iri.K. 



KEPEATINQ CHI' II 



of Bunk u by no means satisfactory for an ntnmmiaU instrument ; 

 it it weak, and heavy, and rickety. But U a pertaUt astronomical 

 circle u wanted, and i. > this elaaa of instruments we should oonfine the 

 repeating circle, we think the following alteration ahould be adopted. 

 The telescope hang* looaely from ita centre,* and whatever care may 

 be taken by the artist, the flexure of each end must be considerable, 

 probably different, and possibly varying from time to time with varia- 

 tion* ill the temperature. It should be grasped by two lining oollan 

 near the enda of a diameter of a remier circle, and the teleecope might 

 then be safely exUaded three or four Inches each way beyond the 

 \gain, the axia damp which hold* the vertical circle 

 should be fixed OB the pillar and embrace, the rim of the inner circle, 

 the clamp of the level (for no aecond teleecope U wanted) might be at 

 the back, above, and quite out of the way. The wbolo circle ahould 

 be brought a cloee to the upright pillar ai possible, and pcrbapi it < 

 axia had better be fixed by toe maker permanently at right angles to 

 the pillar. This would take away much Wright and give great firm- 

 neat to the whole instrument. 



It must however be admitted that imlcea there are two intelligent 

 obBerven, or unleia the baae on which the instrument atandi in so 

 steady a to prevent the poaaibility of any derangement when the 

 observer movea from the teleecope to read the level, that errors may 

 creep in, though not, as it seems to us, greater than in all other iuxtru- 

 mrnU not reflecting. We have previously cautioned circle observers, 

 and the warning cannot be too strongly pressed upon our countrymen 

 at least, that the lent must alirayt be noted contemporaneously with 

 the Aurcfioa of the star. If the foundation 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 

 instrument is affected by the weight or motion of the observer, the 

 lurl after bisection is no test of the position ai bisection, and two 

 observers are absolutely necessary. In Borda's repeating circle, where 

 the clamp is necessarily imperfect from the shortness of its bearing, it 

 is impossible to move the front telescope without shifting the circle a 

 little at the same time ; but this U .of uo importance, for the level 

 shows the change, and the reading off of the level, wheu properly 

 applied, corrects this error. 



In judging of the repeating principle as applied to any instrument, 

 attention should be paid to the perfect independence of the telescope 

 and level with respect to each other, and to their perfect connection 

 with the circle when they are clamped to it. In some 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 unclamping is going on, and the construction has, 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 hold 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 off. 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 come within 1" of the truth. 



It may be worth mentioning that with the circle of Borda the 

 measurements may be made by moving the telescope contrary to the 

 order of divisions, that is, if the first observation is made with the 

 face to the right hand instead of the left. There is no advantage in this 

 modification, except perhaps that, as the screws are handled a little 

 differently, any discrepancy between an angle measured in the two 

 ways would show an error in one or both the methods. It would be 

 advisable, where several series are taken, to vary the direction in which 

 the telescope is brought to its new position, and that in which the 

 circle is turned upon the star. The tangent screw might be worked 

 either constantly one way or the other, or alternately, but we should 

 not expect any sensible difference in the results if the instrument is 

 well made and the observers careful If two steady observers can be 

 found, the double altitude of any star may be repeated, with the 

 genuine Borda and its two telescopes, exactly as a terrestrial angle/that 

 is, by measuring the angle between the star seen directly and by 

 reflexion from mercury. This would in theory appear to be the most 



If the object nd eye end bend equally, there U no alteration In the 

 direction of thr line of light ; the only evil i* that the ob'.ique Incidence of the 

 rays on the object glau dcfornu the Image when the obliquity U considerable. 

 Tbs German trtit of Relchenbsch'i wliool apply lever* to telescope* hung by 

 the middle. In order to counteract flexure. We prefer, on the whole, obtaining 

 a maximum of itlffnr**, and then determining the effect of flexure which mutt 

 be allowed for. Tin-re ii no possibility of avoiding the investigation in any 

 cue where accuracy li demanded. Osmbey takes a longer hold of the telescope, 

 but In providing a motion for nrreytng when the circle la horicuntal, wp 

 think he hat lott something In liability when tin- circle It vertical. 



perfect application of the instrument, as flexure has no effect upon the 



ingle measured, being equal and in the same direction in i>tl, 

 tiona of the telescopes. The level U not wanted fur thin observation 

 at all, but the circle must be set truly vertical A single observer might 

 indeed make the same observation with one telescope, as the level 

 would show and measure any shifting of the circle. And here again 

 the effect of flexure U eliminated from the observed double altitudes. 

 Finally, double nadir distances may be observed of a star reflected 

 from a mercurial horizon, exactly as double zenith distances are 

 observed in the ordinary method. This last species of observation 

 may have the advantage of being sometimes more eonvi nicnt. Imt tin- 

 chief reason why it is pointed out is, that the effect oi tl. \un- upon 

 double nadir distances is equal, but in a contrary d,i.. ti..n. to its 

 effect on double zenith distances; the observer has thus an easy 

 f ascertaining whether flexure exists, and of measuring ita 

 amount and law. We suppose that the apparent nadir distance of a 

 reflected star is the same as the zenith distance of the star seen 

 directly. The horizontal points of all the large circles which we 1. 

 vary to some extent with the altitude of the star observed, whi> h 



contrary to what is here supposed. Thin lat mention 

 creponcy is one of the most perplexing points in modern practical 

 astronomy. The amount is, however, so small as scarcely to - 

 sensibly any conclusion drawn from reflected observations with so 

 lunall on in-t runiciit as a repeating < 



What, pi-credes refers almost entirely to the repeating principle 

 when applied to measurements in altitude. Instead of the circle of 

 Borda and its two telescopes, later artiste have given a motion in 

 azimuth to their theodolites, in addition to the motion of the tele- 

 scopes and verniers, by which the angle can be measured precisely as 

 r's original instrument. But in several instruments which we 

 have seen there is a considerable probability of disturbing the 

 clamp while moving the telescope or using ita tangent screws. It is to 

 secure the detection of any similar motion that a watch telescope, as 

 it is called, is frequently added to English theodolites, and is indeed 

 required for many, spoiled as they are by an unnecessary adjustment 

 to zero, to save indolent or ignorant surveyors a simple subtraction. 

 A watch telescope can scarcely be applied to a repeating theodolite, 

 and we think that the repeating tripod may be so mode as to be free 

 from any objection. This was first constructed by Mr. Dollond on 

 the suggestion of the late Astronomer Royal, and has been found very 

 useful in the trigonometrical survey of Irrl.-md. 



The three foot-screws of an ordinary theodolite ore placed in the 

 three notches which are seen on the table of the tripod. This ui>; .T 

 I-art turns heavily on a stout short centre, it is fixed by a cl.iin; 

 and there is a tangent screw at i> for giving slow motion. The steady 

 action of the tangent screw is secured by a spring at c. It is evident 

 that if, in using an ordinary theodolite, R (the right hand object) is 

 first bisected, the circle read off, and then L (the left hand object) is 

 bisected, the circle being again read off, that the difference b> 

 the two readings is the angle to be measured, if the inttruw id 

 been tkifted, and if the bisection, reading off, 4c., are perfect. Now 

 suppose the whole instrument to be taken up and set down exactly 

 concentric with its first position, without any other alteration, but 

 with the telescope on R ; if L be a second time bisected, the difference 

 between this latter and the preceding reading will lie also the 

 angle to be measured, and therefore the vernier will have passed 

 over twice the angle, reckoning from the beginning. If, instead of 

 this impracticable taking up and setting down again, the stand 

 on which the theodolite rests con be turned round concentrically 

 so that R is bisected by the telescope, the theodolite itself 

 untouched, it is clear that the operation is equivalent to that just 

 described, and consequently that the telescope being brought on L by 



Fig. 3. Repeating Stand by Menem. Trougliton and Slmrn*. 



motion, the measure is obtained of twice the angle re 

 ..ml the process may be continued ad libitum, until the errors of read- 



