In the Parthenon, the stylobate has an upward curvature of more than four inches on the sides of the edifice and of more than two and a half inches on the east and west fronts. Vertical features were made to incline inward in order to correct the common appearance of leaning outward at the top. In the Parthenon, the axes of the columns are not vertical, but they are inclined inward nearly three inches. They are said also to be inclined toward each other to such a degree that they would meet at an altitude of one mile above the ground. The eleven-foot frieze and architrave is inclined inward about one and one-half inches. In Fig. 85, _a_ represents the front of a temple as it should appear; _b_ represents its appearance (exaggerated) if it were actually built like _a_ without compensations for optical illusions; _c_ represents it as built and showing the physical corrections (exaggerated) in order that it may appear to the eye as _a_ does. Tall columns if they are actually straight are likely to appear somewhat shrunken in the middle; therefore they are sometimes made slightly swollen in order to appear straight. This outward curvature of the profile is termed an entasis and in the Parthenon column, which is thirty-four feet in height, amounted to about three-fourths of an inch. In some early Grecian works, it is said that this correction was overdone but that its omission entirely is quite unsatisfactory. Some authorities appear to believe that an excellent compromise is found in the Parthenon columns. [Illustration: Fig. 85.--Exaggerated illusions in architecture.] One of the conditions which is responsible for certain illusions and has been compensated for on occasions is represented in Fig. 86. On the left are a series of squares of equal size placed in a vertical row. If these are large so that they might represent stories in a building they will appear to decrease in size from the bottom upward, because of the decreasing projection at the eye. This is obvious if the eye is considered to be at the point where the inclined lines meet. In order to compensate for the variation in visual angle, there must be a series of rectangles increasing considerably in height toward the top. The correction is shown in the illustration. It is stated that an inscription on an ancient temple was written in letters arranged vertically, and in order to make them appear of equal size they were actually increased in size toward the top according to the law represented in Fig. 86. Obviously a given correction would be correct only for one distance in a given plane. [Illustration: Fig. 86.--Illustrating the influence of visual angle upon apparent vertical height.]