The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t17: Chapter 20: The Construction of Fire-Altars in the Form of a Tortoise (Kūrmacit)—First Type with Twisted Limbs
The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t17
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- English
Chapter 20: The Construction of Fire-Altars in the Form of a Tortoise (Kūrmacit)—First Type with Twisted Limbs
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**20.1-20.2.** Fire-altars in the form of a tortoise are of two types, (1) the tortoise with twisted limbs (*vakrāṅgāḥ*) and (2) the tortoise with rounded limbs (*parimaṇḍalāḥ*). The construction of the first type is described in this chapter.
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**20.3-20.7.** *The construction of the fire-altar.* A square of side 10 *prakamas* or 300 *aṅg* is first constructed and the four corners are cut off by 30 *aṅg* (that is, an isosceles triangle of two equal sides, each 30 *aṅg* is removed from each corner. *A B C D E F G H* is the shape of the body thus obtained (Fig. 72). Note that AB = CD = EF = HG = 60√2 aṅg. and BC = DE = FG = AH = 180 aṅg. Four squares, each of side 30 *aṅg*. are placed side by side in contact with the middle of the eastern side of the body *AH*. Outer halves of the two side squares are diagonally cut off so as to get the figure *a b c d*. Note that *ab* equals 60 *aṅg*. Similar figures are constructed in the middle of the other three sides of the body *BC*, *DE* and *FG*.
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Fig. 72. Fire-altar in the form of a tortoise with twisted limbs. (a) Lay-out. (b) Brick types.
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The head is constructed by placing a rectangle on *ab* (ab = 60 aṅg) of which length or height is 75 *aṅg*; the two eastern corners are then cut off by 30 *aṅg* each so as to get the shape *efabg* for the head.
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For each foot, a rectangle 30√2 aṅg. broad by 60√2 aṅg long is placed in the middle of the cut off corner, say on *HG* for the south-east corner. Thereupon, the eastern corner of this rectangle is cut off by 30√2 aṅg so as to obtain *hijk* for the shape of the foot. Similar constructions are made upon *EF*, *CD* and *AB* to build the remaining feet.
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The distribution of areas in the different parts of the fire-altar is as follows : The body (*ātman*) with the four projected areas : $1/(120²)[300² - 2 × 60 × 60 + 12 × 30 × 30] = 13/2 sq. pu. or 104 caturthi.$ The head : 1/(120²)[75 × 60 - 30 × 30] = ¼ sq. pu. or 4 caturthis. The feet : 4/(120²)[60 × 60 - 30 × 30] = ¾ sq. pu or 12 caturthis. The total area = (13/2 + ¼ + ¾)sq. pu = 7½ sq. pu. or 120 caturthis.
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Note that 1 sq. pu = 16 caturthis or 16 ṣoḍaśīs. The *caturthi* unit is mentioned here because the commentator has given the measurements in this unit as follows: *ātmani catuḥ śataṃ caturthyaḥ śirasi catasraścaturthyaḥ pādeṣu dvādaśa evaṃ viṃśaśataṃ caturthyaḥ /*
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**20.8-20.11. Bricks.** The following 6 types of bricks have been prescribed for covering the fire-altar :—
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B₁ — square brick of side 1/4 pu, caturthi ; 30 × 30 sq. ang. B₂ — triangular brick (diagonally cut), half of *caturthi*, *ardhyā* ; two sides 30 ang each, diagonal side 30√2 ang. B₃ — triangular brick, one fourth of *caturthi*, *pādyā* ; two sides 15√2 ang each, the diagonal side 30 ang. B₄ — four-sided brick of area 1½ padya ; its sides are 15 ang., 15 ang., 30 ang. and 15√2 ang. B₅ — brick formed by joining 2 B₄ bricks along the longest side, hamsamukhi. B₆ — square brick of area equal to half *caturthi* ; 15√2 × 15√2 sq. ang.
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Fig. 73. Fire-altar in the form of a tortoise, showing arrangement of bricks in the first layer.
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**20.12-20.15.** *The placement of bricks in the first layer.* As per *sūtras*, 1 *B*₆ is to be placed at the tip of the head and below it 2 *B*₅s (Fig. 73). In each foot 5 *B*₆s and 2 *B*₃s are placed as shown in the figure. In the remaining space, *B*₂s are placed wherever the corners are cut diagonally and *B*₁s in the rest. Clearly, the number 200 cannot be arrived at in this way; so *B*₁s are replaced by *B*₂s as necessary. According to the commentary, this can be done in the following way. Excluding the feet, the whole space of the fire-altar can be divided into 12 vertical rows, — 6 on the southern side of the line passing through the centre of the body and the tip of the head and 6 on its northern side. In the first 6 rows from the southernmost one, the arrangement is as follows :—
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1st row : *B*₁ — 2 ; *B*₂ — 2 ; total — 4
2nd row : *B*₁ — 6 ; *B*₂ — 2 ; ,, — 8
3rd row : *B*₁ — 2 ; *B*₂ — 14 ; ,, —16
4th row : *B*₁ — 3 ; *B*₂ — 14 ; ,, —17
5th row : *B*₁ — 3 ; *B*₂ — 16 ; ,, —19
6th row : *B*₁ — 6 ; *B*₂ — 14 ; *B*₅ — 1 ,, —21
(*B*₆ at the tip is excluded) total —85
Likewise, in 6 rows north of the central line; total —85
In the feet : *B*₃ — 8 ; *B*₆ — 20; total —28
Total 198
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With *B*₆ at the tip of the head, the total comes to 199. So the commentator observes that to complete the number and for the sake of symmetry *B*₆ at the tip is replaced by 2*B*₃s (*śirasi sūtroktāṃ caturaśreṣṭakāmuddhṛtyāntadīrghapārśve pādeṣṭake nidadhyāt |*). The arrangement of bricks is shown in Table 13.
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TABLE 13. *Number and types of bricks in different parts of the kūrmacit fire-altar—first layer.
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| Parts of the *citi* | Brick type | | | | | Total |
| | *B₁* | *B₂* | *B₃* | *B₄* | *B₅* | *B₆* | |
| Head | 2 | | 2 | | 2 | | 6\* |
| Body | 42 | 124 | | | | | 166\* |
| Feet | | | 8 | | | 20 | 28 |
| Total | 44 | 124 | 10 | — | 2 | 20 | 200 |
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**20.16-20.21.** *The placement of bricks in the second layer.* In the second layer, 1 *B*₅ is placed at the tip of the head, flanked on each side by 1 *B*₃. Below each *B*₃ on either side 2 B₄s and 1 B₃ are placed as shown in Fig. 74. In each foot, 2 B₁s and 3 B₂s are placed in such a way that half of 1 B₁ lies in the body to avoid overlapping of
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Fig. 74. Fire-altar in the form of a tortoise, showing arrangement of bricks in the second layer.
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edges. In the projected part of the body at the centre of each side, 5 B₃s are placed at the end followed by 3 B₁s, part of which lie in the body.
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As in the first layer, the second can be divided into 13 vertical rows, excluding part of each foot (containing 4 bricks) as shown in the figure. Starting from the southernmost row, we have :
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| | total | — 5 |
| 1st row : B₃ — 5 ; | | |
| 2nd row : B₁ — 3 ; B₂ — 2 ; B₃ — 4 | ,, | — 9 |
| 3rd row : B₁ — 9 ; B₂ — 2 ; | ,, | —11 |
| 4th row : B₁ — 9 ; B₃ — 4 ; | ,, | —13 |
| 5th row : B₁ — 9 ; B₂ — 2 ; | ,, | —11 |
| 6th row : B₁ — 11 ; B₃ — 4 ; B₄ — 2 | ,, | —17 |
| | total | —66 |
| 7th (central) row : B₁ — 13 ; B₃ — 1 ; B₅ — 1 ; | ,, | —15 |
| The remaining 6 rows on the northern side as in the southern | ,, | —66 |
| Remaining parts of 4 feet : B₁ — 4 ; B₂ — 8 ; | ,, | —12 |
| | Total | 159 |
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Thus there is a deficit of 41 bricks (*ekacatvāriṁśadūnāḥ*). This deficit is met by replacing 40 B₁s (5B₁s from each of the 3rd, 4th, 5th and 6th rows of each of the southern and the northern halves of the *agnikṣetra*) by 80 B₂s. Also 1 B₁ in the head is replaced by 2 B₂s. Dvārakānātha says: *tṛtīyādiṣu catasṛṣu pañca pañca caturthiruddhṛtyaṁ catvāri-* *ṁśadardhyā dakṣiṇottarasaviśeṣa upadheyāḥ | evamuttarasminpārśve viparītasaviśeṣāḥ | śirasyekām caturthīmuddhṛtya dve ardhye upadheye |* The final arrangement of bricks in different parts of the fire-altar is shown in Table 14.
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TABLE 14. *Number and types of bricks in different parts of the fire-altar—2nd layer.
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| Parts of the *citi* | Brick Type B₁ | Brick Type B₂ | Brick Type B₃ | Brick Type B₄ | Brick Type B₅ | Brick Type B₆ | Total |
| Head, including part of body. | 1 | 2 | 4 | 4 | 1 | — | 12 |
| Body, excluding portions accounted for in head and feet. | 49 | 88 | 31 | — | — | — | 168 |
| Feet, including part of body. | 8 | 12 | — | — | — | — | 20 |
| Total | 58 | 102 | 35 | 4 | 1 | — | 200 |