:o6 



• • • • 



2. c-\-2eccs, ni=9 \ 



}■ . " ' " 'i 



.. . ., am j therefore c=e ' J, 2;n and w=J^ J, 2OT 



iu=c—c s^ OT 



-: ..... ^ 



3. c+2^xccs, m — c s, m=o j 



:M='c— ^ccam —'c ' -t^'e'cs, %n therefore w=4<? s m=yin—s, ims 



» I 



s, m s , m J 



Hcnee ■w=m+le s, im+[e . s, m — -j, y?i+kc. / 



which terms are equivalent to the two correftions applied by Sir Ifaac 



Newton. 



On the fecond Caffitii's method.* 



The method of Caflini, now in order to be examined, is perhaps 

 both the mod elegant that has yet been invented, and the mofl readily 

 Fig. 4. deduced from the equable defcription of areas, and is alfo, in the plane- 

 tary orbits, of very great praftical value. 



Let P be the place of the planet, and AI the excentric anomaly. SB 

 perpendicular to CI. Let AD = the mean anomaly, and draw DT per- 

 pendicular, and DO parallel to CI. Then becaufe DA is the mean 

 anomaly, the area DCA = SAI = SIC -\- ICA, and therefore SCI =DCI 

 conlequently SB = the arch DI. 



Hence three approximations are derived by Caffini. i. SD is nearly 

 parallel to CI, therefore if the angle SDC be computed, DCI will be 

 found nearly, and confequcntly ACI the excentric anomaly. 



2. SO =. DI — DT. And therefore when the excentricity is not 

 great, the meafure of the angle SDO^DI — DT nearly. This latter 

 quantity being taken from SDC, the angle DCI is obtained. 



3. SD: 



* Mem. Acad. 1719. Caffini Elem. Aftr. vol. i. p. 143. 



I 



