As soon as Piazzi, Olbers, and Harding had discovered three of the numerous telescopic planets now known, Herschel proposed to himself to determine their real magnitudes; but telescopes not having then been applied to the measurement of excessively small angles, it became requisite, in order to avoid any illusion, to try some experiments adapted to giving a scale of the powers of those instruments. Such was the labour of that indefatigable astronomer, of which I am going to give a compressed abridgment.
The author relates first, that in 1774, he endeavoured to ascertain experimentally, with the naked eye and at the distance of distinct vision, what angle a circle must subtend to be distinguished by its form from a square of similar dimensions. The angle was never smaller than 2' 17"; therefore at its maximum it was about one fourteenth of the angle subtended by the diameter of the moon.
Herschel did not say, either of what nature the circles and squares of paper were that he used, nor on what background they were projected. It is a lacuna to be regretted, for in those phenomena the intensity of light must be an important feature. However it may have been, the scrupulous observer not daring to extend to telescopic vision what he had discovered relative to vision with the naked eye, he undertook to do away with all doubt, by direct observations.
On examining some pins' heads placed at a distance in the open air, with a three-foot telescope, Herschel could easily discern that those bodies were round, when the subtended angles became, after their enlargement, 2' 19". This is almost exactly the result obtained with the naked eye.
When the globules were darker; when, instead of pins' heads, small globules of sealing-wax were used, their spherical form did not begin to be distinctly visible till the moment when the subtended magnified angles, that is, the moment when the natural angle multiplied by the magnifying power, amounted to five minutes.
In a subsequent series of experiments, some globules of silver placed very far from the observer, allowed their globular form to be perceived, even when the magnified angle remained below two minutes.
Under equality of subtended angle, then, the telescopic vision with strong magnifying powers showed itself superior to the naked eye vision. This result is not unimportant.
If we take notice of the magnifying powers used by Herschel in these laborious researches, powers that often exceeded five hundred times, it will appear to be established that the telescopes possessed by modern astronomers, may serve to verify the round form of distant objects, the form of celestial bodies even when the diameters of those bodies do not subtend naturally (to the naked eye), angles of above three tenths of a second: and 500, multiplied by three tenths of a second, give 2' 30".
Refracting telescopes were still ill understood instruments, the result of chance, devoid of certain theory, when they already served to reveal brilliant astronomical phenomena. Their theory, in as far as it depended on geometry and optics, made rapid progress. These two early phases of the problem leave but little more to be wished for; it is not so with a third phase, hitherto a good deal neglected, connected with physiology, and with the action of light on the nervous system. Therefore, we should search in vain in old treatises on optics and on astronomy, for a strict and complete discussion on the comparative effect that the size and intensity of the images, that the magnifying power and the aperture of a telescope may have, by night and by day, on the visibility of the faintest stars. This lacuna Herschel tried to fill up in 1799; such was the aim of the memoir entitled, On the space-penetrating Power of Telescopes.
This memoir contains excellent things; still, it is far from exhausting the subject. The author, for instance, entirely overlooks the observations made by day. I also find, that the hypothetical part of the discussion is not perhaps so distinctly separated from the rigorous part as it might be; that disputable numbers, though given with a degree of precision down to the smallest decimals, do not look well as terms of comparison with some results which; on the contrary, rest on observations bearing mathematical evidence.