8o INTRODUCTION 



or principle of the series which enables us to say that the 

 ' infinitely little ' difference may be neglected because the 

 character of the series is not affected by it. 



But in neglecting this * infinitely little ' difference, 

 because of the special character or law of the series, we 

 have virtually passed from the unity of mere quantity to 

 a unity of character, a unity in which the parts are not 

 entirely indifferent to the whole and to one another, but 

 are connected in accordance with some special principle. 

 We have thus given an indefinite increase of elasticity to 

 the formulae of Algebra and have prepared the way for 

 an algebraic representation and calculus not merely of the 

 elementary space-unities (figures) of the Greek Geometry, 

 but also of more comprehensive geometrical unities of 

 which these are elements, and further of physical unities 

 and indeed of any unity the elements of which are in 

 themselves capable of a sufficiently accurate quantitative 

 expression. For instance, the phenomena with which 

 Physics deals are differences of a unity, elements in 

 a whole. But the unity, the whole, is not one of quantity 

 merely. And yet its elements are capable of quantitative 

 expression with a degree of accuracy such that its dif- 

 ference from absolute accuracy may be neglected so far as 

 physical science is concerned. Consequently it becomes 

 possible to state and to work out nggfelems of physical 

 science in terms of Algebra. 



The Infinitesimal Calculus and the Principle of Becoming 

 or System. 



The practical development of this possibility is the 

 function of the Infinitesimal Calculus of Leibniz and 

 Newton 3 . As we have already seen, the Analytical 



1 A succinct account of the famous controversy regarding the 

 discovery of this method, and of the different forms in which 

 Leibniz and Newton expressed it/will be found in Dr. William- 

 son's article * Infinitesimal Calculus ' in the pth ed. of the Encyclo- 

 paedia Britannica. Cf. Merz, History of European Thmight in the Nineteenth 

 Century, i. 100-103. 



