142 EULOGY ON AMPERE. 



movements into the domain of analysis, it wonld be necessary to sur- 

 mount obstacles a tliousaud times greater than those met by the modern 

 geometer, when he wishes, with the assistance of mathematics, to follow 

 in all their ramifications the various phenomena discovered and studied 

 by physicists. However general this opinion may be, it is not the less 

 an error. The smallness of the planets, when compared to the sun ; the 

 immensity of the distances 5 the almost spherical form of the celestial 

 bodies ; the absence of all matter caj^able of oiiering any sensible resist- 

 ance in the vast regions where the elliptical orbits are described, are so 

 many circumstances extremely simplifying the problem, and bringing 

 it within the abstractions of rational mechanics. If, instead of the 

 movements of the planets — I mean of distant bodies capable of being 

 considered reduced to simple points — the only guide had been the 

 phenomena of attraction of irregular polyhedrons, acting on each other 

 at short distances, the laws of universal gravity would remain yet to be 

 discovered. 



These words Avill suffice to give an idea of the real obstacles which 

 render the progress of mathematical physics so slow. No one need, 

 therefore, be sui'prised to learn that the propagation of sound, or of 

 luminous vibrations; that the movement of the light waves ruffling 

 the surface of liquids ; that the atmospheric currents caused by irregu- 

 larities of pressure and temperature, etc., are much more difficnlt to 

 calculate than the majestic course of Jupiter, Saturn, or Uranus. 



The phenomena of terrestrial physics Amx)ere proposed to unravel 

 were certainly among the most complex. The attractions and repul- 

 sions observed between conducting wh-es resulted from the attraction 

 and repulsion of all their parts. Xow, to pass from the whole to the 

 determination of the numerous and different elements which compose 

 it, or in other words to the investigation into the manner in which the 

 mutual actions of two infinitely small parts of two currents vary, when 

 their relative distances and inclinations are changing, offered unwonted 

 difficulties. 



All these difficulties have been overcome. The four conditions of 

 equilibrium, which have rendered so much assistance to the author in 

 developing phenomena, will be called the laws of Ampere, as the three 

 great consequences, deduced by that celebrated genius from the obser- 

 vations of Tycho, are called the laws of Kepler. 



The oscillations, turned to so great profit by Coulomb in the measure- 

 ment of small magnetic or electrical forces, imperatively exact that the 

 bodies for experimeiit should be suspended by a single film without tor- 

 sion. The conducting wire cannot be i^laced in such a position, as it 

 Avould be in danger of losing its virtue unless in permanent communi- 

 cation with the two poles of the battery. 



Oscillations give very exact measurement, but coupled with the 

 express condition of being numerous. The conducting wires of Ampere 

 never fail to be at rest after a very small number of oscillations. 



