THE UNITY OF SCIENCE 17 



composed. But this is a consequence of the very nature of a 

 scientific law. For such a law, if properly drawn up, is al- 

 ways (to borrow a convenient term from the mathematicians) 

 a statement of some constant relation or ratio between two or 

 more variables ; it does not prescribe the limits of variation of 

 the variables. The law of gravitation tells us that bodies at- 

 tract one another directly as their masses and inversely as the 

 squares of their distances; it does not tell us how many 

 bodies there are in the universe, or even the solor system, nor 

 what their actual masses are, nor their initial distances from 

 one another. To find the position of Mars on a given even- 

 ing next month with the aid of the formula of gravitation, 

 you must have some information upon these last-mentioned 

 points. This constitutes no logical imperfection in the law; 

 the variables in question are expressly provided for in the 

 law itself, and the possession of empirical knowledge about 

 them is presupposed as the condition of the rightful applica- 

 tion of the law to particular cases. But it is one thing to be 

 unable to deduce a particular phenomenon from a general law, 

 without the aid of the supplementary empirical knowledge 

 for which the law calls, and quite another thing to be unable 

 to make such a deduction even when you have that empirical 

 knowledge which was the apparent situation in the problem 

 of the deduction of the monkey's position from the laws of 

 physics or chemistry. It is these two wholly disparate sorts 

 of non-deducibility which seem to have been confused in the 

 passage I last cited. Scientific unification, then, takes place 

 in so far as diverse classes of phenomena come to be recog- 

 nized as deducible from a single, relatively simple general- 

 ization concerning the correlation of certain variables pro- 

 vided that in each particular case the actual natures or values 

 of the variables be known. And unification fails of attain- 

 ment in so far as two or more kinds of phenomena appear (in 

 the light of existing knowledge) as undeducible from any 

 single, already verified law, even were the actual values of the 

 variables referred to by any such law precisely ascertained 



