Prof. Thomson on the Dynamical Theory of Heat. 435 



suitable to the ch-cumstauces. It might be doubted, indeed, 

 whether these nine coefficients can be perfectly independent of 

 one another ; and indeed it might appear very probable that they 

 are essentially reducible to six independent coefficients, from the 

 extraordinary nature of certain conclusions which we shall show 

 can only be obviated by supposing 



& = ^", 6"=f, and (/)'=A/r". 



Before going on to investigate any consequences from the unre- 

 stricted fundamental equations, I shall prove that it is worth 

 while to do so, by demonstrating that a metallic structure may 

 be actually made, which, when treated on a large scale as a con- 

 tinuous solid, according to the electric and thermal conditions 

 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 equa- 

 tions with nine arbitrarily prescribed values for the coefficients 

 e, 4>, &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 different metals, forming right 

 angles at the successive junctions, be placed in perpendicular 

 planes, and not touching one another at any point, but with a 

 common straight line joining the points of bisection of the small 



straight parts of each conductor. Let an insulating substance 

 be moulded round them so as to form a solid bar of square sec- 

 tion, just containing the two zigzags imbedded in it in planes 

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

 of electi'icity, 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 elec- 

 tric 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 chfi'erent 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 conduction. 



