98 ; REPORT—188). 
5. Theories which are based upon dynamical considerations, and which: 
take into account the action of the dielectric. 
This class includes the theories of Maxwell and v. Helmholtz. 
We shall now proceed to the detailed consideration of these theories. 
Theories in which the action between elements of current is deduced by 
geometrical considerations combined with certain assumptions which 
are not explicitly, at any rate, founded on the Principle of the Oonser- 
vation of Energy. 
The best known theory of this class is that of Ampére. Others, 
however, have been giveu by Grassmann, Stefan, and Korteweg, which 
we shall consider in order. 
Ampere’s Theory. 
This theory was first published in 1820. In 1823 appeared his great. 
paper, the ‘ Mémoire sur la Théorie Mathématique des Phénoménes 
Electro-dynamiques,’ Mémoires de I’ Institut, t. vi., which Maxwell de-- 
scribes as ‘ perfect in form and unassailable in accuracy,’ and which at 
once brought the action between electric currents under the power of 
mathematics. Ampere founded his theory on certain postulates which 
he attempted to establish by experiment; inasmuch, however, as he 
always dealt with closed circuits in his experiments and elements of 
circuit in his postulates, the experimental evidence is not quite satis- 
factory. Ampere’s experiments have been repeated by v. Ettingshausen ! 
with much more delicate apparatus. 
The postulates used by Ampére are as follows. The first four are 
given in the words of Professor Tait :—? 
I. ‘ Equal and opposite currents in the same conductor produce equal 
and opposite effects on other conductors; whence it follows that an 
element of one current has no effect on an element of another which lies 
in the plane bisecting the former at right angles.’ 
II. ‘ The effect of a conductor bent or twisted in any manner is 
equivalent to that of a straight one, provided that the two are traversed 
by equal currents and the former nearly coincides with the latter.’ 
Ill. ‘No closed cirenit can set in motion an element of a circular 
conductor about an axis through the centre of the circle and perpendicular 
to its plane.’ 
IV. ‘ In similar systems traversed by equal currents the forces are 
equal.’ 
V. ‘ The action between two elements of current is a force along the 
straight line joining them, and proportional to the product of the lengths 
of the elements and the currents flowing through them.’ 
It follows from IV. that the force between two elements of current 
varies inversely as the square of the distance between them. 
The assumption V. is one that can only be justified by the correctness 
of the results to which it leads. We have no right to assume @ priori 
that the action is equivalent to a single force, and not to a force and a 
couple: and we have no more right to assume that the force is along the 
line joining the elements than we have to assume that the force between 
1 © Ueber Ampére’s elektrodynamische Fundamentalversuche,’ Wien. Ber, (11), 77. 
p. 109, 1878. 
? Tait’s Quaternions, 2nd edit. p. 249. 
