246 [TYPES OF FILAR (fig. 13). The means for changing the length of the tube and the distance of C from the scale are omitted in the figure. These appli ances are required if the "run" has to be accurately adjusted. By " run " is meant the difference between the intended whole number of screw-revolutions and the actual measure of the space between two adjacent di visions of the scale in turns of the screw divided by the number of intended revolutions. In delicate researches two divisions of the scale should always be read, not < merely for increased accuracy but to obtain the corrections for "run" from the observations themselves. Eepsold s Fig. 14 represents an important type of reading micrometer by the reading Repsolds. Here the web-frame is mounted on the screw itself. The micro- limiting plane of motion is at p, where the end of the micrometer meter. screw bears upon the hardened, flattened end of the screw s, and is kept in bearing against this plane by the spiral spring q. Rotation 13. Fig. 14. of the wire-frame is prevented by the small stud m which passes through the web-frame and projects slightly on both sides of it, just barely touching the inner surfaces of the top and bottom of the micrometer box. The web-frame thus rests solely on the screw and on the point m, and therefore follows it absolutely and accurately. Micro- The comparative merits of the various micrometers are discussed meter by Lord Lindsay and Mr Gill (Dunecht Publications, vol. ii. pp. errors. 53-55, 1877). If the screw of the Repsold micrometer is bent, so that, for example, the end of the frame next the screw-head is raised and that next the end p lowered, a tvist will be given to the web- frame, and the centre of the wire will be moved nearer to the micro meter head than it should be, while the reverse effect will follow when the head has been turned through 180. The effect of a similar error on the other micrometers described would be of a much less amount. They are, however, liable to errors of another character. If, as in Troughton s original micrometer, the shoulder is square, the hole in the end of the box may be left sufficiently wide to allow for a small error in the parallelism of the screw-matrix with the motion of the slide, but the smallest bend in the screw causes the shoulder no longer to bear flat, but to ride on its edge, thus intro ducing an extremely uncertain form of error. If the shoulder is spherical, fitting into a hollow cone on the end of the box, as in the micrometers of Simms, Cooke, and Grubb, an almost inconceivable accuracy of construction is implied in drilling the matrix of the screw in the slide so that its axis and that of the cone shall be in the same straight line, and both parallel to the motion of a point in the slide. Any departure from perfect accuracy in this respect has the effect of bringing different portions of the spherical shoulder to bear on different parts of the cone for different revolutions, and introduces errors of a character by no means easy to deal with. In addition to these objections there always is the greater objection of employing as a delicate contact-measuring surface one that is exposed where oil is used. Dust and oil will arrange themselves in layers of variable and uncertain thickness and defeat all attempts to secure absolutely consistent results. In Repsold s micrometer the point d appui is a small hardened and polished bearing, requir ing little lubrication, and perfectly protected from dust; the errors of the screw (some of them exaggerated, certainly) are faithfully reproduced, and consequently determinable, and beyond this the work to be done by the screw is reduced to a minimum, no slide- friction having to be overcome. If we are to regard as the most perfect instrument, "not that which has absolutely the smallest errors, but that which reproduces its errors with the most perfect consistency," undoubtedly Repsold s form of micrometer is best. In order to avoid the exaggeration of the screw-errors produced by the non-symmetrical position of the screw in Repsold s micro meter, Stone, in December 1879, exhibited at the Royal Astronomical Society, and described (Monthly Notices, p. 270), a modification of Repsold s instrument. But, both in his statement of the compara tive merits of the Troughton and Repsold micrometers and in the new form which he figures, Stone overlooks a strong point in the Rep- Lindsay- sold form, and in that proposed by Lord Lindsay and Gill three years Gill mi- previously, 1 namely, the avoidance of all friction of the slide, and croineter. the elimination of all error or strain that may occur from a want of parallelism in the axis of the matrix and the motion of the slide. The Lindsay-Gill micrometer will be better understood from the following description. In fig. 15 Ss is the micrometer screw ; its 1 Dunecht Publications, vol. ii., footnote p. 56, Dunicht, 1^77. cylindrical axis is nicely ground to fit a hole in the side of the box at a ; 2 the same axis, but ground to a somewhat smaller cylinder, fits neatly but smoothly a hole in the web-frame at b. A screw, cut on the same axis, is tapped into the web- frame at s, and the axis terminates in a pivot which fits a hole in a brass plate cc. The end of the pivot hardened and slightly rounded rests on a flat agate 3 bearing , which is imbedded in the plate B, and securely held in situ by pressure of the plate cc. The plate B is firmly attached to the bottom of the box. q, q are spiral springs mounted on pins. Both springs and pin pass freely through the web-frame at p, p, and the pins (but not the springs) pass freely through the frame at n, n. 4 The parallel webs for observing the division (fig. 13) are mounted on the forked end of the frame at ma. The web-frame is narrower and thinner than the breadth and height of the interior of the box, and is only prevented from rotat ing by the delicate touch of the projecting ends of the pin m on the inner surfaces of the top and bottom of the box. It appears that a frame so mounted fulfils all theoretical con ditions of accuracy. It is perfectly free to follow the motion of the screw and accurately to reproduce its errors, notwithstanding any reasonable faults of workmanship ; and no permissible shake or fouling of the bearing Fig. 15. at a can produce sensible error in the distance between the bearing surface of the agate plane and the spider webs. The motion is pro duced with the minimum of friction; and the "feel" of the screw is therefore as delicate and perfect as it is possible to make it. The micrometer of type D shown in fig. 16 has recently Repsold s been made by the Repsolds for the Cape Observatory. As this micro- instrument combines meter. all their most recent s modifications, we de scribe it in detail. Fig. 17 represents the same micrometer with the upper side of the box removed. The letters in the descrip tion refer to both figures. S is the head of the micrometer screw, s that of the screw by which the micrometer box is moved relative to the plate/ (fig. 16), s that of the screw which moves the eye piece slide. K is the clamp in position angle, P the slow mo tion screw in position angle ; pp is the posi tion circle, R, R its two readers. The lat ter are in fact little microscopes carrying F - 16 _ a vernier etched on glass, in lieu of a filar micrometer. These verniers can be read to 1 , and estimated to 2. D is the drum-head which gives the frac tion of a revolution, d that which gives the whole number of revo lutions, I is the index or pointer at which both drums are read. This index is shown in fig. 17, but only its mode of attachment (X, fig. 17) in fig. 16. The teeth of the pinion z, fig. 17, are cut on the axis of the micrometer screw. The drum/; and its attached tooth wheel are ground to turn smoothly on the axis of the screw. The pinion z and the toothed wheel d are connected by an intermediate wheel and pinion Y; the numbers of teeth in the wheels and pinions are so proportioned that twenty-four revolutions of the micrometer screw produce one revolution of the drum and wheel d. (This is the description of Repsold s counter referred to under type A. ) The divisions of both drums are conveniently read, simultaneously, by 2 There would be some advantage in allowing the screw s axis to pass with a. little shake through the hole in the end of the box at a, and then, extending the length of the larger cylinder, transfer the bearing from a to a well-fitting hole In a piece fixed like B to the bottom of the box. This form would also give some facilities of construction, and all the oiled surfaces would be perfectly protected. 3 Sapphire is better ; the agate bearing of such a screw has been found very sensibly worn. . 4 If it is desired to prevent possible contact of these pins with the frame, t.ie
ends of the pins may be m;ide to enter guiciing holes in cc.