CYLINDER. 357 



Lastly, the induction on the axis in the interior is 

 Fj = 47rl - F = 27J-I (cos a + COS ft) 



it is parallel to the magnetisation and varies very slowly so long as 

 the point in question is at a considerable distance from the bases. 



If / is the length of the cylinder and a its radius, the value 

 of the induction F at the centre of the cylinder is 



= 27rl. 



v= 



When the length of the cylinder is very great as compared with 

 its diameter, we may take the approximate expression 



F = 4 Tl| i-- 



The induction is then sensibly the same throughout the whole extent 

 of the median section, and the expression for the total flow of induc- 

 tion Q which traverses it is 



If the cylinder is so long that the quantity in brackets does not 

 sensibly differ from unity, the flow of induction in the median 

 section is equal to (2Tra) 2 I. This flow is proportional therefore to 

 the square of the contour ; it has sensibly the same value in any 

 given section sufficiently distant from the ends. 



