A.—MATHEMATICS AND PHYSICS. 23 
Tf now the oil is made to flow along the length of the tank a new force is 
called into play, due to the earth’s rotation. This force is horizontal and 
in the northern hemisphere tends to drive the moving oil to the right of 
its motion. If the partition.is on the right of the motion, the oil cannot 
move in that direction and the partition takes the additional pressure due 
to the deflecting force of the earth’s rotation. Before the motion started, 
the difference of pressure on the two sides of the partition obviously 
increased from the top to the bottom. It is possible to conceive the 
~ motion of the oil increasing with the depth at such a rate that the deflecting 
force of the earth’s rotation would just balance the difference of pressure 
at each depth due to the difference in density. If this could be arranged, 
the pressure on each side of the partition at each point would be equal 
and the partition could be withdrawn without disturbing the equilibrium. 
We should then have the oil and water existing side by side in equilibrium 
without any tendency of the water to flow under the oil. 
In practice, however, the oil could not be caused to flow in the required 
artificial manner without introducing forces which themselves would 
destroy the equilibrium. The mathematical investigation shows, however, 
that the deflecting force of the earth’s rotation, combined with gravity, 
- leads to a system of forces which produces the same effect, except that the 
surface dividing the oil and water does not remain vertical but slopes at a 
definite angle. If the oil moves with the same velocity throughout, the 
surface of discontinuity remains plane and the angle of its slope depends 
only on the difference in density between the oil and the water, the velocity 
of motion, and the latitude in which the experiment takes place. When 
equilibrium has been reached in this way the sloping boundary between 
the oil and water is stable to small disturbances, and deformations only 
produce waves which travel along the boundary with a definite velocity. 
The mathematical investigation of the similar problem as applied to 
discontinuities in the atmosphere has shown that the result is the same. 
Two bodies of air at different temperatures will remain in equilibrium 
side by side if suitable motion parallel to the boundary is given to the air 
on each side. The angle which the surface of discontinuity makes with 
the horizontal depends on three factors, namely, the latitude and the 
difference in temperature and relative motion of the warm and cold 
currents. Given steady motion, these three factors adjust themselves in 
a perfectly definite way, with the cold air lying as a rule in the acute angle 
which the boundary makes with the horizon. 
V. Bjerknes considers that there are three great permanent surfaces 
of discontinuity of this kind in the atmosphere, and that the slope of the 
surface in each is in accordance with the discontinuities of the wind and 
density observed on the two sides. 
Taking these in turn, the first is the great surface of discontinuity 
between the troposphere and the stratosphere. In this case the strato- 
_ sphere is relatively the warm body of air and the troposphere is relatively 
the cold body of air. The air in the troposphere has an easterly drift 
relatively to the air in the stratosphere, and therefore, according to the 
formule, the surface of discontinuity should slope downwards towards the 
poles. Now we know from observation that the stratosphere is lower 
over the poles than over the equator, and Bjerknes considers that the 
observed values of the changes in wind and temperature on passing from 
