ATMOSPHERIC TIDES AND OSCILLATIONS 
of the twelve calendar months (for many years). Fig- 
ures 10b, c, d, e, f show sets of twelve dial points, one 
for each month, for (6) Taihoku [43], (c) Batavia [22, 
23, 96-99], (d, inset in c) Potsdam and Hamburg |12] 
combined, (e) Hong Kong [29], and (f) the three Iberian- 
peninsular stations Coimbra, Lisbon, and San Fernando 
combined (using 112 years’ data in all) [57]. Similar dia- 
grams have been drawn for several other stations. Their 
most remarkable feature is the large lag of high tide, by 
nearly two hours, in January and February as compared 
with some of the J and # months. This is shown as well 
by the southern station Batavia as by the other (north- 
ern) stations. 
The Lunar Tidal Variation of Temperature. The heat- 
ing of the atmosphere by moonlight is quite negligible, 
but the moon nevertheless does produce a lunar semi- 
diurnal variation of the air temperature, as a secondary 
consequence of its mechanical tidal action. The changes 
of air density accompanying the tidal variation of pres- 
sure will be different according as they take place iso- 
thermally or adiabatically, or in some intermediate way 
between these extremes. A similar question arises in the 
theory of sound waves. Newton [85b], who first calcu- 
lated the speed of sound, assumed that the density 
variations are isothermal, and obtained a result that 
disagreed with his measurements. Laplace [74f] realized 
that the density variations are too rapid to allow the 
heat of compression to be conducted away during the 
brief period of each oscillation, and the assumption that 
the variations are adiabatic led him to the correct for- 
mula for the speed of sound. 
The lunar atmospheric tide is a double tidal wave 
travelling round the earth each lunar day; the period is 
long—half a lunar day—but the distance between the 
places of high and low pressure, or condensation and 
rarefaction, is also great (except near the poles). Cal- 
culation shows that the density changes must be adia- 
batic as regards heat flow (either horizontal or vertical) 
un the atmosphere (except at very great heights—of the 
order 120 km—where the thermal conductivity of air is 
much increased owing to the long molecular free paths). 
The only possibility of the tidal oscillation being nearly 
isothermal is by interchange of heat with the liquid 
under surface (the solid earth does not conduct suffi- 
ciently to modify the tidal adiabatic temperature vari- 
ations near ground level). 
The adiabatic nature of the tidal air wave has been 
tested by determining the lunar semidiurnal variation 
of air temperature at Batavia, from sixty-two years’ 
bihourly observations. Figure 11 shows’ the resulting 
dial vector with its probable error circle, within which 
lies the point C that corresponds to the adiabatic tem- 
perature variation, calculated from the known pressure 
‘variation L,. Thus the determined and calculated tem- 
perature variations agree within the margin of accuracy 
of the determination [36]. 
It would be of interest to compute the lunar semi- 
diurnal variation of air temperature from a long series 
of records from the windward side of some small flat 
tropical island in a great ocean. This would throw light 
on the degree of interchange of heat between air and 
519 
sea. Bartels has suggested that it might prove advan- 
tageous, in such a study, to use only the night varia- 
tions of air temperature, if these were less variable from 
day to day than the daytime values. 
BATAVIA 
(1866-1928) 
(0) 0.005°C 
Fie. 11—Harmoniec dial specifying (with probable-error 
circle) the lunar semidiurnal tidal variation of air temperature 
at Batavia. The point C represents the variation calculated 
from the lunar semidiurnal variation of barometric pressure at 
Batavia, on the assumption that the density variations are 
adiabatic. 
The Lunar Tidal Wind Currents. The tidal variations 
of sea level are accompanied by tidal currents (super- 
posed on any other motions present, such as those in 
the Gulf Stream). Similarly in the atmosphere the L» 
pressure variation must be accompanied by tidal wind 
variations. These are best determined from bihourly 
values of the east-west and north-south component 
wind speeds. Only a few observatories, such as Mauri- 
tius and Bombay, have published such data, calculated 
from the usual wind records of direction and total 
speed. For this reason but little work has been done on 
the daily wind variations, whether solar or lunar. The 
only available lunar results are illustrated in Fig. 12a 
[47], which shows the Lp dial vectors, with probable 
error circles, for the eastward and northward wind 
speeds at Mauritius, from sixteen years’ observations 
(1916, 1917, 1920-83). The ratio l/r (see p. 514) is less 
than three, so that the determinations should be 
strengthened by using more data (which are available 
for Mauritius); similar investigations should be made 
also for other stations. 
Figure 126 [47] shows in a similar way the dial vectors 
for the S» (solar semidiurnal) variations of east and 
north wind speed at Mauritius, derived from the same 
data, the amplitude scale being ten times less open than 
in Fig. 12a. 
The ratios of the solar to the lunar amplitudes are of 
the order 20, rather greater than for the S» and Ls pres- 
sure variations, for which at Mauritius the ratio is 17. 
The amplitude of the ZL. wind variations, about 1 cm 
see, is of the right order of magnitude according to 
the mathematical theory of these oscillations. 
