and the general element will be designated by N^j^. 



These 5400 points cover an extensive area of the sea surface such that 

 quite a few waves are involved. Were they measured with respect to a zero 

 determined by the level of the water in the absence of the waves., they would 

 average to zero and the sum of their squares would be a minimumo However, 

 they were read witli reference to an arbitrary tilted plane instead of with refer- 

 ence to the sea level. 



The values desired with respect to zero level are given by equation {8, 1) 

 where the unknown constants a, b, and c absorb the effects of the grid spacing 



{S= 1) N*^ = N.^ - aj - bk - c 



j = Oj . . , , , n-1 k = Oj . „ , . , m-1 



n = 60 m = 90 



Consider equation (8. 2), 



m-1 n-1 m-l n-l 



(8. Z; Y = i: ^ "^^* '^ 



k= 



2 (n1)^- S S (N-1^ - ai - bk - c)' 

 :0j = J^ k-0 j=0 J^^ 



The value of V should be a minimum with reference to true sea level {if 

 the area covered by the points is large enough), and this can be accomplished if 



8a 



(8o 3) aT = ° ' 



8V 

 and Qi = , 



dc 



Equations (8,3) lead to equations (8.4). 



59 



