Prof. Thomson on the Dynamical Theory of Heat. 433 



be observed that probably the depth inferred from tidal intervals 

 and ages may be the depth of the sea at a greater distance from 

 the coast ; while the depth deduced from heights is the depth of 

 the sea after it has begun to shoal, the tide being composed 

 partly of a derivative and partly of the original Atlantic tide. 



Is it impossible, or improbable, that the result deduced from 

 times, viz. 11-65 miles, is the depth of the central channel of the 

 South Atlantic and of the Antarctic Oceans, while the depth 

 deduced from heights, viz. 5*12 miles, is the mean depth of 

 the whole Atlantic ? 



These and many other interesting questions suggest them- 

 selves, which I shall leave for the consideration of those concerned 

 in the mathematical theory of the tides. The separation of the 

 effects of the sun and moon in the diurnal tide, which has never 

 before been made, must prove of value in correcting the bases 

 on which the mathematical theories of the tides rest ; theories 

 which, notwithstanding the amount of mathematical genius ex- 

 ercised on them, must be considered as still in a most imperfect 

 and unsatisfactory condition. 



Trinity College, Dublin, 

 May 7, 1856. 



LV. On the Dynamical Theory of Heat.—Vavt VI. Thermo- 

 electric Currents. By William Thomson, M.A., Professor 

 of Natural Philosophy in the University of Glasgoio. 

 [Concluded from p. 388.] 



§§ 156-170. On the Thermal Effects and the Thermo-electric 

 Excitation of Electrical Currents in Homogeneous Crystalline 

 Solids. 

 156. rriHE Propositions I. and II., investigated above, sugges t 

 J- the kind of assumptions to be made regarding the 

 reversible thermal effects of currents in uniformly heated crystal- 

 line solids, and the electromotive forces induced by any thermal 

 circumstances which cause inequalities of temperature in different 

 parts. The formulse expressing these agencies in the particular 

 case which we have now investigated, guide us to the precise 

 forms required to express those assumptions in the most general 

 possible manner. 



157. Let us first suppose a rectangular parallelopiped {a, h, c) 

 of homogeneous crystalline conducting matter, completely sur- 

 rounded by continuous metal of the standard thermo-electric 

 quality touching it on all sides, to be traversed in any direction 

 by a uniform electric current, of which the intensity components 

 parallel to the three edges of the parallelopiped arc h, i, j, and to 



