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History of Three-Color Photography
there are ten units, each having two boundaries 30 mm. long, and multiplying this by half the units, or by 5, the result is the same, 300 mm. If one line be crossed the total of the boundaries is 4X150, or 600 mm., as before. If the lines of an alternating line and mosaic plate run the short way of the plate, then there are fifteen line units, each with boundaries of 20 mm., thus 15X10, or 150 square units, each with a periphery of 4 mm. ; the total is, therefore, 20X7^ added to 4X75, which equals 150+300, or 450 mm. In the case of an equilateral triangle mosaic, Fig. 109, assuming that each triangle is equal in area to one of the squares before considered, there are then 300 units. But as the periphery of each triangle is 4.56 mm., the total length of the boundaries is greater, that is 684, instead of 600 mm. If there are 300 hexagons, Fig. 110, then as the periphery of the hexagon is only 3.72 mm., the total of the boundaries is reduced to 558 mm. If the area of the units be increased, or diminished, other results will
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Fig. 112
Fig. 113
Fig. 114
obviously be obtained. Taking the square first, then if the sides of the square are doubled, that is 2 mm., instead of 1, the periphery is doubled and the area quadrupled, which reduces the total number to one-fourth; therefore, there are 75 squares, each with a periphery of 8 mm., so that the total of the boundaries is 300, instead of 600 mm., as before. If the sides are halved the peripheries are halved and the area reduced to onefourth, and the total number quadrupled, with the result that there are 1200 squares of 2 mm. periphery, so that the total is 1200 mm. From this it is clear that the smaller the unit the greater the length of the dividing lines.
In considering the diaper pattern screens, in which one color unit forms the ground on which two other color units are in the form of quite separate units, larger results are obtained. Assume the blue units to be merged together so as to form a blue ground, and the other units are uniformly distributed thereover, Fig. 109, the total boundary of the lines is equal to the periphery of each of these units, 200 multiplied, therefore, for the square pattern the total is 800, instead of 600 mm., as before. If the squares are changed to circles, Fig. 112, the periphery of each unit is only 3.54 mm., and the length of the dividing lines is reduced to 708 mm. With a diaper of triangles, Fig. 114, it would be necessary to nearly