to be a very scientifical work. I have not yet had time to
engage in it; but I find that the conclusions of his demonstrations are,
that every part of the catenary is in perfect equilibrium. It is a great
point, then, in a new experiment, to adopt the sole arch, where the
pressure will be equally borne by every point of it. If any one point is
pushed with accumulated pressure, it will introduce a danger, foreign to
the essential part of the plan. The difficulty you suggest, is, that the
rails being all in catenaries, the tubes must be of different lengths,
as these approach nearer or recede farther from each other, and
therefore you recur to the portions of concentric circles, which are
equidistant in all their parts. But I would rather propose, that you
make your middle rail an exact catenary, and the interior and exterior
rails parallels to that. It is true, they will not be exact catenaries,
but they will depart very little from it; much less than portions of
circles will. Nothing has been done here on the subject since you went
away. There is an Abbe D'Arnal at Nismes, who had obtained an exclusive
privilege for navigating the rivers of this country by the aid of the
steam-engine. This interests Mr. Rumsey, who had hoped the same thing.
D'Arnal's privilege was published in a paper of the 10th of November.
Probably, therefore, his application for it was previous to the delivery
of Mr. Rumsey's papers to the secretary of the Academy of Sciences,
which was in the latter part of the month of August. However, D'Arnal is
not a formidable competitor. He is not in circumstances to make any use
himself of his privilege, and he has so illy succeeded with a steam-mill
he erected at Nismes, that he is not likely to engage others to venture
in his projects. To say another word of the catenarian arch, without
caring about mathematical demonstrations, its nature proves it to be in
equilibrio in every point. It is the arch formed by a string fixed at
both ends, and swaying loose in all the intermediate points. Thus at
liberty, they must finally take that position, wherein every one will
be equally pressed; for if any one was more pressed than the neighboring
point, it would give way, from the flexibility of the matter of the
string.

*****

I am, with sentiments of sincere esteem and attachment, Dear Sir, your
friend and servant,

Th: Jefferson.

LETTER CLXXVII.--TO JOHN JAY, January 11, 1789

TO JOHN JAY.

Paris, J