1903.] T/ie Ultra-violet Spectrum of Radium. 303 



Rule. 



First calculate the approximate value of X 2 by the following 

 formula : 



A 3 2 (% - n 2 ) 



(1). 



Next, in a similar way, find the approximate value of A 4 , using the 

 following formulae : 



" 3 X "V _ = A 4 2 (approx.) 



Then 



A 4 (true) = A 4 (approx.) E 4 . 



calculate E 2 by the following equation : 

 (Approx.) A 2 8 (7i 2 



(Approx.) A 4 3(7i 4 - m) (% - %) 

 Then 



(Approx.) X 2 E 2 = X 2 . 



[In fact, writing y for X~ 2 , of which the refractive index is a 

 function, and x for 7i, the graph of the relation between y and x may 

 in this neighbourhood be identified with a parabola. The formulae (1) 

 and (2) neglect the effect of its curvature, by taking the points 2 and 

 4 to be on the chord connecting the points 1 and 3. The corrections 

 E 2 and E 4 are thus connected with the distances from the points on 

 this chord to the true points on the curve by the formula 8y = - 2E/A 3 ; 

 and the formula (3) connecting them is the expression of a well-known 

 geometrical property of a parabola.] 



Example. 

 Calculate a radium line from adjacent iron lines as standards. 



HI = 0-000000. A! = 2813-388 (Rowland). 



7i 2 = 0-005310. A 2 = A radium line. 



% = 0-107143. X 4 = 2823-389 (Rowland). 



7i 8 = 0-131020. A 3 = 2825-667 (Rowland). 



2 log A! 6-8984593 2 log A 3 6-9022420 



log 0-00531 B-7250945 log 0-125710 1*0993698 



log 42029-46 4-6235538 log 1003718-32 6-0016118 



42029-46 



log 1045747-78 = 6-0194269 



