always four external pillars at the angles, so that the square shape is retained, with twelve pillars, of which the eight internal pillars may be taken as mere insertions to support the long architrave between the four angular pillars. [Illustration: 113. Diagrams of Roofing. 114. ] [Illustration: 115. Diagram of Roofing.] It is evident that here again we come to a limit beyond which we cannot progress without using large and long stones. This was sometimes met by cutting off the angles of the octagon, and making the lower course of sixteen sides. When this has been done an awkwardness arises in getting back to the square form. This was escaped from, in all the instances I am acquainted with, by adopting circular courses for all above that with sixteen sides. In many instances the lower course with sixteen sides is altogether omitted, and the circles placed immediately on the octagon, as in the temple at Vimala Sah (Woodcut No. 130, p. 236). It is difficult to say how far this system might be carried constructively without danger of weakness. The Indian domes seldom exceed 30 ft. in diameter, but this may have arisen more from the difficulty of getting architraves above 12 ft. or 13 ft. in length to support the sides, than from any inability to construct domes of larger diameter in themselves. This last difficulty was to some extent got over by a system of bracketing, by which more than half the bearing of the architrave was thrown on the capital of the column, as shown in Woodcut No. 116. Of course this method might have been carried to any extent, so that a very short architrave would suffice for a large dome; but whether this could be done with elegance is another matter. The Indians seem to have thought not; at least, so far as I know, they never carried it to any extent. Instead of bracketing, however, they sometimes used struts, as shown in Woodcut No. 116, but it is questionable whether that could ever be made a really serviceable constructive expedient in stone architecture. [Illustration: 116. Diagram of Indian construction. B. Form of bracket capital in the angle of an octagonal dome.]