on the Motion of the Moon. 109 



is evident that the beat generated by friction in the rising of the 

 water to form the wave before the moon's meridian is reached is 

 as truly at the expense of the earth's rotation as the heat gene- 

 rated after the meridian is passed. 



Suppose that in the rising of a given mass of water in the 

 formation of the wave, a unit of heat, 1390 foot-pounds, is gene- 

 rated and dissipated into space before the water passes the 

 moon's meridian. The question suggests itself, where has this 

 1390 foot-pounds of energy come from ? The only answer that 

 we can give is that it conies from the vis viva of rotation. In 

 my former paper I showed that the rising of the water to form 

 the wave tends to diminish the vis viva of rotation, and that the 

 vis viva thus lost is completely restored as the water descends to 

 its original level. But if any heat be generated during the 

 rising and falling of the water, the vis viva will not be wholly 

 restored. If, for example, 1390 foot-pounds of energy in the 

 form of heat be generated by the friction of the water as it rises 

 and falls, then the water on reaching its original level will owe 

 to rotation 1390 foot-pounds of the energy borrowed as it as- 

 cended which it can never pay back. And hence the vis viva of 

 rotation must be diminished by that extent. 



The same result follows when mechanical work is performed 

 by the water as it ascends or descends if heat be generated. A 

 tide-mill, as Professor Tyndall remarks, tends to diminish the 

 rotation of the earth. 



The way in which the phenomena of the tides are usually 

 viewed has the effect of preventing the rationale of the process 

 from being clearly seen*. Take, for example, the lunar wave. 

 All physicists agree that it depends upon two causes, viz. the 

 attraction of the moon, and the centrifugal force of the earth's 

 motion around the common centre of gravity of the earth and 

 moon. But practically, however, in explaining the phenomena 

 the kinetic element is almost entirely overlooked, and an undue 

 prominence is given to the static element. It is well known, for 

 example, that students have a considerable difficulty in under- 

 standing how the water can rise on the side furthest from the 

 moon. But no possible difficulty could be felt if the student 

 was shown (what in theory is admitted) that the rise of the water 

 at that place is a necessary result of the centrifugal force of the 

 earth's motion around the common centre of gravity, that being 

 the point furthest from the centre of rotation. By viewing the 

 phenomena from the kinetic stand- point instead of the static, 

 new light is cast upon the subject. We can then, as has been 

 shown t, perceive how it is that heat generated by friction as the 



* Phil. Mag. for April 1864, p. 286. 

 t Ibid. pp. 289, 290. 



