210 



MICROMETER. 



Double preaching to, or receding from, the observer, will be 

 Image Mi- found in Dr. Brewster's Treatise on New Philosophical 



rromeiers. f n/t /,. l/mc , llSt J} oo k HI. C h ap U 



The principle upon which this instrument is found- 

 ed, may also be applied to Ramsden's dioptric micro- 

 meter, and to the reflecting micrometer which we have 

 Described in Chap. III. as applied to a Cassegrainian 

 o.r Gregorian telescope. 



CHAP. VI. 



On Angular or Position Micrometers. 



towards r, the angle mso, will open, and if drawn from On 



r towards , it will shut again. The case c, c, must laror 1 '"''' 

 * (ion Micro- 



SirWilliara 

 Hrrsclii'l's 

 I'ositiun 

 Microme- 

 ters. 

 FLATZ 

 CCCI.XXVI. 

 Fig. 4, 5, 

 <i, 1. 



Fig. 5. 



Fig. 6. 



Fig. 7. 



meters. 



The first micrometer of this kind, that we are ac- 

 quainted with, was invented and used by Sir William 

 Herschel, 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 this 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 com- 

 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 Fig. 4, inclosed 

 in a turned case of wood, as it is put together, ready to 

 be 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 containing the brass work, showing 

 the index plate a projecting at one side, where the case 

 is cut away to receive it. D is a piece, having a screw 

 b at the bottom, by means of which the micrometer is 

 fastened to the telescope. To the piece C is given a 

 circular motion, in the manner the horizontal motion 

 is generally given to Gregorian reflectors, by the lower 

 part going through the piece D, where it is held by the 

 screw E, which keeps the two pieces C and D toge- 

 ther, but leaves them at liberty 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 consists of two parts in- 

 closing the eye lens. This figure also shows how the 

 piece C passes through D, and is held by the ring E : 

 the brass 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 brass 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. The pinion e turns the wheel d, and carries 

 the index plate a. One of its pivots 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 e, c. The piecey projects over the cen- 

 tre of the index plate to receive the upper pivot of the 

 pinion m, n, the fixed wire fastened to c, c. o, 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 finger is 

 drawn over the milled edge of the index plate from q 

 7 



have a sharp corner t, which serves as a hand to point 

 out the divisions on the index plate." Phil. Trant. 1781, 

 p. 509. 



In this instrument the two wires always cross each Dr.^Brevr- 

 other at the centre of the field, and consequently their ter' Poei- 

 angular separation is produced uniformly by the mo- tlon * 

 tion of the pinion. This very circumstance, however, '" 

 which, though it renders it easy for the observer 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 centre of the 

 field, as appears from Fig. 8, and the use of the in- Fig. 8. 

 fat r union t is limited to those cases in which S s is less 

 than the radius SC. The greatest disadvantage of the 

 instrument, however, is the shortness of the radius SC, 

 for the error of observation must always diminish as 

 the length of this radius increases. This disadvantage 

 does not exist in measuring the angle of position of two 

 stars S, s, for the distance S s remains the same what- 

 ever 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 re- 

 mote vertex. If the distance of the nearest extremi- 

 ties of theae lines is greater than the chord of the angle 

 which they form, measured upon the radius SC, then 

 it is impossible to measure that angle, for the lines can* 

 not be brought to coincide with the two lines by which 

 it is contained. Nay, when the chord of the angle 

 does exceed the distance between the nearest extremi- 

 ties, the portion of the wires that can be brought into 

 coincidence with the lines is so small, as to lead to very 

 serious errors 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 cir- 

 cle. If any two chords AB, CD, Fig. 9. intersect each Fig. 9. 

 other in the point O within the circle, the angle which 

 they form at O will be equal to half the sum of the 

 arches AC, BD ; but if these chords do not intersect 

 each other within the circle, but tend to any point O 

 without the circle, as in Fig. 10, then the angle which Fig. 10. 

 they form is equal to half the difference of the arches 

 AC, BD ; that is, calling <p the angle, we have in the 



AC + BD 



first case <p = ! , and in the second case (f = 



. Hence if AB, CD be two wires, placed in 



the focus of the first eye-glass of a telescope, the move- 

 able one AB may be made to form every possible an- 

 gle with the fixed one CD, and that angle may be rea- 

 dily found from the arches AB, CD. 



The apparatus by which these arches are measured 

 is represented in Fig. 11, where the graduated circular pig. u. 

 head may be divided only into 1 80, in order to save 

 the trouble of halving the sum, or the difference of the 

 arches AC, BD ; but as it would still be necessary to 

 measure tno arches before the angle could be ascertain- 

 ed, we have adopted another method, remarkable for 

 its simplicity, and giving no more trouble than if the 

 wires always intersected each other in the centre of the 

 field. 



