The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t16: Chapter 19: The Construction of Fire-Altars in the Form of a Pyre (Śmaśānacit)
The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t16
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Chapter 19: The Construction of Fire-Altars in the Form of a Pyre (Śmaśānacit)
c8.t16.2
**19.1-19.2.** The fire-altar in the form of a pyre, as we shall presently see, is a trapezium. For its measurements and constructions as also for the bricks, a new unit has been introduced. Let p be this unit. According to rule 19.2, $p² = 1/15 of the area of the fire-altar = 1/15 × 15/2 sq. pu.$ $= ½ sq.pu.$ $p = 1/(√2) pu. = √7200 ang. = 84 ang. 28 tila.$ Dvārakānātha explains : *agnikṣetraṃ\dots pañcadaśadhā vibhajya labdhaṃ saptasahasrāṇi dve śate cāṅgulayaḥ | tasya bhāgasya samacaturaśrakaraṇī ṣaṭtilonapañcāśītyaṅgulā (85 aṅg. — 6 ti.).*
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Fig. 69. (a) Fire-altar in the form of a pyre (*śmaśānacit*)—first layer. (b) Method of making isosceles and double isosceles triangular bricks.
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The fire-altar is in the form of a trapezium ABCD, of which the western side BC is 2p units (= 170 aṅg. - 12 tila), the eastern side AD is 3p (= 254 aṅg. + 16 tila) and the height, that is, the distance between AD and BC is 6p (= 509 aṅg. - 2 tila) (Fig. 69). For the word trapezium, the word *ekato'nimaddirghacaturaśra* is used. It means a rectangle of which one side is shorter (than the opposite parallel side). The area of the trapezium is given by $2p × 6p + p/2 × 6p = 15p² = 15/2 sq. pu. = 7½ sq. pu.$ which satisfies the area of the *agnikṣetra*.
c8.t16.5
*First layer.* For purposes of making the bricks, a rectangle ABCD is formed such that its length AB is 3p and breadth BC is ½p. From the mid-point E of AD, join EB, EC. EBC is an isosceles triangle (*prauga*) of area ¾p². 20 such *praugas* equal 15p² or 7½ sq. pu. and can be accommodated within the fire-altar. To attain the number 200, each such isosceles triangle is divided into 10 parts in the manner shown in Fig. 69(b). The sides EB, EC and BC are each divided into 4 equal parts by marking 3 equidistant points on each side. The points on the sides are joined with those on the base as shown, so as to obtain 4 isosceles triangles at the base and 6 double isosceles triangles above them. About the formation of such triangles, the commentator says : *evam vibhakte pṛthvanikasthāḥ praugākārāścatasra iṣṭakāḥ / tatastisra ubhayataḥ praugākṛtayaḥ / tato dve / tata ekā cubukāntā /*
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Regarding the placement of 20 isosceles triangles EBC of area ¾p², a line EF is drawn in the middle of the body (Fig. 69a). In the eastern half, 11 such triangles can be placed, 6 with vertices turned west and 5 with vertices turned east. In the western half, 9 such triangles can be accommodated, 5 with vertices turned west and 4 with vertices turned east. This represents the arrangement of bricks in which 80 *praugas* and 120 *ubhayata praugas* are used.
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Fig. 70. Types of bricks used in the second layer of the *śmaśānacit*.
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Fig. 71. Arrangement of bricks in the *śmaśānacit*—2nd layer.
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**19.5-19.7.** *Bricks and their placement in the second layer.* The entire space of the fire-altar (*agnikṣetra*) can be divided into five large isosceles triangles of base *p* and height (from vertex to base) 6*p*. Three of them have their vertices turned towards west and the vertices of the two in between them are turned towards east. The two isosceles triangles, one on the southern side and the other on the northern, which have their vertices turned towards west, are bisected by perpendicular lines drawn from the vertex to the base (Fig. 71). The *agnikṣetra* is thus divided into three portions, (1) half isosceles triangle *CDE* on the southern side, (2) the half isosceles triangle *BAF* on the northern side, and (3) the rectangle *BCEF* in the middle. Note that, since *ED* and *AF* are each ½p, EF = BC = 2p.
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To make the different types of bricks, the half isosceles triangle on either side is divided into six parts (Fig. 70). *AB*, *BC* and *AC* are divided into three equal parts each by the points, *a*, *b*, *c*, *d*, *e*, and *f*. Join *bc*, *ad*, *de* and *cgf*. The space is thus divided into 3 half isosceles triangles *Bbc*, *cdg* and *dce* which constitute the first type of brick B₁. Note that Bb = 2p, bc = p/2. Through the above division, we get the second type B₂, the rectangular bricks *abcg*, *Aagf* and *fgde*, of which the sides are 2p and p . The third type B₃, called the *bṛhatī*, is a rectangular brick *ABCD* (Fig. 70(b)), of which AB = ⅙p and AD = ¼p. The fourth type B₄ is half *bṛhatī* (Fig. 70(c)), a rectangular brick measuring p/4 by p/6.
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The arrangement of bricks in the second layer is shown in Fig. 71. 3B₁s and 3 B₂s are placed in each of the two half-isosceles parts of the fire-altar. 8 B₄s are placed on the eastern and the western parts each of the rectangular part of the fire-altar, with the longer side turned north-south. (Note that 2p/¼p = 8). These two rows use up ⅓p and the remaining vertical distance is (6p - p/3) = 17p/2. The remaining space in the rectangular part of the fire-altar can be divided into 17 horizontal and 8 vertical rows in which 136 B₃ bricks can be fitted with their longer sides turned east. Thus, the number of bricks used in this way totals as follows : $B₁ - 6 ; B₂ - 6 ; B₃ - 136 ; B₄ - 16 ; total - 164.$ There is still a deficit of 36 bricks. According to the commentator, the deficit can be met by replacing 36 B₃ bricks (9 from each of the 4 corners) by 72 B₄s. Dvārakānātha says : *pārśvayorupahitapraugārdhayordvādaśeṣṭakāḥ | madhyabhūtacaturasra (pūrvā) parāntayoḥ ṣoḍaśārdheṣṭakāḥ | madhye ṣaṭtriṁśaccataṁ bṛhatyaḥ prāgāyatāḥ | evaṁ catuḥṣaṣṭi śatamiṣṭakāḥ | ṣaṭtriṁśannyūnā bhavanti | śroṇyaṁseṣu nava nava bṛhatīścaturasrākṛtā uddhṛtyāṣṭādaśāṣṭādaśārdhyā nidheyāḥ | evaṁ dviśataḥ prastāraḥ |*
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**19.9-19.11.** These *sūtras* deal with the height of the fire-altars and do not call for much comment.