THICKNESS AND ELECTRICAL RESISTANCE OF THIN LIQUID FILMS. 511 
Table VII.—Hard Soap; 1 part to 70 of water. 
Percentage of 
KNOg. 
Thickness in /t./t., measured 
electrically. 
Mean. 
3 
9-6, II-6, 12-3, 7-7, lO-O, 12-5 
10-6 
2 
12-3, 20-0, 8-3, 10-7, lO'S, II-3, II’I, 17-3 
12-7 
1 
20-1, 28-0, 22-1, 30-3, 21-6 
24'4 
O’o 
29-8, 29-8, 25-2, 25'8, 22-0, 26'4, 26-4 
26-5 
0-0 
146, 103, 139, 215, 197, 240, 134. 98, 149, 
155, 129, 79, 118, 167 
148 
0 -0* 
156, 84, 213, 240, 159, 250 
184 
The first thing to notice with regard to this table is that when the solution 
contained 3 per cent, of KNOg, both the variations in the results of the individual 
experiments and the mean value of the thickness are in close agreement with the 
corresponding values obtained by us in 1883 (“Limiting Thickness,” &c., loc. cit., 
p. 661). This fact is proved by the following table, in which the thicknesses are as 
usual expressed in /r.ju. 
Table VIII. 
Date. 
Largest value. 
Smallest value. 
Mean of all values. 
1882 . . . 
14-5 
7-2 
11-7 
1891 . . . 
12-5 
7-7 
10-6 
Next we note that in Table VII. the indications of an increase in the calculated 
thickness are unmistakable when the quantity of dissolved salt is reduced to 1 per 
cent. When no salt is used, and the proportion of soap to water is as 1 to 40, the 
mean thickness is in one case no less than 184 p,./r. The colour corresponding 
approximately to this would be the beginning of the yellow or of the red of the first 
order, according as the incidence of the light was grazing or normal. 
Under no possible circumstances could a film of this thickness appear black. The 
beginning of the black, according to Newton, occurs when the thickness is 36 /r./r., 
which is only about one-fourth or one-fifth of the mean value obtained for unsalted 
solutions. We are therefore driven to the conclusion that the close agreement 
between the results of the optical and electrical measures of the thickness of black 
* One part of soap to 40 of water. 
