ATMOSPHERIC TIDES AND OSCILLATIONS 
By SYDNEY CHAPMAN 
Queen’s College, 
The oscillations considered in this article are those of 
world-wide character, on a scale greater than that of 
the ordinary local or regional weather distributions. It 
is convenient to call them “tides” even when their origin 
is thermal and not gravitational. 
Most of our information concerning these tides comes 
from the barometer, which shows an excess or deficit of 
pressure as the motion heaps up the air or draws it 
away above a locality. 
GRAVITATIONAL TIDES 
The sea tides, with their twice-daily rise and fall, 
have been known since the dawn of history. The time 
of high tide advances from day to day in evident asso- 
ciation with the moon’s moiton. Our understanding of 
this goes back to Newton [85a], who showed how, on 
the basis of his laws of mechanics, a universal inverse- 
square “gravitational” attraction between all material 
particles would explain the weight that makes bodies 
near the earth fall towards it, explain the planetary 
motions, and also, less simply, the sea tides. 
The gravitational attraction exerted by the sun on a 
particle of the earth is GS/r? per unit mass, where G 
denotes the gravitational constant, S the sun’s mass, 
and r the distance from the sun’s centre O to the ter- 
restrial particle. On the average this force provides the 
orbital centripetal acceleration wr towards the sun, 
where w denotes the orbital angular velocity of the 
earth (27 per year). The average values of these accel- 
erations are those at the earth’s centre C, for which 
r = 1, Where ro = OC. Hence GS/ry? = wry or w? = 
GS/r.3. 
But the gravitational attraction is greater, and the 
centripetal acceleration less, over the hemisphere nearer 
the sun, than at the earth’s centre, leaving a distribu- 
tion of unbalanced force over this hemisphere, directed 
sunwards (at most places obliquely upwards, partly 
acting against the earth’s pull). Over the opposite hemi- 
sphere the gravitational acceleration is too weak to 
supply the whole centripetal acceleration, and there is 
a distribution of unbalanced acceleration away from 
the sun, here also obliquely upward, partly against the 
earth’s pull. Particles free to move, like those of the 
sea water or air, will doso under the action of these un- 
balanced forces; the water surface will tend to become 
spheroidal, with its long axis along the line OC joining 
the centres of the sun and earth. 
If the earth did not rotate relative to this line, such 
a steady distribution of level would actually be attained. 
It is called the equlibriwm solar tide. This is proportional 
to the gradient along OC, at C, of the unbalanced accel- 
eration wr — GS/r?, that is, to w? + 2GS/r3 or 3G'S/r03. 
The moon exerts a similar tidal influence, propor- 
Oxford, England 
tional to 3 Gi/r3, where M and 7, denote the moon’s 
mass and distance (from C); M/S and 7/7 are both 
very small, but it turns out that the lunar tidal action 
is 2.4 times as great as the solar, and on this account 
the moon chiefly governs the sea tides, though the sun 
at different epochs in the month adds to or reduces the 
_ lunar tides. 
In the eighteenth century Newton’s successors ex- 
tended his planetary theory to explain the motions in 
the solar system in almost every detail. They began also 
to develop the theory of the tides. Laplace [74a] recog- 
nized the powerful influence of the earth’s rotation on 
the tides, which are a dynamical, not statical, phe- 
nomenon. The ‘‘equilibrium tide” is only a theoretical 
conception providing a convenient standard of com- 
parison for the real tides. 
Laplace developed his tidal theory in a series of re- 
markable memoirs, later summarized in his Mécanique 
céleste. He restricted his analysis for the most part to 
the idealized case of an ocean of uniform depth cover- 
ing the whole earth. Hence his results have only a 
limited application to the actual sea tides, which are 
complicated by the irregular outlines and interconnec- 
tions of the oceans, and by their nonuniform depth. 
These complications present problems with which tidal 
theorists still wrestle arduously. 
Laplace showed that his ideal ocean tides might be 
greater or less than the equilibrium tides, according to 
the depth of the ocean; and also that they might not 
be “‘direct,”’ with high tide “‘under”’ the tide-producing 
body, and also on the other hemisphere: they might be 
“reversed,’’ with low tides at points on the earth near- 
est to and farthest from the tide-producing body, and 
high tides intermediate between them. 
THE ATMOSPHERIC TIDES S,, L, 
Newton realized that the tidal forces must act on 
the atmosphere as well as on the seas. The lack of lateral 
boundaries renders the atmosphere a better subject for 
Laplace’s idealized theory. This theory treated the 
sea water as incompressible, but he showed that the 
theory could be adapted surprisingly well to the com- 
pressible air if its temperature were assumed uniform, 
and unchanged throughout the compressions and rare- 
factions accompanying the air tides—that is, if the 
changes of air density were supposed to take place iso- 
thermally. On this basis he calculated the air tides for 
an atmosphere agreeing in total mass and average tem- 
perature with the actual atmosphere, and showed that 
the tides would be direct, that is, the air would be 
heaped up with high pressure under the tide-producing 
body, and on the opposite side of the earth. 
Thus the tide should produce a twice-daily variation 
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