12 



To investigate this question suppose tluit a reflecting grating is used and 

 that we look in tliu direction of the collimator, towards the "-ratins; 



let = angle between telescope and normal on the right 



"i — )) n I) )) J) )) >) 'Clt. 



n = ,, „ collimator ,, ,, 



h = ,, ,, ,, ,, telescope ou the right 



"l~- I) !» 11 U '1 )) ^) Icit. 



b,= ., „ ,, ,, ,, tor strictly normal incidence, 



then b := '> — a and 6i := " + rt 



and we have for the S[iectrnm of the first order — • 



;, 



s 



sin (b -\- a) + sin a (R) 



sin (/', — (■() — sin a (L) 



the nonn.il to tlie grating hciiig snp[>ns<'il In he thrown sliglilly to the Icl't. 

 Ditfercnliating and sup|)osing a ;= we have 



(//' = — (1 + Sl\' b) lift 



(//j, = ( ] 1 sec b^ ) (III » 



and tli(> error in taking — - — '- for b„ will lie 



(sec b^ — sec b) da 



An exandnation will show that if />„ he 4.")'^ and the grating lie as nrifli as "r' 

 away from ils trno position this error will he less llian lialf a second. To 

 facilitate and increase the accuracy of this ailjustnicnt the hr.iss jaws of the 

 slit were hlackcncd and then when the colliii; iting eye piece was placed in front 

 of the slit ami properly illnniinafed a very clear and well defned innige was 

 produceil liy reflection from the grating. It was fonnd that the adjustment 

 could le made very quickly and within one or two seconds. It is safe, tiiercfore, 

 to assert that the results aie entirely ficc from any sensil le eiror oriL:;inating 

 in this adjustment. 



COlUilCCTIoX FOR TKMI'KK.VI'l'KK. 



To make the reductions for temperature it is necessary to know the tem- 

 perature at which settings were made and the co-etiioient of t'xpinsion of the 

 m.iterial of which the grating is composed. It is believed that the lirst has heen 

 (vccomplished with a degree of accuracy exceeding that in the case of any series 

 of measurements Idtherto made. Angström admits and deplores the difficulty 



