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.