unloading the veins in the immediate neighborhood of the heart, and so remove some part of the resistance to be overcome by the contractions of the cardiac muscle. When we come to the detailed study of the heart it will appear also that a slight force of suction is generated by the heart itself, which force adds its effects upon the flow of venous blood to those of the elasticity of the lungs and of the contraction of the muscles of inspiration.

It must here be repeated, however, that the heart is quite competent to maintain the circulation unaided. This is proven as follows: If in an anæsthetized mammal a cannula be placed in the windpipe, the chest be widely opened, and artificial respiration be established, the circulation, though modified, continues to be effective. By the opening of the chest its aspiration has been ended, and can no longer assist in the venous return. If, further, the animal be drugged in such a manner as completely to paralyze the skeletal muscles throughout the body, their contractions can exert no influence upon the venous return; yet the circulation is still kept up by the heart, unaided either by the elasticity of the lungs, by the contractions of the muscles which produce inspiration, or by those of any other skeletal muscles.

E. THE SPEED OF THE BLOOD IN THE ARTERIES, CAPILLARIES, AND VEINS.

If we keep as our text, in discussing the circulation, the character of the capillary flow, it will be seen that we have now accounted for the facts that the capillary flow is toward the veins; that it shows much friction; that it is continuous, pulseless, and under low pressure. We have not yet accounted for the fact that it is slow. We must now do so, but must first state and account for the speed of the blood in the arteries and veins.

The Measurement of the Blood-speed in Large Vessels; the "Stromuhr."-The speed of the blood in the larger veins and arteries must be measured indirectly. We can picture to ourselves the volume of blood which moves. past a given point in a given blood-vessel in one second, as a cylinder of blood having the same diameter as the interior of the blood-vessel. The length of this cylinder will then be expressed by the same number which will express the velocity with which a particle of the blood would pass the given point in one second, provided that this velocity be uniform and be the same for all the particles. In order, then, to learn the average speed of the blood at a given point of an artery or vein during a certain number of seconds, we have only to measure the calibre of the blood-vessel and the quantity of blood which passes the selected point during the period of observation. From these two measurements the speed can be obtained by calculation. But these two measurements are not quite easy. The physical properties of the blood-vessels, especially of the veins, make their calibres variable and hard to estimate justly as affected by the conditions present during an experiment. The means adopted for measuring the quantity of blood passing a point in a given time necessarily alters the resistance encountered by the flow, and so of itself affects both the rate of flow and the blood-pressure; and, with the

B

FIG. 17.-Diagram of longitudinal section of Ludwig's "Stromuhr." The arrows mark the direction of the bloodstream. For further description see the text.

latter, the calibre of the vessel. For these reasons any measurement of the average speed of the blood by the above method is only approximately correct. The best instrument for measuring the quantity of blood driven past a point during an experiment is the so-called "stromuhr" or "rheometer" of Ludwig, a longitudinal section of which is given diagrammatically in Figure 17.1 This is essentially a curved tube shaped like the Greek capital letter 2. Each end of the tube is tied into one of the two stumps (a and b) of the divided vessel. These ends of the tube are as nearly as possible of the same calibre as the vessel selected. Each limb of the tube is dilated into a bulb, and the upper part of the tube, including the two bulbs, is of glass; the lower part of each limb is of metal. At the top, between the bulbs, is an opening for filling the tubes, which can easily be closed when not in use. Each end of the tube is filled with defibrinated blood before being tied into the blood-vessel. In the limb of the tube (B, (Fig. 17) which is the farther from the heart if an artery be used, or the nearer to the heart if a vein, the defibrinated blood is made to fill the cavity up to the top of the bulb. In the other limb (4, Fig. 17) the blood fills the tube only up to a mark (e, 'Fig. 17) near the bottom of the bulb. Through the opening between the bulbs the still vacant space, which includes the whole of the bulb A, is filled with oil, all air being excluded. The opening is then closed. If now the clamps be removed from the blood-vessel, the blood of the animal will enter the tube at a and drive before it the contents of the tube. Thus defibrinated blood from B will be driven into the distal stump of the vessel at b, and will enter the circulation of the animal. Oil will at the same time be driven over from A to B. The bulb A has upon it two marks, d and e, one near the top of it, the other near the bottom. The instant when the line between the oil and the advancing blood reaches the mark near the top of A is the instant when a volume of blood equal to that of the displaced oil has entered A, past the mark near the bottom of it. The capacity of the tube between the two marks is accurately known. The time required for this space to be filled with the entering blood is measured by the observer. The calibre of the metal tube at a is accurately known, and is assumed to be equal to the calibre of the blood-vessel. From these measurements the average speed of the blood-stream at a is calculated.

1 J. Dogiel: "Die Ausmessung der strömenden Blutvolumina," Berichte über die Verhandlungen der k. sächsischen Gesellschaft der Wissenschaften zu Leipzig, Math.-physische Classe, 1867, S. 200.

The metallic lower part of the instrument, which includes both limbs of the tube, is completely divided horizontally at c. The two parts are so built, however, as to be maintained in water-tight apposition. This arrangement permits the whole upper part of the instrument, including the glass bulbs, to be rotated suddenly upon the lower, so that the bulb B may correspond with the entrance for the blood at a, and the bulb A with the exit for the blood at b. If this rotation be effected at the instant when the space between the two marks on A has been filled with blood, the bulb B, now charged with oil, will be filled by the blood which enters next, and the first charge of the animal's own blood will make its exit at b. Oil will now pass over from B to A; when the line between it and the blood which is leaving A has just reached the lower mark on A, the bulbs are turned back to their original position. Thus, by repeated rotations, each of which can be made to record upon the kymograph the instant of its occurrence, a number of charges of blood can be received and transmitted in succession; it is always the same space, between the marks on A, which is used for measuring the charge; and the time of the experiment can be much prolonged. By this procedure the errors due to a single brief observation can be greatly reduced. Indeed, the time of entrance of a single charge of blood would be quite too short to give a satisfactory result.

The use of the stromuhr not only affords necessary data for the calculation of the average speed of the blood, but seeks directly to measure the volume of blood delivered in a given time by an artery to its capillary district. It is evident that this volume is a quantity of fundamental importance in the physiology of the circulation. Could we ascertain it, by direct measurement or by calculation, for the aorta or pulmonary artery, we should know at once the volume of blood delivered to the capillaries in one second, and thus the time taken for the entire blood to enter either those of the lungs or of the system at large. By this knowledge, many important problems would be advanced toward solution.

The Measurement of Rapid Fluctuations of Speed.-The stromuhr can give only the average speed of the blood during the experiment. To study rapid fluctuations of speed, another method is needed. If, in a large animal, a vessel, best an artery, be laid bare, a needle may be thrust into it at right angles. If the needle be left to itself, the end which projects from the artery will be deflected toward the heart, because the point will have been deflected toward the capillaries by the blood-stream. The angle of deflection might be read off, could a graduated semicircle be adjusted to the needle. If the stream be arrested, the needle returns to its position at right angles to the artery. The greater the velocity of the stream, the greater is the deflection of the needle. If, later, the same needle be thrust into a tube of rubber through which water flows at known rates of speed, the speed corresponding to each angle of deflection of the needle may be determined. If the needle were made to mark upon a kymograph, variations of the speed would be recorded

as a curve.

An instrument based on the principles just described is valuable for the study of rapid changes of velocity. In an artery, its needle oscillates rhythmically, showing that there the speed of the blood varies during each beat of the heart, being greatly accelerated by the systole of the ventricle, and retarded by the cessation of the systole. It will be remembered that the microscope directly shows faint rhythmic accelerations in the minute arteries of the frog. In the veins rhythmic changes of speed do not occur except near the heart from respiratory causes.

The Speed of the Blood in the Arteries.-The stromuhr shows that the speed of the blood is liable to great variations. This fact, and the range of speed in the arteries, are fairly exhibited by the results obtained by Dogiel from the common carotid artery of a dog, the experiment upon which lasted 127 seconds. During this time six observations were made which varied in length from 14 to 30 seconds each. For one of these periods the average speed was 243 millimeters in one second; for another period, 520 millimeters. These were the extremes of speed noted in this case. The speed in the arteries diminishes toward the capillaries.

The Speed of the Blood in the Veins.-The speed in a vein tends to be slower than that in an artery of about the same importance, but is not necessarily so.3 It increases from the capillaries toward the heart.

The Speed of the Blood in the Capillaries.-The rate of the capillary flow may be measured directly under the microscope. Certain physiologists have also observed the movement of the blood in the retinal capillaries of their own eyes, and have measured its rate there. Both methods show that in the capillaries the speed is very much less than in the large arteries or large veins. In the capillaries of the web of the frog's foot it is only about 0.5 millimeter in one second. In those of the mesentery of a young dog it has been found to be 0.8 millimeter; in those of the human retina, from 0.6 to 0.9 millimeter.

Speed and Pressure of the Blood Compared.—If now we compare the speed with the pressure of the blood in the arteries, in the capillaries, and in the veins, we shall be struck by both similarities and differences. In the arteries both pressure and speed rhythmically rise and fall together; and both the mean pressure and the mean speed decline from the heart to the capillaries. In the capillaries both pressure and speed are pulseless and low,—very low compared with the great arteries. In the veins, however, the pressure is everywhere lower than in the capillaries and falls from the capillaries to the heart; the speed is everywhere higher than in the capillaries and rises from 1 M. L. Lortet: Recherches sur la vitesse du cours du sang dans les artères du cheval au moyen d'un nouvel hémodromographe, Paris, 1867.

2 J. Dogiel: loc. cit.

3 E. Cyon und F. Steinmann: "Die Geschwindigkeit des Blutstroms in den Venen," Bulletin de l'Académie Impériale des Sciences de St. Pétersbourg, 1871; also in E. Cyon: Gesammelte physiologische Arbeiten, 1888, S. 110.

*K. Vierordt: Die Erscheinungen und Gesetze der Stromgeschwindigkeiten des Blutes, etc., 1862, S. 41, 111.

the capillaries to the heart. It is apparent, therefore, that there is no direct connection between the pressure and the speed of the blood at a given point, inasmuch as they change together along the arteries and change inversely along the veins. How varied the combinations may be of pressure and speed will be seen in studying the regulation of the circulation.

In the great veins, as in the arteries, the speed is very high compared with the capillaries. In the capillaries the speed of the blood is least, while in the tubes which supply and which drain them the speed is great. The physiological value of these facts is clear. It has already been pointed out that the blood moves slowly through the short and narrow tubes, where its exchanges with tissue and with air are effected, and swiftly through the long tubes of communication. What are the physical conditions which underlie these physiological facts?

The speed of the blood varies inversely as the collective sectional area of its path. If the circulation in an animal continue uniform for a time. -during several breaths and heart-beats-it is evident that the forces concerned must be so balanced that, during that time, equal quantities of blood will have entered and left the heart, the arteries, the capillaries, and the veins, respectively. If the arteries, for instance, lose more blood than the heart transmits to them, this blood must accumulate in the veins till the arteries become drained and the supply to the capillaries fails. The very maintenance of a circulation, then, implies that equal quantities of blood must pass any two points of the collective blood-path in equal times, except when a general readjustment of the rate of flow may lead to a temporary disturbance of it. It will be seen at once that this principle is consistent with the widest differences of rate between individual arteries of the same importance, or between individual veins or capillaries. If in one artery the flow be increased by onehalf, and in another be diminished by one-half, the total flow in the two arteries collectively will be the same as before.

If the principle just stated be considered in connection with the anatomy of the blood-path, the differences of speed in the arterial, capillary, and venous systems will at once be understood. The wider arteries and veins are few. Dissection shows that when an artery or vein divides, the calibre, and, with the calibre, the "sectional area" of the branches taken together, is commonly larger than that of the parent trunk. In general it is a law of the arterial and venous anatomy that the collective sectional area of the vessels of either system increases from the heart to the capillaries. The smaller the individual vessels are, the wider is the blood-path which they make up collectively. Widest of all is the blood-path where the individual vessels are smallest-that is, in the capillary system. The collective sectional area of the capillaries is several hundred times that of the root of the aorta. The collective sectional area of the veins which enter the right auricle is greater, perhaps twice as great, as that of the root of the aorta. The venous system, regarded as a single tube, is of much greater calibre than the arterial. It is perhaps better to make these general statements than to compare the different figures given