HALL, ABERRATION CONSTANT. 



55 



180° 



= Zi + ai sin z + bi cos z + a,2 ^i" 2z+ bj cos 2z 



- (180° + N) + bi - b.j (1) 



. Z = zo + ai sin z — b| cos z — aj sin 2z + b^ cos 2z 



- (180° + N) + bi - ba (2) 



After the instruiiient is reversed the corresponding formulas are 



360 — Z = Z3 — 111 sin z -\- b| cos z — 32 sin 2z + ba cos 2z 

 - (180° + N) +bi -ba 



ai sin z — bi cos z + a2 sin 2z + b2 cos 2z 



— (180^ + N) +bi -b2 



180° + Z = Z4 ■ 



(3) 



(4) 



By combining formulas (1) and (3) the cosine coefficients can be ob- 

 tained. Accordingly stars were observed north and south of the zenith 

 in both positions of the instrument for this purpose. 



From 22 south stars is obtained 



bi = -1.13 , b, 



-0.-17 



and from 26 north stars 



bi = -1.50", bo = -0.49" 



The term 6^. seems" really to exist, though it will require a good many 

 observations to determine it with accuracy, since the weights of observa- 

 tions made at large zenith distances are small. The following table of 

 approximate weights has been computed with the zenith distance as 



argument : 



By measuring the distance on the circle between north and south stars 

 of about 60° zenith distance the coefficient a, of the sine flexure was 

 obtained, 



ai =-- 



-1.20" 



Some attempts were made to find the flexure coefficients by treating 

 the north and south stars separately. But the cosine coefficients enter 

 with -such large relative weights that the process is not accurate. It was 

 necessary to insert, also, a term to represent any correction of the lati- 

 tude, and this has a large relative weight. The latitude was assumed to 

 be +48° 16' 49.3''. 



Taking then the north and south stars separately, these values were 

 obtained : 



Clamp West- 

 North stars. 

 South stars 



Clamp East- 

 North stars 

 South stars 



A-l" 



+0.40' 

 —0.36 



+0.03 

 —0.53 



