Intelligence and Miscellaneous Articles, 319 



1. With H=K, 



F= 



2. With H=K^±^ 



which leads to 



2nba(a + 2r) 



Bab 

 a+2r 



2M(a'+ry 



F a'+r 



7r6«(« + 2r) 7r6a' 1 1 , ,— — — — - 



And as then we have s a", we deduce a = V «(a + 2r), 



and consequently 



F' = « + 2r 



F Va 3 + 2«r + / 



As « + 2>- can be put in the form */ a 2 -\~2ar+r 2 -\-r, it is at once 

 seen that F' is greater than F. 



The experimental verification of the above-exhibited deduction 

 not being easy to realize, on account of the too great sensitiveness 

 of galvanometers with resistant helices and with continual varia- 

 tions of the resistance of the exterior circuit with galvanometers of 

 short helix, I made the experiment with electromagnets, the attrac- 

 tive force of which, reckoned according to the laws of MM. Dub 

 and Jacobi, admits of the same conditions of a maximum relative to 

 the resistance of the magnetizing helices, as I have shown in my 

 researches on the best construction of electromagnets. Now the 

 following are the results I obtained with one and the same electro- 

 magnet excited by a Daniell pile of 20 elements, to which I applied 

 successively magnetizing coils of two different resistances, viz. a 

 resistance of 75 kilometres of telegraphic wire of 4 millims. dia- 

 meter, and a resistance of 200 kilometres. In order to avoid static 

 reactions, the attractive forces were measured with 1 millimetre 

 distance of separation from the armature. 



(1) Forces of the electromagnet with coils of 75 kilometres re- 

 sistance. 



Attractive force, 

 metres, metres. grammes. 



The exterior circuit having 18620+ 80 



18620 + 100000 15 

 „ „ „ 18620 + 200000 5-5 

 „ „ „ 18620 + 370000 



(2) Forces of the electromagnet with coils of 200 kilometres re- 

 sistance. 



The exterior circuit having 18620+ 5S 



18620 + 100000 25 



18620 + 200000 14 



18620 + 370000 



The wire of these circuits was perfectly insulated; and the time 



