Professor TyndaVs Lecture on Force. 243 



Now the work done — or, as it is sometimes called the mechan- 

 ical 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 eflfect 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 eflfect would be represented by wv^. 

 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 eflfect. Hence the importance of augmentine the 

 velocity of a projectile, and hence the philosophy of Sir William 

 Armstrong in using a 50 pound charge of powder in his recent 

 striking experiments. 



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

 multiplied by the square of its velocity. 



Now, in firing a ball against a target, the projectile, after col- 

 lision, is often found hissing hot. Mr. Fairbairn informs me that 

 in the experiments at Shoeburyness it is a common thino- to see 

 a flash of light, even in broad day, when the ball strikes the tar- 

 get. And if I examine my lead weight after it has fallen from a 

 height, I also find it heated. Now, here experiment and reason- 

 ing lead us to the remarkable law that the amount of heat gen- 

 erated, like the mechanical eflfect, 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 qua- 

 druple your amount of heat. Here then we have common me- 

 chanical motion destroyed and heat produced. I take this Wolin 

 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. ^Ye 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 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 



