76 



O. A. Åkesson 



{^^) ^ = — ^ K ^ ^" northern hemisphere 



and 



(49) V^^+^l^f' in the southern. 

 From the equations of Vg^ and v^g we deduce 



3 



(50) »^iLZlZüji^^l/^. 



î?j 7?., Oy ' Sy 



That this expression may not be inconsistent with the preceding expressions, aS'^ and Sy 

 must necessarily have the same sign in the southern hemisphere and different signs 

 in the northern, a cotulition not fulfilled in the present case. Moreover, that a division 

 of our frequency- snrfaces into two normal components of the form given in (42) 

 may be practicable, the relation 



hrh 



must exist. This condition can, however, only be succesfnlly used when skewness 

 and excess are not too small. Otherwise the quotients will be very inaccurately 

 determined. 



In computing the unknown quantities, and are first to be determined. 

 This may be done by means of the expression for v^^ combined with tlie expressions 

 of the third or fourth moment. In the former case we obtain 

 NN V ^ 



(52) 



NN V3,v„3 + 4v,,^ 4(S.A+'i' 

 in the latter 



N^N,, _ 



^""^^ 'NN - 6r^ ± 8l7^1^, ■ 



In this equation the sign + shall be used when E_^- and Ey are ^ 0 or, what is 

 the same, when 



Since 



N ^ N 



JVj and N^ are determined. Having computed N^ and N^, the other unknown 

 quantities w?^, m^, m^, n^, a.^ and are easily obtained. Since we have previously 

 seen that the condition of dividing our frequency-surfaces was not fulfilled, we can- 

 not make a numerical computation of the characteristics of the two frequency- 

 functions (42) in the present case. 



