THE ELECTRICAL RESISTANCE OF THIN LIQUID FILMS. 
485 
ance of the film, the specific resistance of the liquid in mass, and the mean specific 
resistance of the surface layer, the thickness of which is equal to the radius of molecular 
attraction respectively. Then we have 
T_T —2ro 2 CT 
R p r 
Now the experiments certainly prove that there is no regular increase or decrease 
in the specific resistance of the film between the thicknesses of 1 3 X 10 -5 and 3 ‘7 X 10~ 5 
centims. amounting to as much as 3 per cent, of its value. But if we assign to 2m the 
value found by Quincke, about 1 X 10~ 5 centims., it may readily be shown from the 
above formula that, if r differed from p by as much as 17 per cent., It would vary 
3 per cent, between those thicknesses. As no such variation is observed we must 
conclude either that the radius of molecular attraction is less than Quincke’s value or 
that the mean specific resistance of the surface layer, the thickness of which is equal 
to the radius of molecular attraction, does not differ by more than 17 per cent, from 
that of the liquid in mass. 
It is obvious that the electrical experiments confirm the accuracy of the revised 
scale of colours. Had Newton’s scale been used, the numbers analogous to those 
given in columns II. and III, of Table IX. would have varied from 0’884 to 1'012. 
Change of composition of the films .—The fact that films formed under constant 
hygrometric conditions obey Ohm’s law having thus been proved, the second part of 
the enquiry refers to the change of composition which might under other circumstances 
be produced. 
This is illustrated by experiments on five films. 
In the case of some of these the observed specific resistance rose as high as 204, 
indicating, as that of the liquid in mass was only 140 - 5, a considerable loss of water. 
To determine this the specific resistance was first reduced to 20° 0. by the formula 
/> =p 20 {l+(O-03 + 0-000138)(20-Q}. (Seep. 475.) 
The number of parts of water lost out of 100 of the original standard solution 
was then approximately calculated from the formula 
p-=10S. (See p. 477.) 
The loss of 25 parts of water having been proved to increase the refractive index by 
O'O L8, a corrected value of that quantity was obtained from the formula 
g = 1-397 + 0-00072^, 
which would be very nearly true up to p=25. 
This number was then used to correct the thickness of the film, and the new value 
of p thus obtained gave a second approximation to the value of p. 
3 r 2 
