RamBaut—Photographic Star Images due to Refraction. 198 
exposure than would in any case be given to a plate intended for 
accurate measuremeut, in which case the exposure will generally 
be limited to fifteen minutes at most. 
Of course if the change in the refraction were uniform and the 
intensity of the light of the star constant, then in all positions, 
although the star image would no longer be a circle but a line of 
some sensible length, still by taking the middle of this short line 
as the point to measure from, and computing our formule for the 
middle of the exposure, we should eliminate the effect of refraction. 
But in the neighbourhood of the horizon the rate at which the 
refraction changes is very rapidly accelerated, and the intensity of 
the light of the star rapidly diminished by atmospheric absorption 
as the zenith distance increases. From both of these causes, there- 
fore, the denser part of the star image will lie nearer the position 
which the star occupied at the beginning of the exposure if the 
star is approaching the western horizon and the measures made 
from it will be in consequence affected with error. Ii the star is 
near its rising, the end of the exposure will have the greatest effect 
in determining the position of the image. 
It is therefore of importance to investigate how far we may 
assume the variation of the refraction to be uniform for a quarter 
of an hour. It will be obvious at once, without calculation, from 
an examination of the curves in figs. 1, 2, 3, and 4, that down to a 
zenith distance of 60° we introduce no sensible error by assuming 
the increase of the differential refraction to be uniform for this 
limit ; and if we compute the amount of distortion in a quarter of 
an hour from this cause, we shall find that in this time a star - 
for which da and dé are each 1000” changes its position on the 
plate, 
at a declination of 0° by 07-15 
i * sg Oi se OF 20 
5 wap’ gai. LO rssh, Cielo, 
3 35 BGO Or09 
In a quarter of an hour, too, the star’s zenith distance will not 
vary by more than 3°, by which it will not lose one-hundredth 
part of its light, so that we need not consider the minute change 
in its photographic activity. 
