92 H. A. Rowland— Concave Gratings for Optical Purposes. 
source of light exist on this circle, the reflected image and all 
the spectra will be brought to a focus on the same circle. 
Thus if we attach the slit, the eye-piece and the grating to the 
three radii of the circle, however we move them, we shall 
always have some spectrum in the focus of the eye-piece. But 
in some positions the line of foci is so oblique to the direction 
of the light that only one line of the spectrum can be seen 
well at any one time. The best position of the eye-piece as 
far as we consider this fact is thus the one opposite to the grat- 
ing and at its center of curvature. In this position the line of 
foci is perpendicular to the direction of the light, and we shall 
show presently that the spectrum is normal at this point what- 
ever the position of the slit, provided it is on the circle. 
Fig. 1 represents this case; A is the slit, C is the eye-piece, 
and B is the grating with its center of curvature at C. In this 
case all the conditions are satisfied by fixing the grating and 
eye-piece to the bar whose ends rest on carriages moving 
on the rails AB and AC at right angles to each other; when 
desired, the radius AD may be put in to hold everything 
steady, but this has been found practically unnecessary. _ 
he proper formulz for this case are as follows. If 2 is the 
wave-length and w the distance apart of the lines of the grating 
from center to center, then we have 
LAN. any 
Oo  . 3 
‘where N is the order of the spectrum. 
Bea bien ‘ 
Now in the given case p is constant and so NA is proportional 
to the line AC. Or, for any given spectrum, the wave-length 
is proportional to that line. - 3 
