DETERMINATION OF THE FICT1VE LAYER. 647 



two masses, and if we consider the points situate in the neighbour- 

 hood of one of them m, the action of the other mass may be 

 neglected. 



If z is the perpendicular force, and x the abscissa of the point P, 

 measured on the axis of the magnet, starting from the mass + m as 

 origin, we may write 



m . my 



x = sm 3 w = - 



y (: 



The curve corresponding to this equation, in which y is con- 

 sidered as a constant, presents exactly the same aspect as those 

 which have been given by Coulomb to represent the distribution 

 of magnetism in cylindrical magnets (419), if we put aside the 

 ordinate relative to the end of the magnet, knowing that this 

 extreme value was the result of an estimate. 



We shall compare, for instance, the values calculated on the 

 hypothesis of a uniform linear magnetisation with an experiment 

 which has been given in detail by Coulomb,* and which he indi- 

 cates as giving in the most complete manner the distribution of 

 magnetic densities on a thin steel rod 2 lines in diameter. 



The small magnet used for the oscillations was 6 lines in length, 

 and was at a distance of 8 lines from the rod investigated. The 

 distance from the centre of the magnet to the axis of the rod 

 was therefore one inch, and Coulomb's numbers represent actions 

 produced at points situate at different distances from the ends. 

 We may then either make y=i inch in the preceding formula, 

 and calculate the constant my by one of Coulomb's numbers, or 

 determine at what distance y the magnet should be placed to 

 satisfy two of the experimental numbers. We find in this way 



Values of z 



* COULOMB. Mem. de FAcad. des Sciences, 1879. 3 rti Mem., 8th Exp. 

 Collection de Mem. de la Societe de Physique, Vol. I., p. 293. 



