The problem appeared truly insoluble, when our associate perceived he could reach his object by 
observing different conditions of equilibrium between conducting wires of certain forms placed one 
before the other. The choice of these forms was the essential point; and it is here the genius of 
Ampère displayed itself in the most marked manner. 
He first enveloped with silk two equal portions of the same conducting wire; he bent this wire so 
that its two covered portions should be in juxtaposition, and traversed from opposite soles by a 
current from the same battery; he was satisfied then that this system of two equal but opposite 
currents exercised no power over the delicately suspended conducting wire, and thus proved that the 
attractive force of a given electrical current is perfectly equal to the force of repulsion it 
exercised when the direction of its course is mathematically inverted. 
Ampère then suspended a very moveable conducting wire exactly between two fixed conducting wires, 
which being traversed from the same side by one and the same current ought to repel the intermediate 
wire; one of these fixed wires is straight, the other bent and twisted, presenting a hundred small 
sinuosities. The communication necessary to give play to the currents being established, the 
moveable intermediate wire will stop exactly between the two fixed wires, and if moved from its 
position will return itself to the same place. From this it follows that if a straight connecting 
wire and a sinuous connecting wire, though their unfolded lengths may be very different, exercise 
powers exactly, equal if they have extremities common to both. 
In a third experiment Ampère established undeniably that no closed current whatever could came a 
circular portion of connecting wire to turn round an axis perpendicular to that one are passing 
through its center. 
The fourth and last fundamental experiment of our associate is an instance of equilibrium, 
involving three suspended circular circuits whose centers are in it straight line, and whose radii 
are in continuous geometrical proportion. 
Our associate made use of those four laws to settle what he had allowed to remain arbitrary in his 
analytical formula, conceived in the most general terms imaginable to explain the mutual action of 
two infinitely small elements of two electrical currents. 
A skillful comparison of the general formula with the observation of the four cases of equilibrium 
shows that the reciprocal action of the elements of two currents is exercised in the direction of 
the line uniting their centers; that it depends on the mutual inclination of these elements, and 
that it varies in intensity in the inverse proportion of the squares of the distances. 
Thanks to the profound researches of Ampère, the law, which governs celestial movements, the law, 
extended by Coulomb to the phenomena of electricity at rest or in tension, and then though with less 
certainty, to magnetic phenomena, becomes one of the characteristic features of