RamBaut—Photographic Star Images due to Refraction. 187 
of less than one-tenth of a second, every possible disturbing 
cause must be examined into and allowed for with all available 
rigour. | 
In order to investigate how far the image of a star on a photo- 
graphic plate can be distorted by the refraction, I take the 
formule which I have given in the “‘ Astronomische Nachrichten ” 
for the correction for refraction in R. A. and declination respec- 
tively. 
If we denote by a and 6 the R. A. and declination of any star, 
and by ¢ the latitude of the observatory, and by @ the sidereal 
time of the observation; if, further, da and dé denote the differ- 
ences in R. A. and declination between this star and another, and 
if Ada and Adé denote the corrections for refraction to da and dé re- 
spectively, and (3 be the coefficient of refraction at the zenith dis- 
tance of the star, we find, 
cos @ Sin v sin (u +6) cot cos (m + 26) 
Ada cos 6 = 3 ee Sein ino) da cos 6 ee Gann) > 
and 
cos d COs v 1 
Adés = B | N sin? n sin?(u + 0) da ee 6 Es sin?(m + 8) \? 
in which m, 7, p, v are determined by the equations, 
tan m = cot ¢ cos (@-a), cot u = tan ¢ cos (0—a), 
cot m=sinmtan(@-a), and cot v=cos m tan (0-a). 
Hence we may write— 
Ada cos 8 = AX + BY, and Add = CX + DY, 
in which X and Y are the rectangular co-ordinates on the plate 
of the second star referred to the first as origin, the axis of X being | 
in the direction of the parallel at the first star, and A, B, C, and 
D are constants computed for the position of the first star at the 
moment of observation. 
This is a form of the expression which is exceedingly con- 
venient where a number of stars on one plate have to be measured. 
