CHAPTER XI.

Telescopes.

73. Roger Bacon, A. D. 1250, has treated, among other Optical Phenomena, upon the apparent magnitudes of objects and spherical foci. He says, "For it is easy to understand, by the canons above mentioned, that the greatest things may appear exceeding small, and contrarily. For we can give such figures to transparent bodies, and dispose them in such order, with respect to the eye and the objects, that the rays shall be bent and refracted towards any place we please; and thus, from an incredible distance, we may read the smallest letter, and may number the smallest particles of dust and sand, by reason of the greatness of the angle under which we may see them; and, on the contrary, we may not be able to see the greatest bodies just by us, by reason of the smallness of the angle under which they may appear. For distance does not affect this kind of vision, excepting by accident, but the angle does." Thus Bacon really produced effects precisely analogous to those produced by our telescopes and microscopes.

In 1570, in the first English edition of Euclid's Elements, by Sir Henry Billingsley, there are mentioned "perspective glasses," clearly the same as our telescope. In 1591, Thomas Digges of Oxford writes thus: "My father, by his continuall painful practises, assisted with demonstrations

mathematicall, was able and sundry times hath, by proportionall glasses, duly situate in convenient angles, not only discovered things farre off, read letters...but also seven miles off declared what hath been doone at that instant in private places."

In 1610, so powerful had these glasses been made, Harriot was able to observe the spots in the sun.

Towards the end of the 16th century, a fortunate concurrence led to the invention of dioptric telescopes in Holland. Borelli informs us that the children of Zachariah Jansen, a spectacle-maker of Middle-Burgh, amusing themselves in their father's shop, placed by chance a convex and a concave lens in such a way, that on looking through them at the weathercock of the church, it seemed to them much larger and nearer than usual...This was about 1590. No sooner was this interesting discovery made known...than Galileo, Kepler, Descartes and other philosophers bent the whole force of their genius to the improvement and employment of so useful an apparatus. (Encycl. Metropol.)

74. It would be well, before discussing what it really was that these children had found out, to give a slight explanation of the words in italics in Bacon's writing quoted above.

If we hold a small circular piece of paper between us and the sun, we can, by placing it at the proper distance, exactly eclipse the sun: and we say then that the sun and the paper appear the same size. If we did not know the distance of the paper or its size, the eye would at once convey to the brain the idea that the sun and paper were of the same size. In a total eclipse, for instance, of the sun by the moon, this occurs.

The moon though much smaller

than the sun, appears to cover the sun, that is, appears to be the same size. Thus size is judged by the relative angles, not by the relative lengths and breadths. It will be necessary constantly to bear this in mind in what follows.

Fig. 54.

75.

Figure 54 will shew how it was that the children of Jansen saw the weathercock larger, by means of a convex (C) and a concave (C) lens.

2

Suppose for the moment that C, was removed. The rays from P of the weathercock would, after refraction at C1, form an image at 1, where PCp, is a straight line, and

according to the usual convention. Similarly Q would have its image at 9,. Now let the concave lens C, be placed so that þ11 is just in its focus. The rays then which are coming from the object-glass to the focus 1, and are intercepted by the lens C, will on emergence from C, form a beam of rays parallel to p,C,. But when rays enter the eye in a parallel beam, they appear as if they came from a point a very long way off. Thus, then, these rays appear to come from some point p (i. e. the eye sees an image) a very long way off, in the direction p1C, produced. Similarly with q. So that, finally, the object PQ, by means of the lenses, is seen under an angle pCq instead of under the angle PEQ or PC,Q, as it would be without the lenses.

We have in the last few words assumed that the eye and

the eye-lens coincide. In order to gain the central rays of the pencil falling on the eye-lens from each point of the object, it is clear that the eye must be placed close to the lens. Whence it follows that there is no object in having an eye-lens much larger than the pupil of the eye. Thus, by the figure, only a very small portion of the rays falling on the object-glass come to the eye.

We have therefore now shewn how an image is formed larger than PQ. But the children saw it also nearer, whereas, by our method, it has been placed at an infinite distance. A very slight alteration in the position of the lenses will accomplish this. Suppose we push in our concave lens very slightly, nearer to C. The result of this, since an object and image move in the same direction, will be to give the emergent rays a slight divergence from some point pon p, C, produced, not at an infinite distance, as before. The size of the final image pq remains the same as before, since it is measured by the angle under which it is seen, and that is not altered, except by the very slight movement of C

2

For objects so distant as the moon, for example, or indeed for objects much closer, at the distance of a few hundred yards, the rays incident on the object-glass may be considered parallel, and p,q, is therefore in the principal focus. Therefore C, C = difference of focal lengths of the two lenses.

76. This combination of lenses is called Galileo's telescope, from the following facts. "Happening to be in Venice in the month of May 1609, he learned in that city that a Belgian had invented a perspective instrument, by means of which distant objects appeared nearer and larger.

This report...excited an intense interest in his mind, and upon his return to Padua he began to ponder upon the probable mode by which such an effect could be produced. He discovered upon the very night of his arrival, that the enlargement of the object depended upon the doctrine of refraction, and on the following day he made his first attempt to execute an instrument upon this principle. Having procured a leaden tube, he fitted in one of its extremities a plano-convex lens, and in the other a planoconcave one, and, having applied his eye to the concave lens, he was delighted to perceive objects pretty much magnified. They appeared to be three times nearer and nine times larger....He immediately gave intimation of his success to his friends in Venice, with whom he had been conversing on the previous day. Having succeeded a few days later in making a better instrument, he joyfully proceeded to Venice, taking it with him.... Galileo's object now was to construct a telescope of superior magnifying power. This he found to be a task of very difficult accomplishment, for the art of grinding and polishing lenses was then in its infancy....Soon afterwards he made another instrument which magnified 60 times in surface, and finally, sparing neither application nor expense, he succeeded in executing an instrument of such excellence as to represent objects almost 1000 times larger, and above 30 times nearer than they appeared to be by the natural power of the eye." (Grant's Hist. of Astron. Vol 1. p. 520.)

Thus Galileo constructed this telescope by theory, by thinking how it could be done, whereas all former constructions had been entirely experimental.

77. There are two great disadvantages attending this construction.