522 
can be perceived (as also often at some Kuropean sta- 
tions and others in moderate latitudes) even in the 
records for individual days. 
By harmonic analysis the components S, of the solar 
daily variation (n = 1, 2,...) can be determined and 
separately studied. 
The diurnal component S, [68, 69] differs remark- 
ably from iS», being (unlike S,) much affected by local 
weather (cloud or sunshine) and topography. At the 
bottom of deep valleys it is greatly magnified. Its 
amplitude s; is much greater in summer than in winter; 
its phase o; is about 90°, the maximum of S, thus oc- 
curring near local noon. It is not a world-wide oscilla- 
tion, but a thermal effect [68, 71] sensitive to local 
influences. It will not be further considered here. 
The components S; and $4, with periods of eight and 
six hours, are also thermal effects (the sun’s tidal action 
has no appreciable components with these periods). 
They result from the corresponding components 73 and 
Ts of the daily variation of air temperature, which they 
resemble in their geographical distribution and sea- 
sonal changes. For example, S; and 73 have opposite 
phases in opposite hemispheres, and these phases are 
reversed from summer to winter. The S3 barometric 
variation manifests a world-wide atmospheric oscilla- 
tion [93], less simple and regular than the S» oscillation; 
the S, oscillation is still less regular [87]. These S; and S, 
oscillations should be further studied to fill in the frame- 
work of the whole subject of atmospheric oscillations 
[12-16, 18, 55, 102, 111]. 
The Solar Semidiurnal Oscillation S.. In modern 
times Hann [63-67]; Angot [3], Schmidt [92, 94], and 
Simpson [95] have taken a leading part in collecting and 
discussing the data for S». The literature is too vast to 
be cited here, but further references may be found in 
the papers quoted, particularly those of Hann. 
Simpson’s study was based on data from 214 stations. 
He illustrated the regularity of phase of S» in low lati- 
tudes by showing that at seventeen stations between 
latitudes +10°, the local time of maximum of Sz lay 
between 9.55 and 105 (a.m. and p.m.) at all but-one, 
at which it was 10.3». 
In the polar regions this uniformity of local time of 
maximum gives place to a different uniformity, that of 
absolute (e.g., Greenwich) time of maximum [2, 9, 62]. 
At ten out of fifteen stations north of latitude 70°, this 
Greenwich time lay between 11.5" and 12.5". As Schmidt 
[92] indicated, this shows that S»2 is a combination of a 
regular double wave travelling westward round the 
earth like the sun, and a semidiurnal oscillation of the 
air, symmetrical about the earth’s axis, between the 
poles and the equator. 
Simpson expressed S_ at each station (in longitude ¢ 
east of Greenwich, expressed in time units, 15° per hour) 
as the sum of two terms corresponding to two such 
oscillations: 
S2 Sin (2¢ + o2) = bsin (2¢+ B) +c sin (Qt — 29 + CQ), 
DYNAMICS OF THE ATMOSPHERE 
wherein ¢ denotes local solar time and ¢ — ¢, Greenwich 
time. From 190 stations divided into eight latitude 
groups, from 10°S to 85°N, he determined b, B, c, C 
for each group, as given in Table I. 
TasBLE I. CONSTANTS FOR THE REPRESENTATION OF S> aT 
Various LatitupEs [95] 
Group Travelling wave Symmetrical wave 
Mean lat. | No: of 5 (mm) B ¢ (mm) Cc 
0 17 0.920 156.8 0.068 —4.0 
18 15 0.835 155.3 0.082 —23.2 
30 12 0.628 149.1 0.059 10.4 
40 46 0.387 153.9 0.043 91.1 
50 60 0.240 153.0 0.041 104.4 
en 18 0.096 158.0 0.062 108.4 
14 0.072 98.6 
80 8 } OI Med) { 0.080 | 116.4 
Mean 154.1 
The phase B of the travelling wave has a remarkably 
small range (9° or +9 minutes of time) in the eight 
zones. The amplitude 6b, decreasing steadily polewards 
from the equator, is well represented by the formula 
(Z = latitude): 
b = 0.937 cos? T. 
Up to about 60° latitude the other wave is of minor 
importance. Wilkes [111] has represented it by the 
formula: 
[0.07 — 0.1|sin Z| ]sin 2(¢¢ — ¢) 
+ 0.075 |sin | cos 2(¢ — ¢), 
where | sin /| denotes the positive magnitude of sin J. 
Figure 15 shows dial vectors for S. (in barometric 
pressure) which relate to the points at their thick ends 
(not their centres, as in Figs. 5 and7 for Lz). It illustrates 
P 
| XK 
20 TN <i \ = 
{o) 0.5 MM. 
Se 
120 WEST 100 80 60 
120 
20 
Fig. 15.—The distribution of the annual mean solar semi- 
diurnal barometric variation (S2) over North America. Each 
dial vector refers to S2 at the point at its thick end (cf. with 
the lunar Figs. 5,7, where each vector refers to Lz at its centre). 
the regularity of Sz in phase and amplitude (decreasing 
northward) over North America; but it shows also 
that S_ like L, (Fig. 7), though to a much less extent, 
a 
