Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/13

CONTENTS

xvii

Art.	Page
409. The potential of a magnetic shell at any point is the product of its strength multiplied by the solid angle its boundary subtends at the point	32
410. Another method of proof	33
411. The potential at a point on the positive side of a shell of strength $\Phi$ exceeds that on the nearest point on the negative side by$4\pi \Phi$	34
412. Lamellar distribution of magnetism	34
413. Complex lamellar distribution	34
414. Potential of a solenoidal magnet	35
415. Potential of a lamellar magnet	35
416. Vector-potential of a lamellar magnet	36
417. On the solid angle subtended at a given point by a closed curve	36
418. The solid angle expressed by the length of a curve on the sphere	37
419. Solid angle found by two line-integrations	38
420. $\Pi$ expressed as a determinant	39
421. The solid angle is a cyclic function	40
422. Theory of the vector-potential of a closed curve	41
423. Potential energy of a magnetic shell placed in a magnetic field	42

Chapter IV.

Induced Magnetization.

424. When a body under the action of magnetic force becomes itself magnetized the phenomenon is called magnetic induction	44
425. Magnetic induction in different substances	45
426. Definition of the coefficient of induced magnetization	47
427. Mathematical theory of magnetic induction. Poisson s method	47
428. Faraday's method	49
429. Case of a body surrounded by a magnetic medium	51
430. Poisson's physical theory of the cause of induced magnetism	53

Chapter V.

Magnetic Problems.

431. Theory of a hollow spherical shell	56
432. Case when $\kappa$ is large	58
433. When $i=1$	58
434. Corresponding case in two dimensions. Fig. XV	59
435. Case of a solid sphere, the coefficients of magnetization being different in different directions	60