must, as has been said, depress the tube with a certain force; that is to say, if we represent by 100 the pressure of the liquid in the tube, the pressure of the lever must be somewhat superior to it, say 105; and it follows that the vototitional force cannot raise the syhygmograph instantaneously, unless it be higher by five at this instant, or, being inferior to this number, it will raise it only, when, in its growing motion, it shall have acquired a force equal to five, which demands time.

Figure 9 represents three supperposed sinuous lines, each formed by the oscillations of a sphygmograph; the most inferior is traced by the one nearest the orifice of ingress, the middle line is traced by the sphygmograph 72 (fig. 6) and the highest, No. 3, by the last sphygmograph.

If the first oscillation on each of these lines be examined, it is seen that the beginning of the lever's ascension is earlier in proportion as the pulsation is taken closer to the orifice of ingress; but it is also seen that the angle, at which the ascending line separates, is so much more open as we are nearer the entrance of the tube; hence this point is on the line No. 1, easier perceived than at any other part.

If to this cause of error, depending on the degree of obliquity of the ascension, we add (as has already been adverted to), that the lever can only be raised when the additional force has acquired a greater intensity than the force which depressed the tube, we can readily apprehend the reason for the production of a retardation in certain sphygmographic tracings.

It remains to be proven, that there is in reality no retardation; and for this purpose we have made use of a medium more sensitive than a sphygmograph, namely: a manometer containing a liquid of small density, and offering the least possible friction.

Experiment. Let us take a long gum elastic tube, fitted by one of its extremities to a raised receiver and terminating by a vertical glass tube, the height of the receiver. When the levels are in equilibrium, let us mark on the glass the summit of the liquid. If we now compress suddenly the elastic tube, it is seen to be always impossible to perceive the least retardation between the instant of compression and that of the rise of the liquid column in the glass tube.

On the contrary, without a mark on the glass, we cannot perceive the small ascension of the beginning, especially if somewhat distant, and the ascentional motion which in this case is manifestly accelerated, is perceivable only after a certain time.

2d. Period of increase in the oscillation, and nature of the motion which produces it.

As soon as the sphygmographic line rises above the horizontal, which it traced at the time of the uniform tension, of the points a a' a", it is seen to describe two curves, which, united, form the shape of an S-at first, with a concavity above, and afterwards, by a convexity in the same direction, united together by a more or less short rectilinear line.

We have said that the first concave portion represents an accelerated motion; it is caused by the increase of tension, which, feeble at the beginning, goes on increasing in power; but as every accelerated motion meets a regulator in friction, bringing it back to an uniform type, it follows, that, at a given moment, the ascensional force becomes uniform; and its tracings are represented by an oblique, though rectilinear line. Finally, the impulsive force decreases, and, owing to he current, the excess of the afflux over the dischargethat is to say, tension-diminishes; the convex curved line,

which represents the diminished motion, then succeeds to the rectilinear portion, until such time, when, the discharge being greater than the afflux, tension begins to decrease.

3d. Summum of the curve; intermediate point between the period of ascension and that of decline in the oscillation.

Owing to the diminution of the ascending motion in the last period, it will happen, after a while, that this motion ceases altogether, the flowing acts only, and tension is reduced. Between the period of increase and that of decline, the sphygmograph remains for a short instant steady (fixè)—the same as seen in a pendulum, between two halves of an oscillation. At this moment, the rotation of the cylinder being the only motion produced, the marking point traces a very short horizontal line, but which we assume, theoretically, as the expression for the maximum tensity.

The height of this line, described by the sphygmograph previous to the intervention of the additional tension, represents the intensity of the force by which the lever is raised in other words, the intensity of the additional force itself in every portion of the tube. Now, we see this height diminishing on each of the lines, in proportion as we rise, by passing from 1 to 3-a further proof of the unequal tension throughout the length of the tube; a result agreeing fully with the one obtained by manometers (fig. 8), hy showing, from the heights of the mercurial columns, that additional impulsions are distributed by decreasing from No. 1 to No. 3. This fact is due to the greater separation of the curves a and a' on the side of the orifice of ingress.

As to the form (shape) of the curve's summit, it varies according to the nature of the motion which the sphygmograph describes: that is to say, according as elasticity has

been more or less efficient in transforming the wave's impul sion (impulsion de l'oudée). If elasticity has but feebly acted, the ascending portion, almost vertical, will make, with the descending oblique portion, a very marked angle (un angle très accusé)-as may be seen on the inferior tracings of figs. 9, 10, 11. If, on the contrary, elasticity has greatly modified the impulsion, the two curves, touching by their summits, give the appearance of a horizontal line.

As to the position which the summit of the curve occupies with respect to the vertical lines (which serve to measure time), it is easy to perceive that this point is so much more removed from the commencement of the pulsation, as we observe the tracings produced at a point farthest removed from the orifice of ingress. The summits of the curves bb' b", are situated at points so much the more removed, even on account of the obliquity of the ascending line. It is hence seen that all the pulsations take place at the same time, as to their beginning (début), but that their maximum is so much more retarded, as we observe them farthest from the orifice of ingress.

4th. Of the period of decline and the nature of the motion which produces it.

The descent of the sphygmograph is composed, like the ascension, of a motion at first accelerated, then diminished; but, as the motion takes place here in an inverse manner, when compared with what took place in the first portion, so, likewise, is its explanation the inverse of the former. To have the same sphygmographic expression, the figure ought to be turned upside down, so as to keep the summum of oscillation below. In the drawing, in its normal position, the accelerated motion of descent is represented by a curved line, convex above. The last half of this descent is a

diminished motion, for the flowing, which is its cause, diminishes with tension: its graphic representation must also be inverse of the diminished ascensional motion, and a curve, with the concavity above, will, in this case, be the result.

5th. End of the pulsation.

The descending period of the pulsation may end in two different ways; either the additional tension is completely extinguished before a second impulsion comes on, or a second impulsion takes place before the effect of the first has subsided.

In the first case, the line of minima is found on the inferior horizontal (as seen at the commencement of figs. 9, 10, 11). In the second case, the minima are seen on an ascending line (a b, a' b', a" b", figs. 10 and 11), thus showing that the mean tension has been raised.

The sphygmograph may serve to verify the laws on tension given by the manometer.

Indeed we have seen that, in cases of increase of tension, by a growing frequency of impulsions, this increase is mainly felt at points nearest the orifice of ingress (this results, on the inspection of the lines a and a' fig. 8; the line a, being