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with which a body, of a given figure and density, would attract a par ticle of matter, occupying any proposed situation in the second, the subject of investigation is the figure itself, which a mass of matter, wholly or partly fluid, would assume, by the joint effect, of the mutual attraction of its particles, and a centrifugal force arising from a rotatory motion about an axis. To render the second of these inquiries more exactly conformable to what actually takes place in nature, the influence of the attractions of the several bodies, that compose the planetary system, ought to be superadded to forces already mentioned.
It is the first of these two researches, of which we propose to treat at present; and we shall even confine our attention to homogeneous bodies, bounded by finite surfaces of the second order.
The theory of the attractions of spherical bodies is delivered by Sir Isaac Newton in the first book of the Principia. In the same place the illustrious author lays down a method for determining the attractions of round bodies (or such as are generated by the revolving of a curve about a right line which remains fixed) when the attracted point is situ ated in the common axis of the circular sections; and he employs this method to compute the attractive force of a spheroid of revolution on a point placed in the axis. Maclaurin was the first who determined the attractions of such a spheroid generally, for any point placed in the sur face, or within the solid. The method of investigation, invented by that excellent geometer, is synthetical, but original, simple, and elegant, and has always been admired by mathematicians. When the attracted point is placed without the solid, the difficulty of solving the problem is greatly increased and it was reserved for Le Gendre to complete the theory of attractions of spheroids of revolution, by extending to all points whether without or within the solid, what had before been investigated for the latter case only. La Place took a more enlarged view of the problem; he extended his researches to all elliptical spheroids, or such solids whose three principal sections are all ellipses; and he obtained conclusions with regard to them, similar to what Maclaurin and Le Gendre had before demonstrated of spheroids of revolution. In this more general view of the problem, the investigation is particularly difficult, when the attracted point is placed without the solid. The method of investigation, which La Place has employed for surmounting the diffic culties of this last case, although it is entitled to every praise for its ingenuity, and the mathematical skill which it displays, is certainly neither so simple nor so direct, as to leave no room for perfecting the theory of the attractions of ellipsoids in both these respects. It consists in shewing that the expressions for the attractions of an ellipsoid, on any external point, may be resolved into two factors; of which one is the mass of the ellipsoid, and the other involves only the excentricities of the solid and the co-ordinates of the attracted point; whence it follows that two ellipsoids, which have the same excentricities, and their principal sections in the game planes, will attract the same external point with forces proportional to the masses of the solids. This theorem includes the extreme case, when the surface of one of the solids passes through the attracted point: and by this means the attraction of an ellipsoid, upon a point placed without it, is made to depend upon the attraction which another ellipsoid having the same excentricities as the former, exerts upon a point placed ia the surface, Le Gendre has given a direct demonstration of the the
orem of La Place, by integrating the fluxional expressions of the attrac tive forces; a work of no small difficulty, and which is not accomplished without complicated calculations. In the Mecanique Celeste, the subject of attraction of ellipsoids is treated by La Place after the method first given by himself in the Memoirs of the Academy of Sciences, founded on the theory of series and partial fluxions.' pp. 345-347.
Mr. Ivory's method, which however he rather indicates than explains, has ingenuity to recommend it. But he has not pursued the investigation far enough to render it very fertile in useful or curious consequences. The two following theorems are all we can extract:
"If two ellipsoids of the same homogeneous matter have the same excentricities, and their principal sections in the same planes; the attractions, which one of the ellipsoids exerts upon a point in the surface of the other, perpendicularly to the planes of the principal sections, will be to the attractions which the second ellipsoid exerts upon the corresponding point in the surface of the first, perpendicularly to the same planes, in the direct proportion of the surfaces, or areas, of the principal sections to which the attractions are perpendicular." 22 9 p. 355.
"If a point be situated within a shell of homogeneous matter, bounded by two finite surfaces of the second order, which are similar and similarly placed; then the attraction of the matter of the shell upon the point, in any one direction, will be equal to, and destroy, the attraction of the same matter, in the opposite direction."'
If we had to compare this paper with Professor Playfair's, on an analogous subject, in the Transactions of the Edinburgh Royal Society, (see Ecl. Rev. Vol. V. p. 1045) we should say that Mr. Ivory's displayed a greater command of ingenious expedients, Mr. Playfair's more fondness for useful deductions; Mr. Ivory's betrays the love of parade so common among mathematicians of the day, Mr. Playfair's, that love of simplicity which ought always to characterize a man of science; the one seems written to be admired, the other, to be understood.
We may take this opportunity of observing, that we have recently detected a mistake in Professor Playfair's paper, which had escaped our notice when reviewing it. The Professor gives 153° for the vertical angle of an isosceles pyramid with a square base which shall attract a particle at its vertex with greatest force (Ecl. Rev. Vol. V. 1049). But, according to Mr. P.'s own investigation, this is erroneous; for adopting his notation, 48° 40′, and sin sin2 », whence sin ท sin ; which gives the semivertical angle 60° 4' very nearly, and not 76° 30', which Mr. Playfair makes it. The resulting vertical angle 120° 8' does not present so wide an anomaly when compared with 125° 32′ the vertical angle of the cone of greatest attraction, as Mr. Playfair's computation. That anomaly we observed with no small surprize; and we are glad to see it thus removed.
XXI. Observations on Albumen, and some other Animal Fluids; with Remarks on their Analysis by electro-chemical Decomposition. By Mr. William Brande, F. R. S. Communicated by the Society for the Improvement of Animal Chemistry. Read June 15, 1809.
Mr. Brande, having found that the usual modes of obtaining mucus did not separate the saline ingredients which it contained, and upon which the agents employed as tests of the presence of mucus have considerable action, was induced to employ the action of Galvanism for the purpose of separating them, and thus to obtain the mucus perfectly pure. Saliva was exposed with this view to the Galvanic current in a glass vessel, connected by filaments of moistened cotton with two other glass vessels containing pure water, the water in one cup being made positive, and in the other negative. In about ten minutes, a quantity of white matter was observed adhering to the cotton on the negative side of the circuit, while that on the positive side remained clean. This appearance being unexpected, the effect of electricity was tried upon the uncoagulated albumen of an eye; and a rapid coagulation was found to take place at the negative wire, when the conductors were brought within two inches of each other, a thin film only surrounding the positive wire. This unlooked for phænomenon being mentioned to Mr. Davy, he suggested the idea, that the fluidity of coagulated albumen might be owing to the presence of an alkali, the separation of which at the negative pole would occasion coagulation to take place. Experiments were made in pursuance of this idea, which appear fully to confirm it. Distilled water in which coagulated albumen had been boiled, afforded a copious coagulation when subjected to the Galvanic current, and the brown viscid fluid observed by Dr. Bostock to separate from white of egg, coagulated and cut into slices, was found by Mr. B. to consist principally of an alkaline solution of albumen. The coagulation of albumen by alcohol and acid certainly admits, as Mr. B. observes, of satisfactory explanation on the same principle. The alkali was found to be soda, and a small quantity of muriat of soda was also detected. Saliva, the mucus of the oyster, trachea, and some other varieties, afforded a copious coagulation of albumen on the application of Galvanism, when none could be detected by acids, heat, or alcohol, alkaline matter being always evolved at the negative wire, and an acid at the positive; but the proportion of alkali was always predominant, although no uncombined alkali was sensible to the usual re-agents. these results lead to new ideas relative to mucus, and even render its existence as a distinct fluid subject to considerable
doubt, Mr. B. asks whether mucus is a peculiar combination of muriat of soda and albumen, or if it may not be a compound of soda and albumen, in which the alkali is not separable by the usual modes of analysis, but which yields to the superior decomposing energy of electricity,-queries, which remain to be decided by future investigation.
Bile, milk, the liquor of the amnios, and pus, all yielded their albumen to electricity; but Mr. B. notices that a marked difference takes place in the effects of a high and low electrical power; that with the former the coagulation goes on rapidly at the negative, and very slowly at the positive pole; but that, with a very low power, the principal coagulation is at the positive wire, and an alkaline solution of the albumen surrounds the negative one.
XXII. Hints on the Subject of Animal Secretions. By Everard Home, Esq. F. R. Š. Communicated by the Society for the Improvement of Animal Chemistry. Read June 22, 1809. Mr. Home informs us that the reflections which led to the present inquiry arose, while preparing his lectures on the Hunterian museum. The recent discoveries of Mr. Davy suggested to him the probability, that animal secretion might depend upon electrical agency; and the actual existence of a Voltaic battery in the torpedo, and electrical eel, and the obvious fact that some circumstances in the structure and arrangement of the nerves do not appear to be at all necessary to the common purposes of sensation, gave considerable support to the conjecture. The experiments detailed in this paper were made by Mr. Brande, aided by the suggestions of Mr. Davy; and their object was, to ascertain if any changes, similar to those connected with secretion, could be produced in the blood by the action of electricity. In two experiments made upon blood, its coagulation was found to oppose an insuperable obstacle to the long continued action of electricity; and in the subsequent ones, therefore, serum was em ployed; the results were strikingly similar to those obtained by Mr. Brande in his experiments on mucus.
By these experiments it is ascertained, that a low negative power of electricity separates from the serum of the blood an alkaline solution of albumen; that a low positive power separates albumen with acid, and the salts of the blood. That with one degree of power, albumen is separated in a solid form, with a less degree it is separated in a fluid form.'
In the queries which close this communication, an opinion is expressed, that a weaker degree of electricity than can be kept up by art, may be capable of separating from the blood the different parts of which it is composed, and of forming them into new combinations; and that the structure of the
nerves may fit them to possess the power required, and as very low powers are not influenced by imperfect conductors, such as the animal fluids, their electricity will not be given out to the neighbouring parts. This conjecture_ receives strong confirmation from a fact noticed by Dr. Berzelius, professor of chemistry at Stockholm, in a work on animal secretion published in 1806, and which is given by Mr. H. in the form of a note, the work having been shewn to Mr. Home, by Mr. Davy, after this paper was put in the press. The subject is so curious and interesting, that we offer no apology for transcribing the following statement, translated from the work and inserted in the note.
Trace all the nerves leading to any secretory organ in a living animal, and divide them, being careful to injure the blood vessels, and the structure of the organ itself, as little as may be: notwithstanding the continued circulation of the blood, the organ itself will as little secrete its usual fluid, as the eye deprived of its nerve can see, or a muscle whose nerve has been divided can move. We may, therefore, easily conceive, that any trifling alteration in the nerves of a gland, may materially affect its secretion, the supply of blood being in every way perfect.' p. 385. XXIII. On the comparative Influence of Male and Female Parents on their Offspring. By Thomas Andrew Knight, Esq. F. R. S. In a Letter to the Right Hon. Sir Joseph Banks, Bart. K. B. P. R. S. Read June 22, 1809.
The facts with which we are presented in this paper have been deduced chiefly from numerous experiments on fruit trees, made with a view to the production of improved and permanent varieties, especially of the apple. The character of the female plant was in general most strongly impressed on the offspring, and Mr. Knight is led from attentive and judicious observation to extend the principle to the animal creation. He opposes, we think successfully, the opinions advanced by Mr. Cline in a communication made to the Board of Agriculture, and offers some suggestions which merit the attentive notice of those who are engaged in improving the breed of domestic animals.
XXIV. On the effect of westerly Winds in raising the Level
of the British Channel. In a Letter to the Right Hon. Sir Joseph Banks, Bart. K. B. F. R. S. By Joseph Rennel, Esq. F. R. S. Read June 22, 1809.
In a communication laid before the Royal Society many years ago, Major Rennel adverted to the effect of strong westerly winds in raising the level of the British channel, and the escape of the superincumbent waters through the straits of Dover into the lower level of the north sea;' and the recent loss of the Britannia East Indiaman, on the Goodwin sands, has led him to a more attentive consideration of the subject, VOL VI