the powers exercised by electricity in motion. The general formula, which gives the value of the 
mutual actions of the infinitely small elements of currents, once understood, the determination of 
the combined actions of limited currents of different forms becomes a simple problem of integral 
analysis.  
Ampère did not fail to follow out these applications of his discoveries. He first tried to 
discover how a rectilinear current acts on a system of circular closed currents, contained in planes 
perpendicular to the rectilinear current. The result of the calculation, confirmed by experiment 
was, that the planes of the circular currents, would, supposing them movable, arrange themselves 
parallel to the rectilinear current. If like transversal currents pass over the whole length of a 
magnetic needle, the cross direction which, in the experiment of Oersted, completed by Ampère, 
seemed an inexplicable anomaly, would become a natural and necessary fact. Is it not evident, then, 
to all how memorable would that discovery be that would rigorously establish the fact that to 
magnetize a needle is to excite, to put in motion around each molecule of the steel, a small, 
circular, electrical vortex? Ampère fully realized the wide reach of the ingenious generalization 
that had taken possession of his mind; and he hastened to submit it to experimental proofs and 
numerical verifications, which, in our day, are the only processes considered entirely 
demonstrative. 
It seemed very difficult to create an assemblage of closed circular currents capable of great 
mobility. Ampère confined himself to an imitation of this composition and form, by causing a single 
electrical current to circulate through a wire enveloped in silk, and coiled like a helix in very 
compact spires. The resemblance between the effects of this apparatus and those of a magnet was very 
striking, and encouraged the illustrious academician to devote himself to a difficult and minute 
calculation of the actions of closed circuits perfectly circular. 
Starting from the hypothesis that like currents exist around the particles of magnetic bodies, 
Ampère, recognized, in elementary actions, the laws of Coulomb. These laws treated with the most 
consummate skill by an illustrious geometer have explained all the known facts of the science of 
magnetism; the hypothesis of Ampère represents them with equal accuracy. 
The same hypothesis, finally applied to the investigation of the action which a rectilinear 
connecting wire exercises over a magnetic needle, leads analytically to the law that M. Biot has 
deduced from extremely nice experiments. 
If, with the almost entire body of ancient physicists, it is thought advisable to consider steel as 
composed of solid molecules, in each of which exist two fluids of opposite properties, fluids 
combined, and neutralizing each other when the metal is not magnetic, fluids more or less separated 
when the steel is more or less magnetized, the theory will cover all that is known at present, even 
in the most subtle numerical particularities of ordinary magnetism. This theory is silent, however,