CHAP. VII., 7.] 



ELECTRICITY. COULOMB POISSON GREEN. 



191 



(875.) 

 Results. 



(876.) 

 Theory of 

 electrical 

 attractions 

 and repul- 

 sions. 



(877.) 

 Its prin- 

 ciples de- 

 veloped by 

 Coulomb, 



ing handle, which being applied flat-wise to the sur- 

 face of an excited body takes off a portion of electri- 

 city, which is found in all cases to be proportioned 

 to the electric excitement of the part which it had 

 touched ; being then presented to the torsion balance 

 properly electrified, it shows by the repulsive effect 

 produced, the relative tension of the part of the 

 body whence the sample was obtained. 



In this manner Coulomb determined the distribu- 

 tion of electricity upon electrified spheres at and after 

 contact with one another ; on spheres inductively 

 electrified, on rods and plates and other figures ; and 

 his results, so far as they have been compared with 

 theory, give evidence of the care and skill with which 

 they were obtained, allowance being in all cases made 

 for the loss of electricity by imperfect insulation. He 

 also laboured with praiseworthy diligence to compare 

 his results with the theory which he adopted of two 

 fluids, each attracting the particles of the other and 

 repelling their own according to the Newtonian law. 

 The uEpinian theory admits of only one fluid, but as it 

 assumes a repulsion between the elementary particles 

 matter it cannot be said to gain much in simplicity, 

 whilst the mathematical results of either hypothesis 

 are in general the same. M. Mosotti has endea- 

 voured recently to revive the view of Franklin and 

 of .^Epinus, so as to include, after the manner of 

 Boscovich, the entire mechanical properties of 

 matter. 



The doctrine of attractions is a complex and diffi- 

 cult one even when the distribution of the attracting 

 matter, as well as the fundamental law of attraction, 

 is known. But it becomes much more so when the 

 distribution of the attracting matter is itself the 

 result of the very effect which it is the object 

 of the problem to discover. If two homogeneous 

 spheres attract one another, molecule to molecule, by 

 the law of gravity, the problem is easy, provided the 

 matter be rigid, and the distribution of it therefore 

 unchanged ; but if two such spheres be charged with 

 the mobile electric fluid (using the term as a mere 

 abbreviation), the case is very different, for now the 

 electricity tends to shun the nearest points of each 

 sphere, and to accumulate itself towards the remoter 

 parts of their surfaces. The distribution of the 

 electricity, and also the repulsive effect at any point, 

 are both to be found simultaneously. The calcula- 

 tions of Coulomb were inadequate (as has been said) 

 to such a solution ; he contented himself with comput- 

 ing the effect of certain simple distributions which evi- 

 dently lay on opposite sides of the truth, and com- 

 paring them with the result of experiment. Though 

 any one such comparison might avail little, the 

 cumulative evidence of many imperfect comparisons 

 argued favourably for the truth of the hypothesis. 



At the very time that Coulomb was pursuing this 

 inquiry, Legendre first, and then Laplace, were in- 

 venting and improving those subtle and powerful 

 mathematical methods at which we have glanced in 



the chapter on Physical Astronomy, Art. 99, &c., Laplace, 

 for estimating attractions by a general method. Le- and Pois ' 

 gendre's principles of calculation applied to cases of SOD * 

 the symmetrical distribution of the attractive sub- 

 stances, but Laplace escaped this restriction. The 

 problem is reduced to finding a quantity usually de- 

 noted by the letter V, called by some writers the 

 potential, for the given body or surface, the expression Potential. 

 for which may in each case be expanded into a series, 

 the co-efficients of the terms of which (known as 

 Laplace's co-efficients) are connected by certain rela- 

 tions which are evolved from the conditions of the 

 problem. It was M. Biot first of all, but principally 

 Poisson, who applied this method to electrical, and 

 subsequently to magnetical phenomena. Poisson, 

 with great labour, succeeded in representing correctly 

 by analysis the conditions of some of Coulomb's ex- 

 periments on spheres and ellipsoids. But it must 

 be owned that the complication of the analysis, the 

 difficulty of applying it to any but the very simplest 

 cases, and the considerable latitude of the errors of 

 experiment, rendered the results rather analytical 

 exercises than solid bases for physical induction ; 

 which may in some degree account for the manner 

 in which Sir John Leslie mentions them in his Dis- 

 sertation. Poisson (as I have elsewhere remarked) 

 had not the talent of conducting his mathematics in 

 a fertile direction, and usually left the fields of ex- 

 perimental physics on which he touched nearly as 

 barren as he found them. But this is no rea- 

 son why other mathematical reasoners may not 

 obtain more pregnant results. We shall see in the 

 next section that Gauss, a distinguished contempo- 

 rary of Poisson, by treating the great problem 

 of the distribution of the magnetism of the globe 

 (in many respects similar to those of the theory 

 of electricity) with the utmost mathematical gene- 

 rality, has obtained results of great novelty and 

 importance ; that he has not only shown experi- 

 menters how to proceed, but has invented instru- 

 ments for them to use. A similar step has not yet 

 been taken in electricity. Notwithstanding the un- 

 questionable beauty of Sir William Harris's methods 

 of measuring electrical attractions (Phil. Trans. 

 1834), they are little adapted for comparison with 

 theory, and Coulomb's experiments still remain the 

 standard ones on the subject. 



The theory of Coulomb has, however, been ably ge- (878.) 

 neralized by Green, a nearly self-taught mathemati- Writings 

 cian of great originality, who died at a premature age. ^ of 6n 

 In a memoir on electricity privately printed about Professor 

 1830 he generalized Poisson's methods and ap-W.Thom- 

 plied them to a number of new cases. His paper 80n * 

 was reprinted a few years since in Crelle's Journal. 

 To him I believe is due the term potential. Several 

 continental mathematicians of eminence have added 

 some steps to the theory of electricity, but probably 

 the most important from its fertility and simplicity 

 is a theorem discovered by Professor William Thorn- 



