Problem 13.-To determine, in the arteries under observation, the rule of the time-relation of the three principal secondary waves to the beginning of the pulsation of which they are parts.

While fully appreciating the difficulty of an exact rendering of the specific facts embraced in the chronometry of the secondary waves, the data in hand are offered as competent for the solution of the problem as stated above.

Solution, by a critical examination of the plates. The position of the lines 1', 2', 3' on the distal trace, as to the summits of the first and second waves, and the aortic notch or beginning of the third wave respectively, shows the relation sought; inasmuch as these numbered lines are placed at the same respective distances from C as 1, 2, 3 on the proximal trace, and exactly cutting the secondary waves, are placed from B.

In the reading it is important to consider that the aortic is truly a double wave, and that the first indentation is prop

erly the aortic notch. The double form is shown distinctly in the carotid, and is more or less indicated in the femoral traces. In the radial, dorsal, and posterior tibial, it scarcely appears. Examination of the pairs of the K series, all shown by reversal, yields the following results:

1. The first and second waves of all the pairs attain their summits as early in the distal as in the proximal arteries—in the dorsalis pedis as in the carotid pulse.

2. The beginning of the third or aortic wave is slightly but clearly delayed in the dorsal as compared with the femoral and carotid pulse, while delay is scarcely shown in the femoral and radial as compared with the carotid pulse, and in the femoral radial pair the correspondence is complete.

Examination of the pairs of the L series (part shown by reversal) yields the following results:

1. The first wave is shown to attain its summit at the same time in the posterior tibial and carotid pulse (shown by reversal); in the femoral and carotid; in the radial and carotid; in the femoral and radial; while the summit is shown very slightly delayed in the posterior tibial as compared both with the femoral and radial.

2. The second wave is shown slightly antecedent in the femoral and subsequent in the radial, as compared with the carotid; delayed in the radial as compared with the femoral, and in the posterior tibial as compared with the femoral, radial, and carotid.

3. The beginning of the aortic wave is shown delayed in the distal pulse of all the pairs except the femoral-radial, in which it marks corresponding time.

Allowing for fallacies, and giving the above results a judicious interpretation, the premises will justify at least the following statement:

Rule 1.-The interval between the beginning of the pulse and its acme of expansion is the same in all parts of the arterial system.

Rule 2.-In certain conditions of the vessels and circulation the second wave keeps close time with the first in the onward flight, while in certain other conditions of the same

the second falls notably behind the first in the progress from the heart.

Rule 3.-The aortic wave rises later in the distal than in the proximal pulses, and latest in the pulse most distant from the heart.

I proceed now to elucidate the significant inquiry, Are the foregoing data reliable? With certain reservations and restrictions, I claim that they are. The time-differences shown on the engravings are not the certain expressions of the exact asynchronisms between the pulsations represented, but they are, indeed, extremely fine approximations thereto. The basal point of ascent from which the measurements were made is notably the most stable of any in a tracing. In the mechanism the lever has descended and become poised for the moment before it mounts up again on the current wave. Thus the basal point is wholly removed from the disturbing influence of inertia of the lever. The other chief obstacle to a good tracing-namely, undue friction of the writing-point against the slide-is so palpable when present, and so easily obviated, that this cause of displacement of the basal point need never be operative. Indeed, so little liable is this point to fallacious deviation, that its indications may be relied upon even in tracings not altogether faultless in form. In the tracings given, the basal point of each and every pulsation is unquestionably in its true position. The instrument, properly charged and adjusted, and used with skill and care, is simply incapable of erroneous registry of this point. Whence come, then, the errors admitted as liable in the representations of the time-differences? The automatic registry is perfect, but the estimation thereof is imperfect.

The measurements are subject to fallacy from two sources: one, the difficulty of exactly locating the basal point, more or less obscured as it is in a curve; the other, an unnoted change in the speed of the carriage taking place within the limits of the time-points from which the measurements are made. The first source, it would seem, is unavoidable, and must be continuous; the second may be obviated when we attain to a mechanism that will move the slide with a certain unvarying speed. As no error attaches to the time