66 ^' Marion" expedition to davis strait and Baffin bay 



bution fills this need. Various coefficients of skewness are used, 

 but the formula Sk = QxQ^/M- is very satisfactory for size distri- 

 butions in which the quartiles are known. If R is the reference 

 diameter, then B=MV^ = Qi/jSo=jSoXQ^. Thus, if the three 

 fundamental constants, M, So, and Sk or log Sk, are given, the 

 significant features of the mechanical composition of the sediment 

 are at once apparent, for by multiplying the median by the square 

 root of the coefficient of skew^ness one obtains the reference diameter, 

 and by dividing or multiplying this by the coefficient of sorting he 

 gets the first and third quartile, respectiveh\ However the main 

 object of the skewness is to determine the approximate position of 

 the mode of the size distribution; that is, the diameter correspond- 

 ing to the apex or crest of the histogram. 



The coefficient of skewness is a ratio of the increase in diameter 

 in the second quartile interval to that in the third quartile interval. 

 For examiDle, in sample 1, Sk is 3.65. This means that the ratio of 

 increase of diameter between the median and the first quartile is 

 3.65 times that between the third quartile and median; because, 

 from M to Q^ the diameter rises from 5 to TO, which is a fourteen- 

 fold increase, and from Qs to M it goes from 1.3 to 5, which is a 

 fourfold augmentation. The second and third quartile intervals, 

 each represent 25 per cent of the weight of the sediments, but the 

 ratio of increase in diameter for the two intervals is 14 to 3.9, or 

 3.65. From this it is evident that in this sample the maximum 

 sorting occurs on the fine side of the median; that is, the mode lies 

 in the third quartile interval. 



The coefficient of skewness is a ratio varying about unity. Con- 

 sequently, when one compares the dissymmetr}^ of two samples, one 

 of which has the mode in the second quartile interval and the other 

 in the third, he obtains an erroneous impression unless the logarithm 

 of the skewness is given. For example, values of Sk of 0.67 and 

 1.5 refer to the same degree of dissymmetry; but unless one is very 

 familiar with reciprocals, the similarity of the two ratios is not 

 evident. However, if they are given in their logarithmic form, 

 namely —0.18 and +0.18, respectively, their equivalence is at once 

 apparent. For this reason the skewness is given as log Sk on 

 Figure 48. 



The interpretation of the coefficient of skewness may be briefly 

 summarized as follows: If Sk is greater than 1.0 or log Sk positive, 

 the maximum sorting of the constituents lies on the fine side of the 

 median ; if Sk is less than 1, or log Sk negative, the maximum sort- 

 ing is on the coarse side of the median ; if Sk is about 1.0 or log Sk 

 near 0, the maximum sorting corresponds approximately with the 

 median; and the greater the divergence of Sk from 1.0, or log Sk 

 from ; the farther the maximum sorting lies from the median. 



Practicability of fundamental constants. — In order to illustrate the 

 practicability of these three fundamental constants let us take sample 

 1, in which %I is 5, So is 7.35, and Sk is 3.65. From these three con- 

 stants it follows that the sediment is a coarse-grained clay; that it 

 is very poorly sorted; that the greatest concentration of particles 

 occurs in the clay group relatively far from the median on the fine 

 side; that 25 per cent of the sample is larger than 70 microns in 

 diameter, and 25 per cent is smaller than 1.3 microns. 



