Moon's Rsivg Q Setting, a the biguation of H®r usp8 269 K/X, Kaving made the calculations prescribed in the preceding pages, we gre now to protect their results, and to exhib + representation of the noon as she will appear at the given time 'Phe annexed figure (in . 88) will lustgte the method of the projection. We first fix upon १ point a s, which shall represent the position of the sun's centre upon the western horison ; the moment of sunset, and we determinein the manner taught at the beginning of the third chapter, the links of cardinal direction of which it is the entire *rom his point we then lay of the base (} $L, necording to lt value in tigits as ascertained by the previous proce8, and northwara or Southward, yoording to its true direcon as determined by whe sathe proces). Fro , ibe extremity, is laid of bho perpendicular (kot), which has the fixt«d value of twelve digit= 'his, boing a line perpendicular to the plane of the horizon, may be regarded a• having no proper direction of its own upon the suete.ce ot projection: but he text direct u& to lay t of westward from L , apparently in rder that the observer bg. 33 standing upon the eastern side of his base SLand lookin westward toward the setting sun. ruay have his figure duly before hit1. he western extreplity of the perpendicular, M, represents the ons place, and trom that as a centre, and with a radius equal ko bhe semi-diupmeter of the noem in digit, ascertained by calcula. tion for the given nmoment, ५ eircle is described, representing the moon's disk. Max; we ure to prolong tho hypothchu$u, SM, to ७ und to drawby the usual , line , at right angles to it: the directions upon the disk meunsthe hus determined by the hypothenuse, as the text phrases it, are called by ॐhe conremary rnoon-directions 't (cadh¢digex). 'The Sun being at S, he illuminated half of the moon's circumference will be 87, the cups will be e6 8 and , and y will be the extremity of the diameter of greatest ilomiaation. From 2, then, 1ay of upon the hypothetuee an annount, up, equal to bhe measure in digits of the , of thbe illuminated part diameterand barough , , and b describe an are of a circle, in the natuer already more than once explained (see abovevi. 1416; bhe crescont roर will represent the the moon'illuminated part at the given amount and direction of fine. Now we once more make a determination of direction upon the disk perpendicular that according to the LM; is to way, we prolong LM to , and draw s' h' at right angles to it: the directions thus established are styled connnenta in bhe "$n-directions (81tryadi¢8, although without obvious propriety: they might rather be called f*appagent directions, or since & should represent a line parallel wh directions on the ap! The line aft in is called the horizon, and age' one perpondicular to {
