ON THE MEASUREMENTS OE WAVE-LENGTHS. 
79 
changes of temperature such as would very nearly account for the discrepancy in the 
readings. Thus, taking the linear coefficient of expansion of wrought iron to be 
0'0000122 for 1° C., the length of screw to be 20 inches, and the change of tempera¬ 
ture 5°, the change in entire length would amount to O'OOl inch, or in 5 inches, which is 
about the measured length of each photograph, to 0'000305. From this must be deducted 
the coefficient of expansion of white glass, which amounts to 0'000215 inch, which 
reduces the error to 0‘00019. The error is generally an increasing one as the distance 
from zero increases. 
We have taken advantage of our numerous measurements to reduce the error to a 
minimum : first, by taking the mean of several readings ; secondly, by observing the 
intervals occurring between the lines and adopting numbers which, while they accord 
with the progressive increase in these intervals, closely approximate the numbers 
obtained by measurement. On comparison of the two sets of figures, it will be found 
that the mean of all readings and the mean of all adopted numbers agree. The 
greatest difference between any two series of mean adopted numbers and mean 
readings amounts to 0'0005 inch, the average error being 0‘00023 inch. The value of 
these fractions in wave-length for any portion of the spectrum is not greater than 
0"2 tenth-metre for the less refrangible, and probably as little as 0'05 for the more 
refrangible rays. 
A difference in the linear measurements of the fiducial lines could occur by an 
unequal contraction of the gelatine film on drying. This was never the case with our 
plates for the reason that the central portion of each film only was used, the films were 
dry when the photographs were taken, and would presumably remain in the same 
position on the glass after developing unless some artificial mode of desiccation were 
employed, such as the elimination of water by steeping in alcohol. This latter method 
was never resorted to. 
In the case of the photographs of the spectra to the right of the reflected image of 
the slit, one series of numbers, those of zinc, do not satisfactorily show the same 
relation between their intervals as can be traced between those of the other two plates, 
thallium and magnesium. The images on these photographs are not so sharp, and 
present consequently a greater difficulty in measurement than those on the spectra to 
the left. That the numbers adopted for the zinc plate are fairly correct is evident 
from the values determined for the cadmium lines. 
The apparently greater dispersion of the portion 17-26 than of the portion 11-18, 
and of the latter than of 6-12, is due to the varying inclination of the plates to the 
axis of the camera lens. The plates, when in focus for the portion 6-12, were but 
slightly if at all inclined, while the plates including 11-18 and 17-26 were taken at a 
very considerable inclination ; the inclination for the latter being the greater. A screen 
of cardboard was placed in front of the upper half of the slit when photographing the 
fiducial lines, in order to prevent them obscuring the spectral lines below to which 
they referred. When the reflections of the slit were too diffuse it was found advan- 
