From Cadwallader Colden
Draft: New-York Historical Society
There is no Question but in the case you mention of a ships being taken up in a Southern latitude and let down in one some degrees more northerly 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 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 60 miles at the Œquator what will it be at 1 second on either side of the Œquator? 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 ships 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 these 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 the going and return will be = o.
The shorter Voyages to Europe without doubt are chiefly owing to the more frequent westerly winds but this does not account for the reason why in going to Europe a ship is generally a head of the reckoning or you meet with the land sooner than by the computation of the ships way if it be well kept, whereas in coming to America the reckoning is generally a head 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 advances daily about twelve degrees eastward and therefor 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 the river you meet the flood sooner than you do the ebb in going up the river 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 other things being alike, I’l u[nder]take to support it against any objection. There are some mistakes that I would be so far from being ashamed of them after I knew them to be such that I would be vain of them because none but those of a lively and quick and pierceing Imagination can fall into them. A Blockhead is uncapable of making such mistakes. There is even a pleasure in telling it after the mistake is discover’d and the person to whom it is told values the ingenuity which occasion’d 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 which please and flatter the Imagination most.
Suppose the difference between the lands end and the coast of America to be 72 degr. 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 lands end and therefor a ship will meet with one whole tide of flood against her there which would be an ebb in her favour on the coast of America and supposing her voyage perform’d in 30 days, every day equally approaching to America, she would every day have that tide lessen’d 1/30 of the time as she approaches. I once had thoughts to calculate an Equation to rectify a ships easting and westing but upon reflecting that a general equation cannot serve for every ship but must be different for every ship according to the several molds by which the ship is built and her being loaded or in ballast, I believe it will be of little use for according to the different molds of a ship and her being deep or light the tides have greater or less force on her way. The heavy dull ships must make much larger allowences than the best saylors and accordingly we generally find these heavy saylers most out in their reckoning.
5. Colden wrote this draft reply on the back of BF’s letter to him (see above, p. 67). Punctuation, omitted in the draft, has been supplied.