ON THE TOTAL SOLAR ECLIPSE OF AUGUST 20, 188G. 
299 
the change of the Sun’s declination in one minute is t seconds of arc, the displace¬ 
ment will be pT, and we get for the longest time of exposure compatible with full 
definition— 
Epr = 2-5. 
In the West Indian Eclipse II was 10 and r was '9, which gives about 17 seconds 
as time of exposure. This is sufficient for obtaining a good image ; and we conclude, 
therefore, that an adjustment of the polar axis to about 3'’5 is sufficient for full 
definition. Photographs taken with longer exposures would chiefly serve to fix the 
fainter parts of the outer corona. 
By the ordinary means of adjusting an equatorial it is not difficult to obtain the 
necessary accuracy; nevertheless, the calculation shows that we can by no means 
neglect to go through the full routine of adjustment, and no equatorial should be sent 
(jut for eclipse purposes without complete appliances in the way of good finders, 
circles which are easily read, &Ci 
The adjustment of the rate of the clock to the necessary accuracy is, as will appear, 
much more difficult. 
We have seen that the angular displacement may reach, but should not exceed, 
1'22 X 10“°/E during the time of exposure. Reduced to seconds of time, this is 
equal to ‘If/R, or, if the exposure is to be q seconds of time, the error of the clock 
should not exceed TT/qR, which for an exposure of 17 seconds and an aperture of 
10 cm. is one part in a thousand. 
The instrument we had at our disposal did not allow an adjustment as accurate 
as this. At Prickly Point it was found difficult to go beyond an accuracy of one per 
cent. No record of the rate was taken at Carriacou, but it was probably no better 
than at Prickly Point. This would show that full definition would not be possible 
with an exposure of more than two seconds.* 
We may finally calculate by how much the efficient aperture is reduced if the errors 
due to adjustment are greater than those we have hitherto allowed. If the centres of 
two star discs are separated bj^ a distance 2@ -fi K, a displacement equal to K would 
just bring them into contact. A telescope which to the eye would resolve two 
stationary stars at a distance 2® will, if during the time of photographic exposure the 
displacement is K, have its effective aperture reduced in the ratio of (20 -p K) : 20. 
Hence, if R’ be the effective aperture 
R - E' _ K 
ir ’ “ 20‘ 
* Some of the statements made here do not agree with those made in the Preliminary Account 
(‘ Roy. Soc. Proc.’ vol. 42, p. 180). The discrepancy is accounted for by the fact that I previously took 
wider limits for the allowable shifting due to the motion of the telescope, and that T have since then 
subjected the photographs to a closer investigation as regards fineness of detail actually shown. 
2 Q 2 
