Prof. Challis on the Force of Gravity. 4-t3 



antecedent and independent principle. This argument altogether 

 leaves out of consideration the part performed by mathematics 

 in physical research. The law of vis viva is a generalization of 

 mathematical deductions from the observed modes of action of 

 accelerative forces, and cannot, therefore, be legitimately adduced 

 as an anterior principle from which the nature of those forces 

 may be inferred. As we have no conception from personal ex- 

 perience and sensation of any other species of force than jwes- 

 sure, the actio in distans does not admit of being explained by 

 any previous or concomitant knowledge, but, if it be a reality, 

 must for ever remain to us incomprehensible. All such argu- 

 mentation as that employed by Professor Briicke is rendered 

 nugatory, if it can be shown by mathematical reasoning that the 

 physical forces are consequences of pressures. 



This is the undertaking in which I am engaged. But mathe- 

 matical reasoning must set out from principles ; and in selecting 

 those which are appropriate to this inquiry, I have been mainly 

 guided by Newton's views on the ultimate properties of matter, 

 especially as embodied in the Regula Tertia P hilosophandi in the 

 Third Book of the ' Principia.' The constituent particles of mat- 

 ter are there said to have finite dimensions, and to be hard, im- 

 ])enetrable, inert, and capable of movement. Whether they are 

 indivisible is considered to be uncertain. Modern chemical 

 science seems to have decided that they are appropriately desig- 

 nated as atoms, the observed constancy of the properties of sim- 

 ple bodies depending most probably on the indivisibility of their 

 constituent particles. Newton concludes the Regula with these 

 words : "Attamen gravitatem corporibus essentialem esse minime 

 affirmo. Per vim insitam intelligo solam vim iuertiaj. Hsec 

 iuimutabilis est. Gravitas recedendo a terra diminuitur." The 

 Jesuits merely i-emark on the last sentence, " ut infrk deraon- 

 strabitur," seemingly not pei'ceiving that it was added to point 

 out the distinction between a quantitative property, and one that 

 is not quantitative. The vis inertia is not quantitative, accord- 

 ing to Newton. There may be more or less of inert matter, but 

 not more or less of inertia. Hence the vis inertice is an essential 

 property. But gravity being a quantitative function of space, is 

 not an essential property of matter. Unless it can be shown 

 that abstract numerical relations are not commensurate with the 

 quantitative relations of natural bodies, it is a legitimate exten- 

 sion of Newton's principles to say that because the word square 

 occurs in the enunciation of the law of gravity, for this reason 

 alone the law is capable of demonstration. It is the j)cculiar 

 province of the science of numbers to aid the understanding in 

 tracing the consequences of hypotheses, and from true hypo- 

 theses to arrive at quantitative laws. 



