10. Somâkara in his commentary on the _Shesha Jyotisha_ quotes a passage from the _Satapatha Brâhmana_, which contains an observation on the change of the tropics, and which is also found in the _Sâkhâyana Brâhmana_, as has been noticed by Prof. Max Müller in his preface to _Rigveda Samhitâ_ (p. xx. foot‐note, vol. iv.). The passage is this: ... “The full‐moon night in Phâlguna is the first night of Samvatsara, the first year of the quinquennial age.” This passage clearly shows that the quinquennial age which, according to the sixth verse of the _Jyotisha_, begins on the 1st of Mâgha (January‐February), once began on the 15th of Phâlguna (February‐March). Now when the 15th of Phâlguna of the first year called Samvatsara of the quinquennial age begins, the moon, according to the _Jyotisha_, is in 3/4th of the Uttar Phâlgunî, and the sun in 1/4th of Pûrva Bhâdrapadâ. Hence the position of the four principal points on the ecliptic was then as follows: The winter solstice in 3°29’ of Purva Bhâdrapadâ. The vernal equinox in the beginning of Mrigashîrsha. The summer solstice in 10 of Purva Phâlgunî. The autumnal equinox in the middle of Jyeshtha. The vernal equinoctial point, we have seen, coincided with the beginning of Krittikâ in 1421 B.C.; and from the beginning of Krittikâ to that of Mrigashîrsha, was, in consequence, 1421 + 26‐2/3 x 72 = 1421 + 1920 = 3341 B.C., supposing the rate of _precession_ to be 50° a year. When we take the rate to be 3°20" in 247 years, the time comes up to 1516 + 1960·7 = 3476·7 B.C. When the winter solstice by its retrograde motion coincided after that with the beginning of Pûrva Bhâdrapadâ, then the commencement of the quinquennial age was changed from the 15th to the 1st of Phâlguna (February‐March). This change took place 240 years after the date of the above observation, that is, in 3101 B.C. This date is most important, as from it an era was reckoned in after times. The commencement of the Kali or Kali Yuga (derived from “kal,” “to reckon”), though said by European scholars to be an imaginary date, becomes thus an astronomical fact. INTERCHANGE OF KRITTIKÂ AND ASHVINÎ.(646)