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tracings which is similar to that of a change in the length of the lines AB in the constructions. This is one more reason why mere inspection of the curves cannot give a satisfactory result.

These constructions show that the sphygmographic curves must show great variations, since the amount of blood pumped into the system, the elasticity of the arteries and friction of the surrounding tissues are subjected very likely not only to individual but also to local and temporal variations. But under given conditions only a certain form of the pulse wave is possible, and this form does not change so long as these conditions do not change. The sphygmograms in Fig. 6 show some of the typical forms of the pulse curve.

No. I shows the influence of high arterial tension, and No. II of low tension. The first corresponds to No. II in Fig. 5, the second

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to Nos. I and III. Nos. IV and V of Fig. 5 show the effect of great friction and small elasticity. The constructions differ in the form of the elastic movement; the position of equilibrium is reached with different velocity in both cases. The resulting movements differ slightly in the form of the catacrotic phase. Both forms may be seen in No. III of Fig. 6. This sphygmogram was taken from an artery with low tension, and this form of the sphygmographic curve is well known as characteristic of the "soft" pulse. If the artery has lost to a large extent the qualities of an elastic body, and if the outflow is very rapid,

the pulse curve shows nothing but the slight elevation of the travelling wave; No. IV in Fig. 6 shows a curve of this character.

This theory explains many surprising facts which resisted every attempt at explanation. The anacrotic part shows a steep ascent, because it is due to the sudden arrival of the blood wave. It seems that an interruption in the descent may be seen only in abnormal cases. The sphygmograms of twelve normal individuals were observed regularly by me during more than a year without once discovering an anacrotic elevation.

The hemautographic curve of Landois is produced in this way. The form of this curve depends on the velocity of the escaping jet of blood. The velocity of the blood flow depends on the resistance of the arterial system in the sense that the velocity decreases when the resistance increases. When the arterial wall is in the negative phase of vibration the lumen of the artery is smaller, and, therefore, the velocity smaller. This is confirmed by the actual tracings of the velocity of the circulation by Marey.

It is also obvious that the dicrotic elevation never can arrive before the primary wave, because the arterial wall cannot perform elastic vibrations before it is expanded by the impulse of the arriving blood wave. Neither is it surprising that the "dicrotic wave" seems to travel in the same direction and with a velocity equal or almost equal to the velocity of the pulse wave. Such a difference can be produced only by a difference in the time of the vibrations of the arteries at different points of the body. The time of one vibration is necessarily very short, and the length of this interval depends on the circumstances which determine the elasticity of the arterial wall and the friction. These conditions may be subjected to local variations. If, therefore, the time-interval between the primary and the secondary elevation is measured at two different points (e. g., at the carotid and at the radialis) a difference of time may be found. Starting from the supposition that the dicrotic elevation is due to a wave travelling in the blood, one could attribute this difference of time to a velocity of the "dicrotic wave" which is slightly different from the velocity of the primary wave. The fact that the dicrotic elevation appears later in places farther from the heart was interpreted as a proof that the wave travelled out from the heart. No theory which assumes that the dicrotic elevation is due to a wave travelling in the blood can give a reason why two waves of the same form and origin should travel through the same liquid at different velocities.

At this point a theory must be mentioned, which was brought for

ward recently, because it is based on measurements of the velocity of propagation of the dicrotic wave. This theory is connected with Krehl's theory of the function of the valves. The blood, according to Krehl, enters the aorta through a small opening, and expanding in a large space it produces fluctuations and eddies, which would close the valves if they were not kept open by the blood which streams through under high pressure. They must, therefore, close at the moment when the aortic pressure is equal to the intraventricular pressure. This occurs shortly after the moment indicated by the beginning of the decline of the intraventricular pressure curve. Now the second sound of the heart is heard somewhere in the descending part of the cardiogram and the measurements of Huerthle 2 have shown that the second sound is heard 0.02" after the beginning of the descent of the cardiogram. This seems to indicate that the second sound of the heart is in a temporal relation to the closure of the valves. Many theories of the origin of the sounds of the heart agree on this one point that the second sound is due to a noise in the muscles. It therefore may be supposed that the second sound is due to the tension of the valves when they close or shortly afterwards. The problem now would seem to be to find an elevation in the descending branch of the curve of intraventricular pressure, or in the tracings of the apex beat, which could be attributed to the closure of the valves. It was taken for granted that the curves of intraventricular pressure and those of the apex beat were identical. In many of these tracings an elevation was found which may be called "the wave f." This elevation is not found in all the tracings, and its position seems to be rather variable. Edgren 3 remarks that the wave ƒ was always found near the abscissa no matter whether the preceding decline of the curve was great or small. In some of Chauveau's tracings the wave f is missing or indistinct, in others it is very well marked and approximately in the middle of the descending branch of the curve.5

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1 Edgren: Kardiographische und sphygmographische Untersuchungen, Skandinavisches Archiv f. Physiologie, vol. 1, pp. 88-91, 1889; Fredericq: Vergleich der Stoss und Druckcurven der rechten Herzkammer des Hundes, Centralblatt f. Physiologie, vol. 7, p. 770, 1893; Einthoven und Geluk: Die Registrierung der Herztöne, Archiv f. d. Ges. Physiologie, vol. 57, p. 631, 1894.

2 K. Huerthle: Beiträge zur Hämodynamik, Archiv f. d. Ges. Physiologie, vol. 60, p. 281, 1895.

3 Edgren: loc. cit. p. 87.

* A. Chauveau: Inscription électrique des mouvements valvulaires, Journal de Physiologie et de Pathologie Générale, vol. 1, p. 388, fig. 4, 1899.

5 Ibid. p. 391, fig. 6 (curve 5); and the same author's La pulsation cardiaque, in the same Journal, vol. 1, p. 795, fig. 5, and p. 796, 1899.

Edgren made experiments on the temporal relation of the wave f and of the dicrotic wave, which to avoid misunderstandings he calls the "wave f'." His experiments were made as follows. A sphygmogram from the carotid and a cardiogram were taken simultaneously, the points of the writing-levers being in the same vertical line. The wave f' appeared a little after the wave f. The length of this interval could be calculated by measuring the distance between these waves, as the speed of the drum was known. From this was subtracted the time of propagation of the dicrotic from the heart to the point where the instrument was fixed. In this way it was found that the time between the appearance of the wave ƒ and of the wave f' was equal to the time of propagation of the dicrotic wave from the heart. Edgren concluded that the dicrotic wave is in close temporal relation to the closure of the valves. To this comes the supposition that the wave f' is due to a change of pressure proceeding from the heart. The wave f', therefore, could be attributed to the tension of the valves.2 Edgren and Tigerstedt are the chief exponents of this theory.

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In so far as this theory assumes that the dicrotic elevation is due to a wave travelling from the heart to the periphery, it is open to all the arguments against a theory of the central origin of the dicrotic wave. Against the more special assertion that the dicrotic elevation is in connection with the closure of the valves, the following facts must be mentioned. We grant that the tracings of the apex beat may be directly substituted for the curves of intraventricular pressure, although this is by no means obvious, since one tracing gives the form of the pressure changes and the other the effect of the shock of the heart against the wall of the chest. It is, furthermore, not proved that the wave ƒ is due to the closure of the valves and that the waves f and f' correspond to each other so closely as Edgren's experiments seem to indicate. His measurements of the length of lines were made with an exactitude of 0.1 mm., but his computations were carried to the third decimal place of a second. The third decimal is generally inexact and the second in a large number of cases. Experimental evidence, furthermore, directly contradicts the statement that the 1 Edgren: loc. cit. p. 114.

2 The exposition of this theory may be found in R. Tigerstedt: Intracardialer Druck und Herzstoss, Ergebnisse der Physiologie, vol. 1, pp. 258-262, 1902. This theory, equally remarkable for its logical beauty and for its confirmation by Edgren's experiments, has not found its way into recently published text-books of physiology, though Edgren's paper belongs to the most frequently quoted publications on sphygmography and cardiography.

3 Tigerstedt: loc. cit. p. 261.

dicrotic elevation corresponds to the wave f. Fredericq1 traced pressure curves in the ventricle and in the aorta, and determined the points of equal pressure in both curves. He thus found that a point near the beginning of the descent of the curve of intraventricular pressure corresponds to the dicrotic. His experiments are rather conclusive against the theory in question, since the wave ƒ is very well marked in these tracings of Fredericq. The following facts, however, are fatal for the theory that the closure of the valves causes the dicrotic elevation: The dicrotic wave disappears in diseases like atheroma and arteriosclerosis which do not impair the function of the valves, but affect the elasticity of the arterial wall, and it is not affected by valvular insufficiency. The independence of the dicrotic from the function of the valves is conclusively proved by v. Kries, who found the dicrotic elevation in the femoral artery of an animal whose heart was replaced by a valveless bag.

All these facts, on the contrary, can be understood easily in the light of the theory that the sphygmographic curve gives the movements of the arterial wall, which movement is conditioned by the decreasing amount of blood in the artery, and the elastic vibrations of the wall around a variable position of equilibrium. In some cases the conditions of the problem are rather simple, and admit an analytic treatment, the results of which fit closely to the experimental facts. This part of the theory, however, has merely physiological interest, and therefore is discussed in a separate paper. It may be mentioned at this point that this theory of normal dicrotism is essentially identical with the theory of abnormal dicrotism as stated by Galen. He believed that the second beat of the pulsus bis feriens was due to an elastic vibration of the arterial wall. "Ex eodem genere sunt dicroti; nam arteria in occursu quasi repellitur, moxque redit. . . . Neque enim tum arteria contrahitur, sed quasi concuteretur, occidit; cuius delapsum a primae distentionis termino nulla dirimit manifesta quies, ut animadvertitur in contractione: sed simulatque attolli destitit, recidit atque ita paulisper vibrata, mox occurrit iterum." 2 Galen, however, is mistaken in his view, and in his observation that sometimes three or more pulse-beats may be felt with the finger. No form of the pulse is known where three or more beats may be felt for every heart-beat, and the actual tracings exclude the possibility

1 Fredericq: La pulsation du cœur chez le chien, no. 5. La comparaison du tracé du choc du cœur avec celui de la pression intraventriculaire, Travaux du Laboratoire de Liège, vol. 5, p. 67, 1896.

2 Galenus: De pulsuum differentiis, lib. 1. c. 16.

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