ABSTEACT-CONCEETE PEOBLEMS. 97 



If I held what Prof. Bain supposes me to hold, my position 

 would be an absurd one ; but he misapprehends me. The 

 misapprehension results in part from his having here, as 

 before, used the word &quot;concrete&quot; with the Comtean mean 

 ing, as though it were my meaning ; and in part from the 

 inadequacy of my explanation. I did not in the least mean 

 to imply that the Abstract-Concrete Science of Mechanics, 

 when dealing with the motions of bodies in space, is limited 

 to the interpretation of planetary movement such as it would 

 be did only a single planet exist. It never occurred to me 

 that my words (see p. 19) might be so construed. Abstract- 

 Concrete problems admit, in fact, of being complicated in 

 definitely, without going in the least beyond the definition. 

 I do not draw the line, as Prof. Bain alleges, between the 

 combination of two factors and the combination of three, or 

 between the combination of any number and any greater 

 number. I draw the line between the science which deals 

 with the theory of the factors, taken singly and in combina 

 tions of two, three, four, or more, and the science which, 

 giving to these factors the values derived from observations of 

 actual objects, uses the theory to explain actual phenomena. 



It is true that, in these departments of science, no radical 

 distinction is consistently recognized between theory and the 

 applications of theory. As Prof. Bain says : 



&quot;Newton, in the First Book of the Principia, took up tho 

 problem of the Three Bodies, as applied to the Moon, and worked 

 it to exhaustion. So writers on Theoretical Mechanics continue to 

 include the Three Bodies, Precession, and the Tides.&quot; 



But, supreme though the authority of Newton may be as a 

 mathematician and astronomer, and weighty as are the names 

 of Laplace and Herschel, who in their works have similarly 

 mingled theorems and the explanations yielded by them, it 

 does not seem to me that these facts go for much ; unless it 

 can be shown that these writers intended thus to enunciate 



the views at which they had arrived respecting the classifi- 

 5 



