
 < 
 
 PUBLICATIONS 
 
 OP THE 
 
 Vassar College Observatory 
 
 No. 1 
 
 MARY W. WHITNEY, Director 
 
 4 
 
 * 
 
 "}■. 
 
 « 
 
 r 
 
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 Cornell University 
 Library 
 
 The original of this book is in 
 the Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924012303529 
 
PUBLICATIONS OF THE VASSAK COLLEGE 
 OBSERVATORY, No. 1. 
 
 Mart W. Whitney, Director. 
 
 Catalogue of Stars 
 
 One Degree of the North Pole 
 
 OPTICAL DISTORTION OF THE HELSINGFORS 
 ASTRO-PHOTOGRAPHIC TELESCOPE 
 
 DEDUCED FROM 
 
 PHOTOGRAPHIC MEASURES 
 
 BY 
 
 CAROLINE E. FURNESS. 
 
 Assistant in the Observatory. 
 
 Submitted in partial fulfillment of the requirements for the degree of Doctor of 
 Philosophy in the Faculty of Pure Science, Columbia University. 
 
 POTJGHKEEPSIE, N. Y. 
 1900. 
 
61B 
 
 PRESS OF 
 
 THE NEW ERA PRINTING COMPANY, 
 
 LANCASTER, PA 
 
INTRODUCTION. 
 
 The Vassar College Observatory was established in 1865, when 
 Vassar College was first opened to the public. It was built and 
 equipped for purposes of instruction, the plan of founder and 
 trustees not including scientific work for publication. The first 
 director was Maria Mitchell, well known as a discoverer of comets, 
 and as the recipient of a medal from the King of Denmark for the 
 dis6overy of a comet in 1847. Professor Mitchell published a 
 series of observations on the surface features of Jupiter and Sat- 
 urn in Silliman's Journal and the American Journal of Science. 
 Since 1890 an effort has been made to carry on a certain amount 
 of observational work outside that involved in instruction, and 
 this has been given mainly to minor planets and comets. Publi- 
 cations have been sent with more or less regularity to the current 
 astronomical journals. The present paper is the first regular 
 publication of the observatory. 
 
 The site of the observatory is on the grounds of Vassar College, 
 about three miles east of the Hudson River, in Poughkeepsie, 
 New York. 
 
 The adopted latitude of the observatory is 41° 41' 18". The 
 adopted longitude of the observatory is 4 h 55 m 33 s .6 west of 
 Greenwich. 
 
 The latitude was obtained by Professor Mitchell in 1872, by the 
 zenith telescope method. The telescope was loaned by the U. S. 
 Coast Survey. The longitude was also obtained by Professor 
 Mitchell, by electric telegraph connection with Harvard College 
 Observatory in 1877. Clock signals were exchanged for one 
 evening only, and there was no change of observers. 
 
 The observatory consists of a central dome, with wings to the 
 south, east and north. The south wing contains a clock room 
 and a class room, the east wing, the meridian room, the north 
 wing the living rooms of director and assistant. In the dome, 
 twenty-five feet in diameter, stands a twelve-inch equatorial with 
 the usual equipment of eye-pieces and filar micrometer. The ob- 
 ject glass of the equatorial was originally made by^ Fitz of New 
 York, but was afterwards [recut by Alvan Clark. The telescope 
 was remounted in 1888 by Warner and Swasey of Cleveland, 
 Ohio. 
 
The meridian room contains a' transit circle made by Young of 
 Philadelphia, and afterward improved in its mounting by Fauth 
 & Co., of "Washington, D. C. The object glass of the transit 
 telescope has an aperture of four inches. The clock room con- 
 tains a Bond sidereal clock and a Bond chronograph ; also a 
 machine for measuring stellar photographs, made by the Repsold 
 firm of Hamburg. As this publication treats only of work upon 
 photographic plates, measured with the Repsold machine, it is not 
 necessary that a more detailed account of the observatory equip- 
 ment should be given at this time. 
 
 The Repsold measuring machine was the joint gift to the ob- 
 servatory of Miss Catherine Bruce and Mr. Frederick Thompson. 
 It is of the pattern described by Scheiner in Photographie der 
 Gestirne, p. 148. The additional details of its construction are 
 given in the following pages. 
 
 The object glass of the equatorial is cut for visual purposes and 
 we possess no correcting lens. It does not seem at present advis- 
 able, with the means and time at our disposal, to attempt to take 
 photographs, but the measurement and reduction of photographs 
 taken elsewhere fit in well with our other duties, and with this 
 purpose in view the Repsold measuring machine was secured. 
 
 The first piece of reduction, based upon stellar photographs, 
 was suggested by Professor Jacoby of Columbia University. He 
 had in his possession twelve polar plates taken by Professor 
 Donner of Helsingfors, Finland, partly measured and awaiting 
 reduction. Miss Caroline E. Furness, assistant in the observatory, 
 was placed in charge of the investigation. 
 
 We express our thanks to Professor Rees and Professor Jacoby 
 of Columbia University, who have given us much aid and sug- 
 gestion. 
 
 Our thanks are also due to our college trustee, Mr. Samuel 
 Coykendall, through whose generosity this publication is made 
 possible. 
 
 Miss Mary E. Tarbox and Miss Louise Ware, graduates of 
 Vassar College, have rendered much assistance in the labor of 
 computation. 
 
 We take this opportunity to give public expression to our 
 thanks for the publications received from other observatories. 
 
 Mary W. Whitney, 
 
 Vassab College. Director of Observatory. 
 
TABLE OF CONTENTS. 
 
 Section. Page 
 
 I. Description of the Plates i 
 
 II. Measurement of the Plates 3 
 
 III. Instrumental Corrections 4 
 
 IV. Method of Determining Right Ascension and Declina- 
 
 tion of a Star from the Measured Co-ordinates 26 
 
 V. Method of Determining the Plate Constants 28 
 
 VI. Method of Determining the Apparent Places of the 
 
 Standard Stars 1 30 
 
 VII. Determination of Plate Constants 36 
 
 VIII. Results of the Measures 42 
 
 IX. Final Results 57 
 
 X. Optical Distortion 63 
 
Catalogue of Stars within One Degree of the North Pole, and 
 
 Optical Distortion of the Helsingfors Astro-photographic 
 
 Telescope, deduced from Photographic Measures. 
 
 Description of the Plates. 
 
 In September, 1895, at the request of Professor Harold Jacoby, 
 of Columbia University, Professor Anders Donner, director of 
 the Observatory at Helsingfors, Finland, made a series of photo- 
 graphs of the region of the North Pole. Professor Jacoby had 
 two objects in view in securing these photographs ; first, to ob- 
 tain a catalogue of stars in "the immediate vicinity of the pole ; 
 and second, to investigate by a new method * the optical distor- 
 tion of the Helsingfors telescope. Twelve photographs were 
 made in all ; four with the telescope pointed at 90 declination, 
 and the remaining eight with it pointed at 89 °. The first four 
 plates furnish material for a catalogue of stars within one degree 
 of the pole, and their reduction forms the greater portion of the 
 present paper. The discussion of optical distortion in Section X 
 is based upon the results embodied in this catalogue. A reduc- 
 tion of the remaining eight plates, and a catalogue of the stars 
 found on them are reserved for a later publication. 
 
 The photographs were taken in the following manner on plates 
 provided with a reseau ; the telescope was set for the desired 
 right ascension and 89 declination, and a plate exposed. It was 
 next moved i° in declination, keeping the same right ascension, 
 and a second plate exposed. The telescope was then moved i° 
 in declination a second time, still keeping the same right ascen- 
 sion, and a third plate exposed. For a second set of three 
 plates the telescope was adjusted to a right ascension differing 
 from the first by 45 , and the changes in declination just described 
 were repeated, and similarly for a third and fourth set. The 
 twelve plates taken together cover a circular area 2° in radius 
 about the pole, with considerable overlapping. The four middle 
 
 * Astronomical Journal, Vol, XIII, p. 190. 
 
 1 
 
2 Stars within One Degree of the North Pole, and 
 
 plates contain the region within i° of the pole. Within this 
 limit they duplicate each other, but are taken with the telescope 
 in different positions. Three exposures were made on each plate, 
 6 m , 3 m , and 20 s in duration, and between consecutive exposures 
 the telescope was moved slightly in declination. Most of the 
 stars were so faint that the 20* images could not be measured ; 
 consequently they form no part of this reduction. The accom- 
 panying figure shows the overlapping of the twelve plates : 
 
 22*21™ 
 
 Fig. i. 
 
 The following table taken from the Helsingfors records gives 
 the data accompanying the exposures for the four central plates : 
 Hereafter the plates will usually be designated by the Roman 
 numeral in the last column. 
 
Optical Distortion deduced from Photographic Measures. 3 
 Table I. 
 
 Plate. 
 
 1895. 
 
 Obs. 
 Barom. 
 
 Tbermom. 
 Att. Ext. 
 R. R. 
 
 Length 
 
 of 
 Expos. 
 
 End of 
 Expos. 
 
 a 
 
 S 
 
 No. 
 
 Sept. 16, No. 
 
 3 
 
 mm 
 Dr. 757-3 
 
 
 
 +8.3 
 
 
 
 +7-7 
 
 m 8 
 
 6 
 
 3 
 
 20 
 
 h m s 
 2314 2 
 
 18 4 
 
 19 5 
 
 h m 
 22 24 
 
 1 
 900 
 
 I 
 
 Sept. 16, No. 
 
 6 
 
 D. 756.6 
 
 +8.0 
 
 + 7.2 
 
 6 
 
 3 
 20 
 
 02759 
 3135 
 32 36 
 
 I 24 
 
 900 
 
 II 
 
 Sept. 18, No. 
 
 2 
 
 Dr. 751.2 
 
 +8.7 
 
 + 8.2 
 
 6 
 
 3 
 
 20 
 
 2042 9 
 
 45 43 
 
 46 34 
 
 I924 
 
 900 
 
 III 
 
 Sept. 21, No. 
 
 14 
 
 D. 764.5 
 
 + 2-5 
 
 +2.1 
 
 6 
 
 3 
 20 
 
 3 18 34 
 
 22 12 
 
 23 2 
 
 4 24 
 
 900 
 
 IV 
 
 D. Donner. 
 
 Dr. Dreyer, assistant. 
 
 II. 
 
 Measurement of the Plates. 
 
 The star images were measured for the most part at the Col- 
 umbia Observatory with the Repsold measuring machine No. 1, 
 by Mrs. Herman S. Davis and Mrs. Annie Maclear Jacoby. A 
 few were measured by me with the Repsold machine of the Vas- 
 sar College Observatory. These measuring machines are of the 
 form described in Scheiner's Photographie der Gestirne, p. 148. 
 The reading microscope is furnished with two sets of movable 
 micrometer threads at right angles to each other. In making the 
 measurements at Columbia the horizontal screw was used through- 
 out, since it was decided after trial that bisections made with ver- 
 tical threads were more accurate than those made with horizontal 
 threads. 
 
 The plate was oriented in the machine so that one set of reseau 
 lines was parallel to the vertical micrometer threads, and the 
 microscope adjusted so that ten revolutions were equal to the 
 distance between two reseau lines, or 5™"- The screw-head was 
 then set at 47.75 and the carriage moved so as to place the parallel 
 threads over the preceding corners of the reseau square. Micro- 
 
4 Stars within One Degree of the North Pole, and 
 
 meter settings was then made in the following order : i° upper 
 left hand corner, 2 lower left hand corner, 3 large image, 4 
 middle image, 5 small image, 6° lower right hand corner, 7 
 upper right hand corner. The last setting was about i4 r -75- The 
 screw was then turned forward half a revolution, to I5 r -25,and the 
 process just described was repeated in the reverse order, ending 
 at 5 r .25- The object of turning the screw half a revolution for- 
 ward was to eliminate as far as possible the periodic errors, and to 
 distribute the wear on the screw. 
 
 It was deemed necessary to observe the corners of each square, 
 because the lines for the most part were too indistinct for accu- 
 rate bisection. In some cases even the corners were invisible and 
 this prevented the measurement of some of the stars. 
 
 Each coordinate was measured in two positions of the circle 
 180 apart, in order to eliminate personal errors entering into the 
 bisection of the star image. 
 
 A specimen sheet showing the form of recording the settings 
 will be found on page 8. The first two lines of the upper and 
 lower sections contain the actual settings on the reseau lines and 
 star images. In addition to the original record of the micro- 
 meter readings, each sheet contains the instrumental correc- 
 tions, and all the steps leading to the determination of the final 
 coordinates. Each image was reduced separately ; in fact, the 
 means were not taken until the final right ascension and polar 
 distance were obtained. 
 
 III. 
 
 Instrumental Corrections. 
 
 1°. Screw Corrections. 
 
 The portion of the screw used lies between 5' and 15'. The 
 variations in pitch of this portion of the screw were determined 
 by comparison with an accurate quarter millimeter scale, espe- 
 cially constructed for this purpose by Repsold, and the property 
 of Professor Jacoby,who kindly lent it to Professor Whitney for 
 determining the corrections of the Vassar screw. The method 
 of comparison is described by Professor Jacoby in the American 
 Journal of Science, 1896, Vol. 1, page 333. The following tables 
 give the corrections to the readings of the horizontal screw in 
 
Optical Distortion deduced from Photographic Measures. 5 
 
 tenths of microns, or units of the fourth decimal place. These 
 screw corrections, as will be seen from the specimen reduction 
 sheet on page 8, were applied to the settings on the star-images 
 only. Since the mean of the settings on each reseau line is very 
 nearly $ or 15', it was assumed that the screw corrections for the 
 four separate settings on each line would nullify one another. 
 
 Table II. 
 
 Micrometer. 
 
 Columbia, No. 1. 
 
 Vassar. 
 
 5E 
 
 +0.0000 
 
 -fo.0000 
 
 6 
 
 +O.OOIO 
 
 -j- 0.0028 
 
 7 
 
 4- 0.0004 
 
 +0.0038 
 
 8 
 
 — 0.0006 
 
 +0.0034 
 
 9 
 
 — 0.0024 
 
 +0.0018 
 
 10 
 
 — 0.0034 
 
 +0.0000 
 
 11 
 
 — 0.0044 
 
 — 0.0006 
 
 12 
 
 — 0.0042 
 
 — 0.0018 
 
 13 
 
 — 0.0044 
 
 — 0.0028 
 
 H 
 
 — 0.0028 
 
 — 0.0030 
 
 15 
 
 +0.0000 
 
 +0.0000 
 
 2°. Reseau Corrections. 
 
 The reseau used, Gautier No. 9, has been investigated by Pro- 
 fessor Donner, and the result published.* On pages 38-40 of his 
 paper will be found two tables of corrections to the measured co- 
 ordinates ; one set for the ^-coordinates, and one set for the Y- 
 cob'rdinates. They give the correction for the intersection of 
 every vertical line with every horizontal line. The unit is a tenth 
 micron. These corrections are applied in the following manner : 
 Suppose I and I + 1 are the numbers of two consecutive .X-lines, 
 and V and V + 1 the numbers of two consecutive F-lines, the 
 four lines enclosing a square. Let K t be the correction for the 
 line I, and K l+1 the correction for the line I + 1. Then E l is the 
 mean of the tabular values for the intersection of the .X-line with 
 the two F-lines V and V + 1; E l+ x is the mean of the tabular 
 values for the intersection of the .X-line I + 1 with the same two 
 F-lines. In other words, we find the correction for the middle of 
 the side of the square. 
 
 *Acta Societatis Seientiarum Fennicse. Tome XXI, Nr. 8. Determina- 
 tion des Constantes necessaires pour la E^duction des Cliches pris a Helsingfors. 
 
6 Stars within One Degree of the North Pole, and 
 
 3°. Error of Runs. 
 
 The error of runs for each square can be obtained directly from 
 the settings on the reseau lines. The method of correcting for it 
 will be given in the derivation of the general formula for finding 
 the star's coordinate from the measurements. 
 
 4°. Method of Obtaining the Corrected Cordinates. 
 
 Let I = number of lower reseau line, 
 l-\- i = number of upper reseau line, 
 
 D = difference between the reading of the lower line and 
 
 the reading of the star image, always positive. 
 Q = error of runs expressed in units of the fourth 
 
 decimal place, 
 R = difference between the readings of the upper 
 and lower reseau lines, always positive, = 
 io.oooo± Q, 
 K t = correction to position of lower reseau line taken 
 from Donner's table, 
 K l+l = correction for upper reseau line, 
 X, Y= final coordinates. 
 
 Then if we measure the coordinates from the line o, e. g., #-co- 
 ordinate, 
 
 X= 5 l + zi + & + (.E + i - K) | . 
 
 Since B will not differ much from io r it will be sufficient if in 
 
 place of -= we use — =f . The formula then becomes 
 
 Ji io ioo 
 
 In case we wish to measure the coordinates from the central reseau 
 lines we should use for 5Z, $(l — 14) and 5(? — 43). 
 
 This method of recording and reducing is due to Professor 
 Jacoby. 
 
 The specimen sheet appended shows in detail the method of ob- 
 taining the final coordinate. The screw correction has been in- 
 corporated with the general sum in order to shorten the process. 
 
Optical Distortion deduced from Photographic Measures. 1 
 
 The succeeding pages contain Table III, the table of corrected 
 coordinates. It includes the coordinates, direct, reversed and 
 mean, for both the big and middle images of every star on the 
 four^plates. 
 
Stars within One Degree of the North Pole, and 
 
 Polar Plate: Hels. Sept. 16, '95. No. 3. 
 
 Line. 
 
 December 2, 1896 : X Direct. 
 
 Line. 
 
 No. 
 
 Micr. 
 
 Big Image. 
 
 9-152 
 9.660 
 
 Sc. 
 
 Mid. Image. 
 
 Sc. 
 
 No. 
 
 Micr. 
 
 20 
 
 4-765 
 •754 
 
 5-250 
 .264 
 
 +15 
 + 6 
 
 9.142 
 9-639 
 
 + 15 
 + 6 
 
 21 
 
 I4-738 
 
 ■748 
 
 15.248 
 
 ■ 244 
 
 
 5.0082 
 
 9.4060 
 5.0082 
 4-3978 
 
 + 10 
 
 9-39°5 
 5.0082 
 
 4.3823 
 
 +10 
 
 
 14-9945 
 
 Low Line Read. 
 
 DifE. = D. 
 
 V*D 
 
 Ki 
 
 (Kh-i—Ki) — 
 , D 
 
 -X «?o 
 
 Screw Corr'n 
 
 Sum 
 
 Lower Line, mm. 
 
 Star's Coord. 
 
 5.OO82 
 9.9863 
 
 Q = —137 
 
 + 2.1989 
 + 6 
 
 + 
 
 + 3° 
 
 + 5 
 + 2.2030 
 
 — 3°- 
 —32.2030 
 
 + 5 
 
 + 2.1912 
 
 + 6 
 
 + 
 
 + 30 
 
 + 5 
 + 2.1953 
 
 — 3°- 
 —32-1953 
 
 + 5 
 
 ■Ki+i +5 
 Ki= +6 
 Diff. = —1 
 
 
 Line. 
 
 Noven 
 
 ber 18, 3 
 
 896: X reverse 
 
 d. 
 
 Line. 
 
 No. 
 
 Mlcr. 
 
 Big Image. 
 
 Sc. 
 
 Mid. Image. 
 
 Sc. 
 
 No. 
 
 Micr. 
 
 21 
 
 4.776 
 
 •737 
 
 5.202 
 
 .232 
 
 10.364 
 10.812 
 
 — 2 
 
 — 5 
 
 10.375 
 IO.842 
 
 — 2 
 
 — 5 
 
 20 
 
 I4-750 
 •773 
 
 I5-229 
 .201 
 
 
 4.9868 
 
 10.5880 
 
 14.9882 
 
 4.4002 
 
 — 4 
 
 IO.6085 
 
 14.9882 
 
 4-3797 
 
 — 4 
 
 
 14.9882 
 
 Low Line Bead. 
 DifE. = D. 
 
 yi d 
 
 Ki 
 
 (zi+i-*i)r 
 
 D 
 
 Screw Corr'n 
 
 Sum 
 
 Lower Line. mm. 
 
 Star's Coord. 
 
 4.980S 
 10.0014 
 
 Q = + 14 
 
 + 2.2001 
 + 6 
 
 + 
 
 — 3 
 
 + 2 
 -f- 2.2006 
 
 —3°- 
 
 — 32.2006 
 
 + 2 
 
 + 2.1898 
 + 6 
 
 + 
 
 — 3 
 
 + 2 
 + 2.1903 
 —30. 
 —32.1903 
 
 + 2 
 
 tfi+i +5 
 Ki= +6 
 DifE. = —1 
 
 
 Mean X 
 
 — 32.2018 
 
 
 — 32.1928 
 
 
 
Optical Distortion deduced from Photographic Measures. 9 
 
 Star 43. Measured by Furness. 
 
 Line. 
 
 No. 
 
 Micr. 
 
 44 
 
 4-752 
 •75o 
 
 5-278 
 •279 
 
 
 5.0148 
 
 Low Line Bead. 
 Diff. = D. 
 
 y* d 
 
 E, 
 
 , D 
 
 -#« To 
 
 Screw Corr'n 
 
 Sum 
 
 Lower Line, mm. 
 
 Star's Coord. 
 
 December 3, 1896 : Y Direct. 
 
 Big Image. 
 
 8.219 
 8.740 
 
 8.4795 
 5.0148 
 
 3-4647 
 
 + l-73 2 4 
 — 9 
 
 + 3 
 
 + 
 
 28 
 
 + 13 
 + 1-7359 
 +5- 
 +6-7359 
 
 +31 
 
 +22 
 
 +26 
 
 + 13 
 
 Mid. Image. Sc. 
 
 8.925 
 9.446 
 
 9-I855 
 5.0148 
 4.1707 
 
 +2.0854 
 — 9 
 
 + 4 
 
 + 34 
 
 + 8 
 +2.0891 
 
 +5- 
 + 7.0891 
 
 +20 
 +10 
 
 + 15 
 
 + 8 
 
 Line. 
 
 No. 
 
 45 
 
 Micr. 
 
 14-733 
 .741 
 
 15-270 
 .250 
 
 Q 
 
 14.9985 
 5.0148 
 9-9837 
 -163 
 
 Ki= 
 Diff. 
 
 —9 
 
 +9 
 
 Line. 
 
 No. 
 
 Micr. 
 
 45 
 
 4.770 ■ 
 .740 
 
 5-241 
 .260 
 
 
 5.0028 
 
 Low Line Bead. 
 Diff. = D. 
 
 E, 
 
 <Zi+i -Ei) - 
 , D 
 
 -XQYo 
 
 Screw Corr'n 
 
 Snm 
 
 Lower Line, mm. 
 
 Star's Coord. 
 
 Mean Y 
 
 November 20, 1896 : Y Reversed. 
 
 Big Image. 
 
 11.299 
 11.790 
 
 11-5445 
 
 15.0055 
 
 3.4610 
 
 + I-7305 
 
 — 9 
 
 + 3 
 
 — 5 
 
 + 8 
 
 + 1.7302 
 
 + 5- 
 
 + 6.7302 
 
 + 6.7330 
 
 Sc. 
 
 -11 
 -20 
 
 -l6 
 
 + 
 
 Mid. Image. Sc. 
 
 IO.590 
 II.072 
 
 10.8310 
 
 15.0055 
 
 4-1745 
 
 + 2.0872 
 
 — 9 
 
 + 4 
 
 — 6 
 
 + 3 
 
 + 2.0864 
 
 4- 5- 
 
 + 7.0864 
 
 T7.0878 
 
 — 4 
 
 — 7 
 
 — 6 
 
 + 3 
 
 Line. 
 
 No. 
 
 44 
 
 Micr. 
 
 14-752 
 •770 
 
 15.263 
 ■237 
 
 Q,- 
 
 15.0055 
 
 5.0028 
 
 10.0027 
 
 +27 
 
 E H i +0 
 
 Ki= —9 
 Diff. = +9 
 
10 
 
 Stars within One Degree of the North Pole, and 
 
 Table III. — Corrected Coordinates. Plate I. 
 
 Star. 
 
 X 
 
 Big Images. 
 
 Y 
 
 Big Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 I 
 
 +22.9453 
 
 .9481 
 
 +22.9467 
 
 —50.8083 
 
 .8062 
 
 — 50.8072 
 
 2 
 
 + 5-3844 
 
 •3885 
 
 + 5.3864 
 
 — 9.7128 
 
 .7157 
 
 — 9- 7 142 
 
 3 
 
 +24.9746 
 
 .9720 
 
 +24-9733 
 
 —44 4794 
 
 ■4753 
 
 —44-4774 
 
 4 
 
 +35-4435 
 
 •4493 
 
 +35.4464 
 
 —32-5757 
 
 •5693 
 
 —32.5725 
 
 6 
 
 +44.1476 
 
 •i55i 
 
 +44-I5I4 
 
 — 25.9000 
 
 .9007 
 
 —25.9004 
 
 7 
 
 +31-3441 
 
 •339° 
 
 +3I-34I6 
 
 —17.7044 
 
 .7070 
 
 —17.7057 
 
 8 
 
 +3I-35I3 
 
 •3477 
 
 +31-3495 
 
 —16.3648 
 
 ■3659 
 
 —16.3654 
 
 9 
 
 +23-3213 
 
 .3258 
 
 +23-3236 
 
 — 1 1 -39°5 
 
 •3858 
 
 —11.3882 
 
 IO 
 
 +45.0110 
 
 .0067 
 
 +45.0088 
 
 —20.5572 
 
 .5529 
 
 —20.5550 
 
 ii 
 
 +21.2718 
 
 .2685 
 
 +21.2702 
 
 — 7-735Q 
 
 •7347 
 
 —11.7348 
 
 12 
 
 +47-7341 
 
 •73i 1 
 
 +47.7326 
 
 — 6.6388 
 
 ■6385 
 
 — 6.6386 
 
 13 
 
 +43.1034 
 
 .1191 
 
 +43.1112 
 
 — 5- 2224 
 
 .2265 
 
 — 5-2244 
 
 14 
 
 +59-5247 
 
 •5303 
 
 +59-5275 
 
 — 2.8530 
 
 .8522 
 
 — 2.8526 
 
 15 
 
 +52.8485 
 
 .8508 
 
 +52.8496 
 
 — 1.8472 
 
 .8619 
 
 — 1.8546 
 
 16 
 
 +58.7837 
 
 .7820 
 
 +58.7828 
 
 + 1-7625 
 
 •7564 
 
 + 1-7595 
 
 17 
 
 +54- 363 
 
 .0407 
 
 +54-0385 
 
 + 2.9028 
 
 •8930 
 
 + 2-8979 
 
 18 
 
 + 19.9844 
 
 .9886 
 
 + 19.9865 
 
 + 2.7839 
 
 .7842 
 
 + 2.7840 
 
 "9 
 
 +38-4077 
 
 .4091 
 
 +38.4084 
 
 + 6. 741 1 
 
 .7464 
 
 + 6.7438 
 
 20 
 
 +34-3779 
 
 .3802 
 
 +34-3790 
 
 + 11.3692 
 
 •3575 
 
 +11-3634 
 
 21 
 
 +27-9325 
 
 ■9345 
 
 +27-9335 
 
 + 14.8407 
 
 .8459 
 
 + I4-8433 
 
 22 
 
 +46.2865 
 
 •2915 
 
 +46.2890 
 
 +29.2586 
 
 .2564 
 
 +29-2575 
 
 23 
 
 + 10.7241 
 
 .7252 
 
 +10.7246 
 
 + 8.8621 
 
 .8614 
 
 + 8.S618 
 
 24 
 
 +47-4451 
 
 • 4495 
 
 +47-4474 
 
 +33.1202 
 
 .1318 
 
 +33.1260 
 
 25 
 
 + I4-7758 
 
 .7806 
 
 + 14.7782 
 
 4-21. 9611 
 
 .9610 
 
 +21.9610 
 
 26 
 
 + 8. 1 195 
 
 .1169 
 
 + 8.1182 
 
 +21.4081 
 
 .4070 
 
 +21.4076 
 
 27 
 
 + I.333I 
 
 •3257 
 
 + I-3294 
 
 +35-1691 
 
 .1702 
 
 +35-1696 
 
 28 
 
 — 4.6425 
 
 .6338 
 
 — 4- 6382 
 
 +39-8213 
 
 .8227 
 
 +39.8220 
 
 29 
 
 — 9-6857 
 
 .6866 
 
 — 9.6862 
 
 +38.2426 
 
 ■ 2424 
 
 +38.2425 
 
 3° 
 
 — 7-7410 
 
 •7415 
 
 — 7-7412 
 
 +27.6632 
 
 .6615 
 
 +27.6624 
 
 3t 
 
 —18. 1 615 
 
 .1605 
 
 — 18.1610 
 
 +42.9125 
 
 .9106 
 
 +42.9116 
 
 32 
 
 —19.8304 
 
 .8352 
 
 —19.8328 
 
 +30.3051 
 
 •3055 
 
 +30.3053 
 
 33 
 
 —24-2575 
 
 ■2595 
 
 —25- 2585 
 
 +36-8582 
 
 .8603 
 
 +36.8592 
 
 34 
 
 —24.3796 
 
 .3800 
 
 —24.3798 
 
 +36.9228 
 
 ■9349 
 
 +36.9288 
 
Optical Distortion deduced from Photographic Measures. 11 
 
 Table III. — (Continued.') Corrected Coordinates. Plate I- 
 
 Star. 
 
 X 
 
 . Big Images. 
 
 Y 
 
 Big Images. 
 
 Direct. 
 
 Beversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 35 
 
 — 24.0960 
 
 .0995 
 
 — 24.0978 
 
 +3I-4850 
 
 .4885 
 
 +31.4868 
 
 38 
 
 — 23.0990 
 
 .0978 
 
 —23.0984 
 
 +17.8260 
 
 .8167 
 
 + 17.8214 
 
 39 
 
 —31-7337 
 
 .7308 
 
 —31.7322 
 
 +20.7775 
 
 •7733 
 
 +20.7754 
 
 40 
 
 —35-7056 
 
 .7096 
 
 —35-7076 
 
 +21.9363 
 
 •9363 
 
 +21.9363 
 
 41 
 
 —22.4889 
 
 ■4895 
 
 — 22.4892 
 
 + 8.7226 
 
 • 7145 
 
 + 8.7186 
 
 4= 
 
 —19.6396 
 
 .6389 
 
 —19.6392 
 
 + 4-9837 
 
 .9840 
 
 + 4-9838 
 
 43 
 
 —32.2030 
 
 .2006 
 
 — 32.2018 
 
 + 6.7359 
 
 .7302 
 
 + 6.7330 
 
 44 
 
 —47.5636 
 
 •5657 
 
 —47.5646 
 
 + 4.0003 
 
 ■99" 
 
 + 3-9957 
 
 45 
 
 —12.7930 
 
 •7933 
 
 —12.7932 
 
 + 0.0078 
 
 .0051 
 
 + 0.0064 
 
 46 
 
 — 20.4808 
 
 .4786 
 
 — 20.4796 
 
 — 3-899I 
 
 .8944 
 
 — 3.8968 
 
 47 
 
 —52.1609 
 
 •1574 
 
 —52.1592 
 
 —I3-5I07 
 
 .5116 
 
 —13-5112 
 
 48 
 
 — 5-8905 
 
 .8946 
 
 — 5.8926 
 
 — 0.1050 
 
 .1047 
 
 — 0.1048 
 
 49 
 
 — 6.0505 
 
 .0540 
 
 — 6.0522 
 
 — 0.2313 
 
 •2348 
 
 — 0.2330 
 
 50 
 
 —47.1179 
 
 .1118 
 
 —47.1148 
 
 — 16.2131 
 
 •2155 
 
 —16.2143 
 
 5i 
 
 —26.2338 
 
 •2347 
 
 — 26.2342 
 
 —12.8866 
 
 ■8903 
 
 —12.8884 
 
 52 
 
 —36-9373 
 
 •9353 
 
 —369363 
 
 — 22.9566 
 
 ■9528 
 
 —22-9547 
 
 53 
 
 —17.4309 
 
 ■4344 
 
 —17.4326 
 
 — 9.7622 
 
 •7598 
 
 — 9.7610 
 
 54 
 
 —32-57I4 
 
 .5758 
 
 —32-5736 
 
 —23.5097 
 
 .5046 
 
 —23.5072 
 
 55 
 
 — 6.6942 
 
 .6922 
 
 — 6.6932 
 
 — 4-2510 
 
 .2476 
 
 — 4-2493 
 
 56 
 
 — 19.6199 
 
 .6221 
 
 — 19.6210 
 
 —17-0983 
 
 .0997 
 
 — 17.0990 
 
 57 
 
 —12.8857 
 
 .8816 
 
 —12.8836 
 
 — 11. 1209 
 
 .1226 
 
 — 11.1218 
 
 58 
 
 —14.6145 
 
 .6116 
 
 —14.6130 
 
 —14.8666 
 
 .8719 
 
 — 14.8692 
 
 59 
 
 — 13.6072 
 
 .6000 
 
 —13.6036 
 
 — 20.6847 
 
 .6791 
 
 — 20.6819 
 
 60 
 
 — 6.9856 
 
 •9834 
 
 — 6.9845 
 
 —1 1- 1557 
 
 .1488 
 
 — n. 1522 
 
 61 
 
 — 10.8260 
 
 .8248 
 
 —10.8254 
 
 — 22.7863 
 
 .7891 
 
 — 22.7877 
 
 62 
 
 — 9-1502 
 
 .1507 
 
 — 9-I504 
 
 — 19.3626 
 
 .3601 
 
 —19.3614 
 
 63 
 
 — 19.0203 
 
 •0235 
 
 — 19.0219 
 
 —49-5376 
 
 •5436 
 
 —49.5406 
 
 64 
 
 — 59269 
 
 •9238 
 
 — 5-9248 
 
 — 17.501 r 
 
 ■5049 
 
 —17.5030 
 
 65 
 
 + 8.6687 
 
 .6674 
 
 + 8.6680 
 
 — 46.0112 
 
 .0084 
 
 — 46.0098 
 
12 Stars within One Degree of the North Pole, and 
 
 Table III. — (Continued.) Corrected Coordinates. Plate I. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. 
 
 Middle Images- 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 I 
 
 + 22.9457 
 
 .9469 
 
 +22.9463 
 
 —50.4622 
 
 •4633 
 
 — 50.4628 
 
 2 
 
 + 5-39!4 
 
 .3870 
 
 + 5.3892 
 
 — 9-3647 
 
 .3662 
 
 — 9.3654 
 
 3 
 
 +24.9746 
 
 •9651 
 
 +24.9698 
 
 —44.1294 
 
 .1266 
 
 — 44.1280 
 
 4 
 
 +35-4477 
 
 •4451 
 
 +35.4464 
 
 —32.2295 
 
 .2312 
 
 —32.2304 
 
 6 
 
 +44-1471 
 
 .1589 
 
 +44.1530 
 
 —25.5588 
 
 .5669 
 
 —25.5628 
 
 7 
 
 +31-3*59 
 
 .3370 
 
 +3I.34I4 
 
 —17.3766 
 
 •3724 
 
 —17-3745 
 
 8 
 
 +3I-343I 
 
 .3402 
 
 +3I-34I6 
 
 — 16.0263 
 
 •0259 
 
 — 16.0261 
 
 9 
 
 +23.3245 
 
 .3262 
 
 + 23.3254 
 
 — II.0444 
 
 .0438 
 
 — 11. 0441 
 
 IO 
 
 +45.0095 
 
 .0092 
 
 +45.0094 
 
 — 20. 2230 
 
 .2150 
 
 — 20.2190 
 
 II 
 
 +21.2705 
 
 .2708 
 
 +21.2706 
 
 — 7-3943 
 
 ■3913 
 
 — 7-3928 
 
 12 
 
 +47-7374 
 
 ■7423 
 
 +47.7398 
 
 — 6.3030 
 
 ■3051 
 
 — 6.3040 
 
 13 
 
 +43.1010 
 
 ■1043 
 
 +43.1026 
 
 — 4.8896 
 
 .8964 
 
 — 4-8930 
 
 14 
 
 +59-5325 
 
 •5367 
 
 +59-5346 
 
 — 2.5175 
 
 •5183 
 
 — 2.5179 
 
 15 
 
 +52.8525 
 
 ■8513 
 
 +52.8519 
 
 — 1.5268 
 
 ■5269 
 
 — 1.5268 
 
 16 
 
 +58.7840 
 
 ■7792 
 
 +58.7816 
 
 + 2.091.1 
 
 .0928 
 
 + 2.0920 
 
 17 
 
 +54.0368 
 
 .0472 
 
 +54.0420 
 
 + 3-2383 
 
 .2299 
 
 + 3-2341 
 
 18 
 
 +19.9924 
 
 .9889 
 
 + 19.9906 
 
 + 3-1240 
 
 .1263 
 
 + 3-1252 
 
 19 
 
 +384134 
 
 .4088 
 
 +38.4III 
 
 + 7-0778 
 
 •0783 
 
 + 7.0780 
 
 20 
 
 +34.3885 
 
 •3762 
 
 +34.3824 
 
 + 11.7005 
 
 .7049 
 
 + 11.7027 
 
 21 
 
 +27.9405 
 
 .9407 
 
 + 27.9406 
 
 + 15.1763 
 
 •1793 
 
 + I5-I778 
 
 22 
 
 +46.3023 
 
 •3025 
 
 +46.3024 
 
 +29.6019 
 
 •5974 
 
 +29-5995 
 
 23 
 
 + 10.7264 
 
 .7283 
 
 + IO.7274 
 
 + 9.2029 
 
 •2047 
 
 + 9-2038 
 
 24 
 
 +47-4523 
 
 •4495 
 
 +47.4509 
 
 + 33.4660 
 
 -47I8 
 
 +33.4689 
 
 25 
 
 + 14.7862 
 
 ■79°3 
 
 +14.7882 
 
 +22.3027 
 
 •3051 
 
 +22.3039 
 
 26 
 
 + 8.1301 
 
 .1256 
 
 + 8.1278 
 
 +21.7507 
 
 • 7551 
 
 +21.7529 
 
 27 
 
 + 1-3337 
 
 •3323 
 
 + 1-333° 
 
 +35-5142 
 
 •5185 
 
 +35-5164 
 
 28 
 
 — 4-6283 
 
 .6248 
 
 — 4.6266 
 
 +40.1664 
 
 .1654 
 
 +40.1659 
 
 29 
 
 — 9-6765 
 
 .6746 
 
 — 9-67S6 
 
 +38.5882 
 
 •5924 
 
 +38.5903 
 
 3° 
 
 — 7-7242 
 
 •7224 
 
 — 7-7233 
 
 +28.0109 
 
 .0077 
 
 +28.0093 
 
 31 
 
 — 18.1630 
 
 •1570 
 
 — 18.1600 
 
 +43-2654 
 
 .2654 
 
 +43.2654 
 
 32 
 
 —19.8218 
 
 .8279 
 
 —19.8248 
 
 +30.6590 
 
 .6546 
 
 +30.6568 
 
 33 
 
 —24-2545 
 
 .2578 
 
 —24.2562 
 
 +37.2014 
 
 .2138 
 
 +37.2076 
 
 34 
 
 —24-3774 
 
 •3770 
 
 —24.3772 
 
 +37-2744 
 
 .2817 
 
 +37.2780 
 
Optical Distortion deduced from Photographic Measures. 13 
 
 Table III {Continued.') Corrected Coordinates. Plate I. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. 
 
 Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 35 
 
 —24.0933 
 
 .0991 
 
 — 24.0962 
 
 +3I-8348 
 
 .8386 
 
 +3I-8367 
 
 38 
 
 — 23.0900 
 
 •0895 
 
 —23.0898 
 
 +18.1781 
 
 .1702 
 
 + 18.1742 
 
 39 
 
 — 31.7220 
 
 .7212 
 
 —31.7216 
 
 +21.1174 
 
 .1019 
 
 +21.1096 
 
 40 
 
 —35-7o6l 
 
 .7109 
 
 —35-7085 
 
 +22.2888 
 
 .2804 
 
 + 22.2846 
 
 41 
 
 —22.4875 
 
 .4820 
 
 — 22.4848 
 
 + 9.0809 
 
 .0721 
 
 + 9-0765 
 
 42 
 
 —19.6368 
 
 •6393 
 
 — 7I9.6380 
 
 + 5-3342 
 
 •3373 
 
 + 5.3358 
 
 43 
 
 —32-I953 
 
 .1903 
 
 — 32.1928 
 
 + 7.0891 
 
 .0864 
 
 + 7-0878 
 
 44 
 
 —47-5546 
 
 •5577 
 
 —47-5562 
 
 + 4-3522 
 
 ■3293 
 
 + 4-3408 
 
 45 
 
 —12.7915 
 
 •79 '6 
 
 — 12.7916 
 
 + 0.3595 
 
 -3586 
 
 + O.3590 
 
 46 
 
 —20.4775 
 
 ■4776 
 
 — 20.4776 
 
 — 3-5418 
 
 •5424 
 
 — 3-5421 
 
 47 
 
 —52.1630 
 
 ■1530 
 
 —52.1580 
 
 —13.1664 
 
 ■1653 
 
 —13-1658 
 
 48 
 
 — 5.8889 
 
 .8894 
 
 — 5-8892 
 
 + 0.2455 
 
 ■ 2429 
 
 + 0.2442 
 
 49 
 
 — 6.0463 
 
 •0505 
 
 — 6.0484 
 
 + 0.1 126 
 
 .1132 
 
 + 0.1 129 
 
 5° 
 
 —47.1164 
 
 .1092 
 
 — 47.II28 
 
 —15-8591 
 
 .8587 
 
 -15-8589 
 
 51 
 
 — 26.2308 
 
 ■2357 
 
 —26.2332 
 
 —12.5344 
 
 •5359 
 
 —12.5352 
 
 52 
 
 —36-93I9 
 
 .9300 
 
 —36.9310 
 
 — 22.6044 
 
 .6066 
 
 —22.6055 
 
 S3 
 
 — 17.4261 
 
 •4334 
 
 —17.4298 
 
 — 9-407I 
 
 .4107 
 
 — 9.4089 
 
 54 
 
 —32-576I 
 
 •5735 
 
 —32.5748 
 
 —23-1595 
 
 ■ 1590 
 
 —23.1592 
 
 55 
 
 — 6.6944 
 
 •6967 
 
 — 6.6956 
 
 — 3-8973 
 
 .9004 
 
 — 3.8988 
 
 56 
 
 —19.6157 
 
 .6201 
 
 — 19.6179 
 
 —16.7459 
 
 •7436 
 
 — 16.7448 
 
 57 
 
 —12.8827 
 
 .87x2 
 
 — 12.8769 
 
 —10.7789 
 
 ■7833 
 
 — 10. 781 1 
 
 58 
 
 — 14.6118 
 
 .6109 
 
 — 14.6114 
 
 —I4-5I4I 
 
 • 5129 
 
 —I4-5I35 
 
 59 
 
 —I3-6I52 
 
 .6015 
 
 — 13.6084 
 
 —20.3245 
 
 .3192 
 
 — 20.3218 
 
 60 
 
 — 6.9868 
 
 •9798 
 
 — 6.9833 
 
 — 10.8071 
 
 .7989 
 
 — 10.8030 
 
 61 
 
 — 10.8260 
 
 .8270 
 
 — IO.8265 
 
 —22.4379 
 
 •4423 
 
 — 22.4401 
 
 62 
 
 — 9-I504 
 
 .1510 
 
 — 9-I507 
 
 — 19.0140 
 
 .0119 
 
 — 19.0130 
 
 63 
 
 — 19.0226 
 
 .0287 
 
 —19.0256 
 
 —49.1951 
 
 •1936 
 
 —49.1944 
 
 64 
 
 — 5.9264 
 
 .9271 
 
 — 5-9268 
 
 —17-1514 
 
 • 1527 
 
 —17.1520 
 
 65 
 
 + 8.6654 
 
 .6670 
 
 + 8.6662 
 
 —45.6624 
 
 .6621 
 
 — 45.6622 
 
14 
 
 Stars within One Degree of the North Pole, and 
 
 Table III. — (Gont.'). Corrected Coordinates. Plate II. 
 
 Star. 
 
 X 
 
 . Big Images. 
 
 Y 
 
 . Big Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 I 
 
 — 19.6722 
 
 •6754 
 
 —19.6738 
 
 —52.2321 
 
 .2267 
 
 —52.2294 
 
 2 
 
 — 2.9149 
 
 .9149 
 
 — 2.9149 
 
 — 10.8103 
 
 .8153 
 
 —IO.8128 
 
 3 
 
 —13-7549 
 
 •7517 
 
 —13-7533 
 
 — 49.2109 
 
 .2070 
 
 — 49.2090' 
 
 i 4 
 
 + 2.0730 
 
 .0677 
 
 + 2.0704 
 
 —48.2452 
 
 .2401 
 
 — 48.2426 
 
 5 
 
 +I3-3367 
 
 •3392 
 
 + i3-338o 
 
 —54.4698 
 
 •4753 
 
 —54.4726 
 
 6 
 
 +12.9355 
 
 -9357 
 
 + 12.9356 
 
 —49.6995 
 
 .7006 
 
 — 49.7000 
 
 7 
 
 + 9-7075 
 
 .7008 
 
 + 9-7042 
 
 —34-8477 
 
 .8472 
 
 —34-8474 
 
 8 
 
 + 10.6696 
 
 .6668 
 
 +10.6682 
 
 —33-9065 
 
 .9013 
 
 —33-9039 
 
 9 
 
 + 8.5342 
 
 -532I 
 
 + 8.5332 
 
 —24.7039 
 
 .7031 
 
 —24.7035 
 
 IO 
 
 +17.3322 
 
 •3345 
 
 +17-3334 
 
 —46.5470 
 
 •5531 
 
 —46.5505 
 
 ii 
 
 4- 9-6825 
 
 .6869 
 
 + 9-6847 
 
 — 20. 6904 
 
 .6824 
 
 — 20.6864 
 
 12 
 
 +29.1205 
 
 .1183 
 
 +29.1194 
 
 — 38.6722 
 
 .6676 
 
 — 38.6699 
 
 13 
 
 +26.8663 
 
 •8633 
 
 +26.8648 
 
 —34-3931 
 
 ■3998 
 
 —343964 
 
 14 
 
 +40.1337 
 
 .1273 
 
 +40.1305 
 
 —44.3621 
 
 .3518 
 
 —44-3570 
 
 15 
 
 +36.1183 
 
 .1181 
 
 +36.1182 
 
 —38.9181 
 
 .9147 
 
 —38.9164 
 
 16 
 
 +42.8825 
 
 .8710 
 
 +42.8768 
 
 —40.5763 
 
 •5748 
 
 —40.5756 
 
 18 
 
 + 16.2412 
 
 ■2347 
 
 + 16.2380 
 
 —12.3442 
 
 ■3442 
 
 —12.3442 
 
 19 
 
 +32.0386 
 
 .0409 
 
 +32.0398 
 
 —22.6153 
 
 .6184 
 
 —22.6168 
 
 21 
 
 +30-3795 
 
 .3881 
 
 +30.3838 
 
 — 9-4727 
 
 .4729 
 
 — 9-4728 
 
 22 
 
 +53-555o 
 
 •5531 
 
 +53-554° 
 
 —12.3302 
 
 •3309 
 
 —12.3306 
 
 23 
 
 +14.0156 
 
 •0159 
 
 +14.0158 
 
 — I-4987 
 
 .4921 
 
 — 1-4954 
 
 24 
 
 +57-1244 
 
 •1235 
 
 +57.1240 
 
 —10.4147 
 
 .4156 
 
 —10.4152 
 
 25 
 
 +26.1679 
 
 .1687 
 
 +26.1683 
 
 + 4.8716 
 
 .8695 
 
 + 4.8706 
 
 26 
 
 +21.0775 
 
 .0767 
 
 +21.0771 
 
 + 9.2026 
 
 .2100 
 
 + 9-2063 
 
 27 
 
 +26.0450 
 
 .0480 
 
 +26.0465 
 
 +23-7I34 
 
 .7149 
 
 +23.7142 
 
 28 
 
 +25.1262 
 
 .1239 
 
 +25.1250 
 
 +31-2233 
 
 ■2350 
 
 +31.2292 
 
 29 
 
 +20.4485 
 
 •4544 
 
 +20.4514 
 
 +33-6936 
 
 .6927 
 
 +33-6932 
 
 30 
 
 + I4-3306 
 
 •3343 
 
 +I4-3324 
 
 +24-8473 
 
 • 8454 
 
 +24.8464 
 
 31 
 
 + 17.7888 
 
 .7866 
 
 + 17.7877 
 
 +42.9988 
 
 .0038 
 
 +43.0013 
 
 32 
 
 + 7.6611 
 
 .6619 
 
 + 7-6615 
 
 +35-2929 
 
 .2878 
 
 +35-2904 
 
 33 
 
 + 9-1945 
 
 •1935 
 
 + 9-J940 
 
 +43-0544 
 
 .0497 
 
 +43.0520 
 
 34 
 
 + 9-I485 
 
 .1499 
 
 + 9-1492 
 
 +43.1841 
 
 .1840 
 
 +43.1840 
 
Optical Distortion deduced from Photographic Measures. 15 
 
 Table III. — ( Continued.') Corrected Coordinates. Plate II. 
 
 
 X 
 
 . Big Images. 
 
 Y. Big Images. 
 
 Star. 
 
 
 
 
 
 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. R 
 
 3versed. 
 
 Mean. 
 
 35 
 
 + 5-4983 
 
 • 5003 
 
 + 5-4993 
 
 +39-!522 
 
 1495 
 
 +39-I508 
 
 36 
 
 + 2.2747 
 
 .2695 
 
 + 2.2721 
 
 + I5-7789 
 
 7828 
 
 +I5-78o8 
 
 37 
 
 + I.0478 
 
 .0460 
 
 -j- 1.0469 
 
 +14.9990 
 
 9954 
 
 +14.9972 
 
 38 
 
 - 3-4856 
 
 .4909 
 
 — 3-4882 
 
 +28.8050 
 
 8140 
 
 +28.8095 
 
 39 
 
 — 7-485I 
 
 .4858 
 
 — 7-4854 
 
 +36-9957 
 
 9978 
 
 +36.9968 
 
 40 
 
 — 9.4610 
 
 .4629 
 
 — 9.4620 
 
 +40.6423 
 
 6505 
 
 +40.6464 
 
 41 
 
 — 9.5169 
 
 • 5147 
 
 — 9-5r58 
 
 +21-9523 
 
 9548 
 
 +21.9536 
 
 42 
 
 —10.1503 
 
 .1478 
 
 — 10.1490 
 
 +17.2989 
 
 2938 
 
 +17.2964 
 
 43 
 
 —17.7676 
 
 •7734 
 
 —17.7705 
 
 +27.4390 
 
 4441 
 
 +27.4416 
 
 44 
 
 —30.5523 
 
 •5473 
 
 —30.5498 
 
 +36-39!4 
 
 3875 
 
 +36.3894 
 
 45 
 
 — 8.8399 
 
 .8456 
 
 — 8.8428 
 
 + 8.9350 
 
 9397 
 
 + 8.9374 
 
 46 
 
 ■ — 17.0272 
 
 ■0235 
 
 —17.0254 
 
 +11.6352 
 
 6376 
 
 +11.6364 
 
 47 ' 
 
 — 46.1929 
 
 .1950 
 
 — 46.1940 
 
 +27.3002 
 
 3040 
 
 + 27.3021 
 
 48 
 
 — 4.0621 
 
 .0623 
 
 — 4.0622 
 
 + 3-9714 
 
 9688 
 
 + 3-9701 
 
 49 
 
 — 4.2688 
 
 .2622 
 
 — 4-2655 
 
 + 3-997Q 
 
 9938 
 
 + 3-9954 
 
 50 
 
 —44.5502 
 
 ■558i 
 
 —44-5542 
 
 +21.8303 
 
 8312 
 
 +21.8308 
 
 5i 
 
 —27.4634 
 
 .4648 
 
 —27.4641 
 
 + 9-3753 
 
 3792 
 
 + 9-3772 
 
 52 
 
 —42.1561 
 
 • 1596 
 
 —42.1578 
 
 + 9-857I 
 
 8541 
 
 + 9-8556 
 
 53 
 
 —19.0463 
 
 .0426 
 
 —19.0444 
 
 + 5-3436 
 
 3415 
 
 + 5-3426 
 
 54 
 
 —39-4752 
 
 .4711 
 
 —39-4732 
 
 + 6.3817 
 
 3772 
 
 + 6.3794 
 
 56 
 
 —25.7946 
 
 • 79 2 5 
 
 —25-7936 
 
 + 1.7060 
 
 7074 
 
 + 1-7067 
 
 57 
 
 —16.8067 
 
 .8082 
 
 — 16.8074 
 
 + 1.1510 
 
 1526 
 
 + 1.1518 
 
 58 
 
 —20.6754 
 
 .6714 
 
 —20.6734 
 
 — 0.2687 
 
 2752 
 
 — 0.2720 
 
 60 
 
 — 12.6714 
 
 .6683 
 
 — 12.6698 
 
 — 3-0427 
 
 0465 
 
 — 3-0446 
 
 61 
 
 — 23.6287 
 
 • 6254 
 
 — 23.6270 
 
 — 8.5265 
 
 5306 
 
 — 8.5286 
 
 62 
 
 — 20.0142 
 
 .0125 
 
 — 20.0134 
 
 — 7-3133 
 
 3099 
 
 — 7-3"6 
 
 63 
 
 —48.3696 
 
 ' -3714 
 
 —48.3705 
 
 — 21.6059 
 
 5957 
 
 — 21.6008 
 
 64 
 
 — 16.4216 
 
 •4256 
 
 — 16.4236 
 
 — 8.2829 
 
 2755 
 
 — 8.2792 
 
 65 
 
 — 26.3480 
 
 •3452 
 
 — 26.3466 
 
 -38.7338 
 
 7305 
 
 —38.7322 
 
16 Stars within One Degree of the North Pole, and 
 
 Table III. — (Continued.') Corrected Coordinates. Plate II. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. 
 
 Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 I 
 
 — 19.6819 
 
 .6807 
 
 —19.6813 
 
 —5I-8459 
 
 .8429 
 
 —51.8444 
 
 2 
 
 — 2.9289 
 
 .9277 
 
 — 2.9283 
 
 — 10.4194 
 
 .4244 
 
 — IO.4219 
 
 3 
 
 —13-7549 
 
 .7617 
 
 —I3-7583 
 
 —48.8222 
 
 .8225 
 
 —48.8224 
 
 4 
 
 + 2.0675 
 
 .0576 
 
 + 2.0626 
 
 —47.8510 
 
 .8485 
 
 —47.8498 
 
 5 
 
 + 13-3322 
 
 .3284 
 
 + I3-3303 
 
 —54.0749 
 
 ■ 0832 
 
 —54.0790 
 
 6 
 
 +12.9340 
 
 .9299 
 
 + 12.9320 
 
 —49.3208 
 
 .3190 
 
 —49-3199 
 
 7 
 
 + 9-6978 
 
 .6910 
 
 + 9-6944 
 
 —34-4527 
 
 •4553 
 
 —34.4540 
 
 8 
 
 + 10.6586 
 
 .6636 
 
 + 10.6611 
 
 —33-5084 
 
 .5108 
 
 —33-5096 
 
 9 
 
 + 8-5275 
 
 .5231 
 
 + 8.5253 
 
 —24.3142 
 
 .3107 
 
 —24.3124 
 
 IO 
 
 + 17-3244 
 
 •3237 
 
 + 17.3240 
 
 — 46.1605 
 
 .1622 
 
 — 46.1614 
 
 ii 
 
 + 9- 6 797 
 
 .6764 
 
 + 9.6780 
 
 — 20.2903 
 
 •2945 
 
 — 20.2924 
 
 12 
 
 +29.1192 
 
 .1116 
 
 +29 1 154 
 
 —3S-2845 
 
 .2796 
 
 —38.2820 
 
 13 
 
 +26.8483 
 
 .8566 
 
 + 26.8524 
 
 —33-9977 
 
 .0040 
 
 — 34.0008 
 
 14 
 
 +40.1204 
 
 .1166 
 
 +40.1185 
 
 —43.9662 
 
 .9672 
 
 —43.9667 
 
 IS 
 
 +36.1131 
 
 .1198 
 
 +36.1164 
 
 —38.5266 
 
 .5280 
 
 —38.5273 
 
 16 
 
 +42.8584 
 
 .8610 
 
 +42.8597 
 
 — 40. 1702 
 
 .1700 
 
 — 40.1701 
 
 18 
 
 + 16.2284 
 
 .2277 
 
 + 16.2280 
 
 —"•9563 
 
 •9520 
 
 —II.9542 
 
 19 
 
 +32.0258 
 
 .0246 
 
 +32.0252 
 
 — 22.2221 
 
 .2226 
 
 — 22.2224 
 
 21 
 
 +30.3745 
 
 •378l 
 
 +30.3763 
 
 — 9-o853 
 
 .0811 
 
 — 9.0832 
 
 22 
 
 +53-5429 
 
 •5405 
 
 +53-5418 
 
 —11.9430 
 
 .9419 
 
 —II.9424 
 
 23 
 
 +14.0034 
 
 .0046 
 
 +14.0040 
 
 — 1.1102 
 
 .1012 
 
 — I- 1057 
 
 24 
 
 +57- 1 1 19 
 
 .1068 
 
 +57-I094 
 
 —10.0175 
 
 .0178 
 
 — IO.O176 
 
 25 
 
 +26.1563 
 
 •1599 
 
 +26.1581 
 
 + 5-2628 
 
 .2611 
 
 + 5.2620 
 
 26 
 
 +21.0685 
 
 .0667 
 
 + 21.0676 
 
 + 9-5909 
 
 •5958 
 
 + 9-5934 
 
 27 
 
 +26.0320 
 
 .0341 
 
 +26.0330 
 
 +24.1101 
 
 .1136 
 
 +24. 11 18 
 
 28 
 
 +25.1196 
 
 .1146 
 
 + 25.1171 
 
 +31.6126 
 
 .6230 
 
 +31.6178 
 
 29 
 
 +20.4415 
 
 .4417 
 
 +20.4416 
 
 +34.0871 
 
 .0904 
 
 +34.0888 
 
 30 
 
 +14.3201 
 
 .3248 
 
 + 14.3224 
 
 +25.2374 
 
 •2329 
 
 +25.2352 
 
 3t 
 
 + 17.7798 
 
 .7788 
 
 +17-7793 
 
 +43.3888 
 
 .3827 
 
 +43-3858 
 
 32 
 
 + 7-6504 
 
 .6446 
 
 + 7-6475 
 
 +35.6858 
 
 •6792 
 
 +35.6825 
 
 33 
 
 + 9-1837 
 
 .1830 
 
 + 9-1834 
 
 +43-4445 
 
 .4448 
 
 +43-4446 
 
 34 
 
 + 9-I365 
 
 •1394 
 
 + 9-1380 
 
 +43-5738 
 
 .5680 
 
 -I-43-5709 
 
Optical Distortion deduced from Photographic Measures. It 
 
 Table III. — (Continued.) Corrected Coordinates. Plate II. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. 
 
 Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 35 
 
 + 5-4868 
 
 .4882 
 
 + 5.4875 
 
 +39-5398 
 
 .5381 
 
 +39-5390 
 
 36 
 
 + 2.2625 
 
 • 2576 
 
 + 2.2600 
 
 + 16.1676 
 
 •1725 
 
 + 16.1700 
 
 37 
 
 -j- 1.0223 
 
 .0110 
 
 -j- 1. 0166 
 
 + I5-3879 
 
 ■3878 
 
 + I5.3878 
 
 33 
 
 — 3-4964 
 
 .4988 
 
 — 3.4976 
 
 + 29.2004 
 
 .2045 
 
 +29.2024 
 
 39 
 
 — 7-4944 
 
 .4991 
 
 — 7.4968 
 
 + 37.3764 
 
 •3753 
 
 +37.3758 
 
 40 
 
 -- 9-4699 
 
 .4667 
 
 — 9-4683 
 
 +41.0273 
 
 .0417 
 
 +41.0345 
 
 41 
 
 — 9-527I 
 
 ■5284 
 
 — 95278 
 
 +22.3445 
 
 •3474 
 
 + 22.3460 
 
 42 
 
 — 10.1631 
 
 •1571 
 
 — 10.1601 
 
 + 17.6895 
 
 .6812 
 
 + 17.6854 
 
 43 
 
 —17.7791 
 
 ■7764 
 
 —17.7778 
 
 +27.8362 
 
 •8309 
 
 + 27.8336 
 
 44 
 
 —30.5611 
 
 ■5525 
 
 —30-5568 
 
 +36.7742 
 
 •7723 
 
 +36.7732 
 
 45 
 
 - 8.8439 
 
 ■8503 
 
 — 8.8471 
 
 + 9.3256 
 
 •3285 
 
 + 9.3270 
 
 46 
 
 —17-0385 
 
 .0412 
 
 —17.0398 
 
 + 12.0241 
 
 .0306 
 
 + 12.0274 
 
 47 
 
 — 46.2009 
 
 .2027 
 
 — 46.2018 
 
 +27.6878 
 
 .6869 
 
 +27.6874 
 
 48 
 
 — 4-0745 
 
 .0768 
 
 — 4-0756 
 
 + 4.3608 
 
 • 3620 
 
 + 4.3614 
 
 49 
 
 — 4-2815 
 
 .2787 
 
 — 4.2801 
 
 + 4-384I 
 
 ■3835 
 
 + 4-3838 
 
 50 
 
 —44-5634 
 
 ■5651 
 
 —44-5642 
 
 +22.2167 
 
 .2185 
 
 + 22.2176 
 
 5i 
 
 — 27.4762 
 
 .4762 
 
 — 27.4762 
 
 + 9.7622 
 
 .7704 
 
 + 9-7663 
 
 52 
 
 —42.1659 
 
 .1746 
 
 —42. 1702 
 
 + IO.2370 
 
 .2390 
 
 + IO.2380 
 
 53 
 
 — 19.0580 
 
 •0557 
 
 — 19.0568 
 
 + 5-7317 
 
 ■ 7279 
 
 + 5-7298 
 
 54 
 
 —39-4882 
 
 .4848 
 
 —39.4865 
 
 + 6.7667 
 
 •7657 
 
 + 6.7662 
 
 56 
 
 —25.8048 
 
 •8031 
 
 — 25.8040 
 
 + 2.0992 
 
 .0994 
 
 + 2.0993 
 
 57 
 
 —16.8216 
 
 .8242 
 
 — 16.8229 
 
 + 1-5430 
 
 ■5405 
 
 + I.54I8 
 
 58 
 
 — 20.6862 
 
 .6824 
 
 — 20.6843 
 
 + 0.1 187 
 
 .1161 
 
 + 0.1174 
 
 60 
 
 — 12.6792 
 
 .6780 
 
 —12.6786 
 
 — 2.6560 
 
 •6565 
 
 — 2.6562 
 
 61 
 
 —23.6384 
 
 ■ 6346 
 
 —23.6365 
 
 — 8.1412 
 
 •1398 
 
 — 8.1405 
 
 62 
 
 — 20.0185 
 
 •0185 
 
 — 20.0185 
 
 — 6.9216 
 
 .9202 
 
 — 6.9209 
 
 63 
 
 —48.3756 
 
 •3799 
 
 —48.3778 
 
 — 21.2167 
 
 .2158 
 
 — 21.2162 
 
 64 
 
 —16.4274 
 
 • 434o 
 
 —16.4307 
 
 — 7.8912 
 
 .8878 
 
 - 7.8895 
 
 65 
 
 —26.3509 
 
 ■3546 
 
 —26.3528 
 
 —38.3480 
 
 •3435 
 
 -38.3458 
 
18 
 
 Stars within One Degree of the North Pole, and 
 
 Table III. — (Continued.') Corrected Coordinates. Plate III. 
 
 Star. 
 
 X 
 
 . Big Images. 
 
 Y 
 
 . Big Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Meaa. 
 
 I 
 
 +51-0658 
 
 •0599 
 
 +51.0628 
 
 — 20.6778 
 
 .6808 
 
 —20.6793 
 
 2 
 
 + 9-58I8 
 
 .5898 
 
 + 9-5858 
 
 — 4-0546 
 
 .0569 
 
 — 4.0558 
 
 3 
 
 +48.OIOI 
 
 .0160 
 
 +48.0130 
 
 —14.7761 
 
 •773° 
 
 —14.7746 
 
 4 
 
 +47.0020 
 
 .0083 
 
 +47.0052 
 
 + I.0397 
 
 •0435 
 
 + 1. 0416 
 
 5 
 
 +53-I907 
 
 .1964 
 
 +53- T 936 
 
 + 12.3321 
 
 ■3352 
 
 + 12.3336 
 
 6 
 
 +48.4349 
 
 •4345 
 
 +48.4347 
 
 + 11. 9217 
 
 .9198 
 
 +II.9208 
 
 7 
 
 +33-5885 
 
 .5896 
 
 +33-5890 
 
 + 8.6413 
 
 ■6444 
 
 + 8.6428 
 
 8 
 
 +32-64I5 
 
 .6342 
 
 +32-5378 
 
 + 9-5983 
 
 ■5973 
 
 + 9-5978 
 
 9 
 
 +234414 
 
 •4503 
 
 +23.4458 
 
 + 7-44oi 
 
 •4399 
 
 + 7-4400 
 
 IO 
 
 +45-2597 
 
 •2645 
 
 +45.2621 
 
 + 16.2984 
 
 •3038 
 
 +16.3011 
 
 II 
 
 +19.4166 
 
 •4055 
 
 +19.4110 
 
 + 8.5704 
 
 .5667 
 
 + 8.5686 
 
 12 
 
 +37-3367 
 
 •3394 
 
 +37-338o 
 
 +28.0599 
 
 .0574 
 
 +28.0586 
 
 J 3 
 
 +33.0674 
 
 .0691 
 
 +33.0682 
 
 +25.7809 
 
 •7803 
 
 +25.7806 
 
 n 
 
 +43-0071 
 
 .0052 
 
 +43.0062 
 
 +39.0894 
 
 .0830 
 
 +39.0862 
 
 16 
 
 +39.2033 
 
 .2032 
 
 +39.2032 
 
 +41.8145 
 
 .8135 
 
 +41.8140 
 
 17 
 
 +35.0600 
 
 .0484 
 
 +35-0542 
 
 +39.2671 
 
 .2731 
 
 +39.2701 
 
 18 
 
 +11.0548 
 
 .0613 
 
 + 11.0580 
 
 +15.0980 
 
 .0968 
 
 + I5-0974 
 
 !9 
 
 +21.2808 
 
 .2885 
 
 +21.2846 
 
 +30.9269 
 
 •9234 
 
 +30.9252 
 
 21 
 
 + 8.1541 
 
 .1521 
 
 + 8.1531 
 
 + 29.2352 
 
 •2343 
 
 + 29.2348 
 
 22 
 
 +10.9249 
 
 .9288 
 
 + 10.9268 
 
 +52.4032 
 
 .4129 
 
 +52.4080 
 
 23 
 
 + 0.2139 
 
 .2141 
 
 + 0.2140 
 
 +12.8408 
 
 .8414 
 
 + 12.8411 
 
 24 
 
 + 9.0017 
 
 .0075 
 
 + 9.0046 
 
 +55-9556 
 
 ■9571 
 
 +55-9564 
 
 25 
 
 — 6.1837 
 
 ■1875 
 
 — 6.1856 
 
 +24.9779 
 
 • 9756 
 
 +24.976S 
 
 26 
 
 — 10.49S6 
 
 .4964 
 
 —10.4975 
 
 +19.8676 
 
 .8666 
 
 + 19.8671 
 
 28 
 
 —32-5342 
 
 ■53oo 
 
 —32-5321 
 
 +23.8727 
 
 .8665 
 
 + 23.8696 
 
 29 
 
 —34-9903 
 
 .9881 
 
 —34.9892 
 
 +19.1727 
 
 ■ 1713 
 
 + 19.1720 
 
 30 
 
 — 26.1369 
 
 •1355 
 
 — 26.1362 
 
 +13.0860 
 
 .0852 
 
 + 13-0856 
 
 31 
 
 —44.2997 
 
 .3009 
 
 —44.3003 
 
 + 16.4858 
 
 .4876 
 
 + 16.4867 
 
 32 
 
 —36.5603 
 
 .5622 
 
 —36.5612 
 
 + 6.3869 
 
 .3902 
 
 + 6.3886 
 
 33 
 
 —44.3225 
 
 .3271 
 
 —44.3248 
 
 + 7-8843 
 
 .8903 
 
 + 7-8873 
 
 34 
 
 —44-4571 
 
 ■4539 
 
 —44-4555 
 
 + 7-8563 
 
 .8518 
 
 + 7-8540 
 
 35 
 
 —40.4034 
 
 .4050 
 
 — 40.4042 
 
 + 4.2092 
 
 .2045 
 
 + 4.2068 
 
Optical Distortion deduced from Photographic Measures. 19 
 
 Table III {Continued, .) Corrected Coordinates. Plate III. 
 
 Star. 
 
 X 
 
 . Big Images. 
 
 Y. Big Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. E 
 
 eversed. 
 
 Mean. 
 
 36 
 
 — 17.0294 
 
 .0277 
 
 — 17.0286 
 
 + 1-0563 
 
 0569 
 
 + I.0566 
 
 38 
 
 —30.0463 
 
 .0419 
 
 —30.0441 
 
 — 4-7414 
 
 738l 
 
 — 4-7398 
 
 39 
 
 —38.2234 
 
 .2221 
 
 —38.2228 
 
 — 8.7677 
 
 7677 
 
 — 8.7677 
 
 40 
 
 — 41.8617 
 
 .8564 
 
 —41.8590 
 
 —10.7570 
 
 7576 
 
 —10-7573 
 
 41 
 
 —23-I587 
 
 •1599 
 
 —23-1593 
 
 —10.7451 
 
 7452 
 
 —IO.7452 
 
 42 
 
 —18.5083 
 
 .50IO 
 
 — 18.5046 
 
 — 11.3711 
 
 3737 
 
 — ir.3724 
 
 43 
 
 — 28.6290 
 
 .6234 
 
 —28.6262 
 
 — 19.0267 
 
 0223 
 
 —I9-0245 
 
 44 
 
 —37-549° 
 
 ■5515 
 
 —37-5502 
 
 —3I-8343 
 
 8300 
 
 —31.8322 
 
 45 
 
 —10.1567 
 
 •1558 
 
 — IO.1562 
 
 — 10.0404 
 
 0393 
 
 — IO.0398 
 
 46 
 
 — 12.8296 
 
 .8305 
 
 — 12.8300 
 
 -18.2378 
 
 2363 
 
 — 18.2370 
 
 47 
 
 — 28.4242 
 
 .4186 
 
 — 28.4214 
 
 —47-4485 
 
 4472 
 
 —47.4478 
 
 48 
 
 — 5-I99I 
 
 .1916 
 
 — 5-1954 
 
 — 5-2482 
 
 2492 
 
 — 5.2487 
 
 49 
 
 — 5-2H5 
 
 .2174 
 
 — 5-2144 
 
 — 5-4449 
 
 4447 
 
 — 5-4448 
 
 50 
 
 — 22.9428 
 
 •9385 
 
 — 22. 9406 
 
 —45.7960 
 
 7905 
 
 —45-7932 
 
 51 
 
 —10.5335 
 
 .5284 
 
 —10.5310 
 
 — 28.6725 
 
 6739 
 
 — 28.6732 
 
 52 
 
 —10.9744 
 
 .9685 
 
 —10.9714 
 
 —43-3558 
 
 3553 
 
 —43-3556 
 
 53 
 
 — 6.5189 
 
 ■5244 
 
 — 6.5216 
 
 — -20.2237 
 
 2259 
 
 — 20.2248 
 
 54 
 
 — 7-49 6 3 
 
 •4987 
 
 — 7-4975 
 
 — 40.6662 
 
 6672 
 
 — 40.6667 
 
 56 
 
 — 2.8678 
 
 .8724 
 
 — 2.8701 
 
 — 26.9716 
 
 9709 
 
 — 26.9712 
 
 58 
 
 — 0.9128 
 
 •9095 
 
 — 0.9112 
 
 — 21.8442 
 
 8440 
 
 — 2.8441 
 
 60 
 
 + 1.8461 
 
 .8504 
 
 + 1.8482 
 
 —13-8325 
 
 83 r6 
 
 —13.8320 
 
 61 
 
 + 7-3 62 ° 
 
 •3679 
 
 + 7-3650 
 
 —24-7739 
 
 7753 
 
 —24.7746 
 
 62 
 
 + 6.1341 
 
 .1292 
 
 + 6.1316 
 
 — 21.1636 
 
 1627 
 
 — 21.1632 
 
 63 
 
 +20.5026 
 
 .5088 
 
 +20.5057 
 
 —49.4836 
 
 4818 
 
 —49.4827 
 
 64 
 
 + 7-0903 
 
 .0912 
 
 + 7.0908 
 
 —17-5685 
 
 5656 
 
 —17.5670 
 
 65 
 
 +37-5742 
 
 •5785 
 
 +37-5764 
 
 —27.3972 
 
 4015 
 
 —27.3994 
 
20 
 
 Stars within One Degree of the North Pole, and 
 
 Table III. — (Continued.) Corrected Coordinates. Plate III. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. 
 
 Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 I 
 
 +51.0823 
 
 .0681 
 
 +51.0752 
 
 — 20.2708 
 
 .2714 
 
 — 20.2711 
 
 2 
 
 + 9- 5958 
 
 .6004 
 
 + 9-598I 
 
 — 3-65I5 
 
 •6499 
 
 — 3-6507 
 
 3 
 
 +48.0306 
 
 .0227 
 
 +48.0266 
 
 —14.3676 
 
 •3654 
 
 — 14.3665 
 
 4 
 
 +47.0215 
 
 .0218 
 
 +47.0216 
 
 + 1-4458 
 
 .4516 
 
 + I-4487 
 
 5 
 
 + 53.2089 
 
 • 2034 
 
 +53.2062 
 
 + 12.7388 
 
 ■7419 
 
 + 12.7404 
 
 6 
 
 +48.4367 
 
 .4402 
 
 +48.4384 
 
 + 12.3301 
 
 •3205 
 
 + 12.3253 
 
 7 
 
 +33-596o 
 
 ■5934 
 
 +33-5947 
 
 + 9-°459 
 
 .0516 
 
 + 9.0488 
 
 8 
 
 +32.6625 
 
 .6418 
 
 +32.6522 
 
 + IO.0008 
 
 .0047 
 
 +I0.0028 
 
 9 
 
 +23-4577 
 
 •4477 
 
 +23-4527 
 
 + 7.8417 
 
 .8479 
 
 + 7-8448 
 
 IO 
 
 +45-2765 
 
 • 2755 
 
 +45.2760 
 
 + 16.7019 
 
 .7087 
 
 + 16.7053 
 
 ii 
 
 4- 19.4301 
 
 .4200 
 
 + 19.4250 
 
 + 8.9789 
 
 ■9737 
 
 + 8.9763 
 
 12 
 
 +37-3534 
 
 ■3520 
 
 +37-3527 
 
 + 28.4715 
 
 .4706 
 
 + 28.4710 
 
 13 
 
 +33- 79i 
 
 .0825 
 
 +33.0808 
 
 +26.1826 
 
 .1962 
 
 +26.1894 
 
 14 
 
 +43.0201 
 
 .0164 
 
 +43.0182 
 
 +39.4910 
 
 •4905 
 
 +39.4908 
 
 16 
 
 +39-2313 
 
 .2293 
 
 +39-2303 
 
 +42.2137 
 
 .2214 
 
 +42.2176 
 
 17 
 
 +35-0781 
 
 .0697 
 
 +35-0739 
 
 +39-6645 
 
 .6872 
 
 +39-6758 
 
 18 
 
 + 11.0678 
 
 •o733 
 
 +11.0706 
 
 + 15-4971 
 
 •5013 
 
 + I5-499 2 
 
 19 
 
 +21.2941 
 
 .2952 
 
 +21.2946 
 
 +3I-332S 
 
 •3370 
 
 +3I-3348 
 
 21 
 
 + 8.1667 
 
 .1621 
 
 + 8.1644 
 
 + 29.6423 
 
 .6380 
 
 +29.6402 
 
 22 
 
 + io.9357 
 
 •9386 
 
 + 10.9372 
 
 +52.8103 
 
 .8136 
 
 +52.8120 
 
 23 
 
 + 0.2264 
 
 ■2253 
 
 + 0.2258 
 
 + 13.2470 
 
 •2483 
 
 +13.2476 
 
 24 
 
 + 9.0190 
 
 • 0175 
 
 + 90182 
 
 +56.3738 
 
 ■3797 
 
 +56.3768 
 
 25 
 
 — 6.1674 
 
 .1720 
 
 — 6.1697 
 
 +25.3889 
 
 • 3864 
 
 +25-3876 
 
 26 
 
 —10.4843 
 
 •4859 
 
 —10.4851 
 
 +20.2742 
 
 .2780 
 
 +20.2761 
 
 28 
 
 —32-5245 
 
 .5220 
 
 —32.5232 
 
 +24.2765 
 
 .2709 
 
 +24.2737 
 
 29 
 
 —34.9821 
 
 .9849 
 
 —349835 
 
 + I9-5785 
 
 .5810 
 
 + 19-5798 
 
 3° 
 
 — 26.1179 
 
 .1182 
 
 —26.1180 
 
 + 13-4934 
 
 • 4944 
 
 + 13-4939 
 
 31 
 
 —44.2997 
 
 ■3031 
 
 —44.3014 
 
 + 16.8885 
 
 .8960 
 
 + 16.8922 
 
 32 
 33 
 34 
 
 —36-5496 
 
 •5542 
 
 —36-55I9 
 
 + 6.7906 
 
 •7965 
 
 + 6.7936 
 
 —44.4461 
 
 •4399 
 
 —44.4430 
 
 + 8.2628 
 
 ■2593 
 
 + 8.2610 
 
 35 
 
 —40.3890 
 
 •3907 
 
 —40.3898 
 
 + 4.6133 
 
 .6127 
 
 + 4-6130 
 
Optical Distortion deduced from Photographic Measures. 21 
 
 Table III. — (Continued.') Corrected Coordinates. Plate III. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. 
 
 Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 36 
 
 — 17.0:30 
 
 .0141 
 
 —17.0136 
 
 + I-459 8 
 
 .4641 
 
 + I.4620 
 
 38 
 
 —30.0325 
 
 •0274 
 
 —30.0300 
 
 — 4-333° 
 
 .3318 
 
 — 4-3324 
 
 39 
 
 —38.2048 
 
 .2110 
 
 —38.2079 
 
 - 8.3518 
 
 •3513 
 
 — 8.3516 
 
 40 
 
 —41.8452 
 
 .8372 
 
 — 41.8412 
 
 —10-3533 
 
 •3514 
 
 —I°-3524 
 
 4i 
 
 —23.I4I3 
 
 •1439 
 
 —23.1426 
 
 —10.3393 
 
 ■339° 
 
 — IO.3392 
 
 42 
 
 —18.4944 
 
 •4934 
 
 —18.4939 
 
 —10.9637 
 
 ■9643 
 
 — IO.9640 
 
 43 
 44 
 45 
 
 — 28.6107 
 
 .6104 
 
 —28.6106 
 
 — 18.6250 
 
 •6163 
 
 — 18.6206 
 
 —10.1459 
 
 •143 1 
 
 —10.1445 
 
 — 9-6337 
 
 •6355 
 
 — 9-6346 
 
 46 
 
 — 12.8163 
 
 •8i35 
 
 — 12.8149 
 
 —17-8313 
 
 .8232 
 
 — 17.8272 
 
 47 
 
 —28.4075 
 
 .4094 
 
 — 28.4084 
 
 —47.0432 
 
 •0555 
 
 —47.0494 
 
 48 
 
 — 5-1797 
 
 ■ 1745 
 
 — 5-I77I 
 
 — 4.8416 
 
 .8400 
 
 — 4.8408 
 
 49 
 
 — 5-I998 
 
 .2049 
 
 — 5.2024 
 
 — 5-039° 
 
 .0384 
 
 — 5-0387 
 
 5° 
 
 — 22.9263 
 
 .9280 
 
 — 22.9272 
 
 —45.3801 
 
 • 3784 
 
 —45-3792 
 
 51 
 
 —10.5238 
 
 .5182 
 
 — IO.5210 
 
 — 28.2661 
 
 .2606 
 
 — 28.2634 
 
 52 
 
 — 10.9606 
 
 .9602 
 
 — IO.9604 
 
 —42.9490 
 
 .9480 
 
 —42.9485 
 
 53 
 
 — 6.5044 
 
 • 5^47 
 
 — 6.5096 
 
 — 19.8209 
 
 .8183 
 
 — 19.8196 
 
 54 
 
 — 7-48I5 
 
 • 4894 
 
 — 7-4854 
 
 —40.2547 
 
 -2545 
 
 —40.2546 
 
 56 
 
 — 2.8581 
 
 .8596 
 
 — 2.8588 
 
 —26.5635 
 
 • 5627 
 
 —26.5631 
 
 58 
 
 — 0.8942 
 
 .8942 
 
 — 0.8942 
 
 —21-4385 
 
 .4400 
 
 —21.4392 
 
 60 
 
 + 1.8561 
 
 •8594 
 
 + 1.8578 
 
 —13.4240 
 
 .4225 
 
 —13.4232 
 
 61 
 
 + 7- 3730 
 
 .3706 
 
 + 7-3718 
 
 —24.3671 
 
 ■3651 
 
 — 74.3661 
 
 62 
 
 + 6. 148 1 
 
 .1421 
 
 + 6. 145 1 
 
 —20.7544 
 
 •7558 
 
 —20.7551 
 
 63 
 
 +20.5170 
 
 .5181 
 
 +20.5 [76 
 
 — 49.0678 
 
 .0706 
 
 — 49.0692 
 
 64 
 
 + 7.1020 
 
 .1005 
 
 + 7. 1012 
 
 —17.1645 
 
 .1623 
 
 —17.1634 
 
 65 
 
 +37-5892 
 
 •5904 
 
 +37-5898 
 
 — 26.9907 
 
 -994° 
 
 — 26.9924 
 
22 
 
 Stars within One Degree of the North Pole, and 
 
 Table III. — (Continued.) Corrected Coordinates. Plate IV. 
 
 Star. 
 
 s 
 
 . Big Imag 
 
 ss. 
 
 y 
 
 . Big Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Eeversed. 
 
 Mean. 
 
 I 
 
 —48.9275 
 
 •9304 
 
 — 48.9290 
 
 — 24.6663 
 
 .6589 
 
 — 24.6626 
 
 2 
 
 — 8.4684 
 
 .4684 
 
 — 8.4684 
 
 — 5.6598 
 
 •6594 
 
 —56.6596 
 
 3 
 
 —42.5129 
 
 • 5169 
 
 —42.5149 
 
 — 26.4724 
 
 • 4715 
 
 — 26.4720 
 
 4 
 
 —30.2553 
 
 .2615 
 
 —30.2584 
 
 —36.5236 
 
 .5188 
 
 —36.5212 
 
 5 
 
 — 26.2267 
 
 .2262 
 
 — 26.2264 
 
 —48.7393 
 
 .7422 
 
 — 48.7408 
 
 6 
 
 —23- 2 733 
 
 •2737 
 
 —23-2735 
 
 —44.9856 
 
 .9842 
 
 —44.9849 
 
 7 
 
 — '5-5405 
 
 ■54" 
 
 —I5-5408 
 
 —31.8829 
 
 .8781 
 
 -3 1. 8805 
 
 8 
 
 — 14.2023 
 
 •1965 
 
 —14.1994 
 
 —3I-8254 
 
 .8296 
 
 —31-8275 
 
 9 
 
 — 9-5185 
 
 .5148 
 
 — 9-5166 
 
 — 23.6276 
 
 .6260 
 
 —23.6268 
 
 10 
 
 — 17.9002 
 
 .9000 
 
 — 17.9001 
 
 —45-6377 
 
 • 6377 
 
 —45-6377 
 
 ii 
 
 — 5-9224 
 
 .9280 
 
 — 5-9252 
 
 —21.4774 
 
 •4735 
 
 —21-4754 
 
 12 
 
 — 3-9°9« 
 
 •9055 
 
 — 3-9076 
 
 —47.8616 
 
 ■ 8594 
 
 —47.8605 
 
 13 
 
 — 2.6538 
 
 • 6571 
 
 — 2-6552 
 
 —43-2025 
 
 .2003 
 
 —43.2014 
 
 14 
 
 + 0.2944 
 
 .2949 
 
 + O.2946 
 
 —59-5I30 
 
 •5237 
 
 —59-5I84 
 
 15 
 
 + 1. 0610 
 
 .0672 
 
 + 1. 0641 
 
 —52.8019 
 
 .8066 
 
 —52.8042 
 
 17 
 
 + 5-8492 
 
 .8541 
 
 + 5-85I6 
 
 —53-8394 
 
 ■8515 
 
 —53-8454 
 
 18 
 
 + 4-5333 
 
 •5309 
 
 + 4-5321 
 
 —19.8166 
 
 .8194 
 
 —19.8180 
 
 19 
 
 + 9- J 447 
 
 .1460 
 
 + 9- r 454 
 
 —38.0768 
 
 .0772 
 
 —38.0770 
 
 20 
 
 + 13.6222 
 
 .6173 
 
 +13-6198 
 
 — 33-9 r 37 
 
 .9084 
 
 — 33-9"o 
 
 21 
 
 + 16.8630 
 
 .8629 
 
 + 16.8630 
 
 —27-3I3I 
 
 •3"7 
 
 —27.3124 
 
 22 
 
 +31.9146 
 
 •9159 
 
 +3i-9 r 52 
 
 —45-I488 
 
 • i55o 
 
 —45-I5I9 
 
 23 
 
 +10.2856 
 
 .2878 
 
 +10.2867 
 
 —10.3259 
 
 .3!74 
 
 — 10.3216 
 
 24 
 
 +35 8404 
 
 .8365 
 
 +35-8384 
 
 — 46.1650 
 
 .1634 
 
 — 46.1642 
 
 25 
 
 +23.5123 
 
 •5 '43 
 
 +23-5133 
 
 —I3-93I3 
 
 ■9365 
 
 —13-9339 
 
 26 
 
 +22.7301 
 
 ■7277 
 
 +22.7289 
 
 — 7-2927 
 
 .2888 
 
 — 7.2908 
 
 27 
 
 +36.2335 
 
 ■2325 
 
 +36.2330 
 
 — 0.0244 
 
 .0236 
 
 — 0.0240 
 
 28 
 
 +40.6579 
 
 .6657 
 
 +40.6618 
 
 + 6.1116 
 
 .1160 
 
 + 6. 1 138 
 
 29 
 
 +38-9I57 
 
 .9089 
 
 +38.9123 
 
 + 11.0894 
 
 .0917 
 
 + ir. 0906 
 
 3° 
 
 +28.4185 
 
 .4239 
 
 +28.4212 
 
 + 8.7695 
 
 .7727 
 
 + 8.7711 
 
 31 
 
 +43-3°68 
 
 •3055 
 
 +43.3062 
 
 + I9-7340 
 
 •7371 
 
 + I9-7356 
 
 32 
 
 +30.6207 
 
 .6205 
 
 +30.6206 
 
 + 20.9627 
 
 .9666 
 
 +20.9646 
 
 33 
 
 +37.0172 
 
 .0171 
 
 +37.0172 
 
 +25.6128 
 
 .6143 
 
 +25.6136 
 
 34 
 
 +37.0657 
 
 .0680 
 
 +37.o668 
 
 +25-7424 
 
 ■7434 
 
 +25-7429 
 
Optical Distortion deduced from Photographic Measures. 23 
 
 Table III. — {Continued.) Corrected Coordinates. Plate IV. 
 
 Star. 
 
 X 
 
 Big Images. 
 
 Y 
 
 Big Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. ' 
 
 35 
 
 +31.6408 
 
 .6401 
 
 +31.6404 
 
 +25.2624 
 
 .2613 
 
 +25.2618 
 
 36 
 
 + I3-3996 
 
 ■3933 
 
 +13.3964 
 
 +10.3004 
 
 • 3027 
 
 +10.3016 
 
 37 
 
 +II.9648 
 
 •9615 
 
 + 11.9632 
 
 +10.5731 
 
 •5747 
 
 + 10.5739 
 
 38 
 
 + 18.0416 
 
 .0413 
 
 + 18.0414 
 
 +23.7814 
 
 .7860 
 
 +23.7837 
 
 39 
 
 + 20.6756 
 
 .6799 
 
 +20.6778 
 
 +32.5166 
 
 ■5151 
 
 +32.5I58 
 
 40 
 
 +21.6936 
 
 .6908 
 
 +21.6922 
 
 +36.5194 
 
 ■5236 
 
 +36.5215 
 
 41 
 
 + 8.9509 
 
 •9529 
 
 + 8.9519 
 
 +22.8479 
 
 .8414 
 
 +22.8446 
 
 42 
 
 + 5-3365 
 
 • 3349 
 
 + 5-3357 
 
 +19.8783 
 
 .8798 
 
 + 19.8790 
 
 43 
 
 + 6.6266 
 
 .6217 
 
 + 6.6242 
 
 +32.4812 
 
 .4841 
 
 +32.4826 
 
 44 
 
 + 3-3449 
 
 • 342t 
 
 + 3-3435 
 
 +47.7300 
 
 •7343 
 
 +47.7322 
 
 45 
 
 + o.5952 
 
 .6022 
 
 + 0.5987 
 
 +12.8595 
 
 .8564 
 
 +12.8580 
 
 46- 
 
 — 3-58ii 
 
 .5801 
 
 — 3-58o6 
 
 +20.3921 
 
 .3908 
 
 +30.3914 
 
 47 
 
 —14.3233 
 
 .3237 
 
 —14.3235 
 
 +51.7107 
 
 .7116 
 
 +5I.7II2 
 
 48 
 
 + 0.7182 
 
 .7213 
 
 + 0.7198 
 
 + 5.9582 
 
 ■9579 
 
 + 5-9566 
 
 49 
 
 + 0.5860 
 
 .5897 
 
 + 0.5878 
 
 + 6. 1 153 
 
 .1171 
 
 + 6. 1 162 
 
 50 
 
 —16.8371 
 
 .8407 
 
 —16.8389 
 
 +46.5679 
 
 ■5683 
 
 +46.5681 
 
 51 
 
 —12.7767 
 
 •7774 
 
 — 12.7770 
 
 +25.8171 
 
 .8199 
 
 +25.8185 
 
 52 
 
 — 23.2184 
 
 .2221 
 
 — 23.2202 
 
 +36.1597 
 
 • 1574 
 
 +36.1586 
 
 53 
 
 — 9-3 2 65 
 
 •3225 
 
 — 9-3245 
 
 +17-1343 
 
 ■1377 
 
 +17.1360 
 
 54 
 
 —23.6144 
 
 .6160 
 
 —23.6152 
 
 +31-7852 
 
 .7872 
 
 +31.7862 
 
 55 
 
 — 3-4494 
 
 .4492 
 
 — 3-4493 
 
 + 6.6076 
 
 .6078 
 
 + 6.6077 
 
 56 
 
 —16.7355 
 
 •7339 
 
 —16.7347 
 
 +19-0579 
 
 .0641 
 
 +19.0610 
 
 57 
 
 —10.5240 
 
 • 5224 
 
 —10.5232 
 
 +12.5441 
 
 ■5452 
 
 +12.5446 
 
 58 
 
 —14.3303 
 
 •3362 
 
 —14-3332 
 
 +14.1304 
 
 ■ 1350 
 
 +14.1327 
 
 59 
 
 — 20. 1089 
 
 .1063 
 
 — 20. 1076 
 
 +12.9172 
 
 .9219 
 
 +12.9196 
 
 60 
 
 —10.3477 
 
 •3467 
 
 —10.3472 
 
 + 6.6407 
 
 .6465 
 
 + 6.6436 
 
 61 
 
 — 22.1260 
 
 .1281 
 
 — 22.1270 
 
 -1- 10.0693 
 
 .0752 
 
 +10.0722 
 
 62 
 
 —18.6324 
 
 .6327 
 
 —18.6326 
 
 + 8.5271 
 
 .5287 
 
 + 8.5279 
 
 63 
 
 —49.1427 
 
 .1466 
 
 —49.1446 
 
 +I7-3J42 
 
 • 3125 
 
 +I7-3I34 
 
 64 
 
 —16.6681 
 
 .6674 
 
 —16.6678 
 
 + 5-3588 
 
 .3622 
 
 + 5-3605 
 
 65 
 
 —44.6232 
 
 .6234 
 
 —44-6233 
 
 —10.2262 
 
 .2300 
 
 — 10.2281 
 
24 
 
 Stars within One Degree of the North Pole, and 
 
 Table III. — ( Continued.) Corrected Coordinates. Plate IV. 
 
 Star. 
 
 X. 
 
 Middlelmag 
 
 es. 
 
 y. 
 
 Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 I 
 
 —48-930S 
 
 •9309 
 
 —48.9307 
 
 — 24.2827 
 
 .2791 
 
 —24.2809 
 
 2 
 
 — 8.4688 
 
 .4691 
 
 — 8.4689 
 
 — 5-2794 
 
 •2751 
 
 — 5.2772 
 
 3 
 
 —42.5195 
 
 •5177 
 
 —42.5186 
 
 —26.0848 
 
 .0849 
 
 —26.0848 
 
 4 
 
 —30.2573 
 
 • 2579 
 
 —30.2576 
 
 —36.1426 
 
 .1365 
 
 —36.1396 
 
 5 
 
 — -26.2306 
 
 .2275 
 
 — 26.2290 
 
 — 48.3606 
 
 •3576 
 
 —48359I 
 
 6 
 
 — 23.2781 
 
 .2802 
 
 —23.2792 
 
 —44.6043 
 
 .6048 
 
 — 44.6046 
 
 7 
 
 —I5-5425 
 
 .5478 
 
 —15-5452 
 
 — 3M999 
 
 .4921 
 
 —31.4960 
 
 8 
 
 —14.2058 
 
 .2060 
 
 —14.2059 
 
 —31.4416 
 
 .4406 
 
 —31-44" 
 
 9 
 
 — 9-5!95 
 
 •5191 
 
 — 9.5193 
 
 —23-2459 
 
 • 2453 
 
 —23.2456 
 
 IO 
 
 — 17.9000 
 
 .9022 
 
 — 17.9011 
 
 —45-2512 
 
 .2491 
 
 —45.2502 
 
 II 
 
 — 59252 
 
 .9290 
 
 — 5-927I 
 
 — 21.0860 
 
 .0873 
 
 —21.0866 
 
 12 
 
 — 3-9075 
 
 .9081 
 
 — 3.9078 
 
 —47-4717 
 
 -4758 
 
 —47-4738 
 
 13 
 
 — 2.6507 
 
 .6568 
 
 — 2.6538 
 
 —42.8175 
 
 .8109 
 
 — 42.8142 
 
 14 
 
 + 0.2939 
 
 .2914 
 
 + 0.2926 
 
 — 59- r 454 
 
 .1421 
 
 —59-I438 
 
 15 
 
 + 1-0556 
 
 •0575 
 
 + 1.0566 
 
 —52.4211 
 
 •4338 
 
 —52.4274 
 
 17 
 
 + 5-849? 
 
 •8515 
 
 + 5-8506 
 
 —53-4517 
 
 ■4569 
 
 —53-4543 
 
 18 
 
 + 4-5284 
 
 •5270 
 
 + 4-5277 
 
 —I9-4338 
 
 •4333 
 
 —I9-4336 
 
 19 
 
 + 9-1397 
 
 •1433 
 
 + 9-I4I5 
 
 —37.6966 
 
 .6980 
 
 —37-6973 
 
 20 
 
 + 13.6214 
 
 .6200 
 
 + 13.6207 
 
 —33-5259 
 
 .5212 
 
 —33 5236 
 
 21 
 
 + 16.8622 
 
 .8629 
 
 + 16.8626 
 
 —26.9335 
 
 •9332 
 
 —26.9334 
 
 22 
 
 +3i-9 I 38 
 
 .9126 
 
 +3I-9I32 
 
 —44.7740 
 
 .7780 
 
 —44.7760 
 
 23 
 
 + 10.2833 
 
 .2840 
 
 +10.2836 
 
 — 9- 9424 
 
 .9368 
 
 — 9- 9396 
 
 24 
 
 +35-8397 
 
 ■8335 
 
 +35-8366 
 
 —45-7798 
 
 •7765 
 
 —457782 
 
 25 
 
 +23-5091 
 
 •5123 
 
 +23-5107 
 
 —13.5486 
 
 • 55io 
 
 —I3-5498 
 
 26 
 
 +22.7285 
 
 .7261 
 
 +22.7273 
 
 — 6.9063 
 
 .9071 
 
 — 6.9067 
 
 27 
 
 +36.2337 
 
 .2282 
 
 +36.2310 
 
 + 0.3554 
 
 .3638 
 
 + 0.3596 
 
 28 
 
 +40.6603 
 
 .6667 
 
 +40.6635 
 
 + 6.4926 
 
 • 5017 
 
 + 6.4972 
 
 29 
 
 +38.9152 
 
 .9101 
 
 +38.9126 
 
 +11.4706 
 
 • 4731 
 
 + 11. 4718 
 
 3° 
 
 +28.4191 
 
 .4222 
 
 +28.4206 
 
 + 9-I536 
 
 •1576 
 
 + 9-I556 
 
 31 
 
 +43-3073 
 
 •3063 
 
 +43-3068- 
 
 +20.1135 
 
 .1123 
 
 +20.1129 
 
 32 
 
 33 
 34 
 
 +30.6227 
 
 .6188 
 
 +30.6208 
 
 +21.3492 
 
 ■3529 
 
 +21.3510 
 
 +37.0662 
 
 .0693 
 
 +37.0678 
 
 +26.1218 
 
 ■1 139 
 
 +26.1178 
 
Optical Distortion deduced from Photographic Measures. 25 
 
 Table III. — (Continued.) Corrected Coordinates. Plate IV. 
 
 Star. 
 
 X. 
 
 Middle Images. 
 
 Y. Middle Images. 
 
 Direct. 
 
 Reversed. 
 
 Mean. 
 
 Direct. R 
 
 eversed. 
 
 Mean. 
 
 35 
 
 +31.6418 
 
 .6416 
 
 +31.6417 
 
 +25-6439 
 
 6421 
 
 +25.6430 
 
 36 
 
 + I3-399I 
 
 •3939 
 
 + I3.3965 
 
 + 10.6837 
 
 6853 
 
 + 10.6845 
 
 37 
 
 + II.9700 
 
 .9632 
 
 + II.9666 
 
 + 10.9728 
 
 9685 
 
 +10.9706 
 
 38 
 
 + 18.0396 
 
 .0410 
 
 + 18.0403 
 
 +24.1685 
 
 1661 
 
 +24.1673 
 
 39 
 
 + 20.6796 
 
 .6825 
 
 + 20.6810 
 
 +32.9026 
 
 9054 
 
 +32.9040 
 
 40 
 
 +21.6951 
 
 .6964 
 
 + 21.6958 
 
 +36.9140 
 
 9206 
 
 +36. 9 1 73 
 
 41 
 
 + 8.9506 
 
 •9537 
 
 + 8.9522 
 
 +23.2243 
 
 2232 
 
 +23.2238 
 
 42 
 
 + 5-3362 
 
 •3352 
 
 + 5-3357 
 
 +20.2603 
 
 2658 
 
 +20.2630 
 
 43 
 
 + 6.6304 
 
 .6252 
 
 + 6.6278 
 
 +32.8633 
 
 8671 
 
 -t-32.8652 
 
 44 
 
 + 3-3522 
 
 .3461 
 
 + 3-3492 
 
 +48.1082 
 
 1255 
 
 +48.1168 
 
 45 
 
 + 0.5934 
 
 .6012 
 
 + 0.5973 
 
 + 13-2394 
 
 2439 
 
 + 13.2416 
 
 46 
 
 — 3-5844 
 
 ■5844 
 
 — 3-5844 
 
 +20.7754 
 
 7769 
 
 +20.7762 
 
 47 
 
 —14.3127 
 
 .3129 
 
 —14.3128 
 
 +52.0979 
 
 0966 
 
 + 52.0772 
 
 48 
 
 + 0.7216 
 
 .7223 
 
 + 0.7220 
 
 + 6.3454 
 
 3473 
 
 + 6.3464 
 
 49 
 
 + 0.5870 
 
 ■5895 
 
 + 0.5882 
 
 + 6.5011 
 
 5028 
 
 + 6.5020 
 
 50 
 
 —16.8363 
 
 .8385 
 
 —16.8374 
 
 +46.9469 
 
 9522 
 
 +46.9496 
 
 51 
 
 — 12.7772 
 
 .7769 
 
 — 12.7770 
 
 +26.2011 
 
 2035 
 
 +26.2023 
 
 52 
 
 — 23.2171 
 
 .2208 
 
 —23.2190 
 
 +36.5401 
 
 5383 
 
 +36.5392 
 
 53 
 
 — 9-3264 
 
 •3231 
 
 — 9-3248 
 
 + I7.52I5 
 
 5235 
 
 +17-5225 
 
 54 
 
 —23.6114 
 
 .6141 
 
 — 23.6128 
 
 +32.1703 
 
 1710 
 
 +32.1706 
 
 55 
 
 — 3-4469 
 
 .4482 
 
 — 3-4476 
 
 + 6.9892 
 
 9975 
 
 + 6.9934 
 
 56 
 
 -16.7358 
 
 • 7332 
 
 —16.7345 
 
 +I9-4458 
 
 4485 
 
 + 19.4472 
 
 57 
 
 —10.5243 
 
 •5231 
 
 —10.5237 
 
 + 12.9294 
 
 9260 
 
 + 12.9277 
 
 58 
 
 —I4-3323 
 
 •3352 
 
 —I4-3338 
 
 + 14.5137 
 
 5143 
 
 + 14.5140 
 
 59 
 
 —20.1055 
 
 .1008 
 
 — 20. 1032 
 
 + 13.3002 
 
 3028 
 
 +13-3015 
 
 60 
 
 —10.3510 
 
 •3482 
 
 —10.3496 
 
 + 7-0274 
 
 0295 
 
 + 7.0284 
 
 61 
 
 — 22.1244 
 
 ■1245 
 
 — 22.1244 
 
 +10.4513 
 
 4586 
 
 + 10.4550 
 
 62 
 
 —18.6321 
 
 • 6319 
 
 — 18.6320 
 
 + 8.9114 
 
 9147 
 
 + 8.9130 
 
 63 
 
 —49.1432 
 
 • 1463 
 
 —49.1448 
 
 +17.6997 
 
 7009 
 
 + 17.7003 
 
 64 
 
 —16. 668 [ 
 
 .6686 
 
 — 16.6684 
 
 + 5-7452 
 
 7452 
 
 + 5-7452 
 
 65 
 
 — 44.6400 
 
 ■6379 
 
 —44.6390 
 
 — 9.8408 
 
 8430 
 
 — 9.8419 
 
26 Stars within One Degree of the North Pole, and 
 
 IV. 
 
 Method of Determining the Right Ascension and Declination 
 of a Star from Its Measured Coordinates. 
 
 The principles upon which this method is based have been eluci 
 dated and published by Professor Jacoby in the Astronomical 
 Journal, Vol. X, p. 120. The same article is to be found in full. in 
 Scheiner's Photographie derGestirne, pp. 159-166, and it is neces- 
 sary to give here only the application of the theorem to the case 
 in hand. 
 
 The problem may be stated thus : 
 
 Given a series of circles and angles on a sphere which are pro- 
 jected upon a plane tangent to the sphere, becoming thus straight 
 lines and -plane angles ; required to pass from the measured 
 straight lines and plane angles to the corresponding spherical 
 parts. 
 
 The solution naturally falls into two divisions. The first case 
 includes those angles which have their vertices at the point of 
 tangency ; the second those which have their vertices elsewhere. 
 The second case is discussed in the paper by Jacoby and is the one 
 that concerns us here. In this treatment it is assumed that the 
 photographic plate is perpendicular to the optical axis of the 
 telescope and is cut by it at the intersection of the two middle 
 reseau lines. This point is the point of tangency of the plane and 
 sphere, and is thus the center of projection. 
 
 Let r be the focal length of the objective. If B (using the 
 notation of the paper referred to) is a plane angle one side of 
 which passes through the center of projection, and the vertex of 
 which is at a distance p from 0, then the correction necessary to 
 change B into B s the corresponding spherical angle is 
 
 1 p 2 
 1? = — ; sin B p cos B p , 
 
 B, = B p + y. 
 
 If d is the linear distance between the vertex m of B and some 
 
 p 
 
 point m' situated on the side of B p not passing through 0, and p' 
 is the corresponding distance between and m'; then if s is the 
 
Optical Distortion deduced from Photographic Measures. 27 
 corresponding distance on the sphere, expressed in seconds of arc, 
 
 , = *-**„>«* B,-l* tPl i+l* t 0. 
 
 r 2 r> 2r or 
 
 In applying these formulas to the case of the polar plates, we 
 shall assume that we know the usual constants for each plate, 
 i. e., the coordinates of the pole, the angle of orientation and the 
 scale value. Accordingly let 
 
 X, Y be the rectangular coordinates of the star, 
 ?, t\ be the rectangular coordinates of the point on the plate 
 corresponding to the pole of the heavens, 
 A toe the right ascension of the .X-axis in the sky, 
 to be the scale value a 
 a, - be the star's apparent right ascension and polar distance 
 
 P/ f xW 
 
 Y-i 
 
 Fig. 2. 
 
 From the figure we have the following relations, viz : 
 
 p sin B = Y— v, p sin B' = — n, 
 
 pcosB=X — f, p cos B' = — f, 
 
 B" = B' — B. 
 
 The angle B is the plane angle which we wish to convert into 
 a spherical angle, but neither of its sides passes through the ori- 
 gin, hence the auxiliary angle B" is used, such that B = B' — B" . 
 
 The correction to be applied to B is 
 
 i p 1 
 n = - -. sin B' cos B' 
 2 r 
 
 ip- 
 
 2 sin B" cos B", 
 
 = - -. sin B. 
 
28 Stars within One Degree of the North Pole, and 
 
 And thence 
 
 a = B 4- - p 2 sin B<->* sin i" + .4, 
 
 it =pu — - pp2 cos 2 .B"" 3 sin 2 i" — - p{X 2 + F 2 )u 3 sin 2 1" 
 
 + ^# 3 <j 3 sin 2 i". 
 
 These formulas hold good if the pole is not more than a degree 
 from the center of the plate. When it is very near the center, as 
 in the 90 plates, certain terms may be omitted. This omission 
 and a slight additional transformation leave the equations in the 
 final form 
 
 a = B + A, 
 
 I [ (0 
 
 v = pa p 3 u 3 s ; n 2 I //_ p (xf + Yn)" 1 sin 2 \" . 
 
 V. 
 
 Method of Determining the Plate Constants. 
 
 The equations (i)can be solved whenever we know the plate con- 
 stants f, rjj A and w, and will furnish the right ascensions and 
 polar distances of the stars on the plates. On the other hand, we 
 can also obtain from them the values of S, >j, A and u> if we know 
 the right ascensions and polar distances of at least two stars. If 
 there are more than two known stars on the plate, the resulting 
 equations can be solved by least squares. Since we can obtain 
 very good approximate values of these constants by a direct so- 
 lution, it will be sufficient to find their corrections by the use of 
 differential formulas derived from equations (1). 
 
 If da and di: are changes in a and i: due to small changes in ?, 
 ■f), A and u>, and we put 
 
 a' = a -f- da, 
 TT> = IT + dir, 
 
 then we have 
 
 . '. sin B cos 2? ... . 
 
 a' = a-\ ; d£ r — -., dn + dA, 
 
 p sin 1" p sin \" ' 
 
 ■x f = it -\- pdu — u cos Bd!j — a sin Biv. 
 
Optical Distortion deduced from Photographic Measures. 29 
 
 Of these quantities a and n are computed from (i) with the 
 approximate plate constants, a' and it' are the apparent places of 
 the standard stars obtained by reduction from some catalogue. 
 Each equation in right ascension should be multiplied by pa> sin i " 
 to give it the same weight as the polar distance equations. If 
 we make this multiplication and adopt the following substitutions 
 
 Ike = (a — a') pa sin \" , 
 
 n v — it — it', 
 
 dA' = <j sin i" dA, 
 
 our equations become 
 
 <j sin Bd% — a cos Bdn -\- pdA' + rtx = o, . . 
 
 — a cos Bd f — a sin Bdi + pdo + % = o. 
 
 Each star furnishes two such equations and a least squares so- 
 lution of the equations furnished by all the standard stars on the 
 plate will give the most probable values of d?, dy, dA' and da>* 
 
 On account of the symmetry of the coefficients in these last two 
 equations the least squares solution can be simplified. Let 
 
 — (J sin B = r, — a cos B = s, 
 then the equations (2) become 
 
 — rdf + sdq -\- pdA' -\- odw -\- n x = o, 
 + sdl; + rdv + odA' + pd a + n y = 0. 
 
 If a, b, c, d, n, and s, have the signification usually adopted in 
 the Gaussian method of elimination, and the terms indicated in 
 the square bracket are formed in the customary way, we have the 
 following relations, 
 
 [66] = [aa] , [a&] = o, [ac] = — [&d] , [ad] = [6e] , 
 [cc] = [dd], [cd] = o. 
 
 We can also make use of the ordinary check formulas, 
 [ao] + [ac] + [ad] + [an] = [as], 
 [aa] + [ad] — [ac] + [6m] = [6s], 
 
 [ac] + [ad] + [ce] + [en] = [cs], 
 
 [ad] — [ac] + [cc] -f- [dn] = [ds], 
 
 * These formulas appear in a paper written by Professor Jacoby entitled 
 "Photographic Researches near the Pole of the Heavens," and published in 
 the Bulletin of the Imperial Academy of Sciences of St. Petersburg, V Series, 
 Volume IX, No. 1 (June, 1898). 
 
30 Stars within One Degree of the North Pole, and 
 
 If we place 
 
 F = [aa] ■ [cc] — [ae] • [ac] — [ad] • [ad], 
 C = [ac] • [en] + [ad] ■ [an] — [cc] ■ [an], 
 D = [ad] • [c»] — [ac] - [dn] — [ce] ■ [In], 
 G = [ac] - [am] + [«d] • [8n] — [aa] ■ [en], 
 J9 r = [ad] ■ [an] — [ac] ■ [bn] — [aa] • [dn], 
 
 then 
 
 ^ C ^ ^ .7,./ G .j ^ 
 df=-, d, = -, d4' = -, da, = -, 
 
 weight of df = weight of dn = = — , 
 
 \_cc] 
 
 F 
 weight of dA' = weight of dw = -. — ; . 
 
 [aaj 
 
 (3) 
 
 Another method of solving these equations has been published 
 by Professor Jacoby,* the study of which suggested to me the 
 above process. The present formulas, however, seem more suit- 
 able for this work, particularly since they give a desirable check 
 to the computation early in its course. Their symmetry and sim- 
 plicity are at once noticeable. 
 
 Before giving the results of the several least squares solutions., 
 it will be necessary to explain somewhat in detail the method of 
 computing a! and -', the apparent places of the standard stars. 
 
 VI. 
 
 Method of Determining the Apparent Places of the Stand- 
 ard Stars. 
 
 The plate constants f and t] are the rectangular coordinates of 
 that point on the plate which is the projection of the pole of the 
 heavens, but since the celestial pole is a moving point its projec- 
 tion is not fixed, and we are at liberty within certain limits to 
 make a choice of the epoch which fixes the exact position of the 
 pole. £ and ij are determined through the solution of equations 
 (2) by comparing the apparent places of the stars in the sky with 
 their positions obtained from the measured coordinates, hence the 
 manner of computing their apparent places must be consistent 
 
 * Monthly Notices E. A. S., May, 1896. 
 
Optical Distortion deduced from Photographic Measures. 31 
 
 ■with the choice of pole. If, pursuing the usual process, we cor- 
 rect the star places taken from some standard catalogue for pre- 
 cession, nutation, aberration and refraction, f and jj will be the 
 coordinates of the pole at the instant of observation, and A will 
 be the right ascension of the .X-axis referred to the equinox of 
 date. The places of the unknown stars obtained by the solution 
 of equations (i) will be the apparent places at the instant of ob- 
 servation, and must be corrected for refraction and reduced to 
 the beginning of the year, after which a further application of 
 precession is necessary to bring them to any desired epoch. 
 
 It is possible to abbreviate quite considerably the labor of this 
 long computation by selecting the position of the pole for some 
 other instant than that of observation, for example, the epoch of 
 the catalogue from which the standard stars are taken. Preces- 
 sion and nutation do not affect the positions of the stars relative 
 to one another, but merely change the planes of reference. Hence 
 if we apply to the right ascensions and polar distances of the 
 standard stars, proper motion, aberration and refraction, the con- 
 stants <?, 7] and A will give the position on the plate of the pole of 
 the epoch of the catalogue. The scale value, w, depends upon the 
 mutual distances of the stars and would not be altered by this 
 method of procedure. The right ascensions and polar distances 
 of the unknown stars computed from equations (i) will be their 
 apparent places, but referred to the pole and equinox of the epoch 
 of the catalogue. 
 
 We can also make a simplification in the computation of refrac- 
 tion, which would ordinarily be an involved process with stars of 
 such high declination. The pole of the selected epoch may be 
 treated as if it were a luminous point and affected by refraction, 
 in which case the right ascensions and polar distances of all the 
 stars will be affected by differential refraction only. This as- 
 sumption is allowable, because the point on the plate, of which f 
 and t) are the coordinates, in an imaginary point, and the point in 
 the sky of which it is the projection can be connected with the 
 real pole by means of a simple differential relation. 
 
 However, precession affects certain quantities which appear in 
 the formulas for aberration and refraction, and must therefore be 
 considered in finding the place of the refracted pole. The aber- 
 ration formulas involve the longitude of the sun and the obli- 
 quity of the ecliptic ; the refraction formulas, the sidereal time, 
 
32 
 
 Stars within One Degree of the North Pole, and 
 
 which is the angle formed at the pole by the equinoctial colure and 
 the meridian, and the zenith distance of the pole, all of which 
 quantities are changed by precession. The modifications intro- 
 duced for each of these changes will be given with the statement 
 of the formulas employed. 
 
 1. Aberration. 
 
 The formulas used are due to Dr. G. W. Hill and are found in 
 the Star Tables of the American Ephemeris, page xxii, where 
 they are numbered (30). 
 
 u — Uj = — 20". 4451 cosec - 1 [sin a t sin Q + cos % cos e cos©] 
 
 — o". 0009329 cosec 2 ir x sin 2a t cos 2 © 
 -f o". 0009295 cosec 2 ji-j cos 20j sin 2 Q 
 + o".3ii cos<p cos (6 — <Zj) cosec -,, , 
 
 *" — ""! = + 20". 4451 cos 7T, cos ^ sin© } (4) 
 
 — 20". 4451 cos [cos ji-j sin Oj cos t — sin «i sin e] 
 + o".ooo4648 cotTj sin 2a,. sin 2 © 
 
 — [o". 0000402 — o". OOOO4665 COS 20j] cot ~ l cos 2 © 
 
 — o".3ii cos f sin (0 — aj) cos w,. 
 
 In these equations a, and ^ are the places unaffected by aber- 
 ration ; a and - are affected by aberration. In order to use the 
 right ascension and polar distance directly from the catalogue it 
 will be necessary to apply to the longitude of the sun for date, 
 precession in longitude from the epoch of the catalogue to date 
 of exposure, and to use for e the mean obliquity of the ecliptic for 
 the date of catalogue. We shall then have the places of the stars 
 affected by aberration but referred to the pole and equinox of the 
 date of the catalogue. The last term in each equation gives the 
 effect of diurnal aberration. 
 
 2. Proper Motion. 
 
 The effect of proper motion can be computed by means of the 
 following equations in which a 2 and n t are the coordinates of the 
 
Optical Distortion deduced from Photographic Measures. 33 
 
 star unaffected by proper motion. They are also taken from the 
 Star Tables of the American Ephemeris and are numbered (10). 
 
 a — a 2 =fit + ftp' cot 7r 2 < 2 [.us cos 2 ^ 2 — ^'( 1 + 3 cot 2 n" 2 )]i 3 , 
 
 1 
 
 7T — 7T 2 = — fl'l-\--/i 2 Sin 2 7T 2 i 2 + - ^' ( I + 2 COS 2 7T„ )<3. 
 4 D 
 
 (5) 
 
 3. Refraction. 
 
 Very precise formulas for differential refraction have been de- 
 rived by Jacoby and used by him in his paper on the Pleiades.* 
 At his suggestion the differential method was also employed in 
 this investigation, though several modifications were necessary 
 because of its application in the vicinity of the pole. These modi- 
 fications were developed by me. Jacoby's formulas give the ef- 
 fect of differential refraction on position angle and distance, hence 
 if we suppose the imaginary refracted pole to take the place of the 
 central star, they will apply equally well to the present case, for 
 the position angle becomes the hour angle, and the measured dis- 
 tance becomes the polar distance. The zenith distance of the 
 pole at Helsingfors is 30 , therefore terms of higher order than 
 the first were omitted. With our notation, Jacoby's group (c) 
 becomes 
 
 a— o/ = + fccot 2 0sin(0 — a')cos(0 — a'), 1 
 
 7T — n-' = + /fc7r[oot 2 0cos 2 (0 — a') + l] sin 1". j * ' 
 
 If we hold to the original signification of these formulas, a' and 
 ■k' are the apparent right ascension and polar distance of a star, 
 is the sidereal time of exposure, z is the zenith distance of the 
 pole, and and a' have their vertices at the same point. But if 
 the quantities a' and ■"' are referred to the pole and equinox of 
 the date of the catalogue, in which case a' has its vertex at this 
 pole, it will be necessary to find the angle at this point corre- 
 sponding to the angle 0, i. e., an angle such that one side passes 
 through the equinox of the adopted epoch, and the other through 
 the zenith at the instant of exposure. By means of differential 
 formulas we can easily pass from one angle to the other in the 
 manner described below. We shall find first the position of the 
 
 * Annals, New Yoke Academy of Science, Vol. VI, p. 253. 
 
34 Stars within One Degree of the North Pole, and 
 
 pole of the adopted epoch referred to the pole of date, and then 
 pass to its refracted position. 
 
 Let 
 
 Fig. 3. 
 
 P = pole at epoch of catalogue, 
 P = pole at date of exposure, 
 P 1 = pole at epoch, when refracted, 
 [] = pole of ecliptic, 
 Z = zenith. 
 P T = equinoctial colure for epoch, 
 Pf = equinoctial colure for date, 
 ZPt = = sidereal time of exposure, 
 
 ZP 9 f t =o v zp 1 ^=e v 
 r a P B=Ji ,rPP ll =A, 
 
 PZ = 
 
 77P = 
 
 P Z=z ,P 1 Z=z 1 , 
 
 PP = *. 
 
 A is the right ascension of the pole of epoch of catalogue re- 
 ferred to the pole of the date of exposure. It is a little greater 
 than 180 . 
 
 A is always less than 180 , and 180 + A is right ascension of 
 P reckoned from P . 
 
 From the figure we have the following relations : 
 
 6 = A — ZPB, e = A o — ZP B, 
 e = e + (A — A) — {ZP B — ZPB). 
 
 (6) 
 
Optical Distortion deduced from Photographic Measures. 35 
 
 Employing a series developed by Jordan,* we have from the 
 triangle IJPP 
 
 (270 — A ) — (270 — A) = Train (270 — A) cote, 
 or 
 
 A — A = ir cos A cot e, 
 and from the triangle ZPP 
 
 ZPB — ZP B = nsm(A—6) cot z. 
 Hence 
 
 O — = ""[cos .4 cot e + sin (0 — A) cot a]. (7) 
 
 We have also 
 
 z — * = — tcos(0 — 4). (8) 
 
 We can use the same differential formula for finding the angle 
 
 ®i — e o = "■ sin O cot P To = o, 
 since 
 
 p c r = 9 o°. 
 
 To find z, we have only to find the mean refraction for the zenith 
 distance z and apply it directly to z . Our formulas then read 
 
 a — a' = + k sin (^o + a') cos (S — a / )isan'z l , ) 
 
 *- — n' = + far' [1 + cos 2 (0 O — a') tan 2 zj sin 1". j ' 9 ^ 
 
 For diurnal aberration also we should use z 1 and d . 
 
 It has been tacitly assumed that we already possess values of 
 A and it which are the right ascension and polar distance of the 
 pole of date of exposure. They may be obtained in several ways. 
 We may use Chauvenet's Astronomy I (664), or the method of 
 Fabritius, or more briefly the ordinary precession constant for 
 t , the epoch of the catalogue, as follows : 
 
 A=i8o° + ±m {t-t ), j (IQ) 
 
 tt ==n [t — 1 ). J 
 
 It is desirable to be more precise with nutation since its effect 
 is much greater. This can be accomplished by using the ordinary 
 Besselian constants A and B of the Berliner Jahrbuch, and im- 
 proving the results by the use of the Fabritius formulas. f The 
 
 * Handbuch der Vermessnngskunde, diitte Auflage, 1890, Vol. Ill, p. 313. 
 t Astr. Nach., 2072 and 2063 ; Oppolzer, Bahnbestimmnng, Vol. I, p. 258. 
 
,36 Stars within One Degree of the North Pole, and 
 
 aberration terms -Gc arid Dd are of course omitted. These im- 
 proved values of A and w should be used in equations (7) and (8). 
 They should not be confounded with the A and n of equation 
 (1) and for convenience might be called A'" and *■'". 
 
 e — 9 = 71-'" [cos A>" cot £ + sin ( S — A'" ) cot z] , J 
 
 a, — s = — ?r w cos {6 — A'"). ) 
 
 If we determine the right ascensions and polar distances of the 
 known stars in this manner arid substitute them in equations (2) 
 for the purpose of finding the plate constants, the values of £ and 
 ■f) thus derived will be the coordinates of the pole of the epoch of 
 the catalogue, considered to be refracted. A will be the right as- 
 cension of the .X-axis reckoned from the equinox of the catalogue, 
 and <d should remain unaffected by the method adopted. 
 
 Conversely, the right ascensions and polar distances of the un- 
 known stars obtained by substituting these values of the con- 
 stants in (1) should be freed from differential refraction, and 
 aberration and they will then be referred to the pole and equinox 
 of the catalogue. 
 
 VII. 
 
 Determination of Plate Constants. 
 
 The standard stars were taken from Elkin's " Heliometer Tri- 
 angulation of Stars in the Vicinity of the North Pole."* The 
 epoch of this catalogue is 1888.0. The Helsingfors plates are two 
 degrees square, and it was therefore decided to include in the 
 present publication only those stars which lie within one degree 
 of the pole, and consequently on all four plates. Unfortunately 
 only two of Elkin's stars lie in this region, hence it was necessary 
 to utilize a few other stars which were farther from the center and 
 lay in the corners of the plates. The following table includes all 
 of Elkin's stars which were available.f There were a few others 
 appearing on some plates which lay farther from the center than 
 10, but they were not included. 
 
 * Transactions of Yale Observatory, Vol. I, part III; 
 tElkin, loc. tit., p. 179. 
 
Optical Distortion deduced from Photographic Measures. 37 
 
 Star. 
 
 s 
 
 t 
 
 V 
 
 P 
 
 * 
 
 ! 
 
 a 
 
 1 II 
 
 41 26 32 
 
 i297.'25 
 
 116° 8' 33 
 3728.37 
 
 193 33 33 
 3718.88 
 
 O 1 II 
 
 246 46 54 
 2685.92 
 
 293°55 5° 
 3735-81 
 
 / // 
 334 27 22 
 
 3953-79 
 
 Table IV contains the rectangular coordinates of these stars as 
 they appear on the four plates. Bach star was measured twice 
 and the mean taken for the final coordinate. 
 
 Table IV. — Coordinates of Standard Stars. 
 
 IB X 
 Y 
 
 IMX 
 Y 
 
 II 
 
 BX 
 Y 
 
 II MX 
 Y 
 
 III BX 
 
 Y 
 
 III MX 
 
 Y 
 
 IV BX 
 Y 
 
 IV MX 
 
 Y 
 
 + 18.7952 
 
 — 7.9222 
 
 + 18.7940 
 
 — 7-58I2 
 
 + 7.8014 
 —19.0512 
 
 + 7.7881 
 —18.6642 
 
 + 17-7945 
 +6.6870 
 
 +17.8049 
 + 7.0924 
 
 — 62153 
 —18.9971 
 
 — 6.2164 
 — 18.6091 
 
 +40.4762 
 +48.3180 
 
 +40.4924 
 +48.6676 
 
 +50.7758 
 —38.6665 
 
 +50.7760 
 —38.2861 
 
 —37.2292 
 
 +51.8052 
 
 —37.2241 
 +52.1562 
 
 — 64.0614 
 + 9-2847 
 —64.0529 
 + 9.6910 
 
 +51-5005 
 +39.1071 
 
 +5I-5053 
 +39-4929 
 
 —45-5262 
 
 + 2.1541 
 
 —45-5230 
 + 2.5078 
 
 —30.4085 
 +33-6557 
 —30.4278 
 +34.0496 
 
 —34-8150 
 —31.6872 
 
 ■34.8028 
 — 31.2800 
 
 + 1-5743 
 +45.6420 
 
 + 1-5742 
 +46.0252 
 
 —43.6778 
 43.6150 
 
 —43.6883 
 ■43.2487 
 
 —61.5584 
 + 0.0757 
 
 —61.5679 
 + 0.4628 
 
 +41.4649 
 —49-4535 
 +41.4721 
 —49.0484 
 
 — 44.0910 
 +42.1716 
 
 —44.0907 
 +42.5576 
 
 48.4102 
 
 ■42.5585 
 
 — 48.4162 
 
 ■42. 1628 
 
 I have also collected in tabular form the various quantities 
 needed in the solution of equations (4), (9) and (11). 
 
38 
 
 Stars within One Degree of the North Pole, and 
 
 w 
 
 pa 
 < 
 
 
 S 
 
 
 « So 
 
 
 ^ O *: ^ % 
 
 m r>- co t*- _. 
 
 
 
 
 hH 
 
 
 
 « v -rf cO cO CO 
 
 
 
 
 o> 
 
 6 
 
 a 
 
 8 " 
 ■* 
 
 <N O . 
 
 co r>. 
 
 
 V *H v _(_ V CN 
 
 OS O i-< ~t~ P* OS 
 
 
 
 j> 
 
 -5 
 3 
 
 K 
 
 1 O _i_ »o to 
 1 ioT or-*. 
 
 8* c\ 
 
 
 
 <D 
 
 "3 
 
 
 
 
 lO v- 
 
 
 
 
 
 l-l 
 
 CN 
 
 
 CO "" 
 
 00 M 
 
 vb V "b *co o _ 
 
 
 
 g 
 
 M 
 
 -*a 
 
 
 M M lO CO ™tf" OS 
 
 
 
 
 0) 
 
 <o " 
 
 a w 
 
 M O 
 
 ■a 00 
 co r- 
 
 
 V V ^ iN.CN 
 
 
 
 
 M 
 
 CO 
 
 
 1^1 IO lO 
 
 o T^ o t->. 
 
 
 
 
 5 
 
 
 
 co as • 
 
 ^3- « OS 
 
 
 
 
 
 
 " 
 
 
 
 
 
 
 a 
 
 
 CO cO 
 
 IH "*1" 
 
 B -cJ-"^ 
 
 
 ^ % % * % 
 
 Tt M VO CO VO ._ 
 
 
 
 
 
 
 CM IO cO CO CN JO 
 v v v | v W 
 
 cn o m -\- M OS 
 
 
 
 
 3 
 ■o 
 
 2 
 
 ri 
 
 
 1 °m 4- o 10 R 
 
 O 
 
 
 HH 
 
 6 
 
 
 
 
 " 00 
 
 CO ff ^ 
 
 o 
 
 OS OS 
 
 !2 ° u 
 
 
 <0 
 
 3 
 
 ~ 
 
 CO 
 
 l-l 
 
 43 
 
 as as 
 co cm 
 
 8 R 
 
 00 " 
 
 
 sO OS -*3 
 
 ■ CD 
 
 
 *; % 5j S; % 
 
 •-« ""*■ cO CO cO 
 
 
 
 a 
 
 60 
 
 
 M 
 
 CN U*J CO CO CN M 
 v v v , v CN 
 
 tN "tf- m -h tN OS 
 
 1 -"T _i_ m io 
 1 o T^ o t^. 
 
 ^ 
 
 
 
 s 
 
 
 
 S 1 ^cf> 
 
 CO 
 
 
 
 
 a 
 
 
 . 8b 
 
 io >o 
 
 
 O "io ^b Vj vo 
 
 
 
 
 ►H 
 
 
 
 CN lO cO cO CN CN 
 
 \b "d- cn -J- CO OS 
 
 
 
 
 "3 
 
 ^5 
 
 j^o* 
 
 1 cr, 
 
 1 CN _|_ IO IO 
 
 1 o T^ o t^. 
 
 N 
 
 
 ,_; 
 
 g 
 
 6 
 
 a 
 
 o g 
 
 ^- OS -i 
 CN OS 
 
 OS M 
 
 
 
 
 
 
 V !>■ 
 
 
 "* n V 
 
 
 CO 
 
 
 VD 
 
 
 
 
 OS o t^ 
 
 
 "3 
 
 
 
 
 
 E 
 
 
 4^ 
 
 05 io 
 
 cO "? 
 
 CO M 
 
 O J % !j ^ 
 rf m |>. ro r- 
 
 «o 
 
 M CN 
 
 
 
 g 
 
 c- 
 
 OS ^ 
 
 M 
 
 H CO CO CO M CO 
 
 
 
 
 
 0) 
 CO 
 
 
 
 ** v v 1 v IO 
 
 v£> co cn -h CO OS 
 
 
 
 
 
 
 cn o 
 
 J3 CO 
 
 
 1 \D i o r>. 
 g 1 oS 
 
 
 
 
 
 
 O (N, 
 
 
 
 
 
 
 
 M 
 
 
 
 
 
 
 a 
 
 
 
 
 CO 5: % ^ 5; 
 
 in r*. cn to cn 
 
 
 
 
 HH 
 
 
 cO iO 
 
 
 . ■ co CO CO CN 
 ^J- CO CN H- CO as 
 
 
 
 
 CD 
 
 to 
 
 «3 ^ 
 
 
 
 
 
 
 M CO 
 
 ^. 
 
 o _|_ IO io 
 1 OS T^ o t-^. 
 
 
 
 
 § 
 
 d 
 
 rO cO 
 
 lO _ 
 
 "* OS • 
 
 
 
 
 n 
 
 CN l"- 
 
 H O 
 
 CO CN OS 
 
 o f 
 
 
 M 
 
 OS 
 
 +^ 
 s3 
 
 
 u5 
 
 M 
 
 M 
 
 vo v * 
 
 
 OS o «^ 
 Sg ^ OS 
 VO co o 
 
 *>■ co O 
 
 
 
 
 ro ^ 
 
 -V 5; ^ ft; 5. 
 
 
 
 
 -e 
 
 M CO 
 
 CO H 
 
 IS rt H CO *-* 
 
 M ^O 
 
 
 
 a 
 
 co 
 
 H 
 
 Tf Tt CO CO CN OS 
 
 't CN -J - CO OS 
 
 "©- 
 
 
 
 60 
 
 
 IH CO 
 
 ja o 
 
 r-t 
 
 
 ■■* _L IO IO 
 
 or (L In 
 
 
 
 
 s 
 
 
 
 ts OS . 
 
 TT CM OS 
 CO 
 
 
 
 
 
 ON 
 00 
 
 l-l 
 
 *> o 
 
 V V 
 
 1 ^° 1 1 *T -g 
 cd « ^ § 
 
 * 1 
 
 Mi 
 
 a 
 
 
Optical Distortion deduced from Photographic Measures. 39 
 
 Remarks. 
 
 j. The Helsingfors sidereal time corresponds to the middle of 
 the time of exposure ; see Table I, page 3. 
 
 2. The longitude of the sun was taken from the Berliner Jahr- 
 buch for 1895. It is there referred to the mean equinox of the 
 beginning of the year 1895 aud was therefore decreased by the 
 precession in longitude for seven years. 
 
 3. The obliquity of the ecliptic is the mean obliquity for 1888.0. 
 It is taken from the Jahrbuch for 1888. 
 
 4. The effect of precession on the pole of 1888.0 was computed 
 by. Chauvenet I. (664). The resulting right ascension and polar 
 distance of pole of 1888 referred to the pole of date are 
 
 A = i8o°2 / 43 // .34 
 ■k = i4o".37 
 
 The values of A'" and rJ" given in the table are obtained by the 
 ordinary " reduction to date." using the Besselian numbers A and 
 B taken from the Jahrbuch. They were further improved by the 
 use of Fabritius's method. 
 
 5. The value of log h was taken from the Pulkowa refraction 
 tables, in accordance with the data given in Table I. It was in- 
 creased by -fa of itself to allow for the difference between visual 
 and photographic refractions. 
 
 I shall now give a rather full outline of the process of reducing 
 one plate, selecting for this purpose plate I, middle images. An- 
 nual aberration was computed according to equations (4); diurnal 
 aberration according to the last term of (4) using O and 90 — z,, 
 for and <p ; differential refraction according to (9). The only 
 standard star whose proper motion has been determined is " <p " 
 or I TJrsse Minoris. Its proper motion was taken from the Ber- 
 liner Jahrbuch, and applied according to the first term of (5). 
 
40 
 
 Stars within One Degree of the North Pole, and 
 
 Star. 
 
 s 
 
 1 
 
 V 
 
 p 
 
 <f> 
 
 a 1888.0 
 Annual aberr. 
 Prop. Motion. 
 Diurn. aberr. 
 Differ, refrac. 
 
 a apparent. 
 
 n 1888.0 
 Annual aberr. 
 Prop. Motion. 
 Diurn. aberr. 
 Differ, refrac. 
 
 tt apparent. 
 
 / a 
 41 26 23 
 
 + 3240 
 
 + 15 
 + 9 
 
 116° 833 
 
 — 924 
 
 — 5 
 
 — 9 
 
 O 1 II 
 
 193 33 33 
 
 — 16 18 
 
 — 8 
 
 + 7 
 
 2464654 
 
 — 648 
 
 — 3 
 
 + 4 
 
 O 1 II 
 
 293 55 50 
 + 854 
 
 — 6 
 + 5 
 
 — 9 
 
 4i 59 36 
 
 1297.25 
 + 13-97 
 
 + 0.12 
 — 0.42 
 
 115 58 55 
 
 3728.37 
 + 15-58 
 
 + 0.12 
 — 1. 19 
 
 193 17 14 
 
 3718.88 
 
 — 6.70 
 
 — 0.06 
 
 — i-35 
 
 37IO-77 
 
 246 40 7 
 
 2685.92 
 
 — 18. 16 
 
 — 0.15 
 
 — 0.77 
 
 294 4 34 
 
 3735-81 
 
 — 16.28 
 
 + 0-05 
 
 — 0.13 
 
 — i- 17 
 
 1310.92 
 
 3742.88 
 
 2666.84 
 
 3718.28 
 
 The plate constants are to be determined from equations (2). 
 Approximate values were found quite easily. A, the orientation 
 angle of the X-axis was placed equal to 66°, i. e., the right ascen- 
 sion of the center of the plate taken from Table V, plus 90 . u> was 
 assumed to be equal to 60" ; f and y, were obtained from the so- 
 lution of the following simple relations : 
 
 07 = 71-'" sin {A'" — A), 
 uf = 7r"/cos {A"' — A). 
 
 A preliminary solution of (2) with equations derived from two 
 stars gave approximate values of all the constants. This ap- 
 proximation was so close that the further corrections did not 
 exceed o^oi for £ and i;, and o".oi for A and u>, and the absolute 
 terms with a few exceptions were less than 1". 
 
 The following specimen equation of condition 
 
 — 26dS — 54<2?? + 22dA' + o".37 = o 
 
 shows that the coefficients and absolute terms are not of the same 
 order of magnitude. In order to simplify the subsequent numer- 
 ical work each coefficient was divided by 100, and each unknown 
 quantity multiplied by 100, and the following substitutions made : 
 
 X = ioodf , y = 100*7, 2 = loodA 1 , t = looda. 
 
 We then have the following. equations : 
 
Optical Distortion deduced from Photographic Measures. 41 
 
 — .26a; 
 
 — -54» 
 
 +.223 
 
 +.ootf 
 
 +-37 = o 
 
 +.45 
 
 —.40 
 
 + .63 
 
 + .00 
 
 — .11=0 
 
 +■49 
 
 +■35 
 
 + .62 
 
 +.00 
 
 + .07 = 
 
 +.01 
 
 + .60 
 
 +■45 
 
 +.00 
 
 +.01 =0 
 
 —•43 
 
 +.41 
 
 +.62 
 
 +.00 
 
 — .29 = 
 
 —•54 
 
 +.26 
 
 +.00 
 
 +.22 
 
 +.19 = 
 
 —.40 
 
 — 45 
 
 +.00 
 
 +.63 
 
 +.11 = 
 
 +■35 
 
 — 49 
 
 +.00 
 
 +.62 
 
 +.00 = 
 
 +.60 
 
 — .01 
 
 + .00 
 
 +•45 
 
 —.43 = 
 
 +•41 
 
 +.43 
 
 +.00 
 
 +.62 
 
 — .84 = 
 
 Solving these equations according to equations (3), we have 
 the following values of the unknown quantities and their weights. 
 
 <7f = + o mm .oo37, 
 dy = + o mm .oo4i, 
 
 dA' = — o".ooo9, 
 
 dA = — 3", 
 
 <f« = + 0".0042, 
 
 weight 16500, 
 weight 16500, 
 weight 13000, 
 
 weight 13000, 
 
 The final coordinates with their probable errors are 
 
 f = — o mm .9734 ±o".ooi4, 
 V= + i n "°.8549 ± o".ooi4, 
 ^ = 67°30'47" ±6", 
 u = 59". 8585 ±o".ooi6. 
 
 : o .0002, 
 
 : O mnl .OO02, 
 
 The probable error r j, of one determination of polar distance 
 is ±o".i8, and of one determination of right ascension is 
 ±o."i8 cosec jr. 
 
 Similar least squares reductions of the remaining plates give 
 rise to the following values of the plate constants. 
 
 Table VI. — Plate Constants. 
 
 Plate. 
 
 £ 
 
 V 
 
 Probable 
 error of 
 Ion,. 
 
 A 
 
 Prob. 
 err. 
 A 
 
 bi 
 
 Probable 
 error of 
 
 a) 
 
 »'i 
 
 IB 
 
 M 
 
 II B 
 
 M 
 
 IIIB 
 
 M 
 
 IV B 
 
 M 
 
 mm 
 —0-9745 
 —0.9734 
 +0.5491 
 +0.5353 
 —2.8448 
 —2.8349 
 +2.4822 
 +2.4825 
 
 mm 
 + I.505I 
 + 1-8549 
 + I.6113 
 + 2.0038 
 —O.6334 
 — 0.2276 
 + I.0837 
 + I.4682 
 
 11 
 ±0.0016 
 ±0.0014 
 ±0.0012 
 ±0.0018 
 ±0.0016 
 ±0.0013 
 ±0.0017 
 ±0.0017 
 
 t u 
 67 30 10 
 
 67 30 47 
 
 112 39 30 
 112 39 18 
 22 29 16 
 22 29 18 
 155 28 17 
 159 28 24 
 
 ±6 
 ±6 
 ±6 
 
 ±7 
 ±6 
 ±6 
 ±6 
 -+-6 
 
 59-8594 
 59-8585 
 59- 8 554 
 59-8579 
 59-8527 
 59-8530 
 59-8568 
 59-8554 
 
 ±0.0018 
 ±0.0016 
 ±0.0017 
 ±0.0021 
 ±0.0019 
 ±0.0016 
 ±0.0019 
 ±0.0019 
 
 a 
 ±0.20 
 ±0.18 
 ±0.11 
 ±0.16 
 ±0.19 
 ±0.15 
 ±0.22 
 ±0.22 
 
42 Stars within One Degree of the North Pole, and 
 
 VIII. 
 
 Results of the Measures. 
 
 The plate constants given in the preceding section were used 
 in determining the right ascensions and polar distances of the un- 
 known stars. 
 
 The process employed was the reverse of that followed on page 
 40. One additional step, however, was necessary in computing 
 the aberration which according to equations (4) involves in the 
 second member a 1 and x 1 which are unaffected by aberration. 
 
 A first determination of aberration was made by using the first 
 two terms of (4) and the resulting Aa and An applied to the right 
 ascensions and polar distances which had been already freed from 
 the effects of differential refraction and diurnal aberration. This 
 gives approximately the true places for 1888.0, and these new 
 values of a and tt were substituted in the complete equations (4). 
 This additional step was taken but once, and the approximate places 
 served as a basis for computing the aberration for all four plates. 
 
 The reductions of the big and middle images have been carried 
 through to the end independently, with the exception of the de- 
 termination of annual aberration. The difference in the times of 
 exposure corresponding to the big and middle images had no 
 effect on annual aberration, hence but one determination was 
 made for each plate. The mean of the values deduced from the 
 big and middle images on each plate was taken as the mean right 
 ascension and polar distance for that plate, and the final right 
 ascension and polar distance is the mean of the four results thus 
 obtained. The residuals are the differences between the final 
 mean and the mean for each plate. 
 
 In the table of mean results immediately following, the figures 
 in the second column refer to the number of the plate and the 
 image " big " or " middle " which is reduced. The columns headed 
 " a " and " *■" give the right ascension and polar distance for each 
 image measured. The columns headed ^(B+M) give the mean of 
 the aon for the big and middle images on any one plate. The 
 " mean " is the mean of these last quantities and not of the quan- 
 tities in the columns " a " or " tt ". The residuals are the differ- 
 ences between this mean and the mean for each plate. 
 
Optical Distortion deduced from Photographic Measures. 43 
 
 The probable error of the mean place was derived from the 
 probable errors, r-± , of the single determinations of right ascension 
 and polar distance for each plate. The means from the four plates 
 were treated as four independent observations, and the ordinary 
 formula for propagation of error was used, 
 
 ,, = ± l/f '' + f ''- +!!-'. (12) 
 
 n 
 
 This will give the same probable error for stars which are found 
 on all four plates, viz : 
 
 for a, r = ± o".o64 cosec w, 
 for 7r, r = ± o".o64. 
 
 The probable errors of the stars which do not appear on all 
 four plates were obtained by substituting in equation (12) only 
 the probable errors of the plates on which the,y were found. The 
 probable errors are attached to the means in the table of mean 
 results. 
 
 It will be noticed that in taking the final mean, equal weights 
 were given to the means from the several plates, although this is 
 not in accordance with a rigorous interpretation of the principles 
 of least squares, whereby these means should be given weights 
 inversely proportional to the squares of the probable errors. 
 
 This method was adopted because the conditions involved did 
 not warrant in my opinion a strict following of the least squares 
 method. In fact if I had proceeded on the basis that the probable 
 errors were equal for the different plates, and had found an aver- 
 age probable error by taking the mean of the eight probable er- 
 rors for the different images, and if I had used this average prob- 
 able error in the formula 
 
 Vnr 1 
 
 r = , 
 
 n 
 
 exactly the same result, r = ± o".o64 would have been obtained. 
 For an explanation of the asterisk in column 1 Table YII see 
 p. 68. 
 
44 Stars within One Degree of the North Pole, and 
 
 Table VII. — Mean Results. 
 
 Star. 
 
 Plate. 
 
 a 
 
 %(B+M) 
 
 Aa sin tv 
 
 IT 
 
 %{B+M) 
 
 Air 
 
 *I 
 
 I B 
 
 IM 
 
 O 1 14 
 
 145 5° 
 4615 
 
 46 2 
 
 —■05 
 
 3441-53 
 1.74 
 
 I.64 
 
 11 
 + ■22 
 
 
 II B 
 
 45 4o 
 
 45 50 
 
 —.26 
 
 0.85 
 
 I. II 
 
 —•31 
 
 
 II M 
 
 45 59 
 
 
 
 i-37 
 
 
 
 
 III B 
 
 4632 
 
 4638 
 
 + .56 
 
 1.05 
 
 I. IO 
 
 —■32 
 
 
 IIIM 
 
 46 45 
 
 
 
 1. 16 
 
 
 
 
 IV B 
 
 45 44 
 
 45 50 
 
 —.26 
 
 1.78 
 
 I.82 
 
 + .40 
 
 
 IV M 
 
 45 56 
 
 
 
 1.87 
 
 
 
 
 Oil' II 
 
 Means 1 46 5 ±4 
 
 
 3441.42 ±.06 
 
 *2 
 
 I B 
 
 IM 
 
 5°4i' 
 4152 
 
 41 26 
 
 —•'24 
 
 768.30 
 8.40 
 
 8'' 3 5 
 
 — .02 
 
 
 II B 
 
 42 33 
 
 42 34 
 
 +•03 
 
 8.38 
 
 8-44 
 
 +.07 
 
 
 II M 
 
 42 34 
 
 
 
 8.50 
 
 
 
 
 III B 
 
 43 1 
 
 43 1 
 
 + .14 
 
 850 
 
 8.58 
 
 + .21 
 
 
 IIIM 
 
 43 1 
 
 
 
 8.65 
 
 
 
 
 IV B 
 
 42 28 
 
 42 43 
 
 +.07 
 
 8.17 
 
 8.12 
 
 —■25 
 
 
 IV M 
 
 4258 
 
 
 
 8.07 
 
 
 
 
 1 a a 
 Means 5 42 28 ±16 
 
 
 768.'37 ±.'06 
 
 *3 
 
 I B 
 IM 
 
 1 a 
 
 636 14 
 
 36 34 
 
 3624" 
 
 —■27 
 
 3I57-I4 
 7.00 
 
 7.07 
 
 +!'2I 
 
 
 II B 
 
 3624 
 
 3638 
 
 —.06 
 
 6-79 
 
 6.96 
 
 +.10 
 
 
 II M 
 
 3652 
 
 
 
 7.14 
 
 
 
 
 III B 
 
 36 43 
 
 3646 
 
 +.06 
 
 6.49 
 
 6.58 
 
 —.28 
 
 
 IIIM 
 
 3650 
 
 
 
 6.67 
 
 
 
 
 IV B 
 
 37 6 
 
 37 2 
 
 +•3° 
 
 6.81 
 
 6.84 
 
 — .02 
 
 
 IV M 
 
 36 57 
 
 
 
 6.86 
 
 
 
 
 1 a a 
 Means 6 36 42 ±4 
 
 
 3i56.'86 ±'.'06 
 
 *4 
 
 I B 
 
 IM 
 
 24° 5 35 
 5 45 
 
 5 4o 
 
 —■14 
 
 2976^85 
 7.08 
 
 6.96 
 
 —'•15 
 
 
 II B 
 
 5 34 
 
 5 4i 
 
 — 13 
 
 6-75 
 
 6.82 
 
 —.29 
 
 
 II M 
 
 5 48 
 
 
 
 6.88 
 
 
 
 
 III B 
 
 5 42 
 
 5 46 
 
 —.06 
 
 6.90 
 
 7.10 
 
 — .OI 
 
 
 IIIM 
 
 5 49 
 
 
 
 7.31 
 
 
 
 
 IV B 
 
 6 4 
 
 6 12 
 
 +•31 
 
 7-55 
 
 7-57 
 
 + .46 
 
 
 IV M 
 
 6 21 
 
 
 
 7-59 
 
 
 
 
 Means 24 5 50 ±5 
 
 
 2977.11 ±.06 
 
 5 
 
 II B 
 
 II M 
 
 35° 16 1" 
 16 11 
 
 16 6" 
 
 —."27 
 
 3431-49 
 1.67 
 
 1.58 
 
 — .10 
 
 
 III B 
 
 16 42 
 
 1643 
 
 + .36 
 
 1.26 
 
 1.36 
 
 —•32 
 
 
 IIIM 
 
 1644 
 
 
 
 i-45 
 
 
 
 
 IV B 
 
 16 14 
 
 16 16 
 
 .IO 
 
 2.02 
 
 2.10 
 
 f.42 
 
 
 IV M 
 
 16 18 
 
 
 
 2.17 
 
 
 
 
 1 a 1 
 Means 35 16 22 ±4 
 
 
 543 1- 68 ±"07 
 
Optical Distortion deduced from Photographic Measures. 45 
 
 
 Table VI] 
 
 . — (Continued.) 
 
 Mean Results. 
 
 
 Star. 
 
 Plate. 
 
 a 
 
 y^b+m) 
 
 An. Sin it 
 
 IT 
 
 %(B + M) 
 
 Aw 
 
 6 
 
 I B 
 IM 
 
 o / li 
 
 35 58 41 
 5838 
 
 58 40" 
 
 — 3° 
 
 3148.36 
 8-74 
 
 8.55 
 
 II 
 + .08 
 
 
 II E 
 
 5832 
 
 5840 
 
 —■3° 
 
 7.66 
 
 8.16 
 
 —•31 
 
 
 II M 
 
 5848 
 
 
 
 8.67 
 
 
 
 
 III B 
 
 59 12 
 
 5913 
 
 +.20 
 
 8.24 
 
 8.05 
 
 — 42 
 
 
 IIIM 
 
 59 14 
 
 
 
 7.86 
 
 
 
 
 IV B 
 
 59 3° 
 
 5928 
 
 +.40 
 
 8.94 
 
 9.12 
 
 + .65 
 
 
 IV M 
 
 59 25 
 
 
 
 9-3i 
 
 
 
 
 Means 35 59 ±4 
 
 
 3148.47 ±.06 
 
 7 
 
 I B 
 
 IM 
 
 / // 
 36 25 11 
 
 24 15 
 
 2443" 
 
 — .02 
 
 2238.16 
 8.65 
 
 8^40 
 
 + .19 
 
 
 II B 
 
 24 2 
 
 24 8 
 
 —.41 
 
 7.88 
 
 7-93 
 
 —.28 
 
 
 II M 
 
 2413 
 
 
 
 7.98 
 
 
 
 
 in b 
 
 24 45 
 
 24 50 
 
 +.06 
 
 8.36 
 
 8.24 
 
 + •03 
 
 
 IIIM 
 
 24 54 
 
 
 
 8.13 
 
 
 
 
 IV B 
 
 25 26 
 
 2518 
 
 +.36 
 
 8.21 
 
 8.26 
 
 + .05 
 
 
 IV M 
 
 25 11 
 
 
 
 8.30 
 
 
 
 
 1 a a 
 Means 36 24 45 ±6 
 
 
 // // 
 2238.21 ±.06 
 
 *8 
 
 I B 
 IM 
 
 1 11 
 
 3813 3 
 
 12 25 
 
 1244' 
 
 11 
 
 —.06 
 
 2198.22 
 8.02 
 
 8.'l2 
 
 // 
 
 -(-.22 
 
 
 II B 
 
 1244 
 
 12 57 
 
 +.09 
 
 7.82 
 
 7.87 
 
 —•°3 
 
 
 II M 
 
 13 10 
 
 
 
 7.92 
 
 
 
 
 III B 
 
 13 2 
 
 12 56 
 
 +.08 
 
 7.92 
 
 8.05 
 
 +.15 
 
 
 IIIM 
 
 1250 
 
 
 
 8.18 
 
 
 
 
 IV B 
 
 1253 
 
 1238 
 
 — .12 
 
 7-53 
 
 7-54 
 
 —36 
 
 
 IV M 
 
 12 22 
 
 
 
 7-56 
 
 
 
 
 1 a a 
 Means 38 12 49 ±6 
 
 
 // // 
 2197.90 ±.06 
 
 *9 
 
 I B 
 IM 
 
 / // 
 
 39 5 3i 
 
 5 3i 
 
 5 3i' 
 
 +"26 
 
 i633'-5i 
 3-69 
 
 3.60 
 
 II 
 
 + .36 - 
 
 
 II B 
 
 432 
 
 4 46 
 
 — .10 
 
 3-°3 
 
 3- 16 
 
 —.08 
 
 
 II M 
 
 5 
 
 
 
 3-29 
 
 
 
 
 III B 
 
 521 
 
 5 22 
 
 +•19 
 
 3-4i 
 
 3.32 
 
 + .08 . 
 
 
 IIIM 
 
 523 
 
 
 
 323 
 
 
 
 
 IV B 
 
 4 16 
 
 4 14 
 
 —•35 
 
 2.79 
 
 2.90 
 
 —•34 
 
 
 IV M 
 
 4 13 
 
 
 
 3.oi 
 
 
 
 
 Means 39 4 58 ±8 
 
 
 1633.24 d=.o6 
 
 
 
 / // 
 
 / // 
 
 „ 
 
 // 
 
 „ 
 
 // 
 
 *IO 
 
 I B 
 
 IM 
 
 4138 11 
 37 56 
 
 38 4 
 
 —.14 
 
 3039-58 
 9.88 
 
 9-73 
 
 +.09 
 
 
 11 B 
 
 3801 
 
 38 
 
 — .20 
 
 9-63 
 
 9-83 
 
 + ■19 
 
 
 II M 
 
 38 
 
 
 
 0.03 
 
 
 
 
 III B 
 
 3820 
 
 3814 
 
 +.02 
 
 9-54 
 
 9.64 
 
 +.00 
 
 
 IIIM 
 
 38 9 
 
 
 
 9-75 
 
 
 
 
 IV B 
 
 38 34 
 
 38 33 
 
 +■3° 
 
 9.46 
 
 9-36 
 
 —.28 
 
 
 IV M 
 
 3832 
 
 
 
 9.26 
 
 
 
 
 
 1 a a 
 Means 41 38 13 ±4 
 
 
 3039.64 ±.06 
 
46 Stars within One Degree of the North Pole, and 
 
 Table VII. — (Continued.') Mean Results. 
 
 Star. 
 
 Plate. 
 
 a. 
 
 H(.B + M) 
 
 Aa sin it 
 
 IT 
 
 %(S + M) 
 
 Air 
 
 *II 
 
 I B 
 
 IM 
 
 1 11 
 
 44 28 27 
 28 2 
 
 1 II 
 
 28 14 
 
 -%e 
 
 1427.54 
 7.67 
 
 7.60 
 
 — .20 
 
 
 II B 
 
 2751 
 
 28 16 
 
 —.24 
 
 8.08 
 
 8.16 
 
 + .36 
 
 
 II M 
 
 28 40 
 
 
 
 8.24 
 
 
 
 
 III B 
 
 2838 
 
 28 40 
 
 —.08 
 
 7.22 
 
 7-34 
 
 —46 
 
 
 IIIM 
 
 2843 
 
 
 
 7-47 
 
 
 
 
 IV B 
 
 30 26 
 
 3° 14 
 
 +.58 
 
 8.19 
 
 8.08 
 
 + .28 
 
 
 IV M 
 
 3° 3 
 
 
 
 7.96 
 
 
 
 
 1 a a 
 Means 44 28 51 ±9 
 
 
 a 11 
 1427.80 ±.06 
 
 *I2 
 
 I B 
 
 IM 
 
 57 5i'ii" 
 5049 
 
 / a 
 
 51 
 
 +.06 
 
 2939.67 
 0.16 
 
 9-92 
 
 +"26 
 
 
 II B 
 
 5044 
 
 5049 
 
 — .10 
 
 9.68 
 
 0.02 
 
 +-36 
 
 
 II M 
 
 5054 
 
 
 
 037 
 
 
 
 
 III B 
 
 5i 8 
 
 51 14 
 
 +.25 
 
 9- 16 
 
 9.40 
 
 —.26 
 
 
 IIIM 
 
 51 20 
 
 
 
 9-63 
 
 
 
 
 IV B 
 
 5038 
 
 5040 
 
 .22 
 
 9.42 
 
 9-32 
 
 —■34 
 
 
 IV M 
 
 5042 
 
 
 
 9.22 
 
 
 
 
 O 1 II II 
 
 
 // // 
 
 
 Means 57 50 56 ±5 
 
 
 2939.66 ±.06 
 
 13 
 
 I B 
 
 IM 
 
 58 39 '16" 
 3822 
 
 3S'49 
 
 —"05 
 
 2653.00 
 2-45 
 
 2.72 
 
 —■07 
 
 
 II B 
 
 3851 
 
 3852 
 
 — .OI 
 
 3°9 
 
 3.10 
 
 + .31 
 
 
 II M 
 
 38 53 
 
 
 
 3-n 
 
 
 
 
 III B 
 
 38 45 
 
 3S48 
 
 —.06 
 
 2.06 
 
 2.18 
 
 —.61 
 
 
 IIIM 
 
 3851 
 
 
 
 2.30 
 
 
 
 
 IV B 
 
 3858 
 
 39 4 
 
 + .14 
 
 3.26 
 
 3-15 
 
 + .36 
 
 
 IV M 
 
 39 9 
 
 
 
 3-04 
 
 
 
 
 Means 58°38's3"±5 
 
 
 2652.79 ±.06 
 
 *i4 
 
 I B 
 
 IM 
 
 63 16 5c 
 1638 
 
 1644 
 
 + .OO 
 
 3614.00 
 4-38 
 
 4-19 
 
 — .01 
 
 
 II B 
 
 17 2 
 
 1656 
 
 + .22 
 
 4.02 
 
 4.18 
 
 — .02 
 
 
 II M 
 
 1650 
 
 
 
 4-34 
 
 
 
 
 III B 
 
 1656 
 
 1653 
 
 +.16 
 
 4.14 
 
 4.18 
 
 .02 
 
 
 IIIM 
 
 1650 
 
 
 
 4.21 
 
 
 
 
 IV B 
 
 1625 
 
 16 25 
 
 —•34 
 
 4.01 
 
 4.27 
 
 + .07 
 
 
 IV M 
 
 1625 
 
 
 
 4-53 
 
 
 
 
 1 11 a 
 Means 63 16 44 ±4 
 
 
 3614.20 ±.06 
 
 15 
 
 I B 
 
 IM 
 
 / // 
 63 49 10 
 48 22 
 
 48'46 
 
 — "18 
 
 3211.09 
 1.20 
 
 i!l4 
 
 +'•13 
 
 
 II B 
 
 48 55 
 
 49 3 
 
 +.10 
 
 o.59 
 
 0.98 
 
 —■°3 
 
 
 II M 
 
 49 " 
 
 
 
 1.36 
 
 
 
 
 IV B 
 
 49 14 
 
 49 3 
 
 +.10 
 
 c.72 
 
 0.92 
 
 —.09 
 
 
 IV M 
 
 4852 
 
 
 
 1. 12 
 
 
 
 
 i a a 
 Means 63 48 57 ±5 
 
 
 3211.01 ±.08 
 
Optical Distortion deduced from Photographic Measures. 47 
 Table VII (Continued.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 WLB+M) 
 
 %(B + M) 
 
 16 
 
 17 
 
 *i9 
 
 I B 
 
 IM 
 
 II B 
 
 II M 
 
 III B 
 
 IIIM 
 
 67 39 55 
 
 39 31 
 4013 
 
 40 24 
 40 19 
 39 34 
 
 39 43 
 
 40 18 
 39 56 
 
 O / 
 
 Means 67 39 
 
 If I H 
 
 1 52 12 
 
 '■ 
 
 ; 52 22 
 
 1 
 
 ! 52 4 
 
 o / 
 
 Means 68 52 
 
 —.27 
 +•32 
 —■05 
 
 59 ± 4 
 
 3559-63 
 9-43 
 9-74 
 9.14 
 8.91 
 9-55 
 
 13 ± 5 
 
 o / 
 
 Means 70 48 
 
 23 ±11 
 
 a I n 11 
 
 Means 75 o 47 ± 6 
 
 953 
 9-44 
 9.23 
 
 +•13 
 +.04 
 
 —.17 
 
 I B 
 
 IM 
 
 O 1 II 
 
 68 52 19 
 52 4 
 
 52 12 
 
 — .02 
 
 3276.41 
 6.60 
 
 II 
 
 6.50 
 
 III B 
 IIIM 
 
 52 35 
 52 10 
 
 52 22 
 
 +.14 
 
 6.57 
 6-97 
 
 6.77 
 
 IV B 
 IV M 
 
 52 3 
 52 6 
 
 52 4 
 
 —.14 
 
 7.45 
 6.98 
 
 7.22 
 
 I B 
 
 O 1 II 
 
 70 48 39 
 
 48' 14" 
 
 II 
 
 —■05 
 
 1238.88 
 
 // 
 8.94 
 
 IM 
 
 4748 
 
 
 
 9.01 
 
 
 II B 
 
 49 1 
 
 4858 
 
 +.21 
 
 8.68 
 
 8.84 
 
 II M 
 
 48 55 
 
 
 
 9.00 
 
 
 III B 
 
 4848 
 
 4826 
 
 +.02 
 
 8-59 
 
 8-55 
 
 IIIM 
 
 48 3 
 
 
 
 8.51 
 
 
 IV B 
 
 4815 
 
 47 55 
 
 —•17 
 
 9.66 
 
 9.64 
 
 IVM 
 
 47 35 
 
 
 
 9.61 
 
 
 I B 
 
 75° 56 
 
 oW 
 
 —•14 
 
 11 
 2360. 10 
 
 0.06 
 
 IM 
 
 12 
 
 
 
 0.03 
 
 
 II B 
 
 1 2 
 
 058 
 
 +.12 
 
 0.13 
 
 0.13 
 
 II M 
 
 055 
 
 
 
 13 
 
 
 III B 
 
 044 
 
 050 
 
 +•03 
 
 9.82 
 
 9.92 
 
 IIIM 
 
 057 
 
 
 
 O.OI 
 
 
 IV B 
 
 058 
 
 46 
 
 — .01 
 
 0.27 
 
 o-35 
 
 IVM 
 
 °33 
 
 
 
 0.43 
 
 It 
 
 I B 
 
 83 5 4 
 
 — .12 
 
 4 52 
 
 2178.63 
 
 8.60 
 
 IM 
 
 441 
 
 
 
 8-57 
 
 
 IV B 
 
 423 
 
 +.12 
 
 4 3° 
 
 0.19 
 
 0. 10 
 
 IVM 
 
 4 38 
 
 
 
 0.00 
 
 
 Means 83 4 4 1 ± 9 
 
 3559-4Q ±.07 
 
 — 23 
 —.06 
 
 +•39 
 
 3276^83 ±!o8 
 
 —•05 
 —•15 
 —•44 
 +■65 
 
 1238.99 =fc.o6 
 —.06 
 +.01 
 — .20 
 +■23 
 
 2360.12 ±.06 
 
 —•75 
 
 +•75 
 
 2179.35 ±.10 
 
48 
 
 Stars within One Degree of the North Pole, and 
 
 Table VII. — (Continued.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 a 
 
 %(B + M) 
 
 Aa SiQ n- 
 
 7T 
 
 Y^b + m) 
 
 Al7 
 
 *2I 
 
 I B 
 
 IM 
 
 92 2 1 54" 
 2044 
 
 1 11 
 21 19 
 
 11 
 —.07 
 
 i88 7 " 5 7 
 7.48 
 
 11 
 
 7-52 
 
 +''33 
 
 
 II B 
 
 22 02 
 
 2153 
 
 + •23 
 
 6.86 
 
 7.10 
 
 —.09 
 
 
 II M 
 
 2144 
 
 
 
 7-34 
 
 
 
 
 III B 
 
 21 4 
 
 21 O 
 
 —.24 
 
 6.96 
 
 6.96 
 
 —■23 
 
 
 IIIM 
 
 2057 
 
 
 
 6-95 
 
 
 
 
 IV B 
 
 21 43 
 
 21 36 
 
 + .OS 
 
 705 
 
 7-17 
 
 — .02 
 
 
 IV M 
 
 21 30 
 
 
 
 7.29 
 
 
 
 
 
 / a 11 
 
 
 ./ // 
 
 
 
 Means 92 21 27 ±7 
 
 
 I887.I9 ±-06 
 
 
 
 1 a 
 
 / // 
 
 // 
 
 „ 
 
 „ 
 
 „ 
 
 22 
 
 I B 
 
 IM 
 
 98 °37 
 25 
 
 031 
 
 + .22 
 
 3263.33 
 3.69 
 
 3-51 
 
 +.43 
 
 
 II B 
 
 21 
 
 8 
 
 —.14 
 
 301 
 
 3.16 
 
 +.08 
 
 
 II M 
 
 59 54 
 
 
 
 3.30 
 
 
 
 
 III B 
 
 °39 
 
 038 
 
 + •32 
 
 2-54 
 
 2.50 
 
 —.58 
 
 
 IIIM 
 
 037 
 
 
 
 2.45 
 
 
 
 
 IV B 
 
 2 
 
 59 53 
 
 -.38 
 
 2.99 
 
 3-14 
 
 +.06 
 
 
 IV JI 
 
 59 44 
 
 
 
 3-30 
 
 
 
 
 
 1 11 a 
 Means 98 17 ±4 
 
 
 // // 
 3263.08 ±.06 
 
 *23 
 
 I B 
 IM 
 
 1 a 
 100 2 59 
 
 143 
 
 2 21 
 
 11 
 — .20 
 
 809^3 1 
 9.12 
 
 9.22 
 
 +"09 
 
 
 II B 
 
 243 
 
 2 20 
 
 — .21 
 
 9.27 
 
 936 
 
 +■23 
 
 
 II M 
 
 156 
 
 
 
 9-45 
 
 
 
 
 III B 
 
 238 
 
 2 26 
 
 —.18 
 
 9.00 
 
 9-°3 
 
 — .10 
 
 
 IIIM 
 
 2 15 
 
 
 
 9.06 
 
 
 
 
 IV B 
 
 6ie 
 
 5 42 
 
 +.60 
 
 8.91 
 
 8.90 
 
 —•23 
 
 
 IV M 
 
 5 13 
 
 
 
 8.90 
 
 
 
 
 
 1 a a 
 Means 100 3 12 ±16 
 
 
 809.13 ±.06 
 
 *24 
 
 I B 
 
 IM 
 
 10044 45" 
 44 55 
 
 44V 
 
 — .22 
 
 3444-60 
 4.44 
 
 4-52 
 
 +:' l8 
 
 
 II B 
 
 4506 
 
 45 8 
 
 + .08 
 
 4-73 
 
 4-74 
 
 +.40 
 
 
 II M 
 
 45 10 
 
 
 
 4.76 
 
 
 
 
 III B 
 
 44 58 
 
 44 58 
 
 —.08 
 
 3-4o 
 
 3-84 
 
 —•50 
 
 
 IIIM 
 
 44 58 
 
 
 
 4.28 
 
 
 
 
 IV B 
 
 45 15 
 
 45 16 
 
 + .22 
 
 4-36 
 
 4.25 
 
 —.09 
 
 
 IV M 
 
 45i8 
 
 
 
 4.14 
 
 
 
 
 
 1 a 11 
 Means 100 45 3 ±4 
 
 
 3444.'34 ±'°6 
 
 *25 
 
 I B 
 
 IM 
 
 120 19 53 
 1859 
 
 19 26 
 
 11 
 
 +.12 
 
 i53o'95 
 0.90 
 
 0.92 
 
 — .22 
 
 
 II B 
 
 19 59 
 
 19 47 
 
 +.27 
 
 1.20 
 
 i-34 
 
 +.20 
 
 
 II M 
 
 19 35 
 
 
 
 1.48 
 
 
 
 
 III B 
 
 19 39 
 
 19 14 
 
 +.04 
 
 1.06 
 
 1. 18 
 
 +.04 
 
 
 IIIM 
 
 1849 
 
 
 
 1.30 
 
 
 
 
 IV B 
 
 18 14 
 
 18 10 
 
 —.41 
 
 1.22 
 
 1. 14 
 
 — .00 
 
 
 IV M 
 
 18 5 
 
 
 
 1.06 
 
 
 
 
 
 1 a 11 
 Means 120 19 9 ±9 
 
 
 I53I-I4 ±"06 
 
Optical Distortion deduced from Photographic Measures. 49 
 Table VII. — {Continued.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 a 
 
 y^B+M) 
 
 Aa sin 77 
 
 IT 
 
 %{B + M) 
 
 a?7 
 
 
 
 1 u 
 
 i 11 
 
 II 
 
 II 
 
 „ 
 
 11 
 
 *26 
 
 I B 
 IM 
 
 133 35 23 
 3429 
 
 34-56 
 
 +•03 
 
 1298.27 
 8.20 
 
 8.24 
 
 —.04 
 
 
 II B 
 
 36 2 
 
 35-24 
 
 +.20 
 
 8.49 
 
 8.58 
 
 +■36 
 
 
 II M 
 
 34 47 
 
 
 
 8.66 
 
 
 
 
 III B 
 
 34 41 
 
 34.26 
 
 —•15 
 
 7.82 
 
 7.88 
 
 —.40 
 
 
 IIIM 
 
 34 10 
 
 
 
 7-95 
 
 
 
 
 IV B 
 
 34 40 
 
 34-38 
 
 —.08 
 
 8.48 
 
 8.42 
 
 +.14 
 
 
 IV M 
 
 34 37 
 
 
 8-35 
 
 
 
 
 1 a a 
 Means 133 34 5 r ±11 
 
 
 1298.28 ±.06 
 
 27 
 
 I B 
 
 IM 
 
 / 11 
 
 154 5 47 
 
 6 7 
 
 5 57 
 
 // 
 
 + •37 
 
 2014.49 
 429 
 
 4-39 
 
 II 
 
 +•13 
 
 
 II B 
 
 5 17 
 
 5 22 
 
 + .02 
 
 4-3° 
 
 4-44 
 
 +.18 
 
 
 II M 
 
 528 
 
 
 
 4.58 
 
 
 
 
 IV B 
 
 4 39 
 
 440 
 
 —.40 
 
 4-03 
 
 3-94 
 
 —•32 
 
 
 IV M 
 
 440 
 
 
 
 3-84 
 
 
 
 
 1 a 11 
 Means 154 5 20 ± 8 
 
 
 2014.26 ±.08 
 
 *28 
 
 I B 
 
 IM 
 
 O / // 
 
 163 25 42 
 25 27 
 
 25'34 
 
 +.06 
 
 2301.82 
 i-35 
 
 i'.'ss 
 
 +'41 
 
 
 II B 
 
 26 19 
 
 25 54 
 
 +.28 
 
 1-25 
 
 1.32 
 
 +•15 
 
 
 II M 
 
 25 29 
 
 
 
 i-39 
 
 
 
 
 III B 
 
 24 35 
 
 2442 
 
 —•52 
 
 1.04 
 
 1.03 
 
 —.14 
 
 
 IIIM 
 
 24 48 
 
 
 
 1.02 
 
 
 
 
 IV B 
 
 2546 
 
 2546 
 
 +•19 
 
 0.76 
 
 0.76 
 
 —.41 
 
 
 IV M 
 
 2546 
 
 
 
 0.76 
 
 
 
 
 1 a a 
 Means 163 25 29 ± 6 
 
 
 2301.17 ±.06 
 
 *29 
 
 I B 
 
 IM 
 
 1 11 
 171 19 21 
 19 10 
 
 1 a 
 19 16 
 
 +■13 
 
 2260.39 
 0.09 
 
 0.24 
 
 II 
 
 +•33 
 
 
 II B 
 
 19 11 
 
 19 11 
 
 +.08 
 
 015 
 
 0.26 
 
 +■35 
 
 
 II M 
 
 19 11 
 
 
 
 o-37 
 
 
 
 
 III B 
 
 1927 
 
 1930 
 
 +.29 
 
 9-45 
 
 9.60 
 
 —•31 
 
 
 IIIM 
 
 1932 
 
 
 
 9-74 
 
 
 
 
 IV B 
 
 1826 
 
 18 20 
 
 -.48 
 
 9.61 
 
 9-55 
 
 -•36 
 
 
 IV M 
 
 18 15 
 
 
 
 9-49 
 
 
 
 
 a 1 11 11 
 
 Means 171 19 4 ± 6 
 
 
 2259.91 ±.06 
 
 
 
 O 1 II 
 
 / // 
 
 it 
 
 tl 
 
 // 
 
 II 
 
 *3° 
 
 I B 
 
 IM 
 
 172 40 36 
 3916 
 
 39 56 
 
 +.41 
 
 1617.85 
 7.41 
 
 7-63 
 
 —•05 
 
 
 II B 
 
 3912 
 
 3846 
 
 — 15 
 
 7-51 
 
 7-5° 
 
 —.18 
 
 
 II M 
 
 3820 
 
 
 
 7-5o 
 
 
 
 
 III B 
 
 39 15 
 
 3852 
 
 — .10 
 
 7-94 
 
 7.72 
 
 +.04 
 
 
 IIIM 
 
 3828 
 
 
 
 7-49 
 
 
 
 
 IV B 
 
 3842 
 
 3846 
 
 — 15 
 
 7.92 
 
 7.88 
 
 +.20 
 
 
 IV M 
 
 3850 
 
 
 
 7-83 
 
 
 
 
 O 1 II // 
 
 Means 172 39 5+ 8 
 
 
 1617.68 ±"06 
 
50 Stars within One Degree of the North Pole, and 
 
 Table VII. — (Continued.') Mean Results. 
 
 Star. 
 
 Plate. 
 
 a 
 
 %(B+M) 
 
 Aa sin it 
 
 IT 
 
 BK(+M) 
 
 Att 
 
 31 
 
 I B 
 
 IM 
 
 Oil 
 
 l8o 26 40 
 27 IO 
 
 26'55" 
 
 +■'30 
 
 2687.00 
 7.20 
 
 7.10 
 
 —.'24 
 
 
 II B 
 
 26 54 
 
 26 30 
 
 —.03 
 
 7-o5 
 
 6.94 
 
 —.40 
 
 
 II M 
 
 26 5 
 
 
 
 6.83 
 
 
 
 
 III B 
 
 2648 
 
 27 
 
 +■36 
 
 7.20 
 
 7-5° 
 
 + .16 
 
 
 IIIM 
 
 27 n 
 
 
 
 7.81 
 
 
 
 
 IV B 
 
 25 53 
 
 25 4i 
 
 —.68 
 
 7-94 
 
 7.82 
 
 + .48 
 
 
 IV M 
 
 25 29 
 
 
 
 7.69 
 
 
 
 
 
 1 a a 
 Means 180 26 32 ±5 
 
 
 2687.34 ±.06 
 
 * 32 
 
 I B 
 
 IM 
 
 I9i°i3 3" 
 13 
 
 13 2 1 —.33 
 
 2067.36 
 7.19 
 
 7.28 
 
 + .II : 
 
 
 II B 
 
 14 
 
 13 55 ! +.20 
 
 6.98 
 
 7.00 
 
 — .17 
 
 
 II M 
 
 1350 
 
 
 7.02 
 
 
 
 
 III B 
 
 1327 
 
 13 3i 
 
 —.04 
 
 7-35 
 
 7-36 
 
 + •19 
 
 
 IIIM 
 
 13 35 
 
 
 
 7.38 
 
 
 
 
 IV B 
 
 13 42 
 
 13 51 
 
 +.16 
 
 7.04 
 
 7.04 
 
 — •13 
 
 
 IV M 
 
 14 
 
 
 
 7-05 
 
 
 
 
 
 a 1 11 11 
 
 Means 191 13 35 ±6 
 
 
 2067.17 ±.06 
 
 33 
 
 I B 
 
 I9i°i6 35" 
 
 
 —■17 
 
 2340^84 
 
 
 + .18 
 
 
 II B 
 
 1654 
 
 
 +.06 
 
 0.65 
 
 
 .OI 
 
 
 III B 
 
 17 12 
 
 
 +.28 
 
 0.67 
 
 
 + .OI 
 
 
 IV B 
 
 1634 
 
 
 —.18 
 
 0.48 
 
 
 —.18 
 
 
 
 1 a ,1 
 Means 191 16 49 ±8 
 
 
 2440.66 ±.09 
 
 34 
 
 I B 
 
 IM 
 
 I9I°2I 35" 
 22 8 
 
 / // 
 
 21 52 
 
 —•'17 
 
 2548'33 
 8.21 
 
 8.27 
 
 + '41 
 
 
 II B 
 
 22 32 
 
 22 18 
 
 +.14 
 
 8.44 
 
 8.05 
 
 + .19 
 
 
 II M 
 
 22 3 
 
 
 
 7.66 
 
 
 m 
 
 
 III B 
 
 21 53 
 
 21 50 
 
 —.19 
 
 7-93 
 
 7.88 
 
 + .02 
 
 
 IIIM 
 
 2147 
 
 
 
 7.82 
 
 
 
 
 IV B 
 
 22 41 
 
 22 25 
 
 +•23 
 
 7-45 
 
 7.24 
 
 —.62 
 
 
 IV M 
 
 22 9 
 
 
 
 7.02 
 
 
 
 
 
 1 a a 
 Means 191 22 6 ±5 
 
 
 2547.86 ±'.'06 
 
 *35 
 
 I B 
 
 IM 
 
 19535 0" 
 35 35 
 
 35' 18" 
 
 — .02 
 
 2274^53 
 4-49 
 
 4.5i 
 
 +"•45 
 
 
 II B 
 
 35 16 
 
 35 3 
 
 —.19 
 
 4-45 
 
 4-38 
 
 + ■32 
 
 
 II M 
 
 34 5° 
 
 
 
 4-30 
 
 
 
 
 III B 
 
 35 19 
 
 35i8 
 
 — .02 
 
 4.04 
 
 3-91 
 
 —•15 
 
 
 IIIM 
 
 35 16 
 
 
 
 3-78 
 
 
 
 
 IV B 
 
 35 44 
 
 35 39 
 
 +.21 
 
 3-52 
 
 3-46 
 
 —.60 
 
 
 IV M 
 
 35 34 
 
 
 
 3-39 
 
 
 
 
 
 i a a 
 Means 195 35 20 ±6 
 
 
 2274.06 ±.'06 
 
Optical Distortion deduced from Photographic Measures. 51 
 Table VII. — (Continued.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 a 
 
 \i{B+M) 
 
 da sin tt 
 
 ir 
 
 B%{+M) 
 
 Air 
 
 36 
 
 II B 
 II M 
 
 i9 6 °53 17 
 5236 
 
 52V 
 
 11 
 
 + .20 
 
 862^39 
 2.21 
 
 2.30 
 
 + •34 
 
 
 III B 
 
 5i 52 
 
 51 52 
 
 —.06 
 
 2.42 
 
 2.27 
 
 + •31 
 
 
 IIIM 
 
 5152 
 
 
 2.12 
 
 
 
 
 IV B 
 
 51 34 
 
 5130 
 
 —.14 
 
 i-38 
 
 I.32 
 
 -.64 
 
 
 IV M 
 
 51 25 
 
 
 
 1.27 
 
 
 
 
 
 / // // 
 Means 196 52 6 ±18 
 
 
 861.96 ±.07 
 
 37 
 
 II B 
 
 II M 
 
 / a 
 
 201 42 56 
 
 4658 
 
 / // 
 
 44 57 
 
 —.04 
 
 1. 
 811.22 
 1. 10 
 
 i"i6 
 
 + •07 
 
 
 IV B 
 
 4427 
 
 4520 
 
 + .05 
 
 0.72 
 
 1.02 
 
 —.07 
 
 
 IV M 
 
 4613 
 
 
 
 1-33 
 
 
 
 
 
 1 a a 
 Means 201 45 8 ±23 
 
 
 811.09 ±-°9 
 
 
 
 1 u\ 1 a 
 
 H 
 
 „ 
 
 a 
 
 1/ 
 
 * 3 8 
 
 I B 
 IM 
 
 211 36 27 36 20 
 36 12 
 
 +.06 
 
 1657.90 
 7.61 
 
 7.76 
 
 —.27 
 
 
 II B 
 
 37 2 j 36 40 
 
 + .22 
 
 8.18 
 
 8.20 
 
 + •17 
 
 
 II M 
 
 36 17 
 
 
 
 8.22 
 
 
 
 
 III B 
 
 35 55 
 
 35 52 
 
 —.16 
 
 8.23 
 
 8 10 
 
 + .07 
 
 
 IIIM 
 
 35 5° 
 
 
 
 7-97 
 
 
 
 
 IV B 
 
 35 52 
 
 35 58 
 
 — .11 
 
 8.12 
 
 8.06 
 
 + •03 
 
 
 IV M 
 
 36 4 
 
 
 
 7-99 
 
 
 
 
 
 Means 211 36 12 zb 8 
 
 
 1658.03 ±.06 
 
 
 
 / // 
 
 / // 
 
 11 
 
 11 
 
 a 11 
 
 *39 
 
 I B 
 IM 
 
 215 48 41 
 49 19 
 
 49 ° 
 
 +•24 
 
 2186.19 
 5.19 
 
 5-69 
 
 + ■05 
 
 
 II B 
 
 4859 
 
 48 55 
 
 +.19 
 
 5-49 
 
 5-12 
 
 —•52 
 
 
 II M 
 
 4851 
 
 
 
 4.76 
 
 
 
 
 III B 
 
 4842 
 
 48 18 
 
 —.22 
 
 5-77 
 
 5-56 
 
 —.08 
 
 
 IIIM 
 
 4753 
 
 
 
 5-35 
 
 
 
 
 IV B 
 
 4815 
 
 4817 
 
 — 23 
 
 6.08 
 
 6.20 
 
 + .56 
 
 
 IV M 
 
 48 19 
 
 
 
 6.31 
 
 
 
 
 
 1 a a 
 
 
 // // 
 
 
 
 Means 215 48 38 ± 6 
 
 
 2185.64 ±.06 
 
 40 
 
 I B 
 
 1 in 1 11 
 217 21 23 ! 21 48 
 
 +"06 
 
 2426.12 
 
 6.14 
 
 + .02 
 
 
 IM 
 
 22 12 
 
 
 
 616 
 
 
 
 
 II B 
 
 21 46 
 
 21 25 
 
 —.26 
 
 6.08 
 
 5-94 
 
 + .06 
 
 
 II M 
 
 21 4 
 
 
 
 5-8r 
 
 
 
 
 III B 
 
 2153 
 
 22 2 
 
 +■23 
 
 5-87 
 
 5-66 
 
 -.46 
 
 
 IIIM 
 
 22 IO 
 
 
 
 5-45 
 
 
 
 
 IV B 
 
 21 44 | 21 54 
 
 + •13 
 
 5-45 
 
 5.76 
 
 -.36 
 
 
 IV M 
 
 22 4 1 
 
 
 6.07 
 
 
 
 
 
 1 11 11 
 
 
 11 11 
 
 
 
 Means 217 21 47 ± 5 
 
 
 2425.88 ±.06 
 
52 Stars within One Degree of the North Pole, and 
 
 Table VII. — (Continued.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 u. 
 
 %(B -i M) \ An sin 7t 
 
 IT 
 
 %(B + M) 
 
 Att 
 
 *4I 
 
 I B 
 
 IM 
 
 / // 
 
 229 24 30 
 
 2348 
 
 24' 9" 
 
 —•32 
 
 I374"5° 
 4.44 
 
 II 
 
 4-47 
 
 11 
 + .29 
 
 
 II B 
 
 2534 
 
 25 21 
 
 + .19 
 
 4.67 
 
 4.66 
 
 + .48 
 
 
 II M 
 
 25 8 
 
 
 
 4.66 
 
 
 
 
 III B 
 
 24 45 
 
 24 59 
 
 +.04 
 
 3-97 
 
 3-78 
 
 —.40 
 
 
 IIIM 
 
 25 13 
 
 
 
 3.60 
 
 
 
 
 IV B 
 
 25 12 
 
 25 9 
 
 +.08 
 
 3-97 
 
 3.80 
 
 -.38 
 
 
 IV M 
 
 25 6 
 
 
 
 3-63 
 
 
 
 
 O I II // 
 
 Means 229 24 54 ±9 
 
 
 1374.18 ±.'06 
 
 *42 
 
 1 n 1 11 
 I B 237 21 26 21 32 
 
 II 
 
 +.04 
 
 H53-88 
 
 3-88 
 
 + '03 
 
 
 IM 2138 
 
 
 
 3.88 
 
 
 
 
 II B 22 6 
 
 2158 
 
 +.20 
 
 3- 80 
 
 3-69 
 
 —.16 
 
 
 11 M 21 51 
 
 
 
 3-58 
 
 ; 
 
 
 III B 22 7 
 
 2158 
 
 + .20 
 
 3-58 
 
 3-52 
 
 —•33 : ! 
 
 
 III M 21 50 
 
 
 
 3-46 
 
 
 
 
 IV B 20 7 
 
 20 12 
 
 —•44 
 
 4-33 
 
 4-3° 
 
 +•45 
 
 
 IV M 20 18 
 
 
 
 4.27 
 
 
 
 
 t u a 
 Means 237 21 25 ±11 
 
 
 ii53'.85 ±'.06 
 
 *43 
 
 I B 
 
 IM 
 
 23 8Cl 4' 15" 
 14 11 
 
 14' 13" 
 
 — -17 
 
 1912.98 
 2.53 
 
 2'.76 
 
 — "06 
 
 
 II B 
 
 14 34 
 
 14 12 
 
 —.18 
 
 3-19 
 
 3.10 
 
 +.28 i 
 
 
 II M 
 
 13 49 
 
 
 
 3.01 
 
 
 
 
 III B 
 
 14 47 
 
 15 4 
 
 + .29 
 
 2.90 
 
 2.80 
 
 — .02 
 
 
 IIIM 
 
 15 20 
 
 
 
 2.70 
 
 
 
 
 IV B 
 
 1448 
 
 1440 
 
 +.07 
 
 2.66 
 
 2.60 
 
 — .22 
 
 
 IV M 
 
 14 33 
 
 
 
 2-53 
 
 
 
 
 / // // 
 Means 238 14 32 ±7 
 
 
 1912.82 ±.06 
 
 *44 
 
 I B 244 33 53" 
 I M 34 48 
 
 34' 20 
 
 — .20 
 
 2811.50 
 1. 00 
 
 1-25 
 
 +.05 
 
 
 n B : 34 51 
 
 3456 
 
 +■31 
 
 0.68 
 
 o-95 
 
 — .20 
 
 
 II M 1 35 
 
 
 
 1.22 
 
 
 
 
 III B 1 34 49 
 
 34 49 
 
 +.21 
 
 1 62 
 
 1.62 
 
 +.47 
 
 
 IV B 34 18 
 
 34 10 
 
 —34 
 
 0.87 
 
 0.84 
 
 — 31 
 
 
 IV Mi 34 1 
 
 
 
 0.80 
 
 
 
 
 Means 244 34 34 ±5 
 
 
 2811.15 ±.06 
 
 *45 
 
 I B 254°56 39" 
 
 56'34" 
 
 +•33 
 
 731-97 
 
 i-94 
 
 +"08 
 
 
 IM 
 
 5630 
 
 
 
 1. 91 
 
 
 
 
 II B 
 
 55 15 
 
 54 38 
 
 —.14 
 
 1.80 
 
 1-54 
 
 —•32 
 
 
 II M 54 
 
 
 
 1.27 
 
 
 
 
 III B 
 
 53 3 1 
 
 53 48 
 
 —■34 
 
 1.81 
 
 1.80 
 
 —.06 
 
 
 IIIM 
 
 54 5 
 
 
 
 1.78 
 
 
 
 
 IV B 
 
 55 28 
 
 55 48 
 
 +.14 
 
 2.21 
 
 2.18 
 
 +-32 
 
 
 IV M 
 
 56 9 
 
 
 
 2-15 
 
 
 
 
 Means 25455 r2 ± l6 
 
 
 731.86 ±"06 
 
Optical Distortion deduced from Photographic Measures. 53 
 Table VII. — (Continued.') Mean Results. 
 
 Star. 
 
 Plate. 
 
 a. 
 
 X(B + M) 
 
 Aa sin it 
 
 IT 
 
 %(B + M) 
 
 Air 
 
 *46 
 
 I B 
 
 IM 
 
 262°59 3" 
 58 53 
 
 58' 58" 
 
 +"16 
 
 1230.59 
 0-59 
 
 o'59 
 
 +:'i6 
 
 
 II B 
 
 57 38 
 
 57 36 
 
 —■34 
 
 0.30 
 
 0.28 
 
 —■15 
 
 
 II M 
 
 57 33 
 
 
 
 0.26 
 
 
 
 
 III B 
 
 57i8 
 
 57 32 
 
 -•36 
 
 0-53 
 
 0.36 
 
 —.07 
 
 
 HIM 
 
 57 46 
 
 
 
 0.19 
 
 
 
 
 IV B 
 
 59 37 
 
 O O 
 
 +■53 
 
 0.48 
 
 0.50 
 
 +.07 
 
 
 IV M 23 
 
 o.53 
 
 
 
 
 t a a 
 Means 262 58 32 ±11 
 
 
 123043 ±.'06 
 
 *47 
 
 I B 
 
 263 50 56 | 51 23 
 
 II 
 
 +.05 
 
 3212.68 
 
 2.69 
 
 +.14 
 
 
 IM 
 
 51 5o 
 
 
 
 2.70 
 
 
 
 
 II B 
 
 5136 
 
 5136 
 
 +.26 
 
 1.85 
 
 2.05 
 
 —■50 
 
 
 II M 
 
 5i 35 
 
 
 2.25 
 
 
 
 
 III B 
 
 50 37 ' 5o 55 
 
 —.40 
 
 2.62 
 
 2.77 
 
 +.22 
 
 
 IIIM 
 
 5i 13 
 
 
 2.92 
 
 
 
 
 IV B 
 
 51 45 [ 51 28 
 
 +■13 
 
 2.76 
 
 2.68 
 
 +.13 
 
 
 IV M 
 
 51 12 
 
 
 2.59 
 
 
 
 
 1 a a 
 Means 263 51 20 ± 4 
 
 
 3212 55 ±.06 
 
 48 
 
 I B 
 
 IM 
 
 265 28 52 
 3030 
 
 2941" 
 
 +'.'01 
 
 328^48 
 8.36 
 
 a'42 
 
 —'23 
 
 
 II B 
 
 25 54 
 
 26 6 
 
 —■33 
 
 8.74 
 
 8.72 
 
 +.07 
 
 
 II M 
 
 26 18 
 
 
 
 8.70 
 
 
 
 
 III B 
 
 2730 
 
 2941 
 
 + .01 
 
 8.70 
 
 8-53 
 
 — .12 
 
 
 IIIM 
 
 3152 
 
 
 
 8.36 
 
 
 
 
 IV B 
 
 33 45 
 
 3238 
 
 +•3° 
 
 8.82 
 
 8.94 
 
 +.29 
 
 
 IV M 
 
 3i 32 
 
 
 // 
 
 9.07 
 
 
 
 
 1 a 
 Means 265 29 32 ±40 
 
 
 328.65 ±.06 
 
 *49 
 
 I B 
 
 IM 
 
 1 a 
 
 266 12 43 
 
 16 16 
 
 1430" 
 
 +'.'18 
 
 339-98 
 9.90 
 
 9'94 
 
 —'13 
 
 
 II B 
 
 8 16 
 
 928 
 
 —•3° 
 
 0.30 
 
 0.27 
 
 +.20 
 
 
 II M 
 
 1040 
 
 
 
 0.24 
 
 
 
 
 III B 
 
 1054 
 
 11 29 
 
 — .11 
 
 9-51 
 
 9.48 
 
 —•59 
 
 
 IIIM 
 
 12 4 
 
 
 
 9-45 
 
 
 
 
 IV B 
 
 15 9 
 
 15 2 
 
 +■23 
 
 o.54 
 
 0.58 
 
 +■51 
 
 
 ivm 
 
 14 56 
 
 
 
 0.61 
 
 
 
 
 1 II II 
 
 Means 266 12 37 ±40 
 
 
 340.07 ±.00 
 
 * S o 
 
 I B 
 IM 
 
 / // 
 268 28 39 
 
 2855 
 
 28V 
 
 II 
 
 —.04 
 
 2978.16 
 7.96 
 
 s!o6 
 
 +"16 
 
 
 II B 
 
 28 41 
 
 28 40 
 
 —.14 
 
 7.89 
 
 8.00 
 
 +.10 
 
 
 II M 
 
 2839 
 
 
 
 8.11 
 
 
 
 
 III B 
 
 28 40 
 
 2841 
 
 —.13 
 
 8.16 
 
 7.90 
 
 + .00 
 
 
 IIIM 
 
 2842 
 
 
 
 7-63 
 
 
 
 
 IV B 
 
 29 10 
 
 29 14 
 
 + •34 
 
 7-79 
 
 7.66 
 
 —.24 
 
 
 IVM 
 
 29 18 
 
 
 
 7-52 
 
 
 
 
 / a a 
 Means 268 28 50 ± 5 
 
 
 2977.90 ±.06 
 
54 Stars within One Degree of the North Pole, and 
 
 Table VII. — (Continued.) Mean Results. 
 
 Star. 
 SI 
 
 Plate. 
 
 a 
 
 %(B + M) 
 
 Aa sin ir 
 
 IT 
 
 MB + M) 
 
 Air 
 
 I B 
 
 1277° 146 
 
 1 II 
 
 154 
 
 — "°3 
 
 1759-12 
 
 it 
 9.06 
 
 + '.14 
 
 
 IM 
 
 2 2 
 
 
 
 9.00 
 
 
 
 
 II B 
 
 1 5 
 
 I 2 
 
 —.55 
 
 8.74 
 
 8.78 
 
 —.14 
 
 
 II M 
 
 058 
 
 
 
 8.82 
 
 
 
 
 III B 
 
 145 
 
 142 
 
 — 13 
 
 9-i5 
 
 9.04 
 
 +.12 
 
 
 IIIM 
 
 1 40 
 
 
 
 8-94 
 
 
 
 
 IV B 
 
 3 8 
 
 3 14 
 
 +.62 
 
 8.84 
 
 8.80 
 
 — .12 
 
 
 IV M 
 
 3 19 
 
 8.76 
 
 
 
 Means 277 1 58 ± 8 
 
 
 1758.92 ±.06 
 
 *52 
 
 I B 
 IM 
 
 281 35 39 
 3630 
 
 36 4" 
 
 — .20 
 
 2622.07 
 1.84 
 
 // 
 I.96 
 
 // 
 +.04 
 
 
 II B 
 
 3640 
 
 3623 
 
 +.05 
 
 1.99 
 
 2.04 
 
 + .12 
 
 
 II M 
 
 36 6 
 
 
 
 2.08 
 
 
 
 
 III B 
 
 35 58 
 
 36 i 
 
 — 23 
 
 1.82 
 
 I.78 
 
 —.14 
 
 
 IIIM 
 
 36 4 
 
 
 
 i-75 
 
 
 
 
 IV B 
 
 3640 
 
 3648 
 
 +.38 
 
 2.03 
 
 I.89 
 
 —•°3 
 
 
 IV M 
 
 3656 
 
 
 
 1-75 
 
 
 
 / // // 
 Means 281 36 19 ± 5 
 
 
 2621.92 ±.06 
 
 *53 
 
 I B 
 
 IM 
 
 / // 
 281 36 29 
 
 3658 
 
 3644" 
 
 +"18 
 
 1212.17 
 2.00 
 
 // 
 2.08 
 
 +"26 
 
 
 II B 
 
 36 6 
 
 35 47 
 
 —.16 
 
 2 04 
 
 2.08 
 
 +.26 
 
 
 II M 
 
 35 28 
 
 
 
 2.13 
 
 
 
 
 III B 
 
 35 53 
 
 36 6 
 
 —•05 
 
 1-54 
 
 1.56 
 
 —.26 
 
 
 IIIM 
 
 3618 
 
 
 
 1-57 
 
 
 
 
 IV B 
 
 3618 
 
 3618 
 
 +.02 
 
 1-53 
 
 1.58 
 
 —.24 
 
 
 IV M 
 
 3619 
 
 
 
 1.62 
 
 
 
 O 1 II 11 
 
 Means 281 36 14 dzii 
 
 
 1211.82 ±.06 
 
 *54 
 
 I B 
 
 IM 
 
 285 41 41 
 42 18 
 
 42 
 
 +.00 
 
 2430-53 
 0.67 
 
 0.60 
 
 — .01 
 
 
 II B 
 
 41 52 
 
 4144 
 
 —.19 
 
 0.67 
 
 O.65 
 
 +.04 
 
 
 II M 
 
 4136 
 
 
 
 0.63 
 
 
 
 
 III B 
 
 42 
 
 42 4 
 
 +.05 
 
 0.68 
 
 0.50 
 
 — .11 
 
 
 IIIM 
 
 42 9 
 
 
 
 0.31 
 
 
 
 
 IV B 
 
 4214 
 
 42 14 
 
 +.17 
 
 0.77 
 
 0.70 
 
 +.09 
 
 
 IV M 
 
 42 13 
 
 
 
 0.62 
 
 
 
 / // ,' 
 Means 285 42 ± 5 
 
 
 2430.61 ±.06 
 
 55 
 
 I B 
 
 IM 
 
 291 37 
 3622 
 
 3641" 
 
 — .12 
 
 502'. 33 
 2.44 
 
 2'.' 3 8 
 
 — .11 
 
 
 IV B 
 
 3858 
 
 38 39 
 
 + .12 
 
 2.6r 
 
 2.60 
 
 +.11 
 
 
 IV M 
 
 3820 
 
 
 
 2-59 
 
 
 
 / // ./ 
 Means 29 1 37 40 ±52 
 
 
 502.49 ±"10 
 
Optical Distortion deduced from Photographic Measures. 55 
 Table VII — (Continued.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 a 
 
 X{B+M) 
 
 Aa Sin ir 
 
 ■n 
 
 %{B+M) 
 
 Air 
 
 •56 
 
 I B 
 IM 
 
 / // 
 
 292 6 21 
 646 
 
 6 34" 
 
 II 
 —.14 
 
 I593-74 
 3-43 
 
 3.58 
 
 +.'10 
 
 
 II B 
 
 7 1 
 
 7 8 
 
 +•13 
 
 3-64 
 
 3-71 
 
 +•23 
 
 
 II M 
 
 7 15 
 
 
 
 3-78 
 
 
 
 
 III B 
 
 7 9 
 
 7 16 
 
 + •19 
 
 3-72 
 
 3-66 
 
 + .18 
 
 
 IIIM 
 
 723 
 
 
 
 3-59 
 
 
 
 
 IV B 
 
 630 
 
 6 29 
 
 —.18 
 
 2-93 
 
 2.95 
 
 —•53 
 
 
 IV M 6 28 
 
 
 2.97 
 
 
 
 / // 11 
 Means 292 6 52 ± 8 
 
 
 1593.48 ±.06 
 
 
 O 1 II 1 II II 
 
 // 
 
 // ti 
 
 57 
 
 I B 
 IM 
 
 293 38 58 
 4137 
 
 40 18 
 
 + .26 
 
 1055.57 
 5-73 
 
 5.65 
 
 +•13 
 
 
 II B 
 
 38 53 
 
 39 2 
 
 — .12 
 
 5.85 
 
 5-92 
 
 +.40 
 
 
 II M 
 
 3910 
 
 
 
 5-99 
 
 
 
 
 IV B 
 
 38 47 
 
 39 
 
 —.14 
 
 5.02 
 
 500 
 
 —■52 
 
 
 IV M 
 
 39 13 
 
 
 
 4-99 
 
 
 
 Oil! II 
 
 Means 293 39 27 ±15 
 
 
 // // 
 1055.52 ±.08 
 
 
 
 / // 
 
 / // 
 
 // 
 
 11 
 
 y/ 
 
 id 
 
 *58 
 
 I B 
 IM 
 
 297 14 11 
 14 15 
 
 14 13 
 
 —■34 
 
 1291.68 
 1-37 
 
 1-52 
 
 + .28 
 
 
 II B 
 
 15 45 
 
 15 34 
 
 +.15 
 
 1.23 
 
 1.28 
 
 +.04 
 
 
 II M 
 
 1523 
 
 
 
 1-34 
 
 
 
 
 III B 
 
 14 34 
 
 15 8 
 
 — .01 
 
 1.16 
 
 1. 21 
 
 —•°3 
 
 
 IIIM 
 
 15 43 
 
 
 
 1.26 
 
 
 
 
 IV B 
 
 15 21 
 
 1540 
 
 +■19 
 
 1. 01 
 
 0.96 
 
 —.28 
 
 
 IV M 
 
 15 59 
 
 
 
 0.90 
 
 
 
 1 a 11 
 
 
 // // 
 
 Means 297 15 9 ±11 
 
 
 1291.24 ±.06 
 
 
 O 1 II 1 II II 
 
 // 
 
 // // 
 
 59 
 
 I B 
 
 IM 
 
 307 21 37 
 2051 
 
 21 14 
 
 —•37 
 
 1542.28 
 1.89 
 
 2.08 
 
 +.24 
 
 
 IV B 
 
 22 40 
 
 2245 
 
 +•36 
 
 1.77 
 
 1 60 
 
 —.24 
 
 
 IV M 
 
 2250 
 
 
 
 1.44 
 
 
 
 a 1 ii 11 
 
 Means 307 22 ±13 
 
 
 I54I-* 
 
 84 ±.10 
 
 *6o 
 
 I B 
 
 IM 
 
 311 832" 
 9 15 
 
 854" 
 
 +.10 
 
 85 1. "70 
 1.72 
 
 1.71 
 
 +'.'10 
 
 
 II B 
 
 6 14 
 
 648 
 
 —.40 
 
 1.88 
 
 1.79 
 
 +.18 
 
 
 II M 
 
 723 
 
 
 
 1.70 
 
 
 
 
 III B 
 
 7 34 
 
 740 
 
 —.19 
 
 1.77 
 
 1.69 
 
 +.08 
 
 
 IIIM 
 
 7 47 
 
 
 
 1. 61 
 
 
 
 
 IV B 
 
 10 20 
 
 1030 
 
 +•49 
 
 1.17 
 
 1.24 
 
 —•37 
 
 
 IV M 
 
 1039 
 
 
 
 1.30 
 
 
 
 1 a 11 
 
 
 // // 
 
 . Means3ii 8 28 ±16 
 
 
 851.61 ±.06 
 
56 Stars within One Degree of the North Pole, and 
 
 Table Til. — (Concluded.) Mean Results. 
 
 Star. 
 
 Plate. 
 
 a. 
 
 %(B + M) 
 
 An sin it 
 
 IT 
 
 y*(b+m) 
 
 Att 
 
 61 
 
 I B 
 IM 
 
 314 53 20" 
 53 47 
 
 5i2,A 
 
 +"06 
 
 I58M3 
 i-59 
 
 i'si 
 
 // 
 — .01 
 
 
 II B 
 
 52 57 
 
 5240 
 
 -•38 
 
 1.41 
 
 1.44 
 
 —.08 
 
 
 II M 
 
 52 24 
 
 
 
 i-47 
 
 
 
 
 III B 
 
 5256 
 
 5250 
 
 — 3° 
 
 i-53 
 
 i-43 
 
 —.09 
 
 
 IIIM 
 
 52 44 
 
 
 
 i-33 
 
 
 
 
 IV B 
 
 54 38 
 
 54 44 
 
 +.62 
 
 1.81 
 
 1.72 
 
 +.20 
 
 
 IV M 54 51 
 
 
 
 1.64 
 
 
 
 
 / // // 
 Means 314 53 27 ± 8 
 
 
 I58i'.52 ±'06 
 
 *62 
 
 I B 
 IM 
 
 315 28 5 
 2834 
 
 28 20 
 
 — .11 
 
 I353'58 
 3-67 
 
 3-62 
 
 +"06 
 
 
 II B 
 
 2923 
 
 29 5 
 
 +.20 
 
 3-36 
 
 3-55 
 
 — .01 
 
 
 II M 
 
 2847 
 
 
 
 3-74 
 
 
 
 
 III B 
 
 2845 
 
 29 6 
 
 +.21 
 
 3.58 
 
 3-56 
 
 +.00 
 
 
 IIIM 
 
 29 26 
 
 
 
 3-55 
 
 
 
 
 IV B 
 
 27 53 
 
 27 54 
 
 —.29 
 
 3-5i 
 
 3 49 —°7 
 
 
 IV M 
 
 27 55 
 
 
 
 3-47 
 
 1 
 
 
 1 a a 
 Means 315 28 36 ± 9 
 
 
 1353.56 ±'.'06 
 
 *6 3 
 
 I B 3i7°45 37" 
 IM| 46 3 
 
 45'5o" 
 
 —■'37 
 
 3252.89 
 3-14 
 
 3.02 
 
 +.16 
 
 
 II B 46 22 
 
 4636 
 
 +•37 
 
 2.96 
 
 2.94 
 
 +.08 
 
 
 II M 46 49 
 
 
 
 2.92 
 
 
 
 
 III B 46 7 
 
 46 18 
 
 +.08 
 
 3-09 
 
 2.91 
 
 +.05 
 
 
 IIIM 1 4630 
 
 
 
 2.73 
 
 
 
 
 IV B | 46 8 
 
 46 7 1 —.10 
 
 2-57 
 
 2.56 
 
 —•30 
 
 
 IV M 46 6 
 
 
 2.55 
 
 
 
 
 1 a a 
 Means 317 46 13 ± 4 
 
 
 3252.86 ±.06 
 
 *64 
 
 I B 
 
 IM 
 
 322° 6 54" 
 6 59 
 
 656" 
 
 — .10 
 
 1186.00 
 5-96 
 
 S-9& 
 
 — .02 
 
 
 II B 
 
 6 5 
 
 630 
 
 +.26 
 
 6.06 
 
 5-95 
 
 —•05 
 
 
 II M 
 
 6 55 
 
 
 
 5.84 
 
 
 
 
 III B 
 
 6 45 
 
 6 42 
 
 —.19 
 
 5.78 
 
 5-86 
 
 —.14 
 
 
 IIIM 
 
 6 40 
 
 
 
 5-93 
 
 
 
 
 IV B 
 
 841 
 
 8 45 
 
 +.55 
 
 6.20 
 
 6.21 
 
 +.21 
 
 
 IV M 
 
 8 49 
 
 
 
 6.22 
 
 
 
 
 1 a a 
 Means322 7 13 ±11 
 
 
 1186.00 ±.06 
 
 *65 
 
 I B 
 
 IM 
 
 348 36 6 36 18 
 3630 
 
 +.00 
 
 2 9 o4."74 
 4.80 
 
 // 
 4-77 
 
 41 
 
 +■07 
 
 
 II B 
 
 35 52 1 36 7 
 
 —•15 
 
 4.80 
 
 4.88 
 
 + .18 
 
 
 II M 
 
 3622 
 
 
 
 4-95 
 
 " 
 
 
 
 III B 
 
 36 10 
 
 3618 
 
 +.00 
 
 4.62 
 
 4.7o 
 
 +.00 
 
 
 IIIM 
 
 3626 
 
 
 
 4-77 
 
 
 
 
 IV B 
 
 3638 
 
 3630 
 
 +.17 
 
 4-03 
 
 4.44 
 
 —.26 
 
 
 IV M 
 
 3623 
 
 
 
 4.86 
 
 
 
 
 Means 348 36 18 ± 5 
 
 
 2904.70 ±.06 
 
Optical Distortion deduced from Photographic Measures. 57 
 
 IX. 
 Final Results. 
 
 The table of final results contains the magnitudes of the stars, 
 their numbers in the Bonn Durchmusterung, and in Carrington's 
 Redhill Catalogue, their right ascensions, north polar distances 
 and declinations for 1888.0, and their rectangular coordinates for 
 this epoch. 
 
 The magnitudes of Carrington's catalogue were adopted for 
 such of his stars as are included in this publication, and were 
 also taken as the standard of comparison for the remaining stars. 
 They were determined by him with considerable care, as will 
 be seen by a reference to his own description.* The faintest star 
 recorded by him is io m .3, which stands for 9 ra .5 on Argelander's 
 Durchmusterung scale. 
 
 The magnitudes of the remaining stars were determined by 
 visual comparisons made with the 12-in. equatorial of the Vassar 
 College Observatory, March 21-23, J 9 00 - This telescope has fre- 
 quently been used for asteroid observations in which the DM 
 stars are used for purposes of identification, so that the Arge- 
 lander scale is familiar to the observers. Accordingly estimates 
 were made on the DM scale, and o m .8 added to reduce to the 
 Carrington scale. Some slight variations in magnitude from the 
 1855 determinations were noticed, one of which was particularly 
 interesting. 
 
 Star 3546 of Carrington's Catalogue, DM 89°.24 shows no 
 trace on any one of the four photographic plates. It is not even 
 included among the stars which were visible but too faint to be 
 measured. It was observed by Carrington on four different 
 nights and estimated at io m .3 each time. It was seen with the 
 Yassar telescope on the above dates, and was estimated at g m .6 
 on DM scale, or io m .4 on Carrington's scale. These facts seem 
 to indicate a variability in magnitude. 
 
 Numbers 33 and 34 form -£1717. 
 
 The rectangular coordinates were computed by the ordinary 
 formulas 
 
 * Catalogue of the 3735 Ciroumpolar Stars observed at Redhill in 1854-55- 
 56, by R. C. Carrington, p. xxv. 
 
58 Stars within One Degree of the North Pole, and 
 
 X = cos a sin it oosec 
 
 : I" . J 
 
 (13) 
 Y = sin n sin n cosec ] 
 
 where a and tc are the mean right ascension and polar distance of 
 a star referred to the equator and equinox of the epoch t . 
 
 If X 1 and Fj are the rectangular coordinates for some other 
 epoch t, they can be found from the following equations, 
 
 
 (14) 
 
 The differential coefficients which are given in Table IX seq. 
 were computed according to the formulas of Fabritius which may 
 be found in several places, but are given in a particularly conve- 
 nient form in Elkin's paper.* 
 
 The corresponding polar coordinates for the beginning of the 
 year t, can be computed by the formulas 
 
 sin Tj cos % =■ X x sin i' , , 
 
 sin Tj cos a 1 = X l sin 1", \ 
 sin 7I-! sin Oj = 1\ sin \" . J 
 
 It is my intention later to determine the proper motions of the 
 stars for which a sufficient number of accurate places exist. This 
 will be deferred until a catalogue of the remaining eight plates 
 has been made, after which the proper motion of the entire group 
 will be deduced. 
 
 *Loc. cit., p. 181. 
 
Optical Distortion deduced from Photographic Measures. 59 
 
 Table VIII. — Final Results. 
 
 
 No. 
 
 Mg. 
 
 Right Ase 
 
 N. P.D. 
 
 Declination, 
 
 X 
 
 Y 
 
 Number in 
 
 
 
 
 1888.0. 
 
 
 1888.0. 
 
 
 
 B. D. M. 
 
 Car. 
 
 
 I 
 
 m 
 10.3 
 
 iV 5 
 
 344 1 '42 
 
 89° 2 38^58 
 
 +3439-63 
 
 + io6"i8 
 
 88.1 
 
 9 
 
 
 2 
 
 10. 1 
 
 5 42 28 
 
 768.37 
 
 894711-63 
 
 + 76456 
 
 + 76.41 
 
 89.I 
 
 a 
 
 
 3 
 
 16.5 
 
 63642 
 
 3156.86 
 
 89 723.14 
 
 +3135-74 
 
 + 363-46 
 
 
 
 
 4 
 
 9-7 
 
 24 5 50 
 
 2977.11 
 
 89 1022.89 
 
 +2717.56 
 
 + 1215.47 
 
 89.2 
 
 201 
 
 
 5 
 
 9.6 
 
 35 16 22 
 
 3431-68 
 
 89 248.32 
 
 +2801.53 
 
 -(-1981.60 
 
 88.IO 
 
 303 
 
 
 6 
 
 10.8 
 
 35 59 
 
 3148.47 
 
 89 7 31-53 
 
 +2547.61 
 
 + 1849.81 
 
 
 
 
 7 
 
 10.3 
 
 36 24 45 
 
 2238.21 
 
 8922 41.79 
 
 +1801.19 
 
 +1328.56 
 
 
 
 
 8 
 
 10.3 
 
 38 12 49 
 
 2197.90 
 
 89 23 22.10 
 
 +1726.88 
 
 + I359-58 
 
 89-5 
 
 288 
 
 
 9 
 
 10.4 
 
 39 458 
 
 1633.24 
 
 893246.76 
 
 + 1267.76 
 
 + 1029.65 
 
 89.4 
 
 c 
 
 
 IO 
 
 10.3 
 
 4i 38 13 
 
 303964 
 
 89 9 20.36 
 
 +2271.65 
 
 +2019.49 
 
 89.6 
 
 345 
 
 
 ii 
 
 10.8 
 
 442851 
 
 1427.80 
 
 8936 12.20 
 
 +1018.70 
 
 +1000.41 
 
 
 
 
 12 
 
 10. 1 
 
 57 50 56 
 
 2939.66 
 
 89 11 0.34 
 
 +1564.30 
 
 +2488.76 
 
 89.7 
 
 475 
 
 
 13 
 
 10.5 
 
 58 38 53 
 
 2652.79 
 
 891547.21 
 
 +1380.19 
 
 +2265.38 
 
 
 
 
 14 
 
 9-7 
 
 63 16 44 
 
 3614.20 
 
 8859 45.80 
 
 +1625.04 
 
 +3228.05 
 
 88.20 
 
 538 
 
 
 15 
 
 10.8 
 
 63 48 57 
 
 3211.01 
 
 89 6 28.99 
 
 +1416.82 
 
 +2881.38 
 
 
 
 
 16 
 
 10.7 
 
 67 39 59 
 
 3559-4Q 
 
 89 40.60 
 
 +1352.50 
 
 +3292.23 
 
 
 
 
 17 
 
 10.7 
 
 68 52 13 
 
 3276.83 
 
 89 523.17 
 
 +1181.19 
 
 +3056.39 
 
 89.8 
 
 579 
 
 
 18 
 
 10.5 
 
 70 48 23 
 
 1238.99 
 
 8939 21.01 
 
 + 407-33 
 
 + 1 170. 1 1 
 
 
 
 
 19 
 
 10.6 
 
 75 047 
 
 2360.12 
 
 892039.88 
 
 + 610.31 
 
 +2279.78 
 
 
 
 
 20 
 
 10.8 
 
 83 4 4i 
 
 2179-35 
 
 89 23 40.65 
 
 + 262.64 
 
 +2163.42 
 
 
 
 
 21 
 
 9-3 
 
 92 21 27 
 
 1887.19 
 
 892832.81 
 
 — 77.63 
 
 +1885.57 
 
 89.9 
 
 d 
 
 
 22 
 
 10.3 
 
 98 17 
 
 3263.08 
 
 89 536.92 
 
 — 454-38 
 
 +3231-15 
 
 89.10 
 
 833 
 
 
 23 
 
 10.5 
 
 100 3 12 
 
 809.13 
 
 89 46 30.87 
 
 — I4T.24 
 
 + 796-70 
 
 
 
 
 24 
 
 10.3 
 
 10045 3 
 
 3444-34 
 
 89 235.66 
 
 — 642.47 
 
 +3383-73 
 
 89.II 
 
 862 
 
 
 25 
 
 10.0 
 
 120 19 9 
 
 I53I-I4 
 
 89 34 28.86 
 
 — 772.94 
 
 + 1321-71 
 
 89.12 
 
 e 
 
 
 26 
 
 10.6 
 
 '33 34 5i 
 
 1298.28 
 
 893821.72 
 
 — 895.00 
 
 + 940.47 
 
 
 
 
 27 
 
 10.3 
 
 154 5 20 
 
 2014.26 
 
 892625.74 
 
 — 1811.75 
 
 + 880.17 
 
 89.16 
 
 f 
 
 
 28 
 
 9.7 
 
 163 25 29 
 
 2301.17 
 
 892138.83 
 
 —2205.50 
 
 + 656.45 
 
 89.17 
 
 9 
 
 
 29 
 
 10.3 
 
 171 19 4 
 
 2259.91 
 
 89 22 20.09 
 
 —2233-97 
 
 + 34I-I4 
 
 89.19 
 
 
 
 30 
 
 9-9 
 
 172 39 5 
 
 1617.68 
 
 89 33 2.32 
 
 —1604.37 
 
 + 206.91 
 
 89.18 
 
 h 
 
 
 31 
 
 10.3 
 
 180 26 32 
 
 2687.34 
 
 8915 12.66 
 
 —2687.18 
 
 — 20.74 
 
 89.20 
 
 
 
 32 
 
 10.5 
 
 191 13 35 
 
 2067.17 
 
 89 25 32.83 
 
 —2027.59 
 
 — 402.44 
 
 
 
 
 33 
 
 10.6 
 
 191 16 49 
 
 2540.66 
 
 89 17 39-34 
 
 —2491.51 
 
 — 496.96 
 
 
 
 
 34 
 
 9-7 
 
 191 22 6 
 
 2547.86 
 
 891732.14 
 
 —2497.81 
 
 — 502.21 
 
 89.21 
 
 i 
 
 1 35 
 
 10.3 195 35 20 
 
 2274.06 
 
 8922 5.94 
 
 —2190.36 
 
 — 611. 10 
 
 89.23 k 
 
60 
 
 Stars within One Degree of the North Pole, and 
 
 
 
 Table VIII. — (Concluded 
 
 .) Final Results. 
 
 
 No. j Mg. 
 m 
 
 36 : 10.3 
 
 Right Asc. 
 1888.0. 
 
 DP d Declination, 
 1888.0. 
 
 X 
 
 Y 
 
 Number in 
 B. D. M.i Cat. 
 
 t 11 
 196 52 6 
 
 // 1 a 
 861.96 894538.04 
 
 — 824!'S7 
 
 — 250.12 
 
 89.26 
 
 m 
 
 37 
 
 11. 
 
 201 45 8 
 
 811.09 89462S.91 
 
 — 753-34 
 
 — 300.58 
 
 
 
 38 
 
 IO.I 
 
 211 36 12 
 
 1658.03 893221.97 
 
 — 1412.12 
 
 — 868.86 
 
 8925 
 
 I 
 
 39 
 
 10.6 
 
 215 48 38 
 
 2185.64 892334.36 
 
 — 1772.42 
 
 —1278.81 
 
 
 
 40 
 
 10.7 
 
 217 21 47 
 
 2425.88 891934.12 
 
 — 1928.06 
 
 —1472.14 
 
 
 41 
 
 10.5 
 
 229 24 54 
 
 1374-18 8937 5.82 
 
 — 894.00 
 
 — 1043.60 
 
 \ 
 
 42 
 
 10.3 
 
 237 21 25 
 
 II53-85 894046.15 
 
 — 622.39 
 
 — 971-59 
 
 89.29 
 
 43 
 
 10.6 
 
 238 14 32 
 
 1912.82 8928 7.18 
 
 — 1006.76 
 
 — 1626.41 
 
 
 44 
 
 10.6 
 
 244 34 34 
 
 2811.15 8913 8.85 
 
 — 1206.82 
 
 -2538.83 
 
 
 
 45 
 
 10.0 
 
 254 55 12 
 
 731.86 894748.14 
 
 — 190.41 
 
 — 706.66 
 
 89-35 
 
 r 
 
 46 
 
 10.3 
 
 262 58 32 1230.43 89 39 29.57 
 
 — 150-47 
 
 — 1221.19 
 
 89-3I 
 
 P 
 
 47 
 
 10.5 
 
 26351 20 3212.55 89 627.45 
 
 — 343-84 
 
 —3I93-96 
 
 
 
 48 
 
 II. 
 
 2652932 328.65 895431.35 
 
 — 25.83 
 
 — 327-63 
 
 
 
 49 
 
 IO.I 
 
 266 12 37 340.07 8954 19.93 
 
 — 22.48 
 
 — 339-33 
 
 89-37 
 
 t 
 
 50 
 
 10.0 
 
 2682850 2977.90 891022.10 
 
 - 78.96 
 
 —2976.75 
 
 89.30 
 
 2818 
 
 5i 
 
 10.3 
 
 277 158:1758.92 893041.08 
 
 4- 215.35 
 
 —1745.66 
 
 89.33 
 
 g 
 
 52 
 
 10.3 
 
 281 36 19 2621.92 891618.08 
 
 + 527-43 
 
 — 2568.24 
 
 89,32 
 
 2977 
 
 53 
 
 10.6 
 
 281 36 14 J1211.82 893948.18 
 
 + 243.75 
 
 — 1187.04 
 
 
 
 54 
 
 9-9 
 
 285 42 2430.61 89 19 29.39 
 
 4- 657.71 
 
 —2339-87 
 
 89-34 
 
 3023 
 
 55 
 
 11. 
 
 291 37 40 
 
 502.49 895137.51 
 
 + 185.20 
 
 — 467.11 
 
 
 
 56 
 
 10.6 
 
 292 6 52 
 
 1593.48 893326.52 
 
 + 599-87 
 
 —1476.24 
 
 
 
 57 
 
 10.8 
 
 293 39 2 7 
 
 1055.52 894224.48 
 
 + 423-54 
 
 — 966.81 
 
 
 
 58 
 
 10.3 
 
 297 15 9 
 
 1291.24 893828.76 
 
 + 59 1 - 2 ? 
 
 —1147.90 
 
 89.36 
 
 s 
 
 59 
 
 10.9 
 
 307 22 
 
 1541.84 893418.16 
 
 + 935-76 
 
 —1225.39 
 
 
 
 60 
 
 10.6 
 
 311 828 
 
 851.61 894548.39 
 
 + 560.29 
 
 — 641.34 
 
 
 
 61 
 
 10.4 
 
 314 53 27 
 
 1581.52 893338.48 
 
 + 1116.16 
 
 — 1120.42 
 
 
 
 62 
 
 10.4 
 
 315 28 36 
 
 I353-56 893726.44 
 
 + 965-03 
 
 — 949- 1 1 
 
 
 
 63 
 
 10.3 
 
 3 J 7 46 13 
 
 3252.86 89 5 47-14 
 
 +2408.50 
 
 — 2186.17 
 
 88.126 
 
 
 64 
 
 10.4 
 
 322 7 13 
 
 1186.00 894014.00 
 
 4- 936-11 
 
 — 728.21 
 
 
 
 65 
 
 9-7 
 
 348 36 18 
 
 2904.70 891135.30 
 
 4-2847-35 
 
 — 573-87 
 
 89.38 
 
 3601 
 
Optical Distortion deduced from Photographic Measures. 61 
 
 Table IX. — Precession. 
 
 Star. 
 
 dy 
 
 dx 
 
 100 d*y 
 
 100 d^x 
 
 10,000 d s y 
 
 10,000 d^x 
 
 I 
 
 +o.'7686 
 
 — 20.0740 
 
 —O.4480 
 
 — 0.0118 
 
 ■ — 0.0008 
 
 +0.01 19 
 
 2 
 
 -j-o. 1708 
 
 — 20.0701 
 
 — 0.4484 
 
 +0.0041 
 
 — 0.0005 
 
 +0.01 19 
 
 3 
 
 +0.7006 
 
 — 20.1320 
 
 —0-4494 
 
 — 0.0100 
 
 — 0.0008 
 
 +0.0119 
 
 4 
 
 +0.6072 
 
 — 20.3226 
 
 —0.4537 
 
 — 0.0077 
 
 — 0.0007 
 
 -fO.0121 
 
 5 
 
 -j-o. 6260 
 
 —20.4931 
 
 —0-4575 
 
 — b.0083 
 
 —0.0007 
 
 +O.OI22 
 
 6 
 
 +0.5692 
 
 — 20.4641 
 
 —O.4568 
 
 — 0.0067 
 
 — 0.0007 
 
 +0.0I2I 
 
 7 
 
 +0.4025 
 
 —20.3487 
 
 —O.4544 
 
 — 0.0023 
 
 — 0.0006 
 
 +O.OI2I 
 
 8 
 
 +0.3859 
 
 —20.3558 
 
 —O.4546 
 
 — 0.0018 
 
 — 0.0006 
 
 +0.0I2I 
 
 9 
 
 +0.2833 
 
 — 20.2826 
 
 —O.4529 
 
 +0.0010 
 
 — 0.0005 
 
 4 0.0I20 
 
 IO 
 
 +0.5076 
 
 — 20.5021 
 
 —O.4578 
 
 — 0.0052 
 
 — 0.0007 
 
 +O.OI22 
 
 ii 
 
 +0.2276 
 
 — 20.2761 
 
 —0.4529 
 
 +0.0025 
 
 —0.0005 
 
 +0.0I20 
 
 12 
 
 —o.3495 
 
 — 20.6072 
 
 — O.4602 
 
 — 0.0010 
 
 — 0.0006 
 
 +O.OI22 
 
 13 
 
 +0 3084 
 
 —20.5576 
 
 —O.4591 
 
 +0.0001 
 
 — 0.0006 
 
 +0.0122 
 
 14 
 
 +0.3631 
 
 —20.7713 
 
 —O.4639 
 
 — 0.0014 
 
 — 0.0006 
 
 +O.OI23 
 
 15 
 
 +0.3166 
 
 —20.6945 
 
 — O.4622 
 
 — 0.0002 
 
 — 0.0006 
 
 +O.OI23 
 
 16 
 
 +0.3022 
 
 —20.7858 
 
 — 0.4642 
 
 -f 0.0002 
 
 : — 0.0005 
 
 + O.OI23 
 
 17 
 
 +0.2639 
 
 —20.7335 
 
 —O.4631 
 
 +0.0012 
 
 — 0.0005 
 
 +O.OI23 
 
 18 
 
 4-0.0910 
 
 —20.3141 
 
 -O.4538 
 
 +0.0060 
 
 — 0.0004 
 
 +O.OI2I 
 
 19 
 
 +0.1364 
 
 — 20.5612 
 
 — o-4593 
 
 -i- 0.0047 
 
 — 0.0004 
 
 +O.OI22 
 
 20 
 
 +0.0587 
 
 —20.5354 
 
 — 4588 
 
 +0.0067 
 
 — 0.0004 
 
 +O.OI22 
 
 21 
 
 —0.0173 
 
 —20.4736 
 
 —o.4574 
 
 +0.0088 
 
 — 0.0003 
 
 +O.OI2I 
 
 22 
 
 — 0.1015 
 
 — 20.7726 
 
 — 0.4642 
 
 +0.0109 
 
 — 0.0003 
 
 +O.OI23 
 
 23 
 
 —0.0316 
 
 — 20.2310 
 
 —0.4521 
 
 +0.0093 
 
 — 0.0003 
 
 -(-0.0I20 
 
 24 
 
 —0. 1436 
 
 —20.8064 
 
 —0.4650 
 
 +0.0119 
 
 — 0.0003 
 
 + O.OI23 
 
 25 
 
 —O.I737 
 
 —20.3479 
 
 —0.4547 
 
 +0.0130 
 
 — 0.0002 
 
 + O.OI2I 
 
 26 
 
 — 0.2000 
 
 — 20.2628 
 
 —0.4528 
 
 +0.0138 
 
 —O.O002 
 
 + 0.0I20 
 
 27 
 
 —0.4048 
 
 — 20.2489 
 
 —0.4526 
 
 +0.0193 
 
 — O.OOOI 
 
 -J-0.0I20 
 
 28 
 
 — 0.4928 
 
 — 20. 1984 
 
 —0.4516 
 
 +0.0216 
 
 O.OOOI 
 
 + O.OI20 
 
 29 
 
 —0.4992 
 
 — 20.1281 
 
 —0.4500 
 
 +0.0219 
 
 — 0000 
 
 + O.OII9 
 
 30 
 
 —0-3585 
 
 — 20.0987 
 
 —0.4492 
 
 +0.0181 
 
 — O.OOOI 
 
 +O.OII9 
 
 31 
 
 ■ — 0.6004 
 
 — 20.0468 
 
 —0.4483 
 
 +0.0246 
 
 — 0.0000 
 
 + O.OII9 
 
 32 
 
 —04530 
 
 — 19.9622 
 
 —0.4463 
 
 +0.0206 
 
 — 0. 0001 
 
 + O.OI 19 
 
 33 
 
 —0.5567 
 
 — 19.9406. 
 
 —0.4458 
 
 +0.0235 
 
 — 0,0000 
 
 -i- 0.0118 
 
 34 
 
 —0.5581 
 
 —19-9394 
 
 —0.4458 
 
 -1-0.0235 
 
 — 0.0000 
 
 +0.0118 
 
 35 
 
 — 0.4894 
 
 —19.9154 
 
 — 0-4453 
 
 -f 0.0217 
 
 ■ — O.OOOI 
 
 +0.0118 
 
62 Stars within One Degree of the North Pole, and 
 
 
 Table IX.— 
 
 ( Concluded.') Precession. 
 
 
 Star. 
 
 dy 
 
 dx 
 
 100 d 2 2/ 
 —0.4470 
 
 100 (Px 
 
 10,000 dpy 
 
 10,000 d s z 
 
 36 
 
 — o."i843 
 
 —19.9970 
 
 + 0.0135 
 
 — 0.0002 
 
 11 
 
 +0.0119 
 
 37 
 
 —0.1683 
 
 —I9-9858 
 
 —0.4467 
 
 +0.0131 
 
 — 0.0003 
 
 +O.OI 19 
 
 38 
 
 —0-3I55 
 
 —198584 
 
 —0.4439 
 
 +0.01 7 1 
 
 — O.OC02 
 
 +0.0118 
 
 39 
 
 —0.3960 
 
 — 19.7663 
 
 — 0.4418 
 
 +0.0193 
 
 — O.OOOI 
 
 +0.0117 
 
 40 
 
 —0.4308 
 
 — 19.7228 
 
 — 0.4409 
 
 +0.0202 
 
 — O.OOOI 
 
 +0.0117 
 
 4i 
 
 — 0.1998 
 
 — 19.S194 
 
 —O.4429 
 
 + 0.0140 
 
 — 0.0002 
 
 +0.0118 
 
 42 
 
 — 0.1391 
 
 —I9-8357 
 
 —0.4433 
 
 +0.0124 
 
 — 0.0003 
 
 +0.0118 
 
 43 
 
 — 0.2249 
 
 —19 6888 
 
 — 0.4400 
 
 +0.0148 
 
 — 0.0002 
 
 +O.OI 17 
 
 44 
 
 — 0.2696 
 
 — 19.4840 
 
 —0.4355 
 
 + 0.0162 
 
 — 0.0002 
 
 +0.0116 
 
 45 
 
 —0.0425 
 
 —19.8951 
 
 — 0.4446 
 
 + 0.0098 
 
 — 0.0003 
 
 +0.0118 
 
 46 
 
 —0.0336 
 
 —19.7798 
 
 —O.4419 
 
 +0.0097 
 
 — 0.0003 
 
 +00117 
 
 47 
 
 —0.0768 
 
 —I9-3370 
 
 —O.4321 
 
 +0.01 10 
 
 — 0.0003 
 
 +0.0115 
 
 48 
 
 — 0.0058 
 
 —19.9799 
 
 —O.4465 
 
 +0.0088 
 
 — 0.0004 
 
 +0.0119 
 
 49 
 
 ■ — 0.0050 
 
 —19-9773 
 
 — O.4464 
 
 +0.0087 
 
 — 0.0004 
 
 +0.0119 
 
 50 
 
 — 0.0176 
 
 —I9-3859 
 
 —0.433I 
 
 +0.0095 
 
 — 0.0003 
 
 +0.0115 
 
 51 
 
 +0.0481 
 
 — 19.6624 
 
 — o-4393 
 
 +0.0075 
 
 — 0.0004 
 
 +0.0117 
 
 52 
 
 40.1178 
 
 —19.4777 
 
 —o.435i 
 
 +0.0059 
 
 — 0.0004 
 
 +0.0116 
 
 53 
 
 + 0.0545 
 
 —19.7876 
 
 • — 0.4421 
 
 +0.0074 
 
 — 0.0004 
 
 +0.0117 
 
 54 
 
 +0. 1470 
 
 —19.5289 
 
 —0.4362 
 
 +0.0050 
 
 — 0.0005 
 
 +0.0116 
 
 55 
 
 4-0.0414 
 
 —19.9487 
 
 —0.4458 
 
 +0.0076 
 
 — 0.0004 
 
 +0.01 18 
 
 56 
 
 +0.1340 
 
 — 19.7226 
 
 —0.4405 
 
 +0.0052 
 
 — 0.0004 
 
 +0.0117 
 
 57 
 
 +0.0946 
 
 —19.8368 
 
 —0.4432 
 
 +0.0062 
 
 — 0.0004 
 
 +0.0118 
 
 58 
 
 + 0.1321 
 
 — 19.7962 
 
 — 0.4422 
 
 +0.0053 
 
 — 0.0004 
 
 +0.0117 
 
 59 
 
 +0.2091 
 
 -19.7788 
 
 — 0.4418 
 
 + 0.0032 
 
 — 0.0004 
 
 +0.0117 
 
 60 
 
 +0.1252 
 
 — 19.9096 
 
 —0.4448 
 
 +0.0054 
 
 — 0.0004 
 
 +O.OI 18 
 
 61 
 
 +0.2494 
 
 — 19.8022 
 
 — 0.4422 
 
 +0.0022 
 
 — 0.0005 
 
 +O.OI 18 
 
 62 
 
 +0.2156 
 
 — 19.8406 
 
 —0.4432 
 
 +0.0030 
 
 — 0.0005 
 
 +O.OI 18 
 
 63 
 
 +0.5382 
 
 —19.5621 
 
 —0.4368 
 
 —0.0054 
 
 — 0.0007 
 
 +0.0116 
 
 64 
 
 + 0. 2092 
 
 —19.8901 
 
 —0.4443 
 
 +0.0031 
 
 — 0.0005 
 
 +0.0118 
 
 65 
 
 + 0.6362 
 
 — 19.9229 
 
 —0.4447 
 
 — 0.0082 
 
 — 0.0007 
 
 +0.01 18 
 
Optical Distortion deduced from Photographic Measures. 63 
 
 X. 
 
 Optical Distortion. 
 
 The subject of optical distortion has been approached from 
 both theoretical and empirical standpoints. Scheiner, in his 
 " Photographie der Gestirne "* gives the theoretical aspect, and 
 treats the subject under the heads of regular and irregular distor- 
 tion. Regular distortion is due to the fact that a spherical sur- 
 face is projected on the flat photographic plate, and its effect can 
 be eliminated by formulas of reduction such as equations (i) of 
 this paper. Irregular distortion is a peculiar property of each 
 telescope, and depends upon the curvature of the lenses and the 
 indices of refraction, i. e., the constants of the system as they are 
 usually understood in optics. Its effect is to change the shape of 
 the star image by elongating it radially, and under certain cir- 
 cumstances to displace the center of density. 
 
 Steinheilf has computed the effect of the Konigsberg heliome- 
 ter objective on a cylinder of rays passing through the lens, sup- 
 posing the photographic plate to be at different distances from 
 the objective. A star image 48' from the principal axis becomes 
 somewhat comet shaped, though it is still symmetrical with re- 
 spect to a line drawn through it from the center of the plate. 
 The consequence is, that there would be difficulty in deciding 
 how to bisect the image, and the measured positions may not rep- 
 resent the positions of the stars in the sky. However, the heliom- 
 eter is corrected for visual rays only. In the case of a photo- 
 graphic objective properly corrected, the image would become 
 elliptical in shape, would be symmetrical in two directions, and 
 the centers of density and figure would coincide, so that the diffi- 
 culty of bisection arising from this cause is removed. 
 
 The subject has been more extensively treated from the empir- 
 ical standpoint. Prof. H. H. Turner, J has published a paper on 
 the errors of star places due to optical distortion in which he 
 shows that the plates of the Oxford Astrophotographic telescope 
 are free from distortion by the examination of forty plates, each 
 containing about thirty stars. Prom the smallness of the resid- 
 
 * Pp. 23-25. 
 
 f Scheiner, pp, 25-27, see footnote, p. 25. 
 
 t Mon. Not., E. A. S. Vol. LIX, p. 438. 
 
64 Stars within One Degree of the North Pole, and 
 
 uals he deduces the fact that there is no optical distortion.* In 
 the second part of his paper, Prof. Turner discusses the possible 
 distortion of a different kind of glass, namely the Bruce photo- 
 graphic doublet, the property of the Harvard College Observa- 
 tory, and now at the Arequipa station. Through Prof. Pickering, 
 a glass positive from Arequipa was secured, and two contact 
 negatives were made of overlapping portions of the positive on 
 the regulation Oxford plates. Two other Oxford plates were ex- 
 posed to the same region in the sky, and were compared with the 
 contact negatives. The residuals obtained by this processf were 
 too large and too systematic to receive the treatment accorded to 
 the residuals from the Oxford plates. After some further exam- 
 ination it was decided that the discrepancies were due to the cur- 
 vature of the plates used in making the photographic copies, to 
 the want of complete contact and to obliqueness in the illumina- 
 tion. J His final conclusion is that there is no optical distortion 
 over an area 4 from the center of the Harvard plate. 
 
 In a later number§ of the same periodical appears an article by 
 Capt. Hills describing another method of finding distortion em- 
 ployed by him. He photographed star trails on a plate, and 
 measuring the actual differences in curvature between them, com- 
 pared them with the computed differences. In applying this 
 method to a Zeiss doublet of 377™™ focal length, he found that 
 there was no measurable distortion over a field of 9 from the 
 center. 
 
 The distortion caused by the Helsingfors telescope with which 
 the polar photographs were taken, and which is the general subject 
 of this section, has already been investigated by Professor Donner, 
 the Director of the Observatory. Tf Briefly described, his method 
 was to compare the measured coordinates of a group of stars with 
 the coordinates computed from their right ascensions and decli- 
 nations, which had been accurately determined by some other 
 method than the photographic. Accordingly he selected a group 
 of stars contained in a circular issued by Dr. Gill for this very 
 purpose. This group formed a portion of the Victoria compari- 
 son stars used by Gill in his heliometer triangulation for solar 
 
 *Loo cit., p. 443. 
 
 fLoo. cit., p. 450. 
 
 JLoc. cit., p. 465. 
 
 § Mon. Not., R. A. S., Vol. LIX, p. 564. 
 
 If See footnote, p. 5, this paper. 
 
Optical Distortion deduced from, Photographic Measures. 65 
 
 parallax, and their places had been determined with great precis- 
 ion. This group was photographed on six plates when near the 
 meridian, with the telescope in the two positions, east and west 
 of the pier. Without going into the details of his method, it may 
 be mentioned that there are nine stars on each plate and that the 
 rectangular coordinates were measured from the star nearest the 
 center. The coordinates were corrected for refraction, aberration 
 and division errors of the reseau, and were then compared with 
 the coordinates of the same stars computed from the places 
 furnished by Gill. With the differences O-C as the absolute terms 
 in the equations 
 
 °=n y +k !l +py — rx, 
 
 o = n x + k x +px + ry, 
 
 the plate constants were computed in the usual way. In solving 
 these equations Donner used the ^-equations and the y-equations 
 both together and separately, with interesting results as regards 
 the scale value. This was found to be 
 
 ^= — 0.002134, 
 
 Pa; = 0.002036, 
 
 J)a3,=: O.0O2O72. 
 
 Thus there appears to be a uniform difference in the two scale 
 values of 
 
 Pv — P* = — 0.000098, 
 
 which is equivalent to C/.0059 at a distance of 60' from the center 
 of the plate. This difference seems to indicate that the object 
 glass flattens the field, making the ^-coordinates longer in pro- 
 portion than the ^-coordinates, and might be taken as an indica- 
 tion of distortion. Donner himself suggests several other expla- 
 nations, but seems to think it is especially due to small errors in 
 the star places. 
 
 There is still another explanation, which latter became available, 
 and which was suggested to me by Professor Jacoby. The cor- 
 rections for refraction were calculated according to Kapteyn's 
 formulas, which were published by him in the Bulletin of the 
 Permanent Committee,* and are also to be found in Scheinerf. 
 
 *Bull. Com. Perm., T. I, p. 101. 
 t Loc. cit., p. 140. 
 
66 Stars within One Degree of the North Pole, and 
 
 In a latter number * Kapteyn published a third term for the re- 
 fraction in x, which is 
 
 — fc tan (Scot (<5+ N)x. 
 
 Wishing to learn the effect of this slight additional term, I 
 made a new reduction of Exposure I, Plate i, Sept. 12, 1892. 
 On this plate p is — 0.002152 and p x — is 0.002052, showing the 
 average difference above referred to. The absolute terms arising 
 from the [^-coordinates are all increased numerically as will be 
 seen by comparing the following set of numbers : 
 
 ni(old). ^(new). 
 
 — .1292 —-I354 
 
 — .1019 — .1069 
 
 — .0734 — .0772 
 
 — .0396 — .0414 
 
 — .0296 — .0311 
 — .0000 — .0000 
 + 0622 + .0666 
 -f- .0967 + .1012 
 + .1285 +.1346 
 
 A second solution of the equations with the new absolute terms 
 leads to the new value of 
 
 j) x = — 0.002164. 
 
 This value accords very well with the value of p v , and hence, as 
 far as the difference in scale values is concerned, there seems to 
 be no evidence of distortion. 
 
 The expression which Donner himself used for this displace- 
 ment was 
 
 as-\-bs 2 + cs 3 +••■ > 
 
 where s is the distance from the center, and a, b and c are con- 
 stants to be determined from the equations. On account of the 
 form of the terms, a cannot be separated from the scale value, 
 hence b is the only constant obtained. The six plates in the Vic- 
 toria region give for b the mean value, 
 
 J = — o.oooooio, 
 
 and the reduction of the two plates of the Pleiades furnishes for 6 
 the mean value, 
 
 6 = +0.0000021. 
 
 * Corrections de Refraction et d'Aberration. Bull. Com. Perm., Tom. 
 Ill, 1896. (Not yet published.) 
 
Optical Distortion deduced from Photographic Measures. 67 
 
 Calling attention to the small magnitude of these quantities 
 and their difference in sign, Donner concludes* that the constant 
 6 of the term 6s 2 in the expression for the distortion does not ex- 
 ceed a few units in the seventh decimal place, and since the cor- 
 rections which might result are for all practical purposes con- 
 fused with the corrections for the scale value of the plate, we can 
 in practice neglect the distortion of the field of the objective. 
 
 It will thus be seen that Donner's and Turner's methods are 
 alike in comparing the measured coordinates with the coordinates 
 obtained from other observations, for which purpose Donner 
 used heliometer measurements and Turner, meridian observa- 
 tions. 
 
 Another similar investigation making use of the same stars in 
 Gill's circular was carried out at the Observatory of San Per- 
 nandof, one of the observatories participating in the astrophoto- 
 graphic survey. The same formula 
 
 e = ps 4- 8s 2 
 
 was employed, and its effect was found to be negligible. The de- 
 tails of the method of research are not published in the Bulletin. 
 It was stated in the introduction to this paper that one of Prof. 
 Jacoby's objects in having a group of polar plates taken was to 
 investigate the distortion of the Helsingfors objective by a new 
 method which did not involve, except indirectly, any previous de- 
 termination of the star places. His plan was to have the same 
 group of stars photographed with the telescope in different posi- 
 tions with regard to the pier, so that the object glass would be 
 situated differently each time with regard to the stars in the 
 group. Two different positions could be obtained by taking a 
 group near the meridian, and reversing the telescope between the 
 two exposures which method was indeed followed by Donner, 
 though for another purpose. But the selection of the group 
 about the pole made it possible to turn the telescope through any 
 angle desired after each exposure. On reference to Table I, page 
 3, it will be seen that the right ascensions of the pole were 
 
 b-, in* , l'-,.m ,!i~ ,m . 
 
 I9»24 m , 22 n 24 m , I n 24 m , 4 n 24 n 
 
 thus differing by 45". Strictly speaking, the pole has every right 
 
 *Loc. cit., p. 65. 
 
 t Bulletin du Comit6 Permanent, 1896; Proces-Verbaux, p. 52. 
 
68 Stars within One Degree of the North Pole, and 
 
 ascension, but those just quoted belong to the hour circles which 
 are perpendicular to the X axes on the different plates. 
 
 As before stated, the usual effect of optical distortion is to dis- 
 place the center of density of a star image. If the displacement 
 is only radial, it will change the distance of the star from the 
 center of the plate, but will not change its position angle, but if, 
 in addition to the radial displacement, there is a displacement in 
 any other direction due to some special peculiarity of the object 
 glass, such as would be suggested by a different scale value in 
 two perpendicular directions, the combination of the two would 
 alter both the position angle and distance of the star, and this ef- 
 fect might be different over different parts of the plate. A dis- 
 placement of this character would not be detected by Donner's 
 method, which assumes that the distortion is the same along dif- 
 ferent radii of the objective. Furthermore, if the plate holder 
 always keeps the same position relative to the object glass, which 
 is usually the case with telescopes employed only for photo- 
 graphic purposes, and if the telescope is changed in position, then 
 the same star appearing on different portions of the plates, will 
 be displaced differently and a proper comparison of the right as- 
 censions and polar distances of a large number of stars, obtained 
 independently from the different plates would give the effect of 
 this kind of distortion. This method of procedure was followed 
 with the polar plates taken at Helsingfors. 
 
 From the Table of Mean Results, forty -two stars (there marked 
 with an asterisk), which appear on all four plates were selected 
 on the basis of their distribution in right ascension and polar dis- 
 tance. They were divided into zones, and about the same num- 
 ber of stars was selected from each zone, as will be seen on refer- 
 ring to the figures given below. 
 
 I o"-i3oo" 2, 23, 42, 45, 46, 49, 53, 58, 60, 64, Total 10. 
 
 II i3oo"-i8oo" 9, 11, 25, 26, 30, 41, 56, 62, " 8. 
 
 III i8oo"-24oo" 8, 19, 2i, 28, 29, 32, 35, 39, 43, " 9. 
 
 IV 24oo"-3ooo" 4, 12, 38, 44, 50, 52, 54, 65, " 8. 
 V 3ooo"-36oo" 1, 3, 10, 14, 24, 47, 63, " 7. 
 
 By means of these forty-two stars the four plates were reduced 
 to a common standard as follows : A new set of corrections to 
 the constants of reduction for each plate was obtained by a least 
 squares solution according to equations (2) using the above forty- 
 
Optical Distortion deduced from Photographic Measures. 69 
 
 two stars for this purpose, and taking for the numerical terms the 
 residuals found in the columns headed Aa sin n and Aiz of Table 
 VII. For example the following equations are obtained from 
 stars i and 2, plate I. 
 
 V 
 
 — 54<if — 25*? + 58^' — 05 = o, + 07 ; 
 
 — 25df + 54di? + 58du + 22 = o, + 08 ; 
 
 — 52df — sodv + I3<U' — 24 = o, — 18 ; 
 
 — 3odf + 52dv + i$du — 02 =o, — 04. 
 
 The new residuals obtained by substituting the dS , dy, dw and dA' 
 in the equations just described, involve only the systematic errors 
 due to distortion. They are given in the above equations under 
 the heading '' i>." In general the effect of this new reduction was 
 to decrease numerically the residuals to a small extent only. In 
 fact it will be noticed in referring to the residuals in Table VII, 
 that they are fairly well distributed both in magnitude and sign, 
 and from this it was inferred beforehand that the corrections to 
 ?, 1, A and <» would be small and would not materially change the 
 characters of the residuals, as indeed turned out to be the case. 
 
 A satisfactory agreement as regards the scale value appeared in 
 the course of this reduction, and in some sense it is a test of the 
 method. It can be quite easily perceived by an examination of 
 the following figures which give the old and new values. 
 
 Plate. 
 
 (o Table VI. 
 
 dot 
 
 to (new). 
 
 IUB + M) 
 
 59".8590 
 
 — // .0026 
 
 59"-8564 
 
 Ui(B + M) 
 
 .8566 
 
 — .0010 
 
 .8556 
 
 Illi{B + M) 
 
 .8528 
 
 + .0021 
 
 .8549 
 
 IVUB + M) 
 
 .8561 
 
 + .0015 
 
 .8576 
 
 Mean 
 
 59".856i±o" 
 
 .0017 
 
 59".856i ± o".ooo8 
 
 The following table gives the new residuals for the forty -two 
 stars : 
 
10 Stars within One Degree of the North Pole, and 
 
 
 
 
 
 Table X. 
 
 
 
 
 
 Star. 
 
 B 
 
 Aa Sin 7T 
 
 P 
 
 Air 
 
 Star. 
 
 s 
 
 Aa sin fr 
 
 p 
 
 Air 
 
 
 o 
 
 // 
 
 mm 
 
 u 
 
 
 
 mm 
 
 
 I 
 
 294 
 
 +.07 
 
 58 
 
 +.08 
 
 12 
 
 350 
 
 +•'14 
 
 49 
 
 + •17 
 
 
 249 
 
 —■31 
 
 
 — 35 
 
 
 3°5 
 
 —.16 
 
 
 + .32 
 
 
 340 
 
 +■54 
 
 
 — .20 
 
 
 36 
 
 +•23 
 
 
 —•17 
 
 
 207 
 
 —•34 
 
 
 +■45 
 
 
 263 
 
 —.24 
 
 
 —•32 
 
 3 
 
 299 
 
 —.16 
 
 53 
 
 +.08 
 
 14 
 
 356 
 
 +.10 
 
 61 
 
 — r 3 
 
 
 254 
 
 — .11 
 
 
 +.07 
 
 
 311 
 
 +.15 
 
 
 —.07 
 
 
 344 
 
 +.04 
 
 
 —.16 
 
 
 4i 
 
 +.14 
 
 
 +.09 
 
 
 211 
 
 +•23 
 
 
 + .02 
 
 
 268 
 
 -■36 
 
 
 + .11 
 
 4 
 
 317 
 
 —.04 
 
 50 
 
 —.26 
 
 19 
 
 8 
 
 —.08 
 
 40 
 
 —.12 
 
 
 272 
 
 —.18 
 
 
 —■32 
 
 
 322 
 
 +.06 
 
 
 — -°3 
 
 
 2 
 
 —.08 
 
 
 +.09 
 
 
 53 
 
 +.01 
 
 
 —•13 
 
 
 229 
 
 +.26 
 
 
 +•49 
 
 
 280 
 
 — .01 
 
 
 +•25 
 
 8 
 
 331 
 
 +.02 
 
 37 
 
 +•15 
 
 21 
 
 25 
 
 —•03 
 
 32 
 
 +.29 
 
 
 286 
 
 + .04 
 
 
 — 05 
 
 
 34o 
 
 +.18 
 
 
 — .11 
 
 
 16 
 
 +.06 
 
 
 +.22 
 
 
 70 
 
 —■25 
 
 
 —.18 
 
 
 243 
 
 — 15 
 
 
 -•36 
 
 
 297 
 
 +.10 
 
 
 — .01 
 
 9 
 
 332 
 
 +•33 
 
 28 
 
 +•32 
 
 24 
 
 33 
 
 —•15 
 
 58 
 
 +.07 
 
 
 287 
 
 —.14 
 
 
 —.09 
 
 
 348 
 
 +.01 
 
 
 + •33 
 
 
 17 
 
 +•17 
 
 
 +•13 
 
 
 78 
 
 —.09 
 
 
 —.40 
 
 
 244 
 
 —•37 
 
 
 —•35 
 
 
 305 
 
 +.22 
 
 
 —•03 
 
 10 
 
 334 
 
 —.04 
 
 51 
 
 — .01 
 
 25 
 
 52 
 
 +•13 
 
 26 
 
 —.26 
 
 
 289 
 
 —.26 
 
 
 +.J5 
 
 
 7 
 
 +.23 
 
 
 +.16 
 
 
 19 
 
 + .00 
 
 
 +.10 
 
 
 97 
 
 +.04 
 
 
 +.07 
 
 
 246 
 
 -f.26 
 
 
 —.26 
 
 
 324 
 
 —38 
 
 
 +•03 
 
 ii 
 
 337 
 
 — .20 
 
 24 
 
 —•23 
 
 26 
 
 65 
 
 +•03 
 
 22 
 
 —.07 
 
 
 292 
 
 —.28 
 
 
 +•35 
 
 
 20 
 
 +.16 
 
 
 +.26 
 
 
 22 
 
 — .10 
 
 
 — 42 
 
 
 no 
 
 — - T 5 
 
 
 — -37 
 
 1 
 
 250 
 
 +.56 
 
 I+.26 
 
 
 338 
 
 —.04 
 
 
 +■17 
 
Optical Distortion deduced from Photographic Measures. 71 
 
 
 
 r 
 
 rABLE X.- 
 
 -( 
 
 Gontir 
 
 ,ued). 
 
 
 
 
 Star. 
 
 B 
 
 An sin n 
 
 P 
 
 Air 
 
 
 Star. 
 
 B 
 
 Ad Sill TT 
 
 P 
 
 Air 
 
 28 
 
 
 
 95 
 
 5o 
 
 140 
 
 8 
 
 +.07 
 
 +.24 
 
 —•51 
 
 +.21 
 
 mm 
 38 
 
 + .32 
 
 +:09 
 —.08 
 —•33 
 
 41 
 
 
 161 
 116 
 206 
 
 73 
 
 —•'31 
 
 +,19 
 
 +.06 
 +.06 
 
 mm 
 23 
 
 +.'i 9 " 
 
 +•44 
 —■35 
 —.29 
 
 29 
 
 i°3 
 58 
 
 148 
 15 
 
 +.14 
 +•05 
 +.3° 
 -.46 
 
 38 
 
 +•23 
 +.29 
 —.24 
 —.27 
 
 
 42 
 
 169 
 124 
 
 214 
 81 
 
 +.05 
 
 +.21 
 +,22 
 -.46 
 
 19 
 
 —.06 
 —.19 
 —.28 
 
 +•53 
 
 3° 
 
 104 
 
 59 
 150 
 
 16 
 
 +.41 
 —•17 
 —.09 
 
 — -13 
 
 27 
 
 — 15 
 —■23 
 
 + .08 
 
 +.27 
 
 
 43 
 
 170 
 
 125 
 
 216 
 
 82 
 
 —.14 
 —.19 
 
 +•31 
 +.04 
 
 32 
 
 —.18 
 +.24 
 +.06 
 —•13 
 
 32 
 
 123 
 78 
 
 168 
 35 
 
 —.32 
 
 +.18 
 — .02 
 
 +•17 
 
 34 
 
 +.01 
 —•23 
 +.25 
 —•°3 
 
 
 44 
 
 177 
 
 132 
 
 222 
 
 89 
 
 —•15 
 +.29 
 +.22 
 
 —•37 
 
 47 
 
 — .11 
 —.26 
 +.58 
 —.19 
 
 35 
 
 128 
 82 
 
 173 
 40 
 
 +.00 
 — .21 
 
 +.00 
 +.21 
 
 38 
 
 +•33 
 +.27 
 —.08 
 —•50 
 
 
 45 
 
 187 
 
 142 
 
 232 
 
 99 
 
 +•34 
 —.13 
 —•32 
 +.11 
 
 12 
 
 +.01 
 
 —34 
 — .02 
 +.38 
 
 38 
 
 144 
 
 98 
 
 189 
 
 56 
 
 +.07 
 +.21 
 —.14 
 — .12 
 
 27 
 
 —•37 
 +.12 
 +.12 
 +.12 
 
 
 46 
 
 195 
 150 
 240 
 107 
 
 +.19 
 —•33 
 —•35 
 +48 
 
 20 
 
 +.07 
 —■17 
 — .01 
 
 +.14 
 
 39 
 
 148 
 
 i°3 
 
 193 
 
 60 
 
 +.26 
 
 +.17 
 — .20 
 
 —.25 
 
 36 
 
 —.07 
 
 —■57 
 +.00 
 
 +.67 
 
 
 47 
 
 196 
 
 151 
 241 
 108 
 
 +.13 
 +.24 
 
 —•39 
 
 +.06 
 
 53 
 
 —.04 
 -.56 
 +•35 
 +■25 
 
T2 
 
 Stars within One Degree of the North Pole, and 
 
 Table X — (Concluded). 
 
 Star. 
 
 49 
 
 5° 
 
 52 
 
 53 
 
 54 
 
 56 
 
 58 
 
 199 
 
 154 
 244 
 III 
 
 201 
 
 156 
 246 
 
 "3 
 
 214 
 169 
 
 259 
 126 
 
 214 
 169 
 
 259 
 126 
 
 218 
 
 173 
 263 
 130 
 
 225 
 1 So 
 270 
 137 
 
 230 
 185 
 275 
 142 
 
 +.19 
 —.28 
 —.10 
 +•19 
 
 +.03 
 —.16 
 — .12 
 +.27 
 
 —.13 
 +.04 
 —•23 
 +-3i 
 
 +.22 
 —.16 
 —■05 
 —.04 
 
 +.09 
 — .20 
 +.05 
 +.10 
 
 — .12 
 
 +.13 
 +.19 
 —•25 
 
 —.29 
 
 +•15 
 — .01 
 
 +•13 
 
 mm 
 5 
 
 49 
 
 43 
 
 40 
 
 26 
 
 —.18 
 +.20 
 -■56 
 +.56 
 
 — .01 
 +.05 
 +.12 
 
 — 13 
 
 — .11 
 +.08 
 
 — -°3 
 +.06 
 
 +.15 
 +•25 
 — .20 
 —.18 
 
 —•15 
 +.01 
 — .01 
 +.18 
 
 +.00 
 +.21 
 +.25 
 
 —■47 
 
 +.19 
 —•05 
 +-°3 
 
 —•23 
 
 Star. 
 
 B 
 
 Aa sin it 
 
 P 
 
 Ajr 
 
 
 
 
 II 
 
 mm 
 
 II 
 
 60 
 
 245 
 
 +.15 
 
 14 
 
 +.04 
 
 
 199 
 
 — 39 
 
 
 +•17 
 
 
 290 
 
 — .20 
 
 
 +•13 
 
 
 157 
 
 +•43 
 
 
 —•35 
 
 62 
 
 249 
 
 —.04 
 
 22 
 
 —.02 
 
 
 203 
 
 +•20 
 
 
 — .01 
 
 
 294 
 
 +.20 
 
 
 +.06 
 
 
 161 
 
 -•36 
 
 
 —.04 
 
 63 
 
 251 
 
 —.26 
 
 54 
 
 +.00 
 
 
 205 
 
 +•34 
 
 
 +.04 
 
 
 296 
 
 +.07 
 
 
 +.18 
 
 
 163 
 
 —.18 
 
 
 — .22 
 
 64 
 
 255 
 
 —.04 
 
 20 
 
 —.09 
 
 
 210 
 
 +.26 
 
 
 —■05 
 
 
 300 
 
 — .20 
 
 
 —.08 
 
 
 167 
 
 +.48 
 
 
 + 23 
 
 65 
 
 281 
 
 +.11 
 
 48 
 
 —.06 
 
 
 236 
 
 —.19 
 
 
 +•15 
 
 
 326 
 
 — .02 
 
 
 +.11 
 
 
 193 
 
 +.09 
 
 
 — .22 
 
 2 
 
 300 
 
 —.18 
 
 13 
 
 —.04 
 
 
 254 
 
 +.02 
 
 
 +.08 
 
 
 345 
 
 +.T2 
 
 
 + .24 
 
 
 212 
 
 +•03 
 
 
 —.27 
 
 23 
 
 32 
 
 —.19 
 
 14 
 
 +.09 
 
 
 347 
 
 —.24 
 
 
 +.21 
 
 
 77 
 
 —.19 
 
 
 —.07 
 
 
 304 
 
 +.64 
 
 
 —.24 
 
Optical Distortion deduced from Photographic Measures. 73 
 
 To facilitate a comparison of the residuals they were plotted as 
 ordinates of points whose abscissas were the position angles B; 
 those for Aa sin jr forming the upper part of the diagram and 
 those for An the lower. Thus the residuals from stars lying on 
 the same section of the plates were grouped together. An ex- 
 amination of the accompanying diagram shows that there is no 
 decided tendency on the part of the residuals toward a grouping 
 such as would indicate the presence of distortion. Indeed two 
 stars close together on the plate have quite different residuals, 
 vide 32 and 35. The plot of the points representing the residuals 
 before the least squares reduction compared with the plot of the 
 residuals after reduction, shows simply that the latter are more 
 crowded together toward the axis of abscissas than the former, 
 but there is no especial distribution. 
 
 The conclusion is therefore reached that this method of com- 
 parison does not show any indication of distortion in the field of 
 the objective. This result is one that was to be expected from 
 Donner's investigation, as well as from optical considerations. 
 The tests to which the instrument maker subjects his lens before 
 it leaves his hands as a finished product are severe and delicate. 
 An elevation equal to the -&m two hundred thousandth part of a?t 
 wave-length of light can be detected, and the tests for striee and 
 variations in densit}' are equally exacting. The radial distortion 
 is a natural consequence of the curve of the glass, but a displace- 
 ment in position angle or a deformation such as was suggested by 
 the discrepant scale values in the two coordinate directions, must 
 in all probability be due to something which happens to a glass 
 after it leaves the hands of the maker, as for instance, a strain 
 due to the position of the lens in its cell. Hence, the general 
 conclusion is reached, that so far as the Helsingfors telescope is 
 concerned, there is no evidence of optical distortion, and that in 
 this respect its performance is most satisfactory. 
 
u 
 
 Stars within One Degree of the North Pole. 
 
 r*7 
 
 X 
 
 Pi 
 
 •a is "a V "*•