From this accumulation of data several striking facts stand out. First there is great difference between individual observers working with telescopes of similar aperture as respects their agreement with “Dawes’ Limit,” showing the effect of variation in the physiological factors as well as instrumental ones.
Second, there is also a very large difference between the facility of observing equal bright pairs and equal faint pairs, or unequal pairs of any kind, again emphasizing the physiological as well as the physical factors.
Finally, there is most unmistakable difference between small and large apertures in their capacity to work up to or past the standard of “Dawes’Limit.” The smaller telescopes are clearly the more efficient as would be anticipated from the facts just pointed out regarding the different effect of the ordinary and inescapable atmospheric waves on small and large instruments.
The big telescopes are unquestionably as good optically speaking as the small ones but under the ordinary working conditions, even as good as those a double star observer seeks, the smaller aperture by reason of less disturbance from atmospheric factors does relatively much the better work, however good the big instrument may be under exceptional conditions.
This is admirably shown by the discussion of the beautiful work of the late Mr. Burnham, than whom probably no better observer of doubles has been known to astronomy. His records of discovery with telescopes of 6, 9.4, 12, 18½ and 36 inches show the relative ease of working to the theoretical limit with instruments not seriously upset by ordinary atmospheric waves.
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.