Lifting Power of the Electro-Magnet. 533 



The action of a helix, -^^ is represented by the quantity of current multi- 

 plied into the number of spires (not the length of wire, as is sometimes stated), 

 and into a coefficient expressing the mean efficiency of these spires ; this effi- 

 ciency decreases as the ratio of the spires' radius to that of the magnet increases, 

 at first rapidly, but afterwards very slowly, for that portion of the magnet which 

 is in its plane. On parts out of the plane the action may even increase with 

 the distance, but it is much feebler than the other. 



The lifting force L is not proportional to any one power or exponential of 

 ^. The increase of it, corresponding to a given increase of ^, lessens conti- 

 nually as ^ increases. This diminution is least in hard steel, but only because 

 that material requires a higher exciting force to develop its magnetism. The 

 rate of this decrease shows that there must be a maximum L for each magnet, 

 which no magnitude of ^ can make it exceed. This maximum is higher the 

 greater the section of the magnet is, and the shorter its circuit. It seems the 

 same for iron and hard steel. 



When the excitation is very feeble, L seems to depend on \, the permanent 

 magnetism, as well as on ^ ; but in the higher powers solely on the latter. A 

 tolerable approximation is given by an empirical formula, 



J- _ Ax li^ 



in which A is the maximum, and B that value of -^ which would excite the 

 magnet to half the maximum. This quantity appears to possess some remark- 

 able properties, and may be considered a sort of modulus ; in steel, for instance, 



A 



it is 14 times greater than in iron, and the fraction ::; ■. — appears to be a 



B X section 



good measure of the efficiency of any magnet. 



VOL. XXIII. 4 A 



