17 



REPEATING CIRCLE. 



REPEATING CIRCLE. 



18 



level will measure small arcs better than any graduated limb or even 

 than any small telescope can do, and it is therefore as safe to correct 

 for an error of level as to adjust. The level readings should be regis- 

 tered as towards the object end and eye end, or and + , along with 

 the times, and the correction may be made to the final arc. It is 

 clear that if the level were always brought -to the same divisions, there 

 would be no level error. The effect of a derangement of the vertical 

 axis, which is shown by the level, is calculated as follows : Let the 

 reading of the level end towards the object be 10" larger than the 

 reading towards the eye. To correct this, the footscrew towards the 

 observer should be raised 5", when the two readings will agree; but 

 now the telescope points 5" below its former position, in which it 

 bisected the star correctly. The telescope therefore must be raised, 

 that is, the zenith distance must be diminished 5" ; hence if 5" be sub- 

 tracted from the multiplied zenith distance on account of that observa- 

 tion, the error would be corrected, and so on with every other instance. 

 " The rule is, add together all the level readings towards the object end, 

 and prefix - ; do the same with those towards the eye end, and prefix 

 + ; take their algebraic sum, 'and Divide by twice the number of 

 observations, and the result is the correction to be applied with its 

 sign to the mean zenith distance. This will generally be a very small 

 quantity. As the great difficulty in observing out of a regular obser- 

 vatory is in the reading off, the division of the level might be to every 

 2", but numbered as single seconds. These would be better seen, and 

 the divisor of the difference would be the number of observations. 

 When the instrument is very small, and the probable circumstances 

 under which the observer may be placed promise few facilities, the 

 scale may be cut to 1CT only, with bold lines. A mistake of one or 

 two tenths in guessing the subdivisions would be very rare, and 

 scarcely cause a sensible error in the final result. 



The circle has been supposed to be adjusted before observing ; this 

 is a very simple operation. First place the instrument with the foot- 

 screws in their cups, and let that footscrew be towards the observer 

 which rests on the slow-motion piece. This is seen at fy. 1, on the 

 right. Place the axis nearly vertical by guess, or, if there is an 

 azimuthal circle, set the plane of that nearly horizontal by a box level. 

 Then place the plane of the vertical circle upright by the cross level, 

 and bring ita plane to be parallel with the two footscrews which are 

 from the observer : that is, if the object is in or near the meridian, 

 set the circle east and west. Bring the bubble of the main level to the 

 same division at each end by its clamp and tangent screws, and then 

 reverse the instrument (turn it 180 in azimuth). The level is to be 

 brought again to the same divisions, half by its tangent screw, half by 

 screwing the two footscrews an equal quantity in opposite directions. 

 Now turn the circle a quarter round (place it in the meridian according 

 to the supposition), and bring the bubble of the level to its proper 

 position by the third footscrew only. This first attempt at adjustment 

 need only be approximate, but it must be performed over again with 

 considerable nicety. The slow-motion piece is, we believe, due to 

 Borda, and is a very ingenious and useful contrivance for making a 

 coarse screw do the work of a fine one. By placing the footscrew 

 nearer to or farther from the line of the two studs, the elevating power 

 of the screw can be reduced in any proportion, and the finest and 

 slowest motion possible given to the instrument. We have used 

 the slow motion for finally bisecting a star in observing with great 

 comfort. It is more ready to the hand than any other part of the 

 instrument, and the disturbance of the axis is of no importance,~as 

 the level must be read off at all events. The approximate bisection 

 is performed by the other screws, and if the observer recollects which 

 way the star is moving, the space through which the instrument is 

 thus moved need only be a very few seconds. The cross level must 

 be originally fixed and adjusted, after the plane of the circle is known 

 to be vertical, either by hanging a plumb-line before the limb, or when 

 the telescope bisects at the same time an object and its image reflected 

 from a fluid. When the cross level is adjusted, the horizontal wire of 

 lescope may be set right by making a star in the meridian run 

 along it, or else by bisecting a fixed object with it, and afterwards 

 moving the circle in azimuth. The object should run along the wire, 

 and by twUting the wire-plate round may be made to do so. 



In the astronomical use of the instrument the azimuthal circle is 

 scarcely required, except to see that you have turned the circle 1 80 at 

 each reversal. It is convenient to have a coarse division to show this ; 

 it is a relief to the eye, and prevents the possibility of catching a 

 wrong star. Any stop which is adjustable and gives notice when the 

 i) ha* reached 180 will do. In many of Troughton's repeating 

 circle! there i a pin which is pressed by a slight spring against two 

 holes in the azimuth circle, which are 180 apart. This is convenient 

 enough if the observations are confined to Polaris, or a very slow 

 moving star, but wholly insufficient for stars near the equinoctial. It 

 supposes besides that the feet of the instrument are almost exactly 

 placed with respect to the meridian, which is not to be done at once. 

 A bar moving rather stiffly on the vertical axis, and coming against a 

 top, seems a better contrivance. 



Kor setting to the approximate zenith distance, there is a graduated 

 semicircle attached to the level, which may be seen in the general 

 view. This has iU diameter parallel to the level. A slender bar is 

 attached to the object end of the telescope, and passes at the back of 

 the circle ; this points out on the semicircle the approximate zenith 



AHT AMD SCI. D1V. VOL. VII. 



distance of the star. In many circles which we have seen there are 

 two slips of brass which slide with a little force on the semicircle, and 

 the slight bar above mentioned ia brought to touch each of these atopa 

 alternately. Nothing can be more convenient, but unfortunately, how- 

 ever well the clamps may be made, the contact between the bar and 

 a stop forces the clamp somewhat, and the essential condition of the 

 instrument, that these should be undisturbed, is destroyed. The bar 

 should not be allowed to touch the semicircle at all, but stand freely 

 from it. In this way, by alternately bringing the bar to the equal and 

 opposite divisions, when either the telescope or the level is moved, the 

 telescope will always be at the proper altitude when the level is hori- 

 zontal. If any one should wish to use the repeating circle as an 

 altitude and azimuth circle, or as a surveying instrument, the wires of 

 the telescope must be set at right angles to the circle axis, by bisecting 

 a distant and distinct object, reading the azimuthal verniers, turning 

 the instrument half round, again bisecting the object, and reading the 

 verniers a second time. If the object be very distant, the azimuth 

 circle may be set to the mean of the readings, and the object bisected 

 by the horizontal screws, which draw the wire-plate ; but if very great 

 accuracy is required, either two marks must be set up having the same 

 distance from each other as lies between the two positions of the axis 

 of the telescope, or the angle which this last space subtends at the 

 distant mark must be allowed for. The instrument is not fitted for 

 nice observation with the azimuth circle. 



We have now explained the chief astronomical use of Borda's circle, 

 which is that of determining the altitudes of stars upon the meridian 

 by several observations near the meridian. There is a correction to be 

 applied to the mean result, which is easily computed when the approxi- 

 mate latitude and exact time are known. The formula) and tables 

 required may be found in several works on astronomy, in Schumacher's 

 ' Hiilfstafeln,' p. 38, and Baily's ' Tables,' p. 154. The length of time 

 during which the observations may be carried on depends on the 

 altitude of the star and its proximity to the pole. Polaris might be 

 observed safely beyond 36 on each side the meridian, which is the 

 extent of the present tables, and, in these latitudes, stars in or below 

 the equinoctial for fully half an hour on each side. It is supposed that 

 the error of the clock is well known, but even this may be wrong to 

 a small amount without causing much error, if the number of obser- 

 vations on each side the meridian and the hour angles are nearly 

 equal. 



The repeating circle may be very well used for getting the time 

 either by equal altitudes, or by absolute altitudes with one or two 

 repetitions. For this purpose there should be three or five horizontal 

 wires, and the instrument should be previously carefully adjusted. 

 The instrument must be moved in azimuth, so that the star passes 

 each wire near the centre, and nothing should be touched which affects 

 the level. For illumination by night, there is an opening with a 

 reflector in the centre of the telescope. This is objected to as weaken- 

 ing the telescope, but the other mode of illuminating by a small 

 central reflector, or outer ring in front of the object glass, is incon- 

 venient. Perhaps by taking a longer hold of the telescope and 

 strengthening the intervening portion of the tube, the former con- 

 %-enient arrangement may be preserved without sensible loss of strength. 

 The repeating circle, on Borda's construction at least, cannot be well 

 employed in observing the sun without very careful screening. The 

 level is so perpetually changing its zero, when exposed to the sun, 

 that there is no possibility of saying what the instrumental zenith is. 



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-screw, 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 Delanibre's ' MfSthodes Analytiques pour la 

 Determination d'une Arc du Me'ridien,' &c. , Paris, An VII.; in the 

 ' Discours Preliminaire,' by the same author, contained in the ' Baso 

 du Systeme Metrique Decimal,' 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 ? We should answer that ( in the first place, the construction 



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