CIRCLE. 



501 



Circle, out having recourse to the divisions at all during the in- 

 ^^V^^ tcrmediate observations. 



An index carrying a microscope at each end, one of 

 which is shewn at k, is applied to the centre of the fore 

 index, by the help of which the four verniers are read ; 

 that is, two of them by each, for one will not read all 

 the four, because the arm cannot pass the telescope. A 

 similar arm is centred upon the base of the pillar, which, 

 moving freely all round, its single microscope serves to 

 read off all the three verniers of the azimuth circle. 

 Adjust- Having now gone through the description of the re- 



menti of peating circle, it only remains that there should be given 

 ihe repeat- an enumeration of its few and simple adjustments. 1st, 

 The azimuth axis is adjusted tertical, or the circle ho- 

 rizontal, by means of the feet screws and levels in the 

 way practised in the corresponding adjustment of other 

 instruments. 2d, The plane of the upper circle is ad- 

 justed vertical for astronomical purposes, by turning it 

 round the cross axis ; and the required position ii as- 

 certained by applying a plumb-line to the face of the 

 circle. This adjustment is, however, obtained much 

 more correctly, by observing any elevated object at rest, 

 pointing the telescope upon it directly, and then obser- 

 ving its image as reflected from the surface of a fluid : 

 the middle vertical wire bisecting, in both cases, is the 

 proof of adjustment, and furnishes an unexceptionable 

 criterion. 3d, The line of collimation of the telescope 

 parallel to the plane of the circle. As both the tele- 

 scopes have their positions eccentric, respecting the ver- 

 tical axis, chuse, for this purpose, a very distant object, 

 and as nearly as can be estimated in the horizon ; bisect 

 that object by the middle vertical wire, and then read 

 off what the verniers of the azimuth circle give ; now 

 turn the face of the circle to the contrary hand, bisect 

 the object in this position, and read the azimuth circle 

 a second time ; now carry the instrument in azimuth 

 through half the angular difference, (abating 180), as 

 shewn at the two positions, and then the plane of the 

 circle will pass exactly through the object ; move now 

 the wires of both telescopes by their proper screws, 

 until they bisect the object. The fourth adjustment is 

 of use only, when taking levels is the end of observation ; 

 it is to set the line of collimation of the back telescope 

 parallel to the level ; a very distant object is also required 

 for this purpose, because the back telescope is lower in 

 position than the front one. With every thing adjusted 

 as before, bisect any object nearly in the horizon by 

 the middle horizontal wire of the fore telescope, and 

 read the divisions of the circle ; reverse the instrument, 

 both in altitude and azimuth, and bisect the object, and 

 read the circle as before. The half difference of the 

 readings will be the altitude or depression of the object ; 

 set the indices, therefore, to this half difference, and 

 turning the instrument round in azimuth, look for a new 

 object that is bisecti-d by the wire; this -object will be 

 in the horizon, and the end will be accomplished by 

 turning the hack index until the level comes to the 

 middle, and adjusting the horizontal wire by the proper 

 screw, so that it may bisect that object. 



Tl:e perspective view of the repeating circle shews all 

 that is provided by the maker, and in the observatory is 

 all that can be required ; but iri the field, as no one 

 would think of placing it upon the ground, a stand is 

 wanting ; but this may be so simple in its construction, 

 as to be made by any one accustomed to work in wood. 

 It sh uld consist of three spreading well braced legs, in- 

 serted at top into the under side of a round table, and 

 united beli. w by three crosses, reaching from leg to leg. 

 The diameter of the table should be at least two inches 

 greater than is required by the feet-screws of the tripod. 



It may be about three feet high, more or less, according Circle, 

 to the stature of the observer ; and if a circular groove V *""Y"*"* ' 

 in the surface of the table receives the feet-screws, the 

 three studs may be dispensed with, and the whole in- 

 strument turned round in order to lay it in the plane of 

 every pair of objects, the angular distance of which is 

 to be taken at the same station ; and that without lo- 

 sing the angular point, as indicated by a plummet sus- 

 pended below the centre of the instrument. 



There will seldom be found ground sufficiently firm 

 to support the weight of the observer, without deran- 

 ging the position of an instrument as he walks round it ; 

 and on this account, in the most accurate operations, it 

 is usual to level the ground, and to secure steadiness by 

 driving three piles of wood to a sufficient depth for the 

 legs of the stand to rest on. 



As perhaps the feet-screws of every instrument are 

 the most unsteady parts, for the purpose of lessening this 

 evil, these are made as short as possible. An observer, 

 therefore, should provide himself with a number of wed- 

 ges for propping the tripod, in adjusting the circle into 

 the proper plane, agreeable to a rule hereafter to be 

 given. 



SECT. II. On the method of observing Terrestrial An- 

 gles with the Repeating Circle. 



The repeating circle, as above described, may be consi- Method of 

 dered either as a geodetical or as an astronomical instru- observing 

 ment ; and it owes much of its celebrity to its having been terrestrial 

 employed in this double capacity by the French astrono- angles with 

 mers, in the great trigonometrical operations lately car- ? he r fPf at " 

 ried on in that kingdom. 1D S clrcle ' 



Of the manner in which the repeating circle was used 

 on this occasion, a most ample account has been given 

 by the National Institute, in two quarto volumes, enti- 

 tled L'arc du Meridien. Much useful information may 

 likewise be found in Puissant's Geodosie, and in a single 

 quarto volume, published separately by Delambre, enti- 

 tled, Methodes analytiques pour la Determination d'un 

 arc du Meridien. 



In all these treatises, a great portion is allotted to cal- 

 culations which become necessary, both from the mecha- 

 nical construction of the repeating circle, and from the 

 circumstances under which it must frequently be unavoid- 

 ably used. Many of these considerations, being common to 

 all instruments, will be given under SURVEYING. And of 

 those which are peculiar to this instrument, our limits 

 oblige us to omit a great many, and to confine ourselves 

 to those which seem to us most likely to be of general 

 utility. 



The repeating circle will not measure the horizontal 

 angle between two objects of different elevations, but it 

 will measure the direct angular distance between two ob- 

 jects, and the zenith distance of each of them, from 

 which data, the horizontal angle may be inferred by 

 spherical trigonometry ; and as, in each of these mea- 

 surements, the repeating property of the instrument may 

 advantageously be employed ; the horizontal angle may 

 no doubt be obtained to a very great degree of precision. 

 Let H h be an arc of the ho- 

 rizon, H', h' two terrestrial ob- 

 jects. Z the zenith, and ZH, 

 Z/i great circles of the sphere 

 passing from the zenith to the ' 

 horizon through the points H', 

 ''' /('. Then in the triangle ZH'A', 



the three sides ZH', Z h', H'h', 



H h being determined by actual mea- 



surement with the instrument ; the angle Z, equal to 



