4th. A metlioil of oliscrvatiitii ami iviluetinii was iiseil by Angstrom in whirli 

 the griitinj^ was made nearly normal to the col'iiiuator, the deviation from strict 

 [)erpendicu1arity heing so great, however, that it could not be ne<j;lec'te 1 in the 

 calcnlations. This method was not used by the writer, because it is especially 

 suitable for transparent ratbi r than reflecting gratings, and also because it was 

 j)erfectly e:\sy to make the grating so iiearlj' normal to the eiillimator that it 

 miijht idways be assumed to be accur.ite'ly so. On account of its bidng the 

 jnethod used by Angstrom and in order that it may be compared with that 

 adopted in tliese observations, it is lu-re included with the otliers. 



Suppose the grating to be of gl.iss and to be adjusted so as to be as nearly 

 as possible normal to the collimator. Readings are then taken with the tek'SC0{)e 

 in three positions: when set on the line on one side; on the image of the slit ; and 

 on the line on the other side. 



Let a, S an;l ",, be these readings 



let ^ = y and —- S = « 



then the formuhu for reiluction used by Angstrom are; — 



/ = s sin ;- cos {o -f <f>) 



cos 7* 



and tan <^ = . n approximately. 



These fornuil.'o are e<isily develo[)ed. As before 



let 4' = angle lietween collimator and normal 



fl =: ,, ,, telescope ,, ,, in one position. 



/9 = ,, ,, ,, ,, ,, in the other position. 



tlien we have 



and 

 but 



/ = .s ( sin I) — sin «^ ) ( 1 ) 

 /= sfsin -\- s\n4>) f'2) 



o 



and d -\- (f> z= - ^ - 



Adding ( 1) and (2) and substituting tliese values, we have; — 

 ^ = « sin ;• cos (ii -|- <f>) 



Also subtracting (2) from ( 1 ) and reducing in the saino way, — 

 sin ^ = cos Y sin ( « t <f> ) 



