- 
E.. F. Burr on the Neptunian Theory of Uranus. 239 
from an imperfect determination of the elements of Neptune, or 
its period is so great that it may be assumed constant, and merged 
in the correction of the longitude of the epoch. 
In deducing the results which follow, we have availed our- 
selves of some considerations for abridging the labor. ‘The gen- 
eral formule for the perturbations of true longitude have been 
subjected to the usual condition that the mean an longitude and the 
equation of the centre be the same in the elliptic and in the 
troubled movement. This enables us»to employ the ae 
given by observation for the epoch. The constants which serve 
to make the origin of the time the origin in ier the perth: 
tions, are not distinctly calculated, but transferred to the equations 
of condition and determined with their general corrections. A 
similar disposal has been made of the effects on the inequalities — 
of the secular: variations of the elements. For several ages 
fore and after the époch, these variations may be regarded as 
changing eigen with the time and all their —, superior 
to the first be neg ected. Hence their effect on the inequalities dur- 
ing the unit of time is “correctly represented. by c = = (#)- As it 
is only appreciable in connection with inequatigjed of — period, 
we may regard it as essentially constant’ during the century and 
a half of observation and, ‘consequently, confound it with the 
correction of the mean motion. 
It may be well also, in passing, vert tob some of the un- 
corrected errors and sources of error "hte we have had occasion 
to notice. In the 3d volume of the Mecanique Celeste of 
La Place, by Bowditch, the following corrections shoul 
made? Page 9, for the third term of the formula for the ine- 
age of the ‘second order in longitude, read 
>. .H. ee’ sin [t (n’t—nt +e <8) t2nt Be — w! —ol]: 
page 63, note 2423, for the last term of the ee of the 
first term of R, read 
M°.¢? . eos Su. cos T’, 
page 235, line 8, for.“‘ these values” read « thesé values multiplied 
into e?, ee’, e’?, y? respectively.” In the “'Theorie Analytique 
du Systeme du Monde” of Pontécoulant, vol..3, p. 30, for the 
terms of R of the third order depending on the ieslisiatiotom read 
N°. ea? . t (n't —nt +e —£)4+3nt+3e — — 217] 
N’. be a (n/t — nt +e = 8) + 3pt-+38 07 — 9). 
It is also deserving of patticular attention, that in these treatises 
thes 6 3 ae quantities A, B, etc., have different ot 
e following are the fundamental quanti sige aon» y Nep- 
tune to the theory of Uranus. : 
* 
e 
