270 PROF. W. THOMSON ON THE MATHEMATICAL THEORY OF MAGNETISM. 
as to constitute what is, as far as regards magnetic action, equivalent to a single 
infinitely thin bar of any form, longitudinally magnetized with an intensity varying 
arbitrarily from one end of the bar to the other. Hence such a magnet may be 
called a complex magnetic solenoid. 
The magnetic strength of a complex solenoid is not uniform, but varies from one 
part to another. 
(3.) An infinitely thin closed ring, magnetized in the manner described in (1.), is 
called a closed magnetic solenoid. 
67. Definitions and explanations regarding Magnetic Shells. 
(1.) A magnetic shell is an infinitely thin sheet of any form, normally magnetized 
with an intensity varying inversely as the thickness in different parts. 
The constant product of the intensity of magnetization into the thickness is 
called the magnetic strength, or sometimes simply the strength of the shell. Hence 
the magnetic moment of any plane portion, or of an infinitely small portion of a 
curved magnetic shell, is equal to the product of the magnetic strength, into the 
area of the portion. 
(2.) A number of magnetic shells of different areas may be put together so as to 
constitute what is, as far as regards magnetic action, equivalent to a single infinitely 
thin sheet of any form, normally magnetized with an intensity varying arbitrarily 
over the whole sheet. Hence such a magnet may be called a complex magnetic 
shell. 
The magnetic strength of a complex shell is not uniform, but varies from one part 
to another. 
(3.) An infinitely thin sheet, of which the two sides are closed surfaces, is called a 
closed magnetic shell. 
68. Solenoidal and Lamellar Distributions of Magnetism. — If a finite magnet of 
any form be capable of division into an infinite number of solenoids which are either 
closed or have their ends in the bounding surface, the distribution of magnetism in 
it is said to be solenoidal, and the substance is said to be solenoidally magnetized. 
If a finite magnet of any form be capable of division into an infinite number of 
magnetic shells which are either closed or have their edges in the bounding surface, 
the distribution of magnetism in it is said to be lamellar*, and the substance is said 
to be lamellarly magnetized. 
69. Complex Lamellar Distributions of Magnetism. — If a finite magnet of any 
form be capable of division into an infinite number of complex magnetic shells, it is 
said to possess a complex lamellar distribution of magnetism. 
70 . Complex Solenoidal Distributions of Magnetism. — Since, by cutting it along 
* The term lamellar, adopted for want of a better, is preferred to “laminated”; since this might be objected 
to as rather meaning “composed of plates,” than composed of shells, whether plane or curved, and is besides 
too much associated with a mechanical structure such as that of slate or mica, to be a convenient term for the 
magnetic distributions defined in the text. 
