188 Proceedings of the Royal Society of Edinburgh. [Sess. 
the mean value of the field throughout the cross-section of the wire in the 
following manner : — 
Let the circle of radius a represent a section of the wire, P any point at 
distance r from the centre O. Then the strength of the field at P, say H, 
is given by 
where c is the current in C.G.S. units, 
by S. 
Mean value of H = 
Denote the area of the cross-section 
il** 
♦ _ 4 c r 3 
~a T J 
oL J 
_ 4c 
3a 
2 
— X current 
15a 
when the current is in amperes. 
For the investigation of cobalt I employed a rectangular strip, and 
determined the mean value of the field as follows : — 
Let the length and breadth of the cross-section be 2a and 2b respectively, 
the centre being the origin. Take any point P (x, y) and draw a rectangle 
Fig. 2. 
through P similar to the strip with sides 2x and 2 y. Also let the element- 
ary rectangle dxdy be drawn, having P for its centre. Suppose i to be 
the current density, and that the current is flowing upwards from the 
paper. Then the current passing through the elementary rectangle is idxdy. 
