44 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
has also remarked ; Gold has used the law sin 3 0, which fits the observations very 
closely. Schuster adopted the law sin 2 6 (or Q 2 2 ), which represents the facts 
moderately well, though distinctly less well than sin 3 6. Schmidt’s expression was 
(29) (0'31 Q, 2 -0'082Q 4 2 ) sin(2£+154°). 
The seasonal variation of amplitude has been represented by Angot by the formula 
(30) cos 3 S/cl 2 , 
where <1 is the sun’s declination and d its distance. Its magnitude is well illustrated 
by the following results of an analysis of the Batavian barometric observations for 
the period 18G6 to 1905 :— 
Spring (February to April) . 
Autumn (August to October) 
Summer (May to July). 
Winter (November to January). 
Mean equinox. 
Mean solstice . . . . 
1’026 sin (2 1 + 156°'0), 
1 '022 sin (2£+163°'9), 
0'935 sin (it + 158°'5), 
I "009 sin (2f +161°'9), 
1’021 sin (2 1+ 159°'9), 
0'971 sin (2t+ 160°'3). 
The mode of origin of the daily barometric variation has been much discussed, but 
the question whether the important semi-diurnal component is of tidal or thermal 
origin, or both, seems still open. If it is fundamentally a tidal effect, resonance with 
a free atmospheric period of 12 hours must be assumed, since the lunar diurnal 
barometric variation (which can hardly be of other than tidal origin) is of much 
smaller magnitude. Probably resonance is necessarily involved also if the cause 
is thermal, as the Kelvin-Margules theory supposes. In any case, however, the 
12-hour variation is clearly much more fundamental than the 24-hour component, 
a fact which has an interesting bearing on the magnetic variations. 
-» • • • • • Q (j) , . 
If <E> is the velocity potential of the atmospheric motion, so that — is the velocity 
CjS 
in the direction of ds, the simplest theory connecting A and the pressure variation Sp 
asserts that 
(31) 
1 dA> _ ^p 
v 2 dt p 
where v is the velocity of sound. At the earth’s surface, taking op as 
(32) 0-3QJ sin (\ + i') + (0'3lQ 3 2 -0'082Q 4 2 ) sin {2 (\ + f')+ 154°} 
in millimetres of mercury (so that, p in the same units is 760), we find that 
(33) <J> = (Nif/27rp) [O'3 cos (A -f f) + {0’ 16QJ — 0'041Q 4 2 } cos {2 (\ + t')+ 154°}]. 
