Physical Aspects of Protoplasmic Streaming 



225 



the lower side. If the curve is periodic, or almost periodic, as in 

 Figure 10, this line can be found easily with the aid of a planimeter, 

 or by any other practical method. When the wave form changes 

 from rhythm to rhythm, as is the case in many of the wave trains 

 with which we are concerned, the line of which we speak is mathe- 

 matically indeterminate. But in practice we can find such a line with 



TIME IN MINUTES 



14 r 



12 



10 



8 



6 



4 - 



2 





 -2 

 -4 

 -6 

 -8 

 -10 

 -12 

 -14 



Fig. 11. 



a certain degree of approximation. This can be done graphically 

 by measuring the successive areas included within common tangents 

 of consecutive crests or troughs, and the experimental curve. These 

 areas divided by the distances between two contact points of the 

 common tangents show the mean distances from the tangents to 

 the line being sought. 



The dash-dot lines XY in Figures 10, 12, and 13 are lines which 

 divide the waves approximately into equal -f- and — parts. These 

 lines show the "true" axes of the waves, the ordinate of which is a 

 measure of the polarity of the plasmodium in its absolute scale. 

 These true axes or "polarity lines," are generally (except Fig. 

 10) not parallel to the base line. Lack of parallelism shows that the 



