18 REPORT—1852. 
spheres placed near one another and subjected to the influence of an electrified 
point, whether in the line joining the centre of the spheres or not; but the formule 
expressing the details were not brought forward. 

On certain Magnetic Curves ; with applications to Problems in the Theories 
of Heat, Electricity, and Fluid Motion. By Professor W. Tomson, 
MA, F.RSL. & FE. 
A method, which had been given by the author in the Cambridge Mathematical 
Journal for integrating the differential equations of the lines of force in any case of 
symmetry about an axis, is applied in this communication to the case of an infinitely 
small magnet placed with its axis direct or reverse along the lines of force of a 
uniform magnetic field. Diagrams containing the curves drawn accurately, accord- 
ing to calculations founded on the result of this investigation, (corresponding to 
series of ten or twelve different values given to the constant of integration,) were 
exhibited to the Section. Certain parts of these curves were shown in a separate 
diagram, as constituting precisely the series of lines of electric force about an insu- 
lated spherical conductor under the influence of a distant electrified body ; and the 
other parts, in a separate diagram, as constituting the lines of motion of a fluid mass 
in the neighbourhood of a fixed spherical solid, at considerable distances from which 
the fluid is moving uniformly in parallel lines so mry as to cause no eddies round. 
the obstacle. The circle representing the section of the spherical conductor, in the 
former of these diagrams, cuts the entire series of curves at right angles, with the 
exception of one curve, which it cuts through a double point at an angle of 45° to 
each branch. The circle representing the section of the spherical obstacle in the 
latter diagram, along with two infinite double branches consisting of the axial dia- 
meter produced externally in each direction, constitutes the limiting curve of the 
series shown, and is not intersected by any of them. A series of diagrams (deduced 
from the former of these by describing a circle of the same size as that shown in it, 
and drawing, on a smaller scale, as much of the curves as lies without this circle,) 
was shown as representing the disturbed lines of magnetic force about balls of ferro- 
magnetic substance of different inductive capacities, placed in a uniform magnetic 
field; and another series, similarly derived from the latter, (that is, the one repre- 
senting the lines of fluid motion about a spherical obstacle,) was shown as represent- 
ing the disturbance caused by the presence of diamagnetic balls of different inductive 
capacities in a uniform magnetic field. These two series of diagrams are also accu- 
rate representations of the lines of motion of heat in a large homogeneous solid 
having heat uniformly conducted across it, as disturbed by spherical spaces occupied 
by solid matter of greater or less conducting power than the matter round them ; 
the two principal diagrams from which they are derived being the corresponding 
representations for the cases of spherical spaces occupied respectively by matter of 
infinitely great and infinitely small conductivity. The author called attention to 
the remarkable resemblance which these diagrams bore to those which Mr. Faraday 
had shown recently at the Royal Institution to illustrate his views regarding the 
action of ferromagnetics and diamagnetics in influencing the field of force in which 
they are placed ; and justified and illustrated the expression ‘conducting power for 
the lines of force,”’ by referring to rigorous mathematical analogies presented by the 
theory of heat. 
On the Equilibrium of elongated Masses of Ferromagnetic Substance in 
uniform and varied Fields of Force. By Professor W. Tomson, M.A, 
FRSL. & E. 
The fact, first discovered experimentally by Gilbert, that a bar of soft iton, held 
by its centre of gravity in a uniform magnetic field, settles with its length parallel 
to the lines of force, is not explained correctly when it is said to be merely due to 
the property of magnetic induction in virtue of which the bar of soft iron becomes 
temporarily a magnet like a permanent magnet in its position of stable equilibrium. 
For exactly the same statement would be applicable to a row of soft iron balls rigidly 
alt: 
