70 THE PRINCIPLES OF SCIENCE. 



with its vibrations, the energy of those vibrations will be 

 unlimited, and may fracture any body. 



Let us now consider what will happen if the strokes be 

 not exactly at the same intervals as the vibrations of the 

 body, but, say, a very little slower. Then a succession of 

 strokes will meet the body in nearly but not quite the 

 same position, and their effects will be accumulated. 

 Afterwards the strokes will begin to fall when the body 

 is in the opposite phase. Thus imagine that one pen 

 dulum moving exactly from one extreme point to another 

 in a second, should be struck by another pendulum which 

 makes 61 beats in a minute ; then, if the pendulums 

 commence together, they will at the end of 30^ beats be 

 moving in opposite directions. Hence whatever energy 

 was communicated in the first half minute will be neutra 

 lized by the opposite effect of that given in the second 

 half. The effect of the strokes of the second pendulum 

 will therefore be alternately to increase and decrease the 

 vibrations of the first, so that a new kind of vibration will 

 be produced running through all its phases in 61 seconds. 

 An effect of this kind was actually observed by Ellicott, 

 a member of the Royal Society, in the case of two clocks y. 

 He found- that through the wood- work by which the 

 clocks were connected a slight impulse was transmitted, 

 and each pendulum alternately lost and gained momentum. 

 Each clock, in fact, tended to stop the other at regular in 

 tervals, and in the intermediate times to be stopped by 

 the other. Many of the most important disturbances in 

 the planetary system depend upon the same principle ; for 

 if one planet happens always to pull another in the same 

 direction in similar parts of their orbits, the effects, how 

 ever slight, will be accumulated, and a disturbance of large 

 ultimate amount and of long period will be produced. The 



y Philosophical Transactions (1739), vol. xli. p. 126. 



