343 
OSMOTIC PRESSURES DERIVED FROM VAPOUR-PRESSURE MEASUREMENTS. 
that in the experiments at 30° C. with dilute sulphuric acid the second vessel scarcely 
changes in weight, but with both cane sugar and a-methyl glucoside there is a small 
hut persistent loss ; this effect may indicate that the latter two substances suffer 
a slight decomposition, but experiments designed to elucidate this point are now in 
progress. 
The Calculation of the Osmotic Pressures .—The osmotic pressures are connected 
with the vapour pressures by Porter’s equation (‘Roy. Soc. Proc.’ A, vol. 79, p. 521), 
p pro rp - P 
■Sj dp — v dp + v dp, 
7T_r d 7T— J TT,, 
(h) 
where P is the osmotic pressure, and p the pressure on the solution ; ir„ and i r 0 are, 
as before, the vapour pressures of the solution and solvent respectively; v and u are 
the specific volumes of the solvent vapour and pure liquid solvent respectively. 
In our paper on calcium ferrocyanicle solutions we give reasons for thinking that 
equation (5) should be modified so as to be applicable to the vapour densities when 
measured in air. From the following discussion, which is contributed by Mr. G. W. 
Walker, it would seem that we were mistaken, and that the air values may be used 
without change. 
In the experiments the pressure on the pure solvent is one atmosphere. Hence (5) 
becomes 
rP+1 r*u r i 
•Si dp = v dp + u dp, 
J TT- J TT- J 7T. i 
but VTr/c/p - u/v K for vapour over the pure solvent. ( Cf. Porter, loc. cit.) 
Therefore 
f 77 o 
u dp = v dp 
J TT n 
where wo 1 is the vapour pressure observed. Again, dir/cp = sp'ir for the vapour over 
the solution. 
Therefore 
J -l p 77 7T 
•s-j dp = v dp. 
77 7T J 
where is the observed vapour pressure of the solution. 
Therefore 
■p+i 
I - u 
v dp* 
* This result might have been anticipated had it been noticed that Sir J. J. Thomson, in articles 90 
and 91 of “Applications of Dynamics,” shows that the increase in vapour pressure of a pure liquid caused 
by the pressure of the atmosphere upon it, precisely balances the lowering brought about by the dissolved 
air in it. 
2 z 
VOL. OCXYIII.-A. 
