The application of the divided object-glass micro meter to a telescope for measuring distances, and to a coming-up glass for ascertaining whether a ship is ap proaching to, or receding from, the observer, will be found in Dr. Brewster's Treatise on New Philosophical Instruments, Book III Chap II The principle upon which 'his instrument is found ed may also be applied to Rainsclen's (Impute micro meter, and to the reflecting micrometer which we have described in Chap. III. as applied to a Cassegrainian or Gregorian telescope.
On ?ngular or Position Micrometers.
The first micrometer of this kind, that we are ac quainted with, was invented and used by Sir William rschel, for the purpose of measuring the angle which a line joining the two stars that compose a double star, forms with the direction of their apparent motion. The object which thit, celebrated astronomer had in view, was to verify a conjecture that the smaller of the two stars revolved round the greater, or rather round their corn mon centre of gravity ; and he actually found, by means of this instrument, that in the double star of Castor this revolution was performed in 342 years.
" The position micrometer is shown in Plate CCCLXXV I. Fig. 4, inclosed in a turned case of wood, as it is put together. ready to he used with the telescope. A is a little box which holds the eye-glass. B is the piece which covers the inside work, and the box A is screwed into it. C is the body of the micrometer con taming the brass work, showing the index plate a pro jecting at one side, where the case is cut away to re ceive it. D is a piece, having a screw b at the bottom, by means of which the micrometer is fasten:LI to the te lescope. To the piece C is given a circular motion, in the manner the horizontal motion is generally given to Gr. gorian reflectors, by the lower part going through the piece D, where it is held by the screw E, which k, t ps the two pieces C and D together, but leaves them at ty to turn on each other Fig. 5, is a section of the case containing the brass work. where may be observed the piece B hollowed out to receive the box A, which t onsists of two parts in closing the eye lens. This figure also shows how the plc e C passes through D, and is held by the ring E : the hrass work, consisting of a hollow cylinder, a wheel and pinion, and index plate, is there represented in its place. F is the body of the br iss work, being a hol low cylinder with a broad rim C at the upper end ; this rim is partly turned away to make a bed for the wheel d. 'I'he pinion e turns the wheel d, and carries the index plate a. One of its pints moves in the arm f, screwed on the upper part of c, which arm serves also to confine the wheel d to its place on c. The other pivot is held by the arm g fastened to F.
Fig. 6, is a plan of the brass work. The wheel d, which is in the form of a ring, is laid on the upper part of F or C, and held by two small arms f and h screwed down to e with the screws i, i.
Fig. 7, is a plan of the brass work ; d, d is the wheel placed on the bed or socket of the rim of the cylinder c, c, and is held down by the two pieces f, h, which are screwed on c, c. The piece f projects over the cen
tre of the index plate to receive the upper pivot of the pinion in, n, the fixed wire fastened to c, c 0, p, the moveable wire fastened to the annular wheel d, d. The index plate a is divided into 60 parts, each sub-divided into two, and milled on the edge. When the linger is drawn over the milled edge of the index plate from q towards r, the angle 7713 0 %% ill open, and if drawn frint r towards q, it will shut again. The case c, c, must have a sharp corner t, which serves as a hand to point out the divisions on the index plate." Phil. Trans. 1781, p. 5u9.
In this instrument, the two wires always cross each other at the centre of the field, and consequently their angular separation is produced uniformly by the mo tion of the pinion. Tnis very circumstance, howt.ver, which, though it renders it easy for the onserver to read off the angle from the scale, is one of the greatest im perfections of the instrument. The observations must obviously be all made on one side of the litre of the field, as appears from Plate CCCLXXVI. Fig. 8, and the use of the instrument is limited to those cases in which S a is less than the radius SC. The greatest dis advantage of the instrument, however, is the shortness of the radius SC, for the error of observation must al ways diminish as the length of this radius increases. This disadvantage does not exist in measuring the an gle of position of two stars S. s, for the distance S a re mains the same whatever be the length of SC but in determining all other angles contained by lines, whose apparent length is greater than SC, this imperfection is inseparable from the instrument. Nay. there are some cases in which the instrument completely fails ; as, for instance, when we wish to measure the angle formed by two lines which do not meet in a point, but only tend to a remote vertex. If the distance of the nearest extre mities of these lines is greater than the chord of the an gle which they form, measured upon the radius SC, then it is impossible to measure that angle, for the lines cannot be brought to coincide with the two lines by which it is contained. Nay, when the chord of the an gle does exceed the distance between the nearest extre mities, the portion of the wires that can he brought into coincidence with the lines is so small, as to lead to very serious ors in the result The new angular micrometer, which we venture to propose as a substitute for this instrument, is complete ly free from the defects which we have just noticed, and is founded on a very beautiful property of the circle. If any two chords AB, C D, Plate CCCLXXVI. Mir. 9, in tersect each other in the point 0 within the circle, the angle which they form at 0 will be equal to half the sum of the arches AC, 131) ; hut if these chords do not inter sect each other within the circle, but tend to any point.
0 without the as in Fig. 10, then the angle which they form is equal to half the difference of the arches AC, 131) ; that is, calling 0 the angle, we have in the