REPEATING CIRCLE. 



till the vernier -bar touches the fecond flop, and during this 

 motion, the revolving verniers have moved backwards juft 

 double tlic rough diftance with the attached circle, that they 

 did forwards before without it ; confequently the fixed ver- 

 niers will now read the fame angle at the riglit of zero, that 

 the revolving verniers did on the left, when the clamping is 

 again made and the contaft completed ; but Hill this is only 

 a fecond mode of reading a fingle meafure of the angle, 

 and nearly all that is yet gained in accuracy, is the exter- 

 mination of the index error, and that of the dark glafs, if 

 ufed ; thefe errors having been alternately pofitive and nega- 

 tive, if any exilted. Thefe two meafures, feparately read, 

 are equivalent to Borda's crojfcd obfervation, as he calls it, 

 becaufe the motion of the vernier-bar croffes the point zero 

 in his fixed circle : here it is prefumed that the two obje£ls, 

 that include the angle, are equally luminous ; but if not, it 

 will be neceflary to invert the face of tlie inltrument before 

 each fecond, fourth, fixth, &c. contaCi, and then the mo- 

 tions will all be forward, or from right to left, which other- 

 wife would be alternate : the iecond reading, however, may 

 be omitted ; the revolving verniers, being unclamped, muft 

 be moved again to the firll ftop in the original pofition, 

 where, the contatt benig complete, they will give a double 

 meafure if examined ; but the readings are yet omitted : the 

 fixed verniers are now unclamped, the inftrument again 

 inverted, and the contaft completed, when thefe verniers, if 

 examined, will alfo give double meafures ; and thus treble 

 and quadruple meafures mull be had fuccefllvely at both the 

 revolving and fixed verniers, or even more, if the circle has 

 not been palled over by each pair of verniers, before the 

 readings are required to be examined, and then the average 

 of all the meafures by the fixed verniers, added to an aver- 

 age of aU the meafures by the revolving verniers, will 

 afford the means of getting an average of the whole number 

 of meafures. 



FroQi this defcription of Hafsler's mode of applying the 

 repeating principle, it will be obvious to the reader, that 

 the diametrical bars of the two pair of verniers muft not be 

 contiguous to each other, when the glafles called the horizon- 

 glafs and index-glafs are parallel ; and accordingly we find, 

 on examining an inftrument of this conftrudlion,that thefe bars 

 crofs one another at right angles before the operations begin ; 

 but as there is but one zero in the circle, one pair of the 

 verniers muft neceflarily begin at 90°, when the other pair 

 begins at o ; confequently ninety degrees muft be deduAed 

 from the fum of the meafures of this pair before their aver- 

 age is taken : otherwife, if neither pair of the verniers begin 

 at zero, the two numbers from which they refpeftively com- 

 mence muft both be dedufted before the averages are taken, 

 in W'hich cafe it will be of no importance at what part of 

 the flying circle the operations begin. Should the reader 

 find any difficulty in comprehending this defcription of 

 Hafsler's repeating circle, without a reference to a drawing, 

 we recommend that he refer to our account of reflefting cir- 

 cles, defcribed under the article Circle, where he will find 

 the account of the two feparate inftruments of which this 

 forms an union ; and at the fame time will fee how it differs 

 from Mendoza's, which gives double refults. 



By way of illuftrating the ufe of Hafsler's repeating cir- 

 cle, we will fuppofe that fome known ftar is to the eaft or 

 weft of the moon, and that the longitude of the place of 

 obfervation is required from an aftual meafurement of tlie 

 diftance of the faid ftar from the moon's limb, when com- 

 pai'ed v.-ith its computed diftance as given for a certain hour 

 on the fame evening at Greenwich, in the Nautical Almanac : 

 •we will fuppofe the glufles of the circle adjufted, and the 

 fmall telefcope fcrewed into its fockct, and fo adjufted both 



14 



for diftinA vifion, and comparative brightnefs of both objefts, 

 that the ftar can be brought to touch the moon's limb, and 

 have a fenfible contaft ; in the firft place, hold the plane of 

 the circle in fucli an inclined pofition that it may pafs 

 through both objects, and get the ftar into the field of view, 

 while the revolving verniers are at zero, and the fixed onefl 

 clamped at 90° ; in the next place, move the revolving 

 verniers with an equable motion, and let the eye follow the 

 ftar, or rather the image of it, till it comes to the edge of the 

 moon, which it may be made to approach by a proper motion 

 of the body ; then clamp the index there till the ftop is put 

 on the femicircle very nearly to touch the edge of the index, 

 where it muft remain ; the fecond ftop muft alfo be put to 

 the fame divifion on the femicircle at the other fide ef its 

 zero, provided this zero be co-incident with the zero of the 

 circle ; or, which is the fame thing, the diftance between 

 the ftops muft be fomewhat more than double the angle 

 to be meafured ; the contaft may now be completed by 

 the tangent-fcrew ; let the fixed verniers be unclamped, and 

 the releafed circle and revolving verniers be made to recede to- 

 gether till the fecond ftop gives them a check, there they mull 

 be clamped and the circle inverted, when the ftar will again be 

 feen nearly in contaft, which muft now be made entirely fo 

 by the fcrew of flow motion ; in the next place the move- 

 able verniers, being firft unclamped, muft be carried again 

 to the tirll ftop and clamped, to make the contaft as before, 

 after the inverCon of th.e circle has again taken place ; and 

 in this manner the revolving verniers muft be moved to the 

 firft ftop, and the verniers and circle together to the fe- 

 cond ftop, before each inverfion and contaft, till five, fix, 

 fevcn, or more alternate operations have been gone through, 

 and the whole circle has been travelled over, which may 

 always be known from the pofition of the ftops. The ex- 

 aft times muft be noted at the beginning and end of thefe 

 operations, which by an expert obferver will be gone 

 through in a few minutes, and the mean time will be 

 had of the moment correfponding to the mean of the re- 

 peated obfervations : at thefe times the affiftants muft alfo 

 take each their two altitudes. Say now that the ftops 

 were required to be nearly at 40° at each fide of zero of 

 the femicircle, or that the diftance between them was So°, 

 ^vithin a few minutes over, and that there were nine ob- 

 fervations thus made with the revolving verniers, and 

 eight with the fixed ones, which numbers fuppofe the firft 

 and laft meafures to be taken with the fame pair of verniers, 

 or with the fame face of the circle uppermoft ; fay alfo, 

 that the final readings by this pair of verniers were refpec- 

 tively i*^ 10' 20", and 181° 10' o", or rather 361° 10' 20", 

 and 541° 10' o", becaufe thefe verniers completed the entire 

 circle ; then if we diminifh the latter reading by 180°, 

 its diftance before the other, we fhall have 361 "' 10' o", 

 and the average of the pair of oppofite verniers will be 

 361° 10' 10", which quantity divided by 9, the number of 

 meafures taken by them, will give a quotient of 40° 7' 8".9 

 for the firft average of the diftance, refulting from the oper- 

 ation of the revolving verniers alone ; again, let the final 

 readings of the fixed verniers be refpeftively 50° 57' 20" 

 and 230° 57' 30" ; but if we increafe the firlt reading by 

 360°, we fliall have 410° 57' 20", which muft be di- 

 rainifhed by 90°, becaufe it ftarted from this number, and the 

 remainder will be the correft reading, namely 320° 57' 20' ; 

 alfo 230° 57' 3c" increafed by 360^ is 590° 57' 39", 

 and this number diminiihed firft by 90°, as before, and 

 tlien by 180°, the diftance by which it precedes its fel- 

 low-vernier, will be 320'' 57' 30", and coniequently the 

 average of the two final readings of the fixed verniers will 

 be 320° 57' 25", which fum divided by S, the number of re- 

 peated 



