24. In the next place, it is very obvious that if we raise the kilogramme two metres in height, we do two units of work--if three metres, three units, and so on. And again, it is equally obvious that if we raise a weight of two kilogrammes one metre high, we likewise do two units of work, while if we raise it two metres high, we do four units, and so on. From these examples we are entitled to derive the following rule:--_Multiply the weight raised (in kilogrammes) by the vertical height (in metres) through which it is raised, and the result will be the work done (in kilogrammetres)._ _Relation between Velocity and Energy._ 25. Having thus laid a numerical foundation for our superstructure, let us next proceed to investigate the relation between velocity and energy. But first let us say a few words about velocity. This is one of the few cases in which everyday experience will aid, rather than hinder, us in our scientific conception. Indeed, we have constantly before us the example of bodies moving with variable velocities. Thus a railway train is approaching a station and is just beginning to slacken its pace. When we begin to observe, it is moving at the rate of forty miles an hour. A minute afterwards it is moving at the rate of twenty miles only, and a minute after that it is at rest. For no two consecutive moments has this train continued to move at the same rate, and yet we may say, with perfect propriety, that at such a moment the train was moving, say, at the rate of thirty miles an hour. We mean, of course, that had it continued to move for an hour with the speed which it had when we made the observation, it would have gone over thirty miles. We know that, as a matter of fact, it did not move for two seconds at that rate, but this is of no consequence, and hardly at all interferes with our mental grasp of the problem, so accustomed are we all to cases of variable velocity. 26. Let us now imagine a kilogramme weight to be shot vertically upwards, with a certain initial velocity--let us say, with the velocity of 9·8 metres in one second. Gravity will, of course, act against the weight, and continually diminish its upward speed, just as in the railway train the break was constantly reducing the velocity. But yet it is very easy to see what is meant by an initial velocity of 9·8 metres per second; it means that if gravity did not interfere, and if the air did not resist, and, in fine, if no external influence of any kind were allowed to act upon the ascending mass, it would be found to move over 9·8 metres in one second.