MR. MACQUORN RANKIN E ON THERMO-DYNAMICS. 
145 
defines a pair of curves of equal transmission. From this and from equation (31.), it 
follows, that for such a pair of curves 
If one of the curves, or lines, of equal transmission is a straight line of equal 
volumes, that is, an ordinate AD parallel to OY, then the other is an ordinate I3C, 
parallel to OY also. Then ABCD is the diagram of maximum efficiency for an air- 
engine with a perfect regenerator, when the air traverses the regenerator without 
alteration of volume ; and by adopting this diagram, the additional expansion from 
V B to V c is dispensed with. 
If one of the curves, or lines, of equal transmission is a straight line of equal 
pressures AD' parallel to OX, then the other also is a straight line of equal pressures 
BC'. The diagram thus formed, ABC’S)', is suitable, when the air, as in Ericsson’s 
engine, has to traverse the regenerator without change of pressure. 
It must be observed, that no finite mass, or extent of conducting surface, will 
enable a regenerator to act with the ideal perfection assumed in Propositions X. and 
XL, and their corollaries. 
Owing to the want of a general investigation of the theory of the action of the 
regenerator based on true principles, those who have hitherto written respecting it 
have either exaggerated its advantages or unduly depreciated them. From this re- 
mark, however, must be excepted a calculation of the expenditure of heat in Captain 
Ericsson’s engine, by Professor Barnard of the University of Alabama*. 
(31.) General Remarks on the 'preceding Propositions. 
The eleven preceding propositions, with their corollaries, are the geometrical re- 
presentation of the theory of the mutual transformation of heat and motive power, 
by means of the changes of volume of a homogeneous elastic substance which does 
not change its condition. All these propositions are virtually comprehended in the 
first two, of which, perhaps, the most simple enunciations are the following : — 
I. The mechanical equivalent of the heat absorbed or given out by a substance in 
passing from one given state as to pressure and volume to another given state, through 
a series of states represented by the co-ordinates of a given curve on a diagram of 
energy, is represented by the area included between the given curve and two curves 
of no transmission of heat drawn from its extremities, and indefinitely prolonged in 
the direction representing increase of volume. 
II. If across any pair of curves of no transmission on a diagram of energy there 
be drawn any series of isothermal curves at intervals corresponding to equal differ- 
ences of actual heat, the series of quadrilateral areas thus cut off from the space be- 
tween the curves of no transmission will be all equal to each other. 
These two propositions are the necessary consequences of the definitions of iso- 
* Silliman’s Journal, September 1853. 
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