H. A. Rowland—Concave Gratings for Optical Purposes. 93 
If a micrometer is fixed at C wecan consider the case as 
follows: 
Bi MN prick ig ? 
dX w 
F (Tea arma. 
If D is the distance the cross-hairs of the micrometer move 
forward for one division of the head, we can write for the 
point C 
pene 
p 
and for the same point sis zero. Hence 
Fy ihe 
Np 
But this is independent of » and we thus arrive at the impor- 
tant fact that the value of a division of the micrometer is 
always the same for the same spectrum and can always be 
determined with sufficient accuracy from the dimensions of the 
apparatus and number of lines on the grating, as well as by 
observation of the spectrum. 
Furthermore, this proves that the spectrum is normal at this 
pene and to the same scale in the same spectrum. Hence we 
ave only to photograph the spectrum to obtain the normal 
Spectrum and a centimeter for any of the photographs always 
represents the same increase of wave-length. 
t is to be specially noted that this theorem is rigidly true 
Whether the adjustments are correct or not, provided only 
that the micrometer is on the line drawn perpendicularly from 
the center of the grating, even if it is not at the center of 
curvature. 
