WASHINGTON OBSERVATIONS FOR 1870.—APPENDIX I. REMOTE ST f - y4 ^ REPORT ON THE DIFFERENCE OF LONGITUDE BETWEEN WASHINGTON AND ST. LOUIS. BY WILLIAM HARKNESS, PROFESSOR OF MATHEMATICS, U. S. NAVY. PREPARED AT THE U. S. NAVAL OBSERVATORY BY ORDER OF REAR-ADMIRAL B. F. SANDS, U. S. N., SUPERINTENDENT. WASHINGTON: GOVERNMENT PRINTING OFFICE. 1872. Vi Lt c^S Z.G?.£2- TABLE OF CONTENTS. Page. I. Introductory.5 II. Description of observing-stations.5 III. Instruments employed at Washington.6 IV. Instruments employed at St. Louis.6 V. Method of reducing the observations for time : Formulae employed.7 Adopted mean right ascensions for 1870.0 of stars used in the determination of the difference of longitude between Washington and St. Louis, together with the constants for azimuth, level, and collimation at each station.'.8 Observations for time at Washington.10 Resulting corrections to the Kessels clock.14 Observations for time at St. Louis.15 Resulting corrections to the chronometer Dent No. 274S.22 VI. Personal equation.23 Relative personal equation of Mr. Frisby and Professor Harkness.33 Relative personal equation of Professors Eimbeck and Harkness.33 VII. Exchange of time-signals, and resulting difference of longitude: The Telegraph line between Washington and St. Louis.34 Programme for the exchange of signals.35 Formulae emplojmd for the reduction of the signals.37 Comparisons of time-pieces obtained by reading off the Washington chronograph-sheets.38 Comparisons of time-pieces obtained by observing coincidences of beats at St. Louis.38 Clock and chronometer corrections at the times of the exchange of signals.39 Observed values of the difference of longitude between Washington and St. Louis, and of the time occupied in the passage of a galvanic signal between those cities..39 Final value of the difference of longitude between Washington and St. Louis.39 Digitized by the Internet Archive in 2017 with funding from University of Illinois Urbana-Champaign Alternates https://archive.org/details/reportondifferenOOhark REPORT ON THE DIFFERENCE OF LONGITUDE BETWEEN WASHINGTON AND ST. LOUIS. United States Naval Observatory, Washington , November 14, 1872. Sir: I have the honor to submit to you the following' report on the determination of the difference of longitude between Washington and St. Louis, of which you directed me to take charge so far as this Observatory is concerned. I.—INTRODUCTORY. The operations described in this report were initiated by the United States Coast Survey, and the Observatory took part in them at the request of that institution, with the understanding that the observations at St, Louis should be made by Coast Survey officers, and those at Washington by Observatory officers; and that at the conclusion of the campaign complete copies of the observations and reductions should be exchanged for each other’s use. The observations here were made by myself and Assistant Ob¬ server Edgar Frisby, and reduced entirely by me. The observations at St. Louis were made by Professor William Eimbeck, of the Coast Survey, and reduced by Professor R. Keith, of the Coast Survey; but, as the right ascensions which the latter gentleman adopted for some of the stars employed differed slightly from those used at this Ob¬ servatory, before his work could be compared with my own it required a few small corrections, which have been introduced by Mr. Frisby and myself. The arrange¬ ments for the use of the Western Union Telegraph Company’s lines between Wash¬ ington and St. Louis were made by the officers of the Coast Survey, but I cannot refrain from expressing my thanks to Mr. M. Marean, the Western Union Company’s electrical superintendent in this city, for his kindness in promptly making the neces¬ sary connections between the different wires at the main office here. II.—DESCRIPTION OF OBSERVING-STATIONS. The observing-station at Washington was the present site of the transit circle, which is 77.8 feet due west of the center of the dome of the Observatory. Its geogra¬ phical position is: Latitude,. +3S°53 / 3 8". 8 Longitude, west of Greenwich, . 5 h 8 ra i2 s .o The station at St, Louis was in a small observatory erected on St. Charles street, between Seventeenth and Eighteenth streets, in the southwest corner of the Wasliing- ton University grounds. These grounds, rectangular in form, are bounded on the north 6 DIFFERENCE OF LONGITUDE, by Washington avenue, and on the south by St. Charles street, occupying the whole space between these streets, which is 150 feet. They are bounded on the east by Seventeenth street, and extend 206 feet 10^ inches toward Eighteenth street. Wash¬ ington avenue and St. Charles streets are parallel to each other, and run in the direction south 75° east. Seventeenth and Eighteenth streets are also parallel to each other and run in the direction south 15 0 west. The small observatory building measured eight feet from north to smith, and ten feet from east to west. It contained two piers, the transit instrument being mounted on the eastern one and the zenith telescope on the western one. The following distances were measured from the station point on the transit pier, viz: to the western boundary of the university grounds, 13 feet 5 inches; to the line of curb-stones on the northern side of St. Charles street, 14 feet 4 inches: and to the produced western face of the Scientific Department building, 10 feet 4 inches. The approximate latitude of the station was + 38° 37'. III.—INSTRUMENTS EMPLOYED AT WASHINGTON. The Transit Circle, whose object-glass has a focal length of 145 inches, and a clear aperture of 8.52 inches, was used with an eye-piece which produced a magnifying-power of 186 diameters. Throughout the whole series of observations the clamp end of the axis was to the east. A description of this instrument is given in Appendix I to the Washington Observations for 1865. J he Kessels Side) cal ( loch, No. 13 2 4? which is the Observatory standard, was employed in connection with A. CJn onoyraph, having a barrel 8.15 inches in diameter and 24.0 inches long - , revolving once each minute. This chronograph will run continuously for four hours without requiring the paper to be changed. It has but a single pen, with which both the clock-signals and those made by the observer are recorded. The Electro-magnetic Apparatus, which was used for sending and receiving the longitude-signals is entirely automatic. It would occupy too much space to explain it here, but a full description may be found in Appendix I to the Washington Observations for 1867. ' IY.—INSTRUMENTS EMPLOYED AT ST. LOUIS. United States Coast Survey Portable Transit Instrument No. 7, made by William A iirdemann, of Washington. Its object-glass has a focal distance of 25^ inches, and a clear aperture of 2.03 inches. A diagonal eye-piece was used, wliicli produced a magnifying-power of 67 diameters. The length of the axis between the Y’s is 14 inches, and the pivots are 0.71 of an inch in diameter. It is provided with two finding-circles, each 4 inches in diameter, graduated to every 2c/, and reading by means of two ver¬ niers to single minutes. A Sidereal Box Chronometer, Kessels and Dent No. 1287. A Mean Time Box Chronometer, Dent No. 2748. 1 he Elect) o-maynetic Apparatus employed was the ordinary Morse receiving mao- net, sounder, and key, together with a break-circuit key; all of which were in the Western Union Telegraph Office in the Merchant’s Exchange, on First street, between Walnut and Market streets. WASHINGTON AND ST. LOUIS. 7 Y.-METHOD OF REDUCING THE OBSERVATIONS FOR TIME. Let a — apparent right ascension of the star observed; T' — observed clock or chronometer time of star’s transit; T 0 — time, by face of clock or chronometer, for which clock or chronometer correction is to be determined; R — rate per hour of clock or chronometer; AT 0 — correction of clock or chronometer at the instant when its face indi¬ cated the time T 0 - v — effect of errors of observation; «, b, and c — respectively, the azimuth, level, and collimation constants; A, B ,and C — respectively, the azimuth, level, and collimation factors, Then each star observed will furnish one equation of condition of the form o= a - \_T + ^T 0 + R (T'-T 0 ) + Aa + Bb + Cc] - v and from all the equations thus obtained the most probable values of the quantities considered as unknown can be found by the method of least squares. When the observations have been made with a fixed instrument, the quantities sought are usually AT 0 and R\ but if a portable instrument has been used they will generally be AT 0 , R, and a. Sometimes it is convenient to make T 0 equal to the mean of the observed times of transit of all the stars in the group, and then R is found from the difference between the values of AT 0 given by two groups of stars separated by an interval of some hours. It is always advantageous to have the unknown quan¬ tities in the equations of condition quite small, and therefore, when possible, it is best to introduce closely approximate values of these quantities, and to solve only for small corrections to these approximate values. Thus, if R is large, and r is an approximate value of it, we write R — dr -f-r, and, substituting that value in the equations of con¬ dition, we determine dr. In the same manner, if A T {) is large, and 0 is an approxi¬ mate value of it, we write AT 0 — 9 -f- 69 , and, substituting that value in the equations of condition, we determine 69 . The factors A, B , and C may be computed by means of the formulae A — sin (— d) sec d — sin — cos g> tan d B — cos (— d) sec d — cos cp -f- sin cp tan d C — sec d in which cp is the latitude of the place of observation, and d the declination of the star observed. For a culmination below the pole, 180° — d must be substituted instead of d. The following rules are sometimes convenient for determining the signs of these quantities. A is positive, except for stars between the zenith and the pole. B and C are positive, except for stars below the pole. Table I gives the adopted mean places of all the stars employed in the longitude operations, together with the corresponding values of A, B, and C, both at Washington and St. Louis. 8 DIFFERENCE OF LONGITUDE, Table I .—Adopted Mean Bight Ascensions for 1870.0 of Stars used in the Determination of the Difference of Longitude between Washington and St. Louis; together with the Constants A, D, and C for Azimuth, Level, and CoUimation at each Station. Name of Star. Right Ascension. Washington. St. Louis. A B c A B c h. m. s. £ Ilydrae .... 8 39 53-45 + 0.529 + 0.857 + 1.01 L Ursae Majoris . 8 50 17.72 - 0.247 + 1.490 + 1.52 K Cancri .... 9 0 42.25 + 0.462 + 0.918 + 1.03 I Draconis 9 18 20.13 - 4-85 + 5-15 + 7.08 a Ilydrae .... 9 21 11.96 + 0.734 + 0.693 + 1.01 p Cephei, S. P. 9 26 58.46 + 2.76 _ 0-939 — 2.92 £ Leonis .... 9 38 28.10 + 0.267 + 1.06 + 1 . 10 1“ Leonis .... 9 45 21.94 + 0.232 + 1.09 + I. 12 79 Draconis, S. P. . . 9 51 15.02 + 3.19 - 1.27 - 3-44 a Leonis .... 10 1 26.82 + 0.449 + 0.920 + 1.02 32 Ursae Majoris . 10 8 33-82 — I .11 + 2.17 + 2-44 7 1 Leonis .... 10 12 48.14 + o. 33 i + 1.02 1.07 9 Draconis 10 23 58.40 - 2.60 + 3-36 + 4-25 l Leonis .... 10 42 25-37 + 0.469 + 0.904 + 1.02 L Cephei, S. P. 10 45 3-53 + 2.34 — 0.589 — 2.41 a Ursae Majoris . 10 55 41.04 — 0.875 + 1.98 + 2.16 cJ Leonis .... II 7 11.52 . . + 0.320 + 1.02 + 1.07 5 Crateris .... II 12 50.58 . . . . + 0.S20 + 0.624 + 1.03 r Leonis .... II 21 15-13 + 0.579 + 0.817 + 1.00 + 0.574 + 0.820 + I.OO 1 Draconis II 23 39-55 • • • V — i -53 + 2.50 4" 2.93 V Leonis .... II 30 17.60 + 0.629 + 0.777 + 1.00 p Leonis .... II 42 25.66 + 0.416 + 0.949 + 1.04 + 0.4II + 0.952 + 1.04 y Ursae Majoris . II 46 58.98 • . . . - 0.468 + 1.65 + 1.72 0 Virginis. II 58 35-22 + 0.498 4~ 0.883 1.01 + 0-493 + 0.886 + 1.01 4 Draconis 12 6 4.78 • * • • — 3-16 + 3.81 + 4-95 V Virginis .... 12 13 15-35 + 0.627 + 0.779 + 1.00 + 0.622 + 0.782 + I .OO P Corvi. 12 27 33-74 + 0.953 + 0.515 + 1.08 a Draconis 12 27 55-31 . . . . - 1.58 + 2.54 + 3.00 12 Canum Venaticorum 12 49 56.63 — 0.002 + r. 29 + 1.29 e Virginis .... 13 3 13-27 + 0.694 + 0.725 + 1.00 Polaris, S. P. . 13 II 17-34 +32.85 25,22 _ 41.42 a Virginis .... 13 18 20.85 + 0.772 + 0.660 + 1.02 ? Virginis .... 13 28 4.26 + 0.626 + 0.779 4- I .OO V Bootis .... 13 48 29.71 + 0.360 + 0.995 + 1.06 a Bootis .... 14 9 43-98 + 0.347 + 1.00 + 1.06 WASHINGTON AND ST. LOUIS. 9 Table 1 .—Adopted Mean Right Ascensions for 1870.0, dee. —Continued. Name of Star. Right Ascension. Washington. St. Louis. A B c A B c h. m. s. £ Bootis. 14 39 18.61 + 0.219 + 1.11 + 1.13 a . 2 Librae. 14 43 41.42 + 0.842 + 0.606 + I.04 + O.S38 + 0.610 + 1.04 ft Ursae Minoris . 14 51 6.66 - 2.13 + 3.06 + 3-79 p Bootis. 14 57 2.89 — 0.046 + 1.32 + 1.32 - 0.052 + 1.32 + 1.32 ft Librae. 15 10 0.87 + 0.750 + 0.679 + 1.01 + 0.746 + 0.683 + I .OI p Bootis. 15 19 34-84 + 0.023 + 1.27 + 1.27 + 0.017 + 1.27 + 1.27 y 2 Ursae Minoris . 15 20 57-15 . . — 1.82 + 2.74 + 3-29 Cl Coronae Borealis . 15 29 11.08 + 0.229 + 1.10 + 1.12 + 0.223 + I . 10 + I .12 a Serpentis .... 15 37 51.99 + 0-535 + 0.853 + I .01 + 0.530 + 0.856 + I .OI e Serpentis .... 15 44 20.27 + 0.562 + 0.832 + I .OO + 0.557 + 0 00 CO 4 - + I .00 c Ursae Minoris . 15 48 45.50 — 3.12 + 3-77 + 4.89 e Coronae Borealis . 15 52 12.44 • . + 0.222 + 1. 102 + I . 12 ft 1 Scorpii. 15 57 52.89 + 0.899 0.559 + 1.06 Groombridge 2320. l6 5 58.46 - i -33 + 2.33 + 2.69 <5 Ophiuchi .... l6 7 32.12 + 0.676 + 0.739 + I .OO r Ilerculis .... l6 15 50.13 — 0.189 + 1.44 + 1.46 V Draconis .... l6 22 14.18 - 0.836 + 1.94 + 2.12 c Ophiuchi .... l6 30 0.16 + 0.764 + 0.668 + 1.02 V Ilerculis .... l6 38 26.43 - 0.005 + 1.29 + I . 29 - O.OII + I . 29 + I.29 K Ophiuchi .... l6 51 30-97 + 0-497 + 0.884 + I .OI + 0.492 + 0.887 I .OI d Herculis .... l6 56 48.28 + O. 107 + 1.20 + 1.20 + 0. IOI + 1.20 + 1.20 e Ursae Minoris . l6 59 22.74 - 5-09 + 5-39 + 7.42 - 5.12 + 5-37 + 7.42 a 1 Herculis .... 17 8 43.26 + 0.426 + 0.941 + 1.03 + 0.421 + 0.944 + 1.03 44 Opliiuchi .... 17 18 26.00 + 0-974 + 0.498 + I.09 + 0.971 + 0.502 + I.09 Groombridge 966, S. P. 17 22 21.68 + 3-53 — i -54 — 3.85 a Ophiuchi .... 17 28 54.07 + 0.453 + 0.919 + I .02 + 0.448 + 0.922 + 1.02 0 ) Draconis .... 17 37 42.96 - i -39 + 2-39 + 2.77 r- Herculis .... 4 i 22.32 + 0.2x6 + 1.11 + 1.13 y Draconis .... 17 53 35-37 . « - 3.60 + 1-57 + I .6l y 2 Sagittari .... 17 57 27.50 + 1.08 + 0.413 + I. l6 P Sagittar i i .... 18 5 59-38 + 0.926 + 0.538 + 1.07 + 0.923 + 0.542 + 1.07 (j Ursae Minoris . 18 14 16.33 12.47 + II -35 + 16.86 —12.52 + 11.28 + 16.86 V Serpentis .... 18 14 35-03 + 0.663 + 0.749 + I .OO I Aquilae. 18 28 8.00 + 0.742 + 0.686 + 1.01 a Lyrae. 18 32 32.26 + 0.006 + 1.28 + 1.28 51 Cepliei, S. P. 18 38 43-17 + 16.73 — 12.21 — 20. 72 + 16.86 — 12. iS — 20. 72 ft Lyrae. 18 45 16.87 + O. 117 + 1.19 + 1.19 c Aquilae. 18 59 26.14 + 0.438 + 0.930 + I.O3 + 0.433 + 0-933 + 1.03 Sagittarii .... 19 10 1.68 + 0.894 + 0.564 + 1.06 (5 Aquilae. 19 18 56.64 + 0.589 + 0.809 + I .00 + 0.584 + 0.812 + I .OO 2—W S 4 IO DIFFERENCE OF LONGITUDE, I able I. Adopted Mean Right Ascensions for 1870.0, dee. —Continued. Name of Sta k Aquilae . y Aquilae . rc Aquilae . ft Aquilae . % Ursx Minoris «* Capricorni . e Delphini « Cygni e Aquarii . v Cygni 1 Pegasi . ft Aquaiii . Righ Ascension. Washington. St. Louis. A B C A B C h. 111 . s. J 9 29 53-85 4 - 0.728 + 0.697 ' + I .01 + 0.724 + 0.701 + I .OI 19 40 4-79 + 0.486 + 0.892 + 1.02 + 0.481 + 0.895 + 1.02 19 4.4 26.46 + 0.511 + 0.872 "!* I .OI + 0.506 + 0.875 + I .OI 19 48 55-68 + O.545 + 0.845 + I .01 + 0.540 + O.848 + I .OI 19 54 16.90 -40.52 + 33-99 + 52.89 40.68 + 33-78 + 52.89 20 IO 50.44 + 0.806 + 0.634 + 1.03 _ 1 _ 0.802 + 0.638 + 1.03 20 27 0.17 + 0 . 4/8 + 0.898 + 1.02 + 0.473 + 0.901 + 1.02 20 37 0.07 — O. 140 + 1.40 + 1.41 20 45 38.47 + 0.747 + 0.674 + I .01 20 52 19.70 0.046 + 1.32 + 1.32 21 l6 4-52 + 0.357 + 0-997 + 1.06 21 24 42.90 + 0.712 + 0.710 + I .01 Washington Observations .—The observations for time made at Washington are given in table II. I lie first and second columns do not require any explanation. The column “Observer” contains the initials of the person who made the observations, as follows: Ha. E. F. S. Professor William Harkness. Professor John If. Eastman. Assistant Observer Edgar Erisby. Assistant Observer Ormond Stone. llie column “J\ 0. of Wires" gives the number of wires over which the transit of the star was observed. All time-stars were observed by the chronographic method, and, as a rule, over nine wires; but azimuth-stars were observed by eye and ear, and generally over only five wires. The column “ Time of Transit over Mean of Wires ” con¬ tains the time of transit over an imaginary wire situated at the mean of the standard set of nine wires.. 1 or stars observed over all the wires of that set the mean of the observed tune* of transit is of course the time of transit over the mean wire, but for other stars the time of transit over the mean wire has been deduced from the observed times of transit by the application of the necessary corrections. The columns “Cc,” “Bbf and “ Aa ” contain the corrections for collimation, level, and azimuth. The numbers in the column Correction for Instrument" are the sums of the quantities in the three preceding cob umns. I he column Corr. lransit ’ contains the clock-time of transit over the merid= ian, obtained by adding together the quantities in the columns “Time of Transit over Mean of Wires" and “ Correction for Instrument." The column “Adopted Right Ascen¬ sion" contains the adopted apparent right ascensions of the stars observed. The column “Observed Clock Corr." contains the difference between the “Corr. Transit" and the WASHINGTON AND ST. LOUIS. “Adopted Right Ascension." The column v contains the difference between the observed and adopted clock corrections; or, in other words, the error of observation. The values of the constants employed during each night are as follows: Date. c b a s. s. s. April 12 — 0.02 - 0.15 + 0.02 23 .01 .14 - 0.15 # 26 .02 .08 .07 30 — 0.02 — O.II — 0.16 The constant c was obtained from observations on a pair of opposing collimators. Ij was obtained from observations of the spirit-level, two readings being made with it in a direct, and two with it in a reversed position, a was computed from the observed transits of Polaris, using for that purpose a closely approximate value of the clock correction. Full details as to the methods of determining these constants are given on pages xxvi—xxviii of the Washington Observations for 1870. DIFFERENCE OF LONGITUDE, I 2 Table II. — Transits of Stars observed at Washington to determine the Corrections to the Jvessels Sidereal Clock. Date. Star. Observer. No. of Wires. Time of Transit over Mean of Wires. Cc Bb A a Correction for Instrument. Corr. Transit. Adopted Right Ascension. Observed Clock Corr. V 1870. h. m. s. s. s. s. s. s. s. s. April 12 T Leonis Ha. 9 I I 21 18. II — 0. 12 — 0. 12 + 0.01 —0.13 17.98 16.00 -1.98 + .02 | V Leonis Ha. 9 30 20.54 .02 . 12 .01 -*3 20.41 18.51 1.90 — .06 P Leonis Ha. 9 42 28.72 .02 .14 .01 • 15 28.57 26.57 2.00 + .04 0 Virginis . Ha. 9 II 58 38.29 .02 -13 .01 .14 38.15 36.20 i -95 — .02 V Virginis . Ha. 9 12 13 18.50 .02 . 12 .01 •13 18.37 16.37 2.00 + .03 e Virginis . Ha. 9 13 3 16.48 — .02 — 0 . II .01 — O. 12 16.36 14-39 1.97 — .01 Polaris, S. P. . Ha. 5 13 10 29.50 +0.83 + 3-78 +0.66 + 5-27 34-77 32.75 — 2.02 April 23 V Leonis F. 9 11 30 24.28 — 0.01 — 0 . II — O.O9 — 0.21 24.07 18.45 —5-62 — .01 p Leonis F. 9 42 32.40 .01 • 13 .06 .20 32.20 26.51 .69 + .05 0 Virginis . F. 9 11 58 41.96 .01 .12 .07 .20 41.76 36.15 .6l -.04 V Virginis . F. 9 12 13 22.21 .01 .11 - .09 .21 22.00 16.35 •65 — .01 12 Canum Venat. F. 9 12 49 3-76 — .01 —0.18 0.00 .19 3-57 57-88 .69 -b.oi Polaris, S. P. . F. 5 13 10 42.10 +■ -41 + 3-53 - 4-93 • 99 41 . II 35-27 .84 S Bootis. F. 9 15 19 42.16 — .01 —0.18 0.00 .19 41.97 36.24 .73 -•03 a Cor. Borealis. F. 9 15 29 18.31 — 0.01 -0.15 —0.03 —0.19 18.12 12.33 - 5-79 + .03 April 26 T Leonis F. 5 II 21 23.19 — 0.02 — 0.07 —0.04 -0.13 23.06 15.90 -7.16 -•03 V Leonis F. 9 30 25.83 .02 .06 .04 . 12 25.71 18.43 .28 + .08 0 Virginis . F. 9 II 58 43-43 .02 .07 - .04 • 13 43.30 36.13 •17 -.05 12 Canum Venat. F. 9 12 50 5.20 •03 . 10 .00 • 13 5-07 57.87 .20 -•05 e Virginis . Ha. 9 13 3 21.70 — .02 —0.06 —0.05 - -13 21-57 14.41 . l6 + .06 Polaris, S. P. . F. 5 10 42.68 + .83 + 2.02 —2.30 + -55 43-23 35-95 .28 S Virginis . F. 9 28 12.88 — .02 — 0.06 0.04 — . 12 12.76 5-42 • 34 + .06 V Bootis. Ha. 9 13 48 38.14 .02 .08 •03 • 13 38.01 30.91 . 10 -■03 a Serpentis . F. 9 15 38 0.63 .02 .07 ,04 • 13 0.50 53-15 • 35 — .02 e Serpentis . Ha. 9 15 44 28.79 — 0.02 — 0.07 — 0.04 —0.13 28.66 21.44 — 7.22 + .01 April 30 0 Virginis . Ha. 9 11 58 45-19 — 0.02 — 0. 10 —0.08 — 0.20 44-99 36.11 -S.8S — .OI V Virginis . Ha. 9 12 13 25-43 .02 .09 . 10 .21 25.22 16.32 .90 + .01 p Corvi . Ha. 9 12 27 44.11 — .02 —0.06 0.15 0.23 43-88 34-93 •95 + .05 Polaris, S. P. . Ha. 5 13 10 48.10 + .83 +2.77 5-26 1.66 46.44 37-53 .91 a Virginis . Ha. 9 18 31.12 — .02 — 0.01 0. 12 0.21 30.91 22.06 .85 — .06 ? Virginis . Ha. 9 28 14-54 .02 .09 . 10 .21 14-33 5-43 .90 — .01 V Bootis. Ha. 9 13 48 40.00 .02 . II .06 .19 39.81 30.93 .88 -•03 a Bootis. Ha. 9 14 9 54-37 — 0.02 — 0 . II —0.06 —0.19 54.18 45.20 —8.98 + .06 WASHINGTON AND ST. LOUlS. 13 Each of the quantities in the column “Observed Clock Corr .” is equal to « — \_T' + Aa + Bb + Cc] which, for brevity, we will represent by n. Then each star observed furnishes an equation of condition of the form o = — n + A T 0 -f- R ( I — Tf) -(- v and from all the equations thus obtained on any given night the values of AT, and II for that night have been found by the method of least squares. Assuming T 0 — 1 i h o" 1 by the face of the Kessels clock, the equations of condition, normal equations, and resulting values of AT, and II, for each night, are as follows: Washington, Equations of Condition. 0 — + : - 9 S + Al, + 0.35 11 O m —b 1.90 -b A I g —f— o. 50 lb o —(- 2.00 —h A J 0 ~h o. 71 R o = + i-95 + AT 0 + 0.98 11 o — + 2.00 + AT, -f 1.22 It o — + 1 -97 H~ Al 0 -f- 2.05 11 April 12, 1870. Normal Equations. o — + 11.80 + 6.00 AT 0 -f- 5.81 11 0 — + 1J -45 + 5 -^ 1 A 1 0 + 7.53 It Hence S. s. AT, — — 1.954 ± 0.010 II —— 0.0133 Washington, 1 Equations of Condition. o = + 5.62 + AT," + 0.51 R o = + 5.69 + AT," + 0.71 R o = + 5.61 -f- ATf -J- 0.98 R o — + 5.65 + A1 0 -f- 1.22 11 o — 5.69 -f- AT, -(- 1.82 R ° — + 5-73 + AT'' -j- 4.33 R o = + 5-79 + AT 0 ' + 4.49 R Washington, I Equations c o — + 7 - I( ^ + AT ," -f- 0.36 R o — + 7.28 + AT ," + 0.51 R o — -j - 7- 1 7 ~h A 1 , -(- 0.98 R o — + 7 - 2 ° "T A 1 , -(- 1.83 II o — + 7.16 + AT , +2.06 R ’RIL 23, 1870. Normal Equations. o — + 39-78 + 7.00 AT," + 14.06 It o =r + 80.46 + 14.06 AT," + 45.43 R Hence AT," — — 5.615 ± 0.008 R — — 0.0335 PRIL 26, 1870. r ' Condition. o — d~ 7-34 + JT o" + 2.47 R o =r + 7.10 + AT, +2.81 R o — + 7-35 + *Tf + 4.63 R o — + 7-2 2 + AT, + 4.74 R DIFFERENCE OF LONGITUDE, H Normal Equations. 8 . ° = + 43 - 5 ° + 6.00 4T 0 " -J- o.oo BT 0 -f- 10.78 11 ° = + 21.48+ 0.00 BTf + 3.00 JT 0 + 9.61 n 0 = + I 47-58 + 10.78 JT 0 " + 9.61 AT 0 + 66.84 It Hence 4 T 0 " = — 7.176 + 0.016 0 = — 7.013 + 0.019 B — — 0.0423 Washington, Equations of Condition. o = + 8.88 + JT , + 0.98 B o =: + 8.90 + JT 0 + 1.22 B 0 — + 8.95 + 4 Tq + 1.46 It 0 — + 8.85 + 4 T 0 + 2.31 B 0 = + 8.90 + 4 T 0 + 2.47 B o z= + 8.88 + BT 0 + 2.81 It o = + 8.98 + 4 T 0 + 3.16 B April 30, 1870. Normal Equations. 8 . o — + 62.34+ 7.00 + 14.4! y> 0 — + 1 28-38 + 14.41 4 T 0 -\- 33.90 It Hence 4 T 0 — — 8.880 + 0.011 B — — 0.0121 As-will be shown farther on, Mr. Frisby observes the transit of an equatorial star o s . 121 later than T, and therefore we have 4 T n — J T 0 " + o s . 121 Hence, on April 23, 4T 0 = — 5 s -6i5+o s .i 2 i--5 s .494 + o«.ooS On April 26, Mr. Frisby’s observations give 4 T , — — 7 s . 176 + o s . 121 — — 71055 + o s .oi6 and my own give 4 B 0 = — 7 s -Q !3 + o s .oi 9 Taking the mean, we find 4B 0 — 7 -°34 i o s .oi4 Collecting our results, we have the expressions given in Table III for the correc¬ tions which must be applied to the time indicated by the face of the Kessels clock, in order to reduce it to sidereal time determined by myself at the meridian of the transit circle. T is the time indicated by the clock at the instant for which the correction is required, and the quantities after the sign + are approximately the probable .errors. Table III. — Corrections to.the Kessels Clock. Date. Correction. , April 12 s - s. h. s. — 1.954 — 0.0133 {T 1 — ir.00) ± 0.010 23 — 5-494 — 0.0335 {T' — 11.00) ± 0.008 26 — 7.034 — 0.0423 (T' — 11.00) ± 0.014 30 — S.8S0 — 0.0121 (T' — 11.00) ± 0.011 WASHINGTON AND ST. LOUIS. 15 St. Louis Observations. —The observations for time at St. Louis were made by Pro¬ fessor William Limbeck, and are given in Table IV. The first column contains the date. The column “Lamp” gives the position of the axis of the transit instrument; L. signifying that the lamp .was to the east, W. that it was to the west. The column “No. of Wires ” gives the number of wires over which the transit of the star was observed. The field of view of the instrument contained nine vertical wires, separated by intervals of about 15 seconds of time, but as a rule only the middle seven wires were used, and all observations were made by the eye and ear method. The column 11 Star” does not require any explanation. The column “Time of Transit over Mean of Wires ” contains the time of transit over an imaginary wire situated at the mean of the standard set of seven wires. For stars not observed over all the wires of that set the time of transit over the mean wire has been deduced from the observed times of transit by the application of the necessary corrections. The column “ b ” contains the observed values*of the level constant, each of them being derived from two readings of the spirit-level, one made with it in the direct, the other with it in the reversed posi¬ tion. The level is of the striding form, and each division of its scale is equal to o s .c>9. The columns “Bb” and’“Cc” contain the corrections for level and collimation. The column “r” contains the correction for rate of the chronometer. The column “Corr. Transit''' contains the sum of the quantities 111 the columns “Time of Transit over Mean of Wires ,” “Bbf “Co” and “r.” The column “Adopt'd Bight Ascension” contains the adopted apparent right ascensions of the stars observed. The column “Obs'd Chron Correction" contains the difference between the “Corr. Transit ” and the “Adopt'd Bight Ascension.'' The column “v” contains the difference between the observed and adopted chronometer correction; or, in other words, the error of observation. Throughout the whole series of time determinations the adopted value of B is —o s .o86; and the adopted value of c is -f- o s .2q for lamp west. The latter constant was obtained from transits of circumpolar stars, each observation being made over one-half the wires with the lamp west, and over the other half with lamp east. i6 DIFFERENCE OF LONGITUDE, Table IV.— Transits of Stars observed at St. Louis to determine the Corrections to the Sidereal Chronometer Kcssels and Dent No. 1287. Date. Lamp. No. of Wires. Star. Time of Transit over Mean of Wires. b Bb Cc r Corr. Transit. Adopt’d Right Ascension. Obs’d Chron. Correction. V 1870. April 12 E. 7 £ Hydras . h. m. s. 8 33 U -99 s. —0.09 s. —0.08 s, — 0.24 s. -0.05 m. s. 33 14-62 m. s. 39 53.6o m. s. + 6 38.98 s. — .02 E. 7 L Ursae Maj. . 43 40.78 • 13 • 19 • 36 .07 43 40.16 50 17.91 37-75 + .04 E. 7 K Cancri . 8 54 4 -Oi • 19 0.17 0.24 .08 54 3.52 0 42.51 38.99 -■13 E. 4 I Draconis . 9 11 54-42 1.09 1.70 .11 11 51.52 18 22.27 30.75 + .06 E. 7 a Hydra: . 14 33 - 6 o -0.15 —0.24 . 12 14 33.09 21 12.38 39-29 — .02 E. 5 p Cephei, S.P. 20 I4.2I .23 + .22 + .70 . 12 20 15.01 26 57.21 42.20 + .14 W. 7 t Leonis . 31 50.04 • 25 + .27 .26 •13 31 49.90 38 28.54 38.64 -.05 W. 7 t i Leonis . 38 43-89 • 17 • 19 • 27 •15 38 43.82 45 22.41 38.59 -.oS W. 4 a Leonis . 9 54 48.57 .09 .09 .24 •17 54 48.55 1 27.37 38.82 + .02 W. 7 P Librae . 15 3 23.16 .20 .14 .24 .01 3 23.25 10 1.90 38.65 + .02 W. 7 s Bootis . 11 58.53 .24 • 30 •03 11 58.56 19 36.07 37-51 + .09 W. 3 y 2 Ursae Min. . 14 25.43 .19 ■ 52 •79 •03 14 25.67 21 0.50 34-83 + .10 W. 5 a Coronae Bor. 22 34.24 • 17 .20 .27 •04 22 34.27 29 12.16 37-89 + .02 W. 7 a Serpentis . 31 14-53 • 15 + .24 •05 31 14.57 37 52.94 38.37 — .02 E. 7 £ Serpentis . 37 43-21 • 15 — 0.24 .06 37 42.76 44 21.21 38.45 — .06 E. 5 UrsaeMin. . 42 19.07 .68 1.17 .06 42 17.16 48 50.29 33-13 -.09 E. 6 yS 1 Scorpii . 15 5 i 15-33 —0.18 — 0.10 -0.25 —0.07 51 14.91 57 53.86 + 6 38.95 — .06 April 23 E. 5 I Draconis . 9 - 11 53-62 +0.10 +0.52 -1.70 -0.03 11 52.41 18 20.82 + 6 28.41 + .29 E. 7 a Hydrae . 14 46.81 + .05 — 0.24 •03 14 46.59 21 12.22 25.63 — .06 E. 6 p Cephei, S.P. 20 33.02 + .01 - .04 + .70 ■03 20 33.65 26 57.90 24.25 + .2S E. 7 £ Leonis . 32 2.9O .00 — . 26 •05 32 2.59 38 28.3s 25-79 + .05 E. 7 Leonis . 38 56.97 — .11 — . 12 •27 .06 38 56.52 45 22.25 25.73 + •13 E. 7 a Leonis . 9 55 1.96 . 16 • 14 0.24 .08 55 1.50 1 27.23 25-73 .OO E. 7 9 Draconis . 10 17 34.12 .18 .60 — 1.02 . 12 17 32.38 24 O.I4 27.76 -•31 W. 7 / Leonis . 36 0.31 • 25 .22 +0.24 . -14 36 0.19 42 25.99 25.80 — .oS W. 7 a Ursae Maj. . 10 49 15.53 .20 .40 • 52 . 16 49 15.49 55 42.23 26.74 — .26 W. 7 ti Leonis . n 0 46.54 .18 • 25 •17 0 46.44 7 12.25 25.81 .00 W. 6 d Crateris 6 26.13 • 17 .11 .24 .is 6 26.08 12 51-45 25-37 +.16 w. 7 A Draconis . 17 14-56 • 15 .38 • 70 .20 17 14.68 23 41-50 26.82 +.05 w. 7 P Leonis . 36 0.89 • 14 ■ 24 .22 36 0.77 42 26.51 25-74 + .02 w. 7 y Ursae Maj. . 40 33-90 • 15 .24 O.4I •23 40 33-84 47 0.29 26.45 — .20 w. 4 4 Draconis . 11 59 40.77 -0.15 -0.57 +1.19 —0.26 59 4 I-I 3 6 8.85 + 6 27.72 — .06 April 26 w. 4 I Draconis . 9 11 5691 0.00 0.00 + 1.70 —0.02 11 58.59 18 20.42 +6 21.83 +.65 w. 7 a Hydrae . 14 52.59 .00 +0.24 .03 14 52.80 21 12.iS I 9 . 3 S .00 w. 7 p Cephei, S.P. 20 40.66 - .07 + .07 - -70 •03 20 40.00 26 58.12 iS. 12 +•13! w. 7 £ Leonis . 32 8.46 • 05 - .05 + .26 •05 32 8.62 38 28.33 19.71 -.07! w. 7 Leonis . 39 2.47 .08 .09 .27 .06 39 2.59 45 22.20 19.61 +■05 ! w. 7 a Leonis . 9 55 7-49 .02 .02 •24 .08 55 7-63 1 27.17 19-54 .00 w. 6 r 1 Leonis . 10 6 28.33 — .01 — .OI 0.25 . 10 6 29.07 12 4S.50 19.49 +.11 w. 5 9 Draconis . 17 36.82 + .04 + -13 + 1.02 . 12 17 37 .S 5 23 59-94 22.09 — .S6 E. 4 a Ursae Maj. . 10 49 22.66 0.00 0.00 —0.52 I 1 —0.16 49 21.98 55 42.15 + 6 20.17 + . 20 1 WASHINGTON AND ST. LOUIS. l 7 Table IV .—Transits of Stars observed at St. Louis , &c. —Continued. Date. Lamp. No. of Wires. .Star. Time of Transit ovei Mean of Wires. b Bb Cc r I Corr. Transit. | Adopt’d Right Ascension. Obs’d Chron. Correction. V 1S70. h. m. s. s. s. s. s. m. s. m. s. m. s. s. April'26 E. 5 4 Lconis . 11 0 53.07 —0.05 —0.05 —0.25 -0.17 0 52.60 7 12.23 + 6 19.63 — . 02 • E. 5 X Draconis . 17 21-79 .06 • 15 .70 . 20 17 20.74 23 41.38 20.64 .OO E. 7 p Lconis . 36 7-57 ■ ■ .09 .25 . 22 36 7 - 0 i 42 26.49 19.48 4-.0S E. 7 7 Ursx Maj. . 40 40.93 .09 .15 •41 •23 40 40.14 47 0.25 20. 11 -.07 E. 7 0 Virginis . 52 17-26 .12 . 10 0.24 .24 52 16.68 58 36.13 19-45 +. 06 E. 6 4 Draconis . 11 59 4S.90 1 .12 .46 r.19 — .26 59 46.99 6 8.69 21.70 [ —. l6 E. 7 a 2 Librae . 14 37 24.30 . . .06 0.24 4- .02 37 24.02 43 42.74 18.72 ' 4- .02 E. 7 p Urspc Min. . 44 51-66 . . • 31 .91 4- .01 44 50.45 51 10.95 20.50 j —.OI E. 5 p Bootis . 14 50 45-57 .10 • 13 •31 .00 50 45-13 57 4-39 19.26 + .01 E. 7 p Librae . 15 3 43-73 ■ 15 . 10 •24 — .01 3 43-38 10 2 .II 18.73 + .07 E. 7 s Bootis . 13 17-57 .20 • 25 •30 .02 13 17.00 19 36.27 19.27 -.04 . E. 7 a Coronac Bor. 22 53.82 .21 • 23 .27 .04 22 53.28 29 12.3s 19.10 .OO E. 7 a Serpcntis . 31 34.So .19 • 1 7 -0.24 •05 3 i 34-34 37 53.17 is.S3 1 + .09 W. 5 c Ursx Min. . 42 29.61 .21 •79 + 1.17 .06 42 29.93 48 50.97 21.04 + .04 w. 7 E Coronx Bor. 45 54-58 •23 0.27 .07 45 54-55 52 13.70 19-15 -•03 w. 4 d 1 Scorpii . 5 i 35-39 • 17 . 10 •25 .08 5 i 35.46 57 54.15 18.69 + .01 w. 5 Groom. 2320 15 59 4i.i6 • . .28 .65 .09 59 41-44 6 1.40 19.96 4 - .06 w. 7 r Ilcrculis 16 9 32.17 .07 . 10 • 35 . 11 9 32.31 15 5 i. 7 o 19-39 — . 02 w. 5 7 Draconis . 15 56.34 .06 . 12 • 5 i . 12 15 56.61 22 16.44 19.83 -.10 w. 7 ? Ophiuchi . 23 42.36 •03 .24 . 12 23 42.45 30 1.27 18.82 -.03 w. 6 V Ilcrculis 16 36 8.33 — 0.04 -0.05 +0.31 —0.13 36 8.64 38 27.76 +6 19.30 .OO April 30 w. 2 I Draconis . 9 12 6.15 0.00 + 1.70 —0.02 12 7.83 18 19.87 + 6 12.04 — .62 w. 7 a Hydra . 14 59-36 .00 +0.24 •03 14 59-57 21 12.12 12-55 + .07 w. 5 /? Cephei, S. P. 20 46.08 — .02 + .02 - -70 •03 20 45.37 26 58.36 12.99 4 - .06 w. 7 £ Lconis . 32 15.66 .08 - .0.3 4 - . 26 •05 32 15.78 38 2S.27 12.49 + .03 w. 7 r Lconis . 39 9.56 .08 .09 4 - .27 .06 39 9-68 45 22.14 12.46 + .05 w. 3 79 Drac., S. P. 45 2.00 + .11 - .83 .07 45 1.21 51 14-50 13.29 -•15 w. 7 • a Lconis . 9 55 14-47 . II — . 10 4 - .24 1 .08 55 14.53 1 27.14 12.61 -•05 w. 4 32 Ursx Maj. . 10 2 21.Si .08 .17 0.59 .09 2 22.14 8 34-35 12.21 + .01 w. 7 9 Draconis . 17 46.74 — .02 - .07 1.02 1 . 12 17 47-57 23 59-64 12.07 — . l6 w. 7 1 Lconis . 36 13.16 .00 4-0.24 .14 36 13.26 42 25.91 12.65 -.09 w. 4 L Cephei, S. P. 38 49.86 .00 .00 - .58 .15 38 49- r 3 45 2.49 13.36 — .40 w. 7 a Ursx Maj.. 10 49 29.29 4- .04 -f- . oS 4- .52 . 16 49 29.73 55 42.01 12.28 — . IO 7 d Lconis . 11 0 59.94 + .02 + .02 - .25 .17 0 59-54 7 12.18 12.64 — .11 E. 5 d Crateris 6 39.22 - .03 . .24 .iS 6 38.77 12 51-37 12.60 + .04 E. 6 T Lconis . i 5 3-83 ; .06 .24 .19 15 3-34 21 15.87 12.53 + .05 E. 4 "k Draconis . 17 30-35 — .11 .28 .70 . 20 17 29.17 23 41.22 12.05 4- .08 E. 7 P Lconis . 36 14.61 .18 .25 .22 36 13.96 42 26.46 12.50 4 -.05 E. 7 7 Ursx Maj.. 40 48.93 •23 .38 .41 1 • 23 40 47.91 47 0.17 12.26 4-.10 E. 7 0 Virginis 52 24.36 •29 0.26 0.24 • 25 52 23.61 58 36.11 12.50 -b.07 E. 5 4 Draconis . 11 59 59.70 1.10 I . 19 ! .26 59 57.15 6 8.45 n.30 -f- . 48 E. 7 V Virginis 12 7 4-55 —0.30 0.23 0.24 . 26 7 3-82 13 16.31 12.49 4-.10 E. 6 K. Draconis . 12 21 47.81 —0.76 —0.72 — O.29 21 64.04 27 57.78 +6 11.74 4 -.14 3 —w s DIFFERENCE OF LONGITUDE, I 8 Each of the quantities in the column “ Obs'd Citron. Correction ” is equal to « - |\r Hb B (T - To) + Bb + 6V] wliich, for brevity, may be represented by n. Then we have O m n —(— A /o -b Ad —|— v But as throughout this series of observations n is very large, we write AT 0 — GfSG and the equation just given becomes o — — n Q SG Aa + v in which the absolute term, — n + G, may be made sufficiently small by choosing a suitable value of G. Each star observed furnishes an equation of condition of this form, and from all the equations so obtained on any given night the values of SG and a for that night have been found by the method of least squares. The adopted values of T 0 and G for each night, together with the equations of con¬ dition, normal equations, and resulting values of SO and a, are as follows: St. Louis, April 12, 1870. Equations of Condition; T , = 7 h 53“ 22 s o — — 8.98 -j- SG -f- 0.529 a o — — 7-75 + — 0.274 a o — — 8.99 -f- SG -j- 0.462 a o — — 0.75 -f- SG — 4.850 a o — — 9.29 -f- 8 G -f- 0.734 a 1st Group, 8 U to 1 o' 1 . G — 6 m 30 s .ooo s. o = - 12.20 + SG 4- 2.760 a o — — 8.64 + SG -f- 0.267 a o — — 8.59 -T -f- 0.232 a or=: — 8.82 -)- SG -f- 0.449 a Normal Equations. o — — 74.01 -f 9.00 SG -f- 0.34 a 0 — 52.10 + 0.34 SG -f 32.56 a Hence 60 = -fo 8.163 « = + o 1.515 41' 0 — + 6 38.163 d= o s .oi9 Equations of Condition; T 0 = 14 11 53 m 22 s o = — 8.65 + SG -)- 0.746 a o — — 7.51 -p + 0.017 a o = — 4.83 -f SG — 1.820 a o — — 7.89 + SG -j- 0.223 a 2 d Group, 15 11 to i6 u . G — -f- 6 m 3o s .ooo s. ° = —8.37 + -f- 0.530 a o — ' 8.45 + SG 4- 0.557 a 0 = — 3- x 3 + ~ 3- I2 o a o — — 8.95 + SG -f- 0.899 a WASHINGTON AND ST. LOUIS. 19 Normal Equations. 8 . o — — 57.78 + 8.00 ( 5 ( 9 — 1.970 o = — 6.97— 1.97 69 + 15.05 a Hence • m. s. <59 — 4-0 7.582 0 = 4-0 1.455 ^ Tq — 4" 6 37.582 + o s .oi8 St. Louis, April 23, 1870. Equations of Condition. T 0 = 8 h 53 “ 34 s o~ - 8.41 4- <59 — 4.850 a o — 5.634-<594-0.7340 O = — 4.25 4- <59 4- 2.760 0 o = — 5.79 4- <59 4- 0.267 a o = — 5.73 4- <594-0.232 o o = —5.73 4 -<59 4-0.4490 o = — 7.76 4- (59 — 2.600 o o = — 5.80 4- (59 4- 0.469 o 9 = -L 6 m 20 s .OOO 8 . o = — 6.74 4- (59 — 0.875 a o = — 5.81 —{- (59 4- 0.320 a o = — 5.37 4- <59 4- 0.820 o o = — 6.82 -f- <59 — 1.530 o o = — 5.74 (59 4- 0.411 a o = — 6.45 -|- <59 — 0.468 o o = — 7.72 -|- <59 — 3.160 o Normal Equations. o = — 93.75 4 - 15.00 <59 — 7.020 0 = 4 - 72 . 07 — 7.02 <59 4 - 53.24 o Hence Ill. S. 69 = + o 4988 o = — o 0.564 — 4 - 6 25.988 + o\o 33 St. Louis, April 26 , 1870 . Equations of Condition; T 0 = 8" 53“ 40 s o = —3.83 4-69 — 4.8500 o — — 1-38 + 694-0.7340 o = — o. 12 + 69 4- 2.760 a o — — 1.71 + 69 + 0.267 a o ~ — 1.61 + 69 + 0.232 o o — 1.54 + (59 + 0.449 o o = — 1.49 + < 5 0 +0.33 1 a o — — 4.09 + 69 — 2.600 o 1st Group, 9 h to 12 11 . 9 = 4-6“ 18 s .ooo s. 0 = — 2. 17 + 69 — 0.875 a o = — 1.63 + 69 + 0.320 o o = — 2.64 + 69 — 1.530 a o = — 1.48 + 69 -]- 0.411 o 0 = — 2. 11+ 69 — 0.468 a 0 = — 1.45 + 694-0.493 o o = — 3.70 + 69 — 3.160 o 20 DIFFERENCE OF LONGITUDE, Normal Equations. 8 . o = —30.95 + 15.00 < 50 — 7.49 a 0 = 4-42.64— 7.49 <50 + 52.70 a Hence m. s. <50 = + o 1.786 « = -o 0.555 4 r l 0 = 4-6 19.786 4 = o s .o57 Equations of Condition T 0 — 14'“ 5 3 m 4i s o = — 0.72 4- <50 4- 0.838 a o = — 2.50 4- <50 — 2.130 a o = — 1.26 -{- <50 — 0.052 a o = — 0.73 -f- <50 -f 0.746 a 0 = — 1.2 7 4- <5 0 4 ~ 0-0 1 7 a 0 = — 1.1 o -j- <50 -f- o.223 « o = — 0.83 4- <50 + 0.530 a o = — 3.04 -(- <50 — 3-120 a ; 2 d Group, 14 11 to 1 7 1 '. 0 = -f- 6 m 18 s .ooo 8 . 0 = — 1.15 4“ <50 4“ 0.222 a o = — 0.69 4- <50 4* 0.899 a o = — 1.96 4- <50 — 1.330 a o = — 1.39 4- <50 — 0.189 a o = — 1.83 4- (50 — 0.836 a o = — 0.82 4- (50 4- 0.764 a o = — 1.30 4- <50 — 0.011 a Normal Equations. o = — 20.59 4- 15-oo (50 — 3.43 a 0 = 4-15.92— 3.43 <50 4- 19.81 a Hence m. s. (50 = 4-0 1.237 a — — o 0.590 4 T 0 = + 6 19.237 4= 01009 St. Louis, April 30, 1870. Equations of Condition. T 0 = 8” 53 m 48 s 8 . o = — 0.04 -f (50 — 4.850 a o = — 0.55 -f 60 + 0.734 a o = — 0.99 -j- <50 4- 2.760 a o = — 0.49 4- <50 4 - O- 2 67 a o = — 0.46 4- <50 -f- 0.232 a o = — 1.29 4- <50 4~ 3.190 a o = — 0.61 4- <50 4- 0-449 a 0 = — 0.21 -f (50 — 1.11 o a o = — 0.07 4- <50 — 2.600 a o = — 0.65 -j- <50 4- 0.469 a o = — 1.36 -j- <50 4- 2.340 a 0 = 4-6™ 12 s . 000 o = — 0.28 4- (50 — 0.875 a o = — 0.64 4- <50 4- 0.320 a o = — 0.60 <50 4- 0.820 a o = —0.53 4- <504-0.574(1 o = — 0.05 4- <50 — 1.530 a o = — 0.50 <50 4 - 0-4 11 a o = — 0.26 <50 — 0.468 a o = — 0.50 + <50 4- 0.493 « 0 = 4- 0.70 <50 — 3.160 a o = — 0.49 -j- <50 -}- 0.622 a 0=4-0264- <50 — 1.580 a H-H- WASHINGTON AND ST. LOUIS. 2 I Normal Equations. S. o — — 9.61 -f- 22.00 dO — 2.49 a 0=1—14.56- 2.49 se + 73.59 a Hence 111. s. 60 — + o 0.461 a — -f o o. 214 AT 0 — A 6 12.461 A o s -031 These values of AT 0 apply to the sidereal chronometer Kessels and Dent No. 1287. But in the exchange of longitude signals the mean-time chronometer Dent No. 2748 was employed, and its corrections were determined every evening, both before carry¬ ing it to, and after bringing it back from, the telegraph-office, by comparing it with No. 1287 by the method of coincidence of beats. The comparisons on each night, together with the resulting expressions for the corrections of No. 2748, are as-follows: April 12.—When No. 1287 indicated y h 53 1,1 12 s its correction was -f- 6 m 38 s . 163 A: o s .oi9, and when it indicated 14 1 ' 53"' 22 s its correction was + 6 m 37 3 .582 A: o s .oi8. It was therefore gaining o s .o 83Q per hour. Chronometer Comparisons. Before going to Telegraph-Office. After returning from Telegraph-Office. No. 1287. No. 2748. No. 12S7. No. 2748. h. m. s. h. m. s. 10 11 14.0= 8 53 36.0 14 20.5 = 56 42.0 17 25.0 = 59 46.0 h. m. s. h. m. s. 14 39 32.0 “ 13 21 10.0 42 39.0 = 24 1C.5 "4 s' 43-0 = 27 20.0 Hence, if T is the sidereal time at the meridian of the transit instrument, and T' the time indicated by No. 2748, we have T — T' A k 1 2 4 ra 3 b s .575 + 9 s -783 (T' — i’i h ) Az o 3 .oiS April 23.—When No. 1287 indicated 8 U 53” 1 34 s its correction was -f- 6 m 25 3 .988 01033; and when it indicated 8 h 53” 1 40 s on April 26, its correction was A 6 m i9 s -786 o s .057. It was therefore gaining o 3 .o86i per hour. Chronometer Comparisons. Before going to Telegraph-Office. After returning from Telegraph-Office. No. 1287. ■ No. 2748. No. 1287. No. 2748. h. m. s. h. m. s. 12 4 24.0 =10 3 25.0 7 29.5 = 6 30.0 10 35.0 = 9 35.0 h. m. s. li. m. s. 15 1 33.0 =13 0 5.0 4 35-0 = 3 6.5 6 39.0 = 6 10.0 T — T ' A 2 11 7 m 33 s - 9 22 + 9 s - 7 6 5 ( t ' ~~ 1 i h ) zb o. s 033 Hence 22 DIFFERENCE OF LONGITUDE, April 26.—When No. 1287 indicated 8 h 53" 1 40 s its correction was + 6 m i9 8 .786 Az o 8 .057; and when it indicated 14'* 53“ 41 s its correction was -f- 6 ra i9 8 .237 Az o\oog. It was therefore gaining o s .09i5 per hour. Chronometer Comparisons. Before going to Telegraph-Office, After returning from Telegraph-Office. No. 1287. No. 2748. No. 1287. No. 2748. h. m. s. h. m. s. h. m. s. h. m. s. 12 9 31.0 = 9 56 45.0 14 22 33.0 = 12 9 25.O 12 40.0 = 9 59 53.5 25 39 -° = 12 30.5 15 42.0 =10 2 55.0 28 39.0 — 15 30.0 Hence T — T' -)- 2’ 1 19 111 i5 s .869 -f- 9- s 862 ( T 1 — 1 i h ) Az 0^030 April 30.—When No. 1287 indicated 8 1 ' 53 111 40 s , on April 26, its correction was -f- 6 m 19 s .786 Az o s .057; and when it indicated 8 h 53™ 48 s , on April 30, its coiTection was + 6 m i2 s .46i Az o s .03i. It was therefore gaining o s .o763 per hour. Chronometer Comparisons. Before going to Telegraph-Office. After returning from Telegraph-Office. No. 1287. No. 274S. I No. 1287. No. 2748. h. m. s. h, m. s. 12 27 10.5 = 9 58 40.0 30 16.0 =10 1 45.0 33 2T.5 = 4 50.0 h. m. s. h. m. s. 14 56 25.0 12 27 30.0 14 59 30.0 =■ 30 34.5 15 2 34.0 = 33 33.0 Hence T —T‘ A- 2 11 34 111 5 2 s . 701 + 9 s -Soi ( T / — 1 i u ) Az o s .o31 Collecting our results, we have the expressions given in Table V for the correc¬ tions which must be applied to the time indicated by the face of the mean-time chro¬ nometer Dent No. 2748 in order to reduce it to sidereal time at the meridian of the transit instrument. T' is the time indicated by the chronometer at the instant for which the correction is required, and the quantities after the sign Az are approximately the probable errors. Table V. —Corrections to the Chronometer Bent No. 2748. Date. Correction. h. m. s. s. h. s. April 12 + 1 24 36.575 + 9.7S3 {T 1 — 11.00) ± 0.018 23 + 2 7 33.922 + 9.765 {T’ — it. 00) ± 0.033 26 + 2 19 15.869 -I- 9.S62 ( T 1 — ix. 00) ± 0.030 3 ° + 2 34 52.701 + 9.801 ( T ' — 11.00) ± 0.031 WASHINGTON AND ST. LOUIS. 2.3 VI.—PERSONAL EQUATION. In the beginning of August, 1870, Professor Eimbeck came to Washington, bring¬ ing with him his sidereal chronometer Ivessels and Dent No. 1287, and his portable transit instrument C. S. No. 7. The latter was soon mounted on the collimator pier to the north of the transit circle and our relative personal equation was determined in the following manner: Professor Eimbeck and I made observations for time simultaneouslv, he using his own chronometer and portable transit instrument, and I using the transit cir¬ cle, the Ivessels clock, and chronograph. As far as possible we both employed the same stars. At the conclusion of each night’s work he took my observing-key, and, by tap¬ ping upon it in coincidence with the beats of his chronometer, recorded upon the chro¬ nograph connected with the Ivessels clock a series of signals similar to those which he sent from St. Louis when making telegraphic comparisons of time for difference of longitude. The correction necessary to reduce the local time determined by him to that determined by myself thus became known, and as his instrument and mine were in precisely the same meridian, this correction is evidently the required personal equa¬ tion. The observations for time made at Washington with the transit circle are given in Table VI, the arrangement, of which is similar to that of Table II. The values of the constants employed during each night are as follows: Date. C b a August 5 s. + O.O4 s. — 0.21 s. — 0.02 8 + .05 - .24 — .01 12 + .05 - -23 - -03 15 0.00 — 0.27 — 0.24 24 DIFFERENCE OF LONGITUDE, Table VI .—Transits of Stars Observed at Washington with the Transit Circle to deter¬ mine the Corrections to the Kessels Sidereal Clock Date. Star. Observer. No. of Wires. Time of Transit over Mean of Wires Cc Bb 1 A a 1 Correction for Instrument. Corr. Transit. Adopt’d Right Ascension. Obs’d Clock Correction. 1870. h. m. s. s. s. s. s. i s. s. s. S. 1 Aug. 5 K Ophiuchi . Ha. 9 16 52 15.60 +0.04 — 0.19 —0 01 —0.16 15-44 32.49 -42.95 — . IO d Herculis . Ha. 9 16 57 33 -H • °5 .25 .00 .20 32.91 49-75 43 -16 + .10 C Sagittarii . IL, 9 18 6 44.63 .04 0 . II — .02 O.O9 44 - 5.4 1.49 43-05 .OO (l Ursx Minoris Ha. 5 ’ 15 13.60 t- .67 +2.38 + -25 -r.46 12.14 2S.55 43-59 51 Ccphei, S. P. . Ha. 5 iS 39 8.75 - -8 3 + 2.56 - -33 + 1.40 10.15 27-94 42.21 7 Aquilx Ha. 9 19 40 50.04 + .04 — 0.19 .01 —0.16 49.88 6.91 42.97 — .OS ft Aquilx ; Ha. 9 49 41.06 0.04 0.18 — .01 0.15 40.91 57.82 43-09 + .05 X Ursx Minoris Ha. 4 19 55 55-55 2. T I 7.14 + .81 4.22 51-33 12.58 38.75 U ' 2 Capricorni Ha. 9 ro O CO O -t-0.04 —0.13 — 0.02 — 0 . II OI U» CO 52.72 —43.06 -j- .02 Aug. 8 n Herculis . Ha. 9 16 39 11.42 +0.06 -0.31 0.00 —0.25 II.17 27.72 - 43-45 -•03 H Ophiuchi . Ila. 9 16 52 16.10 • 05 0.21 .00 . 16 15-94 32.45 43-49 + .01 E Ursa; Minoris Ha. 5 17 0 9.59 • 37 1.29 + .05 .87 8.72 25.49 43-23 a 1 Herculis . Ha. 9 9 2S.43 • 05 0.23 .OO .18 28.25 44.81 43-44 -.04 44 Ophiuchi . Ila. 9 17 19 11.53 • 05 0. 12 — .or 0.08 11.45 27.94 43-51 + .03 6 Ursx Minoris S. 7 18 15 11.70 +0.84 -2.72 + .12 -1.76 9-94 27-54 42.40 5 i Cephei, S. P.- . S: 5 39 8.50 — 1.03 +2.93 — -17 + I -73 10.23 29.17 41.06 0 Lyrx . S. 9 18 46 2.64 +0.06 — O.29 .00 -0.23 2.41 18.87 43-54 + .02 K . Aquilx Ila. 9 19 30 39.67 • 05 • 17 — .01 •13 39-54 56.02 43-52 + .04 y Aquilx Ha. 9 40 50.52 • 05 .21 .00 . l6 50.36 6.91 43-45 -.°3 0 Aquilx S. 9 49 4 I -48 0.05 0.20 — .01 0.16 41.32 57 -S 2 43-50 — .02 X Ursx Minoris S. 4 19 55 58.82 +2.64 -8.16 +0.41 - 5 - n 53-71 IO.65 — 43 -o 6 Aug. 12 Polaris, S. P. . S. 5 13 12 38.60 — 2.07 + 5-80 —0.98 + 2-75 4.1 • 35 56.82 - 44-53 a Virginis . F. 9 19 5.91 +0.05 -0.15 .02 — O. 12 5-79 21.23 44-56 + .01 Virginis . F. 9 13 28 49.31 • 05 . 18 .02 • 15 49.16 4-63 44-53 — .02 £ Bootis. F. 9 14 40 3.89 .06 • 25 .01 . 20 3-69 I 9 -I 5 44-54 .OI a 2 Librae . . F. 9 44 26.97 • 05 .14 - -03 . 12 26.85 42.31 44-54 — .OI 0 Bootis. F. 9 14 57 48.23 .07 • 30 .00 • 23 48.00 3 37 44-63 . oS 0 Librx . F. 9 15 10 46.53 • 05 . l6 — .02 • 13 46.40 1.87 44-53 — .02 a 1 Herculis . Ha. 9 17 9 29.46 • 05 2° .01 .iS 29.28 44-76 44-52 +.05 a Ophiuchi . Ha. 9 29 40.32 •05 .21 • OI • 17 40.15 55.68 44-47 .00 i u Herculis . Ha. 9 17 42 8.61 .06 .26 .OI .21 8.40 23-93 44-47 .00 c Sagittarii . Ha. 9 iS 6 46.07 .05 O. 12 - -03 O. 10 45-97 1.44 44-53 +.06 6 Ursx Minoris Ha. 5 15 11.65 .84 2,60 + -37 i -39 10.21 26.22 43-99 I Aquilx Ha. 9 28 54.62 •05 0.16 — .02 0.13 54-49 10.00 • 44-49 +.02 a Lyrx . Ha. 9 33 18.79 +.0.06 — O.29 .OO —0.23 18.56 34-20 44-36 —. 11 51 Cephei, S. P. . S. 5 j8 39 13.22 -1.05 +2.81 - -50 + 1.27 14.49 30.77 43-72 6 Aquilx S. 9 19 19 43.36 +0.05 — O.I9' .02 —0.16 43-20 58.73 44-47 -.oS K Aquilx S. 9 30 40.76 •05 . 16 .02 • 13 40.63 56.02 44.61 +.06 7 Aquilx s. 9 40 51.61 0.05 0.21 — 0.01 0.17 51-44 6.90 44-54 — .01 X Ursx Minoris s. 5 19 55 56.26 2.64 7.82 + 1.22 3-96 52.30 7.82 44 - 4 S £ Delphini . s. 9 20 27 47.08 0.05 0.21 — 0.01 O. 17 46.91 2.36 44-55 .00 I Pegasi s. 9 21 .16 51.49 •05 •23 .01 .19 5 I -30 6.79 44-51 -.04 0 Aquarii s. 9 21 25.29.87 +0.05 —0.16 — 0.02 — 0.13 29.74 45 -i 6 - 44 - 5 S + .03 WASHINGTON AND ST. LOUIS. 25 Table VI. — Transits of Stars Observed at Washington, dec. — Continued. Date. Star. Observer. No. of Wires. Time of Transit over Mean of Wires. Cc Bb A a ! Correction for Instrument. Corr. Transit. Adopt’d Right Ascension. Obs’d Clock Correction. V 1870. h. m. s. s. s. s. s. s. s. s. s. Aug.15 a Ophiuchi . E. 9 17 29 41-47 0.00 —0.25 —0.11 — 0.36 41. II 55-63 -45-48 + .03 u Herculis . Ha. 9 42 9-52 .00 • 30 •05 ■35 9.17 23.88 45-29 — .06 y 2 Sagittarii . E. 9 m CO 15-44 .00 . II .26 • 37 15.07 29.67 45-40 -.04 C Sagittarii . Ha. 9 is 6 47.19 .00 0.15 —0.22 • 37 46.82 1.41 45-41 + .07 6 Ursae Minoris H.&E. II 15 IO.QI .00 3.06 +3.00 .06 vn 00 6 25-30 45-55 I Aquilae Ha. 9 28 55-69 .00 0.19 —0.18 ■ 37 55-32 9.98 45-34 .00 a Lyrae . E. 9 33 19.88 .00 -0.35 0.00 • 35 19-53 34-15 45 - 3 S -.05 51 Cephei, S. P.. H.&E. i 1 39 18.31 .00 + 3.29 -4.01 • 72 17-59 31.82 45-77 p Lyrae . Ha. 9 18 46 4.49 .00 —0.32 0.03 • 35 4.14 18.79 45-35 + .02 ? Aquilae E. 9 ig 0 13.90 .00 • 25 . 11 •36 13-54 2S .09 45-45 .02 (5 Aquilae Ha. 9 19 44.41 .00 . 22 .14 •36 44-05 58.71 45-34 .OI n Aquilae E. 9 30 41-83 .00 .19 .17 • 36 41.47 56.01 45.46 + .04 y Aquilae Ha. a 40 52-53 .00 .24 . 12 • 36 52.17 6.89 45.28 -.04 a Aquilae E. 9 19 45 14-37 0.00 — O. 24 — 0.12 —0.36 T 4 . 0 I 28.60 - 45-41 — .01 Assuming T 0 — i6 b o m by face of the Kessels clock, and 0 — — 4 o s .ooo, the equations of condition, normal equations, and resulting values of 69 and R for each night are as follows : Washington, August 5, 1870. Equations of Condition. Normal Equations. o o o o o o — T 2.95 + 60 -(- 0.87 R — -}- 3.16 -j- < 5<9 -f- 0.96 R — + 3-05 + 60 + 2.11 R — + 2.97 + 69 + 3.68 R — + 3-°9 + d# + 3-^3 A — + 3.06 + 69 -f- 4.19 R o = +18.28 + 6.00 69 + 1 5.64 R o ~ + 47.62 + 15.64 69 + 51.90 R Hence s . 69 — — 3.046 R — + 0.0004 RT 0 — — 43.046 + o s .o2 2 Washington, August 8, 1870. On this evening observations were made by two persons, and therefore two values of RT 0 have been introduced in the equations. 4—w s 26 DIFFERENCE OF LONGITUDE, Equations of Condition. 8 . Or= +3.45 + ( 50 + o + 0.65 72 0 — H“ 3-49 89 + o + 0.87 H 0 — + 3-44 + 89 + o + 1.16 It 0 = + 3 - 5 1 f 89 f- o +1.32/1! ° = + 3-54 + 0 + 89 "'f- 2.77 It o = + 3 .52 + ( 50 + o +3.51/2 o — + 3-45 + 89 + o +3.68/2 0=r + 3. 5 0+ O + 69 "' + 3.83 It Normal Equations. o = + 20.86 + 6.00 39 + 0.00 39 "' +11.19 72 o — + 7-°4 “l - 0.00 39 + 2.00 89 "' + 6.60 72 o = + 62.16 + 11.19 39 + 6.60 39 "' + 52.47 11 Hence 89 — 3.475 89 '" — — 3-518 72 — — 0.0011 s 4 T 0 = — 43.475 + 0.010 JT 0 '" = — 43-518 + 0.014 Washington, August 12, 1870. On this evening observations were made by three persons, and therefore three values of the clock correction have been introduced in the equations. Equations of Condition.. 0 = + 4.56 + 39" + 0 + 0 - 2.68/2 ° = + 4-53 + 89" + 0 + 0 — 2.52 72 °- + 4-54 + 89 " + 0 + 0 — i-33 72 0 — + 4-54 + 89" + 0 + 0 — 1.26/2 0 = + 4-63 + 80" + 0 + 0 — 1.03 72 0 = + 4-53 + 89" + 0 + 0 - 0.82 72 0=1 + 4.52 + 0 + 89 + 0 + 1.16 72 0 — + 4-47 + 0 + 39 + 0 + 1.49 72 0 — + 4-47 + 0 + 39 + 0 + 1.70 72 0 — + 4-53 + 0 + 89 + 0 + 2.11 72 0 — + 4-49 + 0 + (50 + 0 + 2.48 72 0=1 + 4.36 + 0 + (50 + 0 + 2.5 6 72 0 — + 4-47 + 0 + oE 89"' + 3-33 72 O nz —(— 4.61 0 + of-39"' + 3 - 5 i 72 0 — + 4-54 + 0 + of- 89 '" + 3-68 72 ° = + 4-55 + 0 + of-89"' + 4.46 72 0 — + 4 - 5 1 + 0 + of-69'" + 5.28 72 0 = + 4-58 + 0 + 0 + 39'" + 5.42 72 WASHINGTON AND ST. LOUIS. * 27 Not mat Equations. O 2= + 27-33 + 6.00 59" + 0.00 59 + 0.00 59"‘ ' — 9-64 R O 2= + 26.84 0.00 59" + 6.00 59 + 0.00 59'" ' + 11.50 R O 2= + 27.26 0.00 59" + 0.00 <50 + 6.00 59"' ' + 25.68 R O 2= + 124.18 — 9.64 59" + 11.50 59 + 25.68 59"' ' + 156.33 R Tice 59" — 8. - 4-554 59 — - 4-474 59'" — - 4-545 R — + 0.0005 S. 4T 0 " 2= - 44-554 ± 0.01 I JT 0 — - 44-474 ± 0.017 JT'" — — 44-545 ± 0.014 Washington, August 15, , 1870. On this evening observations were made by two persons, and therefore two values of the clock correction have been introduced in the equations. Equations of Condition. S. o = + 5.48 + 59 ' + o + 1.50 It 0=2 + 5.29+ 0 + 59 +1.70 It o = + 5.40 + 59 ' + 0+1.97 It o —+ 5.41+ o + d <9 + 2.11 12 o = + 5.34 + o + < 50 + 2.48 E o — + 5-38 + 8d ' + o + 2.56 12 0=2 + 5.35 + o + <50 + 2.77 R o = + 5.45 + 59 ' + o + 3.00 R 0=2 + 5.34+ o + 60 + 3.33 R o =2 + 5.46 + 59 ' + o + 3.51 R o — + 5.28 + o + 59 + 3.68 R 02= + 5.41 + 59 ' + o + 3.75 R Normal Equations. o = + 32.58+ 6.00 59' + 0.00 59 + 16.29 12 o = + 32.01+ 0.00 59' + 6.00 <50 + 16.67 12 o = + 174.11 + 16.29 + 16.07 6# + 93.86 R 59' =2— 5.465 59 —— 5.370 R — + 0.0129 s . 4 T 0 ' — — 45465 ±'0.010 4 T„ 2= —45.370 + 0.013 Hence 28 DIFFERENCE OF LONGITUDE, The observations for time made at Washington by Professor Eimbeck with the poitable tiansit instinment ( . S. iso. 7 are given in I able VII, the arrangement of which is similar to that of Table IV. These observations were reduced by*Professor Keith of the Coast Survey, who adopted, throughout the whole series, U —_o s . 032 , and c — + o s -547 with lamp west. The latter constant was determined from measures made with the right-ascension micrometer of the transit circle; that instrument being- used as a collimator to the portable transit instrument. As already explained, some of the right ascensions employed by Professor Keith differed slightly from those used at this Observatory, and on that account a few small changes have been made in his reductions by Mr. Frisby and myself. WASHINGTON AND ST. LOUIS. 2 9 Table VII. —Transits of Stars Observed at Washington bg Professor William Eimbeck with the Portable Transit Instrument C. S. No. 7 , to determine the Corrections to the Sidereal Chronometer Kessels and Dent No. 1287 . Date. d, S No. of Wires. Star. Time of 1 Transit over Mean of Wires. b Bb Cc r Corr. Transit. Adop’d Right Ascension. Obs’d Chron. Correction. V 1870. h. m. s. s. s. s. s. 111. S. m. s. m. s. s. Aug. 5 E. 3 £ Ursae Min.. l6 4 13-32 +0.09 4-0.48 — 4.08 4-0.03 4 9-75 59 25-97 +5516.22 +0.76 E. 7 44 Ophiuchi . 23 10.53 .06 ■ 03 0.60 .02 23 9.98 18 27.97 17.99 .02 E. 6 CJ Draconis . 42 29.12 • 07 • 17 1-52 4- '.01 42 27.78 37 45-31 17.53 + .08 E. 7 y Draconis . l6 58 20.28 • 04 .06 0.89 .00 58 19-45 53 37-33 17.88 - • 65 E. 5 S Sagittarii . 17 10 43.62 0.04 0.59 .00 10 43-07 6 1.50 18.43 - • 43 E. 4 J Ursae Min. . 19 21.20 . 11 4-1.25 - 9-30 .00 19 13-15 14 28.44 15.29 + • 44 E. 5 51 Cephei, S.P. 17 42 57.81 . 11 -i -34 4-11.40 — .02 43 7.85 38 28.06 20.21 + .44 E. 5 j Aquilae . r3 23 41.14 4-0.09 - 0-55 .04 23 40.64 18 58.74 18.10 - . l6 E. 7 li Aquilae . 34 38.39 . 11 .oS •55 .04 34 37-88 29 56.03 18.15 .18 E. 6 y Aquilae. 44 49-43 . 10 •56 • 05 44 48.92 40 6.92 18.00 • 07 E. 7 a Aquilae . 18 49 11.02 . 10 • 55 • 05 49 10.52 44 28.61 18.09 . l6 E.? 7 a * Capricorni. 19 15 35-19 + 0 . II 4-0.07 — 0-57 —0.06 15 34-63 IO 52.72 +5518.09 0. 11 Aug. 8 E. 7 / 3 1 Scorpii . 15 2 38.51 4-0.01 — 0.58 4-0.06 2 a 38.00 57 54-34 +5516.34 +0.10 E. 6 r Herculis . 20 36.03 +0.02 .03 .80 • 05 20 35-31 15 51-24 15-93 - .08 E. 7 r S Ophiuchi . 34 45-89 4 - .03 .02 -56 •04 34 45-39 30 1.69 16.30 + .08 E. 7 7 Herculis . 43 12.50 4- .02 • 7 i .04 43 11.85 38 27.72 15-87 .07 E. 7 K Ophiuchi . 15 56 16.83 .00 •56 .04 56 16.31 5 i 32.45 16.14 .09 E. 6 Herculis I C ) 1 34-50 • i - -03 0.66 • 03 I 33-84 56 49-70 15-86 .14 E. 4 £ Ursae Min.. 4 17-18 - -07 •38 4-05 • 03 4 12.79 59 25.50 12.71 + .46 E. 7 a 1 Herculis . 12 29.16 .oS .08 0.56 • 03 12 28.55 8 44.81 16.26 - .08 E. 7 44 Ophiuchi . 23 11.96 - .04 - 0.60 • 03 23 n-35 18 27.94 16.59 .11 E. 3 Gr’m.g66,S.P. 27 0.51 4 - .11 4- 2.10 .02 27 2.74 22 21.15 18.41 • 54 E. 6 a Ophiuchi . 33 40.08 .06 - -05 - 0.56 .02 33 39-49 28 55-72 16.23 - .04 E. 6 0) Draconis . 42 31-92 . 11 .26 - 1.52 4- .01 42 30.15 37 45 •16 15.01 +0.18 W. 7 y Draconis . 16 58 20.79 .09 • 14 4 - 0.88 .00 58 21-53 53 37-25 15-72 - I . 72 w. 7 C Sagittarii . 17 10 44.36 •03 0.59 .00 10 44-92 6 1.48 16.56 - O. II w. 3 <5 Ursae Min.. 19 10.24 .01 — .11 4 - 9.24 .00 19 19-37 14 27.43 8.04 + 1.10 w. 4 5 i Cephei, S.P. 17 43 15-74 - .04 -H • 4 ^ - H -34 - .01 43 4.87 38 29.28 24.41 + 0.70 w. 7 c Aquilae . 18 4 11.40 4- .01 .01 4 - 0. 56 •03 4 11.94 59 28.14 16.20 - .01 w. 7 d Sagittarii . 14 46.86 .01 • 58 • 03 14 47.42 10 3-95 16.53 + .10 w. 7 6 Aquilae . 23 41.88 •03 .02 •55 .04 23 42.41 18 58.74 16-33 - .06 w. 7 Aquilae . 34 39-23 .01 • 55 .04 34 39-75 29 56.03 16.28 + . 12 w. 7 y Aquilae . 44 50.15 .02 • 56 • 05 44 50.68 40 6.91 16.23 - .02 w. 7 a Aquilae . 18 49 H -77 4-0.02 4-0.02 4 - 0-55 —0.06 49 12.28 44 28.61 + 55 16.33 — O. 10 Aug. 12 E. 7 6 Ophiuchi . T 5 12 20.33 —0.04 -0.03 — 0.55 4-0.06 12 19.81 7 33-40 + 55 13-59 + 0.12 E. 7 V Draconis . 27 3-49 — .01 — .02 I . l6 • 05 27 2.36 22 15.14 12.78 . l6 E. 7 Ophiuchi . 15 34 48.44 .00 0.56 ■ 05 34 47-93 30 1.61 13-68 0.17 Ef 3 £ Ursae Min.. l6 4 19-65 + .05 4-05 •03 59 15-68 59 24.86 9.18 + 1.04 E. 7 a 1 Herculis . l6 13 31.96 4-0.03 4-0.03 — 0.56 4-0.03 13 34-46 8 44-75 + 55 13-29 +0.03 / DIFFERENCE OF LONGITUDE, O Table VII .—Transits of Stars Observed at Washington, dee. —Continued. Date. Lamp. No. of Wires. | Star. Time of Transit Over Mean of Wires. b Bb Cc r Corr. Transit. Adop’d Right Ascension. Obs’d Chron. Correction. V 1870. h. m. s. s. s. S. s. m. s. m. s. m. s. s. Aug. 12 E. 7 44 Ophiuchi . 16 23 14.74 + 0.02 +0.01 — 0.61 +0.03 23 14-17 18 27.89 +5513-72 —0.09 E. 7 a Ophiuchi . 33 42.86 + .03 + .03 0.56 .02 33 42.35 28 55.68 13-33 + .01 E. 6 (j Draconis .. 42 34.22 - .04 — . 10 1.52 + .01 42 32.61 37 44-96 12.35 —0.04 E. 7 y Draconis . 16 58 25.01 — .02 - -03 0.88 .00 58 24.10 53 37-15 13-05 — 1.98 E. 7 /1' Sagittarii . 17 10 48.43 • • + .01 0.59 .00 10 47.85 6 i -44 13-59 + 0.01 E. 3 S Ursae Min. . 19 29.99 + .05 + -57 - 9.24 .00 19 21.32 14 26.11 4-79 + 1.30 E. 2 51 Cephei,S.P. 42 56.32 + .01 — . 12 + H -34 — .02 43 7-52 38 30.78 23.26 -0.75 E. 2 51 Cephei,S.P. 17 43 20.54 — .06 + -73 -H -34 .02 43 9 - 9 1 38 30.78 20.87 + 1.64 W. 7 £ Aquilae. iS 4 14.27 — .02 — .02 + 0.56 •03 4 I 4-78 59 28.11 13-33 —0.08 W. 7 (5 Aquilae . 23 44.78 .OO .OO ■55 •03 23 45-30 18 58.72 13-42 .01 W. 7 it Aquilae . 34 42.00 .OO .OO •55 .04 34 42.51 29 56.02 I 3 - 5 I .02 W, 7 y Aquilae . 44 52.83 .OO .56 .05 44 53-34 40 6.90 13-56 .20 W. 7 a Aquilae . 49 14.50 — .OI •55 •05 49 15.00 44 28.60 13.60 • 23 W. 7 P Aquilae . 18 53 43 -S3 .OI •55 •05 53 44-32 48 57 - 8 i 13-49 . IO, W. 7 e Delphini . 19 31 48.44 — .02 .02 • 56 .07 31 48.91 27 2.36 13-45 . 10 W. 6 a Cygni . 19 41 48.88 — 0.02 —0.03 + 0.77 —0.08 41 49.54 37 2.62 + 55 13-oS —0.07 Aug. 15 W. 7 r ) Herculis 15 43 16.34 — 0.01 — 0.01 + 0.71 +0.04 43 17 -oS 3 S 27.58 + 55 10.50 — 0. 10 W. 7 k Ophiuchi . 15 56 21.03 + -03 0.56 •03 56 21.65 5 i 32.35 10.70 - .09 w. 3 e Ursae Min.. 16 4 12.34 + .05 .26 4-05 •03 4 16.68 59 24-35 7.67 + .28 w. 7 44 Ophiuchi . 23 16.26 .04 0.60 •03 23 16.93 18 27.85 10.92 + .05 w. 7 a Ophiuchi . 33 44 -iS .14 . 12 0.56 .02 33 44-88 28 55.61 10.73 - .oS w. 7 w Draconis . 42 33-24 .09 .22 1.52 + .02 42 35-00 37 44-79 9-79 0.07 w. 7 y Draconis . 16 58 25.80 .08 . 12 •0.88 ,.00 58 26.80 53 37-07 10.27 2.00 w. 7 ft 1 Sagittarii . 17 10 49.97 .05 •59 .00 10 50.61 6 1.41 10.80 0.14 w. 7 7 Serpentis . 19 25.41 . II +0.08 + 0.55 .00 19 26.04 14 36.87 10.83 - -05 w. 4 51 Cephei.S.P. 43 26.07 . 12 — 1.46 — 11-34 — .01 43 13-26 38 31-84 18.58 +0.27 E. 3 51 Cephei,S.P. 17 43 1.48 .20 —2.44 + H -34 .02 43 10.36 38 31-84 21.4S 1.06 E. 7 f Aquilae . 18 4 18.09 • 25 +0.23 — 0.56 .02 4 17-74 59 28.09 10.35 0.0S E. 7 d Sagittarii . 14 53-79 • 25 .14 .58 •03 14 53-32 10 3.93 10.61 .08 E. 7 (5 Aquilae . 23 48.66 • 19 • 55 . •03 23 48.27 18 58.71 10.44 .08 E. 7 k Aquilae . 34 45-99 .22 • 15 • 55 .04 34 45-55 29 56.01 10.46 .20 E. 7 y Aquilae . 44 5 6 -86 .10 • 56 .04 44 56.45 40 6.89 10.44 + .10 E. 7 a Aquilae. 49 18.52 .10 •55 •05 49 18.09 44 28.59 10.50 — .02 E. 7 P Aquilae . 18 53 47.92 .19 0.10 0-55 •05 53 47-47 48 57-So 55 10.33 + -17 E. 2 /I Ursae Min. . 19 0 51.84 . IO 3 - 4 i 29.05 .06 0 26.14 55 6.05 54 39-91 .58 E. 7 ft Aquarii. 50 30-75 0.08 0.56 .08 50 30.19 45 40.78 55 10.59 • 03 E. 7 v Cygni . 19 57 12.74 | +0.12 +0.16 — 0.72 —0.09 57 12.09 52 22.19 + 55 10.10 +0.01 WASHINGTON AND ST. LOUIS. The adopted values of T 0 and 0 for each night, together with the equations of con- ition, normal equations, and resulting values of 60 and a, are as follows: Washington, August 5, 1870. Equations of Condition. T 0 = 17’ 1 4™ 42 s s. O rr + 1.78 + SO — 5.120a O rr + O.OI + SO -(- 0.971a o — + 0.47 + do — 1.390 a o — -)-o. 12 + ( 50 — 3.600 a o = - 0.43 + 60 + 0.923 a o — + 2.71 + 60 — 12.520 a Normal 0 — + 55 m 18 s .000 o — — 2.21 + SO -]- 16.860 a o — — 0.10 + SO -f- 0.584 a o — — 0.15 + SO -(- 0.724 a o rr 0.00 +60 + 0.481a o —— 0.09 + SO + 0.506 a o — — 0.09 + 50 + 0.802 a Equations. 0=2+ 2.02+12.00 69 — 0.78 a o — — 82.06— 0.78 SO + 485.89 a Hence 111. S. 60 — — o 0.158 a — + o 0.169 JT 0 = ES5 1 7-84 2 rt o s .o 8 o Washington, August 8, 1870. Equations of Condition. a 1 _ T . ui . . s h — 1 7 4 44 S. Or: - O.34 + SO + 0.899 a o rr + 0.07 + SO — 0.189 a o = — 0.30 + SO + 0.764 a orr + o. 13 + dO — 0.011 a o — — 0.14 + SO + 0.492 a o rr + 0.14 + 60 + 0.101 a O rr + 3.29 + SO — 5.1 20 a o rr — 0.26 + SO + 0.421 a o — — 0.59 + SO + 0.971 a Orr— 2.41 + SO + 3.530 a O rr — 0.23 + SO + 0.448 a 0 — + 55“ i6 s .ooo S. Orr+ O.99+ 60— 1.390 a O rr + 0.28 + 60 — 3.600 a Or — 0.56 + 60 + 0.923 a o =r + 7.96 + 60 — 12.520 a o — — 8.41 + 60 + 16.860 a Orr: — 0.20 + 60+ 0.433 a Orr — 0.53 + 60+ 0.894 a o — 0.33 + 60 + 0.584 a Orr — 0.28 + 60+ 0.724 a o —— 0.23 + 60+ 0.481a Orr —0.33 + 60+ 0.506 a Normal Equations. Orr — 2.28 + 22.0060+ 6.20 a o == — 272.33 + 6.20 60 + 500.77 a SO — — o 0.050 a — + o 0.543 z/T 0 rr + 55 15.950 rb O.071 Hence DIFFERENCE OF LONGITUDE, Washington, August i 2, 1870. Equations of Condition. To — 17" 4 ’" 47 s 8 . o — — 0.59 + 60 + 0.676 a o — + 0.22 + 60 — 0.836 a o — — 0.68 + 69 + 0.764 a o — + 3.82 + 60 — 5.120 a o — — 0.29 -f- 60 + 0.421a 0 = — 0.72 + 604- 0.971 a 03 — 0.33 + 60+ 0.448 a o —+ 0.65 + 60 — 1.390 a 0 = — 0.05 + 60 — 3.600 a o — — 0.59 + 60+ 0.923 a o — + 8.21 +60 — 12.520 a 6 — + 55 m 1 3 8 -°°o o — — 10.26 + 60 + 16.860 a 0 = — 7.87 + 60+16.860 a o = — 0.33 + 60 + 0.433 a o — 0.42 + 60 4“ 0.584 a o 13 — 0.51 + 60 + 0.724 ^ 0 = — 0.56 + 60+ 0.481 a o — — o.6o + 60 + 0.506 a o 3; — 0.49 + 60+ 0.540 a o = — 0.45 + 60 + 0.473 a o 3; — 0.08 + 60 — o. 140 a Normal Equations. o — — 11.92 + 21.0060+ 18.06 a o 3i — 433.16 + 18.06 60 + 772.36 a Hence 60 3:+ O 0.087 « = + o 0.559 3: + 55 13-087 db o s . 109 Washington, August 15, 1870. A preliminary reduction of tlie observations showed that there was something wrong about the adopted value of the collimation constant, and therefore a term involv¬ ing a correction to it has been introduced in the equations of condition. Equations of Condition. T 0= 1 y h 4 U1 50 s s. 03:— 0.50 + 60+ 1.296c— 0.011 a o — — 0.70 + 60+ 1.01 6c + 0.492 a o = + 2.33 + 60+ 7.426c— 5.120 a 03 — 0.92 + 60+ 1.09 6c + 0.971 a o 3= — 0.73 + 60+ 1.02 6c + 0.448 a 03:+ 0.21+60+ 2.776c— 1.390 a 0 = — 0.27 + 60+ 1.61 6c— 3.600 a 03=— o. 8 o + 60 + 1.07 6c + 0.923 a 03— 0.83 + 60+ 1.00 6c + 0.663 a 03 — 8.58 + 60 — 20.72 6c + 16.860 a 03— 11.48 + 60 + 20.72 6c + 16.860a 03 + 55'" io s .ooo s. 03— 0.35 + 60— 1.03 6c + 03— o. 6 i + 60 — 1.06 6c + 03— 0.44 + 60— 1.00 6c + 03— 0.46 + 60— 1.01 6c + 03— 0.44 + 60— 1.02 6c + 03— 0.50 + 60— 1.01 6c + 03— 0.33 + 60— 1.01 6c + o 3 + 30.09 + 60 — 52.89 6c — 03— 0.59 + 60— 1.01 6c + 03— 0.10+60— 1.326c — 0-433 a 0.894 a 0.584 a 0.724 a 0.481 a 0.506 a 0.540 a 40.680 a 0.747 a 0.046 a WASHINGTON AND ST. LOUIS. 33 Normal Equations. o r= + 4 .oo+ 2 i.oo( 50 — 44.08 dc — 8.72 a or - 1634.97 — 44.08 89 + 3738.42 8 c + 2102.63 a or — 1578.74 — 8.72 89 + 2102.63' 8 c + 2270.36 a Hence 89 — + o 0.274 8 c z r + o o. 102 a — + o 0.602 zJT 0 rr + 55 10.274 ± O s .o85 C r + o 0.649 Relative Personal Equation of Mr. Frisby and Processor Harhiess .—If RT 0 represents the correction to the Kessels clock at any given instant, as determined by me; and RT 0 ", the same correction as determined by Mr. Frisby; then the observations of April 26 give, R Pq — Rd 0 +0/163 and those of August 12 give, ' RT 0 = RT 0 " + o s .o8o The mean is, RT,- RT 0 " + o s .i2i which I adopt. Relative Personal Equation of Professors Eimbeck and Harkness .—111 any case in which it is desired to determine personal equation, suppose that a comparison of the time-pieces of the senior and junior observers shows that when the face of the former indicates the time T s , the face of the latter indicates the time Tq and let RT S be the correction to the time-piece of the senior observer, as determined from his observa¬ tions; RT j: the correction to the time-piece of the junior observer, as determined from his observations; and m, the interval by which the .junior observer notes the transit of an equatorial star later than the senior observer. Then, if RT S and Rl) have been determined at the same meridian, T s + RT S — Tj + R Tj + m and hence m=T s -T j + RT s -RT j In the case of a single time-piece, if at any given instant its correction is RT' s from the observations of the senior observer, and RT- from the observations of the junior observer, then R T s — RTj + m Considering all differences of longitude as essentially positive, if the senior observer occupies the station, rn, taken with regard to its proper sign, must be j subtracted from j the observed difference of longitude in order to free it from the effects of personal equa¬ tion. ( western l eastern 5 —W S 34 DIFFERENCE OF LONGITUDE, Designating by 'J\ the time indicated by the Kessels clock, and by 1 ) the time indicated by the chronometer Kessels and Dent No. 1287; the comparisons of time¬ pieces, and the computation of m from the observations given above are as follows: Comparisons of Time-Pieces to determine Personal Equation. Date. No. of Signals. T , Tj r , - Tj 1870. h. m. s. h. m. s. m. t s. August 5 37 21 O Cl II xrs T Cl O 14 11.66 + 56 0.79 8 37 20 10 11.04 = 19 14 n.66 55 59-38 12 37 21 2 9.25 == 20 6 11.66 55 57-59 15 37 20 4 7-30 = 19 S 11.66 1 + 55 55-64 Each line in the column 11 No. of Signals n gives the number of signals read from the chronograph-sheet, the mean of which furnished the comparison recorded on the same line. Computation of the Value of m. Date. A T , A Tj * AT , - A Tj c : 1 ! m 1870. m. s. m. s. m. s. m. s. s. August 5 - 0 43.04 + 55 17.76 - 56 0.80 + 56 0.79 - 0.01 8 0 43.48 55 15.88 55 59-36 55 59-38 + 0.02 12 0 44.47 55 12.99 55 57-46 55 57.59 0.13 15 - 0 45.32 + 55 10.21 - 55 55-53 + 55 55-64 + 0 . II 1 he values ot m apparently divide themselves into two groups—the results of the first two nights agreeing with each other, and the results of the last two nights agree¬ ing with each other. However, as there is no reason for supposing that the observa¬ tions on one night are better than those on another, I have adopted the general mean, which is o m — + o s .o 62 i o 8 .c>2 5 As Professor Eimbeck occupied the western station during the exchange of longi¬ tude signals, this quantity must be subtracted from the observed difference of longitude in order to free it from personal equation. VII.—EXCHANGE OF TIME-SIGNALS, AND RESULTING DIFFERENCE OF LONGITUDE. The telegraph-line between Washington and St. Louis is made up entirely of wire stretched in the air, but, as it is 990 miles long, it cannot be worked in a single circuit. It was therefore divided into three circuits, and the signals were transmitted from each circuit to the next following by means of automatic repeaters, which were placed at Graf- WASHINGTON AND ST. LOUIS. 35 ton and Cincinnati. The number of statute-miles of wire, exclusive of that on the magnets, and the amount of battery, in each circuit, were as follows: Washington to Grafton , 335 miles: at Washington, 60-modified Grove cells coupled up for quantity in two parallel series of 30 cells each; at Grafton v 50 Grove cells. Grafton to Cincinnati , 310 miles: 50 Grove cells at Grafton; 64 Grove cells at Cincinnati. Cincinnati to St. Louis , 345 miles: 62 Grove cells at Cincinnati; 60 Grove cells at St. Louis. The signals employed in determining the difference of longitude were made by breaking 1 a closed galvanic circuit; a method which seems best because the magnets used in telegraphing are much more certain to open promptly when the circuit is broken than to close promptly when it is re-established. This is true of a circuit including only a single magnet, but it applies with far greater force when, as in the present case, the signals are transmitted through several circuits by means of repeaters. As the observer at St. Louis had neither a clock, a break circuit chronometer, nor a chronograph, it was necessary to employ other means in making the telegraphic com¬ parisons of time-pieces there. The plan adopted is fully explained in the PROGRAMME FOlt THE EXCHANGE OF LONGITUDE-SIGNALS. 1. Local sidereal time will be determined at each station by observing- transits of stars in the usual manner. As the telegraph-wires do not extend to the observing-station at St. Louis, whenever signals are to be exchanged it will be necessary for the observer there to go to the telegraph-office in the Merchant’s Exchange, carrying with him a mean time box-chronometer beating half-seconds. The distance between the observing-station and the telegraph-office is about one and a half miles, and to avoid the chance of undetected tripping of the chronometer while being carried, it must be compared with the standard sidereal chronometer each evening immediately before starting from, and immediately after returning to, the observing-station. 2. Every afternoon the observer at St. Louis will notify the observer at Washington as to the state of the weather, and if it is clear at both places arrangements will be made to exchange signals in the evening. The hour of making the exchange will necessarily depend very much upon the convenience of the telegraph company, but it will usually be practicable to obtain the use of the wires some time between 10 p. m. and midnight. 3. The telegraph-office in the Merchant’s Exchange at St. Louis, and the United States Naval Observatory at Washington, having been put in communication, the observer at the former will ask the observer at the latter if he is ready to receive signals, and, upon getting an affirmative reply, the St. Louis observer will wait until his mean-time chronometer indicates 50 seconds, and then he will send a rattle by means of his break-circuit key. This rattle will consist of ten or fifteen dots made at the rate of about five per second. At the beginning of the next minute he will com¬ mence sending his first series of signals. This will consist of thirteen taps on his key, made in exact coincidence with the beats of his chronometer at o, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and o seconds; a pause of five seconds, and a rattle. At the beginning of the next minute he will com¬ mence sending his second series of signals. This will consist of eleven taps on his key, made in coincidence with the beats of his chronometer at o, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 seconds; a pause of five seconds, and a rattle. At the beginning of the next minute he will commence sending his third series of signals. This will consist of thirteen taps on his key, made in coincidence with the beats of his chronometer at o, 10, 20, 30, 40, 50, o, 10, 20, 30, 40, 50, and o seconds; a pause of five seconds, and a rattle. The three series of signals, from the beginning of the first rattle to the end of the last rattle, will occupy about four minutes and twenty seconds; and immediately upon their 3 6 DIFFERENCE OF LONGITUDE, completion the observer at Washington will notify the observer at St. Louis whether or not they have been properly received. If they have not been, they will be repeated ; if they have been, the observer at St. Louis will telegraph to the observer at Washington the hour and minute indicated by the chronometer at the beginning of the first series. The observer at St. Louis will of course preserve a record of the hour and minute indicated by the chronometer at the commencement of each of the series of signals. These signals will all be transmitted to Washington, where they will record themselves upon the chronograph sheet along with the beats of the Washington clock, and, as the probable error of a single signal is only about T o s .o34, they will furnish a very accurate comparison of time-pieces. 4. As soon as the observer at Washington has been notified of the hour and minute corre¬ sponding to the beginning of the first series of signals from St. Louis, he will ask the observer there if he is ready to receive signals from Washington, and upon receiving an affirmative reply he will connect the Washington sidereal clock with the telegraph-line in such a manner that its pendu¬ lum will break the circuit for somewhat less than one-tenth of a second every time it passes the central point of its arc, thus making a break once every second. In addition, the beginning of each miuute will be marked by a double break—that is, by a break interpolated midway between the break corresponding to o seconds and that corresponding to 1 second. These signals will be transmitted to St. Louis and there rendered audible bj- means of a sounder so adjusted that its back stroke is much louder than its forward one. Sitting beside this sounder, and keeping his eye upon his mean time chronometer, the observer at St. Louis will wait until the back stroke 1 of the sounder coincides with the beat of the chronometer; and when this occurs he will note the time indicated by the latter, and also the time of arrival of the next follow¬ ing double break. Three such coincidences will be recorded, and, as they occur at intervals of about three minutes, the time required for so doing will not generally exceed twelve minutes. As soon as the double break following the third coincidence has been received, the observer at St. Louis will open the circuit and ask the observer at Washington what hour and minute of his clock corresponded to the break in question. The observer at Washington having furnished the desired information, the two stations will bid each other “good night,” and this will close the exchanges for the evening. N. B.—Although there will generally be an uncertainty of three or four seconds as to the exact instant when the beat of the sounder coincides with that of the chronometer, still special care must always be taken to note whether the coincidence occurs at a whole or at a half-second beat of the chronometer. " , The record of signals received at St. Louis, from Washington, on the evening of April 12, together with their reduction, is appended in order to show how the com¬ parison of time-pieces is deduced from the coincidences of beats observed in the manner just described. Coincidence of breaks with beats of chronometer. Next follow ing double break. h. tn. s. s. to 45-0 32.0 20 44-5 31-5 23 40.0 31.0 — 14’ 1 42™ o s .o Wash. Clock. As the double break corresponds to o seconds of the Washington clock, if from the seconds of the time of coincidence of beats, (increased by 60 when necessary,) the seconds of the time of the next following double break are subtracted, the remainder will be the seconds indicated by the face of the Washington clock at the time of the coincidence of beats. Thus, for the first coincidence recorded aboye, 45 s -0 — 32 S -Q = i3 s -o 1 The back stroke is used because it corresponds to the break. The forward stroke corresponds to the subsequent closing of the circuit. WASHINGTON AND ST. LOUIS. 37 The last recorded coincidence and doable break give, not only the seconds of the Washington clock, but the hour and minute also ; thus furnishing the means of sup¬ plying the hour and minute to each of the other coincidences. Applying this pro¬ cess to the record given above, we obtain: Kessels Clock. Chronometer Dent No. 2748. h. m. S. ll. 111. s. H 35 13.0 z= 12 17 45 -o 38 13.O = 20 44-5 4 1 9.0 =z 23 40.0 If we let AX — difference of longitude between two stations; west longitudes being taken as positive; T e — time by face of eastern clock when it sends a signal, and T w — time by face of western clock when that signal is received at the western station; T' w — time by face of western clock when it sends a signal, and T' e = time by face of eastern clock when that signal is received at the eastern station; t.— time occupied in the passage of a signal from one station to the other; AT e , z 1 T W , AT' e , AT' w — respectively, the corrections necessary to reduce the times indicated by the faces of the eastern and western clocks to true local time at the instants T e , T w , T' e , T' w , then, neglecting personal equation, when the eastern clock sends and the signals are received at the western station, we have AX - t = (T-T w ) + (AT-AT W ) and when the western clock sends, and the signals are received at the eastern station, we have zbl + t = ( T' e -T ' w ) + (. AT'-AT' W ) Hence + ( ^T e -AT W ) + ( AT' e — AT' w ) 2 ' 2 - (T e — T l0 ) (AT' e -AT' w )-(AT e -AT w ) 2 2 If the rates of the clocks are small, the second term in the expression for the value of t may usually be neglected. The following are the results of the telegraphic comparisons of time-pieced, both at Washington and St. Louis, together with their reduction by means of the formulae just given, used in connection with the data contained in the preceding pages. By way of explanation it is only necessary to remark that each line in the column headed 11 No. of Signals ” gives the number of signals read off from the chronograph-sheet, the mean of which furnished the comparison recorded on the same line. 38 DIFFERENCE OF LONGITUDE, Comparisons of Time-Pieces obtained bg reading off the Washington Chronograph-Sheets. Date. No. of Signals. j Kessels Clock at Washington. Dent 2748 at St. Louis. Means. T ' , - T'u 1870. h. m. s. h. m. s. h. m. s. h. m. s. h. m. -! s. j April 12 13 14 3 53.22 == 11 46 30.