This micrometer will require a table for correcting a small error which arises from the eccentric motion of the half mirrors. By this motion their centres of cur vature will approach a little towards the large mirror. The equation for this purpose in small angles is insensi ble ; but when angles to be measured exceed ten minutes, it must not be neglected. Or, the angle mea sured may be corrected by diminishing it in the pro portion the versed sine of the angle measured, suppos ing the eccentricity radius, bears to the focal length of the small mirror.
As the aberration is less in the Cassegrainian tele scope than either in those of the Gregorian or Newto nian lorm, Mr. Ramsden preferred it for the application of this micrometer, the aberrations being nearly as 3 to 5.
Mr. Ramsden's dioptric micrometer, represented in Fig. 24, is applied to the erect eye-tube of a refracting telescope, and is placed between the third and louith eye-glasses. In order to understand its application, let x y, Fig. 23, be the principal pencil of rays from the object-glass 0 ; t t and u u, the axis of two oblelue pencils ; a, the first eye-glass ; in, its conjugate focus, or the place of the micrometer ; b the second eyeglass; c the third, and d the fourth. or that which is nearest the eye. Let p be the diameter of the object-glass, e the diameter of a pencil at in. and,/ the diameter of the pencil at the eye ; it is evident, that the axes of the pencils from every part of the image will cross each other at the point in ; and e, the width of the mi crometer-glass, is to 17, the diameter of the object-glass, as in a is to g o, which is the proportion of the mag nifying power at the point in; and the error caused by an imperfection in the micrometgr-glass placed at M will be to the error, had the micrometer been at 0, as 711 is top.
The micrometer itself is shown in Fig. 24, whdre A is a convex or concave lens, bisected by a plane across its centre ; one of these semi-lenses is fixed in a bathe and the other in the frame E ; which two frames slide on a plate H. and are pressed against it by thin plates a a; the frames B and E are moved in contrary directions by turning the button D : L is a scale of equal parts on the frame B ; it is numbered from each end towards the middle. There are too verniers on the frame E, one at M. and the other at N. for the con
venience of measuring the diameter of a planet. E,-..e. on both sides the zero. The first division on both these verniers coincides at the same time wit!, the two zeros on the scale L ; and if the frame is moved to wards the right, the relative motion of the two frames is shown on the scale by the vernier M ; but- if the frame B be moved towards the left, the relative motion is shown by the vernier N. This micrometer has a motion round the axis of vision, for the convenience of measuring the diameter of a planet, Ste. in any direc tion. by turning an endless screw F, and the inclina tion of the diameter, which is measured to the hori zon, is shown in the circle g by a vernier image. See Savary, Phil. Trans. 1753, p. 165. Bnuguer, Par. 1748, p. I I, and Hist. p. 87. Dollond, Phil. Trans. 1753, p. 178, and 1754, p. 551. Mask,lync's Phil. Trans. 1771, p. 536, and 1777, p. 799, and Ramsdcn, Phil. Trans. 1779, p. 419.
On Double Image Micrometers. in which the Lenses or Mirrors are opened and shut optically.
The method of varying the angular distance of a pair of fixed wires has been successfully applied by Dr. Brewster to the construction of a divided object glass micrometer, which possesses peculiar advan tages. It is represented in Plate CCCLXXVI. Fig. I, where LL is an achromatic object-glass. having two achromatic B, represented in Fig.
moveable between it and its principal focus 1. These semilenses are completely fixed, so that their centres are invariably at the same distance ; but the angle subtended by the two images which they form, is va ried by giving them a motion along the axis Of of the lens LL. When the semilenses are close to LL, the two images are much separated, and lorm a great angle ; but, as the lenses are moved towards j; the centres of the images gradually approach each other, and the angle which they form, is constantly increas ing. By ascertaining, therefore, experimentally, the angle formed by the centres of the images, when the semilenscs are placed close to LL, and also the angle which they subtend when the semilenses are at j; the other extremity of the scale, we have an instrument which will measure, with the utmost accuracy, all in termediate angles.