M I C R M E T E R. 



207 



Fit- tO. 



rig. si. 



and is refracted by the prism RS to 2, undergoes the 

 refraction NR 2e; and the ray WGR, which belongs to 

 the axis WCO, and is refracted by the prism PR to if, 

 undergoes the refraction OR tc. Now NC it, part of 

 the angle measured, is to NR Zt, the refraction of the 

 prism RS, as R to to C w ; and OC n>, the other part of 

 the angle measured, is to OR n, the refraction of the 

 i PR, in the same ratio of R ir to C w : therefore 

 OCN, the whole angle measured, is to ORN, the sum 

 of the refractions of the two prisms, as R m to C n ; 

 that is, as the distance of the prisms from the focus of 

 the object-glass to the focal distance of the object glass. 



When the prisms are placed in the manner repre- 

 sented in Fig. 20. the point e of the image it e is illu- 

 minated only by the rays which fall on the object- 

 glass between A and F, and the point 2w only by the 

 rays which fall on the object-glass between B and G. 

 Now the angles CRF, CRG, equal to the refractions 

 of the prisms, being constant, the spaces FC, CG, will 

 increase in proportion as the distances RF, RG, in- 

 crease, and the spaces AF, GB, diminish as much ; 

 and therefore, the images at the point of mutual con- 

 tact, *2ir, will be each illuminated by half the rays 

 which fall on the object-glass when the pri<ms are 

 placed close to the object-glass ; but will be enlightened 

 MM and leas the nearer the prisms are brought to the 

 focus of the object-glass. 



But when the prisms are placed in the manner shewn 

 in Fig 21. the images at the point uf contact, as the 

 prisms are removed from the object-glass towards the 

 eye-glass, will be enlightened with more than half the 

 rays that fall on the object-glass, and will be most en- 

 lightened when the prisms are brought to the focus 

 itself ; for the point 2e of the image tw2e will be en- 

 lightened by .-ill the rays EE that fall on the object- 

 glass between B and F, and the point tr of the image 

 tfe will be enlightened by all the rays WW which fal. 

 on the object-glass between A and G. But the differ- 

 ence of the illuminations is not very considerable in 

 achromatic telescopes, on account of the great aperture 

 of the object glass ; as the greatest space FG is to the 

 focal distance of the object-glass, as the sum of the 

 tines of the refractions of the prisms is to the radius. 



There is a third way, and perhaps the best, of plac- 

 ing the prisms, so as to touch one another along their 

 ides which are at right angles to the common sections 

 of their refracting planes. In this disposition of the 

 prisms, the images will be equally enlightened, namely, 

 each with half the rays which fall on the object glass, 

 wherever the prisms be placed between the object-glass 

 ami eye-glass. 



1 mm what has been shewn it appears, that this in- 

 strument, which may be properly called the prismatic 

 micrometer, will measure any angle that does not ex- 

 ceed the sum of the refractions of the prisms, except- 

 ing only very small angles, which cannot be taken 

 with it on account of the vanishing of the pent 

 rays at the juncture of the two prisms near the 

 ofthe object-glass ; that it will afford a very large scale, 

 namely, the whole focal length of the object-glass for 

 the greatest angle measured by it ; and that it will ne- 

 ver be out of adjustment ; as the point of the scale 

 where the measurement begins (or the point of O) an- 

 swers to the focus of the object-glass, which is a fixed 

 point for olntial objects, and a point very easily found 

 for terrestrial objects. All that will be necessary to be 

 lone, tn order to find the value ofthe scale of this mi- 

 cromotor, will be to measure accurately the distance of 

 from the focus when the instrument is set 



to measure the apparent diameter of any object sub- Double 

 tending a known angle at the centre of the object- ' n 

 glass, which may be easily found by experiment, as by ' "j* 

 measuring a base, and the diameter ot the object ob- ^_ - ^-f 

 served placed at the end of it, in the manner practised 

 with other micrometers : for the angle subtended by 

 this object will be to the angle subtended by a celes- 

 tial object, or very remote land object, when the dis- 

 tance of the prisms from the principal focus is the same 

 as it was found from the actual focus in the terrestrial 

 experiment, as the principal focal distance of the object- 

 glass is to the actual focal distance in the said experi- 

 ment. 



It will, I apprehend, be the best way in practice, in- 

 stead of one prism to use two prisms, refracting con- 

 trary ways, and so divide the refraction between them 

 (as represented in Fig. 20. and 21.) Achromatic 

 prisms, each composed of two prisms of flint and crown- 

 glass, placed with their refracting angles contrary ways, 

 will undoubtedly be necessary for measuring angles 

 with great prcci.-ion by this instrument. 



Two or more sets of prisms may be adapted to the 

 same telescope, to be used each in their turn, for the 

 more commodious measurement of different angles. 

 Thus it may be very convenient to use one set of prisms 

 for measuring angles not exceeding 36', and conse- 

 quently fit for measuring the diameters of the sun and 

 moon, and the lucid parts and distances of the cusps 

 in their eclipses ; and another set of prisms to measure 

 angles not much exceeding one minute, and conse- 

 quently fit for measuring the diameters of all the other 

 planets: This latter set of prisms will be the more 

 convenient for measuring small angles, on account of a 

 small imperfect ung the u-e of this microme- 



ter, as before mentioned ; namely, that angles cannot 

 be measured with it when the prisms approach very 

 near the focus of the object glass, the pencils of rays 

 being there lost at the point where the prisms touch 

 one another." 



This micrometer has not been found to answer in 

 practice. In addition to the ordinary unconnected co- 

 lours of the object glass, it it injured by the imcorrect- 

 ed colours of the achromatic prism, which most parti- 

 cularly affect the touching limbs. 



A catoptric double image micrometer analogous to 

 that of Dr. Maskelyne, but much more simple in its 

 construction, in consequence of no additional prisms, 

 lenses, or mirrors, being used, has lately been proposed 

 by Dr. Brewster. It is applied to the Newtonian te- 

 lescope, and has the advantage of not being affected by 

 any change in the focal length of the eye. An account of 

 this micrometer will be found in the Edinburgh I'/ulo- 

 tojitticul Journal for 1 820. 



In the year 177<>, the late ingenious Mr. Ramsden 

 communicated to the Royal Society an account of two 

 micrometers ; a catojtiric one, which formed two im- 

 ages by means of two semi-mirrors ; and a dioptric one, 

 which formed a double image by means of two semi- 

 lenses placed in the eye-piece of the telescope. 



The first of these instruments is represented in Plate RimtUen'. 

 CCCLXX V. Fig. 22, and has been thus described by its catoptric 

 inventor. " Beside the advantage it derives from the ">leron>c- 

 principle of reflection, of not being disturbed by the hete- p f 

 rogeneity of light, it avoids every defect of other mi- C ccL*xr. 

 cromcters, and can liave no aberration, nor any defect Fig. 99. 

 arising from the imperfection of materials or of execu- 

 tion ; as the extreme simplicity of its construction re- 

 quires no additional mirrors or glasses to those required 

 for the telescope ; and the separation of the images be- 



