In the posts of April 29th, July 18th, and July 24th, 2012, reference was made to material by Hans Malmstedt that was cited by David Pratt. The two articles by Hans Malmstedt have now become easily available in their source journal, The Theosophical Path, posted at the Theosophical University Press website. I have extracted the two articles and now post them here. They are:

“The Cycles of the Cosmos, Hans Malmstedt 1931”

“Our Position in Time on Globe D, Hans Malmstedt 1933“

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An english translation of the SURYA-SIDDHANTA has been uploaded on this site library under the REFERENCES index, INDIAN TRADITIONS header : http://prajnaquest.fr/downloads/BookofDzyan/IndianTraditions/Others/Surya%20Siddhanta.pdf

It was translated from the sanskrit by Pandit Bâpû Deva Shâstri, and published in 1860 by the Asiatic Society of Bengal.
It is bounded with a translation of the SIDDHANTA SHIROMANI, translated by Lancelot Wilkinson and Pandit Bâpû Deva Shâstri, published in 1861.

In his postscript of the SURYA-SIDDHANTA, Bâpû Deva explained that eighteen Siddhanta were written, of which only four were procurable during his time (SÛRYA-Sid., BRAHMA-Sid., SOMA Sid., and VASISHTA-Sid.). The SURYA Sid. is supposed to be the oldest.

Page 108 (SIDDHANTA SHIROMANI) gives another calculation for the elapsed-time-since-the-beginning-of-this-kalpa :

“Of the present KALPA, 6 Manus with their 7 Sandhis, 27 Yugas ans their 3 Yuga’Nghri (Krita, Treta, and Dwapara), and 3179 sidereal years of the fourth Yuga’Nghri of the 28th Yuga of the 7th Manu, that is to say 1,972,947,179 sidereal years have elapsed from the beginning of the present Kalpa to the commencement of the Sa’liwa’hana era.”
Note : Saliwahana was a king of southern India, born in 78 A.D., starting the “Saka Era”.

Compared to H.P.B. number given in the S.D (vol II, page 68), there is a gross difference of 1,972,947,179 – 1,955,884,687 = 17,062,492 years for the elapsed time since the beginning of cosmic evolution.

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Thanks once again to the efforts of Dr. N. C. Ramanujachary, we now have the data from the 1879-1880 Tiru Ganita Panchanga. This allows us to correct two typographical errors in the data given from the 1880-1881 issue (16645009981 for 1664500981, and 1972948980 for 1972948981), which in turn allowed us to correct a typographical error in the data given from the 1884-1885 issue (1955884687 for 1955884987) as copied by H. P. Blavatsky in The Secret Doctrine. All this data from three different issues enables us to eliminate the typographical error factor: the eighteen million years figure is not a mistake. Moreover, since this figure increases rather than decreases, it must in fact be the elapsed years of the Vaivasvata manvantara as stated, rather than the years remaining of the Vaivasvata manvantara lacking one digit, as can be calculated from the extant Sūrya-siddhānta. Since the eighteen million years figure cannot be derived in any known manner from the data given in the extant Sūrya-siddhānta, we are left with only one conclusion. The compiler of the Tiru Ganita Panchanga used a manuscript of the Sūrya-siddhānta that had additional verses in chapter one giving the data necessary to make this calculation.

At the time the Tiru Ganita Panchanga was first published, 1869-1870, there was only one printed edition of the Sūrya-siddhānta. It was published in 1859 in Calcutta (see May 15 posting), far from Madras. Astronomers in India then routinely used their own manuscript copies of texts such as the Sūrya-siddhānta. We must therefore assume that a fuller manuscript of the Sūrya-siddhānta exists in south India. Perhaps it still remains with the descendants of the compiler of the Tiru Ganita Panchanga.

Here is the data from the 1879-1880 Tiru Ganita Panchanga, kindly supplied by Dr. Ramanujachary in his email reply to me dated Aug. 29, 2012:

I had occasion to visit the Adyar Library on this errand today.
Obtained a copy of the first page giving figures.
Yes, your two corrections of years are validated.
——————————————————————————–
The translated version of the page is as below:

Almanac for the year PRAMADI,
corresponding to Kaliyuga year 4981; and English year 1879-80
The figures are in accordance with SURYASIDDHANTA.
years that passed  in Brahmanah kalpa: 1972948980
years that passed after Srishti(Manifestation); 1955884980
years that passed after SWAYAMBHAVU: 1664500980
years that pased in VAIVASWATA : 18618720

Kali age: 4981
Vikrama Satabda: 1937
Salivahanasak: 1802
Kollamandu: 1054-55
English: 1879-80
Hijari: 1296-97
Phasali: 1288-89
Drik Ganita year: 11

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As can easily be seen from the sources mentioned in the May 15 posting on the Sūrya-siddhānta, the information on yugas, manvantaras, and kalpas in the Sūrya-siddhānta is found in chapter 1, verses 15-24, and 45-47 (or 44-46 in the Sanskrit edition with the commentary by Parameśvara). There are adequate English translations, by Rev. Ebenezer Burgess (1860), by Bāpū Deva Śāstrī (1861), and by Bimalā Prasāda Siddhānta Sarasvatī (from Sanskrit to Bengali,1894 or 1896, and from Bengali to English, 2007). Nonetheless, these verses are here given in Sanskrit and English translation, primarily for convenience of reference. Unless the compiler of the Tiru Ganita Panchanga had access to a more complete manuscript of the Sūrya-siddhānta, this is the data on which the figures for the elapsed years of various epochs given at its beginning would have been based.

The Sanskrit text given here is based primarily on the 1957 edition of the Sūryasiddhānta by Kripa Shankar Shukla with the Sanskrit commentary by Parameśvara (1432 C.E.), in comparison with the 1859 edition by Fitzedward Hall with the Sanskrit commentary by Raṅganātha (1603 C.E.). I have also compared the 1871, 1891, and 1911 editions, and the 1991 edition by Śrīcandra Pāṇḍeya with the Sanskrit commentary by Kamalākara Bhaṭṭa (born 1618 C.E.). Shukla’s edition gives in footnotes variant readings from the text as found with the Sanskrit commentaries by Mallikārjuna Sūri (1178 C.E.), Yallaya (1472 C.E.), and Rāmakṛṣṇa Ārādhya (1472 C.E.). Shukla also consulted the commentaries by Bhūdhara (1572 C.E.) and Tamma Yajvā (1599 C.E.) for questionable readings. The fact that all these major commentaries were used by Shukla for his edition does not leave a very high probability that a more complete manuscript, having additional verses here, was available to the compiler of the Tiru Ganita Panchanga.

When putting the Sanskrit into roman script I have divided the words with spaces and hyphens as much as possible. Also I have made my English translation fairly literal, so that the Sanskrit can more easily be followed. There seems to be no possibility of deriving a figure of eighteen million years for the age of the Vaivasvata manvantara from this data, and this is all that can be found on this topic in the extant Sūrya-siddhānta.

Sūrya-siddhānta, chapter 1

tad-dvādaśa-sahasrāṇi catur-yugam udāhṛtam |

sūryābda-saṅkhyayā dvi-tri-sāgarair ayutāhataiḥ || 15 ||

sandhyā-sandhyāṃśa-sahitaṃ vijñeyaṃ tac catur-yugam |

kṛtādīnāṃ vyavastheyaṃ dharma-pāda-vyavasthayā || 16 ||

15-16. Twelve thousand of those [divine years, divyaṃ varṣam] are called a fourfold yuga (age). By the count of solar years, that fourfold yuga together with its [opening] sandhi period and [closing] sandhi period is to be understood as four hundred and thirty-two multiplied by ten thousand [i.e., 4,320,000]. This fixed limit of the kṛta and other [yugas] is by way of the fixed limit of the legs of dharma (righteousness).

Notes: fourfold yuga, consisting of the kṛta, tretā, dvāpara and kali yugas; sandhi or sandhyā = “junction, interval, twilight”; four hundred and thirty-two, dvi-tri-sāgara = “two three ocean,” where ocean is a word-number standing for “four,” and the whole number is to be read backwards.

yugasya daśamo bhāgaś catus-tri-dvy-eka-saṅguṇaḥ |

kramāt kṛta-yugādīnāṃ ṣaṣṭho ’ṃśaḥ sandhyayoḥ svakaḥ || 17 ||

17. The tenth part of a yuga [i.e., 432,000] multiplied by four, three, two, and one in sequence [is the length] of the kṛta and other yugas. Their own sixth part [is the length] of the two sandhi periods [combined].

yugānāṃ saptatiḥ saikā manvantaram ihocyate |

kṛtābda-saṅkhyā tasyānte sandhiḥ prokto jala-plavaḥ || 18 ||

18. Seventy plus one yugas are here called a manvantara. At the end of it is said to be a sandhi period having the number of years of a kṛta [yuga]. It is an inundation by water.

sa-sandhayas te manavaḥ kalpe jñeyāś caturdaśa |

kṛta-pramāṇaḥ kalpādau sandhiḥ pañcadaśaḥ smṛtaḥ || 19 ||

19. Those manus together with the sandhi periods are to be understood to be fourteen in a kalpa (eon). At the beginning of a kalpa is recollected to be a fifteenth sandhi period having the measure of a kṛta [yuga].

itthaṃ yuga-sahasreṇa bhūta-saṃhāra-kārakaḥ |

kalpo brāhmam ahaḥ proktaṃ śarvarī tasya tāvatī || 20 ||

20. Thus a kalpa, with a thousand yugas, bringing about the destruction of beings, is said to be a day of Brahmā. His night is of the same extent.

param āyuḥ śataṃ tasya tayāhorātra-saṅkhyayā |

āyuṣo ’rdham itaṃ tasya śeṣāt kalpo ’yam ādimaḥ || 21 ||

21. His complete life is a hundred [divine years] by this count of days and nights. Half of his life has passed. Of the remainder, this is the first kalpa.

Note: the reading śeṣāt kalpo, found in the edition with the commentary by Parameśvara (and read in the three other commentaries cited in the footnotes), is preferable to the reading śeṣa-kalpo, found in the editions with the commentary by Raṅganātha.

kalpād asmāc ca manavaḥ ṣaḍ vyatītāḥ sa-sandhayaḥ |

vaivasvatasya ca manor yugānāṃ tri-ghano gataḥ || 22 ||

22. Of this kalpa six manus have passed with their sandhi periods. Of the Vaivasvata manu, three cubed [i.e., 27] yugas have passed.

aṣṭāviṃsād yugād asmād yātam etat kṛtaṃ yugam |

ataḥ kālaṃ prasaṅkhyāya saṅkhyām ekatra piṇḍayet || 23 ||

23. Of this twenty-eighth yuga, this kṛta yuga has passed. For calculating time after this, one should combine into one the number.

graha-rkṣa-deva-daityādi sṛjato ’sya carācaram |

kṛtādri-vedā divyābdāḥ śata-ghnā vedhaso gatāḥ || 24 ||

24. Four hundred and seventy-four times one hundred divine years passed of the creator [Brahmā], he creating the moving and the unmoving, i.e., planets, stars, gods, demons, etc. [at the beginning of the kalpa].

Note: four hundred and seventy-four, kṛta-adri-veda, word-numbers for four (kṛta, the four dots on a winning dice, also the kṛta yuga where dharma stands on all four legs), seven (adri, mountain, the seven mountains), and four (veda, the four vedas). Then the whole number is to be read backwards, although with this particular number it would not matter.

. . . . . . . . . . . . . . . . .

ṣaṇ-manūnāṃ tu sampīḍya kālaṃ tat-sandhibhiḥ saha |

kalpādi-sandhinā sārdhaṃ vaivasvata-manos tathā || 45 ||

yugānāṃ tri-ghanaṃ yātaṃ tathā kṛta-yugaṃ tv idam |

projjhya sṛṣṭes tataḥ kālaṃ pūrvoktaṃ divya-saṅkhyayā || 46 ||

sūryābda-saṅkhyayā jñeyāḥ kṛtasyānte gatā amī |

kha-catuṣka-yamādry-agni-śara-randhra-niśākarāḥ || 47 ||

45-47. Having combined the time of the six [past] manus together with their sandhi periods, along with the sandhi period at the beginning of the kalpa, also of the Vaivasvata manu the passed three cubed [i.e., 27] yugas, plus this kṛta yuga; having subtracted from that the time of creation previously stated by the count of divine [years]; the passed [years] at the end of the kṛta [yuga] by the count of solar years are to be understood as these: four skies, twins, mountain, fire, arrow, bodily openings, moon [i.e., 1,953,720,000].

Notes: kha-catuṣka, a group of four skies, where sky or space equals 0, so 0000; yama, twins, 2; adri, mountain (the seven mountains), so 7; agni, fire (the three fires), so 3; śara, arrow (the five arrows), so 5; randhra, opening (the nine apertures of the body), so 9; niśākara, “night-maker,” the moon, so 1. Then all these digits must be read backwards, yielding 1,953,720,000. As the word-number nine, the reading randhra is superior to the reading nanda, found only in the edition with the commentary by Parameśvara (based on a transcript of a single manuscript from the Adyar Library). The other commentaries cited in the footnotes read randhra. The nine Nanda brother-kings in Indian history come far later than the age of the Sūrya-siddhānta is supposed to be. The variant sampiṇḍya for sampīḍya in 45a, being synonyms, and the preceding ca for tu, make little difference.

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When introducing Stanza II of the anthropogenesis portion of the “Book of Dzyan,” given in volume 2 of The Secret Doctrine, H. P. Blavatsky informs us that the commentary thereon refers to Nārada and Asura Maya (p. 47):

“Stanza II., which speaks of this Round, begins with a few words of information concerning the age of our Earth. The chronology will be given in its place. In the Commentary appended to the Stanza, two personages are mentioned: Narada and Asura Maya, especially the latter. All the calculations are attributed to this archaic celebrity; and what follows will make the reader superficially acquainted with some of these figures.”

Blavatsky then gives a section titled, “Two Antediluvian Astronomers” (pp. 47-51), which begins with this paragraph:

“To the mind of the Eastern student of Occultism, two figures are indissolubly connected with mystic astronomy, chronology, and their cycles. Two grand and mysterious figures, towering like two giants in the Archaic Past, emerge before him, whenever he has to refer to Yugas and Kalpas. When, at what period of pre-history they lived, none save a few men in the world know, or ever can know with that certainty which is required by exact chronology. It may have been 100,000 years ago, it may have been 1,000,000, for all that the outside world will ever know. The mystic West and Freemasonry talk loudly of Enoch and Hermes. The mystic East speaks of Narada, the old Vedic Rishi, and of Asuramaya, the Atlantean.”

The asura named Maya is indeed a famous astronomer, writer of the most authoritative Sanskrit text on astronomy, the Sūrya-siddhānta. Nārada is certainly a well-known rishi in Indian tradition, and astronomy is in fact one of the subjects that he is said to have mastered, but he is primarily known for his mastery of music. There is no Sanskrit astronomical treatise in use that is attributed to him, and the classical Indian astronomers do not refer to or quote him. In Blavatsky’s statement, “To the mind of the Eastern student of Occultism,” we have to emphasize the words, “of Occultism”; and in her statement, “The mystic East speaks of Narada,” we have to emphasize the word “mystic.” To the mind of the Eastern student in general, Nārada is the divine musician; and the East in general speaks of Nārada the musician, not Nārada the astronomer. Yet, for Blavatsky and her contacts, Nārada was the great astronomer Nārada. We must inquire why this would be so.

As just seen, the secret commentary on the “Book of Dzyan” is reported to refer to the astronomers Nārada and asura Maya. Then, in the section titled, “The Chronology of the Brahmins” (pp. 66-74), figures are given including the age of humanity as 18,618,728 years (in 1887 C.E.), taken from the Tirukkanda Panchanga = Tiru Ganita Panchanga, based on the Sūrya-siddhānta. After giving these figures, Blavatsky writes (p. 70): “These sacred astronomical cycles are of immense antiquity, and most of them pertain, as stated, to the calculations of Nārada and Asuramaya.” So is there some astronomical text that we perhaps no longer have, but that is associated with Nārada, even mythologically?

Ebenezer Burgess, introducing his 1860 translation of the Sūrya-siddhānta, writes (p. 142):

“Among the different Siddhāntas, or text-books of astronomy, existing in India in the Sanskrit language, none appeared better suited to my purpose than the Sūrya-siddhānta. That it is one of the most highly esteemed, best known, and most frequently employed, of all, must be evident to any one who has noticed how much oftener than any other it is referred to as authority in the various papers on the Hindu astronomy. In fact, the science as practised in modern India is in the greater part founded upon its data and processes. In the lists of Siddhāntas given by native authorities it is almost invariably mentioned second, the Brahma-Siddhānta being placed first: the latter enjoys this preeminence, perhaps, mainly on account of its name; it is, at any rate, comparatively rare and little known.”

We see that, at least mythologically, there is a text that is regarded even more highly than the Sūrya-siddhānta, namely, the Brahma-siddhānta. But the genuine original Brahma-siddhānta is apparently no longer extant; otherwise it would surely be in wide use. Nonetheless, there is an extant text called the Brahma-siddhānta, and this tells us why Nārada would be so highly regarded as an astronomer: in it, the god Brahmā teaches astronomy to Nārada. So we may assume that in the original Brahma-siddhānta also, Nārada is the recipient of the knowledge of astronomy from Brahmā. This is like in the Sūrya-siddhānta, where the asura named Maya is the recipient of the knowledge of astronomy from an incarnation or part (aṃśa) of the sun, sūrya.

The now extant text called Brahma-siddhānta calls itself the second praśna or section of the Śākalya-saṃhitā. There is no English translation of it. It was first published in 1912 in the Sanskrit collection titled, Jyautiṣa-siddhānta-saṃgraha, edited by Vindhyesvari Prasad Dvivedi, in the Benares Sanskrit Series, no. 39. The puzzle of why it calls itself the second praśna was not solved until several decades later. When D. G. Dhavale was preparing a critical edition of the Brahma-siddhānta, he saw that one of the eight manuscripts he had gathered contained many additional verses in its first chapter. These verses showed that the various praśnas or sections of the Śākalya-saṃhitā each summarized an astronomical siddhānta. The first section summarized the Sūrya-siddhānta, and the second section summarized the Brahma-siddhānta. Six more sections summarized the Pauliśa-siddhānta, the Soma-siddhānta, the Romaśa-siddhānta, the Gārgya-siddhānta, the Bṛhaspati-siddhānta, and the Vāsiṣṭha-siddhānta. Of these sections of the Śākalya-saṃhitā, only the summary of the Brahma-siddhānta is now extant. It provides our only window into this long lost text. It shows us that the original Brahma-siddhānta was taught by Brahmā to Nārada.

Even though the original text by Nārada is long lost to us, although perhaps not to the Theosophical Mahatmas (see SD 1.47-51), the tradition of the two great antediluvian astronomers remained known to astronomers in India. A verse from the seventeenth century C.E. Indian astronomer Kamalākara’s Siddhānta-tattva-viveka (verse 65 of the bhagaṇa-māna-adhyāya, chapter on elements of revolutions) is quoted by Sankar Balakrishna Dikshit in his Bharatiya Jyotish Sastra, English translation, vol. 2, p. 47, saying: “That pure (science of astronomy) which was revealed to Maya by the god Sun, was described to Nārada by Brahmā, to Śaunaka by Himaguru (Moon or Soma) and to Māṇḍavya by the sage Vasiṣṭha.”

As for the astronomical contents of the Brahma-siddhānta according to its summary in the Śākalya-saṃhitā, already in 1896 Sankar Balakrishna Dikshit had determined that this summarized version copies the modern Sūrya-siddhānta. He writes (Bharatiya Jyotish Sastra, English translation, vol. 2, p. 4): “The basic principles, propounded by the Śākalya Brahma Siddhānta, even it be more ancient than Brahmagupta, are exactly the same as those propounded by the modern Sūrya-siddhānta.” Again, he says (p. 49): “The number of revolutions and other elements in this tally entirely with those of the Sūrya-siddhānta in all respects and have already been given.” This was confirmed by D. G. Dhavale when preparing his Sanskrit critical edition, The Brahmasiddhānta of Śākalyasaṃhitā (Pune: Bhandarkar Oriental Research Institute, 1996). He writes in his English Introduction (pp. xi-xii): “It is generally agreed that this Brahmasiddhānta is based on the modern Sūryasiddhānta. In order to compare the two siddhāntas I prepared a line index to the S.S. [Sūryasiddhānta] . . . On comparison it was found that agreement in actual wording of the two siddhāntas occurs in 65 lines or caraṇas. . . . The present Brh. [Brahmasiddhānta] closely follows the modern S.S. in data about the planetary motions etc.” It seems certain, then, that like the Sūrya-siddhānta, where we have only a modern revision of the original text, so the summary of the Brahma-siddhānta in the Śākalya-saṃhitā is only a modern revision.

Nonetheless, although this summary apparently does not preserve the original astronomical data of the original Brahma-siddhānta, Sankar Balakrishna Dikshit noticed that it was unique in a couple of ways. First, “the subject of religion also, which is never met with in an astronomical work, has been included in it” (op. cit., p. 49). Further on this, D. G. Dhavale found in the one manuscript that had additional verses in the first chapter, an entire additional chapter, a seventh adhyāya. It, too, apparently pertains to religion. He writes (op. cit., p. ix): “The contents of the seventh Adhyāya, however, do not justify its inclusion in a treatise on astronomy. In fact the chapter reads more like a Purāṇa than an astronomical essay. Whatever astronomical references there are in it are about the same as are found in some of the Purāṇas.” For this reason, he unfortunately did not include this otherwise unknown chapter in his edition, so we do not know exactly what is in it. There is an astrological text attributed to Nārada, the Nāradīya-saṃhitā, on divination and muhūrta. A Sanskrit edition of it was prepared by Haridāsagupta and published in 1905. Much of its contents are included in the Nārada-purāṇa, according to a comparison made by K. Damodara Nambiar (published in the journal, Purāṇa, Jan. 1974, pp. 103-112, and cited in Ganesh Vasudeo Tagare’s Introduction to his English translation of The Nārada-Purāṇa, Part 1, Delhi, 1980, p. 30). Perhaps some of this material in fact came from the original Brahma-siddhānta.

Second, the Brahma-siddhānta is also unique in that it gives otherwise unknown information about the seven stars of what we call the Great Bear or Big Dipper constellation, known as the Seven Rishis (saptarṣi). Sankar Balakrishna Dikshit writes (op. cit., p. 50): “It is the specialty of this work that it gives the latitudes and longitudes of the Saptarṣi group (i.e. Great Bear), which are not given by any other siddhānta.” There is a very unusual cycle associated with the Seven Rishis, taught by the ancient astronomer Vṛddha Garga in a now lost text (quoted by Bhaṭṭotpala in his commentary on Varāha-mihira’s Bṛhat-saṃhitā, chapter 13). These stars are supposed to move through one asterism or nakṣatra in exactly one hundred solar years. Of course, the fixed stars have no such physical motion. Nonetheless, the cycle is real, and has been in use in parts of India and Kashmir from ancient times, as seen in stone inscriptions, and right up to the present. It has been studied in detail by John E. Mitchiner in his 1982 book, Traditions of the Seven Ṛṣis. I have written a little about it and its relation to Theosophical teachings in my article, “The Centennial Cycle” (Theosophical History, vol. 11, no. 4, Oct. 2005, pp. 5-15; http://www.easterntradition.org/centennial%20cycle.pdf). According to David Pingree, Nārada is “one of the interlocutors in the Vṛddhagārgīsaṃhitā” (Census of the Exact Sciences in Sanskrit, Series A, vol. 3, 1976, p. 148; see also vol. 2, 1971, p. 118). Whether or not Nārada and Vṛddha Garga here discuss the cycle of the Seven Rishis, the fact that Nārada gives unique information on the Seven Rishis associates him with old teachings on astronomical cycles.

It is clear from the above that Nārada is considered to be an ancient astronomer, one of the very most eminent as the recipient of the astronomical teachings from Brahmā that formed the original but now lost Brahma-siddhānta.

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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.

Category: Occult Chronology | 2 comments

As noted in the posting dated May 20, 2012 (The Mystery of the Age of Humanity: Still Unsolved), Prof. C. A. Shinde (Librarian of the Adyar Library) kindly informed me that although the Adyar library does not have the particular issue that H. P. Blavatsky used, for kali yuga 4986 or 1884-1885 C.E., it does have several previous years of the Tirukkanda Panchanga, 1870-1881. This was wonderful news, since any one of these should give the epochs used in this long-defunct almanac, and that HPB used in The Secret Doctrine (vol. 2, pp. 68-69). I then requested the help of Dr. N. C. Ramanujachary with this, who has taken out time from his full schedule to carefully check the 1880-1881 issue and to write up a detailed reply. His extremely helpful reply has elucidated and clarified much for us. I have received his permission to post it here. It is dated July 15, 2012. He wrote:

“I am sorry for the delay but it was unavoidable because of my tours and non-availability of time.

But I am glad I was able to do some useful work on the way that was puzzling you, with the kind help of Prof. C A Shinde, the Librarian of the Adyar Library.

I will place the points in numbers:

1. The Adyar Library has not got the said Panchangam for 1884-5, but luckily they have the number for 1880-81. By adding 4 years to the figures available in this, we get the actual years for 1884-5, I am sure you will agree.
2. The name of the Panchanga is actually “Tiru (=Sri) Ganita (=mathematical) Panchangam” in Tamil and “Drik-Ganita-Panchangamu” in Telugu. Evidently the person who informed HPB of the names did not spell it well or the variation in pronunciation made it ‘Tirukkanda Panchangam’ – which is obviously wrong. The Panchangam is printed by ‘Vyavahara Tarangini Mudrakshara Sala’ at Chennapuri (=Madras). The compilers of the Panchangam are: Chintamani Raghunathacharyulu and Tadakamalla Venkata Krishna Rao living in Nungumbakkam and Triplicane (both are part-wards of Madras City). You will find the names of compilers were also defectively noted in The Secret Doctrine, as also all other records of literature derived from that.
3. This Panchangam is published year after year in Tamil (Dravid) and Telugu. Happily as I know Telugu, I was able to fish out the material you wanted.
4. I am holding photo-copies (2) of the title page and the Inner page where the figures are enumerated, given kindly by the Adyar Library; and will be able to post them by Air Mail if you can send me the Postal address, which I do not have now. If you need exact English translation of the pages, I can also give it.
5. Now, coming to the figure/number part:

Calendar for the Vikrama year (1880-81)

According to Sri Surya Siddhanta :

Years that passed since Brahman-kalpa:                      1972948980

Years that passed since Creation (Srishti)                     1955884981

Years that passed since SWAYAMBHAVA Manu          16645009981

Years that passed in Kaliyuga                                                     4982

Years that passed in Vikrama Satabda                                         1938

Years that passed in Salivahana Saka                                           1803

KOLLAMANDU                                                                                1054-55

ENGLISH                                                                                          1880-81

HIZARI                                                                                             1297-98

PHASALI                                                                                           1289-90

MY NOTE [Dr. Ramanujachary]: The years in between the 2 border lines do not concern us now.

When you add 4 years (duration between 1880-81 & 84-85) to the years that passed in Vaivaswata Manu, we get the figure 18,618,725, which was adopted by HPB.  Please also note the Tiru Ganita Panchangam clearly says the figures are according to SURYA SIDDHANTA.”

. . . . . . . . . . . . . . . . . .

Dr. Ramanujachary then had scans of the relevant pages made and sent to me. They are here attached, so that anyone can see these things for themselves: tiruganitapanchangam.

First, we see that the title Tirukkanda Panchanga is incorrectly written. Using a phonetic spelling like HPB used, it is the Tiru Ganita Panchanga, following the Tamil, or the Drik Ganita Panchanga, following the Telugu. It is in fact the Dṛg-gaṇita Pañcāṅga, described in Sankar Balakrishna Dikshit’s book, Bharatiya Jyotish Sastra (references and link given at the end of the posting on the Tirukkanda Panchanga dated May 30).

Next, we see that there is indeed a typographical or clerical error in the figure 1,955,884,687 years given in The Secret Doctrine, vol. 2, p. 68, which should be 1,955,884,987. This was deduced by Hans Malmstedt in his 1933 article, as reported by David Pratt (references and links given in the April 29, 2012 posting, Occult Chronology: The Age of the World, part 2). The figure 1,664,500,987 years given in The Secret Doctrine is also confirmed (see HPB’s footnote on this, vol. 2, p. 68), showing that Malmstedt has again provided the correct solution to this problem.

Last and most important, the figure for the age of the Vaivasvata manvantara, given in The Secret Doctrine as 18,618,728 years (vol. 2, p. 69), is confirmed as being correctly copied from the Tiru Ganita Panchanga. It is not a mistaken transcription, as I suggested may have been the case in my posting dated May 30, 2012. This puts us on firm ground to proceed with our investigation. We now have to determine how this figure was arrived at, based on information given in the Sūrya-siddhānta. Everyone else gets a figure of about 120 million years for the age of the Vaivasvata manvantara based on this data. It is possible that the compilers of the Tiru Ganita Panchanga had access to a more complete copy of the Sūrya-siddhānta. As stated in the posting on the Sūrya-siddhānta, dated May 15, 2012, manuscripts of this text vary widely. Most of the Sanskrit commentaries on it remain unpublished. The Indian astronomers who produced the Tiru Ganita Panchanga somehow got a figure of 18 million years for this. As Dr. Ramanujachary confirmed, in agreement with what HPB reported (SD 2.49-51), “the Tiru Ganita Panchangam clearly says the figures are according to SURYA SIDDHANTA.”

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While awaiting the arrival of material from a Tirukkanda Panchanga held by the Adyar Library, all my attempts to arrive at the needed eighteen million years figure have failed, whether using the 1:2:3:4 ratio or the 1:2:3:4:5:6:7 ratio. At the same time, I have found no hint of anything but the traditional figures in any of the pañcāṅga material that I have. The 18,618,725 or 18,618,728 years figure that we seek is beginning to look suspiciously like a mistaken transcription from the Tirukkanda Panchanga, or possibly a misprint in it.

A traditional pañcāṅga may give the length of a manvantara, which as stated earlier is 306,720,000 years (before the addition of the 1,728,000 years sandhi period at the end). It may give the elapsed years of the current or Vaivasvata manvantara, which as stated earlier is 120,532,986 years up to the year 1884 C.E. It may then give the number of years still remaining in the current or Vaivasvata manvantara, which in the year 1884 C.E. would be 186,187,014 years (again not counting the 1,728,000 years sandhi period at the end of the manvantara). If one of the last three digits was mistakenly omitted from this figure when it was transcribed from the Tirukkanda Panchanga (or even if there was a misprint in that issue of the Tirukkanda Panchanga), we would have 18,618,701 or 18,618,704 or 18,618,714, suspiciously like the 18,618,725 or 18,618,728 years figure that we seek.

Background information on what must be the Tirukkanda Panchanga, although it is not called that, may be found in Sankar Balakrishna Dikshit’s book, Bharatiya Jyotish Sastra, vol. 2, pp. 181-182, and 285-286 (available online, http://www.scribd.com/doc/76935732/Bharatiya-Jyotish-Sastra-2). It is there called the Dṛggaṇita Pañcāṅga, by Cintāmaṇi Raghunāthācārya. It began being published in Śaka 1791, or 1869 C.E.

Category: Occult Chronology | 1 comment

For those who may not have easy access to all the relevant Indian texts, here is an article that gives the teaching on the yugas and kalpas as found in the Purāṇas, in comparison with that found in the Manu-Smṛti (The Laws of Manu), the epic Mahābhārata, and Sanskrit astronomical treatises (Jyotiṣa Siddhāntas) such as the Sūrya-siddhānta. The article is titled, “The Purāṇic Theory of the Yugas and Kalpas—A Study,” by Anand Swarup Gupta, published in Purāṇa [Half-yearly Bulletin of the Purāṇa Department, All-India Kashiraj Trust, Varanasi], vol. 11, no. 2, July 1969, pp. 304-323. It also includes the teaching on the manvantaras. At the end it gives the geological time scale taken from Principles of Physical Geology, by Arthur Holmes, originally published in 1944. For the link I have titled the file, Yugas and Kalpas – Puranic Theory of.

Category: Occult Chronology | 1 comment

No one has yet posted a solution to the riddle of the eighteen million years age of physical humanity versus the one hundred and twenty million years age of our current humanity. There seems to be no obvious explanation of why the Tirukkanda Panchanga gave the eighteen million years age for the current Vaivasvata manvantara, quoted in full agreement in The Secret Doctrine (vol. 2, pp. 68-69), while according to all known sources the age of the Vaivasvata manvantara should be one hundred and twenty million years. The answer to this may have been given by H. P. Blavatsky in a fragmentary article published posthumously as “On Cosmic Cycles, Manvantaras, and Rounds” (Blavatsky Collected Writings, vol. 13, pp. 301-306), if anyone who is good at numbers can figure it out.

In this article, HPB writes (p. 302): “The astrological work states that: — 3. ‘The number of years that elapsed since the beginning of Vaivasvata Manvantara — Equals 18,618,725 years.’” This very same statement is made in The Secret Doctrine (vol. 2, pp. 68-69), where it is taken from the Tirukkanda Panchanga (the one for the kali yuga year 4986; see SD vol. 2, p. 51). So obviously “the astrological work” referred to in HPB’s fragmentary article is the Tirukkanda Panchanga. The calculations that she gives in this article may therefore pertain to how the eighteen million years figure is obtained. We should here recall that, for HPB, this figure is the age of humanity “on our planet D, in the present Round” (p. 302). In the Tirukkanda Panchanga, this figure is apparently given for the age of the Vaivasvata manvantara as a whole, an age that from other sources should be one hundred and twenty million years. I am hoping that someone who is good at numbers can figure this out.

In a small book that Daniel Caldwell called my attention to, Occult Chronology, by James Arther (Adyar: Theosophical Publishing House, 1943; http://blavatskyarchives.com/theosophypdfs/early_theosophical_publications_chrono.htm; http://hpb.narod.ru/Occult_Chronology.htm), the author refers to the Tirukkanda Panchanga and says (near the end of the book, no page number): “The Adyar Library is not in possession of a copy, and I have not yet been able to secure one. If anybody is the fortunate possessor of, or can lay his hand on, a copy, it would be greatly appreciated if he would make the Adyar Library the happy recipient of it.” This may have happened. I contacted the Adyar Library and learned from Prof. C. A. Shinde that although the Adyar library does not have the particular issue that HPB used, for kali yuga 4986 or 1884-1885 C.E., it does have several previous years of the Tirukkanda Panchanga, 1870-1881. These should all give the same epochs that the 1884-1885 issue gives. I have requested material from these. When it arrives, it may (or may not) be possible to determine how the Tirukkanda Panchanga arrived at its eighteen million years age of the Vaivasvata manvantara.

The ratio and calculations given by HPB in the fragmentary article referred to above are highly unusual, and do not fit in with other things she gave. Nonetheless, no one has yet been able to figure out how the eighteen million year figure was derived by the normal calculations, using the ratio 1:2:3:4. So perhaps further efforts using the ratio 1:2:3:4:5:6:7 will solve this riddle. Right now, the eighteen million years age of humanity is based only on an occult claim, apparently supported by reference to a once used calendar/almanac, the Tirukkanda Panchanga. But unless we can determine how the Tirukkanda Panchanga arrived at this figure, its evidence is little more than one more unverifiable claim. I have not found any other reference in any other Hindu text supporting this age for the Vaivasvata manvantara.

Category: Occult Chronology | 2 comments

Current Science has developed many disciplines to assess Earth history. Obviously, this is based on the Universe, Solar and Earth genesys models, with all possible hypothesis, starting with the Big Bang theory, the solar nebulae accretion, and the earth generation from planetoides accretion and collisions. What is of some value is the consistancy between many observations and models like baryogenesis and the quantity and diversity of elements in the universe and on the earth. It gives some credibility to it. The purpose of this post is to give the scientific understanding in regard with earth history and life genesis vs time in order to compare with the traditions time-lines. It comes from Geology, and it is called the stratigraphic scale.

4 major eras have been identified (numbers are in million of years) : Precambrian (4,600 M to 550 M), Paleozoic (550 M to 250 M), Mesozoic (250 M to 65 M), and Cenozoic (65 M to now).

They are divided in sub-periods which may be of some interests in our search, in regard with life development on earth. They will be listed together with the sequence of events.

According to lastest findings and models :

– Earth accretion process started 4,600 M years ago. Accretion started when the protosolar cloud temperature decreased, triggering materials condensation. Then the combined energy of gravitational collapse and radioactive elements disintegration  generated the fusion process, melting the compound of materials. The final cooling phase creates the different layers of the earth. The complete process is supposed to have lasted for 100 M years. (to be compared to the 300 M years from the SD)

– Life emerged first on earth between 4,600M and 3,500M years ago  (blue-green algae) – The SD says that first appearance of “humanity” on planetary chain was 1,664 M years ago.

– Invertebrates and lower vegetals started 2,500 M years ago

– First vertebrate (fish) appeared during Cambrian era ( 550 M years ago )

– First batracian = Carboniferous era, 350 M years ago

– First reptiles = Permian era, 280 M years ago

– First mammal = Trias era, 235 M years ago

– First birds = Jurassic era, 200 M years ago

– Oldest man discovered = Pleistocene era, 1.8 M years ago. The S.D says that the human period, up, to year 1887 lasted for 18.6 M years.

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The age of the world as taught in Hindu Sanskrit texts, which is in general agreement with that taught in The Secret Doctrine, can be readily ascertained from the data given in the Hindu Sanskrit texts. This is not the case, however, for the age of humanity. The basis of the age of our present humanity as taught in The Secret Doctrine, in agreement with that taught in the Hindu Tamil Tirukkanda Panchanga for Kali Yuga 4986, is a mystery. We do not know either the data that formed the basis of the calculation, or the method used in making the calculation, of the 18,618,725 years up till Kali Yuga 4986, or 1884-1885 C.E., given for this (BCW 13.302; given in SD 2.69 as 18,618,728 up to the year 1887). Since this age of humanity as more than eighteen million years is of central importance to the anthropogenesis taught in the Book of Dzyan, I request that interested persons try to solve this problem.

The figure given from the Tirukkanda Panchanga for the age of the world (SD 2.68) can clearly be traced to the Sūrya-siddhānta, as can the deduction of the time taken for “creation” (sṛṣṭi) at the beginning of the kalpa (17,064,000 years) in the second figure given from it (1,664,500,987). The Secret Doctrine also claims the author of the Sūrya-siddhānta, Asuramaya, as one of its two sources. So we might reasonably expect the data regarding the more than eighteen million years figure for the age of our present humanity to be found in that book. I have not yet found such data there, or figured out how to deduce this figure from the data given there. The English translation by Ebenezer Burgess, despite being published in 1860, appears to be accurate for the most part. It was published in the Journal of the American Oriental Society. This older material from this journal is now available free from JSTOR. Here is the link to this translation: http://www.jstor.org/stable/592174. Five editions of the Sanskrit text can be downloaded from the Digital Library of India, at the links provided by Capt. Anand in his comment on April 27. Some of the basic information from the Sūrya-siddhānta is summarized as follows:

A kalpa (eon) is four billion, three hundred and twenty million (4,320,000,000) years.

One thousand mahā-yugas make a kalpa (chap. 1, verse 20); therefore:

A mahā-yuga (great age) is four million, three hundred and twenty thousand (4,320,000) years (chap. 1, verse 15).

Seventy-one mahā-yugas (yielding 306,720,000), to which must be added a sandhi period (1,728,000) at the end, make a manvantara (chap. 1, verse 18); therefore:

A manvantara (period of a manu) is three hundred and eight million, four hundred and forty-eight thousand years (308,448,000).

Fourteen manvantaras (yielding 4,318,272,000), to which must be added a sandhi period (1,728,000) at the beginning, make a kalpa (chap. 1, verse 19); i.e., 4,320,000,000 years.

Of the present kalpa, six manvantaras are past (6 x 308,448,000 = 1,850,688,000), and of the present Vaivasvata manvantara, twenty-seven mahā-yugas are past (27 x 4,320,000 = 116,640,000) (chap. 1, verse 22). Also past is the sandhi period (1,728,000) at the beginning of the kalpa. This yields 1,969,056,000 years. At the time the Sūrya-siddhānta was taught to the asura named Maya, the kṛta-yuga (1,728,000) of the twenty-eighth mahā-yuga had also passed (chap. 1, verse 23). This yields 1,970,784,000 years. From this must be deducted the time taken for “creation” at the beginning of the kalpa (17,064,000) (chap. 1, verse 24; note the typo here, “plants” for “planets,” uncorrected in the 1935 Calcutta reprint edition, and copied uncorrected in A. K. Chakravarty’s 2001 book, The Sūryasiddhānta, p. 64). This yields 1,953,720,000 years.

This whole calculation is summarized in chap. 1, verses 45-47, giving the result in word numbers so that there is no mistake: khacatuṣkayamādryagniśararandhraniśākarāḥ. That is: kha-catuṣka, a group of four skies, where sky or space equals 0, so 0000; yama, twins, 2; adri, mountain (the seven mountains), so 7; agni, fire (the three fires), so 3; śara, arrow (the five arrows), so 5; randhra, opening (the nine apertures of the body), so 9; niśākara, “night-maker,” the moon, so 1. Then all these digits must be read backwards, yielding 1,953,720,000. This is the number of years from the beginning of the epoch (not of the kalpa itself) to the end of the last kṛta-yuga.

To come up to the year 1884 C.E., we must add to this the time of the tretā-yuga (1,296,000), the dvāpara-yuga (864,000), and the number of years of the kali-yuga that have passed (4,986) of this twenty-eighth mahā-yuga, a total of 2,164,986 years. This yields 1,955,884,986 years. Once we correct the typo of 6 for 9 in the hundreds place, as discussed in the previous post, this is essentially the same figure as that given in BCW 13.301 (1,955,884,685) and SD 2.68 (1,955,884,687), both derived from the Tirukkanda Panchanga. This is the number of years from the beginning of the epoch to the year 1884 C.E.

Now we want to find out the age of just our own Vaivasvata humanity, the number of years that have elapsed in the Vaivasvata manvantara. We can do this in two ways. Using the data from the Sūrya-siddhānta, that twenty-seven complete mahā-yugas have already passed in the Vaivasvata manvantara (chap. 1, verse 22), we calculate 27 x 4,320,000 = 116,640,000 years. To this we must add, of the twenty-eighth mahā-yuga, the passed kṛta-yuga (1,728,000), the passed tretā-yuga (1,296,000), the passed dvāpara-yuga (864,000), and the elapsed years of the kali-yuga up to the year 1884 C.E. (4986), or 3,892,986 years. This yields 120,532,986 for the number of years that have elapsed from the beginning of the Vaivasvata manvantara to the year 1884 C.E.

This should match the number arrived at earlier by calculating from the beginning of the epoch to the year 1884 C.E. (1,955,884,986), minus the number of years up to the beginning of the Vaivasvata manvantara. For the number of years up to the beginning of the Vaivasvata manvantara, we get the following: the six past manvantaras (6 x 308,448,000 = 1,850,688,000), plus the sandhi period at the beginning of the kalpa (1,728,000), yields 1,852,416,000; minus the time taken for “creation” at the beginning of the kalpa (17,064,000), yields 1,835,352,000 years. Indeed, 1,955,884,986 minus 1,835,352,000 gives us 120,532,986 years. This is merely a check to be sure that the figures we are using match.

So we have 120,532,986 elapsed years of the Vaivasvata manvantara up to the year 1884 C.E., from which we must figure out how the 18,618,725 year age of physical humanity was derived. Subtracting 18,618,725 years from 120,532,986 years, we have 101,914,261 years to account for. We can try to do this in two ways. We may try to do this in terms of the yugas, which is the only information that the Sūrya-siddhānta gives us. Or we may try to do this in terms of the root-races, since we are told that the 18,618,725 year age of physical humanity is to the middle of the third root-race, and we are now past the middle of the fifth root-race.

According to The Secret Doctrine, each “round” or manvantara has 49 root-races, with seven on each of seven postulated “globes.” Since a Theosophical “round” equals two manus or manvantaras (because the second of these is a “seed” manu), the Sūrya-siddhānta information that we are in the seventh or Vaivasvata manvantara agrees with The Secret Doctrine information that we are in the fourth round (SD 2.309). But neither the Sūrya-siddhānta (chap. 1), nor the Viṣṇu-purāṇa (book 1, chap. 3, and book 3, chap. 1), nor The Laws of Manu (chap. 1) speak about 49 root-races or about seven globes. Yet if we cannot calculate how the 18,618,725 year figure was derived by the Tirukkanda Panchanga from just the yuga information, then we may try calculating this figure from the root-race information.

We may recall that for the age of humanity in this kalpa (also called a “day of Brahmā,” and consisting of fourteen manvantaras), the Tirukkanda Panchanga gave 1,664,500,987 years (SD 2.68). This represents a deduction of about 300,000,000 years from the beginning of evolution (1,955,884,987 years), allowing for the kingdoms up to the human kingdom to evolve. This 300 million years is apparently referred to in the stanzas from the Book of Dzyan given in The Secret Doctrine, vol. 2, stanza II, śloka 5, “The wheel whirled for thirty crores more,” and, “. . . After thirty crores she turned round.” A crore, Sanskrit koṭi, is ten million; so thirty crores is three hundred million. This deduction as made in the Tirukkanda Panchanga is 291,384,000 years, the length of a manvantara (308,448,000) minus the time taken for “creation” (sṛṣṭi) at the beginning of the kalpa (17,064,000 years). But I have not found in the Sūrya-siddhānta any mention that such a deduction for the evolution of the lower kingdoms should be made. So perhaps the compilers of the Tirukkanda Panchanga did have access to a more complete manuscript of the Sūrya-siddhānta than is now available, as Blavatsky suggests (SD 2.50-51, 67).

However we do it, via the yugas or via the root-races, we must account for the 101,914,261 preceding years, and the 18,618,725 year age of physical humanity, totaling 120,532,986 elapsed years of the Vaivasvata manvantara up to the year 1884 C.E. The 101,914,261 preceding years would be distributed over the seven root-races of the first globe, the seven root-races of the second globe, the seven root-races of the third globe, and the first two and a half root-races of our present fourth globe. That is, the 101,914,261 years would be distributed over twenty-three and a half root-races, while the 18,618,725 years would cover the period of about two root-races. We must figure out how the Tirukkanda Panchanga arrived at the 18,618,725 year figure. Can it be derived from the Sūrya-siddhānta? What is the data that formed the basis of the calculation of the 18,618,725 years up till Kali Yuga 4986 (1884-1885 C.E.)? What is the method used in making the calculation of the 18,618,725 years up till Kali Yuga 4986?

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Regarding HPB’s fragmentary article, “On Cosmic Cycles, Manvantaras, and Rounds” (BCW 13.301-306), Daniel Caldwell called my attention to a discussion of this by David Pratt. This is part of his larger article, “Secret Cycles,” section 9, titled, “The unfinished article controversy” (http://davidpratt.info/secretcyc.htm#s9). Note 2 of that article refers readers to another article of his, “Geochronology: Theosophy and Science,” of which the fourth section is, “The age of the earth” (http://davidpratt.info/geochron.htm#g4). In this section, it seems to me, the problems of the discrepancies between the various dates for the age of the earth quoted by HPB in The Secret Doctrine have been solved. The solutions given by David Pratt in this article were arrived at by Hans Malmstedt in an earlier article entitled “Our Position in Time on Globe D” (The Theosophical Path, October 1933, pp. 226-235: http://www.theosociety.org/pasadena/ttp/ttp_v43n02.pdf; David also refers us to the July 1931 issue, pp. 63-69).

First, in the 1,955,884,687 (SD 2.68, or 1,955,884,685, BCW 13.301) years given from the Tirukkanda Panchanga for Kali Yuga 4986 there is apparently a typographical error. The last three digits, 687, should be 987. David Pratt reports that Hans Malmstedt suggested that the 9 was simply placed upside down, making 6, by the typesetter. This error, however, would have occurred before The Secret Doctrine was set in type, as we now know from the BCW 13 article (which gives the same number, but two years earlier). This article was not published until 1958, so would not have been known to Malmstedt, writing in 1933. So the error would have been either a typographical error in the Tamil Tirukkanda Panchanga itself, or a clerical error in the English translation of relevant parts of this made for HPB. It is unfortunate that no copy of this pañcāṅga can now be found. When all the rest of the figure can be fully explained, it seems certain that this is merely a typographical error, and that the 6 should be 9.

For the figure 1,664,500,987, gotten after 300,000,000 was supposed to have been subtracted from 1,955,884,687 (SD 2.68), this yields 291,384,000 after changing the typo 687 to 987. As Malmstedt has shown, this matches the length of a full manvantara, 308,448,000 years, less the time taken for “creation” (sṛṣṭi, emanation or manifestation) at the beginning of the kalpa, 17,064,000 years. This last figure, from Sūrya-siddhānta 1.24, is an important part of its calculations, even though some other astronomical treatises do not use it (e.g., Brahmagupta’s Brahmasphuṭa-siddhānta, and Bhāskara II’s Siddhānta-śiromaṇi). This shows that the figure 300,000,000 given by HPB (SD 2.68) was merely an approximation, whether of 291,384,000 or of 308,448,000 years. The fact that the Tirukkanda Panchanga uses the former figure is another demonstration that it, like other pañcāṅgas, was based on the Sūrya-siddhānta.

Then, the figure given by Dayanand Saraswati and the Arya Samaj, 1,960,852,987 years, is also explained. Malmstedt, as reported by David Pratt, showed that it is the standard number, but it does not include the numbers for the sandhi periods. Since the Sūrya-siddhānta prescribes calculating for these sandhi periods, we see that Dayanand has disregarded this. He has also disregarded the time taken for the “creation” given in the Sūrya-siddhānta. In other words, Dayanand does not follow the Sūrya-siddhānta.

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In The Secret Doctrine (1888), H. P. Blavatsky gives a figure for the age of the cosmos or solar system (SD 2.68), derived from the Tirukkanda Panchanga for Kali Yuga 4986, or 1884-1885 C.E. (SD 2.51), as 1,955,884,687 years. In a posthumously published writing fragment tentatively titled “On Cosmic Cycles, Manvantaras, and Rounds” (Blavatsky Collected Writings, vol. 13, pp. 301-306), HPB gave the same figure, obviously from the same source, but before it was adapted for 1887 by adding two years to it, 1,955,884,685. Here, rather than the age of the cosmos as a whole, or narrowed down to the age of the solar system, she applies this figure to our planetary chain (the seven rounds). Then, presumably in support of such an unusually large figure, she notes (SD 2.68 fn.) that the school of Dayanand Saraswati, the Arya Samaj, on the cover of their Arya Magazine for a similar year, gives the date, “Aryan era 1,960,852,987.”

The Tirukkanda Panchanga is a calendar or almanac, written in Tamil, and published in south India. Pañcāṅgas are published throughout India for each year. This one, HPB says, was compiled “from fragments of immensely old works attributed to the Atlantean astronomer, and found in Southern India” (SD 2.50). The “Atlantean astronomer” is Asuramaya, as she says in the section, “Two Antediluvian Astronomers” (SD 2.47-51). She takes for granted that her readers know what book Asuramaya wrote, the Sūrya-siddhānta, so does not there mention it. From a secret book ascribed to Pesh-Hun or Nārada, called the “Mirror of Futurity,” and from the work of Asuramaya (i.e., the original Sūrya-siddhānta), she tells us, come “the figures of our cycles” (SD 2.49). I say “the original Sūrya-siddhānta,” because we know that the current one is a later redaction. We know this because the old Sūrya-siddhānta as summarized in Varāha-mihira’s Pañca-siddhāntikā differs significantly from the current one.

The Sūrya-siddhānta is quite the most influential astronomical work in India, and only in the last century has it become superseded in many circles by modern astronomy. The figures given in the Tirukkanda Panchanga, like other traditional pañcāṅgas (Indian calendars, almanacs), and also the date given in the Arya Magazine, are based on the Sūrya-siddhānta. It gives (chapter 1, verse 47) 1,953,720,000 solar years since the beginning of the kalpa (eon) to the end of the last kṛta-yuga (“perfect age”), less the time taken for “creation” (sṛṣṭi, emanation or manifestation) at the beginning of the kalpa, 17,064,000 years. This figure, 1,953,720,000, is possibly original, because it is given in a verse using word-numbers. This avoids typographical errors that are frequent when using numerals. From this figure, one can calculate to the beginning of the Śaka era (78 C.E.), much used in India, as 1,955,883,179 years. Similarly, Ebenezer Burgess, in his English translation of the Sūrya-siddhānta, published in 1860, calculated to the year 1859 C.E., the figure 1,955,884,960 years (p. 173). This is only a few hundred years different from the figure given in the Tirukkanda Panchanga, and adopted by HPB in The Secret Doctrine.

Burgess noted (pp. 142, 144) that the manuscripts of the Sūrya-siddhānta used by him had somewhat different readings and arrangement than the first published Sanskrit edition (edited by Fitzedward Hall and published in 1859 in the Bibliotheca Indica series, Calcutta). This same basic text, as commented on by Raṅganātha, was also published in Calcutta in 1871, and again there in 1891 edited by Jīvānanda Vidyāsāgara. Despite the fact that at least 36 Sanskrit commentaries on the Sūrya-siddhānta are known, only two other traditional commentaries on it have been published, as far as I know. The first is that by Parameśvara. This was edited by Kripa Shankar Shukla and published in 1957 (by Lucknow University). The verse in question, 1.47, giving the figure in question, is verse 1.46 in this edition, and it has the variant reading nanda rather than randhra (both standing for “nine”). The second is that by Kamalākara Bhaṭṭa. This was edited by Śrīcandra Pāṇḍeya and published in 1991 (by Sampurnanand Sanskrit University, Varanasi). We do not have a critical edition of the Sūrya-siddhānta, in the known redaction, nor do we have any manuscript of the old version as summarized by Varāha-mihira in his Pañca-siddhāntikā.

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