LIBRARY OF THE UNIVERSITY OF CALIFORNIA. RECEIVED BY EXCHANGE Class THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS BY EDITH D. KAST A THESIS PRESENTED TO THE FACULTY OF PHILOSOPHY OF THE UNIVERSITY OF PENNSYLVANIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY lnESS OF LANCASTER. PA. 1909 THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS BY EDITH D. KAST A THESIS PRESENTED TO THE FACULTY OF PHILOSOPHY OF THE UNIVERSITY OF PENNSYLVANIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY PRESS OF THE NEW ERA PRINTING COKPANT LANCASTER, PA. 1909 THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. The stars whose right ascensions and proper motions are discussed in this paper are the stars now used by Prof. C. L. Doolittle in his investigation of the variation of latitude at the Flower Observatory of the University of Pennsylvania. For his work the declina- tions of these stars have been reduced in the same way as the right ascensions are in this paper. With Prof. Doolittle's permission the data of the declinations and the results of that investigation are given tor the sake of completeness in this. THE CATALOGS. The following catalogs were employed as the basis of the reduction. For all catalogs for which Boss* gives systematic corrections and weights these have been used. In other cases such corrections and weights have been derived indirectly through Auwers'f system but Auwers' weights have been multiplied in right ascension by .694 and in declination by 1.414 to bring them more nearly into accordance with Boss 1 weights. For a few, weights were derived through Davis' J assignment by comparing with catalogs common to both Boss and Davis. In a few cases, special methods were used which are designated in the explanatory notes that accompany. In these notes s designates the systematic correction in right ascension, s' that^in declination,^* the weight in right ascension and p' that in declination. 1. BRADLEY. 1755. Neue Reduction der Bradleyschen Beobachtungen aus den Jahren 1750 bis 1762. Von Arthur Auwers. St. Petersburg, 1888. 2. LALANDE. 1800. A Catalogue of those Stars in the Histoire Celeste Frangaise of Jerome de Lalande for which tables of reduction to the epoch 1800 have been published by Prof. Schumacher. Francis Bailey, Esq. 5 and 5' same as 4. Very small weights were given Lalande's places, t was taken from the Paris catalogs. 3. D'AGELET. 1800. Reduction of the Observations of Fixed Stars made by Joseph Lepante dAgelet at Paris in 1783-1785 with a catalog of the Corresponding Mean Places referred to the equinox of 1800.0. By B. A. Gould. Washington, 1866. 5 = o'.i2 + reduction from Auwers to Boss 5' == Piazzi i".42 o h to XIP 5' = Piazzi + i".22 XIP to XXIV * Cf. Astronomical Journal, Nos. 549-550. f For the reduction to Auwers' system cf. Auwers' "Tafeln zur Reduction von Sterncatalogen auf das System des Fundamentalcatalogs des Berliner Jahrbuchs " published as Supplement No. 7 to Astronomische Nackrichten, also Ast. Nach., Bd. 134, Nos. 3195-3196 for a few other catalogs. For the reduction from Auwers' system to Boss' cf. Ast. Journal, v. 23, p. 22. For Auwers' weights cf. Ast. Nach., Bd. 151, No. 3615. JCf. "Declinations and Proper Motions of Fifty-six Stars." 3 228152 4 THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. 4. PIAZZI. 1800. Prascipuarum stellarum inerrantium Positiones Media; Ineunte Seeculo XIX ex observationibus habitas in Specula Panormitana ab anno 1792 ad annum 1813. Panormi, 1814. 5. GROOMBRIDGE. 1810. A catalog of Circumpolar Stars deduced from the observations of Stephen Groombridge at Blackheath Observatory. Edited by George Biddell Airy, Esq. London, 1838. The new reduction of Groombridge by Dyson and Thackeray of the Royal Observatory, Greenwich, came after the work was finished but the reduction in declination was revised for those stars whose place in the new differed more than .5" from that in Airy's. For Airy's s' as in Boss' Declinations of Fixed Stars. U. S. Northern Boundary Commission. Report of the Chief Astronomer. Appendix H. 6. DORPAT. 1815. 7. WEISSE-BKSSEL. 1825. Bessel's zone observations reduced by Maximillian Weisse. p = .i, s' = o. 8. AUWERS' KONIGSBERG. 1825. Auwers' reduction of some newly found zone observations made by Bessel. The reduction based on Auwers' system. 9. ABO. 1830. DLX Stellarum Fixarum Positiones Mediae ineunte anno 1830 ex observa- tionibus Aboee habitas deduxit. Fredr. Guil. Aug. Argelander. Helsingforsias, 1835. 10. STRUVE. 1830. Stellarum Fixarum imprimis duplicium et multiplicium pro epocha 1830. Petropli, 1852. 11. STRUVE. 1832. 12. STRUVE. 1836. 5, 5', p and -p' as for Dorpat, 1830. 13. MADRAS. 1835. A General Catalog of the Principal Fixed Stars from Observations made at the Honorable East India Company's Observatory at Madras in the years 1830 to 1843. By Thomas Glanville Taylor. Madras, 1844. 14. RUMKER. 1836. Mittlere Oerter von 12,000 Fixsternen fur den Anfang von 1836, abgeleitet aus den Beobachtungen auf der Hamburger Sternwarte von Carl Rumker. Hamburg, 1852. 15. ARMAGH. 1840. Places of 5345 Stars observed from 1828 to 1854 at the Armagh Ob- servatory. By Rev. T. R. Robinson. Dublin, 1859. 16. GREENWICH. 1840. Catalogue of 2156 Stars formed from the Observations made from 1836 to 1841 at the Royal Observatory, Greenwich. London, 1849. 17. OELTZEN'S ARGELANDER. 1842. Annalen der K. K. Sternwarte in Wien. Bd. i. Wien, 1851. s, s', -p and p' same as for Abo. 18. GREENWICH. 1845. Catalogue from Observations from 1842 to 1847. 19. PARIS. 1845. Catalogue de 1' Observatoire de Paris. Etoiles observees aux Instru- ments Meridiens de 1837 a 1853. 20. RADCLIFFE. 1845. The Radcliffe Catalogue of 6317 Stars, chiefly Circumpolar reduced to the Epoch 1845. Formed from the Observations made at the Radcliffe Observatory under the Superintendence of Manuel John Johnson. Oxford, 1860. 21. GILLISS. 1850. A Catalogue of 1963 Stars and of 290 Double Stars observed by the U. S. Naval Astronomers during the Expedition to the Southern Hemisphere. Appendix i to Wash- ington Yearly Observations for 1868. 22. GREENWICH. 1850. Catalogue of 1576 Stars formed from Observations made during Six Years, from 1848 to 1853, at the Royal Observatory, Greenwich. 23. MADRAS. 1850. A Subsidiary Catalogue of 1440 Stars selected from the British Asso- THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. 5 ciation Catalogue, reduced to Jan. i, 1850, from Observations made at Madras in the years 1849 to 1853. Madras, 1854. 24. SONNTAG. 1850. Mittlere Oerter fur 1850 von Vergleichsternen zum Cometen I 1850. Ast. JVach., Bd. XXXIV. -p same as 19 ; 5= .050 + reduction from Auwers to Boss; 5' as in Auwers for Busch 1838 + reduction from Auwers to Boss. 25. WROTTESLEY. 1850. A Catalogue of the Right Ascentions of 1009 Stars contained in the Catalogue of the British Association for the Advancement of Science. By Lord Wrottesley. Memoirs R. A. S., Vol. XXIII. Based on Nautical Almanac. 26. ALTONA. 1855. 5 and s 1 as for Sonntag 1850. 27. POULKOVA. 1855. Positions Moyenne deduites des observations faites au cercle meridien 1840-1869 et reduites a 1'epoque 1855.0. Observations de Poulkova, Vol. VIII. St. Petersburg, 1889. 28. GREENWICH. 1860. Seven Year Catalogue of 2022 Stars deduced from Observations extending from 1854 to 1860 at the Royal Observatory, Greenwich. 29. PARIS. 1860. Catalogue de I'Observatoire de Paris. Etoiles observees de 1854 a 1867. 30. RADCLIFFE. 1860. Second Radcliffe Catalogue, containing 2386 Stars deduced from observations extending from 1854 to 1861 . Oxford, 1870. 31. YARNALL. 1860. Catalogue of Stars Observed at the United States Naval Observatory during the years 1845 to 1877. Third edition revised . Washington, 1889. 32. GREENWICH. 1864. New Seven Year Catalogue of 2760 Stars, deduced from Observa- tions extending from 1861 to 1867 at the Royal Observatory, Greenwich. 33. BRUSSELS. 1865. Catalogue de 10,792 Etoiles observees a I'Observatoire Royal de Bruxelles de 1857 a 1878 . Par Ernest Quetelet. Bruxelles, 1887. 34. POULKOVA. 1865. Ascensions droites Moyenne des Etoiles occasionnellement observees pour 1865.0. Observations de Poulkova, Vol. XII. 35. GLASGOW. 1870. Catalogue of 6415 Stars for the Epoch 1870, deduced from Obsert vations made at the Glasgow University Observatory during the Years 1860 to 1881. By Rober- Grant. Glasgow, 1883. 36. GREENWICH. 1872. Nine Year Catalogue of 2263 Stars deduced from Observations extending from 1868 to 1876, made at the Royal Observatory, Greenwich. 37. BONN. 1873. (One observation from this was taken from Kiistner's Veroffentlichung der Koniglichen Sternwarte zu Bonn, No. 2, but Bonn 1873 was not found.) 38. ASTRONOMISCHE GESELLSCHAFT ZONES. 1875. These include all of this series between 26 and 53. p and f taken as i.o. Based on Auwers' system. 39. ARMAGH. 1875. Second Armagh Catalogue of 3300 Stars for the Epoch 1875, deduced from Observations made at the Armagh Observatory during the Years 1859 to I &&3- Dublin, 1886. 40. BECKER. 1875. Resultate aus Beobachtungen von 521 Bradley'schen Sternen am grossen Berliner Meridiankreise von Dr. E. Becker. Berlin, 1881. Based on Auwers'. 41. KAM. 1875. Catalog von Sternen deren Oerter durch selbstandige Meridian Beobach- tungen bestimmt worden sind aus Band 67 bis 112 der Ast. Nach. reducirt auf 1875.0. Amster- dam, 1901. The original observations were looked up and given such weights as seemed best in each case. 42. WASHINGTON. 1875. The Second Washington Catalogue of Stars prepared under the Direction of J. R. Eastman. 43. PARIS. 1875. Catalogue de I'Observatoire de Paris. Etoiles observees de 1868 a 1881. 6 THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. 44. POULKOVA. 1875. Catalog von 5634 Sternen fur die Epoche 1875.0, aus den Beobach- tungen am Pulkowaer Meridiankreise wahrend der Jahre 1874-1880 von H. Romberg. St. Petersbourg, 1891. 45. STOCKHOLM. 1875. Results of Meridian observations found in the first five volumes of the publications of the Stockholm Observatory, p and^V same as 43. Based on Auwers' S3 r stem. 46. RESPIGHI. 1875. Catalogo delle Declinazione Medie pel 1875.0 di 1463 Stelle comprese fra i paralleli 20 e 64 nord . Roma, 1880. 47. GREENWICH. 1880. Ten Year Catalogue of 4059 Stars, deduced from Observations extending from 1877 to J 886 at the Royal Observatory, Greenwich. 48. DE BALL. 1880. Declinationen von 200 Sternen innerhalb der Zone, + 49 bis 51, nach Beobachtungen im ersten Vertical am Passagen-instrumente der Herzoglichen Sternwarte zu Gotha. Ast. Nach., Bd. ci, 353. s and 5' reduction from Auwers' to Boss'. 49. CAPE OF GOOD HOPE. 1890. A Catalogue of 3007 Stars for the Equinox 1890 from Observations made at the Royal Observatory, Cape of Good Hope, during the years 1885 to 1895. 50. CINCINNATI. 1890. A Catalogue of 2000 Stars for the Epoch 1890. Publications of the Cincinnati Observatory, No. 13. Based on Auwers' system. 51. DUNSINK. 1890. Mean Places of 717 Stars deduced from Observations made with the Meridian Circle at Dunsink. Dublin, 1896. p and p' same as 50. 5 and s' the reduction from Auwers' to Boss'. 52. GLASGOW. 1890. Second Glasgow Catalogue of 2156 Stars for the Epoch 1890 deduced from Observations made at the Glasgow University Observatory during the Years 1886 to 1892. Glasgow, 1892. 53. GREENWICH. 1890. Catalogue of Stars from Observations extending from 1887 to 1896. 54. BERLIN. 1890. (Kiistner refers to several of these in Veroffentlichung der Koniglichen Sternwarte zu Bonn, No. 2. They were his own observations but I could find them nowhere else.) 55. RADCLIFFE. 1890. Catalogue of 6424 Stars for the Epoch 1890. Formed from Observations made at the Radcliffe Observatory, Oxford, during the Years 1880 to 1893. 56. BATTERMANN. 1895. Resultate aus Beobachtungen von 379 Anhaltsternen und 1640 durch Anschluss bestimmten Sternen, angestellt in den Jahren 1892-1897 am Grossen Berliner Meridiankreise von Dr. H. Battermann. Berlin, 1899. 5 and 5' the reduction from Auwers' to Boss'. 57. CINCINNATI. 1895. Catalogue of 2030 Stars for the Epoch 1895. Publications of the Cincinnati Observatory, No. 14. 5 and 5' the reduction from Auwers' to Boss'. 58. TUCKER. 1897. Publications of the Lick Observatory, Vol. VI, Meridian Circle. ^' = 3-0. 59. CINCINNATI. 1900. Reobservations of more than 4000 Piazzi stars. Based on Auwers'. 60. DUNSINK. 1900. Mean Places of noi Stars deduced from Observations made with the Meridian Circle at Dunsink. p, p' , 5 and s' as for 51. 61. KUSTNER. 1900. Veroffentlichung der Koniglichen Sternwarte zu Bonn. Nos. 5 and 6. 5 and s' the reduction from Auwers' to Boss'. 62. WASHINGTON. 1901. Observations made in the prime vertical by Prof. Hill, s' = o, /' = 5-o. 63. LICK OBSERVATORY. 1906. Observations made by Tucker. Based on Newcomb's system. 5 and 5' reduction from Newcomb to Boss ; p = 5.0, p' = 5.0. THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. 7 YEARLY SERIES. 64. 1835 to 1869. EDINBURG. Astronomical Observations at the Royal Observatory, Edin- burg. Only a few of these places were used. 5' as in Boss' Declinations of Fixed Stars. 65. 1862 to 1876. RADCLIFFE. Results of Astronomical Observations made at the Radcliffe Observatory. 5, p and p' same as Radcliffe, 1860 ; s' from 1867 to 1873 from Boss' Declinations of Fixed Stars ; s' from 1874 to ^76 the mean of reductions for 1871, 1872 and 1873. 66. 1862 to 1887. MADRAS. Meridian Circle Observations. 67. 1879 to 1882. BRUSSELS. Annales de 1'Observatoire Royal de Brusselles, Nouvelle Series. 5 and s' same as for Nautical Almanac. METHOD OF REDUCTION. Approximate places for 1875.0 were obtained and with these the differential coeffi- cients for 1875 were computed, using the constants of Struve and Peters. The formulae for these differential coefficients are as follows : da. ~T t 3*-7 22 5 + [0.126 115] sin at tan S + /tt -jj = [i .302 206] cos a + /*' -J7= [5-988] p cos a tan 8 -f [4.812] /*' sin a. sec 2 8 -f [4.99] MM' tan 8 -gp = [4.63380,,] ( -^ /* J + [5 .98778] ( -^ + /* j cos a tan 8 + [4.81 169] (-^ + yJ J sin a sec 2 8 \ / \ / \ / 4- [4.9866]^' tan 8 -f o s .ooo 032 210 -jjT = [4-6338oJ^- -/*') + [7-16387,,]^ + /i)sin a + [6.7367,,] M Z sin 28 d*S (da. fj\ (d^a. dfj\ _ (da. -TX = [2.098711 -j- + - Ism a + [7. 1630.] -T72 + ~ 1 smot + [3. 0255.] I -j- 4 OF - i \d 2J oy *\dt dt ) *\dt where the numbers enclosed in brackets are logarithms a = the right ascension, 8 = the declination, ji = proper motion in right ascension, and /i/ = proper motion in declination. For calculating d 3 a/ df the tables of Oppolzer were used (Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. I, Table XII) which, because of the small zenith dis- tances of all the stars on the list, were sufficiently accurate. For checking these values use was made of Gould's Tables*; for checking the other differential coefficients Oppol- zer's Tables were used. * Catalogo de Las Zonas Estelares, Appendix, Table IV. Cordoba, 1884. In using this table the value of/* as given in column four should be doubled. Cf. Ast. Nach., Bd. 137, s. 295. da 8 THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. Then the assumed places for 1875.0 were reduced to the epochs of the various cata- logs in which the star was found, making use of the formulae where T= epoch of the catalog. If in the catalog in question proper motion was assumed in deriving the star's place, there is need of applying a correction for proper motion. If T= epoch of the catalog t = mean date of observation JLI,, = proper motion used in the catalog p. = proper motion assumed in this investigation then the correction A^o. = (T /)(/* /A O ). Comparing the catalog place, corrected by the systematic correction and the correc- tion for proper motion, with the assumed place, carried back as explained to the epoch oi the catalog we get an equation of the form A + A/A T = obscrv ed "computed = where Act is the correction to our assumed right ascension, A/* the correction to our assumed proper motion and T is the difference 1875 /. Giving the equation such a weight as the catalog is thought to merit, it takes the form Vp(b.a. -\-Ap.r = ri) where p is the weight. Each catalog will give such an equation and solving the system of equations so obtained for the star, by the method of least squares, the most probable values of Aa and AJU, will be determined. The method of solving the system of equations was the following: Let 4 be the weighted mean of the epochs of observation of the various catalogs. t\, t t n be the epochs of observation of the respective catalogs then *.. V " T .- ('. - 0. (', - '). (< - '.) and 2,pT should be zero. Aa and A/A are given by Aa = and A/i= Aa i8 75 = Aa + ( I8 75 - The final check is The lollowing example will illustrate the various steps in the process. = 69-81 2X- THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. = 1869.81 1,pn 2 = .0455 n = .0242 (2j)Aa = .0057 9- 6 S + 4.1720 A/a = -v- 1 - = + .00065 6412.07 Aa 187 .= .0242 + (.00065 x 5.19)= .0208 = .0027 Check .0371 ASSUMED COORDINATES AND PROPER MOTIONS FOR 1875.0. a = 17 49 13.980 fi =+.0005 d = 4o I 57.56 /i' = +.o64 Epoch. No No. Catalog. Cat Obs. Obs. MO M Mo Tt v "O a e -V ""O a c n p ft r f> > t* /T V = T = t I Bradley 1755 1755-6 I +.0005 OOOO - 0.6 ooo .046 .046 .1 -4-44 114.21 11.42 .0046 1304.16 + -5253 .052 2 Lalande 1800 93-6 + .0005 + 6-4 +.003 -.356 .353 05 -32 - 76.21 -3-8i .0176 290.32 + I-34I I +.279 3 Piazzi oo 10 .03 + .0305 .056 .056 .1 o.oo 69.81 6.98 .0056 487.20 + -3909 .014 4 D'Agelct 00 1803.5 +.0005 - 3-5 .002 -.189 .191 05 .18 66.31 3-32 .0096 220.12!+ .6365 +.124 5 Groombridge 10 io-5 6 +.0005 0.5 OOO +.087 +.087 .1 1.05 59-31 5-93 +.0087 351.65 -5I59 .150 6 Madras 35 37-1 7 + .0005 2.1 .001 -.277 .278 .2 7.42 32.71 6.54 .0556 213.86 + 1.8181 +.232 7 Riimker 36 40.0 i +.0005 4.0 .002 -.189 .191 05 2.OO 29.81 1-49 .0096 44.40 + .2861 +.147 8 Armagh 40 37-2 7 +.0005 + 2.8 + .001 .018 -.017 .2 7-44 32.6l - 6.52 .0034 212.55 f- .1108 .028 9 Edinburg 43 43-5 3 + .0005 0.5 ooo .107 .107 .2 8.70 26.31 -5-26 .0214 138.34 f .5628 +.066 10 Radcliffe 45 47-3 6 +.0005 2.3 .001 .064 -.065 5 23.65 - 22.51 11.26 .0325 253-35 + -7312 +.026 ii Paris 45 49-7 7 +.0005 4-7 .002 +.054 +.052 .8 39.76 2O.II 16.09 +.0416 323-41 - .8362 .089 12 Pulkova 55 5 1.8 4 +.0005 0000 + 3-2 ooo .063 .063 5 25.90 18.01 9.00 0315 162.09 + -5670 +.027 13 Yarnall 60 53-6 4 +.0005 + 6.4 +.003 .021 .018 .4 21.44 16.21 - 6.48 .0072 104.98 + .1166 .017 14 Paris 60 67.0 2 +.0005 - 7-0 .004 .162 .166 .2 1340 2.8l 0.56 0332 1-57 + -0930 +.140 15 Greenwich 64 66.3 3 .004 +.0045 2.3 .010 +.019 +.009 .6 39.78 - 3-51 2. II +.0054 7.38 .0189 -.035 16 Brussels 65 63.6 2 +.0005 + 1-4 + .001 .004 .003 .2 12.72 - 6.21 1.24 .0006 7.69 + -0037 .025 17 A. G. 75 89.5 6 +.0005 14-5 .007 .010 .017 I.O 89.50 + I9.69 + 19.69 .0170 387.89 -3349 +.006 18 A. G. 75 71.6 +.0005 0000 + 3-4 ooo +.031 +.031 I.O 7I.6o + 1-79 + 1-79 +.0310 3.22 + .0558 .054 19 Romberg 75 78.7 2 +.0005 OOOO 3-7 ooo +.005 +.005 3 23.6l + 8.89 + 2.67 +.0015 23.76 + .0134 .023 20 Greenwich 80 86.3 4 +.0005 OOOO -6.3 ooo .050 .050 1.2 103.56 + 16.49 + 19-79 .0600 326.54 -9894 +.036 21 Greenwich 90 95.9 3 +.0005 OOOO 5-9 ooo +.006 +.006 -7 67.13 + 26.09 + 18.26 +.0042! 476.59 + .1096 .013 22 Bonn 1900 98.5 2 +.0005 + i.5 + .001 .019 .018 5 49.25 + 28.69 + 14-34 .0090! 411.56 - -2583 +.012 23 Cincinnati 1900 1900.5 3 -I-.0005 0.5 ooo .Oil .Oil 7 70-35 + 30.69 +21.48 .0077 659-44 -2363 + .007 9.65 673.68 + O.OI .2337 6412.07 +4.1720 FINAL VALUES. 0=17 49 13-959 The proper motions derived by this reduction were changed later by the necessary amount to pass over to Newcomb's constants from Struve and Peter's. THE RESULTS. The list of stars which follows includes 5 (N) found in Newcomb's Fundamental Catalog, and i (B) found in H. B. Evans' Mean Right Ascensions and Proper Motions of 254 Stars. The places of these have been taken from these sources and corrected by amounts necessary to reduce them to Boss' system and Newcomb's constants. There were also 5 (F. O.) Flower Observatory stars whose declinations had been previously determined by Prof. Doolittle and i (D) Davis star. The declinations of these six were taken from the sources indicated and the necessary corrections applied to bring them to Boss' system and Newcomb's constants. The differential coefficients da/ dt and include the proper motions ju, and ju,'. IO THE MEAN RIGHT ASCENSIONS AND PROPER MOTIONS OF 130 STARS. DEFINITIVE POSITIONS 1875.0. Me a !875 da d*a (loo) d'a. /* *17 6.6 6.Q 23 13 22.602 23 20 25.667 2.88264 2.88091 + 1745 + 2124 +.015 +.018 +.00086 .OO027 35 8 31.46 | 39 42 18.56 + 19.6262 + I9-573I + 765 + 637 .136 .137 .0094 -.1778 12 5 II 5 he me tare 328153