We have remarked above, that thefe experiments were made in a particular state of the air; and the law of diffipation ascertained by them is of courfe adapted only to that given state. In a different state of the air, even if this thould be impregnated with the fame pro portion of moisture, the law of diffipation may be different. The inference which M. Coulomb expected to draw from his experiments was, that the ratio of diffipation would prove to be lefs than the cube of the quantity of water held in folution, except when that quantity of water was what the air was capable of holding in folution at the given temperature. This is agreeable to obfervation; for we know that air which is confidered as dry, that is, when it is not nearly faturated with moisture, is the most favourable to electrical phenomena. Such is the general refult of Coulomb's experiments on the diffipation of electricity into the air. The method in which M. Coulomb examined the diffipation along imperfect conductors, by means of this inftrument, was, by completely infulating the ball t, and then after obferving the lofs sustained by a body in contact with it from the air, fliding a metallic rod down the infulating ftalk, till the diffipation began to exceed what took place only by the air. From his experiments refpecting the diffipation along imperfect conductors, he found that this took place in a different manner from that in which electricity escaped by communication with the contiguous air. The elec tricity feems to be diffufed chiefly along the furface of the infulator, and appears principally to be produced by the moisture that is more or lefs attached to it. M. Coulomb illuftrates this in the following manner. Water is found to adhere to the furface of all bodies from which it is prevented by adhesion from efcaping ter. particle is juft fufficient to clear the coercive interval. Electromes Some fluid will come over; and the repulfion of this, acting now in the oppofite direction, will prevent any fluid from coming to fupply its place in the particle which it has juft quitted; the transference of fluid will therefore ftop here, and beyond this point the infulation will be complete. Hence we perceive that there is a mathematical relation between the infulating power, and the length of the canal; and this may be afcertained by the theory which we adopted in the article ELECTRICITY. We shall here give an inftance of this investigation; and, for the fake of fimplicity, we shall take a very probable cafe, viz. where the infulating interval, or, as we may more properly call it, the coercive interval, is equal in every part of the canal. when the bodies are electrified, and is thus rendered capable of receiving a greater degree of electric power. Let us fuppofe that the particles of moisture are difpofed uniformly over the furface, with intervals between them; the electricity that is communicated to one particle, muft acquire a certain degree of denfity, before it can fly from this particle to the next, across the intervening infulating space. When an imperfect conductor of this kind is electrified at one extremity, the communicated electricity, in paffing to the other extremity, muft be weakened every step in paffing from particle to particle, Suppose we have three adjacent particles, which we may call a, b, and c; we infer from N° 374. of the article ELECTRICITY, that the motion of b is fenfibly effected, only by the difference of a and r: and therefore the paffage of electric fluid from b to c, requires that this difference be fuperior, or at least equal to the force neceflary for clearing this coercive interval. Let a particle pafs over. The denfity of fluid of the, particle b is diminished, while the denfity of the particle on the other fide of a remains as before. Therefore fome fluid will pass from a to b, and from the particle preceding a to a; and fo on, till we come to the electrified end of this infulator. It is plain, from this confideration, that we must at laft arrive at a particle beyond c, where the whole repulfion of the preceding VOL. VIII. Part I. Let R reprefent the coercive power of the infulator, or the degree of force required to clear the coercive interval between two particles. Suppofe a ball C, fig. 16. fufpended by a filken thread AB; and let us de-Fig. 16 note the quantity of a redundant fluid in the ball by C, and let the denfities at the different points of the canal be denoted by AD, P d, &c. ordinates to fome curve DdB, cutting the axis in B, the point where the thread AB begins to infulate completely. Let Pp be an element of the axis; draw the ordinate pf, a tangent to the curve df F, the normal d E, and draw fe perpendicular to Pd. Suppofe AC=r, AP=x, and P day. Then we shall have Ppx, and de--y. It was fhewn in N° 374. of the article ELECTRICITY, that the only fenfible action of the fluid on a particle at P iswhen the action of the redundant fluid in the globe on the particle at P, having the denfity y, is denoted by Therefore is R, the coercive power of Pdx de Cy yy PP But P P (r+ x) * ° the thread, which is supposed to be constant, is therefore equal to fome conftant line R. (or f e): de Pd: PE. The fubnormal, PE, is therefore a conftant line. But as this is the property of a parabola, the curve of denfity D d B muft be a parabola, of which 2PE 2R, is the parameter. COR. 1. The denfities at different points of an imperfect infulator are in the fubduplicate ratio of their diftances from the point of complete infulation: for Pď: AD-BP: BA. COR. 2.-The lengths of canal requifite for infulating different densities of the electric fluid are in the duplicate ratio of their denfities; for AB= is a conftant quantity. For AB AD' 2PE' and PE COR. 3. The length of canal requifite for infulation is inverfely as its coercive power, and may be repreD2 ᎠᎪ D' fented by = • R 2PE 2R If we reflect on this theory, we shall perceive, that our formulæ determine the diftribution of fluid along the furface of an imperfect conductor, only in a certain manner, fuppofing that the ball C has received a certain determinate portion of fluid, for this portion diffufing itself, particle by particle, through the conducting matter, will extend to b in such a manner, as that ter. Electrome- the repulfion fhall be every where in equilibrio with the the charging of coated glafs plates. Now we may fuppofe Electromecoercive power of the infulating interval, taken at a that the efcape of the fluid from this body into the air, ter. maximum. We must here remark that this refiftance is begins as foon as it is electrified to 6o, and that it will not active, but only coercive, and may be compared to fly to the infulated plate with the degree 2, if it be the refiftance afforded by vifcidity or friction. Any brought nearer. But if we can prevent this commurepulfion of electric fluid, which falls fhort of this, nication to the infulated plate, by interpofing an elecwill not disturb the stability of the fluid that is fpread tric, we may electrify the cover again, while fo near along the canal, according to any law whatever. So So the metallic plate, to 6°, before it will pafs off into that if AD reprefent the electric denfity of the globe, the air. If now it be removed from the lying plate, and remain conftant, any curve or denfity will anfwer, the fluid would cause the electrometer to rife to 10°, if dd it did not immediately pafs off; and an electric excitement of any kind which could raise this body only to 6° by its intensity, will, by means of this apparatus, raife it to the degree 10, if it be fufficiently copious in extent. If we do the fame thing when the wire which connects the lying plate with the ground is taken away,. we know that the fame diminution of the electricity of the other plate cannot be produced by bringing it down. near the lying infulated plate. provided that be everywhere lefs than R. It is there x fore an indeterminate problem, to affign in general the x The reafonings which have thus been deduced from theory, were confirmed by M. Coulomb in a numerous fet of experiments. These are chiefly valuable for having stated the relation that subfifts between the electric denfity, and the length of fupport neceffary for complete infulation. But as M. Coulomb has not given us the fcale of his electrometer, according to which the abfolute measures of the denfities were determined, the experiments can be of but little ufe till this be known. We hinted, at the end of the theoretical part of ELECTRICITY, that the theory of Volta's condenfer might be more fatisfactorily explained after we had confidered the above experiments of Coulomb. The account which we gave of the condenfer in Chap. xiii. of that article, (chiefly from Cavallo), was the only one we could properly give in that early part of our view of the science. We are now prepared for a more fcientific account of the effects of that inftrument. The following is nearly the manner in which Dr Robifon confidered the fubje&t. Let the cover of an electrophorus be furnished with a graduated electrometer, fuch as may indicate the proportional degrees of electricity; electrify it pofitively to any degree, we shall fuppofe fix, while it is held in the hand, at a little diftance, directly over a metallic plate lying on a wine glafs, or fuch like infulating ftand, but made to communicate with the ground by a wire. Now bring it gradually down towards the plate. The ory teaches, and we fee it confirmed by experiment, that the electrometer will gradually fubfide, and will perhaps fall to 2o, before the electricity is communicated in a fpark: but let us ftop it before this happens; the attraction of the lying plate produces a compenfation of four degrees of the mutual repulfion of the parts of the cover, by condenfing the fluid on its inferior furface, and forming a deficient ftratum above. This needs no farther explanation, after what we faid under ELECTRICITY, on The theory of Volta's condenfer now becomes very fimple. M. Volta feems to have obfcured his conceptions of it, by being intent on the electrophorus which he had lately invented, and was thus led into. fruitless attempts to explain the advantages of the imperfect conductor above the perfect infulator. But the condenfing apparatus is wholly different from an electrophorus; its operations are more analogous to thofe of a coated plate not charged, and infulated only on one fide; and fuch a coated plate lying on a table will be a complete condenfer, if the upper coating be of the fame dimenfions as the plate of the condenfer. All the directions given by M. Volta for preparing the imperfect conductors prove, that the effect produced is to make them as perfect conductors as poffible for any degree of electricity that exceeds a certain fmall intenfity, but fuch as fhall not fuffer this very weak electricity to clear the first step of the conducting space. The marble must be thoroughly dried, and even heated in an oven, and either used in this warm flate, or must be varnished, fo as to prevent the reabforption of moisture. We know that marble of slender dimenfions, fo as to be completely dried throughout, will not conduct electricity till it has again become moift. A thick piece of marble is rendered dry only fuperficially, and ftill conducts internally. It is then in the beft poffibleftate for a condenfer. The fame is the cafe with dry unbaked wood. Varnishing the upper furface of a piece of marble or wood is equivalent to covering it. with a thin glafs plate. Now by this method of covering the top of the marble, a book, or even the table, with a piece of clean dry filk, they all become moft perfect condenfators. This view of the matter has great advantage. We learn from it how to form a condenfing apparatus much more fimple and at the fame time much more efficacious. We require only the fimple moveable plate, which must be covered on the under fide with a very thin coating of the finest coachpainters varnish. By connecting this, by a wire, with the fubftance whofe weak electricity is to be examined, this electricity will be raised in the proportion of the thickness of the varnish to the fourth of the plate's diameter. This condenfation will be produced by detaching the wire from the infulating handle of the condensing plate, and then lifting this from the table on which it was lying. It will then afford fparks, though the original electricity |