Notes A and B

The statement here should have been more explicit, as it has reference to a state of things not to be realised in practice. Like the well-known “first law of motion,⁵³ it can neither be demonstrated à priori, nor proved by any direct and simple experiment. The first law of motion asserts that a body in motion, not acted on by any external force, will continue to move in a straight line, and with a uniform velocity. Now we cannot place a body in such a position that it will not be acted upon by some external forces; but the more we lessen the effect of external forces, the more nearly is the motion straight and uniform. Similarly in the case supposed, the intention is to show that the weight carried up is in a position to do just as much work as was done upon it. We must suppose several impracticable but conceivable conditions in order to eliminate considerations which do not concern the theoretical question; w^re must suppose the cord to be weightless and absolutely devoid of rigidity; the pulley to have no mass or inertia, that is to require no force to set it in motion, and to move without any friction \ the air to offer no resistance; and the force of gravity to be uniform throughout the space. Some approximation to these conditions is practicable, as, for example, the pulley might be the lightest possible, and turn on friction wheels, the cord might be the finest silk thread, and so on. But it is not the influence of these external forces we are considering, but only the energy due to the position of the raised weight. Assuming, therefore, the disturbing conditions absolutely eliminated, it is not difficult to see that no downward force or pressure, however small, could be applied for ever so short a time, to the upper weig’ht without setting the system in motion. The motion would be an accelerated one so long as the force was applied, it would become uniform when the force ceased to act; it would have a velocity proportionate to the force. In any case, after a time the descending weight would reach the ground, and for our point of view it is quite immaterial whether the time occupied by the movement were 5 minutes or 5,000 years, for be it observed, time does not enter into the definition of work as it does into that of “ horse-power.” Then by pushing the conceived conditions to their limits, we may see that without considering any question of conversion of motion into heat, the raised weight can, in theory at least, give back again the energy spent upon it.