ATMOSPHERIC TIDES AND OSCILLATIONS 
per day are available, a method depending on the dif- 
ferences between them, thus eliminating their absolute 
values, is desirable. Laplace [74], and in recent years 
also Bartels [17], used such a method. Almost all deter- 
minations other than those on the early Paris data 
have been based on hourly values, or (better, as Bartels 
urged [17]) on bihourly values, which give almost equal 
accuracy with much less labour [53]. 
In most of the determinations up to about 1935 the 
lunar day was taken as the basis, and the observations 
were rearranged according to lunar time (actual, not 
mean). Usually, though not always, the solar daily vari- 
ation was removed before or after the retabulation. It 
is very important to remove, or allow for, any non- 
periodic change of pressure in the course of each day. 
This was only gradually realized (29, 32, 51, 54]. 
In 1917 reasonably certain determinations of L»2 had 
been made at only three stations [22, 28, 61, 91, 96-99]; 
it is now known at over sixty-five stations [12, 17, 28— 
46, 48-57, 88, 89]. More than half of these determina- 
tions have been made by the method [54] that now 
seems most suitable where hourly or bihourly data are 
available. The method is based on solar daily sequences 
of twenty-five hourly or (better) thirteen bihourly val- 
ues, the last value for each day, which is also the first 
for the next day, being added so that the aperiodic 
change in the day can be removed. The daily sequences 
are separated in twelve lunar-phase groups, using tables 
[19, 20] constructed by Bartels and Fanselau for this 
purpose. The grouping is facilitated if each daily se- 
quence of twenty-five or thirteen (three-figure) values, 
with its identifying and lunar-classification data, is 
entered on a punched card, using Hollerith sorting and 
adding machines in the later work; but these devices 
are not necessary for the application of the method. A 
practical description of the method, with examples, in- 
cluding the probable-error computation, is available 
[103]. The solar daily component variations S, are com- 
puted in the course of the work, and are thus available 
for comparison with L». from the same material. 
The determination of these variations, and especially 
of L2, from the records of air pressure, wind, and tem- 
perature, may be likened to the extraction of a rare 
constituent from a great mass of crude ore—or of a 
needle from a haystack! It is an example of the unex- 
hausted value of the long series of meteorological (as 
also of magnetic) data garnered at many observatories 
decade after decade. There is great need and scope for 
such work on many series of data not yet dealt with. 
THE LUNAR ATMOSPHERIC TIDE L, 
Geographical Distribution: Annual Mean. Figure 5 
indicates the annual mean value of L» so far as results 
are now available [47, 57]. The world map shows arrows 
which in direction and length (on the scales given) rep- 
resent the dial vector for Ls at the point corresponding 
to the centre of the arrow shaft. All the stations lie be- 
tween 60°N and 40°S; there are large areas in this belt, 
however, where J is not known—notably Central Asia, 
the western Pacific, and parts of South America. Some 
515 
determinations made for Russian stations may have 
been omitted because the literature is not accessible. It 
is to be hoped that these gaps will gradually be filled, 
and the limits of our knowledge pushed polewards, us- 
ing the improved computing methods [54, 103] men- 
tioned in the foregoing section. 
If the lunar air tide were in phase with the tidal force, 
all the arrows in Fig. 5 would be upright; actually most 
of them point to the right, implying a lag of high atmos- 
pheric tide (by about half an hour on the average) after 
lunar transit; but some well-determined arrows point 
leftward, as at Mauritius and Kimberley, and at the 
five north European stations, where high tide definitely 
precedes the lunar transit. Later diagrams (e.g., Figs. 8, 
10) indicate the uncertainties of amplitude and phase 
at several stations. 
The L2 component of lunar tidal force decreases 
steadily polewards from the equator, and on the whole 
so do the arrow-lengths representing J, in Fig. 5; but 
there are several departures from this regularity, defi- 
nitely not due to errors in the determinations. The ab- 
normalities in the distribution of LZ» are illustrated 
(rather tentatively, so far as the data will allow) in 
Fig. 6, which shows lines of equal amplitude /2.; where 
the lines are ill-determined they are drawn ‘‘broken.” 
There is a belt of specially high tidal amplitude across 
the South Indian Ocean; and along the west coast of 
North and South America J. is abnormally low. Also at 
Buenos Aires, on the east coast, J, is much less than at 
Melbourne, in nearly the same latitude. 
The remarkable anomaly of the small lunar air tide 
near the northwestern American coast is illustrated in 
Fig. 7 [46, 47, 57], which gives the distribution of Le 
over North America as in Fig. 5, but on a larger scale 
and with additional details (cf. the next section). 
The Annual Variation of Z.. The lunar tidal force 
undergoes no regular annual variation, though it in- 
cludes a semimonthly change of L2 inseparable [30] from 
a semiannual change of S». Nevertheless, LZ», unlike the 
sea tides, varies notably in the course of each year. 
This must be due to a large-scale annual change in our 
atmosphere, the system on which the lunar tidal force 
acts. 
World meteorological charts of isotherms and isobars 
show marked seasonal changes of distribution—seasonal 
in the sense that on the whole, as the sun crosses the 
equator northward or southward, these changes alter- 
nate, the summer state of one hemisphere being approx- 
imately reproduced in the other hemisphere in its sum- 
mer. The lunar air tide is not seasonal in this sense; its 
main changes of J) and 2 occur simultaneously in both 
hemispheres. 
Figure 8 (a, b) illustrates this in one way, 8a (above) 
showing Jz, and 8b (below) showing 2, for the D (De- 
cember solstitial) group of four months November to 
February. The black dots indicate /2 and )» for about 
fifty stations, in the latitudes to be read on the scales of 
the abscissas; the lines centred on these dots indicate 
the uncertainty of ly and Xs, in the manner described in 
the foregoing sections. The curved lines indicate the 
