269 
boulder hypothesis ; he only differed from Mr Fisher in think- 
ing that the valley existed before the iceberg came. He quoted 
some instances of large included boulder-like masses, especially 
one recorded by Professor Morris, in Lincolnshire. 
Mr O. FisHer expressed his pleasure at the corroboration 
which his hypothesis had received. He thought the valley 
could hardly have existed before, because the clay would have 
formed sides sloping more than the limits of the Kimeridge clay 
appeared to do. He had, since writing his paper, sometimes 
thought that the boulder might have been dropped on the top 
of the Kimeridge clay and crushed its way down into its present 
position. 
Mr Bonney, in reply, gave reasons for the supposed pre- 
existence of the valley, and thought it doubtful whether the 
boulder would be heavy enough to crush out the beds below. 
May 27, 1872. 
The VicE-PRESIDENT (PROFESSOR BABINGTON) in the Chair. 
Communications made to the Society : 
(1) On some properties of Bernoulli's numbers, and, im 
particular, on Clausen’s Theorem respecting the 
fractional parts of those numbers. By Professor 
J. C. Apams, F.R.S. 
The author stated that the theorem enunciated by Clausen 
for the determination of Bernoulli's numbers had not been 
proved by him or by any other mathematician—the memoir 
proposed by Clausen not having ever been published. The 
author gave a comparatively simple proof of the theorem. 
Thirty-one of Bernoulli’s numbers are already known; the 
