104 ANNUAL OF SCIENTIFIC DISCOVERY. 



the velocity of starting seven times, we should raise the weight to 

 forty-nine times the height, or to an elevation of seven hundred and 

 eighty-four feet. 



Now, the work done, or, as it is sometimes called, the mechanical 

 effect, as before explained, is proportional to the height, and as a 

 double velocity gives four times the height, a treble velocity nine 

 times the height, and so on, it is perfectly plain that the mechanical 

 effect increases as the square of the velocity. If the mass of the 

 body be represented by the letter m, and its velocity by v, then the 

 mechanical effect would be represented by m v 2 . In the case consid- 

 ered, I have supposed the weight to be cast upward, being opposed in 

 its upward flight by the resistance of gravity ; but the same holds 

 true if I send the projectile into water, mud, earth, timber, or other 

 resisting material. If, for example, you double the velocity of a 

 cannon ball, you quadruple its mechanical effect. Hence the impor- 

 tance of augmenting the velocity of a projectile. 



The measure then of mechanical effect is the mass of the body 

 multiplied by the square of its velocity. 



Now, in firing a ball against a target, the projectile, after collision, 

 is often found hissing hot. Mr. Fairbairn informs me that in the 

 experiments at Shoeburyness it is a common thing to see a flash of 

 light, even in broad day, when the ball strikes the target. And if I 

 examine my lead weight after it has fallen from a height, I also find 

 it heated. Now, here experiment and reasoning lead us to the 

 remarkable law that the amount of heat generated, like the mechan- 

 ical effect, is proportional to the product of the mass into the square 

 of the velocity. Double your mass, other things being equal, and 

 you double your amount of heat ; double your velocity, other things 

 remaining equal, and you quadruple your amount of heat. Here, 

 then, we have common mechanical motion destroyed and heat pro- 

 duced. I take this violin bow and draw it across this string. You 

 hear the sound. That sound is due to motion imparted to the air, and 

 to produce that motion a certain portion of the muscular force of my 

 arm must be expended. We may here correctly say that the me- 

 chanical force of my arm is converted into music. And in a similar 

 way we say that the impeded motion of our descending weight, or 

 of the arrested cannon ball, is converted into heat. The mode of 

 motion changes, but it still continues motion ; the motion of the mass 

 is converted into a motion of the atoms of the mass, and these small 

 motions communicated to the nerves produce the sensation which we 

 call heat. We, moreover, know the amount of heat which a given 

 amount of mechanical force can develop. Thus, for example, the 

 force of a leaden ball falling sixteen feet is sufficient, if suddenly 

 arrested, to raise its temperature three-fifths of a degree Fahrenheit. 

 Its velocity, when arrested, at the end of the sixteen feet, was at the 

 rate of thirty-two feet a second ; but a rifle bullet has at least forty 

 times the velocity of a body falling for one second ; hence, when sud- 

 denly arrested, as by an iron target, the heat generated, provided it 

 could be concentrated in the bullet, would raise its temperature to 

 about nine hundred and sixty degrees, sufficient to melt the lead. 

 In reality, however, the heat developed is divided between the lead 

 and the body against which it strikes ; nevertheless, it would be worth 



