MICROMETER. 



199 



Uarwh!e another at right angles at f, the centre of the rings ; 

 .Mierome- ant ] wnen the telescope is so placed that the image of a 



._'"*' tar falls upon /; let us suppose it to move in any 



line fe ; then by turning the nut D, and consequent- 

 ly the hair fd about the fixed point f, till it tout-In-- the 

 star at ij, it will then coincide with the direction of the 

 tar's motion, and then all other star* will move paral- 

 lel 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 bras* bars g i to, g k p fixed to 

 the ring a be, and equally inclined to its diameter g h, 

 at an angle of 26" 34', when /'X and / i will be each one 

 half ofj'g, and k i=/"i. Hence the difference of i X- 

 and / n will be equal to j'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 / M will be 

 the difference of their declination, as already ex- 

 plained. 



A very simple and useful micrometer, invented by 

 .ivallo, is represented in Fig. 3. It consist* of 

 a thin and narrow slip of mother-of-pearl, finely di- 

 vided into i-'OOdth parts of an inch, by lines which 

 reach from one edge to near the middle of the 

 scale. It i* about the 24th part of an inch broad, 

 and it* thickness i* equal to that of common writ- 

 ing paper. The simplest way of fixing it, is to 

 tick 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 

 feet achromatic telescope, magnifying about 84 times, 

 had each of it* division* nearly equal to a minute, and 

 a* |th part of a division could be estimated by the 

 eye, it was capable of measuring angle* within 7 J se- 

 conds of a degree. M. Cavallo determines the value 

 of the divisions, by observing the (pace which any 

 number of divisions subtend* at a measurable distance, 

 and computing trigonomctrically the angle lubtended 

 by that space. It it preferable, however, in all cases, 

 to ascertain the angular extent of the field of view, 

 by the time of the passage of an equatoreal star, ami 

 to observe the number of division* of the micrometer 

 which correspond to that angle. 



" This simple micrometer," says Dr.Brewster, "u very 

 convenient in portable telescopes, where the eye-piece 

 ha* a motion about it* axis ; but in telescope* lupport- 

 ed upon stands, where the eye-piece i* moved 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 contriv- 

 ance for turning the diaphragm about it* centre, or 

 more simply, by giving a motion of rotation to the 

 tube which contains the first and second eye-glasses. 

 As such a change in the eye-piece, however, i often 

 inconvenient and difficult 'to be made, Mr. Cavallo'* 

 micrometer ha* this great disadvantage, that it cannot 

 be used in reflecting telescopes, or in any achromatic 

 telescope where the adjustment of the eye-piece i* 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 pawing through the centre of the field. 

 The picture in the focus of the eye-glass is broken 

 into two parts, and the view u rendered still more un- 

 pleasant by the inequality of the segments into which 

 the field is divided. In addition to these disadvantage* 

 the different divisions of the micrometer are at unequal' 

 distance* from the eye-glas* which view* them, and 



therefore can neither appear equally distinct, nor sub- Invariable 

 tend equal angles at the eye." 



In order to remedy these inconveniences, Dr. Brew- _^ c '*'__, 

 ster was led, in 1805, to contrive the circular mother- nr Brew . 

 of-pearl micrometer, which is free of all these disad- s<t; r's m- 

 vantages, and has likewise the benefit of a kind of di- thcr-of. 

 agonal scale, increasing in accuracy with the angle to p' 

 be measured. This micrometer, which he has often ""meter. 

 used, both in determining small angles in the heavens, c ^" STi 

 and such as are subtended by terrestrial objects, is re- j,- ^ 

 presented in Plate Ci 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 lube, 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 focirs of the 

 glass next the eye. When the micrometer i* 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 equatoreal star ; 

 and the angles subtended by any number of divisions 

 or degrees will be found by a table constructed in the 

 following manner. 



Let A m p m b, Fig. 5. be the interior circumfe- Fig. -. 

 rence of the micrometer scale, and let m n be the 

 object to be measured. Bisect the arch mn in p, 

 and draw CM, C p, CM. The line C /> will be at 

 right angles to m , and therefore m n will be twice the 

 sine of half the arch IH p n. Consequently, AH : m n= 

 I Cad : Sine of .J mp n; therefore m n X R = sin. -'> mp n X 



AB, and mp n = 



x AB ; a formula by 



which the angle subtended by the chord of any num- 

 ber of degree* may be easily found. The first part of 

 sin. \ m /> n 



the formula, vix. 



T 



is constant, while AB va- 



ries with the sioe of the micrometer, and with the mag- 

 nifying power which U applied. Dr. B. therefore 

 computed the following Table, containing the value of 

 the constant part of the formula for every degree or di. 

 vision of the scale. 



