Page:The Solar System - Six Lectures - Lowell.djvu/102



the middle of the line in the Saturnian system. The chance, if chance arranged it, that it should occupy the like position in the solar system is one out of three, or two to one that it did not. That it should also do so in the Jovian system is $$\scriptstyle \frac {1}{3}$$ of $$\scriptstyle \frac {1}{3}$$, or eight to one against it. That furthermore the Uranian system should show the same is $$\scriptstyle \frac{1}{3}\times\frac{1}{3}\times\frac{1}{3}$$.

In other words, it is twenty-six to one that the largest satellite would not be found to occupy in all the same position. And it does. Twenty-six to one in betting is very much better than certainty odds.

This is not all. Consider the four systems more carefully. It will be seen that the second largest mass is in each of them found outside the first and in three out of the four next to it. In the fourth, it comes next but one. Now the chances against this being accident are much greater than for the first coincidence; while the chance that the two chances should occur together as they do is the product of both. You will see that we are getting outside any chance in the matter at all, and have come face to face with some cause working to this end.

But we are by no means done with the analogies yet. If we construct a curve of positional sizes, we discover that it has two maxima, not one.