Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/205

the induction current is proportional to the primary current. Hence $\gamma$ enters simply as a factor, the other factor being a function of the form and position of the circuits $A$ and $B$.

We also know that the value of this function depends on the relative and not on the absolute positions of $A$ and $B$, so that it must be capable of being expressed as a function of the distances of the different elements of which the circuits are composed, and of the angles which these elements make with each other.

Let $M$ be this function, then the total induction current may be written

where $C$ is the conductivity of the secondary circuit, and $M_{1}$, $\gamma _{1}$ are the original, and $M_{2}$, $\gamma _{2}$ the final values of $M$ and $\gamma$.

These experiments, therefore, shew that the total current of induction depends on the change which takes place in a certain quantity, $M\gamma$, and that this change may arise either from variation of the primary current $\gamma$, or from any motion of the primary or secondary circuit which alters $M$.

540.] The conception of such a quantity, on the changes of which, and not on its absolute magnitude, the induction current depends, occurred to Faraday at an early stage of his researches^[1]. He observed that the secondary circuit, when at rest in an electromagnetic field which remains of constant intensity, does not shew any electrical effect, whereas, if the same state of the field had been suddenly produced, there would have been a current. Again, if the primary circuit is removed from the field, or the magnetic forces abolished, there is a current of the opposite kind. He therefore recognised in the secondary circuit, when in the electromagnetic field, a 'peculiar electrical condition of matter,' to which he gave the name of the Electrotonic State. He afterwards found that he could dispense with this idea by means of considerations founded on the lines of magnetic force^[2], but even in his latest researches^[3], he says, 'Again and again the idea of an electrotonic state^[4] has been forced upon my mind.'

The whole history of this idea in the mind of Faraday, as shewn in his published researches, is well worthy of study. By a course of experiments, guided by intense application of thought, but without the aid of mathematical calculations, he was led to recognise the existence of something which we now know to be a mathematical quantity, and which may even be called the fundamental

1. Exp. Res., series i. 60.
2. Ib., series ii. (242).
3. Ib., 3269.
4. Ib., 60, 1114, 1661, 1729, 1733.