THE EXPLANATION OF LAWS 87 



So far the truth of a theory has been based on two 

 grounds ; first, that the laws to be explained can be 

 deduced from it ; second, that it really explains in the 

 sense that has been indicated. But actually there is in 

 addition, a.tliirdjtest_pf the truth of a theory, which is 

 of great importance ; a true theory will not only explain 

 adequately the laws that it was introduced to explain ; 

 it will alsojDrfidict and xplain~in-^vaiLce,laws.wiuch were 

 ~unFnQwn before . All the chief theories in science (or 

 aTTeast in physics) have satisfied this test ; they have 

 all led directly to the discovery of new laws which were 

 unsuspected before the theory was proposed. 



It is easy to see how a theory may predict new laws. 

 The theory, if it is worthy of consideration at all, will 

 be such that the old laws can be deduced from it. It may 

 easily be found on examination that not only these laws, 

 but others also can be deduced from it ; so far as the 

 theory is concerned, these others differ in no way from the 

 known laws, and if the theory is to be true, these laws 

 that are consequences of it must be true. As a matter of 

 fact, it is very seldom that a theory, exactly in its original 

 form, predicts any laws except those that it was proposed 

 to explain ; but a . very small and extremely natural 

 development of it may make it predict new laws. Thus, 

 to take our example, in order to explain the laws (Boyle's 

 and Gay-Lussac's) to which the theory was originally 

 applied, it is unnecessary to make any assumption about 

 the size of the molecules ; those laws can be deduced from 

 the theory whatever that size (so long as it is below a 

 certain limit) and the 'assumption was at first made for 

 simplicity that the molecules were mathematical points 

 without any size at all. But obviously it was more 

 natural to assume that the molecules, though extremely 

 small, l have some size and once that assumption is made, 



1 If a drop of water were magnified to the size of the earth, the 

 molecules would be about the size of cricket balls. 



