188 Scientific Proceedings, Royal Dublin Society. 
But it will be seen’ that 0, the sidereal time, occurs in the quanti- 
ties A, B, C, D, which consequently are not absolutely constant 
when the exposure lasts for an appreciable time. In the neighbour- 
hood of the horizon, too, the value of ( changes so rapidly that 
another source of variation is introduced. 
In taking astronomical photographs of a group of stars it is 
usual to select one star as guider, and setting this on the intersee- 
tion of a pair of cross lines in the focus of the guiding telescope 
before the plate is exposed, to keep it exactly on this intersection 
all the time the exposure continues. The driving clock of the 
telescope, of course, if correctly rated will keep the instrument 
continually pointing at the star, but it is necessary, in order to 
correct the minute irregularities which are inseparable from even 
the best of clocks, and to eliminate the effect of the changes of 
refraction on the motion of the guiding star, to control the move- 
ment with the hand by means of the fine-motion-apparatus pro- 
vided for that purpose. But even with these precautions, it is 
still only possible to keep one star fixed in position on the plate. 
Hence the amount by which the image of another star is disturbed 
on the plate is measured by the change which takes place in the 
differential refraction relatively to the first star between the 
beginning and the end of the exposure. 
Hence, if A., Bo, Co, Do are the values corresponding to the 
beginning of an exposure, and Aj, Bi, C,, D, those calculated for 
the end of it, we shall find the amount of distortion— 
in RA = (4,- A,) X + (Bi-B) Y=aX + bY, 
and in declination = (C, - C)) X + (D,- Dy) VY = cX + dV. 
From these equations I have computed the following tables 
which give the values of the quantities a, 0, c, d, for 0°, 20°, 40°, 
and 60° of declination, and for every fifteenth degree of hour angle, 
the quantities Ao, B,, C,, Do being taken as referring to the time 
of the meridian passage of the star, and » being taken as the 
latitude of Dunsink Observatory, viz. 53° 28’ 13”. 
