Still another factor governs the _best length_ in any cla.s.s, viz.

lightness of construction; and this depends on four other factors: cost, design, workmanship, and strength of materials.

We are therefore met by quite a crowd of considerations when endeavouring to determine _best length_; but in comparing the rating rules we can eliminate many of them by making a few a.s.sumptions and reasoning therefrom.

_First_, a.s.sume that a new boat is built with the lightest possible hull consistent with strength, and of the best possible design for the 40-R. cla.s.s 1894, and that her L.=62 ft., therefore S=3,871. (See preceding table.)

_Second_, a.s.sume that a longer boat and a shorter boat equally well built and designed are tried and are beaten, and that 62 ft. is then acknowledged to be _best length_ for 40-ratings in our climate.

_Third_, a.s.sume that the cla.s.s is converted in 1895 into one rated at 61.5 American R., 'Queen Mab' being thereby placed at the top of the cla.s.s by the Seawanhaka rule without alteration. The 62-ft. yacht, however, must clip to 3,721, or 150 off her S. as a 40-rater.

But the shorter boat, say a 'Queen Mab' 59 ft. L.W.L., which we a.s.sumed to fail when racing under our rule, could now _add_ 30 ft. and sail against the crack 62-footer with an advantage of no less than 180 sq. ft. of canvas.

Evidently, the best length under our rule being 62, the best length under the American rule is something less; how much less being only determined by trial, and depending on the numerous factors before mentioned. Moreover, an arbitrary limit of L.W.L. is thus shown to be less necessary under the American rule than under ours; and with L. so greatly developed in our racers at the present time, it may be that we have already gone beyond the best length for the American rule, especially in the small cla.s.ses. This was carefully pointed out by the present writer in two letters to 'Land and Water,' October 5 and 9, 1892. Mr. R. E. Froude also stated the case very clearly in the 'Field,' December 31, 1892; but it is very difficult to convince the defenders of the Y.R.A. rule that any other rule is superior.

Mr. Dixon Kemp, in his excellent work on 'Yacht Architecture,' says (p. 15, 2nd edition) in comparing rules I., III., IV.: 'Of these rules, that of the Y.R.A. admits of the employment of the greatest length for any given rating'; and the length referred to was evidently _best length_ in a given climate.

The Seawanhaka rule is therefore superior to ours if excessive length be feared; and being a plus formula, it lends itself readily to the adoption of any desired tax on other linear dimensions.

For instance, Mr. Watson's proposal (II.) might be put into the plus form, thus:--

American R = (2L + 2B + D + [V]S) 3.8 (VI.)

This shows the value of a plus rule over a multiplying rule and the value is not lost when a plus rule is converted into an English rating rule by cubing the former and dividing by a constant. Thus, the recent Rule Committee proposed to convert the Seawanhaka rule into an English rating rule by cubing it and dividing by 6,000, the result being:

English R = (L + [V]S){3} constant, say 48,000 (VII.)

The variable within brackets in VI. can be cubed and divided by a constant in a similar manner. But the cubic forms of the 'plus' rules are clumsy, and seem difficult to those who cannot compute by logarithms. No real advantage is gained by adhering to the English rating and time scale and cla.s.sification. In fact, the American time scale is simpler. If, therefore, a 'plus form' of rating be ever adopted, it would be much better to adopt 'corrected length' as the rating, together with the American time scale. The cla.s.sification could, of course, be chosen in such a manner that our own racing yachts would be at the top of the cla.s.ses without any important alterations.

Another rule was proposed in a leading article of the 'Field' on October 15, 1892. It is:--

English R = L{2}[V]S constant, say 6,000 (VIII.)

It gives a sail-curve nearly parallel to the one produced by the New York rule, and may almost be regarded as that rule dressed in Y.R.A.

uniform; but the advantages of a plus rule are lost, whereas in the conversion of the Seawanhaka rule proposed by the Y.R.A. Committee 1892 they are retained.

Similarly, the Y.R.A. rule--varying as [3V]L.S. (see V.), or as [3V]L. [V]S. [V]S.--may be considered as equivalent to the plus formula L. + 2 [V]S. constant, and the English and American rules may therefore be regarded to vary as follows:

In linear measure New York as 2 L + [V]S Seawanhaka as L + [V]S Y.R.A. as L + 2[V]S

Mr. Herreshoff has recently proposed a rule of rating based on L. [V]

S., which is an area, but the cube root of tonnage is placed in the divisor; and this being linear, it converts the rating into linear measure, an area divided by a line being a line. The result being linear, it is translatable into American rating and time allowance.

Mr. Herreshoff's proposed rule is:--

American R = ( L [V]S / [3V]T ) constant, say 15 (IX.)

A critique on this rule by the editor of the 'Field,' December 17, 1892, suggests that the cube root of 100 T. should be taken, as there are 100 cubic feet in a registered ton. This is unnecessary. So long as S. is superficial, and T. cubic, the [V]S. and the [3V]T. will be linear; and a constant can be selected which will convert the quotient resulting from the rule into corrected feet or inches, or metres, as required for the linear rating adopted.

Mr. Herreshoff's rule when tested is not encouraging; 'Doreen's'

length so corrected being 2-1/2 per cent. smaller than 'Decima's.' The rule evidently does not encourage that compactness of hull-dimension which Mr. Watson considers desirable. It also appears to put a premium on abnormal freeboard, so as to increase T. by means of a large body over the water-level.

This was pointed out by the editor of the 'Field,' December 24, 1892, and an improved rule suggested in which displacement was used as a divisor in place of tonnage. W. the total weight of yacht in English tons dead weight is of course her displacement, and the rule proposed may be written:--

English R = ( L{2}S / [3V]W ) 10,000 (X.)

So far as L. and S. are concerned this rule would produce a similar sail-curve to the Y.R.A. rule (see diagram); but the divisor would encourage a large powerful hull, and the rule would therefore produce a shorter type with more sail than now exists in English racers. The practical difficulty of discovering W., either by measurement or by some system of weighing the yacht complete, has to be considered in connection with this rule.

The most important point to be noted about these rules (IX. and X.) is the fact that Mr. Herreshoff and Mr. Dixon Kemp proposed them--showing that two of the leading experts consider it necessary to encourage greater displacement by means of the rating rules. The question, therefore, arises whether the desired result cannot be effected in a less objectionable manner; and it appears to the writer that dividing the present Y.R.A. rule by some area proportional to that of the immersed mid-section would have the desired effect, and would avoid the difficulties already mentioned. The actual area of M.S. cannot be found without encroaching on the secrets of a yacht's design; but M.

the area of immersed mid-section can be easily found if measured internally, and the Y.R.A. rule may take the form:--

American R = LS constant (say 72) (XI.) -- M

L.S. being cubic, and the variable divisor M. being superficial, the quotient is linear, and a constant divisor can be chosen which will convert the result into American rating, which is expressed in 'corrected' feet.

The general tendencies of the Y.R.A. rule would be modified by the introduction of M. as proposed in XI., a large immersed M.S. being encouraged, without the necessity of employing a deep narrow body, as may be seen on the following table, where 'Bedouin' figures out very well owing to her large but not deep immersed M.S. The author claims with some confidence that this modified rule presents the best solution of the problem yet suggested. But there is really no problem requiring solution at present. So long as yachts like 'Britannia' and 'Satanita' are built for racing under the Y.R.A. existing rule of rating, grumblers will not command an audience. In the event, however, of yachts like 'Pilgrim' or 'Jubilee' winning in our waters a change of some sort will be required.

The measurement of M. can be easily done in a few minutes, with yacht afloat, as described on p. 87 of the 'Field,' January 21, 1893.

The Seawanhaka rule (III.) can be treated similarly, the divisor 2 being thereby avoided. It becomes

American R = L + [V]S - [V]72M (XII.)

The action of these rules may be seen from the table on p. 180; column headed XI. giving the rating under the modified Y.R.A. rule, and column headed XII. giving the rating under the modified Seawanhaka rule. Each result is in 'corrected length.'

The dimensions in above were obtained from the drawings in Dixon Kemp's 'Yacht Architecture,' 2nd ed., except 'Decima's' and 'Doreen's,' which were kindly given by their designers.

It will be found on trial that 72 M. is approximately equal to the mean value of S and L{2} in successful yachts.

_The New French Rule_

On November 5, 1892, it was announced in the 'Field' that the Union des Yachts Francais had decided to adopt a hull-and sail-area rating, it being considered by the 'active element in French yacht racing'

that 'the type ... produced by the French length and girth rule is inferior to the type produced by the British and American rules ...

British yachts having defeated those of France, although handicapped by the French rule of rating.' The conclusion was scarcely a logical sequence from the premisses. It should have been that French racing yachts were not the correct evolution of the French rule of rating.

But we are now concerned with the new French rule (proposed by M.

G.o.dinet) in which sail is an important factor.

+---------------+-------+-------+--------+--------+--------+-------+ | Name of yacht | L | S | [V]S | M | XI. | XII. | +---------------+-------+-------+--------+--------+--------+-------+ | Genesta | 81.0 | 7,643| 101.40 | 91.27 | 94.21 | 87.39 | | Volunteer | 85.9 | 10,270| 87.43 | 105.42 | 100.24 | 93.30 | +---------------+-------+-------+--------+--------+--------+-------+ | Chiquita | 45.5 | 2,636| 51.36 | 31.32 | 53.20 | 49.35 | | Ghost | 46.5 | 2,577| 50.77 | 34.60 | 48.10 | 47.38 | | Minerva | 40.0 | 2,700| 52.00 | 29.73 | 50.39 | 46.00 | +---------------+-------+-------+--------+--------+--------+-------+ | Dis | 36.0 | 1,658| 40.71 | 22.37 | 36.23 | 36.00 | | Decima | 35.67| 1,679| 40.94 | 22.17 | 37.23 | 36.71 | | Doreen | 38.05| 1,572| 39.62 | 21.67 | 38.34 | 38.23 | +---------------+-------+-------+--------+--------+--------+-------+ | Oread | 28.2 | 1,063| 32.60 | 13.33 | 31.25 | 29.82 | | Quinque | 33.0 | 900| 30.00 | 13.33 | 30.93 | 32.02 | | Valentine | 29.8 | 996| 31.56 | 14.47 | 28.50 | 29.08 | | Bedouin | 30.0 | 1,000| 31.62 | 14.96 | 28.00 | 28.92 | +---------------+-------+-------+--------+--------+--------+-------+ | Madcap | 21.0 | 714| 26.72 | 9.97 | 20.89 | 20.97 | | Lady Nan | 23.0 | 653| 25.55 | 8.63 | 24.16 | 23.63 | | Dolphin | 25.7 | 581| 24.10 | 8.27 | 25.07 | 25.41 | +---------------+-------+-------+--------+--------+--------+-------+

In its simplest form, it is:--

English R = (4L - G) G[V]S 520 (XIII.)

G. being the greatest girth from top of deck planking port, round keel to ditto starboard, plus extreme beam. Each of the three factors L. G.

[V]S. being linear (metric measure) the result is given in cubic form, and is converted into English rating by the divisor selected, and the Y.R.A. time scale has been adopted by the Union des Yachts Francais.

The editor of the 'Field' considers that 'the rule is calculated to produce a poor kind of vessel for match sailing or anything else'; but it is hazardous to prophesy the evolution of any rule, more especially one which taxes L., B., D., bilge, and S. No doubt the tax on D. is doubtful policy, and it seems very unnecessary when we consider the small depth of water in many French harbours, which is the most efficient check on D. it is possible to conceive for large yachts, and in the small cla.s.ses D. gives grip and power to windward, and seaworthiness.

A careful a.n.a.lysis of the rule by the writer leads him to believe that the conclusion arrived at by the editor of the 'Field' is correct. It certainly appears that the rule has a sail-curve nearly as steep as the New York rule, which has been abandoned because it encouraged such large sail-plans. For this reason, therefore, if for no other, the new French rule seems to be inferior to the Y.R.A. and the Seawanhaka rules. A good letter on the subject of girth, by one of our leading designers, was published in the 'Yachtsman,' September 8, 1892.