A36. This I know has been pretended to. But it is easy to make geometrical conclusions come out as we would have them, when the data they are founded on, are so uncertain that we may chuse them as suits our purpose.

A37. This circumstance tends gradually to lessen the variety of the seasons.

A38. This was Tobias Mayer, who was born at Marbach in the principality of Wurtemberg, in the year 1723: he rendered himself celebrated in astronomy, by having calculated the best tables of the moon, and by an excellent catalogue of stars. He died at Gottingen in 1762, at the age of thirty-nine years. W. B.

A39. It may happen that any of the planets, about the time they become stationary, shall describe a loop about some small fixed star, in such manner as might be easily mistaken for the star making part of a revolution about the planet. This I suspected to have been the case with the above observation of Montaigne. But the times set down do not confirm the suspicion.

A40. See page 320 of the foregoing Memoirs.

A41. See page 154 of the foregoing Memoirs.

A42. Mr. T. T. proceeding on a different supposition, has computed twenty-seven billions of years necessary for that purpose.

A43. “The main-wheel, which is fixed on the barrel on which the cat-gut runs.” Mr. Voight.

A44. “A perpetual rochet is a spring lying between the main-wheel, and a plate which is so high in diameter as to be nearly of a height with the bottom of the main-wheel teeth, and is cut with fine teeth all round, in the shape of a fine saw. A click on an axis is fixed between the two frame-plates, with a weak spring that forces this click into the fine saw-teeth, which keeps the plate from moving backwards when the clock is winding up. This fine rochet-wheel is fixed on the barrel-arbour or axis, the same as the main-wheel. The barrel-rochet comes close against the plate of the fine rocket, which has a click screwed on the front, corresponding with the barrel-rochet, and a spring above that rochet’s click, which forces that click into the barrel-rochet’s teeth: it is this that makes the clattering noise, which is heard when a clock is winding up: There is a middling strong spring placed between two arms of the cross of the main-wheel, bent like the space of the two arms between which it acts; and this spring is as broad as the thickness of the cross-arms. One end of that spring is fastened to the inside of the fine rochet-plate: the other end lies on the other cross-arm, and acts on that like a gun-lock mainspring on the cock-tumbler. When the clock or time is set a going, and the maintaining power or weight of the fusee or barrel, this power will raise that spring so far as to resist the maintaining power, and becomes stationary as long as the time-piece is going; and when it is wound up, this spring in the main-wheel cross will expand itself, press on the cross-arm, and force that wheel forward, with nearly the same power as the maintaining power would give: the click for the fine-teethed rochet falls into one of those fine teeth, and keeps that rochet steady, without having the least motion, as long as the winding-up of the clock continues; and by this means a time-piece can lose no time in winding up: hence it is called a perpetual rochet; which requires the most accurate workmanship, in its construction.” Mr. Voight.

A45. This description is drawn up from two separate accounts of the instrument, with which the Writer of these Memoirs was obligingly furnished, in writing, by Robert Patterson and the late David Rittenhouse Waters, Esquires, of Philadelphia. Mr. Patterson mentions, that he recollects his having seen the Hygrometer so described, in Dr. Rittenhouse’s Observatory, about thirty years ago.

A46. The second volume of the Transactions of the American Philosophical Society contains a letter, written on the 13th of November, 1780, by Dr. Benjamin Franklin, then in France, to Mr. Nairne, of London: but it was not communicated to the Society, until January, 1786.

In that letter, Dr. Franklin suggests to Mr. Nairne (an eminent optician, and mathematical instrument maker,) the idea of an Hygrometer made of wood; in preference to metalline instruments, for the purpose of discovering “the different degrees of humidity in the air of different countries;”—an idea which occurred to the Doctor, in consequence of a casual circumstance, mentioned in his letter.

Dr. Franklin supposed “a quick sensibility of the instrument, to be rather a disadvantage” to it; “since,” says he, “to draw the desired conclusions from it, a constant and frequent observation day and night, in each country—when the design is, to discover the different degrees of humidity in the air of different countries—will be necessary for a year or years, and the mean of each different set of observations is to be found and determined.”—“For these reasons,” continues the Doctor, “I apprehend that a substance which, though capable of being distended by moisture and contracted by dryness, is so slow in receiving and parting with its humidity that the frequent changes in the atmosphere affect it sensibly, and which therefore should, gradually, take nearly the medium of all those changes and preserve it constantly, would be the most proper substance, of which to make an Hygrometer:”—and he believes good mahogany wood to be that substance. In the concluding part of this letter, Dr. Franklin says to his correspondent: “I would beg leave to recommend to you—that you would take a number of pieces of the closest and finest grained mahogany that you can meet with; plane them to the thinness of about a line, and the width of about two inches across the grain, and fix each of the pieces in some instrument that you can contrive, which will permit them to contract and dilate, and will shew, in sensible degrees, by a moveable hand upon a marked scale, the otherwise less sensible quantities of such contraction and dilatation.”

Hence it appears, that Franklin and Rittenhouse conceived an idea of the same kind, nearly at the same time: but that the latter carried his invention into practice, three or four years before the theory of the former, founded on similar principles, had been announced to the American public, or, as it is believed, was made known to any other person than Mr. Nairne. W. B.

A47. In a table (in the 2d vol. of Lalande’s Astronomie,) entitled, “Passages de Mercure sur le Soleil, calculés pour trois sièclessiècles par les nouvelles Tables,” the transit of that planet, above referred to, is thus set down by Lalande, at Paris; viz.

A48. The calculations are here wanting, in Dr. Smith’s MSS.

A49. Here Dr. Rittenhouse’s ends: The remainder of the versification is continued by another hand.

A50. He never professed the business of making watches: the first mechanical occupation he assumed was that of a clock maker, an employment he pursued many years, in the earlier part of his life. W. B.

A51. Having, in the preceding note, adverted to the unimportant error in the text, wherein our Philosopher is stated to have pursued the employment of a watch-maker, instead of that of a clock-maker; it becomes necessary to notice, in this place, another mistake, though likewise an inconsiderable one, into which the liberal and candid writer of the article, above quoted, has been led. Dr. Rittenhouse’s Observatory, at Norriton—the place of his original residence and the seat of his farm-house—was erected prior to the celebrated “Astronomical Observations” made by him, in the year 1769; which were those relating to the Transit of Venus over the Sun’s disk, on the 3d of June in that year. W. B.

A52. The time above referred to, is supposed to have been in the year 1790 or 1791; though perhaps it may have been somewhat earlier. Dr. Sproat died in the autumn of 1793. W. B.

A53. An uncle of Copernicus was Bishop of Warmia, (in Ermeland, a little province of Poland,) and gave him a canonry in his cathedral of Frawenberg, a city in ducal Prussia, situated on the Frische Haff, at the mouth of the Vistula: it was there he began to devote himself to astronomy, at the age of twenty-eight years. His great work, De Revolutionibus Orbium Cœlestium, was completed about the year 1530: but his apprehensions of meeting with persecution from the bigotted ignorance of the age, in consequence of the system he therein promulgated, deterred him from publishing it until thirteen years after that period; and it is supposed that the agitation of his mind, occasioned by its appearance in the world, produced the sudden effusion of blood, which terminated his life on the 24th day of May, in the year 1543. W. B.