526 
temperature associated with weather and annual varia- 
tions, and also on account of the difficulty the S: wave 
would have in twice daily surmounting the heights of 
Central Asia and the Rocky Mountains without losing a 
material fraction of its energy. These irregularities, 
however, are on a relatively small scale. The possibility 
that the variations of mean temperature from year to 
year might affect the tuning was examined by Bartels 
[12], but no such effect was found. 
Taylor also was led to doubt the validity of the 
resonance hypothesis, despite the strength of the general 
arguments in its favour. Lamb had assumed, on the 
basis of the work already mentioned, that free oscilla- 
tions of the atmosphere can exist which are identical, in 
distribution and period, with those of an ocean of such 
depth that long waves are propagated in it with the 
speed that he calculated for plane atmospheric waves. 
This assumption was used by Taylor [100] to estimate 
the period of the oscillation of S2 type to be expected in 
an atmosphere in which the speed of propagation of long 
waves was that of the waves produced by the Krakatoa 
volcanic eruption of 1883. This great atmospheric pulse 
was propagated more than once round the entire earth, 
with a speed of 319 m sec, which corresponds to an 
equivalent depth h = 10.4 km, a value markedly too 
great to give a free period (for an oscillation of S» type) 
nearly equal to 12 hours. 
Lamb’s assumption may be regarded as an extension 
of Laplace’s theory of waves in an isothermal atmos- 
phere. As realised later by Taylor, it involves the 
possibility that the atmosphere may have many equiva- 
lent depths, a contingency not possible in the atmos- 
pheres of the special type considered by Laplace and 
Lamb, for which h = Ho. Lamb’s assumption is not 
obviously true, but in 1936 Taylor [101] proved its 
validity, and further developed Lamb’s investigation of 
oscillations that are distributed in a similar way geo- 
graphically (that is, as functions of longitude » and 
colatitude @), but have different height distributions of 
motion. In this work he was the first to take account of 
the cessation, at the tropopause, of the upward decrease 
of temperature. 
The following year Pekeris [86] applied Taylor’s meth- 
ods to determine the free periods of an atmosphere in 
which the stratospheric temperature increases upwards 
above a certain height. This temperature distribution 
had been inferred from studies of the abnormal propa- 
gation of sound to great distances (beyond a zone of 
silence surrounding the source of sound), as well as from 
the heights of occurrence of meteors. Pekeris showed 
that, subject to a certain condition, the atmosphere 
could oscillate in ways corresponding to two equivalent 
oceanic depths. One of these was about 10 km, associ- 
ated with a speed of propagation equal to that of the 
Krakatoa wave; the other gave a period (for a geo- 
graphical distribution of S. type) of very nearly 12 
hours, though the uncertainty of the upper atmospheric 
data precluded an exact calculation of the free period. 
The condition referred to was that the atmospheric 
temperature, after increasing upward above the strato- 
sphere, should reach a maximum and thereafter decrease 
DYNAMICS OF THE ATMOSPHERE 
upwards to a low value. This was in agreement with the 
temperature distribution proposed by Martyn and Pul- 
ley [80] in 1936. 
An important conclusion reached by Pekeris on this 
basis was that at high levels the pressure variation may 
be reversed in phase and highly magnified. This fitted 
well with the dynamo theory of the solar and lunar 
daily geomagnetic variations, the phases of which dis- 
agree with those of S, and L» at the ground, and the 
amplitudes of which, in the light of present knowledge 
of the electrical conductivity of the ionosphere, must be 
much greater than those of S. and Ls at the ground. 
The magnified amplitude of L. there is confirmed by 
the determination [6] of the lunar tide in the E-layer, 
though the phase in the E-layer (over England) does 
not show the predicted reversal. 
Pekeris [86] in 1939 re-examined the barometric traces 
for the Krakatoa waves and found evidence of a minor 
component wave propagated with the speed of 280 m 
sec, corresponding to an equivalent depth of 7.9 km, 
accordant with a free oscillation (of S. type) with a 
period nearly equal to 12 hours. He showed that as the 
explosion occurred at a low level most of the energy of 
the pulse should go into the faster-travelling wave. (He 
estimated this energy as about 10” ergs, roughly 1000 
times that of the waves set up by the Nagasaki atomic 
bomb explosion.) The waves set up by the 1908 Si- 
berian meteorite have been similarly examined [110] by 
Whipple. 
The discussion by Pekeris has been extended by 
Weekes and Wilkes [107, 111], who have shown that 
according to theory the height distribution of the ampli- 
tude and phase of L, may differ materially in the iono- 
sphere from that of S., if there is an upward rise of 
temperature in the E-layer followed by an upward 
decrease above some height in that layer, where the 
temperature has another maximum (with a further rise 
of temperature in the F-layer). The observational stud- 
ies of the tidal motions and tidal changes of electron 
density in the different ionospheric layers, now being 
actively pursued [4, 5, 26, 76-81], will throw light on this 
possibility. Reliable measurements of ionospheric tem- 
peratures by rocket-borne instruments naturally pro- 
vide a valuable additional basis for a detailed theory of 
the oscillations. 
In the free oscillations of a liquid ocean of uniform 
depth h, the velocity components u, v, and w, and the 
departure Ap of the pressure from its mean value p (at 
each depth), have a relative geographical distribution 
(or variation with @ and ¢) that is independent of depth. 
These dependent variables u, v, w, and Ap are taken 
to be proportional to (the real part of) exp i(se + ot), 
where 27/o is the free period t;. Laplace obtained a 
“tidal” equation which, for given values of s and h, 
determines a series of values of c, and a corresponding 
series of functions representing the variation of u, 2, 
w, and Ap with the colatitude 0. 
The same equation is applicable to the forced oscilla- 
tions of an atmosphere, whatever its temperature-height 
distribution (supposed uniform over the globe); in this 
case o (as well as s) is known (27/o is the imposed 
