xii.] THE INDUCTIVE OR INVERSE METHOD. 263 



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. The agree- 

 ment was so close that it might have proved more than 

 casual, but its fortuitous character is now 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 tiiis be not a law to be ultimately ex- 

 tended to all the elements, as supposed by Frout, 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 connection with the 

 principles of physical astronomy. Front's Law bears more 

 probability because it would bring the constitution of the 

 elements themselves in close connection with the atomic 

 theory, representing them as built up out of a simpler 

 substance. 



In historical and social matters, coincidences are fre- 

 quently pointed out which are due to chance, although 

 there is always a strong popular tendency to regard them 

 as the work of design, or as having some hidden meaning. 

 If to 1794, the number of the year in which liobespierre 

 fell, we add the sum of its digits, the result is 1815, the 

 year in which Napoleon fell ; the repetition of the process 

 gives 1830 the year in which Charles the Tenth abdicated. 

 Again, the French Chamber of Deputies, in 1830, consisted 

 of 402 members, of whom 221 formed the party called 

 "La queue de liobespierre," while the remainder, 181 in 

 number, were named " Les honuetes gens." If we give to 

 each letter a numerical value corresponding to its place in 

 the alphabet, it will be found that the sum of the values 

 of th(^ letters in each name exactly indicates the number 

 of the party. 



