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The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t3: Chapter 3: Positions, Relative Distances and Areas of Sacrificial Fires and Altars

The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t3

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English

Chapter 3: Positions, Relative Distances and Areas of Sacrificial Fires and Altars

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This and the following four chapters 4-7 deal with the positions, relative distances, and areas of various sacrificial fires and altars as also the types of bricks used in the construction of some of them. For a fuller appreciation of the details of mensuration presented by the *śulbakāras* in these chapters, a general idea regarding the plan of the sacrificial ground and the various fires and altars mentioned will be helpful. These details have been given at various places of the *Brāhmaṇas*, particularly of the *Yajurveda* school. Karavinda, the commentator of the *Āpastamba-Śulba-sūtra* has also made available a good summary.

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PLAN OF THE SACRIFICIAL GROUND

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The place for worship and performance of the various sacrificial rites is selected where the ground is high, even and firm, inclining towards the east or the north and rising towards the south.a It should be spacious enough for the laying of the sacrificial hall, the *mahāvedi* and various pits, structures and elements required. After drawing the east-west line in the sacrificial ground, the sacrificial hall, the *prācīna-vaṃśa* or *prāgvaṃśa*, as called by Baudhāyana, Kātyāyana and others, is erected at the western end, lying along, and symmetrically about, the east-west line (Fig. 26). The name is derived from the use of horizontal beams (*vaṃśa*) supported by four corner posts, on which corner beams are fastened to serve as lintels of the eastern and western doors.b In this hall, besides the priests, the members of the family and friends of the person performing the sacrifice can assemble.

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Inside this sacrificial hall are set up the *gārhapatya* fire at the western end, the *āhavanīya* fire at the eastern, the *dakṣiṇāgni* on the southern side more towards west and the *utkara* on the northern side more towards east. In between the *āhavanīya* and the *gārhapatya* fire is placed the *dārśapaurṇamāsika* altar for the full-moon sacrifice or such other altars as may be required.

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a *Śat. Br.* III. 1. 1. 1-3.

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b *Śat. Br.*, III. 1.1.6; also see Eggelling's note, *SBE*, 26, 3.

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The *gārhapatya* is the householder's fire received from his father and transmitted to his descendants. It is a perpetual sacred fire from which other sacrificial fires are lighted. This fire is used by the priests for cooking oblations.a The *āhavanīya* is a consecrated fire taken from the householder's perpetual fire and is also used for cooking oblations. The *dakṣiṇāgni*, also called by the name of *anvāhārya-pacana*, is used for cooking food. Eggeling says that, at the new-and full-moon sacrifice, the *anvāhārya* mess of rice, the priest's *dakṣiṇā*, is cooked at this fire. The *utkara* placed near the north-east side of the sacrificial hall is a rubbish pit dug out in the ground.

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East of the *prāgvaṁśa* and separated by a narrow space, the *mahāvedi* or the *saumikī vedi* (the *soma* altar) is placed symmetrically about the east-west (*prācī*) line. This is a trapezium measuring 30 units on the western side, 24 on the eastern side and 36 units east-west along the spine. The setting up of the *mahāvedi* is described in the *Śatapatha Brāhmaṇa* as follows (Eggeling's translation)b :

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"1. From the post which is the largest on the east side (of the hall) he now strides three steps forwards (to the east), and there drives in a peg,—this is the intermediate (peg).

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2. From the middle peg he strides fifteen steps to the right, and there drives in a peg,—this is the right hip.

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3. From the middle peg he strides fifteen steps northwards, and there drives in a peg,—this is the left hip.

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4. From that middle peg he strides thirty-six steps eastwards, and there drives in a peg,—this is the fore-part.

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5. From the middle peg (in front) he strides twelve steps to the right, and there drives in a peg,—this is the right shoulder.

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6. From the middle peg he strides twelve steps to the north, and there drives in a peg,—this is the left shoulder. This is the measure of the altar."

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After the area of the *mahāvedi* is thus marked out, the *sadas* tent is erected near the western base of the *mahāvedi*. The tent is rectangular in area, the longer side lying south-north symmetrically about the east-west line, and is provided with doors on the western and the eastern side. This tent is reserved for the priests to sit and conduct various operations:—"And because all the gods sat (*sad*) in it therefore it is called *sadas*—and so do these Brāhmaṇas of every family now sit therein."{a} Clearly the tent is divided by the *prācī* line into two parts. In the middle of it, a post of *udumbara* wood (*Fiscus glomerata*) is fixed to the ground.{b}

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a *Śat. Br.*, I. 1.2.23.

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b III. 5.1. 3-6.

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{a} *Śat. Br.* III. 5. 3. 5.

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{b} *Śat. Br.* III. 6. 1. 2.

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Fig. 26. Plan of the Sacrificial Ground.

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Inside the *sadas*, six *dhiṣṇya* hearths, *Dh*, are prepared. These are subordinate or side altars, generally a heap of earth covered with sand on each of which a fire is placed. There are actually eight *dhiṣṇyas*, of which two, *e.g.*, the *āgnīdhra* and the *mārjālīya* are placed outside the *sadas* as will be seen in what follows. Of these six hearths placed in the tent, five are placed on the northern part parallel to the cast side and belong, in order from the south to the (1) *Hotṛ*, (2) *Brāhmaṇācchaṁsi*, (3) *Potṛ*, (4) *Neṣṭṛ*, and (5) *Acchāvāka*. The *dhiṣṇya* hearth belonging to the *Maitrāvaruṇa* or *Praśāstṛ* priest is placed on the southern half of the tent near the east side.

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The two other *dhiṣṇya* hearths, *e.g.* the *āgnīdhra*, *Āg*, and the *mārjālīya*, *M*, are placed in the middle part of the northern and the southern side respectively of the *mahāvedi*. Both these hearths are set up under square sheds with four posts erected over them, open on the east side and the side facing the *havirdhāna* cart-shed in the middle of the altar. The *Brāhmaṇa* says: "In the north—with regard to the back part of the Soma-carts—he then raises the *āgnīdhra* (shed). One half of it should be inside the altar, and one half outside; or more than one half may be inside the altar and less outside; or the whole of it may be inside the altar......."{c} *Āgnīdhra* is the sacred fire and is to be thrown up first. The *mārjālīya* is a heap of earth on which sacrificial vessels are cleansed and is the last to be thrown up.

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{c} *Śat. Br.* III. 6. I. 26.

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In the middle region of the *mahāvedi*, east of the *sadas* and in line with the *āgnīdhra* and the *mārjālīya*, the *havirdhāna* shed, *H*, is erected. This is the shed for the Soma-cart used for carrying soma plants to the sacrificial ground. Regarding the derivation of the name, the *Brāhmaṇa* says: 'And because Soma is therein—Soma being *havis* (material for offering) for the gods—therefore it is called *Havirdhāna* (receptacle of *havis*)'.{d} The cart-shed is provided with doors on the eastern and the western side and possibly on the southern and northern sides. Regarding the construction of the cart-shed, Eggeling, following Sāyaṇa and Kātyāyana, explains that, in front of the carts and behind them, beams are driven into the ground, six on each side.{e} The two middle ones, one cubit north and south of the *prācī* line respectively, forming a gateway on each side. On these two rows of beams other beams are laid, running from south to north, and forming, as it were, the lintels of the gates; the tie beams running west-east rest on them. This frame of timber is to form a square of nine (or ten) cubits. Mats of seed-grass are spread over the tie beams.

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{d} *Śat. Br.* III. 5. 3. 2.

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{e} *Śat. Br.* III. 5.3.9. Eggeling's notes, SBE, 27, 128.

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*Uparavas* are sounding holes dug out in the ground near the *havirdhāna*. The *soma* plants are ground over this hole, emitting the sound of the grinding stone, which gave it the name. The exact location of these sounding holes is not clear. The *Śatapatha Brāhmaṇa* says: ‘He digs just beneath the fore-part of the shafts of the southern cart.’a Karavinda says that the *uparavas* are located in the south-west corner of the southern part of the cart-shed,—*dakṣiṇahavirdhānasya dakṣiṇāśronyāmu-paravāḥ*.

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The *uttara vedi, UV*, is raised near the eastern side of the *mahāvedi*, with the *prācī* line passing through its middle. It literally means ‘higher or upper altar’ and so is likened to the nose of the sacrificer: ‘That high altar (*uttara vedi*) is the nose oft he sacrificer; because they throw it up so as to be higher than the altar, therefore it is called ‘high altar’.b The altar is built with the earth dug out of the *cātvāla* pit. This *cātvāla* pit is dug out at a little distance towards north from the north-east corner of the *mahāvedi*. The *Brāhmaṇa* says: ‘....and from where the northern peg of the front side is, he strides three steps backwards and there marks off the pit (*cātvāla*).’c It is of the same measure as that of the *uttara vedi*. Karavinda’s comments on the *cātvāla* is as follows: *uttarasmādvedyaṃsādudakprakrame cātvāla uttaravedisammitah*. West of the *cātvāla* is the rubbish heap *utkara, U*. Eggeling has observed that the exact distance of the *cātvāla* is left to the discretion of the Adhvaryu priest, provided it is in front of the *utkara* and a narrow passage is left between them. He also says that the *cātvāla* pit should be contiguous to the north edge of the large altar, that is, the *mahāvedi*.

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DISTANCE AND RELATIVE POSITION OF GĀRHAPATYA, ĀHAVANĪYA, DAKṢIṆĀGNI AND UTKARA

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**3.1-3.5** According to Baudhāyana, the *āhavanīya* is constructed at a distance of 8 *prakramas* from the *gārhapatya* fire, when it is made by 4 Brāhmaṇas. The distance is sometimes 11 or 12 *prakramas* for peoples other than the Brāhmaṇas and followed traditionally from the time of the *Śatapatha Brāhmaṇa* (*Śat. Br.* I. 7.3. 23-25). For finding the relative positions of *gārhapatya*, *āhavanīya* and *dakṣiṇāgni* fires, Baudhāyana has prescribed the following three methods :

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b *Śat. Br.* III. 5.1.12.

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*First method.* Let *A*, *G*, and *D* stand for *āhavanīya*, *gārhapatya* and *dakṣiṇāgni* fires. The distance *AG* is divided into three equal parts, and with each third part, three squares are drawn touching each other; then the north-west corner of the western square, south-east corner of the same square and north-east corner of the eastern square mark the places for *gārhapatya*, *dakṣiṇāgni* and *āhavanīya* fires respectively (Fig. 27). When *A* and *G* are interchanged the corresponding position of *D* i.e. *U* will denote the place for *utkara*. Kātyāyana has given a similar method for fixing the positions of *A*, *G*, *D* and *U* (vide *Kśl.* 1.11).

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a *Śat. Br.* III. 5.4.3.

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c *Śat. Br.* III. 5.1.26.

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Fig. 27.

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Fig. 28.

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Fig. 29.

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Here, if a be the distance between the *gārhapatya* and the *āhavanīya*, then $AD = √((⅔ a)² + (a/3)²) = (√5)/3 a$ and GD = √((a/3)² + (a/3)²) = (√2)/3 a

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*Second method.* According to this method, $AD & = ⅔ (a + a/7) or ⅔ (a + a/6) / & = 16/21 a or 7/9 a$ and GD = 8/21 a or 7/18 a

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*Third method.* Here AD = ⅗ (a + a/5) = 18/25 a and GD = ⅖ (a + ⅕) = 12/25 a.

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The second method is given by Āpastamba (*Āśl.* 4.4) and the first method by Kātyāyana (*Kśl.* 1.11).

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From these three methods, the approximate values of √5 and √2 have been calculated by Dattaa as follows:— $√5 = 16/7, 7/3, 54/25 = 2.285, 2.333, 2.16 respectively.$ and √2 = 8/7, 7/6, 36/25 = 1.142, 1.166, 1.44 respectively.$

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a Datta (2), 203-205.

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The values √5 = 2.285 and √2 = 1.44 are correct upto first place of decimal and others are fairly approximate values.

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DĀRŚAPAURṆAMĀSIKA VEDI

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**3.6-3.8.** The *dārśapaurṇamāsika vedi* is placed towards the west side of the *āhavanīya* and is in the form of an isosceles trapezium having face equal to 48 *aṅgulas*, base 64 *aṅgulas* and altitude 96 *aṅgulas*.

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Here AD = 48 *aṅgulas*
BC = 64 *aṅgulas*
and EW = 96 *aṅgulas*.

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A cord of length 2 *BC* is taken and a mark is given at its middle. Two ends of the cord are fixed at the southern poles *A* and *B* and is stretched towards south by the middle mark and a pole is fixed at it. Fixing two ends of the cord at this pole an arc is drawn through *AB* by the middle mark of the cord. Similar arcs are drawn in other sides. This is the *vedi* (Fig. 28).

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This has been referred to in *Āśl.* 4.5 and *Mśl.* 1.4. The *vedi* has a long tradition and is mentioned in the *Taittirīya Saṃhitā* (II. 6.4. 2-3) and *Taittirīya Brāhmaṇa* (III. 2.9. 10).

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PAŚUBANDHA AND UTTARA VEDI

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**3.9-3.10.** The *paśubandha vedi* is in the form of an isosceles trapezium whose face equals 8 *padas*, base 10 *padas* and altitude 12 *padas*. Sometimes the *vedi* is measured by *akṣa*, *īṣā* and *yuga* units of a chariot. The *uttara vedi* according to Baudhāyana is a square pit of side 10 *padas*.

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PAITṚKĪ VEDI

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**3.11.** The *paitṛkī vedi* is a square altar and its four corners are placed in four cardinal directions *viz.* east, west, north and south. The side of the *paitṛkī vedi* is one-third of the units in *mahāvedi*, which is an isosceles trapezium of 972 sq. *padas*, having its face of 24 *padas*, base 30 *padas* and altitude 36 *padas*. Hence the corresponding units in *paitṛkī vedi* are 8, 10, 12 and its area ½ (8 + 10) × 12 = 108 sq. *padas*. This justifies Baudhāyana's statement that the *paitṛkī vedi* is one-ninth in area of the *mahāvedi*.

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Again, when one-third of the *mahāvedi* (i.e. *sautrāmaṇikī vedi*) is turned into a square, its side becomes 18 *padas* (*Bśl.* 3.12). Baudhāyana says in this rule that the side of the *paitṛkī vedi* is 18/(√3). This is also quite proper, for by the first method the side of the *paitṛkī vedi* equals √108 or 18/(√3).

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Kātyāyana, however, prescribes that in a square *ABCD* of 2 sq. *puruṣas*, the figure obtained by joining the middle poles *E*, *G*, *W*, *H*, that is the figure *EGWH* will be the required *paitṛkī vedi*. The area *EGWH* is undoubtedly a square of 1 sq.

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*puruṣa* (Fig. 29). Here again the area varies from that of Baudhāyana but agrees with that of Āpastamba (*Āśl.* 6.7-6.8). Though there is some difference in area, it is, however, a fact that the *paitṛki vedi* is a square pointing towards the cardinal directions.

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SAUTRĀMAṆIKĪ VEDI

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**3.12.** The rule of Baudhāyana suggests that the *Sautrāmaṇikī vedi* may be a square of 18 *padas* or an isosceles trapezium whose area is one-third of that of *mahāvedi*, having area of 972 sq. *padas*. Baudhāyana made no explicit mention of how to construct an isosceles trapezium similar to a given isosceles trapezium but with one-third of its area. Āpastamba (*Āśl.* 5.8) constructed it with 1/(√3) of the units used in *mahāvedi* or 8√3 and 10√3 as face and base and 12√3 as altitude. The *mahāvedi* is an isosceles trapezium having face 24, base 30 and altitude 36 units. Hence the *sautrāmaṇikī vedi* is an isosceles trapezium of face 24/(√3) or 8√3, base 30/(√3) or 10√3, and altitude 36/(√3) or 12√3. Hence the area of the figure in the above two cases comes out as,

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(i) ½(24/(√3)+30/(√3))×36/(√3)=½·54/(√3)·36/(√3)

and (ii) ½(8√3+10√3)×12√3=324.

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This equals one-third the area of a *mahāvedi*. The same method is also given by Kātyāyana (*Kśl.* 2.11-2.12).

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