CIRCLE. 



487 



Circle, tended to a sextant, so as to measure 1 20 or more de- 

 * T * 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 coun- 

 try, the sextant was immediately adopted for the nicer 

 nautical purposes, to the exclusion of the octant and cir- 

 cle which preceded it. 



It bar. just been said, that the accuracy of Bird's di- 

 viding caused the rtfiVcting 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 instru- 

 ment to be adopted there. 



SECT. II. Description of Borda' s Reflecting Circle. 



Bordi'i About the year 1775, the justly celebrated Chevalier 



reflecting <J e Borda, turned his thoughts to the improvement of the 

 circle. reflecting circle of Mayer, and, after 12 years application 



to the subject, gave his laboun 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 di- 

 rections for finding the longitude by the lunar method, 

 together with new rules and tables for this and other 

 nautical purposes. 



QLLJV Flg- 2 of Plate CXLIV - " * representation of Bor- 



da's circle, which, upon a comparison with the figure of 

 Mayer's, may probably at first sight eem 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 wai, 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, give the instrument new and useful pro- 

 perties. On looking at the figures, it will be seen thai 

 the telescope is drawn back, so that no part of it ex- 

 tends beyond the i dex-glass ; and, that the horizon- 

 glass is carried forward nearly to the opposite limb : these 

 alterations, simple as they are, accomplish his greatest 

 improvement. We have now two ways of making ob- 

 servations ; for reckoning from the point of parallelism 

 as the glasses are represented in the figure, we can carry 

 the reflected image either to the left, by moving the in- 

 dex A forwards, or to the right, by moving the index 

 B forwards ; for the incident rays may now fal! on the 

 index-glass through a long range, either above or be- 

 low the horizon-glass. The point of parallelism is of 

 no more use, for we are now enabled to observe, at each 

 step of either index, the correct double angular distance. 

 Borda calls half of this distance an observation to the 

 right, tbe other half, one to the left, and both together, 

 he calls a crossed observation : he calls it crossed, be- 

 cause 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 index B at zero, and then by 

 the motion of A to make the reflected image of the ob- 

 ject on the left, pass beyond the point of parallelism, 

 following it with the circle until it arrives at, and coin- 



cides with, the object on the right ; all this is prepara- 

 tory. Looking now to the right, bring the glasses pa- 

 rallel, by moving B forwards ; but pass that point, fol- 

 lowing the reflected image until it cornea to the object 

 on the left ; the double angular distance will no.v 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 manner, by alternate motions of 

 the indices, until you have completed a sufficient set. 

 The whole number of degrees now read off at B, divid- 

 ed by double the number of times which that index was 

 carried forwards, will give the angle sought ; and where 

 the observations are connected with time, as in taking 

 lunar distances, 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 

 preparatory step, another result might have been obtain- 

 ed 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. 



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 pre- 

 paratory step ; and suppose the objects to be the sun to 

 the right, ar.d the moon to the loft ; 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 seldom be done. But an 

 easy and obvious expedient prevents the necessity of this ; 

 for, by turning the instrument with the divided side down- 

 wards, we place it in a position which changes an obser- 

 vation to the right into one to the left ; and, consequent- 

 ly, 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 ; but 

 is out of the way of those rays, when they pass again 

 reflected from the horizon-glass to the eye. Close be- 

 hind the horizon glass, is a similar socket for tbe same 

 purpose ; a dark glass applied here, will soften the di- 

 rect rays, in cases where both objects are too bright for 

 the eye, and in the few cases where the fainter image 

 may be reflected. But as dark glasses, in either posi- 

 tion, would intercept the incident rays, in very small 

 angles, we find another application of darkening glasses 

 for the reflected rays, the position of which is immedi- 

 ately before the index-glass, which they completely co- 

 ver ; these are not half so dark as those first describ- 

 ed, because the rays of light pass twice through them, 

 once before reflection, and again afterwards ; three or 

 more glasses of different colours and shades are applied 

 at each of the three positions, but only one at a time 

 can be used at any of them. 



Circte. 



Analogous to this, it should have been stated, in the method of observing with Slayer's circle, that when the brighter ob- 

 i to tbe right, the face of the circle must be used upwards : but when it is on th Jeft, the face jnust be used down- 



