112 Sugg-Sidth%ta. the length given to the equinoctial shadow corresponds to that which it hB in the latitude of Washington It is not, howevey, on account of the coincidence of th' with Bhe pnth of the equinoctial shadow that it is directed to be pgmanently drawn upon the dial-face : its use is to determine for any given shadow its agrk, or meature of amplitude. Thus, let ad, ba, Bk, b!, 8, be shadows cast by the gnomon, under vious conditions of time and dec linkton : then the distance from the extrernity of each of thers to the line of the equinoctial shadow, or dx, d'e, ke, c", 18 respectively, is denominated the ord of that shadow or of that time, The term uyurf we have translatel measure of amplitude,’’ because it does in fact cpresent the sine of the Sun's amplitudo -understanding by < amplitude "" lie distance of the sun at rising or Retting from the east or West point of the hoxizo--vaying with the hypotheruse of the shadow, and always maintaining to that hypothenuse the fixed ratio of the sine of omplitude to radius. Ththis is so, is assumed by the text in its treatment of the g7d, but is nowhere istinctly fated, nor is the cornmentafor ut the prins of demonstrating the principle. Since, how ever, it is not an intmediately obvious ne, we wil} take the liberty of giving the proof of it. In ]ho onnexed figure (Fig. 10) act C represent the top of the gnomon, and let be any given position of the sun in the hehens. From K draw KB at right ongles to the plane of the prime vertical, meeting that plane in B ', and let the point of its inforsection with हुig 10, the plane of the equator be in E. Join KC, C/C, and ByThen KG is radius, and I'K cqual to the sine of the sun's amplitude : for it, in the sun's daily revolution, the point K is brought to the horizon, E/JB will disappear, KEC will become a right angle, KI/ will be the atnplitude, and D'K its sine; but, with a given declination, the value of JEW K remains always the same, since it is a line drawn in a constant airection between $wo parallel planes, that of the circle of declination and that of the squator. Now conceive the three lines interesting in
