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or astronomy. These Vedāngas find brief treatment in the Brāhmaṇas or Upanishads and acquire the necessary scientific cast in the age we have come to just now.

This development leads us on to the so-called Sūtra period, because this growing mass of literature required to be put in a shape which could easily be mastered. The alphabet, no doubt, had been invented already (or adapted thoroughly to Indian requirements), though perhaps it was not brought quite into common usage. This period overlaps the next and may be taken to occupy the four centuries between 750 B.C. and say 350 B.C. So far then we have to rely entirely upon such evidence as is available in our sacred literature, and scholars have allotted these to very varying periods.

The Aryan home is placed within the Arctic Circle by Mr. Tilak, and he ascribes a very early period (7000 B.C.) indeed for the earliest hymns of the Rig-Veda; while European scholars would bring it to 1500 B.C. Mr. Tilak rests his arguments upon certain solar and other astronomical phenomena referred to in the earlier hymns which upon his hypothesis find clear explanation. The late Mr. Shankar Balakrishna Dikshit refers certain at least of the Brāhmaṇas to 3800 B.C.; there being a reference in the Śatapada Brāhmaṇa to the Pleiades being in the Equinox, which is verifiable astronomically. Dr. Thibaut considers that the verse referred to is a late interpolation. So our position here is not very secure, and therefore our chronology respecting this period cannot lay claim to much accuracy. The ultimate downward limit of our period may be taken to be accurate, as it brings in an unlooked for synchronism. Pythagoras,^[1] the Greek philosopher, is believed to have learned in India not only his theory of transmigration, but also his theory of numbers from our Sankya system. Drs. Goldstücker