L. Bell — Absolute Wave-length of Light. 



551 



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

 the form for the method here used, 



c=sin cp cos d. 



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

 between the telescopes, 



(5 , <p=tan cp tan Odd. 



Taking now dd = 1" and <p as found in these experiments 



d>=0"-089. 



By this means the necessary correction could be introduced in 

 the angle of deviation, but the angle between the telescopes 

 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 d 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 10<p from which the 

 errors of the circle were completely eliminated. The results in 

 detail were as follows, corrected to 20° on thermometer used, 



1887. 



Date. 





Nov 



• 2, 



a 



3, 



a 



4, 



a 



5, 



(C 



5 > 



u 



9, 



cc 



16, 



a 



16, 



u 



iv, 



cc 



22, 



cc 



29, 



a 



29, 



a 



29, 



a 



30, 



cc 



30, 



a 



30, 



Dec. 



1, 



i< 



1, 



36° 



0' 



21" 



19 



36 







25 



87 



36 







24 



40 



36 







24 



95 



36 







26 



83 



36 







26 



14 



36 







27 



40 



36 







27 



37 



36 







27 



57 



36 







25 



16 



36 







25 



69 



36 







25 



99 



36 







25 



91 



36 







26 



10 



36 







25 



SO 



36 







25 



SI 



36 







25 



OS 



36 







25 



so 



The last decimal place is retained simply for convenience in 

 averaging. The mean value of <p is 36° 0' 26" "07 which reduced 

 for the error of thermometer at 20° gives finally, 



<p=36° 0' 2b"-\1. 



The probable error of this value is ,f '14z. The effect of a 

 small error in <p on the resulting wave-length is given at once by 



$A = cos cpdcp. 



