Permanent Contraction of the Planetary Orbits. 97 



I have shown in my previous papers that the theoretic 

 atomic weights of several allied series of elements so closely 

 agree with those obtained experimentally, that the differ- 

 ences amount to less than half of 1 per cent, of the whole 

 of these series. It will, therefore, be evident to philosophic 

 thinkers in every department of science, that the experi- 

 mental atomic weights, or any other property of matter 

 which the same numbers represent, are only approxima- 

 tions and subordinate to the theoretic law itself, just as the 

 actual planetary orbits differ from those perfectly elliptical, 

 as deduced from the law of gravitation. 



It is not a little remarkable that in my comparison of 

 the atomic weights and the radii vectores of the planetary 

 orbits, I should have to encounter the same kind of objec- 

 tion against a law of multiple proportions of planetary 

 distances as that which has been advanced against the 

 multiple proportions of the atomic weights. 



As the quantitative determinations of observational 

 astronomy and molecular physics require the same qualities 

 of mind and methods of investigation, it is not surprising 

 to find that, when a number of recurring instances ap- 

 proaching the nature of a law are brought under the notice 

 of an astronomical computer, he will pronounce for, or 

 against, the assumed law according to his particular bias or 

 idiosyncrasy. Hence it is that Bode's law of planetary 

 distances is considered by some only as an aid to astrono- 

 mical research, while others reject it altogether. 



This law, briefly stated, is as follows :: — The radii vectores, 

 or the relative mean distances of the planets from the sun, 

 proceed in multiple proportions ; each one after the second 

 being double the one which precedes it, and by adding 4 to 

 each progression, we obtain approximately the distances of 

 the planets, as shown in the following table :— 



