290, 291] THE EARTH AS A TIME-KEEPER. 369 



So long as the time measuring process is the rotation of the 

 Earth relative to the stars, the question whether the length of 

 the day is liable to change is meaningless. Now it has been 

 stated by astronomers that the day is increasing in length, or 

 that, in long past ages, the angular velocity of the Earth was 

 sensibly greater than it is now. This statement should imply 

 that there is some other process for measuring time than the 

 rotation of the Earth, and that at one time less of this process 

 would have taken place while the Earth turned through four 

 right angles than would be the case now. It might be meant, 

 for example, that such a process is the vibration of the lumin- 

 iferous medium in transmitting a certain kind of light, and that a 

 particular measurable interval is the period of such a vibration, 

 and then the statement would be that the number of such periods 

 in a day is increasing. In such a form however the statement 

 would be quite unverifiable. Again, it might be meant by the 

 statement (that the length of the day is increasing) that time 

 measured by a function of sidereal time fulfils better than sidereal 

 time the requirements of the Law of Gravitation and the theory 

 of energy, and that this function has a positive second differential 

 coefficient with respect to sidereal time. 



Now it is quite conceivable that the change made in the 

 equations of motion of bodies of the solar system by changing 

 the independent variable from the number representing sidereal 

 time to a function of that number which varies very slowly, while 

 producing no change of importance in the mechanical description 

 of most of the motions of the solar system, might help to bring 

 some particular facts under the Law of Gravitation. In such a 

 case it would be simpler to say that time can be measured so 

 that the length of the day varies and the particular fact accords 

 with the law than to keep to the measurement of time by the 

 diurnal rotation and seek a formulation of the fact as an exception 

 to the application of the law. It is known that the existence of 

 one of the inequalities in the motion of the Moon can thus be 

 accounted for. 



Again, the Earth and Moon, with the fluid ocean on the Earth, 



form a system showing various internal relative motions, among 



which the tides are conspicuous. Such internal relative motions 



generally involve dissipation of energy in a system, for they do 



L. 24 



