movements into the domain of analysis, it would be necessary to surmount obstacles a thousand 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; the almost spherical form of the celestial 
bodies: the absence of all matter capable of offering any sensible resistance 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 will suffice to give an idea of the real obstacles which render the progress of 
mathematical physics so slow. No one need, therefore, be surprised 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 irregularities of pressure and temperature, etc., 
are much more difficult to calculate than the majestic course of Jupiter, Saturn, or Uranus. 
The phenomena of terrestrial physics Ampère proposed to unravel were certainly among the most 
complex. The attractions and repulsions observed between conducting wires resulted from the 
attraction and repulsion of all their parts. Now, 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 Ampère, as the 
three great consequences, deduced by that celebrated genius from the observations of Tycho, are 
called the laws of Kepler. 
The oscillations, turned to so great profit by Coulomb in the measurement of small magnetic or 
electrical forces, imperatively exact that the bodies for experiment should be suspended by a single 
film without torsion. The conducting wire cannot be placed in such a position, as it would be in 
changer of losing its virtue unless in permanent communication 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 Ampère never fail to lie at rest after a very small number of oscillations.