plained the principles and extent of his method. With regard to its prac- 

 tical value for the planetary orbits, it yields to feveral of the methods that 

 have been mentioned, and with refpeft to elliptical orbits in general, it 

 certainly yields to Newton's method, and perhaps to Machin's, Mr. 

 Ivory remarks the fame inconvenience in his method as was obferved above 

 with refpeft to Newton's ; the computation of the excentric anomaly in 

 orbits very excentric, when the body is near perihelion. This inconveni- 

 ence does not exirt: in Machin's foiution ; in that part of the orbit his firil 

 approximation is as exaft as can be defired. In the extreme cafe when 

 the ellipfe is evanefcent, the foiution derived from Newton's method is 

 much more fimple than that of Mr. Ivory. And alfo, in that cafe, Machin's 

 foiution is more commodious than that in the Edinburgh Tranfaftions. 

 It is with concern I have made thefe remarks on the labours of a perfon who 

 has* merited fo much by his moft elegant and ufeful foiution of a 

 problem connefted with phyfrcal agronomy. A problem on which the emi- 

 nent mathcmaticions of Europe had neceflarily exerted their ingenuity for 

 nearly half a century ; and whofe folutions have ail been furpafled by that 

 of Mr. Ivory. In his foiution of Kepler's problem, he has added the me- 

 thod of deriving the place of a comet, moving in an excentric ellipfe from 

 the place in a parabola having the fame perihelion diftance. He confiders 

 the problem as new, although, befide Simpfon and Laplace above referred 

 to, Lalande mentions the problem. Mr. Ivory has given two terms of the 

 feries derived by his method. 



• Edinb. Tranfaflions, Vol. 4. 1798. 



