Firz Grratp— Hypothesis as to Electro-Magnetic Actions. 58 
confined to the actions already described between the spirals and 
the accompanying flows within and near them. On this hypo- 
thesis these vortex spirals would be representatives of the Faraday 
lines of force. 
The hypothesis here put forward very tentatively does not 
include any supposition as to the nature of matter, nor as to how 
the singular points that represent electric charges, or electrons, can 
be connected with matter. At the same time it goes some way 
towards showing that the hypothesis—that the ether is a turbu- 
lent liquid—has great possibilities underlying it. 
In explanation of the above, it may be well to state clearly 
the assumptions underlying it. It is asswmed that the spirality 
described is propagated unchanged as a wave. This is justified by 
pointing out that this spirality is essentially the laminar motion 
investigated by Lord Kelvin, because it involves a flow in the 
direction of the axis of the spiral, and such a flow cannot take 
place along the direction of a vortex filament without a spiral 
deformation of the filament. Lord Kelvin illustrated his theorem 
by reference to a system of vortex rings which would, however, 
diffuse among one another in a way that was contrary to one of 
his fundamental assumptions: while I am citing, as an example 
of his theorem, the case of infinite approximately straight vortex 
filaments which he has shown might, certainly if empty, exist in 
steady motion in presence of one another. 
It has further been assumed that, initially, SAH=0. This may 
be justified as follows :—If we assume that, initially, the singular 
points are points from which a large number of long spirals pro- 
ceed in various directions, it is evident the same number must enter 
as leave any surface which does not surround one or more of these 
singular points, and that the excess of those entering above those 
leaving, will be a measure of the number of their singular points 
within the surface. Calling this latter p, per unit volume, we get 
at once SAH = 4zp, initially. Where p=0, we have SAF = 0, and 
as SAE =0 at all these points, we see that, even though the 
original distribution in long spirals rearranges itself among the 
surrounding vortices, nevertheless SAH will continue to vanish 
at all these places where there are no singular points. 
Tt may also be worth while calling attention to the method ot 
analysis used in this note. I have taken a vector H, to represent 
