Fitz Gmratp—AHypothesis as to Electro-Magnetic Actions. 51 
‘to fill space with a series of approximately straight hollow vortex 
filaments which would be in stable steady motion. This seems to 
finally dispose of the objection that diffusion of vortices must take 
place, at least in the case of hollow vortices; and by making the 
vortex filaments sufficiently fine, the space might be filled with full 
vortices whose rate of diffusion could be made as slow as necessary 
to explain the ether, even if it could be shown that such an arrange- 
ment of full vortices would not be stable. 
What I now desire to call attention to, is a hypothesis as 
to the nature of the wave motion which can be transmitted by a 
system of vortex filaments. 
A vortex filament can have a spiral wave superposed upon it. 
‘The irrotational motion in the neighbourhood of this screw will be 
essentially the same as the distribution of magnetic force near a 
similar spiral wire carrying an electric current. There will be, on 
the whole, a flow along the inside of the spiral, but the motion 
of the fluid is complex. It could, however, be defined by a vec- 
tor, whose direction was parallel to the axis of the spiral, and 
whose magnitude was measured by the square root of the mean 
square of the additional energy per unit length of the moving 
fluid above that of the undisturbed vortex. If then a space were 
filled with spiral vortices, all parallel to a given line, and causing 
flow in the same direction, there would be an increase in the 
energy per unit volume which could be measured by the square 
of a vector, say H. There would be, on the whole, a flow of fluid 
along the axes of these spiral vortices. Now, consider the case 
of a single spiral vortex surrounded by other parallel straight ones. 
These latter would not stay straight. ‘They would be bent by the 
action of their spiral neighbour, and spiral waves would be set up 
along them. How can we describe this transference of spirality 
from one vortex to one of its neighbours? It depends upon two 
vectors—one the vector parallel to the axis of the spiral, and the 
other a vector perpendicular to the two vortices. ‘The vector then 
defining the transference, being itself defined by two rectangular 
vectors, must be a vector perpendicular to both, ¢.e. must, in the 
ease of a spiral vortex surrounded by others which it is setting in 
motion, be distributed in circles round the spiral vector. What 
will the magnitude of this new vector depend on, and how can we 
define it further? Its magnitude will depend on how fast the 
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