L × S = constant in any class,
so these rules can take the forms
L + √S = constant, in any class III.
2L + √S = constant, in any class IV.
It then becomes evident that any sacrifice of S. to obtain greater L. under Rule IV. is only half as effective as the same process under Rule III. Conversely, any sacrifice of L. to obtain more S. is twice as effective under Rule IV. as under Rule III.
Again, as comparisons between L. and S. must be brought to some common measure, the Y.R.A. form ... L. × S. = constant in any class, may be read L. × √S. × √S. = constant, and it then becomes clear that any sacrifice of S. to get L. is twice as effective as in Rule III., and four times as effective as in Rule IV.; and conversely, that any sacrifice of L. to get more S. is half as effective as in Rule III., and one-fourth as effective as in Rule IV.
The author of the Y.R.A. rule has pointed out that it can be converted into the American form of 'corrected length,' thus:—
American R = [3]√L × S (V.)
See his second edition of 'Yacht Architecture.' The sail curve is precisely the same as that from the Y.R.A. rule.