Wave-length of Light. 367 



Applying now the relations found for grating I. in the 

 foregoing section, 



5=0-002500226 millim. 

 And since <£ = 45° V 48"-24, 



X=5896-18. 

 Similarly for grating II., 



s=0-003519041 millim., 

 4> = 42°4'59"-28, 

 \ = 5896-23. 



Computing the similar quantities for the speculum-metal 

 gratings III. and IV., for grating III., 



s =0-003519358 millim., 

 <^> = 36 o 0'25 // -17, 

 0=6° 59' 58"'56 ? 

 \= 5133-89; 



and for grating IV., 



s = 0-002534306 millim., 

 ^, = 35°59'59 // -06, 

 <9 = 6°58'31"-0, 

 X.=5914-37. 



Reducing now these latter wave-lengths to the corresponding 

 values of Dj, introducing the barometric corrections and com- 

 bining, the final results for that line are : — 



Grating. W. L. 



1 5896-18 



II 5896-23 



III. . .' 5896-15 



IV 5896-17 



Finally, then, the mean value of the absolute wave-length of 

 D x in terms of the mean value assigned to S a 3 is 



5896-18 

 in air at 760 millim. pressure and 20° C. temperature, or, in 

 vacuo, 5897-90. 



It is no easy matter to form an estimate of the probable error 

 of this final result. So far as errors of observation go, the 

 result should be correct to within one part in half a million, 

 but there are so many complex sources of constant errors in 

 this problem that such a statement means little. My present 

 result exceeds the estimated probable error of my former 

 result considerably, though it falls within the limit set by 

 Prof. Rowland and myself for the possible error, and noted 

 in his paper on " Relative Wave-lengths " of the same date as 



