Now this medium by absorbing energy sets movements going. And that movements do not neutralize one another—i.e., that movements in opposite directions do not mutually destroy one another—has this result, that a given amount of this absorption produces the greatest possible amount of motion. If motion came to a rest in any other way, more of this absorption by the ultimate medium would be needed. Hence, by a given amount of absorption in the ultimate medium the greatest possible amount of motion is produced. That is, the absorption of motion into the ultimate medium is a minimum, and the law of the conservation of energy is the expression of this being a minimum.
But here again a further remark is called for. We start by assuming energy to be an absolute existence. But why not assume this action on the part of the ultimate medium to be the real action, and consider the phenomena of motion and energy as the mode of its action.
What this action of the ultimate medium may be needs examination. All that we can say at present is that relatively to that which we call energy, the action of this medium is that of being acted on.
CHAPTER VI.
In the preceding, however, it must be remembered that this conception of an ultimate medium was merely a supposition to enable us to see and roughly map out the relations of the things we are investigating. Where we were really landed was in an infinite series—we were brought logically to the conception of an infinite series of media, one behind the other.
What does an infinite series indicate?
Let us turn to a region of thought where infinite series are familiar objects, and we can learn about them.
In algebra infinite series are common. Thus take series 1 - x²/2 + x⁴/4 and so on for ever. This is the attempt in algebra to represent a trigonometrical idea. In trigonometry it is expressed as cos. x. But in algebra it needs this infinite series.
In algebra infinite series occur when the object which it is wanted to represent in algebraical terms cannot be grasped by algebra. When there is no single term or set of them in algebra which will serve, the object is represented by means of an infinite series. Thus we may say that in any calculus, when the object to be treated of cannot be expressed in the terms of the calculus, it is represented by means of an infinite series.
Now, dealing with material considerations, going on in the calculus of matter, we have come to an infinite series. This indicates that we have gone as far as the material calculus will carry us. We have now to bring in an idea from a different quarter if we will simplify our expression.