DISCONTINUOUS PERIOD IN CYCLOGRAM ANALYSIS 63 



to the slit ; but these lines will differ one from another in density on account 

 of the variations in the curve K that obstruct one or another opening in G. 

 Now if we start the curve K in motion, the longitudinal lines on the film W 

 will remain straight but will change in density according to the variations in 

 the curve K as each part of it passes across each opening in G ; and eventually 

 each longitudinal line will make a reproduction of the complete original data 

 with ordinates represented by photographic density. The result is a "multi- 

 ple plot" with complete reproductions of the data in equidistant parallel 

 lines. It is easily seen that if the film W moves very slowly in relation to 

 the speed of the curve K, the horizontal offset between these reproductions 

 will be very small; but as the film goes faster the horizontal offset between 

 the reproductions on the film W will be greater. Thus, the offset in the 

 resulting multiple plot depends on the relative rates of motion of K and W. 



In our original attempts at analysis there was no fundamental difference 

 between multiple plot and our present cyclogram, merely differences of con- 

 venience in production and use. Discontinuous periods were seen in either 

 one. There was a little difference in the formula for getting the cycle length. 

 The multiple plot could be described as a cyclogram in which the two plot- 

 ting axes are not perpendicular to each other. To get them perpendicular 

 we choose an axis of x, in time, not perpendicular to the multiple lines of 

 the data (the analyzing lines) but perpendicular to the "sweep" lines. It is 

 noticeable that in the cyclogram as commonly reproduced the analyzing 

 lines slant to right or left of the perpendicular (referring to publications 

 subsequent to 1920). Changing the slant from right to left, or the reverse, 

 inverts the resulting plot (fig. 20) . The same effects are readily produced in 

 Stumpff's apparatus by giving his grating a slow constant motion ; the direc- 

 tion of this motion corresponds to the direction of slant of our analyzing 

 lines and the rate of motion corresponds to the angular amount of slant. 



An important difference between the two analyzing methods is that 

 while each can produce a photograph, ours also gives instantaneous visible 

 results and is very readily and rapidly applied to a large range of cycle length. 

 If we understand Dr. Stumpff's instrument correctly it is not so well adapted 

 as ours to the study of discontinuous periods. 



In describing Dr. Stumpff's instrument in the last few paragraphs, I have 

 exemplified the production of a form of multiple plot and a cyclogram by his 

 process. Dr. Stumpff's operation of the instrument produces a periodogram. 

 This is done by imparting an accelerated motion to the grating G. When 

 this motion comes into a definite speed ratio to the motion of different cycle 

 maxima in the curve K, a critical resonance point is passed which goes on 

 record on the film in the form of a parabola vertex which can be nicely located, 

 thus giving data for an accurate determination of the cycle length. 



APPLICATIONS OF THE DISCONTINUOUS PERIOD 



There seem to be several fields in which the discontinuous period should 

 find special usefulness. The first is the determination of the terrestrial areas 

 (meteorological districts) in which similarity in climatic cycles may be found. 



