192 Scientific Proceedings, Royal Dublin Society. 
is the same thing, a star at a distance of 1414” and position angle 
45°, we find the distortion— 
in RA 
= 0°00243 x 1000” + 0:00343 x 1000” = 2743 + 37-43 = 57:86, 
and in declination 
= 0:00348 x 1000” + 0:004538 x 1000” = 3°48 +4:538 =7 -96. 
Hence we see that the centre of the image of the second star 
will be drawn out through a length of nearly 10”, and will make 
an angle of about 386° with the direction of the parallel in which the 
diurnal motion takes place. 
This is, of course, rather an extreme case, as it will be seen from 
the ‘‘ Zenith Distance Curve”’ that, while the hour angle changes 
from 4" to 5%, the star passes from a zenith distance of 73° to 
about 81°, a position in which no very great precision could be 
expected. 
If, however, we refer to the curve corresponding to 40° decli- 
nation (fig. 3), and investigate the distortion which the star under- 
goes in passing from 60° to 75° zenith distance, we shall find the 
following quantities. Corresponding to a zenith distance of 60° 
we find the hour angle 6°12, and to 75° an hour angle 8-25, and 
for these hour angles we find, 
(a) (2) (c) (@) 
at 612 0:00014 000067 0-00070 0-00040 
at 8-25 -00028 + 00183 + -00204 += -00270 
0:00014 0:00116 0:00184 0:00230 
If therefore as before we take da and dé each equal to 1000” 
we shall find, 
aX = 014, cX = 1°34, 
bY =1°16, dY = 2°30, 
“OX + OY =f 30," eX Ad Yo — one: 
Hence the distortion amounts to 3”°87 in a direction inclined 
to the parallel by an angle of about 17°. 
It should, however, be remarked that in this case the exposure 
would last for more than two hours which is a much longer 
