318 Prof. Challis on the Principles of Theoretical Physics. 



made the supposition that they are all spherical, but not without 

 regard to antecedently known facts, such as the following. The 

 properties of bodies in a fluid or gaseous state are in no respect 

 altered by any change of the relative positions of the parts — a 

 fact which would hardly be conceivable if the atoms had any 

 other than the spherical form, because in that case their mutual 

 actions would have relation to directions in space. Light is 

 found to traverse some substances without modification, or 

 change of velocity, on changing the direction of its passage 

 through them ; and though this is not the case in other sub- 

 stances, yet as the latter are known to be crystalline, it is reason- 

 able to attribute the circumstance to the arrangement of the 

 atoms, and not to deviations from the spherical form. Lastly, I 

 have adopted the Newtonian doctrine that inertia is an essential 

 quality, but not quantitative, and that consequently all atoms 

 have the same specific inertia. According to this and the preced- 

 ing hypothesis, atoms differ from each other only in magnitude. 



The foregoing hypotheses relating to the aether and the qualities 

 of atoms are the only ones that I have employed in laying the 

 foundation of a general mathematical theory of the physical 

 forces. This circumstance, while it may give an idea of the 

 difficulty of the undertaking, at the same time affords a presump- 

 tion that the hypotheses are true, it being extremely improbable, 

 if that were not the case,, that in the varied and extensive appli- 

 cations that have been made of them, some obvious and fatal 

 contradiction would not have been encountered. The Newtonian 

 dictum, " hypotheses non fingo," must be taken with reservation, 

 as it is not possible to frame a physical theory without hypotheses. 

 The theory of gravitation, for instance, rests on the hypothesis 

 of the law of the inverse square. But they ought, no doubt, to 

 be few and fundamental, and to be such as admit of being tested 

 by means of mathematical reasoning founded on them. The 

 multiplication of hypotheses, and making them pro re natd, are 

 sure signs of a failing theory. 



It will be right here to draw a distinction as to kind and 

 degree between the verifications which the two classes of hypo- 

 theses admit of in the actual state of science. The verification 

 of the first class may be effected by comparing results deduced 

 from them by rigid mathematical reasoning directly with observed 

 phenomena. If, for instance, such deductions admit of being 

 brought into satisfactory comparison with the eleven different 

 kinds of phenomena of light which I previously enumerated (as, 

 I believe, may be done), there would be a strong presumption, 

 almost amounting to a proof, of the reality of the existence of 

 the aether, and of its being such as it was assumed to be. And 

 to arrive at this conclusion with so much of certainty as to allow 



