314 THE PRINCIPLES OF SCIENCE. 



the difference of absolute and relative gravity, as if it 

 were a new discovery proceeding from his theory 6 . More 

 than a century elapsed before other apparent exceptions 

 to the Newtonian philosophy were explained away. 



Newton himself allowed that the motion of the apsides 

 of the moon's orbit appeared irreconcilable with the law 

 of gravity, and it remained for Clairaut to remove the 

 reproach bj more complete mathematical analysis. There 

 must always indeed remain, in the motions of the tides 

 or of the heavenly bodies, discrepancies of some amount 

 between theory and observation ; but like discrepancies 

 have so often yielded in past times to prolonged investi- 

 gation that all physicists have come to regard them as 

 merely apparent exceptions, which will afterwards be found 

 to be new confirmations of the law with which they now 

 seem to conflict. 



The most beautiful instance, perhaps, which can be 

 adduced of an apparent exception, is found in the total 

 reflection of light, which occurs when a beam of light 

 within a medium falls very obliquely upon the boundary 

 separating it from a rarer medium. It is the general 

 law that when a ray strikes the limit between two media 

 of different refractive indices, part of the light is reflected 

 and part is refracted, but when the obliquity of the ray 

 within the denser medium passes beyond a certain point 

 there is a sudden apparent breach of continuity, and the 

 whole of the light is reflected. A very clear reason can 

 be given for this exceptional conduct of the light ; for 

 according to the law of refraction the sine of the angle of 

 incidence always bears a fixed ratio to the sine of the angle 

 of refraction, so that the greater of the two angles, which 

 is always that in the less dense medium, may increase up 

 to a right angle, but when the media differ in refractive 

 power, the less angle cannot become a right angle, as this 



e 'Principia/ bk. II. Prop. 20. Corollaries, 5 and 6. 



