ON THE TOTAL SOLAR ECLIPSE OF AUGUST 29, 1886. 301 
greater. The photographs would be larger and more convenient to copy, which would 
be an advantage, but it seems more rational to improve the definition obtained with a 
4-inch lens, before larger apertures are used. 
If we could increase the aperture without increasing the focal length, we could 
reduce the time of exposure and gain an advantage, provided that the clock motion 
is sufficiently uniform. All our investigations, then, seem to point to the desirability 
of an improvement not only in the average rate of the clock motion, for that could 
easily be effected, but in the steadiness and regularity of the motion. 
I give, in conclusion, collected together, some formulse which may be useful to future 
eclipse observers. 
In the equations (/» is the displacement in seconds of arc which is allowable, con¬ 
sistent with full definition as above defined. 
H is the true aperture of the lens in centimeters. 
R' is the effective aperture of the lens. 
q is the time of exposure in seconds. 
Q is the longest time of exposure compatible with full definition. 
y is the greatest allowable angle between the true pole and the pole of the 
instrument in seconds of arc. 
T is the change of Solar declination measured in seconds of arc per second of time. 
e is the error of the clock rate, measured in per cent. 
In equations (2), (4), and (6) it is assumed that in adjusting the pole of the 
equatorial no account is taken of the change of the Solar declination during the 
eclipse. 
<f>=2'5lR ..( 1 ), 
Q = 2-5/Rt .(2), 
y = 34600/%.(3) ; 
or, if the longest exposure Q is to be used, 
y= 13840T.(4). 
Finally, to determine R', we easily find 
1; — ^ 60 X X eq .(.5). 
This equation will allow us to determine the time of exposure allowable for a given 
effective aperture R' if the clock rate is known. If the longest exposure Q is to be 
used, we get 
K-P/ P5 X 10-s X e 
11 ' 
T 
( 6 ). 
