०७

न खण्डामुपदध्यात् । न भिन्नामुपदध्यात् । न कृष्णामुपदध्यात् । न जीर्णामुपदध्यात् । न लक्ष्मणामुपदध्यात् । न स्वयमातृण्णां स्वयञ्चितावुपदध्यात् १

One should not use (for the laying of the fire-altar) a broken brick, a brick which is cleft, a blackened brick (due to over or under heating), a damaged brick and a brick with scratching marks. In the layer where a brick full of natural holes (svayamātṛṇṇa) is used it is not to be covered (by a brick).

न खण्डामुपदध्यात् । न भिन्नामुपदध्यात् । न कृष्णामुपदध्यात् । न जीर्णामुपदध्यात् । न लक्ष्मणामुपदध्यात् । न स्वयमातृण्णां स्वयञ्चितावुपदध्यात् १

ऊर्ध्वप्रमाणमिष्टकानां जानोः पञ्चमेन कारयेत् । अर्धेन नाकसदां पञ्चचोडानां च २

The height of the brick is to be made a fifth of the jānu (that is, 6% angula); that of the nākasat and the pañcacoḍā half of that measure (that is, 3 añgula).

ऊर्ध्वप्रमाणमिष्टकानां जानोः पञ्चमेन कारयेत् । अर्धेन नाकसदां पञ्चचोडानां च २

यच्छोषपाकाभ्यां प्रतिह्रसेत पुरीषेण तत्सम्पूरयेत् पुरीषस्यानियतपरिमाणत्वात् ३

What is lost by drying and burning is to be made good by loose earth because of the flexibility of its quantity.

HEIGHT AND CHARACTERISTICS OF DIFFERENT LAYERS OF ALTAR AND BRICKS

5.7-7.3. In the usual five-layer construction, the height of the altar is 32 aṅg., height of each layer being \(\frac{32}{3}\) aṅg. (Bśl. 5.7 and 7.2). According to Karavindasvāmī, it is 6 aṅg. Actually two layers are constructed. Construction of other layers is not required, since the 3rd and the 5th layer are the replica of the 1st and the 4th that of the 2nd. In the placement of bricks in different layers clefts between two layers are avoided. An altar of daily fire like the gārhapatya has 21 bricks in each layer, while a kāmya fire-altar is constructed with 1000 bricks, each layer containing 200 bricks. A fire-altar of \(7\frac{1}{2}\) sq. purușas is the normal construction. Pañcacoḍā and nākasat bricks have half the thickness of ordinary bricks; hence one pañcacoḍā and one nāksat taken together are considered as one brick (Bśl. 5.17 and 7.2). They are usually on the fifth layer placed at the top. The spoiled or broken bricks or bricks of black colour are not used in the construction ( Bśl. 7.1).

Usually all the fire-altars from \(1\frac{1}{2}\) sq. purușas (one fold)\(8\frac{1}{2}\) to \(101\frac{1}{2}\) sq. purușas (101 fold) are not constructed. In some cases they are constructed without wings and tails.
In the construction of fire-altars from 8 to 101 sq. purușas, how the units in sq. purusas are proportionately increased has been discussed. After all these are not normal constructions and are done in the construction for second and third time. In the second and third construction the fire-altar is constructed with more bricks and increased height. As regards its height and the number of bricks to be used in its construction, the Taittiriya Samhitā writes: “He should pile (the fire) of a thousand (bricks) when first piling (it); this world is commensurate with a thousand; verily he conquers this world. He should pile (it) of two thousands, when piling a second time, the atmosphere is commensurate with two thousands; verily he

conquers the atmosphere. He should pile (it) of three thousands, verily he conquers yonder world. Knee-deep should he pile (it) when piling for the first time, verily with the gayatri he mounts this world; naval-deep should he pile it when piling for the second time, verily with the triṣṭubh, he mounts the atmosphere; neck-deep should he pile (it) when piling for the third time, verily with the jagati, he mounts the yonder world”.¹ (Keith’s translation).

The fire-altar (Chapter 6) has the characteristics of an animal. The head of the animal lies in the east and its back is compared with the east-west line. The east-west line is the central line of the altar and measurements are given with reference to this central east-west line. The bricks marked for south and north are placed accordingly on the southern and northern side of the altar. Diagrams of circle, a bull, a woman without ears, line, darbha grass are depicted on the bricks for their use for specific purposes. The bricks with different markings and symbols are also mentioned by Mānava in Chapter 7 of his Mānava-śulbasūtra.

यच्छोषपाकाभ्यां प्रतिह्रसेत पुरीषेण तत्सम्पूरयेत् पुरीषस्यानियतपरिमाणत्वात् ३

व्यायाममात्री भवतीति गार्हपत्यचितेर्विज्ञायते ४

According to tradition, the gārhapatya fire has the measure of 1 vyāyāma.

व्यायाममात्री भवतीति गार्हपत्यचितेर्विज्ञायते ४

चतुरश्रेत्येकेषां । परिमण्डलेत्येकेषाम् ५

It (gārhapatya fire) is a square by one tradition and a circle by another.

चतुरश्रेत्येकेषां । परिमण्डलेत्येकेषाम् ५

चतुरश्रं सप्तधा विभज्य तिरश्चीं त्रेधा विभजेत् । अपरस्मिन्प्रस्तार उदीचीरुपदधाति ६

The (gārhapatya fire in the form of) square is to be divided into 7 parts (length-wise) and then into 3 parts transversely. In the second layer, bricks are to be placed towards north (that is, the division in the first layer as aforesaid is to be reversed).

चतुरश्रं सप्तधा विभज्य तिरश्चीं त्रेधा विभजेत् । अपरस्मिन्प्रस्तार उदीचीरुपदधाति ६

समचतुरश्राश्चेदुपदध्याद्व्यायामषष्ठेनेष्टकाः कारयेच्चतुर्थेन तृतीयेनेति । तासां नव प्रथमा द्वादश द्वितीया इति पूर्वस्मिन्प्रस्तार उपदधाति । पञ्च तृतीयाः षोडश प्रथमा इत्यपरस्मिन् ७

To place square bricks (instead of rectangular ones as indicated above), (square) bricks of sides one-sixth, one-fourth and one-third of 1 vyāyāma are made. Of them, 9 bricks of the first type and 12 of the second are placed in the first layer; 5 of the third type and 16 of the first are placed in the second layer.

CONSTRUCTION OF GARHAPATYA FIRE-ALTAR (SQUARE). 7.4-7.7. Baudhāyana says the garhapatya fire-altar has the form of a square according to one tradition and of a circle according to another. The area is always one sq. vyāyāma. It is constructed with 21 bricks in each layer. For the placing of bricks in the square garhapatya, the following two methods are adopted.

First Method.
One side of the square is divided into 3 parts by drawing 3 parallel lines and the other into 7 parts by drawing 7 parallel lines. These lines divide the square area into 21 rectangles and the bricks are accordingly made. This is for the first layer. For the second layer, the bricks are arranged differently in the square.

Second Method.
Three kinds of square bricks are made with 6th, 4th and 3rd part of a vyāyāma. The first layer is prepared with 9 bricks of the first kind and 12 bricks of the second, and the second layer with 6 bricks of the third kind and 16 bricks of the first.

How the ancient altar builders determined the size of the bricks of different kinds and the number of bricks of each kind required for the construction of each layer is not known. The solution was obtained possibly on the following line.[^b]

Empirical Method.
Suppose the sides of the three new types of bricks be p, q, and r th part of a vyāyāma, where p, q, r are rational integers. The minimum number of bricks must be three, since in each layer there are two types of square bricks and no two layers have identical arrangement of bricks.

[^b] Datta (2), 180-183.

Let the first layer have m number of bricks of the first kind and n bricks of the second kind, so that

m + n = 21

and \(\frac{m}{p^2}+\frac{n}{q^2}=1\) ….(1)

Similarly we can have another set of equations, if the second layer consists of s bricks of the third kind and t bricks of the first kind, as follows:

m + n = 21 and \(\frac{r}{r^2}+\frac{t}{p^2}=1\) ….(2)

Baudhāyana’s solutions are :

(i) x = 9, y =12, p = 6, q=4

(ii) x =5, y=16, p = 3, q=6

These two sets of values obviously satisfy equations (1) and (2) respectively.

Solutions of equations (1) and (2) lead to the problem of solution of the simul- taneous indeterminate equation of the type:

\(\frac{x}{p^2}+\frac{y}{q^2}=1\)
x + y = 21 …..(3)

Solving three, we write :

\(x = p^2 \frac{(21-q^2)}{p^2 - q^2}, y = \frac{q^2(p^2-21)}{p^2-q^2}\)

The numbers x and y are considered positive by the śulbakāras. Hence

if p > q, p^2 > 21 > q^2
since, s^2>21 > 4^2, p>5, q\leqslant 4
if p < q, q\geqslant 5, p\leqslant 4

Putting q= 1, 2, 3, 4, the values of p can be determined by trial, considering the value of x to be integral.

समचतुरश्राश्चेदुपदध्याद्व्यायामषष्ठेनेष्टकाः कारयेच्चतुर्थेन तृतीयेनेति । तासां नव प्रथमा द्वादश द्वितीया इति पूर्वस्मिन्प्रस्तार उपदधाति । पञ्च तृतीयाः षोडश प्रथमा इत्यपरस्मिन् ७

परिमण्डलायां यावत्सम्भवेत्तावत्समचतुरश्रं कृत्वा तन्नवधा विभजेत् प्रधींस्त्रिधा त्रिधेति । अपरं प्रस्तारं तथोपदध्याद्यथा प्रध्यनीकेषु स्रक्तयो भवन्ति ८

Within the (gārhapatya fire in the form of) circle a square of the maximum size possible is drawn and divided into 9 parts (squares). The segments of the circle (between the circumference and the square) are divided into 3 parts each. The second layer is placed in such a way that the corners (of the square within the circle) lie at the centres of the segments (of the first layer).

परिमण्डलायां यावत्सम्भवेत्तावत्समचतुरश्रं कृत्वा तन्नवधा विभजेत् प्रधींस्त्रिधा त्रिधेति । अपरं प्रस्तारं तथोपदध्याद्यथा प्रध्यनीकेषु स्रक्तयो भवन्ति ८

धिष्ण्या एकचितीकाश्चतुरश्राः परिमण्डला वा ९

The dhiṣnya fires are one-layered in the form of a square or a circle.

CONSTRUCTION OF GĀRHAPATYA FIRE-ALTAR (CIRCULAR)

7.8. For construction of a circular gārhapatya a square ABCD as large as possible is inscribed within a circle (Fig. 31) Āpastamba has directed that with half a vyāyāma as radius this circle is to be drawn; the end points of two diameters standing at right-angles to each other when joined give the largest possible square (Āsl. 7.5.).

The square ABCD is then divided into 9 equal parts by 3 parallel lines from one side and 3 from the other side, and each segment is divided into 3 equal parts. Hence the whole circle is divided into 21 parts and the bricks are accordingly made for the first layer.

In the second layer the square is so adjusted that the corners A, B, C, and D are placed in the middle points E, F, G and H of the segments.

Baudhāyana and Āpastamba have considered the problem of quadrature of the circle whose area falls short of the circle.

धिष्ण्या एकचितीकाश्चतुरश्राः परिमण्डला वा ९

तेषामाग्नीध्रीयं नवधा विभज्यैकस्याः स्थानेऽश्मानमुपदध्यात् १०

Of these (dhisnya fires), the āgnīdhrīya is divided into 9 parts, and in one part a stone is to be placed (instead of a brick.)

तेषामाग्नीध्रीयं नवधा विभज्यैकस्याः स्थानेऽश्मानमुपदध्यात् १०

अथ होतुर्धिष्ण्यं नवधा विभज्य पूर्वांस्त्रिभागानेकैकं द्वेधा विभजेत् ११

The dhiṣṇya fire of the hoty priest is divided into 9 parts and the 3 parts on the eastern side are divided into 2 parts each.

अथ होतुर्धिष्ण्यं नवधा विभज्य पूर्वांस्त्रिभागानेकैकं द्वेधा विभजेत् ११

अथेतरान्नवधा नवधा विभज्य मध्यमपूर्वौ द्वौ भागौ समस्येत् १२

The others (dhiṣṇya fires) are each divided into 9 parts and then two parts, one in the centre and the other in the east, are combined.

अथेतरान्नवधा नवधा विभज्य मध्यमपूर्वौ द्वौ भागौ समस्येत् १२

अथ मार्जालीयं त्रेधा विभज्य पूर्वापरौ भागौ पञ्चधा विभजेत् १३

Now the mārjālīya fire is divided into 3 parts and then the eastern and the western parts (taken together) are divided into 5 parts.

अथ मार्जालीयं त्रेधा विभज्य पूर्वापरौ भागौ पञ्चधा विभजेत् १३

उख्यभस्मना संसृज्येष्टकाः कारयेदिति १४

The bricks are to be made by mixing with ashes from the caldron.

उख्यभस्मना संसृज्येष्टकाः कारयेदिति १४

संवत्सरभृत एवैतदुपपद्यते न रात्रिभृतः १५

This applies to those whose consecration lasts a year and not to those undergoing it for a smaller number of nights.

संवत्सरभृत एवैतदुपपद्यते न रात्रिभृतः १५

एवमस्य मन्त्रवती चितिकॢप्तिः १६

Thus (the laying of) the fire-altar is completed with the sacrificial formulas (recited by the priest).

एवमस्य मन्त्रवती चितिकॢप्तिः १६

छन्दश्चितं त्रिषाहस्रस्य परस्ताच्चिन्वीत कामविवेकात् तस्य रूपंश्येनाकृतिर्भवतीति १७

After (a fire-altar made of) three thousand (bricks), a fire-altar to be piled with metres (of the sacred hymns) is to be laid. This is because of a difference in the wish. This (fire-altar) is falcon-shaped, as it is natural (for all such fire-altars).

CONSTRUCTION OF DHIṢṆYA, Āgnidhrīya, MĀRjĀLĪYA AND CHANda Fire-altars.

7.9-7.17. The dhisnya has one layer only. It may be a square or a circle. Generally it is covered with sand on which the fire is placed.

The āgnidhriya may also be a square or a circle. When it is in the form of a square, it is divided into nine small squares, and the central brick is replaced by a piece of stone. The same method is also given by Manava (Mśl. 6.10). When it is circular, a round stone of 8 angulas diameter is placed in the centre of the circle and the remaining area divided into eight equal parts (Fig. 32).

The mārjāliya is divided into 3 equal parts by lines parallel to the north-south line. The eastern and western parts together are divided into 5 parts. No detail is available in the Baudhāyana fulba as to how the eastern or western part is to be divided. The commentator Dvārakānātha gives the idea of dividing the eastern slab into two and western slab into three parts. Mānava has, however, suggested different constructions (Mśl. 6.11). The mārjāliya, when circular, is divided into six equal parts.

The chandaścit is the fire-altar of mantras, not of bricks. The shape of the fire-altar is drawn on the ground and the whole ceremony performed. Instead of placing bricks, the sacrificer only touches the places on which the bricks are to be placed and mutters the same mantras at the appropriate time.

छन्दश्चितं त्रिषा-हस्रस्य परस्ताच्चिन्वीत कामविवेकात् तस्य रूपंश्येनाकृतिर्भवतीति १७