458 
PROFESSORS A. W. REINOLD AND A. W. RUCKER ON 
coloured ring of the same width, even when the colour is of the second or first 
order. 
In discussing the method it is necessary to show that no sensible error was caused 
by the disturbance of the equipotential lines which accompanied the introduction of 
the needle points into the films. The distance between any two needles being greater 
than those between the upper and lower needles and the metal rings by which the 
cylinder was supported, it will be sufficient to consider the extremities of the film 
only. 
A small aggregation of liquid was always observed around the needle points. Its 
dimensions were variable, but the diameter was never greater than a millimetre and a 
half. If we assume that the resistance of this mass (of radius a) was infinitely small, 
compared with that of the surrounding film, and that the dimensions of the cylinder 
were infinitely greater than a, the equation to each of the disturbed equipotential 
lines would be of the form 
y 
= constant, 
where the axes of x and y are horizontal and vertical respectively. 
The maximum displacement, by the introduction of a needle, of the equipotential 
($• 
line which passes through x= 0, y — y would therefore be —. The condition of accuracy 
is that this quantity shall be negligible at a distance from the needle equal to that of 
the metal ring which bounds the cylinder. This distance was generally greater than 
5 millims., and therefore O'll is the limit of error. The distance between two needles 
being 15 millims., it is therefore possible that an occasional error of 0'75 per cent, may 
have been caused, but we doubt whether it ever reached this amount; and in all the 
more important experiments, viz.: those made after September 20, 1880, it certainly 
did not, as the two lower needles were exclusively used, and the error must therefore 
have been halved. 
The thickness of the film between two needles was taken as the mean of the 
thicknesses at the needles. These were measured in turn, the time of each observation 
being noted, and curves were drawn of which the ordinates represented the thicknesses 
and the abscissae the times. It was found that to make and record a measure of the 
thickness occupied about half a minute, but, when the film was thinning slowly, 
observations were made at longer intervals. The curves were used to correct errors of 
observation by smoothing off irregularities. On a few occasions errors amounting to 
2 per cent, of the thickness were thus detected. In the curves themselves the error 
of observation probably nowhere exceeds 1 per cent., and approaches that amount only 
when the films were very thin. 
The electrical observations on the resistance of the film were carried on simultaneously 
with the above, and curves showing the relation between the resistance and time were 
