318 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND C. Y. BURTON: 
If either the barometer or the driving pressure varies, this formula is not strictly 
correct, and in general we should have to evaluate the integral numerically from a 
record of the pressures ; we may still, however, write 
k = t( an d l 0 = t U ) , 
\JPl TTtj./ mean ^To' m eau 
where the quantities involved must now be given some mean value, which is not 
necessarily the arithmetic mean. 
But in the experiments the magnitude of the quantities makes it clear that the 
arithmetic mean is a very close approximation to the true value, and hence equation 
(4) is sufficiently accurate if B is the mean barometer. 
To make quite sure that this is correct we have verified it in an extreme case, 
where during the experiment the barometer varied irregularly by some 30 mm., but 
no sensible error was introduced. Nevertheless cases may arise in which the error 
might be important, and attention is therefore drawn to it so that the correction may 
not be overlooked. For instance, during high winds the barometer fluctuates rapidly, 
and it is conceivable that equilibrium is not established throughout the apparatus 
instantaneously. In this case the assumptions made in the formula are not valid, and 
indeed we have some experimental evidence that the results are affected by rapid air 
pulses. 
As regards a change in the temperature of the bath, obviously the quantities in¬ 
volved in the calculation are also affected, but equation (4), in which the values 
appropriate to the mean temperature are used, is still a close approximation provided 
the temperature changes are sufficiently small. 
In our experiments IJi\ is always less than 1'22, hence the osmotic pressure, which 
is proportional to lo g e l 0 /li, is approximately proportional to {l 0 —li)/l 0 ', thus it is only 
with the loss of weight of the water vessel that the highest accuracy is required. 
We will now endeavour to estimate the errors involved should the assumptions 
made at the beginning of the preceding analysis not be strictly accurate. 
Solution and Solvent not at same Temperature *—-Although the effect of a difference 
between the temperatures of the solution and solvent could be investigated fully from 
the equations already established, yet it is thought that the following simple method 
of considering the matter is sufficient. Take the case of a weight normal solution of 
cane sugar at 30" C. This solution is the most dilute that we have investigated, and 
it is here that the error due to a temperature difference has the largest effect. 
Suppose l 0 = 20 gr. (i.e., 20 gr. of water are evaporated from the whole system during 
the run) and l a —l x = 0'5 gr. Now assume a persistent difference in temperature 
during the whole run of 0°"001 C ; this is equivalent to a change of 0'006 per cent, in 
the vapour density of water ; so that the loss in the water vessel will differ from the 
* See note at end of paper. 
