SEXTANT. 



SEXTANT. 



last position of the index-bar, and those alone, which may be as inope- 

 rative on the measurement of the angle as the observer pleases or has 

 patience for. This would seem a great advantage ; but when Bird was 

 ordered to make a circle on this model, the divisions were found to be 

 so good that repetition added little to the accuracy of which a single 

 observation was capable, and the fresh determination of a position of 

 parallelism after every observation was too much trouble to be taken 

 when not absolutely necessary. The reflecting circle of Mayer was not 

 adopted in England, but great pains were employed in constructing 

 and dividing the sextant, in which our artists were eminently suc- 

 cessful. 



In France it is probable that the art of instrument-making was at 

 this time less advanced, and therefore the merit of Mayer's principle 

 was more readily appreciated. The celebrated Borda, who was a seaman 

 and navigator, first had an improved instrument on this construction 

 made about 1775,* and published a full description of its form and use 

 in 1787 (' Description et Usage du Cercle de Be'flexion, par le Chevalier 

 de Borda,' Paris, 1787), to which we refer the reader as a standard 

 acd classical work. The accompanying figure will explain Borda's 

 instrument, though it is not precisely similar to that which he 

 recommended. 



rive-Inch Diameter. 

 Borda't Reflecting Circle, by Troughton and Simiiis. 



The index-glass, with its bar, vernier, and tangent screw, and the 

 excentric bar which carries the telescope, horizon-glass, with its vernier 

 and tangent screw, require no explanation. The telescope hag a 

 parallel-ruler motion to bring the images to equal brightness, which is, 

 we believe, Bird's construction. Borda holds his telescope by two ears, 

 each of which can be raised or depressed separately, and he has a 

 graduation for each, so as to move them equal quantities. Dollond, in 

 his very beautiful repeating circles, has an up-and-down piece abort 

 the bar. The important and essential conditions of the repeating 

 circle are, that moving one index shall in no way affect the other ; that 

 the clamps when fixed shall not be liable to move from looseness, bad 

 balancing, or bad centering when the position of the circle is changed ; 

 and finally, that the axis of the index-glass and the collar on which the 

 horizon-bar turns shall both be so true, and of such a length, that the 

 motions of each bar are parallel to the plane of the divided circle. 

 The same precautions must be taken as in the sextant in trying the 

 index and horizon glasses, in placing the prismatic edges of the dark 

 glnnfim up and down alternately, in setting the glasses perpendicular to 

 the plane of the circle, and the telescope parallel to it : and it is 

 scarcely necessary to add, that the directions given above for using 

 dark glasses, equalising brightness, &c., apply to one reflecting instru- 

 ment as well as another. The cells into which the dark glasses are 

 inserted, when wanted, are seen between the two glasses and also in 

 front of the horizon-glass. 



On looking at Borda's circle as it is here represented, the opening of 

 the angle between the two glasses is towards the spectator ; hence an 

 observer looking through the telescope would see an object directly in 

 the line of the telescope, and some other object, call it A, which lies 

 towards the spectator, by reflexion. Now suppose the index-bar to 

 be moved through the position of parallelism and until the glasses 

 make the same angle as before, but with the opening from the 

 spectator, it is clear, first, that the angle read off Iwtween the first and 

 second positions will be twice the original angle ; and secondly, that 

 the observer, still looking at the same object as before seen directly, 

 will see by reflexion an object on his right hand (call it B), which 

 mates the same angle with the axis of the telescope as A did, but on 

 the other side. Now if we suppose the whole instrument to turn 

 half round upon the telescope as an axis, it is evident that A will be 

 seen exactly as at first, while the index-bar has been moved forwards 

 twice the angle between A and the axis of the telescope produced. 

 This is exactly the complete observation with Troughton's circle, and 

 thus while we have got double the angle by two observations, we have 

 got rid of index error, and have only two readings to which error of 



Borda'i alteration* were apparently very simple : he drew the telescope 

 back until it object-glau fell short of the index-glass, while Mayer's projected 

 beyond it, and he carried the horizon-glass forward almost to the edge of the 

 circle, which Mayer planted close before his telescope. Yet these slight modi- 

 fications completely changed the instrument. 



ARTS AlfD SCI. DIT. VOL. VII. 



division and reading off can apply.* Now suppose the instrument to 

 be returned to its original position, and, leaving the index-k'.r securely 

 clamped, move the horizon-bar, which carries the telescope and horizon- 

 glass, through the same angle and in the same direction as the index- 

 bar has travelled. If the original object be again viewed through the 

 telescope, and the contact between that and A perfected by the tangent 

 screw of the horizon-bar, it is clear that everything is exactly as at 

 starting, except that the index and horizon-bar have each moved over 

 the divided circle exactly twice the angle to be measured. Let the 

 operation which has been described be repeated, and everything will be 

 as at starting, except that the indices will have moved over four times 

 the angle, and it is evident that there is no limit to the number of 

 repetitions except the will of the observer. So that, theoretically at 

 least, the influence of bad division, bad centering, and bad reading off 

 upon the final angle may be reduced below any sensible quantity. 

 There is another very considerable advantage, namely, that there are 

 only two readings off of each vernier + for any number of repetitions. 



On looking at the figure again it will be seen that the rays of light 

 which fall on the index-glass pass between the telescope and the horizon- 

 glass, and there is a particular angle at which they pass through the 

 horizon-glass before falling on the index-glass. This occasions some 

 inconvenience, as the reflected image in that case is scarcely ever quite 

 perfect, and if the sun be the reflected object, the interposed dark glass 

 increases the imperfection. When Borda's circle is used in the hand 

 for observing altitudes, the instrument is to be held alternately in the 

 left and right hand for the crossed observations, but in taking lunar 

 distances there is the same difficulty as in the sextant when the face 

 is downwards. A handle with curved tube may however be applied 

 pretty much as in Troughton's circle, and if it is fixed into a collar 

 which turns on the centre, it may be kept out of the way of the 

 telescope, &c. There is a part of this circle which, though not actually 

 necessary, will be found of great convenience, the graduated semicircular 

 arc which is attached to the horizon-bar. The index-bar, either by its 

 edge or by a fiducial line, points out the reading on the semicircle, and 

 shows on each side when the glasses are parallel. By the help of 

 this it is easy to set roughly to any angle on one side or the other, and 

 thus save the trouble which nice setting would require, or seeking for 

 an object, which is still more troublesome. In some circles two small 

 pieces which slide easily can be fixed on this semicircle, and the proper 

 opening is given by the touch alone, that is, when the index-bar just 

 feels the stop. But there is always a risk of forcing a clamp which is 

 supposed to be fixed, by the slightest touch, and therefore we prefer 

 setting by a coarse-reading. As the chronometer must be noted and 

 read off at every observation, there will generally be light enough for 

 this purpose. Borda's original circles were much too large, and very 

 weak and ugly. Six inches diameter seems to us quite sufficient for 

 an instrument of this construction, which is intended to be used 

 according to its principle. The telescope and glasses are nearly the 

 same for all sizes, and the repetition reduces the errors of division and 

 reading off so rapidly that we should prefer rather a coarse division, 

 which is easily seen, to a fine one. A boldly cut division to 30" would 

 probably be best for general purposes ; the circle should be as light as 

 is consistent with strength, but the main points to be looked to are 

 the independence of the index and horizon-bars, the truth and per- 

 pendicularity of the centerings, and the firmness of the clamps. 

 Whether the want of balance in both bars, and especially the horizon- 

 bar, is wholly innoxious, is a point of some doubt, otherwise there 

 would seem to be no theoretical objection to a well-made repeating 

 circle. Hitherto this instrument has not been much used in England. 

 By some it may have been thought more troublesome than the 

 sextant ; it has generally been made too large and cumbersome, and 

 perhaps prejudice may be added as one of the causes why it has not 

 been properly valued. At the same time, though warm partisans of 

 the repeating principle, we conceive that the results with a repeating 

 circle will not be superior to those which may be attained by the sextant 

 or by Troughton's circle when in the best hands ; but it is more inde- 

 pendent, requires less thought and care and skill than the sextant, and 

 is neither so troublesome nor so cumbrous as Troughton's circle. 



An alteration was proposed in Troughton's construction by Mr. 

 Hasslar, director of the survey of the coast of the United States. The 

 circle turns freely round the centre, and is clamped at pleasure either 



Some observers use the repeating circle as a sextant. They change the 

 readings from time to time by altering the position of the horizon-bar and 

 determining the zero position uf the index-bar. This mode of observing will 

 undoubtedly tend to destroy errors of division and excentricity, but it is a com. 

 plete sacrilice of the best qualities of a repeating circle. At any rnte index 

 irror should be destroyed in tbc way we have pointed out, which would be somo 

 compensation for the reduced radius of the divided arc. Borda calls the pair 



tfrrationt croisfet, or crofted observations. 



t The index-vernier is usually read off and the horizon vernier neglected. 

 Lieutenant Rapcr has pointed out the following use of the second vernier. 

 1'lacc the glasses parallel and read off both verniers ; then if you wish to 

 measure two angles rapidly, observe one by moving the index-bar, and the 

 other by moving the horizon-bar. In observing altitudes of two stars In 

 uncertain weather and in maritime surveying, this recommendation may be of 

 great service. Let the greater angle be first measured by moving the index. 

 bar, then the angle moved over by the index-bar is the greater angle, and the 

 difference between this angle and that moved over by the horizon-bar is the 

 less angle. 



K K 



