220 
MR. IVORY ON THE THEORY 
Let n 2 = ~s, n being the constant of the mean motion in the primitive ellipse, 
when t — 0: then 
"I 
[... (13) 
d^ = & c. I 
Taking next the semi-parameter h 2 , we have, by equation (3), 
hdh = r 2 ( < d'R-~dr ): 
but J'R = dv + dr ; wherefore, 
hdh =(^) -r 2 dv = 3. 2 J.\-e 2 . (^)d?,. 
In order to find the value of let the expressions of ^yand^ in the 
d i) d v 
formulas (C), be added: then, since it has been shown that -^- s + = 1, we 
get. 
ndt = d{(\ + nf i -^dl)- 
J R J R / d R\ (dr dr\./d R\ 
' dv \dr) \d v ' d v) ' \dv) 
d t d v 
and, because r is a function of v — v, ^ = 0 ; wherefore, 
JR JR _/JR\ 
de + dv~ \dv)‘ 
Further, because s always accompanies or which is the same thing, because 
R is a function of £ + 2, we have ^ = ^7 : 
consequently, 
JR . JR 
J? 
.JR_/J R\ 
' dv \dv )’ 
By substituting this value. 
^=avra(^f+^)<*e 
•** = «( I - 2 ) + 2/ a 2 + ^)dZ, 
( 14 ) 
