THE TROCHOIDED PLANE. 63 
If I have succeeded in communicating my views with regard to 
the motion of a plane surface when acted on by an undulati 
one, and the converse, it will be obvious that if the undulating 
surface is rolled up into a cylinder, with the axis parallel to the 
direction of propagation of the waves, the same reasoning will 
hold good, fon reduce the examples of cylindrical waves to plane 
waves ; but when we consider the action of the particles com- 
sing the axis of the cylinder, it becomes necessary to explain 
the spherical wave. 
Let us suppose a sncpagier shell to be composed of any elastic 
medium, also, the polar axis to be similarly constituted ; let the 
pane of bisection of ws ms 0 axis come exactly between two of 
which two particles we will set approach: 
and receding | eee one another ; this will send an equal series 
of waves of extension and compression through the two halves of 
the polar axis, culminating in the pushing out and pulling in of 
the poles synchronously, and the generation of a series of 
waves passing over each hemisphere, meeting at the equator, and 
crossing each other to the opposite poles. The orbits of the par- 
ticles Somponnia the sphere will at first be long ellipses ; ; as the 
waves recede further from the poles the orbits become circular ; 
one wave length from the equator they become elliptic again ; at 
the equatorial plane they move radially to the sphere, and after 
one wave has reached the opposite pole, every particle of the 
spherical shell will be moving radially and harmonically with the 
two central vibrating particles. Any number of atoms may be 
conceived as being at the centre, and completely filling the sphere, 
vibrating in every direction, causing an capa ef spherical 
waves on se spherical shell, crossing in every direct 
If e the converse of this, and suppose the. equatorial 
ei, or ‘dane in any parallel of latitu de, to be set vibrating 
in unison, radially, the resultant will be an intensified vibration of 
the polar axis longitudinally ; this is closely analogous to a sea 
wave meeting a vertical obstruction, and causing that horizontal 
downward-moving vortex that is so destructive to the foundations 
of steep smooth marine structures in shallow water. Where 
occurs, the practice is to tumble in loose blocks of stone or con 
crete, the effect of which is to break up the vortex, and rob it of 
its 
dur 83 Sydney summer thunder-storms often show this atmospheri- 
cally; the sun’s heat over the land causes the sea-breeze to come 
in from the N.E. with increasing force as the day advances, and 
the heated air returns to the sea by an upper current from the 8. W. 
There is an upward current at the Blue Mountains, or where the 
sea-breeze takes off in force, and heavy cumulus ‘clouds gather, 
their tops being drawn out by the return current in long streaks 
pointing seaward ; towards evening, if more air comes in than can 
