39 2 ON MAGNETS. 



We may observe that if the perpendicular components do not 

 give the distribution, they enable us to calculate the total mass of 

 magnetism by Green's theorem. This mass is obviously null for the 

 whole magnet; but the total flow of force on either side of the 

 neutral line is equal to 477 by the mass of the fictive layer corre- 

 sponding to this side. This total mass is represented by the area of 

 the curve obtained by taking as ordinates the values found for the 

 perpendicular component at all points of the axis of the magnet, 

 imagined to be indefinitely prolonged, or more simply by the 

 maximum ordinate of the curve of demagnetisation. 



419. CYLINDRICAL MAGNETS. Coulomb determined experi- 

 mentally, and by means of the methods mentioned above, what he 

 calls the distribution of magnetism in cylindrical needles. 



He first found that for short magnets those, that is to say, 

 whose length is less than fifty times the diameter the perpendicular 

 force at each point (which he confounded with the density) is pro- 

 portional to the distance from the middle. 



The linear density would then be the same as for a sphere or an 

 ellipsoid uniformly magnetised. 



The curve of distribution is then figured by a right line OB 

 (Fig. 86), making a certain angle a with the axis OA of the bar. 



Fig. 86. 



A straight line OB', forming the prolongation of the former, would 

 represent the negative magnetism on the other half of the bar. The 

 centre of gravity of the surface is projected, as for a sphere, at a 

 third of the semi-length of the bar measured from the ends. 



This law ought to represent the true distribution of magnetisation 

 with tolerable approximation, for Coulomb proved that, other things 

 being equal, the magnetic moment of short bars is proportional to 

 the cube of the length. 



If the bar is long that is to say, if the length is more than fifty 

 times the diameter d the magnetism is imperceptible for a certain 

 length on either side of the centre, and may still be represented by a 



