440 
MR, R, T. GLAZBBROOK ON DOUBLE REFRACTION 
Now when 
we see from Table X. 
But 
0= =90° 17' 56" 
/u,= 1*48457 
M 
1 _cos 2 8 ^ sin 2 8 
2 ' 
Mi 
1 cos 2 8 
/V 
M 
Mi 
cosec 2 d 
Substituting the values of /x, /x l5 and d we get 
/u a = 1-48456 
The values given by Mascart and Rudberg are 
1 ‘48455 
1‘48474 
ihe middle column of Table X. gives the values of /x in the directions given by the 
first column for the values 
fjij = 1 ‘65436 
/a 2 = 1-48456 
The Roman numerals I., II., &c., in the first column refer to the tables of experi¬ 
mental results from which the values of /x in the fourth column are taken. The fifth 
column gives the excess of experiment over theory. 
These differences it vdll be seen are much greater in the case of prism II. than for 
any of the others. 
They are also greater for the first part of the results in Table II., in which the face 
of incidence was P, than for the latter, when the light was incident on the face Q. 
Postponing, then, for the present the consideration of this point, let us compare the 
differences between theory and experiment for prisms I., IIL, and IV. We notice at 
once their extreme smallness—the greatest is only ‘00014, and only in eight out of the 
sixty measurements taken do they amount to as much as *0001. The mean irrespective 
of sign is ‘000055. The differences are, on the whole, negative near the major axis. 
They tend to become least at about 15° away from either axis. From that point they 
are positive and reach a maximum value at from 45° to 50° away from the major axis. 
So that the curve given by experiment would, though very nearly coincident with 
an ellipse, lie inside the ellipse near the major axis, cut it at about 15 from that axis, 
and lie outside for the rest of its course. 
The difference, however, between the radii vectors to the two curves drawn in the 
same direction would never be greater than To oo oth part of either. 
My first inference from these results was that Huyghen’s construction represented 
nature to a degree of exactness comparable with the probable error of experiment. 
