UC-NRLF UNITED STATES NOETHERN BOUNDARY COMMISSION. DECLINATIONS OF FIXED STARS. BY LEWIS BOSS, <\ NOW DIRECTOR OF DUDLEY OBSERVATORY. .'o\S ' l * f *. r * x REPORT ON THE DECLINATIONS OF THE STARS EMPLOYED IN LATITUDE WORK WITH THE ZENITH TELESCOPE, EMBRACING SYSTEMATIC CORRECTIONS IN DE- CLINATION DEDUCED FOR VARIOUS AUTHORITIES, AND A CATALOGUE OF FIVE HUNDRED STARS FOR THE MEAN EPOCH 1875, BY ASSISTANT LEWIS BOSS, NOW DIRECTOE OF DUDLEY OBSERVATORY. DUDLEY OBSERVATOBY, Albany, N. T., February 21, 1877. DEAK SIR: After unexpected delay I Lave the honor to transmit, herewith, my report ou the accuracy of the declinations adopted by the United States Commission in the latitude work ol' the Northern Boundary Survey. In doing this, permit me to thank you most cordially for the kind interest and generous support which you have throughout accorded to this undertaking. The sense of obligation is the more keenly felt, when I reflect upon the many imperfections and deficiencies of the work; but your intercourse with me has been uniformly such as to cause me to forget the debt, and leaves only the most pleasant recollections. I have the honor to be, very respectfully, your obedient servant, LEWIS BOSS, Director of Dudley Observatory, and late Assistant Astronomer of the United States Northern Boundary Commission. Capt. WILLIAM J. TWINING, United States Engineers, Chief Astronomer and Surveyor of the United States Northern Boundary Commission. INTRODUCTORY. The method of obtaining latitudes with the zenith telescope, which was adopted by the United States Northern Boundary Commission, rendered it necessary, in 1872, to calculate the declinations of a large number of stars. The short time allowed lor preparation rendered a critical discussion of these star-places quite impracticable. The declinations adopted in the work of 1872 were, therefore, derived from a limited number of authorities; but were subsequently revised whenever additional material 409 340729 410 UNITED STATES NORTHERN BOUNDARY COMMISSION. [4] could be secured. Thus the catalogue for 1874 was compiled from nearly all the authorities which could be obtained from the library of the United States Naval Observatory. The method of reduction was substantially that employed by Argelander in the seventh volume of Bonn observations.* The principal deviations from this plan con- sisted in the smaller weights given to declinations from the older authorities, and in applying no systematic corrections to those -of a mean date later than 1860. Upon the accuracy of the adopted declinations depend the latitudes of twenty-two stations in the vicinity of the forty-ninth parallel. There is every reason to believe that for the majority of the stations the error in location due to instrumental causes is practically insignificant, and that if any considerable correction is needed it may sateiy be ascribed to systematic error in the values of declination assigned to the determining stars. To ascertain the numerical limits between which the value of such a correction is likely to exist, and, as far as practicable, to compute its actual amount, was the original purpose of this discussion. When the work was about half completed, it appeared that the systematic correc- tions and the declinations of the principal stars, adopted as standard in this paper, might prove acceptable to others engaged in certain classes of astronomical reductions. This circumstance led to a considerable enlargement of the original scope of the work. Only stars of the northern hemisphere, with a few in the first ten degrees of south declination, had hitherto been considered. The list was uowextended so as to include all the stars of the American Ephemeris. Quite recently, upon my appointment to the astronomical direction of Dudley Observatory, the work received an additional impulse from my determination, in reducing observations made with the transit circle, to use a standard catalogue in declination as well as right ascension. This course was adopted for the reason that, whenever the places of the principal fixed stars can be predicted from observations already made, with greater accuracy than they can be determined at any one observa- tory by a single series of a few years duration, a desire for the greatest economy of labor and accuracy in results should dictate one of two courses : either a special and rigorous research, having in view the independent determination of the places of a small number of the brighter stars; or, the use of a standard catalogue, compiled from the best available sources, to which the observations of all other objects should be essentially referred. It is much to be regretted that owing to unavoidable circumstances this change in plan was made too late for the most advantageous disposition of materials available for the purpose in view. On the other hand, the corrections and the resulting declin- ations are probably very near those which would have resulted from a more systematic and elaborate discussion, adopting the same general principles. This considerable extension of the original plan was determined upon at a time when it was out of the question that the computations should be completed during the existence of the boundary commission; so that in the performance of the work it has been necessary for me to incur many obligations. For material assistance I am especially indebted to Prof. Simon Newcomb, of the United States Naval Observatory. * Bonn Seob., Band VII., Abth. I., " Untersuchungeu iibur tiic Eigenbewegungen von 200 Sternen." [5] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 41 1 Without bis generous intervention it would have been impossible for me to Lave com- pleted the work in its present extent, within the prescribed limits of time, For further aid, I am under the greatest obligations to the office of the American Ephemcris and Nautical Almanac ; and to the Dudley Observatory, where the later computations have been carried on partly for the purpose of constructing a standard catalogue of declin- ations, for use with the transit circle, as already explained. The services of several computers have been engaged from time to time, generally for short periods. For such services, I am chiefly indebted to Assistant C. L. Doolittle, since Professor of Mathematics and Astronomy in the Lehigh University, Pennsylvania, and to Assistant O. S.Wilson, who have labored on the work in a most disinterested and competent manner. My thanks are also due to Thomas R. Featherstouhangh, A. M., formerly assistant at the Dudley Observatory. The facilities of the Observatory at Washington were most kindly extended to me by Admiral B. F. Sands, Superintendent, and by his successor in office, Admiral C. H. Davis. To the various members of the astronomical corps at that institution I desire to express my acknowledgments; particularly to Professors Eastman, Harkness, and Nourse, for special courtesies. PEELIMINAEY STATEMENT AND GENERAL PLAN OF THE WORK. It is well known that troublesome systematic discordances exist even among inde- pendent declination determinations of the highest rank, while the differences which were found between the earlier results of Bessel, Brinkley, and Pond, and even between different results by the same astronomer, were such as to provoke an acrimonious con troversy and to lead to most erroneous theories. The science of exact measurement of zenith distances was no doubt very much stimulated by the latter circumstances, for in the period extending from 1820 to 1850 we have more than one-half the entire material now available for researches upon the absolute declinations of the fundamental stars. For the purpose here proposed, it will not be necessary to make any extensive enumeration of the attempts which have been made from time to time to ascertain and reconcile these differences. Since the appearance of Bessel's reduction of Bradley's observations,* the uniform practice has been to consider these places for 1755 as abso- lute, and to compare them with the results of a single modern series, or with the mean of two or more. With the declinations and proper motions thus formed, the corrections necessary to reduce any given series to the standard could be ascertained. Miidler compared a number of modern catalogues with Pond's Catalogue of 1,112 stars, the proper motions being derived from the Fundamental Dr. Gould reduced the star- places now adopted in the American Ephemeris in a similar manner, using for the modern catalogue the Abo Catalogue of the late Dr. Argelander.f Dr. Wolfers cor- rected the declinations of Bessel's Tdbulce Regiomontancc, using for that purpose eleven modern catalogues. Many series of observations were adapted to the system thus formed through the labors of Dr. Argelauder and Dr. Auwers. The latter has con- * Fundamenta Astronomiai pro anno 1755, ex obtervationibua J. Bradley, Aitctore F. \V. Bessel. Begio- monti, 1818. tDorpat observations, vol. xiv. J. II. MUdler. t Dr. B. A. Gould's Standard Watts of Fundamental Stars, Untied Stales Coast Survey, 18GC. $ Tabulce Ileductionum, Auctore J. Pb. Wolfers. Berollni, 1858. Dr. Auwers in Astronomische Xachrich- ten. Dr. Argelander, Astroitomische Nachrichten, Bonn liiob. lid. vii, etc. 412 UNITED STATES NORTHERN BOUNDARY COMMISSION. [6] tributed an exhaustive independent investigation of declination corrections in Astro- nomisclie Nachrichten, Baud 04 (pp. 305 to 382). Taking the Abo Catalogue, referred to the Fundamenta^, as the medium of comparison, the corrections necessary to reduce the principal modern series of observed declinations to the system of the Abo are first ascertained and afterward corrected by the mean of fourteen catalogues judged most suitable for the purpose, in such a, way that, for the epoch 1755, the system is that of the Fundamenta as at first ; but for the mean modern date (about 1837) that of the mean of the fourteen catalogues. Shortly afterward (A. N., Bd. 64, p. 193) Dr. Auwers used these corrections in discussing the declinations of thirty-four fundamental and nine circumpolar stars. Similar discussions and compilations relating to star declinations have also been made by Baily,* Laugier,t Safford,f Bruhns, and others. It is evident in the cases cited that, it' we denote by J N the correction required by n normal system for the epoch T, which corresponds to the mean of the modern catalogues employed in its formation, and by A B the correction required for the same system or what is the same thing, Bessel's Fundamenta at the epoch 1755, the cor- rection of the system for any other epoch T' will be, If we put AN=G and T=1835, wo shall have as the correction of the normal system, when T 1 = 1875, -\AB. Thus, if declinations are required for the epoch 1875, a single determination at that date having weight 5, when the unit of weight is the corresponding determination by Bradley, is worthy of more confidence than that which is derived from a discussion which assumes the Fundamenta as absolute at the epoch 1755, even though modern determinations be absolutely without error for the epoch 1835. After the time of Bradley we meet with uo important independent determination of declination until that of Piazzi for the mean epoch 1800. But the instrument used in this series was entirely inadequate for the purpose, and although all the elements of reduction precession, nutation, and aberration (-xcepted were derived from the obser- vations themselves, the execution of the work is not such as to command our entire confidence. Passing over the circumpolar catalogue of Groombridge (epoch 1810), the first which appears to answer our requirements results from observations made with the Eeicheubach circle, in 1820 and 1821, by Bessel (Eonigslerg Beob., vol. vii). This may be regarded as the first example in the new era of declination determinations with meridian instruments. The form of discussion there employed has, with slight modifi- cations, served as a model for similar independent researches of I he highest order ever since that time; and since this epoch there is no lack of material for the formation of standard catalogues of declination. * Catalogue of the Royal Astronomical Society for 1830. British Association Catalogue of 8,377 stars for the epoch 1850, etc. t Memoire sur la Determination da Distances Polaires dcs Eloiks Fondamcntales par E. Laugicr. Deux- ibme section, p. 75. t Annals of Harvard College Ohservatory ; Memoirs American Academy, New Series, vol. iii ; Mean dcclinatious .of 981 stars for 1875, Washington, 1873, etc. $ Gencralbcrichl dcr Eitropaisclien Gradmessung, 171. [7] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 413 It will be shown tbat the interval of time between the group of early determina- tions by Bessel (1821), Struve (1824), and Argelander (1829), and the later ones at Leiden, Melbourne, Greenwich, and Washington observatories (not to mention inter- mediate catalogues), is quite sufficient for an independent judgment as to the approxi- mate accuracy and consequent weight of Bradley's results, and that a reliable system of corrections to the various catalogues may be founded on a discussion of recent cata- logues alone, taking as the earliest that of Bessel for the mean epoch 1821. Having premised this much, for the purpose of a more exact understanding of the scope and contents of the succeeding pages, the successive steps and objective points will be indicated in brief. These are: 1. The selection of stars to form the catalogue, and particularly of a list of stars most frequently observed, which shall serve as the basis of the normal system and as a medium of comparison between the various series of observations. 2. The formation of approximate positions and proper motions for the fictitious epoch 1875.0. These will be necessary for the computation of precession coefficients. Furthermore, the values of the assumed d and /j.' should be fair approximations, for reasons which will appear in the proper place. 3. The computation of precession coefficients, and with the aid of these (and in the case of close circumpolar stars by the rigorous formula) the reduction of the individual declinations to the required epochs, in order that the assumed declinations may be cor- rected by comparison with the observed values. 4. The selection of catalogues and series of observations, which shall serve in various stages of the work to correct the assumed declinations. These will be divided into three classes. 5. The application to the declinations given by these catalogues of certain correc- tions deemed advisable from an inspection of the constants and methods of reduction, and numerous compilations of the results of several successive years at the same obser- vatory into single catalogues embracing convenient intervals of time. These correc- tions are such as can be determined without recourse to comparisons of the determina- tions of one instrument with those of another. The compilations are for the purpose of rendering available a large mass of material that would otherwise be inconvenient or unsuitable for the purpose here proposed. Generally, published catalogues, which combine in one determination the results of several years, have been used without change. 6. The collection of results and formation of the approximate normal system from a discussion of the declinations of the fundamental and principal circumpolar stars, using for this purpose only those series of observations which are supposed to give determinations of sufficient independence and weight. 7. By the aid of the approximate corrections to the selected list of authorities to enlarge the number of standard declinations, and, in turn, with these to derive the systematic correction required by Bradley's observations as reduced by Bessel in the Fundamenia Astronomies. 8. With this correction together with those previously found, and with an increased list of stars, to ascertain corrections to the assumed declination and proper motion of each star; and taking them as a basis, to compute definitive corrections and weights for all the catalogues except those of the third class; with which final weights and 414 UNITED STATES NORTHERN BOUNDARY COMMISSION. [8J corrections, the definitive declinations are computed (as they appear in the cata- logue at the end of this paper), a few excepted which depend on a small number of authorities. 9. The computation of a few systematic corrections to catalogues of the third class; and the formation of all remaiuing declinations for the final catalogue. 10. A few deductions relative to the accuracy of the declinations formerly adopted in obtaining latitudes on the Northern Boundary. SECTION I. SELECTION OP STAGS. The preliminary catalogue necessarily embraces all the stars used in zenith tele- scope work of the United States Northern Boundary Commission, 1872-187/5. All of the stars of the American Ephemeris for which apparent places are given in that publication are added to this list, Sirius and Procyon excepted. The great majority of these stars are required for the purpose of constructing the normal system. These were supplemented by a considerable number of the Poulkova Hauptsterne, preference being given to those most frequently observed at Poulkova and elsewhere. At the suggestion of others a few stars were added which might servo for latitude determinations with zenith telescope on or near the parallel of 39 north latitude. Effectively, the selection may be regarded, for convenience, as embracing at least five different classes of stars : a. The fundamental and principal circumpolar stars which have been by common consent quite universally observed. 6. A class of stars less frequently observed, but with the observations so distrib- uted in time, that reliable determinations of declination and proper motion can be had without recourse to Bradley's observations; and which, together with the fundamental stars, may serve to construct an approximate normal system for the epoch 1755. c. A class of stars similar to the last, but lacking in satisfactory authorities for the epochs included between 1820 and 1840. After the systematic corrections of the older authorities are ascertained, these will serve equally with the preceding in deter- mining the systematic corrections required by the principal authorities. d. A considerable number of stars, which do not furnish proper material for ascer- taining systematic corrections to the principal authorities, but which will be found valuable for the purposes of perfecting the system of corrections adopted for a few catalogues of small weight, and for extending the system to catalogues deficient in observations of the first three classes of stars. e. The remaiuing declinations are such as depend on few authorities, and are prac- tically of no service in ascertaining systematic corrections. They belong to the class of stars selected and used for observation with the zenith telescope; and it is desirable to calculate their declinations with whatever precision can be attained by the use of all authorities that are conveniently accessible. [9] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 415 SECTION II. APPROXIMATE POSITIONS FOB 1875.0. Our plan contemplates the assumption at a given epoch of approximate values of the right ascension and declination, and of proper motion in both co-ordinates. These will serve for the accurate computation of the precession coefficients. For this pur- pose it is simply necessary to avoid errors which are largo enough to introduce appre- ciable errors in those terms of precession in declination that depend on the higher powers of the time, and in the geometrical part of the annual variation. It is, however, desirable in order to facilitate subsequent computations that the declination and its proper motion should be so determined that the corrections they may require will not be inconveniently large; and that the difference between the assumed and con- cluded proper motions will not be so large, that the neglect of the small difference between the adopted mean epoch of observation for each catalogue and the particular mean for a given star will seriously affect the final result for declination and proper motion. The epoch of reduction selected for the catalogue is the fictitious or Besselian epoch 1875.0. Right ascension. For the fundamental stars this is copied from Professor Newcomb's paper, Appen- dix III., Washington Observations for 1870. The proper motions are from the same source. Except for stars south of declination 30, the remaining right ascensions are taken from the American Ephemeris for 1875, as far as possible. The following incon- siderable corrections are, however, applied in most cases. They are intended to reduce these right ascensions to the standard of Professor Newcomb's paper, above cited. Hour. Correction. Hour. Correction. Hour. Correction. 8. s. 8. + .03 8 .03 1C + .01 1 + .02 9 .02 17 + .02 a + .01 10 .02 18 + .03 3 + .01 11 .02 19 + .03 4 00 12 .01 20 -t- .03 5 .01 13 .01 21 + .03 C .01 14 - .00 22 + .03 7 .02 15 + .01 23 + .03 8 .02 16 + .01 24 + .03 The proper motions, in A. R., of these stars were taken from the Star Tables of American Ephemeris (Wu., 1869). They are mostly those of Dr. B. A. Gould's Stand- ard Places of Fundamental Stars, United States Coast Survey, second edition (Wn., 18GC). For other stars the A. R. and /* were computed, if possible, from at least two good modern authorities compared with either Bradley, Piazzi, or Groombridge, and 416 UNITED STATES NORTHERN BOUNDARY COMMISSION. [10] occasionally with all three. The authorities were first corrected by the tables of Pro- fessor Newcomb's paper just mentioned. In a few cases where older authorities were wanting the assumed A. R. and /x were computed with greater care. Declinations. In computing assumed declination and proper motion in declination, the preference was given: first, to the Northern Boundary catalogue of latitude stars for the epoch 1874.0; second, to the declinations for 1870.0 reduced by Brnhusfor the Gradmessung, and contained in Qeneralbericht dcr Europaisclien Gradmessung fur 1871;* third, exclud- ing stars south of 30 declination, to the declinations for 1875.0 of the American Ephemeris ; and fourth, in the failure of these three sources of supply, declinations were computed in a manner entirely analogous to that adopted with right ascensions, except that no systematic corrections were applied. Nearly all the declinations of stars south of 30 declination were formed from the mean of Mr. Stone's recent catalogue of Maclear's observations at the Cape for I860, and the First Melbourne Catalogue for 1870, the assumed proper motions being copied from the latter. ' In " Details of Corrections to Assumed Places " the preliminary a and 8 with their assumed variations are given at the head of the table for each star. SECTION III. COMPUTATION OF PRECESSION TERMS. The constants of Peters and Struve have been adopted. They aref: TO = 46".0623 + 0".0002349 (t 1800) n = 20".0607 - 0".00008C3 (t 1800), where t is expressed in years. These are now in very general use, and probably are not far from the correct values. J At any rate, since our object is not so much to ascertain the exact amount of proper motion as to know the total change produced by the annual movement, great accuracy is required only in terms of precession involving higher powers of the time. The effect of proper motion has been considered in every case, and for this purpose the formula given by Professor Hill in Star Tables of the American Ephemeris (p. xix) have been adopted. The coefficient of t 3 has received a slight modification due to the neglect of small terms. So that, if the first and second differential coefficients in both * " Die Declinationen der bei der Gradmessung zu Bnitenbestimmungen benutzten Fixsterne," C. Sruhns. The declination and n' of a Cephei there given appear to lie in error. Taking the geometrical precession as computed on p. 14, the seconds of (! for Bradley 's observations reduced to 1870, should he 04".23 instead of 06".26 as printed in the last column of p. 7. The corrected proper motion will be -f- ".024 instead of + ".006, and the seconds of T\ sin a sec 2 S + 2 /* // tan 3. If a, //, m, and -^i are expressed in time, and the factor -= supplied, when necessary, tit ft we have the following tables of logarithmic values for the coefficients, the arguments being the year, and quantities depending on the place of the star, except for the first table, which simply gives the values of m and n for various epochs: Year. M 7!. logrc 10 *1T 8. /. 1750 3. 06987 20. 0650 1. 30243&5 0. 126348 1775 3. 07035 20. 0629 1. 30239^8 0. 126302 1800 3. 07082 20. 0607 1. 3023461 0. 126255 1825 3. 07129 20.0585 1. 3022994 0. 126208 1850 3.07177 20. 0564 1. 3022527 0.126162 1875 3.07225 20. 0542 1.3022059 0. 126115 1900 3. 07272 20.0521 1. 3021592 0. 126068 N B- -27 418 UNITED STATES NORTHERN BOUNDARY COMMISSION. [12] (Pa Log. coefficients of Year. Constant. -/ dt p ( |^ + /i J cos a tan )- 1750 (-10) 6.73673m (-10) 4. 63357 re (-10) 7.164105m 1775 4. 63362 re 7. 104059 n 1800 4. 63366 ra 7.164012m 1825 4. 63371 m 7. 103965m 1850 4. 63376 re 7. 16391 8 re 1875 4. 63380 n 7. 163872 re 1900 4.63385n 7. 163825 n (P6 dt 3 Log. coefficients of Year. /da ft\ (S+3) /^a \ /^da\ 1750 (-10) 2.09871 (-10) 7. 16411 re (-10) 3. 02577 n 1775 7. 16406 re 3. 02573 re 1800 7. 16401 re 3. 02568 re 1825 7. 16396 re 3. 025G3 re 1850 7. 16392 re 3. 02558 m 1875 7. 16387 n 3. 02554 n 1900 7. 16383 n 3. 02549 re [13] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 419 With these tables, and with the assumed values of a, d, //., and //.', ~, ", , -_ and were computed for the epoch 1875 for every star. The values of all these will dt 3 be found in the definitive catalogue (end of this Appendix), except that of , for which the catalogue gives the corrected value. The assumed value of and - ? - will be found with assumed values of a and //) cos (EI' + EI) ( s/ *) == tan (. This series embraces observations with the Washington mural circle in the years 1853-1858. They are reduced and the results printed in Appendix II., Wash- ington observations for 1870. Prof. A. Hall has formed the declinations of the funda- mental stars into a single catalogue, printed in Ast. Nacli. 1947. I have taken the declinations from the original source. Gh 57. The Greenwich Seven-year Catalogue of 2022 Stars reduced to the epoch 1860.0. The observations embrace the years 1854-1860 inclusive. C. G. H. 58. Observations made with the Cape circle in the years 1856-'61 by Sir Thomas McClear, reduced to the epoch 1860 by E. J. Stone, astronomer royal at the Cape of Good Hope, and printed in " The Cape Catalogue of 1159 Stars," etc., Cape Town, 1873. Wn 64. Eesults of observations with Washington mural circle for the years 1861- 1865, printed in the annual catalogues of the respective years. Gh 64. The new Seven-year Catalogue of Greenwich, embracing the results of observations with the Greenwich transit circle, for the years 1861-1867, both inclusive. Lu 67. This series is taken from " Mittlere Declinationen von 57 Fundamental 'sternen, abgeleitct aus Leidener Merldiarikreisbeobachtungen in den JaUren 1864-1868," W. Val- entine (Ast. Nach. K 902 Bd. 80, s. 93); and from "Annalen der Sternwarte in Leiden, herausgegcben von Dr. F. Kaiser." Me 68. "The First Melbourne General Catalogue of 1227 Stars, for the Epoch 1870. Deduced from Observations extending from 1863 to 1870, made at the Melbourne Observatory," etc. 11. L. J. Ellery, Melbourne, 1874. Wn 68. Eesults of observations made with the Washington transit circle in the years 186G-1869, taken from the annual volumes. Ee OS. Eesults of observations made with the Cariingtou circle at the Badcliffo observatory in the years 1862-1873. These are taken from the annual catalogues of the Eadcliffe observatory. They are finally divided into two series Ee 66, including years 1862-1869; Ee 72, including years 1870-1873. Gh 70. Eesults of observations made with the Greenwich transit circle and printed in the annual catalogues of the Greenwich observatory, 1868-1872. Wn 72. Eesults of observations with the Washington transit circle 1870-1874, printed in annual volumes. The results of 1874 in manuscript were generously placed at my disposal by Prof. J. E. Eastman. [17] EBFOET OF THE CHIEF ASTEONOMEE, APPENDIX H. 423 CLASS II. This embraces catalogues supposed to be unsuitable for use in founding the normal system ; but excludes a few catalogues of small extent, or weight, which are used only with stars of class e. Many of these are the results of observations, which in turn depend on the places of a standard list of stars; others are independent, but of small weight; or their use for other reasons may be regarded as of doubtful propriety. Gli 1752 or Gh 1755. " Fundamenta Astronomies pro Anno MDCGLV. deducta ex Observationibus Viri Incomparabilis James Bradley in Specula Astronomica Grenovicensi per Annos 1750-1762 institutis, Auclore Fredcrico Wilhelmo Bessel." Regiowonti 1818. This is in effect the result of two series of observations the one of northern stars (stars north of Greenwich zenith), mean epoch about 1752; the other of southern stars, mean epoch 1755 or 1750. Po 1800. " Precipuarum Stcllarum Inerrantium Positiones Media inuente sceculo XIX. Ex observationibus kabitis in Specula Panormilana ab anno 1792 ad annum 1813," Panormi 1814, by Joseph Piazzi. Bh 10. "A Catalogue of Circumpolar Stars, deduced from the Observations of Ste- phen Groombridge, Esq.", &c., at Blackheath observatory. Eeduced to January 1, 1810, and edited by Sir G. B. Airy. Lond. 1838. Va 29. Professor Littrow's declinations of fundamental stars, from observations made at the Vienna observatory in the years 1827-'8-'9. They are reduced to 1830, and printed in Mem. Boyal Ast. Soc. IV., p. 328. Dt 30. Struve's Positiones Medice, above cited, Catalogus Generalis, These places are quite numerous and appear to be when correctiones ultimw are applied, systemati- cally the same as the results of Catalogus Primarius. The observations from which the catalogue is constructed extend over the period 1822-1843, however, and there were consequently doubts whether Dt 24 and Dt 30 should be classed together. Gh 30. Pond's catalogue of 1112 stars reduced to 1830. These are the results of observations made with two mural circles from January 1, 1825, to January 1, 1833. C. G. H. 31. Eesults obtained by Fallows, in 1830 and 1831, at the Cape of Good Hope; reduced to 1830, and printed in Mem. E. A. S. vol. XIX. The catalogue con- tains but few declinations, and has only been used with a few stars south of 30. Mh 34. The results of Lamont's observations at Munich in the years 1829-1840. Most of the observations were made in 1833 and 1834, and are found in " Observations Astromicos in Specula Regia Monacliiensi^ etc., for those jears. I have for convenience taken all from ''Annalen der Koniglichen Stermcarte bei Munchm," Bd. XX., Miiucben, 1874; and from the detailed positions, commencing p. 264. Ah 41 and Ah 52. Ejbinson'n Armagh catalogue of 5345 stars. Owing to the great period o" time embraced in the observations of this catalogue, I have divided them into two series the first, for the years 1835-1846; the second, 1847-1854. This I have done by a method which will be explained (p. 39). So 51. The observations of Captain Gillis made at the observatory of Santiago, in Chili, in the years 1850-1852. The catalogue reduced to 1850 is printed in Appen- dix I., Washington Astronomical Observations for 1868. Bs 66, Bs 60, Bs 05. These are to be found in " Annales de VObservatoire Eoyal de Bruxelles ", for years 1855-1867. The groups are: 1855-1856; 1857-1862; 1803-1807. Ps 56 and Ps CO. These are found in " Annales de VObservatoire Imperial de Paris." 424 UNITED STATES NOETHEEN BOUNDAEY COMMISSION. [18] The first group covers the years 1854-1857, the second 1858-1862; and both are the results of observations of the Gambey mural circle. Ps 64 and Ps 66. These are in continuation of the series just mentioned, bat the observations are principally made with the great meridian circle of Eichens and Secre- tan. The groups are 1863-1864, and 1865-1867. Ce 56. This series embraces the annual catalogues in the volumes of the Cam- bridge (Eng.) observatory for the years 1852-1860. Ee 58. " Second Kadclifi'e Catalogue containing 2386 stars; deduced from observa- tions, extending from 1854 to 1861, at the Badcliffe observatory, Oxford; and reduced to the epoch 1860." Me 62. "Astronomical Observations made at the Williamstown Observatory in the years 1861, 1862 and 1863, under the direction of Eobert L. J. Ellery," etc. Eeduced to 1860. Melbourne, 1869. Bn 66. Argelander's observations with the transit circle at Bonn observatory. These are found partly in Ast. Nach. No. 1719, and partly in Bonn Beob. Bd. VI. Lc 67. " Rexultata aus Beobachtungen avf der Leipziger Stcritwarte," Dr. Eugle- mann, 1870; also " Die Declinationen der bei Gradmesstmg" etc., Dr. C. Bruhns. CLASS III. When an authority is of small weight, and especially when it has few declinations in common with the standard stars of Section VIII, there is danger that the error in adopted systematic correction for computing the definitive declinations may work a disadvantage, which will more than counterbalance any benefit to be derived from supposed additional weight. This objection will be, in a measure, removed by the computation of a large number of definitive places, giving more and better standards for comparison. In making up this list a few series of observations have been omitted, either because they were not at my disposal, or because it was believed that the labor of collating them and ascertaining the proper reductions and correclions would not be repaid by the weight of new material thus acquired. Zone observations for the most part are neglected on account of their small weight in a discussion of this kind. A very few of Lalande's and D'Agelet's observations were, however, used in extreme cases. Ms 35. "General Catalogue of the Principal Fixed Stars, from Observations made at Madras, by T. G. Taylor." Madras, 1845. The declinations are reduced to the epoch 1845. Ms 50. Astronomical observations made at Madras for the years 1848-1852. Mad- ras, 1856. Wn 48. Declinations from the prime vertical transit at Washington, principally in the years 1847 and 1848. Eh 08, Eh 63, and Eh 67. Edinburgh astronomical observations. The groups are respectively 1854-1860; 1861-1864; and 1865-1869. The declinations are taken from the annual catalogues. Pa 62. " Observations faites a Vlustrumtnt des Passages e"labli dans le premier Verti- cal," volume iii, " Observations de Poulkova," pp. 224 to 237. The declinations are determined by Mr. F. A. Oom. 1 19] KEPOET OF THE CHIEF ASTEONOMEE, APPENDIX H. 425 Wu 70. Declinations by Prof. M. Yarnall with the mural circle of tbe Washington observatory, 1SGG-1873, taken from the detailed results in annual volumes of Wash- ington Astronomical Observations. Pa 71. In the ninth volume of " Viertcljahrsschrift der Astroncmisclien Gesellschaft (pp. 83 to 88), is given a catalogue of the u Zusatzsterne" from observations of the Poulkova observatory. The declinations are undoubtedly of a high order of accuracy; but feeling some uncertainty about the proper manner of deducing systematic correc- tion from them, I have placed them in Class III. ; and in consequence use but one of the declinations for definitive purposes. SECTION V. EXPLANATION OF PBELIMINABY COBEECTIONS AND COMPILATION OP EESULTS. Before proceeding to actual discussion of normal declinations, it will be necessary to examine each catalogue for the purpose of applying such corrections as shall appear advisable from inspection. These corrections may be regarded as of three classes : First. Those required on account of the reduction of the observations from appar- ent place to the true epoch of the catalogue. These are principally for nutation and proper motion actually employed. In a few cases small corrections have been applied to reduce from epoch "Jan. 1" (Greenwich), or =281 to the fictitious epoch = 280; and rarely, a correction for precession which is always practically insignificant. Modern researches appear to show that no considerable correction to Peters's nutation is needed; and that value is now universally used. This value for 1800 is (Numerus Constans Nutationis p. 37) : 9".223 cos & sin a 6".865 sin & cos a. Among other rvalues of autation that have been used in reducing observations are these : Value employed by Bessel in Fund. Ast 9".C48 Bradley's (original value) 9".00 Maskelyue's ' 9".55 Groombridge's 9".G3 Lindenau's 8".977 Baily's (A. S. 0. and B. A. C.) . . . 9".25. The individual corrections applied to each catalogue are for the principal terms, and are of the form 17 sin a + r/ cos a, which appears to require no explanation. In most cases requiring it the correction for proper motion has been applied. It' t denotes the epoch of reduction of the catalogue and t' the mean epoch of the obser- vations of a particular star in the same, //, the assumed proper motion (Section III.), and n" the proper motion which was applied in the reductions of the catalogue, we shall have corrections for proper motion, where (t I') is expressed in years : (P.' - M ") (t - I'). Where the correction is practically insignificant, where the epoch of observation 426 UNITED STATES NORTHERN BOUNDARY COMMISSION. [20] is not conveniently ascertained, where redactions are inaccurate, or not carried beyond first decimal place of seconds, and, especially, in a few of the cases where proper motions have been determined by comparison with Bradley, this correction is com- monly neglected. The correction, for epoch, i. e., from sun's longitude 281 or from "Jan. 1" to O = 280, is applied to most of the English catalogues whose epoch is previous to 1857, and to Wn 47. The correction for precession is generally insignificant, and is often included in the form, An. Var. assumed An. Var. of Catalogue. In case of catalogues which had been reduced by help of the Astronomical Society's Catalogue (Baily 1'830) it was convenient to include a correction for precession with that for epoch and nutation. Second. In many catalogues, corrections which have been derived by special exami- nation of the instrument, or discussions of the observations, are indicated in the intro- ductions, but not applied to the results. Similar corrections sometimes occur through the neglect of certain precautions, and which, discovered too late for correction of the printed results, are in the nature of errata, to be applied by the reader. Correctiones Ultimcc, in Struve's Pos. Ned., are of the former class ; certain corrections in the intro- ductions to the two Radcliffe catalogues are of the latter class. Finally, under this head come errata wherever found. Third. In a limited number of cases it has been thought advisable to examine cer- tain series of annual catalogues in order to reduce the discordances in the results of separate years, and, if possible, to ascertain corrections which seem to be required by preliminary inspection. This is analogous to the work already done by the authors in many cases, where catalogues have been formed from those of several separate years. Under the designation of each catalogue will be enumerated all the corrections above specified which have actually been applied in this discussion. Some of the peculiarities in methods of observation or reduction which appear to invite special attention will be noticed in the same connection. The reasons for grouping, and the methods of combining the results of partial catalogues, will be explained. The corrected catalogue declinations are then compared with the assumed declina- tions of this paper (Sections II. and III.), and the residuals, in the sense Observed- Assumed Declinations are exhibited in column " C," in "Details of Corrections to Assumed Declinations". To facilitate comparisons of separate years in the case of compilation, the subtraction, Observed Assumed Declination is made at the out- set, by which means the various catalogues are effectively referred to a common mean epoch, with the assumed annual variations (Section II.). These residuals are then com- bined with or without correction, as the case may require. Gh 1752-1755. The coefficient of nutation adopted by Bessel in the reductions is 9".G48. Taking the mean epoch of observation for northern stars to be 1752, and for southern 1755, the corrections to the declinations will be : Northern stars ".34 sin (a 53.9) Southern stars ".425 sin (a 2.7) Before discussing the systematic correction, the corrections applied by Bessel to Bradley's declinations between the parallels + 14 and 14 are subtracted from the catalogue places. No attempt was made to ascertain proper motion corrections on [21] EEPOET OF THE CHIEF ASTRONOMER, APPENDIX H. 427 account of the difficulty of finding the mean epochs of observation, and also from the fact that Bessel has applied the correction, approximately, by comparison with Po 1800. In Dr. Bruhnt? reduction of Gradmessung stars is found a list of declinations which have been computed by Dr. Auwers from the observations of Bradley. But these are not definitive, nor are they at this stage of their reduction independent, because Bessel's (Konigsberg) refractions have been employed. It will be seen that the weight of testimony is in favor of refractions, on the average, at least as small as those which Bessel deduced from Bradley's observations. Professor Newcomb kindly placed at my disposal similar results for a limited list of stars which he was reducing. But both the lists combined embrace less than half the stars required in this discussion, so that the old results were used. Po 1800. I have applied correction to this catalogue only for proper motion in a few cases where the latter is large. The effect of the nutation correction is included in the A. R. term of the declination correction subsequently ascertained. Bh 10. The mean epochs of observation are secured from the first Radcliffe cata- logue, and the proper motion correction applied iu every case. As the catalogue was not included iu Class I., the application of nutation correction was not made, but it is included in the A. R. term subsequently found. In the use of this catalogue I have encountered a difficulty which introduces some uncertainty iu the results. For many of the stars most frequently observed two results for declination are given iu the catalogue. In the introduction this is explaiued by say- ing that the first of the two results was originally reduced to 1807, and the second to 1812. I have assumed that the observations are distinct, and that the epoch given for these stars in Re 45 is the epoch of the first set. In all these cases the mean of the two results has been taken, without correction for proper motion, as the mean epoch is probably very near 1810. The history of the reductions, for reasons partly unavoidable, is an unfortunate one, and this is the more to bo regretted, for the editor says (p. ix, Int.), "There can be no doubt, I conceive, that this instrument at the time of its erection, and for several years afterward, was the finest in the world." It appears to have been well handled, and was reversed ten times at least during the active period of the observations making up this catalogue. The materials were probably suited to the formation of an independent cat- alogue, which would have been no mean contribution to the solution of the problem of absolute declinations. Kg 21. To the results as given by Dollen has been applied the correction ".24 sin (a + 7.5), duo to the use of Lindenan's nutation. Gh 22. The correction ".'2'J sin (a + 32.l) is applied for nutation. Dt 24. No correction is applied to this catalogue. Ao 29. Correction for Lindenau's nutation + ".24 sin (a 9Q.3), is adopted. Va 29. The same nutation correction as for Ao 29 is used. The observations are reduced with Bessel's Kb'uigsberg refractions, but no details are given whereby an independent judgment may be formed of the character and accu- racy of the declinations. Dt 30. To all the results have been applied " Correctiones Ultimas" (Pos. Med., pp. 351 to 371), which is considered as bringing them systematically in accordance with those of Dt 24. It may be doubted whether this is completely accomplished for the 428 UNITED STATES NOKTHERN BOUNDARY COMMISSION. [22] entire series, aud so this catalogue has not beeu used in formation of Normal System. Wherever the proper motions have not beeu ascertained by comparison with Fund. Ast. this correction has been applied, using for the purpose the mean date of observa- tion, always supplied in such cases iu the Catalogus Generalis. S. H. 31. The observations were reduced with Young's refractions. This table is given in the introduction, p. 22, for "adapting the St. Helena declinations to Bessel's refractions." a Correction. t Correction. ' o a o a 85. 0.0 + 5 + 1.4 75 + -4 + 15 + 1.5 65 + .6 + 25 + 1.6 55 + .* + 35 + 1.8 45 + .9 + 45 + 2.0 35 + 1.0 + 50 + 2.2 25 + 1.1 + 55 + 2.4 15 + 1.2 + 60 + 2.6 5 + 1.3 + 65 + 2.2 + 5 + 1.4 These corrections are applied at the outset to all the declinations. The position of the observatory (

*>4, = Correction to nadir divisions respectively of 1841, 1842, 1843, and 1844, for accidental error, or deviation from the law expressed by x sin 2 R + x 1 cos 2 R. A . The application of any of the above quantities is restricted to a given year by the use of subscript figures, 1, 2, 3 and 4, respectively for 1841, 1842, 1843, and 1844. The declinations are referred to the common epoch 1843.0 by means of the reduction of assumed places (Section III). The corrected declination will then be: (1) R' + I' + 180 + is required before the declinations can be regarded as definitive. The discussion of A

, weights were computed for the few that required it on the same assumption as in the preceding portion of the discussion. The latitude observations are all on stars of declination greater than 74, so that the refraction cannot be examined, and the observations may be assumed to be of equal accuracy in the small range of zenith distance. The results are these : Year. A , as given above, take into account the probable error of the formulae derived for division correction. The probable error of the mean value of A

d, we Lave by the proper substitutions, the following corrections to the decli- nations of Eh 43, as printed in the annual catalogues : (1841) - ".47 + ".S94_(280 2 8) + Jc t (1842) - 1".05 + ".894 (228 - 2 d) + k 2 (1843) + ".63 + ".894 (218 -25)+ 7r 3 (1844) + ".09 + ".894 ( 78" - 2 S) + 7,- 4 where Arj. etc., are to be taken, as before, from the tables of division correction in the annual volumes. The following table exhibits in column I. the values of this expression, computea for every five degrees of declination (and includes ft). Column II. is the sum of column I. and the definitive correction found for Eh 43 in Table IX. at the end of this paper. To this is still to be added a small correction depending on right ascension. Table of corrections to Edinburgh, 1841-1844. S 1841. 1842. 1843. 1844. I. II. I. II. I. II. I. II. S.P. // // // // // a // // 75 + .13 + .13 + 1.24 + 1.24 1.37 1.37 + .34 + .34 SO + .01 + .01 + 1.16 + 1.16 1.39 1.39 + .37 + .37 85 .17 .17 + 1.06 + 1.08 1.36 1.36 + .37 + .37 90 .23 .23 + .94 + .94 1.29 1.29 + .36 + .36 Above pole. + 90 + .23 + .23 .94 .94 + 1.29 + 1.29 .36 .36 + 85 + .28 + .28 .80 .80 + 1.18 + 1.18 .34 .34 + 80 + .28 + .28 .67 .67 + 1.04 + 1.04 .31 .31 + 75 + .25 + .25 .56 .56 + ;90 + .90 .28 .28 + 70 + .16 + .16 .44 .44 + .75 + .75 .26 - .26 + 05 + .05 + .03 .36 .38 + .59 + .57 .24 .26 + 60 .08 .13 .31 .36 + .46 + .41 .23 .23 + 55 .23 .31 .30 .38 + .35 + .27 .23 .31 + 50 .39 .47 .33 .41 + .26 + .18 .23 .31 + 45 .54 .60 .40 .46 + .20 + .14 .21 .7 + 40 .67 .70 .51 .54 + .17 + .14 .20 - ,23 + 35 .78 .78 .65 .65 + .13 + .18 .16 .16 + 30 .86 .81 .78 .73 + .18 + .23 .10 .or. + 25 - .91 .79 .94 .82 + .20 + .32 .02 + .10 + 20 .93 .74 1.09 .90 + .23 + .42 + .09 + .28 + 15 .93 .66 1.23 .96 + .27 + .54 + .21 + .48 + 10 .92 .58 1.34 1.00 + .28 + .62 + .34 + .68 + 5 .89 .53 1.43 1.07 + .30 + .66 + .47 + .83 .87 .53 1.48 1.14 + .31 + .65 + .59 + .93 5 .84 .59 1.51 1.26 + .31 + .56 + .71 + .93 10 .82 . .69 1.51 1.38 + .32 + .45 + .79 + .92 15 .80 .78 1.50 1.48 + .33 + .35 + .83 + .85 20 .80 .88 1.48 1.56 + .35 + .27 + .83 + .75 25 .80 .95 1.46 1.61 + .38 + .23 + .81 + .66 30 .79 1.00 1.44 1.65 + .45 + .24 + .74 + .53 [33] HEPOET OF THE CHIEF ASTRONOMER, APPENDIX H. 439 With the corrections of column I. added to those for nutation and proper motion all the results for a given star were formed into a single mean, with the following table of weights : Weights. Observations. 1 1 2 2 a 3 2.5 4 3 5 to 9 4 10 to 35 5 36, or more. Eh 58, Eh 63 and Eh 67. There are few observations in this series ; but many of them relate to stars for which few observations are found elsewhere. The unimportant corrections for nutation applied to Cambridge annual catalogues of corresponding years previous to 1857 are used. The proper motion correction is generally neg- lected : the difference between t' oso assumed in this paper and those of B. A. 0. used in reduction of Edinburgh observations being usually small, for the short interval of time intervening between the mean epoch of observation and the beginning of the year. The grouping is determined by constancy of zenith circle readings, which, how- ever, were often changed during the period embraced in Eh 58. Kg 43. The reduction by Luther, in Ast. Na^li. 1070, employs Bessel's refractions (1821) and derives the latitude f rom a. Urs. Miu., a Aurigao andaCygni. I have followed the lead of Dr. Auwers (Ast. Nacli. 1549), talsic;; the latitude from a Urs. Min. alone and applying the correction ".17 to the declinations of all stars, except a Auriga and a Cygni, whose declinations are taken from upper culmination alone, and the cata- logue places corrected respectively by ".44 and ".41. Tho observations were originally reduced with Peters's nutation. GREENWICH CATALOGUES, 1836-1672. This long and valuable series of observations is remarkable for the uniformity of its plan and methods, the thoroughness and accuracy of its numerical reductions, and the vast amount of material it contains, chiefly relating to places of sun, moon, planets, and stars of the sixth magnitude, or brighter. The observations are made with non reversible instruments, and the problem of absolute declinations is rendered altogether subordinate to the requirements of routine work on a large number of ob- jects.* This robs the series oi an interest it might otherwise possess ; but when syste- matic corrections to its various catalogues are once ascertained, it becomes the richest mine of information on the ik elinations of the brighter stars. Two mural circles were used until Marcb, 1839, then a single mural circlet until 1851, when the great transit circle was mounted, and has been used until the present time. The position of the telescope on each of Ihe mural circles was changed at the beginning of each year. The relation of the telescope and circle of the transit circle is invariable. * In a critical examination of Greenwich polar distances for 1851-1854 Mr. A. Marth has pointed out very conclusively the defects of the Greenwich transit circle, as applied to the problem of absolute declinations. ( Ast. Nach., 12CiO.) t In 1848, for a short time, the Jones Cape circle was used. 440 UNITED STATES NORTHERN BOUNDARY COMMISSION. [34] The observations were reduced with Bessel's refractions (Tab. Reg.) until 1868, when tbe refractions of the Fwndamenta multiplied by 0.99797 were adopted on the authority of a discussion by Mr. E. J. Stone (Month. Not., vol. 28, p. 27), who uses for tbe purpose observations made with the transit circle of Greenwich 1857-1805. Gh S9 and Gh 45. The observations of separate years are usually reduced to the beginning of the year with no proper motion, or with values of that element taken from A. S. C. Wherever the error from this is considerable, it has been carefully attended to in the errata of later catalogues. 1 have not investigated any cases inde- pendently of these. The proper motions of the B. A. C. were used in compiling the general from the special catalogues. Where the difference between these and those assumed in this paper is worth regarding the proper correction has been applied, using for the purpose the mean epochs of the Twelve-year catalogue, which are only given to the nearest year. For reduction to apparent place the special catalogues de- pend upon the Nautical Almanac. The following mean corrections for nutation and epoch have been applied : Gh 39. + ".04 sin (a + 305) Gh 45. ".02 sin (a + 61) Gh 50. The nutation correction is : - ".05 sin (a + 76) The remarks under the preceding catalogues are generally applicable. A portion of the time the mural circle was used in a temporary observing-room, and the circum- stances under which much of the work was done were necessarily unfavorable. Some uncertainty in the systematic correction of this catalogue must arise from the fact that it combines results from two distinct instruments at different times. Gh 57. This catalogue may be regarded as containing the work of the transit circle in its best estate, when the observers had become accustomed to its peculiarities, and before any appreciable imperfection or wear had resulted from long use. Though the instrument was used in a single position during the entire period, the circle readings were made with six microscopes. Furthermore, the error of division was carefully examined for every degree and for some special divisions, and the high reputation of the makers is a guarantee that the accidental errors of division are probably small. The proper motions of this and succeeding catalogues of Greenwich are generally in fair agreement with the assumed proper motions, so that this correction is seldom applied by me. The special catalogues, until 1857, require small corrections for nuta- tion and epoch; after that year the observations were reduced with Peters's nutation, and to epoch = 280. The resulting small correction was neglected. Gh 64. The series embraced in this catalogue is essentially a continuation of the preceding. No correction is needed save that for proper motion, which is usually insig- nificant. During the long period of its use the instrument underwent slow changes from wear, which might be quite sufficient to cause a real difference in the systematic correction required (see Gh 70). Gh 70. The slight corrections required by the annual variations of the special cat- alogues were sometimes regarded. The results of separate years were then combined with weights according to number of observations in each year. I became aware of the [35] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 441 large error due to wear of the micrometer screws too late to make any use of a special correction on that account. I have taken my information from Mr. Christie's paper in Month. Not. R. A. S., for November, 187G. The series of reflection observations made during the period 183G-1872, at Green- wich, has attracted wide attention, and has been the subject of some interesting memoirs. A brief consideration of the principal points involved will be of use in judging the value of the declinations in the absolute sense. During most of the period occupied by observations with the mural circles, the correction ^ was found to be Jt so small and so irregular that it could not safely be applied.* The corrections of earlier years, and for 1850, were small. It may, therefore, be assumed that the declinations of that period (183G-1850) are practically uninfluenced by the discordance in question. On the introduction of the great transit circle in 1851 this discordance was at once noticeable, and a correction has always been applied to all polar distances deduced from the observations of this instrument this correction being assumed to be equal for the two classes of observations (direct and reflected), but applied with opposite signs. The division error was discussed for every degree of pointer reading, first in 1851-'2, again in 1856, and lastly in 1871. The results of the three investigations essentially confirm each other. The first table of corrections was used in the years 1851-1856 ; the second, 1857-1867; the third, which is the mean of the first and second, 1868 and later. The horizontal flexure was several times determined by the opposing horizontal colliraators. Until 1866 the telescope was raised from 'its bearings in order to render the collimators intervisible. In the latter part of 1865 the telescope cube was pierced in such a manner as to dispense with the raising. Owing to construction of the instrument a single circular opening could not be cut, but several radiating apertures in the form of sectors were made. This necessitated the use of .very large collimators (aperture 7 inches). The value of the horizontal flexure suddenly changed at this time nearly one second, passing from a decided plus value to a minus value. In the table to be given it will be observed that there is a simultaneous change in the opposite direction of the sign of the coefficient of sin Zcos? Z. As Professor Newcomb suggested to me recently that the entire series of observations with the transit circle could be reconciled to the supposition of a uniform coefficient of flexure, depending on sin Z, I have examined this question, not, however, in any very critical or conclu- sive manner. It is necessary to remark that the formula of correction was, until 1862, assumed to be (1) a + b sin Z; subsequently to that time (2) a + b' sin Z cos 2 Z. I have reduced b' to make it comparable with 6, by supposing that the mean Z, where D R occurs, is effectively about 25, and, therefore, that b would have been about .8 b', had the law expressed in (1) been used instead of (2). The groups are partly determined by the periods during which the same coefficient determined from opposing collimators was used. The following table exhibits approximate results. The first column gives the year or period ; the second, adopted value of flexure depend- *Airy says, p. xli, Int. Gh. Obs., 1840, " The values of E D are so small, and the existence of any law among them so uncertain, that I have thought it best to adopt the circle-results without any correc- tion for B D." This remark is substantially repeated in each volume until 1850. 442 UNITED STATES NORTHERN BOUNDARY COMMISSION. [30] ing on sin Z, obtained from observation of collimators ; the third, the average value of & for the given period for the first three groups directly derived for all after 1862 from V in the manner explained ; the fourth, the average value of the constant term a; the fifth, the sum of second and third columns; the sixth, the weight the result of one year being the unit. The spaces indicate epochs of change in division correction used : Period. Colliruator flexure. 6, or. 8&' (t Residual flexure. Weight. // II II a 1851 1852 1853-1856 + .73 + .73 + .50 .24 [- .24] .31 + .10 [ :o 3 ] + .49 + .19 1 4 1857-1861 1862-1864 1865 1866-1870* + .56 + .56 + .76 .37 .42 .43 .62 + .62 + .04 + .01 .04 + .10 + .14 + .13 + .14 + .25 5 3 1 5 1871 and 1872 .12 + .51 .01 + .39 2 + .21 21 * The actual change in division correction used took place in 1868, and is unimportant. Thus it appears that, if the uniform value of sine flexure, + ".21, had been employed throughout ths series, we should have had sufficiently good agreement between direct and reflection observations. This appears to me to throw discredit upon the value of flexure derived from opposing collimators, and forces me to the belief that the change in the collimator flexure between 1865 and 1866, if it has indeed any reality in fact, was much -smaller than has been supposed. In this particular case, at least, the fore- going discussion appears to argue strongly for the utility of reflection observations. . If there is a real residual discordance, E D, it would appear from the discus- sions of Airy (Mem. R. A. S. xxxiii, and Seven-year Catalogue, p. viii); Faye (Comptes .Eewrfws, xxi, pp. 401, 635, 757); and Van de Sande Backhuyzen* (Ast. Nach. 1720), that it is probably due in some measure to the effect of variations of temperature at different altitudes in the observing room. It is quite likely, that the reflection obser- vations are principally affected as Henderson and others have supposed. It may be interesting to note that, if we assume the latitude derived by Bessel from Bradley's observations (Fund. Astr.) to be near the truth and there is good reason for believing it is and if we suppose the mean latitude for the period 1836- 1860 to be that which is affected by the correction R-D we shall have : 1755 :

will be constant; and J>, F and F' will depend upon the reading of the circle used. Values of JZ,F and F 1 . During the years 1867 and 1868 circle B was used. It was reversed at the begin- ning of 1868, but was not shifted relatively to the telescope. In each year there is a considerable number of reflection observations, both north and south. The neces- sary conditions are thus established for ascertaining the quantities JZ67, dZG8,F and F'. F and F' have been already investigated as stated above* (p. 44) ; but that portion of F' which depends upon the flexure of the telescope could only be roughly inferred, and was taken as .00. So far as this assumption is supported by the present investigation, it will be found to be substantially correct. However the discordance between the direct and reflected observations of these and other years may originate, if one of the possible causes of error is known, and if the form of the differences can be reconciled, within a fair degree of probability, to represent the effect of that cause, we are bound to accept the latter, provisionally, as the most probable, or at least as an important source of the difficulty. If other means of measuring the effect of the known disturbing agency exist and have been employed, the question then relates to the weight of each determination or method, and, except for considerations of expediency, neither should be adopted to the exclusion of others, unless there is great disparity of weights. It is a priori possible that the whole or a part of the discordance in question may be produced by flexure. The horizontal flexure (F) has been measured by opposing collimators and also by the aid of leveled collimators, in the manner detailed in the Washington volume for 1865-t The definitive result was taken from the former method. The values given by leveled collimators, for reasons stated, are justly regarded as of little weight, though it will be seen that their mean is very near the mean finally adopted in this discussion. Professor Newcomb considers the flexure of the circles and of the telescope separately. The former was ascertained by a method of comparing simultaneous readings of the two circles, combined with a systematic rotation in their relative positions. The flexure of the telescope in the horizontal position was deter- mined by subtracting from the value of F, found by opposing collimators, that pre- viously found for the circle read in the observation. A rough check on the zenithal flexure of telescope was obtained in an analogous manner by the aid of nadir observa- tions combined with readings on leveled collimators. The result is confessedly of small "Washington Astronomical Observations for 1866, Appendix I, $ 60 to $ 67. t $ (65) App. I., Wn. Obs., 1865. [51] REPORT OP THE CHIEF ASTRONOMER, APPENDIX H. 457 weight. Many of tbe determinations by opposing collimators were known to be influ- enced by temperature in the room varying at different altitudes, and such were rejected. It is not altogether improbable that the measures accepted may have been affected injuriously by the same cause, though in a smaller degree. They are also liable to error from other causes, among which may be mentioned personal error, and the error possibly arising from the small aperture of the collimators.* It would be difficult to estimate the probable error in the determination of F and F' ; but perhaps enough has been said to show that a considerable correction to the adopted values is not altogether inadmissible. The reflection-observations of 1867 and 1868 will first be examined to ascertain whether the differences A P (Ref ) J Pt will tolerate the supposition that they are caused wholly or mainly by a constant error in adopted zenith point combined with an error in the assumed coefficient of sin Z in the formula for flexure. And for the purpose of assigning proper weights to A P(Ref) A P in each case e, will be ascertained by approximation. In 1867 there are a few observations of "miscellaneous stars" by reflection, and as these are situated almost exclusively near the zenith they will afford additional evidence as to the character of the change near the zenith in the value of A P(Ref ) A P. The following table exhibits the results from these stars arranged in order of zenith distance of stars observed directly, zenith distances being counted from to 360. The first column gives the name of the star; the second is P cor- rected wherever necessary by ".34, to reduce to adopted zenith points; the third is seconds of P (Ref), reckoned from reflected pole through nadir, etc. ; the fourth gives the number of observations respectively for P and P (Ref), separated by a hyphen ; the fifth shows the respective weights on the unit whose probable error is 1".00. These weights are deduced on the supposition that the value of e, is ".25. The sixth column shows the values of P(Ref) P, and the last column shows the values of Z. Name. P P(Ref) Obs. 71-' P(Ref) P Z B. A. C.I 144 o ' // 24 52 46.60 27 33 15.02 32 55 18.32 33 59 05.38 35 25 36.07 35 50 31.17 36 48 07.39 40 14 03.10 41 29 61.03 41 34 11.07 stars north of zenitl 46.16 13.48 16.99 05.73 36. 85 30.97 08.28 02.81 58.57 11.36 ,) 2-1 1-1 2-2 2-1 2-1 3-1 2-1 2-1 1-2 4-1 2 1.5 2.5 2 2 2 2 2 2 2 // .44 1.54 1.33 + .35 + .78 .20 + .89 .29 2.46 + .29 o 334 337 342 343 344 345 346 349 350 350 6 Ursae Majoris /3 Ursa Majoris 81 Ursse Majoris 21 Ursse Mnjoris 1 Can. Ven 51 Draconis o Auri" f a3 X Ursas Majoris z Hercnlis Recapitulation (t 20 - .39 .23 344 * The apertnre of the collimators is only 2J inches, while that of the telescope is 8.5 inches. AP,-f .D. 458 UNITED STATES NORTHERN BOUNDARY COMMISSION. [52] Name. P P(Ref) Obs. *? P(Ref) Z 15. A. C. 4962 o / // 62 24 32. 79 62 44 46.97 63 17 29.45 64 17 29.63 65 58 27. 14 67 19 60.39 67 47 30. 42 68 50 40.27 68 56 22.20 74 00 47.13 76 38 37.05 79 37 07.15 stars south of zenit 33.74 47.64 28.28 29.70 28.04 59.80 31.71 40. 13 22. 83 46.32 36.77 07.43 i) 2-1 2-1 2-1 3-1 3-1 2-1 2-1 2-1 2-1 2-1 2-1 2-1 2 2 2 2 2 2 2 2 2 2 2 y ti + .95 + .67 1.17 + .07 + .90 .9 -|- 1.29 .14 + .6:1 .81 .28 + .28 o 11 12 12 13 15 16 17 18 18 23 25 28 B. A. C. 4809 y Cor. Borealis . d Bootia 26 Bootis B A C 1970 B A C 2788 f Tauri BAG. 5620 Recapitulation ( 24 + . 15 . 14 17 The probable errors are deduced from the actual residuals ; had they been esti- mated from I it' in each case, they would have been ".22 and ".20, respectively, for the northern and southern groups. At about 18 zenith distance on each side there are gaps without stars observed, more than 5 wide in each instance. Taking only the stars nearest the zenith, we have: 7T P(Ref) P Z 16 5 it 27 o 346 [Same, excluding % Ursse Majoris. 14.5 18 + .03 + . 15 345] 15 The evidence in favor of an abnormal change appears to be wanting. The result has, however, but small weight. Collecting now all the material which exists in 1867 and 1868 for determining A ZQ7, A Z 68, and F, and collecting the values of AP (Ref ) A P into groups, including in each group a zone nearly 5 wide, we have the fol- lowing tables : 1867. No. Meau AP(Ref) AP + ".16 sin Z v> I. II. III. o II II ti II (D 309 .54 15 .49 .13 + .11 (2) 315 .87 17 .05 + .21 + .50 (3) 323 .77 31 00 + .12 + .48 W 329 .66 34 + .02 + .02 + .43 (5) 334 .56 31 + .03 .07 + .39 (6) 345 -- .29 28 + .03 .32 + .26 (7) 350 .81 22 + .67 + .21 + .84 (8) 12 + .58 40 .15 + .23 .26 (9) 18 + .48 28 + .10 + .35 .08 (10) 25 + .49 50 + .25 + .35 .00 (11) 32 +1.01 46 .11 .16 .44 (12) 38 +1.65 15 .61 .79 1.02 (13) 46 +1.49 30 .42' .61 .78 (14) 49 + .78 18 + .44 + .10 .05 (15) 53 +1.13 6 + -17 .24 .36 [53] EEPOET OP THE CHIEF ASTRONOMER, APPENDIX H. 459 The correction + ".16 sin #, in column A P(Eef ) A P, is the reduction for differ- ence of latitudes of instrument and reflecting surface in reflection observations. The weight, -', supposes =t l/'.OO as the probable error of the unit. By successive trials it was found that, taking c, = ".25, the assumed and concluded probable errors of unit of weight in 1868 were exactly alike; and the latter for 1867 was 1".07, while from the assumption it should have been 1".00. The approximation is considered quite sufficient, especially when it is remembered that there is great uncertainty in the appli- cation of the law adopted to represent /JP(Bef) JP. We therefore have for any given number (n) of observations the weight 1.00 The table gives : .0625 + - n Values of n' with arguments e and n. E = i.oo e, == .25 n e = ".52 ".54 ".60 ".70 ".80 '.90 1".00 1 3.0 2.8 2.4 1.8 1.4 1.1 .9 2 5.2 4.8 4.1 3.2 2.6 2.1 1.8 3 6.6 6.3 5.5 4.4 3.6 3.0 2.6 4 7.7 7.4 6.6 5.4 4.5 3.8 3.2 5 8.6 8.3 7.4 6.2 5. 3 4.5 3.8 6 9.3 9.0 8.2 6.9 5.9 5.1 4.4 7 9.9 9.6 8.8 7.5 6.5 5.6 4.9 8 10.4 10.1 9.3 8.1 7.0 6.1 5.3 9 10.8 10.5 9.8 8.6 7.5 6.6 5.8 10 11.2 10.9 10.2 9.0 7.9 7.0 6.2 15 12.4 12.2 11.7 10.5 9.5 8.6 7.7 20 13.2 13.0 12.4 11.5 10.6 9.7 8.9 25 13.6 13.5 13.0 12.2 11.4 10.6 9.8 30 14.0 13.9 13.4 12.7 11.9 35 14.' 2 14. 1 13.7 13 1 40 14.4 14.3 14.0 13.4 50 14!7 14.6 14.3 13.8 These can easily be converted into any other scale whose standard probable error is e, by means of the factor _. The value of e is found on p. 49. The weight n , _ *' (Dir.) X *' (Bef.) . taken to (he nearest unit- JT' (Dir.) + -K' (Kef.) Recurring again to the table of comparisons, ^P(Bef) JP, (1867), the numbers in column headed I. are the residuals (calc. obs.J, which result from the employment of the following values deduced directly from the observations of 1867, assuming that the differences A P (Eef ) J P are due to constant error and flexure. F= + ".74 ".052. The column marked II. is constructed on the supposition: j Z > or A Z" = ^(Bef.)-JP + M sin z . 460 UNITED STATES NORTHERN BOUNDARY COMMISSION. 154] t. e., assuming AZio be different for northern and southern stars, and excluding the supposed flexure, except that of + ".06 deduced from opposing collimators. We have for northern stars, A Z' = ".29 ; for southern stars, A Z" = + ".40. Professor Newcomb found*: A Z' = - ".45 A Z" = + ". 15. The difference is mainly the effect of the correction ".34 to reduce systematically to zenith points derived from collimators. In the first solution the small value of AZ shows that the zenith points thus derived are practically free from constant error. While the numbers in column I. do not show that agreement of fact with hypoth- esis, which is desirable, they ought to have some preference over those of column II., especially when we consider that the manner of usiug the corrections AZ/ and AZ" , is at least highly questionable on a priori grounds. It may be noted that of the eight comparisons making up line (7), we have: Stars. Z AP(Ref.)-AP, etc. w' I. o // II 1st 4 349 1.51 13 + 1.3 ad 4 352 -f .22 9 .4 Whatever the source of these anomalies it is undoubtedly quite irregular in its action, and is suggested with some probability by Faye's hypothesist as to columns of heated air in the observing-room, which may principally or solely affect observations by reflection. Explanation of column III. will follow later, (p. 57). We have a similar table for 1868: No. Mean Z the N B - 30 466 UNITED STATES NORTHERN BOUNDARY COMMISSION. [60] numbers in column "Calc. obs." must be divided by 2. Excluding all observations where Z > 75, the results of separate years, for latitude are: // // 1866 - .46 .08 1867 .26 .06 1868 - .46 .06 1869 - .22 .12 Mean by weights .37 The differences are not much greater than the probable errors would lead us to expect, especially when we consider the uncertainty of J Z for each year. The adopted latitude, 38 53' 38".43, is more than 0".8 less than that found in 1845,* with the mural circle, and ".35 less than the result with the same instrument in 1861-2-3-4.t The difference between the earliest and latest determination is appar- ently greater than the sum of any probable instrumental errors in the two series. If the flexure from opposing collimators had been adopted, the seconds of latitude would have been 38". 66 very nearly. If, on the other hand, we take the results of comparison of Me 68 with Wn 68, and suppose, accordingly, that the refractions of the latter ought to be multiplied by .9953 the seconds of latitude are 38".83 ; leaving a difference not accounted for of ".42 ; and this, too, under the extreme supposition that the refractions of 1845 are correct, while the same refractions for 1868 need to be multiplied by .9953. Combining with table (A) the correction + ".37, for A q> already determined, we arrive at the following definitive correction to P and A P: n a 1866 - .41 .95 sin (312.5 + P) 1867 + .45 + .69 sin (252.6 + P) + j ".34 to nadir values of P and A P. j ( B ) isfis fit* -n/ ^9-L.P^.i.J Irregular corrections for error of + .08 + .69 sin ( 5.2 + P) + 4 pointg gee 1869 + .81 + .69 sin (252.6 + P) Column (B) of the subjoined table is constructed from these. In column "Final" are found the systematic corrections necessary to reduce the North Polar Distances, after they are first corrected for division error and error of certain zenith points, to the Nor- mal System of this paper. It is formed by subtracting from (B) the declination cor- rection of Wn 68, taken from Table IX. "Appendix to Washington Astronomical Observations for 1845. 1 Appendix to Washington Astronomical Observations for 1864. [01] REPORT OP THE CHIEF ASTRONOMER, APPENDIX H. 467 Wn GG- Wn GO. Table of corrections to Polar Distances by direct observation.* 136G. 1867. 1868. 18G9. P () Final. () Final. (JB) Final. () Final. o // // // // // // // // 3155 + .50 + .70 .05 4- .15 .15 4- .05 + .30 + .50 340 + .47 + .62 .09 4- .06 .10 + .05 + .^.'6 + -41 345 + .43 + .53 .13 .03 .04 + .06 + .23 + .33 350 -f- .39 + .44 .16 .11 4- .02 4- .07 + .20 + .25 355 + .34 4- .36 .18 .16 + .08 + .10 + .17 + .19 3GO + .29 + .29 .20 .20 + -14 + .14 + .15 + .15 5 + .23 4- .21 .21 .23 4- .20 + .18 + . 14 | + . 12 10 + .17 + .12 .23 .28 + .26 + .21 + .13 + .08 15 + .10 00 .23 .33 4- .32 + .22 + .12 + .02 20 + .03 .12 .23 .38 4- .37 4 .22 4- -13 .03 25 .04 .24 .23 .43 + .43 + .23 + .13 - .07 30 .12 .38 .22 .48 + .48 4 .22 + -14 - . 12 35 .20 .52 .20 .52 4- .52 + .20 + .15 . 17 40 .28 .64 .18 .54 + .57 + .21 + .17 .19 45 ^ 37 .76 .16 .55 + .61 + .22 + .0 JC) 50 ! 45 .87 .13 .55 4- .64 + .22 4- .22 .'so 55 .53 - .93 .09 .54 + .. 1867. 186 3. 186 3. d a 1 6 n' a *' S _/ a Androiuedse O / /' 4- 28 21 41 36 44 n 41.6 11 n 41 4 12 a 41 7 10 II 40 7 9 y Pegasi + 14 26 57. 84 45 58.4 19 58. 14 56 9 10 57 9 q a Cassiopea3 + 55 48 45.69 23 45 9 fi 45 9 8 45 6 7 44 6 a (3 Ceti 18 42 42.44 34 42.1 11 42. 2 12 43.1 q 42 9 2 21 Cassiopeas + 74 15 57. 51 38 57.6 7 56.2 3 57 5 i 21 Cassiopeaa, S. P 58.3 6 57.3 8 57 1 *; 58 1 4 e Piscium 4- 7 10 42. 72 35 43.0 14 42. 6 12 42 4 q v Piscium 4- 26 34 08.94 7 08. 9 7 a Uri-sB Minoris 4- 88 36 20. 33 112 20.7 15 20. 2 15 20 2 14 19 9 1 a Ursse Mirjoris S. P. . 20.4 TS 20. 3 15 20 2 11 20 7 13 6 Ceti 8 51 55.48 28 55.6 10 55. 4 10 55 4 R A Cassiopeaa 4- 69 35 02. 07 3 02 1 S i? Piscium + 14 39 51. 18 39 51.3 11 50 7 14 51 3 10 52 6 o Piscium + 8 29 31. 44 32.3 11 30 9 13 31 2 10 31 5 3 j3 Ariel is 4- 20 09 41. 09 41 41.4 II 40 3 13 41 2 q 42 5 50 Cassiopeos + 71 46 49.78 31 50.6 8 49 1 3 51 S 49 5 50 Cassiopeas, S. P 48.6 /\ 49 9 5 49 4 12. 2 13 12 2 8 10 5 5 Cephei(48H) 4- 77 14 42.20 41 41.8 7 42 5 42 5 7 Cephei (48 H.) S. P 42.8 7 42 1 7 41 5 6 43 5 2 C Arietis . .. ..... 4- 20 33 11.28 27 11.6 8 11 10 11 3 7 11 3 2 n Persei 4- 49 23 18.20 24 18.5 10 18 4 7 17 5 5 17 6 (5 Persei . 4- 47 21 43 94 8 43 3 Q 46 2 ri Tauri 4- 23 41 39.92 36 40.1 10 40 1 12 39 9 q 39 1 5 f Persei 4- 31 29 19.16 18 18 8 fi 17 9 5 20 4 7 y 1 Eridani 13 53 10.10 25 10.5 q 10 3 7 09 6 7 09 1 2 y Tauri + 15 18 22.20 30 21.8 q 22. 1 12 22 5 7 23 7 e Tauri 4- 18 53 05.69 32 05.7 7 05.7 2 05 9 11 05 4 10 Tauri + 16 14 28. 12 45 28.1 11 28. 2 14 28 4 10 27 7 8 a Caaielopardalis . . 4- 60 06 49. 30 19 49.4 7 49.0 5 49 4 1 49 5 ? i Aurigae . ... 4- 32 57 13.72 36 13.8 q 13. 8 12 14 1 8 13.0 7 11 Orionia. . 4-' 15 13 02.29 26 02.9 q 02.0 9 01.6 6 03 <> a Auriga). . .- 4- 45 51 36.35 16 36.5 4 36. 5 35.8 5 38 3 /3 Orionis ... . . 8 21 23.54 35 23.4 11 23. 8 12 22.9 7 24 4 \ /3 Tauri 4- 28 29 33.98 44 34.2 11 34. 13 33.9 11 33 7 7 Groombridge 986 4- 74 56 58. 71 5 57.7 3 Groombridge 966, 8 P 60.3 f 6 a> & IT' Camclopardalis (22 H) o / // + 69 21 38 95 12 a n n 39 7 6 n 38 2 6 [i Geiuinoruffl. ... + 22 34 41.69 26 41.7 10 41.6 8 41 6 4 41 9 4 + 16 30 32. 63 46 32.7 11 32.3 13 3.3 g 32 7 11 Cepbei (51 H) -f- 87 14 28.83 68 29.0 T' 28 5 V> 29 4 7 28 4 7 Cephei (51 H.) S. P 28.8 1 29 4 8 28 5 10 28 47 40 55 32 40 3 10 40 3 9 41 2 5 40 7 g 26 11 08 42 15 07 8 7 08 9 7 09 2 1 A Geminorum. .. .- ..... 16 46 30.87 3 30.9 T + 22 13 20. 62 42 20.7 11 20 4 1 20 2 9 21 1 10 Pi. VII 67 -(- 68 43 50. 22 8 51 4 49 8 6 o 2 Geniiuorum.. . ... .... + 32 10 20.41 41 28.9 11 29 7 11 29 4 11 29 8 g ? Geminorum -. + 28 20 32.07 48 31.9 11 32 2 n 32 2 12 32 9 Geminorum. ........ . + 27 06 16.71 35 16.4 8 16 2 9 17 3 g 17 10 Ursse Majoris (3 H) -f 68 51 30.47 2 30 5 2 15 Argus . 23 55 32.28 30 32 9 4 32 4 11 31 5 g 32 3 9 + 6 54 03.44 39 03.3 7 03 7 T> 03 5 9 03 3 11 + 48 33 27 60 23 27.7 4 28 1 47.0 in 46 6 7 + 56 01 31. 96 5 32.0 B B.A. C. 4596 + 41 45 05.79 8 05.8 8 77 Bootis .,__.. ...... ...... + 19 Oil 37.23 44 37.0 14 37.1 13 37 6 10 37 5 7 77 Ursro Majoris .... .. ....... + 49 58 22.25 32 22.7 8 22.0 1 23.0 7 21 3 B 11 Bootis + 28 01 31. 09 7 31.1 7 a Draconis ...... + 65 00 26.27 26 25.6 fi 26. 6 C) 26.9 l\ 26 7 4- 25 43 04.59 7 04 6 7 a Boo" is.. .......... . + 19 52 14. 46 48 14.8 11 14 5 n 14 3 12 14 1 q 6 Bootis ........ + 52 27 41.90 22 41 6 6 42 1 q 41 4 4 42 7 T y Boot is...... ..... + 38 53 13. 10 5 13 1 5 5 Ursae Minoris . . . + 76 16 57.98 38 57 1 8 58 3 q 59 3 7 56 8 fi 5 TJrero Minoris, S. P 58.7 <> 58.4 fi B.A C 4827 -f- 47 21 56.77 g 56 8 8 e 1 Bootis . . . + 27 37 E5.24 45 55 3 T> 55 2 14 55 7 10 54 6 q (i 3 Librse . ..... 15 29 29.70 38 29 8 11 29 6 11 29 6 8 29 8 8 B.A.C.4897 + 38 21 22. 96 7 23.0 7 + 74 41 41 58 48 42 4 8 41 6 11 41 8 7 41 4 8 P Ursae Minoris, S. P. ...... .... 40 8 5 40.9 *, 41.7 /| t Bootis . \ 9H* " (04. 72) (5) (04.7) (5) 4- 41 50 09.02 8 09.0 g /? Bootis 4- 40 r>4 44. 85 24 45. I 10 45.2 7 44.1 7 8 53 38.79 40 38 3 1 39.7 1-> 38.3 8 38.7 8 fj. 1 Bootis + 37 50 29.36 34 29 2 10 29.8 11 29.4 7 28.8 6 y 3 Urese Minoris - . ...... .. + 72 18 13.48 22 14 8 fi 13.4 ^ 13 6 fi 11.7 1 y 3 Ursae Minoris, S. P 12.2 3 a CoroHse Borealis .-.. + 27 09 37. 30 46 37 5 14 36 9 11 37.9 q 37.1 q B.A. C. 5157 + 43 36 20.97 7 21 7 Bootis ....... 4- 40 47 04.51 7 04.5 7 y Coronse Borealis 4- 26 42 54. 00 5 54 5 a Serpentis + 6 50 33 37 43 33 5 1"> 33 5 13 32.2 10 33 1 8 e Serpentia 4- 4 52 36 73 35 36 5 q 36 8 1 36 9 g 36 8 fi Ursse Minoris ........ ..... 4- 78 11 57 04 27 57 8 8 56 9 5 56.3 5 56 4 i\ f Ursae Minoris, S. P. .. -- 57.3 5 e Coronas Borealis + 27 15 41 54 4 41.5 4 (j Scorpii . 22 14 37 14 20 37 9 6 37 1 q 36.2 3 36 4 B. A. C. 5313 4- 55 07 25 31 B 25.3 8 /3 1 Scorpii ...... 19 26 30 28 32 31 2 10 2r<. 9 11 30.7 fi 30 9 5 Groombridge 2320 + 66 09 29 24 3 29.2 S tJ Ophiuchi ... 3 21 08 86 36 08 9 10 08.5 T> 08.9 q 09.5 fi 16 Herculis ....... 4- 19 08 35 21 7 35 2 7 + 46 37 44 02 33 44 1 10 44 4 10 43.8 fi 43 6 7 4- 32 38 33 47 7 33 5 7 26 08 11 36 32 11 5 10 11 10 11 8 8 11.0 4 + 61 48 48 77 14 49 8 48 5 fi 4- 69 03 12 81 17 13 6 4 12 4 12 5 fi 13.3 a 10 17 50 81 30 50 7 10 50 9 10 50.7 fi 51.2 4 4- 39 10 28 74 29 28 8 10 29 5 11 27.5 fi 28 1 o K Ophiuchi 4- 9 34 56.06 37 55.8 10 57.0 11 55.7 q 55.5 7 J Herculis -(- 33 45 39 36 9 39 7 40 5 <> 4- 82 14 59 46 36 59 6 11 59 3 10 59.3 8 59 2 S e Ursa^ Minoris, S. P. 59.9 4 [Goj REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 471 Wn 68 Catalogue Continued. A 1 .. | ; - _/ 18 186 r. 186S i. 186 }. ,! 7T' i K 1 f! IT 1 18.9 4 18.2 14 18.7 13 18.6 q 18 5 10 2 55 50.64 18 51.4 7 50. 1 6 50.3 *> 8 20 01. 75 30 01.5 10 01.8 9 01.9 9 02.1 9 + 38 39 44.05 49 44.4 15 43.9 14 43.6 11 44.2 q 110 Herculis + 20 25 18.77 7 18.8 7 + 33 12 39. G3 34 39.6 11 39.9 10 39.3 7 39.5 6 26 27 27. 97 go 27.8 7 28.0 8 28.1 7 f>{) Draconis -f 75 16 36.67 27 30. 3 8 36.6 H 37.4 5 50 Draconis, S.P 36.5 5 36.9 1 AquilsB -. ...... + 13 40 09. 68 31 09.7 9 09.8 11 10.0 q 07.7 9 + 32 17 42 44 7 42.4 7 + 65 45 27.60 8 27.7 a d Sagittarii. 19 11 06.82 7 06.8 7 + 67 25 45.74 23 45.2 7 46.0 9 45. 3 5 47.7 f T Draconis .... + 73 06 34.66 11 34.5 5 35.4 4 r Draconis SP 33.6 9 + 2 51 13.44 28 13.7 8 13.5 13 13.1 7 4- 34 10 25.39 7 25.4 7 7 19 07.38 29 07.2 9 07.2 10 07.7 10 BAG 6748 * _|_ 54 40 54 77 7 54 8 7 4- 10 17 36.26 41 36.2 11 36.3 13 37.0 10 35.2 7 + 831 17. 88 42 18.1 13 17.5 13 18.7 11 16.4 5 4- 69 55 53.81 14 54. 1 8 53.4 6 (3 Aquilse + 6 04 44.04 32 44.4 9 44.2 12 43.8 9 42.6 2 + 88 54 44.93 72 44.6 11 45.1 13 44.9 11 45.2 8 44.9 7 44.8 11 45.1 11 -f 6 54 26. 07 25 26.0 9 26.6 a 25.6 a 12 57 06.64 33 06.9 V? 06.7 11 06.3 10 4- 77 18 44.85 25 45.2 5 44.8 7 K Cepliei S P 44.9 7 44.6 3 44.5 3 18 38 82.68 28 32.9 9 32.1 10 33.2 9 40 Cygni 4- 38 00 28.51 8 28.5 a + 36 00 55. 14 7 55.1 7 4- 10 51 22.68 28 22.3 8 23.3 11 22.3 9 ft Cveni .. ... -f 44 48 34. 59 35 34.9 Is? 34.9 10 34.0 9 34.4 4 9 28 36. 60 27 36.4 8 37.1 q 36.3 10 v ^yj? 1 ** -f 40 39 35.75 30 35. 4 11 36.4 19 35.2 7 GUCvirni 4- 38 06 05.91 30 05. 8 11 06. 2 19 05.6 7 C CvffQi 4- 21) 41 11.90 38 11.9 11 12.2 19 11.7 9 11.5 6 472 UNITED STATES NOBTHEEN BOUNDARY COMMISSION. [C6J Wn 68 Catalogue Continued. * i ORO n _/ 186 6. 186 7. 186 S. 186 9. 6 TT' (5 *' & n' 29.6 7 38 Pegasi -f 31 53 51. 40 6 51.4 6 a Lacertos -f 49 36 15.38 3 15. 4 3 TI Aqnarii 47 50.03 30 49.9 11 49.7 10 50.7 7 50.2 2 Cephei (226 13) + 75 32 47. 16 7 47.1 fi Cephei. (226 B), S. P 47.3 1 C Pejrasi . . -f 10 08 34 33 29 34 10 34 o 10 35 3 7 34 1 2 Cephei .. -(- 65 30 24 08 17 23 6 8 24 1 3 24 6 6 \ Aquarii ........ 8 16 53 20 24 53 6 7 52 5 g 53 5 9 d Piscia Australia . 30 19 16 74 21 16 8 7 16 2 7 17 2 7 a Pegasi ...... -f- 14 29 43 51 43 43 7 12 43 4 13 43 1 9 44 9 3 Andromedse + 49 20 05.40 7 05.2 4 05.6 3 o Cephei + 07 23 22.58 18 23.0 q 22.2 q 8 Piscium + 5 39 14.32 28 13.9 q 14 6 10 14.5 q i Piscium ... 4 54 39 27 30 39 2 q 39 6 10 38 5 9 41 4 2 y Cephei -f 76 53 44. 68 32 45.3 q 44.8 44.5 ^ 7 Cephei, S.P 41.9 44.8 8 44.2 3 Groombridge 4163. -f 73 40 32.42 7 32 4 7 o Piscium + 6 07 56.46 30 56.8 q 56.1 1' J 56.6 q The value of " C" in "Details of Corrections," etc., is computed from these declina- tions ; and in column " obs." the values of d are given instead of the number of obser- vations. A comparison of this catalogue with the polar distances of the Melbourne General Catalogue (Me 68) may not be devoid of interest. The mean epochs of observation in each are nearly identical, so that erroneous proper motions will be practically with- out influence in the comparison. In the comparison* by E. J. Stone, of Greenwich and Melbourne (to which reference is elsewhere made), the refraction at the latter place Is supposed to be different for equal zenith distances north and south. From circum- polar stars observed at Melbourne, with a correction of + "-15 to y, it was found that the adopted refractions should be multiplied by .99628. From comparisons of stars common to Greenwich and Melbourne the latter quantity was found to be .99086. These resnlta were adopted in formation of Me (i8. Though possible ou a priori grounds, this hypothesis is open to serious objections, when we consider the difficulty E. J. Stone, Month. Not., 28, p. 27 [67] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 473 of determining ( 1 k) independently, at the latitude of Melbourne, and the small weight of the actual determination, with a circle which was throughout used in a single position. Before comparing I have, therefore, reduced the polar distances of Me 08 to those which would have resulted from circumpolar stars alone. This I have accom- plished by the application of the correction .00542 p to all polar distances less than 127 50'. The individual weights are so uniform that to each comparison I have assigned weight 1, these excepted, a Aurigse, a Cygni, S Scorpii, a Sagittarii, and a Columbae, which received weight 0.5 j and a Persei and i Urs Majoris, which were rejected for obvious reasons. If p be the computed and (1 Ic) p the required mean refractions at Washington for a given star, p 1 and (1 fc') />', the corresponding quantities for the same star at Mel- bourne, and if M = P (Wu) P(Me), we shall have from each comparison (n), n' being the weight : \P + 72.") & + (/>' + 75.") k' + n = 0}V-' The two catalogues furnish 87 such equations which, though separately formed, are combined for convenience of solution in the following groups : Residuals after substitution. 65 k -f 538 k' 72 314 79 234 83 205 90 175 95 159 100 148 105 138 109 132 117 122 124 115 136 107 151 100 165 95 176 91 191 88 219 84 260 79 3. 31 = 1 -1.06 .96 3 + .51 .73 4 + .49 1.01 6 + .12 1.02 9 + .03 1.60 5 - .58 1.21 8 - .21 1.15 6 - .16 .98 8 + .01 .80 7 + .18 1.05 6 - .05 .87 6 + .15 1.13 5 - .06 .72 2 + .40 1.00 2.5 + .15 1.29 3.5 - .08 1.47 - .14 1.79 0.5 - .29 The solution gives Probable error (when k = + .00468 .00061 Jc' = + .00362 .00045 ' = 1) = ".41 The refractions at Melbourne are already (as assumed), Bessel's (Tab. Beg.) x .99628. They now become 0.99628 x (1 .00362), or .99267 x (Bessel's). Those at Washington become .99532 x (Bessel's). Admitting that e, for Melbourne is only .20, the probable error of an average single P, (wher> rJ = 1) for Me 68 is roughly ".37. 474 UNITED STATES NORTHERN BOUNDARY COMMISSION. [68] Judging from this, the hypothesis adopted to explain the differences Wn 68 Me 08 is uot repugnant, to the facts, especially when we bear in mind that the Melbourne circle has remained in an invariable position during the period for which the com- parison holdy good. But, on the other hand, this very circumstance throws a doubt upon the whole discussion ; for we can form but an imperfect idea of the degree to which our work may be affected by errors in adopted division and flexure correction, and by uncorrected flexure, such as has been suspected in the Cape circle. (Month. Not., vol. 33, p. 69.) I have formed the following table of Corrections to polar distances of Wn 68 and Me 68. P. Wn 63. Me 68. P Wn 68. Me 68. I. II. III. IV. I. .11. III. IV. r> 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 // 00 .06 .10 .14 .17 .21 .23 .26 .29 .31 .33 .36 .38 .40 .43 .46 .49 .51 .56 // 00 .02 .05 .10 - .15 .20 .26 .32 36 // /; o 90 95 100 105 110 115 120 125 130 135 140 145 ICO lf.5 100 1(>5 170 175 180 // .56 .60 .65 - .71 .79 .89 1. 04 1.27 // .59 .59 .60 .63 .70 .80 .93 1.09 // + .19 + .*0 + .22 + .23 + .24 + .25 + .27 + .27 + .26 + .25 + .23 + .21 + .19 + .16 + -14 + -11 + .Od + .04 .00 // + .16 + .18 + .21 + .20 + .30 + .32 + .36 + .38 + .40 + .34 + .22 + .12 + . 05 .00 .39 .42 .45 .47 .50 .53 .55 .57 - .58 .59 .20 .06 + .02 + .07 + -11 + .lit + .16 + .17 + .19 .67 .48 .11 + .08 + .15 + .15 + .15 + .15 + .16 Column I. exhibits the results of the correction (/> + 72") X .00468 for Wn 68. Column II., for purposes of comparison, gives the final correction of Wn 68 to Normal System. Column III. shows the correction just established for Me 68 by comparison with Washington. For stars of north polar distance less than 127 50', this correction is ".27 .0018/>; for the remainder it is, (p+ 75") x .00362. These corrections are applicable to the results as printed in the ''General Catalogue." Column IV. gives the adopted correction of Me 684:o Normal System. The agreement between 1. and II., as well as between III. and IV., is such as to strengthen the beliuf that a great part of the difference Wn 68 Me 68 is due to error in the adopted refractions at each observatory. Wn 72. The mean corrections to polar distance of American Ephemeris, or simply polar distance, with the correction for "Div. Flex., etc.," are taken as printed from sec- tions entitled " Corrections to the Star Positions of the American Ephemeris," etc., and " Mean Places of Miscellaneous Stars," etc., without change for stars of polar distance less than 46. From polar distance 56 southward certain corrections, which are in- [GO] REPOET OF THE CHIEF ASTEONOMEB, APPENDIX H. 475 eluded in the reductions on account of discordance between direct and reflected obser- vations, are rejected. The effect of this is to apply the following corrections to polar distances, or what is the same thing, to the correction for "Div. Flex, etc.," before adding the latter to the polar distance: Year. Correction. 1870 // + .31 1871-2 00 1873 - .42 1874 .82 Between the limits 56 and 40 (P. D.) these corrections are interpolated so as to become zero at the northern limit. By some accident the correction ".82 for 1874 was neglected for stars between polar distances 102 and 125. The effect of this has been, quite insignificant, however, since the preliminary systematic corrections depend chiefly on residuals of stars whose polar distance is less than 102. Proper motion has not been applied in the reductions of " Miscellaneous Stars." These, I have corrected accordingly. As the results of separate years so taken exhibit considerable systematic discord- ances, for use in the discussion of systematic corrections I have pursued a course entirely analogous to that explained under Ee 66 and 72. Following is a list of correc- tions to assumed places, thus resulting : // .19 .43 .68 .41 .46 + .02 .32 1.14 .35 .54 +1.60 .34 + .18 .17 .34 .12 +1.49 + .12 1.04 .04 .30 .45 .56 .12 + .57 J3 Tauri // .26 + .20 .21 n .61 +1.00 .20 .17 .31 +2.08 .27 .24 + .53 .49 .91 .50 +1. :!8 .CO .55 d Oriouis a. Ursoe Majoris 3 Ceti + .21 .52 .12 +1.23 .41 .51 .41 1.11 .85 + .04 .25 1.10 .72 J Crateris T Loon is . . a Ursaa Minoris Ceti 7} Geiuiuorum. ...... v Leonis a Geminorum. ...... /3 Leonis y Genrinorum e Can is Majoris (j Canis Majoris y Ursa} Majoris o Virginis ri Virginis (j Corvi .. f Ceti /5 Gcminorum. ...... K Draconis v Ceti Geininorum a CanamVen.. Virginis + .13 1.25 .17 .67 + .09 .74 .50 + 1.35 + .27 .67 i Ursse Majoris a* Ureae Majoris + .40 + 1.84 .Ti f Virgiuis 77 Tauri rj Ursa) Majoris 7j Boot is . e Tauri a Hydras + .41 + .49 50 a Draconis E Leonis n Bootis + .18 .94 .16 5 Ursa? Miuoris e Bootis r -- a 2 Libras 476 UNITED STATES NORTHERN BOUNDARY COMMISSION. [70J (3 Urase Minoris ... n -f .34 y 2 Sagittarii // .51 (3 Cephei n -4- 53 8 Bootis -1- .13 M 1 Sagittaiii. .. ...... .68 4- 21 (3 Librae .34 <5 UrsiS Minoris ..... -1- .28 1 05 ft Bootis ............ .67 T] Serpentis - --. .58 4- .32 77 4- 29 81 (i Coronas Borealis .. .19 8 Lyras . . , .33 7] Acjuarii ...... 4- .07 .21 .58 4- .18 76 02 4- 27 43 3 82 81 22 4- 19 28 .18 + .31 a Pesrasi.. .28 22 1 81 4-1 33 51 4- .09 4-1 17 34 4- 55 57 Q Aquilaa . ... .92 1 01 a 2 Capricorn! 11 K Ophiuchi 4- 23 4-1.57 a Herculis. . ... -t- .81 1.55 44 Ophiuchi .72 4- 44 j3 Draconis . .... 4- .86 1 19 a Ophiuchi -|- .34 4- -11 -1- .73 61 Cygni 4- 80 u Herculis .. . . .04 Cveni 45 tp l Draconis ... .46 4- 10 v Draconis .08 B Aquarii -1- .13 Discussion of 3669 residuals of stars most frequently observed in the years 187 1-'73 gives for the probable error of pointing : e= V .4554 ( .0122) + .0415 ( .0076) tan 2 Z. The values tabulated according to zenith distance are these : Z It, e Z c o // o n o /t .675 40 .696 60 .762 10 .676 45 .705 65 .804 20 .679 50 .717 70 .877 30 .685 55 .735 75 1.02 In the final reductions, separate systematic corrections have been deduced for each year. These are shown in Table IX. With these corrections and the following system of weights, the definitive values of (vide " Details of Corrections to Assumed Dec- linations") have been computed : Weights for combination of Wn 70-74. Number of observations. Weight. Number of observations. Weight. 1 1 8 to 11 5 2 2 12 to 16 6 3 2.5 17 to 27 7 4 3 28 to 51 8 5 to 7 4 52, or more 9 [71] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 477 SECTION VI. FIRST APPROXIMATION TO NORMAL SYSTEM. It will be assumed that the catalogues to be used in tbe formation of the Normal System have received all the corrections which can be applied solely on the authority of the observations composing each of them. It will also be taken for granted that the correction furnished by a given catalogue to the assumed declination is of the form: rpi m A 8 + A ,j.i , 100 ' where A 5 is the correction of S for a given epoch, T (T 1 being the mean epoch of each A u! catalogue), and ~, the correction to the assumed annual variation. This course is only proper when the path of proper motion does not deviate sensibly from the arc of a great circle. That there is such deviation in the cases of Sirius and Procyon has been pretty well established by Dr. Auwers and others; but these stars are omitted in our catalogue. It is possible that variable proper motion may ultimately be found in the large majority of cases, but, a few binary systems excepted, the evidence of such variability at present appears to be wanting. If now no discrepancies of a constan t character were found to exist between the determinations of different observatories, nothing further would remain except to deter- mine the relative weights, and by means of conditional equations, derive a correction for each assumed declination. On the other hand, granting the existence of these dif- ferences, we should be justified in adopting the samecour&e, if the declination of every star in a given catalogue were made with equal weight, and if each of the stars under consideration had been determined in each of the authorities. This, however, is by no means the case, and in order to prevent the undue influence of large systematic errors in case of stars for whose declinations there are few authorities, it remains to be ascer- tained what corrections of a constant and periodic character can be applied to each catalogue. This can be accomplished by means of comparison with standard declina- tions, which are free from any such error. From the nature of the case this standard can never be attained. The best that can be done is to consider the combined testimony of all independent determinations available for the purpose. To take any two determinations as standard, to the exclu- sion of all others, would be manifestly an error, for it would be assuming that the weight of these selected catalogues in comparison with the remainder is as infinity to zero, while all experience teaches that the best independent determinations of declination are subject to comparatively large errors. There is, however, great difference in the quality of these so-called independent determinations, which vary from such special investigations as those of Kg 21, Dt 24, Ao 30, and Pa 45, where every precaution has been exercised to remedy the inevitable defects of instruments by variety in the circumstances of observation, and the utmost skill and rigor in the computations, with determination of the various elements of atmos- pheric refraction, to those which assume their refractions from alien authority, which are made with non-reversible instruments, and with little attention to those details of ob- servation and reduction so essential in the delicate problem of measuring absolute decli- nation. It seems but reasonable to suppose that declinations of the former class are 478 UNITED STATES NOETHEBN BOUNDABY COMMISSION. entitled to much greater confidence tban those of the latter. This I have endeavored to express through the following system of weights to be employed in the preliminary discussion : Weights. Authority. Weight. Authority. Weight. Authority. Weight. Kg 21 Gh22 4 1 Kg 43 Eh 43 2 1 Gh 57 CGH58 2 1 Dt24 5 Gh45 2 Wn64 1 Ao29 5 Pa 45 10 Gh64 2 Sh31 1 Ee45 1 Ln67 8 CGH33 a Wn47 I Me 68 2 Ce34 i Ce48 1 Wn68 3 Eh 37 i Gh51 1 Re 68 2 Kg 38 2 Ps 53 3 Gh?0 2 GU39 2 So 55 1 Wn72 1 Ce40 1 Wn56 1 For the purpose proposed in this section, weight zero was assigned to all other catalogues. A few are excluded on the ground that, although independent, their weight is so small that they would merely encumber the computation with useless material. These weights are not those which might seem to be required by comparisons with an approximate mean system, but are derived from an independent study of each cat- alogue, considered solely on the basis of internal evidence, with the assistance of such critical reviews as have been found conveniently accessible. They result from careful study, but are necessarily arbitrary, and can only bo regarded as mere expressions of opinion concerning the relative contribution made by each determination to the problem of finding an absolute system of declinations. It would therefore be superfluous, and at all events a tedious task to mention in detail the facts and arguments relied upon in support of each individual weight. It will be sufficient to notice some of the principles adopted, which are of general application and tolerably definite and well established. An investigation, founded on a series of observations for declination, will be regarded as independent, or absolute, in proportion to its freedom from any assumption whatever founded upon results from other series of observations, having in view the same or any other purpose. Practically, however, the determination of aberration, nutation, and precession can be left to special investigations. On the other hand, it may be doubted whether the constant of refraction or of atmospheric expansion is sensibly the same for different regions and climates ; even if it were, in practical influ- ence on observations, much would still depend upon local conditions and upon the character and situation of the meteorological instruments. Add to this the uncertainty of any existing single determination, and it will hardly be maintained that any series of declination observations is strictly independent, which does not include the determina- tion of refraction constant and coefficient of expansion for atmospheric air, by proper methods and adequate means, from the observations themselves. Every series of observations professing to give independent declinations should contain satisfactory evidence as to the character and amount of its instrumental cor- rections. In this connection the excellence of the mechanical construction of the [73] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 479 instrument becomes an important consideration. Thus the work of the older instru- ments labors under disadvantage. It is plain that the greater the variety of circum- stances under which an instrument may be used, other things being equal, the greater will be the freedom from constant errors due to instrumental causes. Therefore, results from instruments which admit of reversal have received the preference over others. Furthermore, when the relation of the circle to the telescope is so altered that its read- ings for a given zenith distance vary from year to year, this has been regarded as a decided advantage. This consideration becomes of less importance, however, with finely graduated instruments read by a large number of microscopes. The real advan- tage of reflection observations is supposed to be an open question. It has been ably debated by Bessel, Faye, Dollen, Airy, Kaiser, and others. In cases where the dis- cordance R D is large, and not accounted for by special investigations of the instru- ment, this circumstance has been regarded as just cause for suspicion. Where we have a long series of observations made at the same observatory, or with the same instrument, the weight of each group is considerably reduced from that which would have been assigned to it when standing as the sole representative of the particular series. Thoroughness and skill in the methods of reduction were allowed to have an important bearing upon the decision of these weights. Lastly, the degree of liability to fortuitous errors is an element which has been considered. With the older catalogues it is a highly important one. The catalogue of Piazzi, for instance, is essentially independent, but its chance errors are such that had we been assured of its entire freedom from systematic error, it would still have received a weight practically insignificant by comparison with the determinations actually used in the present discussion. In a less degree the same is true of Bradley's declinations for 1755. These weights were applied, without alteration, to all the declinations of the respect- ive authorities, where the star was observed at least four times at a zenith distance of 70 or less; beyond 70, weights were diminished by the use of empirical factors, diminishing nearly in proportion to the reciprocal of the square of the refraction; being zero for all zenith distances greater than 80, and in cases where the weight multiplied by the factor is less than .5. The results of the various series of determinations made by observatories in the southern hemisphere, were never used beyond 70 zenith distance; so that from the pole down to and including a Virginis, there was no diminution of weights for this cause. The factors are these : z Factor Z Factor. o // o // 70 1.0 76 .5 71 .9 77 .4 72 .8 78 .3 73 .7 79 .3 74 .6 60 .2 75 .6 480 UNITED STATES NOETHEEN BOUNDAET COMMISSION. [74] Two or three observations received half- weight; a single observation, weight zero. Now while there is great disparity in the number of authorities relating to differ- ent stars, fortunately a considerable number of stars have been quite universally observed. They are known as the fundamental stars, to which may be added a Persei, tj Ursa? Majoris, f Draconis, /9 Draconis, ? Ursae Majoris, a Cassiopesp, a Cephei, a Ursae Mnjoris, /3 Cephei, /? Ursae Minoris, f Cephei, C Ursae Minoris, <5 Ursae Minoris, and a Ursae Minoris. Tb ise have each been frequently observed in a majority of the series of observations enumerated above (Class I). It will be possible, therefore, in the case of these stars, without the intervention of systematic corrections, to compute declina- tions which shall be measurably free from error, and thus answer the purpose of an approximate normal system, to be subsequently revised and improved. The results of this preliminary discussion are exhibited in Table I. The first column contains the name of the star ; the second and third, respectively, values of [J d] and [J fi'] determined in the following manner. For each catalogue an equation of condition was constructed of the form : , -0 = The values of are those given in column G of Table A, " Details of Corrections to Assumed Declinations." The epoch 1845 is selected to facilitate the solution of the equations. T' is the designation for mean epoch and is sufficiently indicated in the numerical part of the designation of the catalogues concerned. These values of [ J d] and [J //] are those which result from the use of Gh 1755, without final correction and with weight 1. The fourth and fifth columns contain A d and J/i', with Bradley's declinations excluded; and these values are used in forming the preliminary system of corrections. The sixth and seventh columns contain, respectively, the probable errors of the adopted J S and A /*'. The eighth contains the probable error of the unit of weight. The last column contains the approximate declination for 1845. TABLE I. Name of star. [AJ] CV] M bpf e M v d (i Virginis // + 045 II 848 a + 052 it 1 003 a 055 // 345 ii .47 o 10.4 P OrioDis ... + 193 . 100 + .187 014 .062 .390 .53 8.4 a HydraB .... 4- 111 .430 + . 128 784 .062 .387 .52 8.0 a Aqnarii ...... . .022 .148 .009 405 .071 441 .60 1.1 . 178 .106 .207 + 487 .035 .340 .46 4-3.5 .149 .493 .136 740 .055 345 .47 4-6.0 a Serpentis . ...... .... .002 + .023 4- .028 569 ,059 .366 .50 4-6.9 -4- .022 075 4- .019 00 .056 .349 .47 4-7.4 a A ({ i ii ] ; n + .022 + .248 4- .040 . 104 051 .319 .43 4-8.5 y Aqnilse .005 .102 + .003 251 .056 .348 .46 4-10.2 + 032 694 + 056 1 177 062 385 52 4-12 7 a Ophiuchi + 105 217 4- 111 1 046 003 394 53 4-12 7 y Pe^asi . , 228 22(5 231 164 061 373 51 4-14 3 Pegasi . ...... ...... 4- 285 914 + 330 1 85 038 268 38 4-14 4 + .173 4- 141 -\- 197 336 060 372 51 +14 6 4- 229 1 844 + 259 141 047 288 39 +15 4 a Tauri . ... + 032 219 4- 060 790 067 415 56 +16 2 [75| REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. TABLE I Continued. 481 Name of star. [AtS] CV] A9 .21 +.17 -.30 -.07 + .40 -.37 - .38 -.20 25 30 -.22 -.60 -.03 +.06 + .28 -.21 +.30 -.12 -.16 +.14 -.30 -.0-i + .38 -.26 - .34 -.20 30 35 -.18 -.65 -.11 +.11 +.28 -.17 +.30 -.22 -.08 +.09 -.30 +.06 + .36 .15 - .31 -.20 :<5 40 - 14 -.70 .15 +.16 +.28 -.13 +.30 00 +.04 -.30 +.20 + .33 -.04 - .29 -.20 40 45 -.10 -.66 -.14 +.22 -.07 +.29 00 00 -.30 + .31 +.06 - .28 -.20 45 50 -.06 -.62 .13 +.28 .. -.02 +.28 00 00 -.28 .... + .29 + .13 - .28 -.20 50 55 -.01 -.51 .11 +.30 +.07 +.26 00 00 -.25 .... + .26 +.17 - .28 -.18 55 60 +.04 -.40 -.10 +.33 +.17 +.25 00 00 -.21 . + .23 +.21 - .SB -.17 60 65 +.12 -.27 -.08 +.31 + .S6 +.23 00 00 -.16 + .21 +.22 - .26 -.13 65 ;o +.20 -.15 -.06 + .30 +.29 +.22 00 00 -.10 + .17 +.18 - .25 -.10 70 75 +.26 -.07 -.04 +.22 +.28 +.16 00 00 00 + .14 +.09 - .20 -.05 75 80 + .25 00 -.03 +.15 + .26 +.11 00 oo 00 + .10 00 - .16 00 80 99 +.10 00 00 00 +.20 90 00 00 00 ' ' + 00 00 00 00 90 * The correction actually used by mistake for Co 48 between the limits of 13 and 30 was + ".13. t As actually naed, the correction from 13 to 30 was about ".20. See explanation (p. 69). The following explanations will servo to show the manner of computing these corrections. As the points of comparison were relatively few, sudden fluctuations in the values of the correction are to be avoided, unless they seem to be completely justified by the testimony of the observations. Whenever a general expression such as a (sin Z + sin Z'), or, a (tan Z + tan Z'), (where Z' is the zenith distance of the pole), was found to represent, approximately, the residuals, r, it was adopted. In the derivation of the corrections from 10 to +90 declination, only stars within those limits were used. From 10 to 34, the corrections are very rough approxima- tions, there being but four standard declinations within these limits to control the curves. In fact, the curves were continued, in many cases, according to the law adopted for them within the limits +90 to 10, where this course was not too strongly opposed to the residuals given by the four southern stars.* We proceed to notice such peculiarities in the individual corrections as appear to bo worthy of remark. * The methods nted in deducing some of the corrections of Table II. are not entirely satisfactory to the writer, but were rendered practically unavoidable for reasons which are given in the introductory. (Seep. [4].) 484 UNITED STATES SOUTHERN BOUNDARY COMMISSION. 178] Kg 21. I have supposed that the systematic error in this catalogue is more likely to be due to error in the constant of flexure employed than to anything else. This is found to correspond well with the residuals. Assuming the correction to be of the form, a (sin Z+ sin Z'), we have for a + ".16, The use of this formula was continued to the extreme southern limit. Gh 22. The correction is so small and so uncertain, that zero has been adopted for all declinations. Dt 24. The correction is assumed to be of the form * . where p and p' are respectively the mean refractions for a given star and the pole. We have : x = - .299 The Dorpat observations are reduced with a refraction constant which is Bessel's multiplied by .99545.* Prom the formula we shall have as the true factor, .99545 X 1.00299 = .99843. The following table shows the agreement of the formula with the means of the several groups of residuals. Mean + .02 19.9 18 + .26 22.0 15 .06 22.0 24 4- .20 Wn 47, Wn 56, Wn 64. The corrections were derived by the graphical process. None of these curves are very certain for declinations north of 40. Gh 51, Gh 57, and Gh 64, Ps 53, C. G. H. 58, Ln 67, Re 68, and Wu 72 were also discussed by means of hand curves. So 55. A uniform value of the correction was adopted, since sufficient material for drawing the cu^ve with requisite certainty was not available. Me 68 and Wn 68. Comparison with the residuals r shows that the results of the discussion of Washington and Melbourne declinations (p. 68) answer sufficiently well for the first approximation to their respective corrections. This opinion is supported by the final discussions. Gh 70. The empirical formula a (sin 3 Z+ sin 3 Z'), which differs little in practical effect from that employed with Dt 24 and Ao -D, though it does not very closely rep- resent the mean values of r, is adopted. Discussion of the separate residuals gives for a 1".17. The comparison with means is as follows : Mean f of group. Number of stars. Mean r. Formula. 0. o n // n 8.9 3 1.12 1.05 + .07 4- 5.2 6 .74 .73 + .01 + 13.8 8 .33 .55 .22 -j- 25.8 6 .35 .39 .04 4- 43.0 3 .38 .29 4- .09 + 52.3 6 .50 .28 + .22 + 62. 3 2 .37 .27 + .10 + 75. 4 .46 .0 + .26 488 UNITED STATES NOKTHEKN BOUNDAKY COMMISSION. |8J] If, for instance, observations have been corrected by the formula a sin Z cos 2 Z, when the true formula is a sin Z, then the correction sin 3 Z would be required for the polar distances, as published. The average correction to zenith distances by direct observation during the years 18G8-'72 for R D is + ".75 sin Z cos 2 Z. If we suppose that this correction should have In-eu approximately + ".75 sin Z, then declinations would require the correction ".75 sin 3 Z + (the proper correction for lat- itude). It is, however, probable that a great part of the correction is due to error in the adopted constant of refraction. SECTION VII. CORRECTION OF BESSEL'S FUNDAMENTA ASTRONOMLE. With the systematic corrections of Table II., and with the system of weights already used, we proceed to correct the assumed declinations of stars of class "i>" (p. 8). The object of this is to secure a greater number of points with which to compare Bradley's declinations, and even this additional number is insufficient for the satisfac- tory solution of the problem. The criterion of selection of these additional stars is that there shall be none for which the weight of A /if is less than .5. The formation and solution of conditional equations was conducted on precisely the same principles as for the fundamental stars. The same authorities were used (Gh 1752 and 1755 being of course excluded), but they were first corrected by Table II. in order to diminish the effect of uneven distribution of systematic errors in the series of corrections for a given star. The results are shown in Table III. where the adopted corrections of fundamental and circumpolar stars (Section VI.) are repeated for convenience. The explanation follows : TABLE III. 17 55. v .. TA ' Cor. to a f> Urea; Miuoris . . 217 1 +76 + 605 27 -4-4 07 83 32 1 1 '! /3 Ursse Miuoris ....... 222 9 +75 2 + 0/0 60 4 +1 05 1 59 3 1 4 -2 X Druconis 276 4 4-72 6 + 456 26 3 1 28 9 4-1 :i 1 1 8 y a UrsiB Miuoris ill 1 Draconis ^ Draconis 230.3 266.6 169. 1 +72.7 +72. :t +70 7 .073 + . Ob6 + 456 43.4 15. 9 40 1.57 .30 4-4 17 1.18 .54 90 +4.0 7 3*5 1.0 1.0 1 +3.8 +1.0 - 3 1 321 4 +69 5 014 61 +1 3f 1 60 3 7 1 " -2 .43 + .53 .25 .24 + .87 .90 + .41 + .94 + .35 .02 1.01 +1.85 .73 + .33 + .06 .68 + .60 + .33 +1.03 .58 + .52 .08 .88 +1.77 1.59 + .06 1.69 + 1.14 1.40 1.31 2.67 . 52 1.14 .90 .25 .00 .60 .60 .35 .75 .57 .95 1.05 .68 1.21 .82 .54 .97 .87 .60 1.63 1.08 1.59 .70 .78 1.19 1.23 1.04 1.00 .74 1.60 .96 .69 1.63 .85 .97 .70 .97 .59 1.66 .71 1.06 1.69 .91 .91 .70 .74 .73 1.05 1.12 1.14 a 3.8 2.0 1.5 .2 .2 .8 3.6 1.6 2.0 1.7 2.2 .5 2.6 1.6 4.2 2. 5 2.3 +4.0 1.8 .1 .4 + -2 + -9 1.2 + -7 .1 + .2 1.1 + .4 + -3 2.5 :l 1.7 .8 1.5 .5 .7 + -9 ?.4 .7 + -2 1.6 ft! + + -9 +1.6 +2.4 .4 1.0 1.0 1.0 1.0 1.0 1.0 .7 1.0 1.0 1.0 1.0 0.4 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.0 1.0 2.0 1.0 2.0 1.0 2.0 2.0 1.5 .4 1.0 1.5 1.0 1.0 1.0 1.5 .4 2.r> .7 2'.0 1.0 '1.0 1.0 1.0 1.0 1.0 1.0 1.5 it 4.3 1.1 0.0 + -2 + -7 .6 2.3 1.7 .5 .8 .6 .3 -1.5 .8 2.6 - .8 .8 +1.9 !9 .2 0.0 +1.0 .2 + -5 + -3 .4 .6 +1.6 + .4 1.5 + -3 .6 .7 + -9 1.4 .3 .5 + 1.1 1.6 .6 .5 1.0 1.3 +1.0 +1.5 + .'<3 + -9 + .9 l IJrsaj Majoris e A urigse Draconis ...... 86.6 2.24 .7 d Ura<6 Minoris . 102.7 +1.13 1.0 d I >ra<:oni.s . . 108.1 +1.17 1.0 Camelop.(32H 12.0 2 74 1.0 ij Draconis . 65.2 5. 64 1.0 e Ursse Minoria . 78.0 .27 1.0 o Draconis ... 101.9 +2.04 1.0 f Ursee Minoris . 58.3 2.85 1.0 6 Ursse Majoris ... 319.1 .24 1.0 The ninth column gives the weight used in solving the equations of condition, following is the scale : The Obs. Weight. 1 .4 2 .7 3-9 1.0 10-25 1.5 over 25 2.0 In estimating these weights, no account is taken of the uucertainty of the standard places. Their probable error seldom exceeds ".45, and for the fundamental stars averages about ".3. The probable error of the unit of weight for the additional stars is approximately ".35. Owing to the uncertain character of the residuals I did not think it safe to attempt the drawing of a curve. Careful preliminary examination showed that the error varies [87 1 REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 493 greatly with the Right Ascension, according to what law it is difficult to conjecture. I assumed at first the simple periodic formula of correction, x sin a + y cos a. The form of the declination correction (order of declination) especially for southern stars, appears to be tolerably well represented by the expression v + w sin 2 Z + u tan Z. For southern stars alone the normal equations are these : + 109.2 v + 77.2 w 0.6 x + 5.9 y + 111 - 100.0 = + 77.2 v + 63.5 w 3.3 x + 3.9 y + 82.3 85.7 = 0.60 3.3 ? + 59.6 # + 1.8 y 9.2 u + 30.1 = + 5.9 v+ 3.9 10+ 1.8 x + 49.0 y + 4.2 u + 8.5 = + 111.0 v + 82.3 w - 9.2 x+ 4.2 y + 245.2 u - 121.8 = From which v = - .21 IP = + 1.50 x= .41 y = - .25 u= + .08 Arranged in four nearly equal 8 roll P s t w have the following values of v, x, and y, the residuals being first corrected for + 1".50 sin 2 Z + ".08 tan Z. Mean i v x 9 Weight of i/. Adopted y. o a it II n 13.0 .20 .17 .88 10 .98 + 08.3 .07 .5-J .72 16 .48 + 25.6 .42 .49 + .09 11 .06 + 43.4 .19 .29 + .36 10 + .37 The constancy of v and x is as good as we might expect, but such is not the case with y. In the uncertainty, I have supposed y to vary directly with the declination, and find The equations for northern stars are : // + 60.9 v 27.6 w 13. L x + 0.5 y 28.9 u + 63.8 = - 27.6 v + 20.3 w + 1.3 x + 0.2 y + 21.5 u 35.2 = 13.1 v + 1.3 w + 31.1 x 1.8 y 3.9 u 13.7 = + .5t>+ 0.2 w 1.8 x + 29.8 y- 2.8 + 17.2 = - 29.0 + 21.5 w 3.9 x- 2.8 y + 43.9 u - 31.5 = 494 UNITED STATES NORTHERN BOUNDARY COMMISSION. [88] Whence ' = - .63 w = + 1.25 x = + .04 y = - .01 u = - .35 The number of stars and the weights are too small to admit of any valid argument from the process of grouping ; the residuals, however, are not remarkably well repre- sented by the formula. The real correction is probably much more variable. The equality of the two values of w derived from northern and southern stars is quite striking. The smalluess of u in each case is an argument that the refraction deduced by Bessel corresponds well with Bradley's observations. For the definitive correction I have dropped u and combined the equations for both northern and southern stars. Two sets of coefficients for sin a and cos a are separately determined. For northern stars these are denoted by x 1 and y'. y is introduced into the equations in order to eliminate its mean influence on the determination of the remaining quantities. The equations follow. + 170.1 v + 49.6 w 13.1 x 1 + + 49.6 v + 83.8 IP + 1.3 x 1 + - 13.1 v + 1.3 w + 31.1 a' - + 0.5 v + 0.2 w 1.8 a;' + 0.6 v 3.3 *r + 5.9 v+ 3.9 w The solution gives : 0.0 x 1 0.0 x' 0.5 y' 0.6 x + 0.2 y' 3.3 x + 1.8 1/' 0.0 a; !9.8 y' 0.0 # 0.0 y' + 59.6 # + 1.8 y + 0.0 y' + 1.8 a; + 49.6 y + 5.9 y 36.2 = 3.9 y - 121.0 = 0.0 y 13.7 = 0.0 y+ 17.2 = 1.8 y + 30.1 = 8.5 = v = - .21 .06 w = + 1.56 .10 x' = + .25 .16 y 1 = - .57 .16 x = .41 .10 y = - -25 The probable error of the unit of weight is ".79. For northern stars it is rfc 1".03 ; and for southern ".65. These probable errors are somewhat larger than can fairly be ascribed to Bradley's declinations, since they include the effect of the prebable error of the normal places themselves. In order to be on the safe side I have adopted the following weights in final discussion, the supposed probable error of the unit being ".30, as will be explained hereafter. Weight. Number of observations. Northern stars. Southern stars. 00 .05 .1 .:> .3 1 2 to 8 9, or more. 1 2, or 3 4 to 20 21, or more. [89J REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 495 In computing Table V., weight .5 is assigned to 4 or more observations, and weight .3 to less than that number. Declinations of Gh 1752-55, from one observation are rejected. If the corrections above determined are combined with those for nutation we liave For northern stars (north of 51.5 <5) ".21 + 1".56 sin Z + ".05 sin a - ".29 cos . For southern stars (south of 51.5 S) .21 + 1.56 sin Z ".82 sin a .24 ( 28 s \ cos a . Z is reckoned in the usual direction from to 360. For convenience the following tables have been constructed : TABLE IV. Definitive corrections for BesseVs Fundamenta Astronomies. Northern stars, + 51.5 to + 90. Correction. S Above Below pole. pole. n " f50 .13 + .82 55 .40 + 1 .06 CO .66 + 1 .27 65 .92 + 1 .46 70 1 .15 + 1 .60 75 -1 .35 + 1 .70 80 -1 .52 + 1 .76 85 -1 .65 + 1 .77 90 J .73 + 1 .73 NOTE. The corrections are applicable to declina- tions directly, whether observed above or below pole. The entire correction for northern stars is A + B. a Corr. a h // h -.29 12 1 -.27 13 2 -.23 14 3 -.17 15 4 -.10 16 5 -.03 17 6 + .05 18 7 + .12 19 8 + .19 20 9 + .24 21 10 + .28 22 11 + .30 23 12 + .29 24 From 12 b to 24 b the correction has the opposite sign. 496 UNITED STATES NOETHEEN BOUNDAEY COMMISSION. [90J C*. For stars south o/51.5<5. A.E. DECLINATION. +50 +45 +40 +35 +30 +25 +20 +15 +10 +05 +00 -05 -10 -15 -20 -25 -30 1 2 3 it + .92 + .70 + .49 + .31 f .42 + .18 - .07 - .33 + .56 + .34 + .09 - .15 + .71 + .48 4- .25 -1- .03 + .82 -- .60 -- .3!) + .19 f:B Iia +1.01 + .60 + .61 + .47 + .99 + .78 + .61 + .49 + .93 + .73 + .57 + .46 f .82 + .62 + .48 + .39 + .C6 + .46 + .33 + .26 + .46 + .27 + -14 + .10 + .21 + .02 - .09 - .12 - .08 - .26 - .36 - .37 - .40 - .5t - .07 - .66 - .75 - .92 -1.00 .91 1. 12 -1.29 -1.35 1.31 4 5 6 - .58 - .79 - .96 - .37 - .55 - .69 - .17 - .32 - .43 + .01 - .11 .19 + .16 + .06 + .02 + .29 + .22 + .21 + .37 4-. 33 + .34 + -41 + .40 + .45 + .41 + .43 + .50 + .36 + - 41 + .52 + .26 + .34 + .46 + .12 + .23 + .40 .07 + .06 + .27 - .30 - .14 - .10 - .5fi - .37 - .10 - .85 - .03 - .33 -1.16 .91 .58 7 8 9 -1.08 -1.13 -1.10 - .77 - .79 - .75 - .48 - .48 - .41 .21 - .18 - .OS + .03 + .09 + -21 f .25 f. 34 + .49 f .42 + .54 + -71 + .55 + .70 + .90 + .64 + .K +1.04 + .69 4- .89 +1.14 + .66 + .91 +1.1* + .62 T.b9 +1.19 + .53 4- .82 +1.14 f .39 + .71 +1.00 + .22 + .57 + .94 + .02 1.40 + .80 - .20 + .22 + .63 10 11 12 -1.02 - .87 - .68 - .65 - .49 - .29 - .28 - .11 + .09 + .00 + .24 + .45 + .37 + .57 + .78 + .67 + .88 +1.0C + .91 +1.13 +1.35 +1.12 +1.34 +1.57 +1.28 +1.52 +1.75 +1.39 +1.65 +1.88 +1.4C +1.72 +1.96 +1.48 +1.76 +2.00 +1.45 +1.77 +1.99 +1.39 +1.69 +1.94 +1.29 +1.61 4-1.86 +1.17 +1.49 +1.75 +1.02 +1.30 +1.62 13 14 15 - .44 - .19 - .07 - .06 + .19 + .43 + .32 + .55 + .77 + .68 + .89 +1.09 +1.00 +1.21 +1.39 +1.31 +1.50 +1.66 +1.56 +1.75 +1.89 fl.78 +1.95 +2.07 +1.95+2.08 +2.11+2.22 +2.22+2.31 +2.15 +2.2C +2.36 +2.19 +2.32 +2.36 4-2.18 +2.29 +2.32 +2.12 +2.22 +2. 23 +2.04 +2.13 +2.12 +1.92 +2.00 +1.97 +1.79 +1.85 +1.81 16 17 18 f .32 + .53 + .70 + .65 + .83 + .97 + .97 +1.12 +1.23 +1.27 +1.39 +1.47 +1.52 +1.64 +1.08 +1.79 4-1. w +1.87 +1.99 +2.03 +2.01 +2.15 +2.10 +2.11 +2.27 +2.25 +2.19 +2.34 +2.29 +2.18 +2.36 +2.28 +2.14 +2.34 +2.23 +2. 06 +2.27 +2.13 +1.93 +2.16 +2.00 +1.76 +2.03 +1.83 +1.56 +1.85 +1.63 +1.33 +1.66 4-1,41 +1.08 19 20 21 + .82 .87 + .84 +1.05 +1.07 +1.03 +1.28 fl.28 +1.21 +1.49 +1.46 +1.36 +1.67 +1.61 +1.49 +1.83 +1.74 +1.59 +1.94 +1.82 +1.65 +2.01 +1.86 +1.06 +2. 04 +2. 01 +1. 86 +1. 81 +1. 64 +1. 56 +1.9: +1.71 +1.44 +1.84 +1.59 +1.27 +1.67 +1.38 +1.06 +1.47 +1.15 -f .80 +1.24 + .89 + .52 + .98 + .60 4..H + .70 + .29 - .13 22 23 24 f .76 + .61 + .42 + .93 I is +1.08 1.91 4-. 71 +1.22 +1.04 + .83 +1.33 +1.13 +0.92 +1.41 +1.20 + .99 +1.45 +1.23 +1.01 +1.44 +1. 22 + .99 +1.40 +1.16 +0.93 +1.31 4-1.05 4-0.82 J1.1C .!!() .66 + .98 f .70 + .46 + .75 + .45 + .21 f .47 + .1' - .08 + .17 - .15 - .40 - .17 - .49 - .75 - .52 - .85 -1.12 * Between +14 and 14, S, the entire correction is, C+ correction taken with opposite sign from table, p. 62, Fund. Ast. SECTION VIII. DISCUSSION OP FINAL CORRECTIONS AND WEIGHTS. With the correction just deduced, we shall be able to add a considerable number of standard stars to the list embraced in Table III. The places of the four extieme southern stars of Table I., as well as the additional stars of Table III., will be revised by the addition of Gh, 1752 or '55, as an authority. Forty fundamental and circuin- polar stars of Table I. would not be materially affected by this addition. For tho present, their declinations as already corrected, will be regarded as standard. Two or three stars, which should have been included in the list, were omitted by accident. The manner of deducing A S and A p! has been sufficiently explained under sections VI. and VII. Their values will be found to be not materially different from those finally deduced. [91] EBPOET OP THE CHIEF ASTRONOMER, APPENDIX H. TABLE V. 497 Values of AS and A/J.' adopted in computing final systematic corrections for the principal catalogues. 18 45. 18 45. Ar> Au' A<5 V o, Atidromedse - .... .... .... if .14 II .90 n Leporis . ,_._. // 14 // 4 17 (3 CassiopesB ........... .. .31 41.11 e Oriouis . . . . .... 35 24 .23 .16 a. Orioois _L 02 02 .13 4 -47 {3 Auricse . . .05 60 4 .02 .43 Ceti .28 41.20 02 -4- 21 ij Cassiopeae . . .... 1.20 41.62 46 1 15 y Cassiopesa ...... .... .39 42. G8 y Geminorum j_ 24 1 f>9 e Pisciuni ...... ...... .26 .39 Cephei, (51H) 4 12 67 (3 A iid romoduo ..... . 4 .24 1.97 67 42 oo + .09 .26 C Gennnorum ... ...... .... 4- 72 1 54 4 .06 4 .82 d Geminorum .... 17 2 48 0i Ceti + .13 .39 4 09 73 .52 2.36 4 81 1 51 51 Andromeda? .35 4- .06 (3 Geminorum . 21 43 54 Andromedae 4 .43 2.92 4 01 1 49 o Piscium .... .13 1.59 o Avsrus .. 10 62 e Cassiopcjjo ..... 4 .18 4 .25 31 4- 04 (3 Arietis . . ..... 04 1.76 o Ursaj Majoris. ...... 4 06 _i_ 95 50 Caesiopea3 .... 4 44 42.02 6 Cancri . ...... ...... 4 03 1 08 y Andromedae ... 4 .26 4 .96 e Hydrse ... .... ...... 27 2 54 a Arietis . ... .13 .65 i Ursa) Majoris . ...... 27 22 {3 Trianguli ......... .31 .38 <7 2 UrssB Majoris ....... 4 78 44 46 ft Ceti 4 .04 .57 K Cancri 12 2 72 f 3 Ceti . ; 13 4 .40 12 20 y Ceti 40 1.14 4 13 78 a Ceti .21 4 .49 Ureas Majoris .. ...... 33 4 60 /? Persei 4 44 .92 4 47 60 a Persei . . .... .23 4- .33 4 03 1 57 f Tauri 41.37 4 .58 v Ursse Majoris 4 .33 .20 25 4 04 u Loon is.. _. ..... 39 15 .13 .84 o, Leonis .... .... ...... .... 4 .06 1.18 44 4 66 /I Ursse Majoris . . 58 41 46 c Tauri 4 18 1 35 33 3 10 4 06 79 a Ursaj Majoris . . .... 4 26 1 11 4 25 4 20 28 1 11 f- 36 2 12 36 2 26 47 76 (3 Ursa3 Majoris.. .... 4 29 2 16 (3 Camelopardalis ... . 4 .23 .12 a Ursse Majoris 4 .02 .45 e Auri"8B . . 4 .13 .91 T/J Ursa Majoris .15 .54 4 .23 1.14 6 Leonis 4 .19 2.09 4- 01 58 6 Crateris ...... 59 4 30 4- 19 01 14 1 80 (3 Tauri .24 4 .35 A Draconis 4 .42 43.2S .48 1.18 N B 32 498 UNITED STATES NORTHERN BOUNDARY COMMISSION. [92] TABLE V Continued. 18 15. 18 15. Ac? AM' M V v Leonis ...... .,... n .G8 // -f 1. 08 a + .35 a 2.31 % UrsoB Mfljoris .. . -4- 04 .43 + .19 .63 $ Leon is 4- .26 2. 44 + .20 .34 /? Virginia ... .. . .01 1.00 p 3 Herculia .... .... .... ..., -.11 1.14 y UrsfB Majoris . . . + .20 25 + .13 + .41 .40 2.54 + .11 1.05 14 16 .31 +1.76 j? Virginia ................ .39 1 76 + .02 1.47 fi Corvi .34 .06 .01 + .59 .63 +2.80 .05 + .35 B.A.C.4342 4- .57 +3.83 .42 + .34 -4- .31 +3.43 + .01 + .66 9 +1.89 2.41 30 36 39 +1 37 03 1 20 .68 2.81 4- 16 48 2. 57 +1.41 15 Drdconis...... .... .. 4- 01 4- 84 O^Cygni + .61 + .10 . 17 4- 45 C Cvcni .. .45 1.39 Herculis ........ ... + 03 4- 28 .07 +1.68 ij Herculis .... ....... .69 3 00 + .07 .34 K Ophiuclii .01 39 (3 Cephei .01 +1.33 [93J REPORT OF THE (JHIEF ASTRONOMER, APPENDIX H. 499 TABLE V Continued. 18 45. 18 45. Arf v A(J Co Mean i! ;r' rv> Co o // // o // II + 86.7 5 .23 .00 + 23.9 4 1.70 1.22 + 76.3 6 + .90 .00 + 22. 1 .88 1.27 + 7-2.0 5 .71 .00 + 19.6 6 .94 1.41 -j- 69.5 4 .54 .00 + 15.3 8 2.02 1.83 -f 67.2 4 + .26 .00 + 13.5 5 2. 17 1.85 + 65.3 2 + .15 .00 + 10.3 9 1.79 1.61 + 62.0 7 + .35 .00 + 8.4 8 1.35 1.36 -f 59.7 8 .11 .00 + 6.6 5 .20 1.20 + 57.3 8 .24 .05 + 3.6 7 .71 1.13 + 55.3 3 + .12 .05 0.5 7 2.04 1.59 + 52.4 7 + .19 .15 3.6 5 a. 72 2.04 + 49.4 7 .60 .22 7.2 3 2. 20 2.24 + 46.8 5 .30 .40 9.1 7 1.76 2. 22 + 44.5 .82 .54 14.1 4 2.40 1.79 + 41.7 5 .24 .90 18.7 3 .80 1.25 + 39.5 7 1.19 1.04 22. 4 4 1.12 1.05 + 37.7 3 3. 33 -1.19 27.1 3 1.08 1.00 + 34.0 6 2. 05 1.44 30.0 1 1.40 1.00 + 31. 4 3 1.19 1.45 35.0 2 + .08 1.00 + 28.4 6 .77 1.30 42.1 5 2.21 1.00 -f 26.6 4 1.33 1.23 In drawing the curve much assistance was derived from the comparison of Ao 29 and Po 1800, made by Argelandcr (Abo Catalogue, p. xi). If we denote by the cor- rection to Gh 1755, and by ft' the definitive correction to Ao29 (Table IX.), we shall have on 90 fr (,9 ft') + ,, + 30, + 15, and + 5, the observations would be much better represented. I did not, however, feel justified in taking this course. The plus residuals from 40 to 90 average much larger than in the former discussion. This appears to be almost solely due to accidental causes. Had r " been constructed without correction for terms in a, the plus residuals would have been reduced less than one-tenth of a second. The probable error of the unit of weight, using only the 329 residuals with weight 1, north of 30, is i ".78, and considerably smaller than before. For stars from + 40 to + 90 it is ".88, + 30 to + 40 1".02, and from 30 to + 30 ".66. I did not think it worth while to repeat the investigation of terms in a. Bh 1810. From r a a preliminary correction was derived and used before discussing terms in o. Column r " is formed, taking into account the effect of these terms. (7 contains values derived from the definitive cui*ve. Residuals in order of declination. Mean i TT' 'o ro" Co // // // 86.5 24 + .35 + .07 + .10 _ 76.2 21 + .66 + .38 + .36 7= 2 70.8 33 + .57 + .33 + .31 / 66.5 22 - .0* + .25 + .19 60.8 58 + .16 .00 + .01 56.7 50 .04 .08 .02 50.9 65 + .25 + .18 + .10 45.6 55 + .03 + .08 + .10 40.2 57 + .06 .01 .00 The residuals are arranged in order of a without separation into zones of S. As has been stated, they result from the use of a preliminary correction derived from column r . Residuals in order of right ascension. Mean a K' v ft. // 0.99 49 .10 3.22 13 .06 5. 09 34 .13 9.34 30 1.20 11.78 48 .30 14.48 49 .10 16.79 52 + .10 19.63 73 + .73 22.30 37 + .57 The discussion gives, in fair accordance with those of Argelander and Auwers, this correction : - ".080 ".054 - (".534 ".077) sin a + (".404 ".073) cos a. 506 UNITED STATES NOETHERN BOUNDARY COMMISSION. With m = 7, we have: E = 1".03.* [100J Kg 21. Within the groups the variation in precision is small. Each r is therefore given weight 1. Residuals in order of declination. Mean t! * n> r, + 87.6 2 .13 + .01 + 76.6 3 .09 + .08 + 70.8 4 + .37 + .12 + GO. 9 7 + .03 + .18 + 56. 3 4 + .39 + .17 + 51.1 7 -.03. + -14 + 44.7 3 .07 + .09 + 40.0 7 + .12 + .06 + 28.1 4 + .29 + .06 + 21.3 2 - .08 + .10 + 14.5 7 4- .07 + .13 + 8.2 4 + .16 + -17 + 4.0 3 + .36 + .20 1.1 1 + .44 + .27 9.1 3 + .29 + .41 14.2 2 + .36 + .53 27.6 2 +1.25 + .84 With catalogue probable errors as an argument, and with the probable error of unit of weight .30, taking m = 4, we have from the outstanding residuals E = .30. The probable errors given in the catalogue are therefore adopted in the construction of definitive weights. Residuals in order of right ascension. Declination limits. Declination limits. 30 to +90 30 to +90 Mean a TT' ro' Mean a ir- iV II n 1 6 + .15 13 3 .03 3 3 .13 15 8 .26 5 7 .21 17 8 .08 7 1 + .10 19 8 .17 9 2 - .05 21 8 + -14 11 5 + .26 23 4 + .08 ' In forming an opinion as to the precision of the declination determinations of various catalogues it is, of course, necessary to consider the value of E in connection with the ratio -. In many cases the value of E does not refer at all to the probahle error of a single observation ; and when it can he so con- strued, it is often and necessarily a rough approximation. The most that can he said is that the adopted law of probable errors for a given catalogue is calculated to give with tolerable fidelity the probable errors due to the numbers of observation most frequently occurring with the stars of Table V. [101] BEPORT OF THE CHIEF ASTRONOMER, APPENDIX H. Gh22. 507 The use of the correction zero adopted in Section VI. is continued, since no further material is available. The correction ".11 actually results. Residuals in order of right ascension. Mean a ** o' Mean a TT' r a ' 1 3 // .06 13 1 II .10 3 1 .70 15 4 + .10 5 4 + .08 17 3 - .12 7 1 .00 19 3 + .08 9 2 .65 21 3 .22 11 i .20 23 2 .35 Dt 24. The weights correspond to the probable errors of the catalogue, and the unit of weight, to a probable error of ".25. Residuals in order of declination. Mean o 19 18 .02 9 11 + .11 21 18 .07 11 19 .02 23 11 + .12 Va 29. Each r receives weight 1. Residuals in order of declination. Mean 6 it Co o II II + 74.8 1 + .50 + .40 + 69.9 1 + .81 + .40 + 62.2 2 .39 + .40 + 55.1 2 + .80 + .38 + 50.3 3 + .61 + .31 + 45.2 2 .03 + .24 + 38.7 1 + .81 + .14 + 28.1 4 .19 - .08 + 21.3 2 .31 .19 + 14.3 7 + .05 .15 + 8.2 4 .14 .13 + 4.8 2 .08 .10 1.1 1 .53 .06 9.1 3 .13 .01 No attempt is made to discuss terms in a. With m = 4, we have: E = ".47. [103] EEPOET OF THE CHIEF ASTEONOMEB, APPENDIX E. Ao29. Residuals in order of declination. 509 Mean S * ro Co o II + 88.9 7 + .20 00 , + 76.6 33 + .00 00 ^=3 4- 71.6 34 .01 00 ' 4- 69.3 33 + .02 00 4- 61.2 .05 00 4- 56.5 58 .02 00 4- 50.6 74 + .09 .02 4- 45.0 77 .13 .07 + 39.3 60 .15 .14 + 34.0 46 .21 .17 4- 27.4 47 .20 .24 4- 20.9 43 .30 .28 + 14.4 68 .33 .32 4- 8.4 41 .32 .38 + 4.6 53 .47 .44 1.5 25 .67 .54 9.1 27 .58 .66 14.0 21 .88 .70 18.8 5 .30 .70 26. 1 9 .70 With m = 4, we have : E = ".46. Residuals in order of right ascension. Declination limits. Declination limits. 30 to + 90 30 to 4- 90 Mean a IT' r,,' Mean a if ro' h. II A. // 1 119 .16 13 49 + .08 3 32 .05 15 90 + .02 o 69 .02 17 80 + .06 7 9 .00 19 88 .09 9 71 + .34 21 98 + .07 11 79 .00 23 56 .05 510 UNITED STATES NORTHERN BOUNDARY COMMISSION. Gh 30. Each r is given equal weight. Residuals in order of declination. [104] Meau d 7T 7 r a Co o it */ + 86.3 6 + .55 + .11 -j- 76.7 5 .18 + .15 + 70.8 9 + .22 + .13 + 66.0 4 .17 + .09 + 60.8 15 .05 + .03 + 57.5 10 .18 .06 + 50.9 14 + .03 .28 + 45.7 12 .47 .50 + 39.9 16 1.00 .76 + 33.1 9 1.14 1.02 + 27.2 11 1.29 1.19 + 21.2 14 1.09 1.29 + 14.6 13 1.51 1.31 + 9.0 19 1.36 -1.81 + 4.1 9 1.11 1.34 1.8 12 1.51 1.41 8.5 10 1.28 1.62 14. 1 4 2.00 1.91 18.7 3 2. 10 2.36 22.4 4 2.75 2.C7 27.9 4 2.9 2.9 34.1 1 +9.3 r * With m = 5, we have: E = ".33. Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. 30 to +5 + 40 to 30 30 to +90 Mean a 7T 7 r ' V ' K* 'V h. n // // 1 2 .25 11 + .15 21 + .20 3 3 + .43 7 + .24 10 + .16 5 4 + .57 10 + .12 16 .04 7 2 + .50 12 + .13 13 + .33 9 1 .30 9 .16 13 + .06 11 4 .10 10 .14 19 .07 13 5 + .12 7 + .09 13 .00 15 5 + .32 12 + .03 20 .04 17 2 .80 10 .45 20 .35 19 5 .06 13 .15 21 .03 21 4 .17 10 .18 20 .16 23 5 + .30 9 + .17 14 + .08 A small correction, depending on the right ascension, may be indicated, discussion was not, however, undertaken. The [105] EEPOET OP THE CHIEF ASTRONOMER, APPENDIX H. 51 1 C. G. H. 31. Residuals in order of declination. Mean <5 TT' r<> Co o H n + 12.7 2 .88 + .35 e + 8.2 9 + .00 + .35 r= 2 - + 3.3 3 + .61 + .35 / 0.7 8.4 17.9 7 11 2 + .55 + .27 +1.0-2 + .35 + .35 + .35 For (he last five groups the weights are estimated. 21.1 4 .60 + .35 26.5 3 + .61 + .35 35.0 2 +1.08 + .17 41.4 2 .51 + .03 52.6 1 + .38 .00 r>9.9 5 .40 .00 78.1 1 + .90 .00 The correction is extremely uncertain, owing to the small number of observations, as well as large probable error. The value of E is estimated to be 1".2. The declinations have not been employed in the reduction of any stars between the limits of declination + 90 and 30. S. H. 31. The values of r are applicable to the catalogue places as reduced with Young's refractions. Residuals in order of declination. Mean 3 * ,o Co o II + 73.1 15 + 1.0 + 1.30 e + 65.1 4 + .1 + 1.30 =2 + 62.4 10 + 1.37 + 1.30 ' + 56.2 11 + 1.20 + .30 + 51.0 19 + 1.76 + .30 + 44.7 7 + 1.20 + .30 + 38.7 8 + .90 + .30 + 33.2 6 + 1.21 + .30 + 27.9 33 + 1.18 + .30 + 21. 3 18 + 1.85 + .30 + 14.6 53 + 1.26 + 1.30 + 82 35 + l.CO + 1.26 + 4.1 24 + 1.35 + 1.21 2.4 55 + .79 + 1.13 8.5 70 + 1.2-2 + 1.00 14. 1 30 + 1.32 + .86 18.5 18 + .24 + -74 23.9 17 1.09 + .65 2H.1 31 + .71 + .61 35.0 2 .13 + .60 42.1 5 + .69 + .60 50.4 2 + 1.41 + .60 59.2 6 + .66 + .41 74.8 3 + .14 + .35 512 UNITED STATES NORTHERN BOUNDARY COMMISSION. [106] There appears to be a well-marked correction depending on a, as is shown in the following table: Residuals in order of right ascension. Declination limits. 30 to +5 Declination limits. + 5 to +60 Declinatiou limits. 30 to +60 Mean a n' ro' Mean a 7r' o' Mean TT' ft' ft. 1.0 3.3 5.8 7.4 9.3 11.2 13.0 15.6 18.9 21.8 16 16 25 14 9 7 22 44 28 56 II + .25 + .73 + .26 .89 .10 4- .50 ft. 23.8 2.5 5.2 7.6 11.2 29 16 18 9 24 // + .58 + .98 + .30 + .10 .75 h. 0.7 3.6 5.7 8.3 11.3 13.2 15.5 18.2 19.9 22.3 46 32 42 24 31 31 69 52 56 52 a + .46 + .86 + .02 .25 .46 .10 .66 .23 .16 + .38 .39 .61 .28 + .18 14.9 18.0 19.9 34 36 32 - .38 .12 .10 r n ' in limits 30 to + 60 gives the correction + ".27 sin + ".47 cos a. The probable error of each coefficient is ".09. With TO = 6, we have : E = l".34. C. G. H. 33. Each r is given weight 1. Residuals in order of declination. Mean i ff' n> Co o n // + 33.2 1 + .35 + .31 + 27.7 7 + -41 + .54 + 21.7 7 + .69 + .48 + 14.2 8 .25 + -11 + 8.4 7 .22 .09 + 3.7 6 + .29 .14 2.2 5 .16 .10 8.6 6 .02 + .10 14.1 4 + .32 + .40 18.7 3 + .70 + .65 22.4 4 +1.05 + .79 27.9 4 + .92 + .89 35.0 2 + 1.15 + -71 4i 1 5 + .04 + .32 55. 1 2 .60 + .05 59.2 7 + .04 + .01 75.1 3 .11 .09 With m = 6, we have: E = + ".30. [1071 REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. Residuals in order of right ascension. 513 Declination limits. Declination limits. + 40 to 30 + 40o to 30 Mean a TT' n,' Mean a K" ro' ft. /; h. // 0.35 5 + .10 13.40 4 + .25 3.00 5 .12 15.53 9 + .02 5.41 8 + .19 18.31 7 + .09 7. 66 5 .34 19.72 5 .04 10.67 7 + .09 22.06 7 .33 Ce 34. Residuals in order of declination. Mean 6 * ro Co o It + 87.3 25 .08 .00 n + 75.5 14 + .06 .04 _=3 e + 69.7 14 .25 .14 + 66.2 17 .18 .24 + 61.2 31 .59 .38 + 56.6 43 .28 .52 + 50.3 23 .71 .70 + 45.0 21 .87 .78 + -59 4 15 .79 .83 + 33.2 8 .57 .82 + 27. 8 48 .83 .86 + 20.4 50 .46 .56 + 14.3 52 .47 .39 + 8.5 67 .25 .36 + 4.1 24 .46 .40 0.8 22 .19 .49 8.4 36 .85 .70 14.0 12 1.22 .85 19.2 10 .62 .96 21.7 9 .79 .99 2H. 4 13 1.25 1.00 34. 1 o 1.4 With m = 5, we have: E ".70. B 33 514 UNITED STATES NORTHERN BOUNDARY COMMISSION. Residuals in order of right ascension. [WSJ Declination limits. Declination limits. Declination limits. Declination limits + 40 to 30 + 40 to + 90 30 to + 5 30 to + 90 Mean a tr 1 r e ' ir' ro' *> )' tf >' h. // // // // 1 35 + .16 32 .23 3 .70 67 .01 3 22 + .58 10 .44 8 + .30 32 + .26 5 31 .21 11 .35 5 .20 4J .25 7 24 + .04 24 -t- 04 9 l!2 + .39 5 .50 8 + .40 27 r ^* + .23 11 32 + .03 34 + .14 8 + .05 66 + .09 13 26 + .11 25 + .23 20 + .20 51 + -17 15 50 .06 9 + .20 14 + .42 59 .02 17 22 -h .03 9 + .12 7 + .48 31 + .06 19 49 .13 17 .05 7 .54 66 .11 21 25 .12 33 + .10 25 .12 58 .00 23 21 .45 7 .06 4 .25 28 .35 No certain correction following a appears to be indicated. Mb 34. In Observations Astronomical, 1833 and 1834, Laniont compares his declinations of fundamental stars with those of Bessel and Struve. The comparisons are used in finding the curve of correction, but no use is made of the declinations of the stars so compared. Eesiduals in order of declination. Mean d ir 1 'o <"o o // II + 74.4 12 .29 .29 e 3 + 62.6 14 .36 .49 e. + 57.6 7 .68 .56 / + 49.6 27 .74 .62 + 40.1 36 .55 .54 + 32.0 15 .28 .24 + 27.7 50 + .01 + .01 + 21.0 66 + .27 + .29 + 14.6 72 + .43 + .47 + 9.1 79 + .63 + .50 + 4.3 42 + .94 + .49 1.5 49 .14 + .38 9.0 43 + .53 + -I? 14.2 19 + .70 .01 19.7 9 .43 .19 26.2 20 .61 .5 [109J REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 515 Inadvertently the nutation correction was not applied to the values of r previous to the above discussion. The outstanding residuals are: Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. 25 to +5 + 5 c> to+75 + 75 to 25 C Mean a TT' n,' J 'o' 7T 7 n>' J>. // // n I 2 + 1.70 42 + .-19 44 + .51! 3 10 + .82 9 + .01 19 + .44 5 17 .11 28 + .11 45 + .03 7 4 1.50 45 .32 49 - .42 9 19 + .10 28 + .16 37 + -14 11 20 .45 55 .40 75 .41 13 20 .04 7 .03 27 .04 15 17 + .34 55 + -17 72 + .21 17 4 .40 44 .17 48 .19 19 13 + .05 31 + .22 44 + -17 21 Id - .07 20 + -17 38 + .06 23 19 + -41 11 + .63 30 + .49 Discussed for terms in a, the last column (+ 75 to 25) gives: + ".03 sin a + ".27 cos a, which agrees well with the nutation correction + ".02 siu + .18 cos . The latter is therefore adopted. With TO = 5, we have : E = 1".05. Eh 37. Residuals in order of declination. Menu (J TT' ID Co o // // + 86.9 24 .18 .21 + 76.6 15 .37 .23 _ y + 70.4 7 .18 .23 K l + 66.3 6 .66 .22 + 61.4 26 .14 .21 + 56.0 21 .18 .18 + 50.8 30 .22 .16 + 45. 4 16 + .01 .15 + 39.3 16 .10 .16 + 33.5 10 .43 .18 + 27.6 36 .15 .20 + 21.2 45 - .31 -.18 + 14.5 46 .25 .04 + 9.0 56 + .31 + .03 + 3.9 27 + .07 .03 1.3 29 .24 .17 8.6 32 .51 .26 14.1 15 .23 .26 18.7 9 .25 .18 21.9 9 + .80 - .09 28.6 7 + .44 + .2 With m = 8, we have: = ".52. 516 UNITED STATES NORTHERN BOUNDARY COMMISSION. [110 1 Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to +5 + 5 to +40 + 40 to +90 30 to +90 Mean a TT' 'o' V? Itf 7T 7 ro' TT' V h. // // II // 1 C 1.05 26 + -14 15 4- .16 47 .00 3 10 4- .25 10 + .08 5 .04 25 + -12 5 14 + .16 20 .56 12 + .30 46 .11 7 24 4- .08 5 .02 29 4- 06 9 4 + .20 18 n **** .17 11 + -14 33 ~ . V\J .02 11 13 + .02 20 + .11 16 - .05 49 4- .03 13 15 + .19 8 .15 10 .00 33 + .03 15 14 4- .66 18 .43 9 .3-2 41 + .34 17 G .15 11 - .04 19 .00 36 ..01 19 7 .42 27 .01 7 + -11 41 .06 21 15 .23 17 + .09 23 .11 55 .08 23 13 .31 18 + .21 10 .06 41 .02 A correction is indicated, such as might be due to an error in the adopted temper- ature coefficient in refraction. Very little correction is shown in the summary. I have thought it safest to neglect the discussion of terms in a. (Tide Eh 43). Kg 38. Each r was given equal weight. The numbers in column r a " result from a redis cussion adopting the value of the periodic formula deduced below for terms in . Residuals in order of declination. Mean " o // // II 4-87.5 2 .05 - .05 .07 + 75.8 2 .21 .26 .11 + 71.2 2 .75 .32 .54 + 62.2 2 .69 .24 .60 4- 55.1 2 4- .44 4- .10 4- .40 + 51.1 7 4- .65 4- .24 + .84 + 45.9 8 4- 1.03 4- .30 4- .80 + 39.8 6 .08 4- .22 .01 + 28.1 4 .07 4- .08 .17 + 21.3 2 .01 + .13 .01 -f- 14.3 7 4- .39 4- .27 + .42 4- 8.2 4 4- .29 4- .46 4- .41 4-4.0 3 4- 1.10 4- .59 4- 1.10 1.1 1 4- 1.10 4- -77 4- 1.05 9.1 3 4- .99 4- 1.09 4- .97 14.2 2 4- 1.36 4- 1.31 4- 1.62 26.1 1 4- 2.8 + 1.8 4- 3.16 The declination curve founded on r is adopted. [Ill] EEPOET OF THE CHIEF ASTBONOMEE, APPENDIX H. 517 Residuals in order of right ascension. Declination limits. Declination limits. 30 to +90 30 to +90 Mean rj Mean 6 TT 7 1%' k. II h. // 0.9 6 + .27 13.3 2 .45 3.1 4 + .75 14.9 7 .44 5.2 5 + .50 17.1 5 + .42 7.0 1 + .20 19.3 8 + .13 9.7 9 .05 20.9 5 + .04 11.5 4 .30 23.3 2 + .15 The correction depending on a is quite marked. The result is + ".14 + ".24 sin a + ".32 cos a. The probable errors of the terms in a are each .07. The formula of correction is adopted. With m = 8, we have : E = ".39. Gh 39. Residuals in order of declination. Mean <5 ff' * ,C o + 86.5 79 II + .or It + .01 + 76.7 71 + .05 + .04 __4 + 70.5 67 + .10 + .08 ' + 66.2 62 .10 + .09 + 60.9 176 + .06 + .10 + 56.8 147 + .07 + .11 + 50.9 138 + .20 + .12 + 45.5 136 + .02 + .12 + 39.7 98 + .07 + .13 + 32. 9 54 + .22* + .14 + 27.4 114 + .19 + .16 + 21.1 134 + .15 + .19 + 14.5 130 + .26 + .24 + 8.9 135 + .29 + .29 + 3.9 85 + .37 + .35 1.6 90 + .40 + .43 8.6 97 + .53 + .56 14.1 51 + .71 + .68 18.7 36 + .53 + .80 22.5 44 +1.04 + .90 28.1 44 +1.24 +1.05 With m = 4, we ha.ve : 518 UNITED STATES NORTHERN BOUNDARY COMMISSION. Residuals in order of right ascension. [112] Declination limits. Declination limits. Declination limits. 30 to +5 + 4Qo to _ 3Qo 30 to +900 Mean a TT' r' TT' './ TT' 'o' h. // // // 1 25 .21 96 .15 212 .13 3 39 .13 57 .24 95 .13 5 48 .41 107 .20 174 .18 7 25 + .31 89 + .H 103 + .10 9 13 .30 73 .11 127 .11 11 33 + .01 89 + .13 207 + .13 13 48 + .17 74 + .08 152 + .09 15 45 + .H 108 + .20 202 + .12 17 25 .04 72 + .09 168 + .05 19 20 + .20 119 .C7 201 + .05 21 45 + .27 89 .21 212 .06 23 36 .13 84 .10 144 .11 A tolerably well-marked correction depending on a is indicated. No discussion is undertaken, however, as the correction would in any case be very small. Ce 40. The weights formed in the manner explained in Section V. evidently increase too rapidly with the number of observations. Residuals in order of declination. Meon i 7T 'o Co K' is therefore formed in this manner : o // + 86.6 75 + .02 .00 Weight com- + 76.6 55 + .12 .00 puted ac- r* + 70.2 33 .11 .07 cording to 71 + 65.8 34 .08 .16 Section V. + 61.2 134 .38 .29 + 56.2 65 .37 .40 + 49.6 57 .54 .55 1 to 5 1 to 5 + 45.3 91 .62 .65 6 6 + 39.0 74 .75' .77 7 6 + 32.9 24 .83 .85 8 and 9 7 + 27.7 85 .83 .89 10 and 11 8 + 21.2 113 .78 .82 12 to 14 9 + 14.4 118 .57 .58 15 to 17 10 + 8.9 116 .37 .47 18 to 21 11 + 3.7 56 .51 .54 22 to 25 12 1.3 57 .78 .64 26 to 30 13 8.6 70 .65 .70 31 to 35 14 14.1 25 .93 .68 36 to 40 15 19.4 11 .35 .56 41 to 46 16 21.9 8 .43 .50 47 to 52 17 26.3 7 .07 .4 53 to 58 18 59 to 65 19 66 to 72 20 73 to 80 21 81 to 88 22 89 to 96 23 97 to 105 24 106, or more 25 [1131 REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 519 Residuals in order of right ascension. Declination limits. 30 to + 5 Declination limits. + 50 to + 40 Declination limits. + 4Qo to 30 Declination limits. + 40 to + 90 Declination limits. 30 to + 90 Mean o vr' ro' V nt sr' ro' TT' r a ' 71"' *t h. I 3 5 7 9 11 13 15 17 19 21 23 6 20 16 // + .45 + .16 + .23 62 13 43 54 44 48 24 63 42 86 32 30 ii .09 .15 + .09 + .26 + .34 + .04 .03 + .14 .02 .04 .19 .28 68 33 59 54 53 61 44 92 52 100 73 54 // .04 + .04 + .13 + .26 + .35 + .12 + .05 + .10 .01 .04 .25 .21 79 30 44 II + .06 .07 .11 147 63 103 54 85 139 90 138 97 150 149 86 II + .01 .01 + .03 + .26 + .U .02 + .12 + .06 .01 .07 .12 .04 9 13 20 29 10 14 41 24 + .40 + .39 + .14 + .02 + .06 .06 .30 .13 32 78 46 46 45 GO 76 32 .28 .12 + .19 .02 .02 .11 + .01 + .25 A correction varying with the right ascension is well marked in the zone + 40 to 30 (and is supported in some degree by Ce 34). I find -f (".15 .025) sin a (".15 .025) cos a. With TO = 8, we have : E= ".46, Ce 48 gives ".62, and Ce 56 ".60. I have adopted H = 60. Ah 41 and Ah 52. These were at first treated as separate catalogues, but the experiment proved that there exists between them no difference, which can be safely predicated from the material. Ooms's very thorough comparison of Robinson's Armagh Catalogue (Ast, Nach. Bd. 59, p. 248), after the proper correction, has been relied upon to a great extent in drawing the curve. 520 UNITED STATES NORTHERN BOUNDARY COMMISSION. [114] Residuals in order of declination. Direct comparison. Through Ao 29. Difference Mean i w 7 r a Co Mean i Number of stare. uncorrectcd, applicable to Armagh dec- Difference corrected. lination. o it it o // // + 76.2 11 + .21 + .20 + 81.2 4 + .52 + .88 + 71.2 20 + .05 + .20 + 77.1 6 + .23 + .56 + 66.4 17 .06 + .20 + 72.4 8 + .34 + .63 + 61.0 3d + .11 + -17 + 66.7 8 .39 - .16 + 56.5 32 + .08 + .05 + 62. 4 11 + .38 + .56 + 51.4 38 + .07 .10 + 57.5 15 .35 .23 + 45.5 46 1.13 .71 + 51.6 15 .31 .27 + 40.1 49 .40 .81 + 47.5 15 .69 .75 + 32.9 20 .66 .54 + 42.9 22 .85 1.02 + 26. 5 24 .20 .30 + 37.5 32 .18 .49 + 21.0 25 .16 .27 + 32.7 17 .10 .52 + 15.1 16 .83 .47 + 27.4 29 + .04 .47 + 9.3 41 .61 .78 + 22.3 23 + .41 .18 + 3.7 15 .24 1.08 + 17.7 31 + .30 .36 - 1.7 22 1.14 1.21 + 12.4 18 + .08 .56 8.2 14 .54 1. 15 + 7.6 22 .45 1.05 + 3.0 31 .46 1.07 2.5 7.7 17 14 1.21 + .38 1.98 .58 it 1 is formed with = 2. e ; 13.1 16.8 19 24 .21 + .58 1.24 .47 23.6 2 2.05 3.0 With TO = 6, we have: E = I'M. Residuals in order of right ascension. Mean a ^ ro' Mean a TT' r' h. tt ft. // 1 48 .03 13 27 .16 3 19 + .05 15 40 + .05 5 33 .34 17 35 .37 7 20 .02 19 35 + .18 9 34 + .64 21 48 + .01 11 59 + .03 23 38 + .26 [115] EEPOET OF THE CHIEF ASTRONOMER, APPENDIX H. 521 Kg 43. The correction in order of declination is adopted as it results from the discussion in Section VI. (Table II.). In the following table, each value of r 1 is supposed to have an equal degree of precision. Residuals in order of right ascension. Declination limits. Declination limits. 30 to + 42 30 to +42 Mean a ff 7 rj Mean a 7T 1 r ' ft. n A. ,1 0.7 3 .40 13.3 1 .20 2.9 1 .40 15.0 4 .12 5.4 5 + .14 17.0 3 + .10 7.6 1 - .30 19.4 4 + .40 9.7 2 .20 20.9 3 + .40 11.7 1 .30 22.9 1 + .20 The division into two zones, which was made, is of no interest, owing to the small number of stars. From the above is found as a correction : (".16 ".06) sin a + (".13 ".07) cos a ; and this is adopted. Dr. Auwers found (Ast. Nach., Bd 65, S. 230) : ".139 sin (a 25 38') ".239 (sin 2 a + 05 270- The term depending on 2 a is indeed indicated, but I have preferred to neglect it, since the number of residuals is small. With m = 4, we have : E = ".26. 522 UNITED STATES NORTHERN BOUNDARY COMMISSION. [1161 Eh 43. Residuals in order of declination. Mean 6 v 1 ro Co o it // + 86.8 156 + .06 .00 The weights (TT') are + 76.5 85 + -14 .00 constructed according + 70.5 24 .44 .00 to Section V., which + 66.5 7 .20 .01 supposes : + 61.3 33 .08 . .04 f + 56.5 54 .14 .07 _ o + 50.6 + 45.5 54 38 + .07 .19 .08 .06 The argu raent for form- ing n 1 is not therefore + 39.4 42 -f .03 .03 the total cumber of ob- + 33.3 18 + .33 + .02 servations, but the sum + 27.4 66 + .14 + .09 of the values of ir 1 in + 21.3 66 .10 + .17 each year. + 14.2 68 + .18 + .28 + 8.6 66 + .40 + .35 + 4.1 42 + .10 + .36 1.4 52 + .40 + .31 8.7 65 + .26 + .16 14.1 31 .07 + .04 18.8 21 .50 - .06 22. 17 .38 .12 27.0 10 + .0 .02 Residuals in order of right ascension. Declination limits. Declination limits. Decl i nation limits. DeclinatioB limits. Declination limits. 30 to + 5 + 5 to + 40 + 40 to 30 -j. 4QO to + 90 30 to + 90 Mean a *> n>' It 1 nf 7T 7 ' *-' n>' *> ro' h. li li // n // 1 15 .54 40 .35 55 .40 75 .11 130 .24 3 19 .40 6 .10 25 .54 15 .13 40 . . ;jf) 5 30 + .01 24 + -12 54 + .61 21 + .04 75 + .'05 7 6 + .50 40 + .03 46 + .09 24 .00 70 + .06 9 9 + .60 37 + .09 46 + .19 14 + .23 60 + .20 11 16 .yj 25 + .20 41 .03 37 + .05 78 + .01 13 14 .30 17 + .64 31 + .22 31 + .06 62 + .14 15 28 .07 36 + .24 64 + .10 63 + .30 127 + .20 17 12 .05 27 + .02 39 - .01 54 + .22 93 + .13 19 21 + .14 42 .07 63 .00 43 + .06 106 + .02 21 33 .08 20 .15 53 .11 57 .09 110 - .10 23 20 + .03 W .22 38 .09 31 .27 69 . 17 A correction depending on a is quite well marked in all the zones. The discussion gives : (".05 ".03) sin a (".19 ".03) cos a. Dr. Auwera found (Ast. Nacli., Bd 64, 8. 343) - ".002 sin a ".310 cos a for the Edinburgh declinations, 1835-1839, assuming Ao 29 and Gh 1755 to require no correc- tion. This corresponds tolerably well with Eh 37, between the declination limits 30 [117] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 523 to + 5, as exhibited above. Later (Ast. Nach., Bd 65, p. 227), Dr. Auwers finds that two-thirds of the correction best corresponds with residuals derived from his discussion of fundamental stars. This accords almost perfectly with the formula given above for Eh 43. But Dr. Auwers supposes this formula not to be applicable to the later obser- vations of Henderson. With m = 8, we have : E = ".67. ".66 results from the discussion in Section V. The former is adopted. ,Gh 45. Residuals in order of declination. Mean to + 90 30 to + 90 Mean a ir> ro' Mean a TT' V h. // Ji, // I 179 + .06 13 130 + .03 3 87 + .01 15 185 + .12 5 146 + .05 17 152 .03 7 101 + .02 19 200 .10 9 116 + .12 21 181 .12 11 164 + .12 23 120 .13 A slight correction following the right ascension is indicated. It differs, however, quite sensibly from that shown in Gh 39, and I have, therefore, undertaken no discussion. Pa 45. In forming *', one observation is given weight 1; two to five, weight 2; six or more, weight 3. Residuals in order of declination. Mean S *' >'o Form. Co // n II + 86.6 13 .02 + .03 .00 + 76.0 12 + .04 + .07 .00 -f 70.9 21 .00 + .10 + .05 + 66.0 12 + .18 + .13 + .11 + 60.7 41 + .18 + .16 + .17 + 56.8 29 + .21 + .19 + .21 + 50.8 39 + .27 + .23 + .25 + 45.6 31 + .24 + .26 + .89 -f 39.9 44 + .36 + .29 + .33 + 33.0 21 + .40 + .32 + .36 + 26.9 28 + .29 + .36 + .38 + 21.0 35 + .34 + .39 + .39 + 14.5 + 9.1 38 46 + .45 + .42 + .41 + .43 + .42 + .44 + 4.3 19 + .59 + .46 + .47 1.9 22 + .60 + .47 + .51 8.4 17 + .54 + .49 + .57 14.1 10 + .59 + .50 + .66 19.4 3 + .38 4- 82 23. 9 3 n w * [+1.04] I **" [+1.0 ] 26.1 3 [+1.7 ] [+1.3 1 L I-*-* " J Column "Form" is derived from the expression (Section VI.) + ".34 (sin #+.503) Had the constant + ".34 been increased to + ".37, the accord with C would have been almost perfect down to 8.4. The curve from which C is taken was drawn without the slightest reference to the previous correction. [119J REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 525 The value of JH, taken from the outstanding residuals, is of no interest, since, on account of the great weight given to Pa 45 in the discussion of standard places, it would be entirely too small. In the introduction to the fourth volume of Poulkova observations, we have a thoroughly reliable discussion of the probable error of the declinations. The final weights were founded on these probable errors, which increase rapidly with the zenith distance. From the final residuals (r f ) of 37 fundamental and circumpolar stars (excluding a and S Ursae Minoris), I derive ".273 as the probable error of the unit of adopted weights. Supposing the average weight of a Poulkova declination 4, and of the final J 3 for 1845, 80, we should have approximately ".29 as the probable error of the unit corresponding to a probable error of i ".30, as given in the introduction of volume iv. A like discussion of the residuals (r t ) of 59 other stars, for which the weight of a posi- tion for 1845 is 40, or greater (averaging about 50), gives ".285, or about ".305 for the corrected probable error, which should correspond to the ".30 assumed. It may therefore be assumed that the weights for Pa 45, constructed in the manner explained above, are entirely reliable, and correspond well with the general system adopted in the definitive discussion of A 8 and A //. Residuals in order of right ascension. Declination limits. Declination limits. 20 to + 90 20 to -f 90 Mean a TT' '' Mean a Tf' ro' h. II h. // 1 56 + .11 13 30 + .03 A 20 .11 15 51 .04 5 37 + .01 17 50 .00 7 33 .06 19 50 + .10 9 33 .06 21 45 - .09 11 47 .02 23 31 + .05 526 UNITED STATES NORTHERN BOUNDARY COMMISSION. [120] Re 45. Residuals in order of declination. Mean <5 TT' ro Co o II II + 86.6 [27] [+ -18] [+ -17] + 76.3 22 -j- .53 + .62 -(- 70.8 28 + .72 + .61 e o + 66.4 21 + .23 + -47 = f / + 60.8 45 + .05 + .30 + 56.8 36 + .30 + .16 + 50.8 45 + .02 .04 + 45.6 38 .06 .18 + 40.0 42 .47 .34 -f 33.4 10 .31 .51 -f- 27.4 27 .44 .58 + 21.1 33 .68 .59 + 14.3 32 .22 .41 + 8.8 53 .22 .14 + 3.9 25 .02 + .08 1.4 26 + .63 + .31 8.6 27 + .29 + .49 14.0 10 + .95 + .48 - 19.0 3 + .18 + .36 22. 3 9 + .36 + .25 28.1 13 .31 + .06 There is some doubt about the correction from + 75 to + 90. For stars observed both above and below the pole, it is probably quite small. With m = 5, we have: E = ".73 I adopt ".77, the mean between this determination and that for Re 58. Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to + 6 + 40 to 30 + 40 to + 90 300 to _)_ MO Mean a 7r' ro' 71-' ro' TT' 'o' x> 'o' h. It // // ;/ 1 3 + .10 29 + .31 37 + .05 66 + .16 3 7 .44 17 .03 8 + .22 25 + .06 5 9 .10 26 + .H 20 .12 46 + .01 7 6 .47 26 + .06 5 .17 31 + .03 9 4 1.70 30 .42 16 .34 46 .39 ' 11 10 + .16 22 .05 30 .22 52 .15 13 13 + .33 17 + .45 21 + .40 38 + .42 15 9 + .66 26 .06 24 .33 50 .19 17 6 + .03 16 + .09 34 .11 50 .05 19 7 .53 26 + .11 26 + .20 52 + .15 21 12 + .60 22 + .07 32 + -14 54 + .H 23 14 .21 28 - .19 19 .04 47 .13 The previous discussion (Section VI.) is substantially confirmed. [121J REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 527 Wn 47. The weights are adopted as they result from the combination of separate years in the manner explained in Section V. This supposes - = 3. e i Residuals in order of declination. Mean 6 TT' l'o c u o // // + 86.9 72 + .10 + .13 + 76.6 51 + .46 + .14 + 69.9 19 + .24 + .10 + 62.3 35 + .07 + .02 + 50.3 31 .14 .05 + 50.6 73 .16 .05 + 45.1 31 .23 .05 + 38.5 58 .05 .05 + 33.2 20 + .66 .06 + 27.8 89 .01 .11 + 21.6 83 .24 .19 + 14.2 122 .35 .28 + 8.6 111 .35 .34 + 3.9 74 .37 .35 1.6 49 .51 .33 8.5 63 .16 .28 14.1 54 .30 .24 19.1 22 + .06 .19 - -22.3 36 .35 .15 28.5 49 .05 .05 Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to + 5 + 40 to 30 + 40 to + 90 30 to + 90 Mean .< TT' I'D' ,_/ 'V fi" I'O T' >o' h. // // it // 1 10 + .02 56 + .19 43 .10 99 + .06 3 49 + .01 56 .08 18 .70 74 .23 5 24 .33 70 .56 12 .40 82 .53 7 25 .13 58 .20 10 + .10 68 .16 9 10 .50 46 .20 11 + .21 . 57 .12 11 11 .60 37 .34 29 + .02 66 .18 13 18 .02 37 .10 14 + .50 51 + .06 15 43 + .34 102 + .30 28 + .65 130 + .37 17 31 + .15 58 + .25 : + .16 93 + .21 19 30 + .15 149 + .25 1.3 .00 102 + .20 21 44 .01 95 + .06 66 .04 161 + .02 23 27 .04 60 .08 23 .10 83 .08 From discussion of the values of r ' in the final grouping ( 30 to +90), I derive: ".27 sin a ".08 cos a. Examination of Wn 56 and Wn 64 shows that they are in need of a similar cor- rection ; and the separation into zones renders it highly probable that this correction is almost equally applicable to all limits of declination. 528 UNITED STATES .NORTHERN BOUNDARY COMMISSION. For Wn 56, we have : [122 and for Wn 64, ".16 sin a ".19 cos a; ".22 sin a ".12 cos a. The same form of correction is indicated in Wn 70. It is undoubtedly real and sensibly constant for the Washington mural circle throughout the period of its use. From the combined residuals ( 30 to + 90) of Wn 47, 56, and 64, we have: - (".21 ".03) sin a - (".12 ".03) cos a as the correction ; and it is adopted. It reduces the sums of squares as follows : Year. Before. After. 1847 144 101 1856 258 236 1864 179 165 From the final residuals for 1847, with m = 7, we have: = ".74. Ce48. The weights are derived in the manner explained under Ce 40. Residuals in order of declination. Mean <5 IT' r a Co o a it + 87.9 35 + .28 .00 + 76.9 15 .15 .00 + 70.2 19 .01 .00 + 65.6 20 + .03 .09 + 61.0 62 .21 .23 + 56.6 36 .44 .37 + 49.5 49 .51 .58 + 45.4 64 .58 .6H + 39.0 35 1.19 .82 + 32.6 16 .71 .86 + 27.8 58 .78 .75 + 21.3 60 .42 .41 + 14.5 82 .02 .09 + 9.1 68 .02 .05 + 4.2 29 .22 .05 1.0 27 .02 .08 8.6 38 .15 .12 14.1 15 + .13 .12 18.5 9 + .20 .09 21. 5 6 .9 .09 26.2 3 .8 .03 With m = 5, we have: E = ".62 .60 is adopted, as explained under Ce 40. [123J RKPORT OF THE CHIEF ASTRONOMER, APPENDIX 11. Residuals in order of rigJit ascension. 529 Declination limits. Decl'nation limits. 30 to +90 30 C to +90 Mean a 4 TO' Mean a 71-' >V h. II A. // 1 84 + .07 13 52 + .10 3 29 .19 15 50 .08 5 74 + .06 17 47 .09 7 47 .03 19 119 .09 9 53 .04 21 79 .02 11 73 + .01 23 35 + .21 Gh 61. Residuals in order of declination. Mean t TT' r<> Co o // II + 86.6 77 .16 .13 e + 76.4 55 .07 .14 7, = 4 + 70.6 56 .25 .15 + 66.4 23 .22 .16 + 61.1 95 .14 .17 + 56.7 78 .17 .19 + 50.9 102 .15 .21 + 45.6 62 .26 .20 + 39.4 98 .17 .15 + 32.5 82 + .05 .03 + 27.3 147 .04 + .06 + 21.2 147 + .15 + .16 + 14.5 165 + .28 + .18 + 9.0 218 + .23 + .15 + 4.1 102 .00 + .1U 1.7 129 .01 + .03 8.5 110 .07 .00 14. 1 52 + .01 + .03 18.8 36 + .17 + -11 22.4 48 + .31 + .16 28.2 43 .03 + .22 With m = 5, we have: E = .70. There is i trace of the same peculiarity in the values of r -, as has appeared with Gh 45. In any case, the required correction is so small that its ueglect is of little consequence to the final result. 530 UNITED STATES NORTHERN BOUNDARY COMMISSION. Residuals in order of right ascension. Declination limits. Declination limits. 30 to +5 30 to +90 Mean a rr' n,' TT' r,' i 27 II .04 214 .15 3 38 .14 94 + .04 5 47 + .01 157 + .06 7 25 .15 131 .11 9 14 .20 129 -1- .01 11 39 + .06 177 + -14 13 60 + .10 126 + .13 15 54 + .01 195 + .03 17 27 .20 169 .06 19 52 + .05 183 + .03 21 40 .31 174 .02 23 54 .06 139 .01 So 51. Residuals in order of declination. Mean <5 TT' r a Co o n II + 45.8 4 + 1.06 + 38.6 13 .03 + .44 + 33.2 4 .04 + .58 = , + 27.5 33 + .77 + -74 / + 21.3 40 + .88 + .87 + 14.5 46 + .92 + .99 + 8.7 42 + 1.23 + .05 + 3.7 26 + 1.01 + .09 2.2 14 + 1.09 + .12 8.5 28 + 1.22 + .12 14.1 15 + 1.16 + .10 18.9 12 + .81 + .06 22.5 16 + .95 + .08 28.2 17 + .90 + 1.00 34.2 1 + .25 + .96 41.9 2 + 1.24 + .91 52.6 1 + .94 + .79 59. 6 6 + .82 + .62 75.1 3 + .28 + .28 REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. Residuals in order of right ascension. 531 Declination limits. Declination limits. 30 to + 40 30 to + 40 Mean a * ro' Mean a K> ro' h. // h. // 0.9 24 .37 13.1 81 .16 3.1 22 + .15 14.9 30 .07 5.1 29 + .49 16.7 19 .31 7.1 32 + .07 19.0 40 .16 9.3 27 + .10 21.2 22 - .19 11.3 22 + .53 22.9 18 .66 There is an evident progression of r c ' with a. The discussion gives, as the correc- tion to be applied : + (".24 ".07) sin a (".185 ".075) cos a. There is some reason to expect such a correction for this series, and it is adopted. With m = 6, we have: ".86. Ps 53. Residuals in order of declination. Mean c! K 1 ro C ' o II // + 86.3 37 .10 + .06 e + 76.7 23 + .18 + .19 o e. + 70.6 31 + .38 + .25 i + 66.0 18 + .20 + .28 + 61.9 29 -j- .40 + .29 + 56.5 40 + .29 + .28 + 50.6 33 + .05 + .23 + 46.0 16 + .48 + .19 + 39.5 26 + .17 + .12 + 33.2 13 .03 + .05 + 27.7 30 .08 - .03 + 21.5 38 .15 .10 + 14.4 38 .01 .19 + 8.7 49 .31 .28 -t-3.9 33 .44 .34 1.2 28 .15 .37 9.0 19 .47 .31 14.1 19 .16 .21 18.7 13 .21 .06 22.3 10 + .12 + .12 28.6 13 + .92 + .6 With m = 5, we have: E= ".57. 532 UNITED STATES NORTHERN BOUNDARY COMMISSION. Residuals in order of right ascension. [126] Declination limits. Declination limits. Declination limits. 30 to + 5 + 40 to 30 30 to + 90 Mean a 7T 1 ro' K 1 ro' TT' ro h. II // II 1 9 .08 39 .02 59 .05 3 16 + .35 24 + .10 41 + .18 5 17 .02 31 + .26 42 + .02 7 6 + .20 25 + -17 31 + .15 9 3 + .60 18 .09 27 .02 11 8 .45 22 .26 56 .11 13 13 + .13 20 + .10 44 .11 15 16 .22 27 .14 55 .11 17 8 + .05 20 .44 50 .18 19 9 .00 36 .21 48 + .12 21 10 .10 35 + .01 61 + .15 23 15 + .10 5 + .60 24 + .35 So 55. Residuals in order of declination. Mean d if 'o Co o /* it + 45.8 1 .56 + 38.3 2 +1.19 + .50 - = 2. e ; + 24. 5 4 + .67 + .48 + 20.9 13 + .51 + .45 + 14.2 27 + .30 + .29 + 8.3 29 .03 + .18 + 3.8 15 + .46 + .18 1.9 12 + .45 + .32 8.7 20 + .35 + .39 14.0 12 + .55 + -17 19.0 7 .07 .03 2-2.2 11 .58 .10 28.6 12 .31 .05 42.8 + 34 4- 27 51.8 1 1 "^ + .42 -f- . Aft + .24 59.3 3 + .19 + .12 78.3 2 .49 .00 With m = 6, we have: = ".91. [127] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. Residuals in order of right ascension. 533 Declination limits. Declination limits. 30 to + 40 30 to -f 40 Mean & v 1 >' Mean 6 TT' ' h. // h. // 1.1 7 + .04 12.9 19 .41 2.5 13 .17 15.2 10 + .01 5.0 14 .09 1C. 7 16 .15 7.0 8 .38 19.2 25 + .02 9.4 13 .39 21.2 13 4- .40 11.3 19 .10 22.7 8 + .21 If there is a real variation of the correction, proceeding with the right ascension, it is apparently of an entirely different nature from that adopted for So 51. The weights are small, and the observations are assumed to be practically Jree from any error of this kind. Wn56. Residuals in order of declination. Mean 6 ' 'o Co o // II + 86.1 63 .18 .07 + 76.7 20 .05 + .10 - 4 e t + 70.2 6 + .55 + -I? H- 66.3 4 4 .30 + .18 + 62. 1 27 + .50 + -17 + 50. 1 15 + .24 + -14 + 50.3 51 .16 4 .10 + 45.3 30 .10 + .05 4 38.9 64 + .08 - .01 + 32.0 15 + .37 .06 + 27.6 80 .05 .11 + 21.5 79 .23 .17 4 14.5 75 .16 .24 + 8.7 86 .16 .26 4 4.2 62 .69 .27 1.5 57 .26 .25 8.5 58 .13 .19 14.0 34 .08 .11 18.9 20 .28 .04 22.2 20 4 .09 4 .02 . 28. 5 31 H- .19 4 .13 The probable error, E, is derived from the outstanding residuals corrected further for the effect of terms in a given under Wn 47. With m = 6, we have: E= ".88. With a smaller value of -, we should have a smaller and probably more accurate / value of E. 534 UNITED STATES NOETHEEN BOUNDAKY COMMISSION. [128] Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to + 5 + 40 to 30 4. 40 to + 90 30 to + 90 Mean a IT 1 o' 7T 7 ro ; ic 1 I'o' 9? ro' ft. // // II // 1 19 . 35 61 .07 22 .10 83 .08 3 27 .77 42 .75 10 1.00 52 .80 5 18 .64 48 .41 12 .45 60 .41 7 12 .22 49 .01 14 .10 63 .04 9 3 .30 24 + .25 10 + .13 34 + .21 11 16 + .19 40 + -17 25 + .46 65 + .28 13 30 .02 47 .00 12 + .08 59 + .02 15 26 + .48 72 + .34 21 .23 93 -f .21 17 17 + .27 53 + .28 28 + .05 81 + .ao 19 18 .25 81 .04 21 .19 102 .07 21 33 + .22 76 + .07 38 .05 114 + .03 23 43 + .18 70 + .12 11 .06 81 + -11 For further explanation see Wu 47. Ps 56. Residuals in order of declination. Mean 6 vr 7 r a Co o ft */ + 86.6 26 .35 .32 1 = 2 Ei + 76.6 15 .31 .22 / + 70.8 15 .04 .16 + 66.2 10 + .06 .13 + 61.0 30 .22 .10 + 56.7 32 .17 .09 + 50.4 25 + .05 .11 + 45.2 30 . 05 .15 + 39.4 25 .47 .21 + 33.0 26 - .52 .26 + 27.6 37 .17 .30 + 21.1 48 .26 .35 + 14.5 53 .37 .36 + 8.9 70 .38 .36 + 4.0 32 .32 .35 1.7 47 .31 .33 8.5 43 .29 .23 14.1 15 .07 .08 18.8 12 + .11 + .12 21.9 13 + .20 + .12 28.1 17 + .42 + .50 After the further correction depending on a (to be explained), the outstanding residuals, with m = 7, give: E= i ".46. [129] REPORT OF TEE CHIEF ASTRONOMER, APPENDIX H. 535 Residuals in order of rifjht ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to + 6 + 40 to 30 .(. 4QO to _j_ 900 30 to + 90 Mean * r ' TT' fg TT' n/ TT' r' ft. n ,1 // II 1 8 - .15 21 + .05 25 + .23 46 + .15 3 11 + .15 23 + .13 13 + .01 36 + .08 5 15 + .07 37 + .09 13 H- .12 50 + .10 7 4 + .70 32 + .17 4 -1- .10 36 + .16 9 4 + .30 24 f .25 4 + .30 28 + .25 11 10 + .55 33 + .11 27 -j- .09 60 + .10 13 22 + .21 30 + .15 22 .11 52 + .04 15 19 + .04 40 .05 23 .01 63 .03 17 10 - .35 33 .25 19 .13 52 .21 19 20 .28 50 .31 14 .01 64 .25 21 19 + .01 44 .17 20 .03 64 .13 23 25 .30 38 .24 11 .23 49 .23 Tbe dependence of r ' on right ascension is undoubted. From the column 30 to + 90, 1 derive: + ".19 sin a ".07 cos . From the tables exhibited success! vely under Ps 60, Ps 64, and Ps 66, I find : Year. Formula of correction. 1860 1864 1866 + . 18 sin a 4- . 17 sin a + . 19 sin a . 04 cos a . 00 cos a . 10 cos n From the proper combination of the four sets, we have: + (".20 ".Ot) sin a (".05 ".01) cos . This is adopted as the definitive correction for each of the four catalogues, since there appears to be no marked increase with the time. This correction might be approximately computed in the following manner: If in the definitive formula of correction* for the declinations of the Fundamenta south of + 51,5 we substitute 30 for S, we shall have for that part of the correction depending on : ".82 sin a + ".07 cos a. If, further, we suppose that the mean declination of the stars of the Paris standard catalogue, chiefly used for obtaining zenith points, is about +31, that the catalogues making up the Paris standard are free from errors depending on , and that their mean epoch is about 1845, we shall have for the epoch 1SG1 (about the mean of the entire Paris series) as a correction to Paris observed declinations : ( + ".82 sin a + ".07 cos a ) x = + ".146 sin a - ".012 cos . Of course, if the mean epoch of the catalogues making up the standard is earlier than 1845, this correction will be larger. SrcttMI. VII. 536 UNITED STATES NORTHERN BOUND AEY COMMISSION. [130J Bs 56. Residuals in order of declination. Mean d IT 'o Co + 86.9 27 // + .30 // + .24 c 1 + 76.4 19 + .23 + .31 ___ O e, + 09.8 11 + .03 + .31 + 01. 8 20 + .30 + .25 -t- 56.9 17 + .15 + .13 + 50.6 39 - .07 .10 + 45.6 16 .93 .33 + 38.3 20 .64 .52 + 32.8 24 .35 .50 + 27.4 36 .23 .41 + 21.2 34 .71 .45 + 14.2 37 .54 .64 + 8.5 36 .44 .72 + 4.6 24 1.50 .74 2.0 21 .73 .59 8.4 18 + .18 .30 14.1 18 .23 .21 19.3 9 .11 .23 22.2 11 .37 .24 28.7 10. .73 .29 1 With m = 7, we have: E = ".95 Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. + 40 to 30 + 40" to _|_ goo 30 to +90 Mean a V? r' K 1 o' It 1 rj h. II // n 1 21 .no 19 .17 40 .36 3 13 1.76 6 .17 19 1.25 5 14 + -41 t + .21 21 + .35 7 10 + .92 1 + .20 11 + .85 9 25 + .14 13 + .40 38 + .26 11 22 .16 16 + .32 38 + .04 13 10 .01 11 + .11 21 + .05 15 46 + .28 13 - .08 59 + .21 17 30 + .03 19 + .09 49 + .05 19 43 + .06 12 .04 55 + .04 21 25 .29 25 .13 50 .21 23 34 .05 10 .24 44 .09 A considerable correction depending on a is indicated. The residuals from limits 30 to + 900 gi v e : ".04 sin a ".28 cos a. But, since this result is entirely opposed to that derived from the later Brussels work, the correction is neglected. This could do but little harm, since the observations receive small weight. [131] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. Ce5G. weights are formed as in the two preceding Cambridge catalogues. Residuals in order of declination. 537 Mriui i TT' o Co o // II + 87.5 32 .10 .22 + 75.8 12 .50 .30 + 70.7 12 .51 .35 + 65.7 11 - .03 .43 + 00.7 44 .64 .53 + 56.9 30 .45 .69 + 49.2 28 1.25 1.16 + 45.4 30 1.39 1.36 -j- 39.3 28 1.47 1.45 + 32.7 14 1.22 1.35 + 27.9 42 1.21 1.22 + 20.5 28 .96 .92 + 14.5 52 .59 .66 + 8.9 33 .56 .58 + 5.2 9 .96 .57 0.9 10 .53 .55 8.3 19 .68 .50 13.9 12 .32 .47 19.1 4 .29 .43 21.6 3 + .77 .41 26.2 4 .47 .38 With m = 5, we have: E = ".GO. Residuals in order of right ascension. Declination limits. Declination limits. 30 to +90 30 to +90 Mean a 7T 7 'c' Mean a K 1 n>' h. // h. // 1 41 + .09 13 39 + .33 3 8 + .06 15 54 .11 5 22 + .02 17 44 .10 7 27 + .01 19 64 + .12 9 41 .24 21 51 - .09 11 48 .02 23 26 + .29 538 UNITED STATES NORTHERN BOUNDARY COMMISSION. [13s the probable minimum error of a difterence of declination, Gh 57 C. G. H. r.8 (V. J. S.. X. 200). 540 UNITED STATES NORTHERN BOUNDARY COMMISSION. [134] Re 58. Residuals in order of declination. Mean <5 JT* o Co // If + 86.3 + 75.8 17 14 [- -02] [+ .11] + .40 + . 6sJ 1=2 E, + 71.3 12 -j- .82 + -71 I + GO. 9 11 + .76 + .71 + 61. I 24 + .55 + .62 + 56.7 26 + .52 + .51 + 50.6 27 + .35 + .23 + 45.8 15 + .48 .07 + 39.4 30 .67 .45 + 33.1 24 .63 .71 + 27.4 30 .82 .77 + 21.1 34 .63 .CO + 14.6 35 .41 .32 + 9.1 48 .11 .03 + 4.3 23 + .18 + .24 1.5 29 + .59 + .57 8.5 22 + .92 + .76 15.9 17 + .6 + .7? 22.4 11 +1.1 + .54 27.9 12 .6 + .22 With m = 5, we have : E = ".80. ".77 is adopted. (See Re 45.) Iii drawing the curve I have been much assisted by the very complete dis- cussion of this catalogue in Volume V. of the Vicrteljahrsschrift der Ast. Ges. The examination for terms in a, however, fails to confirm Table IV., given in the place cited, as will appear from the following : Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. 30 to + 5 30 to + 40 30 to +90 Mean a TT' ro' 7T' ro'. IT' r<> ft. if // a 1 4 1.45 28 .35 54 .01 3 7 .37 13 .30 19 + .02 5 12 .32 28 .51 37 .32 7 6 .15 31 + .05 34 .01 9 3 + .90 25 .01 37 .12 11 9 + .23 25 .02 37 .25 13 11 + .01 19 + .25 32 -f .26 15 13 .06 29 + .17 45 .18 17 5 .06 25 .35 44 .32 19 9 .31 31 .07 44 + .04 21 9 + .83 27 + .53 41 + .51 23 14 .03 26 + .27 43 + .36 The correction depending on a, if it exists, is so uncertain, from the small weight, that no attempt at discussion is made. The probable error of the residuals in last column varies from ".12 to ".18. [135] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 541 Ps 60. Residuals in order of declination. Mean 3 71-' '"0 Co o a // + 86.8 20 .15 .19 1_0 + 70. (i 13 .47 .12 e t ' ' + 70.8 13 .03 .05 + 66. 2 8 + .03 .00 -f- 60.8 29 + .05 + .04 + 56.6 28 + .03 + .06 + 49.7 25 + .07 + .10 + 45.2 27 + .23 + .10 -f- 39.5 26 .12 + .10 + 3:5.0 31 .19 + .03 + 27.4 47 .06 .03 + 21. 1 57 .03 . .11 + 14.6 58 .12 .16 + 9.1 86 .26 .19 + 4.1 33 .15 - .20 1.7 52 .16 .16 8.7 45 .08 .06 14.1 17 + .03 + .07 18.9 12 + .35 + .24 21.9 13 + .21 + .41 27.9 16 + .76 + .62 The outstanding residuals are first corrected for the effect of terms in a, as found for the entire Paris series. (See Ps 56.) With m = 7, we have : E = ".35. Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to +5 30 to +40 -f-40 to +90 30 to +90 Mean a if rj is 1 ro' it 1 ro' ?r' 'o' A. II // // // 1 10 .05 47 .00 26 + .08 73 + .03 3 13 + .07 26 .10 11 + .32 37 + .02 5 15 + .25 44 + .16 12 + .21 56 + .17 7 4 -j- .50 39 + .17 1 + .50 40 + .18 9 5 .00 35 + .23 5 .02 40 + .20 11 12 + .25 40 + .12 24 + .08 64 + .10 13 23 + .07 32 + .0-2 15 .09 47 .02 15 19 .04 43 .11 24 .13 67 .12 17 10 .10 37 .14 31 .11 68 .13 19 19 .24 49 .25 35 .15 84 .21 21 20 .07 50 .27 20 .05 70 .20 23 25 .02 40 + .01 8 .10 48 .00 For general explanation sec Ps 56. 542 UNITED STATES NOKTHEKN BOUNDAKY COMMISSION. BsGO. Residuals in order of declination. Mean 6 TT' 'o Co o It // + 86.7 38 + .21 + .'24 + 76.6 19 + .31 + .36 e -j- 71.4 18 + .64 + .40 / + 66.4 7 + .32 + .39 + 61.6 32 + .53 + .30 + ">6.2 31 + .03 + -14 + 51.2 43 .15 .11 + 45.6 19 .47 - .28 + 38.6 32 .44 .31 + 33.0 27 - .20 .21 + 27.5 57 .14 .04 + 21.5 64 + .11 .03 + 14.8 65 - .32 .08 + 9.2 83 .01 .09 + 3.2 38 .27 .05 1.6 53 + .10 .02 8.5 45 - .10 .00 14.0 24 + .03 .00 18.8 14 + .13 .00 >;2.4 19 + .21 .00 28.2 19 .25 .00 The curve from which Co is taken is derived from the mean of Bs 60 and Bs 65, since there is no reason for supposing the two to difler. Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to +5 30 to + 40 + 40 to + 90 30 to + 90 Mean a 7T 7 ro' n 1 'V TT' ro' w> o' ft. ,1 // // 1 11 .05 47 .16 29 + .01 76 .10 3 18 .24 30 + .07 8 + .20 38 + .10 5 18 + .31 50 + .16 12 .08 62 + -11 7 11 + .75 46 + .40 6 + .60 52 + .42 9 7 .10 33 .09 18 + .12 51 .02 11 15 4. .05 43 + .05 18 .31 61 .05 13 28 .28 40 .17 14 .39 54 .23 15 18 .14 54 .22 14 .32 68 .24 17 12 .40 49 .28 25 + .09 74 .16 19 16 + .13 53 .07 20 .17 73 .10 21 20 + .04 46 .02 34 + .09 80 + .03 23 20 + .15 46 - .12 12 .12 58 .12 There is n tolerably well-marked correction indicated, which is substantiated by the examination of Bs 65. From the combined values of r ' in the limits 30 to -f 90, we have : - (".17 ".03) sin a + (".005 ".03) cos a. [137J EEPOET OF THE CHIEF ASTEONOMER, APPENDIX H. 543 This is very nearly what might have beeii predicted from the discussion of Brad- ley's declination, the zenith-points at Brussels being derived from a standard catalogue of a much earlier epoch, with proper motions computed from the Fundamenta. Correcting the values of r for the curve and the above formula, with m = 8, we have for Bs 60 : E = ".59, Me 62. Residual* in order of declination. Meau A vr' n> Co o n // + 48.6 3 1.77 p _ + 45.4 5 .99 1 = 2 + 38.7 4 + .98 + .49 e i + 32.4 10 + .58 + .44 + 27.1 25 + .54 + .40 + 21.0 28 + .36 + .38 -j- 14.7 37 + .22 + .38 + 9.2 39 + .35 + .56 + 4.2 22 + .75 + -74 1.2 81 + 1.13 + .88 8. 5 24 + .83 + .87 14.0 15 + .48 + .77 18. 6 11 + 1.33 + .66 22. C 12 j. .90 + .57 28.2 14 + .33 -j- .46 34.8 2 + .52 + .21 41.1 1 .08 + .06 50.1 2 .12 .04 59.4 6 .30 .20 75.1 3 .19 .14 The correction here determined is applicable in addition to the correction given in Introduction to Williamstown, 1861-'63 (pp. xxi and xxii). With m = 6, we have : E = ".90. This large probable error, nearly twice that of Me 68, found in precisely the same way, may be partly owing to the neglect of correction proceeding according to a. The observations themselves are known to be less exact* than those of Me 68, but appar- ently not in the ratio indicated above. In the comparison of Gh 57 Me 62t Dr. Gylden finds : + ".07 cos a + ".14 sin a ".40 cos 2 a ".34 sin 2 a. Something like this is indicated in the examination below, and probably has a real existence. On the whole, I thought it not advisable to investigate the correction, what- ever it is, depending on a. Fide V. J. S., vol. v, p. 289. tI6W.,p.291. 544 UNITED STATES NORTHERN BOUNDARY COMMISSION. Residuals in order of right ascension. [138J Declination limits. Declination limits. Declination limits. 30 to + 5 + 5 to + 40 30 to + 40 Mean a * V 7T 1 ro' tt> r a ' ft. // II II 1 1 .17 19 .08 26 .10 3 11 .20 3 .30 14 .24 5 16 + .18 26 .64 42 .33 7 8 + .10 18 .13 26 .06 9 4 + .10 14 + .15 18 + .14 11 10 -f .12 14 + .41 24 + .29 13 14 + .69 2 + .60 16 + .65 15 9 + .28 10 + .92 19 + .62 17 C .70 12 .19 18 .36 19 7 .05 14 .25 21 .31 21 12 + .37 10 + .29 22 .07 23 18 + .19 10 + .12 28 + .16 Wn 64. The weights (n 1 ) are constructed as explained in Section V. Residuals in order of declination. Mean <5 7!-' ro' Co o // // + 87.1 95 + .10 + .10 + 76.1 56 + .26 + .11 + 70.7 51 + .27 + .08 + 66.1 38 .03 + .06 + 62.0 43 .41 + .03 + 50.2 19 .or .01 + 50.6 26 + .32 .05 + 45.7 22 + .11 .09 + 38.8 24 + .08 .14 + 33.0 11 .04 .21 -f 27.4 59 .33 .29 + 21.4 67 .44 .38 + 14.5 79 .31 .45 -j- 8.9 80 .59 .46 + 4.5 38 .44 .44 1.3 40 .11 .39 8.8 37 .38 .29 13.9 15 .60 .21 18.9 8 -f -4 .12 21.4 5 + .0 .07 28. a 15 .1 + .06 Correcting the outstanding residuals by the formula embracing terms in (see Wn 47) and with m = 6, we have: J?= ".71. [139] EEPOET OF THE CHIEF ASTRONOMER, APPENDIX H. 545 Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to +5 30 to +40 + 40 to + 90 30 to -f- 90 Mean a m 1 *' TT' r,' W r ' 7T 7 ro' h. II II // // 1 3 .50 50 .19 62 .05 112 .12 3 8 .25 22 .12 8 .36 30 .18 5 11 + .04 36 .53 17 .03 53 .37 7 2 .20 29 .24 11 .50 40 .31 9 2 + .20 29 + -17 10 + .48 39 + .25 11 6 .20 35 .16 29 .32 64 .23 13 20 + -47 34 + .32 32 + .28 66 + .30 15 16 + .33 45 + .40 48 + .25 93 + .31 17 12 + .10 41 + .34 32 + .26 73 -f .30 19 12 .37 54 .08 31 .37 85 .19 21 20 + .21 41 .02 45 + .23 86 + .H 83 30 .09 51 + .05 25 .06 76 + .01 The general explanation is given under Wn 47. Gh 64. Residuals in order of declination. Mean 6 71-' ra Co H II + 86.7 47 + -11 .00 + 76.5 41 .23 .00 = O + 70.7 47 .12 .00 1 + 66.4 41 + .06 .00 + 61.4 54 + .07 .00 + 55.9 28 .14 .00 + 51.0 53 + .20 .00 + 45.6 53 .12 .00 + 40.2 68 + .12 .00 + 32.8 55 .03 + .07 + 27.2 87 + .16 + .12 + 21.1 101 + .13 + .15 + 14.6 102 + .15 + .12 + 8.9 122 + .05 + .05 + 4.2 50 + .19 .00 - 1.2 64 .22 .09 8.6 65 .07 .03 - 14.1 26 + .07 + .H 18.8 17 + .61 + .24 22.1 21 + .25 + .32 28.1 23 + .55 + .49 With m = 5, we have : E = ".49. ".48 is adopted for the definitive weights, as explained under Gh 57. N B 35 546 UNITED STATES NOETHEEN BOUNDAEY COMMISSION. Residuals in order of right ascension. [140J Declination limits. Declination limits. Declination limits. 30to + 5 30 to +40 30 to + 90 Mean a 7T 7 V a 1 n>' TT' rj h. it II II 1 11 + .57 76 + .14 114 + .05 3 16 + .09 37 .09 54 .01 5 25 .01 73 + .03 104 + .04 7 7 .49 68 .15 77 .13 9 7 .40 58 .14 76 .02 11 21 .14 60 .05 91 .11 13 33 .14 49 .12 79 .05 15 28 .06 76 + .01 116 .03 17 9 .00 61 + -11 103 + .09 19 22 + .02 78 - .02 121 -.06 21 27 + .23 69 + .18 138 + .14 23 33 + .05 00 + .13 85 + .04 For remarks see Bn 66. Ps 64. Residuals in order of declination. Mean <5 TT' 'o Co o // // + 86.6 20 .18 .22 C - + 76.6 12 .40 .26 =2 P + 70.7 11 .16 .27 / + 66.2 8 .04 .27 + 61.1 21 .30 .25 + 56.3 21 .17 .22 + 50.6 30 .17 .22 + 45.3 25 .33 .26 + 39.5 25 .39 .30 + 32.8 33 .31 .28 + 27.2 47 .15 .16 + 21. 56 .03 - .06 + 14.6 53 .06 .07 + 9.1 77 .21 .16 + 4.0 25 .29 .22 - 1.8 51 .16 .21 8.5 40 .15 .13 14.1 15 + .02 + .04 18.9 10 + .41 + .29 21.9 13 .08 + .43 27.9 15 +1.01 + .90 With the correction depending on a, and with m = 9, we have :- E = ".37. From Ps 66, we have : E = ".41. The mean is adopted, since both series are essentially the same. [141] REPOET OF THE CHIEF ASTEONOMEE, APPENDIX H. 547 Residuals in order of riglit ascension. Declination limits. Declination limits. Declination Iimit8. Declination limits. 30 to + 5 30 to + 40 + 40 to + 1)0 30to + 90 Mean a If' ro' ' rtf If 1 ro' ' ro' li. ,1 II // // 1 8 - .25 42 + .04 25 + .14 67 + .08 3 12 + .13 24 + .05 13 + .05 37 + .05 5 16 + .38 45 + .19 9 .07 54 + -14 7 4 + .60 40 + .13 1 + .30 41 + -14 9 5 + .20 36 + .08 8 + .30 44 + -12 11 10 + .22 37 -.01 23 + .16 60 + .05 13 23 .10 32 .03 14 + .03 46 -.01 15 20 + .03 42 .15 15 .09 57 .14 17 10 .06 34 .15 15 .17 49 .16 19 13 .05 48 .27 12 .24 60 .27 21 21 + .05 39 .19 17 .01 56 .14 83 16 .08 32 + .50 4 .00 36 + .04 The correction is derived under Ps 56. Bs65. Residuals in order of declination. Mean 6 7T rt Co o n II + 87.0 22 + .27 + .24 f + 76.6 18 + .22 + .36 - = 3 f f + 70.5 9 + .47 + .40 + 67.3 1 + .f5 + .39 + 61.8 16 + .37 + .31 -f 55.9 17 .01 + .10 + 50.2 30 .06 .17 + 45.2 21 .22 .29 -f 39.0 26 .30 .31 -f 32.5 26 + .12 .19 + 27.4 51 .05 .03 + 21.3 47 + .27 + .0:J + 14.4 48 .08 .08 + 8.8 67 + .07 .09 + 4.2 27 + .14 .05 1.6 47 .12 .02 8.6 42 + .02 .00 14.0 22 + .26 .00 18.8 15 + .15 .00 22.3 18 + .13 .00 28.2 8 .05 .00 From the final residuals, corrected as in the case of Bs 60, we have (with m = 8): E = ".44. I have considered this large increase in precision to be real, and have adopted the respective values of E, as determined, in constructing the definitive table of weights lor Bs CO and Bs 65. 548 UNITED STATES NORTHERN BOUNDARY COMMISSION. [142] Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to +5 30 to +40 4. 4QO to _j_ goo 30 to +90 Mean a 7T 7 rj K 1 rd n 1 tV TT' r' h. a it n // I 11 + .35 43 + .16 20 .09 63 + .08 3 13 + .55 23 + .39 7 + .10 30 + .32 5 13 + .12 37 + .35 7 + .13 44 + .32 7 5 + .50 28 + .32 3 + .20 31 + .31 9 7 .00 28 + .14 10 + .29 38 + .18 11 12 + .12 36 + .20 18 + .26 54 + .23 13 26 .20 38 .06 10 + .10 48 .03 15 20 + .04 41 .00 13 + .07 54 + .01 17 10 .06 44 .04 15 .11 59 -.06 19 13 .05 45 .18 7 + .19 52 .13 21 21 + .05 43 + .05 19 -.07 62 + .01 23 16 - .08 34 .00 8 .34 42 -.06 For farther explanations see Bs CO. Ps 66. Residuals in order of declination. Mean 6 7T 7 n> Co o // II + 87.4 16 .32 .20 e + 76.7 7 .10 .20 7= 2 + 70.9 5 .15 .18 c / + G6.0 5 .19 .12 + 60.9 19 + .01 .03 + 56.5 19 + .07 .00 + f>0.4 20 + -14 - .01 + 45.2 27 .13 .07 + 39.4 26 .26 .15 + 32.9 34 .19 .16 + 27.4 47 .06 .10 + 21.2 51 .03 .06 + 14.7 52 - .11 .16 + 9.1 78 .29 .25 + 4.1 26 .32 .27 1.8 43 .21 .24 8.5 41 .25 .19 14.1 14 + .01 .09 18.7 12 .14 + .02 21.9 12 + -11 + -14 27.9 15 + .56 + .39 In the same manner as with Ps 64, we have : H = ".41. .39 is adopted, as previously explained. [143 REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 549 Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to + 5 30 to + 40 + 40 to + 90 30 to +90 Mean a TT' 'o' T n,' TT' ro' K ro' *. // II It // 1 8 + .35 45 .08 18 + .18 63 .00 3 10 .22 22 .21 13 + .18 35 .07 5 16 + .10 42 + .26 8 + .05 50 + .26 7 3 +1.40 36 + .28 .00 36 + .28 9 4 + .30 33 + .11 8 .07 41 + .08 11 10 + .52 32 + .24 16 + .12 48 + .20 13 22 + .14 31 + .10 11 + .37 42 + .17 15 16 .15 40 .17 12 + .27 52 .07 17 9 + .39 35 .20 9 + .02 44 .15 19 19 .11 45 .21 10 .64 55 .29 21 16 .08 46 .14 16 .22 62 .16 23 20 + .04 36 + .03 7 .31 43 .02 The discussion of correction is given under Ps 56. Bn66. Each value of r receives weight one. Residuals in order of declination. Mean 6 7T 'o Co o // // + 85.6 2 + .34 + .41 + 70. 3 4 + .47 + .67 + 71.0 6 + .82 + -71 + 66.1 3 + .72 + .57 + 62.0 5 + .26 + .25 + 56.0 4 .45 .28 + 50.6 10 .58 .54 + 45.4 6 .63 .59 + 39.2 3 .6-2 .56 + 32.8 5 .27 .45 + 27.0 5 .58 .32 + 20.7 9 .19 .25 + 15.0 4 .43 .20 + 9.0 8 .00 .21 + 4.1 4 .34 .27 - 1.3 8 .36 .35 8.2 4 .35 .40 14.0 2 + .05 .40 18.7 3 .76 .40 22.5 3 .48 .40 28.8 1 [+.51] [- .40] The correction in order of declination, as well as right ascension, appears to re produce in proper proportion and with opposite signs the peculiarities noticed in the correction for Bradley's declinations. 550 UNITED STATES NORTHERN BOUNDARY COMMISSION. Residuals in order of right ascension. [144] Declination limits. Declination limits. Declination limits. 30 to + 6 30 to + 40 + 40 to 4- U0 Mean a * ro' if rj w' >v fi. II II // 1 2 .30 6 .20 5 + .14 3 2 + .25 4 + .37 2 4- .10 5 3 + .13 6 4- .07 4 + .08 7 2 4- .CO 5 4- .48 9 3 + .03 4 + .12 11 2 -f .65 6 4- .57 4 .33 13 4 -f- -07 6 .00 2 + .25 15 2 .55 4 .45 4 .30 17 1 .30 4 - .10 5 .14 19 2 .64 4 .31 2 + .90 21 1 + .10 5 .32 6 .30 23 4 .10 5 .06 3 .03 The "Northern stars" were reduced on other principles than those adopted for the zone 30 to + 40. Argelander has given (in Volume VI. of the V. J. S. derAst. Oes., p. 100) the results of a very careful comparison of the difference of declination between Gh 64 and Bu GG. He finds (p. 114, ibid) for the zone - 30 to + 40: (1; ".425 + 0".313 sin a 0".201 cos a, as the difference "Gr. Bonn." From the above table, declination limits 30 to + 400, I find : _ (2) + 0".309 sin a 0".151 cos a, as the correction to Bn 66. This coincidence between the periodic terms of (1) and (2) tends to prove that the discrepancy between Gh 64 and Bn 66 is almost wholly due to error of the latter. Taking the mean epoch of the catalogues upon which are based the declinations of Wolfer's Tabulce Reductionum (also Berlin Jahrbuch, on which Argelander's (1866) decli- nations are founded) to be 1832, and assuming their mean to be practically free from error, proceeding according to right ascension, we shall have as the correction to these declinatious (Berlin Jahrbvch) for 18GG, and for + 20 declination: x (+ ".84 sin a + ".17 cos a) . + ".37 sin a + ".06 cos a.* Considering the great uncertainty of the individual positions of Wolfer'a catalogue for 1866, this may be regarded as a very fair approximation to (2), which is adopted as the definitive correction for the zone 30 to + 40. The Northern stars appear to require no such correction. With m = 8, we have : E = ".31. * Argelander finds (V. J. S., Vol. V., p. 110.) Gr. 1864 Wolfer's== + 0".475 sin (a 2 58'.) [145] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 551 Re 66. Owing to the extreme uncertainty of the individual corrections, the comparisons with definitive curves are of little interest, and for convenience they are here omitted. The residuals were all plotted on a single sheet, so that peculiarities common to all the years were easily detected. Residuals in order of declination. Meand Re 62. Re 63. Re 64. Re 65. Re 60. Re 67. Re 68. Re 69. * r a V 1 fa ir 7 TO nf n> K> r<> TT' *? r a TT' TO o H it it ii 11 II it ii + 87 34 .25 38 . 12 34 + .33 27 + .21 22 + .84 20 + .16 33 + .08 36 + .05 + " 12 .63 8 1.41 18 + .32 8 + .i 6 1.60 1 1.00 6 1 * vv .32 5 +1 90 17 .82 10 r * .16 36 .46 r * + 45 5 1.50 1 + .60 2 -1.10 3 +1.03 9 j *. v v + .14 6 1.03 6 +1.26 22 .44 -j- 39 4 1.45 6 4- .05 7 .37 40 .98 89 + .07 54 .55 + 4 30 1.44 28 .37 24 + .43 26 .16 19 .67 12 1.80 10 1.14 18 .58 31 .85 40 + .15 24 + .07 23 + .22 80 1.16 14 .67 16 .71 27 .70 8 34 .61 31 .27 18 + .86 30 + .46 21 .5<>' V ' ir 1 V ' ' h. II it II n II II // II i 37 + .18 37 .11 38 .25 44 + .53 40 + .05 33 .04 40 .19 61 + .17 3 18 .04 21 .30 11 + .04 16 + .24 19 + .22 21 .89 H .29 18 + .28 5 37 + .29 31 .18 12 - .CO 22 - .06 .-,() + .18 26 .19 86 + .79 21 + .13 7 32 + -41 36 + .30 22 .39 21 .36 36 .43 30 .19 88 + .67 24 .28 9 27 + .52 26 .50 19 .07 14 + .13 11 .02 16 + .35 1! - .05 39 .10 11 26 + .09 34 .24 28 .25 27 .03 93 .12 38 + .37 :*7 + .39 57 .05 13 27 + .06 30 + .28 17 .25 17 .21 21 + .12 30 + .03 81 .04 52 + .20 15 r.2 .11 45 + .10 31 + .15 44 .02 :!~ + .18 44 + .27 46 .06 69 + .11 17 39 .65 45 + -17 15 + .77 31 .98 46 .25 46 + .06 43 + .OS 88 - .06 19 51 .48 43 + .34 33 + .31 37 .66 38 .58 35 + .12 30 .28 74 .15 21 54 + .13 52 .07 .19 53 + .17 ;;i + .19 32 - .39 38 .21 56 + .16 23 34 .04 39 + .32 37 + .50 41 + .44 80 + .31 25 .08 2-2 .88 46 + .11 There appears to be no consistent, well-defined correction depending on A. R. The division into zones proved equally unavailing for the discovery of such a correction. Lc67. Each value of r receives weight one. Residuals in order of declination. Mean <5 7T 7 r a Co o H II + 86.7 5 + .38 + .38 + 76.8 4 + .82 + .87 + 71.0 6 + 1.20 + .99 + 66.4 5 + 1.18 + .93 + 60.8 13 + .89 + .74 + 56.5 8 + .36 + .52 + 50.9 14 .00 + .23 + 45.6 11 .23 .01 + 40.1 11 + .10 .23 + 33.3 8 .09 .40 + 27.5 9 .49 .50 + 21.2 10 .81 .55 + 15.5 11 .48 .53 + 8.8 13 - .33 .46 + 4.0 7 .35 .43 1.7 11 .54 .43 8.6 7 .51 .43 14.0 2 .32 .40 18.7 3 .00 .32 22.5 3 .32 .24 28.8 1 .40 .08 With m 8, we have : E = ".27. [147] EEPOET OP THE CHIEF ASTBONOMEE, APPENDIX H. Residuals in order of right ascension. 553 Declination limits. Declination limits. Declination limits. 30 to + 5 30 to +40 30 to +90 Mean a it o' * ' *> ro' ft. // II a 1 2 .05 10 .00 18 .03 3 3 + .07 5 + .12 8 - .04 5 4 + .25 10 + .14 17 + .16 7 2 .00 7 + .01 8 - .01 9 1 .00 5 + .22 10 + .06 11 3 + .10 8 .00 17 .15 13 5 .23 7 .33 10 .12 15 2 + .05 7 + .14 14 + .04 17 1 + .10 7 + .21 15 + .16 19 3 + .20 10 + .07 18 + .04 21 2 .30 8 + .09 16 + .02 23 4 .20 3 -.19 12 -.14 Ln 67. Each value of r receives equal weight. Residuals in order of declination. With m = 4, we have : E= ".137. Mean 30 to +40 30 to + 90 Mean a _/ 'o' 5T 7 'V JT* ro' h. a // II 1 11 .02 74 + .01 146 .03 3 11 + .53 33 + .23 46 + -I? 5 24 + -11 70 .04 111 + .02 7 5 + .88 65 .09 74 .08 9 7 .20 55 + .02 82 .01 11 17 .14 60 + .01 121 .14 13 33 .18 49 .02 84 .08 15 32 .00 78 + .01 128 .13 17 15 .17 72 .05 133 + .05 19 23 + .40 84 + .09 116 + -11 21 18 + .02 64 - .03 129 .00 23 29 .33 59 .26 84 .14 Re 72. The corrections for this series of annual catalogues are determined in tho came manner as those for Re 66. Residuals in order of declination. Mean S Re 70. Re 71. Re 72. Re 73. v> 'o TT' r a * ft 71"' >" o II If n II + 87 36 + .21 31 + .27 36 + .21 34 -t- .20 + 76 22 - .06 19 + .26 20 + .30 21 + .63 + 70 32 + .31 32 + .38 33 + .46 30 + .52 + 65 15 + .22 16 + .97 19 + .79 15 + .85 + 62 45 .10 46 + .38 46 + .-10 28 + .71 + 56 38 + .33 39 + .r>8 40 + .92 39 +1.09 + 51 35 + .09 28 + .45 33 + .42 27 + .39 + 45 30 + .25 21 .01 19 + .42 17 + .9 + 39 28 - .29 21 + .29 26 + .17 27 + .08 + 32 31 .66 20 .23 20 .29 29 .04 + 27 53 .68 60 .29 56 .22 53 .35 + 21 43 .56 44 .11 48 .02 38 + .17 + 15 51 .04 51 + .17 55 + .33 68 + .22 + 9 60 + .45 60 + .48 54 + .46 60 + .31 + 4 22 .11 22 + .85 24 + .23 19 .33 26 .15 30 + .14 28 + .37 31 + .07 8 25 .46 22 -.04 22 + .13 18 .97 14 11 .90 9 + .04 10 + .15 10 .12 19 5 1.04 6 .70 3 + -17 7 + .02 22 6 .15 7 + .30 9 .32 5 1.56 28 8 1.65 6 .38 6 .40 9 + .12 We have:- E = ".9. 1".00 is adopted, as previously explained. 558 UNITED STATES NORTHERN BOUNDARY COMMISSION. [152] Residuals in order of right ascension. Meau a Be 70. Re 71. Re 72. Re 73. Re 62-73. tf ro' TT 1 ro' JT' V JT' ro' ro' A. If // II II II 1 67 + .03 64 .93 58 4 .55 59 + .46 -4- .10 3 25 + .03 17 4 .49 20 + .37 22 4 .37 4 .01 5 46 + .55 35 4 .37 36 .14 41 4 .40 4 .19 7 3d .28 43 .05 41 .15 27 + .09 .07 9 29 .21 32 + .24 30 + .15 26 + .23 + .03 11 60 .09 57 .17 48 .21 59 -j- .04 .04 13 36 .14 52 .02 45 4 .06 35 .09 + .04 15 67 .27 76 + .03 66 .24 69 .08 .01 17 71 .20 55 + .05 65 .07 59 .46 .12 19 69 + .33 56 .23 70 .15 72 .45 .12 21 75 4 -14 59 .08 76 .04 67 .02 .00 23 39 .09 44 4 .06 42 + .60 36 .01 4 .16 For Re 73 there is an apparently well marked correction depending on a; but as it is not supported by the results of other years, I have thought it best to omit the discussion. Wn 72. The residuals are computed from the standard places for each year. In the dis- cussion, - = 3 is assumed. / Residuals in order of declinatioi DECLINATION SUB POLO. Wn70. Wn71-2. Wn73. Wn 74 * TUT A *' r Co n-' ro C 7t' ro Co *> ro Co 68 5 -"10 00 9 -'.'03 'OO // // 8 -'.'25 4 .% 75 14 4 -57 00 12 4 .00 00 7 .30 on 19 4 .36 4 .38 87 21 4 .07 00 35 4 .24 00 27 CO 00 34 4 .76 4 .21 ABOVE POLE. 4 87 27 4 .12 00 36 .39 00 29 4 .20 00 33 .24 .21 4 76 16 4 -14 00 8 4 .34 00 4 4 .20 4 .02 18 .35 .26 4 70 12 .56 00 9 .03 00 6 .29 4 .04 14 .19 .33 4 05 22 .09 00 23 4 -15 00 10 4 .31 4 .07 31 .48 .41 4 56 5 4 .62 00 2 4 1.19 .04 7 .16 4 -13 10 .72 .55 4 50 25 .45 .06 24 .04 ' .10 13 4 .36 4 .18 24 - .45 .62 4 46 15 .45 .08 18 4 .09 .15 16 .15 4 .23 20 .72 .67 4 39 29 4 .00 .11 32 .25 .23 32 4 -38 4 .32 44 .76 .74 4 33 9 .18 .13 13 .60 .28 13 4 .15 4 .41 15 .58 .79 4 27 54 .14 .15 69 . 35 .31 51 4 .49 4 .49 63 .91 .82 4 21 56 .00 .16 71 .27 .34 56 4 .56 4 .63 72 . 85 .84 4 14 41 .36 .16 76 .53 .33 58 4 .CO 4 .56 73 .69 .81 4 9 67 .27 .16 9 .26 .32 63 4 .48 4 .57 95 .64 .76 4 4 ii9 4 .19 .14 39 .06 .31 33 4 .81 4 .59 43 .87 .76 1 46 4 .02 .09 56 .29 .30 37 4- .51 4 .63 46 .74 .83 8.5 37 4 .08 .02 60 .49 .28 49 4 .79 4 -75 50 1.09 .815 14 16 4 .04 00 23 .09 .25 16 4 .86 4 .84 20 1.18 - .78 19 6 .59 00 11 .43 .23 8 4 1.57 4 .92 12 .36 .67 22 14 4 .41 00 13 .24 .22 12 4 1.81 4 .98 16 .78 ,60 28 13 .24 00 15 .09 - .20 11 4 52 4 l.l 18 .32 .45 34 1 1.3 2 4 -6 2 4 l.l * See explanation, p. 157. [153] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 559 The probable error is derived by comparing the corrected residuals (collected as cue for each star) with the standard A5'. With m 4:, we have: E =".84. Taking s as found in Section V., and e, as found for Wu 68 in the same section, we have: E = V(.70) 2 + (.25 f = ".74. The agreement is far from satisfactory. The former result, ".84, is adopted. The combined results of all the years are next arranged in order of right ascen- sion. Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. Declination limits. 30 to + 5 + 5to + 40 + 40 to + 90 30" to +90 Mean a 7T 7 '<>' IT 'V 7T 7 r a ' tf r<> ft. // n II // 1 39 + .34 162 + .16 88 + .37 289 + .25 3 15 + .08 40 .18 35 .07 90 .10 5 64 - .35 109 + .23 24 + .25 197 + .04 7 33 + .15 119 + .05 42 .36 194 .02 9 20 .13 88 .14 19 .08 127 .13 11 58 .16 131 .09 36 .57 225 .18 13 119 .05 53 + .23 60 + .12 2ii2 + .06 15 87 + .08 121 + .16 100 + .01 308 + .09 17 33 .05 113 .29 80 + .03 226 .14 19 64 + .01 148 + .01 70 .02 282 + .00 21 68 .44 62 .10 111 .14 241 .22 23 69 + .05 51 + .39 27 .17 147 + .13 As shown under Wn 68, the correction in order of A. R. found for the declina- tions of the mural circle is peculiar to that instrument or observing-room alone. The following tables exhibit the results deduced for systematic correction and weight of the various catalogues. 560 UNITED STATES NORTHERN BOUNDARY COMMISSION. [154 TABLE IX. Corrections to declinations. ORDER OF DECLINATION. & 1 o T-l 00 tS J3 m 1-4 OJ bC w -M- 8 .a C5 i p s gj o < o C-3 a O s w O d * ,-H CO A 02 Si K O O * CO m O // 00 00 00 .04 .14 .27 .42 .57 .70 .78 .83 .84 .80 .70 .54 .40 .35 .38 .47 .60 .74 .88 .98 1.00 1.00 TT CO & S M m 6 o +90 +85 +SO +75 +70 +65 +60 +55 +50 +45 +40 +35 +30 +25 +20 +15 +10 + 5 - 5 10 15 20 25 30 35 40 50 60 70 80 90 // // II II -.19 .22 .22 .23 .23 .22 .20 .18 .16 .15 .16 .17 .20 .21 .17 .05 +.04 00 .15 .24 .27 .25 .15 00 +.2 o +90 +85 +80 +75 +70 +65 +60 +55 +50 +45 +40 +35 +30 +25 +20 +15 +10 +05 5 10 15 20 25 30 35 40 50 60 70 80 90 00 00 00 00 00 00 00 .05 .20 .50 1.00 1.40 1.40 1.20 1.40 1.85 1.60 1.10 1.50 2.15 2.20 1.70 1.15 1.00 1.00 1.00 1. 00 00 +.14 +.29 +.38 +.30 +.14 .02 .01 +.12 +.10 .00 00 +.08 +.06 +.10 +.13 +.16 +.18 .+.16 +.13 +.09 +.06 +.06 +.06 +.07 +.10 +.13 +.16 +.19 +.25 +.33 +.43 +.55 +.67 +.78 +.90 "66 00 00 00 00 00 00 00 00 00 00 00 00 00 00 .05 .12 .17 .21 .24 .26 .27 .25 .22 .19 .15 .13 .12 .15 .21 .29 .38 .49 .60 .72 .84 .96 00 00 00 00 00 00 00 00 .02 .07 .13 .16 .22 .20 .29 .32 .36 .43 .52 .60 .68 .70 .70 + .10 + .12 + .15 + .15 + .13 + .08 00 .12 .31 .54 .76 .95 1.12 1.24 1.30 1.31 1.31 1.33 1.37 1.49 1.68 1.97 2. 50 2.85 2.95 +.40 +.40 +.40 +.40 +.38 +.31 +.24 +.17 +.07 .03 .16 .20 .17 .14 .10 .07 .03 00 .28 .38 .40 .52 .60 -.62 .60 .54 .38 .14 +.17 +.32 +.47 +.50 +.50 +.41 +.30 +.14 .03 -.20 .40 +."35 +.35 +.35 +.35 +.35 +.35 +.35 +.35 +.32 +.17 00 00 00 00 00 00 [+1.30] +1.30 +1.30 +1.30 +1.30 +1.30 +1.30 +1.30 +1.30 +1.30 +1.30 +1.28 +1.23 +1.17 +1.09 + .96 + .84 + .70 + .62 + .60 + .60 + .60 + .60 + .50 + .40 + .30 + .20 2." 66 1.10 .34 + .20 + .52 + .57 + .43 + .14 .06 .14 .14 .04 + .16 + .46 + .71 + .88 + .90 + .71 + .47 + .10 i .00 .08 .10 .00 * This correction is subsequently revised with the definitive AJ and Ap'. t Dollen's reduction. t A small minus correction deduced. || This correction is considered as applicable to Dt 30, after " com cliones ultima" (p. 357, Struve's Pos. Med.) have been added. ' The correction for S H 31 is applicable directly to the catalogue results as reduced with Young's refractions. ttFor the years 1833 and 1834 corrections must be applied for defective reading of barometer (see Cambridge Observations, 1835). To get actual corrections to catalogue results for those years, the effect of this correction must be added to the above. [165| REPORT OP THE CHIEF ASTRONOMER, APPENDIX H. 561 TABLE IX. Corrections to declinations Continued. ORDER OF DECLINATION. [+10] +.70 00 +.44 +.10 [+.55] 30 35 4-. 13 00 _1_ 01 35 40 +.27 + .05 +.08 40 50 + 7 + . 15 .14 50 60 +.11 -4- 27 20 60 70 00 + 26 20 70 80 00 + 13 08 80 90 00 00 00 90 * The correction for error of n-sumed latitude, flexure, division, &c., given in the introduction to the Williamstown catalogue, must also be applied. The true correction is, therefore : Correct on taken from introduction Me 62 + correction of above table. tTo the catalogue declinations from direct observations above pole for 1861 and 1862 \vaslirst added the correction ". 68 (+ ".68, below pole); and to the declinations of years 186:?-18(>5 =p".47, according as the declination results from observations above or below the polo. The actual correction is, therefore: These qunntities+ corrections from above table. [157] KEPOKT OF THE OUIEF ASTKONOMEE, APPENDIX H. 563 TABLE IX. Corrections to declinations Continued. OEDEE OP DECLINATION. 6 J CD & g CO m s CO to 6 J ts a i? g 1 g 1 o F a O -- o l~ a i 1 1 r* 1 Wn73. +f <* t- c * & o +90 +85 +80 +75 +70 +65 +60 +55 +50 +45 +40 +35 +30 +25 +20 +15 +10 +05 5 10 15 20 25 '10 it 20 ii +.20 +.26 +.32 +.38 +.40 +.39 +.26 +.06 .17 .29 .32 .27 .11 +.04 +.03 .08 .10 .06 .03 00 00 00 00 00 00 II .20 .20 .20 .20 .17 .11 -.01 00 .01 .07 .15 .18 .14 .06 .06 .15 .24 .27 .28 .24 .17 .07 +.07 +.25 +.48 +.75 II +.40 +.41 +.55 +.71 +.71 +.54 +.05 .36 .56 .60 .57 .50 .38 .28 .24 .20 .20 .25 .33 .40 .40 .40 .40 .40 [-.40] li 4- .22 + .47 + .72 + .94 +1.00 + .90 + .70 + .44 + .18 .04 .23 .37 .47 .54 .55 .52 .47 .43 .43 .43 .43 - .39 .30 .18 .05 II 00 00 00 .01 .05 .10 .17 .22 .25 .26 .2o .26 .26 .26 .26 .25 .23 .19 .12 .05 +.03 +.11 a a 00 + .02 + .05 + .10 + .15 + .20 + .26 + .32 + .36 + .39 + .42 + .45 + .47 + .50 + .53 + .55 + .57 + .58 + .59 + .59 + .60 + .63 + .70 + .80 + .93 +1.09 a 00 .09 .15 .20 .25 .30 .34 .37 .40 .41 .42 .42 .37 .33 .33 .40 .52 .65 .80 1.00 1.20 1.43 1.66 1.93 r oi o +90 +85 +80 +75 +70 -t-65 +60 +55 +50 +45 +40 +35 +30 +25 +20 +15 +10 +05 5 10 15 20 25 30 35 40 50 60 70 SO 90 .00 .00 .00 .00 .00 .00 .00 .03 .06 - .09 .11 .13 .14 .15 .16 .16 .16 .15 .10 .05 .00 00 00 00 00 00 00 00 00 00 00 00 00 .05 .10 .16 .22 .26 .30 .33 .34 .33 .32 .31 .30 .29 .27 .25 .23 .21 19 00 00 00 + .02 + .04 + .07 + .10 + .14 + .18 + .24 + .30 + .38 + .46 + .51 + .54 + .56 + .57 + .58 + .61 + .69 + .77 + .86 + .94 +1.03 +1.11 +.07 .04 .14 .24 .33 .41 .49 .56 .62 .68 .73 .77 .81 .83 .84 .82 .76 .75 .82 .85 .86 .76 .65 .53 40 2'j .25 .26 .27 .27 .25 .21 .22 . 26 .30 .30 .22 .10 .05 .06 .15 .22 .23 .19 - .10 + .07 + .35 + .66 +1.00 +1.35 i+i~25] [+1.00] [+ -67] + .48 + .11 .08 .15 .15 .15 .15 .16 .18 .21 .26 .30 .32 .36 .38 .40 35 40 50 60 70 80 90 .17 .29 .34 .22 .12 .05 00 'Applicable to declinations derived in this paper (Section V.). t Applicable to declinations of annual catalogues after correction, as explained in Section V. tAs explained elsewhere the correction, +".82, to the declinations of 1874, south of Wn. zenith was neglected by accident for stars south of 12 declination, and the error discovered too late to be corrected in the succeeding results. As actually used in making up the definitive C,, of the final dis- 564 UNITED STATES NORTHERN BOUNDARY COMMISSION. [158J TABLE IX. Corrections to declinations Continued. EADCLIFFE ANNUAL CATALOGUES. 6 62.* 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. <5 it II II a II II // II It o +00 00 00 +.40 + .10 + -74 00 + .10 00 + .10 +.23 +.17 .00 +90 +1-5 .26 .17 +.2C + .2? +1.00 00 + .15 00 + .13 +.27 +.94 +.21 +85 +80 .48 .34 +.13 + .38 +1.26 00 + .18 00 + .17 +.31 +.3y +.39 +80 +75 .66 .50 00 + .41 +1.43 00 + .19 .03 + .19 +.36 + .40 +.52 +75 +70 .86 .63 .13 + .40 +1.50 00 + .20 .06 + .20 +.40 +.48 +.07 +70 +65 1.03 .73 .26 + .31 +1.41 00 + .18 .12 + .19 +.42 +.50 +.80 +65 +60 1.21 .81 .40 + .20 +1.21 00 + .13 .23 + -17 +.44 +.51 +.86 +60 +55 1.36 .87 .55 + .08 + .96 .10 + .08 .30 + .12 +.41 +.49 +.82 +55 +50 1.49 .90 .70 .03 + .60 .22 00 .34 + .11 +.35 +.42 +.70 +50 +45 1.56 .90 .75 .10 + .47 .37 .06 .32 .01 +.23 +.33 +.47 +45 +40 1.60 .90 .80 .14 + .20 .46 .10 .27 .22 +. 1C +.15 +.21 +40 +35 1.60 .85 .74 .18 .02 .48 .09 .28 - .50 .10 .07 .02 +35 +30 1.52 .85 .62 .18 .14 .47 + .03 .28 .63 .27 .21 .13 +30 +25 1.51 1.00 .55 .18 .30 .49 + .12 .33 .65 .25 . 17 .06 +25 +20 1.60 1.20 .50 .21 .51 .58 + .07 .48 .40 .10 +.08 +.10 +20 +15 1.68 1.23 .50 .33 .88 .73 .06 .62 00 +.20 +. 32 +.21 +15 +10 1.67 1.20 .42 .42 1.06 .88 .10 .66 + .26 +.40 +.44 +.23 +10 + 5 1. 54 .87 .20 .26 1. 11 1.00 .10 .56 + .20 +.36 +.40 +.11 + 5 1.14 .38 +.25 + .13 .93 .88 - .10 .47 00 +.18 +.30 -.09 5 .78 + .10 +.48 + .40 .91 .74 .20 .40 .25 +.02 +.18 .26 5 10 .59 + .02 +.56 + .53 1.06 .79 .35 .40 .50 .11 +.07 .34 10 15 .43 + .09 +.56 + .62 1.30 .89 .51 .40 .65 .24 -.02 .35 15 20 .30 + .13 +.58 + .80 1.57 1.05 .67 .40 .80 .34 .11 .30 20 25 .20 + .16 +.65 + .90 1.83 1.22 .83 .35 - .90 .42 .20 .25 25 30 .10 + .18 +.72 +1.00 2.10 1.40 1.00 .30 1.00 .50 .28 .20 30 cussion of declinations, Wn 74 was used as above from + 90 to + 15. From that point the corrections were virtually computed according to this table : (5 Corr. 6 Corr. o // o // + 10 .78 15 .99 + 5 .72 20 .77 00 - .65 25 .55 05 .55 30 .34 10 .38 35 .13 That is, as actually used, a declination of Wn 74 (+ 10 to 35 C ), a given in the catalogue, was corrected by + ".82 -f- the values given in this table. As explained under Re 66, the corrections from + 35 to + 90, for (he annual catalogues He 62- Kc 66 are deserving of little confidence. 159] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 565 TABLE X. Corrections to declinations. ORDER OF RIGHT ASCENSION. S~ IS j . I a a II 1 O 11 f-H n | * o ti n o 1-t g 8 i a gj cc w 1 O M JS a h. a II II II n II II II if ft .18 +.40 +.47 +.32 . 15 +.13 .19 .12 .18 .05 +.01 .15 12 1 .04 +.25 +.53 +.38 .11 +.08 .19 .17 .12 00 +.05 .07 13 2 +.11 +.08 +.55 +.40 .06 +.03 .19 .21 .04 +. 05 +.09 +.02 14 3 +.25 .09 +.53 +.40 .00 .02 .17 .23 +.04 +.10 +.12 +.11 15 4 +.37 .26 +.47 +.37 +.06 .07 .14 .24 +.12 +.14 +.15 +.19 16 5 +.46 .41 +.39 +.32 +.11 .12 .09 .24 +.19 +.17 +.16 +.26 17 6 +.53 .53 +.27 +.24 +.15 .16 .05 .21 +.24 +.20 +.17 +.31 18 7 +.56 .62 +.14 +.15 +.18 .19 00 .18 +.28 +.20 +.16 +.34 19 8 +.55 -.66 00 +.05 +.20 .20 +.05 .13 +.30 +.19 +.14 +.34 20 9 +.50 .66 .14 -.06 +.21 .20 +.10 .07 +.30 +.17 +.12 +.33 21 10 +.42 .62 .27 .16 +.20 .19 +.14 .00 +.28 +.14 +.08 +.29 22 11 +.31 .53 .39 .25 +.18 .16 +.17 +.06 +.24 +.10 +.04 +.23 23 12 +.18 .40 .47 .32 +.15 .13 +.19 +.12 +.18 +.05 .01 +.15 24 NOTE. When a is taken from right-hand (12A to 24A) the signs of the table are reversed. * The corrections for Ce 40 and Bn 66 are applicable only within the declination limits 30 to + 40. In computing from tbe values of J7, given in the preceding pages, the definitive weights to be used in the final discussion, ".30 was taken as the probable error of tho unit, and 5 (corresponding to a probable error of ".134) as the maximum weight. Weight .05 is used in a few cases. As the probable errors are somewhat uncertain, especially in their respective relation to number of observations, only the denomina- tions of weight presented in the table were actually used. For convenience, a few weights deduced in Section IX. are also collated here. With the "Catalogue" as an argument, the corresponding horizontal line is fol- lowed until the number of observations is reached, or, at least, the limits which include it. At the top of the column is found the corresponding weight. The second argument is, however, often a probable error (as Kg 21, Dt 24, etc.), or weight resulting from the system of compilation (as with Ce 40, Eh 43, etc.). 566 UNITED STATES NORTHERN BOUNDARY COMMISSION. [160J TABLE XL Weights used in discussion Catalogue. Weights. .05 .1 .2 .3 .4 .5 .6 .7 .8 Number of observations, preliui GIi 1732 2 to 8 . 2 or 3 4 to 20 . All Ior2 errors 3 to 5 6tol8.... 19 or more. Kg 21 Probable .44 to .41.. .40 to .37.. .36 or 35... .34 or .33.. Bt 24 and 30. Same as Kg 21 or Ao 29, acco rding as pro bable error All or number of observati ons is the argument . . 1 2 All C G H 31 land 2.... 8 or 3 3 to9 to9 10 or more. 10 to 21... S. 11.31 1 22 to 85... 85 or more. 1 2... 3 4 5 and 6 7 M h '14 1 and 2... 3 4to6 7 loll .... 12 to 18... 19 to 35 ... 36 or more . ils35 Eh 37 2 or 3 4 or more 1 2... 3 4 All Gh 39 I 3 3 4 5 6 Weights 1 2 3 Eh 43 Weights 1 S... 3 4 Gh 45 1 2 3 4 Pa 45 Sec table Ue 45 1... 2or3 5tol4 4and5.... 6 to 10 .... 11 to 23 ... 24 or more. Ah 4 land 52. Wn 47 1 2 to 4 .... 1. Weights . Same as 2 3 4 5 O 48 Ce40 Wn48(P.T.) Ms 50 1 2 3 4 3to5 . ... Gh 51 Same as Gh39 So 51 1 2 3 to 5 ... 6 to 11 .... 12 to 37 .. 2 38 or more. Pa 53 1 3 So 55 1... . 2 and 3 2 4to7 3 8tol9.... 4 20 or more. WD 56 1 7 8 and 9. . . 2... 10 to 12 ... Ps 56 . 1 Bs 56 1 2 Sand 4.... 5to7 8and9.... 10 to 16... 17 to 27 ... 28 to 52 ... Co 56 Same as Ce 40 Gh 57 1 2 C.G. H. 58... 1 2 3 Re 58 Same as Re 45 Eh 58 . 1 2 3 4 or 5 6to8 9 to 15.... 16 or more . 1 psGO BsCO 1... 2 3 4 Me 02 1. 2 and 3 4to6 7tol7 .... 18 or more. Pa62(P.V.). Eh 63 Wn64 Gh64 Same as Weights Same as Eh 58 ... 1 8 3 4 Gh57 Ps64 1 Bs65 1 8 P 8 60 Same as Ps 64 BnC6 ... Lc67 Ln 67 Eh 67 2 to 5 Me 68... 1 2... Wn 68 Ee 66 and 72. Gh70 Weights . 1... 2 3 4 and 5 6 7 S 9 1 2or3 4or5 1 6to9 10 to 14 ... 2 15 to 23 ... 24 to 44 ... 3 45 to 152 .. 4 Wn70 Ior2 3 to 5 Wn72 Weights . 2 . 3 4 5 6 [161] REPORT OF THE CHIEF ASTRONOMER, APPENDIX H. 567 of definitive decimations. Weights. Catalogue. 1.0 1.5 3.0 2.5 3.0 3.5 4.0 5.0 imiry weight, or probable error. Gh 1752. Gh 1755. Po 1600. Bh 1810. KR 21. Gh22. Dt24and30. Va29. Ao29. Gh30. C. G. H. 31. S. II. 31. C. G. H. 33. Ce34. Mh34. Ms 35. Eh 37. Kg 38. Gh39. Co 40. Kg 43. Eh 43. Gh45. Pa 45. Ee 45. All -tUndra. Wn47. Ce48. Wn48(P.V.) Ma 50. Gh 51. So 51. PS 53. So 55. Wn S6. Ps 56. Bs56. Co 56. Gh57. C. G. H. 58. Ee58. Eh 58. Ps 60. Bs60. Me 62. Pa62(P.T.) Eh 63. Wn64. (J'u ci. PsC4. Bs65. PsC6. Bn66. Lc fi7. Lu07. Eh 67. Mo 68. Wn68. Ke 66 and 73. Gh 70. Wn70. Wn73. .32 to .37 ... All .26 to .33.. .22 to .20.... .19 .18 and .17 .. .16 .15 .14 or less . . . 3 4to6 7 to 10 11 to 16... 17 to 29 30to68 All 8 to 18 5 to 12 13 or more. 7 to 11 12 to 21 . . 5to8 All 22 to 45 9 to 13 46 to 156.. 14 to 19... 4 20 to 28 ..T.. 29to38 39 to 55 56 or more . . 5 and 6 7 and 8... 9 to 14 .... 9 to 11 .. 15 to 26 13 and 13.. 27 to 50... 14 to 16 ... 51 to 139 17 and 18 19 to22 33 or more . . 5 to 8 6 and 7 8 to 10 11 to 13 i4to"l6... 17 to 19 20 "to" 22 23 to 27 38 or more . . 4 to 7 8 to 15 .... 16 to 39 40 or more. 13 to 27 3to5 23 to 124 .. 6tol8 .... 125 and more 3 and 4 5to7 10 or more. 8 to 12 13 to 21 ... 22 to 44 45 to 207 .... 208 or more . 4 to 9 2 5 to8 3... 9to 18 .... 4toG 19 to no 7tol2.... 61 or more. 13 to 30 1 2 3 or more . . . 5 and 6 7to9 10 to 12 13 to 15 ... 16tol8 .... 19 and 20 2 3to5 4 aiid 5 (i to 13 ... C to 8 13 to 52 ... 9tol3 .... 53 or more . . 14 to 21 'm'd 37* .'."".' 38 and more 3 All All All not fun- damental or circnm polar. Fundamental and circum- polnr. 3 to 6 .. 7toS4.... 14tol9... 10 to 13 20 to 25 26 to 30 ... 31 to 36 37 to 41 42 to 49 50 or more . - 5to7 8 to 17 .... 18 to 47 48 or more. 7 to9 . 10 to 13 ... 14 to 17 18 to 21 ... 22 to 25.... 26 to 29 30 to 35 36 or more . . 568 UNITED STATES NORTHERN BOUNDARY COMMISSION. [162] NOTE 1. The Poulkova observations are weighted according to the probable errors given on pp. (29) and (30) of introduction (Vol. V.). The weight is slightly reduced in two cases. Following is the table of weights. Between + 55 and -f- 65 declination, when the observations are above the pole, the weights of the first line are multiplied by .4 : 6 1 obs. 2 obs. 4 obs. 8 obs. 16 obs. + 40 to 55 and 65 to 80 ... -)- 30 or + 90 1 1 9 9 3 3 4 4 5 6 + 20 or -f 80 S P 1 2 a 4 5 + 10 or + 70 SP .8 1.5 2.5 3.5 4 + 00 or + 60 S P .5 1.0 1.5 2.5 3.5 10 or + 50 S P 3 .5 1.0 1.5 2.5 15 or + 45 S. P .2 .3 .7 1.0 2.0 NOTE 2. When the zenith distance of a star observed at a given observatory is greater than 7U U the above weights are multiplied by the following arbitrary numbers: Z D Factor. ZD Factor. o o 70 1.0 76 5 71 .9 77 4 72 .8 78 3 73 .7 79 3 74 .6 80 9 75 .5 NOTE 3. In nsiug the later Greenwich catalogues (Gh 57, 64, and 70), Ps 64 and Ps 66, and Bs 60 and Bs 65, a considerable modification of the above weights takes place, whenever the same star is observed in two or more series at each observatory. The maximum weight given to Gh 57, 64, and 70 combined, is 7.0 ; to Ps 64 and Ps 66, 4.0 ; and to Bs 60 and Bs 65, 5.0. Where the combined weights were smaller than these totals, arbitrary reductions of each are made; these reductions being proportionally less, the fewer the observations. This course is taken because, strictly speaking, the catalogues of the respective groups are really parts of the same series and have to some extent the same errors. Of course, when either of the above-mentioned catalogues stands as the sole representative of its observatory it receives the full tabular weight. In a less degree this reduction of weights is applicable to groups of catalogues not included in the above enumeration ; but in all such cases it is believed that the reduction of weights required is without practical consequence to the final result. With the values of C computed in Section V., and with the corrections and weights of Tables IX., X., and XI., the definitive values of J >'o Co o // // + 86 5 + .43 + .54 + 78 8 + .62 + .62 + 73 10 + .92 + .67 + 69 15 + .78 + .69 + 64 12 + .41 + .64 + 59 22 + .44 + .60 + 54 14 + .59 + .62 + 49 27 + .80 + .72 + 44 20 + .71 + .70 + 39 30 + .47 + .59 + 34 17 + .06 + .44 + 30 21 + .69 + .26 + 26 22 .05 + .04 + 21 24 .28 .26 + 16 19 .88 .53 + 11 14 .50 .66 + 6 20 .42 .67 + 1 11 .88 .62 5 7 .37 .57 9 11 .72 .51 14 5 .42 .42 19 5 00 .32 23 5 + .68 .22 - 28 5 .99 .10 ?5 2 + .70 + .05 42 5 + .18 + .20 50 2 + .45 + .40 59 6 + .54 + .62 69 roi F+ .531 L v J 1 1 v " J Three hundred and thirty-two residuals, from 35 to + 90, which received weight one, give, with m = 8: E = ".62. Residuals in order of right ascension. Declination limits. Declination limits. Declination limits. + 15 to + 90 + 15 to 35 35 to +90 Mean a 7T 7 ro' K 1 ro' TT' r' A. // II n 1 28 .26 6 .45 34 .29 3 22 .34 7 + .14 29 .32 5 19 .14 7 + .31 26 .02 7 15 + .07 3 .07 18 + .05 9 13 .00 6 .25 19 .08 11 16 .39 8 + .08 24 .24 13 13 .39 5 .02 18 .09 15 26 + .78 7 + .89 33 + .80 17 30 + .49 8 + .16 38 + .42 19 25 - .12 13 + .14 38 .03 21 33 .38 13 .08 46 .30 23 23 .18 11 .11 34 .15 572 UNITED STATES NORTHERN BOUNDARY COMMISSION. [16GJ Wn 48 (prime vertical transit). Sixty-one observations in 1847 of 13 stars gave as the mean correction: ".82 ".09. The probable error, E, of a single observation, is ".70. Ms 50. The correction is ascertained from the declinations of the principal stars given in the introduction. Each residual is given weight oue. Residuals in order of declination. Mean 6 71-' fo Co o // // + 87 5 + .10 + .06 -+75 4 + .37 4- .25 + 63 2 + .54 + .30 + 52 8 + .16 4- .30 + 41 5 4- .37 + .23 + 29 + 22 8 8 .06 .41 .08 - .40 + 14 8 .96 .13 + 08 9 .64 .93 7 1.17 1.05 9 6 .99 .99 With m = 4, we have, probable error of a single declination : E = ".32. If we assume - = 2, we shall have for 3 to 5 observations, approximately, weight .3 in the system of Table XI. Residuals in order of right ascension. Mean re TT' n/ Mean a 7T- ro' h. // k. II 1 5 .17 13 4 .00 3 5 .20 15 7 4- .19 5 (i .29 17 6 .01 7 5 4- .28 19 9 + .35 9 5 .37 21 8 + .40 11 5 .34 23 4 .26 REPORT OP THE CHIEF ASTRONOMER, APPENDIX H. 573 Eh 58, Eh 63, and Eh 67. -1 = 2. Eh 58. Eh 63. Eh 67. Mean rf TT' ro Co Mean ' if w Co' ft. II // II // 1 11 + .21 25 .14 36 .04 .17 3 12 + .02 15 .59 27 .32 .23 5 4 .75 13 .77 17 - .76 .24 7 14 4- .09 5 .30 19 .01 .18 9 9 -!- .20 11 .21 20 .03 .07 11 4 .75 15 .29 19 .38 4- .06 13 9 .36 15 .23 24 .28 4- .17 15 6 + .70 19 + .80 25 4- .78 4- .23 17 12 + .60 20 4- .33 32 + .43 4- .24 19 15 .78 17 + .26 32 .23 4- .18 21 16 4- .35 21 4- .04 37 4- .18 4- .07 23 12 .26 18 .16 30 .20 -.06 Column GO' is taken from the correction found to be applicable to the previous series of observations with the Washington mural circle. There is sufficient resem- blance between it and the values of r ' iu the last column to justify its continued use for this catalogue. TABLE XII. Corrections to catalogues of Class III (and to Po 1800). ORDER OF DECLINATION. Mean 6 PolSOO Ms >. Ms 50. Wn 70.* Mean 6 Po 1800. Ms 35. Ms 50. Wn70. o // n // II o // a It It 4- 90 00 + .50 00 00 4- 15 1.62 .56 .70 .75 4-85 4- -16 + .55 4- .10 00 + 10 1. 35 .68 .86 .75 4- 80 4- .30 4- .60 4- .20 00 4- 05 1.29 .67 1.00 .70 4-75 4- .44 4- .65 + .25 00 1.56 - .61 1.05 .59 4-70 4- .52 4- .70 4- .30 .14 - 03 1. 86 .57 1. C5 .44 4- 65 4- .52 4- .65 4- .30 .25 10 1.96 .50 .97 .25 4- 60 4- .48 4- .60 4- .30 .37 15 1.82 .40 4- 55 4- .35 4- .60 4- .30 .43 20 1.5(1 .30 4- 50 4- .10 4- .72 4- .30 .50 25 1.16 .17 4- 45 .30 4- .72 4- .28 .57 30 1.08 .05 4- 40 .80 4- .62 4- .22 .62 35 1.21 4- .05 4- 35 1.03 + .48 4- .10 .66 40 1.40 4- .15 4- 30 1.10 4- .26 .04 .70 50 4- .40 4- 25 1.33 -.02 .26 *3 60 4- .65 + 20 1.62 .32 .49 .75 " If the ac'ual correction for Wn 1872 and 1873 is desired, given in the above table for Wn 70. ".45 must be added to the quantities [169] KBPOET OF THE CHIEF ASTBONOMEB, APPENDIX H. 575 TABLE XII. Continued. Catalogue. Correction. Remarks. Wn 48 // .82 Constant. Eh 58 .S3 Constant from 10 to -f- 60. Eh 63 -t- .51 Constant from 10 to + 60. Pa 62 + .25 Constant. Eh 67 00 Constant from 10 to + 60. The corrections in order of a for Po 1800 and Wn 70 are to be taken from Table X. With these additional corrections the values of A 8 and A /j.' were computed for the 62 remaining stars. These are sufficiently indicated in the "Details of Corrections to Assumed Declinations" by the use of one or more of the catalogues of Class III. SECTION X. GENERAL REMARKS RESPECTING THE CORRECTIONS AND PROBABLE ERRORS OF STARS USED BY THE NORTHERN BOUNDARY SURVEY FOR LATITUDE. The preceding pages afford the means, to some extent, for answering the question as to the probable errors of the declinations used in latitude work on the Northern Boundary. These declinations in the general catalogue of 500 stars at the end of this paper are distinguished by an asterisk, affixed to the current number. Opposite each star, on the right-hand page (and in the third column), will be found its probable error estimated in the manner described in Section VIII. This, taken together with the cor- responding value of J5, given on the left-hand page, will aid informing some judgment as to the probable limits within which any correction is likely to be included. These values of A5 refer to the declinations adopted in the work of 1874. Those of the pre- ceding years are less accurate, and differ slightly from these, but the differences are not systematic. The general correction required by the latitude work of 1874 has been roughly computed in three different ways: First. Fifty different pairs (100 stars) were observed for latitude during the year. Six of these, however, were used but once; one, three times; three, four times; nine, live times; and others more frequently eighteen times being the maximum. Taking the simple mean of all the values of A S for the one hundred stars, we have: + ".042 as the common correction to the declinations actually used ; and this is, of course, applicable to the latitudes. 8ec:>nd. If, however, we take into account the number of times each pair was used, giving weights proportional to the numbers, we have: + ".OG8 as the common correction to all the latitudes. Third. If, still further, we take into account the weights of the stars as computed in this paper, and if we suppose that each observation of a pair with the zenith tele- 576 UNITED STATES NORTHERN BOUNDARY COMMISSION. [170| scope gives an instrumental probable error for latitude of ".3, we have as the mean correction : + ".OO3. I regard it as quite improbable that a common correction larger than i ".1 is needed for the latitudes as actually established in the field. In this paper the stars of the latitude list were reduced without the slightest reference to the previous work performed on them even the seconds of declinations being transcribed from the vari- ous catalogues anew. Under these circumstances the present work may be regarded as an efficient check on the values of declination adopted in the former discussion. EXPLANATION OF TABLES. RECAPITULATION OP SYSTEMATIC CORRECTIONS. This table shows as nearly as possible the total systematic corrections applied by me (either before or after discussion of Normal System) to the catalogue places as I find them. If to these be added errata and corrections due to proper motion, with a few corrections specified in the notes at the end of the table, we shall have declinations according to the system adopted in this paper. In order, however, to accertain the degree of confidence to be placed in certain values from the curves (especially those from 10 to 30), it will be necessary to recur to the detailed reductions. DETAILS OP CORRECTIONS TO ASSUMED DECLINATIONS. These embrace Table A, Table B, and Table C. Table A contains particulars of reduction for the fundamental and principal cir- cumpolar stars. However, four southern stars, usually regarded as fundamental, and a 2 Gemiuorum will be found elsewhere. Table B contains details for all other stars (i. e., stars not included in Table A) situated between +90 and 10 declination. In this region the weights are in no case affected by the question of zenith distance. Table C contains details for all stars situated south of 10 declination. With one exception the construction of all the tables is alike. At the head of the tabular statement for each star is given its assumed right ascension and declina- tion, with the annual variation of each as computed in Sections II. and III. Column " Cat." contains the designation of each catalogue or series of observa- tions. The explanation of these designations is found in Section IV. It is sufficient here to state that the figures refer to the mean year of observation, and the letters are usually the first and last in the name of the observatory according to the English spelling. Column " Obs." contains either the number of observations, weight, or probable error, according as either is made an argument for computation of weight from Table XI. Column C contains the correction to assumed declination given by the respective catalogues in the manner detailed in Sections III. and V. For the later Iladcliffe cat- alogues, and for Wn 72, values of C are contained in Section V. [171] EEPOET OF THE CHIEF ASTRONOMER, APPENDIX H. 577 Column G n in Tables B and C, contains for a limited number of stars the sum of C and of the systematic correction taken from Table II. The place of this is supplied in Table A by column r /t , which contains the correc- tion given to each authority by the declination computed according to the principles of Section VI., but with the addition of the Fundamenta as an authority, with weight one. Column r contains the quantities from which definitive systematic corrections were computed. It is formed by subtracting C from the value of the expression J5 + ( T '~ ] ^) ^V) J 5 an(1 -V bein g taken fr m Tables V. and VII. Column C,, is formed by the addition of the systematic corrections of Tables IX. and X. to column G. For Re 66 and Re 72, as well as Wn 72 and S H 31, the value of C,, is specially computed. Column TT contains the weight computed from Table XI., with the argument in column "Obs." Column r, contains the outstanding residual found by subtracting C,, from s rr\ _ 1S75\ AS + dp!C- - J, where AS and J/t' are to be taken from the left-hand page of the "Catalogue of 500 Stars" at the end of this paper. CATALOGUE OF 500 STABS. On the left-hand page : Columns 1, 2, 3, and 4 appear to require no explanation except the caution that the latter column is simply copied from the catalogue of the British Association. Column 5 contains the approximate right ascension as deduced in Section VII. Column 6 contains the annual variation, and column 7 the secular variation in Right Ascension given in units of the fifth decimal place. The eighth and ninth columns give A 8 and A p.' as they result from the final com- putation, using columns C,, and K of "Details," etc. On the right-hand page, in column 1, the current number is repeated for con- venience. Column 2 is the definitive declination formed from the assumed declination given with each star in "Details," etc., by the addition of Ad from the preceding page. Column 3 contains the probable error ascertained in the manner explained near the end of Section VIII. In a few cases this column is left blank. It is to be understood in such cases that a definite estimate is declined, either because the error is large or cannot readily be ascertained. Column 4 contains the weight to nearest unit, from which the preceding column is estimated. The probable error of this unit is supposed to be uniformly ".30. It is likely to be smaller than larger (p. 1C3). When this column is left blank it ia to be understood that the computed weight is less than .5 Column 5 contains the definitive annual variation, computed by adding to the A I annual variation of "Details," etc., --; Ay! being taken from the left-hand page. 578 UNITED STATES NORTHERN BOUNDARY COMMISSION. [172] Column 6 contains the probable error of the annual variation computed from the weight of J/t' iii conditional equations. Columns 7 and 8 contain the secular variation and third term of precession in declination which are given respectively to the sixth and eighth places of decimals. The mode of their computation is fully explained in Section III. Column 9 contains the proper motion formed by subtracting from the annual variations 20".0542 cos a. The number is Peters' constant of precession (n) for 1875. RECAPITULATION Of SYSTEMATIC COBRECTIONS TO DECLINATIONS. [173] 579 RECAPITULATION OF SYSTEMATIC CORRECTIONS. i r-t O M o t i 30 K IO Q H bo i v ea - ^3 (N 5 so M s a O 5 sS ^r o c*co 4B Q si ; gj 1 36 4- 07 4- .60 00 .12 .16 .25 1.24 4- 25 4- 20 1 62 4- .10 + -74 CO .15 .20 .29 1.30 4- 20 4. 15 1 62 4- .13 + .81 CO .21 .17 .32 1.31 + 15 4. 10 1 35 4- . 16 4- .88 00 .29 .14 .36 1.31 4- .35 + 10 4- 5 1 29 4- .19 4- .95 00 .38 .10 .43 1. 33 4- .35 + 5 5 1.56 1 86 + .25 4- .33 4-1.04 4-1.15 00 00 .49 .60 .07 .03 .52 .60 1.37 1.49 4- .35 4- .35 5 10 1 96 4- .43 4-1.31 00 .72 00 .68 1.68 4- .35 10 15 1 82 _L 55 4-1.44 00 .84 .70 1.97 4- .35 15 20 25 1.50 1 16 4- .67 4- 76 4-1.59 +1 76 00 00 .96 .70 2. 50 2.8 4- .35 4- .'.55 20 2o 30 1 08 2.9 4- .32 30 35 1 21 + -17 35 40 1 40 00 40 50 00 50 60 00 60 70 00 70 80 00 HO 90 00 90 A.B. r-t & 1 :3 ^ 55 .S H Kg21(Bes- sel). si J3 o ^* W -*3 Q gj a > a o 4 8 J3 O -i M E eJ o A.E. h. o 11 18 4- "40 -:'o3 -:'os -:'i3 II -:'o4 -"04 II + "08 A. 12 1 04 + 25 09 09 18 4- 02 4- .02 4- .13 13 2 4- 11 4- 08 15 15 20 4- 09 4- 09 + .18 14 3 4- 2 r i 09 19 .19 22 4- 14 + 14 4- .21 15 4 4- 37 26 22 22 22 -4- 19 4- .19 4- 23 16 5 4- 46 .41 .24 .24 .21 4- .22 + .22 4- .23 17 g 4- r >'< 53 24 24 18 4- 24 4- .24 4- .22 18 7 4- r ifi go 22 22 14 4- 24 4- 24 4- .19 19 8 _j_ 55 6fi .19 .19 .09 4- .23 4- .23 4- .15 20 9 4- 50 66 .15 .15 .03 4- .20 4- .20 4- .10 21 10 11 + .42 4- 31 .62 53 .09 03 .09 03 4- .03 4- 08 -f .15 4- 10 4- . 15 4- 10 + .04 .02 2'i 23 12 4- 18 40 4- 03 4- 03 4- 13 4- 04 4- 04 .08 24 [175J When the argument is 12 b to 24 h the signs are to bo reversed. . r :8l 582 UNITED STATES NORTHERN BOUNDARY COMMISSION. [176] Recapitulation of systematic corrections Continued. (J !"H CO w 02 CO CO K O 6 *r CO U 3 fi U IB O 3 A 23 GC $ a H o . !< CQ | 00 CO 3 ci CO ja O c <> O 6 o 4- 90 // a "oo "oo H + !'50 a .19 "oo "oo II .09 o + 'JO -4- 85 .02 00 + .55 .22 .10 + .01 .09 + 85 + 80 .05 00 + .60 .22 .20 + .03 .09 + 80 4- 75 .11 .04 .28 + .65 .23 .27 + .05 .09 + 75 4- 70 .23 . 14 .38 + .70 .23 .33 + .08 .16 + 70 4- 65 r-H.3oi .38 .27 .46 + .65 .22 .36 + .09 .27 + 65 4- 60 4-1.30 .55 .42 .52 + .60 .20 .15 + .10 .41 + CO + 55 4-1. 30 .72 .57 .60 + .60 .18 + .10 + .11 .52 + 55 4- 50 4-45 4- 40 4-35 4- 30 + 25 4- 20 4- 15 4- 10 4- 5 5 10 15 20 25 30 4-1.30 +1.30 41.30 4-1.30 41.30 41.30 +1.30 41.30 41.28 4-1.22 41.17 4-1.09 4- .96 4- .84 4- .70 4- .C2 4- .60 2.00 1.10 .34 + .20 + .52 + .57 + .43 4- .14 .OG .14 .14 .04 + .16 + .46 + .71 + .88 + .90 .86 .95 1.02 1.05 1.03 .95 .81 .70 .68 .75 .87 1.06 1.26 1.50 1.73 1.98 .70 .78 .83 .84 .80 .70 .54 .40 .35 .38 .47 .(.0 .74 .88 .98 1.00 .62 .CO .54 .38 .14 + .17 + .32 + .47 + .50 + .CO + .41 + .30 + .14 .03 .20 .40 + .72 + .72 + .62 + .48 + .26 .02 .32 .56 .6S .67 .61 .57 . f,0 .40 .30 .17 .05 .16 .15 .16 .17 .20 .21 .17 .05 + .04 00 .15 .24 .27 .25 .15 00 + .2 + .28 + .30 + .24 + .11 + .08 + .09 + .15 + .25 + .41 + .56 + .73 + .94 +1.13 +1.34 +1.55 +1.77 +2.00 + .12 + .12 + .13 + .14 + .15 + .17 + .19 + .23 + .28 + .34 + .41 + .49 + .59 + .70 + .83 + .97 +1.10 .63 .74 .84 .92 .97 .99 .89 .69 .55 .59 .71 .79 .79 .77 .64 .5 .4 +*50 + 45 + 40 + 35 + 30 + 25 + 20 + 15 + 10 + 5 - 10 15 20 25 30 35 4- .CO + .71 + .05 35 40 4- .CO + .47 + .15 40 50 + .60 + .10 + .40 50 CO 4 .50 .00 + .65 60 70 4- .40 .08 70 80 4- .30 .10 80 90 4- .20 00 90 A.E. n n ai & K 6 u t O Sf a O 8 X> O i J3 3 ri GO S a) H If U & 5 Ce40(+40 c to +90). A.R. ft, + "47 -"07 -"07 - "oo + "18 a - :'of. + !'34 - :'o.3 -:'04 h. 12 1 4- .53 .07 .07 .05 + its .05 + .34 .02 .03 13 2 4- .55 .07 .06 .05 + .17 04 + 30 .01 .03 14 3 4- .53 .06 .05 .04 + .15 .03 + .24 .01 .02 15 4 4- .47 .05 .03 .02 + .11 .02 + .17 00 .01 16 5 + .39 - .03 .02 .01 + .07 00 + .09 + .01 00 17 6 4- .27 .01 00 + .01 + .02 + .02 .01 + .02 + .02 18 7 4 .14 + .01 + .02 + .02 .02 + 03 .10 4- 02 + .03 19 8 00 + .03 + .04 + .03 .07 + .04 . 18 + .03 + .03 20 9 .14 + .04 + .'5 + .04 .11 + .05 .25 + .04 + .04 21 10 11 .27 .39 + .05 + .06 + .06 + .07 + .05 + .06 .15 .17 + .06 + .015 .31 .34 + .03 + .03 + .04 + .04 22 23 12 .47 + .07 + .07 + .06 .18 + .06 .34 + .03 + .04 24 When the argument is 12 h to 24 h the sisus are to be reversed. J177] RECAPITULATION OF SYSTEMATIC CORRECTIONS. 583 Recapitulation of systematic corrections Continued. 6 Ce38toCe44. A -t- 80 00 4- .20 4- .28 .67 4-1.04 .31 00 00 4- 50 + 80 4. 75 00 4- .20 + .25 .56 4- .90 .28 4- .02 .00 + .66 4- 75 4- 70 .07 4- .10 4- .16 .44 4- .75 .26 4- .04 + 06 + .60 4- 70 4- 65 .]8 4- .20 4- .03 .38 4- .57 .26 4- .16 + .12 + .42 + 65 4- (10 .32 4- .16 .13 .36 + .41 .28 + .08 + .18 + .28 + 60 + 55 + 50 + 45 + 40 + 35 + 30 -f- 25 -I- 20 + 15 + 10 + 5 5 10 15 .43 .54 .65 .75 .83 .88 .90 .80 .60 .46 .50 .62 - .70 .70 .68 .00 .35 .75 .81 .63 .42 .25 .27 .47 .74 1.04 1.20 1.24 -1.11 .87 4- .30 4- .29 4- .27 4- .26 4- .24 + .23 4- .21 4- .20 + .18 4- .16 + .13 4- .10 + .06 00 .31 .47 .60 .70 .78 .81 .79 .74 .66 .58 .53 .53 .59 .69 .78 .38 .41 .46 .54 .65 .73 .82 .90 .96 1.00 1.07 1.14 1.26 1.38 1.48 4- .27 + .18 + -14 + .14 4- .18 + .23 + .32 4- .42 + .54 4- .62 + .66 + .65 4- .56 4- .45 4- .35 .31 .31 .27 .23 .16 .05 + .10 + .28 4- .48 4- .68 + .83 4- .93 + .96 4- .92 4- .85 4- .06 4- .00 .04 .02 4- .05 + .12 + .15 + .14 + .10 + .05 + .05 + .08 + .12 + .15 + .18 + .23 + .26 + .30 + .33 + .35 + .37 + .38 + .39 + .41 + .44 + .46 + .49 + .53 + .59 + .68 + .10 .07 .20 .34 .48 .56 .60 .59 .45 .20 + .04 + .26 + .44 + .51 + -47 + 55 + 50 + 45 + 40 + 35 + 30 + 25 + 20 + 15 + 10 + 5 5 10 15 yo 55 .48 .88 1 56 4- .27 4- .75 + .22 4- .84 + .33 20 25 4 .95 1.61 4- .23 4- .66 4- .26 4-1.1 4- .16 25 30 3 1.00 1.65 4- .24 + .53 + .30 00 30 35 35 40 40 50 50 CO 60 70 70 80 HO 90 90 A.H. ii i 1 rr *t af 00 20 9 4- .25 .20 4- .15 4- .13 4. . 11 4- .10 4- .01 21 10 + .24 .19 4- .19 4- .17 + .16 4- .14 + .01 52 11 4- .aa .16 4- .22 4. .21 4- . 19 4- . 17 + .02 23 12 4- .19 .13 4- .24 4- .23 4- .21 4- .19 -1- .02 24 Wben the argument is 12 h to 24 h the signs are to bo reversed. 584 UNITED STATES NORTHERN BOUNDARY COMMISSION. [178J Recapitulation of systematic corrections Continued. 6 Wn45. Wn 46 to Wn 48. > ?i^ ooH a * Ce45toCe51. f 5 A o 3 & O S XI i cc IB & *o u5 & a o ^8 iO a 6 o + un it ir; n 4- 10 // "43 "12 it "oo "oo n - :'ir, o 4- yo i Wf- 11 4- 14 43 13 4- 10 4- .08 .05 4- 85 T + QI) 10 4- 1 r > 43 13 4- 20 4- .14 4- .05 4- HO _l- 7^ 11 4- 14 43 14 4- 25 4- 21 4- .12 4- 75 + 70 15 4- 10 43 15 + 30 4- .26 4- . 17 + 70 i gfj 19 _j_ ()(; 53 16 4- 30 4- 28 4 . 18 4- 03 i (jo 7 02 69 18 4- 30 4- .29 4- .16 4- 60 i 55 30 05 85 20 4- 30 4- 27 4- . 13 + 65 -f- 5U -U 4^ .30 30 .05 05 1.00 1 12 .21 20 4- .30 4 28 4- .22 4- 18 4- .10 4- .05 4- 50 + 45 + 40 -f- 35 4- 30 _i_ 25 .30 .30 .33 39 .05 .05 .08 14 .82 .82 1.24 1.30 1.27 1.08 .16 .08 + .02 -1- .10 + .40 + .5.) 4- .68 -j- .80 4- .2V 4- .10 .04 .26 4- .12 + .07 4- .01 4- .on 4- .50 4- .50 4- .49 + .48 .00 .04 .09 .13 4- 40 4- 35 4- 30 4- 25 _j_ 20 46 21 .76 -i- 17 4- .90 .49 .12 4 .44 .18 4- 20 4- 15 54 29 .53 4- .18 4- .99 .70 .18 4- .31 .23 + 15 j_ 10 59 34 .48 4- . 16 4-1.04 .86 .26 4- .20 .26 4- 1 _L 5 60 35 .48 4- .11 4-1.08 1.00 .;;3 4- .15 .27 4- 5 59 .34 .50 4- 04 41.11 1.05 .37 4 .27 .26 5 .56 .31 .54 00 41.13 1.05 .36 4- .40 .23 5 10 15 .52 48 .27 23 .56 .55 00 4- 05 4-1. 12 4-1 09 .97 .30 .19 4- .38 4- .12 .17 .10 10 15 20 .43 .18 .51 4- 13 4-1 00 .02 .07 .02 20 25 36 11 .47 J. 20 4-1 Oa 4- .27 .14 4- .06 25 30 28 .03 43 -L. 24 4- 99 4 7 .02 4- .16 30 35 4- 96 4- . 13 35 40 4- .92 4- .27 40 50 4- 85 4 .27 50 60 4- 63 4- 11 - 60 70 -j- 38 00 70 80 4 l c 00 80 90 00 00 90 A.R. o ^- a * _o "~oo <0*f ** a f fe- 5^ c> * *r a> O -5 in jt O r-5 ift 3 S s & S o co -S 4 f A.E. It. - : ; 87 a .17 n !'05 - :'o5 -"18 n II // :'i2 A. 12 1 .27 .23 .05 .05 .12 .17 13 I .26 .27 .05 .04 .04 - .21 14 3 .23 .28 .03 04 4- 04 23 15 4 .19 .29 .04 03 4- 12 24 16 5 .14 .28 .03 02 4- 19 24 17 8 .07 .23 .02 01 4 24 21 Irt 7 00 .19 .01 00 4- 28 18 19 8 4- .07 .13 00 4- 01 4- 30 13 20 9 4- .14 .05 4- .02 4- .0:? 4- 30 07 21 10 4- .20 4- .03 4- .03 4- .03 4- 28 00 22 11 4- .24 4- .10 4- .04 4- .04 4- .24 4 .06 23 19 4- .27 4- .17 4- .05 4- 05 4- 18 4- . 12 24 When the arentrcnt is 12 h to 24 h the sic;na aro to hfi reversed. 1 179] RECAPITULATION OF SYSTEMATIC CORRECTIONS. 585 Recapitulation of systematic corrections Continued. c! Ps 54 to Ps 57. & a tf 4 in Ce52toCe60. g a o 8 K O O f~\ * v_^ s & Ps 58 to Ps 62. Bs57toBs67. ** ri o a > fc ^ h (! 4- 90 - '35 4- "22 -:'20 "oo it + :'> - ."20 it + .20 n rt o 4- 90 4- 8f> .30 4- .20 .23 4- .02 + .44 .19 4- .26 4- 85 4- 80 .25 4- .30 .26 4- .05 4- .56 .16 4- .32 4- 80 4- 75 .20 4- .31 .31 4- .09 4- .60 .10 4- .38 4- 75 + 70 .15 4- .31 .36 4- . 15 4- .73 .04 4- .40 4- 70 4- 05 .12 4- .30 .44 4- .21 + .70 + .01 4- .39 4- 65 4- 60 .10 4- .22 .55 4- .23 4- .60 + .04 4- .26 4- .25 4- 60 4- 55 .09 4- .07 .77 4- .21 4- .46 4- .07 4- .06 4- 55 4- 50 .11 .13 1.12 4- . 15 [4-2.4 1 4- .20 4- .10 .17 4- 50 4- 45 .15 .36 1.40 4- .11 F 1. 51 . 12 4- .10 .29 4- 45 4- 40 .20 .52 1.45 4- 11 .80 .42 4- .08 .32 -f .50 4- 40 4- "A .24 .52 1.41 4- . 15 .30 .65 4- .04 .27 4- .46 4- 35 4- 30 .28 .46 1 29 4- .24 .06 .80 .00 .11 4- .42 4- 30 4- 25 .33 .37 1 12 4- 33 .05 .74 .00 4- .04 4- .39 4- 25 4- 20 4- 15 .35 .36 .47 62 .87 67 + .37 + 38 .10 .15 .56 .35 .12 15 4- .03 .08 4- .38 + .38 4- 20 4- 15 4- 10 4- 5 .36 .35 .70 .75 .58 :7 4- .35 4- 28 .18 .20 .09 4- 20 .19 20 .10 .06 4- .52 4- .71 + JO 4- 5 34 68 55 4- 20 23 4- 51 18 03 4- 87 5 30 45 53 4- 15 26 -1- 70 13 00 4- 90 5 10 20 23 49 4- 21 26 4- 79 04 00 + 86 10 15 .05 .20 .40 4- .26 .20 4- .79 4- .10 00 4- .75 15 20 4- .14 .23 .42 4- .26 .15 4- .68 4- .28 00 4- .63 20 25 30 + .35 4- .60 .27 .30 .39 r .351 4- .25 f-i_ .201 .10 .05 4- .40 F4- . 101 + .50 4- .70 00 00 4- .f>0 4- .44 25 30 35 .00 4- .21 35 40 + .05 4- .Ori 40 50 + .15 . 14 50 60 + .27 .20 60 70 4- .26 .20 70 80 4- 13 08 80 90 .00 00 90 A.E. & o . S 10 & Bs55andBs 56. S3 O o . -"o M p PH o . ^o* 8<= (3 s^ t~<= m IB m % > P^ ^ (2 A.R. h. "05 "03 // it " . // -"05 + '!oi II // It. 14 1 00 .03 .CO 4- .05 13 "2 4- .05 .02 4- .05 4- .09 14 3 4- . 10 .01 4- .10 4- .12 15 4 4- .14 00 4- . 14 4- .15 16 5 4- 17 4- .01 4- .17 4- .10 17 G 4- .20 4- .02 4- .20 4- .17 18 7 4- 20 4- .03 + .20 4- .16 19 8 4- 4- .03 f + .19 -1- .14 20 9 4- 17 4- 04 4- .17 4- .12 21 10 4- 14 4- .04 4- .14 4- .08 n 11 4- . 10 4- .04 -4- . 10 4- .04 S3 12 4- 05 4- 03 4- 05 . 01 24 When the argument is 12 h to 24 h the signs are to be reversed. 586 UNITED STATES NORTHERN BOUNDARY COMMISSION. [180] Recapitulation of systematic corrections Continued. 89 S S Wu 63 to Wn 65. "JP 3 j tO t LO O 00 a s H o ;s j a K ~^ -*r s< a W a o jg H ^ to 9 a n (5 + 1)0 "GO "39 "oo "20 tl -4- 20 .''20 // a tl 4 "40 4 9) + wr. 57 '36 00 23 -t- 20 .20 4 .41 + 85 TO) + KO 50 35 00 25 4- 32 20 4 .55 + 80 ou + 7^ 57 36 oo 26 4 38 20 4 .71 4 75 /o 4. 70 CO 59 00 27 4- 40 17 4 -71 4 70 T C> . (IS 4 00 27 4. 39 11 4 .54 4 65 4 CO + 55 + 50 + 45 4 40 -j- 35 4 30 4 25 + *>. + 15 + 10 + 5 5 10 15 .66 .70 .73 .75 .81 -- .86 .93 I. 01 l.OS 1.13 1.14 1.12 1.08 1. 03 .96 87 .45 .49 .52 .50 .60 .65 .72 .80 .87 .92 .93 .91 .67 .82 .7.-, GO 00 00 00 00 00 + .05 + .10 + .13 + .15 + .12 + .07 .02 .09 .10 00 _i_ 14 .25 .21 .22 .26 .30 .30 .22 .10 .05 .00 .15 - .22 - .23 .19 .10 -1- .07 + .26 -j- .ou .17 .29 .32 .27 .11 + .04 4 -03 .08 .10 .06 .03 00 00 00 .01 00 .01 .07 .15 .18 .14 .06 .00 .15 .24 .27 .28 .24 .17 04 .33 .33 .33 .33 .33 .33 .33 .33 .33 .33 .33 .33 .33 .33 .33 + .61 4 .51 4 -51 4 .51 4 .51 + .51 4 .51 4 .- r 'l 4-51 4 .51 4 .51 + .51 4 .51 4 .51 4 -51 00 00 00 00 00 00 00 00 00 00 00 00 00 00 CO 4 .05 .30 .50 .00 .57 .50 .38 .28 .24 .20 .20 .25 .33 .40 .40 .40 4 60 4 65 4 50 4 45 4 40 4 35 4 30 4 25 4 20 + 15 4 10 + 5 5 10 15 20 78 57 4- 27 _i_ H5 oo _i_ 07 .40 20 25 6d 47 4. 40 -j- .66 00 J_ 25 .40 25 30 58 r 37 T4- 551 [.(-1 00] 00 4- 48 [ .40] 30 35 _4_ 75 35 40 40 50 50 60 CO 70 70 80 80 90 90 A.R. -3 -! o 8 50 Q i* 3 o s 00 CH s X a s M n 89 .a a s ja H BnC6( 30 10 + 40). A.R. ft, -fis -"19 a -."06 + "oi - :'or, ir a ft // .15 h. 12 1 .17 .17 00 -4- .05 00 .07 13 2 .21 .21 + .05 4 .09 4- .05 4 .02 14 3 .23 .23 + .10 + . 12 4 .10 + .11 15 4 .24 .24 + . 14 + .15 4 .14 + .19 16 5 .24 .24 4- 17 -L. 16 -t- 17 -1- .26 17 6 .21 .21 + 20 _L 17 _L 20 4 31 18 7 .18 .18 + 20 4 16 _i_ 20 4 .34 19 8 .13 .13 + . 19 _L 14 4- 19 -t- .34 20 9 .07 .07 + .17 _L 12 4- 17 4 33 21 10 .00 .00 + . 14 4 .08 4- 14 4 .29 22 11 + .06 + .00 + . 10 4 04 4 10 4 23 23 12 + .12 + .12 + .05 .01 4 05 4 . 15 24 When the argument is 12 h to 24 h the signs are to be reversed. [181] RECAPITULATION OF SYSTEMATIC CORRECTIONS. 587 Recapitulation of systematic corrections Continued. 6 ri s 3 op to S o F A O is ' " B rfl to- 5 a -3 Q 1 ^_^ ^2^-r" *N p|2 *<^i"Z il! fc-S a li ^.<->"Z |S ^ o GO'S *l c ^, j"3 is fe o A c ^ ^ "3 i 4- yo + :'22 "oo II "oo -"29 + "20 it 4- 54 -"14 -:'is 4- o'o 4- 85 4- .47 00 .03 .21 4- .23 4- 57 .18 .12 + 85 -t- 80 4- .72 00 .15 .12 4- 28 4- 62 .21 .08 -t- HO + 75 4- .94 .01 .20 00 4- 33 4- 67 .22 .02 4- "5 + ?0 4-1.00 .05 .25 + . 12 -j- 38 4 72 .22 4- .03 4 70 4- C5 4- 90 10 30 _|_ 24 -4- 43 -1- 77 23 4- 07 -j- 65 4- 60 4- .70 .17 .34 + .38 4- .48 4- 82 .22 4- 12 -4- CO 4- . r ). r ) 4- .44 .22 .37 4- .52 4- .52 -j- 86 .0 -t .17 -j- 55 4- 50 4 45 4 40 4- 35 + 30 -f 25 4- 20 + 15 + 10 + 5 5 10 15 20 4- .18 .04 .23 .37 .47 .54 .55 .52 .47 .43 .43 .43 .43 .39 .30 .25 .2(i .26 .26 .26 .26 .26 .25 .23 .19 .12 .05 + .03 4- .11 [4-1.25] [4-1.00] [4- .67] + .48 4- .11 .08 .15 .15 .15 .15 .16 .18 .21 .26 .30 .40 .41 .42 .42 .37 .33 .33 .40 . 52 .65 .80 1.00 1.20 1.43 1 66 4- .64 + .76 4- -87 4 .98 4-1.09 4-1.20 4-1.30 41.40 4-1.49 H-1.57 4-1. 64 +1.70 4-1.76 4-1. 84 -j-1 95 4- .54 4- .55 -j- .55 4- .54 4 .52 4- .51 4- .50 4- .47 4- .43 4 .39 4- .34 + .29 4- .24 4- .21 -L 22 4- .88 4- .89 4- .89 4- .68 4- .86 4- .85 4- .84 + .81 4- -77 4- .73 4- .68 4- .63 4- .57 + .55 + 56 .21 .22 .22 .23 - .23 .23 .21 .21 .19 .19 .19 .19 .14 .09 00 + .19 4- .19 4- .20 4- .19 4- .17 4- .16 4- .14 + .11 4- .08 + .03 .01 .07 .12 .15 14 4- 50 4- 45 4- 40 4- 35 4- 30 4 25 4-20 4- 15 4- 10 + 5 5 10 15 20 25 . 18 .32 1 U3 4-2 09 -i- 2(> 4- 60 4- .13 10 25 30 .05 .36 r_2 201 4-2 25 4. 33 -4- 67 4- .29 03 30 35 .38 +2 43 4- 43 -i- 77 4- .49 4- 08 35 40 .40 40 50 .34 50 CO .22 60 70 .12 70 80 .05 80 90 .00 90 A.E. s a J C 2 1 o t~ i o e's f -g . * t^ c w a a>-5 |c SB 1 o' o 1 A.R. h. // // n // II It II // // 7i, 12 1 13 2 14 3 15 4 16 5 17 6 18 7 19 8 20 9 21 10 22 11 21 18 24 When the argument is 12' to 24 h tbe signs are to be reversed. 588 UNITED STATES NOETHEEN BOUNDAEY COMMISSION. [182] Recapitulation of systematic corrections Continued. 6 Wn 70, tran- sit circle. (/i) Wn 71 and Wn 72, tran- sit circle.(A) 1! 4 a 3 Wn 74, tran- sit circle.( h) 3 5 f a 8 B ** M 3 M <4 a 0> K 6 o + 90 + 85 + BO + 75 + 70 + 05 + 60 + E5 + + 45 + 40 + 35 J- 30 + 25 -)- 20 + 15 + 10 + 5 5 10 15 "CO . 00 00 00 00 00 .00 .03 .06 .09 .23 .41 .45 .46 .47 .47 .47 .46 .41 .:<6 .31 31 "oo 00 00 00 00 00 .00 .05 .10 .16 .22 .26 .30 .33 .34 .33 .32 .31 .30 .29 .27 25 "CO 00 00 + .02 + .04 + .C7 + .10 + -14 + .18 + .24 + .46 + .75 + .88 + .93 + .96 + .98 + .99 +1.00 +1.03 + 1.11 +1.19 +1 28 + :'o7 .04 .14 .24 .33 .41 .-19 .56 .62 .68 .40 .03 00 00 00 00 00 00 CO 00 00 -1- 04 "oo 00 00 00 .14 .25 - .37 .43 .50 .57 .62 .66 .70 .73 .75 .75 .75 .70 .59 .44 .25 + : 7 45 + .45 + .45 + .45 + .31 + .20 + .08 + .02 .05 .12 .17 .21 .25 .28 - .30 .30 .30 .25 .14 + .01 + .20 "00 .26 .48 .66 .H6 1.03 1.21 1.36 1.49 .56 .60 .60 .52 .51 1.60 1.68 1.67 1.54 1.14 .78 .59 43 "oo .17 .34 .CO .63 .73 .81 .87 .90 .90 .90 .85 .85 1.00 1.20 1.23 1.20 .87 .38 .10 + .02 + 09 + "40 + .26 + .13 00 - .13 .26 .40 .55 .70 .75 .80 .74 .62 .55 .50 .50 .42 .20 + .25 + .48 + .56 56 + 90 + 85 + 80 + 75 + 70 + 65 + 60 + 55 + 50 + 45 + 40 + 35 + 30 + 25 + 20 + 15 + 10 + 5 5 10 15 20 .31 .23 +1 36 + .16 .30 + .13 + .58 20 25 31 21 +1 45 -4- 29 20 _L Ifi -4- 65 25 30 31 .19 +1.53 + .42 .10 + .18 -4- .72 30 35 .31 .17 -1- .53 35 40 .31 .15 40 50 50 GO 60 70 70 80 t-0 90 90 A.R. o t- a * -o Sol ^f f $ ' a Wn74. '$ o Ss 4 g A 8 a s H A. B. It. // II it // II a it // // A. 12 1 13 2 14 3 15 4 16 5 17 6 18 7 19 8 20 9 21 10 22 11 23 12 24 When the nrgnment is 12 h to 24 h the signs are to be reversed- [183] RECAPITULATION OF SYSTEMATIC CORRECTIONS. 589 Recapitulation of systematic corrections Continued. <5 8 K g o M g g K g ?. 3 n o & n r- 3 W s o i- 3 ^H |> 3 a " 3 o 2 a+3 a JJ a "3 o s o a'S a i - 00 "3 "1 g 3* Probable error of anunal va- riation. . = t Argus.. . . i Argus ...... a Hydras ... 24 Ureas Majoris . ... Q Ursai M;t joris ...... e Leouis - . .... v Ursae Majoris jt Leouis . ri Leonis a Leonis . 32 Ureoe Majoris + .95 + .41 2.65 1.36 1.11 .98 .38 2.78 2. 70 + .04 .18 2.34 1.22 1.28 + .35 1.20 +3.84 - l.fc'O .52 2.51 1.05 .05 1.22 +2. < i t a - 3 g o 2 p ! Probable error of annual va- riation. cPi dl* (P6 di : > Proper motion in "3 a a o D' a a o * < ^ cs n 3 V Probable error of annual va- riation. dM 53 d?i dfl a o 'S o a-o H d 1 1 o / " II // // // it // 181 78 37 04. 29 .22 2 19.9878 .0094 + 323 + 133 4- . 0432 182 + 01 40.75 .07 18 20. 0472 .0032 + 349 + 100 .0278 183 62 24 21.76 .25 1 20. 0219 .0090 4- 495 4- 121 .0417 '184 + 27 57 38.99 .20 2 20. 0038 .0056 + 471 4- 94 .0270 *185 + 69 53 36. 16 .14 4 20. 0038 .0061 + 505 4- 66 .0652 186 22 42 18.75 .09 12 19.9725 .0039 4- 637 4- 105 .0659 187 + 70 28 38.85 .10 9 19.8980 .0031 + 548 4- 61 4- .0053 "188 4- 41 33 45.55 .28 1 19.8729 .0066 4- 688 4- 84 .0232 189 + 84 05 32.73 .11 8 19.5990 .0042 4- 191 4- 69 4- .0128 "190 + 56 38 18.77 .12 6 19.6318 .0042 4- 895 + 64 .0254 191 + 38 59 37.72 .07 20 19.5274 .0027 4- 970 4- 76 4- . 0481 192 -j- 57 02 25.55 .30 1 19.4966 .0098 4- 993 4- 60 . 0246 193 4 52 16.10 .07 16 19.331) . 0034 4- 1319 + 100 .0412 194 4- 28 30 44.08 .13 5 18.3458 .0044 4- 1220 + 74 4- . 8816 "195 4- 40 48 55.48 .37 1 19.1607 .0114 4- 1:49 4- 69 4- .0161 196 10 30 29.68 .06 26 18.9239 .0021 4- 1625 4- 103 .0378 197 4- 55 34 43.01 .10 10 18.9095 . 0031 4- 1281 4- 49 .0317 "198 + 73 02 27.83 .22 2 18.7748 .0083 4- 866 4- 20 .0197 *199 -)- 24 52 56.68 18.69-25 4- 1585 4- 76 200 + 02 38.03 .07 18 18.5432 .0031 4- 1743 4- 93 4- . 0401 201 + 55 59 22.25 .24 2 18.5713 .0084 + 1365 4- 44 .0208 *202 4- 41 42 58.88 .34 1 18. 1897 .0110 4- 1672 4- 56 .0485 203 4- 49 56 15.80 .06 24 18. 1020 .0021 4- 1570 + 46 .0245 204 + 21 53 07. 12 .24 9 18.0229 .0076 4- 1892 + 74 4- . 0093 *205 4- 18 32 58.49 .27 1 17.9231 . 0062 4- 1965 + 76 . 0247 206 4- 19 01 30.42 .07 21 18.2001 .0028 4- 1979 + 75 . 3009 *207 + 79 36 44.94 .23 2 17.7777 .0093 133 4- 124 . 0092 208 59 46 07. 14 .23 2 17.6344 .0091 + 2997 + 218 . 0531 *209 4- 27 59 28.11 .16 4 17.5600 .0047 4- 1998 4- 65 + . 0007 210 4- 64 58 25.33 .07 17 17.3174 .1028 4- 1262 + 27 + . 0059 211 4- 25 41 04. 84 .25 1 17.2238 .0116 4- 2142 + 6, . 0656 "212 4- 70 01 10.40 .19 3 16.9961 .0081 + 933 + 33 .0708 213 + 19 50 02.58 .06 27 18.9148 .0020 4- 2151 + 66 J.9994 214 + 46 39 47.01 .13 6 Hi. 6817 .0043 4- 1868 + 41 4- . 1548 215 + 52 25 45. 12 .09 11 16.7873 . 0032 + 1767 4- 34 .4072 '216 + 50 24 1H. 17 .24 2 16.2565 .0060 + 1833 4- 33 . 0468 217 + 30 55 15.53 .09 11 15.9845 .0040 + 2313 + 53 + . 1132 218 + 38 51 21. 11 .15 4 15.9247 .0041 4- 2170 4- 45 4- . 1416 219 + 76 .15 06.01 .09 10 16.0100 .0031 108 4- 106 + . 0159 *220 + 47 20 04.78 .36 1 15.9744 .0109 + 2009 + 37 .0393 221 60 19 11.63 .23 2 15. 4245 .0090 + 3347 + 176 + . 4257 222 + 27 03 36.91 .25 1 15.4814 .0069 + 2515 + 55 .0031 223 + 27 36 07.83 .07 20 15.3787 .0028 4- 2515 + 54 + . 0102 224 15 31 15.67 .07 21 15.2156 .0024 + 3224 + 100 .0786 *225 + 38 19 37.78 .25 1 15.0076 .0094 + 2302 4- 41 + .1158 N B- -76 602 UNITED STATES NORTHERN BOUNDARY COMMISSION. [196] Catalogue of 500 stars Number. a a . tH 0,2 ! m Name. Magnitude. Approximate right ascen- sion, 1875.0. .3 'E . C3 O * a 13 9 0.2 a -3 a < Annual varia- tion 1875.0. Probable error of annual va- riation. $>& dt" M dt 3 a o -3 o i-d t> a IT 8 fi o / n II // u ft u :/ 271 26 09 09. 18 .09 11 8. 3734 .0041 + 4900 4- 71 .0367 272 4- Cl 47 51. 11 .07 17 8.2376 .0026 4- 1107 4- 26 4- . 0546 273 4- 42 09 28. 15 .27 1 8.1111 .0083 + 2656 4- 20 4- 0026 274 + 2 15 32.64 .11 8 8.2062 .0043 4- 4068 4- 44 . 0982 275 4- 49 14 02. 15 .43 8. 0040 .0109 + 2230 4- 18 .0612 276 4- 69 02 18.29 .13 6 7.7958 .0047 157 4- 55 4- . 0209 277 -j- 30 45 45.25 .20 2 7. 7908 .0106 + 3158 4- 24 . 0047 278 -f 42 41 45.08 .12 6 7.6334 .0041 + 2637 4- 19 4- . 0350 270 10 11 43.56 .11 8 7.6308 .0047 + 4480 4- 52 + . 0212 280 4- 46 52 01.93 .40 1 7. 4570 .0116 4- 2379 + 17 -t- . 0116 281 + 49 10 25.04 .19 2 7.2184 . 0052 + 2335 + 17 4- . 0209 282 68 47 39. 59 .22 2 7.2882 .0094 4- 8085 4- 268 . 0563 283 4- 31 49 49.47 .08 15 6. 7387 .0032 + 3068 + 20 4- .4010 284 + 39 09 39.91 .10 9 7. 0633 .0030 + 2844 4- 19 .0903 *285 4- 28 35 15.28 .30 1 6.8077 .0087 4- 3302 + 22 4- . 0421 286 + 57 00 20.98 .16 4 6.5672 . 0103 + 1596 + 17 4- . 0505 *287 4- 42 27 45.06 .29 1 6.6194 .0104 4- 2668 + 16 . 0350 *288 + 55 37 54. 61 .29 1 6.5260 .0122 + 1751 + 17 . 0216 "289 + 31 54 35.34 .19 2 6.2002 .0056 + 3159 + 19 . 0220 290 4- 46 44 31.22 .34 1 6.0105 .0131 4 2428 + 14 .0412 291 + 9 34 15.45 .07 19 5.8897 .0032 + 3947 4- 27 .0056 292 4- 31 06 42. 18 .10 9 5.5476 .0042 4- 3230 4- 17 4- . 0215 293 4- 33 45 01.75 .15 4 5.4424 . 0058 + 3120 4- 16 4- . 0021 294 4- 82 14 22.49 .07 18 5.2906 .0028 8926 4- 552 .0029 295 4- 48 58 37. 19 .30 1 5.153S .0113 + 2285 + 13 .0911 296 43 04 17. 25 .29 1 5.1936 .0109 4- 6083 4- 63 .2743 297 4- 55 55 38.90 .48 4. 6937 .014 4- 1652 4- 14 4- .039 *298 4- 05 52 06.96 .11 7 4.4578 .0039 + 251 n *^ 4- 27 4- .0168 299 + 14 32 03.76 .06 23 4. 4039 . 0022 4- 3905 4- 19 4- . 0204 300 4- 36 57 03.65 .11 7 4.2959 .0050 4- 2987 4- 12 . 0147 301 + 37 25 24.62 .18 3 4.0069 .0049 4- 2920 4- U 4- . 0461 *302 4- 49 49 33.75 .30 1 4.0157 . 0123 4- 2190 + 10 4- .0142 303 + 40 05 54.51 .26 1 3.7564 .0100 + 2840 4- 10 .0697 304 24 03 29. 05 .13 6 3.7222 .0060 + 5260 4- 27 .1311 305 + 37 15 43.15 .11 7 3.5458 .0042 + 2985 4- 10 .0092 "306 + 48 21 56.68 .18 3 3.2029 .0058 4- 2299 4- 9 . 0159 307 4- 58 45 24.50 .25 1 3.0992 .0110 + 1303 + 12 4- . 0199 308 4- f>2 23 40.57 .07 17 2.8255 .0025 4- 1959 4- 8 . 0006 309 4- 12 39 09.44 .06 24 2.9299 .0022 4- 4044 4- 12 .2371 310 4- 43 31 58.67 1. 9728 4- 2650 4- 6 4- .050 311 4- 68 48 5S.74 .11 7 1.6258 .0041 499 1 4- 14 4- . 3237 31-2 4- 27 47 42. 17 .07 20 2. 3701 .0031 4- 3380 4- 8 .7589 313 + 25 39 56.97 .18 3 1.4703 .0057 + 3538 4- 5 .0497 314 4- 47 39 22. 19 .41 1 1. 4053 .014 4- 2358 4- 5 4- .013 *315 + 72 12 34.25 .11 7 1.6576 .0040 1565 4- 30 .2731 606 UNITED STATES NORTHERN BOUNDARY COMMISSION. [L'OOJ Catalogue of 500 stars "l Number. s a dj < ri Name. Magnitude. Approximate right ascen- sion, 1875.0. OJ 'go >_a 'a a s o a'S a *4 *333 6289 39 Draconis 5 22 04 9 -f- 874 18 4- 22 3:>4 6302 X Draconis 4 5 23 18 6 1 075 9 15 1 56 '335 6318 jj 25 58 8 -f 820 j + 38 4-1 61 336 6325 1 AqnilsB . 5 5 28 24 3 4- 3 272 -f 05 g. 337 6355 a Lyras 1 32 42 4 4- 2 031 4- 1 00 1 16 *338 6365 6 35 58 1 4- 2 036 4- 2 12 48 339 6390 e 1 L/yrse 5 40 11 9 4- 1 986 _L i 76 04 340 6387 110 Herculis 5 40 17 4- 2 582 4- 2 + 08 4- (>5 341 6397 111 Hercnlis 5 5 41 30 1 4- 2 649 _i_ i -)- 03 1 29 342 6421 6 44 16.0 4- 1. 547 + .35 +2*08 343 6429 /3 Lyrai 3 45 27.9 + 2. 214 -L 1 .53 2 51 344 6440 a Sagittarii. .. 3 47 30.8 -f 3. 723 ^ 03 + 2H 345 6463 5 49 21 4 -f 0. 887 4 00 62 346 6478 50 Draconia 5 50 23 6 1 901 55 +1 18 +1 65 *347 6476 6 51 29 3 4- 1 580 o +1 45 4-1 54 348 6487 e Auiiihr . 3 5 53 57 + 2 721 _i_ i 05 4- 74 349 6491 y Lvrse . 3 54 16 -f- 2 242 4- 1 50 1 3H 350 6526 X Aquilse 3 59 36 9 -f 3 184 2 16 57 351 6528 f AquilsB 3 18 F9 39 8 -J- 2 755 OS 1 03 352 6553 17 Lyra} e 19 02 42 + 2 266 4. i 12 42 353 6586 55 Draconis .. 6 09 17 7 -f 238 17 -f- 24 4- 56 354 6584 43 Sagittarii 5 10 19 2 4- 3 514 6 3 50 5 74 355 6585 22 Aqnilffi 6 10 19 9 -f- 2 969 1 73 1 78 3C6 6C12 <5 Draconis . . . 3 12 31 3 + 033 23 4- 25 4- 74 357 60-J8 K Cvuni . . 4 14 12 8 + 1 388 3 14 4- 40 358 6024 6 14 47 4 + 2 005 I 04 -(- 60 359 6650 T Draconis . .- 4.5 17 56 7 1 108 58 4- 70 +1 06 360 6646 S Ai|llil;r 3.5 19 11.7 -f 3.024 _ 2 -4- 11 4- 03 [201] CATALOGUE OF 600 STAES. 607 for the epoch 1875.0 Continued. Number. Declination, 1875.0. Probable error of S, 1875. - Ji .3 *S Annual varia- tion, 1875.0. Probable error of annual va- riation. (Pi 23 340 -)- 20 25 41. 18 .18 3 -f- 3. 1592 .0054 + 3692 13 .3475 341 + 18 02 37.70 .21 2 + 3.7118 .0060 + 3791 15 + .1001 *342 + 49 17 39.20 .30 1 + 3.8772 .0109 + 2198 6 + .0278 343 -j- 33 13 07.21 .06 22 + 3.9352 . 0025 + 3150 11 .0171 344 26 26 59. 03 .12 7 + 4.0506 .0049 + 5296 42 .0772 345 + 59 14 09.28 .12 7 + 4.2994 .0036 + 1257 9 -f .0138 346 + 75 17 07.67 .12 6 + 4.4487 .0059 2730 86 + . 0745 347 + 48 42 14.32 .56 ...... -f 4. 3480 .0131 4- 2216 8 .1196 348 + 14 54 00.16 .13 5 + 4.5926 .0045 4 3831 21 .0846 349 + 32 31 09.33 .11 7 + 4. 6905 .0041 4 3157 13 .0138 350 5 04 05.79 .10 9 + 5.0622 .0041 + 4462 34 .0957 351 -f- 13 40 45.01 .07 20 + 5. 0587 .0030 -f 3856 23 .1033 352 + 32 18 21.38 .23 2 + 5. 4360 .0064 4 3170 16 + . 0178 353 -f 65 46 10.12 .19 2 + 5.9941 . 0072 + 303 24 + . 0226 354 19 10 24. 10 .12 6 + 6.0397 .0045 4 4855 52 .0174 355 + 4 36 57.77 .41 1 + 6.0443 .0079 4 4102 33 .0138 356 -f 67 26 30. 05 .08 16 + 6. 3259 .0025 + 45 32 + .0854 357 + 53 08 18.45 .11 8 4- 6.4911 .0035 + 1901 12 + .1100 "358 4- 40 07 51.59 + 6. 4379 4- 2742 17 -4- .009 359 4- 73 07 22. 06 .14 5 + 6.7984 .0051 1589 82 [ , WUW + . 1086 360 + 2 52 01.79 .07 19 + 6. 8691 .0028 + 4142 39 + .0763 608 UNITED STATES NOETHEEN BOUMDAEY COMMISSION. [202] Catalogue of 500 stars Number. a l a cjj <3 CQ Name. Magnitude. Approximate right ascen- sion, 1S75.0. Annual varia- tion in a. &a dP M v 361 6657 5.5 h. m. s. 19 20 15 4 8. 4 2 480 8. 4 2 a 33 II 1 65 362 6661 6.5 20 45 9 4 2 619 4- 1 _|_ 03 04 363 6681 6.5 23 31 2 4 1 090 6 07 -1- 7 r > 364 6690 Cvcni . 3 25 40 8 4 2 417 -L 1 _|_ 06 04 365 6697 t 2 Cvcni . 5 26 33 3 4 1 514 2 _j- 08 4 55 396 6698 8 Cygui 6 27 08. 3 + 2.234 4 1 10 1 33 367 6713 K AquilsB 4 30 10 4- 3 230 4 1 92 JO "368 6728 5.5 32 33.9 + 1.910 4- 62 41 70 3(i9 6734 Cveni . 4 33 05 4 4 1 609 a 08 41 15 370 6748 5 35 52 7 _j_ i 356 n 4- 17 41 90 371 6758 10 Vulpeculse. 6 38 31. 1 + 2.493 JL I 13 1 45 372 6772 3 40 19 4- 2 852 1 1 08 34 *373 6780 5 40 48.6 + 1. 178 y 48 57 374 6779 6 Cvffni. . 3.5 41 04. 1 + 1.876 o 10 1 12 375 6802 1.5 44 41. 1 4 2.928 2 4 14 4 31 *376 6817 5 46 20 -f 2.062 4. l 10 4 05 *377 6830 6 48 26 2 -|- 1.763 56 68 378 6836 e Draconis ...... 5.5 48 35.1 0. 173 44 41 40 43 11 379 6833 /? Acjuilse.. 3.5 49 10.4 + 2.947 1 34 89 380 6999 (5) 49 17.8 60 647 29716 4 57 41 16 381 6rt56 ih Cvfirni . . 5.5 52 23 9 -f 1.554 _ 2 4 20 43 19 *382 0865 6 53 19.9 4 1 639 2 4 40 41 50 383 6879 15 Vulpeculte. .. 5 55 57.2 -f 2 463 -L 1 2 01 5 04 384 6893 T Aquilse . 5.5 58 02 4 2 933 2 1 33 1 14 "385 6937 28 Cvgni 5 20 04 47.2 4 2 226 -L 2 1 14 2 53 *386 6970 68 Draconis . 6 09 31 9 4 992 14 4 51 42 09 387 6965 o 2 Cygni ...... 4 09 41 8 + 1 889 17 4 17 388 6974 3 11 07 + 3.331 8 23 -)- 03 389 7005 K Cephei . .. 4.5 13 03 7 1 899 165 41 28 42 93 390 7004 2 15 44 7 4 4 787 59 33 4 02 *391 7024 71 Draconis . 6 5 17 31 3 4 1 014 14 4- 36 -1 fli 392 7022 y Cygni 3 17 44 5 4 2. 152 J- 2 16 1 89 393 7031 TT Capricorni ... ... 5 20 09 9 4 3 441 11 1 5 -1-1 27 394 7061 40 Cygni 6 22 56 4 4 2 241 -4- 2 C7 2 41 *395 7073 42 Cygni 6 24 34 4 4 2 287 _)_ 2 13 41 04 396 7088 e Delphini 4 27 14.4 4- 2. 866 1 .43 19 397 7098 8 Cepbei 5 27 28.8 + 1.016 15 4 .20 4 29 "398 7100 6 28 31 3 -j- 2 086 -J- 2 06 00 399 7124 5 5 30 31 9 210 67 33 4 24 400 7121 4 31 41 2 4 2 811 o 23 1 41 401 7140 29 Vnlpecul 5 5 32 56 3 4 2 676 _L 1 4 44 88 402 7149 a Delphini . . 3.5 33 50 4 2 789 05 18 403 7166 6 35 46 3 + 1 560 3 17 4 07 404 7171 a Cygui . .... . 1 37 10 3 4 2.044 4- 2 25 94 405 7173 6 Delphi ni 4 37 37 4 4 2 800 o 33 1 fil [203] CATALOGUE OF 500 STARS. 609 for the epoch 1875.0 Continued. Number. Declination, 1875.0. Probable error of <5 di? Proper motion in S. o / // II // it H II it 361 + 24 41 17.62 .21 2 4- 6. 328(5 .0057 4- 3348 22 .6515 362 + 19 51 03.13 .25 1 + 6.8874 .0061 + 3555 27 .0344 *363 -f 57 46 3-2.43 .40 1 4- 7.1371 .0103 + 1455 15 .0105 364 4- 27 41 54.06 .09 11 4- 7.3094 . 0038 + 3247 24 .0144 365 4- 51 27 51. 12 .12 7 + 7.5195 .0033 + 2024 14 4- . 1245 366 + 34 11 17.40 .17 3 4- 7.1381 .0068 + 3001 21 .0043 3G7 7 18 13.08 .10 9 + 7. 6886 .0044 4- 4317 52 4- . 0008 308 -f 43 25 38. V 3 -j- 7. 9023 + 2526 17 4- . 0-21 369 + 49 55 56.07 .11 8 + 8. 1709 .0034 4- 2122 16 -f- . 2475 "370 -f- 54 40 52.85 .35 1 + 8. 3070 .017 + 1783 15 4- .160 371 + 25 28 26.27 .19 2 + 8.3641 .0057 4- 3269 29 + .0065 37-2 4- 10 18 36.31 .06 25 4- 8. 4920 .0021 + 3732 41 .0084 373 -j- 57 43 08.02 .28 1 + 8.4776 .0 06 4- 1545 17 .0617 374 -j- 44 49 35.66 . 12 6 + 8. 5908 .0044 4- 2444 18 + . 0308 375 + 8 32 22.75 '.06 27 + 9.2151 .0020 4- 3841 46 4- . 3701 376 + 40 1G 56. 92 .41 1 + 8.9377 . 0132 + 2647 21 . 0365 *377 + 47 36 34.95 .24 2 + 9.1196 .0095 4- 2256 18 .0188 378 4- 69 56 58.38 .12 7 + 9. 1772 .0041 - 245 56 4- .0271 379 4- 6 05 45.45 .06 24 + 8. 7049 . 0021 4- 3783 - 46 .4909 380 + 88 55 51. 48 .06 22 4- 9.2170 .0026 78715 56385 + .0116 381 4- 52 06 28.04 .13 5 4- 9. 4175 .0047 4- 1955 17 .0281 382 4- 50 34 02. 65 .56 + 9. 5436 .015 4- 2066 18 + . 026 383 4- 27 24 32.89 .24 2 4- 9. 7185 .0067 -j- 3110 33 .0004 384 4- 6 55 35.57 .15 4 4- 9. 8854 .0064 -f 3684 51 4- . 007(1 385 4- 3G 28 21.23 .22 2 4- 10.3933 .0067 + 2733 28 4- . 0057 *3S6 4- 61 42 01.60 .26 1 + 10.8185 .0076 4- 1196 24 4- . 0779 387 + 46 21 46.84 .12 7 4- 10.7554 .0042 + 2279 22 + . 0027 388 12 55 50. 43 .07 19 + 10.8577 . 0025 4- 4039 77 4- . 0003 389 + 77 20 02. 43 .10 9 4- 11.0284 .0038 2360 220 4. .0283 390 57 07 59. 13 .24 2 4- 11.1055 .0100 4- 5741 212 .0902 *391 + 61 51 39.15 .37 1 + 11.3494 .0094 4- 1166 24 4- . 0251 39-2 + 39 51 26.82 .09 12 4- 11.3333 .0026 + 2539 28 .0069 393 18 37 11.65 . 11 7 4- 11.4971 .0041 + 4060 89 .0173 394 4- 38 01 50.23 .18 3 4- 11.6583 .0070 + 2576 30 .0541 *395 + 36 02 18. 19 .19 2 + 11.8195 .0072 + 2642 32 .0086 396 4- 10 52 47.17 .08 15 4- 11.9939 .0024 4- 3294 56 .0219 397 4- 62 34 27. 40 .12 6 4- 12.0075 . 0038 + 1138 25 .0251 398 -j- 42 46 00.62 4- 12. 1784 4- 2374 28 4- . 073 399 4- 7-2 06 28. 99 .15 4 + 12.2255 .0060 '299 77 . 0196 400 H- 14 09 41.07 .22 2 -f 12.2709 .0064 + 3187 55 .0541 401 + 20 45 48. 44 .27 1 + 12.3925 .0078 + 3015 49 .0188 402 4- 15 28 20.30 .10 8 4- 12.4808 .0042 4- 3138 54 4- . 0082 *403 4- 55 33 52.71 4- 12.5450 4- 1711 22 .060 404 + 44 50 03:97 .06 24 4- 12.6916 . 0020 4- 2253 28 .0084 405 4- 14 37 37.87 .22 9 4- 12.6675 .0000 + 3098 54 .0631 G10 UNITED STATES NORTHERN BOUNDARY COMMISSION. [204] Catalogue of 500 stars Number. | 3 a dj i Name. Magnitude. Approximate right ascen- sion, 1875.0. ls > a ~* a 3.2 o-S q HO 400 7795 y Aquarii .... . . 3 15 12 + 3 102 4 Q." -i 0^ *461 7800 2 Lacerta} . ......... 5 15 P2 + 2 468 4- 14 ''3 462 7814 TT Aquarii . .... 5 18 53 6 + 3 065 j 17 7 .. . ... .. 5 19 27 -f- 2 419 J- 1 r i 54 7-1 464 7843 38 Pegasi . 6 24 18 9 4- 2 738 -I- 1 1 00 F9 4(35 7848 6 1 Cephei 4 5 24 31 9 + 2 215 4- 17 + 56 4-" 01 466 7855 a Lacertae. 4 26 OS. 6 -)- 2. 4">9 4. 17 + 05 + 55 467 7868 17 Aqnarii 4 28 56.0 -f 3 084 4-1 "8 468 7881 5 5 30 04 4 _|_ i 082 '!'! -I 59 4- 1 1 *469 7882 6 30 42 + 2 479 -4- 17 07 i i 40 *470 7907 6 34 31 9 -)- 1 301 18 4- 7fi 1 'i 80 471 7908 f Pegasi 3 35 13.6 -f 2 988 4. 2 00 +1 63 472 7923 TI Pegasi 3 37 08.7 + 2 K)4 4. 11 30 1 18 *473 7945 A Perils! .. 4 5 40 30 6 + 2 883 4- H 11 Ori 474 7958 ft Pegasi 4 43 58.3 -f 2 888 _L 9 0'? 4- 07 *475 7962 14 LacertcB . e 44 43 7 _j_ 2 694 -)- 17 4- 1S 5 476 7967 ( Cepbei 4 45 14.0 -)- 2 119 4- 22 + 26 4- 30 477 7970 A Aquarii 4 40 05.5 -f- 3 131 99 1 73 478 7992 a, Piscis Australis ...... 1 50 44. 3 -J- 3 327 21 28 4- ( )2 479 8023 o Andromeda} 4 5(5 10.4 + 2 747 4- l l > 04 ; (J4 *480 8024 6 5 56 14 + 2 519 4- '2fi 10 1 31 481 8032 2 57 43 1 + 2 904 4- 12 - ^fi 1 47 482 8034 a Pegasi . ... 2 58 32 1 + 2 984 4- fi "3 1 81 483 8036 3 AudromedjB ......... 5 5 58 34 5 _|_ g (576 4- 2'i . _ 0.1 + ri *484 8059 5 Andromeda) . ..... 6 23 02 01 9 + 2 708 + 24 + 01 _L Ql 4tf5 8083 6 07 16 2 + 2 8U1 . 37 00 i 09 486 8124 5.5 13 30 1 -f 2 438 + 41 +1 61 +3 6 487 8128 6 13 55 7 -f- 2 842 + 01 4K i (i r * 483 8177 6 Pieoium... . 5 21 37 6 + 3 041 4- 3 1 64 3 O'l "483 8206 72 Pegasi 5.5 27 45 1 + 2 9(i3 4- 16 "1 53 490 8224 A Andromeda) . . 4.5 31 27 1 + 2 917 4- 28 4- 02 00 491 8229 ( Andromedss 4 23 32 00 6 + 2 923 4- 25 4- 2R 1 70 492 8233 i Pisciuui 4 5 33 31 4 + 3 085 3 . 10 _i_i i -j 493 8238 y Cepliei 3 34 13 * -f 2 405 4- 73 4- 4 -j-1 15 494 8237 K Andromeda? 4.5 34 15 4 -f 2 937 4- 26 4- 47 11 *495 8273 5 41 56 6 -f- 2 8''3 60 - Q> - i *m [207] CATALOGUE OF 500 STAES. for the epoch 1875.0 Continued. 613 Number. Declination, 1875.0. Probable error of 6, 1875. 4J 1 V M-\J + .041 471 + 10 10 45.77 .07 18 4- 18.6852 .0031 + 1497 89 .0127 472 + 29 34 04.43 .11 7 4- 18.7101 . 0042 4- 1366 74 .0478 473 + 22 54 29.73 .12 6 4- 18.8352 .0040 4- 1347 80 .0248 474 + 23 56 31. 11 .12 6 4- 18.9105 .0043 4- 1294 81 .0503 *475 + 41 17 31.12 .30 1 + 18.9721 .0076 4- 1185 66 .0102 476 4- 63 32 35.59 .10 9 4- 18.8635 .0031 + 903 35 . 1330 477 8 14 39.10 .09 11 4- 19.0501 .0037 + 1364 103 4- . 0357 478 30 17 03. 08 .12 7 4- 18.9746 .0057 4- 1371 123 .1708 479 + 41 39 15.78 .12 6 + 19.2431 .0043 4- 1019 70 .0381 *480 + 56 26 02.61 .33 1 4- 19.2638 .0134 4- 926 55 .0191 481 4- 27 24 18.34 .12 7 4- 19.4466 .0038 + 1001 83 .128'} 482 4- 14 31 5!'. 01 .06 24 4- 19.2872 .0022 4- 1071 90 .0501 483 4- 49 22 22.11 .18 3 4- 19.4886 .0053 4- 959 66 4- . 1503 *484 4- 48 36 54.6-2 .25 1 4- 19.5354 . 0062 4- 909 68 4- .1181 '485 4- 56 28 41.74 .22 2 + 19.7947 .0076 4- 919 79 4- . 2689 486 4- 67 25 40.26 .19 6 4- 19.6601 .0044 + 636 51 4- . 0172 *487 4-41 23 38.04 .23 1 4- 19.6509 .0067 + 742 78 + . 0005 488 -j- 5 41 33.03 .12 6 4- 19.7175 .0039 4- 652 96 .0563 *4i-9 4- 30 38 07.66 .25 1 4- 19.8347 . 0060 4- 520 89 .0213 4'JO -j- 45 43 51.87 .19 3 4- 19.4689 .0047 4- 446 85 .4300 491 4- 42 34 34.26 .13 6 4- 19.8999 .0050 4- 434 86 .0050 492 4- 4 56 56.19 .07 19 4- 19.4773 .0029 4- 437 102 4432 49:? 4- 76 56 04.87 .07 21 4- 20.0711 .0022 4- 304 49 + . 1435 494 4- 43 3:! 31. 17 .25 2 4- 19.9077 .0060 + 395 87 .0-201 M95 + 67 06 44. 16 .16 4 + 19.9722 .0051 4- 238 78 .0198 614 UNITED STATES NOKTHEKN BOUNDARY COMMISSION. [208] Catalogue of 500 stars a Igd a 1 . C O iO e3 a t4 ojj Name. o 1 1- r a ii (Pa 44 V e -1j fi-.^f o c -^ 3 o * X