It is true that the divergence of these radii recurs as a difficulty, in getting the rails on upon the bolts; but I thought this fully removed by the answer you first gave me, when I suggested that difficulty, to wit, that you should place the rails first, and drive the bolts through them, and not, as I had imagined, place the bolts first, and put the rails on them.  I must doubt whether what you now suggest will be as good as your first idea; to wit, to have every rail split into two pieces longitudinally, so that there shall be but the halves of the holes in each, and then to clamp the two halves together.  The solidity of this method cannot be equal to that of the solid rail, and it increases the suspicious parts of the whole machine, which, in a first experiment, ought to be rendered as few as possible.  But of all this the practical iron men are much better judges than we theorists.  You hesitate between the catenary and portion of a circle.  I have lately received from Italy a treatise on the equilibrium of arches, by the Abbe Mascheroni.  It appears 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.