30 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
improbable, indeed next to impossible, that one uniform phase should extend over 
more than a very minute portion of superficies at a given instant, consistently with 
the conditions of continuity. 
30. The fairest way of considering the subject without assuming the uniformity of 
phase, is to take a section of the incident ray PQ parallel 
to the refracting surface, and therefore and upon 
every particle of this section to erect ordinates representing 
the phases of the different particles : the rippled surface 
which passes through the extremities of these ordinates 
PA 
will possess a kind of type, which after the time — will be 
transferred to the surface AB, through which it will be 
transmitted, with diminished intensity, into the refracting 
AP 
medium, and after a time — - will be brought into the 
a i 
position P / Q ; parallel to AB and PQ. 
Presented under this point of view, the question affords no hold whatever for the 
determination of 0 P and 1 think I am entitled to conclude that the formula 
• „ °l • A 
sin 0,=- sin 0, 
1 a 5 
a 
or 
r a , 
rests on no other foundation than an uncertain analogy drawn from the theory of 
sound, whereas the demonstrations 1 have given of the formulae 
ga sin $ 
^ — gp—sin 
1 ga sin d 
[ Jj ‘ 1 -f- s g l a j sin 
are quite independent of such analogy, and are true whatever may be the type of the 
rippled surface at the front of the waves. 
I may mention, by the way, that I think it arises from the existence of such a 
rippled front of wave, that the fringes of interference, which border the margin of a 
small aperture, upon which a conical pencil of light is incident, are found to vanish 
when the aperture exceeds a very small limit ; in fact, when the aperture is enlarged 
so as to admit a comparatively large chequered surface of the wave’s front, the several 
portions destroy each other’s effect by interference ; but when the aperture is so small 
as only to admit a portion which presents a uniformity of phase, then the fringes 
present themselves and admit of the usual explanation. The hypothesis of a rippled 
front is therefore not only the most probable when we consider the origin of the 
beam, but it accounts simultaneously for the non-spread of the wave and the disap- 
pearance of the fringes when the aperture is large. 
It may perhaps be urged in favour of the hypothesis of uniformity of phase in the 
