3io ELEMENTS OF SCIENCE 



It is true that the dictum "whatever you can assert 

 of all things contained under a class, can be asserted of 

 that class." This is manifest, obvious, and even trivial, 

 and of no practical value. 



The form of induction is as follows : 



a + b + c is Z. 

 but a + b + c = all X. 



therefore X is Z. 



It is, however, only in very rare instances that a + b + c 

 are all X. 



The practical dictum of induction is : " What you can 

 say of a sufficient number of particulars of any class 

 under a required diversity of circumstances and condi- 

 tions, you can fairly predicate of the whole class." It is 

 the main process used in the development of the physical 

 sciences. 



It is the process of discovering laws from facts, and 

 causes from effects. 



a + b + c is Z, 



but a + b + c though not all X may, from the peculiarity 



of their circumstances, be taken as practically = all X, 



therefore X is Z. 



Deduction, as we have now seen, derives facts from laws, 

 and effects from causes. 



We all notice, with more or less readiness and facility, 

 resemblances and differences, and we group these in 

 relation to their antecedents and consequences. As an 

 example, we may take the fact before noticed * that 

 while almost all bodies tend to fall, they fall differently 

 in the open air and under the bell-glass of an air pump. 



We study nature always by observations, but we can 



* See ante, p. 60. 



