of Edinburgh, Session 1881-82. 741 
He also announced that the limits of the mean distance which 
would satisfy the observed perturbations of Uranus were 35 ‘04 and 
37 '90. He founded this conclusion on a supposed inadmissible 
increase of the outstanding differences between theory and observa- 
tion, as the mean distance was diminished below 35. But when 
the planet was discovered its mean distance was found to be only 
30 ; and yet the observations of Uranus were as well satisfied as by 
Leverrier’s hypothetical planet. It was, therefore, an expression of 
Peirce’s high confidence in the accuracy of Leverrier’s conclusions 
that led him to announce that there were two solutions to the 
problem 3 the one being that found by Leverrier, and the other that 
corresponding to the actual case. He also sought to show a cause 
for the two solutions in a supposed discontinuity in the form of the 
perturbations, when the period was brought to the point at which 
five revolutions of Uranus would be equal to two of Ueptune. As 
a matter of fact, however, it has been shown by Professor Adams 
that there was no such discontinuity in the actual perturbations 
during the limited period ; from which it would follow that 
Leverrier must have made a mistake in tracing out the conclusions 
which would follow when the mean distance of the disturbing 
planet was diminished. 
I 11 1849 the preparation of the American Epliemeris and Nautical 
Almanac was commenced at Cambridge, by Lieutenant C. H. Davis, 
and Peirce, in the capacity of consulting astronomer, took an active 
part in planning the work. It being especially desired that accurate 
tables should be employed in the new Ephemeris , Peirce made use 
of Airy’s reduction of the Greenwich lunar observations, then 
recently published, to prepare new tables of the moon. He pre- 
pared the formula and plans for the table which were executed in 
the office of the Ephemeris. Gould's Astronomical Journal was 
commenced at this time, and Peirce contributed a number of short 
papers, the most important of which related to the theory of Saturn’s 
rings. The suspicion had been expressed by Bond and others, 
that temporary divisions took place in the rings from time to time, 
thus showing that they could not be solid. Peirce showed that the 
equilibrium of a fluid ring was necessarily unstable, as well as that 
of a solid one, and therefore suggested that the equilibrium was pre- 
served by the attraction of the satellites. The research, however, was 
