Rcjiect'ion and Refraction of Light. ]47 



But if the repulsive forces are less than this, the ray, as R' S', will pro- 

 ceed, in the iietv nriedium, in a direction P'Q', depending on the magnitude 

 of the forces j and, as is completely demonstrated on the principles of 

 dynamics, rays of the same kind will be so deflected that the sines of 

 incidence and refraction will be in a constant ratio. This explains the 

 sixth fact. Hence it follows, that the velocity of light must be greater in 

 more refractive media. 



Of the nature of the curves between S and P, and of their lengths, and 

 degree of curvature, we know nothing at all ; but the whole of the curved 

 part, as to sense, is a mere physical point, so that S and P apparently co- 

 incide, and the force must be incomparably greater than gravity. 



The media being given, those particles of light which have a greater 

 momentum, will be less refracted by the given forces, than those wiiich 

 have a less momentum ; but that the rays may deviate in different propor- 

 tions in media of different natures, it is necessary that the attractions and 

 repulsions should be elective j to secure this, Newton required the fifth pos. 

 art. 5, which establishes the seventh fact. 



We should expect, that when a ray of a given sort, at a given incidence, 

 is reflected or refracted, at the confines of given media, the whole of it 

 would always be reflected or refracted, which is contrary to the third and 

 fourth facts ; hence Newton was obliged to introduce the seventh postulate, 

 wliich suflSces for an imperfect solution of these facts : the eighth and ninth 

 are evident consequences of the preceding conclusions. 



13. To shew the enormous forces here required. Sir John Herschel, on 

 data far within the bounds of probability, calculates that the force must be 

 2 X 10''^, or two hundred septilliou times greater than the ordinary intensity 

 of gravity. He adds : "In the undulatory hypothesis, numbers not less 

 immense will occur ; nor is there any mode of conceiving the subject, which 

 does not call upon us to admit the exertion of mechanical forces, which may 

 well be termed infinite." See Treatise on Light, art. 561. 



It is not easy to form a right conception of the above mentioned number: 

 take grains of sand so fine that one hundred will just lie in an inch, so that 

 one million will fill a cubic inch, how vast the quantity to form a body 

 large as the eartli. But two hundred septillions of such fine grains would 

 be sufficient, not to form one, or one million, but three millions of millions 

 of globus, each equal in magnitude to the earth ; and as much as the grains 

 in all these bodies is more than one grsiu, so much is the force required to 

 reflect or refract light, greater than the ordinary force of gravity. 



But if the Newtonian theory be admitted, incomprehensibly great as the 

 above estimate is, it falls vastly short of what is necessary for the efiect j 

 for in the calculation Sir .John Herschel has omitted one essential particu- 

 lar, which is, that the bending of the ray is produced, not by the whole 

 force of citiier, but by the differences of the forces which affect the particles 

 of the two media : because we know, as a fact, that there is no reflection 



