90 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 reproduc- 

 tions 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 dis- 

 placement 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 Aline- 

 ments 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 coor- 

 dinate 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 



Theory. The formula for the period is very simple : 

 Let y = length of curve in years or other time-unit employed. 



1 = 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 - = number of analyzing lines in curve when lines are parallel to 

 sweep. 



= number of years in 1 line when lines are parallel to sweep. 

 i 



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 com- 

 monly employed in half-tone engraving. 



