.540
MIC
bright in every part of the field of the telescope, Fig. 10, repre-sents the glasses of a refracting telescope ; xy, the principal pen-cil of rays from the object-glass o\ 11 and u u, the axis of the twooblique pencils; a, the first eye-glass; m, its conjugate focus orthe place of the micrometer ; b the second eye-glass ; c the third ;and d the fourth, or that which is nearest the eye. Let p be thediameter of the object-glass, e the diameter of a pencil at m, and/the diameter of the pencil at the eye ; it is evident, that the axisof the pencils from every part of the image will cross each other atthe point m ; and e, the width of the micrometer-glass, is top thediameter of the object-glass as m a is to g n, which is the propor-tion of the magnifying power at the point m ; and the error causedby an imperfection in the micrometer-glass placed at m will he tothe error, had the micrometer been at o, as m is top. Fig. 11,represents the micrometer, formed by a convex or concave lensdivided into two equal parts by a plane across its centre; one ofthese semi-lenses is fixed in a frame B, and the other in the frameE; which two frames slide on a plate H. and are pressed againstit by thin plates a a; the frames B and K are moved in contrarydirections by turning the button D ; I, is a scale of equal parts onthe frame B; it is numbered from each end towards the middlewith 10, 20, &c. There are two verniers on the frame E, one atM and the other at N, for the convenience of measuring the di-ameter of a planet, &<:. on both sides the zero. The first divisionon both these verniers coincides at the same time with the two ze-ros on the scale L ; and if the frame be removed towards theright, the relative motion of the two frames is shewn on the scaleL by the vernier M ; but if the frame B be moved towards theleft, the relative motion is shewn by the vernier N. This micro-meter has a motion round the axis of vision, for the convenienceof measuring the diameter of a planet, &c. in any direction, byturning an endless screw F ; and the inclination of the diametermeasured with the horizon is shewn cn the circle g by a vernier onthe plate V. The telescope may be adjusted to distinct vision bymeans of an adjusting screw, which moves the whole eye-tube withthe micrometer nearer or farther from the object-glass, as tele-scopes are generally made ; or the same effect may be producedin a belter manner, without moving the micrometer, by sliding thepart of the eye-tube m on the part n, by help of a screw or pinion.The micrometer is made to take off occasionally from the eve-tube, that the telescope may be used without it. Mr. Herschelhaving long had much occasion for micrometers that would mea-sure exceeding small distances exactly, was led to bend his atten-tion to the improvement of these instruments; and .the result ofhis endeavours has been a very ingenious instrument called a lamp-micrometer, which is not only free from most of the imperfectionsof other micrometers, but also possesses the advantages of a•very large scale. This instrument is described iri the Philos.Trans, for 1782. In the Philos. Trans, for 1791, a very simplemicrometer for measuring small angles with the telescope is de-scribed by Mr. Cavallo; who introduces his description with thefollowing observations upon the different sorts of teiescopical mi-crometers in use: “ These instruments may be divided into twoclasses; namely, those which have not, and those which have,some movement amongst their parts. The micrometers of the for-mer sort consist mostly of fine wires or hairs, variously disposed,and situated within the telescope, just where the image of the ob-ject is formed. In order to determine an angle with those micro-meters, a good deal of calculation is generally required. The mi-crometers of the other sort, of which there is a great variety, some Ibeing made with moveable parallel wires, others with prisms, othersagain with a combination of lenses, and so on, are more or less jsubject to several inconveniences, the principal of which are thefollowing: 1. Thetr motions generally depend upon the action of
a screw ; and of course the imperfections of its threads, and thegreater or less quantity of lost motion, which is observable inmoving a screw, especially when small, occasion a considerableerror in the mensuration of angles. 2. Their complication andbulk rendersthem of difficult application to a variety of telescopes,especially to the pocket ones. 3. They do not measure the anglewithout some loss of time, which is necessary to turn the screw, orto move some other mechanism. 4. And lastly, they are con-siderably expensive, so that some of them cost even more than atolerably good telescope.” After having had long in view (ourauthor informs us) the construction of a micrometer which might
be in part at least, if not entirely, free from all these objections ihe, after various attempts, at last succeeded with a simple contri-vance, which, after repeated trials, has been found to answer thedesired end, not only from his own experience, but from that alsoof several friends, to whom it has been communicated. Thi*micrometer, in short, consists of a thin and narrow slip of mother-of-pearl finely divided, and situated in the focus of the eye-glassof a telescope, just where the image of the object is formed. Itis immaterial whether the telescope be a refractor or a reflector,provided the eye-glass be a convex lens, and not a concave one asin the Galilean construction. The simplest, and therefore the best,way of fixing it is to stick it upon the diaphragm which generallystands within the tube and in the focus of the eye-glass. Whenit is thus fixed properly in this situation, if you look through theeye-glass, the divisions of the micrometrical scale will' appearverv distinct, unless when the diaphragm is not exactly in thefocus; in which case, the micrometrical scale must be placed ex-actly in the focus of the eye-glass, either by pushing the dia-phragm backwards or forwards, when that is paacticable ; or elsethe scale may be easily removed from one or the other surface ofthe diaphragm by the interposition of a circular piece of paper orcard, or by a hit of wax. This construction is fully sufficient,,when the telescope is always to be used by the same person ; butwhen different persons are to use it, then the diaphragm which sup-ports the micrometer must be constructed so as to he easily movedbackwards or forwards, though that motion needs not he greaterthan about a tenth or an eight of an inch. This is necessary, be-cause the distance of the focus of the same lens appears differentto the eyes of different persons; and, therefore, whoever is goingto use the telescope for the mensuration of any angle, must firstof all unscrew the tube which contains the eye-glass of the micro-meter from the rest of the telescope, and, looking through the eye?glass, must place the micrometer where the divisions of it may ap-pear quite distinct to his eye. In case any person should not liketo see always the micrometer in the field of the telescope, thenthe micrometrical scale, instead ot being fixed to the diaphragm,may be fitted to a circular perforated plate of brass, woodj oreven paper, which may be occasionally placed upon the said dia-phragm. Mr. Cavallo has made several experiments to deter-mine" the most useful substance for this micrometer. Glass , whichhe had successfully applied fora similar purpose to the compoundmicroscope, seemed at first to be the most promising; but it wasat last rejected after several trials: for the divisions upon it gene-rally are either too fine to be perceived, or too rough ; and thoughwith proper care and attention the divisions may be proportionedto the sight, yet the thickness of the glass itself obstructs in somemeasure the distinct view of the object. Ivory, horn, and wood,were found useless for the construction of this micrometer, on ac-count of their bending, swelling, and contracting, very easily ;whereas mother-of-pearl is a very steady substance, the divisionsupon it may be marked very easily, and when it is made as thin ascommon writing paper it has a very useful degree of transparency.Fig. 12, exhibits this micrometer-scale,, but shews it four timeslarger than the real size of one, which he has adapted to a threc-feet-achromatic telescope that magnifies about 84 tildes. It issomething less than the 24th part of an inch broad ; its thickness isequal to that of common writing paper; and the length of it isdetermined by the aperture of.the diaphragm, which limits thefield of the telescope. The divisions upon it are the200ths of aninch, which reach from one edge of the scale to about the middleof it, excepting every fifth and 10th division, which are longer*The divided edge of it passes through the centre of the field ofview, though this is not a necessary precaution in the constructionof this micrometer. Two divisions of the above described scalein my telescope are very nearly equal to one minute; and as aquarter of one of those divisions may be well distinguished by es-timation, therefore an angle ol one-Sth part of a minute, or of7 "{,may be measured with it. When a telescope magnifies more,the divisions of the micrometer must be more minute ; and Mr.Cavallo finds, that when the focus of the eye-glass of the tele-scope is shorter than half an inch, the micrometer may be dividedwith the five hundredth of an inch ; by means of which, and tfietelescope magnifying about 200 times, one may easily and accu-rately measure an angle smaller than half a second. On the otherhand; w hen the telescope docs not magnify above 30 times, the
divisiow*