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, p, &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 
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 
