After the invention of Borda's repeating reflecting circle, Troughton, who was averse to the principle, produced a non-repeating circle, which he called the British circle; but it more commonly goes by his name. This may be understood by conceiving the circle, of which the sextant is a part, to be completed, and that while the telescope and glasses nre at the front of the instrument, the divisions and three equidistant verniers Ittached to the index•glalss are at the back. The observations ought always to be made in pairs, and for this purpose there are two handles, one to the front and another nt the back. Thus, suppose it were required to take the altitude of the sun : this is first observed exactly as with the sextant, and the three verniers read off, the index glass being above the line which joins the telescope aria horizon-glass.
Let the instrument be conceived to turn round this line through 180', then the index•glass is below, and with the face downwards. By moving the index backwards to zero, it will become parallel to the horizon-glass, and continuing this motion until it is nt the original angle, but on the back arc, the sun will be brought down exactly as in the former observation ; when the contact is to be made with the tangent-screw, and the indices again read off. By combining the observations it is clear the index error is destroyed, and this is one point of superiority to the sextant Again, the three readings wholly destroy any effect of excentricity, and very greatly diminish those errors which may arise from accidental injury to the figure of the circle, while the six readings greatly reduce the errors of division. The errors caused by defects in the dark glasses and horizon-glass are eliminated, and such as nrise from a defect in the index•glaass are diminished, and this too by the principle of the instrument, using it independently upon one object. These advantages are undoubtedly very great ; but the additional weight of the circle and trouble in handling it, the trouble of reading three verniers for every observation, the shortness of the radius, and consequent necessity of limiting the subdivision to 20", seem to overbalance them in the opinion of most seamen. We think that an intelligent observer will get results of nearly equal value from the sextant or from Troughton'a circle, but that the sextant requires much care in selecting and balancing observa tions, which the circle does not. Whenever time or latitude is to be deduced from observations of one object at one time, as where the sun alone is used on geographical expeditions, or where lunar distances are taken from the sun alone, or from one star, the sextant cannot enter into coinparisou with the circle. A very excellent Spanish observer, Don J. J. Ferrer, determined the obliquity of the ecliptic with one of Troughton's circles more accurately than the Greenwich quadrant could do, at a time when that quadrant was still the prin cipal declination instrument in the Royal Observatory. And if frequent
reading off is not too great an objection, Troughton's circle may be recommended as the safer and more independent instrument, and as detnanding less thought and care from the observer.
We have already, in the article REPEATI5P3 CIRCLE, described the original discovery of the principle by Tobias Mayer, and his first appli cation of it After Mayer had greatly improved the lunar tables, be proposed the following construction for measuring the angle between the moon and any other object with the greatest exactness. (` Tabula) motuutn Solis at Luise, auctore Tobias Mayer,' London, 1770.) The instrument is an entire circle, on the centre of which the index-bar turns, the index•gllss being over the centre. The telescope and horizon-glass nre fixed on a second bar, which also turns, but excen trically, on the sauna centre. The two bars can be clamped indepen dently of each other, nnd each in any position, and there is an index or fidueial line to each, by which the divisions of the circle may be read off. Now, suppose a distance between the moon and sun to be required (the dark shades, fie., may be understood from what has been said on the sextant): First, having fixed the index-bar at zero, bring the horizon-glass to be parallel to it by observing the sun (as in deter mining index correction) ; then move forward the index-bar, and observe the distance between the moon and sun's nearest limbs, as with the sextant. If the angle were now read off, we should have the simple distance affected with the whole error of graduation, and obtain no advantage over the sextant. By moving the horizon-bar, bring the two glasses to be parallel exactly as before, and make the measure between the limbs of the moon and sun also as before, by moving the index-bar alone. The angle, if read off now, would be twice the angle required, but the errors of division and reading off would be only those which affect the first and Lila position of the index-bar. In this way the angle may be repeated as often as you please, until the bars have travelled once, twice, or even oftener round the circle; and it is evident that the errors of division and reading off are those at the first and 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 sue ces4u1.