mouth, denotes the orbit in which the planet will revolve to eternity. Or if the serpent be supposed to eat its tail, the orbit will diminish so that the planet would ultimately fall to the centre of force, the sun.

A caryatid pilaster, at Medinet-abou, 24 feet high, in

cluding the high cap, has the hands at the lower part of the chest resting upon a support rising from between the feet,

and presenting in front a parallelogram having a breadth about

length.

If the parallelogram were divided into

1 1 1 2' 22' 23'

&c.,

the sum of all the parts, how far soever continued, would never equal the parallelogram itself; so the parallelogram would be symbolical of infinity or eternity.

One hand holds the whip, or outline of the obelisk, the other the crosier or curve of Osiris. The beard is obeliscal. Above the cap is the globe and serpents with obeliscal or parabolic wings.

The high cap itself is bounded on each side at the lower part by two serpents, and with feathered-like appendages of uniform breadth and of contrary flexure, extending the whole length of the sides.

Fig. 55.

B

Fig. 55. If the focal distance as of the parabola Aα = BC= latus rectum = 36.

SB=

So AB = BC=latus rectum = 6 x 6 36. Parabolic area = 6 times area of obelisk.

The ordinates Pp SP at the different sections, ap will be a curve of contrary flexure traced by p.

SP2=SQ2 + PQ2

= (AQ—AS)2 + PQ'

= (axis - L)2 + ordinate2

= axis2-L x axis + L2 + ordinate2

= axis2 + + L2

.. SP and Pp will always be greater than the axis, and the curve of contrary flexure ap will continually approach to, but can never touch the axis Aq.

Hence the curve ap will be infinite, and the high cap of Osiris will be symbolical of eternity.

The two feathered-like appendages along the curved side of the cap denote that the breadth of the cap will increase as the focal distance A s increases.

If the focal distance were increased, the feathered-like appendages would become more like the curve which Osiris holds in his left hand. Thus the curve of Osiris will be typical of the parabolic curve of contrary flexure, or of infinity.

The top of the cap and feathers being rounded off may denote their infinite extension.

The serpents on the sides of the cap are typical of the obelisk or of infinity.

The serpent here represented is perhaps the most common of all the Egyptian hieroglyphics. It is known by its erect position, swollen neck, and the entwining folds of the lower part of the body. Denon has given a sketch of this serpent

in the same attitude as we see it on the sculptured stone. It is the Naia Haje, a most venomous snake, which the ancient Egyptians assumed as the emblem of Cneph or the Good Deity. It is also a mark of regal dignity, and is seen on the fore part of the tiara of almost all Egyptian statues of deities and kings.

This serpent in the erect position with its swollen neck resembles the parabolic curve of contrary flexure, the same as that of the cap, and the curve in one hand of Osiris.

The Ibis, like the Naia Haje, may have been held sacred from its head and long beak having a resemblance to the parabolic curve of contrary flexure.

In the other hand Osiris holds the obeliscal whip, by means of which he urges the heavenly bodies onwards in their orbits. Hence the myth of Phaeton driving the chariot of his father Sol. The Sun was worshipped by the Egyptians under the name of Osiris.

1 ordinate'

The sun is the centre of force round which the planets revolve with velocity ∞ and P T area obelisk, that is, the planets are urged onwards in their orbits by laws indicated by the obelisk; or, metaphorically, they are driven by Sol or Osiris with the obeliscal whip.

As the focal distance increases, the parabola increases, which is denoted by the feathered-like side of the cap; for the short lines made by a series of increasing parabolas will be more inclined as they recede from the axis of the parabola, and thus give the outside of curve of contrary flexure a feathered appearance. The axis of the curve ordinate of parabola, and ordinate of curve ∞ SP axis of parabola. The revolution of the curve on its axis would generate a solid like the cap.

The obeliscal beard typifies eternity.

If equal parabolas, having their axes in the same straight line and their apices coinciding in A, but on opposite sides of Ap, then the parabolas described on one side of Ap will feather the curve generated by the parabolas on the opposite side of Ap.

Again, if the apex of each parabola passed through the focus of the other, the sun would be in the axis of the curve, like the globe over the forehead of the figure; then the two parabolas would represent the paths of two comets describing parabolas or ellipses round the sun as the common focus. The other globe on the top of the cap might denote a fixed star, or another sun placed beyond any definite distance from the sun.

The Egyptian deities, when in a state of repose, are seated on hyperbolic steps, which decrease as 1, 1, 1, &c. So that the legs and thighs form a right angle, like the side and top of the seat; the thighs and trunk form another right angle, like the top and back of the seat; the arms also form a right angle, like the back and top of the seat. This hyperbolic attitude, which is typical of infinity, gives them a constrained appearance.

Buddha, in the attitude of sitting cross-legged, assumes the form of the hyperbolic solid; the Virginian Okee also assumes the same form; so that by their constrained positions they may be said to represent infinity or eternity.

Wilkinson remarks that the same veneration for ancient usage, and the stern regulations of the priesthood, which forbade any alteration in the form of the human figure, particularly in subjects connected with religion, fettered the genius of the Egyptian artists, and prevented its development. The same formal outline, the attitudes and postures of the body, the same conventional mode of representing the different parts, were adhered to, at the latest as at the earliest periods: no improvements resulting from experience and observation were admitted in the mode of drawing the figure; no attempt was made to copy nature, or to give proper action to the limbs. Certain rules, certain models, had been established by law, and the faulty conceptions of early times were copied and perpetuated by every successive artist. For, as Plato and Synesius inform us, sculptors were not suffered to attempt anything contrary to the regulations laid down regarding the figures of the gods; they