Intelligence and Miscellaneous Articles. 235 



projection makes with the v axis, we have 



, clT , ., 

 a =—- = tan i . 

 dv 



This value of a' is obtained by differentiating (10), and is found 

 to be 



__ = -_(^_l )= __(^l ) (11) 



Here also the condition of constant pressure gives a constant 

 value for a!. Hence, at any point along any line of constant pres- 

 sure, the production of an element of the isentropic line upon the 

 v, T plane makes a constant angle with the projected line of great- 

 est slope at the same point. 



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



tan i = ; /i o\ 



tan* W 



from which it will appear that for either very high or very low 

 pressure the isentropic line runs at right angles to the direction 

 of greatest slope. The condition that it shall coincide with the 

 direction of greatest slope is 



tani= V&— 1 = — , 



"VET "* ™ 



For air this pressure is about 3-2 millimetres of mercury ; and 

 for other gases it is proportional to the volume 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 upper- 

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

 equation of the surface, we have 



v= s/h-lT, (14) 



which is independent of E. 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 maximum 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 condition, 

 (14) shows that they will also have a common density, which, when 

 T is 273 = , will be 0-000058 gramme to the cubic centimetre. 



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

 practically the same as that at which Maxwell's law for viscosity 

 begins to fail. This, however, is a mere coincidence. The two 

 phenomena have nothing in common, as is evident both from theo- 

 retical considerations and from experimental results. — Silliman's 

 American Journal, August 1882. 



