THE INDUCTIVE OR INVERSE METHOD. 303 



pretends to give, is the result in the long run, as it is 

 called, and this really means in an infinity of cases. 

 During any finite experience, however long, chances may 

 be against us. Nevertheless the theory is the best guide 

 we can have. If we always think and act according to 

 its well interpreted indications, we shall have the best 

 chance of escaping error ; and if all persons, throughout 

 all time to come, obey the theory in like manner, they 

 will undoubtedly thereby reap the greatest advantage. 



No rule can be given for descriminating between 

 coincidences which are casual and those which are the 

 effect of law or common conditions. By a fortuitous or 

 casual coincidence, we mean an agreement between events, 

 which nevertheless arise from wholly independent and 

 different causes or conditions, and which will not always 

 so agree. It is a fortuitous coincidence, if a penny thrown 

 up repeatedly in various ways always falls on the same 

 side ; but it would not be fortuitous if there were any 

 similarity in the motions of the hand, and the height of 

 the throw, so as to cause or tend to cause a uniform 

 result. Now among the infinitely numerous events, ob- 

 jects, or relations in the universe, it is quite likely that 

 we shall occasionally notice casual coincidences. There 

 are seven intervals in the octave, and there is nothing very 

 improbable in the colours of the spectrum happening to 

 be apparently divisible into the same or similar series of 

 seven intervals. It is hardly yet decided whether this 

 apparent coincidence, with which Newton was much 

 struck, is well founded or not 1 , but the question will 

 probably be decided in the negative. 



It is certainly a casual coincidence which the ancients 

 noticed between the seven vowels, the seven strings of the 

 lyre, the seven Pleiades, and the seven chiefs at Thebes k . 



i 'Nature,' vol. i. p. 286. 



k Aristotle's ' Metaphysics,' xiii. 6. 3. 



