BL. But actually on account of the eccentricity of the earth there is an unbalanced component of gravity urging it toward the north. This force is just sufficient to deflect the motion of the point from the great circle to the circle BQS corresponding to the parallel of latitude.

In the short time dt, the velocity U if unaffected would carry the point a distance U dt represented in figure 4 by BL. In the same space of time the ellipticity of the earth produces a deflection towards the north equal to LQ, so that at the end of the time dt, the point is not at L but at Q.

Now, let us consider the case of a frictionless body at the point B moving in any direction on the earth's surface, with an initial relative velocity V. If the earth were stationary and spherical the body would in the time, dt, move a distance V dt to a position K. Since the earth is in rotation the absolute velocity of the moving body is the resultant of U and V. In the time, dt, therefore, if no deflecting force were acting the motion of the body would be found by combining BL and BK, which would take the body to the point F. But the ellipticity of the earth produces during this same interval of time, dt, a movement FG equal to LQ. Hence, at the end of the time, dt, the body actually is at the point, G. In figure 4, BK, LF, and QG are all equal and parallel.

It is next desired to find the path described on the earth's surface by the moving body during the motion described above. Since at the point B the body has a relative velocity V in the direction BK, the path, if a curve, must be tangent at B to the line BK, and the center of curvature must be on a line drawn through B perpendicular to BK. After the time, dt, the point B has moved to the position, Q. During this time the line BK has turned through an angle so that it is no longer parallel to its original position like QG, but occupies a position QH such that the angle GQH equals the angle BMQ. Hence, drawing QO perpendicular to QH, the center of curvature, O, lies on this line at such a distance from Q that a circle drawn through Q shall pass through the point, G. Hence, referring to the equations on page 42,

But QH = V dt, and from the similar triangles QHG and MQB,

This is based upon the assumption that the earth rotates once upon its axis in 24 hours. Since the sidereal day is about four minutes shorter than the mean solar day, this assumption introduces a small

error.

Equation 7 shows that a slowly moving body on the earth's surface, when not near the equator, tends naturally to move around a closed curve, approximately a circle, of relatively small size. For example, with a velocity of 10 miles per hour in latitude 30 degrees, the radius of the circle would be about 40 miles. In the northern hemisphere the deflection from a straight line is toward the right, or in other words the motion is in the clockwise direction. In the southern hemisphere the deflection is toward the left, or the circular motion is counter-clockwise.

INFLUENCE OF EARTH'S ROTATION ON BAROMETRIC

GRADIENT

When the movements of the atmosphere follow the curved paths described in the preceding paragraph the rotation of the earth has no influence on the pressure distribution. However, when they depart from these paths, as they generally do, there must be a barometric gradient at right angles to the line of motion of sufficient magnitude to cause the departure.

The force necessary to change the motion of a mass of air from the curved path derived in the preceding pages to a straight line motion relative to the rotating earth, is just equal to the force that would change the motion on a still earth from a straight line to the curved path. Therefore, by substituting the value of p given by equation 7 in equation 6, there is at once obtained an expression for the barometric gradient at right angles to the direction of motion which is necessary, on account of the rotation of the earth, when the atmosphere moves in an approximately straight line. The equation thus obtained is:

Barometric gradient

=

TV sin o
24g

= .004V sin inches per 100 miles (8)

For many conditions this will be a larger gradient than that in simple circular motion given above by equation 6. For example, with a velocity of 20 miles per hour in a latitude of 30 degrees the barometric gradient at right angles to straight line motion would be .04 inch of mercury per 100 miles. If the wind is moving in a curved path in a counter-clockwise direction, the total radial barometric gradient will be given by the sum of equations 6 and 8. If the motion is in the clockwise direction the gradient is found by taking the difference of the two equations.

GENERAL WIND CIRCULATION FOR EASTERN UNITED

STATES

The immediate cause of the general wind circulation is the variation in air temperature. As a hypothetical illustration consider the relative pressure distribution above two points where the air temperatures average 60 and 80 degrees, respectively. At the colder point the barometric pressure would decrease upward at a rate at first of about 0.1 inch of mercury for each 100 feet of vertical rise and would continue to decrease at a rate which would be not quite a constant but a slowly decreasing quantity. At the warmer point the air would be about 4 per cent lighter for the same pressure, and at all higher altitudes would continue to be lighter than the colder air in about the same ratio. The consequence of this is that the decrease of pressure in rising a stated vertical distance would not be so much at the warmer point as at the colder. In rising 1 mile the pressure at the colder point would decrease 0.2 inch of mercury more than the decrease at the warmer point. If the pressure at the surface of the earth were the same at the two points then the pressure 3 miles above the earth's surface would be 0.6 inch of mercury less at the colder point. Or, if the pressure at the earth's surface were 0.3 inch greater at the colder point, at an altitude of 3 miles it would be 0.3 inch less than for the same altitude at the warmer point. In this latter case, then, there would be a surface wind from the colder to the warmer region and at high altitudes a wind from the warmer towards the colder region. Similarly, any variation in temperature between two points. on the earth prevents the existence of a state of equilibrium and starts an air circulation.

The latter case typifies the condition existing over a large part of

the earth's surface during much of the time. The high temperatures prevailing in the equatorial region lead to an unequal pressure distribution with the result that around the earth there is a fairly permanent belt of high pressure at the surface in latitude 30 to 35 degrees north, accompanied by corresponding low pressures at great altitudes above the earth. The resulting surface winds blowing constantly towards the equator over the oceans are called the trade winds. Where deepest they attain an altitude of about 2 miles. The belt of high surface pressure is affected by the seasons as the sun moves north and south of the equator, and by the relations of the continents to the oceans, since land areas are warmer than water areas during the summer, and correspondingly colder during the winter.

Hence the

The region of the trade winds only barely touches the most southern part of the United States, but our winds are affected by their influence. As previously explained on page 47, any wind in the northern hemisphere tends to be deflected toward the right. trade winds in blowing toward the equator turn toward the southwest. Similarly, the air currents at high altitudes moving north from the equator blow toward the northeast, and since they are probably much less retarded by friction on account of their separation from the earth's surface, their easterly component of velocity persists sufficiently to give a decided drift towards the east to all the atmosphere throughout the range of latitude occupied by the United States. The latter is said to lie in the region of the prevailing westerlies and this constant steady drift of our atmosphere toward the east is the basis of all our weather predictions.

Throughout the region of the prevailing westerlies the air temperatures, and their resulting winds, are much affected by the presence of the water vapor and clouds in the air, and by the vertical movements in the air masses. The mechanism controlling changes in these elements has not yet been completely determined, and for this reason long-range weather forecasts are still in only a partially developed state.

The general circulation of the atmosphere between tropical and extra tropical regions by means of high-altitude currents in one direction and low-altitude currents in the reverse direction, might be spoken of as a continuous circulation in vertical planes. In the latitudes of the United States this simple circulation, during much of the time, becomes converted into what might be called for contrast a circulation in horizontal planes. Over a large area the air will be moving toward the north, at a particular instant, while over a different but correspondingly large area at the same time the air will be moving toward the south. The whole system has a continual drift towards

the east in correspondence with the prevailing westerlies of these latitudes, with the result that at a given geographical station the winds are intermittently southerly and northerly.

Neither the origin of these changes nor the mechanism which controls their movements is well enough worked out yet so that accurate predictions of their movements can be made for any extended advance period. But the principle of continuity and the data which is being accumulated each year by the Weather Bureau are continually extending the range of possible prediction. The disturbance of temperature conditions by continental areas and by water vapor and clouds in the air doubtless have a large effect in the intermittent wind circulation. Also, the region of prevailing westerlies, by producing a constant circulation around the north pole, sometimes called the circumpolar whirl, must produce a constant tendency for a low altitude current to creep along the earth's surface in a northerly direction as explained on page 43.

STORMS

A storm may be defined as a movement of the air accompanied by precipitation. Precipitation in any storm is very unevenly distributed, even within limited areas. "A difference of 50 per cent within five miles or 100 per cent within ten miles can easily occur. From a study of many gages located within ten miles of Berlin, Hellman found that even in monthly totals, gages 1500 feet apart were as likely as not to differ 5 per cent, while of course in special rains they would differ 100 per cent."*

The distribution of normal annual rainfall over the eastern United States is shown on figure 5, a map of the country east of the 103d meridian, on which are drawn isohyetal lines (lines of equal rainfall) for each 10 inches. The map is the latest issued by the Weather Bureau, and is based on records of about 1600 stations for the 20-year period 1895-1914, and 2000 additional records from 5 to 19 years in length, uniformly adjusted to the same period.

Rainfall is dependent originally upon the evaporation of water into the air. In the form of water vapor it may then be transported long distances by the winds. Before precipitation can occur condensation must be produced by cooling. The cooling may be caused by contact with cold surfaces or with cold layers of air, by adiabatic expansion while rising to greater altitudes, by radiation, and by mixing with colder air. The oceanic areas of the torrid zone are the most extensive source for evaporation, although it is to be remembered that even on land surfaces a large fraction of the annual rainfall is re* Willis L. Moore, Descriptive Meteorology, New York, 1910, page 209.