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CAPTAIX L. DARWIN, DR. A. SCHUSTER, AND MR. E. W. MAUNDER 
time in making the angle y smaller than that given by the above value, as a closer 
adjustment may in some cases make matters worse instead of better. 
Special considerations may of course induce observers to adjust their iustruments 
more accurately. If, for instance, the equatorial adjustment is to be done once for all 
about a fortnight or a week before the eclipse, and if the conditions of tlie foundation 
on which the pillar rests give grounds for fear that the position may slightly change, 
it would be wise to aim at a greater accuracy in the first instance, so as to give some 
play for change. 
So far the adjustments do not depend on the size of the object-glass, but, if we want 
to make the best use we can of the aperture, an apparent shifting of the Sun’s image 
during the time of exposure must be confined within small limits, which we have now 
to fix. 
The central disc of a star, or of a small object at a great distance, has an angular 
radius @ in the focal plane of the telescope, given by 
@ = l-22\/Pt, 
when R is the diameter of the objective. Experience shows that small objects can, 
under favourable circumstances and with strong illumination, be resolved when the 
centre of one diffraction disc coincides wdth the first dark ring ; but for objects having 
no well-defined boundaries we must give wider limits, and I therefore take the point 
of fair resolution to be reached when the first two dark rings touch, so that the star 
discs stand perfectly clear of each other. In order to find out experimentally to 
what extent a small shifting of the images, such as might be produced by defective 
adjustment of the equatorial, might influence the possibility of resolution, I drew on 
a piece of paper two circles touching each other, corresponding to the two star discs, 
and another similar set above them slightly displaced in the line joining the centres. 
It was found that a displacement of one-tenth of the distance between the centres 
of the disc could only affect tiie resolution to a slight degree. We may, therefore, 
consider a displacement through one-fifth of the radius of each disc allowable with¬ 
out impairing definition. There is always something arbitrary in the fixing of these 
limits, but it must be done in every investigation in which we want to determine the 
accuracy to be aimed at. As object-glasses of diffei-ent makers Avould probably differ 
10 per cent, in their observed resolving powers, the limit chosen seems a fair and 
reasonable one. 
We may allow then an angular shifting of 
</> = 0/5 = 1-22 X/5II = 1-22 X 10 "VR 
if we substitute for X its mean value of about 5 X 10“® cm. This gives a value 
for cf> which varies inversely with the aperture, and is equal to 2‘5 seconds of arc 
for one centimeter aperture. If the exposure takes place during p minutes, and if 
