THE TROCHOIDED PLANE. 65 
I will now state my views as to the formation of vortices, by an 
imperfect plane passing end on through a viscous medium. 
If the plane is perfect and of no thickness, and the medium 
homogeneous, no vortex can be formed; but if the plane has 
the leading end of the plane, the stratification of the medium 
parallel to the plane becoming prolate-cycloidal. When the pro- 
portion between the amplitude of the disturbances, and the wave 
length or distance apart of two zones of compression, exceeds 
that of one to II, or the prolate-cycloid passes into a curtate- 
system of waves, or begin a fresh series farther out from the plane. 
If the force acts at right angles to the plane, a vortex is generated 
behind the plane. 
A breaker shows the vortex initiated vertically, but gravity 
prevents its complete formation. 
A common instance of this action is seen in the skin of eddying 
screw-propeller blades in the unaccountable manner we so often 
see them. I may also add that the pitting of the interior of steam- 
boilers at and near the water-line is to my mind clearly the 
mechanical action of vortices formed by the rapid circulation of 
Th us to a considerable distance from where I started 
with the plane wave, but I thought it best to indicate the natural 
sequence an » WORE a< il 4 £1) fr 4} 4 } Lge 1 pl aaa 
vortex, and will now try to show some natural movements of matter 
and mechanisms that I associate with the different sorts of waves. 
irst, about ocean waves, we find much has been written by 
the late Mr. Scott Russell and others, dealing with their form, 
and the motion of the particles composing them, about the forced 
wave and the free wave ; but no one, as far as I have read, seems 
to note when dealing with the trochoidal form, the motion of the 
imaginary line that I call the connecting-rod, and which appears 
to me to be as important in describing that wave as the radius is 
to the circle (this is probably due to the form of long free ocean 
waves being approximately trochoidal) ; and I do not hesitate in 
saying that the connection of the trochoidal wave and trochoided 
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