Fig. 190.—Resolving Power of the Eye.
Increased acuity will of course be gained for the same magnification in using an objective of greater diameter, to say nothing of increased resolving power, at the cost, of course, of relatively greater atmospheric troubles.
To come down to figures as to the resolving power of the eye, often repeated experiments have shown that two points offering strong contrast with the background can be noted as separate by the normal eye when at an angular separation of about 3′ of arc. People, as we have seen, differ considerably in acuity so that now and then individuals will considerably better this figure, while others, far less keen sighted, may require a separation of 4′ or even 5′.
The pair of double stars ε1, ε2, Lyræ, separated by 3′ 27″ mags. nearly 4 and 5 respectively, can be seen as separate by those of fairly keen vision, while Mizar and Alcor, 11′ apart, seem thrown wide to nearly every one. On the other hand the writer has never known anybody who could separate the two components of Asterope of the Pleiades, distant a scant 2½ but of mags. 6.5 and 7.0 only, while Pleione and Atlas, distance about 5¼′, mags. 6.5 and 4, are very easy.
Assuming for liberality that the separation constant is in the neighborhood of 5′ one can readily estimate the magnification that for any telescope will take full advantage of its resolving power. As we have already seen this resolving power is practically 4.″56/A for equal stars moderately bright. An objective of 4.56′ inches aperture has a resolving constant of 1″ and to develop this should take a magnification of say 300, about 65 to the inch of aperture, requiring a focal length of ocular about 0.20 to 0.25 inch for telescopes of normal relative aperture, and pushing the emergent pencil down to little more than 0.02 inch,—rather further than is physiologically desirable. Except for these extreme stunts of separation, half to two thirds this power is preferable and conditions under which one can advantageously go above this limit are very rare indeed.
A thoroughly good objective or mirror will stand quite 100 magnification to the inch without, as the microscopist would say, “breaking down the image,” but in at least nine cases out of ten the result will be decidedly unsatisfactory.
As the relative aperture of the instrument increases, other things being equal, one is driven to oculars of shorter and shorter focus to obtain the same magnification and soon gets into trouble. Very few oculars below 0.20 inch in focus are made, and such are rarely advisable, although occasionally in use down to 0.15 inch or thereabouts. The usual F/15 aperture is a figure quite probably as much due to the undesirability of extremely short focus oculars as to the easier corrections of the objective.
In the actual practice of experienced observers the indications of theory are well borne out. Data of the habits of many observers of double stars are of record and the accomplished veteran editor of The Observatory, Mr. T. Lewis, took the trouble in one of his admirable papers on “Double Star Astronomy” (Obs. 36, 426) to tabulate from the original sources the practice of a large group of experts. The general result was to show the habitual use with telescopes of moderate size of powers around 50 per inch of aperture, now and then on special occasions raised to the neighborhood of 70 per inch.
But the data showed unequivocally just what has been already indicated, that large apertures, suffering severely as they generally do from turbulence of the air, will not ordinarily stand their due proportion of magnification. With the refractors of 24 inches aperture and upwards the records show that even in this double star work, where, if anywhere, high power counts, the general practice ran in the vicinity of 30 per inch of aperture.