498 HENRY A. ROWLAND 



whose ends rest on carriages moving on the rails AB and AC at right 

 angles to each other; when desired, the radius AD may be put in to hold 

 everything steady, but this has been found practically unnecessary. 



The proper formula? for this case are as follows: If ^ is the wave- 

 length and w the distance apart of the lines of the grating from centre 

 to centre, then we have 



1 _ IN _ sin v 



~~d~ %w~ ~T~ 



where N is the order of the spectrum. 



w sin v 



/ = 



Now in the given case p is constant and so NX is proportional to the 

 line AC. Or, for any given spectrum, the wave-length is proportional 

 to that line. 



If a micrometer is fixed at C we can consider the case as follows : 



1 )N 

 -tf ^^(sin^ + sinv), 



d). w 



7i~ = ~W cos /* 

 a/i N 



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 



A., = I- 



!' 



and for the same point ft is zero. Hence 



But this is independent of v and we thus arrive at the important 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 accu- 

 racy 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 point 

 and to the same scale in the same spectrum. Hence we have only to 

 photograph the spectrum to obtain the normal spectrum and a centi- 

 meter for any of the photographs always represents the same increase 

 of wave-length. 



It 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 centre of the grating, even 

 if it is not the centre of curvature. 



