186 On the Dynamical Theory of Deep-sea Tides. 



as we obtained from friction. That is, friction without perma- 

 nent current does act, as Sir W. Thomson's calculations presup- 

 pose, simply as a conductor of the external force*. 



I do not suppose friction really acts as here supposed, or that 

 the theory of the equatorial tide with friction is perfect. But 

 it does seem clear to me that the moving force of friction at the 

 bottom, if its accelerating force there be proportional to the velo- 

 city, must be in proportion to the mass above (as it is in solid 

 friction) ; it produces the retardation at the bottom against the 

 opposing friction of the faster-moving layers of water above it, 

 and must be greater in proportion to the greater number of those 

 layers. I think, therefore, there must be some effect of what 

 one may call clinging friction, whether there be any current fric- 

 tion or not. 



But any argument tending to show a predominating current 

 tends to show that it is subject to a force which is increasing 

 it; so that Mayer is quite right in looking out for visible effects, 

 however infinitesimally small the cause. And then, taking the 

 existence of a preponderance of eastward protuberances of ascer- 

 tained magnitude and position as a datum, the more the current 

 the less the total effect on the rotation of the solid earth. For 

 the law of the conservation of areas cannot be affected by inter* 

 nal friction ; and the moon's motion round the centre of gravity 

 of the system depends solely on the shape, in nowise on the cur- 

 rents, of the earth's surface. Therefore, if the water is slacken- 

 ing in its eastward motion, the solid earth is not slackening so 

 much as the calculation founded on the shape would bring out. 



There still remains a question which I wish some astrono- 

 mer would work out. Will this action go on at such a rate as 

 ever to reach the limit of a coincidence of the day and the side- 

 real month ? or will it, with whatever fluctuations, on the whole 

 get less and less, so as never to reach some definite limit ? If 

 one might assume that the moon's orbit would remain (looking 

 only to the luni-terrestrial system) nearly circular, a relative esti- 

 mate of the various changes in the whole system (moon's dis- 

 tance, length of day, magnitude of tide, and change of figure of 

 the earth) might be made, though perhaps not of the time it 

 would take to arrive at any given stage. 



* He has obtained a numerical result assuming the elevation (c) to be 

 1 foot, which is about what the formula (K) would give for a sea between 



7T 



3 and 4 miles deep at the equator. But he assumes S = j, which is the 



greatest purchase the moon's force can have, and which, by analogy, pro- 

 bably belongs to a sea in which l—h, or about 7 miles. But we seem a 

 long way from the state of knowledge in which numerical estimates can be 

 of much value. 



