The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t27: Chapters 15, 16 and 17: 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.t27

Language: English

Chapters 15, 16 and 17: Construction of a Fire-Altar in the Form of a Falcon with Curved Wings and Extended Tail—First Type

c8.t27.2

We have already met with Baudhāyana's construction of two types of fire-altars in the form of a falcon with curved wings and extended tail (1st. type, *Bśl.* 10.1-10.20, 2nd. type, *Bśl.* 11.1-11.13). Āpastamba gives the construction of two other types, of which the first one is described in these three chapters, and the second one in chapters 18 to 20 to follow. We have thought it convenient to deal with these three chapters together because of the continuity and overlapping of the subject matter.

c8.t27.3

**15.2.** In the falcon-shaped fire-altar, a head is to be provided, the tail should be spread out and each wing must be curved. According to rule 15.2, the curving of the wing is to be done by pushing the west side upwards and the east-side downwards. Karavinda explains that what actually should be done is to raise upwards towards east the first half of the wing from its root at the body to the middle and to press downward towards west the second half from the middle to the end. (*prathama pakṣārdhaṃ mūlādārabhya paścātprabhṛti prāgunnayet |.. dvayaṃ pakṣārdhaṃ madhyādārabhya purastāt prabhṛti pratyagunnayet |*). The method is further explained in rule 15.6.

c8.t27.4

**15.2-15.5.** *Areas of different parts of the falcon.* A simple rectilinear śyenacit, as we have already noticed (*Bśl.* chs. 8 and 9; *Āśl.* chs. 10 and 11), consists of a square body of 240 × 240 sq. *aṅg.* (4 sq. *pu.*), two rectangular wings each of 144 × 120 sq. *aṅg.* (1⅕ sq. *pu.*) and a rectangular tail of 132 × 120 sq. *aṅg.* (1 1/10 sq. *pu.*). Some areas are taken out from the tail and the body (*ātman*) of the rectilinear *śyenacit* to build up the head and extend the area of each wing in the following manner :

c8.t27.5

Area taken out of the tail—120 × 12 sq. *aṅg.* or 1/10 sq. *pu.*
Area taken out of the head—(120 × 120 + 8 × 900) sq. *aṅg.* or 1½ sq. *pu.*
*Caturbhāgīyā* is the area of a square of side 30 *aṅg.*, that is 900 sq. *aṅg.*
The area of the head, which is built out of 3 caturbhāgīyās, is 2700 sq. *aṅg.* or 3/10 sq. *pu.*
The area of the tail, after the *prādeśa* portion is taken out, is 14400 sq. *aṅg.* or 1 sq. *pu.*
The area of the body, after 1½ sq. *pu.* are taken out, is 2½ sq. *pu.* or 36,000 sq. *aṅg.*
Since the area taken out of the tail and the body less that used for making the head is added to the wings, the area of each wing is determined as follows :

c8.t27.6

The total area added = (120 × 12 + 120 × 120 + 5 × 900) sq. *aṅg.* = 20, 340 sq. *aṅg.* or 113/80 sq. *pu.* The area added to each wing = 10, 170 sq. *aṅg.* = 120 × 84¾ sq. *aṅg.* The area of each extended wing = (120 × 144 + 120 × 84¾) sq. *aṅg.* = 120 × 228¾ sq. *aṅg.*

c8.t27.7

The area of two extended wings = 2 × 120 × 228¾ sq. *aṅg.* or 9⅛ sq. *pu.* The rules direct to increase the length of the rectangular wing without changing its breadth of 1 *puruṣa* or 120 *aṅg.* The new length of the extended rectangular wing is clearly 228¾ *aṅg.* or 9½ *aratnis* plus ¾ *aṅg.*, according to the definition of the units given in rule 15.4. This new length of the wing is stated in rule 15.5. Note that the total area, after distribution, of the fire-altar, remains 7½ sq. *pu.* (= 3/16 + 1 + 5/2 + 61/16).

c8.t27.8

*Shapes of different parts of the falcon.* The constructions of the different parts of the falcon are given in rules 15.6-15.9 and 16.1.

c8.t27.9

**15.6.** *The wing.* For the construction of the wing, a rectangle *ABCD* is taken, such that *AB* equals 120 *aṅg.* and *AD* 228¾ *aṅg.* (Fig. 15(a)). Upon *BC* and *AD*, the triangles *BFC* and *AED* are constructed. *BF*, *CF*, *AE*, *DE* each equals 120 *aṅg.* *AEDCFB* is the new shape of the wing in which the bending (*nirṇāma*) takes place at *E* and *F*.

c8.t27.11

Fig. 15. Different parts of the falcon with curved wings and extended tail : (a) wing, (b) body, (c) tail, and (d) head.

c8.t27.12

**15.7-16.1.** *The body* : A rectangle *ABCD*, of which *AB* equals 240 *aṅg.* and *AD* 180 *aṅg.*, is formed (Fig. 15(b)). At each of the 4 corners an isosceles triangle of side equal to 60 *aṅg.* is formed and cut off from the rectangle by transverse lines *EL*, *FG*, etc. as shown. The length *EF* at the eastern and *IJ* at the western side equals 60 *aṅg.*, *GH* on the southern and *KL* northern side equals 120 *aṅg.* The area of the figure *EFGHIJKLE* exactly equals 36,000 sq. *aṅg.* or 2½ sq. *pu.*

c8.t27.13

**15.8.** *The tail.* The rectangle *ABCD*, of which *AB* equals 120 *aṅg.* and *AD* 60 *aṅg.* is flanked on its southern and northern sides by two rectangles *DEFC* and *AGHB* which are cut off by the diagonals *DF* and *AH* respectively, leading to the figure *ADFHA* which is the shape of the tail (Fig. 15(c)). *AD* equals 60 *aṅg.* and *HF* 180 *aṅg.*

c8.t27.14

**15.9.** *The head.* A square *ABCD* of which each side equals 60 *aṅg.* is constructed (Fig. 15(d)). From the mid-point *E* of *AD*, *EF* and *EG* are drawn to the mid-points *F* and *G* of *DC* and *AB* respectively. *EFCBGE* is the shape of the head.

c8.t27.15

Note that either side of the wing *AB*, *CD* will join exactly with either the south side *GH* or the north side *KL*. Similarly, the base of the head *BC* will fit in exactly with the eastern side *EF* of the body and the eastern side *AD* of the tail with the western side *JI* of the body. These junction lines are the *apyayas*. The four corners of the body are thus cut by lines *EL*, *FG*, *HI*, and *JK* joining the extremities of the *apyayas*, as proposed in the rule 16.1.

c8.t27.16

Fig. 16. Nine types of bricks for the falcon-shaped fire-altar.

c8.t27.17

**16.2-16.10.** *Types of Bricks.* Nine types of bricks have been used in covering the alternate layers of this fire-altar. These are : B₁ — the first type,—a parallelogram *abcd*, of which ab = cd = 24 *aṅg.* and ad = bc = 20 *aṅg.* (Fig. 16). The sides are parallel to those of the parallelogram *ABEF* or *CDEF*, so that this type can fit in the wings. Sundararāja gives the values of the longer diagonal *ac* as 35 *aṅg.* 20 *ti* and of *bd* as 26 *aṅg.* 6 *ti*. He also gives the breadth *ed* between the longer sides as 19 *aṅg.* 2 *ti*, which is 1/12 of 228¼ *aṅg.* (the length of the wing). B₂ — the second type, obtained by joining 2 B₁s along the longer side such that the brick is bent at the middle (*madhye nirṇatā ekapārśve unnatā*—Karavinda) and suitable for use in the wing at the bending (17.5). B₃ — the third type, obtained by joining the parallelogram *abcd* (B₁) with the rectangle *aefb* along *ab*; ae = 15 *aṅg.* This is so designed that it can be used at the junction between the wing and the body, *abcd* lying within the wing and *aefb* in the body (17.5). B₄ — the fourth type, obtained by first making the square *abcd* of side equal to 30 *aṅg.* extending it by half *defc*, and then cutting off the square by the diagonal *bd*; *defbd* is the brick, used in several places. de = 15 *aṅg.*, bf = 45 *aṅg.* ; and bd = 30√2 *aṅg.* B₅ — the fifth type is a rectangle, 30 *aṅg.* by 15 *aṅg.*; *caturbhāgīyārdha*. B₆ — the sixth type is derived from B₅ by dividing it diagonally. B₇ — the seventh type, *gbfdg*, is made by constructing three equal rectangles, so that ad = de = ag = 12 *aṅg.* and ab = ef = gh = 24 *aṅg.* and cutting the outer rectangles by the diagonals *df* and *gb*. The direction of the diagonal is determined by *dakṣiṇāvarayoḥ koṭyorālikhet*. B₈ — the eighth type *ahfda*, is done in the same way as the seventh, with the difference that the northern rectangle is cut off by *ah*, as determined by *uttarāṃ tūttarasyāḥ kotyā* etc. B₉ — the ninth type, an isosceles triangle of base 30 *aṅg.* and side 30 √2 *aṅg*, is obtained by dividing the square *abcd* (ab = 30 *aṅg.*) diagonally.

c8.t27.18

**16.11-17.4.** *Placement of bricks in the first layer.* The placement of bricks in the first layer is best explained in Fig. 17. In each wing 60 B₁s are placed, with their longer sides, 24 *aṅg.* directed towards north. There are 10 rows east-west, each accommodating 6 B₁s.

c8.t27.19

In the tail, 8 B₆s are placed on either side, in two groups each containing 4. Karavinda explains the disposition as follows—*pucchāgre tisraḥ tāsāṃ purastādekam* | *evamuttarasmin pārśve viparyasya kāritāḥ* | At the junction between the tail and the body, 2 B₄s are placed in such a way that the portion diagonally cut lies in the body. West of them are placed 2 B₅s. The space now left in the tail consists of a rectangular strip, 30 *aṅg.* × 60 *aṅg.*, followed west of it by two equal rectangular strips, each 30 *aṅg.* × 120 *aṅg.* ; 10 B₄s (2 + 4 + 4) can be placed in these three strips (17.1).

c8.t27.20

The body (*ātman*) can be divided into three distinct rows, east-west by the lines *GH*, *FI*, *EJ* and *LK*. The breadth of each row is 60 *aṅg*. In the four corner regions, 4 equal areas *EQRL*, *FMNG*, *IOPH* and *JSTK* can be marked out such that *EQ* = *FM* = *OI* = *JS* = 75 *aṅg*.; and *RL* = *NG* = *PH* = *TK* = 15 *aṅg*. In each of these four corner areas, 2 *B*₄s can be placed, with their diagonally cut edges pointing outwards and with their longer sides turned either towards east or west. (*ātmanaḥ śroṇyaṃseṣu dve dve bāhyaviśeṣe*-Sundararāja). Still an area 30 × 30 sq. *aṅg*. is left,

c8.t27.21

Fig. 17. Arrangement of bricks in the first layer of a śyenacit with curved wings and extended tail (after Thibaut ). (North wing not shown).

c8.t27.22

which can be filled by 1 *B*₅ and 2 *B*₆s, thus requiring 4 *B*₅s and 8 *B*₆s as stated in the rule 17.2. The rectangular area *MNPO* and *QRTS* each measures 60 × 90 sq. *aṅg*. and can accommodate 6 *B*₄s each. In the central row 14 *B*₄s can be arranged as shown, leaving two isosceles triangular spaces of side 30 *aṅg*. Kapardi calls the central row *viṣayānāṃ mārga*, as bricks at the junctures (*apyaya*) partly lie on either side; he also confirms 14 *B*₄ bricks in this row—*viṣayānāṃ mārge tiryagātmani caturdaśa caturthyaḥ* / The space available in the head together with the two isosceles triangular areas can be exactly filled with 4 *B*₄ bricks as shown. The number of bricks and their types in the different parts of the fire-altar are given in Table 5.

c8.t27.23

Table 5. *Bricks in different parts of the citi—first layer.*

c8.t27.24

| Parts of the *citi* | Brick types | | | | Total |
| | B₁ | B₄ | B₅ | B₆ | |
| Head, including part of body | | 4 | | | 4 |
| Body | | 34 | 4 | 8 | 46 |
| Wings | 120 | | | | 120 |
| Tail, including part of body | | 12 | 2 | 16 | 30 |
| Total | 120 | 50 | 6 | 24 | 200 |

c8.t27.25

**17.5-17.10.** *Placement of bricks in the second layer.* The arrangement of bricks of different types is shown in *Fig.* 18. In each wing, after placing 5 B₂s at the bending and 5 B₃s at the juncture between the wing and the body such that the extended rectangular part (15 × 24 sq. *aṅg*) lies in the body, the remaining space can accommodate 45 B₁s. 25 B₁s lie on the southern side and 20 B₁s on the northern side of the bending in the southern wing. In the northern wing the arrangement is opposite.

c8.t27.26

In the tail, 5 B₇ bricks are placed on either side, and the whole space is divided into 5 rows west-east. In the second and the fourth row from the bottom 1 B₇ each is placed by the side of the B₇s on either flank. This makes the total number of B₇s 12. (*evaṃ dvādaśa saptamya upahitā bhavanti* /-Karavinda). The remaining space in the tail is covered by 13 B₈ bricks. Their disposition is described by Karavinda as follows: *pucchāgre pārśvagatayossaptamyormadhye pañcāṣṭamyau | nanāgra dvitīyāyām tisrāṇāṃ saptamināṃ madhye tisro'ṣṭamyaḥ | tṛtiyāyāṃ ca tisraḥ | caturtharityām tisrāṇāṃ saptamināṃ madhye ekā | pañcamarityāṃ saptamyormadhye ekā | evaṃ trayodaśāṣṭamyaḥ yathāyogaṃ prāgarāḥ pratyagagrāśca bhaveyuḥ* ||

c8.t27.27

Fig. 18. Arrangement of bricks in the second layer (after Thibaut).

c8.t27.28

In the body, 2 B₄s, with their longer sides turned either towards north or towards south, but the diagonally cut side always facing outwards, are placed at each of the four corners. The remaining space can be divided into five rows east-west. The two rows on the south of the central row are filled with 10 B₄s, of which 5 are turned towards east and 5 towards west. The two rows north of the central are similarly filled with 10 B₄s. (*ātmano dakṣiṇe pārśve daśa caturthyaḥ | pañca-prācīḥ evamuttare pārśve*—Kapardi). The middle row can be filled with 32 B₆ bricks; but, to make the total number of bricks 200, 30 B₆s and 1 B₅ are used.

c8.t27.29

| Parts of the *citi* | Brick types | | | | | | | | | Total |
| | B₁ | B₂ | B₃ | B₄ | B₅ | B₆ | B₇ | B₈ | B₉ | |
| Head | | | | 2 | | | | | 4 | 6 |
| Body | | | | 28 | 1 | 30 | | | | 59 |
| Wings, including part of body | 90 | 10 | 10 | | | | | | | 110 |
| Tail | | | | | | | 12 | 13 | | 25 |
| Total | 90 | 10 | 10 | 30 | 1 | 30 | 12 | 13 | 4 | 200 |

c8.t27.30

In the head, 2 B₄ bricks and east of them at the tip 4 B₉ bricks are placed. The number of bricks and their types used in the different parts of the fire-altar are shown in Table 6.

Linked texts (2)

Baudhāyanaśulbasūtra — Baudhāyana, Sanskrit
Āpastambaśulbasūtra — Āpastamba, Sanskrit