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IN the Velocities of two equal and like Ships; which Velocities, I say, are the square Roots of the Powers which either drive or draw them; as, for ex∣ample, Such two Ships having sails near double
to each other, or as 49 to 25, the Velocity will be as 5, the square Root of 25 unto 7, the like Root of 49. Again, if the sails be near triple, or as 49 to 16, there the Velocity shall be as 7 (the Root of 49) to 4 (the Root of 16.) So as a quadruple Sail is re∣quisite to double swiftness, and noncuple to treble; that is, The sails must be in du∣plicate proportion to the swiftness of the Ship; or this, in subduplicate to that.
Again, let there be two Ships of Equal sails, but of unlike or unequal sharp∣ness, suppose the head of one extremely obtuse or quite flat, and the head of the other to be an Isosceles Triangle added thereunto; I say, the swiftness of these Bodies shall be as the Roots of the Perpendicular of that Triangle to the Root of half the Base, or half breadth of the same. Se∣condly, Or if the same Tri∣angular head be cyphered
away into an Angle from bottom to top; then, as the Root of the same Per∣pendicular is to the Root of the Depth or Thick∣ness, so are the Velocities. Thirdly, If the said head be cyphered both wayes together, then the Pro∣portion of Velocities shall be as half of one of the above mentioned Propor∣tions added to the other whole Proportion: Ex. gr. Suppose the Perpendicu∣lar of the triangle-head
be 36, the half breadth 9, and the whole depth be 4; then the one Proportion shall be as 6, the Root of 36, to 3, the Root of 9: The half of which Proportion is as 6 to 6; and the other Proportion is as 6, the Root of 36, to 2, the Root of 4. Now add the Pro∣portions of 6 to 6, to that of 6 to 2, the sum will be, as 36 to 12, or as 3 to 1.
Fifthly, Suppose two Pa∣ralellepipedons of unequal heads or resistances, Ex. gr.
as 8 to 5, or 64 to 40: And suppose the Sail on the big∣ger, to that on the lesser, to be as 9 to 4, or 72 to 32; then the Velocity of the bigger shall be to the Velo∣city of the lesser, as the Root of 45 is to the Root of 32. For if the Resistan∣ces be as 64 to 40; then, if the sail of the bigger to that of the less were pro∣portionable to the Resi∣stances, the sail of the less should be 45, whereas we suppose it but 32. Where∣fore
the Velocity shall be as the Root of 45, which is almost 7, to the Root of 32, which is about 5½, that is, as about 14 to 11.
Memorandum, That wet∣ting of Sails (by lessening the intersperst apertures between the threds of the Sail-cloth) doth make the Sail, as it were, bigger; which biggerness may be known and measured by the increase of the Ships velocity upon such wet∣ting. For, if the Ship should
move one tenth part quick∣er after wetting than be∣fore, we may conclude the Sails are swollen to the equivalent of about ⅕ part bigger; for 100 (whose Root is 10) exceeds 81, whose Root is 9, by about ⅕ of 100.
By these ways the diffe∣rent Velocities, arising from the different Trim of the same Ship, may be al∣so computed, the best Trim being that which makes least resistance, caeteris pa∣ribus.
Now, having said thus much of the Effects of Sharpness and Sails, (the two principal causes of Velocity in shipping, and unto which all others may be referred;) I shall add, That the want of these two Advantages are the chief cause, why short, bluff, un∣dermasted Vessels sail chea∣per than others.
For suppose two Ships▪ of equal burthens, but of unlike dimensions, the main Beam of the one be∣ing
scarse ⅓ of the Keels length, and in the other, a full ⅕th; I say first, that the Hull of the latter shall cost ⅓ part more than that of the former, and the advantage as to sailing shall be scarce ⅙ part. Again, suppose, the sharper could carry ½ as much sail more as the bluf∣fer, whereof the advantage in sailing would be ⅙ part more, in all ⅓. Now, where the Sails are as 2 to 3, the Masts and Yards must be as 4 to 9 in substance;
and in value much more: And where the Masts and Yards are as 4 to 9 in weight and bulk, the Cord∣age and Rigging must be answerable: And where the Masts, Yards, Sails, and Rigging are great, the Wind-taught of the Ship will correspond, and will require proportionable Ca∣bles; and the weight of the Anchor must follow the size of the Cable, and the number of hands must be proportionable to all the
premisses: So as the one Ship will cost at least double as much as the o∣ther, and will sail at double charge of Wages and Vi∣ctuals, Ware and Tare, &c. Now if no trading Ship be (one time with another) above 1/10 of her whole reign under sail, or 6 days in 60, suppose the sharper and larger-sail'd Ship sail in 4 dayes what the other performs in 6; the diffe∣rence will be but 2 dayes in 60, or 1/30 part of the Wa∣ges,
and Victuals, and o∣ther charges; whereas the charges is supposed to be more than double. I say, this consideration is of great weight in Vessels of burden, especially such as carry gross and cheap bul∣ky Commodities, neither liable to damage or perish∣ing: Of which goods 7 parts of 10 of all Sea∣carriage do consist. But on the other hand, where safety against Enemies, speedy dispatch upon im∣portant
occasions, or pre∣occupation of a Market are in the case, there sharpness and great Sails may be ad∣mitted to the greatest pro∣portions practicable.
Having thus digressed, I mind you that we said, Velocities are the Roots of Resistances and Extent of Sails, &c. It may be well askt, How we know the same, since that very few Seamen or Shipwrights, ei∣ther in their writing or dis∣courses seem to understand
or own this important Po∣sition. To which I answer, that I have by many Ob∣servations, Calculations, and Comparisons, found the same to be praeter propter true, although there be ma∣ny circumstances which in∣termingle themselves in this Experiment, so as to disturb and confound it: As namely, The ill placing of Masts, The ill cutting and standing of Sails, The ill Trim of the Vessel, with the Cleanness or Foulness
of the same; The Sails more or less worn or wet; as also taught or slack Rig∣ging, &c. Wherefore not onely to avoid these last mentioned Intricacies, but also to make these Positions Examinable by every one that desires it; I say, that the different Velocity of Bodies (of several sharp∣nesses, and as drawn or dri∣ven by different Powers of knocks or falling weights,) have been by my self and others much experimented
in large Canales, or Troughs of water, fitted with a con∣venient Apparatus for that purpose, and by no man more, nor more judi∣ciously, than by the Right Honorable the Lord Brounc∣ker, President of this So∣ciety. For I do not think it hard to conceive, that Weights and Sails are pow∣ers of like Effect, and redu∣cible to the same Principle; so as if a Body have moved in double velocity, when drawn by a quadruple
weight; and in triple, when by a noncuple weight; I doubt not but the same will hold in Sails, or other impellent Powers of the same proportions.
And for the further clear∣ing or easier trying hereof, I offer two small Machina∣ments heretofore made in this Society: The one, to measure the Velocity of the Wind, and the other its Power or Equivalency to Weight; whereby it did and will appear, when the
wind is of double velocity, it will stir a quadruple weight; and the like in o∣ther cases according to the proportions of Roots and Squares above mentioned. The same may also be seen even in any good Turnspit-Jack, where a quadruple weight makes double Velo∣city (at the same distances of Time from the begin∣ning of the Motion) both in the time of the Weights descent, as also in the Revo∣lutions of the Fly, and each
intermediate Wheel. Now perhaps the reason of these Phaenomena may be here expected; to which I an∣swer, that the many parallel Instances above and here∣after mentioned, do, like concurrent witnesses, prove the premisses, at least as to any practical use. And as for giving other reasons (which I take to be Ex∣plaining this Subject from the very first Principles of Atomical Matter, and Moti∣on) I leave it to discourse,
as too long for this Exer∣cise.