213 
 
 UC-NRLF 
 
3 uncLer signed, on^foeficulf-Qj 
 
 +, begs leave to request 
 
 the a,Goept CL7iGe of the 
 
 Director of the Ciuoinnati Observatory. 
 
ERRATA. 
 
 PAGE 
 
 LINE 
 
 FOR 
 
 / READ 
 
 7 
 
 35 
 
 third 
 
 thread 
 
 8 
 
 16 
 
 than demanded 
 
 than is demanded 
 
 13 
 13 
 
 19 
 33 
 
 pure 
 
 j mere 
 
 16 
 
 4 
 
 otherwhere 
 
 j elsewhere 
 
 20 
 
 36 
 
 its principal step 
 
 * in its principal steps 
 
 22 33 
 23 
 
 ,34 
 
 48 
 
 j thereby measured 
 { labor proves itself 
 
 here 
 
 f increase of labor thereby 
 ^ j produced proves 
 
 herewith 
 
 24 
 
 24 
 
 has 
 
 " have 
 
 25 
 
 9 
 
 a (in 1st column) a 
 
 27 
 
 2 
 
 3640 (" " " 
 
 ) 3540 
 
 28 
 
 8 
 
 219 ( 7th 
 
 )v210 
 
 28 
 
 29 
 
 13720 ( " 5th " 
 
 ) v 1272( 
 
 28 
 
 47 
 
 345 ( " 7th " 
 
 ) v344 
 
 33 
 
 3 
 
 clock-chronometer 
 
 ^ clock or chronometer 
 
 33 
 
 9 
 
 right 
 
 v night 
 
 33 
 
 12 
 
 swerving 
 
 ^reversing 
 
 33 
 34 
 
 53 
 34 
 
 (Omit the last commas/and close up the line.) 
 \/ 
 near one thread over one thread 
 
 35 
 
 37 
 
 for either of 
 
 ^ for the first three of 
 
 36 
 
 25 
 
 methods 
 
 V method 
 
 37 
 
 42 
 
 bi+bo+Aip+Aip 
 
 y b^bo+Aip+Asp 
 
 38 
 
 7 
 
 Erase and insert: 
 
 bO cos Z (To L\)^sin Z 
 
 38 48 
 
 ,49 
 
 sin a (and) cos a 
 
 sin^d (and) cos/d 
 
 39 
 
 11 
 
 J=&c. 
 
 J t^- &C. 
 
ERRATA. 
 
 PAGE LINE 
 
 FOR READ 
 
 39 45 
 
 quantity ,n <J quantity n 
 
 39 3 
 
 (cotg ^ tg <J) v (cotg <p tg rf cotg 2 ^) 
 
 40 1^ 
 
 v= tg <p cotg rf v v =tg G> cotg 6 l 
 
 40 47 
 
 2 cotg 2 V 2 cotg 2 d> 
 
 41 29, 39 
 
 n 2 C 2 c y u 2 qz C 2 c 
 
 42 12 
 
 factors v functions 
 
 42 14 
 
 Wrangel v/ Westphal 
 
 
 GENERAL STAR CATALOGUE. 
 
 STAR NO. 
 
 COLUMN FOR READ 
 
 4, 29, 53 
 
 3 Hydrae Hydri 
 
 59 
 
 5 20 m ^ 29 m 
 
 92 
 
 3 Geminorum v E Geminorum 
 
 109 
 
 p Cancri v 6 Cancri 
 
 112 
 
 3 * (15) Argus . 15 (i) Argus 
 
 154 
 
 5 27 s 25* 
 
 170 
 
 a 1 GruciN a Crucis 
 
 170 
 
 7 v)-\ 22\^ 
 
 171 
 
 3 b Corvi 5 Corvi 
 
 199 
 
 3 ? Bootis {/6> Bootis 
 
 200 
 
 7 30 /x */36 /x 
 
 219 
 
 3 A 2 Ursae Minoris ^ 7 2 Ursae Minor 
 
 251 
 
 7Q10 y^-LOTO 
 Gi -rol 
 
/c/ t^JLt fist - /Y 4f- < 
 
 / 
 
 THE 
 
 PORTABLE TRANSIT INSTRUMENT 
 
 VERTICAL OF THE POLE STAR, 
 
 TRANSLATED 
 
 FROM THE ORIGINAL MEMOIR OF WM. DOLLEN, 
 
 BY 
 
 CLEVELAND ABBE, 
 
 DIRECTOR OF THE CINCINNATI OBSERVATORY. 
 
 WASHINGTON. 
 
 GOVERNMENT PRINTING OFFICE. 
 1870. 
 
4 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 in and of itself be sufficiently trustworthy, we shall often do well, for the 
 sake of observing Polaris, to renounce the other advantages that accom 
 pany an observation made as near as possible to the meridian. 
 
 This will, however, be absolutely necessary, if perhaps, as only too 
 easily happens with the traveler, the mounting is by no means solid enough 
 to sufficiently assure the invariability of the instrument during the entire 
 interval necessary to a complete time determination in the meridian. In 
 fact, under such" circumstances no other method remains than to limit 
 the duration of the observations to the shortest possible time, and to 
 effect this, therefore, it is necessary to not wait until the proper stars, 
 especially those situated near the pole and necessary for orientation, have 
 reached the meridian, but to leave the meridian and to seek the most 
 appropriate of them all, Polaris itself, wherever it may be in. its diurnal 
 circle. The dexterity of the observer will then show itself in the short 
 ness of the interval which elapses after or even before the transit of Po 
 laris over one of the threads of the reticule and the observation of the 
 transit of the time star proper, (of course on all or at least as many 
 threads as possible;) and we know from much experience that with a 
 little practice this interval need be only a few minutes. The observa 
 tion in the first position is completed by a careful determination of the 
 inclination of the horizontal axis, or, as is very desirable, by two determi 
 nations inclosing the observations of the stars, and whose agreement 
 bears testimony to the actual invariability of the instrument. It is, how 
 ever, important immediately to execute a similar series of observations 
 in the other position of the instrument, in order to free the result from 
 the influence of the error of collimation and the difference in diameters 
 of the pivots, without being under the necessity of taking these quanti 
 ties from other sources. 
 
 It is easy, and will certainly also be intended in these observations, to 
 observe Polaris both times upon the same thread, by preference the mid 
 dle thread, and the succeeding computation will, in fact, be thereby 
 somewhat simplified. One easily sees, however, that so far as concerns 
 the true object of the observation, this is quite without serious import 
 ance, while in the execution of the observation a great relief may result 
 from not being bound to any such condition. This stands in connection, 
 however, with certain imperfections of the transit instruments in their 
 present construction, to which the attention of the observer deserves to 
 be especially called. 
 
 3. The instrument to which the following remarks are especially ap 
 plicable is theErtel portable transit instrument, although they certainly 
 have also a more general importance. This instrument, in different 
 forms, but all of nearly identical construction, has attained an extensive 
 distribution, and may, indeed, through the descriptions given in words 
 and drawings in different authorities, be considered as generally known. 
 It differs chiefly from the formerly much-used Trough ton s transit in the 
 broken telescope and the possibility of the motion about the vertical 
 axis. The former secures a marked facility in the observation, especially 
 in the neighborhood of the zeriith,.and by reason of the shortening of the 
 supports of the horizontal axis conduces much to give a greater rigidity 
 to the entire instrument. The other change had certainly as immediate 
 object to facilitate the exact adjustment in any azimuth, especially in 
 the prime vertical, but the slow-motion screw serving thereto and the 
 careful divisions of the horizontal circle, for reading which four verniers 
 are provided, as well as the circumstance that by the pressure of a sup 
 porting spring the motion of the limb, in respect to the alidade, can be 
 facilitated at will, give reason to suspect that the additional design was 
 
THE VERTICAL OF THE POLE STAR. 5 
 
 entertained of rendering possible the exact measuring of horizontal 
 angles. 
 
 But since any such intention is, through the absence of the assurance 
 (or watch) telescope, only to a limited degree attainable, the greater mo 
 bility in azimuth therefore directly and very seriously endangers the 
 excellence of the instrument as a transit. The clamp that ought to hold 
 fast the two circles, with^ efereiice to each other, and thereby, therefore, 
 the moveable upper, with reference to the immoveable lower portion, 
 performs this service very imperfectly, not only because it operates only 
 on one point, and that a point on the circumference, but also because of 
 the slow motion that is combined with it. Very soon, therefore, it was 
 that two simple clamping screws, distant 180 from each other, were ap 
 plied, wfiich are to be tightened as soon as the instrument is brought 
 into the proper azimuth ; and these are quite well adapted to greatly 
 increase the security of the mounting. 
 
 On the other hand, not only is the exact adjustment in a known azi 
 muth, as given by the readings of the circle, made almost impossible by 
 reason of these clamping screws, since their greater or less tightness is 
 accompanied by sensible flexures and corresponding derangements in 
 the azimuth, but, furthermore, directly through these flexures is the ful 
 fillment of the other condition, that the inclination of the horizontal axis 
 shall be always the least possible, made much more difficult. These 
 clamp screws can, moreover, if they are not applied to the proper points, 
 give rise to a further danger, against which one must be forewarned. 
 Evidently they should only be placed at the points where the supports 
 of the horizontal axis are. In the earlier instruments they are, indeed, 
 always found at these points, and only recently they have been placed 
 90 distant therefrom, probably for the sake of greater convenience in 
 the manipulation; this is, however, precisely where they least of all re 
 alize their object; for if the previously-mentioned supporting spring be 
 even very slightly compressed, then, notwithstanding the tightening of 
 the misplaced clamp screws, the supports of the Y s will remain in a more 
 or less unstable position, and thereby is generated the danger that the 
 inclination of the axis may change when the level is set upon it. 
 
 We have persuaded ourselves, by direct trials, that the danger is not 
 a fancied one, but that in the above way very sensible errors can arise. 
 These become very apparent if on such an instrument with the spring 
 compressed a series of levelingsin alternate positions is made, as though 
 for the determination of the difference of the pivot diameters. In case 
 the necessary care in the reversions has been taken, we may certainly 
 receive very accordant but entirely deceptive values ; for, the influence 
 of the unequal pivot diameters will have entirely disappeared, in com 
 parison with that of the unequal weights of the two sides of the instru 
 ment. Therefore it is indispensable that in using such an instrument 
 the spring should be perfectly slack, in order that before the tightening 
 of the clamp screws the upper portion may rest entirely around with its 
 Avhole weight, even though thereby the slow motion in one direction will, 
 to a great extent, refuse to work. On no account, however, should the 
 circumspect observer neglect to make a special investigation with the 
 object of determining whether the application of the level itself does not 
 still alter the inclination of the axis. 
 
 4. What precedes will quite suffice to show that some experience is 
 necessary in order successfully to conduct the series of observations in 
 that rapid succession which constitutes the importance of this method, 
 as also that it affords a very important relief to be allowed to observe the 
 Pole Star on any thread, but especially upon different threads, in the 
 
6 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 two positions. This latter finds its full importance if it is thereby made 
 possible to preserve the former azimuth alter the reversion. Independ 
 ent of the convenience which thus results to the observer, since he needs 
 only once to clamp his instrument and adjust it for the inclination of the 
 axis, the accuracy of the observation itself will thereby undoubtedly be 
 increased, since it is well known that for some time alter every change 
 in the position of the instrument there remains the danger of a reaction 
 ary change; and finally one finds a very acceptable control for the entire 
 operation in that for each position the same azimuth should result, al 
 though so far as the determination of time is concerned it is only neces 
 sary that the position of the instrument should not have changed during 
 the observation in each position by itself. 
 
 This, however, it must be confessed, at least for our present instru 
 ments, assumes that the Pole Star has a definite motion in azimuth. 
 Therefore, in the immediate neighborhood of its elongation this advan 
 tage must be renounced, and we are reduced to the necessity of adjusting 
 anew the instrument in each position upon the almost motionless star. 
 For, that Polaris becomes in general in this portion of its daily orbit 
 less proper for our object, and therefore may, or even must, be replaced 
 by another star in the neighborhood of the pole, perhaps by 3 Ursae Mi- 
 noris, is, as it seems, a wide-spread yet manifest error. This has proba- 
 ably arisen, first, from the fact that the determination of the moment 
 when the star bisects the thread will truly be then very inaccurate, and 
 that, secondly, the reduction of such a transit from the thread to the 
 great circle will always be large, and, under some circumstances, infinite. 
 
 Now, as concerns the first point, we shall, on consideration, recognize 
 that therein not only no disadvantage exists, but there even results an 
 advantage to the actual object of the observation, since precisely then 
 the orientation of the instrument is achieved as accurately as the opti 
 cal force of the telescope will at all allow; and in reference to the sec 
 ond point it is to be remarked, that this is a difficulty existing only in a 
 certain method of computation, and therein is a proof that this method 
 is not the proper one. No, if we are to leave the meridian at all it must 
 be only for the sake of the advantage which the Pole Star offers; there 
 is really no sufficient reason for choosing any other star for the orienta 
 tion than Polaris. 
 
 At the same time, however, it is not to be denied that the observation 
 in the neighborhood of the elongation has its special difficulties. We 
 must, that is to say, not Avait until the star, by its motion, is brought 
 upon the thread, but must adjust the instrument directly upon the star, 
 Avhile, as above remarked, the azimuth will again be changed by the 
 fastening of the clamping screw. With some practice, however, this 
 difficulty is oveicome, in that the clamp screw itself can, up to a certain 
 point, replace the slow motion; but it is thereby always necessary care 
 fully to watch that the simultaneously changing inclination of the hori 
 zontal axis remains small enough to allow of its accurate measurement. 
 Furthermore, the correction of the inclination by means of the foot 
 screws offers a means of changing a little the position of the star with 
 reference to the threads, which can be occasionally very serviceable to 
 the expert observer for the attainment of his object, especially if the con 
 struction of the instruments allows the level to remain upon the axis 
 during the observation. Still another means of facilitating the observa 
 tion at the elongation consists in the use of a somewhat inclined thread ; 
 we have, however, on this point no experience as to how advantageous 
 this would prove itself in practice. 
 
 5. I allow myself, finally, two further remarks concerning the arrange- 
 
THE VERTICAL OF THE POLE STAR. 7 
 
 merit of the observations, regard to which can be of practical importance 
 under certain conditions. If we relinquish the maintenance of the same 
 azimuth in both positions of the instrument, it is then occasionally pos 
 sible to secure the other, in some circumstances not unimportant, ad 
 vantage of being able to observe the same time star in both positions. 
 This is especially important if no other time star of sufficient brilliancy 
 is at hand ; so that one must, without this resort, content one s self with 
 observations in one position. The application of such a method fails on 
 the approach of the time star to the zenith, on account of its increased 
 azimuthal change. Neglecting the error of collimation and the advance 
 of the Pole Star in azimuth, both which can affect the circumstances as 
 well favorably as unfavorably, then in the latitude of 60 a change in 
 azimuth of nearly 1 corresponds to a thread interval of 15 ; that is to 
 say, after the reversion the instrument must be changed in azimuth by 
 this quantity in order still to be able to observe the Pole Star on the 
 same thread ; and it is easy to decide what change in the hour angle of 
 the time stars corresponds to this change in azimuth. For a Bootis, for 
 instance, it amounts to nearly three minutes of time, and it depends only 
 upon the expertness of the observer and the arrangement of the instru 
 ment whether this interval suffices for the reversion and adjustment in 
 azimuth. 
 
 The other remark refers to the difficulty known to all observers of ob 
 serving the transit of Polaris if the star is very faint. Often one catches 
 the star very fairly at some distance from the thread, while on approach 
 ing it it completely disappears. The observation is then usually made 
 by noting the disappearance of the star on one side of the thread and its 
 reappearance on the other, and the mean of both moments is considered 
 as the time of transit. Of course, however, such an observation is far 
 less accurate than if the star remains visible upon the thread itself, and 
 it will therefore be the less available the longer the interval between the 
 disappearance and reappearance. Now, we have in such cases, with the 
 best results, replaced the observations upon the thread by the observa 
 tion in the middle between two threads, and find that with an appro- 
 J priate thicd. interval there results thereby scarcely an appreciably di 
 minished accuracy of observation. 
 
 6. If we review the previous remarks it results that for the determi 
 nation of time by means of a portable transit instrument, the method of 
 observation here considered is only in very special cases inferior to the 
 observation in the meridian ; on the other hand, in other circumstances 
 which far more frequently present themselves, it will, by this method 
 only, be possible to realize any determination at all ; and therefore the 
 advice seems to be authorized, that we do not shun the labor of putting 
 ourselves by means of the necessary practice, to a certain extent at least, 
 in possession of all the means which the instrument can offer to the ob 
 server to whom it is intrusted. 
 
 The judgment must, however, be quite different if it should be possi 
 ble to give to the instrument an arrangement by which the various diffi 
 culties, above mentioned, are still further removed from the observation. 
 And this is now in reality very completely attainable, and that through 
 changes which have already proved themselves as individually quite ap 
 plicable, although their aggregate combination has still first to stand the 
 proof of actual experience. Now, for our purpose, the most important 
 addition to our present transit instruments seems to me to be the intro 
 duction of a movable thread, whose position, with respect to the fixed 
 threads, will be any time recognized by means of the micrometer screw 
 that carries it. This change, since it only affects the ocular, is also com- 
 
8 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 paratively easy to effect in the existing instruments. The decisive 
 success which is actually attained with the large fixed instruments in 
 different places shows that by proper care and circumspection in the ap 
 plication and use of such a micrometer, an accuracy and reliability can 
 be attained that quite suffices for our purpose. But the importance due 
 to the movable thread in the portable instrument will be only A~ery im 
 perfectly estimated by the advantage that has resulted from its applica 
 tion to the large fixed instruments 5 for, important as may be, for these 
 latter instruments, the facility of observation thereby secured, the method 
 of observing remains unchanged, since, if we will free ourselves as com 
 pletely as possible from the assumption of the invariability of the mount 
 ing, then a meridian mark is indispensable. On the other hand, the 
 movable thread, to a certain degree, provides a meridian mark for the 
 portable instrument. This is the Polar Star itself, that can now on any 
 point of its daily orbit be with equal convenience and reliance observed 
 without a greater consumption of time than demanded to direct the tel 
 escope and point the micrometer thread upon the star, precisely as if a 
 mark were observed. 
 
 Together, however, with this important auxiliary to the achievement 
 of an accurate orientation of the instrument at any instant, provided al 
 ways the optical force of the instrument allows the Pole Star to be actu 
 ally perceived, are still two further changes in the instrument extremely 
 desirable, if we would impart to the entire determination of time the 
 greatest degree of security and convenience. That is to say, it is to this 
 end necessary, first, that not only during the observation itself but also 
 during the reversion of the instrument the level should remain, upon the 
 axis ; and second, that this reversion should be accomplished much more 
 rapidly, and especially more safely that is to say, without danger of any 
 other change than is attainable in the reversion with the unaided hand. 
 
 The possibility of a perfect execution of these arrangements, even in 
 smaller instruments, is circumstantially shown by experience; but 
 truly they affect the construction of the entire instrument so vitally that 
 they must, in planning it, necessarily be kept in view. The increased 
 labor and care to be expended in the construction of such an instrument, 
 and the increased costliness dependent thereon, should not, it seems, 
 come into consideration in contrast with the important increase in the 
 value of the observations resulting therefrom. Such expenditure will 
 be, even in a brief use, richly repaid by the saving in labor at every ap 
 plication, without its being necessary especially to mention the further 
 advantage that is found in the diminution of the danger of seeing the 
 series of observations that has been commenced interrupted before its 
 completion. 
 
 How important in reality is the diminution of the duration of the ob 
 servations which results from our method with instruments specially 
 constructed therefor, will be recognized if one once considers the course 
 pursued in a complete determination of time. As to what concerns the 
 preparation for the observation, that consists mostly in clamping the in 
 strument with sufficiently small inclination of the axis in such an azi 
 muth that the Pole Star appears approximately in the middle of the 
 reticule. As soon, then, as the observation of the transit of a proper 
 time star is finished, the level and Pole Star are read off; a re version of 
 the level upon the axis is not necessary if we at once reverse the instru 
 ment itself and thereby intentionally disturb neither inclination nor azi 
 muth. A second time star in this other position of the instrument with 
 the thereto belonging readings of level and Pole Star, completes the de 
 termination of time. 
 
THE VERTICAL OF THE POLE STAR. 
 
 It is seen that the duration of the whole depends mostly only upon 
 ho\v quickly the proper time stars follow each other in the heavens, and 
 will, therefore, in general, not need to exceed a very small number of 
 minutes. Finally, however, it is, after all, not this decided saving- of 
 labor, important as it in itself may be, that gives the desired contraction 
 of the duration of the observations its proper value, but this rests rather 
 upon the increase of the accuracy that arises therefrom. I estimate this 
 to be very considerable. But to enable any such opinion to claim a 
 universal recognition, it must be based upon unalterable numerical 
 values, which can only be obtained by actual application continued for 
 a long time and under the greatest variety of exterior circumstances. 
 Such numbers are at this moment not at my command, and I therefore 
 content myself with illustrating, by the following considerations, the 
 opinion that I have formed after many years experience in the matter. 
 
 One s first thought may be to increase the accuracy of the time deter 
 mination, if not to any at least to a considerably higher degree, by the 
 repetition of the observations. If we estimate about fifteen minutes for 
 the duration of a complete determination, which, according to what 
 precedes, is considerably more than what will generally be necessary, 
 then, in an hour, which in general certainly would not suffice for a com 
 plete time determination in the meridian, this may be four times 
 repeated, whereby the probable error of the final clock correction, in so 
 far as it depends upon the astronomical observation, would be reduced 
 to one-half. Xow I am of the opinion that this would be practically of 
 no use whatever. That is to say, I think that already the single deter 
 mination possesses such a degree of accuracy that, independent of error 
 in the star places, it cannot be further increased by multiplication of 
 observations ; even the circumstance that a uniformity in the chronom 
 eter rate must then be assumed for so much longer an interval, suffices 
 alone to annul the advantage of reducing by one-half the error of obser 
 vation. I mean, in all seriousness, that the probable error of such a 
 time determination, so far as the observation has an influence on it, 
 depends principally i\pon nought else than the accuracy of the observed 
 transits over the single threads, which evidently is the limit of accuracy 
 that any method whatever can afford. And should this, as I confidently 
 hope, be confirmed by unprejudiced examination, then will the expres 
 sion not seem too venturesome that in the construction of a portable 
 transit instrument, of moderate dimensions, according to the principles 
 above laid down, and in artistic perfection, such as we shall in a short 
 time receive from the hands of Brauer, a new epoch begins in the solu 
 tion of that very important problem, the absolute determination of time. 
 
 7. Finally, I cannot refrain from noticing Avith a few words more par 
 ticularly the especial occasion which has been before alluded to, and 
 which renders it extremely desirable that precisely now the great ad- 
 
 VW1 i"tl O*4-*t2 f\T "f"li-i 1 vi oi"l k /"wl /"v~f* /I ^ rf-nvi v* iTi 1 11 rv i-in^n \\ m*s\ ^/-ii r4 *! s^-rn-\ /I ^.T-* ^.-.-.1 /I 
 
 vantages of the method of determining time here considered should 
 
 given a start to which is a fit conclusion of the labors by which W. 
 Struve has so ably promoted geodesy during his whole life. 
 
 Already is the determination of the astronomical differences of longi 
 tudes along the entire arc appointed for the next two years. The trans 
 mission of time will everywhere, when possible, be made by means of 
 the electric telegraph. Since, however, at present the telegraph does 
 not directly connect the different points of the arc, the desired differ- 
 
10 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 ences of longitude Avill be obtained by means of the central telegraph 
 stations of the different States. Tims it will be possible that all the 
 time determinations upon the entire arc shall be made by the same 
 observer with the same instrument ; and furthermore, it is provided 
 that this shall be entirely independently carried out by the two different 
 observers, so tbat for each individual difference of longitude the neces 
 sary clock correction shall depend upon the quite independent time 
 determination of each observer. It is, however, equally designed that 
 each observer should be assigned to one and the same instrument. 
 Now, this instrument will indeed, in order to facilitate the labor, be 
 provided with a level that does not need to be removed during the 
 observation, and with a special apparatus for reversion. And still I 
 hold decidedly to the opinion that, independent of other difficulties, the 
 fulfillment of the programme for any night s observation, under the con 
 ditions connected with a complete time determination in the meridian, 
 will be possible only under very specially favorable, and therefore seldom 
 occurring, exterior conditions, especially if we, as certainly must be 
 considered necessary, will not relinquish the condition that the trans 
 mission of time be each time, and as closely as possible, included by 
 time determinations at each place. 
 
 Now, under these circumstances, the method here recommended 
 seems to be an especially fortunate expedient. Assuming our reticule 
 to consist of seven threads, then the two stars twice observed by each 
 observer give a sum total of fifty-six individual thread transits, and thus a 
 time determination that is quite comparable with a time transmission 
 by means of as many telegraphic signals. And the whole time neces 
 sary for this operation need be scarcely an hour. It seems useless to 
 attempt to increase the accuracy of the determination for one night by 
 repetition, as is easily possible ; imperative, however, is the repetition 
 on different nights, as is also prescribed in the adopted programme. 
 The final determination of the details in this respect, as also in general, 
 properly remains deferred until the accurate investigations which will be 
 made in the immediate future, as preparatory to the work of the next years, 
 be completed. For the present we are concerned only with the acknowl 
 edgment of a fundamental principle which I would thus enounce: 
 
 FOR THE ATTAINMENT OF A TIME DETERMINATION AT A GIVEN MO 
 MENT, THE PORTABLE TRANSIT INSTRUMENT WILL, UNDER ALL CIR 
 CUMSTANCES, BE BEST MOUNTED, NOT IN THE MERIDIAN BUT IN THE 
 VERTICAL OF THE POLE STAR. 
 
 The next months will bring us the final practical proof of the truth 
 of this thesis. 
 
 8. When the question as to the practical value of the method of obser 
 vation here considered is once settled, then will the overcoming of the 
 greater labor of computation be an object of comparatively secondary 
 importance. A nearer consideration shows, however, that this is by no 
 means so excessive as it appears at the first view ; and the relation is 
 even reversed in those cases where, for the meridian time determination, 
 we dare not be contented without the exact solution according to the 
 method of least squares. 
 
 The deduction of methods of computation which shall unite the great 
 est convenience of execution with the necessary accuracy of the results, 
 has been undertaken at different times and in different places, especially 
 lately on the part of Hanseu, in an exhaustive manner, in an article in 
 No. 1136, Vol. XLYIII, of the Astronomische Nachrichten. Starting 
 from the known general equation for the transit instrument, Hansen 
 gives first a direct exact solution by purely analytical means, which is 
 
THE VERTICAL OF THE POLE STAR. 11 
 
 well worthy of consideration by reason of the art with which the 
 unknowns are found from the transcendental equations. Since, how 
 ever, there can ne>ver be sufficient ground to make use of this exact but, 
 therefore, more tedious solution, there are next deduced approximate 
 formulae for actual use, which really leave scarcely anything more to 
 be desired. Although after this every further discussion of the subject 
 might seem idle, yet I venture in what follows to present the somewhat 
 different method that 1 for years have followed in treating this problem, 
 and that in very frequent applications has always proved itself to my 
 mind thoroughly appropriate. The direct exact solution to which I 
 arrive at first seems to me to recommend itself as very advantageous, 
 by reason of the exceeding clearness of the geometrical considerations 
 on which it is based; afterwards, however, this leads to approximate 
 formula} and precepts for computation which are so simple and conve 
 nient, and especially so entirely free from uncertainty in reference to 
 the signs of all the quantities coming under consideration, that they 
 perhaps deserve consideration even when compared with Hansen s. 
 
 9. For greater generality, and in conformity with the above remarks, 
 I in the following development assume that the two stars are not observed 
 on the same thread. After w r hat more immediately follows will be 
 found the reduction that is necessary if the time star is observed on 
 more than one thread. For the present tjie thread on which the time 
 star is observed is called the middle thread, and the thread for the 
 Pole Star is distant by /from this 5 thus, 90 + c and 90 -f c-f/ desig 
 nate the distance from the west end of the horizontal axis of the transit 
 instrument of the celestial points determined by these two visual lines. 
 
 The exact solution of our problem consists fundamentally in this, to 
 find the diagonal WP and the angle WPS of a spherical quadrilateral 
 WSPS , in which the four sides and the angle P are given. Let us 
 represent by W and P the points in the heavens to which the axes of 
 revolution of the instrument and of the earth are directed, and, to leave 
 nothing uncertain, the west pole of the instrument and the north pole 
 of the equator; S and S <, on the other hand, the places of the Time Star 
 and of the Pole Star at the moment of observation; we thus kuow r at 
 first, 
 
 c, WS =9(P + 
 
 PS=90 3, PS / 
 
 Finally, the angle SPS 7 , which Ave will designate by r, would be simply 
 the difference of the right ascensions of the two stars, if both were 
 observed at the same moment. Since, now, some time at least must 
 elapse between these two observations, this difference is still to be 
 changed by the hour angle corresponding to this interval; and in this 
 nothing further is assumed than that we know the clock rate sufficiently 
 well to make this change in hour angle with an accuracy corresponding 
 to the accuracy of the observations. If, however, the observations are 
 arranged as is proper, then even without the movable thread would 
 this interval never be greater than from five to six minutes, and then a 
 correction on account of the clock rate would scarcely be further 
 demanded, even if the chronometer kept mean time instead of sidereal 
 time; the estimation of the moment when the Pole Star is on the thread 
 is assuredly, with a portable transit instrument, not certain to within a 
 second, even in the neighborhood of the culmination. The concluded 
 clock correction belongs, of course, to the moment of observation of the 
 time star. 
 
 Let a great circle be drawn through the points S 7 and S ; then is the 
 
12 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 exact deduction of WP and the angle WPS given by the following- 
 equations : 
 
 f (1) sinSS siiiPSS ^BinPS sinSPS 
 
 (I) A S P S : ? (2) sin S S cos P S S == sin P S cos P S cos P S sin P S cos S P S 
 ( (3) cos S S = cos P S cos P S -f sin P S sin P S cos S P S 
 
 (II) A W S S : cos W S S = cosWS -cosWS cosSS 
 
 sin W S sin S S 
 
 t (1) sin \V 1* sin W P S = sin W S sin W S P 
 
 (III) A W P S: J (2) sin W P cos W P S = sin P S cos W S cos P S sin W S cos W S P 
 t (S) cos W P = cos P S cos W S + sin P S sin W S cos W S P 
 
 We will now introduce the above-chosen notation, , <$ , e,/, r, into 
 these equations, and also the following: 
 
 (7, PS 8 =*; 
 
 whose immediate object is merely to indicate at once such quantities as, 
 in the application, can never be other than small. In case the arc S S , 
 or the distance of the two points in which the stars are observed, is 
 neither very near 180 nor near 0, both which cases are excluded by 
 the nature of the problem, then is r t of the same order as c and/, while 
 r, w, <r, as also the difference d <J, are of the same order as P S . 
 
 But, entirely without reference to the magnitudes of all quantities, our 
 exact formulae are now the following : 
 
 c (1) cos d sin = cos 6 sin - 
 
 (I) A SPS :< (2) cosdcosf=cosJ sin <5 sin dcosrf cos 7 
 (3) sin d sin d sin 6 -f cos 6 cos 6 cos r 
 
 (II) A W S S : sin n = ^ 
 
 cos c cos d 
 
 ( (1) COSH COS = COS6 COS(-f r/) 
 
 (III) AW PS: < (2) COSH sin -= cos 6 sine + sin 6 cose sin 
 
 ((3) sin n = sin 6 sine -j-cosdcoscsin^-f?;) 
 
 Thus far, as is seen, everything is entirely independent of any refer 
 ence to the place of observation upon the surface of the earth, which 
 reference will be first obtained by the knowledge of the position of the 
 zenith, Z, with respect to the quadrangle hitherto considered. To this 
 end are used the distances of the point Z from the points P and W, 
 which are given by the latitude of the place and inclination of the hori 
 zontal axis of the instrument. If we put, as usual, 
 
 Z P = 9()o ^ Z W == 90^ Z>, 
 
 where ft is positive if the west end of the axis lies above the horizon : 
 also, further, 
 
 Z P W = 9Qo , P Z W = 900 -f- , 
 
 there results : 
 
 (IV) A W P Z- ~~ cc " sec ^ 
 
 { (2) sin a = tg & tg 9 + sin sec /> sec 9 
 
 by means of which our problem is"now completely solved. For 
 
 (90o _ m) _ (90o - _ x}=x m = 15 1 
 
 is the western hour angle of the time star at its observation at S, and 
 consequently the sidereal time of this observation is 
 
 a + t = S + ., 
 
THE VERTICAL OF THE POLE STAR. 13 
 
 if S signifies the observed clock time and u the correction at this moment 
 of the chronometer to sidereal time. Therefore, finally, 
 
 10. Should one at any time have reason to make use of these exact 
 formuhe, I Avould recommend that they be applied as they here stand, 
 without thinking of the introduction of auxiliary angles. These auxil 
 iary angles have, for the computations of the present day thanks to 
 the increasing dissemination of the Gaussian logarithms lost, to a great 
 extent, their former importance; they afford a real relief in the compu 
 tation generally, only Avhen we have to do, not with a single case but 
 AAnth many connected together, to Avhich certain quantities are common, 
 as, for example, often in the computation of tables. 
 
 On the other hand, the experienced computer will certainly not fail 
 to make full use of the adA^antages offered by the smallness of most of 
 the desired quantities, and that, too, without impairing in the least the 
 perfect exactness of the result. ftwuL^ 
 
 Here, hoAvever, such a computation has always a p*e theoretical in 
 terest. In actual practice approximate formuhe suffice, as aboA e several 
 times remarked, even in the extremest cases which can be likely to occur. 
 These approximate formuhe are obtained, if Ave derive the desired quan 
 tities from the above equations, under the assumption that & = 0, c = 0, 
 / =0, and thereupon develop the coefficients of these quantities, Avith 
 whose assistance we can at pleasure compute their influence if they are 
 not equal to zero, a method of solution which will be necessary, in refer 
 ence to c, as soon as the error of collimation is not assumed as known, 
 but must first be found from these same observations themselves. 
 
 If we indicate by the subscript o the A^alues resulting under the assump 
 tion mentioned, and by a prefixed J the correction then necessary, so 
 that, for instance, u = u lt -f J ?/, the above given strict formula; giA T e, 
 without trouble, the following : 
 
 1 sin d 1 f 
 
 = A;;= 7 . c + - ,./ 
 
 o cos d cos d 
 
 cos ?? cos X Q = cos 
 
 cos n o sin #o sin 6 si n$ cos it cos x . A.T sin u s mjc . A n = cos (5 . c-{- sin 6 cos .f . A ?/ 
 
 sin -HO = cos d sin f cos n . A tt = sind.c-f- cos d cos f . A 
 
 sin w = tg (j) tg n {> cos m . A m = sec n sec (j> . J) -f- sec 2 n tg . A n 
 
 sin () = sec o sin H () cos a . A a = tg <t> . & -f- cos n sec . ^ n 
 
 Hence, with help of equations I, there folloAA^s: 
 
 sin o cos 8 sin - 
 
 tff .r,, = Sill d tg C . ; 
 
 COS d Sill d Sin d COS d COS r ; 
 
 tg n = cotg d sin .r ; 
 sin M O = tg (p cotg o sin ,r {> . 
 If, therefore, we put 
 
 tg d COtg o = /, tg <p COtg d = <>. 
 
 then Avill 
 
 / sin r 
 tg ,? = ^ - , sin m n = <>. sin ^ ; 
 
 1 / COS r 
 
 and finally, 
 
14 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 But, 
 
 . J x Am 
 
 = + 1:> 
 
 therefore, 
 
 J tn A x t 
 
 15 
 for which we will write, 
 
 in which the divisor 15 in the coefficients B, C, F, which are now to be 
 immediately developed, need not be further considered if we have ex 
 pressed 6, c,/, in time. We remark, first, in reference to this develop 
 ment, that in the above-given differential formula? the cosines of the small 
 angles, fr, c,/, have been put equal to unity, and the sines proportional 
 to the angles themselves, while in the case of the small quantities, ?, x, 
 n-, m, ., this simplification has not yet been introduced. This is proper, 
 since that these latter, although small in themselves, are, or at least can 
 become, many times larger than the former. Of course b will naturally 
 amount only to a- few seconds of arc, since larger inclinations cannot be 
 measured with the level. The intelligent observer will furthermore take 
 care that c be always very small, but it is not at all meant to advise to 
 attempt to make it zero every time. Finally, in the most extreme cases 
 f can certainly be so large as 15 minutes of arc; the extreme threads will 
 certainly never stand further than this from the middle one ; but even 
 then cosine /does not differ from Radius by a unit in the fifth decimal 
 place. We will most easil} T receive an idea of the magnitudes of the 
 other quantities if we represent their approximate values as functions of 
 any one, most conveniently of n. Our formulas give us at once : 
 
 a = n sec y, m = n tg cr, z = n sec ), ,r = n tg o. 
 Therefore, if we put 
 
 1 cos n =pi 
 
 there results, approximately, 
 
 1 cos a =p sec 2 ^, 1 cosw==ptg 2 c?, 1 cosr==psec 2 <7, 1 cos,r=^tg 2 <S; 
 further, 
 
 sin n = \/ 2pi sin x = tg d -\/ "Ip^ 
 therefore, 
 
 sin n sin x = 2p tg d 
 
 t and we will now easily be able to judge how far these small fractions 
 still demand notice. Since we adopt the rule to use no other star than 
 the Pole Star for orientation, therefore n can never be greater than 
 1 26 , to which corresponds ^ = 0.0003 ; and therefore for a latitude of 
 60 and the observation of zenith stars, none of the above quantities be 
 come greater than about 0.001. Xow this is entirely evanescent, both 
 in respect to b and to c, but not in respect to the extreme value of /, 
 especially in case we would, as we ought, retain the hundredths of a sec 
 ond of time in our results. If we therefore may neglect these fractions 
 at first, for the sake of perspicuity, in the deduction of the coefficients, 
 B, C, F, still we must finally develop for F the small corrections de 
 manded by this omission in order that this may always, when necessary, 
 be brought into account. The differential equations, simplified by the 
 first mentioned assumption, now are : 
 
 A x = cos o . c + sin o . J TJ 
 J n =4- sin 3 . c 4- cos 3 . J r t 
 j m = 4- sec <f . b + tg c . J n. 
 
THE VERTICAL OF THE POLE STAR. 15 
 
 From these, by substitution of J n from the previous equations, there 
 results, 
 
 j m = sec <p . 1) 4- tg <p sin d.c + tg<p cos d . J r t ; 
 therefore, 
 
 j )n J x = sec (p . b 4- (tg ^ sin o 4- cos 8) . c 4- (tg ^ cos <? sin 3) ,Ar h 
 
 or 
 
 j m j # sec <p . b 4- sec c^ cos . c 4- sec ^ sin 2 . J r/ , 
 
 where we have put 
 
 (p d = Z. 
 
 Finally, if we substitute the value 
 
 j -/} = (sec d tg d) . c 4- sec d ./, 
 
 and unite the two terms dependent upon c, the desired coefficients result, 
 B = sec <p 
 
 C = sec tp sec d [sin z + cos (d + z)] 
 F = sec (p sec tf sin z -{- G^>, 
 
 Avhere G is a factor still to be deduced, namely, the coefficient of the 
 hitherto neglected term in the value of F dependent upon p. In order 
 to obtain this we must return to the complete differential equations and 
 seek the value of the partial differential coefficients with reference to/, 
 which, we will designate by dx, dn, d m ; this will at the same time be a 
 control over the accuracy of the previously-found principal terms of the 
 factor F, independent of p. 
 We have 
 
 drj = sec rf, 
 and therefore 
 
 cos n cos x . d x sin n sin x d n = cos I sec d sin 3 
 cos n d n = cos I sec d cos d 
 cos m d m = sec 2 n tg <p . d n. 
 
 If, by means of the second equation, we eliminate the dn from the two 
 others, we obtain : 
 
 cos n cos x.dx = cos c sec d sin 3 -f- tg n sin ,r cos I sec d cos 3 
 
 cos m . d m = sec 3 n tg <p cos c sec d cos o, 
 or remembering that 
 
 cos n cos x = cos r , 
 we have 
 
 d x = sec d sin <? + tg n sin ^ sec d cos 3 
 
 dm = tg c0 sec 2 n sec m cos x sec d cos , 
 and therefore 
 
 dm d x = F = sec d cos d (tg ^ sec 2 n sec w cos x tg n sin x tg 3). 
 But, from the previous remarks, there follows : 
 
 sec 2 n sec m cos x = I 4- p ( 2 4- tg 2 c tg 2 o ) 4- &c. 
 
 2 tff 3 
 tg M sin x =- y- = 2^> tg d 4- &c., 
 
 therefore, 
 
 F = seod cos 3 I tg ? tg 5 4- # [2 tg ? + (tg 2 ^ tg 2 <5) tg 2 tg d] } 
 = sec d cos o (tg <p tg (5) { 1 4- ^ [2 4- (tg <P 4- tg 5) tg f ] } 
 = sec 9 sec d sin* { 1 +^ [2 + (tg <? 4- tg 5) tg ?] }. 
 
 The portion independent of p agrees, as it should, with that pre- 
 
16 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 viously deduced. If we indicate it temporarily by F and by h, the factor 
 of jp, then will 
 
 F = F (1 + p h) = F (1 + p)* = F (sec n)\ 
 
 We now remark that sec n does not otherwhere occur in our computa 
 tion, and that, therefore, it would be convenient to replace it in some 
 way by seem, which is found, without further trouble, in taking from 
 the tables the angle belonging to m. From m = ntg <p there results 
 sec n = (sec m) cot 2 0, therefore (sec n) h = (sec w) 11 cot s 2 0, 
 
 thus, finally, 
 
 F = sec (f sec d sin z (see m) k 
 where 
 
 k = 1 + 2 cotg 2 ^ + cotg <p tg d. 
 
 A similar remark is to be made with reference to the arc d, the comple 
 ment of the distance between the two points of the heavens S and S, 
 in w r hich the two stars are found at the time of their observation. This 
 arc can be found, with all desirable accuracy, from the equations (I.) 
 But in all cases actually occurring this arc passes, within a few seconds, 
 through the zenith ; and further, since it is only used in the computa 
 tion of the differential coefficients C and F. it is more than sufficiently 
 accurate if we put 
 
 00 d = z 1 -f z, therefore d -f z = 1)0 z 1 , 
 
 and take for z the actual zenith distance of the Pole Star, counting it 
 always positive, while z remains = <p d. If, as is for these observa 
 tions always desirable, we have an ephemeris of the Pole Star, that is to 
 say, a table of azimuths and zenith distances with the argument, sidereal 
 time, which indeed is indispensable if the observations are made by day 
 or twilight, then z 1 can, at any time, be taken therefrom. If we have 
 no such table, or none sufficiently accurate, we need only to read the ver 
 tical setting circle simultaneously with the observation ; and if this be 
 also done for the time star then the difference of the two readings, even 
 without any knowledge of the position of the zenith, gives directly the 
 complement of the arc d. 
 
 I will not here omit to call attention to a general remark that has very 
 often proved itself to be one of great importance. We make it an inva 
 riable rule in the accurate observation of either co-ordinate also to ap 
 proximately determine the other, which is always possible by means of 
 the finding circle. Thus, in the observations of transits one always 
 reads also the altitude circle ; in measuring the zenith distances one 
 reads also the horizontal circle; or rather, we do not neglect to record 
 these readings, which will generally be made in order to set the instrument. 
 Independent of the thus-secured sure solutions of many doubts arising 
 in consequence of mistakes, &c., these quantities are always of import 
 ance, and have a direct application as soon as we have to do with the 
 differential coefficients 5 and, although these latter are not always used in 
 the deductions of the results themselves, it is still very desirable not to 
 neglect their development, when not entirely too tedious, since they con 
 duce very much to the attainment of a correct judgment as to the relia 
 bility of the determination obtained. 
 
 11.. The following group gives a complete review of the process of the 
 computation, according to the approximate formulae just developed. Let 
 there be 
 
 For the Pole Star. For the Time Star. 
 
 S S the clock time of observation. 
 
 u + -f u the correction to sidereal time. 
 
THE VERTICAL OF THE POLE STAR. 17 
 
 For the Pole Star. For the Time Star. 
 
 the apparent right ascension. 
 
 o the apparent declination. 
 
 z z the zenith distance, z 1 is always posi 
 
 tive, z=<f> 3. 
 We now form the quantities : 
 
 S/ + ; = I) tg d COtg 8 = / tg X (> = r _ 
 
 S a = T> 
 
 15 (D D) = r tg <p cotg d == <j. sin m {) = >j. sin .r 
 
 thus we have: 
 
 where 
 B==sec0 ft the inclination of the horizontal azis. 
 
 C = sec^ sl c the error of collimation of the middle 
 
 thread. 
 
 F = sec <p . -. (sec wi-) k / the distance of the middle thread from 
 
 sin (z +z] that ou W } 1 i c j 1 tue p ole Star is observed. 
 
 The inclination b is positive if the west end of the axis lies above the 
 horizon ; the signs of c and /are to be understood so that 90 -f c and 
 90+ c +/ represent the distances of the respective points of the heav 
 ens from the west ends of the axis. All three, fr, o, /, are expressed in 
 time, and u will be obtained in time. 
 
 The introduction of the term F/ could evidently be avoided by always 
 considering the thread on which the Pole Star is observed as the middle 
 thread, and reducing the transit of the time star to this. Of course, then, 
 the error of collimation would, in general, be variable both in sign and 
 also in magnitude in the different positions by the known value of the 
 distance of the middle threads adopted in the two positions. No advan 
 tage results, however, in practice from this consideration, correct as it is 
 in and of itself. For, since in this case the collimation error could have 
 a much larger value than otherwise need be assumed, therefore the 
 exact development which is now considered necessary for the factor F 
 would be demanded for the factor C, and this would lead to expressions 
 still more complicated than those found for F. At least I have not my 
 self been able to represent the correction demanded in such a case for 
 the above-given value of c more conveniently than in the form of a factor, 
 
 (sec w)*, where q = cosec 2 y -f cotg <p tg z ~~ i 1 - 
 
 J V /* 
 
 which factor is, therefore, to be made use of if ever the. collimation error 
 should have an especially large value. 
 
 If, moreover, many time determinations are to be made under the same 
 latitude according to our method, it is then certainly most convenient to 
 compute the factors C and F once for all, for the always moderate num 
 ber of stars that can come into consideration ; as we are, indeed, already 
 accustomed to do for the much simpler factors that are used to free the 
 transits observed in the immediate neighborhood of the meridian from 
 the influence of the different instrumental errors. 
 
18 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 12. The endeavor to further simplify the deduction of the clock cor 
 rection by any application of serial developments has but little prospect 
 of. success ; for, because of the magnitude to which the angles x and m 
 can attain, so many members of the series are required in order to ob 
 tain accurate results, that the computation according to the exact form 
 ula is decidedly more convenient. If, however, we will be content with 
 an accuracy of about s . 1, we may write : 
 
 log 1 = log (/? Sin r) + r COS r, 
 
 where 
 
 ;.(/,_ i) cot 3 (tg y tgJ) 
 15 sin 1" 15 sin 1" 
 
 and 
 
 r = mod . A = 0.4343 cotg 8 tg d. 
 
 Although these formulae may be only seldom used in the proper com 
 putation of the observations, they at least offer the advantage of an easy 
 insight into the dependence of the desired clock corrections upon the 
 imperfections of the observations and the errors of the adopted elements 
 of reduction. 
 
 If we also neglect the second term of the formula just given as it evi 
 dently, for the present purpose, does not come into consideration and, 
 besides, allow ourselves to put 
 
 z = 90 y, and therefore d = d, 
 
 whereby in the worst case only so much will be lost as depends upon 
 the polar distance of the Pole Star, we receive 
 
 = D 
 
 " 
 
 -f 1) . sec <p 
 * + c ..(tg <? + sec d tg 8} 
 
 which expression seems quite well suited to serve as a starting point for 
 such considerations. We will, however, here content ourselves with no 
 ticing only that which has reference to the choice of the star which we 
 thus far have spoken of under the name of the Time Star, without thereby 
 having intended to determine anything further as to its place in the 
 heavens. The first thought is to direct the choice by preference to equa 
 torial stars in consideration of the, in itself, correct geometrical principle, 
 that two points on the sphere determine the corresponding great circle 
 the more accurately the nearer their mutual distance approaches a right- 
 angle ; to which the further reason is added, that for the equatorial 
 stars not only the observed transit S, but also the assumed known right 
 ascension , are liable to the smallest absolute errors. 
 
 On closer consideration, however, one perceives that although the 
 latter reason here may certainly have some weight, on the other hand 
 the geometrical consideration is not here in place ; that is to say, the 
 two points that determine the meridian, i. e., the pole and zenith, have, 
 at every place, a given distance for each other which we cannot alter, 
 and upon which, of course, directly depends the accuracy with which the 
 plane of the meridian can in any way be determined. But the determi 
 nation of absolute time consists, principally, in the perception of that 
 part of the heavens with which the zenith of the place of observation 
 coincides at a given instant, and will, therefore, be most directly attained 
 by the observation of the transits of zenith stars. This is already shown 
 
THE VERTICAL OF THE POLE STAR. 19 
 
 in that for zenith stars the influence of the azimuth of the instrument 
 disappears. Our formula makes the relations thus brought into con 
 sideration still plainer, and, if the necessary data were known with suf 
 ficient accuracy, would even allow a numerical estimation of the proba 
 ble errors corresponding to the different cases. But also, independent 
 of this, we see that on account of the factor tg^> tgd, the influence of 
 an error in the angle r and in the adopted value of the quantity /* dis 
 appears in the zenith, whereby it deserves to be particularly mentioned 
 that the latter will be of special importance in the application of a mova 
 ble thread. As to error in the inclination and in the error of collima- 
 tion, the former influence is constant for all stars; the latter is greater 
 the farther the star is removed from the pole. It is, therefore, as above 
 already remarked, only the reliability in the determination of D which 
 diminishes with increasing inclination. But the principal law of this 
 diminution is known to be very dependent upon the peculiarity of the 
 observer, and the diminution, in general, first becomes noticeable at 
 great declinations, so that finally results a very decided advantage for 
 the zenith stars. This advantage will now be increased by the circum 
 stance that for the observation in the zenith, in both positions of the 
 instrument, the same portions of the pivots are used ; their irregulari 
 ties, therefore, are completely eliminated. On the other hand, it is to 
 be allowed that the greater perfectness of the instrument in and of itself, 
 and more especially the shortening of the duration of the observation, 
 essentially diminishes all these different sources of error, and therefore 
 gives a relatively greater weight to the error of the quantity D, which 
 is not affected by them. 
 
 On taking a general view, therefore, the opinion appears authorized 
 that zenith stars certainly have an advantage, but that, in our method, 
 this is less important than in the establishment in the meridian; for in 
 this latter the observation of zenith stars offers the only means of free 
 ing ourselves from the unwarranted assumption of the invariability in 
 azimuth, while in respect to the inclination, the possibly-existing changes 
 at any moment can be recognized by means of the level. Such a greater 
 freedom in the choice of the stars to be observed constitutes, if I am not 
 mistaken, a further not unimportant advantage of our method. 
 
 13. It now, finally, remains to mention, with a few words, the reduc 
 tion that is necessary for the Time Star, if this is observed on more than 
 one thread. Because of the exhaustive treatment that this subject has 
 received in different places, especially by Hansen, it suffices here to 
 merely give the formulae for computation. The time, f, that a star whose 
 declination is d needs in order to pass from any great circle of the sphere 
 to the parallel circle, distant /therefrom ? will be expressed with an accu 
 racy entirely sufficient for our purposes by the formula : 
 
 t =f V sec (d + n) . sec (d n) , 
 
 where n denotes, as previously, the distance at which the great circle 
 passes by the pole. A knowledge of n, sufficient for this reduction, is 
 always at hand; if not otherwise, then it is offered by our computa 
 tion itself, since for the redaction of the angle r, the simple passage of 
 the Time Star through the middle thread, or if this, perhaps, is not ob 
 served, a preliminary reduction of the side thread, with the factor seed, 
 will suffice, without the least prejudice to the accuracy of the computa 
 tion 5 and, in general, the exact reduction has only an importance if the 
 observed threads do not lie symmetrical with respect to the middle 
 thread. 
 
 14. It seems proper, in conclusion, to demonstrate, by some numerical 
 
20 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 example, the accuracy and convenience of the above-given formula for 
 computation. As a first example, I choose that given by Hansen at the 
 conclusion of the memoir in No. 199 of the AstronomischeNachrichteu. 
 The data, according to the notation adopted by us, are as follows : 
 
 h. m. s. " 
 
 a = 9 59 18.86 d = 12 47 33.6 
 
 = 18 27 22.5 (S = 86 35 19.9 
 
 The Time Star was observed on three threads, the Pole Star only on 
 the third. I give here the individual transits, together with the corre 
 sponding thread intervals : 
 
 Time Star. Thread interval. Pole Star. 
 
 h. m. s. s. 
 
 10 51 47.7 +39.50 
 
 52 28.2 h. m. s. 
 
 53 7.5 38.30 11 5 51 = S. 
 Finally, 
 
 <p == 500 56> 0" : & == _ 3//.4 . c = __ 48.70 = _ 70 // t6> 
 
 We content ourselves at first in reference to S with the observation 
 of the middle thread, without considering the two others, since we will 
 not yet reduce them exactly $ thus we have 
 
 7i. m. 8. 
 
 S =D = 53 9.34 
 S a ==D = 16 38 28.5 
 
 D= 15 45 19.16 
 
 19 47". 
 
 We will now at first compute according to the exact formulae of article 
 9, in order to test thereby the .succeeding computation according to the 
 approximate formulae. I use six-figure logarithms in this in order that 
 nowhere, by reason of the length of the computation, can the hundredths 
 of a second of time be rendered doubtful through accumulation of errors 
 in the last place ; but I give the computation, not completely, but only 
 its principal step3. 
 A The formulae I give : 
 
 Q I II O / " 
 
 = 2 53 25.6 d=+IQ 53 10.9 
 thence from II follows : r t = 10 43.3 
 
 therefore, + r, = 3 4 8.9 
 
 And with this, according to III : 
 
 x = 39 39.87 n= 2 59 50.0 
 finally, from IV : m = 3 41 59.69 
 
 therefore, x m = + 3 2 19.82 
 
 With the ?t, thus found, follows 
 
 log V sec (d + n) . sec (d n) = 0.01154, 
 
 and with this the reduction for the time stars to the middle thread be 
 comes 4- 40 S .56 and 39 S .33. The three transits through the middle 
 thread are, therefore, 
 
THE VERTICAL OF THE POLE STAR. 21 
 
 therefore, more accurately, 
 and 
 
 x 
 
 Rnr WA nQ.Ara 
 
 h. 
 
 10 
 
 m. 
 52 
 
 8. 
 
 28.56 
 
 28.2 
 28.17 
 
 8=10 
 D= 
 
 m 
 
 52 
 53 
 
 19 
 
 28.21 
 9.35 
 
 Q QO 
 
 therefore, finally, u= 41 0.03 
 
 For the computation, according to the formulae of article 11, now to 
 be given, I borrow from the foregoing the value of 
 
 o / 
 
 d=W 53.2 
 
 Then is 00 d = z + z= 79 6.8 
 
 further, <p d = z = 38 8.4 
 
 whence, z = 40 58.4 
 
 which I assume to have been read from the finding circle or taken from 
 an ephemeris of the Pole Star. As above remarked, these quantities 
 are only necessary in the computation of the coefficients C and F. In 
 respect to the former I remark, that, in general, not its logarithm but 
 the number itself will be first used, at least in case the error of collima- 
 tion is not assumed as known, but is first to be deduced from the ob 
 servations themselves. In such cases the above-given expression for C 
 is quite convenient, especially if we observe that one portion of it recurs 
 again in F. In other cases, as therefore in the present, it is more con 
 venient to change it into 
 
 = sec (p cos ( z "~ i sec 
 
 As regards the term B ft, we sliould not hesitate to connect its compu 
 tation with the equally necessary conversion of the level divisions, as 
 directly given, into the corresponding value in arc 5 that is to say, we 
 seek not 
 
 1) = 3".4, but at once B b = ~ . sec <p = O s .360. 
 
 lo 
 
 From the given values of z 1 and z follows 
 
 o // 
 
 ?-t?=:<r=39 33.4 
 Z -.= A = 1 25.0 
 
 and, with these, the complete computation of the terms C c and F/ be 
 come the following : 
 
 log cos A = 9.99987 log = 0.3133 log F = 9.99909 
 
 log sec o = 0.11295 log c = 0.6721ra log / = 1.58320& 
 
 log sec <p = 0.20050 log C c = 0.9854/& log F / = 1.58229& 
 
 log sin z = 9.79070 q . log sec m = 0.0015 Jc log sec m = 0.00227 
 
 log sec d = 0.00789 log C c = 0.9869^ log F/ = 1.58456/1 
 
22 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 The corrections dependent upon sec m have been later introduced, after 
 obtaining the values of <j. and in. Their omission would have introduced 
 an error of only O s .033 in C c but of O s .200 in F/. 
 
 I have thus previously executed the computation of the terms C c and 
 F/, because, as above remarked, in the actual application of our method, 
 I suppose the factors C and F to be, once for all, computed and brought 
 into a table. I will hereafter give a portion of such a table. The fol 
 lowing is the computation that is now to be independently executed for 
 each separate observation : 
 
 o . / // 
 
 log tg? = 0.090598 #o = 38 25.90 
 
 log tg 3 = 9.356140 m = 3 28 38.63 
 
 log cotg<5 = 8.775291 x m = + 2 50 12.7 
 
 log denominator = 3247 
 
 s. 
 
 . . 
 
 log sin r = 9.920250ft ?> = + 53 9.35 
 
 logA = 8.131431 B6 = 0.360 
 
 log COST = 9.74383^ Cc = 9.703 
 
 Argum =2.12474 <r ~Pf= 38.420 
 
 log fi = 0.734458 + 52 20.83 
 
 = 11 20.85 
 
 lo 
 
 log cos # = 27 u = 40 59.98 
 
 log sin m = 8.782865^ 
 
 that is to say, differing by O s .05 from the result of the exact computa 
 
 tion. Now, it is not difficult to see where the cause of this discordance 
 
 is to be sought. By reason of the magnitude of the term F/, it is cer 
 
 tainly not surprising that the terms of the higher order neglected therein 
 
 have not been entirely evanescent. But instead of developing these, it 
 
 x is certainly much more convenient, in such a case, to ^ex^cutejthe compu- 
 
 ^VXtation rigorously as regards J^ and tbe^thereby m&m&=3sbo? proves 
 
 ^J itself to btTso slight, especially in consideration that the F/ now en 
 
 tirely falls out, that it seems advisable always to choose this solution if 
 
 the factor F is not already elsewhere given. The system of equations 
 
 will be as follows : 
 
 , ^ _ sec d cotg d 1 sin r 
 
 ~ 1 tg o COtg d 1 COS r 
 
 sin/ 
 
 sin mi = cos d tg ( + r t ] tg <p cos #1 
 
 ii =f 5L_^ (B + B& + Cc) 
 
 These being applied to our example, the following computation results, 
 which I here give without any omission : 
 
 o / // 
 
 log tg 6 = 9.356140 log /= 2.75929^ f = 2 53 25.5? 
 
 log cotg <i = 8.775291 log sin (* + *) = 9.99211 rj = 9 45.03 
 
 log sec d = 0.010916 log n = 2.76718w ^^ = 3 3 10.6 
 log tg 6 cotg 6 = 8.13143 log sin d = 9.345224 
 
THE VERTICAL OF THE POLE STAR. 23 
 
 o / // 
 
 logcosr=9.74383n log tg ( s c + ?) = 8.727007/1 xi= 40 35.77 
 
 Arguin. =2.12474(7 log cos 6 = 9.989084 mi = 3 40 24.58 
 
 log seed cotg <J = 8.786207 log tg = 0. 090598 JT] HI = + 2 59 48.81 
 
 m. s. 
 log shir = 9.920250w logcosjci= 30 ~ m \ = -f 11 59.254 
 
 J-O 
 
 log denominator = 3247 log tg x l = 8.072231 n D-f-B6+Cc=+ 52 59.287 
 
 log tgf = 8.703210 log sin )! = 8.806659 11= 41 0.03 
 
 15. The previous example is treated with abundant fullness, in order 
 to leave no doubts as to the way to be pursued in all cases that can 
 occur. It. is, however, in fact more unfavorably conditioned than is 
 necessary to assume in actual practice. First, Ursa? Minoris should 
 be always observed ; and, secondly, a collimation error of nearly five 
 seconds of time is an aggravation that can be avoided with s ome atten 
 tion. The example is, also, evidently only a fictitious case. I will now, by 
 the computation of an observation actually made, and noways specially 
 favorable, show the process that we are accustomed to follow in the 
 treatment of this problem. To this end we have computed, once for all, 
 the coefficients and F, for our latitude 59 46 20", for a number of the 
 more frequently observed stars, under the assumption that the Time Star 
 is observed some six minutes after the Pole Star, which corresponds very 
 nearly to the interval that occurs in the actual observations. In the 
 example here to be considered the following come into use : 
 
 C logC logF 
 
 13 Draconis - - - - 2.060 0.3139 9.6151 
 
 r Draconis - - - - 2.069 0.3158 9.6576 
 
 a Lyr 2.201 0.3427 9.9613 
 
 C Aquilse - 2.507 0.3997 0.1688 
 
 In reference to the computation itself, I make now, further, the follow 
 ing remarks: 
 
 For 3 = the coefficient v attains an infinite value ; since, however, at 
 the same time A becomes 0, our equations in this case are 
 
 tg x = sin m == tg <p cotg $ sin -. 
 
 But this indicates, that in order to be able, in all cases, to conduct the 
 computation according to quite similar ways, whereby it is known that 
 in the actual application no slight relief is attained, we must subject our 
 formulae still to a small change. We put ^ 
 
 A . p. = tg <? COtg V = v 
 
 and Sinr =, 
 
 1 A COS r 
 
 then will tg X Q = A . p 
 
 and sin m = v . p . cos x ; 
 
 and the further advantage is here connected that the factor v can be 
 considered as constant for all observations of the same evening. 
 
 Since we always observe the Pole Star, the entire angle to be computed 
 does not reach 3 even for a latitude of 60. For such angles as is well 
 known, the excellent five-figure logarithmic tables of Westphal, by the 
 use of the small auxiliary tables headed "Corr.," in connection with the 
 logarithms of the numbers, make the use of the trigonometric tables 
 quite unnecessary : and it may be hereremarked that we have, with 
 
 A- 
 
24 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 great regret, missed this addition in the otherwise perfect tables of 
 Bremiker. On this account, principally, we confine ourselves to five 
 decimals in this computation, although thereby, under some circum 
 stances, the hundredths of a second of time certainly become unsafe; 
 but this can be considered as no noticeable diminution of accuracy in 
 the observation of the transit of a single star. 
 
 As to the following observations, they have been made by a talented 
 and industrious young officer, Mr. Koverski, who at present, as a pupil 
 of the military academy, takes part in the two-year practical course at 
 Poulkova; and, indeed, at that time he had had an experience of only 
 the first few weeks in such observations. The instrument is an Ertel 
 portable transit instrument of larger dimensions, but with the above- 
 mentioned erroneous position of the clamp screw. The reticule consists 
 of nine threads, and we are accustomed to indicate these with the num 
 bers I to IX in fixed order, namely, according to their increasing dis 
 tances from the ocular end of the axis. The otherwise customary nota 
 tion, according to the order in which the observed stars pass through 
 them, becomes ambiguous when the Pole Star stands very near its elonga 
 tion. Small marks upon the threads themselves make a confusion im 
 possible in our method of numbering 5 and this is important, since in the 
 observation of the Pole Star upon only one thread an error, in this re 
 spect, would be very dangerous. In the use of a moveable thread, the 
 numbers upon the micrometer are also quite as safe a means of indicating 
 the fixed threads. The distances from the middle thread, that hasfcome 
 into use, are the following : 
 
 VI = 5 S .731, VII = 17 S .701. 
 
 These refer to the first of our examples, in which the observations in 
 both positions are made in the same azimuth ; while in the second, the 
 Pole Star was too near the elongation, and therefore by changing the 
 azimuth of the instrument, it was each time observed upon the middle 
 thread. The following table contains the entire computation, exactly in 
 the form in which we always conduct it. It needs certainly scarcely 
 any further explanation, except that the factor sin V is omitted on the 
 lines distinguished by the angular brackets. The star positions are 
 those of the British Xautical Almanac. The constants for the evening 
 are: 
 
 a = l h 9 m 43 s 
 log cot 8 = 8.39474 
 log v = 8.62933 
 
THE VERTICAL OF THE POLE STAR. 
 
 25 
 
 Date. 
 
 1863, July 29. 
 
 1863, July 29. 
 
 Position. 
 
 East, 
 
 West. 
 
 West. 
 
 East. 
 
 Time star. 
 
 j3 Draconis. 
 
 y Draconis. 
 
 a Lyrae. 
 
 Aquihe. 
 
 
 h. m. 8. 
 
 7*. m. 8. 
 
 /(. m. s. 
 
 h. m. 8. 
 
 g/ , 
 
 17 25 4 VI 
 
 17 55 2 VII 
 
 18 34 44 M 
 
 19 4 20 M 
 
 S 
 
 17 32 44.55 
 
 17 59 9.69 
 
 18 40 51. 39 
 
 19 10 45.44 
 
 a 
 
 17 27 23. 05 
 
 17 53 28. 54 
 
 18 32 21. 35 
 
 18 59 10.47 
 
 D 
 
 16 15 21 
 
 16 45 19 
 
 17 25 1 
 
 17 54 37 
 
 o 
 
 5 21.50 
 
 5 41. 15 
 
 8 30. 04 
 
 11 34.97 
 
 
 0.50 
 
 0.18 
 
 0.15 
 
 0.27 
 
 F/ 
 
 2.36 
 
 4 8.05 
 
 0.00 
 
 0.00 
 
 
 h. m. 8. 
 
 h. m. s. 
 
 n. m. s. 
 
 h. m. s. 
 
 D D 
 
 16 9 59.5 
 
 16 39 37. 8 
 
 17 16 3l . 
 
 17 43 2.0 
 
 
 o / 
 
 o / 
 
 O 
 
 o / 
 
 T 
 
 242 29.9 
 
 249 54.5 
 
 259 7.8 
 
 260 45.5 
 
 (5 
 
 52 24.5 
 
 51. 30. 6 
 
 38 39. 8 
 
 13 40.0 
 
 log tg 6 
 log sin r 
 
 0. 11358 
 9. 94792H 
 
 0. 09955 
 9. 97274w 
 
 9. 90314 
 9. 99214* 
 
 9. 38589 
 9. 99881 
 
 log denominator 
 
 642 
 
 463 
 
 162 
 
 19 
 
 Argument 
 
 1. 82725(7 
 
 1.96975(7 
 
 2. 42662a 
 
 3. 3504(7 
 
 log cos r 
 
 9. 66443 n 
 
 9. 53596 
 
 9. 27550/t 
 
 8. 8690 M 
 
 & 
 
 log A 
 
 8. 50832 
 
 8. 49429 
 
 8. 29788 
 
 7. 78063 
 
 [log p] 
 
 5. 25593/< 
 
 5. 28254-w 
 
 5. 30495w 
 
 5. 31305/* 
 
 log cos x 
 [logtgzo] 
 [log sin ] 
 
 17 
 3. 76425w 
 3. 88509/j 
 
 18 
 3. 77683/j 
 3. 91169 
 
 8 
 3. 60283 
 3. 93420w 
 
 1 
 3.09368H 
 3. 94237 
 
 
 / // 
 
 o / // 
 
 O / / 
 
 / " 
 
 X 
 
 1 36 49.5 
 
 1 39 40. 1 
 
 1 6 46.6 
 
 20 40.7 
 
 /HO 
 
 2 7 57.0 
 
 2 16 2.0 
 
 2 23 16. 6 
 
 2 26 0. 
 
 X /o 
 
 -|- 31 7. 5 
 
 4 36 21. 9 
 
 4 1 16 30. 
 
 42 5 19.3 
 
 
 m. s. 
 
 m. s. 
 
 7/1. 8. 
 
 W. 8. 
 
 i_ /^ Wo ) 
 
 4 2 4. 50 
 
 4- 2 25. 46 
 
 {- 5 6.00 
 
 4 8 21.29 
 
 i>4B&4F/ 
 
 4 5 18.64 
 
 -j- 5 49.02 
 
 4 8 29. 89 
 
 4 11 34.70 
 
 w + Cc 
 
 3 14. 14 
 
 3 23. 56 
 
 3 23.89 
 
 3 13.41 
 
 Clock rate 
 
 0.04 
 
 4 0.04 
 
 0.04 
 
 4 0.04 
 
 The chronometer gained 4 8 .0 in twenty-four hours sidereal time, and 
 corresponding to this rate are the reductions to the mean mom nit of 
 each pair of determinations, as given in the last line of the individual 
 clock corrections. Such a reduction is necessary to the exact deduction 
 of the collimation error. If we indicate this by -f c for position west, 
 and therefore c for the position east, we have now, by means of the 
 coefficients 0, the following determinations : 
 
 m. s. 
 
 w_ 2.060. c = 3 14.18 
 u + 2.069 . c = 3 23.52 
 therefore, + 4.129. c= 9.34 
 and thence. c= 2.262 
 
 u = 3 18.84 
 for 17 h 46 
 
 . 
 
 M + 2.201. c= -3 23.93 
 u 2.507 . c = 3 13.37 
 4.4.708.6 =: 10.56 
 c = 2.243 
 u = 3 18.99 
 for 18 h 56 m 
 
 The agreement of the two values of c is thoroughly satisfactory, and 
 the change in value of u corresponds, within O s .04, to the above-given 
 rate of the chronometer. 
 
26 
 
 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 TABLE I. 
 FINDING EPHEMERIS OF POLARIS. J = 88 37 . 
 
 
 0=+20. 
 
 0=+30. 
 
 0=^40. 0=+50o. 
 
 0=4-60. 
 
 <fr= + 70. 
 
 
 Hour 
 
 
 
 
 
 
 
 Hour 
 
 angle. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 angle. 
 
 
 Z. 
 
 A. 
 
 Z. 
 
 A. 
 
 Z. 
 
 A. 
 
 Z. 
 
 A. 
 
 Z. 
 
 A. 
 
 Z. 
 
 A. 
 
 
 k. 
 
 o / 
 
 / 
 
 o / 
 
 o / 
 
 o / 
 
 / 
 
 o / 
 
 o / 
 
 o / 
 
 o / 
 
 o / 
 
 o / 
 
 h. 
 
 
 
 68 37 
 
 
 
 58 36 
 
 
 
 48 37 
 
 
 
 38 36 
 
 
 
 28 37 
 
 
 
 18 37 
 
 
 
 24 
 
 1 
 
 40 
 
 23 
 
 39 
 
 24 
 
 40 
 
 28 
 
 39 
 
 34 
 
 40 
 
 45 
 
 39 
 
 1 7 
 
 23 
 
 2 
 
 48 
 
 44 
 
 48 
 
 48 
 
 48 
 
 55 
 
 47 
 
 1 6 
 
 49 
 
 1 26 
 
 48 
 
 2 9 
 
 22 
 
 3 
 
 69 1 
 
 1 3 
 
 59 2 
 
 1 8 
 
 49 1 
 
 1 18 
 
 39 1 
 
 33 
 
 29 3 
 
 2 1 
 
 19 2 
 
 3 
 
 21 
 
 4 
 
 19 
 
 17 
 
 18 
 
 24 
 
 18 
 
 35 
 
 18 
 
 53 
 
 20 
 
 27 
 
 20 
 
 3 37 
 
 20 
 
 5 
 
 39 
 
 26 
 
 39 
 
 33 
 
 39 
 
 45 
 
 39 
 
 2 6 
 
 40 
 
 42 
 
 40 
 
 3 58 
 
 19 
 
 6 
 
 70 
 
 1 28 
 
 60 
 
 36 
 
 50 
 
 48 
 
 40 
 
 9 
 
 30 2 
 
 46 
 
 20 1 
 
 4 3 
 
 18 
 
 7 
 
 21 
 
 25 
 
 21 
 
 32 
 
 21 
 
 44 
 
 21 
 
 2 4 
 
 20 
 
 39 
 
 24 
 
 3 50 
 
 17 
 
 8 
 
 41 
 
 16 
 
 42 
 
 22 
 
 42 
 
 34 
 
 42 
 
 1 50 
 
 39 
 
 21 
 
 42 
 
 3 23 
 
 16 
 
 9 
 
 59 
 
 1 2 
 
 59 
 
 1 7 
 
 59 
 
 1 16 
 
 59 
 
 30 
 
 30 56 
 
 1 54 
 
 20 59 
 
 2 44 
 
 15 
 
 10 
 
 71 12 
 
 44 
 
 61 12 
 
 47 
 
 51 12 
 
 53 
 
 41 19 
 
 1 3 
 
 31 10 
 
 1 20 
 
 21 11 
 
 1 55 
 
 14 
 
 11 
 
 20 
 
 23 
 
 21 
 
 24 
 
 21 
 
 28 
 
 21 
 
 32 
 
 20 
 
 41 
 
 20 
 
 59 
 
 13 
 
 12 
 
 23 
 
 
 
 24 
 
 
 
 23 
 
 
 
 24 
 
 
 
 23 
 
 
 
 22 
 
 
 
 12 
 
 A is to be added to 180 to obtain the azimuth when the hour angle is >12 h . 
 
 A is to be subtracted from 180 to obtain the azimuth when the hour angle is <l2 b . 
 
 TABLE II. 
 COEFFICIENT OF AZIMUTHAL CHANGE FOR A UNIT OF HOUR ANGLE. 
 
 S 0=+20. 
 
 30. 
 
 40. 
 
 50. 
 
 60. 70. 
 
 i 
 
 o 
 
 
 
 
 
 i 
 
 o 
 
 50 
 
 + 0.68 
 
 
 - - 
 
 
 . . 
 
 50 
 
 40 
 
 0.81 
 
 + 0.82 
 
 
 
 
 40 
 
 30 
 
 1.13 
 
 1.00 
 
 + 6.92 
 
 
 
 30 
 
 20 
 
 1.46 
 
 1.23 
 
 1.08 
 
 + i. 06 
 
 
 20 
 
 10 
 
 1.97 
 
 1.53 
 
 1.28 
 
 1.14 
 
 + 1. 05 
 
 10 
 
 
 
 2.92 
 
 2.00 
 
 1.56 
 
 1.30 
 
 1.15 + 1.06 
 
 
 
 + 10 
 
 + 5. 67 
 
 2.88 
 
 1.97 
 
 1.53 
 
 1. 28 1. 14 
 
 + 10 
 
 20 
 
 oo 
 
 4- 5.41 
 
 2.75 
 
 1.88 
 
 1. 46 ! 1. 23 
 
 20 
 
 30 
 
 4.99 
 
 CO 
 
 + 4.99 
 
 2.53 
 
 1. 73 ! 1. 35 
 
 30 
 
 40 
 
 2.14 
 
 4.41 
 
 OO 
 
 + 4.41 
 
 2. 24 1. 53 
 
 40 
 
 50 
 
 1.28 
 
 1.88 
 
 3.70 
 
 OO 
 
 + 3.70 1.88 
 
 50 
 
 60 
 
 0.78 
 
 1.00 
 
 1.46 
 
 2.88 
 
 CO + 2.88 
 
 60 
 
 70 
 
 0.45 
 
 0.53 
 
 0.68 
 
 1.00 
 
 1. 97 ; CO 
 
 70 
 
 110 ! 
 
 + 6.35 
 
 + 6.36 
 
 + 6.40 
 
 + 0.45 |+ 6.53 
 
 110 
 
 120 [ 
 
 
 + 0.51 
 
 0.53 
 
 0. 58 I 0. 65 
 
 120 
 
 130 
 
 
 
 + 0.65 
 
 0. 68 0. 74 
 
 130 
 
 140 
 
 
 
 
 
 + 0. 78 ! 0.82 
 
 140 
 
 + 150 . . 
 
 
 
 
 . . + 0.88 
 
 + 150 
 
THE VERTICAL OF THE POLE STAR. 
 
 27 
 
 TABLE III. 
 
 Angle. 
 
 S. 
 
 T. 
 
 Angle. 
 
 S. 
 
 T. 
 
 /; 
 
 , 
 
 
 // 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 3600 
 
 1 
 
 22 
 
 44 
 
 60 
 
 I 
 
 
 
 
 
 3660 
 
 1 1 
 
 23 
 
 45 
 
 120 
 
 2 
 
 
 
 
 
 3720 
 
 1 2 
 
 24 
 
 47 
 
 180 
 
 3 
 
 
 
 3780 1 3 
 
 24 
 
 48 
 
 240 
 
 4 
 
 
 
 3840 
 
 1 4 
 
 25 
 
 50 
 
 300 
 
 5 
 
 o 
 
 . 3900 
 
 1 5 
 
 26 
 
 52 
 
 360 
 
 6 
 
 
 
 3960 
 
 1 6 
 
 27 
 
 53 
 
 420 
 
 7 
 
 .0 
 
 
 
 4020 
 
 1 7 
 
 28 
 
 55 
 
 480 
 
 8 
 
 1 
 
 1 
 
 4080 
 
 1 8 
 
 28 
 
 57 
 
 540 
 
 9 
 
 1 
 
 1 
 
 4140 
 
 1 9 
 
 29 
 
 58 
 
 600 
 
 10 
 
 1 
 
 1 
 
 4200 
 
 1 10 
 
 30 
 
 60 
 
 660 
 
 11 
 
 1 
 
 1 
 
 4260 
 
 1 11 
 
 31 
 
 62 
 
 720 
 
 12 
 
 1 
 
 2 
 
 4320 
 
 1 12 
 
 32 
 
 63 
 
 780 
 
 13 
 
 1 
 
 2 
 
 4380 
 
 1 13 
 
 33 
 
 65 
 
 840 
 
 14 
 
 1 
 
 2 4440 
 
 1 14 
 
 34 
 
 67 
 
 900 
 
 15 
 
 2 
 
 3 4500 
 
 1 15 
 
 35 
 
 69 
 
 960 
 
 16 
 
 2 
 
 3 4560 1 16 
 
 36 
 
 71 
 
 1020 
 
 17 
 
 2 
 
 3 
 
 4620 1 17 
 
 36 
 
 73 
 
 1080 
 
 18 
 
 2 
 
 4 
 
 4680 1 18 
 
 37 
 
 74 
 
 1140 
 
 19 
 
 2 
 
 4 
 
 4740 1 19 
 
 38 
 
 76 
 
 1200 
 
 20 
 
 3 
 
 5 4800 1 20 
 
 39 
 
 78 
 
 1260 
 
 21 
 
 3 
 
 5 
 
 4860 1 21 
 
 40 
 
 80 
 
 1320 
 
 22 
 
 3 
 
 6 4920 1 22 
 
 41 
 
 82 
 
 1380 
 
 23 
 
 3 
 
 6 4980 1 23 
 
 42 
 
 84 
 
 1440 
 
 24 
 
 4 
 
 7 5040 1 24 
 
 43 
 
 86 
 
 1500 
 
 25 
 
 4 
 
 8 5100 
 
 1 25 
 
 44 
 
 88 
 
 1560 
 
 26 
 
 4 
 
 8 
 
 5160 
 
 1 26 
 
 45 
 
 90 
 
 1620 
 
 27 
 
 5 
 
 9 
 
 5220 
 
 1 27 
 
 46 
 
 93 
 
 1680 
 
 28 
 
 5 
 
 9 
 
 5280 
 
 1 28 
 
 48 
 
 95 
 
 1740 
 
 29 
 
 5 
 
 10 
 
 5340 
 
 1 29 
 
 49 
 
 97 
 
 1800 
 
 30 
 
 6 
 
 11 5400 
 
 1 30 
 
 50 
 
 99 
 
 1860 
 
 31 
 
 6 
 
 12 
 
 5460 
 
 1 31 
 
 51 
 
 101 
 
 1920 
 
 32 
 
 6 
 
 12 
 
 5520 
 
 1 32 
 
 52 
 
 104 
 
 1980 
 
 33 
 
 7 
 
 13 
 
 5580 
 
 1 33 
 
 53 
 
 106 
 
 2040 
 
 34 
 
 7 
 
 14 
 
 5640 
 
 1 34 
 
 54 
 
 108 
 
 2100 
 
 35 
 
 8 
 
 15 
 
 5700 
 
 1 35 
 
 55 
 
 110 
 
 2160 
 
 36 
 
 8 
 
 16 
 
 5760 
 
 1 36 
 
 57 
 
 113 
 
 2220 
 
 37 
 
 9 
 
 17 
 
 5820 1 37 
 
 58 
 
 115 
 
 2280 
 
 38 
 
 9 
 
 18 
 
 5880 1 38 
 
 59 
 
 118 
 
 2340 
 
 39 
 
 9 
 
 18 
 
 5940 1 39 
 
 60 
 
 120 
 
 2400 
 
 40 
 
 10 
 
 19 6000 
 
 1 40 
 
 61 
 
 122 
 
 2460 
 
 41 
 
 10 
 
 20 6060 
 
 1 41 
 
 63 
 
 125 
 
 2520 
 
 42 
 
 11 
 
 21 
 
 6120 
 
 1 42 
 
 64 
 
 127 
 
 2580 
 
 43 
 
 11 
 
 28 
 
 6180 
 
 1 43 
 
 65 
 
 130 
 
 2640 
 
 44 
 
 12 
 
 24 
 
 6240 1 44 
 
 66 
 
 132 
 
 2700 
 
 45 
 
 13 
 
 25 
 
 6300 
 
 1 45 
 
 68 
 
 135 
 
 2760 
 
 46 
 
 13 
 
 26 
 
 6360 
 
 1 46 
 
 69 
 
 138 
 
 2820 
 
 47 
 
 14 
 
 27 
 
 6420 
 
 1 47 
 
 70 
 
 140 
 
 2880 
 
 48 
 
 14 
 
 28 
 
 6480 
 
 1 48 
 
 72 
 
 143 
 
 2940 
 
 49 
 
 15 
 
 29 
 
 6540 
 
 1 49 
 
 73 
 
 145 
 
 3000 
 
 50 
 
 15 
 
 30 
 
 6600 1 50 
 
 74 
 
 148 
 
 3060 
 
 51 
 
 16 
 
 32 6660 1 51 
 
 76 
 
 151 
 
 3120 
 
 52 
 
 17 
 
 33 
 
 6720 
 
 1 52 
 
 77 
 
 154 
 
 3180 
 
 53 
 
 17 
 
 34 
 
 6780 
 
 1 53 
 
 78 
 
 156 
 
 3240 
 
 54 
 
 18 36 
 
 6840 
 
 1 54 
 
 80 
 
 159 
 
 3300 
 
 55 
 
 19 
 
 37 
 
 6900 
 
 1 55 
 
 81 
 
 162 
 
 3360 
 
 56 
 
 19 
 
 38 
 
 6960 
 
 1 56 
 
 83 
 
 165 
 
 3420 
 
 57 
 
 20 
 
 40 
 
 7020 
 
 1 57 
 
 84 
 
 168 
 
 3480 
 
 58 
 
 21 
 
 41 
 
 7080 
 
 1 58 
 
 85 
 
 170 
 
 3jd40 
 
 59 
 
 21 
 
 43 
 
 7140 
 
 1 59 
 
 87 
 
 173 
 
 3600 
 
 60 
 
 22 44 
 
 7200 
 
 1 60 
 
 88 
 
 176 
 
THE PORTABLE TRANSIT INSTRUMENT, ETC. 
 
 TABLE III. Continued. 
 
 Angle. 
 
 S. 
 
 T. 
 
 Angle. 
 
 S. 
 
 T. 
 
 
 
 o / 
 
 
 
 M 
 
 o / 
 
 
 
 7200 
 
 2 
 
 88 
 
 176 
 
 10800 
 
 3 
 
 199 
 
 397 
 
 7260 
 
 2 1 
 
 90 
 
 179 
 
 10860 
 
 3 1 
 
 201 
 
 401 
 
 7320 
 
 2 2 
 
 91 
 
 182 
 
 10920 
 
 3 2 
 
 203 
 
 406 
 
 7380 
 
 2 3 
 
 93 
 
 185 
 
 10980 
 
 3 3 
 
 205 
 
 411 
 
 7440 
 
 2 4 
 
 94 
 
 188 
 
 11040 
 
 3 4 
 
 207 
 
 415 
 
 7500 
 
 2 5 
 
 96 
 
 191 
 
 moo 
 
 3 5 
 
 
 419 
 
 7560 
 
 2 6 
 
 9? 
 
 194 
 
 11160 
 
 3 6 
 
 212 
 
 424 
 
 7620 . 
 
 2 7 
 
 99 
 
 198 
 
 11220 
 
 3 7 
 
 214 
 
 428 
 
 7680 
 
 2 8 
 
 100 
 
 201 
 
 11280 
 
 3 8 
 
 217 
 
 433 
 
 7740 
 
 2 9 
 
 102 
 
 204 
 
 11340 
 
 3 9 
 
 219 
 
 438 
 
 7800 
 
 2 10 
 
 104 
 
 207 
 
 11400 
 
 3 10 
 
 221 
 
 442 
 
 7860 
 
 2 11 
 
 105 
 
 210 
 
 11460 
 
 3 11 
 
 223 
 
 447 
 
 7920 
 
 2 12 
 
 107 
 
 213 
 
 11520 
 
 3 12 
 
 227 
 
 452 
 
 7980 
 
 2 13 
 
 108 
 
 217 
 
 11580 
 
 3 13 
 
 229 
 
 456 
 
 8040 
 
 2 14 
 
 110 
 
 220 
 
 11640 
 
 3 14 
 
 231 
 
 461 
 
 8100 
 
 2 15 
 
 112 
 
 223 
 
 11700 
 
 3 15 
 
 233 
 
 466 
 
 8160 
 
 2 16 
 
 113 
 
 227 
 
 11760 
 
 3 16 
 
 235 
 
 471 
 
 8220 
 
 2 17 
 
 115 
 
 230 
 
 11820 
 
 3 17 
 
 237 
 
 476 
 
 8280 
 
 2 18 
 
 117 
 
 233 
 
 11880 
 
 3 18 
 
 240 
 
 481 
 
 8340 
 
 2 19 
 
 118 
 
 237 
 
 11940 
 
 3 19 
 
 242 
 
 486 
 
 8400 
 
 2 20 
 
 120 
 
 240 
 
 12000 
 
 3 20 
 
 245 
 
 490 
 
 8460 
 
 2 21 
 
 122 
 
 243 
 
 12060 
 
 3 21 
 
 247 
 
 495 
 
 8520 
 
 2 22 
 
 124 
 
 247 
 
 12120 
 
 3 22 
 
 250 
 
 500 
 
 8580 
 
 2 23 
 
 125 
 
 250 
 
 12180 
 
 3 23 
 
 252 
 
 505 
 
 8640 
 
 2 24 
 
 127 
 
 254 
 
 12240 
 
 3 24 
 
 255 
 
 510 
 
 8700 
 
 2 25 
 
 129 
 
 258 
 
 12300 
 
 3 25 
 
 257 
 
 515 
 
 8760 
 
 2 26 
 
 131 
 
 261 
 
 12360 
 
 3 26 260 
 
 521 
 
 8820 
 
 2 27 
 
 132 
 
 265 
 
 12420 
 
 3 27 
 
 263 
 
 525 
 
 8880 
 
 2 28 
 
 134 
 
 268 
 
 12480 
 
 3 28 
 
 266 
 
 530 
 
 8940 
 
 2 29 
 
 136 
 
 272 
 
 12540 
 
 3 29 
 
 268 
 
 535 
 
 9000 
 
 2 30 
 
 138 
 
 276 
 
 12600 
 
 3 30 
 
 271 
 
 540 
 
 9060 
 
 2 31 
 
 140 
 
 279 
 
 , 12660 
 
 3 31 
 
 273 
 
 545 
 
 9120 
 
 2 32 
 
 142 
 
 283 
 
 %/ 1)720 
 
 3 32 
 
 275 
 
 551 
 
 9180 
 
 2 33 
 
 144 
 
 287 
 
 / 12780 
 
 3 33 
 
 278 
 
 556 
 
 9240 
 
 2 34 
 
 145 
 
 291 
 
 y 12840 
 
 2 34 
 
 281 
 
 561 
 
 9300 
 
 2 35 
 
 147 
 
 294 
 
 12900 
 
 3 35 
 
 284 
 
 566 
 
 9360 
 
 2 36 
 
 149 
 
 298 
 
 12960 
 
 3 36 
 
 286 
 
 572 
 
 9420 
 
 2 37 
 
 151 
 
 302 
 
 13020 
 
 3 37 
 
 289 
 
 577 
 
 9480 
 
 2 38 
 
 153 
 
 306 
 
 13080 
 
 3 38 
 
 291 
 
 582 
 
 9540 
 
 2 39 
 
 155 
 
 310 
 
 13140 
 
 3 39 
 
 294 
 
 588 
 
 9600 
 
 2 40 
 
 157 
 
 314 
 
 13200 
 
 3 40 
 
 297 
 
 593 
 
 9660 
 
 2 41 
 
 159 
 
 318 
 
 13260 
 
 3 41 
 
 300 
 
 598 
 
 9720 
 
 2 42 
 
 161 
 
 322 
 
 13320 
 
 3 42 
 
 302 
 
 604 
 
 9780 
 
 2 43 
 
 163 
 
 325 
 
 13380 
 
 3 43 
 
 305 
 
 610 
 
 9840 
 
 2 44 
 
 165 
 
 330 
 
 13440 
 
 3 44 
 
 307 
 
 615 
 
 9900 
 
 2 45 
 
 167 
 
 334 
 
 13500 
 
 3 45 
 
 310 
 
 621 
 
 9960 
 
 2 46 
 
 169 
 
 338 
 
 13560 
 
 3 46 
 
 313 
 
 626 
 
 10020 
 
 2 47 
 
 171 
 
 342 
 
 13620 
 
 3 47 
 
 316 
 
 632 
 
 10080 
 
 2 48 
 
 173 
 
 346 
 
 13680 
 
 3 48 
 
 318 
 
 637 
 
 10140 
 
 2 49 
 
 175 
 
 350 
 
 13740 
 
 3 49 
 
 321 
 
 643 
 
 10200 
 
 2 50 
 
 177 
 
 354 
 
 13800 
 
 3 50 
 
 324 
 
 649 
 
 10260 
 
 2 51 
 
 179 
 
 358 
 
 13860 
 
 3 51 
 
 327 
 
 654 
 
 10320 
 
 2 52 
 
 181 
 
 362 
 
 13920 
 
 3 52 
 
 330 
 
 660 
 
 10380 
 
 2 53 
 
 183 
 
 367 
 
 13980 
 
 3 53 
 
 333 
 
 666 
 
 10440 
 
 2 54 
 
 186 
 
 371 
 
 14040 
 
 3 54 
 
 335 
 
 671 
 
 10500 
 
 2 55 
 
 188 
 
 375 
 
 14100 
 
 3 55 
 
 338 
 
 677 
 
 10560 
 
 2 56 
 
 190 
 
 380 
 
 14160 
 
 3 56 
 
 341 
 
 683 
 
 10620 
 
 2 57 
 
 192 
 
 384 
 
 14220 
 
 3 57 
 
 34* tfl 
 
 688 
 
 10680 
 
 . 2 58 
 
 194 
 
 388 
 
 14280 
 
 3 58 
 
 347 
 
 695 
 
 10740 
 
 2 59 
 
 196 
 
 393 
 
 14340 
 
 3 59 
 
 350 , 
 
 701 
 
 10800 
 
 2 60 
 
 199 
 
 397 
 
 14400 
 
 3 60 
 
 352 
 
 707 
 
APPENDIX AND TABLES, 
 
 BY THE TKANSLATOB. 
 
APPENDIX. 
 
 The memoir here presented to the readers notice was published in 
 1863 by the Imperial Central Observatory at Poulkova, (near St. Peters 
 burg,) after the methods herein given had been carefully elaborated by 
 their author and often tested in the course of his experience as senior 
 astronomer at that institution and as professor of geodesy to the Impe 
 rial Military Academy. 
 
 Until 1864 the practical application of Dolleii s method was seriously 
 embarrassed, inasmuch as no instrument specially proper to this class 
 of observations had been constructed, and the use of u universal instru 
 ments" and Hansen s formulae could only be said to have given promise 
 of what would be achieved with a suitable instrument. In the spring 
 of this year, however, there were finished by Brauer, the then mechani 
 cian of the observatory, three portable transits, two of which were de 
 signed for the immediate use of the observers engaged in determining 
 the longitudes of points on the Yaleutia-Orsk parallel ; the third, soon 
 after its completion, passed into the hands of Professor Schidloifski, 
 director of the observatory at Kieff, who took it with him on returning 
 home in August from the quarter-century inauguration anniversary at 
 Poulkova. 
 
 This latter instrument it was that, having been during the summer at 
 the disposal of Mr. Dollen, would, as he hoped, enable him to carry out 
 such special studies as would decide definitively upon the advantages 
 resulting from its use, the instrument having been made by Brauer, 
 under his own supervision, and with direct reference to the convenient 
 application of his method for the determination of time. 
 
 But the series of observations then begun, unfortunately, could not be 
 completed, and they still remain unpublished, and probably not fully 
 discussed a delay necessitated by the pressure of imperative duties 
 consequent upon Dollen s appointment ad interim to the directorship of 
 the observatory, and an illness that for months threatened his life, and 
 finally compelled him to a year s absence from Poulkova. 
 
 In the summer of 1864 Messrs. Thiele and Zylinski, engaged on the 
 above-mentioned arc of longitude, being in England, their instruments 
 were brought so favorably to the notice of the astronomer royal that 
 Professor Airy ordered from Brauer a similar portable transit for the 
 Greenwich Observatory. This was finished in the winter of 1865- 66, 
 and the accuracy of its construction was sufficiently tested during a few 
 clear days in the following spring, the writer having himself improved 
 the opportunity of examining the cyliudricity of its pivots by means of 
 the microscope apparatus supplied with it. 
 
 Simultaneously with the construction of the latter instrument Brauer 
 took in hand two others, (Nos. Y and VI,) which he was not then able 
 to complete, owing to his other engagements and the removal of his 
 workshop to St. Petersburg, but which he has promised shall be even 
 superior to their predecessors, and which, if not now finished, certainly 
 can be within a few months. 
 
32 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 THE BRATJER PORTABLE TRANSIT. 
 
 The Brauer portable extra-meridional transit instrument consists, as 
 to its chief features, of an objective of 2.5 to 3.0 inches aperture and 30 
 to 36 inches focal length, bearing a power of 150. The ocular being at 
 one end of the axis of revolution, the light for the field illumination 
 enters through the opposite pivot ; the total reflection prism within the 
 central cube admits of proper adjustment. To the stationary reticule of 
 five wires is added a pair of close double wires, moved by a fine microme 
 ter screw. The hanging level need never be removed from its position 
 on the pivots. An unusually expeditious reversing apparatus is always 
 in place, and works with scarcely any possibility of detriment to the sta 
 bility of azimuth or level. This apparatus is so contrived as not to inter 
 fere with nadir observations, made by means of a dish of mercury placed 
 on the pier and below the base of the tripod. The three foot screws rest 
 on corresponding blocks, one of which is itself moveable by a horizontal 
 adjusting screw, allowing the instrument to be accurately placed at any 
 azimuth within a range of six or seven degrees. Microscopes and levels 
 for the examination of the pivots are also provided. 
 
 The excellence of these instruments depends so much upon the con 
 venient arrangement and conscientious workmanship of all the parts, 
 that actual use and the critical study of the results can alone (as it act 
 ually does) suffice to persuade one of their superior merits. 
 
 While the Brauer transit is unusually convenient for use in any verti 
 cal plane, it may, of course, be very advantageously mounted in the me 
 ridian ; it is in this way that the International Commission, having the 
 Yalentia-Orsk arc in charge, have decided to employ it, preferring, it 
 would seem, to sacrifice time rather than risk the introduction of un 
 known errors by the adoption of new methods in a work of such magni 
 tude and importance. That they, in 1863, may have been justified in 
 this discussion will be admitted, but their own, as well as Dollen s, sub 
 sequent experience has removed all serious objections to the methods 
 proposed and advocated by the latter. On the other hand, the experi 
 ence of Messrs. Thiele and Zylinski has brought out in stronger light a 
 peculiar personal equation that had been long known to exist in the use 
 of meridian transit instruments and of the vertical circle for time deter 
 minations. It is found, namely, that the personal equation varies (in eye 
 and ear observations very decidedly, but far less so in eye and hand ob 
 servations) with the direction of the motion of the star s image over the 
 retina. This. source of error is not eliminated by the reversion of the 
 ordinary direct- vision transit in the Y s, but may be so if a reflecting 
 eye-piece be properly employed. 
 
 On account of the great saving of time and labor afforded by the use 
 of the Brauer transit and Dollen s formulae, these especially commend 
 themselves to travelers and to those who are placed in unfavorable at 
 mospheric conditions ; the extra-meridional method here developed must 
 be considered indispensable when the stability of the transit in azimuth 
 or the visibility of the appropriate stars cannot be relied upon for sev 
 eral hours, but may be for perhaps five or ten minutes. 
 
 It will often be found highly advantageous for the observer to apply 
 any ordinary portable transit to observations of this class however incon 
 venient the instrumental arrangements may seem to be. 
 
 For perspicuity and the observer s convenience we take the liberty of 
 appending the following review of Dollen s method, together with a few 
 simple tables. 
 
THE VERTICAL OF THE POLE STAR. 33 
 
 ORIENTATION. 
 
 a-, 
 
 Arrived at any new station whose latitude as well as our clock^hro- 
 nometer correction are approximately known, we determine, first, the 
 zenith point of the setting circle by observation of the nadir point or of 
 a distant terrestrial object. Then a finding ephemeris (such as is given 
 in the appended Table I) enables us to set a ^the proper zenith distance 
 for Polaris, and to sweep in azimuth until that star is found. This, if it 
 benight, or if the north point be accurately known, will require but a 
 few minutes. 
 
 In the day-time it will be more convenient to raise the telescope by 
 means of its" sworvmg apparatus and sight upon the sun. The observed 
 time of transit (T) and the zenith distance (z] of the sun s center give us 
 his azimuth (A) and the clock correction ( J T) by the following well- 
 known fornmlse : 
 
 Put 
 
 90 8 = a s a = a 
 
 900 ^l) S & = /9 
 
 where the double computation of 2 s serves as a check : 
 
 Vsin a sin ft sin Y 
 ; 
 sins 
 
 where the last equation again serves as a che.ck. 
 
 Knowing thus the sun s azimuth, A, and hour angle, t, we have 
 
 North point = observed azimuth i A 
 Clock correction = T (right ascension of sun + t). 
 
 The ordinary portable transit offers no very convenient means for 
 measuring azimuths or for turning the instrument around through any 
 given azimuthal angle. In the Brauer instrument this may be easily 
 effected by means of a simple graduation on the vertical face of the ex 
 terior rim of the circular base of the transit, or more elegantly by means 
 of a graduation in the circular base of the reversing apparatus or the 
 adjacent bed-plate. 
 
 If the instrument does not contain too much iron in the construction 
 of its parts an attached compass needle will be found convenient. 
 
 Polaris being found in the field of view, the careful observer will, after 
 leveling the axis, reverse upon that star, or upon a distant terrestrial 
 object, and see that the collimation error is not too large. 
 
 The choice of a time star will, in the day time, depend upon its own 
 brightness, and a general catalogue of all stars, to the third magnitude 
 inclusive, will afford a number of convenient stars at any time or in any 
 latitude. We have appended such a catalogue^ compiled by - - , 
 including all stars given, as of the third or brighter magnitudes, in the 
 British Association Catalogue, or Argelander s Uranometria Nova, or 
 in Taylor s General Catalogue ; to these stars we have, however, pre- 
 3 
 
34 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 ferred to affix Argelander s magnitudes, excepting for those south of 
 25 of declination j for the variable stars we have adopted the limit 
 ing magnitudes given by Schonfeld. These are all converted into the 
 decimal system of notation, assuming Argelander s 1.2 and 2.1, &c., equal 
 to 1.4 and 1.6, &c., of the decimal system. For night observations the 
 brightness of the star is not always a matter of so much importance, 
 though it will be conducive to greater uniformity of personal equation if 
 stars of equal magnitude be habitually employed. On the other hand, 
 as we may save some little labor by using the stars whose apparent places 
 are given in the Annual Astronomical Ephemerides, we have therefore 
 added to our list of 200 bright stars all others given in the American 
 Astronomical Ephemeris, (A,) in the British Nautical Almanac, (B,) in 
 the Berliner Jahrbuch, ( J,) or in the Coimaissance des Temps, (0,) and have 
 indicated the occurrence of a star in either of these almanacs by an ap 
 propriate letter in the second column of the resulting catalogue of 3G8 
 stars. 
 
 It will be noticed that we thus obtain a sufficient number of points 
 for use in observing moon culminations should the traveler have time or 
 inclination to resort to that method of determining longitude. 
 
 METHODS OF OBSERVATION. 
 
 The course now to be pursued by the observer. depends, to some extent, 
 upon the manner in which he proposes to nse his instrument for the ac 
 curate determination of his clock corrections, but chiefly upon the atmo 
 spheric conditions and the stars of his ephemeris. Either of the follow 
 ing methods may be adopted ; for simplicity we shall, as usual, speak of 
 the observer as being in the northern hemisphere : 
 
 I. 
 
 The instrument being moved in azimuth until Polaris is within the 
 reticule, and by preference near the middle thread, we read the level in 
 both positions of the axis, observe the transit of Polaris liear oue thread 
 and that of a time star immediately before or afterwards, and again read 
 the level in both positions. Then, supposing the inequality of the pivots 
 and the collimation to be known, we have the material for determining 
 the clock correction. The collimation had best be at once determined 
 by observations of Polaris in both positions of the axis. 
 
 But this method ought never to be resorted to except in extreme neces 
 sity : it is always of importance to institute observations of the time 
 stars as well as of Polaris in both positions of the axis, as in the follow 
 ing methods. 
 
 IT. 
 
 Eead the level ; observe the time star, and then Polaris, over any 
 thread, by preference the middle one, or, still better, make several bisec 
 tions by means of the micrometer thread; read the level ; reverse the 
 axis : read the level ; observe Polaris again, as also another time star. 
 
 The observations of the time stars may either precede or follow those 
 of Polaris. 
 
 This method, in which the azimuth remains the same in the two posi 
 tions of the axis, is specially applicable when the azimuthal motion of 
 Polaris is rapid, and differs from the ordinary use of the transit only in 
 that Polaris is observed at any hour angle whatever. 
 
THE VERTICAL OF THE POLE STAR. 35 
 
 III. 
 
 Read the level ; observe Polaris on the middle thread and a time star; 
 read the level ; reverse the axis ; read the level ; alter the azimuth 
 slightly, so that Polaris will again cross the middle thread in a few sec 
 onds ; read the level ; observe Polaris on the middle thread and a time 
 star; read the level; reverse the axis, and again read the level. 
 
 The last reversion and level reading may be omitted if we have no 
 reason to doubt the stability of the instrument. 
 
 In this method, which is commonly the most convenient and expedi 
 tions both as regards the observations and the computations, we alter 
 the azimuth only by a small amount, so as to overtake Polaris in its di- 
 nrnal motion. This method is specially applicable when no micrometer 
 is provided for the instrument. 
 
 IY. 
 
 By the azimuthal motion bring the extreme western thread of the ret 
 icule to Polaris ; read the level ; observe the time star and Polaris ; read 
 the level ; reverse the axis ; read the level ; bring the same thread, now 
 become the extreme eastern one, to Polaris ; read the level ; observe 
 Polaris and the same time star ; read the level ; reverse the axis, and 
 again read the level. 
 
 The last reversion and level-reading may be omitted if the mounting 
 is sufficiently stable. 
 
 The fixed thread of the reticule may be advantageously replaced by 
 the extreme micrometer thread, if such an one is provided in addition to 
 the central thread. In this method we reverse upon Polaris in order not 
 to alter the azimuth so much as to leave that star outside the reticule. 
 It is, however, more expeditious and quite safe to observe Polaris before 
 the time star ; then reverse and set upon the same time star, alter the 
 azimuth so as to again observe its transit, and, finally, observe Polaris, 
 which will certainly be found in the field. 
 
 In this method the azimuth is altered by a large amount, not exceed 
 ing, however, the angular distance of the extreme wires of the reticule. 
 
 PREPARATORY COMPUTATIONS. 
 
 In preparing for eifcta? of the preceding methods of observation we 
 make use of a solution of the problem giving the positions of two stars 
 and of the observer s zenith, required the moment at which these three 
 points are in the same vertical plane. Instead of a rigorous solution, 
 however, we may, by means of Table II, attain a sufficiently approximate 
 determination of the required moment. 
 
 For a star in the meridian the movement in azimuth is, approxi 
 mately, 
 
 ,- . cos 3 T. 
 
 d A = -^r d t. 
 
 sin (tp 8) 
 
 Table II gives the values of dA for dt = l; its use will be apparent 
 from the following example: 
 
 Example. At, latitude + 33, and about 16 h of sidereal time, we desire 
 to determine the clock correction ; we select d Ophiuchi and Y Herculis 
 as appropriate time stars, whose places are 
 
 /. m. 
 
 . No. 234, 3 Ophiuchi ; 3 ; a = 16 7.5 3 = 3 21 
 
 No. 237, Y Herculis ; 3 ; a = 10 10.2 d = + 19 28 
 
36 
 
 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 For these two moments the ephemeris of Polaris gives 
 
 h. in. /(. m. o 
 
 At = 330 atl 7: f = U 56 5 = 68 0; A = l 
 at 16 16: t = I5 5: z = 5757; "A = l 
 From Table II we find 
 
 5 = 181 5 
 
 8 = 181 8 
 
 f For d Ophiuclii = + 1.8 
 
 dA 
 [ For r Herculis ^== + 2.2 
 
 Whence the hour-angle of 5 Ophiuchi, when at the azimuth, 1 5 , is 
 
 0.GO = 2 m .4 
 
 10 y 
 =r ?- 
 
 1.0 
 
 and for r Herculis, = -^ _0.51 = 2 m .l 
 
 and the moments at which the time stars are to be observed will be, 
 respectively, 16 h 9 m .9 and 16 h 18 m .3. 
 
 In setting for the time stars we may use meridian zenith distances, 
 <p d, but having brought the star between the horizontal wires, when 
 once it has entered the field, we should, for accuracy and security, record 
 the reading of the setting circle, and that, too, if possible, to the fraction 
 of a minute. 
 
 In following method^ IV of observation we need to know the space of 
 time within which the observation, reversal, &c., must be accomplished, 
 or the change of azimuth that can be made without throwing Polaris 
 too far from the middle wire. 
 
 We have, with sufficient accuracy, 
 
 sin z 
 
 where i = the equatorial distance of the extreme from the middle thread, 
 and z is the zenith distance of the time star to be observed. Assuming 
 i = l m = 15 , we obtain the d A of the following tables : 
 
 z. 
 
 6 A. 
 
 
 
 
 
 / 
 
 10 
 
 1 
 
 26 
 
 15 
 
 
 
 58 
 
 20 
 
 
 
 44 
 
 25 
 
 
 
 36 
 
 30 
 
 
 
 30 
 
 z. 
 
 (5- A. 
 
 o 
 30 
 
 o 
 
 
 30 
 
 40 
 
 
 
 23 
 
 50 
 
 
 
 20 
 
 60 
 
 
 
 18 
 
 70 
 
 
 
 16 
 
 The azinmthal change to be given to the transit is, evidently, double 
 the A of the preceding table, since the same wire is to be observed first 
 w r hen on the extreme west, and again when on the extreme east. 
 
 Example. At latitude 54, at about 12 h 35 m sidereal time, we propose 
 to observe f Yirginis for clock correction. We have : 
 Polaris z = 37 22 A = + 19 t = ll h 24 m d A = 25 
 
 fj A 
 
 r Virginia z= 
 
THE VERTICAL OF THE POLE STAR. 37 
 
 Whence, if l m is the equatorial distance of the extreme wire, the two 
 setting s must be between the azimuths 
 
 AI = + 19 + 25 = + Oo 44/ ? aiu j A 2 = + 19 (P 25 = 6 ; 
 
 and the time elapsed between the time star transits over the middle 
 threads of the diaphragm will be 
 
 QQ50 / _3 1 ".33 
 ~L2T = = 1.1M 
 
 leaving thus at least forty seconds for reading the level and setting cir 
 cle, reversing, reading the level, and setting at the proper zenith distance 
 and azimuth. This is, indeed, as unfavorable a case as need occur. By 
 omitting to observe the time star on the extreme wires, we can mate 
 rially increase the interval of forty seconds. In instruments properly 
 constructed the level is always* in place and its reading occupies but a 
 few seconds. 
 
 METHODS OF COMPUTATION. COLLIMATION. 
 
 In case the collimation is to be independently determined by observa 
 tions of Polaris in reversed positions of the axis, we may use the follow 
 ing method for deducing the value of that quantity : 
 
 The several micrometric bisections being made in rapid succession in 
 each position of the axis, it will be sufficiently exact to consider the mean 
 reading of the micrometer as belonging to the mean of the observed 
 times. We have, then, as also in case any two fixed wires are observed, 
 
 At time T 1? first position, Polaris distant from the middle wire - - ii 
 At time T 2 , reversed position, Polaris distant from the middle wire - i 2 
 
 the collimation c, and the distances ii and i 2 , being always supposed to 
 increase in the direction of the positive motion of the micrometer screw 
 and to be expressed in seconds of time, being known by observations of 
 equatorial and polar stars. 
 Now, the ordinary formula for azimuth instruments give, 
 
 At time T 1? AI = i -f &i cotg Z x + (c + ii) cosec Zi, 
 At time T 2 , A 2 = 2 -f & 2 cotg Z 2 -f (c -f i 2 ) cosec Z 2 . 
 
 Where A! and A 2 are the azimuths, Z 1? Z 2 the zenith distances of Po 
 laris, Oi = & 4- 3&P and 2 = <> + ( ^aP the azimuths of the axis of revo 
 lution in the direct and reversed positions, and which will be identical 
 if the pivots are of perfect form, (or o a p = and 3 f a p = 0.) So, also, will 
 the inclinations^^ b -f J/^> 4- 4%p and b 2 = b -f A\p + A 2 p be identi 
 cal if the pivots are of equal diameters and perfect form, (or A l p = ; 
 J !|) = 0; J a # = 0; ^^ = 0.) 
 
 For Z l and Z 2 we may use the mean zenith distance, Z, taken from the 
 finder, or the finding epheineris for the mean moment, J (Ti -f T 2 ) = T. 
 
 As the observations are supposed to be made in rapid succession, we 
 ma assume 
 
 
 
 where 
 
38 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 Q being the parallactic angle, which is given with sufficient accuracy by 
 
 sinQ = cos^t-^. 
 sinZ 
 
 There now results, for the collimatiou, 
 
 *!tTq^^ 
 
 c will be negative if the middle thread or micrometer zero is too far in 
 the direction of positive motion. 
 
 TIME. 
 
 The deduction of the clock correction js to be effected by slightly dif 
 ferent processes of computation, according as we have followed one or 
 the other of the previous methods of observation. The formulae- given 
 by Dollen may be systematically arranged as follows, using the follow 
 ing notation as adopted from the preceding memoir : 
 
 Pole Star. Time Star. 
 
 S S the observed times of transit. 
 
 u = U-\-Y u the clock correction^ on sidereal time ; y the correc 
 
 tion for clock rate during S S. 
 a a the apparent right ascensions, corrected for diurnal 
 
 aberration, if necessary. 
 d d -the apparent declinations. 
 
 z =o y z=y<l the zenith distances, z being always positive. 
 
 / the interval for the thread on which Polaris is ob 
 
 served, (+ when west of the middle.) 
 c the error of collimation, (positive when the middle 
 
 thread lies too far to the west.) 
 
 1) the inclination, (positive for west end high.) 
 
 a the azim.uth of the axis, (positive when its west end 
 
 lies south of west point.) 
 
 COLLIMATION KNOWN. 
 
 One pole star and one time star, observed in either position of the 
 axis; the inclination, (&,) the latitude, (&,) and thread interval, (/,) 
 known. 
 
 1. Rigorous -solutioy. 
 
 (See Dollen, 14, first solution.) 
 (.) Compute r from 
 
 S + r a = D ; S a = D; 15(D D) = r. 
 <L/ (6.) Compute sin |c, cos d, and from 
 
 1 Ji,/ cos / sin c = cos d sin r 
 
 cos d cos c = cos d sin d sin d cos d cos r 
 sin d = sin 8 sin d + cos d cos d cos r. 
 (c.) Compute >? from 
 
 sin (c +/) sin c sin d 
 sin 79 = . 
 
 cose cos d 
 
THE VERTICAL OF THE POLE STAR. 39 
 
 (d.) Compute n, x, and m from 
 
 COSMCOS# = + cose cos ( 4- r ; ) 
 cos n sin x cos 3 sin c -f sin d cos c sin (* -f- r t ) 
 sin n = -f sin (5 sin c + cos 5 cos c sin ( + -//) 
 
 sin w = tg n tg 9? + sin h sec ?i sec ^ 
 
 and deduce ^ (a? m). 
 
 JLO 
 
 (e.) Eeduce each observed thread to the middle one by the reductions 
 
 ~~tr/ ~*&-=f Vsec (d + n) sec (d n) 
 
 and derive a new S from the mean of all, whence a new D is to be found. 
 This will rarely necessitate a correction to the ^ (xm) already com- 
 
 puted. 
 
 (/.) With the corrected D compute 
 
 u = ^~(x m) D 
 
 2. Approximate solution . 
 
 When F/ is large, or the factor F is not given. (See Dollen, 14, 
 third solution.) 
 
 (a.) Compute r as in (1 . a) from 
 
 g/ + r _ a / = D ; S = D; 15(D D) = r. 
 
 (6.) Compute from 
 
 sec cotg <5 X sin r 
 
 4- 0< : ___ _____ o ______ ^ 
 
 "1 tg 5 COtg d COS r 
 
 (c.) Compute -/? from 
 
 sin/" 
 
 8111 * = tin (* + *) 
 
 (d.) Compute x\ and ?! from 
 
 Sin Wi = COS ^ tg (I + r y ) COS iPi tg ^. 
 
 (e.) We now have 
 
 15 v 
 
 and there remains only to reduce all the transits of the time star to the 
 middle thread, to correct D thereby, and to compute the terms Bb + Cc. 
 
 If the value of S, first used, be the mean of all threads systematically 
 disposed about the mean thread, it will, generally, not require any cor 
 rection for the quantity^ n. 
 
 (f.) The inclination, o, is given in level divisions, one of which has 
 the value, _p, expressed in seconds of time ; whence we can easily com 
 pute 
 
 B 1) = l)p sec (p. 
 
 (g.) The collimation, c, is expressed in seconds of time, and we have to 
 compute 
 
 C = sec <f> cos J (z 1 z) sec (z 1 -f z) *. ^ > 
 
 q = cosec 2 <p + (cotg <p tg jrttg J (z 1 z) f f / 
 
 C = C (sec mi) i; /^\ 
 
 whence results C . c. 
 
40 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 It will, if c be moderately small, be always allowable to use C instead 
 ofC. 
 
 3. Approximate solution. 
 
 When F/is not large or the factor F is given. (See Dollen, 14, sec 
 ond solution.) 
 
 (a.) Compute r, as before, from 
 
 S + r a ==D ; S a = D- 15 (D D) = r; 
 
 where we shall not materially increase the probable error of our result 
 by adding to the threads, observed symmetrically, any others reduced to 
 the mean thread, by the ordinary formula, 
 
 t (&.) Compute A, fjL 7 v, and />, from 
 
 A = tg d cotg 3 
 
 si n ""* 
 
 /ti=tg?eotg<5 /> = i- - 
 
 v = A // = tg c? COtg d 1 
 
 (c.) Compute x and M O from 
 
 tg x > />, sin M = v p cos ,r . 
 rf. We now have 
 
 and it remains to compute the three terms, 
 
 B6 + Cc+F/. 
 
 (e.) As in (2 ./) we have, for the inclination, 
 
 (/.) For the collimation we have, as in (U . //), 
 
 sin ^^ --I-- mil 2j 
 = S6C * ~~ = S 
 
 = cosec 
 
 + f^ 1 - jcotg ^ tg J (^ x 
 
 and C = 
 
 where, as before, for all ordinary values of c, we may assume C equal to 
 C . 
 
 (g.) The equatorial thread, or micrometer interval, /, being expressed 
 in seconds of time, we have 
 
 sin (z 1 + z) 
 
 and F == F (sec m ) k . 
 
 If F is not given by appropriate tables, then, for very small values of 
 /, we may assume F equal to F . 
 
 COLLIMATION UNKNOWN. 
 
 Each of the three methods of computation previously given assumes 
 the collimation (c) to be previously known, and is adapted to the inde 
 pendent deduction of a clock correction for each pair of stars observed 
 
THE VERTICAL OF THE POLE STAR. 41 
 
 in either position of the instrument. But it is evident that we have only 
 to make a very slight change in the order of computation so as to deduce 
 both colliraation and clock correction from the observation of two pairs 
 of stars, one in each position. It is this class of observations that is to 
 be highly recommended and especially enjoined. 
 
 We may leave out of consideration the rigorous methods of computa 
 tion and confine ourselves to the more generally useful approximate 
 methods. 
 
 4. Approximate solution. 
 
 When F/is large, or the factor F not given. (See Dollen, 15, first 
 example.) 
 
 The azimuth may have remained the same and two different stars have 
 been used for time stars, (as in the II method of observation,) or the azi 
 muth may have been altered in order to observe the same time star in 
 both positions, (as in the IY method of observation.) In either case we 
 have S i and S L for the observations of the Pole Star and Time Star in the 
 first position, but S 2 and S 2 for the observations in the reversed posi 
 tion, and we have to compute the observations of each position inde 
 pendently, according to the method 2 merely in article (2.0), stopping 
 at the computation of 
 
 C , #, and C. 
 
 We thus obtain, by (2 . e), from the first time star, 
 
 w 1 C 1 c= 1 1 5 (a? 1 ii) (D.+ B^), 
 and from the second time star, 
 
 Since each clock correction, Ui and u^ is supposed to hold for the mo 
 ment of the observation of the time star, we reduce them (by adding the 
 quantities YI and -^ computed with an approximate clock rate) to a com 
 mon moment, for which let u be the clock correction ; we then have 
 
 where the upper signs hold when the first position of the instrument is 
 the normal one. The half sum and difference of O x and O 2 now give us 
 the complete solution of our problem. 
 
 5. Approximate solution. 
 
 When F/is small, or F previously given. (See Dollen, 15, second 
 example.) 
 
 The azimuth may have remained the same and Polaris have been 
 observed over side threads or the micrometer wire, (as in the II method 
 of observation,) or the azimuth may have been changed and Polaris ob 
 served on the middle thread, (as in the III method of observation.) 
 
 We, in the first case, follow the method 3 with a modification precisely 
 similar to that given in the previous method, 4, and we obtain, as there, 
 from the values of 1/1 + n do and of u + r 2 C 2 c the correct u and c. 
 (See Dollen, 15, first example.) 
 
 In the second case, following method III, F/is zero ; the computation 
 
42 THE PORTABLE TRANSIT INSTRUMENT IN 
 
 is made according to 2 and 4, but becomes simplified since TJ =0. This 
 is, probably, the best of all the methods of observation and computation. 
 (See Dollen, 15, second example.) 
 
 NOTE 1. If we have pursued the IV method of observation, we may assume Ci C 2 
 without sensible error and obtain it without computing C ore. But it is always desira 
 ble not to omit the determination of the collimation. 
 
 NOTE 2. We have now reviewed the five methods of computation, some one of which 
 is specially appropriate to the use of the transit instrument^accordiug to either of the 
 four methods of observing previously given. The expert observer will not find it diffi 
 cult so to arrange his observations that five-place logarithms may be used in the com- 
 nutations, and, as in the use of small angles the ordinary five-figure tables of logar- 
 ithmic-trigonometric footers may be advantageously replaced by the tables of logar 
 ithms of numbers, we have reproduced, in Table III, the numbers alluded to by Dollen, 
 as given by WwwtgeJl, by means of Avhich one easily passes from the logarithm of any 
 number of seconds of arc to the corresponding logarithmic sine or tangent. If there 
 be required the logarithmic sine or tangent of the angle x, which, expressed in seconds, 
 we denote by x", then we have 
 
 Briggiau log sine x Briggiau log x 1 -f- 4.685575 S 
 Briggian log tangent x = Briggiau log x" -f- 4.685575 -f T. 
 
 Our Table III gives the numbers S and T in units of the sixth place of decimals. It 
 will be most convenient to omit the addition of the constant logarithm 4.685575, in 
 cases where it is eventually eliminated from the result. In using six-figure logarithms 
 the computer will find it advantageous to copy into Bremiker s six-figure tables the 
 numbers S and T, given in the Avell-known edition of Vega by the same author. 
 
 The conversion of arc into time, and vice versa, should be avoided, if possible, by the 
 use of tables in which the arguments are given, in parallel columns, both in time and 
 arc. 
 
THE VERTICAL OF THE POLE STAR. 
 GENERAL STAR CATALOGUE. 
 
 43 
 
 No. 
 
 A. B. J. C. 
 
 Name. 
 
 Mag. 
 
 a 1870.0 
 
 Annual 
 variation. 
 
 (51870.0. 
 
 Annual 
 variation. 
 
 
 
 
 
 ft. m. s. 
 
 g 
 
 o / n 
 
 
 
 1 
 
 A B J C 
 
 a Andromedae . 
 
 2 
 
 1 40 
 
 + 3.1 
 
 + 28 22 22 
 
 - 19.9 
 
 2 
 
 
 Cassiopea3 . . 
 
 2.4 
 
 2 13 
 
 + 3.1 
 
 + 58 26 
 
 + 19. 9 
 
 3 
 
 A B J C 
 
 y Pegasi , . 
 
 2.6 
 
 6 33 
 
 + 3.1 
 
 + 14 27 39 
 
 - 20. 
 
 4 
 
 A B 
 
 Hydrw u . . . . 
 
 3 
 
 18 53 
 
 + 3.3 
 
 77 59 14 
 
 J- 20.2 
 
 5 
 
 C 
 
 a Phoenicia . . . 
 
 2 
 
 19 50 
 
 + 3.0 
 
 43 38 
 
 J - 19. 7 
 
 6 
 
 B 
 
 12 Ceti 
 
 6 
 
 23 24 
 
 + 3.1 
 
 4 49 33 
 
 + 19. 9 
 
 7 
 
 
 6 Andromedae . 
 
 3.4 
 
 32 23 
 
 + 3.2 
 
 +30 8 55 
 
 19.7 
 
 8 
 
 A B J C 
 
 a CassiopeaB . . . 
 
 2. 2-2. 8 
 
 33 9 
 
 + 3.4 
 
 + 55 49 26 
 
 + 19.8 
 
 9 
 
 A B J 
 
 Ceti .... 
 
 2 
 
 37 4 
 
 -f 3.0 
 
 18 42 2 
 
 - 19.8 
 
 10 
 
 A 
 
 21 Cassiopea; 
 
 6 
 
 37 6 
 
 + 3.8 
 
 + 74 16 34 
 
 19.7 
 
 11 
 
 
 y Cassiopege . . 
 
 2 
 
 48 53 
 
 + 3.5 
 
 +60 44 
 
 - 19.6 
 
 12 
 
 A B C 
 
 Piscium .... 
 
 4 
 
 56 12 
 
 + 3.1 
 
 + 7 11 22 
 
 19.5 
 
 13 
 
 
 rj Ceti 
 
 3 
 
 123 
 
 + 3.0 
 
 10 52 11 
 
 19.2 
 
 14 
 
 C 
 
 Andromeda? . . . 
 
 2.4 
 
 1 2 28 
 
 + 3.3 
 
 + 34 55 53 
 
 + 19. 3 
 
 15 
 
 A B J C 
 
 a Ursc e Miuoris . . 
 
 2 
 
 1 11 16 
 
 + 20.1 
 
 + 88 36 59 
 
 - 19.1 
 
 16 
 17 
 
 A B 
 
 8 Cassiopeee 
 9 Ceti 
 
 3 
 3 
 
 1 17 21 
 1 17 31 
 
 + 3.8 
 + 3.0 
 
 + 59 33 30 
 8 51 18 
 
 + 18.9 
 + 18.7 
 
 18 
 19 
 
 A 
 
 A (38) Cassiopere . . 
 y Phomicis . . . 
 
 6 
 3 
 
 1 21 36 
 1 22 44 
 
 + 4.4 
 + 2.6 
 
 + 69 35 39 
 43 59 2 
 
 18.7 
 r 18. 6 
 
 20 
 
 A B 
 
 TI Piscium .... 
 
 3.6 
 
 1 24 32 
 
 + 3. 2 
 
 + 14 40 30 
 
 + 18.7 
 
 21 
 
 A B C 
 
 a Eridani .... 
 
 1 
 
 1 32 52 
 
 + 2.2 
 
 57 53 51 
 
 + 18.4 
 
 22 
 
 B 
 
 v Piscium .... 
 
 4.6 
 
 1 34 40 
 
 + 3.1 
 
 + 4 49 43 
 
 + 18.3 
 
 23, 
 
 C 
 
 (54) Aiidromeda3 . 
 
 4. 4 
 
 1 35 32 
 
 + 3.7 
 
 + 49 49 44 
 
 + 18. 4 
 
 .24 
 
 A 
 
 o Piscium .... 
 
 4 
 
 1 38 32 
 
 + 3.2 
 
 + 8 30 8 
 
 + 18. 3 
 
 25 
 
 
 g Ceti 
 
 3 
 
 1 45 3 
 
 r 3.0 
 
 10 58 45 
 
 + 17.9 
 
 26 
 
 
 Cassiopea) . 
 
 3.4 
 
 1 45 4 
 
 + 4.2 
 
 + 63 1 44 
 
 -4- 18.0 
 
 27 
 
 A B C 
 
 Arietis . . . 
 
 2.6 
 
 1 47 28 
 
 + 3.3 
 
 + 20 10 17 
 
 - -17.8 
 
 28 
 
 A 
 
 50 Cassiopea) 
 
 4 
 
 1 52 23 
 
 + 5.0 
 
 + 71 47 24 
 
 - 17.7 
 
 29 
 
 
 a Hydrss. JV 
 
 3 
 
 1 54 40 
 
 + 1.9 
 
 62 12 2 
 
 - 17. 6 
 
 30 
 
 
 y Andromedae 
 
 2.4 
 
 1 55 55 
 
 + 3.6 
 
 + 48 17 40 
 
 - 17.6 
 
 31 
 
 A B J C 
 
 a Arietis .... 
 
 2 
 
 1 59 51 
 
 + 3.4 
 
 + 22 50 48 
 
 + 17. 2 
 
 32 
 
 
 Trianguli . . . 
 
 3 
 
 2 1 49 
 
 + 3.5 
 
 + 34 12 28 
 
 - 17.3 
 
 33 
 
 A 
 
 l (65) Ceti .... 
 
 4. 4 
 
 267 
 
 + 3.2 
 
 + 8 14 8 
 
 17.1 
 
 34 
 
 B 
 
 67 Ceti 
 
 6 
 
 2 10 30 
 
 + 3.0 
 
 71 21 
 
 + 16. 7 
 
 35 
 
 c 
 
 o Ceti 
 
 1. 7-OO 
 
 2 12 47 
 
 + 3.0 
 
 3 34 10 
 
 + 16.6 
 
 36 
 37 
 
 A C 
 B 
 
 i (35) Cassiopea? . . 
 f 2 Ceti 
 
 4 
 4 
 
 2 18 23 
 2 21 15 
 
 + 4.8 
 + 3.2 
 
 + 66 48 56 
 + .7 52 33 
 
 J- 16.5 
 + 16.3 
 
 33 
 
 A B J 
 
 y Ceti 
 
 3.4 
 
 2 36 34 
 
 + 3.1 
 
 + 2 41 10 
 
 - 15.4 
 
 39 
 
 C 
 
 41 Arietis .... 
 
 4 
 
 2 42 20 
 
 + 3.5 
 
 + 26 43 26 
 
 - 15.2 
 
 40 
 
 
 77 Eridani .... 
 
 3 
 
 2 50 4 
 
 + 2.9 
 
 9 25 1 
 
 ~ 14.6 
 
 41 
 
 
 y Persei .... 
 
 3 
 
 2 55 24 
 
 + 4.3 
 
 + 52 59 42 
 
 - 14. 6 
 
 42 
 
 A B J C 
 
 a Ceti 
 
 2.4 
 
 2 55 29 
 
 + 3.1 
 
 + 3 34 41 
 
 14. 4 
 
 43 
 
 C 
 
 Persei .... 
 
 2. S...4. 
 
 2 59 43 
 
 + 3.9 
 
 + 40 27 10 
 
 + 14. 3 
 
 44 
 
 A 
 
 48 Cephei .... 
 
 6 
 
 3 3 55 
 
 + 7.3 
 
 + 77 15 9 
 
 - 13. 9 
 
 45 
 
 B J 
 
 i Arietis .... 
 
 4.4 
 
 3 4 12 
 
 + 3.4 
 
 + 19 14 
 
 - 13.9 
 
 46 
 
 A 
 
 Arietis .... 
 
 4.4 
 
 3 7 26 
 
 + 3.4 
 
 + 20 33 39 
 
 13.7 
 
 47 
 
 A B J C 
 
 a Persei .... 
 
 2 
 
 3 15 3 
 
 + 4.2 
 
 + 49 23 45 
 
 - 13. 2 
 
 48 
 
 
 Eridani .... 
 
 3 
 
 3 26 45 
 
 + 2.9 
 
 9 54 3 
 
 + 12.4 
 
 49 
 
 A C 
 
 J Persei .... 
 
 3 
 
 3 33 44 
 
 + 4.2 
 
 + 47 22 9 
 
 - 11.9 
 
 50 
 
 
 J Eridani .... 
 
 3 
 
 3 37 2 
 
 + 2.9 
 
 10 12 20 
 
 + 10.0 
 
 51 
 
 A B 
 
 rj Tauri .... 
 
 3 
 
 3 39 46 
 
 + 3.6 
 
 + 23 42 3 
 
 + 11.5 
 
 52 
 
 A 
 
 g Persei . . . 
 
 3 
 
 3 45 58 
 
 + 3.8 
 
 + 31 29 42 
 
 -i- 11.0 
 
 53 
 54 
 
 A B 
 
 y Hydm*/ . . . 
 
 y Eridani / . . . . 
 
 3 
 3 
 
 3 49 18 
 3 51 58 
 
 1.0 
 
 + 2.8 
 
 74 38 16 
 13 52 49 
 
 - 10.9 
 
 4- 10.5 
 
 55 
 
 B 
 
 o 1 Eridani .... 
 
 4.4 
 
 4 5 31 
 
 + 29 
 
 7 10 42 
 
 + 9.7 
 
 56 
 
 A C 
 
 y Tauri ...... 
 
 4 
 
 4 12 24 
 
 + 3.4 
 
 + 15 18 41 
 
 + 9.1 
 
 57 
 
 A B 
 
 Tauri 
 
 3.6 
 
 4 21 3 
 
 + 3.5 
 
 + 18 53 22 
 
 + 8.4 
 
 58 
 
 A B J C 
 
 a Tauri 
 
 1 
 
 4 28 28 
 
 + 3.4 
 
 + 16 14 45 
 
 + 7.6 
 
 59 
 
 
 52 Eridani .... 
 
 3 Ct f 
 
 4 29-30 
 
 + 2.3 
 
 30 49 47 
 
 + 7.7 
 
 60 
 
 
 a Doradus .... 
 
 3 // 
 
 4 31 11 
 
 + 1.3 
 
 55 13 53 
 
 4- 7.6 
 
 61 
 62 
 
 A 
 C 
 
 a (9) Camelopardalis 
 Tr 1 Orionis .... 
 
 4 
 5 
 
 4 41 8 
 4 42 47 
 
 + 5.9 
 + 3.3 
 
 + 66 7 4 
 + 6 43 56 
 
 -r 6.8 
 6.7 
 
 63 
 
 A B 
 
 t Aurigae .... 
 
 3 
 
 4 48 32 
 
 + 3.9 
 
 + 32 57 27 
 
 -r 6.1 
 
 64 
 65 
 
 C 
 A 
 
 (10) Camelopardalis 
 11 Orionis .... 
 
 4 
 5 
 
 4 51 52 
 4 57 9 
 
 + 5.3 
 + 3.4 
 
 + 60 14 55 
 + 15 13 14 
 
 + 6.0 
 ~ 5.4 
 
44 
 
 THE PORTABLE TRANSIT INSTRUMENT IN 
 GENERAL STAR CATALOGUE Continued. 
 
 Xo. 
 
 A. B. J. C. 
 
 Nam*. 
 
 Mag. 
 
 a 1870.0. 
 
 Annual 
 variation. 
 
 <J 1870.0. 
 
 Annual 
 variation. 
 
 
 
 
 
 h. m. s. 
 
 s. 
 
 o / // 
 
 
 
 66 
 
 B 
 
 e Leporis .... 
 
 3.6 
 
 4 59 57 
 
 4- 2.5 
 
 22 32 51 
 
 4- 5.1 
 
 67 
 
 
 ft Eridani .... 
 
 3 
 
 5 1 28 
 
 + 2.9 
 
 5 15 25 
 
 -r 5.0 
 
 66 
 
 A B J C 
 
 d A 11 ri gffi 
 
 1 
 
 575 
 
 4- 4. 4 
 
 4- 45 51 45 
 
 4- 4.2 
 
 69 
 
 A B J C 
 
 Oriouis . 
 
 1 
 
 5 8 17 
 
 4- 2.9 
 
 8 21 15 
 
 4- 4.5 
 
 70 
 
 A B J C 
 
 Tauri 
 
 2 
 
 5 18 5 
 
 + 3.8 
 
 4- 28 29 41 
 
 4- 3.5 
 
 71 
 
 C 
 
 y Orionis .... 
 
 2 
 
 5 18 10 
 
 + 3.2 
 
 4- 6 13 49 
 
 4- 3.7 
 
 72 
 
 A 
 
 966 Groom bridge . . 
 
 6.4 
 
 5 22 22 
 
 4- 8.0 
 
 4- 74 57 5 
 
 4- 3.3 
 
 73 
 
 A B C 
 
 (5 Orionis .... 
 
 2. 2... 2. 7 
 
 5 25 22 
 
 4- 3.1 
 
 23 53 
 
 4- 3.0 
 
 74 
 
 A B 
 
 a Leporis .... 
 
 3 
 
 5 27 
 
 + 2.6 
 
 17 55 3 
 
 4- 2.9 
 
 75 
 
 
 i Orionis .... 
 
 3 
 
 5 29 4 
 
 4- 2.9 
 
 5 59 50 
 
 4- 2.8 
 
 76 
 
 A B C 
 
 c Orionis .... 
 
 2 
 
 5 29 37 
 
 + 3.0 
 
 1 17 14 
 
 4- 2.6 
 
 77 
 
 C 
 
 g Orionis .... 
 
 2 
 
 5 34 12 
 
 4- 3.0 
 
 2 49 
 
 + 2.3 
 
 76 
 
 A B C 
 
 a ColamlNB . . . 
 
 2 
 
 5 34 57 
 
 + 2.2 
 
 34 8 40 
 
 4- 2.2 
 
 79 
 
 
 K Orionis .... 
 
 2.6 
 
 5 41 35 
 
 + 2.8 
 
 9 43 5 
 
 4- 1.7 
 
 80 
 
 
 Columbse . . . 
 
 3 
 
 5 46 23 
 
 4- 2.1 
 
 35 49 14 
 
 4- 1.5 
 
 81 
 
 A B J C 
 
 a Orionia .... 
 
 1.0.. .1.4 
 
 5 48 8 
 
 -f 3.2 
 
 4- 7 22 49 
 
 -f 1.1 
 
 82 
 
 
 AurigsB .... 
 
 2 
 
 5 49 
 
 4- 4.4 
 
 4- 44 55 52 
 
 + 1.0 
 
 83 
 
 
 Aurig .... 
 
 3- 
 
 5 50 51 
 
 + 4.1 
 
 4- 37 12 4 
 
 4- 0.8 
 
 84 
 
 B 
 
 v Orionis .... 
 
 4.6 
 
 609 
 
 4- 3.4 
 
 4- 14 46 53 
 
 
 
 85 
 
 A 
 
 22 Camelopardalis 
 
 4.6 
 
 6 4 31 
 
 4- 6.6 
 
 4- 69 21 36 
 
 0.5 
 
 86 
 
 A B 
 
 p G-eminorum . 
 
 3 
 
 6 15 6 
 
 + 3.6 
 
 4- 22 34 38 
 
 1.4 
 
 87 
 
 
 g Canis Majoris . 
 
 2.6 
 
 6 15 20 
 
 + 2.3 
 
 30 28 
 
 1.3 
 
 88 
 
 C 
 
 Canis Majoris . . 
 
 2.4 
 
 6 16 58 
 
 4- 2.6 
 
 17 53 36 
 
 1.4 
 
 89 
 
 A B C 
 
 a Argus .... 
 
 1 
 
 6 21 4 
 
 4- 1.3 
 
 52 37 32 
 
 1.8 
 
 90 
 
 A B 
 
 y Geminorum . . . 
 
 2.4 
 
 6 30 12 
 
 + 3.5 
 
 4- 16 30 28 
 
 2.7 
 
 91 
 
 
 v Argus .... 
 
 3 
 
 6 33 47 
 
 4- 1.8 
 
 43 4 57 
 
 2.9 
 
 92. 
 
 
 IS Geminorum . . . 
 
 3.4 
 
 6 35 59 
 
 4- 3.7 
 
 + 25 15 26 
 
 3.0 
 
 93 
 
 A B 
 
 51 Cephei .-... 
 
 5 
 
 6 38 42 
 
 4- 30.3 
 
 4- 87 14 23 
 
 3.4 
 
 94 
 
 A B J C 
 
 a Canis Majoris . . 
 
 1 
 
 6 39 26 
 
 f 2.6 
 
 16 32 22 
 
 4.6 
 
 95 
 
 A B 
 
 Cauis Majoris . . 
 
 1.6 
 
 6 53 31 
 
 + 2.4 
 
 28 47 50 
 
 4.6 
 
 96 
 
 B 
 
 y Canis Majoris . 
 
 4.4 
 
 6 57 53 
 
 4- 2.7 
 
 15 26 35 
 
 5.0 
 
 97 
 
 A 
 
 6 Canis Majoris . . 
 
 2 
 
 736 
 
 4- 2. 4 
 
 26 11 18 
 
 5.2 
 
 96 
 
 A B 
 
 6 Geminorum . 
 
 3.4 
 
 7 12 21 
 
 4- 3.6 
 
 4- 22 13 8 
 
 6.2 
 
 99 
 
 
 IT Al gUS .... 
 
 3.4 
 
 7 12 34 
 
 + 2.1 
 
 36 51 55 
 
 6.2 
 
 100 
 
 A 
 
 Piazzi VII, 67 . . 
 
 6 
 
 7 17 20 
 
 4- 6.3 
 
 4- 68 43 35 
 
 6.7 
 
 101 
 
 
 ?7 Canis Majoris . 
 
 2.6 
 
 7 18 57 
 
 4- 2.4 
 
 29 3 4 
 
 6.7 
 
 1C2 
 
 C 
 
 Canis Minoris . . 
 
 3 
 
 7 20 4 
 
 4- 3.3 
 
 4- 8 32 58 
 
 6.8 
 
 103 
 
 A B J "C 
 
 a 1 Geminorum . . . 
 
 1.6 
 
 7 -20 Id 
 
 4- 3.8 
 
 4- 32 10 15 
 
 7.4 
 
 104 
 
 A B J C 
 
 o Canis Minoris . . 
 
 1 
 
 7 32 30 
 
 4- 3.1 
 
 4- 5 33 22 
 
 8.9 
 
 105 
 
 A B J C 
 
 Geminorum . . . 
 
 1.4 
 
 7 37 22 
 
 4- 3.7 
 
 4- 28 20 16 
 
 8.3 
 
 106 
 
 C 
 
 Argus .... 
 
 3.4 
 
 7 43 50 
 
 + 2.5 
 
 24 32 7 
 
 8.7 
 
 107 
 
 A 
 
 Geminorum . 
 
 5 
 
 7 45 32 
 
 4- 3.7 
 
 + 27 5 58 
 
 8.9 
 
 108 
 
 
 % Argus .... 
 
 3 
 
 7 53 28 
 
 4- 1.5 
 
 52 38 4 
 
 9.5 
 
 109 
 
 B 
 
 TO. Caucri .... 
 
 5 
 
 7 55 32 
 
 4- 3.7 
 
 4-28 9 23 
 
 9.8 
 
 110 
 
 
 Argus .... 
 
 2.5 
 
 7 59 1 
 
 4- 2.1 
 
 39 38 20 
 
 10.0 
 
 111 
 
 A C{ 
 
 55 Camelopardalis ^ 
 3 Ursre Majoris . 5 
 
 6 
 
 j 7 59 51 
 
 4- 6.1 
 
 + 68 51 10 
 
 10.0 
 
 119 
 
 113 
 
 A B 
 C 
 
 T\(15J; Argus . . . 
 y 2 Argus .... 
 
 3 
 
 2 
 
 820 
 8 5 31 
 
 4- 2.6 
 
 4- 1.8 
 
 23 55 52 
 46 57 19 
 
 10.1 
 10.5 
 
 114 
 
 C 
 
 Cancri .... 
 
 3.6 
 
 8 9 27 
 
 4- 3.3 
 
 4- 9 35 3 
 
 10.7 
 
 115 
 
 
 e Argus .... 
 
 2 
 
 8 19 51 
 
 4- 1.2 
 
 59 5 27 
 
 11.3 
 
 116 
 
 B 
 
 i? Cancri .... 
 
 6 
 
 8 25 11 
 
 4- 3.5 
 
 4- 20 52 50 
 
 11.9 
 
 117 
 
 C 
 
 f Hydros .... 
 
 4.4 
 
 8 30 46 
 
 4- 3.2 
 
 4- 6 9 21 
 
 12.2 
 
 118 
 
 A B 
 
 Hydrae .... 
 
 3.4 
 
 8 39 53 
 
 4- 3.2 
 
 + 6 53 39 
 
 12. 9 
 
 119 
 
 
 <5 Argus .... 
 
 3 
 
 8 41 7 
 
 1.7 
 
 54 14 
 
 13.1 
 
 120 
 
 A B J 
 
 i Ursae Majoris . 
 
 3 
 
 8 50 18 
 
 4- 4.1 
 
 4- 48 33 
 
 13.8 
 
 
 
 
 
 
 
 
 
 121 
 
 A 
 
 <r* Ursa? Majoris . . 
 
 5 
 
 8 58 55 
 
 4- 5.4 
 
 4- 67 39 32 
 
 14.2 
 
 122 
 
 A 
 
 K Cancri .... 
 
 5 
 
 9 42 
 
 4- 3.3 
 
 4- 11 11 22 
 
 14.2 
 
 123 
 
 e/ 
 
 Cancri .... 
 
 5 
 
 9 1 53 
 
 4- 3.5 
 
 4- 22 34 13 
 
 14.2 
 
 124 
 
 
 A Argus .... 
 
 3 
 
 9 3 13 
 
 4- 2.2 
 
 42 54 33 
 
 14.4 
 
 125 
 
 B 
 
 83 Cancri .... 
 
 6 
 
 9 11 43 
 
 4- 3.4 
 
 4- 18 15 17 
 
 15.1 
 
 126 
 
 C 
 
 Argus .... 
 
 1 
 
 9 11 46 
 
 4- 0.8 
 
 69 10 57 
 
 14.8 
 
 127 
 
 A B C 
 
 t Argus .... 
 
 2 
 
 9 13 37 
 
 4- 1.6 
 
 58 43 47 
 
 14.9 
 
 128 
 
 
 K Argus .... 
 
 4 
 
 9 18 5 
 
 4- 1.9 
 
 54 27 26 
 
 15.3 
 
 129 
 
 A 
 
 1 Draconis .... 
 
 4. 4 
 
 9 18 20 
 
 4- 9.2 
 
 + 81 53 50 
 
 15.3 
 
 130 
 
 A B J C 
 
 o Hydra? .... 
 
 2. 3.. .2. 7 
 
 9 21 12 
 
 4-3.0 
 
 8 5 47 
 
 15.4 
 
THE VERTICAL OF THE POLE STAR. 
 GENERAL STAK CATALOGUE Continued. 
 
 45 
 
 No. 
 
 A. B. J. C. 
 
 Name. 
 
 Mag. 
 
 a 1870.0. 
 
 Annual 
 ariation. 
 
 J 1870.0. 
 
 Annual 
 variation. 
 
 
 
 
 
 h. m. s. 
 
 . 
 
 o / // 
 
 
 
 131 
 
 A 
 
 24 (d) Ursae Majoris . 
 
 4.6 
 
 9 22 56 
 
 + 5.4 
 
 + 70 23 57 
 
 15.5 
 
 132 
 
 A B J 
 
 6 Ursae Majoris . . 
 
 3 
 
 9 24 9 
 
 4- 4.1 
 
 4- 52 16 4 
 
 16. 2 
 
 133 
 
 A B 
 
 Leonia .... 
 
 3 
 
 9 38 28 
 
 \- 3.4 
 
 4- 24 22 17 , 
 
 16.4 
 
 134 
 
 
 u Argus .... 
 
 3 
 
 9 43 51 
 
 + 1.5 
 
 64 28 10 | 
 
 16.6 
 
 135 
 
 A C 
 
 ft Leouia .... 
 
 4 
 
 9 45 22 
 
 + 3.4 
 
 4- 26 37 4 
 
 16.7 
 
 136 
 
 B 
 
 TT Leonia .... 
 
 5 
 
 9 53 21 
 
 + 3.2 
 
 4- 8 40 
 
 17.1 
 
 137 
 
 A B J C 
 
 a Leonis 
 
 1.4 
 
 10 1 27 
 
 4- 3.2 
 
 + 12 36 6 
 
 17. 4 
 
 138 
 
 A 
 
 32 Ursa? Majoris . 
 
 6 
 
 10 8 34 
 
 + 4.4 
 
 -f 65 45 19 
 
 17.8 
 
 139 
 
 
 Leouis .... 
 
 3 
 
 10 9 28 
 
 4- 3.4 
 
 4-24 3 52 
 
 17.7 
 
 140 
 
 A B J C 
 
 y 1 Leonis .... 
 
 2 
 
 10 12 48 
 
 4- 3.3 
 
 4- 20 29 53 
 
 18.0 
 
 141 
 
 
 /x Ursa? Majoris . 
 
 3 
 
 10 14 35 
 
 + 3.6 
 
 f 42 9 10 
 
 17.9 
 
 142 
 
 A 
 
 9 Draconis .... 
 
 4.6 
 
 10 23 58 
 
 + 5.3 
 
 4- 76 22 52 
 
 18.4 
 
 143 
 
 A B C 
 
 p Leonis .... 
 
 4 
 
 10 25 58 
 
 4- 3.2 
 
 -f 9 58 28 
 
 - 18.4 
 
 144 
 
 
 Argus .... 
 
 3 
 
 10 38 19 
 
 + 2.1 
 
 63 42 4H 
 
 18.8 
 
 145 
 
 A B C 
 
 7] Argus .... 
 
 1 6 
 
 10 40 1 
 
 + 2.3 
 
 59 3 
 
 18.8 
 
 146 
 
 
 It Argus .... 
 
 3 
 
 10 41 12 
 
 4- 2.6 
 
 48 44 
 
 18.9 
 
 147 
 
 A B 
 
 I Leonis .... 
 
 5 
 
 10 42 25 
 
 + 3.2 
 
 4- 11 13 56 
 
 18.9 
 
 148 
 
 C 
 
 v Hydrae . .. 
 
 3.4 
 
 10 43 3 
 
 + 2.9 
 
 15 30 52 
 
 18.7 
 
 149 
 
 C 
 
 (3 Urae Majoris . . 
 
 2.4 
 
 10 53 59 
 
 + 3.7 
 
 +57 4 43 
 
 19.2 
 
 150 
 
 A B J C 
 
 a Ursa3 Majoris . . 
 
 2 
 
 10 55 41 
 
 + 3.8 
 
 + 62 27 7 
 
 19.4 
 
 151 
 
 B J 
 
 X Leonis .... 
 
 5 
 
 10 58 19 
 
 + 3.1 
 
 + 8 2 17 
 
 19.4 
 
 152 
 
 
 rl Ursee Majoris . 
 
 3 
 
 11 2 21 
 
 + 3.4 
 
 4- 45 12 10 
 
 19.5 
 
 153 
 
 A B J 
 
 o Leouis .... 
 
 2.4 
 
 11 7 12 
 
 + 3.2 
 
 4- 21 14 8 
 
 19.6 
 
 154 
 
 
 Leouis .... 
 
 3.4 
 
 11 7 2} 
 
 + 3.1 
 
 4- 16 8 24 
 
 19.5 
 
 155 
 
 A B J 
 
 J Crateris .... 
 
 3.4 
 
 11 12 51 
 
 + 3.0 
 
 14 4 32 
 
 19.4 
 
 156 
 
 A 
 
 T Leonis .... 
 
 5 
 
 11 21 15 
 
 + 3.1 
 
 4- 3 34 19 
 
 19.8 
 
 157 
 
 A C 
 
 A Draconis .... 
 
 34 
 
 11 23 39 
 
 4- 3.6 
 
 + 70 2 52 
 
 .19.9 
 
 158 
 
 A B 
 
 v (91) Leouis . . . 
 
 4.6 
 
 11 30 18 
 
 + 3.1 
 
 6 22 
 
 19.8 
 
 159 
 
 A B J C 
 
 13 Leonis .... 
 
 2 
 
 11 42 26 
 
 + 3.1 
 
 + 15 17 56 
 
 20.1 
 
 160 
 
 J C 
 
 ft Virginia .... 
 
 3.5 
 
 11 43 55 
 
 4- 3.1 
 
 4- 2 29 50 
 
 20.3 
 
 161 
 
 A B J C 
 
 y Ursa) Majoris . 
 
 2.4 
 
 11 46 59 
 
 4- 3.2 
 
 + 54 25 3 
 
 20.0 
 
 162 
 
 A 
 
 o Virginia .... 
 
 4 
 
 11 % 58 35 
 
 4- 3.1 
 
 4- 9 27 18 
 
 20.0 
 
 163 
 
 B 
 
 s Corvi 
 
 3 
 
 12 3 26 
 
 + 3.1 
 
 21 53 48 
 
 20. 
 
 164 
 
 A 
 
 4 Draconis .... 
 
 4.6 
 
 12 6 5 
 
 + 2.9 
 
 4- 78 20 18 
 
 20.1 
 
 165 
 
 
 6 Crucis .... 
 
 3 
 
 12 8 15 
 
 4- 3.1 
 
 58 1 29 
 
 20.0 
 
 166 
 
 C 
 
 6 Ursae Majoris . 
 
 3.4 
 
 12 8 59 
 
 4- 3.0 
 
 -f 57 45 16 
 
 20. 1 
 
 167 
 
 
 Y Corvi 
 
 2 
 
 12 9 7 
 
 4- 3.1 
 
 16 49 10 
 
 20.0 
 
 168 
 
 A B 
 
 (1 Chamreleontis . . 
 
 5 
 
 12 10 46 
 
 + 3.3 
 
 78 35 26 
 
 20.0 
 
 169 
 
 A B C 
 
 TJ Virginia .... 
 
 3.4 
 
 12 13 15 
 
 4- 3.1 
 
 4- 3 21 
 
 20.0 
 
 170 
 
 A B C 
 
 a* Crucis .... 
 
 1 
 
 12 19 23 
 
 + 3.3 
 
 62 .2 38 
 /v 
 
 19.9 
 
 171 
 
 C 
 
 / Corvi 
 
 2.4 
 
 12 23 9 
 
 4- 3. I 
 
 16 47 28 
 
 20. 1 
 
 172 
 
 
 y Crucis .... 
 
 2 
 
 12 23 58 
 
 + 3.3 
 
 56 23 
 
 20.1 
 
 173 
 
 A B 
 
 /3 Corvi 
 
 2.4 
 
 12 27 34 
 
 + 3.1 
 
 22 40 40 
 
 20. 
 
 174 
 
 A 
 
 K Dracouis . . 
 
 3.4 
 
 12 27 55 
 
 + 2.6 
 
 4- 70 30 17 
 
 19. 9 
 
 175 
 
 
 y Centauri 
 
 3 
 
 12 34 21 
 
 4- 3.3 
 
 48 14 45 
 
 19. 9 
 
 176 
 
 B C 
 
 y 1 Virginia .... 
 
 2.6 
 
 12 35 4 
 
 + 3.0 
 
 44 12 
 
 19.8 
 
 177 
 
 J I 
 
 Y* Virginia .... 
 
 2.6 
 
 12 35 5 
 
 4- 3.0 
 
 44 6 
 
 19.8 
 
 178 
 
 C 
 
 p Crucis .... 
 
 2 
 
 12 40 8 
 
 + 3.4 
 
 58 58 34 
 
 19.7 
 
 179 
 
 A 
 
 32 Camelopardalis 
 
 4.6 
 
 12 48 12 
 
 + 0.4 
 
 + 84 7 9 
 
 19.6 
 
 180 
 
 C 
 
 e L T rsa3 Majoris . . 
 
 2 
 
 12 48 18 
 
 + 2.7 
 
 4- 56 39 56 
 
 19.7 
 
 181 
 
 1 
 
 J Virginia .... 
 
 3 
 
 12 49 4 
 
 + 3.0 
 
 4- 4 6 15 
 
 19.7 
 
 182 
 
 A B J 
 
 12 Canum Venat. . . 
 
 3 
 
 12 49 57 
 
 + 2.8 
 
 4-39 1 16 
 
 19.5 
 
 183 
 
 C 
 
 e Virgin is . . . 
 
 2.6 
 
 12 55 43 
 
 + 3.0 
 
 4- 11 39 32 
 
 19.5 
 
 184 
 
 A B 
 
 Virginia .... 
 
 4.4 
 
 13 3 13 
 
 + 3.1 
 
 4 50 40 
 
 19.3 
 
 185 
 
 
 y Hydra .... 
 
 3 
 
 13 11 51 
 
 4- 3.2 
 
 22 29 2 
 
 19. 1 
 
 186 
 
 
 t Centauri .... 
 
 3 
 
 13 13 18 
 
 + 3.4 
 
 36 1 34 
 
 19.1 
 
 187 
 
 A B J C 
 
 Virginia . . . 
 
 
 13 18 21 
 
 4- 3.2 
 
 10 28 55 
 
 18.9 
 
 188 
 
 
 Uraa> Majoris . 
 
 2 
 
 13 18 41 
 
 4- 2.4 
 
 4- 55 36 17 
 
 18.9 
 
 189 
 
 A B J C 
 
 ? Virginia .... 
 
 3.4 
 
 13 28 4 
 
 + 3.1 
 
 + 4 11 
 
 18.5 
 
 190 
 
 
 Centauri .... 
 
 3 
 
 13 31 40 
 
 + 3.7 
 
 52 48 15 
 
 18.6 
 
 191 
 
 A B J C 
 
 7 Ursa 1 Majoria . . 
 
 2 
 
 13 42 25 
 
 4- 2.4 
 
 + 49 57 47 
 
 18.1 
 
 192 
 
 
 Centauri 
 
 3 
 
 13 47 26 
 
 4- 3.7 
 
 46 38 50 
 
 18.0 
 
 193 
 
 A B J 
 
 1 Bootis . . . 
 
 3 
 
 13 48 30 
 
 4- 2.9 
 
 4- 19 3 1 
 
 18.2 
 
 194 
 
 A B C 
 
 P Centanri .... 
 
 1 
 
 13 54 40 
 
 4- 4. 2 
 
 59 44 40 
 
 17.7 
 
 195 
 
 B 
 
 T Virginia .... 
 
 4 
 
 13 55 2 
 
 + 3. 
 
 4- 2 10 28 
 
 17.6 
 
46 
 
 THE PORTABLE TRANSIT INSTRUMENT IN 
 GENERAL STAK CATALOGUE Continued. 
 
 Xo. 
 
 A. B. J. C. 
 
 Name. 
 
 Mag. 
 
 a 1870.0. 
 
 Annual 
 variation 
 
 J 1870.0. 
 
 Annual 
 variation. 
 
 
 
 
 
 h. m. s. 
 
 s. 
 
 o / // 
 
 
 
 196 
 
 c 
 
 6 Centauri . . . . 
 
 3 
 
 13 59 3 
 
 + 3.5 
 
 35 43 48 | 18. 1 
 
 197 
 
 A C 
 
 a Draconis .... 
 
 3.4 
 
 14 52 
 
 + 1.6 
 
 4- 64 59 50 17. 4 
 
 198 
 
 A B J C 
 
 a Bootis .... 
 
 1 
 
 14 9 44 
 
 4r 2.7 
 
 4- 19 51 38 18.9 
 
 199 
 
 A 
 
 jp. Bootis .... 
 
 3.6 
 
 14 20 46 
 
 4- 2.0 
 
 4- 52 27 9 16. 8 
 
 200 
 
 B 
 
 p Bootis .... 
 
 3.6 
 
 14 26 14 
 
 4- 2.6 
 
 4- 30 56 3<\ 16.0 
 
 201 
 
 
 y Bootis .... 
 
 2.6 
 
 14 26 51 
 
 4- 2.4 
 
 4- 38 52 40 ! 16. 
 
 202 
 
 
 .77 Centauri .... 
 
 3 
 
 14 27 15 
 
 4- 3.8 
 
 41 35 9 j 16. 2 
 
 203 
 
 A 
 
 5 Ursre Minoris . 
 
 4.7 
 
 14 27 50 
 
 0.2 
 
 4- 76 16 25 16. 
 
 204 
 
 A B C 
 
 a 2 Centauri .... 
 
 1 
 
 14 30 48 
 
 4- 4.0 
 
 60 17 39 15. 
 
 205 
 
 
 a Lupi 
 
 3 
 
 14 33 16 
 
 4- 3.9 
 
 46 49 43 
 
 15.9 
 
 206 
 
 C Bootis .... 
 
 3.4 
 
 14 34 57 
 
 4- 2.9 
 
 4- 14 17 14 
 
 15.7 
 
 207 
 
 A B Bootis .... 
 
 2.4 
 
 14 39 19 
 
 4- 2.6 
 
 + 27 37 24 
 
 15.4 
 
 208 
 
 J i a 1 Libra} .... 
 
 6 
 
 14 43 27 
 
 4- 3.3 
 
 15 27 2 
 
 15.2 
 
 209 
 
 A B J C 
 
 a 2 Libra} .... 
 
 2.4 
 
 14 43 41 
 
 + 3.3 
 
 15 29 59 
 
 15.2 
 
 210 
 
 
 /? Lupi 
 
 3 
 
 14 50 2 
 
 4- 3.9 
 
 42 36 31 
 
 15.0 
 
 211 
 
 
 K Centauri .... 
 
 3 
 
 14 50 43 
 
 4- 3.9 
 
 41 24 56 
 
 14.8 
 
 212 
 
 A B J C 
 
 (i Ursa? Minoris . 
 
 2 
 
 14 51 7 
 
 0.3 
 
 + 74 41 11 
 
 14.8 
 
 213 
 
 A C 
 
 li Bootis .... 
 
 3 
 
 14 57 3 
 
 4- 2.3 
 
 4- 40 54 15 
 
 14.4 
 
 214 
 
 B J 
 
 ip Bootis . . . . 
 
 4.4 
 
 14 58 53 
 
 4- 2.6 
 
 + 27 27 22 
 
 14.2 
 
 215 
 
 
 y Trianguli Australis 
 
 3 
 
 15 6 49 
 
 4- 5 5 
 
 68 11 47 
 
 13.9 
 
 216 
 
 A B 
 
 Libra} .... 
 
 o 
 
 15 10 1 
 
 + 3.2 
 
 8 54 5 
 
 13.6 
 
 217 
 
 
 J Bootis .... 
 
 3 
 
 15 10 16 
 
 4- 2.4 
 
 4- 33 48 6 13. 7 
 
 218 
 
 A 
 
 /*i Bootis .... 
 
 3.6 
 
 15 19 35 
 
 4- 2.3 
 
 4- 37 50 4 12. 8 
 
 219 
 
 A C 
 
 \ 2 Ursa, 1 Minoris . . 
 
 3 
 
 15 20 57 
 
 0.1 
 
 - 72 17 48 12. 8 
 
 220 
 
 
 t Draconis . . 
 
 3 
 
 15 22 3 
 
 4- 1.3 
 
 + 59 25 2 J 
 
 12.8 
 
 221 
 222 
 
 
 y Lupi 
 J Serpentis 
 
 3 
 3.4 
 
 15 26 29 
 15 28 36 
 
 + 4.0 
 
 4- 2.9 
 
 40 43 44 
 
 4- 10 58 34 
 
 12.7 
 12.3 
 
 223 
 
 A B J C 
 
 a Corona} Borealis . 
 
 2 
 
 15 29 11 
 
 4- 2.5 
 
 4-27 9 15 j 12. 3 
 
 224 
 
 A B J C 
 
 a Serpentis ... 2. 4 
 
 15 37 52 
 
 4- 3.0 
 
 4- 6 50 12 1 11. 6 
 
 225 
 
 
 Trianguli Australia 
 
 3 
 
 15 43 43 
 
 4- 5.2 
 
 63 1 30 
 
 11.7 
 
 226 
 
 A C 
 
 Serpentis . . 
 
 3.4 
 
 15 44 20 
 
 4- 3.0 
 
 4- 4 52 15 
 
 11.1 
 
 227 
 
 A B J 
 
 Ursa} Minoris . . 
 
 4.4 
 
 15 48 45 
 
 2.3 
 
 4- 78 11 35 10. 9 
 
 228 
 
 
 y Serpentis 
 
 3.6 
 
 15 50 26 
 
 4- 2.8 
 
 4-16 5 19 12. 
 
 229 
 
 
 IT Scorpii .... 
 
 3 
 
 15 51 
 
 4- 3.6 
 
 25 44 17 10. 8 
 
 230 
 
 A 
 
 Corona} Borealis . 
 
 4 
 
 15 52 12 
 
 + 2.5 
 
 4- 27 15 21 
 
 10.6 
 
 231 
 
 A 
 
 S Scorpii .... 
 
 2.4 
 
 15 52 39 
 
 4- 3.5 
 
 22 14 57 
 
 10.6 
 
 232 
 
 A B 
 
 l Scorpii . . . 
 
 2 
 
 15 57 53 
 
 - 3.5 
 
 19 26 50 
 
 10.2 
 
 233 
 
 
 Draconis 
 
 3.6 
 
 15 59 28 
 
 4- 1.1 
 
 4- 58 54 46 
 
 9.8 
 
 234 
 
 235 
 
 A 
 
 A B 
 
 2320 Groombriclge . . 
 6 Ophiuchi . . . 
 
 5.6 
 3 
 
 16 5 58 
 16 7 32 
 
 4- 0.1 
 4- 3.1 
 
 4-68 9 10 
 3 21 27 
 
 9.5 
 9.6 
 
 236 
 
 j Ophiuchi . . . 
 
 3.4 
 
 16 11 26 
 
 4- 3.2 
 
 4 22 25 
 
 - 9.2 
 
 237 
 
 A T Herculis .... 
 
 3.4 
 
 16 15 50 
 
 -f 1.8 
 
 4- 46 37 27 
 
 8.8 
 
 238 
 
 
 y Herculis .... 
 
 3 
 
 16 16 11 
 
 4- 2.6 
 
 4- 19 28 6 
 
 8.8 
 
 239 
 
 A B J C 
 
 a Scovpii .... 
 
 1.4 
 
 16 21 26 
 
 4- 3.7 
 
 26 8 26 
 
 8.4 
 
 240 
 
 A B 
 
 r) Draconis .... 
 
 2.6 
 
 16 22 15 
 
 4- 0.8 
 
 4- 61 48 33 
 
 8.2 
 
 241 
 
 
 Herculis . . . 
 
 2.4 
 
 16 24 38 
 
 4- 2.6 
 
 4- 21 46 21 
 
 8.2 
 
 242 
 
 A 
 
 15 (A) Draconis . . 
 
 5 
 
 16 28 15 
 
 0.1 
 
 4- 69 2 58 
 
 7.8 
 
 243 
 
 A 
 
 t Ophiuchi . , . 
 
 2.6 
 
 16 30 
 
 4- 3.3 
 
 10 18 5 
 
 7.6 
 
 244 
 
 A B C 
 
 a Trianguli Australia 
 
 2 
 
 16 34 56 
 
 6.3 
 
 68 47 4 
 
 7.4 
 
 245 
 
 B J 
 
 g Hercinis . . . 
 
 2.6 
 
 16 36 23 
 
 4- 2.3 
 
 - 31 50 24 
 
 6.8 
 
 246 
 
 A 
 
 7 Herculis 
 
 3 
 
 16 38 26 
 
 4- 2.1 
 
 -L 39 10 16 
 
 -J 7.0 
 
 247 
 
 c 
 
 Scorpii .... 
 
 3 
 
 16 41 45 
 
 + 3.9 
 
 34 3 17 
 
 7. 1 
 
 248 
 
 
 H l Scorpii .... 
 
 3 
 
 16 42 4 
 
 4- 4.0 
 
 37 49 21 
 
 6.8 
 
 249 
 
 
 S* 2 Scorpii .... 
 
 3 
 
 16 45 26 
 
 4- 4.2 
 
 42 8 14 
 
 - 6.9 
 
 250 
 
 A B J 
 
 K Ophiuchij . . . 
 
 3.4 
 
 16 51 31 
 
 4- 2.8 
 
 4- 9 34 45 
 
 5.9 
 
 251 
 
 C j Herculis .... 
 
 3.4 
 
 16 55 19 
 
 4- 2.3 
 
 4- 31 7 12 
 
 5.6 
 
 252 
 
 A j d Herculis .... 
 
 5 
 
 16 56 48 
 
 4- 2.2 
 
 4- 33 45 30 
 
 5.4 
 
 253 
 
 A B Ursa} Minoris . . 
 
 4.4 
 
 16 59 23 
 
 - 6.4 
 
 4- 82 14 49 
 
 5.2 
 
 254 
 
 n Ophiuchi . . . 
 
 2.4 
 
 17 2 53 
 
 4- 4.3 
 
 - 15 33 40 
 
 5.4 
 
 255 
 
 Draconis .... 
 
 3 
 
 17 8 25 
 
 4- 0.2 
 
 4- 65 52 29 
 
 4.5 
 
 256 
 
 A B J C a 1 Herculis .... 
 
 3.1. ..3. 9 
 
 17 8 43 
 
 4- 2.7 
 
 4- 14 32 27 
 
 4.4 
 
 257 
 
 6 Herculis .... 
 
 3 
 
 17 9 41 
 
 4- 2.5 
 
 - 24 59 38 
 
 4.6 
 
 258 
 
 B & Ophiuchi . . . 
 
 3.4 
 
 17 14 2 
 
 3.7 
 
 - 24 51 59 
 
 4.0 
 
 259 
 
 
 y Ara} 
 
 3 
 
 17 14 28 
 
 4- 5.0 
 
 56 15 4 
 
 4.1 
 
 260 
 
 
 /? Ar 3 17 14 30 
 
 4- 5.0 
 
 - 55 24 13 
 
 4.2 
 
THE VERTICAL OF THE POLE STAR. 
 GENERAL STAR CATALOGUE Continued. 
 
 47 
 
 Xo. 
 
 A. B. J. C. 
 
 Name. 
 
 Mag. 
 
 a 1870.0. 
 
 Annual 
 variation. 
 
 (5 1870.0. 
 
 Annual 
 variation. 
 
 
 
 
 
 h. m. s. 
 
 g 
 
 / II 
 
 n 
 
 2G1 
 
 A 
 
 b (44) Ophiuchi . . 
 
 5 
 
 17 18 26 
 
 + 3.7 
 
 24 3 11 
 
 3.7 
 
 26-2 
 
 
 a Aric 
 
 3 
 
 17 21 48 
 
 r 4.6 
 
 49 46 10 
 
 3.6 
 
 263 
 
 
 A Scorpii .... 
 
 3 
 
 17 24 47 
 
 r 4. 1 
 
 37 19 
 
 3.1 
 
 264 
 
 A B J 
 
 ft Dracoiiis .... 
 
 2.6 
 
 17 27 30 
 
 -;- i. 4 
 
 4- 52 23 55 
 
 2.8 
 
 263 
 
 
 Scorpii .... 
 
 3 
 
 17 27 56 
 
 + 4.3 
 
 42 54 47 
 
 3.1 
 
 266 
 
 A B J C 
 
 a Opliiuchi .... 
 
 2 
 
 17 28 54 
 
 4- 2.8 
 
 4- 12 39 54 
 
 2. 9 
 
 267 
 
 
 * Scorpii .... 
 
 3 
 
 17 33 30 
 
 + 4.1 
 
 38 57 38 
 
 2.5 
 
 268 
 
 C 
 
 Opliiuchi .... 
 
 3 
 
 17 37 3 
 
 4- 3.0 
 
 + 4 37 25 
 
 1.9 
 
 26 
 
 A 
 
 oj Draconia .... 
 
 5 
 
 17 37 43 
 
 0,4 
 
 4- 68 49 2 
 
 1. 6 
 
 270 
 
 A B J 
 
 H Herculis .... 
 
 3.4 
 
 17 41 22 
 
 + 2.3 
 
 + 27 47 54 
 
 2. 4 
 
 271 
 
 A 
 
 i// 1 Herculis, (pr.) . . 
 
 4. 4 
 
 17 44 15 
 
 1.1 
 
 -f 72 12 43 
 
 1.6 
 
 272 
 
 A B J C 
 
 y 1 Dracoiiis .... 
 
 2 4 
 
 17 53 35 
 
 4- 1.4 
 
 + 51 30 18 
 
 0.6 
 
 273 
 
 A 
 
 y 2 Sagittarii 
 
 a 4 
 
 17 57 27 
 
 -t- 3.9 
 
 30 25 23 
 
 0.4 
 
 274 
 
 A B 
 
 H l Sagittarii . . . 
 
 4 
 
 18 5 59 
 
 + 3.6 
 
 21 5 25 
 
 4- 0.5 
 
 275 
 
 A B 
 
 <r Octantia .... 
 
 6 
 
 18 6 19 
 
 + 109.2 
 
 89 16 43 
 
 4- 0. 6 
 
 276 
 
 A B J C 
 
 6 Ursa; Miuoris . 
 
 4.4 
 
 18 14 16 
 
 19.4 
 
 4- 86 36 20 
 
 4- 1.3 
 
 2*77 
 
 278 
 
 A 
 
 77 Serpentis 
 e Sagittarii . . . 
 
 3 
 
 2.6 
 
 18 14 35 
 18 14 52 
 
 + 3.1 
 
 + 4.0 
 
 2 55 49 
 34 26 33 
 
 4- 0.6 
 4- 1.2 
 
 279 
 
 
 A Sagittarii . . . 
 
 3 
 
 18 19 57 
 
 4- 3.7 
 
 25 29 30 
 
 4- 1.4 
 
 280 
 
 A 
 
 1 Aquilie .... 
 
 4.4 
 
 18 28 8 
 
 + 3.3 
 
 8 19 58 
 
 4- 2.2 
 
 281 
 
 A B J C 
 
 a Lyric 
 
 1 
 
 18 32 32 
 
 4- 8.0 
 
 + 38 39 51 
 
 4- 3. 1 
 
 282 
 
 A B J C 
 
 l Lyne 
 
 3. 5... 4. 5 
 
 18 45 17 
 
 + 2.2 
 
 + 33 12 47 
 
 4- 3.9 
 
 283 
 284 
 
 A 
 
 A 
 
 o Sagittarii 
 50 Dracoiiis .... 
 
 o 4 
 6 
 
 18 47 12 
 18 50 33 
 
 + 3.7 
 1.9 
 
 26 27 19 
 4- 75 16 44 
 
 + 4.0 
 4.4 
 
 285 
 
 
 y Lyric 
 
 3.4 
 
 18 54 5 
 
 + 2.2 
 
 4- 32 30 48 
 
 + 4.6 
 
 286 
 
 C 
 
 g Sagittarii . . . 
 
 3.4 
 
 18 54 20 
 
 + . 3. 8 
 
 30 3 50 
 
 4- 4.6 
 
 287 
 288 
 
 A B 
 
 A Aquilse .... 
 g Aquila> .... 
 
 3.4 
 3 
 
 18 59 21 
 18 59 26 
 
 + 3.2 
 
 + 2.8 
 
 5 4 30 
 + 13 40 21 
 
 J- 5.0 
 4- 5.1 
 
 289 
 
 
 TT Sagittarii . . . 
 
 3 
 
 19 2 2 
 
 + 3.6 
 
 21 13 38 
 
 4- 5.3 
 
 290 
 
 A 
 
 d Sagittarii . . . 
 
 5 
 
 19 1U 2 
 
 + 3.5 
 
 19 10 55 
 
 4- 6.1 
 
 291 
 
 B 
 
 a) Aquilas .... 
 
 5.6 
 
 19 11 43 
 
 + 2.8 
 
 + 11 21 46 
 
 4- 6.2 
 
 292 
 
 A C 
 
 S Dracoiiis . . . 
 
 3 
 
 19 12 31 
 
 0.0 
 
 4- 67 25 58 
 
 4- 6.3 
 
 293 
 
 A 
 
 T Dracoiiis 
 
 5 
 
 19 18 2 
 
 1.1 
 
 4- 73 6 47 
 
 4- 6.8 
 
 294 
 
 A B J 
 
 S Aquilie. 
 
 3.4 
 
 19 18 57 
 
 4- 3.0 
 
 + 2 51 23 
 
 4- 6. H 
 
 295 
 
 C 
 
 Cygni .... 
 
 3 
 
 19 25 29 
 
 + 2.4 
 
 -f- 27 41 20 
 
 4- 7. J 
 
 296 
 
 B 
 
 ft 2 Sagittarii . . . 
 
 4.6 
 
 19 28 47 
 
 4- 3.7 
 
 25 10 3 
 
 4- 7.6 
 
 297 
 
 A 
 
 K Aquilas .... 
 
 5 
 
 19 29 54 
 
 + 3. 2 
 
 7 18 51 
 
 4- 7.7 
 
 298 
 
 A B J C 
 
 y Aquilae .... 
 
 3 
 
 19 40 5 
 
 + 2.9 
 
 + 10 17 55 
 
 + 8.5 
 
 299 
 
 
 3 Cvgui 
 
 3 
 
 19 40 55 
 
 + 1 9 
 
 4- 44 48 50 
 
 1 HI 
 
 300 
 
 A B J C 
 
 ~:J o ., 
 a Aquiloe .... 
 
 1.4 
 
 19 44 26 
 
 A. J 
 
 + 2.9 
 
 + 8 31 37 
 
 -t" C. O 
 
 4- 9.2 
 
 301 
 
 
 >7 AquilsE .... 
 
 3. 5.. .4. 7 
 
 19 45 51 
 
 + 3.1 
 
 + 40 26 
 
 + 8.8 
 
 302 
 
 A 
 
 e Dracoiiis . . 
 
 4 
 
 19 48 36 
 
 0.2 
 
 + 69 56 11 
 
 4- 9.2 
 
 303 
 304 
 
 A B J C 
 
 A B 
 
 Aquila3 .... 
 A TJrsaj Minoris . 
 
 4 
 6.4 
 
 19 48 56 
 19 54 17 
 
 + 2.9 
 59.2 
 
 + .6 5 2 
 
 -f 88 55 4 
 
 4- 8.7 
 9. 6 
 
 305 
 
 A 
 
 T Aquilae .... 
 
 5.6 
 
 19 57 47 
 
 4- 2.9 
 
 4- 6 54 46 
 
 4- 9.9 
 
 306 
 
 C 
 
 Aquilie .... 
 
 3 
 
 20 4 36 
 
 + 3.1 
 
 1 12 17 
 
 4- 10.3 
 
 307 
 308 
 309 
 
 J 
 
 A B J C 
 A 
 
 a 1 Capricorni . . . 
 a 2 Capricorni . 
 K Cephei .... 
 
 4.4 
 3.4 
 4.4 
 
 20 10 26 
 20 10 50 
 20 13 13 
 
 + 3.3 
 -j- 3.3 
 1.9 
 
 12 54 28 
 12 56 44 
 + 77 19 
 
 4- 10.8 
 4- 10.8 
 4- 11.0 
 
 310 
 
 
 Capricorni . . . 
 
 3 
 
 20 13 42 
 
 + 3.4 
 
 15 11 22 
 
 4- 11. 
 
 311 
 
 A B C 
 
 a Pavonis .... 
 
 2 
 
 20 15 21 
 
 + 4.8 
 
 57 8 54 
 
 4- 11. 1 
 
 312 
 313 
 
 C 
 A 
 
 y Cygui .... 
 v Capricorni . . . 
 
 2.6 
 5 
 
 20 17 34 
 20 19 53 
 
 + 2.2 
 + 3.4 
 
 + 39 50 31 
 18 38 8 
 
 f 11. 3 
 4- 11.5 
 
 314 
 
 315 
 
 B 
 A 
 
 p Capricorni . . . 
 e Delphini .... 
 
 5 
 4 
 
 20 21 26 
 
 20 27 
 
 + 3.4 
 
 4- 2.9 
 
 18 14 28 
 4- 10 51 48 
 
 4- 11.6 
 4- 12. 
 
 316 
 
 
 a Incli .... 
 
 3 
 
 20 28 25 
 
 4- 4. 3 
 
 47 44 31 
 
 1 1. 9 
 
 317 
 318 
 319 
 
 A 
 C 
 
 3241 Groombridge . 
 13 Pavonis . 
 a Delphini .... 
 
 6.4 
 3 
 3.6 
 
 20 30 33 
 20 33 13 
 20 33 36 
 
 0.2 
 + 5.5 
 
 + 2. 8 
 
 4- 72 5 28 
 66 39 58 
 4- 15 27 19 
 
 4- 12! 2 
 4- 12. 3 
 12.4 
 
 320 
 
 A B J C 
 
 a Cygni 
 
 1.6 
 
 20 37 
 
 + 2.0 
 
 4- 44 49 
 
 4- 12.7 
 
 321 
 
 
 Cygni .... 
 
 2.6 
 
 20 40 57 
 
 4- 2.4 
 
 4- 33 29 5 
 
 - 13. 2 
 
 322 
 323 
 
 A 
 B 
 
 H Aquarii .... 
 32 Vulpeculaj . 
 
 4.6 
 5.4 
 
 20 45 38 
 20 49 1 
 
 + 3.2 
 + 2. 6 
 
 9 28 9 
 4- 27 33 52 
 
 4- 13. 2 
 4- 13.5 
 
 324 
 325 
 
 A 
 A 
 
 v Cygni 
 1879 Twelve year C. 
 
 4 
 6 
 
 20 52 20 
 20 53 24 
 
 + 2.2 
 2.5 
 
 4- 40 40 4 
 
 4-80 3 47 
 
 4- ]3. 7 
 
 4- 13. 7 
 
48 
 
 THE PORTABLE TRANSIT INSTRUMENT, ETC. 
 GENERAL STAR CATALOGUE Continued. 
 
 No. 
 
 A. B. J. C. 
 
 Name. 
 
 Mag. 
 
 a 1870.0. 
 
 ; Annual 
 variation. 
 
 6 1870.0. 
 
 Annual 
 variation. 
 
 
 
 
 
 h. in. s. 
 
 s. 
 
 o / // 
 
 i, 
 
 326 
 
 A B J 
 
 61 l Cvgni .... 
 
 5.4 
 
 21 1 4 
 
 + 2.7 
 
 4-38 6 41 
 
 4- 17.5 
 
 327 
 
 A B 
 
 Cygni 
 
 3 
 
 21 7 24 
 
 + 2.6 
 
 4- 29 41 42 
 
 + 14.6 
 
 328 
 
 A B J C 
 
 a Cephei .... 
 
 2.6 
 
 21 15 28 
 
 + 1.4 
 
 4- 62 2 6 
 
 4- 15.1 
 
 329 
 
 
 y Pavouis .... 
 
 3 
 
 21 15 40 
 
 4- 5.1 
 
 65 57 11 
 
 4- 15.7 
 
 330 
 
 A 
 
 1 Pegasi .... 
 
 4.4 
 
 21 16 4 
 
 + 2.8 
 
 4- 19,15 
 
 + 15.2 
 
 331 
 332 
 
 A B C 
 A B J 
 
 ft Aquarii .... 
 ft Cephei .... 
 
 3 
 3 
 
 21 24 43 
 
 21 26 58 
 
 + 3.2 
 
 + 0.8 
 
 6 8 30 
 
 4- 69 59 24 
 
 4- 15.6 
 4 15.7 
 
 333 
 
 A 
 
 Aquarii .... 
 
 4.6 
 
 21 30 50 
 
 + 3.2 
 
 8 26 9 
 
 4- 15.9 
 
 334 
 
 A B 
 
 e Pegasi .... 
 
 2.4 
 
 21 37 48 
 
 4- 2.9 
 
 -f 9 16 49 
 
 + 16.3 
 
 335 
 
 C 
 
 J Capricorn! . . . 
 
 3 
 
 21 39 51 
 
 4- 3.3 
 
 16 42 54 
 
 + 16.1 
 
 336 
 
 A 
 
 11 Cephei .... 
 
 5 
 
 21 40 
 
 + 0.9 
 
 4 70 42 46 
 
 + 16.5 
 
 337 
 
 
 Y Gruis 
 
 3 
 
 21 46 3 
 
 4- 3.7 
 
 37 58 33 
 
 4 16.5 
 
 338 
 
 A 
 
 \L Capricorui . . 
 
 5 
 
 21 46 12 
 
 + 3.3 
 
 14 9 45 
 
 4 16.8 
 
 339 
 
 B 
 
 16 Pegasi .... 
 
 5.4 
 
 21 47 9 
 
 + 2.7 
 
 4- 25 18 52 
 
 4- 16.8 
 
 340 
 
 A 
 
 79 Draconis .... 
 
 6.4 
 
 21 51 15 
 
 4- 0.7 
 
 4 73 5 14 
 
 + 17.0 
 
 341 
 
 A B J C 
 
 a Aquarii .... 
 
 3 
 
 21 59 6 
 
 4- 3.1 
 
 57 1 
 
 + 17.3 
 
 342 
 
 A B C 
 
 a Gruis 
 
 2 
 
 22 2 
 
 4- 3.8 
 
 47 35 20 
 
 4- 17.2 
 
 343 
 
 C 
 
 g Cephei .... 
 
 3.6 
 
 22 6 21 
 
 + 2.1 
 
 + 57 33 39 
 
 4- 17.6 
 
 344 
 
 
 a Tucanae .... 
 
 3 
 
 22 9 34 
 
 + 4.2 
 
 60 54 20 
 
 4- 17.7 
 
 345 
 
 A B 
 
 Aquarii .... 
 
 4.4 
 
 22 9 58 
 
 + 3.2 
 
 8 25 46 
 
 4- 17.8 
 
 346 
 
 C 
 
 y Aquarii .... 
 
 3.6 
 
 22 14 57 
 
 + 3.1 
 
 2 2 28 
 
 -1- 18. 
 
 347 
 
 A 
 
 TT Aquarii .... 
 
 4.6 
 
 22 18 38 
 
 + 3.1 
 
 4- 43 6 
 
 4- 18.1 
 
 348 
 
 A B 
 
 TI Aquarii .... 
 
 3.6 
 
 22 28 40 
 
 + 3.1 
 
 47 12 
 
 4- 18. 4 
 
 349 
 
 A 
 
 2-26 Cephei .... 
 
 5.4 
 
 22 29 59 
 
 4 1.1 
 
 4- 75 33 23 
 
 + 18.5 
 
 350 
 
 
 Gruis 
 
 3 
 
 22 34 54 
 
 -f 3. 6 
 
 47 33 40 
 
 + 18.6 
 
 351 
 
 A B 
 
 S Pegasi .... 
 
 3.4 
 
 22 34 58 
 
 + 3.0 
 
 +10 9 14 
 
 4- 18.7 
 
 352 
 
 
 T] Pegasi .... 
 
 3 
 
 22 36 55 
 
 4- 2.8 
 
 4- 29 32 32 
 
 + 18.7 
 
 353 
 
 A 
 
 i Cephei .... 
 
 3.6 
 
 22 45 3 
 
 + 2.1 
 
 -r 05 31 1 
 
 + 18.8 
 
 354 
 
 A 
 
 X Aquarii .... 
 
 4 
 
 22 45 50 
 
 f 3. 1 
 
 8 16 13 
 
 + 19. 1 
 
 355 
 
 
 <5 Aquarii .... 
 
 3 
 
 22 47 45 
 
 4 3.2 
 
 16 30 40 
 
 4- 19.1 
 
 356 
 
 A B J C 
 
 a Piscis Australia 
 
 1.4 
 
 22 50 28 
 
 + 3.3 
 
 30 18 38 
 
 4 19.0 
 
 357 
 
 
 Pegasi .... 
 
 2. 2...2. 7 
 
 22 57 28 
 
 + 2.9 
 
 4- 27 22 43 
 
 + 19.5 
 
 358 
 
 A B J C 
 
 o Pegasi .... 
 
 
 
 22 58 17 
 
 4- 3.0 
 
 4- 14 30 24 
 
 4- 19.3 
 
 359 
 
 B J C 
 
 y Piscium .... 
 
 4 
 
 23 10 26 
 
 + 3.1 
 
 -f 2 34 20 
 
 4- 19.6 
 
 360 
 
 A 
 
 o Cephei .... 
 
 5.6 
 
 23 13 18 
 
 + 2.4 
 
 + 67 24 
 
 + 19. 6 
 
 361 
 
 B 
 
 K Piscium .... 
 
 4.6 
 
 23 20 16 
 
 4- 3.1 
 
 + 32 39 
 
 + 19.6 
 
 362 
 
 A 
 
 6 Piscium .... 
 
 4.4 
 
 23 21 22 
 
 4- 3.0 
 
 + 5 39 54 
 
 + 19.7 
 
 363 
 
 A B J 
 
 i Piscium .... 
 
 4.4 
 
 23 33 16 
 
 + 3.1 
 
 4- 4 55 18 
 
 + 19. 5 
 
 364 
 
 A B 
 
 y Cephei .... 
 
 3.4 
 
 23 34 2 
 
 + 2.4 
 
 4- 76 54 25 
 
 + 20.1 
 
 365 
 
 B 
 
 o Sculptoris . . . 
 
 4.4 
 
 23 42 9 
 
 + 3.1 
 
 - 28 50 55 
 
 + 19.9 
 
 366 
 367 
 
 A 
 A B J 
 
 4163Groombridge . . 
 w Piscium .... 
 
 7 
 4 
 
 23 48 32 
 23 52 38 
 
 4- 2.8 
 4- 3.1 
 
 + 73 41 12 
 -r 6 8 36 
 
 + 20. 
 + 19.9 
 
 368 
 
 c 
 
 2 Ceti . 
 
 4.4 
 
 23 57 5 
 
 + 3.1 
 
 18 3 34 
 
 4- 20. 1 
 
 
 
 
 
 
 
 
 
14 DAY USE 
 
 RETURN TO DESK FROM WHICH BORROWED 
 
 LOAN DEPT. 
 
 This book is due on the last date stamped below, or 
 
 on the date to which renewed. 
 Renewed books are subject to immediate recall. 
 
 8 Oct 58 ? 
 
 LD 21-50m-8, 57 
 (,C8481slO)476 
 
 General Library 
 
 University of California 
 
 Berkeley 
 
^^ 
 
 PAMPHIET BINDER 
 
 Syracuse, N. Y. 
 Stockton. Colif.