472 NOTE ON SIR WILLIAM THOMSON'S CORRECTION. [58 



It should be remarked that every inland sea or detached sheet of 

 water on the globe has in the same way a set of five constants, peculiar 

 to itself, which enter into the expression of the height of the tide at any 

 time in that sheet of water. 



By taking such constants into account the formulae which apply to the 

 Oceanic tides are rendered equally applicable to the tides of such a sea 

 as the Caspian, which are thus theoretically shewn to be very small, as 

 they are known to be practically. 



In the work above cited reference is made to a passage in a memoir 

 by Sir William Thomson on the Rigidity of the Earth, published in the 

 Philosophical Transactions for 1862, as being the only one known to the 

 writers in which any consciousness is shewn that such a correction of the 

 ordinary equilibrium theory as that above mentioned is required. 



However just this remark may be in reference to modern writers on 

 the equilibrium theory, it is only fair to Bernoulli, the originator of the 

 equilibrium theory, to point out that in his prize essay on the Tides he 

 distinctly recognises the fact that when the sea is supposed to have only 

 a limited extent the rise and fall of its surface cannot be the same as 

 if the Earth were entirely covered by it. In particular, he shews that the 

 Tides are so much the smaller as the sea has less extent in longitude, 

 and thus explains why they are altogether insensible in the Caspian and 

 in the Black Sea and very small in the Mediterranean, of which the com- 

 munication with the Ocean is almost entirely cut off at the Straits of 

 Gibraltar (see Bernoulli, Traite sur le Flux et Reflux de la Mer, Chap. XL 

 sect. ii.). It may be as well to mention that this treatise of Bernoulli, as 

 well as the dissertations of Maclaurin and Euler on the same subject, is 

 published in the 3rd volume of the Jesuit's edition of Newton's Principia 

 and also appears in the Glasgow reprint of that edition. 



