The ratio between the angles under which an object would be seen by the naked eye, and that by which it is seen in the telescope, is com pounded of the ratios of the focal lengths of the several lenses; thus, if r ba the focal length of the object-lens, f", ", f '" those of the eye-lenses, reckoned in order towards the eye, the expression )7-7, will denote the magnifying power.
But both the spherical aberration and the chromatic dispersion in such a telescope are very considerable ; and before the invention of the achromatic object-glass, Mr. Dollond endeavoured to diminish the former by an eye-tube consisting of five lenses disposed so as to divide the bendings of the pencils nearly equally between them. Such telescopes are not now used ; and Mr. Dollond succeeded at length in constructing telescopes with four eye-glasses, from which both dis tortiOn and colour are removed as much perhaps as a removal is possible.
This is accomplished by placing the first eye-glass beyond the image formed by the object-glass, and at a distance from it less than the focal length of that eye-glass; by this disposition the rays of mean refrangibility in each pencil which diverges from the Image are not, after refraction, parallel to one another, but go on with diminished divergency. A little way beyond the place where the axes of the oblique pencils cross the axis of the telescope there is placed the second eye-glass, which is of such focal length that the mean refrangi ble rays in each pencil, after passing through it, meet in a point, and thus a second image of the object is formed near the eye : the use of these two lenses, therefore, Is to cause the second image to be formed by a gradual convergence of the rays in each pencil. But the several pencils of rays are intercepted by the third eye-glass (commonly called the field-glass), and the second image is thereby formed rather nearer to the first than it would be without such field-lens : from this imago the rays in each pencil diverge, and by the refractive power of the fourth eye-glasa they are made to enter the eye in parallel directions : thus distinct vision of the external object is obtained. The field-glass might have been placed between the eye and the second image, as in the Ittlyghenian eye-piece before described ; but the aberration arising from the spherical form of the glasses is a little less by the construc tion just mentioned. _ Now, in each pencil, the red and violet rays which had been united at the image formed by the object-glass, and which there creased each other, go on from thence diverging from each other till, on the oppo site side of the axis of the telescope, they fall upon the surface of the second eye-glaas : after passing through this lens, the violet ray, which is always more refracted than the red ray, gradually converges towards the latter, and at length meets it in some place short of that at which the rays of mean refraction unite to form the second image. The
practice is to fix the third or field-glass exactly or nearly at the place where the red and violet rays so unite in all the pencils; for the different coloured rays crossing each other in that place, they are finally, by the refractive power of the fourth eye-glass, made to cuter the eye m parallel directions, and thus afford a view of the object nearly or wholly free from colour.
In forming the eye-glasses of telescopes it may be observed that they should be such as will allow the incident and emergent pencils of rays to be nearly equally inclined to their surfaces : on this account the first and fourth eye-glasses are of the plauo-convex form; the flat side of that which is nearest to the object-glass being towards the latter, and that of the other towards the eye.
Besides the power of magnifying objects, that of affording distinct vision with given quantities of light is often an essential requisite, in telescope, particularly to naval men, who have occasion during the obscurity of the night to keep in view a ship of which they may be in chase. This subject was investigated by the late Sir William Herschel, and an account of his researches on what ho calls the trating power of telescopes" was printed in the 'Philosophical Transac tions' for 1800.
Herschel states that he was aware of this property of telescopes as early as the year 1777, when he had constructed a Newtonian telescope with a speculum whose focal length was 20 feet : for, on directing the instrument to a church-steeple at a considerable distance, he could distinguish the hour by the clock, though with the naked eye he could not see the steeple itself. In order to obtain a formula for the space axis x T of the instrument, which is supposed to be of the Gregorian kind. A n is the tube yvhich contains the specula, and is open at the end C B ; and at the extremity nearest to the eye of the observer is a tube K F containing two lenses. it N is the anterior surface of the great speculum, which has a circular perforation, rah, at its centre : is a small speculum, concave like the former, its surface being either spherical or parabolical It is connected with the side of the tube A n by the arm it K, and is capable of being moved in the direction of the axis X Y by means of the rod Y8 : the latter passes through a knob Q, which is fixed to the side of the tube, and works in the knob n, which pasties through an oblong perforation in the side of the tube, and is attached to the part K of the arm BK. This movement is given to the mall mirror in order that its focus may be made to coincide with the place of the imago formed by the great speculum ; that image being at different distances from the latter according to the distance of tho object from the observer.