634 
In the other alternative, namely, a>g, we have two 
cases to distinguish : 
a2 
(1) (—@) <7 
In this case \, and A, are both real and negative. The 
equilibrium at U, I is stable, the disease will become 
definitely established, if once started. The approach 
to equilibrium is aperiodic, asymptotic. 
(2) a*m m at 1) 
aie ae <4 NY bade 
44 te” be 
In this case \, and \, are complex, with negative real 
parts. The equilibrium at U, I is still stable, but will 
be approached by a periodic process of damped oscilla- 
tions. 
It may be remarked that a solution can still be 
given if the coefficients a, m, g, which have here been 
treated as constants, are regarded as periodic or even 
as general functions of the time. However, the 
numerical evaluation of the coefficients appearing in 
the solution then becomes very onerous, It will 
suffice, on this point, to refer to the pertinent mathe- 
matical literature, as, for example, Picard, ‘‘ Traité 
d’Analyse,”’ 1908, vol. 3, pp. 187, 188, 194, 197; 
Goursat, “‘ Traité d’Analyse,” vol. 2, 1918, pp. 482, 
498. 

ALFRED J. LOTKA. 
Johns Hopkins University. 

The Cause of Anticyclones. 
IF space permits, I should like to reply to one or 
two points in the letter contributed by Mr. W. H. 
Dines to Nature of April 14, p. 495. , 
(1) In the first place, when one is dealing with 
two different sorts of air, probably of unequal fre- 
quency of occurrence, it appears to me to be unsafe 
to depend very greatly on comparison with mean 
values derived from all cases considered en masse. 
Has not the Bjerknes theory been elaborated as the 
result of an attempt to deal with the problem of 
atmospheric circulation on the assumption that dis- 
continuities might exist, and that therefore—as other 
methods would probably fail to reveal them—only 
close study of individual cases could hope to succeed ? 
Apart from this, Mr. Dines deals with departure 
of temperature from the mean for the height and 
date. In the paper (Q.J.R. Met. Soc., Jan. 1923) 
to which reference was made in my earlier letter 
(Nature of March 31, p. 429) temperature is dealt 
with throughout in relation to given isobaric surfaces. 
This seemed particularly desirable in the case of 
polar air, for a mass of such air, leaving polar regions 
with high velocity and low barometric pressure, 
may eventually find itself, with -much reduced 
velocity and with a pressure increased by some 
20 to 30 millibars, forming the surface layers of an 
anticyclone in temperate regions. The correspond- 
ing adiabatic increase of temperature (communica- 
tion of heat from warmer seas, etc., being left out of 
account as being more or less common to all polar 
air moving southward) would be 3° to 5° F., or 
enough to bring the temperature at a fixed height 
up to about the mean temperature for that height. 
If the fifty-two cases of anticyclones referred to by 
Mr. Dines are considered from the point of view of 
normal temperature fora given pressure it will be 
evident that about half must be of polar air up to 
1 km., and I think this is about as large a proportion 
as I should claim for that level. Rather more than 
one-fifth would then be polar up to 3 km., and so on. 
(2) The question in regard to humidity is very 
NO. 2793, VOL. 111] 
NATURE 


[May 12, 1923 
complex; but I have always taken exception to 
the view that humidity (either relative or absolute) 
would be of much value in distinguishing between — 
polar and equatorial air apart, that is, from its value 
for locating the discontinuity. In particular, polar 
air, in its passage over warmer seas, should have > 
its humidity at all heights affected quite as greatly 
as its temperature. Equatorial air, on the other 
hand, is being cooled in its surface layers in, the 
course of its northward journey, and the cooling 
effect does not tend to be propagated upward to any 
comparable extent; such factors as are at work 
within equatorial air tend rather to rob it of its 
water vapour without renewing the supply. 
I do not, therefore, consider that where polar air 
lies under equatorial air the inversion of tempera- 
ture need necessarily be associated with any particular 
peculiarity as to relative humidity. At the same time, — 
the conspicuous decrease of relative humidity is well 
known and appears to be common, at least to all 
inversions in anticyclones. It may, therefore, be a 
natural sequel to the inversion itself, and I offer an 
explanation which seems to me not altogether im- 
possible. It is that the inversion of temperature 
once formed acts as a non-return valve to moisture 
(in the same way that it almost certainly does to 
dust and haze in the atmosphere), and that very soon 
the ‘‘ convectional lid ’’ accumulates a concentration 
of water vapour just beneath it; the layer of air 
just above, on the other hand, succeeds in passing 
on upward or allowing to drop below the greater 
part of both its dust and its moisture while re- 
plenishment of these from below has ceased. ‘ 
A. H.-R. GorpiEs 
Wimbledon, S.W.19, if 
April 26. 

TuE reply of Mr. W. H. Dines, in Nature, April 14, 
p- 495, to Maior Goldie’s letter, brings out very 
convincingly the peculiar fact that the temperature 
conditions of the troposphere, both in cyclones and 
anticyclones, are such as would rather obliterate 
than maintain them. Indeed, when we consider the 
problem of pressure distribution, we find that the 
conditions are generally exactly the reverse of those 
required by the ordinary accepted theory, except in 
latitudes within the tropics of Capricorn and Cancer. 
We are thus faced with a very striking theoretical 
difficulty ; for the winds of the earth do not appear, 
in the main, to derive their force and direction from 
the temperature conditions at or near the earth’s 
surface. 
One of the most marked effects of surface tempera- 
ture on the pressure distribution, other than the 
phenomena of the trade winds, is the fact that 
along the high-pressure belts of the tropics the 
pressure is greatest over the cold land masses during 
the winter and lowest over the heated land masses 
during the summer. Another clear effect of surface 
temperature is the fact that the North Pacific cyclone 
and the North Atlantic cyclone (the eyes of the 
North Polar cyclone) are more powerful during the 
summer than they are during the winter. However, 
we have to set against these considerations the 
striking facts that throughout the year the great 
low-pressure areas are over the frigid poles, which — 
are not even exposed to the sun’s rays during the 
winter, and that the high-pressure belts are near the 
tropics of Cancer and Capricorn, and cover the 
intensely-heated desert lands of the continents. To 
surface temperatures, on the other hand, must be 
ascribed the great seasonal changes of pressure 
and temperature which occur over the elevated 
areas of Asia. ; 


