372 MR, R, T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
reference to the planes m / to', we have made an error in the observed angles P M, P M' 
(Section IL), and hence in the position of P referred to the axes. 
Or, secondly, that the position of P relatively to to to' has been accurately found, 
but that the axes of elasticity differ slightly in direction from their assumed positions, 
so that O C is not parallel to the intersection of to to', and O B does not bisect the 
angle M 0 M'. 
We will take the first hypothesis first, and consider what must be the error in P M, 
P M' to give rise to the required change in the position of P. 
Fig. 14. 
Let P' be the new position of P, we require M P' M' P'. 
Let P Iv be perpendicular on LP' 
LK=LP approximately 
KP =0° 17' approximately 
KP = PLK sin 35° approximately 
= 60' X '57 
= 34' approximately 
Now PK P' is approximately a small plane triangle with a right angle at K. 
PP'=yPK 2 +P'K 3 
= v /34 2 +l7 3 
= 17V5 
whence 
PP'=38' 
Again 
cos CP'= cos CL cos LP'— sin CL sin LP' cos ALP' 
whence 
CP'= 35° 58' 
CP =35° 43' [Section II. (12)] 
PP'= 0° 38' 
