CIRCLE. 



B*tlt. Whatever we hire yet uid respecting Borda's princi- 



v< "~/"^ pal improvement, it mu*t hive ill value appreciated ful- 

 ly u much for economy of time as accuracy of result. 

 But when we consider that circle* like Mayer's, as well 

 at octant* and tenants, have the angle* which are mea- 



* turcd by them charged with the full amount of the er- 



ror* in the darkening glastrt, Borda's construction must 

 ri*c greatly in our estimation, and set its competitors at 

 a distance. Hi* method of making crossed observations 

 completely destroys these errors ; for, affecting the con- 

 tact* to the right and left, by equal quantities, in con- 

 trary directions, they will, in every pair, correctly ba- 

 lance each other. 



ltvt The telescope of Borda's circle is attached to the in. 



" dex A by two cocks ; these have each a slider, by which 



r 'f- * it* line of coUimatmn may be set parallel to the plane 

 of the circle, as well as raised or depressed for the pur- 

 potc of daikening or brightening the reflected image, by 

 placing less or more of its aperture opposite the silvered 

 part of the horizon-glass. Both the indices A and B 

 are furnished with apparatus for quick and slow motion. 

 A handle is screwed to the back of the circle at the 

 centre, and stands perpendicular to its plane. This in- 

 strument ha* usually been made of 10 inches diameter, 

 and divided to every minute ; the whole limb compre- 

 hending, like all reflecting instruments, 720. This is 

 owing to the well known law iu catoptrics, that the 

 angle of reflection is, in all cases, equal to the angle of 

 incidence, and not on account of double reflection, as 

 tome authors have erroneously stated. 



SJJCT. III. Description of TrougMon't Reflecting 

 Circle. 



Many of the circles of Borda had been made in Lon- 

 don by several differert artists, chiefly for foreign or- 

 der*, and for the late Mr J. H. de Magellan, who made 

 a few trifling alteration* in its construction, and who 

 put in an ineffectual claim to the invention of the me- 

 thod of making crossed observations. It was in 1794- 

 that one of those artists, Troughton, imposed upon 

 himself the taik of bringing forward, in an improved 

 form, an instrument which hitherto seemed to have drawn 

 towards it the attention of foreigners alone. We have 

 heard Mr Troughton say, that it was with the utmost 

 hesitation he dispensed with the repeating principle in 

 his new construction ; but considering that a well divid- 

 ed instrument can derive little or i.o advantage from its 

 employment, and seeing that its rejection would afford 

 him the means of a simpler and firmer fabric, he deter- 

 mined to put into the hands of his customers an instru- 

 ment which, though greatly superior in precision, wa* 

 in use and management not much different from those 

 they had been accustomed to handle. 



Plate CXLIV. Vig 3. is a representation of this in- 

 strument, exhibiting (he face or side on which the divi- 

 sions are made ; and Fig. 4>. as well as the perspective 

 view, (Plate CXLV.) shews the construction on the re- 

 verse side, or side of the glasses. The simple border, with 

 bar* radiating from the centre, answers sufficiently well 

 in Borda's instrument, where the weight is sustained on 

 the handle at the centre; but, in the case now before 

 us, where there are two handle* applied parallel to the 

 plane of the circle, and one of them bent round from 

 the *ide to which it is fixed, a different figure was re- 

 quired. After many forms had been tried, that which 

 is here given wa* alone found to preserve it* shape unva- 

 ried in all positions. The handle* are attached to the 

 frame by screw* at two opposite parts, where the bars 

 orott each other ; but betides this, they are alto stayed 



JVwrin- 



i .... i 

 \ .- ' - 



I I. :L. 



circle. 



PLAT* 

 CXLIV. 



I 



**.< 



FIAT* 



CXLV. 



at the centre. The index hat three branchet, at equal 

 distances from each other ; one of them carnrs the usual 

 apparatus for quick and slow motion, which being set 

 fast, or put in gradual action, governs also the other 

 two. To this index is fastened an axis, which, after 

 passing through a socket about two inches long, carries 

 at the cither end the index-glass. A secondary frame, 

 attached to the main one by five pillars, is situated near- 

 ly an inch below it ; upon this secondary frame are firm- 

 ly fixed the horizon-glass and the telescope ; on the same 

 frame are ako placed two *ets of coloured glasses, one 

 between the index and horizon glasses, and the other 

 behind the latter of them ; the first for darkening tin- 

 reflected image of a bright body, the second for darken- 

 ing one seen directly. The distance between the two 

 frames affords a relief, whereby the coloured glasses may 

 be turned down, round a joint, for placing them out of 

 the way when they are not wanted. The telescope with 

 different powers screws into a collar, whose squared 

 stem having its four angle* worked through its whole 

 length into a screw, passes through a barrel, which con- 

 nects the mam and secondary frames : the bore of the 

 barrel is square next the telescope, and receives the 

 squared stem of the collar ; but higher, it is cylindrical 

 and large. In this part, a spiral spring is enclosed, which 

 exerting its force against the enlarged higher end of the 

 stem, draws it along with the telescope upwards, while, 

 at the exterior end of the barrel below, a female finger 

 screw, acting on the stem, draws it downwards, and 

 both together affords, by one action, the means of ad- 

 justing the telescope respecting the line of separation 

 between the silvered and unsilvcred parts of the horizon- 

 glass j by this contrivance, the two objects under obser- 

 vation may be made of equal brightness, without taking 

 the eye off them. There is also in the collar into which 

 the telescope screws, the usual adjustment for making 

 the line of collimation parallel to the plane of the circle. 



Jt has already been said, that Bird's construction of 

 Mayer's circle is, in this respect, preferable to Borda's; 

 the latter is indeed very inconvenient, because with it 

 an observer has to read the divisions of the two sliders, 

 by which the height of the telei-cope, from the plane of 

 the circle, is regulated ; for should he, while observing, 

 attempt any alteration, by using the two screws to suit 

 the objects as their brightness varies, and happens to 

 turn one of them more than the other, he would derange 

 the parallel positi.-n of the telescope, and thereby ren- 

 der his observations of no value. The circle of Borda 

 is, in many respects, mechanically defective j that high- 

 ly important part, the centering of the indices, is very 

 much so, for they move round the circle upon bearings 

 no longer than their own thickness ; and, consequently, 

 want that steadiness which is derived from an axis. 



The author of the reflecting circle now under consi- 

 deration, had many reasons for furnishing its only index 

 with three verniers. In the first place, he was desirou* 

 that as the repeating principle had been abandoned, gome 

 contrivance should be substituted tor the purpose of re- 

 ducing the error* of even good dividing. Three read- 

 ings which, upon the principle of taking means, in a 

 crossed observation, (a term we need no longer employ), 

 probably reduce the error of dividing to one sixth part 

 of its simple value; while, at the same time, they per- 

 fectly correct the error arising from any eccentric mo- 

 tion of the index. Thin ktnd uf error, a very import- 

 ant one, is never entirely corrected in Borda's circle. 

 except in the case of beginning and leaving off at the 

 ame point ; for, should the lepeutiont be continued to 

 more than a complete round, the error which at that 

 point mot have vanished, would be again generated'. 



Circle. 



