in Prof. Rowland's Concave Gratings. 193 



that the slit is made movable along the rail that carries the 

 grating. 



Let G X G 2 (fig. 1) be the grating, C its apex, its centre 

 of curvature, CLOM the theoretical focal circle, CLiOiOM^ 

 the true focal curve that passes through 0, L the slit in 

 its original place at the point of the right angle which 

 is formed by the rails LC and LO. Then, on displacing 

 the slit along LC or its elongation to a certain point L x , 

 it will always be possible to obtain distinct images of the 

 spectra, supposing in all cases that such can be given by the 

 grating. This point L x belongs to the curve in question, 

 whose polar coordinates will be determined by measuring the 

 radius of curvature CO (p), the displacement LL X (d), and 

 the angle LCO (/uu). For then, supposing d to be positive, 

 when the slit is moved away from the mirror, the radius 

 vector L 1 C = ^ = pcos n + d and the vectorial angle =/*. 



Denoting the wave-length by X, the number of order of 

 the spectrum by n, the distance between two adjacent lines of 

 the grating by co, we should have, if the theory were exact, 



LO rik - (o 

 sin a= — = — , n\— - . LO. 

 p a> p 



To decide whether the same formula can be applied in the 

 present case, it will be sufficient to displace the slit along the 

 rail LC and to observe if any change is produced in the 

 spectrum, viz., if the same value of p, always corresponds to 

 the same value of X independently of the value of r. In 

 reality small irregular variations were found, which did not 

 seem to exceed one of Angstrom's units, and which were 

 doubtless due to imperfections in the rails and the adjust- 

 ment. According to the theory of concave gratings a dif- 

 ference of one Angstrom's unit in the spectrum corresponds to 

 a lateral displacement of the slit varying in the spectra of 

 different orders between 0*25 and 1 millim. Consequently 

 the formula is exact within the limits of error of our 

 experiments. It follows that the angle e of the segment CL x 

 is determined by the equation 



d dco 



cot 6 



LO p.n\' 



In this formula d and nX being the only variables, we see 



that it is sufficient that their quotient — be constant, in 



n\ 



order that the angle e may be so too. 



III. The measurements were executed in such a way that 



the spectroscope was directed on some known line of the 



