174 BARUS— ADJUSTMENT FOR PLANE GRATING [April 24, 



Rowland's value of D^ is 58.92 X lO"^ cm. ; the mean of the two 

 values of 2x just stated will give 58.87 X lO"® cm. The difference 

 may be due either to the assumed grating space, or to the value of R 

 inserted, neither of which were reliable absolutely to much within 

 .1 per cent. 



Curious enough an apparent shift effect remains in the values of 

 2X for stationary and rotating grating, as if the collimation were 

 imperfect. The reason for this is not clear, though it must in any 

 case be eliminated in the mean result. Possibly the friction involved 

 in the simultaneous motion of three slides is not negligible and may 

 leave the system under slight strain equivalent to a small lateral 

 shift of the slit. 



9. Discussion. — The chief discrepancy is the difference of values 

 for 2x in the single lens system (for D^, 118.7 and 118.5 cm., re- 

 '■ Apctively) as compared with a double lens system (for D^, 118.2 

 1.) amounting to .2 to .4 per cent. For any given method this dif- 

 ference is consistently maintained. It does not, therefore, seem to 

 be mere chance. 



We have for this reason computed all the data involved for a 

 fixed grating 5 cm. in width, in the two extreme positions, Fig. 5, 

 the ray being normally incident at the left hand and the right hand 

 edge respectively for the method of § 6. The meaning of the sym- 

 bols is clear from Fig. 5, vS being the virtual source, g the grating, e 

 the diffraction conjugate focus of 5" for normal incidence, so that 

 & = r is the fixed length of rod carrying grating and eye-piece. It 

 is almost sufficient to assume that all diffracted rays b' to h" are 

 directed towards e, in which case equations ( i ) would hold ; but this 

 will not bring out the divergence in question. They were therefore 

 not used. Hence the following equations (2) to (5) successively 

 apply where d is the grating space. 



(i) coi6'-={h/g-]-s,\ne)/Qose; cotO" = (b/g — sin 0) /cos 0; 



(2) o = &/cos-^; a' =: o" = V^^ + «" ; 



(3) sm i' = s'm i" ^g/a' ; 



(4) — s'm i' + s'm (0 + 6')= \/d; s'm6 = X/d; 



smi"-\-sm(e—d")=X/d; 



(5) cos- i' / a' = cos- (6 + 0')/b'; cos^ i"/ a" = cos- (0—8") /b". 



i 



