=e hehe 
REFRACTIVE POWER. 141 
in the 10th book of the Mécanique Céleste, and founded 
on the corpuscular hypothesis, the formulas would be dif- 
ferent for opaque and for transparent bodies. It is on 
A set of waves propagated circularly from any source, when they 
get to a considerable distance, may be regarded as proceeding in par- 
allel planes. In all cases, the portions of circles or spheres which are 
their true form have a common tangent which marks what is called 
the “ front’’ of the wave. . 
But whenever waves encounter any kind of obstacle, or enter any 
new medium, then, from and round each point of such encounter, a new 
set of spherical waves begins to spread. In denser media these new 
waves spread more slowly than in rarer, but when the obstacle is still 
surrounded by the same medium, then the velocity is unaltered. 
On these principles the ordinary laws of reflexion and refraction are 
proved on the theory of waves. 
In reflexion, if parallel waves u w! follow at equal intervals /, u im- 
pinging on the surface at 0, will cause a new circular wave to spread 
backwards from that point as a centre; when the next wave w! im- 
pinges at o/, it will do the same, and so on in succession. But when 
the wave from o/ has spread to a radius =A, that from o will have 
spread to a radius =2/A, and so on. Hence to these contemporaneous 
circular waves drawing a common tangent v v/ ¢ this will be the front 
of the reflected waves, and the radii to the points of contact o v, of v/, 
will give the inclination of the reflected rays, which is easily seen to be 
equal to that of the incident, since of v! =o! u=/, and o v=2o! v, whence 
o ol=o t, and the triangles upon these equal bases being right-angled, 
the angle v ¢ osu o o/, or the angle of incidence, is equal to that of 
reflexion. 
