MICROMETER. 



203 



Wi ' at their various distances from the earth; but, in order 

 *""*"" to show the resources of the principle on which the in- 

 _"**' - strument is founded, we shall take another example, 

 better adapted to this purpose. 



Let us suppose that the pair of fixed wires subtends 

 only an angle of 40", for the purpose of measuring the 

 distance between double stars, or the diameters of some 

 of the smaller planets, that the telescope magnifies 300 

 times, and that the lens L in its motion from /" to L, 

 through a space of 10 inches, diminishes the power of 

 the instrument to 240 ; then when the lens is at L, 

 the angle of the wires will be 50", for 240 : 300= 

 40" : 5O". Hence we have a scale of 10 inches to 

 measure 40" 30*, or 10*, so that every inch of the 

 scale corresponds to \'', and every 19th of an inch to 

 6"".) From this it follows, that the accuracy of the scale 

 increases as the angle subtended by the fixed wires di- 

 minishes. 



If it should be found convenient to make each divi- 

 sion of the scale correspond to greater variation in 

 the angle than in any of the examples which we have 

 given, it would then be proper to make use of a ver- 

 nier for subdividing the units of the scale. 



In order to show more clearly the method of com* 

 pleting the scale, we have represented a telescope fur- 

 XTt nished with a micrometer, in Plate CC'CI.XXV. Fig. 

 CUST. 9, where AB is the principal tube, with the object 

 If. 9. gla*s at B ; CD secondary tube, at the right hand 

 extremity of which is fixed the lens L, (Fig. 8.) which 

 is moved backwards and forwards with the tube, by 

 the milled head F ; and E the eye-piece, which is ad- 

 justed to distinct vision by the milled head G. The 

 small index i projecting from the principal tube below 

 A, and furnished with a vernier scale if necessary, 

 points out the division* on the scale. Let it now be 

 required to construct the scale for the 2d Example, 

 where the lens L, by moving from f to L, changes the 

 power of the telescope from 40 to 35. Having moved 

 the tube CD as far out as possible, by the milled head 

 F, mark the point of it at n to which the index i points, 

 and this will be the beginning or zero of the scale. 

 Adjust the eye tube E to distinct vision, and find by 

 experiment the angle subtended by the fixed wires: 

 Let this angle be 29 minute*. Move the tube CD as 

 far in as possible by means of the nut F, till the index 

 i points to m, and mark this as the other extremity of 

 the scale. Let the eye tube E be again adjusted to 

 (It met viiion, and the angle subtended by the wires 



whole scale, is to 10 inches, the length of the scale, so 

 is 9" to 36 hundredths of an inch, which being set 

 from m to o, will mark out the point o as correspond- 

 ing to Sy. The space o n being divided into four parts 

 for minutes, and each minute into as many divisions as 

 possible, the micrometer will be ready for use. If 

 great accuracy is required, every unit of the scale 

 might be determined experimentally, by any of the 

 methods mentioned in the preceding note. 



The instrument thus constructed, is capable of mea- 

 suring angles only between 29* and 33' 9", and is 

 therefore peculiarly fitted for determining the diame- 

 ters of the sun and moon. Its range, however, could 

 easily have been extended, by lengthening the tube 

 CD, or by employing a moveable lens, of smaller focal 

 length ; or instead of one pair of wires, we might use 

 several pairs, as AB, CD, a b, cd, <8, yj, Fig. 10, so Fig. \o. 

 placed that only one pair should be in the field of view 

 at a time, and th.it the least angle of the second pair 

 should be equal to the greatest angle of the first pair, 

 and the lean angle of the third pair equal to the great- 

 est angle .:' the setond. 



When the micrometer is constructed on these prin- 

 ciples, it is certainly free from almost all those sources 

 of error with which the wire micrometer is affected. 

 The imperfections of the screw, the errors arising from 

 the uncertainty of the zero, from the bad centering of 

 the lenses, from the want of parallelism in the wires, 

 and from the minuteness of the scale, are completely 

 removed. Nay, if the scale is formed by direct expe- 

 riments, whatever errors may exist in the instrument, 

 are actually corrected ; for a* the sources from which 

 these errors proceed existed in the instrument during 

 the formation of the scale, they cannot possibly afl'oct 

 the result of any observation. The scale is in fact the 

 record of a series of experimental results, and the ob- 

 servation must be as free from error as the experiments 

 by which the scale was formed. It would, therefore, 

 be of great advantage, in micrometrical observations, 

 to make the points B, C, Fig. 1 1, with which the wires Fig. 11. 

 appear to come in contact, as luminous as the object* 

 to which it is intended to apply the instrument, or ra- 

 ther to have a series of result* for object* of various 

 degrees of illumination. 



In the preceding micrometer, the angle of a pair of Dr. Brew, 

 fixed wire* i* increased and diminished, by the motion xer'i tyt- 

 of a second object-glass along the axis of the telescope ; P<< mi- 

 while, in the present instrument, the variation of the "ometer. 



again determined experimentally ; and let this angle angle i* effected by separating the two part* which * ' z> 

 be now 3f 9". In order to find the point of the scale compose an achromatic eye-piece ; or, when the eye- 

 corretponding to 33', say, As 4' 9", the value of the piece consists of two or three lenses, by separating the 



ID order to find the angle mtomitA by a piir of worn AB, CO, Fig. 7, direct the teleaeope, the objeet*la*i of which u luppowd 

 to be at the point A, Fig. 11. to any upright object MN. with pbfa M&C*. porpendenler to tb axk of the Mlesoepe, and placed at . 

 convenient dirtanee, MO AM to example, and oboerre the iptc* which the wins appear lo occupy, or UK point* B. C, which the wire. 

 MB to carer, taking particular can that the Kne joining theee point, i, perpendicular M the wire.. Let the apace DC be 4 feet 2.5T 

 mcbea. BiMct BC in L>. and draw DA ; then ta the right angled triangle ADD. we hare AD-MO feet, and BO.t feet 1.285 inch- 

 t. 10 detornaM the aagk BAD, which, by the empfert CM a? plan tjigeoemotry, win be found to be IV SO", 10 that the whole angU 

 BAC, or that Bftttoded by the wire*, win be W. 



It i* obriooa. bcwevar. that on account of the proximity of the object MN, the image of it in the lilimii ie famed by rayi which 

 &U dirting upon the object glad O, and therefore Uu. image wffl be farmed at /", Fig. 8. at a greater diuance than the principal fo- 

 miprfryiag power "ill be greater, and the angle of the wire* lea. than they would hare b 

 II M Mceaaw, therefore, to fad die 



at /", 



of the wire* lea. than they would hare been had the object MN been 

 angle BAC, that we may hare the real ralue of that angle when the 



"" 



i. directed to *e hmmtly bodiea. Let O/. the (heal length of O, Fig. 8. be called f ; D the diattnce of the object M N ; a 

 anBt; r the correct angle ; F the focal length of L ; and t the dfeanee of the km L from the focu./. Then 



thoa.giefeuf.iby 



we have, by the principle, of Optics, 



.//.the 



of focal length. Calling this ralue of//* m, we hare 6-t-m-I./', and, 





Vy the principle* of Optics, F+J+* ! F.H* : for the new value of LF or for LF'. Hence LF : LFW t ; that it, 



F Ft. 



1 *~~ T +^~ - : * ' wnnula ftom which the corrected angle * may be rradfly found. 



4 



