The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t8: Chapter 10: Construction of a Fire-Altar in the Form of a Falcon with Curved Wings and Extended Tail—First Type

The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava: With Text, English Translation and Commentary c8.t8

Language: English

Chapter 10: Construction of a Fire-Altar in the Form of a Falcon with Curved Wings and Extended Tail—First Type

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**10.1.** This type of fire-altar is constructed more in the likeness of a falcon. To achieve this the two wings are to be curved or bent and the tail is to be extended, that is, spread out. The body (*ātman*) itself should be cut out at its four corners, and there should be a head. The end of each wing is serrated to give it the appearance of being provided with feathers (*patra*). The laying of this type of fire-altar on the part of those who desire heaven has been greatly emphasized in the *Brāhmaṇas*. Here are a few excerpts from the *Śatapatha Brāhmaṇa* : "Prajāpati was desirous of going up to the world of heaven ;…… He saw this bird-like body, the fire-altar, and constructed it. He attempted to fly up, without contracting and expanding (the wings), but could not do so. By contracting and expanding (the wings) he did fly up : whence even to this day birds can only fly up when they contract their wings and spread their feathers"a . Again, "He contracts (the right wing) inside on both sides by just four finger-breadths, and expands it outside on both sides by four finger-breadths;…… In the same way with regard to the tail, and in the same way in regard to the left wing."b

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**10.2-10.3.** *Types of bricks.* For building a fire-altar of this shape which is fully described in what follows, rectilinear bricks alone would not do. Bricks of other geometrical shapes are needed, which are first dealt with. In the first type under consideration in this chapter, the following five types have been prescribed (Fig. 37).

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B₁ — one-fourth (*caturthī*) square brick—30 × 30 sq. *aṅgulas*; that is, a square whose side AB is ¼ *pu.* or 30 *aṅgulas*.

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B₂ — half brick (*ardhā*) obtained by cutting the one-fourth square brick diagonally; each of 2 sides *AB*, *AC* equals 30 *aṅgulas* and the diagonal side or hypoteneuse BC 30 √2 *aṅgulas*.

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a *Śat. Br.* X. 2.1.1. (Eggeling’s translation).

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b *Śat. Br.* X. 2.1.4.

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B₃ — quarter brick (*pādyā*), obtained by cutting the one-fourth brick diagonally; each of 2 sides *AB*, *AC* equals 15 √ 2 *aṅg.* and the hypoteneuse *BC* 30 *aṅgulas*.

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B₄ — four-sided quarter brick (*caturaśra-pādyā*), of which *CD* equals 1⅚ *aṅgulas*, *BC* 15 *aṅgulas*, *AB* 22½ *aṅgulas*, *AD* 15 √ 2 *aṅgulas*. 1 *pada* being 15 *aṅgulas*, the measures are given here in *aṅgulas*. *padasaviśeṣa* means the diagonal of a square of side 1 *pada* or 15 *aṅgulas* or the hypoteneuse of a right-isosceles triangle of side 15 *aṅgulas*. Clearly, such a figure is obtained by joining the rectangle *EBCD* with the isosceles right triangle *AED* along the common side *ED*. Its area is (15 × 15)/2 + (15 × 15)/2 sq. *aṅgulas* = 15 × 15 sq. *aṅgulas*, the same as that of the quarter brick B₃.

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B₅ — half brick *ABCDE* obtained by joining 2 B₄s along their common longest side *AF*; this is also called swan-beaked, *haṁsamukhī*.

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Fig. 37. Brick types.

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AREAS AND SHAPES OF DIFFERENT PARTS OF THE FIRE-ALTAR.

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**10.4-10.9.** *The body*: A rectangle *ABCD* is drawn with *AB* equal to 2 *pu.* or 240 *aṅg.* and *AD* 10 *padas* or 150 *aṅg.* (Fig. 38 (a) ). *FD*, *DG*, *HC*, *CI*, *BJ*, *BK*, *AL* and *AE* are measured out such that each equals 45 *aṅg.* (= 1½ *prakrama*). Join *FG*, *HI*, *JK* and *LE*. *EFGHIJKL* is the body of the altar, with its four corners cut off as laid down in the rule. The area is (240 × 180 - 2 × 45 × 45) sq. *aṅgulas* or ⅞¼ sq. *pu.* The commentator measures the area in a unit of *ṣoḍaśī* which is 1/16 sq. *pu.* or 30 × 30 sq. *aṅgulas*, also called a *caturthī*, the area of B₁. In this unit, the area of the body reduces to 35½ *caturthīs*,—*evamātmaśroṇyaṁseṣvardhapañcamāścaturthyo nirastā bhavanti | atha śiṣṭā ardhaṣaṣṭhāstriṁśaccaturthyo bhavanti* |—*D.*

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*The head*: A rectangle *ABCD* is formed with *AB* equal to 82½ *aṅg.* and BC = 60 *aṅg.* (Fig. 38 (b)). From the centre *E* of *AD*, *EF* and *EG* are joined, *AE*, *ED*, *AG*, *DF* each being equal to 30 *aṅg.* *EGBCF* is the head measuring 4¼ *caturthīs* or 7/32 sq. *pu.* (*itarā ardhapañcamāḥ śiro bhavanti*—*D.*).

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*The tail* : The tail is formed out of a rectangle *ABCD*, of which *AB* is 90 *aṅg*. and *BC* 240 *aṅg.*, by cutting off the two triangles *ABE* and *CDF*, where *AB* = *AE* = =*CD* = *FD* = 90 *aṅg.* (Fig. 38 (c) ). The areas of the tail *EBCF* is 15 *caturthis* or 15/16 sq. *pu*.

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*The wings* : A rectangle *ABCD*, of which *AB* is 150 *aṅg*. and *BC* 180 *aṅg.*, is formed (Fig. 38 (d)). At the mid-point *P* of *BC* a perpendicular *PE* is drawn towards east so that *PE* is 90 *aṅg*. Then the triangle *EBC* is cut off and placed on the eastern side *AD* as the triangle *FAD*. The area of the figure *ABECDF* remains the same as the rectangle *ABCD*. In this way the wing is bent or curved (*nirṇāma*). That the area is not affected by bending in this way is clearly recognized in the *Śatapatha Brāhmaṇa* : "He then makes the wings crooked, for a bird's wings are crooked.........he thus draws them out by just as much as he draws them in; and thus, indeed, he neither exceeds (its size) nor does he make it too small."a

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For the construction of the plumages, five squares DGK₁L₁, L₁K₁K₂L₂ etc. are drawn with side 30 *aṅg*. and intersected by the diagonals DK₁, L₁K₂ etc. The outer triangular halves DGK₁, L₁K₁K₂ etc. are cut off.

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This is the construction of the southern wing; the northern wing is constructed in the same manner. The area of each wing is 32½ *caturthis* and of two wings 65 *caturthis* or 65/16 sq. *pu*.

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Fig. 38. Different parts of the Falcon with curved wings and extended tail—(a) body, (b) head, (c) tail, and (d) wing with plumages (*patra*)—first type.

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a *Śat. Br.* X. 2·1.7 ; Eggeling's translation.

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The total area of the fire-altar, including the body, the head, the tail and the two wings is (35½ + 4½ + 15 + 65) or 120 *caturthīs* (or *ṣoḍaśīs*), that is, 120/16 = 7½ sq. *pu.* (*atra ātmani sārdhapañcatriṃśaccaturthyaḥ* | *śirasyardhapañcamāḥ* | *pucche pañcadaśa* | *daśasu patreṣu pañca* | *pakṣayoḥ ṣaṣṭiḥ* | *evaṃ viṃśatyadhikaṃ śataṃ ṣoḍaśyaḥ* | *puruṣakṣetre ṣoḍaśa ṣoḍaśyaḥ śerate* |—D.)

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**10.10-10.14.** *Placement of bricks in the first layer.* The placement of bricks is shown in Fig. 39 (a) and (b). Two methods are given for the head; the second method is shown in (b). In each case the number of bricks employed is 14. At the eastern and the western end of the body near the junctions with the head and the tail 5 B₃s are placed. In the truncated parts, B₂s and B₃s are placed. Since the head has already been covered, this means placement in the 4 corners of the body, 2 sides of the wing (excluding the western end), eastern and western sides of the curved wings and the feathers at the end. The rest is filled with B₁ bricks.

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Fig. 39. (a) Arrangement of bricks in the *śyenacit* with curved wings and extended tail (north wing not shown); (b) alternative placement of bricks in the head. First layer.

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As pointed out by Thibaut, the bricks specifically mentioned in the *sūtras* 10.10-10.12 total 68; the remaining space, as per *sūtra* 10.13, can be filled with 91 B₁ bricks thus giving a total number of 159 bricks which fall short of 200 bricksa.

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The deficit is to be made good by using B₂s and B₃s as necessary. Dvārakānātha explains that there are 12 rows south-north in the tail and the body excluding the head and the wing (*śirovarjaṃ pucchena sahātmanyudicyo dvādaśa rītayaḥ*). Starting from the end of the tail, 4 B₁s in the 2nd row are replaced by 16 B₃s, 2 B₂s in the 3rd row by 4 B₃s and the middle B₁ in the 8th row by 2B₂s. In each wing, excluding the feathers, there are 6 rows west-east. In each of the 3rd and the 4th row from the south, 3 B₁s are replaced by 6 B₂s and 1 B₁ is substituted by 4 B₃s. In the 5th row, 1 B₁ at the bottom is replaced by 2 B₂s. The total number and types of bricks used in the various parts of the fire-altar are shown in Table 5.

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a Thibaut, 210.

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Table 5. *Number and types of bricks used in different parts of the fire-altar—first layer.*

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| Parts of the *citi* | Brick type | | | | | Total |
| | B₁ | B₂ | B₃ | B₄ | B₅ | |
| Head | 1 | | 6 | 6 | 1 | 14 |
| Body | 30 | 6 | 10 | | | 46 |
| Wings | 30 | 62 | 16 | | | 108 |
| Tail | 8 | 4 | 20 | | | 32 |
| Total | 69 | 72 | 52 | 6 | 1 | 200 |

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10.15-10.20.

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*Placement of bricks in the second layer.* *Svayamātṛṇṇā* is the central place of the fire-altar. Here it means the centre of the body. To accommodate 4 B₅s, a

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Fig. 40. Arrangement of bricks in the second layer.

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rectangle ABCD with *AD* equal to 60 *aṅg.* (2 *prakramas*) and *AB* 45 *aṅg.* (3 *padas*) is taken in the centre of the body (Fig. 40). The placement of 4 B₅s and 4 B₃s is shown as per explanation of the commentator : *svayamātṛṇṇāvakāśamadhyam gṛhītvā padatrayavyāsaṃ prakramadvayadirgham dīrghacaturaśram dakṣiṇottaram buddhyā parikalpya caturaśrapūrvapārśve pratyagagre dve haṃsamukhyau paścimapārśve prāgagre dve haṃsamukhyau | tāsāṃ madhye dakṣiṇottarāgre antardīrghapārśve pādeṣṭake | caturaśradakṣiṇottarapārśvayormadhyabhūtāntarālayorbahirdīrghapārśve dakṣiṇottarāgre dve pādeṣṭake | evamaṣṭeṣṭakaṃ dīrghacaturaśraṃ bhavati |*

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At the junction *EF* between the tail and the body 2 B₅s and 3 B₃s are placed and at the end of the tail 15 B₃s. The end of the wing containing the plumages, TJKLMNOPQRST, is divided into 5 sections in each of which 1 B₂ and 2 B₃s can be placed. The bricks thus mentioned total 58,—centre of the body 8, junction of the tail with body 5, tail end 15, and plumages at two wings 30.

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In the truncated areas, bendings of the wings and junctions (other than already mentioned), B₂s and B₃s are to be placed; as per Fig. 40, these are : B₂—28; B₃—14, total 42. In area, these 100 bricks are equivalent to 36 *caturthīs*. Since the total area is 120 *caturthīs*, the remaining space can be filled by only 84 B₁s, leaving a deficit of 16 bricks. This is met by replacing 16 B₁s by 32 B₂s. D. proposes to do this in the following manner. In the wings, the body including the head, there are 18 rows westeast starting from the south. In Fig. 40, 9 rows are marked from the south to the central east-west line, there being another such 9 rows in the other half. 6 B₁s in the 8th row between the two extreme B₂s and 2 B₁s west of B₂ in the head in the 9th

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TABLE 6. *Number and types of bricks—second layer.

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| Parts of the *citi* | Brick types | | | | | Total |
| | B₁ | B₂ | B₃ | B₄ | B₅ | |
| Head, including part of body at the junction | | 10 | | | | 10 |
| Body, excluding portions accounted for in other parts | 12 | 28 | 4 | | 4 | 48 |
| Wings, including part of the body | 48 | 28 | 34 | | | 110 |
| Tail, including part of the body | 8 | 4 | 18 | | 2 | 32 |
| Total | 68 | 70 | 56 | | 6 | 200 |

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row are replaced by 16 B₂s. Likewise, 8 B₁s in rows 10 and 11 are substituted by 16 B₂s. The final arrangement of bricks in the different parts of the fire-altar is shown in Table 6, in agreement with D's commentary ; *evaṃ pucche dvātriṃśadiṣṭakāḥ | aṣṭapañcāśadātmaśirasoḥ | pakṣayordaśaśatam | asminprastāre’ṣṭaṣaṣṭiścaturthyaḥ | ardheṣṭakāḥ | saptatiḥ | ṣaṭpañcāśatpādeṣṭakāḥ | haṃsamukhyaḥ ṣaṭ* | Note that the number of bricks in the head and the body has not been separately stated.

Linked texts (1)

Śatapathabrāhmaṇa — Yājñavalkya & Śāṇḍilya (Vedic teacher), Sanskrit