46 CLIMATIC CYCLES AND TREE-GROWTH 



On the other hand, some will object, and correctly, that the cy olo- 

 graph process does not give in figures the harmonic constants. Two 

 points answer this; the first is that the cycle must first be caught out 

 of a very complex combination of variables, and second, when the 

 cycle is known it is easy to get its constants by mathematics, if desired 

 (or by photometric means from a cyclogram). 



PRINCIPLE OF THE CYCLOGRAPH 



The earlier forms of the instrument have been described in the 

 previous volume and need no repetition. The principle also was 

 explained, and is briefly outlined here only as an introduction to the 

 present form. The maxima of the curve to be analyzed are cut out, 

 so that light passes through in proportion to the ordinates, as already 

 described under the title Cycle plots. The horizontal spacing of the 

 maxima of light is emphasized if the cutting-line is high, leaving the 

 extreme minima without illumination. Now let us imagine a plot of 

 this sort consisting of a series of evident maxima which seem to be 

 equally spaced (as in the sunspot curve), and we wish to find if they 

 are strictly periodic. We illuminate the curve from the back, place 

 a lens at some distance before it, find the image cast by the lens, and 

 compare the white spots in the image with an adjacent series of dots 

 which we have placed on exactly equal spaces. If the dots are closer 

 than the maxima, the lens is carried farther from the curve, reducing 

 the separation of the focal images until they coincide in the average 

 with the equally spaced dots. Then we see clearly that the maxima 

 largely match the dots but in certain places; let us say, they draw 

 away. These departures let us call differentials. 



So long as differentials take place in their own line (like the longi- 

 tudinal vibrations of sound) it is hard to estimate them, but if these 

 differentials can be turned out perpendicular to the line of the curve, 

 that is, made transverse (like fight- waves), it is very easy to see and 

 measure them. This is very easily done by extending both maxima 

 and dots indefinitely in the transverse direction but at a small angle 

 to each other. This effect is produced on the curve image by adding 

 a cylindrical lens which converts each maximum of the focal image 

 into a vertical band. The same effect is produced on the dots by 

 inserting in their place a series of equally spaced nearly vertical opaque 

 parallel lines. To give these lines accurately, a ruled screen such as 

 that used in photo-engraving is placed at the focus of the lens and 

 the row of vertical bands comes through the slightly inclined trans- 

 parent spaces between the lines. This produces an interference which 

 should be seen to be appreciated. If the maxima are equally spaced, 

 they come through as straight horizontal rows of white spots, but 

 where differentials occur, the spots are displaced above or below the 

 i straight line. Departures from a perfect period are at once recognized, 



