288 Dr. TyudtiU on the Lows of Mat^mtism. 



distances of the position of equilibrium from the respective poles 

 av,^ directly proportional to the sti'eugths of the uiai;nets. 

 . 29. This conclusion, however^ would be altogether opposed'to 

 the experinaental results detailed in § 3. The error lies in the 

 tacit assumption^ that the forces exerted at the unit of distance 

 arc proportional to the strengths of the magnets. With the 

 theoretic poles this assumption was correct^ for there the mag- 

 netism of the little steel ball was constant, and hence the attrac- 

 tions between it and the respective poles at the unit of distance 

 were the products of a constant with the strengths of these poles, 

 these products being therefore in the ratio of the strengths. But 

 with the sphere of soft iron every change in the magnet is ac- 

 companied by a corresponding change in the magnetism of the 

 sphere, which circmnstance puts the proportionality existing iii 

 the other case cntu'cly out of the cpicstion. i ' \:\ ' 



,,,\30. It has been already proved (IC), that if one miagnVt nWe 

 twice the strength of anothei', and if the latter exercise* a c6rtain 

 force upon the iron ball at a certain distance*, the former will 

 exercise the sanic force at four times the said distance. Hence, 

 adopting the disposition of the poles above described, if the ball 

 be placed at a leaf thickness distant from the weaker pole, to be 

 in equilibrium it must be four leaves distant from the stronger, 

 which is here supposed to be underneath the former ; and in 

 general, if m and m' be the strength of any two magnets, and d 

 and d' the distances.at which they c^ert!.«q,\val atU'aetJofis^-iipLpii 

 the sphere, we ha\e ^^ ^^j "' 



''""^^f'ifd" 



friofitf 'which we'4'Aferjthat the distances of the pmid of jequiUbymv^ 

 ofi/iespfwcfi-omthe reupcctive poh& are dii'ecthj ^prQporMQTf^ Jtff 

 the squares of the streiuiths of the inacinets. 



rforrr ffp ^o rft.J. , torr:2nr§ ^nr. >\h(\ rnov/jocf ■rnis'&iid 

 Proposition \1.-^To determine the relation, between the strength 

 of an elect ro-maf/net and the mutual attraction of the magnet and 

 a mass of soft iron, ivhen Loth are separated by a fixed distahce. 



3L, li" v>-e suppose the space above the magnet to be intersected 

 by a liuniber of infinitely thin horizontal planesj placed, say the 

 thickness of one of our leaves asunder, each of these planes will 

 denote a certain section of force. Let the force on the tirst'plane 

 be called /; we know that, by doubling the streng-th of the mag- 

 net, the. force /will be exerted on the fourth plane; by trebling 

 it, on the ninth plane, and so on. Supposing the ball placed on 

 the nnifh plane with the magnetic force thus trebled; let ti^ ask 



* It is, scared v,nccessary to .i;cuiark, tliat tjje tcnii ilistance, as here used, 

 refers to the intcr\'al hctxvceu the magnet and the nearest pomt of the sphere. 



