OSMOTIC PRESSURES DERIVED FROM VAPOUR-PRESSURE MEASUREMENTS. 319 
true value by 20 x 0'006/100 = 0'0012 gr., entailing a per cent, error of 0'2 both in the 
loss in this vessel and on the calculated osmotic .pressure. 
Several attempts to explore the distribution of temperature throughout the bath 
were made with Beckman thermometers and with thermocouples, but, except within 
about 3 cm. of the surface, no certain indication of a difference approaching to 0°'001 C. 
could be detected ; further, as a check to this, vapour pressure experiments in which 
the bath was stirred 50 per cent, faster than the normal rate (in the normal rate, the 
surface of the water immediately over the stirrer is raised about 1 cm. above the 
general level) resulted in no change. 
Similarly, should the pressure p x (see ecpiation (3)) over the solution differ from p 0 
over the solvent by as much as 0'015 mm. Hg, an amount which represents a change 
of 0'02 per cent, on the volume of air passed, we get an error on the loss of weight of 
the solvent of 0'0004 gr., and this is nearly O'l per cent, on the osmotic pressure 
derived from experiments on a weight normal solution at 30" C. Direct observations 
(by means of a sensitive oil manometer) of the difference between p 1 and p 0 show that 
in no case is this quantity greater than 0'004 # mm. Hg, and the consequent correction 
will be, for the most dilute solutions, about 1 part in 5000. It should be pointed out, 
however, that the magnitude of the correction is proportional to the vapour pressure 
of the pure solvent, so that for very volatile liquids or water at a higher temperature 
the air passages must be wide so as to offer as little resistance to flow as possible. 
Air Space between Solution and Solvent. —An error, due to the air space between 
the two vessels, may arise thus. When the barometer is varying no steady state is 
reached, and it is easy to see that as it takes a finite time for the air to travel 
from one vessel to the other, r, p 1 and r 0 p 0 are no longer equal, and a time lag 
results. 
An estimate of the maximum error due to this cause is the following. 
From the dimensions of the apparatus it is computed that, supposing 500 litres of 
air to pass in 125 hours, it will take 25 seconds to pass from one vessel to the other. 
If the barometer rises 30 mm. during the run, it is readily found that the solvent 
vessel will have lost 0'00005 gr. in excess of the amount given by the approximate 
formula (4). 
Slovmess of Air Stream and Turbulent Motion. —There seems to be no means of 
subjecting these two factors to mathematical analysis; but in both cases we may 
safely assume that any effect there may be will be enhanced when we increase the 
rate at which water vapour is taken from the system. Experiments, the details of 
which need not be given, were made in this direction, but without any variation in 
the result; also a further safeguard is provided by the fact that in experiments 
where there were two or more vessels (containing the solution) in series, the last 
vessel scarcely changes in weight. It is as well however to point out that owing 
to the irregular contours of the air passages some turbulent motion must set up, 
* This is for Apparatus A ; for Apparatus D the fall of pressure is about O ’001 mm. Hg. 
VOL. CCXVIII.-A. 2 U 
