own languages have nevertheless sometimes found it con-

venient to invent new ones. Thus the scholars of India, ages ago, selected a set of words from a memoria technica in order to record dates and numbers. These words they chose for reasons which are still in great measure evident ; thus 'moon' or 'earth' expressed 1, there being but one of each; 2 might be called 'eye,' 'wing,' 'arm,' 'jaw,' as going in pairs; for 3 they said 'Rama,' 'fire,' or 'quality,' there being considered to be three Ramas, three kinds of fire, three qualities (guna); for 4 were used 'veda' 'age,' or 'ocean,' there being four of each recognized; 'season' for 6, because they reckoned six seasons; 'sage' or 'vowel' for 7, from the seven sages and the seven vowels; and so on with higher numbers, 'sun' for 12, because of his twelve annual denominations, or 'zodiac' from its twelve signs, and 'nail' for 20, a word incidentally bringing in a finger notation. As Sanskrit is very rich in synonyms, and as even the numerals themselves might be used, it becomes very easy to draw up phrases or nonsense- verses to record series of numbers by this system of arti- ficial memory. The following is a Hindu astronomical formula, a list of numbers referring to the stars of the lunar constellations. Each word stands as the mnemonic equi- valent of the number placed over it in the English trans- lation. The general principle on which the words are chosen to denote the numbers is evident without further explanation: —

'Vahni tri rtvishu gunendu kritâgnibhuta Bânâsvinetra çara bhûku yugabdhi râmâh Rudrâbdhirâmagunavedaçatâ dviyugma Dantâ budhairabhihitâh kramaço bhatârâh.

3 3 6 5 3 1 4 i.e., 'Fire, three, season, arrow, quality, moon, four-side of die, 3 5 fire, element, 5 2 2 5 1 1 4 4 3 Arrow, Asvin, eye, arrow, earth, earth, age, ocean, Rama,