162 



SCIENCE 



[N. S. Vol. XLIX. No. 1259 



least until the pressure of the upper atmos- 

 pliere has become readjusted, they establish at 

 the base of the stratosphere a layer of min- 

 imirm temperature. 



These conclusions are in full accord with 

 Figs. 2 and 3. 



Similarly, whatever the origin of the migra- 

 tory cyclone, another of the many meteorolog- 

 ical problems that needs further investigation, 

 one of its chief features is a deep wind in its 

 eastern portions from lower to higher lati- 

 tudes. In this ease the rotation of the earth 

 leads to a speeding up of the eastward com- 

 ponent of the velocity. Hence this air may be 

 expected to run forward and up and thus to 

 produce a low pressure to its rear. Because 

 of the upward trend thus given to much of 

 the air in the cyclone that portion of it below 

 the stratosphere is more or less dynamically 

 cooled. At the same time the stratosphere 

 bodily drops to lower levels wherever air has 

 been removed from beneath it. Hence its 

 pressure is increased at every level in propor- 

 tion to the initial pressure at that level and 

 its temperature thereby raised by an equal 

 amount throughout. 



Radiation and absorption probably also have 

 some part in determining the temperature con- 

 ditions and interrelations of migrant cyclones 

 and anticyclones, but the chief cause appears 

 to be purely mechanical, as above explained. 



THE LAW OF WIND-INCREASE WITH ELEVATION 



The fact that wind-velocity generally in- 

 creases with elevation has long been known, 

 but the 'law of this increase was not formu- 

 lated for any levels until only a few years ago, 

 nor the cause back of this law revealed until 

 still more recently. The law in question ap- 

 plies only to that portion of the atmosphere 

 that lies between the elevations of 3 to 4 and 

 . 8 to 9 kilometers. Nor could it in any modi- 

 fied form be satisfactorily extended to other 

 levels — not much below 3 kilometers, because 

 of the irregular disturbances due to surface 

 friction, innumerable barriers, and convec- 

 tional turbulence; nor much beyond 9 kilo- 

 meters, because not far from this level the 

 vertical temperature gradient, upon which the 



winds largely depend, rather abruptly and 

 greatly changes. The form of this law, that 

 applies as a first approximation to so much of 

 the atmosphere, is very simple. It says 

 merely that the velocity of the wind varies in- 

 versely with its density, or, in other words, 

 that the mass-flow is a constant. This was 

 determined empirically first by Clayton, of 

 this country, who hid his discovery in a 

 journal of small circulation; and subsequently 

 by Egnell of France, whose proper publication 

 won for the same discovery the appreciative 

 name Egnell's law. 



To show the rationale of this law it is con- 

 venient to assume the well known fact that 

 the velocity of a steady wind half a kilometer 

 or more above the surface and thus nearly 

 frictionless, is given approximately (neglect- 

 ing the generally small deflective force due 

 to cyclonic motion) by the equation 

 „ G 



p2u sin ((> 



in which G is the horizontal pressure gradient, 

 or difference in pressure per unit distance 

 normal, horizontally, to the local isobar, p the 

 density of the air, w the angular velocity of 

 the earth's rotation and <^ the latitude. From 

 this equation it follows at once that at any 

 place, the mass-flow, pv, is directly propor- 

 tional to the horizontal pressure gradient. 

 Hence to find the relation of mass-flow to ele- 

 vation it is sufficient to determine the relation 

 of horizontal pressure gradient to elevation. 



Consider, then, two adjacent columns of 

 air initially exactly alike, and let the tem- 

 perature of one be increased over that of the 

 other by the same amount throughout. Each 

 isobaric level in the warmed column will 

 thereby be raised in direct proportion to its 

 original height, and the horizontal pressure 

 thus established at each height h will be pro- 

 portional to the product of this lift by the 

 local density. That is 



hp 



But from the height of 3 or 4 kilometers 

 above sea level up to that of 8 or 9, the density 

 of the atmosphere is roughly inversely proper- 



