206 



MICROMETER. 



Double 

 Image 

 Microme- 

 ters. 



PLATE 

 OCCLXXV. 

 Fig. 18. 



Dr. Maske 

 lyne's Pris 

 malic Mi- 

 crometer. 



ig. 19. 



ascensions of their centres, allowing for the motion of 

 the planet in the interval of the observations, without 

 any regard to the error of adjustment, for the same rea- 

 son as before. For if you take any point in the chord 

 of a circle, half the difference of the two segments is 

 manifestly the distance of the point from the middle 

 of the chord ; and as the planet runs along HR, the 

 chord is parallel to the equator. 



In like manner, the distances of their limbs may be 

 measured in lines perpendicular to the equator, by 

 bringing the micrometer into the position already de- 

 scribed, and instead of bringing V to HR, separate 

 the segments till the northernmost limbs coincide as at 

 V ; and in the same manner make their southernmost 

 images to coincide, and half the difference of the two 

 measures, allowing for the planet's motion, gives the 

 difference of the declinations of their centres. 



Hence the true place of a planet in the sun's disc 

 may at any time of its transit be found ; and conse- 

 quently the nearest approach to the centre and the time 

 of ecliptic conjunction may be deduced, although the 

 middle should not be observed." Phil. Trans. 1771- 



In using the divided object glass micromtter, it has 

 been found in practice to give different measures of the 

 same angle at different times. This error arises from 

 an alteration in the focus of the eye of the observer ; 

 for if the eye is not suited to see distinctly the inter- 

 section of the two pencils PF, QF, Fig 13, at the point 

 F, the two images will either appear separate or overlap 

 one another, according as the eye is adapted to a nearer 

 or a more distant object than F. In order to remedy 

 this inconvenience, Dr. Maskelyne contrived, in the 

 year 1776, the prismatic micrometer, which we shall 

 describe in his own words. 



"Let ACB (Fig. 19.) represent the object-glass, and 

 d the eye-glass of a telescope, and PR a prism placed 

 to intercept part of the rays coming from an object, 

 suppose the sun, before they fall on the object-glass. 

 The rays EE proceeding from the eastern limb of the 

 sun, and refracted through the object- glass ACB with- 

 out passing through the prism, will form the corre- 

 sponding point of the sun's image at e ; and the rays 

 WW proceeding in like manner from the western limb 

 of the sun will be refracted to form the correspondent 

 point of the sun's image at tu. But the rays 2E, 2E, 

 2W, 2W, proceeding in like manner from the eastern 

 and western limbs of the sun, and falling on the prism 

 PR, and thence refracted to the object-glass ACB, will, 

 after refraction through it, form the correspondent 

 points of the sun's image at 2e, 2w. Let the refraction 

 of the prism be equal to the sun's apparent diameter : 

 in this case, at whatever distance the prism be placed 

 beyond the object-glass, the two images of the sun, 

 n> e, 2n> 2e, will touch one another externally at the point 

 eZtv ; for the rays 2W, 2W, proceeding from the wes- 

 tern limb of the sun, being inclined to the rays EE, 

 proceeding from the eastern limb in the angle of the 

 sun's apparent diameter, will, after suffering a refrac- 

 tion in passing through the prism equal to the sun's 

 apparent diameter, emerge from the prism, and fall 

 upon the object-glass parellel to the rays EE, and con- 

 sequently will have their focus 2ro coincident with the 

 focus e of the rays EE, and therefore the two images 

 of the sun, n e, 2tv2e, will touch one another external- 

 ly at the point e2w, and the instrument will measure 

 the angle EC2W, and that only. 



But if the prism be placed within the telescope, the 

 angle measured by the instrument will be to the re- 

 fraction of the prism as the distance of the prism from 



Double 



Image 



Mlcrom e- 



the focus of the object-glass is to the focal distance of 



the object-glass; or if two prisms be used to form the 



two images, with their refracting angles placed con- 



trary ways, as represented in Fig. 20. and 21. the angle 



measured will be to the sum of the refractions of the 



prisms as the distance of the prisms from the focus of CCCLXXV. 



the object-glass is to the focal distance of the object- Fig. 20 and 



glass. For let ACB (Fig. 20. ) represent the object- 21 - 



glass, and d the eye-glass of a telescope, and PR, RS, 



two prisms interposed between them, with their re- 



fracting angles turned contrary ways, and the common 



sections of their refracting planes touching one another 



at R. The rays proceeding from an object, suppose 



the sun, will be disposed, by the refraction of the ob- 



ject-glass, to form an image of the sun at the focus'; 



but part of them falling on one prism, and part on the 



other, will be thereby refracted contrary ways, so as 



to form two equal images n e, 2tv2e, which, if the re- 



fractions of the prisms be of proper quantities, will 



touch one another externally at the point e2tv. Let 



ECN be the axis of the pencil of rays EE proceeding 



from the sun's eastern limb ; and WCO the axis of the 



pencil of rays WW. proceeding from the sun's western 



limb ; and the point N the place where the image of 



the sun's eastern limb would be formed, and the point 



O v.'here that of the western limb would be formed, 



were not the rays diverted from their course by the re- 



fractions of the prisms. But, by this means, part of 



the rays EE, which were proceeding to N, falling on 



the prism PR, will be refracted to form an image of 



the sun's eastern limb at e, while others of the rays 



EE, which fall on the prism RS, will be refracted to 



form an image of the sun's eastern limb at 2e. In like 



manner, part of the rays W W, which were proceeding 



to form an image of the sun's western limb at O, fall- 



ing on the prism RS, will be refracted to form an 



image of the sun's western limb at 2ts coincident with 



e, the point of the image correspondent to the sun's 



eastern limb : while others of the rays WW, which 



fall on the prism PR, will be refracted to form the 



image of the sun's western limb at IT. The two images 



we, ZmZe, are supposed to touch one another externally 



at the point e2>. The ray EFR, which belongs to 



the axis ECN, and is refracted by the prism PR to e, 



undergoes the refraction NR e, which (because small 



angles are proportional to their sines, and the sine of 



NR e is equal to the sine of its supplement NRC) is to 



NCR as NC or C e is to NR or R e. In like manner, 



the ray WGR, which belongs to the axis WCO, and is 



refracted by the prism RS to 2w or e, undergoes the 



refraction ORe, which is to OC e as OC or Ce is to 



RO or Re: therefore, by composition, ORN the sum 



of the refractions ORe, NRe, is to OCN the sum of 



the angles OC e, NC e, or the sun's apparent diameter, 



as C e to R e ; that is, as the focal distance of the ob- 



ject-glass to the distance of the prisms from the focus 



of the object-glass. 



Or let the prisms PR, RS, be placed with their re- 

 fracting angles P, S, turned from one another as in Fig. Fig. 21. 

 21.: the refraction of the prism PR will transfer the 

 image of the sun from ON to m e, and the refraction of 

 the prism RS will transfer the image ON to 2w2e, the 

 two images 2rv2e, n> e, touching one another externally 

 at the point Ze tv. Let ECN, WCO, be the axes of the 

 pencils of rays proceeding from the two extreme limbs 

 of the sun, and N, O, the points where the images of 

 the sun's eastern and western limbs would be formed 

 by the object-glass, were it not for the refraction of the 

 prisms ; the ray EFR, which belongs to the axis ECN, 



