MICROMETER. 



Let AB, tor example, Fig. 9, be the fixed wire, and 

 or Piwition CD the moveable one, and let it be required to find, at 

 Micn>m- observation, the angle AOC or $. Let the index 

 ._'*"_. of the vernier be at zero, when the point D coincide-. 

 )'i > A with B ; and as it is obvious that the extremity C will 

 rccixxvi. be at c when U is at B, the arch <: A will be a constant 

 *' * quantity, which we sl.a'.l call b. Making \( =m and 



BD=, we have, = * '"; but since the extremity 



C will move over the space C c while D describes the 

 pace DB, these arches must be equal, consequently 

 b = m ; hence adding 2 n to each side of the equa- 



tion, we obtain b + '2n=m -J- n, or 



4 + "= p-, 



consequently $=$ A -f- n. Hence the angle AOC is 

 equal to half the arch A c added to the arch DB ; or 

 since A c i- invariable, the half of it is a constant 

 quantity, and the angle required is equal to the sum 

 of this constant quantity and the arch OB. 



When the wires do not intersect each other, as in 



Fig. 10, we have, p = - and, b = m 



it ; hence 



subtracting 2 n from each side of the equation, we hare 

 6 2=w *, and dividing by 2 b n= ; --, con- 

 sequently $ = $6 n. That is, the angle AOB is 

 equal to the difference between half the arch A c and 

 the arch DB, or to a constant quantity, diminished by 

 the arch DH. 



In finding the angle AOB, therefore, we have mere- 

 ly to observe the place of the index when the wire* 

 are in their proper position ; and as the scale commen- 

 ces at B, or when D and B coincide, and is numbered 

 both ways from li, the degree pointed out on the cir- 

 cular head, when increased or diminished l>y the con- 

 stant quantity, will give the angle of the wires which 

 is sought. The semicircle on each side of a diameter 

 drawn through B, is divided into 180', the IbOth de- 

 gree being at the opposite end of that diameter. 



The method of reading off the angle AOB, may be 

 still farther simplified, to a* to save the trouble even 

 of recollecting the constant quantity, and of adding 

 and subtracting it from the arch pointed out by tin- 

 index of the vernier. This effect is produced by mak- 

 ing the index of the vernier point to the constant quan- 

 tity upon the part of the scale below B, Fig. 9, when 

 the points D, B, coincide, or when the wire CD is in 

 the position e B ; for it is obvious that if . is the aro 

 of the scale, and B : equal to the constant quantity, 

 the arch D - . Inch is pointed out by the index of the 

 vernier, will be equal to J6 + , or the angle AOB. 

 In like manner in Fig. 10, where the wires do not cross 

 each other within the field, and where B : is the con- 

 stant quantity, the arch D z marked out by the index 

 of the vernier, it obviously equal to J b n, or the an. 

 gle AOB, which the wires tend to form at O. By 

 means of this adjustment, therefore, we are enabled to 

 read off the angle AOB with the same facility as if the 

 wires intersected each other in the very centre of the 

 field, when the arches are accurate measure* of the an. 

 gles at the centre. 



It is not necessary that the two wiret should be plac- 

 ed in the focus of the first eye-glass. Dr. Brewster 

 has constructed an instrument of this kind, in which 

 the fixed wire AB is placed in the focus of the whole 

 eye-piece, or, what is the tame thing, in the focus of 

 the object glass, while the moveable wire CD revolv. 

 ed in the focus of the first eye-glass. In this case the 

 wire AB is more magnified than the other ; but if Uut 



should be regarded as an inconvenience, it might easi- Angular, 

 ly be removed by using a more delicate fibre. or Position 



The end of the eye-tube is represented in Fig. 11, " 

 where CD is the circular head, divided into 360 3 , and -_ '_- 

 subdivided by the vernier V ; L is the level, and AB 

 the part of the eye piece which contains the diaphragm 

 with the fixed and moveable wires. The head CD, 

 and the level L, are firmly fixed to the eye tube T, and 

 from the head CD there rises an annular shoulder con- 

 centric with the tube, and containing the diaphragm 

 across which the fixed wire is stretched. This dia- 

 phragm, which is represented in Fig. 12, with the wire Fig. II. 

 extended across, projects through the circle of brass 

 EF. All these parts remain immoveable, while the 

 outer tube AB, and the other half EF of the circular 

 head which contains the vernier V, have a rotatory mo. 

 tion upon the shoulder which rises from CD. The 

 tube AB is merely an outer case to protect a little tube 

 within it, ijhich contains the eye-glass, and the move- 

 able diaphragm with iU fibre extended across it. The 

 inclosed tube is screwed into the ring EF, and the 

 outer tube is also screwed upon the same ring ; so that 

 by moving AR, a motion of rotation is communicated 

 to the vernit-r V. and to the diaphragm and wire be- 

 longing to tin' imu-r tube, while the rest of the eye- 

 piece, containing the other diaphragm with its wire, 

 remains stationary. By this means the moveable wire 

 is made to form every possible angle with the fixed 

 wire, and the angle is determined by the method which 

 we have already explained. The fixed wire is placed 

 a little out of the centre of the diaphragm to which it 

 belong*, and the diaphragm itself is placed in a cell, 

 in which it can be turned round, so as to adjust the 

 wire to a horizontal line, when the level is set. The 

 moveable wire is likewise placed at a little distance 

 from the centre of its diaphragm, as represented in Fig. 13. 

 Fig. 13 ; but by means of screws which pass through 

 the inner tube into the edge of this diaphragm, it can 

 be moved in a plane at right angles to the axis of the 

 eye-piece, so that the moveable wire may be plaoed ei- 

 ther in the centre of the field, or at different distances 

 from it. See Trealite on \cie Phil. Intl. p. 112. 



( HAI'. VII. 

 On I.Hcid Ditc, and I.uminom Image Micrometeri. 



In measuring the distance of dose double stars, Sir Sir William 

 William Herschel found it difficult to apply the common Hcnchel'i 

 ire micrometer, from the various sources of imperfec- lam P * 

 tion to which it in liable, but particularly from the neces- 

 sity of illuminating the wires. He therefore set himself tor"' 

 to construct a micrometer for this particular purpose, PLATT 

 and in this way he contrived the lamp micrometer. CCCLXXTI. 



This instrument is represented in Plate CCCLXX VI. Ki - 

 Fig. 14, " where ABGCFE is a stand nine feet high, on 

 which a semicircular board qhogp is moveable up- 

 ward or downward, in the manner of some fire- screen.", 

 as occasion may require, and is held in its situation by 

 peg p put into any one of the holes of the upright 

 piece AH. This board is a segment of a circle of II 

 inches radius, and is about three inches broader than a 

 semicircle, to give room for the handles r D, e I', to 

 work. The use of this board is to carry an arm L, 30 

 inches long, made to move on a pivot at the centre of 

 the circle, by means of a string, which passes in a 

 groove on the edge of the semicircle pgohi/; the 

 string is fattened to a hook o, (not expressed in the fi- 

 gure being at the back of the arm L,) and, passing 

 along the groove from o h to y, is turned over a pulley 

 t q, and goes down to small barrel e, within tb 



