of various Iron Bodies. 203 



dimensions of which in all directions are of the same order*. In 

 order to calculate a priori, with satisfactory accuracy, the mag- 

 netization of bodies so formed, a rough estimation of the coeffi- 

 cient k is sufficient. The magnetization-functions of such bodies, 

 ascertained by experiments, will always exhibit much less varia- 

 bility than that of a thin bar or ring, of a thin plate or scale, 

 and may almost be regarded as constant. But if, starting from 

 such mean value, we try to calculate the magnetization of any 

 body of the category last mentioned, we may arrive at very in- 

 accurate results ; for, with bodies one or two dimensions of which 

 are very small in comparison with the third, the tangential compo- 

 nent of the magnetic moment will, with the same decomposing 

 force, increase proportionally with k-f. The influence of the 

 specific qualities of the substance appears here, therefore, in full 

 intensity. If we wish to bring such bodies also within the range 

 of our considerations, we must take into account the specific 

 quality of the substance, and the knowledge of the magnetiza- 

 tion-functions of bodies of this sort will be indispensable. The 

 function k perfectly suffices for this purpose, and has the advan- 

 tage that in it abstraction is made of the transverse dimensions 

 of the thin body. 



Those bodies the dimensions of which are of different orders 

 of magnitude play a peculiar part in several branches of physics. 

 In hydrostatics their theory is most essentially conditioned by 

 the capillary forces. In the science of elasticity they require a 

 special method of treatment ; in that of paramagnetic magneti- 

 zation they make a very precise knowledge of the magnetization- 

 functions absolutely indispensable. 



Christmas (0. S.) 18/3. 



* Compare pp. 56-67, vol. ii. of Maxwell's Treatise — for example, 

 " When k is a large positive quantity, the magnetization depends princi- 

 pally on the form of the body, and is almost independent of the precise 

 value of k, except in the case of a longitudinal force acting on an ovoid so 

 elongated/' &c. (p. 66). We always presuppose here that the magnetiza- 

 tion is uniform. 



t More strictly, proportionally with s , , , where e is a number vanish- 

 ing with the transverse dimensions, and the value of k is not referred to the 



T 

 whole tangential force of decomposition T, but to rrr . For a limited 



bar e=0. These considerations explain, for example, the experiments of 

 Von Waltenhofen on the magnetization of bundles of thin wires, thin- 

 walled tubes, &c. (Wiedemann's Galvanismus, 2nd ed. vol. ii. p. 430). The 

 great power of the magnets composed of thin bands of steel (rubans d'acier) 

 of M. Jamin (Comptes Rendus, vol. lxxvi. p. 789) appears also to stand in 

 relation therewith (compare especially art. X. p. 794). 



