MOTION OF THE NODES.

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(629.) This is the case with the planetary orbits. They do notall intersect each other in a common node. Although perfectlytrue, therefore, that the node of any one planet would recede onthe orbit of any and each other by the individual action of thatother, yet, when all act together, recess on one plane may be equi-valent to advance on another, so that the motion of the node ofany one orbit on a given plane, arising from their joint action,taking into account the different situations of all the planes, be-comes a curiously complicated phenomenon whose law cannot bevery easily expressed in words, though reducible to strict numeri-cal statement, being, in fact, a mere geometrical result of what isabove shown.

(630.) The nodes of all the planetary orbits on the true ecliptic,as a matter of fact, are retrograde, though they are not all so ona fixed plane, such as we may conceive to exist in the planetarysystem, and to be a plane of reference unaffected by their mutualdisturbances. It is, however, to the ecliptic, that we are underthe necessity of referring their movements from our station in thesystem ; and if we would transfer our ideas to a fixed plane, itbecomes necessary to take account of the variation of the eclipticitself, produced by the joint action of all the planets.

(631.) Owing to the smallness of the masses of the planets, andtheir great distances from each other, the revolutions of their nodesare excessively slow, being in every case less than a single degreeper century, and in most cases not amounting to half that quan-tity. It is otherwise with the moon, and that owing to two distinctreasons. First, that the disturbing force itself arising from thesun’s action, (as appears from the table given in art. 612,) bearsa much larger proportion to the earth’s central attraction on themoon than in the case of any planet disturbed by any other. Andsecondly, because the synodic revolution of the moon, withinwhich the average is struck, (and always on the side of recess) isonly 29 ; \ days, a period much shorter than that of any of theplanets, and vastly so than that of several among them. All thisis agreeable to what has already been stated (art. 407, 408,) re-specting the motion of the moon’s nodes, and it is hardly neces-sary to mention that, when calculated, as it has been, a priori froman exact estimation of all the acting forces, the result is found tocoincide with perfect precision with that immediately derived from