The Tiru Ganita Panchanga is the only known source that supports the 18 million years age of physical humanity. This is a key figure in The Secret Doctrine, given many times there. It is very important to try to determine how this figure was arrived at in the Tiru Ganita Panchanga. The figure that everyone else gets for the age of the Vaivasvata manvantara from the data given in the Sūrya-siddhānta is about 120 million years. It so happens that this latter figure, too, is given in The Secret Doctrine, from a secret commentary translated in vol. 2, p. 312 (followed by HPB’s comment):

“The last change took place nearly twelve crores of years ago (120,000,000). But the Earth with everything on her face had become cool, hard and settled ages earlier. (Commentary, xxii.)”

“Thus, if we are to believe esoteric teaching, there have been no more universal geological disturbances and changes for the last 120 millions of years, and the Earth was, even before that time, ready to receive her human stock. The appearance of the latter, however, in its full physical development, as already stated, took place only about eighteen millions of years ago, . . .”

So the 120 million years figure refers to one thing, and the 18 million years figure to another. The question is how the 18 million years figure is derived from the same data that yielded the 120 million years figure. David Pratt called my attention to a note in his “Secret Cycles” article, which mentions that Hans Malmstedt thought he had figured it out, but did not give it. See: http://davidpratt.info/secretcyc.htm#s9, where we read:

“It would be interesting to know how the figure of 18,618,841 years (SD 2:69) for Vaivasvata manvantara (up to 2000) was calculated. The last digit (1) indicates that it could be based on the yugas, since the present maha-yuga began 3,893,101 years ago. The period of 18,618,841 years began 826,260 years after the start of the treta-yuga of the fourth maha-yuga prior to the current maha-yuga. The significance of the period of 826,260 years (= 13,771 x 60) is not immediately evident.
Hans Malmstedt says that if we consider the period of 18,618,740 years preceding the present kali-yuga, and deduct 1075 periods of 1,728,000 years each (i.e. 18,576,000 years), we are left with 37,740 years. He adds: ‘This number of years has a certain relation to a far greater period, closely connected with the five globes above the seven manifested globes of our planetary chain’ (‘Our position in time on globe D’, The Theosophical Path, Oct 1933, pp. 226-35). Unfortunately, he does not expand on this bold assertion!”

In trying to figure these things out, we must take note of a typo in the 1880-1881 Tiru Ganita Panchanga that Dr. Ramanujachary kindly transcribed for us. In the line, “Years that passed since SWAYAMBHAVA Manu — 16645009981,” there is an extra “9”. The figure should be 1664500981, as confirmed by the figure given by HPB in The Secret Doctrine (vol. 2, p. 68) from the 1884-1885 issue. It is always the case that when figures are given, two or more printings must be checked in order to see if there are misprints. That is one reason why the 18 million years figure was in question. In this case, we can see the page for ourselves, and can see the typo. It is in the third of the scanned pages, near the top. A chart is there given, with the four main figures given first, then the eight other figures in two columns with a separating line. So the figure in question is the third of the main figures (or the seventh line from the top of the page, on the right hand side of that line). We can see that that figure has eleven digits rather than ten; and it does not take long to learn (by comparison) enough of the Telugu digits to see that the 9 is indeed doubled by mistake. Dr. Ramanujachary transcribed it correctly for us. It is a typographical error in the original.

The Telugu name of this panchanga that we learned from Dr. Ramanujachary, the Drik Ganita Panchanga, or Dṛg-gaṇita Pañcāṅga, is interesting. The Sanskrit term dṛg-gaṇita usually refers to astronomical calculations (gaṇita) that are based on, or corrected by, observation (dṛg = dṛk = dṛś = “see”). There is always a small margin of error in astronomical constants given in texts, so that over time, the calculated planetary positions no longer match the observed planetary positions. But because of the great authority of texts such as the Sūrya-siddhānta or the Āryabhaṭīya, people are hesitant to change the astronomical constants given in them. Thus, for example, the parahita system of calculations used in Kerala state in south India, put forth by Haridatta, was based directly on the astronomical constants given in the Āryabhaṭīya. Several centuries later, the Indian astronomer Parameśvara saw that the calculated positions no longer matched the observed positions. So he introduced the dṛg-gaṇita system of calculations, which incorporates corrections based on observation. See on this the English “Introduction” by the eminent scholar of Hindu astronomy K. V. Sarma (late of the Adyar Library) to his Sanskrit edition of Dṛggaṇita of Parameśvara (Hoshiarpur: Vishveshvaranand Vedic Research Institute, 1963).

Similarly, we learn that in the 1900s “A new type of almanac, called Dṛggaṇita, whose calculation is based on modern Nautical almanacs and ephemerides is becoming popular” (T. S. Kuppanna Sastry, “A Brief History of Tamil Astronomy,” Madras University Journal, reprinted in his posthumously published book, Collected Papers on Jyotisha, Tirupati, 1989, pp. 329-344, quote from p. 342; he does not mention the Tiru Ganita Panchanga in this article). In fact, shortly after Indian independence, lack of uniformity in panchangas led to the establishment by the new government of a Calendar Reform Committee in 1952. Its recommendations were published in 1955. The government then began publishing a national panchanga, the Rashtriya Panchang, in 1957. It is based on the Nautical Almanac prepared and published in India, according to the issues of it that I obtained in India in the 1970s. It does not list elapsed years since creation, or of any manu or manvantara, nor does it refer to the Sūrya-siddhānta.

What a panchanga is and its place in Indian society is well described by S. K. Chatterjee and A. K. Chakravarty in their chapter, “Indian Calendar from Post-Vedic Period to AD 1900,” of the book, History of Astronomy in India (ed. S. N. Sen and K. S. Shukla, New Delhi: Indian National Science Academy, 1985, second revised edition 2000, pp. 276-336, section on “Pañcāṅga or Indian Almanac,” pp. 290-304), p. 290:

“Pañcāṅga is a very important book published yearly and is the basic book of the society giving calendrical information of various nature on daily basis, and is extensively used by the people all over India. This publication is also one of the basic books of the astrologers for making astrological calculations, casting horoscopes, and for making predictions. It is also used considerably by a large section of the people as an astrological guide book for finding out auspicious time for undertaking various social and other activities and the inauspicious time for avoiding such activities. This book shows the date and time of various religious festivals, and is used by the priests for determining the auspicious moments for carrying out various religious rites, and as such it is a fundamental book which is referred to by a very large section of the people in this country.”

They go on to describe the five constituents of a pañcāṅga (literally, “five limbs”):

“(a) Vāra, that is, week day;

(b) Tithi, that is, lunar day. It is indicative of the phase of the Moon.

(c) Nakṣatra, that is, position of the Moon in the nakṣatra division.

(d) Yoga means literally addition. It is the time period when the longitudinal motions of the Sun and the Moon when added amounts to 13° 12’ or its integral multiple.

(e) Karaṇa means half period of a tithi.”

More detail about pañcāṅgas, their constituents, and the recommendations of the government Calendar Reform Committee is given by B. V. Subbarayappa in the chapter titled “Pañcāṅga” of his book, The Tradition of Astronomy in India: Jyotiḥśāstra (History of Science, Philosophy and Culture in Indian Civilization, Vol. IV, Part 4, New Delhi: Centre for Studies in Civilizations, 2008), pp. 203-234. I am giving only references to these books rather than scanning and posting the chapters themselves, unless requested. This information is peripheral to our immediate purpose of trying to understand how the elapsed years of the Vaivasvata manvantara given in the Tiru Ganita Panchanga were calculated from the data given in the Sūrya-siddhānta. As seen, these elapsed years are given at the beginning of the Tiru Ganita Panchanga as added information, and it does not form part of what constitutes a panchanga. It is not given in modern panchangas.

In the last fifty years the majority of research articles published on the Sūrya-siddhānta and related texts have been appearing in Indian Journal of History of Science. It began in 1966, and is published by the Indian National Science Academy, New Delhi. Recently, all the issues from 1966 to the present have become available online, at: http://insa.nic.in/INSAuth/OurPublications.aspx. You have to sign up to be able to download articles. If you are fortunate enough to live near a major academic library that carries this journal, note that the title is Indian Journal of History of Science, not Indian Journal of the History of Science, or you will not find it in the library catalogue. As may be expected, the great majority of these articles are concerned with astronomical calculations of planetary motions based on data given in the Sūrya-siddhānta. In the Sūrya-siddhānta, the data on the yugas and manvantaras precedes the main part of the text, and is found in chapter one. The yugas and manvantaras are usually considered by today’s intelligentsia as part of mythology rather than the history of science. The Secret Doctrine is usually considered by today’s intelligentsia as fantasy rather than mythology. So to have the support of even mythology is a decided gain.