This reticulum was much improved by our eminent countryman, Dr. Bradley. In order to avoid the incon venience of turning the telescope about its axis, he placed the ring a b c, (Plate CCCLXXV. Fig. 2.) of the reticulum, in a groove cut in the fixed ring ABC, and having confined it laterally by-three small plates of brass at A, B, C, he gave it a motion round the axis of the tube by the endless screw DEF, working in a tooth ed arch d e fixed to the moveable ring a b c. The hairs g h, i k cross one another at right angles at I, the centre of the rings ; and when the telescope is so placed that the range of a star falls upon f, let us suppose it to move in any line f g ; then, by turning the nut D, and conse quently the hair,/ d about the fixed point f, till it touches the star at q, it will then coincide with the direction of the star's motion, and then all other stars will move pa rallel to it. In order to find the difference of declination of two stars, he observes the times of their arrival at the edges of two slender brass bars g i o, g k p fixed to the ring a b c, and equally inclined to its diameter g at an angle of 26° 34', when/ k and/ i will be each one half of fg, and k i=f i. HmIce the difference of i and 1 n will be equal to f m, the difference of their heights : that is, the difference of the times of the tran sits of the stars over any two bars i k and 1 a will be the difference of their declination as already explained.
A very simple and useful micrometer, invented by M. Cavallo, is represented in Plate CCCLXXV. Fig. 3. It consists of a thin and narrow slip of mother-of pearl, finely divided into 200dth parts of an inch, by lines which reach from one edge to near the middle of the scale. It is about the 24th part of an inch broad, and its thickness is equal to that of common writ ing paper. The simplest way of fixing it, is to stick it by strong cement, on the diaphragm or field bar, placed in the focus of the eye-glass next the eye. The micrometer which M. Cavallo adapted to a three fret achromatic telescope, magnifying about 84 times, had each of its divisions nearly equal to a minute, and as part ol a division could be estimated by the eye, it was capable ol measuring angles within se conds of a degree. Al. Cavallo determines the value of the divisions, by observing the space which any number of divisions subtends at a measurable distance, and computing trigonometrically the angle subtended by that space. It is prelerable, however, in all cases, to ascertain the angular extent of the field of view by tne time of the passage ol an equatorial star, and to obset ve the number ol divisions of the micrometer which correspond to that angle.
"This simple micrometer," says Dr. Brewster, "is very convenient in portable telescopes. %viler:: the eye-piece has a motion about its axis; but in telescopes support ed upon stands, wnere the eye-piece is moven by a rack and pinion, the slip of mother-of-pearl cannot turn round upon its axis, and, consequently, can only measure angles in one direction. This difficulty., in
deed, might be surmounted by a mechanical contri vance for turning the diaphragm about its centre, or, more simply, by giving a motion of rotation to the tube which contains the first and second eyeglasses. As such a change in the eye-piece, however, is often inconvenient and difficult to be made, Mr. Cavallo's micrometer has this great disadvantage, that it cannot he used in reflecting telescopes, or in any achromatic telescope where the adjustment of the eye-piece is ef fected by rack-work, unless the structure of these in struments is altered for the purpose. Another disad vantage of this micrometer arises from the slip of mo ther-of-pearl passing through the centre of the lick!. The picture in the focus of the eye-glass is broken into two parts, and the view is rendered still more un pleasant by the inequality of the segments into which the field is divided. In addition to these disadvantages, the different divisions of the micrometer are at unequal distances from the eye-glass which views them, and therefore can neither appear equally distinct, nor sub tend equal angles at the eye." In order to remedy these inconveniences, Dr. Brew ster was led, in 1805, to contrive the circular mother of-pearl micrometer, which is free of all these disad vantages, and has likewise the benefit of a kind of di agonal scale, increasing in accuracy with the angle to be measured. This micrometer, which he has often used, both in determining sm ill angles in the heavens, and such as are subtended by terrestrial objects, is re presented in Plate CCCLXXV. Fig. 4. which exhibits its appearance in the focus of the first eye-glass. The black ring, which forms part of the figure, is the dia phragm, and the remaining part is an annular portion of mother-of-pearl, having its interior circumference divided into 360 equal parts. The mother-of-pearl ring, which appears connected with the diaphragm, is com pletely separate from it, and is fixed at the end of a brass tube, which is made to move between the third eye-glass and the diaphragm, so that the divided cir cumference may be placed exactly in the focus of the glass next the eye. When the micrometer is thus fit ted into the telescope, the angle subtended by the whole field of view, or by the diameter of the innermost circle of the micrometer, must be determined either by mea suring a base, or by the passage of an equatorial star ; and the angles subtended by any number of divisions or degrees will be found by a table constructed in the following m Inner.