ATMOSPHERIC TIDES AND OSCILLATIONS 
Figure 2 (full line) shows the mean lunar daily vari- 
ation of Greenwich pressure obtained [28] from these 
N days, by a method of rearrangement of solar hourly 
values according to lunar time. Happily, this method 
avoided a pitfall, then unsuspected but afterwards dis- 
closed by Bartels [12], associated with the use of selected 
barometrically ‘‘quiet”’ days [41]. 
The total range of pressure in Fig. 2 is less than 0.001 
in., and the change from one lunar hour to the next 
averages about 0.00015 in. This exceeds the average 
random error in Fig. 2, namely, 0.00010 in., and the 
systematic nature of the lunar daily variation is clearly 
manifest. Apart from its meteorological and dynamical 
interest, this determination has great statistical interest 
as a remarkable illustration of the “law of combination 
of random errors’”—an example confirmed by many 
later air-tide determinations, most notably by that of 
the tidal variation of air temperature at Batavia [36]. 
(See p. 519.) 
—— 
pp ees 
|x = Tooo INCH OF MERCURY 
A 
+0.01 
Y MERCURY 
a 
2 
OF MERCURY 
= 
SCALE IN MM. 
SCALE IN MM. 
4 = (CHO) 
kK bE ! kK 
x10 xnrA ala 
jac || Wiz wie 
alc Sa ala 
=| Or eacs 
F == SiS 
Fra. 2.—The average lunar daily variation (full line) of 
barometric pressure at Greenwich, computed from 6457 days’ 
hourly data, 1854-1917; the broken line shows the lunar semi- 
diurnal component of the variation. 
Harmonic Analysis and the Harmonic Dial: Units. 
In Fig. 2 the broken curve represents the lunar semi- 
diurnal harmonic (or Fourier) component obtained by 
harmonic analysis of the calculated variation (full line). 
This component curve represents the type of variation 
due to the moon, and the difference between the two 
curves must be ascribed to random variation due to 
weather. 
Any variation which is periodic m an interval 7 can 
be harmonically analyzed and represented as a sum of 
harmonic terms, 
Y cn sin (N9 + Yn), (1) 
where n = 1, 2,...and 6 denotes time reckoned in 
angle at the rate 360° per interval 7. The integer n is 
the order of the harmonic, c, and y, are its amplitude 
and phase. This harmonic has maxima at the time 
6 = (90° — y,)/n and at intervals T/n thereafter 
throughout the period T. 
In the case of a solar or lunar daily variation, 7 
signifies a (mean) solar or lunar day, and @ signifies 
solar time ¢ at the rate 15° per mean solar hour, or 
lunar time 7 at the rate 15° per mean lunar hour. It is 
513 
convenient to reckon ¢ from local mean midnight, and 
t from local lower mean lunar transit. It is also con- 
venient to denote the nth harmonic (S, or L,) by the 
distinctive notations: 
Sn Sin (nt + on) (2) 
for S,, and for Lp, 
1, sin (nt + Xz). (3) 
The only harmonics yet detected in the lunar air tide 
(see p. 511) are the second (m = 2) and the two for 
which n differs only slightly from 2; the other har- 
monics obtainable by analysis of the full-line curve in 
Fig. 2 represent only residual accidental error. 
LOCAL MEAN HOURS 
(0) 6 12 18 24 
ELVE-HOURLY 
SINE-WAVE 
+0.4 
MILLIMETERS 
fo) 
—0.2 
=0.4 
90° (a) 
270° (b) 
Fra. 3.—The solar semidiurnal component (S2) of the daily 
barometric variation at Washington, D. C., represented (Fig. 
3a, above) by a graph, specified (Fig. 3b, below) by a harmonic 
dial. 
In this article lz, for the lunar tidal variation of 
barometric pressure, will be expressed either in micro- 
metres (um) of mercury (1 um = 10-'m = 0.001 mm) 
or in microbars (1 microbar = 0.001 mb or 1 dyne em, 
or 0.00075 mm of mercury). The unit of speed used for 
I, the amplitude of the lunar tidal wind variation asso- 
ciated with Ls, will be 1 em sec (= 0.036 km hr“). 
In graphical illustrations showing both S. and Ls, the 
