MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



Oaven- o f other matter with a force varying inversely as some 

 d , lsh ' 8 . less power of the distance than the cube. Common 



electrical , .. , i J.L j. -i j. 



theory and matter repels its own particles and attracts electric 

 experi- particles according to the same law. The limitation 

 menta - as to a power below the inverse cube of the distance 

 is necessary, since were the decrease of force more 

 rapid, a particle would not be sensibly affected by the 

 repulsion of any portion of the fluid except what was 

 placed close to it. The hypothesis of Cavendish and 

 his mode of reasoning from it were in general the 

 same as those of JEpinus ; but Cavendish was not 

 aware of the researches of the Swedish philosopher 

 until his own memoir was completed. The number 

 of facts accurately ascertained concerning electricity 

 was at that time too small to admit of very precise 

 numerical comparisons, but the ordinary cases of at- 

 traction, repulsion, and induction, were perspicuously 

 explained by the theory ; and had the inverse square 

 of the distance been assumed (as it very safely might 

 have been) to represent the law of diminishing re- 

 pulsion, several of the theorems would have as- 

 sumed a much more definite character, as was 

 shown by Robison. Cavendish first demonstrated 

 in his paper of 1771 that electricity must be 

 confined close to the surface of a spherical body. 

 This memoir also includes a correct theory of 

 the Leyden phial, a just approximation to the law 

 of attraction as the inverse square of the distance, 

 a theory of conduction, and of the distribution of 

 electricity on insulated conductors placed at a dis- 

 tance but connected by a fine wire or electric canal ; 

 and it was only the prelude to other researches never 

 published, but of which some remarkable fragments 

 exist amongst his manuscripts. Professor William 

 Thomson, who has partly examined these, informs 

 me that they contain the experimental solution of 

 problems such as the following : " To compare the 

 quantities of electricity on a spherical conductor, 

 and a plane disk of equal diameter connected by a 

 long conducting wire." Cavendish found that the 

 sphere holds 1*57 times the electricity of the plate, 

 a result exactly coincident with the deductions of 

 theory. 



(872.) I may here (for the sake of biographical connection) 

 He makes men ti on Cavendish's paper on the Torpedo, as a re- 

 ficial " markable instance of the explanation of an obscure 

 torpedo, natural phenomenon, by the analogous effects of an 

 artificial imitation. The experiments of Walsh on the 

 Electrical Fishes have been cited in the preceding Dis- 

 sertation. Cavendish undertook the bold task of prov- 

 ing, that all the external effects of the shock under 

 varied circumstances, might be reproduced by a com- 

 bination of Leyden jars duly protected. He made an 

 artificial torpedo, consisting of 49 jars in a frame 



covered with leather, and he succeeded in obtaining 

 shocks in air as in water, exactly comparable to those 

 obtained from the live fish by Walsh. But perhaps the 

 most striking part of the paper is the incidental men- 

 tion of several laws of electricity then certainly new, and 

 which he had deduced from experiment. Thus, he af- 

 firms the conducting power of iron for electricity to 

 exceed 400,000 times that of distilled water, which he 

 states to be equivalent to the fact, that a conductor of 

 equal diameter will transmit as much electricity if the 

 iron be 400,000 times longer than the water a law 

 conformable to that of Ohm. He farther estimates 

 the conducting power of sea-water at 100 times, but 

 of saturated brine at 720 times that of pure water. 

 Again, the quantity of electricity required to raise the 

 charge on different jars or plates to the same inten- 

 sity he finds to be directly as the area of the coating, 

 and inversely as the thickness of the plate, and he 

 applies this just conclusion with great ingenuity to 

 explain the surprising power of the torpedo's shock 

 by the extreme fineness of the membranes separating 

 the columns of the electrical organs. 



COULOMB (born 1736, died 1806 1 ) was a person of (873.) 

 less genius and less mathematical attainment than Coulonib j 

 Cavendish, yet he had very considerable geometrical exper i_ 

 ability and much facility in applying it to the results ments. 

 of experiments, which he conducted with the greatest 

 ingenuity and accuracy. In the latter respect he has 

 seldom been surpassed. His methods, and even his 

 numbers, are still, after a lapse of more than half a 

 century, in many cases the best we can quote. 

 Like Cavendish, he was devoted to quantitative esti- 

 mations of phenomena. 



His two greatest inventions were the balance of ( 87 *-) 

 torsion and the proof plane. In the course of his i ance O f 

 strictly mechanical researches (which, as we have torsion 

 seen in the chapter on Mechanics, Art. 339, &c., were and ttte 

 numerous and important) he ascertained the laws of p | 

 torsion. Within the limits of perfect elasticity, he 

 found that the force is as the angle of torsion of the 

 wire or fibre, and inversely as its length. An almost 

 indefinite minuteness may thus be attained in the mea- 

 sure offerees which maybe balanced by the elastic tor- 

 sion of a wire. We have seen (Astronomy, 1, Art. 

 156) how it was applied by Michell and Cavendish to 

 measure the gravitation of bodies. Coulomb's inven- 

 tion dates at least from 1784. By means of it he 

 established (in a different and perhaps more satisfac- 

 tory way than had been done by Kobison in 1769) that 

 the electric and magnetic forces vary according to the 

 Newtonian law; 2 and with the aid of the "proof 

 plane" he obtained exact measures of the electric 

 tension on any part of an excited body. The "proof 

 plane" consists of a small gilt disk with an insulat- 



1 For a farther account of Coulomb, see the chapter on Mechanics, 2. 



2 Besides this law, Coulomb experimentally proved two others of great importance : 1. That the electricity of an elec- 

 trified conductor resides wholly on its surface. 2. That the interior of such a conductor is in a condition absolutely undisturbed 

 by the presence of other external excited bodies. 



