With the 6 inch aperture Burnham reached in the average 0.53 of Dawes’ limit, quite near the rough figure just suggested, and he also fell well inside Dawes’ limit with the 9.4 inch instrument. With none of the others did he reach it and in fact fell short of it by 15 to 60%. All observations being by the same notably skilled observer and representing discoveries of doubles, so that no aid could have been gained by familiarity, the issue becomes exceedingly plain that size with all its advantages in resolving power brings serious countervailing limitations due to atmosphere. But a large aperture has besides its possible separating power one advantage that can not be discounted in “light grasp,” the power of discerning faint objects. This is the thing in which a small telescope necessarily fails. The “light grasp” of the telescope obviously depends chiefly on the area of the objective, and visually only in very minor degree on the absorption of the thicker glass in the case of a large lens. According to the conventional scale of star magnitudes as now in universal use, stars are classified in magnitudes which differ from each other by a light ratio of 2.512. a number the logarithm of which is 0.4, a relation suggested by Pogson some forty years ago. A second magnitude star therefore gives only about 40% of the light of a first magnitude star, while a third magnitude star gives again a little less than 40% of the light of a second magnitude star and so on. But doubling the aperture of a telescope increases the available area of the objective four times and so on, the “light grasp” being in proportion to the square of the aperture. Thus a 10 inch objective will take in and deliver nearly 100 times as much light as would a 1 inch aperture. If one follows Pogson’s scale down the line he will find that this corresponds exactly to 5 stellar magnitudes, so that if a 1 inch aperture discloses, as it readily does, a 9th magnitude star, a 10 inch aperture should disclose a 14th magnitude star. Such is substantially in fact the case, and one can therefore readily tabulate the minimum visible for an aperture just as he can tabulate the approximate resolving power by reference to Dawes’ limit. Fig. 186 shows in graphic form both these relations for ready reference, the variation of resolving power with aperture, and that of “light grasp,” reckoned in stellar magnitudes. It is hardly necessary to state that considerable individual and observational differences will be found in each of these cases, in the latter amounting to not less than 0.5 to 1.0 magnitude either way. The scale is based on the 9th magnitude star just being visible with 1 inch aperture, whereas in fact under varying conditions and with various observers the range may be from the 8th to 10th magnitude. All these things, however convenient, must be taken merely at their true value as good working approximations.