s 
270  -REPORT—1862. 
working them to the same thickness, and then interposing them in the paths 
of two streams of light proceeding to interfere, as well as by the method of 
prismatic refraction ; and he states as the result of his observations that he 
can affirm the law to be, at least in the case of topaz, mathematically exact. 
The same result follows from the observations by which Rudberg so accu- 
rately determined the principal indices of Arragonite and topaz*, for the 
principal fixed lines of the spectrum. Professor MacCullagh having been led 
by theoretical considerations to doubt whether, in Iceland spar for instance; 
the so-called ordinary ray rigorously obeyed the ordinary law of refraction, 
whether the refractive indices in the axial and equatorial directions were 
strictly the same, Sir David Brewster was induced to put the question to the 
test of a crucial experiment, by forming a compound prism consisting of two 
pieces of spar cemented together in the direction of the length of the prism, 
and so ent from the crystal that at a minimum deviation one piece was tra- 
versed axially and the other equatorially?. The prism having been polished 
after cementing, so as to ensure the perfect equality of angle of the two parts, 
on viewing a slit through it the bright line D was seen unbroken in passing 
from one half to the other. More recently Professor Swan has made a very 
precise examination of the ordinary refraction in various directions in Iceland 
spar by the method of prismatic refraction t, from whence it results that for 
homogeneous light of any refrangibility the ordinary ray follows strictly the 
ordinary law of refraction. 
It is remarkable that this simple law, which ought, one would expect, to 
lie on the very surface as it were of the true theovy of double refraction, is 
not indicated @ priori by most of the rigorous theories which have been ad- 
vanced to account for the phenomenon. Neither of the two theories of Cauchy, 
nor the second theory of Green, lead us to expect such a result, though they 
furnish arbitrary constants which may be so determined as to bring it about. 
The curious and unexpected phenomenon of conical refraction has justly 
been regarded as one of the most striking proofs of the general correctness of 
the conclusions resulting from the theory of Fresnel. But I wish to point 
out that the phenomenon is not competent to decide between several theories 
leading to Fresnel’s construction as a near approximation. Let us take first 
internal conical refraction. The existence of this phenomenon depends upon 
the existence of a tangent plane touching the wave surface along a plane 
curve. At first sight this might seem to be a speciality of the wave-surface 
of Fresnel; but a little consideration will show that it must be a property of 
the wave surface resulting from any reasonable theory. For, if possible, let 
the nearest approach to a plane curve of contact be a curve of double curva- 
ture. Leta plane be drawn touching the rim (as it may be called) of the 
surface, that is, the part where the surface turns over, in two points, on 
opposite sides of the rim; and then, after having been slightly tilted by 
turning about one of the points of contact, let it move parallel to itself towards 
the centre. The successive sections of the wave-surface by this plane will 
evidently be of the general character represented in the annexed figures, 
1 2 
3 + 5 6 
ti en ) 
° Ww eS 
* Annales de Chimie, tom. xlviii. p. 225 (1831). 
+ Report of the British Association for 1843, Trans. of Sect. p. 7. 
{ Transactions of the Royal Society of Edinburgh, vol. xvi. p. 375. 
