Of the MOON from the SUN. 197 



ZSp (fig. i.) will be the fupplement otZSM, and ZMP (fig. 2.) 

 will be the fupplement of Z MS to 180. 



Zp being perpendicular to MS t the two triangles ZpM and 

 ZpS will both be right-angled at p. The hypothenufes MZ 

 and SZ are the zenith diftances of the objects, or the comple- 

 ments of their apparent altitudes, and the legs MP or SP are 

 the fecond or third arches. Then (by cafe 6. right ang. fpher. 

 triang.} the cotangent of the hypothenufe, or, which is the 

 fame, the tangent of the altitude, multiplied by the tangent of 

 the leg, and divided by radius, gives the cofine of the angle 

 between the hypothenufe and that leg j by which the angles 

 ZMS and ZSM will be found. 



THE other method of finding the angles is prop. 17. fpher. 

 triangles^ prefixed to SHERWIN'S Tables, revifed by CLARK ; and 

 is the fame with that given in the reqttifite tables for finding the 

 horary angle. 



THE fine of the horizontal parallax being to the fine of the 

 parallax in altitude, as radius to the fine of the zenith diftance, 

 (KEIL'S AJlron. left. 21.) the fine of the horizontal parallax, 

 multiplied by the fine of the zenith diftance, or, which is equal 

 to it, by the cofine of the altitude, and divided by radius, will 

 give the fine of the parallax in altitude. 



LET Lq reprefent the parallax in altitude, and Mq the re- 

 fraction in altitude, then Mq fubtracted from Lq will leave LM 

 the corrected parallax, equal to the difference between the ap- 

 parent and true altitude of the Moon. Let SR be equal to the 

 Star's refraction ; then L will be the true place of the Moon, 

 and R the true place of the Star, and LR the true diftance. 

 Let La be a perpendicular arc from L, falling upon MS, pro- 

 duced if neceflary, and let Re be a perpendicular arc from R, 

 falling upon LS, produced if neceflary with the diftance LS 

 draw Lb, and with the diftance LR draw Rd ; then LR and Ld 

 being radii from the fame centre, or rather arches from Z,, as a 

 pole, to the fame parallel, will be equal to one another 5 and, 



for 



