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IQ 26 22 7 Which taken from the mean longitude of Mercury 5 20 51 15 Remains fint commutation 6 24 29 8 The elongation for which is 12 50 12 Sun's longitude once equated , 10 20 22 7 Mercury's geocentric longitude once equated • 10 IS 31 55 See<md Operation. Mercury's geocentric longitude onoe equated 10 13 31 55 Mercury's aphelion subtnct , , , 7 J4 54 40 Remains anomaly , . , , . , 2 28 37 15 The equatiOB for which is ^ 6 3 15 Digitized by Google 228 APPENDIX. Sun's meati longitude !!• ^ ^ 6*^ Sun's longitude twice equated 10 26 5 5r Which taken from Mercury's mean longitude • • 5 20 61 15 Leaves second commutation '. G 24 45 24 The elongation for which is — 12 56 49 Sun's longitude twice equated 10 26 5 31 Mercury's geocentric louf^itude twice equated ;... 10 13 8 42 Third Operation. Mercury's geocentric longitude twice equated 10 13 8 42 Mercury's aphelion, subtract 7 14 64 40 Anomaly 2 28 14 2 The equation for which is _ 6 3 10 Sun's mean longitude • 11 2 9 6 Sun's longitude thrice equated -. 10 26 5 56 Which taken from Mercury's mean longitude 5 20 51 15 Leaves the third commutation 6 24 45 19 The elongation for which is — 12 67 6 Sun's longitude thrice equated 10 26 5 56 Mercury*s geocentric longitude thrice equated . • 10 13 8 50 Fourth Operation, Mercury's geocentric longitude thrice equated 10 13 8 50 lion, subtract 7 14 54 40 .,. 2 28 14 10 r which is _ 6 3 lO e same as in the third operation, all the rest will be the same also ; !Ocentric place of Mercury is found to be 10" 13° 8' 60'', and the 57' 6''. Yenus's geocentric longitude and elongation is found in the T^finA.the, mean heliocentric longitude from the true geocentric longitude, aU the ' requisite data being given. This is the reverse of the former operations. An example will be sufficient. Required the mean heliocentric longitude of Saturn, from His tliie gebcentiSc longitude ibund above 0* 22° 31^ 24^ S&tdl^t tie saiiie from the sun's mean longitude. ...l...*.* 11 2 9 6 L^aveB'firat^coalmutatlpxi ..... ..••.. 10 9 37 42 Plu*allax of the orb for Yrbioh \, with a centrary sign .4- 4 33 59 G^oentciolDoptude^ add .••... •..,... 0 22 31 24 vSiHii.i:.^i^w.^.=..... ..*...>... 0 27 6 29 Subtract place of the aphelion •;.,...••....•• 8 20 54 27 Anomaly 4 6 10 56 Equation of the orbit for which is, with a contrary sign .... + 6 25 59 Add 0 *27 5 23 The sum is the mean heliocentric longitude • • • • . . 1 3 31 22 Second Operation, Sun's mean longitude • 11 2 9 6^ Subtract mean longitude last found ..•••••.•>• 1 3 31 22' Digitized by Google APPENDIX. 229 Seeond oommatetioo •••••• 0 2^ S7' 44^ Parallax of the orb for which, with a contrary sign + 5 17 18 Add geocentric place as before •• 0 22 tl 24 Thesnmis 0 27 48 42 Subtract the aphelion ...... • 8 20 54 27 Anommlj ••••. •• 4 6 54 16 The equation for which it, with a contrary fligB .•••• <f 6 22 28 Add 0 27 48 42 The aom is the mean heliocentric longitude 1 4 11 10 Third Operatum. Son's mean longitode •• •••••••• 11 2 0 6 Subtract mean lengitnde last foond • 1 4 11 10 Third commntation .••..••• 0 27 67 56 Parallax of the orb for which is, with a contrary sign ......•(• 5 19 25 Geocentric longitvde, add ..••••• 0 22 tl 24 Thesnmis 0 27 50 49 ^nbtraot place of the aphelion 8 20 54 27 Anomaly 4 6 56 22 Equation of the orbit for which is, with a contrary sign •••••• 0 6 22 27 Add • 0 27 50 49 The snm is the mean heliocentrio longitode 1 4 IS 16 Fomih OpertUum. Snn's longitude 11 2 0 6 Subtract the mean heliocentric longitude • • • • • 1 4 19 16 Fourth commutation •• • • 0 27 55 50 Parallax of the orb for which is, with a contrary sign <f 5 19 42 Add geocentric longitude • 0 22 SI 24 Thesumis 0 27 51 6 Subtract place of the aphelion ^ • 8 20-54 27 Remains the anomaly • 4 6 56 S9 Equation of the orbit for which is, with a contrary sign • . • • •!• 6 22 17 Add 0 27 51 6 The sum is the mean heliocentric longitude 1 4 IS 2S Fifth Operaium. Sun's mean longitude ••••••• 11 2 9 6 Subtract mean longitude last found 1 4 IS 2S Fifth commutation • 9 27 55 4S ParaHax of the orb for which is, with a contrary sign 4- 5 19 42 Which being the same as in the fourth operation, puis an end to aqy further eatoa- lation : so that 1* 49 IS^ 26"^ is the mean heliooeotrio longitode required, diffiBriof only about 27^ from the original in page 225. Digitized by Google 2m APP£NJ>IX TtMe ^ the CktWKtferenees^ SemidiameterSy and EccentriciHeM qf thi Orbits qf the PlanetSy in Yi^ana*, according to Dada Bhai, a Commentator^on thg Surya Siddhanta. Orbits. ECCEMTRIOITIBS. Pluifftff Circum/er. Leut. QruA€9t. Mtim. Sod • • • • 4S3^6000 684871 26018 45 7 26018 45 7 26018 45 7 Moon.. S24000 51229 4523 48 19 4523 48 19 4523 48 19 MercuT 1043208 164946 12868 14 44 60663 28 24 36765 51 34 Vennii,. 2664637 421316 12879 23 4 304426 10 1 158652 46 32 Man .. 8146909 1288140 262941 35 0 847254 18 40 555097 56 50 Jupiter.. 51376764 8123828 724922 53 2 1631114 5 471178018 29 24 Satain.. 18768255 201861401 215690 0 38 2262097 7 48 123934S 34 8 • The Yojan is about 9. 1-1 1th EogUshmileSf according to the Zri/ivofi. Bat the Mtronomert reckon the eqaetorial circumference of the earth about 5050 Yojans : the degree^ therefore, becomes equal to 14.1-lOth Yojans nearly, which makes the Yojan something less than ftve miles, taking the degree on the equator to be 00 miles. Digitized by Google No. II. REMARKS o THE CHINESE ASTRONOMY. Digitized by Google Digitized by Google APPENDIX. 233 No. II. REMARKS ON THE CHINESE ASTRONOMY. In the course of my inyestigatioii of the antiquity- of the Hindu astronomy, I was induced to take a cursory view of the Chinese, in hopes of finding some analogy between them, and thence be able to draw some conclusion which of the two was the most ancient. In this enquiry, however, I met with nothing that could induce me to believe that any connexion existed between them, at least in ancient times. I found that the Chinese were not only far behind ^e Hindus in the knowledge of astronomy, but that they were indebted to them, in modem times, for the introduction of some improvements into tiiat science, which they themselves acknow- ledge. With respect to tiie Lunar Mansions of tiie Chinese^ they differ entirely from those of the Hindus, who invariably make theirs to contain Id^ 20" each on the ecliptic ; whereas the Chinese have tiieirs of various extents, from upwards of 30^ to a few mi- nutes, and marked by a star at the beginning of each, which makes them totally to differ from the Hindus. The Arabs were the only people that I knew of beside the Hindus that had Lunar Asterisms ; and as they are said to have communicated some of their astronomy to the Chinese about eight or nine hundred years ago, a comparison with tiieir mansions, I thought, might throw some light on the subject, and in this idea I was not mistaken ; for, on comparing the Arabian and Chinese Lunar Asterisms together, I found, to my surprise, that not less than thirteen out of the whole number, which consists of 28, were precisely the same, and in the same order, with scarcely a break between them. Here then there appeared sufficient evidence to shew, that there must have been a connexion between them at some former periods and that the one must have borrowed from the other : but the question then was, who borrowed fiom tb<^ H H Digitized by VjOOQ IC 234 APPENDIX. other, — was it the Chinese from the Arabians, or the Arabians from the Chinese? If the Chinese were the borrowers, somje means might be found of determining the antiquity of the mansions among the Arabs> but if the Arabians were the borrowers, then we must have recourse to the names of the Chinese mansions, to see if they afforded some clue.