MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
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great; as to enable it to receive and emit heat instantaneously without there being 
any sensible difference of temperature between any part of the regenerator and the 
contiguous portion of the working substance ; and from which no appreciable amount 
of heat is lost by conduction or radiation. In theoretical investigations it is con- 
venient, in the first place, to determine the saving of heat effected by a perfect re- 
generator, and afterwards to make allowance for the losses arising from the non- 
fulfilment of the conditions of ideally perfect action ; losses which, in the present 
imperfect state of our knowledge of the laws of the conduction of heat, can be 
ascertained by direct experiment only *. 
(2 7.) Proposition X. — Problem. The true indicator-diagram of any thermo-dyna- 
mic engine being given, to determine the amount of heat saved by a perfect regenerator. 
(Solution.) Let ABCD (in fig. 17) be the given indicator-diagram. Across it 
draw any two indefinitely-close isothermal curves ; q l q l intersecting it in a, b ; and 
q 2 q. 2 intersecting it in d, c. To the stripe between those two curves, speaking generally. 
Fig. 17. 
a certain layer or stratum of the regenerator corresponds, which receives heat from 
the working substance during the change from b to c, and restores the same amount 
of heat during the change from d to a. The amount of heat economized by the layer 
in question is thus found. Through the four points a, b, c, d, draw the indefinitely- 
prolonged curves of no transmission, ah, hi, cm, dn ; then the smaller of the two 
indefinitely-prolonged areas, Ibcm, hadn, represents the heat saved by the layer of 
the regenerator corresponding to the indefinitely-narrow stripe between the isothermal 
curves q x q^ and q 2 q 2 . 
Draw two curves of no transmission, BL, DN, touching the diagram ; and through 
* It is true that the problem of the waste of heat in the action of the regenerator is capable of a hypothetical 
solution by the methods of Fourier and Poisson ; and I have by these methods obtained formulas which are 
curious in a mathematical point of view ; hut owing to our ignorance of the absolute values and laws of varia- 
tion of the coefficients of conductivity contained in these formulae, they are incapable of being usefully applied ; 
and I therefore for the present refrain from stating them. 
