LET. XXI. OF THE SUN, MOON, AND PLANETS. 359

And as the tops of these mountains are consi-derably elevated above the other parts of tstesurface, they are frequently illuminated whenthey are at a considerable distance from the con-fines of the enlightened hemisphere, and by thismeans afford us a method of determining theirheights.

Thus, let E G D be the moon’s enlightened r>- xv.hemisphere, E C D the diameter of the circlebounding light and darkness, and A the top ofa mountain when it first begins to be illumi-nated : Then, since the ray of light SEA is atangent to the moon at the point A, the angleCE A will be a right angle; the line A E, orthe distance of the point A from the boundaryE C D, can also be measured by means of a mi-crometer ; and C E is the known radius of themoon. We have therefore the two sides CEand E A, of the right-angled triangle C E A,from whence we can find the third side C A ;and subducting the radius C B, the remainderA B will be the height of the mountain re-quired. Riccioli observed the top of the hillcalled St. Catherine, upon the fourth day afterthe new moon, to be illuminated when it wasdistant from the confines of the enlightenedhemisphere about one-sixteenth part of themoon's diameter; and by this means found itsheight to be nine miles : So that from this, andother similar observations, it appears, that theA a 4 lunar