454 
PROFESSORS A. W. REINOLD ART) A. W. RECKER OX 
being known, the inner pair could be used as reference lines for colours in their 
immediate neighbourhood. On one occasion, four measures, each made on a single 
ring, gave 431, 429, 431 and 438 millionths of a millimetre as the wave length 
respectively ; on another occasion two measures gave 432 and 438. As none of 
these numbers differ from their mean by more than 1*2 per cent, these measure¬ 
ments enable us to estimate the accuracy of the method. Red glass (coloured with 
oxide of copper) was used in the same way, and two measures agreed in giving 
the wave length as 615. In the case of the blue of the second order the difficulty 
was much increased by the fact that the boundary of a colour so near the centre 
of the rings is very irregular. If we except this tint, however, no measurement 
ever differed from the mean of the measures on the same colour by more than 
1'6 per cent. As three sets of measurements were taken at intervals of nine and 
six months respectively, and as in most cases three, and in some five, observations 
were made in each colour, it seems that the errors of recognition and measurement 
combined did not (except in the case mentioned) exceed 1*6 per cent. 
Side by side with these experiments, which were purposely made at long intervals 
to test the constancy of the colour estimations, other supplementary observations 
were made upon the films themselves. The scale of colour at first used was obtained 
by assigning to each tint the thickness ascribed to that of the same name in Newton’s 
second scale, and adjusting the boundaries so that the number thus assigned to any 
tint should be the mean of those assigned to its boundaries. The scale so formed was 
then tested in the following way. The angles of incidence and the refractive index 
being' known, the ratio of the cosines of the angles of internal incidence could be 
calculated. The colours at the points where the horizontal cross wire cut the 
illuminated bands on the film having been noted, the air-thicknesses corresponding 
to them at normal incidence were taken out from the table of colours, and the ratio 
of the larger to the smaller calculated and divided by the ratio of the cosines. The 
number so obtained will be referred to as the quotient, and the difference between it 
and unity was taken as a measure of the accumulated errors of the scale and of the 
observation. The mean apparent thickness of the film was easily deduced from the 
Cjuotient. 
As has been already stated, the observations proved that the table of colours required 
revision. This was effected by assigning the quotients to the colours shown by the 
more obliquely illuminated band in the observations by which they were obtained, and 
re-arranging the table so as to make the mean of the quotients assigned to each colour 
as nearly as possible unity. Care was taken to make the revised table agree closely 
with the observations on Newton’s rings. 
In January, 1879, 600 double colour observations were made on the two illuminated 
bands, and the table of colours as corrected by them was again revised by me ans of 
1,142 observations made in September and October, 1879. No further change has 
been found necessary, although the accuracy of the table thus corrected has been 
