Remarks on the Form of Numbers, the Method of Using Them, and the Numerical Categories Found in the Mahābhārata

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Remarks on the Form of Numbers, the Method of Using
them, and the Numerical Categories found in the Mahd-
bhdrata. — By E. Washbtjkn Hopkins, Professor in Yale
University, New Haven, Conn.

These Remarks on Numbers are incidental notes which I
made a short time ago, while collecting from the great Hindu
epic some material intended for another purpose. They were
presented in outline as one paper at the meeting of the Society
in April of this year, but as they are rather too long to be
printed all at one time in the Journal, I purpose to bring them
out in sections in successive half -volumes. The general plan of
arrangement is as follows :

The form of epic numbers.

How numbers are handled in arithmetical processes.

How space (dimension, etc.) is measured (norms and syntax).

Time-words and methods of measuring time (months, aster-
isms, etc. ) ; syntax of time expressions ; time-phrases ; age ; epic
dates (excursus).

The epic world according to the categories of the poets (phys-
ical, ethical, etc.).

Various problems, historical as well as philological, serve to
relieve the dryness of the subject, but these will be touched
only by the way, as my chief object is to get data together,
though I have not avoided mention of obvious differences in
matters pertaining to the growth of the epic. The present
paper includes the first three divisions. The next will treat of
time- words (to epic dates), with subsequent divisions according
to circumstances.

Before taking up seriatim peculiar forms of numbers, I would
call attention to certain fanciful number- words which belong to
the later epic. The most striking of these is dapardha, not
merely as "five," dapardhasamkhyah (pardh), i. 188. 20;
dapardhahaviratmakah, xii. 47. 42, * but as "fist" (the half -ten
fingers) :

1 Compare the abstract, da.Qardhat&=pancatva, xii. 187. 27, dissolu-
tion into five elements (ib. 291. 10, daQdrdhapravibhakta).

110 M W. Hopkins, [1902.

xii. 114. 20, Jcruddho dapdrdhena hi tddayed va.

Analogous is pancapakha, "having five branches," the hand:

xi. 17. 30, svapirah pancapdkhdbhydm abhihatya,

which illustrates Nala v. 5. In the Ramayana, vi. 59. 55, this
word is still an adjective to bdhu. Compare RV. x. 137. 7,
dapapakhdbhydm {hastdbhyam) .

I have elsewhere suggested that the word for four appears to
be a combination of "three and." That the digits, as well as
the higher numbers, were indicated by addition is shown by
many examples of "and" combinations to express them, for
example, in i. 234. 15, six is expressed by "five and one," pafica
cai 'kam ca. Double-six (satka for six) reflects a common
doublet, the year consisting of two six-month "courses" of the
sun, dvisatkapadaydmin, xi. 5. 15. Such "double" terms are
not rare: "double-five-headed," dvipaneapirasah kecit, v. 103.
7; dvipaficaratra, Hi. 230. 37 ; dvisadaksa, " with twelve eyes,"
xiii. 86. 19; while for twenty-one, "thrice seven" is normal,
trisaptan, sic, trihsaptakrtvah.

I have no record of alternate adjective numerals, such as
dvitra or tricatura among epic material ; but unexpressed alter-
nates are found: " five or six mouthfuls," pafica sat ; " for seven
or eight days," saptdsta divasdn, v. 160. 40; "even (opposed
to fifty) five or six or seven," api va pafica sat sapta, vi. 3. 83,
also xii. 102. 21; "often or twelve" (years), dapadvadapa-,
iii. 188. 60. Compare dvyeka-, "of two or of one," Manu, x.
7. For triad, tritayam and trayam (in i. 2. .329, etc., patatra-
yam) are used indifferently; in xiii. 111. 18-19, side by side:

dharmap ca 'rthap ca kdmap ca tritayam jivite phalam
etat trayam avdptavyam.

This is the usual triad to be desiderated, but it is often alluded
to as a triad without definition, as in ix. 64. 21, tritayam sevi-
tam sarvam. It is possible that it means trinity in xiii. 147.
53, where Civa says of Visnu:

tatra ca tritayam drstam bhavisyati na sampayah
samasta hi vayam devds tasya dehe vasamahe,

though even here it may, as usual, be equivalent to the trivarga
called tritaya above (rather than the three times, as suggested
in PW.). Iretd for triad is rather affected in the later epic

Vol. xxiii.] Remarks on Numbers. Ill

and (without the implied complement) stands alone for a Yuga
and for the group of three fires (ref. PW.); trika is used spar-
ingly, pancatrika, having a triad of five, fifteen; tritva is a late
solecism (ref. below). A group of four is catustayam or catus-
kam; a group of five, pancakam, etc.

Metaphorical number-names I have illustrated by a passage
cited in my Great Epic, p. 206, where paragni is 5 X 7. The
passage, however, is late and unique in the epic.

I turn now to the regular numbers.

The epic is not so careless of art as to change the grammati-
cal form of all the numbers, but it contains several abnormal
numerals. I shall speak of the form of the numbers three, four,
seven, eight, nine, ten, adding something on derivatives of the
word for one, and the use of the higher numbers.

Tri. In the Sanatsujata Parvan, which is a late imitation of
ancient matter, occurs this verse :

v. 43. 15, tathd nrpansani da fa tri, rajan.

In cl. 19 are mentioned seven cases of cruelty, which appar-
ently led Telang, SUM, viii. p. 168, to translate the words
above "and likewise the seven cruelties." But the seven of
§1. 19 are expressly differentiated from six that precede, ete pare
sapta, "seven other cases," and it is these six and seven together
which make up the thirteen, dapa tri, mentioned in the intro-
ductory fifteenth cloka. Consequently, Nilakantha is right in
saying that dapa tri is for trayodapa, or, in other words, tri
here stands for trlni.

In the last number of this Journal, xxii, p. 345 ff . , I pointed
out an epic case of a dropped ending, dapa-dvddapabhir vd ''pi,
where the vd shows clearly that dapa stands for dapabhih, which
has lost its ending because it is supplied by the next word. 1 A
still more extraordinary case of dislocated ending is found in
that book which historical critique has pronounced later than
the early epic:

iv. 62. 14, avaruddho '■carat Pdriho varsdni tri dapdni ca,

1 The meter here shows that the corrupt form is intentional. The
case differs, therefore, from that of the QB. yajus, Mitraya Varutyaya
ca, which all MSS. of JB., Professor Oertel informs me, have as Mitrd-
varmyaya ca, since the latter form spoils the meter.

112 E. W. Hopkins, [1902.

where tri dapdni stands for thirteen. Here we cannot read tri-
dapdni, for two reasons. First, this word means thirty and not
thirteen, and thirteen is the required meaning. Second, even if
we took tridapani as an adjective meaning thirteen, there would
still remain the ca, which only a very strained interpretation
could dispose of otherwise than as Nilakantha has said {trini ca
dapa ca). There remains only the explanation that in tridapani
the poet has transposed the endings for metrical purposes and
not only written tri for trini but dapdni for dapa, helped
thereto undoubtedly by the preceding varsdni. Such a mon-
strosity is one that need not surprise us among the many evi-
dences of lateness found in the Virata, which, as a whole, lies
nearest to the pseudo-epic in its disregard of Sanskrit grammar
as in other particulars. So in Virata we find the slovenly con-
struction of iv. 39. 10, jitvd vayam nesyati ca ''dya gdvah,
" conquer us and carry off the cows," a verse admitted by Nila-
kantha (compare 47. 34), and quite comparable with the loose-
ness of form found in Qanti.

The PW. has already noticed, i. 113. 21, vihrtya tridapd
nipah, for trinpat ; tridapdu, iii. 123. 1 ( Apvinau) ; and trida-
pdh, 3X10 (=33) gods, passim.

Catur. Professor Holtzmann, in his Anhang to Whitney's
Grammar, § 482, mentions caturah as nominative in xii. 24. 27
and catur as accusative, vedan, in iii. 45. 8. Both forms are
found elsewhere as well. In vii. 149. 22, gdyanti caturo veddh;
vii. 202. 74, vedan krtvd Hha caturap catur apvdn mahepvarah.
Also in viii. 34. 70, tathdi \a vedap caturo haydgrydh. All these
passages are late laudations or describe metaphorical "cars" of
religion, the four Vedas being made the steeds. "Unique is viii.
20. 49, sa tu dvipah pancabhir uttamesubhih Jcrtah sadanpac
caturo nrpah tribhih ("the elephant with five arrows made six-
fold [cut into six pieces] and the king with three (arrows made)
four "), krto dapdnpah Jcupalena yudhyatd yathd havis tad dapa-
ddivatam tathd ("was made ten-fold [qut into ten pieces] by
the skillful warrior, like an oblation offered to ten divinities").

Here caturah is plainly caturdnpah in sense, but as to the
form, it is difficult to say whether by analogy with late com-
pounds in catura it is nominative singular, or by analogy with
"make one four" accusative plural, or by analogy with the
cases above, nominative plural. I think it belongs to the last

Vol. xxiii.] Remarks on Numbers. 113

group, "made-six-fold, made four." The awkward sentence
means as a whole that the six parts of the elephant and the four
parts of the king were like an oblation cut into ten parts. 1

Saptan. By analogy with the cases already mentioned it
may be suspected that sapta stands for saptasu in xii. 343. 106,
where Kandarlka is said to have arrived at Yoga-perfection
because of his excellence, mukhyatvdd, "reflecting often on the
sorrow caused by birth and death, saptajatisu.'''' The commentator
says "the sorrow of seven births," saptajanmikam, which would
imply "in seven births," and not the compound "among those
having seven births," which is the natural interpretation. As to
the meaning, it is probably the indefinite sense of "many,"
which in most examples is hard to verify (i. e. to show that
'seven ' is used without any reference to a fixed number). For
in "seven paces," "seven flames," "seven seers" and "seven
rivers," seven, for all we know, may have been intended liter-
ally. There are two cases, however, where saptan clearly means
"many" simply; once where, instead of elephants tridha pra-
sravantah (an oft-repeated phrase), we find saptadha / for the
parallel sarvatah is used in the same way :

i. 151. 4, trihprasrutamadah,

vi. 64. 58, tridha rajan prasravanto madam bahu,
vii. 26. 6, ksarantah sarvato madam,

vi. 95. 33, saptadha sravata madam, parvatena yatha toyam
sravamanena sarvapah.

The second case is where bhuvanani vipva interchanges with
bhuvanani sapta, or, in the gender of the later epic, bhuvanah
sapta (see hereafter).

Asta. The final vowel is short or long according to metrical
convenience, long when the length is indifferent:

iii. 102. 3, apitih patam astau ca nava ca 'nye,
astau required by the meter;

vii. 146. 134, aksauhinir asta hatvd,
asta required by the meter;

1 The havis called dacadaivatam, represented here by da^anga (the
man and elephant together) " in ten parts," is called dafdngo homah in
xviii. 6. 105.

vol. xxiii. 8

114 E. W. Hopkins, [1902.

xiii. 111. 69, bhutva mlno l sta varsdni, also required,
v. 86. 9, dapd ''sta ca, and vii. 82. 8. and 16, patam asta ca,

cases of diianibus, brevis required;

ix. 46. 74, mahisam ca ' 'stabhih padmdih,
short vowel required;

viii. 22. 6, astdbhir apt, Bhdrata,

long vowel required; ib. 17, JVakuldya patdny astdu, indifferent.
Respecting the alleged difference between astdgava and asta-
gava, PW. i. 531, there are two verses, one of which is

viii. 67. 6, astdgavdm asta patdni bdnan (sc. vahanti),

which Nllakantha interprets as " eight eight-cow wagons carry
hundreds of arrows," his tesdm astdgavdm implying a short
genitive modelled on gavdm [astdu gdvo yasmins tad astdga-
vam pakatam tesdm, astdgavdm asta astasamkhydni pakatdni,
nudabhava drsah, patani bdnan anekapatasamkhydn vahanti).
One is tempted to read astdgavdny, as in the next passage,
which, however, has the short vowel :

viii. 20. 30, astav astagavany uhuh pakatdni yad dyudham
ahnas tad astabhdgena Drdunip ciksepa, marisa,

"Drona's son, Sir, threw as many missiles in an eighth of a day
as eight eight-cow wagons carry," which repeats with elaborate
definiteness the statement of the preceding verse that the hero
poured arrows as Piisan's "younger brother," Pusanuja, that is
Parjanya, pours rain. The scene is late and instructive for the
critique of the epic. The hero here particularly lauded is a cer-
tain Pandya, quite unnoticed previously but now extolled as the
ablest warrior on the Pandu side. It is he who, as explained
above, is quartered and made with his elephant a ten-fold obla-
tion. There appears to be no grammatical difference between
astdgava and astagava. 1

In regard to astacakra, the Petersburg lexicon gives only the
Yedic astacakra, but astacakra is found (of Hari's wagon,
ydna) in vi. 8. 16 ; xii. 335. 11 ; and (of a demon's car, ratha)

1 Compare for these compounds, hasti?a#gava, viii. 38. 7, of a war-
car, and sa^gavlyarii cahatam, ib. 76. 17. In xii. 37. 32, sixteen cows
are yoked to a war-car.

Vol. xxiii.] Remarks on Numbers. 115

in vii. 156. 61; 167. 38; 175. 13; and (of an a$ani) in vii. 175.
96. In the first three Drona cases, samdyukta is added, a set
formula. In the first case, from Bhlsma, the word also begins
a pathya and the whole verse is repeated in the next Canti case,
astacakram hi tad ydnam bhutayaktam manoramam. As the
last case, too, stands at the head of a pathya and in this situa-
tion astacakram would be metrical, the choice must be due to
preference for the later form.

Nava. The Vedic phrase jaghana navatlr nava I have
already, Journal, vol. xxii. p. 389, located in the epic, ii. 24.
19. To this example should be added also the same phrase
occurring at ix. 51. 36 and xii. 22. 11. The last is farthest
removed in context from the original, while the passage in
Calya gives the Vedic text very closely in making the weapon
the bones of Dadhlca (epic form) :

RV. i. 84. 13, Indro Dadhlco astabhir vrtrdny apratiskutah

jaghana navatlr nava,
Mhb. ii. 24. 19, yena (rathend) @akro ddnavdndm

jaghana navatlr nava,
ib. ix. 51. 36, (Dadhlca, tasya 'stibhih) daityadanavavlrdnam

jaghana navatlr nava,
ib. xii. 22. 11, ("Indra the son of Brahman became a Ksatriya

by his acts and ") jndtlndm pdpavrttlndm,

jaghana navatlr nava.

In each case (but the first is not annotated) Nilakantha says
that the number is (not ninety-nine but) eight hundred and ten
(nine nineties). In i. 32. 24, navatyd navatlh (krtvd), v. 1.
navatyo, the multiplication is definite, 8100.

To the forms recognized in grammars and lexicons I am
tempted to add navaih as instrumental plural. Otherwise we
must assume that new arrows are especially used when their
number is ninety, whereas generally there is a natural predilec-
tion for such conjuncts as six and sixty, seven and seventy, and
nine and ninety. So by analogy with navatyd navabhiy ca in
viii. 30. 25 we find navair navatyd ca pardih in viii. 90. 60.
At the same time, "nine" and "new," owing to their like
sound, are found together, as in viii. 48, 50, navair navabhir
dyasdih, but in the case above ca seems to show that navaih is
a numeral.

116 K W. Hopkins, [1902.

I would remark, by the way, on the partially formulaic char-
acter of most of the shooting in the battle-scenes. The test of
an archer's skill is not only to shoot one arrow well but to shoot
many arrows at once. Among digits the object shot at deter-
mines, for the main part, the number of arrows used. With
four arrows one shoots the four steeds; with three, the arms and
forehead or the three charioteers, etc. But even here there is
an occasional irruption of eights, the favorite number of the
later epic. Thus in viii. 89. 63, ten and eight; 65, eight; 68,
eight hundred and eight thousand; 76, eight; all in a bunch,
though up to this passage the whole preceding eighty odd sec-
tions show only half a dozen cases. So in the late wonder-tales
of the first book, larger numbers are by preference expressed in
terms of eight or its multiples, e. g., i. 100. 20, to express thirty-
six years, "years sixteen and eight and also four and eight
more." I shall have occasion in a later section of this paper to
show how this Buddhistic number has driven out the more
ancient holiness of nine.

In the ' ' down-pour " of arrows said to be shot by decades
there is a certain preference for stereotyped groups. Twelve,
fourteen, fifteen, and sixteen are shot more often than seventeen
and eighteen. Twenty-one, trisaptan, is a favorite for the
same reason that endears trisaptati, as three and seven (ty) are
sacrosanct numbers. In this decade, twenty-five is also a
favorite, while twenty-seven is the rarest; in the third decade,
thirty-six is the conventional number, with a few cases of thirty
and thirty-two. The fourth decade is almost ignored; the fifth
appears rarely as fifty ; then come sixty and six and sixty (less
common are three and four and sixty) ; seventy and seven and
seventy (less common are two and three and seventy) ; eighty
(rare) ; ninety (nine and ninety as above) ; and occasionally one
hundred, three hundred, five hundred, and even ten thousand
arrows all discharged from one bow at one shot !

Da£a. The da fata of vi. 2,700 (rightly condemned in
PW.) is replaced in B. 61. 21, by trinpata. The epic has
dapati, analogous to saptati, navati, not as decade but as one
hundred (as who should say "ninety, tenty"),the form, how-
ever, being formulaic like navatir nava (above), and probably
a new formation, as it occurs only in the later part of the epic.
The decisive cases as regards the meaning are (i. 16. 8-13 and) v.
108. 14, the latter:

Vol. xxiii.] Memarks on Numbers. 117

Omkdrasyd 'tha jay 'ante srtayo dapatlr da fa,

where a "thousand branches" is Nllakantha's undoubtedly cor-
rect interpretation. In xiii. 30. 21, the ten might be decades
or hundreds (of days)j though here also Nilakantha admits only
the latter and says the word is Analogie-Sildung '.'

Holtzmann, op. cit. , § 483, has spoken of saptadapesu at iii.
268. 11. I think Nilakantha's explanation (having eight royal
acts and nine siddhis and paktis) is quite inadmissible. Families
' ' having seventeen " would be more likely to be thought sinful
than virtuous. Compare the " seventeen fools and sinners " of
v. 37. 1-6. Then in v. 36. 22, the "great families " are defined
as those which ete saptaguna vasanti, "seven virtues" being
their possession, which suggests saptagunesu as the right read-
ing. But here the meter alone is enough to change saptadapasu
to saptadapesu (vayam punah saptadapesu Krsne hulesu sarve
i navamesu jdtdh).

Higher numbers. Nineteen is not navadapa in the epic
but, as in Latin undeviginti, ehonavihpati? In xiii. 107. 87,
ekonavinpat serves as an ordinal, ekonavinpati dine standing
parallel to sodape, saptadapame, astddape, and purne vinpe
(divase). At C. xi. 561, parivinpat offers a form parallel to
trinpat (also trinpati) ; but B. 19: 15 has papya Krsna for pari-
vinpat (Vivincatim). In i. 2. 330, B. has vincat, C, trincat ;
ib. 379, vinpac chlokapatani. The late Ramayana also admits
vinpat in ekavinpat (ref. PW.). The epic accusative of the
following decades is frequently identical with the nominative;
for example, in i. 86. 15, abhaksah paradas trinpat, either form
doing duty for either case. Examples of trinpat and panodpat,
as accusatives of object and duration respectively, are given
below, and in xiii. 168. 5 and 27, respectively, pancapat is
accusative, parvarih pancapat, and pancdpatam is nominative,
astapancdpatam rdtryah paydnasyd ''dya me gatah, as in the
further case cited below. The corresponding ordinals in the
text (the adhydyas are counted by -tarna forms as well) are
short, ekavinpa, dvdvinpa, trayovinpa, caturvinpa, pancavinpa,
sadvinpa, saptavinpa, astdvinpa, ekonatrinpa (compare ekona-
sasti, ekonasaptati, i. 2. 204, 289, etc.), xiii. 107. 93-121.

1 For thousand the later epic uses dacacatam : tathe 'spudm dacaca-
tam prapnuvanti, xiii. 102. 36, etc. (meter, Great Epic, p. 305).

•2

Or vincatir ehona, vi. 4. 15.

118 E. W. Hopkins, [1902.

Before leaving this subject I would say a few words on cer-
tain declined forms of eka, not because they are irregular as
forms, but on account of the way they are used. The first point
is the parallelism between the adverbial ablative and the instru-
mental, as shown in

v. 43. 21, tribhir dvabhyam ekato vd , rthito yah.

According to the commentator, arthita here means possessed
of or furnished with, artha, a meaning hot usually recognized,
but in accordance with the sense of the passage, which says that
one who has in his power all the twelve virtues is fit to rule the
earth, while "he that is furnished with three, two, or one," is
to be known as one having wealth, tasya svam astl Hi sa vedi-
tavyah. In any case, ekatah is used freely here as a correlative
of the instrumental. 1

The same form has a meaning almost recognized in the Pet.
lexicon, which ascribes to it, besides the ablative sense and that
of "on the one hand, " the meaning of ' ' together, " or " in one. "
By a slight extension of meaning ekatah means altogether,
solely, or, quite literally, one-ly, only, as in vi. 107. 20,

yathd prajvalitam vahnim patamgah sarnabhidravan
ekato mrtyum abhyeti tathd ''ham Shismam iyivan,

"As an insect entering a blazing fire meets only with death, so
I, on having encountered Bhisma." This, at least, is Nllakan-
tha's exposition, who takes the word as equivalent to (ekant)
kevalam, mrtyum eva, rather than as contrasting the insect "on
the one hand " with the speaker. The plural eke meaning
"alone" may be used as well as the singular, ndi 'ke 'pnanti
susampannam, "eat dainties alone," xii. 228. 44.

Examples of the correlation by two ekatah are not uncommon.
One is found in

xii. 12. 12, ekatap ca trayo rajan grhasthdframa ekatah,

where against the other three orders is weighed that of the
householder, which is said to be equal to all the others put
together.

1 For the usual meaning if applied here would be "he who on the one
hand is furnished with three or two." Compare the parallel use of
prathamalah in xii. 83. 1, e?a prathamato vrttir dvitiyaih qrnu, Bha-
rata.

Vol. xxiii.] Remarks on Numbers. 119

In the following stanza I think we may see an extension of
Vedic usage surviving in the epic :

xii. 21. 7, anye sama prapahsanti vyayamam aparejanah

nai'kam na ca ''pare Jcecid ubhayam ca tatha ''pare.

The commentator admits the double negative as an affirmative
and according to him the stanza would mean : " Some praise mild-
ness, others praise a strenuous life, still others praise the one
(Yoga-discipline, dhyana), and others again praise both." But,
although the affirmative double negative is not an impossibility,
it carries with it a strength of affirmation 1 that is quite uncalled
for in this passage, where ekam certainly has no right to be
represented by dhyanam. In the continuation it is said that
some sit in quiet meditation, some are active in governing, and
others are ekantapilinah, which may have led the commentator
here to set up a third object of devotion. But with the antithe-
sis of ubhayam there can be no doubt that ekam is one of the
two already mentioned, and the meaning to be expected is that
some praise mildness, some praise energy, some praise neither,
and some praise both ; which, in my opinion, is what the pas-
sage was intended to mean when it was first written. In other
words, for naPkam na ca, we should read nai 'kaih ca na, which
preserved the old phrase found in BAIT. vi. 2. 2, na ''ham ata
ekam ca na veda ; ib. 3, tato nai , karh ca na veda. Otherwise
na ca na survives only in indefinites, na katham ca na, etc.
The sense of nai , kam as "many a" is here excluded. This
latter meaning is common, e. g., nai ''kam yugaviparyayam
(avasam), "many an age," xii. 229. 49. 2

1 It is used, however, generally, where two clauses are distinguished,
e. g., na cai 'va na prayunjita, sarhktrnam parivarjayet, "not that one
should not commit (these faults, but) one should avoid excess," xii. 56.
42 ; or in strong affirmation, na sa yajno na bhavitd, i. 88. 2, "it will
surely occur ;" nahi tvdih no 'tsahe hantum, xii. 227. 80, " assuredly I can
kill thee." Compare the parallel in the same scene (repeated) in xii.
224. 88, evarh nai 'va na cet kalah . . . patayeyam aham iva 'dya, " I
could kill you now ; if it were not so, if Time did not (prevent)." Com-
pare xii. 239. 4-6, ending etad evarh ca nai 'varh ca na co 'bhe na 'nubhe
tatha.

2 In xiv. 49, a similar but longer string of opinions is given by kecit,
anye, apare, and eke, indifferently, ending with §1. 12, sarvam ekepra-
gansanti na sarvam iti ca'pare, "some praise everything and others
nothing."

120 E. W. Hopkins, [1902.

In regard to the choice between eka or ekatara, the epic uses
either, as in xii. 81. 9, vrnomy ekataram na ca ; 10, ekasya
jay am dpanse, ("like the mother of two gamblers) I prefer
neither, hope for victory of the one." In i. 119. 15, vdsydi
, kam taksato bdhurii candanendi 'kam uksatah na 'kalydnam na
kalydnam eintayann ubhayos tayoh, ' ' not thinking ill or good
to appertain to [these both] either of these, him cutting one
arm with an axe and him anointing one with sandal-paste " (for
anyataram) . In triads, one, another, and a third, any a, apara,
para; eka, apara, eka, and so forth, xii. 86. 30; 137. 4.
Though katara is used quite regularly, kirn may take its place,
as in xii. 126. 16, where, after two are mentioned, we find kim
nu jydyastaram, "which (of these two) is more greater?" So
katama and ka, xii. 167. 2.

On the form of other epic numbers I may refer to what
has already been given in the Petersburg lexicon and in Profes-
sor Speyer's Sanskrit Syntax. I will only register another pan-
cdpatam (gunah proktah) for paflcdpat, xii. 256. 8, and observe
that dvisaptati appears in Manu, vii. 157, but epic dvdsaptati (in
the same passage) at xii. 59. 71; at the same time remarking as
to patd for patdni, in iii. 67. 6, where C. has patam patdh, that
masculine fata belongs to the more recent parts of the epic,
whence patd, like vipvd, may have been the original. As to
the feminines, tripatl, etc., which have been noticed by Speyer,
op. cit. , § 294, these forms are also late in the epic, tripatl and
saptapafl (i. 2. 324) and cognate forms are found in still
later works. Further: besides dapapatam, above (and dapasd-
hasram), "a ten-hundred," there is the uncommon uncom-
pounded singular form (as if plural), as in xiii. 112. 14-15,
where, parallel to dapapatam vedaviddm (in cl. 28), appears
brahmandndm patam dapa.

The question as regards appositional construction may be dis-
cussed here though it pertains to syntax rather than to form.
All substantive numerals may take this construction, sahas-
ram parivatsardn, i. 94. 41, etc., which is not irregular if we
understand "years, a thousand," rather than "thousand (of)
years." But with the higher numbers the noun is usually either
compounded, varsdyutdni, etc., or is in the genitive, purusame-
dhdndm ayutam, i. 95. 20.

Vol. xxiii.] Remarks on Numbers. 121

The particular example just given has indeed a sort of stereo-
typed form, especially when "eleven thousand years" are
referred to. As one says bahuvarsagandn, "many year- rows,"
e. g. xiii. 111. 98, so one says year-hundreds or thousands, pan-
cavarsapata, etc., and uses a formula with eleven, ten thousand
and ten hundred: dapa varsasahasrani dapa varsapatdni ca,
iii. 12. 12; dapa kalpdyutdni, ib. 200. 121. A modifying
number is placed in the same construction, as a general thing,
ayutdni pancdpat (accusative) with genitive, xiii. 107. 31; yud-
dham varsasahasrani dvatrincat abhavat Mia, "the war (of the
gods and their elder brothers, the devils) lasted thirty-two year-
thousands," xii. 33. 26. But here also a genitive is often found
(more correct), dve yugdnam sahasre, xiii. 107. 113, etc., and
an inverted order, as in patavarsa, not as adjective but noun, is
permitted, vdyasah patavarsdni (jlvati), xiii. 111. 86 (compare
patapdradam), in this instance due, perhaps, to the meter (to
avoid a third vipuld after a trochee), but found also ib. 118,
krmir vinpativarsdiii. The very unusual construction found in
i. 90. 1 is probably due to meter also. Here we have samvat-
sardndm ayutam patdndm, "a ten-thousand of hundred years."
Close by occurs another case of apposition, i. 93. 24, tadd
''dadam gdh patam arbuddni, "then I gave cows, a hundred
hundred-millions. "

An adjective may or may not agree with the implied genitive ;
both together, for example, in iii. 127. 2 and 13, bhdrydpatam
sadrplnam and sadrpam. Possessives, by the way, put the
numeral either first or last, with possessive ending, dapagu,
sahasragu, gopatin, xiii. 78. 11. Compare with the last, ib.
102. 43, yo gosahasrl patadah sarndih samdrn, gavdm patl
dadydc ca.

In regard to the syntax of decades, both genitive and appo-
sition are common, and, beginning with vinpati, we find, for
example, sarhsardn vinpatim, xiii. 111. 117; trinpad agriin
(ayajam), xiii. 103. 36. An interesting case historically is
found in xii. 335. 35-37, ekavinpatir utpannds te prajapatayah
smrtdh, not only because "twenty-one Prajapatis" are late-
epic, but because in the twenty names given as those of the sons
of Narayana one has been left out, the list being Brahman,
Sthanu, Manu, Daksa, Bhrgu, Dharma, Yama, Marici, Angiras,
Atri, Pulastya, Pulaha, Kratu, Vasistha, Paramesthin, Vivas-
vat, Soma, Kardama, Krodha, Vikrita.

122 E. W. Hopkins, [1902.

The singular noun (an unusual case, compare Speyer, 8. Syn-
tax, § 294) occurs with trinpat in xiii. 101. 15, narakam trin-
patam prapya (v. 1. in C). The plural decade also is found in
the later epic, e. g. trinpato l bdan, xiii. 103. 34.

The word vinpati gives the name Vivincati, a hero whose
foregone fate is to be attacked with twenty arrows, in a repeated
phrase : Vivinpatirh ca vinpatya viratham krtavan prabhuh, vi.
117. 44=vii. 14. 27, etc. Such number-names are not confined
to this hero and the three wise men, Ekata, Dvita, Trita, as they
are found also in the satyrs' names, Astaka and Navaka, Skan-
da's goat-faced sons, iii. 228. 12 ; and in xiv. 4. 5 are mentioned
Iksvaku's descendants Vinca and Vivinca, who are unknown to
the early epic but appear in the Puranic literature and the
pseudo-epic so clearly associated with it.

An ordinal may be employed to take the place of a cardinal pre-
fixed to another cardinal, as in i. 95. 37, caturvihpam putrapat-
am babhuva, "a twenty -fourth son-century was born," that is
one hundred plus twenty-four, which leads eventually to catur-
vinpa being used for caturvinpati as in caturvinpdksara for the
Gayatri in the Harivaiica (v. PW.), a meaning that may belong
to the passage above as well.

The ordinal may (but does not generally) agree with distrib-
uted singulars, although combined with one, as in the verse of
ii. 77. 31 repeated at xiii. 148. 61, Duryodhanasya Karnasya
fiakunep ca . . . Duhpasanacaturthanam bhumih pdsyati poni-
tam. The ordinal in such a phrase as ' ' five went and she too
(as) sixth " needs no comment, and almost as common is such a
turn as "they five set out having her (as) sixth;" but "with
self as" is probably a late locution, though like the Greek
idiom. It is found in (xii. 177. 52, atmana saptamam kamarii
hatva) the same passage from which examples of these construc-
tions may be taken, namely, "seventh with himself (instrumen-
tal) went the king," xvii. 1. 23-25, prasthitan Draupadlsasthan
. . . bhratarah panca Krsna ca sasthl pva cat 'va saptamah, fol-
lowed by atmana, saptamo raja niryayau Gajasahvayat (late
addition to Panini, vi. 3. 6, PW. Ram. examples). As atman,
plural reflexive in singular, is not very fully illustrated in PW. ,
I will add ndthavantam ivd Hmanam menire, "they regarded
themselves as having a savior," i. 183. 10.

"Vol. xxiii.] Remarks on Numbers. 123

The word dvitiya, "second," passes in compounds from the
meaning "having as second" to that of "with," and independ-
ently to that of alter (ego), i. e., a friend. Familiar examples are
those given by Speyer, chdyadvitlya, " (doubled) with his shad-
ow," asidvitlya "seconded by his sword." An example of the
personal construction is Yuyudhdnadvitiya, "along with Y. ,"
xiv. 66. 11 ' (compare dvitiyavat, with instrumental, iii. 313. 47) ;
me dvitlyah, "my friend," xiii. 102. 57. The idiom, though
perhaps not new, is not often used, — generally in late passages.
Another case occurs in v. 50. 26, Krsnadvitiyah, a passage not
removed from the suspicion of being a late adornment.

The second ordinal answers to our ' ' another " in such phrases
as dvitiyasagaranibha, "like another ocean ;" while the "same"
is expressed by the first cardinal : ekaduhkhah prthaksukhah,
"having the same sorrows but separate pleasures," i. 10. 4 and
50; ekdrtha, ekabhojana, "having the same aim, food," etc. 2

Ordinals are occasionally used to indicate time. First in
time, as contrasted with a subsequent event, is, indeed, gener-
ally given by purv a, "former," purvarupdni, "preliminary
symptoms," xii. 228. 1; or purastat, "previously," i. 189. 22;
but prathama is used in the same way, prathamam . . . pa f. cat,
"at first and afterwards," xii. 227. 68, etc. A "second time"
is dvitlyam, iii. 60. 7; dvih purvam idam trtlyam, "twice
before and now for the third time," iii. 92. 9; purvam . . .
punah . . . idam trtlyam, ' ' first, then again, and now for the
third time," xviii. 3. 35; often as adj., esd trtlyd jijndsd tava
krta, "this is the third examination you have taken," ib. 32.

Before passing on to the epic methods of indicating arithme-
tical processes in detail, I may remark that with the exception
of time (and religious observances), 3 where the duodecimal sys-

1 The next stanza, xiv. 66. 12, has a form not recognized in the lexi-
con, pitrsvasdm, as compared with the regular pitrsvasaram, the latter
found in v. 90. 1 ; viii. 87. 16 ; xiv. 52. 53. Another late passage, vi.
116. 3, has svasdm (like duhitam in Virata; the last noticed by Holtz-
mann, Anhang, § 371).

'' Occasionally ambiguous. Thus, ekapatnitd is the condition of hav-
ing "the same wife"; but in R. v. 28. 13, ekapatnitvam is having
"only one wife." But the context makes the meaning clear.

3 The expansion is rather wide on this side and varies between time-
divisions (twelve years of fasting, sacrificing, etc.) and religious num-
bers, for example, the twelve syllables of the pacta of the jagati verse,
iii. 134. 19 (observe navdksara bxhatl, ib. 16).

124 E. W. Hopkins, [1902.

tern, 12, (30) 60, etc., is naturally selected, the decimal system
is in ordinary use, both for the system of administration, xii.
87. Iff., and for the army, ih. 100. 31, etc. But it does not
appear in any system of measures and only once is used of
weights, though it should be added that the indications of
values are so rare as to be of little importance (in iii. 134. 15,
astdu panah patamanam vahanti ; also draunika, ref. PW.).

COUNTING AND ADDITION.

Except in counting up money, sampidayati, and a poetical
use of yuj and yoga (navdi 'va yogo ganandme 'ti papvat, of
the nine digits in counting, iii. 134. 16 ; tarn muhurtam ksa-
nark velam divasam ca yuyoja ha, " she reckoned the time," ib.
296. 7), the usual word for count (counting is ganand) is (pra) 1
ganayati, as in iii. 193. 28, yatrd 'hdni na ganyante, "where
days are not counted ;" samganana na 'sti, "there's no count-
ing," xiv. 73. 24; ganayasva, "count," iii. 72. 23; a word
that passes into the sense of reckon, think, especially with vi,
and regard, na ca tan ganayam dsuh, "disregarded them," viii.
37. 10 (ganaye in R. vii. 16. 42 appears as gane, manusan na
gane, "I don't regard men "). Often follows the object compared
in the instrumental, na ganayamy etdns trnend 'pi, "I do not
care a straw for them," ii. 44. 34. Though ganeya is used, yet
the corresponding adjective, calculable, is usually parimeya or
samkhyeya, samkhya, i. 74. 33; iii. 121. 11, etc.; i. 55. 2, pak-
rasya yajfiah patasamkhya uktah ; xiii. 107. 36, samkhya ati-
guna, ' ' incalculable number. " The idea of addition is given
both by simple juxtaposition, usually prefixing, of cardinal or
even ordinal (above) numbers, whereby it is sometimes doubtful
whether, as in dapapatam, the modification is by addition or by
multiplication; and by adhikam, as in ekd patddhiJca (i. 115. 21
and 41, ekadhikapatam purnam, patarn pancadhikam, or pre-
fixed) ; that of completeness, by purna, full, sdgra, all, and api
anA pari. Only the last requires a word. 2 The native scho-

1 total), praganayam ami), kasya vdro 'dya, "they calculated whose
turn it was," i. 164. 14.

2 For purqa : "they say that ten hundreds are a full, purna, thou-
sand," iii. 134. 17. For sagra: catarh sagram, " a whole hundred," xii.
112. 6 ; R. Q. v. 7. 28; for api: "still be to thee even (full) ninety-nine
sons, but abandon this one," eatam ekonam apy astu putranatn, tyajdi
'nam eJcam, i. 115. 87.

Vol. xxiii.] Remarks on Numbers. 125

liast gives to pari not the sense of completeness but of addition.
Unfortunately he does not recognize the reading parivinpat,
given above, but he renders paricaturdapa by fifteen at iii. 1.
11 and iii. 93. 28, and at ii. 3. 37 by "fourteen over" (more).
On parisodapa, at iii. 78. 2, he says nothing. Completeness
would seem to be the real meaning by analogy with parisamvat-
sara, for example in iii. 108. 13 ff., sahasraparivatsardn . . .
samvatsarasahasre tu gate divye.

Less common is the use of uttara. In i. 128. 18, patam ekot-
tararh tesdm, "a hundred of them with one more." So in iii.
308. 1, dapottara in the phrase pukle dapottare pakse, "on the
eleventh bright half -month" (after ten full months). This
accords not only with the scholiast's explanation but also with the
usual allotment of ten (whole) months of pregnancy. Other
examples of uttara as plus will be found correctly given in the
Petersburg lexicon. Colloquial is Mm uttaram,, "what more?";
" not to have uttaram " is to be unable to reply to a remark.
Another word for "more" is urdhvam, over, beyond, with
ablative. An adjective with paras or param also does duty for
" more ": pddaraksdn parahpatdn "beyond a hundred guards,"
vi. 95. 36; para/ihsahasrd viprdh, "over a thousand priests,"
xii. 38. 24; as para itself is used, ekap cd ''pi patdt parah, " one
more than a hundred," i. 115. 1; sarhvatsarapardh ksapdh,
"more than a year (of) nights," i. 221. 13 (viii. 90. 61; 78. 55,
parahpata and pararhpata have already been cited by Professor
Holtzmann, Zur Geschichte, i. p. 161. Examples are not
numerous). Nilakantha follows an improbable tradition in
attributing the meaning of ' ' more " to nis in nistrinpa, (a
sword) "more than thirty" thumbs in length, trinpadanguld-
dhikah, iv. 42. 16, and elsewhere.

The word, adhika or abhyadhika, is used to convey a com-
parative notion, "more than," dirghebhyap ca manusyebhyaJi
pramdndd adhiko bhuvi, "greater in size even than tall men,"
xiii. 160. 15; which leads to the sense "superior to," Idghave
sdustavesu sarvesdm abhyadMkah, i. 132. 15, and even to that
of "more happy." The ablative usually follows. Examples :

viii. 35. 4, ipvardd adhikah, (Brahman) "greater than Civa."
vii. 74. 25, yogdt tvatto l dhiko i rjunah, "superior to you

through practice."
viii. 32. 61, Karno hy abhyadMkah Pdrthdt, the same.

126 E. W. Hopkins, [1802.

viii. 83. 31, abhyadhiko rasah, "a better taste."
iii. 92. 15, ko namd , bhyadhikas tatah, "more blessed (supe-
rior, better off) than he."

So (abhy) adhikam is used as the comparative-maker of adjec-
tives : Somo Rohinydm abhy adhikam pritimdn bhutah, ' ' Soma
was more in love withRohini," xii. 343. 57; sa , dhikam pobha-
mdna, "she was more lovely," i. 221. 20. But adhika may-
mean "too great," as in the only defect of Arjuna: pindike
'syd , dhike, xiv. 87. 8 (his cheekbones were too prominent). 1

SUBTRACTION.

The farmer's crop which is sadbhdgaparipuddha is ' ' cleared "
of the royal tax, that is, the sixth part of it has been subtracted,
xiii. 112. 19. The usual term to indicate that one number has
been subtracted from another is una, lacking, deficient, panco-
nam patam, "a hundred less five," iii. 72. 11. The independent
use of this word is rare: une dviyojane gatvd, "two incomplete
leagues" (not quite two), ix. 5. 50. Nilakantha recognizes the
meaning of nyuna, the usual word for almost, in avara, which
occurs in ii. 15. 22, evam sarvdn vape cakre Jardsandhah patd-
varan, "he has overcome almost all a hundred," after it has
been said that the kings overcome were a hundred and one, and
just before the more precise statement that they numbered
eighty-six and that fourteen remained, pesd rdjanp caturdapa,
cl. 18 and 25, to complete the tale of one hundred. As one and
a hundred means only a large number, nyuna, "not quite," is
supported by the context as the probable meaning of avara, and
another passage also seems to show that this meaning, not recog-
nized in the lexicon, which gives only "at least" with numbers,
is possible. This is na kap aid aharat tatra sahasravaram
arhanam, "no one brought as tribute there less than a thou-
sand," ii. 35. 11, literally "a tribute having a diminished thou-
sand," so that avara, "less," forms the counterpart to uttara,
"more." The other meaning, from the idea of "less," that of
"at least," is, however, the usual one, as in mantrinah trya-

1 For " a half more than all " we have " all and more by " in xiii. 125.
10 (extension of Manu iv. 85); ardhenai 'tani sarvani nrpatil} kathyate
'dhikal}.. The scholiast says adhika]}, is in antithesis to a little, k§udra,
king (equal to all these by a half is a great king).

Vol. xxiii.J Remarks on Numbers. 127

varah, "at least three," xii. 83. 47. The "deficient" idea is
common enough with nouns, for example, gundvara, "deficient
in qualities," and glides naturally into the combination with
numbers. Another example of the rarer sense may, I think, be
found in xii. 321. 158: sa (raja) tusyed dapabhdgena tatas tv
anyo dapdvardih, where "at least ten" scarcely .makes the
required antithesis of not even ten ; for the sense seems to be
that a very energetic warlike king " should be satisfied with a
tenth and any other with still less." 1 Opposed, by the way, to
avara in the usual sense is parama. As shown above, para
means "more;" but parama means "at most," sahasraparama,
"at most a thousand," and this "most" is used for "whole,"
trivarsaparamosita , of seeds kept to the highest point of three
years, or, as we should say, three whole years, xiv. 91. 16.

The "remainder" is pesam or pistam, as in pancapatam sat.
ea pesam dindnam tava jivitasya, "the remainder of thy life is
fifty-six days," xii. 51. 14; pistam alpaih nah, "our life's rem-
nant is short;" pepesv anyesu kalesu "at other times, on remain-
ing occasions," i. 122. 26; pese, "as for the rest," apesatah,
"wholly" (without remainder). The participle is more com-
mon than the noun, varsani trlni pistdni, "three years remain,"
xv. 20. 32, and so often, especially with other participles, hata-
pistah, "those left from the killed," still alive, xii. 54. 5, etc.
The verb commonly used is My ate, "is less" (avapisyate,
"remains," avapistam= pistam), opposed to atiricyate "is
more;" samibhavati, "is equal" (equal in size is generally sam-
mitam) ; for ' ' equal " as quit, the same word, ubhayam tat saml-
bhutam, "both sides are quit," xii. 139. 24; equal, of scales,
tula me sarvabhutesu sama tisthati (samo 'harii sarvabhutesu),
xii. 263. 10. Compare xii. 176. 10:

akimcanyam ea rajyam ca tulayd samatolayam
atyaricyata daridryam rajyad api gunddhikam,

' ' I weighed in the scale poverty and kingship ; poverty having
more good qualities surpassed even kingship." The measure is
given by pramana, either of size (as usual) or of number, as in

1 Just before, the daeavarga is the group of imperial factors, but this
does not seem to be referred to in this verse. The king, sa, is expressly
mahotsdha and fond of military duties.

128 E. W. Hopkins, [1902.

xiii. 107. 32, lomnam pramdnena samam,

sc. rksacarmapatasya, (he is exalted in the Brahman world)
' ' equally (as to years) with the number of hairs " (of a hundred
bearskins). "Less" as inferior, secondary, is gauna (see the next
paragraph) .

MULTIPLICATION.

While the word for times in its literal sense is (-varam)
krtvah, pancakrtvas tvayo 'ktah, i. 197. 49 ; trihsaptakrtvah,
passim, the verb for times, multiply, is gunay, whence gunita,
multiplied by (the number preceding), literally "qualified." In
later texts, gunikrta, is used in just the same way, but in the
epic this word is, I think, used only in dvigunikrtavikramah
(Great Epic, p. 419). In the same way, gunibhuta is used in
later texts for gunita, multiplied, but in the epic it means infe-
rior (compare gauna), gunibhuta gundh sarve tisthanti hi para -
krame, "all qualities are qualified in (inferior to) valor," ii. 16.
11. But usually no verb is needed to express multiplication,
which as a f orma,l arithmetical process the epic has as little occa-
sion to make use of as subtraction. But the informal multipli-
cation of ordinary language, double, thrice, a hundred-fold,
without formal sums, is as common as in any other language,
and the times thus indicated is regularly expressed either by
simple juxtaposition of numbers, whereby, as has already been
said, one is uncertain whether addition or multiplication is
intended, as in pancapatam, one hundred and five or five hun-
dred, iv. 43. 6 (only the syntax sometimes shows decidedly, nard-
ndm pancapaficdpad esa pattir vidhlyate, ' ' a patti is reckoned as
five [and] fifty men," v. 155. 28) ; or by the noun guna, as in
satpira dvigunaprotrah, "having six heads and double as many
ears," iii. 225. 17; ekaikam trigunaih pardih, "each one (he
wounded) with three times the number of arrows " (each had
used), viii. 48. 70; tatah sastigune kale, "in a time sixty times
longer than that," xiii. 28. 10. In this last case the same idea
is expressed in the following stanzas without gtma, but perhaps
only because this word has been used several times already.
Thus in 11, tatas tu dvipate kalelabhate kandaprsthatdm, "in a
time two hundred (times longer) than that." As an adverb:
tatah patagunam duhkham idam. mam asprpad bhrpam, "this
grief has afflicted me sorely, a hundred times worse than that,"

Vol. xxiii.] Remarks on Numbers. 129

xi. 27. 33. In this use guna has ousted almost completely the
old vrt of trivrt, which survives only in a few hereditary turns.
A very uncommon equivalent is samkhya, as in xv. 3. 63, yasya
nagasahasrena patasamkhyena vdi balam, "whose strength is
comparable with a thousand elephants 1 a hundred times over "
(numbered a hundred). Between the qualitative and temporal
meaning, where the word is equivalent to krtvah, "times,"
lies the application found in ii. 24. 6, where, in a wrestling-
match, one is whirled about a hundred times, patagunam, a
description, by the way, copied in many details by the writer of
iv. 13, where cl. 36, for example, has the same expression.
Here dvigunam occurs in a physical sense also, rakso dvigunam
cakre, "he doubled that demon up," i. 163. 27 and elsewhere.

A combination of adding and multiplying, as in " more than
so many times that " is expressed by the gunated numeral (to
use this word thus) plus the word for "more." Thus, "he
gave them wealth more than five times what they had asked
him for " is prdddc ca dravinarn . . . yatho , ktavantas te tas-
mins tatah pancagunddhikarn, ii. 12. 15. Without "more":
yatho 'padistam deary dih kdryah paiicaguno rathah, " let my
chariot be furnished with five times (as many arrows) as the
teachers enjoin," vii. 112. 48; yatho, veda dvigunam vetsi,
"you know twice as much as he knows," viii. 32. 62. Here
partial correlation takes the place of the comparative (ablative)
idea. The more elaborate construction is also common, as in
xiii. 100. 7 : yathd ca grhinas tosah . . . tatha patagund prltir
devatdndm, " a hundredfold so great is the joy of the divinities
as is the satisfaction of the householder."

Sometimes, when the completion of the clause is easily under-
stood, it is left out entirely, and we find (of the ahlna sacrifice)
daksindm trigundm kuru, tritvarh vrajatu, "make the fee
threefold, let it reach treble," xiv. 88. 14, that is, make it three
times more (than ordinary).

Some curiously awkward methods of multiplying are found.
In i. 55. 2, after saying that Indra's sacrifices are a hundred in

1 So in using the ablative it is not necessary, any more than in Greek,
to be precise in the application of the case following "times that;"
acvamedhad dacagnnam phalam ahull, "they say the fruit is ten-fold
(that of) a horse-sacrifice," iii. 82. 37.

VOL. xxiii. 9

130 E. W. Hopkins, [1902.

number, samkhya, the poet adds: "But your sacrifice here, O
Bharata, is tathd param tulyasamkhyarh patam vai," which the
scholiast explains as equal to an ayuta of Qakra's (100X100),
hut perhaps only another hundred is intended. In xiv. 65. 18,
however, there is no escaping the awkwardness with which one
number is multiplied into another of a separate category. What
the poet wants to say is sixty thousand camels and twice as
many hundred horses, which he expresses by "twice as many
horses hundreds," sastir ustrasahasrani patani dviguna hay ah.
This is followed by tavad eva with the plural noun, pakatani
rathdp cafva tavad eva karenavah, that is, "just as much"
instead of "as many." So in iii. 281. 10-12, "fourteen crores
of Pieacas, twice as much of Raksasas, dvistavat (with genitive
and with kotyah supplied), and three times as many Yaksas,"
tatah triguna yaksdh. Similarly, ydvat tasya bhavet pustis tejo
(etc.), Krsne tattrigunam, "however much may be Arjuna's
prosperity, glory, etc., Krsna's is three times that," xiii. 148.
34. Ordinarily the numeral adjectives agree with the nouns
compared, as in iii. 122. 27, yavantah pdvakdh proktdh somas
tdvanta eva tu ; vii. 201, 59, sastim varsasahasrani tavanty
eva patani ca. A connecting link is furnished by tavat as part
of a compound yavanti tasya romani tavadyugasahasrani, iii.
200. 71, etc.

Another case of comparing numerically different sorts of
things is found in vii. 65. 9, but here the number is the same :
varksap ca yupa yavantah . . . te tathai 'va punap ca 'nye
tavantah kancand 'bhavan.

Distribution is expressed by repetition, with or without an
adverb: navame navame 'hani . . . dapahe vai gate gate, " each
ninth day ... as often as the tenth day passed," xiii. 107. 39,
43; trayanam mithunam sarvam ekaikasya prthak prthak,
"each one separately has two of the three," xiv. 18. 27. This
relieves one of the necessity of distinguishing between each and
all; for example, in xiv. 90. 34, kudavam kudavam sane vya-
bhajanta, "they all divided (so that each' obtained) one
kudava ;" iii. 124. 21, catasrap ca 'yatd danstra yojanynam
patam patam, " four fangs extending a hundred leagues each."
But ekaika is usually expressed, as above and in ii. 52. 21, dat-
tvai 'kaiko dapapatan kunjaran, "each giving ten hundred
elephants." The noun used alone may be singular, jatamjatarh

Vol. xxiii.] JRemarks on Numbers. 131

ca sdputram ksipaty ambhasi, "she throws in the water (each)
son when born," or -plural, jdtdn jdtdn praksipd 'smart, (putrdn),
i. 98. 13 and 99. 43. The verb may agree with the singular:
ekdikas te tadd pdpdh kramapah parimoksyate, xii. 227. 116,
perhaps only metrical, as in the same chapter pocimi for pocdmi,
cl. 88. The late derivative ekdikapyena is found in xii. 326.
38, tad antahpurakdnanam suramyam darpaydm asur ekdika-
pyena (here the grove opens out from the third kaksyd of the
palace).

With adjectives the cardinal stem prefixed multiplies the
adjective, caturbhadrataras 1 tvayd, "four times as happy (com-
pared) with you," in vii. 55. 49. and xii. 29. 30, two scenes
where all the "kings that died" are spoken of at length in two
different but related accounts, of some value for the history of
the epic. 2 In vii. 70. 25, the phrase is intensified: caturbha-
drataras tvayd bhadrapatddhikdh.

Finally, there is the multiplication expressed by dhd as an
ending, which gives not only the times of division and conse-
quent multiplication of parts, and time literally, ekadha, "at
one time," but also the multiple times in numbers, saptadhd,
"seven times (over)." Sapta tridhd is thus equivalent to sapta
trigundni. In xii. 223. 22, the Gandharvas dance sat sahasrdni

1 The instrumental is not so very rare. Compare eko hi bahubhih
greydn, "one (sage) better than many" (fools), iii. 99. 22; ko riu svan-
tataro maya, ix. 64. 21 ; sa 'fd krgatari mayd, xii. 128. 14 ; durmarsar^a-
taras tvayd, xii. 227. 81. The ablative is used after a positive, mama
balam bhlmam vdyor api, " my strength is greater than the wind," xii.
155. 6. One case expresses comparison, the other the distance from,
sukhdt sukhataram prdptah, "coming from joy to more joy," xiii. 119.
11. The ablative is found with only an implied comparison, rdjydd
devatvam icchanti, "they wish godship from kingship," xii. 180. 20,
leading to preference (vrne and abl. ; also greydn daho na bhaksanam, i.
230. 21, etc.; Holtzmann, §292 b). Noticeable is the double ablative
showing clearly the construction's origin, svavlrydd rdjavirydc ca sva,
vlryam balavattaram, "from (of) his own and a king's, his own power
is stronger," xii. 165. 18. Holtzmann, at §281, gives a few more exam-
ples of the instrumental. To the gen. comparat., my Great Epic, p.
473, add maranam gobhanam (—varam) tasya, i. 79. 13.

2 The introduction of the former is in the latter put at the end of the
account and the latter omits the second Rama, which completes the list
of sixteen in Drona. Bhara,ta, too, changes places, being the antepe-
nultimate king in Qanti but the fifth in Drona, which has several later
features.

132 M W. Hopkins, [1903.

saptadha, literally in seven groups of six thousands, or seven
times six thousand, that is, a not unusual amplification by a
sacred multiple of an old group, for the Atharva Veda, xi. 5. 2,
gives the same conventional satsahasrdh, though here three
hundred thirty-three are added. The epic itself gives to the
Gandharvas another conventional number at iii. 139. 6, where
they are eighty -eight thousand in number and the Yaksas are
four times as many, astdpitisahasrani Gandharvdh . . . Yaksap
cdi '«<$ caturgundh. Another example is furnished by the list
of Munis in seven groups of seven each, at xiii. 151. 42: ity ete
munayo divyd ekdikah sapta saptadha, etc. , ' ' seven, one by
one, reckoned sevenfold " (a different account in xiii. 166. 37 ff.).
Compare also saptadha sapta saptasu ; janma saptadha, xiv.
20. 23 and 27. The number of times a multiplied god appears
is often expressed thus, as when Rudra, kind and terrible, one-
eyed and three-eyed, appears as ekadhd, dvidhd, bahudhd,
patadhd, sahasradha, patasahasradha, xiii. 161. 43. One of
his forms, by the way, is dhumra, which gives, it is said, his
name of dhurjati(n) , a title found only here, xiii. 162. 9, and
vii. 202. 129, two passages of the saine period and content, a
late epic " Catarudriya."

DIVISION.

Halving is expressed by dvdidhlbhu or -Tear or dvidhdkar •
other divisions by tridhd (trdidham), caturdhd, and so on, with
har or vibhaj, e. g., dapadhd hdryam pesam, "the remainder
is to be divided tenfold;" dvidhd krtd jihvdh, ("therefore the
snakes') tongues were cloven," i. 34. 23 (dvijihvdp ca hrtdh,
24) ; gavdth dvdidhlkrtah hhurdh, hhurdn dvidhd , karot,
" Rudra clove the hoofs of his bull and other cattle," viii. 34.
105. The half, ardha, is used no more with nouns than with
participles: ardhdsanam labdhavdn, "he got half of Indra's
throne," iii. 126. 38; ardhacyutdsandh, "half flung from
their seat," vii. 196. 15; also of course with other numbers.
With words of time, ardha follows or precedes in masd-
rdha, ardhamdsa, and means either the middle (of day or
night, ardhadivasa, -rdtra) or half: ardharatrasamaye, "at
midnight" (so passim) ; yady ardhadivasam yudhyate, "if he
fights half a day," vii. 190. 46 {ardhadivasam gatvd, "going
half a day," R. vii. 46. 24).

Vol. xxiii.] Remarks on Numbers. 133

Besides ardhamasa, "a month and a half" may of course be
expressed in full. Thus, where ma is used exactly as in ma
dram, in iv. 21. 17, ma dvrgham ksama halam tvam masam
ardham ca sammatam, "have patience for a short time, a
month and a half" (=sdrdha).

The use of ardha with other numbers shows that, as in the
case of two numbers joined and indicating that the former influ-
ences the latter without specifying how (e. g. dapapata=110 or
1000), the prefixed ardha modifies the word with which it is
connected, but does not specify whether by addition or sub-
traction or ' multiplication. So ardhapatam is one hundred
modified by one half, just as ekapatam is one hundred modified
by one, and the hearer is left to determine whether this means
half a hundred or one hundred plus a half (hundred). With
other fractions, however, there is understood a conventional
modification of subtraction. Thus " half -fourth " is always (as
adjective) three and a half, that is four as modified by a half.
For example, up to two and a half koss is "to the half -third
koss," i. e. to the third koss as modified by a half, kropad
ardhatrtlydt. '

When not defined, bhdga and anpa, "part," mean a quarter,
catitrbhdga=pdda, a (fourth) part (of a quadruped). For three
quarters is used either "three quarter parts" or "three parts."
The usual meaning of "three-part," tribhdga, is one third, but
it occurs also in the later epic (as in still later literature) in the
meaning of three quarters. For other divisions, the part is

made explicit, apltibhdga, -fa, etc. Only hold is almost always

i

16-

iii. 190. 10, (krte catitspad dharmah) adharmapddaviddhas tu

tribhir ancdih pratisthitah;
ib. 11 and 12, tribhir anpdih, caturthdnpena.

In the pseudo-epic, the same situation is expressed by pddono
dharmah (in Treta), dvipdda, pada {adhare yuge), to which is
added the unique idea that even this quarter in Kali is so dimin-
ished as to leave one sixty-fourth, bhavet kdlavipesena hold
dharmasya sodaph, xii. 268. 33-34 (caturthanpa also xii. 283. 51).

1 The passage is cited in full on p. 147, below. I fail to understand
Speyer's explanation, S. Syntax, § 301, that ardhatrtlya in such a case
means " having the third being [but] half."

134= E. W. Hopkins, [1902.

ii. 68. 78, ardham harati vdi gresthah pddo bhavati kartrsu.

iv. 52. 17, balacaturbhdga, "one fourth the army."

xii. 24. 12, dddya balisadbhdgam yo rdstram nd 'bhiraksati
pratigrhndti tatpdpam caturanpena bhumipah.

ii. 5. 70,

kaccid dyasya cd 'rdhena caturbhdgena vapunah
pddabhdgdis tribhir vd 'pi vyayah sam$nddhyate tava,
"are your expenses covered by a half or a quarter, or
at any rate by three quarters of your income ?"

vii. 186. 1,

tribhdgamdtrapesdydm rdtrydm yuddham dvartata,
"the battle was renewed when one third the night was
left."

vii. 191. 9,

tasya cd 'hnas tribhdgena ksayarh jagmuh patattrinah,
" in the course of one third of that day."

The "third" may of course be expressed, as in xii. 285. 23,
labheta bhdgam . . . ardham tathd bhdgam atho trtlyam. In xiii.
168. 28, tribhdgapesa means "having three quarters left."

In i. 96. 21 (as ardhdrdha still later means a fourth) one
eighth is expressed by "half a fourth," turly ardham pradds-
ydmo vlryasydi'kdikapo vayam, "we shall severally give a half
of the fourth of our power," said by the eight Vasus. It is
rather remarkable that Krsna is described in xii. 281. 62 as this
fraction of God: mulasihdyl mahddevah . . . tatsthah srjati tan
bhdvdn . . . turlydrdhena tasye 'mam viddhi Kepavam.

When quarters are mentioned, as when Ori is quartered,
caturdhd vibhaktd, and the quarters are enumerated, the first is
pdda alone, the others are dvitlya, trtvya, caturtha, pddas, xiii.
225. 19 ff.

According to the commentator, triguna, threefold, like tri-
bhdga, also means one third in v. 55. 66, where, after eleven
armies have been contrasted with the seven which in comparison
are called nyundh, "deficient," the deficiency is declared to be
great enough to warrant a battle, for

balath trigimato hinam yodhyam prdha JBrhaspatih
parebhyas trigund ce 'yam mama rdjann anlkim,

whereto N. remarks that the adverb means (deficient) by a
third, tryanpena, and the adjective "a third more." And cer-

Vol. xxiii.] Remarks on Numbers. 135

tainly if number is implied at all, eleven are not thrice seven but
may be loosely reckoned as a group of three fours, deducting
one of which would leave seven, so the "deficient" host would
be "a third less" and the host of eleven would be "a third
more " (measured by itself) . There seems, however, to be a
conscious play on words here, for in the next stanza the "defi-
ciency," nyiinatd, is explained as giinahlnam or a moral lack.

In vituperation, which exercises the epic poets a good deal, it
is customary to say that an opponent is not worth a half, a
quarter, or a sixteenth of the other man. In praise, on the other
hand, one says that the object of praise is worth one and a half
of the other. One sixteenth, expressed either as "sixteenth par-
ticle " or simply a particle or a particle-part, denotes the smallest
part usually taken into account. The word gives the last
imperishable fraction of the moon visible before it disappears
(xii. 305. 4, so the pure soul, kola suksmd, ib. 6 and 335. 40).
The adjective full is sometimes added to the part. Twice this
fraction is exceeded, once by saying that one eighteenth will not
express the relation of inferiority, once by descending to one
hundredth part to express contempt. Apart from vituperation,
the "sixteenth particle" is employed in a few old phrases. It
is found also in Manu and in Buddhistic literature. Examples :

i. 100. 68, agnihotram tragi vidyd santdnam api ca 'ksayani
sarvdny etdny apatyasya kaldm nd 'rhanti sodapim.

ii. 41. 27, istam dattam adhltam ca yajnap ca bakudaksindh
sarvam etad apatyasya kaldm nd 'rhanti sodapim.

iii. 91. 23, na sa Pdrthasya samgrdme kaldm arhati sodapwi.

So iii. 174. 3; 254. 27; 257. 4 (your sacrifice is inferior); vii.
36. 7 (the army); vii. 111. 30 1 . With purna: iv. 39. 14, na
ca 'rjunah kola purna"" mama, "Arjuna is not (as much as) one
whole (sixteenth) part of me;" v. 49. 34, nd ''yam kald 'jri sarn-
purnd Pdndavdndm, "he is not even one whole (sixteenth) par-
ticle of the Pandus." So in vii. 197. 17,

yah kaldm sodaclm purndm Dhanamjaya na te 'rhati.

1 In the next stanza, nd 'lam Pdrthasya samyuge (rare genitive), " not
equal to."

8 So I read (compare the next citation). PW. accepts the text, kald-
purno, s. v.

136 E. W. Hopkins, [1902.

In viii. 15. 28 it is said, "all weapons are not worth a sixteenth
part of him." As an equivalent of ^, prastha (^ of a measure)
is used where it is appropriate, xiv. 90. 7, "this sacrifice is not
equal to a prastha of grain of (given by) a man living by glean-
ing corn," saktuprasthena na tidy ah.

In religious writing, besides the phrase above is found a
(Buddhistic) comparison, repeated, xii. 174. 46 ; 177. 51 ; 277. 6 :

yac ca kamasukham loke yac ca divyam mahat sukham
trsndksayasukhasydi He na 'rhatah $odaclm kalam.

This stanza is in fact attributed to the same Buddhistic king
who sings of his happiness in having nothing, and it is associated
with that famous stanza in the last two passages. In the same
way is used kola alone :

apvamedhasahasrasya vdjapeyapatasya ca
yogasya kalayd tdta na tulyam vidyate phalam,
xii. 324. 9 (a Yoga improvement of Spruch 791).

I have found the ' ' sixteenth " phrase but once in a tristubh
stanza, with a slight alteration in form and sense (truth sur-
passes all possessions) :

iii. 34. 22, rajyam caputrdp ca yapo dhanaih ca
sarvam na satyasya kalam upditi.

A curious account of the distribution of the world's wealth in
vi. 6. 23 asserts that Kubera has one quarter of the valuables
of Meru, out of which he dispenses one particle-part to mankind,
equivalent to one sixty-fourth of all, as in the case of Kali's
virtue (above) :

tasmdt kubero bhagavang, caturtham bhdgam apnute
tatah kaldnpam vittasya manusyebhyah prayacchati.

Examples of other fractions in scorn: i. 201. 13, (yuddhe)
Uddheyasya na padabhak, "not worth a quarter of him;" iii.
253. 9, na ca 'pi padabhak Karnah Pdndavdndm (dhanurvede) ;
vii. 76. 1, tesdrk viryam mama 'rdhena na tulyam, "their
power is not equal to half of me;" xii. 155. 6, kalam astadapim 1
pranair na me prapnoti marutah ; x. 12. 17, na samd mama
vlryasya patdnpend 'pi pinditah, "they all together are not
equal to one hundredth part of my power."

1 This -j^ for the older iV is a pseudo-epic alteration of the old phrase.
It occurs in the Wind and Qalmali fable.

Vol. xxiii.] Remarks on Numbers. 137

A back -handed boast of Karna, which, I think, the poet
intentionally makes incoherent, is that of viii. 43. 9, rte Qalya-
sahasrena vijayeyam aham pardn, "I could conquer the enemy
without (the help of) a thousand Calyas," i. e., "I am equal to
a thousand Calyas," or rather "without 9m a thousand times
over." Qalya mockingly replies that Karna talks nonsense;
whereupon Kama returns "more and double abuse," parusam
dvigunam bhuyah.

On the other hand, in lauding a friend, one and a half is the
norm of comparison, as in the following examples :

vii. 72. 34, mayo, ' ' dhyardhagunah (putrah), "my son is
equal to me one and a half times over " (some-
times simply ' ' equal to me ") .

xi. 20. 1, adhyardhagtmam ahur yarn bale . . . pitrd tvayd
ca, "who in power they say is equal to one and a
half times his father and you" (Krsna!). But the
comparison, too, is once used scornfully :

ix. 33. 19, adhyardhena gunene 'yam gada gurutarl mama
na tatha Dhartarastrasya, "this club of mine is
one and a half times heavier than that of D."

Apart from this belligerent use, one and a half is used of
measurement of numbers, i. 1. 103, adhyardhapata, "having
one hundred and fifty;" of land, viii. 88. 10, adhyardhamdtre
dhanusam sahasre, " on (land) measuring one and a half thou-
sand bow-lengths;" v. 8. 2, tasya sendnivepo '■bhud adhyardham
iva yojanam, "his camp was about a league and a half."

In reckoning interest, pddikam patam is twenty-five per cent. ,
but the verse in which this occurs, ii. 5. 78, padikam ca catam
vrddhya, dadasy rnam anugraham, has a varied reading, praty
ekam ca patam (metrical for prati patam ca ekam) . '

As observed above, the current words for fraction are pada,
bhaga, and anpa. In xiii. 26. 97, appears in this sense ekadepa,
a single part of a whole : udahrtah sarvatha te gunanam mayai
'kadepah . . . paktir na me . . . gunan sarvan parimatum, "a
single part of (Ganges') virtues I have told thee, I cannot count
them all."

1 The later epic, by the way, has two coins not previously recognized,
besides the Roman denarius (implied), namely, the kakint and as{dpa-
dapada (a gold karsapana), xii. 294. 16 ; 299. 40.

138 K W. Hopkins, [1902.

DIMENSIONS, TERMS, VALUES, SYNTACTICAL CON-
STRUCTION.

The usual dimension, parimdna, mentioned in the epic is
length, and with few exceptions distance (length) or height is
the pramdna, a general word for size and extent. Certain
measurements are made in the case of the few small things
measured, hut short distances are loosely cast in such forms as
"near by," "not far," "within sight," or "within hearing,"
and indefinite smallness of extent in the same natural manner is
described as "not an atom," "nor a bit," etc.

Distance: tesdth sampravane, "within hearing of them," xv.
18. 21 (ib. 20, aviduratah, "not far off," like samlpatah,
"near," with genitive; also with ablative, na 'tidurena naga-
rarh vandd asmdd dhi laksaye, i. 151. 44; avidure vandt, 152.
1; na duram vanat, 154. 35; abhydpe, 156. 10, "in the neigh-
borhood"); dpramam prati, utsasarja garbham, i. 8. 7, "near
the asylum " ; also antikam and antike, according to the verb.
In the case of sakapa, "with (in) sight," proximity, the original
sense in many cases has well-nigh disappeared, mdtuh sakdpdt
(am pdpam prutvd, "hearing of the curse on the part of his
mother," i. 37. 1.

The Ramayana has another, more modern, phrase to indicate
proximity, namely mula, as in aham gamisydmi Yamasya
mulam, v. 28. 17; mama mulam, ii. 64. 49, which belongs
rather to Puranic than to epic diction.

Extent: na tasydh suksmam api, "no (superficial) atom of
her," i. 211. 16; na tasya kdye antaram, "no space on his
body," iii. 21. 7; hayandm na 'ntaram, "no interval between
the horses," iii. 172. 6; chidram na rathayoh, "no chink
between the two chariots," i. 226. 3. Indeterminate size is
given by compounds, much as in English, gaja acalasamkapdh,
"mountain-size elephants," xv. 23. 9, etc.

The verb extend, dyam, is used of extending a circle, syn-
onymous with utsarj, mandalam utsrjya, v. 195. 15. The cir-
cumference is, par indha, the diameter, viskambha. To express
the idea of equal distance from a center, the term usually em-
ployed is samanta, "on every side," in adverbial form, vedi
samantdt pancayojand, "five leagues on every side," iii. 129.
22. Generally, the geometrical figures implied by battle-arrays,
called vyuhas, are described in figurative language, as a bird, a

Vol. xxiii.] Remarks on Numbers. 139

needle, a dolphin, and the troops are stationed on the beak, tail,
and wings. Thus karna, ear, becomes "corner" in vi. 60. 10,
oaticpcaturvyalasahasrakarnah, "(an array) with four thousand
elephants on each corner" (N. karnesu vidigbhagesu). But
there is a peculiarity here in that no figure has been mentioned,
and according to the account this array should be like a former
one of crescent shape with two horns, pruge, but, not to speak
of the plural, we cannot take this statement too literally, and I
do not know that karna is even cornu.

A prhgataka, named from a triangular nut which has
"horns," is used to describe one of these vyuhas in vi. 87. 17,
and may be a triangle, though here also the scholiast gives the
usual epic meaning "shaped like a four-road place," just as at
iv. 68. 25, catuspatha, etc. A triangle is trikona, rplywvos,
(triguna), of the garuda, late, as explained in my Great Epic,
p. 372. A city square is a "four place," catvara, xii. 69. 52,
squares and markets being mentioned together in descriptions
of cities. In xii. 73. 21, in antithesis to the whole, krtsna, city,
this word may mean as in English a town-quarter; but in xii.
86. 8, catvarapanapobhita is simply "beautified by squares and
markets." The "four" of a square is used also to give the idea
of a four-square house, catuhpdla, and anta, boundary, is also
used to imply a square, as in dapakiskitsahasranta, of a hall,
"ten thousand cubits square," a meaning made clear by a paral-
lel passage, where samantat, "on all sides," is expressly added,
ii. 1. 21; 3. 23, and no circle can be intended. Earth, catur-
anta, "has four boundaries," that is, it is bounded by the
"four seas." In xiv. 64. 10, a camp is satpada or satpatha
(and navasamkhycma or samsthana), with three streets running
north and south and three east and west, according to the
scholiast; but in xv. o. 16 he explains satpadam puram as hav-
ing six (traversable) places within the seven walls (up to the
inner city), which is not a likely meaning, since the word is fol-
lowed by sarvatodipam, "in all directions." Octagonal is astti-
pri and other numerals are used with the same word, but only
of edges, eight-edged posts and clubs.

Land is measured by bow-lengths (above), and by cow-hides,
api gocarmamatrena bhmnidanena pity ate, "purified by giving
even a cow-hide measure of land," xiii. 62. 19; and the length of
a cord is measured in the same way, na tarn vadhrt parina'hec

140 E. W. Hopkins, [1902.

patacarma, "a cord of a hundred hides could not encircle it," i.
30. 23. A "span of land" and "as much land as a needle's
point could cover " are contemptuous terms.

From these general methods of measurement I turn to the
more exact specifications found in the epic, arranging them on
an ascending scale of comparison, from the "smallest finger"
to the indefinite yojana, which is best rendered league, because
its length varies like that of a league, while it approximates
most closely to the three-mile league, though it ranges from that
extent to about ten miles, according to later authorities; but
nothing in the epic determines its length.

Finger-measurement : A thumb-joint serves as the meas-
ure of a small bit in general, aiigusthaparvamdtrd garbhdh, i.
115. 20, and " thumbkin " spirits are perhaps conceived as being
of thumb-size in relation to breadth as well as height. God
himself, as a spirit, is measured by the size of a thumb-joint,
hrdayam sarvabhutandm parvana 'ngusthanidtrakah, xii. 313.
15 ; as all spirits are described as angusthamatra, thumb-size. ' All
shortest measured distances are calculated by this norm, usually
by twos and fours, the application showing, however, that
"two thumbs" and "four thumbs" refer to thumb-breadths.
Thus there is a stereotyped battle-phrase, na tasya , sld anir-
bhinnam gatre dvyangulam antaram, "there was not an
unwounded space of two thumbs on his limb," vi. 119. 86; 175.
54; iv. 55. 5 (v. 1.) ; xii. 77. 27. The same phrase is found in
R. vi. 45. 20, with the verb of the Virata passage but with only
one "thumb": na hy aviddham tayor gatre babhuva , ngidam
antaram, perhaps to be corrected as in Mbh. Earth is flung up
"four thumbs," caturangulam, by a chariot, viii. 90. 106. In
a late scene, Yudhisthira's chariot floats four thumbs from the
earth, prthivyap caturangulam ucchritah, vii. 190. 56.

The " littlest finger " serves as a comparison in the descrip-
tion of xii. 127. 7-8 (Tanum) :

anyair narair mahabtiho vapusa 'stagundnvitam . . .
parlram api rajendra tasya kanisthikasamam,

"eight times in shape compared with other men (i. e. eight
times as tall), 2 the body being (slender) as the littlest finger";

1 References in my Great Epic, p. 32.

2 A man's height is often given by saying how many cubits he has (as
below). For tall and short are used praiicu and hrasva, respectively,

Vol. xxiii.] Remarks on Numbers. 141

where the poet has to change the regular form of the word kan-
isthikd on account of the meter. I do not know whether in i.
52. 7, snakes that are the size of a gokarna, in antithesis to
those that are leagues long, gokarnasya pramanatah, kropayoja-
namdtrdh, are imagined to he the length of a gokarna-nrrow or
of a thumb-and-finger-span, a late meaning of the word. When
subsequently re-described, they are yojandydmavistard (also a
Ramayana phrase) dviyojanasamdyatdh, i. 57. 23, that is, meas-
ured hy leagues only.

Hand and span : The triangular altar referred to above is
described as "of eighteen hands," astddapakardtmakah, xiv.
88. 32. The hand, however, is usually reckoned as a two-span
cubit and not as a hand-length. Probably the "hand-tip"
gives a double-span, for in the description of a slender woman
it is said that her waist measures "a hand-tip," kardgrasamrni-
tam madhyam, iv. 13. 22. So in xi. 18. 5, anavadydiigl kara-
sammitamadhyamd, "of irreproachable form, measuring a
'hand' about the waist." This measurement shows that the
kara is equivalent to the hasta, a synonymous term, and equal
to about a cubit (eighteen inches nominally, but perhaps only
about sixteen) , ' ' eighteen inches round the waist " being (as I
am informed) the boast of slender maids to-day, and Hindu
women being petite. Double this length, two hastas, is given
in Hindu tables as the circumference of a man's body, about the
average thirty-four to thirty-six-inch waist.

The span, prddepa, is used of the measure of the breast about
the spirit: prddeparndtre hrdi nihsrtam yat, "what is made
manifest in the span-measured breast," xii. 246. 28, that is, in the
vital circle, measured as twelve thumbs in extent from the cen-
ter; a late view if this reading be accepted. 1 Elsewhere the
prddepa is mentioned a few times in the epic, but never in such
a way as to betray what is meant. It measures, for example,
the difference in height between the Pandus and other men, and

jajrle gdilagurufy prangur mahimna prathitdfy prabhulj,, ix. 51. 34; the
fever born of Qiva's sweat is a hrasvo 'timatram ("excessively short")
devil, xii. 284. 40.

1 Beading pradeQamatram we should have a reflex of Chand. v. 18. 1;
Maitri, vi. 38. The Aditya Purana, cited by Colebrooke, Essays, vol.
i. p. 539, says that Vyasa makes the pradeca only one thumb-breadth,
and not ten or twelve, as taught by others.

142 E. W. Hopkins, [1902.

between Bhlsma and Arjuna, for "Bhlsma in size was more by
a span than Arjuna," pramanato JBhlsmasenah pradepend
, dhiko i rjundt, v. 51. 19, and (the same expression except for
the instrumental case) in v. 169. 8, the Pandus are a span taller
than all others, prddepend 'dhikdh pumbhir anydis te ca pramd-
natah.

Another word for span is vitasti, whence the arrows "called
span-long," vditastikd ndma, used only by special warriors at
short distances in the descriptions of the late seventh book and
nowhere else till they are met with again in the Harivanca and
in the later Ramayana. Thus in vii. 191. 42 and in R. vi. 49.
49 of the Gorresio edition, but not in the Bombay text. This is
one of the many little indications that show how close Drona
stands to the latest additions made to the epic. On the other
hand, it helps to a terminus ad quern to find that husta is never
used for a measure in the epic, though common in the Puranas,
and reckoned as two vitastis or twenty-four thumb-breadths.

Cubits : The cubits mentioned are kisku, in vii. 134. 10, "a
club of four cubits," and ctratni, in i. 167. 25, "a bow (of
Drona) of six cubits " (catuskisku and sadaratnidhanuh, respec-
tively, as possessive and determinative compounds). Post-epical
authorities (cited by Colebrooke) make the aratni equal to
twenty-one thumb-breadths, and two aratnis are one kisku;
though some reckon a kisku as equal to four cubits. In vii. 175.
19, both these names, as if synonymous, are united in the
description of a demon's bow, "a twelve-cubit-bow a cubit
round," vyaktam kiskuparlndham dvddapdratnikdrmukam.
Arjuna's bow, i. 189. 20; v. 160. 108, is as long as himself, tola-
mdtra, "palm-tree tall," a common though indefinite measure,
which according to i. 197. 39 is the height of all the Pandus.
The five-cubit (kisku) bow of x. 18. 6 is allegorical but may
indicate the usual length. Arrows are " axle-long," aksamdtra,
passim, and the afijalika arrow mentioned in viii. 91. 41 is three
cubits, tryaratni. A later form, ratni, is used in this same book.
Here, viii. 72. 30, it is said that Karna was astaratnih, "eight
cubits" tall (in iii. 126. 32 a man "grew thirteen cubits," avar-
dhata kiskun trayodapa, but he was Mamdhatar, and enjoyed
peculiar nursing). We might almost suppose that this so-called
cubit, whether kisku or aratni, was really a foot, or about
twelve inches instead of eighteen. For the actual length of

Vol. xxiii.] Remarks on Numbers. 143

Hindu bows and arrows are for the ordinary bow five feet and
for the ordinary arrow two and a half to three feet (Ruling
Caste, pp. 270, 276), and both five and six " cubits " are the size
of the epic bows, while the one arrow measured is given as three
cubits, the heroes being a little above but not much over the
normal height and only Karna being of eight ratnis. Even he
is not extolled as a giant, as a man of eight cubits would be.
"Palm-tree tall" and another phrase used of the heroes, pala-
stambhd ivo , dgatdh, "lofty as Qal trees," v. 169. 7, are more
grandiose than exact. As the later schemes reckon the cubits
in thumbs (or fingers), the twenty-one and twenty-four thumbs
that go, respectively, to an aratni and hasta must be estimated
by the size of a Hindu hand, which at present is rather small.
Further, the relation between thumb-joints and span, reckoned
as from the end of the thumb to the outstretched fore-finger, is
given as twelve, which is too many, for the distance corre-
sponds rather to the relation between the span and the finger-
breadth. Reckoned as eight inches, a normal span, the later
cubit would be nearer sixteen than eighteen inches and the
ratni, being still shorter, would not be much over a foot.
According to the Sucruta, a man's height is one hundred and
twenty thumbs, i. 126. 11, or ten spans, which at nine inches to
a span would make the average Hindu seven and a half feet tall
and at seven inches would still make him nearly six feet.

Foot and Pace : The measure by foot-pace is almost con-
fined to a conventional "eight paces," paddni, often used in
battle-scenes, but always, if I am not mistaken, in the same way,
dplutya, or abhyetya, padany astdu, as in vii. 15. 28; ix. 12.
20. Even a deer "went eight paces and then turned," tatah sa
harino gatv a padany astdu nyavartata, xii. 273. 14. Accord-
ing to the Markandeya Purana, cited by Colebrook, Essays,
vol. i., p. 539, a pada is a foot-breadth and not a pace, being
only half a vitasti span or six fingers (thumbs). In the epic, as
in "seven paces" in the marriage-rite, and in the colloquial
phrase pade pade, "step by step," the word means a general
pace-length or step. " Not a step " is almost equivalent to the
French ne pas; for example, na 'kampata padat padam, "he
did not budge a step" (at all), a common phrase, as in ix. 57.
46. The later epic has padakam padakdrh pandih, " step by
step, slowly," xiii. 53. 35, and another passage has ekapadam
in the sense of "in one word," iii. 313. 69.

144 M W. Hopkins, [1902.

Arms and fathom : Estimated at four or five cubits in
later works, the vydma, space between the outstretched arms,
is used a few times, but only of trees and sacrificial appurte-
nances. A bough dapavydma, ten vyamas long, is mentioned
in a repeated phrase, iv. 23. 21, etc., and a vedl dapavydnidyatd
navotsedhd, "ten vyamas long and nine high," in iii. 117. 12;
while the circumference of a sacrificial post, as made in the good
old days of marvels, is given as one hundred, yupah patavyd-
mah parindhena, vii. 68. 12. The divine discus of Krsna is
vyamantara, which the scholiast says is "five cubits, the space
between the outstretched arms," prasdritayor hastayor ydvdn
vistarah pancahastamitah tdvat, v. 68. 2. It may be called in
general (cf. Qat. Br. i. 2. 5. 14, etc.) a sacerdotal measure, not
employed in the tables, and, except for the measurement of
trees, it keeps this character in the epic.

Rods and Bows : Another sacerdotal implement was the
pamya rod, the cast of which, according to the epic, measures the
interval between the altars set up by a very pious man. The rod,
according to the scholiast, is pointed at one end and has a thick
knob at the other, and is thirty-six thumbs, two and a half stat-
ute cubits, in length. When one " sacrifices by the rod-cast,"
one goes around the earth sacrificing at intervals, which are
measured by the distance a strong man can fling the rod, pamyd
in the epic, or, according to the scholiast, sampd, from its fall,
sampatati. The technical expression is pamydfcsepena (vidhind)
or pamyaksepaih (devdn yajati), "sacrifice to the gods by the
cast of the rod," iii. 90. 5; xii. 223. 24; xiii. 103. 28. The
only varying usage is found in iii. 84. 9, where a Tirtha is
described as being "six rod-casts from an anthill," satsu pam-
ydnipdtesu valmlkdt, but this is still in a sacerdotal connection.
Measure by arrow-casts is confined to estimating time, as will
be shown hereafter.

Bows are used for measurement, but the epic examples give no
clue to the length, though later authorities reckon this as equal to
a staff, danda, or four cubits, which must be regarded as the
length of a bow (six feet). In the three epic cases, two forms
of the word are used, dhanus and dhanu: " dragged eight dha-
nunsi, i. 153. 40; "struck ten dhanvantardni" viii. 83. 9;
"land measuring one and a half thousand of bows," dhanusdm,
viii. 88. 10 (cited above, p. 137).

Vol. xxiii.] Remarks on Numbers. 145

Yuga : This is said to be a measure of four cubits. In iii.
296. 10, yugamatrodite surye, "when the sun is up a yuga"
(N. yugarh hastacatuskam) , when the matutinal-rites are per-
formed (krtvd pdurvdhniJcih Jcriydh). I have not found the
word elsewhere in this sense, and as a measure it does not appear
to be an old term.

Nalva : I am not aware that the nalva or nala is an early-
term of measurement. In the great epic it is confined to the
seventh book and to the mass which I call pseudo-epic, espe-
cially to the Harivaiica. It is, further, not in the Ramayana
in its earlier form but it has been added to it in the later re-writ-
ing of that poem. The word epitomizes the gradual growth of
the epic. The Bombay text has nala and nalva, but not with-
out metrical reason for the choice. We find in vii. 70. 16 (the
latest addition to the chronicles of kings), vedlm astanalotse-
dhdm, which is repeated in xii. 344. 60. In the former case it
is defined by the scholiast as four cubits; in the latter, as a
finger, with tala as v. 1. Again, vii. 156. 58, mahdratham
trinpannalvdntardntaram, and, in a scene which in many points
is a mere repetition 1 of this, vii. 175. 12, nalvamdtram maha-
ratham, which is repeated in 176. 15 (written nalla in these two
verses in C), but nowhere else till we get to xii. 29. 143,
where, also in the chronicles of the "kings that died," we find
that Prthu Vainya gave to the priests hdiranydns trinalotsed-
han parvatdn ehaving,atim. It is interesting to see that the
Drona account of the " sixteen kings," in adding the sixteenth,
has taken from Prthu this laudation and inserted it in the next
and last (lacking in Qanti). i n v ii # g2. 13, the phrase is hair-
anydn yojanotsedhdn dyatdn patayojanam, giving height and
length. In the cases cited it will be observed that nala is not
simply a falsche Schreibart (PW.), but a necessary metrical
alteration (nalla alone being wrong). In xii. 154. 7, a tree is
nalvamdtraparlndhah (where N. defines the measure as hastd-
ndm fatacatustayam, which removes the doubt expressed in
PW. as to catuhpatam), "four hundred cubits in circumfer-
ence " (this attributes the greatest circumference to the tallest

1 It repeats the preceding text, but adhyaya 175 is the original.
Besides the one nalva raised to thirty in 156, we have the cakra, which
in 175. 46 has still only 1000 spokes while in 156. 77 it has 100,000.

vol. xxiii. 10

146 M W. Hopkins, [1902.

tree known, the pdlmali). A Kalamra tree is yojanotsedhah, vi.
15 (not a Dvipa, PW., but a tree that gives perpetual youth).
A following stanza tells of another wonder-tree, estimated as
being one thousand and one hundred leagues tall, which meas-
ures the utseclha or height from earth to sky, vi. 7. 21. Its cir-
cumference is "of aratnis one thousand and hundreds ten and
five" (2500 cubits).

KrO£a : The kropa, Anglo-Indian koss, which means literally
a "scream" and is estimated in later works as two thousand
" bows " or a fourth of a yojana, is the usual number to indicate
travelling distances, not in multiples but always as a koss, as if
one always went just one koss unless he went at least as much
as half a yojana (rare, ii. 2. 22, yojandrdham atho gatvd, in
accompanying a departing guest) or a yojana, which latter is
used for all long stretches. The almost universal use of yojana
for this purpose rather than two or three koss would indicate
that the yojana was shorter than is usually assumed. It is not
often that a koss indicates height, but the examples below will
show one case of mountains thus measured. For journeys,
besides the use of the half-league in the example just given
and the league, as in vii. 112. 12, itas triyojanam manye tarn
adhvanam . . . yatra tisthati, "I think it is a course of three
leagues from here (to) where he stands," we have in the follow-
ing examples the regular (single) koss: iii. 271. 53, kropamd-
trdgatdn apvdn ; vii. 99. 9, rathe kropam atikrdnte ; ix. 29. 42,
kropamdtram apakrdntah ; xi. 11. 1, kropamdtram tato gatva.
In other measurements: vii. 103. 37, tasthdu kropamdtre sam-
antatah, "at a distance of a koss on every side."

A great archer shoots a koss: " He seized several arrows and
when he had fitted them to his bow quickly as if they were one,
they fell at a distance of a koss," kropamdtre nipatanti, viii. 79.
57; rathasthito i gratah kropam asyati pardn, vii. 99. 9. Moun-
tains "raised a koss " are mentioned in vii. 65. 10, parvatdh kro-
pam ucchritdh. Most of the other cases of the use of koss are
quite as useless in helping to a determination of its real length.
They are as follows : For a koss on every side around a beleagured
city the earth is broken up and mined, samantdt kropamdtram,
iii. 15. 16; ponds are of this extent, vdpyah kropasammitdh,
vii. 56. 7; the heroine can be smelt up to a koss, gandhap od
'sydh kropamdtrdt pravdti, i. 197. 36; kropdt pradhdvati, i.

Vol. xxiii.] Remarks on Numbers. 147

167. 46 (see below on yojana). The only passage that seems to
cast light on the epic measure is found in xiii. 90. 37, where
speaking of the purifying effects of the men "fit for the row"
and of the dapapurusa (cl. 27), that is, a man tenth in descent
in inherited Vedic wisdom (one who has nine generations of
pious and learned ancestors), the poet says: "They purify as
far as they see . . . even one such would purify to a distance of
two and a half koss," yavad ete prapapyanti panktyas tavat
punanty uta . . . kropdd ardhatrtlydc ca (above, p. 133) pdvayed
eJca eva hi. Here, as two and a half koss are regarded as less
than the limit of ordinary ability to see a person, and five and a
half miles far exceeds this, it would seem that in the epic the koss
was not two miles and a quarter but nearer one mile, as is the
estimate of the Visnu Purana (which ascribes to it, Colebrooke,
loc. eit. , four thousand cubits, a thousand bows, against the Aditya
Purana's estimate of eight thousand cubits) , or, exactly one mile
and one eighth rather than two miles and a quarter. This, how-
ever, is based on two surmises, first, that the "even one" clause
introduces a restriction applicable also to the distance as less than
that previously mentioned, which seems to me legitimate, and,
second, that the expression "as far as they can see" means as
far as they can see a person (that person becomes pure by being
seen). This latter surmise also seems to me to rest on the
intended meaning, though it is possible that the expression
merely means as far as eyesight can reach, in which case the
passage is as useless as the others.

Gavyuti: After the koss comes the gavyuti, estimated by
later writers as two koss. It is used in the epic to give dis-
tance, gavyutimdtre nyavasat, "stayed at a distance of four
miles," iii. 239. 29; and, in the bombast of the late book of
Drona, the battle-array is estimated as extending twelve gav-
yutis or forty-eight miles, dlrgho dvadapagavyittih (papca
'rdhe pafica vistrtah, and twenty in the rear), vii. 87. 22, a
statement the more remarkable as the whole battle-field is only
five leagues in extent, v. 195. 15. In vii. 87. 14 is found also
the expression, gavyutisu trimdtrdsu (tisthata). The gavyuti
is seldom used for travellers, but often for stationary extent of
hall, camp, and quiescent distance, as in xii. 125. 18, where a
deer springs ahead, but stands a gavyuti distant, gavyutima-
trena, banapatham muktvd, tasthivan. At least, it is not till the

148 E. W. Hopkins, [1902.

late "house of lac" scene, i. 151. 20, gavyutimdtrdd dgatya,
" coming up to a distance of a gavyuti" and in the (also late)
scene at (Gorresio) R. i. 79. 27, gatva gavyuUmdtrakam, that
I find it with a verb of motion. This is doubtless because of
its meaning originally a meadow, that is a field or acre, rather
than a measure of length. According to Nilakantha, goytita is
the equivalent of gavyuti, as used in xiv. 65. 22, goyute goyute
cai f va nyavasat, "he rested (camped) at every gavyuti"
designating a daily march retarded by the weight of treasure
carried. In any case the term is a solecism. A march like this,
by the way, is described as being made kramena, step by step,
"slow march," xv. 23. 16.

Yojana: The "yoking" called yojana, estimated at two
gavyuti, four koss, eight thousand bows, and consequently six-
teen thousand cubits in the Aditya Purana, is reckoned in the
Visnu Purana as only half of this distance, that is, as nine
miles in the former and four and a half in the latter work (Cole-
brooke, loc. cit.), but in the Markandeya Purana as four gav-
yuti or eight koss (cit. PW,). I shall render it league. It is
the longest measure and is used in estimating extent of length
and surface. As the syntactical construction of this word
includes that of all the others previously mentioned, I have
reserved the subject for this paragraph. The construction
varies between adjective compounds in the modifying word,
adjective compounds with yojana, and accusative (nominative)
or ablative of extent, as follows :

i. 30. 23, sa tatah patasdhasram yojandntaram dgatah
kdlena nd 'timdtrena,
"in a short time he went a hundred-thousand league-interval,"
i. e. a distance (measured by) a hundred thousand leagues.

xiv. 9. 34-35 : sahasraih dantdndm patayojandnam . . . dan-
strap catasrd dve pate yojandndm, "a thousand of hundred-
league teeth . . . four fangs two hundred of leagues." i. 175.
43, tat sainyam k&lyamdnam triyojanam, "the army was
driven three leagues;" xii. 170. 15, itas triyojanam gatva,
"going three leagues from here."

ii. 7. 2 : vistlrnd yojanapatam patam adhyardham dyatd . . .
paflcayojanam ucchritd, (a hall, sabhd) "one hundred leagues
broad, one hundred and fifty long . . . five leagues high ;" ib. 8. 2,

Vol. xxiii.] Remarks on Numbers. 149

patayojand vistdraydmasampamia bhuyasi ca'pi, (a hall) "of
a hundred-leagues, complete in breadth and height, and even
more"; ib, 10. 1, thus in B:

sabha Vaipravanl, rdjan, patayojanam ayata
vistirna saptatip cat , va yojana 'tisitaprabha,

where C. has yojandni sitaprabhd. C. has the right reading ;
the construction is "broad, seventy leagues" (in the nomina-
tive), and not "seventy were broadened" (leaving yojana to be
construed as a Vedic form with saptatih), for the construction
throughout, as is customary with vistirna and vistrta, is to
make vistirna agree with sabha.

Ordinarily, the accusative, as in Tcropam iicehritah (above,
p. 146), expresses the extent, and this may be assumed to be the
construction when the form leaves the case ambiguous, as in the
answer to the question, "How long is the road between the
world of Yama and the world of men?" (given as) "between
(etc., is) eighty-six thousands of leagues," Tamalokasya ca
\lhvdnam antaram manusasya ca kldrpam Mm pramanam
vaif sadapltisahasrdni yojandndm narddhipa Ycimalokasya
ca 'dhvdnam antaram manusasya ca, iii. 200. 44 and 46. Here
it is clear that the numeral is in the accusative, and it is prob-
ably governed, as is adhvanam, by gantavyam, as in the fol-
lowing: kiyad 1 adhvanam asmdbhir gantavyam imam Idrpam?
etdvad gamanarh tava, xviii. 2. 26 and 28. The locative may
take the place of the accusative when the word "way" is used,
as in xiv. 27. 3, kiyati adhvani tad vanam, "(on) how great a
way is that forest ?"

I do not find the nominative used to measure distance of
movement (evidently because it is impossible to say one goes to
a nominative) but only of stationary distance, that is, where no
progress toward is implied. For example, one may not say the
way is a kropah but only hropam by analogy with "one goes
a kropam. " But, as in the example above, one may say a hall
is extended so much and use the nominative, because the word
extended does not mean goes to that distance; but extended
is broad, and this ptc. adj. is equivalent to the noun breadth.

1 But kiyantarti kalam, ib. 5. 4. There is a passage, i. 126. 8, where
adhvan appears as a neuter, prasanna dlrgham adhvdnaih sarhksiptam
tad amanyata (N. supplies gamanam).

150 K W. Hopkins, [1902.

So in estimating the (stationary) height of a mountain one says
that it is ' ■ upraised " so much in a compound preceding, as in
sadyojanasamucchritah (ITailasah), "a six-league-upraised"
(mountain), iii. 139. 11; or that it is so many leagues, without
anything to indicate that the numeral is not a predicate nomina-
tive, as in trayastrinpat sahasrani yojanani hiranmayah,
"golden (Meru is) thirty-three thousand leagues," iii. 261. 8;
yojananam sahasrani panca san Malyavan atha, "Malyavat
(is) five-six (eleven) thousands of leagues," vi. 7. 29 ;' or that it
is "upraised" so many leagues in the nominative, as in

Meruh kanakaparvatah . . . sc. tisthati
yojananam sahasrani caturapitir ucchritah
adhastdc caturapitir^ yojananam,

"golden Meru . . . (stands) eighty-four (nom.) thousands of
leagues upraised, (and) under (-ground) eighty-four (nom., sc.
thousands) of leagues," vi. 6. 10-11.

Further, there is the one construction where, instead of saying
that the height or breadth of a mountain is so much, one may
employ partitive apposition with (apparently) a nominative
(predicate), as in

astadapa sahasrani yojanani, vipampate,

sat patani ca pnrnani viskambho Jambuparvatah

lavanasya samudrasya viskambho dvigunah smrtah,

"eighteen thousand leagues and six full hundreds the breadth
(is) Jambu-dvipa, and the salt sea's breadth (is) recorded (as)
twice as much," vi. 11. 5-6. The ordinary construction in such
a case is to prefix the number, if it is easily managed, as part of
a compound, as in adityaparvatam dapayojanavistdram, "of
ten-league-extent," xii. 328. 23; or to put the dimension in an
oblique case, as in

ekaikam yojanapatarh vistarayamatah samam,

"each (city was) one hundred leagues (of a league-hundred)
alike in respect to breadth and length," viii. 33. 19 (compare
pramanayamatah sarnah, of a man, i. 222. 31) ; but with such

1 Here occurs a word rare enough in early texts to be noticed, maha-
rajata as gold- (colored people). Cf. JAOS., xx., p. 221 for hiranya as
silver.

2 For the meter, cf . No. 37 in the Qloka-forms of my Great Epic.

Vol. xxiii.] Remarks on Numbers. 151

an unmanageable number as that above it is more natural to
have the construction of the second part of the sentence a geni-
tive, with the dimension in the nominative.

The locative gives the extent only when this is implied or
conditioned by the context, as "on the way" (above) and in
ekadaca sahasrani yojananam samucehritam, adho bhumer
sahasresu tavatsv eva pratisthitam, (Mt. Mandara), "eleven
thousand of leagues upraised, and supported on just as many
thousands below the earth," i. 18. 3. So "at six-rod-casts from
the anthill" (above, p. 144), is only a location of place, not of
extension; also kropamatre (p. 146).

Finally, 1 in estimating distance to a certain extent, the abla-
tive may be used with some prepositions to convey the notion
of exceeding the limit, or simply, beyond, while the ablative
alone or with a indicates the limit itself up to which the dis-
tance implied extends. Of the first case an example is found
united with the instrumental in

xii. 336. 9, Meroh sahasraih sa hi yojananam

dvatrinpato 'rdhvam kavibhir niruktah,

"this (white island) is said by the poets (to be) from Meru more
than thirty-two thousands of leagues " (by thousands more than
thirty-two) .

The antique expression mulat, "up to the root," is used,
though rarely, both in this sense and in that of "from the root,"
that is from the beginning, but it is significant that the epic
usually expresses the idea by a compound, as in

tatah saniido hriyate nadikulad iva drumah,

xii. 95. 21 ; or it is paraphrased, for example, na mulaghatah
kartavyah, xii. 268. 12. Moreover, in words expressing dis-
tance, the examples leave it a little doubtful whether the abla-
tive means "from" or "up to," but by analogy with the same
phrase with the preposition it would seem that the latter idea
was that of the simple ablative. Thus, to express the idea of a
smell extending a koss we find kropamatrat pravati and kropat

1 Of course I omit idioms which may be translated to give extent
without really expressing this, such as brahmadisu trydntesu bhutesn
parivartate, "pervades all beings from Brahman to grass," iii. 2. 72 (a
common phrase).

152 M W. Hopkins, [1902.

pradhdvati (above, p. 146) ; tasyds tu yojanad gandham djigh-
ranta nard bhuvi, i. 63. 82; ayojanasugandhin, i. 185. 21; and,
in the province of sight, yojanad dadrpe, ii. 24. 22 ; ayojana-
sudarpana; and finally, d with the ablative, as in locandir anu-
jagrnus te tarn a drstipdthdt tadd, ' ' then they followed him with
the eyes up to the limit of their vision," ii. 2. 26. As with
time- words, ydvat is also used, ydvac Carmanvatl, "as far as
the river," i. 138. 74.

Another reason for taking the ablative as one expressing the
limit up to (rather than the origin) is that it thus oilers a perfect
parallel to the use of the ablative with time-words, for, as I
shall show in the next section of this article, the idea of a simple
time-ablative expressing the time after which any thing occurs
is erroneous, though this is the only explanation of this ablative
given by Speyer (and adopted by Whitney). On the contrary,
the time-ablative, unless expressly accompanied with urdhvam
or its equivalent in the sense of "beyond," always indicates
time up to the limit expressed by the ablative, and so the
extent-ablative indicates the extent up to the limit expressed by
this case. With adhi the ablative means above, over. '

When the name of a dimension is given, it is usually com-
pounded with the number, and this has led Speyer in his excel-
lent Sanskrit Syntax, § 54 a), to remark that "when naming
the dimension of a thing one does not use this accus. [of space],
but avails one's self of bahuvrihi compounds." With few
exceptions this is quite correct and as a general rule is perfectly
unimpeachable. Thus in iii. 82. 107 :

ardhayojanavistard pancayojanam ayatd
etdvatl Devihd tu,

" of half -league-breadth, five leagues long (extended) — such is
the size of Devika."

vii. 66. 16, sattrinpadyojandydmd* tring,adyojanam ayatd

pag,cdt purag, caturvinpad vedi hy dsid dhiranmayl,

1 I take yojanad adhi in C. ii. 619 in this sense, but B. 14. 54 has yoja-
nav adhi (triyojandyataih sadma triskhandharh y. a.), and PW. inter-
prets C. as "a Tojana high." This preposition, by the way, is used (in
a way not recognized in PW. or pw.) with gen. of place, in H. ii. 79.
12, sapatnindm adhi nityam bhaveyam, " over my rivals."

2 C. has sadvingad", gl. 2,349, which inverts the ratio and makes
ayama, length, into breadth.

Vol. xxiii.] Remarks on Numbers. 153

"of thirty-six-league-length, thirty leagues broad (extended),
in the rear (and) in front twenty -four (leagues), was the golden
vedi."

This arrangement, by which one member is made a compound
of the noun of dimension and the other has the participle, is
quite a favorite. The following example illustrates it again,
together with another illustration of the extent given by a num-
ber-word, apparently in the accusative :

xiv. 58. 33, ito hi ndgaloko vcti yojanani saharapah,
"from here the dragon-world (is) leagues by the thousand;"

ib. 37 and 40, nagalokam vivepa ha, dadarpd nagalokam ca
yojanani sahasrapah . . . dvdrarh sa dadarpa pancayojana-
vistdram ayatam patayojanam, "he went to the dragon-world,
and he saw the dragon-world, leagues by the thousand . . . and
he saw the' five-league-size gate, a hundred leagues extended."

Another example of the exceptional usage, whereby when
naming the dimension of a thing one uses the accusative, is
given by this case :

xii. 282. 7-8, (dadarpa) Vrtram dhisthitam parvatopamam,
yojandndm patdny urdhvam pancocchritam, arimdama, patani
vistarena Hha triny evd ''bhyadhiJcani vai, "he saw Vrtra stand
like a mountain five hundreds of leagues upraised on high (tall),
and three hundred more in extent."

When two dimensions are given, they may follow adverbially,
as in one of the examples above and in xii. 339. 9, g,atayojana-
vistare tiryag urdhvam ca, "hundred-league-extent (peaks)
transversely and up," that is, two peaks having this extent in
both directions ; for vistar, vistdra is extent in general (akhya-
nam bahuvistaram, "a long story," vii. 52. 37; patayojana-
and anekayojana-vistirna, of ocean, "leagues broad," iii. 282.
59 and 45), and may even limit, as a general term, ayama,
which is always length, as in (dviyojanasanmtsedha) yojandya-
mavistard, "(two leagues high and) a yojana-length-extent
weapon," vii. 175. 97 (not in C).

This last sentence (compare also the nalva citations, above, p.
145) gives the regular word for height, which is construed in
compound form, as here and in i. 29. 30: sad ucchrito yojanani
gajas taddvigundyatah kurmas triyojanotsedho dapayojana-

154 M W. Hopkins, [1903.

mandalah, "an elephant six leagues upraised and twice as
extended ; a three-league-height and ten-league-circle tortoise "
(in English, three leagues tall and ten round).

ON Jr.

Although no word in the epic expresses the relation between
the diameter and the circumference, yet this relation is given
in figures, as applying to the size of the sun, the moon, and the
"planet" that swallows them, the moon being rather larger
than the sun. 1 The account of the size will be found at vi. 11.
3 (Rahu); 12. 40 ff . ; of -the cause of eclipse, i. 19. 9 (rahic-
m/ukhd). The relation between the diameter and the circum-
ference differs inversely according to the size of the object, the
greatest circle having the smallest ratio. Of the three heavenly
bodies, Svarbhanu or Rahu (the devouring planet) is circular,
parimandala, no less than the moon and the sun, so that ir
can be established in this case as well as in the others. Its
diameter, viskambha (breadth), is twelve thousand leagues, yoja-
nas, and "in its circumference and extent," parinahena vipulat-
vena ca, it is "thirty-six thousand sixty hundred" or 42,000
leagues, as say the Pauranic sages, budhah pauranikah. The
moon's diameter, viskambha, is eleven thousand and its circle,
mandala, is thirty-three (thousand) and "sixty-less-one" (hun-
dreds, given in the text as the viskambha, but this must be
parinaha, as in the preceding case), making the sum in thou-
sands (33) and in hundreds (59) equal in all to 38,900. The sun
in diameter is "eight thousand and two more," anye, and its
circle is equal to thirty (thousand), mandalam trinpata samam,
and fifty-eight (hundred) in extent, vipulatvena, or 35,800.
Thus (instead of it— 3.1416) :

1 This is riot strange. In fact, the full moon in India on a clear night
certainly looks larger than the sun even when the latter is on the hori-
zon. Especially at the end of a dusty day; when the moon seems
twice the size even of the harvest moon of this country. But this is
not the only reason for the great size attributed to the heavenly bodies
as compared with that assigned by the Greeks. Even the stars are
regarded as huge worlds "because though small as lamps in appearance
they are so far removed " (the passage is given in my India, Old and
New, p. 59, from iii. 42).

Vol. xxiii.] Remarks on Numbers. 155

R&hu, 12,000: 42,000 tt=3.50
Moon, 11,000: 38,900 tt=3.53+
Sun, 10,000: 35,800 ir=3.58

There is nothing to indicate that the yojana here used is the
special astronomical yojana of later works. According to the
Suryasiddhanta, iv. 1, the sun's diameter is 6,500 (astronomical)
yojanas, and the moon's is 480, while ir in that work is 3.1623
and 3.14136, according to circumstances (Whitney's notes,
JAOS. vi. pp. 183 and 201). A little later, in the fifth cen-
tury, Aryabhata (Thibaut, Astronomie, etc., p. 75, in Btthler's
Grundriss) knew that ir= 3. 1416, and it seems grotesque enough
that even an epic poet could give such statements as those made
above, if he had an approximate notion of the true relation.
For it is not as if the author carelessly (poetically) said that
the sun's circumference is about three and a half times its diam-
eter. The numbers are given in detail for three different circles
and show that the calculation had been made in each case. But
any boy with a string and a tree-stump could get nearer to the
true ratio than 3.5.

[To be continued.]