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I.—Prqfessor Schlegel’s Enigma-Mode of expressing numerals in the Sanskrit and Tibetan languages.

AT the end of the pamphlet lately addressed by Professor Scnnnonn to Sir JAMES Mncxmrosn, on the subject of the Oriental Translation Committee of the Royal Asiatic Society*, we find a morceau of enlightenment for the continentalorientalists, on the Hindu method of expressing numerals by symbolical words, which the learned author states himself to be the first to expound to European scholars.

It is certainly a curious circumstance that neither Connnnooxn, Dnvrs, nor BENTLEY, when quoting, translating, and commenting on the text of Sanskrit astronomical works, should have taken occasion to explain the system invariably used by their authors in expressing verbally the numbers occurring in their computations and formulae; it must doubtless be attributed to their considering the subject too trite and obvious to need any remark, or otherwise the very passage quoted by Professor Scnmonn would surely have elicited some observation by the translator. It is true however that many of the terms thus technically adopted by the Sanskrit arithmeticians and astronomers, as the only mode perhaps of screwing the uncouth elements they had to deal with into the procras

‘ This pamphlet contains also an attack upon Dr. H. H. Wrnsorz, which that gentleman will doubtless answer for himself, and some severe criticism on the careless manner in which oriental works are issued from the press by Calcutta Editors generally. We trust our Orientalists will be able to shew that such censure is not deserved, or at any rate that it applies but partially; and we should like to have the opportunity of pointing out those works (such as the Shah nérna) to the accuracy of which real editorial-‘care was devoted, and on which the confidence of the reader may be implicitly placed.—En.

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Iextract thèäÿçäfessoïs remarks at length, since equal credit is due to his._ingenulty in unravelling the mystery, in the absence of native pundit§,_vvlio would have cleared it up in a moment, as if it had altogpîtlieffrlieen a sealed book of hieroglyphics to the more fortunate

'.-.et\1dent on this side the water, as to the rising schools of Sanskrit

ZOPlIIlOSOPhY in Germany and France.

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Explication d'une Enigma.

“ Dans les Recherches Asiatiques, vol. xii. p. 231, M. Connnnooxn cite un auteur qui dit que le nombre des jours sidéraux compris dans la grande époque, appelée Calpa, est: 1,582,236,450,000. Il donne le texte même, dont les mots qui répondent à ce nombre, signifient litteralementf: quatre espaces vides (ou zero), cinq, céda, go1lt,feu, jumeaux, aile, huit, flêche, lune. Tout ces mots sont réunis en un seul composé agrégatif.

Qu'on se figure maintenant Pembarras des écoliers interpellés pour expliquer comment cette bigarrure fait precisément un trillion cinq cents quatre-vingt-deux billions, deux cen'ts trente six millions, et quatre cents cinquante mille. La chose est pourtant bien sure: il ne peut y avoir erreur. Voici le mot de Penigme. Les mathématiciens Indiens ont une méthode d’exprimer les chiffres par des noms restreints à un certain nombre d’objets. Ils commencent à la droite par les unités, et remontent vers les chiffres d’un ordre supérieur. Cela a Pair d'une puérilité, il y a pourtant là-dessous un but raisonnable. Ou a voulu se prémunir contre l'altératiqn des chifires qui se glisse si facilement dans les livres copiés à la main. Quand le traité etait rédigé en vers, comme c’est un ancien usage dans I’Inde d’employer la versification même dans les livres scientifiques, la. garantie en devenait d’autant plus forte.

Voici l'explication. Les deux premiers termes, étant des chiffres sans déguise. mgnnirîen ont besoin. Vêda ; ces livres sacrés sont au nombre de quatre. Goût .on en, compte six espéces principales : le doux, Pamer, le salé, Paigre, le poignant et lïrstringent. Feu signifie trois ,- par rapport aux trois feux sacrés que les brah. manes entretiennent. Jumeaux, aile, signifient naturellement deuz‘ ; le dernier mot est employé aussi pour les deux moitiés d'une lunaison._ Flèche signifie cinq: ce sont les cinq flèches du dieu de l'amour, dont les pointes sont armées de fleurs. Ces flèches sont un emblème des cinq sens‘ par lesquels l'amour pénètre dans l’ame. Lune est un, parcequ'il n'y à qu'une seule lune.

On voit cependant quïil y a là dedans quelque chose de conventionnel. Par exemple, le mot de goût, chez les Indiens comme chez nous, est employé aussi métaphoriquement, pour les différentes impressions que produit la. poésie. Alors Pénumération varie de huit à dix. Il faut dont savoir que, lorsque ce mot est substitué à un chiffre, l’on doit entendre le goût matériel.

Un autre auteur cité par M. Connnnoxs, exprime le même nombre de la mu

niere suivante, ôcc.’ ’ \

The only difierence in the second enumeration quoted by the Professor consists in the substitution of ocean, quality, vas‘u, and lunar day, for 4, 3, 8 and 15, respectively: of which vasu alone requires explanation, being the name of a species of inferior divinities, eight in number.

The astronomical pundit of the Sanskrit College has enabled me to publish a catalogue of the principal terms thus numerically employed in the Surya-siddhdnta, the Arya-siddhdnta, the Bhcisvatis, and the other numerous astronomical works of the Hind1’1s. It does not seem necessary to offer any explanation, beyond a simple translation of the terms-, since in most cases their origin is obvious to such as are acquainted with the metaphysical or mythological systems of the Hindus. The only equivocal expression in the list appears to be 8'5}, occean,’ which may either represent four or seven .- but it is invariably employed in the former sense in the Surya-Siddhanta and other best authorities.

The mode of expressing any number greater than nine is, by placing consecutively the term for each figure, beginning with the lowest or right-hand figure, as will readily be understood from the example quoted by Professor SCHLEGEL; and as there are numerous synonymes of most of the simple terms, which may be selected as they may be the best adapted to the metre of the intended aslok, an infinity of compounds may be thus formed which must be perplexing enough to a student, in addition to all the other difliculties of a science of calculations. For a. few compounds, however, as ll, l2, 15, 32, &c. single expressionshave been created, founded on the names of Siva, the signs of the zodiac, the days in a half-lunation, the number of human teeth, and other similar analogies, that are easily retained in the memory. ‘

The following is the list alluded to, omitting most of the synonymes of each word, which would have swelled it to an inconvenient length.

0 or 0. Q kha ,- vacuity,,_Wi[=‘rI, ‘WWI 80:. space, heaven, zero, cypher. \ or 1. __q€’tprithvz’ ,- the earth, (and its synonymes i;I\ffl', 1;, -:5 &<;,) W ckandra; the moon, (i1§Kr,‘(§, rm, &c.) 51: ru'p ,- form, colour, &c. R or 2. W paksh; a wing, the half of a lunar mouth, 5? nétra ,- the eye, (‘M3, 3?, ‘fit, &c.) Hm bhuja; an arm, (‘I133 iii, &c.) "2?! _1/am ,- twin, also the deity of Naraha or hell. qfqa; ashwina; the twin sons of Surya. - Q1{ chhada ,- jaw, (the two jaws.) Q or 3, ‘fig banhi ,- fire, (‘iIf£l3 and its synonymes.) (“II Rdma, the deity Rdma ,- (the three are Rdma, Balanima, and Parasurar_nq.)

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ft; chhidra ,- an inlet, (the nine orifices of the body.)

11$ gr-aha ,- a planet, (the 7 planets and two lunar nodes.)

F{IU dishzi; a side, quarter, (and its synonymes,) the eight cardinal points, with the zenith and nadir. For this and all

‘ numbers composed of two or more figures other compound

expression: may be formed, as ti‘; cypher-earth cypher-moon, meaning zero, one, or 10, as explained in the foregoing remarks : the following numbers however have simple expressions likewise.

in Isha ,- a name of Rudra or Siva, (and his other 11 names.)

E05‘ Szirya ,- the sun, (from his l2 monthly appellation,s.)

qt chakra; a wheel, the zodiac.

few Vishva ,- the universe, (the 14 bhuwanas, deducting baikunt on Vz'slmu”s heaven): see the next number.

m Kzima ,- Cupid; the Swdmiorlordof the l3thtz’tl_n’orlunarday. \ X8 or 14. $18? bhuwana; the world, or universe: the seven upper and

* Only used in the Granthu of South lndia.

seven lower heavens. ' ‘(K Indra, aname of the god Indra, (renewed atfourteen epochs.) Hi Manu ,- the fourteen munoos, or saints. ‘ ‘J or 15. Fife; tithi ; a lunar day, (fifteen in a semilunation.) W aha ,- a day, (from the same analogy.) ‘Q or 16. WT kald ,- a digit, one-sixteenth of the moon's diameter. qfi akhri ,- a metre, consisting of four lines, having sixteen syllables in each. Itq nripa ,- a king, (and its synonymes, from the tale of the 16 raids in the Maluibhdrat.) is or 17. wig atyakhri ,- a stanza of four lines, with seventeen syllables to the line. 11: or 18. Efit dhriti ,- ditto having eighteen syllables in a line. \¢ or 1'9. !If?l'Y!'FF|' atidhriti, ditto with nineteen syllables in each line. R0 or 20. ‘FIE nakh; a finger nail. K\ or 21. {iii Swerga; heaven. The twenty one heavens. ‘(R or 22. INF?!‘ J¢iti,.kind, sort; race, family, cast. is or 24. fit? Jina ,~ the 24 Jinas of the Buddh religion. ‘(s or 25. THE tatwa; the 25 essences : the five quintuple elements. (Q or 26. ‘G?T:5f%[ utlrriti ,- in prosody, a stanza of four lines of twentysix syllables each. R0 or 27. ‘H or ‘H1-rfi nakshatra ,- a star, the 27 lunar mansions. as or 32. (ii! danta; a tooth, the number of human teeth. 5‘: or 33. ii: Deva, a god, for the 33 crores of Hindu gods; or by other accounts, 11 Rudras, 1 2 Suryas, 8 Vasus, and 2Viswadevas. at or 49. HTH tdna; tune; the seven octaves (of seven notes each.) ‘GT3 vdyu, the air, the 7 vayus and their 7 subspecies.

On looking over Mr. A. CsoMA’s manuscript translations and extracts from the Tibetan works in the Society’s library, my attention was attracted to the passage in his life of SHAKYA, where the Tibetan author quotes the epoch of BUDDHA from a variety of diiferent authorities : here the same numerical system is seen to prevail ;—-the printed Tibetan text has the dates in figures above, and written at length in the body of the text, in the same kind of symbolical words, as if to secure them from the danger of alteration ; this system in fact gives the same safeguard against the incertitude of figures as the mode of writing values and sums at length in European documents is intended to secure. To elucidate the subject at the time, a separate note was drawn up by Mr. Csomn, showing that the symbolioal terms employed by the Tibetan writers were chiefly if not entirely derived, like their literature in general, from Sans

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