'82 THE PRINCIPLES OF SCIENCE. 



square of the radius. This part of the law of gravity 

 may be considered as due to the properties of space, and 

 there is a perfect analogy in this respect between gravity 

 and all other emanating forces or substances, as was pointed 

 out in a most comprehensive and clear manner by Keill 11 . 

 Thus the undulations of light, heat, sound, and the attrac- 

 tions of electricity or magnetism obey the very same law 

 so far as we can ascertain. If the molecules of a gas or 

 the particles of matter constituting odour were to start 

 from a point and move from it in straight lines uniformly, 

 their distances would increase and their density decrease 

 according to the same principles. 



The other known laws of nature stand in a precisely 

 similar position. Dal ton's laws of definite combining 

 proportions never have been, and never can be exactly 

 proved ; but chemists having shown, to a considerable 

 degree of approximation, that all the more common 

 elements combine together as if each element had 

 atoms of an invariable mass, assume that this is ex- 

 actly true. They go even further. Prout pointed out 

 in 1815 that the equivalent weights of the elements 

 appeared to be simple commensurable numbers ; and 

 Dumas, Pelouze, Marignac, Erdmann, Stas, and others 

 have gradually rendered it likely that the atomic weights 

 of hydrogen, carbon, oxygen, nitrogen, chlorine, and 

 silver, are in the ratios of the numbers i, 12, 16, 14, 

 35*5, and 108. Chemists then step beyond their data; 

 they throw aside their actual experimental numbers, and 

 assume that the true ratios are not those exactly indicated 

 by any weighings, but the simple ratios of these numbers. 

 They boldly assume that the discrepancies are due to 

 experimental errors, and they are justified by the fact 

 that the more elaborate and skilful the researches on the 

 subject, the more nearly their assumption is verified. 

 11 'An Introduction to Natural Philosophy/ $rd. edit., 1733, p. 5- 



