MR. MILL S VIEW. 99 



its equations. And just in the same way that these concrete 

 problems, solved by its aid, cannot by any possibility bo 

 incorporated with the Abstract Science of Algebra ; so I 

 contend that the concrete problems of Astronomy, cannot by 

 any possibility be incorporated with that division of Abstract- 

 Concrete Science which develops the theory of the inter 

 actions of free bodies that attract one another. 



On this point I find myself at issue, not only with Prof. 

 Bain, but also with Mr. Mill, who contends that : 



&quot;There is an abstract science of astronomy, namely, the theory 

 of gravitation, which would equally agree \vith and explain the 

 facts of a totally different solar system from, the one of which our 

 earth forms a part. The actual facts of our own system, the di 

 mensions, distances, velocities, temperatures, physical constitution, 

 etc., of the sun, earth, and planets, are properly the subject of a 

 concrete science, similar to natural history ; but the concrete is 

 more inseparably united to the abstract science than in any other 

 case, since the few celestial facts really accessible to us are nearly 

 all required for discovering and proving the law of gravitation as 

 an universal property of bodies, and have therefore an indispensable 

 place in the abstract science as its fundamental data.&quot; Auguste 

 Comte and Positivism, p. 43. 



In this explanation, Mr. Mill recognizes the fundamental 

 distinction between the Concrete Science of Astronomy, 

 dealing with the bodies actually distributed in space, and 

 a science dealing with hypothetical bodies hypothetically 

 distributed in space. Nevertheless, ho regards these sciences 

 as not separable; because the second derives from the first 

 the data whence the law of inter-action is derived. But 

 the truth of this premiss, and the legitimacy of this infer 

 ence, may alike be questioned. The discovery of the law of 

 inter-action was not due primarily, but only secondarily, to 

 observation of the heavenly bodies. The conception of an 

 inter-acting force that varies inversely as the square of the 

 distance, is an a priori conception rationally deducible from 

 mechanical and geometrical considerations. Though unliko 

 in derivation to the many empirical hypotheses of Kepler 



