120
The difference of ac and bc in any orbit is not, however, avery important matter. On the contrary, the difference of thegreatest and least distances of a planet from the Sun, whichmay be represented respectively by sa and sz, is of the utmostimportance.
The only remarkable fact connected with the point b is thatbs is found to be always equal to ca or cz ; i.e., to one-lialf ofthe sum of sa, the greatest distance from s, and sz, the leastdistance from s, in consequence of which bs is often called theMean Distance. We may also observe, that, in such a case asthat which we previously supposed, in which sc equals Ith ofac, the difference of the greatest and least distances from swill be twice sc, or fths of ca (or sb), the mean distance. Itis interesting to notice that such a degree of ovalness as thiscorresponds very nearly to that of the orbit of the planetMercury, and is more than double that of the orbit of Mars ;while it much exceeds that of the orbits of any other of theprincipal planets. And yet, according to the rule previouslystated, such an orbit would only vary from a circular form, sofar as to make the difference of its greatest and least distancesfrom its centre , c, amount to about Ajih part of the larger,which in the case of Mercury would be about 865,000 miles.The fact of the Sun being situated at a point correspondingto s and not to c, in the case of such a planetary orbit (whichwas Kepler’s first great discovery), lias therefore a much moreimportant effect in causing thedistance of a planet from it to vary,than the actual deviation of the orbit from a circular form *would produce if the Sun were situated at its centre.
When Sir Isaac Kewtou, near to the close of the seventeenth
* It is found, that if we denote the ovalness of theoibit by the ratio ofOS to CA , \ .e., by ith for that of Mercury :—
it will only be about .... ,I„th for Venus ,
„ „ about .... ^th for the Earth ,
„ „ rather more than ^th for Mars ,
„ ,, about . . . . ' ^th for Jupiter ,
„ „ rather mere than ^th for Saturn ,
,, „ rather less than ¥ ’ ff th for Uranus ,
„ „ rather more than T { v th for Neptune ;
the largest of which fractions is less than o:re-half of that for Mercury.