106 APPLICATION OF THE PRELIMINARY RESULTS 



may be situate, the same will hold good when, instead of P, we 

 substitute a body of any figure whatever magnetized at will. 

 The only condition to be observed, is, that the distance between 

 p and every part of the inducing body be not a very great quan- 

 tity of the order . 



On the contrary, when the distance between p and the 



(1 a)r' 



inducing body is great enough to render ^J a very con- 



t 



siderable quantity, it will be easy to show, by expanding F in 

 a descending series of the powers of /, that the actions exerted 

 upon p are very nearly the same as if no plate were interposed. 



We have before remarked (art. 15), that when the dimensions 

 of a body are all quantities of the same order, the results of 

 the true theory differ little from those, which would be obtained 

 by supposing the magnetic like the electric fluid, at liberty to 

 move from one part of a conducting body to another; but when, 

 as in the present example, one of the dimensions is very small 

 compared with the others, the case is widely different; for if we 

 make g rigorously equal to 1 in the preceding formulae, they 

 will belong to the latter supposition (art. 15), and as .Fwill then 

 vanish, the interposing plate will exactly neutralize the action 

 of any magnetic bodies however they may be situate, provided 

 they are on the side opposite the attracted point. This differs 

 completely from what has been deduced above by employing 

 the correct theory. A like difference between the results of the 

 two suppositions takes place, when we consider the action ex- 

 erted by the earth on a magnetic particle, placed in the interior 

 of a hollow spherical shell, provided its thickness is very small 

 compared with its radius, as will be evident by making g 1 in 

 the formulas belonging to this case, which are given in a preced- 

 ing part of the present article. 



17. Since COULOMB'S experiments on cylindric wires magnet- 

 ized to saturation are numerous and very accurate, it was thought 

 this little work could not be better terminated, than by directly 

 deducing from theory such consequences as would admit of an 

 immediate comparison with them, and in order to effect this, we 





