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stop (says he) at an even number of terms, the sum is o; if at an odd number, the sum is 1 : but, as there is no more reason for taking an even than an odd number, consequently the sum is neither o nor 1, but a mean number, or _.” In this kind of reasoning, Leibnitz was nearly followed by Daniel Bernouilli, in volume xvi. of the new Commentaries of Petersburgh. He endeavoured to shew, by the doctrine of chances, that the sums of periodic series are equal to the sum of the different partial suns which can be formed by adding successive terms together, divided by the number of those partial sums; thus
z=1—*+(0.x2)+*3+*++ (0.x5)-*? &c. Hence, putting *=1, the series is 1-1 +(0.1)+ı &c.; and the three partial sums are 1, 0, 0; hence Sum = , and so on for other series.
The above method, however, rather justifies the rule of Berncuilli in those cases in which it has been accused of being false, than exemplifies his mode of reasoning.
MM. La Grange and Bossut shew that the result, given by the method for finding the sum of a recurring series, verifies the principle of Bernouilli ; and they conclude with commending the author of the memoir for having directed the attention of mathematicians to the paradoxes which periodical series present, and for having argued against the application of metaphysical reasonings to questions which, belonging solely to pure analysis, can be decided only by the first principles and fundamental rules of calculation.
Report on a Memoir of M. Bict, on the Integrals of Equations of finite Differences.--This report proceeds from MM. La Place and Prony, who not only commend the memoir, but ap. laud its young author for his previous investigations, and for his zeal and application in the pursuit of abstract science. In the course of the report, are noted the errors and paradoxes into which the late M. Charles (of the Academy of Sciences) was beirayed when treating of a memoir (year 1788) on the plurality of the integrals of which equations of finite differences are susceptible..
Mechanics.-- Report on a new Telegraph, the Invention of MM. Breguet and Betancourt. By MM. La Grange, La Place, Borda, Prony, Coulomb, Charles, and Delambre. - As we coulel 10t, without a long description, hope to convey an adequate notion of the construction and advantages of this new mstrument, we must refrain from the attempt. The very karned men, who have made their report on it, state it to be
essentially different from all other telegraphs, and much more commodious.
Physics.--Observations on the Tides at Teneriffc.-We learn from this paper that M. Baussard, who resided nine months at Teneriffe, has found the establishment of the port * at Sainte Croix at mid-day; in other respects, the tides are subject to RW, great irregularities. -, Chemistry.—Report on a Memoir by M. Cossigny, containing a Project for extracting real Indig, from Wond.-M. Cossigny is of opinion that indigo may be obtained with advantage from woad, and from the blue scabious, by treating them like the indigo plant in America: but MM. Guyton and Fourcroy, while they acknowlege the great importance of the object, remark that the author's memoir does not present, either in principle or practice, any suflicient reason for asserting that the proposed undertaking will probably be atiended with success.
Extract from a Report on a Metallic Alloy sent by the Commissione of Finances of the Legislative Body. - The Commission, wishing i to be informesi, ist, of the composition of this alloy, and, 2dly, whether it could be easily imitated, sent an ingot to the Institute; and the examination of it was perfornied by MM. Bayen, Pelletier, l'auquelin, Chaussier, and Lelièvre.--- According to the assayer of the Mint, this ingot was estimated at 5 dwts. 21 grs.; the external colour of it was white, but its fracture and filings had a tinge of yellow : the specific gravity was 9,4776. By cuppellation and analysis, it was found to consist
Silver - - 50
100 A similar ingot was afterward synthetically formed. Extract from a Report on Colours for painting on Porcelain, invented hy M. Dihl.—The art of painting on porcelain is very analogous to that of painting in enamel; since, in both, the colours are applied on a white vitrified ground, which forms the light parts, and serves to modify the shades. In these arts, only fossil or mineral colours can be used, and they are employed either in the state of oxide or that of glass. The oxides unite well with oils, and form an uniform mass, which flows with
* Etablissement du port ;-for an explanation of this term, sce La Place's Exposition du Systeme du Monck, p. 78.
freedom from the point of the pencil: but the vitrified colours, however well they may be ground, will not unite properly with oil; they therefore separate, and fall from the pencil like sand ringled with water ; which is a most serious inconvenience in these arts. The coloured glasses have nevertheless one very great advantage, viz. that, when they have been employed and fused, they nearly assume the colour which they possessed before pulverization ; while the oxides are liable to many variations in tiut and shade, in consequence of vitrification. The painter is therefore obliged to work according to an imaginary pallet, and to expose certain colours many times to the fire; applying successively those which are powerful or feeble, or bright or obscure ; for it is by long experience alone that he can be capable of estimating the changes produced on colours by the action of fire. It must therefore be regarded as a great advantage, if colours for porcelain can be so prepared as to retain, under every circumstance, an uniformity of tint and shade : which desideratum appears to have been accomplished
by M. Dihl, whose invention has consequently been approved . by the National Institute.
Dattribution of Prizes. M. Bouvard, and M. Burg, assistant Astronomer in the Observatory of the University at Vienna equally share the prize due to the solution of the mathematical question ; which prize the Institute, on account of the great merit of the solution, thought it proper to double.- No answers having been sent to the following questions, the Institute again proposes them: It is required to shew what earthy substances and processes are proper for making an earthern ware, that shall resist sudden transitions from cold to heat, and shall be sufficiently cheap to be purchased by all members of the community. To investigate, by exact experiments, what is the influence of the atmospherical air, of light, of water, and of earth, in the process of vege:tion.'
An Account of the Life and Works of M. Daubenton. By M. Cuvier. We are here presented with a distinct picture of the venerable coadjutor of the great Buffon. The intimacy between these celebrated - men appears to have been particularly fortunate, since each seemed to possess quali. ties that were exactly adapted to moderate, by their opposi. tion, those of the other:
• Buffon, (says the Eulogist,) of a vigorous form, an imposing air, an imperious disposition, prone to passion, and eager for immediate gratification in his mental pursuits as well as in his pleasures, appeared desirous of divining truth and not of observing it. His imagination was continually interposing between him and nature ; and his elo.
quence seemed to be exerted against his own reason, before it bac been employed in captivating that of others.
• Daubenton, of a feeble temperament, a mild countenance, and possessing a moderation which was more the gift of nature than the fruit of wisdom, employed in all his researches the most scrupulous circumspection. He neither believed nor affirmed any thing which he had not seen and touched : so far was he from being desirous of persuading by other means than by evidence itself, that he studiously banished from his conversation and writings every image or expression that had a tendency to mislead : he never suffered by a delay: he recommenced the same work until he had succeeded to his wish; and, by a method too rarely found perhaps among nten who are occupied in real science, all the resources of his mind appeared to unite to anni. hilace his imagination. Buffon believed that he had only taken a hard-working assistant, who would level the inequalities of his route: but he soon found that he had engaged a faithful guide, who pointed out to him the straggling roads and precipices. A hundred times did the half sarcastic smile, which escaped from his doubting friend, recall him from his first thoughts: a hundred times did one of those words, which that friend knew so well where to interpose, stop him in his precipitate march ; and the wisdom of the onc, thus uniting with the strength of the other, at length gave to the history of quadrapeds (the only common performance of the two authors) that excellence which makes it, if not the best of those performances which compose the history of Buffon, at least the most exempt from errors, and most likely to remain for the longest time a classic among naturalists.
• It is not, then, less by what he did for him, than by what he prevented him from doing, that Daubenton was useful to Buffon.'. ,
Some parts in this contrasted description are ably executed : yet we must confess that it is Buffon who gives it interest and dignity.
The biographer then relates the advancement of Daubenton to the place of keeper of the cabinet of natural history, by the interest of Buffon ; his exercicns in that employment; the separation of the two friends; their subsequent reconciliation ; the real improvements which Daubenton made in natural history, &c.
The labours of Daubenton were not calculated solely to gratify the curiosity of the speculative naturalist, but were frequently undertaken with a view to practical utility. Agriculture was indebted to him for its progress; and he endeavoured to introduce into France a breed of sheep with finer wool, by means of sheep brought from Spain.
• He acquired on this account a species of popular reputation, which, in a time of peril, proved of great benefit to him. In the second year of the Revolution, when the most ignorant portion of the people decided on the fate of the most liberal and instructed, the octogenary Daubenton was obliged, in order to preserve a place which he had
dignified by his talents and his virtues, to demand of a section that called itself the Sans Culottes, a paper of which the extraordinary name was a Certificate of Civism. A Professor, a member of the Academy, would have procured such a paper with difficulty; and therefore some sensible persons, who mixed with the furious in the hope of restrainting them, presented him under the title of Shepherd; and it was the Shepherd Daubenton who obtained the certificate necessary for the Di. rector of the National Museum of Natural History. This paper is in existence : but it is a document perhaps less useful in writing the life of Daubenton, than in composing the history of that disastrous cpoch.'
Many interesting particulars are given concerning Daubenton in this eulogy. The naturalist seems to have been a simple-minded, unambitious man; indefatigable in his researches, cautious in his inferences, and sure in his conclusions : more eager to advance science than to acquire fame; and even quietly allowing that another should engross applause, part of which was justly due to him not only for his unremitting assiduity, but for the exertion' of talents which were rare in themselves, and beneficial to society in their effects.
Account of the Life and Works of A1. Lemonnier. By M. Cuvier.-The person here commemorated is Lemonnier the botanist and physician, brother of the famous astronomer. He was introduced to the notice of Louis 15th by the Marshall Duke of Noailles, and the manner of the introduction is here thus shrewdly related :
• Louis 15th, whom his favourite frequently entertained with those pursuits to which he was partial, was desirous of partaking of them by himself: he saw the Dukc's plantations; he heard with in. terest the history and the properties of each vegetable ; and, astonished at finding that instructive pleasures were worth at least as much as those which only fatigue, he wished also to have a botanical garden, and asked for the person' wbo had so well arranged that of the Duke. The latter, eagerly seizing this occasion of serving his friend, ran to seek him, and, without preparation, conducted him to the presence of the monarch. The young man, surprized and intimidated, turned pale, and felt himself indisposed. Kings themselves are not insensible to the little vanity of appearing to inspire awe; and from that moment Louis 15th gave to Lemonnier marks of regard which were soon converted into real favour, when he knew him more intimately.' ,
Were not the quotation too long, we should extract the biographer's explanation of the fact that men, when weary of the unmeaning ceremonies and pompous farces of the world, or wounded by the injustice and wrongs of society, find recrea; tion and comfort in an intimacy with plants, and prefer the study of botany to that of zoology. - i