ON THE LIMITING THICKNESS OF LIQUID FILMS. 
G57 
improbable range. The phenomenon was always transient, and the whole of the 
curvature took place within a distance of one or two millimetres. 
The measurement of the shift of the zero was a matter of some nicety. The field of 
view was scarcely large enough to make it convenient to take the readings when the 
vertical wire bisected the interval between two dark fringes. The observations were 
therefore made by causing them to touch the vertical cross wire, and, as their outline 
was irregular, it required some care to decide upon the particular phenomenon which 
should be called contact. Two readings might easily differ by a degree or more, i.e., 
by from ygth to y^-th of a wave length. As a rule the errors were much less, and the 
mean of five readings was always taken. Another reading as large or as small as the 
largest or smallest would hardly ever have altered the mean by more than 6', and we 
think the extreme possible error of the mean is not more than 1 O'. The most serious 
difficulty was due to the instability of the zero. The two tubes were mounted, as has 
been described, side by side, and the distance travelled by the interfering rays in 
unenclosed air was not more than 30 centims. Owing, however, either to slight 
changes in temperature or hygrometric state, or to some other undetected cause, the 
zero was continually moving. The motion was generally though not always in one 
direction. It was very variable in amount. Sometimes it was negligible, sometimes 
it produced a change of 4° or 5° in as many minutes. It is evident that the thickness 
of the films, given by any particular experiment, would be greater or less than the true 
value according as the motion of the zero was, or was not, in the same direction as that 
produced by the rupture of the films. The observed facts were in accordance with 
this, and the numbers obtained w T ere generally larger or smaller than the mean 
according to the direction of the motion of the zero before the experiment. If there¬ 
fore the motion remained constant during observations made on the two tubes, the 
results given by each would be oppositely affected, and the mean value would be 
correct. Even if, as was the case, it was impossible to ensure such constancy, the 
error of the mean would probably be much less than that of the individual observa¬ 
tions. In all our experiments, therefore, the result of each was taken to be the mean 
of the numbers obtained by breaking the films first in one tube, and then in the other. 
The following are the details of the last experiment performed with the liquide 
glycerique. The zero was on this occasion remarkably steady. 
The ruby glass having been placed in front of the lamp, the angles through which 
it was necessary to turn the compensator to bring the fringes to the right and left of 
the central dark fringe into the position it previously occupied, were measured. These 
were always taken in the order—centre, left, centre, right, centre. The readings 
i'ight and left were compared with the means of the two readings for the centre 
between which they were taken, to reduce the effect of any zero movement which 
might be in progress. 
The angles gi ven by two such sets of measures were 
13° 4E, 13° 31', 13° 25', and 13° 59' ; mean 13° 39'. 
