In applying to the reflecting telescopes of Gregory and Casscgrain the principle which has been already explained, we are led to the formation of a micrometer, remarkable for the simplicity of its construction; and what, at fist sight. may appear paradoxical, we may convert a Gregorian or a Cassegrainian telescope into a-very accurate micrometer, almost without the aid of any additional ap paratus.
It will be readily seen, by those who understand the theory of these telescopes, that their magnifying power may be increased merely by vary ing the distance be tween the eye-piece and the great speculum; and then preducing a distinct vision by a new adjustment of the small mirror. Hence a pair of wires fixed in the eye piece may he made to subtend different angles, solely by having that part of the instrument moveable along a portion of the common axis of the two mirrors.
In order to understand this, let SS, (Peite CCCLXXV. Fig. 13) he the great speculum ol a Gregorian tele scope, having a round hole in its centre, and placed at the extremity of the tube AA ; and let M be the small speculum, whose focus is G, and centre II, attached to an arm MQ, and moveable along the axis of the instru ment by means of a screw and milled head. The rays RR, proceeding from the lower part ,of any object, and falling upon the speculum SS, will be reflected to R', and will there form an image of that part of the object. In like manner, the rays rr will form an image of the upper part of the object at r'. The rays diverging from the image R' r', and intercepted by the small spe culum M, will form another image R" r", at the distance MI..; which being viewed by the eye-glass at E, whose focal distance is FE, will appear distinct and magnified to the observer.
Let us now suppose that the lens E, or the eye-piece of the telescope, (which is generally a Huygenian eye piece, with two glasses,) is moved by a suitable appa ratus into the position L', and that a point is taken, so that F' E' may be equal to FE. Then it is manifest, that, in order to have a distinct view of the object in this new position of the eye-piece, the image formed by the small speculum must be brought to F' in the focus of the lens E'. But as the place of the first image R' r' is in no respects changed by the change of position in the eye-piece, the formation of the image at F can be effected only by bringing the small mirror 111 into a po sition AI', nearer the image R' r' than it was before; and as the space MM' through which it has been moved, in order to converge the rays to F', must necessarily be less than EE', the space through which the eye-glass has moved ; the distance M' F' of the new image at F' from the small mirror must be greater than MF, the dis tance of the other image at F, in the ratio of M' F' to ; and the magnifying power of the instrument must at the same time be increased, and the angle subtended by the wires diminished.
In the formation of this micrometer, we may either construct the scale from calculation, after the two ex treme points of it have been fixed experimentally, by the method already described ; or all the points of the scale may be determined by direct experiment. It would perhaps be more convenient to divide the scale into equal parts, and to construct a table from experi ment, for the purpose of sheaving, by inspection, the angle which corresponds to any number of these equal divisions." On Double Image Micrometers, in which the Lenses, Mirrors, and Prisms, are opened and shut mechani cally.
The first hint of a double image micrometer seems to have been communicated, in 1675, by the celebrated Danish astronomer M. Roemer. ft appears, however, to have remained so entirely unnoticed, twat it was not even known to Mr. Servington Sivary of Exeter. in the year 1743, when he communicated to the R yal Society- of London an account of a double image micro meter, consisting of two lenses, capable of being sepa rated from and of being brought near to one another by mechanical means. When the two images of the sun, or ol any other body, were in contact, the distance of the lenses becomes a measure of the angular magnitude of the sun, the value of the scale having been previously determined by experiment. The account of Savory's micrometer was extracted from the minutes of the So ciety by Mr. Short, and published in the Phil. Trans. for 1753. In 1748, Al. Bouguer proposed a similar instrument which he called a heliometer ; and in 1753, Mr. Dollond made a farther improvement on this kind of micrometer, by substituting in place of two object glasses a single object•glass cut in two. As a drawing and description of Mr. J. Dollond's divided object-glass micrometer has already been given in our article As TaoNomy, and in Plate XLVIII. Fig. 4 and 5, it is un necessary to enlarge the present article by any description of the more imperfect instruments of Savory and Bou guer. We shall content ourselves with explaining the general principle of all instruments of this kind.