1887.] Mr J. Y. Buchanan on Distribution of Temperature. 149 
The density (at 15°*56 C.) of the sea-water which comes in contact 
with the lower surfaces of the icebergs is 1 *0255, which represents 
a chlorine percentage of 1*90. Ice actually melting in this water 
would produce a temperature of - 1 0, 92 C. When ice is immersed 
in this water it lowers its temperature, and a portion of the ice is 
melted, producing dilution. The concentration, therefore, or chlorine 
percentage, which will determine the melting temperature of the 
ice, will be a little lower than that of the original sea- water. From the 
“ Challenger ” observations we see that, on the confines of the pack 
ice, the cold stratum of water has a uniform temperature of 29° F. 
( — 1°*67 C.). Ice melts at this temperature in sea-water containing 
1 *65 per cent, of chlorine. In this process ice is melted, so that 
100 grammes pure warm sea- water become 119 grammes of diluted 
cold sea-water. It will he observed that the ice which has been 
formed in the atmosphere at a temperature of 32° F. comes in this 
way to he melted at a temperature of 29° F. ; and the pressure 
exerted by the 300 fathoms of sea-water, though it may assist in 
the lowering of the melting temperature, is insufficient to account 
for the amount. 
Monday , Min April 1887. 
Dr J. MUBBAY, Yice-President, in the Chair. 
The following Communications were read : — 
1. Note on a Formula for A w 0 l jn l when n, i are very large 
Numbers. By Professor A. Cayley. 
The following formula 
q = e~ (i+1)ln 
is given by Laplace ( Theorie Analytique des Probcibilites, 2 ed. 
Paris, 1814, p. 195) as an approximate value of A n 0 i /n\ when n and 
i are very large numbers, and is applied immediately afterwards to 
the case where i is of the order n log n. As remarked by Professor 
