Figure 190 shows from Cobb’s experiments (Am. Jour. of Physiol., =35=, 335) the effect of reduction of ocular aperture upon acuity. The curve shows very plainly that for emergent pencils below a millimeter (1/25 inch) in diameter, visual acuity falls off almost in direct proportion to the decreasing aperture. Below this figure there can be only incidental gains, such as may be due to opening up double stars and simultaneously so diminishing the general illumination as to render the margins of the star discs a little less conspicuous. An emergent pencil of this diameter is not quite sufficient for the average eye to utilize fully the available resolving power and some excess of magnification even though it actually diminishes visual acuity materially, may be of some service. [Illustration: 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 ε_{1}, ε_{2}, 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.