ELECTRICITY. 



545 



Theoretical 

 Electricity. 



Explanation 

 of the elec- 

 ie spark. 



I the theo- 



i of two 



)! : .: 



duced, is sufficient to overcome the pressure of the at- 

 mosphere, much less that it is sufficient to burst the 

 glass vessels in Beccaria's and Lane's experiments. 



This is confirmed by Prop. 12. For, let an under- 

 charged body be brought near to, and opposite to the 

 end of a long cylindrical body, communicating with the 

 ground, the pressure of the electric fluid against the 

 base of the cylinder, is scarcely greater than the force 

 with which the two bodies attract each other, provided 

 that no part of the cylinder is undercharged ; and con- 

 sequently, if the spark was produced by the air be- 

 ing pushed aside, by the force with which the fluid 

 endeavours to issue from the cylinder, no sparks should 

 be produced, unless the electricity was so strong, that 

 the force with which the bodies attracted each other 

 was as great as the pressure of the atmosphere against 

 the base of the cylinder ; whereas it is well known, that 

 a spark may be produced, when the force, with which 

 the bodies attract, is very trifling in respect of that. 



In discharging a Leyden phial, if the two knobs are 

 brought together very slowly, a hissing noise will be 

 perceived before the spark ; which shows, that the fluid 

 begins to flow from one knob to the other, before it 

 passes in the form of a spark." 



CHAP III. 



On the Theory of two Fluids. 



. THE theory of two fluids originated in the discovery 

 made by M. Dufay of vitreous and resinous electricity; 

 and was afterwards warmly supported by our country- 

 man Mr Symmer, who thought that he discovered in 

 the mechanical effects of the electric spark indubita- 

 ble proofs of two opposite currents. For a long time, 

 however, the question of one or two fluids scarcely oc- 

 cupied the attention of philosophers, who were more 

 solicitous to discover new facts, than to connect to- 

 gether, by any general principles, the scattered phe- 

 nomena of electricity. 



In the theories of ,-Epintu and Cavendish, the doc- 

 trine of a single fluid was adopted ; but, in order to 

 accommodate this hypothesis to the phenomena, they 

 were obliged to assume, contrary to every physical 

 analogy, that the particles of solid bodies repelled each 

 other with the same force with which they attracted 

 the particles of the electric fluid, or with which these 

 particles mutually repelled each other. From this part 

 of the hypothesis it will follow, that while all the par- 

 ticles of solid bodies are endued with- an attractive 

 force diminishing as the square of the distance in- 

 creases ; they are also endued with a repulsive force, 

 following the same law, but infinitely greater in point 

 of i:itci-.-.ity, than the attractive force of gravity. This 

 assumption we conceive to be most unphilosophical, u 

 it ascribes to the particles of solid bodies, a new property 

 almost the very reverse of that which they are known 

 to possess ; and wliatever simplicity may appear in the 

 doctrine of a single fluid, we consider it as merely no- 

 minal, and more than counterbalanced by the assump- 

 tion which is necessary to its existence. 



The doctrine of two fluids, which has never been 

 adopted in this country since the time of Symmer, waa 

 supported by Coulomb, who has employed it in calcu- 

 lating the various phenomena which he observed. 



In this hypothesis it it assumed, that there are two 

 electric fiuios, the viireoui end the retinout. The par- 

 ticles of the viireout fluid repel one another with a force 

 in tin- inverse ratio of the square of the distance, while 

 a the particles of the resinous fluid with n 

 force following the same law ; and the particles of the 



Mil. PAH i II. 



resinous fluid repel one another, while they attract those 

 of the vitreous fluid according to the same law. 



'Die fine experiments of Coulomb on the distribution 

 of electricity over the surface of conductors, have afford- 

 ed an excellent opportunity of comparing the theory 

 with observation ; and in so far as this lias been done, 

 the agreement is very surprising. 



Coulomb has demonstrated, both by theory and 

 experiment, that when electricity is communicated 

 to any conducting body, it will be drawn from the inte- 

 rior of the body, and would diffuse itself indefinitely in 

 ?pace, if it were not arrested in its progress by the sur- 

 rounding air, which, being a non-conductor, will oppose 

 a resistance to its farther diffusion, and force it to distri- 

 bute itself on the surface of the conducting body, in a thin 

 envelope or coating, the thickness of which will vary in 

 different parts with the form of the body. His demon- 

 stration, however, only applies to the case of a spherical 

 body, in which the coating of fluid will be equally thick 

 in every part of its surface. 



This part of the theory has occupied the atten- 

 tion of the illustrious La Place, who has applied to it, 

 in a most elegant manner, the formula; which he em- 

 ployed in determining the figure of the earth. He 

 has shewn, by a method purely synthetical, that, in all 

 ellipsoids of revolution, the electric fluid will distribute 

 itself over their surface, and that the repulsive force 

 of the fluid, or its tension at the pole of the ellipsoid, 

 will be to that of the fluid at the equator, as the polar 

 is to the equatorial axis. 



These interesting results have been extended by M. 

 Biot to all spheroids differing but little from a sphere, 

 whatever be the irregularity of their figure. This 

 eminent mathematician has also examined analytically, 

 the law which regulates the losses of fluid sustain- 

 ed by the two surfaces of a jar, or plate of coated 

 glass, when discharged by successive contacts; and 

 baa shewn, that the losses of fluid form a geometri- 

 cal progression. He has also found the same law to 

 obtain in the discharge by successive contacts of a series 

 of jars or plates in a state of mutual communication, 



The analytical investigation of this subject has been 

 carried to a very great length by M. Poisson of the In- 

 stitute of France, a mathematician of the very first 

 eminence, who had already distinguished himself by 

 some improvements on the higher analysis, and by 

 several fine discoveries on some of the most abstruse 

 branches of physical astronomy. We expected, through 

 the kindness of M. Poisson, to have had it in our 

 power to present our readers with a very full account 

 of his important researches; but we believe that the 

 last memoirs, which he has drawn up, have not yet 

 been printed. We must therefore content ourselves 

 with giving as copious an abstract as we can of his two 

 first memoirs on the distribution of electricity on the 

 * iirface of conductors. 



In order to determine in what manner electricity is 

 distributed on the .surface of a conducting body, "M. 

 Poisson has shewn, that the problem may be reduced 

 to this, to find what ought to b the thickness of the 

 coat of fluid on each point of the surface, in order that 

 the action may be nothing in the interior of the elec- 

 trified body. If the thickness of the coat of fluid is sup- 

 posed to be very small, we shall have the distribution of 

 electricity on the surface of a spheroid, differing very 

 little from a perfect sphere. By the application of tho 

 formula for the attraction of spheroids, M. Poisuon has 

 calculated the attraction of the coating, for a point pla- 

 ced within or without the conductor ; and he has found, 

 Si 



Theoreiu < 

 Electricitv 



Labours of 

 La Place. 



Of M. Biot. 



Researches 

 of M. Pois4 

 ion. 



Case of a 

 tingle bo<U-. 





