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scale can never be out of adjustment, as the point 0, where themeasurement begins, answers to the focus of the object-glass,which is a fixed point for all distant objects, and we have only tofind the value of the scale answering to some known angle: forinstance, bring two limbs of the sun’s images into contact, andmeasure the distance of the prisms from tTie focus, and look inthe nautical almanac for the sun’s diameter, and you get the value ofthe scale. In fig. 6, the limb Q, of the image Qc, is illuminatedhy the rays falling on the object-glass between A and F, and onthe image Qd by those falling between B and G ; but in fig. 7, thesame limbs are illuminated by the rays falling between B and F,A and G respectively, and'therefore will be more illuminatedthan in the other case; but the difference is not considerable, inachromatic telescopes, on account of the great aperture of the ob-ject-glass compared with the distance FG. It might be conve-nient to have two sets of prisms, one for measuring angles not ex-ceeding 30’, and theretote fit for measuring the diameters of thesun and moon, and the lucid parts and distances of the cusps intheir eclipses; and another for measuring angles not much greaterthan V, for the eonveniency of measuring the diameters of theplanets. For as QC : QIl: : sum of the refractions of the prisms :angle aCb, the apparent diameter of the object, it is evident thatif you diminish the third term, you must increase the second indie same ratio, in order to measure tiie same angle: and thus bydiminishing the refractive angle of the prisms, you throw themfurther from Q, and consequently avoid the inconvenience ofbringing them nearer to Q, for the reason afterwards given ; andat the same time you will increase the illumination in a small de-gree. The prisms must be achromatic, each composed of twoprisms of flint and crown glass, placed with their refracting anglescontrariways, otherwise the images will he coloured. In the con-struction here described, the angle measured becomes evanescentwhen the prisms come to the principal focus of the object-glass,and therefore 0 on tin: scale then begins: but if the prisms beplaced in the principal focus they can have no effect, because thePencil of rays at the junction of the prisms would then vanish, andtherefore it is not practicable to bring the two images togetherto get 0 on the scale. Dr. Maskeiyne, therefore, thought ofplacing another pair of prisms within, to refract the rays beforethey came to the other prisms, bv which means the two imagesWould be formed into one before they came to the principal fo-cus, and therefore 0 on the scale could be determined. But to^vokl the error arising from the multiplication of mediums, he, in-stead of adding another pair of prisms,, divided the object-glassthrough its centre, and sliding the segments a little it separatedthe images, and then by the prisms he could form one image verydistinctly, and consequently could determine 0 on the scale; forhy separating the two segments you form two images, and youwill separate the'two pencils so that you may move up the twoPrisms, and the two pencils will fall on each respectively, anil therivo images may be formed into one. In the instrument whichIlr. Maskeiyne had made, 0 on the scale was chosen to be aboutf of the focal length of the object-glass, and each prism refracted^7'. By these means all angles are measured down to 0. In thechilos. 'Frans, for 1 779, Mr. Ilamsden has described two new mi-crometers,'which he contrived with a view of remedying the de-lects of the object-glass-micrometer. 1. One of these is a catop-tric micrometer, which, beside the advantage it derives from thePrinciple of reflection, of not being disturbed by the heterogeneity°f light, avoids every defect of other micrometers, anil can have’Hi aberration, nor any defect arising from the imperfection of ma-terials or of execution ; as the extreme simplicity of its construc-tion requires no additional mirrors or glasses to those required forthe telescope ; and the separation of the image being effected bythe inclination of the two specula, and not depending on the focus°t any lens or mirror, any alteration in the eye of an observer''aniiot affect the angle measured. It lias peculiar to itself the ad-vantages of an adjustment, to make the images coincide in a di-action perpendicular to that of their motion ; anil also of measur-the diameter of a planet on both sides of the zero, which willa Ppear no inconsiderable advantage to observers, who know bow*”uch easier it is to ascertain the contact of the external edges ofwo images than their perfect coincidence. A, fig. 8, representsj ® small speculum divided into two equal parts ; one of which«sed on the end of the arm B; the other end of the arm is fixed
on a steel axis Z, which crosses the end of the telescope C. Theother half of the mirfior A is fixed on the arm D, which arm at theother end terminates in a socket y, that turns on the axis Z ; botharms are prevented from betiding by the braces a a. G representsa double screw, having one part e cut into double the number ofthreads in an inch to that of the part g : the part e having 100threads in one inch, and the part g 50 only. The screw e worksin a nut F in the side of the telescope, while the partg turns in anut H, which is attached to the arm B ; the ends of the arms Band D, to which the mirrors are fixed, are separated from eachother by the point of the double screw pressing against the stud A,fixed to the arm D, and turning in the nut H on the arm B. Thetwo arms B and D are pressed against the direction of the doublescrew e g by a spiral spring within the part n, by which means altshake or play in the nut H, on which the measure depends, is en-tirely prevented. From the difference of the threads on the screwat e and g, it is evident, that the progressive motion of the screwthrough the nut will be half the distance of the separation of thetwo halves of the mirror; and consequently the half-mirrors willbe moved equally in contrary directions from the axis of the tele-scope C. l lie wheel V fixed on the end of the double screw liasits circumference divided into 100 equal parts, and numbered atevery fifth division with 5, 10, &c. to 100, and the index I shewsthe motion of the screw' with the wheel round its axis, while thenumber of revolutions of the screw is shwen by the divisions onthe same index. The steel-screw at R may be turned by the keyS, and serves to incline the small mirror at right angles to the di-rection of its motion. By turning the finger-head T, tig. 9, thedye-tube P is brought nearer or farther from the small mirror, toadjust the telescope to distinct vision ; and the telescope itselflias a motion round its axis for the ijonveniency of measuringthe diameter of a planet in any direction. The inclination of thediameter measured with the horizon is shewn in degrees and mi-nutes by a level and vernier on a graduated circle, at the breechof the telescope. Besides the table lor reducing the revolutionsand parts of the screw to minutes, seconds, &c. it may require atable for correcting a very small error which arises from the ec-centric motion of the half-mirrors. By this motion their centres ■of curvature will (when the angle to be measured is large) approach -a little towards the large mirror: the equation for this purpose insmall angles is insensible ; but when angles to be measured exceed 'ten minutes, it should not be neglected. Or, the angle measuredmay be corrected by diminishing it in the proportion the versed sineof the angle measured, supposing the eccentricity radius, bears tothe focal length of the small mirror. Mr. Ramsden preferredCa-segrain’s construction of the reflecting telescope to either the •Gregorian or Newtonian ; because in the former, errors caused byone speculum are diminished by those in the other. From a pro-perty of the reflecting telescope (which, he observes, has not beenattended to,) that the apertures, of the two specula are to eachother very nearly in the proportion of their focal length, it fol-lows, that their aberrations will be to each other in the same pro-portion ; and these aberrations are in the same direction* if the twospecula are both concave; or in contrary directions, if one spe-culum is concave and the other convex. In the Gregorian con-struction, both specula being concave, the aberration at the secondimage will be the sum of the aberrations of the two mirrors ; butin the Cassegrain construction, one mirror being concave and theother convex, the aberration at the second image will be the diffe-rence between their aberrations. By assuming such proportionsfor the foci of the specula as are generally used in the reflectingtelescope, which is about as 1 to 4, ^the aberration in the Casse-grain construction will be to that in Gregorian as 3 to 5. 2. The
other is a dioptric micrometer, or one suited to the principle of'j refraction. This micrometer is applied to the erect eye-tube of a ■refracting telescope, and is placed in the conjugate locus of thefirst eye-glass: in which position, the image being considerablymagnified before it comes to the micrometer, any imperfection in 1its glass will be magnified only by the remaining eve-glasses,which in any telescope seldom exceeds five or six times. By thisposition also the size of the micrometer-glass will not be the onelOOdth part of the area which w’onld be required if it wms placedin the object-glass; and notwithstanding this great disproportionof size, which is of great moment to tne practical optician, .thesame extent of scale is preserved, and the images are uniformly
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