## Of the true places of the planets ||2||

^{1}Forms of Time, of invisible shape, stationed in the zodiac (Bhagana), called the conjunction (Cighrocca), apsis (Mandocca), and node (fata), are causes of the motion of the planets.

^{2}The planets, attached to these beings by cords of air, are drawn away by them, with the right and left hand, forward or backward, according to nearness, toward their own place.

^{3}A wind, moreover, called provector (Praoaha) impels them toward their own apices (Ucca); being drawn away forward and backward, they proceed by a varying motion.

^{4}The so-called apex (Ucca), when in the half-orbit in front of the planet, draws the planet forward; in like manner, when in the half orbit behind the planet, it draws it backward.

^{5}When the planets, drawn away by their apices (Ucca), move forward in their orbits, the amount of the motion so caused is called their excess (Dhana); when they move backward, it is called their deficiency (Rina).

^{6}In like manner, also, the node, Rahu, by its proper force, causes the deviation in latitude (Vikshepa) of the moon and the other planets, northward and southward, from their point of declination (Apakrama).

^{7}When in the half-orbit behind the planet, the node causes it to deviate northward; when in the half-orbit in front, it draws it away southward.

^{8}In the case of Mercury and Venus, however, when the node is thus situated with regard to the conjunction (Cighra), these two planets are caused to deviate in latitude, in the manner stated, by the attraction exercised by the node upon the conjunction.

^{9}Owing to the greatness of its orb, the sun is drawn away only a very little; the moon, by reason of the smallness of its orb, is drawn away much more;

^{10}Mars and the rest, on account of their small size, are, by the supernatural beings (Daivata) called conjunction (Cighrocca) and apsis (Mandorca), drawn away very far, being caused to vacillate exceedingly.

^{11}Hence the excess (Dhana) and deficiency (Rina) of these latter is very great, according to their rate of motion. Thus, do the planets, attracted by those beings, move in the firmament, carried on by the wind.

^{12}The motion of the planets is of eight kinds: retrograde (Rakra), somewhat retrograde (Anuwakra), transverse (Kutila), slow (Manda), very slow (Mandatara), even (Sama), also, very swift (Cigratara), and swift (Cighra).

^{13}Of these, the very swift (Aticighra), that called swift, the slow, the very slow, the even all these five are forms of the motion called direct (Riju); the somewhat retrograde is retrograde.

^{14}By reason of this and that rate of motion, from day to day, the planets thus come to an accordance with their observed places (Dric), this, their correction (Sphutikarana), I shall carefully explain.

^{15}The eighth part of the minutes of a sign is called the first sine (Jyardha); that, increased by the remainder left after subtracting from it the quotient arising from dividing it by itself, is the second sine.

^{16}Thus, dividing the tabular sines in succession by the first, and adding to them, in each case, what is left after subtracting the quotients from the first, the result is twenty-four tabular sines (Jyardhapinda), in order, as follows:

^{17}Two hundred and twenty-five; tour hundred and forty-nine; six hundred and seventy-one; eight hundred and ninety, eleven hundred and five; thirteen hundred and fifteen;

^{18}Fifteen hundred and twenty; seventeen hundred and nineteen; nineteen hundred and ten; two thousand and ninety-three;

^{19}Two thousand two hundred and sixty-seven; two thousand four hundred and thirty-one; two thousand five hundred and eighty-five; two thousand seven hundred and twenty-eight;

^{20}Two thousand eight hundred and fifty-nine; two thousand nine hundred and seventy-eight; three thousand and eighty-four three thousand one hundred and seventy-seven;

^{21}Three thousand two hundred and fifty-six; three thousand three hundred and twenty-one; three thousand three hundred and seventy-two; three thousand four hundred and nine;

^{22}Three thousand four hundred and thirty-one; three thousand four hundred and thirty-eight. Subtracting these, in reversed order, from the half-diameter, gives the tabular versed sines (Utkramajydrdhapindaka):

^{23}Seven; twenty-nine; sixty-six; one hundred and seventeen; one hundred and eighty-two; two hundred and sixty-one; three hundred and fifty-four;

^{24}Four hundred and sixty; five hundred and seventy-nine; seven hundred and ten; eight hundred and fifty-three; one thousand and seven; eleven hundred and seventy-one;

^{25}Thirteen hundred and forty-five; fifteen hundred and twenty-eight; seventeen hundred and nineteen; nineteen hundred and eighteen;

^{26}Two thousand one hundred and twenty-three; two thousand three hundred and thirty-three; two thousand five hundred and forty-eight; two thousand seven hundred and sixty-seven;

^{27}Two thousand nine hundred and eighty-nine; three thousand two hundred and thirteen; three thousand four hundred and thirty-eight: these are the versed sines.

^{28}The sine of greatest declination is thirteen hundred and ninety-seven; by this multiply any sine and divide by radius; the arc corresponding to the result is said to be the declination.

^{29}Subtract the longitude of a planet from that of its apsis (Mandocca); so also, subtract it from that of its conjunction (Cighra); the remainder is its anomaly (Kendra); from that is found the quadrant (pada); from this, the base-sine (Bhujajya), and likewise that of the perpendicular (Koti).

^{30}In an odd (Vishama) quadrant, the base-sine is taken from the part past, the perpendicular, from that to come; but in an even (Yugma) quadrant, the base-sine (Bahujya) is taken from the part to come, and the perpendicular-sine from that past.

^{31}Divide the minutes contained in any arc by two hundred and twenty-five; the quotient is the number of the preceding tabular sine (Jyapindaka). Multiply the remainder by the difference of the preceding and following tabular sines, and divide by two hundred and twenty-five;

^{32}The quotient thus obtained add to the tabular sine called the preceding; the result is the required sine. The same method is prescribed also with respect to the versed sines.

^{33}Subtract from any given sine the next less tabular sine; multiply the remainder by two hundred and twenty-five, and divide by the difference between the next less and next greater tabular sines; add the quotient to the product of the serial number of the next less sine into two hundred and twenty-five the result is the required arc.

^{34}The degrees of the sun’s epicycle of the apsis (Mandaparidhi) are fourteen, of that of the moon, thirty-two, at the end of the even quadrants; and at the end of the odd quadrants, they are twenty minutes less for both.

^{35}At the end of the even quadrants, they are seventy-five, thirty, thirty-three, twelve, forty-nine; at the odd (Oja) they are seventy-two, twenty-eight, thirty-two, eleven, forty-eight,

^{36}For Mars and the rest; farther, the degrees of the epicycle of the conjunction (Cighra) are, at the end of the even quadrants, two hundred and thirty-five, one hundred and thirty-three, seventy, two hundred and sixty-two, thirty-nine;

^{37}At the end of the odd quadrants, they are stated to be two hundred and thirty-two, one hundred and thirty-two, seventy-two, two hundred and sixty, and forty, as made use of in the calculation for the conjunction (Cighrakarman).

^{38}Multiply the base-sine (Bhujajya by the difference of the epicycles at the odd and even quadrants, and divide by radius (Trijya); the result, applied to the even epicycle (Vritta), and additive (Dhana) or subtractive (Rina), according as this is less or greater than the odd, gives the corrected (Sphuta) epicycle.

^{39}By the corrected epicycle multiply the base-sine (Bhujajya) and perpendicular-sine (Kotijya) respectively, and divide by the number of degrees in a circle: then, the arc corresponding to the result from the base-sine (Bhujajyaphala) is the equation of the apsis (Mdnda Phala), in minutes, etc.

^{40}The result from the perpendicular-sine (Kotiphala) of the distance from the conjunction is to be added to radius, when the distance (Kendra) is in the half-orbit beginning with Capricorn; but when in that beginning with Cancer, the result from the perpendicular- sine is to be subtracted.

^{41}To the square of this sum or difference add the square of the result from the base-sine (Bahuphala); the square root of their sum is the hypothenuse (Karina) called variable (Cala). Multiply the result from the base-sine by radius, and divide by the variable hypothenuse:

^{42}The arc corresponding to the quotient is, in minutes, etc., the equation of the conjunction (Caighrya Phala); it is employed in the first and in the fourth process of correction (Karman) for Mars and the other planets.

^{43}The process of correction for the apsis (Manda barman) is the only one required for the sun and moon : for Mars and the other planets arc prescribed that for the conjunction (Caighrya), that for the apsis (Manda), again that for the apsis, and that for the conjunction—four, in succession.

^{44}To the mean place of the planet applies half the equation of the conjunction (Cighraphala), likewise half the equation of the apsis; to the mean place of the planet apply the whole equation of the apsis (Mandaphala), and also that of the conjunction.

^{45}In the case of all the planets, and both in the process of correction for the conjunction and in that for the apsis, the equation is additive (Dhana) when the distance (Kendra) is in the half orbit beginning with Aries; subtractive (Rina), when in the half orbit beginning with Libra.

^{46}Multiply the daily motion (Bhukti) of a planet by the sun’s result from the base-sine (Bahuphala), and divide by the number of minutes in a circle (Bhacakra); the result in minutes, apply to the planet’s true place, in the same direction as the equation was applied to the sun.

^{47}From the mean daily motion of the moon subtract the daily motion of its apsis (Manda), and, having treated the difference in the manner prescribed by the next rule, apply the result, as an additive or subtractive equation, to the daily motion.

^{48}The equation of a planet’s daily motion is to be calculated like the place of the planet in the process for the apsis: multiply the daily motion by the difference of tabular sines corresponding to the base-sine (Dorjya) of anomaly, and then divide by two hundred and twenty-five;

^{49}Multiply the result by the corresponding epicycle of the apsis (Mandaparidhi) and divide by the number of degrees in a circle (Bhagana); the result, in minutes, is additive when in the half-orbit beginning with Cancer, and subtractive when in that beginning with Capricorn.

^{50}Subtract the daily motion of a planet, thus corrected for the apsis (Manda), from the daily motion of its conjunction (Cighra); then multiply the remainder by the difference between the last hypothenuse and radius.

^{51}And divide by the variable hypothenuse (Cala Karina): the result is additive to the daily motion when the hypothenuse is greater than radius, and subtractive when this is less; if when subtractive, the equation is greater than the daily motion, deduct the latter from it, and the remainder is the daily motion in a retrograde (Vakra) direction.

^{52}When at a great distance from its conjunction (Cighrocca), a planet, having its substance drawn to the left and right by slack cords, comes then to have a retrograde motion.

^{53}Mars and the rest, when their degrees of commutation (Kendra), in the fourth process, are, respectively, one hundred and sixty-four, one hundred and forty-four, one hundred and thirty, hundred and sixty-three, one hundred and fifteen.

^{54}Become retrograde (Vakrin): and when they respective commutation are equal to the number of degrees remaining after subtracting those numbers, in each several case, from a whole circle, they cease retrogradation.

^{55}In accordance with the greatness of their epicycles of the conjunction (Cighraparidhi) Venus and Mars cease retrograding in the seventh sign, Jupiter and Mercury in the eight, Saturn in the ninth.

^{56}To the nodes of Mars, Saturn, and Jupiter, the equation of the conjunction is to be applied, as to the planets themselves respectively; to those of Mercury and Venus, the equation of the apsis, as found by the third process, in the contrary direction.

^{57}The sine of the arc found by subtracting the place of the node from that of the planet or, in the case of Venus and Mercury, from that of the conjunction, being multiplied by the extreme latitude, and divided by the last hypothenuse or, in the case of the moon, by radius—gives the latitude (Vikihshepa).

^{58}When latitude and declination (Apakrama) are of like direction, the declination (Kranti) is increased by the latitude; when of different direction, it is diminished by it, to find the true (Spashta) declination: that of the sun remains as already determined.

^{59}Multiply the daily motion of a planet by the time of rising of the sign in which it is, and divide by eighteen hundred; the quotient add to, or subtract from, the number of respirations in a revolution: the result is the number of respirations in the day and night of that planet.

^{60}Calculate the sine and versed sine of declination: then radius, diminished by the versed-sine, is the dav-radius: it is either south or north.

^{61}Multiply the sine of declination by the equinoctial shadow, and divide by twelve ; the result is the earth-sine (Kshitijya); this, multiplied by radius and divided by the day radius, gives the sine of the ascensional difference (Cara): the number of respirations due to the ascensional difference.

^{62}Is shown by the corresponding arc. Add these to, and subtract them from, the fourth part of the corresponding day and night, and the sum and remainder are, when declination is north, the half-day and half-night.

^{63}When declination is south, the reverse; these, multiplied by two, are the day and the night. The day and the night of the asterisms (Bha) may be found in like manner, by means of their declination, increased or diminished by their latitude.

^{64}The portion (Bhoga) of an asterism (Bha) is eight hundred minutes; of a lunar day (Tithi), in like manner, seven hundred and twenty. If the longitude of a planet, in minutes, be divided by the portion of an asterism, the result is its position in asterisms: by means of the daily motion arc found the days, etc.

^{65}From the number of minutes in the sum of the longitudes of the sun and moon are found the Yogas, by dividing that sum by the portion (Bhoga) of an asterism. Multiply the minutes past and to come of the current yoga by sixty and divide by the sum of the daily motions of the two planets: the result is the time in Nadis.

^{66}From the number of minutes in the longitude of the moon diminished by that of the sun are found the lunar days (Tithi), by dividing the difference by the portion (Bhoga) of a lunar day. Multiply the minutes past and to come of the current lunar day by sixty and divide by the difference of the daily motions of the two planets: the result is the time in Nadis.

^{67}The fixed (Dhruva) Karanas, namely Cakuni, Naga, Catushpada the third, and Kinstughna, are counted from the latter half of the fourteenth day of the dark half-month.

^{68}After these, the Karanas called movable (Cara), namely Bava, etc., seven of them: each of these Karanas occurs eight times in a month.

^{69}Half the portion (Bhoga) of a lunar day is established as that of the Karanas Thus has been declared the corrected (Sphuta) motion of the sun and the other planets.