262 THE PRINCIPLES OF SCIENCE. . [CHAP. 



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 discriminating between 

 coincidences which are casual and those which are the 

 effects of law. By a fortuitous or casual coincidence, we 

 mean an agreement between events, which nevertheless 

 arise from wholly independent and different causes or con- 

 ditions, 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, objects, 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. 2 

 The accidents connected with the number seven have mis- 

 led the human intellect throughout the historical period. 

 Pythagoras imagined a connection between the seven 

 planets and the seven intervals of the moiiochord. The 

 alchemists were never tired of drawing inferences from 

 the coincidence in numbers of the seven planets and the 

 seven metals, not to speak of the seven days of the 

 week. 



A singular circumstance was pointed out concerning 

 the dimensions of the earth, sun, and moon ; the sun's 

 diameter was almost exactly no times as great as the 



1 Newton's Opticks, Bk. I., Part ii. Prop. 3 ; Nature, vol. L p 286 



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



