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t'.on. But, besides these two uses to which the instrument seemswell adapted, Dr. Maskelyne lias shewn, in the Philos. Trans, for5771, how it may be applied to find the difference of right ascen-sions and declinations. For this purpose, two wires at right anglesto each other, bisecting the field of view, must be placed in theprincipal focus of the eye-glass, and moveable about in their ownplane. LetHCRc, fig. 2, be the field of view, HR and Cc thetwo wires; turn the wires till the westernmost star (which is thebest, having further to move) run along IlOII; then separate thetwo segments, and turn about the micrometer till the two imagesof the same star lie in the wire Cc; and then, partly by separatingthe segments, and partly bv raising or depressing the telescope,bring the two innermost images of the two stars to appear and runalong KOH, as a, b, and the vernier will give the difference oftheir declinations; because, as the two images of one of the starscoincided with Cc, the image of each star was brought perpendi-cularly upon IIR, or to HR, in their proper meridian. And, forthe same reason, the difference of their times of passingthe wire COcwill give their difference of right ascensions. These operationswill be facilitated, if the telescope be mounted on a polar axis.If two other wires KL, MN, parallel to Cc, be placed near II andIt, the observation may be made on two stars whose difference ofmeridians is nearly equal to HR, the diameter of the field of view,by bringing the two images of one of the stars to coincide withone of these wires. If two stars be observed whose difference ofdeclination is well settled, the scale of the micrometer will beknown. It lias hitherto been supposed, that the images of the twostars can be both brought into the field of view at once upon thewire HOR : but if they cannot, set the micrometer to the dif-ference of their declinations as nearly as you can, and make theimage which comes first run along the wire llOR, by elevatingor depressing the telescope ; and when the other star comes in, ifit do not also run along HOR, alter the micrometer till it does,and half the sum of the numbers shewn by the micrometer, at thetwo separate observations of the two stars on the wire HOR, willbe the difference of their declinations. That this should be true,it is manifestly necessary that the two segments should recedeequally in opposite directions; and this is effected by Mr. Dollond in his new improvement of the object-glass-micrometer. The dif-ference of right ascensions and declinations of Venus or Mercuryin the sun’s disk and the sun’s limb may be thus found. Turn thewires so that the north limb n of the sun’s image AB, fig. 3, or thenorth limb of the image V of the planet, may run along the wireR H, which therefore will then be parallel to the equator, and con-sequently Cc a secondary to it; then separate the segments, andturn about the micrometer till the two images Vo of the planetpass Cc at the same time, and then by separating the segments,bring the north limb of the northernmost image V of the planet totouch HR, at the time the northernmost limb ji of the southernmostimagcABofthesun touches it,and the micrometer shews the differenceof declinations of the northernmost limbs of the planet and sun, forthe reason formerly given, we having brought the northernmostlimbs of the two innermost images V and AB to HR, these twobeing manifestly-interior to s; and the northernmost limb N of theimage PQ. In the same manner we take the difference of decli-nations of their southernmost limbs ; and half the dillerence of thetwo measures, (taking immediately one after another) is equal tothe difference of the declinations of their centres, without anv re-gard to the sun’s or planet’s diameters, or error of adjustment ofthe micrometer ; for as far as it affects both equally, the differenceis the same as if (here were no error: and the difference of thelimes of the transits of the eastern or western limbs of the sun andplanet over Cc gives the difference of their right ascensions. In-st- ad of the difference of right ascensions, the distance ef the planetfrom the sun’s limb, in lines parallel to the equator, may he moreaccurately observed thus: Separate the segments, and turnabouttlve wires and micrometer, so as to make both imagesV.r, fig. Trimalong IiB, or so that the two intersections I, T, of the sun’s imagemay pass Cc at the same time. Then bring the planet’s and sun’slimbs into contact, as at V, and do tiie same for the other limb ofthe sun, and half the difference gives the distance of the centre of(he planet from the middle of the chord on the sun’s disk parallelto the equator, or the difference of the right ascensions of theircentres, allowing for the motion of the planet in the interval of theobservations, without any regard to the error of adjustment, for the
same reason as before. For if you take any point in the chord ofa circle, half the difference of the two segments is clearly the dis-tance of the point from the middle of the chord ; and as the planetruns along HB, the chord is parallel to the equator. In like nian-I ner, the distances of their limbs may be measured in lines perpen-dicular to the equator, by bringing the micrometer into the po-sition already described, and instead of bringing V to HR, fig. 5*separate the segments till the northernmost limbs coincide as at V ;and in the same manner make their southernmost images to coin-cide, and half the difference of the two measures, allowing for theplanet’s motion, gives the difference of the declinations of theircentres. Hence the true place of a planet in the sun’s disk mayat any time of its transit be found; and consequently the nearestapproach, to the centre and the time of ecliptic conjunction muybe deduced, although the middle should not be observed. Buthowever valuable the object-glass-micrometer undoubtedly is,difficulties sometimes have been found in its use, owing to tiiealteration of the focus of tiie eye, which will cause it togive different measures of the same angle at different time*. Forinstance, in measuring the sun’s diameter, the axis of the pencilcoming through the two segments from the contrary limbs of thesun, as I’F, QF , fig. 1, crossing one another in the focus F underan angle equal to tiie sun’s semidiameter, the union of the limbscannot appear perfect, unless tiie eye be disposed to see objectsdistinctly at tiie place where tiie images are formed ; for if the eyebe disposed to see objects nearer to orfurther off than that place,in the latter case tiie limbs will appear separated, and in tiie formerthey will appear to lap over. 'I his imperfection led Dr. Maske-lyne to inquire whether some method might not be found of pro-ducing two distinct images of tiie sun, or any oilier object,by bringing the axis of each pencil to coincide, or very nearlyso, before the formation of the images, by which means thelimbs when brought together would not he able to appear se-parated from any alteration of the eye ; and this lie found wouldbe effected by tiie refraction of two prisms, placed either withoutor within the telescope ; and on this principle, placing the prismswithin, he constructed a new micrometer, and had one executedby Mr. Dollond , which upon trial answered as he expected. Theconstruction is as follows : let AB be the object-glass; see fig. 6,and 7; ab tiie image, suppose of the sun, which would have beenformed in the principal iocus Q ; hut let tiie prisms PR, SR, beplaced to intercept the rays, and let EF, \VG, lie two rays pro-ceeding from tiie eastern and western limbs of the sun, converg-ing, alter refraction at the lens, to a and b ; and suppose the re-fraction of the prisms to be such, that in fig. (5, the ray EFR, af-ter refraction at R by the prism PR, may proceed in the directionRQ ; and as all tiie rays which were proceeding to a suffer thesame refraction at the prism, they will all be refracted to Q ; atultherefore, instead of an image ab, which would have been formedby Hie lens alone, an image Qc is formed by those rays which fallon the prism PR ; and for the same reason, ihe rays falling on theprism SR will form an image Qd : and in fig. 7, tiie image of thepoint b is brought to Q, by tiie prism PR, and consequently animage Q d is formed by those rays which fall on PR : and for thesame reason, an image Qc is formed by the rays falling on SR-Now in both cases, as the rays EFR, M GR, coming from the *woopposite limbs of ihe sun, and forming the point ot contact of thetwo limbs, proceed in the same direction KQ, they must thus ac-company each other through the eye-glass, and also through theeye, whatever refractive power it lias, and therefore to every eyetiie images must appear to touch. Now the angle 'alib is twice therefraction of tiie prism, and the angle aCb is the diameter ot thesun ; and as these angles are very small, and have tiie same rsub-lense ab, we have the angle tilib : angle aCb : : CQ : HQ. —Nowas CQ is constant, and also the angle alib, being twice the refrae-I lion of tiie prism, the angle aCb varies as 11Q. Hence the e*'"I tent of the scale for measuring angles becomes the focal length °*j the object-glass, and tiie angle measured is in proportion to thedistance of the prisms from the principal locus of the object-glass*and the micrometer can measure all angles (very small ones ex-cepted, for the reason afterwards given,) which do not exceed thesum of the refractions of the prisms; for the angle aCb, the di-ameter of the object to be measured, is always less than the angleali'b, tiie sum of the refractions of the prisms, except when tj lCprisms touch the object-glass, and then they become equal. 'I ,