508 - 2" - 



Now, usinj (121) we nave F (O) = W2 or 1.5, and, taking the latter for simpler arithmetic, 

 we obtain from (122) anO (l26): 



^ = F-j(O) = ^ >"_^'"' (127) 



" m 



For. all Box Model snots 5' > i S_ so tnat: 



/S < I (128) 



while from (122) anO (117) wo find: 



K„ = -^ (8 /S^ - 12 /2 + 15) (129) 



" 10 5 



It is then edsy tc show that in the r-inje Q^^<^, 



0.1^ K^ < O.H (130) 



We have previously seen that K. ^ K, ~ 11 su that, for a/O - 1.52 as in Box Model shots we 

 find from (il9) and (130) that K lies in the range 10 to 40, 



We shall therefore assume that: 



K = 25 (131) 



jives a reasonable expected value for K, while: 



K = HO (132) 



proDably overest inHtos K. 



As a final point, wg require a value for A in order to estimate S froni the mean "deflect ion 

 Dy use of (70). 



Using (120) or (121) and a/b = 1.52 we fino from (ll7) and (116) that 



A, = 32.7 for cosine shape 



A = 31.4 for parabolic shape 



^ - 1.52 (133) 



E 



Further, the value of A for the soap bubble shape and a/b = 1.5 is implicit in equation (38) 

 of the report mentioned on the previous page, and is: 



A, = — X 5.76 = 30.8 for soap bubble shape I = 1.5 (l34) 

 1 3 b 



The difference in A for a/b varying from 1.5 to 1.52 Is undoubtedly negligible so that for 

 the three shapes of cosine, parabola and soap bubble we find A varying from 32.7 to 30. 8. It may 

 be noted that the same three shapes give values 2.47, 2.25 and 2.06 respectively for the ratio of 

 central to mean deflection and this range covers most of the box model shots. For smooth shapes, 

 A is thus relatively insensitive to the precise shape and we shall take: 

 • 



Aj = 31-6 (135) 



as a mean value for application to Box Model trials. This value wauld only lead to pronounced 



error if "ripples" were present since such ripples give a relatively large contribution to Increase 



of area compared with any contribution to mean deflection. Fortunately, the dishing In Box Model 



trials is relatively smooth and the use of (135) is unlikely to introduce errors of more than about 



5» in the deduced values of S„. 



m 



