DISTANCE, SIZE, AND HASS.

27

the earth’s equatorial diameter would always coversuch an arc. But the moon traverses a path of con-siderable eccentricity. Its mean shape (for it variesin shape) is exhibited in fig. 10, Plate III., where 0 isthe centre of the orbit, E the earth, M the place of themoon when nearest to the earth, or in perigee, M' herplace when farthest from the earth, or in apogee, mand m' her positions when she is at her mean, distance(in other words, m m' is the minor axis of the moon’sorbit). Thus E C is the linear eccentricity of the• orbit.* E C is about the eighteenth part of C M, andis thus not at all an evanescent quantity even on thesmall scale of fig. 10. The distance E C is equalto about 13,113 miles. It will be observed, however,that though the eccentricity of the orbit is shown infig. 10, the ellipticity, that is the departure from thecircular shape, is not indicated. In reality, it wouldnot be discernible on the scale of fig. 10.f

But the eccentricity of the moon’s orbit is not

* The true eccentricity is represented by the ratio of E C toE M ; that is, in the case of the lunar orbit, it is about when theorbit is in its mean condition. When the orbit has its maximumeccentricity, the ratio rises to about -fa, and when the eccentricityis at its minimum, the value is about 7 ‘ T .

t By a well-known property of the ellipse, the distances E mand E m' are equal to C M and C M'. Hence C m is easily found.If, for convenience, we represent CM or Em by the number 18,E C will be represented by unity. Hence C m will be representedby \/(18) 2 — 1, or by \/323, or by 17 - 9722. The semi-arcs CMand C to may be approximately represented by the numbers 1,800and 1,797 ; that is, by the numbers 600 and 599 ; or C m is lessthan C M by less than l-600th part of either.