planets and their satellites present. There is one kind of disturbances, however, of which possibly some notion may be given; they are the most remarkable in Jupiter and Saturn. There are many books, written as late as the beginning of the present century, in which the motions of Jupiter and Saturn are spoken of as irreconcilable with the theory of gravitation. It was one of the grand discoveries of La Place, that the great disturbances of those two planets are caused by what is called the "inequality of long period," requiring some hundreds of years to go through all its changes.
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Fig. 60.
Let Figure 60 represent the orbits of Jupiter and Saturn.
You must observe that they are both ellipses, and the positions of their axes do not correspond. Now, the thing which La Place pointed out as regards these planets, affecting their perturbations, is one which applies more or less to several other planets; it is this: that the periodic times of Jupiter and Saturn are very nearly in the proportion of two small numbers, namely 2 to 5. Upon the proximity of that proportion depend entirely some of the peculiarities of their disturbances. And the effect of this will be seen if we consider in what part of their orbits their successive conjunctions will happen.
Inasmuch as these periodic times are in proportion of 2 to 5, it follows that when Saturn is describing two-thirds of a revolution in its orbit, Jupiter is describing almost exactly five-thirds of a revolution
