6 Existence ancl Position of [January, 
valuable. But we see the impossibility to separate into 
distinct parts the research of the elements of Uranus, and 
of the elements of the disturbing body. It would be vain 
to hope that in forming empirical equations we might dis- 
cover, d priori, the law of disturbance, but we should run the 
risk to grossly deceive ourselves, because we should only 
have obtained an expression qualified to represent the ex- 
cesses of the disturbances over the errors arising from the 
inexactitude of the elliptical elements, but not at all the 
disturbances themselves. There is only one way ; it is to 
form the expressions of the disturbances caused by the new 
body into functions of its mass, and of the elements of the 
ellipsis it describes : these disturbances have to be introduced 
into the co-ordinates of Uranus, calculated by means of the 
unknown elements of the ellipsis this planet describes round 
the Sun. Equalising these co-ordinates so obtained to those 
observed, we take for unknown in the equations of condition 
which thereby result not only the elements of the ellipsis 
described by Uranus, but also the elements of the ellipsis 
described by the disturbing planet of which we want the 
position.” 
But when the ellipticity and half the great axis of the 
orbit and the mass, and everything attributed to the unknown 
by Le Verrier, differ so much from those of Neptune, how 
could he be found in the longitude of the predicted ? 
The answer shall prove the existence and give the approx- 
imate longitude, and more or less the other elements of the 
two planets A and B. 
“ The observations extend only over 155 years.” The 
155 must be embraced in a second solution, “ regardless of 
the amount of labour,” after 78 years proved too little. 
9. “ We conclude that e' falls between 94 0 40' and 189° 55', 
or between 263° 8' and 358° 71', to make the value of m' 
positive. 
10. “ We so might get a negative value of nt' correspond- 
ing to the positive value of e 1 , whereby the true solution of 
the problem would be misapprehended. I freely avow that 
this is what first happened to me, and that the difficulty 
long detained me.” 
11. “ We see that the value of in' actually changes sign 
for values of e' included between the points of the circum- 
ference obtained.” 
12. “ To definitively know if there exists in this extent a 
convenient value of c ' , we had now to attribute different ar- 
bitrary quantities to this variable, calculate the corresponding 
values of in', in' h', and in' l', and examine if one of the 
