46 THE PRINCIPLES OF SCIENCE. 



In mathematical and scientific theories we often meet 

 with simple identities capable of expression in the same 

 form. Thus in mechanical science ' The process for finding 

 the resultant of forces = the process for finding the re- 

 sultant of simultaneous velocities a .' Theorems in geometry 

 often give results in this form, as- 

 Equilateral triangles = Equiangular triangles. 

 Circle = Finite plane curve of constant curvature. 

 Circle = Curve of least perimeter. 



The more profound and important laws of nature are 

 often expressible in the form of identities ; in addition to 

 some instances which have already been given I may 

 suggest 



Crystals of cubical system = Crystals incapable of 



double refraction. 



All definitions are necessarily of this form of simple 

 identity, whether the objects defined be many, few, or sin- 

 gular. Thus we may say 



Common salt = Sodium chloride. 



Chlorophyl = Green colouring matter of leaves. 



Square = Equal-sided rectangle. 



It is an extraordinary fact that propositions of this 

 elementary form, all-important and very numerous as 

 they are, had no recognised place in Aristotle's system of 

 Logic. Accordingly their importance was overlooked until 

 very recent times, and logic was the most deformed of 

 sciences. But it is quite impossible that Aristotle or any 

 other person should avoid constantly using them ; not a 

 term could be defined without their use. In one place at 

 least Aristotle actually notices a proposition of the kind. 

 He observes: 'We sometimes say that that white thing 

 is Socrates, or that the object approaching is CalliasV 

 Here we certainly have simple identity of terms ; but he 



a Thomson anil Tait, 'Treatise on Natural Philosophy,' vol. i. p. 182. 

 b ,' Prior Analytics,' I. cap. xxvii. 3. 



