386 PROCEEDINGS OF THE AMERICAN ACADEMY. 



where \_Dn /<] represents the normal derivative of li with respect 

 to fl. 



If the equation CI = k happens to represent a set of parallel surfaces, 

 h, if not constant, is a function of Q alone, so that the h and O surfaces 

 are coincident : in this case cos (f2, h) = 1 and D s 2 O can vanish only 

 where h! vanishes. In general, Z) s 2 O vanishes when the h and O sur- 

 faces cut each other at right angles. 



If Si, s 2 , s 3 are any three mutually perpendicular directions, 

 h 2 + I* + V 2 = V + w 2 2 + ™3 2 = n{ 2 + n 2 2 + « 3 2 = 1 , 

 l x m x + l 2 m 2 + h m 3 = m x n x + m 2 n 2 + m 3 n 3 — l l n 1 + J 2 n 2 + h n 3 = , 



9 2 n 3 2 o 9Hi 



and A 2 " + A 2 " + A 2 " = %r 2 + ^ + ^r 



i 2 3 9x z 3y 9z 



, sa r PZ, , 3/ 2 , % J 9l x 9l 2 , 3/ 3 "I 



3n [ Swij <9w 2 , 3m 3 5>wi , 7 9m 2 9m 3 ~\ 



50 f, 3«i 7 0» 2 , 7 3« 3 , 9n x 9n 2 9n 3 1 



(27) 

 The Jefferson Physical Laboratory. 



