RECTIFICATION of the ELLIPSIS* §cc. 189' 



fm m' - tan^" "^, and fo on : And i + c" - kc'' '^ ; i -f c'" - 

 fee' — , and fo on. Thus : 



2 



A = fec= - X fee' ^ X fee' "-^ X &c. 



To find the logarithm of A, we have then only to add toge- 

 ther the logarithm fecants of the angles 7> 7» "Y"' ^^- ^'^ dimi- 



nifh the fum by as many times the radius as there are fecants, 

 and to take twice the remainder. As the angles m, m', m\ &c. 

 decreafe very faft, it will feldom be necefl'ary to compute more 

 than two or three of them. 



f fit f " Iff 



The feries (^ + ~ + 7- ^4" j- 7' 2 "f" ^<^*) ^^ ^'^° readily com- 

 puted from the tables ; becaufe the logarithms of c', c\ c'", &c. be- 

 ing the fines of the angles m\ m", &c. are all found in the ta- 

 bles. 



As an example, let c ■=. 0.72333 : which is the fradlion that 

 arifes from dividing the mean diftanee of Venus from the fun, 

 by the mean diftanee of the Earth; and this is the moft unfa- 

 vourable cafe that occurs in the theory of the planets : Then to 

 compute A, 1 find, in the table of natural fines, that 0.72333 cor- 

 refponds to 46° i9'48f": we have therefore 

 m =46° 19' 48^' 

 L. tan f = 1. tan 23° 9' 54-5''' = 9.6313206 



2 



L. fin m' zz 

 L. m' z= 10° 32' sf 



9.2626412 



L. tan ^ = 1. tan 5° 16' aS^'' = 8.9652949 



L.-fin m" ■=. 

 L. m":=z o* 29' 18* 



7.9305898 



L. fee 7 =: 10.0365070 



L. fee — = 10.0018429 



L. tan 



