274 THE PRINCIPLES OF SCIENCE. [CHAP. 



Herschel said, and as all natural objects exist in space, and 

 involve molecular movements, measurable in velocity and 

 extent, there is no apparent limit to the ultimate extension 

 of quantitative science. But the reader must not for a 

 moment suppose that, because we depend more and more 

 upon mathematical methods, we leave logical methods 

 behind us. Number, as I have endeavoured to show, is 

 logical in its origin, and quantity is but a development of 

 number, or analogous thereto. 



Division of the Subject. 



The general subject of quantitative investigation will 

 have to be divided into several parts. We shall firstly 

 consider the means at our disposal for measuring phe- 

 nomena, and thus rendering them more or less amenable 

 to mathematical treatment. This task will involve an 

 analysis of the principles on which accurate methods of 

 measurement are founded, forming the subject of the 

 remainder of the present chapter. As measurement, how- 

 ever, only yields ratios, we have in the next chapter to 

 consider the establishment of unit magnitudes, in terms of 

 which our results may be expressed. As every pheno- 

 menon is usually the sum of several distinct quantities 

 depending upon different causes, we have next to investi- 

 gate in Chapter XV. the methods by which we may disen- 

 tangle complicated effects, and refer each part of the joint 

 effect to its separate cause. 



It yet remains for us in subsequent chapters to treat of 

 quantitative induction, properly so called. We must 

 follow out the inverse logical method, as it presents itself 

 in problems of a far higher degree of difficulty than those 

 which treat of objects related in a simple logical manner, 

 and incapable of merging into each other bj> addition and 

 subtraction. 



Continuous Quantity. 



The phenomena of nature are for the most part mani- 

 fested in quantities which increase or decrease continu- 

 ously. When we inquire into the precise meaning of 

 continuous quantity, we find that it can only be described 



