( 561 ) 



to tlie fre(|ueiK'ies fOiTesi)(mdiii'>' witli the deviations — 0.5 uim.. 

 as given in Talile 1, so thai the greater or less degree of agreement 

 hetueeii tiiesc \aluos may be taken as a criterion for the proposed 

 assnnijition //r=r //. 



In order to show that this agreement is fairly satisfactory, the 

 observed trecpiencies between the limits and 0.5 are given once 

 more besides the calcnlatod valiies of A- 



If we compare the situation of the intersection points as shown in 

 Table II and as calculated according to form. (10), we see that the 

 situation of the first point of intersection agrees well with the 

 observed facts, i)ut that the second [)oints «.^, as calculated, cor- 

 respond with greater de\ iations than occur in reality. 



As this second point of intersection naturally coincides with small 

 trecpiencies the degree of precision of which is questionable, it seems 

 difficult to decide whether these differences may be ascribed to 

 insuiTiciency of material, to the omission of a possible fourth term in 

 form. (4), 01' to an error introduced by the supposition //= A; as the 

 calculated values of «^ are jointly too great, the latter cause has to 

 be regarded as the most |(rol)able one. 



4. The fact that in Table HI, in which a measure is given for 

 the skewness of the curves, except for e ^ 0, only one zero-value 

 occurs, proves that in fc/rm. (5) the addition of a third term is cer- 

 tainly not retiuired. The calculation of the constants 5 and Z) as well 

 as the deternunatioii of I he point of intersection ,? can, therefore, 

 easil}- be made. 



As: 



we find immediatelv 



I 



r.rd.v = 



3 I) 

 B -\ = (11) 



whereas 



r B D 



I Ydx = - -^- =r—p~ n. . 

 J h" ^ h' ' 



;i2) 



denotes the surplus of positive over negative deviations. 



If we take the absolute sum of positive and negative deviations 

 as a measure for the skewness *■ : 



/3 « (5 



« = jo -f « = 2 I Ydx — I Yd.v = - r Ydx — V, 



39* 



