1870.] BARKER— ON VITAL AND PHYSICAL FORCES. 433 



5 Rankine, W. J. M., Philosophical Magazine, Feb. 1853. Also 

 Edinburgh PhilosophicalJournal, July, 1855, 



6 Armstrong, Sir TTm. In his address as President of the British 

 Association for the Advancement of Science. Kep. Brit. Assoc, 1863, li. 



7 Grove, W. R., in 1842. Compare " ]N'ature" i, 335, Jan. 27, 1870. 

 Also Appleton's Journal, iii, 324, March 19, 1870. 



8 Id., in Preface to The Correlation of Physical Forces, 4th ed. Re- 

 printed in the Correlation and Conservation of Forces ; edited by E. L. 

 Youmans, p. 7. New York, 1805, D. Appleton & Co. 



9 Id., ib.. Am. ed., p., 33 et seq. 



10 Joule, J. P., Philosophical Transactions, 1850, p. 01. 



1 1 See American Journal of Science, II, xxxvii, 290, 1804. 



12 The work {W) done by a moving body is commonly expressed by 

 the formula W=MV^ in which M, or the mass of the body, is equal to 



w 



— ; i. e., to the weight divided bv twice the intensity of gravity. The 

 2g " IX (1100)'' 



work done by our cannon-ball then, would be =9,404" 14 foot- 



2X64^ 



tons. If, further, we assume the resisting body to be of such a character 



as to bring the ball to rest in moving i of an inch, then the final pressure 



would be 9,404-14x 12X4=451,3987 tons. But since, "in the case of a 



perfectly elastic body, or of a resistance proportional to the advance of the 



centre of gravity of the impinging body from the point at which contact 



first takes place, the final pressure (provided the body struck is 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 (451,3987 X2)=902,797 tons as the 



crushing pressure of the ball under these conditions. [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.] 



13 The unit of impact being that given by a body weighing one pound 

 and moving one loot a second, the impact of such a body falling from a 

 height of 772 feet— the velocity acquired being 222i feet per second 

 (= V 2s^)— would be 1 X (222^)2 =49,408 units, the equivalent in impact 

 of one heat-unit. A cannon ball weighing 1000 lbs. and moving 1100 

 feet a second would have an impact of (1100)2X1000=1,210,000,000 

 units, Dividing this by 49,408, the quotient is 24489 heat-units, the 

 epuivalent of the impact. The specific heat of iron being 1138, this 

 amount of heat would raise the temperature of one pound of iron 215,- 

 19rF., (24,489 X -1138) or of 1000 pounds of iron 215° F. 24489 pounds 

 of water heated one degree, is equal to 136J pounds, or 17 gallons U. 

 S., heated 180 degrees ; i. e., from 32° to 212^ F. 



14 Assuming the density of the earth to be 5-5, its weight would be 

 6,500,000,000,000,000,000,000 tons, and its impact— by the formula given 

 above — would be 1 ,025.000,000,000,000,000,000,000,000,000 foot-tons. 



