1:885.] Two Planets beyond Neptune. 7 
solutions so obtained may represent the motions of Uranus 
in 1690 and 1747.” 
13. “ When we exclude the negative values of m', and 
the positive ones too considerable not to be rejected, ac- 
cording to reasons particular to the motions of Saturn, we 
have to admit that the value of e' suiting the problem, or 
examining the errors of the theory, leaves it in the position 
of the planet in 1690 to 1747 for all the values of e' between 
the limits just indicated, we see that the calculations always 
differ from observation for at least one of these positions,— 
a quantity much too great to be attributed to an error of 
observation, so that the consequence resulting from the dis- 
cussion seems to me the impossibility to represent the 
march of Uranus by means of the perturbing aCtion of the 
new planet.” 
14. Le Verrier arrives at a contraction of the more or 
less opposite arcs ; “ we have to admit that the value of e' 
suiting the problem must be comprised between 108° and 
162°, or between 297 0 and 333 0 ,” but “calculation always 
differs from observation for one at least of these two posi- 
tions,” and we again arrive at the “ impossibility to repre- 
sent the march of Uranus by the disturbing influence of the 
new planet.” 
15. “ Let us remark ” “ that the conclusions at which we 
would arrive may not be the expression of the truth. The 
motives given, to legitimate this way of judging, will receive 
new force by the following remark. Imagine that we went 
through the preceding discussion omitting the two following 
inequalities in longitude.” (— — .) “ These two disturb- 
ances are so feeble that it seems they might be omitted 
without affedting the final result. But nothing of this.” 
16. “ The preceding details seemed indispensable to make 
the reader understand all the difficulties in questions like 
that before us. Without them we could not have seized the 
importance of the modification made in the preceding march 
to definitively solve the problem.” “ The result to be 
arrived at will confirm in a remarkable manner the previsions 
of No. 8. We shall prove, contrary to the conclusions which 
seemed to follow from the preceding discussion, that it is 
possible to represent the march of Uranus, in accounting 
for the disturbing influence of the new planet ; that the 
length of the epoch e' of this new star must be 240° ; and 
that this hypothesis, the expression of the truth, would be 
repulsed by the negative value found for the mass.” 
1 7. “ It is sufficient to discuss in the same manner the 
error of the theory in 1758, and, in attributing increasing 
