38 THE PRINCIPLES OF SCIENCE. [CHAP. 



concerning single circumstances. To prove that the 

 Homeric %a7U'6<? is copper we must show the identity of 

 each quality recorded of ^aX/to? with a quality of copper. 

 To establish Deal as the landing-place of Ccesar, all material 

 circumstances must be shown to agree. If the modern 

 Wroxeter is the ancient Uriconium, there must be the like 

 agreement of all features of the country not subject to 

 alteratio?i by time. 



Such identities must be expressed in the form A = B. 

 We may say 



Colour of Pacific Ocean = Colour of Atlantic Ocean. 



Smell of rotten egg = Smell of hydrogen sulphide. 

 In these and similar propositions we assert identity of 

 single qualities or causes of sensation. In the same form 

 we may also express identity of any group of qualities, as 

 in 



^oX/co? = Copper. 



Deal = Landing-place of Caesar. 



A multitude of propositions involving singular terms fall 

 into the same form, as in 



The Pole star = The slowest-moving star. 



Jupiter = The greatest of the planets. 



The ringed planet = The planet having seven satel- 

 lites. 



The Queen of England = The Empress of India. 



The number two = The even prime number. 



Honesty = The best policy. 



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." 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 simple identities; in 

 addition to some instances which have already been given, 

 I may suggest, 



Crystals of cubical system = Crystals not possessing 

 the power of double refraction. 



