108 Mr. J. Croll on the Influence of the Tidal Wave 



The Astronomer Royal, in an elaborate paper read before the 

 Astronomical Society in April last, arrives at the following con- 

 clusions of an opposite character : — 



(1) That the effect of friction is to accelerate the time of each 

 individual tide, 



(2) That friction does not retard the earth's rotation. 



(3) That it is a further result of this friction and the conse- 

 quent disturbance of the form of the waters that the moon's 

 motion is affected; her orbit is made to become large, and her 

 motion in longitude is retarded. 



It may be stated that the latter conclusion was arrived at a 

 year or two ago by Professor W. Thomson*. In regard to the 

 second conclusion, the Astronomer Royal, in a note appended to 

 his paper, says that he has at length discovered two terms which 

 appear to exercise a real effect on the rotation of the earth. 

 "There is," he says, "a constant acceleration of the waters as 

 following the moon's apparent diurnal course. As this is oppo- 

 site to the direction of the earth's rotation, it follows that from 

 the action of the moon there is a constant retarding force on the 

 rotation of the water, and therefore (by virtue of the friction 

 between them) a constant retarding force on the rotation of the 

 earth's nucleusf. 



In a paper published in the Philosophical Magazine for April 

 1864, I showed that the solar wave retards the motion of the 

 earth around the common centre of gravity of the earth and 

 moon in precisely the same way as the lunar wave retards the 

 motion of the earth around the earth's centre of gravity; 

 and that as the vis viva of the earth's motion around the com- 

 mon centre of gravity of the earth and moon is being gradually 

 converted into heat by the friction of the solar wave and dissi- 

 pated into space, the earth must therefore be continually ap- 

 proaching nearer to the moon. The moon being thus moving 

 in an orbit which is gradually becoming less and less, its period 

 of revolution must also be diminishing. Or, in other words, 

 there is an actual acceleration of the moon's angular motion. 



The reason which has prevented this important consequence 

 from being recognized is no doubt the way in which the question 

 is at present viewed by physicists in general. They still continue 

 to view the influence of the wave in the way in which it first 

 suggested itself to the mind of Mayer. They consider with him 

 that the whole retarding effect is due to the attraction of the 

 moon pulling the wave back to the moon's meridian against the 

 motion of rotation. This, however, is only a part of the effect. 

 The question must be viewed under a more general form ; for it 



* Phil. Mag. for April 1864, p. 293. 



t Monthly Notices of the Royal Astronomical Society, April 1866, p. 235. 



