fee* -; I 4- ^ — 



RECTIFICA'TION of the ELLIPSIS; ^c. 189 



fin nf — tan' -? and fo oh : And i -{• C-' 



fec^ — , and fo on. Thus : 



A = fec= - X fee 

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

 ther the logarithm fecants of the angles 7» ~^j -^j &c. to dimi- 



■ ^ ::iXfec^ —X &c. 

 2 2 



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

 and to take twiee the remainder. As the angles m^ m', ///'', &c. 

 decreafe very faft, it will feldom be neeeflTary to eompute more 

 than two or three of them. 



(c' r' c" c' c" c'" \ . 



I H h ~- — *l" , • ""• -„ 4- &c. ) is alfo readily com- 



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

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

 bles. 



As an example, let c — 0.72333 : whieh is the fradlion that 

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

 by the mean diftance 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 45° 1948^": we have therefore 

 m =1 46* 19' 487^'' I 



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



2 



L. m' 



L. fin m' =: 

 10° 32' sf 



9.2626412 



7«' 



L. tan - = 1. tan 5° 16' 28^^^ = 8.9652949 



2 



L.rfin/«^ = 

 L. m'— o' 29' 18'' 



7.9305898 



L. fee- n: 10.0365070 



L. fee — =z 10.0018429 



L. tan 



