THICKNESS AND ELECTRICAL RESISTANCE OE THIN LIQUID FILMS. 509 
therefore, not too much to say that the average thickness, measured optically, of a 
black soap film formed of a solution of I part soap in 50 of water, but containing no 
KNOg, is double that of a similar film made of a solution of the same composition in 
which 3 per cent, of KNOg has been dissolved. 
The results obtained with the plain hard soap solution are confirmed by experiments 
on liquide glycerique. 
Table V .—Liquide glycerique. No Salt dissolved. 
Proportion of 
Thickness of black film in 
Mean. 
soap to water. 
measured optically. 
I to 40 
23-9, 25-4 
24-6 
I „ 60 
28-6, 30-0, 327, 27-9 
29-8 
In this case, again, a decrease in the proportion of soap produces an increase in the 
apparent thickness of the black. 
When the solution contains 3 per cent, of KNOg, variation in the proportion of 
dissolved soap has comparatively little influence on the thickness of a black film. 
This statement is justified by the figures given in Table VI. 
Table VI. — Hard Soap. 3 per cent, of KNOg. 
Proportion of 
soap to water. 
Mean thickness of black in /(./<., 
measured optically. 
Greatest and least 
values. 
Date. 
1 in 40 
130 
13-5-12-7 
April, 1891 
1 „ 50 
I2I 
12-9-I1-6 
1 ,, 60 
11-55 
Single observation 
July, 1892 
1 „ 70 
12-1 
14-4-10-3 
1883 
■ The question now arises whether the large increase in the thickness of black films, 
formed from what we may, perhaps, for convenience, call an unsalted solution is real, 
or whether it is due to some incorrect assumption. The only point where error is 
possible is in the hypothesis that the refractive index is the same as in the liquid in 
mass. The thickness of the film varies inversely as n — 1 [n being the refractive 
index), and as the refractive index of the soap solution is about 1‘34, itvvould have to 
be reduced to about 1T7 in order that the calculated thickness might be doubled. 
It appears, therefore, d priori, extremely improbable that the mere addition of 
3 per cent, of KNOg should so completely change the optical properties of the liquid 
that, whereas, if the salt be added, the refractive index is practically the same in 
thin films and in the liquid in mass, as is proved both by our experiments of 1883 
