A telescope does not magnify real objects only, but magnifies also the apparent irregularities arising from atmospheric refractions; now, all other things being equal, these irregularities of refraction must be so much the stronger, so much the more frequent, as the stratum of air is thicker through which the rays have passed to go and form the image.
Astronomers experienced extreme surprise, when in 1782, they learned that Herschel had applied linear magnifying powers of a thousand, of twelve hundred, of two thousand two hundred, of two thousand six hundred, and even of six thousand times, to a reflecting telescope of seven feet in length. The Royal Society of London experienced this surprise, and officially requested Herschel to give publicity to the means he had adopted for ascertaining such amounts of magnifying power in his telescopes. Such was the object of a memoir that he inserted in vol. lxxii. of the Philosophical Transactions; and it dissipated all doubts. No one will be surprised that magnifying powers, which it would seem ought to have shown the Lunar mountains, as the chain of Mont Blanc is seen from Maçon, from Lyons, and even from Geneva, were not easily believed in. They did not know that Herschel had never used magnifying powers of three thousand, and six thousand times, except in observing brilliant stars; they had not remembered that light reflected by planetary bodies, is too feeble to continue distinct under the same degree of magnifying power as the actual light of the fixed stars does.
Opticians had given up, more from theory than from careful experiments, attempting high magnifying powers, even for reflecting telescopes. They thought that the image of a small circle cannot be distinct, cannot be sharp at the edges, unless the pencil of rays coming from the object in nearly parallel lines, and which enters the eye after having passed through the eye-piece, be sufficiently broad. This being once granted, the inference followed, that an image ceases to be well defined, when it does not strike at least two of the nervous filaments of the retina with which that organ is supposed to be overspread. These gratuitous circumstances, grafted on each other, vanished in presence of Herschel's observations. After having put himself on his guard against the effects of diffraction, that is to say, against the scattering that light undergoes when it passes the terminal angles of bodies, the illustrious astronomer proved, in 1786, that objects can be seen well defined by means of pencils of light whose diameter does not equal five tenths of a millimetre.
Herschel looked on the almost unanimous opinion of the double lens eye-piece being preferable to the single lens eye-piece, as a very injurious prejudice in science. For experience proved to him, notwithstanding all theoretic deductions, that with equal magnifying powers, in reflecting telescopes at least (and this restriction is of some consequence), the images were brighter and better defined with single than with double eye-pieces. On one occasion, this latter eye-piece would not show him the bands of Saturn, whilst by the aid of a single lens they were perfectly visible. Herschel said: "The double eye-piece must be left to amateurs and to those who, for some particular object, require a large field of vision." (Philosophical Transactions, 1782, pages 94 and 95.)
It is not only relative to the comparative merit of single or double eye-pieces that Herschel differs from the general opinions of opticians; he thinks, moreover, that he has proved by decisive experiments, that concave eye-pieces (like that used by Galileo) surpass the convex eye-piece by a great deal, both as regards clearness and definition.
Herschel assigns the date of 1776 to the experiments which he made to decide this question. (Philosophical Transactions, year 1815, p. 297.) Plano-concave and double concave lenses produced similar effects. In what did these lenses differ from the double convex lenses? In one particular only: the latter received the rays reflected by the large mirror of the telescope, after their union at the focus, whereas the concave lenses received the same rays before that union. When the observer made use of a convex lens, the rays that went to the back of the eye to form an image on the retina, had crossed each other before in the air; but no crossing of this kind took place when the observer used a concave lens. Holding the double advantage of this latter sort of lens over the other, as quite proved, one would be inclined, like Herschel, to admit, "that a certain mechanical effect, injurious to clearness and definition, would accompany the focal crossing of the rays of light."[20]
This idea of the crossing of the rays suggested an experiment to the ingenious astronomer, the result of which deserves to be recorded.
A telescope of ten English feet was directed towards an advertisement covered with very small printing, and placed at a sufficient distance. The convex lens of the eye-piece was carried not by a tube properly so called, but by four rigid fine wires placed at right angles. This arrangement left the focus open in almost every direction. A concave mirror was then placed so that it threw a very condensed image of the sun laterally on the very spot where the image of the advertisement was formed. The solar rays, after having crossed each other, finding nothing on their route, went on and lost themselves in space. A screen, however, allowed the rays to be intercepted at will before they united.
This done, having applied the eye to the eye-piece and directed all his attention to the telescopic image of the advertisement, Herschel did not perceive that the taking away and then replacing the screen made the least change in the brightness or definition of the letters. It was therefore of no consequence, in the one instance as well as in the other, whether the immense quantity of solar rays crossed each other at the very place where, in another direction, the rays united that formed the image of the letters. I have marked in Italics the words that especially show in what this curious experiment differs from the previous experiments, and yet does not entirely contradict them. In this instance the rays of various origin, those coming from the advertisement and from the sun, crossed each other respectively in almost rectangular directions; during the comparative examination of the stars with convex and with concave eye-pieces, the rays that seemed to have a mutual influence, had a common origin and crossed each other at very acute angles. There seems to be nothing, then, in the difference of the results at which we need to be much surprised.
Herschel increased the catalogue, already so extensive, of the mysteries of vision, when he explained in what manner we must endeavour to distinguish separately the two members of certain double stars very close to each other. He said if you wish to assure yourself that η Coronæ is a double star, first direct your telescope to α Geminorum, to ζ Aquarii, to μ Draconis, to ρ Herculis, to α Piscium, to ε Lyræ. Look at those stars for a long time, so as to acquire the habit of observing such objects. Then pass on to ξ Ursæ majoris, where the closeness of the two members is still greater. In a third essay select ι Bootis (marked 44 by Flamsteed and i in Harris's maps)[21], the star that precedes α Orionis, n of the same constellation, and you will then be prepared for the more difficult observation of η Coronæ. Indeed η Coronæ is a sort of miniature of ι Bootis, which may itself be considered as a miniature of α Gem. (Philosophical Transactions, 1782, p. 100.)