THERMODYNAMIC PROPERTIES OF SUBSTANCES. 41 



It is evident that the sign of inequality holds in (e) if it holds in 

 either (6) or (c), therefore, it holds in (e) if there are any differences 

 of pressure or temperature between the different parts of the body 

 or between the body and the medium, or if any part of the body has 

 sensible motion. (In the latter case, there would be an increase of 

 entropy due to the conversion of this motion into heat.) But even if 

 the body is initially without sensible motion and has throughout the 

 same pressure and temperature as the medium, the sign < will still 

 hold if different parts of the body are in states represented by points 

 in the thermodynamic surface at different distances from the fixed 

 plane representing P and T. For it certainly holds if such initial 

 circumstances are followed by differences of pressure or temperature, 

 or by sensible velocities. Again, the sign of inequality would neces- 

 sarily hold if one part of the body should pass, without producing 

 changes of pressure or temperature or sensible velocities, into the 

 state of another part represented by a point not at the same distance 

 from the fixed plane representing P and T. But these are the only 

 suppositions possible in the case, unless we suppose that equilibrium 

 subsists, which would require that the points in question should have 

 a common tangent plane (page 37), whereas by supposition the planes 

 tangent at the different points are parallel but not identical. 



The results of the preceding paragraph may be summed up as 

 follows: Unless the body is initially without sensible motion, and 

 its state, if homogeneous, is such as is represented by a point in the 

 primitive surface where the tangent plane is parallel to the fixed plane 

 representing P and T, or, if the body is not homogeneous in state, 

 unless the points in the primitive surface representing the states of 

 its parts have a common tangent plane parallel to the fixed plane 

 representing P and T, such changes will ensue that the distance 

 of the point representing the volume, entropy, and energy of the 

 body from that fixed plane will be diminished (distances being con- 

 sidered negative if measured from points beneath the plane). Let 

 us apply this result to the question of the stability of the body when 

 surrounded, as supposed, by a medium of constant temperature and 

 pressure. 



The state of the body in equilibrium will be represented by a point 

 in the thermodynamic surface, and as the pressure and temperature of 

 the body are the same as those of the surrounding medium, we may 

 take the tangent plane at that point as the fixed plane representing 

 P and T. If the body is not homogeneous in state, although in 

 equilibrium, we may, for the purposes of this discussion of stability, 

 either take a point in the derived surface as representing its state, or 

 we may take the points in the primitive surface which represent the 

 states of the different parts of the body. These points, as we have 



