[PLASKETT] RADIAL VELOCITY DETERMINATION 79 
results to be discussed were derived. In order to clearly explain how 
the probable errors were obtained it is necessary to briefly describe the 
comparator and the method of measurement. In the first place a 
standard spectrum of the sun is obtained by the same spectrograph 
and this plate has impressed upon it, on each side of the sun spec- 
trum, a strip of the same comparison asin the star spectrum. This 
standard sun spectrum and the star spectrum are viewed by a special 
double objective, single ocular microscope, with a Lummer-Brodhun 
cube in the ocular, which serves to superpose the two spectra so that a 
narrow strip of star spectrum is seen between and touching two strips of 
sun spectrum, while on each side a narrow strip of the star comparison 
lies between and touching strips of sun comparison. The standard 
sun spectrum is moved by a micrometer screw until the corres- 
ponding lines of the star and sun spectra are in exact coincidence 
and then again moved until the comparison lines of the two 
spectra are coincident. The difference in the micrometer readings 
evidently gives us the displacement, due to radial velocity, of 
the star lines with respect to the sun lines, which on multiplication by 
a constant gives, after adding with the proper sign the known 
velocity of the sun, the velocity of the star with reference to the 
observer. 
The coincidences are made at a number of chosen regions, marked 
by dots on the sun spectrum, which correspond, in a sense, to the lines 
in an early type spectrum, on which the cross wire is set. The accidental 
errors can thus evidently be determined from the probable error of the 
determination of the points of coincidence in these regions. After the 
spectra have been measured with the red end to the right for example, 
they are reversed on the comparator and the same regions remeasured. 
The differences of displacement, corrected for a systematic effect due to 
reversal, are evidently wholly due to accidental errors of setting, and 
from these the probable error of a region is readily obtained in the well 
known way, giving a measure of the purely accidental error. 
In addition to the purely accidental errors of setting are others also 
of an accidental character due to irregular arrangement of the silver 
grains or distortion of the film, to the forming of the coincidences to one 
side or other of the dot or centre of the region and consequent incorrect 
value of the velocity constant by which the displacement is multiplied, 
and to numerous other causes. A measure of the total accidental 
error is evidently obtained by computing the velocities separately for 
the mean of the two measures red right, and red left of each region, 
by obtaining the residuals from the mean velocity of the plate, and the 
probable error in the usual way. This probable error should be and is, 
as is seen below, somewhat greater than the purely accidental error of 
setting. 
