xx.J METHOD OF VARIATIONS. 455 



half minute will be neutralised 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 in- 

 crease and decrease the vibrations of the first, so that a 

 new kind of vibration will be produced running through 

 its phases in 61 seconds. An effect of this kind was 

 actually observed by Ellicott, a member of the Eoyal 

 Society, in the case of two clocks. 1 He found that 

 through the wood-work by which the clocks were con- 

 nected a slight impulse was transmitted, and each pen- 

 dulum alternately lost and gained momentum. Each 

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

 and in the intermediate times to be stopped by the other. 

 Many 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, however slight, will be 

 accumulated, and a disturbance of large ultimate amount 

 and of long period will be produced. The long inequality 

 in the motions of Jupitei <md Saturn is thus due to the 

 fact that five times the mean motion of Saturn is very 

 nearly equal to twice the mean motion of Jupiter, causing 

 a coincidence in their relative positions and disturbing 

 powers. The rolling of ships depends mainly upon the 

 question whether the period of vibration of the ship 

 corresponds or not with the intervals at which the waves 

 strike her. Much which seems at first sight unaccount- 

 able in the behaviour of vessels is thus explained, and the 

 loss of the Captain is a sad case in point. 



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



