80 
PROFESSOR W. N. HARTLEY AND MR. W. E. ADENEY 
tageous to photograph four or five spectra on one plate, the photographs of the slit 
falling on the uppermost spectrum only, any error arising from adjustment of the 
plates for the reception of the different spectra being corrected by means of the 
cadmium lines. 
The fiducial fines of the portions 6-12 were sufficiently close together for distances 
between any two of them to be taken as proportional to wave-lengths, with a 
maximum error of about 0‘1 tenth-metre. Owing, however, to the inclination of the 
plates for the other two portions of the spectrum, the error in taking the distances as 
proportional to wave-lengths was too large ; three points were therefore interpolated 
between each pair of fiducial fines. This was easily accomplished, as the intervals 
between the reflections were simply related to one another. The maximum error of 
the curves constructed with the fiducial lines and the interpolated points was about 
Off to 0’25 tenth-metre for the portions 11-18 and 17-26 respectively. Corrections 
were made for the latter error with the plates 17-26. 
The curves were constructed on millimetre paper, 4 millims. were allowed for each 
difference of a tenth-metre of wave-length and 1 millim. for each two-thousandth of an 
inch of the scale numbers. 
The wave-lengths of the cadmium lines. 
As stated in the introduction to this paper, on taking photographs from metallic 
electrodes an electrode of cadmium was always used to furnish a spectrum in reference 
to which all other spectra could be measured. In the adjoining table will be found 
the values we have adopted for the wave-lengths of the cadmium fines, together with 
the numbers afforded by each plate employed in their determination. The latter 
numbers, it will be seen, do not give the true wave-lengths, but require a small 
correction, which will be found in the table. The correction for the numbers calcu¬ 
lated for the fines 12, 17, 18, on the portion 11-18, from photographs of spectra on 
either side of the reflections of the slit, are shown by the table to be as nearly as pos¬ 
sible 2'9 and 3’3 tenth-metres, of negative sign for the spectra to the right and positive 
sign for those to the left. Guided by these corrections, and owing to the fact that 
the fines 12a, /3, y occur also on the photographs of the portion 6-12, the fines 17 and 
18 on the photographs of the portion 17-26, the corrections for the remaining fines 
have been deduced. Thus, for the portion 17-26 the corrections for the lines 17, 18 
were found to be 3‘6 and 3'8 respectively, and a correction of 4'0 was consequently 
made to remaining fines of this portion of the spectrum. In a like manner the 
corrections for the fines of the portion 6-12 were found. The explanation of the 
necessity of these corrections will be given later on, when considering the errors 
introduced by uncorrected lenses. 
