1818.J Charles Augustin Coulomb. 83 



which the wire endeavours to regain its natural position is in the 

 direct ratio of the distance to which it has been removed from 

 it ; and hence, when we obtain the measure of the distance, we 

 have that of the force. The power which operates upon the 

 wire is called the force of torsion 5 and the angle formed by the 

 index in its natural position, and that to which it is brought by 

 the operation of the twisting power, is called the angle of torsion. 

 This is accurately measured on the scale ; and assuming that the 

 force of torsion is equal to the angle of torsion, we are able to 

 ascertain this force with the most perfect accuracy. Proceeding 

 upon this principle, a number of experiments were performed 

 with a view to ascertain the action of different wires, so far as 

 respected their length, their thickness, and the nature of the 

 materials of which they were composed ; and he deduced from 

 them a series of propositions which afford very important data 

 for estimating the amount of very minute, attractive and repulsive 

 forces.* 



Coulomb had been elected a member of the Academy in 1781, 

 and now made Paris his residence, devoting himself for some 

 years almost exclusively to the investigation of the sciences of 

 electricity and magnetism, more especially in endeavouring to 

 perfect their theory. In this investigation he was materially 

 assisted by his torsion balance, and was enabled, by means of it, 

 to execute some very delicate experiments, which may be con- 

 sidered as forming the basis of his most important speculations. 

 He proved by it that electrical attractions and repulsions follow 

 the general law of the inverse ratio of the squares of the dis- 

 tances, a law which had been assumed by preceding philoso- 

 phers as highly probable, and as agreeing generally with the 

 phenomena, but which had not before obtained the sanction of 

 direct experimental proof. In the further prosecution of his 

 researches on the subject of electricity, Coulomb was induced 

 to adopt the hypothesis of the two electric fluids, which had been 

 originally proposed by Dufay, and supported by Symmer, but which, 

 at least in this country, had been almost unanimously renounced 

 for the more simple doctrine, which attributes all the effects 



* Coulomb's essay on torsion is in the ninth volume of the Mem. Scav. 

 Etrang. and is entitled, " Researches theoretical and experimental on the 

 Force of Torsion, and on the Elasticity of metallic Threads; Application of this 

 Theory to the Employment of Metals in the Arts and in different philosophical 

 Experiments; Construction of different Torsion Balances, for the Purpose of 

 measuring very small Degrees of Force ; Observations on the Laws of Elasticity 

 and uf Cohesion." His general theorem is as follows: that the momentum of the 

 fore- of torsion is, for threads of the same kind of metal, in the compound ratio of 

 the angle of torsion, the fourth power of the diameter, and the inverse ratio of 

 the length of the thread ; so that if we call the angle of torsion B, the diameter I), 

 and the length /, we shall have as the expression which represents the force of 



torsion — f where u is a constant coefficient, which depends upon the natural 



atiffness of every metal ; this quantity ,u, which is invariable for the threads of 

 euch particular metal, may be easily determined by experiment. 



f2 



