To these principal uses of the mirror of Archimedes, I could add many other particular ones; but I have confined myself to those only which appeared the most useful, and the least difficult to be put in practice; nevertheless I have subjoined some experiments that I made on the transmission of light through transparent bodies, to give some new ideas on the means of seeing objects at a distance with the naked eye, or with a mirror, like that spoken of by the an cients, and by the effect of which vessels could be perceived from the port of Alexander, as far as the curvature of the earth would permit.
Naturalists at present know, that there are three causes which prevent the light from uniting in a point, when its rays have passed the objective glass of a common mirror. The first is the spherical curve of this glass, which disperses a part of the rays in a space terminated by a curve. The second is the angle under which the object appears to the naked eye: for the breadth of the focus of the objective glass has a diameter nearly equal to the chord of which this angle measures. The third is the different refrangibility of the light; for the most refrangible rays do not collect in the same place with the lesser.
The first cause may be remedied by substituting, as Descartes has proposed, elliptical, or hyperbolical, glasses to the spherical. The second is to be remedied by a second glass, placed to the focus of the objective, whose diameter is nearly equal the breadth of this focus, and whose surface is worked on a sphere of a very short ray. The third has been found to be remedied, by making telescopes, called Acromatics, which are composed of two sorts of glasses, which disperse the coloured rays differently; so that the dispersion of the one is corrected by the other, without the general refraction, which constitutes the mirror, being destroyed. A telescope 31/2 feet long, made on this principle, is in effect equivalent to the old telescopes of 25 feet.
But the remedy of the first cause is perfectly useless at this time, because the effect of the last being much more considerable, has such great influence on the whole effect, that nothing can be gained by substituting hyperbolical, or elliptical glasses to spherical, and this substitution could not become advantageous, but in the case where the means of correcting the effect of the different refrangibility of the rays of light might be found; it seems, therefore, that we should do well to combine the two means, and to substitute, in acromatic telescopes, elliptical glasses.
To render this more obvious, let us suppose the object observed to be a luminous point without extent, as a fixed star is to us. It is certain, that with an objective glass, for example, of 30 feet focus, all the images of this luminous point will extend in the form of a curve to this focus, if it be worked on a sphere; and, on the contrary, they will unite in one point if this glass be hyperbolical; but if the object observed have a certain extent, as the moon, which occupies half a degree of space to our eyes, then the image of this object will occupy a space of three inches diameter in the focus of the objective glass of thirty feet; and the aberration caused by the sphericity producing a confusion in any luminous point, it produces the same on every luminous point of the moon’s disk, and, consequently, wholly disfigures it. There would be, then, much disadvantage in making use of elliptical glasses or long telescopes, since the means have been found, in a great measure, to correct the effect produced by the different refrangibility of the rays of light.
From this it follows, that if we would make a telescope of 30 feet, to observe the moon, and see it completely, the ocular glass must be at least three inches diameter, to collect the whole image which the objective glass produces to its focus; and if we would observe this planet with a telescope of 60 feet, the ocular glass must be at least six inches diameter, because the chord which the angle measures under which the moon appears to us, is, in this case, nearly six inches; therefore astronomers never make use of telescopes that include the whole disk of the moon, because they would magnify but very little. But if we would observe the planet Venus with a telescope of 60 feet, as the angle under which it appears to us is only 60 seconds, the ocular glass can only have four lines diameter; and if we make use of an objective of 120 feet, an ocular glass of eight lines diameter would suffice to unite the whole image which the objective forms to its focus.
Hence we see, that even if the rays of light were equally refrangible we could not make such strong telescopes to see the moon with as to see the other planets, and that the smaller a planet appears to our sight the more we can augment the length of the telescope, with which we can see it wholly. Hence it may be well conceived, that in this supposition of the rays, equally refrangible, there must be a certain length more advantageously determined than any other for each different planet, and that this length of the telescope depends not only on the angle under which the planet appears to our sight, but also on the quantity of light with which it is brightened.
In common telescopes the rays of light being differently refrangible, all that could be done in this mode to give them perfection would be of very little advantage, because, that under whatever angle the object, or planet, appears to our sight, and whatever intensity of light it may have, the rays will never collect in the same part; the longer the telescope the more interval it will have between the focus of the red and violet rays, and consequently the more confused the image of the object observed.
Refracting telescopes, therefore, can be rendered perfect only by seeking for the means of correcting this effect of the different refrangibility, either by composing telescopes of different densities, or by other particular means, which would be different according to different objects and circumstances. Suppose, for example, a short telescope, composed of two glasses, one convex and the other concave; it is certain that this telescope might be reduced to another whose two glasses would be plain on one side, and on the other bordering on spheres, whose rays would be shorter than that on the spheres on which the glasses of the first telescopes have been constructed. However, to avoid a great part of the effect of the different refrangibility of the rays, the second telescope may be made with one single piece of massive glass, as I had it done with two pieces of white glass, one of two inches and a half in length, and the other one inch and a half; but then the loss of transparency is a greater inconvenience than the different refrangibility which it corrects, for these two small massive telescopes of glass are more obscure than a small common telescope of the same glass and dimensions; they indeed give less iris, but are not better; for in massive glass the light, after having crossed this thickness of glass, would no longer have a sufficient force to take in the image of the object to our eye. So to make telescopes 10 or 20 feet long, I find nothing but water that has sufficient transparency to suffer the light to pass through this great thickness. By using, therefore, water to fill up the intervals between the objective and the ocular glass, we should in part diminish the effect of the different refrangibility, because water approaches nearer to glass than air, and if we could, by loading the water with different salts, give it the same refringent degree of power as glass, it is not to be doubted, that we should correct still more, by this means, the different refrangibility of the rays. A transparent liquor should, therefore, be used, which would have nearly the same refrangible power as glass, for then it would be certain that the two glasses, with their liquor between them, would in part correct the effect of the different refrangibility of the rays, in the same mode as it is corrected in the small massive telescope which I speak of.
According to the experiments of M. Bouguer, the thickness of a line of glass destroys 2/7 of light, and consequently the diminution would be made in the following proportion: