﻿XIII. 



A New Method for Correcting a Planets Orbit. 

 Br TRUMAN HENET SAFFORD, A.B. 



( Communicated hy Professor Peirce.) 



1. It will be assumed that values of the elements are so nearly knoAvn, that the 

 squares of their de\iation from the true ones can be neglected ; the mass of the planet 

 will also be neglected. 



2. The approximate elements will be denoted as follows : — 

 M° the mean anomaly at the origin of time ; 



p° the semi-parameter of the orbit ; 



(p° the angle of eccentricity (e° = sin 90°) ; 



71° the longitude of the perihelion ; 



i2° the longitude of the ascending node ; 



f the inclination ; 



L° (the mean longitude at the time t^j) = M° -f- 71°; 



a° (the mean distance) = p° sec- (p° ; 



fi° (the mean daily motion) ^ '^-■rr, (i°~^i where log k = 8.2355814 — 10; 



log h — log sin 1" = 3.5500066. 



The corrected elements to be found will be denoted by the same letters without the ° ; 

 and the prefix 8 to any of these letters denotes the correction to be applied to, or any 

 variations of, these same elements. 



Analogous modifications of all functions of these quantities will be expressed in the 

 same way. 



We shall use the expressions D„, &c., however, to denote the partial difierential co- 

 efficients Avith respect to M, &c. of their functions, even when, for instance, M has the 

 value M° ; and so with the rest. 



3. But instead of computing directly the partial differentials of any coordinates with 



VOL. VI. NEW SERIES. 69 



