Scientific Leciures. 287 



in temperature, knowing the distance tlirongh wliich the weights 

 have fallen, it is easy to calcnlate the quantity of heat which corres- 

 ponds to a given amount of motion. In this way, and as a mean of 

 a hxrge number of experiments, Mr. Joule found that the amount of 

 mass motion in a body weighing one pound, which had fallen from a 

 height of 772 feet, was exactly equal to the molecular motion which 

 must be added to a pound of water, in order to heat it one degree 

 Fahrenheit. If we call the actual energy of a body weighing one 

 pound which has fallen one foot, a foot pound, then we may speak of 

 the mechanical equivalent of heat as being 772 foot pounds. 



The significance and value of this numerical constant will appear 

 more clearly if we apply it to the solution of one or two simple 

 problems. During the recent war two immense iron guns were cast 

 in Pittsburgh, whose weight was nearly 112,000 pounds each, and 

 which had a caliber of twenty inches.* Upon this diagram is a 

 calculation of the effective blow which the solid shot of such a gun, 

 assuming its weight to be 1,000 pounds, and its velocity 1,100 feet per 

 second, would give; it is 902,797 tons ! f Now, if it were possible 

 to convert the whole of this enormous mechanical power into heat, 

 to how much would it correspond? This question may be answered 

 by the aid of the mechanical equivalent of lieat ; here is the calcula- 

 tion, from which we see that when seventeen gallons of ice cold water 

 are heated to the boiling point, as much energy is communicated as 

 is contained in the death-dealing missile at its highest velocity.:}; 



* See American Journal of Science, II., xxxvii., 296, 1864. 



t Thie work (W) done by a moving body iu commonly expressed by the formula W-=MV2, in which 



M, or the mass of the body, is equal to ^- ; i. <>., to the weight divided by twice the intensiity of 



ixnioo")2 

 Uravity. The work done by our cannon ball then would be --^ ; =-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 movinij 

 Ji' of an inch, then the flnal pressure would be 9,404. 14Xl-iX4=-4.51,;W8.7 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 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 (451.398.7X2) 9ii2,797 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. A. N. Skinner, for suggestions 

 on the relation of impact to statical pressure.] 



X The unit of impact being that given by a body weighing one pound and moving one foot a sec- 

 ond, the impact of such a body falling from a height of 772 feet— the velocity acquired being 222^^ 

 feet per second (— Z.^) would be 1X(2223^)"=49,408 units, the equivalent in impact of one heat unit. 

 A cannon hall weighing 1,000 pounds, and moving 1,100 feet a second, would have an impact of 

 (1100) X100=l,210,000,000 units. Dividing this by 49,408, the quotient is 24489 heat-uiiils, the equiva- 

 lent of the impact. The specific heat of iron being 'H.^S, this amount of heat wouM raise the tem- 

 perature of one pound of iron 215,191=' F. (24,489X-11S8) or of 1000 pounds of iron 215= F. 

 2448;t pounds of water heated one degree, is equal to 130;^ pounds, or 17 gallons U. S., heated 160= ; 

 i.e., from 32= to 212= F. 



