of the Thermodynamic Properties of Substances. .391 



subsists, wliicli would require that the jjoints in question should have 

 a common tangent plane (page 3SG), whereas by supposition the planes 

 tangent at the diiferent points are parallel but not identical. 



The results of the preceding paragraph may be summed up as fol- 

 lows : — Unless the body is initially without sensible motion, and its 

 state, if homogeneous, is such as is represented by a jjoiut 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 7^, 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 

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

 pressui'e. 



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

 in the thermodynamic sixrface, 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 7! If the body is not homogeneous in state, although in equi- 

 librium, 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 diiferent parts of the body. These points, as we have 

 seen (page 386), have a common tangent plane, which is identical with 

 the tangent plane for the point in the derived surface. 



Now, if the form of the surface be such that it falls above the tan- 

 gent plane except at the single point of contact, the equilibrium is 

 necessarily stable ; for if the condition of the body be sliglitly altered, 

 either by imparting sensible motion to any part of the body, or by 

 slightly changing the state of any part, or by bringing any small 

 part into any other thermodynamic state whatever, or in all of these 

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

 whole body will then occupy a position above the original tangent 

 plane, and the proposition above enunciated shows that processes 

 will ensue which will diminish the distance of this point from that 

 plane, and that such processes cannot cease until the body is brought 

 back into its original condition, when they will necessarily cease on 

 account of the form supposed of the surface. 



