Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/186

 These spheres intersect in the circle which cuts the plane of the paper in $$D$$ and $$D'$$, so that $$B$$ is the centre of this circle and its radius is 12. This circle is an example of a line of equilibrium, for the resultant force vanishes at every point of this line.

If we suppose the sphere whose centre is $$A$$ to be a conductor with a charge of 3 units of positive electricity, and placed under the influence of 20 units of positive electricity at $$C$$, the state of the case will be represented by the diagram if we leave out all the lines within the sphere $$A$$. The part of this spherical surface within the small circle $$DD'$$ will be negatively electrified by the influence of $$C$$. All the rest of the sphere will be positively electrified, and the small circle $$DD'$$ itself will be a line of no electrification.

We may also consider the diagram to represent the electrification of the sphere whose centre is $$C$$, charged with 8 units of positive electricity, and influenced by 15 units of positive electricity placed at $$A$$.

The diagram may also be taken to represent the case of a conductor whose surface consists of the larger segments of the two spheres meeting in $$DD'$$, charged with 23 units of positive electricity.

We shall return to the consideration of this diagram as an illustration of Thomson’s Theory of Electrical Images. See Art. 168.

122.] I am anxious that these diagrams should be studied as illustrations of the language of Faraday in speaking of ‚lines of force,‘ the ‚forces of an electrified body‘, &c.

In strict mathematical language the word Force is used to signify the supposed cause of the tendency which a material body is found to have towards alteration in its state of rest or motion. It is indifferent whether we speak of this observed tendency or of its immediate cause, since the cause is simply inferred from the effect, and has no other evidence to support it.

Since, however, we are ourselves in the practice of directing the motion of our own bodies, and of moving other things in this way, we have acquired a copious store of remembered sensations relating to these actions, and therefore our ideas of force are connected in our minds with ideas of conscious power, of exertion, and of fatigue, and of overcoming or yielding to pressure. These ideas, which give a colouring and vividness to the purely abstract idea of force, do not in mathematically trained minds lead to any practical error.

But in the vulgar language of the time when dynamical science was unknown, all the words relating to exertion, such as force,