Professor Tyndall's Lectures on Force and on Heat. 535 



earth's rotation) are unaffected by the fluctuations and friction 

 of the tides. But I will not take upon myself to say their proofs 

 are conclusive; and indeed my impression is that all Laplace 

 means is that the difference, if any, is of an order that may be 

 neglected in comparison with the disturbances he takes account 

 of. The following considerations, which have suggested them- 

 selves, or partly have been suggested to me on this subject, are 

 only added in the hopes of eliciting some remarks from one or 

 other of the accomplished mathematicians who write in this 

 Magazine. 



If m be the mass of the moon, r its distance, and -sj its angular 

 velocity (both projected on the equatorial plane), MK 2 the mo- 

 ment of inertia of the earth and sea taken in its instantaneous 

 shape, to its angular velocity ; and if P be taken to represent 

 twice the sum of the products of each molecule of the sea by the 

 square of its distance from the polar axis and by its relative velo- 

 city eastward ; we shall have, from age to age, by the principle of 

 the conservation of areas, 



mr 2 -57 + MK 2 o> -f P = a constant quantity. 



P is an extremely small quantity compared with the other terms; 

 and MK 2 , though it may vary, must do so within narrow limits. 

 If therefore r 2 cr, or the area described by the moon in a second, 

 vary much, it must be "at the expense of" cd, the earth's velocity 

 of rotation. 



Now it seems very precarious to assume as a permanent law 

 of nature, or even as an established existing fact, that the confi- 

 guration of the ocean under tidal influence may be even roughly 

 likened, as to its attraction on the moon, to a prolate spheroid. 

 A glance at a tide-map will show but little outward resemblance 

 to this figure ; and as to theory, the Astronomer Royal warns us 

 (p. 285) that " the amount of elevation of the water depends in 

 a remarkable degree upon other circumstances than the magni- 

 tude of the forces In two parallel canals of different depths 



acted on by precisely the same forces, there might be high water 

 in one when there was low water in the adjacent part of the 

 other : or there might be elevations and depressions at the same 

 time in both, but their magnitudes might bear any proportions 

 whatever." 



But if this common representation has so much substantial 

 truth as to justify us in assuming two wave-crests exactly anti- 

 podal to each other, and either equal in elevation or the nearest 

 to the moon not less than the other, we should then have an ex- 

 ceedingly small tangential force (being the difference of two small 

 attractions multiplied by the sines of two small and nearly equal 

 angles) in the direction of the moon's motion ; and this would 



