One of the first operations which the observer must engage in, is to determine the scale of his level at different temperatures, and then he may, for small deviations, use the indications of the level, instead of worrying himself and losing his time in attempting to produce a perfect adjustment. The value of the scale is thus measured :---Bring the bubble towards one end, bisect a very well defined object with the telescope, and read off both scale and verniers. Then, by the slow motion foot-eerew, bring the bubble towards the other end, bisect the object again by the telescope, and read off the level scale. Now bring the bubble to its original position by the circle-axis clamp, and the telescope on the object by its own clamp, when everything is as at starting, except that the telescope has moved over the circle the sum of the angular motions pointed out by the level. This may be repeated till a sufficiently accurate value is got for the whole scale. To try the equality of the divisions of the level, place the foot-screw near the line passing through the studs of the slow-motion piece, and note the motion of the level for every whole revolution of the screw.
For geodesical purposes Borda's circle is an excellent instrument, as the great French survey proves, but as the same advantages can be obtained by a different application of the repeating principle, it is now but little used. For an account of its employment and the directions for its use we refer to Delambre's M5thodes Analytiques pour la Determination dune Arc du 3Idridien; &c., Paris, An VII. in the Discours Prdliminaire; by the same author, contained in the 'Baas du Systeme Metrique D6eimal; vol. i. Paris,1806.
Borda's repeating circle possesses two most valuable properties ; mere errors of division may be diminuted by sufficient patience ; and the fatigue of reading off the divisions, the most ungrateful part of an observer's task, is greatly reduced. Hence, it may be asked, why is not the repeating circle in general use as a portable astronomical instru ment I We should answer that, in the first place, the construction of Borda is by no means satisfactory for au astrottomind Instrument ; it is weak, and heavy, and rickety. But if a portable astronomical circle is wanted, and to this class of instruments we shored confine the repeating circle, we think the following alteration should be adopted. The telescope hangs loosely from Its centre,• and whatever care may be taken by the artist, the flexure of each end must be considerable, probably thillrent, and possibly varying from time to time with vane tient; iu the temperature. It should be grasped by two strong collars near the ends of a diameter of a vernier circle, and the telescope might then be safely extended three or four Inches teach way beyond the divided circle. Again, the axle clamp which holds the vertical circle should be fixed on the pillar and embrace the rim of the inner circle, the clamp of the level tier no second telescope is wanted) might be at the back, above, and quite out of the way. The whole circle should be brought as close to the upright pillar sa possible, and perhaps its axis had better be fixed by the maker permanently at right angles to the pillar. This would take away much weight and give great firm
ness to the whole instrument.
It must however be admitted that unless there are two intelligent observers, or unless the base on which the instrument stands is au steady as to prevent the possibility of any derangement when the observer move* from the telescope to read the level, that errors may creep in, though not, as it seem, to us, greater than in all other intern ments not reflecting. We have previously cautioned circle observers, and the warning cannot be too strongly pressed upon our countryinen at least, that the lercl must a/trays be noted contemporaneously with the bisedion of the star. If the fouudation of the instrument is im moveable, this will be the same as the level a minute after bisection, and so only one observer be required. But if the position of the internment is affected by the weight or motion of the observer, the kid after bisection is no teat of the position at bisection, and two observers are absolutely necessary. In Bowie's repeating circle, where the clamp is necessarily imperfect from the shortness of its bearing, it is imponsible to move the front telescope without shifting the circle a little at the same time ; but this is ,of no importance, for the level shows the change, and the reading off of the level, when properly applied, corrects this error.
In judging of the repuatiug principle as applied to any instnnnent, attention should be paid to the perfect independence of the telescope and level with respect to each other, and to their perfect connection with tho circle when they are clamped to it. In soma instruments a sort of repetition has been attempted by having the circle turn freely on the telescope axis, and clamping it alternately to the telescope and to a vernier circle which carries the level. It seems difficult in any such construction to secure the immoveability of the circle while clamping and unekunping is going on, and the construction 11M, we believe, gone out of use. There are some precautions which should be observed in every repeating circle, which we shall describe in reference to Borda's construction. Besides the perfect independence of the level, the telescope with its verniers and clamps should be perfectly self-balanced, so as not to apply any force to the clamp in any position; the telescope should be moved on the circle by two fingers pressing in opposite directions towards the extremities ; the circle should be turned in its own plane by laying held of the circle itself, and so gently that no jar can take place, or any springing back or forward of the telescope or its verniers from the moment of inertia : finally, the level must have time to settle before it is read of When these pre •cautions are duly observed, great accuracy may be obtained ; in two instances, to our knowledge, where the latitude has been determined by unexperienced but intelligent observers, the results even of a single night have conic within I' of the truth.