PAPER BY PROF. BEZOLD. 235 



through b au adiabatic and prolong both curves until they cut each 

 other in a point, c; then is Q br = 0, and the quantity of heat is given 



by- 



or, 



Qa.>~ <?».< = A F, 



and therefore, also, 



Qa. b = AF+Q ttte . 



When now Q a e is determined by computation, but F is found by plan- 

 imetric method, this formula gives the value of Q„ h . 



If the curve ac is the curve of constant energy (or isodynamic), then 

 Q ac =ALj where L is the exterior work and is therefore also directly 

 obtained as a surface from the diagram, and then we have to execute the 

 well-known graphic construction for the determination of the quantity 

 of heat gained or lost by a given change of condition. But the method 

 here given possesses the advautage of greater generality and much 

 easier applicability. 



This consideration also holds good when we have to do with limited 

 reversible changes, only one has then to remember that the closed curve 

 projected upon the plane of PQ must also be the projection of a dosed 

 curve in space. If the curve in space that represents the change in 

 condition is not closed, but if it only has the peculiarity that at the 

 initial and linal condition the coordinates p and v have equal values, 

 then it indeed gives a closed projection, but the quantity of heat com- 

 puted by the above-given method is erroneous, and that too by the 

 quantity which corresponds to the increase in internal energy ac the 

 passage from the initial to the final point, that is to say, by the addi- 

 tion of the necessary quantity of vapor. 



The circumstance that one and the same point of the PV plane can 

 correspond to very different conditions appears at first sight to exclude 

 the general presentation of the processes in this plane alone, and thereby 

 to materially diminish not only the applicability of the last-given con- 

 struction but in general to detract from the whole conception here 

 described. But by a closer consideration this is seen not to be the case; 

 rather does it specially apply when for every point in the plane of P Tone 

 has given the corresponding dew-point curve. An example will eluci- 

 date this: Let us assume that one desires to obtain an idea of the dif- 

 ference in the internal energy that is present in the dry stage for equal 

 values of p and v, but different quantities of vapor. If, iu Fig. 32, P 

 is the point having the coordinates p and v, but the quantity of vapor 

 is in one case x m and in the other x„, then these latter correspond to two 

 different dew-point curves, 8 m and 8„. One can now convert the whole 

 internal energy as it existed in the initial condition into external work 

 by moving from the point P forwards adiabatically to the absolute 



