ATMOSPHERIC TIDES AND OSCILLATIONS 
of atmospheric pressure as recorded by the barometer, 
invented by Torricelli at about the time of Newton’s 
birth. Already in the seventeenth century [21] the value 
of this instrument in the study of weather began to be 
realized, and in Newton’s lifetime it became known 
that the barometric changes in the tropics are quite 
different from those in temperate latitudes. Instead of 
the mercurial height varying through several centi- 
metres, as it does in temperate latitudes because of the 
irregular weather changes, the tropical barometer is 
almost steady except when hurricanes sweep the region. 
It shows, however, a small rise and fall twice daily, 
with a range of about 2 mm, almost as simple and 
regular as the tidal changes of sea level; but unlike 
these, the times of high pressure show no perceptible 
change throughout the month; they recur daily at 
nearly the same local solar time, about 10:00 a.m. and 
10:00 p.m. This is illustrated in Fig. 1, which shows the 
barometric changes at Batavia and Potsdam (on differ- 
ent scales) for the same few days [14]. 
NOVEMBER, 1927 
750 
740 
Fic. 1—Barometric variations (on different scales) at Batavia 
and Potsdam, November 5-9, 1927. 
This regular twice-daily barometric change is clearly 
due to the sun, so the “tidal” régime of the atmosphere 
differs greatly from that of the oceans, where the moon 
is the controlling agent. The moon’s effect on the barom- 
eter is very small, though it can be determined with 
much labor from sufficient data. 
The solar semidiurnal barometric variation is our 
chief indication of the greatest world-wide oscillation 
of the atmosphere. For brevity, this oscillation, with 
its associated barometric and wind changes, will be de- 
noted by the symbol S», in which S signifies solar, and 
the suffix 2 indicates the number of its cycles or swings 
per day. Similarly, S, will denote an oscillation whose 
barometric and other changes at each place are re- 
peated 7 times each mean solar day, and L, one with n 
repetitions in each mean lunar day. 
The moon’s capacity to exert any appreciable dy- 
namical influence on the atmosphere lies solely in its 
tidal force, so potent on the oceans. The harmonic de- 
velopment of the lunar tidal potential [58] clearly in- 
dicates the values of n to be expected, and their relative 
importance in the lunar tidal force; for the chief term n 
equals 2, as in the sea tides, and there are two other 
terms for which n differs only slightly from 2; these in- 
crease or decrease the main semidiurnal tide according 
511 
as the moon is nearer to or farther from the earth. 
There is also a term for which v is nearly equal to unity, 
but this depends on the moon’s declination (namely, its 
angular ‘‘distance” from the equatorial plane) and is 
reversed in sign twice monthly as the moon moves 
northward or southward across the equator. This oscil- 
lation L;, has not been detected in the barometric 
records [80]. 
THE SEARCH FOR THE LUNAR ATMOSPHERIC 
TIDE L, 
The Tide at Paris. Laplace’s theory [74a] indicated a 
“direct”? lunar tidal variation of the barometer with a 
range in the tropics of half a millimetre. He considered 
that such a change, though small, should be determina- 
ble from a considerable series of tropical readings; but 
no such series was available to him in 1823, when he 
developed an active interest in the air tide, an interest 
which he maintained for the rest of his life. Instead, he 
was able to obtain from Bouvard, of the Paris observa- 
tory,' an eight-year series (October 1, 1815 to October 1, 
1823) of barometric readings made daily at 9, 12, 15, 
and 21 hours. He used only part of the three daytime 
readings, 4752 in all, and from these, by a well-designed 
method, he sought to compute the lunar semidiurnal 
tide Ly. He calculated its range as 0.054 mm, and the 
lunar times of maximum pressure as 3519™ after upper 
or lower transit. He attached limited significance to 
this result, after calculating the probability [74c] that 
it was not merely due to chance, that is, to the continual 
irregular “weather” variations of the barometer. He 
asserted that to determine so small a variation from 
such data with adequate certainty would require at 
least 40,000 observations. 
Bouvard [74/] in 1827 repeated Laplace’s calculation 
with four more years’ data (in all, twelve years, Jan- 
uary 1, 1815 to January 1, 1827), and from 8940 read- 
ings found a lunar tidal range of 0.0176 mm, with max- 
ima at 258™ and 14°8™. The great difference from La- 
place’s result confirmed the inference that the data used 
were still far too few. 
In 1843 Hisenlohr [60] renewed the attempt with 
twenty-two years’ data (1819-1840), using all the four 
daily readings. Unfortunately he departed from La- 
place’s excellent method of computation, which in- 
volved only differences between readings on the same 
day, thus eliminating the influence of the large changes 
of pressure from day to day. Hisenlohr rearranged his 
data according to the nearest lunar hour (0 to 23) at the 
time of each reading; with unlimited data this method 
would be satisfactory, showing the complete average 
change of the barometer according to lunar time. But 
with his limited data, the number of readings per lunar 
hour ranged from 1302 to 1377, and the hourly means 
1. In references [28, 29] the source of Laplace’s data for the 
air tide was wrongly given as Brest, through confusion with 
his use of Brest sea-level data for comparison with his theory 
of sea tides. It may also be added that in the translation of 
(Vols. 1-4 only, of) Laplace’s great work, by N. Bowditch, 
ref. [74a] is to be found on pp. 793-801 of Vol. 2 (Boston, 1832). 
