Benjamin Peirce. 171 
with either party. Leverrier and Adams each, as Professor 
Peirce has himself shown, by his own laborious researches, did 
point out correctly a place where a planet should be looked for, 
and assigned paths which that planet could have been traveling 
for more than one hundred and twenty years previously, and 
have caused the observed irregularities. Yet the elements of 
that planet’s orbit and its mass and those of Neptune differ 
widely enough to justify the assertion that for the latter ‘hey 
were not correctly given. 
On the other hand, astronomers will not probably agree with 
Professor Peirce in regarding the change of character of the per- 
turbations when the mean motions of the new planet and of 
Uranus pass through the exact ratios 2:5 and 1: 2 as of vital 
importance. In the usual form of development these fractions 
do indeed make certain terms infinite. That belongs, however, 
to the form of the development, not to the perturbations. In 
i is the disturbing body?” th 
solution need not have involved these forms; and it has not 
been shown that they entered into the work of either Leverrier 
or Adams in such a way as to vitiate it. 
? » 
rs. 
In 1852, Professor Bache, then Superintendent of the United 
