42 Mr. G. H. Bryan. [Nov. 22, 



have maximum concentrative power (semi-vertical angle = 54 44'). 

 Under these circumstances the magnetic force at the vertex due to 

 the free magnetism on the conical faces is 



18,930 lo glo l, 

 a 



where b is the diameter of the poles at the base of the cones, and 

 a the diameter of the central neck. 



The following are probable values of the intensity of magnetism 

 when saturation is reached in the particular metals examined : 



Saturation 

 yalue of J. 



Wrought iron 1700 



Cast iron 1240 



Nickel (with 0'75 per cent, of iron) .... 515 

 Nickel (with - 56 per cent, of iron) .... 400 

 Cobalt (with 1'66 per cent, of iron) 1300 



Experiments were also made with specimens of Vickers' tool steel, 

 and other crucible steels, Whitworth's fluid-compressed steel, Bessemer 

 steel, Siemens steel, and Hadfield's manganese steel. This last 

 material, which is noted for its extraordinary impermeability to mag- 

 netic induction, was found to have a constant permeability of about 

 l - 4 throughout the range of forces applied to it, namely, from 2000 

 to nearly 10,000 c.g.s. 



The results are exhibited graphically by curves drawn in Rowland's 

 manner to show the relation of the permeability to the magnetic 

 induction. In the highest field examined, the permeability of wrought 

 iron had fallen to about 2. 



V. "The Waves on a" rotating Liquid Spheroid of finite 

 Ellipticity." By G. H, BRYAN, B.A. Communicated by 

 Professor G. H. DARWIN. Received November 6, 1888. 



(Abstract.) 



The hydrodynamical problem of finding the waves or oscillations 

 on a gravitating mass of liquid which when undisturbed is rotating 

 as if rigid with finite angular velocity in the form of an ellipsoid or 

 spheroid, was first successfully attacked by M. Poincare in 1885. 



In his important memoir " Sur 1'Equilibre d'une Masse fluide 

 animee d'nn Mouvement de Rotation,"* Poincare has ( 13) obtained 

 the differential equations for the oscillations of rotating liquid, and 

 * ' Acta Mathematical vol. 7. 



