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MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
i.e., 
cos 1 n. 2 — cos 1 n 1 
not less than 55° 44' — 49° 35' 
or 6° 9 r 
But the angle between these radii is the difference between the two corresponding 
values of </>', or 
= 31° 42' 34" — 28° 1' 21" 
= 3° 41' 13" 
Again, taking the second and third, the angle deduced from theory is not less than 
cos 1 no —cos 1 n 3 
or 55° 44' —47° 56' 
or 7° 48' 
but from experiment it is 
31° 42' 34" —26° 19' 10" 
— 5° 23' 24" 
In both these cases the angle, as given by theory, must be very much larger than 
that given by experiment. 
Thus, in order that the three pairs of values of p. p 2 may correspond to three radii 
of the surface of wave slowness on Fresnel’s theory, the angles between them must 
be half as large again as they are found to be. 
Hence no section of the surface of wave slowness on Fresnel’s theory can agree 
with the results of the experiments. We may remark, in addition, that the differences 
between consecutive values of p for the outer sheet given by experiment are about 
double those given by theory. 
After this investigation it seems needless to discuss possible alterations in the posi¬ 
tion of the plane of the second prism, with a view to bringing the results of experi¬ 
ment more nearly into accordance with theory. While as regards the constants a, b, c, 
it has already been seen that they have received their most probable values. 
Thus our results, so far as they go, point to the fact that Fresnel’s construction 
does not represent Nature, and that some other theory must be sought to explain the 
phenomena of double refraction. 
And as regards the rival theories already proposed, Lord Rayleigh’s, we have seen, 
is even more than Fresnel’s at variance with observed appearances, while I can hardly 
think that sufficient data have yet been collected to repay the labour of comparison 
with the theories of Green and Cauchy, for on account of the undetermined constants 
it would be necessary to force theory and experiment to agree in so many points that 
they must, perforce, almost agree exactly along the small arcs investigated. 
