CHAPTEE XV. 



ANALYSIS OF QUANTITATIVE PHENOMKNA. 



IN the two preceding chapters we have been engaged 

 in considering how a phenomenon may be accurately 

 measured and expressed. So delicate and complex an 

 operation is a measurement which pretends to any con 

 siderable degree of exactness, that no small part of the 

 skill and patience of physicists is usually spent upon this 

 work. Much of this difficulty arises from the fact that 

 it is scarcely ever possible to measure a single effect at a 

 time. The ultimate object must be to discover the 

 mathematical equation or law connecting a quantitative 

 cause with its quantitative effect ; this purpose usually 

 involves, as we shall see, the varying of one condition at 

 a time, the other conditions being maintained constant. 

 The labours of the experimentalist would be compara- 

 tively light if he could carry out this rule of varying one 

 circumstance at a time. He would then obtain a series of 

 corresponding values of the variable quantities concerned, 

 from which he might by proper hypothetical treatment 

 obtain the required law of connection. But in reality it 

 is seldom possible to carry out this direction except in an 

 approximate manner. Before then we proceed to the 

 consideration of the actual process of quantitative induc- 

 tion, it is necessary to review the several devices by 

 which a complicated series of effects can be disentangled. 

 Every phenomenon measured will usually be the sum, 

 difference, or it may be the product or quotient, of 

 two or more different effects, and these must be in some 



