ATMOSPHERIC TIDES AND OSCILLATIONS 
period ¢;), and the equation determines a series of 
values of A and a corresponding series of functions 
representing the latitudinal variation. 
The height distribution of u, v, w, Ap, and Ap (the 
departure of the density at any height from its mean 
at that height) is determined by a separate equation, 
conveniently expressed in terms of the pressure at 
each height, as an independent variable, by taking x 
=— In (p/po). If we write 
— D In (p + Ap)/Dt = (po/p)*y, 
where v denotes the vector velocity, and D/Dt the 
“mobile operator” [73], the equation is 
dy lo Wap i dH | 
T+] tif y He | Wal; 
in which the height-distribution of the atmosphere 
(depending on the temperature 7 and the mean molecu- 
lar mass m), is involved through H. In so far as y can 
be considered as of fairly constant order of magnitude 
(and this is a matter for examination by means of this 
equation), the expression for div v above indicates an 
upward increase of div v inversely proportional to p’, 
that is, by 1000-fold at about the height of the E-layer. 
Weekes and Wilkes have given an interesting inter- 
pretation of this equation by analogy with the propaga- 
tion of electromagnetic waves in a medium having a 
variable refractive index. In the atmospheric case the 
expression for the analogous “equivalent” refractive 
index 1s 
2. ot, Dens = 
roe pal ry ie 
If the height-distribution of H, for any value of h, 
makes 2 negative at a certain level, upward propaga- 
tion of the energy, mainly put into the atmosphere by 
tidal or thermal causes in the lower layers, is effectively 
blocked. The air at that height acts as a barrier, total 
or partial, trapping the energy, and building up the am- 
plitude in the whole spherical shell between the ground 
and the barrier, giving rise to resonance. If p? is nega- 
tive, not for all heights above the level Z at which it 
first becomes zero, but only for an interval of height, 
the barrier is partially transparent, and some of the 
oscillatory energy passes through it, either to a second 
(or third) barrier where there is a height interval of 
negative w?, or to the high levels at which thermal 
conductivity and dissipation of the energy into heat by 
viscosity become important. At these high levels the 
condition that Ap/p or Ap/p is small, as assumed in the 
equation, ceases to hold, and the modified differential 
equations will become nonlinear. 
The conditions favouring negative yw? are that H 
should be small and that dH/dx should be either posi- 
tive and small, or negative, corresponding to an upward 
decrease of temperature, because « increases upwards. 
The number of barriers to energy flow depends on the 
number of such regions of upward-decreasing tempera- 
ture, but they alone are not sufficient to give a barrier, 
unless the value of h is appropriate, which in turn 
div v = 
527 
depends on the mode and period of the oscillation under 
consideration. 
The boundary conditions in the equation for y are 
that at high levels the energy flow is upwards, and that 
at the ground (Z = 0 and x = 0) the vertical velocity 
is zero—unless the influence of the tidal motions of the 
under surface of the atmosphere (the tides in the oceans 
and in the solid earth) is being taken into account 
[12, 55], in which case at Z = O the vertical velocity w 
must have the corresponding distribution of values. 
Wulf and Nicholson [112] have made a bold and 
imaginative attempt to explain the main irregularities 
of the geographical distribution of L», and its remarkable 
annual changes, stressing in particular the much greater 
and more widespread surface irregularities over the 
earth’s Northern Hemisphere than over the Southern 
Hemisphere. Their suggestions need to be formulated 
and analysed mathematically, and tested also by ref- 
erence to So, with its somewhat different geographical 
pattern and annual change. 
The part of S. that is symmetrical about the earth’s 
axis must be due to some inequality in longitude in the 
distribution of the semidiurnal component of the daily 
variation of air temperature, but no detailed study of 
this has yet been made. 
SUGGESTIONS FOR FUTURE WORK 
There is still great scope for useful extensions of our 
knowledge of the facts of the atmospheric oscillations, 
both solar daily and lunar daily. The newest and richest 
field of such observational and computational study is 
offered by the ionosphere with its several layers, each of 
which needs separate examination as regards the solar 
and lunar daily changes in its height, electron density, 
and other properties. Another new and almost untilled 
field of study is offered by the continuous records of 
cosmic radiation, whose components with different pene- 
trative powers likewise deserve independent treatment. 
An older but far from exhausted field is that of the daily 
magnetic variations, which are causally due to the at- 
mospheric cscillations in the ionosphere. Meteoric data 
may also add to ourknowledge ofthe oscillations, though 
their more sporadic nature renders them less convenient 
for statistical treatment; this disadvantage may pos- 
sibly be mitigated in the future if practical methods of 
radio observation of meteors, continuous throughout 
the day and night, are developed. 
Even as regards the manifestation of the oscillations 
at ground level, where they have been studied for over 
a century, there remains much useful work to be done; 
the daily variations of pressure still need further study, 
and an improved treatment of the solar daily variation 
of air temperature is required to elucidate the thermal 
part of the solar half-daily tide. The lunar tide in air 
temperature found at Batavia might usefully be con- 
firmed by a similar reduction for some continental 
station, and a reduction for some station on a small iso- 
lated island in mid-ocean would throw light on the 
systematic heat interchange between the air and the 
ocean. 
The study of the lunar tidal winds has barely been 
