12 



RICE 



ART. B 



a point which are at right angles to one another then c + c' is a 

 constant quantity at the point and is equal to Ci + C2. 



On page 229 of Vol. I Gibbs uses an important theorem 

 concerning the increase in size of a small portion of a surface 

 produced by an elementary displacement of each element of the 



Fig. 1 



surface by an amount BN in the direction of its normal. Let the 

 element of surface he ABE F (Fig. 1) bounded by normal sections 

 which are at right angles to one another. Let C be the "center 

 of curvature" of the element AB of one of the sections, i.e., the 

 position in the limit where the normals in the plane to the curve 

 at the points A and B meet.* Let C be the center of curvature 



* The reader unacquainted with the geometry of surfaces is warned 

 that for the sake of simplicity we have neglected a detail which is of no 



