52 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES vou. 138, No. 4 
That a gale may exist across a mountain crest while the air is 
relatively calm below, is obvious from the facts (a) that adjacent layers 
of the air frequently have very different velocities, especially when the 
upper part of the under layer is colder than the under part of the 
upper layer, a condition that often occurs, and that permits the two 
distinct layers to flow, the one over the other, with but little inter- 
mingling, much as air flows over water; and (b) that in mountainous 
regions cold air, whatever its origin, tends, through its increased 
density, to fill the valleys and to become entrapped in them. Occa- 
sionally, therefore, the valley atmosphere, up nearly to the crests of 
the flanking mountains, is comparatively quiet while the air next 
above is moving rapidly directly across the trend of the ridges, and, of 
course, up so much of the windward sides of the mountains as pro- 
jects into this over current. 
But at the same time this wind of such obvious origin is blowing 
up one side of a mountain near its crest, a wind in the opposite diree- 
tion, and also shallow, is rushing toward the crest up the other side. 
The explanation of this counter current, the second portion of the 
problem under discussion, requires a little of that strait-jacket logic 
of the physicist. 
Let, then, the wind be in a steady state, constant at any place in 
direction, velocity, temperature, and density, and consider a tube of 
flow, that is, an imaginary tube of whatever size along which the air 
is flowing and across whose walls no air passes either in or out, Just 
above the top of the mountain; let m, be the mass of air that passes 
the crest during a given interval of time along this tube; let v; be the 
volume of this mass as it passes, p: its pressure, and wu its velocity. 
Similarly, let 7.2, v2, pe, Ws, be the corresponding values during the 
same interval of time for any cross section of the tube beyond the 
crest. Then, since the wind is in a steady state, m: = m2. Further- 
more, the simultaneous flows of energy along the tube by these two 
cross sections are also equal, because, as specified, no changes are 
occurring at any place. Finally, if the change of temperature of the 
surrounding air with change of altitude is strictly in keeping with the 
corresponding change in pressure—and in winds that are of the breeze 
order or stronger it is nearly so owing to their considerable stirring 
up, or turbulence—then the gravity contribution to the potential 
energy of a mass of air as it passes from one level to another is negli- 
gible, or, in other words, no appreciable work is required to lift a mass 
of air to a greater height or to pull it down to a lower level. There- 
