GENERALIZATION. 275 



one law phenomena which really belong to different laws. 

 It is generally known, for instance, that a spherical 

 shell of uniform matter attracts an external particle of 

 matter with a force varying inversely as the square of the 

 distance from the centre of the sphere. But this law 

 only holds true so long as the particle is external to the 

 shell. Within the sheU the law is wiiolly different, and 

 the aggregate gravity of the sphere becomes zero, because 

 the force in every direction is neutralized by an exactly 

 equal force. If an infinitely small particle be in the 

 superficies of a sphere, the law is again different, and the 

 attractive power of the shell is half what it would be 

 on particles infinitely close to the surface of the shell. 

 Thus in approaching the centre of a shell from a distance, 

 the force of gravity evinces a double discontinuity in 

 passing through the shell d . 



It may well admit of question, too, whether discontinuity 

 is really unknown in nature. We perpetually do meet 

 with events which are real breaks upon the previous law, 

 though the discontinuity may then be a sign that some 

 wholly independent cause has come into operation. If 

 the ordinary course of the tides is interrupted by an 

 enormous and irregular wave, we attribute it to an earth- 

 quake, or some gigantic natural disturbance. If a meteoric 

 stone falls upon a person and kills him, it is clearly a 

 discontinuity in his life, of which he could have had no 

 anticipation. A sudden sound may pass through the 

 air neither preceded nor followed by any continuous 

 effect. Although, then, we may regard the Law of Con- 

 tinuity as a principle of nature holding rigorously true in 

 many of the relations of natural forces, it seems to be a 

 matter of difficulty to assign the limits within which the 



d Thomson and Tait, 'Treatise on Natural Philosophy,' vol. i. pp. 



346-351' 



T 2 



