436 M. J. Jamin on the Theory of the Normal Magnet, and 



F is proportional to the magnetic intensity at each point, and 

 that we can put F = I 2 ; then 



^-Vf (2) 



W*Vl (3) 



Equation (3), which may be written l]=k% shows that the 

 magnetic intensity at the extremity of the normal pile varies as 

 the ordinates of a parabola A Q P tangent in A to the y-axis ; 

 and from equation (2) we gather that the intensity on the dif- 

 ferent points of a bar of length 21 is figured by a right line 



which makes with the #-axis an angle whose tangent is — ■=. 



For 1= AB, this line is AP; it would be A Q for a pile termi- 

 nated at the point D. 



VII. This total M is the area of the triangle ABP, or 



ixW~i=kn. 



If a be the width of the plates, and e their thickness, and if we 

 neglect the augmentations of intensity produced at the corners 

 and angles of the pile, this quantity must be multiplied by the 

 perimeter 2(#-f ne), n being the number of plates; we have 

 therefore 



VIII. When a contact is placed under the magnet, all free 

 magnetism disappears if the contact is large enough and con- 

 tains a sufficient quantity of iron. The whole of the magnetism 

 M, therefore, is concentrated upon the surface of adhesioD, which 

 I name S. Its intensity there (that is, the quantity of magne- 



M 



tism on the unit of surface) is -~- ; and the carrying-force will 



M 2 M 2 M 2 



be 02-; for the whole surface it will be -^-Sor--^- 



