56 CLIMATIC CYCLES AND TREE GROWTH 



overlapping), thus reducing the number of dots and bringing them nearer 

 their center. If by this means the location of the cloud is found to remain 

 distant from the pole, the reality of the period becomes more and more 

 evident. 



The summation dial, figure 26, is of special interest to us, for it represents 

 the same phases and amplitudes stretched out into a time sequence, though 

 an irregular one. It is, therefore, an extended curve, for it gives facts at 

 successive equal intervals of time through the full data. Figure 26 doubtless 

 was his basis for introducing the middle term in his series of three classes of 

 effects: random, quasi-persistent, and persistent. The diagram at first 

 glance could be divided into "tangles," or random motions, and "arcs," which 

 have a directional effect; in these last the quasi-persistences are more easily 

 found. 



Since the harmonic method uses a constant period of 27 days, any actual 

 change in it becomes expressed as a change in phase ; and since phase is repre- 

 sented as a position angle (direction from pole or a line parallel to such direc- 

 tion), a slight semi-persistent departure in period from the assumed value 

 is expressed by a series of amplitudes pointing progressively in a changing 

 direction; this produces an arc. 



To look at this diagram and think of its possible solar meaning is perhaps 

 perfectly natural. As the period here used is the time of rotation of the sun, 

 the tangles which occur at sunspot maxima and minima mean that at such 

 times magnetic forces are reaching us from widely distributed solar longitudes. 

 This is to be expected at maxima. Dr. Bartels has observed its occurrence 

 also at the beginning of each new sunspot cycle, which explains its presence 

 at minima. The "arcs" indicate a tendency for magnetic forces to emanate 

 for considerable intervals from some localized longitudes of the sun. 



Quasi-Persistence in the Summation Dial — The important feature in 

 Bartels' summation dial, figure 26, is the representation on an extended time 

 scale of certain changes in cyclical character and their evidence of temporary 

 stability, if we can so term it, which he calls quasi-persistence and which I 

 shall indicate in these paragraphs by the initials QP. Amplitude QP's in the 

 summation dial are indicated by the number of equal lengths in succession in 

 the short, straight lines, without regard to direction, such as shown in figure 

 27a. A quasi-persistence in period is indicated by successive, equal angles 

 between these short, straight lines. This develops as a curve and may not 

 have any QP in amplitude, as in figure 27b. A complete reversal of phase by 

 180° has often been suspected in climatic cycles. Such a change in a summa- 

 tion dial would make a pattern somewhat like that in figure 27c. It is pos- 

 sible that a change in phase occurs by some other fraction than \. 



Quasi-Persistence in the Cyclogram — The cyclogram is an automatic plot 

 in three dimensions capable of instant adjustment over a wide range of cycle 

 lengths. In this analysis the portion of the curve below a "cutting line" 

 along the lower minima is commonly omitted during analysis, which is analo- 

 gous to the usage of harmonic analysis in taking values from a mean and not 



