CONTEMPORARY ADVANCES IN PHYSICS 299 



positive magnetism as negative; so also does any smaller fragment 

 broken ofif from the piece, and any still smaller bit broken oat of the 

 fragment, and so forth until the original piece is crumbled into dust, 

 each particle of which still contains as much magnetism of either 

 sign as of the other.* 



Now this requires that when we subdivide a magnetized piece of 

 iron into tiny parcels or volume-elements, not by the hammer nor the 

 file but by the exercise of the imagination, these volume-elements 

 must themselves be imagined as magnets each invested with a positive 

 pole and a negative pole and a magnetic axis pointing in some partic- 

 ular direction. I am not implying atoms by these "parcels" — we 

 shall as yet have nothing to do with atoms. The process of dividing 

 a substance into imaginary small volume-elements has nothing in 

 common with the construction of atoms or atom-models; quite the 

 contrary! It is a process which every physicist undertakes, whenever 

 he desires to analyze the flow of water or the vibrations of air or the 

 strain of a twisted rod or any of a multitude of problems concerning 

 pieces of matter, which, whatever his views about atoms, he intends 

 to regard as continuous media for the nonce. Well! in dealing with 

 magnetism, it is not sufficient to conceive these volume-elements as 

 cubical or otherwise-shaped bits of matter entirely uniform and 

 isotropic in their qualities; they must be conceived as being little 

 magnets themselves. 



This is the reason why we are taught to imagine a piece of magnetized 

 iron as a collection of tiny cubes, each bearing positive magnetism 

 spread like a coat of paint over one side, and negative magnetism over 

 the side opposite; or as a bundle of filaments which, where they come 

 out to the surface of the piece, divide it into a pattern of area-elements 

 each of which is overspread with magnetism positive or negative; 

 or as a pile of laminae, somewhat like a nest of saucers, each of which 

 is covered with magnetism of the two signs on its two sides. This is 

 the reason why, developing the first of these conceptions (which 

 contains implicitly the other two), we are taught to picture a function 

 called the intensity of magnetization, which has a definite value at 

 each point within the magnet, and may be visualized with the aid of 

 the imaginary cubes. Select a point in the interior of the magnet, 

 and imagine it surrounded by a cubical volume-element of thickness d 

 and face-area rf' and volume d^; and imagine two opposite sides of 

 the cube to be covered with magnetism of opposite signs painted on 

 with a surface-density /, so that each side bears a quantity Q which 



* The best evidence for this statement is the fact that magnets in a uniform 

 magnetic field such as that of the earth experience no force tending to displace them 

 bodily though they experience a torque tending to orient them. 

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