656 
PROFESSORS A. W. REINOLD AND A. W. RUCKER 
change of thickness was ever given by the electrical experiments, but it is, of course, 
possible that the behaviour of the cylindrical and plane films might in this respect be 
different. 
Let n and n be the number of the films in the two tubes. Let the mean thick¬ 
nesses of the films in the first tube at the levels where the fringes crossed the 
boundary into the dark (transmitted) band, and where they became vertical, he 
t L and t. 2 , and in the second let them be t{ and t. 2 '. Then the difference of the paths 
of the interfering rays would be 
g 
{( nt l — n't 2 ) — (iit 2 — n — 
where 8 is the angular displacement of the compensator corresponding to the distance 
between the centre of one of the vertical fringes and the point where it cuts the 
boundary. Now since t 1 and are greater than A and t 2 respectively, A.S (p ,—\)na 
is an inferior limit of the quantity t 1 — t 2 . 
The following table gives the data by which the value of this limit was determined 
on several occasions. Lengths are given in terms of millionths of a millimetre. 
Table II.—\=615, p—1 = 0‘4. 
$/a. 
n. 
ty — t.y. 
1-26 
36 
53-8 
075 
49 
23-5 
0-92 
31 
45-6 
0'84 
58 
22 - 2 
Th is table shows that a very considerable change of thickness is necessary to 
account for the phenomenon. If the average thickness of a black film be taken as 
12 X 10 -6 millims., the films in one tube at the boundary of the black must have been 
from 3 to 5 times as thick as elsewhere. 
This explanation is not without its difficulties. The thickness of the “ beginning of 
the black,” when the proper correction for the refractive index is made, is, according 
to Newton’s tables, 36 X 10" 6 millims., whereas one of our experiments (if we adopt 
the above hypothesis) shows the average thickness of the thickest black parts of the 
film to be (53‘8-}-12) X 10 -G = 65‘8 X 10~ 6 millims. 
This discrepancy may, perhaps, be explained by the fact we have already referred 
to (Phil. Trans., 1881, p. 453) that measures on the diameters of Newton’s rings are 
of little value near the central black patch. 
It is, however, difficult to understand why all the films in one tube should behave 
so differently from those in the other, while, if it be assumed that the difference is caused 
by a few films only, it becomes necessary to extend the limits of the black through an 
■ !. 
