318 The Orbit and Motion of 



FOR this purpofe, bifedl AE in F, draw OFx and SFc ; make 

 x.c to Cc, as cS to cF ; draw CpS, and draw OK parallel AE : It 

 is evident that c maybe confidered as a ftraight line parallel to 

 EA ; the fegments ExF, FA, are equal, and the triangles EFS, 

 FSA, are equal ; therefore the elliptical fpaces ExFS, xFSA are 

 equal; but the triangles *cF, CcS are equal, their altitudes be- 

 ing reciprocally as their bafes j therefore, the elliptical fectors 

 ACS, CSE, are equal, and C is the place of the Planet at the 

 third oppofition. Now, cF is nearly equal to the verfed line of 

 cA, which is an arch of about 9, and is therefore about 



of cS. xc is to cF as OK to KF; and therefore xc is nearly 



OO 



ofcF, or -T- ofcS. Ccis^ of xc. or 5 of cS. 

 20 looo 80 128000 



Therefore the angle CSc does not exceed two feconds. If a fi- 

 milar conftruc"lion be made for the points B and D, it will be 



found that the angles BSb, DSd, will not exceed -g- of a fecond. 

 For BS, CS, DS, are nearly equal, and bH and dG are nearly 

 of cF j therefore Bb and Dd are nearly ? of Cc. 



HENCE it is evident, that this fimple and obvious conflruc- 

 tion will give the elements of the orbit with all the accuracy 

 that can be attained by any direct methods from our obferva- 

 tions, becaufe the errors of obfervation are much greater than 

 this j and if the obfervations are not equalifed according to 

 fome probable principle, as has been attempted above, elements 

 cannot be obtained which will be confiflent with them all. The 

 corrections which muft be made for this equalifation are much 

 greater than this error ; and, therefore, no direct methods can 

 give more accurate elements. 



THIS error, fmall as it is, may be very eafily corrected, by 

 computing its quantity in the ellipfe already conftrucled. This 



computation 



