298 
MR. R, T. GLAZEBROOK OR PLANE WAVES IN A BIAXAL CRYSTAL. 
sin AL = 
sin AP, sin AP 7 L 
sin ALP, 
AL = 2° 31' 58" . 
(10) 
The solution of the triangle ALP leads to the same results. 
We now come to the experimental determination of the deviation and the calcula¬ 
tions of the refractive indices. 
Throughout the work for this prism, <f> represents the angle between the normal to 
the wave incident on or emerging from the face P, when in air, c// the corresponding 
angle in the crystal, while \p i]/ are the angles for the face P. I propose then to give a 
table of the values of <f> or xjt according as the wave was incident on P, or P. 
(2.) Of D+ i, i being the angle of the prism, D-pi is given because the expression 
which is equal to ^ ^ \ occurs in the formula, and it saved trouble to calculate 
D +i at once from the readings. 
(3.) Of the values of <p deduced from the formulae 
tan 
2 
i 
tan - tan cot 
</> + -p 
— 2 
proved in the first section and =i. 
(4.) Of the values of /x the refractive index as the mean of the results, given by 
the two formulae 
sin p —jx sin 
sin i p=n sin xp' 
Any difference in the two values of /x found from these two formulae was due only to 
the errors necessarily arising from the use of proportional parts, and rarely exceeded 
• 00001 . 
I also introduce a list of errors in the calculated quantities which would occur from 
errors of 10" in each of the observed quantities, taken so as to produce the maximum 
effect in the result. 
This list was obtained by setting down from the tables the errors to which the 
supposed errors in D and <f> would give rise. 
The numbers in the table of errors for /x are the digits in the fifth place of decimals. 
The next page gives the complete work for one observation as a sample. 
