464 THE PRINCIPLES OF SCIENCE. [CHAP. 



the properties of space, and there is a perfect analogy 

 in this respect between gravity and all other emanating 

 forces, as was pointed out by Keill. 1 Thus the undulations 

 of light, heat, and sound, and the attractions of electricity 

 and 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 spread uniformly, their distances would increase and 

 their density decrease according to the same principle. 



Other laws of nature stand in a similar position. Dalton'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 

 the elements combine together as if each element had 

 atoms of an invariable mass, assume that this is exactly 

 true. They go even further. Prout pointed out in 1815 

 that the equivalent weights of the elements appeared to 

 be simple numbers ; and the researches of Dumas, Pelouze, 

 Marignac, Erdmann, Stas, and others have gradually ren- 

 dered 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 as- 

 sumption is verified. Potassium is the only element whose 

 atomic weight has been determined with great care, but 

 which has not shown an approach to a simple ratio with 

 the other elements. This exception may be due to some 

 unsuspected cause of error. 2 A similar assumption is 

 made in the law of definite combining volumes of gases, 

 and Brodie has clearly pointed out the line of argument 

 by which the chemist, observing that the discrepancies 

 between the law and fact are within the limits of ex- 

 perimental eiTor, assumes that they are due to error. 3 



1 An Introduction to Natural Philosophy, 3rd edit. 1733, p, 5. 



2 Watts. Dictionary of Chemistry, vot i. p. 455. 



3 Philosophical Transactions, (1866) vol. clvi. p. 809. 



