For the sake of simplicity, these directions have hi therto been carried on, as if the two objects could be either of them reflected one to the other ; but this will seldom be practicable ; and it therefore becomes neces sary, that the brighter of the two should be reflected to the fainter, as the sun to the moon, the moon to a'star, &c. To make this appear, let the indices be supposed to stand as they did on completing the preparatory step ; and sup pose the objects to be the sun to the right, and the moon to the left ; make the first observation by reflecting the sun beyond the point of parallelism, as described above, until it coincides with the moon ; to proceed further, would be to reflect the moon to the sun, which can sel dom be done. But an easy and obvious expedient pre vents the necessity of this ; for, by turning the instrument with the divided side downwards, we place it in a posi tion which changes an observation to the right into one to the left ; and, consequently, in this position, the sun may again be reflected to the moon ; thus, by alternate motions of the indices B and A, in alternately reversed positions, we gain a set of repeated observations, always reflecting the image of the brighter object to the fainter.* Upon the index A, and half-way between the centre and horizon-glass, is a socket for holding a dark glass, which being screwed there, modifies the rays of a bright object, after being reflected from the index-glass ; hut is out of the way of those rays, when they pass again reflec ted from the horizon-glass to the eye. Close behind the horizon-glass, is a similar socket for the same purpose ; a dark glass applied here, will soften the direct rays, in cases where both objects are too bright for the eye, and in the few cases where the fainter image may be reflect ed. But as dark glasses, in either position, would inter cept the incident rays, in very small angles, we find ano ther application of darkening glasses for the reflected rays, the position of which is immediately before the in dex-glass, which they completely cover ; these are not half so dark as those first described, because the rays of light pass twice through them, once before reflection, and again afterwards ; three or more glasses of different co lours and shades are applied at each of the three posi tions, but only one at a time can be used at any of them.
Whatever we have yet said respecting Borda's princi pal improvement, it must have its value appreciated ful ly as much for economy of time as accuracy of result. But when we consider that circles like as well as octants and sextants, have the angles which are mea sured by them charged with the full amount of the er rors in the darkening glasses, Borda's construction must rise greatly in our estimation, and set its competitors at a distance. His method of making crossed observations completely destroys these errors ; for, affecting the con tacts to the right and left, by equal quantities, in con trary directions, they will, in every pair, correctly balance each other.
The telescope of Borda's circle is attached to the in dex A by two cocks ; these have each a slider, by which its line of collimation may be set parallel to the plane of the circle, as well as raised or depressed, for the purpose of darkening or brightening the reflected image, by pla cing 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 cen tre, and stands perpendicular to its plane. This instru ment has usually been made of 10 inches diameter, and divided to every minute ; the whole limb comprehending, like all reflecting instruments, 720°. This is owing to the well known law in catoptrics, that the angle of reflec tion is, in all cases, equal to the angle of incidence, and not on account of double reflection, as some authors have erroneously stated.
Many of the circles of Borda had been made in London by several different artists, chiefly for foreign orders, and for the late Mr J. H. de Magellan, who made a few tri
fling alterations in its construction, and who put in an ineffectual claim to the invention of the method of mak ing crossed observations. It was in 1794 that one of those artists, Troughton, imposed upon himself the task of bringing forward, in a improved form, an instrument which hitherto seemed to have drawn towards it the at tention of foreigners alone. We have heard Mr Trough ton say, that it was with the utmost hesitation he dispen sed with the repeating principle in his new construction ; hut considering that a well divided instrument can derive little or no advantage from its employment, and seeing that its rejection would afford him the means of a shn pler and firmer fabric, he determined to put into the hands of his customers an instrument which, though greatly su perior in precision, was in use and management not much different from those they had been accustomed to handle.
Plate CXLIV. Fig. 3. is a representation of this instru ment, exhibiting the face or side on which the divisions are made ; and Fig. 4. as well as the perspective view, (Plate CXLV.) spews the construction on the reverse side, or side of the glasses. The simple border, with bars 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 handles applied parallel to the plane of the circle, and one of them bent round from the side to which it is fixed, a different figure was required. After many forms had been tried, that which is here given was alone found to preserve its shape unvaried in all positions. The handles are attached to the frame by screws at two oppo site parts, where the bars cross each other ; but besides this, they are also stayed at the centre. The index has three branches, at equal distances from each other ; one of them carries the usual apparatus for quick and slow mo tion, which set fast, or put in gradual action, go verns also the other two. To this index is fastened an axis, which, after passing through a socket about two in ches long, carries at the other end the index-glass.. A secondary flame, attached to the main one by five pillars, is situated nearly an inch below it ; upon this secondary frame are firmly fixed the horizon-glass and the tele scope ; on the same frame are also placed two sets of coloured glasses, one between the index and horizon-glass es, and the other behind the latter of them ; the first for darkening the reflected image of a bright body, the se cond for darkening one seen directly. The distance be. tweets the two frames affords a relief, whereby the colour ed glasses may be turned down, round a joint, for pla cing 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 angles worked through• its whole length into a screw, passes through a barrel, which connects the main and secondary frames : the bore of the barrel is square next the telescope, and receives the squared stein 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 togetner affords, by one action, the means of adjusting the telescope respecting the line of separation between the silvered and unsiivered parts of the horizon-glass ; by this contrivance, the two objects under observation may be made of equal brightness, without taking the eye of them. There is also in the collar into which the tele scope screws, the usutd adjustment for making the line of collimation parallel to the plane of the circle.