ON THE MEASUREMENTS OF WAVE-LENGTHS. 
67 
The wave-lengths corresponding with these deviations were calculated, and those of 
the spectral lines were determined from them by interpolation. 
Calculation of the wave-lengths corresponding to the fiducial lines .—For the con¬ 
venience of future reference the photographs of the three portions of the spectrum for 
which the plates were focussed, will he designated by the numbers G-12, 11-18, and 
17-26. These numbers have been assigned to the prominent cadmium lines by 
Mascart, and they serve to fix the limits of the less and more refrangible ends 
respectively of each portion of the spectrum. 
The grating was placed so that to get the three portions of the spectrum into focus 
it was only necessary to move the plate-carrier, without shifting either the lens of the 
camera or the grating itself. The calculations of the wave-lengths corresponding to 
the deviations of the fiducial lines were made from the formula 
a (sin i fi-sin §) = n\, 
where n is positive for the diffracted rays on the same side of the reflected ray as 
the normal, and negative for those on the other side, is the deviation of the line 
reckoned from the normal to the grating, and positive when situated on the same side 
of the normal as the incident ray ; i is the inclination of the normal of the grating to 
the incident ray. This is, of course, at once determined from the position of the 
grating, when its normal is parallel to the incident ray. This position was found in 
the following way. A piece of plate-glass was placed in the small mahogany box at 
the end of the collimator tube (for a description of which see the paper already 
referred to in the Scientific Proceedings of the Royal Dublin Society, p. 10) in such 
a way as to allow the light from the slit to pass through it to the grating, and to 
reflect upwards the image of the slit reflected back from the grating. The grating 
was moved about till the image coincided with the slit. A wide slit was used to 
ascertain approximately the position of the grating, the slit was then narrowed as far 
as necessary, and the grating accurately adjusted. After this adjustment neither slit 
nor grating was moved during the time the whole of the series of photographs were 
being taken. 
• • • • % - s $ _^ 
The deviation S„ is not measured directly. One measures or — according as 
the spectrum observed is to the right or to the left of the regularly reflected image of 
the slit. The following calculation of the wave-lengths corresponding to the fiducial 
line I. for the spectra to the left will serve as an example. 
