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Xr. A Mathematical Theory of Magnetism. — Continuation of Part I. By William 
Thomson, Esq., M.A., F.R.S.E., Fellow of St. Peters College, Cambridge, and 
Professor of Natural Philosophy in the University of Glasgow. Communicated 
by Lieut. -Colonel Sabine, For. Sec. R.S. 
, Received June 20, — Read June 20, 1850. 
Chapter V. On Solenoidal and Lamellar Distributions of Magnetism. 
65. In the course of some researches upon inverse problems regarding distributions 
of magnetism, and upon the comparison of electro-magnets and common magnets, I 
have found it extremely convenient to make use of definite terms to express certain 
distributions of magnetism and forms of magnetized matter possessing remarkable 
properties. The use of such terms will be of still greater consequence in describing 
the results of these researches, and therefore, before proceeding to do so, I shall give 
definitions of the terms which I have adopted, and explain briefly the principal pro- 
perties of the magnetic distributions to which they are applied. The remainder of 
this chapter will be devoted to three new methods of analysing the expressions for 
the resultant force of a magnet at any point, suggested by the consideration of these 
special forms of magnetic distribution. A Mathematical Theory of Electro-Magnets, 
and Inverse Problems regarding magnetic distributions, are the subjects of papers 
which I hope to be able to lay before the Royal Society on a subsequent occasion. 
66. Definitions and explanations regarding Magnetic Solenoids. 
(1.) A magnetic solenoid* is an infinitely thin bar of any form, longitudinally 
magnetized with an intensity varying inversely as the area of the normal section in 
different parts. 
The constant product of the intensity of magnetization into the area of the normal 
section, is called the magnetic strength, or sometimes simply the strength of the 
solenoid. Hence the magnetic moment of any straight portion, or of an infinitely 
small portion of a curved solenoid, is equal to the product of the magnetic strength 
into the length of the portion. 
(2.) A number of magnetic solenoids of different lengths may be put together so 
* This term (from ffojXrjy, a tube,) is suggested by the term “ electro-dynamic solenoid ” applied by Ampere 
to a certain tube-like arrangement of galvanic circuits which produces precisely the same external magnetic 
effect as is produced by ordinary magnetism distributed in the manner defined in the text. The especial ap- 
propriateness of the term to the magnetic distribution is manifest from the relation indicated in the foot-note 
on § 76 below, between the intensity and direction of magnetization in a solenoid, and the velocity and direc- 
tion of motion of a liquid flowing through a tube of constant or varying section. 
