# Page:Climatic Cycles and Tree-Growth - 1919.djvu/112

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CLIMATIC CYCLES AND TREE-GROWTH.

plate 9, e. When the analyzer is turned at a small angle to the lines of the sweep, each transparent line shows the full curve or a substantial part of it in its varying light intensities. 'These numerous reproductions are all parallel to each other, separated by equal dark lines, and each one is displaced longitudinally with reference to its neighbors, thus presenting the characteristics of the differential pattern. By twisting the analyzer with reference to the sweep while the two remain in parallel planes, different periods may be tested; for as the analyzer twists, each reproduction varies in respect to its length and its displacement from its adjoining neighbors above and below. When a period is formed it shows itself, just as in the original differential pattern, by rows of dark and light spots in alinement more or less perpendicular to the analyzing lines, as in plate 9, e. These light and dark rows are analogous to interference fringes and are identical with the elaborate but provokingly useless designs on a wire screen in front of its reflection in a window, or with the parallel fringes when two sets of parallel lines are held at a slight inclination to each other.[1] Alinements are always best recognized by holding the paper edgewise and looking at the diagram at a low angle rather than in a perpendicular direction.

The analyzing plate resembles a coarse grating with equally spaced parallel lines. Much difficulty was experienced in making it. It is most satisfactory if made on glass with strong contrast between the opaque and transparent parts. The grating now in use was produced by photographing a 10-foot sheet of coordinate paper upon which 165 lines of black gummed paper had been carefully fastened. The coordinate lines permitted the spacing to be done with exactness. The width of the transparent space throughout was three-tenths of the distance from center to center. This was carefully photographed by a good lens at different distances. Glass prints were made from each negative and are still in use.[2]

<poem>﻿Theory. — The formula for the period is very simple: Let﻿ y = length of curve in years or other time-unit employed. ﻿l = length of curve image across sweep lines in centimeter or other unit of length. ﻿s = spacing center to center of analyzing lines in unit of length. Then﻿${\displaystyle {l \over s}}$ = number of analyzing lines in curve when lines are parallel to sweep. ﻿${\displaystyle {ys \over l}}$ = number of years in 1 line when lines are parallel to sweep.

1. Roever (1914), has used somewhat similar interference patterns to illustrate very beautifully certain lines of force.
2. A very superior analyzing plate has recently been made from a ruled screen such as is commonly employed in half-tone engraving.