To be brief, it is January the 4th which ought to be selected by the Theosophists —
the Esotericists especially — as their New Year. January is under the sign of Capricornus, the mysterious Makara of the Hindu mystics — the “Kumaras,” it being stated, having incarnated in mankind under the 10th sign of the Zodiac. For ages the 4th of January has been sacred to Mercury-Budha, or Thoth-Hermes. Thus everything combines to make of it a festival to be held by those who study ancient Wisdom.
Whether called Budh or Budhi by its Āryan name, Mercurios, the son of Cælus and Hecātē truly, or of the divine (white) and infernal (black) magic by its Hellenic, or again Hermes or Thoth, its Greco-Egyptian name, the day seems in every way more appropriate for us than January 1st, the day of Janus, the double-faced “god of the time”-servers. Yet it is well named, and as well chosen to be celebrated by all the political opportunists the world over.
H.P. Blavatsky Article: 1890 The New Year’s Morrow