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187 140 51 18 18 135 327 444 446 324 104 12 18 54 130 182 187 188 47 12 19 143 333 445 444 318 96 11 19 56 183 183 187 135 48 11 20 150 338 447 441 312 87 10 20 59 135 184 186 132 40 10 21 157 348 448 438 306 78 9 21 62 137 185 185 180 36 9 22 164 348 450 435 800 69 8 22 65 140 186 183 127 82 8 28 171 358 452 432 294 61 7 23 68 143 187 182 124 29 7 24 178 358 458 429 288 52 6 24 71 144 187 181 121 25 6 25 185 362 454 425 282 44 5 25 78 145 188 180 119 22 5 26 193 367 455 423 274 35 4 26 76 149 188 179 116 18 4 27 199 371 456 420 267 27 3 27 79 152 189 178 113 15 8 28 206 376 457 417 260 9 2 28 81 153 189 176 110 11 2 29 213 380 458 414 253 I 1 29 88 155 189 175 108 5 1 30 219 385 459 411 245 0 ^ 30 86 11 156 190 174 105 0 0 • 11 10- 9* 8 T 6 , 10 9 8 7 6 1 + + + + -r + 9 1 . „ _ . I Q Q Q P UseqftheTa bU. Use qftl leTabU. Supp. Saturn's mean long. !• 4 =>12'56" Saturn's true longitu de.. 0*28 021' 56" Saturn's aphelion 8 20 54 27 Subtract from sun's long. 11 2 9 6 Mean anomaly 4 13 18 29 Commutation .... 10 3 47 87 The equation for which is - 5 51 27 The semipar. for wh ich is — 2 29 39 Saturn's mean longitude 1 4 12 56 Its double is .... - 4 59 18 Saturn's true helioc.long. 0 23 21 29 Saturn's true longits de.. 0 28 21 29 Saturn's geocentric long. 0 28 22 11 Digitized by Google APPENDIX. 225 The preceding examples exhibit the usual mode of the Hindu astronomers in general. There are, however, some who pretend to greater accuracy, and go through ten or a dozen operations to get the geocentric place of a planet ; the method of iduch I will now show from the Tatwa Chintamami of Lakshmi Dasa, a com- mentary on the Siddhanta Sirawumi. Lei the geocentric UmgUude ^ Sktmm be required, mid ki$ mean Helioeentrio place, m ia the last example 1* 4^ 12^ 50*' Place of the aphelioo subtract 8 20 64 27 Remains the mean anoBialj 4 18 18 29 Eqaation of the orbit for which is • — 6 47 50 Satom's mean longitode. ••• 1 4 12 56 Satam's tme longitade once equated 0 28 25 6 .Which taken from the son's mean longitode 11 2 9 6 Remains the first commotation • . • 10 S 44 0 The parallax of the orb for which is ^ 4 58 26 Which taken from his longitode once equated • 0 28 25 6 Leares the geocentric place once equated 0 2S 36 40 Second Operation. From the geocentric place once equated • 0 23 36 40 Subtract place of his aphelion 8 20 54 27 Remains.the second anom'alj * • • 4 2 42 IS The equation of the orbit for which is ..••.... 6 40 52 Saturn's mean longitude 1 4 12 56 Saturn's heliocentric longitude twice equated •'• 0 27 32 4 Which subtract from the sun's mean longitude 11 2 9 6 Remains the second commutation •••• 10 4 37 2 The parallax of the orb for which is — 4 57 0 Saturn's heliocentric longitude twice equated 0 27 32 4 Saturn's geocentric longitude twice equated 0 22 85 4 Third Operation. From Saturn's g^eocentric place twice equated 0 22 35 4 Subtract place of his aphelion ,j 8 20 54 27 Remains third anomaly • •• 4 1 40 37 The equation of the orbit for which is — 6 46 57 Saturn's mean longitude • 1 4 12 56 Saturn's heliocentric longitude three times equated 0 27 25 59 Which subtract from the sun's longitude •• • ••••••• 11 2 9 6 Remains third commutation • • 10 4 43 7 ParaOax of the orb for which is •... ^0 4 54 21 Saturn's longitude thrice equated 0 27 25 59 Saturn's geocentric longitude thrice equated. . • • • 0 22 31 38 Fourth Operation. Saturn's geocentric place ihrioe equated. ••.•••• 0 22 31. 36 Subtract place of his aphelion 8 20 54 27 G G Digitized by Google 226 APPENDIX. Remains fourth anomaly ^...., 4* 1<> 91' ll"" The equation of the orbit for which is , • • • • - 6 47 12 Satom's mean longitade. • • • • • 1 4 18 166 Saf am's faeliocentrio longitade (bar times equated 0 27 2S 44 Subtract the same from the sun's mean longitude 11 2 9 6 Remains the fourth commutation • • 10 4 43 22 Parallax of the orb for which is <> 4 54' 20 datum's fourth equated longitade 0 27 95 44 Saturn's geocentric longitude four times equated 0 22 81 . 24 Fifih Operation. datum's geocentric longitude four times equated 0 22 SI 24 Subtract his aphelion as before 8 20 54 27 Remains the fifth anomaly 4 1 36 57 The equation of the orbit for which is r . . — 6 47 12 Saturn's mean longitude 1 4 12 56 Saturn's heliocentric longitade fiye times equated 0 27 25 44 Which coming out the same as in the fourth operation, the calculation terminatef , and the geocentric and heliocentric longitudes of Saturn remain as in the foartk operation. The same method also serves for Ju^ter ; but Mars requires a different om. Thus £ Mars : — Suppose the mean longitude of Mars ss 2* 7° 35^ 16^ Place of his aphelion subtract 4 8 24 57 Remains the anomaly 0 29 10 21 Equation of the orbit for which is -• 9 46 16 Itshalf + 4 53 8 Mean longitude, add 2 7 35 18 The sum is Mars' longitude onoe equated. 2 12 28 26 Which taken from the sun's mean longitade 11 2 9 6 Remains the first commutation ••• 8 19 40 40 Semiparallax of the orb for which is — 18 28 43 Which taken from tiie longitade once equated 2 12 28 26 Leaves Mars' geocentric longitude once equated .••••••••. 1 23 59 42 ' Second Operation. Mars' geocentric longitude once equated • • 1 23 59 43 Subtract his a^elion (eorrected once) •.... 4 6 43 35 Anomaly • • 9 17 16 42 Equation of the orbit for which is -f 10 41 37 Mars' mean longitude 2 7 35 18 Mars' heliocentric longitade twice equated ..•••......•.• 2 18 16 55 Which subtract from the sun's mean longitade. .••••.••••• 11 2 9 6 Remains second commutation ......••• ••• 8 13 52 It Pardlax of the orb corresponding — 1 8 10 7 Mars' longitude twice equated 2 18 16 6S Mars' geocentrio longitude twice equated. • 1 9 57 46 Third Operation. Mars' geocentric longitude twice equated 1 0 57 48 Subtract the aphelion (twice eorrected) 4 5 47 66 Anomaly.. 9 4 9 S6 Digitized by Google APPENDIX. 227 t%m i|^llw fcr wkidi ii + • 50 34' 1^ M i'f BMB loBghode 9 7 M 18 Man' lidioocBtrie longitude thrioe 6qated 9 It 10 S6 Wki^ Mbtnet froB tlie sun'* meaa longitude 11 9 0 6 Hf ebt the third eomantetion. I...... 8 18 58 SO S— yeraUeaL of the orb oonrmponding , — 0 18 SS 14 Man* longitnde thrice equated 9 It 10 t8 Van* geoeeatric lottgitade thriee equated 1 24 t7 2 Fourth Opermtum, Man' geoceatrie loBgitode thrice equated 1 94 t7 9 Sobtract the q>hdioB (thrice corrected) 4 6 tO 44 '^■•■■•'J 9 18 0 18 Eqoalion of the orbit for which ia 4. 10 tO 8 Man' mean loDgitade 2 7 tfi 18 Man' heliooeotrie loBgitnde four timea equated • 2 18 14 26 Which aahtract firofli the sun'a mean longitude 11 2 9 6 Remaina foorth commatation 8 It 54 40 Panllax of the orb corresponding — 1 8 18 29 Man' longitnde four times equated 2 18 14 26 Man' geocentric longUade four times equated 1 9 55 67 Fifth OperaHon, Man' geocentric longitade foar times equated.... 1 9 55 57 Subtract the aphelion four times corrected 4 1 48 14 AsumMlj 9 8 7 4t Half the equation of the orbit , , 4. 5 55 19 Man' mean longitode ...•• 2 7 35 18 Man' helioeentric longitude fire times equated 2 It 10 57 'Which being the same with that found in the third operation, puts an end to the o|d* culation, as all the rest comes out the same ; therefore the heliocentric longitude of Man ia 2> IZ° W t7^ and the geocentric longitude 1* 9 55^ 57^ T0JM the Ehftgatum mtd geocentrk Ltmgitnie ^f Mercury, Suppose the sun's place or mean longitode •••...... * 11* 2^ 9^ 6'*' Subtract place of Mercury's aphelion , . . , 7 14 54 40 Bemains the anomaly ,,., 3 17 14 S6 The equation for which is , , ^ 5 46 59 Sun's mean longitude 11 2 9 6 Sun's fint equated longitude , .