Rowland's Method for the Concave Grating. 93 



so as to give clearance for the to and fro motion of the rail, R. 

 This admits of measurement of x on both sides of the slit, so 

 that 2x, the distance apart of the two symmetrical positions for 

 a given spectrum line, is again observed. 



11. Rowland's Concave Crating. — For the case of the con- 

 cave grating, the accurate adjustment for symmetrical meas- 

 urement on both sides of the slit is not feasible, because the 

 slit and eye-piece would have to pass through each other. It 

 is possible, however, to find conjugate foci at different distances 

 from the grating in the normal position, which approximately 

 answer the purposes of measurement. Rowland's equation 

 (cos i I p — 1 I JR) cos i + (cos 9 / p — lip') cos 0=0 



where p and p' are the conjugate focal distances for angles of 

 incidence and deviation i and 0, may for 6 = be written 

 1 111 



p I cos" i It I cos i p H 



where p is the normal distance of the eyepiece, so that 



1 1 _ 2 



p~ ~p~:'-r- 



If in figure 6, the slit S is put at p > R from the grating 

 G (normal position), the image is at Eat the end of p from 

 C, where p < R < p'. If p be used as a rail instead of R 

 and put at an angle of incidence i, for the eye-piece at E or E", 

 p cos i > p. But this excess need not be so large as to inter- 

 fere with adequately sharp focusing. 



The following table gives an example, in which the difference 

 of p and p ' iu the normal position is even over 1 foot, an 

 excessive amount, as the distance necessary for clearance need 

 not be more than a few inches. The grating has 14436 lines 

 to the inch and a radius about R = 191 cm . 



Table II. 



Conjugate foci of the concave grating. 

 5683 lines to cm. D = -000,176. 



p = 166 cm . p=198 cm . p-p = 32' :m . 

 i = 1/D. 



E = 191 c ™, 14436 lines to inch, 

 1/po -1/-R = '000788. = 0, sin 













Frannhofer 







i° 



P 

 cm. 



p cos i 



Diff. 

 cm. 



(p/cos l')' 2 



Lines 



t 





0° 



166-0 



166 



•o 



27500 



B 



22° 



59' 



5 



165-3 



165-3 



•o 



27500 



C 



21° 



54' 



10 



163-2 



163-5 



— -3 



27400 



D 



19° 



34' 



15 



159-6 



160-3 



- -7 



27300 



E 



17° 



26' 



20 



154-7 



156-0 



— 1-3 



27100 



F 



16° 



02' 



25 



148-5 



150-4 



— 1-9 



26800 



G 



14° 



10' 



30 



140-9 



143-7 



— 2-8 



26500 









35 



132-2 



136-0 



— 3-8 



26000 









40 



122-3 



127-1 



—4-8 



25500 









