The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t9: Chapter 11: Construction of a Fire-Altar in the Form of a Falcon with Curved Wings and Extended Tail—Second Type

The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t9

Language: English

Chapter 11: Construction of a Fire-Altar in the Form of a Falcon with Curved Wings and Extended Tail—Second Type

c8.t9.2

**11.2-11.3.** *Measurement of the different parts.* We have noticed the use of a new unit of square measure, the *caturthī*, 30 × 30 sq. *aṅgulas* in the case of the *śyenacit* of the first type. Now another unit, the *pañcamī*, 24 × 24 sq. *aṅgulas* or 1 sq. *aratni* (a square of side one-fifth of a *puruṣa*) is introduced. Clearly, 7½ sq. *pu.* is equivalent to (15 × 120 × 120)/(2 × 24 × 24) or 187½ *pañcamīs*, as stated in the rule 11.2. These units are distributed in the various parts of the fire-altar as follows:

c8.t9.3

| The head | ... | 3⅛ *pañcamīs* or sq. *aratni*. |
| The body | ... | 52 ,, ,, |
| The two wings | ... | 117 ,, ,, |
| The tail | ... | 15 ,, ,, |
| | | ----- |
| Total | ... | 187½ ,, ,, |
| | | ----- |

c8.t9.4

These given areas must be satisfied in constructing the figures of the various parts as we shall see in the following *sūtras*.

c8.t9.5

**11.4.** *Construction of different parts of the falcon.* Unlike the falcon of the first type detailed measurements of the various rectangles involved have not been given. However, with the indications given in the rule and the areas in the previous rules, the various parts can be constructed without difficulty.

c8.t9.6

The body is made out of a rectangle *ABCD* (Fig. 41(a) ), of which AD = 144 *aṅgulas* or 6 *aratnis*, AB = 240 *aṅgulas* or 10 *aratnis* and the area 60 sq. *aratnis*. By the cutting of the corners at distances of 2 *aratnis* (48 *aṅgulas*), 8 sq. *aratnis* are removed so that *EFGHIJKL* measures exactly 52 sq. *aratnis*.

c8.t9.7

The head is constructed out of a rectangle 48 × 54 sq. *aṅg.* (AE = AG = ED = DF = 24 *aṅgulas*) such that *EFCBG* measures 3⅛ sq. *aratnis*.

c8.t9.8

The tail is done in the same way as before. Here *AD* equals 8 *aratnis* (192 *aṅgulas*), *AB* 3 *aratnis* (72 *aṅgulas*) and the area 24 sq. *aratnis* (Fig. 41 (c) ). *AB*, *AE*, *FD*, *DC* being equal to 3 *aratnis*, 9 sq. *aratnis* are removed, leaving the area of the tail *EBCF* as 15 sq. *aratnis*.

c8.t9.9

For the wing, the rectangle to be taken should have its side *AD* as 9 *aratnis* (= 216 *aṅgulas*) and *AB* 6 *aratnis* (144 *aṅg.*); the area is 54 sq. *aratnis*. The bending (*nirṇāma*) is made as before, the distance *EP* being 3 *aratnis* (72 *aṅgulas*). For the plumages, 6 rectangles DGK₁L₁, L₁K₁K₂L₂ etc. are fitted at the end of the tail, diagonally intersected and outer halves rejected. Now, each such rectangle is *adhyardhā-pañcamī*, that is, 36 × 24 sq. *aṅgulas* or 1½ sq. *aratni*; the area of 6 of them is 9 sq. *aratnis* and that of the 6 plumages (*patra*) after rejection of half is 4½ sq. *aratnis*. The total area of each wing is, therefore, 58½ sq. *aratnis* and that of two wings 117 sq. *aratnis*.

c8.t9.10

Fig. 41. Different parts of the falcon with curved wings and extended tail : (a) body, (b) head, (c) tail, and (d) wing with plumages—second type.

c8.t9.11

**11.5-11.6.** *Type of bricks.* The following ten types of bricks have been prescribed for covering the fire-altar (Fig. 42) :—

c8.t9.12

| *B*₁ | — square brick of side 1/5 *pu*, *pañcamī*: | 24 × 24 sq. *aṅg.* |
| *B*₂ | — rectangular brick longer than *pañcamī* by half, *adhyardhā-pañcamī*: | 24 × 36 sq. *aṅg.* |
| *B*₃ | — rectangular brick longer than *pañcamī* by a quarter, *pañcamī-sapādā*: | 24 × 30 sq. *aṅg.* |
| *B*₄ | — triangular brick, half of one-fifth, *pañcamī-ardhā*: | 24, 24, 24 √2 *aṅg.* |
| *B*₅ | — triangular brick, quarter of one-fifth, *pañcamī-pādyā*: | 24, 12 √2, 12 √2 *aṅg.* |
| *B*₆ | — triangular brick, half of *adhyardhā*, *adhyardhārdhā*: | 36, 24, 12 √13 *aṅg.* |
| *B*₇ | — triangular brick, quarter of *adhyardhā*, with longer base, *BC* = 36 *aṅg.*, also called *dīrghapādyā*. | |
| *B*₈ | — triangular brick, quarter of *adhyardhā*, with a short base, *BC* = 24 *aṅg.*, also called *śūlapādyā* (pointed like a spear). | |

c8.t9.13

B₉ — triangular brick obtained by joining one one-eighth of a *pañcamī* brick ABD with one one-eighth of an *adhyardhā* brick ADC along the common side AD (= 12 *aṅg*); also called *ubhayī*.

c8.t9.14

B₁₀ — triangular brick, one-eighth of a *pañcamī*, 12, 12, 12 √2 *aṅg*.

c8.t9.16

Fig. 42. Brick types.

c8.t9.17

**11.7-11.9.** *Placement of bricks in the first layer.* The arrangement of bricks is illustrated in Fig. 43. As the *sūtras* have not given details further than some general directions, D's commentary has been followed to explain the disposition of 200 bricks.

c8.t9.18

The fire-altar from the western end of the tail, through the body, upto the eastern tip of the head, excluding the wings, is divided into 15 rows south-north. Beginning with the western end as the first layer, the number and types of bricks are as follows :—

c8.t9.19

1st row, in the tail — B₁ — 6 ; B₄ — 2 ; total — 8 2nd row, " — B₁ — 4 ; B₄ — 2 ; total — 6 3rd row, " B₄ — 6 ; " — 6 4th row, in the body B₄ — 6 ; " — 6 5th row, " — B₁ — 4 ; B₄ — 2 ; " — 6 6th-11th row " — B₁ — 6 × 6 ; " — 36 12th row (like 5th) " — B₁ — 4 ; B₄ — 2 ; " — 6 13th row (like 4th) " B₄ — 6 ; " — 6 14th row, in the head — B₃ — 2 ; " — 2 15th row, " B₄ — 2 ; " — 2 — 84 —

c8.t9.20

In each wing, there are six rows, west-east plus the 7th row of plumages, of which brick placements in the southern wing are as follows:—

c8.t9.21

| 1st row (immediately after the body) | — B₂ — 5 ; | B₆ — 2 ; | Total — 7 |
| 2nd row ,, | — B₂ — 5 ; | B₆ — 2 ; | ,, — 7 |
| 3rd row ,, | — | B₆ — 12 ; | ,, —12 |
| 4th row ,, | — | B₆ — 12 ; | ,, —12 |
| 5th row ,, | — B₂ — 5 ; | B₆ — 2 ; | ,, — 7 |
| 6th row ,, | — B₂ — 5 ; | B₆ — 2 ; | ,, — 7 |
| 7th row of plumages (*patra*) | — | B₆ — 6 ; | ,, — 6 |
| | | | ——— |
| | | | 58 |
| In the northern wing, the arrangement is same, but reverse | | ,, | —58 |
| | | | ——— |
| | | Total | 116 |
| | | | ——— |

c8.t9.22

Fig. 43. Arrangement of bricks in the syenacit—second type, first layer.

c8.t9.23

c8.t9.24

TABLE 7. *Number and types of bricks used in different parts of the fire-altar—first layer*

c8.t9.25

| Parts of the *citi* | Brick types | | | | | Total |
| | B₁ | B₂ | B₃ | B₄ | B₆ | |
| Head | | | 2 | 2 | | 4 |
| Body | 44 | | | 16 | | 60 |
| Wings | | 40 | | | 76 | 116 |
| Tail | 10 | | | 10 | | 20 |
| Total | 54 | 40 | 2 | 28 | 76 | 200 |

c8.t9.26

**11.10-11.13.** *Placement of bricks in the second layer.* By placing B₉ bricks (*ubhayi*) at the eastern and the western end of the junction line between the wing and the body such that 12 *aṅg.* of the base lies in the body and 18 *aṅg.* in the wing, the *sūtrakāra* avoids the overlapping of edges of bricks in the two layers (Fig. 44). This is also the purpose of placing B₉s on each side of the head and B₂s at the end of the tail flanked at the western corners by B₅s and B₁₀s. For the complete arrangement of bricks, we again follow the commentator who this time divides the tail, the body and the head in 12 rows beginning with the 1st row at the western end of the tail and ending with the the 12th row at the head. In this division the wing with part of the junction lying in the body is separately treated as before.

c8.t9.28

Fig. 44. Arrangement of bricks in the *śyenacit*—second type, second layer.

c8.t9.29

| 1st row, | in the tail (western) | —B₂ — 5 ; | B₄ — 2 ; B₅ — 4 ; | B₁₀ — 2 ; | Total | 13 |
| 2nd row, | ,, (middle) | —B₁ — 3 ; | B₄ — 2 ; | | ,, | 5 |
| 3rd row, | ,, (junction with body, *sandhirītyā*) | —B₁ — 1 ; | B₄ — 2 ; B₅ — 2; | | ,, | 5 |
| 4th row, | in the body | —B₁ — 3 ; | B₄ — 2 | | ,, | 5 |
| 5th row | ,, | —B₃ — 5 ; | | | ,, | 5 |
| 6th row, | ,, | —B₂ — 5 ; | | | ,, | 5 |
| 7th row, | ,, (middle) | —B₂ — 2 ; | B₆ — 4 ; B₇ — 2 ; | B₈ — 2 ; | ,, | 10 |
| 8th row, | ,, | —B₂ — 5 | | | ,, | 5 |
| 9th row, | ,, | —B₃ — 5 ; | | | ,, | 5 |
| 10th row, | ,, | —B₁ — 3 ; | B₄ — 2 ; | | ,, | 5 |
| 11th row, | ,, (at the junction with the head, *śiropyaya*), | | | B₁ — 1 ; B₄ — 2 ; | ,, | 3 |
| 12th row, | in the head | —B₃ — 1 ; | B₅ — 1 ; B₉ — 4 ; | | ,, | 6 |
| | | | | | | 72 |

c8.t9.30

In each wing there are six rows, west-east, beginning at the junction layer plus the seventh row of plumages.

c8.t9.31

| 1st row of the southern wing in the junction (12 *aṅg.* within body and 18 *aṅg.* in the wing) | | —B₃ — 5 ; | B₅ — 2 ; | B₈ — 1 ; | B₉ — 2 ; | Total | 10 |
| 2nd row | | —B₂ — 5 ; | B₆ — 2 ; | | | ,, | 7 |
| 3rd row | | —B₂ — 5 ; | B₆ — 2 ; | | | ,, | 7 |
| 4th row | (at the bending, *nirṇāma*) | —B₂ — 5 ; | B₆ — 1 ; | B₇ — 1 ; | B₈ — 1 ; | ,, | 8 |
| 5th row | | —B₂ — 5 ; | B₆ — 2 ; | | | ,, | 7 |
| 6th row | | —B₂ — 5 ; | B₆ — 2 ; | | | ,, | 7 |
| 7th row | of plumages (*patrarītyā*) | —B₆ — 6 ; | B₇ — 12 ; | | | ,’ | 18 |
| | | | | | | | 64 |
| In the northern wing, the arrangement is the same, but reverse | | | | | | ,, | 64 |
| | | | | | | Total | 128 |

c8.t9.32

The number and types of bricks used are shown in Table 8.

c8.t9.33

TABLE 8. *Arrangement of bricks in different parts of the fire-altar—second layer.

c8.t9.34

| Parts of the *citi* | Brick type | | | | | | | | | | Total |
| | B₁ | B₂ | B₃ | B₄ | B₅ | B₆ | B₇ | B₈ | B₉ | B₁₀ | |
| Head (including portion of body at junction, 12, 11) | 1 | | 1 | 2 | 1 | | | | 4 | | 9 |
| Body (excluding portions at junctions with head, tail and wings, 4-10) | 6 | 12 | 10 | 4 | | 4 | 2 | 2 | | | 40 |
| Wings (including junction with body and *patras*) | | 50 | 10 | | 4 | 30 | 26 | 4 | 4 | | 128 |
| Tail (including junction with body, 1-3) | 4 | 5 | | 6 | 6 | | | | | 2 | 23 |
| Total : | 11 | 67 | 21 | 12 | 11 | 34 | 28 | 6 | 8 | 2 | 200 |

c8.t9.35

In his commentary, *D.* states 9 bricks in the head, 62 in the body, 21 in the tail and 108 in the wings; that is, he includes in the body 20 bricks at the two junctions of the wings with the body and 2 B₅s at the junction of the tail with the body. In the number of brick types, there is no discrepancy : *asminprastāre ekādaśa pañcamyaḥ | dvādaśa tadardhyāḥ | ekādaśa tatpādyāḥ | dve aṣṭamyau | ekaviṁśatiḥ | ubhayyo’ṣṭau | sapta-ṣaṣṭiradhyardhāḥ | catustriṁśadardhyāḥ | aṣṭāviṁśatidīrghapādyāḥ | ṣaṭ śūlapādyāḥ |.*