DYNAMICAL THEORY OF HEAT. 



161 



tions specified for the substance with reference to which the equations (31) and 

 (32) have been applied, shall exhibit the precise electric and thermal properties 

 respectively expressed by those sets of equations with nine arbitrarily prescribed 

 values for the coefficients 6, cp> &c. 



159. Let two zigzag linear conductors of equal dimensions, each consisting of 

 infinitely short equal lengths of infinitely fine straight wire alternately of two dif- 

 ferent metals, forming right angles at the successive junctions, be placed in per- 

 pendicular planes, and touching one another at any point, but with a common 

 straight line joining the points of bisection of the small straight parts of each 



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conductor. Let an insulating substance be moulded round them, so as to form a 

 solid bar of square section, just containing the two zigzags imbedded in it in planes 

 parallel to its sides. Although this substance is a non-conductor of electricity, 

 we may suppose it to have enough of conducting power for heat, or the wires of 

 the electric conductors to be fine enough, that the conduction of heat through the 

 bar when it is unequally heated may be sensibly the same as if its substance were 

 homogeneous throughout, and, consequently, that the electric conductors take at 

 every point the temperatures which the bar would have at the same point if they 

 were removed. Let an infinite number of such bars, equal and similar, and of the 

 same substance, be constructed ; and let a second system of equal and similar bars 

 be constructed with zigzag conductors of different 

 metals from the former ; and a third with other 

 different metals : the sole condition imposed on the 

 different zigzag conductors being that the two in 

 each bar, and those in the bars of different systems, 

 exercise the same resistance against electric con- 

 duction. 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 number of bars of the second system similarly disposed relatively 

 to one another ; place on these again bars of the first system, constituting another 

 layer similar 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 



