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Method of using it.
Experiments made with it
To use it, a boat being anchored in the stream, the log is to be thrown into the water, and suffered to float away, till the whole of the green cord alone remains on the reel, which is stopped at this point by a catch. One person then looking at a seconds watch gives the signal, when the second hand begins its revolution, and instantly the other, who holds the reel, sets loose the catch; the log floats on, and the time it takes to run out the ten yards of line shows the velocity*.
To determine the absolute force of the current on the cube, slip the loop at the end of the cord off the knob on the reel, and hook it to the hole of the little dynamometer, and the number of degrees shown by the index will express the maximum of the action of the water on a surface of 16 square inches.
This action is not constantly the same, not only from the effect of the waves, but from the natural current, which appears not to be always regular. In fact we have observed in calm weather, without any apparent waves, that the force of impulse varied from one instant to another in the proportion of 6 to 8, or even more.
But the velocity has a great action, as will appear from a table of the experiments we made at Paris between the Pont des Arts and Pont-Royal, on the 20th of July, 1809. The weather was calm, and the Seine a little below its mean height, being at 14 met. [4 feet 11 in.] on the graduated scale of the Pont-Royal.
on the Seine. First situation, 10 yards from the side, opposite the wickets of
261 Force in hectog. 2 to 3: in oz. avoird. 7 to 10 26
The person who holds the reel in his right hand might dispense with an assistant, by holding in his left a stop watch, stopped at the end of the revolution of the seconds hand. He would only have to set loose the stop with the forefinger of the left hand, at the instant he disengaged the catch with the right, and stop the watch again the moment the line was run off the reel. C.
Third situation, 15 yards from the side, opposite the street
Though these data are not very ample, it is obvious,
1st, That the water at the sides of rivers has but little clusions. velocity: and
2dly, That the velocity of the middle of the stream increases in an extraordinary degree the impulsive force; since the action produced on the log by a velocity of 10 met, [32f. 9 in.] in 14 seconds was from 21 ounces to 31; while by a velocity of 28 seconds it was only from 34 oz. to 7,
ments of Mari
On comparing afterward our experiments with those of The experiMariotte, made about 1666 in the same place, we found a otte in the great deal of similarity in the results. By means of little 17th century. balls of wax, ballasted so as to swim level with the surface, he estimated the velocity of the Seine, at its mean height, to be 150 feet in a minute, or 30 inches in a second. But when we made our experiments the Seine was only 4 feet high, and at the time of Mariotte's it was 5 feet; a difference in height answering to the difference of velocity. And hence we may infer, that a century and half has made no change in the current of the river at this part.
The same experiments led us to compare the velocity of Velocity of the the Danube with that of the Seine, In the Journal de Danube.
Paris, of the 11th of July, 1809, is a note from Baron Pakali, who says, that the velocity of the Danube, at its mean height, at Ebersdorf, is 4 feet in a second; so that we may consider it twice as rapid as the Seine at Paris.
Explanation of the Plate.
Pl. II, fig. 3. a, a cube of cork, 4 inches square, bound Explanation of round with packthread to strengthen it.
b, a plate of lead, fastened to the bottom, to ballast the cube, so as to float level with the surface.
cc, knots from which proceeds a silk cord, forming an acute angle at the point d.
'e, hook in the loop of the red cord about two yards long, tied to a green cord of ten yards, rolled up on the reel ƒ, to measure the velocity.
g, a flat piece of hard wood forming a base to the reel, in the centre of which is a small rod of polished steel, on which, as an axis, the reel turns freely,
h, tail of the catch, on which the thumb rests, to let the reel move at the signal given.
Fig. 4. i, a small dynamometer, with an index, to mark on the arch the maximum of the impulse of the current.
Fig. 5. k, the log, floating in the stream.
7, the observer in a boat, holding in his hand the dynamometer, to estimate the force of the current, after having measured the velocity.
Trench Insti tute.
Stability of the planetary sys
Rotation of the Earth.
AN analysis of the proceedings of the mathematical and physical class, during the year 1809, by Mr. Delambre, perp. sec., has just reached us.
The question of the stability of the planetary system has been still farther pursued by Mr. Lagrange, who has examined it in a more general point of view, extending it to a system of bodies acting on each other in any manner whats ever. He also purposes to investigate the relation of the planet round their centre of gravity, considering the deviation of their figure from a sphere, and the attraction the other planets exert on each of their particles.
Mr. Pois on, as a continuation of his inquiry on the variations of the elements of the planets, has composed a pas per on the rotation of the Earth. As Mr. Lagrange has noticed the extreme difficulty of this problem, we cannot
be surprised to find, that formula have occurred to Mr. Poisson, the absolute summing up of which appeared to him impracticable. His object was to examine the influence of the term of the second order in the expression of the velocity of the Earth's rotation. These terms arise from expanding into a series the function expressing the sum of the products of the mass of each body attracting by that of the body attracted, divided by the mutual distance of these bodies. As it is impossible to calculate all these terms, the object is to bring forward only those that merit attention. Mr. P. accordingly examines in the first place, whether even those that depend on the Sun might not be neglected: and he finds, that they are always in fact very small.
As to the figure of the Earth, Mr. P. supposes, that, without the action of the Sun and Moon, the Earth would turn precisely round, one of its principal axes. This is justified by the physical state of things, since we do not perceive in the altitudes of the pole, observed at different places, any of the oscillations, that would result from a different hypothesis, and the duration of which would be about one year, By similar considerations he expunges the terms relative to the other two principal axes, which can never become sensible but on hypotheses of little probability, which would give to the rotary motion of the Earth periods of less than two years, which have never been observed. He afterwards shows, that the equations to be summed up in the successive approximations preserve the same form; whence he concludes, that the axis of rotation will always coincide nearly with the shortest of the Earth's principal axes, and that the poles will always answer to the same points on the surface,
But, though the latitudes may not vary so as to deserve any attention, or to be perceptible to astronomers, is the rotary motion so uniform, as has been supposed? If its inequalities be of a very short period, and not very perceptible, they may escape our notice, and yet in a certain degree affect all our observations, and the consequences deduced from them. Suppose, for example, that the pole, instead of the 360° of its circle, passes only through $50°; and that the
not be irregularities in it!
latitude of Paris observed at a given period should appear, in consequence of an oscillation then at its maximum, too great by 1", the errour being proportional to the cosine of 0; the year following at the same time it would be proportional only to the cosine of 350°, and so on, till at the end of 9 years it would be nothing. At the end of 18 years however it would be 1" in the opposite direction, whence a difference of 2′′ might appear in the altitude of the pole; but so small an inequaArguments for lity in so long a period would not be noticed. To show the probability of this we might say, that Bradley, from a number of observations of the polestar in 1753, found the lati tude of Greenwich 51° 28′ 41-5", though from a still greater number he had before found it only 51° 28′ 38′′. We may suppose therefore an oscillation of 2" with a short period; or a greater oscillation, of which only a part has been observed. The latitude of the observatory at Paris too was found to he 48° 50′ 10′′ at one time, and 48° 50′ 14′′ at other times, by Lacaille, Cagnoli, Mechain, and myself. These. differences might be ascribed to oscillations of at least 2',. and a period of about 15 years, so that there would have been 24 periods between Lacaille and Cagnoli, and one only between Cagnoli and us. But I must add, that, having examined at large the observations of Bradley for. five successive years, I have perceived no trace of these oscillations; that if there were one of 2", it might frequently be confounded with the errours of observation; and that the difference of 3.5" between the two results of Bradley might arise from his having changed his quadrant in the interval, and particularly from the errour of collimation, which for his old quadrant was 1·74", and for the other 8", not being known with sufficient precision, of which there are many instances. Thus we may take it for granted for the present with Mr. P. and astronomers in general, that there is no oscillation, or a very minute one; but of this we have no demonstration, and it is a point of remains to be sufficient importance, to be worth ascertaining with an inproved. strument, in which no errour in the collimation is to be. apprehended. For this it would be sufficient to observe for some years with Borda's circle the meridian altitudes of the polestar above and below the pole during.
But probably there are none.