436 Prof. Thomson 07i the Dynamical Theory of Heat. 



Let an infinite number of bars of the first set be laid on a plane 

 parallel to one another, with 

 intervals between every two 

 in order, equal to the breadth 

 of each. Lay perpendicularly 

 across them an infinite num- 

 ber of bars of the second system 

 similarly disposed relatively to 

 one another; place on these 

 again bars of the first system, 

 constituting another layer si- 

 milar and parallel to the first; 

 on this, again, a layer similar 

 and parallel to the second; and 

 so on till the thickness of the 

 superimposed layers is equal to 

 the length of each bar. Then let an infinite number of the bars of 

 the third system be taken and pushed into the square prismatic 

 apertures perpendicular to the plane of the layers ; the cubical 

 hollows which are left (not visible in the diagram) being previously 

 filled up with insulating matter, such as that used in the composi- 

 tion of the bars. Let the complex solid cube thus formed be coated 

 round its sides with infinitely thin connected sheets of the stand- 

 ard metal, so thin that the resistance to the conduction of elec- 

 tricity along them is infinitely great, compared to the resistance 

 to conduction experienced by a current traversing the interior of 

 the cube by the zigzag linear conductors imbedded in it, (For 

 instance, we may suppose the resistance of four parallel sides of 

 the cube to be as great as, or greater than, the resistance of each 

 one of the zigzag linear conductors.) Let an infinite number of 

 such cubes be built together, with their structural directions pre- 

 served parallel, so as to form a solid, which, taken on a large 

 scale, shall be homogeneous. A rectangular parallelopiped, ahc, 

 of such a solid, with its sides parallel to the sides of the elemen- 

 tary cubes, will present exactly the thermo-electric phsenomena 

 expressed above by the equations (31) nnd (32), provided the 



thermo-electric powers ot,, 



'1 J 



', and 



OT3, ■073', 3t"3, CTg'" of the metals used in the three systems fulfil 

 the following conditions : — 



i(t!r, + ^/ + <' + <") = ^, 

 i(^,-^/) = 6', l(^/'-^/") = ^", 



i (^2 + W + OTg" + W") = (/>, 



i(^2-0 =</>', i«-<')=0". 



\ 





(33). 



