for Optical Purposes. 203 
since these values satisfy the equation. The line of foci is 
then a circle with a radius equal to one half p. Hence, if a 
source of light exist on this circle, the reflected image and all 
the spectra will be brought to a focus on the same circle. This 
is, if we attach the slit, the eyepiece, and the grating to the 
three radii of the circle, however we move them, w r e shall 
always have some spectrum in the focus of the eyepiece. 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 eyepiece, as 
far as we consider this fact, is thus the one opposite to the 
grating and at its centre 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 whatever the position of the slit, provided it is on the 
circle. 
Kg. 1. 
Fig. 1 represents this case. A is the slit, C is the eyepiece, 
and B is the grating with its centre of curvature at C. In 
this case all the conditions are satisfied by fixing the grating 
and eyepiece to the bar B 0, whose ends rest on carriages 
moving on the rails A B and A C at right angles to each 
other. When desired, the radius A D may be put in to hold 
every thing steady; but this has been found practically unne- 
cessary. 
The proper formulae for this case are as follows. If X is 
the wave-length, and w the distance apart of the lines of the 
grating from centre to centre, then we have 
1_XN 
C~2to 
where N is the order of the spectrum; 
sm 2' 
N 
Now in the given case p is constant, and so NX. is propor- 
