It may also be considered as the sum of the very different accelerations represented by A D and D B, where A D is almost the opposite of A C. And it is clear that there is an immense variety of ways in which A B might be resolved into the sum of two accelerations.
After this tedious explanation, which I hope, in view of the extraordinary interest of the conception of force, may not have exhausted the reader's patience, we are prepared at last to state the grand fact which this conception embodies. This fact is that if the actual changes of motion which the different particles of bodies experience are each resolved in its appropriate way, each component acceleration is precisely such as is prescribed by a certain law of Nature, according to which bodies in the relative positions which the bodies in question actually have at the moment,[1] always receive certain accelerations, which, being compounded by geometrical addition, give the acceleration which the body actually experiences.
This is the only fact which the idea of force represents, and whoever will take the trouble clearly to apprehend what this fact is, perfectly comprehends what force is. Whether we ought to say that a force is an acceleration, or that it causes an acceleration, is a mere question of propriety of language, which has no more to do with our real meaning than the difference between the French idiom "Il fait froid" and its English equivalent "It is cold." Yet it is surprising to see how this simple affair has muddled men's minds. In how many profound treatises is not force spoken of as a "mysterious entity," which seems to be
- ↑ Possibly the velocities also have to be taken into account.
