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'e 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 0 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 aro 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'e circle when in the best hands ; but it is more hid& 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 to the frame which supports the horizon-glare and telescope, or to the Index-bar which carries the index-glass. The arrangement is exceedingly ingenious, but we suspect that the clamping and unthimping must affect each other, notwithstanding the beauty of the workmanship. They are also made much too heavy for the hand, and, considering the principle, unnecessarily eo. Mr. liasslar employed them, we believe, in his survey, but we have not hoard of their use elsewhere. The idea of a moveable or flying circle was probably taken from De Mendoza ltioe, who proposed a flying vernier, as well as circle. (' Phil. Trans.'-1801, p. 362.) The of this construction, and the practical objections to it, were, we presume, fatal to its adoption ; for we are not aware that it has ever been successfully used. In observing altitudes at sea, it is presumed that the horizon is always visible, which in hazy weather, or in dark nights, is frequently not the case. There have been several proposals for overcoming the difficulty by adapting a plumb-line or level to the sextant when required.
Several modifications, additions, and supposed improvements have been made in this class of instruments, but none of sufficient import ance to require notice here. The sextant and circle, such as we have described them, are sufficient for the cases which practically occur; and without disputing the ingenuity and even utility of certain modifications in peculiar and exceptional cases, we believe that there is little to be gained by such alterations as have been hitherto propoeed.
I- or reducing observations made with reflecting instruments, w'e must refer to the usual works on nautical astronomy. The tables of Thomp son, or Riddle, or Inman, or Raper, will afford sufficient information. Bordie memoir, already mentioned, should be carefully studied by every one who proposes to use a repeating circle ; and Troughton's article CIRCLE, in Brewster's Edinburgh Encyclopedia,' will be found of great value, especially as a guide to the circle known by his name. We have ventured very frequently to modify their opinions and directions. and the intelligent reader may decide for himself.