the figures for average abundance during comparable periods of time in the 

 two years are of the same order of magnitude. For the period late May - 

 early October, which is cormon to both years, the average count of diatoms 

 was 91 thousand units in 1929, and 88 thousand units in 1930 (Tables 5l and 

 53). For the same period, the average count of greens was 37 thousand in 

 1929, and 38 thousand in 1930. Corresponding figures for the blue-greens 

 were 52 thousand and 63 thousand units. It is recognized that absolute 

 agreement in the averages given above would not prove the reliability of 

 the averages given in Tables $1 and $3. On the other hand, the fact that 

 they are not widely discrepant is suggestive of reliability. That is, v« 

 should expect to find differences in abundance in the same lake in suc- 

 cessive years, yet we should expect that these differences in abundance 

 in the two years would not be great. 



The second reason is that the curves for the two years (Fig. 1$, 

 16, and 17) are in close agreement with respect to (1) the times of 

 changes in abundance, and (2) the degree and direction of change. This 

 relationship can be brought out best by determining the coefficient of 

 correlation and its probable error for each pair of curves by means of 

 the well-known Pearsonian formulae. Data for comparison of the curves 

 were obtained as follows. Points on the curves for 1929 (late May to 

 late September) were taken as X, and corresponding values for 1930, Y, 

 were obtained by running a line vertically to the curves for 1930, These 

 corresponding values were then applied in the following formulae: 



E xy 



r = \ ^ r, 3nd 



•^Ex'^Ey'^ 



P.^A'i: 0.67n$ (1 - ^ 



The values of the coefficients of correlation (r) for the three 

 groups of phytoplankton organisms shown in Figs. 15, I6, and 17, are as 

 follows J 



Diatoms, ,80 + ,082 



Greens, .50 + ,0U2 



Blue-greens, ,99 + .005 



These figures indicate a high degree of correlation between the 

 curves for the two successive years. Agreement is especially close for 



172 



