DAVIS. — A Pa PLANE FOK THERMODYNAMIC CYCLIC ANALYSIS. G31 



it lies, and then a statement of (say) tlie specific volume at b settles 

 everything. So doos a knowledge of P {= P/,/Pa)- So also does a 

 knowledge of Q (that is, the heat that must be supplied to the working 

 substance per unit mass to carry it from b to c). In such cases, there 

 exists a relation, /(/*, Q) = 0, by means of which either of these quan- 

 tities can be expressed in terms of the other (and the parameters). On 

 the P Q plane this equation is a curve ; and the graphical statement of 

 these facts is that it is impossible to construct a cycle of the given type 

 corresponding to any point of the P Q plane which is not also a point 

 of this curve. Such cycles (which may be called cycles of the first order) 

 fill, not a whole P Q plane, but only a line in such a plane, and the 



FiGL'ItE 1. 



Figure 



PQX surface is defined only along this line, and degenerates into a 

 curve drawn upon the surface of a cylinder erected on the line as a 

 directrix. In such special cases, it is sometimes best to discard entirely 

 the contour-line method of studying the surface, and to use instead 

 either a development of the cylinder, or some picture of it, for example 

 such an orthographic projection as will eliminate P. This last is exactly 

 what Dr. Lucke did (although from a different point of view) whenever 

 he had a first order cycle to deal with.* The reason that some such 



* Of the cycles of pp. 225-234 of his paper, Numbers I, IC, VI and VIII are 

 of the first order (Cycle VIII being a special case of the cycle discussed above) ; 

 and the lines marked I and IC in the figures of pp. 418-429 are orthographic pro- 

 jections of the kind described. All the other lines in these figures may be thought 

 of as the intersections of a P QX surface with a plane perpendicular to the P Q 

 plane along either the line P = 2 or the line P = 10. 



