July 20, 1871 | 
NATURE 
227 

By whatever cause so great a difference in the baro- 
metric pressure in the different regions might be produced, 
it may be shown from the principles of dynamics that the 
equilibrium would be restored in a very short time, if there 
was not some constant force tending to drive the atmo- 
sphere from the polar regions towards the equator, or 
from the centre of the cyclone to the exterior, and to keep 
it in that position. Such a force may be found in the in- 
fluence of the earth’s rotation. Ina paper by the writer 
in the Mathematical Monthly in 1869, published in 
Cambridge, U.S., a full abstract of which was also pub- 
lished in the January No. of S7//iman’s Fournal for 
1861, the following very important principle was demon- 
strated :—In whatever direction a body moves on the 
surface of the earth, there is a force arising from the in- 
fluence of the earth’s rotation, which tends to deflect 
the body to the right in the northern hemisphere, and 
to the left in the southern hemisphere. This force, which 
is the key to the explanation of many. phenomena in 
connection with the winds and currents of the ocean, 
does not seem to be understood by meteorologists and 
writers on physical geography. We see it frequently 
stated that the drift of rivers and currents of the ocean 
running north or south always tends to the rig St in our 
hemisphere, and that a railroad car running north. or so th 
presses to the right ; and this is the case. But the same is 
true, and to exactly the same amount, of a current or of a 
railroad car running east or west, orin any other direction. 
The amount of this deflecting force, when the velocity 
of the body is small in comparison with that of the earth’s 
ae. lied as 2 : ; 
rotation, is expressed by 2. =a, + — COS 6 g; in which v is 
2 n 
the lineal velocity of the body relatively to the earth’s sur- 
face, 2 that of the earth’s rotation at the equator, 6 the 
angle of polar distance, and ¢ the force of gravity. Ifthe 
velocity is expressed in miles per hour, the expression in 
uv cos 6 
round numbers becomes ———— 
yocoo £; that is, for each mile 
~ 2 
: 2 I é 
of velocity per hour, the force is. of gravity, mul- 
yp ) 150,000 g y> 
tiplied into the cosine of the polar distance. Hence a 
railroad car on the parallel of 45° north, running in any 
direction at the rate of forty miles per hour, presses to the 
right with a force equal to about ; 5a part of its weight. 
? 
The effect of this deflecting force upon what Mr. 
Stevenson calls the barometric gradient is easily estimated. 
Since the strata of equai pressure of the atmosphere, so 
far as this force is concerned, must be perpendicular to the 
resultant of this force and gravity, the sine of inclination 
uv cos 6 
150,000, 
and the change in barometric pressure for any given dis- 
tance is equal to the weight of a column of atmosphere of 
a height equal to the change of level of the stratum of 
equal pressure, and of a density equal to that at the 
earth’s surface. The barometric gradient, then, as ex- 
pressed by Mr. Stevenson, for any distance d expressed in 
ne ES 
miles is ————— 
5 x 150,000 
height of a homogeneous atmosphere, and thirty inches 
for the pressure at the earth’s surface. Round numbers 
are used throughout, since it is only the order of the effects 
we wish to determine, and not their exact amount. 
According to all observations, there isa steady and very 
strong wind blowing all around the earth in the middle 
and higher latitudes of the southern hemisphere, with a 
velocity of at least twenty-five or thirty miles per hour at 
the surface of the ocean, and this is perhaps much greater 
inthe upper strata of the atmosphere. If at the parallel of 
50° we suppose the velocity of the wind v to be thirty 
miles per hour, the preceding expression of the barometric 
gradient for a distance @ of 5° or 350 miles, using the 
of any such stratum to the earth’s surface must be 
xX 30 inches ; putting five miles for the 

cosine of 40°, is 0°33 inches of mercury. By reference to 
§ 113 of Mr. Buchan’s Meteorology, it will be seen that 
the barometric gradient for that parallel is only 028 
inches for 5° of latitude, and that this is about the maxi- 
mum gradient in the southern hemisphere. Hence a 
velocity less than 30 miles per hour at the surface of the 
sea, especially if we suppose that it increases in the 
higher regions, is sufficient to account for this maximum 
barometric gradient ; and, according to observations, 20 
or 30 miles per hour for the wind in that region is no un- 
reasonable assumption. The eastward velocity of the 
wind in the different latitudes being known, and, conse- 
quently, the corresponding barometric gradients, the 
difference of barometric pressure between any parallel 
near the pole and one toward the equator, is readily 
obtained by integration. As the wind near the equator is 
toward the west the deflecting force there is /oward instead 
of from the pole, and hence the greatest barometric pres- 
sure is about the parallel of 30°, and there is a slight 
depression at the equator. The deflecting force and the 
consequent depression are small, then, on account of the 
small value of @ near the equator. 
Since there is more land and mountain ranges in the 
northern than in the southern hemisphere to obstruct the 
eastward motion of the atmosphere, its velocity is not so 
great, and consequently the polar depression is much less 
there than in the southern hemisphere. According to Mr. 
Buchan the barometric depression in the Arctic regions is 
much greater in the northern part of both the Atlantic 
and Pacific oceans, than it is in the same latitudes on the 
continents. The explanation of this is, that the eastward 
velocity of the atmosphere over the oceans being much 
greater than it is on the continents, where it is obstructed 
more by friction and mountain ranges, the force driving 
the atmosphere from the poles toward the equator is less, 
and consequently the barometric pressure is less in the 
northern part of both oceans than it is on the continents 
in the same latitudes. 
Upon the relative strength of the forces tending to 
drive the atmosphere from the poles towards the equator, 
depend the positions of the equatorial and the tropical 
calm belts. This force being strongest in the southern 
hemisphere on account of less resistance from friction and 
mountain ranges, the mean position of the equatorial calm 
belt is a little north of the equator, and the positions of 
the others a little farther north than they would otherwise 
be. The prime motive power also in both hemispheres 
being the difference of density of the atmosphere between 
the polar and the equatorial regions, arising from a dif- 
ference of temperature and of the amount of aqueous 
vapour, during our summer when this difference is less 
than the average in the northern nemisphere, and greater 
in the southern, these calm belts are forced a little north 
of their mean positions. Of course, just the reverse of 
this happens during our winter ; hence we have an ex- 
planation of the annual variations of the positions of 
these belts. 
In the case of cyclones, the atmosphere at the earth’s 
surface being forced in from all sides towards the centre, 
by the force arising from a difference of density of the 
atmosphere in the central and exterior parts, it cannot, on 
account of the detlecting force which has been explained, 
move toward the centre, without, at the same time, receiving 
a gyratory motion around that centre. Neither can it 
have a gyratory motion without also having a motion 
towards that centre, since in that case there would be no 
force to overcome the frictions of gyration. Hence, neither 
the radial theory of Espy, nor the strictly gyrating theory 
of Reid and others, can be true, though either of them 
may be approximately so in special cases. But the gyra- 
tory part of the motion is not caused by the motion of 
the atmosphere from the north and south only toward the 
centre of the cyclone, as stated by Mr. Buchan and others, 
but equally by the different parts moving in from all sides, 
