Popular Science Monthly/Volume 6/February 1875/Marey's New Results in Animal Movements
By Prof. ALFRED M. MAYER,
OF THE STEVENS INSTITUTE OF TECHNOLOGY.
THE publication of Marey's "Animal Mechanism" in the "International Scientific Series" has put the general reader in possession of one of the most interesting works ever published on experimental physiology. The simplicity and precision of the author's experimental methods, his conscientiousness in being sure of one step before he takes the next, and the skill displayed in interpreting and combining his experimental results—all these admirable characteristics have rendered his book instructive and entertaining to those who merely follow from afar the progress of science, while, at the same time, he has furnished a model of precise research and clear exposition to the professed scientist.
Marey arrives at his facts directly, not inferentially, and this is the charm of his book. The mind of the reader does not rest on the fallible judgment or mere opinion of the author, but is brought face to face with the very records made by the phenomena themselves.
In studying the progress of science, one cannot help remarking certain periods of sudden acceleration in the progress of discovery. These periods of unusual activity are not always, but certainly are very often, due to the invention of some precise and readily-applicable instrument, which gives, as it were, a new scientific sense, and brings into the range of our intellectual vision phenomena and numbers whose existence were barely suspected, until revealed by the aid of some comparatively simple contrivance. Such epochs of sudden progress followed the inventions of the telescope, the spectroscope, the ophthalmoscope, the galvanometer, and the tuning-fork chronoscope. For the latter instrument, men of science are indebted to Dr. Thomas Young, that wonderful man, who touched no department of knowledge that he did not adorn. The application of the sinuous traces of a vibrating tuning-fork on a rolling cylinder, to divide a second of time into as many parts as the number of times the fork swings to and fro in a second, was described by Young in 1807, and published in his "Lectures on Natural Philosophy and the Mechanical Arts," vol. i., p. 191. Like Young's discoveries of the theory of colors, and of the undulatory theory of light, this beautiful invention laid fallow for many years, until reinvented in 1840 by Duhamel, and subsequently brought into general use in physics and physiology. It is now the essential element of the chronoscopes, or, more accurately speaking, of the chronometers, used to measure the velocities of projectiles, and to solve such problems as the rates of progress of the nervous influence and of the muscular wave.
To make any tuning-fork a chronoscope, it is only necessary to know the number of vibrations which the fork makes in a second at a known temperature. This number is determined to the last degree of precision by the following method, devised by the author of this article: A break-circuit clock is placed in the primary or battery circuit of an induction-coil; while one terminal wire of the secondary coil is connected with a metallic cylinder covered with smoked paper, the other terminal wire is led to the tuning-fork, which traces its vibrations, by means of a delicate metallic point, on the paper-covered cylinder. At each second the break-circuit clock sends a spark from the point attached to the vibrating fork, through the smoked paper to the metallic cylinder. It is evident that, on counting the number of sinuosities made by the vibrating fork between two contiguous spark-holes, we have the number of vibrations per second made by the fork. After the above determination has been made, the tuning-fork becomes the most accurate and uniformly rated chronometer yet devised by men of science. But the time-recording tuning-fork is only one part of the apparatus required in the study of physiological motions. We must also be in possession of some contrivance which can be readily applied to an organ, the durations and varied velocities of whose motions we would study, and this contrivance must make a graphic record of these motions alongside of the time-record drawn by the tuning-fork. To Marey we are indebted for many effective recording instruments, but the apparatus which he has most extensively used, and which is admirably adapted to the study of the motions in some of the vital functions and in locomotion, consists of a small drum of shallow depth, one of whose ends is covered with an elastic membrane. The interior of this drum is connected with the interior of a similar drum by a rubber tube of very small internal diameter. The membrane of one of these drums presses against the surface whose motions we would study. A delicate lever rests on the membrane of the other drum, and the end of this lever is armed with a delicate point which touches a revolving cylinder covered with smoked paper. On this cylinder the tuning-fork also simultaneously traces its time-record. Now, as both drums, and the tube which connects them, form an air-tight space, it follows that any depression, given to the membrane which touches the moving surface, will compress the air in this drum, in the connecting tube, and in the drum which carries the delicate lever. The membrane of the latter drum will move outward and cause the pointed lever to move and make its trace on the revolving cylinder. Of course an elevation of the membrane in the first drum will cause a depression in the membrane of the second drum, accompanied by a movement of the lever opposite to that described above. Thus the lever records accurately every movement of the membrane of the distant drum, and the intervening flexible tube allows one to attach the drum to the limb of a moving man, or quadruped, to the wing of a flying-bird, or to the chest, to obtain the traces of the motions of the lungs and of the heart.
In 1863 Marey first began to apply the graphic method to biological studies, in his "Physiologie médicale de la Circulation du Sang." In 1868 he published his "Du Mouvement dans les Fonctions de la Vie." In the preface of this truly valuable work he says: "By the use of the graphic method the illusions of the observer, the tediousness of descriptions, and the confusion of facts, disappear. These two ruling qualities, clearness and conciseness, become every day more desirable, by reason of the enormous increase in biological publications." In his last work, "Animal Mechanism," be has illustrated this remark; for surely no "tediousness" will be experienced in the perusal of this work, in which we are taught, with such "clearness and conciseness," how men and quadrupeds walk and run, and how birds and insects fly.
The desire to see Marey's work on Animal Mechanism fully appreciated by the public has induced us to put the reader in possession of his quite recent discoveries, which could not be incorporated in the book published in the "International Series." We refer to two of his most important researches, one on "Human Locomotion," taken from the Comptes Rendus, of July 13, 1874; the other, "On the Resistance of the Air under the Wing of a Bird during its Flight," we take from the Journal de Physique of July, 1874.
I. New Experiments on Human Locomotion.—The brothers Weber believed that in human locomotion the oscillation of the leg in walking was due alone to the action of gravity; this is to say, that the foot, while off the ground, has the motion of a pendulum. For a long time this opinion has held its place in physiology, but it has been opposed, in recent years, by arguments of various kinds. First, by M. Duchenne, of Boulogne, who showed that the leg is not entirely passive during its displacement, for certain muscular paralyses prevent its oscillation; M. Giraud-Teulon has attacked the theory of Weber, by showing the mathematical errors on which it is founded; and, finally, M. Carlet has determined, experimentally, the active function of certain muscles in the displacement of the leg during walking.
If gravity does not alone act in producing the oscillation of the leg, it becomes impossible to foresee what motion will result from its combination with muscular action. I have appealed to the graphic method for the experimental answer to this question.
When a body moves in a straight line, with variable velocities at each instant, it is easy to obtain the graphic representation of its motion, provided the space moved over is not too extensive. It suffices to join the body, by means of a rigid connection, with a writing-lever, which touches a revolving cylinder, covered with smoked paper. The tracer on the writing-lever, moved with variable velocities, and in a direction parallel to the axis of the cylinder, will draw sinuous curves, whose parts will indicate by their inclination the velocities of the motions which produced them.
But the motions in walking are too extended to be traced on the revolving cylinder in their real magnitudes; in order to reduce them, while at the same time I preserved their characteristics unaltered, I had recourse to a train of wheel-work. In this apparatus, each wheel working into another, whose teeth are ten times more numerous than those of the former, it follows that the motion communicated to the first axis will be reproduced by the second with a reduction of 1; the third axis will reproduce the motion reduced to 1; and the fourth axis will reduce it to 1 etc.
If we attach to the foot of a walker a thread, which is wrapped around the wheel on the first axle of the wheel-work, and if to the third axle we connect the writing-lever, we can obtain traces on the revolving cylinder which will have only 1th of the extent of the paths gone over by the foot of the walker.
Fig. 1 shows five traces obtained from the foot when walking with various velocities. A has been produced by the slowest walk; "B" is the ordinary gait; while C is the most rapid: the remaining traces have been obtained from gaits less rapid than that of C.
(The figure represents the smoked paper, unrolled from the revolving cylinder after the experiment. The paper revolved with the cylinder in the direction from O to Y. Therefore, the axis of the cylinder was parallel to OX, and the tracer on the writing-lever moved parallel to OX. It follows that, if the foot had remained stationary while the cylinder revolved, the tracer would have described a straight line parallel to OY. CH is the trace of the vibrating tuning-fork; each bend of its sinuous line is equal to 1th of a second of time. This chronographic trace gives us the means of estimating accurately the duration of each step and the velocity of the foot at each instant while it is swinging in the air. The spaces gone over by the tracer, as before stated, are 1th of the real distances traversed by the foot; that is, one centimetre on the paper equals one metre gone over by the foot.) Hence, every thing relative to the transport of the foot in walking is expressed in this figure.
1. Velocity of the Gait.—This is expressed by the general inclination of the curve, or by the relation existing between the lengths parallel to OX and to OY. As the different traces contained in the figure correspond to the same distance (three metres and a half; marked on the left-hand vertical line of the figure) gone over in variable times, it follows that the relation of these times to this distance will give the velocities of the different gaits. If we count on the chronograph-trace the time included between the beginning of each curve, and its termination in the line A, B, C, we shall have the measure of this time. (For example, the time occupied in going over 31 metres with the gait B is given by counting the bends of the tuning-fork trace contained between 2 and the perpendicular line let fall from B on to the chronograph-trace.) Thus, for the slow walk from 1 to A, we count thirteen seconds; the more rapid walk from 2 to B occupied six and a half seconds; while with the rapid gait the distance from 5 to C was traversed in two seconds.
2. Alternate Periods of Rest and of Motion of the Foot.—It is evident that, whenever the traces show an horizontal line (that is, a line parallel to OY), those portions of the traces correspond to the traces made while the foot touched the ground and was immovable, since the spaces then gone over are nothing. The traces show that the duration of the periods of repose decreases as the gait is accelerated. The time during which the foot is in motion is shown by the oblique lines whose projection on the trace of the chronograph increases, relatively to the periods of repose, as the gait is more rapid. This proves that the length of the step increases with the velocity of the gait.
We can also, from the traces, estimate with precision the relation of the velocity of gait to the length of step, the relative variations of the duration of the periods of repose and of motion of the foot, etc.; but we will not here dwell on these details; the essential point under consideration is the following:
3. The Nature of the Movement of Translation of the Foot.—The trace of this movement is shown in a line which is nearly straight in all of its parts; the motion of the foot is therefore uniform during nearly the whole of its translation; the inflections of the line at its beginning and at its end show that, in rapid gaits especially, the motion of the foot begins and ends in short periods of variable velocities. From the above we are now able to judge how far the oscillation of the leg is analogous to that of a pendulum.
But we must not exclusively attribute to the action of the muscles of the leg this uniformity in the translation of the foot. In fact, we know that, during this translation, two distinct causes are working:
1. The angular movement which the leg has around the pelvis.
2. The horizontal translation of the pelvis itself; that is to say, of the point of suspension of the leg while the latter oscillates.
We may conceive that, by the combination of these two movements, the motion of the leg may tend to become uniform; this will happen if the minima of the velocities due to the first-named species of motion correspond with the maxima of the second kind of motion. It therefore becomes very interesting to determine what is really the motion of the trunk of the body during different gaits.
The apparatus already described has also served for the solution of this problem.
A cord attached to the waist transmitted to the registering apparatus the motion of translation of the trunk. By experimenting successively on various gaits, we obtained the following figure, whose analysis gives some interesting results:
The undulations are far greater when the walking is very slow than when it is more rapid. Thus, the motion of the body becomes more uniform by reason of a higher velocity. This is the reverse of what happens with the vertical oscillations of the body, which increase with the velocity of progression and with an increase in the length of the steps.
The number of alternations of motion is double that produced by the movement of a single foot, as shown in Fig. 1. This is readily understood when it is remembered that the two feet, repeating the same acts, give alternately to the body a new impulsion.
To make clear this action we have traced, parallel to the line 2 of Fig. 2, the curves P, produced by the motions of the right and of the left foot. These curves, of which one is dotted, and the other full, are at once recognized as similar to those of the line 2 B, of Fig. 1. In fact, on observing the superposition of the different parts of these curves with the curve of translation, we see that the body receives an increase of velocity about the middle of the period when either foot is on the ground. This fact is in harmony with experiments which I have already published.
I will add, in concluding, that one of the most important results obtained by these researches is, the idea which they give of the variability of the movement of translation of the body during walking and running.
In another publication I shall show the applications which can be deduced from these studies to the best utilization of the work of animals.
II. On the Resistance of the Air to the Wings of a Bird during its Flight.—I have presented to the Academy of Sciences a memoir which proves that the wings of a bird, during their downward movements, meet with more resistance from the air when the bird has an horizontal motion of progression than when the bird, depressing his wings with the same velocity, has no horizontal motion of translation.
The explanation of this phenomenon appears to me to be as follows: a wing, or any surface whatever, which moves against the air, meets, at the beginning of its motion, a considerable resistance, on account of the inertia of the air, which resists every displacement; but, little by little, the air yields, and the velocity of its motion gradually increases, until it may equal that of the moving surface which displaces it; this phase of motion having been reached, the resistance diminishes. Finally, when the moving body stops, the moving air tends to continue its journey, and it thereby produces before the moving surface a true aspiration, or negative pressure. But a bird, which moves horizontally during the depressions of its wings, acts, during successive instants of that depression, on a series of columns of air over which it passes. From each column it meets with that maximum resistance which the inertia of the air presents at the first instants of the action of the wing. Finally, when the wing has reached the lowest point of its depression, it is not over the mass of air which it has just set in motion, because the motion of translation of the bird continually brings it into regions where the air is at rest. All of these conditions are evidently favorable to flight, since they increase the resistance of the air, which alone furnishes to the bird its support, and the reaction to its moving wing.
To prove the exactness of this theory, I have made certain experiments in which a uniform quantity of work was applied to produce the elevation and depression of the wings of an artificial bird. In some experiments the motions of the wings took place while the machine was stationary; they had a great amplitude of motion. In other experiments we gave the artificial bird a motion of translation, and then we observed that the amplitude of the flaps of the wing diminished considerably, which fact showed an increase in the resistance of the air.
MM. Planavergne claim the priority of the theoretic idea which I have enunciated, and show, in fact, that they had published, some years since, a memoir, in which this theory is explicitly stated. However, these authors have furnished no experimental demonstrations of their views; consequently, it has appeared to me that it would be interesting to continue the researches which I had begun, and to determine, as accurately as possible, on one hand, the phases and variable conditions of the resistance of the air to a moving body which displaces it with a uniform motion; on the other hand, to find the increase of the resistance of the air under the wings of an apparatus which is transported with determinate velocities.
First Series of Experiments.—Determination, of the variable and constant resistances opposed by the air to a moving body which displaces the air with a uniform motion.
In a solid framework, which glides easily on an horizontal plane, I placed a light screen, with its plane vertical and perpendicular to the direction of its motion. This screen turns around an horizontal axis; and an arm attached to it is charged with an additional weight until perfect equilibrium is established between the arm and the screen itself. This having been done, we have no fear of the inertia of one or another part of the system causing the screen to revolve around its axis at the beginning of its motion of translation. If such a movement of rotation does take place, we must attribute it to the resistance offered by the air.
Behind the screen is placed a little manometric apparatus, which communicates, by means of a tube, with a drum, having a lever resting on its membrane.
The apparatus having been thus arranged, we give to it a uniform motion of translation which lasts half or a quarter of a second, and we obtain on a revolving cylinder the above trace of the point of the writing-lever attached to the membrane of the recording drum.
When the screen is at rest, the apparatus traces an horizontal line x x, which corresponds to the zero of pressure on the dynamometer. At the instant of the beginning of the translation the apparatus shows an energetic pressure (a) on the dynamometer; this is the initial variable resistance caused by the inertia of the air against which the screen pushed. Very soon afterward the curve falls, announcing that the resistance of the air has diminished, although the motion of the disk had remained uniform. This is owing to the fact that the air had then partly acquired the motion of the screen. The pressure falls thus to the level b, which marks the constant resistance of the air during the whole remaining period of the translation.
Finally, when the apparatus is suddenly stopped, we see that the trace of the recording-lever is suddenly depressed at the point c; this is due to the variable terminal condition: it consists in the carrying of the screen forward by the column of air already set in motion by it. This negative resistance gradually ceases, and the tracer returns to zero.We were not able to determine with this rough apparatus the absolute value of the resistance of the air corresponding to different instants of uniform translation, but we can readily see that there exist two variable states, of which one precedes and the other follows the constant resistance of the air. The studies of physicists have heretofore been directed only to the determination of the constant resistance corresponding to different velocities.
Second Series of Experiments.—Increase of the resistance of the air to the downward movement of the wing of a bird, caused by the horizontal translation of the bird.
In making the above determination, I have roughly imitated the construction of the bird, by reducing each of the wings to a thin and rigid plane of a 1 metre in length, and 1 a metre in breadth. These two wings are simultaneously depressed by the action of a spring.
A constant amount of work is thus employed for each blow of the wings. The translation of the artificial bird takes place in gliding along an horizontally-stretched iron wire. Two large wheels, one of them furnished with a crank-handle, move an endless cord parallel to the iron wire. The apparatus with wings is attached to this cord, and can thus be moved horizontally with greater or less velocities.
It is now necessary to determine with precision the velocity of translation and the duration of the depression of the wings. The graphic method gives readily these two measurements:
1. Measurement of the Velocities of Translation of the Apparatus.—This velocity is evidently the velocity of a point on the endless cord, to which the winged apparatus is attached. This cord passes around a little pulley, whose revolutions are counted and registered on a revolving cylinder by means of a lever which is worked pretty much as the lever in the registering apparatus of Morse's telegraph.
The little pulley which serves to measure the velocities is exactly 4 of a metre in circumference; one-half of its circumference is covered with a metallic band, the other half is formed of insulating material. Metallic springs press against the periphery of the pulley, so that, while they touch the metallic band, a current from a battery depresses the lever which traces on the revolving cylinder. Hence the lever is depressed, while 2 of a metre of the cord pass, and it is elevated during the next 2 of a metre of passage of the cord. Thus are registered, in an indented line, the velocities of translation of the artificial bird. Evidently the greater the velocity of the bird the greater will be the number of indentations inscribed in a second on the uniformly-revolving cylinder.
2. Measurement of the Duration of the Depression of the Wings.—A second electrical recorder, similar to that which registers the turns of the pulley, serves to determine the duration of the depression of the wings. For this purpose it is necessary that, at the beginning of the depression, the current of a battery should be broken, and this action is registered on the revolving cylinder by an indentation in the trace of the writing-lever; also, at the end of the depression of the wings, the current must be closed again, and this instant is likewise registered on the cylinder.
We have thus obtained simultaneously the traces of the velocities of translation of the artificial bird, and the durations of the depressions of its wings, and we have obtained a series of determinations of which the preceding figure (4) furnishes some examples:
Experiment No. 1.—The upward indentation in the line a shows the duration of the depression of the wings. Taking that length on the scale of time, we see that the downward movement of the wing lasted less than 1 of a second. In that experiment there was no translation of the bird. The line b does not show any indentation.
Experiment No. 2.—The duration of the depression of the wings (line a) is already greater; it exceeds one-half of a second. The translation was then nearly three metres per second. We find this by taking in the dividers the length on the line b of the 31 double indentations of the tracer, which show that 31 times 4 of a metre, or 1.4 metre, have been traversed by the artificial bird. We carry this length to the scale of time, and we find that it is contained about twice in a second. We thus see at once that the duration of the downward motion of the wing increases with the velocity of translation of the artificial bird.
Experiments Nos. 3-6.—In the remaining experiments, proceeding as we have already done, we find that the duration of the depression of the wing increases with the velocity of translation, and that with a velocity of 51 metres the downward movement of the wing lasts about one second. I have not been able to find the accurate relation between the velocity of translation and the duration of the downward motion of the wing. Experiments made in precisely the same conditions sometimes present slight differences, which are due to the fact that the slightest oscillation of the iron wire, which serves as a support and guide for the artificial bird, slightly changes the durations of the phenomena. From the first series of experiments, it would appear that the duration of the depression of the wing increases in proportion to the velocity of its translation, at least within the limits of the velocities with which I have experimented.