of a Finite Conservative System. 381 



when the pendulum is at one end of its range. The clock 

 instantly begins to go forward ; and goes on retracing every 

 step, and repeating every one of the numerous impacts, of its 

 first forward motion ; till the weight strikes the bottom exactly 

 when each of the sixty balls is striking its field-stop, and 

 when the pendulum is at one end of its range, the same end 

 of its range as when the weight struck the bottom the first 

 time. Thus a perfectly periodic motion goes on for ever. 



16. During any of the half-periods in which the clock is 

 going forward, and the weight running down, any moderate 

 disturbance, such as a slight blow on the pendulum, or a 

 holding of the escapement-wheel stopped for some time, large 

 or small, will make no noticeable difference in the subsequent 

 motion : till the weight readies the bottom of its range, when 

 we find that the periodicity is lost, and the state of things 

 described in §§ 13, 14 supervenes. But any such disturbance 

 during a half-period when the clock is going backwards causes 

 the backward motion to cease and regular forward motion to 

 follow, immediately, or after a few beats, a greater or less 

 number according as the disturbance is exceedingly infini- 

 tesimal or but moderately small. This is a true dynamical 

 illustration of the " dissipation of energy," and helps to show 

 the vanity of attempts which have been made to found 

 " Carnot's Principle," or " the Second Law of Thermo- 

 dynamics," or theories of chemical action, on Lagrange's 

 generalized equations of motion. 



17. Consider the "problem of the three bodies," in two 

 varieties ; first " the Lunar Theory," secondly " the Planetary 

 Theory." One body (the Sun) is in each case vastly larger 

 than either of the two others. In the first case the two others 

 (the Earth and Moon) are so near one another in comparison 

 with the Suirs distance from either that his force produces 

 but a small disturbance of the relative motion of the Earth 

 and Moon under their own mutual attraction. In the second 

 case, two planets move each chiefly under the Sun's influence 

 with comparatively small disturbance by their own mutual 

 attraction. In each case we shall, for simplicity, neglect the 

 motion of the Sun's centre of gravity, and consider him as an 

 absolutely fixed " centre of force."" 



18. Taking first the lunar theory, suppose the centre of 

 gravity, I, of Earth and Moon to move very approximately in 

 a circle round the Sun. Now (without necessarily considering 

 that the Moon is much smaller than the Earth) at an instant 

 when the line M I E passes through S give equal and opposite 

 momentums to M and E in the line M E so as to annul their 

 relative motion in this line if they had any, and to cause each 



