38G PROCEEDINGS OF THE AMERICAN ACADEMY. 



where [Z^n^] represents the normal derivative of h with respect 

 to n. 



If the equation fi = ^ happens to represent a set of parallel surfaces, 

 A, if not constant, is a function of 12 alone, so that the h and U surfaces 

 are coincident : in this case cos (ft, A) = 1 and D^ D, can vanish only 

 where h' vanishes. In general, D^ ft vanishes when the h and Q sur- 

 faces cut each other at right angles- 



If Si, $21 S3 are any three mutually perpendicular directions, 

 /i' + 4' + l:^ = W + nh^ + W = n,^ + no" + 71^' = 1 , 

 h ''^1 + h '"2 + 4 ^^3 =^ '>^h '>h + ^h fh + '"3 ^'3 = ^1 «i + ^2 ^2 + ^3 ^3 == ^ j 



9^n 5^0 52^2 

 _^c)nr 5/, 5/0 9h^ 91. 91. 5/3 1 



dx [_ dy dy dy dz dz o'z _j 



50 r 9mi 9m<, 9nis , 9mi , 9m.2 , 9ni,~\ 



o'^/ |_ S2 0^2 c/2 dx 9x 9x J 



(27) 

 The Jefferson Physical Laboratory. 



