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THE ART OF COUNTING.

own languages have nevertheless sometimes found it convenient 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 artificial 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 equivalent of the number placed over it in the English translation. The general principle on which the words are chosen to denote the numbers is evident without further explanation:—

'Vahni tri rtvishu gunendu kritâgnibhûta
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,