REFRACTIVE POWER. 



141 



in the 10th book of the Mecanique Celeste, 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 u> follow at equal intervals A, u im- 



pinging on the surface at o, will cause a new circular wave to spread 

 backwards from that point as a centre; when the next wave u' 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 =/l, that from o will have 

 spread to a radius =2/1, and so on. Hence to these contemporaneous 

 circular waves drawing a common tangent v v' t this Avill be the front 

 of the reflected waves, and the radii to the points of contact o v, oi v>, 

 will give the inclination of the reflected rays, which is easily seen to be 

 equal to that of the incident, since ul v' =o! u=.\ and o v2o> v, whence 

 o o'=ot t, and the triangles upon these equal bases being right-angled, 

 the angle v t o=u o o', or the angle of incidence, is equal to that of 

 reflexion. 



