OF ASPECT, ROTATION, LIBRATION, ETC. 165

note, in passing, that 19 to 17 is about the ratio inwhich the moon’s apparent linear dimensions aregreater when she is in perigee than when she is inapogee, while 5 to 4 is the apparent ratio in whichher disc when she is in perigee exceeds her disc whenshe is in apogee.) As the eccentricity of her orbit isvariable, its mean value being about O'055, while itsgreatest and least values are about 0'066 and 0'044,there is a different range in her rates of real andapparent motion, according to the amount of eccen-tricity when she is in perigee or apogee respectively.The actual maximum rate of the moon’s motion isattained when she is in perigee and her eccentricityhas its maximum value 0'066, while the actual mini-mum is attained when she is in apogee at such a time.The ratio between her real motions, under thesecircumstances, is that of 1,066 to 934, or about 8to 7 j the ratio between her apparent motions in herorbit being rather greater than 13 to 10.

These variations are sufficiently great'to modify, ina remarkable degree, the movements of the moonwhen considered with reference to the change ff om dayto day in her apparent place in the heavens, and there-fore, in her apparent course from horizon to horizon.We saw that this must be so, when we inquired

means in the following considerations :—The ratio {a + 2) 2 : a? isnearly the same as the ratio (a + I) (a + 3) : (a — 1) (a + 1); thatb, is nearly the same as the ratio (a + 3) : (a — 1). In the abovenase this gives 20 to 16, or 5 to 4. The real value of the ratio9l) 2 : (19) 2 is not 4-fifths or - 8, but '80056, which differs from® by less than the fourteen-hundredth part.