UC-NRLF *C 3M SOb .-,." ; - m $p mi W*$ *"-* - Y ~'fe'i3' : ^$~''^ *j ~ /srX" '^^- "" ^^ r /5^ TO ^P^'''--- ^^ir^"^^-'-^^ \^^^ v ''^^-" v^ J* r**^r- *A' '^^^^^^S^^f^^ $$lw$$S* ' SlW^i ir fe .^^^- f '')^ b ; ^^b^^w'l . ;^$^~f3fe$^ '^^^^"n&^lfe-^f ^/^ ; y. fr Mwr*aFKi ?o^^3*lr^^ ' ^Cln3) JtkJtJp- -yw? '*.:2^) ^-^ *JL* /*>** a^TzF^flOf V*. Sr^**i.-sg^ '^5^* ** \U(^ **b"t ./!( ^^r "V^Alf^ **v-.rf ZlK w i^f*'+ i^^Mi^ * jS^h^i^sij^3*-5^te^^ j i ^^^^fe'^s^^lsl rY 'W^^i^s^' o ( ^% ^^^Z^^r^j^v^ %^^^^ilf*^ -'^>^^jjv^rOv-^ JflSfc aJFfOSaWa S V& liiLjZ/^ ''ffif^" ^*cr*' i<~$k i A/ 5 ->*r* C=s>' D ^St JIA ^^S >% * i'' ^** W ^^>s>" ^ S ^V^^TV I W^^^ V + s^te^eEEwSrs^jg . -'' TABLES OF MELPOMENE, BY E. SCHUBERT. COMPfTEI) FOB THE AMERICAN EPHEMERIS AND NAUTICAL ALMANAC, rNDER THE SUPERINTENDENCE OF COMMANDER CHARLES HENRY DAVIS, U. S. N. UNIVERSITY BUREAU OF ORDNANCE AND HYDROGRAPHY, WASHINGTON. I860. CAMBRIDGE: ELECTROTYPED AND PRINTED BY WELCH, BIGELOW, & CO., UNIVERSITY PRESS. ASTRONOMY UBRARY TIVBESITY) / J VI W. REPORT TO COMMANDER C. H. DAVIS, U. 8. N. I. ON THE COMPUTATION OF THE GENERAL PERTURBATIONS OF MELPOMENE BY JUPITER. BY ERNEST SCHUBERT. FOB the computation of these perturbations, Professor ENCKE'S method, published in the Berliner Jahrbuch for 1857, lias been used in order to try it by a complete application to a special case. The basis of the work are the following elements : MELPOMENE. JUPITER (from BOUVARD'S Tables). 1854, Jan. 0, Washington Mean Time ; (osculating). 1854, Jan. 0, Washington Mean Time. M = 79 56 36".81 o , , 1 M = 269 43 ' 3 9 " 1 * = 15 14 31.52) M E n' = 16 16 53.3) n = 11 58 43.2 8 = 150 1 8.21 ) 8' = 19 16 43.7 [-^^^ Q = 98 56 38.7 i = 10 9 4.77 v = 15 28 17.2) i = 1 18 39.5 * = 5.5760322 in units of the seventh decimal-place, and for the Julian year as the unit of time. Each point of the Melpomene orbit is combined with all 1C points of the Jupiter orbit, which gives 16 X 16 = 256 values of m . On page 854, Professor ENCKE says that those values can be checked only by double calculation, since it cannot be done by the differences in the series obtained for the different M. But I found that, if we arrange the m' if quantities 77." This sketch needs no further explanation ; the principle for the arrangement in B from A is very simple, and it is obvious that it is the vertical series in B which can be tested by differences. m' if In Table A the values of ^ are functions of M, and they are developed in series of the form, t ~ = a 4- a 1 cosM + V sin M' 4- a" cos 2 M + 5" sin 2 M. It is evident that now in these series the coefficients are functions of M, and they must be developed in series of the same form, that is, for instance, a = + a' cos M + /?' sin M -\- a" cos 2 M+ p" sin 2 M Each of the latter series must be multiplied with the cos f' M 1 or sin i 1 M belonging to it, and then, finally, m! if by resolving the products of two cosines or sines into sums and differences, we obtain ^- developed in series of the general form oj' cos (t M i' M) + ^ sin (f Jf f' jlf ). In order to have throughout t' JM 7 we only have to change the sign of t' and that of the coefficient of the sine. The formulas for the components of the disturbing force (page 392) are : z . = -'" {(?-?)*'} m' if Therefore, after having developed M according to the above precepts, we subtract from it = 2684.3 -f 388.2 cos M + 28.1 cos 2 M + 2.0 cos 3 M 4- 0.1 cos 4 M and pot tliii* m' ' ( , V TliU prriixliral --- i- to l>c multipli *' l == 0.03518 + 0.49698 cos M> + 0.68709 sin Jf -j- 0.01336 ccw 2 Af + 0.01657 sin 2 .' -j- 0.00185 cos 3 M' + 0.00060 sin 3 Jf' |- 0.00 144 cos 4 M 1 + 0.00142 cos 5 M' + 0.00142 cos 6 M' + 0.001 42 cos 7 M' + 0.00071 cos 8 AT m' if After that, the periodical series -^j- must be multiplied with x t and y,. We have , = +0.74808 2.25537 cos M 0.24159 cos 2 M 0.03886 cos 3 M 0.00741 COB 4 M - 0.00155 cos 5 M 0.00035 cos 6 M y, = 2.22785 sin M 0.23961 sin 2 Jf 0.03861 sin 3 M - 0.00737 sin 4 M 0.001 55 sin 5 M 0.00035 sin 6 M Finally, after these fire multiplications, by forming the sums, we obtain the series for X,, Y,, Z,. I subjoin here now the terms tf-yf and of m' x' ( -^J retained for multiplication, the terms smaller than 0.5 having been omittc.1. m? P a 1. f CM sin ', CM sin '. f cos tin , f CO* in +434&S 0.0 -4 - - 7.3 0.0 6 -1 + 5.6 - 5.8 -a -2 - 1.1 + 0.6 1 - MM M -3 - + 6.3 - 1.6 7 -1 - 2.7 + 6.6 -1 -2 - 14.0 - 8^ 3 + 19.8 -60.9 -8 - - 6.0 + 2.H 8 -1 0.0 - 3.7 -2 + 195.3 + 33.7 3 - 1.3 - 5.1 -1 - + 109.0 64.1 1 -2 -1174.9 I.Mi.- 4 - 1.6 - -1384.0 + 90.2 -8 -2 0.0 + 0.5 a -2 +2618.4 -301.3 1 - .:._,>-. -305.3 -7 -2 -f 0.5 - 1.1 3 -2 + 350.1 - 13.4 -S -1 0.0 - 3.7 9 - . I-.-..-J -( 26.4 -6 -a - C.8 + 0.7 4 -2 + 77.3 - 27.7 -7 -1 + 2.9 + 6.7 3 - + 48.1 - 43.1 -5 -2 + 1.0 - 0.5 5 -2 + 16.1 - 8.6 - -1 - 54 - 5.1 4 - + 18.5 - 7.9 -4 -2 - 1.2 0.0 6 -2 + 4.7 - 1.5 -o -1 + 6.6 + 3.9 5 - - 4.4 + 0.8 -3 -2 + 0.9 + 0.5 7 -2 0.0 - 1.7 TO'*' p" , i' cos sin .', '' cos sin .', .'' cos sin , >' cos sin 8 -2 0.0 + 0.5 -2 -4 + 0.8 + 1.1 6 -5 + 96.3 - 21.5 -5 -7 + 5.3 + 2.6 -1 -4 1.1 1.8 7 -5 + 38.0 - 11.8 -4 -7 7.4 0,0 -8 -3 + 0.5 + 1.2 -4 + 3.0 + 3.7 8 -5 + 4.5 1.2 -3 -7 + 6.8 - 3.0 -7 -3 - 0.9 - 2.9 1 -4 31.4 - 5.3 -2 -7 5.3 + 5.3 -6 -3 + 2.0 + 2.1 2 -4 + 158.1 - 19.3 -8 -6 + 12.7 1.2 -1 -7 + 2.4 - G.7 -5 -3 2.8 1.2 3 -4 - 447.7 +120.2 -7 -6 + 4.4 - 5.8 -7 0.0 + 7.4 -4 -3 + 2.8 0.0 4 -4 + 506.8 -117.6 -6 -6 + 2.7 0.0 1 -7 3.1 6.5 -3 -3 - 2.9 + 1.1 5 -4 + 181.6 - 30.1 -5 -6 + 1.2 - 1.0 2 -7 + 4.3 + 5.1 -2 -3 + 1.8 - 2.4 6 -4 + 52.8 - 15.4 -4 -6 1.0 0.0 3 -7 2.3 - 2.7 -1 -3 0.0 + 4.8 7 -4 + 14.7 - 4.9 -3 -6 + 0.9 0.0 4 -7 6.7 + 4.7 -3 - 27.6 - 12.0 8 -4 + 2.2 1.6 -2 -6 1.1 - 0.8 5 -7 + 33.9 - 11.6 1 -3 + 202.1 + 1.6 -1 -6 0.0 + 1.0 6 -7 - 45.4 + 23-5 2 -3 - 778.5 +153.7 -8 -5 + 4.5 1.2 -6 0.0 1.0 7 -7 + 23.5 - 2-9 3 -3 +1199.2 -205.2 -7 -5 + 2.8 - 4.0 1 -6 1.2 + 0.8 8 -7 + 6.9 - 10.9 4 -3 + 232.1 - 30.9 -6 -5 + 2.6 + 1.5 2 -6 + .5.7 0.0 5 -3 + 73.9 - 21.2 -5 -5 - 2.5 1.5 3 -6 - 22.5 + 4.0 -8 -8 + 3.6 0.0 6 -3 + 15.1 - 5.3 -4 -5 + 2.9 0.0 4 -6 + 68.9 - 20.7 -7 -8 6.9 - 8.9 7 -3 + 5.8 - 4.7 -3 -5 2.8 + 1.1 5 -6 - 116.8 + 48.6 -6 -8 + 13.0 + 3.8 8 -3 + 0.5 + 1.2 -2 -5 + 1.9 - 2.1 6 -6 + 75.3 - 25.2 -5 -8 3.6 - 2.4 -1 -5 1.3 + 2.8 T D + 46.2 - 18.2 -4 -8 + 1.9 0.0 -8 -4 + 2.2 - 1.6 -5 0.8 - 3.2 8 -6 + 12.7 1.2 4 -8 + 1.9 0.0 -7 -4 0.0 + 0.8 1 -5 + 5.7 + 4.3 5 -8 3.6 + 2.4 -6 -4 + 1.3 1.2 2 -5 - 30.7 1.1 -8 -7 + 6.9 - 10.9 6 -8 + 13.0 - 3.8 -5 -4 1.4 + 0.6 3 -5 + 111.6 - 23.4 -7 -7 + 24.3 + 8.4 7 -8 6.9 + 8.9 -4 -4 + 1.5 0.0 4 -5 - 240.3 + 80.8 -6 -7 6.4 - 9.8 8 -8 + 3.6 0.0 -3 -4 1.6 - 0.6 5 -5 + 204.6 - 59.9 "'(-) ', cos sin i', i cos sin >', i cos sin ', i cos sin +1663.9 0.0 6 -1 - 1.2 - 0.8 -4 -3 - 1.6 - 0.6 1 -4 + 18.5 + 7.9 1 -1772.6 - 90.2 7 -1 3.1 + 6.5 -3 -3 - 2.9 + 1.1 2 -4 + 77.3 + 27.7 2 + 167.2 - 33.7 -2 -3 + 0.9 + 0.5 3 -4 + 282.1 + 30.9 3 - 29.6 + 12.0 -7 -2 - 5.3 + 5.3 -1 -3 + 6.3 1.6 4 -4 + 506.8 +117.6 4 + 2.9 - 3.7 -6 -2 1.1 - 0.8 -3 + 1.3 + 5.1 5 -4 - 240.3 - 80.8 5 - 0.8 + 3.2 -5 -2 + 1.9 - 2.1 1 -3 + 48.1 + 43.1 6 -4 + 68.9 + 20.7 6 0.0 + 1.0 -4 -2 + 0.8 + 1.1 2 -3 + 350.1 + 13.4 7 -4 6.7 - 4.7 7 0.0 - 7.4 -3 -2 + 1.8 - 2.4 3 -3 +1199.2 +205.2 8 -4 + 1.9 0.0 -2 -2 1.1 + 0.5 4 -3 - 447.7 -120.2 -7 -1 + 2.4 - 6.7 -1 -2 6.0 + 2.8 5 -3 + 111.6 + 23.4 -8 -5 - 3.6 - 2.4 -6 -1 0.0 + 1.0 -2 + 19.8 + 60.9 6 -3 - 22.5 - 4.0 -7 -5 + 5.3 + 2.6 -5 -1 1.3 + 2.8 1 -2 + 185.2 - 26.4 7 -3 2.3 + 2.7 -6 -5 + 1.2 1.0 -4 -1 1.1 1.8 2 -2 +2618.4 +301.3 -5 -5 - 2.5 1.5 -3 -1 0.0 + 4.8 3 -2 - 778.5 -153.7 -8 -4 + 1.9 0.0 -4 -5 1.4 + 0.6 -2 -1 - 14.0 - 8.8 4 -2 + 158.1 + 19.3 -7 -4 7.4 0.0 -3 -5 - 2.8 - 1.2 -1 -1 + 109.0 + 64.1 5 -2 - 30-7 + 1.1 -6 -4 1.0 0.0 -2 -5 + 1.0 - 0.5 -1 - 602.6 - 25.8 6 -2 + 5.7 0.0 -5 -4 + 2.9 0.0 -1 -5 + 6.6 + 2.9 1 -1 +5208.0 +305.3 7 -2 + 4-3 - 5.1 -4 -4 + 1.5 0.0 -5 0.0 0.0 2 -1 -1174.9 -156.8 -3 -4 + 2.8 0.0 1 -5 4.4 - 0.8 3 -1 + 202.1 1.6 -7 -3 + 6.8 - 3.0 -2 -4 1.2 0.0 2 -5 + 16.1 + 8.6 4 -1 - 31.4 + 5.3 -6 -3 + 0.9 0.0 -1 -4 7.3 0.0 3 -5 + 73.9 + 21.2 5 -1 + 5.7 - 4.3 -5 -3 2.8 + 1.1 -4 0.0 + 1.6 4 -5 + 181.6 + 30.1 "(*-*) ', 1 tin i'. * cos sin ', ' cos sin ', i cos sin 5 -5 + 204.6 a -6 + 4.7 - i.:. -1 -7 + 2.9 + 6.7 -6 -8 + 4.5 1.2 6 -5 - 116.8 - 48.6 3 -6 + l.">.i + 5.3 -7 0.0 0.0 -4 -8 + 2.2 1.6 7 -5 + 33.9 + 11.6 4 -6 + 58.8 i:..4 1 -7 - 2.7 6.6 -3 -8 + 0.5 + 1.2 8 -5 3.6 J.I 5 -6 + 96,3 -ji.:> 8 -7 0.0 + 1.7 -2 -8 0.0 + ii.:. 6 -6 + 75.3 J.-..-J 3 -7 + 5.8 + 4.7 -1 -8 0.0 - 3.7 -8 - + 13.0 + 3.8 7 -6 1"..! j.:.;, 4 -7 + 14.7 + 4.9 -8 0.0 0.0 -7 -6 6.4 - 9.8 8 -6 + 13.0 + 3.8 6 -7 + 38.0 + 11.8 1 -8 0.0 + 3.7 -6 -6 + 2.7 0.0 6 -7 + 46.2 + 18.2 2 -8 0.0 i - 0.5 -5 - + 2.(i {JS -8 -7 - 6.9 - 8.9 7 -7 + 23.5 + 8.9 3 -8 + 0.5 - 1.2 -4 - + 1.3 I.-J -7 -7 + 84.3 + 8.4 8 -7 6.9 - 8.9 4 -8 + -'.-' + 1.6 -3 -6 + 2.0 + 2.1 - -7 + 4.4 - 6.8 5 -8 + 4.5 + 1.2 -2 -6 0.8 + 0.7 -5 -7 + 8.8 - 4.0 -8 -9 + 3.6 0.0 6 -8 + 12.7 + 1.2 -I -6 5.1 -4 -7 0.0 + 0.8 -7 -8 + 6.9 - 10.9 7 -8 + 6.9 + 10.9 -6 0.0 0.0 -3 -7 0.9 8.9 -6 -S + 12.7 1.2 .8 -8 + 3.6 0.0 1 -6 + M + W -2 -7 + 0.5 1.1 Retained Term* of the Force*. X, T. Zi Xi T, Zi cos sin cos sin COB sin cos sin cos sin cos sin 1*73.1 0.0 + 66.7 0.0 - 550.6 0.0 3 -2 + 441.0 - 143.0 - 64.6 + 280.1 + 356.7 + 329.5 1 + :i7n7> - 224.0 - 180.6 + 3507.2 +1456.4 +1647.6 4 -2 + 149.4 - 0.2 - 20.1 + 51.7 . eu + 85.8 2 + 271.4 + 29.2 - (il.n + 290.6 + 40.6 !!.".. 4 5 -2 + 23.8 - 9.4 + 11.4 + 46.9 + 2J.!t + 23.3 3 :..-,. i 36.5 + 43.1 + 22.9 + 33.4 + 6.7 6 -2 + 15.9 - 12.6 16.2 - 13.1 4 11. (i - 7.4 + 7.5 + 49.4 + 7.8 + 7.2 7 -2 - 1.5 + 7.7 + 24.8 + 11 .7 5 1.2 - 3.8 13.1 31.6 8 -2 1.2 - 3.9 15.0 0.1 6 1.8 0.0 + 27.5 + 27.0 7 1.1 _ 1.1 34.1 14.4 -3 -3 - '.0 + 2.2 + 4.8 - 8.8 - ,, 1.0 0.0 + 19.0 0.0 -2 -3 + 0.3 _ 1.2 - 4.2 + 6.7 -1 -3 - 18.7 - 6.4 - 3.9 + 10.7 -5 -1 - 17.4 + 4.8 3.7 + 1.3 -3 + 174.3 + 60.3 + 50.5 - 170.8 + 60.7 - 32.6 -4 -1 1.9 + 7.6 3.4 1 -3 -1941.3 + 366.8 + 416.3 +1909.7 - 252.3 + 367.8 -3 - Jl.l 4.8 + 2.7 + 0.2 2 -3 +5242.4 - 845.2 - 9f,.4 -5136.7 + 641.7 - 9:Ci.l -2 - i,. > . 79.6 + 72.3 - 30.3 + 33.6 + 6.8 3 -3 + 715.6 - 40.8 - 93.8 - 902.6 - 120.1 - 238.2 -1 - 298.8 - 56.1 - 5.9 + 290.8 - 156.4 + 148.1 4 -3 + 264.1 - 91.3 46.1 - 51 .J + 165.7 + 109.8 - J.VJ1.:, - 9.2 - 274.4 - 2319.6 + 946.0 -1066.3 5 -3 + 87.3 - 26.9 - 21.3 + 18.1 + 55.0 + 49.7 1 - l.:i".- - ll-.-J + 146.4 + 239.5 -712.7 - 136.9 6 -3 17.8 - 4.8 + 1.9 + 2.3 + 19.4 + 1X1 2 - 1100.5 - 208.3 - 83^ + 1111.2 + 742.9 + 793.3 7 -3 1 6^8 - 8.8 - 4.0 + 7.0 3 - 170.0 - 14.4 - 22.2 + 189.0 + 93.1 + 126.7 8 -3 - 4.9 1 4.3 - l.i. - 5.4 4 - 60.0 - 18.5 + 4.5 + 46.9 + 30.0 + 21.6 1 5 - . 7.9 - 0.8 + 11.4 + 5.3 -2 -4 13.6- 8.6 - 0.4 + 1.3 + 18.5 + 1.5 6 - 15.4 _ 11.4 4-1 + 7.7 -1 -4 - 9.4 + 16.2 + 2.6 - 3.2 15.4 + 0.5 7 - 8 - 6.9 2.2 t 8.3 6.5 + 145 + 5-4 6.8 + 2.1 -4 1 -4 2 -4 48.1 - 24.1 + 327.4 1+ 6.0 -1374.1 + 339.5 - 10.2+ 48.4 14.5 - 315.9 + 377.7+1337.6 - 9.5 + 5.2 + WJI- 58.1 1 :,.-,. 1 + 274.1 -4 -2 13.7 - 1.2 0.4 + 25.9 3 -4 +2445.8 - 526.! - 576.6 -2365.7 + 290.1 - 439.8 -3 -2 11.1 - 2.4 - 7.6 24.2 4 -4 + 567.4 - -1.7 - 116.2 - 665 :: 48.3 - 162.0 -2 -2 - 4.1 9.2 + 22.3 + 12.4 5 -4 Jii4.ii - 65.5 - 43.2 - 113.2 + 75.9 + 24.5 -i -a 1211.-) + 109.7 + 86.1 135.!! + 63.1 i .-..:? 6 -4 t 39.5 - 14.6 13.4 21 1 + 31.9 + 22.7 o -a - 3339.0 + 294.1 + 393^ + 3296.3 - 428.2 + 589.8 7 -* 1 31.2- 17.1 - 8.3 + 1 ' 1 -2 +10242.4 -1049.0 -1302.1 -10042.0 -1317.9 -1799.0 8 -4 - 13.2 + 6-9 - J.7 16.7 2 -2 337.0 + 61.6 + 21.0 - P20.1 :; >::. - 271.8 Retained Terms of the Forces. Xi Yi Z. X, Yi Zi i, i' cos sin cos sin CO9 sin cos sin cos sin cos sin -1 -5 - 2.3 + 4.6 - 5.3 + 0.9 + 33.3 + 2.5 9 -6 - 21.0 + 3.9 - 3.9 - 20.8 -5 + 2.5 - 2.0 + 8.7 1.4 14.4 - 0.2 1 -5 - 46.7 - 0.6 - 11.0 + 44.7 - 8.7 4 7.8 1 -7 - 6.0 13.2 + 4.5 + 6.9 + 32.3 1.5 2 -5 + 261.0 44.9 - 43.0 - 252.9 + 44.5 - 52.1 2 -7 + 21.2 + 10.3 4.7 12.5 - 2.5 1.0 3 -5 - 804.6 + 266.5 + 276.2 + 790.9 - 81.9 + 168.1 3 -7 - 53.6 + 1.2 + 12.9 + 42.8 5.0 + 8.0 4 -5 +1037.1 - 288.1 - 306.7 -1000.8 + 122.8 - 191.4 4 -7 + 133.3 - 42.0 - 51.5 - 120.4 + 13.2 - 27.0 5 -5 + 385.4 - 77.0 - 96.6 - 407.2 18.8 - 95.6 5 -7 - 223.6 + 106.2 + 113.6 + 229.7 - 15.5 + 50.5 6 -5 + 119.0 - 37.1 - 38.9 - 98.4 + 31.6 2.1 6 -7 + 149.6 - 58.5 - 79.5 - 171.2 + 17.1 - 30.6 7 -5 + 40.8 - 29.4 - 3.0 - 37.0 + 18.4 + 5.6 7 -7 + 148.6 - 45.4 - 39.2 - 83.3 - 0.5 - 20.7 8 -5 - 16.9 + 9.9 - 19.2 - 29.0 8 -7 + 23.1 - 7.7 6.3 - 45.1 9 -5 - 12.4 + 3.4 - 3.3 12.3 9 -7 - 9.7 + 12.0 - 11.9 - 9.7 -2 -6 - 11.2 + 6.2 - , 19.4 - 19.9 -1 -8 + 5.2 - 17.5 17.5 5.1 -1 -6 + 1.7 - 7.3 + 24.2 + 11.4 - 30.3 - 2.1 -8 + 2,8 + 19.0 + 18.9 1.2 + 24.0 + 1.6 -6 + 0.3 + 9.0 - 26.7 + 0.5 + 25.7 + 1.6 1 -8 - 12.6 - 16.4 - 16.2 + 9.1 - 37.9 + l.fl 1 -6 + 0.4 6.0 + 25.9 16.4 - 8.3 2.4 2 -8 + 13.1 + 12.6 + 12.4 - 12.1 + 16.8 2.3 2 -6 - 37.7 + 10.0 15.1 + 64.1 - 9.8 + 11.9 3 -8 - 8.7 - 7.3 6.3 + 9.4 1.9 + '0.8 3 -6 + 175.4 - 55.6 - 44.8 - 205.8 + 25.6 - 43.0 4 -8 9.8 + 9.3 + 9.4 + 10.2 - 0.7 + 3.1 4 -6 - 424.6 + 177.8 + 181.2 + 459.3 - 38.5 + 98.1 5 -8 + 62.0 - 26.9 - 28.9 - 66.9 + 5.6 13.7 5 -6 + 411.7 - 136.9 - 159.7 - 422.5 + 49.2 - 80.5 6 -8 - 93.5 + 50.5 + 58.8 + 104.6 3.6 + 21.0 6 -6 + 228.2 - 55.2 50.9 - 192.7 - 5.7 - 47.5 7 -8 + 42.2 4.2 16.6 - 72.7 + 5.3 9.6 7 -6 + 89.2 - 22.3 54.2 93.4 + 10.5 - 8.1 8 -8 + 24.9 - 38.7 - 19.7 - 10.6 8 -6 - 22.5 - 8.9 + 0.8 50.31 For the computation of and yro dt we have the above series for x t and y t with reversed signs, and ^! = +0.00003 + 4.02388 cos M + 0.86552 cos 2 M + 0.20922 cos 3 M + 0.05330 cos 4 M + 0.01 392 cos 5 M + 0.00380 cos 6 M + 0.00112 cos 7 M + 0.00028 cos 8 M These multiplications furnish us now finally the material for the formation of the differential equation for r 8 r, namely, of = 4.07365 sin M 0.87270 sin 2 M 0.21058 sin 3 M 0.05352 sin 4 M 0.01402 sinSJUf 0.00375 sin 6 M 0.00 100 sin 7 M + ! m) rR-\- 2fc Ternu of 2 retained fur integration. i, f CO* tin , ' cot >in i, ' co in i. i' cot tin n + 9109.8 0.0 -1 -2 -.'11.7 nu 4 -4 +8063.0 I-.-.H.M 6 -6 rhn:i.r, -350.0 1 - 7en.it + 561. (i -2 4- 311:1.1; + 435.3 5 -4 +3015.7 MSJ 7 - + 677.6 Mfcl a o I3J - 877.8 1 -2 BMU -.i-.".; 6 -4 + 950.1 - 251.7 8 - . aau -129.7 3 :u .4 1 I-J.-J 9 -2 M-.'.-,I..-. -6036.5 7 -4 i:i:,.i; - 60.2 4 '-T-li 3 -2 + 8109.5 - 413.2 1 -7 + 28.7 + 535 :, n - 35.0 I-.'J 4 -2 I.M-.I ITU 1 -5 + 77.2 in.'! 9 -7 + 157.4 - 70.3 6 30.0 U 6 -2 i- 431.0 - 90.6 2 -5 i, :!-..' 16.8 3 -7 + 130.5 + 2.7 7 - 29.5 + ai.7 3 -5 +1875.3 - 439.1 4 -7 - 307.2 + 62.4 8 + 14.1 n.'. -3 - 206.1 1 !!>.!> 4 -5 -3827.3 1 .'-". 1 5 -7 + 609.7 -243.4 9 + 3.0 -">.'. 1 -3 . :.(, !>.:. + 26.7 5 -5 +2916.8 - 851.0 6 -7 - 783.2 .:'.--.- 2 -3 -15678.7 +3104.7 6 -5 +1588.1 - 379.9 7 -7 + 289.9 -139.6 J 1 + 10.1 - 80.2 3 -3 1-90)61.9 :n,u-,.i 7 -5 + 501.0 - 127.7 8 -7 + 365.4 -123.3 -1 - + 686.0 4 -3 . M.M.I i. .'-..i 8 -5 + 192.7 - 75.1 - 11.5 5 -3 . l:\in.,, - 321.7 2 -8 + 101.2 +120.2 1 - -1084.2 6 -3 + 330.1 - 126.3 -6 - 29.7 - 74.4 3 -8 + 105.6 + 96.9 a - HM4 -t- 760.8 1 - + 92.7 + 123.8 4 -S - 28.5 - 313 3 - - 361.1 HU -4 + 67.5 + 56.3 9 -6 + 370.1 + 256.6 5 -8 - 85.7 + 51.5 4 - 99.9 - 116.9 1 -4 + 399.3 + 32.9 3 -6 - 440.1 + 30.6 6 -8 + 272.2 -123.8 5 - + 34.7 IV 1 2 -4 :;-." 1.'' - 388.5 4 -6 +1089.6 - 344.7 7 -8 - 311.7 4 15M.il 3 -4 :>' ;:,.i 'iOTl.li 5 -6 -1794.8 + 723.2 8 -8 ii:i.:' - iT.r, For ilie computation of the coefficients of integration we have, 3.008587 logp, 9.87395 7.248165 " Pl 0.35322 log/i . 365.25 g 208266 log /i' 2.4758o8 " /i + 0.256752 " p! + 9.724023 M 1.806142 /i' 0.529691 p and q are the coefficients in the series for x, and y t . p t 9.38308 p t 8.58950 p 4 7.86982 p, 7.19033 p, 6.54407 log q, 0.34788 y, 9.37951 9, 8.58670 " q, 7.86747 " & 7.19033 " y, 6.54407 9.288603 log 9.743248 1.806142 0.529691 2p 3.612284 2/i' 1.059382 3,. 5.418426 8/1' 1.589073 4 p 7.224568 4 M ' 2.118764 5 M 9.030710 5/i' 2.648455 / 10.836852 6/ 3.178146 7 M 12.642996 7 /i' 3.707837 8/> 14.449136 8/ 4.237528 9 M 16.255278 9 M ' 4.767219 10/i 18.061420 ll/i 19.867562 10 Log of the " Entwickelungs-Factoren." t H i -I- 4 and i 4 < ( 4 - +3, +1 +4, 68480 7.33105 +5, -H, -1 5 i -f- 3 and t 3 +2, +1 6.02698w 4-3, 0, 3 7.92534 +4, -1 +5, -2 . 7J90573 6.40380* +2, +3, -1 +4, -2 +, -3 . , 0, 2 +1, 3 +2, -4 -1-3, 5 ., 8.54206 8.52827n 7.01565 5.66881n t'+landt 1 +1, -f 2, -1 +3, -2 +4, -3 . , 0, 1 +1, -2 +2, -3 +3, * . . 9.20940 9.19653w 7.65594 6.28942n +1, -1 +2, 2 +3, -3 +4, 1 . , 9.98970 8.35223w 6.94297 5.62793n The numbers above the logarithms are those which constitute x in i Specimen of the Tables of Divisors. For the Class i' = 0. ( _, 2 -1 +1 +2 +3 +4 H +8 +7 +8 +9 9.141 19 n 9-26613,, 9-44221 n 9-74325,, 00 9-74325 9-44221 9-26613 9-14119 9-04428 8-96510 8-89815 8-84016 8-78900 -5 9-04428,, 8.18547 8-31041 8-48649 8-78753 8-08856,, 8-78753,, 8-48649 n S. 31011,, -4 9-14119,, 8.40732 8-58340 8-88444 8-28238,, 8-88444, 8 -68340,, 8.40732,, 8-28238, -3 9-26613,, 8-70834 9-00938 S-53226 n 9-00938B 8-70S34n 8.53226,, 8-40732, 8-31041, -2 9-44221,, 9-18546 8-88442,, 9-18566,, 8-88442,, 8- 70834, 8-56340, 8-48649, 8-40731, -1 9-74325, 9-48650 n 9-48650 n 9-18546 n 9-0093R, 8-88444, 8-78753, 8-70835,, 8-64140, 00 9-48650 n 8-8844 2n 8-53226, 8-28238, 8-08856, 7-93020,, 7-79630, 7-68032,, +1 9-74325 9-18546 9-00938 8-88444 8-78753 8-70835 8-64140 8-58341 8-53225 +2 9-44251 8-70834 8-58340 8-48649 8-40731 8-34036 8-28237 8-23121 +3 9-26613 8-40732 8-31041 8-23123 8-16428 8-10629 8-05513 +4 9-14119 8-18547 8-10629 8-03934 7.98125 7-93019 +5 9-04428 8-00938 7-94243 7-88444 7-83328 +6 8-96510 7-86325 7-80526 7-75410 +7 8-89815 7-73831 7-68715 +8 8-84016 7-62916 When for this class t' = 0, one of the divisors in j-. ^ T-. ^ , becomes zero we have to put down the negative square of that divisor which retains a real value. This table of the divisor for i' = and for the coefficients of integration ff (i -\- x) is changed into the table of the divisors for f\ (i -\- x) by squaring all the numbers and by adding to the logarithms of the squares log (c -(- c 1 ) fi. Excepted herefrom are the terms for which c or c' becomes zero. Those terms are to be multiplied by or . 11 S/H-riiifn "f' tin' '/'//iii|>nti- the values on one side of the diagonal line of asterisks, since tin- values ap|>oar on both sides arranged in the same manner as [o 6], [a c~], [i c], with respect to [o a], [64] in iln- method of least squares. By means of the horizontal sums ? the coefficients are checked because of v f /,' _L . ^ _ n + 1, o c - 2 * . ( + 2. o ( - 2. 89, . ( r'ir , ' CO* lin i, i' cos sin >, ' CO* in i i' p CO* Mil + 4I.67< 0.0 -2 + 9933.9 - 7.VI.7 5 -4 - 61.9 +11.5 -1 -7 + 1.3 - 3.6 1 (1 -I-.0.6M -3607..VJ' 1 -2 -12287.5 +1166.2 6 -4 - 15.0 + 3.9 -7 + 7.9 - 21.8 2 o - i:u - 397.60< 2 -2 -21290.5 +2442.7 7 -4 - 1.8 + 0.5 1 -7 + 64.1 -210.9 3 - 2.6U - 64.08/ 3 -2 - 2306.4 + 229.2 2 -7 - 31.3 + 22.5 4 0.0 - 12.83/ 4 -2 - 371.6 + 50.1 -1 -5 + 2.2 - 0.7 3 -7 +148-5 + 87.3 .-, tl 0.0 - 2.5K 5 -2 - 46.1 + 6.0 -5 + 14.2 - 4.0 4 -7 + 51 .3 + :u 1 -5 +127.2 - 9.3 5 -7 - 19.2 + 10.6 + 2936.7 0.0 -3 -3 1.0 - 0.6 2 -5 -138.4 -29.3 6 -7 + 17.3 8.0 1 - !*>.2 + 19.8 -2 -3 - 44.5 - 3.4 3 -5 -433.7 +80.6 7 -7 - 3.7 1.9 2 - 210.4 + 105.3 -1 -3 - 276.0 - 23.1 4 -5 +184.0 -67.4 8 -7 - 3.3 + 1.1 3 - 25.8 + 11.-.' -3 - 2694.8 - 192.4 5 -5 - 77.9 +21.7 4 6.2 + !.'-> 1 -3 - 3380.5 Ill-.l 6 -5 -25.7 + 5.8 -8 + 1.7 + 2.1 2 -3 +18286.1 -3229.5 7 -5 - M + 1.5 1 -8 + 13.0 + i:>.7 -3 - - 15.5 3.7 3 -3 - 155.7 + 30.7 8 -5 - 1.4 0.0 2 -8 + 14.3 + 22.4 -a - - 111.9 - 1 :..-.' 4 -3 + 17.1 - 13.5 3 -8 + 32.1 + 24.5 -i - - 969.8 - 5i:i.:t 5 -3 + 3.3 - 0.4 -1 - + 0.2 + 1.2 4 -8 + 13.9 + :-'.- - - 4613.1 + 388.3 6 -3 9.6 + 2.4 -6 + 6.3 +17.9 5 -8 + 5.6 1.1 i - +10401.0 - 584.0 1 -6 - 27.4 +15.8 6 -9 - 6.3 + 3.1 2 - + 2177.7 - 221.7 -2 -4 + 1.5 - 0.4 2 -6 + 28.2 +51.6 7 -8 + 4- r > - 2.3 3 - + 1M.> + 3.1 -1 -4 + 4.6 - 2.3 3 -6 +279.0 +42.3 8 -8 1.2 0.0 4 - + 0.4 -4 + 32.0 - 33.7 4 -6 K.1 +30.5 1 -4 - 716.1 + 96.8 5 -6 + 59.2 -21.5 6 -9 + 1.5 - 0.9 -3 -2 + 8.3 + 1.5 2 -4 + 2107.7 - 14.-..9 6 -6 - 17.3 + 6.0 7 -9 - 2.2 + 1.0 -2 -2 + 1 i-.-.r. 2.2 3 -4 + 1322.9 - ,'-... 7 - - 7.9 + 2.4 8 -9 + 0.4 - 0.8 -1 -2 + 960.0 + 17.4 4 -4 - 264.9 + 66.3 8 -6 - 2.8 + 1.0 9 -9 - 0.1 0.0 For the formation of the differential equations for J, and i^ it is necessary to multiply r" 8 r with 12 3 ^' X L 4- 1.04488 4- 5.01118 cos M ~ . + 3.00 130 cos 2 M 4- 1.38657 cosSJf 4- 0.56905 cos4Jif + 0.2 1828 cos 5 M 4- 0.08089 cos 6 M 4-0.03161 cos7M 4- 0.00979 cos 8 M Having performed these multiplications we obtain for integration . K 4- 4.39501 sin Jf 4- 2.81725 sin 2 Af -f. 1.33137 sin 3 M + 0.55228 sin 4 Jf 4- 0.21 259 sinSJSf 4-0.07719 sin6J!f 4- 0.02454 sin 7 J!f and simply ~df~* d*6 - df i li. , '' Jj *2 t, "' ** ** cos sin cos sin COS sin cos sin - 293.0* 0.0 - 8731.9* 0.0 4 -1 + 9901.6 - 687.9 + 639.9 + 9298.1 1 - 157.8* + 878.7* - 6465.1* + 28.9* 5 -1 + 4485.2 - 293.2 + 293.5 + 4324.0 2 - 300.4* - 7176.5* + 5387.1* - 241.4* 6 -1 + 1848.4 128.2 + 108.6 + 1792.8 3 204.0* - 5548.1* + 4985.9* 187.2* 7 -1 + 707.7 - 35.2 + 42.0 + 685.0 4 - 103.3* - 2019.2* + 2747.8* - 98.1* 5 44.5* - 1300.9* + 1255.3* 42.8* -5 -2 + 642.1 + 12.6 + 10.6 - 722.2 6 17.7* - 525.2* + 523.1* 16-7* -4 -2 + 1486.2 + 29.1 + 24.1 - 1432.4 7 6.5* - 205.2* + 214.3* 5.8* -3 -2 + 2815.4 + 1C6.1 + 100.8 - 2580.8 8 2.5* - 86.7* + 72.6* 2.2* -2 -2 + 2684.3 + 452.4 + 471.5 - 1797.5 9 1.0* - 29.0* + 9.4* 0-3* -1 -2 - 7484.1 + 1745.8 + 1767.9 +10518.1 10 0.1* 3.9* + 1.6* 0.0 -2 -54730.2 + 6308.1 + 6527.9 +64290.9 CHECK. CHECK. 1 -2 -33213.1 + 4804.2 + 6058.7 +63561.3 I a' a />+! Sa' a p m = +0.72b' m q^ +0.2 = +0.2 =-1.3 2 -2 -43437.6 + 5071.7 - 911-5 - 7514.1 3 -2 -67573.3 + 7582.9 - 6459.1 -56034.2 - 1018.5 0.0 + 266.3 0.0 4 -2 -43662.0 + 4902-5 - 4521-2 -40231.6 1 +15182.5 - 28.1 + 162.6 +15375.4 5 -2 -21547.8 + 2409.7 - 2290-0 -20489.0 2 + 5564.4 + 173.9 34.7 + 5736.0 6 -2 - 9236.7 + 1028.4 - 1022.1 - 8963.1 3 + 1767.9 + 254.2 - 196.5 + 1794.1 7 -2 - 3643.3 + 418.6 - 375.7 - 3553.1 4 + 493.1 + 187.1 172.2 + 546.1 8 -2 - 1396.3 + 152.9 - 165.9 - 1351.0 5 + 117.3 + 92.0 105.0 + 88.9 6 + 27.6 + 40.7 12.6 + 52.6 -4 -3 - 651.5 85.0 81.9 + 655.5 7 + 12.2 + 15.1 - 50.0 14.3 -3 -3 - 1374.1 - 208.3 - 196.8 + 1267.2 -2 -3 - 1941.2 493.8 - 469.4 + 1623.6 -5 -1 - 406.2 85.9 90.4 + 427.5 -1 -3 + 389.6 - 1075.9 - 986.1 - 1536.3 -4 -1 - 982.6 - 212.8 - 197.2 ' + 914.4 -3 +15466.8 - 2231.2 - 1968.7 -19070.7 -3 -1 - 1719.4 - 439.9 - 409.9 + 1568.1 1 -3 +32924.0 - 7039.1 - 6188.3 -44406.5 -2 -1 - 1636.9 - 655.5 - 551.2 + 1006.6 2 -3 +11266.3 - 1666.8 - 3073.1 -16238.7 -1 -1 + 4032.3 - 612.7 - 215.2 - 6026.3 3 -3 +39386.4 - 6595.6 + 5534.2 +32608.6 -1 +24638.8 - 2220.4 - 1199.6 -30750.9 4 -3 +24184.2 - 4154.3 + 374!).3 +22344.9 1 -1 + 2392.2 - 642.0 633.8 -16574.1 5 -3 +11285.6 - 1951.6 + 1832.9 +10799.1 2 -1 +22618.3 - 1611.4 + 943.3 +16076.1 6 -3 + 4654.2 - 807.3 + 782.0 + 4512.8 3 -1 +18183.6 - 1301.6 + 1150.8 +16159.8 7 -3 + 1770.4 - 314.5 + 294.3 + 1739.2 13 1. ' {,,, +J i, ' s j co fin co* Mil cot cot tin - a 4 64X7 10&8 4 106.7 4 636.1 9 -6 4 584.2 + 270.1 -1- 47.8 - 556.3 3 -6 4 437.0 + 203.4 uu 1265 -2 -4 + nio.t; - 68.2 - 56.7 - 288.9 4 -6 + 358.0 + 366.4 - 36.9 + 995.9 l I 4 810.7 101.6 - 103.4 - 7 5 -6 4 709.5 + 42.1 - 309.6 - 87.7 c l ,-Jl.l - l< - 2134.8 6 - + 450.4 3.1 84.7 + 71.9 l l 4 6730.5 - 7-."." - <;i... . - 6538.2 7 -6 + 162.7 + 6.0 - 73.3 + 0.4 a -4 4 1!).V..I - l-..7 - 317.0 - 2674.6 4 7290.6 - 885.8' - 204.7 + 1960.0 -2 -7 4 645 - 161.6 - 161.9 67.0 4 -4 . - 860.7 + 698.4 4 4901.3 -1 -7 + l .1.1, - 346.6 304.2 128.3 I 4 ;-!. - 3HG.5 + 300.1 + 2412.3 ' -7 -1- 239.2 - 450.1 367.1 - 210.4 6 -4 + 906.7 llll.l + '.i-'.n 4 861.4 1 -7 4 '-'- 101.8 + 234.0 144.11 7 1 4 293.8 - 37.9 4 14.6 + 267.7 2 -7 + 602.1 - 301.2 + e>2.7 Jl'>.- 3 -7 4 23.'..-. 165.7 + 292.0 - 25.8 -1 -5 4 23.6 - Zt.!> - 30.9 - 13.7 4 -7 4 533.2 + 74.6 117.3 + 228.1 -5 - 1*1.0 - : - 13.9 4 166.0 5 -7 + 140.3 + 187.4 + 9.8 + 518^ 1 -5 - 770.1 - 13.7 + 9.7 + - 6 -7 + 283.7 + 4.4 151.0 31.0 - 414.6 4 1 '.:. + 81.9 4 801.6 7 -7 4 228.1 - 28.0 - 54.4 + 9.6 - in: 4 128.4 + 243.3 + 400.4 4 -5 - 210.8 - !!:!.' - 378.3 - l - I-- 1 -1 -8 4 49.6 + 35.3 + 32.3 - 47.1 - 18.1 - 108.7 - 24.7 - 603.6 -8 + 85.2 + 114.7 + 104.7 755 6 -5 - 169.1 - 1 - 32.8 - 3(W5 1 -8 + 99.9 + 107.1 + 71.3 74.1 - 1.V..7 8.3 - 20.1 - 207.0 2 -8 4 166.9 + 158.9 + 46.6 73.9 8 -5 - 124.0 + 95 - 33.9 - 128.7 3 -8 4 121.3 + 131.4 50.9 + 24.9 4 -8 4 123.3 + 129.5 - 865 + 104.0 -1 -6 4 71.7 4 112.7 r 134.3 - 55.7 5 -8 4 154.8 + 65.2 107.3 + 30.4 -6 4 164.4 4 1- + 112.6 - 154.6 6 -8 - 27.9 + 89.5 + 13.8 + 155.1 1 - 4 453.6 4 265.6 + 173.0 - 434.8 7 -8 + 57.3 ' + 18.4 40.2 - 55.8 The integration of the preceding three differential equations gives finally the perturbations of the rectangu- lar co-ordinates. ', ' | Ti ti cos tin cot sin cot sin - 84.94* 0.0 -1022^1* 0.0 4 148J6TJ 1 - 4.74* 44279.97* -4154.40* - 11.92* HH. 2 4 25.65* 41241.89* -1226.46* 4 24.06* - 48.01* 3 4 8.30* 4 325.86* - 322.92* 4 8.27* - 7.72) 4 4 2.50* 4 86.21* - 85.92* 4 2.37* 1.4lf< 5 4 0.68* 4 22.96* - 22.70* 0.0 - 0.3K 6 4 0.16* 4 6.19* - 6.02* 0.0 - 0.07* 4 0.08* 7 0.0 4 1.31* - 1.37* 0.0 0.0 0.0 - 699.7 0.0 4 755 0.0 1 411185 - 6.6 9.4 4 901.6 0.0 2 4 463-6 - 31.7 4 28.9 4 433.4 4 143.4 :t 4 100.7 1.1.4 4 13.1 4 97.4 4 42.2 4 4 23.3 - 5.2 4 4.9 4 21.1 4 gJi 5 4 6.8 - 15 4 1.7 4 6.1 4 1.0 6 4 0.8 0.4 4 0.1 4 05 4 048 4 i'.-' -5 -I 4 4.1 4 1.1 4 1.0 - 4.0 0.0 -4 -\ 4 32.1 4 3.7 4 35 32-4 4 0.8 - 0.9 i '' 14 I % Si *) l COS sin cos sin COS sin -3 -1 + 122.3 + 11.8 + 11.8 - 122.9 + 4.2 4.5 -2 -1 + 494.5 + 26.8 + 26.3 - 491.7 + 2-J.7 26.9 -1 -1 + 2208.5 - 55.3 72.4 - 2188.4 + 226.2 - 236.6 -1 + 7732.7 - 671.7 - 325.3 - 7809.7 + 428.1 318.4 1 -1 - 1340.7 - 82.3 0.9 - 1289.8 - 554.G + 231.4 2 -1 - 3739.2 + 227.2 - 192.7 - 3658.9 - 202.1 114.3 3 -1 - 1092.5 + 72.3 70.3 - 1081.8 - 22.9 10.7 4 -1 - 300.6 + 19.9 19.6 - 300.2 4.2 1.6 5 -1 _ 79.0 + 5.0 5.4 84.8 0.6 0.3 6 -1 21.9 + 1.3 1.1 - 20.7 7 -1 6.3 0.0 0.0 6.1 -5 -2 6.6 0.2 0.2 + 7.2 -4 -2 - 50.0 + 1.9 + 2.0 + 52.5 -3 -2 - 192.0 + 7.5 + 7.8 + 192.5 1.7 + 2.1 -2 -2 - 778.1 + 36.1 + 36.1 + 779.4 9.2 + 12.0 -1 -2 - 3513.0 + 213.1 + 218.7 + 3500.3 - 72.0 + 85.4 -2 -19149.5 + 2127.3 + 2083.7 +19003.2 - 428.6 + 600.3 1 -2 - 8330.7 + 1305.0 + 754.2 + 9254.2 + 525.7 - 767.6 2 -2 +10930.4 - 1159.0 + 1065.5 +10367.5 + 244.1 146.5 3 -2 + 4932.9 - 540.5 + 540.7 + 4849.2 + 3.7 46.1 4 -2 + 1507.9 - 166.7 + 166.1 + 1497.3 + 1.5 7.4 5 -2 + 428.2 - 47.6 + 47.9 + 432.3 + 0.3 1.4 6 -2 + 122.5 - 13.7 + 12.7 + 112.6 7 -2 + 30.7 3.5 + 3.0 + 29.9 8 -2 + 8.0 0.8 + 0.9 + 7.7 -4 -3 1.9 + 3.0 + 2.8 + 4.8 -3 -3 + 65.9 + 3.6 + 3.5 - 66.1 + 0.6 0.7 -2 -3 + 245.3 + 13.5 + 13.2 - 263.7 + 3.3 3.6 -1 -3 + 1128.7 + 45.6 + 42.7 - 1120.9 + 21.1 22.1 -3 + 5724.9 + 4.2 15.3 - 5630.2 + 187.9 - 208.4 1 -3 + 9598.9 - 2097.8 - 1894.6 - 9736.8 + 145.1 - 246.1 2 -3 - 5031.4 - 17.9 + 509.0 - 2272.5 - 842.5 + 1273.3 3 -3 - 3779.0 + 539.8 - 523.1 - 3638.3 - 69.4 + 141.1 4 -3 - 1034.5 + 161.6 156.4 - 1022.7 18.6 + 16.8 5 -3 - 268.1 + 43.2 - 42.6 - 269.3 - 3.7 + 3.0 6 -3 80.4 + 13.6 9.6 56.7 0.7 + 0.5 7 -3 17.7 + 3.1 3.0 - 17.2 8 -3 4.0 + 0.7 0.6 3.9 -4 -4 1.1 + 1.1 -3 -4 . + 1.4 1.3 -2 -4 3.2 + 1.4 + 0.9 + 2.7 a 0.3 -1 -4 -4 8.9 + 1.4 + 1.2 12.1 + 1.2 - 22.6 + 9.3 4.0 + i 3 + 27.9 2.5 - 21.9 1 -4 + 1826.7 - 182.2 135.1 - 1854.9 + 59.7 - 91.2 2 -4 + 748.2 120.8 - 111.6 - 32.3 - 1&7 + 217.7 3 -4 - 833.4 + 99.3 1.6 - 402.4 56.4 + 80.2 4 _4 - 294.8 + 40.7 - 33.9 - 250.5 2.5 + 14.8 5 -4 - 72.0 + 10.1 8.1 66.4 2.4 + 0.9 6 -4 14.5 + 1.8 1.8 16.4 0.5 7 -4 3.4 + 0.3 2.9 -2 -5 1.6 + 1.7 15 * ft f, ', *' tin CM tin CO* fin -1 -5 10.1 + I.'' + 2.1 10.4 - .! + M -5 47.7 + '.'.' + 4.1 + 46.9 + ': + 1.3 1 -5 J -5 --.>.'. 1 - 148.9 13.4 + 21.4 UfJ + fr.VJ + 218.3 + 188.6 + i:;.- + 104 I'.l 3 -r. + 204.2 - 30.9 40.0 + 7.4 + 80.9 39.4 4 -5 + 20.8 + 7.8 + 20.2 M:;.:I 64 + 84 G -5 + 2.5 + '' ' 1 + 1.1 + 20.6 04 + 24 6 -5 + 3.1 0.6 + 04 + i..l 04 7 -5 + 1.7 + 2.4 8 -5 + 0.9 + 0.9 -2 -6 + 0.7 - 0.3 + 0.2 0.7 -1 -6 + 1.3 24 4.2 1.9 + 1.8 -6 + 14.0 2.3 -r 2.1 14.4 4.0 $.3 1 -6 + 101.1 141.0 + 1264 1874 1.4 2.7 2 -4 f 1664 + 64.2 - 62.6 - 66.6 + 2.7 84 3 -6 153.2 - : + 95.3 - 77.5 - 144 + 22.4 4 -6 37.1 - 324 + 114 - 87.9 + 1.6 54 -6 - 25.6 3.1 + 11.6 14 1.7 + 2.6 6 -6 0.0 0.3 + 1.9 2.2 0.9 7 -6 - 23 T 0.0 -3 -7 04 + 04 0.2 + 0.4 -2 -7 2.0 + 4.3 + 4.3 + 2.1 -1 -7 9.4 + 164 + 15.9 + 9.2 1.0 -7 41.5 + 57.1 + 544 + 41.9 -53 04 1 -7 - 237.0 + 146.4 + 103.9 + 2344 - J3.3 2 -7 162.0 - 86.7 + 110.3 - 238.0 *'.'< Jfft 3 -7 + 290.3 153.9 + 1374 + 272.2 8.9 + 17.- 4 -7 - 20.6 - 30.8 + 37.4 0.0 2.5 + 4.9 5 -7 2.3 11.4 + 4.1 17.7 + 0.3 14 6 -7 5.4 1.0 + 4.1 + 04 0.4 + 0.7 7 -7 2.4 0.3 + 1.3 0.3 -1 -8 - 14 1.4 1.4 + 1.7 -8 6.8 8.3 8.4 + 6.1 - . 04 1 -8 - 16.8 21.4 - 22.0 + 18.8 + 15.5 1.0 2 -8 + 46.1 + 43.3 + 30.6 434 + 1.4 0.7 3 -8 - 44.0 - 50.4 46.7 - 394 4.0 + 0.9 4 -8 - 12.4 - 11.7 -f 94 14.1 - I'. | 0.4 :. -- 7.7 3.0 + 5.4 2.0 - 04 + 0.7 6 -8 04 2.2 0.1 4.0 04 7 -8 0.9 + 0.3 + 04 + 04 Normal Placet referred to the Mean Equinox 1854.0. Berlin M. T. 3 Berlin M. T. a S 1852, July 1.0 271 35 1643 - 8 35 16.00 1855, April 26.0 223 23 31.65 - 58 1&38 1852, October 1.0 274 56 46.02 -18 24 28.78 1856, October 22.0 39 13 48.02 - 5 12 50.07 1853, January 1.0 322 28 46.75 -16 2 17.53 !>, March 90.0 182 4 41.86 + 7 34 3.35 1854, January 28.0 128 3 16.18 +12 2 48.34 1859. July 8.0 278 7 52.10 - 9 19 9.96 16 The perturbations computed with the above coefficients for the times of the normals are : Si +11421 + 4084 + 1750 +39074 + 2042 + 1754 + 5642 + 8584 -15176 -19862 -33592 - 4084 - 2185 -14556 - 2660 -10494 -2756 -2823 -2105 +3665 + 532 - 380 +2672 -^500 +14787 + 9001 +10510 +38902 + 2592 + 5556 + 6360 +10653 -10133 -16524 -30074 + 6322 - 1580 -12885 - 1575 - 6160 - 6858 - 8192 -11002 + 1899 - 98 - 4268 + 1788 - 7252 For J, , j, , f, , the plane of the orbit of Melpomene is the fundamental plane, but J, rj, J are referred to the equator. The transformation is effected by means of the formulas on pages 391 and 392, IB U" /?5"7. We derive from n' = 16 16' 53".3, Q' = 19 16' 43".7, and ' = 15 28' 17".2 for 1854.0: cos (*, x) = + 0.959273 cos (y,*) = 0.268411 cos (z, at) = -f 0.088074 cos (a:, y) = + 0.282146 cos (y, y) = -f- 0.925742 cos (z, y) = 0.251799 cos (or, z) = 0.013949 cos (y, z) + 0.266394 cos (z, z) = -|- 0.963765 The computation of the normal places from the osculating elements for 1854.0 with the perturbations J, TJ, , gives the following equations of condition for the determination of the corrections of the elements : +1.72507 -3.46371 +1.76341 -0.01327 +0.11791 - 9.60585 + 157.29' +1.05428 -2.12179 +0.96271 -0.00356 +0.03244 - 5.53250 + 26.24 +0.98888 -1.13494 +0.69111 -0.02955 +0.01693 - 3.91254 - 184.68 +1.54040 +3.09070 +1.69341 -0.05026 -0.05610 + 0.38965 - 508.67 +1.05335 -1.21848 +1.51267 -0.04736 +0.35622 + 5.19856 + 75.05 +3.21295 +1.63979 +2.06075 -0.07675 +0.47456 +33.30130 -1902.90 +1.01318 +0.73413 +1.50797 -0.08393 +0.19514 +15.62610 - 219.44 +1.85143 -3.64800 +1.80356 -0.01777 +0.07135 +37.14650 - 606.95 dM S XIV r= 2M- M' XXIX = 3M- M> XLIV 5M8M' XV = 4M- M' XXX = 5M M' XLV = 5M7M' the perturbations are : 19 i ' k { cot in CO* (in CM in* ii M -I.'M' -1022.4 If + 14O67* M 1.7 If +427" HV|.40f mm - 44.23f + 493Bf J M + 25-ti.V i.'ll.89f -1226.4 + 24.!Wf l-.ul/ + 53.1* :\M + t.:M + 325.8 - 3*a.'.w + 8.27f - 7.72T + 8.561 4.1A + 2.50* + 86.2U 85.9* + 2UJ7f 1.47< + 1^3f :. M + o.6* + aa/.iK/ 22.7W 0.3U i 0.34/ G.I/ + 0.1W + O.i:c !...'." - OM7t + 0.08f 7 .!/ + 1.31f 1.37< I + 7732.7 - 671.7 - 325J - 7809.7 + 428.1 312.4 I i 'ir.i.r. + 2127.3 + 2083.7 +19003.2 MM + 600.3 :t : .!. + 4.2 15.3 - 5630.2 + 187.9 208.4 4 + 1.4 12.1 ..M; 4.0 + 27.9 21.9 I 47.7 + -.:> + 4.1 + 46.9 + 1.8 + 1.3 6 + 14.0 2.3 2.1 14.4 4.0 0.3 7 41.5 + r,7.i + 54.6 + 41.9 5.3 0.5 81 &a 8.3 M + 6.1 0.5 II - 1340.7 -.'.: (1.0 - 1289.8 - 654.6 + 231.6 J II M - 1150.0 + 1065.5 +10367.5 + 244.1 MM 311 - 3779.0 + 639.8 - :>.':!. i - 3638.3 .,-.1 + 141.1 4 II - !fiW.H + 4t>.7 - 33.9 - 250.5 2-5 + 14.8 .1 II + 2.5 + 2.9 + 1.1 + 20.6 0.6 + 5 611 9.0 ii.it + 1.9 2.2 + 0.9- 7 II 2.4 0.3 + 1.3 0.3 III + !tt!>8.9 - 2097^ - 1894.6 T>.8 + 145.1 261.1 2 III + 166^ ) 64.2 i, -.'.(, - 66.6 + 2.7 2.5 IV - 8330.7 + 1305.0 + 754.2 + 9954.2 + 525.7 - 787.6 2 IV + 748.2 120.8 lll.i. - 32.3 131.7 + 217.7 31V 1. vi.; 78^ + !>:>.:! - 77.5 14.6 + 22.4 4 IV 12.4 11.7 :M; - 14.1 0.4 0.4 V - 5031.4 - 17.9 + 509.0 - 2272^ -IV.:. + 1273.3 av 37.1 - 32.5 + 11^ - 87.9 + 1.6 5^ VI + 49:v..!i - 540.5 + 540.7 + 4849.2 + 3.7 46.1 a vi 144 f 1^ 1.8 16.4 VII - 3739.2 + 227.2 - 192.7 - 3658.9 - 202.1 114.3 2 VII + 1507.9 166.7 + 166.1 + 1497.3 + 1.5 7A 3 VII 80.4 -) 13^ 9.6 - 56.7 0.7 + 03 vin - 3513.0 + 213.1 + 218.7 + 3500.3 - 72.0 + 85.4 9 VIII 3^ + 1.4 - 0.9 + 2.7 IX + 2208.5 :.:>.:! 72.4 - 218M + 226.2 - 236.6 _' IX 77-.I + 36.1 + 36.1 + 779.4 9.2 + 12.0 SIX + 65.9 + &6 + 3-5 66.1 O.li 0.7 4 IX 1.1 + 1.1 X + 1826.7 182.2 135.1 - 1854.9 + 69.7 - 91.2 ax + 46.1 + 43.3 + 39.6 v. ,i..r will then, in not very eccentric ellipses, describe nearly the true anomaly. This auxiliary anomaly, denoting with r', we have, simply, cot v> = cot M. The logarithm of the constant factor - ^ is for Melpomene = 9.8078595, and log p = 0.3398226 for the computation of the nidi us vector by means of r = , ' 1 + co a The correetion c, to be added to v 1 in order to get the true anomaly , is given in Table IL, with M as the argument For the construction of this table I hud c developed in the following series : c = 526.495 sin M + 2232.957 sin 2 M + 819.532 sin 3 M -j- 245.033 sin 4 M e = + 68.825 sin 5 M + 18.848 sin 6 M -j- 5.096 sin 7 M -f 1.395 sin 8 M c = + 0.373 sin 9 M + 0.103 sin 10 M + 0.053 sin II M Example for computing a Place from the Tables. 1861, Feb. 5 d 5" 58" 15' Washington M. T. = Feb. 5" 12' Berlin M. T. We write down on a scrap of paper the constants to be used. From Table V. the logarithms of log* 9.337800 1 9.807860 0.339823 co* (xix) 9.982068 co* (jrix) 9.427362n co* (zi x) 8.943100 co*(njp) 9.449004 co* (yiy) 9.966656 co* (n jr) 9.400622n co* (n z) 8.144356n 9.424948 CO* (:i i) 9.984015 and from Table VI., A' 105 34' 42".6 & 16" 53' 23".8 C' 357" O 7 0".6 log sin a 9.998323 log lin b 9.985806 log lin e 9.425543 M = mean anomaly, and t time since 1854.0 are taken from Table I. M t 1861, 84 42 59".56 -f 7.00068 Feb. 8 47 3.72 0.08488 5 days 1 25 0.60 0.01369 5 hours 3 32.53 0.00057 58 minutes 41.09 15 seconds 0.17 94 59 17.67 +7.09982 1 e 1+e COt ^ M cot M = cot $ t/ 47 29 38".8 9.962142 59 30 30.4 9.770002 v> 119 1 0.8 From Table IL c - 26 10.1 v 118 34 50.7 cos v 9.679789n e cos v 0.104133 9.017589 1 + cos v 0.895867 9.952243* r 0.387580 22 Formation of the Arguments from Talk HI.* I. n. III. IV. V. VI. VII. VHI. IX. 1861, 237.828 322.545 78.202 200.37 162.92 9.81 47.26 30.94 153.11 Feb. 357.425 6.209 1.058 3.63 9.85 21.20 14.99 346.07 348.64 5 days 359.584 1.001 0.171 0.59 1.59 3.42 2.42 357.75 358.17 6 hours 359.979 0.050 0.008 0.03 . 0.08 0.17 0.12 359.89 359.91 234.816 329.805 79.439 204.62 174.44 34.60 64.79 14.65 139.83 XI. xn. xrii. XIV. XV. XVI. xvn. xvni. 1861, 316.03 84.72 131.98 125.46 68.40 216.7 268.8 332.4 179.2 Feb. 358.48 8.78 23.78 16.05 339.85 32.6 343.5 27.4 38.8 5 days 359.76 1.42 3.84 2.59 356.75 5.3 357.3 4.4 6.3 6 hours 359.99 0.07 0.19 0.13 359.84 0.3 359.9 0.2 0.3 314.26 94.99 159.79 144.23 44.84 254.9 249.5 4.4 224.6 XIX. XX. XXI. XXII. xxm. XXIV. XXV. XXVI. XXVII. 1861, 118.9 57.1 184.1 309.5 193.9 3.3 221.5 71.7 34.2 Feb. 8.3 36.2 334.7 350.8 355.9 13.5 328.5 353.3 359.5 5 days 1.3 5.8 355.9 358.5 359.3 2.2 354.9 358.9 359.9 6 hours 0.1 0.3 359.8 359.9 0.0 0.1 359.8 0.0 0.0 128.6 99.4 154.5 298.7 189.1 19.1 184.7 63.9 33.6 xxvin. XXIX. XXX. XXXI. XXXII. xxxin. XXXIV. XXXV. XXXVI. 1861, 278.6 343.7 301.4 294.9 356.8 259.0 348.7 50.6 26.1 Feb. 4.7 331.1 41.3 33.6 5.7 322.3 56.3 28.5 50.1 5 days 0.8 355.3 6.7 5.4 0.9 353.9 9.1 4.6 8.1 6 hours 0.0 359.8 0.3 0.3 0.1 359.7 0.5 0.2 0.4 284.1 309.9 349.7 334.2 3.5 214.9 54.6 83.9 84.7 XXXVII. XXXVIII. XXXIX. XL. XLI. xm. XLHL XLIV. XLV. 1861, 88.0 203.7 187 226 24 140 147 166 288 Feb. 22.3 17.1 348 54 338 333 341 23 26 5 days 3.6 2.8 358 9 357 356 357 4 4 6 hours 0.2 0.1 > 114.1 223.7 173 289 359 109 125 193 318 With these Arguments the perturbations are computed from Table IV. * These Arguments being expressed in degrees and decimals, 360.0, 720.0, or 1080 0, must be subtracted when one of the sums is greater than one of those numbers. 23 Ti-nus with / I II III IV V VI VII VIM IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII X X X I V XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII XLIV XLV i * & + ma me. 41U.3 7.vt.4 mjt m. 136.1 UM 73.6 37.1 6.1 8.7 22.1 18.3 19.1 21.2 8.7 7.0 44 U 3.6 LI 1.9 0.6 n.- M 4:i.: 334.7 165.2 1 !'.'.( 1:1.- 101. ! -T.-J 30.1 21.7 24.2 5.7 7.9 6.9 2.8 0.6 0.1 0.2 0.9 14) + 264.9 liV.T.- WJ MM 127.3 79.7 m 104.2 12.7 10.2 0.9 2.0 U 2.6 U 2.4 1.5 0.2 0.3 0.7 U ::>:.- ..-..- 460.7 (,-.- M J17.4 37.1 23.1 M J :i:!.- 4 12.3 15.6 2.0 :!.:, 2.5 11.3 3.9 17.0 4.4 0.1 2.1 2.7 0^ + .-..I'.', m 9M 10^ 1.8 9.9 4 \A 0.1 l.i 0.3 1.0 0.7 0.1 2.2 1.2 M 1.0 0.1 50.1 21.3 8^ 2.J 19.6 4.8 33.9 12.0 0.3 1.7 OJ> 34i 0.3 0.3 0.4 0.1 !.."> 0.2 0.4 cos(r,r)S, + 4890.0 cos (jri x) ti 265.9 co* (zi x ) Ci + 49.0 Reduction to the appar- ent equinox. /+2o".03 9 ,0.9765 G 338 24 sin(G+o')Hl 99.9697 tan ' 9.3529 + l'.99 oTaii'.H J o' +22.22 coe(G + o) 9.5573. JV - 3.42 0.5338. o=13245 :i.-,'.':, i - +12 42 3.4 E - 4603.1 co(r,y){i + 1412.5 cos (jri jf) ft + 920.2 cot(ij)ti - 14U.4 1 -I- 2192J CD* (l *) Ei - 70.0 cot (jn ) >n + 264.3 cos (*i *) Ci + 537.9 C + 732.2 sin (4' + r) 224 9 33.3 9.843018. r sin a 0.385903 * 0.228921. sin (B 1 + r) 135 28 14.5 9.845888 r sin 6 0.373386 y 0^i:i-'7) sin (2 Y -0.614699 ^cosa'sina' +1.044308 0.018828 * -1.694031 J + 4603 X +0.723955 ^cosa'cosa' -0.965473 9.984740. in a' , , 9^65861 tan a' 132 45 13.3 0.034088. * +0.586568 C + 732 Z -0.266747 J sin *' +0.320553 9^05900 JcotV 0.152967 cos** ( f 9.989240 tan J> +12425^ 9.352933 J 0.163727 a' and f arc referred to the mean equinox 1861.0. 6. o.77 26.IHH37 I8H /' j-7 17 ao.-c, 2.00137 I--I 354 42 34.48 27.00C68 1 -:,7 :n> i.; i 3.00068 1 J 98 8 18.90 28.00000 1868 134 8 46.89 4.00000 i--n 201 34 1.92 28.99932 J:t7 34 32.01 4.1' 1884 n 305 16 45.75 30.001 37 1-1,1 /; nil 17 i 6.0(il :!7 I:. 48 42 21.47 31.00C68 1-1,1 84 4'J 511.56 7.00068 i-i, 158 8 13.18 B4MOO I-*.-. 1 I-i 8 43.88 8.00000 1--7 255 33 56.90 Mjna 1861 I'll ni 2ti.'.'!i 1 >n2 I--H B :i--!i 16 40.74 34.0(11 :!7 1-1,1 /; :f, 17 10.83 10.001:17 |-~i in.' I-J 21.45 35.00C68 I86B in- 42 .M. .v. 11.00068 l-'.ni -'Hi - -.17 36.00000 1866 JIJ 8 38.86 fc 12.00000 !-''! 309 33 51.88 36.991i:J2 1867 :V45 34 21.98 12.99932 1-2 B 5:t Ki :i5.72 :t-.i:ol37 l-i i-i B 89 17 5.81 14.00137 IBM 156 42 19.44 39.00068 I-,.' I! >2 42 49.53 15.00063 i-'i 260 8 3.15 40.00000 1-7 1 j-.Hi - nn.-j:, 16.00000 I-T, 3 33 46.87 4I>.!I9!>32 1-71 jl IJ4 Iti.'Hi 16.!" 1896 B 107 16 30.70 42.00137 i-7-j /; II.: 17 0.80 18.00137 1897 210 42 14.42 43.00068 1-7:: JH, 42 4i.:.i 1!U>0068 I-,- 314 7 58.14 44.00000 1-71 350 8 2-. 90.00000 1- ,, 57 33 41.85 44.!' 1 .'!i::2 1-7'. 93 :n n.'.'.-. 20.'t9932 1900 B 161 16 25.(i!i +46.00137 l-7ii /( 197 16 55.78 +32.00137 Month*. if l Day*. it t o il January 0.00 +0.00000 1 o 17 0.12 +O.OC374 Ki l,niary 8 47 3.72 0.08488 8 34 0.24 0.00548 March 16 43 7.08 0.16154 3 51 0.36 O.IKIH2I April J.-> 30 10.78 0.24642 4 1 8 0.48 0.01(!i5 May 34 11 0.32856 5 1 25 (1.60 (i.oi:a;:i June 42 47 18.10 0.41344 6 1 42 0.72 i . 1643 July 51 17 2148 0.49558 7 1 59 0.84 0.01917 August 60 4 25.40 0-58046 8 2 16 0.96 O.G2I!N) inber li- .'.I 211.12 046534 9 2 :n 1."- O.i 2464 i Irtohcr 77 21 :fj.72 0.74748 10 2 50 1.20 0.027:1* NoTemhoi* 86 8 36.44 0.83236 93 5 40 2.40 d.i 5476 Dftmber 94 38 40.04 +1.91450 30 8 :m +0.08214 In BUscxtile Yean one day most be subtracted from the date in the fir*! two months. 26 TABLE I. Concluded. FOR THE MEAN ANOMALY. The times are referred to the meridian of Washington. Hours. M 1 Hours. M t 1 H i a 1 42.51 +0.00011 13 9 12.57 +0.00149 2 1 25.01 0.00023 14 9 55.07 0.00160 3 2 7.52 0.00034 15 10 37.58 0.00172 4 2 50.02 0.00046 16 11 20.08 0.00183 5 3 32.53 0.00057 17 12 2.59 0.00195 6 4 15.03 0.00069 18 12 45.09 0.00206 7 4 57.54 0.00080 19 13 27.60 0.00218 8 5 40.04 0.00092 20 14 10.10 0.00229 9 6 22.55 0.00103 21 14 52.61 0.00241 10 7 5.05 0.00114 22 15 35.11 0.00252 11 7 47.56 0.00126 23 16 17.62 0.00264 12 8 30.06 +0.00137 24 17 0.12 +0.00275 M M For Minutes. For Seconds. For Minutes. For Seconds. 1 o".71 o'.'oi 31 2K96 0.'36 2 1.42 0.02 32 22.67 0.37 3 2.13 0.03 33 23.38 0.39 4 2.83 0.05 34 24.09 0.40 5 3.54 0.06 35 24.80 0.41 6 4.25 0.07 36 25.50 0.42 7 4.96 0.08 37 26.21 0.44 8 5.67 0.09 38 26.92 0.45 9 6.38 0.11 39 27.63 0.46 10 7.08 0.12 40 28.34 0.47 11 7.79 0.13 41 29.05 0.48 12 8.50 0.14 42 29.76 0.50 13 9.21 0.15 43 30.47 0.51 14 9.91 0.16 44 31.17 0.52 15 10.62 0.17 45 31.88 0.53 16 11.33 0.19 46 32.59 0.54 17 12.04 0.20 47 33.29 0.55 18 12.75 0.21 48 34.00 0.57 19 13.46 0.22 49 34.71 0.58 20 14.17 0.23 50 35.42 0.59 21 14.88 0.25 51 36.12 0.60 22 15.58 0.26 52 36.83 0.61 23 16.29 0.27 53 37.54 0.62 24 17.00 0.28 54 38.25 0.64 25 17.71 0.29 55 38.96 0.65 26 18.42 0.31 56 39.67 0.66 27 19.13 ' 0.32 57 40.38 0.67 28 19.84 0.33 58 41.09 0.68 29 20.54 0.34" 59 41.80 0.70 30 21.25 0.35 60 42.51 0.71 '11 TABLE II. H.U TIIK CORRECTION C TO BE ADDED TO THE AUXILIARY ANOMALY v 1 . Argument -> M. For J/> 180 the Argument U 360 31, and the lign of c to be ravened. Arg. c Diff. Arg. 1 Diff. Arg. c Diff. c Diff o 1 H , 1 M o i H , , 0.0 0.00 22.5 . Ji. .-.-.'.I. 45.0 +311 29.45 67.5 + 8 45.17 + 1 831 '"-' B4 41 9630 >..! .5 39 0.24 -.3I 68.0 7 59.33 -4-84 1.0 2 17.58 .-." 41 5338 .:"- 46.0 38 30.16 30-08 A 7 13^7 44.76 A 3 V.1..-1, 24.0 42 r.i.:>i 34-81 .5 37 59.23 30-93 69.0 6 27.'JO 4647 2.0 4 :t4.79 ,,-. .1 i-j 4:i.iii 34-U 47.0 37 27.48 11-76 A 6 42-35 46.66 5 43.14 -.!. 25.0 It li..t-t 41 A 36 54.H3 11-66 70.0 4 56.!'3 46-43 3.0 6 5I.-T 86.13 A 43 27.56 31-31 48.0 36 21.61 11-31 .5 4 11.65 46-18 A 7 59.10 7-81 26.0 43 47.30 19-74 A 35 47.54 14-07 71.0 3 264>3 46-13 4.0 9 6^1 87-61 A 44 5.57 18-17 49.0 35 12.75 14-79 A 9 41.56 44-96 A 10 13.75 87-14 27.0 44 22.37 16-80 A 34 37425 34-50 72.0 1 5632 44-76 "<:: 16-33 16-18 44-67 5.0 +11 20.47 .5 +44 37.69 50.0 +34 1.07 A + 1 12.25 1:2 -J6.74 +8.17 28.0 44 .M..-.., +11-87 A 33 24425 -M-M 73.0 + 27.90 -44-16 6.0 13 32.50 86-78 A 45 3.96 11-40 51.0 324630 17-46 A - 16423 44-11 1 1 :!7.71 6-31 29.0 45 14.90 10-94 A 32 8.74 18-08 74.0 1 0.13 41 90 7.0 15 4:2.3:1 '''' : A 45 24.40 9-60 52.0 31 30.10 18-84 A 1 43.78 41-66 16 46.31 3-98 30.0 45 32.46 8-08 .5 30 50.90 19-10 75.0 2 27.17 43-39 8.0 17 49.61 81-JO A 45 39.07 8-61 53.0 30 11.17 19-71 A 3 10.29 41-11 A 18 52.20 81.69 31.0 45 44.27 6-30 A 29 30.93 40-34 76.0 3 53.12 43-81 9.0 1 54.04 61-84 A 45 48.04 1-T7 54.0 28 50.19 40-74 A 4 35.67 43-66 A .' i 55.08 61-04 32.0 45 5ii.4ii 3.M A 98 8.99 41-30 77.0 5 17.91 43-34 80-10 + 0-88 41-63 41-91 10.0 +21 55.28 .5 +45 51.38 55.0 +27 27.36 A - 5 5934 .5 2254.61 +69-11 33.0 4650.97 - 0-41 A 26 45.30 -43-08 78.0 6 41.45 -4141 ll.n 23 53.03 68-41 A 45 49.19 1-78 56.0 26 234 43-46 A 7 22.73 41-38 .5 24 50.51 67-48 34.0 45 46.05 1-14 A 25 20.01 43-81 79.0 8 3.66 40-91 12-0 17.02 68-61 A 45 41.57 4-4* 57.0 24 3632 41-19 A 8 44.24 40-68 J 26 42-51 66.49 35.0 45 35.76 6-81 A 23 53.31 41-41 80.0 9 24.46 40-31 13.0 27 36-96 64-41 A 45 28.65 7-11 58.0 23 9.48 41-81 A 10 4.31 19-86 A 28 30.33 61-17 36.0 45 20.23 8-U A 22 25.37 44-11 81.0 10 43.79 19-48 14.0 29 22.60 M-*7 A 45 10.53 9-70 59.0 21 404)9 M-H .5 11 2238 19-08 30 13.73 61-11 37.0 44 69.58 10-96 A 90 56-37 44-81 82.0 12 1.57 19-69 49-97 11-19 44-86 38-10 154 +31 3.70 .5 +44 47.39 60.0 +20 11.52 A -123937 .5 31 52.48 +48-7S >.ii 44 33.97 -11-43 .5 19 26.47 -46-06 83.0 13 17.76 -17.89 lli.il 3940.04 47-68 A 44 19.35 14-63 61.0 18 41.24 44-11 A 13 55.23 17*47 .5 XI 26.36 46-3-1 39.0 44 3-55 16.90 A 17 55.84 46-40 .-l.ii 14 32429 17-06 17.0 34 11.42 46-08 A 43 46.58 18-97 62.0 17 10.30 46-64 .5 15 8.92 lti-63 J 34 .V,.l:' 41-77 40.0 43 28.48 18-10 .5 16 24.63 46-67 85.0 15 45.11 18-18 18.0 3.-. 37.66 41-47 A 43 9425 19-H 63.0 15 3836 46-77 A 16 2036 16-76 .5 36 1830 41-14 41.0 42 48.93 30-13 .5 14 53.01 46-86 86.0 16 56.17 16-11 19.0 36 58.60 T..-I 42 27.52 31-41 64.0 14 7.H- 46-91 A 17 31.03 14-88 A 37 37.03 18-41 42.0 42 5.07 33-46 A 13 21.11 46-97 87.0 18 5.43 14-40 1746 H-49 46-01 tt-94 20.0 +38 14.08 A +41 11.-.- 65.0 +12 35.10 A -18 39.37 _5 38 49.75 +16-87 43.0 41 17.08 -*4-80 .5 11 49.07 -4841 88.0 19 1-J.-5 -M-48 21.0 39 24.01 14-18 A 40 51.60 .''.. !- 66.0 11 3.05 4841 A 19 4535 33.1(1 5 39 56.85 31-84 44.0 40 25.15 36-4S A 10 17.05 46-00 89.0 20 18.38 11-61 22.0 40 29.27 11-41 A 39 57.76 97-19 67.0 9 31.08 46-97 A 20 50.42 32-04 +40 58.26 +49-99 I5.il +39 29.45 -M.11 A + 8 45.17 -46-91 90.0 -21 21.98 -11-66 28 TABLE II. Concluded. FOR THE CORRECTION c TO BE ADDED TO THE AUXILIARY ANOMALY v'. Argument = M. For J/> 180 the Argument is 360 M, and the sign of c to be reversed. Arg. c Diff. Arg. c Diff. Arg. c Diff. Arg. c Diff o i ii u o i u o i u u o i H ii 90.0 .5 -21 21.98 21 53.05 -31.07 112.5 113.0 -36 9.15 36 16.91 - 7-76 135.0 .5 -34 18.97 34 6.94 +12-03 157.5 158.0 -20 16.21 19 51.85 +24-36 91.0 22 23.63 30-58 .5 36 24.18 7-27 136.0 33 54.55 12-39 .5 19 27.32 24-53 .5 22 53.72 30-09 114.0 36 30.94 6-76 .5 33 41.80 12-75 159.0 19 2.61 24-71 92.0 23 23.31 29-59 .5 36 37.20 6 26 137.0 33 28.70 13-10 .5 18 37.73 24-68 .5 23 52.40 29-09 115.0 36 42.97 5-77 .5 33 15.25 13-45 160.0 18 12-68 25-05 93.0 24 20.98 28-58 .5 36 48.25 5.28 138.0 33 1.46 13-79 .5 17 47-47 25-21 .5 24 49.05 28-07 116.0 36 53.03 4-78 .5 32 47.32 14-14 161.0 17 22-10 25-37 94.0 25 16.62 27-57 .5 36 57.33 4-30 139.0 32 32.85 14-47 .5 16 56-58 25-52 .5 25 43.67 27-05 117.0 37 1.14 3-81 .5 32 18.04 14-81 162.0 16 30-90 25-68 26-54 3-32 15-14 25-82 95.0 -26 10.21 .5 -37 4.46 140.0 -32 2.90 .5 -16 5.08 .5 26 36-24 -26-03 118.0 37 7.31 - 2-85 .5 31 47.44 + 15-46 163.0 15 39.11 +25-97 96.0 27 1.75 28-51 .5 37 9.67 2-36 141.0 31 31.65 15-79 .5 15 13.00 26-11 18S 16-10 26-24 .5 27 26.74 :j4-yy 119.0 37 11.55 .5 31 15.55 164.0 14 4G.7G 97.0 27 51.20 24-46 .5 37 12.97 1-42 142.0 30 59.13 16-42 .5 14 20.38 26-38 .5 23 15.14 23.94 120.0 37 13.91 0-94 .5 30 42.41 16-72 165.0 13 53.68 26-50 98.0 28 38.56 23-42 .5 37 14.38 0-47 143.0 30 25.37 17-04 .5 13 27.25 26-63 .5 29 1.45 22-89 121.0 37 14.39 - 0-01 .5 30 8.04 17-33 166.0 13 0.51 26-74 99.0 29 23.82 22-37 .5 37 13.93 + 0-40 144.0 29 50.41 17-63 .5 12 33.65 26-86 .5 29 45.66 21-84 122.0 37 13.01 0-92 .5 29 32.48 17-93 167.0 12 6.68 26-97 21-32 1-37 18-22 27-07 100.0 -30 6.98 .5 -37 11.64 145.0 -29 14.26 .5 -11 39.61 .5 30 27.77 -20-79 123.0 37 9.81 + l.RS .5 23 55.75 +18-51 168.0 11 12.43 +27-18 101.0 30 48.03 20-26 .5 37 7.53 2.28 146.0 28 36.96 18-79 .5 10 45.15 27-28 .5 31 7.76 19-73 124.0 37 4.81 2-72 .5 28 17.89 19-07 169.0 10 17.78 27-37 102.0 31 26.97 19-21 .5 37 1.64 3-17 147.0 27 58.54 19-35 .5 9 50.32 27-46 .5 31 45.64 18-67 125.0 36 58.04 3-60 .5 27 38.93 19-61 170.0 9 22.77 27-55 103.0 32 3.79 18-15 .5 36 54.00 4-04 148.0 27 19.05 19-88 .5 8 55.14 27-63 .5 32 21.41 17-62 126.0 36 49.53 4-47 .5 26 58.91 20-14 171.0 8 27.43 27-71 104.0 32 38.50 17-09 .5 36 44.63 4-90 149.0 26 38.51 20-40 .5 7 59.64 27-79 .5 32 55.06 16-56 127.0 36 39.31 5-3-2 .5 26 17.86 20-65 172.0 7 31.79 27-85 16-04 5-74 20-90 27-92 105.0 -33 11.10 .5 -36 33.57 150.0 -25 56.96 .5 - 7 3.87 .5 33 26.61 -15-51 123.0 36 27.41 + 6-16 .5 25 35.81 +21.15 173.0 6 35.89 +27-98 106.0 33 41.59 14-98 .5 36 20.83 6-58 151.0 25 14.41 21-40 .5 6 7.85 28-04 .5 33 56.05 14-46 129.0 36 13.84 6.99 .5 24 52.78 21-63 174.0 5 39.76 28-09 107.0 34 9.99 13-94 .5 36 6-44 7-40 152.0 24 30.92 21-86 .5 5 11.62 28-14 .5 34 23.40 13-41 130.0 35 58.63 7-81 .5 24 8.83 22-09 175.0 4 43.44 28-18 108.0 34 36.30 12-90 .5 35 50.41 8-22 153.0 23 46.51 22-32 .5 4 15.21 28-23 .5 34 48.68 12-38 131.0 35 41.80 8-61 .5 23 23.98 22-53 176.0 3 46.94 28-27 109.0 35 0.54 11-86 .5 35 32.79 9-01 154.0 23 1.23 22-75 .5 3 18.65 2S-29 .5 35 11.88 11-34 132.0 35 23.39 9-40 .5 22 38.27 22-96 177.0 2 50.32 28-33 10-83 9-79 23-17 28-35 110.0 -35 22.71 .5 -35 13.60 155.0 -22 15.10 .5 - 2 21.97 .5 35 33.02 -10-31 133.0 35 3.43 +10-17 .5 21 51.72 +23-38 173.0 1 53.60 +28-37 111.0 35 42.82 9-80 .5 34 52.87 10-56 156.0 21 28.14 23-58 .5 1 25.21 28-39 .5 35 52.10 9-28 134.0 34 41.94 10-93 .5 21 4.36 23-78 179.0 56.81 28-40 112.0 36 0.88 8-78 .5 34 30.64 11-30 157.0 20 40.38 23-98 .5 - 28.41 28-40 .5 -36 9.15 - 8.27 135.0 -34 18.97 +11-67 .5 -20 16.21 +24-17 180.0 0.00 +28-41 29 TABLE III. FOR THE AR i: 3.418 303.47 187.00 310.63 67.10 2%.:ia 236.37 i--.<; n . .:t:i 316.8% 1 5.H05 346.37 303.1!) 2X'."I 244.12 nun loa.a.-, I-.-.7 :i5i>.ai:i mm a8.:c,7 29. 14 .-,....7 327.71 :i-.-.:.'i wet MMM 4U.8IO 174.1*6 340.22 237.18 163.63 194.74 i ' 562 17ti.i:i- 53.963 114.70 290.84 229.85 53.71 359.55 li v.io I860 D i.-.i MiVMI 749 1.-.7.59 47.04 iai.17 230.73 1 '.'..OS J-I..-7 l-(,l :.-<28 78.202 200.37 1'.. !.-! 47.26 HUM 1.VI.11 1-..-J 207.503 35.64H 90^54 243.15 278.80 259.44 223.7:i 326.86 MJ6 1863 177.178 i -.: . .108 885.! i.l 34.68 149.08 40.33 tut 245.60 1-61 11 1 H..769 182.056 11 328.82 1MI.88 ::".!" 217.34 MB 111.48 1-.,-, llii.444 255.1 Vi 128.047 11.60 266.76 389.03 33^7 94.17 337.7:1 I-,,, 86.119 323.263 140.500 64.:W 22.64 178.67 210.41 290.00 2rej.!>7 ]-<,: man 41.366 152. 97.16 138.53 68.30 KM 126.01 nM 186- /; -T..3S5 114.670 165.440 140.05 254.72 31H.62 203.05 321.48 296.10 1869 :i55.o60 l'.'7.774 177. 182.83 10.62 208.26 20.49 157.41 162.35 1-7. :;.'!. 734 260-877 190.346 225.01 126.49 97.90 197.02 353.33 BAH i-;i 294.409 333.981 902.79'.) 268.39 242.37 :U7..V! 1U6 189.25 254.84 i-;-.' /; 264.001 47.284 -.' 15.286 311.29 :i:.-..-,7 237.85 190 .57 24.72 12.t.7-_' 1-7:1 .U76 120.388 337.740 354.06 114.45 127.49 7.10 220.64 346.% 1-71 -.'a.350 193.492 240. loa 36.84 230.33 17.12 183.63 56.56 213.21 1-7.-. 173.025 252.646 79.62 346.22 266.76 0.17 252.48 79.46 1-76 D 1 lv!.617 339.899 265.134 122.52 102.42 157.08 177.18 87.95 305.34 1-77 112.2i 47.489 357.a r >3 92.031 44.54 dJD 303.67 306.62 145.41 97.92 1*92 B 17.080 ?o.:v,7 104.517 87.44 157.79 193.99 121.63 340.88 323.80 1- : 346.755 143.460 116.070 130.23 273.68 -::.i,.! 300.17 176^1 190.05 1- '! 316.430 216.564 129.423 172.99 -"..v; 333.26 116.70 12.73 56.30 I-'C, 286.104 Meg 141.876 215.77 145.44 222.90 293.23 BUB 282~ r >4 1896 fl 255.696 2.JI71 I.-V4.363 358.67 261.64 113.22 110.2.5 44.12 148.42 1897 225.371 76.075 166.816 301.40 i7..-,a 2.85 386.78 240.04 14.67 1-,- 105.045 140.178 179.268 344.22 133.30 252.40 103.31 75.96 240.01 1899 164.720 MM 191.721 27.00 249.28 142.12 279.84 271.88 107.16 1900 fl 134.IU 1 a n. aw 5.48 32.44 107.35 333.04 30 TABLE III. Continued. FOR THE AEGUMENTS. A. For the different Years. The times are referred to the meridian of Washington. Years. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. 1852 B 116.98 233.29 130.80 22357 44^34 o 4.1 219.5 305.9 o 28.3 1853 99.11 336.72 50.76 52.55 167.16 27.5 25.1 268.7 124.8 1854 81.24 80.15 330.72 241.53 289.98 50.9 190.7 231.4 221.3 1855 63.37 183.58 250.68 70.52 52.79 74.3 356.3 194.1 317.8 1856 B 45.44 267.29 171.41 260.02 174.06 98.7 161.3 157.8 55.5 1857 27.57 30.72 91.37 89.01 297.78 122.1 326.9 120.5 152.0 1858 9.70 134.15 11.33 277.99 60.59 145.5 132.5 83.3 248.5 1859 351.82 237.58 291.29 1(56.98 183.41 168.9 2D8.1 46.0 345.0 186t) B 333.90 341.29 212.02 296.48 305.58 193.3 103.2 9.6 82.7 1861 316.03 84.72 131.98 125.46 68.40 216.7 268.8 332.4 179.2 1862 298.16 188.15 51.94 314.45 191.21 240.1 74.4 295.1 275.7 1863 280.29 291.57 331.90 143.43 314.03 263.5 240.0 257.8 12.2 1864 B 262.36 35.29 252.63 332.93 76.20 287.9 45.0 221.5 1.10.0 1865 244.49 138.72 172.59 161.92 199.01 311.3 210.6 184.2 2C6.5 1866 226.62 242.14 92.55 350.91 321 .,83 334.7 16.2 146.9 303.0 1867 208.75 345.57 12.51 179.89 84.65 358.1 181.8 109.7 39.5 1868 B 190.82 89.29 293.24 9.39 206.81 22.5 346.9 73.3 137.2 1869 172.95 192.71 213.20 198.38 329.63 45.9 152.5 36.0 233.7 1870 155.08 296.14 133.16 27.37 92.45 69.3 318.1 a r >8.8 330.2 1871 137.21 39.57 53.12 216.35 215.27 92.7 123.7 321.5 66.7 1872 B 119.29 143.28 333.85 45.85 337.43 117.1 288.7 285.1 164.4 1873 101.42 246.71 253.81 234.84 100.25 140.5 94.3 247.9 260.9 1874 83.54 350.14 173.77 63.83 223.07 163.9 259.9 210.6 357.4 1875 65.67 93.57 93.74 252.81 345.89 187.3 65.5 173.4 93.9 1876fi 47.75 197.28 14.46 82.32 108.05 211.7 230.6 137.0 191.6 1877 29.88 300.71 294:42 271.30 230.87 235.1 36.2 99.7 288.1 1878 12.01 44.14 214.39 100.29 353.69 258.5 201.8 62.5 24.6 1879 354.13 147.57 134.35 289.27 116.50 281.9 7.4 25.2 121.1 1880 B 336.21 251.28 55.08 118.78 238.67 306.3 172.4 348.8 218.9 1881 318.34 354.71 335.04 307.76 1.49 329.7 338.0 311.6 315.4 1882 300.47 98.14 255.00 136.75 124.31 353.1 143.6 274.3 51.9 1883 282.60 201.57 174.96 325.73 247.12 16.5 309.2 237.0 148.4 1884 B 264.68 305.28 95.69 155.23 9.29 41.0 114.3 200.7 246.1 1885 246.80 48.71 15.65 344.22 132.11 64.4 279.9 163.4 342.6 1886 228.93 152.14 295.61 173.20 254.92 87.7 85.5 126.1 79.1 1887 211.06 255.57 215.57 2.19 17.74 111.1 251.1 88.9 175.6 1888 B 193.14 359.28 136.30 191.69 139.91 135.6 56.1 52.5 273.3 1889 175.26 102.71 56.26 20.68 262.73 159.0 221.7 15.2 9.8 1890 157.39 206.14 336.22 209.66 25.54 182.4 27.3 338.0 106.3 1891 139.52 309.56 256.18 38.65 148.36 205.7 192.9 300.7 202.8 1892 B 121.60 53.28 176.91 228.15 270.53 230.2 358.0 264.3 300.5 1893 103.73 156.71 96.87 57.14 33.34 253.6 163.6 227.1 37.0 1894 85.85 260.13 16.83 246.12 156.16 277.0 329.2 189.8 133.5 1895 67.98 3.56 296.79 75.11 278.98 300.4 134.7 152.6 230.0 1896 B 50.06 107.28 217.52 264.61 41.15 324.8 299.8 116.2 327.8 1897 32.19 210.70 137.48 93.59 163.96 348.2 105.4 78.9 64.3 1898 14.31 314.13 57.44 282.58 236.78 11.6 271.0 41.7 160.8 1899 356.44 57.56 337.40 111.56 49.60 35.0 76.6 4.4 257.2 1900 B 338.52 161.27 258.13 301.07 171.76 59.4 241.7 328.0 355.0 31 TABLE III. Gmtbuud. mi; TIII: AUGI-.MKNTS. A. For the different Yeui. The time* are referred to tho meridian of Washington. Twn. \1 \ \\ \\I XXII \\lll XX1\ XXV. XXVL XXVII o o O o O o o o l-v_- /; :tli,.:i 17 '.-.' MU MM 867.9 14.5 322.0 58.8 83.0 MJ MM i-.i MM ttft.7 173.1 311.0 340.3 77.6 I-.M I.VJ.I :tn.ti MM.:, 352.1 171.:. 331.8 300.0 261.8 IM MM 17.7 172.7 123.3 130.5 MM MJ 1 -. ,6 B ::i-.i; -.'..I 234.0 134.1 75.0 MM 277.2 104.5 61.3 1-57 r.i.-j 396.2 -'.-...' 26.8 68.2 MM 26.0 55.9 MM 1-1.7 217.4 :i:.-.i MM MM MM 255.3 307.5 50.5 tan --.'. 7 MM 60.5 167.5 290.4 TV, 244.4 MM 45.1 letxi /; .". ' 1-JI.'' :.-. i 242.1 204.6 -: :.'.! 150.2 39.7 tan iias .-,7.1 184.1 MM 193.9 3.3 221.5 71.7 34.2 I-.-.- JI7.il MM MM 200.7 145.7 162.0 210.6 353.2 28.8 URJ I-.M 3U-.I 91.8 97.5 MM 199.6 274.6 23.4 1864 /; Mil :;,,'. 7 342.7 49.1 1 19.7 187.7 195.9 18.0 1-,,-, 151.3 71. i 233.8 0.9 278.4 176.7 117.4 12.5 29.1 134.1 125.0 312.7 77.0 11,:..- 38.9 7.1 1867 95.2 16.1 264.5 235.7 1. M.'i 320.3 1.7 1868 B -.-..'. MM J-.7.I, 267.0 216.2 34.8 MM 241.6 356.3 Ml 183.6 MB.? B9.7 l.-.-.l MM 193.4 132.0 163.1 350.8 1-7U MU mj 21.9 49.3 119.8 352.1 121.0 MJ :vi.-,.4 1-71 I''.'. 1.1 84.1 300.4 71.6 150.8 110.1 6.0 340.0 1-7-2 D 117.9 o.i 1 1:.. 1 191.3 23.3 309.9 98.2 MM 334.6 l-7:i m&ja 134.6 207.G --M 335.I in-.:, 87.2 MM 329.2 1-71 :ti:t.'i 2no.8 333.6 MM 267.2 76.3 130.2 323.7 1 -7.-, '.1. j 9 MJ1 224.7 238.7 65.8 65.3 51.7 318.3 1-76 B 334.3 33.3 115.G 190.4 224.9 53.4 333.0 :u _>.! 1-77 .'I-..' 40.4 95.5 6.8 142.2 23.6 42.5 254.5 307.5 1-7- 346.2 106.6 mjs a-.7.ii 94.0 182.3 31.5 17:.. ' 302.0 1-7' -I.-.' 17-J.- 140.0 45.8 340.9 20.6 97.4 296.6 l-*0 D 1-.'.-. 240.1 281.1 39.9 357.5 140.0 8.6 18.7 291.2 1-1 MJ 343.3 MU 309.3 298.7 357.7 300.2 MM 1 .' 18.5 12.4 4r..-> 182.2 261.1 97.3 346.8 221.6 260.4 l-l IMU 78.6 107.6 7:1.4 212.9 256.0 335.8 143.1 274.9 1884 fi Jll.- II.V' 169.0 324.2 164.5 .-,-,.! 323.9 64.4 26! 1.5 1---. KU 212.1 231.2 2I.-..4 116.3 213.7 318.9 345.9 264.1 !--.; 293.3 KKi.r, (,-.! 12.4 302.0 267.3 1-7 148.8 344.4 av,.:, 357.7 MJ 171.1 291.0 1-.- 253.2 1888 B 247.1 51.8 :..,.- 248.5 331.6 330.2 279.1 110.1 247.8 1889 MB.1 ll-.'i HM 139.7 283.4 !'-.- 268.2 31.5 242.4 UN 83.1 184.1 i-i.-j 30.8 23.J.2 MTJ 257.2 313.0 237.0 MM 181.1 250.3 243.3 MM 187.0 86.1 246.3 Mtfi 231.5 1892 B 279.4 317.6 304.7 172.8 U-.7 245.2 234.3 MM 226.1 1893 17.4 6.9 64.0 903 43.! ."."..I 77.2 220.7 1894 II. '..I 90.0 69.0 315.1 42.3 202.6 212-5 358.7 215.3 1 - 15 213.4 r.',.i 131.2 j .,.: 354.1 1.2 201.5 MM 209.9 1896 fi 311.7 MM 97.1 305.8 160.3 MM 201.4 MM 1897 49.7 '.- Mi 254.7 MM 257.6 319.0 178.6 MU 199.0 1898 147.7 MM 316.9 239.4 209.4 117.0 167.7 44.4 UM 1899 245.7 62.0 19.0 130.6 161.2 27G.3 156.8 188.2 1900 B 344.0 !_".:! 8-1.1 Sl.fi I !-.'.- 7r,.4 11!.- 247.1 1 -.'.7 32 TABLE III. Continued. FOR THE ARGUMENTS. A. For the different Years. The times are referred to the meridian of Washington. Years. XXVIII. . XXIX. XXX. XXXI. XXXII. XXXIII. XXXIV. XXXV. XXXVI. o o o o O o O 1852 B 141.2 171.1 237.4 330.1 107.3 297.8 134.9 272.0 110.7 1853 196.4 190.4 4.2 6.0 174.9 213.7 78.2 247.2 340.9 1854 251.7 209.7 131.0 41.8 242.6 129.7 21.6 222.4 211.2 1855 306.9 229.2 257.8 77.7 310.3 45.6 324.9 197.6 81.4 1856 B 2.3 247.7 26.0 114.6 18.2 320.4 270.1 173.7 313.3 1857 57.5 267.1 152.8 150.4 85.9 236.3 213.5 148.9 183.5 1858 112.7 286.4 279.6 186.3 153.5 152.3 156.8 124.1 53.8 1859 168.0 305.8 46.4 222.1 221.2 68.3 100.2 99.3 284.0 I860 B 223.4 324.3 174.6 259.1 289.1 343.0 45.3 75.4 155.9 1861 278.6 343.7 301.4 294.9 356.8 259.0 348.7 50.6 26.1 1862 333.8 3.1 68.2 330.7 64.5 174.9 292.0 25.7 256.4 1863 29.0 22.5 195.0 6.6 132.1 90.9 235.4 0.9 126.6 1864 B 84.4 40.9 323.2 43.5 200.0 5.6 180.5 337.0 358.5 1865 139.6 60.3 90.0 79.4 267.7 281.6 123.9 312.2 228.7 1866 194.9 79.7 216.8 115.2 335.4 197.5 67.2 287.4 99.0 1867 250.1 99.1 343.7 151.0 43.1 113.5 10.6 262.6 329.2 1868 B 305.5 117.5 111.8 188.0 110.9 28.2 315.8 238.7 201.1 186!) 0.7 136.9 238.6 223.8 178.6 304.2 259.1 213.9 71.3 1870 56.0 156.3 5.4 259.7 246.3 220.2 202.5 189.1 301.6 1871 111.2 175.7 132.3 295.5 314.0 136.1 145.8 164.3 171.8 1872 B 166.6 194.1 260.4 332.4 21.9 50.9 91.0 140.4 43.7 1873 221.8 213.5 27.2 8.3 89.5 326.8 34.3 115.6 274.0 1874 277.0 232.9 154.1 44.1 157.2 242.8 337.7 90.8 144.2 1875 332.3 252.3 280.9 80.0 224.9 158.7 281.0 66.0 14.4 1876 B 27.6 270.8 49.0 116.9 292.8 73.5 226.2 42.1 246.3 1877 82.9 290.2 175.8 152.7 0.5 349.4 169.6 17.3 116.6 1878 138.1 309.5 302.7 188.6 68.2 265.4 112.9 352.5 346.8 1879 193.3 328.9 69.5 224.4 135.8 181.4 56.3 327.7 217.1 1880 B 248.7 347.4 197.6 261.3 203.7 96.1 1.4 303.8 88.9 1881 304.0 6.8 324.5 297.2 271.4 12.1 304.8 279.0 319.2 1882 359.2 26.2 91.3 333.0 339.1 288.0 248.1 254.2 189.4 1883 54.4 45.5 218.1 8.9 46.8 204.0 191.5 229.4 59.7 1884 B 109.8 64.0 346.2 45.8 114.6 118.7 136.7 205.5 291.5 1885 165.0 83.4 113.1 81.6 182.3 34.7 80.0 180.7 161.8 1886 220.3 102.8 239.9 117.5 250.0 310.7 23.4 155.9 32.0 1887 275.5 122.2 366.7 153.3 317.7 226.6 326.7 131.1 262.3 1888 B 330.9 140.6 134.9 190.2 25.6 141.4 271.9 107.2 134.1 1889 26.1 160.0 261.7 226.1 93.2 57.3 215.2 82.4 4.6 1890 81.3 179.4 28.5 261.9 160.9 333.3 158.6 57.6 234.6 1891 136.6 198.8 155.3 297.8 228.6 249.2 101.9 32.8 104.9 1892 B 192.0 217.3 283.5 334.7 296.5 164.0 47.1 8.9 336.7 1893 247.2 236.6 50.3 10.6 4.2 79.9 350.4 344.1 207.0 1894 302.4 256.0 177.1 46.4 71.8 355.9 293.8 319.2 77.2 1895 357.6 275.4 303.9 82.2 139.5 271.9 237.1 294.4 307.5 1896 B 53.0 293.9 72.1 119.2 207.4 186.6 182.3 270.6 179.3 1897 108.3 313.3 198.9 155.0 275.1 102.6 125.6 245.7 49.6 1898 163.5 332.6 325.7 190.8 342.8 18.5 69.0 220.9 279.8 1899 218.7 352.0 92.5 226.7 50.4 294.5 12.4 196.1 150.1 1900 B 274.1 10.5 220.7 263.6 118.3 ' 209.2 317.5 172.2 22.0 33 TABLE III. GmtimutL FOH THE ARGUMENTS. A. For the different Team. The time* are referred to the meridian of Washington. y. MI XXXVII. XXXVIII XXXIX XI. XLI. XI. II XI. Ill XLIV. XLV. 1852 1! '.'17.- l-.ui 1 o in 161 o 103 O 10 214 O 63 ] -:.:) 1 1 '.'I 31.1 m m 147 146 128 8 l-.VI -::.'.'. 112 11 192 281 43 313 1855 314.0 7:I.H 303 35 116 236 56 317 HI MM G 216.8 J7.VI 164 M a 979 IM 233 903 1887 ll-. > 117.4 M 213 325 m HI 147 148 i--.- 21.0 318.8 M 126 70 8 101 69 93 MM J-i.l 160.2 106 39 17.-, 59 237 336 38 i-i;.i /; 1 -.Vl 2.2 327 313 279 96 371 HI 344 i-i,i 88.0 ',>i:t.7 187 226 94 140 147 166 Hi i -<;. Htt.1 4.-,. I 48 140 199 184 HI 81 233 i-.;i HU 246.5 269 53 234 J 57 HI 178 M;I /; . i:.r..o 88.5 129 HI 339 M 192 271 194 1865 r>7.i 290.0 350 240 84 316 327 1-:, 69 1866 319.2 131.4 211 153 188 1 102 100 14 1S67 --.'I.:! 332.8 72 67 293 45 238 14 318 1868 B i-.'l.i 174.8 292 341 38 88 12 290 264 1-.,' 26.2 16.3 153 254 143 133 148 204 209 1870 -.'--..' 217.7 14 167 248 177 HI 119 154 i-7i 190.3 59.2 235 80 352 221 58 33 99 1872 B 93.1 261.1 95 355 97 265 193 308 44 1873 355.2 102.6 316 968 202 309 328 223 349 1874 257.3 304.0 177 181 307 353 103 138 294 I-7-. 139.4 145.5 38 94 52 38 239 52 239 1876 D 62.2 347.4 M 9 156 81 13 327 185 1877 324.3 188.9 119 M 261 125 148 262 130 1878 -j.;. i 30.3 340 195 6 170 284 156 74 l-7:i 1-'-.'. 231.8 201 Ml 111 214 59 71 19 1880 B 31.3 73.8 61 23 215 257 194 346 325 1-1 293.4 275.2 -,'-_' 296 320 M 329 261 270 I.' 1 :>:,.:, 116.6 143 209 65 346 104 175 215 l--:i 97.6 318.1 4 122 170 30 239 90 160 1884 B 0.4 160.1 224 37 274 74 14 5 105 1-.-, 262.5 1.5 85 310 19 118 149 280 50 1886 164.5 202.9 306 223 124 162 285 194 355 1887 66.6 44.4 166 136 229 207 60 109 HI 1888 B 329.4 306.4 27 00 333 950 195 23 246 I--:- 231.5 87.8 248 323 78 294 330 299 1!1 1- .,, 133.6 HM 109 236 183 339 105 213 135 1891 :r,.7 130.7 329 149 ne S3 840 128 80 1892 B 298.5 332.7 190 64 32 66 15 43 96 1893 200.6 174.1 51 7 137 111 150 318 331 1894 102.7 15.5 m 250 M 155 H6 Hi 976 I-'.', 4.8 217.0 132 163 347 199 61 147 991 1896 B 267.6 59.0 353 78 91 243 195 62 166 1897 169.7 260.4 214 Ml 196 ma 331 336 111 1898 71.8 101-8 74 264 301 331 106 251 56 1899 333J3 303.3 177 46 15 241 166 1 1900 B 136.7 145.3 l.V, M ISO 59 16 81 307 34 TABLE III. Continued. FOR THE ARGUMENTS. D. Variations of the Arguments for the different Months. The times are referred to the meridian of Washington. Months. I. II. III. IV. V. VI. VII. VIII. IX. January 0?000 o!ooo o!ooo 0.00 000 0.00 o.oo o.oo o.oo February 357.425 6.209 1.058 3.63 9.85 21.20 14.99 346.07 348.64 March 355.098 11.817 2.014 6.91 18.74 40.35 28.53 333.48 338.38 April 352.523 18.026 3.072 10.54 28.59 61.55 43.52 319.55 327.02 May 350.031 24.035 4.096 14.06 38.12 82.07 58.03 306.07 316.03 Jane 347.456 30.244 5.154 17.69 47.97 103.27 73.02 292.14 304.67 July 344.964 36.253 6.178 21.21 57.50 123.79 87.53 278.66 293.68 August 342.389 42.462 7.236 24.84 67.35 144.99 102.52 264.73 282.32 September 339.814 48.671 8.294 28.47 77.19 166.19 117.51 250.80 270.96 October 337.322 54.680 9.318 31.99 86.72 186.71 132.02 237.32 259.97 November 334.747 60.889 10.376 35.62 96.57 207.91 147.01 223.39 248.61 December 332.255 66.898 11.400 39.14 106.10 228.43 161.52 209.01 237.62 Months. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. January o.oo o.oo o.oo 000 o.oo o 0.0 o 0.0 o 0.0 o 0.0 February 358.48 8.78 23.78 16.05 339.85 32.6 343.5 27.4 38.8 March 357.11 16.72 45.26 30.55 321.65 62.0 328.6 52.2 73.8 April 355.59 25.50 69.04 46.60 301.50 94.6 312.1 79.6 112.6 May 354.12 34.00 92.05 62.13 282.00 126.1 296.1 106.1 150.1 June 352.60 42.78 115.83 78.18 261.85 158.7 279.6 133.5 188.9 July 351.13 51.28 138.84 93.71 242.35 190.2 263.6 160.0 226.4 August 349.61 60.06 162.62 109.76 222.20 222.8 247.1 187.4 265.2 September 348.09 68.84 186.39 125.81 202.05 255.3 230.6 214.8 303.9 October 346.62 77.34 209.40 141.34 182.55 286.8 214.6 241.3 341.4 November 345.10 86.12 233.18 157.39 162.40 319.4 198.1 268.7 20.2 December 343.63 94.62 256.19 172.92 142.90 350.9 182.1 295.3 57.7 Months. XIX. XX. XXI. XXII. XXIII. XXIV. XXV. XXVI. xxvn. o o o o o o o o o January 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 February 8.3 36.2 334.7 350.8 355.9 13.5 328.5 353.3 359.5 March 15.8 68.9 311.9 342.4 352.8 25.6 300.1 347.3 359.1 April 24.1 105.1 286.6 333.2 348.1 39.1 268.6 340.6 358.6 May 32.2 140.1 262.1 324.2 344.1 52.2 238.1 334.2 358.2 June 40.5 176.3 236.8 315.0 340.0 65.6 206.6 327.5 357.7 July 48.6 211.3 212.3 306.1 336.0 78.7 176.1 321.0 357.3 August 56.9 247.5 187.0 296.8 331.9 92.1 144.6 314.3 356.8 September 65.2 283.7 161.7 287.6 327.8 105.6 113.1 307.6 356.3 October 73.3 318.7 137.2 278.6 323.8 118.6 82.6 301.2 355.9 November 81.6 354.9 111.9 269.4 319.7 132.1 51.1 294.5 355.4 December 89.7 29.9 87.4 260.5 315.7 145.2 20.6 288.0 355.0 In Bissextile Years subtract one day from the date in the first two months. TABLE III. Continued. FOR THE ARGUMENTS. n. Variation* of the Arguments for the different Month*. The time* are referred to the meridian of Washington. Monthi. XXVI II XXIX XXX. XXXI. XXXII. XXX11I XXXIV. XXXV. XXXVI. o o o o o o o Q January 0.0 0.0 0.0 0.0 0.0 0.0 0X1 0.0 0.0 February 4.7 331.1 41.3 33.6 5.7 322.3 56.3 BU 50.1 March 8.9 ii'H.'i 78.7 64.0 10.9 IBM 107.2 54.2 95.4 April in.:, 276.0 120.0 97.6 16.6 250.6 163.5 BU n:..:. M : 18.0 2i.O 160.0 130.2 22.2 214.1 218.0 110.2 194.0 June 22.7 219.1 201.3 KM 27.9 176.4 274.4 au 244.1 July 27.2 llil.l 241.3 196.4 33.5 139.9 HU 166.2 2)2.6 August 31.8 1 .,.'.-. BM _-.:,..,, 39.2 102.2 HJ 194.6 342.7 Septemlicr :wi.r, 133.3 ::.-.;.' KS4 44.9 i,l.-, 814 223.1 32.8 I triober 41.0 105.3 3.9 296.2 50.5 28.0 136.1 MM 81.3 Noremlior 45.6 194 45.2 ::-. '- 56.2 350.3 192.4 279.1 131.4 December :->.l 48.4 B5.2 2.4 61-8 ::i:;.- 246.9 3C6.6 179.9 Monthi. XXXVII. xxxvin. XXXIX. XL. XLI. XI.II. X I.IIl. XLIV. XLV. o o o o o o o January 0.0 0.0 February 22.3 17.1 348 54 338 333 341 23 26 March 42.4 32.5 338 102 319 309 324 44 50 April 64.6 49.6 326 156 297 282 305 67 76 May 86.2 66.2 314 m 276 256 MB 90 101 June 108.4 83.3 303 262 J.-, 1 229 267 113 127 July 130.0 99.9 291 314 233 203 ' 248 136 152 August 152.2 117.0 279 7 212 177 229 159 178 KMlHeiuber 171.:. 134.1 268 61 190 150 210 182 204 October 196.0 150.6 256 113 169 124 192 205 229 Norember 218.3 167.7 244 167 147 97 173 228 255 December 239.8 184.3 333 219 126 71 154 250 260 In Bissextile Years subtract one day from the date in the first two months. 3G TABLE III. Continued. FOR THE ARGUMENTS. C. Variations of the Arguments for the different Days. The times are referred to the meridian of Washington. Days. I. II. III. IV. V. VI. VII. VIII. IX. 1 359?917 0^200 0?034 0.12 0.32 0.68 o 0.48 359.55 359.63 2 359.834 0.401 0.068 0.23 0.64 1.37 0.97 359.10 359.27 3 359.751 0.601 0.102 0.35 0.95 2.05 1.45 358.65 358.90 4 359.667 0.801 0.137 0.47 1.27 2.74 1.93 358.20 358.53 5 359.584 1.001 0,171 0.59 1.59 3.42 2.42 357.75 358.17 6 359.501 1.202 0.205 0.70 1.90 4.10 2.90 357.30 357.80 7 359.418 1.402 0.239 0.82 2.22 4.79 3.39 356.85 357.43 8 359.335 1.602 0.273 0.94 2.54 5.47 3.87 356.40 357.07 9 359.252 1.803 0.307 1.06 2.86 6.16 4.35 355.95 356.70 10 359.169 2.003 0.341 1.17 3-18 6.84 4.84 355.51 356.34 20 358.338 4.006 0.683 2.34 6.35 13.68 9.67 351.01 352.67 30 357.508 6.009 1.024 3.52 9.53 20.52 14.51 346.52 849.01 Days. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. 1 359.95 o 0.23 o 0.77 052 359.35 o 1.1 3595 o 0.9 o 1.3 2 359.90 0.57 1.53 1.04 358.70 2.1 358.9 1.8 2.5 3 359.85 0.85 2.30 1.55 358.05 3.2 358.4 2.7 3.8 4 359.80 1.13 3.07 2.07 357.40 4.2 357.9 3.5 5.0 5 359.76 1.42 3.84 2.59 356.75 5.3 357.3 4.4 6.3 6 359.71 1.70 4.60 3.11 356.10 6.3 356.8 5.3 7.5 7 359.66 1.98 5.37 3.62 355.45 7.4 356.3 6.2 8.8 8 359.61 2.27 6-14 4.14 354.80 8.4 355.7 7.1 10.0 9 359.56 2.55 6.90 4.66 354.15 9.5 355.2 8.0 11.3 10 359.51 2.83 7.67 5.18 353.50 10.5 354.7 8.8 12.5 20 359.02 5.67 15.34 10.36 347.00 21.0 349.4 17.7 25.0 30 358.53 8.50 23.01 15.53 340.50 31.5 344.0 26.5 37.5 Days. XIX. XX. XXI. XXII. XXIII. XXIV. XXV. XXVI. xxvn. 1 0.3 o 1.2 359^2 359^7 3599 o 0.4 3590 359.8 o 0.0 2 0.5 2.3 358.4 359.4 359.7 0.9 358.0 359.6 0.0 3 0.8 3.5 357.6 359.1 359.6 1.3 356.9 359.4 0.0 4 1.1 4.7 356.7 358.8 359.5 1.7 355.9 359.1 359.9 5 1.3 5.8 355.9 358.5 359.3 2.2 354.9 358.9 359.9 6 1.6 7.0 355.1 358.2 359.2 2.6 353.9 358.7 359.9 7 1.9 8.2 354.3 357.9 359.1 3.0 352.9 358.5 359.9 8 2.2 9.3 353.5 357.6 358.9 3.5 351.9 358.3 359.9 9 2.4 10.5 352.7 357.3 358.8 3.9 350.9 358.1 359.9 10 2.7 11.7 351.8 357.0 358.7 4.4 349.8 357.9 359.9 20 5.4 23.4 343.7 354.0 357.4 8.7 339.7 355.7 359.7 30 8.1 35.0 335.5 351.1 356.0 13.0 329.5 353.6 359.6 37 TABLE III. Continwd. FOR Tin: AKI.I MI: NTS. C. Variations of the Arpuraenu for the different Duys. The time* are referred to the meridian of Washington. XXVIII. XXIX XXX. XXXI XXXII. XX XIII. X X XIV. XXXV. XXXVI. 1 O ii.-j K0J O 14 1.1 o 0.2 o o 0.9 14 o 0.3 :;:.-.! 2.7 2.2 0.4 3T)7.6 34 13 3.2 :t ii.r, VIA 4.0 3.3 0.6 356.3 U 83 4.9 4 ii. i, H6J 5.3 4-3 0.7 388.1 7.3 3.7 6.5 5 03 IBM 6.7 54 0.9 9.1 44 8.1 I 0.9 354.4 8.0 6.5 1.1 352.7 10.9 54 9.7 7 1.1 9.3 74 1.3 :i.M.:, 12.7 6.4 11.3 8 1..' :t-vj.:, 10.7 8.7 1.5 3.%o.:i 14.5 7.3 12.9 9 1.4 12.0 9.8 1.7 343.0 16.4 8.3 144 Ml 1.5 K0.7 13.3 10.9 1.9 347.8 18.2 9.2 Hi.-.- 30 14 341.3 26.7 21.7 3.7 335.7 36.3 18.4 :w.:t 30 4.5 i 332-0 40.0 :.r, 54 :i23..-, :.|..-, .'7.:, i-.:, Un- XXXVII. XXXVIII. XXXIX. XL. XLI. XLII. XI. Ill XLIV. XLV. o O o o 1 0.7 0.6 2 359 359 359 1 1 2 1.4 1.1 359 3 359 SBG 359 2 2 3 2.2 1.7 359 5 358 357 358 2 3 4 2-9 2.2 359 7 357 357 :'-,- 3 3 5 3.6 .'.- 358 9 357 356 357 4 4 6 4.3 3.3 358 10 356 KB 356 5 5 7 5.0 3.!) 357 12 355 354 356 5 6 8 5.7 4.4 357 14 354 353 355 6 7 9 C.5 5.0 357 16 354 352 354 7 8 10 7.2 U 356 17 353 351 354 8 8 20 144 11.0 352 35 346 343 MB 15 17 30 2145 164 349 52 339 334 342 2! 25 38 TABLE III. Continued. FOR THE ARGUMENTS. D. Variations of the Arguments for the different Hours. The times are referred to the meridian of Washington. Hours. I. II. III. IV. V. VI. vn. VIII. IX. 1 359.997 0.008 o!ooi o!oo o 0.01 0.03 0.02 359.98 35999 2 359.993 0.017 0.003 0.01 0.03 0.06 0.04 359.96 359.97 3 359.990 0.025 0.004 0.02 0.04 0.09 0.06 359.94 359.95 4 359.986 0.033 0.006 0.02 0.05 0.11 0.08 359.92 359.94 5 359.983 0.042 0.007 0.03 0.07 0.14 0.10 359.90 359.92 6 359.979 0.050 0.008 0.03 0.08 0.17 0.12 359.89 359.91 7 359.976 0.058 0.010 0.03 0.09 0.20 0.14 359.87 359.89 8 359.972 0.066 0.011 0.04 0.11 0.23 0.16 359.85 359.88 9 359.969 0.075 0.013 0.04 0.12 0.26 0.18 359.83 359.86 10 359.965 0.083 0.014 0.05 0.13 0.29 0.20 359.81 359.85 20 359.930 0.166 0.028 0.10 0.26 0.57 0.40 359.62 359.70 Hours. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. o o o o o o O O o 1 0.00 0.01 0.03 0.02 359.97 0.0 0.0 0.0 0.1 2 0.00 0.02 0.06 0.04 359.95 0.1 0.0 0.1 0.1 3 359.99 0.04 0.10 0.07 359.92 0.1 359.9 0.1 0.2 4 359.99 0.05 0.13 0.09 359.89 0.2 359.9 0.2 0.2 5 359.99 0.06 0.16 0.11 359.87 0.2 359.9 0.2 0.3 6 359.99 0.07 0.19 0.13 359.84 0.3 359.9 0.2 0.3 7 359.99 0.08 0.22 0.15 359.81 0.3 359.9 0.3 0.4 8 359.98 0.10 0.26 0.17 359.78 0.4 359.8 0.3 0.4 9 359.98 0.11 0.29 0.20 359.76 0.4 359.8 0.3 0.5 10 359.98 0.12 0.32 0.22 359.73 0.4 359.8 0.4 0.5 20 359.96 0.24 0.64 0.24 359.46 0.9 359.6 0.7 1.0 Hours. XIX. XX. XXI. XXII. XXIII. XXIV. XXV. XXVI. XXVII. o o o o O o o o 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.0 0.1 359.9 0.0 0.0 0.0 359.9 0.0 0.0 3 0.0 0.2 359.9 0.0 0.0 0.1 359.9 0.0 0.0 4 0.0 0.2 359.9 0.0 0.0 0.1 359.8 0.0 0.0 5 0.1 0.2 359.8 359.9 0.0 0.1 359.8 0.0 0.0 6 0.1 0.3 359.8 359.9 0.0 0.1 359.8 0.0 0.0 7 0.1 0.3 359.8 359.9 0.0 0.1 359.7 0.0 0.0 8 0.1 0.4 359.7 359.9 0.0 0.1 359.7 0.0 . 0.0 9 0.1 0.4 359.7 359.9 0.0 0.2 359.6 . 0.0 0.0 10 0.1 0.5 359.7 359.9 o.o 0.2 359.6 0.0 0.0 20 0.2 1.0 359.3 359.8 0.0 0.4 359.2 0.0 0.0 39 TABLE III. Conchil.l. FOR THE ARGUMENTS. D. Variation* of the Argument* for the different Hour*. The tirae arc referred to the meridian of Washington. Hour*. XXVIII. XXIX. XXX. XXXI XXXII. xxxni. \XXIV. XXXV. XXXVI. o o o o o o p 1 0.0 0.0 0.1 0.0 0.0 0.1 0.0 0.1 2 0.0 IBM 0.1 0.1 0.0 :ivi.:i 0.2 0.1 0.1 :t 0.0 0.2 0.1 0.0 359.8 0.2 0.1 0.2 4 0.0 0.2 0.2 0.0 359.8 0.3 0.2 0.3 :. 0.0 3894 0.3 0.2 0.0 3BB.7 0.4 0.2 0.3 G 0.0 :c,<>.- 0.3 0.3 0.1 359.7 U 0.2 0.4 7 0.0 :r,! 1.7 0.4 0.3 0.1 :i.-,:u, 0.5 0.3 0.5 8 0.0 my 0.5 0.4 0.1 BfiM 0.6 0.3 0.5 :i 0.0 3BB.7 M 0.4 0.1 359.5 0.7 0.3 M u 0.0 IBM 0.6 0.5 0.1 359.5 U 0.4 0.7 90 0.0 359.2 1.1 0.9 0.2 359 J) LB M 1.3 Honrn. \\\V1I XXXVIII. XXXIX. XL. XLI. XLII. XI. III. XLIV. XLV. 1 o 0.0 o 0.0 o o o o 2 0.1 0.1 3 0.1 0.1 - 4 (I.I 0.1 5 0.2 0.1 6 0.2 0.1 7 0.2 0.2 8 0.2 0.2 1 9 0.3 0.2 1 10 0.3 0.2 1 20 M 0.5 1 359 359 1 1 40 TABLE IV. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. Terms multiplied with t. Argument = M. Arg. Ji Diff. ft Diff. Cl Diff. Arg. 6 Diff. T!l Diff. Si Diff. o o - 5.24 -684.22 -35.71 45 +437.82 -360.75 +24.69 1 + 9.15 +14-39 683.87 + 0-35 34.59 +1-12 46 440.91 +3-09 350.43 + 10-32 26.00 + 1-31 2 23.51 14-36 683.09 0-78 33.45 1-14 47 443.73 2.82 340.15 10-28 27.29 1-29 3 37.83 14-32 681.88 1-21 32.29 1-16 48 446.27 2.54 329.91 10-24 28.57 1-28 4 52.09 14-26 680.23 1.65 31.11 1.18 49 448.56 2.29 319.74 10-17 29.84 1-27 5 66.27 14-18 678.17 2-06 29.91 1-20 50 450.58 2.02 309.63 10-11 31.10 1-26 6 80.37 14-10 675.69 3*48 28.69 1-22 51 452.36 1.78 299.58 10-05 32.34 1-24 7 94.35 13-98 672.80 3-89 27.45 1-24 52 453.88 1.53 289.61 9-97 33.57 1-23 8 108.20 13.85 669.51 3-29 26.19 1-26 53 455.17 1.Q9 279.72 9-89 34.79 1-22 9 121.91 13-71 665.82 3-69 24.92 1-27 54 456.22 1-05 269.90 9-82 35.99 1.20 13-56 4-09 1.29 0-82 9-73 1-18 10 +135.47 -661.73 -23.63 55 +457.04 -260.17 +37.17 11 148.84 +13-37 657.27 + +.46 22.33 +1-30 56 457.64 +0-60 250.53 + 9.64 38.34 +1-17 12 162.03 13-19 652.42 4-S5 21.01 1-32 57 458.02 0-38 240.98 9.55 39.50 1-16 13 175.01 112-98 647.19 5-23 19.68 1.33 58 458.19 +0-17 231 .53 9-45 40.64 1.14 14 187.77 12-76 641.62 6-57 18.34 1-34 59 458.16 -0-03 222.18 9.35 41.77 1-13 15 280.31 lfc.54 635.69 6-93 . 16.99 1.35 60 457.94 0-22 212.93 9-25 42.88 1-11 16 212.60 12-29 629.42 6-27 15.63 1-36 61. 457.53 0-41 203.79 9.14 43.97 1-09 17 224.65 12-05 622.84 6-68 14.25 1.38 62 456.94 0-59 194.75 9-04 45.05 1-08 18 236.45 11-80 615.94 6-90 12.87 1-38 63 456.17 0-77 185.82 8-93 46.11 1-06 19 247.98 11-53 608.74 7-20 11.48 1*39 64 455.23 0-94 177.01 8.81 47.15 1-04 11.24 7-48 1-39 1-11 8-70 1-03 20 +259.22 -601.26 -10.09 65 +454.12 -168.31 +48.18 21 270.19 +10-97 593.51 + 7-78 8.69 +1-40 66 452.85 -1-27 159.72 + 8.59 49.19 + 1-01 22 280.86 10-67 585.50 8-01 7.28 1-41 67 451.42 1.43 151.25 8-47 50.18 0-99 23 291.23 10-37 577.25 8-25 5.87 1-41 68 449.84 1.58 142.89 8-3G 51.16 0-98 24 301.29 10-06 568.77 8-48 4.45 1-42 69 448.12 1-72 134.65 8-24 52.12 0-96 25 311.04 9-75 560.07 8-70 3.03 1-42 70 446.26 1-86 126.53 8-12 53.06 0-94 26 320.46 9.42 551.17 8-90 1.61 1-42 71 444.26 2-00 118.54 7-99 53.98 0-92 27 329.56 9-10 542.08 9-09 - 0.19 1-42 72 442.13 2-13 110.66 7-88 54.89 0-91 28 3^8.32 8-76 532.81 9.27 + 1.23 1-42 73 439.88 2-25 102.91 7-75 55.78 0-89 29 346.74 8-42 523.39 9-42 2.65 1-42 74 437.51 2-37 95.28 7-63 56.65 0-87 8-09 9.58 1-42 2-49 7-51 0*85 30 354.83 -513.81 + 4.07 75 +435.02 - 87.77 +57.50 31 +362.62 + 7-79 504.09 + 9-72 5.48 +1-41 76 432.42 -2-60 80.39 + 7-38 58.33 +0-83 32 370.07 7-45 494.25 9-84 6.90 1-42 77 429.72 2-70 73.12 7-27 59.15 0-82 33 377.21 7-14 484.30 9-95 8.31 1-41 78 426.92 2.80 65.98 7-14 59.94 0-79 34 384.01 6-80 474.25 10-05 9.71 1-40 79 424.02 2-90 58.96 7-02 60.72 0-73 35 390.48 6.47 464.12 10-13 11.11 1-40 80 421.02 3-00 52.07 6-89 61.48 0-76 36 396.63 6-15 453.91 10-21 12.51 1-40 81 417.93 3-09 45.29 6.78 62.23 0-75 37 402.45 5.82 443.65 10.28 13.89 1-38 82 414.76 3-17 38.64 6-65 62.95 0-72 38 407.95 6-50 433.35 10-30 15.27 1-38 83 411.50 3-26 32.10 6.54 63.66 0-71 39 413.13 5-18 423.01 10-34 16.65 1-38 84 408.17 3.33 25.68 6-42 64.35 0-69 4.87 10-36 1.36 3-41 6.30 0-67 40 +418.00 -412.65 +18.01 85 +404.76 - 19.38 +65.02 41 422.57 + 4-57 402.27 +10-38 19.37 +1.36 86 401.29 -3-47 13.20 + 6-18 65.67 +0-68 42 426.82 4-25 391.88 10-39 20.72 1*35 87 397.75 3*54 7.13 6-07 66.30 0-63 43 430.78 3-96 381.49 10-39 22.05 1-33 88 394.14 3.61 1.18 5.95 66.92 0-62 44 434.45 3-67 371.11 10-38 23.38 1-33 89 390.47 3-67 + 4.66 5-84 67.51 0-59 45 +437.82 + 3-37 -360.75 +10-36 +24.69 +1-31 90 +386.75 -3.72 + 10.39 + 5-73 +68.09 +0-68 II TABLE IV. Cunt, I'KUTI lil'.ATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. Terms multiplied with (. Argument = M. Ar* 5, Diff. 1l Diff. ,& Diff. Ji Diff. Th Diff. f, Diff. 90 - H).:P.I +68.09 m +173.00 +76.34 :>1 --T8 II..IHI +5.61 +o.& 136 188.14 -4-47 174.96 +I.M 76.16 -0-18 '.'.' :i7'.i.i4 S.3 -M..-.I 6.41 8MO 0.46 137 183.66 4*48 i7i;.-i 1*90 T:,/I, 0.90 n 37MI J.8H 4-39 0.41 138 179.18 4-47 178.70 1-84 75.75 O-'Jl M :i7i.: 3-93 B.19 4-39 nx 0-40 174.72 4-47 l-ii.in 1W 75JJ3 o-w B6 :;:.:i7 3.98 :i7.:t7 4-18 70.71 0-48 140 170.25 4-47 182.23 1-74 75.29 0-94 96 :ui:t.:i 4-01 i-. 1 . i:. 4.08 71.1- 0.47 141 h,,.T- 4-47 18*41 149 75.03 0--M \<7 S69JO 4 -04 17. l:l 4-98 7l.t,.i 0-49 142 161.32 4-46 185.56 1-M 74.77 0-98 ;j.V).-zt Ml B&90 4-87 72.07 0.44 143 1.VJ.87 4-44 187.14 1-46 74.49 0-98 M ::.,l.n t-i-j :,7.o7 4-T7 0.43 144 1 .VJ.M 4-4 188.68 1-44 74.20 0-39 4-U 4.T 0-40 4-44 l-4 0-31 100 H346JK + 61.74 +72.89 145 +147.% + i:Mi.i7 +73.69 Ml -4-18 66.32 +4.18 73.27 +0-38 146 143..VJ -4-44 Ml.i.l +144 73.57 -0-39 UN 4-JO 70.79 4'4T 73.63 0-M 147 139.07 ' 4.44 193.00 39 73.24 0-33 108 334.36 4*31 7.-..1- 4-39 73.98 0.34 148 134.64 4.43 194.34 34 72.S9 0-34 104 330.09 4-M 7' Mi, 4-28 74.31 0-3* 140 130.20 4-44 I'.u.i.l 30 72.53 0-36 105 4-98 83.66 4.90 74.62 0-31 150 lv>:,.77 4-43 HKi.'.MI 98 72.16 0-37 106 3-JI..-.I 4-80 87.76 4-10 74.92 0-30 151 121.34 403 196.11 31 71.77 0-39 107 317.19 4-3J 91.78 4411 75.l:i 0-97 152 in,, -j 4.43 199.28 17 71.38 0-39 108 312.85 4-34 95.70 3.93 1MB 0-tt 153 112.50 I-I-J 200.40 19 70.97 0-41 109 n&ao 4-34 99.54 3.84 75.70 0-'J4 154 108.08 4-43 201.48 140 70^4 0-43 4-37 3-76 0.33 l-ll 1-04 0-43 110 +304.13 +103.30 l.V, +103.67 +202.52 +70.11 111 -4-38 106.97 +.7 76.13 +0.31 156 90.26 -4-41 203.52 + 1-00 69.66 -0-44 II.' 4-40 II"..-,.-, 3.48 76.32 0-19 157 94.85 441 204.48 0-98 60.20 0*48 111! 4-41 114.06 3.41 76.50 0-18 158 90.45 4-40 20.-..40 0-99 68.73 0-17 114 286.52 4.4-] 117.4* 3-49 76.66 0-16 159 86.05 4-40 206.28 0-88 68.25 0-48 US M&68 4-4* 120.83 3-34 7ii.-.i 0-14 160 81.65 4*40 207.12 0-84 67.75 0-40 116 277.66 4.4* 124.10 3-37 7i;.":i 0-13 161 77.25 4-40 207.92 0-80 67.24 0-41 117 273.21 4-44 127.29 3-19 77.04 0-11 162 72.86 4.39 208.68 0-76 66.72 0-49 118 4-44 130.41 3.13 77.13 0-09 163 68.47 4-89 809.40' 0-79 66.19 0-43 ll'.i 264.30 4.46 133.45 3-04 77.21 0-08 164 64.08 4-39 210.09 0.9 65.65 0-M 4-Hi M7 0-0 I..TO 0-68 0.44 130 +259.84 +136.42 +77.27 165 + 59.69 +210.74 +65.10 ! 121 -4-47 139.32 +1.90 77.32 +0-0 166 55.30 -4-39 211.35 +0-1 64.54 -o. i -- -.:. >.- 4.48 142.14 9.82 77.35 0-03 167 50.92 4*38 211.!I2 0-7 63.96 0-68 123 J|.,.rj I- IT 144.90 8-76 77.36 +0-01 168 4MB 4*39 2)2.46 0-44 63.37 0-59 124 241.94 4-48 147.60 S-70 77.36 0-00 169 42.15 4-38 212.96 0-40 62.78 0-49 198 4-18 I60J9 a.i 77.34 -0-09 170 37.77 4-38 213.42 0-46 62.17 0-81 196 j :_'. ; 4-49 158.76 3-M 77.31 0-0$ 171 33.38 4.39 2IH.K-, 0-43 61.55 127 UM0 4-48 15M7 -49 77.26 0-06 172 29.00 4.38 214.24 0-39 60.02 0-63 123 SMI 4.49 157.70 9.4* 77.20 0-08 173 24.62 4*38 -Jll.V. r.34 60.29 0-83 129 21931 4.49 160.07 2-17 77.12 0*08 174 20.23 4-39 2)4.91 0-39 .Vi..,! 0-S4 4-48 I'M 0-09 4-38 0-99 O.M 130 ..[.-..in +162.37 +77.03 175 + 15.65 +2I5J20 .:.-.- 131 -'M..-.4 -4-49 164.62 +J.S* 76.92 -0.11 176 11.46 -4-39 215.44 +0^4 :.-.:: l -047 132 206.06 4-48 166.80 9.18 TfcfiQ 0-19 177 7.08 4.38 215.65 0.91 57.63 0-88 133 201.58 4-4H 168.92 I'll 76.66 0-14 178 + 269 4-39 215.82 0-17 56.95 0-88 134 107.00 4-49 170.09 3-07 7i,.:,l 0-16 179 - 1.70 4-39 215.96 0-14 56.25 0-70 138 +192.61 -4-48 +173.00 +9*1 1-76.34 -0-17 180 - 6.09 -4-39 +216.06 +0-10 +55.54 -0-71 42 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. Terms multiplied with t. Argument = M. Arg. li Diff. h Diff. & Diff. Arg. Si Diff. h Diff. 1 Diff. o o 180 - 6.09 +216.06 +55.54 225 -208.16 +178.25 +15.94 181 10.48 -4-39 216.12 +0-06 54.82 -0-73 226 212.78 -4-62 176.30 1-95 14.94 -1-00 182 14.88 4-40 216.15 +0-03 54.10 0-72 227 217.40 4-62 174.29 2.01 13.94 1-00 183 19.27 4-39 216.13 -0-03 53.36 0-74 228 222.02 4-62 172.23 2-06 12.93 1-01 134 23.67 4.40 216.09 0-04 52.62 0.74 229 226.64 4-62 170.11 2.12 11.92 1-01 185 28.07 4.40 216.00 0-09 51.86 0-76 230 231.27 4-63 167.92 2-19 10.91 1-01 186 32.48 .4-41 215.88 0-12 51.10 0-76 231 235.90 4-63 1G5.68 2 24 9.90 1.01 187 36.88 4-40 215.72 0-16 50.33 0-77 232 240.53 4-63 163.37 2.31 8.88 1 02 188 41.29 4-41 215.52 0-30 49.55 0-78 233 245.16 4-63 160.99 2-38 7.86 1-02 189 45.71 4-43 215.29 0-33 48.77 0-78 234 249.79 4-63 158.55 2-46 6.84 1-02 4-42 0-27 0-80 4.03 2-51 1-02 190 - 50.13 +215.02 +47.97 235 -254.42 +156.04 + 5.82 191 54.55 -4-42 214.71 -0-31 47.17 -0-80 236 259.05 -4-63 153.46 -2-68 4.80 -1 02 192 58.97 4-43 214.37 0-34 46.36 81 237 263.67 4-62 150.80 2 66 3.78 1 02 193 63.40 4-43 213.99 0-38 45.54 0-82 238 268.30 4-63 148.08 2-72 2.76 1-02 194 67.84 4.44 213.57 0-42 44.71 0-83 239 272.92 4-62 145.28 2-tO 1.73 1.03 195 72.28 4.44 213.11 C-16 43.87 84 240 277.54 4-63 142.40 2-88 + 0.71 1 02 196 76.72 4-44 212.61 0.50 43.03 0-84 241 282.16 4-62 139.44 2-96 - 0.31 1 02 197 81.17 4-45 212.07 0-54 42.18 0.85 242 286.77 4-61 136.40 3 04 1.34 1.03 198 85.63 4-46 211.49 0-58 41.32 o-ee 243 291.37 4-60 133.28 3-12 2.36 1-02 199 90.09 4.46 210.87 0-G2 40.46 0-86 244 295.96 4-59 130.08 3-CO 3.39 1-03 4-46 0-67 0-87 4-59 3.28 1-02 200 - 94.55 +210.20 +39.59 245 -300.55 +126.80 - 4.41 201 99.02 -4-47 209.50 -0-70 38.71 -0-88 246 305.13 -4-58 123.44 -3.36 5.43 -1 02 202 103.50 4.48 208.75 0-75 37.82 0-89 247 309.70 4-57 119.99 3.45 6.45 1-02 203 107.98 4.46 207.95 0-80 36.93 0-89 248 314.25 4*55 116.45 3.54 7.47 1-02 204 112.47 4-49 207.10 0*85 36.03 0-90 249 318.79 4-54 112.83 3 62 8.49 1-02 205 116.97 4-50 206.21 0-89 35.13 0-90 250 323.32 4.53 109.12 8.71 9.51 1 02 206 121.47 4*50 205.28 0-93 34.22 0-91 251 327.83 4-51 105.32 S 80 10.52 1-01 207 125.98 4-51 204.30 0-99 33.30 0-92 252 332.33 4-50 101.43 3.89 11.53 1-01 208 130.49 4-51 203.28 1-02 32.38 0-92 253 336.81 4-48 97.45 3-93 12.54 1 01 209 135.01 4.53 202.20 1-08 31.45 0-93 254 341.27 4.46 93.38 4-07 13.55 1 01 4-53 1-12 0-93 4*44 4-16 i no 210 -139.54 +201.08 +30.52 255 -345.71 + 89.22 -14.55 211 144.07 -4-53 199.91 -1-17 29.58 -0-94 2T>6 350.12 -4-41 84.96 -4-26 15.55 -1.00 213 148.61 4.54 198.70 1-21 28.63 0*95 257 354.51 4-39 80.60 4-36 16.54 0-99 213 153.16 4-55 197.43 1-27 27.68 0.95 258 358.88 4-37 76.14 4-46 17.54 LOO 214 157.71 4-55 196.12 1.31 26.73 0-95 259 363.21 4-33 71.58 4-56 18.52 0.98 215 162.27 4-56 194.75 1.37 25.77 0-96 260 367.51 4-30 66.92 4-66 19.51 0-99 216 166.83 4*56 193.34 1-41 24.81 0.90 261 371.79 4-38 62.16 4-76 20.49 0-98 217 171.41 4.58 191.87 1-47 23.84 0>97 262 376.03 4.34 57.29 4-87 21.46 0-97 218 175.98 4-87 190.35 > 1.S2 22.87 0-97 263 380.23 4-20 52.32 4-97 22.43 0-97 219 180.56 4.58 188.79 1-56 21.89 0-98 264 384.39 4-16 47.24 5-08 23.39 0-% 4.89 1.03 98 4-13 6.19 0-96 220 -185.15 +187.16 +20.91 265 -388.51 + 42.05 -24.35 221 189.74 4-59 185.49 -1-67 19.92 -0-99 266 392.59 -4-08 36.75 -5.30 25.30 -0.95 222 194.34 4-60 183.76 1-73 18.93 0-99 267 396.62 4-03 31.34 5-41 26.24 0-94 223 198.94 4-60 181.98 1-78 17.94 0-99 268 400.60 3.98 25.82 6-52 27.18 0-94 224 203.55 4*61 180.14 1-84 16.94 1-00 269 404.53 3-93 20.18 6-64 28.11 0-93 225 -208.16 4-61 +178.25 -1.89 +15.94 -1-00 270 -408.40 3-87 + 14.43 -6-76 -29.03 -0-92 43 ~1 TABLE IV. Cmitimud. I'KIHTKIi.VTIOXS OF TIIK CO-ORDIXATKS IN I NITS OF TIIK SIXTH DECIMAL. Terrai multiplied with I. Argument if. Si HiiV. 1l Diff. & Diff. Arg. l Diff. ',: Diff. tl Diff. o o -Til 14.43 -29.03 us -457.24 -365 J2 -56.92 -.Tl out -1-81 MB - 5-87 _>.:>:, -0.93 316 + 1.W 375.78 -HM6 57.09 -0.17 -:.' ll&M 1.76 S-99 0.91 at) 44'.l.75 3-90 386.26 10-48 57.23 0-14 03 IT'...:, M| I1..M t.-ll 31.76 0-90 :-.!- 445.57 4*18 ::(,.::. 10.49 57.35 0-13 tn : 9.77 6.73 M4B .-, 319 441.07 4-M 407.22 10.47 57.44 009 I-.- ..-.' 1-M 16.11 604 :u.:,:i 0.88 BH 436.26 4*81 417.67 10-45 5750 0-06 1-47 -".'.:.- 6-47 34.40 0-87 321 431.15 .-11 mm 10-43 57.54 0-04 an 433.68 j'.l- MO 35.26 0.88 322 6.44 438.48 10-19 57.55 -0-01 436.'. LSI ::.-..- Ml KJI 0-86 323 419.95 6.76 44-.-J 10-14 r.7.:.:t +0-03 :: ' 4IH.-JI ..-: 42.73 6.84 36.96 0-84 324 413^7 8-08 459.11 10-19 67.48 0-0* 1-1.1 6.M 0-83 6-41 10-31 0-08 BM -37.79 M -407.46 -469.34 -57.40 --i 446.38 -144 HJG - 7^ ::-.i. 1 MB 400.72 + 8-74 479.48 -10-14 :.7.-.-,' +0-11 M 3-94 6U0 7-11 39.41 O-t-0 327 3JI3.66 7-06 -l-'.:,:i 1005 B7.J5 0-14 M 168.18 9.8) 744 40.21 0-80 328 HM| 7-40 499.48 9-M 56.98 0-17 --I 2-73 7-.-<> 7-47 40.!!l 0-78 329 mju 7-71 509.30 9-83 56.78 C-30 ->-. 2-82 BUB 7- 41.76 0-77 330 370.4H 519.00 9-70 5655 0*31 M 3.49 94.10 7.71 tut 0-76 331 362.10 - .. .v,'-.:,i 9-M 56.2!l O.M M 462.36 3.18 101.94 7.84 43.26 0-74 M ai:t.:Ki 8-71 537.91 9-17 56.00 0-39 ..... !.!.'.' 0.34 101.90 7.M 43.W 0.71 333 344.36 9.01 547.12 9*31 sue 0-13 M 466.72 Ml 117.!C.l ..,,, 44.71 0-75 334 335.01 B-3S 556.14 9*03 55.33 0-35 1-M 8--J1 0-70 9-G7 8.81 0-18 290 -468.70 -126.20 -45.41 335 -325.34 5M4B _"i 47n-.il -1-84 - 8-U 46.10 336 3i.i.:v. + 9-90 B7U6 - 8.61 54.54 +0-41 ITJ.-J: 1.69 II-.'.- 8.4ft 46.77 0-7 337 :>r,.ii:i 10-3-J KIM en 54.10 "II 293 47:f.7(J 1.&3 1.11. .1.1 8.57 IT.U 0-6S 338 294.42 1041 590.06 8-U 53.62 0-48 ZM 47.".. 11 |.8 160.24 48.06 064 339 2K1.51 10-91 597.95 7-89 r.:f.i-.> 0-10 M 476.36 1-M 169.05 8.81 48.66 O.M 340 272.30 11--J1 605.56 7-61 sue 0-64 296 477.40 144 177.97 B.M 49.23 0.61 341 269.82 11-48 612.89 7-11 52.01 0-57 47-.-J7 0-87 187.01 '"1 49.87 0-8 342 249.07 11-75 <;io.'.i3 7-04 51.42 0-59 M 478.96 0-89 I'M. .11. *! 50.44 0-S7 343 237.06 1Q-01 626^6 6-71 50.79 0.61 M 479.46 0.90 205.42 M 50.99 0-U 344 224.81 !.' .,:;:;.ri. 8-40 50.13 0-86 0-33 9-M 0-tl IJ-40 049 300 -479.78 -214.78 -51.12 345 -212.31 -639.14 -49.44 Hill 479.00 -0-13 224.2T, - -47 .v.'.n:; -0-1 346 UM9 -I-U-7H 644.88 - 5-74 48.72 +O.TS 302 47*81 -H).09 -.'..::.-.' .57 ma 0-49 347 186.65 13-94 6S046 6-18 47.97 0.75 47'.t.VJ 0-29 J 1:1.4- 9.86 0-47 348 I7:!..m 13-15 85UB 6-03 47.19 0-78 304 479.00 0-53 -76 53.44 0-4S 349 160.15 13-U 6B0JH 4-61 46.39 0-90 305 17-. -.-7 0.7* 263.09 9.8* 53^7 0-43 350 146.64 13-61 664.16 4*35 4.-...V, 0-84 306 477.30 0.7 273.02 9-ra 54.28 0-41 an M.. . 668.09 1-86 44.69 0-86 307 476.10 I'M 10-00 54.67 0-39 352 119.11 13-84 671.48 1-48 43.79 0-90 M 474.65 1-45 293.10 10-08 65.03 0-38 3.13 105.16 13-95 674.13 1-OJ 42.87 0-91 309 472.06 149 303.26 10-18 65.37 0-34 3.14 91.08 :;.. - 677.18 2-5 41.93 0-94 1-M io. 0-34 11.17 3.34 0-98 310 -471.01 -31.1.48 a.Vi - 76.91 -679.42 -40.95 311 46-1.79 +3. Sil.Tr. -lo-r: -0-10 aie i ..'. ,7 +14-14 681.24 - 1-83 :v.t.'.ir. +1-00 1 312 466.32 3-47 334.08 10.33 56.26 0-77 a-,7 048 11.31 682.63 1 39 :\2 -o- 360 - 5.24 ; i-;. -6-4.22 - " -M.71 -H-10 1 44 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT I. Arg. Si Diff. % Diff. tl Diff. Arg. fi Diff. ft Diff. & Diff. o -577 4177 421 45 4 303 4928 437 1 570 4 7 201 424 21 46 339 436 933 4 5 38 41 2 562 8 225 24 21 47 375 36 936 3 38 3 554 8 248 23 22 +1 48 412 37 938 2 39 1 4 545 9 271 23 22 49 450 38 940 4 2 40 1 Q 23 Q 38 1 5 536 294 22 50 488 939 41 1 6 526 10 316 22 22 51 527 39 938 1 41 JJ '*'' 1 40 3 7 515 338 23 52 567 935 42 1 8 504 11 360 22 23 53 607 40 930 5 43 1 9 493 11 381 21 23 54 648 41 925 5 44 1 12 21 41 8 1 10 -481 4402 423 55 4 689 4917 445 11 468 413 423 421 24 41 56 731 442 908 - 9 46 41 12 455 13 444 21 24 57 773 42 898 10 46 13 441 14 464 20 24 58 815 42 885 13 47 1 14 427 14 484 20 24 59 857 42 871 14 48 1 15 413 14 503 19 24 60 900 43 856 15 49 1 16 398 15 522 19 25 1 61 942 42 838 18 50 1 17 383 15 542 20 25 62 985 43 819 19 50 18 367 16 560 18 25 63 1027 42 798 21 51 1 19 350 17 579 19 25 64 1069 42 775 23 51 17 18 1 42 25 1 20 -333 4597 426 65 41111 4750 452 21 316 417 615 418 26 40 66 1153 442 723 -27 52 4o 22 298 18 633 18 26 d 67 1194 41 695 38 53 1 23 279 19 650 17 26 68 1234 40 665 30 53 24 260 19 667 17 27 1 69 1274 40 632 ?3 54 4i 25 241 19 684 17 27 70 1314 40 598 34 54 26 220 21 701 17 27 71 1352 38 563 35 54 27 200 20 717 16 28 1 72 1390 38 525 38 54 28 178 22 733 16 28 73 1427 37 485 40 54 29 156 22 749 16 28 74 1463 36 444 41 54 23 15 1 35 43 -1 30 -133 4764 +29 75 41498 4401 453 31 109 424 779 415 29 40 76 1532 434 356 -45 53 -0 32 85 24 793 14 29 77 1564 32 310 46 53 33 60 25 807 14 30 1 78 1595 31 262 48 52 1 34 34 26 821 14 30 79 1625 30 212 60 51 1 35 - 8 26 834 13 31 1 80 1653 28 161 51 51 36 4 20 28 847 13 31 81 1680 27 108 53 50 1 37 48 28 859 12 32 1 82 1705 25 4 54 54 49 1 38 77 29 870 11 32 83 1729 24 - 2 56 47 2 39 107 30 881 11 33 1 84 1751 22 59 57 46 1 30 10 20 59 1 40 +137 4891 +33 85 41771 -118 445 41 169 432 900 4 9 34 41 86 1789 418 178 -60 43 -2 42 201 32 908 8 35 1 87 1805 16 239 61 41 2 43 234 33 916 8 35 88 1819 14 301 62 40 1 44 268 34 923 7 36 1 89 1831 12 365 64 38 2 45 4303 435 4928 4 6 +37 4l 90 410 -64 +36 -2 TABLE IV. Continued, IM.Ull UP. \TIo.\S OF TIIK CO-OKDINATKS IN UMTS OF THE SIXTH DECIMAL. AROUMKNT I. t Dilf. 1l Diir. fi Diff. Atg. i. Diff. ft Diff. fi Diff. o 90 1-11 - 420 + 36 135 - 408 teat -116 n 1848 + 7 - 34 - 136 506 -98 2H40 - l 11!) -a 03 1864 a 561 i 31 * 137 605 M + a 122 i 93 l-',7 + i M 89 1 138 704 W 2831 a 125 3 94 iaa 6% 37 i 139 80S || MM n 127 9 '.'. - i 765 , 84 3 140 902 M _'-. <; 14 130 a 96 i--,i i 634 oe 21 3 141 101)1 J7-- 18 132 a 97 i-ii 7 904 - 18 3 142 1100 ' 2767 9) 134 a 96 i - ..-, >::. :i i:. * 143 1198 2741 . 136 I 99 1333 11 mi 70 12 a 144 1295 7 2712 it 138 * IS 71 a 90 S3 100 +1806 -1116 + 9 145 -1391 -2679 -140 101 17'l -17 1187 -71 6 - 146 1487 - 2643 + ai 141 -i m 1771 -.11 + 3 * 147 l.'.-l II 2608 40 143 9 103 1748 i:: 1,1 71 14- 1674 . KM 44 144 1 104 17-23 1401 71 - 4 4 MB 1766 W 2510 48 145 1 105 I6M 1471 70 7 I 150 !-:,(, M MM 61 146 1 106 i., ,i ai 1542 71 11 4 161 1944 88 2405 M 147 1 107 16 u 1612 70 14 t 152 2030 2347 - 148 1 108 i:.- i 17 n,-l ,', 18 4 153 2114 84 2286 61 148 109 i:,i- 41 171'' 23 4 154 2196 SI 2221 M 149 -1 41 t 80 <-, 110 hUM -1817 - 35 155 -2276 -2154 -149 111 n .- -4 1-:! - 29 -4 156 2tr>4 -18 2083 + 71 149 11-.' 14W i i 1949 M 33 4 ir.7 2429 - 2009 74 149 Ill li-tf S3 2013 64 37 4 158 9501 72 1!I33 76 148 4i IM 1301 J '7.-. 41 4 159 2571 70 1854 9 148 iir. r.'i:t 2136 81 45 4 160 tea M 1772 147 I in; 1 1 -. 1 JI'HJ 00 48 t 161 2701 4 1688 84 146 1 117 m- M 2253 57 4 162 2762 1601 87 145 1 118 1052 M 2309 M 56 4 163 2819 1512 8 144 1 11 ' M at Ha 60 4 164 -'-71 &4 1420 K 143 1 -.: 4 SI a 9 130 Oil -2414 -64 165 -2925 -1327 -141 l-.'l -17 -74 M63 -49 68 -4 166 2973 -4 1232 + M 140 + 1 m 760 77 4 72 4 167 3017 44 1135 87 138 2 123 681 79 8553 44 75 1 168 MM 41 1036 09 136 2 IM 600 81 MM 41 79 4 169 3095 37 935 101 134 2 IX 516 81 HH H 83 4 170 3128 ,; 833 10* 132 2 1-36 431 81 nee M 86 3 171 3158 H 730 H3 12 3 127 344 87 2701 ;i 90 4 172 3184 2 M 104 127 2 128 M - ' 2730 94 4 173 3206 521 IM 124 3 129 164 91 2756 24 97 3 174 3224 18 414 107 121 a 99 3 IS 107 a 130 + 71 4778 -100 175 -3239 - 307 -118 131 - 22 - ma -i 104 -4 176 3249 -10 200 + 107 115 fa 132 117 M 2813 it 107 I 177 3255 - 98 108 112 a 133 213 M j-r, 19 110 3 178 3258 - 1 + 17 IM 109 a 134 310 MM 1 113 3 179 3256 + a 125 108 105 4 135 - 408 -t -:; i - t -116 -t 180 MN + + 234 + 109 -102 +a 46 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT I. Arg. & Diff. h Diff. tl Diff. Arg. Ji Diff. ft Diff. & Diff. O 180 -3251 + 234 -102 225 + 122 +2878 +78 181 3241 + 10 342 +108 98 +4 226 220 +98 2857 -51 80 +2 182 3228 13 450 108 94 4 227 316 96 2832 25 82 2 18 108 3 95 183 3210 558 91 228 411 2804 2o 84 2 184 3188 22 664 106 87 4 229 505 94 2773 31 86 I 185 3163 25 771 107 83 4 230 596 91 2738 35 88 2 186 3133 30 876 105 79 4 231 686 90 2700 38 90 2 187 3099 34 980 104 75 4 232 774 88 2659 41 92 2 188 3062 37 1083 103 70 5 233 859 85 2615 44 93 1 189 3020 42 1184 101 66 4 234 942 63 2568 47 94 1 45 100 4 61 50 1 190 -2975 +1284 - 62 235 +1023 +2518 +95 191 2926 4- 49 1382 + 98 57 +5 236 1101 +78 2466 -53 96 + 1 192 2874 52 1478 96 53 4 237 1177 76 2411 65 97 1 193 2817 57 1572 94 49 4 238 1250 73 2354 57 98 1 194 2758 59 1664 92 44 6 239 1320 70 2294 60 98 195 2695 63 1754 90 40 4 240 1388 68 2233 61 98 196 2628 67 1841 87 35 5 241 1453 65 2169 64 98 197 2558 70 1926 85 31 4 242 1514 61 2103 66 99 +1 198 2485 73 2008 82 26 5 243 1573 59 2036 67 98 -1 199 2410 75 2087 79 22 4 244 1629 56 1967 69 98 79 76 5 53 71 200 -2331 +2163 - 17 245 +1682 +18P6 +98 201 2249 + 82 2236 + 73 13 +4 246 1732 +50 1824 -72 97 -1 202 2165 84 2306 70 8 5 247 1778 46 1751 73 97 203 2079 86 2372 66 - 4 4 248 1822 44 1676 75 96 1 204 1990 89 2435 63 + 1 5 249 1862 40 1601 75 95 1 205 1899 91 2495 60 5 4 250 1899 37 1524 77 94 1 206 1806 93 2551 56 10 5 251 1933 34 1447 77 93 1 207 1711 95 2603 52 14 4 252 1963 30 1369 78 92 1 208 1614 97 2651 48 18 4 253 1990 27 1291 78 90 2 209 1516 98 2696 45 23 5 254 2015 25 1212 79 89 1 99 41 4 20 78 2 210 -1417 +2737 + 27 255 +2035 +1134 +87 211 1316 +101 2774 + 37 31 +4 256 2053 +18 1055 -79 86 -1 212 1214 102 2807 33 35 4 257 2067 14 976 79 84 2 213 1112 102 2836 29 39 4 258 2079 12 897 79 82 2 214 1008 104 2861 25 43 4 259 2087 8 818 79 80 2 215 905 103 2882 21 46 3 260 2093 6 740 78 78 2 216 801 104 2900 18 50 4 261 2095 + 2 663 77 76 2 217 697 104 2913 13 54 4 262 2094 - 1 586 77 74 2 218 593 104 2922 9 57 3 263 2090 4 509 77 72 3 219 489 104 2927 5 60 3 264 2083 7 434 75 70 2 104 + 2 3 9 74 2 223 - 385 +2929 + 63 265 +2074 + 360 +68 221 282 +103 2926 - 3 67 +4 266 2061 -13 286 -74 66 -2 222 180 102 2920 6 70 3 267 2046 15 214 72 63 3 223 - 78 102 2910 10 72 2 268 2029 11 143 71 61 2 224 + 22 100 2896 14 75 3 269 2008 21 74 69 59 2 225 + 122 + 100 +2878 - 18 + 78 +3 270 +1985 -23 + 6 -68 +56 -3 47 V ^ v *5lkS77T*]\ TABLE IV. ConHnnnl. I'KinVK!'. VTHiNS OF TIIK COORDINATES IN r.MTs oF TIIK SIXTH DECIMAL. ARGUMENT I. Ar_- ft Dirt; t. Diff. b Diff. Arg. ft Diff. '.: Diff. Cl Diff. o o -'7 n + 6 +56 - 90 -969 -10 '.'71 1981 -9 - 61 -ft 54 "* 316 55 -i* + 18 9 +1 m 27 126 89 n 1 317 89 M M 19 9 I'M:! I l-.i 61 4!) * 318 129 n .' 8 l 274 1-71 12 m 61 46 1 B9 154 884 21 8 l-:t7 14 309 . 44 1 BH ]-:. 31 21 7 i ua 19 367 98 42 1 321 Ji:. M 841 .. 6 i m I7M I 422 99 39 i 322 243 - -1- * 6 278 17-:. ' . 475 91 37 2 323 .'7 n 27 795 5 1 K.-l 41 M : 34 1 324 296 -. 771 M 4 1 41 49 2 29 94 1 J-i +1641 - 576 +32 325 -321 -747 - 3 J-I -44 623 -47 30 1 326 345 -24 722 +28 2 +1 M 49 668 49 27 1 327 366 - i 697 . 1 1 -'-:: 47 710 49 25 2 BB8 390 22 671 .. - 1 j-l 1 1.-.- 47 750 40 23 2 329 410 - 645 ' 1 1409 49 7- M 21 9 330 430 20 619 ... + 1 1 1360 -Jl M 18 1 331 448 18 593 ... 2 1 .'-: nut I 857 n 16 9 332 465 n 566 27 3 1 j-- 1980 91 --- 11 14 9 333 481 16 539 27 4 1 out 91 916 " 12 9 334 497 1 512 97 5 1 99 28 9 14 27 1 ZX) + 1 1 .">2 610 + 1 - 24 28 18 1 308 y, 44 1059 9 10 3T>3 609 1 + 9 28 18 309 217 41 1049 10 10 3T>4 606 1 98 28 19 1 42 12 1 29 310 + 17.', -1037 -10 355 -603 + 53 +19 311 134 -41 in-JI +11 10 356 599 + 4 79 +26 19 +0 312 94 40 1010 14 10 357 595 4 104 29 20 1 313 55 to 0M 19 10 358 590 * 129 99 90 314 + 17 M TOI 18 10 3.1 1 1 584 G 153 24 20 315 - 20 -n - 962 + 17 -10 360 -577 + 7 +177 +44 .'l +1 48 TABLE IV. Continued. PEETURBATIONS OF THE CO-ORDINATES IN UJJITS OF THE SIXTH DECIMAL. ARGUMENT II. Arg. Ji Diff. h Diff. fl Diff. Arg. 6 Diff. m Diff. & Diff. o o +551 + 51 -38 45 + 118 +727 -23 1 550 - i 65 + 14 37 +1 46 92 ~16 739 +12 23 -o 2 548 4 78 13 37 47 66 26 750 11 23 3 547 i 91 13 36 i 48 39 27 760 10 24 i 4 546 i 105 14 35 i 49 + 12 27 769 9 24 5 544 2 118 13 34 i 50 - 17 29 777 8 24 6 542 3 134 14 34 51 46 29 785 8 24 7 540 2 146 14 33 1 52 76 30 791 6 25 1 14 t On 8 538 160 32 53 106 oU 797 25 9 536 2 174 14 31 i 54 137 31 802 6 25 2 14 32 3 1 10 +534 +188 -31 55 - 169 +805 -26 11 531 - 3 202 +14 30 +1 56 201 -32 808 + 3 26 -o 12 528 3 217 15 29 1 57 233 32 810 + 2 26 13 525 3 231 14 28 1 58 266 33 810 27 1 14 521 4 246 15 28 59 299 33 809 - 1 27 15 517 4 261 15 27 1 60 333 34 807 2 27 16 513 4 276 15 27 61 367 34 804 3 27 17 508 S 292 16 26 1 62 401 34 799 5 27 18 503 i 307 15 25 1 63 435 34 793 6 28 -1 19 498 6 323 16 25 64 470 35 786 7 28 16 1 34 8 20 +492 +339 -24 65 - 504 +778 -28 21 485 - 7 355 +16 24 +0 66 538 -34 768 -10 28 22 478 7 371 16 24 67 573 35 756 12 28 23 470 8 387 16 23 1 68 607 34 744 12 28 24 462 8 404 17 23 69 641 34 730 14 28 25 453 9 420 16 22 1 70 674 33 714 16 28 26 444 9 437 17 22 71 708 34 697 17 28 27 434 10 453 16 22 72 740 32 679 18 28 28 423 11 470 17 22 73 773 33 660 19 27 +1 29 411 12 487 17 22 74 805 32 638 20 27 12 16 +1 31 22 30 +399 +503 -21 75 - 836 +616 -27 31 386 13 520 +17 21 76 866 -30 592 -24 26 +1 32 372 14 536 16 21 77 896 30 567 25 26 33 358 14 553 17 21 78 925 29 540 27 26 34 342 16 569 16 21 79 953 29 512 28 25 1 35 326 16 585 16 21 80 980 27 483 29 24 1 36 309 17 601 16 21 81 1006 26 453 30 24 37 291 18 617 16 21 82 1031 25 421 32 23 1 38 273 18 632 15 21 83 1055 24 388 33 22 1 39 253 20 647 15 21 84 1077 22 354 34 22 20 14 -1 21 35 1 40 +233 +661 -22 85 -1098 +319 -21 41 211 22 676 +15 22 86 1118 -20 282 -37 20 +1 42 189 22 689 13 22 87 1137 19 245 37 19 1 43 166 23 703 14 22 88 1154 17 206 39 18 1 44 142 24 715 12 22 89 1170 16 167 39 17 1 45 +118 -24 +727 +12 -23 1 90 -1184 -14 +127 -40 -15 +2 49 TABLE IV. Continued. ri.KTi mi.vno.Ns OF THE CO-ORDINAI i> IN \ \ns ur TIIK SIXTH DECIMAL. ARGUMENT II. A*. fi Diff. !l Diff. & ONE Arg. fc Diff. It Diff. tl Diff. O 90 -1184 + 137 -15 UB + 5 MN + 76 91 I1M H 86 -41 14 +1 136 61 +M 1424 " 77 +1 M 1207 11 44 49 13 i 137 117 56 1 !.'-. ~ 79 a M TJII, + 1 43 11 i 138 174 67 1424 + 81 a M aau 7 i-j 41 10 i 139 230 M 1421 83 a m 1 85 41 9 i 140 266 M 1416 65 a 96 I'.'!-' 4 130 7 a 141 342 M 1406 8 66 i 97 1M - 1 174 44 5 a 142 398 M 1399 I 88 a 98 I-.MI 319 45 4 1 143 453 55 1387 la 89 i 99 + a M . - 3 a 144 509 56 1374 11 91 a 4 4i a M 18 i 100 IM - 310 145 + 563 -1358 + 99 101 i .-.-,' + 6 356 -4 + 1 +1 146 617 +44 1340 +18 93 +1 IM l-'ll 8 401 49 3 a 147 670 U 1320 JO 94 i 103 ISM 10 447 46 5 a 148 723 S3 1298 aa 96 a Hi4 UM 11 492 41 7 a 149 774 11 1274 a4 97 i 105 117' 14 538 48 9 a 150 M 51 1248 36 96 1 106 1163 16 583 45 11 a ir.l -7:. 50 1231 97 99 i 107 1146 n 627 44 13 a 152 923 48 1191 30 99 106 1136 .' 671 44 15 a 153 97J 48 1159 I 100 i 109 1104 :: 715 44 17 a 154 1017 4 1126 n 101 i n 41 i 44 u 110 -1061 - 758 +20 155 +1061 -1091 +101 111 1056 + -0,1 -42 33 +a 156 1105 +44 1054 +n 102 +1 11-J 1038 843 43 84 a 157 1147 4a 1016 18 102 113 40 26 a 158 1187 40 976 40 102 114 968 923 40 99 i 159 1325 38 934 43 102 115 936 a 961 39 31 a 160 1262 i; 891 43 103 +1 116 'Ml H 999 18 33 a 161 1297 15 847 44 103 117 m i , 1035 35 a 162 1330 801 103 -1 118 ~.'7 :l- 1070 Si 38 i 163 1363 la 755 46 102 11:' 788 M 1104 14 40 a 164 1391 a* 707 48 102 41 U 9 38 M m -747 -1137 +49 165 +1419 - 657 +103 rji 705 +49 1168 -11 46 +1 166 1445 +96 607 +tt 101 -1 122 661 44 1197 a 47 a 167 146S 556 51 101 133 616 41 1325 .- 49 a 168 1489 91 504 59 100 1 134 MR 47 1253 37 52 i 169 1509 ao Ml 53 99 1 135 47 1277 54 a 170 1526 n M 54 99 136 473 1300 :i 56 a 171 1541 15 344 54 98 1 137 1-.". M 1331 31 59 i 172 1554 n 390 54 97 1 138 372 81 1340 19 61 i 173 1564 10 235 U 96 1 139 .'.-.' i M 1357 17 63 a 174 1573 179 58 96 1 51 18 a 6 55 a 130 - 267 -1373 465 175 +1579 - 134 + 93 131 314 + IM -11 67 +9 176 1563 + i 68 +M 93 -i 133 160 M 1398 11 69 a 177 1584 + a 13 58 91 i 133 106 1408 10 73 i 178 1583 ~ ' + 44 56 90 i 134 - 50 M 1415 7 74 a 179 l.-.-u i 100 50 86 a m -'. +M 1490 + 5 +76 +a 180 U575 + 156 +5 + 87 -i 50 TABLE IV .Continued. PERTURBATIONS OP THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT II. Arg. ft Diff. * Diff. fl Diff. Arg. li Diff. % Diff. ?! Diff. o o 180 +1575 + 156 +87 225 - 291 +1353 - 6 181 1567 - 8 211 +55 85 -2 226 342 -51 1337 -16 8 -2 182 1557 10 266 55 83 2 227 393 61 1318 19 10 2 183 1545 12 321 55 82 1 228 443 50 1298 20 11 1 184 1531 14 375 54 80 2 229 492 49 1276 22 12 1 185 1514 17 428 63 78 2 230 539 47 1252 24 14 2 186 1496 18 481 53 76 2 231 586 47 1226 26 15 1 187 1475 21 533 52 74 2 232 631 45 1199 27 . 17 2 188 1452 23 584 51 72 3 233 675 44 1170 29 18 1 189 1427 25 635 51 70 2 234 717 42 1140 30 19 1 27 49 2 41 32 1 190 +1400 + 684 +68 235 - 758 +1108 -20 191 1372 -28 732 +48 66 -2 236 798 -40 1075 -33 21 -1 192 1341 31 779 47 64 3 237 836 38 1040 35 22 1 193 1308 33 825 46 62 2 238 872 36 1004 36 23 1 194 1274 34 870 45 60 3 239 907 35 967 37 24 1 195 1238 36 913 43 57 3 240 940 33 929 38 25 1 196 1200 33 955 42 55 2 241 971 31 890 39 26 1 197 1160 40 995 40 53 2 242 1001 30 850 40 27 1 198 1119 41 1033 38 51 2 243 1028 27 809 41 27 199 1076 43 1071 38 48 3 244 1054 26 767 42 28 1 44 35 2 24 43 1 200 +1032 ^ +1106 +46 245 -1078 + 724 -29 201 987 -45 1140 +34 44 -3 246 1100 -22 681 -43 29 -o 202 941 46 1172 32 41 3 247 1120 20 637 44 30 1 203 893 48 1202 30 39 2 248 1138 18 593 44 30 204 844 49 1230 28 37 3 249 1154 16 548 45 31 1 205 794 50 1256 26 34 3 250 1168 14 503 45 31 206 743 51 1281 25 32 3 251 1181 13 458 45 32 1 207 691 62 1303 22 30 3 252 1191 10 412 46 32 208 639 52 1324 21 28 2 253 1199 8 367 45 32 209 585 64 1342 18 25 3 254 1205 6 321 46 33 1 64 16 2 6 45 210 + 531 +1358 +23 255 -1210 + 276 -33 211 477 -54 1373 +15 21 -2 256 1212 2 230 -46 33 -o 212 422 55 1385 12 19 2 257 1213 - 1 185 45 33 213 367 55 1395 10 17 2 258 1211 + 3 141 44 33 214 311 56 1403 8 15 3 259 1208 3 96 45 34 1 215 256 55 1409 6 12 3 260 1203 5 52 44 34 216 200 56 1413 4 10 3 261 1196 7 + 9 43 34 217 144 56 1414 + 1 8 3 262 1187 9 - 34 43 34 218 89 55 1414 6 2 263 1177 10 76 42 34 219 + 33 66 1412 - 2 4 2 264 1165 13 118 42 34 65 5 1 14 40 220 - 22 +1407 + 3 265 -1151 - 158 -34 221 77 -56 1400 - 7 + 1 -2 266 1136 + 15 198. -40 34 -o 222 131 64 1391 9 - 1 2 267 1119 17 237 39 34 223 185 54 1381 10 3 2 268 1101 18 274 37 34 224 238 53 1368 13 5 2 269 1081 20 311 37 34 225 - 231 53 +1353 -15 -6 -1 270 -1060 +21 - 347 -36 -34 -o 51 TABLE IV. Continued. IT.UTt Kr.ATloNS OF T1IK CO-ORDIN A TI.S IN 1MTS OF THE SIXTH DECIMAL. ARGUMENT 11. Arg. fi Ditr. * KilV & Diff. Aig. t Diff. * Diff. b Diff. o o 270 -1060 -347 -34 315 . 986 -647 -46 271 1037 4 :.-.' -u 34 ~* 316 305 4so 631 4l 46 -o 272 1U13 34 415 S3 34 317 324 19 615 16 46 aee 3A 447 13 34 318 M 18 599 16 47 i r,\ 962 M 478 11 34 319 359 17 683 16 47 vrr:, !>:t5 .: MM 10 34 320 375 18 566 17 48 1 276 007 .- 536 :- 34 321 301 16 549 17 48 277 -T- - ' 564 II 34 322 405 14 532 17 48 273 -1- to | H I an 34 323 419 U .-,7:, 17 49 1 01 818 10 614 34 34 324 432 11 Me 17 49 3-J 31 13 17 MO 7-.; -637 -34 325 4444 -481 -49 2S1 4M 668 -ai 34 -o 326 455 411 463 418 49 -o M 722 n .,7-* 30 84 827 466 11 446 17 60 -1 981 aee S3 607 19 34 328 476 10 429 17 60 j-i IK 14 714 17 34 329 485 9 412 17 50 >:. i.-Ji 14 730 18 36 1 330 493 8 394 18 60 'J 1 1 ."> 7 34 744 14 35 331 601 8 377 17 50 -'-7 652 U 787 It 35 332 508 7 360 17 50 517 15 769 13 35 333 514 343 17 60 HO 483 14 779 10 36 334 620 327 16 60 U 9 1 A 17 293 - 448 -788 -36 335 4525 -310 50 291 413 4iA 790 - 7 36 -0 336 530 4 294 418 50 292 ::?- 34 801 6 36 337 534 4 277 17 50 203 :;il 31 806 A 36 338 538 4 261 16 60 ."I MM 15 810 4 37 1 339 541 1 245 16 60 275 34 812 a 37 340 544 a 230 1A 49 4i . , 241 M 813 - i 37 341 547 i 214 16 49 297 208 t3 813 38 1 342 549 a 199 15 49 m 175 33 811 4 a 38 343 551 a 184 15 49 299 143 I 809 3 38 344 652 i 169 15 48 1 81 4 1 i 15 300 301 ' - Ill 79 414 -805 800 4 A -39 39 -o 345 346 4553 554 4 1 -154 140 414 -48 47 41 308 48 11 795 5 40 1 347 555 1 125 15 47 303 - 18 30 7- 7 40 348 556 4 I 111 14 46 1 304 4 12 to 780 8 40 349 556 97 14 46 305 41 39 772 8 41 1 350 556 83 14 45 1 306 69 38 762 10 41 351 556 69 14 45 307 96 37 752 10 42 1 352 556 66 13 44 1 308 123 37 741 11 42 353 556 42 14 43 1 309 148 3t 729 13 43 1 354 555 - 1 29 It 43 35 13 o 14 1 310 4 173 -717 -43 355 ..-..v, - 15 -42 311 197 434 704 411 44 -1 356 664 - ' - 2 411 41 41 312 221 34 690 14 44 357 553 1 4 11 11 40 1 313 243 33 676 14 45 1 :.:,- 553 35 14 40 314 265 St 662 14 45 552 1 38 11 39 1 315 4 285 430 -647 413 -46 -1 360 - 1 4 51 411 -38 4i 52 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT III. Arg- Ji Diff. fll Diff. Cl Diff. Arg. ft Diff. 1l Diff. & Diff. O o +977 -196 +15 45 +537 -829 - 7 1 973 - 4 213 17 46 522 -15 838 -9 2 969 4 230 17 -2 47 506 16 847 9 -2 3 965 4 247 11 13 48 491 15 856 9 9 4 960 5 264 17 49 475 16 865 9 5 955 5 281 17 1 50 460 15 873 8 1 6 950 5 298 17 12 51 444 16 881 8 10 16 16 g 7 945 314 52 428 889 8 939 6 331 17 1 53 412 16 896 7 2 9 933 6 347 16 11 54 395 17 903 7 12 6 17 16 7 10 +927 -364 55 +379 -910 11 920 - 7 380 -16 2 56 363 -16 917 -7 1 12 913 7 396 16 9 57 346 17 923 6 13 13 906 7 412 16 58 329 17 929 6 g 16 1 17 g 14 898 428 59 312 935 . 15 890 8 444 16 8 60 296 16 941 6 14 16 882 8 459 15 61 279 17 946 5 17 874 8 475 16 2 62 261 19 951 5 2 18 865 9 490 15 6 63 244 17 955 4 16 19 856 9 505 15 64 227 17 960 5 9 15 1 17 4 1 20 +847 -520 65 +210 -964 21 838 - 9 535 -15 5 66 192 -18 967 -3 17 22 828 10 550 15 67 175 17 971 4 23 818 10 564 14 2 68 ' 158 17 974 3 1 24 808 10 578 14 3 69 140 18 977 3 18 25 797 11 592 14 70 123 17 979 2 26 786 11 606 14 1 71 105 18 981 2 1 27 775 11 620 14 + 2 72 87 18 983 2 19 28 764 11 633 13 73 70 17 985 2 29 752 19 647 14 2 74 52 18 986 1 1 12 13 17 1 30 +740 -660 75 + 35 -987 20 31 723 -12 673 -13 76 + 17 -18 988 -1 32 716 12 685 12 1 77 - 1 18 989 -1 1 33 703 13 698 13 - 1 78 18 17 989 21 34 691 12 710 12 79 36 13 989 35 678 13 722 12 2 80 53 17 988 +1 1 36 665 13 734 12 3 81 71 18 987 1 22 37 651 14 745 11 82 88 17 986 1 38 638 13 756 11 1 83 106 IS 985 1 1 39 624 11 768 19 4 84 123 17 983 2 23 14 11 18 2 40 +610 -779 85 -141 -981 41 595 -16 789 -10 2 86 158 -17 979 +2 1 42 581 14 800 11 6 87 175 17 977 2 24 43 567 14 810 10 88 192 17 974 3 44 552 15 820 10 -1 89 209 17 971 3 -1 45 +537 -15 -829 - 9 - 7 90 -226 -17 -967 +4 -25 63 TABLE I V. Continued. PERTURBATIONS OF THE CO-OKDINATKS IN UNITS OF THE SIXTH DECIMAL. ARGUMENT m. A*. t Diff. Diff. f. Diff. At*. t Diff. Jl Diff tl Diff. M -226 -967 -to OB -834 -648 -27 91 343 -17 ..I + 136 -1-J -8 534 +14 M ni 17 960 -1 137 850 8 519 19 + 277 17 m 96 138 see 8 ;,,,-, 14 37 94 -."I 17 951 139 866 8 490 16 95 310 18 946 140 874 8 475 16 l 96 327 17 '.Ml 36 141 881 T 460 19 26 97 343 18 936 143 --- 7 445 16 96 M 18 Hi l 143 -.14 ' nq 19 99 375 18 '.-I 37 144 901 7 415 19 36 18 8 | 18 100 -391 M 145 -907 -399 101 407 -18 911 + 7 146 913 ~t 384 +16 i M at 18 905 8 27 147 918 9 368 18 35 103 438 li -,- 7 148 8M 8 353 18 104 454 18 890 8 -I 149 939 9 336 18 105 469 19 --:: 7 38 150 933 4 320 10 35 106 l-l 19 875 8 151 938 9 304 18 107 499 19 767 6 153 M 4 M; 16 I 106 513 14 an 8 38 153 946 4 273 18 34 109 528 19 850 1 154 950 4 355 17 14 1 16 1 110 -549 - 11 155 -953 -239 + 9 _ 4-IT 111 BBf at 98 156 956 ^9 323 ' 17 23 112 571 14 m 9 157 959 1 206 H 113 584 13 813 10 158 961 3 189 17 1 114 .vi- 14 803 10 38 159 963 ' 173 17 32 11.-. 611 13 793 10 160 965 3 155 17 116 mt 14 783 10 161 967 3 139 16 1 117 638 13 ::.- 11 38 163 968 1 133 17 21 118 651 13 763 10 163 969 1 105 17 119 663 11 751 11 164 970 -1 88 17 1 13 11 17 130 -676 -740 98 165 -970 - 71 20 131 M -1 na +1? 166 970 54 +17 123 700 11 717 11 167 970 37 17 1 133 711 11 705 H 98 168 970 30 17 19 134 m 13 693 13 169 969 +' - 3 17 135 734 11 i,-l 13 t 170 968 1 + 14 17 1 136 745 11 668 13 38 171 967 1 31 17 18 127 756 U M 13 173 965 5 48 17 128 767 U 643 13 173 964 1 65 17 1 139 777 18 630 IS 98 174 963 3 83 17 17 11 14 3 17 130 -787 -616 175 -959 + 99 131 797 -11 603 + 13 176 at +1 116 + 17 t 133 806 * r,!o 13 98 177 .,-,! 3 133 17 15 133 816 11 576 14 178 950 4 150 17 134 825 * m 14 +1 IT'.I 947 3 166 16 +1 i.r, -834 - * + 14 -27 l-'i !M3 +4 fl3 +17 II 54 TABLE IV . Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT III. Arg. b Diff. 111 Diff. tl Diff. Arg. fi Diff. % Diff. tl Diff. o o 180 -943 +183 -14 225 -524 +816 + 7 181 939 + 4 200 +17 226 510 + 14 826 +10 182 935 4 217 17 +1 227 496 14 835 9 +1 183 930 5 233 16 13 228 482 14 844 9 8 184 925 5 250 17 229 467 15 853 9 185 920 5 266 16 l 230 453 14 862 9 2 186 915 5 283 17 12 231 438 15 871 9 10 187 909 6 299 16 232 423 15 879 8 188 903 6 315 16 2 233 409 14 .887 'B 1 189 897 6 331 16 10 234 394 15 895 8 11 6 16 16 7 190 -891 +347 235 -378 +902 191 884 + 7 363 +16 1 236 363 +15 909 + 7 1 192 877 7 379 16 9 237 348 15 916 7 12 193 870 7 395 16 238 332 16 923 7 194 663 7 411 16 1 239 317 15 929 6 2 195 855 8 426 15 8 240 301 16 935 6 14 196 847 8 442 16 241 285 16 941 6 197 839 8 457 15 2 242 269 16 947 6 1 198 831 8 472 15 6 243 253 16 952 6 15 199 822 9 487 15 244 237 16 957 6 9 15 1 16 4 1 200 -813 +502 245 -221 +961 201 804 + 9 517 +15 5 246 205 +16 966 + 5 16 202 795 9 531 14 247 189 16 970 4 203 785 10 546 15 2 248 173 16 974 4 1 204 776 9 560 14 3 249 156 n 977 3 17 205 766 10 574 14 250 140 16 980 3 206 755 11 588 14 1 251 123 n 983 3 2 207 745 10 602 14 - 2 252 107 . 16 986 3 19 . 208 734 11 615 13 253 90 n 988 2 209 724 10 629. 14 2 254 74 16 990 2 1 11 13 17 2 210 211 -713 701 +12 +642 655 +13 255 256 - 57 40 +n +992 993 + 1 20 212 690 11 668 13 1 257 24 16 994 1 1 213 678 12 681 13 + 1 258 - 7 n 995 1 21 214 666 12 693 12 259 + 10 17 995 215 654 12 705 12 2 260 26 16 995 1 216 642 12 717 12 3 261 43 17 995 22 217 630 12 729 12 262 60 17 995 218 617 13 741 12 1 263 77 n 994 - 1 1 219 604 13 752 11 4 264 93 16 993 1 23 13 11 n 2 220 -591 +763 265 +110 +991 221 578 + 13 774 +11 1 266 127 +17 990 - 1 1 222 565 13 785 11 5 267 143 16 988 2 24 223 551 14 796 11 268 160 17 985 3 224 538 13 806 10 +2 269 177 n 983 2 +0 225 -524 + 14 +816 +10 + 7 27(1 +193 +16 +980 - 3 +24 55 TABLE IV. Gmtum-,1. I'l.UIl KliATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT HI. Arg. 6 Diir. T ,\ Diff. f, Diff. lot ft Diff. fll Diff. tl Diff. o o 270 +1W ..-,i +24 315 +821 +561 +28 01 210 + 17 .'77 - 316 MO + 8 547 -14 272 236 M 973 4 +l 317 840 10 533 14 -o 273 242 M Ml 4 25 318 849 9 518 It 28 274 KB 17 HE 4 319 -:,- Ml 18 m 871 14 m 4 i m 867 9 486 18 i m j>i M M 1 26 321 -::. 8 471 19 27 277 m M 951 I 883 t 455 18 J> m 17 MI a 323 891 8 439 16 279 340 16 940 6 26 324 899 8 423 16 27 It 6 7 16 j-,i +355 +934 325 +906 +407 >l 371 + 16 M - i 326 913 + 7 391 -16 ' M in 18 921 7 27 327 MO 7 375 16 26 M 403 M 915 8 MB 927 T 359 16 j-i 418 19 908 7 329 933 8 342 17 i 433 13 900 e 27 330 939 8 325 17 25 M 449 16 m 7 331 945 6 309 16 in 464 16 885 8 1 332 950 f 292 17 i --- 479 M 876 I 28 333 955 275 17 24 M 494 19 868 8 334 960 t 258 17 15 1 4 17 290 +509 +859 335 +964 +241 291 523 +14 850 - 9 28 336 969 + 6 224 -17 24 2!t2 533 I 841 9 337 973 4 206 18 210 552 M 831 10 Mi 976 1 169 17 1 294 566 14 822 9 28 339 m 1 172 17 23 M :,-n 14 812 10 340 Mi 1 154 18 296 594 14 801 11 +1 341 985 1 137 17 1 297 608 14 791 10 29 342 987 3 120 17 22 MO 621 II 780 11 343 989 1 102 18 299 635 14 769 11 344 991 1 84 18 1 11 11 1 17 300 +648 +757 29 345 +993 + 67 21 301 661 +1 746 -M 346 994 + 1 49 -18 m 673 19 734 11 347 995 + 1 32 17 1 303 686 11 7M 11 29 348 995 + 14 18 20 304 698 11 710 11 349 995 - 4 18 305 711 1* 697 11 350 995 21 17 1 306 723 11 685 11 29 351 M6 39 18 19 307 734 11 672 11 352 994 - 1 56 17 308 746 11 659 11 -1 353 993 1 74 18 1 309 757 11 645 14 98 354 992 1 91 17 17 11 11 * 18 310 +768 +632 355 T.filU -109 311 779 + 11 618 -14 356 988 126 -17 1 312 790 11 604 14 28 3T.7 985 144 18 16 313 801 11 590 14 358 963 161 17 314 811 10 576 14 359 980 178 17 -1 315 + -JI +10 +561 -It +28 360 +077 -1% -18 +15 IT ABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT IV. Arg. 6 Diff. 1l Diff & Diff. Arg. 1 Diff 1l Diff t, Diff. -775 + 75 +38 o 45 -502 +691 + 6 I 773 + 2 90 +15 46 492 + 10 702 +11 2 772 1 106 16 -2 47 482 10 713 11 -4 3 770 2 121 15 36 48 471 11 723 10 + 2 4 768 2 137 16 49 460 11 734 11 5 765 3 152 15 1 50 450 10 744 10 4 6 763 2 167 15 35 51 439 11 754 10 - 2 7 760 3 182 15 52 427 12 763 9 8 757 3 197 ia 1 53 416 11 773 10 4 9 754 3 213 16 34 54 405 11 782 9 V 6 4 15 12 9 10 -750 +228 55 -393 +791 11 747 + 3 243 +15 2 56 382 +11 800 + 9 4 12 743 4 257 14 32 57 370 12 309 9 10 13 739 4 272 15 58 358 12 817 8 14 735 4 287 13 2 59 346 12 825 8 5 15 730 5 302 15 30 60 334 12 833 8 15 16 725 5 316 14 61 322 13 841 S 17 720 5 331 15 1 62 310 12 848 7 5 18 715 5 345 14 29 63 298 12 856 8 20 19 710 5 359 14 64 285 13 863 7 6 15 5 12 6 5 20 -704 +374 65 -273 +869 21 699 + 5 388 +14 27 66 260 +13 876 + 7 25 22 693 6 402 14 67 248 13 882 6 23 687 6 416 14 3 68 235 13 888 6 5 24 680 7 430 14 25 69 222 13 894 6 30 25 674 6 443 13 70 209 13 899 5 26 667 7 457 14 2 71 196 13 904 5 5 27 660 7 470 13 23 72 183 13 909 5 35 28 653 7 484 14 73 170 13 914 5 29 645 8 497 13 3 74 157 13 918 4 6 7 13 13 4 30 -638 +510 21 75 -144 +922 41 31 630 + 8 523 +13 76 130 + 14 926 + 4 32 622 8 536 13 3 77 117 13 929 3 5 33 614 8 549 13 18 78 103 14 932 3 46 34 605 9 562 13 79 90 13 935 3 35 597 8 574 13 3 80 76 14 937 2 6 36 588 9 587 13 15 81 63 13 940 3 52 37 579 9 599 12 82 49 14 942 2 38 570 9 611 13 3 83 35 14 943 1 5 39 561 9 623 12 12 84 21 14 944 1 57 9 12 13 1 40 -552 +635 85 - 8 +945 41 542 + 10 646 +11 3 86 + 6 + 14 946 + 1 6 42 532 10 658 12 9 87 20 14 946 63 43 523 9 669 11 88 34 14 946 44 513 10 680 11 -3 89 48 14 946 -5 45 -502 +11 +691 + 11 + 6 90 + (i',> + 14 +945 - 1 -68 57 TABLE IV. Continued. PKlMTUr.ATIOXS OF THE CO-ORDINA IKS IN I MT> til-' TIIK SIXTH DECIMAL. ARGUMENT IV. Ai* t Diff. 1l Diff. & Diff. Aig. i Diff. 1l Diff. tl Diff. o O 90 + 62 -68 135 +678 +605 -114 91 77 +u 944 - i 136 BM + 11 -14 02 M 14 943 i - 137 701 11 578 11 93 105 U 'II a 73 138 712 u 564 u 114 94 119 11 a 139 723 u 550 14 95 133 14 M a I 140 734 11 536 14 +1 96 147 U m i 78 141 745 u 522 14 113 97 162 13 932 * 142 755 10 507 II 98 176 14 M * 143 MB 10 493 14 1 99 . 190 It M 4 83 144 775 10 478 1ft 112 14 4 9 16 100 :! +921 145 7-1 +463 101 UB +13 '.117 - 4 4 146 794 +10 448 -1ft 3 109 233 14 912 I 87 147 803 1 433 1ft 110 103 247 14 .,- 4 11- -rj 418 1ft 1>U m 14 903 1 149 -.M 8 403 1ft | 105 276 U 897 a 92 150 828 8 :i- 1ft 108 106 ,"i U -Jl 6 151 836 g 372 18 107 305 la --:, - 4 152 814 1 357 15 1 108 319 u 879 6 96 153 851 7 341 1C 105 109 333 14 -7-J 1 154 858 7 325 16 14 7 1 7 It 3 110 4347 an 155 +865 +309 111 30 + 14 858 - 7 99 156 -7'J + 7 293 -1 102 112 376 u 851 7 157 878 < 277 16 113 390 14 Ml 8 4 158 -I 6 261 16 1 114 MM It M 8 103 I.V.I 889 1 245 16 99 115 418 14 BM 160 894 1 229 16 116 M 14 817 1 161 899 6 213 16 4 117 446 14 808 106' 162 904 I 197 16 95 118 M 11 ;,., 163 908 4 181 16 ir.i 473 14 790 1 164 912 4 164 17 4 14 10 16 130 +487 +780 106 165 +915 +148 91 l-'l 500 +11 770 -10 166 918 + 3 132 -18 122 514 14 7,,. 10 * 167 921 115 17 ft 123 as ia 749 11 110 168 923 3 99 16 86 124 541 14 738 11 169 925 1 83 16 125 554 IS 727 11 1 170 927 2 67 16 ft 126 567 11 716 11 112 171 928 1 60 17 81 127 580 11 7"! 11 172 929 + 1 34 16 123 :, :( 11 I,'-:! 11 1 173 929 18 16 ft 129 606 11 681 11 113 174 929 + 1 17 76 11 11 16 130 +618 +669 175 +929 - 15 131 630 +1* 656 -11 -1 176 928 - 1 31 -18 6 132 643 11 644 11 114 177 927 1 47 16 70 133 G.V, H 631 11 178 926 1 63 16 134 667 11 618 11 179 924 t 7!l 16 +8 135 ..,;- +11 .1,1-, -11 -114 180 +922 - 3 - 95 -16 1,1 58 TABLE IV .Continued. PEETURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT IV. Arg. & Diff. ft Diff. ?1 Diff. Arg. Ji Diff. fl Diff. tl Diff. O o 180 +922 - 95 -64 225 +481 -700 +38 181 919 3 111 -16 226 465 -16 710 -10 182 916 3 127 16 +6 227 450 15 719 9 +6 183 913 3 143 16 58 228 434 16 729 44 184 909 4 158 15 229 419 15 738 9 185 905 4 174 16 6 230 03 16 747 9 6 186 901 4 190 16 52 231 387 16 756 9 50 187 896 5 205 15 232 371 16 764 8 188 891 5 221 16 7 233 355 16 773 9 6 189 885 6 236 15 45 234 339 16 781 8 56 6 15 16 8 190 +879 -251 235 +323 -789 191 873 - 6 266 -15 7 236 307 -16 797 - 8 5 192 866 7 281 15 38 237 291 16 805 8 61 193 859 7 296 15 238 274 17 812 7 194 852 7 311 15 7 239 258 16 819 7 5 195 844 8 326 15 31 240 242 16 826 7 66 196 836 8 340 14 241 226 16 833 7 197 828 8 355 15 7 242 210 16 839 6 5 198 819 9 369 14 24 243 193 17 846 7 71 199 810 9 383 14 244 177 16 652 6 9 14 7 16 5 4 200 +801 -397 245 +161 -857 201 791 -10 411 -14 17 246 145 -16 863 - 6 75 202 781 10 425 14 247 129 16 868 5 203 771 10 438 13 7 248 113 10 873 5 4 204 760 11 452 14 10 249 97 16 878 5 79 205 749 11 466 14 250 81 16 883 5 206 738 11 479 13 7 251 65 16 887 4 207 727 11 492 13 - 3 252 49 16 891 4 82 208 715 12 505 13 253 34 15 895 4 209 703 12 518 13 7 254 18 16 899 4 3 13 12 15 3 210 +691 -530 + 4 255 + 3 -902 85 211 678 13 543 -13 256 - 13 -16 905 3 212 665 13 555 12 7 257 28 15 908 3 3 213 652 13 567 12 11 258 43 15 911 3 88 214 639 13 579 12 259 58 15 913 2 215 626 13 591 12 7 260 73 15 915 2 2 216 612 14 603 12 18 261 88 15 917 2 90 217 598. 14 614 11 262 102 14 919 2 218 584 14 626 12 7 263 117 15 920 1 2 219 570 14 637 11 25 264 131 14 921 1 92 15 11 14 1 220 +555 -648 265 -145 -922 221 541 14 658 -10 6 266 160 -15 922 1 222 526 15 669 11 31 267 174 14 922 93 223 511 It 679 10 268 187 13 922 224 496 15 690 11 +7 269 201 14 922 +1 225 +481 -15 -700 -10 +38 270 -214 -13 -921 + 1 +94 59 TABLE IV.Gmtiim,;!. I'F.inTKi; \TIn\s ,F TIIF. ( ( )-( Mil H N A TF.S IN UNITS OF THE SIXTH HF.CIMAI.. AR<;r.\IKNT IV. Arg. *. our fll itiir. (l Diff. An?. & Diff. Diff. Cl Diff. o 270 -214 -921 +94 315 6M -600 +71 -'71 M -14 MO + i 316 .,:.- -* 587 + 18 .'II 11 919 i +1 317 664 6 574 la -a 273 U '.M7 9 u 318 670 6 561 la 68 '.'71 K7 11 MB 1 319 676 6 M- 11 :-. m 11 013 1 320 t.-I 8 535 11 a 276 11 '.'11 9 95 321 667 6 521 u 65 277 304 19 .,. 3 322 692 8 507 u 316 19 00B a -1 323 697 8 4!3 14 a 279 m 19 902 i 94 M IM 8 479 u 62 19 4 8 14 M -340 -898 325 -707 -465 .'-1 m -19 894 + 4 m 712 -9 450 +18 9 M :,:; 11 M 4 94 327 716 4 436 14 60 -.'-:! 375 11 --., 4 328 721 9 421 19 .'-1 :'.-, 11 --i 8 1 329 725 4 406 18 a 397 11 tn 8 93 330 729 4 3; >2 U 57 -.'-I, 1 1- 11 871 8 331 733 4 377 18 --7 418 10 MB 6 1 332 737 4 362 18 i M 429 11 859 6 92 333 741 4 347 19 55 289 10 853 6 334 744 a 332 14 10 6 3 4 10 a 290 -449 -847 335 -748 -316 291 459 -10 MO + 7 90 336 751 -8 301 +18 52 469 10 833 7 337 754 8 286 18 293 479 10 -.'. 8 11 338 757 a 270 16 8 294 1- 9 818 7 88 339 760 a 255 18 50 497 9 810 8 340 762 9 239 16 296 507 10 -ii-,! 1 1 341 765 a 223 16 9 516 9 7.;: g 86 342 767 9 208 18 48 298 524 8 785 8 343 769 1 192 16 299 533 9 776 9 3 344 771 9 177 f6 1 9 9 9 16 300 -542 -767 84 345 -773 -161 46 Ml 550 - 8 + 10 346 774 -1 145 + 10 302 608 747 10 a 347 775 1 129 16 9 303 566 8 737 10 81 MB 776 1 114 18 44 3M 574 8 727 10 349 777 1 98 H 305 tea 8 717 10 a 350 778 1 82 16 1 306 590 8 706 11 79 351 779 1 66 16 43 307 607 7 .. -, 11 352 779 -0 51 19 308 604 7 684 II * 353 779 35 16 9 309 612 8 673 II 76 354 779 9 19 16 41 7 19 1 310 -619 -661 355 -779 - 3 311 626 - 7 649 +11 1 356 779 + 12 + 19 9 312 632 6 637 19 73 357 778 +1 24 16 39 313 630 7 625 11 358 777 1 44 16 314 645 6 613 11 i 359 776 1 59 19 -1 315 -652 ' (,'MI + 18 +71 -775 +1 + 75 + 16 m 60 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT V. Arg. & Diff. 1l Diff. & Diff. Arg. li Diff. % Diff. & Diff. o o -507 + 52 - 84 135 +358 -188 +150 3 507 39 -13 77 +7 138 376 + 18 181 + 7 148 -2 6 505 + 2 26 13 70 7 141 392 16 174 7 146 2 JJ 13 16 g 9 502 + 13 63 7 144 408 166 144 J 12 497 5 13 56 7 147 422 14 158 8 141 3 15 491 6 - 13 13 49 7 150 436 14 150 8 137 4 18 484 7 26 13 41 8 153 448 12 141 9 133 4 21 475 9 39 13 33 8 156 459 11 132 9 329 4 24 465 10 52 13 25 8 159 469 10 122 1C 125 4 27 454 11 64 12 18 7 162 477 8 113 9 120 5 13 13 8 7 10 5 30 -441 - 77 - 10 165 +484 -103 +115 33 427 +14 89 -13 - 2 +8 168 490 + 6 92 + 11 109 -6 36 412 15 100 11 + 6 8 171 494 4 82 10 103 6 39' 396 16 112 12 14 8 174 497 3 71 11 97 6 42 379 17 123 11 22 8 177 499 + 2 61 10 91 6 45 360 19 133 10 30 8 180 499 50 11 84 7 48 340 20 143 10 38 8 183 498 ~ 1 39 11 78 6 51 320 20 153 10 45 7 186 496 2 28 11 71 7 54 299 21 163 10 53 8 180 493 3 16 19 63 8 57 277 22 171 8 60 7 192 488 5 - 5 11 56 7 23 8 8 6 11 8 60 -254 -179 + 68 195 +482 + 6 + 48 63 230 +24 187 - 8 75 +7 198 474 - 8 18 + 12 41 -7 66 206 24 194 7 82 7 201 465 9 29 11 33 8 69 181 25 201 7 88 6 204 455 10 40 11 25 8 72 156 25 207 6 95 7 207 444 11 51 11 17 8 75 130 26 212 5 101 6 210 432 12 63 12 9 8 78 104 26 216 4 107 6 213 418 14 74 11 + 1 8 81 78 26 220 4 112 5 216 404 14 84 10 - 7 8 84 51 27 224 4 118 6 219 388 16 95 11 15 8 87 - 25 26 226 2 123 5 222 371 17 106 11 23 8 27 2 4 17 10 8 90 + 2 -228 +127 225 +354 +116 - 31 93 29 +27 230 - 2 131 +4 228 335 -19 126 +10 39 -8 96 55 26 231 - 1 135 4 231 316 19 136 10 47 8 99 81 26 231 139 4 234 295 21 145 9 54 7 102 107 26 230 + 1 142 3 237 274 21 154 9 61 7 105 133 26 229 1 145 3 240 252 22 163 9 69 8 108 159 26 228 1 147 2 243 230 22 172 9 76 7 111 184 25 226 2 149 2 246 207 23 180 8 83 7 114 208 24 223 3 151 2 249 183 24- 187 7 89 6 117 232 24 219 4 152 1 252 . 158 25 194 7 C6 7 23 4 + 1 25 7 6 120 +255 -215 +153 255 +133 +201 -102 123 277 +22 211 + 4 153 258- 108 -25 207 + 6 107 -5 126 298 21 206 5 153 261 83 25 213 6 113 6 129 319 21 200 6 152 -1 264 57 26 218 5 118 5 132 339 20 194 6 . 151 1 267 31 26 222 4 123 5 135 +359 + 19 -188 + 6 +150 -1 270 + 5 -26 +226 + 4 -127 -4 61 TABLE IV. Continued. PEItTl KHATIONS OF T1IK ro-OKDINATKS IN UNITS OF THE SIXTH DECIMAL. ARGUMENT V. Aig. fi Diff. * Diff. d Diff. A*. t Diff. i)i Diff. Ci Diff. o o 270 +5 +226 -127 315 -351 mi -149 - 21 +' in 318 370 - t0 g 147 276 47 M 135 321 HI 191 145 78 234 J 139 17 j ., 142 ' 98 " M 1 142 327 420 175 139 ' 124 M +l 145 330 434 14 166 136 * 149 236 147 333 447 13 156 132 4 M 17, 235 149 336 I. Vi 15 146 10 128 -."1 198 m 1 150 ' 339 I7.i 11 136 124 4 297 222 m ' 151 ' 342 479 125 11 119 I -1 8 13 5 300 -245 +229 345 -487 +113 -114 303 268 -" 226 M 348 494 102 109 M i n in A :i H, 290 M 152 351 499 90 103 309 311 217 i:.l 354 503 4 77 97 312 M 211 150 357 506 65 11 91 315 IM 1 -149 360 -507 1 + 52 1 -84 ARGUMENT VI. Arg. 1 Diff. m Diff. frl A* Jl Diff. Diff. & o +492 + 54 69 +127 +471 3 1" - 4 79 +8 72 102 -9* 477 + 8 -4 6 4-:i 5 104 35 75 77 35 482 5 9 477 8 129 35 78 51 36 485 * 4 12 470 7 153 34 -1 81 + 25 * 487 1 15 461 9 177 34 84 - 1 * ' I-- + 1 4 18 451 10 200 2* 1 87 27 98 1-7 - 1 21 440 11 223 3) 90 53 94 I-:, 1 5 24 428 13 245 88 2 93 78 3* 1-J * 27 414 14 267 11 96 104 38 477 8 5 14 11 35 8 30 +400 .1 } 2 99 -129 +471 33 -1 MB + 102 154 -as 464 - 7 5 1^ 35 g 36 367 327 IV 2 105 179 455 39 349 18 346 19 108 203 34 446 9 4 43 330 19 363 17 3 111 226 9 435 11 45 311 19 379 18 114 24!t as 422 U 4 48 _ 31 395 M 3 117 271 93 409 1* 51 960 11 409 14 120 2-13 93 394 U 4 54 247 ;; 423 U 3 123 314 91 379 U 57 224 i 435 11 126 333 19 362 17 4 M H , 19 18 60 +201 +446 4 129 -352 -344 63 177 -M 455 + 9 132 370 -18 326 -18 4 66 152 m 464 9 -4 135 387 17 306 30 69 +127 * +471 + 7 138 -403 -18 --'' ~* -3 62 TABLE IV .Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT VI. Atg. Si Diff. ni Diff. Si Arg. Si Diff. % Diff. l o 138 -403 +286 -3 o 249 -125 -473 141 418 -16 265 -21 252 100 +25 479 - 6 +4 145 431 13 243 22 3 255 74 26 483 4 147 444 13 220 23 258 48 26 486 3 4 1 J 23 26 150 455 197 3 261 - 22 488 J, 153 465 10 173 24 264 + 4 26 488 5 156 474 9 149 24 2 267 30 26 487 + 1 159 481 7 124 25 270 56 26 485 2 5 163 487 6 99 25 2 273 81 25 481 4 165 492 5 74 25 276 107 26 476 5 5 3 26 25 6 168 -495 + 48 1 279 +132 -470 171 497 - 2 + 23 -25 282 157 +25 462 + 8 5 174 498 - 1 - 3 26 -1 285 181 24 453 9 177 497 + 1 29 26 288 205 24 443 10 5 180 495 2 54 25 291 228 23 432 11 183 491 4 80 26 294 251 23 420 12 4 186 486 5 105 25 'o 297 273 22 406 14 189 480 6 130 25 300 294 21 391 15 4 192 472 8 155 25 +1 303 314 20 376 15 195 464 8 179 24 306 334* 20 359 17 4 10 23 19 18 198 -454 -202 1 309 +353 -341 201 442 +12 225 -23 312 370 +17 323 +18 4 204 430 12 248 23 2 315 387 17 303 20 207 416 14 270 22 318 402 15 283 20 3 210 401 15 291 21 2 321 417 15 262 21 213 385 16 311 20 324 430 13 240 22 3 216 368 17 330 19 2 327 442 12 217 23 219 349 19 349 19 330 453 11 194 23 3 222 330 19 366 17 3 333 463 10 171 23 225 310 20 383 17 336 472 9 147 24 2 20 15 7 25 228 -290 -398 3 339 +479 -132 231 268 +22 412 -14 342 4a5 + 6 98 +24 2 234 246 23 426 14 4 345 489 4 73 25 237 223 23 438 12 348 492 3 47 26 1 240 199 24 448 10 4 351 494 2 - 22 25 243 175 24 458 10 354 495 + 1 + 3 25 +1 246 150 25 466 8 +4 357 494 - 1 29 26 249 . -125 +25 -473 - 7 360 +492 - 2 + 54 +25 TABLE IV. Continued, 1-i.ini ur- vriiixs OF TIIK CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT VIL A*. t Diff. 1l Diff. & Ai* 6 Diff. 1 Diff. fl o -231 4 -20 135 +292 MO 3 ~ ' 8 ~ 138 322 +10 tea +17 + 8 .. M 1 13 21 141 350 364 19 9 -.".I i 18 144 377 97 342 91 10 19 m i 23 22 147 403 M 319 91 15 m 1 29 150 426 91 203 M 13 18 240 i 35 23 153 448 99 266 7 243 i 42 156 MB 90 216 10 u 24 9 GO 2-1 159 485 17 n 11 27 Jl- 1 58 162 500 II 173 19 16 9 1 11 U 30 -250 -67 24 165 +r,13 -140 33 - I 77 -10 168 M + 106 +M 1* 36 255 9 88 n 24 171 520 7 70 M 39 256 1 99 11 174 533 4 - 35 U 10 49 258 - 3 112 11 23 177 534 + 1 + 1 M 45 m 126 M 180 533 - 1 37 M 20 48 M 140 14 23 183 528 t 72 a 51 n 155 It 186 521 7 107 u 21 54 256 + a 171 18 22 l-'.i 511 10 142 U 57 253 .1 187 10 192 498 11 175 .: *J 4 n 1 19 60 -249 -204 21 195 - I-J +207 63 244 + 6 222 -18 198 464 -18 238 +11 22 66 237 7 230 17 10 201 444 90 267 99 69 229 8 257 18 204 422 29 2!t4 97 23 72 220 9 275 18 18 207 398 94 320 9 75 IOB 11 203 18 210 372 M 343 91 23 78 196 11 311 ia 16 213 345 97 364 91 81 182 U 328 n 216 316 99 383 19 22 84 166 18 345 n 14 219 .'-. M 400 17 87 149 17 362 17 222 M M 414 14 22 ia 11 11 90 -129 -377 12 225 +225 +425 93 109 +90 391 -14 228 194 -11 434 + 9 21 96 88 91 404 11 9 231 162 39 441 1 99 62 :i 416 19 234 131 11 445 4 20 102 37 15 426 10 1 237 100 11 447 + 9 !:, - 10 47 434 8 240 69 11 447 10 108 + 18 98 441 7 4 243 40 99 444 - 1 111 47 99 445 4 246 + 11 99 440 4 18 114 76 99 448 - 1 - 2 2-10 - 17 98 433 7 117 107 11 448 252 44 424 9 17 11 + 1 10 120 +138 -446 + 1 255 - 69 +414 123 169 +11 442 + 4 258 93 -94 402 -19 15 126 200 11 435 7 3 261 li:. 99 389 11 129 231 11 426 1 264 136 91 375 14 13 132 262 11 414 19 + 6 267 155 19 360 M 135 +202 + -400 +14 270 -172 -n +344 -w +11 64 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT VII. Arg. ?! .Diff. * Diff. Ek Arg. li Diff. * Diff. & o o 270 -172 +344 +11 315 -259 +100 273 188 -16 327 -17 318 257 +2 88 -12 - 7 276 202 14 309 IS 9 321 255 2 78 10 279 214 12 2!)2 17 324 252 3 68 10 9 282 225 11 274 18 7 327 249 3 59 9 285 234 9 256 18 330 247 2 51 8 11 288 242 8 238 18 5 333 244 3 43 8 291 248 6 220 18 336 241 3 36 7 13 294 253 5 203 17 + 3 339 239 2 30 6 297 257 4 186 n 342 237 2 24 6 15 3 16 2 5 300 -260 +170 345 -235 + 19 303 261 - I 155 -15 348 233 +2 14 5 17 306 262 - I 140 15 - 2 351 232 1 9 6 309 262 126 14 354 231 +1 5 4 19 312 261 + 1 112 14 - 4 357 231 + 1 4 315 -259 + 2 +100 -12 360 -231 - 4 - 5 -20 ARGUMENT VIII. Arg. li Diff. m Diff. & Arg. ft Diff. rn Diff. fl o -352 + 22 -7 69 -106 +335 3 350 + 2 40 +18 72 88 +18 340 + 5 + 6 JJ 18 18 ^ 6 347 58 6 75 70 344 9 344 3 76 18 78 52 is' 347 3 7 e Ifi 18 2 12 339 94 lo 5 81 34 349 15 334 6 112 18 84 - 15 19 350 1 8 18 328 6 129 17 4 87 + 3 18 351 + ! 21 320 8 146 17 90 22 19 350 - 1 9 a 18 24 312 163 3 93 40 348 27 303 9 179 16 96 58 18 346 2 9 9 15 18 4 30 -294 +194 2 99 + 76 +342 33 283 +11 209 +15 102 94 +18 338 - 4 10 36 272 11 224 15 -1 105 112 18 332 6 39 260 12 238 14 108 129 17 326 6 10 42 247 13 251 13 111 146 17 319 7 45 233 14 263 12 114 162 16 311 8 11 14 12 16 Q 48 219 275 +2 117 178 302 51 204 15 286 n 120 194 16 292 10 11 54 189 15 296 10 3 123 209 15 281 11 57 173 16 306 10 126 224 15 270 11 11 16 8 14 12 60 -157 +314 4 129 +238 +258 63 140 +17 322 _+ 8 132 251 +13 245 -13 11 66 123 17 329 7 +5 135 263 12 232 13 69 -106 +17 +335 + 6 138 +275 +12 +218 -14 +11 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATI.^ IX UNITS OF THE SIXTH DECIMAL. ARGUMENT VIII Arg. fc Diff. I, Diff. Ci A*. {, Diff. ll Diff. Ci Q o --'?". +218 +11 249 +106 -335 - 6 141 J-<, +11 Ml -is 252 89 -17 340 - s 144 M n 188 i> 11 MB 71 18 344 4 7 147 306 9 172 18 258 53 18 347 S BU 9 l .. 18 11 261 34 n 349 1 a ID 322 7 139 n 264 + 16 18 350 1 IM MI 7 122 17 10 267 - 3 19 351 1 9 IflB MB 8 105 17 270 21 18 350 + 1 162 340 87 18 9 273 39 18 349 1 9 165 344 4 69 18 276 58 19 346 S 4 18 18 4 168 +348 + 51 9 279 - 76 -342 10 171 NQ + 1 33 -18 -.'--' 94 -18 338 + 4 171 351 1 + 15 18 8 285 111 n 333 1 10 177 352 + 1 - 3 18 288 129 18 323 7 180 - 1 22 19 7 291 146 n 319 7 11 183 349 1 40 18 2)4 162 18 311 8 186 347 2 66 18 6 2)7 178 18 302 9 11 189 343 4 76 18 300 194 18 2)2 10 192 339 4 94 18 5 303 209 IS 282 10 11 195 334 S 112 18 306 224 IS 271 11 7 17 14 11 196 901 +327 MB - 7 -129 146 -17 4 309 312 -238 251 -IS -259 246 +1S 11 '.Ml 312 8 162 18 3 315 264 IS 232 14 11 207 303 9 178 18 318 276 13 218 14 S10 _"l 9 194 18 2 321 J-7 11 203 IS 11 213 MB 11 209 IS 324 297 10 1-- IS 216 n 11 MB 14 + 1 327 306 9 173 IS 11 Jl > MB 11 237 14 330 315 9 156 17 222 247 13 250 IS 333 323 8 140 18 10 225 233 14 263 IS 336 330 7 123 17 14 13 8 18 MB +21!) HBM - 2 339 -336 -105 9 231 905 -14 286 -11 342 341 - S 87 + 18 234 MB 18 2)6 10 3 345 345 4 70 17 9 237 173 18 305 9 348 MB S 51 19 240 157 18 314 9 4 351 351 S 33 18 8 243 141 18 322 8 354 352 - 1 - 15 18 M6 194 n 329 7 - 5 357 BBi + 4 19 + 7 M9 +106 -M -M6 - * 360 -MB -4 ---' +IS 66 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT IX. Arg. & Diff. * Diff. ?! Arg. li Diff. 111 Diff. tl o +150 - 3 +22 o 180 -305 + 3 + 11 +34 -24 5 150 11 ~~ 8 20 185 302 45 21 10 150 18 7 18 190 294 8 78 33 19 15 151 + i 26 8 16 195 282 12 110 32 16 20 152 i 34 8 13 200 267 15 140 30 13 25 153 + i 43 9 11 205 247 20 167 27 10 30 153 53 10 8 210 225 22 192 25 7 35 153 63 10 6 215 200 25 212 20 4 40 153 75 12 + 3 220 172 28 230 18 - 1 45 152 - 1 87 12 225 144 28 243 13 + 2 3 13 29 9 50 55 +149 146 -3 -100 114 -14 - 2 5 230 235 -115 86 +29 +252 257 + 5 + 5 8 60 141 6 128 14 8 240 57 29 259 + 2 11 65 134 7 143 15 10 245 29 28 257 2 13 70 126 8 158 15 13 250 - 3 26 252 6 16 75 116 10 173 15 16 255 + 22 25 244 8 18 80 104 12 188 15 18 260 45 23 234 10 21 85 89 15 202 14 20 265 65 20 222 12 23 90 72 17 216 14 23 270 83 18 209 13 25 95 53 19 228 12 25 275 99 16 194 15 26 22 10 14 16 100 + 31 -238 -27 280 +113 +178 +28 105 + 7 -24 246 - 8 28 285 . 124 +11 163 15 29 110 - 18 25 252 6 30 290 132 8 147 16 30 115 45 27 255 - 3 31 295 139 7 131 16 31 120 73 28 255 32 300 144 6 116 15 31 125 101 28 251 + 4 33 305 148 4 102 14 32 130 130 29 243 8 34 310 150 2 89 13 32 135 159 29 232 11 34 315 152 + 2 76 13 32 140 186 27 217 15 34 320 152 64 12 31 145 212 26 198 19 34 325 152 54 10 31 24 2S 10 150 -236 -176 -33 330 +152 + 44 +30 155 257 -21 150 +26 32 335 151 - 1 35 9 29 160 274 17 121 29 31 340 150 1 27 8 28 165 288 14 90 31 29 345 150 19 8 27 170 298 10 58 32 28 350 150 11 8 25 175 304 6 - 24 34 26 355 149 - 1 + 4 7 24 180 -305 - 1 + 11 +86 -24 360 +150 + 1 - 3 - 7 +22 tt TABLE IV .Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT X Arg. ft Diff. ft Diir. Arg. 6 Diff. 1l Diff. & o +187 - 10 + 6 1-0 -178 + 17 - 6 5 186 - l 26 -w 5 185 175 + i 33 +l 5 10 183 I 43 17 4 190 171 4 48 16 4 15 178 4 60 n 3 195 166 5 62 14 :t 20 ITS 76 18 3 200 159 1 76 14 2 25 164 8 91 H 2 205 152 7 90 14 I 30 155 1(16 19 + 1 210 143 1 103 13 _ | 35 145 10 120 14 215 134 115 13 40 133 19 133 13 - 1 220 123 11 126 11 + 1 1. 121 13 145 12 2 225 112 11 136 10 1 14 11 H 10 50 +107 -156 - 3 230 -100 +146 + 3 58 92 -14 165 - 4 235 87 +11 l. r >4 + 8 4 60 77 IS 173 8 5 240 74 n 162 8 5 65 61 Id l-n 7 6 245 60 14 168 a 6 TO 45 H 1-:, ft 7 250 46 14 173 4 6 75 28 17 1-- 1 7 255 32 14 177 4 7 80 + 11 17 190 9 8 HO 17 15 180 1 8 85 - 6 17 m - 1 9 265 - 2 It 181 1 8 90 23 17 i- + a 9 270 + 14 la 182 + 1 39 19 187 a 10 275 29 15 180 - 9 9 16 4 15 9 100 - 55 -183 -10 280 + 44 +178 +10 105 71 -1 177 + 10 285 59 + 14 174 - 4 in 110 86 H 170 7 11 290 73 14 16!) 5 11 118 100 14 162 8 11 295 87 14 163 6 11 120 113 " in 10 11 300 101 14 156 11 125 125 13 141 11 11 305 114 13 147 11 130 136 11 130 11 11 310 126 19 137 10 11 136 146 10 117 13 11 315 138 19 126 11 11 140 155 104 13 10 320 148 10 114 13 11 145 163 8 90 14 10 325 158 10 101 11 in u 8 14 150 -169 - 75 -10 330 +166 + 87 +10 155 174 - 5 60 +15 9 335 173 + 7 72 -14 9 169 177 1 45 U 9 340 179 67 15 9 Ml 179 3 29 M 8 345 183 4 41 M 8 170 180 - 1 - 14 15 7 350 186 > 24 17 8 175 180 + 2 H 7 355 187 + 1 + 7 17 7 180 -178 + 1 - 17 Mi - 6 no -1-7 1<> -17 + 6 ft 68 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XI. Arg. Ji Diff. 1)1 Diff. fc Arg. b Diff. * Diff. Si o o +101 + 11 - 3 180 -144 + 10 -30 5 98 - 3 30 +19 - 1 185 144 8 - 2 31 10 92 6 48 18 + 1 190 144 6 2 31 15 83 9 65 17 2 195 145 - 1 + 3 3 32 14 A 3 20 72 a 79 3 200 145 32 25 58 14 92 13 4 205 145 - 3 3 33 30 43 15 102 10 4 210 146 - 1 6 3 34 35 27 16 110 8 4 215 146 10 4 34 40 + 11 16 116 6 4 220 146 14 4 35 Ifl g A 45 - 5 10 119 3 225 146 18 36 16 + i + 1 5 50 - 21 +120 + 2 230 -145 - 23 -36 55 36 -15 119 - i + 1 235 144 + 1 28 - 5 37 60 51 15 117 2 240 142 2 34 6 37 65 64 13 114 3 - 2 245 140 2 41 7 37 70 76 12 110 4 3 250 137 3 47 6 38 75 87 11 105 6 5 255 133 4 54 7 38 80 97 10 99 6 7 260 128 5 61 7 38 85 106 9 93 6 9 265 122 6 69 8 38 90 113 7 86 7 10 270 115 7 76 7 38 95 120 7 80 6 12 275 106 9 83 7 37 5 7 9 7 100 -125 + 73 -14 280 - 97 - 90 -37 6 +1 1 105 130 67 15 285 86 11 96 36 110 133 3 61 6 17 290 74 12 101 5 35 115 136 3 55 6 18 295 60 14 106 5 34 120 139 3 . 49 6 19 300 46 14 109 3 32 125 140 1 44 5 21 305 30 16 111 - 2 30 130 141 1 40 4 22 310 - 13 17 111 28 135 142 1 36 4 23 315 + 4 17 108 + 3 26 140 143 1 32 4 24 320 21 17 103 5 24 145 143 29 3 25 325 38 17 96 7 21 3 16 9 150 -143 + 26 -26 330 + 54 - 87 -19 155 143 - o 23 - 3 26 335 68 +14 75 +12 16 160 143 20 3 27 340 80 12 60 15 13 165 143 18 2 28 345 90 10 44 16 10 170 143 15 3 29 350 97 7 26 18 8 175 144 - 1 13 2 29 355 101 + 4 - 7 19 5 180 -144 + 10 - s -30 360 +101 + 11 +18 - 3 * TABLE IV .Continued. Pl.lMl UBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XIL Arg. fc Diff. Diff. b Arg. fc Diff. * Diff. Q o o - 97 - 6 -2 ISO +132 + 8 +3 5 96 + i 13 - 7 185 130 - !l 30 +u 10 95 i 21 8 2 190 117 31 n 2 i:. 94 i 38 7 195 114 43 11 20 93 3 35 7 3 200 109 53 10 3 j-, gg a 43 8 M 103 63 10 30 86 a 50 7 3 210 96 71 9 3 83 4 67 7 315 88 8 79 8 40 78 4 64 7 2 220 80 8 86 7 2 45 74 4 70 1 225 71 9 93 7 e 7 10 6 50 -68 - 77 2 230 + 61 + 98 2 55 63 + 83 235 51 -10 103 + 4 61) 56 88 2 340 41 10 106 a 3 65 49 7 93 245 31 10 109 a 70 41 8 98. 2 250 20 11 110 i 2 Q 10 * | 33 102 255 + 10 111 80 34 9 I,.:, 1 260 10 110 - i 1 85 15 9 108 265 - 10 10 109 i 90 - 5 10 109 1 270 19 9 107 9 1 10 M + 5 110 275 39 104 10 8 4 100 + 15 -110 -1 280 - 37 +100 +1 1".-, 35 +10 109 + 1 385 45 - 8 96 - 4 110 36 11 107 9 390 53 8 91 * 11.-, 46 10 105 9 395 60 7 86 1 m 56 10 101 4 300 66 a 80 a 135 66 10 96 6 305 73 ' 74 ' 130 75 9 90 A +1 310 77 s 67 7 -1 UB 84 9 83 7 315 81 4 60 7 140 93 8 75 8 1 320 85 4 53 7 1 145 99 7 66 9 325 88 a 46 7 7 9 a 7 150 +106 - 57 1 330 - 91 + 39 1 155 111 + I 47 +10 335 93 - 9 32 - 7 160 lir, 4 37 10 2 340 95 3 34 8 2 165 119 4 36 11 345 96 1 17 7 170 121 9 15 11 2 350 97 - 1 8 2 175 122 + 1 - 3 11 355 97 + 3 7 1-d + 8 +11 +3 360 - 97 - 6 - 8 -3 i 70 * TABLE IN .Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XIII. Arg. ii Diff. * Diff. fl Arg. Ji Diff. 4k Diff. Si o o -83 - 6 180 +83 + + 6 5 82 +1 - 4 -4 185 82 -i 3 +3 10 80 3 7 3 4 190 80 2 7 4 4 15 78 2 11 4 195 78 2 10 3 20 75 3 14 3 - 2 200 75 3 14 4 + 2 25 72 3 17 3 205 71 4 17 3 30 68 4 21 4 210 67 4 20 3 35 63 5 24 3 215 62 6 23 3 40 58 5 26 2 + 1 220 57 5 26 3 - 1 45 52 6 29 3 225 52 5 28 2 6 2 6 3 50 -46 -31 3 230 +46 +31 3 55 40 +6 33 -2 235 39 -7 33 +2 60 33 7 35 2 5 240 33 6 35 2 5 65 26 7 37 2 245 26 7 36 1 70 19 7 38 1 7 250 19 7 38 2 7 75 12 7 39 1 255 12 7 39 1 80 - 5 7 40 -1 8 260 + 5 7 40 +1 8 85 + 3 8 40 265 - 3 8 40 90 10 7 40 9 270 10 7 40 9 95 17 7 40 275 17 7 40 7 +1 7 100 +24 -39 10 280 -24 +40 10 105 31 +7 39 +0 285 31 -7 39 -1 110 38 7 39 1 10 290 38 7 38 1 10 115 44 6 36 2 295 44 6 37 1 120 50 6 34 2 11 300 50 6 35 2 11 125 56 6 32 2 305 56 6 33 2 130 61 5 30 2 11 310 61 5 31 2 11 135 66 6 28 2 315 66 6 29 2 140 70 4 25 3 10 320 70 4 26 3 10 145 74 4 23 2 325 74 4 23 3 3 3 3 3 150 +77 -20 9 330 -77 +20 9 155 80 +3 17 +3 335 80 -3 17 -3 160 82 2 13 4 8 340 82 2 14 3 8 165 83 1 10 3 345 83 1 10 4 170 84 +1 7 3 7 350 84 -1 7 3 7 175 84 - 3 4 355 84 + 3 4 180 +83 -1 +3 + 6 360 -3 +1 -3 - 6 TABLE IV.Gmlimud. I'KUri Kl'.ATIONS OF THE CO-ORD1.VVI KS IN INITS OF TIIK SIXTH 1>I.< IMAL. ARGUMKNT XIV. An: fi Diff. fli Diff. b AIR. fl Diff. Diff. fi o +44 + 3 tt I -u -54 - 2 -2 5 i:. 41 - 1 4 165 64 4 3 4 10 45 4 3 2 190 64 8 ft 2 u 44 -i 7 3 M 63 +1 13 30 44 11 4 1 200 51 9 18 1 43 i 14 3 Ml 49 9 23 30 4-.' 1 18 4 +1 210 47 9 27 -1 :tr, 41 i 21 I 215 44 ' 31 40 3: i 9 34 3 M 40 4 35 45 37 9 38 4 225 37 a 38 a 9 3 4 a 50 -t;iT, -31 -1 230 -33 +41 +1 .V, 33 -3 34 ~* 235 29 +4 44 +* 60 30 9 37 3 1 240 24 1 46 9 1 27 3 40 3 245 20 4 47 1 TO 23 4 42 9 2 350 15 1 48 1 2 n 20 3 44 9 255 11 4 49 1 80 16 4 46 9 2 260 6 i 60 + 1 2 85 12 4 48 9 365 - 2 4 49 -I 90 8 4 49 1 3 270 + 2 4 49 3 Be + 3 8 50 1 275 7 1 48 1 4 -1 4 1 100 _ i 51 3 _>-! 1 +11 +47 3 105 6 ~* 61 385 14 43 45 -9 110 11 6 51 3 390 18 4 44 1 3 in 15 4 50 +1 395 22 4 42 9 130 20 * 49 1 3 300 25 3 39 3 3 at 25 1 47 9 305 28 3 37 2 130 39 4 45 9 4 310 30 9 34 3 4 i:Ci 33 4 42 3 315 33 a 31 a 140 37 4 39 a 3 320 35 9 28 a 3 145 41 4 35 4 325 37 2 25 a a 4 2 3 150 -44 -31 3 330 +39 +22 3 l.V, 47 ~* 27 +4 335 40 +1 19 -a 160 60 * 23 4 3 340 42 2 16 3 3 165 53 9 18 5 345 43 1 13 3 170 53 1 13 1 3 350 43 10 3 3 175 64 -1 8 4 355 44 + 1 6 4 I-" M -2 +0 -8 360 +44 + 3 -a 48 TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XV. Arg. li Diff. Diff. & Arg. li Diff. * Diff. fl o o -29 _ 2 180 +31 + 2 5 29 4 -2 185 31 5 +3 10 29 7 3 190 30 -1 7 o 15 28 +1 9 2 195 29 1 10 3 20 27 1 12 3 200 28 1 13 3 25 26 I 14 2 205 27 1 15 3 30 25 1 16 2 210 25 2 17 2 35 23 2 18 2 215 24 1 20 3 40 22 1 20 2 220 22 2 22 2 45 20 1 22 2 225 20 2 23 1 2 2 2 2 50 -18 -24 230 +18 +25 55 16 +2 25 -1 235 15 -3 26 +1 60 14 2 26 1 240 13 2 28 3 65 11 3 27 1 245 10 3 29 1 70 9 2 28 1 250 8 2 29 i g _(-j 75 7 m 29 255 5 30 q j 3 Q 80 4 30 260 + 2 30 85 - 1 3 30 265 2 30 90 + 1 2 30 270 - 3 3 30 95 4 3 30 275 5 2 30 2 3 -1 100 + 6 -30 280 - 8 +29 105 9 +3 29 +1 285 10 -2 28 1 110 12 3 28 1 290 13 3 27 1 115 14 2 27 1 295 15 2 26 1 120 16 2 26 1 300 17 2 24 2 125 19 3 24 2 305 19 2 23 1 130 21 2 23 1 310 21 2 21 2 135 23 2 21 2 315 23 2 19 2 140 25 2 19 2 320 24 1 17 2 145 26 1 16 3 325 25 1 15 2 2 2 2 2 150 +28 -14 330 -27 +13 155 29 +1 11 +3 335 28 -1 10 -3 160 30 1 9 2 340 28 8 2 165 30 6 3 345 29 -1 6 2 170 31 +1 3 3 350 29 3 3 175 31 - 1 2 355 29 + 1 2 180 +31 + 2 +3 360 -29 - 2 -3 TABLE IV.Gmtinued. I'KIMTKIIATIMNS OF TIIK t'O-OKDINATKS IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XVI ARGUMENT XVII. Arg. t Diff. 1, Diff. Ei Arg. ft Diff. Diff. & o + 113 + 4 +2 -103 - 16 -9 5 113 - 6 -10 5 102 +I 94 ~* 10 119 - i 15 1 2 10 99 33 2 15 110 9 25 10 15 96 49 90 108 1 34 1 90 92 50 - 1 104 4 43 95 87 57 7 30 100 4 59 +1 30 89 64 7 -1 35 96 ft 61 35 76 71 7 40 89 8 69 40 69 7 78 7 45 83 8 76 1 45 62 7 83 1 7 7 8 * 50 + 76 - 83 50 -54 - 88 55 68 ~ 89 - 8 55 46 +8 93 ~* 60 60 8 96 a -1 60 38 96 1 +1 65 59 8 100 1 65 99 99 1 70 43 * 104 4 1 70 90 101 9 1 75 34 I 107 1 75 11 103 -3 80 94 10 110 * 2 80 - 9 103 1 85 14 10 111 1 85 + 7 103 90 + 5 B 119 ~ l 2 90 16 109 + 1 2 96 - 5 10 119 95 95 101 1 10 + 1 B I 100 - 15 -111 3 100 + 34 - 96 2 in:, 95 -10 109 + 9 105 49 +8 95 +1 110 34 107 9 3 110 50 8 91 4 2 in 43 103 4 115 58 8 86 5 m 59 99 4 3 120 66 8 81 * 2 U6 61 94 I 125 73 7 75 130 69 88 8 3 130 79 8 68 2 UB 77 8 89 8 135 85 6 61. 140 84 7 75 7 3 140 90 ' 54 7 3 145 90 a 68 7 145 94 4 46 8 1 8 .4 8 150 -96 -60 3 150 + 96 - 38 2 155 100 51 + 9 155 101 * 99 + 160 105 49 9 3 160 103 3 20 B 2 165 106 33 9 165 104 1 11 9 170 110 24 * 2 170 105 +1 _ a 9 2 175 119 14 10 175 104 1 + 7 9 180 -113 ~ 4 + 10 -2 180 +103 -I + 16 ** +2 180 are to be subtracted from the Arguments > 180, and Si, n, and d to be taken with the reversed iign. 10 TABLE IV .Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XVIII. ARGUMENT XIX. Arg. fi Diff. % Diff. ?i Arg. 1 Diff. 1l Diff. Ci o o +43 + 5 +29 +14 -1 10 41 -3 12 +7 10 26 -8 18 +4 -1 20 39 2 19 7 20 22 4 22 4 30 35 4 26 7 30 17 6 26 4 40 30 6 31 6 40 12 5 28 2 50 24 6 36 5 50 7 6 30 +2 +1 60 17 7 40 4 60 + 1 6 30 1 70 10 7 42 2 70 - 5 6 30 1 80 + 3 7 43 +1 80 10 5 20 -1 2 90 - 5 8 43 90 15 5 27 2 2 7 -1 5 3 100 -12 +42 100 -20 +24 +2 110 19 -7 39 -3 HO 24 -4 21 -3 2 120 26 7 35 4 120 28 4 17 4 2 130 31 5 30 5 130 30 2 12 6 2 140 36 5 24 6 140 32 2 7 6 2 150 39 3 17 7 150 33 -1 + 2 5 1 160 42 3 10 7 160 33 - 4 6 1 170 43 -1 + 3 7 170 31 +2 9 5 1 180 -43 - 5 -8 180 -29 +2 -14 -5 +1 ARGUMENT XX. ARGUMENT XXI. ARGUMENT XXII. Arg. fit 1)1 fi Arg. Si % & Arg. & h fi o o o -27 - 4 +25 + 1 -24 +10 -8 10 26 9 10 24 - 3 10 21 14 8 20 24 13 20 24 8 20 17 18 8 30 21 . 17 30 22 12 30 13 21 7 40 18 21 40 20 16 40 9 23 7 50 14 23 50 17 19 50 - 4 25 6 60 10 25 60 13 22 60 + 1 26 5 70 - 5 27 70 10 24 70 6 26 3 80 27 80 6 26 80 10 25 2 90 + 4 27 90 + 1 26 90 15 23 -1 100 + 9 -26 100 - 3 -26 100 +19 +21 +1 110 13 24 110 7 25 110 22 19 2 120 17 21 120 11 24 120 25 15 4 130 21 18 130 15 21 130 26 11 5 140 23 14 140 18 18 140 28- 7 6 150 25 10 150 21 14 150 28 + 3 7 160 27 - 5 160 23 10 160 27 - 2 8 170 27 170 24 6 170 26 6 8 ISO +27 + 4 180 -25 - 1 180 +24 -10 +8 180 are to be subtracted from the Arguments > 180, and |i, iji, and ti to be taken with the reversed sign. 75 TABLE IV. Continued. P1.RTURBATIONS OF THE CO-OUDINATES IN t NITS OF THE SIXTH DECIMAL. AUt.rMI.N I' XXIII AK'.I'M! NT XXIV. ARGUMENT XXV. Arg. 6 1i & Arg. fi 1i Ci Arg. k h fi o -aa - 3 -i +30 -4 +2 -19 + 1 10 23 + 3 i 10 30 4 1 10 19 4 30 . ai 6 -i 30 18 4 +1 30 18 7 30 90 10. 30 1C 3 30 16 10 40 18 i:t 40 14 3 -1 40 14 13 50 15 16 50 11 2 2 50 13 15 60 13 18 60 8 1 2 60 9 17 70 9 30 +1 70 + 4 -1 3 TO 6 18 80 1 B 1 80 80 - 3 19 90 - 1 23 1 90 - 3 +1 90 + 1 19 100 + 3 +22 +1 100 - 7 +1 -4 100 + 4 +19 110 6 81 1 110 10 2 110 7 18 m 10 20 2 120 13 3 120 10 16 no 13 18 2 130 16 3 130 13 14 MO 16 15 2 140 18 4 140 15 13 150 18 12 2 150 19 4 150 17 9 160 30 9 1 160 90 4 3 160 18 6 170 22 1 1 170 21 4 3 170 1! + 3 IfO ---.' + 3 +1 180 -90 + 4 -9 1-0 +1!) - 1 ARGUMENT XXVI. ARGUMENT XXVII. ARGUMENT XXVIII. Arg. fi h fi Arg. ft 1l fi Arg. t fli & o O o +19 +13 +16 +11 +3 -15 + 5 +1 10 21 9 10 14 7 3 10 14 8 1 80 23 6 20 12 + 2 3 20 13 11 1 30 34 + 2 30 10 - 2 2 30 13 14 +1 40 34 - 2 40 7 7 2 40 10 16 50 83 6 50 4 11 2 50 8 18 60 82 10 60 + 1 15 1 60 6 19 b 70 30 13 70 - 3 19 +1 70 - 3 20 80 17 16 80 6 22 80 19 - 90 14 19 90 9 24 90 + 2 19 100 +11 -21 100 -11 -35 -1 100 + 5 +18 - 110 7 22 110 14 96 1 110 7 16 120 + 3 83 120 16 26 2 120 9 14 130 - 1 23 130 17 25 2 130 11 11 2 140 6 22 140 18 24 3 140 13 8 2 150 10 20 150 18 21 3 150 14 5 2 160 13 18 160 18 19 3 160 15 + 2 2 170 16 16 170 17 15 3 170 15 - 3 2 180 -19 -13 180 -16 -11 -3 at +15 - 5 -1 180 are to be subtracted from the Argument* > 180, and -,, n, and ti to be taken with the rerersed sign. TABLE IV. Continued. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XXIX. ARGUMENT XXX. ARGUMENT XXXI. Arg. 1 1i & Arg. & fe & Arg. li & o o o +12 + 1 -8 __l -7 -1 10 12 - 1 10 8 2 10 7 2 20 12 3 20 7 3 20 6 3 30 11 5 30 7 5 30 6 4 40 10 7 40 6 6 40 5 5 50 9 9 50 5 7 50 4 6 60 7 10 60 4 8 60 3 6 70 5 11 70 2 8 70 -2 7 80 3 12 80 -1 8 80 7 90 + 1 12 90 +1 8 90 +1 7 100 - 1 -12 -1 100 +2 -8 100 +2 -6 110 3 12 1 110 3 8 110 3 6 120 5 11 1 120 4 7 120 4 5 130 7 10 1 130 5 6 130 5 5 140 9 9 1 140 6 5 140 6 4 150 10 7 1 150 7 4 150 7 3 160 11 5 -1 160 8 2 160 7 -2 170 12 3 170 8 -1 170 7 180 -12 - 1 180 +8 +1 180 +7 +1 ARGUMENT XXXII. ARGUMENT XXXIII. ARGUMENT XXXIV. Arg. fi fli t, Arg. li Ji & Arg. & ni & o +4 -5 o +3 O +3 10 5 4 10 3 10 3 +1 20 6 3 20 3 _j 20 3 i 30 6 2 30 3 1 30 2 2 40 7 -1 40 3 2 40 2 2 50 7 50 2 2 50 2 2 60 7 +1 60 2 3 60 1 3 70 6 2 70 1 3 70 +1 3 80 6 3 80 +1 3 80 3 90 5 4 90 3 90 3 100 +4 +5 100 -3 100 -1 +3 110 3 5 110 _j 3 110 1 3 120 2 6 120 1 3 120 2 2 130 +1 6 130 2 3 130 2 2 140 6 140 2 2 140 3 2 150 -1 6 150 3 2 150 3 1 160 2 6 160 3 1 160 3 +1 170 3 5 170 3 -1 170 3 180 -4 +5 180 -3 180 -3 180 are to be subtracted from the Arguments > 180, and I,, n, and ti to be taken with the reversed sign. 77 TABLE IV. CiHifini','1. 1'I.KTrRBATIOXS OF THK CO-ORDIXATKS IX l.NITS OF THE SIXTH DECIMAL. ARI;UMI:M xxxv. ARGUMKNT XXXVI AKtifMKNT XXXVII. 6 li f, AIR. i 180, and li, ui, and ft to be taken with the reversed sign. 78 TABLE IV. Concluded. PERTURBATIONS OF THE CO-ORDINATES IN UNITS OF THE SIXTH DECIMAL. ARGUMENT XLI. ARGUMENT XLII. ARGUMENT XLIII. Arg. Ii 'ji & Arg. & ^i 1 Arg. & ii Si o o -1 0-1 +20 -100 20 1 +1 20 2 20 100 40 -1 i 40 2 40 -1 +1 60 i 60 +1 2 60 010 80 i 80 1 1 80 010 100 i 100 2 +1 100 010 120 +1 i 120 2 120 +110 140 1 +1 140 2 -1 140 1 +1 160 1 160 1 1 160 100 180 +1 180 +1 -2 180 +100 ARGUMENT XLIV. ARGUMENT XLV. Arg. fl % i Arg. { t *ii Si o -1 +1 20 1 20 -1 40 1 40 1 -1 60 -1 60 1 1 80 80 1 2 100 100 1 2 120 120 1 2 140 -1 140 -1 1 160 +1 1 160 -1 180 +1 -1 180 180 are to be subtracted from the Arguments > 180, and ii, n, and Ci to be taken with the reversed sign. TABLE V. LOGARITHMS Fou UF.FF.KIM \(. THK I'KIMTUHATIONS TO THE EQUATOR. Mean Equinox of the beginning of the Tear. Yean. o (*i *) o(jnx) (!) * (1) coi (yi jf) (*iy) cot (i) o(jn*) (*.) I-.v.'/J ' . -.:ii. 9.423945* 8.944771 7 /i &MMM MMOT 9.966852 9.400858M -.H.I-Ju./i 9.425243 y*iooy^w l-;,:, MM068N 8.944t2l5 '.'.117012 gUK6-.'l MOOK.'4'i 8.161 466n 9.425201 9.9tKKi2 i- I B M9M6BN 17345 9.9667116 9.400791 n 8.156674M 9.425159 9.983iN I-.-.7 Jl7:i 9.423.S4*n 8.943844 '.117, .77 9.966766 9.400757 8.155432M 9.425117 9.964000 B81 9.426227n 8.943658 MMOM 9.966740 9.400723n 8.152!l9l'i 9.495075 9.964004 1H.V.I i-.". 9.4266C6n 8.943473 9.448341 '1712 9.400669 8.1501 42n 9.425033 9.084C06 1-1, i /.' ii.'i- 1 9.426964n 8.943266 :i. 11-673 9.966664 9.400656n 8.147263n 9.4241KH) 9.964011 1961 9.427362n 8^4:ilii :i.li 9.966056 9.400622 8.144356n '.'.l-T'l- 9.964015 M,-J i.i-.c7r 8.942914 9.4J 9.966628 9.400568n -.11111 9.424905 9.984019 1-.,:: -M12 9.4981 17n 8.94 V728 9.44!>666 9.966600 9.400554n 8.136472 9.424863 9.964C23 MB '.'.'-1984 9.438494n 8.942M1 9.44 9.H 9.40U.V.'l;i 8.135514n 9.4VM--"' 9.964C27 i-.,-, 9.981956 9.42867 in 8.942355 9.450326 9.966544 9.400487 8.132546n 9.424778 9.984031 i-.-, -1938 9.429247n -."r.'h,- !U.. 9.966516 9.400454n 8.129549n 9.424735 9.934035 1667 9.981-.MKI 9.429623n 8.941981 9.4.V)!e6 9.f!664rt6 9.400420n -.I-J.V.'I" 9.424693 9.984039 i-.,- /; -1*79 9.429999* 8.941794 9.451315 9^66459 9.400387n 8.123466n 9.424650 9.984042 tM 9.961844 9.430374n -.'ll, 7 9.4:>1G44 i.!W6431 9.400353n 8.120409n 9.424608 9.984(!46 1870 1316 9.430749n 8.941420 an 9.966403 9.400320 8.117336n 9.424565 9.984050 1871 9.981788 1.4:11 134n 8.941233 9.4r>2301 '.i.'. '66375 :M .-.-., 8.11424 l/< 9.45M.V.".' 9.984064 i -:./; 9.981760 9.431498* 6.941045 5)89 9.!6346 9.4002.->:t; -.11 11 1 I// 9.424479 9.964068 1873 9.9817:tt n.4-.U672 8.940868 9.4.-,* 157 9.966318 9.40021 On 8.107956n 9.424437 9.964C62 1874 9.981704 9.432--' .|:.; 8.940670 '.M.-.3284 9.966290 9.400166n 8.104794n 9.424 394 9.984C66 1875 9.981676 9.432618n 8.940463 i..|r,36l2 9.966262 9.400152n 8.101610n 9.424351 9.984070 i-;.;/,' ncir 9.438!)!iln 8.940205 9.453-139 9.966233 9.4001 19n 8.0963(*7 9.424308 9.984073 1677 9.981619 9.43X)64n 8.940107 9.454266 9.966205 9.400065n 8.0951 34 9.424265 9.964077 1-7- 9.961 .V>1 9.433736n 8.939919 9.966177 9.400052n 8.091878n 9.424222 9.964C81 !-:> 9.981563 9.434106n 8^3!>7:il 9.454918 9.966149 9.400019n 8.08NVI7H 9.424179 9.964085 i --,,/; 9.981534 9.43447;>n 8.93!t:.i:i 9.455244 1.966120 9.399986n 8.085275H 9.424136 9.984068 1881 9.961506 9.4:H-:.u; t U9HH 9.455.-.70 9.966092 9.399952 8.081923n 9.424093 ., ., ._, 1-- .' 9.981478 9.43Slu 8.939167 :i.l.Vj895 9.!66063 9.39991 9n 8.078529n 9.424050 UK6 l--:t -1450 9^36Ti!M 9.456220 9.966' KIT, 9.3996S6n 8.0751 10n 9.424007 9.964100 I I /( 1 lv!l 9.4350611 MMM 9.456545 9^)66006 9.39853n 8.07171 in 9.423TG4 94)84103 l-v-. 9.981393 9^36:Ciln 8.938632 !'. 156869 9.965978 rt.;eii6i9n 8.C6fti65n 9.423H21 9.984107 1--., 9.981364 9.43670(W 8.936413 :i.i:,7193 9.965949 9.399786n 8.064795* 9.423878 9.964111 1 7 9.961336 9.437069n 8.938224 9.457517 9.965!)21 9.399753n 8.C61302n 9.423^:1". 1115 1888 B -1307 9.437438n 8.938035 9.457841 9.965892 9.399720W 8.057762n 9.423791 9.984119 l-i -1279 9.437807n 8.937846 9.456164 9.965864 9.399687n 8.054 l!i*i 9.423748 9.984123 I-MI -1250 I178N 8.937657 9.458487 9.965835 9.3!W654n 8.050612n 9.423704 9.964127 l-.ll 9.96)223 9.438543n 8.937468 9.456610 9.965806 9.3!>n621n 8.046982R 9.423661 9.964131 LMtl '.i.!i*1193 9^3)10n Mmn 9.459133 9.965777 9.399586H 8.043323n 9.423617 9.964134 I8H -1165 9.4:0277n 8.937089 9.459455 9.965749 9.399555n 8.039652n 9.423573 9.984138 1894 9.961136 9.439644/1 8.936*19 9.4511777 9.965720 9.399522n 8.035950n 9.42352!! 9.964142 !-', 9.981108 9.44001 in 8JKK709 9.460099 9.965691 9.399489 8.032211* 9.423485 9.984146 1-N,/.' 9.961079 9.440377n 8.936S19 9.460420 9.965662 9.399456 8.028449n 9.423442 9.984149 1897 9.961051 9.440743n 8^36329 9.460741 9.965634 9.399423W 8.024650K 9.423398 9.984153 1-,- 9.981022 9.441 108H 8.936139 9.461061 9.965605 9.399390n 8.020817n 9.423355 9.984157 1899 9.980993 9.441474K 8.935949 9.461 :i-j 9.965576 9.399357n 8.016950n 9.42331 1 9.994161 '.l.'.MIIMit !).441^:!!bi 8.93T.7.-.- 9.46 17i )2 !i.'. *>:.:> 17 !>.:!. i32T>n 8.013046n !'.423268 9.984164 80 TABLE VI. CONSTANTS FOR THE EQUATOR. Equator and mean Equinox at the beginning of the Year. Tears. A' B' C' log sin a. log sin b. log sin c. O 1 It O 1 II O 1 II 1852 B 105 27 14.0 16 46 17.2 356 49 20.7 9.998310 9.985785 9.425995 1853 105 28 3.8 16 47 4.6 356 50 31.7 9.998311 9.985787 9.425945 1854 105 28 53.6 16 47 52.0 356 51 42.7 9.998313 9.985790 9.425895 1855 105 29 43.5 16 48 39.2 356 52 53.8 9.998314 9.985792 9.425844 1856 B 105 30 33.4 16 49 26.8 356 54 5.0 9.998316 9.985794 9.425794 1857 105 31 23.2 16 50 14.2 356 55 16.1 9.998317 9.985797 9.425744 1858 105 32 13.0 16 51 1.6 356 56 27.1 9.998319 9.985799 9.425694 1859 105 33 2.9 16 51 49.0 356 57 38.2 9.998320 9.985801 9.425644 1860 B 105 33 52.8 16 52 36.5 356 58 49.5 9.998321 9.985804 9.425593 1S61 105 34 42.6 16 53 23.8 357 0.6 9.998323 9.9858C6 9.425543 1862 105 35 32.4 16 54 11.2 357 1 11.7 9.998324 9.985808 9.425493 1863 105 36 22.2 16 54 58.6 357 2 22.9 9.998326 9.985811 9.425443 1864 B 105 37 12.2 16 55 46.1 357 3 34.2 9.998327 9.985813 9.425302 1865 105 38 2.0 16 56 33.5 357 4 45.4 9.998329 9.985815 9.425342 1866 105 38 51.8 16 57 20.9 357 5 56.5 9.998330 9.985818 9.425292 1867 105 39 41.6 16 58 8.2 357 7 7.7 9.998331 9.985820 9.425242 1868 B 105 40 31.6 16 58 55.8 357 8 19.1 9.998333 9.985822 9.425192 1869 105 41 21.4 16 59 43.1 357 9 30.3 9.998334 9.985825 9.425142 1870 105 42 11.2 17 30.5 357 10 41.5 9.998336 9.985827 9.425092 1871 105 43 1.0 17 1 17.9 357 11 52.7 9.998337 9.985829 9.425042 1872 B 105 43 50.9 17 2 5.4 357 13 4.1 9.998339 9.985831 9.424991 1873 105 44 40.7 17 2 52.8 357 14 15.4 9.998340 9.985834 9.424941 1874 105 45 30.5 17 3 40.2 357 15 26.6 9.998342 9.985836 9.424891 1875 105 46 20.3 17 4 27.6 357 16 37.9 9.998343 9.985838 9.424841 1876 B 105 47 10.3 17 5 15.1 357 17 49.3 9.998344 9.985840 9.424791 1877 105 48 0.1 17, 6 2.5 357 19 0.6 9.998346 9.985843 9.424741 1878 105 48 49.9 17 6 49.8 357 20 11.9 9.998347 9.985845 9.424691 1879 105 49 39.7 17 7 37.2 357 21 23.2 9.998349 9.985847 9.424641 1880 B 105 50 29.7 17 8 24.7 357 22 34.7 9.998350 9.985849 9.424591 1881 105 51 19.5 17 9 12.1 357 23 46.0 9.998352 9.985852 9.424541 1882 105 52 9.3 17 9 59.5 357 24 57.3 9.998353 9.985854 9.424491 1883 105 52 59.1 17 10 46.9 357 26 8.7 9.998354 9.985856 9.424441 1884 B 105 53 49.0 17 11 34.4 357 27 20.2 9.998356 9.985858 9.424391 1885 105 54 38.8 17 12 21.8 357 28 31.6 9.998357 9.985660 9.424341 1886 105 55 28.6 17 13 9.1 357 29 42.9 9.998359 9.985863 9.424291 1887 105 56 18.4 17 13 56.5 357 30 54.3 9.998360 9.985865 9.424241 1888 B 105 57 8.4 17 14 44.0 357 32 5.9 9.998361 9.985867 9.424191 1889 105 57 58.2 17 15 31.4 357 33 17.3 9.998363 9.985869 9.424141 1890 105 58 48.0 17 16 18.8 357 34 28.7 9.998364 9.985871 9.424C91 1891 105 59 37.8 17 17 6.2 357 35 40.2 9.998366 9.985874 9.424041 1892 B 106 27.7 17 17 53.7 357 36 51.8 9.998367 9.985876 9.423991 1893 106 1 17.5 17 18 41.1 357 38 3.2 9.998369 9.985878 9.42394] 1894 106 2 7.3 17 19 28.5 357 39 14.7 9.998370 9.985880 9.423891 1895 106 2 57.2 17 20 15.9 357 40 26.2 9.998371 9.985882 9.423841 1896 B 106 3 47.1 17 21 3.4 357 41 37.8 9.998373 9.985884 9.423792 1897 106 4 36.9 17 21 50.8 357 42 49.4 9.998374 9.985886 9.423742 1898 106 5 26.7 17 22 38.1 357 44 0.9 9.998376 9.985888 9.423692 1899 106 6 16.5 17 23 25.5 357 45 12.4 9.998377 9.985890 9.423642 1900 B 106 7 6.5 17 24 13.0 357 46 24.1 9.998379 9.985893 9.423592 OF THE UNIVERSITY CALIFORNIA BERKELEY Return to desk from which borrowed. 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