The cinema as a graphic art : on a theory of representation in the cinema (1959)

1 THE CINEMA AS A GRAPHIC ART Theorem 6. Given the same movement, the speed of change of the area c the perspective is in direct proportion to the speed of the figure and the squar of the focussing distance, and in converse proportion to the cube of the distanc to the lens. Theorem 7. Given the same movement, the speed of change of the area c the perspective is in direct proportion to the square of the focussing distanc and the speed of the figure, and in converse proportion to the degree of distanc from the lens. Theorem 8. The depth 1 of the perspective of the object is in direct pro portion to the focussing length and in converse proportion to the square of th distance from the object to the lens. (Note. — The analogous theorems (3, 4, 5, 6 and 7) are deduced in regard to a mov< ment of the object not along but parallel to the main ray.) Theorem 9. Given the movement of a line parallel to the main ray, alonj itself, the dimension of its image is proportional to the focussing distance, it distance from the main ray, and its dimension, and is in converse proportion t< the projection of the space between its two ends to a neutral plane.2 Theorem 10. Given the same movement, the speed of movement of am point of the perspective is in proportion to the speed of the corresponding poin in space, and in converse proportion to the speed of the retrogression of th( point in space from the neutral plane. Theorem 11. Given the movement of a point parallel to the picture, th< speed of movement of its perspective is in proportion to the speed of movemem of the point itself and the focussing distance, and in converse proportion to the retrogression of the line of movement of the point from the lens. Theorem 12. Given the movement of a perpendicular line parallel to the picture, the dimension of the perspective changes in direct proportion to the retrogression of the line from the main plane 3 and in converse proportion to the distance of its ends from the neutral plane. Theorem 13. Given the same movement, the speed of movement of perspective of any point along a line is in proportion to the speed of movement of the line itself, and in converse proportion to the retrogression of a point on the same line from the neutral plane. We must close this section with a few words on aerial perspective. In linear perspective the impression of spatial depth is created mainly by the distribution of dimensions and the lines marking them. But in aerial perspective the same effect is achieved by the tonal differentiation of planes and dimensions, distributed at various distances from the foreground. The closer the object is to the foreground, the more intensively do our eyes perceive light and shade, and the stronger are the light contrasts of the image. Our impression of the form and outline of the object also changes equally in correspondence with the object's distantial relationship to the foreground. At a close distance the object is clearly outlined, and as it recedes into the depths of the image it loses its distinct outlines and is perceived as a tonal mass. Aerial perspective is in direct dependence upon the laws of the strength of 1 ' Depth of the perspective ' is the relation of the height of the perspective of the body's depth to its actual depth.— AT. 2 ' Neutral plane ' denotes the plane passing through the centre of the lens parallel to the picture. — N. 3 ' Main plane ' is used to denote the plane perpendicular to the picture, passing through the centre of the lens and parallel to one (vertical) side of the picture. — N. 54