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18 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.

Now, it is well known to those who have studied the laws of motion, that a body, shot upwards with the velocity of 9.8 metres in one second, will be brought to rest when it has risen 4.9 metres in height. If, therefore, it be a kilogramme, its upward velocity will have enabled it to raise itself 4.9 metres in height against the force of gravity, or, in other words, it will have done 4.9 units of work; and we may imagine it, when at the top of its ascent, and just about to turn, caught in the hand and lodged on the top of a house, instead of being allowed to fall again to the ground. We are, therefore, entitled to say that a kilogramme, shot upwards with the velocity of 9.8 metres per second, has energy equal to 4.9, inasmuch as it can raise itself 4.9 metres in height.

27. Let us next suppose that the velocity with which the kilogramme is shot upwards is that of 19.6 metres per second. It is known to all who have studied dynamics that the kilogramme will now mount not only twice, but four times as high as it did in the last instance—in other words, it will now mount 19.6 metres in height.

Evidently, then, in accordance with our principles of