meister-geometry and measure in hindu temples

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Geometry and Measure in Indian Temple Plans: Rectangular Temples Author(s): Michael W. Meister Source: Artibus Asiae, Vol. 44, No. 4 (1983), pp. 266-296 Published by: Artibus Asiae Publishers Stable URL: http://www.jstor.org/stable/3249613 Accessed: 09-07-2018 16:20 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms

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MICHAEL W. MEISTER University of Pennsylvania

GEOMETRY AND MEASURE IN INDIAN TEMPLE PLANS: RECTANGULAR TEMPLES

he stone temple in North India generally uses a square-based p

temple to the square altar of Vedic ritual and to the square of th A square diagram, the Vdstumandala, generated by geometric rules th

in Sulba-Sitra texts as early as the fourth century B.C., was used in altars, and recent studies have demonstrated that such a grid diagram

application for the creation of temple ground plans in North India from

through the tenth century A. D.2 Measured at the base of the sanc

the plan of a temple most frequently was related to a grid of 8 x 8 = a grid prescribed for temples in a sixth-century text, the Brhat Safhita

The inner space (Brahmasthdna) of a sanctum was defined by the c walls were each two squares thick. This grid was applied in varyi

temple ground plans in this period, and architects, while retaining refer

significant grid, were able to vary the aesthetic configuration of the sto

ably (fig. 3).4 A small number of rectangular shrines in Central India, be

of their construction, offer a particular opportunity to test the line bet freedom and his constraints.

The study of temple plans can reveal principles of ritual as well as practical organization; it can also begin to suggest the flexibility left in the hands of artisans faced with ritual

constraints. Rectangular temples in Central India can act as a further test for the practical application of the ritual grid; at the same time, because of the peculiar problems faced by

architects in designing elevations to fit such shrines, this group can reveal, more clearly than can square shrines, pragmatic possibilities and the aesthetic independence allowed the architect.

Rectangular shrines exist in order to reflect the form of certain images used for worship.

Among these are images of reclining Visnu, a scene of a mother reclining to suckle a child 1 See Stella Kramrisch, The Hindu Temple, Calcutta 1946; C.P.S. Menon, Early Astronomy and Cosmology, London 1932;

R.N. Apte, "Some Points Connected with the Constructive Geometry of Vedic Altars," Annals of the Bhandarkar Oriental Research Institute, VII (1926), p. 14: "though all the surface of the earth is vedi, still selecting a particular part of it and measuring it they should perform theyajna there." 2 Michael W. Meister, "Mandala und Practice in Nagara Architecture in North India," Journal of the American Oriental Society, 99.2 (1979), pp. zo204-219. 3 LVI. lo: "Let the area of a temple always be divided into sixty-four squares." In Varahamihira temple building is only

a special case of building, and the Vastumandala is described in detail in an earlier chapter, LII, "on architecture." Buildings other than temples are specified to use a grid of 9 x 9= 81 squares. Other texts allow a variety of grids. 4 Meister, "Mandala."

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(usually thought to represent the birth of Krsna or a Jina), sets of deities such as the Saptamdtrkds, larger sets of goddesses, the Navagrahas, and Visnu's Dasdvatdras.s Such shrines are sometimes subsidiary parts of larger temple complexes, as at Dhamnar; but on

some occasions, particularly for Goddess shrines, the main temple has been given a rectangular plan.6 In the seventh century, such temples, in all parts of India, were given oblong "wagonvault" roofs referring back to the quasi-barrel-vaulted wooden structures that formed so

prominent a part of ancient India's urban landscape.7 Well-known among such "cialdfikhara" forms are those of the Bhima and Gane'a rathas at Mahabalipuram, south of Madras; but such "Valabhl" (oblong-vaulted) roofs appear also at Khimeivara in Saurdstra, at Jageivara in Himachal Pradesh, on the Vaithal Deul in Bhubane'vara (Orissa), and at Naresar and on the Teli-kd-mandir at Gwalior in Central India (figs. 19, 22).8

This "iala likhara" in South India continued to be used as roof for oblong temple gateways (gopura). From at least the eighth century A.D. in Western India, oblong structures used some variety of pent-roof (Phdrhsand).9 In Central India, where the square-

based curvilinear tower of North India (the Latina Nagara fikhara) had become preeminent, two prominent rectangular temples built in the ninth and early tenth centuries

abandon the wagon-vault of the Teli-kd-mandir and the small shrine at Naresar, and join two Ndgara towers together (fig. 2 5) as roof for rectangular sanctums. That the condensed

symbolism of the Ndgara tower had become an essential marker for a Hindu structure in Central India by the ninth century seems implicit in this decision.10 Because the joining together of two square-based structures to house a rectangular sanctum posed unusual problems for the temple's architect, these two examples offer a unique test of his freedom to improvise. The grandest and earliest of the rectangular temples preserved in Central India is the Teli-kd-mandir in the Gwalior fort (figs. 5-6, 20-22), which dates to the first half of the

eighth century A.D., probably in the reign of Yasovarman of Kannauj (ca. A.D.

720-75 3).11 The temple is Saivite, originally dedicated perhaps to Saivite Matrkds12 (the s J.M. Nanavati and M.A. Dhaky, The Maitraka and the Saindhava Temples of Gujarat, Artibus Asiae Supplementum XXVI, Ascona 1969, figs. I2-1I3, 22, 29. The Gadarmal temple at Badoh had once a number of goddess images lying around its sanctum, in particular a large image of a suckling mother now in the Archaeological Museum, Gwalior (A.K. Coomaraswamy, History oflIndian and Indonesian Art, New York 1927, fig. 178). The Vaithal temple in Bhubanesvar, which has a Valabhi wagon-vault over its rectangular sanctum, houses a set of Mdtrkds surrounding a large image of Durgd (K. C. Panigrahi, Archaelogical Remains at Bhubaneswar, Bombay 1961). 6 Michael W. Meister, "Phrihsand in Western India," Artibus Asiae, XXXVIII (1976), pp. 167-M88. Dhamnar, fig. 22; Osidfi, figs. 1, 3-4; Auwa, fig. 2. 7 A.K. Coomaraswamy, "Early Indian Architecture: I. Cities and City Gates"; "III. Palaces," Eastern Art II (1930), pp. 209-236; III (1931), pp. 181-2z 17, illustrates such cityscapes. 8 Kramrisch, Hindu Temple, p. 413. Nanavati and Dhaky, Maitraka..., Plate 55; S.K. Saraswati in The Struggle for Empire, Bombay 1957, plate IX. 9 Meister, "Phri-sand." 10 See also Michael W. Meister, "Construction and Conception: Mandapikd Shrines in Central India," East and West, 26 (1976), pp. 409-418. " H. Goetz proposed an early seventh-century date for this temple in "The Last Masterpiece of Gupta Art," Indian Arts andLetters, XXIX (1955), PP.47-59. Coomaraswamy called the temple 1 Ith century, H.I.I.A., fig. 212, as did Percy Brown, Indian Architecture (Buddhist and Hindu), 4th ed., Bombay 1959, p. i 28. Krishna Deva, Temples of North India, New Delhi 1969, pp. 22-24, thought it might date to ca. A.D. 85o in the reign of Mihira Bhoja (A.D. 836-888), but

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bust of a goddess from Gwalior now preserved in the National Museum, New Delhi, may have come from this temple).13 The Teli-kd-mandir is sometimes talked of as if it showed "Southern" influence because of its large rectangular keel-roof, which resembles those of the Bhima and Ganesa rathas at Mahabalipuram, or those on later South Indian templegateways (gopura).14 Coomaraswamy, instead, compared it to the Vaithal temple at Bhuba-

nesvara (ca. eighth century A.D.).15 Other shrines exist in the north with similar Valabhi keel-roofs in the eighth century (e.g. at Gopesvar and Jageivar in the hills, and Naresar near Gwalior). These temples use bhumi-khandas (corner units of cornices separated by ribbed amalaka-stones) to support the keel vault (figs.I7, i9), thus separating themselves morphologically from South Indian shrines. Such shrines as the Bhima and Ganeia rathas

can properly be called Valabhi DrIvida Vimdnas; the Tell temple and other such shrines in North India are Valabhi Ndgara PrIsddas. The Tell temple reflects in its proportions a careful expansion of the grid system known

from square temples in Central India in the eighth century. In fig. 4 I give a ground plan for the Tell temple. Several plain bhitta platforms support the base moldings (vedibandha) of the temple walls (figs. 6, zo20). These consist of khura, kumbha, a broad antarapatta-setback (decorated with a vediki pattern of small pillarets with a broad cross-beam of foliage), and

a kapotaplhhood. The frieze of the wall (jahgha) has doors on the central bhadra projections which lead to broad recesses which now lack their images. On the corners, smaller niches in the form of shrine models with entry doorways (fig. 20) also lack images. Percy Brown records the inner dimensions of the sanctum of this temple as 15 x 30 ft. (a ratio of I :2).16 This is not correct. The sanctum measures ca. 6 x 9 meters, the ratio being

2:3. In fig. 5, I give a diagram of one quarter of the temple's ground plan showing the grid from which the architect has generated his plan. The sanctum is defined by 4 x 6 squares; the walls are two squares thick, measured from the corners. (Each square of this grid is ca. .5 meters on a side.) Corner buttresses measure 2 x 2 squares at the kbura-hoof of the wall's moldings (fig. 6). The central bhadra projection on each side projects a full square.17 The opening into the bhadra shrine is ca. two squares wide. Each bhadra has subsidiary offsets (three on the short walls, three on the longer back wall) which are each a third of a square wide and step back a third of a square (fig. 5). On

he has recently confirmed that the short graffiti remaining on the temple are all "assignable to the mid 8th century"

(personal correspondence). 12 Cunningham thought the temple Vaisnavite. The Garuda over the door, however, is only ornamental, holding the tails of the ndga-idkhbd bands. The end pediments of the superstructure preserve images of Durgd (S) and possibly Virabhadra (N). Images in the recess of the vedibandha mouldings are largely Saivite. Krishna Deva points out Saiva Dvarapilas at the outer door and Sikta Dvarapdlas inside the praggriva entry (op. cit., p. z3).

13 This image has recently appeared on the cover of a catalogue, Inde, cing mille Ans dArt, Paris 1978, where it is identified

as "Vardhana dynasty, 7th century." See also Leigh Ashton, ed., The Art of India and Pakistan, London 1949, P. 5 5 and fig. 240. 14 Guides often repeat a story of a king married to a southern queen, or of kings from the south marching far into the north to build the temple.

15 Coomaraswamy, H.LL..A., p. io9.

16 Brown, Indian Architecture, p. i28. 17 The degree the bhadra projects can vary from temple to temple (Meister, "Mandala"); the one-square projection seen here parallels that at Mahua, fig. 2.

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the longer western wall, pratiratha offsets to either side of the central bhadra, each one-and-

one-third squares wide and having niches, separate the bhadra from the corner piers (figs.

5, 22).

Effectively, the architect of this temple has taken a square sanctum of 4 x 4 squares and

increased it by half. The karna (corner) piers mark the two-square thickness of the outer walls. On the shorter sides, the central bhadra by itself marks the four-square dimension of the inner sanctum (fig. 5). On the longer wall, the bhadra and pratiratha offsets together

measure the six-square width of the inner sanctum. The small, offset, pratibhadra corners of the bhadras act as a significant means to rationalize the ratios governing the long and short walls of this rectangular shrine. On a square temple of this period (cf. fig. 2) the ratio

of karna (corner) to central bhadra offset is :'I; of pratiratha to bhadra, 1:2 (the whole rhythm of the wall is thus 2: " :2: " :2). (If the pratibhadras were to be taken as a "pratiratha" and the doorway [fig. 5] taken as the bhadra measure, then the wall's rhythm would remain

2: 1:2:"1:2.) On the long wall, because of the fractions introduced by the use ofpratiratha offsets, the ratio of karna to bhadra becomes 3"5 (the bhadra is three and one-third pada-

squares). The ratio ofpratiratha to karna is 2: 3; ofpratiratha to bhadra is 2: 5 (the pratiratha

is one-and-one-third squares in width); the overall rhythm of the wall thus is 3:2:5: 2: 3. The ratio of karna plus pratiratha to bhadra is : i. This complex interlocking of ratios of prime integers follows directly from the architect's subtle expansion of his original 8 x 8 grid.

The Teli-kd-mandir enlarges such a grid by increasing the sanctum, not the entire structure, by 5o percent (from 4 x 4 to 4 x 6 squares, a ratio of 2: 3), thus enlarging the outer dimensions from 8 x 8 to 8 x io squares (a ratio of 4: 5). The ratio of thickness of wall to sanctum is 1:2 on the temple's shorter sides, I:3 on the longer wall.8 Ratios that emerge from this analysis of the Teli-kd-mandir's plan thus include I1, 1:2, 1:3, 2:3, and 3: 5 as well as 2:5 and 4: 5. These simple ratios governing the plan and created by the grid might be compared to harmonic ratios. I know of no evidence to suggest a deep commitment in India to "musical" harmonies in architecture;'9 yet few structures better embody

harmonious proportions than the eighth-century Teli-kd-mandir. The group of small eighth-century shrines clustered together in a gorge near Gwalior airport at a site known as Naresar poses a number of problems for the historian of Indian architecture. What are probably the two earliest structures stand on largejagatf platforms, entry-stairways to the western side (fig. 17). I choose to number the eighth-century shrines

at the site from the east to west: no. i high in the gorge; no. 2 nestled against thejagatf of no. i, facing nos. 3 and 4 at the same level; no. 5, a west-facing, Valabhi-roofed shrine on ajagatt slightly behind and below nos. 3 and 4 (figs. 17-19); and no. 6 facing east below the Valabhi shrine.20 Thejagatr platform on which the rectangular, Valabhi-roofed temple 18 Wall thickness here is measured to the corner face, not through the thickness of the bhadra projections (cf. Meister,

"Mandala").

19 As in the European Renaissance; R. Wittkower, Architectural Principles in the Age of Humanism, New York 1965. 20 Temple nos. I and 5 were built first; nos. 2-4 and 6 were added slightly later. O. Viennot, Temples de lInde centrale et occidentale, Paris 1976, uses different numbers for these temples. See also D.R. Patil, The Descriptive and Classified List of Archaeological Monuments in Madhbya Bharat, Gwalior 195 2, for these and other shrines discussed from Central India.

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stands abuts the rock level on which temple nos. 3 and 4 are built; its heavy vedtbandha-like

moldings support an upturned lotus-molding and apatta paving-slab (fig. 7). The platform has a projection on the west paralleling the shrine's prdggriva-entry; a long flight of steps leads up to the platform on the west.

The shrines at Naresar are very small, and quite crude compared to the much grander Tell-kli-mandir in Gwalior. All have thin walls, betraying contact with constructional

conventions used for building small temples in2rhythm the same century.21 walls of temple no. 1, however, as example, stillman.dapikd display the same2: 1: 2: 1i: of parts

The outer

found on other square masonry shrines in Central India in the eighth century.

The rectangular temple no. 5 has two niches projecting on its back wall (fig. I8) that contain images of Surya and Visnu. A single niche on the north wall shows Pdrvati; on

the south, Gane'a. On the jukandsa, Durg. is shown seated on a lion. The sanctum, which

now preserves no image, has a ratio of depth to width of 3:5. Overall proportions of the

outer walls are ca. 7: 10i. While the thin walls and broad sanctum of this temple cannot suggest construction by use of a grid, care has been taken to maintain certain simple proportions on the outer walls. On the shorter sides, the ratio of karna to bhadra projection is 2:5 ; the ratio ofpratibhadra

to central niche projection is also 2:5; the ratio of karna to bhadra niche is 3:4 (the ratio of pratibhadra to karna thus becomes 8:15).

On the long wall, the ratio of karna to bhadra is i: 2; that ofpratibhadra to bhadra niche

is 2:5; karna to niche projection is 9: io (pratibhadra to karna thus becomes 4:9). The recess between the two broad bhadra projections is half the pratibhadra, two ninths the karna face, or one fifth the niche projection. Significant in this example is the use of simple measure; constructing the temple using

thin walls the against architect has face preserved simple ratios,(following but withoutman.dapikd-like reference to a grid.conventions) Niches are applied the wall (fig. 18) and do not extend as offsets into the superstructure (fig. 8, right). Bhadra offsets

a system of

in the wall extend into the superstructure (fig. g19) as udgama pediments on the first story, beneath the Valabhi vault. Aesthetic order on this Valabhi temple has resulted, not directly

from the manipulation of a grid but from the builder's pragmatic adjustments of simple measure.

Square shrines in Central India in the ninth century continue to us

to control the laying out of the ground plan, but adaptation of a applying the grid to the plan results in new wall proportions. Th seventh and eighth centuries in Central India measures the thick

corners (karna-vyasa); that adopted in the ninth century measur

21 Meister, "Construction and Conception." Such shrines have pillared walls reflecting a w using thin slabs between, producing walls much thinner than in the masonry tradition. to suggest that temples no. I and 5 both had an ambulatory enclosure of pillars with int

to those surrounding the Jain temple, no. z2, at Deogarh late in the 8th century (cf Temples in Central India," Aspects of Jaina Art and Architecture, ed. U.P. Shah and

pp. zz223-24i). A small flat-roofed Devi shrine exists at Mahua built of thin mand rectangular plan. 270

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through the bhadra projections (bhadra-vyasa), pulling the corners inside the grid.22 (In fig. i i, I give a diagram to represent the differences between application of these two systems.) Bhadra measure had been used in Western India in the seventh and eighth centuries

A.D. and probably was adopted in Central India from that region as a result of the expanded hegemony of the Imperial Gurjara-Pratihdras in the ninth century. The shift can be seen by comparing the Sarya temples at Umri and Madkheda in District Tikamgarh;23

Umri obscures its 2: :2: I:2 proportions by an overlay of niches; Madkheda has been built using a rhythm of 2 : 1.5:3 : 1.5 :2 that is the result of using the bhadra-vydsa method to place the plan within the ritual grid. The Nakti-Mdtd temple near Jaipur in Western India (fig. 3,

upper right) also uses bhadra-vydsa measure and shows a wall rhythm of 2:I.5:3:I.5":2. The ornate tendencies at Umri, Madkheda, and Nakti-miti, with saliladntara recesses gradually introduced between each part of the wall, sur and sub offsets provided, and ornamental niches applied at different levels, almost guarantee that a system of sub measures had to be in effect. The grid might still help to determine the measure of sanctum

and wall, and the full measure of each wall part, but the subdivisions of each part seem to have been aesthetically determined. Pragmatic and aesthetic determinations, but with a reference to the primary proportions initially generated by use of the mandala's grid, help explain, and can be tested by, the two rectangular shrines at Badoh and Barwasagar, the first built early in the ninth, the

second by about the beginning of the tenth century. The large temple called the "Gadarmal" at Badoh as well as the Jarai Math at Barwasagar do not use Valabhi vaults as roofs, but once had curvilinear towers over their rectangular sanctums made by joining together two Latina Ndgara towers (figs. 23, 25). Niches with Dikpdla images appear on the corner faces at Badoh; the pratiratha offsets take the form of ornamented pilasters; bhadra niches project as small cellas, two on back and one on each short wall (figs. 9, 23). The long back wall of the Gadarmal temple shows the karnas, pratirathas, and bhadras of two square shrines, joined by eliminating the karna piers at the point of juncture (fig. 23; and thus also the corner venukos'a bands in the

superstructure above). (Because of the damage here and at Barwasagar [figs. 23, 25] we can only guess at the nature of the uppermost levels of such a conjoined superstructure.) The moldings of the temple rest on a low manca platform (figs. I2 B, 23), which partly follows the projections, but not the indentations, of the temple's plan (fig. 9). Fronted by a unique ratgamandapa (open pillared hall) with broad balconies on either side mimicking the rectangularity of the shrine itself (fig. 9), the whole complex stands on an extensive jagatz platform surrounded by the ruins of seven subsidiary shrines (fig. Io). On the north, a kind of causeway extends from the platform, broadening out to support a torana gateway

marking the entry to the entire complex (figs. Io, 24).

Because of its damaged condition (fig. 2 3), the massiveness of this temple's construction

(and reconstruction) has been exposed. Because of that massiveness, and the experimental, 22 Meister, "Mandala." 23 Ibid., figs. 12-i3; Viennot, plates zz229, 240.

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even odd, nature of its plan and superstructure, certain compromises have apparently been

necessitated. The nature of those compromises, however, helps measure the system applied. Because the rectangular shrine at Badoh was roofed by two Nigara towers, one might expect its sanctum to be the product of two square sanctums joined together. The ratio of the sanctum's depth to breadth is actually only I: 1.85 (not quite the i: 2 one might expect; the sanctum measures 3.9I x 7.26 meters). In fig. I3, I have given a diagram to show the measured plan of this temple on the left in comparison to the proportions produced by use of a square grid (right). A certain constriction of the plan at Badoh is apparent; parts of the back wall have been compressed compared to the side walls, which use the grid. (To emphasize this compression, I provide, for comparison, the plan of the temple [fig. 14] expanded to fit the proportions of the grid.)

To meld two N.gara as here attempted suchhave sleight of the back wall, using the grid structures system, the pratirathas paired at therequires center would merged

hand. On

(the measure of the absent karnas would include the salildntara recess). In this experiment, pratiratha and bhadra measurements on the back wall have been reduced, perhaps partially to retain this visually essential separation at the khura level (fig. 23). (The karna measure remains the same on the back and side walls.) Reduction in size of paired bhadra projections

on the back wall of a rectangular shrine had also occurred on temple no. 5 at Naresar (fig. 18), where careful use of measure had still retained simple ratios between all parts. At Badoh as well, though architects were willing to "fudge" in using the grid, rational measurements are still apparent on both side and back walls.

At Badoh, the karna faces on both long and short walls show the same measure. Pratiratba and bhadra parts have been reduced on the long wall. On the side walls, the ratio

of pratiratha to bhadra is 1:2, of karna to bhadra 2:3, and of pratiratha to karna 3:4. (The overall rhythm of the shorter walls, therefore, remains 2:1.5: 31.5:2, appropriate for bhadra vyasa application of the Vastumandala's grid.) On the long back wall, however, the ratio ofpratiratha to karna is 1: 2, of karna to bhadra and ofpratiratha to karna approximately 7: I0o. (The recess between central paired pratirathas is ca. half the breadth of each pratiratha

at the khura molding, making the overall rhythm of the back wall approximately

7:"5 :10:which 5:[2.5]5: Each of course, is made recesses, must"10"5: follow :7. their ownpart, subordinate measurements.)

up of sub projections, offsets, and

The square grid of the Vastumandala had been an appropriate starting point for constructing a square temple plan, and it retained utility long after the aesthetic indepen-

dence ofIndia. the exterior hadcentury, radically transformed the outer appearance of the in North In the eighth this grid system could still readily be expanded to N.gara temple produce a rectangular plan for the Teli-ki-mandir at Gwalior; the very precision with which that plan was laid out reflects the utility of the grid. To merge two Nigara towers, as at Badoh, however, put demands on the architect and engineer that could be met more adequately by use of simple measure than by strict adherence to a grid. What Badoh provides us better than square temples in the ninth century is a measure of the architect's freedom to manipulate his monument, at times for an aesthetic effect. Let me be clear about "measure". The proportions that the laying out of a ground plan 272

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by use of a grid provided still had to be translated into actual measurements that stone

masons and engineers could use. Proportions suitable for architects because of their relation to the grid were located in the khura hoof of the wall moldings, at floor level (where the walls of most temples through the eighth century touched the foundation). As structures began to be given ornamented sub moldings (as at Badoh, fig. i2), and as the variegation and indentation of the wall increased, the grid proportions that I have located became more and more a conceit, built into the plan by a system of interlocking measurements used for actual construction. Badoh's ground plan can demonstrate dramatically the degree to which measure (still preserving a system of simple proportions) could substitute for the grid where the latter had become inconvenient to an architect facing problems of elevation and construction.

That the Badoh temple was not an aberrant experiment can be demonstrated by the Jarai Math at Barwasagar, District Jhansi, built probably around A.D. 900.24 The architect of this rectangular shrine again has merged two Ndgara towers (fig. 25), but has done so with a more experienced facility than had the architect at Badoh. The temple stands on an elegant pgtha basement (figs. i z, 26) consisting of plain khura and kumbha moldings and a capping lotus-patterned kapotapdl-molding fronted by an ornamental band of kirttimukha

masks. As in previous temples, significant measurement continues to be located in the

khura hoof of the vedibandha moldings (fig. i z), not in this pptha base. Karnas and pratirathas

are encrusted with ornamental niches with tall pediments; the bhadras have small antardla porches projected in front of their small cella-shrines (fig. 26).

The proportions of the rectangular inner sanctum are 2: 3, as in the earlier Teli-kdmandir (proportions that present, presumably, fewer engineering problems to the constructing architect than the : 1.85 attempted at Badoh). Along the shorter outer walls, the ratio of pratiratha to bhadra is i':2, of karna to bhadra 2: 3, and of pratiratha to karna 3: 4 (the overall rhythm thus is 2: i. :5 3: 1. 5: 2). On the longer back wall, where karna faces are

of the same dimension as on the short walls but pratiratha and bhadra parts have been reduced by one third, the ratio of pratiratha to bhadra is 1:2, karna to bhadra i:i, and pratiratha to karna 1:2. (The recess between paired central pratirathas on the back wall begins only above the khura molding [figs. I 5-16], making the overall rhythm of the back

wall 2: I:2:"[I+ I]:2: :2.)

By reducing parts of the back wall by thirds, the architect has managed to maintain rational proportions on both long and short walls and to fit his temple to the grid. The aesthetic balance of the Barawasagar plan (fig. 15) compared to that at Badoh (fig. 9) is the result of this precision. That such proportions have been generated in reference to a grid is demonstrated in fig. 26, where I show the ground plan of the Jarai Math (measured at

the khura hoof) in relation to a grid of 8 x Io squares. As in the Tell temple (fig. 5), the sanctum measures 4 x 6 squares. The bhadra on the short wall is two squares wide, the pratiratha a single square, the karna one-and-a-third squares. On the long wall, the karna 24 A. Fiihrer, Monumental Antiquities and Inscriptions, Allahabad I891, p. I '5, refers this temple to the 9th century A.D. Hargreaves, Circle Report, Archaeological Survey of India, Northern Circle (Hindu and Buddhist), 19153--16, pp. 5, io--i 2, Appendix A, cites a lintel inscription apparently of the "later half of the 9th or beginning of ioth century A.D."

273

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remains one-and-a-third squares; the pratiratha measures two-thirds of a square; and the bhadra one-and-a-third squares. Proportional measure, as at the Teli-kU-mandir, has been maintained by using one-third fractions of the grid's measure.25 The analyses presented here are the result, not of studying the drawings of these temple's plans, but of measuring (to the millimeter) the moldings of standing temples in order to reconstruct their ground plans. The logic of placing significant measurements at

floor level, at the base of the wall moldings where the temple structure rests on its foundation, is inescapable in early shrines (figs. 1-2). Such rational measure continues to be applied to the khura molding (figs. 6, i2), at the base of the sanctum walls, even when

thethestructure is built above an ornamental socle The (manca p.tha), itself indented at level of which actual construction had to begin. ritualorsignificance of the grid and offset, required that it continue to frame the sanctum, enclosed by these walls, in its web of ratios.

Concentric measurements, derived from but not demonstrating the simple ratios of the

grid, then be usedastoa constructional locate the p.tha bases.26 Thecould grid loses significance mechanism as the sanctum is raised higher and higher on ornamental bases, yet it survives. The architect in his design, not the constructing engineer, utilizes the simple ratios that the grid provides. To translate these into the permutations of an increasingly variegated wall surface (fig. 25), or to transmit

them out to theas bottom edge of the p.tha baseof(or to the moldings ofcontrol an enclosing ambulatory wall, at Khajuraho), required a system fractional measure, the of which we can see developing in temples throughout the ninth century A.D., and for which the peculiar problems of rectangular temples can act as a test.

25 A rectangular temple, its sanctum dimensions measuring 2:3, that fails to maintain such precision in the placement

and measure of its outer walls is the Harihara temple no. 3 at Osidfi (see Meister, "Phdthsand," figs. I, 9). 26 "The Udaye'vara Temple Plan," in the K.R. Srinivasan Felicitation Volume, Madras (in press) points out that this eleventh-century "stellate" temple seems to use a system relating the grid at the sanctum level to a process of construction using circles at the pitha level.

274

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Fig. z Mahua, Dist. Shivpuri, Madhya Pradesh. Siva templ with constructing grid. (ca. A.D. 650o-700)

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b

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atj

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279

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A. Fig. 7 Jagati mouldings: A. Naresar, temple no. 5; B. Badoh, Gadarmal temple

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Karna vyasa Bhadra vyasa

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Fig. 16 Barwasagar, Jarai Math. Ground plan with constructing grid (lower left: section at khurd-moulding; upper left: grid and plan at khurd-moulding; upper right: section atjadghd without ornamental niches; lower right: section atjadghd showing ornamental niches)

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Fig. 26 Barwasagar, Ja