468 ON THE CONSTRUCTION 



moon's relative orbit; the points 23, 0, 1, 2, and 3, on the 

 line PQ, are the moon's places at the hours denoted by the 

 numbers ; the sun's place being supposed to be at S. All 

 these are obtained as in the usual method. 



Make the arcs AF and CH, each equal to the reduced 

 latitude of the place, and join FH. With the centre N and 

 radius NF, describe the quadrantal arc FU. Make FI 

 and FK, each equal to the sun's declination, and join KI 

 and FS. Draw ar and Iiv, parallel to FN and SD re- 

 spectively. On NH, make NT equal to Sr, and complete 

 the rectangle NTXU. On XU, produced if necessary, take 

 UV, equal to \w, taking it to the right of SU, when the 

 sun's declination is north, but to the left, when the decli- 

 nation is south, and join VN. Take the hour angles from 

 noon, corresponding to the hours marked on the relative 

 orbit ; and on the arc UF, produced if necessary, set off from 

 U, arcs equal to these angles, marking their extremities with 

 the numbers of the hours' to which the arcs correspond. 

 From the extremities of the arcs, draw lines parallel to UX 

 or FH, as the lines 1, x; 2, x\; &c. meeting NU in the points 

 m, and NV in the points v. Then will the distances 1, w ; 

 2, w ; &c. be the moon's parallax in right ascension at the 

 23d, 1st, 2d, &c. hours; and the corresponding distances vx, 

 will be the parallax in declination. 



From the hour points on the moon's relative orbit, draw 

 lines as 23, n; I, n; &c. parallel to FH or AC ; drawing 

 them to the left hand, when the time is in the forenoon, but 

 to the right hand, when the time is in the afternoon, and 

 make them respectively equal to the parallax in right ascen- 

 sion at these hours. From the points n, draw the lines 

 w, xxiii ; n, O ; &c. parallel to SU, drawing them below the 

 point, n, and make them respectively equal to the moon's pa- 

 rallax in declination at the corresponding hours. Join xxiii, O ; 

 O, 1 ; &c. Then will the broken line thus formed be a near 

 representation of the moon's apparent relative orbit ; and the 

 points xxiii, O, 1, &c. will be the moon's places in the appa- 

 rent orbit at those times. 



