354 Mr. Louis Bell on the Absolute 



The temperature being thus obtained, the necessary cor- 

 rection was introduced directly into the angle of deviation. 

 Writing the formula for wave-length in the form 



A,= Cssin cf), 



where C is a factor depending on the method in which the 

 grating is used, and differentiating we obtain 



— = — cot <f)8(f), 



where, if we take 1° for the temperature variation, — is the 

 coefficient of expansion. Whence 



B l 



^ ~ cot <f> 



correction for 1° variation in temperature. For grating III., 

 for instance, 8cj> = 2""688; and by this means all the deviations 

 were reduced to 20°. Writing again the equation for wave- 

 length in the form for the method here used, 



c=sin <£> cos 6. 



Now to obtain the variation in <p due to a change in the angle 

 between the telescopes, 



8$ = tan (f> tan 686. 



Taking now 86=1" and <J> as found in these experiments, 



S<£ = 0"-089. 



By this means the necessary correction could be introduced 

 in the angle of deviation, but the angle between the tele- 

 scopes was so nearly constant as to render this correction 

 needless. 



The line selected for measurement with III. was a sharp 

 one in the green at 5133*95 of Rowland's map. The angle 

 6 between the telescopes was adjusted so that in the eighth 

 order the double deflection was 72°. Eighteen complete 

 series of observations were then obtained, each giving a value 

 of 100, from which the errors of the circle were completely 

 eliminated. The results in detail were as follows, corrected 

 to 20° on thermometer used : — 



