ptolemy versus copernicus.

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ing between them, first announced by Titius, in a translationof Bonnet’s “ Contemplation de la Nature,” published atLeipzig , in 1766, which, being afterwards brought into moregeneral notice by Bode, about a.d. 1778, is consequently usuallytermed Bode’s Law. A series is formed by taking the number4, and adding to it in succession 3, twice 3, four times 3, eighttimes 3, sixteen times 3, and so on ; so that we obtain thenumbers:

4, 7, 10, 16, 28, 52, 100, 196.

These numbers, if we pass over the fifth (which, however,corresponds to the gap between Mars and Jupiter , in which somany small planets have of late been discovered), are found toagree very approximately with the ratios of the distances ofMercury, Venus, the Earth, Mars, Jupiter, Saturn, and Uranus ,from the Sun. For if we multiply the terms of Bode’s seriesrespectively by 10, we obtain:

• 40, 70, 100, 160, 280, 520, 1000, 1960 ;

whereas, if the Earth ’s distance be represented by 100, theactual distances of the various planets are respectively;—

for Mercury Venus the Earth Mars Jupiter Saturn Uranus

as the numbers 39 72 100 152 520 954 1918.

The near agreement of these two sets of numbers is there-fore very remarkable. The rule, however, fails for the last-discovered major planet Neptune , the next term of Bode’sseries being 3880, which differs greatly from the number 3005,which would represent the real value.

The truth is that Bode’s arrangement hardly deserves to betermed, as it frequently is, a lam, no theory having yet beensuggested which gives a satisfactory reason for its existence,although occasional attempts have been made to connect it withthe gradual formation of the planets in succession, according toLaplace’s nebular hypothesis. It bears no comparison withthe three laws of Kepler, which, although originally discoveredwithout their cause being understood, have since been provedto be, in the very strictest and minutest possible degree,necessary consequences of the action of gravitation. Bode’sso-called law must at present be looked upon as little morethan an example of a curious coincidence.