304 THE PRINCIPLES OF SCIENCE. 



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 monochord. 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 

 earth's diameter, while in almost exactly the same ratio 

 the mean distance of the earth was greater than the sun's 

 diameter, and the mean distance of the moon from the 

 earth was greater than the moon's diameter 1 . The agree- 

 ment was so close that it might have proved more than 

 casual, but its fortuitous character is sufficiently shown 

 by the fact, that the coincidence ceases to be remarkable 

 when we adopt the amended dimensions of the planetary 

 system. 



A considerable number of the elements have atomic 

 weights, which are apparently exact multiples of that 

 of hydrogen. If this be not a law to be ultimately ex- 

 tended to all the elements, as supposed by Prout, it is a 

 most remarkable coincidence. But, as I have observed, 

 we have no means of absolutely discriminating accidental 

 coincidences from those which imply a deep producing 

 cause. A coincidence must either be very strong in 

 itself, or it. must be corroborated by some explanation or 

 connection with other laws of nature. Little attention 

 was ever given to the coincidence concerning the dimen- 

 sions of the sun, earth, and moon, because it was not very 

 strong in itself, and had no apparent connexion with the 



1 Chambers'^ 'Astronomy/ ist. ed. p. 23. 



