Page images
PDF
EPUB

and two, upon corresponding points, taken on two sides of the plane of x, z, and of which the co-ordinates will be + x, y, z for the one, and + 1, −y + for the other.

582. It remains, then, to consider the components of the pressures, taken parallel to the co-ordinates; that is, parallel to the straight line which joins the centres Cc, of the two spheres; and, indeed, from the symmetrical disposition of electricity round the straight line, it is evident that it cannot have any motion but in this single direction; and, consequently, these components alone must produce the tendency of the two spheres towards each other.

583. To obtain, in the simplest manner, the sum of all these components, it must be remarked,

[ocr errors]
[ocr errors]

that their general expression K - E2 contains no variable but r; for cos. u, which enters into the value of E' is equal to -; it hence follows

that their intensities are equal in the points relatively to which the co-ordinate x is the same, and which are consequently situated upon one small circle, parallel to the plane of the co-ordinates y, z. Besides, as all these points are equally distant from the line of the centres, it is clear that the total result of the equal forces which are applied to them will be in the direction of this line; consequently, this will also be the direction of the general result of all the efforts of this kind exerted upon the whole surface of the sphere A.

[merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

587. Since we suppose the two spheres very di tant from each other, compared with the magnitude of their radii, will be a very small frac tion; hence we may develope this expression fo E-E into a converging series of the ascending powers of, this will be effected by the binomisi

theorem; and taking only the first power of which, in the case we are considering, will cortain an infinitely great proportion of the total result, compared with the other powers, it wi

become

584. To obtain now, easily, the sum of all these forces, parallel to the line of the centres, which is here that of the co-ordinates r, let us begin by joining together the values of r which are equal and contrary; for the thicknesses E, of the electric stratum on the two hemispheres of A being almost equal, from the supposition that the two spheres are very distant, the pressures corresponding to opposite values + and -x, must be almost equal also; and, as the compo- E-E nents which they give parallel to the co-ordinates r are in a contrary direction, their sum must be reduced to a very small quantity. To introduce this circumstance, call E, what E becomes when we change into ; then the expressions of the corresponding components parallel to the co-ordinates r will be, On the side of the

[merged small][ocr errors]

Tending to move +KE the air in the direction A B Tending to move E2 the air in the direction BA

negative co-ordinates-x, 585. We preserve the superficial element w always of the same value, as it is exactly alike in the two cases, on account of the symmetrical form of the sphere on the two sides of the plane of the co-ordinates y, z; adding these two components to each other, with their actual sign, their sum will express the element of the total resulting force, which tends to carry the air in the direction A B. This, then, will be

K(E2— E3), or, what is the same thing,

K≈w (E+ E) (E—E).

[blocks in formation]

or by reduction E-E=
This value of E-E must now be multiplied by
E+E, to form the factor E-E2 which enters
into the expression of the total resulting force;

2

but since E-E is already of the order it is
a2
evident that, in E+E we must confine our-
selves to the terms which are not divided by a,
this limitation reduces the value of E+E to 2 e,
and employing this to multiply E-E, there
results

[merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small]

It might be shown for this case, as well as for the other, that there cannot be any inequality of pressure but in the direction of the co-ordinates x; then comparing the points of the surface, which correspond to the two sides of the plane of the co-ordinates y, z, we shall find that the element of the resulting force of the pressures parallel to the co-ordinates r, is in general ex

Κτω

589. Each of these partial results is proportional to the superficial element w, and to the square of the cosine of the angle, which these elements form with the axis of the co-ordinates x. But, if we compare them together upon different spheres, this angle will always be expressed by the same values; for the equal values of u, however, the superficial element will vary in magnitude proportionally to the square of the radius of the sphere. Consequently, the sum of all the values of the factor o cos. u, extended to every sphere, will only vary from each other in the E' what E' becomes when we change + into ratio of the square 72; it may be represented, that is to say, cos. u into then by K'r2, K' being a constant and numerical co-efficient which may be found, and which, in reality, is found by the processes of the integral calculus. Supposing it known then, the total result of the pressures parallel to the co-ordi

[blocks in formation]

It will be directly proportional then to the quantities 4re, 4 of external electricity which they possess, and inversely proportional to the square of the distance of the two centres. When the quantities of electricity given to the two spheres are of the same nature, whether vitreous or resinous, the values of e and of e' must be considered as having the same sign. In that case the expression (1) is negative; that is to say, according to what has been previously admitted, that, in this case, the air which surrounds the sphere A, is more pressed in the direction BA, than in the direction A B. It will not then press equally the sphere A, as it did before it was electrified; it will press it less on the side which is most distant from the other sphere, since it is in that direction that the electric reaction is the strongest. Consequently, if the sphere A is at liberty to move, and deprived of its weight, or if its weight be sustained by a thread of suspension, it will put itself in motion from the side where the atmospheric pressure has become the weakest, that is to say, that it will recede from the other sphere B.

590. The contrary would happen, according to our formula, if the quantities e, e', of electricity introduced into the two spheres were of a different nature, for then it would be necessary in the calculation to give to them different signs. The formula (1), which represents the total result of the pressures exerted against the air parallel to the line of the centres, will then become positive; that is to say, according to what has been already agreed on, the external air will be more pressed in the direction A B, than in that of BA; the sphere A will move then in the direction in which the external pressure will have become the weakest, that is towards the sphere B, agreeably to observation.

591.We have hitherto only considered the effect of the pressures round the sphere A, but the same reasonings and calculations will apply to the other sphere; only we must then employ, instead of E and E, the expressions of the electric strata which correspond to them, and which

we have seen to be

[ocr errors][merged small][merged small][merged small][merged small]

pressed by (EE) in representing by

[ocr errors]

-cos. u', the angle u being here reckoned from the point a, situated on the side of A upon the line of the centres. By next considering the spheres as very distant, we shall obtain in the same manner the value of E'-E'. Approximating no farther than the first power of this will give E'-E'

[ocr errors]

-6er2
a2

E+E'

a

[ocr errors]

cos. u. We have then only to take

2e', and putting these values in the expressions of the partial resulting force, it will -12Kee'r cos. u become It may be dea2 monstrated as above, that the sum of the factors the radius of the sphere B, and may besides be cos. u will be proportional to the square of represented by K2; K' being the same numethe total resulting force then, the expression will rical co-efficient we have already employed. For finally become —12KK′ee′r2zd#2

a2

[ocr errors]

that is, exactly

the same which we have obtained for the other sphere, which ought to be the case, since in these sort of phenomena action and re-action are always equal. Here, as in the example immediately above, the positive sign of the expression will signify that the resulting force of the pressures exerted against the air round the sphere B, is directed towards the other sphere, and the negative sign will signify that this resulting force is directed the opposite way. The first case will take place when the electric charges e e' are of a contrary nature; in that case, the sphere B will advance from the side where the atmospheric pressure is weakest, that is towards A; the other case will happen when the electric charges e e' are of the same nature, then B will recede from A.

592. The common expression for the result of the pressures vanishes for both the spheres, when e or e' is nothing, that is, when one of them is in the natural state. This seems to indicate that they would then neither approach nor recede from each other, while, in reality, we know that in this case they always approach. This apparent contradiction is owing to the degree of approximation at which we stopped our development of the above expression. We have supposed our two spheres very distant from each other, compared with the radii of their surfaces; the result of this is, that whatever be the quantity 4re, 4πre of external electricity which we have introduced into each of them, it will distribute itself almost uniformly over the two hemispheres, anterior and posterior; so that the

difference of the pressures exerted against the air by these two hemispheres, which is the only cause of motion, will be very small; and it is to this degree of minuteness that we have confined our approximations in developing E2-E". 593. If, however, the one of the two spheres, B for example, is only electrified by the influence of the other, which we always suppose very distant, the development of its natural electricities will be still very feeble, and of the same order of minuteness with that to which we have confined our approximations; but this weak electricity still dividing itself between the two hemispheres of B, in a manner nearly equal, as in the example immediately above, the difference of pressures round the two hemispheres will become very minute in a still lower degree-will become a quantity of the second order of minuteness, and, consequently, cannot be found in our developments, such as we have limited them. To obtain it complete, we must not, in the calculation of E+E' confine ourselves to quantities, independent of, but take its whole value. We shall then have, first of all,

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small]

power of the distance of the centres of the two spheres, instead of the simple square which we had in the other approximation. It is obvious, that experiments of this kind, made with the electric balance, by charging only one of the balls, might produce an error as to the true law of the phenomena, if the theory did not throw light upon them; for one might be led to conclude from them, that the apparent attraction determined in this case is not reciprocally as the square of the distance of the centres of the two spheres, which nevertheless would be contrary to the truth: consequently, when it is meant to put this simple law of the square to the test, the balls must not be allowed to approach so near to each other, that the electricity developed by their reciprocal influence, may bear any sensible proportion to the quantities of external electricity introduced into them; and this is the reason that, in these experiments, it is always more certain to employ, instead of balls, small circular discs of gilt paper; for, on account of the thinness of these discs, the quantities of vitreous or resinous electricity developed at their surfaces, having scarcely any room to separate from each other, their actions on the exterior bodies must be always nearly alike, and cannot, therefore, alter the results any more than if their development had not taken place.

597. The theory, which we have thus explained in regard to spheres, applies equally well to bodies of any form whatever; but here the difficulty of the analysis prevents us from anticipating any thing but the general effects which the different pressures produce, without our being able to reduce them to numbers. Here it will suffice to have established the general mode of reasoning applicable to all the questions of this kind, and to have followed out the whole development for the single case, which analysis has been able as yet completely to surmount.We shall add, that before the theory had acquired its actual precision, it could not be clearly conceived how the attractions and repulsions, which in reality only take place between the electrical principles themselves, were communicated to the material particles of the electrified bodies; and philosophers were reduced to the necessity

with these values, the expression of the partial of denoting this effect by the vague word tension, resulting force

[ocr errors]

(EE), or K (E-E) cos. u 30 Ke2 ^

تی

becomes cos.u'(1-3 cos.2u). 595. It only remains to take the sum of it over all the extent of the surface of the sphere B; but, in this operation, the variable factor, o cos. u (1-3 cos. u), will give a result proportional to the square of the radius of the sphere B, and which we may consequently represent by K" r', K' being a constant numerical co-efficient different from K'; thus, the total resulting force

will at last be

[ocr errors]

ئی

596. This force, then, will be an order of minuteness, much inferior to that which we obtained at first, when e was not supposed to be nothing, since the radii there are divided by the fifth

which represented the electricity like a kind of spring placed between the bodies and tending to make them approach or recede. A few miscellaneous illustrations, including the latest and most important discoveries, must conclude our article.

NEW GALVANIC BATTERY FOR MEDICAL

PURPOSES.

598. The object of this battery is to increase the galvanic power, ad libitum, and to continue it for a great length of time, without any fresh excitation. These most desirable results are ef fected by a metallic and a semi-metallic substance, combined with another less oxidable metal, the surfaces of which are acted on by one or two mineral acids diluted with pure water. The power and duration obtained by these means are very great, though contrary to the hitherto acknowledged laws of galvanism, which require

two dissimilar metals and one interposed fluid to develope the galvanic influence. This apparatus is designed for philosophical experiments on animals, and for the use of an operator in full practice. It is not only capable of increased power, but, by a simple contrivance, it perpetuates its action to almost any length of time for a succession of operations; these advantages are obtained by the shape and position of the plates; for, instead of being square and stationary, as in the common battery, they are circular and made to revolve on an axis at the will of the operator. As only one segment of the circle is used at one time, several different operations may be effected in each revolution of the entire circle, without the trouble of wiping any part of the circle. A constant stream of galvanic fluid may thus be exhibited almost ad infinitum, and the unpleasant effluvia arising from the frequent addition of acid, as in the common mode, is prevented. The apparatus being concealed from view, in a handsome covered box, cannot give alarm to the most timid patient. The greatest facility is afforded in removing the oxide from the surfaces of the plates by a few revolutions round its axis, and the virtue of the acid solution in the cells remains in full strength for a very long time.

599. M. La Beaume's portable galvanic battery consists of a box containing four series of plates, and four divisions made with pieces of glass and baked wood, which are interposed to divide the box for the plates; the ends of each series are connected by a hole in the plates, so that a connecting wire is not required. There is also a space for a bottle of acid. The inside of the box cover contains the apparatus necessary for the galvanic operation. By a few simple directions the battery may be preserved in good order for some months, or even years. The cover, after the apparatus is taken out of it, is placed on the box, and, sliding into a groove, is fastened by a pin.

600. Another portable galvanic battery for suspended animation. This apparatus possesses a very great galvanic power in a small compass, and its action can be perpetuated for as long a time as may be necessary, which is accomplished by the combination of different metals. It consists of 300 or 400 plates in a box about three feet long, three inches deep, and three inches wide; the circular plates are about the size of half a crown, and when the apparatus is taken out, the box is filled with diluted nitric acid, and the row of stringed plates is placed horizontally on the two supports of the battery.

601. A third portable galvanic battery intended to be used in suspended animation from drowning, &c., is contained in a walking-stick, for the convenience of town or country practitioners, when no conveyance can be immediately obtained for a larger battery. This galvanic apparatus is contained in a hollow stick, with three divisions; the first division contains a bottle of acid, salt, and linen rag, covered by a metal cap affixed to the handle of the stick, and which is to be used as a cup to mix the acid with water. The second division is composed of two parts, one sliding on the other by means of a groove;

when opened, it forms a pair of galvanic batteries of 300 or 400 plates of combined metal, which are connected together by an arched wire. The third division, which is the smaller end of the stick, contains a small lancet, the conducting wires, &c., and is also held by the hand during the operation. This stick contains all that is necessary for the galvanic process except water, which can be obtained on the spot. The power of this battery is rendered equal to the following, by the combination of the plates, the strength of the acid, and the horizontal position of the plates, which prevents the circuit of communication being formed by the expressed moisture of the interposed cloths, which must result from a perpendicular position of the pensile pile, as invented by professor Aldini, and improved by Dr. de Sanctis.

602. The most portable battery consists of a series of plates of the form and size of a shilling or a sixpence; each pair being intersected by a piece of cloth, on the principle of professor Aldini; and this battery is more powerful than his, because the semi-metal is combined with one of the other metals. This battery consists of 200 or 300 plates, and may be conveyed with perfect ease in the pocket.

ELECTRICITY DEVELOPED IN CAPILLARY
ATTRACTION.

603. M. Becquere! is said to have demonstrated, that there is a sensible development of electricity during the ascent of liquids in capillary tubes. He first obtained this result by increasing the sensibility of Schweigger's galvanometer. He placed three of these instruments together, so that the magnetic needle of the middle one deviates from its ordinary direction, by the lateral effects produced upon each of its poles by the contrary poles of the two other needles. From this arrangement it follows, that, when an electric current passes into the apparatus, tending to bring the needle into the plane of the magnetic meridian, the middle needle will be as much less retarded in its process as the poles, opposite to its own, of the other two needles are more remote from it, consequently, the oscillations will have a wider extent than if there were only one galvanometer.

604. In order to observe the electricity of capillary action, M. Bacquerel could not employ glass, as it is not a conductor of electricity; but he employed sponge of platinum, aud small pieces of charcoal. Pure hydrochloric acid, much diluted with water, is poured out into the platinum dish, which communicates with one of the ends of the wire of the galvanometer; and into the dish is plunged sponge of platinum, which is fixed at the other end of the wire. At this contact there is produced an electric current, which goes from the sponge to the acid, and the direction of which is contrary to that of the current which would have been obtained if the acid had been attacked by the metal. As the interstices of the sponge are filled with the fluid, the current diminishes, and it ceases when the sponge has absorbed all the liquid which it can contain. Sometimes the current takes another direction, but the cause of that is not known.

[ocr errors]

The same effect is produced with nitric acid, but it is less marked. The same result was obtained with a small piece of charcoal, prevented from ouching the platinum by a band of papier Joseph.

ELECTRICITY DEVELOPED IN SOLUTIONS AND

MIXTURES.

605. By means of the same apparatus, M. Becquerel has discovered that an electrical current goes from the acid to the water, when sponge of platinum, that has imbibed distilled water, is plunged into the dish of platinum, containing hydrochloric acid.

606. In order to observe the electricity of solutions of alkalies in water, he fixed in the platina pincers a fragment of hydrate of potassa or soda, enveloped in papier Joseph, and then plunged it into distilled water in the platina cup. A current was thus produced from the water to the alkali.

607. M. Becquerel also found that electricity was developed during the mixture of sulphuric

and nitric acids.

ELECTRICAL EFFECT.

608. The following effect is attributed by Mr. Fox, who observed it, to electricity. A piece of iron pyrites was fastened with a piece of brass wire in a moss-house, the moss being damp. On the following day, the wire was found broken and excessively brittle, and, in those parts in contact with the pyrites, much corroded. On one occasion, after the brass wire had been fastened once or twice round a piece of iron pyrites, and had remained for some days enveloped in damp linen, the constituents of the brass wire were separated, and it was converted copper wire coated with zinc.

into

CONDUCTION OF ELECTRICITY BY AMADOU. 609. It is remarked, in a late number of the Journal de Physique, that the effect of a piece of amadou, in drawing off electricity from charged surfaces, is equal to that of a metallic point. For this purpose, it requires to be dry; and, it may be observed, that at the time a number of fibres rise up and point towards the electrified surface. For the rapid abstraction of electricity, it requires, however, that besides offering points, the body should possess a high conducting power, which was not previously known to belong to this substance.

EFFECT OF VOLTAIC ELECTRICITY UPON AL

[blocks in formation]

the pile, has the same polarity as when it is employed along with oxide of manganese. The reason of this is, that a pile of tinned paper has electrical poles. But, whatever be the kind of paper which is used, the pile always increases in energy, and its polarity always coincides with that of a pile of tinned paper and oxide of manganese, when the paper has been impregnated with a solution of sulphate of zinc, and afterwards dried. In preparing the paper, M. Zamboni avails himself of a dry season, He spreads the solution of sulphate of zinc over the face of the paper which is not covered with tin, and having dried it, but without taking away from the paper its own natural humidity, he covers this face with very dry oxide of manganese. The pile being thus constructed, it is carefully defended from the air. If the paper is not fine and unsized, a little alcohol should be added to the solution of sulphate of zinc. The best manner of preserving the pile, as Zamboni has ascertained by long experience, is to enclose it in a glass tube, whose diameter is somewhat greater than that of the discs, and to run into the intermediate space a moderately warm cement of wax and turpentine. A pile of 2000 discs, constructed in this manner, gives a spark visible in day-light. M. Zamboni recommends the perfect insulation of all the parts of the pile that require to be insulated.

THERMO-ELECTRICITY.

612. It was proved, by professor Sebeck, that antimony, brought into contact with another metal, and unequally heated, would cause the magnetic needle to deviate from its meridian. With a view to ascertain this fact, and to investigate whether this property was restricted to antimony, or extended to other metals, the following experiments were made.

A

613. (1.) A parallopiped of antimony was procured, about fifteen inches long, and one inch square. This bar was prepared by treating crude antimony with sulphate of potassa and tartrate of potassa. A slip of copper was attached to both ends of the antimony. It was kept in close contact with the antimony by means of copper rings. This bar was laid in the direction of the magnetic meridian. needle was placed on the antimony, and the ends of the bar were successively heated by a spirit-lamp. When the heat was thus applied to the south end, the magnetic needle immediately, and strongly, deviated to the east. extent of this deviation depends on the length, mobility, and strength of the needle. It has been seen as much as 68°. When the heat spreads more uniformly through the metal, the deviation decreases, and the needle gradually returns to the magnetic meridian.

The

614. Supposing the deviation to the east at its maximum, the lamp burning under the end placed under the end facing the north, the devifacing the south, if it then be removed, and

ation to the east will decrease, and it will change into a deviation to the west.

615. In general, if the heat is applied under the north end of the bar, the needle will deviate to the west.

« PreviousContinue »