ABSTRACT
The first thing to be remembered is-what physicists now-a-days will scarcely deny-that force is a mathematical fiction, not a physical entity. The second point is that, in virtue of the philosophy of the calculus, acceleration is a mere mathematical limit, and does not itself express a definite state of an accelerated particle. It may be remembered that, in discussing derivatives, we inquired whether it was possible to regard them otherwise than as limits-whether, in fact, they could be treated as themselves fractions. This we found impossible. In this conclusion there was nothing new, but its application in Dynamics will yield much that is distinctly new. It has been customary to regard velocity and acceleration as physical facts, and thus to regard the laws of motion as connecting configuration and acceleration. This, however, as an ultimate account, is forbidden to us. It becomes necessary to seek a more integrated form for the laws of motion, and this form, as is evident, must be one connecting three configurations.
