500 HENRY A. EOWLAND 



in place. We then carefully adjust the focus by altering the length of 

 D until the cross-hairs are at the exact centre of curvature of the grat- 

 ing. On moving the bar the whole series of spectra are then in exact 

 focus, and the value of a division of the micrometer is a known quan- 

 tity for that particular grating. The wooden way AC, on which the 

 carriage moves, is graduated to equal divisions representing wave- 

 lengths, since the wave-length is proportional to the distance AC. Wo 

 can thus set the instrument to any particular wave-length we may wish 

 to study, or even determine the wave-length to at least one part in five 

 thousand by a simple reading. By having a variety of scales, one for 

 each spectrum, we can immediately see what lines are superimposed on 

 each other and identify them accordingly when we are measuring their 

 relative wave-length. On now replacing the eye-piece by a camera, we 

 are in a position to photograph the spectrum with the greatest ease. 

 We put in the sensitive plate, either wet or dry, and move to the part 

 we wish to photograph; having exposed for that part, we move to 

 another part, raise the plate to another position and expose once more. 

 We have no thought for the focus, for that remains perfect, but simply 

 refer to the table giving the proper exposure for that portion of the 

 spectrum and so have a perfect plate. Thus we can photograph the 

 whole spectrum on one plate in a few minutes, from the F line to the 

 extreme violet in several strips, each 20 inches long. Or we may photo- 

 graph to the red rays by prolonged exposure. Thus the work of days 

 with any other apparatus becomes the work of hours with this. Fur- 

 thermore, each plate is to scale, an inch on any one of the strips repre- 

 senting exactly so much difference of wave-length. The scale of the 

 different orders of spectra are exactly proportional to the order. Of 

 course the superposition of the spectra gives the relative wave-length. 

 To get the superposition, of course, photography is the best method. 



Having so far obtained only the first approximation to the theory of 

 the concave grating, let us now proceed to a second one. The dividing 

 engine rules equal spaces along the chord of the circular arc of the grat- 

 ing: the question is whether any other kind of ruling would be better, 

 for the dividing engine is so constructed that one might readily change 

 it to rule slightly different from equal spaces. 



The condition for theoretical perfection is that C shall remain con- 

 stant for all portions of the mirror. I shall therefore investigate how 

 nearly this is true. 



Let p be the radius of curvature and let R and r be the true dis- 

 tances to any point of the grating, R and r being the distances to the 



