Unfortunately the mathematics of the rule make it difficult, if not impossible, to do so, because the blow on L. is lessened when it is shared by other quantities. Thus by Mr. Watson's modification of the rating rule, proposed in October 1892, viz. English R = (2L + 2B + D) × S ÷ {constant, say 17,000} (II.) 'Doreen' is of smaller rating, although both longer and more beamy than 'Decima.' They are of the same rating for racing by the Y.R.A. rule. Mr. Watson's formula would therefore encourage even greater length of hull than the Y.R.A. rule. No such difficulty is encountered by the introduction of such taxes into the Seawanhaka rule, where the plus sign replaces the multiplying sign used by us. This rule was adopted by the American Yacht Club of its name in 1882, the form being American R = (L + [V¯]S) ÷ 2 (III.) The New York Yacht Club has raced for a number of years under a similar rule for time allowance,[6] viz. American R = (2L + [V¯]S) ÷ 3 (IV.) and just as the Y.R.A. rule can take the form L × S = constant in any class, so these rules can take the forms L + [V¯]S = constant, in any class III. 2L + [V¯]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. [Footnote 6: But not for classification, which latter has been simply the length of hull on water-line. Hence, yachts built for the same class have varied much in their sail-area; 'Vigilant' and 'Valkyrie' for instance.] 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. × [V¯]S. × [V¯]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 = [3V¯]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. An examination of this form of the Y.R.A. rule is interesting. By cubing V. and comparing it with I., it will be seen that six thousand times the English rating equals the cube of the American rating derived from formula V. [Illustration: Diagram of sail curves, showing the relation of sail to L.W.L. in the Y.R.A., New York, and Seawanhaka Rules. 40-rating class.]