of Edinburgh, Session 1885-86. 405 
The value of this (which Meyer obtains by expanding in an infinite 
series, integrating, and summing) may he obtained by noting that 
while the two parts must, from their meaning, be equal , the second 
part can be integrated at once as it stands. 
Or we may change the order of integration in the first, and find, 
that it is transformed into the second. 
Or we may obtain it by inspection, if we merely transform the 
double integrals by the assumptions 
v = r cos 6 , v 1 = r sin 0 . 
Note now that the limits for r are 0 to oo in both ; but those for fl- 
are 0 to 7r/4 in the first, and 7r/4 to tt/ 2 in the second. When this 
is done we find that the mean number of collisions is 2 ^2 tt a ns 2 . 
Dividing, by this, the mean speed 2 a/ Jv, we have Clerk-Maxwell’s. 
value of the mean path — tx —5 • 
r v'2.7 ms 2 
PEI V ATE BUSINESS. 
The following Candidates were balloted for, and declared duly 
elected Fellows of the Society : — Dr A. B. Griffiths, F.C.S., Technical 
College, Manchester; Daniel M. Connan, Esq., Education Depart- 
ment, Cape Town; and David Cunningham, M.Inst.C.E., Dundee. 
Monday, 21 st December 1885. 
Peofessor DOUGLAS MACLAGAN, M.D., Vice-President* 
in the Chair. 
The following Communications were read : — 
1. On the Distribution of Temperature in Loch Lomond during 
the Autumn of 1885. By J. Y. Buchanan. (Plate XI.). 
In the course of the autumn of this year (1885) I have taken 
several occasions to determine the distribution of temperature in the 
water of Loch Lomond. The results of these observations are 
interesting, as indicating the march of temperature in the different 
layers at different localities in the lake, and also the gain and loss 
of heat with the changing seasons. 
Loch Lomond is divided naturally into three basins. If the level 
