Professor Mayer proposed, that his new instrument should be 16 inches diameter; and for the purpose of relieving the arm of the observer from the weight of so heavy all' apparatus, recommended that it should be sup ported by a staff, which should rest upon the ground or deck. Bird, who probably made the first of these in struments, improved upon that idea. He made the staff communicate with a belt, which buckled round the loins of the observer.' The staff was double, being compo sed of two sliding tubes. These moved one within the other, for the purpose of adjusting the height of the cir cle to the eye of the observer, and by the help of a ball and socket attached to the centre of the instrument, he was enabled to accommodate its plane to the position of the objects. Bird also applied darkening glasses to the reflecting circle,and gave it every useful appendage which Hadley's quadrant had borne before. In particular it should be mentioned, that the telescope was attached to the index A by two double levers, which acted exactly in the same manner that the single ones do in the common parallel ruler. On these levers the telescope rose and fell, respecting the line of separation between the silvered and unsilvered parts of the horizon-glass. A consequent backward and forward motion necessarily took place. This is a much better contrivance for regulating the brightness of the two images, than that which was adopted afterwards for the same purpose by Bor da. It is a curious circumstance, that Bird divided his circles into 360° instead of 720°, as the nature of all reflecting instruments require ; whence it became neces saryto double the angle read off in a single observation, i and in continued ones, to divide the accumulated angle by only half the number of repetitions.
It may be considered an unfortunate circumstance for the credit of the reflecting circle, that Bird was its ori ginal maker ; for the correctness of his dividing deter mined Admiral Campbell to neglect the repeating prin ciple altogether, which he deemed a troublesome mode of observation, and to use a single portion of the limb. He then saw, that the arc of the octant ought to be ex tended to a sextant, so as to measure 120 or more de grees, and represented to the Board of Longitude, that a sextant, the radius of which should be double that of the circle, would be equally manageable at sea. He was ably seconded by Bird in these speculations ; and such was the opinion of astronomers and others, concerning the judgment of these two individuals, that, in this country, the sextant was immediately adopted for the nicer nau tical purposes, to the exclusion of the octant and circle which preceded it.
It has just been said, that the accuracy of Bird's di viding caused the reflecting circle to be laid aside in this country ; and we may add with equal truth, that the rude state of that art in France, occasioned that instrument to be adopted there.
About the year 1775, the justly celebrated Chevalier de Borda, turned his thoughts to the improvement of the reflecting circle of Mayer, and, after 12 years application to the subject, gave his labours to the public in an ex- • cellent pamphlet, which appeared at Paris in 1787. In this work, the chevalier minutely describes the former construction, gives a particular account of his own im provements, as well as ample instructions for using the instrument, and accompanies these, with complete direc tions for finding the longitude by the lunar method, toge ther with new rules and tables for this and other nauti cal purposes.
• Fig. 2. of Plate CXLIV. is a representation of Borda's circle, which, upon a comparison with the figure of Mayer's, may probably at first sight seem to exhibit a trifling difference for a work of 12 years ; but when we come to comprehend the effects that proceed from these alterations, we must acknowledge, with satisfaction, that the time was not spent in vain.
The great objection to Mayer's circle was, that it re quired two operations in order to obtain one result ; namely, one for the parallelism of the glasses, and another for the angular distance of the objects. Borda removed this inconvenience in the neatest manner possible ; and in doing this, gave the instrument new and useful pro perties. On looking at the figures, it will be seen that the telescope is drawn back, so that no part of it extends beyond the index-glass ; and that the horizon-glass is carried forward nearly to the opposite limb : these altera tions, simple as they are, accomplish, his greatest im provement. We have now two ways of making observa tions; for, reckoning from the point of parallelism as the glasses are represented in the figure, we can carry the re flected image either to the left, by moving the index A forwards, or to the right, by moving the index 13 forwards; for the incident rays may now fall on the index-glass through a long range, either above or below the ho•izon glass. The point or parallelism is of no more use, for we are now enabled to observe, at each step of either index, the correct double angular distance. Honda calls half of this distance an observation to the right, the other half, one to the left, and both together, he calls a crossed ob servation ; he calls it crossed, because the image of the reflected object crosses the point of parallelism. To use the instrument, it is best, in the first place, to set the in dex B at zero, and then by the motion of A to make the reflected image of the object on the left, pass beyond the point of parallelism, following it with the circle until it arrives at, and coincides with, the object on the right ; all this is preparatory. Looking now to the right, bring the glasses parallel, by moving B forwards ; but pass that point, following the reflected image until it comes to the object on the left ; the double angular distance will now be marked by B, but this is not yet to be noted. Perform a similar operation by the index A, reflecting from left to right, and a second by B, reflecting from right to left : proceeding in this manlier, by alternate motions of the indices, until you have completed a sufficient set. The whole number of degrees now read oil at B, divided by double the number of times which that index was carried forwards, will give the angle sought ; and where the ob servations are connected with time, as in taking lunar dis tances, that angle will correspond with the mean of the times at which the contacts were made. It should be remarked, that had the index A been read after the pre paratory step, another result might have been obtained from it ; but it would have been required, that the set had concluded with a motion of A, or else that the crossed observations had been, respecting it, reckoned one less in number.