374 Mr. J. S. Ames on the Concave Grating 



distance it is out of focus at any point is then 



y = /)(! + a sin V— Scos v)— /) (1 — S) 



=p (a sin v + S — S cos v), 



.x=a sin (a + v) ; 



.'. y — ax + ah— B^a^ — x^. 



Since a and S are both small, this curve is the sum of those 

 found in Cases I. and III. 



V. Suppose the slit is displaced along AC. See fig. XI. 

 We have 



AD=b, 

 DC = ^. 

 As before, 



pR 



■J' r= 



R + R cos v—p cos'^v' 

 But W=p^-.v'-2bx, 



\/ o^ ~~ x^ . h 

 and cos v= — —. since -is small. 



P P 



p^p' 



hx 



y — r — T^^^ — 



Vp'-x^' 



By the principle of addition of small displacements, the 

 effect of any combination of these four displacements can be 

 found by addition — one can be used to counteract another, 

 and so on. Thus, displacement lY. can correct a combination 

 of I. and III. This has been found true in practice. 



Any small displacement, as long as the distance from the 

 gratuig to the camera-box is unaltered, does not affect the 

 constant of the instrument (i. e. the ratio of A to d\\ for, as 

 we saw above, that depends on this distance alone. 



General Description. 



Before giving the adjustments and precautions necessary in 

 mounting a concave grating properly, I will briefly describe 

 the various parts of the apparatus as used in Professor Row- 

 land's Laboratory. 



The instrument is mounted in a room, the walls and fix- 

 tures of which are blackened, and whose windows are of 

 " ruby '^ glass and provided with black shades. Opening off 



