DYNAMICAL THEORY OF HEAT. 147 
136. A very close analogy subsists between the thermo-dynamical circum- 
stances of an electrical current in a circuit of two metals, and those of a fluid 
circulating in a closed rectangular tube, consisting of two vertical branches con- 
nected by two horizontal branches. Thus if, by the application of electro-motive 
force in one case, or by the action of pistons in the other, a current be instituted, 
and if, at the same time, the temperature be kept uniform throughout the circuit, 
heat will be evolved and absorbed at the two junctions respectively in the former 
case, and heat will be evolved in one and absorbed in the other of vertical branches 
of the tube in the latter case, in consequence of the variations of pressure expe- 
rienced by the fluid in moving through those parts of the circuit. If the temperature 
of one junction of the electrical circuit be raised above that of the other, and if the 
temperature of one vertical branch of the tube containing fluid be raised above that 
of the other, a current will in each case be occasioned, without any other motive 
appliance. Ifthe current be directed to do work with all its energy, by means of 
an engine in each case, there will be a conversion of heat into mechanical effect, 
with perfectly analogous relations as to absorption and evolution of heat in dif- 
ferent parts of the circuit, provided the engine worked by the fiuid current be 
arranged to pass the fiuid through it without variation of temperature from or to 
either of the vertical branches of the tube. Ifo, and c, denote the specific heat 
of unity of mass of the fluid, under the constant pressures at which it exists in 
the lower and upper horizontal branches of the tube in the second case; m(T), 
11(T’) the quantities of heat evolved and absorbed respectively by the passage of 
a unit mass of fiuid through the two vertical branches kept at the respective 
temperatures T, T’; and if F denote the work done by a unit mass of the fluid in 
passing through the engine; the fundamental equations obtained above, with re- 
ference to the thermo-electric circumstances, may be at once written down for 
the case of the ordinary fiuid, as the expression of the two fundamental laws of 
the Dynamical Theory of Heat, both of which are applicable to this case, without 
any uncertainty such as that shown to be conceivable as regards the application 
of the second law to the case of a thermo-electric current. The two equations thus 
obtained are equivalent to the two general equations given, in §§ 20 and 21 of the 
First Part of this series of papers, as the expressions of the fundamental laws of 
the Dynamical Theory of Heat applied to the elasticity and expansive properties 
of fluids. In fact, when we suppose the ranges of both temperature and pressure 
in the circulating fluid to be infinitely small, the equation F=J uf ‘ odt, reduced 
‘ U i 
to the notation formerly used, and modified by changing the independent va- 
riables from (¢, p) to (/, v), becomes 
_t dp 
MT ae 
VOL. XXI. PART I. 2R 
