' 
E. F. Burr on the Neptunian Theory of Uranus. 241 
d? " : = A 
logy —__¥ =1- log. __* =1-5611 
og 5 59356, og pve 1 9 
log. b, =0-71354, log. b, =0-44757 
2 cf 
by =029534, b= 0°13666 
2 
(4) (5) 
db. : 
log. _? =1-29207, log. 52 = 119331. « 
da da 
With these values, and supposing the terms depending on the 
mean anomalies included in the elliptic Nae ti the ape 
principal inequalities of true longitude are ved. The 
expressed in terms of the sail of the. pte 
m’'. 
3°251 sin (n't—nt-+e’—) 
++79°230 sin 2(n/t—nt-+-s’—e) 
< — 1351 +-¢/—« 
— 0 305 sin re ‘pai . 
a": 102 sin 5(n' t— ie 
| +-0°321 sin-(n't-e’—) 
—248'890 si hs ery ae 
1 i 
—0°205 sin ( saith} Dnt e4 20 
—4-594 sin (—2n’'t+-3nt—2e'4-3e—w 
+0-090 sin (—3n’ oe tna 
-+-0:024 sin are * 
—0-048 sin (n't+-e'—w/ 
| — 0-063 sin (Sn't—4nt-+-5e —4e—o’) 
—12-188 sin (2n't--2¢ 121° .:33' -43”) 
—12-061 sin ( alae ve Hi ae s tA 
11 t—2nit-+4¢ —2«+2° 
T0396 sin (Gx toanid 640-4 2° 00-27) 
pri in (6n!'t—Bnt-}-6e' +Be-$5°'-2'-14") 
It will readily be seen, that the approximation has been carried 
as far as terms of the fourth order in eccentricities and inclina- 
tions. ‘The secular variations * the’ eccentricity an 
of the perihelion corresponding to two different values of Nep- 
tune’s mass, and for three synodic revolutions of Uranus, are the 
following : 
