496 Electrical Resistance of Thin Metallic Films. 



the above is, however, not absolutely true. Suppose, for 

 example, that we imagine the direction of the field to remain 

 fixed, and the whole of the material to be rotated through an 

 angle a about one of the lines where the bounding gaps meet, 

 say the lines whose end is represented by the point 0. A 

 constant field, with V adjusted in the above manner, would 

 satisfy (3) and it would satisfy (2), as far as those planes 

 are concerned which intersect on lines parallel to the lines of 

 rotation, for the angles which these planes now make with 

 MP, counting in a counter-clockwise direction from the- 

 plane which was originally perpendicular thereto, are 



IT IT 



so 



that 



lV b - a Y c — c^b= oXF(a)XJcos«— cos i^—uj 



-~ cos ( .j- +aU = 0. 



If we consider any of the planes which are not included 

 in the above class, however, we shall see that this condition 

 will not strictly hold. This tells us that a uniform field 

 throughout the hexagonal figures would not satisfy the con- 

 ditions of the problem. A little consideration will, however, 

 show that the conditions are not violated to any large extent, 

 and when we consider that as the direction of the field is 

 varied throughout a solid angle of 2w there are seven dif- 

 ferent positions in which the ideal condition represented by 

 fig. 8 become satisfied, we see that there is no direction in 

 which the field can act in which the condition departs very 

 far from the ideal condition represented by that figure, 

 and we are, I think, justified in assuming that the solution 

 given for that case, and represented by equation (10) ,. 

 is a very good approximation to that for the most general 

 case. 



Department of Terrestrial Magnetism, 



Carnegie Institution of Washington, 

 February 25, 1914. 



