84 ROYAL SOCIETY OF CANADA 
from 1: 2 to 1: 1-1/2 can thus be accounted for. In the single prism 
spectrograph, however, the linear dispersion, angular dispersion, resol- 
ving power, and purity of spectrum are practically only one third of 
those of III L, and the errors should be three times as great. Instead of 
that the total error of a plate, which is of course the most important 
quantity to be determined, is only 40 per cent. greater with the lower 
dispersion and an examination of the last two columns shows that the 
systematic (due to changing instrumental factors) part of this error is 
nearly the same in III L and I, while the accidental part is nearly in 
proportion to the dispersions. 
This would seem to indicate either that the single prism spectro- 
graph is less likely to give systematic displacements of the spectrum 
lines than III L or that the kilometre rather than the linear value of the 
systematic displacements remains constant. So far as the first supposi- 
tion is concerned, although the single prism instrument! is undoubtedly 
less affected by flexure than III L and is probably better controlled and 
regulated as regards temperature, these two factors will not have much 
influence in the short exposure required on Arcturus. There is no 
ground for supposing on the other hand that kilometre rather than 
linear values of the systematic displacement should remain constant 
except in the case of displacements due to temperature changes in the 
prisms. 
A partial explanation of the relative superiority of the low disper- 
sion instrument is that it may be due to the fact that the three prism 
plates were mostly made on different dates and at varying hour angles 
though never far from the meridian, while the one prism plates were 
made in four groups only, the plates being obtained consecutively and 
probably under similar conditions in each of the groups. 
In any case it seems to be evident that radial velocity determina- 
tions of second type stars may be made with low dispersion instruments 
with an accuracy not much less than that obtainable with the high dis- 
persion instruments at present in use. This fact, if considered established 
by the present investigation, is one of much importance as it admits the 
carrying of the spectrographic survey of the heavens to stars more than 
a magnitude fainter than those at present available. 
It may be of interest to compare the values of the probable errors 
of a region and plate in the solar type star Arcturus with those obtained, 
in my investigations on the effect of slit width? of the probable errors 
of an average line and of a single plate in the case of the early type star 
1 Journal R.A.S.C., III., p. 287. 
2? Astrophysical Journal XX VIII, 259 and Trans. Royal Society of Canada 1909, 
p. 209. 
