MICROMETER. 



213 



proached or removed to the same distance of the two 

 stars, so that the two lucid points may be exactly co- 

 vered by, or coincide with the stare. A little practice in 

 this business toon makes it easy, especially to one who 

 has already been used to look with both eyes open. 



What remains to be done is very simple. With a 

 proper rule, divided into inches and 40th parts, the dis- 

 tance of the lucid points is taken, which may be done 

 to the greatest nicety, because, as observed before, the 

 little boles are made with the point of a very fine needle. 

 The measure thus obtained is the tangent of the mag- 

 nified angle under which the stars are seen, to a radius 

 of 10 feet; therefore, the angle being found, and di- 

 vided by the power of the telescope, gives the real an- 

 gular distance of the centres of a double star. For in- 

 stance, Se| ' -l, Sir William Herschel measured 

 Herculis with thi-, instrument. Having caused the 

 two lucid points to coincide exactly with the stars centre 

 on centre, be found the radius, or diftmrf of the central 

 lamp from the eye, 10 feet 4.15 inches ; the tangent or 

 di*nnr of the two lucid points M.fi fortieth part* of an 

 inch ; this gives the magnified angle 55', and dividing 

 by the power 460, which he used, he obtained 4* S4' r/ 

 for the distance of the centres of the two stars. The 

 scale of the micrometer at this very convenient dis- 

 tance, with the power of -WJO( which his telescope bears 

 so well on the fixed stars that for near a twelvemonth 



She hardly used any other) is above a quarter of an 

 to a second ; and by putting on his power of 9M, 

 which in very fine evening* is exOcmely distinct, be ob- 

 tained a scale of more than half an inch to a second, 



whereas the most perfect of his former micrometers, 

 with the same instrument, had a scale of less than the 

 2000th part of an inch to a second. 



The measures of this micrometer are not confined to 

 double stars only, but may be applied to any other ob- 

 jects that require the utmot accuracy, such as the dia- 

 meters of the planet* or their satellites, the mountains 

 of the moon, the diameti -tan, &c. For 



instance, Oct. -'*, 1 7 .ilium Herschel measured 



the apparent diameter of I.\ ne ; and judging it of the 

 greatest importance to increase his scale as much as con- 

 venient, he placet! tin- micrometer at the greatest conve- 

 nient distance and (with some trouble, for want of longer 

 handles, which might easily be added ) took the diameter 

 of this star by removing the two lucid point* to such a 

 distance as just to inclose the apparent diameter. When 

 be measured his radius, it was found to be 82 feet 6 

 inches. The distance of the two lucid points was 

 about three inches ; for extreme nicety could not be ob- 

 tained in thi* observation, on account of the very great 

 power he used, which was 6450. From these measures 

 we have the magnified angle 38' 10" : this divided by 

 the power gives O".S55 for the apparent diameter of 

 Lyrz. The scale of the micrometer, on this occasion, 

 was no less than 8.443 inches to a second, as will be 

 found by multiplying the natural tangent of a second 

 with the power and radius in indies. In Nov. 1781, he 

 measured the diameter of the new star ; but the air 

 was not very favourable, for this singular star was not 

 so distinct with 227 that evening as it generally is with 

 460 : therefore, without laying much stress on the ex- 

 actness of the observation, he only report* it, to ex- 

 emplify the use of his micrometer. His radius was 

 35 feet 1 1 inches. The diameter of the star, by the 

 distance of the lucid points, was 2.4 inches, and the 

 power he used 287 : hence the magnified angle is found 

 1$, and the real diameter of the star 5".022. The 

 scale of this measure is .474 millesimals of an inch, or 

 almost half an inch to a second." 



A lucid disc micrometer was also used by M. Schroe- Lucid. 

 ter of Lilienthal, in his observations on the new pla. Diso < u" 

 nets, but we are not acquainted with the principles of 

 its construction. 



. . _ 



A luminous image micrometer, in which the angle, 

 subtended by two lucid points, is measured by expand- 

 ing them into circular discs, and marking the instant 

 of contact, has been described by Dr. Brewster in his 



Treatise on AVar Philosophical Instruments, p. 40. 



CHAP. VIII. 

 On Doubly Hrfracting Micrometers. 



The first person who proposed to employ the sepa- Doubly n- 

 ration of two images, formed by double refraction, firming mi- 

 as the principle of a micrometer, was the late inge- cr o me ' er - 

 nious Abbe Rochon. On the 5th March 1 777, Messrs. 

 Leroi, Lemonnier, and Condorcet, gave a favourable 

 report of this new invention, which was brought to a 

 considerable degree of perfection by successive im- 

 provements with which M. Rochon was constantly 

 occupied till the time of his death, which took place 

 in 1817. 



If we suppose ABC, Plate CCCLXXVI. Fig. 19. PIATE 

 a priiro of rock crystal, so cut out of the bexaedral CCCLXXVI. 

 priim in which this substance is generally formed, v> 8- l9 - 

 that AC is the axis of the prism, and BCD another 

 prism, so cut out of the same crystal, that BC is the 

 axis of the prism, then a ray of light UR incident per- 

 pendicularly at H, will go on to It' without being di- 

 vided into two pencils, aa the doubly refracting force 

 vanishes in the direction of the axis; but when it 

 reaches R' it will be divided into two pencils 11' If, 

 R' {, one of which, R R", the ordinary pencil will go 

 on in the direction R' E without any deviation, as it is 

 in no way affected with the doubly refracting force of 

 the second prism BCD, while the extraordinary pencil 

 R' { will deviate from the line R K, in virtue oi 

 doubly refracting force of the second prism BCD. 

 An eye placed at E will obviously not receive the two 

 rays U'K and R' i, hut if we draw E r", r" r' , r' r re- 

 spectively parallel to i j, r R', r" R' R, a ray rr incident 

 perpendicularly at r, will give an extraordinary ray 

 r" E, which will reach the eye E at the same time 

 with the ordinary ray R' E, and the observer will see 

 two distinct images of the object from which these 

 rays proceed. 



In order to apply this compound prism to the pur- 

 poses of a micrometer, M. Rochon introduces it be- 

 tween the object-glass and the eye-glass of an astrono- 

 mical telescope, as shewn in Fig. 20. ; and by moving Fig. 20. 

 it along the axis of the telescope, the angular separa- 

 tion of the two images of the object *t is made to vary 

 in a manner similar to what has been already describ- 

 ed in the prismatic micrometer of Dr. Maskelyne. 



In the year 1812, M. Rochon proposed another form 

 of his micrometer, from which he expected great ad- 

 vantages. He took a parallelepiped of rock crystal, 

 formed of two prisms, cut with angles of about 30", 

 and so as to make the images of the sun overlap one 

 another about five minutes. W hen joined together 

 by mastic, it was ground into a convex lens, and was 

 united with a concave lens of glass, so as to form an 

 achromatic object-glass. This object-glass, which had 

 focal length of about three decimetres, separated the 

 centres of the images of the sun about 28 minutes. 

 He then adapted to this object-glass a common mi- 

 crometer, which measured angles of 10 minutes, and 

 he had thus three decimetres or 10 minutes to com. 

 plete the measure of the diameters of the sun or moon. 



