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Popular Science Monthly/Volume 9/July 1876/Blasius's Theory of Storms

< Popular Science Monthly‎ | Volume 9‎ | July 1876

BLASIUS'S THEORY OF STORMS.[1]
By Prof. VICTOR L. CONRAD, M. A.

I PROPOSE to give some account of a new theory of storms put forth by Prof. Blasius, of Philadelphia, formerly Professor of Natural Sciences in the Lyceum of Hanover, Germany. His attention was first drawn to the subject of storms in the year 1851. Having witnessed the destructive effects of a tornado at West Cambridge, Massachusetts, he made a careful survey of its entire track. The facts discovered about the middle of its course, where the most damage had been caused, favored the rotary theory of Redfield; those near the end of its path seemed to confirm the inblowing theory of Espy; but those at the beginning could not be explained by either theory. Discouraged and perplexed by these conflicting results, he resolved to apply to storms the analogy drawn from the life of an animal in its origin or embryo, its development to maturity, and its end. From this he argued that storms must have a beginning, a duration, and an end, with phases peculiar to each stage of their development and progress, like an animal; and, guided by this analogy, he made a careful reexamination and application of all the facts he had discovered, and came to the following conclusion respecting the origin and distinct character of tornadoes and storms:

Origin of Storms and Tornadoes.—"I had found the existence of two opposing currents of air of different temperature, coming respectively from northwest and southwest, acting suddenly against each other after a sultry calm of some duration; and shortly, a third gyratory force making its appearance between them, traveling in their diagonal, growing to such magnitude as to obliterate all trace of the straight-line forces of the opposing currents, and finally abruptly disappearing. The two currents must have been, during the period of sultry calm, in a state of equilibrium, since the clouds were observed to remain for some time almost stationary. South of the tornado's track the southwest wind prevailed until the beginning of the tornado, and, from information obtained for me by ex-President Hill, it appeared that a storm had traveled from northwest to southeast over the States of New Hampshire and Vermont, and that during its progress a southwest wind was replaced by a northwest wind. I was thus led to conclude that the storm announced that afternoon by the black bank of cloud consisted in the conflict of two aërial currents of different temperature—that the colder northern current displaced the warmer southern current in the direction from northwest to southeast, gradually decreasing in velocity until, north of Waltham, West Cambridge, and Medford, it came to a perfect standstill, producing the sultry calm felt before the tornado.
"Here the two currents, being in equilibrio, exerted a great compressive force against each other. The equilibrium was disturbed by the uneven configuration of the earth around Prospect Hill. This disturbance produced the tornado, which traveled, not in the direction of the storm toward the southeast, but in the diagonal of the two opposing currents over their region of calm at their line or meeting, and in and underneath the black bank of clouds stretched out from west to east which must have marked this line of meeting.
"I came thus to two distinct phenomena—the tornado, and the storm in the ordinary sense of the word—both different in their origin, nature, direction, progress, and appearance, and governed by entirely different laws."

Continuing his observations for several years, he came to the conclusion—

"That storms in the temperate zone at least, and over the United States, are the effect of the conflict of opposing aërial currents of different temperatures, and not the cause of these currents and temperatures, as seems to be assumed by some cyclonists."

Continuing and extending his observations and studies in the general held of meteorology, our author compares his own method of procedure with that usually pursued by others, as follows:

"Having found, during my investigations, that tornadoes and other storms are different phenomena, and that they follow different laws, I endeavored to investigate storms in general by the same method I had used with the tornado.
"My researches were not made by filling out the ordinary meteorological formulas from observations made three or four times daily, as is the custom. I had learned that no storm will be accommodating enough to develop itself just at the specified periods for observing; I do not believe that this method will ever lead to any definite results.
"A storm must be treated as an individual which is subject to development. This is difficult, on account of the nature of the subject, but it is possible and essential. We must take the storm at its earliest appearance, and not lose sight of it for one moment until we know it throughout its whole extent, in all its parts, from beginning to end."

This view of Prof. Blasius coincides with that of Sir William Herschel, who says:

"In endeavoring to interpret the weather, we are in the position of a man who hears at intervals a few fragments of a long history related in a prosy, unmethodical manner. A host of circumstances omitted or forgotten, and the want of connection between the parts, prevent the hearer from obtaining possession of the entire story."
 

Definition of a Storm.—But leaving methods and passing to results, our author defines a storm in general to be "the movement of the air caused by its tendency to reëstablish an equilibrium which has been disturbed; and we may call all such movements storms, whether they are gentle breezes or furious hurricanes, whether accompanied by more or less condensation of moisture or clouds, or even by none at all," as in deserts.

Classification of Storms.—As the result of his investigations in aerial movements in the northern hemisphere, Prof. Blasius presents the following classification of all storms:

1.Local or Vertical Storms. Stationary. Centripetal.—Produced by a tendency of the atmosphere to reëstablish in a vertical direction an equilibrium that has been disturbed. Characteristic cloud—cumulus.
2. Progressive or Lateral Storms. Traveling.—Produced by a tendency of the atmosphere to reëstablish in a lateral direction an equilibrium that has been disturbed. They are of two kinds:
(a.) Equatorial or Northeast Storms. Winter storms.—Produced by a warm current displacing a cool one to supply a deficiency toward the poles. Temperature changing from cool to warm.—Direction to the northeastern quadrant. Characteristic cloud—stratus.
(b.) Polar or Southeast and Southwest Storms. Summer storms.—Produced by a cool current displacing a warm one to supply a deficiency toward the equator. Temperature changing from warm to cool. Direction to the southern semicircle. Characteristic cloud—cumulo-stratus.
3. Loco-Progressive or Diagonal Storms. Traveling locally. Rotary—tornadoes, hailstorms, sandstorms, water-spouts, etc.—Produced by a tendency of the atmosphere to reestablish the equilibrium of a polar storm which has been disturbed in the plane of meeting by a peculiar configuration of the ground.—Direction, the diagonal of the forces of the two opposing currents transversely through the polar storm.—Characteristic cloud—conus.
 

In order that the significance of the above classification may be clearly understood, it will be well to notice in brief outline the general movements of the atmosphere surrounding the globe, more especially those in the northern hemisphere.

Atmospheric Currents.—All storms owe their origin to the heat of the sun, which produces differences of temperature in different portions of the earth, and thereby causes all the movements and currents which take place in the atmosphere around the globe. As the air at the equator is more highly heated by the sun than that of any other region, it expands, becomes lighter and rises, causing a partial vacuum or deficiency there at the surface of the earth. The air north and south of it at once moves forward from opposite directions to supply this deficiency at the equator, and this in turn becomes heated and ascends. Other air again moves forward from north and south to replace it, and thus an upward current at the equator, and a north and south polar current at the surface toward the equator, are established. These north and south polar currents cause a deficiency of air at the poles, and the heated air which has risen at the equator into the upper region of the atmosphere divides and moves forward toward the opposite poles to supply the deficiency caused there. Thus, upper currents in opposite directions from the equator to the poles are also established in order to restore the equilibrium disturbed by the surface polar currents flowing toward the equator.

But by the time the air of the upper currents has reached the region of the tropics, it has become cooler and heavier, and descends to the surface of the earth. Here it divides into two currents—one flowing back to the equator, forming the trade-winds; and the other, becoming warmer again at the surface, flows toward the poles, meeting the polar current somewhere north of the tropic in the northern hemisphere, and south of it in the southern. This meeting of the equatorial or tropical and polar currents in the temperate zone, and the various phenomena attending and resulting from it, are the most significant and important facts which constitute the basis of Prof. Blasius's theory of storms, in distinction from the centripetal theory of Espy, and the rotary theory of Colonel Clapper, as developed by Piddington, Thorn, Dove, and others, and better known in this country as the cyclone theory of Redfield.

The following diagram (Fig. l) will serve to indicate the movements and courses of the general atmospheric currents of the earth, as above described, the arrows showing the directions in which they move.

The two currents above referred to—the polar and the equatorial or tropical—are of different temperatures, and move horizontally in opposite directions toward each other. When they meet they overlap each other somewhat like two wedges with their sharp ends forward. The warmer current, being lighter, glides obliquely over the cooler current, and moves northward; and the cooler current, being heavier, moves beneath it on the surface of the earth southward, just as two currents, warm and cold, flow over each other in opposite directions through an open window or door of a heated room.

The plane of meeting between these two currents is more or less inclined northward in the northern hemisphere, for the reason just stated; and the lower end of the plane, or the space of air between these two currents where they meet on the surface of the earth,[2] constitutes the centre line or area proper of the storm, and the region of lowest barometer. The horizontal plane beneath this inclined plane[3]

PSM V09 D320 Atmospheric currents.jpg
Fig. 1.—Atmospheric Currents.

is the geographical extent of the region affected by the storm and the region of low barometer. The place where the currents meet is constantly changing with the changing seasons, following the sun northward in summer and southward in winter. These changes of locality do not, however, take place in one continuous movement of the atmosphere; but with successive oscillations, like the waves of a rising tide, each succeeding wave advancing farther and receding less than the one before it, until its most northern or southern limit is reached as represented by the numbers 1 and 2 in the diagram when the oscillations in the opposite direction again begin. Whenever the lower end of the plane of meeting between the two opposing currents at B oscillates or passes over any place on the surface of the earth, it will cause storm or change of weather there a change of wind, of temperature, and of atmospheric pressure.

The inclination of the plane of meeting, or the slope of the tropical current over the polar, varies with the seasons and local circumstances. In winter the slope between the two currents is very gradual, as there is less difference of temperature, and less power of resistance between them. The warm current passes over the cold at a gentle inclination (as represented by the line B H in Fig. 1); and thus the horizontal or geographical extent of the storm beneath it—from B to D—which is the region of low barometer, is much enlarged, and sometimes its oscillations extend or move over several hundred miles.

In summer, however, the difference of temperature between the two currents, and their power of resistance, are greater, and when they meet they bank up against each other with more momentum and force, and the plane of meeting or conflict is often very steep and sometimes almost vertical (as indicated by B H in Fig. 2). Hence, the geographical extent of a storm in summer is much less than in winter, and the region of low barometer which moves with it is correspondingly small.

Clouds the Precursors of Storms.—Whenever a warm current of air, saturated with moisture, meets or mingles with a cold current, the invisible moisture of the warm air is condensed into visible vapor or clouds. As storms are produced by the movements and conflicts of warm and cold currents of air, the formation of clouds always indicates to the observer the region in the atmosphere where such movements are taking place, which would otherwise be invisible. Clouds, therefore, are the invariable precursors of storms, and the kind of clouds formed will indicate the kind of storm or atmospheric movements which produce them.

This general fact, however, does not apply to deserts, where the moisture of the warm air is condensed and precipitated before it meets the cooler air, and hence rain-clouds are seldom or never formed by the sand-storms of deserts.

Classification of Clouds.—Whenever, on account of some topographic circumstances, the sun heats any locality on the surface of the earth more than the surrounding region, a gentle current or column of heated air rises, and its invisible moisture is condensed into small masses of clouds called cumuli, which spread and produce the mottled appearance commonly known as "mackerel sky," as indicated at 1 in the accompanying illustration (Fig. 2).

But when, as is frequently the case in summer, a valley or plain, or island, or any other place, is much more highly heated by the sun than the surrounding region, the heated air over such locality rises more rapidly and with more ascensional momentum; and, as it reaches the higher and cooler regions of the atmosphere, its moisture is condensed into large rounded volumes, or mountain-like masses of cumulus clouds, as indicated at 2 in the illustration. Such cumulus clouds always precede and characterize a local summer storm or shower.

When the warm horizontal current from the south, as in winter, meets with the cold current from the north, it slopes upward over the cooler current, and forms stripes or bands of stratus clouds along the horizon, as shown in Fig. 3.

PSM V09 D322 Cumulus clouds.jpg
Fig. 2.—Cumulus Clouds.

These stratus clouds indicate to the observer the fact that a warm current is coming northward.

When in summer a cool current is moving southward, it encounters the warm equatorial or tropical current, which again glides upward and over it, and forms horizontal bands of stratus clouds along the upper line of contact, as in winter storms; but, in addition, the denser cold air from the north, moving with more momentum, will lift up the warm and saturated air from the tropics, and its moisture will be condensed into masses of cumulus clouds banked up against the top of the cold current, and arranged over the horizontal stratus clouds. Thus is produced the combination of cumulo-stratus cloud, as represented in Fig. 4, and which is characteristic of progressive summer storms.

PSM V09 D323 Stratus clouds.jpg
Fig. 3.—Stratus Clouds.

To the tornado-cloud produced by a whirl of air, and resembling an inverted cone, Prof. Blasius gives the name of conus, which is both distinctive and appropriate.

These four typical classes of clouds—viz., cumulus, stratus, cumulo-stratus, and conus—indicate and characterize the four different classes of storms.

Prediction of Storms.—With the foregoing facts and classifications in view, Prof. Blasius's method of predicting the approach of storms, "by their embodiments the clouds," can be verified by any careful observer of ordinary intelligence.

Winter Storms.—When in winter, while the wind is blowing from the north, thin, hazy bands or stripes of stratus clouds appear low in the southern horizon, it indicates that the warm current from the south is flowing northward, sloping over the polar current, and that the condensation of its vapor into clouds, by successive undulations, has commenced in the upper and colder regions of contact. More and more of these stratus clouds gradually appear, until they cover the entire southern sky and reach the zenith. This may require from twelve to twenty-four hours, or longer. Sometimes these clouds, before reaching the zenith, will recede and disappear beneath the southern horizon. This indicates a backward oscillation of the southern current, caused by the greater resistance of the polar current. But in such case the stratus clouds will reappear next day, or sooner, and uniting and, becoming denser, they will advance over the zenith, and cover the whole heavens, discharging rain, snow, or sleet, according to the thermal conditions present.

PSM V09 D324 Cumulo stratus clouds.jpg
Fig. 4.—Cumulo-Stratus Clouds.

Thus, by observing the clouds, a northeast or winter storm may always be predicted from one to three days beforehand, while the barometer shows no change until the stratus clouds from the south have reached and passed over the zenith, when it begins to fall; but the thermometer indicates no change.

At this stage of the storm the wind from the north rises and blows more violently, while the clouds move northward against the wind, and the rain or snow, driven by the prevailing wind, comes down obliquely from the north. After some time the direction of the wind changes, and there is a calm. The air is warmer, the thermometer rises suddenly, the barometer has reached its lowest point, and the rain or snow falls vertically. This calm continues for a longer or shorter time, and the wind gradually changes until it comes from nearly or quite the opposite quarter from which it came at the beginning of the storm, and blows more powerfully than before. The barometer now rises again, but is not as high as before the storm, because it is in the tropical current which has reached the locality. If, now, the wind from the south, which has prevailed and driven back the northern current, continues in the same direction until the entire atmospheric area of the storm passes over the zenith northward, and the sky clears up from the south or southwest, as is generally the case in early autumn or late spring, then the next storm or change of weather will come from the north. But if the wind changes its direction again before the storm is over, as is mostly the case in mid-winter, and blows from the north, as it did at the beginning, until the entire atmospheric area of the storm is carried backward over the zenith, and the sky clears from the north, then the next storm or change of weather will come from the south, as described above. In this case the polar current has prevailed, the air is colder, the thermometer falls, the barometer rises higher than in the other case, and the atmospheric conditions existing before the storm are gradually reestablished.

Summer Storms.—Before a progressive summer storm, the air is usually warm and sultry, the sky cloudless but somewhat dim, and a light southerly breeze is blowing. Suddenly the sound of distant rumbling thunder is heard, and large masses of dark cumulus clouds rise and arrange themselves on a long bank of stratus clouds in the northern or northwestern horizon. This is the cumulo-stratus combination of clouds which is the herald of a polar or progressive summer storm. Soon the south wind increases in violence, and drives clouds of dust before it. The thunder, rolls, and lightning flashes more frequently. The clouds bank up higher and higher, and advance more slowly, until at last they become stationary. These are the ordinary indications of a violent progressive summer storm, which sometimes ends in a tornado.

Like a winter storm, it is produced by the meeting and conflict of the polar and tropical currents under greater differences of temperature and other conditions, and is therefore attended with more violent and complex phenomena than those of a winter storm. The changes of wind, and of the barometer and thermometer, during its development at any locality, are similar to those of a winter storm in its return, oscillation southward; that is, these changes occur in a reverse order to those of a winter storm during the regular progress of the tropical current northward, in the same order as during its oscillation southward.

In most cases of this kind of summer storms, after the clouds have remained stationary for some time, discharged their rain and restored the disturbed equilibrium of the atmosphere, the polar current which produced it by moving southward oscillates back to the north again, and the storm at this locality is over—although similar phenomena and changes will be occasioned by it later at other localities over which it sweeps in its oscillation northward.

The cumulo-stratus cloud, which is the precursor of this kind of storm, can usually be observed only from one to eight hours, and, in some cases of the most violent kind, only about twelve hours before it will burst upon a place. Although these storms are the most dangerous and destructive—not unfrequently ending in tornadoes and hurricanes—the barometer is of no practical service in predicting it. This is explained by the fact that in such storms the plane of meeting of the two currents moves southward with its lower extremity, or region of lowest barometer, in front, while the plane itself is more or less inclined northward. Hence the barometer shows no change until this region of lowest barometer moves over it, when it suddenly falls g but it is then already in the most dangerous part of the storm, and its warning, therefore, comes too late; while the clouds, if properly observed, always give warning in time to provide against the dangers of such a storm.

Tornadoes.—This class of storms includes hailstorms, waterspouts, hurricanes, and all storms in which rotary and lateral motions are more or less combined. They are the most violent and destructive of all storms, as well as the most complicated and difficult to understand and explain. They are the offspring of progressive polar or summer storms, and in the temperate zone occur only during summer.

When in the development of a summer storm, as above described, the two conflicting currents attain a state of equal power or resistance, and thus balance each other, which is indicated when the dense cumulus clouds over the plane of conflict become stationary, then the storm is at its crisis. The air within the region of conflict is compressed and very sultry, and this condition is always felt before a tornado by persons within its area. If, now, during this critical stage of the storm, no topographic or other disturbance of its tension take place in its plane of meeting, a return oscillation of the polar current northward will set in, and the storm will gradually clear away. But if, in this crisis of the storm and during this high state of compression and resistance, either current becomes stronger, and forces back the other over some hill or valley, or if some other obstruction or configuration of the surface of the earth breaks the tension or disturbs the resistance between the two currents at any point, so that the polar current will sink as in a valley, then the tropical current will suddenly rush into this depression and generate a succession of violent whirling and zigzag motions along the diagonal of the two currents within the plane of conflict, as the waters of a dam would rush through a sudden break or depression in an embankment. This conclusion respecting the origin of tornadoes Prof. Blasius reached after his careful study of the West Cambridge tornado of 1851, and it was subsequently confirmed by the facts and phenomena connected with the tornado of Iowa and Illinois, in May, 1873, as obtained from the report of the United States Signal Service for that year, as well as by those of other tornadoes.

The characteristic cloud of a tornado is the conus, which appears first above as a dense, dark disk, and is formed by the whirl of the tropical current rushing into the depression of the polar current which starts the tornado, and it is enlarged and lengthened by alternate and rapid condensations above and below, as the tropical air whirls and zigzags along the diagonal of conflict, until sometimes the conus above and below unite—as in the case of water-spouts at sea—and a rotating column of mingled air, dense cloud, dust, or water—as the case may be—is thus formed, and sweeps along the plane of meeting between the opposing currents, and beneath the bank of cumulus clouds which mark the area of a tornado's path of destruction.

The conus cloud, however, as above described, is only formed when the tornado has already commenced, and is therefore of no use to indicate its occurrence beforehand.

But when the dark and dense masses of cumulus clouds in a summer storm cease moving forward or laterally, but bank up higher and higher, and there is great commotion among them, and when there is an oppressive sultriness about the air, these phenomena always indicate that the suspended storm is in a crisis or condition to generate a tornado, in case some local obstruction or other cause disturb the equilibrium of resistance between the two conflicting currents.

Scientific Aspects.—The condensed result of modern meteorological science is the general fact announced by Prof. Buys-Ballot, of Utrecht, that "the wind always blows from the place of highest to that of lowest barometer, turning by the rotation of the earth to the right on the northern hemisphere, and to the left on the southern hemisphere." This is known as "Ballot's Law," and is the chief basis of all scientific weather predictions at the present day.

The first part of this law, given in italics, is found to be universally correct. The second part, however, has many exceptions, and is as often "honored in the breach as in the observance;" for, in polar storms, the winds from the northern semicircle do not conform to it.

Among other definite results attained by barometric observations and deduced from Ballot's law, is the fact that the rain-area of a storm extends over that of lowest barometer and also surrounds it. The isobars, or elliptic lines, of equal barometer, surround the area of lowest barometer, and the most distant isobar marks the limit of the region of low barometer, and may be regarded as the boundary between the regions of high and low barometer. The gradients indicate the differences of pressure between the isobars on a line extending at right angles from that of highest to that of lowest barometer.

The shape of the area of lowest barometer in a progressive storm is that of an irregularly elongated ellipse, moving sideways, or in the direction of its shortest diameter; and the gradients are found to be much more steep on the southward than on the northward side of this area; from which it follows that the rain-area is much less on the southward than on the northward side of a progressive storm.

All the atmospheric changes and phenomena above stated result from the same general cause, but under different conditions and circumstances. This cause is the meeting of the polar and tropical currents in their movements northward and southward, to restore a disturbed equilibrium in the atmosphere toward the equator or the poles.

Applying this theory in brief explanation of the facts stated in connection with Ballot's law, we find the area of lowest barometer at the place where the two currents meet on the surface of the earth. It is produced by the obliquely upward movement of the tropical current over the polar current, and by its rising more or less vertically in the vicinity of contact, after its horizontal progress northward has been checked by encountering the polar current. This oblique and upward movement of the tropical current diminishes the atmospheric pressure there, as shown by the barometer, and produces that depressing calm which is always felt by persons in any locality where this meeting of currents takes place, or over which its area moves or oscillates during the continuance of a storm. The elongated, elliptical shape of this area is accounted for by the fact that it is the narrow space between the two currents where they meet, and extends eastward and westward between them. It is rounded at the ends or margins of the currents, where the wind, in accordance with Ballot's law, blows inward toward the centre line of contact, which is also the centre line of lowest barometer. And, as the two currents force each other backward and forward during a storm, they necessarily carry along the elliptical space between them, and thus its movements in the direction of its shorter axis are accounted for.

The rain-area, or that of low barometer, which surrounds the elliptical region of lowest barometer where the currents meet on the surface, as just explained, extends horizontally beneath the plane of meeting, which is inclined northward. It is produced chiefly by the oblique and upward movement of the tropical current over the polar.

The gradients, or different degrees of pressure within the rain-area, are caused by the same upward movement of the tropical current over the polar, in connection with the constantly-varying heights or depths of both polar and tropical air, which are vertically above the space beneath the inclined plane from the region of lowest to that of highest barometer northward; and the steeper or more abrupt gradients southward are explained by the fact that when the tropical current meets the polar current it is suddenly checked, and while a portion of it moves obliquely over the polar current, as stated, another portion of it rises, more or less vertically, for some distance around the vicinity of contact, and the pressure is thus more suddenly diminished on the southward side of this area of low barometer than on the northward, where it slopes more gradually beneath the inclined plane of meeting, as above explained.

For obvious reasons, the region of high barometer is within the polar current before it meets the tropical, and also within the tropical current before it is disturbed, or its horizontal movement checked by meeting the polar current; but the barometer is highest in the polar current, because it is colder and denser.

In addition to the foregoing facts which barometric observations have established, this theory of opposing currents explains a great many other aerial problems and phenomena which have not heretofore been adequately accounted for. Among these are the real causes of different kinds of storms and how they originate; why they move forward and backward, carrying the lines and areas of high and low barometer, of isobars and gradients, with them, and why they cease; why the barometer indicates the approach of some storms in advance, but is useless in others; why it falls in some storms but rises in others; why a progressive storm travels against the prevailing wind, and why the wind changes during its progress; why there is a region of calm, and why the wind is stronger around this region of calm. It explains how snow-storms change to rain, or sleet and rain, and why it falls obliquely toward the direction from which the storm is coming; also why in some storms the rain falls in advance of the area of low barometer and in the rear of it in others. It accounts for the origin of tornadoes, water-spouts, hail-storms, and all other whirling storms, and explains why these always move in an eastward direction on our continent. It explains why the rain-areas of winter storms are more extended than those of summer, why their approach is slower and their continuance longer, and why they produce sudden changes of temperature in their progress over any place. It greatly simplifies and corrects previous explanations respecting the formation of different kinds of clouds, and accounts for the development of electricity both in summer and in winter storms.

 

  1. "Storms: Their Nature, Classification, and Laws, with the Means of predicting them by their Embodiments the Clouds." By William Blasius. Philadelphia: Porter & Coates.
  2. As shown at B in the diagram.
  3. 2 From B to D.