Prof. Challis on Newton's "Foundation of all Philosophy" 287 



fingo," of wliicli the history of physical science has afforded too 

 many examples. 



The foregoing discussion has prepared the way for making 

 the proper distinction between the theoretical and the experi- 

 mental departments of natural philosophy. The province of 

 experiment is to discover facts and the relations of facts, i. e. 

 laws, without respect to causation, or the operation of force. 

 Kepler's discovery of the laws of the motions of the planets is 

 an instance. Experiment also furnishes the data necessary for 

 making theoretical calculation apply to actual instances, and for 

 verifying the results of such calculation. The province of 

 theory is to deduce, by reasoning, from the fundamental ideas of 

 matter and force, the explanations of facts and laws established 

 by experiment, and so to refer them to their causes. In the 

 experimental department, a law is a grouping of observed facts; 

 in the theoretical, the law is shown to be the consequence of 

 certain primary facts. Every fact and every law which experi- 

 ment makes known, is a problem for the theorist to solve by 

 mathematical reasoning. 



It should here be remarked that physical astronomy does not 

 immediately come under the above definition of theory, because, 

 while it refers the observed motions of the heavenly bodies to 

 the action of forces, it rests on two particular hypotheses, made 

 pro hdc vice, viz., that all bodies attract in proportion to their 

 masses, and that the attraction varies according to the law of 

 the inverse square. The truth of these hypotheses is established 

 by the coincidence of the results of calculation founded on them 

 with facts of observation. That being the case, the hypotheses 

 may be regarded as facts, to be placed in the category of facts 

 in general, which require to be referred, for their explanation, to 

 the fundamental ideas of matter and force. Thus the law of 

 gravity, being a quantitative law, should be deducible by 

 reasoning. 



The theoretical reasoning above spoken of is, of course, 

 mathematical reasoning conducted by symbols. It would not 

 be possible, without the aid of such means, to embrace with the 

 deductive faculty the consequences of the fundamental hypo- 

 theses. In physical astronomy the symbolic reasoning consists 

 in the formation and solution of differential equations of the 

 first order in regard to the number of variables. A general 

 physical theory in which force is regarded as the action of a 

 fluid medium by pressure, evidently demands the determina- 

 tion by mathematics of the laws of the motion and pressure of 

 the fluid, to effect which the application of a higher and more 

 comprehensive order of differential equations is required. Per- 

 ceiving; the absolute necessity of this research for making pro- 



