BODE'S LAW, an arithmetical relation subsisting between the distances of the planets from the sun. It may be thus stated: Write, in the tir,t instance, a row of fours, r.nd under these place a geometrical series beginning with 3, and increasing by the ratio 2. putting the 3 under the second 4; r.nd by addition we have the series 4, 7, 10, rte., whica gives nearly the relative distances of the planets from the sun.
4 4 4 4 4 4 4 4 4 3 6 12 24 48 96 192 384 4 7 10 16 2S 52 100 19G 388Tints, if 10 be taken es the distance of llte earth front the sun, 4 will give that of Mercury, 7 that of Venus. and so forth. The actual relative distances are its follow, making 10 the distance of the earth— Mercury. Venus. Earth. Liars. Asteroids. Jupiter. Saturn. 'Uranus. Neptune.
3.9 7.2 10 15.2 27.4 • 52 95.4 102 300 Close as is the correspondence between the law and the actual distances, no physical reason ];as been given to account for it, although there is little room fordoubt that such exists.
13. I.., therefore, in the present state of ecienee, is termed empirical. Kepler was the first to perceive the law, and Bode argued from it that a planet might be found between Mars and Jupiter, to fill up the gap that existed at the time in the series. The discovery of the asteroids has proved the correctness of this prediction. The greatest deviation from the law is seen in the ease of Na ',tune; hut if we were acquainted with the princi ples from which the law proceeds, we might also be able to account for the discrepancy. similar relations, though expressed in different numbers, are found to subsist in the distances of the satellites of Jupiter and Saturn from their primaries.