DISTANCE, SIZE, AND MASS.

33

values reduced for the effects of irradiation, give forthe diameter,—

(1) When the moon is nearest to the earth, 33' 30'1" or 2010'1"

(2) „ „ at her mean distance, 31 51 or 18651

(3) „ „ farthest from the earth, 29 20'9 or 1760'9

It has been already mentioned (p. 28) that the meandistance is not the arithmetic mean between thegreatest and least distance; it necessarily follows thatthe mean apparent diameter is not the arithmetic meanbetween the greatest and least apparent diameters.

Now, the apparent surface of the lunar disc varies,not as these diameters, but as the squares of thesediameters. It is easily calculated that if the size ofthe lunar disc, when the moon is at her mean distance,is represented by the number 10,000, then, when sheis nearest to the earth, her disc shows a surface of11,615; while, when she is farthest, the apparentsurface is but 8,914. Or, if we call the surface of themoon’s disc when nearest to us 10,000, then, whenshe is farthest from us, the surface of her disc wouldbe represented by the number 7,674. We may verynearly represent the apparent size of the moon’s discwhen she is nearest to us, and when she is farthestfrom us, by the numbers 4 and 3; in other words,when the moon is full and farthest from the earth, shegives only three-fourths of the amount of light whichshe gives when full and at her nearest to the earth.But there is a very convenient way of representingthe relative dimensions of the moon’s disc when she18 at her nearest and farthest. It is very easily shown

D