208 



MICROMETER. 



Double 



Image 



Microme 



tcr. 



Kamsden's 

 dioptric 

 microme- 

 ter. 



Figs. 23, 

 N> 



ing effected by the inclination of the two specula, and 

 not depending on the focus of any lens or mirror, any 

 alteration in the eye of an observer cannot affect the 

 angle measured. It has also the advantages of an ad- 

 justment, to make the images coincide in a direction 

 perpendicular to that of their motion ; and also of mea- 

 suring the diameter of a planet on both sides of the ze- 

 ro, which will appear no inconsiderable advantage to 

 observers who know how much easier it is to ascertain 

 the contact of the external edges of two images than 

 their perfect coincidence. In this micrometer, the small 

 speculum A is divided into two equal parts; one of 

 which is fixed on the end of the arm B ; the other end 

 of the arm is fixed on a steel axis X, which crosses the 

 end of the telescope C. The other half of the mirror 

 A is fixed on the arm D, which arm at the other end 

 terminates in a socket^, that turns on the axis X ; both 

 arms are prevented from bending by the braces a a. 

 G represents a double screw, having one part e cut into 

 double the number of threads in an inch to that of the 

 partg; the part e having 100 threads in one inch, and 

 the part g 50 only. The screw e works in a nut F in 

 the side of the telescope, while the part g turns in a 

 nut H, which is attached to the arm B ; the ends of the 

 arms B and D, to which the mirrors are fixed, are se- 

 parated from each other by the point of the double 

 screw pressing against the stud h, fixed to the arm D, 

 and turning in the nut H on the arm B. The two arms 

 B and D are pressed against the direction of the double 

 screw eg, by a spiral spring within the part n, by which 

 means all shake or play in the nut H, on which the 

 measure depends, is entirely prevented. 



From the difference of the threads on the screw at 

 e and g, it is evident that the progressive motion of the 

 screw through the nut will be half the distance of the 

 centres of the two halves of the mirror; and conse- 

 quently the half mirrors will be moved equally in con- 

 trary directions from the axis of the telescope C. 



The wheel V fixed on the end of the double screw has 

 its circumference divided into 100 equal parts, and the 

 index I shows the motion of the screw with the wheel 

 round its axis, while the number of revolutions of the 

 screw is shown by the divisions on the same index. 

 The steel screw at R may be turned by the key S, and 

 serves to incline the small mirror at right angles to the 

 direction of its motion. The telescope itself has a mo- 

 tion round its axis for the conveniency of measuring the 

 diameter of a planet in any direction ; and the inclina- 

 tion of the diameter measured with the horizon is 

 shown by a level and vernier on a graduated circle, at 

 the breech of the telescope. 



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 mi- 

 nutes, 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 form, 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 fourth 



Double 

 Image 



* 



' 



eye-glasses. In order to understand its application, 



let xy, Fig. 23, be the principal pencil of rays from 



the object-glass O ; / 1 and u u, the axis of two oblique 



pencils; a, the first eye-glass ; m, its conjugate focus, _ _ 



or the place of the micrometer; b the second eye-glass ; 



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 m ; and e, the width of the mi- 



crometer-glass, is to p, the diameter of the object-glass, 



as m a is to g o, which is the proportion of the mag- 



nifying power at the point m ; and the error caused by 



an imperfection in the micrometer-gJass placed at m 



will be to the error, had the micrometer been at O, as 



m is to p. 



The micrometer itself is shewn in Fig. 24, where A F'g- ** 

 is a convex or concave lens, bisected by a plane across 

 its centre; one of these semi-lenses is fixed in a frame 

 B, 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 two verniers on 

 the frame E, one at M and the other at N, for the con- 

 venience of measuring the diameter of a planet, &c. 

 on both sides the zero. The first division on both 

 these verniers coincides at the same time with 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, &c. 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. Bouguer, Mem. Acad. 

 Par. 1748, p. 1 1, and Hist. p. 87. Dollond, Phil. Trans. 

 1753, p. 178, and 1754, p. 551. Maskelyne's Phil. 

 Trans. 1771, p. 536, and 1777, p. 799, and Ramsden, 

 PhiL Trans. 1779, p. 4 19. 



CHAP. V. 



On Double Image Micrometers, in which the. Lenses or 

 Mirrors are opened and shut optically. 



The method of varying the angular distance of a Dr.^Brew- 

 pair of fixed wires has been successfully applied by **." 3 dl ~ 



Dr. Brewster to the construction of a divided object- 7" Jed . oh " 



... .. , J ject-glass 



glass micrometer, which possesses peculiar advanta- microme- 



ges. It is represented in Plate CCCLXXVI. Fig. 1. tcr, PLAT* 

 where LL is an achromatic object-glass, having two cccixxvi. 

 achromatic semilenses, A, B, represented in Fig. 2, F'g- l > % 

 moveable between it and its principal focus f. 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 O f of 

 the lens LL. When the semilenses are close to LL, 

 the two images are much separated, and form a great 

 angle ; but, as the lenses are moved towards f, 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 

 semilenses are placed close to LL, and also the angle 



