But among the yachts the old {L - B × B × (1/2 B)}/94 prevailed, and gradually builders discovered that, by increasing draft and amount of ballast, beam could be pared down, and a boat of nominally the same tonnage made longer and to carry more sail than her predecessor. Lead ballast was slowly introduced, despite all sorts of adverse prophecies from old salts that it would strain the ship and would cause her to plunge so heavily as to go under; and presently, when some unknown genius first put lead outside, and from a timid hundredweight or two this increased to tons, the veterans gave the new type up altogether as past praying for, and left them to their well-merited fate. I have been unable to get any definite information as to the first application of outside ballasts, but in 1834 Messrs. Steele built the 'Wave' for Mr. John Cross Buchanan, and on this vessel a metal keel was fixed. There may, however, have been earlier instances of this in the South. But Providence was on the side of the heavy lead keels, and each year yachts got longer, and deeper, and narrower, and had more and more lead outside, until there was none left inside at all, while they more and more nearly approached Euclid's definition of a line as having length but no breadth. _A propos_ of these proportions, a good, and it may possibly be true, story is told of an enthusiastic cutter-man on the other side of the Atlantic, who, intensely prejudiced against the fine broad ships of America, asked a friend here to buy, and have sent across to him, a typical British 5-ton cutter, stipulating only that she should be fast, and at least as narrow as anything of her class. The little craft was safely brought across and put in the water in New York Bay, and after a trial sail the owner invited one or two friends to come off for a day's pleasuring in the new ship, with the object of showing the advantages of five feet of beam against ten. But, on coming alongside, the first to get out of the dinghy took hold of the runner, and taking a nice wide step, so as to get well into the centre of the boat, stepped clean into the water on the other side. But long before the advantage of substituting untaxed depth for the heavily taxed beam was discovered, and about 1850 Mr. Wanhill, of Poole, introduced the raking sternpost, thus getting, on a given length of keel, a much longer water-line. But even this device was used in moderation, 50° to 60° being the utmost rake given, with the sternpost showing at the water-line, and such vessels as our modern cutaway fives, tens, twenties, or forties, with the keel a fourth of their over-all length, were as yet unthought of, though the direct inducement to build them was far stronger then than now. [Illustration: 'Cygnet' cutter, 35 tons. Built by Wanhill, of Poole, in 1846.] [Illustration: Midship section.]