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The first step is to ascertain the number of revolu- tions made by the planet Venus, from the instant of midnight at the beginning of the Kali Yuga, to the end of the year 4029, which will be found to be 6549. Add these to the position of the planet at the end of the year 4029, =4" 2° 49' 39*, the sum will be Venus's entire motion in 4029 Hindu years, = 6549rev. 4. 2° 49' 39^ ; thcu say, as 4029 years give g549rev. 4. 2° 49' 39", so 1080000 years will give 1755594'^- 0 22° 55' 8', which, rejectmg the frac- tion, (being under six signs), it will be 1755594 revolutions .in 1080000 years: this number being multiplied by four, we have 7022376, the revolutions in a Maha Yuga, or 4320000 years ; and the revo- lutions in a Mahd Yuga being multiplied by 1000, we have 7022376000, the revolutions in a Kalpa, the same as given in the Table. Having thus shown how the number of revolutions of the planet in the primary cycle of 1080000 years is found, let it now be applied in determining the posi- tion of the planet. In doing this, there is no occa- sion to reckon from the beginning of the Kalpa, as in the system of Brahma ; for in this system, we may commence our calculation from any point of time/ Digitized by Google 122 THE MODERN ASTRONOMY at which the planets are assumed to have been in a line of mean conjunction : and as the last mean con- junction is assumed to have taken place at midnight, at the beginning of the KaH Vuga, .we commence our calculation from thence, in preference to any other, asi being the commencement of the cycle of 1080000 years. Suppose we wanted to know the mean heliocen- tric longitude of Venus at the end of the year 4029 of the Kali Vuga, (A.D. 928,) then we say, as the number of years in the cycle, is to the number of revolutions in the same, so the years elapsed since the beginning of Kali Vuga, to the planet's heliocen- tric longitude, in revolutions, signs, &c. Thus, for the year 4029 of the Kali Yuga, we have 2*^^= 6549^- 4* 2° 44' 31' 12*', which differs from the actual position of Venus by only 5' T 48*" : this difference arises from the fraction 0* 22° 55' 8", being rejected in forming the number of revolutions, which must be always entire. The motions of the nodes and apsides of the planets being slow, making a revolution in a great many years, are reckoned from the beginning of a system, and their revolutions determined in the same manner as^ those of the planets in the system of Brahma, already explained. It must be obvious from the above example, that the method of ctmiputing' the mean place of a planet by this system, is less troublesome by fer in the operation, than in the system of Brahma. If we wanted to find the meaai longitude of Venus for the end erf the year 4CQ9 of the Kali Yutga^ by the latter systranfi, we must find the time elapsed from the ere- 9lion,tbus^: — Digitized by Google OF THE HINDUS. 123 To sunrise at die begiaaing of the Kali Vuga, it is . 1972044000 Add, 4029 To the end of the year 4029 of tke Kail VugUy .... 1972946029 The number of revolutions of Venus in 4320000000 years is 7022389492 : therefore the mean heliocen- tric longitude of Venus at the end of the year 4029 of the Kali Yuga, by this system, will be expressed by the formula : '''''''^:i,::r^ ='^?5^S^^= 3207131830 revolutions, 4' S" 58' 33' 23", the mean longitude of Venus at the end of the year 4029 of the KaU Yuga. This shows not only the great labour in the calcula- tion, but also partly the error in position : to gel the whole error we must compare die time ; for the end of the year 4029 of the KaH Yuga, by the system of Bratuna, does not coincide widi the end of iht same year by the system of Varaha. For, 4029 years, by the system of Brahma, =365^' 15^ 30' 22' 30^ X 4029 = 1471626^'- 14^- 40' 52" 30^ and 4029 years, by the system of Vaiaha, = 147 1627** 3 1**47* 30' 36* the difference is, 1^- 17^ 6' 38* 6'' but the for- mer begins from sunrise, and the latter from mid- night : therefore we must diminish the difference by six hours, or 15 dandas, which will make 1*^2*^ 6" 88' 6''= 1*- 0^ 50*- 39" 14" 24*^- the real difference in A. D. 928. We must therefore add the mean motion of Venus for this difference = T 39' 30" to 4 5"* 58" 83" 23*" die sum is 4' 7^ 38' 3" 23* the mean longitude of Venus by the system of Brahma in A.D. 928, at the moment the lon^tude by the system of Varaha was 4*2^44'3r 12*" which, as the latter only differed 5* T 48* from the truth, shows how erroneous the sy^em of Brahma had become at that time ; though in A. D. 538, when it was framed, it gave the place Digitized by Google > \ \^ 124 THE MODERN ASTRONOMY of Venus to within 6' 41' of the truth. This is, in fact, the case with every system: they are all cor- rect, or nearly so when framed, but not. so at any considerable distance of time, either before or after. The mean longitude of Venus, by the system of Varaha at the end of the year 4029 of the Kali Yuga, was found above not to diflfer 6' from the truth ; but will it give the position of that planet in A. D. 538, or the end of the year 3639 of the Kali Yuga, with the same degree of correctness ? Most cer- tainly not, because it was not then framed. The mean longitude of Venus at the end of the year 3639 of the Kali Yuga, by the system of Varaha = '^5^j^= . . 4- 15° 31' 19' 12" By LaLande's Tables for the same instant, H. sphere, 4 18 46 3 44 Error in A. D. 538, . 0 3 14 44 32 And if we carried our calculations still farther back into antiquity, the error would be found to increase in proportion to the time, so that at the beginning of the Kali Yuga the error would amount to 32°4S'36''. Upon this change in the error in proportion to the time, is founded the method of determining the an- tiquity of astronomical systems or books ; and, in fact, it is not only the surest, but the very best that can be employed. If there were no errors, or if the errors were always the same, then we should have no data to proceed on; but this supposition is in its nature impossible : there never yet was found any set of astronomical tables or systems, whether Eu- ropean or otherwise, that did not in progress of time become more and more inaccurate^ by the continual accumulation of the errors in the mean annual motions. Digitized by Google OF THE HINDUS. 125 We shall now proceed to show the antiquity of the system of Varaha, in the same manner as we did that of Brahma, by dividing the errors in position at the beginning of the Kali Yuga by the errors in the mean annual motions. The following Table shows the positions of the planets, both by the system and La Lande's Tables, at the instant of midnight, at the beginning of the Kali Yuga, on the meridian of ZQein, 75*^ 50' east of Greenwich. THE TABLE. BjlAliftDde, H. Sphere. Bj the Sjttem. Enron or Differeooet. Sod, 0* Oo O' 0^ .. 0 Oo O' 0* ..0000 0 0 O' 0^ - 0 0 5 56 Mood, 0 0 5 56 Apogee, 4 0 11 25 ..3000 ~ 1 0 11 25 Node, ft 6 22 S9 ..6000 + 0 23 27 31 Mereuy,.... 10 26 84 25 ..'0000 + 1 3 25 35 VeDu., 1 2 43 36 .. 0 0 0 0 - 1 2 43 36 Man, 11 17 54 18 ..0000 + 0 12 5 42 Jopiter, 0 17 2 53 ..0000 . 0 17 2 53 SatoTD 11 9 0 57 ..0000 + 0 20 59 3 And the following Table exhibits the mean annual motions of the planets, both by the system and LaLande's Tables, with the differences or errors. Mean Annual Motions of the Planets, ^c . Hindu Sphere. By La Laode't Tables. Bj the System. Differeoces. Sod, 12 Oo O' 0^ Mood,.... 4 12 46 40,613 Apogee, 1 10 40 35 ,591 Node, 0 19 21 31,090 Mereory, .. 1 24 45 36 ,943 Veoat, .... 7 15 11 23 ,635 Man, .... 6 11 24 19,15 Jnpiter, ... 1 0 20 50,483 SatnrD,.... 0 12 13 9,343 .. 12 Qo (/ (/" .. 4 12 46 40 ,8 .. 1 10 41 00 ,9 .. 0 19 21 11 A .. 1 24 45 7 ,2 .. 7 15 11 52 ,8 .. 6 11 24 9 ,6 .. 1 0 21 6 ,0 .. 0 12 12 50 ,4 .... + 0^,187 .... + 25 ,309 .... - 19 ,690 .... .29,743 .... + 29 ,165 .... 9 ,55 .... + 15 ,517 ....