366 Mr C. T. Heycock and Mr F. H. Neville, On the [June 3, 
This series proceeds according to powers of p/m,, which lies 
between — a and 8, and therefore canisnes 7 in the limit, and there- 
fore ultimately 
tye” i( pe ) 
WO = tm, —=—, v=e Om) 
2m, 
a 
Now between the limits (1—a)m, and (1+) m, of m con- 
secutive terms of the series Xv are ultimately equal, and we may 
replace =v by fudm or Judy; and the limits of » are — am, and 
+8m,, that is in the limit —o« and +2. Hence in the limit 
Sy = [ 1 vdp = fm Gita. 
1-t 
S/O eel (2 at) eg ae (D), 
which may be expressed by (C) in terms of p. 
The function of p to which the complete series 2w,, bears 
ultimately a ratio of equality when p is infinite is thus found, 
without the necessity of expressing the series in the first instance 
for general values of p by means of a definite integral. 
The same method will evidently apply to the series whose 
general term is formed from (A) by integrations or differentiations 
with or without intervening multiplications by powers of #, since 
this process will merely introduce factors of the form m-+c¢ into 
the numerator or denominator or both, and in passing to the 
limit for p= 00 these factors may be put outside after writing m, 
for m. 
(2) On the lowering of the freezing point of tin caused by 
the addition of other metals. By C. T. Hrycocx, M.A., King’s 
College, and F. H. NEviiuz, M.A., Sidney Sussex College. 
WHEN considering the researches of Raoult on the lowering of 
the freezing point of solutions, it occurred to us that the solution 
of one element in another might present the simplest case. 
We have therefore determined the freezing point of pure tin 
and of tin containing known quantities of other metals. Tin was 
first chosen, because its melting point is fairly low and permitted 
the use of a mercurial thermometer, and also on account of its 
well-known power of dissolving many metals. As in the case of 
other liquids, the moment of incipient solidification is sharply 
indicated by surfusion. The experiments were made in a crucible 
consisting of a block of cast iron six inches high and five inches in 
diameter, having a cylindrical hole one inch in diameter and four 
inches long bored along its axis; this arrangement ensured slow 
cooling. Into this hole, which served as a cavity for containing 
