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 THK AMERICAN El'HKMERIS AND iNAUTICAL ALMANAC. 
 
 BY 
 
 GEORGE W. HILL. 
 
 
 BUREAU OK NAVIGATION, 
 
 \V A s il | N <; To X. 
 18 
 
\ -'University of California. 
 
 . HFT OF 
 
TABLES 
 
 OK 
 
 VENUS, 
 
 I'RKPARKJ) I'T>R Till. HSK. Ol' 
 
 THE AMERICAN EPHEMERIS AND NAUTICAL ALMANAC 
 
 BV 
 
 GEORGE W. El ILL. 
 
 I'unusur.n BV AUTHORITY OK THE SECRETARY OK THK NAVY. 
 
 BUREAU OF NAVIGATION, 
 
 WASHINGTON. 
 
 1872, 
 

PBEFACE. 
 
 Tin: following tallies of Venus have liccn prepared to take the place of the unsatisfactory 
 elements and tallies heretofore used in the preparation of tho Antrrirtni I''/>l/rn/"i-ix <nnl 
 .\tnif iral AlnniiHti-. 
 
 The elements given in Li: VKIMMKH'S Aitmilr* <!< FObserwttoire Inij>cri(il tie I'tirix, Tome 
 \'l., have heen corrected by the discussion of au extended series of observations; Lr. 
 VKUUIKU'S e.\]iressions for the perturbations have been modified by changes in the adopted 
 values of the planetary masses; and the tables have been carefully arranged so as to 
 facilitate the computation either of particular places, or of an Kphemeris, of the planet. 
 
 The work has been performed by .Mr. (ii:oi;cK W. HILL, who has long been one of 
 I he most elh'cient Assistants in the preparation of tho works published by this office. 
 
 J. H. C. COFFIN, 
 
 Prof. Mat}/. ('. .V. A r ., 
 Superintendent nf Xtiufira/ Alnmnnr. 
 WASIIIXCTOX, May, 
 
S T E \ T S . 
 
 IxTKoprcTio*. C+mjtrmctum fmJ j tf tkt TmUf* . t 
 
 EI*iDDUofU:Ocbltof\>B,l?oOjO . I 
 
 Preceio of the iqmimmti . * 
 
 Have* of the pbaeto t 
 
 Varriag elt rf the ettit mfVcmm* ... . . . 1 
 
 3 
 
 . ....... 4 
 
 . 
 
 Arptaentt oflht tabl** .6 
 
 OWMjoitr of Ux- rrlipuc id ngtiUon ...... C 
 
 of a fixed 4ate . . 
 
 1 to XV ....... 9 
 
 XVI to XXV . . ! 
 
 XXVI : XXXV - _ .... .11 
 
 XXXVI to XL . li 
 
 XLI t, XLVI 13 
 
 Dmrtim*ftr Ik' mtt if tJki TfUtt 14 
 
 Euapie . . ... . . W 
 
 TrauitofVN*iB 1761 ......... VI 
 
 ' 1769 . . *i 
 
 CWratiw ) tin rlrmtmtt ^ (ftc fr*it *f I'tmm* ... *1 
 
 L<-\rmrr" rlffmt f tfce ortm of Vrnn* ....... 21 
 
 1769 - .... 2J 
 
 r part * the orfcit . . 34 
 
 rpartof theorfcii * 
 itbel 
 
 31 
 
 Sonul nnatiau 34 
 
 Ooroltabon ei MeicwT by Ve 
 
 TABLE& 
 
 Tblr 
 
 14 
 IT 
 
 - 
 I? 
 
i CONTENTS. 
 
 Page. 
 
 Table- . \.\VI. l.ii^arillllll iil'llic elliptic radius vector . . ...... 4<> 
 
 X.NVII. iii \\.\VI. Perturbation* of log r .... 51 
 
 XXXVII., XX Will. Perturbations of the latitude Oi 
 
 XXXIX. Values <>t'A" x , A'j, &c., iind Arg.s. XV. :ind XVI for tliu beginning of each year ..... ?'J 
 
 ,\l.. Corrections of T Z , f y , &c., due to lunar Natation .......... 7(i 
 
 XLI. " " " " due to sular -Nnlation 77 
 
 XLII. Kai tors lor finiling corrections of x, y, z, due to perturbations of the latitude 7tj 
 
 XI, HI. 1'arallax and semidiiiiuetcrs ............... "8 
 
 XI. IV. Motions of the Argumentg for centuriei ............ 79 
 
 XLV. A trnn of lung p'-riod in the perturbation of the longitude ......... 80 
 
 Xl.VJ. Reduction to tlie Ecliptic .... 80 
 
'UNIVERSITY! 
 
 INTRODUCTION. 
 
 CONSTRUCTION AND USE OF THE TABLES. 
 
 THE Tables arc based on ihe following 
 
 Epoch, 1850, Jan. 0.0, Washington Mean Time. 
 
 L' = 244 18 18.32 
 -' = 129 27 42.86 
 &' = 75 19 53.10 
 V = 3 23 35.01 
 c' = 0.006843113 
 n' = 2106611".35447 
 
 Those elements have heen derived from a discussion of the data furnished by the transits of Venus in 1761 
 and 1769, and by observations made at Greenwich in the interval 1836-1870, at Paris in the interval 1S38-1866, 
 and at Washington in the interval 1863-1867. In this discussion the Solar Theory of HANSEN and OLUFSKN was 
 used.* Consequently these Tables should be used in conjunction with the Tables du Soleil of these authors.! 
 
 The value of the Precession of the Equinoxes, according to PETERS,^ is 
 
 50".2411 1 + 0".0001134< 2 , 
 
 where the unit of t is the tropical year, and it is counted from 1800. If we make the unit the Julian year, and 
 count t from 1850, the formula will be 
 
 50".25351 t + 0".0001134 t 2 . 
 The formulae which define the motion of the plane of the ecliptic are, according to HANSEN and OLUFSEN, 
 
 sin i" sin Q" = + 0".053916 t + 0".00001887 < 2 , 
 sin i" cos Q" = 0".467839 t + 0".00000562 f. 
 
 In order to obtain the tropical motion of the planet, it is necessary to add, to the sidereal motion, the preces- 
 sion, and the small term, 
 
 sin i' sin i" sin ( Q' Q"), 
 the numerical value of which is + 0".01382 t. This it is also necessary to add to the longitude of the perihelion. 
 
 * Tallies du Solril, riiruttis il'ii/irls les ordres dc la SociM Royalc tics Sciences de Copenhafrue, par MM. I' .1. llnnsrn et C. F. 
 R. Olufsen. Co/Hiili(i<?if 1~">:5. 
 
 I Tlic Pulkowa constant of aliorration 20".44.">1 should however be employed instead of 20" i">."i. 
 t Peters' JVumerus Cunsluns A'ututionis, p. 71 Tables du Soleil, p. 21. 
 
 1 
 
INTRODUCTION. 
 
 The values of the planetary masses, adopted, are 
 
 Mercury = i^;.---,), Mars ;'" = {.)()()()()()' 
 
 Venus m' = Jupiter t lv = inr.ri ' 
 
 'iUOl'Vl \7JU 
 
 The Earth and Moon w" = .j;,.,^/,,, , Saturn 
 
 Tlic mass of Mercury is that of ENCKE,* the mass of the Earth and Moon is that found hy Prof. S. NEWCOMB,! 
 and which corresponds to the value 8". 848 of the mean horizontal parallax of the Sun ; the values of the other 
 masses arc those adopted by HANSEN and OLUFSEN. On these values of the disturbing masses depend the expres- 
 sions of the secular and periodic perturbations used, with the single exception, that, since the discussion of the 
 observations inc!>c.it< d 32". 515 as ihe value of the annual tropical motion of the node, this value has been preferred 
 to the value 32 // .2!).il. given by theory. If \ve suppose that the modification of the values of the masses, necessary 
 <> |>i"j.liiot: the li'-:-i number, should be applied to Venus alone, the mass of this planet would be reduced to 
 
 1 
 421240 ' 
 
 Thus the following are the expressions of the varying elements, the longitudes being referred to the mean 
 equinox and eeliplie of date, and / reckoned from 1850, Jan. 0.0, Washington Mean Time: 
 
 L' = 241 18 18.32 + 2 10669 L62 180 t + o!'o001134 t 2 , 
 -' = 129 27 42.86 + 50.0494 t - 0.000592 t\ 
 
 &' = 75 19 53.10 + 32.5150 t + 0.000151 t*, 
 
 i> = 3 23 35.01 + 0.03814 t 0.0000016 /, 2 , 
 
 e' = 0.006843113 0.00000050009 / + 0.0000000000128 < 2 , 
 = 1411".494 - 0".10315 t + 0".00000265 t?. 
 
 The value of the semi-axis major of the planet's orbit is given by the equation 
 
 a , = rlj2L. *"l // 
 
 LI + m" n'-J 
 
 To be consisient, \ve must employ the same linear unit for the radius vector of Venus as that which HANSEN 
 and OUTFSKN have used for the radius vector of the Earth. From an examination of their formula-, it appears 
 that they have taken as unity, not n", but, in the notation of LAPLACE, the quantity 
 
 I denoting summation with respect to all the masses which produce sensible perturbations in the motion of the 
 Earth. Hence their value of a" is 
 
 , v , /2 d A^ 
 
 | -* 1 "-*I5 ' 
 
 And, the numerical values being substituted, we obtain 
 
 log a" = 9.9999998786. 
 The tropical motion of the Sun, in a Julian year, is, according to the Tables du Soldi, equal to 
 
 360 22".56009 0".380853 X 0.01677 + 50".23414. 
 If from this is subtracted 50".25351, our value of the precession, the value of ", we adopt, is obtained, 
 
 n" = 1295977".41415. 
 And consequently, 
 
 log a' = 9.8593376699. 
 
 * .l.tlriiiiiiniisr/ii- .Viirliririttrn, J\"o. 443. 
 
 t Astronomical and XMiarologtcal Observations made at the United States Naval Observatory during the year 1865 Appendix 
 
 u., p. ao. 
 
 2 
 
I INTRODUCTION. 
 
 Tin; expression of the equation of the ccntn-, for llir epoch 1S5P.O, is 
 
 + 2822".971 sin .V + 12".071 sin 2 M + 0".072 sin :; M. 
 
 Tin- expression of the logarithm of the elliptic radius vc-rlor for llie same time is 
 
 9.8593127 is - 0.00-2971871 cos ji/ - o.ooooi5253 cos -2 M - 0.000000099 cos 3 ,u. 
 
 The elliptic heliocentric latitude referred to tin; ecliptic of date may be found from the formula 
 
 log sin 1,-it. = 8.7722149 + 13.51 / + log sin [orh. Ion-. + (360' - Q')]. 
 The secular perturbation of the orbit longitude is given In the formula, 
 
 ( - 0". 12691 sin ,17 - 0".0()1()S sin -I M) in. 
 IU ilciiotini; the number of anomalistic revolutions of llic planet from the epoch. 
 
 The secular perturbation of the logarithm of the radius vector is -riven by the formula, (in units of llic eighth 
 
 decimal), 
 
 ( 0.016 + 13.360 cos M + 0.137 ens > .\f ) in. 
 
 The following are the expressions lor the periodic perturbations of Venus; /. /' iVc. denoting (he mean longi- 
 tudes of the several planets in their order, referred to the mean equinox of 1850.0. They have been obtained bv 
 multiplying the expressions given in Li: YKKKIKK'S, ' Aiuiuli '* ilc /' (ilwn-uluii-c l/ii/in-in/ i/r i'tirix" Tonic VI, 
 by the pmper faciors. 
 
 Perturbation* n/' // (>/-/:ii \.<ni>:\imli-. 
 
 ACTION or MI.KCURY. 
 
 + 0.011 sin (/ - /') 
 0.010 sin -2 (I - /') 
 - 0.005 sin :i (/ - /') 
 4- 0.0:21 sin (2 I I 1 + 281) 
 
 4- 0.328 sin (/ 2 /' + 251.8) 
 4- 0.015 sin (2 / - 3 /' 4- 7 I ) 
 4- 0.047 sin (3 /' - / + 35) 
 4- 0.139 sin (-Z I 4 /' 4- .'WH".3) 
 4- 0.453 sin (2 / 5 /' 4- 35. 1). 
 
 ACTION OF THE EAISTII. 
 
 4.!)81 sin (/' - /") 
 
 - 11,189 sin -Z (/' - /") 
 
 4- 7.-260 sin (3 /' - 3 /" 4- 7'.6) 
 
 4- 1.050 sin (4 /' - 4 /" 4- D 10') 
 
 4- 0.3:!5 sin (5 /' - 5 /" 4- 1.5) 
 
 4- 0.143 sin 6 (/' - /") 
 
 4- 0.0(57 sin 7 (/' - /") 
 
 4- 0.035 sin 8 (/' /") 
 
 4- 0.0 19 sin <)(/'-/") 
 
 + 0.013 sin 10 (/' /") 
 
 4- 0.007 sin 11 (/' - /") 
 
 + 0.004 sin 12 (/' - /") 
 
 4- 0.003 sin 13 (/' - /") 
 
 4- 0.059 sin (4 /' - 3 /" 4- 227.7) 
 
 4- 0.099 sin (3 /' 2 /" 4- 53V2) 
 
 4- 0.019 sin (-2 /' /" 4- 51) 
 
 4- 0.070 sin (/" 4- 109.2) 
 
 4- 0.093 sin (-2 /" - /' 4- 18.2) 
 
 4- 3.515 sin (-2 /' - 3 /" 4- 208 7'.f>) 
 
 4- 0.687 sin (3 /' - 4 /" + 268. 1) 
 4- 1.620 sin (4 /' 5 /" 4- '268 24'.5) 
 4- 0.210 sin (5 /' 6 /" 4- 89.5) 
 4- 0.055 sin (6 /' 7 /" 4- 89) 
 4- 0.0-24 sin (7 /' 8 /" 4- 88) 
 4- 0.013 sin (8 /' 9 /" 4- 90) 
 4- 0.0-2-2 sin (-2 /" 4- 210) 
 4- 0.044 sin (3 /' /' 4- 53) 
 4- 1.495 sin (5 /" - 3 /' 4- 198 21') 
 4- 0.188 sin (4 /' fi /" 4- 340.7) 
 4- 0.096 sin (5 /' - 7 /" 4- 337.. r >) 
 4- 0.155 sin (6 /' 8 /" 4- 163.l) 
 4- 0.015 sin (7 f - 9 /" 4- 160) 
 4- 0.013 sin (5 /" 2 /' + 77) 
 4- 0.218 sin (5 /' - 8 /" 4- 66.5) 
 4- 0.013 sin (7 /' 10 /" 4- 67) 
 4- 0.067 sin (9 /' 13 /" + 346".2) 
 + 2.820 sin (8 /' 13 /" 4- 227 ' 5S') 
 4- 0.026 sin (13 /" - 7 /' 4- 198). 
 
INTRODUCTION. 
 
 ACTION OF MAI:S. 
 
 0.0 IS sin (/' I 1 " 
 
 + 0.0.-)!) sin 2 (/' /"') 
 
 4- 0.019 sin (/' 2 I 1 " + 155) 
 
 + 0.657 sin (2 /' - 3 /"' 4- 332 
 
 sin (/' - /'-' + 31') 
 + 0.8SO sin 2 (/' - / iv ) 
 + 0.0-11 sin 3 (/' / iv ) 
 + 0.007 sin 4 (/' - / iv ) 
 4- 0.0-26 sin (2/' - /' v 4- 113) 
 + 1.557 sin (/ iv + 169 50 7 ) 
 
 0.178 sin (/' - / v ) 
 .f- 0.050 sin '2 (/'- /"] 
 
 4- 0.009 sin 
 + 1.168 sin 
 4- 0.019 sin 
 4- 0.021 sin 
 + 0.08-2 sin 
 
 (3 // _ 4 P" + 333) 
 (// _ 3 /"' 4- 1 17 56') 
 (2 /' _ 4 /"' + 1^6) 
 (3 /' - 6 /'" + 281) 
 (o // _ fi //// + 740.8). 
 
 ACTION OF Jui'lTER. 
 
 + 0.477 sin 
 + 0.167 sin 
 + 0.019 sin 
 4- 0.094 sin 
 + 0.055 sin 
 + 0.046 sin 
 + 0.027 sin 
 
 ACTION OF SATURN. 
 
 + 0.205 sin 
 4- 0.025 sin 
 + 0.010 sin 
 
 (/' _ 2 / iv + 155.6) 
 (2/' - 3/ iv + 12. 1) 
 (3 // _ 4 / + 12) 
 (// 4. /iv 4. o.3) 
 (2 / iv + 143) 
 (// _ 3 /* 4- 164) 
 (2 /' - 4 /iv 4. 2-\). 
 
 (/ v + 190) 
 
 (2 /' - 3 r + 90). 
 
 of I In: aeronil onlrr, depending on the product of t lie musses of Ike Earth and Mars. 
 + 0".282 sin (4 /'" 4. 3 /' - 7 /" + 147. 1). 
 
 ]'i-rturbation.i of tin' Common Logarithm of the Radius Vector, in units of the eighth decimal. 
 
 ACTION OF MERCURY. 
 
 + 4.3 
 
 4- 8. 1 cos (/ /') 
 
 4- 1.1 cos 2 (/- /') 
 
 4- 6.1 cos (2/- /' + 285) 
 
 4- 4.3 cos (/' + 105) 
 
 4- 15.3 cos (2 / 4 /' 4- 150.7) 
 + 22.2 cos (/ 2 /' 4- 75. 1) 
 + 1.9 cos (2 / - 3 /' 4- 75) 
 + 3.5 cos (3 /' - / 4- -207) 
 4- 7.5 cos (2 / - 5 /' + 226). 
 
 ACTION OF THE EARTH. 
 
 - 18.6 
 
 4- 228.2 cos (/' /") 
 4; 998.6 cos 2 (/' /") 
 
 - si 1.8 cos (3 /' - 3/" + 8') 
 
 145.2 cos 1 (/' - /") 
 
 - 52.2 cos (5 /' - 5 /" 4- 20') 
 
 23.0 cos 6 (/' /") 
 
 11.5 cos 7 (/' /") 
 - 6.4 cos 8 (/' /") 
 
 3.5 <-os 9 (/' - /") 
 
 2.6 cos 10 (/' - /") 
 
 4- 7.2 cos (4 /' - 3 /" + 45) 
 + 11.7 cos (3 /' 2 /" + 230.5) 
 + 6.6 cos (2 /' /" + 230) 
 + 3.1 cos (/' 4- 105) 
 
 + 4.7 cos (/" 4- 286) 
 4- 3.2 cos (2 /" /' 4- 114) 
 
 4- 76.8 cos (2 /' - 3 /" 4- 89.8) 
 
 4- 46.1 cos (3 /' - 4 /" + 88.9) 
 
 4- 162.2 cos (4 /' - 5 /" + 88 52') 
 
 4- 25.6 cos (5 /' - 6 I" + 268.7) 
 4- 7.7 cos (6 /' 7 /" 4- 268) 
 4- 4.2 cos (7 /' - 8 I" 4. ^70) 
 4- 3.7 cos (2 /" + 30) 
 + 4.5 cos (3 /" /' 4- 249) 
 
 + 17.2 cos (5 /" 3 /' 4- 21.8) 
 + 7.2 cos ( 1 /' _ 6 /" + 159) 
 + 7.1 cos (5 /' 7 /" 4- 172) 
 
 4- 17.2 cos (6 /' - 8 /" + 338.2) 
 4- 6.9 cos (9 /' 13 /" + 158) 
 + 2.4 cos (13 /" 7 /' 4. 25). 
 
INTRODUCTION. 
 
 + 3.5 cos (/' /'") 
 7.9 cos 2 /' I" 1 ) 
 
 19.-2 
 
 4- 299.2 cos (/' I* 4- 'JO') 
 - I33.it cos -.' (/' / iv ) 
 7.0 coa 3 (/' f lv ) 
 + 1.1 cos (:>/* / iv 4-237) 
 
 4- is.7 coa (/' /' ) 
 4.3 cos 2 (/' / v ) 
 
 [OH oi- MA IIS. 
 
 4- (is.i coa (*>!' 3 i'" + i.vr.ii). 
 
 ACTION OF JUI-ITKR. 
 
 -f- N.8 cos (/ iv 4- 352) 
 
 + 10. 9 cos (/' 2 /"' 4- 335.0) 
 
 4- -2 l.s coa (-2 /' 3 / lv 4- 192". l) 
 
 4- !).(! cos (/'-)- /"' 4- 1N2 ) 
 
 _(_ i.i ,,, s (/' 3/ lv + 3 
 
 ACTION oi- SATIIKN. 
 
 of /In- Latitude. 
 ACTION OF THE EARTH. 
 
 + O.Ol'-i sin (',' /' \i I" + 175) 
 + O.OK! sin (3 /' 3 /" + 356) 
 -f 0.013 sin (4 /' 3 /" + - 
 4- 0.0-2G sin (3 /' -^ /" 4- -. 
 4- 0.07S sin (-J /' /" 4- '285) 
 4- 0.1-J1 sin (/' + 104.5) 
 4- 0.09-2 sin ( -2 /" /' 4- 10 I .5 
 
 4- 0.075 sin (-2 /' 3 i" 4- 75.r,) 
 4- 0.081 sin (3 V 4 /" 4- 75.5) 
 4- 0.308 sin (4 f 5 I" 4- 75.3) 
 4- 0.050 sin (5 /' 6 /" 4- 2r ( (; ') 
 4- 0.014 sin (6 /' 7 I" -\- -2-58 ) 
 4- 0.020 sin (3 /" /' 4- '20) 
 4- 0-28 sin (6 /' 8 /" 4- 343) 
 4- .015 sin (9 V 13 I" 4- 143 11 ). 
 
 ACTION OF JUPITER. 
 
 4- 0.0-20 sin V I" 4- 153) 
 4- 0.159 sin (/' '2 / lv 4- Cl.8) 
 
 4- 0.023 sin (V 4- I 4- 284) 
 4- 0.018 sin (/' 3 / iv + 74). 
 
 ACTION OF SATURN. 
 4- 0".017 sin (V 2 / v 4- 28). 
 The tropical motion of Venus in diflbrc-nt intervals of time, for the epoch 1850.0, is, 
 
 in one mean solar day 
 in 3(i5 " " days 
 in 366 " " days 
 in 100 Julian years 
 
 1 36 7.807315, 
 224 47 29.669971, 
 2'26 23 37.477286, 
 199 12 42.180000, 
 
 in 100 Julian years less one day 197 36 34.372685. 
 
 Denoting by d the number of days elapsed from the epoch (1850, Jan. 0.0, Washington mean time), the 
 values of/, /', <Scc., are 
 
 / = 32 1OG5G + 4?0923387467 d. 
 
 I' = 211.3050 4- 1.6021304695 ,1. 
 
 1" = 100.0159 4- 0.985609 1-2-2M d, 
 
 I'" = 83.2669 + 0.52 1032N5 15 d. 
 
 / iv = 159.9594 4- 0.083091276-2 ,1. 
 
 / v = 14.8203 4- 0.0331596753 d. 
 5 
 
INTRODUCTION. 
 
 The Arguments employed in these tables have severally the following meanings: 
 
 The Argument m is an integer, which denotes the number of times Venus has passed through its perihelion 
 since the beginning of 1850; it is negative before ibis epoeh. and remains constant during an anomalistic revolu- 
 tion of tho planet. 
 
 Argument I is the number of menu solar days since M = 0. 
 
 II is the number of Julian years since 8 I' 13 /" -(- 318 47' = 0. 
 " III is the number of mean solar days since j" - .'! V" = 0. 
 " IV is the number of mean solar days since 5 /" 3 /' -f- 288 27' = 0. 
 '' V is the number of mean solar days since 2 I' 3 /" = 0. 
 " VI is the number of mean solar days since I' /" = 0. 
 " VII is the number of mean solar days since 4 /' 5 /" -j- 1 50' = 0. 
 " VIII is the number of mean solar days since 2 V 3 I'" + 65 32' = 0. 
 " IX is tiic number of mean solar days since V 7 IV = 0. 
 
 X is the value of?, when last /' = 129 27 14".5,* in parts of 60 to a circumference. 
 " XI is the value of/", when last V = 129 27' M".5, in parts of 210 to a circumference. 
 " XII is the value of/"' when last /' = 129 27' 1 l".f>. in parts .if GO to a circumference. 
 ' XIII is the value of / iv , when last /' == 129 27' 14".5, in parts of 60 to a circumference. 
 " XIV is the value of ? v , when last /' = 129 27' 14".5, in parts of 36 to a circumference. 
 
 ' . XV is Arg. XI -{- Arg. XIII -j- 0.22 -|- day of the year, of Hanscn and Olufsen. 
 " XVI is Arg. I -j- 22052 -f- 0.01791 -f- day of the year, of Hanscn and Olufseii. 
 
 Arguments X XIV remain constant during a period of Argument I, and are augmented, in each case, by a 
 certain fixed quantity, when Venus passes through its perihelion and m is increased by a unit. 
 
 From the data previously given, are readily obtained the following expressions for the value of the different 
 ari;iiinents; i denoting an integer, in general so taken that the Argument may be less than its period: 
 
 I = 71' 1 .G81535 + d -j- 0''.0000001224 t 2 22 I' 1 . 700777864 ul ,t 
 
 II = 167 V .9 + / 238-V.92 i, 
 
 III = 11H01'.26 + d 11987'V25?, 
 
 IV = ir/T'Ua? -f d 2959 a .209 i. 
 V = 762 d .072 + d 1454 d .9358 i, 
 
 VI = 234 d .0375 -\- d 583 rt .92137 i, 
 
 VII = 80 d .466 -j- rf 243 d . 16487 i, 
 
 VIII = 186 d .467 + d 220 d .56628 i, 
 
 IX = 55 d .526 -f- d 236 d .99191 i, 
 
 X= 5.1 167 + 33.25863 MI 60 ,, 
 
 XI = 19.5741 + 147.64477 m 240 i 
 
 XII = 7.6168 + 19.62509 m 60 i, 
 
 XIII = 25.6671 + 3.11178 m 60 i, 
 
 XIV = 1.2122 + 0.75181 m 36 i, 
 XV = 4037 d .4 -f d 6798 d .262 i, 
 
 XVI = l d .64 + d 365' 1 .24219 i. 
 
 The values of the obliquity of the ecliptic and of the nutation, employed ill thoso Tables, arc those given in 
 the Tables du So/ciV, 
 
 e = 23 27' 31".42 0".46784 t 0".000001405 * 2 , 
 
 J <; = 17".332 sin Q ( + 0".208 sin 2 Q -- 1''.254 sin 2 Q, 
 J i -f- 9".271 cos S ^ 0".089 cos 2 Q ^ + 0".551 cos 2 Q, 
 Q, being the longitude of the Moon's ascending node, and Q the Sun's true longitude. 
 
 Tliis is tlic value of tliu longitude of the perihelion ut the epoch 1850.0, which was employed in computing llie tables of 
 the perturbations to double entry. 
 
 t Rigorously, the Argument which should be employed as the horizontal Argument of tlie tables of perturbations to double 
 entry, lias this expression, 
 
 7 I'UMMI +tl 224'1.7<>080I100 m, 
 But Argument I may safely be used in Its stead, as thr emir, iu llic interval from 850 A. I), to 2850 A. D. cannot exceed 0".()05' 
 
 6 
 
INTRODUCTION. 
 
 The reetaiiL'ular coordinates of a planet, referred to the equinox and equator, are most readily computed by 
 means of the formula* 
 
 X = /.\ /' sin (/. 4~ h\) 4~ /' " i''i 
 
 y = A\ /' sin (/. 4" ^"y 1 + 1>. 
 
 z = k, r sin (/. 4- A',.) 4- p f n ,1, 
 
 uhere /. is ihe orbit longitude, and <" ,i the perturbation of the latitude, expressed in parts of the radius 
 
 The quantities A\, A",, iVc.. are obtained from the following formula): 
 Find /i, //, if. <! from the equations 
 
 /i sin // = sin- sin ;! 8; " S ' M ^ = s '" * cos 8' 
 
 A cos // -= sin / sin 8? g cos G = 1 2 sin 1 ' cos'-'8i 
 
 & 
 
 then 
 
 A- x sin A' x = 1 '2 siir ' sin 2 8^ *y s ' n ^y = '* sin ( H + ')i 
 
 /.\ cos A' x = /( sin H, A-y cos AT V = g cos (G 4~ ^), 
 
 k, sin A",, = h cos (H 4- J )i 
 
 A- z cos Kt = g- sin (G 4~ ') 
 
 The values of /\, f\ and /( z arc, A' denoting the longitude reduced to the ecliptic, 
 
 ^> x = r sin ,5 cos /.', 
 
 ]> y = r sin ft cos s sin // r cos /9 sin e, 
 
 ;; = / sin 'J sin ; sin /.' 4~ r cos ft cos e. 
 
 These formula; avail for obtaining .1-, (/, and : relV'rred to any equinox and equator, provided that the longitudes 
 /!, 8 al ' ( ' I'l'ferred to the same equinox, and the proper values are assigned to the inclinations i and e. 
 
 Rut when the values of /t x , JT X , &c., have been computed for mean equinox of date, the effect of nutation on 
 these quantities will be most easily computed by the aid of these differential coefficients, 
 
 d. log A-j _ ft 
 
 = _ . cos (Kj _ K ^ y = , sn (r _ 
 
 Ky fty 
 
 COB *- *X 
 
 ,., - 
 
 ^ = _ 2 sin 2 .j sin ( JT S + 2 Q ), 
 
 48*. 
 
 cos . gin 
 
 ^j?y = 1 fa sin 2 1 cose cos (K s 4-2 a) 4- sin t sin e cos (A r v 4- 8)1, 
 d Q k,f L 2 J 
 
 * gin (^ _|_ 2 Q ) _ sin f cos s in ( AT Z 4- 
 
 8 A ' z L 
 
 ^ z = - f'2sin z y sine cos (A' z 4-2 8) sin i cos cos (K z 
 rf 8 k z L 
 
 where 3f denotes the modulus of common logarithms. In computing the variations of log i x , log k y , and log A- z , 
 J ; and J ft or J < must be expressed in parts of the radius. 
 
 In computing the aberration, the constant of Struve should be used. The aberration time is then given by 
 the formula, J being the distance of the planet from the Earth. 
 
 log. aberration time in days - 7.76052 4~ 'g- J- 
 
 7 
 
INTRODUCTION. 
 
 The parallax is given hy the formula 
 
 and the semi-diameter by the formula 
 
 8".848, 
 
 parallax = 
 
 . ,. 8". 516. 
 
 semi-diameter = 
 
 A 
 
 In the: computation of the perturbations produced by Venus on other planetary bodies, the values of the incli- 
 nation of the orbit and the longitude of the ascending node referred to the ecliptic and equinox of some fixed date 
 are needed; also the reduction of the longitude to this ecliptic and equinox is wanted. If the current time be 
 1850 -f- /, and the fixed date 1850 -f- *, and c'' denote the general precession from 1850 to 1850 -)- <, and /. denote 
 the nrbit longitude, and <!' denote the general precession from 1850 to 1850 -(- <, the formulae, we are in quest 
 of. are 
 
 i = i 0".06634 (t /), 
 a o = (c-< c\,) + 7".8616 (/ t a ), 
 
 ;. = ;. (v- c'< ) 0".oi382 (t /,,). 
 
 Or, with sufficient accuracy for our purpose, 
 
 i = 3 23' 35" + 0".03814 t 0".02820 (/ * ), 
 = 75 19' 53" -4- 32".515 t a 9". 882 (t /), 
 ;. = ;. 50".273 (t O- 
 
 In the American Ephcnieris the heliocentric coordinates of the planets are given, for the purpose of the com- 
 putation of special perturbations, referred to the ecliptic and equinox of the 2400000 th day of the Julian period, 
 and of every 5000 th day thereafter. If d denote the number of days between the epoch and the current time, (it 
 will be negative when the current time is before the epoch,) the formulae for the computation of these coordinates, 
 for Venus, are ; 
 
 Epoch = 2400000 th day of the Julian Period = 1858, Nov. 16. 
 
 ;, o = ;. 0". 13763d, 
 
 x = [9.99929] r sin (/> -4- 89 58' 32"), 
 
 y o = [9.99995] r sin (/>. -f 1' 29") 
 
 z o = [8.7722] r sin (;. + 284 35' 18" + 0".027 d). 
 
 Epoch = 2405000 th day of the Julian Period == 1872, July 25. 
 
 /! o = /. 0". 13764 d, 
 
 ic o = [9.99929] r sin (;. + 89 58' 32"), 
 
 y a = [9.99995] r sin (A -f 1' 28"), 
 
 z = [8.7722] r sin (/>. -f- 284 27' 53" + 0".027 d). 
 
 Epoch = 2410000 th day of the Julian Period = 1886, Apr. 3. 
 
 ;. o =/ 0". 13765 d, 
 
 x = [9.99928] r sin (i + 89 58' 33"), 
 
 ?/ = [9.99995] r sin (/> + 1' 27") 
 
 2o = [8.7723] r sin (;. + 284 20' 28" -f 0".027 d). 
 
 Epoch = 2415000 th day of the Julian Period = 1899, Dec. 11. 
 
 ;. o = ;. 0". 13766 d, 
 
 x = [9.99928] r sin (/> o + 89 58' 34"), 
 
 y = [9.99995] r sin (A + 1' 26") 
 
 z = [8.7723] r sin (* + 284 13' 3" + 0".027 d). 
 
 Epoch = 2420000 th day of the Julian Period = 1913, Aug. 20. 
 
 / o = /I 0". 13766 d, 
 x = [9.99928] r sin (x o -f 89 58' 34"), 
 y a = [9.99995] r sin (/ -f 1' 24"), 
 s = [8.7723] r sin (/, -4- 284 5' 37" -f- 0".027 d). 
 
 8 
 
INTRODUCTION. 
 
 In the above expressions nf the rectangular coordinates, (lie logarithms of the constant factors, inclosed in [I, 
 li:i\e been given, instead of tlie constants themseU es ; and the pertnrl>::tioiis of tin- latitude liave lieen neglected. 
 
 Table I. contains the longitudes of tlie principal Observatories from Washington, as given by Dr. GOULD in 
 the American Epheineris for 1.S70. West longiludes arc' considered as positive. 
 
 Tables II., III., and IV. are tables of Astronomical Date's in mean solar days, from which any date, given in 
 the usual form of reference to the Christian era. may be reduced to its value in days and decimals of a day of the 
 Julian period. They are taken from lYna i.'s Lunar Tables. l}\ adding the days given for the current century 
 to the days of the previous centennial date, we obtain the number of days elapsed ot the Julian Period for Jun. 0"' 
 Mean Noon in common years and for Jan. I' 1 in bissextile years. To this should be added the days and decimals 
 of a day for fractional parts of a year given in Tables 111. and IV. 
 
 Table V. contains ihe periods of the various argu nts, and multiplies of them, which it is sometimes neces- 
 sary to subtract, to render the arguments less than their periods. 
 
 Table VI. contains for Washington Mean Noon of Jan. O' 1 in common years, Jan. I' 1 in bissextile years, of 
 each year from 1750 to 1950, the following quantities : 
 
 L = -211 IS' 1N".:W O n 17' HV'.OO 4- 2106691".6218 / 
 
 + 0".0001l:il /- 4- 0".282 sin (1 /" 4- 3 /' 7 /" 4- 147.l), 
 
 the hteger i!>. the Arguments I. XIV., the logarithm of the sine of the inclination, and the supplement to 360 
 of the mean longitude of the ascending node. The term 47' 40".00 in L is equivalent to the sum of all the 
 constants which have been added to the quantities in the tables of the equation of the centre, and of the periodic 
 perturbations of the orbit longitude, in order to render them always positive. 
 
 Table VII. contains for every day of the year, the motion of the mean longitude, and the motion of the sup- 
 plement of the node, and the fraction of the year from the beginning of the year. 
 
 Table VIII. contains the motion of L for hours, minutes and seconds; also for tenths, hundrcdths and thous- 
 undihs of a dav. 
 
 Table IX. contains the factor of a small correction to be applied to L, on account of the inequality of its 
 motion. The quantity taken from this table must be multiplied by the fraction of the year obtained from the 
 preceding table, and the product added to L. 
 
 Table X. contains the lunation of the Centre for every tenth of a day of Argument I. Its secular variation, 
 corresponding to the fractional part of the anomalistic period, is included in the numbers of the table. The con- 
 stant added, to render all the numbers positive, is 47' 3".50. 
 
 Tables XI. XXV. contain the perturbations of the Orbit Longitude. They are given in units of hundredths of 
 a second -of arc. 
 
 And particularly, Table XI. contains the factor of the secular perturbation for each day of Argument I. The 
 quantity taken from this table must be multiplied by the integer ill. The logarithm of the factor is also given, as 
 some may prefer making the multiplication by the aid of logarithms. 
 
 Table XII. contains the factor of that part of the secular perturbation which varies as the square of the time. 
 It is given at intervals of 4 days of the Argument I. The quantity taken from this uible, must be multiplied by 
 ( i* 1 */ 'l' ne lg ar ithm of the factor is also given. The formula for the numbers of this table is 
 
 4- 2.01 sin M. 
 
 Table XIII. contains the long period term, due to the action of the Earth, 
 
 4- 2".820 sin (8 P 13 I" -f 227 58'). 
 
 It is given at intervals of 2 years of the Argument II. The constant added to render all the numbers positive is 2".82. 
 Table XIV. contains the terms 
 
 + 1".168 sin (/ 3 /'" 4- 117 56') 
 + 0".082 sin (2 V 6 V" + 74.8) 
 
 due to the action of Mars. They are given at intervals of 200 days of the Argument III. The constant added is 1". 15. 
 Table XV. contains the term 
 
 4- 1".495 sin (5 I" 3 f 4- 198 24'), 
 
 due to the action of the Earth. It is given at intervals of 40 days of the Argument IV. The constant added is 1".50 
 2 V '> 
 
INTRODUCTION. 
 
 Fable XVI. contains the terms 
 
 4- 3".515 sin (2 /' 3 1" + 268 7'. 5) 
 4- 0".188 sin (4 /' 6 /" + 340.7), 
 
 due to the action of the Earth. They are given at intervals of 16 days in the Argument V. The constant added is 
 3".GO. 
 
 Table XVII. contains the terms 
 
 4.984 sin (I' /") 
 - 11.489 sin (2/' 2 /") 
 4- 7.260 sin (3 I' 3 I" + 7'.6) 
 + 1.050 sin (4 /' 4 /" 4- 0.10') 
 -|- 0.335 sin (5 /' 5 /" + 1.5) 
 4- 0.143 sin (61' G I") 
 
 ilur in the: action of the Earth. 
 is 16".G. r ). 
 
 Table XVIII contains the term 
 
 + a067 sin ( 7 /' 7 I") 
 4- 0.035 sin (8 /' 8 /") 
 4- 0.019 sin (9 V 9 /") 
 4- 0.013 sin ( 10 V 10 I") 
 -\- 0.007 sin (11 /' 11 I") 
 4- 0.004 sin (12 V 12 /") 
 4- 0.003 sin (13d' 13/"), 
 
 They arc given at intervals of 2 days in the Argument VI. 
 
 The constant added 
 
 4- 1".620 sin (4 I' 5 I" + 268 24'.5), 
 
 due to the action of the Earth. It is given at intervals of 4 days in the Argument VII. The constant added is 1".62. 
 Table XIX. contains the term 
 
 4- 0".657 sin (2 /' 3 I'" + 332 44'), 
 due: to the action of Mars. It is given at intervals of 4 days in the Argument VIII. The constant added is 0".6fi. 
 
 Table XX. contains the terms 
 
 2".959 sin (/' / iv 4- 31') 4- 0".041 sin (3 /' 3 Z iT ) 
 
 4- 0".880 sin (2 V 2 I") 4- 0".007 sin (4 /' 4 I"), 
 
 due to the action of Jupiter. They are given at intervals of 2 days in the Argument IX. The constant added is 3". 35. 
 
 Table XXI. contains the perturbations due to the action of Mercury. The formula has already been given at 
 page 3. The tabulation is to double entry, the horizontal argument being L, and the vertical argument X., which 
 remains constant during a period of Argument I. When Argument I. surpasses the limit of the table, 224 (1 .7 should 
 be subtracted from it, and 33.26 should be added to Argument X.; and if this last surpasses 60, 60 may be subtracted 
 from it. The constant added to the numbers, to render them positive, is 0".85. 
 
 Table XXII. contains the residual perturbations due to the action of the Earth. The analytical expression is 
 that given on page 3 with the omission of the terms which have been tabulated in Tables XIIL, XV., XVI., XVII., 
 and XVIII. The tabulation is to double entry, the horizontal argument being L, and the vertical argument XL, 
 which remains constant during a period of Argument I. When 224 d .7 is subtracted from Argument L, 147. (il 
 should be added to Argument XL; and if this last exceeds 240, 240 may be subtracted from it. The constant 
 added to the numbers of this table is 1".40. 
 
 Table XXIII. contains the residual perturbations due to the action of Mars. The analytical expression is that 
 given at page 4, with the omission of the terms which have been tabulated in Tables XIV. and XIX. The tabula- 
 tion is to double entry, the horizontal argument being L, and the vertical argument XII., which remains constant 
 during a period of Argument L When 224 d .7 is subtracted from Argument L, 19.6 must be added to Argument 
 XII.; and if this last exceeds 60, 60 may be subtracted from it. The constant added to the numbers of this table is 
 
 Table XXIV. contains the residual perturbations due to the action of Jupiter. The analytical expression is 
 tint given at page 4, with the omission of the terms which have been tabulated in Table XX. The tabulation is 
 to double entry, the horizontal argument being L, and the vertical argument XIIL, which remains constant during a 
 period of Argument I. When 224 d .7 is subtracted from Argument L, 3.11 must be added to Argument XIIL; and 
 if this last exceeds 60, 60 may be subtracted from it. The constant added to the numbers of this table is 2".35. 
 
 Table XXV. contains the perturbations due to the action of Saturn. The analytical expression is given on 
 page 4. The tabulation is to double entry, the horizontal argument being L, and the vertical argument XIV., which 
 
 
 10 
 
I NTIIODUCTION. 
 
 remains constant during a period of Argument I. When 22 I' 1 . 7 is subtracted (V<ini Argument I.. O.S inn I In- added 
 10 \ i L'ument XIV.. and if this last exceeds ;{(i, :j(i may lie subtracted from it. The constant added Id I 
 of this talile is 0". 10. 
 
 The preeedinic tallies give the t )rhit Longitude of Venus referred to the mean eijuiimx of dale. 
 
 TaMe \\ \ I. eonlains the eoiiiinon logarithm of the Elliptic lladius Vector, for every lentil of a da\ of Argu- 
 nent I. Its secnlar variation, corresponding In the- fractional |iarl of the anomalistic period is included. The 
 formula tabulated is 
 
 !).,S5!)31275 - 0.0000257 - 0.00297187 cos M 
 - 0.00001525 cos -2 M 0.00000010 cos 3 M 
 
 1 ' 7 (<l'i!iitity from Tab. XXVII). 
 
 The term 0.0000'J.">7 is equivalent to the sum of all the constants, which have been added in the tables of the peri- 
 odic perturbations, in order to render the numbers al\va\s positive. 
 
 Tahles XXVII. X\XV. contain the perturbations of log. r; they are given uniformly in units of the eighth 
 decimal ; and specially : 
 
 Table XXVII. contains (lie factor of the secular perturbations for each day of Argument I. The quaniity 
 taken from this table must be multiplied by the integer 111. The logarithm of the factor is also given. 
 
 Table XXVIII contains the factor of that part of the secular perturbation which varies as the square of the 
 time. It is given for intervals of 1 days in the Argument I. The quantity taken from this table must be multi- 
 
 by ( 
 
 The formula for the numbers of this table is 2.1 cos M. 
 
 Table XXIX. contains the terms 
 
 - 1N.6 23.0 cos (6 I' G I") 
 + 22S.2 eat (/' - /") - 11.5 cos (7 /' - 7 /") 
 + 998.6 cos (2 /' - 2 /") 6.4 cos (8 /' 8 /") 
 _ H 11.8 cos (li /' 3 /" + 8') 3.5 cos (9 /' - 9 /") 
 
 - 145.2 cos ( 1 /' - 4 /") 2.6 cos (10 /' - 10 /"), 
 
 - 52.2 cos (5 I' - 5 /" + 20') 
 
 due to the action of the Earth. The constant added is 1594. 
 
 Table XXX. contains the term 
 
 + 162.2 cos {4 f 5 /" + 88 52'), 
 due to the action of the Earth. The constant added is 162. 
 
 Table XXXI. contains the terms 
 
 19.2 133.0 cos (2 f 2 / iv ) 
 
 + 299.2 cos (/' - /* + 20') - 7.0 cos (3 /' - 3 /"), 
 
 due to the action of Jupiter. The constant added is 445. 
 
 Table XXXII. contains the perturbations due to the action of Mercury. The formula has already been given 
 on page 4. The constant added is 34. The tabulation is to double entry, and the remarks which have been 
 made with regard to Table XXI. also apply here. 
 
 Table XXXIII. contains the residual perturbations due to the action of the Earth. The formula is that given 
 at page' 1 with the omission of the terms which have been tabulated in Tables XXIX. and XXX. The constant 
 added is 150. The tabulation is to double entry, and the remarks made with regard to Table XXII. apply here. 
 
 Table XXXIV. contains the perturbations due to the action of Mars. The formula has been given at page 5. 
 The constant added is 80. The tabulation is to double entry, and the remarks made with regard to Table XXIII 
 apply here. 
 
 Table XXXV. contains the residual perturbations due to the action of Jupiter. The formula is that given on 
 page 5, when the terms tabulated in Table XXXI. are omitted. The constant added is 80. The tabulation is to 
 double entry, and the remarks made with regard to Table XXIV. apply here. 
 
 Table XXXVI. contains the perturbations due to the action of Saturn. The formula has been given at pa-e .">. 
 
 11 
 
INTRODUCTION. 
 
 The constant added is 25. The tabulation is to double entry, and the remarks made with regard to Table XXV 
 apply here. 
 
 These tables (XX VI. XXX VI.) sutlicc tor finding the logarithm of the radius vector. 
 
 Tables \X\VII. and XXXVIII. contain the perturbations of the latitude expressed in units of hundredths of a 
 second o!' an-. 
 
 Table XXXVII. contains the perturbations due to the action of the Earth. The formula has been given at 
 page 5. The constant added is 0".62. The tabulation is to double entry, and the remarks made with regard to 
 Table XXII. apply here. 
 
 Table XXXVIII. contains the perturbations due to the action of Jupiter. The formula has been given at page 
 5. The constant added is 0".21. The tabulation is to double entry, and the remarks made with regard to Table 
 XXIV. apply here. 
 
 The latitude of Venus is then obtained in the following way. The elliptic latitude is obtained from the formula 
 
 log sin (elliptic hit.) = log sin i + log sin [orbit long. + (360 ft)], 
 in which the orbit longitude is corrected for perturbations. Then the true latitude is given by the formula 
 
 True Latitude = Elliptic Latitude + the sum of the quantities derived from Tables XXXVII. and XXXVIII. 0"83.* 
 
 Table XXXIX. contains, for the beginning of each year between 1750 1950, the values of the quantities K It 
 K y , K 2 , log /t x , log /.-,., log k.,. and the Arguments XV. and XVI. on which depend respectively the lunar and solar 
 nutation. 
 
 The beginning of the year for Arguments XV. and XVI. must be understood as being the Washington mean 
 noon of Jan. 0, (Jan. 1 in bissextile years,). But the other six quantities of this Table are given for this time of the 
 beginning of the year only for 1850, and backwards and forwards from this epoch they proceed by intervals of a 
 tropical year. This modification has been made, in order that the motion of these quantities for the fractional 
 part of the year might be included in Table XLI. From each of the quantities /(T x , K y , and K%, there has brrn 
 subtracted the constant 20".00, and from log y the constant 0.0000089, and from log k t the constant 0.0000560. 
 These constants are equivalent, in each case, to the sum of the constants which have been added to the quantities 
 in Tables XL. and XLI. to render them positive. Moreover to K^ has been added the small correction, due to 
 lunar nutation, over and above the lunar nutation itself; and to log fc x has been added the small correction due to 
 lunar nutation. 
 
 Table XL. contains the variations of the quantities K^, K y , K z , log fc y , and log k 7l which are produced by lunar 
 nutation. The two last arc expressed in units of the seventh decimal place. These quantities have all been com- 
 puted for the epoch 1850, and are subject to small secular changes, which, except in the case of the correction of 
 K x , arc barely sensible in the course of a century. The variation of A K 2 in a century has therefore been given 
 in the adjacent column. 
 
 The constants which have been added to render the numbers positive, are 18".00 to A K, 18". 00 to A K y , 
 17".00 to A K z , 88 units to J log i y , 430 units to J log k,.. The lunar nutation of the equinox can be obtained 
 from the value of A K% by subtracting 18".00. The formulae for the quantities tabulated arc 
 
 A K K = 18".00 + A </>, 
 A K y = 18".00 + 1.0044 A { + 0.0690 A E, 
 A K, = 17".00 + 0.9498 A <,' + 0.3323 A e, 
 sec. var. of A K,, = + 0.0030 A 3, 
 
 A log k y = 88 + 0.5469 A f - 9.480 A e, 
 J log k t = 430 2.534 A <J> + 45.71 J E, 
 
 when for A $ and J E are substituted those parts of the values of these quantities given on page 6 which depend 
 on 1 ([ . The part of A K^ which has been applied to K^ in Table XXXIX is 
 
 + 0.0015 J v\ 
 
 untl tne value of J log fc x which has been added to i- x in the same Table is 
 
 - 0.0181 J </'. 
 
 "The single term in the perturbations of the latitude, due to the action of Saturn, has not II.HMI tabulated. It seemed super, 
 fluous to take account of it, when the corresponding term in the latitude of the Kartli, producing, at maximum, an effect in the 
 geocentric position of Venus, nearly three times greater, is neglected by llansen and Olufsen in their " Tables du Soldi." 
 
 12 
 
INTRODUCTION. 
 
 Table XL I. contains the variations of the quantities A' . A\ , A"., K, L r /-^ -,111] log /.-. \vhicli arc produced by 
 solar nutation. augmented hy the niolioii oi'tlie quantities in the tVac-tional part of the tropical year. J log /. 
 J loir l; f are expressed in units of the seventh decimal place. The quantities have been computed t'ur the epoch 
 1 >.">(>. The secular variation J A',, becoming sensible ill the course of a eentur\ , is given in the adjacent column. 
 The last column contains the solar nutation of the equinox. The constants which have been added are 2".00 to 
 J A., ^".00 to J A" v , ;}".00to J A',., 1 unit to J log t,, and 130 units to J log /.-,. The formula 1 lor the quantities 
 tabulated are, 
 
 J A' v = 2".00 + 0".05 r + J v \ 
 
 j A', = ->".(>(> 4- 0".12G r + J ,,' 4- 0".03N sin (2 O + 98.2), 
 J K 7 . = 3".00 - l".H(il r 4- J v'> 4- 0". lift sili (2 O + 71.0), 
 sec. var. J A' 2 = + 0".049 -, 
 
 J log /t v = 1 4- 22.145 r 4- 5.3 sin (2 O + 263.5), 
 
 J log /.-, = 130 - 103.110 - 4- 25. 1 sin (> O + N3 3 .8), 
 
 r denoting tlie fraction of the year, and the value of J <,' being 
 
 - 1".254 sin 2 Q. 
 
 The proper values of A' x , A' y &c., needed for computing the values of .r, //, anil z referred to the true equinox 
 and equator of date, are therefore obtained, by adding the quantities obtained from Tables XL. and XLI. to the 
 quantities given in Table XXXIX. for th<;,beiiinin<!! of the i/car. And there is no need of interpolation in this 
 laM Table, except for log. A\, which however is nearly constant. 
 
 Table XLI 1. contains the values of the factors by which the perturbation of the latitude, obtairrcd from Tables 
 XXXVI.I. and XXXVIII. by subtracting 0".83, and expressed in hundredths of a second of arc, must be multi- 
 plied, in order to obtain the corresponding corrections of the coordinates a;, y, and z expressed in units of the seventh 
 decimal place. The Argument is the Orbit Longitude. 
 
 Table XLI 1 1. contains the 1'arallax and Seinidiameter. The Argument is the logarithm of the planet's 
 distance from the Earth. The formula? have already been given at page 8. The value of the semidiameter here 
 given lias still need to be increased by a constant quantity for the effect of irradiation, but varying for different 
 observers and instruments, when the reduction ot observations is in question. 
 
 Tables XLIY. and XLV. give Ihe means of obtaining the mean longitude and arguments for a time not con- 
 tained between the limits 1750 1950. 
 
 Table XLIV. contains the quantities which must be added to the quantities of the 19 th century contained in 
 Tables VI. and XXXIX., to obtain the mean longitude and arguments for the beginning of the corresponding 
 year of any other century between 300 B. C. and 2300 A. D. The numbers in the columns headed I' 50, must 
 lie multiplied by (f 50), t' denoting the number of years from the beginning of the century, and the products 
 added to the numbers of the preceding column. In the case of log sin i, the numbers of the column headed 
 I' 50 must be understood as being in units of the last decimal place of log sin i. In using this Table for dates 
 which are B. C. the given year must be conceived as increased algebraically by a unit. It will be noticed that 
 two lines occur for the argument 1500: the first is for dates which are according to the Julian calendar (Old 
 Style), and the second Tor those which are according to the Gregorian calendar (New Style). The Julian calendar 
 ends with Oct. 4, 1582 ; and the Gregorian begins with Oct. 15, 1582. 
 
 Table XLV. contains the values of the inequality of the longitude to long period, 
 
 4- 0".282 sin (4 V" 7 I" + 3 V 4- 147. 1), 
 
 and of certain multiples of the period of the argument in years. As this inequality has been added to the numbers 
 of the column headed L in Table VI., we must enter the Table first with the argument equal to the corresponding 
 year of the 19"' century and take the equation with the opposite sign ; and next with the argument equal to the year 
 of the given date, and take the corresponding equation: then both these quantities must be added to the L resulting 
 from the previous Tables. If the year of the given date is not found in the limits of this Table, that multiple of 
 the period of the argument, which is requisite, must be added to it or subtracted from it. 
 
 Table XLVI. contains the Reduction of the Orbit Longitude to the ecliptic. The Argument is the "Orbit 
 Longitude 4- 360 ft", or this angle diminished by 180 when it exceeds 180. It is given for every 10' of the 
 
 13 
 
INTRODUCTION. 
 
 Argument. The arrangement of the Table will be easily understood. The Table is constructed for the epoch 
 lsr,0.(), and the variation in a century, of the numbers tabulated, is given in the last column but one, for every 
 ee. The 1'imnilii for the reduction to the ecliptic is 
 
 ISO".!) It sin 2 (I + 360 ft) + 0".079 sin 4 (A + 360 &), 
 
 and for its secular variation 
 
 - 0".113 sin -2 (/- + 360 - a). 
 
 DIRECTIONS FOR THE USE OF THE TABLES. 
 
 The given time must be reduced to Washington Mean Time by the aid of Table I. The hours, minutes and 
 see, ,11,1s can then lie reduced to the equivalent decimal part of a day by Table IV.; and the whole number of clays 
 which have elapsed since the beginning of the year can be found from Table III. 
 
 The values of the mean longitude L, m and the fourteen arguments of the perturbations are taken from Table 
 VI. for the given year, if it lies between 1750 and 1949. If we do not want the heliocentric longitude and latitude 
 of the planet, but intend to compute the geocentric coordinates by the Gaussian process, the quantities, in the 
 columns of this Table, headed Log. sin i and 360 & , will not be needed. 
 
 From Table VII. will be obtained the motion of L from the beginning of the year to the given day; and also 
 the fraction gf^he year; from Table IX. the factor which must be multiplied by the fraction of the year and the 
 product added to L ; and from Table VIII. the motion of L for hours, minutes and seconds, or for decimal parts of 
 a day. The quantities obtained from Tables VII. IX. being added to the L from Table VI., we obtain the tabular 
 mean longitude of the planet for the given date. 
 
 To Arguments I. IX., II. excepted, we add the number of days and decimal part of a day which have 
 elapsed since the beginning of the year ; to Argument II. we add the fractional part of the year. If any argument 
 thus obtained, exceed its period given in Table V., we subtract as many multiples of the period as may be neces- 
 sary to reduce il below its period. To the Argument in, we add as many units, as we have subtracted multiples 
 of its period from Argument I., and to Arguments X. XIV. we add severally the same number of multiples 
 of the numbers 33.26, 147.64, 19.6, 3.11, and 0.8. The values of these multiples are given in Table V. If any 
 Argument X. XIV. exceed its period given in Table V., we may subtract from it the largest contained multiple 
 of its period. 
 
 The Equation of the Centre is obtained from Table X. with the Argument I. The perturbations of the longi- 
 tude in hundrcdlhs of a second of arc will be obtained with the proper arguments from Tables XI. XXV- 
 The number obtained from Table XI. must be multiplied by the integer m, and the number from Table XII. by 
 
 . -2 
 
 the factor | m ) ;'the logarithms of the numbers in these two tables have also been given in the adjacent column, 
 
 in order that, if preferred, the multiplication may be performed by their aid. The Equation of the Centre and 
 these perturbations being added to the mean longitude, we obtain the orbit longitude referred to the mean equinox 
 of date. 
 
 The Logarithm of the Elliptic Radius Vector is obtained from Table XXVI. with the Argument I ; and its 
 perturbations, in units of the eighth decimal, with the proper arguments from Tables XXVII. XXXVI. The 
 number obtained from Table XXVII. must be multiplied by the integer us, and the number from Table XXVIII. 
 
 by the factor ( .VJY ! tnc logarithm of the number is also given in Table XXVII., in order that, if preferred, the 
 
 multiplication may be performed by its aid. If the sum of the numbers thus obtained from Tables XXV1I.-XXXVI. 
 be divided by 10, and the quotient be added to the last figures of the quantity obtained from Table XXVI., we shall 
 have the common logarithm of the radius vector of the planet. 
 
 If we diminish by 83 the sum of the numbers, obtained from Tables XXXVII. and XXXVIII. with the proper 
 arguments, we shall have, in hundredths of a second of arc, the perturbations of the latitude. 
 
 The values of 7i x , K s , &c., and Arguments XV. and XVI. arc to be taken from Table XXXIX. for the 
 given year. And to Arguments XV. and XVI. should be added the number of days and the decimal part of a day 
 elapsed since the beginning of the year ; and if Argument XV. exceed its period, given in Table V., the period 
 
 14 
 
1 NTRODUGTION. 
 
 should !>< subtracted from it. The corrections of' A . /v" . &c., arc obtained from Tables X I,, and XLI., with the 
 respective Arguments XV. and XVI. In the ease of K, in carl. Table, the variation in 100 years, given in the 
 adjacent column, must be taken into account; we multiply it by the fractional part of the eentur\ elapsed since 
 L850, and add the product to the quantity obtained from the preceding column. T nations being added 
 
 to the- values of A".. A"., &C., obtained iritlwut iiitff illation from Table XXXIX., we have the proper values of 
 these' quantities for computing the rectangular coordinates of the planet referred to the true equinox and equator 
 of date. 
 
 It' r denote the radius vector, and / the orbit longitude of the planet, these coordinates are obtained by the 
 
 formula' 
 
 x = i'x r sin (). + K^), 
 
 y = k,. r sin (/. -f- A" y ), 
 
 ; = /,', / sill (/ + K, ). 
 
 The values of the coordinates thus found need correction for the effect of perturbations in latitude. To 
 obtain these corrections we multiply the perturbations of the latitude, expressed in hundredlhs of a second of arc, 
 respectively by the three factors obtained from Table XI, 11. with the argument /., and the products are the respec- 
 tive corrections of the coordinates expressed in units of the seventh decimal. 
 
 If A", V'and Z denote the coordinates of the Sun referred to the same system of planes as j , i/ and z, the- 
 atric right ascension a, declination , and distance from the Earth J, of the planet, are obtained from the 
 equations, 
 
 J cos a. cos <5 = x + -Y, 
 A sin a. cos ft = y + Y, 
 
 J sin = 2 + Z. 
 
 The '/ and <t thus obtained have still to be corrected for aberration, if we desire' the apparent position of the 
 planet. The aberration time T in days is given by the equation 
 
 log T = 7.7(J052 + log J ; or, T = .005761 J. 
 
 If ' ami ' denote the daily variation of a and o at the given date, the corrections for aberration are 
 
 /I I d t 
 
 . rpd a 
 
 J,_-T_, 
 
 Finally, from Table XLIII., we can obtain, with the argument log J, the parallax and scmidiameter of the 
 planet. 
 
 If we desire to have the heliocentric longitude and latitude, we take from Table VI. the values of log. sin i 
 and :J60 Q for the given year. The motion of 360 Q, for the fraction of the year is given in Table VII.; 
 that of log sin i can readily be inferred from Table VI. Then if the latitude be computed from the equation, 
 
 log sin lat. = log sin i + log sin (A + 360 $) 
 
 and the perturbations of the latitude, which have already been obtained, be added to it, we shall have the helio- 
 centric latitude required. The ecliptic heliocentric longitude, referred to the mean equinox of date, will be got by 
 adding to /. the reduction to the ecliptic, from Table XLVI. As the value of the reduction, given in the body of the 
 Table, is for the epoch 1850, we must apply to it the variation in 100 years multiplied by the fraction of a century 
 elapsed since 1850. The heliocentric longitude referred to the true equinox of date will be found by adding the 
 nutation of the equinoxes in longitude. The lunar nutation will be obtained by subtracting 18" from J A\ in 
 Table XL.; the solar nutation is given in the last column of Table XLI. 
 x, y, and z may then be obtained by the formulae 
 
 x = r cos / cos V 
 
 y = r cos / sin // cos e' r sin / sin e' 
 
 ~ = r cos / sin /' sin 3' + ; sin / cos c' 
 
 in which /' and / are the heliocentric longitude anil latitude, and e' = -f J , the apparent obliquity of the ecliptic. 
 
 15 
 
INTRODUCTION. 
 
 If the given year is not between the limits 17501949, we take from Tables VI. and XXXIX, the values 
 of L, m, the Arguments 1. XVI., log sin i and 360 - , for the corresponding year of the 19 th century, 
 (remembering to add algebraically a unit to the year if the given date is before the Christian era.) 
 
 We add to these the quantities obtained from Table XLIV., with the given century as the Argument. More- 
 over we add to L, I, log sin i and 360 Q respectively the quantities given in the adjacent columns, headed 
 I' 50, multiplied by this factor, (I' denoting the number of years of the given century,) noticing that in the case 
 of log sin i, the quantities in the column headed I' 50 are in units of the last decimal of this quantity. It will be 
 observed that the argument 1500 occurs twice in Table XLIV.; the first line is to be employed for dates in old 
 style, the second for dates in new style. 
 
 After this, we proceed precisely as before, except that Table VIII. not being available, we employ in its stead 
 Table XLV., which we enter twice, first with the corresponding year of the 19 th century as the argument, and 
 subtracting from L the equation obtained; next with the given year, as the argument, or this augmented or dimin- 
 ished by the requisite number of multiples of the period, which will be found at the bottom of the Table ; and 
 adding to L the equation thus obtained. 
 
 In this case, we must necessarily deduce the heliocentric longitude and latitude of the planet, since the tables 
 for finding 7f x , A',., &c., arc restricted to the years 1750 1949. The method of computing by rectangular coor- 
 dinates is only to be preferred when we have the coordinates of the sun ready at hand. 
 
 In computing an ephemeris we shall avoid the horizontal interpolation in the tables to double entry, if, instead 
 of computing the perturbations, for the Washington Mean Noon of some particular day, and for equal intervals 
 thereafter, we compute the value of the perturbations, for the times, when Arg. I. is an exact multiple of 8 days, 
 and then the interpolation, with reference to Arg. I., can be performed on the sums. It will be found that the 
 interval of 8 days is not too long for the secure interpolation of intermediate values. However, if m should be 
 quite large, that is, if the given time is quite distant from 1850, the terms of the perturbations, which involve this 
 factor, may be computed separately, for the times, for which, the ephemeris is wanted. In all cases, the interpola- 
 tion of the sums of the perturbations, to the times of the ephemeris, will be easier, if these sums are first interpolated 
 into the middle, that is, for every 4 days. In the computation of an isolated position even, this method of obtaining 
 the perturbations, first for the times when Arg. I. is a multiple of 8 days, can bo followed with advantage, at least 
 as far as regards the tables to double entry. 
 
 The following examples will sufficiently illustrate the foregoing precepts: 
 
 1. Required an ephemeris of the heliocentric position of Venus, for Washington Mean Noon, at intervals of 2 
 days, and covering the time of the Transit on Dec. 8 th , 1874. 
 
 We will commence the calculation of the perturbations at 310 d .3195 from the beginning of the year = Nov. 
 6 a .3195, when the value of Argument I. is 160 d . 
 
 Preparation of the Arguments. 
 
 Table VI., 1874, 
 Day of Year, 
 Table V., Periods, 
 
 Arguments for Date, 
 
 No. of days to end of period 
 
 Table V., Periods, 
 
 Ill 
 
 I. 
 
 II. 
 
 HI. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 IX. 
 
 39 
 
 74.3513 
 
 19L9 
 
 8583 
 
 d 
 
 346 
 
 d 
 
 798.5 
 
 24L22 
 
 d 
 92.5 
 
 129.8 
 
 d 
 
 52.83 
 
 
 310.3495 
 
 0.8 
 
 310 
 
 310 
 
 310.3 
 
 310.35 
 
 310.3 
 
 310.3 
 
 310.35 
 
 1 
 
 -224.7008 
 
 
 
 
 
 
 -243.2 
 
 -220.6 
 
 -236.99 
 
 40 
 
 160.0000 
 
 192.7 
 
 8893 
 
 656 
 
 1108.8 
 
 551.57 
 
 159-.6 
 
 219.5 
 
 126.19 
 
 eric 
 
 id 
 
 
 
 
 
 40.00 
 
 
 8.0 
 
 
 
 
 
 
 
 
 -583.92 
 
 
 220.6 
 
 
 7.65 
 
 6.9 
 
 16 
 
INTRODUCTION. 
 
 X. M XII. XIII 
 
 XIV. 
 
 XV. 
 
 XVI. 
 
 42.20 
 
 17.72 53.0 
 
 27.03 
 
 30.6 
 
 6005.2 
 
 d 
 1.8 
 
 :{:!.v!ti 
 
 147.(il 19.6 
 
 3.11 
 
 0.7 
 
 310.0 
 
 310.0 
 
 -60.00 
 
 -60.0 
 
 
 
 
 
 Table VI.. iv; I, 
 
 Table V., Incr. of in = 1, 
 
 Periods, 
 
 Arguments for Date, 15.46 165.36 12.6 301.4 31.3 
 
 Perturbations of the Lon<fitii<!i', in Iniml ri'iltlis of a srcontl. 
 
 6315.2 311.8 
 
 Arg. I. 
 
 160 
 
 l<i:s 
 
 176 
 
 181 
 
 192 
 
 200 
 
 208 
 
 216 
 
 221 
 
 Table XI .... 
 
 + 491 
 
 + 507 
 
 + 198 
 
 +4(> I 
 
 +406 
 
 + 328 
 
 +282 
 
 + 121 
 
 + 10 
 
 Table. XIII . . . 
 
 188 
 
 187 
 
 187 
 
 187 
 
 187 
 
 187 
 
 187 
 
 187 
 
 186 
 
 Table XIV . . . . 
 
 157 
 
 157 
 
 157 
 
 158 
 
 158 
 
 159 
 
 156 
 
 159 
 
 160 
 
 XV .... 
 
 128 
 
 126 
 
 128 
 
 181 
 
 134 
 
 136 
 
 188 
 
 141 
 
 144 
 
 Table XVI .... 
 
 847 
 
 834 
 
 821 
 
 308 
 
 Jill 
 
 281 
 
 266 
 
 255 
 
 242 
 
 Table XVII . . . 
 
 1793 
 
 1708 
 
 1665 
 
 1656 
 
 1667 
 
 1679 
 
 1672 
 
 1631 
 
 1548 
 
 Table XV11I . . . 
 
 2GO 
 
 231 
 
 200 
 
 167 
 
 134 
 
 101 
 
 72 
 
 46 
 
 25 
 
 Table XIX .... 
 
 
 
 1 
 
 5 
 
 12 
 
 22 
 
 34 
 
 48 
 
 62 
 
 77 
 
 Table XX .... 
 
 431 
 
 519 
 
 591 
 
 642 
 
 668 
 
 670 
 
 650 
 
 612 
 
 563 
 
 Table XXI . . . . 
 
 22 
 
 28 
 
 25 
 
 27 
 
 29 
 
 31 
 
 31 
 
 39 
 
 44 
 
 Table XXI I . . . 
 
 189 
 
 138 
 
 139 
 
 141 
 
 113 
 
 145 
 
 145 
 
 141 
 
 135 
 
 Table XXIII . . . 
 
 34 
 
 23 
 
 22 
 
 20 
 
 18 
 
 16 
 
 18 
 
 12 
 
 10 
 
 Table XX IV . . . 
 
 2:> i 
 
 244 
 
 234 
 
 225 
 
 219 
 
 216 
 
 216 
 
 218 
 
 222 
 
 Table XXV . . . 
 
 36 
 
 33 
 
 82 
 
 82 
 
 :u 
 
 36 
 
 40 
 
 45 
 
 51 
 
 Sums .... 
 
 1205 
 
 4231 
 
 4204 
 
 4170 
 
 4113 
 
 4019 
 
 3875 
 
 3672 
 
 3417 
 
 \>ii. Tlie inequality from Table XII. is insensible at tins epoch, as is also the corresponding one of Log. r in 
 Table -\\VII1 
 
 Perturbations of Log r, in units of the eighth decimal. 
 
 Arg. I. 
 
 160 
 
 168 
 
 176 
 
 184 
 
 192 
 
 200 
 
 208 
 
 216 
 
 224 
 
 Table XXVII . . . 
 
 -133 
 
 -15 
 
 + 104 
 
 +219 
 
 +323 
 
 +411 
 
 +478 
 
 + 522 
 
 + 538 
 
 Table XX IX . . . 
 
 2146 
 
 1989 
 
 1850 
 
 1753 
 
 1716 
 
 1748 
 
 1841 
 
 1978 
 
 2136 
 
 Table XXX . . . 
 
 292 
 
 309 
 
 320 
 
 321 
 
 321 
 
 311 
 
 295 
 
 274 
 
 248 
 
 Table XXXI . . . 
 
 17 
 
 66 
 
 141 
 
 236 
 
 339 
 
 440 
 
 528 
 
 594 
 
 636 
 
 Table XXXII . . . 
 
 50 
 
 46 
 
 36 
 
 24 
 
 13 
 
 9 
 
 9 
 
 12 
 
 11 
 
 Table XXXIII . . 
 
 231 
 
 221 
 
 214 
 
 210 
 
 211 
 
 216 
 
 224 
 
 235 
 
 245 
 
 Table XXXIV . . 
 
 85 
 
 70 
 
 57 
 
 46 
 
 36 
 
 29 
 
 23 
 
 20 
 
 19 
 
 Table XXXV . . . 
 
 140 
 
 184 
 
 125 
 
 112 
 
 99 
 
 85 
 
 73 
 
 65 
 
 60 
 
 Table XXXVI . . 
 
 36 
 
 32 
 
 27 
 
 22 
 
 17 
 
 11 
 
 6 
 
 3 
 
 
 
 Sums .... 
 
 2864 
 
 2852 
 
 2874 
 
 2946 
 
 3075 
 
 3260 
 
 3177 
 
 3703 
 
 3893 
 
 Perturbations of the Latitude, in hundrcdths of a second. 
 
 Arg. I. 
 
 160 
 
 168 
 
 176 
 
 184 
 
 192 
 
 200 
 
 208 
 
 216 
 
 224 
 
 Table XXXVII . 
 Table XXX VI 11 . . 
 Constant 
 
 39 
 34 
 
 83 
 
 43 
 35 
 
 S3 
 
 46 
 36 
 
 83 
 
 53 
 36 
 
 83 
 
 59 
 35 
 
 83 
 
 65 
 34 
 
 83 
 
 71 
 82 
 
 83 
 
 76 
 30 
 
 83 
 
 80 
 
 27 
 
 83 
 
 
 
 
 
 
 
 
 
 
 
 Sums .... 
 
 -10 
 
 5 
 
 - 1 
 
 + 6 
 
 + 11 
 
 + 16 
 
 +20 
 
 +23 
 
 +24 
 
 17 
 
INTRODUCTION. 
 
 Interpolating the perturbations of the longitude and log r to intervals of 4 days, we have, 
 
 Arg. I. 
 
 I'm. of the 
 Long. 
 
 uiir. 
 
 Pert of 
 Log r. 
 
 Diff. 
 
 Arg. 
 
 Pert, of the 
 Long. 
 
 Diff. 
 
 Pert, of 
 
 Log,. 
 
 Diff. 
 
 d 
 
 
 
 
 
 d 
 
 it 
 
 
 
 
 160 
 164 
 
 168 
 172 
 176 
 180 
 184 
 188 
 192 
 
 42.65 
 
 12. 17 
 
 42.31 
 
 42.18 
 42.04 
 41.89 
 
 41.70 
 41.45 
 41.18 
 
 18 
 1C 
 
 13 
 
 14 
 15 
 19 
 95 
 
 :V2 
 
 2864 
 
 2855 
 2852 
 2858 
 2874 
 2903 
 2946 
 3003 
 3075 
 
 9 
 3 
 + G 
 16 
 
 89 
 
 43 
 
 57 
 
 + 72 
 
 192 
 196 
 200 
 204 
 208 
 212 
 216 
 220 
 221 
 
 41.13 
 40.72 
 40.19 
 39.51 
 38.75 
 37.80 
 36.72 
 35.50 
 34.17 
 
 41 
 53 
 05 
 79 
 95 
 108 
 139 
 133 
 
 3075 
 3162 
 3260 
 3365 
 3477 
 3592 
 3703 
 3804 
 3893 
 
 + 87 
 98 
 105 
 112 
 115 
 111 
 101 
 + 89 
 
 The Orbit Loin'Jludc and Log. r. Washington Mean Noon. 
 
 Date. 
 
 
 
 Sloan Longitude 
 
 Eqtia. of the 
 
 Pert, of 
 
 
 Log. Elliptic r 
 
 Pert, of 
 
 
 
 
 Arg. I. 
 
 from Tablrs 
 
 Centre from 
 
 the Long. 
 
 Orbit Long. 
 
 from Table 
 
 Log. r. 
 
 Log. /. 
 
 1-71. 
 
 
 
 VI.-VIII. 
 
 Table X. 
 
 
 
 XXVI. 
 
 
 
 Dec. 3 
 
 d 
 
 337 
 
 186'.6505 
 
 1 II 
 
 68 3 8.37 
 
 5 45J20 
 
 it 
 
 41.54 
 
 a i a 
 
 68 9 35.11 
 
 9.8578827 
 
 298 
 
 9.8579125 
 
 5 
 
 339 
 
 188.6505 
 
 71 15 23.98 
 
 7 5.00 
 
 41.40 
 
 71 23 10.38 
 
 9.8577382 
 
 301 
 
 9.85776H3 
 
 7 
 
 341 
 
 190.6505 
 
 74 27 39.59 
 
 8 32.38 
 
 41.24 
 
 74 36 53.21 
 
 9.8575986 
 
 305 
 
 9.8576291 
 
 9 
 
 313 
 
 192.6505 
 
 77 39 55.21 
 
 10 7.11 
 
 41.07 
 
 77 50 43.39 
 
 9.8574644 
 
 309 
 
 9.8574953 
 
 11 
 
 345 
 
 194.6505 
 
 80 52 10.82 
 
 11 48.87 
 
 40.87 
 
 81 4 40.56 
 
 9.8573358 
 
 313 
 
 9.8573671 
 
 13 
 
 347 
 
 196.6505 
 
 84 4 26.44 
 
 13 37.36 
 
 40.64 
 
 84 18 44.44 
 
 9.8572135 
 
 318 
 
 9.8572 153 
 
 Inequalities of 7t x , K y , fyc. 
 
 
 4E*. 
 
 AK,. 
 
 4Jk 
 
 A log k r 
 
 I):iv of 
 
 
 
 
 
 Year. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Table 
 
 Table 
 
 Sum. 
 
 Table 
 
 Table 
 
 Sum. 
 
 Table 
 
 Table 
 
 Sum. 
 
 Table 
 
 Table 
 
 Sum. 
 
 
 XL. 
 
 XLI. 
 
 
 XL. 
 
 XLI. 
 
 
 XL. 
 
 XLI. 
 
 
 XL. 
 
 XLI. 
 
 
 d 
 
 310 
 
 KX68 
 
 it 
 0.78 
 
 // 
 
 11.46 
 
 // 
 
 11.23 
 
 if 
 0.83 
 
 12!o6 
 
 // 
 
 12.81 
 
 a 
 0.24 
 
 13!05 
 
 5 
 
 19 
 
 24 
 
 320 
 
 10.82 
 
 0.85 
 
 11.67 
 
 11.37 
 
 0.90 
 
 12.27 
 
 12.96 
 
 0.19 
 
 13.15 
 
 5 
 
 21 
 
 26 
 
 330 
 
 10.96 
 
 1.07 
 
 12.03 
 
 11.52 
 
 1.11 
 
 12.63 
 
 13.11 
 
 0.28 
 
 13.39 
 
 5 
 
 23 
 
 28 
 
 310 
 
 11.11 
 
 1.39 
 
 12.50 
 
 11.66 
 
 1.42 
 
 13.08 
 
 13.26 
 
 0.49 
 
 13.75 
 
 4 
 
 25 
 
 29 
 
 350 
 
 11.25 
 
 1.80 
 
 13.05 
 
 11.81 
 
 1.83 
 
 18.64 
 
 13.10 
 
 0.80 
 
 14.20 
 
 4 
 
 27 
 
 31 
 
 360 
 
 11.40 
 
 2.26 
 
 13.66 
 
 11.95 
 
 2.30 
 
 14.25 
 
 13.55 
 
 1.19 
 
 14.74 
 
 4 
 
 28 
 
 32 
 
 370 
 
 11.54 
 
 2.68 
 
 14.22 
 
 12.10 
 
 2.72 
 
 14.82 
 
 13.70 
 
 1.57 
 
 15.27 
 
 3 
 
 28 
 
 31 
 
 
 J log Ar z . 
 
 
 
 
 
 
 
 Day of 
 Year 
 
 
 ^x- 
 
 E r 
 
 K* 
 
 Log x . 
 
 Log k y . 
 
 Log i- z . 
 
 
 
 
 
 Table 
 
 Table 
 
 Sum. 
 
 
 
 
 
 
 
 
 XL. 
 
 XLI. 
 
 
 
 
 
 
 
 
 <1 
 310 
 
 828 
 
 46 
 
 874 
 
 89 58 23.90 
 
 o / // 
 
 1 27 22.22 
 
 352 44' 25.01 
 
 9.9992854 
 
 9.9598380 
 
 9.6179435 
 
 320 
 
 829 
 
 34 
 
 863 
 
 24.11 
 
 22.43 
 
 25.11 
 
 4 
 
 82 
 
 424 
 
 3.'5() 
 
 830 
 
 23 
 
 853 
 
 24.47 
 
 22.79 
 
 25.35 
 
 4 
 
 84 
 
 414 
 
 310 
 
 831 
 
 14 
 
 845 
 
 24.94 
 
 23.24 
 
 25.71 
 
 4 
 
 85 
 
 406 
 
 350 
 
 833 
 
 7 
 
 840 
 
 25.49 
 
 23.80 
 
 26.16 
 
 4 
 
 87 
 
 401 
 
 360 
 
 834 
 
 3 
 
 837 
 
 26.10 
 
 24.41 
 
 26.70 
 
 4 
 
 88 
 
 398 
 
 370 
 
 835 
 
 2 
 
 837 
 
 26.66 
 
 24.98 
 
 27.23 
 
 4 
 
 87 
 
 398 
 
 18 
 
INTRODUCTION. 
 
 <\>mjilii:'iiin !' /lie Ri-r/fiiiHiilnr Co'i'irili 
 
 
 
 
 
 
 
 Dai.-, 1-71 
 
 /. + K, 
 
 a + / v . 
 
 t. -f /> 
 
 
 (- A, i. 
 
 f- A A 
 
 
 Q 1 It 
 
 o / // 
 
 / // 
 
 
 
 
 IN-.-. : 
 
 \:^ 7 5!uio 
 
 n:> 3ii :.s.-2<> 
 
 60 51 0.70 
 
 9.5708516 
 
 :>.!>:u7:>n 
 
 !).55!)3398 
 
 5 
 
 K;I -21 3.V27 
 
 72 50 33..V, 
 
 ni 7 : ;.(>:> 
 
 9.5039252 
 
 9.9400684 
 
 9.5720679 
 
 r- 
 
 K;I :i:> 1N.-20 
 
 71; I 16.50 
 
 (17 -^i is.'ii; 
 
 !). |-j:!7(ill 
 
 9.9468769 
 
 9.5880998 
 
 9 
 
 1(>7 1!) S. l!l 
 
 7!) IN (5.79 
 
 70 :5."> il.'J-.' 
 
 y.:w:{. r )(is l 
 
 9.9522237 
 
 9.59-25170 
 
 ll 
 
 171 3 r>.7(i 
 
 :i'2 1.07 
 
 73 W (i. IN 
 
 9.1911412 
 
 9,9561415 
 
 9.6003850 
 
 13 
 
 171 17 9.75 
 
 s.-i Hi M.Oli 
 
 77 3 10.15 
 
 8.9973798 
 
 9.958(5533 
 
 !).(i()(i7. r .li:) 
 
 Dal.-, 1-71 
 
 log I. 
 
 log y. 
 
 log :. 
 
 X. 
 
 y- 
 
 i 
 
 Dec. 3 
 
 9.4282640 
 
 9.7896669 
 
 9.4173623 
 
 + 0.26S0798 
 
 + 0.6161-2-23 
 
 + 0.'2613i;si) 
 
 5 
 
 9.36 16935 
 
 9.7978367 
 
 9.4998362 
 
 0.2-299818 
 
 0.6-27N-2-23 
 
 0.-2(i!)05-20 
 
 7 
 
 9.-2H 1390-2 
 
 9.8045060 
 
 9,1 107-^89 
 
 0.1911570 
 
 0.6375879 
 
 0.2758855 
 
 9 
 
 9.1810(537 
 
 !).K097190 
 
 9.4500123 
 
 0.1517273 
 
 0.645-2366 
 
 0.2818463 
 
 11 
 
 9.0 185083 
 
 9.8185086 
 
 9.4577521 
 
 0.1118171 
 
 0.6508!) 15 
 
 0.-2N(i!)l 1-2 
 
 IS 
 
 8.851(5-251 
 
 9.8188986 
 
 !),!<) 100 18 
 
 +0.07155-25 
 
 +0.6511833 
 
 + 0.-29107-2!> 
 
 TABLE XI.ll. 
 
 I):iti:,l874. 
 
 Factors (or 
 
 Pert, of the 
 
 Lat. 
 
 A * 
 
 Ay- 
 
 AZ. 
 
 A i- 
 
 A y. 
 
 A z- 
 
 llr,-. 3 
 
 13 
 
 +0.001 
 0.000 
 
 -0.147 
 -0.141 
 
 + 0.323 
 + 0.3-21 
 
 + 7 
 + 14 
 
 
 
 
 j 
 -2 
 
 +2 
 + 4 
 
 Dal.-, 1-71 
 
 X. 
 
 jr. 
 
 s. 
 
 Date, 1874. 
 
 a;. 
 
 y- 
 
 z. 
 
 l>rr. 3 
 
 5 
 
 7 
 
 +0.2680798 
 0.2299818 
 +0.1911570 
 
 + 0.6161222 
 ().(i-27s-2-2-2 
 +0.6375377 
 
 +0.2613682 
 0.2690523 
 
 +0.2758858 
 
 Dec. 9 
 11 
 13 
 
 +0.1517273 
 0.1118171 
 +0.07155-25 
 
 + 0.6452364 
 0.6508913 
 +0.6544831 
 
 + 0.2818167 
 0.28(59146 
 + 0.2910733 
 
 "2. Required the heliocentric longitude and latitude and the logarithm of the radius vector of Venus for 1769, 
 June 3' 1 10 1 ' 10 Paris mean time. 
 
 This is equivalent to June 3 d 4 b 52 m 26 8 .98 Washington mean time = 154 d .20309 from the beginning of 
 
 the year. 
 
 Preparation of the Arguments. 
 
 
 m 
 
 I. 
 
 11. 
 
 111. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII 
 
 VIII. 
 
 IX 
 
 Table VI., 1769 . 
 
 1 ):i\ .if Yoiir 
 Table V., Periods . 
 
 Arguments for date 
 
 -132 
 1 
 
 148.1850 
 154.2031 
 -224.7008 
 
 86.9 
 0.4 
 
 6195 
 154 
 
 a 
 465 
 151 
 
 276,8 
 
 154.2 
 
 430.08 
 
 154.20 
 583.92 
 
 162.6 
 151.2 
 -243.2 
 
 d 
 
 158.4 
 154.2 
 -220.6 
 
 95.51 
 151. -20 
 236.99 
 
 -131 
 
 77.6873 
 
 87.3 
 
 6349 
 
 619 
 
 431.0 
 
 0.31 
 
 73.6 
 
 92.0 
 
 12.72 
 
 
 X. 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 log sin i. 
 
 3600 - a . 
 
 XV. 
 
 XVI. 
 
 Tables VI., XXXIX, 
 1769 . ... 
 
 54.98 
 33.26 
 -60.00 
 
 210.46 
 147.64 
 
 -240.00 
 
 57.1 
 19.6 
 -60.0 
 
 34.91 
 3.11 
 
 10.0 
 0.8 
 
 8.7721047 
 5 
 
 285 23 59^5 
 -13.7 
 
 1646.5 
 
 154.2 
 
 ,1 
 2.3 
 154.2 
 
 Tables V., VII. . . 
 
 Args., &c., for date . 
 
 28.24 
 
 118.10 
 
 16.7 
 
 38.02 
 
 10.N 
 
 8.7721052 
 
 285 23 45.8 
 
 1800.7 
 
 156.5 
 
 19 
 
INTRODUCTION. 
 
 Mean Longitude. 
 
 L. 
 
 Table VI., 1769 
 Table VII., June 3 
 Table IX. 4 1 ' 
 
 tt tt 52m 
 
 " " 26 S .98 
 
 VIII., 1769, (-0" 
 
 Table 
 
 Mean Longitude, 
 
 4 57 7.69 
 246 44 2.33 
 16 1.301 
 3 28.282 
 1.801 
 .015 X 0.4) = -0.006 
 
 252 41.40 
 
 Longitude. 
 
 Logarithm Radius Vector. 
 
 Mean Longitude 
 
 252 6 4L40 
 
 Log. Elliptic r, Table XXVI., 
 
 9.8610042 
 
 Equation of tbe Centre 
 
 1 25 39.70 
 
 Table XXVII., - 7.66 X (- 131) 
 
 + 1003 
 
 Table XI., - 10.363 X (- 131) 
 
 -f 13.57 
 
 Table XXV1IL, + 1.2 X (-.1.31) 2 
 
 + 2 
 
 Table XII., + 1.66 X (- 1.31) 2 
 
 + 0.03 
 
 Table XXIX., 
 
 1716 
 
 Table XIII., 
 
 4.66 
 
 Table XXX., 
 
 6 
 
 Table XIV., 
 
 0.32 
 
 Table XXXI., 
 
 600 
 
 Table XV., 
 
 1.12 
 
 
 
 Table XVI., 
 
 4.45 
 
 Arg. I. 72 80 
 
 
 Table XVII., 
 
 16.68 
 
 
 
 Table XVIII., 
 
 2.05 
 
 Table XXXII., 48 49 
 
 
 Table XIX., 
 
 1.21 
 
 Table XXXIII., 39 36 
 
 
 Table XX., 
 
 2.93 
 
 Table XXXIV., 40 51 
 
 
 
 
 Table XXXV., 82 77 
 
 
 Arg. L, 72 80 
 
 
 Table XXXVI., 14 10 
 
 
 Table XXI., 82 80 
 
 
 Sums, 223 223 
 
 
 Table XXII., 145 150 
 
 
 Interpolated, 
 
 223 
 
 Table XXIII., 10 8 
 
 
 
 
 Table XXIV., 310 308 
 
 
 Log. r, 
 
 9.8610377 
 
 Table XXV., 15 17 
 
 
 
 
 Sums 562 563 
 
 
 Latitude. 
 
 
 Interpolated, 
 
 5.63 
 
 
 O / // 
 
 
 
 Orbit Longitude, 
 
 253 27 13.75 
 
 
 Orbit Longitude, 
 
 253 27 13.75 
 
 360 - Q, 
 
 285 23 45.8 
 
 Red. to Ecliptic, Table XLVL, 
 
 +7.26 
 
 
 
 Lunar Nutation, Table XL., 
 
 + 17.29 
 
 Arg. of Latitude, 
 
 178 50 59.5 
 
 Solar Nutation, Table XLL, 
 
 - 0.68 
 
 
 
 
 
 Log sin Arg. of Latitude, 
 
 8.3025984 
 
 
 Heliocentric Longitude, 
 
 253 27 37.62 
 
 Log sin i 
 
 8.7721052 
 
 
 
 Log sin Latitude 
 
 7.0747036 
 
 
 
 Elliptic Latitude 
 
 o / // 
 
 + 04 4.98 
 
 
 
 Arg. I. 72 SO 
 
 
 
 
 Table XXXVII., 65 57 
 
 
 
 
 Table XXXVIII., 17 15 
 
 
 
 
 Sums 82 72 
 
 
 
 
 Interpolated 
 
 0.75 
 
 
 
 Constant 
 
 - 0.83 
 
 
 
 Latitude 
 
 + 04 4.90 
 
 
 
 20 
 
 
INTRODUCTION. 
 
 Kncke's reduction of tho observations of the Transit of Venus in 17(!i) gives 253* 27' 13". 17 and +0" 4' 4".5fi 
 as the orbit longitude and latitude.* I'.ut according to the Tnhlrx tin So/ril of Hansen and Olufsen, the longitude 
 and latitude of tin- Sun, adopted b) Kncke, must be eorreeteil, respectively, by + 0".G4 and + 0".01. Thus we 
 ina\ adopt 2.~i3 27' 13".81 and +0 4' 4".52 as the values given by observation, ;uid the residuals, ( )hs. Cal., 
 are respectively + 0".06 and 0".38. 
 
 If Enekc's reduction of the Transit of 1761 is compared with the Tables, in the same way, the residuals will 
 DC found to be 0".33 and + 0".40. 
 
 3. Required the heliocentric position of Venus for 1639, Dec. I' 1 3 h ll m 55" Paris mean time. 
 This time is equivalent to Dec. 3 tl 22 h '27'" 21 S .9H Washington mean time = 337' 1 .93567 from the beginning 
 of the year. 
 
 Preparation of the Arguments. 
 
 
 lit 
 
 1. 
 
 u. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 IX. 
 
 Table VI.. 1KJ9 . 
 Table XI, IV, 1600. 
 Terms X (f 50), 
 Dav of Year, 
 Periods, .... 
 
 - 18 
 
 -326 
 + 2 
 
 96.2956 
 
 204.4585 
 +0.0005 
 337.9357 
 -449.4016 
 
 i.-)6:9 
 
 38.9 
 0.9 
 
 7786 
 10863 
 
 338 
 
 -11987 
 
 2358 
 932 
 
 338 
 
 -2959 
 
 1108 d 9 
 1153.7 
 
 337.9 
 -1454.9 
 
 303.49 
 526.09 
 
 337.94 
 -583.92 
 
 196.3 
 144.6 
 
 337.9 
 -486.3 
 
 138.7 
 180.0 
 
 337.9 
 -440.1 
 
 66.39 
 182.50 
 
 337.94 
 -473.98 
 
 Arguments for date, 
 
 -342 
 
 191.2887 
 
 196.7 
 
 7000 
 
 669 
 
 1145.6 
 
 583.60 
 
 192.5 
 
 216.5 
 
 112.85 
 
 
 X 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 log sin i. 
 
 *-Q. 
 
 XV. 
 
 XVI. 
 
 Tab^s VI., X.XXIX. 
 
 1839 ' 
 
 6.46 
 
 1.97 
 
 14.4 
 
 29.66 
 
 237 
 
 87721999 
 
 a 1 II 
 
 284 46 46 
 
 d 
 
 194 
 
 a 
 1 3 
 
 Table XUV., 1600 . 
 
 Terms X (>' - 50), . 
 
 1 Li \ of Year, or Periods 
 Periods 
 
 17.69 
 6.52 
 
 107.80 
 55.29 
 
 22.2 
 
 39.3 
 600 
 
 5.56 
 6.22 
 
 6.9 
 1.5 
 
 -0.0002732 
 -24 
 + 12 
 
 + 1 48 17.0 
 0.6 
 30.1 
 
 1732.9 
 337.9 
 
 +0.4 
 337.9 
 
 
 
 
 
 
 
 
 
 
 
 Arguments for date, . 
 
 30.67 
 
 165.06 
 
 15.9 
 
 41.44 
 
 32.1 
 
 8.7719255 
 
 286 33 50.9 
 
 2090.2 
 
 339.6 
 
 Mean Longitude. 
 
 L. 
 
 O / // 
 
 Table VI., 1839 285 59 48.72 
 
 Table XLIV., 1600, 324 46 55.79 
 
 Term X ('' - 50), + 0.458 
 
 Table VII., Dec. 3, 179 55 51.07 
 
 Table IX., 22 1 ', 1 28 7.157 
 
 " " 27 1 ", 1 48.146 
 
 " " 21 9 .98, 1.466 
 
 Table XLV., 1839.9 with opp. sign, 0.176 
 
 " " 1942.3 = 1639.9 + 302.4, 0.279 
 
 Mean Longitude, 72 12 32.35 
 
 * Der Venns-clurolignng von 17GO, p. 1(17. 
 21 
 
INTRODUCTION. 
 
 Longituilr. 
 
 Mi -:ni Longitude, 
 
 Kipmtion of the Outre, 
 
 Table XI., + lO.JJO!) X (- 3 12), 
 
 Table XII., - 1.61 X (3.12)', 
 
 Table XIII., 
 
 Table XIV., 
 
 Table XV.. 
 
 Table XVI., 
 
 Table XVII., 
 
 Table XVIII., 
 
 Table XIX., 
 
 Table XX., 
 
 Arg. I. 
 
 184 
 
 102 
 
 Table XXI., 
 
 107 
 
 109 
 
 Table XXII., 
 
 140 
 
 142 
 
 Table XXIII, 
 
 25 
 
 25 
 
 Table XXIV., 
 
 428 
 
 436 
 
 Table XXV., 
 
 35 
 
 34 
 
 Sums 
 
 735 
 
 746 
 
 Interpolated 
 
 
 
 Orbit Longitude, 
 Red. to Ecliptic, Table XLVI., 
 Lunar Nutation, Table XL., 
 Solar Nutation, XLI., 
 
 Heliocentric Longitude, 
 
 72 12 32.35 
 
 9 1.83 
 
 -35.26 
 
 -0.19 
 
 1.60 
 
 0.59 
 
 1.27 
 
 2.87 
 
 16.67 
 
 1.30 
 
 0.01 
 
 2.69 
 
 7.45 
 
 72 21 33.18 
 
 +6.79 
 
 + 16.34 
 
 - 0.73 
 
 72 21 55.58 
 
 Logarithm Radius Vector. 
 
 Log. Elliptic r, Tnbl.> XXVI, 
 Table XXVIL, + 7.86 X (- 342), 
 Table XXVIII., 
 Table XXIX., 
 Table XXX., 
 Table XXXI., 
 
 Arg. I. 
 
 184 
 
 192 
 
 Table XXXII., 
 
 24 
 
 28 
 
 Table XXXIII., 
 
 210 
 
 212 
 
 Table XXXIV., 
 
 108 
 
 96 
 
 Table XXXV., 
 
 35 
 
 52 
 
 Table XXXVI., 
 
 26 
 
 20 
 
 Sums 403 
 
 Interpolated 
 
 Log. r, 
 
 408 
 
 Latitude. 
 
 Orbit Longitude, 
 360- Q, 
 
 Arg. of Latitude, 
 Log sin Arg. of Lat. 
 Log sin i, 
 
 Log sin Latitude, 
 
 Elliptic Latitude, 
 
 Arg. I. 184 
 
 Table XXXVII., 54 
 
 Table XXXVIII., 
 
 Sums 
 
 Interpolated, 
 Constant 
 
 Latitude, 
 
 9 
 63 
 
 192 
 
 61 
 12 
 
 73 
 
 9.8575552 
 -2697 
 15 
 
 1716 
 
 321 
 
 9 
 
 408 
 
 9.8575527 
 
 72 21 33.18 
 286 33 50.9 
 
 358 55 24.1 
 
 n 8.2739219 
 
 8.7719255 
 
 n 7.0 158 17 I 
 
 o / // 
 
 -0 3 49.23 
 
 0.72 
 -0.83 
 
 -0 3 49.34 
 
 If Enckc's reduction of Horrox's observations of (be Transit at this time be corrected to conform with the 
 position of the Sun as derived from Hanson and Olufscn's Tables, the residuals of the orbit longitude and helio- 
 centric latitude arc found to be respectively + 1 1".4 and 18". 9. 
 
 22 
 
INTRODUCTION. 
 CORRECTION OF THE ELEMENTS OF THE ORBIT OF VENUS. 
 
 Tin' Elements adopted tor comparison with oh.-ervation, arc. in the main, those on which LKVKIUUKR \\;\-~ 
 
 \\i-i Tables. 
 They arc 
 
 Epoch, IViO, Jan. 1.0, Paris Mean Time. 
 
 -' = 129 27 1 1.5 
 
 Q' = 75 19 52.3 
 
 /' = 3 23 31.83 
 
 c' = 0.00(581331 
 
 ' = 21 06(51 1 
 
 The value of ' has iii-cn changed in order to make the adopted tropical motion coincide with LKVKKRIKK'S 
 value. The values ot the disturbing masses, and, in fuel, of all the constants needed in the theory, are, with two 
 exceptions, those i;iven ill the Introduction. But the annual tropical motion of the node at the epoch 1850 
 employed is 32".2!)31 as it results from the adopted values of the planetry masses : and the true longitude of tho 
 Sim is derived from the apparent longitude of I IAX.SKX'S and OLUFSEN'S Tables du Soleil by subtracting the effect 
 of aherration Corresponding to the constant 20".2.">5. 
 
 All the elements, except the mean motion, are ' determined, with nearly all the precision possible by tho 
 modern observations; that is to say, those comprehended in the interval from 1686 up to toe present time. The 
 addition of the observations made previously to 183(5 to the discussion, would scarcely increase this precision. 
 For the mean motion we must employ ancient observations ; anil for this purpose it seems better to depend on the 
 data furnished by the Transits of 17(il and 17(5!), than on the somewhat uncertain observations of Bradley. 
 
 Encke's reduction of these Transits, corrected to conform with the positions of the Sun derived from the 
 Tiililm dn Soli'H, will be adopted. All the longitudes mentioned hero are referred to the mean equinox of date. 
 
 For the Transit of 17(51 Encke gives 
 
 Paris Moan Time = 1761, June 5 d 17 h 30'". 
 
 Q f II 
 
 True Longitude of the Sun = 75 35 49.6, 
 
 Latitude of the Sun + 0.6, 
 
 Orbit Longitude of Venus = 2553534.45, 
 
 Heliocentric Latitude of Venus = 3 45.91, 
 
 Hut the Tnbli-x ilit So/i' it give 75 35' 52".05 and -f 0".53 as the longitude and latitude of the Sun. Consequently 
 the adopted position of Venus is 
 
 o / // 
 Orbit Longitude = 255 35 36.90, 
 
 Heliocentric Latitude = 3 45.84. 
 For the Transit of 1769, Enckc gives 
 
 Paris Mean Time = 17(59, June 3' 1 10 1 ' 10'". 
 
 a I II 
 
 True Longitude of the Sun = 73 27 13.8, 
 
 Latitude of the Sun = 0.0, 
 
 Orbit Longitude of Venus = 2532713.17, 
 
 Heliocentric Latitude of Venus = +4 4.56. 
 
 The Tn/>li'n /In N/a/ give 73 27' 14".25 and -f-0".04 as the longitude and latitude of the Sun. Consequently 
 the adopted position of Venus is 
 
 O I II 
 
 Orbit Longitude of Venus = 253 27 13.62, 
 
 Heliocentric Latitude of Venus = +4 4.52. 
 
 23 
 
INTRODUCTION. 
 
 The meridian observations have been corrected to conform with the constant 8".848 of solar parallax, anil to 
 the following expression for the semi-diameter : 
 
 8^516 Q// - ; 
 
 A 
 
 In other respects Leverricr's reduction has been adopted. With regard to the Greenwich and Paris observations 
 which have accumulated since Levcrricr made his investigation, that is, from 1858 forward, as, on comparing the 
 places, given in the several annual volumes, for the fundamental time-stars, with Dr. GOULD'S Standard Places, 
 SfC., no sensible average difference in the right ascensions could be discovered, no correction for difference of 
 equinoxes has been applied to them. To the Washington observations in declination in the years LS66, 1867, 
 has been applied the correction +0".7f>. (Sec Washington Observations for 1867, Appendix III., pp. 20, 21.) 
 
 In forming the following normals, Paris observations have been combined with Greenwich; but Washington 
 observations have been kept separate. The normals, formed from them, are those given for Washington Mean Noon. 
 The Paris Observations used are not in great number, and belong to the years 1838 and 1856 1866. The com- 
 parisons arc Obs. Cal. 
 
 Normals in the inferior part of the Orbit. 
 
 No. 
 
 Greenwich M. T. 
 
 App. K. A. 
 
 App. Dec. 
 
 No. Obs. 
 
 A 
 
 A, 
 
 
 d 
 
 h in H 
 
 all' 
 
 
 8 
 
 n 
 
 1 
 
 1836, June 9.0 
 
 8 16 6.380 
 
 --21 53 40.12 
 
 4 
 
 + 0.082 
 
 + 0.62 
 
 2 
 
 July 2.0 
 
 8 52 43.140 
 
 -- 16 16 11.35 
 
 5 
 
 0.057 
 
 + 0.63 
 
 3 
 
 July K5.0 
 
 8 43 59.799 
 
 --14 17 35.12 
 
 4 
 
 0.054 
 
 0.32 
 
 4 
 
 Aug. 7.0 
 
 7 47 48.091 
 
 --13 41 44.35 
 
 3 
 
 + 0.228 
 
 0.60 
 
 5 
 
 Aug. 30.0 
 
 7 56 5.580 
 
 -- 15 11 1.98 
 
 4 
 
 + 0.083 
 
 1.71 
 
 6 
 
 1838, Jan. 12.0 
 
 22 36 4.483 
 
 - 8 23 42.65 
 
 ' 
 
 + 0.079 
 
 + 0.48 
 
 7 
 
 Feb. 2.0 
 
 23 19 4.936 
 
 5 1.83 
 
 5 
 
 -0.163 
 
 + 5.07 
 
 8 
 
 Feb. 22.0 
 
 23 11 48.498 
 
 + 3 26 16.93 
 
 3 
 
 + 0.050 
 
 + 2.00 
 
 9 
 
 March 12.0 
 
 22 33 39.400 
 
 1 38.66 
 
 3 
 
 + 0.178 
 
 + 1.75 
 
 10 
 
 March 24.0 
 
 22 23 12.226 
 
 - 3 12 55.39 
 
 10 
 
 + 0.111 
 
 1.18 
 
 11 
 
 April 7.0 
 
 22 37 31.008 
 
 - 4 49 5.56 
 
 13 
 
 + 0.096 
 
 1.02 
 
 12 
 
 1839, Sept. 21.0 
 
 12 58 21.552 
 
 14 51 58.87 
 
 4 
 
 0.147 
 
 0.66 
 
 13 
 
 Oct. 12.0 
 
 12 19 41.626 
 
 9 44 43.41 
 
 9 
 
 + 0.047 
 
 + O.S2 
 
 14 
 
 1841, May 1.0 
 
 3 50 40.864 
 
 + 25 34 44.55 
 
 6 
 
 + 0.009 
 
 + 0.39 
 
 15 
 
 May 27.0 
 
 2 59 23.728 
 
 + 17 13 40.10 
 
 5 
 
 f 0.254 
 
 + 1.95 
 
 16 
 
 June 12.0 
 
 2 59 45.783 
 
 + 14 23 34.07 
 
 4 
 
 -0.021 
 
 0.92 
 
 17 
 
 1842, Dec. 15.0 
 
 17 56 8.706 
 
 22 32 23.92 
 
 5 
 
 -0.140 
 
 + 2.34 
 
 18 
 
 1843, Jan. 10.0 
 
 17 15 35.705 
 
 17 35 57.26 
 
 2 
 
 - 0.042 
 
 + 0.29 
 
 19 
 
 1844, May 31.0 
 
 7 46 25.585 
 
 + 23 55 35.09 
 
 6 
 
 0.047 
 
 + 1.23 
 
 20 
 
 July 30.0 
 
 7 49 49.182 
 
 + 13 59 37.34 
 
 6 
 
 0.046 
 
 0.68 
 
 21 
 
 1846, Jan. 16.0 
 
 22 44 36.217 
 
 6 45 4.41 
 
 3 
 
 0.074 
 
 + 0.13 
 
 22 
 
 Feb. 8.0 
 
 23 14 37.585 
 
 + 1 8 50.95 
 
 4 
 
 0.092 
 
 + 0.20 
 
 23 
 
 March 18.0 
 
 22 15 8.390 
 
 3 5 52.55 
 
 2 
 
 + 0.210 
 
 3.17 
 
 24 
 
 1847, Aug. 15.0 
 
 12 16 12.840 
 
 4 47 4.42 
 
 4 
 
 + 0.052 
 
 + 0.69 
 
 25 
 
 Sept. 23.0 
 
 12 43 32.402 
 
 13 41 51.42 
 
 4 
 
 0.203 
 
 + 0.64 
 
 26 
 
 Nov. 15.0 
 
 12 36 33.246 
 
 3 37 36.16 
 
 5 
 
 + 0.206 
 
 - 0.82 
 
 27 
 
 1849, May 2.0 
 
 3 36 3.678 
 
 + 24 41 22.91 
 
 5 
 
 + 0.187 
 
 + 0.09 
 
 28 
 
 June 8.0 
 
 2 49 10.035 
 
 + 14 4 37.76 
 
 10 
 
 - 0.087 
 
 + 3.60 
 
 29 
 
 1850, Nov. 23.0 
 
 18 8 47.037 
 
 26 55 13.20 
 
 3 
 
 -0.159 
 
 2.65 
 
 30 
 
 Dec. 17.0 
 
 17 33 52.085 
 
 21 38 46.95 
 
 2 
 
 0.033 
 
 0,17 
 
 31 
 
 1851, Jan. 20.0 
 
 17 20 48.740 
 
 17 41 28.31 
 
 4 
 
 + 0.296 
 
 0.76 
 
 32 
 
 1852, July 10.0 
 
 8 24 23.066 
 
 + 15 40 33.60 
 
 9 
 
 + 0.040 
 
 + 0.44 
 
 33 
 
 Aug. 16.0 
 
 7 25 42.850 
 
 + 15 24 38.50 
 
 4 
 
 + 0.182 
 
 0.78 
 
 34 
 
 Sept. 5.0 
 
 8 4 29.218 
 
 + 15 58 35.33 
 
 4 
 
 + 0.126 
 
 1.14 
 
 35 
 
 1854, Jan. 20.0 
 
 22 50 6.361 
 
 5 16 4.06 
 
 6 
 
 + 0.061 
 
 -0.04 
 
 36 
 
 Feb. 3.0 
 
 23 6 4.528 
 
 34 39.68 
 
 3 
 
 + 0.012 
 
 + 1.67 
 
 37 
 
 Feb. 20.0 
 
 22 49 33.074 
 
 + 1 19 46.87 
 
 5 
 
 + 0.221 
 
 + 0,45 
 
 38 
 
 1855, Aug. 18.0 
 
 12 20 36.824 
 
 - 5 57 52.34 
 
 7 
 
 + 0.007 
 
 + 0.32 
 
 39 
 
 Sept. 20.0 
 
 12 35 48.073 
 
 - 12 52 25.49 
 
 5 
 
 -- 0.120 
 
 + 2.32 
 
 40 
 
 Oct. 12.0 
 
 11 55 6.943 
 
 6 28 37.38 
 
 4 
 
 - - 0.076 
 
 1.62 
 
 41 
 
 Nov. 16.0 
 
 12 36 57.050 
 
 - 3 23 38.44 
 
 5 
 
 -- 0.148 
 
 0.90 
 
 42 
 
 1857, Feb. 16.0 
 
 49 21.025 
 
 + 6 27 10.65 13 
 
 - - 0.063 
 
 + 0.46 
 
 43 
 
 March 18.0 
 
 2 36 3.575 
 
 + 19 31 12.35 5 
 
 0.058 
 
 0.37 
 
 44 
 
 April 16.0 
 
 3 35 55.521 
 
 + 25 33 57.52 7 
 
 + 0.027 
 
 0.85 
 
 45 
 
 May 21.0 
 
 24250.763 +165935.65 8 +0.118 
 
 + 0.56 
 
 46 
 
 June 13.0 
 
 2 50 20.725 + 13 31 18.27 13 + 0.020 
 
 + 0.81 
 
 24 
 
INTRODUCTION. 
 
 No. 
 
 GrciMiwii-li M. T. 
 
 App. K. A. 
 
 App. 1 > 
 
 .V, 01,, 
 
 An 
 
 A-i 
 
 
 .1 
 
 ll III fl 
 
 off/ 
 
 
 | 
 
 // 
 
 17 
 
 1*57. June 26.0 
 
 3 20 19.536 
 
 + 11 46 16.18 
 
 12 
 
 + 0.08 1 
 
 + 1.07 
 
 18 
 
 1858, AMU. 17.0 
 
 12 21 4.321 
 
 - 2 10 32.51 
 
 !) 
 
 -0.139 
 
 + 1.03 
 
 I!) 
 
 Sept. 18.0 
 
 11 31 :>7.:>11 
 
 - 17 21 17.16 
 
 4 
 
 0.05*. 
 
 1.56 
 
 50 
 
 ( tet 10.0 
 
 16 2 1.666 
 
 -24 12 17.26 
 
 10 
 
 O.ON6 
 
 - 0.62 
 
 51 
 
 Nov. 7.0 
 
 17 37 19.017 
 
 28 1 51.96 
 
 11 
 
 + 0.050 
 
 3.2 1 
 
 
 V,v. 29.0 
 
 17 55 !).<;:>! 25 :>i 3i.n 
 
 3 
 
 + 0.311 
 
 -4.70 
 
 53 
 
 !)-. 21.0 
 
 17 7 52.155 
 
 20 4 43.16 
 
 4 
 
 + 0.203 
 
 2.23 
 
 54 
 
 IS.')!), .Ian. 10.0 
 
 16 5S 27.618 
 
 17 21 53.14 
 
 7 
 
 + 0.051 
 
 + 3.60 
 
 55 
 
 .l:ill. 29.0 
 
 17 10 25.353 is 26 821 
 
 8 
 
 + 0.138 
 
 + 0.17 
 
 56 
 
 I860. M ;IV ;{.() 
 
 5 53 lts.561 +26 36 37.27 
 
 4 
 
 + 0.03 1 
 
 + 1.13 
 
 57 
 
 .M:iv 23.0 
 
 7 16 2.x 13 
 
 + 25 23 36.95 
 
 5 
 
 + 0.0)2 
 
 + 1.53 
 
 58 
 
 June lit!) 
 
 s 23 55.S23 
 
 
 - 19 58 30. 1 1 
 
 5 
 
 f 0.103 
 
 + 2. 13 
 
 59 
 
 July 10.0 
 
 8 11 15.899 
 
 
 - 16 8 22.57 
 
 6 
 
 + 0.103 
 
 + 2.50 
 
 60 
 
 An;,'. 31.0 
 
 7 4N 10.699 
 
 
 - 16 21 11.53 
 
 7 
 
 + 0.203 
 
 + 0.18 
 
 61 
 
 Sept. 22.0 
 
 !) 1 57.720 
 
 
 - 14 11 21.01 
 
 11 
 
 + 0.174 
 
 -0.67 
 
 89 
 
 1861, Doc. 10.0 
 
 20 31 32.S10 
 
 21 9 42.31 
 
 4 
 
 0.020 
 
 - 1.11 
 
 68 
 
 Dec. 26 
 
 21 37 51.N53 
 
 -15 29 11.52 
 
 7 
 
 + 0.036 
 
 - 1.41 
 
 (it 
 
 1862, Jan. 16.0 
 
 22 38 21.3S1 
 
 - 6 59 2.66 
 
 9 
 
 + 0.063 
 
 0.43 
 
 66 
 
 Feb. 12.0 
 
 22 50 59.987 
 
 + 17 57.58 
 
 2 
 
 + 0.201 
 
 2.41 
 
 66 
 
 March 11.0 
 
 21 58 59.897 
 
 - 3 59 31.67 
 
 5 
 
 + 0.211 
 
 + 3.72 
 
 67 
 
 April 23.0 
 
 23 14 6.685 
 
 4 20 27.06 
 
 9 
 
 f 0.061 
 
 + 0.09 
 
 68 
 
 .May 13.0 
 
 26 3. 17!) 
 
 + 1 19 59.00 
 
 4 
 
 - 0.069 
 
 + 2.83 
 
 69 
 
 1863, July 11.0 
 
 10 21 37.937 
 
 + 10 53 34.89 
 
 7 
 
 - 0.014 
 
 + 0.74 
 
 70 
 
 An"},'. 1.0 
 
 11 35 5.196 
 
 + 1 22 1.05 
 
 6 
 
 - 0.004 
 
 2.34 
 
 71 
 
 lug. 12.0 
 
 12 1 25.882 
 
 - 3 26 49.57 
 
 7 
 
 + 0.106 
 
 4.25 
 
 n 
 
 Sept. i.o 
 
 12 35 55.785 
 
 - 10 23 46.78 
 
 6 
 
 -0.108 
 
 + 0.38 
 
 73 
 
 Sept. !!).() 
 
 12 21 5 1.20C 
 
 - 11 49 46.67 
 
 6 
 
 + 0.117 
 
 + 1.85 
 
 ' 1 
 
 Oct 2s.o 
 
 11 50 36.106 
 
 1 43 20.76 
 
 2 
 
 + 0.117 
 
 3.63 
 
 75 
 
 NOT. 20.0 
 
 12 47 33.27 1 
 
 3 53 37.08 
 
 5 
 
 + 0.202 
 
 -2.15 
 
 76 
 
 1865, Feb. 13.0 
 
 38 41.720 
 
 
 -58 4.61 
 
 4 
 
 0.012 
 
 - 1.17 
 
 77 
 
 March 25.0 
 
 2 51 9.362 
 
 
 -21 44 33.17 
 
 7 
 
 0.008 
 
 + 0.69 
 
 78 
 
 April 9.0 
 
 3 23 1.559 
 
 
 -21 16 29.99 
 
 10 
 
 + 0.057 
 
 + 0.96 
 
 78 
 
 April 25.0 
 
 3 20 45.JJ53 
 
 
 -21 31 33.5!) 
 
 11 
 
 + 0.102 
 
 0.08 
 
 NO 
 
 May 7.0 
 
 2 56 28.201 
 
 + 21 8 3.49 
 
 7 
 
 + 0.201 
 
 + 1.48 
 
 81 
 
 May 21.0 
 
 2 28 59.092 
 
 
 - 14 58 17.96 
 
 9 
 
 + 0.233 + 1.59 
 
 83 
 
 June 11.0 
 
 2 12 18.317 
 
 
 - 13 4 19.64 
 
 8 
 
 + 0.208 + 0.26 
 
 83 
 
 June 22.0 
 
 3 7 28.235 
 
 
 - 14 5 20.47 
 
 7 
 
 + 0.139 
 
 0.07 
 
 84 
 
 July 11.0 
 
 4 9 16.618 
 
 
 -17 22 1.01 
 
 9 
 
 + 106 
 
 + 0.31 
 
 85 
 
 1866, Sept. 25.0 
 
 15 1 14.407 
 
 20 15 30.52 
 
 3 
 
 + 0.066 
 
 + 0.55 
 
 86 
 
 Oct. 16.0 
 
 16 24 17.041 
 
 26 5 30.30 
 
 7 
 
 + 0.017 
 
 1.53 
 
 87 
 
 Oct. 27.0 
 
 17 2 22.875 
 
 27 36 58.50 
 
 3 
 
 0.002 
 
 + 0.46 
 
 88 
 
 Nov. 15.0 
 
 17 44 28.584 
 
 27 42 20.26 
 
 9 
 
 - - 0.208 
 
 -0.31 
 
 86 
 
 Nov. 30.0 
 
 17 39 2,104 
 
 25 25 42.81 
 
 4 
 
 -- 0.417 
 
 + 0.05 
 
 90 
 
 Dec. 28.0 
 
 16 44 36.668 
 
 - 18 5 53.53 
 
 2 
 
 -. 0.359 +0.19 
 
 91 
 
 1867, Feb. 7.0 
 
 18 9 47.537 
 
 19 2 58.09 
 
 6 
 
 -- 0.174 +1.04 
 
 99 
 
 March 30.0 
 
 21 52 48.772 
 
 12 51 21.47 
 
 2 
 
 --0.015 0.29 
 
 93 
 
 1868, May 6.0 
 
 6 7 11.8:51 
 
 
 -26 42 54.56 
 
 6 
 
 0. 1 1 1 
 
 + 0.76 
 
 94 
 
 May 19.0 
 
 7 21.501 
 
 
 -25 57 6.61 
 
 3 
 
 + 0.05 1 + 0.95 
 
 95 
 
 May 29.0 
 
 7 31 52.111) 
 
 
 -21 29 40.91 
 
 4 
 
 + 0.103 +0.71 
 
 96 
 
 June 12.0 
 
 8 8 50.822 
 
 -21 11 50.55 
 
 9 
 
 + 0.05!) + 0.79 
 
 97 
 
 June 29.0 
 
 8 16 30.999 + 18 13 10.72 
 
 7 
 
 + 0.203 
 
 0.09 
 
 98 
 
 July 14.0 
 
 7 47 9.381 
 
 
 - 16 9 52.23 
 
 6 
 
 + 0. 177 
 
 + 1.23 
 
 99 
 
 July 28.0 
 
 7 14 21.065 
 
 
 - 15 34 15.57 
 
 4 
 
 + 0.173 
 
 1.35 
 
 100 
 
 Aug. 15.0 
 
 7 11 41.426 
 
 
 -16 13 52.9!) 
 
 1 
 
 + 0.050 
 
 0.96 
 
 101 
 
 Aug. 26.0 
 
 7 32 23.633 
 
 
 - 16 38 18.77 
 
 4 
 
 + 0.104 
 
 + 0.03 
 
 102 
 
 Sept. 4.0 
 
 7 57 43.509 
 
 
 - 16 35 5.21 
 
 4 
 
 0.069 
 
 0.37 
 
 103 
 
 Sept. 18.0 
 
 8 46 43.419 
 
 
 - 15 25 27.66 
 
 6 
 
 + 0.00 1 
 
 0.63 
 
 104 
 
 1869, Doc. 1.0 
 
 19 55 0.713 
 
 23 33 19.35 
 
 2 
 
 + 0.033 
 
 + 0.09 
 
 105 
 
 Dec. 23.0 
 
 21 26 28.614 
 
 16 37 52.39 
 
 1 
 
 + 0.038 
 
 + 0.94 
 
 106 
 
 1870, Jan. 3.0 
 
 22 2 46.591 
 
 -12 18 0.76 
 
 1 
 
 + 0.092 + 1.72 
 
 107 
 
 Jan. 27.0 
 
 22 48 13.855 
 
 - 3 24 26.46 
 
 4 
 
 + 0.339 + 2.6 1 
 
 108 
 
 Feb. 21.0 
 
 22 19 12.992 
 
 1 14 10.51 3 
 
 + 0.257 + 2.49 
 
 109 
 
 March 19.0 
 
 21 49 6.160 
 
 - 6 42 37.21 2 
 
 + 0.196 +1.21 
 
 110 
 
 April 5.0 
 
 22 18 31.S56 
 
 - 7 18 36.33 2 
 
 + 0.087 + 2.55 
 
 111 
 
 April 12.0 
 
 22 37 59.072 
 
 6 36 2.61 3 
 
 + 0.266 + 2.67 
 
 119 
 
 April 22.0 
 
 23 10 0.139 1 16 21.21 3 +0.060 +2.31 
 
 4 V 
 
 25 
 
INTRODUCTION. 
 
 No. 
 
 Greenwich .M. T. 
 
 .\pp. R. A. 
 
 AI>]>. D'-c. . 
 
 No.Obs. 
 
 A 
 
 A<! 
 
 
 (i 
 
 ll 11) S 
 
 I It 
 
 
 s 
 
 // 
 
 113 
 
 1H70, May 23.0 
 
 1 5 55.5 18 
 
 + 4 54 43.03 
 
 7 
 
 + 0.036 
 
 + 0.63 
 
 111 
 
 June 13.0 
 
 2 33 32. 55N 
 
 4- 12 34 56.06 
 
 4 
 
 + 0.148 
 
 -0.12 
 
 115 
 
 July 13.0 
 
 4 53 4.820 
 
 -j-20 50 51.48 
 
 5 
 
 + 0.047 
 
 + 1.00 
 
 116 
 
 Aug. S.O 
 
 7 5 26.170 
 
 4-22 6 39.93 
 
 3 
 
 - 0.032 
 
 !- i.oo 
 
 117 
 
 Aug. '25.0 
 
 8 32 16.460 
 
 |- 19 12 2.24 
 
 5 
 
 0.107 
 
 + 0.3 I 
 
 18 
 
 Sept. 15.0 
 
 10 14 53.930 
 
 (- 12 4 3.63 
 
 2 
 
 0.060 
 
 + 0.89 
 
 li) 
 
 Sept. '26.0 
 
 11 6 24.896 
 
 - 7 13 14.54 
 
 5 
 
 0.026 
 
 + 0.78 
 
 20 
 
 Oct. 1-2.0 
 
 12 19 50.532 
 
 31 51.43 
 
 5 
 
 0.170 
 
 + 1.03 
 
 21 
 
 Nov. i.O 
 
 13 52 35.280 
 
 10 14 46.16 
 
 4 
 
 0.157 
 
 - 0.24 
 
 23 
 
 Nov. 18.0 
 
 15 15 37.167 
 
 17 20 12.09 
 
 3 
 
 0.012 
 
 + 1.06 
 
 123 
 
 Dec. -21.0 
 
 18 28 7.770 
 
 23 56 17.07 
 
 1 
 
 - 033 
 
 - 1.33 
 
 124 
 
 l:i~l, Jan. 4.0 
 
 19 28 19.110 
 
 -22 55 7.73 
 
 1 
 
 0.029 
 
 + 1.12 
 
 No. 
 
 Wellington -M. T. 
 
 A|i>. 1!. A. 
 
 App. Dei'. 
 
 No.Obs. 
 
 An 
 
 A'i 
 
 
 .1 
 
 li in s 
 
 / // 
 
 
 B 
 
 // 
 
 1 25 
 
 1863, Aug. 19.0 
 
 12 19 46.295 
 
 6 19 30.41 
 
 13 
 
 + 0.078 
 
 + 1.33 
 
 126 
 
 Sept. 1-2.0 
 
 12 34 6.510 
 
 - 12 5 24.23 
 
 9 
 
 4-0.071 
 
 + 1.08 
 
 127 
 
 Oct. 19.0 
 
 11 42 32.127 
 
 - 2 57 57.34 
 
 10 
 
 -|- 0.236 
 
 -0.94 
 
 128 
 
 Nov. 15.0 
 
 12 32 43.563 
 
 2 56 9.17 
 
 11 
 
 4-0.071 
 
 + 0.35 
 
 1-.") 
 
 1865, Feb. 7.0 
 
 16 19.073 
 
 + 2 10 43.90 
 
 6 
 
 4- 0.034 
 
 + 0.11 
 
 130 
 
 Feb. -23.0 
 
 1 16 59.279 
 
 -|- 10 9 15.R1 
 
 4 
 
 - 0.039 
 
 --0.44 
 
 131 
 
 March 11.0 
 
 2 13 1.700 
 
 -j- 17 6 32.28 
 
 o 
 
 + 0.037 
 
 - - 1.02 
 
 132 
 
 March 28.0 
 
 3 2 8.034 
 
 + 22 35 31.27 
 
 o 
 
 0.113 
 
 -- 1.20 
 
 133 
 
 April 18.0 
 
 3 26 40.672 
 
 4-25 11 16.40 
 
 6 
 
 + 0.010 
 
 -- 1.81 
 
 J.-J1 
 
 May 2.0 
 
 3 7 27.361 
 
 -j-22 47 40.20 
 
 4 
 
 + 0.240 
 
 4-0.61 
 
 135 
 
 May 18.0 
 
 2 34 22.761 
 
 + 16 46 48.36 
 
 7 
 
 + 0.091 
 
 + 1.46 
 
 136 
 
 .limr 4.0 
 
 2 32 28.520 
 
 4-13 9 9.64 
 
 8 
 
 + 0.095 
 
 j-0.42 
 
 137 
 
 June 26.0 
 
 3 19 28.164 
 
 4- 14 43 23.83 
 
 9 
 
 + 0.079 
 
 0.00 
 
 138 
 
 July '20.0 
 
 4 45 13.373 
 
 4- 18 57 33.95 
 
 8 
 
 + 0.080 
 
 + 1.11 
 
 139 
 
 1866, Sept. 1-2.0 
 
 14 9 6.234 
 
 - 15 7 32.81 
 
 5 
 
 0.062 
 
 - 0.62 
 
 110 
 
 Oct. 6.0 
 
 15 46 27.321 
 
 -23 49 35.82 
 
 4 
 
 - 0.031 
 
 - 0.75 
 
 111 
 
 Oct. 19.0 
 
 16 36 2.1)52 
 
 -26 39 2.71 
 
 8 
 
 + 0.061 
 
 -2.11 
 
 142 
 
 Nov. 9.0 
 
 17 36 3.668 
 
 -28 1 18.33 
 
 7 
 
 + 0.134 
 
 - 1.56 
 
 143 
 
 Nov. 28.0 
 
 17 42 2.599 
 
 -25 52 0.26 
 
 6 
 
 + 0.385 
 
 - 1.88 
 
 111 
 
 Dec. 19.0 
 
 16 55 50.052 
 
 -20 53.68 
 
 2 
 
 + 0.570 
 
 + 2.20 
 
 145 
 
 1867, Jan. 22.0 
 
 17 17 25.170 
 
 17 59 43.41 
 
 10 
 
 + 0.222 
 
 0.14 
 
 Normals in the superior part of the Orbit. 
 
 No. 
 
 Greenwich M. T. 
 
 App. a. A. 
 
 App. Dec. 
 
 No.Obs. 
 
 A 
 
 At! 
 
 
 ,1 
 
 li m s 
 
 / // 
 
 
 g 
 
 // 
 
 146 
 
 1858, Jan. 23.0 
 
 19 46 16.637 
 
 21 53 48.46 
 
 3 
 
 + 0.022 
 
 2.26 
 
 117 
 
 April 23.0 
 
 2 56 59.252 
 
 + 16 35 27.79 
 
 5 
 
 0.005 
 
 -0.10 
 
 us 
 
 June 14.0 
 
 7 27 55.977 
 
 + 23 33 18.26 
 
 13 
 
 + 0.078 
 
 -0.13 
 
 119 
 
 July 19.0 
 
 10 17 52.788 
 
 + 12 10 47.22 
 
 5 
 
 0.035 
 
 + 0.11 
 
 150 
 
 1859, Feb. 23.0 
 
 19 14 56.589 
 
 - 19 15 37.66 
 
 7 
 
 + 0.022 
 
 -0.82 
 
 151 
 
 March 18.0 
 
 20 57 4.220 
 
 - 16 1 1 30.29 
 
 6 
 
 + 0.188 
 
 + 2.39 
 
 152 
 
 June 17.0 
 
 3 46 35.988 
 
 + 18 29 1.65 
 
 4 
 
 + 0.033 
 
 - 0.40 
 
 158 
 
 July 19.0 
 
 6 31 41.515 
 
 + 23 6 57.50 
 
 11 
 
 - 0.021 
 
 - 0.31 
 
 164 
 
 Aug. 23.0 
 
 9 32 0.652 
 
 4- 15 49 11.42 
 
 8 
 
 -0.016 
 
 -0.44 
 
 155 
 
 Nov. 13.0 
 
 16 1 34.918 
 
 -20 45 38.42 
 
 5 
 
 + 0.0 14 
 
 - 1.75 
 
 158 
 
 Dec. 17.0 
 
 19 5 56.987 
 
 23 55 27.75 
 
 4 
 
 + 0.043 
 
 - 3.39 
 
 157 
 
 1860, Jan. 17.0 
 
 21 46 14.280 
 
 15 10 47.89 
 
 5 
 
 + 0.016 
 
 2.66 
 
 158 
 
 Feb. 29.0 
 
 1 24.170 
 
 + 6 15 55.78 
 
 3 
 
 - 062 
 
 0.77 
 
 159 
 
 April 19.0 
 
 4 48 31.013 
 
 -j-25 10 19.92 
 
 4 
 
 -0.014 
 
 - 0.04 
 
 160 
 
 Oct. 24.0 
 
 11 13 17.826 
 
 + 5 r>l 46.41 
 
 5 
 
 + 0.086 
 
 - 0.82 
 
 161 
 
 Dec. 10.0 
 
 14 42 35.914 
 
 - 13 40 52.46 
 
 5 
 
 - 0.060 
 
 0.81 
 
 162 
 
 1867, May 14.0 
 
 1 11 9.973 
 
 + 5 34 41.60 
 
 6 
 
 + 0.113 
 
 + 0.44 
 
 163 
 
 June 17.0 
 
 3 49 8.762 
 
 + 18 38 58.87 
 
 5 
 
 + 0.050 
 
 + 1.11 
 
 16 i 
 
 Aug. 18.0 
 
 9 10 1.066 
 
 + 17 23 4 1.04 
 
 6 
 
 0.059 
 
 + 0.60 
 
 165 
 
 Oct. 15.0 
 
 13 11 6.075 
 
 - 9 28 37.18 4 
 
 + 0.009 
 
 1.01 
 
 26 
 
I INTRODUCTION. 
 
 jYii;'w/.v in I In- sii/irrinr /iiir/ /' // Orlil. 
 
 No. 
 
 Gri'cnwirli M. T. 
 
 A|i|>. ft. A. 
 
 A ji|i. n 
 
 No. Ob*. 
 
 Aa 
 
 A.! 
 
 166 
 
 |si;-. Nov. 19.0 
 
 h in a 
 16 36 3.11s 
 
 / // 
 
 22 2."> 31.:.1 
 
 5 
 
 0*001 
 
 - a:> i 
 
 167 
 
 1868, Oct. 16.0 
 
 10 10 13.171 
 
 + 8 3s :J!I.S2 
 
 9 
 
 + 0.100 
 
 + 0.01 
 
 168 
 
 Dec. 17.0 
 
 15 IS Hi.5l.Vi 
 
 - 16 23 36.5)5 
 
 6 
 
 + 0.083 
 
 f 0.83 
 
 169 
 
 Is<;<), .Ian. 12.0 
 
 17 32 57.506 
 
 22 22 25.57 
 
 5 
 
 + o.ino 
 
 1.18 
 
 170 
 
 \:K : | 20.0 
 
 1 36 7.1!).") 
 
 + 8 13 5!).!)5 
 
 6 
 
 - 0.070 
 
 + 0.55 
 
 171 
 
 .lime 17.0 
 
 (i 29 55.7s 1 
 
 + 2! 7 55.16 
 
 5 
 
 - 0.020 
 
 + 0.32 
 
 172 
 
 Jnlv Ki.O 
 
 9 1 6.0!)0 
 
 + 18 33 2,s7 
 
 1 
 
 - 0.208 
 
 + 0.78 
 
 173 
 
 An-. 2(i.O 
 
 12 10 o.t;si 
 
 - 7 31.79 
 
 5 
 
 -0.010 
 
 f 0.29 
 
 174 
 
 Sep,. 21.0 
 
 1 1 : 2C. --:;:! 
 
 -13 7 17.72 
 
 1 
 
 0.183 
 
 + 1.02 
 
 178 
 
 Oct. 13.0 
 
 15 11) 16.3li8 
 
 -21 12 11.S7 
 
 5 
 
 0.026 
 
 + 1.13 
 
 In order to have as few unknown quantities. in the ci|ii;itioiis of condition, ;i^ possible, the dillrrciiccs J n and 
 Jo |i,-i\i. I ice n i-liiiiiircd into cos r r J II and J i, ; W di -noting th<' ^cciccnlric lon^ilndc of Venus ivl'm-rd in a plane 
 dmwii tlirongli the e.-utre of the Kartli parallel to the plane of the orhil of Venus, and T, denoting the corresponding 
 latitude. The forniuhr used are given in WATSON'S T/ii-off/irnl .\xlrnnomii. pp. 153 159. 
 
 In the following eipiations, \vc have put 
 
 l ' 
 
 a; = J L'o- 2 sin j ',' J Q', 
 
 y = 100 J ', 
 
 c' ( J -' - 
 
 2 t J 
 
 all expressed in seconds of arc; and .r', //',;' and u' denote the similar quantities in reference to the solar ele- 
 
 ments. In the computation of the coefficients of the last, roughly approximate formula; have heen used. 
 
 A mean of the Transits of 17G1 and 17G9 gives 
 
 + 0.992 j' - 0.839 y + 1.61 : + 1.17 u + 1.00 x> - 0.84 y + 0.83 z' - \.82u' = + 1".745. 
 
 The indeterminate correction of the Sim's semi-diameter nearly disappears from this mean. 
 
 The following equations of condition are numbered with the same number ;>s the normals, from which they 
 are derived. The last column contains tin; residuals which remain after the elements have been corrected as 
 shown in the sequel. 
 
 No. 
 
 1 
 2 
 3 
 4 
 5 
 
 6 
 7 
 8 
 9 
 10 
 
 11 
 12 
 13 
 14 
 15 
 
 16 
 17 
 18 
 19 
 20 
 
 Equations of condition. 
 
 Residuals. 
 
 - 0.40 *+ O.OSy 0.36: 1.44+ 1.4&/ 0.19/ 0.21 z' 3.06u' = + L01 + 0.97 
 
 -1.37 +0.180.872.97+2.41 -0.32 -1.45 -4.69 =0.95 1.02 
 
 -2.05 +0.280.874.16+3.08 -0.41 -2.17 -5.74 = -0.69 0.71 
 
 -2.07 +0.280.024.28+3.11 -0.41 -2.65 -5.57 =+3.37 +3.37 
 
 -0.80 +0.11+0.312.15+1.80 -0.24 -2.22 3.16 =+1,11 +1,13 
 
 -0.31 +0.040.12+1,11+1.30 -0.16 +1.86 +2.32 =+1.27 +0.68 
 
 -0.98 +0.12 0.93 +2.31 + 1.98 -0.21 +3.56 +2.59 =0.23 1.25 
 
 -2.27 +0.272.31+4.06+3.27 -0.39 +5.84 +3.12 =+1.48 0.38 
 
 _--j. U +0.293.04+3.85+3.10 -0,10 +6.26 +2.85 =+3.13 +1.22 
 
 -1.70 +0.202.53+2.69+2.70 -0.32 +5.18 +2.00 =+1.13 0.27 
 
 -0.90 +0.111.76+1.56+1.91 -0.22 +3.95 +1.01 =+0.96 +0.08 
 
 -2.06 +0.21+3.532.38+3.08 -0.32 -6.12 -0.14 =1.66 2.07 
 
 -2.51 +0.26+4.642.02+3.51 -0.36 -7.01 +0.39 =+0.29 0.34 
 
 -2.00 +0.174.120.54+3.00 -0.26 +4.57 3.99 =+0.22 0.91 
 
 -2.09 +0.184.051.48+3.10 -0.27 +4.28 -4.47 =+4.08 +3.09 
 
 -1.12 +0.102.391.18+2.12 -0.14 +2.72 -3.49 =0.59 1.11 
 
 -2.69 +0.19+3.71+3.87+3.69 -0.26 -1.82 +7.26 =2.09 120 
 
 1.58 +0.11 + 1.80 +2.98 +2. 5s -0.18 -0.65 +5.38 = O.(i3 -2.10 
 
 0.07 +0.21 -2.76 = -0.81 (i.id 
 
 0.18 2.17 +6.18 =0.57 1.14 
 
 - 0.27 
 
 - 2.40 
 
 + 0.01 0.63 1.18 + 1.27 - 
 + 0.13 0.41 1.N2 +3.10 
 
 27 
 
INTRODUCTION. 
 
 No. 
 
 Equations of condition. 
 
 Residuals. 
 
 21 
 
 - 0.47.T 
 
 + 0.02.y 0.17-. 
 
 + 1.64+ 1.47^ 
 
 0.06y' 
 
 + 2.19;' 
 
 + 2.48w' 
 
 0.98 
 
 1.79 
 
 22 
 
 - 1.51 
 
 + 0.06 
 
 1.31 
 
 + 3.16 
 
 + 2.54 
 
 0.10 
 
 + 1.37 
 
 + 3.00 
 
 - 1.19 
 
 -2.93 
 
 23 
 
 - 1.95 
 
 + 0.07 
 
 -2.61 
 
 + 3.15 
 
 + 2.95 
 
 0.11 
 
 + 5.79 
 
 + 2.51 
 
 = + 1.84 
 
 - 0.20 
 
 21 
 
 -0.40 
 
 + 0.01 
 
 + 1.03 
 
 - 1.15 
 
 + 1.40 
 
 -0.03 
 
 2.79 
 
 -1.18 
 
 = +0.42 
 
 + 0.24 
 
 25 
 
 2.29 
 
 + 0.05 
 
 + 8.87 
 
 2.60 
 
 + 3.28 
 
 -0.07 
 
 6.58 
 
 0.29 
 
 = 2.95 
 
 3.92 
 
 26 
 
 0.55 
 
 + 0.01 
 
 + 1.78 
 
 0.38 
 
 + 1.55 
 
 0.03 
 
 3.33 
 
 + 1.04 
 
 = +3.15 
 
 + 2.75 
 
 27 
 
 2.22 
 
 + 0.02 
 
 -4.51 
 
 -0.53 
 
 + 3.22 
 
 0.02 
 
 + 4.94 
 
 -4.09 
 
 = +2.47 
 
 + 0.72 
 
 28 
 
 1.22 
 
 + 0.01 
 
 2.59 
 
 1.14 
 
 + 2.22 
 
 0.01 
 
 + 3.02 
 
 -3.46 
 
 = +0.04 
 
 0.85 
 
 29 
 
 1.55 
 
 -0.01 
 
 + 2.84 
 
 + 1.97 
 
 + 2.55 
 
 + 0.02 
 
 2.07 
 
 + 4.94 
 
 = 2.24 
 
 -3.81 
 
 30 
 
 2.73 
 
 0.03 
 
 + 3.75 
 
 + 3.93 
 
 + 3.72 
 
 + 0.04 
 
 2.06 
 
 + 7.28 
 
 = 0.41 
 
 3.18 
 
 31 
 
 0.88 
 
 0.01 
 
 + 1.17 
 
 + 2.02 
 
 + 1.88 
 
 + 0.02 
 
 1.96 
 
 + 4.10 
 
 = +4.28 
 
 + 3.11 
 
 32 
 
 2.18 
 
 -0.05 
 
 1.24 
 
 4.31 
 
 + 3.18 
 
 + 0.08 
 
 -L77 
 
 6.06 
 
 = 0.38 
 
 - 1.61 
 
 33 
 
 1.26 
 
 -0.03 
 
 + 0.04 
 
 2.92 
 
 + 2.26 
 
 + 0.06 
 
 2.00 
 
 -4.22 
 
 = +2.07 
 
 + 1.48 
 
 34 
 
 -0.44 
 
 0.01 
 
 + 0.19 
 
 -1.60 
 
 + 1.44 
 
 + 0.04 
 
 1.92 
 
 2.50 
 
 = + 1.59 
 
 + 1.39 
 
 35 
 
 0.68 
 
 0.03 
 
 -0.51 
 
 + 1.96 
 
 + 1.68 
 
 + 0.07 
 
 + 2.58 
 
 + 2.70 
 
 = +0.46 
 
 -0.68 
 
 36 
 
 - 1.37 
 
 0.06 
 
 - 1.02 
 
 + 2.96 
 
 + 2.37 
 
 + 0.10 
 
 + 3.95 
 
 + 3.09 
 
 = +0.71 
 
 - 1.20 
 
 37 
 
 -2.43 
 
 0.10 
 
 -2.15 
 
 + 4.44 
 
 + 3.42 
 
 + 0.14 
 
 + 5.83 
 
 + 3.70 
 
 = +2.52 
 
 0.59 
 
 38 
 
 -0.51 
 
 0.03 
 
 + 1.14 
 
 -1.33 
 
 + 1.51 
 
 + 0.09 
 
 -3.10 
 
 - 1.20 
 
 = 0.19 
 
 0.52 
 
 39 
 
 -2.27 
 
 -0.13 
 
 + 3.71 
 
 2.77 
 
 + 3.27 
 
 + 0.19 
 
 -6.49 
 
 -0.59 
 
 = +0.25 
 
 -1.20 
 
 40 
 
 -2.32 
 
 -0.13 
 
 + 4.26 
 
 2.04 
 
 + 3.27 
 
 + 0.19 
 
 6.59 
 
 -0.07 
 
 = + 1.31 
 
 -0.27 
 
 41 
 
 0.46 
 
 -0.03 
 
 + 1.64 
 
 0.39 
 
 + 1.46 
 
 + 0.09 
 
 -3.12 
 
 + 0.99 
 
 = +2.17 
 
 + 1.73 
 
 42 
 
 + 0.13 
 
 + 0.01 
 
 0.89 
 
 + 0.28 
 
 + 0.87 
 
 + 0.06 
 
 + 1.91 
 
 + 0.52 
 
 = + 1.01 
 
 + 0.85 
 
 43 
 
 0.25 
 
 -0.02 
 
 -1.34 
 
 + 0.16 
 
 + 1.21 
 
 + 0.09 
 
 + 2.71 
 
 0.68 
 
 = 0.68 
 
 1.18 
 
 44 
 
 1.37 
 
 0.10 
 
 3.10 
 
 + 0.07 
 
 + 2.37 
 
 + 0.17 
 
 + 4.12 
 
 2.66 
 
 = +0.01 
 
 1.57 
 
 45 
 
 -2.17 
 
 0.16 
 
 -4.30 
 
 - 1.15 
 
 + 3.17 
 
 + 0.23 
 
 + 4.76 
 
 -4.18 
 
 = + 1.79 
 
 -0.31 
 
 46 
 
 0.86 
 
 0.06 
 
 2.06 
 
 -0.91 
 
 + 1.86 
 
 + 0.14 
 
 + 2.50 
 
 3.03 
 
 = +0.55 
 
 -0.31 
 
 47 
 
 0.41 
 
 0.03 
 
 1.38 
 
 -0.72 
 
 + 1.41 
 
 + 0.11 
 
 + 1.57 
 
 -2.63 
 
 = + 1.49 
 
 + 1.01 
 
 48 
 
 + 0.28 
 
 + 0.02 
 
 + 0.81 
 
 0.23 
 
 + 0.72 
 
 + 0.06 
 
 1.45 
 
 -0.59 
 
 = 2.32 
 
 -2.18 
 
 49 
 
 + 0.13 
 
 + 0.01 
 
 + 0.92 
 
 + 0.17 
 
 + 0.87 
 
 + 0.08 
 
 - 1.91 
 
 + 0,13 
 
 = 0.21 
 
 - 0.26 
 
 50 
 
 0.05 
 
 0.00 
 
 + 1,06 
 
 + 0.48 
 
 + 1.01 
 
 + 0.09 
 
 1.96 
 
 + 1.41 
 
 = 0.98 
 
 1.26 
 
 51 
 
 0.80 
 
 0.07 
 
 + 1.95 
 
 + 1.01 
 
 + 1.79 
 
 + 0.16 
 
 2.15 
 
 + 3.30 
 
 = +0.98 
 
 -0.08 
 
 52 
 
 -2.13 
 
 -0.19 
 
 + 3.57 
 
 + 2.60 
 
 + 3.10 
 
 + 0.28 
 
 2.37 
 
 + 5.96 
 
 = +4.52 
 
 + 1.97 
 
 53 
 
 2.58 
 
 -0.23 
 
 + 3.49 
 
 + 3.83 
 
 + 3.54 
 
 + 0.32 
 
 2.09 
 
 + 6.93 
 
 = +3.16 
 
 -0.06 
 
 54 
 
 1.28 
 
 -0.12 
 
 + 1.70 
 
 + 2.46 
 
 + 2.26 
 
 + 0.20 
 
 0.80 
 
 + 4.79 
 
 = +0.13 
 
 - 1.67 
 
 55 
 
 0.48 
 
 -0.04 
 
 + 0,81 
 
 + 1.49 
 
 + 1.47 
 
 + 0.13 
 
 + 0.19 
 
 + 3.29 
 
 = + 1.94 
 
 + 1.03 
 
 56 
 
 + 0.09 
 
 + 0.01 
 
 0.55 
 
 0.78 
 
 + 0,92 
 
 + 0.09 
 
 + 1.02 
 
 -1.78 
 
 = +0.55 
 
 + 0.58 
 
 57 
 
 -0.17 
 
 0.02 
 
 0.62 
 
 1.07 
 
 + 1.18 
 
 + 0.12 
 
 + 0.55 
 
 2.81 
 
 = +0.44 
 
 + 0.27 
 
 58 
 
 1.03 
 
 0.11 
 
 1.08 
 
 2.31 
 
 + 2.05 
 
 + 0.21 
 
 0.57 
 
 -4.25 
 
 = +0.95 
 
 + 0.14 
 
 59 
 
 2.27 
 
 0.24 
 
 - 1.37 
 
 4.41 
 
 + 3.29 
 
 + 0.35 
 
 -1.62 
 
 6.32 
 
 = + 1.02 
 
 0.62 
 
 60 
 
 0.52 
 
 0.05 
 
 + 0.10 
 
 - 1.72 
 
 + 1.52 
 
 + 0.16 
 
 -1.83 
 
 2.76 
 
 = +2.87 
 
 + 2,49 
 
 61 
 
 0.06 
 
 0.01 
 
 + 0.16 
 
 1.09 
 
 + 1.07 
 
 + 0.11 
 
 - 1.89 
 
 1.47 
 
 = +2.61 
 
 + 2.58 
 
 62 
 
 + 0.07 
 
 + 0.01 
 
 0.02 
 
 + 1.02 
 
 + 0.92 
 
 + 0.11 
 
 + 0.26 
 
 + 2.12 
 
 = 0.58 
 
 0,88 
 
 63 
 
 -0.12 
 
 0.01 
 
 0.16 
 
 + 1.21 
 
 + 1.11 
 
 + 0.13 
 
 + 1.00 
 
 + 2.37 
 
 = +0.07 
 
 -0,48 
 
 61 
 
 0.62 
 
 0.07 
 
 0.36 
 
 + 1.89 
 
 + 1.61 
 
 + 0.19 
 
 + 2.35 
 
 + 2.74 
 
 = +0.72 
 
 0.48 
 
 65 
 
 2.12 
 
 - 0.26 
 
 1.60 
 
 + 4.07 
 
 + 3.07 
 
 + 0.37 
 
 + 5.13 
 
 + 3.73 
 
 = + 1.87 
 
 - 1,35 
 
 
 
 
 
 
 
 28 
 
 
 
 
 
[NTRODUOTION. 
 
 No. 
 
 Equation* <>l cui/di/ion. 
 
 66 
 
 2.11. 
 
 , _ 0.26// 2.45*+ 3.60u+ 3.07-t' + 0.37./ + 5. 11-.' + 3. 15' = 
 
 + 4.21 
 
 + 1.01 
 
 67 
 
 o.2:t 
 
 0.03 
 
 0.97 
 
 + 0.86 
 
 + 1.22 
 
 + 0.15 
 
 + 2.71 
 
 + 0.18 
 
 = 
 
 + 0.87 
 
 + 0.23 
 
 86 
 
 + 0.03 
 
 0.00 
 
 - O.SO 
 
 + 0.55 
 
 + 0.96 
 
 + 0.12 
 
 + 2.05 
 
 0.56 
 
 = 
 
 + 0.23 
 
 -0.06 
 
 69 
 
 + 0.09 
 
 + 0.01 
 
 + 0.47 
 
 - O.S2 
 
 + 0.92 
 
 + 0.12 
 
 - 1.17 
 
 - 1.65 
 
 = 
 
 - 0. 15 
 
 -0.51 
 
 70 
 
 -0.17 
 
 - 0.02 
 
 + 0.73 
 
 1.00 
 
 + 1.18 
 
 + 0.16 
 
 2.14 
 
 - 1.1!) 
 
 = 
 
 + 0.89 
 
 + 0.73 
 
 71 
 
 0.11 
 
 - ().().-, 
 
 + 0.98 
 
 1.22 
 
 + l.ll 
 
 + 0.19 
 
 2.7!) 
 
 1.31 
 
 = 
 
 + 3.22 
 
 + 2.87 
 
 72 
 
 - 1.19 
 
 -0.16 
 
 + 1.98 
 
 2.02 
 
 + 2.20 
 
 + 0.30 
 
 - 4. 19 
 
 - 1.05 
 
 = 
 
 - 1.61 
 
 2.63 
 
 73 
 
 - 2.2!) 
 
 -O81 
 
 + 3.67 
 
 - 2.8!) 
 
 + 3.29 
 
 + 0. 15 
 
 6.57 
 
 0.78 
 
 = 
 
 + 0.77 
 
 -1.19 
 
 71 
 
 - 1.13 
 
 0.16 
 
 + 2.56 
 
 0.97 
 
 + 2.11 
 
 + 0.29 
 
 - 1.55 
 
 + 0.11 
 
 = 
 
 + 3.09 
 
 + 1.95 
 
 75 
 
 -0.31 
 
 0.01 
 
 + 1.11 
 
 0.36 
 
 + 1.31 
 
 + 0.18 
 
 2.7? 
 
 + 1.06 
 
 = 
 
 + 3.6 1 
 
 + 3.21 
 
 74 
 
 + 0.13 
 
 + 0.02 
 
 0.88 
 
 + 0.33 
 
 + 0.97 
 
 + 0.15 
 
 + 1.93 
 
 + 0.85 
 
 = 
 
 - 1.08 
 
 - 1.21 
 
 77 
 
 0.48 
 
 0.07 
 
 - 1.66 
 
 + 0.23 
 
 + 1.61 
 
 + 0.25 
 
 + 3.39 
 
 0.81 
 
 = 
 
 + 0.13 
 
 - 0.74 
 
 78 
 
 - 1.09 
 
 -0.17 
 
 2.6 1 
 
 + 0.21 
 
 + 2.25 
 
 + 0.3 1 
 
 + 1.25 
 
 1.90 
 
 = 
 
 + 1.03 
 
 0.58 
 
 79 
 
 2.05 
 
 0.32 
 
 - 1.2 1 
 
 0.17 
 
 + 3.16 
 
 + 0. IS 
 
 + 5.41 
 
 3.27 
 
 = 
 
 + 1.30 
 
 - 1.37 
 
 80 
 
 -2.51 
 
 0.39 
 
 -4.99 
 
 0.6 1 
 
 + 3.50 
 
 + 0.54 
 
 + 5.80 
 
 3.80 
 
 = 
 
 + 3.15 
 
 + 0.05 
 
 81 
 
 - 1.81 
 
 0.28 
 
 3.75 
 
 1.02 
 
 + 2.67 
 
 + 0.11 
 
 + 4.11 
 
 3.2 t 
 
 
 
 + 3.72 
 
 + 1.53 
 
 82 
 
 -0.78 
 
 -0.1 2 
 
 2.03 
 
 -0.71 
 
 + 1.61 
 
 + 0.25 
 
 + 2.66 
 
 2. 17 
 
 = 
 
 + 2.94 
 
 + 1.95 
 
 83 
 
 0.45 
 
 0.07 
 
 - 1.47 
 
 0.65 
 
 + 1.27 
 
 + 0.20 
 
 + 1.89 
 
 2.22 
 
 = 
 
 + 1.89 
 
 + 1.30 
 
 81 
 
 -0.07 
 
 0.01 
 
 0.98 
 
 0.51 
 
 + 0.94 
 
 + 0.15 
 
 + 0.91 
 
 -2.01 
 
 = 
 
 + 1.51 
 
 + 1.32 
 
 85 
 
 + 0.01 
 
 + 0.01 
 
 + 1.02 
 
 + 0.20 
 
 + 1.08 
 
 + 0.18 
 
 2.25 
 
 + 0.55 
 
 = 
 
 + 0.69 
 
 + 0.53 
 
 86 
 
 0.2 1 
 
 - 0.0 1 
 
 + 1.28 
 
 + 0.45 
 
 + 1.39 
 
 + 0.23 
 
 2. 1!) 
 
 + 1.68 
 
 = 
 
 + 0.95 
 
 + 0.41 
 
 87 
 
 ().:>! 
 
 0.09 
 
 + 1.62 
 
 + 0.66 
 
 + 1.67 
 
 + 0.28 
 
 2.61 
 
 + 2. 17 
 
 = 
 
 0.10 
 
 - 1.00 
 
 88 
 
 1.36 
 
 0.23 
 
 + 2.76 
 
 + 1.48 
 
 + 2.52 
 
 + 0,43 
 
 2.92 
 
 + 4.38 
 
 = 
 
 + 2.78 
 
 + 0.78 
 
 89 
 
 2.36 
 
 -0.10 
 
 + 3.97 
 
 + 2.75 
 
 + 3. 15 
 
 + 0.58 
 
 3.24 
 
 + 6.23 
 
 = 
 
 + 5.62 
 
 + 2.27 
 
 90 
 
 1.95 
 
 -0.33 
 
 + 2.75 
 
 + 3.06 
 
 + 2.73 
 
 + 0,46 
 
 -2.12 
 
 + 5.43 
 
 = 
 
 + 4.99 
 
 + 2.07 
 
 91 
 
 0.20 
 
 -0.03 
 
 + 0.64 
 
 + 1.14 
 
 + 1.02 
 
 + 0.17 
 
 + 0.16 
 
 + 2.49 
 
 = 
 
 + 2.58 
 
 + 2.00 
 
 92 
 
 + 0.24 
 
 + 0.04 
 
 -0.01 
 
 + 0.86 
 
 + 0.66 
 
 + 0.11 
 
 + 1.23 
 
 + 0.92 
 
 = 
 
 + 0.53 
 
 + 0.47 
 
 93 
 
 + 0.04 
 
 + 0.01 
 
 0.58 
 
 0.82 
 
 + 0.97 
 
 + 0.18 
 
 + 0.98 
 
 1.93 
 
 = 
 
 -1.45 
 
 -1.45 
 
 94 
 
 -0.11 
 
 0.02 
 
 0.64 
 
 1.01 
 
 + 1.15 
 
 + 0.21 
 
 + 0.65 
 
 2.46 
 
 = 
 
 + 0.68 
 
 + 0.49 
 
 95 
 
 0.35 
 
 0.06 
 
 0.76 
 
 1.27 
 
 + 1.36 
 
 + 0.25 
 
 + 0.34 
 
 2.95 
 
 = 
 
 + 1.31 
 
 + 0.90 
 
 96 
 
 0.81 
 
 -0.15 
 
 1.05 
 
 -1.93 
 
 + 1.83 
 
 + 0.34 
 
 0.20 
 
 3.87 
 
 = 
 
 + 0.68 
 
 -0.18 
 
 97 
 
 -1.75 
 
 0.32 
 
 1.47 
 
 3.45 
 
 + 2.78 
 
 + 0.51 
 
 -1.00 
 
 5.52 
 
 = 
 
 + 2.86 
 
 + 1.13 
 
 98 
 
 -2.47 
 
 0.46 
 
 -1.39 
 
 -4.75 
 
 + 3.49 
 
 + 0.65 
 
 -1.61 
 
 6.68 
 
 = 
 
 + 2.36 
 
 + 0.02 
 
 99 
 
 -2.10 
 
 -0.39 
 
 0.73 
 
 4.28 
 
 + 3.12 
 
 + 0.58 
 
 - 1.72 
 
 5.98 
 
 = 
 
 + 2.60 
 
 + 0.64 
 
 100 
 
 1.05 
 
 -0.20 
 
 -0.11 
 
 2.57 
 
 + 2.06 
 
 + 0.38 
 
 - 1.67 
 
 3.99 
 
 = 
 
 + 0.79 
 
 0.19 
 
 101 
 
 0.60 
 
 -0.11 
 
 + 0.02 
 
 -1.85 
 
 + 1.61 
 
 + 0.30 
 
 -1.70 
 
 3.02 
 
 = 
 
 + 1.48 
 
 + 0.92 
 
 102 
 
 0.35 
 
 0.06 
 
 + 0.06 
 
 - 1,47 
 
 + 1.35 
 
 + 0.25 
 
 -1.75 
 
 -2.40 
 
 = 
 
 -0.92 
 
 -1.26 
 
 103 
 
 - 0.0!) 
 
 0.02 
 
 + 0.11 
 
 -1.13 
 
 + 1.09 
 
 + 0.20 
 
 -1.82 
 
 - 1.62 
 
 = 
 
 + 0.20 
 
 + 0.12 
 
 101 
 
 + 0.12 
 
 + 0.02 
 
 + 0.09 
 
 + 0.96 
 
 + 0.87 
 
 + 0.17 
 
 0.09 
 
 + 2.01 
 
 = 
 
 + 0.46 
 
 + 0.23 
 
 105 
 
 0.09 
 
 0.02 
 
 -0.10 
 
 + 1.21 
 
 + 1.10 
 
 + 0.22 
 
 + 0.87 
 
 + 2.40 
 
 = 
 
 + 0.79 
 
 + 0.26 
 
 106 
 
 0.32 
 
 0.06 
 
 0.20 
 
 + 1.48 
 
 + 1.31 
 
 + 0.26 
 
 + 1.49 
 
 + 2.60 
 
 
 
 + 1.84 
 
 + 0.95 
 
 107 
 
 1.21 
 
 0.25 
 
 0.70 
 
 + 2.84 
 
 + 2.22 
 
 + 0.44 
 
 + 3.45 
 
 + 3.30 
 
 = 
 
 + 5.70 
 
 + 3.37 
 
 108 
 
 2.63 
 
 0.53 
 
 -2.15 
 
 + 4.76 
 
 + 3.5S 
 
 + 0.72 
 
 + 5.86 
 
 + 4.25 
 
 = 
 
 + 4.49 
 
 -0.01 
 
 109 
 
 - 1.44 
 
 0.29 
 
 -1.91 
 
 + 2.58 
 
 + 2.42 
 
 + 0.49 
 
 + 1,11 
 
 + 2.42 
 
 = 
 
 + 3.11 
 
 + 0.51 
 
 110 
 
 0.63 
 
 0.13 
 
 1.27 
 
 + 1.40 
 
 + 1.62 
 
 + 0.33 
 
 + 3.34 
 
 + 1.13 
 
 = 
 
 + 2.10 
 
 + 0.78 
 
 29 
 
INTRODUCTION. 
 
 Equations of condition. 
 j^ o Residuals. 
 
 Ill 
 
 __ 0.42.r 0.09.I/ 1.09;+ 1.13+ 1.4Lr' + 0.29/ + 3.02;' + 0.72 ' = 
 
 + 4.67 
 
 + 3.68 
 
 112 
 
 - 0.20 
 
 -0.04 
 
 - 0.92 
 
 + 0.87 
 
 + 1.20 
 
 + 0.2 1 
 
 + 2.65 
 
 + 0.23 
 
 = 
 
 + 1.74 
 
 + 1.08 
 
 113 
 
 + 0.11 
 
 + 0.03 
 
 0.76 
 
 + 0.10 
 
 + O.SG 
 
 + 0.17 
 
 + 1.70 
 
 - 0.82 
 
 = 
 
 + 0.76 
 
 + 0.63 
 
 111 
 
 + 0.2 4 
 
 + 0.05 
 
 0.80 
 
 + 0.21 
 
 + 0.75 
 
 + 0.15 
 
 + 1.09 
 
 1.20 
 
 = 
 
 + 1.98 
 
 + 2.03 
 
 115 
 
 + 0.39 
 
 + 0.08 
 
 -0.49 
 
 0.22 
 
 + 0.08 
 
 + 0.14 
 
 + 0.2 4 
 
 1.39 
 
 = 
 
 + 0.96 
 
 + 1.27 
 
 116 
 
 + 0.37 
 
 + 0.08 
 
 0.55 
 
 -0.61 
 
 + 0.01 
 
 + 0.13 
 
 0,12 
 
 1.24 
 
 = 
 
 0.50 
 
 0.12 
 
 117 
 
 + 0.3S 
 
 + 0.08 
 
 - 0.29 
 
 0.77 
 
 + 0.62 
 
 + 0.13 
 
 0.77 
 
 1.00 
 
 = 
 
 - 1.55 
 
 - 1.11 
 
 118 
 
 + 0.40 
 
 + 0.08 
 
 + 0.15 
 
 0.82 
 
 + 0.60 
 
 + 0.12 
 
 -1.07 
 
 0.59 
 
 = 
 
 - '.13 
 
 0.63 
 
 119 
 
 + 0,41 
 
 + 0.08 
 
 + 0.33 
 
 0.77 
 
 + 0.60 
 
 + 0.12 
 
 -1.16 
 
 0.34 
 
 = 
 
 -0.66 
 
 -0.17 
 
 120 
 
 + 0,11 
 
 + 0.09 
 
 + 0.60 
 
 -0.59 
 
 + 0.59 
 
 + 0.12 
 
 1.19 
 
 + 0.28 
 
 = 
 
 -2.75 
 
 xJ.27 
 
 121 
 
 + 0.42 
 
 + 0.09 
 
 + 0.81 
 
 -0.23 
 
 + 0.58 
 
 + 0. 12 
 
 1.08 
 
 + 0.48 
 
 = 
 
 2.23 
 
 -1.81 
 
 122 
 
 + 0.42 
 
 + 0.09 
 
 + 0.84 
 
 + 0.12 
 
 + 0.58 
 
 + 0.12 
 
 0.85 
 
 + 0.80 
 
 = 
 
 -0.45 
 
 0.09 
 
 123 
 
 + 0.42 
 
 + 0.09 
 
 + 0.43 
 
 + 0.73 
 
 + 0.57 
 
 + 0.12 
 
 0.12 
 
 + 1.10 
 
 = 
 
 -0.44 
 
 0.21 
 
 124 
 
 + 0.42 
 
 + 0.09 
 
 + 0.22 
 
 + 0.82 
 
 + 0.57 
 
 + 0. 12 
 
 + 0.14 
 
 + 1.16 
 
 = 
 
 0.25 
 
 0.05 
 
 125 
 
 0.62 
 
 0.08 
 
 + 1.24 
 
 -1.44 
 
 + 1.63 
 
 + 0.22 
 
 3.30 
 
 -1.23 
 
 = 
 
 + 0.50 
 
 0.03 
 
 126 
 
 1.88 
 
 -0.26 
 
 + 2.98 
 
 3.12 
 
 + 2.88 
 
 + 0.39 
 
 -5.80 
 
 0.87 
 
 = 
 
 + 0.49 
 
 -1.02 
 
 127 
 
 1.65 
 
 - 0.24 
 
 + 3.29 
 
 -1.47 
 
 + 2.65 
 
 + 0.37 
 
 5.52 
 
 + 0.04 
 
 = 
 
 + 3.61 
 
 + 2.02 
 
 128 
 
 -0.43 
 
 -0.06 
 
 + 1.57 
 
 0.43 
 
 + 1.43 
 
 + 0.20 
 
 -3.07 
 
 + 0.93 
 
 = 
 
 + 0.82 
 
 + 0.31 
 
 12!) 
 
 + 0.18 
 
 + 0.0& 
 
 -0.85 
 
 + 0.36 
 
 + 0.81 
 
 + 0.12 
 
 + 1.70 
 
 + 0.76 
 
 = 
 
 + 0.51 
 
 + 0.43 
 
 130 
 
 + 0.06 
 
 + 0.01 
 
 -1.00 
 
 + 0.24 
 
 + 0.96 
 
 + 0.14 
 
 + 2.18 
 
 + 0.27 
 
 = 
 
 0.35 
 
 - 0.56 
 
 131 
 
 -0.15 
 
 0.02 
 
 -1.22 
 
 + 0.19 
 
 + 1.15 
 
 + 0.17 
 
 + 2.58 
 
 0.38 
 
 = 
 
 + 0.88 
 
 + 0.42 
 
 132 
 
 -0.57 
 
 -0.09 
 
 -1.81 
 
 + 0.19 
 
 + 1.56 
 
 + 0.24 
 
 + 3.19 
 
 1.29 
 
 = 
 
 - 1.10 
 
 - 2.05 
 
 133 
 
 - 1.62 
 
 -0.25 
 
 -3.52 
 
 + 0.03 
 
 + 2.67 
 
 + 0,41 
 
 + 4.51 
 
 2.92 
 
 = 
 
 + 0.68 
 
 - 1.50 
 
 134 
 
 -2,41 
 
 -0.37 
 
 -4.84 
 
 -0.46 
 
 + 3.57 
 
 + 0.55 
 
 + 5.46 
 
 -4.03 
 
 = 
 
 + 3.34 
 
 + 0.29 
 
 135 
 
 -2.21 
 
 -0.34 
 
 -4.40 
 
 -1.02 
 
 + 3.22 
 
 + 0.49 
 
 + 4.97 
 
 -4.07 
 
 = 
 
 + 1.74 
 
 -0.93 
 
 136 
 
 1.18 
 
 -0.18 
 
 2.60 
 
 0.95 
 
 + 2.18 
 
 + 0.34 
 
 + 3.20 
 
 -3.21 
 
 = 
 
 + 1.44 
 
 0.00 
 
 137 
 
 -0.35 
 
 0.05 
 
 - 1.32 
 
 0.03 
 
 + 1.36 
 
 + 0.21 
 
 + 1.51 
 
 -2.54 
 
 = 
 
 + 1.09 
 
 + 0.56 
 
 138 
 
 + 0.02 
 
 0.00 
 
 -0.83 
 
 + 0.52 
 
 + 0.97 
 
 + 0.15 
 
 + 0.35 
 
 -2.12 
 
 = 
 
 + 1.32 
 
 + 1.23 
 
 139 
 
 + 0.15 
 
 + 0.03 
 
 + 0.92 
 
 + 0.09 
 
 + 0.84 
 
 + 0.14 
 
 - 1.89 
 
 + 0.22 
 
 = 
 
 -0.60 
 
 -0.59 
 
 140 
 
 -0.07 
 
 0.01 
 
 + 1.10 
 
 + 0.35 
 
 + 1.07 
 
 + 0.18 
 
 2.09 
 
 + 1.26 
 
 = 
 
 - 0.20 
 
 - 0.50 
 
 141 
 
 -0.30 
 
 0.05 
 
 + 1.35 
 
 + 0.52 
 
 + 1.29 
 
 + 0.22 
 
 -2.13 
 
 + 1.99 
 
 = 
 
 + 1.23 
 
 + 0.64 
 
 142 
 
 -1.01 
 
 -0.17 
 
 + 2.28 
 
 + 1.15 
 
 + 2.00 
 
 + 034 
 
 -2.30 
 
 + 3.70 
 
 = 
 
 + 2.00 
 
 + 0.49 
 
 143 
 
 -2.22 
 
 - 0.38 
 
 + 3.80 
 
 + 2.57 
 
 + 3.21 
 
 + 0.54 
 
 2.68 
 
 + 6.05 
 
 = 
 
 + 5.49 
 
 + 2.34 
 
 144 
 
 -2.54 
 
 -0.43 
 
 + 3.0(5 
 
 + 3.57 
 
 + 3.51 
 
 + 0.00 
 
 -2.36 
 
 + 6.78 
 
 = 
 
 + 7.55 
 
 + 3.84 
 
 145 
 
 -0.61 
 
 0.10 
 
 + 1.02 
 
 + 1.61 
 
 + 1.60 
 
 + 0.27 
 
 -1.65 
 
 + 3.56 
 
 = 
 
 + 3.16 
 
 + 1.98 
 
 146 
 
 + 0.42 
 
 + 0.03 
 
 + 0.30 
 
 + 0.80 
 
 + 0.58 
 
 + 0.05 
 
 + 0.38 
 
 + 1.13 
 
 = 
 
 0.00 
 
 0.06 
 
 147 
 
 + 0.41 
 
 + 0.03 
 
 0.80 
 
 - 0.24 
 
 + 0.59 
 
 + 0.05 
 
 + 1.02 
 
 -0.58 
 
 = 
 
 -0.11 
 
 + 0.11 
 
 148 
 
 + 0.39 
 
 + 0.03 
 
 -0.04 
 
 -0.83 
 
 + 0.62 
 
 + 0.05 
 
 + 0.06 
 
 - 1.26 
 
 = 
 
 + 1.08 
 
 + 1.40 
 
 149 
 
 + 0.34 
 
 + 0.03 
 
 + 0.56 
 
 -0.61 
 
 + 0.60 
 
 + 0.06 
 
 -0.81 
 
 - 1.12 
 
 = 
 
 -0.51 
 
 - 0.25 
 
 150 
 
 0.02 
 
 0.00 
 
 + 0.38 
 
 + 1.00 
 
 + 1.04 
 
 + 0.10 
 
 + 1.03 
 
 + 2.11 
 
 = 
 
 + 0.79 
 
 + 0.40 
 
 151 
 
 + 0.16 
 
 + 0.01 
 
 + 0.12 
 
 + 0.89 
 
 + 0.83 
 
 + 0.08 
 
 + 1,43 
 
 + 1.18 
 
 = 
 
 + 3.21 
 
 + 3.00 
 
 152 
 
 + 0.38 
 
 + 0.04 
 
 0.83 
 
 -0.03 
 
 + 0.62 
 
 + 0.06 
 
 + 0.61 
 
 - 1.11 
 
 = 
 
 + 0.34 
 
 + 0.49 
 
 153 
 
 + 0,40 
 
 + 0.04 
 
 - 0.58 
 
 - 0.59 
 
 + 0.00 
 
 + 0.0!) 
 
 -0.13 
 
 - 1.19 
 
 = 
 
 -0.29 
 
 0.00 
 
 151 
 
 + 0.42 
 
 + 0.04 
 
 + 0.06 
 
 + 0.83 
 
 + 0.59 
 
 + 0.08 
 
 -0.83 
 
 - 0.83 
 
 = 
 
 -0.08 
 
 -0.03 
 
 155 
 
 + 0,42 
 
 + 0.0 I 
 
 + 0.72 
 
 + 0,13 
 
 + 0.58 
 
 + 0.06 
 
 -0.81 
 
 + 0.85 
 
 = 
 
 + 1.01 
 
 + 1.21 
 
 30 
 
INTRODUCTION. 
 
 No. 
 
 Tin' equations derived from ihc latitudes ; contain two more unknown quantities, 
 
 v = J ?' , to = sin t'. -I Q', 
 
 lint in them tlic variation ol'tlic solar elements will be neglected. 
 Tlio mean oflhe Transits of 17(il and 17(59 gives 
 
 -0.059 x + 0.050 // 0.095: 0.069 u + 0.00 v + 1.000 w = I". 165. 
 From tins mean the indeterminate correction of the Sun's semi-diameter is nearly eliminated. 
 
 Equations of condition. 
 
 No. 
 
 
 
 
 
 
 
 
 
 H 
 
 1 
 
 - 0.01* 
 
 + 0.000 
 
 - 0.0 Iz 
 
 + 0.00 
 
 + 
 
 0.6 lv 
 
 + 1.24w 
 
 = + 
 
 0.82 
 
 2 
 
 -0.10 
 
 + 0.01 
 
 -0.21 
 
 -0.08 
 
 
 
 0.36 
 
 + 1.95 
 
 = + 
 
 0.41 
 
 3 
 
 - 0.12 
 
 + 0.02 
 
 -0.31 
 
 -0.11 
 
 
 
 1.09 
 
 + 2.04 
 
 = 
 
 0.49 
 
 4 
 
 + 0.17 
 
 -0.02 
 
 -0.41 
 
 + 0.25 
 
 
 
 2.13 
 
 + 0.88 
 
 = 
 
 0.14 
 
 5 
 
 + 0.20 
 
 -0.03 
 
 -0.37 
 
 + 0.17 
 
 
 
 .1.60 
 
 - 0.40 
 
 = 
 
 1.51 
 
 6 
 
 + 0.09 
 
 - 0.01 
 
 - 0.14 
 
 0.10 
 
 + 
 
 0.12 
 
 - 1.35 
 
 = + 
 
 0.02 
 
 7 
 
 + 0.20 
 
 - 0.02 
 
 - 0.23 
 
 - 0.35 
 
 + 
 
 1.17 
 
 - 1,12 
 
 = + 
 
 5.62 
 
 8 
 
 + 0.19 
 
 - 0.02 
 
 -0.30 
 
 -0.49 
 
 + 
 
 2.32 
 
 -0.77 
 
 = + 
 
 1.51 
 
 9 
 
 -0.14 
 
 + 0.02 
 
 - 0.51 
 
 -0.16 
 
 + 
 
 2.12 
 
 + 0.46 
 
 = + 
 
 0.64 
 
 10 
 
 -0.23 
 
 + 0.03 
 
 -0.54 
 
 - 0.07 
 
 + 
 
 1.88 
 
 + 1.10 
 
 = 
 
 1.70 
 
 11 
 
 - 0.18 
 
 + 0.02 
 
 -0.36 
 
 -0.10 
 
 + 
 
 1.05 
 
 + 1.38 
 
 
 1.48 
 
 12 
 
 - 0.22 
 
 + 0.02 
 
 - 0.01 
 
 - 0.58 
 
 
 
 2.3 1 
 
 -0.09 
 
 = 
 
 1.49 
 
 13 
 
 + 0.11 
 
 -0.01 
 
 - 0.33 
 
 - 0.36 
 
 
 
 2.06 
 
 - 1.55 
 
 = + 
 
 1.04 
 
 14 
 
 + 0.12 
 
 -0.01 
 
 + 0.21 
 
 -0.24 
 
 + 
 
 1.57 
 
 + 1.68 
 
 = + 
 
 0.31 
 
 15 
 
 - 0.03 
 
 0.00 
 
 - 0.02 
 
 - 0.0!) 
 
 + 
 
 0.06 
 
 + 2.31 
 
 = + 
 
 0.63 
 
 
 
 
 
 31 
 
 
 
 
 
 
 156 
 
 4-0. i\.i 
 
 4- 0.0 [it 0.25* 0.814-0.69a 
 
 > 4- 0.064 
 
 ,/_o.ioy 4- i.2iH'= 4- 
 
 0.38 
 
 4-0.75 
 
 157 
 
 4-0.3!) 
 
 4- o.o i 
 
 0,11 
 
 4- 0.72 
 
 4- 0.60 
 
 4-0.06 
 
 4- 0.65 
 
 4- i.os 
 
 = 
 
 0.61 
 
 0.57 
 
 158 
 
 4- 0.35 
 
 4-0.01 
 
 - 0,s:, 
 
 4-0.01 
 
 4- 0.65 
 
 4-0.07 
 
 4- 1.38 
 
 4- 0.2 1 
 
 = 
 
 1.16 
 
 - 1.04 
 
 159 
 
 4-0.1!) 
 
 4- 0.02 
 
 -0.61 
 
 - O.(i5 
 
 4-0.81 
 
 4- o.08 
 
 4- 1.26 
 
 - 1.29 
 
 = 
 
 0.19 
 
 - 0.07 
 
 160 
 
 4-0.21 
 
 4- 0.02 
 
 -)- 0.35 
 
 0.80 
 
 4-0.77 
 
 4- 0.08 
 
 - 1.76 
 
 -0.15 
 
 = 4- 
 
 i..-,o 
 
 4- 1.69 
 
 161 
 
 4- 0.3 1 
 
 4-0.01 
 
 4-o.Ni 
 
 0.21 
 
 4- 0.66 
 
 4-0.07 
 
 -O.iM 
 
 4- 1.06 
 
 = 
 
 0.53 
 
 0.30 
 
 162 
 
 4-o.:ii 
 
 4- 0.06 
 
 0.63 
 
 4- 0.52 
 
 4- 0.66 
 
 4-0.11 
 
 4- 1.25 
 
 0.55 
 
 1 
 
 1.72 
 
 4- 1.80 
 
 163 
 
 4- 0.3S 
 
 4- 0.07 
 
 - 0.82 
 
 - 0.05 
 
 4- 0.62 
 
 4- o. 1 1 
 
 4-0.60 
 
 - 1.10 
 
 = + 
 
 0.98 
 
 4- 1.22 
 
 161 
 
 4- o. 12 
 
 4- 0.07 
 
 - 0.02 
 
 0.85 
 
 4- 0.59 
 
 4-0.10 
 
 - O.7.") 
 
 - 0.90 
 
 = 
 
 0.97 
 
 - 0.50 
 
 165 
 
 4- o. 12 
 
 4-0.07 
 
 4- O.S3 
 
 0.13 
 
 4- 0.5S 
 
 4-0.10 
 
 - 1.13 
 
 4- 0.28 
 
 = 4- 
 
 0.52 
 
 4- 0.89 
 
 166 
 
 4- o. 1 1 
 
 4-0.07 
 
 4- 0.6 1 
 
 4- 0.55 
 
 4- 0.58 
 
 4-0.10 
 
 -0.70 
 
 4- 0.!)5 
 
 = 4-0.01 
 
 4-0.24 
 
 167 
 
 4-0.17 
 
 4- 0.03 
 
 4- 0.2!) 
 
 - O.N5 
 
 4- O.S3 
 
 4-0.16 
 
 - 1.81 
 
 - 0. 13 
 
 = 4- 
 
 1.38 
 
 4- 1.57 
 
 168 
 
 4- 0.35 
 
 4- 0.07 
 
 4- 0.82 
 
 - 0. 10 
 
 4- 0.65 
 
 4-0.12 
 
 - 1.16 
 
 -f-0.75 
 
 = 4- 
 
 0.61 
 
 4-0.90 
 
 16!) 
 
 4- 0.38 
 
 4- 0.07 
 
 4- 0.75 
 
 4- 0.38 
 
 4-0.61 
 
 4-0.12 
 
 0.07 
 
 4- 1.29 
 
 = + 
 
 0.85 
 
 4- 1.09 
 
 170 
 
 4- 0. 12 
 
 4- 0.08 
 
 - 0.7!) 
 
 4- 0.24 
 
 4-0.58 
 
 4-0.11 
 
 4- 1.10 
 
 0.35 
 
 = 
 
 0.73 
 
 -0.48 
 
 m 
 
 4- o. 12 
 
 4-0.08 
 
 0.35 
 
 -0.76 
 
 4- 0.5!) 
 
 4-o.li 
 
 4-0.18 
 
 - 1.15 
 
 = 
 
 0.27 
 
 4- 0.20 
 
 17--' 
 
 4- o. 12 
 
 4-0.08 
 
 4-0.27 
 
 -0.81 
 
 4- 0.58 
 
 4- o. 1 1 
 
 -0.50 
 
 - 1.05 
 
 = 
 
 3.06 
 
 2.55 
 
 173 
 
 4- 0.3S 
 
 4-0.07 
 
 4-0.79 
 
 - 0.27 
 
 4- 0.62 
 
 4-0.12 
 
 - 1.27 
 
 -0.50 
 
 = 
 
 0.26 
 
 4-0.10 
 
 11 1 
 
 4-0.31 
 
 4-0.06 
 
 4-0.81 
 
 4 0.20 
 
 4- 0.6 I 
 
 4-0.13 
 
 - 1.35 
 
 4-0.18 
 
 = 
 
 2.86 
 
 2.65 
 
 L75 
 
 4- 0.32 
 
 4- o.oe 
 
 4- 0.65 
 
 4- 0.55 
 
 4-0.68 
 
 4-0.13 
 
 1.25 
 
 4-0.80 
 
 = 
 
 0.73 
 
 0.60 
 
No. 
 
 INTRODUCTION. 
 
 Equations of condition. 
 
 
 
 
 
 
 
 
 // 
 
 16 
 
 + 0.02x 
 
 O.OOy 
 
 + 0.01% 
 
 + O.OSw 
 
 - 0.75i. 
 
 + 1.69w 
 
 = -0.77 
 
 17 
 
 + 0.01 
 
 0.00 
 
 - 0.07 
 
 + 0.04 
 
 + 0.27 
 
 -2.68 
 
 = + 2.21 
 
 18 
 
 -0.15 
 
 + 0.01 
 
 -0.12 
 
 + 0.32 
 
 + 1.60 
 
 1.45 
 
 = + 0.21 
 
 19 
 
 + 0.01 
 
 0.00 
 
 + 0.02 
 
 0.00 
 
 + 0.78 
 
 + 0.97 
 
 = + 1.13 
 
 20 
 
 + 0.10 
 
 0.00 
 
 0.38 
 
 + 0.18 
 
 -2.05 
 
 + 1.36 
 
 = - 0.77 
 
 21 
 
 + 0.11 
 
 0.00 
 
 -0.17 
 
 - 0.11 
 
 + 0.33 
 
 - 1.45 
 
 = + 0.53 
 
 22 
 
 + 0.23 
 
 -0.01 
 
 0.28 
 
 -0.45 
 
 + 1.G3 
 
 - 1.35 
 
 = + 0.73 
 
 23 
 
 - 0.23 
 
 + 0.01 
 
 - 0.57 
 
 0.06 
 
 + 2.13 
 
 + 0.86 
 
 - 1.07 
 
 24 
 
 - 0.13 
 
 0.00 
 
 0.12 
 
 0.25 
 
 - 0.86 
 
 + 1.09 
 
 = + 0.95 
 
 25 
 
 0.17 
 
 0.00 
 
 0.07 
 
 -0.56 
 
 - 2.43 
 
 - 0.35 
 
 = - 0.67 
 
 26 
 
 + 0.07 
 
 0.00 
 
 - 0.09 
 
 - 0.11 
 
 + 0.09 
 
 1.54 
 
 = + 0.53 
 
 27 
 
 + 0.10 
 
 0.00 
 
 + 0.18 
 
 - 0.2 1 
 
 + 1.52 
 
 + 1.83 
 
 = - 0.65 
 
 
 1 
 
 
 
 
 
 
 
 28 
 
 + 0.01 
 
 0.00 
 
 0.00 
 
 + 0.02 
 
 - 0.62 
 
 + 1.79 
 
 = + 3.82 
 
 29 
 
 -0.06 
 
 0.00 
 
 + 0.14 
 
 -0.05 
 
 - 1.03 
 
 - 1.91 
 
 = 2.56 
 
 30 
 
 0.00 
 
 0.00 
 
 -0.07 
 
 + 0.07 
 
 + 0.49 
 
 - 2.67 
 
 = - 0.52 
 
 31 
 
 0.15 
 
 0.00 
 
 - 0.15 
 
 + 0.29 
 
 + 1.60 
 
 - 0.73 
 
 = - 0.13 
 
 32 
 
 - 0.10 
 
 0.00 
 
 0.30 
 
 -0.06 
 
 - 1.04 
 
 + 2.13 
 
 == + 0.55 
 
 33 
 
 + 0.21 
 
 + 0.01 
 
 -0.38 
 
 + 0.27 
 
 - 1.92 
 
 + 0.18 
 
 = - 0.52 
 
 34 
 
 + 0.16 
 
 0.00 
 
 -0.30 
 
 + 0.10 
 
 - 1.27 
 
 - 0.63 
 
 = - 0.79 
 
 35 
 
 + 0.14 
 
 + 0.01 
 
 - 0.21 
 
 - 0.20 
 
 + 0.59 
 
 - 1.51 
 
 = - 0.38 
 
 36 
 
 + 0.22 
 
 + 0.01 
 
 -0.27 
 
 -0.39 
 
 + 1.41 
 
 - 1.47 
 
 = + 1.29 
 
 37 
 
 + 0.16 
 
 + 0.01 
 
 -0.37 
 
 - 0.44 
 
 + 2.39 
 
 -0.81 
 
 = - 0.72 
 
 38 
 
 -0.16 
 
 -0.01 
 
 - 0.12 
 
 -0.30 
 
 -0.98 
 
 + 1.12 
 
 = + 0.33 
 
 39 
 
 - 0.18 
 
 0.01 
 
 -0.09 
 
 - 0.56 
 
 -2.43 
 
 - 0.21 
 
 = + 2.84 
 
 40 
 
 + 0.17 
 
 + 0.01 
 
 -0.42 
 
 0.29 
 
 - 1.88 
 
 - 1.59 
 
 = - 1.00 
 
 41 
 
 + 0.06 
 
 0.00 
 
 -0.08 
 
 - 0.10 
 
 + 0.20 
 
 - 1.44 
 
 = + 0.10 
 
 42 
 
 + 0.06 
 
 0.00 
 
 -0.06 
 
 - 0.11 
 
 + 031 
 
 - 0.86 
 
 = + 0.03 
 
 43 
 
 + 0.13 
 
 + 0.01 
 
 + 0.04 
 
 -0.25 
 
 + 1.18 
 
 - 0.46 
 
 = + 0.64 
 
 44 
 
 + 0.18 
 
 + 0.01 
 
 + 0.22 
 
 - 0.32 
 
 + 1.78 
 
 + 0.86 
 
 = - 0.92 
 
 45 
 
 -0.05 
 
 0.00 
 
 - 0.03 
 
 -0.14 
 
 + 0.33 
 
 + 2.36 
 
 = - 0.04 
 
 46 
 
 + 0.02 
 
 0.00 
 
 + 0.01 
 
 + 0.05 
 
 0.80 
 
 + 1.48 
 
 = + 0.66 
 
 47 
 
 + 0.05 
 
 0.00 
 
 0.01 
 
 + 0.10 
 
 - 1.04 
 
 + 0.90 
 
 = + 0.64 
 
 48 
 
 0.03 
 
 0.00 
 
 -0.05 
 
 0.05 
 
 + 0.03 
 
 + 0.70 
 
 = + 0.07 
 
 49 
 
 - 0.07 
 
 -0.01 
 
 -0.02 
 
 -0.13 
 
 - 0.68 
 
 + 0.61 
 
 = - 1.75 
 
 50 
 
 -0.09 
 
 0.01 
 
 + 0.09 
 
 - 0.16 
 
 1.15 
 
 + 0.14 
 
 = - 0.90 
 
 51 
 
 0.11 
 
 -0.01 
 
 + 0.19 
 
 - 0.12 
 
 - 1.37 
 
 1.06 
 
 = - 3.16 
 
 52 
 
 -0.03 
 
 0.00 
 
 + 0.09 
 
 - 0.03 
 
 0.71 
 
 - 2.35 
 
 - 4.41 
 
 53 
 
 - 0.03 
 
 0.00 
 
 -0.07 
 
 + 0.13 
 
 + 0.84 
 
 2.49 
 
 = 1.78 
 
 51 
 
 - 0.14 
 
 - 0.01 
 
 - 0.10 
 
 + 0.29 
 
 + 1.54 
 
 1.26 
 
 = + 3.67 
 
 55 
 
 - 0.12 
 
 -0.01 
 
 - 0.14 
 
 + 0.19 
 
 + 1.45 
 
 - 0.21 
 
 = + 0.35 
 
 56 
 
 + 0.04 
 
 0.00 
 
 + 0.06 
 
 -0.05 
 
 + 0.93 
 
 + 0.14 
 
 = + 1.39 
 
 57 
 
 + 0.03 
 
 0.00 
 
 + 0.05 
 
 - 0.02 
 
 + 0.90 
 
 + 0.79 
 
 = + 1.57 
 
 58 
 
 -0.05 
 
 0.00 
 
 0.10 
 
 - 0.02 
 
 + 0.18 
 
 + 1.80 
 
 = +2.67 
 
 59 
 
 -0.08 
 
 0.01 
 
 - 0.30 
 
 0.03 
 
 - 1.11 
 
 + 2.13 
 
 = + 2.72 
 
 60 
 
 + 0.16 
 
 + 0.02 
 
 0.31 
 
 + 0.13 
 
 1.37 
 
 0.50 
 
 = + 0.58 
 
 
 
 
 
 32 
 
 
 
 
 
 
 
No. 
 
 INTRODUCTION. 
 
 iif riin/liliiin. 
 
 61 
 
 4- O.I Or 
 
 4- 0.01// 
 
 -0.19; 
 
 - 0.01 it 
 
 0.63r 
 
 - O.'IOrc = 
 
 - 0.01 
 
 69 
 
 0.00 
 
 0.00 
 
 0.01 
 
 
 0.00 
 
 
 
 0.70 
 
 - 0.73 = 
 
 - 1.35 
 
 63 
 
 4- 0.0 1 
 
 D.OD 
 
 -0.07 
 
 
 
 0.02 
 
 
 
 0.37 
 
 4- 
 
 1.15 
 
 = 
 
 - 1.50 
 
 61 
 
 4- 0.13 
 
 4- 0.01 
 
 - 0.20 
 
 
 
 0.17 
 
 4 
 
 0.11 
 
 - 1.54 = 
 
 - 0.74 
 
 65 
 
 4- 0.22 
 
 4- 0.03 
 
 - 0.3 1 
 
 
 
 0.17 
 
 + 
 
 2.01 
 
 - 1.19 = 
 
 - 3.3S 
 
 66 
 
 0.-2 I 
 
 0.03 
 
 0.59 
 
 
 
 0.02 
 
 4- 
 
 2.26 
 
 + 
 
 0.54 
 
 = 
 
 4- 2,16 
 
 67 
 
 0.0s 
 
 0.01 
 
 - 0.14 
 
 
 
 0.09 
 
 f 
 
 0.1(1 
 
 f. 
 
 1.2.') 
 
 mm 
 
 -0.29 
 
 6S 
 
 0.03 
 
 0.00 
 
 -0.03 
 
 
 
 ().().-, 
 
 
 
 0. 10 
 
 + 
 
 0.89 
 
 = 
 
 4- 3.00 
 
 69 
 
 -0.01 
 
 0.00 
 
 0.07 
 
 
 
 0.03 
 
 + 
 
 0.2(i 
 
 f 
 
 0.90 
 
 = 
 
 4- 0.62 
 
 70 
 
 0.07 
 
 -0.01 
 
 0.09 
 
 
 
 0.11 
 
 
 
 0.36 
 
 4 
 
 1.15 
 
 = 
 
 -2.16 
 
 71 
 
 -0.11 
 
 0.02 
 
 - 0.13 
 
 
 
 0.2.-. 
 
 
 
 0.80 
 
 4- 
 
 1.15 
 
 
 
 - 3.21 
 
 72 
 
 - 0.23 
 
 0.03 
 
 - 0.07 
 
 
 
 0.49 
 
 
 
 1.74 
 
 4- 
 
 0.76 
 
 = 
 
 0.32 
 
 73 
 
 -0.17 
 
 0.02 
 
 - 0.12 
 
 
 
 o..-.( ; 
 
 
 
 2.41 
 
 
 
 0.21 
 
 = 
 
 4- 2. 10 
 
 71 
 
 4- 0.16 
 
 4- 0.02 
 
 0.2s 
 
 
 
 0.18 
 
 
 
 0.74 
 
 
 
 1.75 
 
 = 
 
 - 2.59 
 
 75 
 
 4-0.04 
 
 4- 0.01 
 
 0.05 
 
 
 
 0.07 
 
 + 
 
 0.33 
 
 
 
 1.30 
 
 = 
 
 -0.70 
 
 76 
 
 4-0.06 
 
 4-0.01 
 
 -0.07 
 
 
 
 0.10 
 
 + 
 
 0.26 
 
 
 
 0.86 
 
 = 
 
 -0.80 
 
 77 
 
 4- 0.16 
 
 4- 0.02 
 
 4-0.09 
 
 
 
 0.30 
 
 4- 
 
 1.13 
 
 
 
 0.21 
 
 = 
 
 4-0.69 
 
 78 
 
 4-0.19 
 
 4- 0.03 
 
 4- 0.21 
 
 
 
 0.31 
 
 4- 
 
 1.75 
 
 4- 
 
 0.50 
 
 = 
 
 4- 0.68 
 
 79 
 
 4- 0.13 
 
 4- 0.02 
 
 + 0.20 
 
 
 
 0.30 
 
 4- 
 
 1.72 
 
 + 
 
 1.54 
 
 = 
 
 -0.50 
 
 80 
 
 4- 0.01 
 
 0.00 
 
 4- 0.03 
 
 
 
 0.17 
 
 4- 
 
 1.22 
 
 4- 
 
 2.20 
 
 = 
 
 4- 0,45 
 
 81 
 
 -0.01 
 
 0.01 
 
 - 0.03 
 
 
 
 0.09 
 
 4- 
 
 0.07 
 
 4. 
 
 2.22 
 
 
 
 4- 0.26 
 
 82 
 
 4- 0.02 
 
 0.00 
 
 4-0.01 
 
 4- 
 
 0.01 
 
 
 
 0.76 
 
 4- 
 
 1.50 
 
 = 
 
 0.82 
 
 83 
 
 4- 0.04 
 
 4- 0.01 
 
 0.00 
 
 4- 
 
 o.os 
 
 
 
 0.99 
 
 + 
 
 1.02 
 
 = 
 
 -0.72 
 
 SI 
 
 4- O.or. 
 
 4- 0.01 
 
 - 0.01 
 
 4- 
 
 0.10 
 
 
 
 1.06 
 
 + 
 
 0.30 
 
 = 
 
 -0.07 
 
 85 
 
 - O.OS 
 
 -0.01 
 
 4- 0.01 
 
 
 
 0.16 
 
 
 
 0.88 
 
 + 
 
 0.49 
 
 = 
 
 4- O.H3 
 
 86 
 
 -0.11 
 
 - 0.02 
 
 4- 0.12 
 
 
 
 0.17 
 
 
 
 1.29 
 
 
 
 0.09 
 
 - 
 
 1.35 
 
 87 
 
 - 0.12 
 
 -0.02 
 
 4- 0.17 
 
 
 
 0.16 
 
 
 
 1.41 
 
 
 
 0.56 
 
 = 
 
 4- 0,15 
 
 88 
 
 0.10 
 
 0.02 
 
 4- 0.20 
 
 
 
 0.09 
 
 
 
 1.26 
 
 
 
 1.63 
 
 = 
 
 -0.07 
 
 89 
 
 - 0.03 
 
 0.00 
 
 4-0.07 
 
 
 
 0.04 
 
 
 
 0.61 
 
 
 
 2.49 
 
 = 
 
 4- 0.5S 
 
 90 
 
 -0.09 
 
 0.02 
 
 -0.05 
 
 4- 
 
 0.23 
 
 4- 
 
 1.23 
 
 
 
 2.00 
 
 = 
 
 4- 1.11 
 
 91 
 
 0.11 
 
 0.02 
 
 -0.17 
 
 4- 
 
 0.15 
 
 4- 
 
 1.24 
 
 4- 
 
 0.17 
 
 = 
 
 4- 0.70 
 
 92 
 
 -0.01 
 
 -0.01 
 
 0.07 
 
 
 
 0.03 
 
 4- 
 
 0.01 
 
 + 
 
 0.75 
 
 
 
 - O.I!) 
 
 93 
 
 4-0.01 
 
 4-0.01 
 
 4-0.06 
 
 
 
 0.05 
 
 4- 
 
 0.96 
 
 4- 
 
 0.26 
 
 = 
 
 4- O.N3 
 
 94 
 
 4- 0.03 
 
 4- 0.01 
 
 4- 0.06 
 
 
 
 0.02 
 
 + 
 
 0.95 
 
 4- 
 
 0.6!) 
 
 = 
 
 4- 0.99 
 
 95 
 
 4-0.02 
 
 0.00 
 
 4- 0.0 1 
 
 
 
 0.01 
 
 + 
 
 0.82 
 
 4- 
 
 1.06 
 
 = 
 
 4- 0.89 
 
 96 
 
 -0.02 
 
 0.00 
 
 0.04 
 
 
 0.00 
 
 4- 
 
 0.44 
 
 4- 
 
 1.61 
 
 
 
 4- 0.92 
 
 97 
 
 -0.09 
 
 - 0.02 
 
 -0.21 
 
 
 
 0.05 
 
 
 
 on 
 
 -f 
 
 2.14 
 
 ^ 
 
 4- 0.44 
 
 98 
 
 - 0.03 
 
 0.00 
 
 -0.31 
 
 4- 
 
 0.05 
 
 
 
 i.ii 
 
 | 
 
 2.02 
 
 = 
 
 4- 1.56 
 
 99 
 
 4- 0.14 
 
 4-0.03 
 
 0.33 
 
 + 
 
 0.27 
 
 
 
 1.96 
 
 4- 
 
 1.25 
 
 = 
 
 - 1.15 
 
 100 
 
 4- 0.20 
 
 4- 0.01 
 
 - 0.3 1 
 
 4- 
 
 0.26 
 
 
 
 1.79 
 
 4- 
 
 0.12 
 
 = 
 
 -0.91 
 
 101 
 
 4- 0.17 
 
 4- 0.03 
 
 0.31 
 
 4- 
 
 0.17 
 
 
 
 1.48 
 
 
 
 0.35 
 
 = 
 
 4- 0.19 
 
 102 
 
 4-0.14 
 
 4- 0.03 
 
 - 0.27 
 
 4- 
 
 0.09 
 
 
 
 1.18 
 
 
 
 0.62 
 
 = 
 
 0.52 
 
 103 
 
 4-0.10 
 
 4- 0.02 
 
 - 0.20 
 
 
 0.00 
 
 
 
 0.72 
 
 
 
 O.S6 
 
 = 
 
 -0.60 
 
 104 
 
 Q.01 
 
 0.00 
 
 4- 0.01 
 
 
 0.00 
 
 
 
 0.79 
 
 
 
 0.52 
 
 = 
 
 + 0.02 
 
 105 
 
 4- 0.03 
 
 4-0.01 
 
 0.06 
 
 
 
 0.01 
 
 
 
 0. 13 
 
 
 
 1.12 
 
 = 
 
 4- 0.74 
 
 5V 
 
 
 
 
 33 
 
 
 
 
 
 
 
 
No. 
 
 INTRODUCTION 
 
 Iniiulionfs of condition. 
 
 106 
 
 + 0.07* 
 
 + 0.01/y 
 
 0.13; 
 
 0.06 
 
 - O.OSy 
 
 - 1.38(0 
 
 = + 1.18 
 
 107 
 
 + 0.20 
 
 + 0.04 
 
 0.28 
 
 -0.33 
 
 + 1.14 
 
 1.61 
 
 = + 0.54 
 
 108 
 
 + 0.05 
 
 + 0.01 
 
 0.46 
 
 0.30 
 
 + 2.47 
 
 - 0.62 
 
 = + 0.96 
 
 109 
 
 - 0.24 
 
 0.05 
 
 0.53 
 
 0.00 
 
 + 1.77 
 
 + 0.94 
 
 = + 0.22 
 
 110 
 
 0.16 
 
 0.03 
 
 - 0.31 
 
 0.07 
 
 + 0.88 
 
 + 1.27 
 
 = + 1.94 
 
 111 
 
 -0.12 
 
 0.02 
 
 0.23 
 
 0.09 
 
 + 0.56 
 
 + 1.28 
 
 = + 1.03 
 
 112 
 
 0.08 
 
 0.02 
 
 0.14 
 
 -0.09 
 
 + 0.16 
 
 + 1.20 
 
 = + 1.81 
 
 113 
 
 -0.01 
 
 0.00 
 
 0.01 
 
 0.03 
 
 0.57 
 
 + 0.65 
 
 = ;- 0.34 
 
 125 
 
 0.17 
 
 0.02 
 
 0.12 
 
 -0.33 
 
 - 1.12 
 
 -f 1.08 
 
 = + 1.69 
 
 126 
 
 - 0.23 
 
 0.03 
 
 - 0.07 
 
 - 0.49 
 
 - 2.24 
 
 + 0.23 
 
 = + 1.42 
 
 127 
 
 + 0.19 
 
 + 0.03 
 
 - 0.39 
 
 0.22 
 
 - 1.30 
 
 - 1.73 
 
 = + 0.59 
 
 128 
 
 + 0.06 
 
 + 0.01 
 
 0.08 
 
 0.10 
 
 + 0.16 
 
 1.43 
 
 = + 0.76 
 
 J29 
 
 + 0.05 
 
 + 0.01 
 
 -0.07 
 
 -0.08 
 
 + 0.11 
 
 -0.85 
 
 = - 0.11 
 
 130 
 
 + 0.08 
 
 + 0.01 
 
 -0.05 
 
 0.16 
 
 + 0.56 
 
 0.85 
 
 = + 0.64 
 
 131 
 
 + 0.12 
 
 + 0.02 
 
 + 0.01 
 
 0.2 1 
 
 + 1.03 
 
 0.61 
 
 = + 0.74 
 
 132 
 
 + 0.17 
 
 + 0.02 
 
 + 0.12 
 
 0.31 
 
 + 1.51 
 
 0.08 
 
 = + 1.60 
 
 133 
 
 + 0.18 
 
 + 0.03 
 
 + 0.24 
 
 - 0.33 
 
 + 1.81 
 
 + 1.08 
 
 = + 1.68 
 
 134 
 
 + 0.07 
 
 + 0.01 
 
 + 0.13 
 
 - 0.29 
 
 + 1.47 
 
 + 1.98 
 
 = -0.50 
 
 135 
 
 -0.06 
 
 0.01 
 
 -0.05 
 
 0.18 
 
 + 0.46 
 
 + 2.34 
 
 = + 0.90 
 
 136 
 
 -0.01 
 
 0.00 
 
 0.00 
 
 0.01 
 
 - 0.51 
 
 + 1.80 
 
 = 0.11 
 
 137 
 
 + 0.05 
 
 + 0.01 
 
 - 0.01 
 
 + 0.09 
 
 - 1.03 
 
 + 0.84 
 
 = - 0.35 
 
 138 
 
 + 0.05 
 
 + 0.01 
 
 -0.06 
 
 + 0.09 
 
 - 0.99 
 
 + 0.03 
 
 = + 0.88 
 
 139 
 
 -0.06 
 
 -0.01 
 
 0.02 
 
 -0.12 
 
 -0.56 
 
 + 0.66 
 
 = -0.91 
 
 140 
 
 -0.09 
 
 0.02 
 
 + 0.07 
 
 -0.17 
 
 - 1.13 
 
 + 0.23 
 
 = -0.84 
 
 141 
 
 -0.11 
 
 - 0.02 
 
 + 0.14 
 
 -0.17 
 
 - 1.34 
 
 0.22 
 
 - 1.90 
 
 142 
 
 -0.11 
 
 - 0.02 
 
 + 0.21 
 
 -0.11 
 
 - 1.37 
 
 - 1.26 
 
 = 1.37 
 
 143 
 
 -0.04 
 
 0.01 
 
 + 0.11 
 
 -0.05 
 
 -0.77 
 
 2.38 
 
 = -0.65 
 
 144 
 
 -0.03 
 
 -0.01 
 
 -0.05 
 
 + 0.12 
 
 + 0.77 
 
 -2.51 
 
 = + 3.52 
 
 145 
 
 0.14 
 
 - 0.02 
 
 0.14 
 
 + 0.24 
 
 + 1.48 
 
 - 0.50 
 
 = + 0.28 
 
 To apply to these equations the rigorous method of least squares would be very laborious: hence a method 
 of " Equivalent Factors" has been used; the equations have been multiplied either by. whole numbers or by frac- 
 tions which are ready multipliers. In this way, the following Normal Equations were derived from tho equations 
 of condition which have cos ij. A for their absolute terms, 
 
 // 
 
 + 195.841- 44.809y + 127.71z + 73.19;t 251.90^ + 43.027/ 85.48;' + 119.25u' =- 8.77 
 _ 44.78 +47.099 - 83.68 62.84 + 41.04 48.460 + 41.17 - 96.06 = 113.43 
 + 120.94 83.889 +427.28 +133.17 -136.59 +82.936 -410.76 +400-15 = +162.30 
 + 70.03 62.965 +135.64 +365.81 - 73.13 +63.350 +114.76 +508.04 = +197.06 
 
 255.15 +42.172 -138.12 - 80.06 +125.64 27.182 + 91.22 132.67 = + 92.63 
 
 + 40.68 -48.373 + 82.84 + 61.99 - 26.27 +51.815 - 41.45 + 94.13 = +121.18 
 
 - 83.42 +41.537 -422.53 +119.76 +102.83 40.091 +644.06 -111.82 = 23.87 
 
 + 112.81 95.792 +406.68 +505.65 -126.69 +94.621 120.34 +902.21 = +264.18 
 
 34 
 
I NTKODUCTION. 
 
 It' ii is eliminated IVoin these equations, tin' result is 
 
 + 
 
 L81.8& 
 
 -32.2130 +100.57: 
 
 -237. 27.' 
 
 + 30.352//' 108 
 
 .11-.' + 17.60' = - 
 
 IS.'-JO 
 
 
 
 
 + 36.\!s 1 - 6().:{s 
 
 + 28. |s 
 
 -37.577 
 
 + 60. ss 
 
 8.78 = 
 
 
 + 
 
 95. 15 
 
 -60.971 +377.!)0 
 
 109.H7 
 
 | 59. si 1 
 
 -452.54 
 
 + 215.20 = 
 
 + 
 
 90.5:; 
 
 281 
 
 + 28.391 ION. 13 
 
 + 109.63 
 
 -13.317 
 
 + 116.31 
 
 - 21. 
 
 18 
 
 - 
 
 + 
 
 135.K; 
 
 + 
 
 28.81 
 
 -37.705 4- 59.N5 
 
 - 13.ss 
 
 + 11. Os() 
 
 - 60.90 
 
 + 8.04 = 
 
 4- 
 
 
 
 
 106.35 
 
 ! 1 17 466.91 
 
 + 126.77 
 
 60.831 
 
 + 606. 
 
 111 
 
 278.15 = 
 
 88.88 
 
 + 
 
 16.01 
 
 _ s.770 +219. IS 
 
 - 25.60 
 
 + 7.0r>3 
 
 -27S.91 
 
 + 199.94 = 
 
 
 And if from tip liminated. the result is 
 
 + 156.13.C -15.9S7// 20S.OO.C' +14 
 
 .US,/' 
 
 + 11.99.:' 
 
 
 -39.67"' 
 
 // 
 = - 72.30 
 
 
 17 
 
 .50 +26.512 + 
 
 1091 28 
 
 .055 
 
 -11.42 
 
 
 +25.60 
 
 = 
 
 
 
 G5 
 
 .11 
 
 212,13 +10.900 +378.0S + 3 
 
 .863 
 
 -13.51 
 
 
 + 10.27 
 
 = 
 
 + 
 
 161 
 
 .74 
 
 
 + 13 
 
 .6!) -28.019 + 
 
 3.51 +31 
 
 .598 
 
 + 10.77 
 
 
 -26.01 
 
 = 
 
 + 
 
 73. 15 
 
 
 + U 
 
 .59 -13.190 
 
 9.11 +13 
 
 .151 
 
 +47.33 
 
 
 12.25 
 
 = 
 
 i- 
 
 23 
 
 .52 
 
 
 - 39 
 
 .35 +26.593 + 
 
 38.18 -27.674 
 
 -16.50 
 
 
 +75.13 
 
 = 
 
 
 
 61 
 
 .46 
 
 It is evident now, that since the principal co-efficients of:' and u' have fallen from <> 1 1.06 and 902.21 to i7.33 
 and 75.13, no very reliable values of these quantities can he obtained from these equations. The elimination ol 
 // gives 
 
 + 145.89J' 
 
 201.13.1' 
 
 - 2.1SO//' 
 
 + 5.112' 
 
 24.25w' 
 
 = 111.52 
 
 -205.2 1 
 
 + 373.60 
 
 + 15.384 
 
 - 8.82 
 
 +29.76 
 
 = +188.48 
 
 - 4.80 
 
 - 15.07 
 
 + 1.950 
 
 - 1.30 
 
 - 1.01 
 
 = + 4.64 
 
 + 2.89 
 
 - 3.69 
 
 - 0.791 
 
 +41.65 
 
 + 0.47 
 
 = - 8.84 
 
 - 21.82 
 
 + 27.25 
 
 + 0.435 
 
 - 5.06 
 
 +49.48 
 
 = + 3.78 
 
 The elimination of # from these gives 
 
 + 90.23^ +11.895)/' 1.63;' 
 
 + 8.11 + 1.868 1.13 
 
 + 0.30 - 0.742 +41.55 
 
 2.88 + O.Ofil 4.30 
 
 - 4.35' 
 + 0.21 
 + 0.95 
 +45.85 
 
 = +31.63 
 = + 0.97 
 = - G.63 
 = -12.89 
 
 The elimination of x' from these gives 
 
 +0.755//' - 0.98.Z' + 0.62w' = - 1.99 
 0.782 +41.56 + 0.96 = 6.74 
 +0.444 - 4.35 +45.71 = -11.88 
 
 The only condition, relative to the solar elements, which can be obtained with any weight, from these equa- 
 tions, is 
 
 x 1 + 0.132 \f + 0".335. 
 
 That is, the mean longitude of the Sun of HANSEN and OLUFSEN'S Tables ought to be increased by a third of a 
 second at the epoch 1863. As, however, these Tables will, probably, be used, for a long time to come, in rom- 
 puting the solar eo<'irdinatfs of the Amrricitu l:'ji/n'mi'ria, i/', ~J and it' will be put severally equal to zero; and as 
 it lias been decided to use the 1'ulkova constant of aberration, ,r' will he put equal to + 0".19. With these 
 assumptions, the values of x, y, z and are 
 
 - 0".502, // = - 2".N63, z = - 0".040, u = + 0".195. 
 
 The equation of condition derived from the Transits of 1761 and 1769 being excluded, the normal equations, 
 determining the corrections of the inclination and the longitude of the ascending node, are 
 
 + 2.51 x + 0.390 y + 1.84 s - 0.67 u + 163.26 v - 0,42 w = + 26".(>2 
 -1,16 -0.105 -(V) -1.06 - 5.86 +188.58 = + 24.11 
 
 35 
 
INTRODUCTION. 
 
 From these arc obtained tlie following values of o and w. 
 
 v = + 0".18 Z w = + 0".12 or J Q' == + 2".0. 
 
 But from the equation furnished by the Transits in 1761 and 17(59, 
 
 J 8' = - 17".84. 
 
 If the first result is suppose,! to belong to 1855.0, and the second to 1765.4, the proper value of the correction is 
 
 J Q' = + 0".9 + W2-J2 I. 
 
 The origin of the pretty large correction 0".02863, of the mean motion of Venus, is easily shown. In his 
 investigation, LEVEKKIKK (Ainin/m, Vol. VI., p. 72) found the following value of J ', 
 J n' = + 0".00085 + 0".0689 v + 0".0959 >' + 0".1207 /'; 
 
 but the value of this quantity used in forming his Tables is the first term only. If the values of v, v 1 and /' cor- 
 responding to the change from LEVERRIER'S values of the masses to those here adopted, be substituted in this 
 expression, the correction of LEVERRIER'S mean motion, from this cause, is found to be 
 
 J .' = 0".01588. 
 
 Moreover, a comparison of the values of the Sun's mean longitude in the Tables of HANSEN and OLUFSEN and 
 of LEVERRIER, gives 
 
 Han. - Lev. = - 0".93 - 0".01074 t. 
 
 From the way in which J n' and J n" are involved in the equations of condition, it may be concluded, that 
 if J n" were left indeterminate in the solution, the value of A n', obtained, would be roughly, 
 
 J' = (J') + 1.2 J ", 
 
 (J n') denoting the value of J n' on the supposition of J n" = 0. Thus on making J n" = 0".01074, the cor- 
 rection of the mean motion of Venus, from this cause is 
 
 J ' = 0".01289. 
 The sum of these two corrections is 
 
 J n' = 0".02877 
 
 which is almost identical with that derived from the equations of condition. 
 
 The increment of the motion of the node, 0".222, requires that the mass of Venus should be reduced from 
 
 408134 to 4-J7-MO' '^' 1 ' s a l ' ees w * t ' 1 LEVERRIER'S result: setting out with the mass 0.0000024885, he found that it 
 should be multiplex! by the factor 0.948, which would make the mass ij 
 
 The corrections to be added to the elements, with which we set out, to obtain the elements, from which the 
 Tables are constructed, are 
 
 J L' = 0".502, 
 
 A -' = + 28".46, 
 
 A Q' = + 0".90 +0".222, 
 
 A V = + 0".18, 
 
 A e' = - 0.000000196, 
 
 J n' = 0".02863. 
 
 The Tables have been compared with the occultation of Mercury by Venus, observed at Greenwich May 28, 
 1737. The observations made are 
 
 Greenwich M. T. 
 
 h m 6 
 
 9 40 3.9. Mercury distant from Venus not more than a tenth part of the diameter of Venus. 
 9 48 10.2. Mercury wholly occulted by Venus. 
 
 36 
 
I XTRODUCTION. 
 
 The position of Mercury heiut; derived from 1'rof. WINLOCK'S '1'ables, the apparent position of the two planets, 
 as seen from (Irecnwich, and in longitude and latitude, are 
 
 <;r-,.,,wirh M.T. /. I. /'. //. I' I. b'l,' 
 
 d ll Q I It O I f Q I II Q I It II II 
 
 Ma> 2S H Mi 21 2:U>:> +2 !) 12.90 89 :M -19.97 4-210 9.98 4-11(5.92 + 5'/.OS 
 
 10 M) :U :).:!."> 4-2 8 r.s.r.i M :i<) :w.<;:! 4-29 l l.2s 50.72 4-15.85 
 
 And interpolating 
 
 (ii. -i-iiw ii-li .M. T. /' /. // li. Out. of Centres. 
 
 ll III 8 // // // 
 
 9 10 :{.> 4- :n.T.1 + 22.(il :w.9<i 
 
 !) is 10.2 1.79 4- 19.87 19.95 
 
 With the addition of 0".;">7 for irradiation, the semi-diameters of Mercury and Venus are respectively .'{".98 
 and 2(i".97 : hence at the first observation, the distance of the limbs of the planet is IS". 01, 2".G more than a lenth 
 part of the diameter of Venus: at the second observation, the distance of the centres is less than the dill'ereiice of 
 semi-diameters; hence the Tables are verified by the statement of the observer. Venus beinjr, at the time, a thin 
 Crescent, and about half of Mercury's disc being illuminated, it is plain that it would be difficult for the obsever 
 .o estimate- the distance in fractional parts of the apparent diameter of Venus. 
 
 LEVKKKIEH'S remarks on this occultatton are impaired by a mistake made in the last line of his computatk n. 
 
 37 
 
TABLES OF VENUS. 
 
TABLE 1. 
 
 LONGITUDE OF THE PRINCIPAL OBSERVATORIES FROM WASHINGTON. 
 
 West Longitudes are marked + 
 
 Place. 
 
 Longitude 
 from VVashingtoi 
 in Time. 
 
 In Decimals 
 of a Day. 
 
 Place. 
 
 Longitude 
 from Washington 
 in Time. 
 
 In Decimals 
 of a Day. 
 
 Abo, 
 
 h m s 
 
 6 37 20.32 
 
 0.2759296 
 
 Lcipsic, 
 
 h m s 
 
 5 57 46.87 
 
 o!2484592 
 
 Albany,* 
 
 13 12.87 
 
 0.0091767 
 
 Leyden, 
 
 - 5 26 8.57 
 
 0.2264881 
 
 Allegheny,* 
 
 -fO 11 50.20 
 
 +0.0082199 
 
 Liverpool, 
 
 4 56 ]-.'.;{ 1 
 
 0.2056984 
 
 Altona, 
 
 5 47 58.54 
 
 0.2416498 
 
 Madras, 
 
 10 29 9.67 
 
 0.1369175 
 
 Ann Arbor, 
 
 +0 26 42.67 
 
 +0.0185494 
 
 Madrid, 
 
 4 53 27.00 
 
 0.2037847 
 
 Armagh, 
 
 4 41 36.92 
 
 0.1955662 
 
 Mannheim, 
 
 - 5 42 3.06 
 
 0.2375354 
 
 Athens, 
 
 6 43 7.58 
 
 0.2799488 
 
 Markree, 
 
 - 4 34 24.00 
 
 0.1905556 
 
 Berlin, 
 
 6 1 47.77 
 
 0.2512473 
 
 Marseilles, 
 
 - 5 29 40.55 
 
 0.2289415 
 
 Bilk, 
 
 5 35 17.77 
 
 0.2328445 
 
 Melbourne, 
 
 14 48 7.17 
 
 0.6167496 
 
 Bonn, 
 
 5 36 36.02 
 
 0.2337502 
 
 Milan, 
 
 - 5 44 58.20 
 
 0.2395625 
 
 Breslau, 
 
 6 16 22.19 
 
 0.2613679 
 
 Modena, 
 
 - 5 51 55.53 
 
 0.2443927 
 
 Brussels, 
 
 5 25 41.29 
 
 0.2261723 
 
 Moscow, 
 
 7 38 29.29 
 
 0.3183946 
 
 Cambridge, (Eng.) 
 
 5 8 35.08 
 
 0.2)42949 
 
 Munich, 
 
 5 54 38.00 
 
 0.2462731 
 
 Cambridge, (Mass.) 
 
 23 41.54 
 
 0.0164530 
 
 Naples, 
 
 - 6 5 10.95 
 
 0.2535990 
 
 Cape of Good Hope, 
 
 6 22 8.09 
 
 0.2653711 
 
 New York,* 
 
 - 12 15.47 
 
 0.0085124 
 
 Chicago, 
 
 +0 42 14.26 
 
 +0.0293317 
 
 Nicolajcw, 
 
 7 16 6.53 
 
 0.3028534 
 
 Cincinnati,* 
 
 +0 29 46.94 
 
 +0.0206822 
 
 Olmiitz, 
 
 6 17 15.43 
 
 0.2519841 
 
 Christiania, 
 
 5 51 6.69 
 
 0.2438274 
 
 Oxford, 
 
 5 3 9.79 
 
 0.2105300 
 
 Clinton, 
 
 6 35.08 
 
 0.0015727 
 
 Padua, 
 
 - 5 55 41.17 
 
 0.2470013 
 
 Copenhagen, 
 
 5 58 31.05 
 
 0.2489703 
 
 Palermo, 
 
 6 1 37.00 
 
 0.2511227 
 
 Cracow, 
 
 6 28 2.80 
 
 0.2694768 
 
 Paramatta, 
 
 15 12 18.64 
 
 0.6335491 
 
 Dorpat, 
 
 6 55 6.02 
 
 0.2882641 
 
 Paris, 
 
 - 5 17 33.02 
 
 0.2205211 
 
 Dublin, 
 
 4 42 50.39 
 
 0.1964165 
 
 Philadelphia,* 
 
 7 33.61 
 
 0.005250.5 
 
 Durham, 
 
 5 1 52.64 
 
 0.2096370 
 
 Prague, 
 
 6 5 53.52 
 
 0.2540917 
 
 Edinburgh, 
 
 -4 55 29.34 
 
 0.2052007 
 
 Pulkowa, 
 
 7 9 31.06 
 
 0.2982757 
 
 Florence, 
 
 5 53 15.12 
 
 0.2453139 
 
 Rome, 
 
 5 58 8.53 
 
 0.2487098 
 
 Geneva, 
 
 5 32 49.24 
 
 0.2311344 
 
 San Fernando, 
 
 - 4 43 22.42 
 
 0. 1967873 
 
 Georgetown,* 
 
 +0 6.20 
 
 +0.0000718 
 
 Santiago, 
 
 25 30.00 
 
 0.0177083 
 
 Gottingen, 
 
 5 47 58.49 
 
 0.241G492 
 
 Senftenberg, 
 
 6 14 3.00 
 
 0.2597570 
 
 Gotha, 
 
 5 51 3.39 
 
 0.2437892 
 
 Spcyer, 
 
 5 41 58.00 
 
 0.2374769 
 
 Greenwich, 
 
 5 8 12.39 
 
 0.2140323 
 
 Stockholm, 
 
 6 20 2!i.::r> 
 
 0.2641939 
 
 Hamburg, 
 
 5 48 5.95 
 
 0.2417355 
 
 St. Petersburg, 
 
 7 9 25.87 
 
 0.2982161 
 
 Hclsingfors, 
 
 6 48 1.32 
 
 0.2833486 
 
 Sydney, 
 
 15 13 12.77 
 
 0.63-11758 
 
 Hudson,* 
 
 +0 17 32.06 
 
 +0.0121766 
 
 Upsala, 
 
 - 6 18 42.70 
 
 0.2629942 
 
 Kasan, 
 
 8 24 41.14 
 
 0.3504761 
 
 Utrecht, 
 
 5 28 43.67 
 
 0.2282832 
 
 Konigsberg, 
 
 30 11.87 
 
 0.2709707 
 
 Vienna, 
 
 6 13 44.09 
 
 0.2595381 
 
 Krcmsmunstcr, 
 
 6 4 45.03 
 
 0.2532990 
 
 Wilna, 
 
 6 49 23.33 
 
 0.2842978 
 
 NIITK. Tlicsc Longitudes, except of pi;,,.,.* ,,,;,,-kr<l u.ll, ;1 *, ;,,-, dependent on lliat ofCamhridge, Mass., the late-t correc- 
 tion of which is -+- 0-'..|<> = O'l .0000053. 
 
TABLE II. 
 
 3 
 
 Ninnbrr tif Days i-liijixnl xiiirr Ike "Beginning < if tin- .1 ill inn I'ir/nil, at the Dnli: .Tun. in Common Years, 
 
 tntil .Inn. 1 IH liixacjlilr Yi'iirx. 
 
 
 
 
 
 vi: \i: i\ 
 
 
 \ i: AH iv 
 
 
 
 Date IE 
 
 1 >:iy. 
 
 V.ar. 
 
 U:tt'- i: 
 Solar 
 
 Tin; CI:N i ri:v. 
 
 plx", : 
 ( Ylirrmiiill 
 
 TIII: <'!:. vi rnv. 
 
 DMVS from 
 previous ( Yn 
 trmiiul Date. 
 
 
 
 
 
 
 
 
 I f N . 
 
 It" I'oMtive. 
 
 Data 
 
 ir N, L'.iti>.- 
 
 If Positive 
 
 
 4718B. 
 
 
 
 1000 
 
 1356173 
 
 100 
 
 1 
 
 
 
 50 
 
 51 
 
 18262 
 
 -1712 
 
 .-{(15 - !)()() 
 
 1392698 
 
 99 
 
 2 
 
 865 
 
 49B. 
 
 52 B. 
 
 18628 
 
 ^1711 
 
 730 - sOO 
 
 1 129223 
 
 98 
 
 3 
 
 730 
 
 48 
 
 53 
 
 18993 
 
 -4710 
 
 1095 
 
 700 
 
 14657 IS 
 
 97B. 
 
 4B. 
 
 1096 
 
 47 
 
 54 
 
 19358 
 
 4709B. 
 
 1461 
 
 - 600 
 
 1502273 
 
 96 
 
 5 
 
 1461 
 
 46 
 
 55 
 
 19723 
 
 470S 
 
 1826 
 
 500 
 
 1538798 
 
 95 
 
 6 
 
 1826 
 
 45B. 
 
 56 B. 
 
 20089 
 
 4707 
 
 2191 
 
 400 
 
 157 5323 
 
 ill 
 
 7 
 
 2191 
 
 44 
 
 57 
 
 20454 
 
 470(1 
 
 2556 
 
 300 
 
 1611848 
 
 93 B. 
 
 8B. 
 
 2557 
 
 43 
 
 58 
 
 20819 
 
 4705 B. 
 
 2922 
 
 200 
 
 1648378 
 
 92 
 
 9 
 
 2922 
 
 42 
 
 59 
 
 21184 
 
 4701 
 
 8287 
 
 100 
 
 1684898 
 
 91 
 
 10 
 
 8287 
 
 41 B. 
 
 GOB. 
 
 21550 
 
 4703 
 
 8652 
 
 1 
 
 1721123 
 
 90 
 
 11 
 
 3652 
 
 40 
 
 61 
 
 21915 
 
 - 1702 
 
 4017 
 
 101 
 
 1757!) is 
 
 89 B. 
 
 12 B. 
 
 4018 
 
 39 
 
 62 
 
 22280 
 
 1701B. 
 
 4383 
 
 201 
 
 171)1173 
 
 88 
 
 13 
 
 4383 
 
 38 
 
 63 
 
 22645 
 
 4700 
 
 4748 
 
 301 
 
 1830998 
 
 87 
 
 14 
 
 4748 
 
 37B. 
 
 64B. 
 
 23011 
 
 4600 
 
 41273 
 
 401 
 
 1867523 
 
 86 
 
 15 
 
 5113 
 
 36 
 
 65 
 
 23376 
 
 1500 
 
 777!>s 
 
 501 
 
 1904048 
 
 85.B. 
 
 16B. 
 
 5479 
 
 35 
 
 66 
 
 23741 
 
 1100 
 
 1 1 13-23 
 
 601 
 
 1910573 
 
 84 
 
 17 
 
 5844 
 
 34 
 
 67 
 
 24106 
 
 4300 
 
 150s IS 
 
 701 
 
 1977098 
 
 83 
 
 18 
 
 6209 
 
 33 B. 
 
 68B. 
 
 24472 
 
 1-200 
 
 187373 
 
 801 
 
 2013623 
 
 82 
 
 19 
 
 6574 
 
 32 
 
 69 
 
 24837 
 
 1100 
 
 223898 
 
 901 
 
 2050148 
 
 81 B. 
 
 20/J. 
 
 6910 
 
 31 
 
 70 
 
 25202 
 
 1000 
 
 260423 
 
 1001 
 
 2086673 
 
 80 
 
 21 
 
 7305 
 
 30 
 
 71 
 
 25567 
 
 8900 
 
 296!) IS 
 
 1101 2123198 
 
 79 
 
 22 
 
 7670 
 
 29 B. 
 
 72J5. 
 
 25933 
 
 3800 
 
 883473 
 
 1201 
 
 2159723 
 
 78 
 
 23 
 
 8035 
 
 28 
 
 73 
 
 26298 
 
 3700 
 
 869998 
 
 1301 
 
 2 1962 IS 
 
 77 B. 
 
 24B. 
 
 8401 
 
 27 
 
 74 
 
 26663 
 
 3600 
 
 406523 
 
 1401 
 
 2232773 
 
 76 
 
 25 
 
 8766 
 
 26 
 
 75 
 
 27028 
 
 3500 
 
 1 13048 
 
 1501 
 
 2269298 
 
 75 
 
 26 
 
 9131 
 
 25 B. 
 
 76B. 
 
 27394 
 
 3400 
 
 179573 
 
 1583 
 
 2299238 
 
 74 
 
 27 
 
 9496 
 
 24 
 
 71 
 
 27759 
 
 3300 
 
 516098 
 
 1584B. 2299604 
 
 73B. 
 
 28 B. 
 
 9862 
 
 23 
 
 78 
 
 28124 
 
 3200 
 
 552628 
 
 1585 
 
 2299969 
 
 72 
 
 29 
 
 10227 
 
 22 
 
 79 
 
 28489 
 
 3100 
 
 589148 
 
 1586 
 
 2300334 
 
 71 
 
 30 
 
 10592 
 
 2 IB. 
 
 SOB. 
 
 28855 
 
 . 3000 
 
 625673 
 
 1587 
 
 2300699 
 
 70 
 
 31 
 
 10957 
 
 20 
 
 81 
 
 29220 
 
 2900 
 
 662198 
 
 15885. 2301065 
 
 69B. 
 
 32 B. 
 
 11323 
 
 19 
 
 82 
 
 29585 
 
 2800 
 
 698723 
 
 1589 
 
 2301430 
 
 68 
 
 33 
 
 11688 
 
 18 
 
 83 
 
 29950 
 
 2700 
 
 7352 IS 
 
 1590 
 
 2301795 
 
 67 
 
 31 
 
 12053 
 
 17jB. 
 
 84B. 
 
 30316 
 
 2600 
 
 771773 
 
 1591 
 
 2302160 
 
 66 
 
 35 
 
 12418 
 
 16 
 
 85 
 
 30681 
 
 2500 
 
 808298 
 
 1592/J. 2302526 
 
 65B. 
 
 36 B. 
 
 12784 
 
 15 
 
 86 
 
 31046 
 
 2100 
 
 S 1 1823 
 
 1593 
 
 2302891 
 
 61 
 
 37 
 
 13149 
 
 14 
 
 87 
 
 31411 
 
 2300 
 
 8813 IS 
 
 1594 
 
 230325(5 
 
 63 
 
 38 
 
 13511 
 
 13B. 
 
 88B. 
 
 31777 
 
 2200 
 
 917873 
 
 1595 
 
 2303621 
 
 62 
 
 39 
 
 13879 
 
 12 
 
 89 
 
 32142 
 
 2100 
 
 954398 
 
 1596/J. 
 
 2303987 
 
 61B. 
 
 40B. 
 
 11215 
 
 11 
 
 90 
 
 32507 
 
 2000 
 
 990923 
 
 1597 
 
 2301352 
 
 60 
 
 41 
 
 14610 
 
 10 
 
 * 91 
 
 32872 
 
 1900 
 
 1027 lis 
 
 1598 
 
 2301717 
 
 59 
 
 42 
 
 14975 
 
 9B. 
 
 92 B. 
 
 33238 
 
 1800 
 
 1063973 
 
 1599 
 
 2305082 
 
 58 
 
 43 
 
 15310 
 
 8 
 
 93 
 
 33603 
 
 1700 
 
 1 100 498 
 
 1600B. 2305448 
 
 57B. 
 
 44B. 
 
 15706 
 
 7 
 
 94 
 
 33968 
 
 1600 
 
 1137023 
 
 1601 
 
 2305813 
 
 56 
 
 45 
 
 16071 
 
 6 
 
 95 
 
 34333 
 
 1500 
 
 11735 IS 
 
 1701 
 
 '23 12337 
 
 55 
 
 46 
 
 16436 
 
 5B. 
 
 96B. 
 
 34699 
 
 1100 
 
 1210073 
 
 1801 2378861 
 
 51 
 
 47 
 
 16801 
 
 4 
 
 97 
 
 35064 
 
 1300 
 
 1246598 
 
 1901 2415385 
 
 58, 
 
 48B. 
 
 17167 
 
 3 
 
 98 
 
 35429 
 
 1-200 
 
 1283123 2001 
 
 2151910 
 
 52 
 
 49 
 
 17532 
 
 2 
 
 99 
 
 35794 
 
 1100 
 
 1319648 
 
 2101 
 
 
 51 
 
 50 
 
 17897 
 
 IB. 
 
 100B. ! 36160 
 
 1000 
 
 1 356 173 
 
 2201 
 
 2524958 
 
 50 
 
 51 
 
 18262 
 
 
 100 
 
 36159 
 
 
 
 
 
 
 
 
 
 
 I 
 
 G V 
 
TABLE III. 
 
 1 
 
 Number of Days from Jan. in Common Years, and Jan. 1 in Bissextile Years. 
 
 
 jANfAi:v. IT:I;UCAKY. 
 
 ! 
 
 
 
 
 
 
 
 
 
 1583. 
 
 ^ 
 
 ;r 
 
 t 
 
 ^ 
 
 | 
 
 
 
 
 
 
 
 pi 
 
 a 
 
 
 gj 
 
 K 
 
 
 
 
 
 c 
 
 IN 
 
 -, 
 
 
 
 
 
 ^' 
 
 
 
 
 
 H 
 
 ca 
 
 a 
 
 A 
 
 M 
 
 H 
 
 a 
 
 s 
 
 
 
 I 
 
 *c 
 
 o 
 
 y. 
 
 i 
 
 H 
 
 u 
 
 " 
 
 A 
 
 t 
 
 K 
 
 b 
 
 'J2 
 P 
 
 H 
 
 o 
 
 N 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 '? 
 
 
 
 
 
 X 
 
 
 '- 
 
 
 p 
 
 
 o 
 
 E 
 
 
 O 
 
 
 B 
 
 
 
 5 
 
 3 
 
 p^ 
 
 <j 
 
 ^j 
 
 t? 
 
 - 
 
 r^ 
 
 
 O 
 
 Pd 
 
 
 o 
 
 H 
 
 n 
 
 
 
 3 
 
 S 
 
 H 
 
 H 
 
 * 
 
 a 
 
 ^ 
 
 * 
 
 
 66 
 
 
 
 
 
 
 fe 
 
 8 
 
 1 
 
 1 
 
 
 
 32 
 
 31 
 
 60 
 
 91 
 
 121 
 
 152 
 
 182 
 
 213 
 
 244 
 
 274 
 
 305 
 
 335 
 
 274 
 
 295 
 
 325 
 
 5 
 
 t) 
 
 4i 
 
 1 
 
 33 
 
 32 
 
 61 
 
 92 
 
 122 
 
 153 
 
 183 
 
 214 
 
 245 
 
 275 
 
 30(> 
 
 336 
 
 275 
 
 296 
 
 326 
 
 
 
 c 
 
 2 
 
 34 
 
 33 
 
 62 
 
 92 
 
 123 
 
 154 
 
 184 
 
 215 
 
 246 
 
 276 
 
 307 
 
 337 
 
 276 
 
 297 
 
 327 
 
 1 
 
 4 
 
 3 
 
 35 
 
 34 
 
 63 
 
 94 
 
 124 
 
 155 
 
 185 
 
 216 
 
 247 
 
 277 
 
 308 
 
 338 
 
 277 
 
 298 
 
 328 
 
 r 
 
 R 
 
 4 
 
 36 
 
 35 
 
 64 
 
 95 125 
 
 15C 
 
 186 
 
 217 
 
 248 
 
 278 
 
 309 
 
 339 
 
 
 299 
 
 329 
 
 
 
 
 
 
 
 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 6 
 
 5 
 
 37 
 
 36 
 
 65 
 
 96 
 
 126 
 
 157 
 
 187 
 
 218 
 
 249 
 
 279 
 
 310 
 
 340 
 
 
 300 
 
 330 
 
 7 
 
 7 
 
 (1 
 
 38 
 
 37 
 
 66 
 
 97 
 
 127 
 
 158 
 
 188 
 
 219 
 
 250 
 
 280 
 
 311 
 
 341 
 
 
 301 
 
 334 
 
 8 
 
 N 
 
 7 
 
 39 
 
 38 
 
 67 
 
 98 
 
 128 
 
 159 
 
 189 
 
 220 
 
 251 
 
 281 
 
 312 
 
 312 
 
 
 302 
 
 332 
 
 9 
 
 9 
 
 8 
 
 40 
 
 39 
 
 68 
 
 99 
 
 129 
 
 160 
 
 190 
 
 221 
 
 252 
 
 282 
 
 313 
 
 343 
 
 
 303 
 
 333 
 
 10 
 
 10 
 
 9 
 
 41 
 
 40 
 
 69 
 
 100 
 
 130 
 
 161 
 
 191 
 
 222 
 
 253 
 
 283 
 
 314 
 
 344 
 
 
 304 
 
 334 
 
 11 
 
 11 
 
 10 
 
 42 
 
 41 
 
 70 
 
 101 
 
 131 
 
 162 
 
 192 
 
 223 
 
 254 
 
 284 
 
 315 
 
 345 
 
 
 305 
 
 335 
 
 12 
 
 12 
 
 11 
 
 43 
 
 42 
 
 71 
 
 102 
 
 132 
 
 163 
 
 193 
 
 224 
 
 255 
 
 285 
 
 316 
 
 346 
 
 
 306 
 
 336 
 
 13 
 
 13 
 
 12 
 
 44 
 
 43 
 
 72 
 
 103 
 
 133 
 
 164 
 
 194 
 
 225 
 
 256 
 
 286 
 
 317 
 
 317 
 
 
 307 
 
 337 
 
 11 
 
 14 
 
 13 
 
 45 
 
 44 
 
 73 
 
 104 
 
 134 
 
 165 
 
 195 
 
 226 
 
 257 
 
 287 318 
 
 348 
 
 
 308 
 
 338 
 
 15 
 
 15 
 
 14 
 
 46 
 
 45 
 
 74 
 
 105 
 
 135 
 
 166 
 
 196 
 
 227 
 
 258 
 
 288 
 
 319 
 
 349 
 
 278 
 
 309 
 
 339 
 
 16 
 
 16 
 
 15 
 
 47 
 
 46 
 
 75 
 
 106 
 
 136 
 
 167 
 
 197 
 
 228 
 
 259 
 
 289 
 
 320 
 
 350 
 
 279 
 
 310 
 
 340 
 
 17 
 
 17 
 
 16 
 
 48 
 
 47 
 
 76 
 
 107 
 
 137 
 
 168 198 
 
 229 
 
 260 
 
 290 
 
 321 
 
 351 
 
 280 
 
 311 
 
 341 
 
 18 
 
 18 
 
 17 
 
 49 
 
 48 
 
 77 
 
 108 
 
 138 
 
 169 
 
 199 
 
 230 
 
 261 
 
 291 
 
 322 
 
 352 
 
 281 
 
 312 
 
 342 
 
 19 
 
 19 
 
 18 
 
 50 
 
 49 
 
 78 
 
 109 
 
 139 
 
 170 
 
 200 
 
 231 
 
 262 
 
 292 
 
 323 
 
 353 
 
 282 
 
 313 
 
 343 
 
 20 
 
 20 
 
 19 
 
 51 
 
 50 
 
 79 
 
 110 
 
 140 
 
 171 
 
 201 
 
 232 
 
 263 
 
 293 
 
 324 
 
 354 
 
 283 
 
 314 
 
 344 
 
 21 
 
 21 
 
 20 
 
 52 
 
 51 
 
 80 
 
 111 
 
 141 
 
 172 
 
 202 
 
 233 
 
 264 
 
 294 
 
 325 
 
 355 
 
 284 
 
 315 
 
 345 
 
 22 
 
 22 
 
 21 
 
 53 
 
 52 
 
 81 
 
 112 
 
 142 
 
 173 
 
 203 
 
 234 
 
 265 
 
 295 
 
 326 
 
 356 
 
 285 
 
 316 
 
 346 
 
 23 
 
 23 
 
 22 
 
 54 
 
 53 
 
 82 
 
 113 
 
 143 
 
 174 
 
 204 
 
 235 
 
 266 
 
 296 
 
 327 
 
 357 
 
 286 
 
 317 
 
 347 
 
 24 
 
 24 
 
 23 
 
 55 
 
 54 
 
 83 
 
 114 
 
 144 
 
 175 
 
 205 
 
 236 
 
 267 
 
 297 
 
 328 
 
 358 
 
 287 
 
 318 
 
 348 
 
 25 
 
 25 
 
 24 
 
 56 
 
 55 
 
 84 
 
 115 
 
 145 
 
 176 
 
 206 
 
 237 
 
 268 
 
 298 
 
 329 
 
 359 
 
 288 
 
 319 
 
 349 
 
 26 
 27 
 28 
 29 
 
 30 
 
 26 
 27 
 28 
 29 
 80 
 
 25 
 
 26 
 27 
 
 28 
 29 
 
 57 
 58 
 59 
 
 56 
 57 
 58 
 59 
 
 85 
 86 
 87 
 88 
 89 
 
 116 
 117 
 118 
 119 
 120 
 
 146 
 147 
 148 
 149 
 150 
 
 177 
 178 
 179 
 180 
 181 
 
 207 
 208 
 209 
 210 
 211 
 
 238 
 239 
 240 
 241 
 242 
 
 269 
 270 
 271 
 272 
 273 
 
 299 
 300 
 301 
 302 
 303 
 
 330 
 331 
 332 
 333 
 334 
 
 360 
 361 
 362 
 363 
 364 
 
 289 
 290 
 291 
 292 
 293 
 
 320 
 321 
 322 
 323 
 324 
 
 350 
 351 
 352 
 353 
 354 
 
 31 
 
 31 
 
 30 
 
 
 
 90 
 
 
 151 
 
 
 212 
 
 243 
 
 
 304 
 
 
 365 
 
 294 
 
 
 355 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
TABLE IV. 
 
 r> 
 
 /,' i! ill-linn nf lluiirx. Miiiu/i-x, <nul Scrnmls nf Tinir In J>i'i'iiiu//.t nf u ])ni/. 
 
 
 Prrimal ol'a 
 Pay. 
 
 Min. 
 
 Pecimal ofa 
 
 Pay. 
 
 If in. 
 
 Drrilllill lifa 
 Pay. 
 
 
 Decimal of a 
 
 See. 
 
 Pi-riina! ol'a 
 
 Day. 
 
 1 
 
 0.0116667 
 
 1 
 
 0.000(1!) 11 
 
 31 0.0215278 
 
 1 
 
 0.0000116 
 
 31 
 
 o.oQpas 
 
 2 
 
 0.0833333 
 
 2 
 
 0.0013889 
 
 32 0.0222222 
 
 2 
 
 0.0000231 
 
 32 
 
 0.000370 1 
 
 :{ 
 
 0.1250000 
 
 :{ 
 
 0.0020S33 
 
 33 0.022!) 167 
 
 3 
 
 0.0000347 
 
 33 
 
 0.000381!) 
 
 4 
 
 0.166 
 
 ;i(i67 
 
 i 
 
 0.0027778 
 
 31 0.0236111 
 
 1 
 
 0.0000 163 
 
 31 
 
 0.00039:!.-) 
 
 5 
 
 0.20N3333 
 
 5 
 
 0.003 1722 
 
 35 0.0243056 
 
 5 
 
 0.0000579 
 
 35 
 
 0.0001051 
 
 6 
 
 0.2500000 
 
 6 
 
 0.0011667 
 
 36 0.0250000 
 
 6 
 
 0.000069 1 
 
 36 
 
 0.0004167 
 
 7 
 
 0.21U6667 
 
 7 
 
 0.0018611 
 
 37 0.02569 1 I 
 
 7 
 
 0.0000810 
 
 37 
 
 0.000 12S2 
 
 8 
 
 0.3333333 
 
 8 
 
 0.0055556 
 
 38 0.0263889 
 
 8 
 
 0.0000926 
 
 :is 
 
 0.000 i:i: 
 
 B 
 
 0.375 
 
 0000 
 
 9 
 
 0.0062500 
 
 39 0.0270833 
 
 9 v 
 
 0.0001012 
 
 39 
 
 0.000151 1 
 
 10 
 
 0.110 
 
 6667 
 
 10 
 
 0.00694 1 1 
 
 40 0.0277778 
 
 10 
 
 0.0001157 
 
 40 
 
 0.0001630 
 
 11 
 
 0. 15S3333 
 
 11 
 
 0.0076389 
 
 41 
 
 0.028 1722 
 
 11 
 
 0.0001273 
 
 41 
 
 0.0004715 
 
 12 
 
 0.5000000 
 
 12 
 
 0.0083333 
 
 12 
 
 0.0291667 
 
 12 
 
 0.0001389 
 
 12 
 
 0.000 iMil 
 
 13 
 
 0.5116667 
 
 13 
 
 0.0090278 
 
 43 
 
 0.0298611 
 
 13 
 
 0.0001505 
 
 13 
 
 0.0004977 
 
 14 
 
 0.5833333 
 
 11 
 
 0.0097222 
 
 44 
 
 0.0305556 
 
 14 
 
 0.0001620 
 
 11 
 
 0.0005093 
 
 rs 
 
 0.6250000 
 
 15 
 
 0.0104167 
 
 45 
 
 0.0312500 
 
 15 
 
 0.0001736 
 
 45 
 
 0.0005208 
 
 16 
 
 0.6666667 
 
 16 
 
 0.0111111 
 
 46 
 
 0.0319414 
 
 16 
 
 0.0001852 
 
 46 
 
 0.0005324 
 
 17 
 
 0.70S3333 
 
 17 
 
 0.0118056 
 
 47 
 
 0.0326389 
 
 17 
 
 0.0001968 
 
 47 
 
 0.0005110 
 
 18 
 
 0.7500000 
 
 18 
 
 0.0125000 
 
 48 
 
 0.0333333 
 
 18 
 
 0.0002083 
 
 48 
 
 0.0005556 
 
 19 
 
 0.7916667 
 
 1!) 
 
 0.0131!) 11 
 
 49 . 0.0340278 
 
 19 
 
 0.0002199 
 
 49 
 
 O.ooo:.!i7 1 
 
 20 
 
 O.S333333 
 
 20 
 
 0.0138889 
 
 50 
 
 0.0317222 
 
 20 
 
 0.0002315 
 
 50 
 
 0.0005787 
 
 21 
 
 O.S750000 
 
 21 
 
 0.0115833 
 
 51 
 
 0.0354167 
 
 21 
 
 0.0002431 
 
 51 
 
 0.0005903 
 
 22 
 
 0.9 If 
 
 6667 
 
 22 
 
 0.0152778 
 
 52 
 
 0.0361111 
 
 22 
 
 0.0002546 
 
 52 
 
 0.0006019 
 
 23 
 
 0.95N3333 
 
 23 
 
 0.0159722 
 
 53 
 
 0.0368056 
 
 23 
 
 0.0002662 
 
 53 
 
 0.00061:!! 
 
 21 
 
 1.0000000 
 
 24 
 
 0.0166667 
 
 51 
 
 0.0375000 
 
 24 
 
 0.0002778 
 
 51 
 
 0.0006250 
 
 
 
 
 25 
 
 0.0173611 
 
 55 
 
 0.0381944 
 
 25 
 
 0.0002894 
 
 55 
 
 0.0006366 
 
 
 
 
 26 
 
 0.0180556 
 
 56 
 
 0.0388889 
 
 26 
 
 0.0003009 
 
 56 
 
 0.0006481 
 
 
 
 
 27 
 
 0.0187500 
 
 57 
 
 0.0395833 
 
 27 
 
 0.0003125 
 
 57 
 
 0.0006597 
 
 
 
 
 28 
 
 0.0191111 
 
 58 
 
 0.0402778 
 
 28 
 
 0.0003241 
 
 58 
 
 0.0006713 
 
 
 
 
 29 
 
 0.0201389 
 
 59 
 
 0.0409722 
 
 29 
 
 0.0003356 
 
 59 
 
 0.0006829 
 
 
 
 
 30 
 
 0.0208333 
 
 60 
 
 0.0416667 
 
 30 
 
 0.0003472 
 
 60 
 
 0.00069 1 I 
 
 TABLE V. 
 
 Periods of the Arguments with their multiples. 
 
 Increments of Arguments 
 
 X-XIVfnr an incri'tiai- 
 
 
 
 of 1,2 and 3 in the integer ill. 
 
 
 
 
 1 Period. 
 
 2 Periods. 
 
 3 Periods. 
 
 
 
 Argument I 
 
 22 1''.7008 
 
 419'UOH! 
 
 674 d .1023 
 
 
 Increment 
 
 Increment Increment 
 
 II 
 
 23S\9 
 
 477-v.S 
 
 716J-.8 
 
 
 
 /. .. f , .1 
 
 01 nl == *i ol HI ^= d. 
 
 III 
 
 11967*. 
 
 23974 d . 
 
 35962' 1 . 
 
 
 
 
 IV 
 
 2969*. 
 
 5918*. 
 
 8878 d . 
 
 
 
 
 V 
 
 1454 d .9 
 
 2909-'.9 
 
 4364 d .8 
 
 Argument X 
 
 33.26 
 
 6.52 39.78 
 
 VI 
 
 583''.92 
 
 1167".84 
 
 175 K76 
 
 XI 
 
 " XII 
 
 147.64 
 19.6 
 
 55.29 202.93 
 39.3 58.9 
 
 VII 
 
 213''.16 
 
 486''.33 
 
 729''.49 
 
 " XIII 
 
 3.11 
 
 6.22 9.34 
 
 " VIII 
 
 220''.6 
 
 440'.1 
 
 661*.7 
 
 " XIV 
 
 0.8 
 
 1.5 2.3 
 
 IX 
 
 236' 1 .99 
 
 473''.98 
 
 710".98 
 
 
 
 
 X 
 
 60 units 
 
 120 units 
 
 180 units 
 
 - 
 
 XI 
 
 240 units 
 
 480 units 
 
 720 units 
 
 XII 
 
 60 units 
 
 120 units 
 
 !>() units 
 
 XIII 
 
 60 units 
 
 120 units 
 
 180 units 
 
 " XIV 
 
 36 units 
 
 72 units 
 
 108 units 
 
 \v 
 
 8796*3 
 
 13596''.5 
 
 2039 l-'.M 
 
 XVI 
 
 365''.2 
 
 730''.5 
 
 1095''.7 
 
TABLE VI. 
 
 Mean Longitude, Arguments, tyc., for Wa^hin^lon Mean Noon of Jan. in common years, Jan. 1 in 
 bissextile, years. 
 
 \ 
 
 Year. 
 
 L 
 
 in- 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 1750 
 
 o / // 
 
 45 54 5.24 
 
 -163 
 
 173.9096 
 
 67:9 
 
 d 
 
 1 12 42 
 
 2403 
 
 d 
 
 611.5 
 
 497.08 
 
 31.2 
 
 1751 
 
 270 41 31.89 161 
 
 89.5080 
 
 68.9 
 
 11607 
 
 2768 
 
 976.5 
 
 278.16 
 
 153.0 
 
 17525. 
 
 137 5 12.35 159 
 
 6.1064 
 
 69.9 
 
 11973 
 
 175 
 
 1342.5 
 
 60.24 
 
 32.7 
 
 1753 
 
 1 52 42.00 
 
 158 
 
 146.4056 
 
 70.9 
 
 351 
 
 540 
 
 252.5 
 
 425.24 
 
 154.5 
 
 1754 
 
 226 40 11.66 
 
 156 
 
 62.0040 
 
 71.9 
 
 716 
 
 905 
 
 617.5 
 
 206.32 
 
 33.2 
 
 1755 
 
 91 27 41.31 
 
 155 
 
 202.3032 
 
 72.9 
 
 1081 
 
 1270 
 
 982.5 
 
 571.32 
 
 155.0 
 
 175GB. 
 
 317 51 18.77 
 
 153 
 
 118.9016 
 
 73.9 
 
 1447 
 
 1636 
 
 1348.5 
 
 353.40 
 
 34.7 
 
 1757 
 
 182 38 48.42 
 
 151 
 
 34.5000 
 
 74.9 
 
 1812 
 
 2001 
 
 258.6 
 
 134.48 
 
 156.5 
 
 1758 
 
 47 26 18.08 
 
 150 
 
 174.7993 
 
 75.9 
 
 2177 
 
 2366 
 
 623.6 
 
 499.48 
 
 35.2 
 
 1759 
 
 272 13 47.73 
 
 148 
 
 90.3977 
 
 76.9 
 
 2542 
 
 2731 
 
 988.6 
 
 280.56 
 
 157.1 
 
 17(507?. 
 
 138 37 25.19 
 
 146 
 
 6.9961 
 
 77.9 
 
 2908 
 
 137 
 
 1354.6 
 
 62.63 
 
 36.7 
 
 1761 
 
 3 24 54.84 
 
 145 
 
 147.2953 
 
 78.9 
 
 3273 
 
 502 
 
 264.7 
 
 427.63 
 
 158.6 
 
 1702 
 
 228 12 24.50 
 
 143 
 
 62.8937 
 
 79.9 
 
 3638 
 
 867 
 
 629.7 
 
 208.71 
 
 37.2 
 
 1763 
 
 92 59 51.15 
 
 142 
 
 203.1929 
 
 80.9 
 
 4003 
 
 1232 
 
 994.7 
 
 573.71 
 
 15^.1 
 
 17645. 
 
 319 23 31.61 
 
 140 
 
 119.7913 
 
 81.9 
 
 4369 
 
 1598 
 
 1360.7 
 
 355.79 
 
 38.7 
 
 1765 
 
 184 11 1.27 
 
 138 
 
 35.3898 
 
 82.9 
 
 4734 
 
 1963 
 
 270.7 
 
 136.87 
 
 160.6 
 
 1766 
 
 48 58 30.92 
 
 137 
 
 175.6890 
 
 83.9 
 
 5099 
 
 2328 
 
 635.7 
 
 501.87 
 
 39.2 
 
 1767 
 
 273 46 0.58 
 
 135 
 
 91.2874 
 
 84.9 
 
 5464 
 
 2693 
 
 1000.7 
 
 282.95 
 
 161.1 
 
 17685. 
 
 140 9 38.04 
 
 133 
 
 7.8858 
 
 85.9 
 
 5830 
 
 100 
 
 1366.7 
 
 65.03 
 
 40.7 
 
 1769 
 
 4 57 7.69 
 
 132 
 
 148.1850 
 
 86.9 
 
 6195 
 
 465 
 
 276.8 
 
 430.03 
 
 162.6 
 
 1770 
 
 229 44 37.35 
 
 130 
 
 63.7834 
 
 87.9 
 
 6560 
 
 830 
 
 641.8 
 
 211.11 
 
 41.3 
 
 1771 
 
 94 32 7.00 
 
 129 
 
 204,0826 
 
 88.9 
 
 6925 
 
 1195 
 
 1006.8 
 
 576.11 
 
 163.1 
 
 17725. 
 
 320 55 44.47 
 
 127 
 
 120.6811 
 
 89.9 
 
 7291 
 
 1561 
 
 1372.8 
 
 358.18 
 
 42.8 
 
 1773 
 
 185 43 14.12 
 
 125 
 
 36.2795 
 
 90.9 
 
 7656 
 
 1926 
 
 282.9 
 
 139.26 
 
 164.6 
 
 1774 
 
 50 30 43.78 
 
 124 
 
 176.5787 
 
 91.9 
 
 8021 
 
 2291 
 
 647.9 
 
 504.26 
 
 43.3 
 
 1775 
 
 275 18 13.43 
 
 122 
 
 92.1771 
 
 92.9 
 
 8386 
 
 2656 
 
 1012.9 
 
 285.34 
 
 165.1 
 
 1776B. 
 
 141 41 50.89 
 
 120 
 
 8.7755 
 
 93.9 
 
 8752 
 
 63 
 
 1378.9 
 
 67.42 
 
 44.8 
 
 1777 
 
 6 29 20.55 
 
 119 
 
 149.0748 
 
 94.9 
 
 9117 
 
 428 
 
 288.9 
 
 432.42 
 
 166.6 
 
 1778 
 
 231 16 50.21 
 
 117 
 
 64.6732 
 
 95.9 
 
 9482 
 
 793 
 
 653.9 
 
 213.50 
 
 45.3 
 
 1779 
 
 96 4 19.86 
 
 116 
 
 204.9724 
 
 96.9 
 
 9847 
 
 1158 
 
 1018.9 
 
 578.50 
 
 167.1 
 
 17801?. 
 
 322 27 57.32 
 
 114 
 
 121.5708 
 
 97.9 
 
 10213 
 
 1524 
 
 1384.9 
 
 360.58 
 
 46.8 
 
 1781 
 
 187 15 26.98 
 
 112 
 
 37.1692 
 
 98.9 
 
 10578 
 
 1889 
 
 295.0 
 
 141.66 
 
 168.6 
 
 1782 
 
 52 2 56.64 
 
 111 
 
 177.4684 
 
 99.9 
 
 10943 
 
 2254 
 
 660.0 
 
 506.66 
 
 47.3 
 
 1783 
 
 276 50 26.29 
 
 109 
 
 93.0669 
 
 100.9 
 
 11308 
 
 2619 
 
 1025.0 
 
 287.74 
 
 169.1 
 
 17845. 
 
 143 14 3.76 
 
 107 
 
 9.6653 
 
 101.9 
 
 11674 
 
 26 
 
 1391.0 
 
 69.81 
 
 48.8 
 
 1785 
 
 8 1 33.41 
 
 106 
 
 149.9645 
 
 102.9 
 
 52 
 
 391 
 
 301.0 
 
 434.81 
 
 170.6 
 
 1786 
 
 232 49 3.07 
 
 104 
 
 65.5629 
 
 103.9 
 
 417 
 
 756 
 
 666.0 
 
 215.89 
 
 49.3 
 
 1787 
 
 97 36 32.73 
 
 103 
 
 205.8621 
 
 104.9 
 
 782 
 
 1121 
 
 1031.0 
 
 580.89 
 
 171.1 
 
 17885. 
 
 324 10.19 
 
 101 
 
 122.4605 
 
 105.9 
 
 1148 
 
 1487 
 
 1397.0 
 
 362.97 
 
 50.8 
 
 1789 
 
 188 47 39.85 
 
 99 
 
 38.0590 
 
 106.9 
 
 1513 
 
 1852 
 
 307.1 
 
 144.05 
 
 172.6 
 
 1790 
 
 53 35 9.51 
 
 98 
 
 178.3582 
 
 107.9 
 
 1878 
 
 2217 
 
 672.1 
 
 509.05 
 
 51.3 
 
 1791 
 
 278 22 39.16 
 
 96 
 
 93.9566 
 
 108.9 
 
 2243 
 
 2582 
 
 1037.1 
 
 290.13 
 
 173.1 
 
 17927?. 
 
 144 46 16.63 
 
 94 
 
 10.5551 
 
 109.9 
 
 2609 
 
 2948 
 
 ' 1403.1 
 
 72.21 
 
 52.8 
 
 1793 
 
 9 33 46.28 
 
 93 
 
 150.8543 
 
 110.9 
 
 2974 
 
 354 
 
 313.2 
 
 437.21 
 
 174.6 
 
 1794 
 
 234 21 15.94 
 
 91 
 
 66.4527 
 
 111.9 
 
 3339 
 
 719 
 
 678.2 
 
 218.29 
 
 53.3 
 
 1795 
 
 99 8 45.60 
 
 90 
 
 206.7519 
 
 112.9 
 
 3704 
 
 1084 
 
 1043.2 
 
 583.29 
 
 175.2 
 
 17965. 
 
 325 32 23.07 
 
 88 
 
 123.3503 
 
 113.9 
 
 4070 
 
 1450 
 
 1409.2 
 
 365.36 
 
 54.8 
 
 1797 
 
 190 19 52.72" 
 
 86 
 
 88.9488 
 
 114.9 
 
 4435 
 
 1815 
 
 319.2 
 
 146.44 
 
 176.7 
 
 1798 
 
 55 7 22.38 
 
 85 
 
 179.2480 
 
 115.9 
 
 4800 
 
 2180 
 
 684.2 
 
 511.44 
 
 55.3 
 
 1799 
 
 279 54 52.04 
 
 83 
 
 94.8464 
 
 116.9 
 
 5165 
 
 2545 
 
 1049.2 
 
 292.52 
 
 177.2 
 
 Constant subtracted from L = 47' 4li". 
 
TABL.E VI. 
 
 Minn Ltnin'iliidf, Arguments, cV''., /<>/' M'n.-i/iiinffiiti Menu J\"<HI;I J Jim. in romuinn yrtirs. Jim. I in 
 l>ixxi'.ili/i- i/i-firx. 
 
 Fear. 
 
 VIII. 
 
 IX. 
 
 X. 
 
 M. 
 
 XII. 
 
 Xlil. 
 
 XIV. 
 
 Log. sin i. 
 
 :wo- Q. 
 
 1760 
 
 a 
 55.9 
 
 2858 
 
 43.96 
 
 193. IS 
 
 4N.7 
 
 58.45 
 
 22.7 
 
 S.77207SS 
 
 / // 
 
 2s.) 31 16.8 
 
 I?.') 1 
 
 200.3 
 
 156.29 
 
 50. IS 
 
 8.71 
 
 28.0 
 
 4.67 
 
 2 1.2 
 
 0802 
 
 33 1 1.3 
 
 1752JB. 
 
 125.2 
 
 
 56.99 
 
 64.06 
 
 7.2 
 
 10.89 
 
 25.7 
 
 OS 15 
 
 33 11.8 
 
 1753 
 
 49.1 
 
 176.31 
 
 30.25 
 
 211.70 
 
 26.9 
 
 14.01 
 
 26.6 
 
 0829 
 
 32 39.3 
 
 1754 
 
 193.5 
 
 67.33 
 
 86.77 
 
 26.99 
 
 6.1 
 
 20.23 
 
 28.0 
 
 OS 12 
 
 32 6.9 
 
 1755 
 
 117.1 
 
 195.31 
 
 10.03 
 
 17 1.63 
 
 25.7 
 
 23.3 I 
 
 28.7 
 
 N.7720856 
 
 285 31 31,1 
 
 ii MI:. 
 
 42.2 
 
 87.85 
 
 16.55 
 
 229. 92 
 
 5.0 
 
 29.5!! 
 
 30.2 
 
 OS70 
 
 31 l.s 
 
 1757 
 
 186.7 
 
 215.36 
 
 23.06 
 
 15.21 
 
 44,2 
 
 35.79 
 
 31.7 
 
 0883 
 
 30 29,1 
 
 1758 
 
 110.5 
 
 10(i.3S 
 
 56.33 
 
 192. Mi 
 
 8.9 
 
 38.90 
 
 32.5 
 
 0897 
 
 2!) 5li.9 
 
 1759 
 
 34.4 
 
 231.3S 
 
 2.S 1 
 
 8.15 
 
 43. 1 
 
 45.12 
 
 34.0 
 
 0911 
 
 29 21.1 
 
 1760B. 
 
 179.8 
 
 12(5.10 
 
 9.36 
 
 63. 1 1 
 
 22. 1 
 
 51.35 
 
 35.5 
 
 8.7720924 
 
 285 28 51.9 
 
 1761 
 
 103.7 
 
 17.12 
 
 42.62 
 
 211.08 
 
 12.0 
 
 54.46 
 
 0.2 
 
 0938 
 
 2S 19.1 
 
 1763 
 
 27.6 
 
 1 15. 13 
 
 49.13 
 
 26.37 
 
 21.2 
 
 0.68 
 
 1.7 
 
 0951 
 
 27 47.0 
 
 1763 
 
 172.0 
 
 3(i. 1 1 
 
 22.39 
 
 n 1.02 
 
 40.9 
 
 3.79 
 
 2.5 
 
 0965 
 
 27 14.5 
 
 1764B. 
 
 9G.9 
 
 165.45 
 
 28.91 
 
 229.31 
 
 20.1 
 
 10.02 
 
 4.0 
 
 0979 
 
 26 41.9 
 
 1765 
 
 20.7 
 
 56.47 
 
 35,13 
 
 44.60 
 
 59.4 
 
 16.24 
 
 5.5 
 
 8.7720992 
 
 285 26 9.5 
 
 1766 
 
 1655 
 
 IS 1.17 
 
 8.68 
 
 192.2 1 
 
 19.0 
 
 19.35 
 
 6.2 
 
 1006 
 
 25 37.0 
 
 1767 
 
 89.0 
 
 75. lit 
 
 15.20 
 
 7.5:! 
 
 5S.2 
 
 25.58 
 
 7.7 
 
 1020 
 
 25 4.5 
 
 17685. 
 
 13.9 
 
 201.50 
 
 21.72 
 
 62.82 
 
 37.5 
 
 31.80 
 
 9.2 
 
 1033 
 
 24 32.0 
 
 1769 
 
 ir>s. i 
 
 95.51 
 
 51.98 
 
 210,16 
 
 57.1 
 
 34.91 
 
 10.0 
 
 1047 
 
 23 59.5 
 
 1770 
 
 82.2 
 
 823.53 
 
 1.49 
 
 25.75 
 
 36,1 
 
 41.14 
 
 11.5 
 
 8.7721060 
 
 285 23 27.0 
 
 1771 
 
 6.1 
 
 1 1 1.5 1 
 
 8475 
 
 173.40 
 
 56.0 
 
 44.25 
 
 12.3 
 
 1071 
 
 22 51.6 
 
 1772B. 
 
 151.5 
 
 6.55 
 
 41.27 
 
 228.69 
 
 35.2 
 
 50.47 
 
 13.8 
 
 loss 
 
 22 22.0 
 
 1773 
 
 7.'.. 1 
 
 134.56 
 
 47.7!) 
 
 48.98 
 
 14.5 
 
 56.69 
 
 15.3 
 
 1101 
 
 21 49.5 
 
 1771 
 
 219.8 
 
 85.58 
 
 21.05 
 
 191.62 
 
 31.1 
 
 59.81 
 
 16.0 
 
 1115 
 
 21 17.1 
 
 1775 
 
 1 13.7 
 
 153.59 
 
 27.5(5 
 
 6.91 
 
 13.4 
 
 6.03 
 
 17.5 
 
 8.7721128 
 
 285 20 44.6 
 
 1776J5. 
 
 68.6 
 
 45.60 
 
 31.08 
 
 62.20 
 
 52.6 
 
 12.25 
 
 19.0 
 
 1142 
 
 20 12.1 
 
 1777 . 
 
 213.0 
 
 173.61 
 
 7.31 
 
 209.85 
 
 12.2 
 
 15.37 
 
 19.8 
 
 1156 
 
 19 39.6 
 
 1778 
 
 136.9 
 
 64.63 
 
 13.86 
 
 25.14 
 
 51.5 
 
 21.59 
 
 21.3 
 
 1169 
 
 19 7.1 
 
 1779 
 
 60.7 
 
 192.64 
 
 47.12 
 
 172.78 
 
 11.1 
 
 24.70 
 
 22.0 
 
 1183 
 
 18 31.6 
 
 1780.B. 
 
 206.2 
 
 84.65 
 
 53.63 
 
 228.07 
 
 50.4 
 
 30.92 
 
 23.5 
 
 8.7721197 
 
 285 18 2.1 
 
 1781 
 
 130.0 
 
 212.66 
 
 0.15 
 
 43.?6 
 
 29.6 
 
 37.15 
 
 25.0 
 
 1210 
 
 17 29.6 
 
 178-2 
 
 53.9 
 
 103.68 
 
 33.11 
 
 191.00 
 
 49.2 
 
 40.26 
 
 25.8 
 
 1224 
 
 16 57.1 
 
 1783 
 
 198.3 
 
 231.68 
 
 39.93 
 
 6.29 
 
 28.5 
 
 46.48 
 
 27.3 
 
 1237 
 
 16 24.7 
 
 17845. 
 
 123.2 
 
 123.70 
 
 46.44 
 
 61.58 
 
 7.7 
 
 52.71 
 
 28.8 
 
 1251 
 
 15 52.1 
 
 1785 
 
 47.1 
 
 1 1.72 
 
 19.70 
 
 209.23 
 
 27.4 
 
 55.82 
 
 29.5 
 
 8.7721265 
 
 285 15 19.6 
 
 1786 
 
 191.5 
 
 142.72 
 
 26.22 
 
 21.52 
 
 6.6 
 
 2.04 
 
 31.1 
 
 127S 
 
 14 47.1 
 
 1787 
 
 115.1 
 
 33.7 1 
 
 59.48 
 
 172.16 
 
 26.2 
 
 5.15 
 
 31.8 
 
 1292 
 
 14 14.7 
 
 17885. 
 
 40.2 
 
 102.75 
 
 6.00 
 
 227.45 
 
 5.5 
 
 11.38 
 
 33.3 
 
 1306 
 
 13 42.1 
 
 1789 
 
 184.7 
 
 53.76 
 
 12.51 
 
 42.74 
 
 41.7 
 
 17.60 
 
 34.8 
 
 1319 
 
 13 9.6 
 
 1700 
 
 108.5 
 
 181.77 
 
 15.77 
 
 190.39 
 
 4.4 
 
 20.71 
 
 35.6 
 
 8.7721333 
 
 285 12 37.2 
 
 1791 
 
 32.4 
 
 72.71) 
 
 52.29 
 
 5.68 
 
 43.6 
 
 26.94 
 
 1.1 
 
 1346 
 
 12 4.7 
 
 17925. 
 
 177.8 
 
 201.80 
 
 58.81 
 
 60.97 
 
 22.9 
 
 33.16 
 
 2.6 
 
 1360 
 
 11 32.1 
 
 17!):! 
 
 101.7 
 
 92.81 
 
 32.06 
 
 208.61 
 
 42.5 
 
 36.27 
 
 3.3 
 
 1374 
 
 10 59.7 
 
 1794 
 
 25.6 
 
 220.82 
 
 38.58 
 
 23.90 
 
 21.7 
 
 42.50 
 
 4.8 
 
 1387 
 
 10 27.2 
 
 1795 
 
 170.0 
 
 111.84 
 
 11.84 
 
 171.51 
 
 11.1 
 
 15.61 
 
 5.6 
 
 8.7721401 
 
 285 9 51.7 
 
 17965. 
 
 91.9 
 
 3.85 
 
 18.36 
 
 226.83 
 
 20.6 
 
 51.83 
 
 7.1 
 
 - 1415 
 
 9 22.1 
 
 1797 
 
 18.7 
 
 131.86 
 
 24.87 
 
 12.12 
 
 59.9 
 
 58.05 
 
 8.6 
 
 112S 
 
 8 49.7 
 
 1798 
 
 163.2 
 
 22.88 
 
 58.13 
 
 189.77 
 
 19.5 
 
 1.17 
 
 9.3 
 
 1442 
 
 8 17.2 
 
 1799 
 
 87.0 
 
 150.89 
 
 4.65 
 
 5.06 
 
 58.7 
 
 7.39 
 
 10.8 
 
 8.7721456 
 
 285 7 41.7 
 
TABLE VI. 
 
 3[ca Luiii/i/iiili', Ariinmnitx, <fr., fur Wellington j\Imn Xo<>n of Jnn. o in cvtomm years, .run. 1 in 
 lii.-inr.i-lilc unit's. 
 
 Year. 
 
 L. 
 
 HI- 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 1800 
 
 / // 
 
 144 42 21.70 
 
 81 
 
 10,1118 
 
 117!9 
 
 553o' 
 
 29 lo" 
 
 llli!2 
 
 73JGO 
 
 <i 
 55.8 
 
 1801 
 
 9 29 51.36 
 
 80 
 
 150.7111 
 
 118.9 
 
 5895 
 
 315 
 
 324.3 
 
 438.60 
 
 177.7 
 
 1802 
 
 234 17 21.02 
 
 78 
 
 66.3125 
 
 119.9 
 
 6260 
 
 680 
 
 689.3 
 
 219.68 
 
 56.3 
 
 1803 
 
 99 4 50.67 
 
 77 
 
 206.6417 
 
 120.9 
 
 6625 
 
 1015 
 
 1054.3 
 
 0.76 
 
 178.2 
 
 18042?. 
 
 325 28 28.14 
 
 75 
 
 123.2401 
 
 121.9 
 
 6991 
 
 1411 
 
 1420.3 
 
 366.76 
 
 57.8 
 
 1805 
 
 100 15 57.80 
 
 73 
 
 38.8386 
 
 122.9 
 
 735G 
 
 1776 
 
 330.4 
 
 1 17.84 
 
 179.7 
 
 1808 
 
 55 3 27,16 
 
 72 
 
 179.1378 
 
 123.9 
 
 7721 
 
 2111 
 
 695.4 
 
 512.84 
 
 58.3 
 
 1807 
 
 279 50 57.12 
 
 70 
 
 94.7362 
 
 121.9 
 
 8086 
 
 2508 
 
 1060.4 
 
 293.91 
 
 180.2 
 
 1808B. 
 
 116 11 31.58 
 
 68 
 
 11. 33 16 
 
 125.9 
 
 8452 
 
 2872 
 
 1426.4 
 
 75.99 
 
 59.9 
 
 1809 
 
 1 1 2 4.24 
 
 67 
 
 151.6339 
 
 126.9 
 
 8817 
 
 278 
 
 336.4 
 
 110.99 
 
 181.7 
 
 1810 
 
 235 49 33.90 
 
 65 
 
 67.2323 
 
 127.9 
 
 9182 
 
 613 
 
 701.4 
 
 222.07 
 
 60.4 
 
 1811 
 
 100 37 3.56 
 
 64 
 
 207.5315 
 
 128.9 
 
 9517 
 
 1008 
 
 1066.4 
 
 3.15 
 
 182.2 
 
 18127?. 
 
 327 41.03 
 
 62 
 
 121.1299 
 
 129.9 
 
 9913 
 
 1374 
 
 1432,1 
 
 369.15 
 
 61.9 
 
 1813 
 
 191 48 10.69 
 
 60 
 
 39.7284 
 
 130.9 
 
 10278 
 
 1739 
 
 342.5 
 
 150.23 
 
 183.7 
 
 1814 
 
 56 35 40.35 
 
 59 
 
 180.0276 
 
 131.9 
 
 10643 
 
 2104 
 
 707.5 
 
 515.23 
 
 62.4 
 
 1815 
 
 281 23 10.01 
 
 57 
 
 95.6260 
 
 132.9 
 
 11008 
 
 2469 
 
 1072.5 
 
 296.31 
 
 184.2 
 
 1816B. 
 
 147 46 47.47 
 
 55 
 
 12.2245 
 
 133.9 
 
 11374 
 
 2835 
 
 1438.5 
 
 78.39 
 
 63.9 
 
 1817 
 
 12 34 17.13 
 
 54 
 
 152.5237 
 
 134.9 
 
 11739 
 
 241 
 
 348.6 
 
 443.39 
 
 185.7 
 
 1818 
 
 237 21 46.79 
 
 52 
 
 68.1221 
 
 135.9 
 
 116 
 
 606 
 
 713.6 
 
 224.46 
 
 64.4 
 
 1819 
 
 102 9 16.45 
 
 51 
 
 208.4213 
 
 136.9 
 
 481 
 
 971 
 
 1078.6 
 
 5.54 
 
 186.2 
 
 18207?. 
 
 328 32 53.92 
 
 49 
 
 125.0198 
 
 137.9 
 
 817 
 
 1337 
 
 1444.6 
 
 371.54 
 
 65.9 
 
 1821 
 
 193 20 23.58 
 
 47 
 
 40.6182 
 
 138.9 
 
 1212 
 
 1702 
 
 35 1.6 
 
 152.62 
 
 187.7 
 
 1822 
 
 53 7 53.24 
 
 46 
 
 180.9174 
 
 139.9 
 
 1577 
 
 2067 
 
 719.6 
 
 517.62 
 
 66.4 
 
 1823 
 
 282 55 22.90 
 
 44 
 
 96.5159 
 
 140.9 
 
 1942 
 
 2432 
 
 1084.6 
 
 298.70 
 
 188.2 
 
 18217?. 
 
 149 19 0.37 
 
 42 
 
 13.1143 
 
 141.9 
 
 2308 
 
 2798 
 
 1450.6 
 
 80.78 
 
 67.9 
 
 18-25 
 
 14 6 30.03 
 
 41 
 
 153,1135 
 
 142.9 
 
 2673 
 
 204 
 
 360.7 
 
 445.78 
 
 189.7 
 
 1826 
 
 238 53 59.69 
 
 39 
 
 69.0119 
 
 143.9 
 
 3038 
 
 569 
 
 725.7 
 
 226.86 
 
 68.4 
 
 1827 
 
 103 41 29.36 
 
 38 
 
 209.3112 
 
 144.9 
 
 3103 
 
 934 
 
 1090.7 
 
 7.94 
 
 190.2 
 
 18287?. 
 
 330 5 6.82 
 
 36 
 
 125.9096 
 
 145.9 
 
 37G9 
 
 1300 
 
 1.8 
 
 373.94 
 
 69.9 
 
 1829 
 
 194 52 36.49 
 
 31 
 
 41.5080 
 
 146.9 
 
 4134 
 
 1665 
 
 366.8 
 
 155.02 
 
 191.7 
 
 1830 
 
 59 40 6.15 
 
 33 
 
 181.8073 
 
 147.9 
 
 4499 
 
 2030 
 
 731.8 
 
 520.02 
 
 70.4 
 
 1831 
 
 284 27 35.81 
 
 31 
 
 97.4057 
 
 148.9 
 
 4884 
 
 2395 
 
 1096.8 
 
 301.09 
 
 192.2 
 
 issjiB. 
 
 150 51 13.28 
 
 29 
 
 11.0041 
 
 149.9 
 
 5230 
 
 2761 
 
 7.8 
 
 83.17 
 
 71.9 
 
 1833 
 
 , 15 38 42.94 
 
 28 
 
 151.3034 
 
 150.9 
 
 5595 
 
 167 
 
 372.8 
 
 448.17 
 
 193.8 
 
 1831 
 
 240 26 12.60 
 
 26 
 
 69.9018 
 
 151.9 
 
 5960 
 
 532 
 
 737.8 
 
 229.25 
 
 72.4 
 
 1835 
 
 105 13 42.27 
 
 25 
 
 210.2010 
 
 152.9 
 
 6325 
 
 897 
 
 1102.8 
 
 10.33 
 
 194.3 
 
 18367?. 
 
 331 37 19.73 
 
 23 
 
 126.7995 
 
 153.9 
 
 6691 
 
 1263 
 
 13.9 
 
 376.33 
 
 73.9 
 
 1837 
 
 196 24 49.40 
 
 21 
 
 42.3979 
 
 154.9 
 
 7056 
 
 1628 
 
 378.9 
 
 157.41 
 
 195.8 
 
 1838 
 
 61 12 19.06 
 
 20 
 
 182.6971 
 
 155.9 
 
 7421 
 
 1993 
 
 713.9 
 
 522.11 
 
 74,4 
 
 1839 
 
 285 59 48.72 
 
 18 
 
 98.2956 
 
 156.9 
 
 7786 
 
 2358 
 
 1108.9 
 
 303.49 
 
 196.3 
 
 18107?. 
 
 152 23 26.19 
 
 16 
 
 14.8940 
 
 157.9 
 
 8152 
 
 2724 
 
 19.9 
 
 85.57 
 
 75.9 
 
 1811 
 
 17 10 55.86 
 
 15 
 
 155.1932 
 
 158.9 
 
 8517 
 
 129 
 
 384.9 
 
 450.57 
 
 197.8 
 
 1812 
 
 211 58 25.52 
 
 13 
 
 70.7917 
 
 159.9 
 
 8882 
 
 494 
 
 749.9 
 
 231.64 76.4 
 
 1843 
 
 106 45 55. IN 
 
 12 
 
 211.0909 
 
 160.9 
 
 9247 
 
 859 
 
 1114.9 
 
 12.72 
 
 198.3 
 
 18447?. 
 
 333 9 32.65 
 
 10 
 
 127.6893 
 
 161.9 
 
 9613 
 
 1225 
 
 26.0 
 
 378.72 
 
 77.9 
 
 1845 
 
 197 57 2.32 
 
 8 
 
 43.2878 
 
 162.9 
 
 9978 
 
 1590 
 
 391.0 
 
 159.80 199.8 
 
 1846 
 
 62 44 31.98- 
 
 7 
 
 183.5870 
 
 163.9 
 
 10343 
 
 1955 
 
 756.0 
 
 521.80 78.5 
 
 1817 
 
 287 32 1.65 
 
 5 
 
 99.1854 
 
 164.9 
 
 10708 
 
 2320 
 
 1121.0 
 
 305.88 200.3 
 
 IS is/;. 
 
 153 55 39.12 
 
 3 
 
 15.7839 
 
 165.9 
 
 11074 
 
 2686 
 
 32.1 
 
 87.96 80.0 
 
 181!) 
 
 18 43 8.78 
 
 2 
 
 156.0831 
 
 166.9 
 
 11439 
 
 92 
 
 397.1 
 
 452.96 
 
 201.8 
 
 Constant subtracted from L = 47' 40". 
 
TABLE VI. 
 
 i 
 
 M i-ii n I.oiii/ititilt', Ari/iniioitx. tr.,/w Wasl/hii/lon Muni Xoon of Jan. in common ymrx, ,Imt. I in 
 binm-j-tilc ynti-N. 
 
 
 VIII. 
 
 IX. 
 
 \. 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 1 '>;_'. *'" ' 
 
 360 - Q. 
 
 
 .1 
 
 1 
 
 
 
 
 
 
 
 / // 
 
 1800 
 
 10.9 
 
 11.90 
 
 11.17 
 
 60.85 
 
 38.0 
 
 13.61 
 
 12.:! 
 
 8.7721469 
 
 285 7 12.2 
 
 1801 
 
 155.3 
 
 169.91 
 
 44.43 
 
 207.99 
 
 57.11 
 
 16.72 
 
 18.1 
 
 UN;! 
 
 6 39.8 
 
 1802 
 
 79.2 
 
 60.98 
 
 50.94 
 
 23.28 
 
 86.9 
 
 22.95 
 
 14.6 
 
 i !!><; 
 
 6 7.3 
 
 1803 
 
 8.1 
 
 188.93 
 
 2 1.20 
 
 170.93 
 
 56.5 
 
 26.06 
 
 15.4 
 
 1510 
 
 5 31. s 
 
 IMII/;. 
 
 1 is.;, 
 
 
 30.72 
 
 226.22 
 
 35.7 
 
 82.3 
 
 16.9 
 
 1523 
 
 5 2.2 
 
 
 7-.'. 1 
 
 206.96 
 
 87.24 
 
 41.51 
 
 15.0 
 
 3S.51 
 
 18.4 
 
 8.7721537 
 
 285 4 29.8 
 
 1806 
 
 -,'l 
 
 99.98 
 
 10.50 
 
 189.15 
 
 84.6 
 
 41.62 
 
 19.1 
 
 1550 
 
 3 57.3 
 
 1807 
 
 1 10.7 
 
 221 
 
 17.01 
 
 1.11 
 
 13.9 
 
 17.84 
 
 20.6 
 
 1564 
 
 3 21.8 
 
 1808B. 
 
 65.5 
 
 120.00 
 
 2;!..-):( 
 
 59.73 
 
 53.1 
 
 51.07 
 
 22.1 
 
 I :.', . 
 
 2 52.2 
 
 1809 
 
 210.0 
 
 11.02 
 
 56.79 
 
 207.37 
 
 12.7 
 
 57.18 
 
 22.9 
 
 1591 
 
 2 19.7 
 
 1810 
 
 183.8 
 
 1:59.02 
 
 8.81 
 
 22.66 
 
 52.0 
 
 3.10 
 
 21.1 
 
 8.7721605 
 
 285 1 47.3 
 
 1811 
 
 57.7 
 
 30.04 
 
 86.! 
 
 170.31 
 
 11.6 
 
 6.51 
 
 25.1 
 
 1618 
 
 1 ll.H 
 
 1812B. 
 
 203. 1 
 
 159.05 
 
 48.08 
 
 225.60 
 
 50.9 
 
 12.71 
 
 26.6 
 
 1632 
 
 42.2 
 
 1813 
 
 127.0 
 
 50.06 
 
 49.60 
 
 40.8!) 
 
 30.1 
 
 18.96 
 
 28.1 
 
 1646 
 
 2*5 9.7 
 
 1814 
 
 50.9 
 
 i: <.o? 
 
 22.86 
 
 1S8.53 
 
 49.7 
 
 22.07 
 
 28.9 
 
 1659 
 
 281 59 37.2 
 
 1815 
 
 195.3 
 
 69,09 
 
 29.37 
 
 8.82 
 
 29.0 
 
 28.30 
 
 30.4 
 
 8.7721673 
 
 284 59 4.U 
 
 ; .;/;. 
 
 120.2 
 
 198.10 
 
 35.89 
 
 59. 1 1 
 
 
 84.52 
 
 31.9 
 
 1686 
 
 58 32.2 
 
 1817 
 
 44.0 
 
 89.11 
 
 9.15 
 
 206.76 
 
 27.9 
 
 87.63 
 
 32.6 
 
 1700 
 
 57 59.7 
 
 
 
 217.12 
 
 15.66 
 
 22.05 
 
 7.1 
 
 48.85 
 
 31.1 
 
 1713 
 
 57 -2'i:'. 
 
 1819 
 
 112.3 
 
 108.14 
 
 48.93 
 
 169.69 
 
 26.7 
 
 48.97 
 
 31.9 
 
 1727 
 
 56 51.7 
 
 18302?. 
 
 37.2 
 
 0.15 
 
 55. 1 1 
 
 221.98 
 
 6.0 
 
 58.19 
 
 0.4 
 
 8.7721741 
 
 281 56 22.2 
 
 1821 
 
 181.6 
 
 128.16 
 
 1.96 
 
 10.27 
 
 45.2 
 
 59.11 
 
 1.9 
 
 1751 
 
 55 49.T 
 
 1823 
 
 105.5 
 
 19.18 
 
 35.22 
 
 187.91 
 
 4.9 
 
 2.53 
 
 2.7 
 
 1768 
 
 55 17.2 
 
 1823 
 
 J!>. 1 
 
 117.19 
 
 11.71 
 
 3.20 
 
 44.1 
 
 8.75 
 
 4.2 
 
 1781 
 
 54 44.7 
 
 1824B. 
 
 174.8 
 
 39.20 
 
 4H.25 
 
 58.49 
 
 23. 1 
 
 14.97 
 
 5.7 
 
 1795 
 
 51 12.2 
 
 1829 
 
 98.7 
 
 167.21 
 
 21.51 
 
 206.14 
 
 43.0 
 
 18.08 
 
 6.4 
 
 8.7721808 
 
 284 53 39.7 
 
 1826 
 
 22.6 
 
 58.23 
 
 28.03 
 
 21.43 
 
 22.2 
 
 21.31 
 
 7.9 
 
 1S22 
 
 53 7.2 
 
 1827 
 
 107.0 
 
 186.23 
 
 1.29 
 
 169.07 
 
 41.9 
 
 27.42 
 
 8.7 
 
 1836 
 
 52 34.7 
 
 10289. 
 
 91.9 
 
 78.25 
 
 7.81 
 
 22 1.36 
 
 21.1 
 
 33.64 
 
 10.2 
 
 1849 
 
 52 2.1 
 
 1829 
 
 15.7 
 
 206.26 
 
 14.82 
 
 39.65 
 
 0.4 
 
 39.87 
 
 11.7 
 
 1863 
 
 51 29.6 
 
 1830 
 
 160.2 
 
 97.27 
 
 47.58 
 
 187.30 
 
 20.0 
 
 12.98 
 
 12.1 
 
 8.7721876 
 
 284 50 57.1 
 
 1831 
 
 84.0 
 
 22558 
 
 51.10 
 
 2.59 
 
 59.2 
 
 49.20 
 
 13.9 
 
 1890 
 
 50 24.7 
 
 1882.8. 
 
 8,9 
 
 117.30 
 
 0.62 
 
 57.88 
 
 38.5 
 
 55.43 
 
 15.4 
 
 1901 
 
 49 52.1 
 
 1S33 
 
 153.3 
 
 8.82 
 
 33.88 
 
 205.52 
 
 58.1 
 
 58.54 
 
 16.2 
 
 1917 
 
 49 19.6 
 
 1834 
 
 77.2 
 
 186.32 
 
 40.39 
 
 20.81 
 
 37.4 
 
 4.76 
 
 17.7 
 
 1931 
 
 48 47.1 
 
 1--:;:, 
 
 1.1 
 
 27,84 
 
 13.65 
 
 168.45 
 
 57.0 
 
 7.87 
 
 18.4 
 
 8.7721911 
 
 284 48 11.6 
 
 18865. 
 
 1 16.5 
 
 156.85 
 
 20.17 
 
 223.74 
 
 86.2 
 
 14.10 
 
 19.9 
 
 1958 
 
 47 42.0 
 
 1887 
 
 70.1 
 
 17.86 
 
 26,69 
 
 39.03 
 
 15.5 
 
 20.32 
 
 21.5 
 
 1971 
 
 47 9.6 
 
 1838 
 
 211.S 
 
 175.37 
 
 59.94 
 
 186.68 
 
 35.1 
 
 23. 13 
 
 22.2 
 
 1985 
 
 46 37.1 
 
 1839 
 
 188.7 
 
 66.39 
 
 6.46 
 
 1.97 
 
 14.4 
 
 29.66 
 
 23.7 
 
 1999 
 
 46 1.6 
 
 is i()/;. 
 
 63.5 
 
 195.40 
 
 12.98 
 
 57.26 
 
 53.6 
 
 35.88 
 
 25.2 
 
 8.7722012 
 
 284 45 32.0 
 
 1841 
 
 208.0 
 
 86.41 
 
 46.24 
 
 20 1.90 
 
 13.2 
 
 38.99 
 
 26.0 
 
 2026 
 
 44 59.5 
 
 1842 
 
 131.8 
 
 21442 
 
 52.75 
 
 20.19 
 
 52.5 
 
 15.21 
 
 27.5 
 
 2039 
 
 44 27.0 
 
 1813 
 
 55.7 
 
 105.44 
 
 26.01 
 
 167.84 
 
 12.1 
 
 18.33 
 
 23.2 
 
 2053 
 
 13 51.5 
 
 1844B. 
 
 201.1 
 
 234.44 
 
 82.53 
 
 223. 13 
 
 51.4 
 
 54.55 
 
 29.7 
 
 2067 
 
 43 21.9 
 
 1845 
 
 12f>.0 
 
 125. 1(5 
 
 39.05 
 
 3S. 12 
 
 30.6 
 
 0.77 
 
 31.2 
 
 8.7722080 
 
 284 42 49.5 
 
 IM ; 
 
 4K.9 
 
 16.48 
 
 12.31 
 
 186.06 
 
 50.2 
 
 3.88 
 
 32.0 
 
 209 1 
 
 12 17.0 
 
 1847 
 
 193.3 
 
 144.49 
 
 18.82 
 
 1.35 
 
 29.5 
 
 10.11 
 
 33.5 
 
 2107 
 
 11 11.5 
 
 IMS/;. ii 
 
 86.50 
 
 25.3 1 
 
 56.64 
 
 8.7 
 
 16.33 
 
 35.0 
 
 2121 
 
 41 11.9 
 
 1849 
 
 12.0 
 
 Hi 1.51 
 
 58.60 
 
 201.28 
 
 28.4 
 
 19. 1 1 
 
 35.7 
 
 8.7722131 
 
 284 40 3!). 1 
 
 
 
 1 
 
 
 
 
10 
 
 TABLE VI. 
 
 Mean Longitude, Arguments, $c., for Washington Mean Xoon of Jan. in common years, Jan. I in 
 bissextile i/ears. 
 
 Year. 
 
 L 
 
 HI- 
 
 I. 
 
 11. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 1850 
 
 243 30 38.45 
 
 
 
 71.6815 
 
 167?9 
 
 11804 
 
 a 
 457 
 
 d 
 
 702.1 
 
 284.04 
 
 SO'!5 
 
 1851 
 
 108 18 8.11 
 
 1 
 
 211.9808 
 
 168.9 
 
 182 
 
 822 
 
 1127.1 
 
 15.12 
 
 202.3 
 
 1862J9. 
 
 334 41 45.58 
 
 3 
 
 128.5792 
 
 169.9 
 
 548 
 
 1188 
 
 38.1 
 
 381.12 
 
 82.0 
 
 1853 
 
 199 29 15.25 
 
 5 
 
 44.1776 
 
 170.9 
 
 913 
 
 1553 
 
 403.1 
 
 102.19 
 
 202.8 
 
 1851 
 
 64 16 44.92 
 
 6 
 
 184.4769 
 
 171.9 
 
 1278 
 
 1918 
 
 768.1 
 
 527.19 
 
 82.5 
 
 1859 
 
 289 4 11.58 
 
 8 
 
 100.0753 
 
 172.9 
 
 1643 
 
 2283 
 
 1133.1 
 
 308.27 
 
 204.3 
 
 185GB. 
 
 155 27 52.05 
 
 . 10 
 
 16.6738 
 
 173.9 
 
 2009 
 
 2649 
 
 44.2 
 
 90.35 
 
 84.0 
 
 1867 
 
 20 15 21.72 
 
 11 
 
 156.9730 
 
 174.9 
 
 231 I 
 
 55 
 
 409.2 
 
 455.35 
 
 205.8 
 
 1858 
 
 245 2 51.39 
 
 13 
 
 72.5715 
 
 175.9 
 
 2739 
 
 420 
 
 774.2 
 
 236.43 
 
 84.5 
 
 1859 
 
 109 50 21.05 
 
 14 
 
 212.8707 
 
 176.9 
 
 3104 
 
 785 
 
 1139.2 
 
 17.51 
 
 206.3 
 
 18605. 
 
 330 13 58.53 
 
 16 
 
 129.4691 
 
 177.9 
 
 3470 
 
 1151 
 
 50.3 
 
 383.51 
 
 86.0 
 
 1861 
 
 201 1 28.19 
 
 18 
 
 45.0675 
 
 178.9 
 
 3835 
 
 1516 
 
 415.3 
 
 164.59 
 
 207.8 
 
 1864 
 
 65 48 57.86 
 
 19 
 
 185.3668 
 
 179.9 
 
 4200 
 
 1881 
 
 780.3 
 
 529.59 
 
 86.5 
 
 1868 
 
 290 36 27.53 
 
 21 
 
 100.9052 
 
 180.9 
 
 4665 
 
 2210 
 
 1 145.3 
 
 310.67 
 
 208.3 
 
 18645. 
 
 157 5.00 
 
 23 
 
 17-5637 
 
 181.9 
 
 4931 
 
 2612 
 
 56.3 
 
 92.75 
 
 88.0 
 
 1865 
 
 21 47 31.67 
 
 24 
 
 157.8629 
 
 182.9 
 
 5296 
 
 18 
 
 421.3 
 
 457.75 
 
 209.8 
 
 1866 
 
 246 35 4.31 
 
 26 
 
 73.4613 
 
 183.9 
 
 5661 
 
 383 
 
 786.3 
 
 238.82 
 
 88.5 
 
 1807 
 
 111 22 31.00 
 
 27 
 
 213.7606 
 
 184.9 
 
 6026 
 
 748 
 
 1151.3 
 
 19.90 
 
 210.3 
 
 18685. 
 
 337 46 11.48 
 
 29 
 
 130.3590 
 
 185.9 
 
 6392 
 
 1114 
 
 62.4 
 
 385.90 
 
 90.0 
 
 1869 
 
 202 33 41.15 
 
 31 
 
 45.9575 
 
 186.9. 
 
 6757 
 
 1479 
 
 427.4 
 
 166.98 
 
 211.8 
 
 1870 
 
 67 21 10.82 
 
 82 
 
 186.2567 
 
 187.9 
 
 7122 
 
 1844 
 
 792.4 
 
 531.98 
 
 90.5 
 
 1871 
 
 292 8 40.49 
 
 31 
 
 101.8551 
 
 188.9 
 
 7487 
 
 2209 
 
 1157.4 
 
 313.06 
 
 212,1 
 
 18725. 
 
 158 32 17.96 
 
 36 
 
 18.4536 
 
 189.9 
 
 7853 
 
 2575 
 
 68.5 
 
 95.14 
 
 92.0 
 
 1873 
 
 23 19 47.63 
 
 37 
 
 158.7528 
 
 190.9 
 
 8218 
 
 2940 
 
 433.5 
 
 460.14 
 
 213.9 
 
 1874 
 
 248 7 17.30 
 
 39 
 
 74.3513 
 
 191.9 
 
 8583 
 
 346 
 
 798.5 
 
 241.22 
 
 92.5 
 
 1875 
 
 112 54 46.97 
 
 40 
 
 214.6505 
 
 192.9 
 
 8948 
 
 711 
 
 1163.5 
 
 22.30 
 
 214.4 
 
 1876 B. 
 
 339 18 24.45 
 
 42 
 
 131.2189 
 
 193.9 
 
 9314 
 
 1077 
 
 71.5 
 
 388.30 
 
 94.0 
 
 1877 
 
 201 5 54.12 
 
 44 
 
 46.8474 
 
 194.9 
 
 9679 
 
 1442 
 
 439.5 
 
 169.37 
 
 215.9 
 
 1878 
 
 68 53 23.79 
 
 45 
 
 187.1466 
 
 195.9 
 
 10044 
 
 1807 
 
 804.5 
 
 534.37 
 
 94.5 
 
 1879 
 
 293 40 53.46 
 
 47 
 
 102.7451 
 
 196.9 
 
 10409 
 
 2172 
 
 1169.5 
 
 315,15 
 
 210,1 
 
 1880 //. 
 
 160 4 30.94 
 
 49 
 
 19.3435 
 
 197.9 
 
 10775 
 
 2538 
 
 80.6 
 
 97.53 
 
 96.0 
 
 1881 
 
 24 52 0.61 
 
 50 
 
 159.6428 
 
 198.9 
 
 11140 
 
 2903 
 
 445.6 
 
 462.53 
 
 217.9 
 
 1882 
 
 249 39 30.28 
 
 53 
 
 75.2412 
 
 199.9 
 
 11505 
 
 308 
 
 810.6 
 
 243.01 
 
 90.6 
 
 1883 
 
 114 26 59.95 
 
 53 
 
 215.5404 
 
 200.9 
 
 11870 
 
 673 
 
 1 175.6 
 
 24.69 
 
 218,4 
 
 18845. 
 
 340 50 37.43 
 
 55 
 
 132.1389 
 
 201.9 
 
 249 
 
 1039 
 
 86.6 
 
 390.69 
 
 98.1 
 
 1885 
 
 205 38 7.10 
 
 57 
 
 47.7373 
 
 202.9 
 
 615 
 
 1404 
 
 451.6 
 
 171.77 
 
 219.9 
 
 1886 
 
 70 25 36.77 
 
 58 
 
 188.0366 
 
 203.9 
 
 980 
 
 1769 
 
 816.6 
 
 536.77 
 
 98.6 
 
 1887 
 
 295 13 6.45 
 
 60 
 
 103.6350 
 
 204.9 
 
 1315 
 
 2134 
 
 1181.6 
 
 317.85 
 
 220.4 
 
 1888 B. 
 
 161 36 43.93 
 
 62 
 
 20.2335 
 
 205.9 
 
 1711 
 
 2500 
 
 92.7 
 
 99.92 
 
 100.1 
 
 1889 
 
 26 24 13.60 
 
 63 
 
 160.5327 
 
 206.9 
 
 2076 
 
 2865 
 
 457.7 
 
 464.92 
 
 221.9 
 
 1890 
 
 251 11 43.27 
 
 65 
 
 76.1312 
 
 207.9 
 
 2111 
 
 271 
 
 822.7 
 
 246.00 
 
 100.6 
 
 1S91 
 
 115 59 12.95 
 
 66 
 
 216.1:!()1 
 
 208.9 
 
 2808 
 
 636 
 
 1187.7 
 
 27.08 
 
 222,1 
 
 18922?. 
 
 342 22 50.43 
 
 68 
 
 133.0289 
 
 209.9 
 
 3172 
 
 1002 
 
 98.8 
 
 393.08 
 
 102.1 
 
 1893 
 
 207 10 20.10 
 
 70 
 
 48.6273 
 
 210.9 
 
 3537 
 
 1367 
 
 463.8 
 
 174.16 
 
 223.9 
 
 1894 
 
 71 57 49.78 
 
 71 
 
 188.9265 
 
 211.9 
 
 3902 
 
 1732 
 
 828.8 
 
 539.16 
 
 102.6 
 
 1895 
 
 296 45 19.45 
 
 73 
 
 101.5250 
 
 212.9 
 
 4267 
 
 2097 
 
 1193.8 
 
 320.24 
 
 224.4 
 
 18965. 
 
 163 8 56.!)3 
 
 75 
 
 21.12:55 
 
 213.9 
 
 4033 
 
 2463 
 
 104.8 
 
 102.32 
 
 104.1 
 
 1897 
 
 27 50 26.61 
 
 76 
 
 161.4227 
 
 214.9 
 
 4998 
 
 2828 
 
 409.8 
 
 467.32 
 
 225.9 
 
 1898 
 
 252 43 56.29 
 
 78 
 
 77.0211 
 
 215.9 
 
 5303 
 
 234 
 
 834.8 
 
 248.40 
 
 104.6 
 
 1899 
 
 117 31 25.96 
 
 79 
 
 217.3201 
 
 216.9 
 
 5728 
 
 599 
 
 1199.8 
 
 29,18 
 
 226.4 
 
 Constant subtracted from L = !?' -10". 
 
TABLE VI. 
 
 11 
 
 M' dit Lunijitiiilr, Ar^uinnilx, <$-r., fur Wiixlihiatoti Mruii Xnon of Jan. /;/ I-IIHIIIKHI i/rrs, Jan. 1 in 
 hixxi-j-ti/r years. 
 
 JTear. 
 
 VIII. 
 
 IX. 
 
 \. 
 
 \l. 
 
 XII. 
 
 Mil. 
 
 XIV. 
 
 Log. sin i. 
 
 360 - Q. 
 
 1850 
 
 186.5 
 
 .1 
 
 6.12 
 
 19.57 
 
 7.6 
 
 25.<57 
 
 1.2 
 
 8.772211!) 
 
 / // 
 
 284 40 6.9 
 
 1851 
 
 ll().:i 
 
 183 
 
 38.37 
 
 167.22 
 
 27.2 
 
 28.78 
 
 2.0 
 
 2163 
 
 39 31.1 
 
 IN.VJ/;. 
 
 85.2 
 
 76.55 
 
 44.89 
 
 222.51 
 
 6.5 
 
 35.00 
 
 3.5 
 
 2176 
 
 39 1.8 
 
 IN:.:; 
 
 179.6 
 
 203.56 
 
 51.41 
 
 87.80 
 
 45.7 
 
 41.23 
 
 5.0 
 
 2190 
 
 38 29.3 
 
 1854 
 
 103.5 
 
 94.57 
 
 2 1.67 
 
 1N5.44 
 
 5.1 
 
 44.34 
 
 5.8 
 
 2203 
 
 37 56.8 
 
 IN;,;, 
 
 87.4 
 
 222.58 
 
 31.19 
 
 0.73 
 
 11. li 
 
 50.56 
 
 7.3 
 
 8.7722217 
 
 284 37 21.3 
 
 IS56B. 
 
 172.8 
 
 114.60 
 
 37.70 
 
 66.02 
 
 28.9 
 
 56.78 
 
 s.s 
 
 2230 
 
 36 51.8 
 
 1857 
 
 96.7 
 
 6.61 
 
 10.96 
 
 203.67 
 
 18.5 
 
 59.90 
 
 9.5 
 
 22 1 1 
 
 36 19.3 
 
 1858 
 
 20.5 
 
 133.62 
 
 17.ls 
 
 18.96 
 
 22.7 
 
 6.12 
 
 11.0 
 
 2257 
 
 35 16. s 
 
 1 s.v.i 
 
 165.0 
 
 24.64 
 
 50.74 
 
 166.60 
 
 42.4 
 
 9.23 
 
 11.8 
 
 2271 
 
 35 14.3 
 
 1860Z?. 
 
 89.8 
 
 168.65 
 
 57.25 
 
 221.89 
 
 21.6 
 
 15.45 
 
 13.3 
 
 8.77222s 1 
 
 284 34 41.7 
 
 1861 
 
 13.7 
 
 (4.66 
 
 :i.77 
 
 37.18 
 
 e.9 
 
 21.68 
 
 14.8 
 
 2298 
 
 31 9.2 
 
 186-2 
 
 158.1 
 
 172.67 
 
 37.03 
 
 IS 1.82 
 
 20.5 
 
 21.79 
 
 15.5 
 
 2311 
 
 33 36.7 
 
 1863 
 
 82.0 
 
 63.69 
 
 43.55 
 
 0.11 
 
 59.7 
 
 31.01 
 
 17.0 
 
 2325 
 
 33 4.2 
 
 1861U. 
 
 6.9 
 
 192.70 
 
 50.07 
 
 55.40 
 
 39.0 
 
 37.23 
 
 18.5 
 
 2339 
 
 32 31.6 
 
 1866 
 
 151.3 
 
 88.71 
 
 23.32 
 
 203.05 
 
 58.6 
 
 40.35 
 
 19.3 
 
 8.7722352 
 
 284 31 59.1 
 
 1866 
 
 75.2 
 
 211.72 
 
 29.84 
 
 18.34 
 
 37.9 
 
 46.57 
 
 20.8 
 
 2366 
 
 31 26.6 
 
 1S67 
 
 219.6 
 
 102.74 
 
 3.10 
 
 165.98 
 
 57.5 
 
 49.69 
 
 21.5 
 
 2379 
 
 30 54.1 
 
 1868J5. 
 
 111.5 
 
 231.74 
 
 9.62 
 
 22 1.27 
 
 36.7 
 
 55.91 
 
 23.0 
 
 2893 
 
 30 21.5 
 
 1869 
 
 68.3 
 
 122.76 
 
 16.13 
 
 36.56 
 
 16.0 
 
 2.13 
 
 21.5 
 
 2406 
 
 29 49.0 
 
 1870 
 
 212.8 
 
 13.78 
 
 1!).39 
 
 181.21 
 
 35.6 
 
 5.24 
 
 25.3 
 
 8.7722 120 
 
 284 29 16.5 
 
 1871 
 
 136.6 
 
 111.7s 
 
 55.91 
 
 239.49 
 
 14.9 
 
 11.47 
 
 26.8 
 
 2 133 
 
 28 44.0 
 
 18725. 
 
 61.5 
 
 83.80 
 
 2.43 
 
 5 1.7!) 
 
 64.1 
 
 17.69 
 
 28.3 
 
 2117 
 
 28 11.5 
 
 1873 
 
 20:>.!> 
 
 161.81 
 
 35.69 
 
 202.43 
 
 13.7 
 
 20.80 
 
 29.1 
 
 2460 
 
 27 39.0 
 
 1S71 
 
 129.8 
 
 52.83 
 
 12.20 
 
 17.72 
 
 53.0 
 
 27.03 
 
 30.6 
 
 2474 
 
 27 6.5 
 
 1875 
 
 53.7 
 
 180.83 
 
 16.46 
 
 165.36 
 
 12.6 
 
 30.14 
 
 31.3 
 
 8.7722487 
 
 284 26 34.0 
 
 1876Z?. 
 
 !!)!).! 
 
 72.85 
 
 21.98 
 
 220.65 
 
 51.9 
 
 36.36 
 
 32.8 
 
 2501 
 
 26 1.4 
 
 1871 
 
 123.0 
 
 200.86 
 
 28.:.() 
 
 35.94 
 
 31.1 
 
 42.59 
 
 34.3 
 
 2515 
 
 25 28.9 
 
 1878 
 
 46.9 
 
 91.87 
 
 1.76 
 
 183.59 
 
 50.7 
 
 45.70 
 
 35.1 
 
 2528 
 
 24 56.4 
 
 1879 
 
 191.3 
 
 219.88 
 
 8.27 
 
 238.88 
 
 30.0 
 
 51.92 
 
 0.6 
 
 25 12 
 
 24 23.9 
 
 18805. 
 
 116.2 
 
 111.90 
 
 14.79 
 
 54.17 
 
 9.2 
 
 58.14 
 
 2.1 
 
 8.7722555 
 
 284 23 51.3 
 
 1881 
 
 40.0 
 
 2.91 
 
 48.05 
 
 201.81 
 
 28.9 
 
 1.26 
 
 2.8 
 
 256!) 
 
 23 18.8 
 
 1882 
 
 1M.:. 
 
 130.92 
 
 54.57 
 
 17.10 
 
 8.1 
 
 7,18 
 
 4.3 
 
 2682 
 
 22 46.3 
 
 1883 
 
 108.3 
 
 21.94 
 
 27.82 
 
 161.75 
 
 27.7 
 
 10.59 
 
 5.1 
 
 2596 
 
 22 13.8 
 
 188 1 /;. 
 
 8&2 
 
 150.95 
 
 31.31 
 
 220.04 
 
 7.0 
 
 16.81 
 
 6.6 
 
 2609 
 
 21 41.2 
 
 1885 
 
 177.6 
 
 41.96 
 
 40.86 
 
 35.33 
 
 462 
 
 23.01 
 
 8.1 
 
 8.7722623 
 
 284 21 8.7 
 
 1886 
 
 101.5 
 
 169.97 
 
 11.12 
 
 182.97 
 
 5.9 
 
 26.15 
 
 8.8 
 
 2636 
 
 20 36.2 
 
 1881 
 
 2:1. 1 
 
 69.99 
 
 20.63 
 
 238.26 
 
 45.1 
 
 82.87 
 
 10.4 
 
 2650 
 
 20 3.7 
 
 18885. 
 
 170.8 
 
 189.99 
 
 27.15 
 
 63.55 
 
 24.4 
 
 38.60 
 
 11.9 
 
 2664 
 
 19 31.1 
 
 1889 
 
 '.) 1.7 
 
 SI. 01 
 
 0.41 
 
 201.19 
 
 44.0 
 
 41.71 
 
 12.6 
 
 2677 
 
 18 58.6 
 
 1N!)0 
 
 is.r, 
 
 209.02 
 
 6.98 
 
 16.48 
 
 23.2 
 
 47.93 
 
 11.1 
 
 8.7722691 
 
 284 18 26.1 
 
 1891 
 
 163.0 
 
 100.01 
 
 40.19 
 
 164.13 
 
 42.9 
 
 51.04 
 
 14.9 
 
 270 1 
 
 17 53.6 
 
 18925 
 
 s7.s 
 
 229.0 1 
 
 46.70 
 
 219.42 
 
 22. 1 
 
 57.27 
 
 16.1 
 
 2718 
 
 17 21.0 
 
 1899 
 
 11.7 
 
 120.06 
 
 63.22 
 
 31.71 
 
 1.4 
 
 3. If) 
 
 17.9 
 
 2731 
 
 16 48.5 
 
 1894 
 
 156.1 
 
 11.08 
 
 2H. is 
 
 1 S2.35 
 
 21.0 
 
 6.60 
 
 18.6 
 
 2745 
 
 16 15.9 
 
 1895 
 
 80.0 
 
 139.08 
 
 33.00 
 
 237.64 
 
 0.2 
 
 12.83 
 
 20.1 
 
 8.7722758 
 
 284 15 43.4 
 
 18965 
 
 1.9 
 
 31.10 
 
 89.51 
 
 52 93 
 
 39.5 
 
 19.05 
 
 21.6 
 
 2772 
 
 15 10.8 
 
 1897 
 
 1 19.3 
 
 159.11 
 
 12.77 
 
 200.5* 
 
 nit. i 
 
 22.16 
 
 22.1 
 
 
 1 1 ;;s,-{ 
 
 ISDN 
 
 7:1.2 
 
 50.12 
 
 19.29 
 
 16.87 
 
 18.4 
 
 28.39 
 
 23.!) 
 
 27!)!) 
 
 1 1 6.8 
 
 1899 
 
 217.6 
 
 178.13 
 
 52.68 
 
 163.51 
 
 58.0 
 
 81.60 
 
 2 1.6 
 
 (2812 
 
 284 13 33.3 
 
 7 \ 
 
TABLE VI. 
 
 Menu Loiit/i/ittk, Arguments, dec., for Washington Mean Koon of Jan. in common years, Jan. 1 in 
 bissextile years. 
 
 Year. 
 
 I. 
 
 in- 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 1900 
 
 / // 
 
 ,'M2 IN 55.61 
 
 81 
 
 132.9188 
 
 217.9 
 
 6093 
 
 a 
 
 964 
 
 109.'9 
 
 394.48 
 
 105'! 1 
 
 1901 
 
 207 6 25.31 
 
 83 
 
 48.5173 218.9 
 
 6158 1329 
 
 474.9 
 
 175.55 
 
 226.9 
 
 1902 
 
 71 53 54.99 
 
 84 
 
 188.8165 219.9 
 
 6823 1691 
 
 839.9 
 
 540.55 
 
 105.6 
 
 1903 
 
 296 11 21.67 
 
 86 
 
 104.4150 220.9 
 
 7188 
 
 2059 
 
 1201.9 
 
 321.63 
 
 227.4 
 
 19042. 
 
 163 5 2.15 
 
 88 
 
 21.0131 
 
 221.9 
 
 7554 
 
 2425 
 
 116.0 
 
 103.71 
 
 107.1 
 
 1905 
 
 27 52 31.83 
 
 89 
 
 161.3127 
 
 222.9 
 
 7919 
 
 2790 
 
 481.0 
 
 468.71 
 
 228.9 
 
 1900 25-2 10 1.51 
 
 91 
 
 76.9111 
 
 223.9 
 
 8284 
 
 196 
 
 846.0 
 
 2 19.79 
 
 107.6 
 
 1907 
 
 117 27 31.19 
 
 92 
 
 217.2104 ' 221.9 
 
 8649 
 
 561 
 
 1211.0 
 
 30.87 
 
 229.5 
 
 19085. 
 
 343 51 8.67 
 
 91 133.8088 
 
 225.9 
 
 9015 
 
 927 
 
 122.0 
 
 396.87 
 
 109.1 
 
 1909 
 
 208 38 38.35 
 
 96 
 
 49.4073 
 
 226.9 
 
 9380 
 
 1292 
 
 487.0 
 
 177.95 
 
 231.0 
 
 1910 
 
 73 26 8.03 
 
 97 
 
 189.7065 
 
 227.9 
 
 9745 
 
 1657 
 
 852.0 
 
 542.95 
 
 109.6 
 
 1911 
 
 298 13 37.71 
 
 99 
 
 105.3050 
 
 228.9 
 
 10110 
 
 2022 
 
 1217.0 
 
 324.03 
 
 231.5 
 
 19127?. 
 
 164 37 15.20 
 
 101 
 
 21.9034 
 
 229.9 
 
 10476 
 
 2388 
 
 128.1 
 
 106.10 
 
 111.1 
 
 1913 
 
 29 2 t 1 1.N8 
 
 102 
 
 162.2027 
 
 230.9 
 
 10841 
 
 2753 
 
 493.1 
 
 471.10 
 
 233.0 
 
 1914 
 
 2.">l 12 14.56 
 
 104 
 
 77.8011 
 
 231.9 
 
 11206 
 
 158 
 
 858.1 
 
 252.18 
 
 111.6 
 
 1915 
 
 11H 59 11.21 
 
 105 
 
 218.1004 
 
 232.9 
 
 11571 
 
 523 
 
 1223.1 
 
 33.26 
 
 233.5 
 
 19165. 
 
 315 23 21.23 
 
 107 
 
 134.6988 
 
 233.9 
 
 11937 
 
 889 
 
 131.2 
 
 399.26 
 
 113.1 
 
 1917 
 
 210 10 51.11 
 
 109 
 
 50.2973 
 
 234.9 
 
 315 
 
 1251 
 
 499.2 
 
 180.34 
 
 235.0 
 
 1918 
 
 174 58 21.09 
 
 110 
 
 190.5965 
 
 235.9 
 
 680 
 
 1619 
 
 861.2 
 
 515.31 
 
 113.6 
 
 1919 
 
 299 15 50.77 
 
 112 
 
 106.1950 
 
 236.9 
 
 1045 
 
 1984 
 
 1229.2 
 
 326.42 
 
 235.5 
 
 19205. 
 
 166 9 28.26 
 
 114 
 
 22.7935 
 
 237.9 
 
 1411 
 
 2350 
 
 110.2 
 
 108.50 
 
 115.2 
 
 1921 
 
 30 56 57.95 
 
 115 
 
 163.0927 
 
 238.9 
 
 1776 
 
 2715 
 
 505.2 
 
 473.50 
 
 237.0 
 
 1922 
 
 255 44 27.63 
 
 117 
 
 78.6912 
 
 1.0 
 
 2141 
 
 121 
 
 870.2 
 
 25 1.58 
 
 115.7 
 
 1923 
 
 120 31 57.31 
 
 118 
 
 218.9904 
 
 2.0 
 
 2506 
 
 486 
 
 1235.2 
 
 35.65 
 
 237.5 
 
 19B4B. 
 
 346 55 34.80 
 
 120 
 
 135.5889 
 
 3.0 
 
 2872 
 
 852 
 
 146.3 
 
 401.65 
 
 117.2 
 
 1925 
 
 211 43 4.49 
 
 122 
 
 51.1873 
 
 4.0 
 
 3237 
 
 1217 
 
 511.3 
 
 182.73 
 
 239.0 
 
 1926 
 
 76 30 34.17 
 
 123 
 
 191.4866 
 
 5.0 
 
 3602 
 
 1582 
 
 876.3 
 
 547.73 
 
 117.7 
 
 1927 
 
 301 18 3.86 
 
 125 
 
 107.0850 
 
 6.0 
 
 3967 
 
 1917 
 
 1241.3 
 
 328.81 
 
 239.5 
 
 11)287?. 
 
 167 41 41.35 
 
 127 
 
 23.6835 
 
 7.0 
 
 4333 
 
 2313 
 
 152.4 
 
 110.89 
 
 119.2 
 
 1929 
 
 32 29 11.04 
 
 128 
 
 163.9827 
 
 8.0 
 
 4698 
 
 2678 
 
 517.4 
 
 475.89 
 
 2H.O 
 
 1930 
 
 257 16 40.72 
 
 130 
 
 79.5812 
 
 9.0 
 
 5063 
 
 84 
 
 882.4 
 
 256.97 
 
 119.7 
 
 1931 
 
 122 4 10.41 
 
 131 
 
 219.8804 
 
 10.0 
 
 5428 
 
 449 
 
 1247.4 
 
 38.05 
 
 241.5 
 
 19325. 
 
 348 27 47.90 
 
 133 
 
 136.4789 
 
 11.0 
 
 5794 
 
 815 
 
 158.4 
 
 404.05 
 
 121.2 
 
 1933 
 
 213 15 17.59 
 
 135 
 
 52.0774 
 
 12.0 
 
 6159 
 
 1180 
 
 523.4 
 
 185.13 
 
 243.0 
 
 1931 
 
 78 2 47.27 
 
 136 
 
 192.3766 
 
 13.0 
 
 6524 
 
 15-15 
 
 888.4 
 
 550.13 
 
 121.7 
 
 1935 
 
 302 50 16.96 
 
 133 
 
 107.9751 
 
 14.0 
 
 6889 
 
 1910 
 
 1253.4 
 
 331.20 
 
 0.4 
 
 19365. 
 
 169 13 54.46 
 
 140 
 
 24.5735 
 
 15.0 
 
 7255 
 
 2276 
 
 164.5 
 
 113.28 
 
 123.2 
 
 1937 
 
 34 1 24.15 
 
 141 
 
 164.8728 
 
 16.0 
 
 7620 
 
 2641 
 
 529.5 
 
 478.28 
 
 1.9 
 
 1938 
 
 258 48 53.83 
 
 143 
 
 80.4712 
 
 17.0 
 
 7985 
 
 47 
 
 894.5 
 
 259.36 
 
 123.7 
 
 1939 
 
 123 36 23.52 
 
 144 
 
 220.7705 
 
 18.0 
 
 8350 
 
 412 
 
 1259.5 
 
 40.44 
 
 2.4 
 
 19405. 
 
 350 1.02 
 
 146 
 
 137.3690 
 
 19.0 
 
 8716 
 
 778 
 
 170.5 
 
 406.44 
 
 125.2 
 
 1941 
 
 214 47 30.71 
 
 148 
 
 52.9671 
 
 20.0 
 
 9081 
 
 1143 
 
 535.5 
 
 187.52 
 
 3.9 
 
 1942 
 
 79 35 0.40 
 
 149 
 
 193.2667 
 
 21.0 
 
 9446 
 
 1508 
 
 900.5 
 
 552.52 
 
 125.7 
 
 1943 
 
 304 22 30.09 
 
 151 
 
 108.8651 
 
 22.0 
 
 9811 
 
 1873 
 
 1265.5 
 
 333.60 
 
 4.4 
 
 19445. 
 
 170 46 7.59 
 
 153 
 
 25.4636 
 
 23.0 
 
 10177 
 
 2239 
 
 176.6 
 
 115.68 
 
 127.2 
 
 1915 
 
 35 33 37.28 
 
 154 
 
 165.7628 
 
 24.0 
 
 10542 
 
 2604 
 
 541.6 
 
 480.68 
 
 5.9 
 
 1946 
 
 260 21 6.97 
 
 156 
 
 81.3613 
 
 25.0 
 
 10907 
 
 10 
 
 906.6 
 
 261.76 
 
 127.7 
 
 1947 
 
 125 8 36.66 
 
 157 
 
 221.6606 
 
 26.0 
 
 11272 
 
 375 
 
 1271.6 
 
 42.83 
 
 6.4 
 
 19485. 
 
 351 32 14.16 
 
 159 
 
 138.2590 
 
 27.0 
 
 11638 
 
 741 
 
 182.7 
 
 408.83 
 
 129.2 
 
 1949 
 
 216 19 43.85 
 
 161 
 
 53.8575 
 
 28.0 
 
 15 
 
 1106 
 
 517.7 
 
 189.91 
 
 7.9 
 
 Constant subtracted from L = 47' 40". 
 
TABLE VI. 
 
 M i-ii it I.niKjitiiilf, Ari/iinii ills. i(-c.,/(//- ]\'xli!/it//un Mrmi \nnit <,/ Jan. in common yriim, -lini. 1 in 
 Itinsi-.rtilf i/i'Urx. 
 
 iTeor. 
 
 VIII. 
 
 IX. 
 
 Y 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 Log. sin /. 
 
 360- Q. 
 
 11100 
 
 a 
 111.5 
 
 69*15 
 
 59.07 
 
 318.80 
 
 37.2 
 
 87.72 
 
 26. 1 
 
 8.772282 1 
 
 / // 
 
 281 13 O.N 
 
 1901 
 
 65.3 
 
 197.16 
 
 
 31.09 
 
 16.5 
 
 48.94 
 
 27.6 
 
 2837 
 
 12 2s.:( 
 
 1903 
 
 209.8 
 
 88.n 
 
 88.84 
 
 IN 1.73 
 
 36. 1 
 
 17.0(1 
 
 2s. 1 
 
 2S5 1 
 
 11 55.N 
 
 1903 
 
 183.6 
 
 216.18 
 
 15.36 
 
 237.02 
 
 15.4 
 
 53 
 
 29.9 
 
 2N6 1 
 
 11 23.3 
 
 19017;. 
 
 .-)S.;, 
 
 ios.20 
 
 51.88 
 
 62.81 
 
 54.6 
 
 59.50 
 
 31.1 
 
 281 
 
 10 50.7 
 
 1905 
 
 JO'.'.il 
 
 236.2 l 
 
 .'.-..13 
 
 199.96 
 
 11.3 
 
 2.62 
 
 32.2 
 
 8.7722891 
 
 2S| 10 is.-.; 
 
 1906 
 
 126.8 
 
 127.22 
 
 31.65 
 
 15.25 
 
 53.5 
 
 8.84 
 
 33.7 
 
 2905 
 
 9 15.7 
 
 1901 
 
 50.7 
 
 18.24 
 
 i.!n 
 
 162.89 
 
 13.1 
 
 11.95 
 
 3 1. 1 
 
 2918 
 
 1) 13.2 
 
 1908B. 
 
 196.1 
 
 li7.-j:> 
 
 11.48 
 
 2 IS. 18 
 
 52. 1 
 
 18.17 
 
 85.9 
 
 2932 
 
 N 10.6 
 
 1909 
 
 120.0 
 
 38J26 
 
 17.95 
 
 33. 17 
 
 81.6 
 
 21.10 
 
 1.5 
 
 2!) 15 
 
 S s. 1 
 
 1910 
 
 B.8 
 
 166.27 
 
 51.20 
 
 lsl.12 
 
 51.3 
 
 27.51 
 
 2.2 
 
 8.7722959 
 
 MM 7 35.6 
 
 11)11 
 
 18&8 
 
 5759 
 
 67.72 
 
 236. 1 1 
 
 30.5 
 
 88.78 
 
 3.7 
 
 21)72 
 
 7 3.0 
 
 1912/;. 
 
 113.1 
 
 1SJ.29 
 
 4.24 
 
 61.70 
 
 9.8 
 
 39.96 
 
 5.2 
 
 2986 
 
 (i 30.4 
 
 1913 
 
 37.0 
 
 77.31 
 
 37. 50 
 
 199.3 1 
 
 29. 1 
 
 43.07 
 
 5.9 
 
 2999 
 
 5 57.!) 
 
 19 It 
 
 181.4 
 
 205.32 
 
 11.01 
 
 1 1.63 
 
 8.6 
 
 49.29 
 
 7.1 
 
 3012 
 
 5 -J.Y 1 
 
 1915 
 
 105.3 
 
 96.33 
 
 n.27 
 
 162.27 
 
 558.3 
 
 52.40 
 
 8.2 
 
 8.7723026 
 
 284 4 52.9 
 
 1916B. 
 
 80.2 
 
 225.3 1 
 
 23.79 
 
 217.56 
 
 7.5 
 
 58.63 
 
 9.7 
 
 303!) 
 
 4 20.3 
 
 1917 
 
 174.6 
 
 116.36 
 
 30.3 1 
 
 32. N5 
 
 46.8 
 
 4.85 
 
 11.2 
 
 3053 
 
 3 -17.H 
 
 1918 
 
 98.5 
 
 7.3S 
 
 3.57 
 
 1N0.50 
 
 (i. 1 
 
 7.96 
 
 11.9 
 
 8066 
 
 3 15.3 
 
 1919 
 
 2&3 
 
 135.:;s 
 
 10.08 
 
 235.79 
 
 45.6 
 
 14.19 
 
 13.4 
 
 3080 
 
 2 42.8 
 
 I90DB. 
 
 1G7.H 
 
 27.40 
 
 16.60 
 
 51.08 
 
 24.9 
 
 20.41 
 
 15.0 
 
 8.7723093 
 
 284 2 10.2 
 
 1921 
 
 91. (i 
 
 155.11 
 
 49.86 
 
 198.72 
 
 1 1.5 
 
 23.52 
 
 15.7 
 
 3107 
 
 1 37.6 
 
 1922 
 
 15.5 
 
 16.42 
 
 56.38 
 
 11.01 
 
 23.S 
 
 29.75 
 
 17.2 
 
 3120 
 
 1 5.1 
 
 1 923 
 
 159.9 
 
 17-1.13 
 
 29.63 
 
 161.66 
 
 43.4 
 
 32.86 
 
 18.0 
 
 3134 
 
 32.6 
 
 19217;. 
 
 848 
 
 66. 15 
 
 36.15 
 
 216.95 
 
 22.6 
 
 39.08 
 
 19.5 
 
 3147 
 
 284 0.0 
 
 [925 
 
 8.7 
 
 191.16 
 
 42.67 
 
 32.2 1 
 
 1.9 
 
 45.30 
 
 21.0 
 
 8.7723160 
 
 283 59 27.5 
 
 1926 
 
 153.1 
 
 S5. 17 
 
 15.93 
 
 179.88 
 
 21.5 
 
 48.42 
 
 21.7 
 
 3174 
 
 58 55.0 
 
 11CJ7 
 
 77.0 
 
 213. is 
 
 22. 15 
 
 235.17 
 
 0.8 
 
 54.64 
 
 23.2 
 
 31K7 
 
 58 22.5 
 
 1928Z?. 
 
 1.9 
 
 105.50 
 
 28.96 
 
 50.46 
 
 40.0 
 
 0.86 
 
 24.7 
 
 3201 
 
 57 49.9 
 
 11)29 
 
 116.3 
 
 233.50 
 
 2.22 
 
 198.10 
 
 59.6 
 
 3.97 
 
 25.5 
 
 3211 
 
 57 17.3 
 
 1930 
 
 70.2 
 
 124.52 
 
 8.74 
 
 13.39 
 
 38.9 
 
 10.20 
 
 27.0 
 
 8.7723228 
 
 283 56 41.8 
 
 1931 
 
 211. (i 
 
 15.51 
 
 42.00 
 
 161.04 
 
 58.5 
 
 13.31 
 
 27.7 
 
 32 1 1 
 
 56 12.3 
 
 I932J3. 
 
 139.5 
 
 111.55 
 
 48.51 
 
 216.33 
 
 37.8 
 
 19.53 
 
 29.2 
 
 3255 
 
 55 39.7 
 
 19:5:t 
 
 63.3 
 
 35.56 
 
 55.03 
 
 31.62 
 
 17.0 
 
 25.76 
 
 30.7 
 
 3268 
 
 55 7.2 
 
 1934 
 
 207.8 
 
 163.57 
 
 js.29 
 
 179.26 
 
 36.6 
 
 28.87 
 
 31.5 
 
 3282 
 
 51 34.7 
 
 1936 
 
 131.6 
 
 51.59 
 
 31.81 
 
 231.55 
 
 15.9 
 
 35.09 
 
 33.0 
 
 8.77232!!.") 
 
 283 51 2.1 
 
 193GB. 
 
 56.5 
 
 183.59 
 
 4-1.32 
 
 49.84 
 
 55.1 
 
 11.32 
 
 31.5 
 
 3309 
 
 53 29.5 
 
 19:57 
 
 200.9 
 
 74.61 
 
 i i..vs 
 
 197.49 
 
 14.8 
 
 44.43 
 
 85.8 
 
 3322 
 
 52 57.0 
 
 1938 
 
 12 1.8 
 
 202.62 
 
 21.10 
 
 12.78 
 
 51.0 
 
 50.65 
 
 0.8 
 
 3335 
 
 52 2-1.5 
 
 1939 
 
 48.7 
 
 93.63 
 
 54.36 
 
 160.42 
 
 13.6 
 
 53.76 
 
 1.5 
 
 3349 
 
 51 52.0 
 
 19405. 
 
 191.1 
 
 222.6 1 
 
 0.88 
 
 215.71 
 
 52.9 
 
 59.99 
 
 3.0 
 
 8.7723362 
 
 283 51 19.4 
 
 1911 
 
 118.0 
 
 113.66 
 
 7.39 
 
 31.00 
 
 32. 1 
 
 6.21 
 
 4.5 
 
 3376 
 
 50 46.9 
 
 1942 
 
 41.8 
 
 4.67 
 
 40.65 
 
 178.64 
 
 51.8 
 
 9.32 
 
 5.3 
 
 3389 
 
 50 11.3 
 
 1913 
 
 186.3 
 
 132.68 
 
 47.17 
 
 233.93 
 
 31.0 
 
 15.55 
 
 6.8 
 
 3403 
 
 49 41.8 
 
 19445. 
 
 111.1 
 
 21.70 
 
 53.69 
 
 19.22 
 
 10.3 
 
 21.77 
 
 8.3 
 
 3416 
 
 49 9.2 
 
 1945 
 
 35.0 
 
 152.71 
 
 26.95 
 
 196.67 
 
 29.9 
 
 24.88 
 
 9.0 
 
 8.7723430 
 
 283 48 36.7 
 
 1946 
 
 179.4 
 
 43.72 
 
 33. 16 
 
 12.16 
 
 9.1 
 
 31.10 
 
 10.5 
 
 8448 
 
 48 1.2 
 
 1917 
 
 103.3 
 
 171.73 
 
 6.72 
 
 159.80 
 
 28.8 
 
 31.22 
 
 11.3 
 
 31 :.7 
 
 47 31.6 
 
 \'.n-^/:. 
 
 28.2 
 
 63.75 
 
 13.21 
 
 215.09 
 
 8.0 
 
 40.44 
 
 12.8 
 
 3 no 
 
 46 511.0 
 
 1!)19 
 
 172.6 
 
 191.76 
 
 19.76 
 
 30.38 
 
 47.3 
 
 46.66 
 
 14.3 
 
 B.7723484 
 
 2N3 16 26.5 
 
TABLE VII. 
 
 Motion of mean Longitude and of Q, ; and Fraction of Year. 
 
 Common 
 
 Bissextile 
 
 Motion of Mran 
 
 .Motion of 
 
 Fract. 
 
 Year. 
 
 Motion of Mran 
 
 Motion of 
 
 Frart. 
 
 Year. 
 
 Year. 
 
 Longitude. 
 
 3600- Q 
 
 of Year. 
 
 
 Longitude. 
 
 3600- Q, 
 
 of Year. 
 
 
 
 o / /' 
 
 n 
 
 
 
 / II 
 
 n 
 
 
 Jan. 
 
 Jan. 1 
 
 0.00 
 
 0.0 
 
 0.000 
 
 Mar. 1 
 
 90 7 48.44 
 
 5.3 
 
 0.164 
 
 1 
 
 2 
 
 1 3(j 7.-I 
 
 O.I 
 
 0.003 
 
 2 
 
 97 43 50.25 
 
 5.4 
 
 0.107 
 
 2 
 
 3 
 
 3 12 i.-).i;i 
 
 0.2 
 
 0.005 
 
 3 
 
 99 20 4.05 
 
 5.5 
 
 0.170 
 
 3 
 
 1 
 
 4 48 23.42 
 
 0.3 
 
 0.008 
 
 4 
 
 100 50 11. 8G 
 
 5.6 
 
 0.173 
 
 4 
 
 5 
 
 6 24 3I.'.>3 
 
 0.4 
 
 0.011 
 
 5 
 
 102 32 19.07 
 
 5.7 
 
 0.175 
 
 5 
 
 6 
 
 8 39.04 
 
 0.4 
 
 0.014 
 
 6 
 
 104 8 27.48 
 
 5.8 
 
 0.178 
 
 6 
 
 7 
 
 9 36 4G.K4 
 
 0.5 
 
 0.016 
 
 7 
 
 105 44 35.28 
 
 5.9 
 
 0.181 
 
 7 
 
 8 
 
 11 12 54.05 
 
 0.6 
 
 0.019 
 
 8 
 
 107 20 43.09 
 
 C.O 
 
 0.183 
 
 8 
 
 9 
 
 12 49 2.40 
 
 0.7 
 
 0.022 
 
 9 
 
 108 50 50.90 
 
 6.1 
 
 0.18C 
 
 g 
 
 10 
 
 14 25 10.27 
 
 0.8 
 
 0.025 
 
 10 
 
 110 32 58.70 
 
 6.1 
 
 0.189 
 
 ID 
 
 11 
 
 1C 1 18.07 
 
 0.9 
 
 0.027 
 
 11 
 
 112 9 0.51 
 
 6.2 
 
 0.192 
 
 11 
 
 12 
 
 17 37 25.88 
 
 1.0 
 
 0.030 
 
 12 
 
 113 45 14.32 
 
 6.3 
 
 0.194 
 
 12 
 
 13 
 
 19 13 33.69 
 
 1.1 
 
 0.033 
 
 13 
 
 115 21 22.13 
 
 6.4 
 
 0.197 
 
 13 
 
 14 
 
 20 49 41.50 
 
 1.3 
 
 0.030 
 
 14 
 
 11G 57 29.93 
 
 0.5 
 
 0.200 
 
 14 
 
 15 
 
 22 25 49.30 
 
 1.2 
 
 0.038 
 
 15 
 
 118 33 37.74 
 
 0.0 
 
 0.203 
 
 15 
 
 16 
 
 24 1 57.11 
 
 1.3 
 
 0.041 
 
 1C 
 
 120 9 45.55 
 
 6.7 
 
 0.205 
 
 16 
 
 17 
 
 25 38 4.92 
 
 1.4 
 
 0.044 
 
 17 
 
 121 45 53.36 
 
 6.8 
 
 0.20C 
 
 17 
 
 18 
 
 27 14 12.72 
 
 1.5 
 
 0.047 
 
 18 
 
 123 22 1.16 
 
 0.9 
 
 0.211 
 
 18 
 
 19 
 
 28 50 20.53 
 
 1.6 
 
 0.04!) 
 
 19 
 
 124 58 8.97 
 
 C.9 
 
 0.214 
 
 19 
 
 20 
 
 30 26 28.34 
 
 1.7 
 
 0.052 
 
 20 
 
 126 34 16.78 
 
 7.0 
 
 0.216 
 
 20 
 
 21 
 
 32 2 30.15 
 
 1.8 
 
 0.055 
 
 21 
 
 128 10 24.59 
 
 7.1 
 
 0.219 
 
 21 
 
 22 
 
 33 38 43.95 
 
 1.9 
 
 0.057 
 
 22 
 
 129 40 32.39 
 
 7.2 
 
 0.222 
 
 22 
 
 23 
 
 35 14 51.70 
 
 2.0 
 
 0.000 
 
 23 
 
 131 22 40.20 
 
 7.3 
 
 0.225 
 
 23 
 
 24 
 
 30 50 59.57 
 
 2.0 
 
 O.OC3 
 
 24 
 
 132 58 48.01 
 
 7.4 
 
 0.227 
 
 24 
 
 25 
 
 38 27 7.38 
 
 2.1 
 
 0.000 
 
 25 
 
 134 34 55.81 
 
 7.5 
 
 0.230 
 
 25 
 
 26 
 
 40 3 15.18 
 
 2.2 
 
 0.068 
 
 20 
 
 130 11 3.02 
 
 7.6 
 
 0.233 
 
 26 
 
 27 
 
 41 39 22.99 
 
 2.3 
 
 0.071 
 
 27 
 
 137 47 11.43 
 
 7.7 
 
 0.230 
 
 27 
 
 28 
 
 43 15 30.80 
 
 2.4 
 
 0.074 
 
 28 
 
 139 23 19.24 
 
 7.7 
 
 0.238 
 
 28 
 
 29 
 
 44 51 38.00 
 
 2.5 
 
 0.077 
 
 29 
 
 140 59 27.04 
 
 7.8 
 
 0.241 
 
 29 
 
 30 
 
 46 27 46.41 
 
 2.6 
 
 0.079 
 
 30 
 
 142 35 34.85 
 
 7.9 
 
 0.244 
 
 30 
 
 31 
 
 48 3 54.22 
 
 2.7 
 
 Q.082 
 
 31 
 
 144 11 42.06 
 
 8.0 
 
 0.240 
 
 31 
 
 Feb. 1 
 
 49 40 2.03 
 
 2.8 
 
 0.085 
 
 Apr. 1 
 
 145 47 50.47 
 
 8.1 
 
 0.249 
 
 Feb. 1 
 
 2 
 
 51 10 9.83 
 
 2.8 
 
 0.088 
 
 2 
 
 147 23 58.27 
 
 8.2 
 
 0.252 
 
 2 
 
 3 
 
 52 52 17.04 
 
 2.9 
 
 0.090 
 
 3 
 
 149 C.08 
 
 8.3 
 
 0.255 
 
 3 
 
 4 
 
 54 28 25.45 
 
 3.0 
 
 0.093 
 
 4 
 
 150 30 13.89 
 
 8.4 
 
 0.257 
 
 4 
 
 5 
 
 56 4 33.20 
 
 3.1 
 
 0.096 
 
 5 
 
 152 12 21.C9 
 
 8.5 
 
 0.200 
 
 5 
 
 6 
 
 57 40 41.06 
 
 3.2 
 
 0.099 
 
 6 
 
 153 48 29.50 
 
 8.5 
 
 0.203 
 
 6 
 
 7 
 
 59 10 48.87 
 
 3.3 
 
 0.101 
 
 7 
 
 155 24 37.31 
 
 8.6 
 
 0.266 
 
 7 
 
 8 
 
 60 52 56.68 
 
 3.4 
 
 0.104 
 
 8 
 
 157 45.12 
 
 8.7 
 
 0.2C8 
 
 8 
 
 9 
 
 62 29 4.49 
 
 3.5 
 
 0.107 
 
 9 
 
 158 30 52.92 
 
 8.8 
 
 0271 
 
 9 
 
 10 
 
 64 5 12.29 
 
 - 3.0 
 
 0.110 
 
 10 
 
 160 13 0.73 
 
 8.9 
 
 0.274 
 
 10 
 
 11 
 
 05 41 20.10 
 
 3.6 
 
 0.112 
 
 11 
 
 101 49 8.54 
 
 9.0 
 
 0.277 
 
 11 
 
 12 
 
 67 17 27.91 
 
 3.7 
 
 0.115 
 
 12 
 
 163 25 10.:!."> 
 
 9.1 
 
 0.278 
 
 12 
 
 13 
 
 68 53 35.71 
 
 3.8 
 
 0.118 
 
 13 
 
 105 1 24.15 
 
 9.2 
 
 0.282 
 
 13 
 
 14 
 
 70 29 43.52 
 
 3.9 
 
 0.120 
 
 14 
 
 106 37 31.96 
 
 93 
 
 0.285 
 
 14 
 
 15 
 
 72 5 51.33 
 
 4.0 
 
 0.123 
 
 15 
 
 168 13 39.77 
 
 9.3 
 
 0.288 
 
 15 
 
 10 
 
 73 41 59.14 
 
 4.1 
 
 0.126 
 
 1C 
 
 109 49 47.58 
 
 9.4 
 
 0.890 
 
 16 
 
 17 
 
 75 18 6.94 
 
 4.2 
 
 0.129 
 
 17 
 
 171 25 55.38 
 
 9.5 
 
 0.293 
 
 17 
 
 18 
 
 76 54 14.75 
 
 4.3 
 
 0.131 
 
 18 
 
 173 2 3.19 
 
 9.G 
 
 0.29G 
 
 18 
 
 19 
 
 78 30 22.56 
 
 4.4 
 
 0.134 
 
 19 
 
 174 38 11.00 
 
 9.7 
 
 0.298 
 
 19 
 
 20 
 
 80 6 30.37 
 
 4.5 
 
 0.137 
 
 20 
 
 170 14 18.80 
 
 9.8 
 
 0.301 
 
 20 
 
 21 
 
 81 42 38.17 
 
 4.5 
 
 0.140 
 
 21 
 
 177 50 26.61 
 
 8.9 
 
 0.304 
 
 21 
 
 22 
 
 83 18 45.98 
 
 4.6 
 
 0.142 
 
 22 
 
 179 26 34.42 
 
 10.0 
 
 0.307 
 
 22 
 
 23 
 
 84 54 53.79 
 
 4.7 
 
 0.145 
 
 23 
 
 181 2 42.23 
 
 10.1 
 
 0.309 
 
 23 
 
 24 
 
 86 31 1.60 
 
 4.8 
 
 0.148 
 
 24 
 
 182 38 50.03 
 
 10.1 
 
 0.312 
 
 24 
 
 25 
 
 88 7 9.40 
 
 4.9 
 
 0.151 
 
 25 
 
 184 14 57.84 
 
 10.2 
 
 0.315 
 
 25 
 
 96 
 
 89 43 17.21 
 
 5.0 
 
 0.153 
 
 26 
 
 185 51 5.65 
 
 10.3 
 
 0.318 
 
 26 
 
 27 
 
 91 19 25.02 
 
 5.1 
 
 0.150 
 
 27 
 
 187 27 13.46 
 
 10.4 
 
 0.320 
 
 27 
 
 28 
 
 28 
 29 
 
 92 55 32.82 
 94 31 40.63 
 
 5.2 
 
 5.3 
 
 0.159 
 0.161 
 
 28 
 29 
 
 189 3 21.26 
 190 39 29.07 
 
 10.5 
 10.0 
 
 0.323 
 
 0.326 
 
TABLE VII. 
 
 Mnl inn nf M, ,1,1 Lnimiluili' unit of Q; mill 1'rurlinn ,,f \'i;ir. 
 
 
 .M, ,11011 of 
 
 Uotii 
 
 l-'r.-irtion of 
 
 * 
 
 .Motion of 
 
 .Motion of 
 
 -.,n of 
 
 
 Mran Longitude. 
 
 - 8 
 
 > i-.-ir. 
 
 i-ar. 
 
 .Mean Lnngiiinlf. 
 
 - Q 
 
 
 
 / ') 
 
 n 
 
 
 
 o / // 
 
 II 
 
 
 April 30 
 
 1. - 
 
 10.7 
 
 
 Jlllu- 29 
 
 2- 23 y 
 
 16.0 
 
 0.403 
 
 .May 1 
 
 103 51 41.60 
 
 
 0.331 
 
 30 
 
 50 33.12 
 
 16.1 
 
 n r. 6 
 
 2 
 
 195 27 52.4'J 
 
 10.0 
 
 0.334 
 
 July 1 
 
 291 35 10.: 3 
 
 16.9 
 
 (i i- - 
 
 3 
 
 197 4 0.30 
 
 10.9 
 
 0.337 
 
 2 
 
 293 11 1-71 
 
 16.3 
 
 0.501 
 
 4 
 
 19" 40 - II 
 
 11 II 
 
 0.340 
 
 3 
 
 291 17 56.55 
 
 16 1 
 
 0.504 
 
 ."> 
 
 200 Hi 15.91 
 
 11. 1 
 
 0.312 
 
 4 
 
 21 4.35 
 
 li,., 
 
 0.507 
 
 6 
 
 201 52 23.72 
 
 11 2 
 
 0.315 
 
 5 
 
 12.16 
 
 16.6 
 
 
 7 
 
 203 2- 31.53 
 
 11.3 
 
 11.31- 
 
 6 
 
 299 36 19.97 
 
 16.7 
 
 0.512 
 
 8 
 
 205 1 : 
 
 11,1 
 
 
 7 
 
 
 16.7 
 
 0.515 
 
 !) 
 
 - in 17.14 
 
 1 1 .5 
 
 0.353 
 
 8 
 
 
 H, - 
 
 11.51" 
 
 Ill 
 
 
 116 
 
 0.356 
 
 
 
 ! 21 43.30 
 
 169 
 
 OJMO 
 
 11 
 
 2,10 53 2.76 
 
 11.7 
 
 (1.359 
 
 10 
 
 51.20 
 
 17.1) 
 
 (1.523 
 
 12 
 
 211 29 1 
 
 11.8 
 
 0.361 
 
 11 
 
 307 36 50.00 
 
 17.1 
 
 0.526 
 
 13 
 
 213 5 1 
 
 11.8 
 
 (1.361 
 
 12 
 
 300 13 (i.-l 
 
 172 
 
 
 14 
 
 214 -II 26.1" 
 
 11.9 
 
 0.367 
 
 13 
 
 310 40 1 1.62 
 
 17.3 
 
 0.531 
 
 15 
 
 216 17 33.90 
 
 12.0 
 
 0.370 
 
 14 
 
 312 25 22.43 
 
 17.1 
 
 0.534 
 
 16 
 
 217 53 41.70 
 
 12.1 
 
 D.372 
 
 15 
 
 314 1 30.23 
 
 -17 1 
 
 0.537 
 
 17 
 
 210 20 49.60 
 
 12.2 
 
 11.3,75 
 
 16 
 
 315 37 38.04 
 
 17.5 
 
 0.539 
 
 18 
 
 221 5 57.41 
 
 12.3 
 
 0.37" 
 
 17 
 
 317 13 1 
 
 17 6 
 
 0.5 12 
 
 10 
 
 222 42 5.22 
 
 121 
 
 0.381 
 
 18 
 
 318 49 53.66 
 
 17.7 
 
 0.545 
 
 20 
 
 221 1- 13.02 
 
 125 
 
 0583 
 
 19 
 
 320 26 1.46 
 
 17.8 
 
 0.548 
 
 91 
 
 225 51 2.I.-3 
 
 126 
 
 0.386 
 
 20 
 
 :22 2 0.27 
 
 17.0 
 
 0.550 
 
 22 
 
 227 30 2".6I 
 
 126 
 
 0.389 
 
 21 
 
 323 38 17.08 
 
 18.0 
 
 n,-,:,:', 
 
 23 
 
 229 6 36,15 
 
 12.7 
 
 0.392 
 
 22 
 
 325 14 24.88 
 
 l-i 
 
 0.556 
 
 24 
 
 230 42 41.25 
 
 12.8 
 
 0.394 
 
 23 
 
 326 50 32.69 
 
 18.2 
 
 0.550 
 
 25 
 
 232 1" 52.1.6 
 
 12.9 
 
 0.307 
 
 24 
 
 328 26 40.50 
 
 1-2 
 
 0.561 
 
 26 
 
 233 54 59.87 
 
 13.0 
 
 0.400 
 
 25 
 
 330 2 4".31 
 
 1 3 
 
 0.564 
 
 27 
 
 235 31 7.68 
 
 13.1 
 
 0.403 
 
 26 
 
 331 38 56.11 
 
 I M 
 
 0.567 
 
 28 
 
 237 7 15.48 
 
 -13.2 
 
 0.405 
 
 27 
 
 333 15 3.92 
 
 18.5 
 
 0.570 
 
 20 
 
 13 23.20 
 
 13.3 
 
 0.408 
 
 28 
 
 334 51 11.73 
 
 18.6 
 
 0.572 
 
 30 
 
 240 10 31.10 
 
 13,1 
 
 0.411 
 
 29 
 
 336 27 19.54 
 
 18.7 
 
 0.678 
 
 31 
 
 241 55 38.90 
 
 134 
 
 0.413 
 
 30 
 
 338 3 27.34 
 
 18.8 
 
 0.578 
 
 June 1 
 
 243 31 46.71 
 
 13,5 
 
 0.416 
 
 31 
 
 339 39 35.15 
 
 18.9 
 
 0.580 
 
 2 
 
 245 7 54.52 
 
 13.6 
 
 0.419 
 
 Aug. 1 
 
 341 15 42.06 
 
 19.0 
 
 0.583 
 
 3 
 
 246 44 2.33 
 
 13.7 
 
 122 
 
 2 
 
 342 51 50.77 
 
 10.1 
 
 0.686 
 
 4 
 
 248 20 10.13 
 
 13.8 
 
 0.424 
 
 3 
 
 344 27 58.57 
 
 19.1 
 
 0.589 
 
 5 
 
 240 56 17.04 
 
 13.9 
 
 0.427 
 
 4 
 
 346 4 6.38 
 
 19.2 
 
 0.591 
 
 6 
 
 251 32 25.75 
 
 14.0 
 
 0.430 
 
 5 
 
 347 40 14.10 
 
 193 
 
 0.594 
 
 7 
 
 253 s 33.56 
 
 14.1 
 
 0.433 
 
 6 
 
 340 Hi 21.00 
 
 191 
 
 0.597 
 
 8 
 
 254 44 41.36 
 
 14.2 
 
 0.435 
 
 7 
 
 350 52 20.80 
 
 19.5 
 
 0.600 
 
 9 
 
 256 20 49.17 
 
 14.2 
 
 0.438 
 
 8 
 
 352 2-i 37.61 
 
 19.6 
 
 0.602 
 
 10 
 
 257 56 56.9- 
 
 14.3 
 
 0.411 
 
 9 
 
 351 -I 45.12 
 
 19.7 
 
 0.605 
 
 11 
 
 259 33 4.79 
 
 II 1 
 
 0,111 
 
 10 
 
 355 -III 5322 
 
 I - 
 
 0.6:)8 
 
 12 
 
 261 9 12.50 
 
 11.-, 
 
 0,1 16 
 
 11 
 
 357 17 1.03 
 
 19.9 
 
 0.611 
 
 13 
 
 262 45 20,10 
 
 14.6 
 
 0.119 
 
 12 
 
 358 53 8.84 
 
 19.9 
 
 0.613 
 
 14 
 
 261 21 2851 
 
 14.7 
 
 0.452 
 
 13 
 
 29 1665 
 
 2 1.0 
 
 0.616 
 
 15 
 
 265 57 36.01 
 
 14.8 
 
 0.455 
 
 14 
 
 2 5 24,15 
 
 BO 1 
 
 0.610 
 
 16 
 
 267 33 43.82 
 
 1 1.9 
 
 0.457 
 
 15 
 
 3 41 32.26 
 
 2,1.2 
 
 0.022 
 
 17 
 
 260 9 51.63 
 
 15.0 
 
 0.460 
 
 16 
 
 5 17 40.07 
 
 20.3 
 
 0.624 
 
 18 
 
 15 5!>,I4 
 
 15.0 
 
 0.463 
 
 17 
 
 6 53 47.88 
 
 20.4 
 
 0.627 
 
 19 
 
 272 22 721 
 
 16.1 
 
 11,165 
 
 18 
 
 8 589 556" 
 
 20.5 
 
 0.630 
 
 20 
 
 273 58 15.05 
 
 15.2 
 
 0.468 
 
 19 
 
 10 6 3.49 
 
 20.6 
 
 0.632 
 
 21 
 
 275 34 22-1, 
 
 -15.3 
 
 0.471 
 
 21) 
 
 11 42 11.30 
 
 20.7 
 
 0.635 
 
 99 
 
 277 10 30.67 
 
 15.4 
 
 0.474 
 
 21 
 
 13 18 10.10 
 
 20.7 
 
 0.638 
 
 23 
 
 27" 46 38.47 
 
 15.5 
 
 0.476 
 
 22 
 
 1 1 51 26.91 
 
 20.8 
 
 0.641 
 
 24 
 
 280 22 46.28 
 
 15.6 
 
 0.479 
 
 23 
 
 16 30 34.72 
 
 20.9 
 
 0.643 
 
 25 
 
 281 58 54.00 
 
 15.7 
 
 0.482 
 
 24 
 
 18 6 42.53 
 
 21.0 
 
 0.646 
 
 26 
 
 283 35 1 - ' 
 
 15.8 
 
 n.!-.-, 
 
 25 
 
 19 42 50.33 
 
 21.1 
 
 0.649 
 
 27 
 
 2-5 II 0.70 
 
 15.8 
 
 0.487 
 
 26 
 
 21 IS 5H.I4 
 
 21.2 
 
 0.652 
 
 28 
 
 2^6 47 17.51 
 
 15.9 
 
 0.490 
 
 27 
 
 22 55 5.95 
 
 21 .3 
 
 0.6.-, 1 
 
TABLE VII. 
 
 Mii/inn nf Mi-mi LoinfiliuJi' unil of Q; and Fraction of Yc.nr. 
 
 Vear. 
 
 Motion (if 
 
 Moan Longiliido. 
 
 Motion ni' 
 360 Q 
 
 Fraction of 
 Year. 
 
 Year. 
 
 Motion of 
 Mean Longitude. 
 
 Motion of 
 360 Q, 
 
 Fraction of 
 Year. 
 
 Aug. 28 
 
 a! 31' IH'.'TO 
 
 -2l"4 
 
 0.657 
 
 Nov. 4 
 
 o / // 
 133 28 4.05 
 
 27.4 
 
 0.843 
 
 " -J!t 
 
 Jli 7 21. .HO 
 
 21 J3 
 
 0.660 
 
 5 
 
 135 4 12.40 
 
 27.5 
 
 0.846 
 
 30 
 
 27 43 29.37 
 
 21.5 
 
 0.663 
 
 
 
 130 40 20.27 
 
 27.0 
 
 0.849 
 
 31 
 
 2!) li) 37.18 
 
 21.6 
 
 0.665 
 
 7 
 
 138 16 28.07 
 
 27.7 
 
 0.852 
 
 Sept. 1 
 
 30 55 44.98 
 
 21.7 
 
 0.668 
 
 8 
 
 139 52 35.88 
 
 27.8 
 
 0.854 
 
 2 
 
 32 31 52.79 
 
 21.8 
 
 0.071 
 
 9 
 
 141 28 43.69 
 
 27.9 
 
 0.857 
 
 3 
 
 34 8 0.00 
 
 21.9 
 
 0.074 
 
 10 
 
 143 4 51.50 
 
 28.0 
 
 0.860 
 
 4 
 
 35 44 8.41 
 
 22.0 
 
 0.076 
 
 11 
 
 144 40 59.30 
 
 28.0 
 
 0.862 
 
 5 
 
 37 20 10.21 
 
 22.1 
 
 0.079 
 
 12 
 
 146 17 7.11 
 
 J8.1 
 
 0565 
 
 G 
 
 38 50 24.02 
 
 82,2 
 
 0.682 
 
 13 
 
 147 53 14.92 
 
 28.2 
 
 0.868 
 
 7 
 
 40 32 31.83 
 
 22.3 
 
 0.685 
 
 14 
 
 149 29 22.73 
 
 28.3 
 
 0.871 
 
 8 
 
 42 8 311.04 
 
 22.3 
 
 0.687 
 
 15 
 
 151 5 30.53 
 
 28.4 
 
 0.873 
 
 n 
 
 43 44 47.44 
 
 22.4 
 
 0.690 
 
 10 
 
 152 41 38.34 
 
 28.5 
 
 0.876 
 
 10 
 
 45 20 55.25 
 
 22.5 
 
 0.693 
 
 17 
 
 154 17 46.15 
 
 28.6 
 
 0.879 
 
 n 
 
 40 57 3.CG 
 
 22.0 
 
 0.695 
 
 18 
 
 155 53 53.90 
 
 28.7 
 
 0.882 
 
 12 
 
 48 33 10.87 
 
 22.7 
 
 0.098 
 
 19 
 
 157 30 1.70 
 
 28.8 
 
 0.884 
 
 13 
 
 50 9 18.07 
 
 22.8 
 
 0.701 
 
 20 
 
 159 9.57 
 
 28.8 
 
 0.887 
 
 14 
 
 51 45 26.48 
 
 22.9 
 
 0.704 
 
 21 
 
 100 42 17.38 
 
 28.9 
 
 0.890 
 
 15 
 
 53 21 34.2!) 
 
 S3.0 
 
 0.700 
 
 22 
 
 102 18 25.18 
 
 29.0 
 
 0.893 
 
 16 
 
 54 57 42.09 
 
 23.1 
 
 0.709 
 
 23 
 
 103 54 32.99 
 
 29.1 
 
 0.895 
 
 17 
 
 56 33 49.90 
 
 23.1 
 
 0.712 
 
 24 
 
 165 30 40.80 
 
 29.2 
 
 0.898 
 
 18 
 
 58 9 57.71 
 
 23.2 
 
 0.715 
 
 25 
 
 107 6 48.61 
 
 29.3 
 
 0.901 
 
 19 
 
 59 46 5.52 
 
 23.3 
 
 0.717 
 
 26 
 
 108 42 56.41 
 
 29.4 
 
 0.904 
 
 20 
 
 01 22 13.32 
 
 23.4 
 
 0.720 
 
 27 
 
 170 19 4.22 
 
 29.5 
 
 0.906 
 
 21 
 
 02 58 21.13 
 
 23.5 
 
 0.723 
 
 28 
 
 171 55 1203 
 
 29.0 
 
 0.91)9 
 
 22 
 
 64 34 28.94 
 
 23.0 
 
 0.720 
 
 29 
 
 173 31 19.84 
 
 29.0 
 
 0.912 
 
 23 
 
 66 10 30.75 
 
 23.7 
 
 0.728 
 
 30 
 
 175 7 27.04 
 
 29.7 
 
 0.914 
 
 24 
 
 07 40 44.55 
 
 23.8 
 
 0.731 
 
 Dec. 1 
 
 176 43 35.45 
 
 29.8 
 
 0.917 
 
 25 
 
 69 22 52.36 
 
 23.9 
 
 0.734 
 
 a 
 
 178 19 43.26 
 
 29.9 
 
 0.920 
 
 20 
 
 70 59 0.17 
 
 23.9 
 
 0.737 
 
 3 
 
 179 55 51.07 
 
 30.0 
 
 0923 
 
 27 
 
 72 35 7.98 
 
 24.0 
 
 0.739 
 
 4 
 
 181 31 58.87 
 
 30.1 
 
 0.925 
 
 128 
 
 74 11 15.78 
 
 24.1 
 
 0.742 
 
 5 
 
 183 8 6.68 
 
 30.2 
 
 0.928 
 
 89 
 
 75 47 23.59 
 
 24.2 
 
 0.745 
 
 6 
 
 184 44 14.49 
 
 30.3 
 
 0.931 
 
 30 
 
 77 23 31.40 
 
 24.3 
 
 0.747 
 
 7 
 
 186 20 22.29 
 
 30.4 
 
 0.934 
 
 Oct. 1 
 
 78 59 39.20 
 
 24.4 
 
 0.750 
 
 8 
 
 187 56 30.10 
 
 30.4 
 
 0.936 
 
 2 
 
 80 35 47.01 
 
 24.5 
 
 0.753 
 
 9 
 
 189 32 37.91 
 
 30.5 
 
 0.939 
 
 3 
 
 82 11 54.82 
 
 24.0 
 
 0.756 
 
 10 
 
 191 8 45.72 
 
 30.6 
 
 0.942 
 
 4 
 
 83 48 2.03 
 
 24.7 
 
 0.758 
 
 11 
 
 192 44 53.52 
 
 30.7 
 
 0.946 
 
 5 
 
 85 24 10.43 
 
 24.7 
 
 0.761 
 
 19 
 
 194 21 1.33 
 
 30.8 
 
 0.947 
 
 6 
 
 87 18.24 
 
 24.8 
 
 0.704 
 
 13 
 
 195 57 9.14 
 
 30.9 
 
 0.950 
 
 7 
 
 88 30 20.05 
 
 24.9 
 
 0.707 
 
 14 
 
 197 33 16.95 
 
 31.0 
 
 0.953 
 
 8 
 
 90 12 33.80 
 
 25.0 
 
 0.709 
 
 15 
 
 199 9 24.75 
 
 31.1 
 
 0.950 
 
 9 
 
 . 91 48 41.00 
 
 25.1 
 
 0.772 
 
 16 
 
 200 45 32.56 
 
 31.2 
 
 0.958 
 
 10 
 
 93 24 49.47 
 
 25.2 
 
 0.775 
 
 17 
 
 202 21 40.37 
 
 31.9 
 
 0.901 
 
 11 
 
 95 57.28 
 
 25.3 
 
 0.773 
 
 18 
 
 203 57 48.17 
 
 31.3 
 
 0.964 
 
 12 
 
 90 37 5.08 
 
 25.4 
 
 0.780 
 
 13 
 
 205 33 55.98 
 
 31.4 
 
 0.967 
 
 13 
 
 98 13 12.69 
 
 25.5 
 
 0.783 
 
 20 
 
 207 10 3.79 
 
 31.5 
 
 0.969 
 
 14 
 
 99 49 20.70 
 
 25.6 
 
 0.786 
 
 21 
 
 208 46 11.60 
 
 31.0 
 
 0.972 
 
 15 
 
 101 25 28.51 
 
 25.0 
 
 0.789 
 
 22 
 
 210 22 19.40 
 
 31.7 
 
 0.975 
 
 10 
 
 103 1 3031 
 
 25.7 
 
 0.791 
 
 23 
 
 211 58 27.21 
 
 31.8 
 
 0.977 
 
 17 
 
 104 37 44.12 
 
 25.8 
 
 0.794 
 
 24 
 
 213 34 35.02 
 
 31.9 
 
 0.980 
 
 18 
 
 100 13 51.93 
 
 25.9 
 
 0.797 
 
 25 
 
 215 10 42.83 
 
 32.0 
 
 0.983 
 
 1!) 
 
 107 49 59.74 
 
 26.0 
 
 0.800 
 
 20 
 
 216 46 50.63 
 
 32.0 
 
 0.986 
 
 20 
 
 109 26 7.54 
 
 20.1 
 
 0.802 
 
 27 
 
 218 22 58.44 
 
 32. 1 
 
 0.988 
 
 21 
 
 111 2 15.35 
 
 20.2 
 
 0805 
 
 28 
 
 219 59 6.25 
 
 32.2 
 
 0.991 
 
 22 
 
 112 38 23.16 
 
 26.3 
 
 0.808 
 
 29 
 
 221 35 14.06 
 
 32.3 
 
 0.994 
 
 33 
 
 114 14 30.97 
 
 26.4 
 
 0.810 
 
 30 
 
 223 11 21.86 
 
 32.4 
 
 0.997 
 
 24 
 
 1 1 5 50 38.77 
 
 20.4 
 
 0.813 
 
 31 
 
 224 47 29-6? 
 
 32.5 
 
 0.999 
 
 25 
 
 117 26 40.58 
 
 26.5 
 
 0.816 
 
 32 
 
 226 23 37.48 
 
 32.0 
 
 1 .002 
 
 20 
 
 119 2 54.39 
 
 20.0 
 
 0.819 
 
 33 
 
 227 59 45.28 
 
 32.7 
 
 1.005 
 
 27 
 
 120 39 2.19 
 
 -20.7 
 
 0.821 
 
 34 
 
 229 35 53.09 
 
 32.8 
 
 1 .008 
 
 28 
 
 122 15 10.00 
 
 20.8 
 
 0.824 
 
 35 
 
 231 12 0.90 
 
 32.8 
 
 1.010 
 
 30 
 
 123 51 17.81 
 
 20.9 
 
 0.827 
 
 30 
 
 232 48 8.71 
 
 32.0 
 
 1.013 
 
 30 
 
 125 27 25.62 
 
 27.0 
 
 0.830 
 
 37 
 
 234 24 16.51 
 
 33.0 
 
 1.010 
 
 SI 
 
 127 3 33.42 
 
 27.1 
 
 0.832 
 
 
 
 
 
 Nov. 1 
 
 128 39 41.23 
 
 27.2 
 
 0.835 
 
 
 
 
 
 2 
 
 130 15 49.04 
 
 27.2 
 
 0.838 
 
 
 
 
 
 3 
 
 131 51 W^, 
 
 27.3 
 
 0.84 1 
 
 
 
 
 
TABLE VIII. 
 
 17 
 
 Mi'liiHI <>/' Mrilll I. n II -ri hi, If. 
 
 Hours. 
 
 For Hours. 
 
 .Minn 
 Hecondi. 
 
 For .Mimitrs. 
 
 Ollcls. 
 
 .Mi nut 
 
 .inU. 
 
 For Jliinr 
 
 For Si'i'oinls. 
 
 1 
 
 o / // 
 
 l 0.325 
 
 1 
 
 / // 
 1.005 
 
 0.067 
 
 31 
 
 / // 
 
 2 1.168 
 
 8,'o69 
 
 1 
 
 8 0.651 
 
 g 
 
 (1 S.OH 
 
 0.134 
 
 32 
 
 2 S.I 73 
 
 2.136 
 
 3 
 
 12 O.!l7(i 
 
 3 
 
 12.016 
 
 0.200 
 
 33 
 
 2 12.17!) 
 
 -.'203 
 
 1 
 
 Hi l.:i()l 
 
 I 
 
 16.022 
 
 0.2(17 
 
 31 
 
 2 16. 1M 
 
 2.270 
 
 :. 
 
 20 1.627 
 
 5 
 
 20.027 
 
 0.331 
 
 35 
 
 2 20.11)0 
 
 2.336 
 
 6 
 
 21 1.952 
 
 <i 
 
 21.033 
 
 0.101 
 
 36 
 
 2 21.195 
 
 2. 103 
 
 7 
 
 28 2.277 
 
 7 
 
 28.038 
 
 0. 167 
 
 87 
 
 2 -js.201 
 
 2.170 
 
 8 
 
 32 2.602 
 
 8 
 
 32.013 
 
 0.534 
 
 :is 
 
 2 32.206 
 
 2.687 
 
 ! 
 
 36 2.M28 
 
 !) 
 
 36.01!) 
 
 0.601 
 
 39 
 
 2 36.211 
 
 2.601 
 
 10 
 
 40 3.253 
 
 10 
 
 (1 10.051 
 
 6.688 
 
 40 
 
 2 10.217 
 
 2.670 
 
 11 
 
 o H 3.57s 
 
 11 
 
 II. Olid 
 
 0.731 
 
 41 
 
 2 1 1.222 
 
 2.737 
 
 13 
 
 is :j.!KI| 
 
 12 
 
 IS. (Ml.-) 
 
 0.801 
 
 12 
 
 2 ls.228 
 
 2.801 
 
 ia 
 
 52 1.22!) 
 
 ia 
 
 52.070 
 
 0.868 
 
 43 
 
 2 52.233 
 
 2.871 
 
 11 
 
 o 56 i.55i 
 
 11 
 
 56.07 U 
 
 0.936 
 
 1! 
 
 2 56.239 
 
 2.1)37 
 
 15 
 
 1 1.8SO 
 
 15 
 
 1 0.081 
 
 .001 
 
 15 
 
 3 0.2 1 1 
 
 3.001 
 
 it; 
 
 1 i 5.205 
 
 16 
 
 1.0S7 
 
 .Oils 
 
 III 
 
 3 1.219 
 
 3.071 
 
 17 
 
 N 5.530 
 
 17 
 
 8.092 
 
 .185 
 
 17 
 
 3 s. >.->.-> 
 
 3.138 
 
 18 
 
 12 5.856 
 
 18 
 
 12.098 
 
 .202 
 
 IS 
 
 3 12.260 
 
 3.204 
 
 1!) 
 
 lii (J.181 
 
 19 
 
 16.103 
 
 .268 
 
 49 
 
 3 16.266 
 
 3.27 1 
 
 JO 
 
 20 6.50(i 
 
 20 
 
 20.108 
 
 .388 
 
 50 
 
 3 20.271 
 
 3.3 
 
 21 
 
 21 6.831 
 
 21 
 
 24.114 
 
 .102 
 
 51 
 
 3 21.277 
 
 3. 105 
 
 22 
 
 28 7.157 
 
 22 
 
 1 28.119 
 
 .469 
 
 52 
 
 3 2N.282 
 
 3.171 
 
 23 
 
 :!2 7.182 
 
 23 
 
 1 32.125 
 
 .536 
 
 63 
 
 3 32.287 
 
 3.5 !' i 
 
 21 
 
 36 7.N07 
 
 21 
 
 1 36.130 
 
 .602 
 
 51 
 
 3 36.293 
 
 3.605 
 
 
 
 25 
 
 1 40.136 
 
 1.869 
 
 55 
 
 3 10.21)8 
 
 3.672 
 
 
 
 26 
 
 1 44.141 
 
 1.736 
 
 56 
 
 3 11.301 
 
 3.738 
 
 
 
 27 
 
 1 IN. 116 
 
 1.802 
 
 57 
 
 3 18.309 
 
 3.N05 
 
 
 
 28 
 
 1 52.152 
 
 1.869 
 
 58 
 
 3 52.314 
 
 3.872 
 
 
 
 29 
 
 1 56.157 
 
 1.936 
 
 59 
 
 3 56.320 
 
 8488 
 
 
 
 30 
 
 2 0.163 
 
 2.003 
 
 60 
 
 4 0.325 
 
 4.005 
 
 Days. Motion of M. L. 
 
 Days. 
 
 Motion of M. 1.. Days. 
 
 Motion of M. L. 
 
 0.1 09 36"781 
 
 0.01 
 
 . o' 5T678 0.001 
 
 5^768 
 
 0.2 19 13.561 
 
 0.02 
 
 1 55.356 0.002 
 
 11.536 
 
 0.3 '28 50.312 
 
 0.03 
 
 2 53.034 0.003 
 
 17.303 
 
 0.4 38 27.123 
 
 0.04 
 
 3 50.712 0.004 
 
 23.071 
 
 0.5 48 :i.!)()l 
 
 0.05 
 
 4 48.390 0.005 
 
 88.889 
 
 0.6 57 40.(i> 1 
 
 0.06 
 
 5 46.068 0.006 
 
 31.607 
 
 0.7 1 7 17.465 
 
 0.07 
 
 6 43.746 0.007 
 
 40.375 
 
 0.8 1 16 51.216 
 
 0.08 
 
 7 41.125 0.008 
 
 46.112 
 
 0.9 1 26 31.027 
 
 0.09 
 
 H 31). 103 0.009 
 
 51.910 
 
 1.0 1 36 7.807 
 
 0.10 
 
 9 36.781 0.010 
 
 57.678 
 
 TABLE IX. 
 
 Factor of a small Correction to be multiplied by the fraction of the year and then added to L. 
 
 Vfiir. Factor. 
 
 rr. 
 
 Factor. 
 
 Year. Factor. 
 
 Year. 
 
 Fin tor. 
 
 1750 -O'blS 
 
 1800 
 
 -o'bn 
 
 1850 O'OOS 
 
 1900 
 
 +o'.007 
 
 1760 0.016 
 
 1810 
 
 0.010 
 
 l.s:;o 0.003 
 
 1910 
 
 0.010 
 
 1770 0.015 
 
 1820 
 
 0.009 
 
 1870 -0.001 
 
 1920 
 
 0.013 
 
 17sO 0.014 
 
 1830 
 
 0.007 
 
 JNMI +0.001 
 
 1930 
 
 0.016 
 
 17!)0 0.012 
 
 1840 
 
 0.006 
 
 1890 0.001 
 
 1940 
 
 0.020 
 
 1800 -0.011 
 
 1850 
 
 -0.005 
 
 1900 +0.007 
 
 1950 
 
 +0.088 
 
18 
 
 TABLE X. 
 
 EQUATION OF THE CENTRE, FOR 111 = 0. 
 
 d 
 
 Constant added 47' 3".5. Period = 224.7008. 
 
 d 
 
 Diff. 
 
 d 
 
 Diff. 
 
 d 
 
 Diff. 
 
 d 
 
 Diff. 
 
 d 
 
 Diff. 
 
 Arg. I. ! O.O 
 
 for 0<l.l 
 
 0.1 
 
 for U'l.l 
 
 O.2 
 
 for 0-1.1 
 
 0.3 
 
 for O-i.l 
 
 O.4 
 
 fur (J'l.l 
 
 6 1 047 5() 
 
 // 
 +7.96 
 
 47' MAG 
 
 u 
 +7.96 
 
 47' 19.42 
 
 ii 
 +7.96 
 
 47 27.38 
 
 u 
 +7.96 
 
 47 3f>.35 
 
 n 
 +7.96 
 
 1 | 48 2*1 1 
 
 7.96 
 
 48 31.07 
 
 7.96 
 
 48 39.03 
 
 7.96 
 
 48 40.98 
 
 7.96 
 
 48 54.! 14 
 
 7.95 
 
 2 i 04!) 42.05 
 
 7.95 
 
 49 50.00 
 
 7.95 
 
 4!) 58.55 
 
 7.95 
 
 50 0.50 
 
 7.94 
 
 50 14.44 
 
 7.94 
 
 3 
 
 51 2.07 
 
 7.93 
 
 51 10.00 
 
 7.93 
 
 51 17.93 
 
 7.93 
 
 51 25.86 
 
 7.93 
 
 51 33.79 
 
 7.92 
 
 4 
 
 52 21.30 
 
 7.91 
 
 52 29.21 
 
 7.91 
 
 52 37.11 
 
 7.91 
 
 52 45.02 
 
 7.00 
 
 52 52.92 
 
 7.90 
 
 5 
 
 53 40.27 
 
 7.88 
 
 53 48.15 
 
 7.88 
 
 53 50.02 
 
 7.88 
 
 54 3.90 
 
 7.87 
 
 54 11.77 
 
 7.87 
 
 (i 
 
 54 58.92 
 
 7.85 
 
 55 0.77 
 
 7.84 
 
 55 14.61 
 
 7.84 
 
 55 22.44 
 
 7.1 1 
 
 55 30.28 
 
 7.83 
 
 7 
 
 50 17.19 
 
 7.81 
 
 50 25.00 
 
 7.80 
 
 50 32.79 
 
 7.80 
 
 56 40.59 
 
 7.79 
 
 50 48.38 
 
 7.79 
 
 8 
 
 57 35.02 
 
 7.76 
 
 57 42.78 
 
 7.75 
 
 57 50.53 
 
 7.75 
 
 57 58.27 
 
 7.74 
 
 58 0.01 
 
 7.74 
 
 
 
 58-52.34 
 
 7.70 
 
 59 0.04 
 
 7.70 
 
 59 7.74 
 
 7.69 
 
 59 15.43 
 
 7.69 
 
 59 23.11 
 
 7.68 
 
 10 
 
 1 9.09 
 
 7.li 1 
 
 10.74 
 
 7.64 
 
 24.37 
 
 7.63 
 
 32.00 
 
 7.63 
 
 39.02 
 
 7.88 
 
 11 
 
 1 1 25.22 
 
 7.08 
 
 1 32.79 
 
 7.57 
 
 1 40.30 
 
 7.56 
 
 1 47.92 
 
 7.56 
 
 1 55.48 
 
 7.55 
 
 12 
 
 1 2 40.05 
 
 7.01 
 
 2 48.15 
 
 7.50 
 
 2 55.05 
 
 7.49 
 
 3 3.14 
 
 7.48 
 
 3 10.02 
 
 7.48 
 
 13 
 
 1 3 55.33 
 
 7.43 
 
 4 2.70 
 
 7.42 
 
 4 10.17 
 
 7.41 
 
 4 17.58 
 
 7.40 
 
 4 24.98 
 
 7.40 
 
 14 
 
 1 5 9.20 
 
 7.31 
 
 5 10.54 
 
 7.34 
 
 5 23.88 
 
 7.33 
 
 5 31.20 
 
 7.32 
 
 5 38.51 
 
 7.31 
 
 15 
 
 1 22.21 
 
 7.20 
 
 6 29.40 
 
 7.24 
 
 30.70 
 
 7.24 
 
 6 43.93 
 
 7.23 
 
 6 51.15 
 
 7.22 
 
 16 
 
 1 7 34.28 
 
 7.16 
 
 1 41.44 
 
 7.15 
 
 7 48.58 
 
 7.14 
 
 7 55.71 
 
 7.13 
 
 8 2.84 
 
 7.12 
 
 17 
 
 1 8 45.37 
 
 7.l)(i 
 
 8 52.43 
 
 7.05 
 
 8 59.47 
 
 7.04 
 
 9 0.50 
 
 7.03 
 
 9 13.52 
 
 7.01 
 
 18 
 
 1 9 55.12 
 
 MB 
 
 10 2.37 
 
 6.94 
 
 10 9.30 
 
 6.93 
 
 10 10.22 
 
 6.92 
 
 10 23.14 
 
 6.1)1 
 
 19 
 
 1 11 4.37 
 
 O.bl 
 
 11 11.20 
 
 6.63 
 
 11 1S.03 
 
 C.82 
 
 11 24.83 
 
 6.80 
 
 11 31.03 
 
 6.79 
 
 20 
 
 1 12 12.17 
 
 6.72 
 
 12 18.89 
 
 6.71 
 
 12 25.59 
 
 6.70 
 
 12 32.28 
 
 6.68 
 
 12 38.9( i 
 
 6.67 
 
 21 
 
 1 13 18.77 
 
 6.60 
 
 13 25.36 
 
 6.58 
 
 13 31.94 
 
 6.57 
 
 13 38.50 
 
 6.56 
 
 13 45.0( i 
 
 6.55 
 
 22 
 
 1 14 24.10 
 
 6.47 
 
 14 30.57 
 
 6.46 
 
 14 37.02 
 
 6.44 
 
 14 43.45 
 
 6.43 
 
 14 49.87 
 
 6.42 
 
 23 
 
 1 15 28.13 
 
 6.34 
 
 15 34.46 
 
 6.32 
 
 15 40.78 
 
 6.31 
 
 15 47.08 
 
 6.29 
 
 15 53.36 
 
 6.28 
 
 24 
 
 1 10 30.80 
 
 6.20 
 
 16 36.99 
 
 6.19 
 
 16 43.10 
 
 6.17 
 
 16 4! 1.32 
 
 6.10 
 
 16 55.47 
 
 6.14 
 
 25 
 
 1 17 32.05 
 
 6.05 
 
 17 38.10 
 
 6.04 
 
 17 44.13 
 
 6.02 
 
 17 50.15 
 
 6.01 
 
 17 50.15 
 
 6.00 
 
 20 
 
 1 18 31.85 
 
 5.90 
 
 18 37.75 
 
 5.89 
 
 18 43.03 
 
 5.87 
 
 18 49.50 
 
 5.86 
 
 18 55.35 
 
 5.84 
 
 27 
 
 1 19 30.15 
 
 0.70 
 
 19 35.89 
 
 5.74 
 
 19 41.02 
 
 5.72 
 
 19 47.33 
 
 5.71 
 
 19 53.03 
 
 5.69 
 
 28 
 
 1 20 20.89 
 
 5.59 
 
 20 32.47 
 
 0.58 
 
 20 38.05 
 
 5.56 
 
 20 43.60 
 
 0.00 
 
 20 49.14 
 
 5.53 
 
 29 
 
 1 21 22.04 
 
 5.4:1 
 
 21 27.46 
 
 5.'I2 
 
 21 32.87 
 
 5.40 
 
 21 38.20 
 
 5.38 
 
 21 43.04 
 
 5.37 
 
 30 
 
 1 22 15.55 
 
 5.27 
 
 22 20.81 
 
 5.25 
 
 22 20.05 
 
 5.23 
 
 22 31.27 
 
 5.21 
 
 22 36.48 
 
 5.20 
 
 31 
 
 1 23 7.38 
 
 5.10 
 
 23 12.47 
 
 5.08 
 
 23 17.54 
 
 5.06 
 
 23 22.59 
 
 0.00 
 
 23 27.63 
 
 5.03 
 
 32 
 
 1 23 57.49 
 
 4.92 
 
 24 2.40 
 
 4.90 
 
 24 7.30 
 
 4.89 
 
 24 12.18 
 
 4.87 
 
 24 17.04 
 
 4.83 
 
 33 
 
 1 24 45.84 
 
 4.75 
 
 24 50.58 
 
 4.73 
 
 21 55.29 
 
 4.71 
 
 25 0.00 
 
 4.09 
 
 25 4.08 
 
 4.07 
 
 34 
 
 1 25 32.39 
 
 4.56 
 
 25 30.95 
 
 4.05 
 
 25 41.49 
 
 4.03 
 
 25 40.00 
 
 4.01 
 
 25 50.50 
 
 4.49 
 
 35 
 
 1 26 17.12 
 
 4.38 
 
 20 21.49 
 
 4.36 
 
 20 25.84 
 
 4.34 
 
 26 30.17 
 
 4.32 
 
 20 34.49 
 
 4.30 
 
 30 
 
 1 20 59.97 
 
 4.19 
 
 27 4.15 
 
 4.17 
 
 27 8.32 
 
 4.15 
 
 27 12.40 
 
 4.13 
 
 27 16.59 
 
 4.11 
 
 37 
 
 1 27 40.93 
 
 4.00 
 
 27 44.92 
 
 3.98 
 
 27 48.89 
 
 3.96 
 
 27 52.84 
 
 3.94 
 
 27 50.77 
 
 3.92 
 
 38 
 
 1 28 19.90 
 
 3.80 
 
 28 23.75 
 
 3.78 
 
 28 27.53 
 
 3.77 
 
 28 31.28 
 
 3.75 
 
 28 35.02 
 
 3.73 
 
 39 
 
 1 28 57.02 
 
 3.61 
 
 29 0.02 
 
 3.59 
 
 29 4.20 
 
 3.57 
 
 29 7.70 
 
 3.55 
 
 29 11.29 
 
 3.53 
 
 40 
 
 1 29 32.10 
 
 3.41 
 
 29 35.50 
 
 3.39 
 
 29 38.87 
 
 3.37 
 
 29 42.23 
 
 3.35 
 
 29 45.57 
 
 3.33 
 
 41 
 
 1 30 5.10 
 
 3.20 
 
 30 8.30 
 
 3.18 
 
 30 11.53 
 
 3.16 
 
 30 14.09 
 
 3.14 
 
 30 17.82 
 
 3.12 
 
 49 
 
 1 30 30.19 
 
 3.00 
 
 30 39.18 
 
 2.98 
 
 30 42.14 
 
 2.90 
 
 30 45.09 
 
 2.94 
 
 30 48.02 
 
 2.92 
 
 43 
 
 1 31 5.15 
 
 2.79 
 
 31 7.93 
 
 2.77 
 
 31 10.09 
 
 2.70 
 
 31 13.43 
 
 2.73 
 
 Jl 10.15 
 
 2.71 
 
 44 
 
 1 31 32.02 
 
 2.58 
 
 31 31.59 
 
 2.56 
 
 31 37.15 
 
 2.04 
 
 31 39.08 
 
 aja 
 
 31 42.18 
 
 2.00 
 
 45 
 
 1 31 50.80 
 
 2.37 
 
 31 59.10 
 
 2.35 
 
 32 1.50 
 
 2.33 
 
 32 3.81 
 
 2.31 
 
 32 6.11 
 
 2.29 
 
 46 
 
 1 32 19.45 
 
 2.16 
 
 32 21.59 
 
 2.14 
 
 32 23.72 
 
 2.12 
 
 32 25.83 
 
 2.09 
 
 32 27.91 
 
 2.07 
 
 47 
 
 1 32 39.90 
 
 l.ill 
 
 32 41.89 
 
 1.92 
 
 32 43.80 
 
 1.90 
 
 32 45.09 
 
 1.87 
 
 32 47.50 
 
 1.85 
 
 48 
 
 1 32 58.32 
 
 1.73 
 
 33 0.04 
 
 1.71 
 
 33 1.73 
 
 1.68 
 
 33 3.40 
 
 1.66 
 
 33 5.00 
 
 1.04 
 
 49 
 
 1 33 14.51 
 
 1.51 
 
 33 10.01 
 
 1.49 
 
 33 17.19 
 
 1.47 
 
 33 18.95 
 
 1.44 
 
 33 20.38 
 
 1.42 
 
 50 
 
 1 33 28.53 
 
 1.29 
 
 33 29.81 
 
 1.27 
 
 33 31.07 
 
 1.25 
 
 33 32.30 
 
 1.23 
 
 33 33.52 
 
 1.20 
 
 51 
 
 1 33 40.30 
 
 1.08 
 
 33 41.42 
 
 1.05 
 
 33 42.40 
 
 1.03 
 
 33 43.48 
 
 1.01 
 
 33 44.47 
 
 0.99 
 
 52 
 
 1 33 49.99 
 
 0.85 
 
 33 50.83 
 
 0.83 
 
 33 51.05 
 
 0.81 
 
 33 52.45 
 
 0.79 
 
 33 53.23 
 
 0.76 
 
 59 
 
 1 33 57.13 
 
 0.63 
 
 33 58.or, 
 
 O.lil 
 
 33 58.05 
 
 0.09 
 
 33 59.23 
 
 0.06 
 
 33 59.78 
 
 0.54 
 
 54 
 
 1 34 2.00 
 
 0.11 
 
 34 3.00 
 
 (1.39 
 
 34 3.11 
 
 0.37 
 
 31 3.80 
 
 0.35 
 
 31 4.13 
 
 0.32 
 
 55 
 
 I 34 5.08 
 
 +0.19 
 
 3 1 5.80 
 
 +0.17 
 
 31 0.02 
 
 +:i.io 
 
 34 0.15 
 
 +0.13 
 
 34 0.27 
 
 +0.10 
 
TABLE X. 
 
 EQUATION OF TIIF. (TATKF.. FOU 111=0. 
 
 .1 
 
 (..nstimt ;!,!. ,! IT' :;" .:,. IVrio.l WM 221 : 
 
 
 d 
 
 Diff. 
 
 ,1 
 
 Diff. 
 
 .1 
 
 Diff. 
 
 .1 
 
 Diir. 
 
 d 
 
 Diff. 
 
 Arg.I. 
 
 0.5 
 
 fur I*' 1 . 1 
 
 0.8 
 
 
 0.7 
 
 f..r U.I.I 
 
 0.8 
 
 f.,r (I'M 
 
 <>.! 
 
 furll'i.l 
 
 d 
 
 
 17 43.31 
 
 II 
 
 IT- 51.27 
 
 n 
 
 47 5:i23 
 
 ii 
 +7.96 
 
 48 1 7'.'l9 
 
 n 
 +7.% 
 
 4^ 15'J5 
 
 n 
 
 1 
 
 19 2.-H 
 
 
 lit in..-:, 
 
 7.95 
 
 49 l-.-ll 
 
 
 49 20.75 
 
 TJt 
 
 49 31.70 
 
 7.95 
 
 a 
 
 :,(i 22.38 
 
 
 50 : 10.32 
 
 7.94 
 
 50 3-.20 
 
 
 50 40.20 
 
 7Jt 
 
 50 51.1 1 
 
 7.1i:i 
 
 3 
 
 :.l 11.71 
 
 
 51 19.03 
 
 
 51 57.55 
 
 
 52 5.17 
 
 
 52 I3.3S 
 
 7.DI 
 
 4 
 
 53 o.s-> 
 
 7.90 
 
 53 -.7 1 
 
 7.89 
 
 53 10.01 
 
 7.89 
 
 53 21.50 
 
 7.89 
 
 53 32.38 
 
 7.88 
 
 :. 
 
 51 19.01 
 
 7.86 
 
 51 27.50 
 
 7.86 
 
 51 35.30 
 
 
 51 43.22 
 
 
 54 51.07 
 
 us 
 
 o 
 
 55 :l-.l 1 
 
 . 
 
 55 15.! '3 
 
 
 55 53.75 
 
 
 50 1.57 
 
 
 50 9.3* 
 
 ',.-1 
 
 7 
 
 50 50.10 
 
 7.78 
 
 57 3.95 
 
 7.78 
 
 57 11.72 
 
 7.77 
 
 57 lit. lit 
 
 7.77 
 
 57 27.20 
 
 tM 
 
 8 
 
 n 5-i 13.75 
 
 7.73 
 
 5< 21.1- 
 
 7.73 
 
 ' '.20 
 
 7.7-_> 
 
 ")"* *{l t ' t"' 
 
 7.72 
 
 58 44.1.1 
 
 7.71 
 
 9 
 
 n 59 30.79 
 
 7.67 
 
 59 3>. 10 
 
 7.117 
 
 59 40.13 
 
 
 59 53.79 
 
 7.66 
 
 00 1.44 
 
 1M 
 
 10 
 
 1 47.21 
 
 7.1! 1 
 
 51.S5 
 
 7.01 
 
 1 2. 15 
 
 7.60 
 
 1 10.H5 
 
 . 
 
 1 17.01 
 
 7- r ,8 
 
 11 
 
 1 2 3.02 
 
 ; .. > i 
 
 2 10.50 
 
 
 
 2 is. |0 
 
 7.53 
 
 2 25.02 
 
 
 2 It!. II 
 
 7.51 
 
 12 
 
 1 3 IS.Oil 
 
 7,17 
 
 3 25.55 
 
 7.16 
 
 3 .33.01 
 
 7,1.-, 
 
 3 40.46 
 
 7.44 
 
 3 47.90 
 
 7.44 
 
 13 
 
 1 4 32.37 
 
 7.39 
 
 4 39.71 i 
 
 7.38 
 
 1 17J3 
 
 7.37 
 
 I 51.50 
 
 7.36 
 
 5 I,-?, 
 
 7 JO 
 
 14 
 
 5 45.S2 
 
 7.30 
 
 5 53.11 
 
 7.-3D 
 
 0,10 
 
 7.28 
 
 7.08 
 
 7.27 
 
 11.95 
 
 7.26 
 
 15 
 
 5S.30 
 
 7JM 
 
 7 5.57 
 
 7.20 
 
 7 12.70 
 
 7.19 
 
 7 lit.! 14 
 
 7.18 
 
 7 27.12 
 
 7.17 
 
 10 
 
 8 it.! 15 
 
 7.11 
 
 8 17.06 
 
 7.10 
 
 8 24.15 
 
 7.09 
 
 8 31.24 
 
 7.08 
 
 8 38.31 
 
 7.07 
 
 17 
 
 it 20.53 
 
 7.00 
 
 9 27.53 
 
 6.99 
 
 it 31.52 
 
 6.98 
 
 it 41.50 
 
 6.97 
 
 9 IS. 17 
 
 6.96 
 
 18 
 
 10 30.04 
 
 6.90 
 
 10 30.! 13 
 
 6.88 
 
 10 43.- 1 
 
 6.87 
 
 10 50.07 
 
 6.86 
 
 10 57.53 
 
 6.85 
 
 19 
 
 11 3-. 12 
 
 6.78 
 
 11 45.19 
 
 6.77 
 
 11 51.96 
 
 6.76 
 
 11 58.71 
 
 6.74 
 
 12 5,15 
 
 6.73 
 
 20 
 
 1 12 45.H3 
 
 6.66 
 
 12 52.28 
 
 tM 
 
 12 :>-'.: >2 
 
 6.63 
 
 13 5.55 
 
 6.63 
 
 13 12.17 
 
 6.61 
 
 21 
 
 1 13 51.00 
 
 m 
 
 13 5s. 12 
 
 6.53 
 
 II I.OI 
 
 6.51 
 
 11 11.14 
 
 6.50 
 
 14 17.03 
 
 6.48 
 
 2-.' 
 
 1 14 50.2s 
 
 6.40 
 
 15 2.0S 
 
 6.39 
 
 15 9.00 
 
 6.38 
 
 15 15.43 
 
 6.36 
 
 15 21.79 
 
 6.35 
 
 23 
 
 1 15 59.01 
 
 6.37 
 
 16 5.90 
 
 
 10 12.11 
 
 tM 
 
 16 18.38 
 
 6.23 
 
 10 24.59 
 
 6.21 
 
 21 
 
 1 17 1.00 
 
 6.13 
 
 17 7.72 
 
 6.11 
 
 17 13.S3 
 
 6.10 
 
 17 19.92 
 
 6.08 
 
 17 25.! til 
 
 6.07 
 
 25 
 
 1 IS 2.11 
 
 5.98 
 
 18 s.ll 
 
 5.96 
 
 18 14.07 
 
 5.95 
 
 18 20.01 
 
 5.93 
 
 18 25.91 
 
 Ml 
 
 26 
 
 1 19 1.19 
 
 5.83 
 
 19 7.01 
 
 5.81 
 
 lit 12.-2 
 
 5.80 
 
 19 IS.OI 
 
 5.78 
 
 lit 24.39 
 
 5.77 
 
 27 
 
 1 lit r,-.7 1 
 
 5.67 
 
 20 4.38 
 
 5.66 
 
 20 10.03 
 
 5.64 
 
 20 15.07 
 
 5.63 
 
 20 21.29 
 
 5.01 
 
 28 
 
 1 20 51.00 
 
 5.52 
 
 21 0.17 
 
 5.50 
 
 21 5.00 
 
 5.48 
 
 21 11.14 
 
 5.47 
 
 21 16.60 
 
 .-,. I. 1 . 
 
 29 
 
 1 21 49.00 
 
 5.35 
 
 21 51.31 
 
 5.33 
 
 21 59.07 
 
 U| 
 
 22 4.! is 
 
 5.30 
 
 22 10.27 
 
 5.38 
 
 30 
 
 1 22 41.07 
 
 5.18 
 
 22 40.85 
 
 5.16 
 
 22 52.01 
 
 5.15 
 
 22 57.15 
 
 5.13 
 
 23 2.27 
 
 5.11 
 
 31 
 
 1 23 32.05 
 
 5.01 
 
 23 37.65 
 
 4.1111 
 
 23 42.64 
 
 4.98 
 
 23 47.60 
 
 4.96 
 
 23 52.55 
 
 4.94 
 
 32 
 
 1 21 21.88 
 
 4.83 
 
 24 20.71 
 
 4.83 
 
 24 31.52 
 
 4.80 
 
 21 30.31 
 
 4.78 
 
 24 41.08 
 
 4.76 
 
 33 
 
 1 25 9.34 
 
 4.66 
 
 25 13.rut 
 
 4.64 
 
 25 1S.02 
 
 4.63 
 
 25 23.23 
 
 4.60 
 
 25 27.82 
 
 4.58 
 
 31 
 
 1 25 51.99 
 
 4.47 
 
 25 59,15 
 
 4.45 
 
 20 3.S9 
 
 4.43 
 
 20 S.32 
 
 4.42 
 
 26 12.73 
 
 4 .XI 
 
 35 
 
 1 20 38.78 
 
 4.38 
 
 20 43.00 
 
 4.27 
 
 26 47.31 
 
 4.a:i 
 
 26 51.55 
 
 4.23 
 
 26 55.77 
 
 4.31 
 
 36 
 
 1 27 20.0! i 
 
 4.09 
 
 27 24.78 
 
 4.08 
 
 27 28.84 
 
 4.06 
 
 27 32.S9 
 
 4.04 
 
 27 36.92 
 
 4.03 
 
 
 1 28 0.09 
 
 3.90 
 
 28 4.5s 
 
 3.88 
 
 28 8.45 
 
 3.86 
 
 28 12.31 
 
 3.84 
 
 28 10.14 
 
 3.82 
 
 38 
 
 1 2- 3S.7I 
 
 3.71 
 
 28 42.43 
 
 3.69 
 
 28 40.11 
 
 3.67 
 
 28 49.77 
 
 3.65 
 
 28 .53,10 
 
 3.63 
 
 39 
 
 1 29 14.81 
 
 3.51 
 
 29 18.31 
 
 3.49 
 
 29 21.79 
 
 3.47 
 
 29 25.25 
 
 3.45 
 
 29 28.68 
 
 3.43 
 
 40 
 
 1 29.48.88 
 
 3.31 
 
 29 52.18 
 
 3.29 
 
 29 55. Hi 
 
 3.37 
 
 29 5S.71 
 
 3.35 
 
 30 1.95 
 
 3.32 
 
 41 
 
 30 20.93 
 
 3.10 
 
 30 24.02 
 
 3.08 
 
 30 27.0! t 
 
 3.06 
 
 30 30.15 
 
 3.04 
 
 30 :t3.I8 
 
 3.02 
 
 49 
 
 30 5! 1.93 
 
 2.90 
 
 30 53.S1 
 
 3.88 
 
 30 50.0S 
 
 
 30 59.52 
 
 3.83 
 
 31 2.31 
 
 3.81 
 
 43 
 
 31 18.85 
 
 2.69 
 
 31 21.52 
 
 2.67 
 
 31 24.18 
 
 MB 
 
 31 26.81 
 
 Ml 
 
 31 29.43 
 
 3.60 
 
 44 
 
 31 41.07 
 
 2.48 
 
 31 47.14 
 
 2.46 
 
 31 49.5! 1 
 
 2.44 
 
 31 52.01 
 
 3.41 
 
 31 51.11 
 
 2.39 
 
 10 
 
 32 S.39 
 
 2.27 
 
 32 lo.oi 
 
 3.34 
 
 32 12.88 
 
 
 32 15.09 
 
 2.20 
 
 32 I7.2S 
 
 2.18 
 
 46 
 
 32 29.97 
 
 2.05 
 
 32 32.01 
 
 2.03 
 
 32 34.03 
 
 3.01 
 
 32 30.03 
 
 1.99 
 
 32 38.00 
 
 1.97 
 
 47 
 
 32 49.11 
 
 1.83 
 
 32 51.23 
 
 1.81 
 
 32 53.04 
 
 1.79 
 
 32 54.82 
 
 1.77 
 
 32 56.58 
 
 1.75 
 
 48 
 
 33 0.09 
 
 1.63 
 
 : S.29 
 
 1.60 
 
 33 9.88 
 
 1.58 
 
 33 11.45 
 
 1.55 
 
 33 12.99 
 
 1.53 
 
 49 
 
 3-3 21.79 
 
 1.40 
 
 33 23. IS 
 
 1.38 
 
 33 24.55 
 
 1.36 
 
 33 25.90 
 
 1.34 
 
 33 27.22 
 
 1.31 
 
 50 
 
 : 34.71 
 
 1.18 
 
 33 35.S9 
 
 1.16 
 
 33 37.04 
 
 1.14 
 
 a3 38.16 
 
 1.13 
 
 33 8! 1.27 
 
 1.10 
 
 51 
 
 33 45.15 
 
 0.96 
 
 :(3 40.40 
 
 0.94 
 
 33 47.:i3 
 
 0.93 
 
 S3 4s.21 
 
 0.90 
 
 33 49.13 
 
 0.88 
 
 52 
 
 33 53.9S 
 
 0.74 
 
 33 51.72 
 
 0.72 
 
 33 55.13 
 
 0.70 
 
 33 50.11 
 
 0.67 
 
 33 50.7 s 
 
 Ml 
 
 53 
 
 34 0.32 
 
 0.52 
 
 34 (),-"{ 
 
 O..V) 
 
 31 1.32 
 
 0.48 
 
 31 1.79 
 
 0.46 
 
 31 2.23 
 
 0.43 
 
 ' 51 
 
 31 l.ll 
 
 0.30 
 
 31 1.73 
 
 0.28 
 
 31 5.00 
 
 0.26 
 
 31 5.25 
 
 0.34 
 
 31 5. IS 
 
 +0.-J1 
 
 55 
 
 31 0.36 
 
 40.08 
 
 34 0.13 
 
 
 31 0.48 
 
 . i."l 
 
 34 0.50 
 
 +0.01 
 
 34 6.51 
 
 -0.01 
 
 8 V 
 
TABLE X. 
 
 EQUATION OF THE CENTRE, FOR in = 0. 
 
 d 
 
 Constant added 47' 3".5. Period = 224.7008. 
 
 
 d 
 
 Diff. 
 
 d 
 
 Diff. 
 
 d 
 
 Dim 
 
 d 
 
 Diff 
 
 d 
 
 Dim 
 
 Arg. I. 
 
 o.o 
 
 for 0<U 
 
 O.I 
 
 for 0>U 
 
 o.a 
 
 for O''.l 
 
 0.3 
 
 forO'U 
 
 0.4 
 
 for IK 1 
 
 56 
 
 1 II 
 
 1 31 6.49 
 
 -0.03 
 
 34 o!-!5 
 
 -0.05 
 
 31 0.39 
 
 II 
 -0.07 
 
 34 6.31 
 
 -0.09 
 
 34 0.20 
 
 ii 
 -0.12 
 
 57 
 
 1 34 5.10 
 
 0.25 
 
 34 4. si 
 
 II.-J7 
 
 34 4.50 
 
 0.39 
 
 34 4.25 
 
 0.32 
 
 34 3.92 
 
 o.:i i 
 
 58 
 
 1 31 1.50 
 
 0.47 
 
 34 1.02 
 
 0.19 
 
 34 0.52 
 
 0.51 
 
 33 59.99 
 
 0.54 
 
 33 59.45 
 
 0.56 
 
 59 
 
 J 33 55.71 
 
 0.69 
 
 33 55.01 
 
 0.71 
 
 33 54.28 
 
 0.73 
 
 33 53.54 
 
 0.75 
 
 33 52.77 
 
 0.78 
 
 60 
 
 1 33 47.72 
 
 0.91 
 
 33 46.80 
 
 0.93 
 
 33 45,-; i 
 
 0.95 
 
 33 44.89 
 
 0.97 
 
 33 43.91 
 
 1.00 
 
 lil 
 
 1 33 37.54 
 
 1.13 
 
 33 30.10 
 
 1.15 
 
 33 35.24 
 
 1.17 
 
 33 34.06 
 
 1.10 
 
 33 32.86 
 
 1.21 
 
 02 
 
 1 33 25.19 
 
 1.34 
 
 33 23.83 
 
 1.37 
 
 33 22.45 
 
 1.39 
 
 33 21.06 
 
 1.41 
 
 33 19.64 
 
 1.43 
 
 03 
 
 1 33 10.67 
 
 1.56 
 
 33 9.10 
 
 1.5S 
 
 33 7.51 
 
 1.60 
 
 33 5.89 
 
 1.62 
 
 33 4.26 
 
 1.65 
 
 01 
 
 I 32 54.00 
 
 1.77 
 
 32 52.21 
 
 1.80 
 
 32 50.41 
 
 1.82 
 
 32 48.58 
 
 1.84 
 
 32 40.73 
 
 1.86 
 
 05 
 
 1 32 35.19 
 
 1.99 
 
 32 33.19 
 
 2.01 
 
 32 31.17 
 
 2.03 
 
 32 29.13 
 
 2.05 
 
 32 27.07 
 
 2.07 
 
 ot; 
 
 1 32 1 1.26 
 
 2.20 
 
 32 12.05 
 
 8.99 
 
 32 9.82 
 
 2.24 
 
 32 7.57 
 
 2.26 
 
 32 5.29 
 
 2.28 
 
 07 
 
 1 31 51.22 
 
 J.tl 
 
 31 48.80 
 
 3.43 
 
 31 40.37 
 
 2.45 
 
 31 43.91 
 
 2.47 
 
 31 41.42 
 
 2.49 
 
 08 
 
 1 31 26.10 
 
 2.63 
 
 31 23.48 
 
 - 2.64 
 
 31 20.83 
 
 2.66 
 
 31 18.16 
 
 2.68 
 
 31 15.47 
 
 2.70 
 
 69 
 
 1 30 58.92 
 
 2.83 
 
 30 50.09 
 
 2.84 
 
 30 53.23 
 
 2.86 
 
 30 50.36 
 
 2.88 
 
 30 47.47 
 
 SUM 
 
 70 
 
 1 30 29.09 
 
 3.03 
 
 30 20.06 
 
 3.04 
 
 30 23.00 
 
 3.06 
 
 30 20.53 
 
 3.08 
 
 30 17.43 
 
 3.10 
 
 71 
 
 1 29 58.15 
 
 3.33 
 
 29 55.21 
 
 3.24 
 
 29 51.90 
 
 3.20 
 
 29 4S.OS 
 
 3.28 
 
 29 45.39 
 
 3.30 
 
 72 
 
 i 29 >.->.: i 
 
 3.43 
 
 29 21.78 
 
 3.44 
 
 29 18.33 
 
 3.46 
 
 29 14.86 
 
 3.48 
 
 29 11.37 
 
 s.r.o 
 
 73 
 
 1 28 50.01 
 
 3.62 
 
 28 46.38 
 
 3.64 
 
 28 42.74 
 
 3.66 
 
 28 39.07 
 
 3.68 
 
 28 35.39 
 
 3.69 
 
 74 
 
 1 28 12.87 
 
 3.81 
 
 28 9.05 
 
 3.83 
 
 28 5.22 
 
 3,85 
 
 28 1.36 
 
 3.87 
 
 27 57.18 
 
 3.89 
 
 75 
 
 1 27 3: (..-.( 
 
 4.00 
 
 27 29.82 
 
 4.02 
 
 27 25.79 
 
 4.04 
 
 27 21.75 
 
 4.05 
 
 27 17.68 
 
 4.07 
 
 76 
 
 1 20 52.91 
 
 4.18 
 
 26 48.71 
 
 4.30 
 
 26 44.50 
 
 4.32 
 
 20 40.27 
 
 4.24 
 
 26 36.02 
 
 4.26 
 
 77 
 
 1 26 10.14 
 
 4.37 
 
 26 5.77 
 
 4.38 
 
 26 1.37 
 
 4.40 
 
 25 50.96 
 
 4.42 
 
 25 52.53 
 
 5.44 
 
 78 
 
 1 25 25.57 
 
 4.55 
 
 25 21.02 
 
 4.56 
 
 25 16.44 
 
 4.58 
 
 25 11.85 
 
 4.60 
 
 25 7.24 
 
 4.62 
 
 79 
 
 1 24 39.23 
 
 4.72 
 
 24 31.50 
 
 4.74 
 
 24 29.75 
 
 4.76 
 
 24 24.98 
 
 4.77 
 
 24 20.20 
 
 4.79 
 
 80 
 
 1 23 51.14 
 
 4.89 
 
 23 46.24 
 
 4.91 
 
 23 41.32 
 
 4.93 
 
 23 30.39 
 
 4.94 
 
 23 31.43 
 
 4.96 
 
 81 
 
 1 23 1.36 
 
 5.06 
 
 22 50.29 
 
 5.08 
 
 22 51.21 
 
 5.09 
 
 22 46.10 
 
 5.11 
 
 22 40.98 
 
 5.13 
 
 82 
 
 1 22 9.92 
 
 5.23 
 
 22 4.0!) 
 
 5.34 
 
 21 59.44 
 
 5.26 
 
 21 54.17 
 
 5.27 
 
 21 48.89 
 
 SM 
 
 83 
 
 1 21 10.86 
 
 5.39 
 
 21 11.47 
 
 5.40 
 
 21 6.06 
 
 5.42 
 
 21 O.(i3 
 
 5.43 
 
 20 55.19 
 
 5.45 
 
 84 
 
 1 20 22.23 
 
 5.54 
 
 20 10.08 
 
 5.56 
 
 20 11.12 
 
 5.57 
 
 20 5.54 
 
 5.59 
 
 19 59.94 
 
 5.60 
 
 85 
 
 1 19 20.00 
 
 5.69 
 
 19 20.36 
 
 5.71 
 
 19 14.64 
 
 5.72 
 
 19 8.91 
 
 5.74 
 
 19. 3.17 
 
 5.75 
 
 86 
 
 1 18 28.39 
 
 5.84 
 
 18 22.55 
 
 5.85 
 
 IS 10.69 
 
 5.87 
 
 18 10.81 
 
 5.88 
 
 18 4.92 
 
 5.90 
 
 87 
 
 1 17 29.29 
 
 5.98 
 
 17 23.30 
 
 5.99 
 
 17 17.30 
 
 6.01 
 
 17 11.28 
 
 6.03 
 
 17 5.25 
 
 6.04 
 
 88 
 
 1 10 28.78 
 
 6.12 
 
 16 22.65 
 
 6.13 
 
 1C 10.51 
 
 6.15 
 
 16 10.36 
 
 6.16 
 
 16 4.19 
 
 ' 6.18 
 
 89 
 
 1 15 20.92 
 
 6.25 
 
 15 20.06 
 
 6.26 
 
 15 14.39 
 
 6.28 
 
 15 8.10 
 
 6.29 
 
 15 1.81 
 
 6.30 
 
 90 
 
 1 14 23.75 
 
 6.38 
 
 14 17.37 
 
 6.39 
 
 14 10.97 
 
 6.40 
 
 14 4.50 
 
 6.42 
 
 13 58.13 
 
 6.43 
 
 91 
 
 1 13 19.33 
 
 6.50 
 
 13 12.82 
 
 6.51 
 
 13 0.30 
 
 6.53 
 
 12 59.77 
 
 6.54 
 
 12 53.22 
 
 6.55 
 
 92 
 
 1 12 13.70 
 
 6.62 
 
 12 7.08 
 
 6.63 
 
 12 0.44 
 
 6.64 
 
 11 53.79 
 
 6.66 
 
 11 47.13 
 
 6.67 
 
 93 
 
 1 11 6.92 
 
 6.73 
 
 11 0.18 
 
 6.75 
 
 10 53.43 
 
 6.76 
 
 10 40.07 
 
 6.77 
 
 10 39.89 
 
 6.78 
 
 94 
 
 1 9 59.03 
 
 6.84 
 
 9 52.19 
 
 6.85 
 
 9 45.33 
 
 6.86 
 
 9 38.40 
 
 6.87 
 
 9 31.58 
 
 6.88 
 
 95 
 
 1 8 50.09 
 
 6.94 
 
 8 43.14 
 
 6.95 
 
 8 30.18 
 
 6.96 
 
 8 29.22 
 
 6.97 
 
 8 22.24 
 
 6.98 
 
 96 
 
 1 7 40.16 
 
 7.04 
 
 7 33.11 
 
 7.05 
 
 7 20.05 
 
 7.06 
 
 7 18.99 
 
 7.07 
 
 7.11.91 
 
 7.08 
 
 97 
 
 1 6 29.27 
 
 7.13 
 
 6 22.14 
 
 7.14 
 
 6 14.99 
 
 7.15 
 
 6 7.83 
 
 7.16 
 
 6 0.07 
 
 7.17 
 
 98 
 
 1 5 17.50 
 
 7.22 
 
 5 10.28 
 
 7.23 
 
 5 3.05 
 
 7.24 
 
 4 55.80 
 
 7.24 
 
 4 48.56 
 
 7.25 
 
 99 
 
 I 4 4.89 
 
 7.30 
 
 3 57.59 
 
 7.31 
 
 3 50.28 
 
 7.32 
 
 3 42.96 
 
 7.33 
 
 3 35.63 
 
 7.33 
 
 100 
 
 1 2 51.51 
 
 7.38 
 
 2 44.13 
 
 7.38 
 
 2 30.71 
 
 7.39 
 
 2 29.35 
 
 7.40 
 
 2 21.94 
 
 7.40 
 
 101 
 
 1 1 37.39 
 
 7.45 
 
 1 29.95 
 
 7.45 
 
 1 22.49 
 
 7.46 
 
 1 15.03 
 
 7.46 
 
 1 7.56 
 
 7.47 
 
 102 
 
 60 22.02 
 
 7.51 
 
 00 15.11 
 
 7.51 
 
 00 7.59 
 
 7.52 
 
 60 0.00 
 
 7.53 
 
 59 52.53 
 
 7.53 
 
 103 
 
 59 7.23 
 
 7.57 
 
 58 59.00 
 
 7.07 
 
 58 52.08 
 
 7.58 
 
 58 44.50 
 
 7.58 
 
 58 36.91 
 
 7.59 
 
 104 
 
 57 51.29 
 
 7.62 
 
 57 43.07 
 
 7.62 
 
 57 30.04 
 
 7.63 
 
 57 28.41 
 
 7.63 
 
 57 20.77 
 
 7.64 
 
 105 
 
 50 34.80 
 
 7.67 
 
 50 27.19 
 
 7.67 
 
 56 19.52 
 
 7.67 
 
 50 11.84 
 
 7.68 
 
 56 4.16 
 
 7.68 
 
 106 
 
 55 17.99 
 
 7.71 
 
 55 10.28 
 
 7.71 
 
 55 2.56 
 
 7.71 
 
 54 51.85 
 
 7.73 
 
 54 47.13 
 
 7.72 
 
 107 
 
 54 0.74 
 
 7.74 
 
 53 53.00 
 
 7.74 
 
 53 45.25 
 
 7.75 
 
 53 37.50 
 
 7.75 
 
 53 29.75 
 
 7.75 
 
 108 
 
 52 43.18 .. 
 
 7.77 
 
 52 35.40 
 
 7.77 
 
 52 27.63 
 
 7*77 
 
 52 19.85 
 
 7.78 
 
 52 12.07 
 
 7.78 
 
 109 
 
 51 25.35 
 
 7.79 
 
 - 51 17.50 
 
 7.79 
 
 51 9.70 
 
 7.80 
 
 51 1.90 
 
 7.80 
 
 50 54.16 
 
 7.80 
 
 110 
 
 50 7.33 
 
 7.81 
 
 49 59.52 
 
 7.81 
 
 49 51.71 
 
 7.81 
 
 49 43.89 
 
 7.81 
 
 49 36.08 
 
 7.82 
 
 111 
 
 48 49.17 
 
 -7.82 
 
 48 41.34 
 
 -7.82 
 
 48 33.52 
 
 -7.82 
 
 48 25.70 
 
 -7.82 
 
 48 17.87 
 
 -7.82 
 
TARIFF X. 
 
 K(,H VHON OF TIIK (TATIiK. Foil ill =0. 
 
 r..ii,.fmt :nlil.-ii 17' ::':.. ivn..,l .'.' i : 
 
 d 
 
 Dili'. 
 
 .1 
 
 Diff. 
 
 ,1 
 
 Dill'. 
 
 d 
 
 Diir. 
 
 d 
 
 Diff. 
 
 Arg 1 )..-> 
 
 tnrlM.I 
 
 o.e 
 
 fbrO l 
 
 0.7 
 
 
 o.s 
 
 fiirli'M 
 
 <).!) 
 
 lurlH.l 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 56 
 
 / // 
 
 ::i (U)7 
 
 ft 
 -<i.M 
 
 31 5'>> 
 
 n 
 
 -0.16 
 
 31 
 
 n 
 
 31 
 
 n 
 -Ml 
 
 :( 5-u 
 
 II 
 -4M 
 
 57 
 
 :tl 3.5s 
 
 
 :il 3.21 
 
 
 
 3 1 '.- 1 
 
 0.40 
 
 31 >.!() 
 
 (1.1:1 
 
 31 I.JKi 
 
 IP. i:. 
 
 56 
 
 33 ' 
 
 
 33 5S.29 
 
 0.60 
 
 :{.-( 57.68 
 
 
 :tt 57.CI 
 
 
 :{-( 50.3S 
 
 
 SB 
 
 :!-( 51. '.19 
 
 o.H> 
 
 33 51. is 
 
 
 :u 50.31 
 
 .- 1 
 
 .'ft 49.49 
 
 
 :ct is.oi 
 
 
 00 
 
 : 42.90 
 
 
 :t II.-; 
 
 l.lll 
 
 33 10.S-> 
 
 1.06 
 
 : :i.7."> 
 
 \M 
 
 :KI 3s.t;o 
 
 1.10 
 
 01 
 
 :{3 31.03 
 
 \M 
 
 33 3(t.: 
 
 i.-.i; 
 
 33 ->!M-.' 
 
 \M 
 
 :tt -J7.-3 
 
 
 :ti 20.52 
 
 IJ 
 
 02 
 
 33 is.2ti 
 
 1 . i."> 
 
 :{{ 10.73 
 
 1.47 
 
 :t !5.-.>5 
 
 i.n 
 
 : 13.71 
 
 
 :i3 i -.'.>-.' 
 
 I...I 
 
 63 
 
 :n 2.00 
 
 
 It) (i.!f 
 
 
 3-.' S 
 
 i /. i 
 
 ::. 57.50 
 
 i.;.i 
 
 32 55.70 
 
 1.78 
 
 01 
 
 : ll.s:; 
 
 1.88 
 
 3-J !-.>.! "7 
 
 1.90 
 
 :w 41.05 
 
 1.99 
 
 32 39.12 
 
 l.:u 
 
 32 37.17 
 
 isn 
 
 05 
 
 : 21.99 
 
 
 : 9 
 
 Ul 
 
 3-i ->0.70 
 
 J.ll 
 
 32 IS.OI 
 
 32 10.15 
 
 
 06 
 
 32 
 
 2.30 
 
 :!-.' o.i! 
 
 tM 
 
 31 5S.35 
 
 
 31 50.00 
 
 
 31 53.02 
 
 
 (17 
 
 :il 3s/>2 
 
 
 ;n 3i;.in 
 
 
 31 :',:{>;; 
 
 2.55 
 
 31 31.29 
 
 
 31 21.71 
 
 
 
 31 K'.77 
 
 
 31 HUH 
 
 a.74 
 
 31 -.-*> 
 
 2.76 
 
 31 4.52 
 
 ' 
 
 31 1.73 
 
 2.80 
 
 69 
 
 30 41.50 
 
 
 30 ll.ltt 
 
 J.'.ll 
 
 30 3S.07 
 
 tM 
 
 30 35.70 
 
 
 30 32.7 1 
 
 3.00 
 
 70 
 
 30 14.32 
 
 Ul 
 
 30 11.1!) 
 
 :i.n 
 
 30 s.o: 
 
 3.16 
 
 30 4 .SO 
 
 3.18 
 
 30 1.00 
 
 3.90 
 
 71 
 
 29 12.(.- 
 
 :).: 
 
 -.71 
 
 :t.:u 
 
 2!t 35.:J!i 
 
 3.3G 
 
 29 32.1.2 
 
 
 29 2S.03 
 
 3.40 
 
 7'.' 
 
 29 
 
 :t..v_> 
 
 2!) 4.:n 
 
 3..-1 1 
 
 99 0.7S 
 
 Ul 
 
 28 57.21 
 
 3M 
 
 53.69 
 
 3.IM 
 
 7:t 
 
 2S 31.IM 
 
 3.71 
 
 > -.;.! 10 
 
 3.73 
 
 98 -i\.-f> 
 
 S.7B 
 
 > 20.10 
 
 3.77 
 
 28 1 O.I IS 
 
 
 71 
 
 .'7 53.59 
 
 3.90 
 
 >: 4! 1.07 
 
 A.-.i-l 
 
 27 45.7 t 
 
 3.UI 
 
 -.'7 41.79 
 
 Ul 
 
 27 37.^2 
 
 3.98 
 
 75 
 
 -.'7 13.00 
 
 4.09 
 
 27 !>..".() 
 
 4.11 
 
 27 5.3- 
 
 4.13 
 
 27 l.-.'l 
 
 tM 
 
 JO 57.08 
 
 4.17 
 
 7(i 
 
 20 31.75 
 
 4.98 
 
 2fi 27. 17 
 
 4.99 
 
 2fi 2:1.10 
 
 4.31 
 
 20 l-.-l 
 
 4.33 
 
 -.'0 11.50 
 
 4..15 
 
 77 
 
 25 
 
 4.46 
 
 -.'.-. 43.0-.' 
 
 4.47 
 
 -.'5 3!M3 
 
 4.19 
 
 25 3l.li3 
 
 i.:.l 
 
 25 30.11 
 
 4. r k) 
 
 78 
 
 r> 2.02 
 
 4.63 
 
 21 57.! is 
 
 4.65 
 
 24 Si.3l 
 
 4.67 
 
 24 4.-.01 
 
 4.fi9 
 
 -'I 43.91 
 
 4.70 
 
 re 
 
 21 15.40 
 
 4.81 
 
 24 10.58 
 
 4.83 
 
 24 5.75 
 
 4.84 
 
 24 0.90 
 
 4.86 
 
 23 5(5.03 
 
 4.88 
 
 HO 
 
 23 20.10 
 
 4.98 
 
 23 21. is 
 
 4.99 
 
 23 10.17 
 
 5.01 
 
 23 11.15 
 
 5.03 
 
 23 0.12 
 
 tM 
 
 81 
 
 22 35.S5 
 
 5.14 
 
 >> 30.70 
 
 5.16 
 
 -,"2 -.'5.5.3 
 
 5.18 
 
 22 20.31 
 
 5.19 
 
 22 15.11 
 
 :..! 1 
 
 83 
 
 21 43.5H 
 
 Ul 
 
 >( a&aa 
 
 :..:;.' 
 
 21 :W.!I5 
 
 tM 
 
 21 27.00 
 
 Ul 
 
 21 22/.' 1 
 
 5J7 
 
 ta 
 
 JO 4!i.7l 
 
 5.17 
 
 .M !l/>7 
 
 5.48 
 
 20 3S.7- 
 
 5.50 
 
 20 33.-.'s 
 
 5.51 
 
 20 27.70 
 
 5Ji3 
 
 i-l 
 
 19 5l.:t3 
 
 5.G1 
 
 10 4,-.7 1 
 
 5.63 
 
 19 43.07 
 
 5.64 
 
 19 37.41 
 
 5.66 
 
 19 31.74 
 
 5.n7 
 
 85 
 
 is 57.11 
 
 S.77 
 
 18 51.03 
 
 5.78 
 
 IS 15.S5 
 
 5.80 
 
 18 40.04 
 
 5.81 
 
 18 34.23 
 
 5.H-2 
 
 86 
 
 1 17 59.02 
 
 5.91 
 
 17 SI. 10 
 
 5.93 
 
 17 47.17 
 
 5.94 
 
 17 41.22 
 
 5.95 
 
 17 35.20 
 
 5.97 
 
 87 
 
 1 10 r>:i.-.>0 
 
 6.06 
 
 1(5 53.15 
 
 6.06 
 
 16 47.07 
 
 6.08 
 
 16 40.99 
 
 6.09 
 
 10 34.8!) 
 
 6.10 
 
 ss 
 
 i 15 saoi 
 
 6.19 
 
 15 51.82 
 
 6.00 
 
 15 45.62 
 
 6.21 
 
 15 39.40 
 
 6.23 
 
 15 33.10 
 
 6.24 
 
 BO 
 
 1 11 55.50 
 
 6.-.1-1 
 
 14 4!i.l7 
 
 6.33 
 
 14 42.SI 
 
 6.34 
 
 14 30.19 
 
 6.35 
 
 14 30.13 
 
 6T7 
 
 !K) 
 
 1 13 51.70 
 
 6.44 
 
 13 4.V>5 
 
 6.45 
 
 13 3S.7!i 
 
 6.46 
 
 13 32.31 
 
 6.48 
 
 13 25.S3 
 
 6.49 
 
 !>1. 
 
 1 12 40.00 
 
 6.J6 
 
 12 40.10 
 
 6J7 
 
 12 33.52 
 
 6.:>9 
 
 12 20.92 
 
 6.60 
 
 12 20.32 
 
 6X1 
 
 09 
 
 1 11 40.15 
 
 6.68 
 
 11 33.77 
 
 6.69 
 
 11 27.07 
 
 6.70 
 
 11 20.37 
 
 6.71 
 
 11 13.05 
 
 6.79 
 
 98 
 
 1 10 33.11 
 
 6.79 
 
 10 20.3-2 
 
 6.80 
 
 10 19.51 
 
 6.82 
 
 10 12.70 
 
 6.83 
 
 10 5.-7 
 
 6.84 
 
 M 
 
 i 9 21.09 
 
 6.89 
 
 ! 17.7H 
 
 6.90 
 
 9 10.88 
 
 6.91 
 
 9 3.97 
 
 6.99 
 
 - 57.04 
 
 6.93 
 
 05 
 
 1 8 15.25 
 
 6.99 
 
 8 8.25 
 
 7.00 
 
 8 1.21 
 
 7.01 
 
 7 54.22 
 
 7.02 
 
 7 47.19 
 
 7.03 
 
 96 
 
 1 7 4.83 
 
 7.09 
 
 57.71 
 
 7.10 
 
 50.01 
 
 7.11 
 
 13.52 
 
 7.13 
 
 30.40 
 
 7.19 
 
 !I7 
 
 1 5 53.50 
 
 7.18 
 
 5 40.31 
 
 7.19 
 
 5 39.1--' 
 
 7.19 
 
 5 31.93 
 
 7.20 
 
 5 24.72 
 
 JM 
 
 96 
 
 1 4 41.30 
 
 7.26 
 
 4 3I.(,3 
 
 7.27 
 
 4 20.70 
 
 7.28 
 
 4 19.IS 
 
 7.29 
 
 4 12.19 
 
 7.29 
 
 'M 
 
 1 3 28.30 
 
 7.34 
 
 3 20.1 5 
 
 7.33 
 
 3 13.00 
 
 7.3J 
 
 3 0.24 
 
 7.36 
 
 2 58.88 
 
 7.37 
 
 100 
 
 1 2 14.51 
 
 7.41 
 
 2 7.12 
 
 7.42 
 
 1 59.70 
 
 7.42 
 
 1 52.'.'7 
 
 7.43 
 
 1 44.84 
 
 7.44 
 
 101 
 
 1 1 0.01) 
 
 7.48 
 
 52.150 
 
 7.48 
 
 45.12 
 
 7.49 
 
 37.02 
 
 7.50 
 
 30.12 
 
 7JO 
 
 102 
 
 50 4 !.!>!> 
 
 7..M 
 
 5!l 37.15 
 
 7.54 
 
 59 29.91 
 
 7..V 
 
 .V.i 22.35 
 
 7.56 
 
 59 14.79 
 
 7J6 
 
 103 
 
 58 
 
 7.59 
 
 .58 21.73 
 
 7.60 
 
 58 14.12 
 
 7.60 
 
 58 6.52 
 
 7.61 
 
 57 58.91 
 
 7.61 
 
 101 
 
 57 13.13 
 
 7.01 
 
 57 5.49 
 
 7.65 
 
 50 57^3 
 
 7.65 
 
 50 50.18 
 
 7.66 
 
 50 ]>.:,> 
 
 7.66 
 
 lor. 
 
 55 50.47 
 
 7.69 
 
 55* 48.78 
 
 7.69 
 
 55 41.09 
 
 7.69 
 
 55 33.39 
 
 7.70 
 
 55 25.09 
 
 7.70 
 
 106 
 
 51 39.41 
 
 -.;> 
 
 51 31. (X 
 
 7.73 
 
 51 '.'3.95 
 
 7.73 
 
 51 10.22 
 
 7.73 
 
 54 H.is 
 
 7.71 
 
 107 
 
 53 21.99 
 
 7.76 
 
 53 14.23 
 
 7.76 
 
 53 0.17 
 
 7.76 
 
 52 58.71 
 
 7.76 
 
 52 50.94 
 
 7.77 
 
 H - 
 
 52 4.2!) 
 
 7.78 
 
 51 50.51 
 
 7.78 
 
 51 4S.7-.' 
 
 7.79 
 
 51 40.93 
 
 7.79 
 
 51 33.11 
 
 7.79 
 
 lOit 
 
 r>() |(i.:!ii 
 
 7.80 
 
 50 .'K50 
 
 7.80 
 
 50 30.75 
 
 7.81 
 
 50 2--'.! "5 
 
 
 50 15.14 
 
 ,.-1 
 
 110 
 
 ii 19 -.'s.-jo 
 
 7.89 
 
 49 20.45 
 
 7.89 
 
 49 12.03 
 
 7.89 
 
 19 l.sl 
 
 7.89 
 
 48 5'i.99 
 
 7.W 
 
 111 
 
 48 10.05 -7.83 
 
 48 2.21 
 
 -7.8S 
 
 47 54.40 
 
 -7.83 
 
 47 46.57 
 
 -7.83 
 
 47 3S.75 
 
 --..:! 
 
TABLE X. 
 
 EQUATION OF THE CENTRE, FOR in = 0. 
 Const;, nt ud.ln! .17' 3".5. Period = 224.7008. 
 
 Arg. 1. 
 
 d 
 O.O 
 
 Ditr. 
 
 for (Kl 
 
 d 
 
 O.I 
 
 Diff. 
 
 for OJ.l 
 
 d 
 
 O.i2 
 
 Diir. 
 
 forlKl 
 
 (i 
 
 0.3 
 
 Diir. 
 
 forOJ.l 
 
 d 
 O.4 
 
 Diff. 
 for (K 1 
 
 112 
 
 61 II 
 47 30.!>2 
 
 ii 
 -7.83 
 
 / // 
 47 23.10 
 
 ii 
 -7.83 
 
 / // 
 
 47 15.27 
 
 II 
 -7.83 
 
 47 7V14 
 
 ii 
 -7.83 
 
 40 5I.M32 
 
 ii 
 -7.83 
 
 li:5 
 
 46 12.66 
 
 7.S2 
 
 46 4.a3 
 
 7.83 
 
 45 57.01 
 
 7.82 
 
 45 49.19 
 
 7.82 
 
 45 41.36 
 
 7.88 
 
 114 
 
 44 54.43 
 
 7.89 
 
 4! 46.61 
 
 7.82 
 
 44 38.80 
 
 7.83 
 
 44 30.98 
 
 7.81 
 
 44 23.17 
 
 7.81 
 
 115 
 
 43 36.31 
 
 7.81 
 
 43 28.50 
 
 7.80 
 
 43 20.70 
 
 7.80 
 
 43 12.90 
 
 7.80 
 
 43 5.10 
 
 7.80 
 
 in; 
 
 42 18.34 
 
 7.79 
 
 42 10.55 
 
 7.78 
 
 42 2.77 
 
 7.78 
 
 41 54.99 
 
 7.78 
 
 41 47.21 
 
 7.78 
 
 117 
 
 41 0.5!) 
 
 7.70 
 
 40 52.82 
 
 7.76 
 
 40 45.07 
 
 7.76 
 
 40 37.31 
 
 7.75 
 
 40 29.56 
 
 7.75 
 
 118 
 
 39 43.1 1 
 
 7.73 
 
 39 35.38 
 
 7.73 
 
 39 27.05 
 
 7.72 
 
 39 19.93 
 
 7.72 
 
 39 12.21 
 
 7.72 
 
 1H> 
 
 38 25.97 
 
 7.09 
 
 38 18.28 
 
 7.09 
 
 38 10.59 
 
 7.69 
 
 38 2.90 
 
 7.08 
 
 37 55.22 
 
 7.68 
 
 120 
 
 37 9.23 
 
 7.C5 
 
 37 1.58 
 
 7.C5 
 
 30 53.93 
 
 7.64 
 
 36 40.29 
 
 7.04 
 
 36 38.65 
 
 7.63 
 
 121 
 
 35 52.93 
 
 7.00 
 
 35 45.33 
 
 7.00 
 
 35 37.74 
 
 7.59 
 
 35 30.14 
 
 7.59 
 
 35 22.56 
 
 7.58 
 
 139 
 
 34 37.15 
 
 7.55 
 
 34 29.01 
 
 7.54 
 
 34 22.06 
 
 7.54 
 
 34 14.53 
 
 7.53 
 
 34 7.00 
 
 7.53 
 
 123 
 
 33 21.91 
 
 7.49 
 
 33 14.46 
 
 7.48 
 
 33 6.97 
 
 7.48 
 
 32 59.50 
 
 7.17 
 
 32 52.03 
 
 7.46 
 
 1-24 
 
 32 7.36 
 
 7.42 
 
 31 59.94 
 
 7.42 
 
 31 52.52 
 
 7.41 
 
 31 45.12 
 
 7.40 
 
 31 37.71 
 
 7.40 
 
 12.-) 
 
 30 53.46 
 
 7.33 
 
 30 46.11 
 
 7.35 
 
 30 38.77 
 
 7.34 
 
 30 31,13 
 
 7.33 
 
 30 24.1 1 
 
 7.32 
 
 1% 
 
 29 40.30 
 
 7.98 
 
 29 33.03 
 
 7.27 
 
 2!) 25.76 
 
 7.26 
 
 29 18.51 
 
 7.25 
 
 29 11.26 
 
 7.24 
 
 127 
 
 28 27.94 
 
 7.19 
 
 28 20.75 
 
 7.19 
 
 28 13.57 
 
 7.18 
 
 28 6.39 
 
 7.17 
 
 27 59.23 
 
 7.16 
 
 128 
 
 27 16.43 
 
 7.11 
 
 27 9.32 
 
 7.10 
 
 27 2.23 
 
 7.09 
 
 26 55.15 
 
 7.08 
 
 26 48.07 
 
 7.07 
 
 12!) 
 
 26 5.82 
 
 7.01 
 
 25 58.81 
 
 7.00 
 
 25 51.81 
 
 6.99 
 
 25 44.83 
 
 6.98 
 
 25 37.85 
 
 6.97 
 
 130 
 
 24 56.18 
 
 0.91 
 
 24 49.27 
 
 0.90 
 
 24 42.37 
 
 6,89 
 
 24 35.48 
 
 6.88 
 
 24 28.60 
 
 6.87 
 
 131 
 
 23 47.55 
 
 6.81 
 
 23 40.75 
 
 6.80 
 
 23 33.95 
 
 6.79 
 
 23 27.17 
 
 0.78 
 
 23 20.39 
 
 0.77 
 
 i:32 
 
 22 39.99 
 
 6.70 
 
 22 33.29 
 
 0.09 
 
 22 26.61 
 
 6.68 
 
 22 19.94 
 
 0.67 
 
 22 13.27 
 
 0.06 
 
 133 
 
 21 33.55 
 
 6.59 
 
 21 26.97 
 
 0.57 
 
 21 20.40 
 
 6.56 
 
 21 13.64 
 
 6.55 
 
 21 7.30 
 
 0.54 
 
 134 
 
 20 28.28 
 
 6.47 
 
 20 21.82 
 
 6.43 
 
 20 15.37 
 
 6.44 
 
 20 8.93 
 
 6.43 
 
 20 2.51 
 
 6.42 
 
 135 
 
 19 24.23 
 
 6.34 
 
 19 17.8!) 
 
 6.33 
 
 19 11.57 
 
 6.32 
 
 19 5.26 
 
 6.30 
 
 18 58,96 
 
 6.29 
 
 136 
 
 18 21.45 
 
 6.31 
 
 18 15.24 
 
 6.20 
 
 18 9.05 
 
 6.19 
 
 18 2.87 
 
 6.17 
 
 17 50.70 
 
 6.16 
 
 137 
 
 17 19.99 
 
 6.08 
 
 17 13.92 
 
 0.00 
 
 17 7.86 
 
 6.05 
 
 17 1.82 
 
 6.04 
 
 16 55.79 
 
 6.113 
 
 1138 
 
 16 19.90 
 
 5.94 
 
 16 13.96 
 
 5.92 
 
 16 8.05 
 
 5.91 
 
 16 2.14 
 
 5.90 
 
 15 56.25 
 
 5.88 
 
 13'J 
 
 15 21.22 
 
 5.80 
 
 15 15.43 
 
 5.78 
 
 15 9.06 
 
 5.77 
 
 15 3.90 
 
 5.75 
 
 14 58.15 
 
 5.74 
 
 140 
 
 14 24.00 
 
 "i.lj.") 
 
 14 18.36 
 
 5.03 
 
 14 12.73 
 
 5.62 
 
 14 7.12 
 
 C.61 
 
 14 1.53 
 
 5.59 
 
 141 
 
 13 28.28 
 
 5.49 
 
 13 22.79 
 
 5.48 
 
 13 17.32 
 
 5.40 
 
 13 11.87 
 
 5.45 
 
 13 6.43 
 
 5.43 
 
 112 
 
 12 34.12 
 
 5.34 
 
 12 28.79 
 
 5.32 
 
 12 23.17 
 
 5.31 
 
 12 18.17 
 
 5.29 
 
 12 12.89 
 
 5.27 
 
 143 
 
 11 41.54 
 
 5.18 
 
 11 36.37 
 
 5.17 
 
 11 31.22 
 
 5.15 
 
 11 26.08 
 
 5.13 
 
 11.20.96 
 
 5.11 
 
 144 
 
 10 50.59 
 
 5.01 
 
 10 45.59 
 
 5.00 
 
 10 40.60 
 
 4.98 
 
 10 35.03 
 
 4.96 
 
 10 30.68 
 
 4.94 
 
 145 
 
 10 1.32 
 
 4.84 
 
 9 56.48 
 
 4.83 
 
 9 51.00 
 
 4.81 
 
 9 46.86 
 
 4.79 
 
 9 42.08 
 
 4.77 
 
 140 
 
 !) 13.75 
 
 4.67 
 
 9 9.09 
 
 4. 65 
 
 !) 4.45 
 
 4.03 
 
 8 59.82 
 
 4.62 
 
 8 55.21 
 
 4.60 
 
 147 
 
 8 27. 3 
 
 4.49 
 
 8 23.45 
 
 4.47 
 
 8 18.98 
 
 4.46 
 
 8 14.54 
 
 4.44 
 
 8 10.11 
 
 4.42 
 
 148 
 
 7 43.90 
 
 4.31 
 
 7 39.00 
 
 4.29 
 
 7 35.31 
 
 4.28 
 
 7 31.04 
 
 4.26 
 
 7 26.80 
 
 4.24 
 
 14!) 
 
 7 1.69 
 
 4.13 
 
 57.57 
 
 4.11 
 
 6 53.17 
 
 4.09 
 
 6 49.38 
 
 4.07 
 
 6 45.32 
 
 4.05 
 
 150 
 
 6 21.33 
 
 3.94 
 
 17.39 
 
 3.92 
 
 6 13.48 
 
 3.90 
 
 6 9.59 
 
 3.89 
 
 6 5.71 
 
 3.87 
 
 151 
 
 5 42.85 
 
 3.75 
 
 5 39.11 
 
 3.73 
 
 5 35.38 
 
 3.71 
 
 5 31.68 
 
 3.69 
 
 5 28.00 
 
 3.03 
 
 152 
 
 5 6.29 
 
 3.56 
 
 5 2,74 
 
 3.54 
 
 4 59.21 
 
 3.53 
 
 4 55.70 
 
 3.50 
 
 4 52.21 
 
 3.48 
 
 153 
 
 4 31.08 
 
 3.30 
 
 4 28.32 
 
 3.34 
 
 4 24.99 
 
 3.32 
 
 4 21. 68 
 
 3.30 
 
 4 18.38 
 
 :u'8 
 
 154 
 
 3 59.04 
 
 3.16 
 
 3 55.88 
 
 3.14 
 
 3 52.75 
 
 3.13 
 
 3 4! MM 
 
 3.10 
 
 3 46.54 
 
 3.08 
 
 155 
 
 3 28.40 
 
 2.96 
 
 3 25.44 
 
 2.94 
 
 3 22.51 
 
 2.98 
 
 3 19.60 
 
 2.90 
 
 3 10.70 
 
 2.b8 
 
 156 
 
 2 59.78 
 
 8.78 
 
 2 57.03 
 
 2.74 
 
 2 54.30 
 
 2.73. 
 
 2 51.59 
 
 2.70 
 
 2 48.90 
 
 2.08 
 
 157 
 
 2 33.21 
 
 2.55 
 
 2 30.67 
 
 2.53 
 
 2 28.14 
 
 2.51 
 
 2 25.64 
 
 2.49 
 
 2 23.10 
 
 2.47 
 
 158 
 
 2 8.71 
 
 2.35 
 
 2 6.38 
 
 2.32 
 
 2 4.06 
 
 2.30 
 
 2 1.77 
 
 2.28 
 
 1 59.50 
 
 2.26 
 
 159 
 
 1 46.31 
 
 2.13 
 
 1 44.18 
 
 2.11 
 
 1 42.08 
 
 2.09 
 
 1 40.00 
 
 2.07 
 
 1 37.94 
 
 2.05 
 
 160 
 
 1 26.01 
 
 1.93 
 
 1 21.10 
 
 1.90 
 
 1 22.21 
 
 1.88 
 
 1 20.34 
 
 1.86 
 
 1 18,19 
 
 1.84 
 
 161 
 
 1 7.84 
 
 1.71 
 
 1 0.14 
 
 1.69 
 
 1 4.47 
 
 1.67 
 
 1 2.81 
 
 1.05 
 
 1 1.17 
 
 1.62 
 
 102 
 
 51.81 
 
 1.49 
 
 50.33 
 
 1.47 
 
 48.87 
 
 1.45 
 
 47.43 
 
 1.43 
 
 46,01 
 
 1.41 
 
 163 
 
 37.94 
 
 J.28 
 
 36.68 
 
 1.26 
 
 35.43 
 
 1.23 
 
 34.21 
 
 1.21 
 
 33.00 
 
 1.19 
 
 164 
 
 26.24 
 
 i.no 
 
 25.19 
 
 1.04 
 
 24.16 
 
 1.03 
 
 23.10 
 
 1.00 
 
 22.17 
 
 0.97 
 
 165 
 
 16.72 
 
 0.84 
 
 15.89 
 
 0.83 
 
 15.08 
 
 0.80 
 
 14.29 
 
 0.78 
 
 13.53 
 
 0.76 
 
 100 
 
 9.39 
 
 0.03 
 
 8.77 
 
 0.00 
 
 8.18 
 
 0.58 
 
 7.01 
 
 0.56 
 
 7.07 
 
 0.54 
 
 167 
 
 4.25 
 
 -11.10 
 
 3.86 
 
 -0.38 
 
 3.49 
 
 -0.36 
 
 3,14 
 
 -0.34 
 
 2.81 
 
 -0.32 
 
TABLE X. 
 
 FETATION (IK TIIK (T.NTlii:, F< >U III = 0. 
 
 Coiislant add.-il -17' T'.5. IVriml = 22 1 : 
 
 
 d 
 
 Diff. 
 
 ,1 
 
 Diff. 
 
 .1 
 
 Diff. 
 
 d 
 
 
 .1 
 
 Diff. 
 
 
 ()..-, 
 
 CorO*.l 
 
 O.6 
 
 
 0.7 
 
 
 O.S 
 
 lurlH.I 
 
 ().:) 
 
 
 ,1 
 
 119 
 
 o / /; 
 40 51.79 
 
 -7.83 
 
 lii 4:i!!Hi 
 
 
 40 30.' 1 1 
 
 -7.*! 
 
 / // 
 lii 2S.3I 
 
 
 lii 20.' 19 
 
 
 113 
 
 45 :t.54 
 
 
 45 25.72 
 
 
 45 17.90 
 
 
 45 10.07 
 
 
 45 2.25 
 
 
 111 
 
 Oil 15.: {5 
 
 
 1 1 7.5 1 
 
 
 43 5! 1.73 
 
 7.-I 
 
 13 51.92 
 
 :.-\ 
 
 43 11.11 
 
 7. s| 
 
 115 
 
 42 57.30 
 
 
 42 19.50 
 
 
 12 41.71 
 
 
 12 :!3.92 
 
 
 42 20.13 
 
 7.7'J 
 
 110 
 
 41 39.13 
 
 7.77 
 
 II 31.00 
 
 7.77 
 
 41 2. 
 
 - "7 
 
 41 10.12 
 
 
 1 1 s.:J5 
 
 7.76 
 
 117 
 
 40 2I.M 
 
 7.7:. 
 
 40 11.00 
 
 7.71 
 
 40 0.32 
 
 7.71 
 
 :t:i 5S.58 
 
 7.71 
 
 :? - -I 
 
 7.71 
 
 us 
 
 39 1.50 
 
 7.71 
 
 3" 50.7S 
 
 7.71 
 
 3s : 
 
 7.71 
 
 11.37 
 
 7.7U 
 
 :;8 :t;.. ,7 
 
 7.70 
 
 119 
 
 37 17.55 
 
 7.li7 
 
 37 :i9,-7 
 
 7.67 
 
 37 32.21 
 
 
 37 01.51 
 
 
 37 Ji>.88 
 
 7.CJ 
 
 120 
 
 30 31.02 
 
 
 3 i 23.39 
 
 
 30 15.77 
 
 
 30 8.15 
 
 7.11. 
 
 30 0.51 
 
 7. lii 
 
 121 
 
 35 11.9," 
 
 
 35 7.10 
 
 
 31 59,-! 
 
 7.57 
 
 31 52.27 
 
 
 31 41.; 1 
 
 
 199 
 
 : 59.47 
 
 
 :Ci 51. 'Hi 
 
 7..M 
 
 33 41.11 
 
 ", . . , 1 
 
 .33 30.91 
 
 
 33 29. ! 1 
 
 
 123 
 
 32 1 1.57 
 
 7. Ill 
 
 32 37.11 
 
 7,1.-, 
 
 32 29.07 
 
 7. i;, 
 
 32 
 
 7.11 
 
 32 14.79 
 
 7.IJ 
 
 121 
 
 31 30.32 
 
 7.39 
 
 31 22.! i| 
 
 
 31 15.50 
 
 7.38 
 
 31 8.18 
 
 7_'I7 
 
 31 0.8-7 
 
 7.36 
 
 125 
 
 30 10.79 
 
 Ml 
 
 30 9.17 
 
 7.;:i 
 
 30 2.17 
 
 7.30 
 
 99 5I,"7 
 
 
 2:l 47.58 
 
 IM 
 
 120 
 
 29 1.02 
 
 7.-J1 
 
 2- 50.7," 
 
 7. Ml 
 
 2" 19.50 
 
 7. _'.! 
 
 2- 12.31 
 
 7.-.M 
 
 15.14 
 
 IM 
 
 127 
 
 27 52.07 
 
 7.15 
 
 27 44.92 
 
 7.11 
 
 27 37.79 
 
 7.13 
 
 27 30.00 
 
 7.1- 
 
 27 23.51 
 
 7.13 
 
 HB 
 
 20 41.01 
 
 7.C6 
 
 2i i 33.! 15 
 
 
 26 26.91 
 
 7.04 
 
 26 19X7 
 
 7 .11.1 
 
 20 12. -I 
 
 7.02 
 
 199 
 
 o 25 :tn.,"s 
 
 6.96 
 
 25 23.! 12 
 
 tM 
 
 25 10.97 
 
 6.94 
 
 25 10.03 
 
 6.93 
 
 25 3.10 
 
 
 130 
 
 021 21.73 
 
 6.86 
 
 24 II, 
 
 i;.-:, 
 
 21 8.03 
 
 6.84 
 
 21 1.19 
 
 6.83 
 
 23 51.37 
 
 6.SJ 
 
 131 
 
 23 13.03 
 
 6.76 
 
 23 0.,-s 
 
 C.73 
 
 23 0.14 
 
 6.73 
 
 22 53.11 
 
 G.72 
 
 22 10.09 
 
 C.71 
 
 132 
 
 22 0.02 
 
 6.64 
 
 21 5! P.! 19 
 
 6.63 
 
 21 53.30 
 
 
 21 40.71 
 
 6.61 
 
 21 40.14 
 
 6.60 
 
 133 
 
 21 0.70 
 
 &:,:i 
 
 20 51.21 
 
 li..M 
 
 20 47.73 
 
 6.50 
 
 20 41.21 
 
 6.19 
 
 20 31.75 
 
 
 134 
 
 19 50.10 
 
 6.40 
 
 19 49.70 
 
 6.39 
 
 19 43.31 
 
 6.38 
 
 19 30.91 
 
 6.37 
 
 19 30.58 
 
 li.X, 
 
 135 
 
 18 52.08 
 
 6.28 
 
 18 40,10 
 
 6.37 
 
 18 40.14 
 
 6.35 
 
 18 33.!>0 
 
 6.24 
 
 18 27.(,7 
 
 6.93 
 
 136 
 
 17 50.55 
 
 6.15 
 
 17 44.11 
 
 6.13 
 
 17 38.28 
 
 6.13 
 
 17 .32.17 
 
 6.11 
 
 17 20.07 
 
 tM 
 
 137 
 
 10 19.77 
 
 6.01 
 
 10 43.77 
 
 
 Hi 37.78 
 
 5.98 
 
 10 31.80 
 
 5.97 
 
 16 25,- 1 
 
 5.95 
 
 138 
 
 15 50.3," 
 
 5.87 
 
 15 11.52 
 
 5.89 
 
 15 38.07 
 
 5.84 
 
 15 32," 1 
 
 5.83 
 
 15 27.02 
 
 '5.M1 
 
 130 
 
 14 52.12 
 
 5.73 
 
 14 40.71 
 
 5.71 
 
 1 1 41.01 
 
 5.69 
 
 14 35.32 
 
 5.68 
 
 14 29.65 
 
 5.66 
 
 140 
 
 13 55.95 
 
 tM 
 
 13 50.38 
 
 
 13 ll.sl 
 
 5.54 
 
 13 39.30 
 
 5.13 
 
 13 33.78 
 
 5.51 
 
 111 
 
 13 1.00 
 
 .'i. !> 
 
 12 55.5! 1 
 
 5.40 
 
 12 50.20 
 
 5.38 
 
 12 1 1,"2 
 
 5.37 
 
 12 39.10 
 
 5-'G 
 
 142 
 
 12 7.03 
 
 5.96 
 
 12 2.:t8 
 
 :,._' I 
 
 11 57.14 
 
 5.33 
 
 11 51.92 
 
 5.21 
 
 II 40.72 
 
 5.19 
 
 143 
 
 11 15.,"0 
 
 5.09 
 
 11 10.77 
 
 5.08 
 
 1 1 5.70 
 
 5.06 
 
 11 0.05 
 
 5.04 
 
 10 55.01 
 
 5.03 
 
 144 
 
 10 25.74 
 
 4.93 
 
 10 20.82 
 
 4.91 
 
 10 15.92 
 
 4.89 
 
 10 11.04 
 
 4.88 
 
 10 6.17 
 
 4.86 
 
 145 
 
 9 37.32 
 
 4.76 
 
 9 32.57 
 
 4.74 
 
 9 27.," 1 
 
 4.72 
 
 9 23.12 
 
 4.70 
 
 9 18.43 
 
 4.69 
 
 110 
 
 8 50.02 
 
 4.58 
 
 8 40.05 
 
 4.56 
 
 8 41.49 
 
 4.M 
 
 8 30.96 
 
 4_M 
 
 8 32. 1 1 
 
 4.51 
 
 147 
 
 8 5.69 
 
 4.40 
 
 8 1.30 
 
 4.39 
 
 7 56.92 
 
 4.37 
 
 7 52.56 
 
 4.35 
 
 7 48.22 
 
 4J3 
 
 148 
 
 7 22.56 
 
 4.32 
 
 7 18.35 
 
 4.90 
 
 7 14.10 
 
 4.18 
 
 7 9.9," 
 
 4.17 
 
 7 5.83 
 
 I.I.-. 
 
 149 
 
 6 41.27 
 
 l.lll 
 
 37.25 
 
 4.<h> 
 
 33.24 
 
 4.00 
 
 6 29.25 
 
 3.98 
 
 6 25.2" 
 
 3.9S 
 
 150 
 
 6 1.85 
 
 3.85 
 
 5 58.01 
 
 3.83 
 
 5 54.20 
 
 3.81 
 
 5 50.40 
 
 3.79 
 
 5 10.01 
 
 3.77 
 
 151 
 
 5 24.33 
 
 3.66 
 
 5 20.08 
 
 3.C4 
 
 5 17.06 
 
 3.62 
 
 5 13.45 
 
 3.60 
 
 5 9.SO 
 
 3.58 
 
 152 
 
 4 4s.7 1 
 
 3.46 
 
 1 15.29 
 
 :i.n 
 
 4 41>5 
 
 :i. i-j 
 
 4 38. 1 1 
 
 3.40 
 
 4 a>.o.-> 
 
 X18 
 
 153 
 
 4 15.11 
 
 3.26 
 
 1 11.,"5 
 
 tM 
 
 4 8.02 
 
 3.23 
 
 4 5.41 
 
 3.30 
 
 4 2.21 
 
 :t.iH 
 
 154 
 
 3 43.46 
 
 3.06 
 
 3 40.11 
 
 3.04 
 
 3 37.38 
 
 3.02 
 
 3 31.37 
 
 3.00 
 
 3 31.37 
 
 3J8 
 
 155 
 
 3 13.83 
 
 2.86 
 
 3 10.98 
 
 2.84 
 
 3 8.15 
 
 2.82 
 
 3 5.31 
 
 2.80 
 
 3 2.55 
 
 2.78 
 
 156 
 
 2 40.21 
 
 2.66 
 
 2 43.59 
 
 2.64 
 
 2 40.97 
 
 2.69 
 
 2 .38.30 
 
 2.59 
 
 2 35.78 
 
 9i7 
 
 157 
 
 2 20.70 
 
 2.45 
 
 2 18.20 
 
 2.43 
 
 2 15.H1 
 
 2.41 
 
 2 13.15 
 
 2.39 
 
 2 11.07 
 
 2J7 
 
 158 
 
 1 57.25 
 
 2.-J 1 
 
 1 55.02 
 
 tM 
 
 1 52.82 
 
 3.20 
 
 1 50.02 
 
 9.18 
 
 1 I".I5 
 
 2.16 
 
 159 
 
 1 35.! 
 
 2.03 
 
 1 33.88 
 
 2.01 
 
 1 31.88 
 
 1.99 
 
 1 29.90 
 
 1.97 
 
 1 27.95 
 
 1.94 
 
 160 
 
 1 10.00 
 
 1.82 
 
 1 14.&5 
 
 1.80 
 
 1 13.07 
 
 1.77 
 
 1 11.30 
 
 1.7.-, 
 
 1 9.50 
 
 1.73 
 
 161 
 
 59.5i i 
 
 1.60 
 
 57.! >7 
 
 1.58 
 
 50,10 
 
 1.56 
 
 54, "5 
 
 1.54 
 
 53.32 
 
 1.59 
 
 162 
 
 41.01 
 
 1.39 
 
 43.23 
 
 IJ7 
 
 41.-- 
 
 IM 
 
 40.51 
 
 IM 
 
 3.>.23 
 
 IM 
 
 ni3 
 
 31.82 
 
 1.17 
 
 30.00 
 
 1.15 
 
 29.53 
 
 1.13 
 
 28.41 
 
 1.10. 
 
 27.32 
 
 IMS 
 
 101 
 
 21.21 
 
 0.95 
 
 20.27 
 
 0.93 
 
 19.35 
 
 0.91 
 
 18.15 
 
 0.89 
 
 17.57 
 
 0.86 
 
 165 
 
 12.78 
 
 0.73 
 
 12.00 
 
 0.71 
 
 11.30 
 
 0.09 
 
 10.. i" 
 
 ojtn 
 
 10.02 
 
 tM 
 
 [66 
 
 0.51 
 
 0.-)I 
 
 6.01 
 
 0.49 
 
 5.50 
 
 0.47 
 
 5.10 
 
 tM 
 
 4.00 
 
 0.43 
 
 107 
 
 2.51 
 
 -0.39 
 
 2.22 
 
 -0.37 
 
 1.90 
 
 -0.35 
 
 1.73 
 
 -OJO 
 
 1.51 -0.91 
 
TABLE X. 
 
 EQUATION OF THE CENTRE, FOR 111 = 0. 
 
 d 
 
 Constant suUK-il 47' :{.o. Period = 224. 7008. 
 
 Arg. L. 
 
 d 
 
 o.o 
 
 Diff. 
 
 forO'l.l 
 
 cl 
 
 0.1 
 
 DilK. 
 
 lor [)'".! 
 
 <1 
 
 0.2 
 
 Diff. 
 
 for (><U 
 
 (1 
 
 0.3 
 
 DifT. 
 
 for (!'".! 
 
 d 
 O.4 
 
 Did'. 
 forO"i.l 
 
 d 
 
 o i n 
 
 it 
 
 / // 
 
 II 
 
 1 11 
 
 n 
 
 / // 
 
 ii 
 
 / // 
 
 u 
 
 168 
 
 1.31 
 
 -0.18 
 
 1.14 
 
 -0.16 
 
 0.99 
 
 -0.14 
 
 0.8! i 
 
 -0.12 
 
 0.70 
 
 -0.10 
 
 Ifi9 
 
 0.58 
 
 +0.04 
 
 0.03 
 
 +0.06 
 
 0.70 
 
 +0.08 
 
 0.79 
 
 +0.10 
 
 0.91 
 
 +0.13 
 
 170 
 
 2.0(5 
 
 0.26 
 
 o 2.33 
 
 0.28 
 
 2.62 
 
 0.30 
 
 2.93 
 
 0.39 
 
 3.27 
 
 ' 0.35 
 
 171 
 
 5.74 
 
 0.43 
 
 6.23 
 
 0.50 
 
 0.75 
 
 0.52 
 
 7.28 
 
 0.54 
 
 7.84 
 
 0.57 
 
 17-3 
 
 11. (54 
 
 0.70 
 
 12.35 
 
 0.72 
 
 13.08 
 
 0.74 
 
 13.83 
 
 0.76 
 
 14.01 
 
 0.79 
 
 17:! 
 
 19.73 
 
 0.92 
 
 20.06 
 
 0.94 
 
 21.01 
 
 0.96 
 
 22.59 
 
 0.98 
 
 23.58 
 
 1.01 
 
 171 
 
 .'!0.02 
 
 1.14 
 
 31.17 
 
 1.10 
 
 32.34 
 
 1.18 
 
 33.54 
 
 1.20 
 
 34.75 
 
 1.22 
 
 175 
 
 42.5 1 
 
 1.:16 
 
 43.88 
 
 1.38 
 
 45.27 
 
 1.40 
 
 40.08 
 
 1.42 
 
 48.11 
 
 1.44 
 
 17(5 
 
 57.18 
 
 1.58 
 
 58.76 
 
 1.60 
 
 1 0.37 
 
 1.62 
 
 2.00 
 
 1.64 
 
 3.05 
 
 1.66 
 
 177 
 
 1 14.02 
 
 1.79 
 
 1 15.82 
 
 1.81 
 
 1 17.05 
 
 1.K4 
 
 1 19.50 
 
 1.86 
 
 1 21.30 
 
 1.88 
 
 178 
 
 1 33.03 
 
 a.oi 
 
 1 35.04 
 
 2.03 
 
 1 37.08 
 
 9.05 
 
 1 3!). 15 
 
 2.07 
 
 1 41.23 
 
 2.09 
 
 179 
 
 1 54.18 
 
 2.22 
 
 1 50.41 
 
 2.24 
 
 1 58.07 
 
 9.26 
 
 2 0.94 
 
 2.29 
 
 2 3.24 
 
 2.31 
 
 180 
 
 2 17.47 
 
 2.43 
 
 2 19.91 
 
 2.46 
 
 2 22.38 
 
 2.48 
 
 2 24.87 
 
 2.50 
 
 2 27.38 
 
 9.52 
 
 181 
 
 2 42.87 
 
 8.05 
 
 2 45.53 
 
 2.07 
 
 2 48.20 
 
 9.09 
 
 2 50.! >0 
 
 2.71 
 
 2 53.02 
 
 2.73 
 
 18'2 
 
 3 10.37 
 
 2.85 
 
 3 13.24 
 
 2.87 
 
 3 16.12 
 
 2.90 
 
 3 19.03 
 
 2.92 
 
 3 21.90 
 
 8.94 
 
 183 
 
 3 39.95 
 
 3.0G 
 
 3 43.02 
 
 3.08 
 
 3 46.12 
 
 3.10 
 
 3 49.23 
 
 3.12 
 
 3 52.30 
 
 3.14 
 
 184 
 
 4 11.59 
 
 3.27 
 
 4 14.87 
 
 3.29 
 
 4 18.16 
 
 3.31 
 
 4 21.48 
 
 3.33 
 
 4 24.82 
 
 3.35 
 
 189 
 
 4 45.2(5 
 
 3.47 
 
 4 48.74 
 
 3.49 
 
 4 52.23 
 
 3.51 
 
 4 55.75 
 
 :i.r,:i 
 
 4 59.29 
 
 3.55 
 
 181) 
 
 5 20.93 
 
 3.07 
 
 5 24.01 
 
 3.69 
 
 5 28.31 
 
 3.71 
 
 5 32.02 
 
 3.73 
 
 5 35.70 
 
 3.75 
 
 187 
 
 5 58.59 
 
 3.86 
 
 6 2.46 
 
 3.88 
 
 (5 0.36 
 
 3.90 
 
 6 10.27 
 
 3.92 
 
 14.20 
 
 3.94 
 
 188 
 
 6 38.20 
 
 4.06 
 
 6 42.26 
 
 4.08 
 
 6 40.35 
 
 4.10 
 
 50.46 
 
 4.11 
 
 6 54.58 
 
 4.13 
 
 189 
 
 7 19.73 
 
 4.25 
 
 7 23.98 
 
 4.27 
 
 7 28.26 
 
 4.29 
 
 7 32.55 
 
 4.30 
 
 7 3(5.87 
 
 4.32 
 
 1!IO 
 
 8 3.14 
 
 4.43 
 
 8 7.59 
 
 4.45 
 
 8 12.05 
 
 4.47 
 
 8 10.53 
 
 4.49 
 
 8 21.03 
 
 4.51 
 
 191 
 
 8 48.42 
 
 4.C2 
 
 8 53.05 
 
 4.64 
 
 8 57.0!) 
 
 4.65 
 
 9 2.36 
 
 4.67 
 
 9 7.04 
 
 4.69 
 
 199 
 
 f9 35.51 
 
 4.80 
 
 9 40.32 
 
 4.82 
 
 9 45.15 
 
 4.83 
 
 9 49.99 
 
 4.85 
 
 9 54.85 
 
 4.87 
 
 199 
 
 10 24.40 
 
 4.98 
 
 10 29.38 
 
 4.99 
 
 10 34.38 
 
 5.01 
 
 10 39.40 
 
 5.03 
 
 10 44.44 
 
 5.01 
 
 ID! 
 
 11 15.02 
 
 5.15 
 
 11 20.18 
 
 5.17 
 
 11 25.35 
 
 5.18 
 
 11 30.55 
 
 5.90 
 
 11 35.75 
 
 5.92 
 
 1!>5 
 
 12 7.313 
 
 5.32 
 
 12 12.68 
 
 5.33 
 
 12 18.03 
 
 5.35 
 
 12 23.39 
 
 5.37 
 
 12 28.7(5 
 
 5.38 
 
 196 
 
 13 1.36 
 
 5.48 
 
 13 6.85 
 
 5.50 
 
 13 12.36 
 
 5.51 
 
 13 17.88 
 
 5.53 
 
 13 23.42 
 
 5.55 
 
 197 
 
 13 5(5.!)!) 
 
 5.04 
 
 14 2.64 
 
 5.66 
 
 14 8.31 
 
 5.67 
 
 14 13.99 
 
 5.69 
 
 14 19.09 
 
 5.71 
 
 198 
 
 14 54.20 
 
 5.80 
 
 15 0.01 
 
 5.81 
 
 15 5.a3 
 
 5.83 
 
 15 11.07 
 
 5.84 
 
 15 17.52 
 
 5.86 
 
 190 
 
 15 52.95 
 
 5.95 
 
 15 58.91 
 
 5.96 
 
 10 4.88 
 
 5.97 
 
 16 10.87 
 
 5.99 
 
 16 16.87 
 
 6.01 
 
 200 
 
 10 53.19 
 
 6.10 
 
 16 59.29 
 
 C.ll 
 
 17 5.41 
 
 6.13 
 
 17 11.54 
 
 6.14 
 
 17 17.69 
 
 6.15 
 
 301 
 
 17 54.87 
 
 6.84 
 
 18 1.12 
 
 6.25 
 
 18 7.38 
 
 6.27 
 
 18 13.155 
 
 6.28 
 
 18 19.94 
 
 6.89 
 
 202 
 
 18 57.95 
 
 0.38 
 
 19 4.*) 
 
 6.39 
 
 19 10.72 
 
 6.40 
 
 19 17.13 
 
 6.42 
 
 19 23.50 
 
 6.43 
 
 20:5 
 
 20 2.37 
 
 6.51 
 
 20 8.88 
 
 6.52 
 
 20 15.41 
 
 6.53 
 
 20 21.95 
 
 6.55 
 
 20 28.50 
 
 0.56 
 
 204 
 
 21 8.09 
 
 6.03 
 
 21 14.73 
 
 6.65 
 
 21 21.38 
 
 0.00 
 
 21 28.05 
 
 6.07 
 
 21 34.72 
 
 6.68 
 
 '205 
 
 22 15.04 
 
 6.7C 
 
 22 21.81 
 
 6.77 
 
 22 28.58 
 
 6.78 
 
 22 35.37 
 
 6.79 
 
 22 42.10 
 
 6.60 
 
 906 
 
 23 23.1!) 
 
 6.87 
 
 23 30.07 
 
 6.88 
 
 23 30.9(5 
 
 6.89 
 
 23 43.80 
 
 6.91 
 
 23 50.77 
 
 6.92 
 
 207 
 
 24 32.48 
 
 6.98 
 
 24 39.47 
 
 6.99 
 
 24 46.40 
 
 7.00 
 
 24 53.47 
 
 7.02 
 
 25 0.50 
 
 7.03 
 
 208 
 
 25 42.84 
 
 7.09 
 
 25 49.! )3 
 
 7.10 
 
 25 57.04 
 
 7.11 
 
 26 4.15 
 
 7.12 
 
 2G 11.28 
 
 7.13 
 
 209 
 
 2(5 54.23 
 
 7.19 
 
 27 1.42 
 
 7.20 
 
 27 8.62 
 
 7.21 
 
 27 15.84 
 
 7.29 
 
 27 23.00 
 
 7.83 
 
 210 
 
 28 (5.5!) 
 
 7.98 
 
 28 13.87 
 
 7.29 
 
 28 21.17 
 
 7.30 
 
 28 28.47 
 
 7.31 
 
 28 35.79 
 
 7.39 
 
 211 
 
 29 19.85 
 
 7.37 
 
 29 27.23 
 
 7.38 
 
 29 34.01 
 
 7.39 
 
 29 42.00 
 
 7.40 
 
 29 49.40 
 
 7.40 
 
 212 
 
 30 33.!)7 
 
 7.45 
 
 30 41.43 
 
 7.46 
 
 30 48.89 
 
 7.47 
 
 30 56.30 
 
 7.48 
 
 31 3.84 
 
 7.48 
 
 213 
 
 31 48.88 
 
 7.5!) 
 
 31 5(5.41 
 
 7.54 
 
 32 3.95 
 
 7.54 
 
 32 11.50 
 
 7.55 
 
 32 19.05 
 
 7.56 
 
 214 
 
 33 4.52 
 
 7.60 
 
 33 12.13 
 
 7.61 
 
 33 19.74 
 
 7.61 
 
 33 27.35 
 
 7.62 
 
 33 34.! )7 
 
 7.63 
 
 215 
 
 34 20.84 
 
 7.06 
 
 34 28.51 
 
 7.67 
 
 34 36.18 
 
 7.67 
 
 34 43.86 
 
 7.08 
 
 34 51.54 
 
 7.69 
 
 2Hi 
 
 35 .37.77 
 
 7.72 
 
 35 45.49 
 
 7.73 
 
 35 53.22 
 
 7.73 
 
 30 0.95 
 
 7.74 
 
 30 8.69 
 
 7.74 
 
 217 
 
 3(5 55.24 
 
 7.77 
 
 37 3.02 
 
 7.78 
 
 37 10.80 
 
 7.78 
 
 37 18.58 
 
 7.79 
 
 37 20.37 
 
 7.79 
 
 218 
 
 38 13.21 
 
 7.82 
 
 38 21.03 
 
 7.82 
 
 38 28.85 
 
 7.83 
 
 38 30.08 
 
 7.83 
 
 38 44.51 
 
 7.83 
 
 219 
 
 39 31.00 
 
 7.86 
 
 39 39.46 
 
 7.86 
 
 39 47.32 
 
 7.87 
 
 39 55.19 
 
 7.87 
 
 40 3.00 
 
 7.87 
 
 220 
 
 40 50.35 
 
 7.89 
 
 40 58.24 
 
 7.89 
 
 41 0.13 
 
 7.90 
 
 41 14.03 
 
 7.90 
 
 41 21.93 
 
 7.90 
 
 221 
 
 42 9.10 
 
 7.92 
 
 42 17.32 
 
 7.92 
 
 42 25.24 
 
 7.92 
 
 42 .33.10 
 
 7.92 
 
 42 41.09 
 
 7.93 
 
 :> 
 
 43 28.158 
 
 7.!)4 
 
 43 30.02 
 
 7.94 
 
 43 41.50 
 
 7.94 
 
 43 52.51 
 
 7.94 
 
 44 0.45 
 
 7.94 
 
 an 
 
 44 48.14 
 
 TJH 
 
 II 50.10 
 
 7.95 
 
 45 4.05 
 
 7.95 
 
 45 12.00 
 
 7.96 
 
 45 19.90 
 
 7.96 
 
 J2-1 
 
 4(5 7.71 
 
 +7.90 
 
 46 15.07 
 
 +7.96 
 
 4(5 23.63 
 
 +7.96 
 
 40 31.59 
 
 +7.96 
 
 4(3 39.55 
 
 +7.90 
 
TABLE X. 
 
 I:QI ATION OF TIII-: CKNTUK, FOII m=o. 
 
 .! 
 
 > .: ,uiii.-,i IT' :!".:>. ivn.ui -= 221 ; 
 
 \rg 1 
 
 d 
 <)..-. 
 
 Dill'. 
 f.irO'U 
 
 .1 
 0.<i 
 
 Diff. 
 
 l.irlf'.l 
 
 .1 
 
 0.7 
 
 Diff. 
 
 .1 
 
 O.8 
 
 Diff. 
 
 f.,ril'i.l 
 
 d 
 0.!> 
 
 Diff. 
 
 r.,r(l''.I 
 
 ,i 
 Ki8 
 
 
 
 ti (i o.or 
 
 n 
 
 -<>.l>7 
 
 d (Mil 
 
 // 
 
 d i 
 
 ii 
 
 1 1 1 1.:,:, 
 
 // 
 HM)I 
 
 6 fa, 
 
 II 
 
 +<l.lll 
 
 108 
 
 1.05 
 
 +0.19 
 
 1.20 
 
 M.n 
 
 l.::s 
 
 
 l.5!l 
 
 I.SI 
 
 I'.-.'l 
 
 170 
 
 :!.li:t 
 
 
 1.01 
 
 
 l.ll 
 
 ii.n 
 
 I.S3 
 
 11. I.I 
 
 5/,'S 
 
 M| 
 
 171 
 
 -.11 
 
 
 (1 il.01 
 
 n.hi 
 
 !Mil 
 
 0.63 
 
 10.28 
 
 
 o lo.: 15 
 
 048 
 
 172 
 
 15.11 
 
 
 o io.23 
 
 o.si 
 
 17.07 
 
 ox. 
 
 17.! >3 
 
 
 I, -..-2 
 
 n.!io 
 
 17:! 
 
 (1 21.00 
 
 l.iti 
 
 (1 25.01 
 
 !.:. 
 
 28.70 
 
 1.117 
 
 27.711 
 
 
 '.'- 
 
 tM 
 
 171 
 
 35.! i! i 
 
 
 37.25 
 
 i .;; 
 
 3S..VI 
 
 
 3:.K{ 
 
 l.:il 
 
 o II. Hi 
 
 l.::l 
 
 17.-, 
 
 (I (I 1 '.:,7 
 
 i.r, 
 
 (1 51.05 
 
 i.i'j 
 
 52.55 
 
 I..M 
 
 51.07 
 
 
 55.01 
 
 tM 
 
 170 
 
 1 5.:t3 
 
 IM 
 
 1 7.02 
 
 1.71 
 
 1 S.7 1 
 
 1.73 
 
 1 10. Is 
 
 
 1 I".'.') 
 
 U71 
 
 177 
 
 1 23.25 
 
 
 1 25.|ii 
 
 
 1 27.10 
 
 IM 
 
 1 2! 1.05 
 
 
 1 3I.C3 
 
 UK 
 
 178 
 
 1 13..33 
 
 J. 1 -J 
 
 1 45.|ii 
 
 .'.i i 
 
 1 !7.';i 
 
 L'.lli 
 
 I 4H.78 
 
 ua 
 
 1 51.! 17 
 
 3.30 
 
 1711 
 
 ii _> 5.50 
 
 
 2 7.: HI 
 
 UB 
 
 2 I0.2(i 
 
 i:i7 
 
 2 12.01 
 
 
 -' 15.01 
 
 -Ml 
 
 180 
 
 (1 '.' 2!>.! l| 
 
 J.:. I 
 
 2 32. l(i 
 
 
 2 35.0-3 
 
 
 2 37.02 
 
 
 2 Kl.-.'l 
 
 
 |S| 
 
 2 r>ii.:{ii 
 
 
 2 5:i.l2 
 
 J.77 
 
 3 l.!i| 
 
 3 4.71 
 
 
 3 7.r>:{ 
 
 
 183 
 
 o :i 2i.:n 
 
 
 3 27.S7 
 
 
 3 30 
 
 :i.oo 
 
 3 :t.!.-; 
 
 tM 
 
 3 30.! 10 
 
 :i.i>4 
 
 183 
 
 o ; 55.52 
 
 
 3 SSJSS 
 
 3.18 
 
 1 1.88 
 
 ;i.-jii 
 
 1 5.10 
 
 tM 
 
 1 s.:n 
 
 
 181 
 
 1 
 
 :I.:IT 
 
 1 31.55 
 
 :i.:w 
 
 1 31.! 15 
 
 :i.n 
 
 1 3S.30 
 
 Ml 
 
 !.80 
 
 .'!. I.', 
 
 185 
 
 d 5 . -, 
 
 :i.:,r 
 
 5 O.l> 
 
 
 5 1 
 
 
 5 13.01 
 
 UK 
 
 5 17.28 
 
 :i.K, 
 
 I . 
 
 d r, 3.1.5.! 
 
 3.77 
 
 5 |:i. i 
 
 
 5 17.0!) 
 
 n.-i 
 
 5 50.! KI 
 
 
 5 51.71 
 
 :i. -I 
 
 187 
 
 d d is.15 
 
 :i.:i(i 
 
 (i 22. U 
 
 :i.9s 
 
 ii :.;.!! 
 
 4.00 
 
 (i :U12 
 
 
 31.15 
 
 -l.nl 
 
 I ; ; 
 
 (i 
 
 i.i.i 
 
 7 a. 
 
 1.17 
 
 7 7.' , 
 
 1.1!) 
 
 7 11.27 
 
 4.31 
 
 7 15.1!) 
 
 
 189 
 
 o 7 -11.20 
 
 r.:n 
 
 7 15.55 
 
 436 
 
 7 4!t.!i2 
 
 ua 
 
 7 51.31 
 
 4.40 
 
 7 58.72 
 
 I.I.' 
 
 190 
 
 8 25.55 
 
 4J3 
 
 s 30.09 
 
 4.54 
 
 s :U.(it 
 
 ut 
 
 8 3:i.2l 
 
 I..V- 
 
 e i3.8i 
 
 \M 
 
 191 
 
 !> 11.71 
 
 4.71 
 
 i) Ki.lii 
 
 4.73 
 
 it 21.20 
 
 i.: , 
 
 ! 2.V. 15 
 
 4.76 
 
 !" 30.72 
 
 4.78 
 
 109 
 
 !) 5! i.73 
 
 4.89 
 
 10 4.03 
 
 4.91 
 
 10 !.."> 
 
 4.IKJ 
 
 10 14.48 
 
 4.94 
 
 10 I!U3 
 
 4.96 
 
 193 
 
 10 4!>.l!) 
 
 5.06 
 
 10 51.57 
 
 5.08 
 
 10 5!Mi5 
 
 5.10 
 
 11 4.70 
 
 ut 
 
 11 9JBS 
 
 
 IIM 
 
 11 40.!)8 
 
 ua 
 
 II 4(i.22 
 
 
 II 51. IS 
 
 5.27 
 
 11 50.70 
 
 5.2S 
 
 12 2.05 
 
 :,.:m 
 
 195 
 
 d 12 31.15 
 
 5.40 
 
 12 3 
 
 :.. i 
 
 12 -1 >.!>! 
 
 5.43 
 
 12 50.43 5.45 
 
 12 S&89 
 
 
 196 
 
 1:1 2s.: is 
 
 
 13 31.55 
 
 538 
 
 13 10.13 
 
 5.59 
 
 13 45.74 :..6l 
 
 13 51.30 
 
 5^1 
 
 197 
 
 14 -C-.K) 
 
 
 11 31.13 
 
 .-..-, 1 
 
 1 1 3(i.8.-l 
 
 :..;:, 
 
 14 42.04 5.77 
 
 1 1 48.4 1 
 
 
 198 
 
 15 2: .3:i 
 
 
 15 2D.27 
 
 5.89 
 
 15 35.17 
 
 5.90 
 
 15 41.08 
 
 5.93 
 
 15 47.01 
 
 
 \'M 
 
 10 ' 
 
 6.03 
 
 10 2s.: 12 
 
 6.04 
 
 Ki 34.90 
 
 6.05 
 
 Ki 41.02 
 
 6.07 
 
 Ki 47.10 
 
 Bjoa 
 
 200 
 
 I/ 23.85 
 
 6.17 
 
 17 30.03 
 
 6.18 
 
 17 :j!i.22 
 
 6.00 
 
 17 42.42 
 
 Mi 
 
 17 is.iii 
 
 
 301 
 
 (1 IS 20.24 
 
 6.31 
 
 is :!2.55 
 
 i;.:w 
 
 18 3S.-- 
 
 6.33 
 
 18 45.22 
 
 ex- 
 
 IS 51..,- 
 
 
 202 
 
 111 2!>.!>!) 
 
 Ml 
 
 III 30.11 
 
 6.46 
 
 l:i 12.! H) 
 
 6.47 
 
 1'J 4!i.:tS 
 
 6.48 
 
 1!) 55,-7 
 
 ii. r.i 
 
 203 
 
 20 :15.07 
 
 6.57 
 
 20 41. (15 
 
 B.58 
 
 20 is.-j| 
 
 6.60 
 
 20 54.84 
 
 6.61 
 
 21 1-10 
 
 6.UJ 
 
 304 
 
 21 41.41 
 
 6.70 
 
 21 48.12 
 
 6.71 
 
 21 54.83 
 
 6.72 
 
 22 1.50 
 
 6.73 
 
 22 8.'J! 
 
 i;.;i 
 
 205 
 
 22 -IS.! 17 
 
 ut 
 
 22 55.71 > 
 
 6.83 
 
 23 2.<i3 
 
 6.84 
 
 23 -I.I7 
 
 
 2:i i <;.: 
 
 6.6 
 
 20(5 
 
 23 57.70 
 
 IM 
 
 21 1.03 
 
 6.94 
 
 21 11.57 
 
 6.95 
 
 24 18.53 
 
 li.M 
 
 21 25.511 
 
 I-..1IT 
 
 207 
 
 25 7.53 
 
 7.04 
 
 25 14.57 
 
 IM 
 
 25 21.02 
 
 7.06 
 
 25 28.0!) 
 
 7.07 
 
 25 35.70 
 
 |J 
 
 7.0U 
 
 208 
 
 2f, IS. 11 
 
 7.14 
 
 '.'li 25.55 
 
 T.1S 
 
 20 :i2.71 
 
 7.16 
 
 20 3! 1.87 
 
 7.17 
 
 2(i 17.05 
 
 7.18 
 
 20!) 
 
 27 30.2:i 
 
 IM 
 
 27 37.53 
 
 ;.-.M 
 
 27 44.78 
 
 -..< 
 
 27 52.01 
 
 -,.-M 
 
 27 5! 1.31 
 
 
 2)0 
 
 28 43.ll 
 
 7J3 
 
 28 50.44 
 
 7J4 
 
 28 57.7S 
 
 7.34 
 
 2!' 5.13 
 
 IM 
 
 2.) 12.1!) 
 
 7.:i 
 
 211 
 
 o aa 5<;.8i 
 
 7.11 
 
 30 4.23 
 
 7.ia 
 
 30 11.G5 
 
 7.43 
 
 30 I'J.08 
 
 7.44 
 
 30 20.52 
 
 -,.ll 
 
 212 
 
 31 11.33 
 
 7.19 
 
 31 18.83 
 
 7^0 
 
 31 20.33 
 
 7..M 
 
 31 33.84 
 
 1AI 
 
 31 41.30 
 
 
 213 
 
 32 20.01 
 
 7.58 
 
 32 31. IS 
 
 7.:>7 
 
 32 41.70 
 
 7^8 
 
 32 4!.3J 
 
 
 32 50.! 13 
 
 ^30 
 
 "1 1 
 
 o 33 I2.oo 
 
 7.63 
 
 : 50.24 
 
 7*1 
 
 3.) 57.88 
 
 7.64 
 
 31 5.53 
 
 7.65 
 
 31 13.18 
 
 7.G6 
 
 215 
 
 34 5! i.23 
 
 7.69 
 
 35 (i.!l3 
 
 7.70 
 
 35 14.03 
 
 7.70 
 
 35 22.31 
 
 7.71 
 
 ;r> 30.05 
 
 7.71 
 
 210 
 
 3() 10.44 
 
 7.75 
 
 3(i 21. lit 
 
 7.r:> 
 
 36 31.! 15 
 
 7.76 
 
 30 3! ".71 
 
 7.76 
 
 ::; 17.17 
 
 7.77 
 
 217 
 
 37 31.17 
 
 7.K) 
 
 37 41.! 17 
 
 7.80 
 
 37 l!>.77 
 
 7.81 
 
 37 57.58 -.xi 
 
 :..3!) 
 
 7.81 
 
 218 
 
 38 52.35 
 
 '..-I 
 
 3't O.lit 
 
 7^4 
 
 ;) s.oi 
 
 7.85 
 
 311 15.811 
 
 7.85 
 
 80 23.71 
 
 7^5 
 
 21!) 
 
 40 IO.H3 
 
 
 40 is.-i 
 
 7.88 
 
 40 20.0. > 
 
 7.68 
 
 40 34.57 
 
 7.88 
 
 40 42.10 
 
 7.89 
 
 220 
 
 41 29.84 
 
 7.01 
 
 II 37.71 
 
 7.91 
 
 41 45.05 7.9i 
 
 41 53.57 
 
 7.91 
 
 !! 1.18 
 
 7.93 
 
 221 
 
 42 4!'.02 
 
 7.33 
 
 42 5l ;.!>5 
 
 7.93 
 
 43 1,-s 
 
 7.93 
 
 43 I2.-I 
 
 7.93 
 
 13 20.75 
 
 KM 
 
 222 
 
 11 S. 10 
 
 7.!>:> 
 
 11 l(i.31 
 
 7.95 
 
 44 2l.2:i 
 
 UB 
 
 II 32.21 
 
 7JB 
 
 II 10.l!> 
 
 
 223 
 
 15 '.'7 .!>> 
 
 7.% 
 
 -15 35.S7 
 
 7.96 
 
 15 4:!.S3 
 
 7.96 
 
 15 5 1.7! > 7.!>6 
 
 15 5H.75 
 
 
 224 
 
 4(5 47.52 
 
 +7.S6 
 
 4(i 55.18 
 
 +7.W 
 
 47 3.44 +7.96 
 
 47 11.40 ; +7.96 47 1 
 
 +7.96 
 
TABLE XI. 
 
 TABLE XII. 
 
 Perturbations /' the Longitude. 
 
 Factor to be multiplied l)y the integer m ; and its Logarithm. 
 
 Pert, of the Long. 
 Fact, to be X f.) 2 
 
 * LOU' 
 
 Arg.I 
 
 Factor. 
 
 Log.Fac 
 
 Arg.I 
 
 Factor. 
 
 Log. Fin- 
 
 Arg.I 
 
 Factor 
 
 L igl-'iic 
 
 Arg.I 
 
 Factor. 
 
 Log.Fac. 
 
 Arg.I 
 
 Fact 
 
 L. Fac. 
 
 d 
 
 
 0.000 
 
 n CO 
 
 d 
 
 63 
 
 12.596 
 
 al .1002 
 
 d 
 
 120 
 
 + 2.049 
 
 0.4231 
 
 d 
 
 180 
 
 +12.109 
 
 1.0831 
 
 d 
 
 
 
 +0.00 
 
 CO 
 
 1 
 
 <>.:!<; r 
 
 9.5575 
 
 61 
 
 1 2.547 
 
 1.0985 
 
 121 
 
 2.990 0.1757 
 
 181 
 
 11.996 
 
 1 .0790 
 
 4 
 
 0.22 
 
 9.349 
 
 a 
 
 0.721 
 
 9.8579 
 
 62 
 
 12.488 
 
 1.0905 
 
 122 
 
 3.328 0.5222 
 
 182 
 
 1 1 .875 
 
 1 .0746 
 
 8 
 
 0,14 
 
 9.043 
 
 3 
 
 1.081 
 
 0.0338 
 
 63 
 
 12.421 
 
 1.0942 
 
 123 
 
 3.063 
 
 0.5638 
 
 183 
 
 11.744 
 
 1 .0698 
 
 12 
 
 0.06 
 
 9.820 
 
 4 
 
 1.441 
 
 j/0.1587 
 
 64 
 
 12.343 
 
 7(1.0914 
 
 124 
 
 + 3.997 
 
 0.6017 
 
 184 
 
 +1 1 .604 
 
 1.0040 
 
 16 
 
 +0.87 9.933 
 
 5 1.7IH) 
 
 0.2550 
 
 65 
 
 1 2.256 
 
 1.0883 
 
 125 
 
 4.320 0.0301 
 
 185 
 
 11.454 
 
 1 .0590 
 
 80 
 
 1.06 
 
 0.027 
 
 6 
 
 2.156 
 
 0.3331 
 
 66 
 
 12.159 
 
 1.0849 
 
 126 
 
 4.052 
 
 0.6670 
 
 136 
 
 11.295 
 
 1 .0529 
 
 24 
 
 1 .25 
 
 0.096 
 
 7 
 
 2.509 
 
 0.3i)95 
 
 67 
 
 12.053 
 
 1.0811 
 
 127 
 
 4.976 
 
 0.0969 
 
 187 
 
 11.128 
 
 1.0404 
 
 28 
 
 1.42 
 
 0.151 
 
 8 I 2.S62 
 
 ;i0.4567 
 
 68 
 
 11.938 
 
 nl.076!) 
 
 128 
 
 -f- 5.295 
 
 0.7239 
 
 1S8 
 
 +10.952 
 
 1.0395 
 
 32 
 
 +1.56 
 
 0.194 
 
 !) 
 
 3.212 
 
 0.51)68 
 
 69 
 
 11.813 
 
 1 .0724 
 
 129 
 
 5.6II 1 0.7490 
 
 189 
 
 10.706 
 
 1.0321 
 
 30 
 
 1 .69 
 
 0.22!) 
 
 Ill 
 
 3.563 
 
 0.5514 
 
 70 
 
 11.680 
 
 1 .0074 
 
 130 
 
 5.922 0.7725 
 
 190 
 
 10.571 
 
 1.0241 
 
 49 
 
 1.80 
 
 0.250 
 
 11 
 
 3.1)04 
 
 0.5915 
 
 71 
 
 11.536 
 
 1.0621 
 
 131 
 
 6.230 
 
 0.7945 
 
 191 
 
 10.36!) 
 
 1.0157 
 
 44 
 
 1.89 
 
 0.277 
 
 19 
 
 4.210 
 
 ((9.02.-<9 
 
 72 
 
 11.385 
 
 n 1.0563 
 
 132 
 
 + 6.532 
 
 0.8150 
 
 192 
 
 +10.158 
 
 1.0068 
 
 48 
 
 +1.95 
 
 0.291 
 
 13 
 
 4.584 
 
 0.6612 
 
 73 
 
 1 1 .220 
 
 1 .0502 
 
 133 
 
 6.829 
 
 0,834 1 
 
 193 i 9.939 
 
 0.9973 
 
 52 
 
 1.99 
 
 0.299 
 
 14 
 
 4.918 
 
 0.6918 
 
 74 
 
 1 1 .056 
 
 1.0436 
 
 134 
 
 7.121 
 
 0.8525 
 
 194 
 
 9.712 
 
 0.9-73 
 
 50 
 
 2.01 
 
 0.302 
 
 15 
 
 5.250 
 
 0.7202 
 
 75 
 
 10.S79 
 
 1.0366 
 
 135 
 
 7.408 
 
 0.8697 
 
 195 
 
 9.478 
 
 0.9767 
 
 6J 
 
 1.9!) 
 
 0.300 
 
 Hi 
 
 5.."7."> 
 
 ?i0.746a 
 
 76 
 
 10.694 
 
 n 1.0291 
 
 136 
 
 + 7.089 
 
 0.8859 
 
 196 
 
 + 9.235 
 
 0.0654 
 
 61 
 
 + 1.96 
 
 0.292 
 
 17 
 
 5.8116 
 
 0.7706 
 
 77 
 
 10.591 
 
 1.0212 
 
 137 
 
 7.! 165 
 
 0.9012 
 
 197 
 
 8.985 
 
 0.9535 
 
 68 
 
 1.90 
 
 0.273 
 
 18 
 
 6513 
 
 0.7933 
 
 78 
 
 10.29!) 
 
 1.0128 
 
 138 
 
 8.235 
 
 0.9157 
 
 198 
 
 8.727 
 
 0.9409 
 
 72 
 
 1.81 
 
 0.253 
 
 1!) 
 
 6.524 . 
 
 0.8145 
 
 7!) 
 
 10.090 
 
 1.0039 
 
 139 
 
 8.498 
 
 0.9293 
 
 199 
 
 8.463 
 
 0.9275 
 
 70 
 
 1.71 
 
 0.232 
 
 30 
 
 6.839 
 
 nO.8344 
 
 8!) 
 
 9.873 
 
 nO.!)944 
 
 140 
 
 -f- 8.756 
 
 0.9423 
 
 200 
 
 + 8.191 
 
 0.91 "S3 
 
 80 
 
 +1.58 
 
 0.1 98 
 
 21 
 
 7.131 
 
 0.85:! 1 
 
 81 
 
 9.048 
 
 0.9844 
 
 141 
 
 9.006 
 
 0.9545 
 
 201 
 
 7.914 
 
 0.8984 
 
 84 
 
 1.43 
 
 0.155 
 
 22 
 
 7.42G 
 
 0.8707 
 
 82 
 
 9.417 
 
 0.973!) 
 
 142 
 
 9.219 
 
 0.9601 
 
 202 
 
 7.62!) 
 
 0.8825 
 
 88 
 
 , 1.26 
 
 0.101 
 
 23 
 
 7.715 
 
 0.8873 
 
 83 
 
 9.177 
 
 0.9627 
 
 143 
 
 9.486 
 
 0.9771 
 
 203 
 
 7.338 
 
 0.8656 
 
 92 
 
 1.03 
 
 0.034 
 
 24 
 
 7.997 
 
 rtO.9029 
 
 84 
 
 8.932 
 
 nO.9509 
 
 144 
 
 -f 9.710 
 
 0.9875 
 
 204 
 
 + 7.042 
 
 0.8477 
 
 96 
 
 +9.88 
 
 9.947 
 
 as 
 
 8.273 
 
 0.9177 
 
 85 
 
 8.079 
 
 0.9385 
 
 145 
 
 9.939 
 
 0.9973 
 
 205 
 
 6.739 
 
 0.8286 
 
 100 
 
 0.68 
 
 ! 1.832 
 
 26 
 
 8.542 
 
 0.9316 
 
 86 
 
 8.421 
 
 0.9254 
 
 146 
 
 10.153 
 
 1.0066 
 
 206 
 
 6.431 
 
 0.8083 
 
 104 
 
 0.46 
 
 9.687 
 
 27 
 
 8.805 
 
 0.9417 
 
 87 
 
 8.155 
 
 0.9114 
 
 147 
 
 10.300 
 
 1.0154 
 
 2J7 
 
 0.118 
 
 0.7860 
 
 108 
 
 0.24 
 
 9.380 
 
 28 
 
 9.060 
 
 H0.9571 
 
 88 
 
 7.883 
 
 7(0.8967 
 
 148 
 
 + 111.559 
 
 1 .0236 
 
 208 
 
 + 5.801 
 
 0.7635 
 
 112 
 
 +0.02 
 
 i(8.293 
 
 2!) 
 
 9.308 
 
 0.9689 
 
 89 
 
 7.006 
 
 0.8812 
 
 149 
 
 10.750 
 
 1.0314 
 
 209 
 
 5.478 
 
 0.7386 
 
 116 
 
 -0.207t9.3IO 
 
 30 
 
 9.548 
 
 0.9799 
 
 90 
 
 7.323 
 
 0.8047 
 
 1 50 
 
 10.933 
 
 1.0337 
 
 210 
 
 5.150 
 
 0.7118 
 
 120 
 
 0.42 
 
 9.029 
 
 :u 
 
 9.781 
 
 04)904 
 
 91 
 
 7.035 
 
 0.8473 
 
 151 
 
 11.108 
 
 1.0456 
 
 211 
 
 4.819 
 
 0.6830 
 
 124 
 
 0.04 
 
 9.807 
 
 32 
 
 10.00.". 
 
 n 1.0002 
 
 92 
 
 6.741 
 
 nO.8287 
 
 152 
 
 + 11.274 
 
 1.0521 
 
 212 
 
 + 4.484 
 
 0.6517 
 
 128 
 
 0.85 
 
 ! 1.929 
 
 33 
 
 10.22:) 
 
 1.0096 
 
 93 
 
 6.442 
 
 0.8090 
 
 153 
 
 1 1 .432 
 
 1.0581 
 
 213 
 
 4.145 
 
 0.6175 
 
 132 
 
 1 .05 
 
 0.020 
 
 34 
 
 lo.4:ii 
 
 1.0183 
 
 94 
 
 6.138 
 
 0.788 i 
 
 154 
 
 11.581 
 
 1 .0037 
 
 214 
 
 3.802 
 
 0.5800 
 
 136 
 
 1 .23 
 
 0.091 
 
 35 
 
 10.031 
 
 1.0266 
 
 95 
 
 5.S30 
 
 0.7657 
 
 155 
 
 11.721 
 
 1 .0690 
 
 215 
 
 3.457 
 
 0.5387 
 
 140 
 
 1.40 
 
 0.140 . 
 
 36 
 
 10*03 
 
 >il. 0343 
 
 96 
 
 5.517 
 
 nO.7417 
 
 156 
 
 fll.851 
 
 1 .0738 
 
 216 
 
 + 3.108 
 
 0,1925 
 
 144 
 
 1 .55 
 
 .0.19I 
 
 37 
 
 11.005 
 
 1.0416 
 
 97 
 
 5.200 
 
 0.710!) 
 
 157 
 
 1 1 .972 
 
 1 .0782 
 
 217 
 
 2.757 
 
 1) 1ID1 
 
 148 
 
 1.68 
 
 0.226 
 
 38 
 
 11.179 
 
 1.0484 
 
 98 
 
 \~7 : .< 
 
 0.6883 
 
 158 
 
 12.085 
 
 1.0S22 
 
 218 
 
 2.404 
 
 0.3800 
 
 152 
 
 1.80 
 
 0.254 
 
 39 
 
 11.344 
 
 1 .05 18 
 
 99 
 
 4.555 
 
 0.0585 
 
 159 
 
 18.189 
 
 1.0800 
 
 219 
 
 2.049 
 
 OJB115 
 
 156 
 
 1.89 
 
 0.275 
 
 40 
 
 11.500 
 
 nl.0607 
 
 100 
 
 4.227 
 
 7(0.0260 
 
 160 
 
 +12.283 
 
 1 .0893 
 
 220 
 
 + 1.091 
 
 0.2281 
 
 160 
 
 1.95 
 
 nO.290 
 
 41 
 
 M.(il7 
 
 1 .0662 
 
 101 
 
 3.897 
 
 0.5!!., 7 
 
 161 
 
 12.367 1.0923 
 
 221 
 
 1 .333 
 
 0.1248 
 
 161 
 
 1.99 
 
 0.2! 19 
 
 42 
 
 1 1 .784 
 
 . .0713 
 
 102 
 
 3.563 
 
 0.55 H 
 
 162 
 
 12.442 
 
 1.0949 
 
 222 
 
 0.974 
 
 9.9886 
 
 168 
 
 2.01 
 
 0.302 
 
 43 
 
 11.91:! 
 
 1 .0760 
 
 103 
 
 3.227 
 
 0.5088 
 
 163 
 
 12.507 
 
 1.0972 
 
 223 
 
 0.613 
 
 9.7875 
 
 172 
 
 2.00 
 
 0.300 
 
 44 
 
 12.031 
 
 1.0803 
 
 104 
 
 2.^8 
 
 7(0.4606 
 
 164 
 
 +12.563 
 
 1 .0991 
 
 224 
 
 + 0.253 
 
 7/1.4031 
 
 176 
 
 1.96 
 
 ((0.293 
 
 45 
 
 12.140 
 
 1.0842 
 
 105 
 
 2.547 
 
 0.406') 
 
 165 
 
 12.60!) 
 
 1.1007 
 
 225 
 
 0.198 
 
 7(9.0334 
 
 180 
 
 1.90 
 
 0.280 
 
 46 
 
 12.839 
 
 1 .0877 
 
 106 
 
 2.205 
 
 0.3434 
 
 166 
 
 12.015 
 
 1.1019 
 
 226 
 
 0,109 
 
 9.6712 
 
 184 
 
 1.82 
 
 0.209 
 
 47 
 
 12.329 
 
 1.0909 
 
 107 
 
 1.860 
 
 0.2095 
 
 167 
 
 12071 
 
 1.1028 
 
 227 
 
 0.829 
 
 9.9185 
 
 183 
 
 1.72 
 
 0.234 
 
 48 
 
 12.408 
 
 7(1.0937 
 
 108 
 
 1.514 
 
 1(0.1^01 
 
 168 
 
 +12.087 
 
 1.1034 
 
 228 
 
 1.189 
 
 nO.0752 
 
 192 
 
 1.59 
 
 nO.201 
 
 4!) 
 
 12.47!) 
 
 1 .0962 
 
 109 
 
 1.167 
 
 0.0071 
 
 169 
 
 12.693 1.1036 
 
 229 
 
 1 .548 
 
 0.1898 
 
 196 
 
 1.44 
 
 0.159 
 
 50 
 
 12.540 
 
 1.0983 
 
 110 
 
 0.819 
 
 9.91 33 
 
 170 
 
 12.690 1.1935 
 
 230 
 
 1.9D6 
 
 0.280 1 
 
 200 
 
 1 .2.8 
 
 0.100 
 
 51 
 
 12.5! 10 
 
 1.1000 
 
 111 
 
 0.471 
 
 9.0730 
 
 171 
 
 12.676 1.1030 
 
 231 
 
 2.202 
 
 0.3545 
 
 204 
 
 1.10 
 
 0.040 
 
 52 
 
 12.630 
 
 7(1.101 1 
 
 112 
 
 0.122 
 
 H.9.0804 
 
 172 
 
 +12.653 1.1022 
 
 232 
 
 2.615 
 
 wO.4175 
 
 208 
 
 0.90 
 
 B9.9S6 
 
 53 
 
 12.660 
 
 .1024 
 
 113 
 
 + 0.227 
 
 p9.3560 
 
 173 
 
 12.61!) 1.1010 
 
 333 
 
 2.967 
 
 0,1723 
 
 212 
 
 0.70 
 
 9.843 
 
 54 
 
 12.681 
 
 .1032 
 
 114 
 
 0.575 
 
 9.7597 
 
 174 
 
 12.576 1.0995 
 
 234 
 
 3.317 
 
 0.5207 
 
 216 
 
 0.48 
 
 9.684 
 
 55 
 
 12.602 
 
 .1035 
 
 115 
 
 0.983 
 
 9.9052 
 
 175 
 
 12.522 
 
 1.0977 
 
 235 
 
 3.664 
 
 0.5640 
 
 220 
 
 0.26 
 
 9.420 
 
 56 
 
 12.692 
 
 7( .K;:!.-. 
 
 116 + 1.271 
 
 0.1011 
 
 170 
 
 + 12,159 
 
 1 .0955 
 
 236 
 
 4.007 
 
 0j6028 
 
 224 
 
 0.04 
 
 H.59I 
 
 57 
 
 12.683 
 
 .1032 
 
 117 
 
 1.617 
 
 0.2087 
 
 177 
 
 12.386 1.0929 
 
 237 
 
 4.348 
 
 0.6383 
 
 228 
 
 +0.18 p9.267 
 
 08 
 
 13.664 
 
 .1026 
 
 118 
 
 U>63 
 
 0.2:12.1 
 
 178 
 
 12.3)1 1.0900 
 
 233 
 
 4.685 
 
 0.6707 
 
 232 
 
 0.11 9.(i09 
 
 09 
 
 12.635 
 
 .1016 
 
 119 
 
 2:307 
 
 0.3630 
 
 17!) 
 
 12.211 1.086U 
 
 239 
 
 5.018 
 
 0.7.105 
 
 236 
 
 0.02 
 
 9.795 
 
 60 
 
 12.5! 6 
 
 .10(12 
 
 120 
 
 + 2.649 
 
 0.4231 
 
 IS;) 
 
 + 12.109 1.0831 
 
 219 
 
 5.319 
 
 7(0.7283 
 
 21:) +0.83 
 
 9.920 
 
 The perturbations arc expressed in limulrcdllis of a second of arc. 
 
TAHLKS. 
 
 TABLE XIII. 
 
 r vui.i: xiv. 
 
 TAIILK XV. 
 
 TAIU.I: xvi. 
 
 I'trt. tif thr 1. illicit Hill I'll Ilir 
 I'.iirth. 
 
 I'rrt. of llit /.' 
 
 /./,, /;/ M 
 
 I'irlurlialiiiH (if III r l.,inyilinlr, 
 by t/ir I-'.:, rill. 
 
 /' rt nrl'iifnut tif' flit l.int^tlittl', />i/ t!i<- 
 ' Larth. 
 
 Arg II 
 
 ,:, 
 
 Arg II. 
 
 Arg. Ill 
 
 
 Ar IV. 
 
 
 t\ 
 
 
 Eqan. 
 
 Ar" V. 
 
 ,:, 
 
 
 
 
 
 
 ,1 
 
 
 ,1 
 
 
 ,i 
 
 ,i 
 
 
 d 
 
 
 
 
 
 
 Jlo 
 
 n 
 
 
 II 
 
 
 
 2960 
 
 
 
 2 
 
 736 
 
 707 
 
 9 
 
 
 
 
 900 
 
 
 10 
 
 I 
 
 2920 
 
 16 
 
 .-, 
 
 758 
 
 708 
 
 4 
 
 i 
 
 836 
 
 400 
 
 913 
 
 m 
 
 3 
 
 
 88 
 
 |) 
 
 768 
 
 708 
 
 6 
 
 3 
 
 234 
 
 600 
 
 804 
 
 190 
 
 .-, 
 
 2-10 
 
 i- 
 
 15 
 
 7-1 
 
 707 
 
 8 
 
 "' 
 
 839 
 
 
 194 
 
 n.i 
 
 9 
 
 
 64 
 
 23 
 
 -;IO 
 
 703 
 
 10 
 
 9 
 
 230 
 
 ten 
 
 I.-3 
 
 2 HI 
 
 il 
 
 9760 
 
 -0 
 
 89 
 
 816 
 
 
 I-J 
 
 13 
 
 228 
 
 1800 
 
 171 
 
 840 
 
 in 
 
 9780 
 
 96 
 
 43 
 
 
 6UI 
 
 14 
 
 17 
 
 886 
 
 1 100 
 
 158 
 
 880 
 
 96 
 
 21,- I 
 
 118 
 
 55 
 
 848 
 
 683 
 
 Hi 
 
 23 
 
 ._,., | 
 
 10:10 
 
 145 
 
 32 1 
 
 34 
 
 
 186 
 
 
 864 
 
 678 
 
 18 
 
 -".1 
 
 889 
 
 1- 
 
 131 
 
 
 12 
 
 
 1 11 
 
 
 880 
 
 663 
 
 90 
 
 86 
 
 990 
 
 20IKI 
 
 117 
 
 400 
 
 .->! 
 
 9660 
 
 Kill 
 
 M 
 
 
 (i!7 
 
 29 
 
 n 
 
 918 
 
 22, M I 
 
 103 
 
 110 
 
 61 
 
 2-VJ.l 
 
 176 
 
 II., 
 
 918 
 
 639 
 
 84 
 
 68 
 
 816 
 
 9400 
 
 90 
 
 480 
 
 71 
 
 2480 
 
 199 
 
 l:;2 
 
 988 
 
 615 
 
 26 
 
 (il 
 
 214 
 
 9600 
 
 7(i 
 
 :,2 1 
 
 83 
 
 211 I 
 
 
 151 
 
 944 
 
 507 
 
 28 
 
 70 
 
 819 
 
 9800 
 
 64 
 
 560 
 
 94 
 
 
 22 1 
 
 170 
 
 960 
 
 .',77 
 
 30 
 
 80 
 
 910 
 
 3000 
 
 89 
 
 GOO 
 
 106 
 
 9960 
 
 Jill 
 
 190 
 
 976 
 
 566 
 
 32 
 
 91 
 
 206 
 
 3800 
 
 41 
 
 640 
 
 118 
 
 8320 
 
 956 
 
 210 
 
 998 
 
 534 
 
 34 
 
 109 
 
 
 3400 
 
 89 
 
 680 
 
 131 
 
 22-0 
 
 272 
 
 231 
 
 loos 
 
 511 
 
 36 
 
 II 1 
 
 804 
 
 3600 
 
 93 
 
 790 
 
 1 II 
 
 2210 
 
 888 
 
 259 
 
 1084 
 
 4-i, 
 
 38 
 
 126 
 
 808 
 
 3800 
 
 16 
 
 TOO 
 
 156 
 
 , 
 
 304 
 
 273 
 
 1040 
 
 461 
 
 40 
 
 199 
 
 j i, i 
 
 4000 
 
 10 
 
 BOO 
 
 169 
 
 9160 
 
 890 
 
 
 1056 
 
 4:w; 
 
 42 
 
 I :,2 
 
 198 
 
 4800 
 
 5 
 
 -n 
 
 181 
 
 2120 
 
 336 
 
 317 
 
 1072 
 
 411) 
 
 II 
 
 165 
 
 106 
 
 1100 
 
 2 
 
 880 
 
 mi 
 
 8080 
 
 369 
 
 339 
 
 1088 
 
 383 
 
 46 
 
 179 
 
 194 
 
 4600 
 
 (1 
 
 090 
 
 206 
 
 8040 
 
 86S 
 
 360 
 
 1104 
 
 856 
 
 48 
 
 193 
 
 199 
 
 HMO 
 
 
 
 '.Kill 
 
 217 
 
 
 884 
 
 389 
 
 1120 
 
 880 
 
 50 
 
 
 190 
 
 5000 
 
 
 
 1000 
 
 998 
 
 I960 
 
 400 
 
 404 
 
 1136 
 
 303 
 
 69 
 
 221 
 
 188 
 
 
 2 
 
 loin 
 
 239 
 
 1980 
 
 416 
 
 12", 
 
 1168 
 
 271 i 
 
 64 
 
 2:!6 
 
 l-t, 
 
 5400 
 
 :, 
 
 lu-il 
 
 949 
 
 1880 
 
 438 
 
 i Hi 
 
 116--! 
 
 2-">0 
 
 66 
 
 950 
 
 1-1. 
 
 5QOO 
 
 I) 
 
 1120 
 
 
 1840 
 
 4 is 
 
 467 
 
 11-1 
 
 286 
 
 58 
 
 265 
 
 Id2 
 
 5800 
 
 14 
 
 1160 
 
 266 
 
 1800 
 
 464 
 
 487 
 
 1200 
 
 200 
 
 GO 
 
 280 
 
 180 
 
 6000 
 
 20 
 
 1200 
 
 271 
 
 1760 
 
 480 
 
 507 
 
 1216 
 
 177 
 
 62 
 
 995 
 
 178 
 
 6200 
 
 26 
 
 1240 
 
 J-n 
 
 1720 
 
 496 
 
 .-,27 
 
 1232 
 
 164 
 
 64 
 
 310 
 
 176 
 
 6400 
 
 34 
 
 1980 
 
 986 
 
 1680 
 
 619 
 
 54.') 
 
 121- 
 
 133 
 
 66 
 
 32 1 
 
 171 
 
 6600 
 
 42 
 
 1390 
 
 891 
 
 1640 
 
 598 
 
 563 
 
 1864 
 
 113 
 
 i,s 
 
 339 
 
 172 
 
 6800 
 
 50 
 
 1360 
 
 898 
 
 1600 
 
 644 
 
 581 
 
 1280 
 
 94 
 
 70 
 
 3.-.3 
 
 170 
 
 7000 
 
 89 
 
 1400 
 
 297 
 
 1560 
 
 560 
 
 597 
 
 12!Ki 
 
 77 
 
 72 
 
 368 
 
 168 
 
 
 (in 
 
 1 110 
 
 909 
 
 1590 
 
 676 
 
 613 
 
 1312 
 
 61 
 
 74 
 
 889 
 
 166 
 
 7400 
 
 78 
 
 1480 
 
 299 
 
 1480 
 
 099 
 
 628 
 
 1388 
 
 47 
 
 76 
 
 395 
 
 164 
 
 7600 
 
 88 
 
 
 
 
 
 1,11 
 
 IS44 
 
 3.-> 
 
 78 
 
 409 
 
 169 
 
 7800 
 
 00 
 
 
 624 
 
 694 
 
 1360 
 
 2T> 
 
 80 
 
 422 
 
 160 
 
 8000 
 
 1IMI 
 
 
 (ill) 
 
 666 
 
 1876 
 
 17 
 
 82 
 
 434 
 
 1 .- 
 
 8200 
 
 120 
 
 
 656 
 
 (>7(> 
 
 1399 
 
 10 
 
 84 
 
 447 
 
 156 
 
 8400 
 
 131 
 
 
 672 
 
 
 1 Ins 
 
 .', 
 
 86 
 
 450 
 
 164 
 
 8600 
 
 141 
 
 
 (, : 
 
 693 
 
 1 121 
 
 3 
 
 88 
 
 470 
 
 188 
 
 8800 
 
 189 
 
 
 7.11 
 
 699 
 
 1110 
 
 2 
 
 90 
 
 481 
 
 160 
 
 9000 
 
 Ki2 
 
 
 720 
 
 703 
 
 1 i:.6 
 
 3 
 
 92 
 
 491 
 
 148 
 
 9200 
 
 172 
 
 
 736 
 
 707 
 
 1472 
 
 5 
 
 M 
 
 .Mil 
 
 146 
 
 9400 
 
 189 
 
 
 
 
 
 
 96 
 
 r.io 
 
 ill 
 
 0600 
 
 1 : i-' 
 
 
 98 
 
 518 
 
 149 
 
 9800 
 
 200 
 
 
 
 
 
 
 
 n 
 
 100 
 
 526 
 
 140 
 
 1 0000 
 
 
 Constant added in Table XIII. 2-2 
 
 102 
 
 633 
 
 138 
 
 10200 
 
 2lli 
 
 " XIV. Li:.. 
 
 104 
 
 539 
 
 136 
 
 10400 
 
 299 
 
 < 11 XV. l.:,o. 
 
 106 
 
 645 
 
 134 
 
 10600 
 
 227 
 
 " 11 XVI. 3.60. 
 
 108 
 
 550 
 
 132 
 
 10800 
 
 231 
 
 
 110 
 
 554 
 
 130 
 
 11000 
 
 234 
 
 y 
 
 
 558 
 
 128 
 
 11200 
 
 286 
 
 Period of Argument II. 238.92. 
 
 114 
 
 660 
 
 1 26 
 
 11400 
 
 935 
 
 "ii III. 11987'!. 
 
 116 
 
 562 
 
 124 
 
 11600 
 
 233 
 
 " " IV. 29.W 
 
 118 
 
 564 
 
 122 
 
 11800 
 
 230 
 
 u it n v. 1454<>9. 
 
 120 
 
 564 
 
 120 
 
 12000 
 
 916 
 
 
 
 9V 
 
 The perturbations arc expressed in liuiiilri-<lili> ol'n nerond of arc. 
 
TABLE XVII. 
 
 Perturbation of I lie Longitude l>y I lie Earth. 
 
 Constant ;:ililoil 16".65. Period of Argument VI., 583''.92. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Eqlia; 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 
 
 166-i 
 
 104 
 
 47 
 
 208 
 
 8720 
 
 312 
 
 912 
 
 416 
 
 2093 
 
 520 
 
 2456 
 
 2 
 
 1671 
 
 106 
 
 31 
 
 210 
 
 2772 
 
 314 
 
 846 
 
 413 
 
 2172 
 
 522 
 
 2405 
 
 4 
 
 1675 
 
 108 
 
 18 
 
 212 
 
 2821 
 
 316 
 
 783 
 
 420 
 
 224!) 
 
 524 
 
 2354 
 
 6 
 
 1677 
 
 110 
 
 8 
 
 214 
 
 2366 
 
 318 
 
 722 
 
 422 
 
 2326 
 
 526 
 
 2303 
 
 8 
 
 1670 
 
 112 
 
 3 
 
 216 
 
 2908 
 
 320 
 
 664 
 
 424 
 
 2400 
 
 528 
 
 2254 
 
 10 
 
 1680 
 
 114 
 
 
 
 218 
 
 2946 
 
 322 
 
 609 
 
 426 
 
 2473 
 
 530 
 
 2205 
 
 19 
 
 1678 
 
 116 
 
 2 
 
 220 
 
 2979 
 
 324 
 
 557 
 
 428 
 
 2544 
 
 533 
 
 > 1 5s 
 
 14 
 
 1676 
 
 118 
 
 7 
 
 222 
 
 3009 
 
 326 
 
 509 
 
 430 
 
 2613 
 
 534 
 
 2112 
 
 16 
 
 1671 
 
 120 
 
 16 
 
 224 
 
 3035 
 
 328 
 
 464 
 
 432 
 
 2680 
 
 536 
 
 2068 
 
 18 
 
 1664 
 
 122 
 
 28 
 
 226 
 
 3057 
 
 33!) 
 
 423 
 
 434 
 
 2744 
 
 538 
 
 2025 
 
 20 
 
 1655 
 
 ISM 
 
 4") 
 
 228 
 
 3074 
 
 332 
 
 385 
 
 436 
 
 2805 
 
 540 
 
 1985 
 
 o-> 
 
 1043 
 
 126 
 
 65 
 
 230 
 
 3087 
 
 334 
 
 352 
 
 438 
 
 2863 
 
 542 
 
 1946 
 
 24 
 
 1623 
 
 128 
 
 90 
 
 232 
 
 3095 
 
 3.36 
 
 322 
 
 440 
 
 2918 
 
 544 
 
 1910 
 
 26 
 
 1611 
 
 130 
 
 118 
 
 234 
 
 3099 
 
 338 
 
 296 
 
 442 
 
 2! 171 
 
 546 
 
 1875 
 
 as 
 
 1591 
 
 139 
 
 149 
 
 236 
 
 3099 
 
 340 
 
 275 
 
 444 
 
 3020 
 
 548 
 
 1843 
 
 30 
 
 1569 
 
 134 
 
 185 
 
 238 
 
 3095 
 
 342 
 
 258 
 
 446 
 
 3065 
 
 550 
 
 1813 
 
 32 
 
 1544 
 
 136 
 
 824 
 
 240 
 
 3086 
 
 344 
 
 245 
 
 448 
 
 3108 
 
 552 
 
 1786 
 
 34 
 
 1517 
 
 138 
 
 266 
 
 242 
 
 3073 
 
 346 
 
 237 
 
 450 
 
 3147 
 
 554 
 
 1762 
 
 36 
 
 1486 
 
 140 
 
 312 
 
 244 
 
 3055 
 
 348 
 
 233 
 
 452 
 
 3188 
 
 556 
 
 1740 
 
 38 
 
 1454 
 
 142 
 
 361 
 
 246 
 
 3033 
 
 350 
 
 233 
 
 454 
 
 3214 
 
 558 
 
 1721 
 
 40 
 
 141!) 
 
 144 
 
 414 
 
 248 
 
 3007 
 
 352 
 
 237 
 
 456 
 
 3241 
 
 560 
 
 1704 
 
 42 
 
 1382 
 
 146 
 
 470 
 
 250 
 
 2977 
 
 354 
 
 246 
 
 458 
 
 3265 
 
 569 
 
 1690 
 
 44 
 
 1343 
 
 148 
 
 523 
 
 252 
 
 2943 
 
 356 
 
 259 
 
 460 
 
 3285 
 
 564 
 
 167!) 
 
 46 
 
 1302 
 
 150 
 
 590 
 
 254 
 
 2905 
 
 358 
 
 277 
 
 462 
 
 3302 
 
 566 
 
 1670 
 
 48 
 
 1250 
 
 152 
 
 654 
 
 256 
 
 2864 
 
 360 
 
 299 
 
 464 
 
 3314 
 
 568 
 
 1663 
 
 50 
 
 1314 
 
 154 
 
 720 
 
 258 
 
 2818 
 
 362 
 
 325 
 
 466 
 
 3323 
 
 570 
 
 1659 
 
 52 
 
 1168 
 
 156 
 
 789 
 
 260 
 
 2770 
 
 364 
 
 355 
 
 468 
 
 3328 
 
 572 
 
 1656 
 
 54 
 
 1120 
 
 158 
 
 860 
 
 262 
 
 2717 
 
 366 
 
 389 
 
 470 
 
 3329 
 
 574 
 
 1655 
 
 56 
 
 107! 
 
 160 
 
 933 
 
 264 
 
 2662 
 
 368 
 
 426 
 
 472 
 
 3327 
 
 576 
 
 1656 
 
 58 
 
 10x22 
 
 162 
 
 1008 
 
 266 
 
 2604 
 
 370 
 
 468 
 
 474 
 
 3320 
 
 578 
 
 1638 
 
 60 
 
 971 
 
 164 
 
 1084 
 
 263 
 
 2542 
 
 372 
 
 514 
 
 476 
 
 331 1 
 
 580 
 
 1661 
 
 62 
 
 920 
 
 166 
 
 1162 
 
 270 
 
 2479 
 
 374 
 
 563 
 
 478 
 
 3297 
 
 582 
 
 1664 
 
 64 
 
 863 
 
 168 
 
 1241 
 
 272 
 
 2412 
 
 376 
 
 615 
 
 480 
 
 3280 
 
 584 
 
 1668 
 
 66 
 
 816 
 
 170 
 
 1321 
 
 274 
 
 2344 
 
 378 
 
 671 
 
 482 
 
 3260 
 
 586 
 
 1671 
 
 68 
 
 764 
 
 172 
 
 1409 
 
 876 
 
 2273 
 
 380 
 
 729 
 
 484 
 
 3237 
 
 588 
 
 1675 
 
 70 
 
 712 
 
 174 
 
 14o3 
 
 278 
 
 2201 
 
 382 
 
 791 
 
 486 
 
 3211 
 
 590 
 
 1677" 
 
 72 
 
 6GO 
 
 176 
 
 1564 
 
 280 
 
 2127 
 
 384 
 
 855 
 
 488 
 
 3189 
 
 592 
 
 1679 
 
 74 
 
 60!) 
 
 178 
 
 1646 
 
 282 
 
 2051 
 
 386 
 
 929 
 
 490 
 
 3150 
 
 594 
 
 1630 
 
 76 
 
 559 
 
 180 
 
 1727 
 
 284 
 
 1975 
 
 388 
 
 091 
 
 492 
 
 3116 
 
 596 
 
 1678 
 
 78 
 
 510 
 
 182 
 
 1808 
 
 286 
 
 1897 
 
 390 
 
 1063 
 
 494 
 
 3079 
 
 598 
 
 1676 
 
 80 
 
 462 
 
 184 
 
 1888 
 
 288 
 
 1819 
 
 392 
 
 1137 
 
 4% 
 
 3039 
 
 600 
 
 1671 
 
 82 
 
 415 
 
 186 
 
 1967 
 
 290 
 
 1740 
 
 394 
 
 1212 
 
 498 
 
 2998 
 
 602 
 
 1664 
 
 84 
 
 370 
 
 188 
 
 21146 
 
 292 
 
 1661 
 
 396 
 
 128!) 
 
 500 
 
 9054 
 
 604 
 
 1655 
 
 86 
 
 327 
 
 ]'.)() 
 
 2123 
 
 294 
 
 1582 
 
 398 
 
 1367 
 
 502 
 
 290!) 
 
 606 
 
 1642 
 
 88 
 
 285 
 
 192 
 
 2198 
 
 296 
 
 1504 
 
 400 
 
 1446 
 
 504 
 
 2862 
 
 608 
 
 1627 
 
 90 
 
 246 
 
 194 
 
 2272 
 
 298 
 
 1426 
 
 402 
 
 1527 
 
 506 
 
 2814 
 
 610 
 
 1610 
 
 99 
 
 210 
 
 196 
 
 2343 
 
 300 
 
 1348 
 
 404 
 
 1607 
 
 508 
 
 2764 
 
 612 
 
 1590 
 
 !)4 
 
 175 
 
 198 
 
 2413 
 
 302 
 
 1272 
 
 406 
 
 1689 
 
 510 
 
 2714 
 
 614 
 
 1568 
 
 '.16 
 
 144 
 
 200 
 
 2479 
 
 304 
 
 1197 
 
 408 
 
 1770 
 
 512 
 
 2663 
 
 616 
 
 1543 
 
 98 
 
 115 
 
 202 
 
 2544 
 
 306 
 
 1193 
 
 410 
 
 1851 
 
 514 
 
 2612 
 
 618 
 
 1516 
 
 100 
 
 89 
 
 204 
 
 2605 
 
 3(18 
 
 1051 
 
 412 
 
 1932 
 
 516 
 
 2560 
 
 620 
 
 1485 
 
 102 
 
 67 
 
 206 
 
 266-1 
 
 310 
 
 980 
 
 414 
 
 2013 
 
 518 
 
 2508 
 
 622 
 
 1 153 
 
 104 
 
 47 
 
 208 2720 
 
 312 
 
 912 
 
 416 
 
 2093 
 
 520 
 
 2156 
 
 624 
 
 1418 
 
 The perturbations are expressed in liimdrcdtlis of a second of arc. 
 
TAI1L.KS. 
 
 E 1155.1 XVIII. 
 
 TAKM-: XIX. 
 
 >^*cT0^E^3 
 Till l,i: XX. / 
 
 
 
 J N J W T3 i 
 
 l'i rt. of tin- Litnaitinli- 
 liy lli<- F.nrlli. 
 
 1'i-rt. n! Hi,- Lnin;i/iifli- 
 l'i/ Mnrx. 
 
 Perturbation /' the Lon^innli- Ay jionVfrX & il 
 
 \ c 
 
 ^ 7PAT3- 
 
 Arg. VII 
 
 Equa. 
 
 Art; VII. 
 
 Ar- \ III 
 
 ,,,, 
 
 Ar| \ III 
 
 Arg. IX. 
 
 ,,,,,. 
 
 Arg. IX. 
 
 Equa. 
 
 "t 
 Arg. IX. 
 
 
 d 
 
 
 il 
 
 948 
 
 d 
 
 
 
 
 .1 
 934 
 
 d 
 
 
 
 339 
 
 d 
 
 -H 
 
 7 
 
 Kill' 
 
 1,71 
 
 4 
 
 
 
 '.Ml 
 
 4 
 
 
 
 ._,._,, , 
 
 2 
 
 :iv!7 
 
 -J 
 
 19 
 
 169 
 
 672 
 
 8 
 
 8 
 
 940 
 
 8 
 
 1 
 
 916 
 
 4 
 
 :i-M 
 
 -1 
 
 P.I 
 
 161 
 
 1,7'.' 
 
 19 
 
 "' 
 
 936 
 
 19 
 
 :l 
 
 212 
 
 6 
 
 316 
 
 96 
 
 98 
 
 166 
 
 67(1 
 
 Hi 
 
 10 
 
 939 
 
 16 
 
 6 
 
 
 8 
 
 300 
 
 as 
 
 
 168 
 
 667 
 
 80 
 
 16 
 
 22* 
 
 90 
 
 B 
 
 _'. ' 1 
 
 HI 
 
 303 
 
 '.Ml 
 
 10 
 
 170 
 
 663 
 
 24 
 
 96 
 
 22 1 
 
 94 
 
 13 
 
 21 Ml 
 
 19 
 
 996 
 
 09 
 
 69 
 
 179 
 
 
 98 
 
 34 
 
 mo 
 
 88 
 
 l- 
 
 106 
 
 1 1 
 
 J-:' 
 
 04 
 
 77 
 
 171 
 
 6T.1 
 
 38 
 
 46 
 
 916 
 
 39 
 
 93 
 
 199 
 
 16 
 
 981 
 
 06 
 
 83 
 
 176 
 
 643 
 
 36 
 
 57 
 
 919 
 
 36 
 
 99 
 
 I-- 
 
 18 
 
 27:1 
 
 
 no 
 
 17- 
 
 634 
 
 in 
 
 71 
 
 jn- 
 
 III 
 
 
 1-1 
 
 -'n 
 
 2(il 
 
 mo 
 
 198 
 
 1- i 
 
 694 
 
 II 
 
 * 
 
 804 
 
 II 
 
 49 
 
 i- 1 
 
 99 
 
 856 
 
 109 
 
 1 i- 
 
 189 
 
 613 
 
 18 
 
 100 
 
 200 
 
 |8 
 
 50 
 
 176 
 
 94 
 
 845 
 
 104 
 
 168 
 
 l-l 
 
 
 59 
 
 116 
 
 196 
 
 59 
 
 57 
 
 172 
 
 26 
 
 935 
 
 106 
 
 100 
 
 186 
 
 600 
 
 56 
 
 1 32 
 
 199 
 
 56 
 
 (il 
 
 168 
 
 28 
 
 -.'-.' 1 
 
 in- 
 
 919 
 
 ]-- 
 
 577 
 
 60 
 
 149 
 
 188 
 
 Gil 
 
 72 
 
 164 
 
 30 
 
 213 
 
 lli) 
 
 936 
 
 100 
 
 164 
 
 64 
 
 163 
 
 1 1 
 
 64 
 
 70 
 
 160 
 
 32 
 
 901 
 
 119 
 
 950 
 
 199 
 
 RBI 
 
 6d 
 
 i-j 
 
 ISO 
 
 &s 
 
 96 
 
 156 
 
 34 
 
 188 
 
 III 
 
 883 
 
 1:14 
 
 .->:'.- 
 
 79 
 
 108 
 
 176 
 
 7-.' 
 
 08 
 
 159 
 
 36 
 
 171, 
 
 116 
 
 807 
 
 196 
 
 
 76 
 
 915 
 
 172 
 
 76 
 
 ion 
 
 1 1- 
 
 38 
 
 163 
 
 118 
 
 332 
 
 198 
 
 511 
 
 
 930 
 
 168 
 
 80 
 
 106 
 
 III 
 
 HI 
 
 150 
 
 PJI 
 
 356 
 
 800 
 
 I - 
 
 84 
 
 946 
 
 164 
 
 84 
 
 119 
 
 140 
 
 49 
 
 137 
 
 122 
 
 :;-i 
 
 909 
 
 ! , 
 
 88 
 
 950 
 
 160 
 
 88 
 
 117 
 
 1 .:i > 
 
 44 
 
 123 
 
 124 
 
 405 
 
 204 
 
 472 
 
 09 
 
 979 
 
 [56 
 
 !I2 
 
 121 
 
 139 
 
 46 
 
 110 
 
 196 
 
 428 
 
 206 
 
 |i,i 
 
 IK; 
 
 963 
 
 152 
 
 % 
 
 125 
 
 198 
 
 48 
 
 08 
 
 198 
 
 159 
 
 908 
 
 448 
 
 100 
 
 804 
 
 1 1- 
 
 100 
 
 198 
 
 124 
 
 50 
 
 96 
 
 130 
 
 471 
 
 210 
 
 436 
 
 104 
 
 303 
 
 1 II 
 
 Illl 
 
 130 
 
 120 
 
 59 
 
 73 
 
 189 
 
 486 
 
 919 
 
 496 
 
 108 
 
 310 
 
 140 
 
 108 
 
 131 
 
 116 
 
 54 
 
 62 
 
 134 
 
 517 
 
 21 1 
 
 415 
 
 119 
 
 316 
 
 136 
 
 119 
 
 132 
 
 112 
 
 56 
 
 51 
 
 136 
 
 537 
 
 216 
 
 405 
 
 116 
 
 321 
 
 138 
 
 
 
 
 58 
 
 41 
 
 138 
 
 556 
 
 918 
 
 386 
 
 190 
 
 323 
 
 12- 
 
 
 
 
 <>0 
 
 38 
 
 140 
 
 r,7:l 
 
 990 
 
 ::-- 
 
 194 
 
 894 
 
 194 
 
 
 
 
 62 
 
 23 
 
 142 
 
 BOO 
 
 222 
 
 
 
 64 
 6G 
 
 16 
 
 10 
 
 1 II 
 
 i it; 
 
 GII:> 
 618 
 
 224 
 996 
 
 372 
 365 
 
 
 se 
 
 6 
 
 148 
 
 630 
 
 998 
 
 350 
 
 
 70 
 
 2 
 
 150 
 
 611 
 
 230 
 
 88i 
 
 
 72 
 
 
 
 169 
 
 850 
 
 232 
 
 346 
 
 
 74 
 
 
 
 154 
 
 658 
 
 234 
 
 311 
 
 
 76 
 
 
 
 156 
 
 664 
 
 836 
 
 335 
 
 
 78 
 
 3 
 
 158 
 
 668 
 
 
 330 
 
 
 80 
 
 7 
 
 160 
 
 671 
 
 240 
 
 394 
 
 " t 
 
 Constant added in Table XVIII. 1.62. Period of Argument VII. 213.16. 
 
 Constant added in Table XIX. IMJ6. Period of Argument VIII. 220.57. 
 
 Constant added in Table XX. 3.35. Period of Argument IX. a36.!>!i. 
 
 The perturbations are expressed in liundredths of a second of arc. 
 
3O 
 
 TABLE XXI. 
 
 Perturbation of the Longitude by Mercury. 
 
 Horizontal Argument = I. 
 Constant added 0''.85. Period of Argument 1., 224'' .7. 
 
 
 tl 
 
 d 
 
 d cl 
 
 d 
 
 rt 
 
 <] 
 
 d 
 
 d 
 
 rt 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 Arg. X 
 
 
 
 
 
 16 
 
 24 
 
 32 
 
 40 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 88 
 
 96 
 
 104 
 
 112 
 
 
 
 139 
 
 131 
 
 131 
 
 132 
 
 135 
 
 137 
 
 138 
 
 138 
 
 138 
 
 141 
 
 146 
 
 152 
 
 158 
 
 162 
 
 162 
 
 J 
 
 I'M 
 
 127 
 
 128 
 
 129 
 
 138 
 
 134 
 
 134 
 
 135 
 
 136 
 
 139 
 
 144 151 
 
 156 
 
 158 
 
 158 
 
 2 
 
 123 
 
 122 
 
 122 
 
 124 
 
 127 
 
 139 
 
 130 
 
 131 
 
 138 
 
 136 
 
 142 
 
 148 
 
 158 
 
 153 
 
 152 
 
 3 
 
 116 
 
 lir> 
 
 116 
 
 118 
 
 121 
 
 121 
 
 125 
 
 125 
 
 128 
 
 132 
 
 138 
 
 143 
 
 147 
 
 116 
 
 143 
 
 4 
 
 1(17 
 
 107 
 
 100 
 
 112 
 
 115 
 
 117 
 
 118 
 
 120 
 
 122 
 
 127 
 
 133 
 
 138 
 
 139 
 
 138 
 
 134 
 
 6 
 
 99 
 
 99 
 
 102 
 
 105 
 
 108 
 
 111 
 
 112 
 
 113 
 
 117 
 
 122 
 
 127 
 
 131 
 
 131 
 
 128 
 
 123 
 
 6 
 
 90 
 
 91 
 
 EM 
 
 98 
 
 102 
 
 104 
 
 105 
 
 107 
 
 III 
 
 116 
 
 121 
 
 123 
 
 122 
 
 118 
 
 112 
 
 7 
 
 81 
 
 84 
 
 87 
 
 92 
 
 95 
 
 97 
 
 99 
 
 llll 
 
 105 
 
 110 
 
 114 
 
 115 
 
 112 
 
 107 
 
 100 
 
 8 
 
 74 
 
 77 
 
 81 
 
 86 
 
 89 
 
 92 
 
 93 
 
 96 
 
 100 
 
 104 
 
 107 
 
 107 
 
 102 
 
 96 
 
 89 
 
 9 
 
 67 
 
 72 
 
 76 
 
 81 
 
 86 
 
 87 
 
 88 
 
 91 
 
 95 
 
 99 
 
 100 
 
 99 
 
 93 
 
 85 
 
 78 
 
 in 
 
 63 
 
 68 
 
 73 
 
 78 
 
 81 
 
 83 
 
 85 
 
 87 
 
 ill 
 
 94 
 
 94 
 
 91 
 
 84 
 
 76 
 
 68 
 
 M 
 
 60 
 
 60 
 
 71 
 
 75 
 
 79 
 
 80 
 
 82 
 
 85 
 
 88 
 
 90 
 
 89 
 
 .-'1 
 
 76 
 
 67 60 
 
 13 
 
 59 
 
 65 
 
 70 
 
 ?" 
 
 77 
 
 79 
 
 81 
 
 83 
 
 86 
 
 86 
 
 84 
 
 78 
 
 69 
 
 6U 
 
 53 
 
 13 
 
 60 
 
 (ili 
 
 72 
 
 76 
 
 78 i 79 
 
 80 
 
 83 
 
 S4 
 
 84 
 
 80 
 
 73 
 
 63 
 
 55 
 
 48 
 
 14 
 
 61 
 
 70 
 
 75 
 
 78 
 
 80 
 
 81 
 
 82 
 
 83 
 
 6M 
 
 82 
 
 77 
 
 69 
 
 59 
 
 51 
 
 45 
 
 IS 
 
 68 
 
 75 
 
 79 
 
 8 
 
 83 
 
 83 
 
 84 
 
 85 
 
 85 
 
 81 
 
 75 
 
 66 
 
 57 
 
 49 
 
 43 
 
 Hi 
 
 75 
 
 81 
 
 85 
 
 86 
 
 87 
 
 87 
 
 87 
 
 87 
 
 86 
 
 81 
 
 74 
 
 65 
 
 56 
 
 49 
 
 44 
 
 17 
 
 84 
 
 88. 
 
 91 
 
 92 
 
 92 
 
 91 
 
 91 
 
 91 
 
 88 
 
 82 
 
 74 
 
 65 
 
 56 
 
 50 
 
 46 
 
 18 
 
 !)3 
 
 97 
 
 9!) 
 
 98 
 
 97 
 
 96 
 
 96 
 
 94 
 
 90 
 
 84 
 
 75 
 
 (ir. 
 
 57 
 
 52 
 
 58 
 
 19 
 
 102 
 
 106 
 
 106 
 
 105 
 
 103 
 
 102 
 
 100 
 
 98 
 
 93 
 
 85 
 
 76 
 
 67 
 
 60 
 
 56 
 
 55 
 
 20 
 
 na 
 
 ill 
 
 113 
 
 111 
 
 109 
 
 107 
 
 105 
 
 101 
 
 95 
 
 87 
 
 78 
 
 69 
 
 64 
 
 61 
 
 60 
 
 21 
 
 181 
 
 122 
 
 120 
 
 117 
 
 114 
 
 112 
 
 108 
 
 104 
 
 98 
 
 89 
 
 80 
 
 72 
 
 68 
 
 66 
 
 66 
 
 22 
 
 130 
 
 129 
 
 126 
 
 122 
 
 119 
 
 115 
 
 112 
 
 107 
 
 99 
 
 90 
 
 81 
 
 75 
 
 72 
 
 71 
 
 72 
 
 23 
 
 137 
 
 135 
 
 131 
 
 126 
 
 122 
 
 118 
 
 114 
 
 108 
 
 100 
 
 91 
 
 83 
 
 78 
 
 76 
 
 77 
 
 78 
 
 24 
 
 143 
 
 139 
 
 134 
 
 129 
 
 124 
 
 120 
 
 115 
 
 108 
 
 100 
 
 91 
 
 84 
 
 80 
 
 .80 
 
 81 
 
 83 
 
 25 
 
 147 
 
 143 
 
 136 
 
 130 
 
 125 
 
 120 
 
 114 
 
 108 
 
 99 
 
 91 
 
 85 
 
 82 
 
 83 
 
 85 
 
 88 
 
 26 
 
 148 
 
 142 
 
 135 
 
 129 
 
 123 
 
 118 
 
 113 
 
 105 
 
 97 
 
 89 
 
 84 
 
 83 
 
 85 
 
 88 
 
 91 
 
 27 
 
 147 
 
 140 
 
 133 
 
 126 
 
 120 
 
 115 
 
 109 
 
 101 
 
 93 
 
 87 
 
 83 
 
 83 
 
 87 
 
 90 
 
 93 
 
 28 
 
 ' 144 
 
 136 
 
 128 
 
 121 
 
 111, 
 
 110 
 
 104 
 
 96 
 
 89 
 
 83 
 
 81 
 
 83 
 
 87 
 
 90 
 
 93 
 
 29 
 
 138 
 
 130 
 
 122 
 
 115 
 
 109 
 
 104 
 
 97 
 
 90 
 
 83 
 
 79 
 
 78 
 
 81 
 
 86 
 
 89 
 
 92 
 
 30 
 
 130 
 
 122 
 
 113 
 
 107 
 
 101 
 
 96 
 
 89 
 
 82 
 
 77 
 
 74 
 
 75 
 
 78 
 
 83 
 
 87 
 
 89 
 
 31 
 
 120 
 
 112 
 
 101 
 
 98 
 
 92 
 
 87 
 
 80 
 
 74 
 
 69 
 
 68 
 
 70 ! 75 
 
 80 
 
 83 
 
 85 
 
 ' 32 
 
 109 
 
 1011 
 
 93 
 
 87 
 
 82 
 
 77 
 
 71 
 
 65 
 
 62 
 
 62 
 
 65 
 
 70 
 
 75 
 
 78 
 
 80 
 
 33 
 
 96 
 
 88 
 
 81 
 
 75 
 
 71 
 
 66 
 
 61 
 
 56 
 
 54 
 
 56 
 
 60 
 
 65 
 
 70 
 
 73 
 
 74 
 
 34 
 
 82 
 
 74 
 
 68 
 
 64 
 
 60 
 
 55 
 
 51 
 
 47 
 
 46 
 
 49 
 
 54 
 
 60 
 
 64 
 
 66 
 
 68 
 
 35 
 
 68 
 
 61 
 
 56 
 
 68 
 
 49 
 
 45 
 
 41 
 
 39 
 
 39 
 
 43 
 
 49 
 
 54 
 
 58 
 
 60 
 
 61 
 
 36 
 
 54 
 
 48 
 
 41 
 
 41 
 
 38 
 
 35 
 
 33 
 
 31 
 
 33 
 
 38 
 
 44 
 
 49 
 
 52 
 
 53 
 
 54 
 
 37 
 
 41 
 
 36 
 
 33 
 
 31 
 
 29 
 
 26 
 
 24 
 
 25 
 
 28 
 
 33 
 
 39 
 
 44 
 
 46 
 
 47 
 
 47 
 
 38 
 
 29 
 
 26 
 
 24 
 
 22 
 
 21 
 
 19 
 
 18 
 
 19 
 
 24 
 
 30 
 
 36 
 
 39 
 
 41 
 
 41 
 
 42 
 
 39 
 
 19 
 
 17 
 
 16 
 
 13 
 
 14 
 
 13 
 
 13 
 
 16 
 
 21 
 
 27 
 
 33 
 
 36 
 
 37 
 
 37 
 
 37 
 
 40 
 
 11 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 11 
 
 14 
 
 20 
 
 26 
 
 31 
 
 34 
 
 34 
 
 34 
 
 34 
 
 41 
 
 5 
 
 5 
 
 6 
 
 7 
 
 8 
 
 8 
 
 10 
 
 15 
 
 21 
 
 27 
 
 31 
 
 33 
 
 32 
 
 32 
 
 32 
 
 42 
 
 2 
 
 3 
 
 5 
 
 7 
 
 8 
 
 9 
 
 12 
 
 17 
 
 23 
 
 29 
 
 32 
 
 33 
 
 32 
 
 32 
 
 33 
 
 43 
 
 2 
 
 4 
 
 6 
 
 9 
 
 10 
 
 12 
 
 15 
 
 21 
 
 27 
 
 32 
 
 35 
 
 35 
 
 34 
 
 34 
 
 35 
 
 44 
 
 4 
 
 7 
 
 10 
 
 12 
 
 14 
 
 17 
 
 21 
 
 27 
 
 33 
 
 37 
 
 39 
 
 39 
 
 37 
 
 37 
 
 39 
 
 45 
 
 8 
 
 12 
 
 16 
 
 19 
 
 21 
 
 24 
 
 29 
 
 35 
 
 40 
 
 44 
 
 44 
 
 43 
 
 42 
 
 43 
 
 45 
 
 46 
 
 16 
 
 20 
 
 24 
 
 27 
 
 89 
 
 33 
 
 38 
 
 43 
 
 48 
 
 51 
 
 51 
 
 50 
 
 49 
 
 50 
 
 53 
 
 47 
 
 25 
 
 30 
 
 34 
 
 36 
 
 39 
 
 43 
 
 48 
 
 53 
 
 58 
 
 59 
 
 59 
 
 57 
 
 57 
 
 58 
 
 62 
 
 48 
 
 36 
 
 41 
 
 45 
 
 47 
 
 50 
 
 54 
 
 59 
 
 64 
 
 68 
 
 68 
 
 67 
 
 66 
 
 66 
 
 68 
 
 72 
 
 49 
 
 48 
 
 53 
 
 57 
 
 59 
 
 62 
 
 66 
 
 71 
 
 75 
 
 78 
 
 78 
 
 77 
 
 75 
 
 76 
 
 79 
 
 84 
 
 50 
 
 61 
 
 65 
 
 69 
 
 71 
 
 74 
 
 78 
 
 82 
 
 86 
 
 88 
 
 88 
 
 86 
 
 85 
 
 87 
 
 91 
 
 96 
 
 51 
 
 74 
 
 78 
 
 81 
 
 83 
 
 86 
 
 91) 
 
 94 
 
 97 
 
 98 
 
 97 
 
 96 
 
 96 
 
 98 
 
 103 
 
 108 
 
 52 
 
 87 
 
 91 
 
 93 
 
 95 
 
 97 
 
 101 
 
 105 
 
 107 
 
 JOS 
 
 106 
 
 1(15 
 
 106 
 
 109 
 
 115 
 
 120 
 
 53 
 
 99 
 
 11)2 
 
 104 
 
 105 
 
 108 
 
 III 
 
 114 
 
 116 
 
 116 
 
 115 
 
 114 
 
 116 
 
 120 
 
 126 
 
 138 
 
 54 
 
 110 
 
 112 
 
 113 
 
 114 
 
 117 
 
 120 
 
 123 
 
 124 
 
 124 
 
 122 
 
 122 
 
 125 
 
 130 
 
 136 
 
 142 
 
 55 
 
 119 
 
 j\ 
 
 121 
 
 122 
 
 124 
 
 27 
 
 130 
 
 131 
 
 130 
 
 129 
 
 130 
 
 133 
 
 139 
 
 145 
 
 150 
 
 56 
 
 126 
 
 27 
 
 127 
 
 128 
 
 130 
 
 33 
 
 135 
 
 135 
 
 135 
 
 134 
 
 136 
 
 140 
 
 146 
 
 153 
 
 157 
 
 57 
 
 I3J 
 
 31 
 
 131 
 
 139 
 
 134 
 
 37 
 
 138 
 
 139 
 
 138 
 
 138 
 
 141 
 
 145 
 
 1 .vj 
 
 158 
 
 162 
 
 58 
 
 134 
 
 34 
 
 133 
 
 134 
 
 136" 
 
 39 
 
 140 
 
 140 
 
 139 
 
 140 
 
 144 
 
 149 
 
 156 
 
 161 
 
 164 
 
 59 
 
 134 
 
 33 
 
 133 
 
 134 
 
 137 
 
 30 
 
 140 
 
 140 
 
 140 
 
 141 
 
 146 
 
 152 
 
 158 
 
 163 
 
 Kit 
 
 GO 
 
 132 
 
 31 
 
 131 
 
 132 
 
 135 
 
 137 
 
 138 
 
 138 
 
 138 
 
 141 
 
 M6 
 
 158 
 
 168 
 
 162 
 
 162 
 
 The perturbation! are expressed in hundredllis of a second of arc 
 
TABLE XXI. 
 
 31 
 
 Perturbation <>f tin- Longitude l>n Mercury. 
 
 Constant iidili-d , ! ,,f Argument X , 60. 
 
 
 d 
 
 ,l 
 
 d 
 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 .1 
 
 d 
 
 ,1 
 
 d 
 
 ,1 
 
 d 
 
 
 120 
 
 12W 
 
 136 
 
 111 
 
 1.12 
 
 160 
 
 16* 
 
 176 
 
 
 1!>2 
 
 200 
 
 20* 
 
 216 
 
 221 
 
 2!I2 
 
 
 
 169 
 
 160 
 
 159 
 
 1 .- 
 
 166 
 
 181 
 
 146 
 
 138 
 
 130 
 
 194 
 
 110 
 
 III 
 
 108 
 
 '.ill 
 
 H 
 
 1 
 
 156 
 
 154 
 
 159 
 
 ISO 
 
 II? 
 
 111 
 
 134 
 
 195 
 
 1 1* 
 
 ill 
 
 106 
 
 '.i? 
 
 BO 
 
 79 
 
 :'. 
 
 2 
 
 1 l:i 
 
 IK, 
 
 143 
 
 Mil 
 
 136 
 
 190 
 
 190 
 
 112 
 
 Ml 
 
 ;i? 
 
 HI 
 
 
 71 
 
 
 59 
 
 3 
 
 1 10 
 
 136 
 
 1:1:1 
 
 199 
 
 193 
 
 115 
 
 Ml, 
 
 97 
 
 90 
 
 
 76 
 
 
 60 
 
 .M 
 
 Ii, 
 
 4 
 
 190 
 
 12.-> 
 
 121 
 
 116 
 
 100 
 
 100 
 
 !l| 
 
 -J 
 
 7.') 
 
 69 
 
 62 
 
 54 
 
 46 
 
 3!) 
 
 34 
 
 5 
 
 II- 
 
 113 
 
 108 
 
 102 
 
 ,,;, 
 
 
 76 
 
 
 (il 
 
 :,:, 
 
 1- 
 
 41 
 
 :u 
 
 27 
 
 M 
 
 6 
 
 i- 6 
 
 10| 
 
 90 
 
 
 80 
 
 71 
 
 
 54 
 
 1- 
 
 19 
 
 36 
 
 99 
 
 98 
 
 18 
 
 16 
 
 7 
 
 94 
 
 88 
 
 89 
 
 75 
 
 G7 
 
 .",? 
 
 
 II 
 
 
 ;t| 
 
 
 in 
 
 14 
 
 10 
 
 9 
 
 8 
 
 82 
 
 76 
 
 70 
 
 G:I 
 
 r,l 
 
 16 
 
 
 
 
 91 
 
 II, 
 
 11 
 
 7 
 
 5 
 
 5 
 
 9 
 
 71 
 
 66 
 
 59 
 
 :,i 
 
 41! 
 
 84 
 
 27 
 
 M 
 
 18 
 
 11 
 
 in 
 
 6 
 
 3 
 
 2 
 
 3 
 
 10 
 
 62 
 
 56 
 
 4! > 
 
 rj 
 
 33 
 
 86 
 
 19 
 
 16 
 
 19 
 
 hi 
 
 6 
 
 3 
 
 2 
 
 9 
 
 4 
 
 11 
 
 61 
 
 48 
 
 41 
 
 34 
 
 21 i 
 
 19 
 
 II 
 
 19 
 
 ID 
 
 8 
 
 6 
 
 3 
 
 3 
 
 5 
 
 8 
 
 12 
 
 47 
 
 42 
 
 86 
 
 98 
 
 JI 
 
 Hi 
 
 12 
 
 II 
 
 hi 
 
 8 
 
 7 
 
 6 
 
 7 
 
 10 
 
 14 
 
 13 
 
 42 
 
 87 
 
 31 
 
 95 
 
 1- 
 
 11 
 
 12 
 
 19 
 
 12 
 
 12 
 
 II 
 
 11 
 
 13 
 
 16 
 
 99 
 
 11 
 
 40 
 
 m 
 
 30 
 
 24 
 
 l!l 
 
 Ii, 
 
 16 
 
 Hi 
 
 17 
 
 17 
 
 17 
 
 19 
 
 a 
 
 27 
 
 89 
 
 15 
 
 39 
 
 35 
 
 30 
 
 95 
 
 21 
 
 M 
 
 20 
 
 22 
 
 21 
 
 95 
 
 26 
 
 29 
 
 33 
 
 38 
 
 43 
 
 16 
 
 40 
 
 37 
 
 32 
 
 
 26 
 
 M 
 
 
 31 
 
 33 
 
 ;; | 
 
 36 
 
 40 
 
 45 
 
 50 
 
 55 
 
 17 
 
 43 
 
 40 
 
 37 
 
 84 
 
 89 
 
 34 
 
 ft? 
 
 40 
 
 43 
 
 46 
 
 48 
 
 52 
 
 57 
 
 63 
 
 68 
 
 18 
 
 48 
 
 45 
 
 42 
 
 41 
 
 41 
 
 43 
 
 47 
 
 
 
 57 
 
 60 
 
 6.'. 
 
 71 
 
 71, 
 
 81 
 
 19 
 
 53 
 
 
 49 
 
 49 
 
 50 
 
 54 
 
 58 
 
 G:! 
 
 66 
 
 G'.l 
 
 73 
 
 78 
 
 84 
 
 89 
 
 93 
 
 20 
 
 59 
 
 58 
 
 57 
 
 57 
 
 60 
 
 65 
 
 70 
 
 74 
 
 78 
 
 81 
 
 85 
 
 91 
 
 96 
 
 101 
 
 104 
 
 21 
 
 65 
 
 66 
 
 (M 
 
 66 
 
 70 
 
 76 
 
 81 
 
 86 
 
 89 
 
 99 
 
 97 
 
 109 
 
 107 
 
 112 
 
 114 
 
 99 
 
 72 
 
 72 
 
 
 7.-, 
 
 -.1 
 
 86 
 
 91 
 
 in; 
 
 99 
 
 lo:t 
 
 107 
 
 119 
 
 117 
 
 190 
 
 122 
 
 
 79 
 
 711 
 
 81 
 
 84 
 
 09 
 
 96 
 
 101 
 
 106 
 
 
 III 
 
 116 
 
 190 
 
 196 
 
 127 
 
 128 
 
 21 
 
 84 
 
 85 
 
 88 
 
 
 97 
 
 103 
 
 108 
 
 112 
 
 116 
 
 118 
 
 122 
 
 127 
 
 130 
 
 132 
 
 189 
 
 2."> 
 
 89 
 
 90 
 
 93 
 
 98 
 
 104 
 
 110 
 
 114 
 
 118 
 
 120 
 
 121! 
 
 127 
 
 131 
 
 183 
 
 184 
 
 134 
 
 26 
 
 92 
 
 94 
 
 98 
 
 108 
 
 109 
 
 III 
 
 118 
 
 191 
 
 193 
 
 126 
 
 129 
 
 139 
 
 134 
 
 134 
 
 133 
 
 27 
 
 94 
 
 96 
 
 100 
 
 106 
 
 119 
 
 117 
 
 120 
 
 199 
 
 12:! 
 
 196 
 
 199 
 
 131 
 
 139 
 
 132- 
 
 131 
 
 
 96 
 
 97 
 
 101 
 
 107 
 
 119 
 
 117 
 
 119 
 
 120 
 
 122 
 
 194 
 
 196 
 
 198 
 
 199 
 
 127 
 
 126 
 
 .;,, 
 
 !tl 
 
 96 
 
 101 
 
 106 
 
 ill 
 
 114 
 
 116 
 
 117 
 
 118 
 
 190 
 
 122 
 
 193 
 
 193 
 
 121 
 
 120 
 
 80 
 
 91 
 
 94 
 
 98 
 
 103 
 
 108 
 
 110 
 
 111 
 
 III 
 
 119 
 
 114 
 
 116 
 
 116 
 
 115 
 
 114 
 
 113 
 
 31 
 
 87 
 
 90 
 
 94 
 
 99 
 
 103 
 
 104 
 
 106 
 
 104 
 
 in:. 
 
 106 
 
 1H7 
 
 108 
 
 107 
 
 105 
 
 105 
 
 39 
 
 B9 
 
 85 
 
 
 98 
 
 96 
 
 H7 
 
 97 
 
 96 
 
 97 
 
 98 
 
 !l!l 
 
 99 
 
 98 
 
 97 
 
 97 
 
 
 76 
 
 79 
 
 83 
 
 86 
 
 88 
 
 88 
 
 83 
 
 87 
 
 88 
 
 89 
 
 89 
 
 8!) 
 
 89 
 
 88 
 
 
 34 
 
 69 
 
 72 
 
 76 
 
 7!l 
 
 80 
 
 79 
 
 78 
 
 78 
 
 78 
 
 80 
 
 80 
 
 80 
 
 80 
 
 80 
 
 81 
 
 36 
 
 62 
 
 66 
 
 63 
 
 70 
 
 71 
 
 70 
 
 69 
 
 68 
 
 70 
 
 71 
 
 72 
 
 79 
 
 71 
 
 72 
 
 7.-, 
 
 3G 
 
 
 58 
 
 61 
 
 63 
 
 63 
 
 61 
 
 60 
 
 60 
 
 Gl 
 
 63 
 
 1,1 
 
 64 
 
 6.". 
 
 66 
 
 70 
 
 
 49 
 
 51 
 
 54 
 
 6fi 
 
 56 
 
 53 
 
 52 
 
 5.1 
 
 55 
 
 56 
 
 .",7 
 
 58 
 
 59 
 
 62 
 
 66 
 
 38 
 
 43 
 
 46 
 
 48 
 
 49 
 
 48 
 
 46 
 
 46 
 
 47 
 
 49 
 
 
 53 
 
 54 
 
 56 
 
 50 
 
 64 
 
 39 
 
 39 
 
 41 
 
 43 
 
 43 
 
 43 
 
 42 
 
 42 
 
 43 
 
 46 
 
 4!) 
 
 50 
 
 69 
 
 55 
 
 59 
 
 64 
 
 40 
 
 36 
 
 38 
 
 40 
 
 40 
 
 39 
 
 38 
 
 3!) 
 
 42 
 
 46 
 
 48 
 
 50 
 
 69 
 
 56 
 
 61 
 
 66 
 
 41 
 
 34 
 
 37 
 
 3D 
 
 38 
 
 38 
 
 38 
 
 89 
 
 42 
 
 46 
 
 50 
 
 59 
 
 55 
 
 69 
 
 lil 
 
 70 
 
 49 
 
 35 
 
 37 
 
 39 
 
 39 
 
 38 
 
 39 
 
 42 
 
 46 
 
 50 
 
 .-,4 
 
 56 
 
 
 (II 
 
 70 
 
 7.') 
 
 4:t 
 
 37 
 
 40 
 
 41 
 
 42 
 
 42 
 
 43 
 
 47 
 
 51 
 
 56 
 
 60 
 
 63 
 
 66 
 
 71 
 
 77 
 
 '-' 
 
 44 
 
 42 
 
 44 
 
 46 
 
 46 
 
 47 
 
 50 
 
 54 
 
 
 64 
 
 68 
 
 71 
 
 75 
 
 79 
 
 85 
 
 90 
 
 45 
 
 48 
 
 61 
 
 52 
 
 53 
 
 55 
 
 58 
 
 63 
 
 69 
 
 73 
 
 77 
 
 80 
 
 84 
 
 89 
 
 BO 
 
 00 
 
 46 
 47 
 
 56 
 66 
 
 -,'.i 
 6!l 
 
 61 
 71 
 
 62 
 73 
 
 64 
 75 
 
 68 
 80 
 
 71 
 86 
 
 - 1 
 
 09 
 
 -1 
 06 
 
 88 
 
 99 
 
 91 
 
 102 
 
 96 
 
 106 
 
 100 
 110 
 
 106 
 
 III 
 
 107 
 
 116 
 
 48 
 49 
 
 77 
 
 88 
 
 80 
 92 
 
 82 
 94 
 
 84 
 97 
 
 88 
 101 
 
 93 
 106 
 
 9!) 
 112 
 
 104 
 117 
 
 190 
 
 111 
 193 
 
 114 
 198 
 
 117 
 128 
 
 191 
 
 130 
 
 194 
 
 1 :.' 
 
 194 
 131 
 
 50 
 
 101 
 
 104 
 116 
 
 106 
 II!) 
 
 110 
 199 
 
 114 
 127 
 
 11!) 
 139 
 
 125 
 
 137 
 
 12!) 
 140 
 
 139 
 
 112 
 
 133 
 149 
 
 135 
 
 137 
 14.') 
 
 139 
 146 
 
 139 
 
 III 
 
 137 
 111 
 
 52 
 53 
 54 
 
 195 
 
 146 
 
 128 
 
 138 
 148 
 
 130 
 
 III 
 1.-.0 
 
 134 
 146 
 
 138 
 
 1 l'i 
 167 
 
 I II 
 I :,:t 
 161 
 
 1 1- 
 156 
 
 ISO 
 157 
 
 163 
 
 150 
 157 
 
 1GI 
 
 160 
 166 
 
 I.V.I 
 
 ISO 
 155 
 197 
 
 150 
 164 
 158 
 
 150 
 
 158 
 189 
 
 148 
 
 148 
 147 
 
 143 
 143 
 140 
 
 55 
 56 
 
 to 
 
 to 
 
 60 
 
 154 
 
 160 
 
 11)1 
 
 16.-. 
 162 
 
 156 
 161 
 164 
 
 166 
 164 
 
 160 
 
 158 
 169 
 166 
 
 166 
 164 
 
 159 
 
 161 
 166 
 
 167 
 1G7 
 164 
 188 
 
 li>l 
 168 
 169 
 167 
 
 I56 
 
 166 
 169 
 160 
 163 
 
 Ilil 
 151 
 
 167 
 
 162 
 I5S 
 148 
 
 165 
 166 
 169 
 156 
 
 1 1- 
 
 161 
 
 |50 
 141 
 
 130 
 
 180 
 
 159 
 148 
 136 
 194 
 
 1.-.7 
 154 
 
 II- 
 
 1 M 
 1 10 
 
 II- 
 
 154 
 
 150 
 143 
 134 
 193 
 111 
 
 i ii 
 187 
 197 
 116 
 
 103 
 
 113 
 137 
 
 r.- 
 II- 
 
 98 
 
 136 
 190 
 190 
 
 ion 
 
 Add 33.26 to Arg. X wln-n 224''.7 is lubtracted from Arg. I. 
 
TABLE XXII. 
 
 Perturbations of the Longitude by the Earth. 
 
 Horizontal Argument = I. 
 
 Constant added 1".40. Period of Argument I. 224 (1 .7. 
 
 
 a 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d d d 
 
 d 
 
 a 
 
 d d d 
 
 Arg.XI 
 
 
 
 8 
 
 16 
 
 21 
 
 32 
 
 40 
 
 48 
 
 56 
 
 61 
 
 72 
 
 
 
 
 
 96 
 
 IO1 
 
 112 
 
 
 
 71 
 
 80 
 
 88 
 
 94 
 
 98 
 
 100 
 
 102 
 
 105 
 
 110 
 
 117 
 
 127 
 
 140 
 
 153 
 
 165 
 
 177 
 
 1 
 
 63 
 
 71 
 
 79 
 
 85 
 
 88 
 
 90 
 
 08 
 
 95 
 
 99 
 
 105 
 
 115 
 
 126 
 
 139 
 
 152 
 
 164 
 
 2 
 
 55 
 
 63 
 
 71 
 
 76 
 
 79 
 
 81 
 
 82 
 
 85 
 
 88 
 
 94 
 
 102 
 
 113 
 
 126 
 
 138 
 
 151 
 
 3 
 
 49 
 
 56 
 
 63 
 
 6S 
 
 71 
 
 72 
 
 ::i 
 
 75 
 
 77 
 
 82 
 
 91 
 
 101 
 
 113 
 
 126 
 
 138 
 
 4 
 
 44 
 
 50 
 
 56 
 
 60 
 
 63 
 
 64 
 
 65 
 
 66 
 
 68 
 
 72 
 
 80 
 
 90 
 
 101 
 
 114 
 
 126 
 
 5 
 
 40 
 
 45 
 
 50 
 
 54 
 
 56 
 
 57 
 
 57 
 
 56 
 
 59 
 
 63 
 
 70 
 
 79 
 
 90 
 
 102 
 
 115 
 
 6 
 
 39 
 
 42 
 
 47 
 
 50 
 
 51 
 
 52 
 
 51 
 
 51 
 
 53 
 
 55 
 
 61 
 
 70 
 
 -1 
 
 92 
 
 105 
 
 7 
 
 39 
 
 42 
 
 45 
 
 47 
 
 48 
 
 48 
 
 47 
 
 47 
 
 47 
 
 49 
 
 54 
 
 62 
 
 72 
 
 84 
 
 95 
 
 8 
 
 42 
 
 43 
 
 46 
 
 47 
 
 47 
 
 47 
 
 45 
 
 44 
 
 43 
 
 45 
 
 49 
 
 56 
 
 65 
 
 76 
 
 87 
 
 9 
 
 47 
 
 47 
 
 48 
 
 49 
 
 49 
 
 48 
 
 45 
 
 43 
 
 42 
 
 42 
 
 45 
 
 51 
 
 60 
 
 70 
 
 81 
 
 10 
 
 54 
 
 53 
 
 53 
 
 54 
 
 53 
 
 51 
 
 48 
 
 45 
 
 43 
 
 42 
 
 44 
 
 49 
 
 56 
 
 65 
 
 75 
 
 11 
 
 63 
 
 61 
 
 01 
 
 60 
 
 59 
 
 57 
 
 53 
 
 49 
 
 46 
 
 44 
 
 45 
 
 48 
 
 54 
 
 62 
 
 71 
 
 13 
 
 73 
 
 71 
 
 70 
 
 69 
 
 67 
 
 64 
 
 61 
 
 56 
 
 51 
 
 49 
 
 47 
 
 49 
 
 53 
 
 61) 
 
 67 
 
 13 
 
 84 
 
 83 
 
 81 
 
 80 
 
 77 
 
 74 
 
 70 
 
 64 
 
 59 
 
 55 
 
 52 
 
 52 
 
 55 
 
 59 
 
 66 
 
 14 
 
 95 
 
 94 
 
 92 
 
 91 
 
 89 
 
 85 
 
 80 
 
 74 
 
 68 
 
 62 
 
 58 
 
 57 
 
 58 
 
 61 
 
 65 
 
 15 
 
 107 
 
 106 
 
 104 
 
 103 
 
 101 
 
 97 
 
 92 
 
 85 
 
 78 
 
 72 
 
 66 
 
 63 
 
 62 
 
 63 
 
 66 
 
 16 
 
 118 
 
 117 
 
 116 
 
 115 
 
 114 
 
 10!) 
 
 104 
 
 97 
 
 89 
 
 82 
 
 75 
 
 70 
 
 68 
 
 67 
 
 69 
 
 17 
 
 12!) 
 
 IsM 
 
 128 
 
 127 
 
 125 
 
 121 
 
 116 
 
 108 
 
 100 
 
 92 
 
 84 
 
 78 
 
 71 
 
 73 
 
 73 
 
 18 
 
 13d 
 
 13d 
 
 133 
 
 137 
 
 136 
 
 132 
 
 127 
 
 119 
 
 111 
 
 102 
 
 94 
 
 87 
 
 82 
 
 79 
 
 78 
 
 19 
 
 146 
 
 146 
 
 146 
 
 146 
 
 145 
 
 141 
 
 136 
 
 129 
 
 121 
 
 112 
 
 103 
 
 95 
 
 90 
 
 86 
 
 83 
 
 20 
 
 153 
 
 1.-.:? 
 
 153 
 
 153 
 
 152 
 
 148 
 
 144 
 
 137 
 
 129 
 
 120 
 
 111 
 
 103 
 
 97 
 
 93 
 
 90 
 
 21 
 
 158 
 
 158 
 
 158 
 
 158 
 
 157 
 
 154 
 
 150 
 
 144 
 
 136 
 
 127 
 
 118 
 
 110 
 
 104 
 
 100 
 
 97 
 
 22 
 
 163 
 
 162 
 
 162 
 
 162 
 
 161 
 
 158 
 
 154 
 
 148 
 
 140 
 
 133 
 
 124 
 
 116 
 
 HI 
 
 106 
 
 103 
 
 23 
 
 1G6 
 
 165 
 
 164 
 
 163 
 
 162 
 
 100 
 
 156 
 
 150 
 
 143 
 
 136 
 
 128 
 
 121 
 
 115 
 
 112 
 
 109 
 
 24 
 
 168 
 
 166 
 
 165 
 
 164 
 
 163 
 
 160 
 
 156 
 
 151 
 
 145 
 
 138 
 
 130 
 
 124 
 
 119 
 
 116 
 
 114 
 
 25 
 
 170 
 
 167 
 
 165 
 
 161 
 
 162 
 
 160 
 
 156 
 
 151 
 
 144 
 
 138 
 
 131 
 
 125 
 
 121 
 
 119 
 
 117 
 
 26 
 
 172 
 
 168 
 
 165 
 
 163 
 
 161 
 
 158 
 
 154 
 
 149 
 
 143 
 
 136 
 
 130 
 
 124 
 
 121 
 
 119 
 
 119 
 
 27 
 
 174 
 
 169 
 
 166 
 
 163 
 
 160 
 
 157 
 
 152 
 
 147 
 
 140 
 
 134 
 
 128 
 
 123 
 
 120 
 
 119 
 
 119 
 
 28 ' 
 
 176 
 
 171 
 
 167 
 
 164 
 
 160 
 
 156 
 
 151 
 
 144 
 
 138 
 
 131 
 
 125 
 
 120 
 
 117 
 
 116 
 
 117 
 
 2'J 
 
 179 
 
 174 
 
 169 
 
 165 
 
 161 
 
 156 
 
 150 
 
 143 
 
 136 
 
 128 
 
 122 
 
 116 
 
 113 
 
 112 
 
 114 
 
 30 
 
 183 
 
 177 
 
 172 
 
 167 
 
 162 
 
 157 
 
 150 
 
 143 
 
 135 
 
 126 
 
 118 
 
 112 
 
 109 
 
 107 
 
 109 
 
 31 
 
 187 
 
 181 
 
 176 
 
 171 
 
 166 
 
 159 
 
 152 
 
 144 
 
 134 
 
 125 
 
 116 
 
 109 
 
 104 
 
 102 
 
 103 
 
 32 
 
 190 
 
 185 
 
 181 
 
 176 
 
 170 
 
 163 
 
 155 
 
 146 
 
 1 35 
 
 125 
 
 114 
 
 106 
 
 100 
 
 97 
 
 97 
 
 33 
 
 194 
 
 190 
 
 186 
 
 182 
 
 176 
 
 169 
 
 160 
 
 150 
 
 138 
 
 126 
 
 114 
 
 104 
 
 96 
 
 92 
 
 91 
 
 34 
 
 198 
 
 195 
 
 192 
 
 188 
 
 183 
 
 176 
 
 166 
 
 156 
 
 143 
 
 12!i 
 
 115 
 
 104 
 
 94 
 
 88 
 
 86 
 
 35 
 
 201 
 
 200 
 
 198 
 
 195 
 
 190 
 
 183 
 
 174 
 
 1G2 
 
 149 
 
 134 
 
 119 
 
 1 05 
 
 94 
 
 86 
 
 82 
 
 36 
 
 204 
 
 204 
 
 203 
 
 2H2 
 
 197 
 
 191 
 
 182 
 
 170 
 
 156 
 
 140 
 
 124 
 
 108 
 
 95 
 
 86 
 
 80 
 
 37 
 
 205 
 
 208 
 
 208 
 
 207 
 
 204 
 
 199 
 
 191 
 
 179 
 
 164 
 
 148 
 
 131 
 
 114 
 
 99 
 
 87 
 
 80 
 
 38 
 
 205 
 
 208 
 
 211 
 
 212 
 
 211 
 
 206 
 
 199 
 
 188 
 
 174 
 
 157 
 
 139 
 
 121 
 
 105 
 
 92 
 
 83 
 
 39 
 
 204 
 
 209 
 
 213 
 
 216 
 
 216 
 
 213 
 
 207 
 
 198 
 
 184 
 
 167 
 
 149 
 
 130 
 
 113 
 
 98 
 
 88 
 
 40 
 
 201 
 
 208 
 
 214 
 
 218 
 
 220 
 
 219 
 
 215 
 
 206 
 
 194 
 
 178 
 
 160 
 
 141 
 
 "123 
 
 107 
 
 95 
 
 41 
 
 197 
 
 205 
 
 213 
 
 219 
 
 223 
 
 224 
 
 221 
 
 215 
 
 203 
 
 189 
 
 171 
 
 153 
 
 134 
 
 118 
 
 105 
 
 42 
 
 192 
 
 202 
 
 211 
 
 219 
 
 225 
 
 228 
 
 226 
 
 222 
 
 213 
 
 200 
 
 183 
 
 165 
 
 147 
 
 130 
 
 116 
 
 43 
 
 186 
 
 197 
 
 208 
 
 217 
 
 225 
 
 230 
 
 231 
 
 229 
 
 221 
 
 211 
 
 196 
 
 178 
 
 161 
 
 143 
 
 12!) 
 
 44 
 
 179 
 
 192 
 
 203 
 
 214 
 
 224 
 
 231 
 
 235 
 
 234 | 
 
 229 
 
 221 
 
 207 
 
 191 
 
 175 
 
 158 
 
 143 
 
 45 
 
 172 
 
 185 
 
 198 
 
 210 
 
 222 
 
 231 
 
 237 
 
 239 
 
 236 
 
 230 
 
 219 
 
 204 
 
 188 
 
 172 
 
 157 
 
 46 
 
 165 
 
 178 
 
 192 
 
 206 
 
 218 
 
 230 
 
 238 
 
 242 
 
 242 
 
 238 
 
 229 
 
 216 
 
 201 
 
 186 
 
 171 
 
 47 
 
 157 
 
 171 
 
 186 
 
 200 
 
 214 
 
 227 
 
 238 
 
 245 
 
 247 
 
 245 
 
 238 
 
 227 
 
 213 
 
 199 
 
 184 
 
 48 
 
 150 
 
 163 
 
 178 
 
 194 
 
 209 
 
 224 
 
 236 
 
 246 
 
 250 
 
 250 
 
 246 
 
 237 
 
 224 
 
 211. 
 
 196 
 
 49 
 
 142 
 
 156 
 
 171 
 
 187 
 
 204 
 
 220 
 
 234 
 
 245 
 
 252 
 
 254 
 
 252 
 
 245 
 
 234 
 
 222 
 
 208 
 
 50 
 
 134 
 
 147 
 
 162 
 
 179 
 
 197 
 
 214 
 
 230 
 
 243 
 
 252 
 
 257 
 
 256 
 
 251 
 
 242 
 
 231 
 
 218 
 
 51 
 
 136 
 
 Kill 
 
 154 
 
 170 
 
 189 
 
 207 
 
 225 
 
 239 
 
 250 
 
 257 
 
 259 
 
 255 
 
 248 
 
 238 
 
 226 
 
 52 
 
 117 
 
 129 
 
 144 
 
 161 
 
 180 
 
 19!) 
 
 218 
 
 234 246 
 
 25<) 
 
 259 
 
 258 
 
 252 
 
 243 
 
 232 
 
 53 
 
 108 
 
 119 
 
 133 
 
 150 
 
 169 
 
 189 
 
 209 
 
 226 
 
 241 
 
 252 
 
 257 
 
 258 
 
 254 
 
 247 
 
 237 
 
 54 
 
 99 
 
 109 
 
 122 
 
 138 
 
 157 
 
 178 
 
 198 
 
 217 
 
 233 
 
 245 
 
 253 
 
 256 
 
 254 
 
 249 
 
 240 
 
 55 
 
 90 
 
 98 
 
 110 
 
 125 
 
 144 
 
 164 
 
 185 
 
 205 
 
 223 
 
 237 
 
 247 
 
 251 
 
 252 
 
 248 
 
 242 
 
 56 
 
 81 
 
 87 
 
 97 
 
 111 
 
 129 
 
 149 
 
 170 
 
 191 
 
 210 
 
 226 
 
 238 
 
 245 
 
 248 
 
 246 
 
 241 
 
 57 
 
 72 
 
 76 
 
 84 
 
 96 
 
 113 
 
 133 
 
 154 
 
 175 
 
 196 
 
 213 
 
 227 
 
 236 
 
 241 
 
 242 
 
 239 
 
 58 
 
 63 
 
 64 
 
 70. 
 
 81 
 
 96 
 
 115 
 
 136 
 
 158 
 
 179 
 
 198 
 
 214 
 
 225 
 
 233 
 
 236 
 
 835 
 
 59 
 
 55 
 
 54 
 
 57 
 
 66 
 
 79 
 
 97 
 
 117 
 
 139 
 
 161 
 
 181 
 
 199 
 
 212 
 
 222 
 
 228 
 
 230 
 
 60 
 
 4!) 
 
 45 
 
 4S 
 
 51 
 
 63 
 
 79 
 
 98 
 
 119 
 
 141 
 
 163 
 
 182 
 
 198 
 
 210 
 
 218 
 
 223 
 
 The perturbations are expressed in hundredths of a second of arc. 
 
TAIILK XXII. 
 
 :*:* 
 
 Perturbations of the Ln->ititili- /<// th<- l-'.nrih. 
 
 llori/.tiiital Argument = I. 
 
 (.umlaut ailil.-il l'..|tl. IVri.ul ufAr.-.!..!. MI \ 1 . _' HI iimls. 
 
 
 .1 
 
 .1 
 
 ,i 
 
 .1 .1 
 
 ,1 
 
 ,l 
 
 ,i 
 
 ,1 
 
 ,i 
 
 ,1 
 
 ,i 
 
 d 
 
 ,i 
 
 4 
 
 Ari M 
 
 120 
 
 13* 
 
 136 
 
 111 
 
 1*3 
 
 100 
 
 li 
 
 IT 
 
 INI 
 
 l3 
 
 300 
 
 30* 
 
 II 
 
 331 
 
 333 
 
 
 
 188 
 
 105 
 
 801 
 
 1 1 
 
 
 
 
 
 
 911 
 
 813 
 
 -.'1 1 
 
 914 
 
 211 
 
 
 1 
 
 17.-. 
 
 183 
 
 iao 
 
 193 
 
 193 
 
 197 
 
 198 
 
 901 
 
 804 
 
 
 919 
 
 915 
 
 816 
 
 816 
 
 .'II 
 
 2 
 
 Ii, -J 170 
 
 177 
 
 189 
 
 1-:, 
 
 1-7 
 
 100 
 
 103 
 
 108 
 
 
 
 813 
 
 -'17 
 
 918 
 
 916 
 
 3 
 
 llii i.> 
 
 166 
 
 171 
 
 171 
 
 ITS 
 
 l-l 
 
 i-:, 
 
 101 
 
 107 
 
 '1 
 
 211 
 
 216 -.'l:i 
 
 -'is 
 
 4 
 
 I3B 
 
 nr 
 
 156 
 
 li,i 
 
 164 
 
 I6t) 
 
 17'J 
 
 177 
 
 183 
 
 u-o 
 
 190 
 
 
 Jl 1 
 
 818 
 
 810 
 
 5 
 
 197 
 
 136 
 
 1 II 
 
 ISO 
 
 155 
 
 158 
 
 163 
 
 168 
 
 17:, 
 
 I-:: 
 
 199 
 
 
 Jin 
 
 816 
 
 810 
 
 6 
 
 III, 
 
 197 
 
 134 
 
 141 
 
 145 
 
 140 
 
 154 
 
 ISO 
 
 166 
 
 176 
 
 186 
 
 1% 
 
 
 211 
 
 ji- 
 
 7 Iu7 
 
 117 
 
 1 25 
 
 139 
 
 137 
 
 1 M 
 
 145 
 
 151 
 
 158 
 
 ton 
 
 170 
 
 I'.HI '.Ml 
 
 -.'II 
 
 91? 
 
 - 
 
 BO 
 
 100 
 
 117 
 
 I-JI 
 
 138 
 
 139 
 
 137 
 
 1 1-J 
 
 150 
 
 ISO 
 
 171 
 
 is: l!Xi 
 
 
 816 
 
 D 
 
 99 
 
 101 
 
 100 
 
 116 
 
 120 
 
 184 
 
 188 
 
 134 
 
 Ml 
 
 161 
 
 164 
 
 177 
 
 191 
 
 J 1 1 
 
 814 
 
 in 
 
 BE 
 
 96 
 
 108 
 
 108 
 
 119 
 
 116 
 
 180 
 
 1 25 
 
 i:i:l 
 
 149 
 
 156 
 
 17(1 
 
 186 
 
 
 813 
 
 ii 
 
 80 
 
 
 06 
 
 101 
 
 106 
 
 100 
 
 113 
 
 117 
 
 194 
 
 135 
 
 1 1- 
 
 164 
 
 i- i 
 
 IIKJ 
 
 Jll 
 
 19 
 
 7(i 
 
 -1 
 
 00 
 
 96 
 
 90 
 
 109 
 
 106 
 
 no 
 
 117 
 
 19} 
 
 1 II 
 
 157 
 
 175 
 
 109 
 
 830 
 
 13 
 
 73 
 
 BO 
 
 
 91 
 
 93 
 
 95 
 
 
 109 
 
 100 
 
 11!) 
 
 134 
 
 150 
 
 160 
 
 188 
 
 
 14 
 
 71 
 
 77 
 
 81 
 
 85 
 
 87 
 
 89 
 
 u 
 
 05 
 
 109 
 
 118 
 
 126 
 
 149 
 
 163 
 
 184 
 
 -.' 'l 
 
 15 
 
 71 
 
 7.'. 
 
 78 
 
 81 
 
 83 
 
 84 
 
 86 
 
 89 
 
 M 
 
 lor, 
 
 Illl 
 
 136 
 
 157 
 
 17'J 
 
 .'ii 
 
 16 
 
 7',> 
 
 75 
 
 77 
 
 79 
 
 80 
 
 80 
 
 -. 
 
 -1 
 
 89 
 
 W 
 
 Ill 
 
 180 
 
 150 
 
 171 
 
 I!i7 
 
 17 
 
 71 
 
 76 
 
 77 
 
 78 
 
 n 
 
 77 
 
 78 
 
 7!l 
 
 83 
 
 99 
 
 106 
 
 1 22 
 
 143 
 
 167 
 
 108 
 
 1- 
 
 78 
 
 78 
 
 7!) 
 
 711 
 
 78 
 
 7li 
 
 76 
 
 76 
 
 7!) 
 
 96 
 
 
 11. -> 
 
 136 
 
 160 
 
 l-:, 
 
 10 
 
 83 
 
 83 
 
 82 
 
 81 
 
 79 
 
 77 
 
 7:, 
 
 74 
 
 76 
 
 82 
 
 92 
 
 108 
 
 128 
 
 161 
 
 177 
 
 90 
 
 HO 
 
 88 
 
 86 
 
 85 
 
 82 
 
 79 
 
 71 i 
 
 73 
 
 74 
 
 78 
 
 87 
 
 101 
 
 119 
 
 1 1-.' 
 
 168 
 
 81 
 
 96 
 
 94 
 
 ga 
 
 90 
 
 87 
 
 
 78 
 
 71 
 
 7:! 
 
 7:. 
 
 -J 
 
 94 
 
 HI 
 
 189 
 
 157 
 
 89 
 
 109 
 
 101 
 
 OB 
 
 96 
 
 99 
 
 87 
 
 82 
 
 77 
 
 74 
 
 71 
 
 78 
 
 
 103 
 
 189 
 
 146 
 
 23 
 
 108 
 
 107 
 
 105 
 
 103 
 
 !> 
 
 93 
 
 87 
 
 81 
 
 7.-, 
 
 73 
 
 75 
 
 83 
 
 95 
 
 119 
 
 134 
 
 M 
 
 114 
 
 113 
 
 112 
 
 110 
 
 105 
 
 100 
 
 99 
 
 
 78 
 
 74 
 
 73 
 
 78 
 
 87 
 
 102 
 
 EU 
 
 85 
 
 118 
 
 118 
 
 117 
 
 116 
 
 111 
 
 106 
 
 98 
 
 90 
 
 82 
 
 76 
 
 79 
 
 71 
 
 HI 
 
 98 
 
 no 
 
 96 
 
 190 
 
 121 
 
 as 
 
 QU 
 
 117 
 
 119 
 
 104 
 
 06 
 
 86 
 
 78 
 
 73 
 
 78 
 
 71, 
 
 
 99 
 
 B7 
 
 131 
 
 123 
 
 i-.v, 
 
 ce 
 
 rag 
 
 117 
 
 110 
 
 101 
 
 90 
 
 -l 
 
 71 
 
 71 
 
 79 
 
 78 
 
 90 
 
 86 
 
 1-J.i 
 
 183 
 
 BK 
 
 127 
 
 1 25 
 
 121 
 
 115 
 
 106 
 
 06 
 
 -1 
 
 76 
 
 71 
 
 (in 
 
 73 
 
 m 
 
 as 
 
 117 
 
 121 
 
 125 
 
 127 
 
 127 
 
 IM 
 
 118 
 
 110 
 
 99 
 
 88 
 
 78 
 
 72 
 
 68 
 
 0:1 
 
 7li 
 
 30 
 
 113 
 
 nr 
 
 122 
 
 126 
 
 127 
 
 126 
 
 121 
 
 113 
 
 IIKI 
 
 92 
 
 81 
 
 74 
 
 69 
 
 87 
 
 71 
 
 M 
 
 107 
 
 112 
 
 II- 
 
 1X3 
 
 MS 
 
 185 
 
 121 
 
 115 
 
 106 
 
 96 
 
 
 77 
 
 70 
 
 67 
 
 69 
 
 SB 
 
 100 
 
 KKi 
 
 112 
 
 118 
 
 122 
 
 183 
 
 191 
 
 117 
 
 108 
 
 09 
 
 88 
 
 
 72 
 
 68 
 
 68 
 
 33 
 
 94 
 
 BO 
 
 106 
 
 113 
 
 118 
 
 121 
 
 190 
 
 117 
 
 no 
 
 101 
 
 98 
 
 83 
 
 7(i 
 
 71 
 
 (ill 
 
 34 
 
 88 
 
 99 
 
 00 
 
 107 
 
 113 
 
 117 
 
 118 
 
 117 
 
 in 
 
 104 
 
 M 
 
 87 
 
 79 
 
 74 
 
 71 
 
 35 
 
 83 
 
 86 
 
 93 
 
 101 
 
 108 
 
 113 
 
 116 
 
 116 
 
 112 
 
 106 
 
 98 
 
 91 
 
 83 
 
 77 
 
 74 
 
 M 
 
 7!) 
 
 82 
 
 88 
 
 96 
 
 103 
 
 no 
 
 114 
 
 115 
 
 113 
 
 108 
 
 109 
 
 !)5 
 
 87 
 
 B8 
 
 78 
 
 37 
 
 78 
 
 7!) 
 
 85 
 
 99 
 
 100 
 
 107 
 
 112 
 
 II 1 
 
 113 
 
 110 
 
 106 
 
 90 
 
 99 
 
 86 
 
 82 
 
 38 
 
 78 
 
 70 
 
 83 
 
 90 
 
 98 
 
 106 
 
 111 
 
 114 
 
 116 
 
 119 
 
 In- 
 
 103 
 
 06 
 
 01 
 
 86 
 
 3! 
 
 82 
 
 81 
 
 84 
 
 90 
 
 98 
 
 III.', 
 
 111 
 
 115 
 
 117 
 
 115 
 
 Ill 
 
 107 
 
 100 
 
 06 
 
 91 
 
 40 
 
 88 
 
 85 
 
 87 
 
 93 
 
 100 
 
 107 
 
 113 
 
 118 
 
 no 
 
 118 
 
 115 
 
 111 
 
 111.-, 
 
 100 
 
 B6 
 
 41 
 
 96 
 
 08 
 
 93 
 
 97 
 
 104 
 
 110 
 
 117 
 
 121 
 
 193 
 
 199 
 
 II!) 
 
 116 
 
 100 
 
 104 
 
 90 
 
 49 
 
 106 
 
 101 
 
 101 
 
 103 
 
 109 
 
 lir, 
 
 121 
 
 126 
 
 127 
 
 127 
 
 124 
 
 180 
 
 114 
 
 109 
 
 104 
 
 43 
 
 118 
 
 III 
 
 110 
 
 112 
 
 116 
 
 122 
 
 187 
 
 131 
 
 133 
 
 133 
 
 rag 
 
 196 
 
 II!) 
 
 114 
 
 10!) 
 
 44 
 
 131 
 
 123 
 
 120 
 
 mi 
 
 MS 
 
 130 
 
 135 
 
 rae 
 
 139 
 
 139 
 
 136 
 
 131 
 
 186 
 
 11:1 
 
 114 
 
 45 
 
 144 
 
 136 
 
 132 
 
 132 
 
 134 
 
 138 
 
 142 
 
 145 
 
 146 
 
 146 
 
 142 
 
 137 
 
 131 
 
 125 
 
 120 
 
 4(3 
 
 158 
 
 14!) 
 
 144 
 
 142 
 
 144 
 
 147 
 
 151 
 
 153 
 
 154 
 
 163 
 
 140 
 
 144 
 
 138 
 
 138 
 
 196 
 
 47 
 
 171 
 
 llil 
 
 156 
 
 153 
 
 153 
 
 156 
 
 ISO 
 
 169 
 
 161 
 
 160 
 
 156 
 
 151 
 
 146 
 
 13!) 
 
 133 
 
 48 
 
 184 
 
 173 
 
 166 
 
 163 
 
 163 
 
 164 
 
 167 
 
 168 
 
 169 
 
 167 
 
 163 
 
 158 
 
 159 
 
 146 
 
 140 
 
 49 
 
 186 
 
 184 
 
 176 
 
 172 
 
 171 
 
 172 
 
 174 
 
 17.', 
 
 176 
 
 174 
 
 170 
 
 res 
 
 160 
 
 i:,3 
 
 148 
 
 50 
 
 2(T> 
 
 104 
 
 185 
 
 181 
 
 179 
 
 179 
 
 180 
 
 181 
 
 182 
 
 180 
 
 177 
 
 ITS 
 
 166 
 
 160 
 
 155 
 
 51 
 
 21:1 
 
 202 
 
 103 
 
 188 
 
 1-:, 
 
 1 86 
 
 186 
 
 '187 
 
 187 
 
 186 
 
 itg 
 
 178 
 
 179 
 
 167 
 
 169 
 
 59 
 
 883 
 
 800 
 
 wo 
 
 194 
 
 191 
 
 190 
 
 191 
 
 192 
 
 192 
 
 191 
 
 i 
 
 I-l 
 
 178 
 
 173 
 
 168 
 
 53 
 
 226 
 
 215 
 
 206 
 
 200 
 
 196 
 
 1!).-, 
 
 1 >:. 
 
 1% 
 
 196 
 
 196 
 
 109 
 
 188' 
 
 183 
 
 178 
 
 173 
 
 :,i 
 
 230 
 
 221) 
 
 211 
 
 
 201 
 
 1W 
 
 l!l 
 
 19!) 
 
 800 
 
 180 
 
 106 
 
 192 
 
 187 
 
 189 
 
 177 
 
 55 
 
 833 
 
 224 
 
 215 
 
 20!) 
 
 205 
 
 202 
 
 202 
 
 m 
 
 202 
 
 201 
 
 I!'- 
 
 roe 
 
 no 
 
 l-l 
 
 179 
 
 56 
 
 234 
 
 226 
 
 818 
 
 213 
 
 208 
 
 206 
 
 204 
 
 805 
 
 805 
 
 203 
 
 800 
 
 107 
 
 1!H 
 
 IS, 
 
 l-l 
 
 57 
 
 234 
 
 227 
 
 221 
 
 215 211 
 
 1 ' 
 
 807 
 
 808 
 
 207 
 
 805 
 
 809 
 
 i e 
 
 199 
 
 186 
 
 180 
 
 :,- 
 
 232 
 
 227 
 
 222 
 
 Jl- 214 
 
 212 
 
 210 
 
 210 
 
 800 
 
 
 80S 
 
 108 
 
 199 
 
 185 
 
 17!) 
 
 BO 
 
 
 B86 
 
 223 
 
 219 
 
 216 
 
 214 
 
 213 
 
 212 
 
 211 
 
 
 -"l 
 
 198 
 
 191 
 
 1-1 
 
 177 
 
 GO 
 
 224 
 
 884 
 
 222 
 
 220 
 
 218 
 
 216 
 
 815 
 
 215 
 
 819 
 
 210 
 
 
 198 
 
 r.M 
 
 1-:; 
 
 171 
 
 Add 147.64 to Arg. XI. when 224'".7 is subtra. t. ,1 iVuni Arg. I. 
 
TABLE XXII. 
 
 Perturbations of tin- Longitude bij the Earth. 
 
 
 Horizontal Argument = I. 
 
 Constant added 1 ; '.40. Period of Argument 1., 224 J .7. 
 
 
 d 
 
 d 
 
 did d 
 
 d 
 
 d 
 
 d 
 
 d d 
 
 d 
 
 rt 
 
 d 
 
 d 
 
 d 
 
 Arg.XI 
 
 
 
 | 
 
 16 
 
 ! 24 
 
 33 
 
 4O 
 
 48 
 
 56 
 
 01 
 
 72 
 
 80 
 
 
 
 96 
 
 104 
 
 112 
 
 | 
 
 60 
 
 49 
 
 45 
 
 45 
 
 51 
 
 63 
 
 .79 
 
 98 
 
 119 
 
 141 
 
 163 
 
 182 
 
 198 
 
 210 
 
 218 
 
 223 
 
 61 
 
 44 
 
 37 
 
 85 
 
 38 
 
 47 
 
 62 
 
 79 
 
 99 
 
 122 
 
 143 
 
 164 
 
 182 
 
 196 
 
 207 
 
 214 
 
 ea 
 
 41 
 
 31 
 
 26 
 
 27 
 
 33 
 
 41 
 
 60 
 
 80 
 
 102 
 
 121 
 
 146 
 
 164 
 
 181 
 
 194 
 
 203 
 
 G3 
 
 41 
 
 28 
 
 21 
 
 18 
 
 21 
 
 30 
 
 44 
 
 62 
 
 83 
 
 105 
 
 127 
 
 147 
 
 164 
 
 179 
 
 191 
 
 64 
 
 43 
 
 .28 
 
 18 
 
 12 
 
 12 
 
 18 
 
 30 
 
 45 
 
 65 
 
 86 
 
 108 
 
 128 
 
 147 
 
 164 
 
 177 
 
 65 
 
 47 
 
 31 
 
 18 
 
 10 
 
 7 
 
 10 
 
 18 
 
 32 
 
 49 
 
 69 
 
 90 
 
 111 
 
 130 
 
 147 
 
 162 
 
 66 
 
 54 
 
 36 
 
 21 
 
 11 
 
 5 
 
 4 
 
 10 
 
 21 
 
 36 
 
 54 
 
 74 
 
 94 
 
 113 
 
 131 
 
 147 
 
 67 
 
 63 
 
 44 
 
 28 
 
 15 
 
 6 
 
 3 
 
 6 
 
 14 
 
 26 
 
 42 
 
 60 
 
 79 
 
 97 
 
 U5 
 
 131 
 
 68 
 
 73 
 
 54 
 
 37 
 
 23 
 
 12 
 
 6 
 
 5 
 
 10 
 
 20 
 
 33 
 
 48 
 
 66 
 
 83 
 
 99 
 
 115 
 
 60 
 
 85 
 
 67 
 
 49 
 
 33 
 
 21 
 
 12 
 
 9 
 
 10 
 
 16 
 
 27 
 
 40 
 
 55 
 
 70 
 
 85 
 
 100 
 
 70 
 
 97 
 
 80 
 
 63 
 
 46 
 
 32 
 
 21 
 
 15 
 
 13 
 
 16 
 
 24 
 
 34 
 
 46 
 
 60 
 
 73 
 
 87 
 
 71 
 
 110 
 
 94 
 
 78 
 
 61 
 
 45 
 
 33 
 
 24 
 
 20 
 
 20 
 
 24 
 
 31 
 
 41 
 
 52 
 
 63 
 
 75 
 
 72 
 
 13 
 
 109 
 
 93 
 
 76 
 
 60 47 
 
 36 
 
 29 
 
 26 
 
 27 
 
 31 
 
 38 
 
 46 
 
 55 
 
 65 
 
 73 
 
 134 
 
 123 
 
 1(18 
 
 92 
 
 76 
 
 62 
 
 49 
 
 40 
 
 35 
 
 33 
 
 34 
 
 38 
 
 44 
 
 51 
 
 58 
 
 74 
 
 144 
 
 135 
 
 122 
 
 107 
 
 92 
 
 77 
 
 64 
 
 53 
 
 45 
 
 41 
 
 40 
 
 41 
 
 44 
 
 48 
 
 54 
 
 75 
 
 153 
 
 145 
 
 135 122 
 
 107 
 
 92 
 
 78 
 
 66 
 
 57 
 
 51 
 
 47 
 
 46 
 
 47 
 
 49 
 
 52 
 
 76 
 
 160 
 
 155 
 
 146 134 
 
 121 
 
 107 
 
 93 
 
 80 
 
 69 
 
 62 
 
 56 
 
 53 
 
 52 
 
 52 
 
 53 
 
 77 
 
 165 
 
 162 
 
 155 145 
 
 133 
 
 120 
 
 106 
 
 93 
 
 82 
 
 73 
 
 66 
 
 62 
 
 59 
 
 57 
 
 56 
 
 78 
 
 169 
 
 167 
 
 162 153 
 
 144 
 
 131 
 
 118 
 
 106 
 
 94 
 
 85 
 
 77 
 
 71 
 
 67 
 
 64 
 
 61 
 
 79 
 
 171 
 
 170 
 
 167 
 
 160 
 
 152 
 
 141 
 
 129 
 
 117 
 
 106 
 
 96 
 
 88 
 
 81 
 
 76 
 
 71 
 
 67 
 
 80 
 
 172 
 
 172 
 
 170 
 
 165 
 
 158 
 
 149 
 
 138 
 
 127 
 
 116 
 
 107 
 
 99 
 
 91 
 
 85 
 
 80 
 
 75 
 
 81 
 
 172 
 
 172 
 
 171 
 
 168 
 
 163 
 
 155 
 
 146 
 
 136 
 
 126 
 
 117 
 
 108 
 
 101 
 
 95 
 
 89 
 
 83 
 
 82 
 
 171 
 
 172 
 
 171 
 
 169 
 
 166 
 
 160 
 
 152 
 
 144 
 
 134 
 
 126 
 
 118 
 
 110 
 
 104 
 
 97 
 
 90 
 
 83 
 
 170 
 
 171 
 
 171 
 
 170 
 
 167 
 
 163 
 
 157 
 
 150 
 
 142 
 
 134 
 
 126 
 
 119 
 
 112 
 
 105 
 
 98 
 
 84 
 
 169 
 
 169 
 
 169 
 
 169 
 
 168 
 
 165 
 
 161 
 
 155 
 
 148 
 
 141 
 
 134 
 
 126 
 
 120 
 
 112 
 
 105 
 
 85 
 
 168 
 
 168 
 
 168 
 
 168 
 
 168 
 
 166 
 
 163 
 
 158 
 
 153 
 
 147 
 
 140 
 
 133 
 
 126 
 
 119 
 
 111 
 
 86 
 
 108 
 
 166 
 
 166 
 
 167 
 
 167 
 
 167 
 
 165 
 
 161 
 
 157 
 
 152 
 
 145 
 
 139 
 
 132 
 
 124 
 
 116 
 
 87 
 
 167 
 
 165 
 
 164 
 
 166 
 
 166 
 
 167 
 
 166 
 
 163 
 
 160 
 
 156 
 
 150 
 
 143 
 
 136 
 
 12!) 
 
 120 
 
 88 
 
 167 
 
 164 
 
 163 
 
 165 
 
 164 
 
 166 
 
 166 
 
 165 
 
 163 
 
 159 
 
 153 
 
 147 
 
 140 
 
 133 
 
 123 
 
 8!) 
 
 167 
 
 163 
 
 161 
 
 162 
 
 163 
 
 165 
 
 166 
 
 166 
 
 164 
 
 161 
 
 156 
 
 151 
 
 144 
 
 136 
 
 126 
 
 90 
 
 167 
 
 162 
 
 160 i 160 
 
 162 
 
 163 
 
 165 
 
 166 
 
 165 
 
 163 
 
 159 
 
 154 
 
 147 
 
 139 
 
 129 
 
 !H 
 
 168 
 
 162 
 
 159 I 158 
 
 159 
 
 161 
 
 164 
 
 165 
 
 165 
 
 164 
 
 161 
 
 156 
 
 150 
 
 142 
 
 132 
 
 9SJ 
 
 168 
 
 161 
 
 157 156 
 
 157 
 
 159 
 
 162 
 
 164 
 
 165 
 
 165 
 
 162 
 
 158 
 
 153 
 
 145 
 
 136 
 
 93 
 
 168 
 
 160 
 
 156 153 
 
 154 
 
 156 
 
 159 
 
 162 
 
 164 
 
 165 
 
 163 
 
 161 
 
 156 
 
 148 
 
 139 
 
 94 
 
 168 
 
 16i) 
 
 154 
 
 151 
 
 151 
 
 152 
 
 156 
 
 159 
 
 162 
 
 164 
 
 164 
 
 163 
 
 158 
 
 152 
 
 144 
 
 95 
 
 169 
 
 159 
 
 153 
 
 149 
 
 148 
 
 149 
 
 152 
 
 156 
 
 160 
 
 163 
 
 165 
 
 164 
 
 162 
 
 157 
 
 149 
 
 96 
 
 169 
 
 159 
 
 152 
 
 147 
 
 145 
 
 146 
 
 149 
 
 153 
 
 158 
 
 162 
 
 165 
 
 166 
 
 165 
 
 161 
 
 154 
 
 97 
 
 170 
 
 159 
 
 151 
 
 145 
 
 143 
 
 143 
 
 145 
 
 150 
 
 155 
 
 161 
 
 165 
 
 168 
 
 168 
 
 166 
 
 160 
 
 08 
 
 171 
 
 160 
 
 151 
 
 145 
 
 141 
 
 140 
 
 143 
 
 147 
 
 153 
 
 159 
 
 165 
 
 169 
 
 171 
 
 171 
 
 167 
 
 9!) 
 
 172 
 
 162 
 
 152 
 
 145 
 
 140 
 
 139 
 
 140 
 
 145 
 
 151 
 
 158 
 
 164 
 
 171 
 
 174 
 
 175 
 
 174 
 
 100 
 
 171 
 
 164 
 
 154 
 
 146 
 
 141 
 
 138 
 
 139 
 
 143 
 
 150 
 
 157 
 
 165 
 
 172 
 
 177 
 
 180 
 
 180 
 
 101 
 
 176 
 
 167 
 
 158 
 
 149 
 
 143 
 
 140 
 
 140 
 
 143 
 
 149 
 
 157 
 
 165 
 
 173 
 
 180 
 
 184 
 
 186 
 
 102 
 
 179 
 
 171 
 
 162 
 
 163 
 
 146 
 
 142 
 
 141 
 
 144 
 
 149 
 
 157 
 
 166 
 
 175 
 
 183 
 
 189 
 
 191 
 
 103 
 
 182 
 
 175 
 
 166 
 
 158 
 
 151 
 
 146 
 
 144 
 
 146 
 
 151 
 
 158 
 
 167 
 
 176 
 
 185 
 
 192 
 
 196 
 
 104 
 
 184 
 
 179 
 
 171 
 
 163 
 
 156 
 
 151 
 
 149 
 
 149 
 
 153 
 
 160 
 
 169 
 
 178 
 
 187 
 
 195 
 
 200 
 
 105 
 
 187 
 
 183 
 
 177 
 
 170 
 
 163 
 
 157 
 
 154 
 
 154 
 
 157 
 
 163 
 
 171 
 
 180 
 
 189 
 
 198 
 
 203 
 
 106 
 
 188 
 
 186 
 
 181 
 
 176 
 
 16!) 
 
 164 
 
 160 
 
 159 
 
 161 
 
 166 
 
 173 
 
 182 
 
 191 
 
 200 
 
 236 
 
 107 
 
 188 
 
 188 
 
 185 
 
 181 
 
 176 
 
 170 
 
 167 
 
 165 
 
 166 
 
 16!) 
 
 175 
 
 184 
 
 193 
 
 201 
 
 208 
 
 108 
 
 186 
 
 18!) 
 
 188 
 
 185 
 
 181 
 
 176 
 
 173 
 
 170 
 
 170 
 
 173 
 
 178 
 
 186 
 
 194 
 
 203 
 
 210 
 
 109 
 
 182 
 
 187 
 
 189 
 
 188 
 
 185 
 
 181 
 
 178 
 
 175 
 
 175 
 
 176 
 
 180 
 
 187 
 
 195 
 
 203 
 
 211 
 
 110 
 
 177 
 
 184 
 
 188 
 
 188 
 
 187 | 184 
 
 181 
 
 179 
 
 178 
 
 179 
 
 182 
 
 188 
 
 195 
 
 204 
 
 212 
 
 111 
 
 170 
 
 178 
 
 183 
 
 186 
 
 186 
 
 185 
 
 183 
 
 181 
 
 180 
 
 180 
 
 183 
 
 189 
 
 195 
 
 203 
 
 211 
 
 112 
 
 161 
 
 171 
 
 177 
 
 182 
 
 183 
 
 184 
 
 182 
 
 181 
 
 180 
 
 181 
 
 183 
 
 188 
 
 194 
 
 202 
 
 210 
 
 113 
 
 150 
 
 161 
 
 168 
 
 171 
 
 177 179 
 
 179 
 
 17!) 
 
 179 
 
 179 
 
 181 
 
 186 
 
 192 
 
 201 
 
 209 
 
 114 
 
 138 
 
 149 
 
 157 
 
 164 
 
 169 
 
 172. 
 
 174 
 
 175 
 
 175 
 
 176 
 
 178 
 
 183 
 
 189 
 
 198 
 
 206 
 
 115 
 
 125 
 
 136 
 
 145 
 
 153 
 
 158 163 
 
 166 
 
 168 
 
 169 
 
 171 
 
 174 
 
 179 
 
 185 
 
 193 
 
 203 
 
 116 
 
 112 
 
 122 
 
 131 
 
 140 
 
 146 152 
 
 156 
 
 159 
 
 162 
 
 164 
 
 168 
 
 173 
 
 179 
 
 188 
 
 198 
 
 117 
 
 99 
 
 108 
 
 117 
 
 125 
 
 132 ! 139 
 
 144 
 
 149 
 
 158 
 
 156 
 
 160. 
 
 165 
 
 172 
 
 181 
 
 192 
 
 118 
 
 87 
 
 95 
 
 102 
 
 110 
 
 118 
 
 125 
 
 132 
 
 137 
 
 142 
 
 146 
 
 151 
 
 157 
 
 164 
 
 174 
 
 184 
 
 119 
 
 76 
 
 82 
 
 89 
 
 96 
 
 104 
 
 111 
 
 11!) 
 
 125 
 
 131 
 
 136 
 
 Ml 
 
 148 
 
 155 
 
 164 
 
 175 
 
 120 
 
 67 
 
 71 
 
 77 
 
 83 
 
 90 
 
 98 
 
 106 
 
 113 
 
 119 
 
 125 
 
 131 
 
 138 
 
 145 
 
 154 
 
 165 
 
 The perturbations arc expressed in Imndredths of a second of arc, 
 
TABLE XXII. 
 
 /' rturbiilinnx .//"// Lmigituih- Inj tlir Kartli. 
 
 Horizontal Argument = I. 
 
 r.m-t:nit aild..,l 1" 1 > IVn-d of Argument XI ,2-10 units. 
 
 
 d 
 
 d 
 
 d 
 
 d 
 
 .) 
 
 ,1 
 
 ,1 
 
 ,l 
 
 d 
 
 d d 
 
 d 
 
 d 
 
 ,1 
 
 .1 
 
 Arg. XI 
 
 
 iaa 
 
 i:tO 
 
 111 
 
 i.ia 
 
 160 
 
 1CN 
 
 176 
 
 INI 
 
 
 aoo 
 
 aoM 
 
 a 10 
 
 aai 
 
 a.ta 
 
 60 
 
 994 
 
 221 
 
 999 
 
 99 ' 
 
 918 
 
 216 
 
 215 
 
 916 
 
 913 
 
 210 
 
 205 
 
 198 
 
 191 
 
 183 
 
 174 
 
 til 
 
 21 a 
 
 910 
 
 21!' 21!) 
 
 21- 21- 
 
 217 
 
 917 
 
 215 
 
 211 
 
 
 109 
 
 100 
 
 l-l 
 
 171 
 
 69 
 
 900 
 
 913 
 
 2 Hi 217 
 
 818 
 
 818 
 
 918 
 
 918 
 
 217 
 
 213 
 
 2, i7 
 
 
 100 
 
 ISO 
 
 170 
 
 63 
 
 199 
 
 2 .0 
 
 210 211 
 
 816 
 
 818 
 
 819 
 
 
 918 
 
 915 
 
 
 2H1 
 
 1!H 
 
 l-o 
 
 KJ8 
 
 01 
 
 188 
 
 106 
 
 803 
 
 
 813 
 
 816 
 
 21- 
 
 990 
 
 819 
 
 916 
 
 211 
 
 903 
 
 193 
 
 180 
 
 168 
 
 05 
 
 175 
 
 1-5 
 
 194 
 
 201 
 
 
 212 
 
 216 
 
 220 
 
 220 
 
 918 
 
 213 
 
 205 
 
 100 
 
 183 
 
 169 
 
 66 
 
 KM 
 
 172 
 
 l-:i 
 
 109 
 
 200 
 
 
 813 
 
 918 
 
 22 ' 
 
 919 
 
 215 
 
 2os 
 
 108 
 
 186 
 
 172 
 
 67 
 
 115 
 
 158 
 
 
 181 
 
 191 
 
 200 
 
 
 215 
 
 918 
 
 219 
 
 217 
 
 211 
 
 202 
 
 100 
 
 177 
 
 68' 
 
 130 
 
 1 i:: 
 
 156 
 
 168 
 
 180 
 
 101 
 
 901 
 
 210 
 
 210 
 
 9111 
 
 217 
 
 21 1 
 
 
 106 
 
 1-2 
 
 69 
 
 115 
 
 12- 
 
 1 12 
 
 155 
 
 168 
 
 l-l 
 
 IBS 
 
 904 
 
 919 
 
 217 
 
 919 
 
 217 
 
 210 
 
 Jil 
 
 1-:' 
 
 70 
 
 100 
 
 114 
 
 127 
 
 1 II 
 
 1 56 
 
 16!) 
 
 l-l 
 
 106 
 
 
 215 
 
 219 
 
 21:1 
 
 214 
 
 206 
 
 1! '5 
 
 71 
 
 -7 
 
 100 
 
 113 
 
 127 
 
 1 12 
 
 157 
 
 173 
 
 188 
 
 2 H 
 
 211 
 
 21- 
 
 22 I 
 
 918 
 
 911 
 
 909 
 
 72 
 
 76 
 
 87 
 
 100 
 
 III 
 
 189 
 
 115 
 
 l',2 
 
 17- 
 
 194 
 
 
 215 
 
 980 
 
 890 
 
 916 
 
 20!) 
 
 73 
 
 67 
 
 77 
 
 88 
 
 101 
 
 116 
 
 133 
 
 151 
 
 1 .- 
 
 1-5 
 
 200 
 
 211 
 
 910 
 
 221 
 
 220 
 
 214 
 
 74 
 
 61 
 
 68 
 
 78 
 
 90 
 
 
 121 
 
 |:l ' 
 
 1 - 
 
 170 
 
 193 
 
 207 
 
 216 
 
 221 
 
 222 
 
 218 
 
 75 
 
 57 
 
 63 
 
 71 
 
 81 
 
 90 
 
 110 
 
 12- 
 
 1 1- 
 
 107 
 
 185 
 
 201 
 
 212 
 
 219 
 
 222 
 
 220 
 
 76 
 
 55 
 
 59 
 
 65 
 
 74 
 
 86 
 
 101 
 
 118 
 
 137 
 
 157 
 
 177 
 
 II 
 
 207 
 
 216 
 
 2-20 
 
 221 
 
 77 
 
 56 
 
 58 
 
 63 
 
 69 
 
 7!) 
 
 93 
 
 100 
 
 138 
 
 148 
 
 107 
 
 185 
 
 200 
 
 211 
 
 217 
 
 919 
 
 7- 
 
 60 
 
 60 
 
 62 
 
 67 
 
 75 
 
 87 
 
 109 
 
 1 i'.i 
 
 138 
 
 158 
 
 177 
 
 109 
 
 904 
 
 212 
 
 215 
 
 n 
 
 65 
 
 63 
 
 63 
 
 66 
 
 72 
 
 81 
 
 
 111 
 
 129 
 
 14!) 
 
 167 
 
 tea 
 
 1% 
 
 205 
 
 210 
 
 80 
 
 70 
 
 67 
 
 65 
 
 66 
 
 70 
 
 77 
 
 
 103 
 
 120 
 
 139 
 
 157 
 
 17:t 
 
 1-7 
 
 197 
 
 203 
 
 81 
 
 77 
 
 73 
 
 69 
 
 67 
 
 (i!) 
 
 75 
 
 84 
 
 
 112 
 
 189 
 
 147 
 
 163 
 
 177 
 
 l-s 
 
 194 
 
 82 
 
 84 
 
 78 
 
 73 
 
 69 
 
 BO 
 
 72 
 
 7!) 
 
 90 
 
 104 
 
 180 
 
 137 
 
 152 
 
 166 
 
 177 
 
 1^5 
 
 83 
 
 90 
 
 -1 
 
 77 
 
 72 
 
 09 
 
 70 
 
 75 
 
 -1 
 
 
 . HI 
 
 126 
 
 III 
 
 156 
 
 107 
 
 175 
 
 84 
 
 97 
 
 89 
 
 81 
 
 74 
 
 70 
 
 68 
 
 71 
 
 77 
 
 88 
 
 101 
 
 116 
 
 130 
 
 1 15 
 
 156 
 
 104 
 
 83 
 
 102 
 
 93 
 
 84 
 
 76 
 
 70 
 
 66 
 
 07 
 
 72 
 
 80 
 
 92 
 
 106 
 
 119 
 
 134 
 
 115 
 
 154 
 
 H6 
 
 106 
 
 97 
 
 86 
 
 77 
 
 70 
 
 64 
 
 03 
 
 Mi 
 
 73 
 
 
 'Kj 
 
 100 
 
 123 
 
 134 
 
 1 13 
 
 >7 
 
 110 
 
 100 
 
 H8 
 
 78 
 
 (i'.i 
 
 62 
 
 59 
 
 60 
 
 65 
 
 71 
 
 86 
 
 
 119 
 
 123 
 
 133 
 
 88 
 
 113 
 
 102 
 
 90 
 
 78 
 
 K 
 
 60 
 
 55 
 
 51 
 
 58 
 
 05 
 
 71 i 
 
 88 
 
 Ml 
 
 113 
 
 122 
 
 89 
 
 116 
 
 104 
 
 
 79 
 
 67 
 
 58 
 
 52 
 
 49 
 
 51 
 
 57 
 
 67 
 
 78 
 
 01 
 
 102 
 
 112 
 
 90 
 
 118 
 
 106 
 
 93 
 
 80 
 
 67 
 
 56 
 
 49 
 
 45 
 
 45 
 
 50 
 
 58 
 
 68 
 
 81 
 
 92 
 
 102 
 
 
 121 
 
 100 
 
 05 
 
 81 
 
 67 
 
 56 
 
 46 
 
 42 
 
 40 
 
 43 
 
 51 
 
 60 
 
 71 
 
 82 
 
 
 92 
 
 124 
 
 112 
 
 98 
 
 83 
 
 69 
 
 56 
 
 45 
 
 39 
 
 30 
 
 38 
 
 44 
 
 52 
 
 03 
 
 73 
 
 
 03 
 
 128 
 
 110 
 
 102 
 
 87 
 
 71 
 
 58 
 
 46 
 
 38 
 
 34 
 
 33 
 
 38 
 
 45 
 
 55 
 
 00 
 
 71 
 
 M 
 
 133 
 
 121 
 
 107 
 
 91 
 
 76 
 
 61 
 
 48 
 
 38 
 
 33 
 
 31 
 
 34 
 
 39 
 
 48 
 
 S3 
 
 (>0 
 
 95 
 
 13!) 
 
 127 
 
 113 
 
 97 
 
 81 
 
 66 
 
 52 
 
 41 
 
 33 
 
 30 
 
 31 
 
 35 
 
 12 
 
 50 
 
 58 
 
 96 
 
 146 
 
 134 
 
 121 
 
 105 
 
 -i 
 
 73 
 
 
 45 
 
 36 
 
 31 
 
 30 
 
 32 
 
 88 
 
 15 
 
 11 
 
 97 
 
 153 
 
 142 
 
 129 
 
 114 
 
 97 
 
 81 
 
 65 
 
 51 
 
 41 
 
 34 
 
 31 
 
 31 
 
 35 
 
 40 
 
 46 
 
 98 
 
 161 
 
 151 
 
 139 
 
 121 
 
 107 
 
 91 
 
 74 
 
 59 
 
 47 
 
 89 
 
 34 
 
 32 
 
 35 
 
 38 
 
 43 
 
 99 
 
 16!) 
 
 160 
 
 14!) 
 
 134 
 
 118 
 
 101 
 
 84 
 
 68 
 
 55 
 
 15 
 
 3!) 
 
 35 
 
 36 
 
 38 
 
 42 
 
 100 
 
 177 
 
 169 
 
 159 
 
 145 
 
 129 
 
 113 
 
 00 
 
 78 
 
 64 
 
 53 
 
 45 
 
 40 
 
 40 
 
 40 
 
 42 
 
 101 
 
 184 
 
 178 
 
 169 
 
 156 
 
 141 
 
 124 
 
 
 90 
 
 75 
 
 61 
 
 51 
 
 47 
 
 45 
 
 44 
 
 45 
 
 102 
 
 191 
 
 187 
 
 178 
 
 100 
 
 159 
 
 136 
 
 11!) 
 
 101 
 
 B6 
 
 73 
 
 63 
 
 55 
 
 52 
 
 50 
 
 11 
 
 103 
 
 197 
 
 104 
 
 187 
 
 176 
 
 163 
 
 117 
 
 130 
 
 113 
 
 97 
 
 84 
 
 73 
 
 05 
 
 01 
 
 58 
 
 .,.- 
 
 104 
 
 203 
 
 201 
 
 1 :'5 
 
 185 
 
 173 
 
 158 
 
 141 
 
 185 
 
 109 
 
 90 
 
 84 
 
 70 
 
 71 
 
 68 
 
 67 
 
 105 
 
 207 
 
 206 
 
 202 
 
 193 
 
 l-l 
 
 107 
 
 152 
 
 136 
 
 120 
 
 106 
 
 96 
 
 87 
 
 -2 
 
 7!) 
 
 7- 
 
 106 
 
 210 
 
 211 
 
 207 
 
 200 
 
 189 
 
 176 
 
 102 
 
 115 
 
 131 
 
 118 
 
 107 
 
 90 
 
 !'l 
 
 91 
 
 80 
 
 107 
 108 
 109 
 
 214 
 216 
 
 217 
 
 215 
 218 
 993 
 
 819 
 
 217 
 
 220 
 
 206 
 211 
 216 
 
 107 
 
 203 
 209 
 
 184 
 192 
 198 
 
 171 
 186 
 
 155 
 164 
 173 
 
 Ml 
 151 
 160 
 
 I3U 
 148 
 
 11- 
 12!) 
 139 
 
 111 
 122 
 132 
 
 106 
 117 
 
 12- 
 
 too 
 
 114 
 
 125 
 
 113 
 121 
 
 110 
 III 
 112 
 113 
 114 
 
 218 
 218 
 218 
 217 
 815 
 
 222 
 223 
 994 
 824 
 
 223 
 
 223 
 
 225 
 227 
 888 
 889 
 
 220 
 223 
 226 
 899 
 
 231 
 
 214 
 218 
 223 
 227 
 230 
 
 205 
 210 
 815 
 
 2-20 
 225 
 
 193 
 200 
 206 
 212 
 217 
 
 180 
 
 188 
 195 
 
 201 
 
 207 
 
 168 
 176 
 
 183 
 
 I'.H) 
 1% 
 
 157 
 165 
 
 173 
 
 1 96 
 
 148 
 
 1.56 
 164 
 170 
 176 
 
 112 
 150 
 157 
 103 
 169 
 
 137 
 146 
 153 
 159 
 164 
 
 136 
 
 I II 
 
 151 
 157 
 
 11,1 
 
 M 
 143 
 
 151 
 
 116 
 
 161 
 
 115 
 116 
 117 
 118 
 119 
 190 
 
 213 
 
 213 
 1% 
 188 
 
 178 
 
 221 
 218 
 214 
 
 2.)0 
 101 
 
 22H 
 227 
 824 
 21!) 
 212 
 204 
 
 232 
 232 
 230 
 227 
 222 
 215 
 
 232 
 934 
 
 234 
 838 
 
 22:) 
 224 
 
 22!) 
 833 
 
 233 
 834 
 
 232 
 
 22- 
 
 222 
 226 
 22!) 
 231 
 831 
 230 
 
 212 
 217 
 221 
 294 
 
 226 
 227 
 
 202 
 
 212 
 216 
 219 
 990 
 
 ini 
 UK 
 
 809 
 
 212 
 
 1-2 
 1-7 
 101 
 105 
 191) 
 202 
 
 171 
 
 17- 
 I-J 
 1-5 
 1-:' 
 
 109 
 
 168 
 172 
 175 
 177 
 180 
 183 
 
 166 
 
 170 
 172 
 171 
 
 171, 
 
 163 
 169 
 
 107 
 
 IW 
 
 160 
 
 I7o 
 
 10 V 
 
 Add 147.64 to Arg. XI. when 224''.7 is subtracted from Arg. I. 
 
TABLE XX11. 
 
 Perturbations oft/if Longitude by the Earth. 
 
 Horizontal Argument = I. 
 
 Constant added 1''.40. Period of Argument I., 224'' .7. 
 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d : d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 Arg.XI 
 
 
 
 8 
 
 1G 
 
 24 
 
 32 
 
 40 
 
 48 
 
 56 
 
 61 
 
 72 
 
 80 
 
 88 
 
 96 
 
 1O4 
 
 112 
 
 120 
 
 67 
 
 71 
 
 77 
 
 83 
 
 00 
 
 98 
 
 106 
 
 113 
 
 119 
 
 125 
 
 131 
 
 138 
 
 145 
 
 154 
 
 165 
 
 181 
 
 50 
 
 62 
 
 66 
 
 71 
 
 78 
 
 86 
 
 93 
 
 101 
 
 108 
 
 111 
 
 121 
 
 127 
 
 134 
 
 143 
 
 154 
 
 122 
 
 53 
 
 55 
 
 57 
 
 62 
 
 67 
 
 75 
 
 83 
 
 90 
 
 98 
 
 " 104 
 
 110 
 
 117 
 
 124 
 
 132 
 
 142 
 
 123 
 
 53 
 
 51 
 
 51 
 
 54 
 
 59 
 
 65 
 
 73 
 
 80 
 
 88 
 
 94 
 
 101 
 
 107 
 
 113 
 
 121 
 
 131 
 
 124 
 
 48 
 
 47 
 
 47 
 
 49 
 
 53 
 
 58 
 
 65 
 
 72 
 
 80 
 
 86 
 
 92 
 
 99 
 
 104 
 
 111 
 
 119 
 
 135 
 
 48 
 
 46 
 
 45 
 
 46 
 
 48 
 
 53 
 
 59 
 
 66 
 
 73 
 
 79 
 
 85 
 
 91 
 
 96 
 
 101 
 
 108 
 
 186 
 
 49 
 
 46 
 
 45 
 
 44 
 
 46 
 
 49 
 
 55 
 
 61 
 
 68 
 
 74 
 
 80 
 
 84 
 
 89 
 
 93 
 
 99 
 
 127 
 
 52 
 
 49 
 
 46 
 
 45 
 
 4r> 
 
 48 
 
 52 
 
 58 
 
 65 
 
 70 
 
 76 
 
 80 
 
 83 
 
 87 
 
 91 
 
 128 
 
 56 
 
 52 
 
 49 
 
 46 
 
 46 
 
 47 
 
 51 
 
 57 
 
 62 
 
 68 
 
 73 
 
 77 
 
 80 
 
 82 
 
 86 
 
 129 
 
 60 
 
 56 
 
 52 
 
 49 
 
 47 
 
 48 
 
 51 
 
 56 
 
 62 
 
 67 
 
 72 
 
 76 
 
 78 
 
 80 
 
 82 
 
 ISO 
 
 05 
 
 61 
 
 56 
 
 52 
 
 50 
 
 49 
 
 52 
 
 56 
 
 61 
 
 67 
 
 72 
 
 76 
 
 79 
 
 80 
 
 81 
 
 181 
 
 70 
 
 66 
 
 61 
 
 56 
 
 53 
 
 51 
 
 53 
 
 57 
 
 62 
 
 68 
 
 74 
 
 78 
 
 80 
 
 82 
 
 83 
 
 132 
 
 76 
 
 71 
 
 65 
 
 60 
 
 56 
 
 54 
 
 55 
 
 58 
 
 63 
 
 69 
 
 75 
 
 80 
 
 83 
 
 85 
 
 86 
 
 133 
 
 82 
 
 76 
 
 70 
 
 64 
 
 59 
 
 56 
 
 56 
 
 59 
 
 64 
 
 70 
 
 77 
 
 83 
 
 87 
 
 90 
 
 91 
 
 134 
 
 89 
 
 82 
 
 75 
 
 68 
 
 62 
 
 58 
 
 58 
 
 60 
 
 65 
 
 72 
 
 79 
 
 86 
 
 92 
 
 95 
 
 97 
 
 135 
 
 96 
 
 88 
 
 80 
 
 73 
 
 66 
 
 61 
 
 60 
 
 62 
 
 66 
 
 73 
 
 81 
 
 90 
 
 96 
 
 101 
 
 104 
 
 136 
 
 103. 
 
 !I5 
 
 86 
 
 77 
 
 70 
 
 64 
 
 62 
 
 63 
 
 67 
 
 75 
 
 83 
 
 92 
 
 101 
 
 107 
 
 111 
 
 137 
 
 112 
 
 || :! 
 
 93 
 
 83 
 
 74 
 
 68 
 
 65 
 
 65 
 
 69 
 
 76 
 
 85 
 
 95 
 
 104 
 
 112 
 
 117 
 
 138 
 
 121 
 
 Ill 100 
 
 90 
 
 80 
 
 72 
 
 68 
 
 67 
 
 70 
 
 77 
 
 86 
 
 97 
 
 107 
 
 116 
 
 123 
 
 139 
 
 131 
 
 12! 109 
 
 97 
 
 86 
 
 77 
 
 72 
 
 70 
 
 72 
 
 78 
 
 87 
 
 98 
 
 109 
 
 119 
 
 127 
 
 140 
 
 111 
 
 m 118 
 
 106 
 
 94 
 
 84 
 
 76 
 
 73 
 
 74 
 
 79 
 
 87 
 
 98 
 
 110 
 
 121 
 
 130 
 
 141 
 
 152 
 
 141 
 
 128 
 
 115 
 
 102 
 
 91 
 
 82 
 
 78 
 
 76 
 
 80 
 
 87 
 
 98 
 
 109 
 
 121 
 
 131 
 
 142 
 
 163 
 
 151 
 
 138 
 
 125 
 
 111 
 
 99 
 
 89 
 
 83 
 
 80 
 
 81 
 
 87 
 
 97 
 
 108 
 
 119 
 
 130 
 
 143 
 
 173 
 
 162 
 
 149 
 
 136 
 
 12,1 
 
 108 
 
 96 
 
 88 
 
 84 
 
 83 
 
 88 
 
 96 
 
 106 
 
 117 
 
 I2H 
 
 144 
 
 183 
 
 173 
 
 161 
 
 147 
 
 132 
 
 117 
 
 104 
 
 94 
 
 88 
 
 86 
 
 88 
 
 94 
 
 103 
 
 114 
 
 125 
 
 145 
 
 193 
 
 183 
 
 171 
 
 158 
 
 142 
 
 127 
 
 113 
 
 101 
 
 93 
 
 88 
 
 89 
 
 93 
 
 100 
 
 110 
 
 121 
 
 146 
 
 201 
 
 193 
 
 181 
 
 168 
 
 153 
 
 137 
 
 122 
 
 109 
 
 98 
 
 92 
 
 90 
 
 92 
 
 98 
 
 106 
 
 116 
 
 147 
 
 208 
 
 201 
 
 190 
 
 178 
 
 163 
 
 147 
 
 130 
 
 117 
 
 104 
 
 95 
 
 91 
 
 91 
 
 95 
 
 102 
 
 111 
 
 148 
 
 213 
 
 207 
 
 198 
 
 186 
 
 172 
 
 156 
 
 139 
 
 124 
 
 110 
 
 100 
 
 94 
 
 92 
 
 93 
 
 99 
 
 107 
 
 14!) 
 
 217 
 
 212 
 
 205 
 
 194 
 
 181) 
 
 164 
 
 147 
 
 131 
 
 116 
 
 105 
 
 97 
 
 92 
 
 93 
 
 96 
 
 103 
 
 150 
 
 219 
 
 216 
 
 210 
 
 200 
 
 187 
 
 172 
 
 155 
 
 138 
 
 123 
 
 110 
 
 100 
 
 94 
 
 92 
 
 94 
 
 100 
 
 151 
 
 219 
 
 218 
 
 214 
 
 205 
 
 194 
 
 179 
 
 162 
 
 146 
 
 130 
 
 115 
 
 104 
 
 97 
 
 94 
 
 94 
 
 98 
 
 153 
 
 218 
 
 219 
 
 216 
 
 209 
 
 199 
 
 185 
 
 169 
 
 1 53 
 
 136 
 
 121 
 
 109 
 
 100 
 
 96 
 
 94 
 
 97 
 
 153 
 
 217 
 
 219 
 
 218 
 
 213 
 
 204 
 
 191 
 
 176 
 
 159 
 
 143 
 
 128 
 
 115 
 
 105 
 
 99 
 
 96 
 
 97 
 
 154 
 
 214 
 
 218 
 
 219 
 
 216 
 
 208 
 
 197 
 
 183 
 
 166 
 
 151 
 
 135 
 
 122 
 
 111 
 
 103 
 
 99 
 
 99 
 
 155 
 
 211 
 
 217 
 
 220 
 
 218 
 
 212 
 
 202 
 
 189 
 
 174 
 
 158 
 
 143 
 
 129 
 
 118 
 
 109 
 
 103 
 
 102 
 
 156 
 
 208 
 
 215 
 
 220 
 
 228 
 
 217 
 
 898 
 
 196 
 
 182 
 
 167 
 
 152 
 
 138 
 
 125 
 
 116 
 
 109 
 
 106 
 
 157 
 
 204 
 
 214 
 
 221 
 
 223 
 
 221 
 
 215 
 
 2114 
 
 I'll 
 
 177 
 
 161 
 
 147 
 
 134 
 
 124 
 
 116 
 
 111 
 
 158 
 
 200 
 
 212 
 
 221 
 
 226 
 
 226 
 
 221 
 
 212 
 
 200 
 
 187 
 
 172 
 
 158 
 
 144 
 
 133 
 
 123 
 
 117 
 
 159 
 
 197 
 
 211 
 
 222 
 
 229 
 
 231 
 
 228 
 
 221 
 
 210 
 
 198 
 
 183 
 
 16!) 
 
 155 
 
 143 
 
 132 
 
 125 
 
 160 
 
 193 
 
 209 
 
 222 
 
 232 
 
 236 
 
 236 
 
 230 
 
 221 
 
 209 
 
 196 
 
 182 
 
 167 
 
 154 
 
 142 
 
 133 
 
 161 
 
 189 
 
 207 
 
 223 
 
 235 
 
 242 
 
 243 
 
 240 
 
 232 
 
 221 
 
 208 
 
 194 
 
 180 
 
 166 
 
 153 
 
 143 
 
 162 
 
 185 
 
 204 
 
 223 
 
 237 
 
 246 
 
 250 
 
 249 
 
 242 
 
 233 
 
 221 
 
 207 
 
 193 
 
 179 
 
 165 
 
 154 
 
 163 
 
 179 
 
 201 
 
 221 
 
 238 
 
 250 
 
 256 
 
 257 
 
 253 
 
 245 
 
 234 
 
 221 
 
 206 
 
 192 
 
 178 
 
 165 
 
 164 
 
 17:i 
 
 197 
 
 219 
 
 238 
 
 252 
 
 261 
 
 264 
 
 262 
 
 255 
 
 245 
 
 233 
 
 219 
 
 205 
 
 191 
 
 178 
 
 165 
 
 167 
 
 191 
 
 215 
 
 236 
 
 252 
 
 263 
 
 269 
 
 269 
 
 264 
 
 256 
 
 245 
 
 232 
 
 219 
 
 204 
 
 191 
 
 166 
 
 159 
 
 184 
 
 209 
 
 232 
 
 250 
 
 264 
 
 272 
 
 274 
 
 271 
 
 265 
 
 256 
 
 244 
 
 231 
 
 218 
 
 204 
 
 167 
 
 150 
 
 176 
 
 201 
 
 225 
 
 246 
 
 261 
 
 271 
 
 276 
 
 276 
 
 272 
 
 264 
 
 254 
 
 243 
 
 230 
 
 217 
 
 168 
 
 141 
 
 166 
 
 192 
 
 217 
 
 239 
 
 256 
 
 269 
 
 276 
 
 278 
 
 276 
 
 270 
 
 263 
 
 953 
 
 242 
 
 230 
 
 169 
 
 131 
 
 155 
 
 181 
 
 206 
 
 229 
 
 249 
 
 263 
 
 272 
 
 277 
 
 277 
 
 274 
 
 269 
 
 261 
 
 252 
 
 242 
 
 170 
 
 120 
 
 144 
 
 168 
 
 194 
 
 217 
 
 238 
 
 254 
 
 266 
 
 272 
 
 276 
 
 275 
 
 272 
 
 267 
 
 260 
 
 252 
 
 171 
 
 110 
 
 132 
 
 155 
 
 180 
 
 204 
 
 B25 
 
 243 
 
 256 
 
 265 
 
 271 
 
 273 
 
 272 
 
 270 
 
 266 
 
 260 
 
 172 
 
 100 
 
 119 
 
 141 
 
 165 
 
 189 
 
 210 
 
 229 
 
 244 
 
 255 
 
 263 
 
 267 
 
 270 
 
 270 
 
 968 
 
 265 
 
 173 
 
 1)1 
 
 108 
 
 128 
 
 150 
 
 173 
 
 194 
 
 213 
 
 230 
 
 242 
 
 252 
 
 259 
 
 264 
 
 267 
 
 268 
 
 268 
 
 174 
 
 84 
 
 97 
 
 115 
 
 135 
 
 1ST 1 
 
 178 
 
 197 
 
 214 
 
 228 
 
 239 
 
 248 
 
 255 
 
 261 
 
 265 
 
 267 
 
 175 
 
 77 
 
 88 
 
 103 
 
 121 
 
 141 
 
 161 
 
 180 
 
 197 
 
 212 
 
 224 
 
 235 
 
 244 
 
 S53 
 
 258 
 
 263 
 
 176 
 
 72 
 
 80 
 
 93 
 
 109 
 
 127 
 
 145 
 
 163 
 
 180 
 
 195 
 
 208 
 
 220 
 
 230 
 
 239 
 
 248 
 
 256 
 
 177 
 
 69 
 
 75 
 
 84 
 
 98 
 
 114 
 
 130 
 
 147 
 
 163 
 
 177 
 
 191 
 
 203 
 
 214 
 
 225 
 
 235 
 
 245 
 
 178 
 
 67 
 
 71 
 
 78 
 
 89 
 
 103 
 
 117 
 
 132 
 
 147 
 
 169 
 
 173 
 
 185 
 
 197 
 
 2J9 
 
 220 
 
 231 
 
 179 
 
 68 
 
 69 
 
 74 
 
 82 
 
 94 
 
 106 
 
 119 
 
 132 
 
 144 
 
 156 
 
 167 
 
 179 
 
 191 
 
 203 
 
 215 
 
 180 
 
 69 
 
 68 
 
 71 
 
 78 
 
 87 
 
 97 
 
 108 
 
 119 
 
 129 
 
 140 
 
 150 
 
 161 
 
 172 
 
 185 
 
 fee 
 
 The perturbations are expressed in hundredths of a second of arc. 
 
TABLE XXII. 
 
 Perturbations of the L ,-th. 
 
 lli'i'i/uiitul Ar^iiiiii-iit = I. 
 r,,u..i;,i>t addi-d I'.ll IVriud ..fArf-iim-m XI , 210 units. 
 
 Ar^.M 
 
 <\ 
 120 
 
 ,l 
 
 a 
 
 i ;<; 
 
 111 
 
 192 
 
 100 
 
 ,1 
 10M 
 
 ,1 
 
 ,1 
 INI 
 
 ,1 
 
 200 
 
 cl 
 
 20* 
 
 210 
 
 22 i' 
 
 .' 
 
 190 
 
 17- 
 
 191 
 
 904 
 
 215 
 
 22 1 
 
 898 
 
 
 
 
 212 
 
 
 199 
 
 1-:; 
 
 I76 
 
 170 
 
 121 
 
 167 
 
 180 
 
 103 
 
 
 916 
 
 893 
 
 
 
 221 
 
 213 
 
 
 106 
 
 l-i, 
 
 1 7'. I 
 
 173 
 
 122 
 
 155 
 
 168 
 
 189 
 
 105 
 
 
 916 
 
 991 
 
 22 1 
 
 910 
 
 21 1 
 
 
 198 
 
 
 1 89 
 
 176 
 
 193 
 
 1 12 
 
 155 
 
 160 
 
 1-:: 
 
 
 
 913 
 
 916 
 
 217 
 
 913 
 
 2 17 
 
 
 193 
 
 Mi 
 
 l-n 
 
 121 
 
 12:1 111 
 
 166 
 
 169 
 
 l-:i 
 
 196 
 
 
 210 
 
 212 
 
 211 
 
 
 
 196 
 
 I no 
 
 l-l 
 
 195 
 
 117 
 
 198 
 
 1 II 
 
 156 
 
 170 
 
 I-:; 
 
 I'.il 
 
 
 207 
 
 2i- 
 
 2.17 
 
 
 lOt) 
 
 I'H 
 
 tan 
 
 I2li 
 
 106 
 
 116 
 
 198 
 
 1 12 
 
 156 
 
 170 
 
 189 
 
 199 
 
 199 
 
 
 2iil 
 
 901 
 
 IU8 
 
 in 
 
 127 
 
 '.17 
 
 105 
 
 III, 
 
 190 
 
 112 
 
 17 
 
 170 
 
 1-2 
 
 IU1 
 
 1 'i7 
 
 
 2 13 
 
 2 '1 
 
 r.ni 
 
 I2S 
 
 
 96 
 
 105 
 
 117 
 
 130 
 
 Ml 
 
 158 
 
 171 
 
 1-2 
 
 191 
 
 197 
 
 201 
 
 903 
 
 2 13 
 
 12!) 
 
 * 
 
 90 
 
 :i7 
 
 107 
 
 119 
 
 133 
 
 Mi, 
 
 11,1 
 
 173 
 
 l-l 
 
 199 
 
 108 
 
 109 205 
 
 2 Hi 
 
 i:; i 
 
 83 
 
 96 
 
 99 
 
 100 
 
 110 
 
 193 
 
 137 
 
 151 
 
 164 
 
 17(i 
 
 186 
 
 194 200 
 
 2 I5 
 
 2i- 
 
 131 
 
 -:> 
 
 85 
 
 99 
 
 95 
 
 |0| 
 
 115 
 
 12- 
 
 1 12 
 
 i.-,-, 
 
 l<, - 
 
 179 
 
 L-.i l'.<7 
 
 2 'I 
 
 909 
 
 132 
 
 
 -7 
 
 89 
 
 93 
 
 100 
 
 no 
 
 191 
 
 134 
 
 117 
 
 li,l 
 
 173 
 
 l-l 193 
 
 903 
 
 
 133 
 
 !U 
 
 91 
 
 !i| 
 
 !I4 
 
 99 
 
 106 
 
 116 
 
 127 
 
 1 |:l 
 
 153 
 
 166 
 
 177 I-- 
 
 ION 
 
 906 
 
 134 
 
 117 
 
 (17 
 
 96 
 
 97 
 
 100 
 
 105 
 
 113 
 
 122 
 
 134 
 
 in, 
 
 159 
 
 171 
 
 1-2 
 
 193 
 
 903 
 
 135 
 
 105 
 
 104 
 
 103 
 
 101 
 
 103 
 
 106 
 
 ill 
 
 11!) 
 
 199 
 
 i r> 
 
 159 
 
 164 
 
 176 
 
 188 
 
 199 
 
 136 
 
 112 
 
 112 
 
 110 
 
 108 
 
 107 
 
 108 
 
 112 
 
 117 
 
 125 
 
 134 
 
 145 
 
 157 
 
 169 
 
 l-l 
 
 IDS 
 
 137 
 
 121 
 
 190 
 
 118 
 
 115 
 
 113 
 
 119 
 
 113 
 
 116 
 
 122 
 
 130 
 
 139 
 
 150 
 
 169 
 
 175 
 
 187 
 
 138 
 
 196 
 
 127 
 
 196 
 
 12:1 
 
 119 
 
 116 
 
 116 
 
 111 
 
 121 
 
 121, 
 
 133 
 
 1 II 
 
 155 
 
 Ki7 
 
 1- , 
 
 139 
 
 133 
 
 134 
 
 133 
 
 130 
 
 125 
 
 121 
 
 119 
 
 117 
 
 118 
 
 122 
 
 198 
 
 137 
 
 117 
 
 160 
 
 173 
 
 Mi 
 
 136 
 
 139 
 
 139 
 
 135 
 
 131 
 
 126 
 
 122 
 
 118 
 
 117 
 
 119 
 
 193 
 
 131 
 
 140 
 
 152 
 
 166 
 
 141 
 
 138 
 
 142 
 
 113 
 
 140 
 
 135 
 
 130 
 
 124 
 
 119 
 
 116 
 
 116 
 
 119 
 
 125 
 
 133 
 
 144 
 
 168 
 
 112 
 
 138 
 
 144 
 
 145 
 
 143 
 
 139 
 
 133 
 
 126 
 
 120 
 
 116 
 
 ill 
 
 115 
 
 119 
 
 196 
 
 136 
 
 ii' 
 
 143 
 
 137 
 
 143 
 
 146 
 
 145 
 
 141 
 
 134 
 
 12- 
 
 12:1 
 
 11.-, 
 
 ill 
 
 III! 
 
 111 
 
 in 
 
 128 
 
 Ml 
 
 III 
 
 134 
 
 141 
 
 145 
 
 145 
 
 112 
 
 138 
 
 128 
 
 121 
 
 Ill 
 
 lll'.l 
 
 106 
 
 108 
 
 111 
 
 190 
 
 132 
 
 145 
 
 130 
 
 137 
 
 142 
 
 143 
 
 141 
 
 138 
 
 12- 
 
 120 
 
 113 
 
 1' ,, 
 
 109 
 
 102 
 
 104 
 
 111 
 
 122 
 
 III, 
 
 195 
 
 133 
 
 13!) 
 
 141 
 
 13!) 
 
 135 
 
 12- 
 
 119 
 
 111 
 
 |0| 
 
 08 
 
 96 
 
 97 
 
 103 
 
 112 
 
 147 
 
 190 
 
 198 
 
 136 
 
 137 
 
 137 
 
 133 
 
 127 
 
 118 
 
 no 
 
 101 
 
 94 
 
 91 
 
 89 
 
 93 
 
 101 
 
 1 1- 
 
 115 
 
 193 
 
 130 
 
 134 
 
 134 
 
 131 
 
 126 
 
 117 
 
 109 
 
 DO 
 
 in 
 
 96 
 
 99 
 
 84 
 
 91 
 
 14!) 
 
 110 
 
 118 
 
 125 
 
 130 
 
 132 
 
 130 
 
 124 
 
 117 
 
 108 
 
 97 
 
 88 
 
 81 
 
 75 
 
 75 
 
 79 
 
 150 
 
 106 
 
 111 
 
 121 
 
 126 
 
 129 
 
 128 
 
 123 
 
 116 
 
 107 
 
 96 
 
 a-> 
 
 76 
 
 (i:i 
 
 67 
 
 68 
 
 51 
 
 103 
 
 no 
 
 117 
 
 123 
 
 126 
 
 126 
 
 123 
 
 116 
 
 107 
 
 
 84 
 
 73 
 
 61 
 
 59 
 
 57 
 
 52 
 
 101 
 
 107 
 
 114 
 
 190 
 
 121 
 
 125 
 
 122 
 
 117 
 
 108 
 
 96 
 
 83 
 
 71 
 
 50 
 
 59 
 
 1- 
 
 53 
 
 too 
 
 106 
 
 112 
 
 118 
 
 193 
 
 194 
 
 199 
 
 117 
 
 109 
 
 97 
 
 83 
 
 70 
 
 57 
 
 47 
 
 40 
 
 54 
 
 101 
 
 105 
 
 111 
 
 117 
 
 121 
 
 194 
 
 123 
 
 118 
 
 110 
 
 99 
 
 85 
 
 71 
 
 56 
 
 43 
 
 34 
 
 55 
 
 102 
 
 105 
 
 110 
 
 116 
 
 121 
 
 12:i 
 
 123 
 
 120 
 
 113 
 
 102 
 
 88 
 
 73 
 
 56 
 
 42 
 
 30 
 
 
 105 
 
 107 
 
 111 
 
 115 
 
 120 
 
 123 
 
 121 
 
 121 
 
 115 
 
 106 
 
 99 
 
 76 
 
 59 
 
 43 
 
 99 
 
 57 
 
 109 
 
 109 
 
 112 
 
 116 
 
 120 
 
 123 
 
 121 
 
 123 
 
 11- 
 
 100 
 
 96 
 
 81 
 
 64 
 
 46 
 
 31 
 
 58 
 
 113 
 
 112 
 
 113 
 
 117 
 
 190 
 
 123 
 
 125 
 
 1 25 
 
 121 
 
 114 
 
 102 
 
 -7 
 
 70 
 
 59 
 
 35 
 
 159 
 
 119 
 
 116 
 
 116 
 
 118 
 
 120 
 
 123 
 
 126 
 
 126 
 
 121 
 
 118 
 
 108 
 
 95 
 
 78 
 
 i, i 
 
 42 
 
 160 
 
 126 
 
 122 
 
 119 
 
 119 
 
 121 
 
 194 
 
 126 
 
 128 
 
 126 
 
 199 
 
 lit 
 
 103 
 
 88 
 
 70 
 
 52 
 
 161 
 
 134 
 
 198 
 
 124 
 
 122 
 
 193 
 
 125 
 
 127 
 
 I2!l 
 
 12!) 
 
 127 
 
 121 
 
 111 
 
 98 
 
 -2 
 
 III 
 
 169 
 
 14 I 
 
 135 
 
 130 
 
 126 
 
 125 
 
 196 
 
 12- 
 
 130 
 
 132 
 
 131 
 
 127 
 
 190 
 
 108 
 
 :n 
 
 77 
 
 163 
 
 154 
 
 144 
 
 136 
 
 131 
 
 12!) 
 
 12- 
 
 130 
 
 132 
 
 134 
 
 135 
 
 133 
 
 12- 
 
 1 l!l 
 
 107 
 
 91 
 
 164 
 
 165 
 
 154 
 
 145 
 
 138 
 
 133 
 
 132 
 
 139 
 
 134 
 
 137 
 
 139 
 
 130 
 
 136 
 
 12!) 
 
 119 
 
 in:, 
 
 165 
 
 178 
 
 165 
 
 155 
 
 146 
 
 140 
 
 137 
 
 136 
 
 137 
 
 140 
 
 142 
 
 Ml 
 
 143 
 
 138 
 
 131 
 
 119 
 
 166 
 
 100 
 
 178 
 
 166 
 
 155 
 
 148 
 
 143 
 
 Ml 
 
 Ml 
 
 113 
 
 146 
 
 148 
 
 149 
 
 117 
 
 141 
 
 131 
 
 167 
 
 204 
 
 101 
 
 17- 
 
 167 
 
 158 
 
 151 
 
 147 
 
 145 
 
 147 
 
 14!) 
 
 159 
 
 155 
 
 154 
 
 150 
 
 1 12 
 
 168 
 
 218 
 
 205 
 
 192 
 
 179 
 
 169 
 
 160 
 
 154 
 
 151 
 
 151 
 
 153 
 
 166 
 
 I.V.I 
 
 159 
 
 157 
 
 169 
 
 
 231 
 
 218 
 
 206 
 
 192 
 
 181 
 
 171 
 
 163 
 
 158 
 
 166 
 
 157 
 
 159 
 
 162 
 
 163 
 
 163 
 
 15!) 
 
 170 
 
 242 
 
 939 
 
 220 
 
 206 
 
 194 
 
 183 
 
 173 
 
 166 
 
 162 
 
 161 
 
 162 
 
 166 
 
 166 
 
 Ki7 
 
 165 
 
 171 
 
 252 
 
 944 
 
 233 
 
 220 
 
 2,17 
 
 r 5 
 
 184 
 
 175 
 
 Hi!) 
 
 166 
 
 166 
 
 11,7 
 
 !(,- 
 
 170 
 
 160 
 
 172 
 
 969 
 
 254 
 
 244 
 
 233 
 
 220 
 
 207 
 
 196 
 
 184 
 
 176 
 
 171 
 
 16!) 
 
 169 
 
 170 
 
 171 
 
 171 
 
 173 
 
 966 
 
 260 
 
 254 
 
 244 
 
 839 
 
 919 
 
 206 
 
 194 
 
 l-l 
 
 176 
 
 172 
 
 171 
 
 170 
 
 171 
 
 172 
 
 174 
 
 268 
 
 266 
 
 261 
 
 253 
 
 243 
 
 230 
 
 216 
 
 203 
 
 191 
 
 1-2 
 
 175 
 
 172 
 
 171 
 
 171 
 
 172 
 
 175 
 
 267 
 
 267 
 
 265 
 
 260 
 
 251 
 
 
 226 
 
 212 
 
 roe 
 
 187 
 
 I7'i 
 
 171 
 
 171 
 
 170 
 
 171 
 
 176 
 
 969 
 
 966 
 
 266 
 
 263 
 
 257 
 
 246 
 
 233 
 
 21!) 
 
 
 1 ". 
 
 1-2 
 
 175 
 
 171 
 
 17'l 
 
 Mil 
 
 177 
 
 254 
 
 260 
 
 264 
 
 263 
 
 25!) 
 
 951 
 
 939 
 
 226 
 
 211 
 
 106 
 
 l-i, 
 
 177 
 
 171 
 
 li, ' 
 
 168 
 
 
 949 
 
 251 
 
 257 
 
 260 
 
 258 
 
 253 
 
 213 
 
 230 
 
 216 
 
 
 189 
 
 179 
 
 172 
 
 168 
 
 11,7 
 
 t!7 ' 
 i 
 
 998 
 
 939 
 
 248 
 
 254 
 
 255 
 
 252 
 
 211 
 
 233 
 
 219 
 
 906 
 
 
 l-l 
 
 173 
 
 I6H 
 
 165 
 
 189 
 
 211 
 
 2-21 
 
 2;t6 
 
 244 
 
 248 
 
 21- 
 
 213 
 
 233 
 
 
 207 
 
 196 
 
 1-3 
 
 171 
 
 167 
 
 H, 1 
 
 Add 147.64 to Arg. XI. wln'ii 22I''.7 in nublracted from Arg. I. 
 
TABLE XXII. 
 
 Perturbations of the Longitude by the Earth. 
 
 Horizontal Argument = I. 
 
 Constant added 1".40. Period of Argument I. 224' ] .7. 
 
 Arg. XI 
 
 d 
 
 o 
 
 ii 
 8 
 
 i 
 16 
 
 | 24 
 
 32 
 
 40 
 
 d 
 
 48 
 
 5 
 
 ,1 
 <1 
 
 tl 
 72 
 
 d 
 
 SO 
 
 d 
 88 
 
 d 
 
 96 
 
 a 
 1O4 
 
 t 
 112 
 
 180 
 
 CO 
 
 68 
 
 71 
 
 78 
 
 87 
 
 97 
 
 108 
 
 110 
 
 129 
 
 140 
 
 150 
 
 161 
 
 172 
 
 185 
 
 198 
 
 181 
 
 72 
 
 70 
 
 71 
 
 75 
 
 82 
 
 00 
 
 09 
 
 107 
 
 116 
 
 125 
 
 133 
 
 143 
 
 154 
 
 166 
 
 170 
 
 182 
 
 75 
 
 72 
 
 72 
 
 74 
 
 70 
 
 85 
 
 91 
 
 08 
 
 105 
 
 111 
 
 118 
 
 126 
 
 136 
 
 147 
 
 160 
 
 183 
 
 70 
 
 75 
 
 74 
 
 75 
 
 78 
 
 82 
 
 86 
 
 90 
 
 95 
 
 09 
 
 104 
 
 110 
 
 119 
 
 129 
 
 141 
 
 184 
 
 83 
 
 70 
 
 77 
 
 77 
 
 78 
 
 80 
 
 82 
 
 85 
 
 87 
 
 89 
 
 93 
 
 06 
 
 103 
 
 112 
 
 123 
 
 is:; 
 
 87 
 
 83 
 
 80 
 
 70 
 
 79 
 
 80 
 
 80 
 
 81 
 
 81 
 
 82 
 
 83 
 
 85 
 
 89 
 
 07 
 
 107 
 
 186 
 
 92 
 
 87 
 
 84 
 
 82 
 
 81 
 
 80 
 
 80 
 
 78 
 
 77 
 
 76 
 
 75 
 
 /o 
 
 78 
 
 83 
 
 93 
 
 187 
 
 96 
 
 92 
 
 88 
 
 86 
 
 84 
 
 82 
 
 80 
 
 77 
 
 75 
 
 72 
 
 69 
 
 63 
 
 69 
 
 73 
 
 81 
 
 188 
 
 101 
 
 06 
 
 03 
 
 89 
 
 87 
 
 85 
 
 82 
 
 78 
 
 74 
 
 70 
 
 66 
 
 63 
 
 62 
 
 64 
 
 71 
 
 180 
 
 105 
 
 100 
 
 97 
 
 94 
 
 01 
 
 88 
 
 85 
 
 80 
 
 75 
 
 6!) 
 
 64 
 
 60 
 
 57 
 
 58 
 
 63 
 
 100 
 
 110 
 
 105 
 
 101 
 
 08 
 
 05 
 
 02 
 
 88 
 
 83 
 
 77 
 
 71 
 
 64 
 
 58 
 
 55 
 
 54 
 
 58 
 
 191 
 
 115 
 
 no 
 
 106 
 
 103 
 
 100 
 
 06 
 
 02 
 
 87 
 
 81 
 
 74 
 
 66 
 
 50 
 
 54 
 
 52 
 
 54 
 
 102 
 
 121 
 
 116 
 
 112 
 
 108 
 
 .105 
 
 102 
 
 97 
 
 92 
 
 85 
 
 78 
 
 70 
 
 62 
 
 56 
 
 52 
 
 52 
 
 193 
 
 127 
 
 122 
 
 117 
 
 114 
 
 111 
 
 108 
 
 104 
 
 98 
 
 01 
 
 83- 
 
 74 
 
 66 
 
 58 
 
 54 
 
 52 
 
 194 
 
 133 
 
 129 
 
 124 
 
 121 
 
 118 
 
 114 
 
 111 
 
 105 
 
 08 
 
 90 
 
 81 
 
 71 
 
 62 
 
 56 
 
 53 
 
 105 
 
 140 
 
 136 
 
 131 
 
 123 
 
 125 
 
 122 
 
 118 
 
 113 
 
 106 
 
 98 
 
 83 
 
 77 
 
 67 
 
 60 
 
 55 
 
 106 
 
 147 
 
 143 
 
 138 
 
 136 
 
 133 
 
 130 
 
 127 
 
 121 
 
 115 
 
 106 
 
 96 
 
 84 
 
 73 
 
 64 
 
 58 
 
 197 
 
 154 
 
 150 
 
 146 
 
 143 
 
 140 
 
 138 
 
 135 
 
 131 
 
 124 
 
 115 
 
 104 
 
 02 
 
 80 
 
 60 
 
 61 
 
 1!)8 
 
 161 
 
 157 
 
 153 
 
 150 
 
 148 
 
 146 
 
 144 
 
 140 
 
 134 
 
 124 
 
 113 
 
 100 
 
 87 
 
 75 
 
 65 
 
 199 
 
 168 
 
 164 
 
 160 
 
 157 
 
 156 
 
 154 
 
 .152 
 
 149 
 
 143 
 
 134 
 
 122 
 
 100 
 
 94 
 
 81 
 
 60 
 
 200 
 
 173 
 
 170 
 
 166 
 
 164 
 
 163 
 
 161 
 
 160 
 
 157 
 
 151 
 
 143 
 
 131 
 
 117 
 
 102 
 
 87 
 
 74 
 
 201 
 
 178 
 
 174 
 
 171 
 
 169 
 
 168 
 
 167 
 
 167 
 
 164 
 
 159 
 
 151 
 
 139 
 
 125 
 
 109 
 
 04 
 
 70 
 
 202 
 
 182 
 
 178 
 
 174 
 
 172 
 
 172 
 
 172 
 
 72 
 
 70 
 
 166 
 
 158 
 
 147 
 
 133 
 
 117 
 
 100 
 
 84 
 
 203 
 
 184 
 
 180 
 
 176 
 
 174 
 
 174 
 
 174 
 
 75 
 
 74 
 
 171 
 
 1G4 
 
 154 
 
 140 
 
 124 
 
 107 
 
 00 
 
 204 
 
 185 
 
 180 
 
 176 
 
 174 
 
 174 
 
 175 
 
 76 
 
 76 
 
 174 
 
 168 
 
 159 
 
 146 
 
 130 
 
 113 
 
 06 
 
 905 
 
 184 
 
 180 
 
 175 
 
 173 
 
 173 
 
 173 
 
 75 
 
 76 
 
 175 
 
 171 
 
 162 
 
 151 
 
 136 
 
 119 
 
 101 
 
 206 
 
 184 
 
 178 
 
 173 
 
 170 
 
 169 
 
 170 
 
 72 
 
 74 
 
 174 
 
 171 
 
 165 
 
 155 
 
 141 
 
 124 
 
 107 
 
 207 
 
 182 
 
 175 
 
 170 
 
 165 
 
 164 
 
 165 
 
 167 
 
 70 
 
 171 
 
 170 
 
 165 
 
 157 
 
 144 
 
 129 
 
 112 
 
 208 
 
 181 
 
 173 
 
 166 
 
 160 
 
 158 
 
 160 
 
 162 
 
 165 
 
 167 
 
 167 
 
 164 
 
 157 
 
 147 
 
 133 
 
 117 
 
 209 
 
 170 
 
 170 
 
 162 
 
 156 
 
 153 
 
 153 
 
 155 
 
 159 
 
 162 
 
 164 
 
 162 
 
 157 
 
 148 
 
 136 
 
 120 
 
 210 
 
 178 
 
 168 
 
 150 
 
 152 
 
 148 
 
 147 
 
 149 
 
 153 
 
 156 
 
 150 
 
 159 
 
 156 
 
 143 
 
 137 
 
 124 
 
 211 
 
 170 
 
 167 
 
 157 
 
 149 
 
 144 
 
 142 
 
 142 
 
 146 
 
 150 
 
 154 
 
 155 
 
 153 
 
 148 
 
 138 
 
 126 
 
 212 
 
 180 
 
 167 
 
 156 
 
 146 
 
 140 
 
 137 
 
 137 
 
 141 
 
 145 
 
 148 
 
 151 
 
 150 
 
 146 
 
 138 
 
 127 
 
 213 
 
 182 
 
 169 
 
 157 
 
 146 
 
 130 
 
 135 
 
 134 
 
 136 
 
 140 
 
 143 
 
 147 
 
 148 
 
 144 
 
 133 
 
 128 
 
 214 
 
 186 
 
 172 
 
 IG;) 
 
 148 
 
 130 
 
 134 
 
 132 
 
 133 
 
 137 
 
 141 
 
 144 
 
 145 
 
 143 
 
 137 
 
 123 
 
 215 
 
 190 
 
 177 
 
 164 
 
 152 
 
 M2 
 
 136 
 
 133 
 
 133 
 
 135 
 
 139 
 
 142 
 
 143 
 
 141 
 
 136 
 
 123 
 
 216 
 
 106 
 
 183 
 
 170 
 
 157 
 
 147 
 
 130 
 
 135 
 
 134 
 
 136 
 
 138 
 
 141 
 
 142 
 
 141 
 
 136 
 
 120 
 
 217 
 
 202 
 
 190 
 
 177 
 
 164 
 
 153 
 
 145 
 
 140 
 
 138 
 
 138 
 
 140 
 
 142 
 
 143 
 
 141 
 
 137 
 
 129 
 
 218 
 
 207 
 
 107 
 
 185 
 
 172 
 
 161 
 
 152 
 
 146 
 
 143 
 
 143 
 
 143 
 
 145 
 
 145 
 
 143 
 
 139 
 
 131 
 
 210 
 
 213 
 
 204 
 
 193 
 
 181 
 
 170 
 
 163 
 
 151 
 
 150 
 
 14!) 
 
 148 
 
 149 
 
 149 
 
 146 
 
 '142 
 
 135 
 
 220 
 
 217 
 
 210 
 
 20!) 
 
 180 
 
 179 
 
 169 
 
 162 
 
 158 
 
 156 
 
 155 
 
 155 
 
 154 
 
 151 
 
 147 
 
 139 
 
 2-31 
 
 220 
 
 215 
 
 207 
 
 197 
 
 187 
 
 178 
 
 171 
 
 166 
 
 164 
 
 162 
 
 162 
 
 161 
 
 158 
 
 153 
 
 146 
 
 222 
 
 222 
 
 210 
 
 212 
 
 21)4 
 
 105 
 
 186 
 
 180 
 
 175 
 
 172 
 
 171 
 
 170 
 
 160 
 
 166 
 
 161 
 
 154 
 
 223 
 
 221 
 
 220 
 
 216 
 
 209 
 
 201 
 
 193 
 
 187 
 
 183 
 
 181 
 
 179. 
 
 179 
 
 178 
 
 175 
 
 171 
 
 163 
 
 224 
 
 219 
 
 220 
 
 217 
 
 212 
 
 205 
 
 109 
 
 194 
 
 190 
 
 188 
 
 187 
 
 187 
 
 187 
 
 185 
 
 181 
 
 174 
 
 225 
 
 215 
 
 218 
 
 217 
 
 213 
 
 208 
 
 202 
 
 198 
 
 195 
 
 104 
 
 104 
 
 105 
 
 106 
 
 105 
 
 192 
 
 186 
 
 226 
 
 210 
 
 214 
 
 214 
 
 211 
 
 238 
 
 204 
 
 201 
 
 1 00 
 
 109 
 
 200 
 
 202 
 
 204 
 
 204 
 
 232 
 
 103 
 
 227 
 
 202 
 
 208 
 
 209 
 
 208 
 
 206 
 
 203 
 
 201 
 
 201 
 
 202 
 
 205 
 
 238 
 
 211 
 
 213 
 
 213 
 
 200 
 
 228 
 
 104 
 
 2(10 
 
 203 
 
 203 
 
 202 
 
 200 
 
 200 
 
 201 
 
 204 
 
 208 
 
 313 
 
 217 
 
 221 
 
 222 
 
 220 
 
 999 
 
 184 
 
 192 
 
 195 
 
 107 
 
 107 
 
 196 
 
 197 
 
 100 
 
 203 
 
 208 
 
 215 
 
 Ml 
 
 226 
 
 230 
 
 22!) 
 
 230 
 
 174 
 
 182 
 
 187 
 
 189 
 
 190 
 
 190 
 
 192 
 
 105 
 
 200 
 
 207 
 
 216 
 
 223 
 
 230 
 
 235 
 
 237 
 
 231 
 
 163 
 
 172 
 
 177 
 
 181 
 
 182 
 
 183 
 
 186 
 
 100 
 
 196 
 
 234 
 
 214 
 
 223 
 
 231 
 
 238 
 
 241 
 
 232 
 
 153 
 
 161 
 
 167 
 
 172 
 
 173 
 
 175 
 
 178 
 
 183 
 
 100 
 
 100 
 
 210 
 
 220 
 
 230 
 
 839 
 
 243 
 
 233 
 
 142 
 
 151 
 
 157 
 
 162 
 
 164 
 
 167 
 
 170 
 
 175 
 
 183 
 
 102 
 
 204 
 
 215 
 
 227 
 
 236 
 
 213 
 
 234 
 
 131 
 
 140 
 
 147 
 
 152 
 
 155 
 
 158 
 
 161 
 
 167 
 
 174 
 
 184 
 
 196 
 
 209 
 
 221 
 
 232 
 
 240 
 
 235 
 
 120 
 
 130 
 
 137 
 
 142 
 
 145 
 
 148 
 
 152 
 
 157 
 
 165 
 
 175 
 
 187 
 
 200 
 
 213 
 
 225 
 
 231 
 
 236 
 
 110 
 
 119 
 
 127 
 
 132 
 
 136 
 
 130 
 
 142 
 
 147 
 
 155 
 
 165 
 
 177 
 
 190 
 
 203 
 
 215 
 
 225 
 
 237 
 
 99 
 
 109 
 
 117 
 
 123- 
 
 126 
 
 120 
 
 132 
 
 137 
 
 114 
 
 153 
 
 165 
 
 178 
 
 102 
 
 234 
 
 215 
 
 238 
 
 80 
 
 09 
 
 107 
 
 113 
 
 117 
 
 110 
 
 122 
 
 127 
 
 133 
 
 1-12 
 
 153 
 
 166 
 
 179 
 
 192 
 
 203 
 
 230 
 
 80 
 
 89 
 
 97 
 
 103 
 
 107 
 
 110 
 
 112 
 
 lib 
 
 122 
 
 130 
 
 140 
 
 153 
 
 166 
 
 179 
 
 101 . 
 
 HMO 
 
 71 
 
 80 
 
 88 
 
 94 
 
 98 
 
 100 
 
 102 
 
 104 
 
 110 
 
 117 
 
 127 
 
 140 
 
 153 
 
 1 65 
 
 177 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 The perturbations are expressed in hundrudtlis of a second of arc. 
 
TABL.E XXII. 
 
 /'< rlurtiiiliuii.-: iift/i*' l.ninjititilf lnj the Eurtli. 
 
 lliiri/iuiiiil Aiguiiiriit = I. 
 
 lit milled I" i i I 1 , riod Of U] .-lit XI , -JIH units. 
 
 
 ,i 
 
 ,i 
 
 ,i 
 
 ,i ,i 
 
 .1 
 
 t 
 
 ii 
 
 .1 
 
 ,1 
 
 
 .1 
 
 d 
 
 ,1 
 
 .1 
 
 Arg.Xl 
 
 120 
 
 law 
 
 i:t<i 
 
 191 
 
 132 
 
 ICO 
 
 1<>M 
 
 170 
 
 INI 
 
 l2 
 
 200 
 
 20* 
 
 210 
 
 UN 
 
 232 
 
 ISO 
 
 211 
 
 j-ji 
 
 936 
 
 Jll 
 
 848 
 
 948 
 
 943 
 
 833 
 
 999 
 
 807 
 
 195 
 
 183 
 
 171 
 
 167 
 
 Hi) 
 
 181 
 
 193 
 
 208 
 
 J-JI 
 
 23d 
 
 339 
 
 849 
 
 831) 
 
 939 
 
 899 
 
 900 
 
 l!>7 
 
 1-5 
 
 17.-. 
 
 L67 
 
 IG3 
 
 1-.' 
 
 IT:. 
 
 190 
 
 805 
 
 918 
 
 898 
 
 933 
 
 834 
 
 'J'J! 1 
 
 829 
 
 910 
 
 198 
 
 186 
 
 I7(i 
 
 168 
 
 163 
 
 183 
 
 IG6 
 
 ITS 
 
 I-- 
 
 903 
 
 816 
 
 J'J 1 
 
 ,'.'7 
 
 22:. 
 
 880 
 
 Jin 
 
 109 
 
 1-7 
 
 71, 
 
 168 
 
 169 
 
 l-l 
 
 13d 
 
 IM 
 
 171 
 
 188 
 
 809 
 
 213 
 
 910 
 
 
 817 
 
 Jll!) 
 
 199 
 
 188 
 
 77 
 
 168 
 
 169 
 
 186 
 
 121 
 
 137 
 
 155 
 
 179 
 
 I-- 
 
 801 
 
 810 
 
 Jl 1 
 
 913 
 
 908 
 
 111!) 
 
 188 
 
 7- 
 
 168 
 
 nil 
 
 l-i, 
 
 106 
 
 131 
 
 139 
 
 107 
 
 175 
 
 100 
 
 801 
 
 
 809 
 
 805 
 
 198 
 
 180 
 
 7!l 
 
 169 
 
 n,i 
 
 187 
 
 n 
 
 101 
 
 195 
 
 III 
 
 169 
 
 179 
 
 199 
 
 801 
 
 804 
 
 : a 
 
 197 
 
 189 
 
 7!) 
 
 169 
 
 Mil 
 
 188 
 
 81 
 
 96 
 
 119 
 
 131 
 
 160 
 
 168 
 
 183 
 
 194 
 
 800 
 
 j i i 
 
 11)6 
 
 189 
 
 1711 
 
 169 
 
 160 
 
 160 
 
 72 
 
 >:, 
 
 mi 
 
 130 
 
 140 
 
 169 
 
 17.-. 
 
 187 
 
 195 
 
 197 
 
 196 
 
 189 
 
 180 
 
 170 
 
 160 
 
 180 
 
 65 
 
 77 
 
 99 
 
 111 
 
 131 
 
 ISO 
 
 167 
 
 181 
 
 190 
 
 104 
 
 194 
 
 i m 
 
 l-l 
 
 171 
 
 li,l 
 
 1!H 
 
 Gl) 
 
 71 
 
 
 1(13 
 
 199 
 
 149 
 
 160 
 
 17.-, 
 
 I-:. 
 
 191 
 
 199 
 
 188 
 
 189 
 
 I7'J 
 
 162 
 
 1'.i2 
 
 57 
 
 66 
 
 79 
 
 96 
 
 115 
 
 135 
 
 153 
 
 Ill:' 
 
 181 
 
 188 
 
 190 
 
 188 
 
 183 
 
 171 
 
 n.l 
 
 193 
 
 G6 
 
 63 
 
 7:. 
 
 mi 
 
 10- 
 
 198 
 
 117 
 
 !(.:< 
 
 17G 
 
 185 
 
 18!) 
 
 188 
 
 l-l 
 
 17G 
 
 166 
 
 1U4 
 
 55 
 
 60 
 
 71 
 
 85 
 
 102 
 
 121 
 
 140 
 
 157 
 
 171 
 
 181 
 
 187 
 
 188 
 
 185 
 
 179 
 
 169 
 
 I!).") 
 
 Gfi 
 
 60 
 
 G7 
 
 80 
 
 96 
 
 115 
 
 133 
 
 151 
 
 166 
 
 177 
 
 I-:, 
 
 188 
 
 l-(i 
 
 l-l 
 
 171 
 
 106 
 
 66 
 
 :.- 
 
 64 
 
 76 
 
 90 
 
 108 
 
 137 
 
 144 
 
 160 
 
 17)1 
 
 I^'J 
 
 186 
 
 1-7 
 
 l-l 
 
 178 
 
 1(17 
 
 67 
 
 67 
 
 69 
 
 72 
 
 -:. 
 
 101 
 
 11!) 
 
 137 
 
 153 
 
 167 
 
 178 
 
 185 
 
 187 
 
 186 
 
 189 
 
 108 
 
 69 
 
 57 
 
 60 
 
 68 
 
 79 
 
 95 
 
 119 
 
 139 
 
 146 
 
 nil 
 
 173 
 
 189 
 
 187 
 
 188 
 
 185 
 
 100 
 
 Gl 
 
 58 
 
 58 
 
 64 
 
 74 
 
 88 
 
 104 
 
 121 
 
 139 
 
 154 
 
 168 
 
 178 
 
 185 
 
 188 
 
 188 
 
 200 
 
 lit 
 
 58 
 
 57 
 
 60 
 
 69 
 
 81 
 
 97 
 
 113 
 
 130 
 
 146 
 
 161 
 
 17:! 
 
 182 
 
 187 
 
 189 
 
 Ml 
 
 G7 
 
 68 
 
 66 
 
 57 
 
 (il 
 
 7r, 
 
 89 
 
 105 
 
 139 
 
 138 
 
 153 
 
 166 
 
 177 
 
 184 
 
 I-- 
 
 909 
 
 71 
 
 61 
 
 56 
 
 .-,:, 
 
 60 
 
 69 
 
 82 
 
 '.17 
 
 113 
 
 139 
 
 145 
 
 159 
 
 170 
 
 I7!l 
 
 1-:. 
 
 903 
 
 76 
 
 G4 
 
 57 
 
 54 
 
 67 
 
 (il 
 
 75 
 
 89 
 
 104 
 
 130 
 
 135 
 
 150 
 
 162 
 
 172 
 
 180 
 
 904 
 
 80 
 
 67 
 
 58 
 
 54 
 
 55 
 
 61 
 
 6!) 
 
 82 
 
 96 
 
 111 
 
 196 
 
 140 
 
 153 
 
 164 
 
 173 
 
 205 
 
 85 
 
 71 
 
 61 
 
 66 
 
 .'I 
 
 58 
 
 65 
 
 75 
 
 88 
 
 101 
 
 116 
 
 129 
 
 1 t-j 
 
 154 
 
 164 
 
 106 
 
 90 
 
 76 
 
 G4 
 
 57 
 
 54 
 
 56 
 
 61 
 
 70 
 
 81 
 
 99 
 
 105 
 
 118 
 
 131 
 
 142 
 
 159 
 
 207 
 
 95 
 
 80 
 
 68 
 
 60 
 
 56 
 
 56 
 
 51) 
 
 66 
 
 74 
 
 -1 
 
 96 
 
 107 
 
 II!) 
 
 139 
 
 110 
 
 208 
 
 Kid 
 
 85 
 
 72 
 
 61 
 
 57 
 
 56 
 
 :,7 
 
 69 
 
 69 
 
 77 
 
 87 
 
 96 
 
 107 
 
 116 
 
 136 
 
 20!) 
 
 105 
 
 90 
 
 77 
 
 67 
 
 60 
 
 57 
 
 56 
 
 60 
 
 65 
 
 71 
 
 78 
 
 -ii 
 
 !)5 
 
 103 
 
 112 
 
 210 
 
 10!) 
 
 94 
 
 81 
 
 70 
 
 62 
 
 58 
 
 56 
 
 58 
 
 61 
 
 66 
 
 71 
 
 .77 
 
 84 
 
 91 
 
 98 
 
 211 
 
 119 
 
 97 
 
 84 
 
 73 
 
 65 
 
 60 
 
 57 
 
 57 
 
 60 
 
 62 
 
 65 
 
 (ill 
 
 71 
 
 7!) 
 
 86 
 
 Bit! 
 
 114 
 
 100 
 
 87 
 
 7G 
 
 67 
 
 61 
 
 58 
 
 57 
 
 57 
 
 59 
 
 61 
 
 -62 
 
 66 
 
 69 
 
 74 
 
 913 
 
 115 
 
 102 
 
 JO 
 
 79 
 
 69 
 
 63 
 
 59 
 
 57 
 
 56 
 
 66 
 
 57 
 
 57 
 
 59 
 
 61 
 
 65 
 
 214 
 
 116 
 
 104 
 
 91 
 
 80 
 
 71 
 
 64 
 
 60 
 
 57 
 
 56 
 
 60 
 
 55 
 
 54 
 
 55 
 
 55 
 
 57 
 
 215 
 
 117 
 
 105 
 
 93 
 
 81 
 
 72 
 
 65 
 
 60 
 
 58 
 
 56 
 
 55 
 
 54 
 
 69 
 
 52 
 
 :.i 
 
 61 
 
 9H> 
 
 118 
 
 106 
 
 94 
 
 82 
 
 73 
 
 66 
 
 61 
 
 58 
 
 57 
 
 66 
 
 .-,1 
 
 51 
 
 50 
 
 4!) 
 
 48 
 
 217 
 
 11!) 
 
 107 
 
 KS 
 
 84 
 
 75 
 
 67 
 
 62 
 
 69 
 
 58 
 
 :.7 
 
 .-,:, 
 
 69 
 
 50 
 
 48 
 
 46 
 
 918 
 
 121 
 
 109 
 
 97 
 
 86 
 
 76 
 
 69 
 
 64 
 
 Gl 
 
 69 
 
 58 
 
 57 
 
 54 
 
 52 
 
 49 
 
 46 
 
 21!) 
 
 194 
 
 113 
 
 100 
 
 89 
 
 79 
 
 71 
 
 66 
 
 63 
 
 61 
 
 61 
 
 59 
 
 57 
 
 55 
 
 52 
 
 48 
 
 990 
 
 129 
 
 117 
 
 104 
 
 93 
 
 83 
 
 75 
 
 6!) 
 
 66 
 
 64 
 
 63 
 
 69 
 
 60 
 
 58 
 
 55 
 
 61 
 
 981 
 
 1 35 
 
 123 
 
 111 
 
 99 
 
 88 
 
 71) 
 
 74 
 
 70 
 
 68 
 
 68 
 
 67 
 
 (.1 
 
 62 
 
 60 
 
 .-,:, 
 
 993 
 
 143 
 
 131 
 
 118 
 
 106 
 
 96 
 
 86 
 
 80 
 
 7.-) 
 
 73 
 
 7'J 
 
 79 
 
 69 
 
 67 
 
 (il 
 
 (in 
 
 33 
 
 1 53 
 
 141 
 
 128 
 
 116 
 
 104 
 
 94 
 
 87 
 
 82 
 
 80 
 
 7') 
 
 77 
 
 75 
 
 73 
 
 69 
 
 Gl 
 
 994 
 
 164 
 
 153 
 
 140 
 
 127 
 
 115 
 
 105 
 
 97 
 
 91 
 
 87 
 
 85 
 
 84 
 
 81 
 
 7!) 
 
 7:. 
 
 6!) 
 
 225 
 
 177 
 
 166 
 
 153 
 
 140 
 
 128 
 
 117 
 
 108 
 
 101 
 
 97 
 
 95 
 
 !)2 
 
 88 
 
 85 
 
 81 
 
 7.-. 
 
 226 
 
 190 
 
 180 
 
 167 
 
 K,4 
 
 142 
 
 130 
 
 120 
 
 113 
 
 107 
 
 103 
 
 100 
 
 96 
 
 92 
 
 87 
 
 80 
 
 9S7 
 
 203 
 
 193 
 
 189 
 
 16!) 
 
 156 
 
 III 
 
 134 
 
 125 
 
 11!) 
 
 114 
 
 110 
 
 105 
 
 100 
 
 94 
 
 86 
 
 228 
 
 2 1 5 
 
 21)7 
 
 1!Ki 
 
 Iri4 
 
 171 
 
 159 
 
 148 
 
 139 
 
 131 
 
 195 
 
 120 
 
 114 
 
 108 
 
 mi 
 
 IK! 
 
 999 
 
 226 
 
 21!) 
 
 209 
 
 198 
 
 186 
 
 173 
 
 162 
 
 152 
 
 144 
 
 137 
 
 131 
 
 194 
 
 117 
 
 108 
 
 100 
 
 930 
 
 231 
 232 
 233 
 234 
 
 234 
 241 
 
 245 
 24G 
 244 
 
 230 
 238 
 244 
 246 
 246 
 
 221 
 231 
 
 338 
 
 242 
 
 244 
 
 211 
 
 222 
 231 
 2:56 
 239 
 
 19!) 
 211 
 221 
 228 
 232 
 
 187 
 900 
 
 210 
 218 
 224 
 
 176 
 
 189 
 200 
 209 
 216 
 
 166 
 178 
 
 190 
 200 
 207 
 
 157 
 
 169 
 181 
 191 
 
 200 
 
 149 
 161 
 172 
 183 
 192 
 
 142 
 153 
 165 
 
 17.-, 
 185 
 
 134 
 145 
 156 
 
 167 
 177 
 
 127 
 137 
 148 
 158 
 169 
 
 118 
 ISti 
 138 
 149 
 159 
 
 109 
 117 
 187 
 
 137 
 148 
 
 235 
 236 
 987 
 
 sea 
 
 939 
 
 240 
 
 240 
 233 
 224 
 213 
 
 201 
 
 188 
 
 243 
 237 
 229 
 219 
 207 
 196 
 
 242 
 238 
 231 
 222 
 211 
 201 
 
 239 
 936 
 
 230 
 223 
 214 
 204 
 
 233 
 232 
 938 
 222 
 214 
 901 
 
 227 
 227 
 224 
 220 
 213 
 206 
 
 220 
 221 
 220 
 217 
 212 
 206 
 
 913 
 
 216 
 217 
 216 
 919 
 
 207 
 
 206 
 211 
 
 Jll 
 Jll 
 Jll 
 209 
 
 200 
 206 
 211 
 212 
 'JI3 
 
 911 
 
 1114 
 201 
 907 
 911 
 213 
 213 
 
 187 
 196 
 203 
 208 
 819 
 814 
 
 179 
 189 
 1*17 
 Jill 
 210 
 214 
 
 170 
 180 
 190 
 196 
 908 
 211 
 
 ISO 
 
 170 
 180 
 
 I'.M) 
 
 1 - 
 
 Add 147.64 to Are. XI. when 224'>.7 is subtracted from Arg. I. 
 
40 
 
 TABLE XX1I1. 
 
 Perturbations of the Longitude by Mars. 
 
 Horizontal Argument = I. 
 
 Constant added 0'M3. Period of Argument 1., 224<1.7. 
 
 Aif. 
 XII. 
 
 4 
 
 
 d 
 
 i 
 
 d 
 
 16 
 
 cl 
 
 24 
 
 d 
 
 32 
 
 d 
 
 40 
 
 i 
 
 48 
 
 d 
 
 158 
 
 d 
 
 61 
 
 d 
 
 72 
 
 d 
 80 
 
 d 
 88 
 
 d 
 96 
 
 104 
 
 d 
 
 112 
 
 
 
 3 
 
 4 
 
 6 
 
 9 
 
 12 
 
 15 
 
 17 
 
 20 
 
 23 
 
 24 
 
 26 
 
 26 
 
 26 
 
 26 
 
 24 
 
 1 
 
 1 
 
 2 
 
 3 
 
 5 
 
 8 
 
 11 
 
 14 
 
 17 
 
 20 
 
 22 
 
 24 
 
 26 
 
 26 
 
 26 
 
 26 
 
 2 
 
 1 
 
 1 
 
 1 
 
 3 
 
 5 
 
 8 
 
 10 
 
 14 
 
 17 
 
 19 
 
 22 
 
 24 
 
 25 
 
 26 
 
 26 
 
 3 
 
 2 
 
 1 
 
 1 
 
 1 
 
 3 
 
 5 
 
 7 
 
 10 
 
 13 
 
 16 
 
 19 
 
 21 
 
 23 
 
 24 
 
 25 
 
 4 
 
 4 
 
 2 
 
 1 
 
 1 
 
 2 
 
 3 
 
 5 
 
 8 
 
 10 
 
 13 
 
 16 
 
 18 
 
 20 
 
 22 
 
 23 
 
 5 
 
 6 
 
 4 
 
 3 
 
 2 
 
 2 
 
 2 
 
 4 
 
 6 
 
 8 
 
 11 
 
 13 
 
 16 
 
 18 
 
 20 
 
 21 
 
 6 
 
 8 
 
 6 
 
 4 
 
 3 
 
 3 
 
 2 
 
 3 
 
 5 
 
 7 
 
 9 
 
 11 
 
 14 
 
 16 
 
 18 
 
 20 
 
 7 
 
 1! 
 
 8 
 
 6 
 
 5 
 
 4 
 
 3 
 
 4 
 
 6 
 
 6 
 
 8 
 
 10 
 
 13 
 
 15 
 
 16 
 
 18 
 
 8 
 
 12 
 
 10 
 
 8 
 
 6 
 
 5 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 9 
 
 12 
 
 14 
 
 16 
 
 18 
 
 9 
 
 14 
 
 12 
 
 10 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 5 
 
 7 
 
 9 
 
 11 
 
 13 
 
 15 
 
 17 
 
 10 
 
 15 
 
 13 
 
 11 
 
 9 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 15 
 
 17 
 
 11 
 
 17 
 
 15 
 
 13 
 
 11 
 
 8 
 
 7 
 
 5 
 
 6 
 
 5 
 
 5 
 
 7 
 
 9 
 
 II 
 
 14 
 
 16 
 
 12 
 
 18 
 
 17 
 
 15 
 
 12 
 
 10 
 
 8 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 7 
 
 9 
 
 13 
 
 15 
 
 13 
 
 20 
 
 19 
 
 17 
 
 15 
 
 12 
 
 10 
 
 8 
 
 6 
 
 6 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 13 
 
 11 
 
 21 
 
 21 
 
 19 
 
 17 
 
 15 
 
 13 
 
 10 
 
 8 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 15 
 
 22 
 
 22 
 
 21 
 
 19 
 
 17 
 
 16 
 
 13 
 
 10 
 
 8 
 
 7 
 
 6 
 
 5 
 
 6 
 
 7 
 
 9 
 
 16 
 
 21 
 
 22 
 
 22 
 
 21 
 
 19 
 
 18 
 
 15 
 
 13 
 
 11 
 
 9 
 
 7 
 
 (i 
 
 6 
 
 6 
 
 8 
 
 17 
 
 20 
 
 21 
 
 21 
 
 21 
 
 20 
 
 19 
 
 J8 
 
 15 
 
 13 
 
 11 
 
 9 
 
 8 
 
 7 
 
 7 
 
 7 
 
 18 
 
 17 
 
 19 
 
 20 
 
 20 
 
 20 
 
 20 
 
 19 
 
 17 
 
 15 
 
 13 
 
 11 
 
 10 
 
 9 
 
 8 
 
 8 
 
 19 
 
 15 
 
 16 
 
 18 
 
 19 
 
 19 
 
 19 
 
 19 
 
 17 
 
 16 
 
 15 
 
 13 
 
 11 
 
 10 
 
 9 
 
 9 
 
 20 
 
 13 
 
 15 
 
 15 
 
 16 
 
 17 
 
 18 
 
 18 
 
 17 
 
 16 
 
 15 
 
 14 
 
 12 
 
 11 
 
 10 
 
 10 
 
 21 
 
 12 
 
 13 
 
 14 
 
 15 
 
 15 
 
 16 
 
 16 
 
 16 
 
 15 
 
 14 
 
 13 
 
 12 
 
 11 
 
 11 
 
 10 
 
 22 
 
 12 
 
 13 
 
 13 
 
 14 
 
 14 
 
 15 
 
 15 
 
 14 
 
 14 
 
 14 
 
 13 
 
 12 
 
 11 
 
 10 
 
 10 
 
 23 
 
 13 
 
 13 
 
 14 
 
 14 
 
 14 
 
 14 
 
 14 
 
 14 
 
 13 
 
 13 
 
 12 
 
 11 
 
 10 
 
 9 
 
 9 
 
 24 
 
 15 
 
 15 
 
 15 
 
 15 
 
 15 
 
 15 
 
 14 
 
 14 
 
 13 
 
 12 
 
 12 
 
 10 
 
 9 
 
 8 
 
 8 
 
 25 
 
 10 
 
 16 
 
 16 
 
 16 
 
 16 
 
 16 
 
 16 
 
 15 
 
 14 
 
 13 
 
 12 
 
 11 
 
 9 
 
 8 
 
 7 
 
 26 
 
 16 
 
 17 
 
 17 
 
 17 
 
 17 
 
 17 
 
 17 
 
 17 
 
 16 
 
 15 
 
 13 
 
 12 
 
 10 
 
 9 
 
 7 
 
 27 
 
 16 
 
 16 
 
 17 
 
 ifl 
 
 18 
 
 19 
 
 19 
 
 18 
 
 18 
 
 17 
 
 15 
 
 14 
 
 12 
 
 10 
 
 8 
 
 28 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 19 
 
 19 
 
 19 
 
 19 
 
 18 
 
 16 
 
 14 
 
 13 
 
 11 
 
 29 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 19 
 
 20 
 
 20 
 
 20 
 
 19 
 
 18 
 
 17 
 
 15 
 
 13 
 
 30 
 
 10 
 
 11 
 
 11 
 
 13 
 
 14 
 
 16 
 
 17 
 
 19 
 
 20 
 
 20 
 
 20 
 
 20 
 
 19 
 
 17 
 
 15 
 
 31 
 
 
 
 9 
 
 9 
 
 10 
 
 12 
 
 13 
 
 15 
 
 17 
 
 18 
 
 19 
 
 20 
 
 20 
 
 19 
 
 18 
 
 17 
 
 32 
 
 !) 
 
 9 
 
 8 
 
 9 
 
 9 
 
 11 
 
 12 
 
 14 
 
 16 
 
 17 
 
 18 
 
 19 
 
 19 
 
 19 
 
 18 
 
 33 
 
 11 
 
 9 
 
 8 
 
 8 
 
 8 
 
 9 
 
 10 
 
 12 
 
 13 
 
 15 
 
 16 
 
 17 
 
 18 
 
 18 
 
 18 
 
 34 
 
 13 
 
 11 
 
 9 
 
 8 
 
 8 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 14 
 
 15 
 
 16 
 
 16 
 
 17 
 
 35 
 
 15 
 
 13 
 
 11 
 
 10 
 
 9 
 
 8 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 15 
 
 36 
 
 18 
 
 16 
 
 13 
 
 11 
 
 10 
 
 9 
 
 9 
 
 9 
 
 10 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 14 
 
 37 
 
 20 
 
 18 
 
 16 
 
 14 
 
 12 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 14 
 
 38 
 
 22 
 
 20 
 
 18 
 
 15 
 
 14 
 
 12 
 
 11 
 
 11 
 
 10 
 
 11 
 
 11 
 
 12 
 
 13 
 
 14 
 
 14 
 
 39 
 
 23 
 
 21 
 
 19 
 
 17 
 
 15 
 
 13 
 
 12 
 
 11 
 
 11 
 
 11 
 
 12 
 
 13 
 
 13 
 
 14 
 
 15 
 
 40 
 
 24 
 
 23 
 
 21 
 
 18 
 
 17 
 
 15 
 
 13 
 
 12 
 
 11 
 
 11 
 
 12 
 
 13 
 
 13 
 
 14 
 
 15 
 
 41 
 
 25 
 
 24 
 
 22 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 12 
 
 11 
 
 18 
 
 12 
 
 13 
 
 14 
 
 15 
 
 42 
 
 26 
 
 25 
 
 24 
 
 22 
 
 20 
 
 18 
 
 15 
 
 14 
 
 12 
 
 12 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 43 
 
 28 
 
 27 
 
 26 
 
 24 
 
 22 
 
 23 
 
 17 
 
 15 
 
 13 
 
 12 
 
 11 
 
 12 
 
 12 
 
 13 
 
 14 
 
 44 
 
 28 
 
 28 
 
 28 
 
 26 
 
 24 
 
 22 
 
 23 
 
 17 
 
 15 
 
 13 
 
 12 
 
 11 
 
 11 
 
 12 
 
 13 
 
 45 
 
 28 
 
 29 
 
 29 
 
 28 
 
 27 
 
 25 
 
 23 
 
 20 
 
 17 
 
 15 
 
 13 
 
 12 
 
 11 
 
 11 
 
 12 
 
 46 
 
 27 
 
 28 
 
 29 
 
 29 
 
 28 
 
 27 
 
 25 
 
 23 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 12 
 
 12 
 
 47 
 
 24 
 
 26 
 
 28 
 
 29 
 
 2!) 
 
 28 
 
 27 
 
 25 
 
 23 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 12 
 
 48 
 
 21 
 
 24 
 
 26 
 
 27 
 
 28 
 
 28 
 
 28 
 
 26 
 
 25 
 
 23 
 
 21 
 
 19 
 
 16 
 
 15 
 
 14 
 
 49 
 
 18 
 
 20 
 
 23 
 
 25 
 
 26 
 
 27 
 
 27 
 
 27 
 
 26 
 
 24 
 
 22 
 
 20 
 
 19 
 
 17 
 
 15 
 
 50 
 
 16 
 
 17 
 
 20 
 
 22 
 
 24 
 
 25 
 
 26 
 
 26 
 
 25 
 
 25 
 
 23 
 
 22 
 
 2!) 
 
 18 
 
 17 
 
 51 
 
 13 
 
 15 
 
 17 
 
 19 
 
 21 
 
 23 
 
 24 
 
 24 
 
 24 
 
 24 
 
 23 
 
 22 
 
 21 
 
 19 
 
 18 
 
 52 
 
 12 
 
 14 
 
 16 
 
 17 
 
 If) 
 
 21 
 
 22 
 
 23 
 
 21! 
 
 23 
 
 22 
 
 21 
 
 20 
 
 19 
 
 18 
 
 53 
 
 12 
 
 13 
 
 15 
 
 17 
 
 18 
 
 20 
 
 21 
 
 21 
 
 22 
 
 22 
 
 21 
 
 21 
 
 20 
 
 19 
 
 17 
 
 54 
 
 12 
 
 14 
 
 15 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 21 
 
 21 
 
 21 
 
 20 
 
 19 
 
 18 
 
 17 
 
 55 
 
 12 
 
 14 
 
 15 
 
 17 
 
 18 
 
 23 
 
 21 
 
 21 
 
 21 
 
 21 
 
 20 
 
 20 
 
 19 
 
 18 
 
 16 
 
 56 
 
 12 
 
 14 
 
 15 
 
 17 
 
 19 
 
 2;) 
 
 21 
 
 22 
 
 22 
 
 22 
 
 22 
 
 21 
 
 20 
 
 18 
 
 17 
 
 57 
 
 10 
 
 12 
 
 14 
 
 17 
 
 19 
 
 20 
 
 22 
 
 2-3 
 
 23 
 
 24 
 
 23 
 
 22 
 
 21 
 
 20 
 
 18 
 
 58 
 
 8 
 
 10 
 
 12 
 
 \:> 
 
 17 
 
 20 
 
 21 
 
 23 
 
 24 
 
 25 
 
 25 
 
 24 
 
 23 
 
 22 
 
 20 
 
 59 
 
 5 
 
 7 
 
 9 
 
 12 
 
 15 
 
 17 
 
 23 
 
 22 
 
 24 
 
 25 
 
 26 
 
 26 
 
 25 
 
 24 
 
 22 
 
 6) 
 
 3 
 
 4 
 
 6 
 
 9 
 
 12 
 
 15 
 
 17 
 
 21 
 
 23 
 
 24 
 
 26 
 
 26 
 
 26 
 
 26 
 
 24 
 
 The perturbation! are expressed in hundredth* of a second of tin: 
 
TABLE \\III. 
 
 41 
 
 Partarfaffow /'// Lin>itu<li- by MII/-.I. 
 
 ll"ii/unl;il Ariiinrnr = I. 
 
 <'i>ii<t:iin aildnl ()' .!.">. IVnoil ot'Argiiinriit XII., GO unite. 
 
 Arg. 
 XII 
 
 lio 
 
 a 
 1* 
 
 .1 
 136 
 
 ,1 
 111 
 
 .1 
 1-52 
 
 160 
 
 IN 
 
 176 
 
 ll 
 INI 
 
 -I 
 192 
 
 too 
 
 SON 
 
 .1 
 216 
 
 J-JI 
 
 M 
 
 
 
 23 
 
 81 
 
 10 
 
 17 
 
 16 
 
 13 
 
 19 
 
 11 
 
 10 
 
 10 
 
 10 
 
 II 
 
 19 
 
 14 
 
 16 
 
 1 
 
 85 
 
 2:1 
 
 81 
 
 1!) 
 
 i; 
 
 16 
 
 14 
 
 19 
 
 11 
 
 11 
 
 11 
 
 II 
 
 ii 
 
 19 
 
 13 
 
 *i 
 
 K5 
 
 M 
 
 83 
 
 89 
 
 80 
 
 Iti 
 
 16 
 
 16 
 
 13 
 
 18 
 
 19 
 
 II 
 
 19 
 
 19 
 
 13 
 
 :t 
 
 85 
 
 
 M 
 
 83 
 
 21 
 
 80 
 
 18 
 
 17 
 
 15 
 
 14 
 
 13 
 
 13 
 
 13 
 
 13 
 
 1:1 
 
 4 
 
 M 
 
 -,'l 
 
 21 
 
 83 
 
 89 
 
 21 
 
 19 
 
 18 
 
 17 
 
 16 
 
 16 
 
 II 
 
 14 
 
 II 
 
 11 
 
 B 
 
 22 
 
 ,':i 
 
 83 
 
 88 
 
 J-' 
 
 20 
 
 I'.i 
 
 IS 
 
 17 
 
 17 
 
 16 
 
 16 
 
 16 
 
 M 
 
 K 
 
 6 
 
 21 
 
 21 
 
 81 
 
 .'i 
 
 M 
 
 80 
 
 1!) 
 
 18 
 
 17 
 
 16 
 
 Hi 
 
 H, 
 
 Hi 
 
 16 
 
 16 
 
 7 
 
 80 
 
 20 
 
 ."i 
 
 80 
 
 
 19 
 
 18 
 
 17 
 
 16 
 
 Hi 
 
 18 
 
 16 
 
 16 
 
 16 
 
 16 
 
 8 
 
 19 
 
 Ji 
 
 80 
 
 80 
 
 19 
 
 18 
 
 17 
 
 16 
 
 16 
 
 14 
 
 II 
 
 14 
 
 14 
 
 M 
 
 K 
 
 y 
 
 19 
 
 80 
 
 80 
 
 20 
 
 1!) 
 
 18 
 
 17 
 
 16 
 
 15 
 
 14 
 
 13 
 
 la 
 
 I'J 
 
 in 
 
 14 
 
 10 
 
 19 
 
 20 
 
 21 
 
 21 
 
 21 
 
 20 
 
 18 
 
 17 
 
 16 
 
 13 
 
 12 
 
 n 
 
 II 
 
 il 
 
 II 
 
 n 
 
 18 
 
 20 
 
 21 
 
 89 
 
 2-2 
 
 81 
 
 80 
 
 18 
 
 16 
 
 II 
 
 13 
 
 n 
 
 10 
 
 !l 
 
 10 
 
 13 
 
 17 
 
 19 
 
 21 
 
 89 
 
 23 
 
 j:t 
 
 89 
 
 JI 
 
 111 
 
 Hi 
 
 14 
 
 12 
 
 11 . 
 
 !> 
 
 :P 
 
 13 
 
 iii 
 
 18 
 
 JI 
 
 J:t 
 
 M 
 
 M 
 
 .'I 
 
 2:! 
 
 21 
 
 10 
 
 17 
 
 n 
 
 N 
 
 10 
 
 9 
 
 14 
 
 13 
 
 16 
 
 19 
 
 21 
 
 23 
 
 24 
 
 r. 
 
 M 
 
 2:1 
 
 21 
 
 N 
 
 17 
 
 14 
 
 M 
 
 111 
 
 15 
 
 11 
 
 M 
 
 17 
 
 80 
 
 22 
 
 24 
 
 86 
 
 86 
 
 25 
 
 23 
 
 22 
 
 20 
 
 17 
 
 HS 
 
 12 
 
 ii; 
 
 10 
 
 19 
 
 IS 
 
 18 
 
 20 
 
 89 
 
 M 
 
 -.'.-, 
 
 86 
 
 86 
 
 24 
 
 22 
 
 80 
 
 17 
 
 H 
 
 17 
 
 !) 
 
 11 
 
 13 
 
 16 
 
 Iti 
 
 21 
 
 23 
 
 94 
 
 86 
 
 96 
 
 96 
 
 M 
 
 22 
 
 111 
 
 17 
 
 Iti 
 
 !) 
 
 in 
 
 12 
 
 14 
 
 17 
 
 W 
 
 .'1 
 
 83 
 
 86 
 
 25 
 
 85 
 
 86 
 
 98 
 
 HI 
 
 n 
 
 1!) 
 
 !) 
 
 10 
 
 11 
 
 111 
 
 re 
 
 18 
 
 20 
 
 ,"-' 
 
 M 
 
 M 
 
 jr, 
 
 25 
 
 24 
 
 23 
 
 ll 
 
 M 
 
 10 
 
 10 
 
 n 
 
 i:t 
 
 K 
 
 17 
 
 1!) 
 
 21 
 
 B 
 
 25 
 
 86 
 
 26 
 
 m 
 
 24 
 
 
 sti 
 
 1 I 
 
 Id 
 
 11 
 
 N 
 
 n 
 
 16 
 
 19 
 
 81 
 
 23 
 
 M 
 
 86 
 
 26 
 
 96 
 
 2r, 
 
 j; 
 
 99 
 
 !i 
 
 10 
 
 n 
 
 12 
 
 13 
 
 15 
 
 18 
 
 20 
 
 81 
 
 Ji 
 
 2:> 
 
 27 
 
 27 
 
 26 
 
 9) 
 
 83 
 
 9 
 
 !t 
 
 9 
 
 HI 
 
 12 
 
 14 
 
 16 
 
 1- 
 
 22 
 
 23 
 
 25 
 
 27 
 
 27 
 
 27 
 
 27 
 
 24 
 
 7 
 
 7 
 
 8 
 
 9 
 
 10 
 
 N 
 
 15 
 
 17 
 
 20 
 
 22 
 
 at 
 
 26 
 
 28 
 
 28 
 
 28 
 
 15 
 
 6 
 
 6 
 
 6 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 17 
 
 20 
 
 22 
 
 25 
 
 27 
 
 28 
 
 29 
 
 % 
 
 6 
 
 .', 
 
 5 
 
 5 
 
 5 
 
 7 
 
 9 
 
 11 
 
 14 
 
 17 
 
 20 
 
 23 
 
 2T> 
 
 27 
 
 88 
 
 27 
 
 7 
 
 5 
 
 5 
 
 4 
 
 4 
 
 5 
 
 6 
 
 8 
 
 11 
 
 14 
 
 16 
 
 20 
 
 2-2 
 
 25 
 
 27 
 
 J- 
 
 8 
 
 7 
 
 5 
 
 4 
 
 4 
 
 4 
 
 4 
 
 6 
 
 8 
 
 10 
 
 18 
 
 16 
 
 l!l 
 
 2-2 
 
 24 
 
 29 
 
 11 
 
 
 
 7 
 
 5 
 
 4 
 
 4 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 13 
 
 16 
 
 I'.I 
 
 21 
 
 30 
 
 13 
 
 11 
 
 9 
 
 8 
 
 6 
 
 5 
 
 4 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 13 
 
 Hi 
 
 18 
 
 31 
 
 i:. 
 
 14 
 
 12 
 
 10 
 
 8 
 
 7 
 
 6 
 
 5 
 
 r. 
 
 6 
 
 7 
 
 9 
 
 11 
 
 13 
 
 16 
 
 n 
 
 17 
 
 15 
 
 1:1 
 
 12 
 
 10 
 
 9 
 
 8 
 
 7 
 
 7 
 
 7 
 
 7 
 
 8 
 
 10 
 
 12 
 
 II 
 
 33 
 
 17 
 
 16 
 
 14 
 
 13 
 
 12 
 
 10 
 
 9 
 
 8 
 
 8 
 
 8 
 
 8 
 
 9 
 
 10 
 
 12 
 
 13 
 
 34 
 
 16 
 
 15 
 
 14 
 
 13 
 
 12 
 
 11 
 
 10 
 
 9 
 
 9 
 
 9 
 
 9 
 
 10 
 
 II 
 
 12 
 
 13 
 
 35 
 
 15 
 
 15 
 
 14 
 
 13 
 
 12 
 
 11 
 
 10 
 
 9 
 
 9 
 
 9 
 
 9 
 
 10 
 
 11 
 
 12 
 
 14 
 
 86 
 
 14 
 
 14 
 
 13 
 
 12 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8, 
 
 9 
 
 9 
 
 10 
 
 19 
 
 14 
 
 37 
 
 14 
 
 13 
 
 IB 
 
 12 
 
 11 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 7 
 
 8 
 
 i 
 
 11 
 
 13 
 
 38 
 
 14 
 
 14 
 
 13 
 
 12 
 
 11 
 
 9 
 
 8 
 
 7 
 
 6 
 
 5 
 
 5 
 
 6 
 
 7 
 
 !l 
 
 II 
 
 39 
 
 15 
 
 15 
 
 14 
 
 13 
 
 11 
 
 10 
 
 8 
 
 6 
 
 5 
 
 4 
 
 4 
 
 4 
 
 5 
 
 6 
 
 8 
 
 40 
 
 16 
 
 16 
 
 15 
 
 14 
 
 13 
 
 11 
 
 9 
 
 7 
 
 5 
 
 4 
 
 3 
 
 2 
 
 3 
 
 3 
 
 ."> 
 
 II 
 
 16 
 
 17 
 
 17 
 
 16 
 
 15 
 
 13 
 
 11 
 
 9 
 
 7 
 
 5 
 
 3 
 
 2 
 
 1 
 
 2 
 
 3 
 
 42 
 
 16 
 
 17. 
 
 17 
 
 17 
 
 17 
 
 15 
 
 14 
 
 12 
 
 9 
 
 7 
 
 5 
 
 3 
 
 2 
 
 1 
 
 1 
 
 43 
 
 16 
 
 17 
 
 18 
 
 18 
 
 18 
 
 17 
 
 16 
 
 14 
 
 12 
 
 !l 
 
 7 
 
 5 
 
 3 
 
 1 
 
 1 
 
 44 
 
 14 
 
 16 
 
 17 
 
 18 
 
 19 
 
 18 
 
 18 
 
 17 
 
 15 
 
 12 
 
 10 
 
 7 
 
 5 
 
 It 
 
 9 
 
 45 
 
 13 
 
 14 
 
 16 
 
 17 
 
 18 
 
 19 
 
 19 
 
 18 
 
 17 
 
 15 
 
 12 
 
 10 
 
 7 
 
 5 
 
 3 
 
 46 
 
 12 
 
 19 
 
 16 
 
 16 
 
 17 
 
 n 
 
 19 
 
 18 
 
 18 
 
 16 
 
 M 
 
 12 
 
 10 
 
 8 
 
 :. 
 
 47 
 
 13 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 18 
 
 18 
 
 18 
 
 17 
 
 Hi 
 
 14 
 
 12 
 
 10 
 
 8 
 
 48 
 
 13 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 18 
 
 18 
 
 18 
 
 17 
 
 16 
 
 14 
 
 I-J 
 
 10 
 
 49 
 
 15 
 
 14 
 
 14 
 
 15 
 
 16 
 
 17 
 
 17 
 
 18 
 
 18 
 
 18 
 
 18 
 
 17 
 
 16 
 
 13 
 
 II 
 
 50 
 
 16 
 
 15 
 
 15 
 
 15 
 
 16 
 
 17 
 
 17 
 
 18 
 
 19 
 
 19 
 
 19 
 
 18 
 
 17 
 
 I.', 
 
 13 
 
 51 
 
 17 
 
 16 
 
 16 
 
 16 
 
 16 
 
 17 
 
 18 
 
 18 
 
 19 
 
 l!l 
 
 111 
 
 19 
 
 1- 
 
 17 
 
 14 
 
 52 
 
 17 
 
 16 
 
 16 
 
 16 
 
 16 
 
 17 
 
 18 
 
 19 
 
 19 
 
 20 
 
 20 
 
 20 
 
 1!) 
 
 18 
 
 16 
 
 5:1 
 
 17 
 
 16 
 
 16 
 
 IB 
 
 16 
 
 17 
 
 17 
 
 18 
 
 20 
 
 20 
 
 21 
 
 91 
 
 21 
 
 88 
 
 Iri 
 
 54 
 
 16 
 
 15 
 
 15 
 
 15 
 
 15 
 
 16 
 
 17 
 
 17 
 
 19 
 
 20 
 
 21 
 
 21 
 
 89 
 
 21 
 
 20 
 
 55 
 
 If! 
 
 14 
 
 16 
 
 13 
 
 13 
 
 14 
 
 15 
 
 1(i 
 
 17 
 
 19 
 
 20 
 
 21 
 
 22 
 
 88 
 
 21 
 
 56 
 
 16 
 
 14 
 
 19 
 
 12 
 
 n 
 
 l-> 
 
 13 
 
 14 
 
 16 
 
 17 
 
 1- 
 
 20 
 
 21 
 
 81 
 
 2-2 
 
 57 
 
 l(> 
 
 14 
 
 i:i 
 
 12 
 
 n 
 
 11 
 
 11 
 
 n 
 
 13 
 
 15 
 
 w 
 
 1- 
 
 l!l 
 
 ji 
 
 21 
 
 58 
 
 18 
 
 16 
 
 II 
 
 M 
 
 n 
 
 11 
 
 10 
 
 10 
 
 11 
 
 a 
 
 14 
 
 18 
 
 17 
 
 18 
 
 19 
 
 n 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 11 
 
 10 
 
 10 
 
 10 
 
 n 
 
 11 
 
 1:1 
 
 14 
 
 H, 
 
 17 
 
 6o 
 
 23 
 
 21 
 
 19 
 
 17 
 
 15 
 
 i:t 
 
 12 
 
 11 
 
 10 
 
 HI 
 
 HI 
 
 11 
 
 u 
 
 II 
 
 IT. 
 
 M 19.6 to Arg. XII. when 224 d .7 is subtracted from Arg. I. 
 
TABLE XXIV. 
 
 Perturbations of the Longitude li Jupiter. 
 
 Horizontal Argument = I. 
 
 Constant added 2".35. 1'eriod of Argument I. 224 ll .7. 
 
 * ,. 
 
 d 
 
 a 
 
 d 
 
 d d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 Aig. 
 XIII. 
 
 
 
 
 
 16 
 
 24 
 
 32 
 
 40 
 
 48 
 
 56 
 
 64 
 
 72 
 
 
 
 8 
 
 06 
 
 1O4 
 
 112 
 
 
 
 205 
 
 209 
 
 216 
 
 226 
 
 237 
 
 248 
 
 259 
 
 268 
 
 275 
 
 278 
 
 280 
 
 279 
 
 276 
 
 271 
 
 268 
 
 1 
 
 1 85 
 
 184 
 
 188 
 
 194 
 
 204 
 
 214 
 
 226 
 
 236 
 
 245 
 
 253 
 
 257 
 
 25!) 
 
 258 
 
 256 
 
 254 
 
 a 
 
 169 
 
 164 
 
 163 
 
 166 
 
 173 
 
 182 
 
 193 
 
 204 
 
 215 
 
 221 
 
 231 
 
 237 
 
 239 
 
 240 
 
 238 
 
 3 
 
 158 
 
 147 
 
 142 
 
 111 
 
 144 
 
 151 
 
 160 
 
 171 
 
 183 
 
 194 
 
 204 
 
 212 
 
 218 
 
 221 
 
 222 
 
 4 
 
 150 
 
 136 
 
 126 
 
 121 
 
 120 
 
 123 
 
 130 
 
 140 
 
 151 
 
 163 
 
 175 
 
 186 
 
 195 
 
 201 
 
 204 
 
 5 
 
 145 
 
 12S 
 
 115 
 
 105 
 
 100 
 
 100 
 
 104 
 
 111 
 
 121 
 
 133 
 
 146 
 
 158 
 
 1,0 
 
 17!) 
 
 185 
 
 6 
 
 143 
 
 125 
 
 108 
 
 95 
 
 86 
 
 82 
 
 82 
 
 86 
 
 04 
 
 1 04 
 
 117 
 
 131 
 
 144 
 
 156 
 
 164 
 
 7 
 
 143 
 
 123 
 
 1(15 
 
 89 
 
 77 
 
 68 
 
 64 
 
 65 
 
 70 
 
 79 
 
 90 
 
 104 
 
 118 
 
 132 
 
 143 
 
 8 
 
 143 
 
 124 
 
 105 
 
 87 
 
 72 
 
 61 
 
 53 
 
 50 
 
 52 
 
 57 
 
 67 
 
 7!) 
 
 93 
 
 108 
 
 121 
 
 9 
 
 143 
 
 126 
 
 108 
 
 89 
 
 72 
 
 58 
 
 47 
 
 40 
 
 38 
 
 40 
 
 47 
 
 58 
 
 71 
 
 85 
 
 100 
 
 10 
 
 142 
 
 128 
 
 111 
 
 93 
 
 75 
 
 59 
 
 46 
 
 36 
 
 30 
 
 29 
 
 32 
 
 40 
 
 51 
 
 65 
 
 79 
 
 11 
 
 140 
 
 129 
 
 115 
 
 99 
 
 81 
 
 65 
 
 4!) 
 
 37 
 
 28 
 
 23 
 
 23 
 
 27 
 
 36 
 
 47 
 
 61 
 
 IS 
 
 136 
 
 . 129 
 
 11!) 
 
 105 
 
 89 
 
 73 
 
 57 
 
 42 
 
 31 
 
 23 
 
 19 
 
 20 
 
 25 
 
 34 
 
 45 
 
 13 
 
 130 
 
 128 
 
 121 
 
 111 
 
 98 
 
 83 
 
 67 
 
 52 
 
 38 
 
 28 
 
 21 
 
 18 
 
 1!) 
 
 25 
 
 34 
 
 14 
 
 124 
 
 125 
 
 122 
 
 116 
 
 106 
 
 94 
 
 79 
 
 61 
 
 50 
 
 37 
 
 27 
 
 21 
 
 19 
 
 21 
 
 27 
 
 15 
 
 116 
 
 120 
 
 122 
 
 120 
 
 114 
 
 105 
 
 92 
 
 73 
 
 64 
 
 50 
 
 38 
 
 29 
 
 24 
 
 22 
 
 24 
 
 16 
 
 109 
 
 115 
 
 12!) 
 
 122 
 
 120 
 
 115 
 
 1C6 
 
 94 
 
 80 
 
 66 
 
 53 
 
 42 
 
 34 
 
 28 
 
 27 
 
 17 
 
 103 
 
 111) 
 
 117 
 
 123 
 
 125 
 
 124 
 
 119 
 
 109 
 
 98 
 
 85 
 
 71 
 
 58 
 
 48 
 
 40 
 
 35 
 
 13 
 
 96 
 
 105 
 
 114 
 
 122 
 
 129 
 
 131 
 
 130 
 
 124 
 
 116 
 
 104 
 
 91 
 
 78 
 
 65 
 
 55 
 
 47 
 
 H 
 
 92 
 
 101 
 
 111 
 
 122 
 
 131 
 
 137 
 
 140 
 
 138 
 
 133 
 
 124 
 
 112 
 
 99 
 
 85 
 
 73 
 
 63 
 
 20 
 
 ni 
 
 99 
 
 10) 
 
 121 
 
 132 
 
 142 
 
 149 
 
 151 
 
 149 
 
 142 
 
 133 
 
 121 
 
 108 
 
 94 
 
 82 
 
 21 
 
 92 
 
 99 
 
 108 
 
 120 
 
 133 
 
 146 
 
 166 
 
 161 
 
 163 
 
 160 
 
 153 
 
 143 
 
 131 
 
 117 
 
 104 
 
 22 
 
 95 
 
 101 
 
 10!) 
 
 121 
 
 135 
 
 149 
 
 161 
 
 170 
 
 176 
 
 177 
 
 173 
 
 165 
 
 154 
 
 141 
 
 128 
 
 23 
 
 100 
 
 105 
 
 112 
 
 123 
 
 136 
 
 151 
 
 166 
 
 178 
 
 187 
 
 191 
 
 190 
 
 186 
 
 177 
 
 165 
 
 152 
 
 24 
 
 108 
 
 111 
 
 118 
 
 127 
 
 139 
 
 154 
 
 170 
 
 184 
 
 196 
 
 204 
 
 206 
 
 205 
 
 199 
 
 189 
 
 177 
 
 
 
 117 
 
 120 
 
 125 
 
 133 
 
 144 
 
 168 
 
 174 
 
 190 
 
 203 
 
 214 
 
 220 
 
 222 
 
 219 
 
 211 
 
 201 
 
 26 
 
 128 
 
 130 
 
 131 
 
 141 
 
 ISO 
 
 163 
 
 178 
 
 194 
 
 210 
 
 223 
 
 232 
 
 237 
 
 237 
 
 2i!2 
 
 224 
 
 27 
 
 139 
 
 142 
 
 1 45 
 
 151 
 
 159 
 
 170 
 
 184 
 
 199 
 
 215 
 
 230 
 
 241 
 
 24!) 
 
 95S 
 
 251 
 
 245 
 
 28 
 
 151 
 
 1 55 
 
 158 
 
 163 
 
 169 
 
 178 
 
 190 
 
 205 
 
 220 
 
 236 
 
 219 
 
 260 
 
 266 
 
 267 
 
 264 
 
 29 
 
 164 
 
 168 
 
 171 
 
 175 
 
 180 
 
 188 
 
 198 
 
 211 
 
 226 
 
 241 
 
 255 
 
 268 
 
 277 
 
 281 
 
 281 
 
 30 
 
 177 
 
 181 
 
 165 
 
 189 
 
 194 
 
 199 
 
 207 
 
 218 
 
 231 
 
 246 
 
 261 
 
 274 
 
 285 
 
 292 
 
 906 
 
 31 
 
 190 
 
 196 
 
 200 
 
 204 
 
 208 
 
 212 
 
 218 
 
 227 
 
 238 
 
 251 
 
 265 
 
 279 
 
 991 
 
 301 
 
 307 
 
 32 
 
 204 
 
 210 
 
 215 
 
 21!) 
 
 222 
 
 226 
 
 230 
 
 237 
 
 245 
 
 256 
 
 269 
 
 283 
 
 296 
 
 307 
 
 316 
 
 33 
 
 21!) 
 
 224 
 
 229 
 
 234 
 
 237 
 
 240 
 
 243 
 
 248 
 
 254 
 
 963 
 
 273 
 
 286 
 
 299 
 
 311 
 
 322 
 
 34 
 
 235 
 
 239 
 
 241 
 
 2-1!! 
 
 252 
 
 255 
 
 257 
 
 260 
 
 264 
 
 270 
 
 278 
 
 289 
 
 301 
 
 314 
 
 326 
 
 35 
 
 251 
 
 254 
 
 259 
 
 263 
 
 267 
 
 26!) 
 
 271 
 
 273 
 
 275 
 
 278 
 
 284 
 
 292 
 
 303 
 
 315 
 
 327 
 
 36 
 
 268 
 
 270 
 
 274 
 
 278 
 
 281 
 
 284 
 
 286 
 
 286 
 
 287 
 
 988 
 
 291 
 
 297 
 
 305 
 
 315 
 
 327 
 
 37 
 
 287 
 
 287 
 
 289 
 
 292 
 
 296 
 
 298 
 
 300 
 
 300 
 
 299 
 
 299 
 
 999 
 
 302 
 
 307 
 
 316 
 
 396 
 
 38 
 
 306 
 
 304 
 
 305 
 
 306 
 
 309 
 
 311 
 
 313 
 
 313 
 
 312 
 
 310 
 
 308 
 
 308 
 
 311 
 
 316 
 
 325 
 
 39 
 
 326 
 
 322 
 
 321 
 
 aai 
 
 322 
 
 324 
 
 325 
 
 325 
 
 324 
 
 321 
 
 318 
 
 316 
 
 316 
 
 318 
 
 324 
 
 40 
 
 346 
 
 341 
 
 337 
 
 325 
 
 335 
 
 336 
 
 337 
 
 337 
 
 336 
 
 333 
 
 328 
 
 324 
 
 321 
 
 321 
 
 324 
 
 41 
 
 366 
 
 359 
 
 354 
 
 350 
 
 348 
 
 347 
 
 348 
 
 348 
 
 346 
 
 343 
 
 339 
 
 333 
 
 32!) 
 
 325 
 
 325 
 
 42 
 
 386 
 
 378 
 
 37.) 
 
 B65 
 
 361 
 
 358 
 
 B68 
 
 357 
 
 356 
 
 353 
 
 348 
 
 343 
 
 336 
 
 331 
 
 327 
 
 43 
 
 405 
 
 3% 
 
 387 
 
 379 
 
 373 
 
 369 
 
 867 
 
 366 
 
 364 
 
 362 
 
 357 
 
 351 
 
 '344 
 
 337 
 
 331 
 
 44 
 
 422 
 
 413 
 
 403 
 
 394 
 
 386 
 
 380 
 
 375 
 
 373 
 
 371 
 
 369 
 
 365 
 
 359 
 
 352 
 
 344 
 
 336 
 
 45 
 
 436 
 
 428 
 
 418 
 
 408 
 
 398 
 
 390 
 
 383 
 
 379 
 
 376 
 
 374 
 
 371 
 
 366 
 
 359 
 
 351 
 
 341 
 
 m 
 
 447 
 
 440 
 
 431 
 
 420 
 
 409 
 
 399 
 
 391 
 
 384 
 
 381 
 
 373 
 
 375 
 
 371 
 
 365 
 
 357 
 
 347 
 
 47 
 
 4. 14 
 
 450 
 
 441 
 
 4:il 
 
 419 
 
 408 
 
 398 
 
 390 
 
 381 
 
 381 
 
 378 
 
 374 
 
 369 
 
 362 
 
 353 
 
 48 
 
 ' 457 
 
 455 
 
 44!) 
 
 43!l 
 
 428 
 
 415 
 
 404 
 
 394 
 
 367 
 
 332 
 
 378 
 
 375 
 
 371 
 
 365 
 
 357 
 
 49 
 
 455 
 
 456 
 
 452 
 
 414 
 
 433 
 
 421 
 
 409 
 
 398 
 
 388 
 
 382 
 
 378 
 
 371 
 
 371 
 
 367 
 
 860 
 
 50 
 
 448 
 
 452 
 
 451 
 
 446 
 
 436 
 
 425 
 
 412 
 
 400 
 
 38!) 
 
 381 
 
 376 
 
 372 
 
 369 
 
 366 
 
 861 
 
 51 
 
 436 
 
 443 
 
 445 
 
 442 
 
 435 
 
 426 
 
 413 
 
 401 
 
 889 
 
 380 
 
 373 
 
 363 
 
 365 
 
 363 
 
 359 
 
 52 
 
 419 
 
 429 
 
 434 
 
 434 
 
 430 
 
 423 
 
 412 
 
 4(10 
 
 388 
 
 377 
 
 36!) 
 
 363 
 
 360 
 
 358 
 
 355 
 
 53 
 
 897 
 
 410 
 
 413 
 
 421 
 
 421 
 
 416 
 
 407 
 
 396 
 
 384 
 
 373 
 
 364 
 
 357 
 
 353 
 
 350 
 
 349 
 
 54 
 
 372 
 
 386 
 
 397 
 
 404 
 
 406 
 
 404 
 
 398 
 
 389 
 
 378 
 
 363 
 
 358 
 
 350 
 
 345 
 
 342 
 
 341 
 
 55 
 
 344 
 
 35!) 
 
 372 
 
 381 
 
 386 
 
 388 
 
 385 
 
 379 
 
 370 
 
 360 
 
 351 
 
 342 
 
 336 
 
 332 
 
 331 
 
 56 
 
 315 
 
 32!) 
 
 343 
 
 354 
 
 362 
 
 367 
 
 368 
 
 365 
 
 358 
 
 350 
 
 341 
 
 333 
 
 326 
 
 322 
 
 320 
 
 57 
 
 385 
 
 298 
 
 312 
 
 :'.2 1 
 
 335 
 
 342 
 
 346 
 
 346 
 
 343 
 
 337 
 
 330 
 
 333 
 
 315 
 
 310 
 
 307 
 
 68 
 
 2:.6 
 
 967 
 
 279 
 
 202 
 
 304 
 
 313 
 
 380 
 
 324 
 
 324 
 
 321 
 
 316 
 
 310 
 
 304 
 
 298 
 
 905 
 
 59 
 
 2','!) 
 
 2:',7 
 
 217 
 
 850 
 
 271 
 
 281 
 
 991 
 
 2! 17 
 
 301 
 
 301 
 
 299 
 
 296 
 
 990 
 
 2-5 
 
 282 
 
 ft 
 
 205 
 
 209 
 
 216 
 
 326 
 
 237 
 
 248 
 
 25!) 
 
 26s 
 
 275 
 
 278 
 
 960 
 
 279 
 
 276 
 
 271 
 
 263 
 
 The perturbations are expressed in liundreilllis of a seeond of arc. 
 
TABLE XXIV. 
 
 43 
 
 Perturbations <>/' tin- Longitude In/ Jii/ii/cr. 
 
 Horizontal Arguinanl = 1. 
 
 Constant added I lVri.,.l nCAr^mn. -ul Mil . (i ' units. 
 
 Arg. 
 XIII 
 
 120 
 
 12N 
 
 i:j 
 
 ail 
 
 ,i 
 
 160 
 
 ION 
 
 176 
 
 1*1 
 
 .1 
 
 00 
 
 20* 
 
 ,i 
 216 
 
 221 
 
 22 
 
 
 
 965 
 
 964 
 
 966 
 
 
 
 
 
 
 949 
 
 
 
 189 
 
 172 
 
 157 
 
 117 
 
 1 
 
 251 
 
 250 
 
 
 251 
 
 959 
 
 
 861 
 
 946 
 
 
 
 
 1-7 
 
 168 
 
 150 
 
 136 
 
 2 
 
 936 
 
 935 
 
 
 935 
 
 936 
 
 937 
 
 
 
 
 817 
 
 
 1-5 
 
 11,0 
 
 146 
 
 190 
 
 3 
 
 891 
 
 .... , 
 
 910 
 
 919 
 
 .j.j , 
 
 -Ml 
 
 999 
 
 991 
 
 2I-* 
 
 910 
 
 198 
 
 I-:; 
 
 11,1 
 
 146 
 
 196 
 
 4 
 
 
 
 
 
 
 905 
 
 206 
 
 
 
 801 
 
 199 
 
 17:' 
 
 163 
 
 146 
 
 195 
 
 5 
 
 188 
 
 1- i 
 
 180 
 
 188 
 
 188 
 
 188 
 
 190 
 
 191 
 
 191 
 
 i- i 
 
 l-l 
 
 175 
 
 161 
 
 115 
 
 196 
 
 6 
 
 171 
 
 171 
 
 171 
 
 171 
 
 
 173 
 
 171 
 
 175 
 
 176 
 
 I7li 
 
 171 
 
 168 
 
 158 
 
 1 II 
 
 198 
 
 7 
 
 169 
 
 157 
 
 nit 
 
 160 
 
 160 
 
 150 
 
 168 
 
 I.V.I 
 
 n,i 
 
 169 
 
 169 
 
 159 
 
 153 
 
 143 
 
 190 
 
 8 
 
 139 
 
 140 
 
 146 
 
 1 17 
 
 117 
 
 146 
 
 1 15 
 
 1 15 
 
 i I,, 
 
 148 
 
 1 i 
 
 II!' 
 
 147 
 
 140 
 
 130 
 
 11 
 
 113 
 
 193 
 
 
 134 
 
 
 134 
 
 139 
 
 139 
 
 139 
 
 134 
 
 
 I: - 
 
 138 
 
 136 
 
 ISO 
 
 10 
 
 83 
 
 105 
 
 115 
 
 191 
 
 193 
 
 193 
 
 I'-!'.' 
 
 190 
 
 190 
 
 191 
 
 193 
 
 I-J7 
 
 190 
 
 130 
 
 !'.'- 
 
 II 
 
 75 
 
 
 100 
 
 106 
 
 1 12 
 
 II 1 
 
 113 
 
 III 
 
 IM 
 
 110 
 
 119 
 
 115 
 
 i-.'o 
 
 193 
 
 194 
 
 12 
 
 69 
 
 73 
 
 - 
 
 96 
 
 Ml 
 
 104 
 
 M", 
 
 103 
 
 109 
 
 mi 
 
 109 
 
 M5 
 
 no 
 
 115 
 
 11!) 
 
 13 
 
 46 
 
 69 
 
 79 
 
 88 
 
 01 
 
 96 
 
 98 
 
 97 
 
 
 94 
 
 94 
 
 97 
 
 101 
 
 M7 
 
 114 
 
 14 
 
 36 
 
 48 
 
 60 
 
 72 
 
 81 
 
 -- 
 
 
 99 
 
 91 
 
 89 
 
 89 
 
 
 
 101 
 
 109 
 
 15 
 
 31 
 
 40 
 
 51 
 
 69 
 
 73 
 
 81 
 
 86 
 
 88 
 
 88 
 
 87 
 
 85 
 
 86 
 
 89 
 
 96 
 
 104 
 
 16 
 
 80 
 
 36 
 
 45 
 
 66 
 
 66 
 
 75 
 
 39 
 
 85 
 
 86 
 
 96 
 
 -1 
 
 84 
 
 87 
 
 92 
 
 101) 
 
 17 
 
 34 
 
 37 
 
 43 
 
 52 
 
 61 
 
 71 
 
 78 
 
 
 86 
 
 86 
 
 85 
 
 85 
 
 87 
 
 !)() 
 
 
 1- 
 
 43 
 
 42 
 
 15 
 
 51 
 
 69 
 
 68 
 
 76 
 
 82 
 
 
 88 
 
 88 
 
 86 
 
 
 89 
 
 98 
 
 1!) 
 
 16 
 
 89 
 
 52 
 
 :,:, 
 
 60 
 
 68 
 
 75 
 
 89 
 
 -7 
 
 91 
 
 09 
 
 93 
 
 93 
 
 06 
 
 100 
 
 20 
 
 73 
 
 66 
 
 69 
 
 62 
 
 65 
 
 70 
 
 77 
 
 84 
 
 90 
 
 95 
 
 97 
 
 98 
 
 II!) 
 
 101 
 
 105 
 
 21 
 
 93 
 
 
 77 
 
 7:! 
 
 7:! 
 
 76 
 
 81 
 
 87 
 
 94 
 
 99 
 
 103 
 
 105 
 
 107 
 
 109 
 
 119 
 
 
 115 
 
 103 
 
 94 
 
 88 
 
 
 85 
 
 88 
 
 93 
 
 
 106 
 
 110 
 
 113 
 
 IHi 
 
 118 
 
 181 
 
 98 
 
 189 
 
 196 
 
 115 
 
 106 
 
 100 
 
 
 98 
 
 Ml 
 
 UK; 
 
 119 
 
 M8 
 
 122 
 
 126 
 
 12!) 
 
 181 
 
 84 
 
 163 
 
 150 
 
 137 
 
 127 
 
 118 
 
 113 
 
 111 
 
 112 
 
 116 
 
 101 
 
 127 
 
 132 
 
 136 
 
 140 
 
 143 
 
 25 
 
 188 
 
 175 
 
 162 
 
 150 
 
 139 
 
 132 
 
 127 
 
 126 
 
 198 
 
 132 
 
 137 
 
 142 
 
 148 
 
 152 
 
 156 
 
 M 
 
 213 
 
 900 
 
 1-7 
 
 171 
 
 169 
 
 153 
 
 146 
 
 ! 13 
 
 1 12 
 
 1 II 
 
 i ri 
 
 164 
 
 169 
 
 16.5 
 
 16!) 
 
 9? 
 
 986 
 
 996 
 
 819 
 
 199 
 
 1-7 
 
 176 
 
 167 
 
 162 
 
 169 
 
 l.v.i 
 
 IfiSI 
 
 166 
 
 179 
 
 178 
 
 1*3 
 
 98 
 
 968 
 
 248 
 
 237 
 
 -"J 1 
 
 212 
 
 900 
 
 190 
 
 183 
 
 178 
 
 17(1 
 
 177 
 
 1-1 
 
 186 
 
 191 
 
 P. 17 
 
 
 277 
 
 270 
 
 260 
 
 949 
 
 987 
 
 095 
 
 214 
 
 206 
 
 100 
 
 196 
 
 104 
 
 196 
 
 200 
 
 905 
 
 211 
 
 3D 
 
 986 
 
 290 
 
 282 
 
 273 
 
 262 
 
 250 
 
 240 
 
 230 
 
 222 
 
 216 
 
 .'i:i 
 
 213 
 
 216 
 
 220 
 
 226 
 
 31 
 
 309 
 
 807 
 
 302 
 
 996 
 
 286 
 
 275 
 
 965 
 
 255 
 
 946 
 
 939 
 
 934 
 
 232 
 
 2:i:i 
 
 236 
 
 240 
 
 32 
 
 321 
 
 899 
 
 390 
 
 815 
 
 308 
 
 899 
 
 989 
 
 96 > 
 
 270 
 
 969 
 
 
 252 
 
 861 
 
 253 
 
 256 
 
 
 330 
 
 834 
 
 335 
 
 333 
 
 898 
 
 321 
 
 313 
 
 304 
 
 996 
 
 286 
 
 870 
 
 J7I 
 
 271 
 
 970 
 
 872 
 
 84 
 
 336 
 
 349 
 
 347 
 
 348 
 
 346 
 
 341 
 
 335 
 
 398 
 
 31!) 
 
 311 
 
 303 
 
 
 991 
 
 
 289 
 
 86 
 
 339 
 
 848 
 
 355 
 
 359 
 
 361 
 
 359 
 
 866 
 
 350 
 
 849 
 
 834 
 
 887 
 
 819 
 
 313 
 
 308 
 
 886 
 
 36 
 
 340 
 
 351 
 
 360 
 
 368 
 
 379 
 
 371 
 
 373 
 
 360 
 
 864 
 
 857 
 
 350 
 
 849 
 
 034 
 
 32!) 
 
 :!.' l 
 
 37 
 
 338 
 
 351 
 
 362 
 
 372 
 
 380 
 
 886 
 
 887 
 
 386 
 
 883 
 
 37fl 
 
 372 
 
 864 
 
 866 
 
 349 
 
 343 
 
 
 336 
 
 849 
 
 361 
 
 374 
 
 384 
 
 399 
 
 398 
 
 400 
 
 1 
 
 807 
 
 399 
 
 886 
 
 
 370 
 
 369 
 
 ::;i 
 
 333 
 
 315 
 
 358 
 
 372 
 
 385 
 
 396 
 
 
 410 
 
 413 
 
 413 
 
 110 
 
 405 
 
 898 
 
 889 
 
 :;-! 
 
 40 
 
 330 
 
 340 
 
 353 
 
 368 
 
 889 
 
 396 
 
 407 
 
 416 
 
 422 
 
 425 
 
 486 
 
 422 
 
 416 
 
 408 
 
 399 
 
 41 
 
 328 
 
 336 
 
 
 361 
 
 376 
 
 899 
 
 406 
 
 4IH 
 
 1-7 
 
 434 
 
 436 
 
 435 
 
 431 
 
 494 
 
 416 
 
 40 
 
 397 
 
 839 
 
 340 
 
 363 
 
 368 
 
 384 
 
 101 
 
 416 
 
 498 
 
 437 
 
 443 
 
 445 
 
 III 
 
 
 130 
 
 43 
 
 898 
 
 389 
 
 3:!4 
 
 345 
 
 358 
 
 375 
 
 3!>2 
 
 409 
 
 494 
 
 437 
 
 446 
 
 451 
 
 469 
 
 449 
 
 443 
 
 44 
 
 380 
 
 32-i 
 
 329 
 
 337 
 
 348 
 
 363 
 
 3SO 
 
 899 
 
 416 
 
 431 
 
 443 
 
 452 
 
 466 
 
 455 
 
 151 
 
 43 
 
 :!:!:! 
 
 888 
 
 326 
 
 330 
 
 338 
 
 351 
 
 367 
 
 
 I 1 
 
 421 
 
 436 
 
 II- 
 
 466 
 
 
 
 46 
 
 
 330 
 
 393 
 
 394 
 
 329 
 
 
 352 
 
 870 
 
 388 
 
 407 
 
 421 
 
 439 
 
 449 
 
 455 
 
 
 47 
 
 343 
 
 333 
 
 885 
 
 
 321 
 
 897 
 
 838 
 
 353 
 
 371 
 
 390 
 
 408 
 
 us 
 
 
 447 
 
 |5| 
 
 48 
 
 347 
 
 887 
 
 887 
 
 !il!) 
 
 315 
 
 317 
 
 324 
 
 336 
 
 359 
 
 370 
 
 
 407 
 
 422 
 
 184 
 
 441 
 
 49 
 
 351 
 
 341 
 
 329 
 
 319 
 
 312 
 
 309 
 
 312 
 
 320 
 
 889 
 
 848 
 
 367 
 
 385 
 
 1 .' 
 
 416 
 
 496 
 
 50 
 
 353 
 
 344 
 
 332 
 
 :!-'! 
 
 311 
 
 304 
 
 302 
 
 305 
 
 314 
 
 397 
 
 843 
 
 36 > 
 
 37- 
 
 804 
 
 406 
 
 51 
 52 
 
 863 
 
 346 
 
 345 
 
 886 
 836 
 
 323 
 
 32 1 
 
 311 
 312 
 
 801 
 909 
 
 2! 15 
 2!H) 
 
 293 
 984 
 
 
 306 
 
 319 
 
 835 
 
 300 
 
 361 
 
 :> 1 
 
 868 
 840 
 
 889 
 
 355 
 
 53 
 
 'illi 
 
 342 
 
 335 
 
 3-.'5 
 
 313 
 
 
 987 
 
 277 
 
 271 
 
 
 275 
 
 
 
 :ilo 
 
 325 
 
 54 
 
 339 
 
 337 
 
 332 
 
 884 
 
 313 
 
 889 
 
 285 
 
 273 
 
 989 
 
 
 
 100 
 
 269 
 
 980 
 
 908 
 
 55 
 
 57 
 58 
 60 
 
 60 
 
 330 
 819 
 306 
 903 
 
 '-'Ii5 
 
 329 
 819 
 307 
 294 
 879 
 964 
 
 326 
 318 
 
 307 
 295 
 280 
 265 
 
 320 
 311 
 305 
 996 
 381 
 266 
 
 311 
 
 -'-I 
 967 
 
 297 
 903 
 987 
 
 978 
 
 266 
 
 284 
 
 2-1 
 277 
 J7I 
 262 
 
 270 
 368 
 266 
 264 
 
 254 
 
 257 
 
 948 
 
 . 1 -. 
 949 
 
 247 
 999 
 
 998 
 
 241 
 229 
 2.' ' 
 914 
 2ID 
 
 240 
 910 
 
 193 
 
 l- i 
 
 944 
 
 999 
 804 
 
 i- i 
 I7'J 
 179 
 
 252 
 895 
 
 I6tl 
 
 157 
 
 96)1 
 
 233 
 1-.' 
 
 ii,-.: 
 
 147 
 
 Add 3.11 to Arg. XIII. when 224< l .7 is subtract.;,! Inmi Arg. 1. 
 
 1 1 IT 
 
44 
 
 TABLE XXV. 
 
 Perturbations of the Longitude by Satiini. 
 
 Horizontal Argument = I. 
 
 Constant added 0".40. Period of Argument I., 224i'.7. 
 
 Ar. 
 XIV. 
 
 a 
 o 
 
 d 
 
 9 
 
 a 
 
 16 
 
 d 
 24 
 
 d 
 32 
 
 d 
 40 
 
 d 
 
 4 
 
 (1 
 56 
 
 d 
 64 
 
 d 
 72 
 
 d 
 
 80 
 
 d 
 S 
 
 d 
 96 
 
 d 
 104 
 
 d 
 112 
 
 
 
 39 
 
 43 
 
 47 
 
 54 
 
 GO 
 
 66 
 
 72 
 
 77 
 
 80 
 
 81 
 
 81 
 
 80 
 
 78 
 
 75 
 
 72 
 
 1 
 
 37 
 
 39 
 
 43 
 
 48 
 
 54 
 
 01 
 
 67 
 
 72 
 
 77 
 
 79 
 
 80 
 
 80 
 
 79 
 
 76 
 
 74 
 
 a 
 
 36 
 
 36 
 
 39 
 
 43 
 
 48 
 
 54 
 
 61 
 
 67 
 
 72 
 
 76 
 
 78 
 
 79 
 
 78 
 
 77 
 
 74 
 
 3 
 
 36 
 
 Oft 
 
 35 
 
 fj/t 
 
 35 
 
 OO 
 
 38 
 
 0,1 
 
 42 
 da 
 
 47 
 Jn 
 
 54 
 
 AC 
 
 60 
 
 66 
 
 Rn 
 
 71 
 fid 
 
 75 
 an 
 
 77 
 
 77 
 
 76 
 
 74 
 
 5 
 
 OO 
 
 37 
 
 O4 
 
 34 
 
 OO 
 
 31 
 
 O** 
 
 30 
 
 ou 
 31 
 
 <*u 
 34 
 
 4o 
 39 
 
 52 
 44 
 
 ov 
 51 
 
 0*1 
 57 
 
 Ut/ 
 
 63 
 
 67 
 
 70 
 
 71 
 
 71 
 
 c 
 
 38 
 
 34 
 
 31 
 
 28 
 
 28 
 
 2!) 
 
 32 
 
 37 
 
 42 
 
 49 
 
 55 
 
 60 
 
 C5 
 
 67 
 
 68 
 
 7 
 
 38 
 
 34 
 
 31 
 
 27 
 
 25 
 
 25 
 
 27 
 
 30 
 
 34 
 
 40 
 
 46 
 
 52 
 
 58 
 
 62 
 
 64 
 
 8 
 
 38 
 
 34 
 
 31 
 
 27 
 
 24 
 
 22 
 
 22 
 
 24 
 
 27 
 
 33 
 
 38 
 
 44 
 
 50 
 
 55 
 
 59 
 
 9 
 
 37 
 
 34 
 
 31 
 
 27 
 
 23 
 
 21 
 
 19 
 
 19 
 
 21 
 
 25 
 
 30 
 
 35 
 
 42 
 
 47 
 
 52 
 
 10 
 
 35 
 
 33 
 
 30 
 
 26 
 
 23 
 
 19 
 
 17 
 
 16 
 
 1C 
 
 18 
 
 22 
 
 27 
 
 33 
 
 39 
 
 45 
 
 11 
 
 33 
 
 31 
 
 29 
 
 26 
 
 22 
 
 19 
 
 16 
 
 14 
 
 13 
 
 14 
 
 16 
 
 20 
 
 25 
 
 31 
 
 37 
 
 12 
 
 30 
 
 29 
 
 27 
 
 25 
 
 22 
 
 19 
 
 15 
 
 12 
 
 11 
 
 10 
 
 11 
 
 14 
 
 18 
 
 24 
 
 29 
 
 13 
 
 27 
 
 do 
 
 25 
 
 23 
 
 21 
 
 18 
 
 15 
 
 12 
 
 9 
 
 8 
 
 8 
 
 9 
 
 12 
 
 17 
 
 22 
 
 14 
 
 25 
 
 24 23 
 
 22 
 
 20 
 
 18 
 
 15 
 
 12 
 
 9 
 
 7 
 
 6 
 
 G 
 
 8 
 
 11 
 
 16 
 
 15 
 
 2:1 
 
 22 21 
 
 20 
 
 19 
 
 17 
 
 15 
 
 12 
 
 9 
 
 7 
 
 5 
 
 4 
 
 5 
 
 7 
 
 11 
 
 1C 
 
 a:i 
 
 21 
 
 20 
 
 19 
 
 18 
 
 16 
 
 15 
 
 13 
 
 10 
 
 8 
 
 5 
 
 4 
 
 3 
 
 4 
 
 7 
 
 17 
 
 24 
 
 21 
 
 19 
 
 18 
 
 17 
 
 1G 
 
 15 
 
 13 
 
 11 
 
 8 
 
 6 
 
 4 
 
 3 
 
 3 
 
 4 
 
 18 
 
 26 
 
 23 
 
 20 
 
 19 
 
 17 
 
 16 
 
 15 
 
 13 
 
 12 
 
 10 
 
 7 
 
 5 
 
 4 
 
 3 
 
 3 
 
 19 
 
 29 
 
 26 
 
 23 
 
 20 
 
 19 
 
 17 
 
 16 
 
 15 
 
 13 
 
 11 
 
 9 
 
 7 
 
 5 
 
 4 
 
 3 
 
 20 
 
 33 
 
 30 
 
 26 
 
 23 
 
 21 
 
 19 
 
 18 
 
 16 
 
 15 
 
 13 
 
 11 
 
 9 
 
 7 
 
 5 
 
 4 
 
 21 
 
 38 
 
 34 
 
 31 
 
 27 
 
 25 
 
 22 
 
 20 
 
 19 
 
 17 
 
 16 
 
 14 
 
 12 
 
 10 
 
 8 
 
 6 
 
 22 
 
 42 
 
 39 
 
 36 
 
 32 
 
 29 
 
 26 
 
 24 
 
 22 
 
 20 
 
 19 
 
 17 
 
 15 
 
 13 
 
 11 
 
 9 
 
 23 
 
 46 
 
 44 
 
 42 
 
 38 
 
 35 
 
 32 
 
 29 
 
 27 
 
 24 
 
 22 
 
 21 
 
 19 
 
 17 
 
 15 
 
 13 
 
 24 
 
 50 
 
 50 
 
 47 
 
 44 
 
 41 
 
 38 
 
 34 
 
 32 
 
 29 
 
 27 
 
 25 
 
 23 
 
 21 
 
 19 
 
 17 
 
 25 
 
 54 
 
 54 
 
 53 
 
 50 
 
 47 
 
 44 
 
 41 
 
 38 
 
 35 
 
 32 
 
 30 
 
 28 
 
 26 
 
 24 
 
 22 
 
 26 
 
 56 
 
 58 
 
 57 
 
 56 
 
 54 
 
 51 
 
 47 
 
 44 
 
 41 
 
 38 
 
 36 
 
 34 
 
 31 
 
 29 
 
 27 
 
 27 
 
 . 58 
 
 60 
 
 61 
 
 61 
 
 59 
 
 57 
 
 54 
 
 51 
 
 48 
 
 44 
 
 42 
 
 39 
 
 37 
 
 35 
 
 32 
 
 28 
 
 58 
 
 62 
 
 64 
 
 65 
 
 65 
 
 63 
 
 60 
 
 57 
 
 54 
 
 51 
 
 48 
 
 45 
 
 43 
 
 41 
 
 36 
 
 29 
 
 58 
 
 63 
 
 66 
 
 68 
 
 69 
 
 68 
 
 66 
 
 63 
 
 60 
 
 57 
 
 54 
 
 51 
 
 49 
 
 47 
 
 44 
 
 30 
 
 57 
 
 62 
 
 67 
 
 70 
 
 72 
 
 72 
 
 71 
 
 69 
 
 66 
 
 63 
 
 60 
 
 57 
 
 55 
 
 52 
 
 50 
 
 31 
 
 54 
 
 61 
 
 66 
 
 70 
 
 73 
 
 75 
 
 75 
 
 74 
 
 71 
 
 69 
 
 66 
 
 63 
 
 60 
 
 57 
 
 55 
 
 32 
 
 52 
 
 58 
 
 64 
 
 69 
 
 74 
 
 76 
 
 77 
 
 77 
 
 76 
 
 73 
 
 71 
 
 68 
 
 65 
 
 62 
 
 60 
 
 33 
 
 48 
 
 55 
 
 61 
 
 67 
 
 72 
 
 76 
 
 79 
 
 79 
 
 79 
 
 77 
 
 75 
 
 72 
 
 69 
 
 67 
 
 64 
 
 34 
 
 45 
 
 51 
 
 57 
 
 64 
 
 69 
 
 74 
 
 78 
 
 80 
 
 81 
 
 80 
 
 78 
 
 76 
 
 73 
 
 70 
 
 68 
 
 35 
 
 42 
 
 47 
 
 52 
 
 59 
 
 65 
 
 71 
 
 76 
 
 79 
 
 81 
 
 81 
 
 80 
 
 78 
 
 76 
 
 73 
 
 70 
 
 36 
 
 39 
 
 43 
 
 47 
 
 54 
 
 60 
 
 66 
 
 72 
 
 77 
 
 80 
 
 81 
 
 81 
 
 80 
 
 78 
 
 75 
 
 72 
 
 The perturbations are expressed in hundredths of a second of arc. 
 
TAIILI-: xxv. 
 
 /' rtitrliiilitiH.-i nfl/if /,.>'/<>("/< />;/ Kilurn. 
 
 linn, audit = I 
 
 CiHisluiit iiddvd II". lil. IViind i.C . \rgmi i.-nl XIV., M units. 
 
 \ r** 
 
 .1 
 
 d 
 
 d 
 
 .1 
 
 d 
 
 d 
 
 d 
 
 .1 
 
 d 
 
 ,! 
 
 d 
 
 d 
 
 d 
 
 
 d 
 
 XIV. 
 
 i*o 
 
 I3M 
 
 186 
 
 III 
 
 154 
 
 100 
 
 ION 
 
 170 
 
 ISI 
 
 
 200 
 
 SON 
 
 310 
 
 9JM 
 
 33 
 
 
 
 70 
 
 G8 
 
 60 
 
 83 
 
 61 
 
 
 68 
 
 69 
 
 18 
 
 4r. 
 
 41 
 
 
 37 
 
 87 
 
 40 
 
 1 
 
 71 
 
 00 
 
 67 
 
 88 
 
 63 
 
 0] 
 
 
 
 5! 
 
 47 
 
 44 
 
 40 
 
 88 
 
 80 
 
 37 
 
 g 
 
 72 
 
 60 
 
 87 
 
 
 03 
 
 61 
 
 
 57 
 
 64 
 
 
 46 
 
 43 
 
 80 
 
 86 
 
 
 3 
 
 79 
 
 (i'.p 
 
 87 
 
 64 
 
 83 
 
 61 
 
 60 
 
 67 
 
 55 
 
 69 
 
 1- 
 
 44 
 
 40 
 
 8fl 
 
 34 
 
 4 
 
 71 
 
 00 
 
 in; 
 
 64 
 
 09 
 
 60 
 
 68 
 
 
 
 
 49 
 
 45 
 
 41 
 
 37 
 
 34 
 
 5 
 
 70 
 
 88 
 
 68 
 
 69 
 
 60 
 
 68 
 
 56 
 
 06 
 
 83 
 
 69 
 
 40 
 
 40 
 
 19 
 
 
 34 
 
 6 
 
 68 
 
 86 
 
 in 
 
 01 
 
 
 56 
 
 54 
 
 
 61 
 
 50 
 
 48 
 
 M 
 
 42 
 
 SB 
 
 36 
 
 7 
 
 88 
 
 64 
 
 69 
 
 60 
 
 67 
 
 :.| 
 
 59 
 
 60 
 
 48 
 
 47 
 
 41) 
 
 44 
 
 49 
 
 38 
 
 86 
 
 8 
 
 00 
 
 61 
 
 GO 
 
 
 68 
 
 59 
 
 49 
 
 47 
 
 40 
 
 44 
 
 43 
 
 1-' 
 
 40 
 
 
 34 
 
 9 
 
 56 
 
 57 
 
 57 
 
 66 
 
 63 
 
 50 
 
 47 
 
 46 
 
 43 
 
 41 
 
 40 
 
 30 
 
 86 
 
 34 
 
 10 
 
 49 
 
 69 
 
 53 
 
 53 
 
 51 
 
 49 
 
 M 
 
 43 
 
 40 
 
 88 
 
 37 
 
 36 :i.i 
 
 34 
 
 39 
 
 11 
 
 49 
 
 46 
 
 4'.) 
 
 60 
 
 49 
 
 47 
 
 45 
 
 49 
 
 38 
 
 36 
 
 34 
 
 33 31 
 
 31 
 
 29 
 
 19 
 
 I!.-, 
 
 40 
 
 41 
 
 46 
 
 47 
 
 46 
 
 44 
 
 41 
 
 38 
 
 86 
 
 32 
 
 30 
 
 28 
 
 27 
 
 13 
 
 18 
 
 83 
 
 38 
 
 42 
 
 43 
 
 44 
 
 43 
 
 40 
 
 37 
 
 34 
 
 31 
 
 29 
 
 27 
 
 26 
 
 94 
 
 14 
 
 91 
 
 27 
 
 32 
 
 37 
 
 40 
 
 41 
 
 41 
 
 40 
 
 37 
 
 34 
 
 31 
 
 28 
 
 96 
 
 Jl 
 
 93 
 
 16 
 
 18 
 
 21 
 
 27 
 
 32 
 
 36 
 
 39 
 
 40 
 
 39 
 
 38 
 
 35 
 
 32 
 
 28 
 
 96 
 
 23 
 
 21 
 
 16 
 
 11 
 
 16 
 
 21 
 
 27 
 
 32 
 
 86 
 
 33 
 
 80 
 
 
 36 
 
 33 
 
 30 
 
 27 
 
 24 
 
 M 
 
 17 
 
 7 
 
 11 
 
 10 
 
 99 
 
 28 
 
 89 
 
 36 
 
 38 
 
 89 
 
 38 
 
 86 
 
 89 
 
 29 
 
 96 
 
 93 
 
 18 
 
 5 
 
 8 
 
 13 
 
 1- 
 
 93 
 
 29 
 
 83 
 
 37 
 
 38 
 
 39 
 
 37 
 
 35 
 
 39 
 
 29 
 
 
 to 
 
 4 
 
 6 
 
 10 
 
 15 
 
 20 
 
 25 
 
 31 
 
 35 
 
 33 
 
 40 
 
 40 
 
 38 
 
 36 
 
 39 
 
 
 20 
 
 4 
 
 6 
 
 8 
 
 12 
 
 17 
 
 23 
 
 28 
 
 33 
 
 33 
 
 40 
 
 41 
 
 41 
 
 40 
 
 37 
 
 33 
 
 91 
 
 6 
 
 6 
 
 8 
 
 11 
 
 15 
 
 20 
 
 26 
 
 3C 
 
 37 
 
 40 
 
 43 
 
 44 
 
 43 
 
 41 
 
 38 
 
 99 
 
 8 
 
 8 
 
 9 
 
 11 
 
 14 
 
 19 
 
 24 
 
 30 
 
 86 
 
 40 
 
 44 
 
 46 
 
 47 
 
 48 
 
 43 
 
 93 
 
 11 
 
 10 
 
 10 
 
 12 
 
 14 
 
 18 
 
 23 
 
 23 
 
 84 
 
 39 
 
 44 
 
 47 
 
 49 
 
 4!) 
 
 43 
 
 Jl 
 
 16 
 
 13 
 
 13 
 
 13 
 
 15 
 
 18 
 
 99 
 
 27 
 
 33 
 
 39 
 
 44 
 
 48 
 
 51 
 
 53 
 
 63 
 
 96 
 
 19 
 
 17 
 
 16 
 
 16 
 
 16 
 
 18 
 
 22 
 
 2G 
 
 32 
 
 38 
 
 43 
 
 49 
 
 53 
 
 .-,:, 
 
 50 
 
 90 
 
 24 
 
 22 
 
 20 
 
 19 
 
 19 
 
 20 
 
 22 
 
 26 
 
 31 
 
 36 
 
 43 
 
 48 
 
 53 
 
 57 
 
 5'J 
 
 27 
 
 30 
 
 27 
 
 25 
 
 23 
 
 99 
 
 22 
 
 23 
 
 26 
 
 30 
 
 35 
 
 41 
 
 47 
 
 53 
 
 
 61 
 
 28 
 
 35 
 
 33 
 
 30 
 
 28 
 
 26 
 
 25 
 
 25 
 
 27 
 
 30 
 
 34 
 
 40 
 
 46 
 
 52 
 
 58 
 
 02 
 
 29 
 
 41 
 
 39 
 
 3G 
 
 33 
 
 30 
 
 29 
 
 28 
 
 28 
 
 30 
 
 34 
 
 38 
 
 44 
 
 50 
 
 57 
 
 69 
 
 30 
 
 47 
 
 44 
 
 41 
 
 38 
 
 35 
 
 33 
 
 31 
 
 30 
 
 31 
 
 33 
 
 37 
 
 42 
 
 48 
 
 68 
 
 60 
 
 31 
 
 53 
 
 60 
 
 47 
 
 44 
 
 41 
 
 38 
 
 35 
 
 33 
 
 33 
 
 34 
 
 36 
 
 40 
 
 46 
 
 69 
 
 
 32 
 
 57 
 
 55 
 
 52 
 
 49 
 
 46 
 
 42 
 
 39 
 
 36 
 
 86 
 
 34 
 
 86 
 
 39 
 
 43 
 
 49 
 
 66 
 
 :i:i 
 
 63 
 
 GO 
 
 57 
 
 54 
 
 51 
 
 47 
 
 44 
 
 40 
 
 38 
 
 36 
 
 36 
 
 37 
 
 41 
 
 45 
 
 51 
 
 34 
 
 65 
 
 63 
 
 61 
 
 58 
 
 55 
 
 52 
 
 48 
 
 45 
 
 41 
 
 39 
 
 37 
 
 37 
 
 39 
 
 42 
 
 47 
 
 35 
 
 68 
 
 66 
 
 64 
 
 61 
 
 59' 
 
 56 
 
 53 
 
 49 
 
 48 
 
 41 
 
 39 
 
 37 
 
 38 
 
 39 
 
 43 
 
 36 
 
 8j 
 
 70 
 
 63 
 
 66 
 
 63 
 
 61 
 
 59 
 
 " 
 
 52 
 
 48 
 
 45 
 
 41 
 
 38 
 
 37 
 
 37 
 
 40 
 
 Add 0.8 to Arg. XIV. when 224-'.7 ia subtracted from Arg. I. 
 
TABLE XXVI. 
 
 Lntrarillim of the Elliptic Radius Vector for BBS = 0. 
 Constant subtracted 0.0000257. Period of Argument I. 'J'JI'1.7008. 
 
 Arg. I. 
 
 a 
 O.O 
 
 a 
 0.1 
 
 a 
 O.2 
 
 d 
 0.3 
 
 a 
 0.4 
 
 a 
 O.5 
 
 ii 
 O.G 
 
 a 
 0.7 
 
 d 
 0.8 
 
 a 
 O.9 
 
 UilT. 
 for 0-1.1. 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 9.8563298 
 
 63298 
 
 63298 
 
 63299 
 
 63300 
 
 63301 
 
 63302 
 
 63304 
 
 63305 
 
 63307 
 
 + 1 
 
 1 
 
 63310 
 
 63312 
 
 63315 
 
 63318 
 
 63321 
 
 63324 
 
 63328 
 
 63332 
 
 63336 
 
 63341 
 
 4 
 
 2 
 
 63345 
 
 63350 
 
 ^3355 
 
 63360 
 
 63366 
 
 63372 
 
 63378 
 
 63384 
 
 63391 
 
 63397 
 
 6 
 
 3 
 
 63404 
 
 63412 
 
 63419 
 
 63427 
 
 63435 
 
 63443 
 
 63451 
 
 63460 
 
 63469 
 
 63478 
 
 8 
 
 4 
 
 63487 
 
 63497 
 
 63507 
 
 63517 
 
 63527 
 
 63538 
 
 635 18 
 
 63559 
 
 63571 
 
 63582 
 
 11 
 
 5 
 
 63594 
 
 63606 
 
 63618 
 
 63630 
 
 63643 
 
 63656 
 
 C3669 
 
 63682 
 
 63696 
 
 63710 
 
 13 
 
 6 
 
 63724 
 
 63738 
 
 63752 
 
 63767 
 
 63782 
 
 63797 
 
 63813 
 
 63828 
 
 63844 
 
 63860 
 
 15 
 
 7 
 
 63877 
 
 63893 
 
 63910 
 
 63927 
 
 63945 
 
 63962 
 
 63980 
 
 63998 
 
 64016 
 
 64035 
 
 18 
 
 8 
 
 64053 
 
 64072 
 
 64092 
 
 64111 
 
 64131 
 
 64150 
 
 64171 
 
 64191 
 
 64211 
 
 64232 
 
 20 
 
 9 
 
 64253 
 
 64274 
 
 64296 
 
 64317 
 
 64339 
 
 64362 
 
 64384 
 
 64407 
 
 64429 
 
 64452 
 
 22 
 
 10 
 
 64476 
 
 64499 
 
 64523 
 
 64547 
 
 64571 
 
 64595 
 
 64620 
 
 64645 
 
 64670 
 
 64695 
 
 25 
 
 11 
 
 64721 
 
 64747 
 
 64773 
 
 64799 
 
 64825 
 
 64852 
 
 64879 
 
 64906 
 
 64933 
 
 64961 
 
 27 
 
 12 
 
 64989 
 
 65017 
 
 65045 
 
 65073 
 
 65102 
 
 65131 
 
 65160 
 
 65189 
 
 65219 
 
 65249 
 
 29 
 
 13 
 
 65279 
 
 65309 
 
 65340 
 
 65370 
 
 65401 
 
 65432 
 
 65464 
 
 65495 
 
 65527 
 
 65559 
 
 31 
 
 14 
 
 65591 
 
 65624 
 
 65656 
 
 65689 
 
 65722 
 
 65756 
 
 65789 
 
 65823 
 
 65857 
 
 65891 
 
 33 
 
 15 
 
 65925 
 
 65960 
 
 65995 
 
 66030 
 
 66065 
 
 66100 
 
 66136 
 
 66172 
 
 66208 
 
 66244 
 
 36 
 
 16 
 
 66281 
 
 66318 
 
 66354 
 
 66392 
 
 66429 
 
 66467 
 
 66504 
 
 66542 
 
 66581 
 
 66619 
 
 38 
 
 17 
 
 66658 
 
 66697 
 
 66736 
 
 66775 
 
 66814 
 
 66854 
 
 66894 
 
 66934 
 
 66974 
 
 67015 
 
 40 
 
 18 
 
 67055 
 
 67096 
 
 67137 
 
 67179 
 
 67220 
 
 67262 
 
 67304 
 
 67346 
 
 67388 
 
 67431 
 
 42 
 
 19 
 
 67474 
 
 67517 
 
 67560 
 
 67603 
 
 67647 
 
 67691 
 
 67734 
 
 67779 
 
 67823 
 
 67868 
 
 44 
 
 20 
 
 67912 
 
 67957 
 
 68002 
 
 68048 
 
 68093 
 
 68139 
 
 68185 
 
 68231 
 
 68278 
 
 68324 
 
 46 
 
 21 
 
 68371 
 
 68418 
 
 68465 
 
 68512 
 
 68560 
 
 68609 
 
 68656 
 
 68704 
 
 68752 
 
 68800 
 
 48 
 
 22 
 
 68849 
 
 68898 
 
 68947 
 
 68996 
 
 69046 
 
 69095 
 
 69145 
 
 69195 
 
 69245 
 
 69296 
 
 50 
 
 23 
 
 69346 
 
 69397 
 
 69448 
 
 69499 
 
 69550 
 
 69602 
 
 69654 
 
 69706 
 
 69758 
 
 69810 
 
 52 
 
 24 
 
 69862 
 
 69915 
 
 69968 
 
 70021 
 
 70074 
 
 70127 
 
 70181 
 
 70234 
 
 70288 
 
 70342 
 
 53 
 
 25 
 
 70396 
 
 70451 
 
 70505 
 
 70560 
 
 70615 
 
 70670 
 
 70726 
 
 70781 
 
 70837 
 
 70893 
 
 55 
 
 . 26 
 
 70949 
 
 71005 
 
 71061 
 
 71118 
 
 71174 
 
 71231 
 
 71288 
 
 71345 
 
 71403 
 
 71460 
 
 57 
 
 27 
 
 71518 
 
 71576 
 
 71031 
 
 71692 
 
 71751 
 
 71809 
 
 71868 
 
 71927 
 
 71986 
 
 72045 
 
 59 
 
 
 
 
 
 
 
 
 
 
 
 
 
 28 
 
 72105 
 
 72164 
 
 72224 
 
 72284 
 
 72344 
 
 72404 
 
 72464 
 
 72525 
 
 72586 
 
 72646 
 
 60 
 
 29 
 
 72707 
 
 72769 
 
 72830 
 
 72891 
 
 72953 
 
 73015 
 
 .73077 
 
 73139 
 
 73201 
 
 73264 
 
 62 
 
 30 
 
 73326 
 
 73389 
 
 73452 
 
 73515 
 
 73578 
 
 73642 
 
 73705 
 
 73769 
 
 73833 
 
 73897 
 
 63 
 
 31 
 
 73961 
 
 74025 
 
 74089 
 
 74154 
 
 74219 
 
 74284 
 
 74319 
 
 74414 
 
 74479 
 
 74544 
 
 65 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 32 
 
 74610 
 
 74676 
 
 74742 
 
 74808 
 
 74874 
 
 74940 
 
 75007 
 
 75073 
 
 75140 
 
 75207 
 
 66 
 
 33 
 
 75274 
 
 75341 
 
 75408 
 
 75476 
 
 75543 
 
 75611 
 
 75679 
 
 75747 
 
 75815 
 
 75883 
 
 88 
 
 34 
 
 75951 
 
 76020 
 
 76089 
 
 76157 
 
 76226 
 
 76295 
 
 76364 
 
 76434 
 
 76503 
 
 76573 
 
 69 
 
 35 
 
 76642 
 
 76712 
 
 76782 
 
 76852 
 
 76922 
 
 76993 
 
 77063 
 
 77134 
 
 77204 
 
 77275 
 
 70 
 
 36 
 
 77346 
 
 77417 
 
 77488 
 
 77560 
 
 77631 
 
 77703 
 
 77774 
 
 77846 
 
 77918 
 
 77990 
 
 72 
 
 37 
 
 78062 
 
 78134 
 
 78207 
 
 78279 
 
 78352 
 
 78425 
 
 78497 
 
 78570 
 
 78643 
 
 78716 
 
 7?i 
 
 38 
 
 78790 
 
 78863 
 
 78937 
 
 79010 
 
 79084 
 
 79158 
 
 79232 
 
 79306 
 
 79380 
 
 79454 
 
 74 
 
 39 
 
 79528 
 
 79603 
 
 79677 
 
 79752 
 
 79827 
 
 79902 
 
 79977 
 
 80052 
 
 80127 
 
 80202 
 
 75 
 
 40 
 
 80277 
 
 80352 
 
 80428 
 
 80504 
 
 80580 
 
 80656 
 
 80732 
 
 80808 
 
 80884 
 
 80960 
 
 76 
 
 41 
 
 81036 
 
 81113 
 
 81189 
 
 81266 
 
 81343 
 
 81419 
 
 81496 
 
 81573 
 
 81650 
 
 81727 
 
 77 
 
 42 
 
 81805 
 
 81882 
 
 81959 
 
 82037 
 
 82114 
 
 82192 
 
 82270 
 
 82348 
 
 82425 
 
 82503 
 
 78 
 
 43 
 
 82582 
 
 82660 
 
 82738 
 
 82816 
 
 82895 
 
 82973 
 
 83052 
 
 83130 
 
 83209 
 
 83288 
 
 78 
 
 44 
 
 83366 
 
 83445 
 
 83524 
 
 83603 
 
 83682 
 
 83762 
 
 83841 
 
 83920 
 
 84000 
 
 84079 
 
 79 
 
 45 
 
 84159 
 
 84238 
 
 84318 
 
 84398 
 
 84477 
 
 84557 
 
 84637 
 
 84717 
 
 84797 
 
 84877 
 
 80 
 
 46 
 
 84958 
 
 85038 
 
 85118 
 
 85199 
 
 85279 
 
 85359 
 
 85410 
 
 85521 
 
 85601 
 
 85682 
 
 81 
 
 47 
 
 9.8585763 
 
 85844 
 
 85924 
 
 86005 
 
 86086 
 
 86167 
 
 86249 
 
 86330 
 
 86411 
 
 86492 
 
 + 81 
 
TABLE XXVI. 
 
 47 
 
 i-ithiH of 1 In- Klliptir ]{u,liu* V, <;,,,- !.,,- tjj = 0. 
 C.,ii!.t:iiit ,.|i!itr:;rtril (I.IIIMI 
 
 Ar-. I. 
 
 .1 
 0.0 
 
 ,1 
 O.I 
 
 .1 
 
 cl 
 
 .1 
 0.1 
 
 0..5 
 
 .1 
 
 .1 
 
 o.r 
 
 .1 
 O.8 
 
 j 
 O.3 
 
 for ii 
 
 .1 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 is 
 
 9.8586573 
 
 86655 
 
 86736 
 
 Mis 17 
 
 86899 
 
 86980 
 
 870(12 
 
 v, 1 1 1 
 
 
 
 
 49 
 
 > N7171 
 
 87552 
 
 
 87716 
 
 s77!is 
 
 87880 
 
 87962 
 
 88!) I] 
 
 88126 
 
 82 
 
 50 
 51 
 
 88208 
 89031 
 
 S8290 
 89111 
 
 SS373 
 89196 
 
 89279 
 
 89362 
 
 88613 
 
 8!) 1 1 1 
 
 89527 
 
 89609 
 
 88861 
 
 89692 
 
 88!) Ill 
 
 81(775 
 
 82 
 83 
 
 52 
 
 89857 
 
 s!)9 10 
 
 90023 
 
 90106 
 
 90189 
 
 
 90354 
 
 ill) 137 
 
 90520 
 
 90608 
 
 S3 
 
 53 
 
 90686 
 
 90769 
 
 908.V.' 
 
 90934 
 
 91017 
 
 91100 
 
 91183 
 
 !H 266 
 
 91349 
 
 91432 
 
 83 
 
 51 
 
 91516 
 
 91599 
 
 ill 68-_> 
 
 91765 
 
 91848 
 
 91931 
 
 9201 1 
 
 92097 
 
 
 92263 
 
 
 55 
 
 92316 
 
 92 129 
 
 92513 
 
 92596 
 
 92679 
 
 92762 
 
 92845 
 
 ! 12928 
 
 98011 
 
 930!) 1 
 
 83 
 
 56 
 
 93177 
 
 93260 
 
 93311 
 
 93 127 
 
 93510 
 
 93593 
 
 98676 
 
 9375!) 
 
 938 12 
 
 93925 
 
 
 57 
 
 94008 
 
 91091 
 
 94174 
 
 1)1257 
 
 91310 
 
 !) 1 123 
 
 91506 915V!) 
 
 94672 
 
 91755 
 
 83 
 
 58 
 
 94838 
 
 91921 
 
 95001 
 
 ! 15086 
 
 95169 
 
 95252 
 
 95335 
 
 95118 
 
 95500 
 
 95583 
 
 
 59 
 
 95666 
 
 957 1!) 
 
 ! 1583 1 
 
 95911 
 
 95996 
 
 96079 
 
 96162 
 
 962 1 1 
 
 96327 
 
 96109 
 
 83 
 
 60 
 
 96493 
 
 9657 1 
 
 96656 
 
 
 
 96821 
 
 96903 
 
 96986 
 
 97068 
 
 97150 
 
 97232 
 
 82 
 
 61 
 
 97311 
 
 97396 
 
 97478 
 
 97560 
 
 976 12 
 
 9772 1 
 
 97806 
 
 !)7sss 
 
 97970 
 
 98052 
 
 
 62 
 
 98134 
 
 98215 
 
 98297 
 
 
 98 160 
 
 98542 
 
 98623 
 
 98705 
 
 98786 
 
 !IS8li7 
 
 82 
 
 63 
 
 98949 
 
 99030 
 
 99111 
 
 9!) If 12 
 
 99273 
 
 99351 
 
 99 135 
 
 !)!).-> 16 
 
 99597 
 
 99678 
 
 81 
 
 61 
 
 9.6599759 
 
 99839 
 
 99920 
 
 tooooi 
 
 00081 
 
 00162 
 
 00212 
 
 00323 
 
 00103 
 
 00183 
 
 80 
 
 65 
 
 9.86005(13 
 
 006 13 
 
 00721 
 
 (HIS01 
 
 00684 
 
 00963 
 
 01013 
 
 01123 
 
 01203 
 
 01282 
 
 80 
 
 66 
 
 01362 
 
 01112 
 
 01 521 
 
 01600 
 
 01680 
 
 0175!) 
 
 01838 
 
 011)17 
 
 0191)6 
 
 02075 
 
 71) 
 
 67 
 
 02151 
 
 02233 
 
 02311 
 
 023!IO 
 
 02469 
 
 02517 
 
 02626 
 
 02701 
 
 02782 
 
 02860 
 
 78 
 
 68 
 
 02938 
 
 03016 
 
 030!) 1 
 
 03172 
 
 03250 
 
 03328 
 
 03105 
 
 03483 
 
 03560 
 
 03638 
 
 7s 
 
 69 
 
 03715 
 
 03792 
 
 03*69 
 
 03!) 16 
 
 01023 
 
 01100 
 
 01177 
 
 125 1 
 
 01330 
 
 01107 
 
 77 
 
 70 
 
 04483 
 
 01560 
 
 01636 
 
 01712 
 
 01788 
 
 Ols6 I 
 
 04940 
 
 05016 
 
 050!) 1 
 
 05167 
 
 7(1 
 
 71 
 
 052 12 
 
 05:; is 
 
 05393 
 
 05168 
 
 05513 
 
 05(518 
 
 05693 
 
 95768 
 
 05843 
 
 05917 
 
 75 
 
 72 
 
 05992 
 
 06066 
 
 06110 
 
 06215 
 
 06289 
 
 06363 
 
 06136 
 
 06510 
 
 0658 1 
 
 06657 
 
 71 
 
 73 
 
 06731 
 
 06801 
 
 06877 
 
 06950 
 
 07023 
 
 07096 
 
 07169 
 
 072 12 
 
 07311 
 
 07387 
 
 73 
 
 74 
 
 0715!) 
 
 07531 
 
 07(i()3 
 
 07675 
 
 07717 
 
 0781!) 
 
 07891 
 
 07962 
 
 08031 
 
 08105 
 
 
 75 
 
 08176 
 
 082 17 
 
 08318 
 
 08389 
 
 08460 
 
 O.s530 
 
 08601 
 
 08671 
 
 08711 
 
 08811 
 
 71 
 
 76 
 
 08881 
 
 08951 
 
 09021 
 
 09090 
 
 09160 
 
 09229 
 
 09298 
 
 09367 
 
 09136 
 
 09505 
 
 69 
 
 77 
 
 0957 1 
 
 096 12 
 
 09711 
 
 09779 
 
 098 17 
 
 09915 
 
 09983 
 
 10051 
 
 Kills 
 
 10186 
 
 68 
 
 78 
 
 10253 
 
 10321 
 
 10388 
 
 10155 
 
 10522 
 
 10588 
 
 10655 
 
 1(1721 
 
 10788 
 
 10854 
 
 67 
 
 79 
 
 10920 
 
 10986 
 
 11051 
 
 11117 
 
 11182 
 
 1 12 is 
 
 11818 
 
 1 137s 
 
 11113 
 
 11507 
 
 65 
 
 80 
 
 11572 
 
 11636 
 
 11701 
 
 1 17(15 
 
 11829 
 
 11893 
 
 11956 
 
 12020 
 
 
 12116 
 
 64 
 
 81 
 
 12210 
 
 12273 
 
 12335 
 
 12398 
 
 12161 
 
 12523 
 
 12585 
 
 12617 
 
 1270!! 
 
 12771 
 
 62 
 
 82 
 
 12832 
 
 12894 
 
 12955 
 
 13016 
 
 13077 
 
 13138 
 
 13199 
 
 13259 
 
 13319 
 
 13380 
 
 61 
 
 83 
 
 13110 
 
 13500 
 
 
 13619 
 
 13678 
 
 
 13797 
 
 13856 
 
 13!ll 1 
 
 13973 
 
 5!) 
 
 81 
 
 1 1031 
 
 11090 
 
 1 11 is 
 
 11206 
 
 1 1263 
 
 14321 
 
 14878 
 
 11136 
 
 14499 
 
 1 1550 
 
 
 85 
 
 14606 
 
 1 1663 
 
 1 1720 
 
 1 1776 
 
 1 1832 
 
 1 ISSN 
 
 14943 
 
 1 1!)!)!) 
 
 15051 
 
 15110 
 
 56 
 
 86 
 
 15165 
 
 15220 
 
 15275 
 
 15329 
 
 15384 
 
 15438 
 
 15499 
 
 15546 
 
 1551111 
 
 15653 
 
 54 
 
 87 
 
 15706 
 
 1575!) 
 
 15812 
 
 15865 
 
 15918 
 
 15970 
 
 16023 
 
 16075 
 
 16127 
 
 16178 
 
 52 
 
 88 
 
 16286 
 
 16281 
 
 16333 
 
 16384 
 
 16131 
 
 Kits;, 
 
 16536 
 
 16586 
 
 16636 
 
 16686 
 
 51 
 
 89 
 
 16736 
 
 16785 
 
 16835 
 
 
 16933 
 
 16982 
 
 17031 
 
 17079 
 
 17127 
 
 17175 
 
 1!) 
 
 90 
 
 17223 
 
 17271 
 
 17319 
 
 17366 
 
 17113 
 
 17160 
 
 17. --07 
 
 17553 
 
 17600 
 
 17646 
 
 17 
 
 91 
 
 17692 
 
 17738 
 
 17783 
 
 17829 
 
 17874 
 
 17919 
 
 17964 
 
 18009 
 
 18053 
 
 180! IS 
 
 45 
 
 K 
 
 18142 | 18186 
 
 18229 
 
 18273 
 
 18316 
 
 I.s35!l 
 
 Is |(I2 
 
 is 115 
 
 18488 
 
 18530 
 
 43 
 
 93 
 
 18572 18614 
 
 18656 
 
 1S697 
 
 18739 
 
 18780 
 
 
 18862 
 
 Is! 102 
 
 181113 
 
 11 
 
 
 18983 19023 
 
 19063 
 
 19102 
 
 19112 
 
 19181 
 
 19250 
 
 19258 
 
 19297 
 
 19335 
 
 39 
 
 95 
 
 9.8619373 19411 
 
 19449 
 
 19487 
 
 19521 
 
 19561 
 
 1115! is 
 
 19635 
 
 19671 
 
 19708 +37 
 
 
 1 
 
 
 
 
 
 
 
 
 
TABL.E XXVI. 
 
 Logarithm of 'tin- Elliptic E/i'/ina Vector for IS1 = 0. 
 Constant subtracted 0.000(;:2.")7. Period of Argument I. a24<>.7008. 
 
 Ar B . I. 
 
 ,1 
 O.O 
 
 a 
 0.1 
 
 <i 
 O.2 
 
 a 
 O.3 
 
 a 
 O.I 
 
 a 
 
 0.9 
 
 <i 
 0.6 
 
 a 
 
 o.y 
 
 cl 
 
 0.8 
 
 a 
 O.9 
 
 Diff. 
 fbrOM. 
 
 d 
 
 
 
 
 
 
 | 
 
 
 
 
 
 96 
 
 9.8619744 
 
 19780 
 
 19815 
 
 19S51 
 
 19886 
 
 19921 
 
 19956 19991 
 
 20025 
 
 20060 
 
 + 35 
 
 97 
 
 20094 
 
 20127 
 
 20161 
 
 20191 
 
 20228 
 
 20261 
 
 20294 
 
 20326 
 
 20359 
 
 20391 
 
 33 
 
 98 
 
 20 123 
 
 20454 
 
 20186 
 
 20517 
 
 20548 
 
 20579 
 
 20610 
 
 20641 
 
 20671 
 
 20701 
 
 31 
 
 99 
 
 20731 
 
 20760 
 
 20790 
 
 20819 
 
 20848 
 
 20877 
 
 20905 
 
 20934 
 
 20962 
 
 20990 
 
 29 
 
 100 
 
 21017 
 
 21045 
 
 21072 
 
 21099 
 
 21126 
 
 21153 
 
 21179 
 
 21205 
 
 21231 
 
 21257 
 
 27 
 
 101 
 
 2128S 
 
 21308 
 
 21333 
 
 21358 
 
 21382 
 
 21407 
 
 21431 
 
 21455 
 
 21479 
 
 21502 
 
 24 
 
 102 
 
 21520 
 
 21519 
 
 21572 
 
 21595 
 
 21617 
 
 21639 
 
 21662 
 
 21683 
 
 21705 
 
 21726 
 
 22 
 
 103 
 
 21748 
 
 21769 
 
 21789 
 
 21810 
 
 21830 
 
 21850 
 
 21870 
 
 21890 
 
 21909 
 
 21928 
 
 20 
 
 104 
 
 21947 
 
 21966 
 
 21984 
 
 22003 
 
 22021 
 
 22039 
 
 22056 
 
 22074 
 
 22091 
 
 22108 
 
 18 
 
 105 
 
 22121 
 
 22141 
 
 22157 
 
 22173 
 
 22189 
 
 22205 
 
 22220 
 
 22235 
 
 22250 
 
 222 G5 
 
 16 
 
 106 
 
 22280 
 
 2229-1 
 
 22308 
 
 22322 
 
 22335 
 
 22349 
 
 22362 
 
 22375 
 
 22388 
 
 22100 
 
 13 
 
 107 
 
 22412 
 
 2-2 12 i 
 
 22436 
 
 22 1 18 
 
 22459 
 
 22470 
 
 22481 
 
 22492 
 
 22502 
 
 22512 
 
 11 
 
 108 
 
 22522 
 
 22532 
 
 22542 
 
 22551 
 
 22560 
 
 22569 
 
 22577 
 
 22586 
 
 22594 
 
 22602 
 
 9 
 
 109 
 
 22610 
 
 22617 
 
 22625 
 
 22632 
 
 22639 
 
 22645 
 
 22651 
 
 22658 
 
 22663 
 
 22669 
 
 6 
 
 110 
 
 22675 
 
 22680 
 
 22685 
 
 22690 
 
 22694 
 
 22699 
 
 22703 
 
 22707 
 
 22710 
 
 22714 
 
 4 
 
 111 
 
 22717 
 
 22720 
 
 22723 
 
 22725 
 
 22727 
 
 22729 
 
 22731 
 
 22733 
 
 22734 
 
 22735 
 
 +2 
 
 112 
 
 22736 
 
 22737 
 
 22737 
 
 22737 
 
 22737 
 
 22737 
 
 22737 
 
 22736 
 
 22735 
 
 22734 
 
 
 
 113 
 
 22733 
 
 22731 
 
 22729 
 
 22727 
 
 22725 
 
 22722 
 
 22720 
 
 22717 
 
 22714 
 
 22710 
 
 3 
 
 114 
 
 22706 
 
 22703 
 
 22698 
 
 22694 
 
 22690 
 
 22685 
 
 22680 
 
 22675 
 
 22669 
 
 22663 
 
 5 
 
 115 
 
 22657 
 
 22651 
 
 22645 
 
 22638 
 
 22632 
 
 22624 
 
 22617 
 
 22610 
 
 22602 
 
 22594 
 
 7 
 
 116 
 
 22586 
 
 22577 
 
 22569 
 
 22560 
 
 22551 
 
 22542 
 
 22532 
 
 22522 
 
 22512 
 
 22502 
 
 9 
 
 117 
 
 22492- 
 
 22481 
 
 22470 
 
 22.159 
 
 22448 
 
 22436 
 
 22424 
 
 22412 
 
 22100 
 
 22387 
 
 12 
 
 118 
 
 22375 
 
 22362 
 
 22349 
 
 22335 
 
 22322 
 
 22308 
 
 2229 1 
 
 22279 
 
 22265 
 
 22250 
 
 14 
 
 119 
 
 22235 
 
 22220 
 
 22205 
 
 22189 
 
 22173 
 
 22157 
 
 22141 
 
 22124 
 
 22108 
 
 22091 
 
 16 
 
 120 
 
 22074 
 
 22056 
 
 22039 
 
 22021 
 
 22003 
 
 21984 
 
 21966 
 
 21947 
 
 21928 
 
 21909 
 
 18 
 
 121 
 
 21890 
 
 21870 
 
 21850 
 
 21830 
 
 21810 
 
 21789 
 
 21769 
 
 21748 
 
 21726 
 
 21705 
 
 21 
 
 122 
 
 21683 21662 
 
 21639 
 
 21617 
 
 21595 
 
 21572 
 
 21549 
 
 21526 
 
 21503 
 
 21479 
 
 23 
 
 123 
 
 21455 
 
 21431 
 
 21107 
 
 21383 
 
 21358 
 
 21333 
 
 21308 
 
 21283 
 
 21257 
 
 21231 
 
 25 
 
 124 
 
 21205 
 
 21179 
 
 21153 
 
 21126 
 
 21099 
 
 21072 
 
 21045 
 
 21017 
 
 20990 
 
 20962 
 
 27 
 
 125 
 
 20934 
 
 20905 
 
 20877 
 
 20848 
 
 20819 
 
 20790 
 
 20760 
 
 20731 
 
 20701 
 
 20671 
 
 29 
 
 126 
 
 20610 
 
 20610 
 
 20579 
 
 20548 
 
 20517 
 
 20486 
 
 20455 
 
 20423 
 
 20391 
 
 20359 
 
 31 
 
 127 
 
 20326 
 
 20294 
 
 20261 
 
 20228 
 
 20195 
 
 20161 
 
 20128 
 
 20094 
 
 20060 
 
 20026 
 
 34 
 
 128 
 
 19991 
 
 19956 
 
 19921 
 
 19886 
 
 19851 
 
 19816 
 
 19780 
 
 19744 
 
 19708 
 
 19672 
 
 36 
 
 129 
 
 19635 
 
 19598 
 
 19561 
 
 19524 
 
 19487 
 
 19449 
 
 19412 
 
 19374 
 
 19335 
 
 19297 
 
 38 
 
 130 
 
 19258 
 
 19220 
 
 19181 
 
 19141 
 
 19102 
 
 19063 
 
 19023 
 
 18983 
 
 18943 
 
 18902 
 
 40 
 
 131 
 
 18862 
 
 18821 
 
 18780 
 
 18739 
 
 18697 
 
 18656 
 
 18614 
 
 18572 
 
 18530 
 
 18488 
 
 42 
 
 OK 
 
 18445 
 
 18402 
 
 18359 
 
 18316 
 
 18273 
 
 18230 
 
 18186 
 
 18142 
 
 18098 
 
 18054 
 
 44 
 
 133 
 
 18009 
 
 17964 
 
 17919 
 
 17874 
 
 17829 
 
 17784 
 
 17738 
 
 17692 
 
 17646 
 
 17600 
 
 46 
 
 131 
 
 17551 
 
 17507 
 
 17460 
 
 17413 
 
 17366 
 
 17319 
 
 17271 
 
 17224 
 
 17176 
 
 17128 
 
 47 
 
 135 
 
 17079 
 
 17031 
 
 1698.2 
 
 16933 
 
 16884 
 
 16835 
 
 16785 
 
 16736 
 
 16686 
 
 16636 
 
 49 
 
 136 
 
 16586 
 
 16536 
 
 16485 
 
 16435 
 
 16384 
 
 16333 
 
 16282 
 
 16230 
 
 16179 
 
 16127 
 
 51 
 
 137 
 
 16075 
 
 16023 
 
 15971 
 
 15918 
 
 15865 
 
 15813 
 
 15760 
 
 15706 
 
 15653 
 
 15600 
 
 53 
 
 138 
 
 15546 
 
 15492 
 
 15438 
 
 15384 
 
 15329 
 
 15275 
 
 15220 
 
 15165 
 
 15110 
 
 15055 
 
 55 
 
 139 
 
 14999 
 
 14944 
 
 14888 
 
 14832 
 
 14776 
 
 14720 
 
 14663 
 
 14607 
 
 14550 
 
 14493 
 
 56 
 
 140 
 
 14436 
 
 14379 
 
 14321 
 
 14264 
 
 14206 
 
 14148 
 
 14090 
 
 14031 
 
 13973 
 
 13914 
 
 58 
 
 141 
 
 13856 
 
 13797 
 
 13738 
 
 13679 
 
 13619 
 
 13560 
 
 13500 
 
 13440 
 
 13380 
 
 13320 
 
 60 
 
 142 
 
 13259 
 
 13199 
 
 13138 
 
 13077 
 
 130] 6 
 
 12955 
 
 12894 
 
 12833 
 
 12771 
 
 12709 
 
 61 
 
 113 
 
 9.8612617 
 
 125H5 
 
 12523 
 
 12461 
 
 12398 
 
 12336 
 
 12273 
 
 12210 
 
 12117 
 
 12083 
 
 -63 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
TABLE XXVI. 
 
 'it/mi ,,/// Elliptic R,,,lins V,;-t,,rJiir BBS = 0. 
 (Hitit.-iiit Miliinn -l.-.l IYrit.il tifArfjiiini'iii 1 
 
 Arg. I. 
 
 ii 
 0.0 
 
 .1 
 O.I 
 
 .1 
 
 o.a 
 
 .1 
 o.:t 
 
 ,i 
 
 0.1 
 
 .1 
 0.5 
 
 ,i 
 0.0 
 
 .1 
 0.7 
 
 .1 
 
 O.M 
 
 .1 
 o. > 
 
 war, 
 
 H.I. 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 111 
 
 9.8612030 
 
 1 l!)5(i 
 
 1 1893 
 
 11829 
 
 11765 
 
 11701 
 
 11636 
 
 11573 
 
 11507 
 
 1 1 1 13 
 
 -61 
 
 146 
 
 1 137S 
 
 11313 
 
 112 IS 
 
 111N2 
 
 11117 
 
 11051 
 
 I09S6 10920 
 
 10854 
 
 107.ss 
 
 86 
 
 146 
 
 10721 
 
 10655 
 
 [0588 
 
 10522 
 
 10455 
 
 10388 
 
 10321 
 
 10251 
 
 10186 
 
 10119 
 
 67 
 
 It? 
 
 10051 
 
 099s:f 
 
 09916 
 
 09s IN 
 
 09779 
 
 09711 
 
 09648 
 
 0957 1 
 
 09505 
 
 09 137 
 
 
 1 is 
 
 09968 
 
 0!)299 
 
 09229 
 
 09160 
 
 09091 
 
 09021 
 
 08951 
 
 
 08812 
 
 OS7 11 
 
 70 
 
 11!) 
 
 (Hi;: i (is(ioi 
 
 08531 
 
 ()s 160 
 
 os:is9 
 
 08318 
 
 08248 
 
 Osl7ii 
 
 08105 
 
 
 71 
 
 . 150 
 
 07963 07S9I 
 
 07819 
 
 077 is 
 
 07676 
 
 07601 07532 
 
 07 159 
 
 07387 
 
 07315 
 
 72 
 
 151 
 
 07 2 12 
 
 071ti!) 
 
 07097 
 
 07034 
 
 06951 
 
 06s 
 
 
 06781 
 
 06858 
 
 06584 
 
 78 
 
 [83 
 
 06511 
 
 OCI37 
 
 063<i.! ( 
 
 06215 
 
 06141 
 
 o;io;;ii 
 
 05992 
 
 059 17 
 
 o.-.sn 
 
 7 1 
 
 15.'} 
 
 05768 
 
 ()5(ii)3 
 
 05(il!t 05511 
 
 05 HiS 
 
 o:.:i!i:i 053 is 052 13 
 
 05167 05991 
 
 78 
 
 164 
 
 05016 
 
 01!) 10 
 
 OIS61 
 
 01712 
 
 on;:!.; oi5;;o OHM 
 
 01107 
 
 01331 
 
 78 
 
 155 
 
 04264 
 
 01177 
 
 04101 
 
 102 1 
 
 03947 
 
 03870 
 
 03793 
 
 037 15 
 
 03688 
 
 03561 
 
 77 
 
 196 
 
 08488 
 
 03106 
 
 03328 
 
 03251 
 
 03173 
 
 03095 
 
 03017 
 
 02989 
 
 
 03788 
 
 7s 
 
 1 57 
 
 03701 
 
 02626 
 
 025 is (' 
 
 02390 
 
 02312 
 
 02283 
 
 02151 
 
 02075 
 
 01997 
 
 79 
 
 158 
 
 01918 
 
 01s:!S 
 
 0175!! OKisO 
 
 OKiOl 
 
 01521 
 
 01442 
 
 OI3i!3 
 
 01283 
 
 01203 
 
 79 
 
 159 
 
 01134 
 
 010 II 
 
 00% 1 
 
 00884 
 
 00804 
 
 00784 
 
 00644 
 
 0!)56 1 
 
 00484 
 
 00103 
 
 B8 
 
 160 
 
 9.8800328 
 
 OIK! 13 
 
 00169 
 
 
 00001 
 
 199931 
 
 99840 
 
 9:!759 
 
 99678 
 
 9959S 
 
 81 
 
 161 
 
 19517 
 
 99436 
 
 99356 
 
 9927 1 
 
 9!) 193 
 
 99 1 1 1 
 
 99030 9 
 
 
 
 81 
 
 163 
 
 98705 
 
 9S62 1 
 
 !)S5 12 
 
 9S161 
 
 98379 
 
 98297 
 
 98216 
 
 98134 
 
 9S052 
 
 97971 
 
 
 169 
 
 97889 
 
 97807 
 
 97728 
 
 97613 
 
 97561 
 
 97479 
 
 97397 
 
 97315 
 
 97388 
 
 97151 
 
 N2 
 
 161 
 
 97088 
 
 96986 
 
 96904 
 
 
 96739 
 
 96657 
 
 96678 
 
 96192 
 
 96110 
 
 9632*3 
 
 N2 
 
 [65 
 
 962)5 96162 !)(i!)s(l !).-,!))7 
 
 95911 
 
 95839 
 
 957 19 
 
 95666 
 
 955S 1 
 
 95501 
 
 88 
 
 166 
 
 !):>! is 95335 
 
 95253 1)5170 
 
 95087 
 
 9500 1 
 
 91921 
 
 9 1S3S 
 
 94756 
 
 91673 
 
 98 
 
 167 
 
 94590 
 
 91507 
 
 9 1 12 1 
 
 91311 
 
 9I2.YS 
 
 91175 
 
 9 1092 
 
 91009 
 
 93926 
 
 98848 
 
 S3 
 
 188 
 
 93760 
 
 93(577 
 
 9359 1 
 
 93510 
 
 93127 
 
 93344 
 
 98361 
 
 98111 
 
 98098 
 
 93012 
 
 
 169 
 
 92999 
 
 92si6 
 
 92768 
 
 92679 
 
 92591 i 
 
 92513 
 
 92 130 
 
 923 17 
 
 9226 1 
 
 921S1 
 
 S3 
 
 170 
 
 92098 
 
 92()i:> 
 
 91932 
 
 91848 
 
 91765 
 
 91689 
 
 91599 
 
 91516 
 
 91133 
 
 91350 
 
 
 171 
 
 91267 
 
 911H1 
 
 91101 
 
 91018 
 
 90935 
 
 90852 
 
 90769 
 
 90686 
 
 90603 
 
 90521 
 
 83 
 
 172 
 
 90 i:is 
 
 90355 
 
 90272 
 
 90189 
 
 90106 
 
 90021 
 
 89941 
 
 89858 
 
 S9775 
 
 S9S93 
 
 
 17:} 
 
 89610 
 
 89527 
 
 S9115 S9362 
 
 89280 
 
 89197 
 
 89115 
 
 WMI32 
 
 88950 
 
 88867 
 
 N3 
 
 171 
 
 887s:> 
 
 88702 
 
 88620 
 
 sv;,:;s 
 
 88456 
 
 88373 
 
 88291 
 
 88209 
 
 88127 
 
 SS015 
 
 N2 
 
 175 
 
 87963 
 
 S7ssi 
 
 87798 
 
 87717 
 
 N7635 
 
 87558 
 
 87471 
 
 
 87308 
 
 87226 
 
 82 
 
 176 
 
 87111 
 
 87063 
 
 86981 
 
 86900 
 
 86818 
 
 86737 
 
 86698 
 
 86574 
 
 86498 
 
 SCI 12 
 
 81 
 
 177 
 
 86330 
 
 N62 1!) 
 
 86168 
 
 86087 
 
 86006 
 
 85925 
 
 S5S I 1 
 
 85768 
 
 
 85602 
 
 si 
 
 178 
 
 85521 
 
 S5 1 1 1 
 
 85360 S52SO 
 
 85199 
 
 85119 
 
 85039 
 
 si: 159 
 
 84878 
 
 84798 
 
 SO 
 
 179 
 
 84718 
 
 N163S 
 
 S155S 
 
 84478 
 
 S1399 
 
 81319 
 
 8 1239 
 
 si 159 
 
 84080 
 
 81000 
 
 NO 
 
 180 
 
 83921 
 
 s:;^ i-j 
 
 88769 
 
 83683 
 
 83601 
 
 88538 
 
 S3 116 
 
 83367 
 
 88988 
 
 H32K) 
 
 79 
 
 181 
 
 83131 
 
 83052 
 
 8297 1 
 
 82895 
 
 S2S17 
 
 82739 
 
 S2661 
 
 82589 
 
 N250 1 
 
 N2 126 
 
 7s 
 
 182 
 
 823 is 
 
 82271 
 
 82193 
 
 82115 
 
 82038 
 
 81960 
 
 81883 
 
 81806 
 
 81728 
 
 81651 
 
 77 
 
 183 
 
 81574 
 
 81497 
 
 81121 
 
 81844 
 
 81267 
 
 81190 
 
 BUM 
 
 81038 
 
 80961 
 
 suss;, 
 
 77 
 
 184 
 
 80809 
 
 S0733 
 
 80657 
 
 80581 
 
 80505 
 
 SO 130 
 
 80894 
 
 80378 
 
 80968 
 
 80128 
 
 76 
 
 185 
 
 80053 
 
 79978 
 
 79903 79S2S 
 
 79788 
 
 79878 
 
 79601 79529 
 
 7!) 155 
 
 79381 
 
 75 
 
 186 
 
 79307 
 
 79233 
 
 79159 7!)S5 
 
 79011 
 
 78938 
 
 7ssii| 7S791 
 
 78717 
 
 7S6 1 1 
 
 71 
 
 187 
 
 78571 
 
 78496 
 
 78426 
 
 78868 
 
 78280 
 
 78208 
 
 78188 
 
 78083 
 
 77991 
 
 77919 
 
 72 
 
 iss 
 
 778 17 
 
 77775 
 
 7770 1 
 
 77689 
 
 77561 
 
 77489 
 
 77418 
 
 77317 
 
 77276 
 
 77908 
 
 71 
 
 189 
 
 771:55 "Oil 
 
 7699 1 76923 
 
 76853 
 
 
 76718 
 
 76843 
 
 7657 1 
 
 76501 
 
 70 
 
 190 
 
 76135 7i;::ii5 
 
 76296 76227 
 
 76158 
 
 76090 
 
 76021 
 
 75952 
 
 75884 
 
 758HJ 
 
 89 
 
 191 
 
 9.85757 is 756sO 75312 75511 
 
 75 177 
 
 75 109 
 
 75312 
 
 75278 
 
 76308 
 
 75111 
 
 67 
 
TABLE XXVI. 
 
 Logarithm of the Elliptic Radius Vector for SBI = 0. 
 
 Constant subtracted 0.0000257. Period of Argument I. 224'' .7008. 
 
 
 a 
 
 (i 
 
 d 
 
 ii 
 
 a 
 
 d 
 
 d 
 
 d 
 
 a 
 
 d 
 
 
 Arg. I. 
 
 0.0 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.4 
 
 0.5 
 
 O.6 
 
 0.7 
 
 0.8 
 
 O.9 
 
 L)iff. 
 
 
 
 
 
 
 
 
 
 
 
 
 for Od.1. 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 102 
 
 9.8575074 
 
 75008 
 
 74941 
 
 74875 
 
 74809 
 
 7 17 13 
 
 ' 74677 
 
 74611 
 
 74545 
 
 74480 
 
 -66 
 
 193 
 
 74115 
 
 74350 
 
 74285 
 
 74220 
 
 74155 
 
 74090 
 
 74026 
 
 73962 
 
 73898 
 
 73834 
 
 64 
 
 194 
 
 73770 
 
 73706 
 
 73643 
 
 73579 
 
 73516 
 
 73 153 
 
 73390 
 
 73327 
 
 73265 
 
 73202 
 
 63 
 
 195 
 
 73140 
 
 73078 
 
 73016 
 
 72951 
 
 72893 
 
 72831" 
 
 72770 
 
 72709 
 
 72648 
 
 72587 
 
 61 
 
 196 
 
 72526 
 
 72465 
 
 72405 
 
 72315 
 
 72285 
 
 72225 
 
 72165 
 
 72103 
 
 72046 
 
 71987 
 
 60 
 
 197 
 
 71928 
 
 718G9 
 
 71810 
 
 71752 
 
 71693 
 
 71635 
 
 71577 
 
 71519 
 
 71462 
 
 71101 
 
 58 
 
 198 
 
 71317 
 
 71289 
 
 71232 
 
 71175 
 
 71119 
 
 71062 
 
 71006 
 
 70950 
 
 70894 
 
 70838 
 
 56 
 
 199 
 
 70782 
 
 70727 
 
 70671 
 
 70316 
 
 70561 
 
 70507 
 
 70152 
 
 70398 
 
 70343 
 
 70289 
 
 55 
 
 200 
 
 70236 
 
 70182 
 
 70128 
 
 70075 
 
 70022 
 
 69969 
 
 69916 
 
 69863 
 
 69811 
 
 69759 
 
 53 
 
 201 
 
 C9707 
 
 69655 
 
 69603 
 
 69552 
 
 69500 
 
 69449 
 
 69398 
 
 69317 
 
 69297 
 
 69246 
 
 51 
 
 202 
 
 69196 
 
 69116 
 
 69096 
 
 69047 
 
 69899 
 
 68948 
 
 68899 
 
 68850 
 
 68801 
 
 68753 
 
 49 
 
 203 
 
 68705 
 
 68657 
 
 68609 
 
 68561 
 
 68514 
 
 68166 
 
 68419 
 
 68372 
 
 68326 
 
 68279 
 
 47 
 
 204 
 
 68233 
 
 68186 
 
 68140 
 
 68095 
 
 68049 
 
 68004 
 
 67959 
 
 67914 
 
 67869 
 
 67824 
 
 45 
 
 205 
 
 67780 
 
 67736 
 
 67692 
 
 67648 
 
 67605 
 
 67561 
 
 67518 
 
 67475 
 
 67432 
 
 67390 
 
 43 
 
 206 
 
 67317 
 
 67305 
 
 67263 
 
 67222 
 
 67180 
 
 67139 
 
 67098 
 
 67057 
 
 67016 
 
 66975 
 
 41 
 
 207 
 
 66935 
 
 66895 
 
 66855 
 
 66815 
 
 66776 
 
 66737 
 
 66698 
 
 66659 
 
 66620 
 
 66582 
 
 39. 
 
 208 
 
 685 1 1 
 
 63506 
 
 66468 
 
 66130 
 
 66393 
 
 66356 
 
 66319 
 
 66282 
 
 66246 
 
 66209 
 
 37 
 
 209 
 
 66173 
 
 66137 
 
 66102 
 
 66066 
 
 66031 
 
 65996 
 
 65961 
 
 65927 
 
 65892 
 
 65858 
 
 35 
 
 210 
 
 65824 
 
 65790 
 
 65757 
 
 6572 1 
 
 65690 
 
 65658 
 
 65625 
 
 65592 
 
 65560 
 
 65528 
 
 33 
 
 211 
 
 65496 
 
 65465 
 
 65434 
 
 65403 
 
 65372 
 
 65341 
 
 65310 
 
 65280 
 
 G5250 
 
 65220 
 
 31 
 
 212 
 
 65191 
 
 65162 
 
 65133 
 
 65101 
 
 65075 
 
 65016 
 
 65018 
 
 64990 
 
 64962 
 
 64935 
 
 28 
 
 213 
 
 64907 
 
 64880 
 
 64853 
 
 61827 
 
 64800 
 
 61771 
 
 61718 
 
 61722 
 
 64697 
 
 64672 
 
 26 
 
 214 
 
 64646 
 
 64622 
 
 64597 
 
 64573 
 
 64548 
 
 64524 
 
 64501 
 
 61477 
 
 64454 
 
 64431 
 
 24 
 
 215 
 
 64408 
 
 64385 
 
 64363 
 
 64311 
 
 64319 
 
 64297 
 
 61276 
 
 61255 
 
 64234 
 
 64213 
 
 22 
 
 216 
 
 61192 
 
 64172 
 
 64152 
 
 64132 
 
 64112 
 
 64093 
 
 64074 
 
 64055 
 
 64036 
 
 64018 
 
 19 
 
 217 
 
 63999 
 
 63981 
 
 63964 
 
 63946 
 
 63929 
 
 63912 
 
 63895 
 
 63878 
 
 63862 
 
 63846 
 
 17 
 
 218 
 
 63830 
 
 63814 
 
 63799 
 
 6378 I 
 
 63769 
 
 63754 
 
 63739 
 
 63725 
 
 63711 
 
 63697 
 
 15 
 
 219 
 
 63684 
 
 63670 
 
 63657 
 
 63611 
 
 63632 
 
 63619 
 
 63607 
 
 63595 
 
 63584 
 
 63572 
 
 12 
 
 220 
 
 63561 
 
 63550 
 
 63539 
 
 63528 
 
 63518 
 
 63508 
 
 63498 
 
 63489 
 
 63179 
 
 63170 
 
 10 
 
 221 
 
 63161 
 
 63 153 
 
 63 1 i I 
 
 63136 
 
 63428 
 
 63420 
 
 63113 
 
 63406 
 
 63399 
 
 63392 
 
 8 
 
 222 
 
 63386 
 
 63379 
 
 63373 
 
 63367 
 
 63362 
 
 63357 
 
 63351 
 
 63317 
 
 63312 
 
 63338 
 
 5 
 
 223 
 
 63333 
 
 63330 
 
 63326 
 
 63322 
 
 63319 
 
 63316 
 
 63314 
 
 63311 
 
 63309 
 
 63307 
 
 3 
 
 224 
 
 9.8563305 
 
 63303 
 
 63302 
 
 63301 
 
 63300 
 
 63300 
 
 63299 
 
 63299 
 
 63299 
 
 63300 
 
 - o 
 
 
TABLE XXVII. 
 
 51 
 
 TAII1YE X\VIII. 
 
 *,,,// of Lo g . r.. 
 
 Prrt. of lag. r. 
 
 F:irtor tn lie multiplied by 111, and its lun.-irithm. I'.-riuil i.l" Ar<-iiiin-iit 1. = I 
 
 Fact, to be X ( ) 2 
 
 Arg.I 
 
 Fartiir. 
 
 In;;, I'll- 
 
 Ar^.l F.-irti.r. i 
 
 
 Factor. 1 
 
 Arg.I 
 
 . Factor 
 
 ,o g .fac 
 
 Arg.I. 
 
 Factor. 
 
 d 
 
 
 
 + 13 15 
 
 1 12- 
 
 d 
 
 (il 
 
 - Mil 
 
 
 d 
 
 -1946 .,1 II 3-. 
 
 l-i 
 
 + 4.06 
 
 06I-: 
 
 d 
 
 
 -2.1 
 
 1 
 
 13.45 
 
 1.12* 
 
 1,1 
 
 1.07 
 
 
 121 
 
 12.90 
 
 I.I IOC 
 
 l-l 
 
 1 II 
 
 iii.ll: 
 
 4 
 
 2.1 
 
 8 
 
 1343 
 
 1.1961 
 
 62 
 
 2:11 
 
 0.36.K 
 
 122 12-1 
 
 1 1071 
 
 1-2 
 
 477 
 
 0.67- i 
 
 8 
 
 2.0 
 
 3 
 
 I:: |.i 
 
 1.1272 
 
 63 
 
 271 
 
 0.4395 
 
 123 
 
 1271 
 
 1 |o| 
 
 1-.: 
 
 .'. 12 
 
 0.709: 
 
 12 
 
 20 
 
 4 
 
 +13.36 
 
 1.1960 
 
 1,1 
 
 - 3.07 
 
 n'l 1-71 
 
 121 
 
 -125!) 
 
 1.1009 
 
 l-l 
 
 + 5.17 
 
 07377 
 
 16 
 
 -l.il 
 
 ."> 
 
 1 3.32 
 
 1 . 1 2 1 1 
 
 
 3.13 i 
 
 1 25 
 
 12 1* 1 H9(,l 
 
 165 
 
 ."> -1 
 
 n 7i,l2 
 
 
 1 - 
 
 6 
 
 13.26 
 
 1 . 1 22 1 
 
 66 
 
 
 0.57-1 
 
 196 
 
 12:15 1.0015 
 
 l-t, 
 
 1, 15 
 
 0.7868 
 
 24 
 
 1.6 
 
 7 
 
 i:: 10 
 
 1. 12.11 
 
 SI 
 
 4.14 
 
 H.6I72 
 
 127 
 
 1221 
 
 
 1-7 
 
 ' 1- 
 
 o.-n- 
 
 
 1 --, 
 
 8 
 
 + 13.10 
 
 1 1171 
 
 6- 
 
 - 1 19 
 
 
 12* 
 
 -12 fi 
 
 14818 
 
 186 
 
 
 04333 
 
 32 
 
 -1.3 
 
 
 
 13.01 
 
 1.1144 
 
 i, ' 
 
 l-l 
 
 n (.-17 
 
 1 2: i 
 
 ll.oo ; 
 
 169 
 
 7.13 
 
 
 36 
 
 I.I 
 
 10 
 
 19.91 
 
 linn 
 
 7 i 
 
 5.1* 
 
 o.7l II 
 
 130 
 
 1171 
 
 1 litiOl, 
 
 100 
 
 7 15 
 
 n -723 
 
 lo 
 
 0.9 
 
 11 
 
 12-0 
 
 1.1072 
 
 71 
 
 
 "7110 
 
 131 
 
 1 1 .56 
 
 1.0630 
 
 101 
 
 7.77 
 
 
 II 
 
 0.7 
 
 12 
 
 + 12.6-1 
 
 1.1030 
 
 72 
 
 - 5 -.-> 
 
 9.7674 
 
 138 
 
 II '- 
 
 ,,1.0561 
 
 199 
 
 
 
 4*. 
 
 - 0.5 
 
 13 
 
 12.54 
 
 1.0984 
 
 73 
 
 6.1* 0.7012 
 
 133 
 
 11.10 l.til-7 
 
 103 
 
 
 0.9229 
 
 Da 
 
 -0.2 
 
 14 
 
 12 ID 
 
 1.0935 
 
 74 
 
 651 
 
 0.8134 
 
 134 
 
 1.0408 
 
 194 
 
 
 0.937!) 
 
 56 
 
 0.0 
 
 10 
 
 12.25 
 
 14880 
 
 75 
 
 6.83 
 
 04348 
 
 135 
 
 10.77 
 
 L4394 
 
 196 
 
 8.95 
 
 84390 
 
 60 
 
 + 0.2 
 
 16 
 
 + 120* 
 
 1 H-22 
 
 76 
 
 - 7.14 
 
 
 136 
 
 -1056 
 
 14836 
 
 196 
 
 + 0.23 
 
 0.9653 
 
 64 
 
 + 0.5 
 
 17 
 
 II .01 
 
 1.0760 
 
 77 
 
 7 15 
 
 04790 
 
 137 
 
 10.33 
 
 1 <il II 
 
 107 
 
 941 
 
 0.9780 
 
 68 
 
 0.7 
 
 18 
 
 11.73 
 
 1.0693 
 
 7- 
 
 7.75 
 
 
 138 
 
 10.10 
 
 1,0041 
 
 19* 
 
 977 
 
 0.9699 
 
 72 
 
 0.9 
 
 10 
 
 1 1 .5 1 
 
 1 nt ,22 
 
 79 
 
 8.05 
 
 04056 
 
 130 
 
 9- , 
 
 
 10!) 
 
 10.03 
 
 1.0013 
 
 76 
 
 1.1 
 
 20 
 
 +11.34 
 
 14546 
 
 80 
 
 - 8.33 
 
 
 140 
 
 - 9.60 
 
 04635 
 
 200 
 
 +10.28 
 
 1.0119 
 
 80 
 
 + 1.3 
 
 21 
 
 11.13 
 
 1 .0465 
 
 81 
 
 -1,2 
 
 0.9364 
 
 III 
 
 0.35 
 
 0.9707 
 
 801 
 
 1049 
 
 l 0990 
 
 84 
 
 15 
 
 22 
 
 10.91 
 
 1.037!) 
 
 n 
 
 8.8!) 
 
 11.0191 
 
 1 12 
 
 
 0.9583 
 
 809 
 
 10.75 
 
 1.0315 
 
 88 
 
 1 Ii 
 
 23 
 
 10.6* 
 
 1 '2-7 
 
 83 
 
 0.16 
 
 0.9621 
 
 113 
 
 8.81 
 
 04451 
 
 
 1048 
 
 1.0405 
 
 92 
 
 1.8 
 
 21 
 
 +10.15 
 
 i mm 
 
 84 
 
 - 9.43 
 
 04749 
 
 1 II 
 
 
 HI).! 13 II 
 
 204 
 
 +11.1!) 
 
 14480 
 
 96 
 
 + 1.9 
 
 25 
 
 10.21 
 
 1 0068 
 
 83 
 
 0.6* 
 
 
 115 
 
 
 04164 
 
 
 II ID 
 
 1.0560 
 
 100 
 
 2.0 
 
 96 
 
 045 
 
 0.9979 
 
 BO 
 
 0.03 
 
 
 1 In 
 
 746 
 
 0.900* 
 
 
 1161 
 
 1.0644 
 
 104 
 
 2.0 
 
 
 9.69 
 
 0.9-61 
 
 87 
 
 10.17 
 
 1.0079 
 
 1 17 
 
 7.61, 
 
 0.8842 
 
 207 
 
 11.79 
 
 i on i 
 
 108 
 
 2.1 
 
 98 
 
 + 9.13 
 
 04743 
 
 88 
 
 -10.40 
 
 1.0 I/O 
 
 148 
 
 - 7.36 
 
 
 
 +11.96 
 
 1.0779 
 
 112 
 
 + 21 
 
 80 
 
 0.15 
 
 ii 961 1 
 
 89 
 
 1062 
 
 1 n2i,2 
 
 149 
 
 7.05 
 
 0.8480 
 
 200 
 
 12 13 
 
 1.0640 
 
 116 
 
 2.1 
 
 
 8.87 
 
 0.917* 
 
 Oil 
 
 lo-l 
 
 1.031!) 
 
 150 
 
 6.73 
 
 n -2-1 
 
 210 
 
 1220 
 
 l 08 '7 
 
 120 
 
 2.0 
 
 31 
 
 8.58 
 
 0.9335 
 
 91 
 
 11.05 
 
 1.0432 
 
 151 
 
 6.41 
 
 
 211 
 
 12 II 
 
 1.0950 
 
 I'M 
 
 2.0 
 
 M 
 
 + 8.28 
 
 0.91-2 
 
 92 
 
 -1 1 .24 
 
 n 1.0509 
 
 I.VJ 
 
 - 6.08 
 
 07849 
 
 212 
 
 (.18.58 
 
 1 0000 
 
 12* 
 
 + 1.9 
 
 33 
 
 746 
 
 09 121 
 
 03 
 
 11,13 
 
 I.058S1 
 
 153 
 
 5.7:, 
 
 
 813 
 
 1271 
 
 1.1043 
 
 139 
 
 I.K 
 
 31 
 
 7.67 
 
 n -- , l 
 
 M 
 
 11.61 
 
 1.0650 
 
 151 
 
 5. 12 
 
 0.733!) 
 
 214 
 
 19.83 
 
 110-3 
 
 136 
 
 1.7 
 
 35 
 
 7.36 
 
 0.8668 
 
 05 
 
 11.79 
 
 1.0714 
 
 l.V, 
 
 5.08 
 
 n.7' l.V. ' 
 
 846 
 
 1844 
 
 1 1120 
 
 up 
 
 1.5 
 
 M 
 
 + 7.04 
 
 03476 
 
 96 
 
 -11.! 15 
 
 itl. 0774 
 
 156 
 
 - 4.73 
 
 nO.6753 
 
 216 
 
 + 13.01 
 
 1 1153 
 
 144 
 
 + 1.3 
 
 
 6.71 
 
 0.8270 
 
 07 
 
 12.10 
 
 1.0630 
 
 157 
 
 4.30 
 
 ' n, 122 
 
 217 
 
 13.13 
 
 1.11*3 
 
 1 I-' 
 
 I.I 
 
 38 
 
 6.38 
 
 04051 
 
 0* 
 
 1 2.25 
 
 l 0661 
 
 158 
 
 I'll 
 
 0.6059 
 
 21* 
 
 13.21 
 
 1 1908 
 
 152 
 
 0.9 
 
 30 
 
 6.05 
 
 0.7816 
 
 90 
 
 12.3:) 
 
 14030 
 
 159 
 
 3.68 
 
 0.5660 
 
 210 
 
 13.2* 
 
 1.1831 
 
 156 
 
 0.7 
 
 40 
 
 + 5.71 
 
 0.7565 
 
 100 
 
 -1251 
 
 n 1.0074 
 
 160 
 
 - 3.32 
 
 04818 
 
 220 
 
 +13.33 
 
 1 121' 
 
 160 
 
 + 0.5 
 
 41 
 
 5.36 
 
 0.7206 
 
 101 
 
 1263 
 
 Moll 
 
 161 
 
 2.% 
 
 0.4716 
 
 221 
 
 13.3* 
 
 I.I 261 
 
 164 
 
 0.3 
 
 42 
 
 549 
 
 0.7004 
 
 102 
 
 18.74 
 
 1.1050 
 
 162 
 
 2.60 
 
 0.4146 
 
 899 
 
 13 II 
 
 1.1275 
 
 168 
 
 + 0.0 
 
 13 
 
 4.66 
 
 061,*- 
 
 103 
 
 12.83 
 
 1.1083 
 
 163 
 
 2.23 
 
 0.3487 
 
 223 
 
 13.11 
 
 1.12*3 
 
 172 
 
 - 0.2 
 
 II 
 
 + 4.31 
 
 0.6314 
 
 till 
 
 -1849 
 
 nl.1113 
 
 161 
 
 - l-t, 
 
 ,,0.2707 
 
 22 1 
 
 + 13.15 
 
 1 12-7 
 
 176 
 
 -0.4 
 
 45 
 
 3.95 
 
 0.5966 
 
 105 
 
 13.00 
 
 I.I 139 
 
 165 
 
 1 .10 
 
 0.1746 
 
 05 
 
 13 15 
 
 1 12- 
 
 l- i 
 
 0.7 
 
 46 
 
 :(.vi 
 
 0.5550 
 
 106 
 
 13.07 
 
 1 1162 
 
 166 
 
 1.12 
 
 0.0511 
 
 226 
 
 13 II 
 
 1 12-5 
 
 1*1 
 
 0.0 
 
 47 
 
 3.22 
 
 04065 
 
 107 
 
 13.13 
 
 f.iiaa 
 
 167 
 
 0.75 
 
 9. -7i,2 
 
 2-27 
 
 13 12 
 
 1.1970 
 
 188 
 
 1.1 
 
 48 
 
 + 2.*6 
 
 0.4589 
 
 108 
 
 -13.17 
 
 nl 119* 
 
 168 
 
 - 0.38 
 
 94766 
 
 22- 
 
 +13.30 
 
 1.1260 
 
 109 
 
 - 1.3 
 
 49 
 
 
 0.3061 
 
 100 
 
 13.21 
 
 1.1210 
 
 16!) 
 
 - 0.01 
 
 n".7*53 
 
 220 
 
 13.35 
 
 1.1956 
 
 l!Hi 
 
 15 
 
 50 
 
 2 12 
 
 0.3265 
 
 110 
 
 3.21 
 
 1.1990 
 
 170 
 
 + 0.37 
 
 /(0.565* 
 
 230 
 
 13.30 
 
 1.1239 
 
 888 
 
 1 Ii 
 
 51 
 
 1.75 
 
 0.2430 
 
 III 
 
 3.26 
 
 1.1225 
 
 171 
 
 0.74 
 
 94704 
 
 231 
 
 1344 
 
 1 121* 
 
 2 il 
 
 14 
 
 52 
 
 1 3* 
 
 O.I 3*0 
 
 112 
 
 - 3.27 
 
 nl.l2iW 
 
 172 
 
 + 1 12 
 
 0.0177 
 
 838 
 
 + 13.17 
 
 1.1193 
 
 20- 
 
 - 1.9 
 
 
 l.oo 
 
 0.0017 
 
 113 
 
 3.27 
 
 1 1 22* 
 
 173 
 
 1.4!) 
 
 0.1726 
 
 233 
 
 I3.0S 
 
 I.I 165 
 
 212 
 
 2.0 
 
 54 
 
 0.63 
 
 0.7993 
 
 114 
 
 3.26 
 
 1 1221 
 
 171 
 
 146 
 
 . 
 
 2:u 
 
 1949 
 
 II 131 
 
 216 
 
 20 
 
 
 + 0.20 
 
 ,9.10-2 
 
 115 
 
 13.23 
 
 1.1217 
 
 175 
 
 2.23 
 
 04489 
 
 J35 
 
 12.88 
 
 1.1099 
 
 220 
 
 2.1 
 
 
 - 0.12 
 
 00719 
 
 116 
 
 -13.20 
 
 1 . 1 2 '7 
 
 176 
 
 + 2.60 
 
 .1151 
 
 886 
 
 +12.77 
 
 1.1060 
 
 221 
 
 -21 
 
 57 
 
 0.19 
 
 9.6:i| | 
 
 117 
 
 13.16 
 
 1.1 193 
 
 177 
 
 2.07 
 
 0. 172.', 
 
 2:17 
 
 121,1 
 
 1.1017 
 
 22- 
 
 21 
 
 KU 
 
 0.-6 
 
 0.036 1 
 
 118 
 
 13.11 
 
 1.1176 
 
 17* 
 
 3.33 
 
 0.523 1 
 
 238 
 
 125 i 
 
 1.0070 
 
 839 
 
 2 1 
 
 JO 
 r.ii 
 
 
 0.0017 
 
 1 Ml 
 
 13.05 
 
 I.I 156 
 
 170 
 
 3.70 
 
 0.56* l 
 
 
 I2:u; 
 
 1.0919 
 
 2:!6 
 
 2.0 
 
 .1. ' 
 
 6) 
 
 1 tM 
 
 nO.2057 
 
 190 
 
 -12.98 
 
 n 1.1 132 
 
 18.) 
 
 + 4.06 
 
 
 211 
 
 + 12.20 
 
 1-0-63 
 
 210 
 
 - 1.0 
 
 11' V 
 
 The purtiirbationu are in units of the eighth decimal place 
 
TABLE XXIX. 
 
 Perturbations of Log. r, by the Earl/i. 
 
 Constant added 1594. Period of Argument VI., 583 d .92. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. 
 
 Equa. 
 
 Arg. VI. Equa. 
 
 <t 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 
 
 1716 
 
 104 
 
 185!) 
 
 808 
 
 550 
 
 312 
 
 2856 
 
 416 
 
 45 
 
 520 
 
 2527 
 
 2 
 
 718 
 
 106 
 
 1795 
 
 210 614 
 
 314 
 
 2811 
 
 418 64 
 
 Bia 
 
 2524 
 
 4 
 
 725 
 
 108 
 
 1 72!) 
 
 212 ' 681 
 
 316 
 
 2762 
 
 420 87 
 
 524 
 
 2518 
 
 6 
 
 736 
 
 110 
 
 1662 
 
 214 
 
 751 
 
 318 
 
 2709 
 
 422 111 
 
 526 
 
 2509 
 
 8 
 
 751 
 
 112 
 
 1593 
 
 216 
 
 829 
 
 320 
 
 2653 
 
 424 1-15 
 
 528 
 
 2496 
 
 ID 
 
 769 
 
 114 
 
 I5SKJ 
 
 218 
 
 896 
 
 322 
 
 25! 14 
 
 426 
 
 179 
 
 530 
 
 2480 
 
 12 
 
 792 
 
 116 
 
 1452 
 
 220 
 
 972 
 
 324 
 
 2531 
 
 428 
 
 216 
 
 532 
 
 2460 
 
 14 
 
 1818 
 
 118 
 
 1381 
 
 2aa 
 
 1049 
 
 326 
 
 2466 
 
 430 
 
 258 
 
 534 
 
 2438 
 
 16 
 
 1846 
 
 120 
 
 1310 
 
 221 
 
 1128 
 
 328 
 
 2397 
 
 432 
 
 302 
 
 536 
 
 2413 
 
 18 
 
 1878 
 
 122 
 
 1238 
 
 226 
 
 1209 
 
 330 
 
 2326 
 
 434 
 
 350 
 
 538 
 
 2385 
 
 20 
 
 1912 
 
 124 
 
 1166 
 
 228 
 
 1290 
 
 332 
 
 2253 
 
 436 
 
 401 
 
 540 
 
 2356 
 
 22 
 
 1948 
 
 196 
 
 10! 15 
 
 230 
 
 1372 
 
 334 
 
 2178 
 
 438 
 
 454 
 
 542 
 
 2323 
 
 24 
 
 1985 
 
 128 
 
 1024 
 
 232 
 
 1455 
 
 336 
 
 2101 
 
 440 
 
 510 
 
 544 
 
 2289 
 
 26 
 
 2(124 
 
 130 
 
 955 
 
 234 
 
 1538 
 
 338 
 
 2022 
 
 442 
 
 569 
 
 546 
 
 2253 
 
 a8 
 
 2064 
 
 132 
 
 886 
 
 236 
 
 1621 
 
 340 
 
 1942 
 
 444 
 
 620 
 
 548 
 
 2216 . 
 
 30 
 
 2103 
 
 134 
 
 818 
 
 238 
 
 1704 
 
 342 
 
 1861 
 
 446 
 
 692 
 
 550 
 
 2177 
 
 32 
 
 21i:i 
 
 136 
 
 752 
 
 240 
 
 1787 
 
 344 
 
 1780 
 
 448 
 
 757 
 
 552 
 
 2138 
 
 34 
 
 2183 
 
 138 
 
 687 
 
 242 
 
 1869 
 
 346 
 
 1697 
 
 450 
 
 823 
 
 554 
 
 2098 
 
 36 
 
 2221 
 
 140 
 
 624 
 
 244 
 
 1950 
 
 348 
 
 1614 
 
 452 
 
 891 
 
 556 
 
 2059 
 
 38 
 
 2259 
 
 149 
 
 563 
 
 246 
 
 2030 
 
 350 
 
 1531 
 
 454 
 
 960 
 
 558 
 
 2019 
 
 40 
 
 22! 14 
 
 144 
 
 505 
 
 248 
 
 2108 
 
 352 
 
 1448 
 
 456 
 
 1029 
 
 560 
 
 1981 
 
 42 
 
 2:32!) 
 
 146 
 
 449 
 
 250 
 
 2185 
 
 354 
 
 1365 
 
 458 
 
 1100 
 
 562 
 
 1944 
 
 44 
 
 2361 
 
 148 
 
 3! 15 
 
 252 
 
 2260 
 
 356 
 
 1283 
 
 460 
 
 1171 
 
 564 
 
 1908 
 
 46 
 
 2391 
 
 150 
 
 345 
 
 254 
 
 2333 
 
 358 
 
 1202 
 
 462 
 
 1243 
 
 566 
 
 1874 
 
 48 
 
 2418 
 
 152 
 
 297 
 
 256 
 
 2404 
 
 360 
 
 1123 
 
 464 
 
 1315 
 
 568 
 
 1843 
 
 50 
 
 2443 
 
 154 
 
 253 
 
 258 
 
 2472 
 
 362 
 
 1044 
 
 466 
 
 1386 
 
 570 
 
 1814 
 
 52 
 
 2465 
 
 156 
 
 212 
 
 260 
 
 8538 
 
 364 
 
 967 
 
 468 
 
 1457 
 
 572 
 
 178!) 
 
 54 
 
 2484 
 
 158 
 
 174 
 
 262 
 
 2600 
 
 366 
 
 891 
 
 470 
 
 1528 
 
 574 
 
 1767 
 
 56 
 
 2500 
 
 160 
 
 140 
 
 264 
 
 265!) 
 
 368 
 
 818 
 
 472 
 
 1598 
 
 576 
 
 1749 
 
 58 
 
 2513 
 
 162 
 
 109 
 
 266 
 
 2715 
 
 370 
 
 746 
 
 474 
 
 1666 
 
 578 
 
 1734 
 
 60 
 
 2522 
 
 164 
 
 83 
 
 268 
 
 2767 
 
 372 
 
 677 
 
 476 
 
 1733 
 
 580 
 
 1724 
 
 62 
 
 2528 
 
 166 
 
 60 
 
 270 
 
 2815 
 
 374 
 
 610 
 
 478 
 
 17! 19 
 
 582 
 
 1718 
 
 64 
 
 2531 
 
 168 
 
 41 
 
 272 
 
 i860 
 
 376 
 
 516 
 
 480 
 
 1863 
 
 584 
 
 1716 
 
 66 
 
 2530 
 
 170 
 
 27 
 
 274 
 
 2901 
 
 378 
 
 485 
 
 482 
 
 1924 
 
 586 
 
 1718 
 
 68 
 
 2525 
 
 172 
 
 17 
 
 276 
 
 2938 
 
 380 
 
 427 
 
 484 
 
 1984 
 
 588 
 
 1725 
 
 70 
 
 2517 
 
 174 
 
 11 
 
 278 
 
 2970 
 
 382 
 
 372 
 
 486 
 
 2041 
 
 590 
 
 1737 
 
 72 
 
 2505 
 
 176 
 
 9 
 
 280 
 
 2999 
 
 384 
 
 321 
 
 488 
 
 2095 
 
 592 
 
 1752 
 
 74 
 
 2490 
 
 178 
 
 12 
 
 282 
 
 3023 
 
 386 
 
 273 
 
 490 
 
 2147 
 
 594 
 
 1770 
 
 76 
 
 2471 
 
 180 
 
 19 
 
 284 
 
 3043 
 
 388 
 
 22!) 
 
 492 
 
 2196 
 
 596 
 
 1793 
 
 78 
 
 2449 
 
 182 
 
 31 
 
 286 
 
 3058 
 
 390 
 
 188 
 
 494 
 
 2242 
 
 598 
 
 1819 
 
 80 
 
 2423 
 
 184 
 
 46 
 
 288 
 
 3069 
 
 303 
 
 152 
 
 496 
 
 2285 
 
 600 
 
 1847 
 
 82 
 
 2393 
 
 186 
 
 66 
 
 290 
 
 3076 
 
 394 
 
 119 
 
 498 
 
 2324 
 
 61)2 
 
 187!) 
 
 84 
 
 2360 
 
 188 
 
 91 
 
 299 
 
 3078 
 
 396 
 
 91 
 
 500 
 
 2361 
 
 604 
 
 1913 
 
 86 
 
 2323 
 
 190 
 
 120 
 
 294 
 
 3075 
 
 398 
 
 67 
 
 502 
 
 2393 
 
 606 
 
 1950 
 
 88 
 
 2284 
 
 192 
 
 153 
 
 296 
 
 3068 
 
 400 
 
 47 
 
 504 
 
 2422 
 
 608 
 
 1987 
 
 90 
 
 2241 
 
 194 
 
 189 
 
 298 
 
 3057 
 
 402 
 
 32 
 
 506 
 
 2448 
 
 610 
 
 2026 
 
 92 
 
 2194 
 
 196 
 
 230 
 
 300 
 
 3041 
 
 404 
 
 20 
 
 508 
 
 2470 
 
 612 
 
 2066 
 
 94 
 
 2145 
 
 198 
 
 275 
 
 302 
 
 3820 
 
 406 
 
 14 
 
 510 
 
 2489 
 
 614 
 
 2105 
 
 96 
 
 2093 
 
 200 
 
 323 
 
 304 
 
 8996 
 
 408 
 
 11 
 
 512 
 
 2503 
 
 616 
 
 2145 
 
 98 
 
 2039 
 
 202 
 
 375 
 
 306 
 
 2! 167 
 
 410 
 
 13 
 
 514 
 
 2515 
 
 618 
 
 2185 
 
 100 
 
 1981 
 
 204 
 
 430 
 
 308 
 
 2934 
 
 412 
 
 20 
 
 516 
 
 2523 
 
 620 
 
 2223 
 
 102 
 
 1921 
 
 206 
 
 488 
 
 310 
 
 2897 
 
 414 
 
 30 
 
 518 
 
 2527 
 
 622 
 
 2261 
 
 101 
 
 1850 
 
 208 
 
 550 
 
 312 
 
 2856 
 
 416 
 
 45 
 
 520 
 
 2527 
 
 624 
 
 2295 
 
 The perturbations are in units of the eighth decimal place. 
 
TABLES. 
 
 
 
 TVHM: xxx. 
 
 TIUI.I: v\\i. 
 
 1'rrtiirlnitioii.t ii f /.cif. r, lif tin- AW///. 
 
 Perturbations i' /<;,'. /, l>y .///(//. 
 
 ronMaiitail.k.l Hi-.'. Period oflrg. \ II. -.M 
 
 ('uiiMaiil a<lil<-il 11 . IVriuJ at \i(_. I.X., .>:!!' .99. 
 
 Arg. \ 1 1 
 
 1 
 
 tit Ml 
 
 l'.c|ll;i. 
 
 Arp IX. 
 
 l'.<|iia. 
 
 Lq l\ 
 
 Ki|ila 
 
 Arg l\ 
 
 I)||1KI. 
 
 1 
 
 
 .1 
 
 
 d 
 
 
 .1 
 
 
 d 
 
 
 II 
 
 171 
 
 198 
 
 I'D 
 
 
 
 
 80 
 
 8n 
 
 H, 1 
 
 368 
 
 4 
 
 154 
 
 139 
 
 l!>7 
 
 1 
 
 585 
 
 -J 
 
 
 169 
 
 380 
 
 - 
 
 IS7 
 
 196 
 
 SI3 
 
 4 
 
 586 
 
 -1 
 
 
 n>i 
 
 III 
 
 Ii 
 
 I-JI 
 
 140 
 
 -.".'- 
 
 (i 
 
 588 
 
 
 .'n 
 
 166 
 
 
 16 
 
 106 
 
 III 
 
 M3 
 
 8 
 
 691 
 
 88 
 
 919 
 
 H.- 
 
 Ii, -J 
 
 -'IP 
 
 m 
 
 146 
 
 J .7 
 
 III 
 
 594 
 
 BO 
 
 194 
 
 170 
 
 l-l 
 
 Jl 
 
 7."i 
 
 in 
 
 '.'TO 
 
 19 
 
 
 09 
 
 171 
 
 179 
 
 
 U 
 
 (il 
 
 158 
 
 tea 
 
 14 
 
 603 
 
 M 
 
 II- 
 
 171 
 
 586 
 
 39 
 
 1!' 
 
 160 
 
 893 
 
 III 
 
 
 06 
 
 187 
 
 176 
 
 546 
 
 36 
 
 :t7 
 
 nil 
 
 3M 
 
 ia 
 
 613 
 
 08 
 
 106 
 
 178 
 
 663 
 
 in 
 
 Iff 
 
 168 
 
 310 
 
 90 
 
 618 
 
 100 
 
 -- 
 
 180 
 
 570 
 
 14 
 
 in 
 
 179 
 
 316 
 
 99 
 
 683 
 
 189 
 
 71 
 
 189 
 
 598 
 
 48 
 
 19 
 
 176 
 
 390 
 
 
 690 
 
 104 
 
 55 
 
 l-l 
 
 606 
 
 N 
 
 6 
 
 180 
 
 393 
 
 96 
 
 6:t:t 
 
 106 
 
 41 
 
 l-i, 
 
 617 
 
 66 
 
 9 
 
 184 
 
 394 
 
 28 
 
 638 
 
 108 
 
 2!l 
 
 188 
 
 627 
 
 GO 
 
 
 
 188 
 
 
 80 
 
 (,!.' 
 
 110 
 
 111 
 
 198 
 
 686 
 
 M 
 
 
 
 199 
 
 891 
 
 
 645 
 
 112 
 
 12 
 
 199 
 
 641 
 
 (:- 
 
 1 
 
 1<I6 
 
 317 
 
 34 
 
 647 
 
 114 
 
 6 
 
 194 
 
 646 
 
 79 
 
 4 
 
 200 
 
 311 
 
 36 
 
 648 
 
 iia 
 
 
 
 1% 
 
 649 
 
 ?6 
 
 8 
 
 204 
 
 804 
 
 38 
 
 Btt 
 
 118 
 
 1 
 
 198 
 
 651 
 
 80 
 
 IS 
 
 208 
 
 BUB 
 
 40 
 
 647 
 
 190 
 
 1 
 
 900 
 
 651 
 
 84 
 
 93 
 
 212 
 
 985 
 
 42 
 
 644 
 
 199 
 
 4 
 
 909 
 
 651 
 
 8 
 
 n 
 
 216 
 
 283 
 
 44 
 
 640 
 
 UN 
 
 9 
 
 204 
 
 649 
 
 BB 
 
 43 
 
 220 
 
 261 
 
 46 
 
 686 
 
 126 
 
 16 
 
 L>IMi 
 
 646 
 
 96 
 
 56 
 
 224 
 
 247 
 
 48 
 
 628 
 
 128 
 
 96 
 
 208 
 
 642 
 
 100 
 
 89 
 
 2-.W 
 
 989 
 
 .-,(1 
 
 61!) 
 
 130 
 
 36 
 
 910 
 
 
 IM 
 
 83 
 
 999 
 
 216 
 
 52 
 
 
 188 
 
 I'.i 
 
 919 
 
 683 
 
 in- 
 
 98 
 
 236 
 
 200 
 
 54 
 
 596 
 
 134 
 
 64 
 
 914 
 
 628 
 
 112 
 
 111 
 
 240 
 
 184 
 
 56 
 
 583 
 
 136 
 
 81 
 
 216 
 
 693 
 
 116 
 
 130 
 
 914 
 
 11,7 
 
 58 
 
 567 
 
 138 
 
 90 
 
 218 
 
 617 
 
 istt 
 
 146 
 
 Ji- 
 
 151 
 
 60 
 
 561 
 
 140 
 
 118 
 
 990 
 
 619 
 
 124 
 
 161 
 
 252 
 
 134 
 
 89 
 
 889 
 
 142 
 
 13!) 
 
 891 
 
 6U7 
 
 1W 
 
 180 
 
 256 
 
 118 
 
 64 
 
 513 
 
 144 
 
 169 
 
 224 
 
 > ,i 
 
 602 
 
 R4V9 
 
 
 66 
 68 
 
 4!)2 
 470 
 
 146 
 148 
 
 i ~ > 
 
 2ll!l 
 
 o 
 998 
 
 .>.'/ 
 
 508 
 
 
 70 
 
 447 
 
 150 
 
 234 
 
 230 
 
 590 
 
 
 72 
 
 423 
 
 152 
 
 958 
 
 989 
 
 588 
 
 
 74 
 
 398 
 
 164 
 
 285 
 
 234 
 
 586 
 
 
 76 
 
 373 
 
 168 
 
 :m 
 
 936 
 
 :,-:, 
 
 
 78 
 
 347 
 
 158 
 
 337 
 
 938 
 
 588 
 
 
 80 
 
 321 
 
 160 
 
 363 
 
 Jin 
 
 586 
 
 'I'!.'- perturbationi) are in units oflhc eighth decimal place. 
 
TABLE XXXII. 
 
 Pcrturliitionn of Lu<;. /, Inj M-n-ury. 
 
 Horizontal Argument = I. 
 
 Consluiit added 34. IVnotI <if Argument I., 224''.7. 
 
 
 <i 
 
 d 
 
 d d 
 
 .1 
 
 d } d 
 
 .1 
 
 ,i 
 
 ,1 
 
 ii 
 
 ,i 
 
 d <i 
 
 d 
 
 Arg.X. 
 
 
 
 8 
 
 16 
 
 24 
 
 32 
 
 40 
 
 43 
 
 56 
 
 61 
 
 72 
 
 
 
 88 
 
 96 
 
 104 
 
 112 
 
 
 
 18 
 
 21 
 
 30 
 
 39 
 
 45 
 
 44 
 
 40 
 
 36 
 
 34 
 
 35 
 
 36 
 
 34 
 
 28 
 
 23 
 
 23 
 
 1 
 
 19 
 
 24 
 
 32 
 
 41 
 
 45 
 
 43 
 
 38 
 
 34 
 
 34 
 
 35 
 
 37 
 
 31 
 
 29 
 
 25 
 
 27 
 
 9 
 
 20 
 
 25 
 
 -34 
 
 42 
 
 44 
 
 41 
 
 36 
 
 33 
 
 33 
 
 35 
 
 37 
 
 35 
 
 30 
 
 27 
 
 31 
 
 3 
 
 21 
 
 27 
 
 36 
 
 42 
 
 43 
 
 39 
 
 34 
 
 33 
 
 33 
 
 36 
 
 38 
 
 35 
 
 31 
 
 30 
 
 36 
 
 4 
 
 21 
 
 28 
 
 37 
 
 42 
 
 42 
 
 37 
 
 32 
 
 31 
 
 34 
 
 37 
 
 39 
 
 36 
 
 33 
 
 34 
 
 42 
 
 5 
 
 2-2 
 
 2!) 
 
 37 
 
 41 
 
 39 
 
 34 
 
 30 
 
 31 
 
 34 
 
 38 
 
 40 
 
 37 
 
 35 
 
 38 
 
 48 
 
 6 
 
 98 
 
 30 
 
 37 
 
 40 
 
 37 
 
 32 
 
 29 
 
 31 
 
 35 
 
 39 
 
 41 
 
 39 
 
 38 
 
 42 
 
 53 
 
 7 
 
 22 
 
 30 
 
 36 
 
 38 
 
 34 
 
 30 
 
 29 
 
 32 
 
 37 
 
 40 
 
 42 
 
 41 
 
 41 
 
 46 
 
 58 
 
 8 
 
 22 
 
 30 
 
 36 
 
 36 
 
 aa 
 
 28 
 
 28 
 
 33 
 
 39 
 
 42 
 
 44 
 
 43 
 
 44 
 
 51 
 
 63 
 
 9 
 
 22 
 
 30 
 
 34 
 
 34 
 
 30- 
 
 27 
 
 29 
 
 35 
 
 41 
 
 44 
 
 45 
 
 45 
 
 47 
 
 55 
 
 67 
 
 10 
 
 22 
 
 29 
 
 33 
 
 32 
 
 28 
 
 27 
 
 30 
 
 37 
 
 43 
 
 46 
 
 47 
 
 47 
 
 51 
 
 59 
 
 70 
 
 11 
 
 22 
 
 29 
 
 32 
 
 30 
 
 27 
 
 27 
 
 32 
 
 39 
 
 45 
 
 48 
 
 48 
 
 49 
 
 54 
 
 63 
 
 7-2 
 
 12 
 
 22 
 
 29 
 
 31 
 
 29 
 
 27 
 
 28 
 
 34 
 
 42 
 
 48 
 
 50 
 
 50 
 
 ->> 
 
 57 
 
 66 
 
 74 
 
 13 
 
 23 
 
 30 
 
 31 
 
 2!) 
 
 27 
 
 30 
 
 37 
 
 45 
 
 50 
 
 52 
 
 51 
 
 54 
 
 59 
 
 68 
 
 75 
 
 14 
 
 25 
 
 30 
 
 31 
 
 29 
 
 28 
 
 33 
 
 41 
 
 49 
 
 53 
 
 53 
 
 53 
 
 56 
 
 61 
 
 69 
 
 75 
 
 15 
 
 26 
 
 31 
 
 31 
 
 29 
 
 30 
 
 36 
 
 45 
 
 52 
 
 55 
 
 55 
 
 54 
 
 58 
 
 69 
 
 69 
 
 73 
 
 16 
 
 28 
 
 32 
 
 32 
 
 31 
 
 33 
 
 40 
 
 49 
 
 55 
 
 57 
 
 56 
 
 55 
 
 59 
 
 64 
 
 69 
 
 71 
 
 17 
 
 31 
 
 34 
 
 34 
 
 33 
 
 37 
 
 44 
 
 53 
 
 58 
 
 59 
 
 57 
 
 56 
 
 59 
 
 65 
 
 68 
 
 6^ 
 
 J8 
 
 34 
 
 36 
 
 36 x 
 
 36 
 
 41 
 
 49 
 
 57 
 
 61 
 
 61 
 
 58 
 
 56 
 
 60 
 
 65 
 
 67 
 
 65 
 
 1!) 
 
 38 
 
 39 
 
 38 
 
 40 
 
 45 
 
 54 
 
 61 
 
 63 
 
 62 
 
 58 
 
 57 
 
 6J 
 
 64 
 
 65 
 
 61 
 
 20 
 
 42 
 
 42 
 
 42 
 
 44 
 
 50 
 
 59 
 
 64 
 
 65 
 
 62 
 
 58 
 
 57 
 
 63 
 
 63 
 
 62 
 
 56 
 
 21 
 
 46 
 
 46 
 
 45 
 
 48 
 
 55 
 
 63 
 
 68 
 
 66 
 
 62 
 
 57 
 
 57 
 
 59 
 
 61 
 
 59 
 
 51 
 
 22 
 
 50 
 
 50 
 
 50 
 
 53 
 
 60 
 
 67 
 
 70 
 
 67 
 
 62 
 
 57 
 
 56 
 
 59 
 
 59 
 
 55 
 
 47 
 
 23 
 
 55 
 
 53 
 
 54 
 
 58 
 
 65 
 
 71 
 
 71 
 
 67 
 
 61 
 
 56 
 
 55 
 
 58 
 
 57 
 
 51 
 
 42 
 
 24 
 
 59 
 
 57 
 
 58 
 
 63 
 
 69 
 
 73 
 
 72 
 
 66 
 
 59 
 
 55 
 
 54 
 
 56 
 
 54 
 
 47 
 
 38 
 
 25 
 
 63 
 
 61 
 
 62 
 
 67 
 
 73 
 
 75 
 
 72 
 
 64 
 
 57 
 
 54 
 
 53 
 
 54 
 
 51 
 
 43 
 
 35 
 
 26 
 
 67 
 
 65 
 
 66 
 
 71 
 
 75 
 
 76 
 
 71 
 
 62 
 
 55 
 
 52 
 
 52 
 
 51 
 
 47 
 
 39 
 
 32 
 
 27 
 
 70 
 
 68 
 
 70 
 
 74 
 
 77 
 
 76 
 
 69 
 
 60 
 
 53 
 
 50 
 
 51 
 
 49 
 
 44 
 
 36 
 
 30 
 
 28 
 
 73 
 
 71 
 
 73 
 
 76 
 
 78 
 
 75 
 
 66 
 
 57 
 
 51 
 
 48 
 
 49 
 
 47 
 
 41 
 
 34 
 
 28 
 
 29 
 
 75 
 
 73 
 
 75 
 
 78 
 
 78 
 
 72 
 
 63 
 
 54 
 
 48 
 
 46 
 
 47 
 
 45 
 
 38 
 
 32 
 
 27 
 
 30 
 
 76 
 
 75 
 
 76 
 
 78 
 
 76 
 
 69 
 
 59 
 
 50 
 
 45 
 
 44 
 
 45 
 
 42 
 
 36 
 
 30 
 
 27 
 
 31 
 
 77 
 
 75 
 
 77 
 
 77 
 
 74 
 
 65 
 
 55 
 
 46 
 
 42 
 
 42 
 
 44 
 
 40 
 
 34 
 
 29 
 
 28 
 
 32 
 
 77 
 
 75 
 
 76 
 
 75 
 
 70 
 
 60 
 
 50 
 
 42 
 
 40 
 
 41 
 
 42 
 
 38 
 
 33 
 
 29 
 
 29 
 
 33 
 
 75 
 
 74 
 
 71 
 
 72 
 
 66 
 
 55 
 
 45 
 
 38 
 
 38 
 
 39 
 
 41 
 
 36 
 
 32 
 
 29 
 
 31 
 
 34 
 
 73 
 
 72 
 
 72 
 
 69 
 
 63 
 
 49 
 
 40 
 
 35 
 
 36 
 
 38 
 
 39 
 
 35 
 
 31 
 
 30 
 
 33 
 
 35 
 
 71 
 
 69 
 
 68 
 
 64 
 
 54 
 
 44 
 
 35 
 
 32 
 
 34 
 
 37 
 
 38 
 
 35 
 
 31 
 
 31 
 
 35 
 
 36 
 
 67 
 
 66 
 
 64 
 
 58 
 
 48 
 
 38 
 
 31 
 
 30 
 
 33 
 
 36 
 
 37 
 
 34 
 
 31 
 
 32 
 
 38" 
 
 37 
 
 63 
 
 62 
 
 59 
 
 52 
 
 42 
 
 32 
 
 26 
 
 28 
 
 32 
 
 36 
 
 36 
 
 34 
 
 32 
 
 34 
 
 40 
 
 sa 
 
 58 
 
 57 
 
 53 
 
 46 
 
 35 
 
 27 
 
 23 
 
 26 
 
 31 
 
 35 
 
 35 
 
 33 
 
 33 
 
 36 
 
 43 
 
 39 
 
 53 
 
 52 
 
 47 
 
 39 
 
 M 
 
 22 
 
 21 
 
 25 
 
 31 
 
 34 
 
 34 
 
 33 
 
 34 
 
 38 
 
 45 
 
 40 
 
 48 
 
 46 
 
 41 
 
 32 
 
 23 
 
 18 
 
 19 
 
 25 
 
 31 
 
 34 
 
 34 
 
 33 
 
 35 
 
 40 
 
 46 
 
 41 
 
 42 
 
 40 
 
 35 
 
 26 
 
 18 
 
 15 
 
 18 
 
 25 
 
 32 
 
 34 
 
 34 
 
 34 
 
 36 
 
 41 
 
 46 
 
 42 
 
 37 
 
 35 
 
 29 
 
 2!) 
 
 14 
 
 13 
 
 17 
 
 25 
 
 33 
 
 35 
 
 34 
 
 35 
 
 38 
 
 42 
 
 46 
 
 43 
 
 32 
 
 2!) 
 
 23 
 
 15 
 
 10 
 
 11 
 
 18 
 
 26 
 
 33 
 
 35 
 
 34 
 
 35 
 
 39 
 
 43 
 
 45 
 
 44 
 
 27 
 
 24 
 
 18 
 
 11 
 
 .8 
 
 11 
 
 19 
 
 28 
 
 34 
 
 35 
 
 34 
 
 36 
 
 40 
 
 43 
 
 44 
 
 45 
 
 23 
 
 19 
 
 13 
 
 7 
 
 6 
 
 12 
 
 21 
 
 30 
 
 35 
 
 36 
 
 35 
 
 36 
 
 40 
 
 42 
 
 42 
 
 46 
 
 19 
 
 15 
 
 9 
 
 5 
 
 6 
 
 13 
 
 23 
 
 32 
 
 36 
 
 36 
 
 35 
 
 37 
 
 41 
 
 42 
 
 40 
 
 47 
 
 15 
 
 19 
 
 6 
 
 4 
 
 7 
 
 15 
 
 25 
 
 34 
 
 37 
 
 36 
 
 35 
 
 37 
 
 41 
 
 41 
 
 37 
 
 48 
 
 13 
 
 9 
 
 4 
 
 3 
 
 8 
 
 18 
 
 28 
 
 39 
 
 38 
 
 37 
 
 35 
 
 38 
 
 41 
 
 40 
 
 34 
 
 49 
 
 11 
 
 7 
 
 3 
 
 4 
 
 11 
 
 21 
 
 31 
 
 37 
 
 38 
 
 37 
 
 36 
 
 38 
 
 40 
 
 38 
 
 31 
 
 50 
 
 9 
 
 5 
 
 3 
 
 5 
 
 14 
 
 25 
 
 34 
 
 39 
 
 39 
 
 37 
 
 36 
 
 38 
 
 39 
 
 35 
 
 27 
 
 51 
 
 8 
 
 5 
 
 4 
 
 8 
 
 17 
 
 29 
 
 37 
 
 40 
 
 39 
 
 37 
 
 36 
 
 38 
 
 38 
 
 32 
 
 24 
 
 52 
 
 8 
 
 5 
 
 5 
 
 II 
 
 21 
 
 32 
 
 39 
 
 41 
 
 39 
 
 37 
 
 36 
 
 38 
 
 37 
 
 30 
 
 21 
 
 53 
 
 9 
 
 6 
 
 7 
 
 II 
 
 25 
 
 36 
 
 41 
 
 41 
 
 39 
 
 37 
 
 36 
 
 37 
 
 36 
 
 28 
 
 18 
 
 54 
 
 9 
 
 7 
 
 10 
 
 18 
 
 39 
 
 39 
 
 43 
 
 41 
 
 38 
 
 36 
 
 36 
 
 37 
 
 34 
 
 26 
 
 16 
 
 55 
 
 10 
 
 9 
 
 13 
 
 22 
 
 33 
 
 41 
 
 44 
 
 40 
 
 38 
 
 36 
 
 36 
 
 36 
 
 32 
 
 24 
 
 15 
 
 56 
 
 12 
 
 12 
 
 17 
 
 26 
 
 37 
 
 43 
 
 44 
 
 40 
 
 37 
 
 35 
 
 36 
 
 35 
 
 31 
 
 83 
 
 15 
 
 57 
 
 13 
 
 14 
 
 20 
 
 30 
 
 40 
 
 45 
 
 44 
 
 39 
 
 30 
 
 35 
 
 36 
 
 35 
 
 30 
 
 21 
 
 16 
 
 58 
 
 15 
 
 10 
 
 24 
 
 34 
 
 42 
 
 45 
 
 43 
 
 38 
 
 35 
 
 35 
 
 36 
 
 34 
 
 29 
 
 21 
 
 17 
 
 59 
 
 16 
 
 19 
 
 27 
 
 37 
 
 44 
 
 45 
 
 42 
 
 37 
 
 34 
 
 35 
 
 36 
 
 34 
 
 28 
 
 22 
 
 1!) 
 
 60 
 
 18 
 
 21 
 
 30 
 
 39 
 
 45 
 
 44 
 
 40 
 
 36 
 
 3-1 
 
 35 
 
 36 
 
 34 
 
 28 
 
 23 
 
 93 
 
 The perturbations an.' in units of the eighth decimal plncu. 
 
TAKLK XXXII. 
 
 r<-rliirl>iiti<nix (>/' /(>,'. r, /<// Mi'rriiry. 
 
 Ilixi/.'HiUl Ar^iniii'iit = I. 
 
 Const ml ;nlc|.-il ill. IVriod c.l'Ar-ii nl X , >',) units. 
 
 Arg. X. 
 
 
 120 
 
 ,i 
 1!IN 
 
 .1 
 
 i:t<> 
 
 111 
 
 .1 
 1 ->.> 
 
 K.;> 
 
 .1 
 
 1M 
 
 17 
 
 .1 
 IW1 
 
 ia 
 
 aoo 
 
 t 
 
 aow 
 
 an 
 
 .1 
 
 aai 
 
 ,\ 
 a:w 
 
 
 
 87 
 
 37 
 
 i- 
 
 
 68 
 
 60 
 
 65 
 
 7:, 
 
 
 03 
 
 04 
 
 88 
 
 -i 
 
 7.-. 
 
 71 
 
 1 
 
 33 
 
 II 
 
 55 
 
 60 
 
 63 
 
 (,-, 
 
 71 
 
 81 
 
 :M 
 
 06 
 
 03 
 
 
 79 
 
 73 
 
 79 
 
 a 
 
 30 
 
 51 
 
 61 
 
 65 
 
 67 
 
 7 i 
 
 76 
 
 
 1)3 
 
 06 
 
 09 
 
 
 7.-, 
 
 70 
 
 60 
 
 3 
 
 45 
 
 57 
 
 66 
 
 60 
 
 71 
 
 7:1 
 
 7J 
 
 88 
 
 05 
 
 06 
 
 
 7:' 
 
 71 
 
 66 
 
 (,:, 
 
 4 
 
 69 
 
 63 
 
 71 
 
 73 
 
 71 
 
 76 
 
 -J 
 
 DO 
 
 06 
 
 03 
 
 85 
 
 71 
 
 66 
 
 69 
 
 61 
 
 B 
 
 58 
 
 
 71 
 
 7.-, 
 
 71 i 
 
 78 
 
 -1 
 
 91 
 
 03 
 
 
 HO 
 
 
 61 
 
 57 
 
 56 
 
 6 
 
 til 
 
 7:s 
 
 77 
 
 77 
 
 77 
 
 78 
 
 
 00 
 
 90 
 
 -l 
 
 73 
 
 69 
 
 55 
 
 59 
 
 
 7 
 
 68 
 
 76 
 
 78 
 
 78 
 
 77 
 
 70 
 
 B6 
 
 88 
 
 
 7- 
 
 66 
 
 
 10 
 
 47 
 
 44 
 
 - 
 
 79 
 
 78 
 
 7:i 
 
 77 
 
 76 
 
 70 
 
 83 
 
 85 
 
 80 
 
 711 
 
 
 48 
 
 43 
 
 41 
 
 :!'.i 
 
 ! 
 
 78 
 
 79 
 
 7!l 
 
 7.-, 
 
 74 
 
 77 
 
 80 
 
 80 
 
 73 
 
 69 
 
 r,n 
 
 41 
 
 37 
 
 :i 
 
 as 
 
 Ill 
 
 77 
 
 79 
 
 77 
 
 73 
 
 72 
 
 74 
 
 76 
 
 71 
 
 66 
 
 54 
 
 19 
 
 34 
 
 31 
 
 31 
 
 -- 
 
 II 
 
 78 
 
 78 
 
 74 
 
 7(1 
 
 611 
 
 71 
 
 72 
 
 68 
 
 
 45 
 
 34 
 
 j- 
 
 
 96 
 
 83 
 
 19 
 
 7- 
 
 7.-. 
 
 70 
 
 66 
 
 65 
 
 67 
 
 67 
 
 61 
 
 50 
 
 :c 
 
 97 
 
 22 
 
 23 
 
 89 
 
 19 
 
 13 
 
 77 
 
 79 
 
 66 
 
 69 
 
 61 
 
 69 
 
 61 
 
 53 
 
 49 
 
 89 
 
 .'I 
 
 17 
 
 18 
 
 18 
 
 15 
 
 14 
 
 74 
 
 68 
 
 61 
 
 57 
 
 57 
 
 57 
 
 55 
 
 46 
 
 34 
 
 22 
 
 15 
 
 13 
 
 IB 
 
 16 
 
 11 
 
 16 
 
 70 
 
 63 
 
 57 
 
 53 
 
 53 
 
 52 
 
 49 
 
 39 
 
 27 
 
 16 
 
 10 
 
 10 
 
 13 
 
 19 
 
 9 
 
 16 
 
 66 
 
 58 
 
 69 
 
 48 
 
 49 
 
 l- 
 
 42 
 
 39 
 
 20 
 
 10 
 
 7 
 
 8 
 
 11 
 
 10 
 
 7 
 
 17 
 
 61 
 
 63 
 
 47 
 
 44 
 
 45 
 
 43 
 
 36 
 
 26 
 
 14 
 
 6 
 
 5 
 
 7 
 
 10 
 
 10 
 
 6 
 
 18 
 
 66 
 
 48 
 
 42 
 
 40 
 
 41 
 
 38 
 
 31 
 
 80 
 
 9 
 
 3 
 
 4 
 
 7 
 
 10 
 
 9 
 
 5 
 
 19 
 
 61 
 
 43 
 
 38 
 
 37 
 
 37 
 
 34 
 
 96 
 
 15 
 
 5 
 
 2 
 
 3 
 
 8 
 
 10 
 
 9 
 
 6 
 
 20 
 
 46 
 
 38 
 
 34 
 
 34 
 
 34 
 
 30 
 
 21 
 
 11 
 
 3 
 
 1 
 
 4 
 
 9 
 
 11 
 
 9 
 
 7 
 
 Bl 
 
 41 
 
 :M 
 
 39 
 
 39 
 
 32 
 
 87 
 
 17 
 
 8 
 
 2 
 
 1 
 
 6 
 
 11 
 
 19 
 
 10 
 
 8 
 
 89 
 
 37 
 
 31 
 
 30 
 
 31 
 
 30 
 
 24 
 
 15 
 
 6 
 
 2 
 
 3 
 
 ! 
 
 13 
 
 13 
 
 11 
 
 10 
 
 93 
 
 33 
 
 28 
 
 99 
 
 30 
 
 28 
 
 99 
 
 13 
 
 6 
 
 3 
 
 6 
 
 19 
 
 15 
 
 14 
 
 19 
 
 19 
 
 24 
 
 30 
 
 26 
 
 28 
 
 21) 
 
 27 
 
 21 
 
 12 
 
 6 
 
 5 
 
 9 
 
 14 
 
 17 
 
 16 
 
 14 
 
 14 
 
 to 
 
 98 
 
 26 
 
 28 
 
 30 
 
 27 
 
 20 
 
 12 
 
 7 
 
 7 
 
 12 
 
 17 
 
 10 
 
 17 
 
 16 
 
 16 
 
 26 
 
 26 
 
 26 
 
 29 
 
 30 
 
 27 
 
 19 
 
 12 
 
 8 
 
 10 
 
 16 
 
 
 21 
 
 19 
 
 17 
 
 19 
 
 87 
 
 25 
 
 87 
 
 30 
 
 31 
 
 27 
 
 19 
 
 13 
 
 10 
 
 13 
 
 1!) 
 
 83 
 
 99 
 
 19 
 
 18 
 
 21 
 
 98 
 
 25 
 
 28 
 
 32 
 
 
 97 
 
 20 
 
 14 
 
 13 
 
 17 
 
 89 
 
 25 
 
 83 
 
 20 
 
 lil 
 
 94 
 
 89 
 
 26 
 
 30 
 
 34 
 
 33 
 
 28 
 
 20 
 
 16 
 
 15 
 
 20 
 
 25 
 
 26 
 
 23 
 
 20 
 
 20 
 
 86 
 
 an 
 
 28 
 
 32 
 
 36 
 
 34 
 
 28 
 
 21 
 
 17 
 
 18 
 
 23 
 
 27 
 
 27 
 
 23 
 
 80 
 
 21 
 
 27 
 
 31 
 
 30 
 
 35 
 
 38 
 
 35 
 
 28 
 
 21 
 
 19 
 
 20 
 
 86 
 
 28 
 
 27 
 
 89 
 
 19 
 
 21 
 
 28 
 
 32 
 
 33 
 
 38 
 
 39 
 
 85 
 
 28 
 
 22 
 
 .20 
 
 23 
 
 97 
 
 28 
 
 26 
 
 21 
 
 18 
 
 21 
 
 29 
 
 33 
 
 35 
 
 40 
 
 40 
 
 36 
 
 27 
 
 22 
 
 21 
 
 24 
 
 28 
 
 28 
 
 24 
 
 19 
 
 17 
 
 21 
 
 29 
 
 34 
 
 33 
 
 42 
 
 41 
 
 35 
 
 27 
 
 22 
 
 22 
 
 25 
 
 28 
 
 27 
 
 22 
 
 17 
 
 16 
 
 21 
 
 89 
 
 35 
 
 40 
 
 44 
 
 41 
 
 34 
 
 26 
 
 21 
 
 22 
 
 25 
 
 27 
 
 25 
 
 19 
 
 14 
 
 IB 
 
 81 
 
 29 
 
 36 
 
 43 
 
 45 
 
 41 
 
 33 
 
 86 
 
 21 
 
 99 
 
 25 
 
 25 
 
 22 
 
 16 
 
 12 
 
 14 
 
 21 
 
 29 
 
 37 
 
 4.-, 
 
 45 
 
 40 
 
 31 
 
 2:! 
 
 20 
 
 22 
 
 24 
 
 23 
 
 19 
 
 13 
 
 10 
 
 13 
 
 21 
 
 80 
 
 38 
 
 46 
 
 46 
 
 38 
 
 28 
 
 21 
 
 19 
 
 21 
 
 22 
 
 90 
 
 16 
 
 9 
 
 8 
 
 13 
 
 21 
 
 ',':> 
 
 39 
 
 46 
 
 43 
 
 36 
 
 25 
 
 19 
 
 18 
 
 19 
 
 20 
 
 17 
 
 11 
 
 6 
 
 7 
 
 14 
 
 89 
 
 29 
 
 40 
 
 46 
 
 41 
 
 32 
 
 99 
 
 17 
 
 16 
 
 17 
 
 18 
 
 14 
 
 8 
 
 4 
 
 6 
 
 14 
 
 23 
 
 29 
 
 41 
 
 4.') 
 
 38 
 
 9t) 
 
 19 
 
 14 
 
 14 
 
 15 
 
 15 
 
 10 
 
 5 
 
 3 
 
 6 
 
 in 
 
 24 
 
 30 
 
 42 
 
 44 
 
 39 
 
 24 
 
 15 
 
 19 
 
 19 
 
 14 
 
 12 
 
 7 
 
 2 
 
 2 
 
 7 
 
 17 
 
 26 
 
 31 
 
 43 
 
 41 
 
 31 
 
 90 
 
 19 
 
 10 
 
 10 
 
 19 
 
 9 
 
 5 
 
 1 
 
 2 
 
 B 
 
 90 
 
 28 
 
 33 
 
 44 
 
 38 
 
 27 
 
 16 
 
 B 
 
 8 
 
 9 
 
 10 
 
 7 
 
 3 
 
 
 
 3 
 
 12 
 
 23 
 
 31 
 
 86 
 
 45 
 
 34 
 
 23 
 
 12 
 
 6 
 
 (i 
 
 9 
 
 9 
 
 6 
 
 2 
 
 
 
 5 
 
 16 
 
 27 
 
 36 
 
 37 
 
 46 
 
 30 
 
 18 
 
 !l 
 
 4 
 
 5 
 
 8 
 
 8 
 
 5 
 
 2 
 
 2 
 
 9 
 
 21 
 
 M 
 
 39 
 
 40 
 
 47 
 
 26 
 
 14 
 
 6 
 
 3 
 
 5 
 
 8 
 
 8 
 
 5 
 
 3 
 
 5 
 
 14 
 
 27 
 
 37 
 
 43 
 
 43 
 
 48 
 
 89 
 
 11 
 
 4 
 
 3 
 
 6 
 
 8 
 
 8 
 
 5 
 
 5 
 
 8 
 
 20 
 
 33 
 
 42 
 
 47 
 
 47 
 
 49 
 
 18 
 
 8 
 
 3 
 
 3 
 
 7 
 
 9 
 
 9 
 
 7 
 
 8 
 
 14 
 
 27 
 
 39 
 
 48 
 
 51 
 
 51 
 
 50 
 
 15 
 
 5 
 
 2 
 
 4 
 
 9 
 
 12 
 
 11 
 
 10 
 
 13 
 
 21 
 
 34 
 
 46 
 
 54 
 
 56 
 
 55 
 
 51 
 
 12 
 
 4 
 
 3 
 
 6 
 
 19 
 
 15 
 
 14 
 
 14 
 
 18 
 
 28 
 
 42 
 
 53 
 
 60 
 
 60 
 
 ED 
 
 E9I 
 
 10 
 
 4 
 
 5 
 
 10 
 
 IB 
 
 18 
 
 18 
 
 19 
 
 85 
 
 36 
 
 50 
 
 60 
 
 65 
 
 64 
 
 62 
 
 53 
 
 9 
 
 B 
 
 7 
 
 14 
 
 1!) 
 
 89 
 
 23 
 
 96 
 
 33 
 
 44 
 
 58 
 
 67 
 
 70 
 
 68 
 
 66 
 
 54 
 
 8 
 
 7 
 
 11 
 
 19 
 
 24 
 
 27 
 
 28 
 
 32 
 
 41 
 
 53 
 
 66 
 
 73 
 
 74 
 
 71 
 
 li'.i 
 
 55 
 
 n 
 
 10 
 
 16 
 
 24 
 
 29 
 
 32 
 
 34 
 
 39 
 
 49 
 
 62 
 
 73 
 
 78 
 
 77 
 
 74 
 
 79 
 
 56 
 
 11 
 
 14 
 
 22 
 
 30 
 
 35 
 
 38 
 
 40 
 
 46 
 
 :.7 
 
 70 
 
 80 
 
 83 
 
 80 
 
 76 
 
 74 
 
 57 
 
 14 
 
 ]!> 
 
 28 
 
 36 
 
 41 
 
 43 
 
 47 
 
 63 
 
 6B 
 
 77 
 
 86 
 
 86 
 
 82 
 
 77 
 
 75 
 
 58 
 
 17 
 
 24 
 
 35 
 
 43 
 
 47 
 
 49 
 
 53 
 
 61 
 
 73 
 
 84 
 
 90 
 
 88 
 
 -.1 
 
 77 
 
 7."> 
 
 69 
 
 22 
 
 30 
 
 42 
 
 4!) 
 
 69 
 
 .-,:, 
 
 59 
 
 68 
 
 80 
 
 89 
 
 09 
 
 89 
 
 82 
 
 76 
 
 75 
 
 60 
 
 27 
 
 37 
 
 48 
 
 55 
 
 58 
 
 60 
 
 86 
 
 78 
 
 85 
 
 93 
 
 94 
 
 88 
 
 rtl 
 
 75 
 
 71 
 
 \\li.Tt 224-" .7 is nulitractccl from Arg. I., add 33.26 to Arg. X. 
 
TABL.E XXXIII. 
 
 Perturbations of Log. r, by l/ic Earth. 
 
 Horizontal Argument = I. 
 
 Constant added 15(1. Period of Argument I., 224''.7. 
 
 Arg. 
 XI. 
 
 d 
 
 o 
 
 d 
 8 
 
 A 
 
 16 
 
 d 
 
 M 
 
 d 
 
 32 
 
 d 
 
 40 
 
 d 
 
 48 
 
 d 
 
 50 
 
 d 
 
 64 
 
 d 
 
 72 
 
 d 
 
 8O 
 
 d 
 
 88 
 
 d 
 
 96 
 
 d 
 
 1O4 
 
 d 
 
 112 
 
 
 
 206 
 
 207 
 
 211 
 
 216 
 
 220 
 
 224 
 
 225 
 
 223 
 
 219 
 
 214 
 
 809 
 
 204 
 
 202 
 
 202 
 
 205 
 
 2 
 
 210 
 
 210 
 
 213 
 
 217 
 
 222 
 
 225 
 
 887 
 
 226 
 
 >>>> 
 
 218 
 
 212 
 
 207 
 
 204 
 
 202 
 
 204 
 
 4 
 
 213 
 
 213 
 
 214 
 
 218 
 
 221 
 
 224 
 
 226 
 
 225 
 
 822 
 
 217 
 
 212 
 
 206 
 
 202 
 
 200 
 
 200 
 
 6 
 
 216 
 
 214 
 
 214 
 
 217 
 
 219 
 
 222 
 
 223 
 
 222 
 
 218 
 
 214 
 
 209 
 
 203 
 
 198 
 
 195 
 
 194 
 
 8 
 
 214 
 
 212 
 
 212 
 
 214 
 
 216 
 
 218 
 
 219 
 
 218 
 
 215 
 
 210 
 
 205 
 
 198 
 
 193 
 
 190 
 
 188 
 
 in 
 
 209 
 
 207 
 
 207 
 
 209 
 
 211 
 
 213 
 
 214 
 
 214 
 
 211 
 
 207 
 
 201 
 
 195 
 
 190 
 
 185 
 
 184 
 
 12 
 
 199 
 
 196 
 
 197 
 
 200 
 
 203 
 
 206 
 
 209 
 
 210 
 
 208 
 
 205 
 
 200 
 
 194 
 
 188 
 
 183 
 
 181 
 
 14 
 
 184 
 
 182 
 
 183 
 
 187 
 
 192 
 
 197 
 
 202 
 
 204 
 
 204 
 
 202 
 
 199 
 
 193 
 
 189 
 
 184 
 
 180 
 
 Hi 
 
 167 
 
 1G6 
 
 i<;~ 
 
 172 
 
 178 
 
 1 rC> 
 
 192 
 
 196 
 
 199 
 
 198 
 
 197 
 
 193 
 
 188 
 
 183 
 
 180 
 
 18 
 
 151 
 
 150 
 
 151 
 
 156 
 
 162 
 
 170 
 
 179 
 
 185 
 
 189 
 
 191 
 
 191 
 
 188 
 
 184 
 
 181 
 
 178 
 
 90 
 
 140 
 
 137 
 
 137 
 
 141 
 
 147 
 
 165 
 
 164 
 
 171 
 
 176 
 
 180 
 
 180 
 
 179 
 
 176 
 
 173 
 
 171 
 
 22 
 
 i:i:i 
 
 129 
 
 127 
 
 130 
 
 134 
 
 141 
 
 14!> 
 
 156 
 
 161 
 
 165 
 
 167 
 
 165 
 
 163 
 
 160 
 
 159 
 
 24 
 
 130 
 
 126 
 
 123 
 
 123 
 
 126 
 
 131 
 
 137 
 
 143 
 
 147 
 
 150 
 
 153 
 
 150 
 
 148 
 
 145 
 
 144 
 
 26 
 
 139 
 
 125 
 
 121 
 
 131 
 
 122 
 
 126 
 
 130 
 
 134 
 
 137 
 
 139 
 
 139 
 
 136 
 
 133 
 
 129 
 
 127 
 
 28 
 
 127 
 
 125 
 
 123 
 
 I'" 
 
 183 
 
 125 
 
 128 
 
 131 
 
 133 
 
 134 
 
 132 
 
 128 
 
 123 
 
 118 
 
 114 
 
 30 
 
 121 
 
 122 
 
 122 
 
 123 
 
 125 
 
 128 
 
 131 
 
 134 
 
 135 
 
 135 
 
 133 
 
 128 
 
 120 
 
 113 
 
 106 
 
 32 
 
 109 
 
 114 
 
 118 
 
 189 
 
 126 
 
 131 
 
 136 
 
 140 
 
 142 
 
 143 
 
 140 
 
 134 
 
 126 
 
 115 
 
 105 
 
 34 
 
 92 
 
 101 
 
 108 
 
 116 
 
 124 
 
 132 
 
 140 
 
 146 
 
 151 
 
 153 
 
 152 
 
 146 
 
 137 
 
 125 
 
 112 
 
 36 
 
 74 
 
 84 
 
 95 
 
 1(16 
 
 117 
 
 128 
 
 140 
 
 150 
 
 157 
 
 162 
 
 163 
 
 159 
 
 150 
 
 138 
 
 123 
 
 38 
 
 55 
 
 66 
 
 79 
 
 92 
 
 106 
 
 120 
 
 134 
 
 147 
 
 158 
 
 167 
 
 170 
 
 169 
 
 162 
 
 150 
 
 136 
 
 40 
 
 41 
 
 51 
 
 62 
 
 76 
 
 90 
 
 106 
 
 123 
 
 138 
 
 152 
 
 164 
 
 171 
 
 172 
 
 169 
 
 160 
 
 147 
 
 42 
 
 33 
 
 39 
 
 48 
 
 60 
 
 74 
 
 90 
 
 107 
 
 124 
 
 140 
 
 IK 
 
 165 
 
 170 
 
 170 
 
 164 
 
 154 
 
 44 
 
 31 
 
 33 
 
 38 
 
 47 
 
 58 
 
 72 
 
 89 
 
 107 
 
 124 
 
 140 
 
 153 
 
 162 
 
 166 
 
 164 
 
 157 
 
 46 
 
 36 
 
 32 
 
 33 
 
 37 
 
 45 
 
 56 
 
 72 
 
 88 
 
 106 
 
 124 
 
 138 
 
 150 
 
 158 
 
 160 
 
 156 
 
 48 
 
 45 
 
 36 
 
 32 
 
 31 
 
 35 
 
 44 
 
 56 
 
 71 
 
 8!) 
 
 107 
 
 124 
 
 138 
 
 148 
 
 153 
 
 153 
 
 r>o 
 
 58 
 
 45 
 
 35 
 
 30 
 
 30 
 
 35 
 
 44 
 
 57 
 
 73 
 
 91 
 
 109 
 
 125 
 
 137 
 
 145 
 
 149 
 
 r>2 
 
 75 
 
 58 
 
 44 
 
 35 
 
 29 
 
 30 
 
 36 
 
 47 
 
 61 
 
 77 
 
 95 
 
 111 
 
 126 
 
 1 35 
 
 142 
 
 54 
 
 90 
 
 76 
 
 58 
 
 44 
 
 34 
 
 31 
 
 32 
 
 39 
 
 50 
 
 65 
 
 81 
 
 98 
 
 113 
 
 124 
 
 132 
 
 56 
 
 121 
 
 100 
 
 79 
 
 61 
 
 46 
 
 36 
 
 33 
 
 34 
 
 42 
 
 53 
 
 68 
 
 83 
 
 98 
 
 110 
 
 120 
 
 58 
 
 150 
 
 128 
 
 106 
 
 83 
 
 64 
 
 49 
 
 39 
 
 35 
 
 37 
 
 44 
 
 55 
 
 68 
 
 81 
 
 94 
 
 104 
 
 60 
 
 181 
 
 160 
 
 137 
 
 112 
 
 89 
 
 69 
 
 53 
 
 42 
 
 38 
 
 39 
 
 46 
 
 55 
 
 66 
 
 77 
 
 87 
 
 62 
 
 211 
 
 193 
 
 171 
 
 145 
 
 120 
 
 95 
 
 74 
 
 58 
 
 47 
 
 42 
 
 43 
 
 47 
 
 55 
 
 64 
 
 72 
 
 64 
 
 236 
 
 223 
 
 203 
 
 180 
 
 154 
 
 127 
 
 102 
 
 82 
 
 65 
 
 54 
 
 49 
 
 48 
 
 51 
 
 57 
 
 63 
 
 66 
 
 253 
 
 245 
 
 231 
 
 212 
 
 188 
 
 163 
 
 136 
 
 113 
 
 93 
 
 77 
 
 67 
 
 61 
 
 59 
 
 60 
 
 63 
 
 68 
 
 261 
 
 259 
 
 251 
 
 238 
 
 219 
 
 197 
 
 173 
 
 149 
 
 127 
 
 109 
 
 94 
 
 84 
 
 78 
 
 75 
 
 73 
 
 70 
 
 259 
 
 263 
 
 263 
 
 256 
 
 244 
 
 228 
 
 207 
 
 186 
 
 165 
 
 146 
 
 129 
 
 116 
 
 106 
 
 100 
 
 94 
 
 72 
 
 251 
 
 260 
 
 265 
 
 265 
 
 261 
 
 251 
 
 236 
 
 219 
 
 201 
 
 183 
 
 166 
 
 152 
 
 141 
 
 131 
 
 122 
 
 74 
 
 241 
 
 252 
 
 261 
 
 267 
 
 269 
 
 265 
 
 257 
 
 245 
 
 231 
 
 216 
 
 201 
 
 187 
 
 175 
 
 164 
 
 154 
 
 76 
 
 233 
 
 244 
 
 254 
 
 263 
 
 269 
 
 271 
 
 268 
 
 262 
 
 253 
 
 242 
 
 23! 1 
 
 217 
 
 206 
 
 196 
 
 186 
 
 78 
 
 228 
 
 237 
 
 247 
 
 257 
 
 264 
 
 270 
 
 271 
 
 270 
 
 265 
 
 258 
 
 249 
 
 240 
 
 231 
 
 223 
 
 214 
 
 80 
 
 228 
 
 233 
 
 241 
 
 249 
 
 257 
 
 264 
 
 268 
 
 270 
 
 270 
 
 266 
 
 261 
 
 255 
 
 250 
 
 243 
 
 237 
 
 82 
 
 231 
 
 232 
 
 236 
 
 242 
 
 249 
 
 2r,6 
 
 262 
 
 267 
 
 269 
 
 26!) 
 
 268 
 
 265 
 
 262 
 
 259 
 
 255 
 
 84 
 
 236 
 
 233 
 
 233 
 
 237 
 
 242 
 
 248 
 
 254 
 
 261 
 
 265 
 
 268 
 
 270 
 
 271 
 
 271 
 
 270 
 
 269 
 
 86 
 
 236 
 
 232 
 
 231 
 
 232 
 
 ,234 
 
 240 
 
 246 
 
 253 
 
 259 
 
 265 
 
 270 
 
 273 
 
 276 
 
 278 
 
 279 
 
 88 
 
 235 
 
 230 
 
 227 
 
 226 
 
 227 
 
 231 
 
 237 
 
 244 
 
 252 
 
 260 
 
 267 
 
 273 
 
 279 
 
 283 
 
 287 
 
 90 
 
 229 
 
 225 
 
 221 
 
 219 
 
 219 
 
 222 
 
 226 
 
 233 
 
 242 
 
 251 
 
 260 
 
 269 
 
 277 
 
 284 
 
 290 
 
 02 
 
 220 
 
 218 
 
 214 
 
 211 
 
 209 
 
 210 
 
 214 
 
 220 
 
 228 
 
 237 
 
 248 
 
 259 
 
 269 
 
 278 
 
 286 
 
 94 
 
 210 
 
 209 
 
 206 
 
 203 
 
 199 
 
 198 
 
 19!l 
 
 203 
 
 210 
 
 218 
 
 229 
 
 241 
 
 253 
 
 265 
 
 276 
 
 96 
 
 198 
 
 199 
 
 197 
 
 194 
 
 189 
 
 185 
 
 184 
 
 is:, 
 
 189 
 
 195 
 
 205 
 
 217 
 
 229 
 
 243 
 
 257 
 
 98 
 
 183 
 
 188 
 
 188 
 
 184 
 
 179 
 
 173 
 
 169 
 
 166 
 
 167 
 
 170 
 
 178 
 
 188 
 
 201 
 
 216 
 
 231 
 
 100 
 
 167 
 
 174 
 
 176 
 
 174 
 
 169 
 
 162 
 
 155 
 
 150 
 
 147 
 
 147 
 
 152 
 
 159 
 
 171 
 
 185 
 
 202 
 
 102 
 
 147 
 
 156 
 
 161 
 
 162 
 
 158 
 
 151 
 
 143 
 
 136 
 
 130 
 
 127 
 
 129 
 
 133 
 
 142 
 
 155 
 
 171 
 
 104 
 
 122 
 
 135 
 
 143 
 
 146 
 
 145 
 
 140 
 
 133 
 
 126 
 
 118 
 
 113 
 
 111 
 
 112 
 
 118 
 
 128 
 
 143 
 
 106 
 
 95 
 
 no 
 
 121 
 
 128 
 
 130 
 
 128 
 
 123 
 
 117 
 
 109 
 
 103 
 
 98 
 
 97 
 
 99 
 
 106 
 
 118 
 
 108 
 
 68 
 
 84 
 
 97 
 
 106 
 
 112 
 
 114 
 
 112 
 
 107 
 
 101 
 
 94 
 
 88 
 
 85 
 
 85 
 
 89 
 
 97 
 
 110 
 
 45 
 
 60 
 
 73 
 
 84 
 
 92 
 
 . 97 
 
 98 
 
 96 
 
 92 
 
 86 
 
 80 
 
 75 
 
 73 
 
 74 
 
 79 
 
 112 
 
 28 
 
 40 
 
 52 
 
 63 
 
 72 
 
 79 
 
 83 
 
 83 
 
 80 
 
 76 
 
 70 
 
 65 
 
 61 
 
 63 
 
 62 
 
 114 
 
 21 
 
 29 
 
 37 
 
 46 
 
 54 
 
 61 
 
 65 
 
 67 
 
 66 
 
 64 
 
 59 
 
 53 
 
 49 
 
 46 
 
 46 
 
 116 
 
 23 
 
 26 
 
 30 
 
 36 
 
 41 
 
 46 
 
 50 
 
 52 
 
 52 
 
 51 
 
 47 
 
 42 
 
 37 
 
 33 
 
 31 
 
 118 
 
 32 
 
 30 
 
 31 
 
 32 
 
 34 
 
 37 
 
 39 
 
 41 
 
 41 
 
 39 
 
 36 
 
 32 
 
 27 
 
 22 
 
 1!) 
 
 ISO 
 
 45 
 
 41 
 
 38 
 
 35 
 
 33 
 
 33 
 
 33 
 
 34 
 
 34 
 
 33 
 
 30 
 
 27 
 
 22 
 
 17 
 
 12 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 The perturbations are in units of the eighth decimal place.. 
 
TABLE XXXIII. 
 
 1'i'rliirtiti/iiiiia of Lin;. /-, tit/ llir i'.iirlli. 
 
 llun/tint;;! Argument = I. 
 
 ("iui>l;ml lidded I.Mi. r.Timl i>f Argument XI., 210 units. 
 
 
 d 
 
 .1 
 
 ,, 
 
 d 
 
 .1 
 
 d 
 
 ,1 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 
 Arg XI 
 
 120 
 
 12* 
 
 136 
 
 111 
 
 142 
 
 160 
 
 16N 
 
 ire 
 
 184 
 
 192 
 
 200 
 
 20N 
 
 216 
 
 
 
 *2 
 
 
 
 310 
 
 217 
 
 224 
 
 931 
 
 935 
 
 
 939 
 
 2:58 
 
 937 
 
 236 
 
 936 
 
 939 
 
 -Ml 
 
 959 
 
 21,2 
 
 3 
 
 JiT 
 
 919 
 
 918 
 
 923 
 
 237 
 
 .'-'.i 
 
 
 
 997 
 
 326 
 
 997 
 
 930 
 
 936 
 
 945 
 
 956 
 
 4 
 
 909 
 
 906 
 
 211 
 
 915 
 
 918 
 
 22', i 
 
 221 219 
 
 -'17 
 
 316 
 
 916 
 
 910 
 
 995 
 
 934 
 
 2H> 
 
 6 
 
 106 
 
 199 
 
 Jl)-' 
 
 J '. 
 
 
 910 
 
 -'ID 
 
 
 
 Jill 
 
 
 906 
 
 911 
 
 990 
 
 939 
 
 8 
 
 189 
 
 11)1 
 
 194 
 
 107 
 
 199 
 
 199 
 
 199 
 
 100 
 
 193 
 
 1:1.1 
 
 188 
 
 10(1 
 
 194 
 
 203 
 
 916 
 
 10 
 
 is:! 
 
 l-l 
 
 l-i, 
 
 188 
 
 189 
 
 188 
 
 186 
 
 183 
 
 178 
 
 171 
 
 171 
 
 171 
 
 173 
 
 181 
 
 193 
 
 19 
 
 170 
 
 180 
 
 l- i 
 
 l-l 
 
 1- i 
 
 178 
 
 171 
 
 169 
 
 169 
 
 156 
 
 150 
 
 1 1- 
 
 1 l:> 
 
 [56 
 
 166 
 
 1 1 
 
 17- 
 
 177 
 
 I7(> 
 
 176 
 
 174 
 
 170 
 
 Mil 
 
 156 
 
 1 17 
 
 138 
 
 130 
 
 125 
 
 194 
 
 [98 
 
 138 
 
 Hi 
 
 177 
 
 176 
 
 17.') 
 
 173 
 
 170 
 
 ! ( ).') 
 
 167 
 
 148 
 
 136 
 
 194 
 
 113 
 
 106 
 
 III! 
 
 109 
 
 100 
 
 IS 
 
 17.') 
 
 171 
 
 173 
 
 172 
 
 169 
 
 164 
 
 166 
 
 145 
 
 131 
 
 117 
 
 102 
 
 01 
 
 83 
 
 81 
 
 -1 
 
 30 
 
 170 
 
 169 
 
 170 
 
 170 
 
 His 
 
 164 
 
 158 
 
 117 
 
 134 
 
 118 
 
 101 
 
 87 
 
 75 
 
 68 
 
 67 
 
 99 
 
 ISO 
 
 160 
 
 163 
 
 165 
 
 167 
 
 166 
 
 H, -J 
 
 153 
 
 1 I-J 
 
 196 
 
 109 
 
 99 
 
 76 
 
 (i"i 
 
 60 
 
 -'1 
 
 1 II 
 
 147 
 
 151 
 
 157 
 
 162 
 
 165 
 
 166 
 
 161 
 
 1 .-,-' 
 
 139 
 
 122 
 
 105 
 
 87 
 
 7-.' 
 
 62 
 
 36 
 
 I'Js 
 
 130 
 
 136 
 
 144 
 
 153 
 
 160 
 
 1 65 
 
 165 
 
 161 
 
 151 
 
 137 
 
 I-JI 
 
 103 
 
 B6 
 
 73 
 
 98 
 
 113 
 
 114 
 
 190 
 
 198 
 
 138 
 
 1 1 
 
 168 
 
 163 
 
 164 
 
 160 
 
 150 
 
 137 
 
 120 
 
 103 
 
 88 
 
 30 
 
 109 
 
 loo 
 
 104 
 
 111 
 
 121 
 
 133 
 
 145 
 
 ,.-,, 
 
 H,i 
 
 161 
 
 156 
 
 147 
 
 184 
 
 119 
 
 111) 
 
 
 '.is 
 
 09 
 
 01 
 
 06 
 
 104 
 
 115 
 
 [98 
 
 139 
 
 149 
 
 154 
 
 156 
 
 I.MI 
 
 149 
 
 130 
 
 118 
 
 34 
 
 Hill 
 
 n i 
 
 85 
 
 84 
 
 89 
 
 98 
 
 100 
 
 199 
 
 133 
 
 149 
 
 147 
 
 147 
 
 143 
 
 136 
 
 198 
 
 36 
 
 lu- 
 
 95 
 
 
 79 
 
 79 
 
 -1 
 
 03 
 
 104 
 
 Hi, 
 
 197 
 
 135 
 
 130 
 
 140 
 
 137 
 
 I.!! 
 
 
 ll!) 
 
 103 
 
 90 
 
 80 
 
 75 
 
 76 
 
 82 
 
 01 
 
 109 
 
 114 
 
 123 
 
 130 
 
 134 
 
 135 
 
 134 
 
 1 1 
 
 131 
 
 113 
 
 98 
 
 86 
 
 78 
 
 7.-, 
 
 77 
 
 84 
 
 93 
 
 1 ! 
 
 III 
 
 122 
 
 128 
 
 131 
 
 133 
 
 4-.' 
 
 11) 
 
 134 
 
 108 
 
 94 
 
 84 
 
 78 
 
 78 
 
 89 
 
 89 
 
 98 
 
 107 
 
 III, 
 
 193 
 
 127 
 
 I'.'i ) 
 
 44 
 
 146 
 
 132 
 
 117 
 
 103 
 
 02 
 
 85 
 
 82 
 
 84 
 
 89 
 
 96 
 
 104 
 
 119 
 
 118 
 
 193 
 
 1J7 
 
 46 
 
 1 in 
 
 137 
 
 I'.'l 
 
 111 
 
 Hill 
 
 99 
 
 88 
 
 87 
 
 90 
 
 95 
 
 109 
 
 108 
 
 114 
 
 119 
 
 122 
 
 48 
 
 149 
 
 141 
 
 [99 
 
 118 
 
 HI7 
 
 99 
 
 93 
 
 91 
 
 92 
 
 95 
 
 100 
 
 105 
 
 HO 
 
 113 
 
 116 
 
 50 
 
 147 
 
 141 
 
 133 
 
 123 
 
 113 
 
 104 
 
 98 
 
 94 
 
 94 
 
 05 
 
 98 
 
 101 
 
 105 
 
 107 
 
 100 
 
 59 
 
 143 
 
 140 
 
 133 
 
 135 
 
 116 
 
 KM 
 
 101 
 
 97 
 
 06 
 
 96 
 
 96 
 
 
 101 
 
 109 
 
 103 
 
 54 
 
 136 
 
 135 
 
 131 
 
 195 
 
 117 
 
 111 
 
 105 
 
 100 
 
 98 
 
 
 98 
 
 98 
 
 99 
 
 100 
 
 09 
 
 
 
 137 
 
 125 
 
 122 
 
 117 
 
 112 
 
 108 
 
 105 
 
 103 
 
 103 
 
 103 
 
 103 
 
 102 
 
 101 
 
 99 
 
 58 
 
 119 
 
 116 
 
 116 
 
 116 
 
 113 
 
 HI 
 
 110 
 
 109 
 
 109 
 
 110 
 
 111 
 
 111 
 
 111 
 
 108 
 
 HIl 
 
 60 
 
 96 
 
 101 
 
 105 
 
 107 
 
 108 
 
 108 
 
 110 
 
 112 
 
 115 
 
 118 
 
 121 
 
 123 
 
 123 
 
 120 
 
 115 
 
 62 
 
 81 
 
 87 
 
 02 
 
 96 
 
 99 
 
 102 
 
 107 
 
 112 
 
 II!) 
 
 I-J.-, 
 
 131 
 
 135 
 
 136 
 
 135 
 
 139 
 
 64 
 
 70 
 
 75 
 
 80 
 
 84 
 
 89 
 
 94 
 
 100 
 
 108 
 
 117 
 
 127 
 
 136 
 
 144 
 
 148 
 
 149 
 
 146 
 
 66 
 
 66 
 
 70 
 
 73 
 
 76 
 
 70 
 
 84 
 
 91 
 
 100 
 
 111 
 
 123 
 
 135 
 
 146 
 
 155 
 
 I.V.I 
 
 i .,- 
 
 68 
 
 73 
 
 72 
 
 72 
 
 73 
 
 74 
 
 76 
 
 81 
 
 98 
 
 100 
 
 114 
 
 129 
 
 142 
 
 [55 
 
 163 
 
 166 
 
 70 
 
 89 
 
 85 
 
 81 
 
 77 
 
 74 
 
 73 
 
 75 
 
 81 
 
 90 
 
 103 
 
 118 
 
 133 
 
 148 
 
 161 
 
 H,- 
 
 72 
 
 114 
 
 107 
 
 99 
 
 91 
 
 84 
 
 78 
 
 76 
 
 77 
 
 83 
 
 93 
 
 107 
 
 123 
 
 140 
 
 155 
 
 11,1, 
 
 74 
 
 144 
 
 134 
 
 193 
 
 112 
 
 101 
 
 99 
 
 84 
 
 82 
 
 83 
 
 90 
 
 101 
 
 115 
 
 132 
 
 148 
 
 162 
 
 76 
 
 176 
 
 16.1 
 
 153 
 
 140 
 
 126 
 
 114 
 
 103 
 
 96 
 
 03 
 
 95 
 
 ID--' 
 
 114 
 
 128 
 
 144 
 
 I.V.I 
 
 78 
 
 205 
 
 195 
 
 183 
 
 170 
 
 156 
 
 142 
 
 129 
 
 118 
 
 111 
 
 109 
 
 112 
 
 J20 
 
 131 
 
 146 
 
 169 
 
 /SO 
 
 230 
 
 232 
 
 212 
 
 200 
 
 187 
 
 172 
 
 158 
 
 145 
 
 136 
 
 130 
 
 no 
 
 133 
 
 141 
 
 l.-.l 
 
 169 
 
 82 
 
 250 
 
 244 
 
 237 
 
 J->7 
 
 215 
 
 202 
 
 1 
 
 174 
 
 163 
 
 154 
 
 150 
 
 150 
 
 155 
 
 161 
 
 171) 
 
 84 
 
 366 
 
 263 
 
 958 
 
 950 
 
 240 
 
 228 
 
 214 
 
 200 
 
 188 
 
 178 
 
 171 
 
 168 
 
 169 
 
 173 
 
 179 
 
 86 
 
 279 
 
 278 
 
 274 
 
 268 
 
 260 
 
 24!) 
 
 236 
 
 222 
 
 208 
 
 107 
 
 189 
 
 l-l 
 
 183 
 
 l-l 
 
 180 
 
 88 
 
 289 
 
 288 
 
 287 
 
 282 
 
 274 
 
 264 
 
 252 
 
 238 
 
 225 
 
 212 
 
 909 
 
 196 
 
 193 
 
 194 
 
 197 
 
 90 
 
 293 
 
 295 
 
 295 
 
 291 
 
 285 
 
 275 
 
 263 
 
 250 
 
 236 
 
 224 
 
 213 
 
 205 
 
 201 
 
 200 
 
 203 
 
 02 
 
 293 
 
 297 
 
 298 
 
 296 
 
 291 
 
 283 
 
 272 
 
 259 
 
 945 
 
 232 
 
 91 
 
 212 
 
 2.16 
 
 905 
 
 
 94 
 
 285 
 
 292 
 
 2!Ki 
 
 297 
 
 204 
 
 287 
 
 277 
 
 265 
 
 252 
 
 23! 
 
 227 
 
 218 
 
 919 
 
 909 
 
 210 
 
 96 
 
 269 
 
 279 
 
 288 
 
 291 
 
 291 
 
 2 : 
 
 280 
 
 270 
 
 258 
 
 MS 
 
 233 
 
 223 
 
 916 
 
 213 
 
 919 
 
 98 
 
 246 
 
 260 
 
 272 
 
 280 
 
 284 
 
 283 
 
 279 
 
 271 
 
 261 
 
 949 
 
 237 
 
 228 
 
 220 
 
 215 
 
 313 
 
 100 
 
 219 
 
 236 
 
 251 
 
 262 
 
 270 
 
 273 
 
 272 
 
 267 
 
 259 
 
 248 
 
 238 
 
 228 
 
 220 
 
 916 
 
 919 
 
 1 AO 
 
 189 
 
 207 
 
 
 240 
 
 251 
 
 258 
 
 959 
 
 257 
 
 251 
 
 949 
 
 933 
 
 224 
 
 2 Hi 
 
 210 
 
 -' '7 
 
 m 
 104 
 106 
 
 108 
 
 160 
 133 
 109 
 
 178 
 150 
 125 
 
 197 
 169 
 142 
 
 214 
 186 
 
 159 
 
 227 
 201 
 174 
 
 237 
 913 
 
 1-7 
 
 241 
 219 
 196 
 
 2 12 
 222 
 
 -Jin 
 
 938 
 
 3:>o 
 
 231 
 214 
 
 196 
 
 999 
 
 207 
 189 
 
 214 
 
 199 
 182 
 
 206 
 192 
 175 
 
 201 
 1-7 
 170 
 
 10.1 
 185 
 
 MO 
 
 110 
 112 
 114 
 116 
 118 
 120 
 
 83 
 
 50 
 32 
 
 18 
 10 
 
 101 
 
 79 
 58 
 39 
 22 
 11 
 
 116 
 99 
 
 7.) 
 4!) 
 30 
 16 
 
 133 
 
 -1 
 62 
 42 
 24 
 
 149 
 121 
 101 
 
 78 
 57 
 37 
 
 162 
 139 
 117 
 96 
 
 71 
 53 
 
 173 
 151 
 
 131 
 112 
 92 
 71 
 
 179 
 169 
 142 
 195 
 
 107 
 
 87 
 
 i- > 
 
 16 1 
 149 
 
 135 
 121 
 103 
 
 17s 
 Hi:: 
 151 
 140 
 
 199 
 116 
 
 173 
 150 
 150 
 149 
 135 
 194 
 
 166 
 153 
 146 
 
 140 
 
 136 
 
 128 
 
 150 
 
 117 
 1:1:1 
 135 
 133 
 199 
 
 166 
 
 142 
 
 134 
 130 
 199 
 127 
 
 153 
 139 
 130 
 196 
 193 
 183 
 
 \Vlicn 2-,M''.7 is subtracted from Arg. 1., add 147.61 to Arg. XI. 
 
TABLE XXXIII. 
 
 Perturbations of Log. ?-, l>y the Earth. 
 
 Horizontal Argument = I. 
 
 Constant added 150. Period of Argument 1., 224<i.7. 
 
 
 d 
 
 d d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 d 
 
 . d 
 
 d 
 
 d 
 
 d 
 
 Arg.X 
 
 
 
 i 
 
 16 
 
 24 
 
 32 
 
 40 
 
 48 
 
 56 
 
 64 
 
 72 
 
 sa 
 
 <*8 
 
 96 
 
 1O4 
 
 112 
 
 120 
 
 45 
 
 41 
 
 38 
 
 35 
 
 33 
 
 33 
 
 .3 
 
 34 
 
 34 
 
 33 
 
 30 
 
 27 
 
 22 
 
 17 
 
 12 
 
 129 
 
 60 
 
 54 
 
 48 
 
 43 
 
 38 
 
 36 
 
 34 
 
 33 
 
 33 
 
 32 
 
 30 
 
 23 
 
 23 
 
 18 
 
 13 
 
 124 
 
 74 
 
 68 
 
 61 
 
 55 
 
 48 
 
 44 
 
 40 
 
 33 
 
 33 
 
 37 
 
 36 
 
 35 
 
 31 
 
 26 
 
 20 
 
 126 
 
 88 
 
 82 
 
 76 
 
 68 
 
 61 
 
 55 
 
 50 
 
 47 
 
 46 
 
 45 
 
 46 
 
 46 
 
 44 
 
 40 
 
 34 
 
 123 
 
 102 
 
 98 
 
 91 
 
 83 
 
 75 
 
 63 
 
 62 
 
 58 
 
 56 
 
 55 
 
 56 
 
 58 
 
 57 
 
 55 
 
 51 
 
 130 
 
 118 
 
 114 
 
 108 
 
 100 
 
 92 
 
 83 
 
 76 
 
 69 
 
 66 
 
 65 
 
 66 
 
 63 
 
 69 
 
 69 
 
 68 
 
 139 
 
 138 
 
 135 
 
 129 
 
 120 
 
 111 
 
 100 
 
 90 
 
 82 
 
 76 
 
 73 
 
 73 
 
 75 
 
 78 
 
 8.) 
 
 81 
 
 134 
 
 162 
 
 158 
 
 152 
 
 144 
 
 133 
 
 120 
 
 107 
 
 96 
 
 87 
 
 81 
 
 79 
 
 80 
 
 83 
 
 87 
 
 91 
 
 136 
 
 187 
 
 184 
 
 178 
 
 16!) 
 
 158 
 
 144 
 
 123 
 
 114 
 
 101 
 
 91 
 
 86 
 
 84 
 
 86 
 
 91 
 
 97 
 
 138 
 
 211 
 
 209 
 
 805 
 
 197 
 
 185 
 
 170 
 
 153 
 
 136 
 
 120 
 
 106 
 
 97 
 
 92 
 
 92 
 
 95 
 
 101 
 
 MO 
 
 232 
 
 232 
 
 22!) 
 
 983 
 
 213 
 
 1!)!) 
 
 \-> 
 
 164 
 
 145 
 
 128 
 
 115 
 
 106 
 
 102 
 
 103 
 
 108 
 
 142 
 
 847 
 
 24!) 
 
 251 
 
 247 
 
 240 
 
 22!) 
 
 213 
 
 195 
 
 175 
 
 157 
 
 13!) 
 
 127 
 
 11!) 
 
 116 
 
 117 
 
 144 
 
 255 
 
 260 
 
 264 
 
 963 
 
 263 
 
 255 
 
 213 
 
 227 
 
 218 
 
 188 
 
 16!) 
 
 153 
 
 141 
 
 134 
 
 131 
 
 146 
 
 256 
 
 264 
 
 271 
 
 277 
 
 27!) 
 
 277 
 
 268 
 
 256 
 
 240 
 
 221 
 
 2i)l 
 
 132 
 
 167 
 
 156 
 
 149 
 
 14H 
 
 252 
 
 262 
 
 273 
 
 282 
 
 288 
 
 2!)] 
 
 288 
 
 279 
 
 266 
 
 350 
 
 230 
 
 211 
 
 193 
 
 179 
 
 163 
 
 ir,n 
 
 244 
 
 256 
 
 268 
 
 281 
 
 291 
 
 297 
 
 299 
 
 295 
 
 286 
 
 272 
 
 255 
 
 237 
 
 218 
 
 201 
 
 187 
 
 152 
 
 233 
 
 245 
 
 35'J 
 
 273 
 
 286 
 
 297 
 
 302 
 
 3D3 
 
 298 
 
 233 
 
 274 
 
 257 
 
 239 
 
 222 
 
 2.16 
 
 1 54 
 
 21!) 
 
 231 
 
 246 
 
 261 
 
 276 
 
 239 
 
 2!)3 
 
 303 
 
 303 
 
 297 
 
 236 
 
 272 
 
 255 
 
 239 
 
 222 
 
 156 
 
 201 
 
 213 
 
 228 
 
 244 
 
 261 
 
 276 
 
 23!) 
 
 21)8 
 
 301 
 
 300 
 
 293 
 
 283 
 
 26!) 
 
 254 
 
 j:!3 
 
 158 
 
 178 
 
 too 
 
 205 
 
 222 
 
 240 
 
 25!) 
 
 275 
 
 237 
 
 295 
 
 298 
 
 296 
 
 290 
 
 230 
 
 267 
 
 253 
 
 16!) 
 
 152 
 
 163 
 
 173 
 
 E96 
 
 216 
 
 236 
 
 255 
 
 272 
 
 284 
 
 292 
 
 296 
 
 294 
 
 233 
 
 27!) 
 
 267 
 
 162 
 
 124 
 
 133 
 
 148 
 
 166 
 
 187 
 
 210 
 
 232 
 
 252 
 
 269 
 
 231 
 
 289 
 
 993 
 
 292 
 
 287 
 
 27!) 
 
 Ki4 
 
 D8 
 
 1(15 
 
 118 
 
 135 
 
 156 
 
 ISO 
 
 204 
 
 227 
 
 217 
 
 263 
 
 276 
 
 235 
 
 289 
 
 289 
 
 286 
 
 166 
 
 77 
 
 81 
 
 91 
 
 106 
 
 125 
 
 148 
 
 173 
 
 197 
 
 219 
 
 239 
 
 256 
 
 26!) 
 
 277 
 
 989 
 
 984 
 
 HH 
 
 66 
 
 65 
 
 70 
 
 81 
 
 98 
 
 118 
 
 141 
 
 164 
 
 183 
 
 208 
 
 227 
 
 243 
 
 256 
 
 265 
 
 272 
 
 170 
 
 65 
 
 59 
 
 59 
 
 65 
 
 77 
 
 93 
 
 112 
 
 133 
 
 154 
 
 174 
 
 193 
 
 211 
 
 225 
 
 238 
 
 250 
 
 172 
 
 74 
 
 63 
 
 58 
 
 58 
 
 64 
 
 75 
 
 89 
 
 106 
 
 124 
 
 141 
 
 tss 
 
 175 
 
 190 
 
 204 
 
 219 
 
 174 
 
 88 
 
 75 
 
 65 
 
 61 
 
 61 
 
 66 
 
 75 
 
 87 
 
 100 
 
 114 
 
 127 
 
 141 
 
 155 
 
 16!) 
 
 184 
 
 176 
 
 105 
 
 90 
 
 78 
 
 71 
 
 67 
 
 63 
 
 71 
 
 78 
 
 87 
 
 96 
 
 105 
 
 114 
 
 125 
 
 136 
 
 14!) 
 
 178 
 
 120 
 
 1C6 
 
 94 
 
 85 
 
 79 
 
 77 
 
 77 
 
 80 
 
 84 
 
 89 
 
 93 
 
 98 
 
 104 
 
 111 
 
 120 
 
 180 
 
 131 
 
 120 
 
 109 
 
 100 
 
 94 
 
 90 
 
 89 
 
 90 
 
 91 
 
 92 
 
 92 
 
 93 
 
 93 
 
 94 
 
 98 
 
 182 
 
 136 
 
 123 
 
 120 
 
 114 
 
 109 
 
 106 
 
 104 
 
 104 
 
 103 
 
 102 
 
 100 
 
 96 
 
 92 
 
 88 
 
 86 
 
 184 
 
 137 
 
 133 
 
 128 
 
 124 
 
 121 
 
 119 
 
 11!) 
 
 119 
 
 118 
 
 116 
 
 112 
 
 105 
 
 97 
 
 88 
 
 81 
 
 186 
 
 135 
 
 134 
 
 132 
 
 131 
 
 129 
 
 12!) 
 
 130 
 
 130 
 
 131 
 
 129 
 
 124 
 
 116 
 
 106 
 
 94 
 
 81 
 
 m 
 
 131 
 
 133 
 
 133 
 
 133 
 
 134 
 
 135 
 
 137 
 
 138 
 
 139 
 
 138 
 
 134 
 
 126 
 
 114 
 
 101 
 
 85 
 
 100 
 
 127 
 
 S30 
 
 132 
 
 133 
 
 135 
 
 137 
 
 139 
 
 142 
 
 144 
 
 143 
 
 140 
 
 133 
 
 122 
 
 108 
 
 91 
 
 199 
 
 123 
 
 126 
 
 129 
 
 131 
 
 133 
 
 135 
 
 138 
 
 142 
 
 145 
 
 146 
 
 144 
 
 13!) 
 
 129 
 
 115 
 
 98 
 
 1!)4 
 
 118 
 
 122 
 
 124 
 
 126 
 
 129 
 
 131 
 
 135 
 
 140 
 
 144 
 
 147 
 
 147 
 
 143 
 
 135 
 
 122 
 
 106 
 
 196 
 
 113 
 
 115 
 
 118 
 
 12:) 
 
 123 
 
 126 
 
 131 
 
 136 
 
 142 
 
 146 
 
 148 
 
 147 
 
 141 
 
 130 
 
 115 
 
 196 
 
 106 
 
 108 
 
 1JO 
 
 112 
 
 115 
 
 119 
 
 124 
 
 131 
 
 138 
 
 144 
 
 149 
 
 150 
 
 147 
 
 139 
 
 126 
 
 200 
 
 101 
 
 102 
 
 103 
 
 104 
 
 106 
 
 111 
 
 117 
 
 124 
 
 133 
 
 141 
 
 147 
 
 152 
 
 151 
 
 146 
 
 136 
 
 202 
 
 i)8 
 
 98 
 
 97 
 
 97 
 
 !)!) 
 
 102 
 
 108 
 
 115 
 
 124 
 
 134 
 
 1 12 
 
 149 
 
 152 
 
 150 
 
 142 
 
 204 
 
 102 
 
 99 
 
 96 
 
 94 
 
 93 
 
 94 
 
 !)3 
 
 104 
 
 113 
 
 123 
 
 133 
 
 142 
 
 147 
 
 148 
 
 144 
 
 206 
 
 11)9 
 
 105 
 
 1 00 
 
 95 
 
 91 
 
 8!) 
 
 90 
 
 94 
 
 101 
 
 111 
 
 120 
 
 130 
 
 138 
 
 142 
 
 141 
 
 208 
 
 122 
 
 117 
 
 no 
 
 102 
 
 95 
 
 89 
 
 86 
 
 86 
 
 91 
 
 98 
 
 107 
 
 117 
 
 125 
 
 132 
 
 134 
 
 210 
 
 137 
 
 132 
 
 124 
 
 114 
 
 104 
 
 94 
 
 87 
 
 84 
 
 84 
 
 89 
 
 96 
 
 105 
 
 114 
 
 121 
 
 125 
 
 919 
 
 151 
 
 148 
 
 140 
 
 130 
 
 118 
 
 106 
 
 95 
 
 88 
 
 85 
 
 86 
 
 90 
 
 93 
 
 106 
 
 113 
 
 11!) 
 
 214 
 
 161) 
 
 160 
 
 155 
 
 146 
 
 134 
 
 121 
 
 109 
 
 99 
 
 93 
 
 92 
 
 93 
 
 98 
 
 105 
 
 112 
 
 118 
 
 216 
 
 163 
 
 167 
 
 166 
 
 160 
 
 150 
 
 138 
 
 126 
 
 116 
 
 108 
 
 104 
 
 104 
 
 107 
 
 112 
 
 118 
 
 123 
 
 218 
 
 160 
 
 169 
 
 171 
 
 170 
 
 164 
 
 154 
 
 144 
 
 134 
 
 126 
 
 121 
 
 120 
 
 122 
 
 126 
 
 131 
 
 135 
 
 220 
 
 154 
 
 166 
 
 173 
 
 176 
 
 173 
 
 167 
 
 159 
 
 151 
 
 144 
 
 139 
 
 137 
 
 139 
 
 143 
 
 147 
 
 152 
 
 222 
 
 148 
 
 162 
 
 172 
 
 173 
 
 17!) 
 
 176 
 
 171 
 
 164 
 
 153 
 
 154 
 
 153 
 
 154 
 
 153 
 
 164 
 
 168 
 
 224 
 
 145 
 
 159 
 
 171 
 
 173 
 
 182 
 
 181 
 
 178 
 
 173 
 
 168 
 
 164 
 
 164 
 
 166 
 
 170 
 
 177 
 
 183 
 
 226 
 
 147 
 
 160 
 
 171 
 
 17!) 
 
 184 
 
 184 
 
 182 
 
 177 
 
 173 
 
 170 
 
 169 
 
 172 
 
 177 
 
 185 
 
 193 
 
 228 
 
 154 
 
 165 
 
 175 
 
 182 
 
 187 
 
 137 
 
 185 
 
 181 
 
 177 
 
 173 
 
 172 
 
 174 
 
 180 
 
 188 
 
 198 
 
 230 
 
 164 
 
 173 
 
 181 
 
 137 
 
 191 
 
 192 
 
 189 
 
 185 
 
 180 
 
 175 
 
 174 
 
 175 
 
 180 
 
 189 
 
 2!)0 
 
 232 
 
 176 
 
 182 
 
 189 
 
 194 
 
 198 
 
 198 
 
 194 
 
 191 
 
 185 
 
 180 
 
 177 
 
 178 
 
 182 
 
 189 
 
 aw 
 
 234 
 
 186 
 
 191 
 
 196 
 
 201 
 
 205 
 
 805 
 
 203 
 
 199 
 
 193 
 
 188 
 
 184 
 
 183 
 
 185 
 
 191 
 
 200 
 
 236 
 
 195 
 
 198 
 
 203 
 
 203 
 
 212 
 
 213 
 
 212 
 
 2!)8 
 
 2)3 
 
 197 
 
 193 
 
 190 
 
 190 
 
 194 
 
 809 
 
 238 
 
 eoi 
 
 204 
 
 2: is 
 
 213 
 
 217 
 
 22;) 
 
 22D 
 
 217 
 
 212 
 
 207 
 
 202 
 
 198 
 
 197 
 
 199 
 
 2.)4 
 
 240 
 
 206 
 
 207 
 
 211 
 
 216 
 
 220 
 
 224 
 
 225 
 
 223 
 
 21!) 
 
 214 
 
 21)!) 
 
 204 
 
 202 
 
 202 
 
 205 
 
 The perturbations are in units of the eighth decimal pla.cc. 
 
TABLE XXXIII. 
 
 I'l-rliir/iii/iniix nf /.n:,'. r, lij tin- I-'.arlh. 
 
 II i \ _ .iini'iii = 1. 
 
 ('"ii-t.-int inlili-il 150 IVrhid oi'Ar^ii nt XI., ','10 unit*. 
 
 Arg.X 
 
 a 
 1 20 
 
 .1 
 12* 
 
 .1 
 
 i::<; 
 
 ,i 
 191 
 
 .1 
 152 
 
 .1 
 160 
 
 !<; 
 
 d 
 
 17 
 
 111 
 
 l<v> 
 
 200 
 
 20W 
 
 i 
 210 
 
 .1 
 221 
 
 ,\ 
 232 
 
 190 
 
 10 
 
 II 
 
 n> 
 
 94 
 
 37 
 
 
 71 
 
 -7 
 
 ID: 
 
 ue 
 
 194 
 
 r.'- 
 
 I3H 
 
 127 
 
 196 
 
 199 
 
 - 
 
 6 
 
 6 
 
 12 
 
 91 
 
 34 
 
 1! 
 
 66 
 
 8* 
 
 06 
 
 IH- 
 
 116 
 
 191 
 
 122 
 
 199 
 
 194 
 
 II 
 
 
 
 6 
 
 6 
 
 ID 
 
 19 
 
 31 
 
 11 
 
 
 71 
 
 -7 
 
 97 
 
 100 
 
 111 
 
 115 
 
 !.'(> 
 
 27 
 
 90 
 
 i:< 
 
 9 
 
 8 
 
 11 
 
 17 
 
 86 
 
 
 51 
 
 64 
 
 76 
 
 86 
 
 06 
 
 11)3 
 
 hid 
 
 II 
 
 87 
 
 J- 
 
 21) 
 
 14 
 
 11 
 
 11 
 
 10 
 
 93 
 
 39 
 
 43 
 
 54 
 
 66 
 
 71, 
 
 86 
 
 130 
 
 63 
 
 66 
 
 47 
 
 37 
 
 28 
 
 21 
 
 16 
 
 IB 
 
 iii 
 
 21 
 
 86 
 
 36 
 
 47 
 
 57 
 
 69 
 
 139 
 
 80 
 
 7(i 
 
 69 
 
 60 
 
 4!) 
 
 40 
 
 31 
 
 -.':> 
 
 21 
 
 90 
 
 88 
 
 37 
 
 34 
 
 42 
 
 52 
 
 134 
 
 09 
 
 D9 
 
 
 33 
 
 71 
 
 64 
 
 63 
 
 44 
 
 36 
 
 39 
 
 87 
 
 26 
 
 86 
 
 33 
 
 40 
 
 136 
 
 109 
 
 105 
 
 i 6 
 
 104 
 
 96 
 
 DO 
 
 7!) 
 
 69 
 
 58 
 
 1- 
 
 40 
 
 34 
 
 31 
 
 30 
 
 33 
 
 138 
 
 109 
 
 115 
 
 190 
 
 191 
 
 110 
 
 114 
 
 106 
 
 96 
 
 83 
 
 71 
 
 
 49 
 
 40 
 
 35 
 
 38 
 
 140 
 
 tie 
 
 193 
 
 130 
 
 13:> 
 
 137 
 
 |36 
 
 199 
 
 121 
 
 109 
 
 06 
 
 81 
 
 67 
 
 54 
 
 44 
 
 35 
 
 149 
 
 193 
 
 130 
 
 139 
 
 145 
 
 ISO 
 
 159 
 
 14!) 
 
 149 
 
 139 
 
 119 
 
 IDI 
 
 87 
 
 71 
 
 56 
 
 44 
 
 1 II 
 
 139 
 
 139 
 
 146 
 
 154 
 
 hi) 
 
 164 
 
 161 
 
 161 
 
 153 
 
 141 
 
 196 
 
 111!) 
 
 Dl 
 
 73 
 
 67 
 
 i ni 
 
 147 
 
 14!) 
 
 164 
 
 Hi:) 
 
 167 
 
 17:1 176 
 
 17.-. 
 
 171 
 
 nil 
 
 II- 
 
 132 
 
 113 
 
 !H 
 
 75 
 
 148 
 
 162 
 
 100 
 
 162 
 
 167 
 
 174 
 
 1- i 
 
 186 
 
 188 
 
 187 
 
 181 
 
 171 
 
 156 
 
 ISO 
 
 II- 
 
 97 
 
 160 
 
 17- 
 
 173 
 
 172 
 
 174 
 
 180 
 
 187 
 
 194 
 
 1!'!) 
 
 801 
 
 190 
 
 193 
 
 182 
 
 166 
 
 147 
 
 196 
 
 IS9 
 
 193 
 
 l-:, 
 
 181 
 
 189 
 
 186 
 
 199 
 
 200 
 
 208 
 
 213 
 
 915 
 
 914 
 
 906 
 
 I9S 
 
 178 
 
 157 
 
 154 
 
 208 
 
 196 
 
 101 
 
 189 
 
 199 
 
 197 
 
 2Dr> 
 
 213 
 
 888 
 
 998 
 
 831 
 
 228 
 
 221 
 
 207 
 
 189 
 
 166 
 
 894 
 
 212 
 
 202 
 
 tee 
 
 197 
 
 200 
 
 207 
 
 216 
 
 996 
 
 935 
 
 241 
 
 244 
 
 849 
 
 233 
 
 219 
 
 158 
 
 239 
 
 226 
 
 916 
 
 207 
 
 204 
 
 204 
 
 208 
 
 916 
 
 224 
 
 2:15 
 
 -'II 
 
 251 
 
 854 
 
 251 
 
 843 
 
 tfiO 
 
 968 
 
 242 
 
 229 
 
 21!) 
 
 212 
 
 90fj 
 
 208 
 
 212 
 
 'Jill 
 
 229 
 
 240 
 
 250 
 
 958 
 
 260 
 
 867 
 
 169 
 
 96U 
 
 957 
 
 ^'11 
 
 2!!2 
 
 888 
 
 214 
 
 210 
 
 210 
 
 314 
 
 221 
 
 931 
 
 841 
 
 253 
 
 850 
 
 863 
 
 164 
 
 979 
 
 969 
 
 258 
 
 246 
 
 934 
 
 983 
 
 915 
 
 911 
 
 .'in 
 
 _'l 1 
 
 881 
 
 930 
 
 94S 
 
 858 
 
 261 
 
 166 
 
 989 
 
 976 
 
 969 
 
 
 -.'17 
 
 
 225 
 
 217 
 
 911 
 
 211 
 
 214 
 
 991 
 
 231 
 
 949 
 
 833 
 
 103 
 
 973 
 
 27.-, 
 
 271! 
 
 267 
 
 356 
 
 248 
 
 837 
 
 228 
 
 819 
 
 914 
 
 213 
 
 216 
 
 884 
 
 233 
 
 811 
 
 170 
 
 258 
 
 964 
 
 268 
 
 268 
 
 265 
 
 258 
 
 350 
 
 .' 1 1 
 
 232 
 
 n i 
 
 220 
 
 218 
 
 222 
 
 889 
 
 237 
 
 17'.' 
 
 232 
 
 943 
 
 963 
 
 960 
 
 963 
 
 963 
 
 260 
 
 254 
 
 246 
 
 
 231 
 
 896 
 
 885 
 
 896 
 
 833 
 
 174 
 
 199 
 
 JI4 
 
 930 
 
 242 
 
 953 
 
 930 
 
 969 
 
 261 
 
 257 
 
 850 
 
 243 
 
 236 
 
 2:12 
 
 830 
 
 232 
 
 176 
 
 164 
 
 l-l 
 
 1!)!) 
 
 216 
 
 939 
 
 845 
 
 954 
 
 
 260 
 
 257 
 
 252 
 
 245 
 
 830 
 
 935 
 
 232 
 
 178 
 
 189 
 
 147 
 
 165 
 
 184 
 
 .' > 1 
 
 929 
 
 236 
 
 248 
 
 954 
 
 8.V, 
 
 253 
 
 248 
 
 818 
 
 837 
 
 833 
 
 180 
 
 106 
 
 117 
 
 132 
 
 150 
 
 171 
 
 I!M 
 
 210 
 
 226 
 
 238 
 
 245 
 
 247 
 
 245 
 
 241 
 
 236 
 
 231 
 
 t9 
 
 87 
 
 99 
 
 103 
 
 117 
 
 136 
 
 157 
 
 178 
 
 19S 
 
 914 
 
 896 
 
 233 
 
 16 
 
 934 
 
 831 
 
 227 
 
 l-l 
 
 76 
 
 75 
 
 79 
 
 89 
 
 105 
 
 193 
 
 144 
 
 166 
 
 186 
 
 21)2 
 
 814 
 
 221 
 
 883 
 
 983 
 
 890 
 
 146 
 
 71 
 
 64 
 
 63 
 
 67 
 
 78 
 
 :>:t 
 
 113 
 
 135 
 
 156 
 
 176 
 
 192 
 
 203 
 
 909 
 
 212 
 
 211 
 
 188 
 
 71 
 
 6!) 
 
 52 
 
 51 
 
 57 
 
 68 
 
 85 
 
 106 
 
 128 
 
 150 
 
 16!! 
 
 184 
 
 1!I4 
 
 200 
 
 201 
 
 190 
 
 74 
 
 Be 
 
 47 
 
 41 
 
 42 
 
 49 
 
 63 
 
 81 
 
 102 
 
 124 
 
 11.-, 
 
 161 
 
 177 
 
 186 
 
 190 
 
 199 
 
 80 
 
 62 
 
 47 
 
 37 
 
 33 
 
 35 
 
 44 
 
 59 
 
 78 
 
 100 
 
 199 
 
 142 
 
 158 
 
 I6B 
 
 176 
 
 194 
 
 88 
 
 69 
 
 61 
 
 37 
 
 28 
 
 26 
 
 2!) 
 
 40 
 
 r,7 
 
 76 
 
 B7 
 
 118 
 
 136 
 
 II!) 
 
 15! t 
 
 l:ni 
 
 W 
 
 78 
 
 58 
 
 41 
 
 28 
 
 21 
 
 20 
 
 85 
 
 36 
 
 58 
 
 71 
 
 !)l 
 
 110 
 
 196 
 
 ISO 
 
 l!H 
 
 109 
 
 88 
 
 69 
 
 49 
 
 32 
 
 20 
 
 14 
 
 14 
 
 20 
 
 :'.! 
 
 47 
 
 65 
 
 83 
 
 M 
 
 114 
 
 200 
 
 121 
 
 101 
 
 81 
 
 60 
 
 40 
 
 85 
 
 13 
 
 H 
 
 9 
 
 15 
 
 26 
 
 40 
 
 56 
 
 7'.' 
 
 87 
 
 909 
 
 130 
 
 113 
 
 94 
 
 73 
 
 r>8 
 
 34 
 
 19 
 
 9 
 
 4 
 
 5 
 
 11 
 
 21 
 
 34 
 
 48 
 
 63 
 
 904 
 
 135 
 
 199 
 
 105 
 
 86 
 
 65 
 
 46 
 
 30 
 
 17 
 
 9 
 
 5 
 
 6 
 
 11 
 
 19 
 
 80 
 
 42 
 
 906 
 
 136 
 
 126 
 
 113 
 
 97 
 
 7!) 
 
 61 
 
 44 
 
 31 
 
 80 
 
 13 
 
 10 
 
 11 
 
 14 
 
 21 
 
 29 
 
 208 
 
 133 
 
 127 
 
 118 
 
 105 
 
 91 
 
 76 
 
 61 
 
 48 
 
 37 
 
 23 
 
 83 
 
 20 
 
 19 
 
 21 
 
 25 
 
 210 
 
 127 
 
 196 
 
 119 
 
 .110 
 
 100 
 
 88 
 
 76 
 
 (-, 
 
 .-,.-, 
 
 46 
 
 40 
 
 35 
 
 31 
 
 30 
 
 29 
 
 212 
 
 122 
 
 139 
 
 190 
 
 114 
 
 106 
 
 98 
 
 88 
 
 80 
 
 72 
 
 64 
 
 58 
 
 63 
 
 47 
 
 43 
 
 38 
 
 914 
 
 121 
 
 193 
 
 191 
 
 117 
 
 111 
 
 105 
 
 !I7 
 
 01 
 
 96 
 
 79 
 
 74 
 
 69 
 
 63 
 
 58 
 
 58 
 
 916 
 
 127 
 
 I9t! 
 
 197 
 
 122 
 
 117 
 
 111 
 
 104 
 
 BO 
 
 05 
 
 90 
 
 87 
 
 83 
 
 78 
 
 72 
 
 <;o 
 
 218 
 
 138 
 
 IJO 
 
 136 
 
 132 
 
 126 
 
 119 
 
 113 
 
 107 
 
 103 
 
 100 
 
 97 
 
 M 
 
 M 
 
 86 
 
 80 
 
 220 
 
 154 
 
 l.->4 
 
 152 
 
 147 
 
 139 
 
 132 
 
 124 
 
 118 
 
 113 
 
 no 
 
 107 
 
 106 
 
 103 
 
 100 
 
 06 
 
 ygjll 
 
 172 
 
 I7:i 
 
 170 
 
 165 
 
 158 
 
 149 
 
 140 
 
 133 
 
 127 
 
 123 
 
 121 
 
 190 
 
 118 
 
 116 
 
 119 
 
 994 
 
 188 
 
 I!IO 
 
 KM) 
 
 186 
 
 17!) 
 
 171 
 
 161 
 
 163 
 
 147 
 
 142 
 
 130 
 
 138 
 
 136 
 
 136 
 
 131 
 
 996 
 
 800 
 
 205 
 
 207 
 
 206 
 
 201 
 
 194 
 
 l-i, 
 
 177 
 
 170 
 
 165 
 
 161 
 
 M,i 
 
 160 
 
 157 
 
 I.M 
 
 998 
 
 21)7 
 
 216 
 
 221 
 
 993 
 
 221 
 
 216 
 
 209 
 
 202 
 
 l!Ki 
 
 190 
 
 186 
 
 185 
 
 184 
 
 182 
 
 17!l 
 
 230 
 
 211 
 
 222 
 
 230 
 
 9M 
 
 236 
 
 234 
 
 230 
 
 224 
 
 218 
 
 213 
 
 210 
 
 209 
 
 208 
 
 207 
 
 gD6 
 
 232 
 
 Iil2 
 
 224 
 
 234 
 
 949 
 
 246 
 
 246 
 
 944 
 
 240 
 
 2:16 
 
 232 
 
 890 
 
 838 
 
 889 
 
 889 
 
 8H 
 
 831 
 
 212 
 
 883 
 
 2:15 
 
 243 
 
 940 
 
 951 
 
 951 
 
 249 
 
 2 15 
 
 949 
 
 941 
 
 241 
 
 243 
 
 846 
 
 -'17 
 
 936 
 
 211 
 
 222 
 
 939 
 
 941 
 
 217 
 
 951 
 
 -:> 1 
 
 350 
 
 -'17 
 
 946 
 
 345 
 
 946 
 
 349 
 
 884 
 
 -'.-,1 
 
 938 
 
 Jll 
 
 00 
 
 22!> 
 
 J37 
 
 949 
 
 -M<; 
 
 247 
 
 246 
 
 '.'11 
 
 943 
 
 949 
 
 945 
 
 340 
 
 85f i 
 
 864 
 
 940 
 
 210 
 
 217 
 
 994 
 
 231 
 
 939 
 
 2:t8 
 
 239 
 
 238 
 
 937 
 
 236 
 
 236 
 
 
 8*4 
 
 252 
 
 869 
 
 13V 
 
 When 224'' .7 is subtracted from Arg. I., add 147.61 to Arg. XI. 
 
410 
 
 TABLE XXXI V. 
 
 Perturbations nf Log. r, by Mars. 
 
 Horizontal Argument = I. 
 
 .Constant added 80. Period of Argument I., 224<i.7. 
 
 
 d 
 
 A 
 
 d 
 
 d 
 
 d 
 
 1 
 
 d 
 
 d 
 
 d 
 
 d 
 
 A 
 
 d 
 
 d 
 
 d 
 
 d 
 
 Arg. 
 XII. 
 
 
 
 8 
 
 1C 
 
 24 
 
 32 
 
 40 
 
 48 
 
 56 
 
 6ft 
 
 72 
 
 80 
 
 88 
 
 96 
 
 SOI 
 
 112 
 
 
 
 !22 
 
 106 
 
 88 
 
 71 
 
 54 
 
 38 
 
 25 
 
 15 
 
 8 
 
 g 
 
 6 
 
 11 
 
 2; 
 
 32 
 
 46 
 
 1 
 
 !38 
 
 124 
 
 111! 
 
 1)3 
 
 76 
 
 61) 
 
 44 
 
 30 
 
 18 
 
 1C 
 
 7 
 
 8 
 
 11 
 
 18 
 
 29 
 
 *> 
 
 14<> 
 
 140 
 
 129 
 
 115 
 
 99 
 
 82 
 
 65 
 
 49 
 
 35 
 
 24 
 
 15 
 
 10 
 
 ( 
 
 11 
 
 17 
 
 3 
 
 153 
 
 14!) 
 
 142 
 
 132 
 
 118 103 
 
 87 
 
 71 
 
 r,r, 
 
 40 
 
 as 
 
 1! 
 
 14 
 
 11 
 
 12 
 
 4 
 
 150 
 
 152 
 
 150 
 
 144 
 
 134 
 
 122 
 
 108 
 
 92 
 
 76 
 
 61 
 
 46 
 
 33 
 
 24 
 
 17 
 
 13 
 
 5 
 
 140 
 
 147 
 
 150 
 
 148 
 
 143 
 
 135 
 
 125 
 
 113 
 
 97 
 
 82 
 
 67 
 
 52 
 
 39 
 
 29 
 
 21 
 
 6 
 
 125 
 
 J36 
 
 143 
 
 147 
 
 147 
 
 114 
 
 138 
 
 128 
 
 115 
 
 102 
 
 88 
 
 73 
 
 58 
 
 45 
 
 34 
 
 7 
 
 106 
 
 120 
 
 131 
 
 140 
 
 145 
 
 146 
 
 144 
 
 139 
 
 131 
 
 121 
 
 107 
 
 93 
 
 78 
 
 64 
 
 50 
 
 8 
 
 85 
 
 101 
 
 115 
 
 126 
 
 133 
 
 142 
 
 145 
 
 144 
 
 139 
 
 132 
 
 123 
 
 112 
 
 DO 
 
 84 
 
 71 
 
 9 
 
 64 
 
 79 
 
 94 
 
 108 
 
 120 
 
 130 
 
 138 
 
 142 
 
 143 
 
 140 
 
 134 
 
 120 
 
 116 
 
 104 
 
 91 
 
 10 
 
 45 
 
 59 
 
 73 
 
 88 
 
 102 
 
 115 
 
 126 
 
 134 
 
 139 
 
 141 
 
 140 
 
 136 
 
 129 
 
 120 
 
 109 
 
 11 
 
 30 
 
 41 
 
 54 
 
 68 
 
 82 
 
 97 
 
 110 
 
 120 
 
 129 
 
 135 
 
 139 
 
 139 
 
 137 
 
 132 
 
 1 24 
 
 12 
 
 19 
 
 27 
 
 37 
 
 49 
 
 61 
 
 75 
 
 DO 
 
 103 
 
 115 
 
 1 25 
 
 132 
 
 137 
 
 139 
 
 137 
 
 133 
 
 13 
 
 16 
 
 1!) 
 
 25 
 
 33 
 
 44 
 
 56 
 
 69 
 
 83 
 
 96 
 
 108 
 
 119 
 
 J27 
 
 133 
 
 i:i~ 
 
 137 
 
 14 
 
 18 
 
 17 
 
 18 
 
 22 
 
 30 
 
 40 
 
 51 
 
 64 
 
 77 
 
 90 
 
 102 
 
 114 
 
 123 
 
 130 
 
 135 
 
 15 
 
 28 
 
 sa 
 
 19 
 
 19 
 
 22 
 
 27 
 
 35 
 
 45 
 
 57 
 
 70 
 
 83 
 
 96 
 
 108 
 
 118 
 
 126 
 
 16 
 
 43 
 
 :!:! 
 
 26 
 
 21 
 
 19 
 
 21 
 
 25 
 
 31 
 
 40 
 
 51 
 
 63 
 
 76 
 
 89 
 
 101 
 
 112 
 
 17 
 
 :>:> 
 
 47 
 
 37 
 
 29 
 
 23 
 
 20 
 
 20 
 
 23 
 
 28 
 
 36 
 
 46 
 
 58 
 
 70 
 
 84 
 
 96 
 
 18 
 
 80 
 
 07 54 
 
 43 
 
 33 
 
 26 
 
 21 
 
 20 
 
 21 
 
 25 
 
 31 
 
 40 
 
 51 
 
 62 
 
 75 
 
 19 
 
 101 
 
 87 
 
 74 
 
 60 
 
 48 
 
 38 
 
 30 
 
 24 
 
 21 
 
 20 
 
 22 
 
 27 
 
 35 
 
 45 
 
 56 
 
 20 
 
 II!) 
 
 106 
 
 92 
 
 79 
 
 66 
 
 53 
 
 43 
 
 33 
 
 26 
 
 21 
 
 19 
 
 21) 
 
 24 
 
 31 
 
 40 
 
 21 
 
 133 
 
 iaa 
 
 111 
 
 99 
 
 86 
 
 73 
 
 59 
 
 47 
 
 37 
 
 29 
 
 23 
 
 19 
 
 18 
 
 2!) 
 
 K 
 
 22 
 
 142 
 
 136 
 
 128 
 
 118 
 
 105 
 
 92 
 
 79 
 
 65 
 
 53 
 
 42 
 
 32 
 
 24 
 
 19 
 
 17 
 
 18 
 
 23 
 
 144 
 
 143 
 
 139 
 
 132 
 
 ^'>> 
 
 111 
 
 99 
 
 86 
 
 72 
 
 58 
 
 46 
 
 35 
 
 26 
 
 20 
 
 16 
 
 24 
 
 141 
 
 144 
 
 144 
 
 141 
 
 135 
 
 127 
 
 117 
 
 105 
 
 N 
 
 78 
 
 63 
 
 51 
 
 39 
 
 29 
 
 21 
 
 25 
 
 132 
 
 139 
 
 143 
 
 144 
 
 143 
 
 138 
 
 131 
 
 122 
 
 111 
 
 98 
 
 85 
 
 70 
 
 56 
 
 43 
 
 31 
 
 26 
 
 117 
 
 127 
 
 135 
 
 141 
 
 144 
 
 144 
 
 142 
 
 136 
 
 127 
 
 117 
 
 105 
 
 91 
 
 76 
 
 61 
 
 47 
 
 27 
 
 98 
 
 111 
 
 122 
 
 132 
 
 139 
 
 143 
 
 145 
 
 143 
 
 139 
 
 132 
 
 122 
 
 110 
 
 96 
 
 82 
 
 66 
 
 28 
 
 78 
 
 93 
 
 106 
 
 118 
 
 128 
 
 137 
 
 143 
 
 146 
 
 145 
 
 142 
 
 137 
 
 128 
 
 117 
 
 103 
 
 88 
 
 2t) 
 
 58 
 
 71 
 
 86 
 
 99 
 
 112 
 
 124 
 
 134 
 
 142 
 
 146 
 
 147 
 
 146 
 
 141 
 
 133 
 
 122 
 
 109 
 
 30 
 
 41 
 
 52 
 
 65 
 
 79 
 
 93 
 
 107 
 
 120 
 
 130 
 
 139 
 
 145 
 
 148 
 
 148 
 
 144 
 
 137 
 
 127 
 
 31 
 
 29 
 
 37 
 
 47 
 
 60 
 
 73 
 
 88 
 
 102 
 
 115 
 
 127 
 
 137 
 
 145 
 
 149 
 
 150 
 
 148 
 
 141 
 
 32 
 
 20 
 
 24 
 
 31 
 
 42 
 
 53 
 
 67 
 
 82 
 
 96 
 
 110 
 
 123 
 
 134 
 
 144 
 
 150 
 
 152 
 
 151 
 
 33 
 
 19 
 
 18 
 
 21 
 
 26 
 
 36 
 
 47 
 
 60 
 
 75 
 
 90 
 
 105 
 
 119 
 
 131 
 
 141 
 
 149 
 
 159 
 
 34 
 
 25 
 
 20 
 
 17 
 
 18 
 
 23 
 
 32 
 
 42 
 
 55 
 
 69 
 
 85 
 
 100 
 
 115 
 
 128 
 
 139 
 
 148 
 
 35 
 
 35 
 
 27 
 
 20 
 
 16 
 
 16 
 
 20 
 
 27 
 
 37 
 
 49 
 
 63 
 
 79 
 
 95 
 
 111 
 
 125 
 
 136 
 
 36 
 
 51 
 
 39 
 
 29 
 
 21 
 
 16 
 
 15 
 
 17 
 
 23 
 
 31 
 
 43 
 
 57 
 
 73 
 
 89 
 
 105 
 
 12U 
 
 37 
 
 69 
 
 55 
 
 43 
 
 32 
 
 22 
 
 16 
 
 13 
 
 15 
 
 19 
 
 27 
 
 38 
 
 52 
 
 67 
 
 84 
 
 100 
 
 38 
 
 90 
 
 76 
 
 61 
 
 48 
 
 34 
 
 24 
 
 16 
 
 13 
 
 12 
 
 16 
 
 23 
 
 33 
 
 46 
 
 61 
 
 78 
 
 39 
 
 110 
 
 97 
 
 82 
 
 66 
 
 51 
 
 38 
 
 27 
 
 18 
 
 13 
 
 11 
 
 13 
 
 19 
 
 29 
 
 41 
 
 56 
 
 40 
 
 128 
 
 116 
 
 102 
 
 87 
 
 72 
 
 56 
 
 42 
 
 29 
 
 19 
 
 13 
 
 10 
 
 11 
 
 16 
 
 25 
 
 36 
 
 41 
 
 140 
 
 131 
 
 121 
 
 108 
 
 93 
 
 78 
 
 61 
 
 46 
 
 32 
 
 22 
 
 14 
 
 10 
 
 10 
 
 13 
 
 21 
 
 42 
 
 148 
 
 144 
 
 137 
 
 128 
 
 114 
 
 99 
 
 83 
 
 66 
 
 50 
 
 36 
 
 24 
 
 15 
 
 10 
 
 8 
 
 11 
 
 43 
 
 148 
 
 150 
 
 148 
 
 142 
 
 132 
 
 119 
 
 105 
 
 89 
 
 71 
 
 54 
 
 39 
 
 27 
 
 17 
 
 11 
 
 8 
 
 44 
 
 141 
 
 148 
 
 150 
 
 150 
 
 145 
 
 136 
 
 124 
 
 110 
 
 94 
 
 77 
 
 59 
 
 44 
 
 31 
 
 20 
 
 12 
 
 45 
 
 130 
 
 140 
 
 148 
 
 152 
 
 152 
 
 147 
 
 140 
 
 130 
 
 116 
 
 99 
 
 82 
 
 64 
 
 49 
 
 35 
 
 23 
 
 46 
 
 112 
 
 127 
 
 138 
 
 147 
 
 153 
 
 154 
 
 151 
 
 144 
 
 133 
 
 120 
 
 104 
 
 87 
 
 69 
 
 53 
 
 38 
 
 47 
 
 90 
 
 108 
 
 123 
 
 136 
 
 146 
 
 152 
 
 155 
 
 153 
 
 147 
 
 138 
 
 125 
 
 109 
 
 92 
 
 75 
 
 58 
 
 48 
 
 68 
 
 88 
 
 104 
 
 119 
 
 133 
 
 145 
 
 152 
 
 155 
 
 154 
 
 149 
 
 141 
 
 129 
 
 114 
 
 97 
 
 81 
 
 49 
 
 46 
 
 62 
 
 81 
 
 98 
 
 115 
 
 130 
 
 142 
 
 151 
 
 156 
 
 156 
 
 152 
 
 144 
 
 133 
 
 119 
 
 103 
 
 50 
 
 27 
 
 41 
 
 57 
 
 76 
 
 93 
 
 111 
 
 127 
 
 133 
 
 149 
 
 155 
 
 156 
 
 154 
 
 147 
 
 136 
 
 123 
 
 51 
 
 13 
 
 23 
 
 36 
 
 53 
 
 70 
 
 89 
 
 107 
 
 122 
 
 136 
 
 146 
 
 154 
 
 156 
 
 155 
 
 150 
 
 140 
 
 52 
 
 3 
 
 9 
 
 19 
 
 39 
 
 48 
 
 65 
 
 84 
 
 102 
 
 118 
 
 133 
 
 144 
 
 J52 
 
 ]5G 
 
 156 
 
 150 
 
 53 
 
 1 
 
 2 
 
 7 
 
 15 
 
 28 
 
 44 
 
 60 
 
 79 
 
 97 
 
 114 
 
 129 
 
 141 
 
 149 
 
 154 
 
 155 
 
 54 
 
 6 
 
 2 
 
 1 
 
 4 
 
 12 
 
 24 
 
 39 
 
 55 
 
 73 
 
 92 
 
 109 
 
 125 
 
 137 
 
 146 
 
 153 
 
 55 
 
 18 
 
 9 
 
 3 
 
 1 
 
 3 
 
 10 
 
 21 
 
 35 
 
 50 
 
 68 
 
 87 
 
 104 
 
 120 
 
 133 
 
 143 
 
 56 
 
 35 
 
 21 
 
 11 
 
 4 
 
 1 
 
 3 
 
 9 
 
 18 
 
 31 
 
 46 
 
 63 
 
 82 
 
 99 
 
 115 
 
 128 
 
 57 
 
 54 
 
 39 
 
 25 
 
 14 
 
 6 
 
 2 
 
 2 
 
 i? 
 
 16 
 
 27 
 
 42 
 
 59 
 
 76 
 
 94 
 
 110 
 
 58 
 
 79 
 
 61 
 
 44 
 
 30 
 
 18 
 
 9 
 
 4 
 
 3 
 
 6 
 
 13 
 
 24 
 
 38 
 
 54 
 
 70 
 
 87 
 
 60 
 
 102 
 
 84 
 
 67 
 
 49 
 
 33 
 
 21 
 
 12 
 
 6 
 
 4 
 
 6 
 
 12 
 
 22 
 
 35 
 
 49 
 
 65 
 
 ' 60 
 
 122 
 
 106 
 
 88 
 
 71 
 
 54 
 
 38 
 
 25 
 
 15 
 
 8 
 
 5 
 
 6 
 
 11 
 
 20 
 
 32 
 
 46 
 
 The perturbations arc in units of the eighth decimal place. 
 
Tilt Li: XXXIV. 
 
 Perturbations f Lu<^. /, A.-/ Mar*. 
 
 rii>riziil;il i = 1. 
 
 ('n-liiut ;icMi IVri"d ,f Argiiinrnl XII., (ill units. 
 
 . 
 
 j 
 
 
 ,j 
 
 ,i 
 
 d 
 
 
 .1 
 
 
 .1 
 
 d 
 
 .1 
 
 d 
 
 
 
 xff 
 
 120 
 
 
 i:ti 
 
 111 
 
 152 
 
 100 
 
 I 
 
 l? 
 
 IM 
 
 19 
 
 200 
 
 20* 
 
 210 
 
 22 1 
 
 2*2 
 
 
 
 1,1 
 
 7,, 
 
 09 
 
 107 
 
 121 131 i:i:> 
 
 1 i:, 
 
 11- 117 
 
 149 
 
 131 
 
 195 
 
 113 
 
 100 
 
 1 
 
 49 
 
 56 
 
 71 
 
 
 109 
 
 III, 127 
 
 136 
 
 III 
 
 li:, 
 
 1 H, 
 
 143 
 
 137 
 
 Itti 
 
 118 
 
 2 
 
 96 
 
 :',7 
 
 51 
 
 63 
 
 8(1 
 
 05 
 
 109 
 
 121 
 
 131 13- 113 
 
 li:, 
 
 143 
 
 IM 
 
 133 
 
 3 
 
 17 
 
 94 
 
 31 
 
 47 
 
 GO 
 
 71 - i 
 
 109 
 
 115 
 
 196 
 
 136 
 
 Ill 
 
 111 
 
 1 II 
 
 149 
 
 4 
 
 12 
 
 IS 
 
 91 
 
 31 
 
 49 
 
 :,:, 
 
 89 
 
 -' 
 
 97 
 
 llll 
 
 191 
 
 131 
 
 138 
 
 143 
 
 144 
 
 - 
 
 16 
 
 16 
 
 16 
 
 21 
 
 99 
 
 38 
 
 r,ii 
 
 a 
 
 7i ; 
 
 
 103 
 
 116 
 
 196 
 
 131 
 
 140 
 
 G 
 
 95 
 
 2 ' 
 
 17 
 
 17 
 
 99 
 
 96 
 
 34 
 
 IS 
 
 ",7 
 
 69 
 
 
 06 
 
 no 
 
 122 
 
 131 
 
 4 
 
 38 
 
 30 
 
 23 
 
 1!) 
 
 18 
 
 1!) 
 
 21 
 
 31 
 
 41 
 
 59 
 
 (il 
 
 77 
 
 91 
 
 106 
 
 117 
 
 8 
 
 57 
 
 4.-, 
 
 3D 
 
 27 
 
 99 
 
 J i 
 
 90 
 
 99 
 
 9B 
 
 36 
 
 16 
 
 ."7 
 
 70 
 
 84 
 
 
 9 
 
 7- 
 
 Gl 
 
 59 
 
 II 
 
 39 
 
 96 
 
 99 
 
 90 
 
 21 
 
 95 
 
 32 
 
 40 
 
 51 
 
 G3 
 
 7- 
 
 ID 
 
 06 
 
 s:( 
 
 7n 
 
 57 
 
 4G 
 
 37 
 
 
 23 
 
 90 
 
 20 
 
 93 
 
 
 3G H, 
 
 ;,, 
 
 11 
 
 114 
 
 109 
 
 !NI 
 
 78 
 
 (>"> 
 
 63 
 
 43 
 
 31 
 
 27 
 
 99 
 
 90 
 
 21 
 
 32 
 
 41 
 
 12 
 
 127 
 
 118 
 
 108 
 
 '.'7 
 
 -1 
 
 71 
 
 50 
 
 47 
 
 37 
 
 90 
 
 93 
 
 2,1 2 i 
 
 99 
 
 98 
 
 13 
 
 135 
 
 130 
 
 123 
 
 II 1 
 
 103 
 
 90 
 
 78 
 
 65 
 
 63 
 
 42 
 
 33 
 
 21 1!) 
 
 21 
 
 14 
 
 137 
 
 136 
 
 133 
 
 127 
 
 11!) 
 
 108 
 
 !I7 
 
 85 
 
 71 
 
 58 
 
 47 
 
 37 
 
 89 
 
 1!) 
 
 15 
 
 139 
 
 136 
 
 137 
 
 136 
 
 130 
 
 194 
 
 116 
 
 104 
 
 99 
 
 7- 
 
 66 
 
 53 41 
 
 31 
 
 23 
 
 Hi 
 
 199 
 
 129 
 
 135 
 
 137 
 
 136 
 
 133 
 
 198 
 
 120 
 
 no 
 
 88 
 
 85 
 
 71 
 
 58 
 
 45 
 
 31 
 
 17 
 
 108 
 
 118 
 
 196 
 
 133 
 
 137 
 
 137 
 
 13G 
 
 132 
 
 1 2~> 
 
 115 
 
 104 
 
 91 
 
 77 
 
 63 
 
 59 
 
 18 
 
 88 
 
 101 
 
 113 
 
 193 
 
 131 
 
 137 
 
 139 
 
 138 
 
 136 
 
 130 122 
 
 111 !H 
 
 84 
 
 60 
 
 1!) 
 
 6!) 
 
 82 
 
 90 
 
 108 
 
 120 
 
 198 
 
 136 
 
 140 
 
 141 
 
 140 
 
 135 
 
 127 
 
 117 
 
 105 
 
 1)1 
 
 90 
 
 51 
 
 63 
 
 76 
 
 89 
 
 103 
 
 11.-, 
 
 125 
 
 134 
 
 140 
 
 112 
 
 142 
 
 138 
 
 132 
 
 122 
 
 no 
 
 
 34 
 
 4.-, 
 
 56 
 
 69 
 
 84 
 
 
 111 
 
 199 
 
 139 
 
 140 
 
 III 
 
 144 
 
 142 
 
 137 
 
 198 
 
 99 
 
 99 
 
 99 
 
 38 
 
 50 
 
 G3 
 
 77 
 
 09 
 
 106 
 
 119 
 
 CIO 
 
 13!) 
 
 144 
 
 146 
 
 145 
 
 in 
 
 98 
 
 1G 
 
 18 
 
 24 
 
 33 
 
 44 
 
 57 
 
 71 
 
 86 
 
 101 
 
 115 
 
 127 
 
 137 
 
 144 
 
 148 
 
 149 
 
 94 
 
 16 
 
 13 
 
 14 
 
 19 
 
 27 
 
 38 
 
 51 
 
 65 
 
 81 
 
 96 
 
 111 
 
 195 
 
 136 
 
 144 
 
 14!) 
 
 86 
 
 99 
 
 1G 
 
 13 
 
 13 
 
 16 
 
 23 
 
 33 
 
 44 
 
 59 
 
 7.'. 
 
 91 
 
 106 
 
 121 
 
 133 
 
 143 
 
 96 
 
 34 
 
 24 
 
 16 
 
 11 
 
 10 
 
 19 
 
 18 
 
 27 
 
 39 
 
 63 
 
 G!) 
 
 85 
 
 109 
 
 118 
 
 131 
 
 27 
 
 59 
 
 3!) 
 
 27 
 
 18 
 
 12 
 
 9 
 
 11) 
 
 15 
 
 93 
 
 34 
 
 48 
 
 63 
 
 80 
 
 08 
 
 114 
 
 88 
 
 71 
 
 55 
 
 42 
 
 29 
 
 18 
 
 11 
 
 7 
 
 7 
 
 11 
 
 18 
 
 99 
 
 42 
 
 
 7.-, 
 
 93 
 
 98 
 
 94 
 
 77 
 
 61 
 
 46 
 
 32 
 
 20 
 
 12 
 
 6 
 
 :, 
 
 7 
 
 14 
 
 24 
 
 37 
 
 52 
 
 70 
 
 30 
 
 114 
 
 99 
 
 83 
 
 66 
 
 50 
 
 36 
 
 23 
 
 13 
 
 7 
 
 4 
 
 5 
 
 11 
 
 20 
 
 32 
 
 47 
 
 31 
 
 131 
 
 119 
 
 105 
 
 89 
 
 71 
 
 56 
 
 40 
 
 26 
 
 16 
 
 7 
 
 3 
 
 3 
 
 8 
 
 16 
 
 27 
 
 32 
 
 145 
 
 136 
 
 1 2 ."> 
 
 no 
 
 04 
 
 7G 
 
 59 
 
 43 
 
 28 
 
 16 
 
 7 
 
 3 
 
 2 
 
 5 
 
 13 
 
 33 
 
 169 
 
 148 
 
 141 
 
 131) 
 
 115 
 
 80 
 
 82 
 
 64 
 
 47 
 
 32 
 
 1:1 
 
 9 
 
 3 
 
 1 
 
 4 
 
 34 
 
 153 
 
 153 
 
 151 
 
 145 
 
 134 
 
 120 
 
 104 
 
 87 
 
 6:1 
 
 51 
 
 35 
 
 21 
 
 11 
 
 4 
 
 1 
 
 85 
 
 14G 
 
 152 
 
 155 
 
 154 
 
 147 
 
 137 
 
 125 
 
 no 
 
 93 
 
 74 
 
 57 
 
 40 
 
 26 
 
 14 
 
 6 
 
 3G 
 
 134 
 
 144 
 
 159 
 
 155 
 
 154 
 
 149 
 
 141 
 
 198 
 
 114 
 
 '.,7 
 
 79 
 
 61 
 
 44 
 
 2.1 
 
 16 
 
 37 
 
 116 
 
 130 
 
 141 
 
 150 
 
 155 
 
 155 
 
 169 
 
 144 
 
 133 
 
 119 
 
 109 
 
 85 
 
 66 
 
 49 
 
 34 
 
 38 
 
 94 
 
 III 
 
 126 
 
 13!) 
 
 149 
 
 155 
 
 156 
 
 153 
 
 146 
 
 137 
 
 121 
 
 107 
 
 00 
 
 72 
 
 54 
 
 39 
 
 72 
 
 90 
 
 107 
 
 123 
 
 137 
 
 147 
 
 I.I 
 
 156 
 
 154 
 
 148 
 
 140 
 
 127 
 
 111 
 
 95 
 
 77 
 
 40 
 
 50 
 
 66 
 
 84 
 
 101 
 
 118 
 
 132 
 
 143 
 
 152 
 
 156 
 
 156 
 
 151 
 
 142 
 
 131 
 
 116 
 
 100 
 
 41 
 
 32 
 
 46 
 
 G2 
 
 79 
 
 97 
 
 114 
 
 128 
 
 140 
 
 14!) 
 
 155 
 
 155 
 
 161 
 
 144 
 
 134 
 
 121) 
 
 42 
 
 18 
 
 28 
 
 41 
 
 57 
 
 74 
 
 92 
 
 109 
 
 194 
 
 137 
 
 146 
 
 159 
 
 154 
 
 151 
 
 146 
 
 137 
 
 43 
 
 10 
 
 15 
 
 24 
 
 37 
 
 69 
 
 68 
 
 86 
 
 103 
 
 119 
 
 133 
 
 113 
 
 150 
 
 153 
 
 159 
 
 148 
 
 44 
 
 9 
 
 8 
 
 12 
 
 21 
 
 33 
 
 48 
 
 G4 
 
 81 
 
 98 
 
 114 
 
 128 
 
 140 
 
 147 
 
 161 
 
 161 
 
 45 
 
 14 
 
 9 
 
 8 
 
 12 
 
 19 
 
 90 
 
 43 
 
 58 
 
 75 
 
 93 
 
 109 
 
 123 
 
 136 
 
 143 
 
 14)1 
 
 46 
 
 25 
 
 16 
 
 10 
 
 8 
 
 10 
 
 16 
 
 26 
 
 39 
 
 54 
 
 7,1 
 
 87 
 
 103 
 
 118 
 
 1311 
 
 141) 
 
 47 
 
 43 
 
 30 
 
 19 
 
 12 
 
 9 
 
 9 
 
 15 
 
 24 
 
 36 
 
 50 
 
 
 81 
 
 08 
 
 113 
 
 196 
 
 48 
 
 63 
 
 47 
 
 34 
 
 23 
 
 14 
 
 10 
 
 10 
 
 13 
 
 21 
 
 31 
 
 45 
 
 60 
 
 76 
 
 
 106 
 
 49 
 
 86 
 
 69 
 
 53 
 
 38 
 
 26 
 
 17 
 
 12 
 
 10 
 
 13 
 
 19 
 
 29 
 
 41 
 
 55 
 
 70 
 
 86 
 
 50 
 
 107 
 
 91 
 
 74 
 
 57 
 
 42 
 
 30 
 
 20 
 
 13 
 
 11 
 
 12 
 
 17 
 
 26 
 
 37 
 
 50 
 
 (i.-, 
 
 51 
 
 127 
 
 112 
 
 07 
 
 80 
 
 63 
 
 48 
 
 35 
 
 24 
 
 17 
 
 13 
 
 13 
 
 16 
 
 24 
 
 34 
 
 46 
 
 59 
 
 142 
 
 131) 
 
 117 
 
 102 
 
 85 
 
 68 
 
 53 
 
 39 
 
 28 
 
 20 
 
 16 
 
 15 
 
 17 
 
 
 31 
 
 53 
 
 161 
 
 144 
 
 134 
 
 122 
 
 106 
 
 90 
 
 74 
 
 58 
 
 44 
 
 33 
 
 23 
 
 17 
 
 18 
 
 16 
 
 91 
 
 54 
 
 155 
 
 152 
 
 147 
 
 138 
 
 126 
 
 111 
 
 96 
 
 80 
 
 64 
 
 49 
 
 37 
 
 27 
 
 21 
 
 17 
 
 17 
 
 56 
 
 150 
 
 i:,:i 
 
 152 
 
 148 
 
 140 
 
 199 
 
 117 
 
 102 
 
 86 
 
 70 
 
 56 
 
 43 
 
 33 
 
 9J 
 
 90 
 
 
 140 
 
 147 
 
 151 
 
 161 
 
 147 
 
 III 
 
 139 
 
 120 
 
 106 
 
 !>l 
 
 76 
 
 61 
 
 1- 
 
 37 
 
 2- 
 
 C7 
 
 101 
 
 
 ! II 
 
 150 
 
 151 
 
 148 
 
 113 
 
 131 
 
 124 
 
 111 
 
 97 
 
 82 
 
 G7 
 
 54 
 
 43 
 
 Dtf 
 
 58 
 
 i - , 
 103 
 
 118 
 
 131 
 
 140 
 
 146 
 
 1 )'' 
 
 149 
 
 145 
 
 138 
 
 129 
 
 117 
 
 1113 
 
 - ' 
 
 75 
 
 80 
 
 Rfll 
 
 --j 
 
 98 
 
 113 
 
 126 
 
 137 
 
 143 
 
 148 
 
 148 
 
 146 
 
 140 
 
 132 
 
 121 
 
 
 06 
 
 81 
 
 Jt' 
 
 69 
 
 61 
 
 76 
 
 92 
 
 107 
 
 121 
 
 131 
 
 13!) 
 
 145 
 
 148 
 
 147 
 
 142 
 
 134 
 
 198 
 
 113 
 
 UN) 
 
 When 2->4 d .7 is subtracted from Arg. I., add 19.6 to Arg XII. 
 
TABLE XXXV. 
 
 Perturbations of Log. /, liy Jupiter. 
 
 Horizontal Argument = I. 
 
 Constant added 30. Period of Argument 1., 224<i.7. 
 
 Arg. 
 XIII. 
 
 d 
 
 
 
 d 
 
 8 
 
 16 
 
 d 
 
 24 
 
 d 
 32 
 
 d 
 40 
 
 d 
 
 48 
 
 ,1 
 56 
 
 i 
 
 61 
 
 .1 
 72 
 
 80 
 
 d 
 
 88 
 
 d 
 
 96 
 
 d 
 
 101 
 
 112 
 
 
 
 81 
 
 61 
 
 46 
 
 35 
 
 23 
 
 27 
 
 31 
 
 39 
 
 50 
 
 61 
 
 72 
 
 80 
 
 85 
 
 88 
 
 83 
 
 ] 
 
 100 
 
 81 
 
 62 
 
 47 
 
 35 
 
 29 
 
 28 
 
 32 
 
 39 
 
 49 
 
 60 
 
 6!) 
 
 76 
 
 80 
 
 83 
 
 2 
 
 119 
 
 100 
 
 80 
 
 62 
 
 46 
 
 34 
 
 23 
 
 27 
 
 31 
 
 S8 
 
 43 
 
 57 
 
 66 
 
 72 
 
 76 
 
 3 
 
 136 
 
 119 
 
 99 
 
 7!) 
 
 60 
 
 44 
 
 33 
 
 27 
 
 26 
 
 30 
 
 38 
 
 46 
 
 55 
 
 63 
 
 69 
 
 4 
 
 150 
 
 136 
 
 118 
 
 97 
 
 76 
 
 57 
 
 42 
 
 31 
 
 26 
 
 25 
 
 30 
 
 37 
 
 45 
 
 54 
 
 61 
 
 5 
 
 159 
 
 149 
 
 134 
 
 115 
 
 94 
 
 73 
 
 54 
 
 39 
 
 29 
 
 24 
 
 25 
 
 29 
 
 36 
 
 45 
 
 53 
 
 6 
 
 165 
 
 160 
 
 148 
 
 132 
 
 113 
 
 90 
 
 69 
 
 50 
 
 36 
 
 27 
 
 23 
 
 24 
 
 29 
 
 37 
 
 45 
 
 7 
 
 165 
 
 165 
 
 158 
 
 145 
 
 128 
 
 107 
 
 85 
 
 64 
 
 47 
 
 33 
 
 25 
 
 22 
 
 24 
 
 30 
 
 ::s 
 
 8 
 
 161 
 
 165 
 
 163 
 
 155 
 
 141 
 
 123 
 
 102 
 
 80 
 
 60 
 
 43 
 
 31 
 
 24 
 
 23 
 
 25 
 
 32 
 
 9 
 
 153 
 
 161 
 
 164 
 
 161 
 
 151 
 
 137 
 
 117 
 
 96 
 
 75 
 
 56 
 
 40 
 
 29 
 
 24 
 
 24 
 
 23 
 
 10 
 
 14'i 
 
 154 
 
 160 
 
 161 
 
 157 
 
 147 
 
 131 
 
 112 
 
 91 
 
 71 
 
 52 
 
 38 
 
 29 
 
 25 
 
 26 
 
 
 129 
 
 142 
 
 152 
 
 158 
 
 158 
 
 153 
 
 141 
 
 . 125 
 
 106 
 
 86 
 
 67 
 
 50 
 
 37 
 
 30 
 
 27 
 
 12 
 
 114 
 
 127 
 
 140 
 
 149 
 
 155 
 
 154 
 
 148 
 
 136 
 
 120 
 
 101 
 
 82 
 
 63 
 
 48 
 
 37 
 
 31 
 
 13 
 
 99 
 
 112 
 
 125 
 
 138 
 
 147 
 
 151 
 
 150 
 
 143 
 
 131 
 
 115 
 
 97 
 
 78 
 
 62 
 
 48 
 
 39 
 
 14 
 
 85 
 
 96 
 
 109 
 
 123 
 
 135 
 
 143 
 
 147 
 
 146 
 
 139 
 
 127 
 
 111 
 
 94 
 
 76 
 
 61 
 
 49 
 
 15 
 
 72 
 
 82 
 
 93 
 
 107 
 
 120 
 
 132 
 
 140 
 
 144 
 
 142 
 
 135 
 
 123 
 
 108 
 
 91 
 
 75 
 
 61 
 
 16 
 
 61 
 
 67 
 
 77 
 
 90 
 
 104 
 
 118 
 
 129 
 
 138 
 
 141 
 
 139 
 
 132 
 
 121 
 
 106 
 
 90 
 
 75 
 
 17 
 
 54 
 
 56 
 
 63 
 
 74 
 
 87 
 
 101 
 
 116 
 
 128 
 
 136 
 
 140 
 
 137 
 
 130 
 
 119 
 
 104 
 
 89 
 
 18 
 
 48 
 
 48 
 
 51 
 
 59 
 
 70 
 
 84 
 
 100 
 
 114 
 
 127 
 
 135 
 
 139 
 
 136 
 
 129 
 
 113 
 
 104 
 
 19 
 
 46 
 
 42 
 
 42 
 
 46 
 
 55 
 
 67 
 
 83 
 
 99 
 
 114 
 
 127 
 
 135 
 
 138 
 
 136 
 
 128 
 
 117 
 
 20 
 
 45 
 
 39 
 
 36 
 
 37 
 
 42 
 
 52 
 
 66 
 
 82 
 
 99 
 
 115 
 
 128 
 
 136 
 
 139 
 
 136 
 
 128 
 
 21 
 
 47 
 
 39 
 
 33 
 
 31 
 
 33 
 
 39 
 
 50 
 
 66 
 
 83 
 
 101 
 
 118 
 
 130 
 
 133 
 
 140 
 
 136 
 
 22 
 
 49 
 
 40 
 
 32 
 
 27 
 
 25 
 
 2!) 
 
 37 
 
 50 
 
 67 
 
 86 
 
 104 
 
 121 
 
 133 
 
 140 
 
 141 
 
 23 
 
 51 
 
 43 
 
 34 
 
 27 
 
 22 
 
 21 
 
 26 
 
 36 
 
 51 
 
 70 
 
 89 
 
 108 
 
 125 
 
 136 
 
 142 
 
 24 
 
 54 
 
 47 
 
 37 
 
 28 
 
 21 
 
 18 
 
 19 
 
 26 
 
 37 
 
 54 
 
 73 
 
 94 
 
 113 
 
 129 
 
 140 
 
 25 
 
 56 
 
 49 
 
 41 
 
 32 
 
 23 
 
 17 
 
 15 
 
 18 
 
 26 
 
 40 
 
 58 
 
 78 
 
 99 
 
 118 
 
 133 
 
 26 
 
 57 
 
 53 
 
 45 
 
 37 
 
 27 
 
 19 
 
 14 
 
 14 
 
 18 
 
 29 
 
 44 
 
 63 
 
 84 
 
 105 
 
 123 
 
 27 
 
 57 
 
 55 
 
 49 
 
 42 
 
 33 
 
 24 
 
 17 
 
 13 
 
 14 
 
 20 
 
 32 
 
 49 
 
 63 
 
 90 
 
 110 
 
 23 
 
 57 
 
 56 
 
 52 
 
 46 
 
 39 
 
 30 
 
 22 
 
 15 
 
 13 
 
 15 
 
 23 
 
 37 
 
 54 
 
 74 
 
 95 
 
 29 
 
 57 
 
 56 
 
 55 
 
 51 
 
 45 
 
 37 
 
 28 
 
 20 
 
 15 
 
 14 
 
 18 
 
 27 
 
 41 
 
 59 
 
 80 
 
 30 
 
 56 
 
 57 
 
 56 
 
 54 
 
 50 
 
 44 
 
 36 
 
 27 
 
 20 
 
 16 
 
 16 
 
 21 
 
 31 
 
 46 
 
 64 
 
 31 
 
 56 
 
 57 
 
 57 
 
 57 
 
 55 
 
 50 
 
 43 
 
 35 
 
 27 
 
 21 
 
 17 
 
 18 
 
 24 
 
 35 
 
 50 
 
 32 
 
 56 
 
 56 
 
 58 
 
 59 
 
 58 
 
 56 
 
 51 
 
 44 
 
 36 
 
 28 
 
 22 
 
 19 
 
 21 
 
 27 
 
 39 
 
 33 
 
 58 
 
 58 
 
 58 
 
 60 
 
 61 
 
 61 
 
 58 
 
 52 
 
 45 
 
 37 
 
 29 
 
 23 
 
 21 
 
 23 
 
 30 ' 
 
 34 
 
 62 
 
 60 
 
 59 
 
 61 
 
 63 
 
 64 
 
 64 
 
 60 
 
 54 
 
 46 
 
 37 
 
 30 
 
 24 
 
 22 
 
 24 
 
 35 
 
 67 
 
 63 
 
 62 
 
 6:! 
 
 65 
 
 63 
 
 69 
 
 67 
 
 63 
 
 56 
 
 47 
 
 33 
 
 30 
 
 24 
 
 22 
 
 36 
 
 74 
 
 68 
 
 65 
 
 65 
 
 67 
 
 70 
 
 72 
 
 73 
 
 71 
 
 66 
 
 58 
 
 43 
 
 39 
 
 30 
 
 24 
 
 37 
 
 83 
 
 75 
 
 70 
 
 68 
 
 70 
 
 72 
 
 76 
 
 78 
 
 77 
 
 74 
 
 63 
 
 59 
 
 49 
 
 S3 
 
 28 
 
 38 
 
 91 
 
 83 
 
 77 
 
 73 
 
 73 
 
 75 
 
 78 
 
 82 
 
 83 
 
 82 
 
 77 
 
 70 
 
 59 
 
 48 
 
 36 
 
 39 
 
 100 
 
 91 
 
 84 
 
 80 
 
 78 
 
 79 
 
 81 
 
 85 
 
 87 
 
 88 
 
 85 
 
 80 
 
 70 
 
 59 
 
 46 
 
 40 
 
 108 
 
 100 
 
 93 
 
 87 
 
 84 
 
 83 
 
 85 
 
 88 
 
 91 
 
 93 
 
 92 
 
 88 
 
 81 
 
 70 
 
 57 
 
 41 
 
 114 
 
 108 
 
 102 
 
 95 
 
 91 
 
 89 
 
 89 
 
 91 
 
 94 
 
 97 
 
 97 
 
 96 
 
 90 
 
 81 
 
 63 
 
 42 
 
 118 
 
 115 
 
 110 
 
 104 
 
 99 
 
 95 
 
 94 
 
 95 
 
 97 
 
 100 
 
 102 
 
 102 
 
 98 
 
 91 
 
 80 
 
 43 
 
 120 
 
 120 
 
 117 
 
 112 
 
 107 
 
 102 
 
 99 
 
 99 
 
 100 
 
 102 
 
 105 
 
 106 
 
 104 
 
 99 
 
 90 
 
 44 
 
 117 
 
 122 
 
 122 
 
 119 
 
 115 
 
 110 
 
 106 
 
 104 
 
 104 
 
 105 
 
 107 
 
 109 
 
 109 
 
 106 
 
 !lil 
 
 45 
 
 111 
 
 120 
 
 124 
 
 124 
 
 121 
 
 117 
 
 113 
 
 109 
 
 108 
 
 108 
 
 109 
 
 111 
 
 112 
 
 111 
 
 107 
 
 46 
 
 102 
 
 115 
 
 123 
 
 126 
 
 126 
 
 123 
 
 119 
 
 115 
 
 113 
 
 111 
 
 111 
 
 112 
 
 114 
 
 114 
 
 112 
 
 47 
 
 91 
 
 108 
 
 119 
 
 126 
 
 129 
 
 128 
 
 125 
 
 121 
 
 117 
 
 114 
 
 113 
 
 113 
 
 115 
 
 116 
 
 116 
 
 43 
 
 77 
 
 96 
 
 111 
 
 122 
 
 129 
 
 131 
 
 129 
 
 126 
 
 121 
 
 117 
 
 115 
 
 114 
 
 115 
 
 116 
 
 117 
 
 49 
 
 62 
 
 82 
 
 101 
 
 115 
 
 125 
 
 131 
 
 132 
 
 129 
 
 125 
 
 121 
 
 117 
 
 115 
 
 115 
 
 116 
 
 118 
 
 50 
 
 48 
 
 69 
 
 88 
 
 105 
 
 118 
 
 127 
 
 131 
 
 131 
 
 128 
 
 124 
 
 119 
 
 116 
 
 115 
 
 115 
 
 117 
 
 51 
 
 34 
 
 53 
 
 74 
 
 93 
 
 109 
 
 121 
 
 128 
 
 131 
 
 130 
 
 126 
 
 121 
 
 117 
 
 114 
 
 113 
 
 115 
 
 52 
 
 23 
 
 40 
 
 60 
 
 79 
 
 
 112 
 
 122 
 
 123 
 
 129 
 
 127 
 
 122 
 
 118 
 
 114 
 
 112 
 
 112 
 
 53 
 
 16 
 
 29 
 
 46 
 
 65 
 
 84 
 
 100 
 
 113 
 
 122 
 
 126 
 
 185 
 
 122 
 
 118 
 
 113 
 
 110 
 
 110 
 
 54 
 
 12 
 
 21 
 
 34 
 
 51 
 
 69 
 
 87 
 
 102 
 
 113 
 
 120 
 
 122 
 
 121 
 
 117 
 
 112 
 
 109 
 
 107 
 
 55 
 
 14 
 
 17 
 
 26 
 
 39 
 
 56 
 
 73 
 
 89 
 
 103 
 
 112 
 
 116 
 
 117 
 
 115 
 
 111 
 
 107 
 
 104 
 
 56 
 
 20 
 
 17 
 
 21 
 
 31 
 
 44 
 
 69 
 
 75 
 
 89 
 
 101 
 
 108 
 
 112 
 
 111 
 
 109 
 
 105 
 
 102 
 
 57 
 
 30 
 
 23 
 
 21 
 
 25 
 
 34 
 
 47 
 
 61 
 
 76 
 
 89 
 
 98 
 
 104 
 
 106 
 
 105 
 
 1D2 
 
 9!) 
 
 58 
 
 44 
 
 32 
 
 25 
 
 24 
 
 23 
 
 37 
 
 49 
 
 62 
 
 76 
 
 87 
 
 95 
 
 99 
 
 100 
 
 98 
 
 96 
 
 59 
 
 62 
 
 46 
 
 34 
 
 27 
 
 26 
 
 30 
 
 39 
 
 50 
 
 62 
 
 74 
 
 84 
 
 90 
 
 93 
 
 91 
 
 92 
 
 60 
 
 81 
 
 61 
 
 46 
 
 35 
 
 23 
 
 27 
 
 31 
 
 39 
 
 50 
 
 61 
 
 72 
 
 80 
 
 85 
 
 88 
 
 88 
 
 The perturbations are in units of the eighth decimal place. 
 
TAI1L.K XXXV. 
 
 <;:* 
 
 /' rt nrlint inns f !,,><;. r, />// .lii/n'/i r. 
 
 llri/'Mital Ar^iiiiifiit = 1. 
 
 < ',,n-i. -int :nlilt ,1 - 1 Period of Arfumnt XIII., 60 unit*. 
 
 An 
 
 MM 
 
 120 
 
 I2N 
 
 .1 
 130 
 
 .1 
 111 
 
 ,,, 
 
 A 
 
 100 
 
 .1 
 ION 
 
 170 
 
 1*1 
 
 192 
 
 200 
 
 ,:>, 
 
 210 
 
 l 
 
 .1 
 
 I) 
 
 87 
 
 86 
 
 Hi 
 
 
 
 105 
 
 116 
 
 190 
 
 III 
 
 150 
 
 166 
 
 156 
 
 15 1 
 
 ISO 
 
 193 
 
 1 
 
 
 -_' 
 
 89 
 
 -1 
 
 80 
 
 vt 
 
 
 191 
 
 135 117 
 
 166 
 
 11,1 
 
 160 
 
 152 
 
 130 
 
 2 
 
 78 
 
 7!) 
 
 7H 
 
 BO 
 
 -1 
 
 
 100 
 
 II-.' 
 
 196 
 
 140 
 
 l.vj 
 
 n, i 
 
 103 
 
 Ilil 
 
 169 
 
 3 
 
 73 
 
 75 
 
 75 
 
 77 
 
 7:i 
 
 -1 
 
 09 
 
 103 
 
 116 
 
 130 
 
 ill 
 
 150 
 
 163 
 
 11,5 
 
 Mil 
 
 4 
 
 07 
 
 70 
 
 72 
 
 73 
 
 75 
 
 70 
 
 
 :u 
 
 106 
 
 r." 
 
 134 
 
 1 1- 
 
 160 
 
 165 
 
 105 
 
 5 
 
 60 
 
 05 
 
 (;:i 
 
 71 
 
 7'.' 
 
 71 
 
 7!l 
 
 86 
 
 96 
 
 rae 
 
 193 
 
 137 
 
 150 
 
 100 
 
 105 
 
 (i 
 
 63 
 
 0'! 
 
 05 
 
 i>- 
 
 70 
 
 71 
 
 71 
 
 70 
 
 87 
 
 96 
 
 111 
 
 125 
 
 139 
 
 151 
 
 II, I 
 
 7 
 
 4(i 
 
 51 
 
 
 05 
 
 07 
 
 60 
 
 71 
 
 71 
 
 - i 
 
 -- 
 
 09 
 
 II-.' 
 
 196 
 
 1 I'l 
 
 151 
 
 B 
 
 10 
 
 48 
 
 56 
 
 (,'J 
 
 05 
 
 i,- 
 
 69 
 
 71 
 
 71 
 
 - i 
 
 88 
 
 00 
 
 112 
 
 196 
 
 130 
 
 9 
 
 35 
 
 43 
 
 51 
 
 58 
 
 63 
 
 66 
 
 i,- 
 
 69 
 
 70 
 
 73 
 
 711 
 
 87 
 
 '.'- 
 
 ill 
 
 125 
 
 10 
 
 31 
 
 38 
 
 46 
 
 51 
 
 61 
 
 65 
 
 67 
 
 66 
 
 68 
 
 60 
 
 71 
 
 77 
 
 
 90 
 
 109 
 
 11 
 
 :!n 
 
 35 
 
 43 
 
 M 
 
 58 
 
 63 
 
 66 
 
 07 
 
 66 
 
 66 
 
 66 
 
 
 74 
 
 82 
 
 93 
 
 19 
 
 30 
 
 34 
 
 40 
 
 47 
 
 55 
 
 61 
 
 05 
 
 07 
 
 66 
 
 ti.'i 
 
 03 
 
 63 
 
 68 
 
 70 
 
 79 
 
 13 
 
 34 
 
 34 
 
 38 
 
 45 
 
 52 
 
 50 
 
 1,1 
 
 66 
 
 66 
 
 01 
 
 69 
 
 
 58 
 
 1,1 
 
 65 
 
 14 
 
 41 
 
 38 
 
 39 
 
 43 
 
 50 
 
 57 
 
 02 
 
 06 
 
 66 
 
 05 
 
 i.-.' 
 
 57 
 
 54 
 
 53 
 
 55 
 
 15 
 
 50 
 
 II 
 
 42 
 
 44 
 
 48 
 
 56 
 
 61 
 
 05 
 
 66 
 
 60 
 
 62 
 
 57 
 
 52 
 
 48 
 
 47 
 
 iii 
 
 62 
 
 52 
 
 47 
 
 46 
 
 48 
 
 53 
 
 50 
 
 63 
 
 66 
 
 66 
 
 63 
 
 
 52 
 
 46 
 
 42 
 
 17 
 
 75 
 
 03 
 
 64 
 
 50 
 
 50 
 
 59 
 
 57 
 
 61 
 
 05 
 
 66 
 
 01 
 
 60 
 
 53 
 
 46 
 
 40 
 
 18 
 
 89 
 
 75 
 
 64 
 
 57 
 
 53 
 
 53 
 
 56 
 
 00 
 
 (>:! 
 
 65 
 
 
 61 
 
 55 
 
 47 
 
 40 
 
 19 
 
 103 
 
 Ml 
 
 76 
 
 66 
 
 59 
 
 56 
 
 66 
 
 
 61 
 
 64 
 
 01 
 
 69 
 
 57 
 
 50 
 
 41 
 
 20 
 
 117 
 
 103 
 
 BB 
 
 76 
 
 67 
 
 61 
 
 68 
 
 68 
 
 60 
 
 02 
 
 62 
 
 62 
 
 
 52 
 
 44 
 
 21 
 
 1 -.'- 
 
 116 
 
 102 
 
 88 
 
 76 
 
 67 
 
 61 
 
 5'.) 
 
 50 
 
 01 
 
 01 
 
 69 
 
 60 
 
 55 
 
 47 
 
 99 
 
 137 
 
 127 
 
 115 
 
 101 
 
 87 
 
 75 
 
 07 
 
 61 
 
 59 
 
 
 60 
 
 61 
 
 60 
 
 56 
 
 50 
 
 23 
 
 II-.' 
 
 137 
 
 l-.il i 
 
 113 
 
 99 
 
 85 
 
 74 
 
 66 
 
 6D 
 
 59 
 
 .VI 
 
 69 
 
 59 
 
 57 
 
 53 
 
 24 
 
 144 
 
 143 
 
 136 
 
 194 
 
 110 
 
 96 
 
 83 
 
 7-J 
 
 64 
 
 6!) 
 
 58 
 
 58 
 
 58 
 
 58 
 
 55 
 
 96 
 
 142 
 
 145 
 
 142 
 
 134 
 
 121 
 
 107 
 
 B9 
 
 7!) 
 
 69 
 
 62 
 
 58 
 
 57 
 
 57 
 
 57 
 
 55 
 
 26 
 
 136 
 
 144 
 
 115 
 
 141 
 
 131 
 
 li- 
 
 103 
 
 88 
 
 75 
 
 66 
 
 i,i 
 
 57 
 
 66 
 
 .51 i 
 
 57 
 
 27 
 
 127 
 
 138 
 
 III 
 
 111 
 
 138 
 
 127 
 
 113 
 
 oe 
 
 84 
 
 7'.' 
 
 63 
 
 5- 
 
 56 
 
 56 
 
 66 
 
 98 
 
 114 
 
 130 
 
 Ml) 
 
 144 
 
 142 
 
 134 
 
 122 
 
 KM 
 
 93 
 
 80 
 
 68 
 
 61 
 
 57 
 
 5( i 
 
 56 
 
 29 
 
 100 
 
 118 
 
 132 
 
 140 
 
 142 
 
 1J9 
 
 130 
 
 117 
 
 102 
 
 88 
 
 75 
 
 65 
 
 60 
 
 57 
 
 56 
 
 30 
 
 84 
 
 103 
 
 120 
 
 132 
 
 139 
 
 140 
 
 131 
 
 194 
 
 111 
 
 98 
 
 84 
 
 72 
 
 64 
 
 59 
 
 58 
 
 31 
 
 69 
 
 88 
 
 106 
 
 121 
 
 132 
 
 137 
 
 136 
 
 130 
 
 119 
 
 106 
 
 92 
 
 80 
 
 70 
 
 63 
 
 60 
 
 
 54 
 
 72 
 
 90 
 
 J07 
 
 122 
 
 131 
 
 134 
 
 139 
 
 124 
 
 114 
 
 101 
 
 89 
 
 77 
 
 O'.l 
 
 64 
 
 33 
 
 41 
 
 57 
 
 71 
 
 92 
 
 108 
 
 121 
 
 128 
 
 130 
 
 127 
 
 120 
 
 109 
 
 97 
 
 86 
 
 76 
 
 69 
 
 34 
 
 
 43 
 
 59 
 
 75 
 
 , !>3 
 
 108 
 
 119 
 
 126 
 
 127 
 
 123 
 
 110 
 
 106 
 
 Hi 
 
 BB 
 
 76 
 
 35 
 
 25 
 
 32 
 
 41 59 
 
 86 
 
 92 
 
 107 
 
 117 
 
 123 
 
 123 
 
 120 
 
 113 
 
 103 
 
 93 
 
 84 
 
 30 
 
 22 
 
 24 
 
 39 
 
 44 
 
 59 
 
 76 
 
 92 
 
 105 
 
 115 
 
 120 
 
 Ml 
 
 117 
 
 110 
 
 102 
 
 93 
 
 37 
 
 22 
 
 20 
 
 24 
 
 31 
 
 44 
 
 59 
 
 75 
 
 !U 
 
 104 
 
 113 
 
 119 
 
 119 
 
 116 
 
 111! 
 
 102 
 
 38 
 
 26 
 
 20 
 
 18 
 
 22 
 
 30 
 
 43 
 
 58 
 
 75 
 
 90 
 
 103 
 
 113 
 
 118 
 
 118 
 
 116 
 
 110 
 
 39 
 
 33 
 
 23 
 
 17 
 
 16 
 
 20 
 
 29 
 
 42 
 
 58 
 
 75 
 
 90 
 
 104 
 
 113 
 
 118 
 
 119 
 
 116 
 
 40 
 
 43 
 
 30 
 
 20 
 
 14 
 
 13 
 
 17 
 
 27 
 
 42 
 
 58 
 
 75 
 
 91 
 
 105 
 
 114 
 
 119 
 
 120 
 
 41 
 
 54 
 
 39 
 
 26 
 
 15 
 
 10 
 
 10 
 
 16 
 
 27 
 
 42 
 
 59 
 
 77 
 
 03 
 
 106 
 
 116 
 
 121 
 
 42 
 
 66 
 
 50 
 
 86 
 
 21 
 
 11 
 
 6 
 
 7 
 
 15 
 
 27 
 
 43 
 
 61 
 
 80 
 
 96 
 
 no 
 
 119 
 
 43 
 
 78 
 
 62 
 
 46 
 
 30 
 
 Hi 
 
 7 
 
 3 
 
 6 
 
 15 
 
 28 
 
 45 
 
 01 
 
 83 
 
 100 
 
 113 
 
 44 
 
 
 75 
 
 59 
 
 41 
 
 25 
 
 12 
 
 1 
 
 1 
 
 6 
 
 16 
 
 31 
 
 49 
 
 69 
 
 88 
 
 mi 
 
 45 
 
 99 
 
 87 
 
 72 
 
 54 
 
 37 
 
 21 
 
 9 
 
 2 
 
 1 
 
 6 
 
 18 
 
 34 
 
 53 
 
 74 
 
 93 
 
 46 
 
 107 
 
 97 
 
 84 
 
 68 
 
 50 
 
 33 
 
 17 
 
 6 
 
 1 
 
 1 
 
 8 
 
 21 
 
 99 
 
 59 
 
 7:1 
 
 47 
 
 113 
 
 106 
 
 
 82 
 
 65 
 
 47 
 
 2!) 
 
 18 
 
 5 
 
 
 
 3 
 
 12 
 
 20 
 
 44 
 
 65 
 
 1- 
 
 117 
 
 113 
 
 100 
 
 94 
 
 79 
 
 62 
 
 44 
 
 27 
 
 14 
 
 5 
 
 9 
 
 6 
 
 16 
 
 31 
 
 50 
 
 49 
 
 118 
 
 117 
 
 113 
 
 105 
 
 93 
 
 78 
 
 60 
 
 42 
 
 26 
 
 13 
 
 6 
 
 4 
 
 9 
 
 21 
 
 37 
 
 50 
 
 118 
 
 120 
 
 11!) 
 
 114 
 
 105 
 
 go 
 
 77 
 
 59 
 
 42 
 
 26 
 
 14 
 
 8 
 
 8 
 
 14 
 
 27 
 
 51 
 
 117 
 
 120 
 
 121 
 
 120 
 
 115 
 
 106 
 
 93 
 
 76 
 
 .V.I 
 
 42 
 
 26 
 
 16 
 
 11 
 
 I-,' 
 
 1!) 
 
 5',' 
 
 114 
 
 118 
 
 121 
 
 123 
 
 122 
 
 116 
 
 107 
 
 93 
 
 77 
 
 59 
 
 41 
 
 28 
 
 18 
 
 M 
 
 16 
 
 63 
 
 111 
 
 115 
 
 119 
 
 123 
 
 196 
 
 124 
 
 119 
 
 109 
 
 115 
 
 78 
 
 61 
 
 44 
 
 30 
 
 21 
 
 18 
 
 54 
 
 108 
 
 111 
 
 116 
 
 122 
 
 126 
 
 129 
 
 128 
 
 122 
 
 111 
 
 H7 
 
 80 
 
 62 
 
 45 
 
 32 
 
 24 
 
 55 
 
 104 
 
 107 
 
 112 
 
 118 
 
 125 
 
 130 
 
 133 
 
 131 
 
 125 
 
 114 
 
 9!) 
 
 82 
 
 64 
 
 47 
 
 34 
 
 66 
 
 100 
 
 102 
 
 106 
 
 113 
 
 121 
 
 129 
 
 135 
 
 137 
 
 136 
 
 129 
 
 117 
 
 101 
 
 83 
 
 65 
 
 49 
 
 57 
 
 97 
 
 98 
 
 101 
 
 107 
 
 116 
 
 125 
 
 134 
 
 140 
 
 113 
 
 140 
 
 132 
 
 119 
 
 103 
 
 84 
 
 66 
 
 58 
 
 94 
 
 94 
 
 
 101 
 
 109 
 
 119 
 
 130 
 
 139 
 
 14(i 
 
 148 
 
 III 
 
 136 
 
 191 
 
 lot 
 
 88 
 
 59 
 
 90 
 
 90 
 
 91 
 
 96 
 
 102 
 
 112 
 
 194 
 
 136 
 
 1 Hi 
 
 151 
 
 159 
 
 148 
 
 138 
 
 1 -.'-' 
 
 mi 
 
 60 
 
 87 
 
 86 
 
 86 
 
 89 
 
 96 
 
 105 
 
 no 
 
 199 
 
 III 
 
 150 
 
 156 
 
 156 
 
 150 
 
 139 
 
 193 
 
 When 224* .7 in subtracted from Arg. I., add 3.11 to Arg. XIII. 
 
TABLE XXXVI. 
 
 Perturbations of Log. r, by Saturn. 
 
 Horizontal Argument = I. 
 
 Constant added 25. Period of Argument I., 224< 1 .7. 
 
 Aif. 
 XIV. 
 
 <l 
 O 
 
 ,i 
 
 
 d' 
 
 16 
 
 d 
 
 24 
 
 d 
 
 32 
 
 d 
 
 40 
 
 d 
 
 48 
 
 d 
 
 56 
 
 d 
 
 64 
 
 d 
 72 
 
 d 
 
 SO 
 
 d 
 
 8 
 
 d 
 
 96 
 
 d 
 
 101 
 
 d 
 
 112 
 
 
 
 13 
 
 8 
 
 4 
 
 1 
 
 
 
 
 
 3 
 
 6 
 
 11 
 
 17 
 
 22 
 
 27 
 
 31 
 
 35 
 
 37 
 
 1 
 
 18 
 
 13 
 
 8 
 
 4 
 
 1 
 
 
 
 1 
 
 3 
 
 7 
 
 12 
 
 18 
 
 23 
 
 28 
 
 32 
 
 35 
 
 2 
 
 23 
 
 18 
 
 12 
 
 7 
 
 3 
 
 1 
 
 
 
 1 
 
 4 
 
 9 
 
 13 
 
 18 
 
 24 
 
 28 
 
 32 
 
 3 
 
 28 
 
 22 
 
 17 
 
 11 
 
 7 
 
 3 
 
 1 
 
 1 
 
 2 
 
 5 
 
 9 
 
 14 
 
 19 
 
 24 
 
 29 
 
 4 
 
 32 
 
 27 
 
 22 
 
 10 
 
 11 
 
 6 
 
 3 
 
 1 
 
 1 
 
 3 
 
 6 
 
 10 
 
 15 
 
 20 
 
 25 
 
 5 
 
 35 
 
 31 
 
 20 
 
 21 
 
 15 
 
 10 
 
 6 
 
 3 
 
 1 
 
 2 
 
 4 
 
 7 
 
 12 
 
 10 
 
 21 
 
 6 
 
 37 
 
 34 
 
 30 
 
 25 
 
 20 
 
 15 
 
 10 
 
 
 
 3 
 
 2 
 
 2 
 
 5 
 
 8 
 
 13 
 
 18 
 
 7 
 
 39 
 
 36 
 
 33 
 
 29 
 
 24 
 
 19 
 
 14 
 
 9 
 
 5 
 
 3 
 
 2 
 
 3 
 
 6 
 
 9 
 
 14 
 
 8 
 
 39 
 
 38 
 
 3G 
 
 32 
 
 28 
 
 23 
 
 18 
 
 13 
 
 8 
 
 5 
 
 3 
 
 3 
 
 4 
 
 7 
 
 11 
 
 9 
 
 39 
 
 39 
 
 37 
 
 35 
 
 32 
 
 27 
 
 22 
 
 17 
 
 12 
 
 8 
 
 5 
 
 3 
 
 3 
 
 5 
 
 8 
 
 10 
 
 39 
 
 39 
 
 38 
 
 30 
 
 34 
 
 32 
 
 26 
 
 21 
 
 16 
 
 11 
 
 8 
 
 5 
 
 4 
 
 4 
 
 G 
 
 11 
 
 38 
 
 38 
 
 38 
 
 37 
 
 30 
 
 33 
 
 29 
 
 25 
 
 20 
 
 15 
 
 11 
 
 7 
 
 5 
 
 4 
 
 5 
 
 12 
 
 37 
 
 38 
 
 38 
 
 38 
 
 36 
 
 35 
 
 32 
 
 28 
 
 24 
 
 19 
 
 14 
 
 10 
 
 7 
 
 5 
 
 4 
 
 13 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 36 
 
 34 
 
 31 
 
 27 
 
 23 
 
 18 
 
 13 
 
 9 
 
 
 
 5 
 
 14 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 36 
 
 35 
 
 33 
 
 30 
 
 26 
 
 21 
 
 17 
 
 12 
 
 8 
 
 6 
 
 15 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 30 
 
 34 
 
 32 
 
 29 
 
 25 
 
 20 
 
 15 
 
 11 
 
 8 
 
 1C 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 30 
 
 35 
 
 33 
 
 31 
 
 27 
 
 23 
 
 19 
 
 14 
 
 10 
 
 17 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 37 
 
 36 
 
 35 
 
 33 
 
 30 
 
 26 
 
 22 
 
 17 
 
 13 
 
 18 
 
 37 
 
 38 
 
 38 
 
 37 
 
 37 
 
 37 
 
 37 
 
 36 
 
 35 
 
 34 
 
 32 
 
 29 
 
 25 
 
 20 
 
 10 
 
 19 
 
 37 
 
 38 
 
 38 
 
 38 
 
 38 
 
 37 
 
 37 
 
 37 
 
 36 
 
 35 
 
 33 
 
 31 
 
 . 28 
 
 24 
 
 19 
 
 20 
 
 3G 
 
 37 
 
 38 
 
 38 
 
 38 
 
 38 
 
 38 
 
 37 
 
 37 
 
 36 
 
 35 
 
 33 
 
 30 
 
 27 
 
 22 
 
 21 
 
 34 
 
 30 
 
 38 
 
 39 
 
 39 
 
 39 
 
 38 
 
 38 
 
 37 
 
 37 
 
 3G 
 
 34 
 
 32 
 
 29 
 
 25 
 
 2'j 
 
 31 
 
 35 
 
 37 
 
 39 
 
 39 
 
 39 
 
 39 
 
 38 
 
 38 
 
 37 
 
 37 
 
 30 
 
 34 
 
 32 
 
 28 
 
 23 
 
 28 
 
 32 
 
 30 
 
 38 
 
 39 
 
 40 
 
 40 
 
 39 
 
 39 
 
 38 
 
 38 
 
 37 
 
 30 
 
 34 
 
 31 
 
 24 
 
 24 
 
 29 
 
 33 
 
 30 
 
 39 
 
 40 
 
 40 
 
 40 
 
 40 
 
 39 
 
 39 
 
 38 
 
 37 
 
 35 
 
 33 
 
 25 
 
 20 
 
 25 
 
 30 
 
 34 
 
 37 
 
 39 
 
 40 
 
 40 
 
 40 
 
 40 
 
 40 
 
 39 
 
 38 
 
 37 
 
 35 
 
 20 
 
 15 
 
 20 
 
 2G 
 
 31 
 
 35 
 
 38 
 
 39 
 
 40 
 
 41 
 
 41 
 
 40 
 
 40 
 
 39 
 
 38 
 
 37 
 
 27 
 
 10 
 
 10 
 
 21 
 
 2G 
 
 31 
 
 35 
 
 38 
 
 40 
 
 if 
 
 41 
 
 41 
 
 41 
 
 40 
 
 40 
 
 39 
 
 28 
 
 6 
 
 11 
 
 10 
 
 22 
 
 27 
 
 32 
 
 30 
 
 39 
 
 40 
 
 41 
 
 41 
 
 41 
 
 41 
 
 40 
 
 40 
 
 29 
 
 3 
 
 7 
 
 12 
 
 17 
 
 23 
 
 28 
 
 33 
 
 3G 
 
 39 
 
 40 
 
 41 
 
 42 
 
 41 
 
 41 
 
 41 
 
 30 
 
 1 
 
 3 
 
 7 
 
 12 
 
 18 
 
 23 
 
 29 
 
 33 
 
 37 
 
 39 
 
 41 
 
 41 
 
 42 
 
 42 
 
 41 
 
 31 
 
 
 
 1 
 
 3 
 
 8 
 
 13 
 
 18 
 
 24 
 
 29 
 
 34 
 
 37 
 
 39 
 
 41 
 
 41 
 
 42 
 
 42 
 
 32 
 
 
 
 
 
 1 
 
 4 
 
 8 
 
 13 
 
 19 
 
 25 
 
 30 
 
 34 
 
 37 
 
 39 
 
 41 
 
 41 
 
 42 
 
 33 
 
 2 
 
 
 
 
 
 1 
 
 4 
 
 9 
 
 14 
 
 20 
 
 25 
 
 30 
 
 34 
 
 37 
 
 39 
 
 41 
 
 42 
 
 34 
 
 5 
 
 1 
 
 
 
 
 
 2 
 
 5 
 
 10 
 
 15 
 
 21 
 
 20 
 
 31 
 
 34 
 
 37 
 
 39 
 
 41 
 
 35 
 
 9 
 
 4 
 
 1 
 
 
 
 
 
 2 
 
 6 
 
 10 
 
 16 
 
 21 
 
 27 
 
 31 
 
 35 
 
 37 
 
 39 
 
 3G 
 
 13 
 
 8 
 
 4 
 
 1 
 
 
 
 
 
 3 
 
 
 
 11 
 
 17 
 
 22 
 
 27 
 
 31 
 
 35 
 
 37 
 
 The perturbations are in units of tlie eighth decimal place. 
 
TABLE XX XVI. 
 
 PwCMrftotfoM <>t Lna. r, lnj Saturn. 
 
 Iliiri/unt.-i! Ar;;il ill = 1 
 
 Cmi-i.-uit a.l.lrd ,'.">. IVriuil nf Argument XIV., 'M units. 
 
 XIV 
 
 ivto 
 
 1 
 I4N 
 
 136 
 
 lit 
 
 1 >. 
 
 IOO 
 
 d 
 Hi* 
 
 I7<i 
 
 d 
 1*11 
 
 102 
 
 200 
 
 SON 
 
 d 
 -Hi 
 
 d 
 tf-.il 
 
 -::-> 
 
 
 
 
 
 40 
 
 11 
 
 41 
 
 
 
 4-> 
 
 41 
 
 41 
 
 :!'. 
 
 :I7 
 
 93 
 
 28 
 
 23 
 
 17 
 
 II 
 
 1 
 
 SI 
 
 
 40 
 
 II 
 
 II 
 
 M 
 
 a 
 
 II 
 
 40 
 
 3B 
 
 36 
 
 n 
 
 
 H 
 
 17 
 
 2 
 
 35 
 
 37 
 
 
 
 40 
 
 n 
 
 41 
 
 41 
 
 41 
 
 11 
 
 40 
 
 38 
 
 36 
 
 91 
 
 27 
 
 n 
 
 3 
 
 3d 
 
 :!.-, 
 
 :!7 
 
 90 
 
 :!'.i 
 
 40 
 
 41 
 
 41 
 
 41 
 
 41 
 
 40 
 
 99 
 
 35 
 
 31 
 
 26 
 
 4 
 
 29 
 
 33 
 
 35 
 
 
 
 
 
 
 40 
 
 40 
 
 41 
 
 41 
 
 40 
 
 39 
 
 37 
 
 34 
 
 31 
 
 :. 
 
 ,>fi 
 
 30 
 
 33 
 
 :r, 
 
 :!7 
 
 38 
 
 
 40 
 
 M 
 
 40 
 
 40 
 
 40 
 
 39 
 
 37 
 
 34 
 
 (i 
 
 a 
 
 97 
 
 n 
 
 n 
 
 36 
 
 :i7 
 
 38 
 
 n 
 
 18 
 
 40 
 
 40 
 
 40 
 
 40 
 
 38 
 
 96 
 
 7 
 
 in 
 
 a 
 
 28 
 
 n 
 
 M 
 
 86 
 
 97 
 
 
 9B 
 
 n 
 
 39 
 
 40 
 
 40 
 
 88 
 
 M 
 
 8 
 
 i:, 
 
 20 
 
 
 
 .*.) 
 
 
 
 31 
 
 36 
 
 37 
 
 
 
 98 
 
 39 
 
 39 
 
 89 
 
 3D 
 
 9 
 
 tt 
 
 17 
 
 It 
 
 26 
 
 
 
 n 
 
 M 
 
 36 
 
 97 
 
 97 
 
 38 
 
 38 
 
 98 
 
 38 
 
 30 
 
 10 
 
 !t 
 
 13 
 
 18 
 
 ti 
 
 .'7 
 
 u 
 
 33 
 
 35 
 
 36 
 
 37 
 
 37 
 
 37 
 
 ae 
 
 :ts 
 
 36 
 
 11 
 
 7 
 
 10 
 
 16 
 
 19 
 
 24 
 
 IB 
 
 :ii 
 
 M 
 
 35 
 
 M 
 
 37 
 
 91 
 
 37 
 
 38 
 
 38 
 
 M 
 
 5 
 
 8 
 
 12 
 
 16 
 
 21 
 
 
 
 29 
 
 
 
 M 
 
 36 
 
 36 
 
 37 
 
 37 
 
 :(7 
 
 37 
 
 13 
 
 I 
 
 G 
 
 9 
 
 13 
 
 18 
 
 ,'-> 
 
 
 
 30 
 
 99 
 
 98 
 
 M 
 
 36 
 
 37 
 
 37 
 
 97 
 
 11 
 
 4 
 
 5 
 
 7 
 
 10 
 
 14 
 
 19 
 
 23 
 
 28 
 
 31 
 
 34 
 
 35 
 
 36 
 
 37 
 
 37 
 
 37 
 
 15 
 
 5 
 
 4 
 
 f> 
 
 8 
 
 11 
 
 16 
 
 20 
 
 -T. 
 
 29 
 
 :;.' 
 
 34 
 
 3(i 
 
 37 
 
 37 
 
 :t? 
 
 1(1 
 
 ~ 7 
 
 B 
 
 4 
 
 I) 
 
 9 
 
 12 
 
 17 
 
 .'1 
 
 M 
 
 30 
 
 93 
 
 35 
 
 37 
 
 91 
 
 :<? 
 
 17 
 
 ! 
 
 (i 
 
 4 
 
 1 
 
 6 
 
 1 
 
 13 
 
 18 
 
 23 
 
 27 
 
 :ti 
 
 34 
 
 36 
 
 37 
 
 37 
 
 18 
 
 12 
 
 8 
 
 5 
 
 4 
 
 5 
 
 7 
 
 10 
 
 14 
 
 19 
 
 24 
 
 28 
 
 32 
 
 35 
 
 37 
 
 38 
 
 1!) 
 
 15 
 
 10 . 
 
 7 
 
 5 
 
 4 
 
 5 
 
 7 
 
 11 
 
 15 
 
 20 
 
 25 
 
 30 
 
 33 
 
 3G 
 
 37 
 
 20 
 
 18 
 
 n 
 
 9 
 
 6 
 
 4 
 
 4 
 
 5 
 
 8 
 
 12 
 
 16 
 
 22 
 
 26 
 
 31 
 
 34 
 
 36 
 
 21 
 
 21 
 
 16 
 
 12 
 
 8 
 
 5 
 
 3 
 
 3 
 
 5 
 
 8 
 
 12 
 
 17 
 
 23 
 
 28 
 
 32 
 
 86 
 
 22 
 
 24 
 
 20 
 
 15 
 
 10 
 
 7 
 
 4 
 
 3 
 
 3 
 
 5 
 
 9 
 
 13 
 
 18 
 
 M 
 
 28 
 
 33 
 
 II 
 
 27 
 
 23 
 
 19 
 
 14 
 
 9 
 
 G 
 
 :! 
 
 2 
 
 3 
 
 5 
 
 9 
 
 14 
 
 M 
 
 
 
 29 
 
 J4 
 
 30 
 
 27 
 
 22 
 
 17 
 
 12 
 
 8 
 
 5 
 
 2 
 
 2 
 
 3 
 
 6 
 
 10 
 
 15 
 
 20 
 
 26 
 
 II 
 
 33 
 
 30 
 
 26 
 
 21 
 
 16 
 
 11 
 
 7 
 
 4 
 
 2 
 
 1 
 
 3 
 
 6 
 
 10 
 
 16 
 
 21 
 
 26 
 
 :c> 
 
 33 
 
 29 
 
 25 
 
 20 
 
 1") 
 
 10 
 
 6 
 
 3 
 
 1 
 
 1 
 
 3 
 
 6 
 
 11 
 
 16 
 
 27 
 
 37 
 
 :!.-> 
 
 Si 
 
 89 
 
 24 
 
 19 
 
 14 
 
 9 
 
 1 
 
 2 
 
 1 
 
 1 
 
 3 
 
 7 
 
 U 
 
 28 
 
 39 
 
 37 
 
 35 
 
 32 
 
 28 
 
 23 
 
 18 
 
 13 
 
 8 
 
 4 
 
 I 
 
 
 
 1 
 
 3 
 
 1 
 
 29 
 
 40 
 
 39 
 
 37 
 
 35 
 
 32 
 
 27 
 
 23 
 
 17 
 
 12 
 
 7 
 
 3 
 
 1 
 
 
 
 1 
 
 4 
 
 30 
 
 41 
 
 40 
 
 N 
 
 37 
 
 3T, 
 
 31 
 
 27 
 
 22 
 
 16 
 
 11 
 
 G 
 
 2 
 
 
 
 
 
 1 
 
 31 
 
 42 
 
 41 
 
 40 
 
 39 
 
 37 
 
 35 
 
 31 
 
 36 
 
 21 
 
 16 
 
 10 
 
 5 
 
 2 
 
 
 
 
 
 32 
 
 42 
 
 42 
 
 41 
 
 41 
 
 39 
 
 37 
 
 34 
 
 30 
 
 26 
 
 20 
 
 15 
 
 9 
 
 5 
 
 1 
 
 
 
 ft 
 
 42 
 
 42 
 
 1-' 
 
 41 
 
 41 
 
 H 
 
 n 
 
 34 
 
 30 
 
 A"> 
 
 20 
 
 14 
 
 !) 
 
 4 
 
 1 
 
 34 
 
 41 
 
 42 
 
 
 
 42 
 
 41 
 
 41 
 
 39 
 
 37 
 
 34 
 
 30 
 
 24 
 
 19 
 
 13 
 
 8 
 
 4 
 
 35 
 
 40 
 
 41 
 
 42 
 
 42 
 
 42 
 
 41 
 
 41 
 
 39 
 
 37 
 
 33 
 
 29 
 
 24 
 
 18 
 
 13 
 
 7 
 
 36 
 
 39 
 
 40 
 
 41 
 
 41 
 
 42 
 
 42 
 
 41 
 
 41 
 
 39 
 
 37 
 
 33 
 
 28 
 
 23 
 
 17 
 
 12 
 
 When 224- 1 .? i nubtracted from Arg. I. add 0.8 to Arg. XIV. 
 
TABL.E XXXVII. 
 
 Perturbations of the Latitude, by the Earth. 
 
 Horizontal Argument = 1. 
 
 Constant added 0".6->. Period of Argument I., 224-1.7. 
 
 Arg. 
 XI. 
 
 A 
 
 
 
 rl 
 
 8 
 
 rt 
 
 16 
 
 24 
 
 ii 
 32 
 
 ,i 
 40 
 
 a 
 48 
 
 d 
 
 56 
 
 d 
 
 61 
 
 d 
 
 72 
 
 d 
 
 8O 
 
 d 
 
 88 
 
 d 
 
 96 
 
 d 
 
 101 
 
 d 
 
 112 
 
 
 
 48 
 
 43 
 
 39 
 
 36 
 
 34 
 
 35 
 
 37 
 
 41 
 
 45 
 
 51 
 
 58 
 
 65 
 
 71 
 
 77 
 
 81 
 
 2 
 
 .V, 
 
 48 
 
 42 
 
 38 
 
 35 
 
 34 
 
 34 
 
 36 
 
 40 
 
 45 
 
 50 
 
 57 
 
 64 
 
 70 
 
 75 
 
 4 
 
 62 
 
 55 
 
 48 
 
 42 
 
 38 
 
 34 
 
 33 
 
 34 
 
 36 
 
 39 
 
 44 
 
 50 
 
 56 
 
 62 
 
 68 
 
 6 
 
 70 
 
 62 
 
 55 
 
 48 
 
 43 
 
 38 
 
 3.-> 
 
 34 
 
 34 
 
 36 
 
 39 
 
 44 
 
 49 
 
 55 
 
 61 
 
 8 
 
 78 
 
 70 
 
 63 
 
 55 
 
 49 
 
 43 
 
 38 
 
 36 
 
 34 
 
 34 
 
 36 
 
 40 
 
 44 
 
 49 
 
 54 
 
 10 
 
 84 
 
 77 
 
 70 
 
 62 
 
 55 
 
 4!l 
 
 43 
 
 39 
 
 36 
 
 35 
 
 35 
 
 37 
 
 40 
 
 44 
 
 48 
 
 12 
 
 89 
 
 83 
 
 77 
 
 69 
 
 62 
 
 55 
 
 49 
 
 44 
 
 40 
 
 37 
 
 36 
 
 36 
 
 38 
 
 40 
 
 43 
 
 14 
 
 94 
 
 89 
 
 83 
 
 76 
 
 69 
 
 62 
 
 55 
 
 49 
 
 44 
 
 40 
 
 37 
 
 36 
 
 37 
 
 38 
 
 40 
 
 16 
 
 97 
 
 93 
 
 88 
 
 82 
 
 76 
 
 69 
 
 62 
 
 55 
 
 40 
 
 44 
 
 40 
 
 38 
 
 37 
 
 36 
 
 37 
 
 18 
 
 98 
 
 96 
 
 1(3 
 
 88 
 
 82 
 
 76 
 
 68 
 
 62 
 
 55 
 
 49 
 
 44 
 
 41 
 
 38 
 
 36 
 
 36 
 
 20 
 
 98 
 
 97 
 
 96 
 
 92 
 
 87 
 
 82 
 
 75 
 
 69 
 
 62 
 
 G6 
 
 50 
 
 45 
 
 41 
 
 38 
 
 36 
 
 22 
 
 96 
 
 97 
 
 97 
 
 95 
 
 92 
 
 88 
 
 82 
 
 76 
 
 69 
 
 63 
 
 56 
 
 51 
 
 45 
 
 41 
 
 38 
 
 24 
 
 92 
 
 95 
 
 96 
 
 96 
 
 95 
 
 92 
 
 88 
 
 83 
 
 77 
 
 70 
 
 64 
 
 58 
 
 51 
 
 46 
 
 41 
 
 26 
 
 86 
 
 90 
 
 93 
 
 94 
 
 95 
 
 94 
 
 92 
 
 88 
 
 84 
 
 78 
 
 72 
 
 66 
 
 59 
 
 53 
 
 47 
 
 28 
 
 78 
 
 82 
 
 87 
 
 90 
 
 92 
 
 94 
 
 93 
 
 92 
 
 89 
 
 85 
 
 80 
 
 74 
 
 68 
 
 61 
 
 55 
 
 30 
 
 69 
 
 73 
 
 78 
 
 83 
 
 87 
 
 90 
 
 91 
 
 92 
 
 91 
 
 89 
 
 86 
 
 81 
 
 76 
 
 70 
 
 64 
 
 32 
 
 60 
 
 64 
 
 69 
 
 73 
 
 78 
 
 83 
 
 87 
 
 89 
 
 91 
 
 91 
 
 89 
 
 87 
 
 83 
 
 77 
 
 73 
 
 34 
 
 52 
 
 55 
 
 59 
 
 63 
 
 68 
 
 74 
 
 79 
 
 83 
 
 87 
 
 89 
 
 90 
 
 90 
 
 88 
 
 84 
 
 80 
 
 36 
 
 47 
 
 47 
 
 50 
 
 53 
 
 58 
 
 64 
 
 69 
 
 75 
 
 80 
 
 84 
 
 87 
 
 89 
 
 90 
 
 89 
 
 86 
 
 38 
 
 44 
 
 43 
 
 43 
 
 45 
 
 48 
 
 53 
 
 59 
 
 65 
 
 71 
 
 77 
 
 81 
 
 85 
 
 88 
 
 90 
 
 89 
 
 40 
 
 4r> 
 
 41 
 
 :i!) 
 
 38 
 
 40 
 
 43 
 
 48 
 
 54 
 
 61 
 
 67 
 
 73 
 
 79 
 
 84 
 
 88 
 
 90 
 
 42 
 
 4S 
 
 41 
 
 37 
 
 34 
 
 34 
 
 35 
 
 39 
 
 44 
 
 51 
 
 57 
 
 64 
 
 71 
 
 78 
 
 84 
 
 88 
 
 44 
 
 W 
 
 44 
 
 38 
 
 33 
 
 30 
 
 30 
 
 32 
 
 35 
 
 41 
 
 47 
 
 55 
 
 62 
 
 70 
 
 77 
 
 83 
 
 46 
 
 59 
 
 49 
 
 41 
 
 34 
 
 29 
 
 26 
 
 26 
 
 28 
 
 32 
 
 38 
 
 45 
 
 53 
 
 61 
 
 70 
 
 77 
 
 48 
 
 67 
 
 55 
 
 45 
 
 36 
 
 29 
 
 24 
 
 22 
 
 22 
 
 25 
 
 30 
 
 36 
 
 44 
 
 52 
 
 61 
 
 70 
 
 50 
 
 75 
 
 63 
 
 51 
 
 41 
 
 32 
 
 y.-> 
 
 21 
 
 18 
 
 19 
 
 22 
 
 27 
 
 35 
 
 43 
 
 52 
 
 61 
 
 52 
 
 83 
 
 71 
 
 59 
 
 47 
 
 36 
 
 27 
 
 21 
 
 17 
 
 16 
 
 17 
 
 20 
 
 26 
 
 34 
 
 42 
 
 52 
 
 54 
 
 92 
 
 80 
 
 67 
 
 55 
 
 43 
 
 32 
 
 24 
 
 18 
 
 14 
 
 13 
 
 15 
 
 19 
 
 25 
 
 33 
 
 42 
 
 56 
 
 100 
 
 88 
 
 76 
 
 63 
 
 50 
 
 39 
 
 29 
 
 21 
 
 15 
 
 12 
 
 12 
 
 14 
 
 19 
 
 25 
 
 33 
 
 58 
 
 106 
 
 96 
 
 84 
 
 72 
 
 59 
 
 47 
 
 36 
 
 27 
 
 19 
 
 14 
 
 12 
 
 12 
 
 15 
 
 19 
 
 26 
 
 60 
 
 111 
 
 102 
 
 92 
 
 81 
 
 68 
 
 56 
 
 44 
 
 34 
 
 26 
 
 19 
 
 15 
 
 13 
 
 13 
 
 16 
 
 20 
 
 62 
 
 112 
 
 106 
 
 97 
 
 87 
 
 76 
 
 65 
 
 53 
 
 43 
 
 34 
 
 26 
 
 20 
 
 16 
 
 15 
 
 15 
 
 18 
 
 64 
 
 111 
 
 107 
 
 100 
 
 92 
 
 82 
 
 72 
 
 62 
 
 52 
 
 42 
 
 35 
 
 28 
 
 23 
 
 19 
 
 18 
 
 18 
 
 66 
 
 107 
 
 104 
 
 100 
 
 94 
 
 86 
 
 77 
 
 68 
 
 60 
 
 51 
 
 43 
 
 36 
 
 30 
 
 26 
 
 24 
 
 22 
 
 68 
 
 100 
 
 100 
 
 97 
 
 93 
 
 87 
 
 80 
 
 73 
 
 65 
 
 58 
 
 51 
 
 45 
 
 39 
 
 34 
 
 32 
 
 28 
 
 71) 
 
 93 
 
 93 
 
 92 
 
 89 
 
 85 
 
 80 
 
 75 
 
 69 
 
 63 
 
 57 
 
 52 
 
 47 
 
 42 
 
 39 
 
 35 
 
 72 
 
 84 
 
 86 
 
 86 
 
 84 
 
 82 
 
 79 
 
 75 
 
 70 
 
 66 
 
 62 
 
 58 
 
 54 
 
 50 
 
 46 
 
 43 
 
 74 
 
 76 
 
 78 
 
 7il 
 
 79 
 
 77 
 
 75 
 
 73 
 
 70 
 
 67 
 
 64 
 
 62 
 
 59 
 
 56 
 
 53 
 
 50 
 
 76 
 
 67 
 
 70 
 
 71 
 
 72 
 
 72 
 
 71 
 
 69 
 
 68 
 
 66 
 
 65 
 
 64 
 
 62 
 
 61 
 
 59 
 
 57 
 
 78 
 
 58 
 
 62 
 
 64 
 
 66 
 
 66 
 
 66 
 
 65 
 
 65 
 
 64 
 
 65 
 
 65 
 
 64 
 
 63 
 
 63 
 
 62 
 
 80 
 
 50 
 
 54 
 
 56 
 
 59 
 
 60 
 
 61 
 
 61 
 
 61 
 
 62 
 
 63 
 
 64 
 
 65 
 
 66 
 
 67 
 
 67 
 
 82 
 
 41 
 
 45 
 
 48 
 
 51 
 
 53 
 
 55 
 
 55 
 
 57 
 
 58 
 
 60 
 
 63 
 
 65 
 
 68 
 
 69 
 
 71 
 
 84 
 
 32 
 
 36 
 
 40 
 
 43 
 
 46 
 
 48 
 
 49 
 
 51 
 
 54 
 
 57 
 
 60 
 
 64 
 
 67 
 
 71 
 
 73 
 
 86 
 
 23 
 
 28 
 
 32 
 
 35 
 
 38 
 
 40 
 
 42 
 
 45 
 
 48 
 
 52 
 
 56 
 
 61 
 
 66 
 
 70 
 
 75 
 
 88 
 
 16 
 
 20 
 
 24 
 
 28 
 
 30 
 
 33 
 
 35 
 
 38 
 
 41 
 
 45 
 
 50 
 
 56 
 
 62 
 
 67 
 
 74 
 
 00 
 
 11 
 
 15 
 
 18 
 
 21 
 
 23 
 
 26 
 
 28 
 
 30 
 
 34 
 
 38 
 
 43 
 
 50 
 
 57 
 
 64 
 
 72 
 
 !)2 
 
 8 
 
 11 
 
 13 
 
 16 
 
 18 
 
 19 
 
 21 
 
 23 
 
 26 
 
 30 
 
 36 
 
 43 
 
 50 
 
 59 
 
 67 
 
 94 
 
 7 
 
 9 
 
 11 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 20 
 
 23 
 
 28 
 
 35 
 
 42 
 
 51 
 
 60 
 
 96 
 
 9 
 
 10 
 
 II 
 
 12 
 
 12 
 
 12 
 
 13 
 
 13 
 
 14 
 
 17 
 
 21 
 
 27 
 
 34 
 
 43 
 
 53 
 
 98 
 
 13 
 
 13 
 
 13 
 
 13 
 
 13 
 
 12 
 
 11 
 
 11 
 
 11 
 
 13 
 
 15 
 
 21 
 
 27 
 
 35 
 
 45 
 
 100 
 
 19 
 
 18 
 
 17 
 
 17 
 
 16 
 
 14 
 
 12 
 
 11 
 
 10 
 
 10 
 
 12 
 
 15 
 
 21 
 
 28 
 
 37 
 
 102 
 
 25 
 
 24 
 
 23 
 
 21 
 
 20 
 
 17 
 
 15 
 
 12 
 
 10 
 
 9 
 
 10 
 
 12 
 
 16 
 
 22 
 
 31 
 
 104 
 
 33 
 
 111 
 
 30 
 
 28 
 
 25 
 
 22 
 
 19 
 
 15 
 
 13 
 
 10 
 
 9 
 
 10 
 
 13 
 
 18 
 
 25 
 
 106 
 
 42 
 
 40 
 
 38 
 
 35 
 
 32 
 
 28 
 
 25 
 
 20 
 
 16 
 
 13 
 
 10 
 
 10 
 
 11 
 
 15 
 
 21 
 
 108 
 
 51 
 
 49 
 
 47 
 
 44 
 
 40 
 
 36 
 
 32 
 
 26 
 
 21 
 
 17 
 
 13 
 
 12 
 
 11 
 
 14 
 
 18 
 
 no 
 
 61 
 
 59 
 
 57 
 
 54 
 
 50 
 
 45 
 
 40 
 
 34 
 
 28 
 
 23 
 
 18 
 
 15 
 
 13 
 
 13 
 
 16 
 
 112 
 
 70 
 
 60 
 
 67 
 
 64 
 
 61 
 
 56 
 
 50 
 
 44 
 
 37 
 
 30 
 
 24 
 
 20 
 
 16 
 
 15 
 
 16 
 
 114 
 
 78 
 
 78 
 
 76 
 
 75 
 
 72 
 
 67 
 
 62 
 
 ,->:> 
 
 48 
 
 40 
 
 33 
 
 27 
 
 22 
 
 19 
 
 18 
 
 116 
 
 84 
 
 85 
 
 85 
 
 85 
 
 83 
 
 Til 
 
 74 
 
 67 
 
 6:1 
 
 52 
 
 44 
 
 36 
 
 30 
 
 25 
 
 23 
 
 118 
 
 86 
 
 90 
 
 92 
 
 93 
 
 92 
 
 911 
 
 86 
 
 80 
 
 72 
 
 64 
 
 66 
 
 48 
 
 40 
 
 34 
 
 30 
 
 130 
 
 85 
 
 91 
 
 95 
 
 98 
 
 99 
 
 BO 
 
 96 
 
 91 
 
 85 
 
 77 
 
 69 
 
 60 
 
 52 
 
 45 
 
 39 
 
 The perturbations are expressed in luiiidredtlis of a second of arc. 
 
TABLE XXXVII. 
 
 /'. rliir/xiliini.-i iifi/ir Lntilitili\ liii l/i-' I'.m-ih. 
 
 lli.riy.tmul Argument = 1. 
 
 nit . -nl, l-'tl \' :i.,il ot'Ar;;iiiii.'iil M., 210 in. 
 
 
 Arg.XI. 
 
 .1 
 
 a 
 14N 
 
 .1 
 130 
 
 .1 
 111 
 
 .1 
 
 
 .1 
 ION 
 
 170 
 
 INI 
 
 194 
 
 400 
 
 40N 
 
 9 , 
 
 221 
 
 2*4 
 
 
 
 85 
 
 87 
 
 
 
 -1 
 
 Bl 
 
 76 
 
 70 
 
 (il 
 
 
 51 
 
 46 
 
 II 
 
 37 
 
 36 
 
 > 
 
 BO 
 
 
 ,-i, 
 
 86 
 
 
 M! 
 
 80 
 
 71 i 
 
 71 
 
 86 
 
 60 
 
 
 to 
 
 44 
 
 II 
 
 4 
 
 73 
 
 7fl 
 
 Bl 
 
 
 84 
 
 1 
 
 
 81 
 
 
 71 
 
 (i7 
 
 
 66 
 
 
 48 
 
 G 
 
 66 
 
 71 
 
 7". 
 
 
 -l 
 
 - 
 
 
 
 7' 
 
 
 
 68 
 
 lil 
 
 00 
 
 66 
 
 8 
 
 
 I.I 
 
 
 7-J 
 
 
 X 
 
 79 
 
 80 
 
 80 
 
 78 
 
 7G 
 
 74 
 
 71 
 
 67 
 
 63 
 
 10 
 
 83 
 
 57 
 
 89 
 
 66 
 
 7 l 
 
 7:! 
 
 76 
 
 
 7!) 
 
 7 ' 
 
 
 77 
 
 75 
 
 73 
 
 70 
 
 I-J 
 
 47 
 
 61 
 
 
 
 63 
 
 1,7 
 
 71 
 
 74 
 
 76 
 
 77 
 
 71) 
 
 7:1 
 
 78 
 
 77 
 
 re 
 
 1 1 
 
 43 
 
 li. 
 
 
 88 
 
 r,7 
 
 I.I 
 
 
 
 79 
 
 7.-) 
 
 7- 
 
 79 
 
 80 
 
 81 
 
 80 
 
 16 
 
 89 
 
 41 
 
 II 
 
 
 61 
 
 
 
 1,1 
 
 
 71 
 
 75 
 
 
 81 
 
 38 
 
 
 18 
 
 86 
 
 37 
 
 40 
 
 HI 
 
 l . 
 
 49 
 
 58 
 
 
 BB 
 
 67 
 
 ~- 
 
 76 
 
 80 
 
 
 
 20 
 
 34 
 
 86 
 
 36 
 
 37 
 
 
 43 
 
 47 
 
 51 
 
 86 
 
 (il 
 
 67 
 
 73 
 
 78 
 
 BB 
 
 86 
 
 99 
 
 86 
 
 34 
 
 BB 
 
 BB 
 
 86 
 
 37 
 
 40 
 
 II 
 
 49 
 
 
 lil 
 
 68 
 
 71 
 
 80 
 
 86 
 
 94 
 
 37 
 
 86 
 
 n 
 
 31 
 
 81 
 
 3'J 
 
 34 
 
 :t7 
 
 49 
 
 47 
 
 54 
 
 lil 
 
 88 
 
 7li 
 
 83 
 
 JO 
 
 49 
 
 
 84 
 
 81 
 
 
 
 
 :ti 
 
 86 
 
 n 
 
 46 
 
 5:t 
 
 iii 
 
 70 
 
 IB 
 
 23 
 
 4!) 
 
 43 
 
 N 
 
 88 
 
 29 
 
 - 7 
 
 Jii 
 
 J7 
 
 23 
 
 89 
 
 38 
 
 M 
 
 52 
 
 61 
 
 71 
 
 30 
 
 87 
 
 51 
 
 44 
 
 38 
 
 33 
 
 99 
 
 26 
 
 Jl 
 
 94 
 
 27 
 
 31 
 
 86 
 
 43 
 
 52 
 
 (i-J 
 
 89 
 
 GG 
 
 60 
 
 53 
 
 4G 
 
 3!) 
 
 33 
 
 
 s, 
 
 83 
 
 98 
 
 86 
 
 88 
 
 84 
 
 43 
 
 89 
 
 34 
 
 75 
 
 68 
 
 (i-J 
 
 
 48 
 
 II 
 
 84 
 
 29 
 
 LT, 
 
 93 
 
 98 
 
 B6 
 
 86 
 
 86 
 
 44 
 
 86 
 
 83 
 
 78 
 
 79 
 
 66 
 
 r>7 
 
 60 
 
 42 
 
 It:, 
 
 
 26 
 
 94 
 
 88 
 
 J.-, 
 
 31) 
 
 36 
 
 BH 
 
 88 
 
 85 
 
 80 
 
 74 
 
 G7 
 
 "'' 
 
 52 
 
 44 
 
 37 
 
 III 
 
 J7 
 
 25 
 
 Jl 
 
 26 
 
 31 
 
 40 
 
 90 
 
 BB 
 
 87 
 
 82 
 
 n 
 
 (i!) 
 
 62 
 
 54 
 
 46 
 
 
 33 
 
 29 
 
 26 
 
 26 
 
 23 
 
 49 
 
 BO 
 
 U9 
 
 Bl 
 
 -- 
 
 - 1 
 
 73 
 
 71 
 
 63 
 
 .'.;, 
 
 1- 
 
 41 
 
 35 
 
 31 
 
 -.'- 
 
 
 44 
 
 83 
 
 Bl 
 
 89 
 
 92 
 
 
 85 
 
 80 
 
 73 
 
 66 
 
 .-,7 
 
 50 
 
 49 
 
 1(7 
 
 83 
 
 30 
 
 46 
 
 -1 
 
 89 
 
 B9 
 
 B4 
 
 B3 
 
 91 
 
 87 
 
 81 
 
 74 
 
 B7 
 
 60 
 
 51 
 
 44 
 
 89 
 
 86 
 
 43 
 
 78 
 
 84 
 
 90 
 
 94 
 
 95 
 
 B6 
 
 88 
 
 
 83 
 
 76 
 
 
 
 63 
 
 46 
 
 41 
 
 50 
 
 70 
 
 78 
 
 86 
 
 !>l 
 
 B6 
 
 87 
 
 87 
 
 94 
 
 90 
 
 84 
 
 77 
 
 70 
 
 62 
 
 BB 
 
 48 
 
 69 
 
 Gl 
 
 71 
 
 80 
 
 
 B9 
 
 B7 
 
 DO 
 
 93 
 
 86 
 
 89 
 
 86 
 
 7'.) 
 
 7J 
 
 Gl 
 
 57 
 
 
 52 
 
 62 
 
 79 
 
 81 
 
 88 
 
 "i 
 
 B8 
 
 100 
 
 100 
 
 1 '7 
 
 88 
 
 87 
 
 81 
 
 7:1 
 
 66 
 
 r.(i 
 
 43 
 
 .'.:) 
 
 63 
 
 71! 
 
 82 
 
 
 BE 
 
 BB 
 
 Ml 
 
 Ml 
 
 
 B4 
 
 89 
 
 --.' 
 
 75 
 
 
 34 
 
 43 
 
 
 63 
 
 73 
 
 82 
 
 90 
 
 96 
 
 BO 
 
 Ml 
 
 101 
 
 08 
 
 86 
 
 90 
 
 84 
 
 GO 
 
 J7 
 
 35 
 
 44 
 
 84 
 
 G4 
 
 73 
 
 82 
 
 90 
 
 86 
 
 99 
 
 101 
 
 101 
 
 II!) 
 
 96 
 
 III 
 
 
 88 
 
 
 :i7 
 
 45 
 
 M 
 
 lil 
 
 73 
 
 -1 
 
 
 94 
 
 97 
 
 Mil 
 
 101) 
 
 B8 
 
 86 
 
 G! 
 
 21 
 
 86 
 
 ::' 
 
 38 
 
 46 
 
 66 
 
 (il 
 
 7-.' 
 
 80 
 
 83 
 
 89 
 
 BB 
 
 BH 
 
 98 
 
 
 66 
 
 j;{ 
 
 25 
 
 2!) 
 
 34 
 
 40 
 
 47 
 
 66 
 
 63 
 
 71 
 
 78 
 
 84 
 
 -:i 
 
 93 
 
 :i5 
 
 96 
 
 63 
 
 27 
 
 27 
 
 39 
 
 32 
 
 3G 
 
 I-J 
 
 43 
 
 66 
 
 69 
 
 69 
 
 75 
 
 81 
 
 86 
 
 89 
 
 
 70 
 
 83 
 
 32 
 
 32 
 
 33 
 
 36 
 
 39 
 
 44 
 
 60 
 
 55 
 
 61 
 
 67 
 
 73 
 
 78 
 
 82 
 
 86 
 
 7'J 
 
 40 
 
 33 
 
 87 
 
 37 
 
 37 
 
 88 
 
 42 
 
 46 
 
 
 68 
 
 60 
 
 BB 
 
 70 
 
 76 
 
 7H 
 
 74 
 
 47 
 
 45 
 
 43 
 
 41 
 
 41 
 
 41 
 
 4'J 
 
 44 
 
 47 
 
 50 
 
 
 
 63 
 
 67 
 
 71 
 
 76 
 
 
 Efl 
 
 49 
 
 47 
 
 46 
 
 44 
 
 44 
 
 44 
 
 18 
 
 47 
 
 60 
 
 53 
 
 67 
 
 61 
 
 65 
 
 78 
 
 61 
 
 58 
 
 56 
 
 53 
 
 51 
 
 48 
 
 47 
 
 46 
 
 45 
 
 46 
 
 47 
 
 49 
 
 52 
 
 55 
 
 59 
 
 80 
 
 66 
 
 G5 
 
 62 
 
 59 
 
 57 
 
 64 
 
 51 
 
 48 
 
 47 
 
 46 
 
 46 
 
 46 
 
 48 
 
 80 
 
 53 
 
 83 
 
 71 
 
 70 
 
 69 
 
 66 
 
 63 
 
 
 56 
 
 52 
 
 49 
 
 47 
 
 45 
 
 45 
 
 45 
 
 4G 
 
 48 
 
 84 
 
 
 7.-, 
 
 7:, 
 
 79 
 
 70 
 
 66 
 
 69 
 
 57 
 
 68 
 
 49 
 
 46 
 
 45 
 
 43 
 
 43 
 
 44 
 
 86 
 
 73 
 
 - ' 
 
 80 
 
 7!) 
 
 77 
 
 73 
 
 68 
 
 64 
 
 
 54 
 
 l i 
 
 46 
 
 43 
 
 41 
 
 41 
 
 88 
 
 79 
 
 
 84 
 
 85 
 
 83 
 
 80 
 
 76 
 
 71 
 
 68 
 
 59 
 
 54 
 
 49 
 
 45 
 
 41 
 
 39 
 
 BO 
 
 7- 
 
 83 
 
 gj 
 
 89 
 
 89 
 
 87 
 
 83 
 
 7!) 
 
 73 
 
 66 
 
 60 
 
 54 
 
 43 
 
 44 
 
 40 
 
 89 
 
 7.-, 
 
 88 
 
 87 
 
 
 89 
 
 92 
 
 90 
 
 
 81 
 
 74 
 
 67 
 
 lil 
 
 54 
 
 48 
 
 i-J 
 
 '.il 
 
 71) 
 
 7- 
 
 88 
 
 Bl 
 
 94 
 
 96 
 
 95 
 
 '.J 
 
 -- 
 
 B8 
 
 7:, 
 
 
 61 
 
 64 
 
 47 
 
 
 
 72 
 
 81 
 
 88 
 
 94 
 
 
 93 
 
 !I7 
 
 '.'I 
 
 89 
 
 83 
 
 77 
 
 69 
 
 Gl 
 
 .", 1 
 
 98 
 
 55 
 
 65 
 
 75 
 
 84 
 
 91 
 
 96 
 
 99 
 
 99 
 
 
 BB 
 
 90 
 
 84 
 
 77 
 
 68 
 
 62 
 
 100 
 
 47 
 
 53 
 
 
 78 
 
 86 
 
 93 
 
 97 
 
 100 
 
 100 
 
 
 B8 
 
 90 
 
 84 
 
 77 
 
 69 
 
 1 1 i-J 
 
 40 
 
 
 61 
 
 71 
 
 81 
 
 83 
 
 94 
 
 93 
 
 100 
 
 HID 
 
 W 
 
 B6 
 
 80 
 
 84 
 
 77 
 
 104 
 
 
 43 
 
 54 
 
 64 
 
 71 
 
 83 
 
 90 
 
 88 
 
 
 100 
 
 iao 
 
 98 
 
 H4 
 
 89 
 
 -'. 
 
 106 
 
 
 37 
 
 47 
 
 57 
 
 68 
 
 77 
 
 84 
 
 91 
 
 
 II! 1 
 
 108 
 
 100 
 
 B7 
 
 B4 
 
 " 
 
 103 
 
 24 
 
 89 
 
 41 
 
 51 
 
 Gl 
 
 70 
 
 7'.) 
 
 86 
 
 
 96 
 
 99 
 
 100 
 
 99 
 
 97 
 
 '.'3 
 
 1 10 
 
 21 
 
 2s* 
 
 36 
 
 45 
 
 54 
 
 64 
 
 7-J 
 
 80 
 
 
 
 96 
 
 99 
 
 99 
 
 H 
 
 96 
 
 1 12 
 
 19 
 
 25 
 
 31 
 
 BB 
 
 1- 
 
 57 
 
 66 
 
 71 
 
 -1 
 
 87 
 
 
 
 
 in) 
 
 
 1 14 
 
 J i 
 
 23 
 
 28 
 
 86 
 
 43 
 
 61 
 
 60 
 
 G7 
 
 71 
 
 Bl 
 
 
 Dl 
 
 BB 
 
 !>7 
 
 
 116 
 
 1 1 . 
 
 22 
 
 24 
 
 28 
 
 J7 
 
 ::-J 
 
 37 
 
 46 
 42 
 
 63 
 
 43 
 
 (, > 
 
 67 
 
 li) 
 
 71 
 
 66 
 
 7-J 
 
 
 
 P3 
 
 87 
 
 98 
 M 
 
 1 I O 
 
 190 
 
 
 34 
 
 33 
 
 35 
 
 37 
 
 11 
 
 45 
 
 
 
 
 lil 
 
 G!) 
 
 74 
 
 79 
 
 84 
 
 Wlicu 22-l''.7 li subtracted trom Arg. I., ;ulel 1 l/.UI lo Ary. XI. 
 
 11 V 
 
TABLE XXX VJ I. 
 
 Perturbations of the Latitude, l>y the Earth. 
 
 Horizontal Argument = I. 
 
 Constant added 0".62. Period of Argument I., 224J.7. 
 
 Arg. 
 XI. 
 
 d 
 
 o 
 
 d 
 
 % 
 
 d 
 
 16 
 
 d 
 
 24 
 
 A 
 
 32 
 
 d 
 
 40 
 
 d 
 
 48 
 
 d 
 
 56 
 
 d 
 
 61 
 
 d 
 
 72 
 
 d 
 
 80 
 
 d 
 
 8 
 
 96 
 
 d 
 
 104 
 
 <i 
 112 
 
 120 
 
 85 
 
 91 
 
 95 
 
 93 
 
 99 
 
 99 
 
 96 
 
 91 
 
 85 
 
 77 
 
 69 
 
 60 
 
 52 
 
 45 
 
 39 
 
 122 
 
 82 
 
 89 
 
 96 
 
 100 
 
 103 
 
 105 
 
 104 
 
 101 
 
 96 
 
 89 
 
 81 
 
 73 
 
 64 
 
 57 
 
 51 
 
 124 
 
 76 
 
 85 
 
 93 
 
 99 
 
 105 
 
 108 
 
 110 
 
 108 
 
 105 
 
 99 
 
 93 
 
 85 
 
 77 
 
 70 
 
 63 
 
 126 
 
 6'.) 
 
 78 
 
 88 
 
 96 
 
 103 
 
 108 
 
 112 
 
 112 
 
 111 
 
 107 
 
 102 
 
 95 
 
 88 
 
 81 
 
 75 
 
 12si 
 
 01 
 
 71 
 
 81 
 
 91 
 
 99 
 
 106 
 
 112 
 
 114 
 
 114 
 
 112 
 
 109 
 
 104 
 
 98 
 
 92 
 
 86 
 
 130 
 
 54 
 
 64 
 
 74 
 
 84 
 
 94 
 
 103 
 
 109 
 
 113 
 
 115 
 
 115 
 
 113 
 
 109 
 
 104 
 
 100 
 
 94 
 
 132 
 
 47 
 
 57 
 
 67 
 
 77 
 
 88 
 
 97 
 
 105 
 
 no 
 
 114 
 
 116 
 
 115 
 
 113 
 
 109 
 
 106 
 
 101 
 
 134 
 
 41 
 
 50 
 
 60 
 
 70 
 
 81 
 
 ill 
 
 99 
 
 107 
 
 112 
 
 114 
 
 115 
 
 114 
 
 112 
 
 110 
 
 106 
 
 136 
 
 36 
 
 44 
 
 53 
 
 63 
 
 74 
 
 84 
 
 94 
 
 101 
 
 108 
 
 112 
 
 114 
 
 114 
 
 113 
 
 112 
 
 110 
 
 138 
 
 32 
 
 39 
 
 47 
 
 56 
 
 67 
 
 77 
 
 87 
 
 95 
 
 103 
 
 108 
 
 111 
 
 113 
 
 113 
 
 112 
 
 111 
 
 140 
 
 29 
 
 35 
 
 41 
 
 50 
 
 5!) 
 
 70 
 
 79 
 
 89 
 
 97 
 
 102 
 
 107 
 
 110 
 
 111 
 
 111 
 
 111 
 
 142 
 
 28 
 
 32 
 
 37 
 
 44 
 
 53 
 
 62 
 
 72 
 
 81 
 
 89 
 
 96 
 
 101 
 
 105 
 
 107 
 
 109 
 
 109 
 
 144 
 
 30 
 
 30 
 
 35 
 
 40 
 
 47 
 
 56 
 
 64 
 
 73 
 
 82 
 
 89 
 
 94 
 
 99 
 
 102 
 
 105 
 
 106 
 
 146 
 
 33 
 
 32 
 
 35 
 
 38 
 
 43 
 
 50 
 
 58 
 
 66 
 
 74 
 
 81 
 
 87 
 
 92 
 
 96 
 
 98 
 
 100 
 
 148 
 
 38 
 
 37 
 
 36 
 
 38 
 
 41 
 
 47 
 
 53 
 
 60 
 
 67 
 
 73 
 
 79 
 
 84 
 
 88 
 
 91 
 
 94 
 
 150 
 
 45 
 
 43 
 
 41 
 
 41 
 
 42 
 
 46 
 
 50 
 
 55 
 
 61 
 
 67 
 
 72 
 
 76 
 
 80 
 
 84 
 
 85 
 
 152 
 
 53 
 
 5!) 
 
 47 
 
 45 
 
 45 
 
 47 
 
 49 
 
 53 
 
 57 
 
 62 
 
 66 
 
 6!) 
 
 73 
 
 77 
 
 78 
 
 151 
 
 61 
 
 57 
 
 54 
 
 51 
 
 50 
 
 50 
 
 51 
 
 53 
 
 56 
 
 59 
 
 62 
 
 64 
 
 67 
 
 69 
 
 70 
 
 156 
 
 68 
 
 Gl 
 
 61 
 
 58 
 
 56 
 
 55 
 
 55 
 
 55 
 
 56 
 
 58 
 
 60 
 
 61 
 
 62 
 
 63 
 
 64 
 
 158 
 
 73 
 
 71 
 
 68 
 
 65 
 
 62 
 
 61 
 
 59 
 
 59 
 
 59 
 
 59 
 
 59 
 
 59 
 
 59 
 
 59 
 
 59 
 
 160 
 
 / 4 
 
 7(i 
 
 74 
 
 72 
 
 69 
 
 67 
 
 65 
 
 63 
 
 62 
 
 61 
 
 60 
 
 59 
 
 57 
 
 56 
 
 55 
 
 162 
 
 80 
 
 80 
 
 79 
 
 77 
 
 75 
 
 73 
 
 70 
 
 68 
 
 66 
 
 63 
 
 62 
 
 59 
 
 57 
 
 54 
 
 52 
 
 164 
 
 83 
 
 83 
 
 83 
 
 83 
 
 81 
 
 79 
 
 76 
 
 74 
 
 71 
 
 68 
 
 65 
 
 61 
 
 58 
 
 54 
 
 50 
 
 166 
 
 83 
 
 86 
 
 87 
 
 87 
 
 87 
 
 85 
 
 83 
 
 80 
 
 77 
 
 73 
 
 69 
 
 64 
 
 60 
 
 54 
 
 50 
 
 168 
 
 83 
 
 87 
 
 90 
 
 91 
 
 92 
 
 91 
 
 89 
 
 87 
 
 83 
 
 79 
 
 74 
 
 63 
 
 63 
 
 56 
 
 50 
 
 170 
 
 80 
 
 86 
 
 90 
 
 94 
 
 96 
 
 96 
 
 95 
 
 94 
 
 90 
 
 86 
 
 80 
 
 74 
 
 67 
 
 60 
 
 52 
 
 172 
 
 75 
 
 83 
 
 89 
 
 94 
 
 98 
 
 100 
 
 100 
 
 100 
 
 97 
 
 93 
 
 88 
 
 81 
 
 73 
 
 65 
 
 56 
 
 174 
 
 6!) 
 
 77 
 
 85 
 
 92 
 
 98 
 
 102 
 
 104 
 
 105 
 
 103 
 
 100 
 
 95 
 
 89 
 
 81 
 
 72 
 
 62 
 
 176 
 
 60 
 
 70 
 
 79 
 
 87 
 
 95 
 
 101 
 
 105 
 
 108 
 
 108 
 
 106 
 
 103 
 
 97 
 
 89 
 
 80 
 
 69 
 
 178 
 
 51 
 
 61 
 
 71 
 
 80 
 
 89 
 
 97 
 
 103 
 
 108 
 
 110 
 
 110 
 
 108 
 
 104 
 
 97 
 
 88 
 
 78 
 
 180 
 
 42 
 
 52 
 
 61 
 
 72 
 
 81 
 
 91 
 
 98 
 
 105 
 
 110 
 
 112 
 
 112 
 
 109 
 
 104 
 
 96 
 
 87 
 
 182 
 
 35 
 
 43 
 
 52 
 
 62 
 
 72 
 
 82 
 
 91 
 
 99 
 
 106 
 
 110 
 
 112 
 
 111 
 
 108 
 
 102 
 
 94 
 
 184 
 
 29 
 
 35 
 
 43 
 
 52 
 
 62 
 
 72 
 
 82 
 
 91 
 
 99 
 
 105 
 
 109 
 
 111 
 
 110 
 
 106 
 
 100 
 
 186 
 
 26 
 
 31 
 
 36 
 
 44 
 
 53 
 
 62 
 
 72 
 
 82 
 
 90 
 
 98 
 
 104 
 
 107 
 
 108 
 
 107 
 
 103 
 
 188 
 
 26 
 
 28 
 
 32 
 
 38 
 
 45 
 
 53 
 
 62 
 
 72 
 
 81 
 
 89 
 
 96 
 
 101 
 
 104 
 
 106 
 
 103 
 
 190 
 
 29 
 
 28 
 
 30 
 
 34 
 
 39 
 
 46 
 
 54 
 
 62 
 
 71 
 
 80 
 
 87 
 
 94 
 
 98 
 
 101 
 
 101 
 
 192 
 
 33 
 
 31 
 
 30 
 
 32 
 
 35 
 
 40 
 
 47 
 
 54 
 
 61 
 
 70 
 
 78 
 
 85 
 
 91 
 
 94 
 
 97 
 
 194 
 
 40 
 
 35 
 
 33 
 
 32 
 
 34 
 
 37 
 
 41 
 
 46 
 
 53 
 
 61 
 
 68 
 
 75 
 
 82 
 
 87 
 
 91 
 
 196 
 
 47 
 
 41 
 
 37 
 
 35 
 
 34 
 
 35 
 
 37 
 
 41 
 
 46 
 
 52 
 
 59 
 
 66 
 
 72 
 
 78 
 
 83 
 
 198 
 
 56 
 
 48 
 
 43 
 
 39 
 
 36 
 
 35 
 
 35 
 
 37 
 
 40 
 
 45 
 
 50 
 
 56 
 
 62 
 
 68 
 
 74 
 
 200 
 
 65 
 
 57 
 
 51 
 
 45 
 
 41 
 
 38 
 
 36 
 
 35 
 
 36 
 
 39 
 
 43 
 
 47 
 
 53 
 
 59 
 
 65 
 
 202 
 
 74 
 
 67 
 
 60 
 
 53 
 
 47 
 
 42 
 
 39 
 
 36 
 
 35 
 
 35 
 
 37 
 
 40 
 
 44 
 
 49 
 
 54 
 
 204 
 
 83 
 
 76 
 
 69 
 
 62 
 
 55 
 
 49 
 
 44 
 
 39 
 
 36 
 
 34 
 
 34 
 
 35 
 
 37 
 
 41 
 
 45 
 
 206 
 
 91 
 
 85 
 
 78 
 
 71 
 
 64 
 
 58 
 
 51 
 
 45 
 
 40 
 
 37 
 
 34 
 
 33 
 
 33 
 
 35 
 
 37 
 
 208 
 
 96 
 
 92 
 
 86 
 
 80 
 
 74 
 
 67' 
 
 61) 
 
 53 
 
 47 
 
 42 
 
 37 
 
 33 
 
 31 
 
 31 
 
 31 
 
 210 
 
 99 
 
 96 
 
 92 
 
 88 
 
 82 
 
 76 
 
 69 
 
 62 
 
 55 
 
 49 
 
 43 
 
 37 
 
 33 
 
 30 
 
 29 
 
 212 
 
 98 
 
 97 
 
 96 
 
 93 
 
 89 
 
 84 
 
 78 
 
 72 
 
 64 
 
 58 
 
 50 
 
 44 
 
 38 
 
 33 
 
 29 
 
 214 
 
 94 
 
 96 
 
 06 
 
 95 
 
 92 
 
 89 
 
 85 
 
 79 
 
 73 
 
 67 
 
 59 
 
 52 
 
 45 
 
 38 
 
 33 
 
 216 
 
 89 
 
 91 
 
 93 
 
 94 
 
 93 
 
 92 
 
 89 
 
 86 
 
 81 
 
 75 
 
 68 
 
 61 
 
 53 
 
 46 
 
 39 
 
 218 
 
 82 
 
 85 
 
 88 
 
 90 
 
 92 
 
 92 
 
 91 
 
 89 
 
 86 
 
 81 
 
 76 
 
 69 
 
 62 
 
 55 
 
 47 
 
 220 
 
 74 
 
 78 
 
 82 
 
 85 
 
 88 
 
 90 
 
 91 
 
 91 
 
 89 
 
 86 
 
 82 
 
 77 
 
 70 
 
 63 
 
 55 
 
 222 
 
 67 
 
 71 
 
 75 
 
 79 
 
 83 
 
 86 
 
 88 
 
 90 
 
 90 
 
 89 
 
 86 
 
 82 
 
 77 
 
 70 
 
 63 
 
 224 
 
 60 
 
 64 
 
 68 
 
 73 
 
 77 
 
 81 
 
 84 
 
 87 
 
 89 
 
 89 
 
 88 
 
 86 
 
 82 
 
 77 
 
 70 
 
 226 
 
 55 
 
 58 
 
 62 
 
 66 
 
 71 
 
 75 
 
 80 
 
 84 
 
 87 
 
 88 
 
 89 
 
 88 
 
 86 
 
 82 
 
 76 
 
 22 
 
 50 
 
 52 
 
 55 
 
 60 
 
 65 
 
 69 
 
 74 
 
 79 
 
 83 
 
 86 
 
 89 
 
 89 
 
 88 
 
 86 
 
 82 
 
 230 
 
 46 
 
 47 
 
 50 
 
 54 
 
 58 
 
 63 
 
 68 
 
 74 
 
 79 
 
 83 
 
 87 
 
 89 
 
 89 
 
 88 
 
 86 
 
 232 
 
 43 
 
 43 
 
 45 
 
 48 
 
 52 
 
 57 
 
 62 
 
 68 
 
 74 
 
 79 
 
 84 
 
 87 
 
 89 
 
 90 
 
 88 
 
 234 
 
 41 
 
 40 
 
 41 
 
 43 
 
 46 
 
 50 
 
 55 
 
 61 
 
 67 
 
 73 
 
 79 
 
 83 
 
 87 
 
 89 
 
 90 
 
 236 
 
 41 
 
 39 
 
 38 
 
 39 
 
 40 
 
 44 
 
 48 
 
 54 
 
 60 
 
 66 
 
 73 
 
 79 
 
 83 
 
 87 
 
 89 
 
 238 
 
 44 
 
 40 
 
 37 
 
 36 
 
 36 
 
 39 
 
 42 
 
 47 
 
 52 
 
 59 
 
 65 
 
 72 
 
 78 
 
 83 
 
 86 
 
 240 
 
 48 
 
 43 
 
 39 
 
 36 
 
 34 
 
 35 
 
 37 
 
 41 
 
 45 
 
 51 
 
 58 
 
 65 
 
 71 
 
 77 
 
 81 
 
 The perturbations are expressed in liundredtlis of a second of arc. 
 
TABLE XXXVII. 
 
 <;*> 
 
 Perturbation* uf // Liiti/mli-, /// ///< /,'// A. 
 
 lloriy.unt.il Argument = I. 
 
 Constant added 0-.62. Peri f Ar,,,,,,,,,, XI , -10 ,,.. 
 
 Arg. 
 
 .1 
 
 .1 
 12N 
 
 .1 
 
 .1 
 1 II 
 
 152 
 
 100 
 
 .1 
 10* 
 
 170 
 
 INI 
 
 .* 
 
 4 
 
 200 
 
 .1 
 20* 
 
 .1 
 210 
 
 221 
 
 .1 
 
 120 
 
 36 
 
 14 
 
 S3 
 
 35 
 
 37 
 
 41 
 
 16 
 
 10 
 
 54 
 
 
 (it 
 
 60 
 
 74 
 
 7:' 
 
 
 199 
 
 4G 
 
 43 
 
 41 
 
 41 
 
 41 
 
 43 
 
 46 
 
 47 
 
 :,,i 
 
 54 
 
 
 61 
 
 $6 
 
 70 
 
 75 
 
 194 
 
 
 54 
 
 50 
 
 48 
 
 47 
 
 47 
 
 47 
 
 48 
 
 49 
 
 51 
 
 
 
 57 
 
 Gl 
 
 65 
 
 196 
 
 69 
 
 65 
 
 61 
 
 58 
 
 66 
 
 54 
 
 53 
 
 59 
 
 51 
 
 51 
 
 :,u 
 
 50 
 
 51 
 
 
 66 
 
 !.>- 
 
 -1 
 
 76 
 
 T - 
 
 69 
 
 67 
 
 1,1 
 
 69 
 
 
 56 
 
 54 
 
 51 
 
 49 
 
 <8 
 
 1- 
 
 40 
 
 130 
 
 00 
 
 86 
 
 83 
 
 
 77 
 
 74 
 
 71 
 
 
 (It 
 
 60 
 
 56 
 
 51 
 
 47 
 
 45 
 
 it 
 
 139 
 
 98 
 
 95 
 
 99 
 
 HO 
 
 ^7 
 
 84 
 
 -1 
 
 77 
 
 7:s 
 
 68 
 
 61 
 
 55 
 
 ia 
 
 45 
 
 49 
 
 134 
 
 104 
 
 101 
 
 90 
 
 98 
 
 96 
 
 93 
 
 '.'1 
 
 87 
 
 82 
 
 76 
 
 68 
 
 69 
 
 54 
 
 47 
 
 49 
 
 136 
 
 108 
 
 107 
 
 105 
 
 101 
 
 lo:t 
 
 101 
 
 !>9 
 
 96 
 
 91 
 
 
 
 70 
 
 61 
 
 59 
 
 15 
 
 138 
 
 111 
 
 109 
 
 IW 
 
 109 
 
 108 
 
 108 
 
 lor- 
 
 104 
 
 100 
 
 94 
 
 87 
 
 78 
 
 Gil 
 
 59 
 
 111 
 
 140 
 
 111 
 
 111 
 
 ill 
 
 112 
 
 112 
 
 112 
 
 114 
 
 111 
 
 108 
 
 103 
 
 96 
 
 87 
 
 77 
 
 67 
 
 55 
 
 149 
 
 lio 
 
 111) 
 
 112 
 
 113 
 
 11 1 
 
 116 
 
 Il- 
 
 IK; 
 
 lit 
 
 no 
 
 mi 
 
 96 
 
 
 75 
 
 63 
 
 144 
 
 107 
 
 108 
 
 lio 
 
 113 
 
 115 
 
 117 
 
 ll!) 
 
 190 
 
 11!) 
 
 in; 
 
 in 
 
 103 
 
 0! 
 
 
 71 
 
 146 
 
 109 
 
 lot 
 
 107 
 
 Illl 
 
 113 
 
 116 
 
 119 
 
 122 
 
 1 ->-,' 
 
 191 
 
 117 
 
 IK) 
 
 109 
 
 91 
 
 7!) 
 
 148 
 
 96 
 
 99 
 
 102 
 
 105 
 
 109 
 
 113 
 
 117 
 
 121 
 
 123 
 
 183 
 
 121 
 
 116 
 
 109 
 
 90 
 
 
 150 
 
 89 
 
 91 
 
 95 
 
 98 
 
 103 
 
 108 
 
 113 
 
 118 
 
 191 
 
 123 
 
 199 
 
 119 
 
 114 
 
 106 
 
 96 
 
 169 
 
 "1 
 
 83 
 
 86 
 
 90 
 
 95 
 
 100 
 
 ! I. 
 
 112 
 
 117 
 
 190 
 
 121 
 
 120 
 
 117 
 
 110 
 
 102 
 
 151 
 
 79 
 
 74 
 
 77 
 
 81 
 
 86 
 
 91 
 
 97 
 
 l"l 
 
 110 
 
 III 
 
 117 
 
 II- 
 
 116 
 
 112 
 
 106 
 
 156 
 
 65 
 
 66 
 
 68 
 
 71 
 
 76 
 
 81 
 
 87 
 
 94 
 
 101 
 
 106 
 
 III 
 
 113 
 
 114 
 
 111 
 
 107 
 
 158 
 
 59 
 
 59 
 
 GO 
 
 63 
 
 66 
 
 71 
 
 77 
 
 84 
 
 90 
 
 97 
 
 102 
 
 106 
 
 108 
 
 108 
 
 105 
 
 160 
 
 51 
 
 53 
 
 53 
 
 54 
 
 57 
 
 61 
 
 .66 
 
 73 
 
 80 
 
 86 
 
 99 
 
 97 
 
 100 
 
 101 
 
 101 
 
 169 
 
 50 
 
 48 
 
 47 
 
 48 
 
 4!) 
 
 53 
 
 57 
 
 63 
 
 60 
 
 7G 
 
 98 
 
 87 
 
 91 
 
 94 
 
 94 
 
 164 
 
 47 
 
 44 
 
 49 
 
 41 
 
 42 
 
 44 
 
 48 
 
 53 
 
 59 
 
 66 
 
 7-j 
 
 77 
 
 B9 
 
 
 -7 
 
 166 
 
 45 
 
 41 
 
 38 
 
 36 
 
 36 
 
 37 
 
 40 
 
 44 
 
 50 
 
 56 
 
 <)'.! 
 
 68 
 
 7:t 
 
 77 
 
 7!) 
 
 168 
 
 44 
 
 38 
 
 34 
 
 31 
 
 30 
 
 30 
 
 32 
 
 36 
 
 41 
 
 46 
 
 53 
 
 51) 
 
 64 
 
 68 
 
 71 
 
 170 
 
 45 
 
 37 
 
 32 
 
 27 
 
 24 
 
 23 
 
 24 
 
 27 
 
 32 
 
 37 
 
 43 
 
 49 
 
 55 
 
 59 
 
 G:! 
 
 172 
 
 47 
 
 38 
 
 31 
 
 86 
 
 SO 
 
 18 
 
 18 
 
 19 
 
 23 
 
 28 
 
 34 
 
 40 
 
 46 
 
 51 
 
 55 
 
 171 
 
 59 
 
 41 
 
 32 
 
 24 
 
 18 
 
 14 
 
 12 
 
 12 
 
 15 
 
 1!) 
 
 25 
 
 30 
 
 36 
 
 1- 
 
 46 
 
 176 
 
 58 
 
 47 
 
 36 
 
 26 
 
 19 
 
 12 
 
 9 
 
 7 
 
 8 
 
 11 
 
 16 
 
 22 
 
 27 
 
 :',:! 
 
 ::- 
 
 178 
 
 67 
 
 54 
 
 42 
 
 31 
 
 22 
 
 14 
 
 8 
 
 5 
 
 4 
 
 6 
 
 9 
 
 14 
 
 19 
 
 -it ' 
 
 89 
 
 180 
 
 75 
 
 63 
 
 50 
 
 38 
 
 27 
 
 17 
 
 10 
 
 5 
 
 2 
 
 2 
 
 4 
 
 8 
 
 12 
 
 17 
 
 21 
 
 182 
 
 84 
 
 72 
 
 59 
 
 47 
 
 35 
 
 24 
 
 15 
 
 8 
 
 3 
 
 2 
 
 2 
 
 4 
 
 7 
 
 11 
 
 15 
 
 184 
 
 91 
 
 80 
 
 G7 
 
 56 
 
 44 
 
 32 
 
 21 
 
 13 
 
 7 
 
 5 
 
 2 
 
 3 
 
 5 
 
 7 
 
 11 
 
 186 
 
 96 
 
 87 
 
 7G 
 
 64 
 
 52 
 
 40 
 
 99 
 
 20 
 
 13 
 
 9 
 
 5 
 
 5 
 
 5 
 
 7 
 
 
 
 
 99 
 
 99 
 
 83 
 
 72 
 
 61 
 
 49 
 
 38 
 
 28 
 
 21 
 
 14 
 
 11 
 
 8 
 
 8 
 
 8 
 
 10 
 
 190 
 
 99 
 
 94 
 
 87 
 
 78 
 
 63 
 
 58 
 
 47 
 
 37 
 
 29 
 
 22 
 
 17 
 
 14 
 
 13 
 
 12 
 
 19 
 
 199 
 
 96 
 
 94 
 
 89 
 
 82 
 
 74 
 
 65 
 
 55 
 
 45 
 
 37 
 
 30 
 
 96 
 
 21 
 
 19 
 
 17 
 
 16 
 
 194 
 
 92 
 
 99 
 
 89 
 
 84 
 
 78 
 
 71 
 
 69 
 
 53 
 
 4G 
 
 39 
 
 33 
 
 2!) 
 
 26 
 
 24 
 
 89 
 
 1% 
 
 86 
 
 88 
 
 87 
 
 85 
 
 81 
 
 75 
 
 68 
 
 60 
 
 54 
 
 48 
 
 42 
 
 38 
 
 34 
 
 it,' 
 
 30 
 
 198 
 
 79 
 
 82 
 
 83 
 
 83 
 
 81 
 
 77 
 
 72 
 
 67 
 
 61 
 
 56 
 
 51 
 
 47 
 
 43 
 
 40 
 
 38 
 
 200 
 
 70 
 
 74 
 
 77 
 
 79 
 
 79 
 
 78 
 
 75 
 
 71 
 
 67 
 
 G:! 
 
 59 
 
 55 
 
 ,VJ 
 
 50 
 
 47 
 
 202 
 
 69 
 
 65 
 
 69 
 
 72 
 
 74 
 
 75 
 
 75 
 
 73 
 
 71 
 
 69 
 
 66 
 
 64 
 
 G'J 
 
 69 
 
 57 
 
 204 
 
 50 
 
 
 60 
 
 64 
 
 68 
 
 70 
 
 72 
 
 73 
 
 73 
 
 73 
 
 72 
 
 71 
 
 70 
 
 68 
 
 67 
 
 206 
 
 40- 
 
 45 
 
 50 
 
 54 
 
 59 
 
 63 
 
 67 
 
 70 
 
 7'J 
 
 74 
 
 75 
 
 76 
 
 76 
 
 7? 
 
 7(i 
 
 208 
 
 33 
 
 36 
 
 40 
 
 45 
 
 50 
 
 54 
 
 59 
 
 64 
 
 68 
 
 72 
 
 75 
 
 78 
 
 80 
 
 83 
 
 -1 
 
 210 
 
 28 
 
 30 
 
 32 
 
 36 
 
 40 
 
 45 
 
 50 
 
 56 
 
 61 
 
 67 
 
 7-> 
 
 77 
 
 81 
 
 a". 
 
 89 
 
 212 
 
 27 
 
 26 
 
 26 
 
 29 
 
 32 
 
 36 
 
 41 
 
 47 
 
 53 
 
 60 
 
 66 
 
 73 
 
 79 
 
 
 90 
 
 214 
 
 28 
 
 26 
 
 24 
 
 24 
 
 85 
 
 29 
 
 33 
 
 38 
 
 44 
 
 51 
 
 59 
 
 66 
 
 74 
 
 82 
 
 
 216 
 
 33 
 
 28 
 
 25 
 
 23 
 
 22 
 
 83 
 
 27 
 
 31 
 
 36 
 
 43 
 
 50 
 
 58 
 
 67 
 
 76 
 
 85 
 
 218 
 
 40 
 
 34 
 
 29 
 
 25 
 
 22 
 
 21 
 
 23 
 
 25 
 
 29 
 
 35 
 
 42 
 
 51 
 
 59 
 
 69 
 
 7:) 
 
 220 
 
 48 
 
 41 
 
 34 
 
 29 
 
 24 
 
 22 
 
 21 
 
 22 
 
 85 
 
 29 
 
 35 
 
 43 
 
 51 
 
 61 
 
 71 
 
 
 56 
 
 47 
 
 41 
 
 34 
 
 28 
 
 24 
 
 22 
 
 21 
 
 22 
 
 25 
 
 30 
 
 36 
 
 45 
 
 54 
 
 ' 1 
 
 994 
 
 63 
 
 66 
 
 48 
 
 41 
 
 34 
 
 29 
 
 25 
 
 22 
 
 22 
 
 23 
 
 86 
 
 31 
 
 38 
 
 47 
 
 57 
 
 226 
 
 70 
 
 63 
 
 55 
 
 48 
 
 40 
 
 34 
 
 29 
 
 25 
 
 23 
 
 22 
 
 24 
 
 28 
 
 33 
 
 41 
 
 50 
 
 228 
 
 76 
 
 70 
 
 63 
 
 55 
 
 47 
 
 40 
 
 34 
 
 29 
 
 25 
 
 23 
 
 23 
 
 25 
 
 30 
 
 36 
 
 44 
 
 230 
 
 81 
 
 76 
 
 69 
 
 G'J 
 
 54 
 
 47 
 
 40 
 
 34 
 
 29 
 
 98 
 
 24 
 
 98 
 
 27 
 
 
 39 
 
 939 
 
 86 
 
 81 
 
 7G 
 
 69 
 
 69 
 
 ."! 
 
 47 
 
 40 
 
 34 
 
 29 
 
 26 
 
 25 
 
 26 
 
 29 
 
 34 
 
 
 88 
 
 86 
 
 61 
 
 76 
 
 69 
 
 62 
 
 55 
 
 47 
 
 41 
 
 34 
 
 30 
 
 28 
 
 27 
 
 88 
 
 
 2:16 
 
 89 
 
 88 
 
 86 
 
 81 
 
 76 
 
 69 
 
 69 
 
 66 
 
 48 
 
 41 
 
 3G 
 
 39 
 
 80 
 
 
 :;i 
 
 938 
 
 -- 
 
 89 
 
 88 
 
 86 
 
 81 
 
 76 
 
 70 
 
 63 
 
 56 
 
 49 
 
 43 
 
 38 
 
 84 
 
 
 
 240 
 
 85 
 
 87 
 
 88 
 
 87 
 
 84 
 
 81 
 
 70 
 
 70 
 
 64 
 
 57 
 
 51 
 
 46 
 
 41 
 
 37 
 
 
 \Vhun 2-J4 J .7 is subtracted from Arg. I., add 147.64 to Arg. XI. 
 
70 
 
 TABLE XXXVIII. 
 
 Perturbations of the Latitude, by Jupiter. 
 
 Horizontal Argument = 1. 
 
 Constant added 0".'J1. Period of Argument I., 234-1.7. 
 
 Arg. 
 Xlll. 
 
 d 
 
 
 
 d 
 
 8 
 
 d 
 
 10 
 
 d 
 
 21 
 
 d 
 
 a a 
 
 d 
 
 40 
 
 d 
 
 48 
 
 d 
 56 
 
 d d 
 
 61 73 
 
 d 
 
 
 
 d 
 
 8 
 
 96 
 
 101 
 
 d 
 113 
 
 
 
 17 
 
 14 
 
 11 
 
 9 
 
 7 
 
 6 
 
 5 
 
 5 
 
 6 
 
 G 
 
 8 
 
 10 
 
 12 
 
 IS 
 
 18 
 
 1 
 
 21 
 
 18 
 
 15 
 
 12 
 
 9 
 
 7 
 
 6 
 
 5 
 
 4 
 
 5 
 
 5 
 
 7 
 
 9 
 
 12 
 
 15 
 
 2 
 
 25 
 
 22 
 
 18 
 
 15 
 
 12 
 
 9 
 
 7 
 
 5 
 
 4 
 
 4 
 
 4 
 
 5 
 
 6 
 
 9 
 
 11 
 
 3 
 
 29 
 
 2G 
 
 22 
 
 11) 
 
 15 
 
 12 
 
 9 
 
 7 
 
 5 
 
 4 
 
 . 3 
 
 3 
 
 4 
 
 6 
 
 8 
 
 4 
 
 32 
 
 29 
 
 2G 
 
 22 
 
 19 
 
 15 
 
 12 
 
 9 
 
 G 
 
 5 
 
 3 
 
 3 
 
 3 
 
 4 
 
 6 
 
 5 
 
 35 
 
 32 
 
 29 
 
 26 
 
 22 
 
 19 
 
 15 
 
 12 
 
 9 
 
 6 
 
 4 
 
 3 
 
 3 
 
 3 
 
 4 
 
 (i 
 
 37 
 
 35 
 
 32 
 
 29 
 
 26 
 
 22 
 
 18 
 
 15 
 
 11 
 
 8 
 
 G 
 
 4 
 
 3 
 
 3 
 
 3 
 
 7 
 
 38 
 
 37 
 
 35 
 
 39 
 
 89 
 
 20 
 
 22 
 
 18 
 
 15 
 
 11 
 
 8 
 
 G 
 
 4 
 
 3 
 
 3 
 
 8 
 
 39 
 
 38 
 
 37 
 
 34 
 
 39 
 
 29 
 
 25 
 
 22 
 
 18 
 
 11 
 
 11 
 
 9 
 
 6 
 
 6 
 
 4 
 
 9 
 
 39 
 
 38 
 
 38 
 
 36 
 
 34 
 
 31 
 
 28 
 
 25 
 
 21 
 
 18 
 
 15 
 
 12 
 
 9 
 
 7 
 
 5 
 
 10 
 
 37 
 
 38 
 
 38 
 
 37 
 
 35 
 
 33 
 
 31 
 
 28 
 
 24 
 
 21 
 
 18 
 
 15 
 
 12 
 
 10 
 
 8 
 
 11 
 
 3G 
 
 37 
 
 37 
 
 37 
 
 36 
 
 34 
 
 32 
 
 30 
 
 27 
 
 24 
 
 21 
 
 18 
 
 15 
 
 13 
 
 11 
 
 13 
 
 33 
 
 35 
 
 36 
 
 36 
 
 36 
 
 35 
 
 34 
 
 32 
 
 30 
 
 27 
 
 24 
 
 22 
 
 19 
 
 16 
 
 14 
 
 13 
 
 30 
 
 32 
 
 34 
 
 35 
 
 35 
 
 35 
 
 34 
 
 33 
 
 31 
 
 29 
 
 27 
 
 25 
 
 22 
 
 20 
 
 17 
 
 14 
 
 27 
 
 29 
 
 31 
 
 32 
 
 33 
 
 34 
 
 34 
 
 34 
 
 33 
 
 31 
 
 29 
 
 27 
 
 25 
 
 23 
 
 21 
 
 15 
 
 23 
 
 26 
 
 28 
 
 30 
 
 31 
 
 32 
 
 33 
 
 33 
 
 33 
 
 32 
 
 31 
 
 30 
 
 28 
 
 26 
 
 24 
 
 16 
 
 20 
 
 22 
 
 25 
 
 27 
 
 28 
 
 30 
 
 31 
 
 32 
 
 33 
 
 33 
 
 32 
 
 31 
 
 30 
 
 2!) 
 
 27 
 
 17 
 
 17 
 
 19 
 
 21 
 
 23 
 
 25 
 
 27 
 
 29 
 
 31 
 
 32 
 
 32 
 
 33 
 
 33 
 
 32 
 
 31 
 
 30 
 
 18 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 27 
 
 29 
 
 30 
 
 32 
 
 33 
 
 33 
 
 33 
 
 33 
 
 32 
 
 19 
 
 11 
 
 13 
 
 15 
 
 17 
 
 19 
 
 21 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 33 
 
 34 
 
 34 
 
 34 
 
 20 
 
 9 
 
 10 
 
 12 
 
 14 
 
 1C 
 
 18 
 
 21 
 
 23 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 34 
 
 35 
 
 21 
 
 8 
 
 8 
 
 9 
 
 11 
 
 13 
 
 is 
 
 18 
 
 20 
 
 23 
 
 26 
 
 as 
 
 31 
 
 33 
 
 34 
 
 35 
 
 22 
 
 7. 
 
 7 
 
 7 
 
 '.) 
 
 10 
 
 12 
 
 15 
 
 18 
 
 20 
 
 23 
 
 26 
 
 29 
 
 32 
 
 34 
 
 35 
 
 23 
 
 7 
 
 6 
 
 6 
 
 7 
 
 8 
 
 10 
 
 12 
 
 15 
 
 18 
 
 21 
 
 24 
 
 27 
 
 30 
 
 89 
 
 34 
 
 24 
 
 7 
 
 " 6 
 
 5 
 
 6 
 
 6 
 
 8 
 
 10 
 
 12 
 
 15 
 
 18 
 
 21 
 
 25 
 
 28 
 
 31 
 
 33 
 
 25 
 
 8 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 13 
 
 15 
 
 19 
 
 22 
 
 25 
 
 28 
 
 31 
 
 26 
 
 9 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 13 
 
 16 
 
 10 
 
 23 
 
 26 
 
 29 
 
 27 
 
 11 
 
 9 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 & 
 
 11 
 
 14 
 
 17 
 
 20 
 
 24 
 
 27 
 
 28 
 
 14 
 
 11 
 
 8 
 
 7 
 
 5 
 
 5 
 
 5 
 
 6 
 
 i 
 
 i) 
 
 12 
 
 15 
 
 18 
 
 21 
 
 24 
 
 29 
 
 16 
 
 13 
 
 10 
 
 8 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 15 
 
 18 
 
 22 
 
 30 
 
 19 
 
 16 
 
 13 
 
 10 
 
 8 
 
 6 
 
 6 
 
 5 
 
 6 
 
 7 
 
 8 
 
 10 
 
 13 
 
 16 
 
 19 
 
 31 
 
 21 
 
 18 
 
 16 
 
 12 
 
 10 
 
 8 
 
 7 
 
 6 
 
 6 
 
 6 
 
 7 
 
 9 
 
 11 
 
 14 
 
 16 
 
 32 
 
 24 
 
 21 
 
 18 
 
 15 
 
 12 
 
 10 
 
 8 
 
 7 
 
 7 
 
 6 
 
 7 
 
 8 
 
 10 
 
 12 
 
 14 
 
 33 
 
 27 
 
 24 
 
 21 
 
 18 
 
 15 
 
 13 
 
 11 
 
 9 
 
 8 
 
 7 
 
 7 
 
 7 
 
 9 
 
 10 
 
 12 
 
 34 
 
 29 
 
 26 
 
 24 
 
 21 
 
 18 
 
 15 
 
 13 
 
 11 
 
 9 
 
 8 
 
 7 
 
 7 
 
 8 
 
 9 
 
 10 
 
 35 
 
 31 
 
 29 
 
 26 
 
 24 
 
 21 
 
 18 
 
 16 
 
 14 
 
 11 
 
 10 
 
 9 
 
 8 
 
 8 
 
 8 
 
 9 
 
 36 
 
 33 
 
 31 
 
 29 
 
 27 
 
 24 
 
 22 
 
 19 
 
 16 
 
 14 
 
 12 
 
 10 
 
 9 
 
 8 
 
 7 
 
 7 
 
 37 
 
 34 
 
 33 
 
 31 
 
 30 
 
 27 
 
 25 
 
 22 
 
 19 
 
 17 
 
 14 
 
 12 
 
 10 
 
 9 
 
 8 
 
 7 
 
 38 
 
 35 
 
 34 
 
 33 
 
 32 
 
 30 
 
 28 
 
 25 
 
 23 
 
 20 
 
 17 
 
 15 
 
 12 
 
 10 
 
 8 
 
 7 
 
 39 
 
 35 
 
 35 
 
 35 
 
 34 
 
 33 
 
 31 
 
 29 
 
 26 
 
 23 
 
 20 
 
 18 
 
 15 
 
 12 
 
 10 
 
 8 
 
 40 
 
 35 
 
 36 
 
 36 
 
 36 
 
 35 
 
 34 
 
 32 
 
 29 
 
 27 
 
 24 
 
 21 
 
 17 
 
 15 
 
 12 
 
 9 
 
 41 
 
 34 
 
 35 
 
 36 
 
 37 
 
 37 
 
 36 
 
 34 
 
 32 
 
 30 
 
 27 
 
 24 
 
 20 
 
 17 
 
 14 
 
 11 
 
 42 
 
 32 
 
 34 
 
 36 
 
 37 
 
 38 
 
 38 
 
 37 
 
 35 
 
 33 
 
 30 
 
 27 
 
 24 
 
 20 
 
 17 
 
 13 
 
 43 
 
 30 
 
 33 
 
 35 
 
 37 
 
 38 
 
 39 
 
 39 
 
 37 
 
 36 
 
 33 
 
 31 
 
 27 
 
 24 
 
 20 
 
 16 
 
 44 
 
 28 
 
 31 
 
 34 
 
 36 
 
 38 
 
 39 
 
 40 
 
 39 
 
 38 
 
 36 
 
 34 
 
 30 
 
 27 
 
 23 
 
 19 
 
 45 
 
 25 
 
 28 
 
 32 
 
 35 
 
 37 
 
 39 
 
 40 
 
 40 
 
 No 
 
 39 
 
 36 
 
 34 
 
 30 
 
 26 
 
 22 
 
 46 
 
 22 
 
 25 
 
 29 
 
 33 
 
 36 
 
 38 
 
 40 
 
 41 
 
 41 
 
 40 
 
 39 
 
 36 
 
 33 
 
 30 
 
 26 
 
 47 
 
 18 
 
 22 
 
 26 
 
 30 
 
 34 
 
 37 
 
 39 
 
 41 
 
 41 
 
 41 
 
 40 
 
 38 
 
 36 
 
 33 
 
 29 
 
 48 
 
 15 
 
 19 
 
 23 
 
 27 
 
 31 
 
 35 
 
 37 
 
 40 
 
 41 
 
 41 
 
 41 
 
 40 
 
 38 
 
 35 
 
 32 
 
 49 
 
 12 
 
 16 
 
 20 
 
 24 
 
 23 
 
 32 
 
 35 
 
 38 
 
 40 
 
 41 
 
 41 
 
 41 
 
 39 
 
 37 
 
 35 
 
 50 
 
 9 
 
 12 
 
 16 
 
 20 
 
 25 
 
 28 
 
 32 
 
 35 
 
 38 
 
 40 
 
 41 
 
 41 
 
 40 
 
 39 
 
 37 
 
 5! 
 
 6 
 
 9 
 
 13 
 
 17 
 
 21 
 
 25 
 
 29 
 
 32 
 
 35 
 
 38 
 
 39 
 
 40 
 
 40 
 
 39 
 
 38 
 
 52 
 
 5 
 
 7 
 
 10 
 
 14 
 
 17 
 
 21 
 
 25 
 
 29 
 
 32 
 
 35 
 
 37 
 
 38 
 
 39 
 
 39 
 
 39 
 
 53 
 
 4 
 
 5 
 
 8 
 
 11 
 
 11 
 
 17 
 
 21 
 
 25 
 
 28 
 
 31 
 
 34 
 
 36 
 
 38 
 
 38 
 
 38 
 
 54 
 
 3 
 
 4 
 
 6 
 
 8 
 
 11 
 
 14 
 
 17 
 
 21 
 
 24 
 
 27 
 
 30 
 
 33 
 
 35 
 
 37 
 
 38 
 
 55 
 
 4 
 
 4 
 
 5 
 
 6 
 
 8 
 
 11 
 
 14 
 
 17 
 
 20 
 
 23 
 
 27 
 
 30 
 
 32 
 
 34 
 
 36 
 
 56 
 
 5 
 
 4 
 
 4 
 
 5 
 
 7 
 
 8 
 
 11 
 
 13 
 
 16 
 
 1!) 
 
 23 
 
 26 
 
 28 . 
 
 31 
 
 33 
 
 57 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 7 
 
 8 
 
 10 
 
 13 
 
 15 
 
 18 
 
 21 
 
 21 
 
 27 
 
 30 
 
 58 
 
 10 
 
 8 
 
 G 
 
 6 
 
 5 
 
 5 
 
 6 
 
 8 
 
 1) 
 
 12 
 
 14 
 
 17 
 
 20 
 
 23 
 
 26 
 
 59 
 
 13 
 
 II 
 
 !) 
 
 7 
 
 6 
 
 5 
 
 5 
 
 6 
 
 7 
 
 9 
 
 11 
 
 14 
 
 16 
 
 19 
 
 22 
 
 GO 
 
 17 
 
 14 
 
 11 
 
 9 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 G 
 
 8 
 
 10 
 
 12 
 
 15 
 
 18 
 
 'Die perturbations are expressed in hundredtlis of a second of arc. 
 
TA1IL.E XXXVIII. 
 
 Perturbations / 'the La/Huilf, Inj ./<//<//.-;. 
 
 Cuii>l.iMl aildi'd II". -'I. IV rind i>r Ariinii-iil M II., l>i> units. 
 
 * r,. 
 
 .1 
 
 .1 
 
 .1 
 
 .1 
 
 
 
 
 .1 
 
 .1 
 
 
 .1 
 
 
 .1 
 
 .1 
 
 
 AFC. 
 
 XIII. 
 
 129 
 
 
 
 131 
 
 13.J 
 
 100 
 
 16* 
 
 170 
 
 1*1 
 
 192 
 
 200 
 
 20* 
 
 210 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 89 
 
 89 
 
 
 81 
 
 83 
 
 35 
 
 87 
 
 
 36 
 
 37 
 
 36 
 
 38 
 
 39 
 
 98 
 
 98 
 
 i 
 
 IS 
 
 81 
 
 83 
 
 
 31 
 
 34 
 
 36 
 
 37 
 
 38 
 
 
 
 37 
 
 35 
 
 33 
 
 80 
 
 9 
 
 II 
 
 ia 
 
 Jl 
 
 93 
 
 88 
 
 31 
 
 34 
 
 36 
 
 
 
 
 30 
 
 37 
 
 38 
 
 33 
 
 3 
 
 II 
 
 II 
 
 17 
 
 Jl 
 
 85 
 
 
 31 
 
 34 
 
 36 
 
 
 .: i 
 
 30 
 
 30 
 
 37 
 
 35 
 
 4 
 
 - 
 
 II 
 
 14 
 
 17 
 
 81 
 
 j:, 
 
 98 
 
 
 
 37 
 
 38 
 
 
 30 
 
 38 
 
 37 
 
 5 
 
 6 
 
 a 
 
 II 
 
 1 1 
 
 18 
 
 21 
 
 95 
 
 90 
 
 39 
 
 34 
 
 37 
 
 
 30 
 
 39 
 
 38 
 
 (i 
 
 1 
 
 6 
 
 8 
 
 II 
 
 II 
 
 18 
 
 89 
 
 96 
 
 
 39 
 
 84 
 
 36 
 
 38 
 
 36 
 
 30 
 
 7 
 
 :! 
 
 5 
 
 (i 
 
 g 
 
 19 
 
 15 
 
 Id 
 
 
 J.-. 
 
 j i 
 
 32 
 
 34 
 
 36 
 
 37 
 
 38 
 
 8 
 
 I 
 
 1 
 
 5 
 
 7 
 
 9 
 
 19 
 
 IS 
 
 10 
 
 89 
 
 96 
 
 88 
 
 31 
 
 33 
 
 36 
 
 36 
 
 
 
 5 
 
 1 
 
 8 
 
 (i 
 
 8 
 
 10 
 
 13 
 
 16 
 
 10 
 
 99 
 
 95 
 
 M 
 
 30 
 
 88 
 
 34 
 
 10 
 
 6 
 
 6 
 
 6 
 
 6 
 
 7 
 
 !) 
 
 11 
 
 19 
 
 16 
 
 19 
 
 99 
 
 21 
 
 27 
 
 
 39 
 
 II 
 
 9 
 
 7 
 
 7 
 
 7 
 
 7 
 
 8 
 
 9 
 
 11 
 
 13 
 
 16 
 
 18 
 
 Jl 
 
 24 
 
 26 
 
 
 19 
 
 19 
 
 10 
 
 B 
 
 8 
 
 8 
 
 8 
 
 8 
 
 10 
 
 U 
 
 13 
 
 18 
 
 18 
 
 90 
 
 93 
 
 85 
 
 13 
 
 15 
 
 13 
 
 11 
 
 10 
 
 g 
 
 8 
 
 8 
 
 9 
 
 10 
 
 11 
 
 13 
 
 IS 
 
 17 
 
 10 
 
 99 
 
 14 
 
 U 
 
 16 
 
 11 
 
 19 
 
 n 
 
 10 
 
 9 
 
 9 
 
 9 
 
 10 
 
 11 
 
 12 
 
 14 
 
 16 
 
 18 
 
 16 
 
 99 
 
 19 
 
 17 
 
 15 
 
 13 
 
 19 
 
 10 
 
 16 
 
 8 
 
 9 
 
 10 
 
 10 
 
 13 
 
 13 
 
 16 
 
 Hi 
 
 96 
 
 83 
 
 91 
 
 18 
 
 16 
 
 n 
 
 19 
 
 11 
 
 10 
 
 B 
 
 a 
 
 9 
 
 10 
 
 11 
 
 19 
 
 17 
 
 88 
 
 86 
 
 94 
 
 
 19 
 
 17 
 
 16 
 
 13 
 
 11 
 
 M 
 
 9 
 
 8 
 
 8 
 
 9 
 
 H) 
 
 Id 
 
 31 
 
 90 
 
 27 
 
 85 
 
 99 
 
 '-' i 
 
 17 
 
 18 
 
 13 
 
 11 
 
 9 
 
 8 
 
 8 
 
 7 
 
 8 
 
 1!) 
 
 89 
 
 39 
 
 30 
 
 38 
 
 26 
 
 93 
 
 20 
 
 Id 
 
 15 
 
 13 
 
 11 
 
 9 
 
 7 
 
 7 
 
 7 
 
 20 
 
 36 
 
 34 
 
 39 
 
 31 
 
 89 
 
 96 
 
 23 
 
 30 
 
 17 
 
 IS 
 
 13 
 
 10 
 
 8 
 
 7 
 
 (i 
 
 Jl 
 
 36 
 
 35 
 
 :H 
 
 33 
 
 31 
 
 89 
 
 26 
 
 8) 
 
 90 
 
 17 
 
 II 
 
 11 
 
 8 
 
 7 
 
 6 
 
 99 
 
 36 
 
 36 
 
 36 
 
 35 
 
 83 
 
 81 
 
 39 
 
 26 
 
 23 
 
 30 
 
 16 
 
 13 
 
 II 
 
 8 
 
 7 
 
 96 
 
 86 
 
 36 
 
 37 
 
 86 
 
 36 
 
 88 
 
 31 
 
 88 
 
 36 
 
 99 
 
 H 
 
 16 
 
 13 
 
 10 
 
 H 
 
 94 
 
 35 
 
 36 
 
 37 
 
 37 
 
 37 
 
 35 
 
 33 
 
 31 
 
 38 
 
 95 
 
 * 33 
 
 18 
 
 18 
 
 12 
 
 9 
 
 25 
 
 34 
 
 36 
 
 37 
 
 37 
 
 37 
 
 36 
 
 35 
 
 33 
 
 30 
 
 97 
 
 94 
 
 Jl 
 
 17 
 
 14 
 
 11 
 
 26 
 
 32 
 
 34 
 
 36 
 
 37 
 
 37 
 
 37 
 
 36 
 
 34 
 
 33 
 
 39 
 
 27 
 
 2:i 
 
 90 
 
 17 
 
 14 
 
 27 
 
 30 
 
 39 
 
 34 
 
 36 
 
 37 
 
 37 
 
 37 
 
 36 
 
 34 
 
 31 
 
 80 
 
 98 
 
 23 
 
 19 
 
 Hi 
 
 96 
 
 97 
 
 30 
 
 33 
 
 88 
 
 36 
 
 37 
 
 37 
 
 36 
 
 88 
 
 89 
 
 31 
 
 98 
 
 
 33 
 
 10 
 
 
 
 25 
 
 38 
 
 30 
 
 33 
 
 35 
 
 36 
 
 36 
 
 36 
 
 36 
 
 34 
 
 32 
 
 30 
 
 37 
 
 35 
 
 21 
 
 30 
 
 22 
 
 25 
 
 38 
 
 30 
 
 33 
 
 34 
 
 35 
 
 36 
 
 36 
 
 35 
 
 34 
 
 32 
 
 30 
 
 37 
 
 Jl 
 
 31 
 
 19 
 
 22 
 
 96 
 
 
 30 
 
 32 
 
 34 
 
 35 
 
 35 
 
 88 
 
 34 
 
 89 
 
 31 
 
 90 
 
 27 
 
 tt 
 
 17 
 
 I'.l 
 
 99 
 
 85 
 
 99 
 
 31) 
 
 33 
 
 33 
 
 34 
 
 35 
 
 35 
 
 84 
 
 88 
 
 31 
 
 29 
 
 33 
 
 14 
 
 17 
 
 W 
 
 89 
 
 96 
 
 27 
 
 39 
 
 31 
 
 33 
 
 34 
 
 38 
 
 34 
 
 34 
 
 i!:i 
 
 31 
 
 34 
 
 M 
 
 14 
 
 16 
 
 19 
 
 33 
 
 24 
 
 37 
 
 30 
 
 31 
 
 33 
 
 34 
 
 34 
 
 34 
 
 M 
 
 33 
 
 35 
 
 10 
 
 11 
 
 13 
 
 16 
 
 18 
 
 21 
 
 34 
 
 36 
 
 39 
 
 31 
 
 32 
 
 34 
 
 34 
 
 86 
 
 34 
 
 36 
 
 8 
 
 9 
 
 11 
 
 13 
 
 15 
 
 18 
 
 31 
 
 33 
 
 36 
 
 38 
 
 31 
 
 39 
 
 34 
 
 86 
 
 35 
 
 37 
 
 7 
 
 8 
 
 9 
 
 10 
 
 19 
 
 15 
 
 17 
 
 30 
 
 93 
 
 35 
 
 38 
 
 31 
 
 83 
 
 84 
 
 88 
 
 38 
 
 6 
 
 6 
 
 7 
 
 8 
 
 ID 
 
 11 
 
 14 
 
 17 
 
 30 
 
 98 
 
 36 
 
 28 
 
 31 
 
 33 
 
 86 
 
 39 
 
 6 
 
 6 
 
 6 
 
 6 
 
 7 
 
 9 
 
 11 
 
 13 
 
 16 
 
 19 
 
 33 
 
 26 
 
 29 
 
 33 
 
 34 
 
 40 
 
 7 
 
 6 
 
 6 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 13 
 
 16 
 
 30 
 
 23 
 
 36 
 
 30 
 
 33 
 
 41 
 
 8 
 
 6 
 
 6 
 
 4 
 
 3 
 
 4 
 
 6 
 
 7 
 
 10 
 
 13 
 
 Hi 
 
 90 
 
 98 
 
 37 
 
 81 
 
 4',' 
 
 ID 
 
 7 
 
 5 
 
 3 
 
 3 
 
 3 
 
 3 
 
 5 
 
 7 
 
 10 
 
 13 
 
 16 
 
 80 
 
 94 
 
 98 
 
 4:) 
 
 19 
 
 9 
 
 6 
 
 4 
 
 3 
 
 2 
 
 3 
 
 3 
 
 4 
 
 7 
 
 10 
 
 13 
 
 17 
 
 21 
 
 25 
 
 44 
 
 15 
 
 11 
 
 8 
 
 5 
 
 3 
 
 2 
 
 1 
 
 1 
 
 3 
 
 4 
 
 7 
 
 10 
 
 14 
 
 18 
 
 99 
 
 45 
 
 18 
 
 14 
 
 10 
 
 7 
 
 4 
 
 2 
 
 I 
 
 1 
 
 1 
 
 2 
 
 4 
 
 7 
 
 11 
 
 14 
 
 18 
 
 46 
 
 89 
 
 17 
 
 13 
 
 10 
 
 6 
 
 4 
 
 3 
 
 1 
 
 
 
 1 
 
 3 
 
 5 
 
 8 
 
 II 
 
 15 
 
 47 
 
 95 
 
 21 
 
 17 
 
 13 
 
 9 
 
 6 
 
 3 
 
 9 
 
 1 
 
 1 
 
 ' 1 
 
 3 
 
 5 
 
 8 
 
 19 
 
 48 
 
 88 
 
 24 
 
 30 
 
 16 
 
 19 
 
 9 
 
 6 
 
 3 
 
 3 
 
 1 
 
 I 
 
 2 
 
 4 
 
 6 
 
 11 
 
 49 
 
 31 
 
 28 
 
 34 
 
 19 
 
 15 
 
 19 
 
 8 
 
 .6 
 
 4 
 
 2 
 
 1 
 
 2 
 
 3 
 
 4 
 
 7 
 
 10 
 
 31 
 
 31 
 
 27 
 
 98 
 
 19 
 
 M 
 
 13 
 
 9 
 
 6 
 
 4 
 
 3 
 
 2 
 
 3 
 
 3 
 
 5 
 
 51 
 
 
 38 
 
 30 
 
 27 
 
 93 
 
 1!) 
 
 16 
 
 19 
 
 9 
 
 7 
 
 5 
 
 4 
 
 3 
 
 3 
 
 4 
 
 69 
 
 37 
 
 SB 
 
 33 
 
 30 
 
 26 
 
 23 
 
 19 
 
 Hi 
 
 13 
 
 10 
 
 8 
 
 6 
 
 4 
 
 4 
 
 4 
 
 63 
 
 38 
 
 37 
 
 85 
 
 33 
 
 30 
 
 27 
 
 33 
 
 20 
 
 17 
 
 II 
 
 11 
 
 9 
 
 7 
 
 6 
 
 5 
 
 
 38 
 
 37 
 
 36 
 
 35 
 
 33 
 
 30 
 
 37 
 
 24 
 
 31 
 
 18 
 
 15 
 
 12 
 
 10 
 
 8 
 
 6 
 
 86 
 
 37 
 
 37 
 
 37 
 
 36 
 
 88 
 
 33 
 
 3') 
 
 28 
 
 96 
 
 
 19 
 
 16 
 
 13 
 
 11 
 
 8 
 
 ' 56 
 
 35 
 
 36 
 
 37 
 
 37 
 
 36 
 
 95 
 
 33 
 
 31 
 
 90 
 
 26 
 
 23 
 
 30 
 
 17 
 
 14 
 
 11 
 
 57 
 
 :i'J 
 
 34 
 
 36 
 
 36 
 
 37 
 
 M 
 
 35 
 
 34 
 
 89 
 
 80 
 
 37 
 
 34 
 
 21 
 
 1- 
 
 15 
 
 53 
 
 
 89 
 
 84 
 
 35 
 
 36 
 
 37 
 
 37 
 
 36 
 
 
 98 
 
 31 
 
 38 
 
 J.-, 
 
 99 
 
 19 
 
 60 
 
 96 
 
 29 
 
 31 
 
 34 
 
 35 
 
 37 
 
 37 
 
 :tr 
 
 37 
 
 86 
 
 84 
 
 89 
 
 91 
 
 36 
 
 
 
 
 
 28 
 
 31 
 
 33 
 
 96 
 
 37 
 
 38 
 
 38 
 
 37 
 
 36 
 
 35 
 
 
 
 39 
 
 98 
 
 When 234 J .7 U subtracted from Arg. I., add 3.11 to Arg. Mil. 
 
TABL.E XXXIX. 
 
 Values, for tin' li-^lnninif of l!n- year, of Ji\, A' v , iV' 1 ., ":nl of tlic Arguments of Nutation, for Washington 
 Mi'ttii J\ovn <f Jan. in Common Yearn and Jan. 1 in Bissextile Years. 
 
 Year. 
 
 A~ x . 
 
 K,. 
 
 K* 
 
 Log /; x . 
 
 Log ky. 
 
 Log k... 
 
 XV. 
 
 XVI. 
 
 
 / // 
 
 / // 
 
 o / // 
 
 
 
 
 d 
 
 a 
 
 1750 
 
 89 58 6.44 
 
 1 20 53.89 
 
 352 48 5.43 
 
 9.9992934 
 
 9.9595611 
 
 9.6191304 
 
 1504.7 
 
 1.9 
 
 1751 
 
 6.48 
 
 54.03 
 
 3.51 
 
 2933 
 
 5033 
 
 1202 
 
 1869.7 
 
 1.7 
 
 17625. 
 
 6.53 
 
 64.17 
 
 352 48 1.60 
 
 2932 
 
 5655 
 
 1100 
 
 2235.7 
 
 2.4 
 
 1753 
 
 6.57 
 
 54.31 
 
 352 47 59.68 
 
 2932 
 
 5677 
 
 0997 
 
 2600.7 
 
 2.2 
 
 1751 
 
 6.61 
 
 54.45 
 
 57.77 
 
 2931 
 
 5699 
 
 0895 
 
 29^5.7 
 
 2.0 
 
 1755 
 
 6.05 
 
 54.59 
 
 55.86 
 
 2931 
 
 5722 
 
 0793 
 
 3330.7 
 
 1.7 
 
 17565. 
 
 6.69 
 
 51.73 
 
 53.95 
 
 2930 
 
 5744 
 
 0691 
 
 3690.7 
 
 2.5 
 
 1757 
 
 6.73 
 
 54.87 
 
 52.04 
 
 2930 
 
 5766 
 
 0589 
 
 4061.7 
 
 2.2 
 
 1758 
 
 6.77 
 
 55.00 
 
 50.13 
 
 2929 
 
 5788 
 
 0480 
 
 4426.7 
 
 2.0 
 
 175!) 
 
 6.81 
 
 55.14 
 
 48.22 
 
 2928 
 
 5810 
 
 0384 
 
 4791.7 
 
 1.7 
 
 17605. 
 
 6.86 
 
 55.28 
 
 46.31 
 
 '2928 
 
 5832 
 
 0282 
 
 5157.7 
 
 2.5 
 
 1761 
 
 6.91 
 
 55.42 
 
 44.40 
 
 2927 
 
 5854 
 
 0180 
 
 5522.7 
 
 2.3 
 
 170-2 
 
 6.96 
 
 55.56 
 
 42.49 
 
 2926 
 
 5876 
 
 9.0190077 
 
 5887.7 
 
 2.0 
 
 17G3 
 
 7.02 
 
 55.70 
 
 40.58 
 
 2926 
 
 5899 
 
 9.6189975 
 
 6252.7 
 
 1.8 
 
 17045. 
 
 7.08 
 
 55.84- 
 
 38.68 
 
 2925 
 
 5921 
 
 9873 
 
 6618.7 
 
 2.5 
 
 17G5 
 
 7.13 
 
 55.97 
 
 36.77 
 
 2924 
 
 5943 
 
 9770 
 
 185.5 
 
 2.3 
 
 1700 
 
 7.18 
 
 56.11 
 
 34.87 
 
 2923 
 
 5965 
 
 9668 
 
 550.5 
 
 2.0 
 
 1707 
 
 7.24 
 
 56.25 
 
 32.96 
 
 2923 
 
 5987 
 
 9565 
 
 915.5 
 
 1.8 
 
 17685. 
 
 7.30 
 
 56.39 
 
 31.06 
 
 2922 
 
 6009 
 
 9463 
 
 1281.5 
 
 2.6 
 
 1709 
 
 7.35 
 
 56.52 
 
 29.15 
 
 2921 
 
 6031 
 
 9300 
 
 1646.5 
 
 2.3 
 
 1770 
 
 7.40 
 
 56.66 
 
 27.25 
 
 2920 
 
 6053 
 
 9258 
 
 2011.5 
 
 2.1 
 
 1771 
 
 7.44 
 
 56.80 
 
 25.35 
 
 2920 
 
 6076 
 
 9150 
 
 2376.5 
 
 1.8 
 
 IT12B. 
 
 7.48 
 
 56.94 
 
 23.44 
 
 2919 
 
 6098 
 
 9053 
 
 2742.5 
 
 2.6 
 
 1773 
 
 7.5-2 
 
 57.07 
 
 21.54 
 
 2919 
 
 6120 
 
 8951 
 
 3107.5 
 
 2.3 
 
 1774 
 
 7.57 
 
 57.21 
 
 19.64 
 
 2918 
 
 6142 
 
 8848 
 
 3472.5 
 
 2.1 
 
 1775 
 
 7.61 
 
 57.35 
 
 17.74 
 
 2918 
 
 6164 
 
 8740 
 
 3837.5 
 
 1.9 
 
 17705. 
 
 7.05 
 
 57,18 
 
 15.84 
 
 2917 
 
 6186 
 
 8644 
 
 4203.5 
 
 2.6 
 
 1777 
 
 7.69 
 
 57.62 
 
 13.94 
 
 2916 
 
 6208 
 
 8541 
 
 4568.5 
 
 2.4 
 
 1778 
 
 7.73 
 
 57.75 
 
 12.04 
 
 2916 
 
 6230 
 
 8439 
 
 4933.5 
 
 2.1 
 
 1779 
 
 7.78 
 
 57.89 
 
 10.14 
 
 2915 
 
 6252 
 
 8336 
 
 5298.5 
 
 1.9 
 
 17805. 
 
 7.83 
 
 58.03 
 
 8.24 
 
 2914 
 
 6275 
 
 8234 
 
 5664.5 
 
 2.6 
 
 1781 
 
 7.88 
 
 58.16 
 
 6.31 
 
 2914 
 
 6297 
 
 8132 
 
 6029.5 
 
 2.4 
 
 1782 
 
 7.94 
 
 58.30 
 
 4.44 
 
 2913 
 
 6319 
 
 8029 
 
 6394.5 
 
 2.2 
 
 1783 
 
 8.00 
 
 58.43 
 
 2.54 
 
 2912 
 
 6341 
 
 7927 
 
 6759.5 
 
 1.9 
 
 17845. 
 
 8.06 
 
 58.57 
 
 352 47 0.65 
 
 2911 
 
 6363 
 
 7824 
 
 327.2 
 
 2.7 
 
 1785 
 
 8.11 
 
 58.70 
 
 352 46 58.75 
 
 2911 
 
 6385 
 
 7722 
 
 692.2 
 
 2.4 
 
 1780 
 
 8.17 
 
 58.84 
 
 56.86 
 
 2910 
 
 6407 
 
 7619 
 
 1057.2 
 
 2.2 
 
 1787 
 
 8.'23 
 
 58.97 
 
 64.96 
 
 2909 
 
 6429 
 
 7517 
 
 1422.2 
 
 1.9 
 
 17885. 
 
 8.'28 
 
 59.11 
 
 53.07 
 
 2909 
 
 6452 
 
 7414 
 
 1788.2 
 
 2.7 
 
 1789 
 
 8.32 
 
 59.24 
 
 51.17 
 
 2908 
 
 6474 
 
 7312 
 
 2153.2 
 
 2.5 
 
 1790 
 
 8.36 
 
 59.38 
 
 49'.28 
 
 2907 
 
 6496 
 
 7209 
 
 2518.2 
 
 2.2 
 
 1791 
 
 8.40 
 
 59.51 
 
 47.39 
 
 2907 
 
 6518 
 
 7106 
 
 2883.2 
 
 2.0 
 
 179:25. 
 
 8.44 
 
 59.64 
 
 45.50 
 
 2906 
 
 6540 
 
 7004 
 
 3249.2 
 
 2.7 
 
 1793 
 
 8.48 
 
 59.78 
 
 43.60 
 
 2906 
 
 6562 
 
 6901 
 
 3614.2 
 
 2.5 
 
 1794 
 
 8.53 
 
 1 26 59.91 
 
 41.71 
 
 2905 
 
 6584 
 
 6799 
 
 3979.2 
 
 2.2 
 
 1795 
 
 8.57 
 
 1 27 0.05 
 
 39.82 
 
 2905 
 
 6000 
 
 6696 
 
 4344.2 
 
 2.0 
 
 17905. 
 
 8.61 
 
 0.18 
 
 37.93 
 
 2901 
 
 0029 
 
 6593 
 
 4710.2 
 
 2.8 
 
 1797 
 
 8.05 
 
 0.31 
 
 36.01 
 
 2903 
 
 0651 
 
 6491 
 
 5075.2 
 
 2.5 
 
 1798 
 
 8.70 
 
 0.45 
 
 34.15 
 
 2903 
 
 6673 
 
 6388 
 
 5440.2 
 
 2.3 
 
 1799 
 
 89 58 8.70 
 
 1 27 0.58 
 
 352 46 32.26 
 
 9.9992902 
 
 9.9596695 
 
 9.6 180286 
 
 5805.2 
 
 2.0 
 
 i c:ii-li of llin <iuuntitic.s A" x ., AT y and K 2 the constant 2J".00 has l>.'.-u : ;ul>tr;irt.'il ; uiiil from log A- y tlie constant 0.0000089, 
 
 and from log k, tliu constant U.UOOOuUi) 
 
TA11L.K X\\I\. 
 
 \'nliii:i,fiir the l- <> hi n in* of tin- iii-fir. /' A',. A",. A-'-., ami of tin- An;iiiiiciii.t of I\'iilii!i,ni,f,ir U'tmhiiigloH 
 
 : .\nnii iif'.ltiii. /;/ Cniii/iion \Vii;'.v mill .Inn. 1 I/I Iiit.-n.iti/,- i'lvirv. 
 
 Year. 
 
 A\. 
 
 K,. 
 
 A'. 
 
 Log A\. 
 
 Log Ay 
 
 Log i-,. 
 
 XV. 
 
 XVI. 
 
 
 / // 
 
 / '/ 
 
 / II 
 
 
 
 
 d 
 
 il 
 
 1800 
 
 89 5N N.NV! 
 
 1 27 0.71 
 
 K.VJ i<; :t(t.:57 
 
 !t.:i!l!l2!)01 
 
 !>.!l.-96717 
 
 9.61861S.-J 
 
 6170.2 
 
 l.s 
 
 1801 
 
 
 0.84 
 
 2S. IS 
 
 2900 
 
 6739 
 
 6080 
 
 6:>35.2 
 
 1.5 
 
 1802 
 
 8.98 
 
 0.98 
 
 ^(i.r.ii 
 
 2900 
 
 6761 
 
 5978 
 
 102.0 
 
 l.:( 
 
 1803 
 
 8.98 
 
 .11 
 
 24.70 
 
 2899 
 
 6783 
 
 6876 
 
 467.0 
 
 1.0 
 
 1804J3. 
 
 !U)1 
 
 .24 
 
 32.81 
 
 2898 
 
 6806 
 
 5778 
 
 S33.0 
 
 1.8 
 
 1805 
 
 9.09 
 
 .:!7 
 
 20.93 
 
 2897 
 
 6828 
 
 5670 
 
 llit.N.O 
 
 1.6 
 
 1S06 
 
 9.16 
 
 .51 
 
 19.04 
 
 2897 
 
 6850 
 
 5667 
 
 1563.0 
 
 1.3 
 
 1807 
 
 9.80 
 
 .64 
 
 17.16 
 
 2896 
 
 6872 
 
 5 16 1 
 
 lifJN.O 
 
 1.1 
 
 isos/;. 
 
 9.2 1 
 
 .77 
 
 15^7 
 
 2896 
 
 UN!) 1 
 
 . r .:!(W 
 
 2-J!M.<) 
 
 1.8 
 
 1S01) 
 
 9.2!) 
 
 .90 
 
 18.89 
 
 2895 
 
 6916 
 
 6259 
 
 j<;:.!).o 
 
 1.6 
 
 1H10 
 
 9.88 
 
 t>.():t 
 
 11.50 
 
 2894 
 
 6889 
 
 5156 
 
 30v! 1.0 
 
 1.1 
 
 1H11 
 
 9.31 
 
 2. Hi 
 
 9.ea 
 
 2894 
 
 6961 
 
 5053 
 
 33N9.0 
 
 1.1 
 
 isiae. 
 
 !>. 1 1 
 
 ..'.:{<> 
 
 7.71 
 
 2898 
 
 6983 
 
 4950 
 
 3755.0 
 
 1.9 
 
 1813 
 
 :>. ir> 
 
 iU3 
 
 :>:. 
 
 2898 
 
 7015 
 
 4848 
 
 4120.0 
 
 1.6 
 
 1814 
 
 9.19 
 
 8.56 
 
 3.97 
 
 2892 
 
 7037 
 
 4745 
 
 1 1S.-..0 
 
 1.1 
 
 1818 
 
 !t.;>3 
 
 2.69 
 
 2.09 
 
 2892 
 
 7059 
 
 4642 
 
 4850.0 
 
 1.1 
 
 18 Hi/;. 
 
 9.58 
 
 2.82 
 
 .i.'.-J -16 0.21 
 
 2891 
 
 7082 
 
 4539 
 
 5216.0 
 
 1.!) 
 
 1817 
 
 9.63 
 
 ZJ95 
 
 :i.vj i.-) rs.:j3 
 
 2890 
 
 7101 
 
 4436 
 
 5581.0 
 
 1.7 
 
 
 9.69 
 
 :{.os 
 
 56.45 
 
 2890 
 
 7 rj<i 
 
 i:c( I 
 
 5!) 16.0 
 
 1.1 
 
 1819 
 
 9.75 
 
 :{.-Jl 
 
 51.57 
 
 2889 
 
 7148 
 
 4381 
 
 6311.0 
 
 1.2 
 
 18207?. 
 
 9.80 
 
 :).:u 
 
 52.69 
 
 2S8S 
 
 7170 
 
 4128 
 
 6677.0 
 
 1.9 
 
 1821 
 
 9.85 
 
 :{,I7 
 
 50.81 
 
 2887 
 
 7192 
 
 4025 
 
 2 13.7 
 
 1.7 
 
 1822 
 
 !).!)! 
 
 3.60 
 
 48.93 
 
 JNN- 
 
 7215 
 
 8922 
 
 608.7 
 
 1.4 
 
 1823 
 
 !).!)7 
 
 :t.7.'{ 
 
 47.06 
 
 2886 
 
 7287 
 
 3820 
 
 973.7 
 
 1.2 
 
 1824A 
 
 10.03 
 
 3.86 
 
 45.18 
 
 2SS5 
 
 7380 
 
 3717 
 
 1339.7 
 
 2.0 
 
 182S 
 
 10.08 
 
 3.99 
 
 43.30 
 
 2885 
 
 7281 
 
 3614 
 
 1704.7 
 
 1.7 
 
 1826 
 
 10.18 
 
 4.12 
 
 41.43 
 
 2884 
 
 7:to:i 
 
 3511 
 
 2069.7 
 
 1.5 
 
 1827 
 
 11.17 
 
 L35 
 
 39.55 
 
 jss:{ 
 
 7825 
 
 3 ION 
 
 2434.7 
 
 1.2 
 
 1S28#. 
 
 10.21 
 
 4.38 
 
 37.68 
 
 jss:t 
 
 7.'5 17 
 
 3305 
 
 2800.7 
 
 2.0 
 
 1829 
 
 10.25 
 
 4.51 
 
 35.80 
 
 ^ss-^ 
 
 7570 
 
 8208 
 
 3165.7 
 
 1.7 
 
 1830 
 
 10.29 
 
 4.63 
 
 33.93 
 
 Jss-> 
 
 7899 
 
 3099 
 
 3530.7 
 
 1.5 
 
 1881 
 
 10.33 
 
 4.76 
 
 32.06 
 
 Jssi 
 
 7414 
 
 2996 
 
 3805.7 
 
 1.3 
 
 18335. 
 
 K).:i7 
 
 4.89 
 
 30.19 
 
 2881 
 
 713G 
 
 2893 
 
 1281.7 
 
 2.0 
 
 1833 
 
 10.42 
 
 5.02 
 
 28.31 
 
 2880 
 
 7 i:.s 
 
 2790 
 
 4626.7 
 
 1.8 
 
 1834 
 
 10.16 
 
 . 5.15 
 
 26.44 
 
 2879 
 
 7480 
 
 MB? 
 
 4991.7 
 
 1.5 
 
 1835 
 
 lO.r. 1 
 
 5.28 
 
 J 1.57 
 
 2879 
 
 7503 
 
 2584 
 
 5356.7 
 
 1.3 
 
 1836 B. 
 
 10.57 
 
 5.40 
 
 22.70 
 
 2878 
 
 7525 
 
 2481 
 
 5722.7 
 
 2.0 
 
 1837 
 
 10.62 
 
 5.53 
 
 20.83 
 
 2877 
 
 784S 
 
 2878 
 
 lids-;.-; 
 
 l.N 
 
 1838 
 
 10.68 
 
 5.66 
 
 18.96 
 
 2877 
 
 7569 
 
 2275 
 
 (i 152.7 
 
 1.6 
 
 1839 
 
 10.73 
 
 5.79 
 
 17.09 
 
 2876 
 
 7591 
 
 2172 
 
 19.4 
 
 1.3 
 
 1840B. 
 
 10.78 
 
 5.91 
 
 15.22 
 
 2875 
 
 7613 
 
 2069 
 
 385.4 
 
 2.1 
 
 1M1 
 
 10.84 
 
 6.04 
 
 18,86 
 
 2875 
 
 7636 
 
 1966 
 
 750.4 
 
 1.8 
 
 1842 
 
 10.90 
 
 6.17 
 
 11.48 
 
 2874 
 
 7668 
 
 1863 
 
 1115.4 
 
 1.6 
 
 IN 13 
 
 10.95 
 
 6.30 
 
 9.62 
 
 2873 
 
 7 CM) 
 
 1760 
 
 1480.4 
 
 1.3 
 
 18442?. 
 
 11.01 
 
 6.42 
 
 7.75 
 
 2872 
 
 7702 
 
 1657 
 
 1846.4 
 
 2.1 
 
 1845 
 
 11.06 
 
 6.55 
 
 5.88 
 
 2872 
 
 7784 
 
 I.V.I 
 
 2211.4 
 
 1.9 
 
 is Hi 
 
 11.10 
 
 6.67 
 
 4.01 
 
 2871 
 
 7746 
 
 lir.i 
 
 2576.4 
 
 1.6 
 
 1847 
 
 11.14 
 
 6.80 
 
 2.15 
 
 2871 
 
 7769 
 
 1848 
 
 2911.4 
 
 1.4 
 
 18482?. 
 
 11.18 
 
 6.93 
 
 :i.vj 15 0.28 
 
 2870 
 
 7791 
 
 1245 
 
 3307.4 
 
 2.1 
 
 1849 
 
 89 58 11.22 
 
 1 27 7.05 
 
 3.VJ -14 58.42 
 
 9.9992870 
 
 9.9597 M3 
 
 9.6181112 
 
 36V..!. 1 
 
 1.9 
 
 From each of the quantities K x , h\ anil A'z, <<"' i.nslant ','H" no !,;,< I,,-. sirlnr.-i.-tnl ; ami IVum log /.,. the cunslant O.OOOOOS'J, 
 ami from lug /., the constant 0.0000560. 
 
74 
 
 TABLE XXXIX. 
 
 Values, for the beginning of ///< i/nir, of K^ 7i v , <^c., and of the Arguments of Nutation, for Washington 
 Mean Noon of Jan. in Common Years and Jan. 1 in Bissextile Years. 
 
 Year. 
 
 AV 
 
 A',. K v 
 
 Log k*. 
 
 Log k s . 
 
 Log k z . 
 
 XV. 
 
 XVI. 
 
 
 o / II 
 
 / // 
 
 a 1 II 
 
 
 
 
 a 
 
 a 
 
 1850 
 
 89 58 11.27 
 
 1 27 7.18 
 
 352 44 56.55 
 
 9.9992869 
 
 9.9597825 
 
 9.6181039 
 
 4037.4 
 
 1.6 
 
 1851 
 
 11.31 
 
 7.31 i 54.69 
 
 2869 
 
 7847 
 
 0936 
 
 4402.4 
 
 1.4 
 
 18525. 
 
 11.35 
 
 7.13 
 
 52.83 
 
 2868 
 
 7869 
 
 0833 
 
 4768.4 
 
 2.2 
 
 1858 
 
 11.40 
 
 7.56 
 
 50.96 
 
 2867 
 
 7891 
 
 0729 
 
 5133.4 
 
 1.9 
 
 1854 
 
 11.44 
 
 7.68 
 
 49.10 
 
 2867 
 
 7914 
 
 0626 
 
 5198,4 
 
 1.7 
 
 1855 
 
 11.50 
 
 7.81 
 
 47.24 
 
 2866 
 
 7936 
 
 0523 
 
 5863,4 
 
 1.4 
 
 18565. 
 
 11.56 
 
 7.93 
 
 45.38 
 
 2865 
 
 7958 
 
 0420 
 
 6229,1 
 
 2.2 
 
 1857 
 
 11.63 
 
 8.08 
 
 43.52 
 
 2865 
 
 7980 
 
 0317 
 
 6591.4 
 
 1.9 
 
 1858 
 
 11.67 
 
 8.18 
 
 41.66 
 
 2864 
 
 8002 
 
 0213 
 
 161.2 
 
 1.7 
 
 185!) 
 
 11.73 
 
 8.31 
 
 39.80 
 
 2863 
 
 8021 
 
 0110 
 
 526.2 
 
 1.5 
 
 18(501?. 
 
 11.79 
 
 8.43 
 
 37.94 
 
 2863 
 
 8046 
 
 9.6180007 
 
 892.2 
 
 2.2 
 
 1801 
 
 11.81 
 
 8.5(5 
 
 36.08 
 
 2862 
 
 8069 
 
 9.6179904 
 
 1257.2 
 
 2.0 
 
 1862 
 
 11.89 
 
 8.68 
 
 3 1.22 
 
 2861 
 
 8091 
 
 9801 
 
 1622.2 
 
 1.7 
 
 1863 
 
 11.91 
 
 8.80 
 
 32.37 
 
 2861 
 
 8113 
 
 9697 
 
 1987.2 
 
 1.5 
 
 18645. 
 
 11.99 
 
 8.93- 
 
 30.51 
 
 2860 
 
 8135 
 
 9594 
 
 2353.2 
 
 2.2 
 
 18(55 
 
 12.03 
 
 9.05 
 
 28.65 
 
 2859 
 
 8157 
 
 9491 
 
 2718.2 
 
 2.0 
 
 1866 
 
 12.07 
 
 9.18 
 
 26.79 
 
 2859 
 
 8179 
 
 9388 
 
 3083.2 
 
 1.8 
 
 18(57 
 
 12.11 
 
 9.30 
 
 24.94 
 
 2858 
 
 8201 
 
 9285 
 
 3448.2 
 
 1.5 
 
 18685. 
 
 12.15 
 
 9.42 
 
 23.08 
 
 2858 
 
 8224 
 
 9181 
 
 3814.2 
 
 2.3 
 
 1869 
 
 12.19 
 
 9.55 
 
 21.23 
 
 2857 
 
 8246 
 
 9078 
 
 4179.2 
 
 2.0 
 
 1870 
 
 12.24 
 
 9.67 
 
 19.37 
 
 2857 
 
 8268 
 
 8975 
 
 4544.2 
 
 1.8 
 
 1871 
 
 12.28 
 
 9.79 
 
 17.52 
 
 2856 
 
 8290 
 
 8872 
 
 4909.2 
 
 1.5 
 
 18725. 
 
 12.33 
 
 9.92 
 
 15.67 
 
 2856 
 
 8312 
 
 8768 
 
 5275.2 
 
 2.3 
 
 1873 
 
 12.39 
 
 10.04 
 
 13.81 
 
 2855 
 
 8334 
 
 8665 
 
 56 10.2 
 
 2.1 
 
 1874 
 
 12.44 
 
 10.16 
 
 11.96 
 
 2854 
 
 8356 
 
 8561 
 
 6005.2 
 
 1.8 
 
 1875 
 
 12.50 
 
 10.28 
 
 10.11 
 
 2854 
 
 8378 
 
 8458 
 
 6370.2 
 
 1.6 
 
 187(55. 
 
 12.56 
 
 10.40 
 
 8.26 
 
 2853 
 
 8401 
 
 8355 
 
 6736.2 
 
 2.3 
 
 1877 
 
 12.62 
 
 10.53 
 
 6.41 
 
 2852 
 
 8423 
 
 8251 
 
 302.9 
 
 2.1 
 
 1878 
 
 12.67 
 
 10.65 
 
 4.56 
 
 2851 
 
 8445 
 
 8148 
 
 667.9 
 
 1.8 
 
 1879 
 
 12.73 
 
 10.77 
 
 2.71 
 
 2851 
 
 8467 
 
 8044 
 
 1032.9 
 
 1.6 
 
 18805. 
 
 12.78 
 
 10.89 
 
 352 44 0.86 
 
 2850 
 
 8489 
 
 7941 
 
 1398.9 
 
 2.4 
 
 1881 
 
 12.83 
 
 11.01 
 
 352 43 59.01 
 
 2849 
 
 8511 
 
 7838 
 
 1763.9 
 
 2.1 
 
 1882 
 
 12.88 
 
 11.14 
 
 57.16 
 
 2849 
 
 8533 
 
 7734 
 
 2128.9 
 
 1.9 
 
 1883 
 
 12.93 
 
 11.26 
 
 55.32 
 
 2848 
 
 8556 
 
 7631 
 
 2493.9 
 
 1.6 
 
 18845. 
 
 12.97 
 
 11.38 
 
 53.47 
 
 2848 
 
 8578 
 
 . 7528 
 
 2859.9 
 
 2.4 
 
 1885 
 
 13.01 
 
 11.50 
 
 51.62 
 
 .2847 
 
 8600 
 
 7121 
 
 3224.9 
 
 2.1 
 
 1886 
 
 13.05 
 
 11.62 
 
 49.77 
 
 2847 
 
 8622 
 
 7321 
 
 3589.9 
 
 1.9 
 
 1887 
 
 13.09 
 
 11.71 
 
 47.93 
 
 2846 
 
 8644 
 
 7217 
 
 395 1.9 
 
 1.7 
 
 18885. 
 
 13.13 
 
 11.86 
 
 46.08 
 
 2846 
 
 8666 
 
 7114 
 
 4330.9 
 
 2.4 
 
 1889 
 
 13.18 
 
 11.98 
 
 44.24 
 
 2815 
 
 8688 
 
 7010 
 
 4685.9 
 
 2.2 
 
 1890 
 
 13.22 
 
 12.10 
 
 42.39 
 
 2844 
 
 8711 
 
 6907 
 
 5050.9 
 
 1.9 
 
 1891 
 
 13.27 
 
 12.22 
 
 40.55 
 
 2844 
 
 8733 
 
 6S01 
 
 5115.9 
 
 1.7 
 
 . 189-25. 
 
 13.33 
 
 12.84 
 
 38.71 
 
 28 13 
 
 8755. 
 
 6700 
 
 5781.9 
 
 2.4 
 
 1893 
 
 13.39 
 
 12,16 
 
 36.86 
 
 2812 
 
 8777 
 
 6597 
 
 6146.9 
 
 2.2 
 
 1894 
 
 13.45 
 
 12.58 
 
 35.02 
 
 2842 
 
 8799 
 
 6493 
 
 6511.9 
 
 2.0 
 
 1895 
 
 13.50 
 
 12.70 
 
 33.18 
 
 2811 
 
 8821 
 
 6390 
 
 78.6 
 
 1.7 
 
 18965. 
 
 13.56 
 
 12.82 
 
 31.34 
 
 2840 
 
 8843 
 
 6286 
 
 111.6 
 
 2.5 
 
 1897 
 
 13.62 
 
 12.!) 1 
 
 29.50 
 
 2840 
 
 8866 
 
 61 S3 
 
 809.6 
 
 2.2 
 
 1898 
 
 13.07 
 
 13.06 
 
 27.66 
 
 
 8888 
 
 6079 
 
 111 1.6 
 
 2.0 
 
 1899 
 
 89 58 13.73 
 
 1 27 13.18 
 
 352 13 25.82 
 
 9.9992838 
 
 9.9598910 
 
 9.6175976 
 
 1539.6 
 
 1.7 
 
 1'ruin each oftlic quantities /vV, /v' y ami k", tin; constant 'i I".')!) h.i . been laliirarti.'cl ; and from lo h y thu constant 0.0000089, 
 
 and from lu;_' /.'., the constant 0.0000500 
 
TABLE \V\I\. 
 
 75 
 
 Vn/iir.f, fur III'' tii-iji luting nl l/i:' i/i-iir. i'/' A" . A",. iVr., mi'.' nU /' \i</iiliuii, far \\'<i*hi,. 
 ; .Von;/ n/' Jim. /;i ('nut/nun \<<ir ii/nl Jim. 1 in JJi 
 
 Fear. 
 
 A', 
 
 A', 
 
 A . 
 
 **. 
 
 fry 
 
 
 XV. 
 
 \\l. 
 
 
 o / /' 
 
 / // 
 
 a 1 II 
 
 
 
 
 ,i 
 
 d 
 
 1900 
 
 89 5S 13.78 
 
 1 27 13.30 
 
 3.VJ 13 -J:t.9s 
 
 9.999-JS3S 
 
 9.959,s!:!2 
 
 9.617:.^: 
 
 1904.6 
 
 1.5 
 
 1901 
 
 13.S-,; 
 
 18.42 
 
 J-4.1 1 
 
 2S37 
 
 6954 
 
 57 (is 
 
 2269.6 
 
 1.3 
 
 1902 
 
 18.87 
 
 18.54 
 
 20.30 
 
 2881 
 
 8976 
 
 5665 
 
 263 1.6 
 
 1.0 
 
 1903 
 
 13.91 
 
 13.65 
 
 is. 17 
 
 2836 
 
 8998 
 
 55(i 1 
 
 2999.6 
 
 0.8 
 
 1904B. 
 
 18.95 
 
 13.77 
 
 16.68 
 
 
 MB! 
 
 5458 
 
 3365.6 
 
 1.5 
 
 1 !)().-> 
 
 13.99 
 
 13.89 
 
 1 1.79 
 
 2835 
 
 9048 
 
 535 1 
 
 3730.6 
 
 1.3 
 
 1906 
 
 1 1.03 
 
 14.01 
 
 12.96 
 
 2835 
 
 9065 
 
 5250 
 
 4095.6 
 
 1.0 
 
 1907 
 
 1 1.08 
 
 14.13 
 
 11.12 
 
 JS3 1 
 
 9081 
 
 5117 
 
 4460.6 
 
 O.s 
 
 1908B. 
 
 1 1.12 
 
 1 I.-J5 
 
 9.28 
 
 
 9109 
 
 5013 
 
 4826.6 
 
 1.6 
 
 1909 
 
 11.17 
 
 14.36 
 
 7. 15 
 
 2838 
 
 9131 
 
 1940 
 
 5191.6 
 
 1.3 
 
 1910 
 
 14J22 
 
 11. is 
 
 5.61 
 
 2832 
 
 9154 
 
 4886 
 
 5556.6 
 
 1.1 
 
 1911 
 
 1 l.'JS 
 
 14.60 
 
 3.78 
 
 2832 
 
 9176 
 
 4732 
 
 5921.6 
 
 O.S 
 
 1912#. 
 
 14.3 1 
 
 1 1.7-4 
 
 1.95 
 
 2831 
 
 9198 
 
 4629 
 
 6287.6 
 
 1.6 
 
 1913 
 
 11.10 
 
 1 IX! 
 
 352 43 0.11 
 
 2830 
 
 9220 
 
 1525 
 
 6652.6 
 
 1.3 
 
 1914 
 
 1 1. 15 
 
 14.95 
 
 352 42 58.28 
 
 2829 
 
 9',' 1;.' 
 
 1 l-j-.' 
 
 219.4 
 
 1.1 
 
 1915 
 
 14.50 
 
 15.07 
 
 66.40 
 
 2829 
 
 9-ji; i 
 
 4318 
 
 584.4 
 
 0.9 
 
 19167A 
 
 14.56 
 
 15.18 
 
 54.62 
 
 2828 
 
 9287 
 
 4214 
 
 950. 1 
 
 l.li 
 
 1917 
 
 14.62 
 
 15.30 
 
 52.79 
 
 2827 
 
 9309 
 
 4110 
 
 1815.4 
 
 1.4 
 
 1!)1H 
 
 14.67 
 
 15.48 
 
 50.96 
 
 2827 
 
 9331 
 
 4007 
 
 1680.4 
 
 1.1 
 
 1919 
 
 1 1.72 
 
 15.53 
 
 49.13 
 
 289i 
 
 9353 
 
 8908 
 
 2045.4 
 
 0.9 
 
 1920//. 
 
 14.76 
 
 15.65 
 
 47.30 
 
 2826 
 
 9375 
 
 3799 
 
 2411.4 
 
 1.6 
 
 19-J1 
 
 14.80 
 
 15.76 
 
 45.47 
 
 2825 
 
 9397 
 
 3695 
 
 277(i. t 
 
 1.4 
 
 l!fJ-^ 
 
 1 1.8 1 
 
 15.88 
 
 43.64 
 
 2825 
 
 9420 
 
 3591 
 
 8141.4 
 
 1.2 
 
 1923 
 
 14.88 
 
 16.00 
 
 41.82 
 
 _>vj 1 
 
 9442 
 
 8488 
 
 8506.4 
 
 0.9 
 
 jtSMB. 
 
 14.93 
 
 16.11 
 
 39.99 
 
 2824 
 
 9464 
 
 3384 
 
 3872. 1 
 
 1.7 
 
 1 !>-,'.-> 
 
 14.97 
 
 16.28 
 
 38.16 
 
 2823 
 
 9486 
 
 3280 
 
 4237. 1 
 
 1.1 
 
 1926 
 
 16.03 
 
 16.34 
 
 36.33 
 
 2823 
 
 9508 
 
 3176 
 
 4602.4 
 
 1.2 
 
 19:27 
 
 15.06 
 
 16.46 
 
 34.51 
 
 2822 
 
 9530 
 
 3072 
 
 4967.4 
 
 0.9 
 
 19283. 
 
 15.11 
 
 16.57 
 
 32.68 
 
 2821 
 
 9552 
 
 2969 
 
 5333. 1 
 
 1.7 
 
 1929 
 
 15.17 
 
 16.69 
 
 30.86 
 
 2821 
 
 9575 
 
 2865 
 
 5698.4 
 
 1.5 
 
 1930 
 
 15.22 
 
 16.80 
 
 29.03 
 
 2820 
 
 9597 
 
 2761 
 
 6063. 1 
 
 U2 
 
 1931 
 
 15.28 
 
 16.92 
 
 27.21 
 
 2819 
 
 9619 
 
 2657 
 
 6428.4 
 
 1.0 
 
 19325. 
 
 15.31 
 
 17.03 
 
 25.38 
 
 2819 
 
 9611 
 
 2553 
 
 6794.4 
 
 1.7 
 
 l!t:t:i 
 
 15,10 
 
 17.14 
 
 23.56 
 
 2818 
 
 9663 
 
 2450 
 
 361.1 
 
 1.5 
 
 1934 
 
 15.46 
 
 17.26 
 
 21.73 
 
 2817 
 
 9685 
 
 23 Hi 
 
 726.1 
 
 1.3 
 
 1935 
 
 15.51 
 
 17.37 
 
 19.91 
 
 2817 
 
 9708 
 
 2-J I'J 
 
 1091.1 
 
 1.0 
 
 1986JB. 
 
 15.57 
 
 17.49 
 
 18.09 
 
 2816 
 
 9730 
 
 2188 
 
 1457.1 
 
 1.8 
 
 1937 
 
 15.62 
 
 17.60 
 
 16.27 
 
 2815 
 
 9752 
 
 203 1 
 
 1822.1 
 
 us 
 
 1938 
 
 15.66 
 
 17.71 
 
 14.45 
 
 2815 
 
 9774 
 
 1930 
 
 2187.1 
 
 1.3 
 
 1939 
 
 15.71 
 
 17.83 
 
 12.63 
 
 2814 
 
 9796 
 
 1826 
 
 2552. 1 
 
 1.0 
 
 1940B. 
 
 15.75 
 
 17.94 
 
 10.81 
 
 2814 
 
 9818 
 
 1722 
 
 2918.1 
 
 1.8 
 
 1911 
 
 15.79 
 
 18.05 
 
 8.99 
 
 2813 
 
 9841 
 
 1618 
 
 3v>s3. 1 
 
 1.6 
 
 194-2 
 
 15.83 
 
 18.17 
 
 7.17 
 
 2813 
 
 9863 
 
 1514 
 
 3648.1 
 
 1.3 
 
 1943 
 
 15.88 
 
 18.28 
 
 5.36 
 
 2812 
 
 9885 
 
 1410 
 
 4013.1 
 
 1.1 
 
 19445. 
 
 15.92 
 
 18.39 
 
 3.54 
 
 2812 
 
 9907 
 
 1306 
 
 1379.1 
 
 1.8 
 
 1915 
 
 15.97 
 
 18.50 
 
 352 42 1.72 
 
 2811 
 
 9929 
 
 1202 
 
 1711.1 
 
 1.6 
 
 1946 
 
 16.02 
 
 18.62 
 
 352 41 59.91 
 
 2811 
 
 9951 
 
 1098 
 
 5109.1 
 
 1.3 
 
 1947 
 
 16.07 
 
 18.73 
 
 58.09 
 
 2810 
 
 9974 
 
 0994 
 
 5474.1 
 
 1.1 
 
 1948#. 
 
 16.12 
 
 18.84 
 
 56.26 
 
 2809 
 
 !l.959i)ii!ii; 
 
 6899 
 
 5s 10. 1 
 
 1.9 
 
 1949 
 
 89 58 16.18 
 
 1 27 18.95 
 
 352 41 54.46 
 
 9.9992M19 
 
 9.9600018 
 
 9.61707 s<; 
 
 6205.1 1.6 
 
 earli of the quantities K',, AT, and k,, l\\<- rmigtant U0".00 has been subtracted; and from log k y tlic coiistaiii 
 
 and from log A, the cnn.staiit 0.00005CO. 
 15 V 
 
TABLE XL,. 
 
 Corrections of K^ 7f v , ($-r., ilur lo Lunar Nutation, for 1850. 
 
 Period of Argument XV., iiTilt-'i.'J. 
 
 Arg- 
 XV. 
 
 A A*. 
 
 A Ay. 
 
 A A;. 
 
 V;ir. in , , , 
 100 yrs. Alogiy.Alog.iz 
 
 Are. 
 XV. 
 
 A K*. 
 
 A Ay. A A',, 
 
 V:ir. ill , 
 
 lOOyre. Al s/ *> 
 
 Alog.i,. 
 
 d 
 
 // 
 
 // 
 
 -/, 
 
 // 
 
 
 
 a // 
 
 // // 
 
 // 
 
 
 
 
 
 18.00 
 
 18.63 
 
 20.05 
 
 +0.03 
 
 1 
 
 850 
 
 2400 32.02 
 
 81.70 
 
 28.47 
 
 -0.02 
 
 148 
 
 140 
 
 50 
 
 18.78 
 
 19.42 
 
 20.79 
 
 0.03 
 
 1 
 
 847 
 
 2450 31.53 
 
 31.18 
 
 27.89 
 
 0.02 
 
 151 
 
 125 
 
 100 
 
 19.56 
 
 20.20 
 
 21.52 
 
 0.03 
 
 2 
 
 844 
 
 2500 31.00 
 
 30.63 
 
 27.28 
 
 0.02 
 
 154 
 
 111 
 
 150 
 
 20.34 
 
 20.98 
 
 22.25 
 
 0.03 
 
 3 
 
 840 
 
 2550 30.45 30.05 
 
 26.64 
 
 0.02 
 
 157 
 
 98 
 
 200 
 
 21.11 
 
 21.75 
 
 22.95 
 
 0.03 
 
 4 
 
 835 
 
 2600 
 
 29.87 
 
 29.45 
 
 25.99 
 
 0.03 
 
 160 
 
 86 
 
 250 
 
 21.87 
 
 22.50 
 
 23.65 
 
 +0.02 
 
 5 
 
 829 
 
 2650 
 
 29.26 
 
 28.82 
 
 25.32 
 
 -0.03 
 
 162 
 
 74 
 
 300 
 
 22.63 
 
 23.25 
 
 24.33 
 
 0.02 
 
 7 
 
 822 
 
 2700 28.63 ' 
 
 28.17 
 
 24.63 
 
 0.03 
 
 164 
 
 63 
 
 850 
 
 23.38 
 
 24.00 
 
 25.00 
 
 0.02 
 
 8 
 
 814 
 
 2750 27.97 
 
 27,19 
 
 23.92 
 
 0.03 
 
 166 
 
 53 
 
 400 
 
 24.12 
 
 21.71 
 
 25.66 
 
 0.02 
 
 10 
 
 806 
 
 2800 27.29 
 
 26.78 23.19 
 
 0.03 
 
 168 
 
 44 
 
 450 
 
 24.85 
 
 25.46 
 
 96.30 
 
 0.02 
 
 12 
 
 797 
 
 2850 
 
 26.59 
 
 26.06 
 
 22.45 
 
 0.03 
 
 170 
 
 36 
 
 500 
 
 25.57 
 
 26.17 
 
 26.93 
 
 +0.02 
 
 14 
 
 787 
 
 2900 
 
 25.87 
 
 25.33 
 
 21.70 
 
 -0.03 
 
 172 
 
 28 
 
 550 
 
 26.27 
 
 26.86 
 
 27.53 
 
 0.02 
 
 16 
 
 777 
 
 2950 ; 25.13 24.58 
 
 20.94 
 
 0.03 
 
 173 
 
 21 
 
 GOO 
 
 26.94 
 
 27.52 
 
 28.10 
 
 0.02 
 
 19 
 
 766 
 
 3000 
 
 24.38 23.81 
 
 20.17 
 
 0.03 
 
 174 
 
 16 
 
 650 
 
 27.60 
 
 28.17 
 
 28.65 
 
 0.02 
 
 21 
 
 754 
 
 3050 
 
 23.61 
 
 23.03 
 
 19.39 
 
 0.03 
 
 175 
 
 11 
 
 700 
 
 28.25 
 
 28.80 
 
 29.19 
 
 0.02 
 
 24 
 
 741 
 
 3100 
 
 22.83 
 
 22.23 
 
 18.60 
 
 0.03 
 
 176 
 
 7 
 
 750 
 
 28.87 
 
 29.41 
 
 29.69 
 
 +0.02 
 
 27 
 
 727 
 
 3150 
 
 22.04 
 
 21.43 
 
 17.81 
 
 -0.03 
 
 176 
 
 4 
 
 800 
 
 29.47 
 
 29.99 
 
 30.17 
 
 0.02 
 
 29 
 
 713 
 
 3200 
 
 21.24 
 
 20.62 
 
 17.02 
 
 0.03 
 
 177 
 
 2 
 
 850 
 
 30.05 
 
 30.55 
 
 30.62 
 
 0.01 
 
 32 
 
 699 
 
 3250 
 
 20.43 
 
 19.80 
 
 16.23 
 
 0.03 
 
 177 
 
 1 
 
 900 
 
 30.60 
 
 31.09 
 
 31.05 
 
 0.01 
 
 36 
 
 684 
 
 3300 
 
 19.62 
 
 18.99 
 
 15.45 
 
 0.03 
 
 177 
 
 
 
 950 
 
 31.13 
 
 31.60 
 
 31.45 
 
 0.01 
 
 39 
 
 668 
 
 3350 
 
 18.80 
 
 18.16 
 
 14.66 
 
 0.03 
 
 177 
 
 1 
 
 1000 
 
 31.63 
 
 32.08 
 
 31.81 
 
 +0.01 
 
 42 
 
 652 
 
 3400 
 
 17.98 
 
 17.34 
 
 13.88 
 
 -0.03 
 
 177 
 
 3 
 
 1050 
 
 32.10 
 
 32.53 
 
 32.14 
 
 0.01 
 
 46 
 
 635 
 
 3450 
 
 17.16 
 
 16.51 
 
 13.10 
 
 0.03 
 
 176 
 
 5 
 
 1100 
 
 32.55 
 
 32.95 
 
 32.45 
 
 0.01 
 
 49 
 
 618 
 
 3500 
 
 16.35 
 
 15.70 
 
 12.31 
 
 0.03 
 
 175 
 
 9 
 
 1150 
 
 32.97 
 
 33.34 
 
 32.73 
 
 0.01 
 
 53 
 
 600 
 
 3550 
 
 15.54 
 
 14.89 
 
 11.59 
 
 0.03 
 
 174 
 
 13 
 
 1200 
 
 33.35 
 
 33.70 
 
 32.97 
 
 +0.01 
 
 57 
 
 582 
 
 3600 
 
 14.73 
 
 14.09 
 
 10.84 
 
 0.03 
 
 173 
 
 18 
 
 1250 
 
 33.70 
 
 34.03 
 
 33.18 
 
 0.00 
 
 61 
 
 564 
 
 3650 
 
 13.93 
 
 13.29 
 
 10.11 
 
 -0.03 
 
 172 
 
 24 
 
 1300 
 
 34.02 
 
 34.32 
 
 33.35 
 
 0.00 
 
 64 
 
 545 
 
 3700 
 
 13.14 
 
 12.50 
 
 9.40 
 
 0.02 
 
 171 
 
 31 
 
 1350 
 
 34.31 
 
 34.58 
 
 33. 19 
 
 0.00 
 
 68 
 
 526 
 
 3750 
 
 12.36 
 
 11.72 
 
 8.70 
 
 0.02 
 
 169 
 
 39 
 
 1400 
 
 34.56 
 
 34.81 
 
 33.60 
 
 0.00 
 
 72 
 
 507 
 
 3800 
 
 11.59 
 
 10.96 
 
 8.02 
 
 0.02 
 
 167 
 
 48 
 
 1450 
 
 34.78 
 
 35.00 
 
 33.67 
 
 0.00 
 
 76 
 
 488 
 
 3850 
 
 10.84 
 
 10.22 
 
 7.36 
 
 0.02 
 
 165 
 
 58 
 
 1500 
 
 34.96 
 
 35.16 
 
 33.70 
 
 0.00 
 
 80 
 
 469 
 
 3900 
 
 10.10 
 
 9.49 
 
 6.72 
 
 -0.02 
 
 163 
 
 68 
 
 1550 
 
 35.10 
 
 35.27 
 
 33.70 
 
 0.00 
 
 84 
 
 449 
 
 3950 
 
 9.38 
 
 8.78 
 
 6.11 
 
 0.02 
 
 160 
 
 80 
 
 1600 
 
 35.21 
 
 35.35 
 
 33.66 
 
 0.00 
 
 88 
 
 429 
 
 4000 
 
 8.68 
 
 8.10 
 
 5.52 
 
 0.02 
 
 158 
 
 92 
 
 1G50 
 
 35.28 
 
 35.39 
 
 33.58 
 
 -0.01 
 
 93 
 
 410 
 
 4050 
 
 8.00 
 
 7.43 
 
 4.95 
 
 0.02 
 
 155 
 
 104 
 
 1700 
 
 35.32 
 
 35.40 
 
 33.48 
 
 0.01 
 
 97 
 
 390 
 
 4100 
 
 7.35 
 
 6.79 
 
 4.42 
 
 0.02 
 
 152 
 
 118 
 
 1750 
 
 35.32 
 
 35.37 
 
 33.34 
 
 -0.01 
 
 101 
 
 370 
 
 4150 
 
 6.72 
 
 6.18 
 
 3.91 
 
 -0.02 
 
 150 
 
 132 
 
 1800 
 
 35.29 
 
 35.31 
 
 33.17 
 
 0.01 
 
 105 
 
 351 
 
 4200 
 
 6.11 
 
 5.59 
 
 3.43 
 
 0.02 
 
 146 
 
 146 
 
 1850 
 
 35.21 
 
 35.20 
 
 32.96 
 
 0.01 
 
 109 
 
 332 
 
 4250 
 
 5.53 
 
 5.02 
 
 2.98 
 
 0.01 
 
 143 
 
 162 
 
 1900 
 
 35.10 
 
 35.06 
 
 32.71 
 
 0.01 
 
 113 
 
 313 
 
 4300 
 
 4.98 
 
 4.49 
 
 2.56 
 
 0.01 
 
 140 
 
 178 
 
 1950 
 
 34.95 
 
 34.88 
 
 32.42 
 
 0.01 
 
 117 
 
 294 
 
 4350 
 
 4.46 
 
 3.99 
 
 2.18 
 
 0.01 
 
 137 
 
 194 
 
 2000 
 
 34.77 
 
 34.67 
 
 32.11 
 
 -0.01 
 
 120 
 
 275 
 
 4400 
 
 3.96 
 
 3.52 
 
 1.82 
 
 -0.01 
 
 133 
 
 211 
 
 2050 
 
 34.55 
 
 34.42 
 
 31.76 
 
 0.02 
 
 124 
 
 257 
 
 4450 
 
 3.50 
 
 3.08 
 
 1.50 
 
 0.01 
 
 129 
 
 22!) 
 
 2100 
 
 34.29 
 
 34.14 
 
 31.3S 
 
 0.02 
 
 128 
 
 239 
 
 4500 
 
 3.07 
 
 2.67 
 
 1.21 
 
 0.01 
 
 126 
 
 247 
 
 2150 
 
 34.00 
 
 33.82 
 
 30.97 
 
 0.02 
 
 132 
 
 221 
 
 4550 
 
 2.68 
 
 2.30 
 
 0.97 
 
 0.01 
 
 122 
 
 265 
 
 2200 
 
 33.67 
 
 33.46 
 
 30.53 
 
 0.02 
 
 135 
 
 204 
 
 4600 
 
 2.32 
 
 1.97 
 
 0.75 
 
 -0.01 
 
 118 
 
 284 
 
 2250 
 
 33.31 
 
 33.07 
 
 30.06 
 
 -0.02 
 
 139 
 
 187 
 
 4650 
 
 1.99 
 
 1.67 
 
 0.57 
 
 0.00 
 
 114 
 
 303 
 
 2300 
 
 32.91 
 
 32.64 
 
 29.55 
 
 0.02 
 
 142 
 
 171 
 
 4700 
 
 1.70 
 
 1.40 
 
 0.43 
 
 0.00 
 
 110 
 
 322 
 
 2350 
 
 32,18 
 
 32.18 
 
 29.02 
 
 0.02 
 
 145 
 
 155 
 
 4750 
 
 1,44 
 
 1.17 
 
 0.32 
 
 0.00 
 
 106 
 
 841 
 
 2400 
 
 32.02 
 
 31.70 
 
 28.47 
 
 -0.02 
 
 148 
 
 140 
 
 4800 
 
 1.22 
 
 0.98 
 
 0.25 
 
 0.00 
 
 102 
 
 360 
 
 A log ky al ><l A log /' : /. i'f" ill units of till! suvuiitli ilcriinal place. 
 
 The constants added arc, 1H".00 to A A" s , J8".()0 to A A' y , ] 7 "- 0() to A A",., ^ t<> A log l; y , and 430 to A log k z . 
 
TABLE XL 
 
 TABLE XL.I. 
 
 Cum ' unnr .\utalinn, / 
 
 / .\ntnlitin, fur 1 
 
 IVrioil ufArsum.'iit XV., 1 
 
 , m \ VI . 966 '-'I 
 
 Ar S . 
 XV. 
 
 AAV 
 
 
 AAV 
 
 Var.in 
 IDOyn. 
 
 
 log*, 
 
 \\ 1 
 
 AAV 
 
 AAV 
 
 AAV 
 
 Vnr. ill 
 
 lililyrs. 
 
 Alg* y 
 
 .I,,./., 
 
 BolM 
 
 iNilIal'll 
 
 ll 
 
 // 
 
 // 
 
 n 
 
 // 
 
 
 
 .1 
 
 II 
 
 // 
 
 // 
 
 n 
 
 
 
 // 
 
 4800 
 
 1.22 
 
 
 0.25 
 
 ().()() 
 
 102 
 
 
 
 
 2.36 
 
 2.33 
 
 3-17 
 
 0.00 
 
 6 
 
 105 
 
 +0.3(i 
 
 1850 
 
 1.04 
 
 0.83 
 
 0.22 
 
 ().()() 
 
 98 
 
 880 
 
 5 
 
 2.57 
 
 2.5 1 
 
 3.36 
 
 0.00 
 
 (i 
 
 105 
 
 0.57 
 
 4900 
 
 0.89 
 
 0.71 
 
 0.22 
 
 o.oo 
 
 94 
 
 100 
 
 10 
 
 2.7(1 
 
 2.7 I 
 
 8.53 
 
 0.00 
 
 6 
 
 106 
 
 0.76 
 
 4950 
 
 0.78 
 
 0.68 
 
 0.25 
 
 0.00 
 
 90 
 
 120 
 
 15 
 
 2.92 
 
 2.9 1 
 
 3.6N 
 
 0.00 
 
 (i 
 
 107 
 
 0.92 
 
 
 0.71 
 
 0.58 
 
 0.83 
 
 +0.01 
 
 Mi 
 
 139 
 
 20 
 
 3.06 
 
 8.05 
 
 3.81 
 
 0.00 
 
 5 
 
 109 
 
 1.06 
 
 5050 
 
 0.68 
 
 0.58 
 
 0.11 
 
 +0.01 
 
 81 
 
 159 
 
 25 
 
 8.16 
 
 8.16 
 
 8.91 
 
 0.00 
 
 5 
 
 111 
 
 + 1.16 
 
 5100 
 
 0.68 
 
 0.61 
 
 
 0.01 
 
 T 1 ) 
 
 479 
 
 30 
 
 3.22 
 
 3.23 
 
 3.9N 
 
 0.00 
 
 4 
 
 114 
 
 1.22 
 
 5150 
 
 0.72 
 
 0.68 
 
 0.76 
 
 0.01 
 
 73 
 
 498 
 
 85 
 
 3.25 
 
 3.26 
 
 1.01 
 
 0.00 
 
 1 
 
 117 
 
 1 .25 
 
 5200 
 
 0.79 
 
 0.7s 
 
 0.91 
 
 0.01 
 
 69 
 
 :. i ; 
 
 40 
 
 3 25 
 
 8.26 
 
 101 
 
 40.01 
 
 3 
 
 120 
 
 1.21 
 
 5250 
 
 0.90 
 
 0.92 
 
 1.2'J 
 
 0.01 
 
 lit; 
 
 586 
 
 (5 
 
 3.20 
 
 3.22 
 
 8.97 
 
 0.01 
 
 2 
 
 123 
 
 1.19 
 
 5300 
 
 .().-, 
 
 1.10 
 
 1.50 
 
 +0.01 
 
 62 
 
 ">5.") 
 
 50 
 
 3. 1 1 
 
 3.11 
 
 3.89 
 
 +0.01 
 
 2 
 
 126 
 
 + 1.10 
 
 5350 
 
 .23 
 
 1 .3 1 
 
 1.81 
 
 0.01 
 
 
 
 55 
 
 
 3.02 
 
 3.77 
 
 0.01 
 
 1 
 
 128 
 
 0.98 
 
 5 100 
 
 .45 
 
 1.56 
 
 2. 1 .'. 
 
 0.02 
 
 54 
 
 
 60 
 
 2.8 1 
 
 
 3.63 
 
 0.01 
 
 1 
 
 131 
 
 0.88 
 
 5 1:.0 
 
 .70 
 
 1.84 
 
 2.52 
 
 0.09 
 
 50 
 
 609 
 
 65 
 
 2.66 
 
 2.7 1 
 
 3.46 
 
 0.01 
 
 1 
 
 132 
 
 0.65 
 
 5500 
 
 .99 
 
 2.16 
 
 2.93 
 
 0.02 
 
 47 
 
 627 
 
 70 
 
 2. 17 
 
 2.52 
 
 3.26 
 
 0.01 
 
 
 
 133 
 
 0.46 
 
 5550 
 
 2.31 
 
 2.51 
 
 3.36 
 
 +0.02 
 
 13 
 
 (ill 
 
 7.') 
 
 2.26 
 
 2.31 
 
 3.0 1 
 
 +0.01 
 
 
 
 133 
 
 +0.25 
 
 5600 
 
 2.67 
 
 2.89 
 
 
 0.02 
 
 40 
 
 660 
 
 80 
 
 2.05 
 
 2.10 
 
 2.82 
 
 0.01 
 
 
 
 133 
 
 *(>.OI 
 
 5650 
 
 3.06 
 
 8.3] 
 
 1.33 
 
 0.02 
 
 37 
 
 676 
 
 85 
 
 1.83 
 
 1.88 
 
 2.59 
 
 0.01 
 
 1 
 
 132 
 
 -0.18 
 
 5700 
 
 3. 17 
 
 8.75 
 
 I.M 
 
 0.02 
 
 33 
 
 692 
 
 90 
 
 1.62 
 
 1.67 
 
 2.35 
 
 0.01 
 
 1 
 
 130 
 
 0.39 
 
 5750 
 
 8.91 
 
 L22 
 
 5.37 
 
 0.02 
 
 30 
 
 707 
 
 05 
 
 1.12 
 
 1.47 
 
 2.12 
 
 0.01 
 
 2 
 
 127 
 
 0.59 
 
 5800 
 
 L39 
 
 4.72 
 
 5.98 
 
 +0.02 
 
 27 
 
 721 
 
 100 
 
 1.21 
 
 1.29 
 
 1.91 
 
 +0.01 
 
 2 
 
 121 
 
 -0.77 
 
 5850 
 
 L89 
 
 5.2 1 
 
 6.52 
 
 0.02 
 
 21 
 
 735 
 
 105 
 
 1.01) 
 
 1.13 
 
 .72 
 
 0.01 
 
 3 
 
 120 
 
 0.92 
 
 5900 
 
 5. 12 
 
 5.80 
 
 7.18 
 
 0.02 
 
 22 
 
 ' is 
 
 110 
 
 0.97 
 
 1.00 
 
 .55 
 
 0.0 1 
 
 4 
 
 115 
 
 1.05 
 
 5950 
 
 5.9* 
 
 6.38 
 
 7.76 
 
 0.02 
 
 19 
 
 760 
 
 115 
 
 0.87 
 
 0.90 
 
 .10 
 
 0.02 
 
 5 
 
 110 
 
 1.15 
 
 6000 
 
 6.56 
 
 6.98 
 
 8.11 
 
 0.03 
 
 17 
 
 772 
 
 120 
 
 0.81 
 
 0.83 
 
 .29 
 
 0.02 
 
 6 
 
 lor, 
 
 1.21 
 
 6050 
 
 7.16 
 
 7.60 
 
 9.07 
 
 +0.03 
 
 14 
 
 783 
 
 125 
 
 0.78 
 
 0.80 
 
 .20 
 
 +0.02 
 
 ' 8 
 
 99 
 
 -1.24 
 
 6100 
 
 7.78 
 
 S.2 I 
 
 9.74 
 
 0.03 
 
 12 
 
 793 
 
 130 
 
 0.78 
 
 0.80 
 
 .15 
 
 0.02 
 
 9 
 
 91 
 
 1.21 
 
 6150 
 
 N. 12 
 
 8.90 
 
 10.13 
 
 0.03 
 
 10 
 
 803 
 
 135 
 
 0.82 
 
 0.83 
 
 .13 
 
 0.02 
 
 10 
 
 88 
 
 1.20 
 
 6200 
 
 9.09 
 
 9.59 
 
 11.11 
 
 0.03 
 
 9 
 
 811 
 
 110 
 
 O.S9 
 
 0.90 
 
 .14 
 
 0.02 
 
 11 
 
 N;{ 
 
 1.13 
 
 6250 
 
 9.77 
 
 10.89 
 
 11.86 
 
 0.03 
 
 7 
 
 819 
 
 115 
 
 1.00 
 
 1.00 
 
 .19 
 
 0.02 
 
 12 
 
 77 
 
 1.02 
 
 6800 
 
 10,17 
 
 11.01 
 
 12.59 
 
 +0.03 
 
 6 
 
 826 
 
 150 
 
 1.13 
 
 1.13 
 
 .27 
 
 +0.02 
 
 13 
 
 72 
 
 -6.89 
 
 6350 
 
 11.18 
 
 11.73 
 
 13.32 
 
 0.03 
 
 4 
 
 832 
 
 155 
 
 1.29 
 
 1 .29 
 
 .88 
 
 0.02 
 
 11 
 
 68 
 
 0.73 
 
 6400 
 
 11.91 
 
 12.47 
 
 1 1.07 
 
 0.03 
 
 3 
 
 838 
 
 160 
 
 1,17 
 
 1.17 
 
 .51 
 
 0.02 
 
 15 
 
 til 
 
 0.55 
 
 6 150 
 
 12.65 
 
 13.23 
 
 1 1.N2 
 
 0.03 
 
 Q 
 
 842 
 
 165 
 
 1.67 
 
 1.67 
 
 .66 
 
 0.02 
 
 16 
 
 60 
 
 0.35 
 
 6500 
 
 13. 10 
 
 13.99 
 
 15.57 
 
 0.03 
 
 2 
 
 846 
 
 170 
 
 1.87 
 
 1.87 
 
 .89 
 
 0.02 
 
 16 
 
 58 
 
 -0.15 
 
 6550 
 
 11. 1C 
 
 14.76 
 
 10.33 
 
 +0.03 
 
 1 
 
 848 
 
 176 
 
 2.08 
 
 2.0s 
 
 1.99 
 
 +0.02 
 
 17 
 
 56 
 
 +0.06 
 
 6600 
 
 1 !.!)-,> 
 
 15.53 17.08 
 
 0.03 
 
 1 
 
 850 
 
 180 
 
 2.28 
 
 2J28 
 
 2.16 
 
 0.02 
 
 17 
 
 54 
 
 0.26 
 
 6650 
 
 15.69 
 
 l(i.31 17. S3 
 
 0.03 
 
 
 
 851 
 
 IK.') 
 
 2. is 
 
 2. 1!) 
 
 2.33 
 
 0.03 
 
 17 
 
 r.l 
 
 0.46 
 
 6700 
 
 16,17 
 
 17.0!) 18.58 
 
 0.03 
 
 
 
 852 
 
 190 
 
 2.67 
 
 2. (IS 
 
 2. 19 
 
 0.03 
 
 17 
 
 51 
 
 0.64 
 
 6750 
 
 17.25 
 
 17.88 
 
 19.33 
 
 0.03 
 
 1 
 
 851 
 
 195 
 
 2.84 
 
 2.85 
 
 2.6 1 
 
 0.03 
 
 16 
 
 56 
 
 0.81 
 
 6800 
 
 1 8.0:5 
 
 18.66 
 
 20.0S 
 
 +0.03 
 
 1 
 
 849 
 
 200 
 
 2.99 
 
 3.01 
 
 2.78 
 
 .0.03 
 
 16 
 
 56 
 
 + 0.96 
 
 685D 
 
 18.81 
 
 19. 15 20.82 
 
 0.03 
 
 1 
 
 847 
 
 205 
 
 3.11 
 
 3.11 
 
 2.89 
 
 0.03 
 
 16 
 
 57 
 
 1 .08 
 
 6900 
 
 19.59 
 
 20.23 
 
 21.55 
 
 0.03 
 
 2 
 
 Ml 
 
 210 
 
 3.19 
 
 8.23 
 
 2.91 
 
 0.03 
 
 16 
 
 60 
 
 1.16 
 
 6950 
 
 20.37 
 
 21.01 
 
 22.27 
 
 0.03 
 
 3 
 
 840 
 
 215 
 
 3.25 
 
 3.29 
 
 3.03 
 
 0.03 
 
 15 
 
 62 
 
 1.22 
 
 7000 
 
 21.11 
 
 81.78 
 
 22.! is 
 
 0.03 
 
 4 
 
 N35 
 
 290 
 
 3.27 
 
 8.39 
 
 8.06 
 
 0.03 
 
 15 
 
 65 
 
 1.21 
 
 7050 
 
 21.90 
 
 22.5 1 
 
 23.68 
 
 +0.02 
 
 :. 
 
 829 
 
 225 
 
 8.26 
 
 3.32 
 
 3.05 
 
 +0.03 
 
 14 
 
 68 
 
 + 1.23 
 
 7100 
 
 22.66 
 
 23.29 
 
 2J.36 
 
 0.02 
 
 7 
 
 822 
 
 230 
 
 3.22 
 
 3.29 
 
 3.02 
 
 0.03 
 
 ll 
 
 71 
 
 1.19 
 
 7150 
 
 23. : i 
 
 2 1.03 
 
 25.03 
 
 0.02 
 
 s 
 
 Nil 
 
 235 
 
 3.11 
 
 3.22 
 
 2.95 
 
 0.03 
 
 13 
 
 73 
 
 1.11 
 
 7200 
 
 22. 1 1 
 
 24.76 
 
 25.68 
 
 +0.02 
 
 10 
 
 806 
 
 2 10 
 
 8.09 
 
 3.11 
 
 2. si 
 
 +0.03 
 
 13 
 
 76 
 
 + 1.00 
 
 A l>g '"> n ml /' ' 'li'i-imal. 
 TABLE XI. 1. r..nstants ad.l.'.l re, -J'Mi i L. A K*, S'MKI to A AT y , 3' to A log t. 
 
TABL.E XL.I. 
 
 TABLE XL1II. 
 
 (' rri'ctions of K*, Ky, 4" f -i lluc l " Solar Nutation, for 1850. 
 
 Parcillti.r end Semi-diameter. 
 
 
 Period of Argument ,\VI.. 3G.j <1 .'.>4. 
 
 
 Arg. 
 XVI. 
 
 A K x . 
 
 A Ky. 
 
 A K,, 
 
 Var. in 
 lOOyrs. 
 
 A.og, y . 
 
 A'og/.-,, 
 
 Solar 
 Niitat'n 
 
 Log. 
 diet. from 
 
 Parallax 
 
 Semi- 
 diam. 
 
 Log. 
 
 ditit.from 
 
 i 
 
 Parallax 
 
 Semi- 
 (liam. 
 
 fl 
 
 
 
 11 
 
 to 
 
 n 
 
 
 
 n 
 
 Earth. 
 
 
 
 Earth. 
 
 
 
 9,lfl 
 
 Q 
 
 A'! 
 
 Q 1 1 
 
 2.84 
 
 +0.03 
 
 13 
 
 76 
 
 +1.00 
 
 
 
 
 
 
 
 ^ iw 
 
 2 15 
 250 
 255 
 260 
 
 L> \J*J 
 
 2.89 
 2.72 
 2.5 1 
 2.35 
 
 f J. 1 A 
 
 2.97 
 2.S1 
 '2.63 
 2.44 
 
 2.71 
 2.54 
 2.36 
 2.16 
 
 0.03 
 0.03 
 0.08 
 0.04 
 
 12 
 12 
 12 
 12 
 
 78 
 79 
 80 
 81 
 
 0.86 
 0.69 
 0.51 
 0.31 
 
 9.40 
 9.41 
 9.42 
 9.43 
 
 35.22 
 34.42 
 
 38.6 1 
 
 32.87 
 
 31.02 
 33.25 
 32,19 
 31.75 
 
 9.85 
 
 9.86 
 
 9.87 
 9.88 
 
 12'.50 
 12.21 
 11.94 
 11.66 
 
 ii 
 
 12.07 
 11.80 
 11.53 
 11.27 
 
 205 
 
 2 
 
 11 
 
 2.23 
 
 1.93 
 
 +0.04 
 
 12 
 
 81 
 
 +0.10 
 
 9.44 
 
 32.13 
 
 81.03 
 
 9.89 
 
 11.40 
 
 11.01 
 
 270 
 
 1 
 
 92 
 
 2.01 
 
 1.70 
 
 0.01 
 
 12 
 
 80 
 
 -0.12 
 
 
 
 
 
 
 
 275 
 
 1 
 
 71 
 
 1.80 
 
 1.47 
 
 0.04 
 
 12 
 
 78 
 
 0.33 
 
 9,45 
 
 81.39 
 
 30.32 
 
 9.90 
 
 11.14 
 
 10.76 
 
 2SO 
 
 1 
 
 51 
 
 1.60 
 
 1.24 
 
 0.04 
 
 13 
 
 76 
 
 0.53 
 
 9.46 
 
 30.68 
 
 29.63 
 
 9.91 
 
 10.89 
 
 10.51 
 
 285 
 
 1 
 
 82 
 
 1.41 
 
 1.02 
 
 0.04 
 
 13 
 
 72 
 
 0.72 
 
 9.47 
 
 29.98 
 
 28.96 
 
 9.92 
 
 10.64 
 
 10.27 
 
 290 
 
 29.0 
 
 1 
 1 
 
 15 
 
 00 
 
 1.23 
 1.08 
 
 0.81 
 0.62 
 
 +0.04 
 0.04 
 
 14 
 15 
 
 69 
 64 
 
 -0.89 
 1.04 
 
 9.48 
 9.49 
 
 29.30 
 28.63 
 
 28.30 
 27.65 
 
 9.93 
 9.94 
 
 10.40 
 10.16 
 
 10.04 
 9.81 
 
 300 
 805 
 310 
 
 0.89 
 O.S2 
 
 0.78 
 
 0.96 
 0.88 
 0.84 
 
 0.46 
 0.34 
 0.25 
 
 0.01 
 0.04 
 0.04 
 
 16 
 17 
 
 19 
 
 59 
 54 
 
 48 
 
 1.15 
 1.22 
 1.26 
 
 9.50 
 9.51 
 9.52 
 
 27.98 
 27.34 
 26.72 
 
 27.02 
 26-40 
 25.81 
 
 9.95 
 9.96 
 9.97 
 
 9.93 
 9.70 
 
 9.48 
 
 9.59 
 9.87 
 9.16 
 
 815 
 
 
 
 79 
 
 0.84 
 
 0.20 
 
 +0.04 
 
 20 
 
 42 
 
 -1.25 
 
 9.53 
 
 26.11 
 
 25.22 
 
 9.98 
 
 9.26 
 
 8.95 
 
 820 
 
 
 
 
 
 0.18 
 
 0.04 
 
 21 
 
 36 
 
 1.21 
 
 9.54 
 
 25.52 
 
 24.65 
 
 9.99 
 
 9.05 
 
 8.74 
 
 825 
 
 
 
 Dl 
 
 Q.i 6 
 
 0.20 
 
 0.04 
 
 22 
 
 31 
 
 1.13 
 
 
 
 
 
 
 
 330 
 
 1 
 
 02 
 
 1.07 
 
 0.25 
 
 0.04 
 
 23 
 
 25 
 
 1.02 
 
 9.55 
 
 24.94 
 
 24.09 
 
 0.00 
 
 8.85 
 
 8.55 
 
 8:35 
 
 1 
 
 17 
 
 1.20 
 
 0.33 
 
 0.05 
 
 24 
 
 20 
 
 0.88 
 
 9.56 
 
 21.37 
 
 23.51 
 
 0.01 
 
 8.65 
 
 8.35 
 
 310 
 8 15 
 350 
 
 1 
 
 1 
 1 
 
 33 
 51 
 72 
 
 1.36 
 1.54 
 1.75 
 
 0.44 
 0.57 
 0.73 
 
 +0.05 
 0.05 
 0.05 
 
 25 
 26 
 
 27 
 
 15 
 11 
 
 8 
 
 -0.72 
 0.54 
 0.33 
 
 9.57 
 9.58 
 9.59 
 
 23.81 
 23.27 
 22.74 
 
 23.00 
 
 22.48 
 21.97 
 
 0.02 
 0.03 
 0.04 
 
 8.45 
 8.26 
 8.07 
 
 8.16 
 7.98 
 7.79 
 
 855 
 360 
 
 1 
 
 2 
 
 95 
 
 18 
 
 1.98 
 2.22 
 
 0.92 
 1.11 
 
 0.05 
 0.05 
 
 27 
 28 
 
 5 
 3 
 
 -0.10 
 +0.13 
 
 9.60 
 9.61 
 
 22.23 
 
 21.72 
 
 21.47 
 
 20.98 
 
 0.05 
 0.06 
 
 7.89 
 7.71 
 
 7.62 
 7.44 
 
 365 
 
 2 
 
 40 
 
 2.44 
 
 1.30 
 
 +0.05 
 
 28 
 
 2 
 
 +0.35 
 
 9.62 
 
 21.22 
 
 20.50 
 
 0.07 
 
 7.53 
 
 7.27 
 
 870 
 
 2 
 
 61 
 
 2.65 
 
 1.49 
 
 +0.05 
 
 28 
 
 2 
 
 +0.56 
 
 9.63 
 
 20.74 
 
 20.03 
 
 0.08 
 
 7.36 
 
 7.11 
 
 
 
 
 
 
 
 
 
 
 9.64 
 
 20.27 
 
 19.58 
 
 0.09 
 
 7.19 
 
 6.95 
 
 A lo" li, and A log ^z are ' n "''* of the seventh decimal. 
 
 
 
 
 
 
 
 Constants added are, 2'_'.0<ho A K*,2".(M to A K y , 3".00 to A K z , 
 
 9.65 
 
 19.81 
 
 19.13 
 
 0.10 
 
 7.03 
 
 6.79 
 
 
 1 to A lo g fc y, antl IM to A log K z . 
 
 9.66 
 
 19.36 
 
 18.70 
 
 0.11 
 
 6.87 
 
 6.63 
 
 
 TABLE XLII. 
 
 9.67 
 9.68 
 
 18.92 
 
 18.49 
 
 18.27 
 17.85 
 
 0.12 
 0.13 
 
 6.71 
 6.56 
 
 6,18 
 6.81 
 
 Factors for obtaining A x, A y, A z/rom A /? . 
 
 9.69 
 
 18.07 
 
 17.45 
 
 0.14 
 
 6.41 
 
 6.19 
 
 Orbit. 
 
 Long. 
 
 For A z- 
 
 For A y- 
 
 For A z. 
 
 9.70 
 
 17.65 
 
 17.05 
 
 0.15 
 
 6.26 
 
 6.05 
 
 
 
 
 
 
 9.71 
 
 17.25 
 
 16.66 
 
 0.16 
 
 6.12 
 
 5.91 
 
 
 o 
 
 
 
 
 9.72 
 
 16.86 
 
 16.28 
 
 0.17 
 
 5.98 
 
 5.78 
 
 6 
 
 180 
 
 + 0-020 
 
 -0.145 
 
 + 0.322 
 
 9.73 
 
 16.48 
 
 15.91 
 
 0.18 
 
 5.85 
 
 5.65 
 
 10 
 
 190 
 
 0.018 
 
 0.148 
 
 0.323 
 
 9.74 
 
 16.10 
 
 15.55 
 
 0.19 
 
 5.71 
 
 5.52 
 
 20 
 
 200 
 
 0.016 
 
 0.150 
 
 0.324 
 
 
 
 
 
 
 
 30 
 
 210 
 
 0.013 
 
 0.152 
 
 0.325 
 
 9.75 
 
 15.73 
 
 15.20 
 
 0.20 
 
 5.58 
 
 5.39 
 
 40 
 
 220 
 
 0.009 
 
 0.152 
 
 0.325 
 
 9.76 
 
 15.38 
 
 14.85 
 
 0.21 
 
 5.46 
 
 5.27 - 
 
 50 
 
 230 
 
 + 0.006 
 
 -0.151 
 
 + 0.325 
 
 9.77 
 
 15.03 
 
 14.51 
 
 0.22 
 
 5.33 
 
 5.15 
 
 60 
 
 240 
 
 0.003 
 
 1 0.149 
 
 0.324 
 
 9.78 
 
 14.68 
 
 14.18 
 
 0.23 
 
 5.21 
 
 5.03 
 
 70 
 
 250 
 
 0.001 
 
 0.146 
 
 0.823 
 
 9.79 
 
 14.35 
 
 18.86 
 
 0.24 
 
 5.09 
 
 4.92 
 
 80 
 
 260 
 
 0.000 
 
 0.143 
 
 0.821 
 
 
 
 
 
 
 
 90 
 
 270 
 
 0.000 
 
 0.139 
 
 0.320 
 
 9.80 
 
 14.02 
 
 13.54 
 
 0.25 
 
 4.98 
 
 4.81 
 
 
 
 
 
 
 9.81 
 
 13.70 
 
 13.24 
 
 0.26 
 
 4.86 
 
 4.70 
 
 100 
 
 280 
 
 + 0.002 
 
 -0.136 
 
 + 0.319 
 
 9.82 
 
 13.39 
 
 12.93 
 
 0.27 
 
 4.75 
 
 4.59 
 
 110 
 
 290 
 
 0.004 
 
 0.134 
 
 0.318 
 
 9.83 
 
 13.09 
 
 12.64 
 
 0.28 
 
 4.64 
 
 4.48 
 
 120 
 
 300 
 
 0.007 
 
 0.132 
 
 0.317 
 
 9.84 
 
 12.79 
 
 12.35 
 
 0.29 
 
 4.54 
 
 4.38 
 
 130 
 
 310 
 
 0.011 
 
 0.132 
 
 0.317 
 
 9.85 
 
 12.50 
 
 12.07 
 
 0.30 
 
 4.43 
 
 4.28 
 
 140 
 
 320 
 
 0.014 
 
 0.133 
 
 0.317 
 
 
 
 
 
 
 
 150 
 
 330 
 
 + 0.017 
 
 -0.135 
 
 -1-0.318 
 
 
 160 
 
 340 
 
 0.019 
 
 0.138 
 
 0.319 
 
 
 170 
 
 850 
 
 0.020 
 
 0.141 
 
 0.321 
 
 
 180 
 
 360 
 
 + 0.020 
 
 -0.145 
 
 + 0.322 
 
 
TAHL.13 XL.IV. 
 
 Mt'fittn of tin' Argument* for O/////r/V.s\ 
 
 Century. 
 
 << 
 
 /' - 50, 
 
 111 
 
 I. 
 
 I' _.-,:!. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI 
 
 VII. 
 
 \ III 
 
 
 O / // 
 
 II 
 
 
 d 
 
 d 
 
 y 
 
 .1 
 
 d 
 
 d 
 
 d 
 
 d 
 
 it 
 
 
 -300 
 
 i.v, .-,:, .-.oo 
 
 -0.1763 
 
 -3111 
 
 11 5.!)! 151 
 
 -0.000514 
 
 50.: 
 
 ! 171 
 
 2381 
 
 1103.1 
 
 359.68 
 
 172.2 
 
 116.5 
 
 
 -2(KI 
 
 :{.-,:> 7 3.60 
 
 0.4536 
 
 3251 
 
 14.7184 
 
 0.000100 
 
 150.: 
 
 { 731 
 
 437 
 
 13 11.7 
 
 581.51 
 
 2-2-2. 1 
 
 27.5 
 
 
 -100 
 
 101 10 Mil 
 
 O.I300 
 
 3089 
 
 138.1447 
 
 0.000165 
 
 II. 
 
 1207 
 
 1451 
 
 II. 1 
 
 310.51 
 
 20,-. 
 
 150.1 
 
 
 
 
 33 :!l I.NI 
 
 0.4082 
 
 2020 
 
 36.8726 
 
 0.1)001 II 
 
 111. 
 
 1061 
 
 2166 
 
 103.0 
 
 57,1( 
 
 70.S 
 
 70.1 
 
 
 100 
 
 232 13 l.:r. 
 
 03856 
 
 2761 
 
 1 60.30: W 
 
 0.000116 
 
 211. 
 
 2121 
 
 521 
 
 311.6 
 
 370.31 
 
 130.1 
 
 201.6 
 
 
 200 
 
 71 55 0.11 
 
 -03639 
 
 -2601 
 
 50.0366 
 
 -0.000302 
 
 72. 1 
 
 
 1535 
 
 106.2 
 
 117.20 
 
 ISO.:) 
 
 112.6 
 
 
 300 
 
 271 7 16.14 
 
 0.3102 
 
 8439 
 
 1-2.1726 
 
 0.000367 
 
 172,1 
 
 3550 
 
 2550 
 
 6I7.S 
 
 430.17 
 
 230.6 
 
 23.6 
 
 K 
 
 100 
 
 III) 10 25.13 
 
 0.3175 
 
 2276 
 
 SI. 2 103 
 
 0.0003 13 
 
 33.5 
 
 4111 
 
 605 
 
 700.1 
 
 i;;. 2 
 
 37.7 
 
 155.2 
 
 d 
 
 500 
 
 300 31 3ti 
 
 0.2: 'is 
 
 3114 
 
 201.6513 
 
 0.0003 IS 
 
 133.5 
 
 1677 
 
 1620 
 
 951.0 
 
 400.00 
 
 --.o 
 
 6i;.2 
 
 a t 
 
 (WO 
 
 148 43 50.82 
 
 0.2722 
 
 1851 
 
 103.3030 
 
 0.000-201 
 
 2:i3.5 
 
 5210 
 
 3634 
 
 1102.6 
 
 236.05 
 
 l:!S.:{ 
 
 187.8 
 
 L. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 - 
 
 700 
 
 347 50 6.1 r> 
 
 -0.210.-, 
 
 -1788 
 
 2.1389 
 
 -0.000269 
 
 94.0 
 
 5809 
 
 no 
 
 12.-, 1.2 
 
 558.83 
 
 I--.:, 
 
 
 3 
 
 soo 
 
 1-7 S -.'5.20 
 
 0.2268 
 
 1626 
 
 I25.5S72 
 
 0.0002 15 
 
 lOl.t 
 
 6: )67 
 
 1704 
 
 1 I05.S 
 
 200.78 
 
 23S.S 
 
 IO.S 
 
 ^ 
 
 000 
 
 26 20 I.--.02 
 
 0.2011 
 
 1463 
 
 21.3372 
 
 0.000-220 
 
 55.7 
 
 6! 130 
 
 27 is 
 
 102.5 
 
 31.73 
 
 45.0 
 
 151.3 
 
 
 
 225 33 
 
 0.1814 
 
 1301 
 
 117.7003 
 
 0.000 l!Mi 
 
 155.7 
 
 7403 
 
 771 
 
 854.1 
 
 356.1 il 
 
 !Ni.2 
 
 62,3 
 
 
 1100 
 
 61 45 33.00 
 
 0.1586 
 
 1 i:(S 
 
 4 6.5 152 
 
 0.000171 
 
 16.S 
 
 8056 
 
 1788 
 
 405.7 
 
 94.56 
 
 116.1 
 
 103.0 
 
 
 1200 
 
 203 58 1.13 
 
 -0.1361 
 
 - 076 
 
 170.0033 
 
 -0.000 1 17 
 
 110.8 
 
 
 2803 
 
 557.3 
 
 116.11 
 
 106.7 
 
 101.0 
 
 
 131X1 
 
 103 10 31.1 1 
 
 O.I 131 
 
 813 
 
 08.7030 
 
 0600189 
 
 2I6.S 
 
 9183 
 
 858 
 
 70S.ii 
 
 154.30 
 
 3.H 
 
 15.0 
 
 
 1400 
 
 30-2 23 :!.!! 
 
 0.0007 
 
 651 
 
 102.2200 
 
 0.0000! 8 
 
 77.8 
 
 0716 
 
 IS72 
 
 860.5 
 
 476.20 
 
 51.1 
 
 147.4 
 
 
 1500 
 
 141 :{.-. 3; 
 
 0.0680 
 
 488 
 
 90.0006 
 
 0.000073 
 
 177.8 
 
 10300 
 
 2887 
 
 1012.1 
 
 211.22 
 
 104.4 
 
 >.l 
 
 S 1500 
 
 125 31 I0.2S 
 
 -0.0680 
 
 . 1" 
 
 8<).!>900 
 
 -0.000073 
 
 177.8 
 
 10-200 
 
 2877 
 
 1002.1 
 
 204.22 
 
 01. 1 
 
 
 1 1600 
 
 :{.'! Hi 55.70 
 
 0.0454 
 
 326 
 
 204.4585 
 
 0.000010 
 
 3S.O 
 
 10863 
 
 032 
 
 lisa? 
 
 526.00 
 
 11 1.6 
 
 ' 
 
 1/vO 
 
 162 23 26.76 
 
 -0.0227 
 
 - 163 
 
 102.2280 
 
 -0.000024 
 
 13S.O 
 
 1 1425 
 
 1016 
 
 1301.3 
 
 263.05 
 
 103.0 
 
 90.' 1 
 
 C : 
 
 000 
 
 
 
 
 0.0000 
 
 0.000000 
 
 0.0 
 
 
 
 
 
 0.0 
 
 0.00 
 
 0.0 
 
 C..I 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 1000 
 
 107 36 35.51 
 
 +0.0-227 
 
 + 162 
 
 1-22.4752 
 
 +0.000024 
 
 100.0 
 
 502 
 
 1013 
 
 150.6 
 
 320.88 
 
 10.3 
 
 130.6 
 
 o 
 jc 
 
 2000 
 
 36 40 21.09 
 
 0.0454 
 
 335 
 
 21.2521 
 
 0.000040 
 
 200.0 
 
 1125 
 
 8688 
 
 302.2 
 
 5s.s:l 
 
 ilO.5 
 
 41.6 
 
 
 
 2100 
 
 234 26 1.13 
 
 40.0680 
 
 + 487 
 
 1 13.73-2-2 
 
 +0.000073 
 
 61.1 
 
 I6SS 
 
 89 
 
 I52.S 
 
 370.70 
 
 1 l-.s 
 
 172.1 
 
 (9 
 
 ,2200 
 
 72 2 43.41 
 
 +0.0007 
 
 + 650 
 
 41.5140 
 
 +0.000098 
 
 101.1 
 
 2250 
 
 1090 
 
 603.4 
 
 116.116 
 
 198.1 
 
 S2. 1 
 
 Century 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 log sin t. 
 
 t' 50. 
 
 363 -Q. 
 
 ' 50. 
 
 XV. 
 
 \V1 
 
 
 -300 
 
 129*81 
 
 35.01 
 
 1S0.76 
 
 10.0 
 
 56.38 
 
 25.2 
 
 -0.0031028 
 
 +21.61 
 
 i 11 
 
 +18 46 55.6 
 
 +<>.'63I 
 
 1190*0 
 
 d 
 
 -1.4 
 
 
 -200 
 
 15S.06 
 
 56.10 
 
 t J."'.~i ^IS.S 
 
 23.00 
 
 3.8 
 
 0.00294$! 
 
 23.11 
 
 17 53 46.0 
 
 0.601 
 
 3721.3 
 
 3.6 
 
 
 -100 
 
 18630 
 
 44.00 
 
 165.31 
 
 3S.1 
 
 47.71 
 
 17.0 
 
 0.0027850 
 
 22.27 
 
 17 33.4 
 
 0.574 
 
 625S.O 
 
 2.H 
 
 
 
 
 211.:,.-, 
 
 5.25 
 
 831.40 
 
 57.0 
 
 11.03 
 
 32.1 
 
 0.0020270 
 
 21.10 
 
 Hi 7 I7.S 
 
 0.544 
 
 1003.4 
 
 2.1 
 
 
 100 
 
 5.80 
 
 53.15 
 
 149.80 
 
 56.3 
 
 39.04 
 
 93 
 
 0.0024719 
 
 10.92 
 
 15 13 50.1 
 
 0.513 
 
 1527.1 
 
 1.3 
 
 
 200 
 
 34.05 
 
 14.30 
 
 215.05 
 
 15.1 
 
 6.26 
 
 24.5 
 
 -0.0023171 
 
 +1S.75 
 
 +14 20 37.4 
 
 +O.I.-3 
 
 262,-. 
 
 -0.5 
 
 
 300 
 
 62.30 
 
 2.20 
 
 134.41 
 
 14.4 
 
 30.37 
 
 2.3 
 
 0.002 K !35 
 
 17.58 
 
 13 27 12.7 
 
 0.453 
 
 2700.2 
 
 +0.3 
 
 fe 
 
 400 
 
 90.54 
 
 
 200.50 
 
 33.3 
 
 57.50 
 
 10.S 
 
 0.0020111 
 
 16.11 
 
 12 :{:{ 45.0 
 
 0.423 
 
 5329.9 
 
 1.1 
 
 c 
 
 500 
 
 II -.7:1 
 
 1 l.-'li 
 
 118.00 
 
 32.6 
 
 21.70 
 
 30.0 
 
 0.0018508 
 
 15.24 
 
 11 40 1 1.3 
 
 0.303 
 
 1065.3 
 
 L8 
 
 B 
 - , 
 
 000 
 
 147.03 
 
 32!l 1 
 
 1S5.05 
 
 51.4 
 
 48.92 
 
 93 
 
 0.0017097 
 
 14.00 
 
 10 40 40.0 
 
 0.362 
 
 35! 10.0 
 
 2.6 
 
 C 
 
 700 
 
 175.28 
 
 53.57 
 
 11.15 
 
 10.3 
 
 16.14 
 
 23.7 
 
 -0.0015008 
 
 +12.89 
 
 + 53 3.8 
 
 +0.332 
 
 6132.7 
 
 +3.1 
 
 IS 
 
 800 
 
 203.53 
 
 41,17 
 
 16; 1.60 9.0 
 
 10.2.-, 
 
 1.5 
 
 0.0014130 
 
 11.72 
 
 S 50 21.0 
 
 0309 
 
 1868.1 
 
 1.2 
 
 * 
 
 000 
 
 231.77 
 
 2.62 
 
 235.70 28.5 
 
 7.47 
 
 16.1 
 
 0.0012665 
 
 10.55 
 
 8 5 41.2 
 
 0.272 
 
 4401.8 
 
 ."..I) 
 
 
 1000 
 
 23.03 
 
 5052 
 
 151.15 
 
 27.8 
 
 31.57 
 
 29.9 
 
 0.0011211 
 
 938 
 
 7 11 55.4 
 
 0.212 
 
 137.3 
 
 .">.- 
 
 
 1100 
 
 51.27 
 
 11.68 
 
 220.25 
 
 40.0 
 
 58.79 
 
 8.4 
 
 0.000076- 
 
 8.20 
 
 18 0.5 
 
 0.211 
 
 2071.0 
 
 6.5 
 
 
 1200 
 
 79.52 
 
 59.58 
 
 138.70 
 
 45.9 
 
 22.90 
 
 22.2 
 
 -0.0008338 
 
 + 7.03 
 
 + 5 24 14.0 
 
 +0.181 
 
 5204.0 
 
 +7.3 
 
 
 1300 
 
 107.70 
 
 20.73 
 
 204.SO 
 
 4.8 
 
 50.12 
 
 0.8 
 
 0.0000010 
 
 5.80 
 
 4 30 10.7 
 
 0.151 
 
 010.1 
 
 S.I 
 
 
 1400 
 
 136.01 
 
 8.63 
 
 123.25 
 
 4.1 
 
 1 1.23 
 
 14.6 
 
 0.000.-,.-, 12 
 
 4.(iO 
 
 3 36 21.8 
 
 0.121 
 
 3173.x 
 
 S.ll 
 
 
 J500 
 
 161.25 
 
 29.79 
 
 189.35 
 
 23.0 
 
 41.45 
 
 29.1 
 
 0.0004110 
 
 3.52 
 
 2 42 20.0 
 
 0.0!) 1 
 
 0007.5 
 
 +9.7 
 
 ij 
 
 1500 
 
 154.25 
 
 29.79 
 
 180.35 
 
 23.0 
 
 41.45 
 
 29.1 
 
 -0.0004116 
 
 + 3.52 
 
 + 2 42 20.0 
 
 +0.001 
 
 5007.5 
 
 -0.3 
 
 fl 
 
 I6IUI 
 
 1. -2.50 
 
 17.60 
 
 I07.SO 
 
 22.2 
 
 -, ;, ; 
 
 6.9 
 
 0.0002732 
 
 2.31 
 
 1 48 17.0 
 
 0.060 
 
 17: f2.! 
 
 40.1 
 
 
 
 1700 
 
 209.75 
 
 
 173.00 
 
 II. 1 
 
 33.78 
 
 21.4 
 
 -0.000 1 3! k) 
 
 + 1.17 
 
 + o :>l 10.0 
 
 +0.030 
 
 4205.6 
 
 +0.2 
 
 cS 
 
 1800 
 
 0.00 
 
 'o!oo 
 
 0.00 
 
 0.0 
 
 0.00 
 
 0.0 
 
 0.0000000 
 
 0.00 
 
 0.0 
 
 0.000 
 
 0.0 
 
 0.0 
 
 c 
 .2 
 
 1000 
 
 27.25 
 
 47.00 
 
 158,15 
 
 :,'; 
 
 24.11 
 
 13.8 
 
 +0.0001310 
 
 - 1.17 
 
 - 51 13.0 
 
 -0.030 
 
 2532.7 
 
 -0.2 
 
 c 
 B 
 
 2000 
 
 55.49 
 
 0.05 
 
 22l,->5 
 
 18/2 
 
 5133 
 
 883 
 
 0.00026-5 
 
 2.34 
 
 1 48 20.0 0.060 
 
 5000.1 
 
 +0.0 
 
 
 2100 
 
 82.74 
 
 56.! 15 
 
 113.00 
 
 17.1 
 
 15.11 
 
 ai 
 
 0.000401 1 
 
 3.52 
 
 2 12 Kl 0.001 
 
 
 0.3 
 
 
 
 2200 
 
 109.98 
 
 18.11 
 
 
 36.3 
 
 12.68 
 
 ' 
 
 20.7 
 
 +0.0005324 
 
 - 1.6.1 
 
 - 3 37 10.2 -0.121 
 
 1 
 
 .{.ecu 
 
 +0.1 
 
8O 
 
 TABLE XL.VI. 
 
 TAIIL1J XI.V. 
 
 Reduction to the Ecliptic for 1850. 
 
 Values of /he Equation 
 
 Argument = Orbit Longitude -f- (360 Q), or this angle diminished by 180. 
 
 + 147.!.) 
 
 Arg. 
 
 0' 
 
 10' 
 
 20' 
 
 30' 
 
 40' 
 
 5O' 
 
 Diff. 
 
 for 10 
 
 Var. in 
 100 yrs. 
 
 
 
 Equa. 
 
 Din", for 
 
 o 
 
 / // 
 
 H 
 
 n 
 
 u 
 
 ii 
 
 n 
 
 n 
 
 n 
 
 o 
 
 Year. 
 
 III yrs. 
 
 
 
 -0 0.00 
 
 1.05 
 
 2.10 
 
 3.15 
 
 4.21 
 
 5.26 
 
 1.05 
 
 0.00 
 
 179' 
 
 
 
 1 
 
 6.31 
 
 7.36 
 
 8 41 
 
 i) ||j 
 
 10 r il 
 
 H<)6 
 
 1 O^i 
 
 o on 
 
 17SJ 
 
 
 
 /, 
 
 
 2 
 
 12.61 
 
 13.66 
 
 O.T: 1 
 
 14.71 
 
 15.76 
 
 J.\/.iJ 1 
 
 16.80 
 
 ,*J\J 
 
 17.85 
 
 1.05 
 
 \j \\j\j 
 
 -0.01 
 
 J. <O 
 
 177 
 
 1800 
 
 H 
 
 -0.281 
 
 - 3 
 
 3 
 
 18.90 
 
 19.94 
 
 20.99 
 
 22.04 
 
 23.08 
 
 24.12 
 
 1.05 
 
 0.01 
 
 176 
 
 1810 
 1820 
 
 
 0.251 
 
 15 
 
 27 
 
 4 
 
 25.16 
 
 26.20 
 
 27.24 
 
 28.28 
 
 29.31 
 
 30.35 
 
 1.04 
 
 0.02 
 
 175 
 
 1830 
 
 
 0.218 
 
 37 
 
 5 
 
 -0 31.39 
 
 32.43 
 
 33.46 
 
 31.50 
 
 35.53 
 
 36.56 
 
 1.03 
 
 -0.02 
 
 174 
 
 1840 
 
 
 0.176 
 
 45 
 
 6 
 
 37.59 
 
 38.61 
 
 39.64 
 
 40.66 
 
 41.69 
 
 42.71 
 
 1.09 
 
 0.02 
 
 173 
 
 
 
 
 
 7 
 
 43.71 
 
 44.76 
 
 45.77 
 
 46.79 
 
 47.80 
 
 48.82 
 
 1.01 
 
 0.03 
 
 172 
 
 1850 
 
 +U.12H 
 
 -51 
 
 8 
 
 49.83 
 
 50.84 
 
 51.85 
 
 52.85 
 
 53.86 
 
 54.87 
 
 1.01 
 
 0.03 
 
 171 
 
 1860 
 1870 
 
 0.073 
 +0.016 
 
 66 
 
 58 
 
 9 
 
 55.87 
 
 56.87 
 
 57.86 
 
 58.86 
 
 59.85 
 
 60-85 
 
 1.00 
 
 0.03 
 
 170 
 
 1880 
 
 -0.043 
 
 58 
 
 10 
 
 -1 1.84 
 
 2.83 
 
 3.82 
 
 4.80 
 
 5.78 
 
 6.76 
 
 0.98 
 
 -0.04 
 
 169 
 
 1890 
 
 
 U.1UU 
 
 54 
 
 11 
 
 1 7.73 
 
 8.71 
 
 9.68 
 
 10.65 
 
 11.62 
 
 12.58 
 
 0.97 
 
 0.04 
 
 168 
 
 1900 
 
 -0.152 
 
 -49 
 
 12 
 13 
 
 1 13.54 
 
 1 19.26 
 
 14.50 
 20.20 
 
 15.46 
 21.14 
 
 16! 41 
 22.08 
 
 17.36 
 23.01 
 
 18.31 
 23.95 
 
 0.95 
 
 0.94 
 
 0.05 
 0.05 
 
 167 
 166 
 
 1910 
 
 
 
 42 
 
 14 
 
 1 24.88 
 
 25.81 
 
 26.74 
 
 27.66 
 
 28.58 
 
 29.50 
 
 0.92 
 
 0.05 
 
 165 
 
 1920 
 
 
 0.236 
 
 31 
 
 
 
 
 
 
 
 
 
 
 
 1930 
 
 
 0.261 
 
 20 
 
 15 
 
 -1 30.41 
 
 31.32 
 
 32.23 
 
 33.13 
 
 34.03 
 
 31.93 
 
 0.90 
 
 -0.06 
 
 164 
 
 1940 
 
 
 0.277 
 
 -10 
 
 16 
 
 1 35.82 
 
 36.71 
 
 37.60 
 
 38.48 
 
 39.36 
 
 40.24 
 
 0.88 
 
 0.06 
 
 163 
 
 1950 
 
 -0.282 
 
 + 2 
 
 17 
 
 18 
 
 1 41.11 
 1 46.28 
 
 41.98 
 47.13 
 
 42.85 
 47.98 
 
 43.71 
 
 48.82 
 
 44.57 
 49.66 
 
 45.43 
 
 50.50 
 
 0.8G 
 0.84 
 
 0.06 
 0.07 
 
 162 
 161 
 
 1960 
 1970 
 
 
 U.V/3 
 
 0.254 
 
 14 
 25 
 
 19 
 
 1 51.33 
 
 52.16 
 
 52.98 
 
 53.80 
 
 54.61 
 
 55.42 
 
 0.82 
 
 0.07 
 
 160 
 
 1980 
 
 
 0.223 
 
 30 
 
 20 
 
 -1 56.23 
 
 57.04 
 
 57.84 
 
 58.64 
 
 59.43 
 
 60.22 
 
 0.80 
 
 -0.07 
 
 159 
 
 1990 
 
 
 0. 182 
 
 44 
 
 21 
 
 2 1.00 
 
 1.78 
 
 2.56 
 
 3.33 
 
 4.10 
 
 4.86 
 
 0.77 
 
 0.08 
 
 158 
 
 2000 
 
 -0.134 
 
 + 51 
 
 22 
 23 
 
 2 5.62 
 2 10.08 
 
 6.37 
 10.81 
 
 T.12 
 11.54 
 
 7.86 
 12.26 
 
 8.60 
 12.98 
 
 9.31 
 13.69 
 
 0.74 
 0.72 
 
 0.08 
 0.08 
 
 157 
 156 
 
 2010 
 2020 
 
 0.080 
 -0.023 
 
 58 
 
 24 
 
 2 14.39 
 
 15.09 
 
 15.79 
 
 16.48 
 
 17.17 
 
 17.86 
 
 O.G9 
 
 0.09 
 
 155 
 
 2030 
 2040 
 
 +0.036 
 0.093 
 
 58 
 55 
 
 25 
 26 
 
 -2 18.54 
 2 22.51 
 
 19.22 
 23.16 
 
 19.89 
 23.80 
 
 20.56 
 24.44 
 
 21.22 
 25.07 
 
 21.87 
 25.70 
 
 O.GG 
 O.C3 
 
 -0.09 
 0.09 
 
 154 
 153 
 
 2050 
 
 +0.146 
 
 50 
 
 27 
 
 28 
 
 2 26.32 
 2 29.94 
 
 26.94 
 30.52 
 
 27.55 
 31.10 
 
 28.16 
 31.67 
 
 28.76 
 32.24 
 
 29.35 
 32.81 
 
 0.60 
 0.57 
 
 0.09 
 O.l'O 
 
 152 
 151 
 
 2060 
 2070 
 
 
 u. iy.i 
 0.231 
 
 33 
 
 29 
 
 2 33.38 
 
 33.94 
 
 34.49 
 
 35.04 
 
 35.58 
 
 36.11 
 
 0.54 
 
 0.10 
 
 150 
 
 2080 
 
 
 0.25!) 
 
 23 
 
 30 
 
 -2 36.64 
 
 37.16 
 
 37.68 
 
 38.19 
 
 38.70 
 
 39.20 
 
 0.51 
 
 -0.10 
 
 149 
 
 2090 
 
 V.X'l'l 
 
 + 12 
 
 31 
 
 2 39.70 
 
 40.19 
 
 40.68 
 
 41.16 
 
 41.64 
 
 42.11 
 
 0.48 
 
 0.10 
 
 148 
 
 2100 
 2110 
 
 +0.282 
 +0.275 
 
 - 1 
 -13 
 
 32 
 
 33 
 34 
 
 2 42.57 
 2 45.25 
 
 2 47.72 
 
 43.03 
 45.68 
 48.11 
 
 43.48 
 46.10 
 
 48,49 
 
 4393 
 46.52 
 
 48.87 
 
 44.38 
 46.93 
 49.25 
 
 44.82 
 47.33 
 49.62 
 
 0.45 
 0.41 
 0.38 
 
 0.10 
 0.10 
 0.11 
 
 147 
 146 
 145 
 
 
 
 35 
 
 -2 49.99 
 
 50.35 
 
 50.70 
 
 51.05 
 
 51.39 
 
 51.72 
 
 0.34 
 
 -0.11 
 
 144 
 
 
 
 36 
 
 2 52.04 
 
 52.36 
 
 52.68 
 
 52.99 
 
 53.30 
 
 53.60 
 
 0.31 
 
 0.11 
 
 143 
 
 Multiples of the Period 
 
 37 
 
 2 53.90 
 
 54.19 
 
 54.47 
 
 54.75 
 
 55.02 
 
 55.28 
 
 0.27 
 
 0.11 
 
 1 12 
 
 nf this El/nation. 
 
 38 
 
 2 55.54 
 
 55.79 
 
 56.01 
 
 56.28 
 
 56.52 
 
 56.75 
 
 0.24 
 
 0.11 
 
 141 
 
 
 
 39 
 
 2 56.96 
 
 57.18 
 
 57.39 
 
 57.60 
 
 57.80 
 
 57.99 
 
 0.20 
 
 0.11 
 
 140 
 
 
 
 40 
 
 -2 58.17 
 
 58.35 
 
 58.52 
 
 58.69 
 
 58.85 
 
 59.01 
 
 0.17 
 
 0.11 
 
 139 
 
 1 
 
 302. 1 
 
 41 
 
 2 59.17 
 
 59. 32 
 
 5!). 16 
 
 59.59 
 
 59.72 
 
 59.84 
 
 0.13 
 
 0.11 
 
 138 
 
 2 
 
 604.8 
 
 42 
 
 2 59.94 
 
 60.05 
 
 60.15 
 
 60.25 
 
 60.3 I 
 
 60.42 
 
 0.09 
 
 0.11 
 
 137 
 
 3 
 
 907.2 
 
 43 
 
 3 0.50 
 
 0.57 
 
 0.64 
 
 0.70 
 
 0.75 
 
 0.79 
 
 0.05 
 
 0.11 
 
 136 
 
 4 
 
 1209.6 
 
 44 
 
 -3 .0.83 
 
 0.86 
 
 0.89 
 
 0.91 
 
 0.93 
 
 0.94 
 
 0.02 
 
 -0.11 
 
 135 
 
 5 
 
 1512.0 
 
 
 GO' 
 
 50' 
 
 4O' 
 
 30' 
 
 20' 
 
 10' 
 
 
 
 Arg. 
 
 6 
 
 1814.4 
 
 
 
 
 
 
 
 
 
 
 
 7 
 
 21J6.8 
 
 
 8 
 
 2419.2 
 
 NDTK. When the degrees of the Argument are read from the right band side of the Table, 
 
 9 
 
 2721.6 
 
 the tens of minutes must he read from the bottom; ami the Reduction and its Secular Variation 
 
 
 
 are affected with the sign -|- instead of . 
 
TA1IL.K XL, VI. 
 
 81 
 
 /,' iliicliiiii la l!u- />//////! /'in- 1S.">(). 
 
 Ar;;ii in = Orliit Longitude -f- (:!UO Q), or this angle diminished l>v 1 
 
 Aff. 
 
 0' 
 
 10' 
 
 20' 
 
 3O' 
 
 10' 
 
 50' 
 
 Diff. 
 
 for III'. 
 
 V.-,r. in 
 ion 
 
 
 
 
 16 
 
 -3 0.95 
 
 
 o'-'i i 
 
 0.93 
 
 // 
 0.91 
 
 II 
 
 0.88 
 
 0.09 
 
 -o'l i 
 
 o 
 
 184 
 
 Hi 
 
 3 O.S5 
 
 0.81 
 
 0.77 
 
 0.72 
 
 0.66 
 
 0.59 
 
 0.05 
 
 0.11 
 
 133 
 
 47 
 
 3 0.;2 
 
 0.11 
 
 0.36 
 
 0.27 
 
 0.18 
 
 0.08 
 
 0.09 
 
 0.11 
 
 139 
 
 48 
 
 2 59.9N 
 
 59.8T] 
 
 68.75 
 
 59.63 
 
 59.50 
 
 5!). 36 
 
 0.13 
 
 0.11 
 
 131 
 
 19 
 
 2 59.21 
 
 59.06 
 
 5S.90 
 
 58.74 
 
 58.67 
 
 68.40 
 
 0.1G 
 
 0.11 
 
 130 
 
 50 
 
 -2 5N.23 
 
 68.05 
 
 57.86 
 
 57.66 
 
 57. Ml 
 
 57.26 
 
 0.-20 
 
 -0.11 
 
 189 
 
 51 
 
 2 57.03 
 
 56.80 
 
 56.57 
 
 56.3 1 
 
 56.10 
 
 55.S6 
 
 0.94 
 
 0.11 
 
 128 
 
 52 
 
 2 55.61 
 
 55.35 
 
 55.09 
 
 54.82 
 
 51.51 
 
 64.96 
 
 0.87 
 
 0.11 
 
 127 
 
 58 
 
 2 53.9N 
 
 58.69 
 
 58.88 
 
 53.09 
 
 52.78 
 
 52. 16 
 
 0.31 
 
 0.11 
 
 126 
 
 54 
 
 2 52.11 
 
 5 LSI 
 
 51.48 
 
 51.14 
 
 50.80 
 
 50. 15 
 
 o.:ti 
 
 0.11 
 
 126 
 
 65 
 
 -2 50.09 
 
 19.73 
 
 49.36 
 
 48.99 
 
 48.61 
 
 48.22 
 
 0.38 
 
 -0.10 
 
 194 
 
 56 
 
 . } \~r QO 
 
 47.48 
 
 47.03 
 
 46.62 
 
 46.2 1 
 
 45.79 
 
 0.41 
 
 0.10 
 
 123 
 
 57 
 
 2 45.37 
 
 11.91 
 
 44.51 
 
 44.07 
 
 43.62 
 
 13.16 
 
 0.44 
 
 O.JO 
 
 122 
 
 58 
 
 2 42.70 
 
 12.23 
 
 41.76 
 
 41.28 
 
 40.80 
 
 40.32 
 
 0.48 
 
 0.10 
 
 181 
 
 59 
 
 2 39.84 
 
 39.35 
 
 38.85 
 
 38.35 
 
 37.84 
 
 37.32 
 
 0.51 
 
 0.10 
 
 120 
 
 60 
 
 -2 36.78 
 
 36.25 
 
 35.72 
 
 35.18 
 
 34.64 
 
 31.09 
 
 0.54 
 
 0.10 
 
 119 
 
 61 
 
 2 33.53 
 
 32.97 
 
 88.41 
 
 31.81 
 
 31.27 
 
 30.69 
 
 0.57 
 
 0.09 
 
 118 
 
 62 
 
 2 30.09 
 
 29.50 
 
 2N.91 
 
 28.31 
 
 27.71 
 
 27.10 
 
 0.00 
 
 0.09 
 
 117 
 
 68 
 
 2 26. 17 
 
 25.85 
 
 25.22 
 
 24.59 
 
 23.95 
 
 23.31 
 
 O.G3 
 
 0.09 
 
 116 
 
 64 
 
 2 22.67 
 
 22.02 
 
 21.37 
 
 20.71 
 
 20.05 
 
 19.38 
 
 O.G6 
 
 0.09 
 
 115 
 
 65 
 
 -2 18.69 
 
 18.01 
 
 17.33 
 
 16.64 
 
 15.95 
 
 15.25 
 
 O.G9 
 
 -0.08 
 
 lit 
 
 66 
 
 2 11.55 
 
 13.84 
 
 13.13 
 
 12,41 
 
 11.69 
 
 10.97 
 
 0.72 
 
 0.08 
 
 113 
 
 87 
 
 2 10.21 
 
 9.51 
 
 8.77 
 
 8.03 
 
 7.29 
 
 6.54 
 
 0.71 
 
 0.08 
 
 112 
 
 68 
 
 2 5.78 
 
 5.02 
 
 4.26 
 
 3.49 
 
 2.72 
 
 1.94 
 
 0.77 
 
 0.07 
 
 111 
 
 69 
 
 1 61.16 
 
 60.38 
 
 59.59 
 
 58.80 
 
 58.01 
 
 57.21 
 
 0.79 
 
 0.07 
 
 110 
 
 70 
 
 -1 56.39 
 
 55.58 
 
 54.77 
 
 53.95 
 
 53.13 
 
 52.30 
 
 0.83 
 
 -0.07 
 
 109 
 
 71 
 
 1 51.48 
 
 50.65 
 
 49.82 
 
 48.98 
 
 48.14 
 
 47.29 
 
 0.84 
 
 0.07 
 
 108 
 
 72 
 
 1 46.44 
 
 45.59 
 
 44.74 
 
 43.88 
 
 43.01 
 
 42.14 
 
 0.8G 
 
 0.07 
 
 107 
 
 73 
 
 I 41.26 
 
 40.39 
 
 39.51 
 
 38.63- 
 
 37.74 
 
 36.85 
 
 0.88 
 
 0.06 
 
 106 
 
 74 
 
 1 35.96 
 
 35.07 
 
 34.17 
 
 33.27 
 
 32.36 
 
 31.45 
 
 0.90 
 
 0.06 
 
 105 
 
 75 
 
 -1 30.54 
 
 29.63 
 
 28.71 
 
 27.79 
 
 26.87 
 
 25.95 
 
 0.92 
 
 -0.06 
 
 101 
 
 76 
 
 1 25.02 
 
 24.09 
 
 23.16 
 
 22.22 
 
 21.28 
 
 20.34 
 
 0.94 
 
 0.05 
 
 103 
 
 77 
 
 1 19.39 
 
 18.44 
 
 17.49 
 
 16.54 
 
 15.58 
 
 14.62 
 
 0.95 
 
 0.05 
 
 102 " 
 
 78 
 
 1 13.66 
 
 12.70 
 
 11.73 
 
 10.76 
 
 9.79 
 
 8.82 
 
 0.97 
 
 0.05 
 
 101 
 
 79 
 
 1 7.84 
 
 6.86 
 
 5.88 
 
 4.90 
 
 3.92 
 
 2.93 
 
 0.98 
 
 0.04 
 
 100 
 
 80 
 
 -0 61.94 
 
 60.95 
 
 59.96 
 
 58.96 
 
 57.96 
 
 56.96 
 
 .00 
 
 -0.04 
 
 99 
 
 81 
 
 55.96 
 
 5 1.96 
 
 53.95 
 
 52.9 1 
 
 51.91 
 
 50.93 
 
 .01 
 
 0.03 
 
 98 
 
 82 
 
 49.92 
 
 48.91 
 
 47.90 
 
 46.86 
 
 45.86 
 
 II. si 
 
 M 
 
 0.03 
 
 97 
 
 N3 
 
 43.H1 
 
 42.79 
 
 41.76 
 
 40.71 
 
 40.71 
 
 39.68 
 
 M 
 
 0.03 
 
 96 
 
 M 
 
 37.65 
 
 36.62 
 
 35.58 
 
 34.55 
 
 33.52 
 
 32.48 
 
 .03 
 
 0.02 
 
 95 
 
 85 
 
 31.45 
 
 30.42 
 
 29.38 
 
 28.34 
 
 27.30 
 
 26.26 
 
 .04 
 
 -0.02 
 
 91 
 
 86 
 
 25.21 
 
 24.17 
 
 23.13 
 
 22.08 
 
 21.03 
 
 19.98 
 
 .or, 
 
 0.02 
 
 93 
 
 87 
 
 18.93 
 
 17.88 
 
 16.83 
 
 15.78 
 
 14.73 
 
 13.68 
 
 M 
 
 0.01 
 
 92 
 
 88 
 
 12.63 
 
 11.58 
 
 10.53 
 
 9.48 
 
 8.42 
 
 7.37 
 
 .05 
 
 -0.01 
 
 91 
 
 89 
 
 -0 6.32 
 
 5.27 
 
 4.21 
 
 3.16 
 
 2. 1 1 
 
 1.05 
 
 .05 
 
 0.00 
 
 90 
 
 
 60' 
 
 50' 
 
 40' 
 
 30' 
 
 90* 
 
 10' 
 
 
 
 Arg. 
 
 NOTE. When the degrees of the Argument are rend from the right hand side of the Table, the tens of minutes must be 
 
 read from the bottom; and the Reduction and its Secular Variation arc affected with ihe sign -f- instead of . 
 

 UNIVERSITY OF CALIFORNIA LIBRARY 
 BERKELEY 
 
 Return to desk from which borrowed. 
 This book is DUE on the last date stamped below. 
 
 1952 
 
 LD 21-95m-ll,'5Q {2877816)476 
 
Hinder 
 
 i.)l.irJ H">- I'"' 
 
 Mk*n 
 
 Slucklnn. Calil 
 ,188 
 
 -Lo.uj.as or 
 
 v or.uo . 
 
 
 -/ ; 
 
 U C BERKELEY LIBRARIES 
 
 i' inn innilin Mil illillllli III lllli Illlil 
 CD37M7bDas 
 
 1937 
 
 UNIVERSITY OF CALIFORNIA LIBRARY