MR. R. T. G-LAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
327 
Considering first tlie inner sheet, we see that theory and experiment agree closely. 
The greatest difference is '00013 ; and in this case, by referring to the adjacent 
experimental values, it is clear that the value 1'53003 is too small. 
We must remember, however, that the investigations are concerned with that sheet 
of the surface of wave slowness of which the section by the plane, x y, is a circle, and 
that the section considered is inclined at an angle less than 5° to this plane; so that 
the form of the curve of section differs but little from a circle, and we may therefore 
reasonably suppose that any theory in which, one of the principal sections of the 
surface of wave slowness is a circle, would also agree fairly closely with our results. 
We therefore proceed to discuss the results for the outer sheet given in the table 
just preceding. 
And here we see at once that there is considerable difference between theory and 
experiment. 
Moreover, from <£'=12° 16' 53” to <f)' = 20° 5' 38”, the theoretical values of /x are 
uniformly greater than the experimental; while from <f>'=20° 35' 20” to <£' = 31° 42' 34” 
the reverse is the case. 
The difference between the two increases on the whole uniformly, and in the last 
case is as great as '0005. 
For the values <£'= 1 9° 13' 4” and <f>'= 20° 5' 38”, theory and experiment agree closely. 
To find the angle between any radius vector and the minimum one of the curve, we 
have to add to the value of <£' the angle M Q, which is 17° 37' 14”. 
Let us call the angle Q O P, 0. 
Then we see that for the angles 6— 0, 0= 37° (about), and 0=90 \ the curves given 
by theory and experiment agree. 
From 0= 29° 54' 7” to 6= 37° (about), the theoretical curve lies outside the 
experimental. 
From 0=37° (about) to 0=49 u 19' 48” the reverse is the case. 
In the neighbourhood of the axes the two must agree more closely. 
These conditions would all be satisfied by a curve which agrees with Fresnel’s 
section at the extremity of the minimum radius vector; lies inside it for about 40°; 
then cuts Fresnel’s curve again, and lies outside for the rest of the quadrant, agreeing 
again at the extremity of the maximum radius vector. 
At first sight there seems some discrepancy between this result and that arrived at 
already in Table XXV. for the first prism. 
But closer examination shows that the two results are corroborative. 
For, in the first place, the observations there tabulated apply to the neighbourhood 
of the major axis of the elliptic section. 
For about 6° on either side of this principal axis, the differences between theory and 
experiment are sometimes positive, sometimes negative ; that is, between these limits 
Fresnel’s section satisfies the results of experiment; but in the last eighteen 
observations there recorded, the experimental value of is always greater than the 
theoretical. 
