No doubt the difficulty in the way of successfully making any experi ments with beam in the direction indicated is the Thames rule of measure ment adopted by the Y.R.A. The penalty put upon beam, and the absence of any restriction upon depth or ballasting, have left, for the purposes of competitive sailing, little opportunity for the naval architect to make extended experiments based on the results of recent investigations of the laws of resistance. His ingenuity, consequently, is almost wholly directed to the question of stability as dependent upon depth of ballasting, and yachts are necessarily of one stereotyped form, as the results of the investigations referred to are not, so far as sailing vessels are concerned, so conclusive as to lead one to suppose that the certain penalty which is imposed upon beam in the tonnage rule for competitive sailing would be balanced by an accession of speed and other essential qualities for match sailing. This condition has been very seriously deprecated ; but it is some satisfaction to know that the Thames rule has encouraged a type of vessels that, for sea-going qualities, cannot probably be surpassed. The practical operation of the rule has been to produce a type of vessel which, although, for any given displacement, incapable of developing the highest speed under favourable circumstances for such, is for general accommodation and comfort, and good behaviour in a sea, excellent ; and no other rule yet proposed has promised to develop such sterling qualities. As a means of comparing the speed or other qualities of yachts for competitive sailing, the Thames rule is approximately a correct one, as all the yachts sailing under it are of one type; but it is contended that the rule, by virtue of the penalty it places on beam, is not just in its operation upon yachts when the ratio of beam to length greatly varies. There is some truth in this ; but, whilst realising the unjustness of the penalty placed upon beam, we must not lose sight of the dangers which would surround its removal.
Beyond these considerations the Thames rule of measurement is generally recommended, as an appropriate means of valuing yachts for competitive sailing, on the assumption that it gives results roughly proportional to sail-carrying power. Disregarding for the present that in the rule breadth is subtracted from length, the Thames rule is Length x Breadth x Half-breadth. The divisor 94 is a constant, and does not alter the relative value of the products obtained under the rule. The rule can be otherwise expressed, thus : L x ), ors x or the relative value under the rule would be maintained if the formula were simply L x This brings us directly to the argument that the Thames rule gives a rough approximation to the sail-carrying power of a yacht, inasmuch as the sail moment of yachts is assumed to be proportional to the square of their breadth multiplied by their length, or L x The sail moment is the area of sail multiplied by the height the centre of effort of the sails is above the centre of lateral resistance; thus we should have a constant proportion from a" te.ight C'E'.
A constant proportion might be obtainable from the foregoing equation if breadth and depth of yachts were proportional through all sizes ; but, as a matter of fact, the proportions of length, breadth, and depth vary a great deal; it is therefore not surprising to find that the sail moment is not uniformly proportional to L x Thus, for the Sappho, 377 tons, we find the sail moment is 4.6
times the product of L x ; for the Kriemhilda, 106 tons, the sail moment is 8 times the product L x for the Freda, 5 tons, the sail moment is 11 times the product L x It is thus quite clear that if an attempt were made to canvas yachts proportionally to the product L x an unsatisfac tory sail plan might very possibly result. It has already been pointed out that the depth of yachts varies nearly as the cube root of their beam ; and their sail spread, if length, breadth, and depth were proportional, would vary nearly as L x hence it may be inferred that the sail spread will be approximately proportional to L or L x It will be gathered from the foregoing that the Thames rule is not so strictly exact in estimating the pretensions of yachts for competitive sailing as some times thought ; but this in practice is of little consequence so long as the yachts sailing under the rule are of one type.
The Y.R.A. rule fails because it takes no cognisance of changes made in the proportional quantities of beam and depth to length; this is of small consequence so long as the ratio of beam to length remains constant, but when that ratio is increased too great a tax becomes placed upon beam; and when the ratio is decreased the tax upon beam is too small. The intention of the Thames rule to class yachts for competitive sailing according to their sail spreads, or, in other words, according to their ability to carry sail, is no doubt a correct one, and we have ascertained how far a rule based on L x 4,/ would give results approaching the sail spread found in existing yachts. The rule it was found required modification, as it gave too much sail spread for comparatively small yachts; but with the I power of the beam modified to power of the beam, or 4y almost the exact sail spread of existing yachts was found, thus : x (L x 6). The constant 6 is merely introduced to bring the proportional sail spread, or " power," up to the exact spread, and does not alter the relative proportion of sail as between yacht and yacht.
The speed performances of yachts will be found to vary very nearly as the power of their sail spreads, and it will be thus easy to make the power for sail spread become the basis for a time allowance. In the table which follows the Sail r d, 1 =( * ) will be found given for a number of yachts. The divisor 1.25 has merely been introduced in order to reduce the value of sail spread' by a regular proportion, so that the time scale of the Y.R.A. might be conveniently used. The Y.R.A. time scale for fifty miles, and applied to each yacht's rating 1.25 on a supposed course of twenty-five miles ; in an adjoining column the actual time for Y.R.A. tons for a twenty-five miles course is given.