270 Mr. L. Bell on the Absolute 



Then if 7 is the angle made by the incident ray with the 

 normal to the grating, and N the order of spectrum, 



Nx /■ . : a\ ■ JL 



— =cos (7 + A) sin <p ; 



also 



sin 7 = sin (7 + A) cos </>, 



and , 



, cos <p K 



tan y— - A — :A. 



' I — COS9 



But from the second of the above equations, 



, A x sin 7 

 sin y + A) = 1 



Now it was found that with the collimating-eyepiece belong- 

 ing to the spectrometer, 7 would never exceed and seldom 

 reach 10", while the angles of deviation observed were about 

 45°. Substituting these values in the last equation, it at 

 once appeared that the cosine of (7 + A) was a quantity dif- 

 fering from unity by considerably less than one part in a 

 million, and hence entirely negligible. Further, it was found 

 that the grating once set could be trusted to remain perpen- 

 dicular through a series of measurements ; and though at the 

 end of each series the grating was adjusted to a new part 

 of the circle, and a close watch kept for its slipping out of 

 adjustment, it was never found necessary to reject a series 

 from that cause. 



The grating was centred and adjusted with reference to 

 the circles and their axes by the ordinary methods. Through- 

 out the experiments the light was concentrated on the slit by 

 an achromatic lens of about half a metre focus, w r hich was 

 placed behind a sheet of deep yellow glass, which served to 

 cut off the overlapping blue rays, which might otherwise have 

 proved troublesome. A heliostat enabled the sun's image to 

 be kept centrally upon the slit. 



The method of observation was as follows : — When instru- 

 ment and grating were in exact adjustment, readings were 

 taken on D : in the spectra on either side of the slit, and the 

 angle measured from three to six times in rapid succession, 

 the last reading being of course on the same side as the first. 



Then the grating was rotated about ten degrees, readjusted, 

 and the process repeated. 



The angles observed in one series were combined to elimi- 

 nate errors of setting, while the use of all portions of the 

 circle served to correct errors of subdivision, since the num- 

 ber of independent series of observations was quite large. 



