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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.]