1862.] on Force. 529 



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

 cal effect would be represented by m v*. In the case considered, 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 importance of aug- 

 menting the velocity of a projectile, and hence the philosophy of 

 Sir William Armstrong in using a 501b. charge of powder in his 

 recent striking experiments. 



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 experi- 

 ments 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 mechanical effect, is pro- 

 portional 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 produced. 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 cer- 

 tain portion of the muscular force of my arm must be expended. We 

 may here correctly say, that the mechanical force of my arm is converted 

 into music. And in a similar way we say that the impeded motion of our 

 descendingweight,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 cadi heat. We, moreover, know the amount of heat which a 

 given amount of mechanical force can develope. Our lead ball, for 

 example, in falling to the earth generated a quantity of heat sufficient 

 to raise the temperature of its own mass three-fifths of a Fahrenheit 

 degree. It reached the earth with a velocity of 32 feet a second, and 

 forty times this velocity would be a small one for a rifle bullet ; multi- 

 plying l^ths by the square of 40, we find that the amount of heat de- 

 veloped by collision with the target would, if wholly concentrated in 

 the lead, raise its temperature 960 degrees. This would be more than 

 sufficient to fuse the lead. In reality, however, the heat developed is 

 divided between the lead and the body against which it strikes ; never- 

 theless, it would be worth while to pay attention to this point and to 

 ascertain whether rifle bullets do not, under some circumstances, show 

 signs of fusion. 



From the motion of sensible masses, by gravity and other means, 



