18 - REPORT—1857, 
this case, we ought to find a permanent augmentation of the intensity of the ecur- 
rent as long as the sphere is in rotation. Different causes, amongst others the con- 
cussion which inevitably accompanies the rapid motion of the sphere, render the 
experiments very difficult. The following, however, are the results which I have 
obtained. When the sphere is set in rotation, as long as its rapidity continues in- 
creasing, a current of induction is developed, and this being added to the primitive 
current, slightly increases its intensity; when the movement of the sphere is uni- 
form, the intensity again becomes the same as when the sphere was without motion; 
lastly, when the rotation becomes slower, the intensity is slightly diminished. 
This case, therefore, does not come under the ordinary rule, which is accounted 
for because we cannot suppose that the current really produces any mechanical 
work: it acts like a force which would tighten a check; the resistance which the 
sphere experiences is analogous to a friction, and becomes converted into heat, 
according to the experiment of M. Foucault. 
Part II,—In his researches upon the theory of electromotors, M. Jacobi has only 
occupied himself with the case in which the movement of the machine takes place in 
he natural direction, But nothing in the formule which he has given prevents their 
application to the case in which the machine is compelled to take a movement oppo- 
site to that which it tends to take under the influence of the electric forces. It is 
sufficient to give a negative value to the rapidity v. We then arrive at singular 
consequences. 
In this case, the current of induction which M. Jacobi has called the counter-cur- 
rent, would become negative, that is to say, it would be in the same direction as the 
principal current, consequently the total current would be stronger whilst the 
machine is animated by a negative rapidity than when it is stopped. 
Giving the rapidity a negative value, = the total current would acquire an in- 
Kk, 
finite intensity (formula 10 of M. Jacobi, ‘Annales de Chimie et de Physique,’ xxxiv. 
p. 451). Now this rapidity would not be very great. At the same time that the in- 
tensity of the current would become infinite, the mechanical work which it would be 
necessary to apply to the machine to give it this rapidity would itself become infinite 
(formula 19). From this it would follow, that by causing the machine to move in 
a direction opposite to its natural movement, the intensity of the current might be 
augmented indefinitely, and consequently mechanical work might be unlimited, con- 
verted into electric current. : 
Lastly, on this negative rapidity being still more increased, the current would 
change its direction. 
It is useless to dwell upon the theoretical and practical importance which would 
be possessed by these consequences if they were realized. 4 priori we might think 
that it was impossible they should be absolutely verified, for the laws upon which 
the calculation is founded have been determined between certain limits and would 
cease to be correct if we passed those limits; moreover, electro-magnetic machines 
present, in their construction, certain obstacles which would prevent the absolute 
realization of these phenomena. 
But, on making the experiment, far from seeing the intensity of the current inde. 
finitely increased, when a reversed motion is given to the machine, we observe that 
the current is weakened almost as much as if the movements were effected in the 
normal direction. Thus, in an experiment made with a small electro-magnetic 
machine, constructed by Froment, the needle of a galvanometer deviated 57° when 
the machine was kept still; on setting the machine in motion so that 242 revolutions 
in a minute were recorded, the deviation fell to 30°; and on making it move in the 
opposite direction with the same rapidity, the deviation was 32°. 7 
The results differ so widely from the deductions of calculation, that we must 
necessarily admit the inexactitude of the formule. 
We have already said that M. Marié Davy had disputed them ; he has indicated 
two elements which have been neglected in the calculation, namely, the electrical 
inertia proper to conductors, and the inertia which arises from these conductors 
being rolled in a spiral, in such a way that the turns of the spire act upon each other 
by induction. M. Jacobi has also neglected a still more important element, which ~ 
M. Marié Davy has perhaps recognized and indicated in a recent memoir presented 
