78 ROYAL SOCIETY OF CANADA 
probable errors in kilometres per second would hence be inversely pro- 
portional to the linear dispersion. That is to say, as we have at the 
Dominion Observatory three different dispersions 10.1, 20.2, and 33.4 
tenth-metres per millimetre at H,, practically as 3, 1-1/2, and 1, we 
should expect to find the probable errors in kilometres per second in- 
versely proportional to these latter numbers or as 1, 2, and 3. 
Most of the radial velocities at the Dominion Observatory have been 
obtained from spectra made with the lowest dispersion, a single prism 
spectrograph, on spectroscopic binary stars of early type in which the 
spectral lines have generally been broad and diffuse. The probable 
errors of the velocity determinations of single plates have been conse- 
quently high, so high as to lead to the belief that the relation above 
expressed was not the true one, but that the probable errors increased 
more rapidly than the dispersion diminished. 
It seemed therefore worth while to make a definite test of the 
matter especially as, although considerable data as to the probable errors 
of high dispersion star spectrographs are available, there is so far as I 
know not much published information in regard to the probable errors 
of one prism instruments. In order to avoid, so far as possible, any 
effect due to diffuseness of the spectral lines, it was decided to use 
spectra of the solar type for the comparison. Further, to eliminate 
difficulties of identification of wave lengths in the blends of lines always 
present in low dispersion second type spectra, it was essential to measure 
the plates by the spectro-comparator, an instrument in which the actual 
displacement of the star lines due to velocity is compared with those in 
a standard plate of the sun whose velocity is known. By this method 
no knowledge of wave length is necessary and errors due to the loss of 
purity inherent with small dispersion can not effect the measurements. 
The brightest solar type star, Arcturus, was selected as a test 
object for the obvious reason that only short exposures would be 
necessary. To produce spectra of Arcturus, of good quality for measure- 
ment, exposures are necessary of about ten minutes with the three 
prism long focus spectrograph designated as III L, 10.1 tenth-metres 
per mm., four to five minutes with the three prism short focus designated 
as III R, 20.2 tenth-metres per mm., and one and a half minutes with 
the single prism spectrograph designated as I, 33.4 tenth-metres per 
mm. at Hy, and consequently the plates required may be quickly made. 
Fortunately when this investigation was begun we had already ob- 
tained nearly thirty plates with III L for another purpose and only 
plates with III R and I were required. Eleven were made with III R 
and about fifty with I. 
Of these plates 24 of III L., 11 of III R and 38 of I were measured 
by myself on the spectro-comparator and from these measures the 
