« AnteriorContinuar »
the world. He pays us very high compliments, admits that we have overcome France, and affirms that Napoleon's antipathy against England was the cause of his destruction.
"" For me,” he exclaims, “I own no conqueror but England, Let all the rest abate their pride; they were but the victor's tools. Those who are paid to fight, have no right to seat themselves in the car of victory. .....England, thy battle has raged through a hundred years thine is the triuinph! Such is the will of heaven. But, at least, thou canst honour heroism, thou wilt not withhold from France the tribute of thy admiration.”
It has been usually taken for granted, that although Napoleon had preferences, he had no attachments. This M. Lavallee contradicts. He calls Eugene Beauharnois, the cherished child;' Lasnes the friend of the heart;' and mentions several others towards whom he felt a strong affection. In connexion with the account of the death of the latter, a story is told of an early prophecy, made in a kind of frolic, by Bonaparte. During the brilliant campaigns of Italy, the generals were almost all young, and much addicted to the pleasures, not always innocent, of youth. One day, they were assembled at the general's lodging, and in a mood of gay and lightsome fancy, he proposed to tell all their fortunes. He took their hands in turn, and promised all the wild and extravagant things imaginable respecting their future destinies. When he came to Lasnes, he looked at his hand, and passed on without speaking; Lasnes. astonished inquired the reason, and the more Bonaparte evaded his questions, the more he urged them. At last, the reluctant oracle, pointing out a certain line, pronounced that it was his fate to fall by a cannon shot. Bonaparte did not hazard a great deal by this prophecy, for Lasnes was always thrusting himself in the way of danger, and was covered with scars. He had been wounded more than thirty times before the fatal ball destroyed him. More anecdotes might be quoted, but we have already extracted the most interesting, and we shall therefore conclude our remarks on these interesting volumes.
Art. IV.-A new Explanation of the Ebbing and Flowing of
the Sea, upon the Principles of Gravitation. By S. Bennett.
New York. 1816. 8vo. pp. 79, MR.
R. BENNETT is, we think, a man of considerable inge...
nuity, and of a great deal of confidence. He says he has meditated on the subject of tides for more than ten years; and now finds himself compelled to lay the result before the world. We admire this patience exceedingly; and as we think the author has escaped just ten times as much ridicule as he would have incurred by publishing the crude results of his
earlier meditations, we advise him—the next time he undertakes to subvert the doctrines of the incomparable sir Isaac Newton' (p. 7. introd.)—to meditate silently, at least twenty years upon the subject, before he runs the venture of meditating aloud. We know how uncivil it is to quote a person against himself; but really Mr. Bennett has hit our own ideas so much better than we could express them ourselves, that we must be permitted to transcribe his phraseology word for word. • Every now and then (says he, Introd. p. 7.) we hear of something under the name of Newton refuted; but when we come to examine what it is, we find nothing but some thoughtless trash, from persons altogether destitute of mathematical information. We do not think this is all applicable to the author before us. There is a plausibility and persuasiveness about him, which is not often found in those persons who publish false theories on mathematics;-a department of human knowledge in which error is, in general, so easily distinguished from truth. His reasoning is peculiarly fitted to take the great majority of readers; who cannot be supposed to comprehend the operations of the various laws and forces which unite in the production of some planetary phenomena,
-and who always lend a willing ear to such explanations as consist of a few simple steps and coincide with what they see every day upon the surface of their own planet. His theory depends, as our readers will soon see, upon what he has given the name of lateral gravitation; a species of force which was first suggested to him by observing how much easier a bale of goods may be pulled into the loft than be hoisted to the gable of a store. Without regarding at all the other forces which must operate upon any body of water on the surface of our globe, he has carried this simple principle into the phenomena of the heavens; and what work he makes among the bodies there by means of his blocks and tackle we shall presently enable our readers to see. In the meantime we are going to show them about as curious a specimen of philosophical disquisition as perhaps they ever encountered. Mr. Bennett attacks a part of the Newtonian system after the following manner:
• I might here add for another reason, if it was necessary, that if there was an actual falling of the earth towards the moon, the further surface of the earth would be most of all attracted, or more correctly, would gravitate more in the direction of the moon than any other part of the earth; for it would gravitate in that line, at once towards the moon, and towards the earth, and its gravitation would amount to the sum of both. Now it would be very singular indeed, if those very particles so situate should lag behind; for to say that they would, would be to say that these very particles gra
vitating more than any other in that direction, that is, in the direction of the fall, yet turn sulky and will not come up so fast as others which are actuated by a less force; in a word, it would be to say, that the greater is not the greater; that a greater cause produces a less effect than a less cause, and so on. Again, once more (" and besides,' he ought to have added); supposing the earth was in a state of actual falling towards the moon, the centre of the earth would be influenced in that direction by the moon only, but the farther surface would be actuated in the same direction by the moon nearly as much as the centre, and by the whole body of the earth into the bargain; which, as has been shown, is 144,000 times greater than the other, and yet we are required to believe that those very particles will still not keep up.'-pp. 40-1-2.
Nobody has ever prétended that the theory of Newton could account for all the phenomena which it was meant to explain; and it has always seemed a very cogent objection to the system, that the least seas should have the greatest tides. During our examination of Mr. Bennett's Theory, we discovered a method of clearing up the subject, which, though it depends upon the application of obvious hydrostatical principles, is, we apprehend, a pretty satisfactory explication of the phenomenon. First, however, we must proceed to construct our diagram, and to disprove our author's hypothesis.
Let C A E represent the earth, D the moon, A B a column of water extending from the centre of the earth to the circumference, and B C a similar column at right angles to B A. Mr. Bennett's theory is founded on these two propositions:
I. That the attraction of the moon D will not cause the water to rise at A.
II. That the waters on the other side of C from the moon, as at N, will begin to move towards C by their lateral gravitation towards the moon D.
Now we grant that if the column of water B A were not connected with any other column running in a different direction, as BC, there could be no elevation of the particles at A by the attraction of the moon D; for the attraction of the moon, on the supposition that she is only one-fortieth of the earth's weight, and 59 semi-diameters * from its surface, would not, at A, be any
1 more than of
of the earth's attraction; 59 x 59
87 while it would be still less at any other part of the column between A and B;-a force which could not by any means counteract the attraction of the earth so much as to lift up the whole column of water, A B, and cause its prolongation at A.-This is the reasoning of our author; and it is unquestionably correct reasoning. But then, not satisfied with the whole truth, he goes on to conclude, that the tides cannot be raised at A, by the greater attraction of the moon for the particles at A, than for those at B:-a conclusion which can only be good upon the supposition, that the column of water A B has no connexion with any other column, running in a different direction, as B C. Let us suppose a communication, however, between A B and BC at the point B;-then, whatever be the magnitudes of the two columns A B and B C, they will balance each other, provided nothing acts upon them but their own gravitation to the centre of the earth; and the surfaces at A and C would, of course, remain for ever at rest. But if we suppose the moon to begin to act at D, the column A B will lose some of its gravity; the equilibrium between the two columns A B and B C will be destroyed; and the water must rise in the column A B, at the same time that it is depressed in the column B C, -until, by lengthening A B and shortening B C, the weights of the two columns become equal.-Again; the gravity of A B will not only be diminished, but that of B C will be increased. For if C M be drawn parallel to B D, the attractive force of the moon CD may
be resolved into the two forces C M and C B; and as C B is one-sixtieth of C M, the column C B will be increased in gravity by one-sixtieth of the moon's attraction at C;—a force which would alone depress the column C B about 200 feet.Nor does it matter in what direction the two columns A B and B C run,- provided they terminate in the points A and C:they may either meet at the centre B; or go straight from A to C; or go round in the curve A O C. The effect will be the same,
-an elevation of the waters at A and a correspondent depression at C; as will be abundantly evident to every person
* Our readers will perceive that on our diagram the moon is by no means 59 semi-diameters from the earth.
understanding the principles of hydrostatics. So much for the incomparable sir Isaac Newton. Now for the incomparable' Mr. Bennett.
He asserts, that, if there be water on the other side of C from the moon D, as at N and P, when the moon is in the horizon C, the waters at N and P will begin to run towards C, by their lateral or horizontal gravitation towards the moon. This proposition, we confess, appears, at first sight, very probable; for if there is nothing to hinder their motion but their natural inertia, the slightest force operating on the particles at N and P, in a horizontal direction, must produce some effect. Now that the moon does actually attract the particles at N and P, is as plain as eyes can make it;—and we should be obliged to grant, therefore, that by this attraction, the particles P and N would run towards C, and form a tide there if they met with the resistance of the land, were it not for a circumstance neglected by our author, which instead of permitting the particles at P and N to move towards C will, as we shall show, cause them to move in the very opposite direction.
Let C Z, N T, and P U, be arcs of concentric circles described round the common centre of gravity of the earth and the moon, passing through the earth; now it is evident, by inspection, that C B Z is the circle in which a particle at the centre of the earth moves, in going round the common centre of gravity; and consequently that there is a perfect balance between the centrifugal force of the particle at the centre B acquired by its motion round the common centre of gravity between the earth and the moon,-and the centripetal force of that particle caused by the attraction of the latter body. The same may be said of all the particles of matter touching the line C Z. As they are at the same distance from the centre round which the earth revolves every lunation; their centripetal and centrifugal forces are the same as those of the particle at B; and therefore a particle at C,-being operated upon by a centrifugal force precisely equal to the attraction of the moon, -is balanced in its situation at C.
But this is not the case as it respects the particles at N, S, and T; for, being farther from the moon, they have a less centripetal force; while, by their movement in a larger circle and with a greater velocity, they have a greater centrifugal force: on both of which accounts the particle N will recede from C, the particles S from B, and the particle T from Z.—The same may be said of the particles in the other circles; that at Preceding from that at N, the one at X from that at S, and that at U from the one at T. The greatest effect will be produced at R; because there the centripetal force is least, while the centri