474 PROFESSOR KNOTT ON THE STRAINS PRODUCED IN IRON, 



becomes an ellipse drawn out radially. In the coiled tubes, on the other hand, this 

 ellipse is drawn out more in the tangential than in the radial direction, a feature which 

 also belongs to the (coiled) cobalt tube. A very similar, indeed almost identical, result 

 is obtained with the iron tubes. The central section of the strain ellipsoid in a 

 plane perpendicular to the axis of the cylinder has its greater axis parallel to the radius 

 of the cylinder ; or, in other words, m is either a greater negative ratio or a smaller 

 positive ratio than v. The onty exceptions are tubes A VI. and VII., B VI. and VII. 

 and the coiled tube C II. 



In general, then, we may draw the following conclusions regarding the behaviour 

 of tubes of the magnetic metals, iron, nickel, and cobalt : — 



1. The strain is one in which there is comparatively little change of volume, but 

 considerable change of form ; in other words, the magnetic st7*esses, acting on the 

 molecular groups, are mainly shearing stresses. This is 'particularly true of nickel. 



2. Except in the case of very thin walls, a circular element in any transverse plane 

 perpendicular to the axis of the cylinder becomes, when the cylinder is magnetized 

 parallel to its axis, an ellipse with its major axis pointing toivards the axis of the 

 tube. When the ivalls are thin, the ellipse into which a small circular element is 

 changed has its minor axis pointing toivards the axis of the tube. The ellipse, in 

 both cases, increases in excentricity as the distance from the axis diminishes. 



To obtain similar results with purely mechanical stresses acting on the surfaces 

 of a tube, we should have to take the normal stress on the external surface greater 

 than that on the internal surface for all but the tubes of widest bore ; and for the 

 wide bored tubes we should have to take the internal normal stress the greater. For 

 nickel and cobalt in all fields, and for iron in high fields, these surface stresses would 

 be tensions ; but for iron in low fields they would be pressures. This comparison is 

 merely intended to illustrate the character of the strain, for there can be no funda- 

 mental resemblance between the magneto-elastic problem discussed in this paper and 

 the purely elastic problem hinted at. In the one case we are dealing with the effect 

 of surface tractions upon a tube of elastic material ; in the other, with the effect of 

 magnetic body forces upon a tube of elastic material of high susceptibility. 



One invariable characteristic of the strain ellipsoid in nickel and cobalt is that the 

 minimum axis is parallel to the magnetizing force. This characteristic holds for iron 

 when the magnetizing force is distinctly higher than that which corresponds to the 

 change of sign of the longitudinal elongation. In other words, when the iron shows 

 marked contraction in the direction of magnetization, its behaviour, as determined by 

 the strain ellipsoid, is very similar to the behaviour of the other metals. 



Then, again, when the magnetizing force is such as to produce distinct positive 

 elongation in a direction parallel to its line of action, in this direction also lies the maxi- 

 mum axis of the strain ellipsoid. It is only during the transition condition, as the 

 longitudinal dilatation changes sign, that the corresponding axis of the strain ellipsoid 

 loses its maximum or minimum characteristic. 





