in a very great degree and in a very curious way, if their conjunctions occurred exactly at the same place.
Now these conjunctions do not occur exactly at the same place. The periodic times are nearly in the proportion of 2 to 5, but not exactly in that proportion. In consequence of the periodic times being not exactly in the proportion of 2 to 5, their places of conjunction travel on, until after a certain time the points of conjunction of the series 1,4,7, &c., would have travelled on until they met the series 3,6,9, &c. Not fewer than 900 years are required for this change.
Now so long as three conjunctions take place at any definite set of points, the effect on the orbits is of one kind. As they travel on, the effect is of another description (because, from the eccentricity of their orbits, the distance between the planets at conjunction is not the same), and so they go on changing slowly until the points of the series 1,4,7, &c., are extended so far as to join the series 3,6,9, &c., and then the conjunctions of the two planets occur at the same points of their orbits as at first, and the effect of each planet in disturbing the other is the same as at first; and thus we have the same thing recurring over and over again for ages. During one-half of each period of 900 years, the effect that one planet has upon the other is that its orbit has been slowly changing, and then during the other half, it comes back to the same thing again. Suppose that, during half the 900 years, one planet has been causing the other to move a little quicker, and that during the other half of that 900 years it has been causing it to move a little slower; although that change may be extremely small as regards the
