Prof. Tyndall on Force. 59 



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

 the mechanical effect would be represented by mv 2 . 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 augmenting the velocity of a projectile, and hence 

 the philosophy of Sir William Armstrong in using a 50 lb. 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 

 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 mecha- 

 nical 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 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 certain portion of the mus- 

 cular 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 descend- 

 ing 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 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 : multiplying J-ths by the square of 40, we find that the 

 amount of heat developed 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 ; nevertheless 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, 

 the speaker passed to the motion of atoms towards each other by 



