308 Intelligence and Miscellaneous Articles. 



part of this subject during the last decade, its theoretical basis ought 

 to be somewhat revised in its essential points. Contrary to Kirch- 

 hoflr's and Duhem's analytical treatment of the question, a more 

 geometrical method is here followed. 



I. General vector distributions are first discussed, Lord Kelvin's 

 well-know r u classification being followed. The conditions are given 

 for (a) solenoidal, (b) lamellar, (c) complex lamellar, (d) lamellar- 

 solenoidal (" Laplacian "), (e) complex lamellar-sole noidal distri- 

 butions. General propositions : — 



(1) If a vector fulfil any of the above conditions, its product 

 into a constant scalar quantity will fulfil it as well. 



(2) The superposition of two solenoidal or lamellar distributions 

 gives a solenoidal or lamellar resultant respectively. 



II. Magnetic vector distributions. — The total intensity is lamellar. 

 In the general case of variable susceptibility (homogeneous isotropic 

 ferromagnetic medium free from electric currents and hysteresis, 

 numerical or directional) the lines of magnetization must still coin- 

 cide with those of total intensity ; however, the magnetization is 

 proved to be complex lamellar (not Laplacian as in the old theory); 

 the susceptibility acts as a scalar "integrating divisor." The fol- 

 lowing theorem holds : — (3) Between any two points of the 

 boundary between a ferromagnetic and an " interferric " the self- 

 iuduced part of the rise of magnetic potential in the latter is 

 numerically equal to the line-integral of the self-demagnetizing 

 intensity in the former. 



The total induction has complex lamellar-solenoidal distribution. 



In case electric currents be flowing through the ferromagnetic, 

 the distribution of intensity and magnetization is no more capable 

 of any particular specification; however, that of the induction 

 remains solenoidal in this case also ; the continuity of the flux of 

 induction thus appears to be a perfectly general fundamental 

 principle. 



Lord Kelvin's theorems regarding similar electromagnetic systems 

 with currents proportional to the linear dimensions remain un- 

 changed in the revised theory. 



III. Magnetic Circuits. — The case of the split-ring is made 

 amenable to sufficiently rigorous treatment by the theory developed ; 

 expressions are given for the value of the demagnet-ring factor and 

 for its relation to the coefficients which measure leakage. 



IY. Finite Cylinder. — From experimental data of Ewing and 

 Tanakadate a table is calculated giving the mean demagnetizing 

 factors for finite cylinders as well as those of the corresponding 

 ovoids ; for a given dimensional ratio the latter are always greater 

 than the former ; an ovoid behaving like a cylinder about 10 to 20 

 per cent, shorter. For cylinders of length exceeding 100 diameters 

 the demagnetizing factor becomes inversely proportional to the 

 square of the dimensional ratio. 



For all details of mathematical treatment the original ( Wied. Ann. 

 xlvi. p. 485, 1892) must be referred to. — Abstract communicated 

 by the Author. 



