DEAR SIR, -- My last letter to you was of the 13th of August last. As you seem willing to accept of the crumbs of science on which we are subsisting here, it is with pleasure I continue to hand them on to you, in proportion as they are dealt out. Herschel's volcano in the moon you have doubtless heard of, and placed among the other vagaries of a head, which seems not organised for sound induction. The wildness of the theories hitherto proposed by him, on his own discoveries, seems to authorise us to consider his merit as that of a good optician only. You know also, that Doctor Ingenhouse had discovered, as he supposed, from experiment, that vegetation might be promoted by occasioning streams of the electrical fluid to pass through a plant, and that other physicians had received and confirmed this theory. He now, however, retracts it, and finds by more decisive experiments, that the electrical fluid can neither forward nor retard vegetation. Uncorrected still of the rage of drawing general conclusions from partial and equivocal observations, the hazards the opinion that light promotes vegetation. I have heretofore supposed from observation, that light affects the color of living bodies, whether vegetable or animal; but that either the one or the other receives nutriment from that fluid, must be permitted to be doubted of, till better confirmed by observation. It is always better to have no ideas, than false ones; to believe nothing, than tobelieve what is wrong. In my mind, theories are more easily demolished than rebuilt.

An Abbe here, has shaken, if not destroyed, the theory of de Dominis, Descartes and Newton, for explaining the phenomenon of the rainbow. According to that theory, you know, a cone of rays issuingfrom the sun, and falling on a cloud in the opposite part of the heavens, is reflected back in the form of a smaller cone, the apex of which is the eye of the observer: so that the eye of the observer must be in the axis of both cones, and equally distant from every part of the bow. But he observes, that he has repeatedly seen bows, the one end of which has been very near to him, and the other at a very great distance. I have often seen the same thing myself. I recollect well to have seen the end of a rainbow between myself and a house, or between myself and a bank, not twenty yards distant; and this repeatedly. But I never saw, what he says he has seen, different rainbows at the same time, intersecting each other. I never saw coexistent bows, which were not concentric also. Again, according to the theory, if the sun is in the horizon, the horizon intercepts the lower half of the bow, if above the horizon, that intercepts more than the half, in proportion. So that generally, thebow is less than a semicircle, and never more. He says he has seen it more than a semicircle. I have often seen the leg of the bow below my level. My situation at Monticello admits this, because there is a mountain there in the opposite direction of the afternoon's sun, the valley between which and Monticello, is five hundred feet deep. I have seen a leg of a rainbow plunge down on the river running through the valley. But I do not recollect to have remarked at any time, that the bow was more than half a circle. It appears to me, that these facts demolish the Newtonian hypothesis, but they do not support that erected in its stead by the Abbe. He supposes a cloud between the sun and observer, and that through some opening in that cloud, the rays pass, and form an iris on the opposite part of the heavens, just as a ray passing through a hole in the shutter of a darkened room, and falling on a prism there, forms the prismatic colors on the opposite wall. According to this, we might see bows of more than the half circle, as often as of less. A thousand other objections occur to this hypothesis, which need not be suggested to you. The result is, that we are wiser than we were, by having an error the less in our catalogue; but the blank occasioned by it, must remain for some happier hypothesist to fill up.

The dispute about the conversion and reconversion of water and air, is still stoutly kept up. The contradictory experiments of chemists, leave us at liberty to conclude what we please. My conclusion is, that art has not yet invented sufficient aids, to enable such subtle bodies to make a well defined impression on organs as blunt as ours: that it is laudable to encourage investigation, but to hold back conclusion. Speaking one day with Monsieur de Buffon, on the present ardor of chemical inquiry, he affected to consider chemistry but as cookery, and to place the toils of the laboratory on a footing with those of the kitchen. I think it, on the contrary, among the most useful of sciences, and big with future discoveries for the utility and safety of the human race. It is yet, indeed, a mere embryon. Its principles are contested; experiments seem contradictory; their subjects are so minute as to escape our senses; and their result too fallacious to satisfy the mind. It is probably an age too soon, to propose the establishment of a system. The attempt, therefore, of Lavoisier to reform the chemical nomenclature, is premature. One single experiment may destroy the whole filiation of his terms, and his string of sulphates, sulfites and sulfures, may have served no other end, than to have retarded the progress of the science, by a jargon, from the confusion of which, time will be requisite to extricate us. Accordingly, it is not likely to be admitted generally.

You are acquainted with the properties of the composition of nitre, salt of tartar and sulphur, called pulvis fulminans. Of this, the explosion is produced by heat alone. Monsieur Bertholet, by dissolving silver in the nitrous acid, precipitating it with lime water, and drying the precipitate on ammoniac, has discovered a powder which fulminates most powerfully, on coming into contact with any substance whatever. Once made, it cannot be touched. It cannot be put into a bottle, but must remain in the capsula, where dried. The property of the spathic acid, to corrode flinty substances, has been lately applied by a Mr. Puymaurin, to engrave on glass, as artists engrave on copper, with aquafortis. M. de la Place has discovered, that the secular acceleration and retardation of the moon's motion, is occasioned by the action of the sun, in proportion as his excentricity changes, or, in other words, as the orbit of the earth increases or diminishes. So that this irregularity is now perfectly calculable.

Having seen announced in a gazette, that some person had found in a library of Sicily, an Arabic translation of Livy, which was thought to be complete, I got the charge des affaires of Naples here, to write to Naples to inquire into the fact. He obtained in answer, that an Arabic translation was found, and that it would restore to us seventeen of the books lost, to wit, from the sixtieth to the seventy-seventh, inclusive: that it was in possession of an Abbe Vella, who, as soon as he shall have finished a work he has on hand, will give us an Italian, and perhaps a Latin translation of this Livy. There are persons, however, who doubt the truth of this discovery, founding their doubts on some personal cricumstances relating to the person who says he has this translation. I find, nevertheless, that the charge des affaires believes in the discovery, which makes me hope it may be true.

A countryman of ours, a Mr. Ledyard of Connecticut, set out from hence some time ago for St. Petersburg, to go thence to Kamtschatka, thence to cross over to the western coast of America , and penetrate through the continent, to the other side of it. He had got within a few days' journey of Kamtschatka, when he was arrested by order of the Empress of Russia, sent back, and turned adrift in Poland. He went to London; engaged under the auspices of a private society, formed there for pushing discoveries into Africa; passed b this place, which he left a few days ago for Marseilles, where he will embark for Alexandria and Grand Cairo; thence explore the Nile to its source; cross the head of the Niger, and descend that to its mouth. He promises me, if he escapes through his journey, he will go to Kentucky, and endeavor to penetrate westwardly to the South Sea.

The death of M. de Buffon you have heard long ago. I do not know whether we shall have any thing posthumous of his. As to political news, this country is making its way to a good constitution. The only danger is, they may press so fast as to produce an appeal to arms, which might have an unfavorable issue for them. As yet, the appeal is not made. Perhaps the war which seems to be spreading from nation to nation, may reach them: this would insure the calling of the States General, and this, as is supposed, the establishment of a constitution.