61 
of Edinburgh, Session 1869 - 70 . 
proved [from § 63 Exam. (2.) ]* that the velocity of the fluid at any 
point in the neighbourhood agrees in magnitude and direction with 
the resultant electro-magnetic force, at the corresponding point, in 
the neighbourhood of an electro-magnet replacing the solid, con¬ 
structed according to the following specification. The “core,” on 
which the “ wire ” is wound, is to he of any material having infinite 
diamagnetic inductive capacity,f and is to be of the same size and 
shape as the solid immersed in the fluid. The wire is to form an 
infinitely thin layer or layers, with one circuit going round each 
aperture. The whole strength of current in each circuit, reckoned 
in absolute electro-magnetic measure, is to be equal to the circulation 
of the fluid through that aperture divided by d ^ r. The resultant 
electro-magnetic force at any point will be numerically equal to 
the resultant fluid velocity at the corresponding point in the 
hydrokinetic system, multiplied by \Z4tt. 
Thus, considering, for example, the particular case of a straight 
tube open at each end, let the diameter be infinitely small in com¬ 
parison with the length. The “ circulation ” will exceed by but an 
infinitely small quantity the product of the velocity within the 
tube into the length. In the neighbourhood of each end, at dis¬ 
tances from it great in comparison with the diameter of the tube and 
short in comparison with the length, the stream lines will be straight 
lines radiating from the end. The velocity, outwards from one end 
and inwards towards the other, will therefore be inversely as the 
square of the distance from the end. Generally at all considerable 
distances from the ends, the distribution of fluid velocity will be the 
same as that of the magnetic force in the neighbourhood of an infi¬ 
nitely thin bar longitudinally magnetised uniformly from end to end. 
Merely as regards the comparison between fluid velocity and re¬ 
sultant magnetic forces, Euler’s fanciful theory of magnetism is thus 
curiously illustrated. This comparison, which has been long known 
as part of the correlation between the mathematical theories of elec- 
* Or from Helmholtz’s original integration of the hydrokinetic equations. 
t Real diamagnetic substances are, according to Faraday's very expressive 
language, relatively to lines of magnetic force, worse conductors than air. 
The ideal substance of infinite diamagnetic inductive capacity is a substance 
which completely sheds off lines of magnetic force, or which is perfectly im¬ 
pervious to magnetic force. 
VOL. VII, 
I 
