110 KEPLIES TO CRITICISMS. 



as a coherent cinder, or as a diffused impalpable powder ; 

 and again, by applying heat, forces it to disclose itself as an 

 clement of animal tissue. Evidently, while thus ascertain 

 ing the affinities and atomic equivalence of carbon, the 

 chemist has nothing to do with any aggregate. He deals 

 with carbon in the abstract, as something considered apart 

 from quantity, form, appearance, or temporary state of com 

 bination ; and conceives it as the possessor of powers or 

 properties, whence the special phenomena he describes re 

 sult : the ascertaining of all these powers or properties being 

 his sole aim. 



Finally, the Abstract Sciences ignore alike aggregates and 

 the powers which aggregates or their components possess; 

 and occupy themselves with relations either with the re 

 lations among aggregates, or among their parts, or the 

 relations among aggregates and properties, or the relations 

 among properties, or the relations among relations. The 

 same logical formula applies equally well, whether its terms 

 are men and their deaths, crystals and their planes of cleav 

 age, or letters and their sounds. And how entirely Mathe 

 matics concerns itself with relations, we see on remembering 

 that it has just the same expression for the characters of an 

 infinitesimal triangle, as for those of the triangle which has 

 Sirius for its apex and the diameter of the Earth s orbit for 

 its base. 



I cannot see how these definitions of these groups of 

 sciences can be questioned. It is undeniable that every 

 Concrete Science gives an account of an aggregate or of 

 aggregates, inorganic, organic, or super -organic (a society); 

 and that, not concerning itself with properties of this or that 

 order, it concerns itself with the co-ordination of the as 

 sembled properties of all orders. It seems to me no less 

 certain that an Abstract- Concrete Science gives an account 

 of some order of properties, general or special ; not caring 

 about the other traits of an aggregate displaying them, and not 



