1878.J Propagation of Plane Waves in a Biaxal Crystal. 501 



CL = 1° 21' 42" 



01/ = 1° 15' 40" 



ALP = 59° 20' 11" 



AL'P = 59° 13' 2" 



while the position of P, the normal to the common face of the two 

 prisms, was given by — 



LP = 35° 0' 19" 

 or L'P = 35° 3' 14" 



Let 0' be the angles between any wave normal and the optic axes. 

 The formulae used to calculate Vi v % were — 



4-£+*-*=* cos (0 + 0'), 



v 2 2 = — Z _ cos (e-o ). 



The values used for a, b, c, were — 



a = 1-68560 

 & = 1-68115 

 c = 1-53013 



These values differ slightly from those used in the first part of the 

 paper, though not by nearly so large amounts as Rudberg found be- 

 tween the values for two different specimens of aragonite. He had 

 differences of more than -0004 (" Pogg. Annalen," xvii, 1). For the 

 outer sheet, which differs least from a sphere, the results of theory and 

 experiment agree fairly closely. But for the inner sheet the curve 

 given by theory agreeing with that given by experiment at the ex- 

 tremity of an axis, lies outside of it throughout the whole of its course 

 away from that axis. The difference is greatest at about 35° away 

 from the principal section, AOC being there as great as - 0009. 



From this point the differences decrease, and at the end of the arc 

 considered, or 74° away from the same axis, the value is 



•0003. 



I found also that no changes in the values of a, b, c, would produce 

 closer agreement, but that if we suppose the arcs LP, L'P, to be in- 

 creased by 17', and the angles ALP, AL'P, by about 1°, the differences 

 between theory and experiment were reduced about -00006, taken 

 throughout the arc, being sometimes positive, sometimes negative. 



I have shown, however, that this change in the position of P in- 

 volves alterations in the measures by which its position relative to the 

 faces mm was determined, which are far in excess of any possible expe^ 

 rimental error, and that the only way of accounting for them is by 

 supposing the axes of elasticity of aragonite to be slightly variable in 

 position relatively to the faces of the crystal. 



