TO CADWALLADER COLDEN.

Conjecture as to the Cause why Ships in crossing the Atlantic have longer Passages in sailing westward than in sailing eastward.

SIR,

[Date uncertain.]

I received yours, with others enclosed for Mr. Bartram and Mr. Armit, to which I suppose the enclosed The persons who brought yours said he would call for answers, but did not; or, if he did, I did not see him.

are answers.

I understand Parker has begun upon your piece. A long sitting of our Assembly has hitherto hindered me from beginning the Miscellany. I shall write to Dr. Gronovius as you desire.

I wish I had mathematics enough to satisfy myself, whether the much shorter voyages made by ships bound hence to England, than by those from England hither, are not in some degree owing to the diurnal motion of the earth; and if so, in what degree. It is a notion that has lately entered my mind; I know not if ever any other's. Ships in a calm at the equator move with the sea fifteen miles per minute; at our Cape suppose twelve miles per minute; in the British Channel suppose

will not be quickly forgotten where he was once known; in whom native taste and talent made up so fully for the deficiencies of early education, that he was the intimate friend and favorite companion of the few literary men of his period; and in whose manners and conversation, frankness and urbanity were so happily blended, that, wherever he went, he softened hostility, conciliated good-will, and turned accidental acquaintance into personal and warm friendship." Several admirable letters from him to his son are printed in Professor Mc Vickar's Memoir; in which are also contained many particulars respecting his intercourse with Franklin. EDITOR.

A printer in New York. - EDITOR.

ten miles per minute. Here is a difference of two miles' velocity per minute between Cape Henlopen and the Lizard. No small matter in so weighty a body as a laden ship, swimming in a fluid. How is this velocity lost in the voyage thither, if not by the resistance of the water? And if so, then the water, which resisted in part, must have given way in part to the ship, from time to time, as she proceeded continually out of parallels of latitude where the earth's motion or rotation was quicker, into others where it was slower. And thus, as her velocity tends eastward with the earth's motion, she perhaps makes her easting sooner. Suppose a vessel lying still in a calm at our Cape could be taken up, and the same instant set down in an equal calm in the English Channel; would not the difference of velocity between her and the sea she was placed in appear plainly by a violent motion of the ship through the water eastward?

I have not time to explain myself farther, the post waiting; but I believe I have said enough for you to comprehend my meaning. If the reasons hinted at should incline you to think there is any thing in this notion, I should be glad of an answer to this question, if it be capable of a precise answer, viz.

Suppose a ship sails in a northeast line from latitude 39 to latitude 52, in thirty days, how long will she be returning on the same line, winds, currents, &c. being equal? Just so much as the eastern motion of the earth helps her easting, I suppose it will hinder her westing. Perhaps the weight and dimensions or shape of the vessel should be taken into consideration, as the water resists bodies of different shapes differently.

I must beg you to excuse the incorrectness of this scrawl, as I have not time to transcribe. I am, Sir, Your most humble servant, B. FRANKLIN.

FROM CADWALLADER COLDEN TO B. FRANKLIN.

Answer to the foregoing Letter respecting the Sailing of Ships across the Atlantic.

SIR,

[Date uncertain.]

There is no question but in the case you mention of a ship's being taken up in a southern latitude, and set down in one some degrees more northerly, at the same moment, she would have a degree of motion eastward; but, that it would shorten a voyage from America to Europe, I cannot think; because, as the alteration is made by insensibly small steps, it can only be so much as an alteration of the velocity in the least conceivable part of a degree of latitude is greater than the resistance of the water, which in all cases remains the same, and equally resists the smallest alteration of the velocity, as the greatest.

Suppose, for example, in the alteration of one second of latitude, how much greater will the velocity be in the southward than northward? If it be sixty miles at the equator, what will it be at one second on either side of the equator? The difference is the force which the ship can acquire from the diurnal rotation of the earth in this second. Now it may be asked, whether this difference will be sufficient to overcome the resistance of the water in any degree whatsoever; that is, whether it be not infinitely small in respect to the resistance of the body of water, which resists the motion of a ship; and if so, it can neither add to, nor diminish, the ship's way in the time she alters her latitude one second; and, if this be the case, it cannot either forward or stop her way in a greater change of latitude, because it is done by a continual addition of seconds,

or rather of less than thirds, or of any imaginable quantity; so that, according to my way of computation, in answer to your question, the difference of time in going and return will be = 0.

The shorter voyages to Europe, without doubt, are chiefly owing to the more frequent westerly winds; but this does not account for the fact, that in going to Europe a ship is generally ahead of the reckoning, or you meet with the land sooner than by the computation of the ship's way, if it be well kept; whereas, in coming to America, the reckoning is generally ahead of the ship. The true reason, I think, is from the tides. The high-water every day is nearly three quarters of an hour more easterly on the globe, than the day before; or, following the course of the moon, advancing daily about twelve degrees eastward. And therefore they every day in sailing westerly meet with the contrary current of the water sooner than they do in sailing easterly; as, in a river, in going down you meet the flood sooner than you do the ebb in going up, where the flood and ebb are nearly equal. For the difference of the force and length of the ebb more than the flood in rivers, from the force of the accumulated fresh water, cannot take place at sea.

If you think proper to give this, in your Miscellany, as the reason of the shorter voyages from America to Europe than from Europe to America, I will undertake to support it against any objection. There are some mistakes that I would be so far from being ashamed of, after I knew them to be such, that I would be vain of them, because none but those of a lively, quick, and piercing imagination can fall into them. A blockhead is incapable of making such mistakes. There is even pleasure in telling it after the mistake is discovered, and the person to whom it is told values the ingenuity

which occasioned the mistake, and, on reflection, is conscious to himself, that he would have valued himself for that very thought. There is a use likewise in mentioning these mistakes to others, to guard them against those conceptions, that please and flatter the imagination most.

Suppose the difference between the Land's End and the coast of America to be seventy-two degrees of longitude, (I choose this number to avoid fractions.) Then the same high-water on the coast of America will happen six hours later at the Land's End, and therefore a ship will meet with one tide flood against her, which would be an ebb in her favor on the coast of America; and, supposing her voyage performed in thirty days, every day equally approaching to America, she would every day have that tide lessened one thirtieth of the time, as she approaches. Some have had thoughts of calculating an equation to rectify a ship's easting and westing; but, upon reflecting that a general equation cannot serve for every ship, but must be different according to the several moulds by which ships are built, and their being loaded, or in ballast, I believe it will be of little use; for, according to the different moulds of a ship, and her being deep or light, tides have greater or less force on her way. The heavy, dull ships must make much larger allowances than the best sailers, and accordingly we generally find these heavy sailers most out of their reckoning.

I am, &c.

CADWALLADER COLDEN.