62 
Proceedings of the Royal Society 
tricity, magnetism, conduction of heat, and hydrokinetics, is merely 
kinematical, not dynamical. When we pass, as we presently shall, 
to a strictly dynamical comparison relatively to the mutual force 
between two hard steel magnets, we shall find the same law of 
mutual action between two tubes, with liquid flowing through each, 
hut with this remarkable difference, that the forces are opposite in 
the two cases ; unlike poles attracting and like poles repelling in 
the magnetic system, while in the hydrokinetic there is attraction 
between like ends and repulsion between unlike ends. 
II. (Proposition.) Consider two or more fixed bodies, such as the 
one described in Prop. I. The mutual actions of two of these 
bodies are equal, but in opposite directions, to those between the 
corresponding electro-magnets. The particular instance referred to 
above shows us the remarkable result, that through fluid pressure 
we can have a system of mutual action, in which like attracts like 
with force varying inversely as the square of the distance. Thus, 
if the exit ends of tubes, open at each end with fluid flowing through 
them, be placed in the neighbourhood of one another, and the enter- 
ing ends be at infinite distances, the mutual forces resulting will be 
simply attractions according to this law. The lengths of the tubes on 
this supposition are infinitely great, and therefore, as is easily proved 
from the conservation of energy, the quantities flowing out per unit 
of time are but infinitesimally affected by the mutual influence. 
III. Proposition II. holds, even if one of the bodies considered 
be merely a solid, with or without apertures ; if with apertures, 
having no circulation through them. In such a case as this the 
corresponding magnetic system consists of a magnet or electro- 
magnet, and a merely diamagnetic body, not itself a magnet, but 
disturbing the distribution of magnetic force around it by its dia- 
magnetic influence. Thus, for example, a spherical solid at rest 
in the field of motion surrounding a fixed body, through apertures 
in which there is cyclic irrotational motion, will experience from 
fluid pressure a resultant force through its centre equal and op- 
posite to that experienced by a sphere of infinite diamagnetic capa- 
city, similarly situated in the neighbourhood of the corresponding 
electro-magnet. Therefore, according to Faraday’s law for the lat- 
ter, and the comparison asserted in Prop. I., it would experience a 
force from places of less towards places of greater fluid velocity, 
