I'.") PROCEEDINGS OP Till' AMERICAS ACADEMY. 



in, we shall hereafter use the scalar values fur //'. // ; . and /. 90 that 

 our first equation will become 



// = //'-//, = //'- NI. 



The only case of a magnetized body not endless, in which we can 

 always calculate what the //, will be, is where an iron ellipsoid i- 

 placed with one of its axes parallel to a uniform magnetizing held // . 

 If the equation of the ellipsoid is 



- + J - + - = 1, 



then it is shown in text-books on the mathematical theory of electric- 

 ity and magnetism, 8 that if there exists on the ellipsoid a surface die 

 tribution of magnetic matter everywhere equal to 



o- = /-cos (.r, n) 



where / is a constant, and {x, n) is the angle between the positive 

 direction of the .r-axis and the exterior normal to the ellipsoid, the 

 volume density p being zero throughout the ellipsoid, then the mag- 

 netic field due to this distribution is constant at every point within 

 the ellipsoid and equal to 



//, = 2-irabcIK . 



where 



*s 



(s + a)*(s + b)*(8 + c)* 



This field fl { is directed parallel to the negative direction of the ar-axis, 

 and tends to demagnetize the iron ; we see furthermore that it is di- 

 rectly proportional to /. The constant / is simply the intensity of 

 magnetization, uniform within the ellipsoid. To keep this magnetic dis- 

 tribution in equilibrium it is sufficient if we apply a uniform magnetic 

 field parallel to the positive .r-axis, of such a strength //'. that when 

 diminished by the demagnetizing field lf„ there will remain in the 

 ellipsoid the uniform resultant held //= /'*.•, where x is the suscepti 

 bility corresponding to the magnetization /, for the kind of iron under 

 consideration. Of course if the a has initially been chosen greater 

 than the maximum value of magnetic intensity attainable, it will be 



» Maxwell, II. §S V~ and 188; Webster, Elec. and Mag., §§ 192, 196 ; Peifce, 

 Newtonian Potential Function, § 09. 



