140 F. K Mpher—The Isentropio Curve. 



Here also the condition of constant pressure gives 

 value for a'. Hence, at any point along any line 

 pressure the projection of an element of the isen 

 upon the v, T plane, makes a constant angle with tl 

 line of greatest slope at the same point. 



From equations (9) and (11) it follows that 



from which it will appear that for either very high i 

 pressure the iscMitroj <■ line i \ .- at i . j it angles to the dii 

 Thee " 



: greatest slope. The condil 

 of greatest slope is 



-Vk=i= z - 



For air this pressure is about 3-2 millimeters of mercury, and 

 for other gases it is proportional to the volumes of a unit mass, 

 at a standard temperature and pressure. 



The thermodynamic surfaces of various gases will lie the one 

 above the other, those having the largest value of E being 

 uppermost. If we now substitute the value of p' of (13) in the 

 original equation of the surface, we have 



v = */k~lT, (U) 



which is independent of R Hence, for all gases which follow 

 the law represented in (1) the lines on their respective surfaces, 

 where the isentropic lines coincide with the direction of maxi- 

 mum slope (13), will all lie in a common plane passing through 

 the axis of P and at right angles to the plane of v, T, its trace 

 upon the latter plane being represented by (14). 



If the gases have a common temperature while in this condi- 

 tio,,, i 14) shows that they will also have a common density, 

 which when T is 273° will be 0-000058 grams to the cubic 



It will be observed that for air, the pressure indicated in (13) 

 is practical! v the sum.- as that at which Maxwell's law for vis- 

 cosity begins to fail. This, however, is a mere coincidence. 

 The 'two phenomena have nothing in common, as is evident 

 both from theoretical considerations and from experimental 



