I909-] SIMILAR TO ROWLAND'S METHOD. 175 



Since 6, g, A, d, b, are given 6' and 6" are found in equation (4), 

 apart from signs. If S^ and 8/' be the distance apart of the projec- 

 tions of the extremities of b' and b, b and b", respectively, on the 

 Hne X, 



8/ =g+ (b — b') s'mO—b'smi' 

 (6) 



8/' = (7 -f (&" — &) sin ^ — 6" sin i" 



If 80' and Sn" be the distance apart of the intersections of the 

 prolongation oi b' and b, b and b", respectively, with the line x, 



8/ =sin(^-f ^')(^cos^/cos (0^9')— b') 



(7) 



83" = sin (e — 0")(b" — b cos $/cos (9 — 6")) 



Given &= 169.4 cm., ^ = 20° 22', about for sodium, g^S cm., 

 the following values are obtained : 



6' =1° ^6', a =192.7 cm., &' = 166.0 cm., 



<9"=i°34', a' = a" ^192.8 cm., r = & = 169.4cm., 



i' = i" = I ° 30', b" = 1 72.4 cm., 



whence 



81' =1.92 cm., 80" ^1.74 cm. 



These limits are surprisingly wide. If, however, they should be 

 quite wiped out on focusing, for any group of rays and symmetrical 

 observations on the two sides of the apparatus, this would be no 

 source of discrepancy. The effect of focusing the two parts of the 

 grating may, in the first instance, be considered as a prolongation 

 of b' till it cuts X, together with the corresponding points for the 

 intersection of b" with x. Thus the values 80' and 8," are here in 

 question and they are 



8,/ = 1.97 cm., 8/ — 8/ = .05 cm. 



whence 

 83" =1.65 cm., 81" — 8. = .09 cm. 



are the conjugate foci for the extreme rays of the grating, respec- 

 tively, beyond the conjugate focus of the middle or normal rays b, 

 on X. Hence the mean of the extreme rays lies at .07 cm. beyond 



