Note 12 — The Correlation of Vital and Physical Forces.

The work (W) done by a moving body is commonly expressed by the formula W = MV2, in which M, or the mass of the body, is equal to w/2g; i.e., to the weight divided by twice the intensity of gravity. The work done by our cannon-ball then, would be (1 × (1100)2)/(2 × 64⅓) = 9,404·14 foot-tons. If, further, we assume the resisting body to be of such a character as to bring the ball to rest in moving ¼ of an inch, then the final pressure would be 9,404·14 × 12 × 4 = 451,398·7 tons. But since, “in the case of a perfectly elastic body, or of a resistance proportional to the advance of the center of gravity of the impinging body from the point at which contact first takes place, the final pressure (provided the body struck 67is perfectly rigid) is double what would occur were the stoppage to occur at the end of a corresponding advance against a uniform resistance,” this result must be multiplied by two; and we get (451,398·7 × 2) 902,797 tons as the crushing pressure of the ball under these conditions. Note: The author’s thanks are due to his friends Pres. F. A. P. Barnard and Mr. J. J. Skinner for suggestions on the relation of impact to statical pressure.