at. Taking, then, the value he obtained, and assuming as before 
that 0 B bisects the angle M 0 M', we have 
/x=58° 28'.* 
Whence from the formulae (1) (2) 
a = 67° 10' 35" 
( 3 ) 
/3= 88° 52' 40" 
( 4 ) 
For the position of P / w r e have similarly, 
0 , = 80° 39' 
0/=lOl° 16' 23" 
Whence, 
a =69° 59' 20" 
£ — 91° 6' 30" 
( 5 ) 
( 6 ) 
* This value of the angle /<. is given in Dana’s ‘Mineralogy,’ for specimens of arragonite coming from 
Silesia. The piece used was obtained from that neighbourhood. 
