72 Formulcefor the Lifting-power of Magnets. 



which can be determined if the law of the distribution of the 

 magnetic induction through the cross-section is known. As- 

 suming this to be a simple uniform distribution (it is generally 

 not quite so at the joint between the polar surfaces and 

 armature of a magnet), this gives the pull (in dynes) as 



P=^B 2 A. 



07T 



This formula* affords a very convenient method of reckoning 

 B from measurements made upon the pull exerted at a given 

 polar surface; the formulae becoming 



A sq. cm.' 



B = 1317 



A sq. in. ' 



The a of Haecker's formula may, therefore, be taken as 

 simply proportional to the square of the magnetic induction 

 through the contact-surface, or 



a = A B 2 . d l . c, 



where d is the density of the steel, and c the ratio of the 

 polar surface to the surface of one face of a cube of equal 

 volume to that of the magnet. 



Haecker found a for horseshoe-magnets twice as great as 

 for bar-magnets. Van der "Willigen found it from three to 

 four times as great for horseshoes. Taking Haecker's figure, 

 this shows that the long return-path through air of the tubes 

 of magnetic induction offered so great a resistance that the 

 steel magnet could only produce across the polar surface in 



this case an induction —7= times as great as when the closed 



horseshoe circuit was used. 



Consideration of the rational formula will show that the 

 greater lifting-power in proportion to their own weight pos- 

 sessed by small magnets, does not require for its explanation 

 the sometimes alleged fact that small pieces of steel can be 

 more highly magnetized than large pieces of steel. For, 

 assuming equal intensity of magnetic induction, B, it is seen 

 that the lifting-power is proportional to surface and not to 

 weight; hence it must necessarily be greater relatively to 

 weight in small magnets. 



* In Mr. Shelford Bidwell's paper, Proc. Koy. Soc. 1886, he uses a 

 formula equivalent to g- (B 2 — H 2 )A, but without giving any reason for 

 deducting H 2 from B 2 . 



