०५

ENLARGEMENT OF FIRE-ALTAR FROM \(7\frac{1}{2}\) SQ. PURUṢAS TO \(101\frac{1}{2}\) SQ. PURUSAS, HEIGHT OF ALTARS AND THEIR PECULIARITIES

अर्धाष्टमाः पुरुषाः प्रथमोऽग्निः । अर्धनवमा द्वितीयः । अर्धदशमास्तृतीयः । एवमुत्तरोत्तरो विधाभ्यास एकशतविधात् । तदेतत्सप्तविध-प्रभृत्येकशतविधान्तम् १

The area of the fire-altar made for the first time is \(1\frac{1}{2}\) square purușa; that for the second time \(8\frac{1}{2}\) (square purușa); that for the third time \(9\frac{1}{2}\) (square puruṣa). Thus by successively adding one-fold (1 square purușa), (one can go) upto 101-fold. Thus it begins with the 7-fold fire-altar ( \(7\frac{1}{2}\) square purușa) and ends with the 101-fold.

अर्धाष्टमाः पुरुषाः प्रथमोऽग्निः । अर्धनवमा द्वितीयः । अर्धदशमास्तृतीयः । एवमुत्तरोत्तरो विधाभ्यास एकशतविधात् । तदेतत्सप्तविध-प्रभृत्येकशतविधान्तम् १

अत ऊर्ध्वमेकशतविधानेव प्रत्याददीत । अनग्निकान्वा यज्ञक्रतूनाहरेत् । अन्यत्राश्वमेधात् २

Thereafter, to continue further, the 101-fold (fire-altar) is to be repeated (that is, after reaching 101-fold, no further increase is to be made). Otherwise, the sacrificial rite is to be performed without a fire-altar.

अत ऊर्ध्वमेकशतविधानेव प्रत्याददीत । अनग्निकान्वा यज्ञक्रतूनाहरेत् । अन्यत्राश्वमेधात् २

अश्वमेधमप्राप्तं चेदाहरेदत ऊर्ध्वं विधामभ्यस्येन्नेतरदाद्रियेत ३

The aśvamedha (sacrifice) is an exception. If the aśvamedha (requiring a fire- altar of 21 square purușa) is performed without (the required agni) being reached, one fold is added to get the next higher fold (that is, \(22\frac{1}{2}.\) puruṣa agni); no other procedure is allowed.

अश्वमेधमप्राप्तं चेदाहरेदत ऊर्ध्वं विधामभ्यस्येन्नेतरदाद्रियेत ३

अतीतं चेदाहरेदाहृत्य कृतान्तादेव प्रत्याददीत ४

If (the required fire-altar is) surpassed, the fire-altar following the one surpassed is to be constructed.

अतीतं चेदाहरेदाहृत्य कृतान्तादेव प्रत्याददीत ४

कथमु खलु विधामभ्यस्येत् ५

But how is one fold to be added ?

कथमु खलु विधामभ्यस्येत् ५

यदन्यत्प्रकृतेस्तत्पञ्चदश भागान्कृत्वा विधायां विधायां द्वौ द्वौ भागौ समस्येत् । ताभिरर्धाष्टमाभिरग्निं चिनुयात् ६

The excess (to be added) to the original form (of the fire-altar) should be divided into 15 parts and two parts be added to each fold (of 1 sq. puruṣa; after 14 parts are in this way added to 7 folds of 7 sq. purușa, the remaining part is added to \(\frac{1}{2}\) sq. puruşa). The (new) fire-altar is to be laid with such (increased) \(7\frac{1}{2}\) folds.

ENLARGED FIRE-ALTAR AND UNITS

5.1-5.6. The fire-altar of the first construction has an area of 71 sq. purușas. This has been discussed in subsequent chapters. The second construction has 8 sq. purusas, and according to Baudhāyana, it is increased by one square puruşa successively from \(7\frac{1}{2}\) sq. purușas to \(101\frac{1}{2}\) sq. purușas. There is a mention of this type of increment upto 101 sq. purusas in the Śatapatha Brāhmaṇa¹. When the fire-altar is increased from the original 7 sq. purusas by p square purusas, Baudhāyana says, the increment in each purușa equals the side of a square of \(1 +\frac{2p}{15}sq.\) purușas. Hence the enlarged unit equals \(\sqrt{1 +\frac{2p}{15}}\) and the area of the enlarged fire-altar \(7\frac{1}{2}(1 +\frac{2p}{15})\) that is, \(7\frac{1}{2}+p.\) sq. purușas (Bśl. 5.6).

With this length as unit of measure, the altar is constructed in the same manner as in original falcon-shaped altar. For obtaining the portion\(\frac{2p}{15}\), Baudhāyana perhaps divided the extra area into 15 equal parts by drawing 15 parallel lines or by drawing 3 parallel lines in one side and 5 parallel lines on the other after p square areas were turned into a square. Then two of these rectangular pieces were combined together with the help of samāsavidi.

Both Āpastamba (Ãśl. 8.6) and Kātyāyana (Kśl. 5.5) have given the same value of Baudhāyana, which equals the side of a square of \(\frac{2}{15}(7\frac{1}{2})\) sq. purușas (where p = 1 sq. puruṣa). Kātyāyana has given the same value of enlarged sq. unit in two other forms as follows:

(i) \(1 + p\left(\frac{5}{5.5} - \frac{1}{3}.\frac{5}{5.5}\right)=1+\frac{2p}{15}\) (Kśl. 5.7);

and (ii) \(1 + p \left(\frac{7}{7.7}-1\times \frac{1\frac{1}{7}}{120}\right) = 1+\frac{2p}{15}\) (Kśl. 5.7);

where p = 1.

This method of Kåtyāyana is known as the method of increment by puruşa (puruṣābhyāsa—Kśl. 5.4). Moreover, Apastamba has devised a method of joining complete purușas in the body, wings and tail. If the increased area of p purușas be an exact mutiple or sub- multiple of the original agni, i.e. \(p = q \times 7\frac{1}{2}\), then the new unit comes out to be \(\sqrt{1 + q.}\) This is known as increment on the whole posts (sarvabhyāsa, Ast. 21.7).
In the enlargement of the falcon-shaped fire-altar (first plan) let s be the enlarged unit in purușa and p the total increment in area. Then in the form of a quadratic equation this can be written as \(body+ 2 wings + tail = 7\frac{1}{2} + p\)

or \(4s^2 + 2 s\left(s+\frac{s}{5}\right)+s\left( s+\frac{s}{10}\right) = 7\frac{1}{2}+p\)

or \(4s^2 + \frac{12}{5}s^2 + \frac{11}{10}s^2 = 7\frac{1}{2}+p\)

or \(\frac{15}{2}s^2 = 7\frac{1}{2}+p\)

or \(s^2= \frac{2}{15}(7\frac{1}{2}+p)= 1+\frac{2p}{15}\)

or \(s= \sqrt{1+\frac{2p}{15}}\)

when p = 94, the maximum enlargement,

\(s= 13\frac{8}{15} = 14\) approx.

The principle of enlargement of agni by increasing the length of the unit of measure was known in the time of the Satapatha Brāhmaṇa.² It has described the construction of the agni of \(101\frac{1}{2}\) sq. purușa, where 14 or \(14\frac{3}{4}\) times enlarged unit in purușa is taken up for its construction.³

यदन्यत्प्रकृतेस्तत्पञ्चदश भागान्कृत्वा विधायां विधायां द्वौ द्वौ भागौ समस्येत् । ताभिरर्धाष्टमाभिरग्निं चिनुयात् ६

ऊर्ध्वप्रमाणाभ्यासं जानोः पञ्चमस्य चतुर्विंशेनैके समामनन्ति ७

The height (of the fire-altar), according to some teaching, should be increased by the twenty-fourth part of the fifth of a jānu (32 aṅgulas).

ऊर्ध्वप्रमाणाभ्यासं जानोः पञ्चमस्य चतुर्विंशेनैके समामनन्ति ७

अथ हैक एकविधप्रभृतीनपक्षपुच्छांश्चिन्वते ८

Some construct the fire-altar from one fold ( \(1\frac{1}{2}\) puruşa) upwards (upto \(6\frac{1}{2}\) sq. purușa) without wings and tail.

अथ हैक एकविधप्रभृतीनपक्षपुच्छांश्चिन्वते ८

तन्नोपपद्यते पूर्वोत्तरविरोधात् ९

This is not justified because it contradicts earlier and later precepts.

तन्नोपपद्यते पूर्वोत्तरविरोधात् ९

अथ हैकेषां ब्राह्मणं भवति श्येनचिदग्नीनां पूर्वा ततिरिति १०

In this connection some Brāhmaṇas maintain that among the fire-altars the making of the falcon-shaped one is the first sacrificial ceremony.

अथ हैकेषां ब्राह्मणं भवति श्येनचिदग्नीनां पूर्वा ततिरिति १०

अथापरेषां न ज्यायांसं चित्वा कनीयांसं चिन्वीतेति ११

Other Brāhmaṇas maintain that after having constructed a larger fire-altar a smaller one should not be laid.

अथापरेषां न ज्यायांसं चित्वा कनीयांसं चिन्वीतेति ११

अथास्माकं । पक्षी भवति । न ह्यपक्षः पतितुमर्हति । अरत्निना पक्षौ द्राघीयांसौ भवतः । तस्मात्पक्षप्रवयांसि वयांसि । व्याममात्रौ पक्षौ च पुच्छं च भवतीति १२

Our Brāhmaṇa teaches as follows: he is winged for the unwinged cannot fly; the two wings are longer (than 1 purușa in each case) by 1 aratni, and this makes the birds strong in their wings; the two wings and the tail measure 1 vyāma (each).

अथास्माकं । पक्षी भवति । न ह्यपक्षः पतितुमर्हति । अरत्निना पक्षौ द्राघीयांसौ भवतः । तस्मात्पक्षप्रवयांसि वयांसि । व्याममात्रौ पक्षौ च पुच्छं च भवतीति १२

नापक्षपुच्छः श्येनो विद्यते । न चासप्तविधस्य पक्षपुच्छानि विद्यन्ते । न च सप्त-विधं चित्वैकविधप्रसङ्गः । तस्मात्सप्तविध एव प्रथमोऽग्निः १३

A falcon without wings and tail does not exist; so the fire-altar which is not seven-fold has neither wings nor tail; moreover, the construction of one-fold fire-altar after the seven-fold has been laid is inadmissible; for all this the seven-fold is the fire-altar to be made for the first time.

नापक्षपुच्छः श्येनो विद्यते । न चासप्तविधस्य पक्षपुच्छानि विद्यन्ते । न च सप्त-विधं चित्वैकविधप्रसङ्गः । तस्मात्सप्तविध एव प्रथमोऽग्निः १३

भेदान्वर्जयेत् । अधरोत्तरयोः पार्श्वसन्धानं भेदा इत्युपदिशन्ति । तद-ग्न्यन्तेषु न विद्यते न स्रक्तिपार्श्वयोः १४

The clefts are to be avoided; the meetings of edges (between bricks) in the upper and lower layer constitute these clefts, as per teachings. Such clefts, however, do not exist either in the peripheries or the two sides of a corner of the fire-altar.

भेदान्वर्जयेत् । अधरोत्तरयोः पार्श्वसन्धानं भेदा इत्युपदिशन्ति । तद-ग्न्यन्तेषु न विद्यते न स्रक्तिपार्श्वयोः १४

साहस्रं चिन्वीत प्रथमं चिन्वान इति १५

One thousand bricks are to be used when (the fire-altar is) constructed for the first time.

साहस्रं चिन्वीत प्रथमं चिन्वान इति १५

पञ्चमायां वा चितौ सङ्ख्यां पूरयेत् १६

This number is to be completed in the fifth layer.

पञ्चमायां वा चितौ सङ्ख्यां पूरयेत् १६

द्विशताश्चेच्चिकीर्षेत्पञ्चचोडाभिर्नाकसदः समानसङ्ख्यं प्रतीयात् १७

Where two hundred bricks are desired (for cach layer), pañcacoḍā and nākasat (bricks) are to be counted together as one (that is, one of each type together to be considered as one brick).

द्विशताश्चेच्चिकीर्षेत्पञ्चचोडाभिर्नाकसदः समानसङ्ख्यं प्रतीयात् १७