SURFACES OF DISCONTINUITY 



531 



volume density cr/f. Consequently de^ will be equal to the 

 product of o-/f and the difference in the volumes of the elements 

 just mentioned. On working this out we shall be able to obtain 

 some information concerning the order of magnitude of C and 

 justify the statements which Gibbs makes on this point in the 

 paragraph beginning at the middle of page 227. It is true he 

 begins the paragraph with the words: "Now we may easily 

 convince ourselves by equation [493] ..." but the reader may 

 well be pardoned if he doubts whether conviction is so readily 



obtained. Since the solid angle subtended by A 'B' at the centre 

 of the sphere is s/W, it is proved by well-known propositions in 

 solid geometry that the volume of the spherical film C'D'E'F' is 



3 R 



-{{R-\-^ -xY- {R-xY], 



since R — x\q the radius of the sphere on which E'F' lies and 

 R -\- ^ — X the radius of that on which CD' lies, R being the 



