METHOD OF VARIATIONS. 51 



F>\vler has well remarked a , the observation of variations 

 is really an integration of a supposed infinite number of 

 applications of the so-called method of difference, that 

 is of experiment in its perfect form. 



In induction we aim at establishing a general law, and 

 if we deal with quantities that law must really be expressed 

 more or less obviously in the form of an equation, or it 

 may be in more than one equation. We treat as before of 

 conditions, and of what happens under those conditions. 

 But the conditions will now vary, not in quality, but 

 quantity, and the effect will also vary in quantity, so that 

 bhe result of quantitative induction is always to arrive at 

 some mathematical expression involving the quantity of 

 each condition, and expressing the quantity of the result. 

 [n other words, we wish to know what function the effect 

 is of its conditions. We shall find that it is one thing to 

 obtain the numerical results, and quite another thing to 

 detect the law obeyed by those results, the latter being an 

 operation of an inverse and tentative character. 



The Variable and the Variant. 



Almost every series of quantitative experiments is 

 directed to obtain the relation between the different 

 values of one quantity which is varied at will, and an- 

 )ther quantity which i* caused thereby to vary. We 

 may conveniently distinguish these as respectively the 

 carialjle and the variant. When we are examining the 

 effect of heat in expanding bodies, heat, or one of its 

 iimensions, temperature, is the variable, length the 

 variant. If we compress a body to observe how much 

 t is thereby heated, pressure, or it may be the dimensions 

 jf the body, forms the variable, heat the variant. In 

 ihermo-electric pile we make heat the variable and the 



a ' Elements of Inductive Logic,' ist edit. p. 175. 

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