1596. TO MADAME HELVÉTIUS

(B. N.)

À Southampton, 27 Juillet 1785 En Angleterre, pres l'Isle de Wight.

Notre Vaisseau arrivait ici nous nous embarquerons. Adieu, ma trés trés trés chere Amie, Souhaitez pour nous bon Voyage, & dites aux bons Abbés de prier pour nous, cela etant leur Metier. Je me trouve tres bien. Si j'arrive en Amerique vous aurez bientot de mes Nouvelles. Je vous aimerai toujours, penses quelquefois de moi, & ecrires quelquefois a

hier de Londres. Aujourdhui

Your learned writings on the navigation of the antients, which contain a great deal of curious information; and your

1 This letter was translated into French, and published at Paris in the year 1787, entitled, "Lettre de Monsieur Benjamin Franklin à Monsieur David Le Roy, Membre de Plusieurs Académies, &c." The following note is prefixed by the French editor. "Cette lettre a été lue à la Société Philosophique Américaine de Philadelphia, le 2 Décembre, 1785. Elle est imprimée dans les Mémoires de cette Société. On lit dans le titre, à M. Alphonse Le Roy. Comme cet Académicien ne se nomme pas Alphonse, nous y avons substitué l'un de ses noms de baptême. Il est de l'Académie des BellesLettres, de celle de Marine, de la Société des Antiquaires de Londres, de la Société Philosophique Américaine, &c." It is here printed from "Transactions of The American Philosophical Society," Vol. II (1786), p. 294. — ED.

very ingenious contrivances for improving the modern sails (voilure), of which I saw with great pleasure a successful trial on the river Seine, have induced me to submit to your consideration and judgment, some thoughts I have had on the latter subject.

Those mathematicians who have endeavoured to improve the swiftness of vessels by calculating to find the form of least resistance, seem to have considered a ship as a body moving through one fluid only, the water; and to have given little attention to the circumstance of her moving through another fluid, the air. It is true, that, when a vessel sails right before the wind, this circumstance is of no importance, because the wind goes with her; but, in every deviation from that course, the resistance of the air is something, and becomes greater in proportion as that deviation increases. I wave at present the consideration of those different degrees of resistance given by the air to that part of the hull which is above water, and confine myself to that given to the sails; for their motion through the air is resisted by the air, as the motion of the hull through the water is resisted by the water, though with less force as the air is a lighter fluid. And, to simplify the discussion as much as possible, I would state one situation only, to wit, that of the wind upon the beam, the ship's course being directly across the wind; and I would suppose the sail set in an angle of forty-five degrees with the keel, as in the following figure; wherein (Plate XII. Fig. 1,) A B represents the body of the vessel, C D the position of the sail, E E E the direction of the wind, M M the line of motion. In observing this figure it will appear, that so much of the body of the vessel as is immersed in the water must, to go forward, remove out of its way what water it meets with between the pricked lines

F F. And the sail, to go forward, must move out of its way all the air its whole dimension meets with between the pricked lines C G and D G. Thus both the fluids give resistance to the motion, each in proportion to the quantity of matter contained in the dimension to be removed. And though the air is vastly lighter than the water, and therefore more easily removed, yet, the dimension being much greater, its effect is very considerable.

It is true, that, in the case stated, the resistance given by the air between those lines to the motion of the sail is not apparent to the eye, because the greater force of the wind, which strikes it in the direction E E E, overpowers its effect, and keeps the sail full in the curve a, a, a, a, a. But suppose the wind to cease, and the vessel in a calm to be impelled with the same swiftness by oars, the sail would then appear filled in the contrary curve b, b, b, b, b, when prudent men would immediately perceive, that the air resisted its motion, and would order it to be taken in.

Is there any possible means of diminishing this resistance, while the same quantity of sail is exposed to the action of the wind, and therefore the same force obtained from it? I think there is, and that it may be done by dividing the sail into a number of parts, and placing those parts in a line one behind the other; thus instead of one sail extending from C to D, figure 2, if four sails, containing together the same quantity of canvass, were placed as in figure 3, each having one quarter of the dimensions of the great sail, and exposing a quarter of its surface to the wind, would give a quarter of the force; so that the whole force obtained from the wind would be the same, while the resistance from the air would be nearly reduced to the space between the pricked lines a b and c d, before the foremost sail.