37 



these tables the wave resistance of practically any assumed normal elementary 

 form with simple midship section can be derived by multiplication with the 

 parameters involved and subsequent summation. A first contribution in this 

 direction has been made by Wigley:*^ He performed calculations for the family 

 (2,H-,6,(/>,t) based on a slightly different form of the polynomial. Although 

 the author has himself used this type of equation in earlier work, he prefers 

 the expanded form 



r, = 1 - ^^e - aj^ - (1 _ a^ - aj^« [l8] 



or in Taylor's notation 



77 = fo(0 +c«f,(0 + tf^d) [19] 



Wigley's work covers only one basic family of ship lines, but it in- 

 cludes a check of calculations by experiments. 



Method of Approximate Discussion ; Pending the computation of tables 

 of complete resistance integrals, a simple if rather coarse procedure has been 

 developed which allows comparison of the relative merits of forms. It is 

 based on the discussion of the integrand of Michell's formula, or rather on 

 only one part of it, which depends on the longitudinal displacement distribu- 

 tion and is formally handled by the M (y) functions previously mentioned. 



This Integral is written in the symbolic form 



R = C J S2{y) *2(y) f(y)^y [20] 



''0 



where y, the variable of integration varies for a given Proude number P 



between y„ = — — and Infinity, 

 2p2 



f(y) is a simple algebraic function, 

 *^(y) is a function dependent upon the vertical distribution of displace- 

 ment, and the product 

 *^(y)f{y) ensures a rapid decrease of the integrand with increasing y. 



S(y) = J l^sinyfd^ [21] 



is an oscillating function dependent upon the longitudinal displacement dis- 

 tribution. S^(y) > represents the most important factor of the integrand. 



