NATURE AND LAW. 377 



It was not until twelve years after the publication of his first 

 two " laws," that Kepler was able to announce the discovery of the 

 third ; which expresses the numerical relation between the re- 

 spective distances of the planets from the sun, and the times oi their 

 revolution around him. This, again, was the outcome of a long 

 series of guesses. And what was remarkable as to the error of the 

 idea which suggested the second law to his mind, was still more 

 remarkable as to the third ; for not only, in his search for the 

 "harmony " of which he felt assured, did he proceed on the 

 erroneous notion of a whirling force emanating from the sun, 

 which decreases with increase of distance, but he took as his guide 

 another assumption no less erroneous, viz., that the masses of the 

 planets increase with their distances from the sun. In order to 

 make this last fit with the facts, he was driven to assume a relation 

 of their respective densities, which we now know to be utterly 

 untrue ; for, as he himself says, " unless we assume this proportion 

 "of the densities, the law of the periodic times will not answer." 

 Thus, says his biographer, " three out of the four suppositions 

 "made by Kepler to explain the beautiful law he had detected, are 

 " now indisputably known to be false ; " what he considered to be 

 the /r^^ of it, being only a mode of false reasoning by which "any 

 "required result might be deduced from any given principles." 

 And yet I cannot doubt that if Kepler had found his " law " to be 

 inconsistent with \}c\.Q.Jacts of which it was the generalized expression, 

 he would have at once surrendered this pet child of his old age, 

 with the same honest zeal for truth that led him to abandon the 

 earlier offspring of his creative brain. 



Neither of the " laws " formulated by Kepler, then, can be 

 regarded as having any higher than an absolutely einpirical value ; 

 being good as expressions of certain classes of uniformities ob- 

 servable in nature ; but, as he left them, quite untrustworthy — 

 except as a guide to further inquiry — beyond the limits of the 

 experience on which they were based. They had (as it seems to 

 me) just the value of what is commonly known as "Bode's formula" 

 (called by Professor Newcome the " law of Titius "), in regard to 

 the distances of the planets from the sun : for this gave a numerical 

 expression of the several distances of Mercury, Venus, the Earth, 

 Mars, Jupiter, Saturn, and Uranus, which not only agreed sufficiently 



