✓ •. tJ. •• • r ■' X \ i i. k- \ ■> * I A « MOVEMENT TKANSLATOK’S NOTE Instantaneous photography, especially that branch of it knoAMi as Chronophotography, has already won for itself a recognized position among the methods of scientific research, and in the near future it is probable that it will be even more generally appre- ciated. Marey and Muybridge must undoubtedly be regarded as the two pioneers of the method ; the works of the latter, written in English and published in America, are within the reach of all who can read the English language ; on the other hand, the works of Marey are for the most part inaccessible to those who are unfamiliar with French. It is for this reason that I applied for and obtained permission to translate this work. “ Le Mouvement ” is one of the most recent and important publications of this eminent physicist and physiologist, and it is, I believe, the most compre- hensive summary hitherto published, of the results and possibilities of instantaneous photography ; every page has its interest not only for the sj)ecialist, but also for the general reader ; and further, the book is replete with suggestiveness of new lines of research. Chronophotography is a new subject, and many of VI TRANSLATOK’S NOTE its tecLmical terms are kno^Mi even to English scientific men only in their French form. For these I have frequently used periphrases, remembering that many of my readers may not be experts. I must acknow- ledge gratefully the continued assistance of my sister, Mrs. Chalmers Mitchell, not only in making the actual translation, but in revising it for the press. 14, Cromwell Place, S.W., August, 1895. EKIC PEITCHAED. PREFACE The graphic method, with its various developments, has been of immense service to almost every brancii of science, and consequently many improvements have of late been effected. Laborious statistics have been replaced by diagrams in Avhich the variations of a curve express in a most striking manner the several phases of a patiently observed phenomenon, and, further, a recording apparatus Avhich aa orks automati- cally can trace the curve of a physical or physiological eA^ent, Avhich by reason of its sloAvness, its feeble- ness, or its rapidity, is othei’Avise inaccessible to observation. Sometimes, however, a curve which represents the phases of a phenomenon is found so misleading that another and more serviceable method, namely, that of chronophotography, has been invented. The development of these new methods of analyzing movement could never have jAroceeded Avithin the confined space of a physiological laboratory. For instance, in comparing- the locomotion of various species of animals, it is essential that each should Ije studied under natural conditions : fish in fresh water or marine aquariums ; insects in the open air ; and ]nan, quadrupeds, and birds in AA'ide spaces in Avhich their movements are unfettered. Vlll PEEFACE The Physiological Station, endowed by the State and the City of Paris, has afforded in this respect unique opportunities, and there, with new appliances, the following investigations have been for the most part carried out. We shall see by a variety of instances to Avhat ex- tent the older methods are applicable for the analysis of certain phenomena, and what progress has been achieved by chronophotography. Each chapter is nothing more than an outline, for any attempt to fill in the details of any section would monopolize the time and attention of a trained specialist. In a few instances such an attempt has been made, for geometricians, hydraulic engineers, naval and military men as well as artists have all had recourse to this method, and at last naturalists have interested them- selves in the matter. It is more especially to this latter class that we dedicate our work, since it appeals to their particular ambition, namely, that of discover- ing among the phenomena of life something that has hitherto escaped the most attentive observation. CONTENTS CHAPTER I / TIME Its Graphic Record ; Time-measurement by means op Photography PAGE Summary. — Graphic record of time — Chronography — Rudiments of the method — Transmission of movement to the recording needle which registers the duration — Chronographic record of a man’s foot in walking, during the phases of rest and motion — The same of the four feet of a horse in its various paces — Record of the fingering of a pianist — Applications of photography to the registration of time — Measurement of the exposure allowed by a photographic shutter — Measure- ment of the time intervals between successive exposures . 1 CHAPTER II SPACE Its Measurement and Representation by Photography Summary. — Tendency to replace outline drawings, plans, and diagrams in relief by photography — Photography traces the various positions in space occupied by a moving body — Photographic trajectory of the movements of a point in space ; its stereoscopic trajectory — Movements of a straight line in space — Solid figures formed thereby: cylinders, hyperboloids, cones, etc. — Movements of a curve- in space; photograifiiy of the figures which it forms : spheres, ellip- soids, etc. — Stereoscojiic pictures of figures of three dimen- sions— Figures formed by the movement of solid bodies; effects of light and shade 18 X CONTENTS CHAPTER HE MOVEMENT Its Measurement, Graphic Eepresentation, and Analysis by MEANS OF CURONOPHOTOGRAPHY TACE Summary. — The understanding of a movement implies a double knowledge, namely, that of space as well as that of time — Graphic representation of a movement — Chart of a train travelling along a line — The curve of a prolonged movement should be recorded in sections — How a moving body can. record its own movement — Proportional enlargement and reduction of the recorded movement — Odography — Photo- graphic record of movement — Photography of the movement of Lippmann’s electrometer — Determination by means of chronophotography of the movements executed by a falling body — Construction of the curves of movement from chrono- irhotographic images — Time-curve of the distance traversed — Curve of velocity — Curve of acceleration . . . .33 CHAPTER IV CHRONOPHOTOGRAPHY ON FIXED PLATES Summary. — Object of chronophotography; principles of the method ; measurement of time and space — Influence of the extent of surface covered by the object which is to be photo- graphed ; influence of the rate of movement — Geometrical chronophotography — Stereoscopic chronophotography — Method of multiplying the number of images without pro- ducing confusion — Alternating images — Separation of the images on the photographic plate ; separation by moving the apparatus — Separation by employing a revolving mirror . ol CHAPTER V DESCRIPTION OF THE APPARATUS Summary. — Construction of the apparatus— Slide, object-glass, circular diaphragms — Erection of the dark background at the physiological station — Dark background for photo- graphing objects in water — Photography of light objects in darkness or in a red light — Colour of objects, and way of illuminating them — Disposition and preparation of the dark field — C.'hoice of the object-glass — Focussing — How to take tlic photographs (57 CONTENTS XI CHAPTER YI APPLICATIONS OF CHRONOPHOTOGRAPIIY TO MECHANICS I'ACE Summary. — Bodies falling in air — Ballistic experiments — The resistance of the air to surfaces variously inclined — ^Applica- tions of chronophotography to hydrodynamics — Fluid veins ; changes in shape of fluid waves; intrinsic movements of fluid waves — Currents and eddies — Influence of the shaj^e of bodies j^laced in currents — Oscillations and vibrations — Rolling of ships — ^Vibrations of metal bridges ... 84 CHAPTER VII CHRONOPHOTOGRAPHY ON MOVING PLATES Principles and History op the Method Summary. — Janssen’s astronomical revolver — Muybridge’s ex- periments : luminous background — Photographic cameras ar- ranged in series — Control of the instantaneous shutter by electrical means — Photographic gun — Internal structure of the instrument— Method of changing the photographic plates — Principles of chronophotography on moving plates — Em- ployment of chronophotography — Necessity for arresting the progress of the film at the moment of exposure — Moment to choose for taking the jihotograph — Form and dimensions of the photographs — Regulation of the number and dimen- sions of the photographs — Reproduction, enlargement, and reduction of chronophotographs 103 CHAPTER VIII HUMAN MOVEMENTS From the Point op View of Kinetics •SusiMARY. — Some movements in man ; the study of them by the graphic method — Speed of difterent paces in man ; relation- ship between the frequency and length of stride — Duration of the rise and fall of the foot in walking and running — Path described by any particular part of the body during different paces; mechanical means of recording it — The study of movements in man by means of chronoirhotography on fixed plates ; long-jumping; high-jumping — Skilled move- ments, fencing, etc. — Jumping from a height — The swing of the leg in walking 12G Xll CONTENTS CHAPTER IX CERTAIN MOVEMENTS IN MAN From the Point of View of DrNAJiics PAGE Summary. — Object of dynamics — Measurement of the forces which play a part in human locomotion — Traction dynamo- graph — Dynamograph for expressing the amount of pressure exercised by the feet on the ground — Combination of the dynamograph with a method of recording movements — The laws of ballistics as applied to the mechanism of jumping — Combined emidoyment of dynamography and chronophoto- graphy — Mechanical work done in human locomotion ; work in the vertical direction ; work in the horizontal direction ; work done in maintaining the movement of the lower limbs during their period of suspension — Kelative amount of work done during different kinds of paces — Practical applications 146 CHAPTER X LOCOMOTION IN MAN From an Artistic Point of View Summary. — Influence of Photography on Art — Different cha- racteristics of ancient and modern works of art — Photo- graphy catches the real attitude — Importance of representing the correct outline of muscles during different actions — Photographs taken from different points of view — Photo- graphs taken from above — Study of the most characteristic altitudes in a movement — Importance of having a series of photographs from which to choose the most expressive attitude — Analysis of facial expression — Choice of the best method for procuring artistic results 166 CHAPTER XI LOCOMOTION OF QUADRUPEDS Summary. — Chronography shows how the feet rise and fall in the different paces of a horse — Transition or passage from one pace to another— Eepresentatiou of the attitudes in all paces of a horse, as shown by chronography and hoof-marks CONTENTS Xlll PAGE — Comparison between diagrams obtained by these methods and those obtained by instantaneous photography — Chrono- photography applied to the representation of a horse in motion — Artistic representation of the horse among the ancients — Locomotion of the horse from the physiological point of view — Geometrical chronophotography of the move- ments taken as a whole — Individual movements of the foot and fetlock 186 CHAPTER XII Locomotion in water SuMJiABY. — Dilferent types of locomotion in water — Method of photographing aquatic animals — Jelly fish : Comatulse — Locomotion by means of undulatory and lateral movements ; the eel — best arrangement for studying its movements — Locomotion by means of undulatory and vertical movements ; the skate — special arrangement for studying its vertical un- dulations from different points of view — Undulatory move- ments of the skate as seen from the side : ditto as seen from in front — The sea-horse : the fresh-water tortoise — Slow movements of star-fish — Locomotion of small marine animals .211 CHAPTER XIII AERIAL LOCOMOTION The Flight of Birds Summary. — Borelli’s theory on the mechanism of the flight of birds— Chronography used for determining the frequency of the movements of the wing, and the relative dura- tion of the rise and fall — Myography — Method of record- ing the phases of contraction and relaxation of the wing muscles — Kecord of the trajectory of a bird’s humerus, and the variations in inclination of the surface of the wing — Photographic trajectory of the tip of the wing — Chrono- photography as showing the successive attitudes of the bird during the different phases of movement of the wings — Photographs of birds taken from difterent aspects — Simul- taneous chronophotography 226 XIV CONTENTS CHAPTEK XIV AERIAL LOCOMOTION The Flight of Insects PAGE Summary. — Frequency of the movements of insects’ wings as estimated by the sound produced in flying — Mechanical re- gistration of the movements of the wings ; frequency among diiFerent species — Synchronous movements of the wings — Changes in inclination of the wing surface — Trajectory of an insect’s wing — Its interpretation — Experiments to de- monstrate the direction of movement of the wing, and its variations in plane — The artiflcial insect — Theory of the flight of insects — Photography as applied to the study of insect flight — Lendenfeld’s experiments — Trajectory of the wing as the insect advances — Photography on moving films — Arrangement of the experiment — Different types of flying insects : Bees, flies, tipulm — Substantiation of the mechanical theory of flight 239 CHAPTER XV COMPARATIVE LOCOMOTION Summary. — Comparative locomotion among terrestrial mammals : the man, the horse, the elephant — Comparative locomotion among different kinds of birds — Classification of different types of locomotion — Comparative locomotion of tortoises and lizards; frogs, toads, and tadpoles; snakes, eels, and fish ; insects and siuders 258 CHAPTER XVI APPLICATIONS OF CHRONOPHOTOGRAPIIY TO EXPERIMENTAL PHYSIOLOGY SUJIMARY. — Numerous applications of chronophotography ; it supplements the information derived from the graphic method — Study of the movements of the heart by means of the graphic method — Photography of the successive phases of cardiac action in a tortoise under conditions of artificial circulation — Variations in shape and capacity of the auricles and ventricles during a cardiac cycle — ^Icchanism of car- diac pulsation studied by means of chronophotograifliy — Comparative advantages of mechanical and chronophoto- graphic registration — Determination of the centres of move- ments in joints 275 CONTENTS XV CHAPTER XVII lillCROSCOPIC CHRONOPHOTOGRAPHY PAGE ScMJiARY. — ^Various movements observable within the field of the microscope — Applications of chronophotograjrhy to the study of these movements — Difficulties of the subject — Special arrangement of the apparatus for chronophotography on fixed plates and on moving films — Retraction of the stalk in vorticella — Movement of the blood in capillary vessels — Movements of the zoospores in the cells of conferva — The use of the solar microscope in chronophotography — The easy application of this method 291 CHAPTER XYIII SYNTHETIC RECONSTRUCTION OF THE ELEMENTS OF AN ANALYZED MOVEMENT Summary. — Plateau’s method; his phenakistoscope — The zoo- trope; its applications to the study of horses’ paces and their relations to one another — The use of instantaneoirs photography in connection with the zootrope — Muybridge, Anschutz — Scientific applications of Plateau’s method — Points of a good apparatus — Improvements made by diffe- rent authors — Attempts at constructing a chronophoto- graphic projector 301 Index . 319 MOVEMENT CHAPTER I TIME Its Graphic Record ; Time-measurement by means OF Photography StsiMARY. — Graphic record of time — Ohrouograpliy — Rudiments of the method — Transmission of movement to the recording needle which registers the duration — Chronographic record of a man’s foot in walking, during the phases of rest and motion — The same of the four feet of a horse in its various paces — Record of the lingering of a pianist — Applications of photography to the regis- tration of time — Measurement of the exposure allowed by a photo- graphic shutter — Measurement of the time intervals between successive exposures. Graphic Record of Time. — Time, like other magni- |t tildes, can be represented in a graphic form by straight ‘ lines of various lengths. In this way the respective duration of several events can be ganged by the ■ various lengths of parallel straight lines placed side by \' side. The order of commencement of these phenomena can be expressed by the relative positions of the begin- nings of the straight lines. With regard to the exact [ order and duration of the events, they can be indicated [• by means of a scale, subdivided into divisions which B 2 moVemi:nt represent years, clays, or fractions of seconds. A diagram will elucidate this method of time-measure- 0 1 1 2|3|4|5|6|7|8|»[iq|ii Fig. 1.— Scale of hours. Time measurement. ment. Suppose we require to express the order and sequence of three events, A, B, C, which occur during a period of 11 hours. Their respective time relations are expressed most clearly by the three lines A, B, C, and by the scale of hours which accomjDanies them. It may be seen by a glance at the diagram that the event A commences at 2 o’clock and finishes at 10 o’clock (its total duration is, therefore, 8 hours) ; that B, commencing at 6 and ending at 11 o’clock, has lasted 5 hours ; and that C, com- mencing at 5 o’clock and ending at a ^ past 8, has only extended over a period of 3^ hours. The sequence of these events is accurately expressed by the divisions on the scale, which correspond to the beginnings of the different lines. Language is as slow and obscure a method of ex- pressing the duration and sequence of events as the graphic method is lucid and easy to understand. As a matter of fact, it is the only natural mode of expressing such events ; and, further, the information which this kind of record conveys is that which appeals to the eyes, usually the most reliable form in which it can be expressed. A celebrated English political economist, W. Playfair, has drawn up a table of the chronological order of the reigns of the various English sovereigns. From it one can see at a glance the age at which each succeeded to the throne, as well as the duration of the •? i TIME 3 reigu. By the side of this chronological table, another series of lines shoAvs the succession of the various ministers, and a third shoAvs the periods of Avar and peace occurring during the respective epochs. Such a table expresses in the most lucid manner the sequence of events. That such a mode of graphic record has been neglected in France cannot be too deeply deplored, xi. someAvhat similar method Avas utilized in France during the last century to express the duration and sequence of certain acts. Vincent and Goiffon * have represented by a chronological record the phases of rest and motion of horses’ feet, as observed in their different paces. This mode of ex- pression is surely preferable to that of language, Avheii it is a question of conveying to the mind the meaning of complicated rhythms. Chronography. — The diagrams of Avhich Ave have just been speaking are, hoAvever, only one mode of representation, clearer, it is true, than others, but reliable only in so far as the data on Avhich they depend are trustAvorthy. In experiments, for instance, Avhich deal Avith time measurements, it is of immense importance that the graphic record should be auto- matically registered, in fact, that the phenomenon should give on paper its OAvn record of duration, and of the moment of pi'oduction. This method, in the cases in Avhich it is applicable, is almost perfect. In other instances photography comes to the rescue, and affords accurate measurements of time events Avhich elude the naked eye. The process Avhich thus serves to register the duration and sequence of events con- stitutes a method called “ chronogra2)hy.” We are about to explain this method, proceeding * Memoire artificielle dcs principcs relatifs ii la lidiile reprcBentation des animaux tant en peiuture qu’en sculpture, par feu Goiffon et M. Vincent. In-fol. 1770. 4 MOVEMENT from the more simple to the more complicated cases. We shall first show how the method can be applied to register the successive phases of rest and motion, as executed by a man’s foot in walking, and then the movements of the four feet of a horse as they occur in its various paces, and, lastly, the automatic method of registering the fingering of a pianist on the keys of his instrument. This last problem must be regarded as one of the most difficult to solve. Rudiments of Chronography. — Let us suppose that a strip of paper is made to travel by clockwork at a uniform rate, and that a pen fixed above the J3aper marks, as it alternately rises and falls, the various periods and intervals. As the pen comes in contact with the paper it leaves its record in the form of “ dashes,” of various lengths, and at various intervals ; and by this means the sequence and duration are registered. If the “ dashes ” are equidistant, it means that the periods of contact follow one another at equal intervals of time. Finally, if it is necessary to obtain an accurate measurement of the duration of contact, and of the intervals between, the exact rate at which the strip of paper is being carried must be known. A control record of the rate may be obtained by allowing the oscillation of a pendulum to mark the seconds on the paper, or, if the movement be very rapid, by allowing the vibrations of a tuning-fork, of which the rate of vibration is kno^VQ, to trace themselves upon the paper.* Transmission of the Movement to the Recording Needle which registers the Duration. — It hardly ever happens that the phenomena, of which one wishes to record the sequence and duration, are capable of acting directly on the recording needle. More often such * For the general principles of chronography, its technique and applications, see “The Graphic Method,” pages 133, 142, 456. TIME 5 movements liave to be observed at a distance and transmitted to the corresponding recording needle. For this purpose transmission by air is employed and found preferable to transmission by electricity. The following apparatus effects this object. Two similar apparatuses are coupled together by pneumatic connecting tubes, and the whole apparatus goes by the name of “ lever-drums.” * Each part con- Fio. 2. — Arrangement designed for transmitting a movement to the needle, wliich ' records the duration and the phases. sists of a metal capsule, with a gutta-percha membrane •stretched over the top ; a lever is attaclied to the membrane by means of a jointed crank. If the first lever is pulled by the hand and lowered, the air in the first tambour is compressed and passes into the second, the corresi>onding lever is raised, and reproduces in all its phases tlie traction exercised on the string. On * Usually called “Marey’s Tambours,” in England. — TiUNShATOit, 6 MOVEMENT the hand being released, the opj)osing force brings the first lever back into its original position, the air returns from the second into the first tambour, and the lever of the second falls in consequence. Thus the movements produced by raising or lowering the hand are transmitted after an inappreciable delay (i.e. that of sound) to a lever which can record them on a revolving cylinder which has been covered with paper. Now, the record can be written in two ways : either according to the Morse Code, by making or breaking the contact between the pen and the surface of the cylinder, or else in the form of a continuous curve, the variations of which express the different phases of the movement.* Chronographic Record of the Foot in Walking, as it touches and leaves the Ground. — A cylinder which turns at a uniform rate is covered with a sheet of paper, while the points of two tracing needles, which are placed side by side, touch the surface of the cylinder, one of them at the moment the right foot, and the other at the moment the left foot reaches the ground. The ob- ject of the arrange- ment is that each Fig. 3. — Shoe for indicating when a man s foot needle shall COme ill comes in contact with the ground; a transmit- . , ting tube effects a communication between the COllTfliCt ItH Til0 Sill* air chamber and the chronographic tambour. the corresponding foot touches tlie ground. The trans- mission is effected by means of pneumatic tubes. A particular kind of shoe (Fig. 3) is fitted to the foot of tlie pedestrian, and the sole is composed of a thick * For the diftcrent applicfitioiis of this sort of written record see “ The orraphic IMethod,” p. t2G. TIME 7 sheet of indiarubber, provided with a hollow chamber. This latter cavity communicates through a long flexible tube with the recording tambour. Each time the foot touches the ground the air within the cavity of the sole is compressed, and passing along the con- necting tube raises the corresponding recording needle. The pedestrian furnished with a pair of these shoes (Fig. 4), carries in his right hand the record- ing apparatus with its registering needles. When he wishes the tracing to commence he squeezes an india- rubber ball which he holds in his left hand ; if, a moment later, he releases the pressure, the needles cease trac- ing. Kecords are thus obtained which vary according to the pace, the weight carried, and the incline. Changes in the se- quence and duration of ■fViQ rnr»+follc! Qi«£j olirviim ^iG, 4. — Pedestrian furnished with Special shoes ine lOOIiailS are snown carrying a chronographic apparatus. by the four figures in the diagram (Fig. 5). In this the contact of the right foot is represented by a white, and that of the left by a diagonally shaded line. The first of the series represents walking on level ground. The steps of the two feet are alternate and regular. The second tracing is obtained by walking upstairs; in this, one foot does not leave the ground until the other one has been down some time. This represents 8 MOVEMENT one of the phases of reduplicated footsteps. The third is that of a runner. The periods of contact are short, and separated from one another by intervals Fig. 5, — Chronograpliic record of the periods of contact of the feet of a man executing various paces. during which neither foot is in contact with the ground — a period of suspension. The fourth tracing is one of a man running at a greater speed, the periods of contact are shorter and the intervals longer. Record of the Rise and Fall of the Four Feet of a Horse in its Various Paces. — For some time past specialists gifted with immense powers of observa- tion have set themselves the task of determining the real character of the various paces of a horse from observations on the se- quence of the heat of the feet. The use of the word heat im- plies an attempt to recognize Ifom the sound of the footfalls tlie sequence of the moment of recording the contacts of a flip miPstlOll of dui’fl- horse’s feet with the ground ; COUiat/l, lue quebLum ui uuut a transmitting tube effects a Epinrr nprrlpptpd IMorPOVPl’ communication between the non Oeillg liegieoieu. iUUXtJtntJl, graphicTambo^u^^ chrono- seiiso of hearing is above all others capable of appreci- ating intervals of time. The effect lias been tried I’’io. G — Special apparatus for TIME 9 of providing horses’ legs with bells which emit different notes as each foot touches the ground. All of these experiments have left doubts as to the exact rhythm of the various paces, doubts which have only been cleared up by the application of chronography. The following method^ has been em- ployed in this research : indiarubber balls stuffed with liair are fixed under the hoofs of the horse, and kept Ito. 7.— Horse at a. full trot. The point indicated on tlie chart corresponds to the position of the horse represented in tlie figure. ill position by calkins which screw into the metal of the shoe. Each of these balls is in connection with a long indiarubber tube which is fastened to the horse’s legs by flannel binders. These tubes communicate with the recording apparatus. The latter is provided with a tracing needle, and held in the liand of the rider (Eig. 7). The pressure of the feet upon the 10 MOVEMENT ground compresses the balls with which they are pro- vided, and forces the contained air into the recording tambours. The method tallies in all respects with that employed in the case of man. However, on account of the multiplication of writing needles, which the greater number of footfalls necessitates, the four needles are grouped in two series, one to record the movements of the fore feet, and the other placed beneath it to record the steps of the hind feet. In both series, the white lines indicate the movements of the right feet, while diagonally shaded ones represent those of the left. Fig. 8 shows results obtained in this way of the three ordinary paces, namely, ambling, walking, and trotting.* It will be noticed that each record is repre- sented as a series of four tracings, such as would be obtained by arranging in parallel series the tracings of two men walking. In fact, a quadruped may be compared to two bipeds — to two men, for instance — walking one behind the other, one to represent the fore, and the other the hind limbs. Such a pair would take the same number of steps ; but the phases of rest and motion would assume different relations in the two cases. It is this which constitutes the difference between the various kinds of paces. For instance, when the corresponding hind and fore feet move simultaneously, the horse is ambling (Fig. 8, first record). If the right fore foot is in the mid phase of rest when the left hind foot reaches the ground, the horse is walking (second record). Lastly, if the anterior and posterior legs move in opposite pairs, Le. if the anterior right reaches tlie ground at tlie * It is more than twenty-one years ago that these experiments were made, and we remember with gratitude the patient assistance witli wiiich Messrs. Pellier and Gai)riel Paillard helped ns to carry them into effect. TIME 11 same time as the posterior left leg, the horse is trotting (third record). It is thus seen with what simj)licity the ordinary paces of a horse may be recorded both as regard sequence and duration.* Paces that involve a springing movement, i.e. the various forms of galloping, can be analyzed with equal facility in spite of their greater complexity. Fig. 9 is the record of the ordinary trii^le-heat gallop, i.e. that in which the combined fall of the hoofs produces three sounds appreciable to the ear. The diagram shows how the three sounds are produced. The simple interpretation of this written record is that, in A, the first sound is made by the left hind foot. The second by the simultaneous fall of tlie left fore, and of the right hind foot. The record demon- strates still another fact, for, in B, it can be seen by what feet tlie body is at any moment supported. It is clear that at first the weight falls only on one leg, tlien on three, and then successively on two, three, * In this record wo liave represented the trot as a walking pace, this is an exceptional case. Tlie ordinary trot is a form of running, and its graphic record shows a moment of “suspension,” ns in the case of a man running. 12 MOVEMENT and one. In the final stage, the horse is momentarily poised in the air before it again comes down on the left hind foot. The Record of the Fingering of a Pianist. — The facility with which chronography can be aj)plied to the most complicated movements of irregular sequence and duration has encouraged an attempt to record movements so complex as to defy the observation of the most practised, namely, the movements of the fingers of a pianist on the keyboard of his instrument. Under each note on the keyboard of a harmonium is placed a tiny pair of bellows, and each of the latter is in communication by means of a special tube with Fic. 9. — Triple-beat gallop. A indicates the exact position of the three beats. B indicates the number of feet by which the horse is supported at any particular moment during a triple-beat gallop. a corresponding pair, which in turn are connected with a tracing needle. The series of needles are placed in a row, and are arranged in the order in which the different notes succeed one another in ordinary music, namely, in an ascending scale of musical pitch. All these needles trace tlieir record on a strip of smoked paper Avhich is moved by clockwork. Finally, a comb with five teeth inscribes the stave on which the various notes are written and recognized by their respective positions in relation to it. The duration of the sound is expressed by tlie length of the stroke. Semitones are distinguished by two tiny parallel stroke.s, instead of a single broad one.* * Tins metliod of notation lins boon made use of by M. V. Tatin in a very able manner. TIME 13 Xt one of tlie scientific soirees at the Sorbonne, during a conference on animal movement,* one of onr associates, a celebrated organist, kindly played some pieces of music which recorded themselves before the eyes of the audience, and of which we here give two examples (Fi 10, A and B). Every one who is A B Fig. 10.— Record of two airs played on the keyboard of a harmonium. accustomed to read ordinary music will easily decipher these examples ; they only differ from the ordinary score by the way in which the duration of the note is expressed. Instead of the conventional method of expressing the duration of different sounds by minims, crotchets, and quavers, and the duration of silence by rests and crotchet-rests, the graphic method conveys See La Nature, 5tli October, 1878. 14 MOVEMENT the same impression by the length of the stroke, that is to say, by a natural graj)hic expression.* The Uses of Photography in recording Time. — If the recording needle cannot be applied to the study of any particular phenomenon, recourse must be had to photography. It is by this means that a system of optical telegraphy has been perfected, by which flashes of light can be transmitted from one point to another, and received as a series of dots and dashes, such as constitute the Morse Code. The luminous point at the transmitting station is alternately, and at various intervals, exhibited and obscured by the movement of a screen. This con- stitutes the transmitting apparatus. The rays of light emanating from this source are rendered parallel by the interposition of a lens, and traverse the inter- vening space to impinge upon a similar lens at the receiving station. At the focal point of this second lens the image of the luminous source is visible in the form of a brilliant spot. If the sensitive surface, upon which this image falls, is allowed to travel at a uniform rate, short flashes of light will produce spots, and sustained flashes will give lines. An arrangement of this kind has many scientific applications, but it is not in this manner that photography has been most usefully employed in time-measurements. It has chiefly been utilized for two purposes. Firstly, to * During late years many inventors have constructed similar machines, and we believe that even this is not the first which auto- matically inscribed an air executed on the piano. Among instru- ments of recent design there is a very remarkable one, which we owe to Messrs. Cros and Carpentier, and which is known as the “Melograph.” This instrument is not intended to register the air as played by the artist, but it perforates a strip of jiaper in such a way that when it is repassed through the machine the piece of music which has been executed by the operator is reproduced by it with perfect fidelity. TIME 15 measure the exjDOSure of a photograjDliic shutter ; and secondly, to measure the intervals of time which separate consecutive exposures. Both of these methods must be described, since it is necessary to be familiar with them, so as to understand the analysis of move- ment by means of photography. ^ Measurement of the Duration of Exposure produced by a Photographic Shutter. — Shutters are generally called instantaneous, when they show in the photograph a representation of a moving object as clearly as would have been the case had the object been at rest. This definition is not, however, strictly true, since shutters, capable of giving a clear picture of passengers in the street, may be incapable of doing so in the case of the hoofs of a trotting horse. A still shorter time is required to catch the various positions of the wing of a fiying bird, and still more so in the case of insects. It must be possible then to measure the exposure of a shutter, and express the time in fractions of a second. We shall see how photo- graphy allows this measure- ment to be made. Let a bright needle rotate on a dial (Fig. 11) covered with black velvet, and graduated by white Fig. n. — Needle spinning round the lines. The movement of the needle must be absolutely uniform. For this purpose with a Foucault’s regulator mechanism is hidden behind the dial, and the needle makes one complete revolution in a second and a half, say 90'". The circumference of the dial is divided into eighteen equal parts, and consequently the con- tained angle of each space corresponds to 5 clockwork machinery is employed. This ’jit 16 MOVEMENT While the needle is constantly rotating, we must focus on the dial a camera provided with the shutter, the exposure of which we wish to ascertain. The opening of the shutter is effected by pressure on an indiarubber ball. If the period of exposure is not extremely short, the image of the needle will not be clearly defined, but will occupy a more or less ex- tensive segment of the dial. In such cases it would be impossible to determine with any exactitude the number of degrees occupied by the image. This is due to the construction of the shutters, which give incomplete illumination at the beginning and end of the exposure.* From the blurred nature of the image, which obscures the exact contour of the needle, one can only approximately estimate that the distance travelled during a single exposure is about three or four degrees, which corresponds to about 2^5 of a second. It is almost impossible for a shutter, which gives a single exposure, to produce one of very short duration. For this object, the spring which moves the shutter must be very powerful, and the weight carried ex- tremely light. With shutters of this kind it is possible to reduce the exposure to 2 J q ^ second. The shutters referred to in this work are of special construction. They consist of fenestrated diaphragms which, by means of continuous rotation, are able to acquire immense velocity. Their fenestrations, moving within the lens with extreme rapidity, produce a succession of illuminations of very short duration. It is this which gives such good definition to the images, which are shown in Fig. 12. Further, the * To obtain a true idea of the outline of the needle, it should bo compared with the image of Eig. 12. In this case the exposure has been short enough to prevent any alteration in its shape through the movement. TIME 17 images succeed one another at absolutely regular intervals, because both the movement of the needle on the dial and that of the circular diaphragms are equally uniform. Measurement of the Intervals of Time which separate Successive Exposures. — By reason of the clear definition of the images, they can be accurately measured, not by the time of exposure, which is too short to be appreciated, but by the in- tervals of time between suc- cessive exposures. Now, this is the important point in the measurements which we shall have to make of the duration of certain phenomena. Provided that one can ar- range a reliable clockwork mechanism so as to move the needle round the dial at a uniform rate, it does not mat- ter what rate of movement is imparted to the circular diaphragms, the interval between two exposures can always be measured by the angle contained between two consecutive images of the needle. If, during the time, an object, visible in the field of the lens, happens to move, there will be found, on the sensitized plate, several of its images in various positions and at various distances from one another. For the purpose of measuring the intervals of time between such successive positions of the object, the changes in position of the needle on the chrono- graphic dial will serve as an index. The further applications of this kind of time measurement will be seen when we come to discuss Chron ophotograph y . a Fig. 12.— Successive positions of the needle on the chronometric dial, measuring the intervals of time separating the successive exposures. CHAPTER II SPACE Its Measueement and Repeesentation by Photogeaphy Summary. — Tendency to replace outline drawings, plans, and diagrams in relief by photography — Photography traces the various positions in space occupied by a moving body— Photographic trajectory of the movements of a point in space ; its stereoscopic trajectory — Movements of a straight line in space— Solid figures formed thereby : cylinders, hyperboloids, cones, etc. — Movements of a curve in space ; photography of the figures which it forms : spheres, ellipsoids, etc. — Stereoscopic pictures of figures of three dimensions — Figures formed by the movement of solid bodies ; etfects of light and shade. Tendency to replace Outline Drawings, Plans, and Diagrams in Relief by Photography. — The positions of bodies in space, their forms and dimensions, find their natural expression in geometrical drawings. Such drawings, executed to a known scale, supply all the information that is required. During the last few years, however, there has been a tendency to substitute photography for outline drawings, and doubtless in the future it will completely replace them. Indeed, it supplies with remarkable ease pictures of undoubted accuracy. The dimensions can be enlarged or reduced as occasion may require, and if thought desirable, a scale for the purpose of measurement may be introduced into the picture, and SPACE 19 the exact dimensions thus indicated. To introduce such a scale into the picture, a rule with very distinct divisions must be placed by the side of the object which is being photographed. When an artist wishes to represent in relief an object of three dimensions, he must obey the laws of perspective, and take into consideration the manner in w'hich the light falls on the object, at the moment of drawing. But the fitful changes of light, during the various times of day, offer innumerable difficulties. Photography, how^ever, gives an instantaneous picture of the most diverse objects, and that, too, with the prevailing conditions of light, and all in correct perspective. The appearance of natural objects, as seen by looking with one eye only, is thus repro- duced by photography. If it is required to get the effect of relief, such as is obtained by looking with both eyes, recourse must be had to stereoscopic pictures. Photography traces the Various Positions in Space occupied by a Moving Body. — When an object changes its position, it is often necessary to notify the posi- tions in space which it successively occupies. In the first place, we must be quite sure that our eyes have been able to folloAv the various phases of movement, and that our memory has been able to retain the details — conditions rarely fulfilled — before we have recourse to drawing, as a means of representing the trajectory described. The diagram traced will be more or less complicated according as we express the movement by a point, a line, a plane superficies, or a solid — in short, according as w'e represent a movement executed in one or more directions. When it is only a question of tlie movement of a point, in certain cases tlie difficulty may be met by making the moving point itself trace the path which 20 MOVEMENT it takes.* It must be possible, however, to fasten this point directly or indirectly to the needle which is to trace the trajector)^, and, further, the propelling force must be sufficient to work the mechanism of the recording instrument, and that, too, without modifica- tion of the movement. But if the point is inaccessible, if the propelling force is too feeble, or if it follows a very complicated course, we must introduce new conditions, and employ photography in the special manner we are about to describe. Principles of Photography with a Dark Background. — When a camera faces a dark background, no impression is made on the sensitized plate, because no light reaches it ; but if a very luminous object is placed between the background and the lens, light will be reflected and an image imprinted on the plate. If, while the object-glass is uncovered, the white object changes its position, there will be reproduced on the plate a track which exactly corresponds to the move- ments of the object. This is the trajectory of the object, or, to put it more precisely, the projection of its trajectory on the surface of the sensitized plate. The image will be more or less reduced in size according to the distance of the object, and according to the focal length of the objective. Photographic Trajectory of the Movements of a Point in Space. — To demonstrate the advantages offered by photography as a means of recording the trajectory of a moving object, we will choose as an example a case in which direct observation ivill afford us no informa- tion, and in which a mechanical method of recording will be impracticable. Suppose, for example, that we wisli to ascertain the various positions in space * Tlie different proceedings for meclmnically recording the move- ments of a point in one or more directions in space have been given in “ The Graphic Method.” SPACE 21 occupied by a particular part of a bird’s wiug during the act of flight, and that this particular part is the tip of one of the quills, called “remiges.” Now, such a quill, by reason of its flexibility, would be incapable of giving the necessary motive power to an apparatus for recording the trajectory of flight ; and, further, this point is inaccessible because birds only fly freely at a certain distance from the observer. A black crow may be used in the experiment, and a small piece of white paper may be fixed to the extremity of one of its Fig. 13. — Trajectory of the tip of a crow’s wing. A brilliant spangle attached to the second of the remiges follows the path indicated by the small arrows. In the lower part of the figure a straight and horizontal arrow shows the direction of fiight. longest “remiges.” The bird is then allowed to fly in front of a dark background, towards which a photo- graphic camera is directed. Since the entire field of the object-glass is dark, that is to say, the bird and its background, the sensitized plate can receive no light except that which is reflected by the small piece of white paper, which is illuminated by the sun. The image of this white spot will leave a record of its track on the sensitized plate. In this way Fig. 13 was obtained, the arrows indicating the direction of flight. Stereoscopic Trajectories. — The trajectory of the 22 MOVEMENT movement of the point of a wing cannot be expressed comprebensively in the form of a plane diagram, since the movement of the wing at the shoulder-joint takes place in three directions. The photographic diagram only gives one projection of this trajectory. It is thus incapable of expressing the real course of flight taken. If a movement takes place in three directions, recourse must be had to a more complicated arrangement, and a stereoscopic trajectory obtained. Let us take the case of a man walking away from us, and concentrate our attention on a particular point of his body. This point is elevated and depressed as the man’s foot rises and falls. Further, it is affected by the side-to-side swing, and according to the direction in which he walks. The pedestrian must be completely dressed in black, and a bright metal button fastened to a part of his body. The man is then made to walk in front of a dark background, and a stereoscopic photographic camera with two lenses is focussed on the spot. Both of these object-glasses, acting precisely as the single one in the preceding experiment, produce two images of the luminous point. Fig. Id was obtained in this manner; it shows two images of the same trajectory taken from two different points of view. Examined with the stereoscope, these images stand out in bold relief.* * Since a considerable number of people arc able to see figures of this sort standing out in relief without having recourse to a stereo- scope, we have published the above figure, and certain others will be found further on. To obtain the full effect of relief without a stereoscope, we must concentrate our vision on a distant point, and then interpose the object between our eyes and the distant point. The page of the book will then be seen double, and consequently the tra- jectory will appear as four separate images. If the book is then very gently moved, and the direction of the eyes slightly altered, the two internal images finally become exactly superimposed. The eye is then accommodated for distinct vision of the central image, which stands out in relief between the two outlying images. With a little practice one can easily dispense with the stereoscope for examining figures of this sort. Sl’ACIil 23 Movements of a Straight Line in Space. Photography of the Solid Figures formed thereby : Cylinders, Hyper- boloids, Cones, etc. — A straight line, which is moved ill various ways on a plane surface, covers the latter with a variety of configurations, or else, if attention is paid only to the various positions which it occupies at certain moments, these positions can be expressed Fig. 14. — Stereoscopic trajectory of a brilliant point placed at the level of the lumbar vertebra; of a man walking away from the photographic camera. as geometrical figures, which can be transferred to jiaper ; but if this straight liue moves in the three directions of sjiace it describes surfaces, the projec- tions of which can only be represented by perspective drawing. In such cases recourse must be had to diagrams in relief, whidi liave tlie advantage of giving beginners a clearer notion of solid forms. By means of threads stretched between metal armatures, one can 24 MOVEMENT sliow how the successive positions of a straight line can produce cylinders, cones, conoids, and hyperboloids by revolution. There is a particularly rich collection of such diagrams at the Academy of Arts and Crafts — very useful as a means of popularizing the study of solid geometry. Now, if the geometry of to-day has become purely a speculative science, there is no doubt that, like all other sciences, it had an experimental origin. It is not likely that the conception of a straight line was evolved from man’s brain as a purely abstract ex- pression, but rather that it entered therein, on seeing a stretched thread, for instance, or some other recti- linear object. In the same way the conception of a plane or a circle found its origin from noticing a flat surface or an object of circular form. There are, so to S2)eak, traces of these concrete origins of geometrical figures in the definitions given to solid figures or to those of three dimensions. Such objects are said to be “ engendered ” by straight lines or curves, which undergo various displacements. Thus a regular cylindrical surface is engendered by a straight line Avhich moves parallel to another straight line, and yet remains at the same distance from it. The straight line which moves is the “ generator ” of the cylinder ; that Avhich remains fixed is its axis. Under such circumstances, let us suppose that the straight line, as it moves in space, leaves a record of its track at every point which it successively passes. Now, this purely imaginary supposition may become an accomplished fact, thanks to photography. Indeed, supposing we take a series of instantaneous views of an illuminated thread as it moves in front of a dark screen, figures are produced Avliich exactly resemble the stereoscopic forms obtained by stretching a series SPACE 25 of threads between metal armatures. This is the method : — A vertical metal rod furnished with two transverse arms, Avhich are exactly opposite to one another, is allowed to rotate in front of a dark screen. This metal frame must be blackened with the smoke of a candle, and thus rendered as nearly invisible as possible. The tAA’o cross-bars must be of equal length, and their free extremities connected by a Avhite thread, which is stretched vertically between them. This thread, by means of the rotatory motion which is imparted to the two cross-bars, moves in a circular manner round the axis, and describes in space the circular outline of a cylinder. A photographic camera directed towards this thread, and kept permanently open, Avould receive an image, which Avould be the projection of a cylinder on a plane surface. But this continuous trajectory Avould not show its method of production with sufficient clear- ness. In order that one may see that such a picture results entirely from the movement of the thread, Avhich at every moment adds a new component- element to the surface of the cylinder, separate images, at successive intervals of time, must be obtained. That is to say, the light must be admitted in an inter- mittent manner. Fig. 15 Avas thus obtained.* If the thread, instead of lying parallel to the axis round Avhich it rotates, is directed obliquely towards it, the figure described will be a hyperboloid by revolution (Fig. 16). And, finally, if the thread is * In this diagram the central axis appears white, because, although the amount of light reflected from such a blackened surface is ex- tremely feeble, nevertheless, this light is always reflected on to the plate every time the objective is uncovered. Now, since the axis remains permanently in one place, each separate impression, however feeble, is superimposed on the same part of the sensitized plate, and ends by being clearly defined. 26 MOVEMENT placed still more oblicpiely — in fact, if it touches the axis at one point — the figure described will be a cone. Photography, with a dark background, is especially adapted for demonstrating the construction of cones and hyperboloids ; and, further, it clearly shows the relations which these two kinds of figures bear to one another. An indefinite number of images can be taken on Fig. 15. — Cylinder engendered by the displacement of a white thread mov- ing round a central axis. Fig. 16.— Hyperboloid by revolution : a single web engendered by the revolution of a thread set obliquely to the axis. the same plate. No sooner has one image been taken than another can be superimjiosed ; the second im- pression is just as good as the first. This method was employed in the production of Fig. 17. After liaving taken a photograph of a hyperboloid by revolution, tlie dark slide was closed, and the thread arranged so as to describe a cone ; the slide was tlien opened again, and the image of the cone obtained. The two pictures SPACE 27 thus superimposed show the hyperboloid on the out- side and its asymptotic cone inside. Conoids. — If the white thread, instead of revolv- ing round the axis, as in the experiment which we have just been reading, has im- parted to it at one extremity a rotatory motion, while the other extremity moves in a straight line, one ob- tains, according to the relationship of the two movements, different SOltS of conoids, of yic. it. — Hyperl'oloid by revolution with iis which Fig. 18 is one asymptotic cone. example. Movements of a Curve in Space. Photography of the Figures which it forms: Spheres, Ellipsoids, etc. — Among Fio. 18. — Conoid engendered by the move- ment of a white thread. Fig. 19. — .Sphere engendered by the rotation of a semi-annular white thread. the forms arising from the movements of a curve, the most easy to })roduce is a sphere ; it is obtained when ‘28 MOVEMENT a semicircular A\ire of Avhite metal rotates round a vertical axis, which is also its diameter. Fig. 19 is the projection of such a sphere on a plane surface. (The imperfections of the figure are due to the fact that it is impossible to impart j)erfect regularity of curvature to the Avire Avhich constitutes the semicircle.) It is unnecessary to multiply examples of figures Fig. 20.— Sphere engendered by the rotation of a semi-annular thread. (Stereoscopic images.) Fig. 21. — Hyperboloid and its asymptotic cone. (Stereoscopic images.) generated by the movement of curves, such as ellip- soids, paraboloids by revolution, etc. In order that these figures of three dimensions may be rendered more intelligible, AAe have reproduced them in the form of stereoscopic pictures by the folloAving proceeding. Stereoscopic Pictures of Figures of Three Dimensions. — We must provide ourselves AA'ith a stereoscopic camera SPACE 29 with two object-glasses of equal focal lengths. The mountings of these objectives must be cleft by a deep slot, perpendicular to their axes ; and within this slot there must rotate a diaphragm perforated by two openings, which are diametrically opposite to one another. This diaphragm rotates at a uniform rate, and simultaneously uncovers the two objectives; during each complete revolution of the diaphragm the objectives are twice uncovered. A mechanical motor turns the circular diaphragm, and, by means of a pulley Fig. 22. — Sphere engendered by the rotation of a semi-annular band, white on the outer surface and black on the inner side. and continuous band, the same motor serves to turn the axis and the white threads. The latter, by their movements, describe the desired figures. Figures formed by the Movement of Solid Bodies; Effects of Light and Shade. — Instead of the fine thread, which has just served our purpose for describing the surface of a sphere in space, let us take a solid body ; the appearance of the figure described will be quite different. A band of Bristol board is ardied lengtli- wise, its convex surface blackened, and its concave 30 MOVEMENT surface left white ; when such a band rotates, a figure such as Fig. 22 will be produced. Except for certain breaches of continuity, due to the intermittent character of the illumination, the surface thus produced will resemble that of a solid sphere, which is illuminated from the left and from above, while the opposite side is only feebly lighted by reflection. This appearance is easily explained. The strip of paper, as it travels over successive meridians of this imaginary circle, is placed under exactly the same conditions of illumina- tion as would be the case if the meridians were those of a real sphere in the same position. Paradoxical Effect produced by Certain Conditions of Illumination. — Instead of the strip of paper used in the preceding experiment, and from which light was only reflected from the convex surface, let us take a strip of similar board, only white on both surfaces. We shall thus obtain a peculiar effect (Fig. 23) which can only be understood when viewed under stereoscopic conditions. Tiie inner and outer surfaces of this sphere can be seen at one and the same time. This is because the arc of Bristol board is white within as well as without, and consequently reflects the light, sometimes from one surface, sometimes from the other, according to the position of rotation. When the convex arc faces the light, i.e. is directed upwards and towards the left, the corresponding portion of the engendered sphere is clearly visible. When the arc is in an exactly opposite phase of rotation, it receives the light on its concave aspect ; that is to say, the interior of the sphere below and on the left is the part illuminated. At first sight this figure appears to be transparent, but on the one hand we know tliat it has been formed l)y an opaque substance, and on tlie other tliat all known transparent media reflect light in a totally different manner. SPACE 31 / 111 reality we are dealing with a hypothetical figure, which finds no counterpart in Nature. Such hypo- thetical figures are still more strange, when, instead of dull substances being employed in their construc- tion, a polislied material is made use of wliich only reflects the sun’s rays from certain points of its snrrace. 32 MOVEMENT Fig. 24. — Paradoxical appearance of a sphere engendered by the rotation of a brilliant metallic thread. Fig. 24 was obtained by allowing a semicircular arc of polished brass to rotate round a vertical axis. There is for each position of rotation only one particular spot on the polished metal arc from which the incidental rays of the sun can be reflected into the body of the camera. Now, as this bright spot changes its position, it is sometimes on the con- vex side and sometimes on the concave side of the metal arc. It is the displacement of this lumi- nous spot which traces the complete rings on the opposite portions of the sphere. In order more clearly to understand the causation of this peculiar appearance, we must have recourse to stereo- scopic figures, with an intermittent series of images. Such figures show that in each position certain portions of the surface of the semicircular arc are dark, that is to say, do not transmit light in the direction of the photographic apparatus ; on the contrary, other points are brilliantly illuminated, because in this position they are “ set,” so to speak, so as to reflect the sun’s rays. These curious effects can never be caused by a real body. The form and ]30sition of the illuminated spots on the sphere can be varied at u ill by changing the direction of incidence of the luminous rays. The mathematical study of these diverse effects would be, perhaps, rather complicated ; in any case, it would afford a very limited amount of interest. It was necessary, however, to mention them, because in the course of our studies, we sliall meet witli analogous forms, produced by tlie movement of certain bodies. CHAPTEK III MOVEMENT Its jMeasueement, Gkaphic Kepresentation, and Analysis by means of Chronophotography Summary. — The understanding of a movement implies a double knowledge, namely, that of space as well as that of time — Grapliic representation of a movement — Chart of a train travel- ling along a line — The curve of a prolonged movement should be recorded in sections — How a moving body can record its own movement — Proportional enlargement and reduction of the recorded movement — Odography — Photographic record of move- ment— Photograi^hy of the movement of Lipi^mann’s electrometer — Determination by means of chronophotography of the move- ments executed by a falling body — Construction of the curves of movement from chronophotographic images — Time-curve of the distance traversed — Curve of velocity — Curve of acceleration. The Understanding of a Movement implies a Double Knowledge, namely, that of Space as well as that of Time. — AVe saw in Chapter II. that photography could reproduce tlie trajectory of a body moving in space ; but tlie idea there conveyed of the successive changes in position was not sufficient to define the movement. The power to do so presupposes a know- ledge of the relationship existing at any moment between the distance traversed and the time occupied. Now, the object of Chapter I. was to demonstrate that [)hotography would permit the exact measurement of time intervals. It follows that, if the two notions of time and space can be combined in photographic 34 MOVEMENT images, we have instituted a chronophotographic method, which explains all the factors in a move- ment which we want to understand. It also affords a very simple experimental solution of certain very complicated mechanical problems. The whole ques- tion of mechaniGS is based on a knowledge of the movement which is imparted to a mass ; for from the movement the force which produces it can be measured. To determine with accuracy the character of a movement, whether it be uniform or irregular, to determine its velocity and degree of acceleration extremely delicate experiments are usually necessary. When the movement is once thoroughly under- stood, its character must be expressed in a j>recise manner. Since the time of Descartes, geometricians have known how to express the characters of move- ments in the form of curves with different variations. But such curves, although they can express certain phenomena, require, like other geometrical figures, a more or less laborious construction. It was a great stej:) in advance when Poncelet and Morin showed that a moving body could itself be made to trace its path in the form of a curve. The first application of this graphic method was made use of in the case of a falling body ; it was soon, however, extended to other branches of Science. Meteorology, Physics, and Physiology all participated in the discovery with advantage to themselves. In spite of the enormous development of this method, it has limitations, which we can only extend by the employment of chronophotography. Thus, when the moving body is inaccessible, wlien it cannot be fastened by mechanical means to the recording apparatus, this new method for determining its movement must be employed ; a metlmd which demands no material link MOVEMENT 35 between the visible point and the sensitized plate on which from moment to moment its movement is recorded. To fully appreciate the advantages of chronophotography, it will doubtless be best to compare it with other methods already employed in the solution of the same problems. Let us take the most simple case, that of recording the displacement in a straight line of a moving body, and let us approach the question in accordance with the two methods. Graphic Eepresentation of Movement. — When a point travels along a straight line, the successive positions can be indicated by means of two straight lines at right angles to one another. These two straight lines, the one horizontal and the other vertical, indicate respectively the time taken and the dis- tance traversed. If the mov- ing body is propelled at a uniform rate of one hecto- metre to the minute, this movement can be expressed by the oblique line which joins the points where the divisions of time and space intersect (Fig. 25). This is the curve of movement. In the case of a uniform movement, this line is always straight : but it will be more or less obliquely inclined according to the speed at which the body travels. Thus, for double speed, that is to say, two hectometres in the minute, the line will pass through the point at which the second division of space and tlie first division of time intersect. It will thus form the diagonal of a series of rectangles, the sides of which will Ije formed of two space-divisions and one time-division. This system of representation ex2U'esses Time in minutes Fig. 26. — Graphic representation of a uniform movement. 36 MOVEMENT all degrees of speed and all kinds of movement. A horizontal line signifies a period of rest, and the length of the line, or, in other words, the number of divisions which it occupies, is a measure of the duration of this period of rest. Irregular movement is expressed by a curve, the inclination of which, i.e. the tangent, indicates from moment to moment the rate of progression. Further, each point of the curve indicates according to its relation to the horizontal and vertical scales the time occupied and the distance travelled since the com- mencement of the movement. Chart of a Train travelling along a Line. — A geometrical expression for all sorts of movement has become now almost universal, since the engineer Ibry made use of it to chronicle the progress of trains along a railway. Nowadays every one is familiar with these charts, in which are to be seen lines intersecting one another in all directions. Variations both as regards inclination and direction express the speed and the route taken by all trains running on the track. Fig. 26 is an example of such a chart placed by the directorate at the service of its employes. To the left of this chart, along the axis of the uprights, are printed in series the names of the various stations. These stopping-places are separated on the cliart by intervals proportional to the number of kilometres which actually intervene as they occur on the line. In the horizontal direction, i.e. along tlie axis of tlie abscissae, time is registered by periods of an lionr; these are again subdivided into periods of ten minutes. To indicate that a train should arrive at a given liour at a particular point on the line, its position is marked on the cliart opposite the station at wliich it is expected, and vertically above the division which corresponds to the time at which it is due. As the MOVEMENT 37 train 231‘oceeds on its way particulars are notified, both as regards the direction in which it is going and the time occupied. But if the train stops, its place on the chart only changes as far as the time-axis is concerned, and consequently the stoppages are ex- Fio. 26.— Cliart to express the movements of trains along a railway. (Ibry’s method.) pressed by horizontal lines more or less elongated. Ihe inclination of the line exjn’esses the speed of the train. The faster the train moves the more nearly vertical does the line become, hlxpress, fast, through, and stopping trains can thus be distinguished at a 38 MOVEMENT glance. The direction of the curve indicates the destination of the train. Lines descending towards the right represent trains going away from Paris, while those which ascend towards the right correspond to trains going towards the capital. The intersections of lines on the chart signify the places and the hours at which trains cross one another en route. This admirable mode of representation is the only one which should be employed to express in a graphic form the trajectory of a moving point. In such tables the rate of progress of the trains is supposed to be uniform, and is represented by straight lines instead of irregular curves. The latter are emj)loyed to express a change of speed as it occurs from moment to moment. This is the only way in which such a mode of graphic representation deviates from what actually occurs. It is improbable, however, that any serious difficulty would arise from this cause. The Curve of a Prolonged Movement should be re- corded in Sections. — Charts used to express the move- ments on a railway are crowded with detail, because they record the progress of every train which moves in one or other direction along a more or less extensive section of the line. The surface of the paper is thus completely utilized. But this would not be the case if we had to record the progress of one train only during a long run extending over many hours. On referring back to Pig. 25 it will be noticed that the diagonal of the square expresses a journey of six hectometres completed in six minutes. Now, for a journey twice as long, and taking twice the time, the diagonal would be double the length, and the square containing it four times as large. According to this geometrical progression, we should have to use a sheet of paper a metre square if we wanted to record the progress of a moving body lor twenty kilometies. MOVEMENT 39 Aud this immense surface would only be broken by a single fine line dividing it diagonally into two parts. This inconvenience would in itself serve to condemn the method from a practical point of view. It can be avoided, how- ever, by dividing the tracing into sections, each of which ex- presses the movement during a given time. Thus Fig. 27 shows concentrated on a narrow strip of paper the various phases of a movement which otherwise would have required a surface six times as large. On this strip of paper the scale representing distance is con- tinuous, but that representing time is broken. After each period of five minutes the curve returns to the first time-division, but remains on the distance-division at which it has actually arrived. From this point a new section of the curve recommences. The sections A, B, C, etc., thus ex- press the progress of the moving body over a distance of 25 hecto- metres, and during a period of 30 minutes, and the curve is quite as intelligible as would be a continuous one requiring a large surface of paper.* * Tlie seetioB A allows that, during the first five minutes, the moving body Time in minutes 0’ I d' T . o' Fig. 27. — Successive sections of the curve of a movement. 40 MOVEMENT How a Moving Body can record its Own Movement. — Poncelet and Morin solved this problem by construct- ing the well-known machine which registers the movement of a falling body. In this machine, the falling body is provided with a needle, which leaves its record on paper, and moves in a vertical direction at the same rate as the falling body. Further, the paper rolled round a revolving cylinder advances in a hori- zontal direction at a uniform rate. When the paper is taken off the cylinder, the needle is found to have traced a curve which is parabolic in form. This is the geometrical manner of expressing a movement of uniform acceleration. This machine is a type of the recording apparatuses of Avhich there are noAvadays a considerable number. It must be mentioned at the same time that, by reason of its construction, it can only record the curves of movement to actual scale ; it could not, therefore, be used to rej)resent movements too small or too extensive to be inscribed on a sheet of paper. It folloAvs that, in order to bring the propor- tions of the movement, the curve of Avhich is to be recorded, AAothin convenient proportions, it must either be enlarged or reduced. Proportional Enlargement and Reduction of the Re- corded Movement. — Very feeble movements, such as occur in living organs, and such as physiologists Avish to understand, usually have to be immensely enlarged. This can be effected by levers Avith needles fixed to has traversed a distance of five hectometres at a uniform rate. This rate is maintained for two minutes longer (section B), then a stoppage occurs for one minute, after which the moving body again advances at an accelerated pace until the tenth minute. This speed of two hectometres a minute is maintained up till the end of the eleventh minute, when it again gives place to a slower move- ment of three hectometres in four minutes. This is maintained during section D and part of E, until the twenty-first minute, at which a period of rest occurs. This stop of three minutes, which is continued during section F, is followed by another period of uniform movement during which the speed is a litllc more than 100 metres per minute. MOVEMENT 41 their extremities. It is in this way that the arterial pulse, as it alternately raises and loAvers the lever, demonstrates in dilferent patients the condition of the circulation.* When a movement is on too large a scale to be recorded in its actual size, it must be Fig. 28. — Enlarged tracings of the pulse in different diseases. reduced before transmission to the recording needle. There are several ways of doing this, the following are the most usual methorls. The movement can be reduced by allowing it to act on the longer arm of a lever, while the writing needle is placed on the sliorter. * See The Circulation. Paris, G-. Masson, 1881. 42 MOVEMENT The relationship which obtains between the lengths of the two arms determines the degree to which the movement is reduced. A movement can be uniformly reduced by means of an indiarubber thread ; this is a c convenient method, and quite reliable enough for most purposes.* “ Let G h (Fig. 29) be an elastic thread ,a- as nearly homogeneous as possible. Under the influence of traction it will become equally extended throughout its length. Let us make fast one of its extremities, c, by means of a nail, for instance. If we exercise traction at the other end, h, so j as to bring it to V, the point a near to c I will only travel the short distance aa'. If ! we have fixed the tracing needle at this j point, it will record on the revolving j cylinder a curve, the amplitude of which 'M will be to that of the real movement as the length of the thread ca is to the length cb. But when the movement has to be immensely reduced, as happens when the path of a body moving through several Fio.29.-Piopor- kilometres has to be traced on a strip of tiondil rcduC” n .. . tion of a move- paper a lew centimetres in length, the of an India- movemeut has to be reduced by means rubber thread. ^ mechauical arrangement of wheels. A system of small pinions and large wheels will effect this object ; in fact, as we know, it will indefi- nitely reduce the amplitude of any movement. We had recourse to this method when we obtained the * This method of reducing the curve by means of an elastic thread was thought of by Admiral Paris and his son. It was made use of in their apparatus described under the name of “Wave Tracers.” — Maritime a7id Colonial i?en’eio, June, 1867. MOVEMENT 43 curve of movement presented in Fig. 27. The in- strument employed in this experiment is applicable for registering the progress of all kinds of machines. It is called an “ Odograph.” The Odograph. — Fig. 30 represents a pedestrian Fig, 30. — Pedestrian pushing an odograph in front of him. pushing before him a light species of wheelbarrow. The track of the wheel upon the ground represents the distance traversed. The wheel of the barrow, by a system of reducing wheels, controls tlie movement of a strip of paper. Further, a tracing needle Avorked by a clock moves across the paper at any desired rate. A 44 MOVEMENT time-curve of the distance traversed results from the combination of these two movements. Figs. 31 and 32 show the details of the a232:>aratns. A strij) of paper, tlie length of which is about one metre, passes between cylindrical rollers which advance it a distance proportional to the space traversed 1)y the moving Fig. 31. — Details of the odograph. The strip of paper, which has already received a tracing of progression and rest, can be clearly seen in position. One needle has completed its journey, and a second, in its turn, is just about to commence. The needles, to the number of five, are arranged at a distance of si.v centimetres from one another, along a steel band wliicli passes round the two rollers G by means of clockwork. At B can be seen the extremity of the sh.aft which imparts tlie movement to the rollers. body. Each revolution of the wlieel, representing a distance of three metres, will advance tlie wheel of the cylindrical rollers throngli a distance of one cog. This is effected liy means of a crank whicli runs along one of the handles of the wheelbarrow. During this time MOVEMENT 45 the strip of paper will have progressed a very short dis- tance, O'l millimetre for instance. It will have com- pletely passed through the rollers at the end of a run of 30 kilometres. The needle, which writes on the paper, is made of brass, and the paper itself is coated with a layer of white zinc, and called paj^ier couclie," in the r lo. 32. — Tlie instrument is seen obliquely from behind. Tlie dial of the clock is visible. The strip of paper is in position between the rollers, and the needle is in the act of tracing. The teeth of the comb have already imprinted hourly sub- divisions on the I aper. At B the end of the shaft acts by means of a clapper on a ratchet-wheel, which in its turn controls the movement of the rollers by means of an endless screw. trade. On tliis latter the brass leaves a very fine and clearly defined track. It never wears out like a pencil, neither does it require ink like a pen. To obtain a curve of the movement, the needle must have imparted to it a uniform motion by means of clockwork, and it 46 MOVEMENT must traverse tlie width of the paper in one lioiir. Besides this, as the strip of paper is drawn through the rollers, it passes beneath a comb, which registers equidistant lines along the length of the paper ; the distance between two teeth corresponds to a duration of ten minutes. This greatly facilitates the reading of the distance traversed in a particular time. Thus during every hour the needle traces a section of a curve analogous to those in Fig. 27, and which are distinguished in order by the letters A, B, C, — F, because the needle takes exactly one hour to cross the width of the paper. As soon as the first curve has been registered another one is commenced, because a second needle in turn begins to register, and at the third hour another needle, and so on indefinitely during the whole of the journey.* When the strip of paper ceases to advance, during periods of rest, the clock nevertheless continues to move the needle, and the latter describes a straight line at right angles to the long axis of the paper. This way of registering move- ment is identical with that which was designed by Ibry. We believe that odography could, with a few special modifications, be applied for registering the progress of a railway train. A novel arrangement of pneumatic tubes can transmit each revolution of the wheels of the engine to the mechanism of the cylindrical rollers, and thus an odograph can be placed in each compartment, and sujDply continuous information of the progress of the train. Thanks to the kindness of M. Millet, chief engineer of the loco- motive department on the Southern Railway (Chemin de fer du Midi), we were able to try the effect of the odograph on express trains running from Dax to Bordeaux, and vice versa. Fig. 33 shows in column A * Tlie npcdles arfi drivpn l>y an cndloss stpol band controlled by the clock. Fro. 33.— Two biographic charts expressing, according to different scales, the advance of a fast train. 48 MOVEMENT a section of tlie original cliart taken on one of these journeys between Dax and Moncenx. To measure from moment to moment the rate of travelling, a small divided scale can be applied to the corresponding part of the diagram. By means of this scale we can measure the length of any portion of the curve, which corresponds to the distance traversed in ten minutes. In this case it can be seen that the speed was 55 kilometres per hour. These charts are exactly like those employed by railway companies ; the method of expressing periods of progression and rest is the same throughout, the only difference is, that Ibry’s charts were theoretical, i.e. the speed of the trains is supposed to be uniform, and is represented by straight lines, and in ours the actual speed is experi- mentally found, and expressed by variations more or less pronounced. It can be seen that from Dax to Eion, and from Kion to Moncenx, the line is not straight but slightly curved, which means that there is a slight variation in the speed. It is generally immediately before, or immediately after, a stojDpage that these variations are noticeable. xU the moment that the train comes to a stop, the curve suddenly changes its direction, which indicates that under the influence of the brake there is a rapid transition from a liigh rate of speed to a condition of rest. On the contrary, at the moment of departure, the curve describes a parabola, which indicates how gradual is tlie acceleration, and how slowly the train gets up speed. The movement of the paper must be con- siderably slowed down, if we want to inscribe all the phases of a long journey within the limits of a single sheet of paper. Column B was obtained in tliis way, and on it is registered a journey from Dax to Bordeaux, representing a distance of GO kilometres. In odography the movement of the paper should be MOVEMENT 49 regulated to suit the average speed of the conveyance the movement of which is to be ascertained, be it carriage, locomotive, or boat, etc.* Wide as is the range of movements capable of being recorded by mechanical means, nevertheless there are, as we re- marked before, cases in which this method ceases to be applicable. It will be seen how valuable the employ- ment of photography becomes in cases of this kind. Photography of the Movements of Lippmann’s Electro- meter.— In 1877, our colleague and friend Lippmann had just invented his capillary electrometer, an in- strument so marvellously sensitive that it was capable of registering the slightest electrical variation that occurred in living tissues. But for this purpose it was necessary to make this electrometer a recording instru- ment. This was managed by means of photography. As the column of the electrometer is exceedingly tine, the movements must be observed under the microscope. This column presents totally different appearances under different conditions of illumination ; on a light background it appears as a dark line ; on a dark back- ground, when illuminated from the sides, it stands out as a very bright line. This column is seen to elongate and contract according to the direction and the in- tensity of the current acting upon it. By receiving its image on a photographic plate a very intense black line will be obtained. If the sensitive plate is moved at a uniform rate at right angles to the axis of the column, all its variations in length will be apparent in the image. The effect of moving the plate is that the image of the column is no longer a simple line ; it is spread out in the form of a band, the sinuous border of which * For the details of tho employment of odograpliy, see La NaturCi No. 278, September 28, 1878. 50 MpVEMENT corresponds to the variations in the length of the column of mercury. To illuminate the column of this instrument, we used a series of flashes from an induction coil furnished with a condenser. This intermittent illumination dis- turbed the continuity of the images, and thus a series of bright lines of unequal length was produced. By this means tracings can be obtained to demon- strate the electrical changes in the hearts of tortoises or frogs, as they occur respectively during the periods of systole and diastole. The sinuous border representing the summit of the column of mercury in such a tracing has a very close resemblance to the curve obtained by mechanically registering the actual movements of the heart during its various phases. The heart, like all other muscular structures, shows changes in its electrical condition, according as it is contracted or relaxed. Determination by Means of Chronophotography of the Movement executed by a Falling Body. — In the study of movement, j)hotography has the advantage of not being obliged to borrow any motive power from the object observed. The following experiment may be made. A black-velvet curtain may be hung vertically so as to form a dark screen, in front of which a white ball, lit up by the sun’s rays, is allowed to fall. A divided scale is placed vertically in front of the dark background, to measure the distance traversed. A chronometric dial is used to measure the intervals between the successive images. When the circular diaphragm has acquired the desired velocity, an assistant pulls the string and the ball falls. The photographic plate receives a series of images of this ball, showing the positions it occupies at each successive exposure. In this way all the necessary elements are obtained for determining “ the MOVEMENT 51 laws of motion.” In order to make it more easy to take measurements from this photograj)h, the original plate is enlarged, and the different positions of the falling body are obtained on a convenient scale. Let ns. draw a horizontal tangent to the ball in each ' of its positions. The distances fallen during the various jieriods since the ‘commencement of the fall will then be seen in series, and it will be ob- served that these distances increase as the square of the time. Tor instance, the distance tra- versed during the second period of fall, that is to say, after the second exposure, is four times as much as that which was tra- versed in the first period. If one wishes to construct a time- 34.— Photography of the movement of a falling body. curve of the dis- tance traversed, the sheet of paper should be divided by vertical lines at equal distances. At the inter- sections of each of these lines with the horizontal tangents a mark is made (a dot in the centre of a circle). The curve E, which joins all of these marks, is a parabola, and rejnesents the time-curve of a body moving at an uniformly accelerated rate. The curve of velocity can be constructed by marking Fig. 36.— Curves of the movement of a falling body. MOVEMENT 53 off from each time-division a distance which represents the space traversed by the ball in the corresponding interval of time. The small crosses mark the lengths of such a series of ordinates. Taken together they form the line V, which is the curve of velocity. Such a line is a straight one, but obliquely inclined, and expresses a velocity of uniform increment. Finally, the curve of acceleration is obtained by marking off on the ordinates, under each of the time- divisions, the excess of velocity of each period over and above that of the one which precedes it, that is to say, the excess of the second over the first, and the third over the second ; in other words, the incre- ment of velocity, or acceleration, in a series of time intervals. A large black dot marks the length of each of these ordinates ; the dots united together by the line A constitute a straight horizontal line showing the acceleration was uniform.* In constructing these figures, the unit of time was represented as any interval. This method answers very well in comparing the relative degrees of speed and acceleration ; but to ascertain the exact degree, these indefinite intervals must represent a second, the recognized unit of time. The chronometric dial provides us with the means of doing this in the same manner as the divided scale measured in meters and fractions of meters the space traversed by a falling body. Thus chronophotography provides us with the means of constructing the curves of movement. * On account of a mistake in the diagram (Fig. 35), the degree of acceleration is half what it ought to be. CHAPTER IV OHRONOPHOTOGRAPHY ON FIXED PLATES Summary. — Object of chronopbotograpby ; principles of the method ; measurement of time and space — Influence of the extent of surface covered by the object which is to be photographed ; influence of the rate of movement — Geometrical chronophoto- graphy — Stereoscopic chronophotography — Method of multiply- ing the number of images without producing confusion — Alter- nating images— Separation of the images on the photographic plate ; separation by moving the apparatus — Sei)aration by em- ploying a revolving mirror. Since the object of chronophotography is to determine with exactitude the characters of a movement, such a method ought to represent the different positions in space occupied by a moving object, i.e. its trajectory, as well as define the various positions of this body on the trajectory at any particular moment. Let us suppose that an ordinary photographic camera is directed towards a dark background, that the lens is uncovered, and that a ball, brightly illuminated by the sun, is thrown across the field of the objective. Luring its passage this ball leaves an impression on various parts of the sensitized plate, and on examining the plate there is found a continuous curved line which exactly represents the path taken by the luminous ball (upper curve. Fig. 36). If we repeat this experiment, but only admit liglit into the dark chamber in an intermittent fashion, and CHRONOPHOTOGKAPHY ON FIXED PLATES 55* at regular intervals of time, an interrupted trajectory will be obtained (lower curve, Fig. 36). This repre- sents the successive positions assumed by the moving object at eacb moment when light is admitted. This is the chronophotographic trajectory. In this method the ii^tervals of time separating two images are of constant and known duration. To obtain the best possible results, the object must be brightly illuminated and the background absolutely dark. The duration of the exposure must be very brief, in order that the object may not move an ap- preciable distance during a single admission of light. P iG. 36. — Simple trajectory and chronophotograpbic trajectory of a bright ball moving in front of a dark background. The original form of the chronophotographic appa- ratus was very simple. It consisted of an ordinary camera and lens. AVithin the body of the camera, in front of the plate, a fenestrated diaphragm was fixed. This rotated at a perfectly uniform rate by means of a crank and regulator. The sensitized plate was held in a frame and fixed in a position so that the object was focussed accurately upon it. As each slit in the diaphragm came into position, the plate received an impression of the illuminated object, representing the actual form and position of the object at that particular moment. Now, as the object became displaced between successive exposures, a series of impressions was ob- tained exactly corresponding to the shape and position 56 MOVEMENT of the object in the various phases of motion. The interval between each image was exactly of a second, and the duration of the exposure of a second. A metre rule with very clearly defined divisions was placed in front of the screen, and in the same plane as the object. The image of this rule reproduced on the sensitized plate served as a scale to measure the real size of the object, and the spaces traversed during each period of of a second. Instead of depending on the absolute regularity of the movement of the diaphragm as a means of measuring the time relations, it would be better in experiments requiring great accuracy to make use of the chronometric dial (Chap. I., Fig. 12). Thus in the experiments on falling bodies described on page 51, the intervals of time between two successive exposures were measured by the angular distance through which the needle moved between two successive images. This proceeding, like that in which the tuning-fork is employed as a mechanical means of registering the rate of movement of the paper, permits of the diaphragm revolving at any speed required. The degree of speed can always be ascertained by referring to the position of the needle on the dial. As for the measurement of space, the image of a divided scale serves, as we said, for measuring the various distances on the photographic plate. But, since all measurements made from a reduced scale necessitate a series of calculations before the real dimensions are ascertained, it is very desirable to find some means of avoiding these tedious calculations. This may be done by enlarging the images, by means of a projection lantern, until the object assumes its actual dimensions, i.e. until the measuring scale on the screen’ appears to be exactly one metre in length. In this case all the dimensions of the image can be directly CHRONOPHOTOGRAPHY ON FIXED PLATES 57 measured. Such chronophotographic pictures contain the two necessary elements for understanding a move- ment, namely, a notion of space as well as that of time ; nevertheless, as we shall see, it is often difficult to harmonize two such incompatible notions without having recourse to certain expedients. Influence of the Extent of Surface covered by the Moving Object. — If the object under observation covers only a small surface in the direction of movement, a large number of images may be obtained without super- position or confusion, as, indeed, we noticed in the case Fig. 37.— a man walking. Chronophotography on a fixed plate. of the moving ball. As far, then, as time is concerned we have a very complete picture, whereas that of space is very restricted. Now, if Ave take a series of images of a man walking, the question of space becomes a most complicated one. Each image must be spread over a considerable surface if it is to shoAV the various positions assumed by the head, arms and legs. Noav, the larger the space covered by the image, the smaller must be the number that can be taken on one plate without superposition and confusion, Witli a large animal, a horse for instance. 58 MOVEMENT Fig. 39.— a man runniDg. Cbronopliotograpliy on a fixed plate. The figures of the runner are much further apart, although the frequency of exposure is the same in botli cases. If tlie runner were to come to a standstill, the images would become superimposed. Sometimes such the number of images has to be very limited, for the length of each, measured in the direction of movement, is so great that they readily overlap, as in Fig. 38. Fro. 38.— Arab horso at a gallop. The large surface covered by each image causes almost complete superposition. Influence of the Rate of Movement. — In different speeds of translation, the number of images which can be taken in a given time Avithout producing confusion, increases as the former become greater. This may be proved by comparing a series of images of a runner (Fig. 39) with those of a man merely walking (Fig. 37). CHRONOPHOTOGRAPHY ON FIXED PLATES 59 a superposition of images can be put to practical use. Thus it gives greater intensity to those images which represent the movements of least rapidity. One of the very first applications of photography to the study of movement was suggested by Messrs. Onimus and Martin, in the year 1865. These investigators exposed the heart of a living animal, and took a photograph of it by leaving the lens permanently uncovered. The photograph was found to have a double outline repre- senting the two extreme positions of contraction and Fig. 40,— a boxer represented in tlie two extreme positions of a movement. dilatation. At these two periods the heart remains momentarily motionless, and its configuration is imparted to the sensitized plate, whereas no clear impression is left of it during the intermediate phases of motion. jMr. Demeny had recourse to this method, which had fallen into unwarranted oblivion, and with which even he himself was previously unfamiliar. In study- ing pliysical exercises, lie took tlie photograpli of a man in the act of boxing in front of a dark screen. 60 MOVEMENT His photograph showed two particular attitudes clearly- defined, and from them Fig. 40 was produced; the latter shows the boxer preparing for a movement, and his position immediately after completing it. The intermediate phases of movement were so rapid that they left no appreciable impression on the plate. Fig. 41.— Man dressed in black, with white lines and points for the chronophotographic study of the movement of the important parts of the body. Geometrical Chronophotography. — This confusion from the superposition of images sets a limit to the applica- tion of chronophotography on fixed plates, yet in many cases, by means of certain appliances, this difficulty may be overcome. The most obvious method CHEONOPHOTOGRAPHY ON FIXED PLATES 61 consists ill artificially reducing tlie surface of tlie object under observation. Such parts of tlie object as are not wanted in the photograph are blackened and thus rendered invisible ; on the other hand, those portions, the movements of which are to be studied, are picked out in white. Thus a man dressed in black velvet (Fig. 41), with bright stripes and spots on his limbs, is reproduced in the photograph as a system of white lines, which indicates the various positions assumed by the limbs. In the diagram thus obtained Fig. 42. — Images of a runner reduced to a system of bright lines for representing the position of his limbs. (Geometrical chronophotography.) (Fig. 42), the number of images may be considerable, and the notion of time very complete, while that of space has been voluntarily limited to what was strictly necessary. Stereoscopic Chronophotography. — In Chapter II. we discussed the method of obtaining stereoscopic pictures of figures described by straight or curved lines moving in space. A series of separate images was thus obtained, that is to say, they were produced by intermittent exposure of the objective. This was done with the double object of explaining the method of producing figures in relief, alid of showing the 62 MOVEMENT successive positions occupied by tbe line which en- gendered them. Now, if the intervals between the exposures are precisely equal, we have an example of stereoscopic chronophotography, and consequently a complete expression of the movement. This method is applicable in a great many cases * in w hich we w^ant to know whether the moving object moves in one plane only or in three. ■ Method of multiplying the Number of Images without producing Confusion. — The applications of chrono- photography are, as w^e have seen, limited by inter- ference from superposition and consequent confusion. Now^, the larger the space covered by the object, and the slower the movement, the sooner does superposition occur. Thus, if the sjDace is large and the movement slow, recourse must be had to certain measures, if we want to obtain a photograph of the various positions occupied in space. One method consists in taking alternating images, another in separating the images on the plate by making them fall on different parts. Alternating Images. — To obtain these, a stereoscopic apparatus with two lenses is employed, both of which are controlled by the same diaphragm. Such a diaphragm should be circular, and contain only one slit, which, as it rotates, alternately admits the light first by the right and then by the left lens. Two series of images will be thus obtained, which lie in two parallel lines. The upper series corresponds to the odd numbers, and the lower to the even numbers, as is shown below — 1 3 5 7 9 2 4 6 8 10 In this way Fig. 43 was obtained, which show^s the various positions of the wings as assumed by a seagull during flight. CIIRONOPHOTOGRAPIIY ON FIXED FLATEB 63 Only live different positions can be represented in a single series without confusion. Now, thanks to the two series, which are the complements of each other, the number of images is doubled^ and the succession of movements represented by them can be followed by passing alternately from the odd to the even number in the natural order, as is indicated by the small arrou s in the diagram. Fig. 43. — Alternating images for multiplying the number of positions afforded by cbronopbotography. It is almost unnecessary to add that these images do not constitute a stereoscopic series, for they are taken successively, and the single slit of the diaphragm never exposes more than one of the two photographic plates. Separation of the Images on the Photographic Plate. — When the object, of which successive images are to be taken, coniines its movements to one particular spot, confusion and sujierpositlon are bound to occur. This 64 MOVEMENT difficulty, however, can be overcome by a variety of expedients, one of which is already known to us, and which depends on the horizontal and forward move- ment of the photographic plate. In speaking of the photographic registration of the variation of Lippmann’s electrometer, we showed how successive images of the illuminated column of mercury formed a continuous series, owing to the onward movement of the plate. This mode of repre- senting the various phases of electrical variation is entirely comparable to the mechanical registration of a movement by means of a needle which traces its record on a moving strip of paper. This kind of sejDaration would be applicable in a great number of cases if it did not require a special and rather complicated apparatus, namely, that of a movable slide and a clockwork motor. But with an ordinary apparatus a similar separation can be obtained by imparting an onward movement to the image itself while the photographic plate remains in position. In order to effect this, a rotatory movement round its own axis must be communicated to the apparatus itself between the periods of exposure. The principal optical axis of the objective is thus displaced in a horizontal plane ; and the image of a man standing- in front of the dark screen will consequently be displaced in a corresponding direction on the plate itself. If this man executes certain movements in the same spot, thus constituting a variety of attitudes, or if he advances excessively slowly, his successive attitudes, instead of being confused and superimposed, will constitute a series of disconnected images, ranged side by side, as if he were moving at a moderate pace in a horizontal direction in front of the dark screen. But it may be urged that the. conception of space CHRONOPHOTOGRAPHY ON FIXED PLATES 65 is false, because a variety of attitudes on the same spot are reproduced in the photograph as if they were onward movements. The real position of each movement must be located in the diagram. This can be done in the following way : — By the side of a man jumping about on the same spot, or walking slowly, a white and perfectly motionless object is placed just in front of the dark background. The images of this object will be arranged in a consecutive series on the T Fig. li.— Rotating mirror for separating the images of an object which moves too slowly. plate. Now, as it is known that these positions corre- spond to a fixed point, they serve as a means of estimating the real positions occupied by the man at the time of each exposure. Such a movement im- parted to the apparatus is a very simple means of obtaining a consecutive series of chronophotographic F 66 MOVEMENT images, but it is difficult to ensure perfect regularity of movement.* A better method of producing the same result consists in reflecting the image of the object by means of a revolving mirror. The image thus be- comes deflected before it enters the camera. The mirror, silvered by Foucault’s method, rotates on a vertical axis, and by means of clockwork it is easy to ensure a uniform movement. Any speed that is desired can be obtained. By these different ways of separating the image, the range of chronophotography on fixed plates can be considerably extended. For thus we are enabled to record movements executed on the same spot, or of extreme degrees of slowness. At the same time the method ceases to be applicable when the duration of the movement is greatly prolonged, when a large number of images are required, or when the dimensions of the plate will not contain the images. Neither is it applicable when the moving object is dark and the background light. Eecourse must then be had to a new method. This is chronophotography on a moving plate ; it will be described further on. * Another inconvenience presented by this method is that there is a risk of the apparatus itself introducing a soui'ce of error. For the circular diaphragm rotating at a great rate tends to preserve its own plane of rotation, and consequently to become distorted when exposed to sudden movement. CHxVPTER Y DESCRIPTION OF THE APPARATUS Summary. — Construction of the apparatus— Slide, object-glass, circular diaphragms — Erection of the dark background at the physiological station — Dark background for photographing objects in water — Photography of light objects in darkness or in a red light — Colour of objects, and way of illuminating them — Disposition and pre- paration of the dark field — Choice of the object-glass — Focussing — How to take the photographs. Chronophotographic Apparatus. — An ordinary photo- graphic camera can be used in chronophotograj)hy, provided that it is furnished with a diaphragm which gives very short periods of exposure at regular in- tervals of time. For this purpose the simplest arrange- ment, and the one we originally employed, is a disc which is provided with small foramina, and which revolves in a slot cut in the mounting of the objective. The disc is made to revolve by a system of pulleys and a continuous chain worked by clockwork and controlled by a good regulator. But there is a diffi- culty in combining a clockwork motor and a photo- graphic camera, as well as in changing the disc from time to time, as the rate and frequency of the exposures may require, and this has induced us to abandon so clumsy an aj)paratus. We determined to construct a special instrument at once portable and capable of being regulated as desired. Such an ar- rangement is the more necessary because there are 68 MOVEMENT certain niovemeiits which cannot be chronophoto- g'raphed on a fixed 2)late, and ^^•hich must be rejDre- sented as a series on a long photographic film, which can be unrolled at the back of the camera. The chronophotographic camera, as shown in Fig. 45, meets all the above requirements ; but, for the present, we must be content to describe only those parts which are necessary for taking photographs on fixed plates. The apparatus consists of two halves united by bellows. The hinder part slides on a rail Fio. 45. — Arrangement of an apparatus adapted for all the purposes of chrono- photography (scale by means of a screw-rack for convenience in focussing, and into this part the dark slides are introduced. The objective is contained in a box (Fig. 46) which is cleft beneath, and accurately fitted so as to slide into the front part of the apparatus. The cleft under the box is continued into the mounting of the objec- tive, and thus divides the object-glass perpendicularly to its principal optical axis, and allows room for the fenestrated diaphragms. Tlie latter by their revolu- tions regulate the intermittent exposures. One end of the bellows fits into the box containing the objective, while tlie other, attached to the hinder part, com- DESCRIPTION OF THE APPARATUS 69 Fig. 4G.— Objective mounted in a sliding box. Below can be seen the opening for the passage of the circular diaphragms. which contains both the ground-glass plate (rig. 47) and the negative (Fig. 50). The only parts which call Fig. 47, — Frame with ground glass for focussing in chronophotography on fixed plates. for special description are the circular diaphragms, and the shaft wliich serves to comnumicate movement to 70 MOVEMENT them. These diaphragms rotate in opposite directions, and as two foramina pass each other an exposure occurs, and the plate is illuminated. By this arrange- ment we can employ discs of small size, and conse- quently greatly reduce the total dimensions of the apparatus. In fact, the dimensions need not exceed the size of an ordinary (24 x 30) camera. The shaft, which determines the revolution of the diaphragms, receives its own motion from wheels, which are worked Fig. 48.— Darlv slide for negative. by a crank. At present, however, we have no space for a detailed description. Now, in focussing, the position of the slide must vary considerably, and the two parts of the apparatus must be more or less separated from one another. The shaft must therefore be able to accommodate itself to these changes in distance, and for this reason is composed of square tubes, which slide one within the other with what is technically called a telescopic action. Erection of a Dark Background for Chronophoto- graphy. — The principles of clironophotography on DESCRIPTION OF THE APPARATUS 71 fixed plates demand that the objects, of which the movements are to be studied, should be the only ones to appear on the sensitized plate, and that the back- ground should not throw a single ray of light into the apparatus. A black velvet curtain may be used for this purpose, provided that the sun does not shine directly upon it, for all substances, however dark their colour, reflect a certain amount of light when strongly illuminated. Chevreul pointed out that the only means of obtain- ing absolute darkness was to blacken the inside of a box, and make a hole in one of its sides. By the side of this dark hole all black material illuminated by the sun appears to be coloured. The nearest approach we have been able to make to these ideal conditions of Chevreul was by constructing a dark and capacious shed (Fig. 49) at the Physiological Station,* the in- terior of which has been painted black, and by hanging a black velvet curtain at the back. The opening of the shed is eleven metres long by four in height. This opening is so situated that the sun cannot penetrate into the interior. * This establishment, by permission of General Assembly and the Municipal Council of Paris, was set up in Princes Park (Park des Princes). Here it is possible to carry out certain researches which would be impracticable in laboratories of the ordinary kind. Such a field for research exists as yet nowhere else. There is a long circular track, perfectly horizontal, and five hundred metres in circumference ; on this the ordinary paces of men and large animals can be studied. By means of a dark background, it is possible to apply chronophoto- graphy on fixed plates to the analysis of long-continued movements. A background, uniformly illuminated, and of even surface, offers facilities for chronophotography on moving films. Registering dyna- mometers, spirometers, pedometers, and various apparatus for the measurement of objects under observation are devoted to the study of human locomotion. In addition, pneumographs, sphygmographs, and cardiographs enable the investigator to study the effect of athletic exercises on the functions of organic life, and to follow step by step the improvement under training. Finally, there is an enclosure, where various kinds of animals can be reared in liberty, and where their normal and modified locomotion can be studied at pleasure. 72 MOVEMENT 111 front of the opening there is a track ])aved with blackened wood, along which, when it is necessary to analyze any particular kind of movement, the man or animal is made to walk. Theoretically, an indefinite number of images may be taken in front of a dark background without any impressions of outside objects appearing on the plate. Practically, when several hundred successive images of a luminous object have Fig. 49. — Arrangement of the dark background at the Physiological Station. In front of it there is a small chamber running on rails for keeping the apparatus. Above the dark background a framework is arranged for holding the camera at a distance of 1 2 metres, when it is necessary to photograph from above. been taken, the plate sometimes appears ‘‘fogged” in the areas which correspond to the dark background. This proves that a small quantity of light emanates from this source. The ajipearance of “ fogging ” curtails the duration of development, and diminishes the intensity of the image. The slightest reflection DESCRIPTION OF THE APPARATUS 73 of light from the dark background must be prevented, because, however feeble may be the light from this source, since it alfects the sensitized plate every time the objective is uncovered, the ultimate sum of these insignificant elfects will finally become appreciable. One of the important factors in obtaining a good negative is a pure atmosphere. Particles of dust floating in the air, when illuminated by the sun, form a sort of luminous haze, which interferes with the clearness of the photographic field. The effect is very noticeable when a horse at a quick pace passes along the track which stretches in front of the background. The track should therefore be kept moist, the soil in the neighbourhood should be turfed, and the inside of the shed kept scrupulously clean. It often hapjDens, however, that the rays of the sun, although they do not penetrate directly into the interior of the shed, nevertheless impinge on the ground which surrounds the entrance, and thus become reflected on to the velvet curtain; the darkness of the photographic field is in consequence considerably reduced. Even if the ground of the shed is composed of asphalte, it is as well to stretch a strip of velvet over those portions of it which are directly illuminated by the sun.* In any case, the chances of light being reflected are minimized by reducing the opening of the shed to the smallest possible dimensions. It seldom happens that the range of movement under observation equals the whole length of the shed, which measures eleven metres in this dimension. Often, too, it is unnecessary to utilize the entire height of the opening, which measures four metres. This can be reduced by means of blinds and * An arrangement which would bo perfect, but of which the resources of the Physiological Stationjlo not admit, would be to lower the level of the ground inside the shed, so as to make it impossible for sunlight to reach it. 74 MOVEMENT black curtains to the smallest dimensions, thus augment- ing the darkness. The majority of experiments do not require such large backgrounds, and can be carried out quite easily under the best conditions. A square box of 0‘50 metre side, lined inside with black velvet, makes an excellent background, especially when the opening in the box is limited in size. In this way photographs can be taken of the movements of small animals, and, generally speaking, of all small objects. The photographs in Chapter II. were taken in front of a box of this kind. They show the figures described in space by a Avhite thread moving in all three directions. Dark Background for photographing Objects in Water. — For the study of the locomotion of fish, and of other movements taking place under water, the objects to be photographed must be themselves brightly illuminated, while their surroundings are in total dark- ness. For this purpose a rectangular tank with glass sides is placed in front of a dark background ; the bottom of the tank is similarly made of glass, and through it the sunlight is allowed to enter after being reflected from a mirror set at an angle on the ground. This arrangement is shoAvn in Fig. 50. Here it will be noticed that the glass tank forms part of an elliptical canal, so that the animals can move round and round, like horses at a circus. The canal is three-parts filled Avith AA^ater, and the transparent part is illuminated by means of an inclined mirror, Avhich receives the sun’s rays direct. The canal, mounted on a high table, is furnished with handles, so that it can be easily moved from place to place. It is set out in front of an open AvindoAV, through Avhich the sunlight can fall upon the inclined mirror. The apparatus is variously disposed according to the time of day, and the inclination of the DESCRIPTION OF THE APPARATUS 75 mirror so set that it reflects the sunlight vertically upwards through the tank. Thus illuminated, all objects floating in the water appear bright, but the water itself, if quite clear, is perfectly invisible. It only now remains to form a dark background by placing a black velvet curtain behind the transparent portion, and to prevent the entrance of any outside light. This is done by means of a light rectangular Fio. 50. — Dark backgroundyor the study of movements occurring in liquids. framework, pyramidal in form, and covered with a black material. The base of the frame envelopes the glass tank, and the other end receives the object-glass. An opening made near the top allows the experimenter to watch what is going on in the water, and to seize an opportune moment for taking the photograph (Fig. 51). Photography of Light Objects in Darkness or in a Red Light. — No dark background is needed at night-time. 76 MOVEMEN'J Vtc. 51. — Arrangement of the oxiieriinent for .stiulyiiig luovoinents la liquids. DESCRIPTION OF THE APPARATUS 77 or in a place illuminated by red light, provided that the object to be photographed is itself a luminous body, such, for instance, as an incandescent lamp ; the latter gives excellent results. L. Soret Avas the first to make use of this arrange- ment. At night, on the stage of a theatre, lighted only by a few red lanterns, he studied the movements of dancers, by fastening little incandescent lamps to their heads and feet. In this way Soret obtained some Fig. 52. — Arrangement employed by Messrs. Demeny and Quenu for studying (by means of chronopbotography) abnormalities in walking. very curious trajectories, in which the curves obtained showed a beautiful and regular interlacement. Messrs. Demeny and Quenu similarly made use of incandescent lamps in analyzing, by means of chrono- photogra2)hy, the characteristic gaits of afflicted Avith various kinds of lameness. A room in a hosj)ital Avas j)rovided Avith red AvindoAvs (Fig. 52), a track Avas marked out on the floor for the jAatient to walk on, and the aiAjDaratus Avas j)laced at a suitable distance. Incandescent lam^Ds Avere fixed 78 MOVEMENT to the joints of the legs, to one of the slionlders, and to the head of the subject. These lamps were con- nected with the battery by means of a carriage, which ran along wire rails, and accommodated itself to the various movements. The negative obtained consisted of a series of bright spots corres|oonding to the succes- sive positions of the different lamps. By connecting the points by straight lines the geometrical chrono- photograph of the gait was obtained.* The combined use of red illumination and the electric light has infinite variations. For instance, if one arranges a powerful electric search-light so that the beams are directed across a room illuminated by red light, only the objects shown up by the electric light will produce a reaction on the photographic plate. Colour of Objects and Way of Illuminating them. — When the objects under observation are white, or of some colour that can be photographed, strong illumi- nation is all that is necessary for obtaining good results, because, if the background against which they are projected is quite dark, by slightly prolonging the process of development the images are made to stand out quite clearly. AVhen, however, the colour of the objects is difficult or impossible to photograph, it is necessary to colour them artificially. * As it would be very diflScult in this long succession of points to recognize those simultaneously formed, the following arrangement was designed : The diaphragm contained five fenestrations, and con- sequently produced five images for every complete revolution. Now, one of these fenestrations was made larger than the rest, and con- sequently the particular image produced by it was of greater intensity than the others on the plate, owing to the longer exposure. In such a negative one can see that in each series of spots every fifth spot is more accentuated than the intermediate ones. These are the main points which must be connected by straight lines, so as to represent in the diagram the axial position of the limbs at successive moments. As for the little intermediate points, they are not without their use, as by their degree of separation one can measure the rapidity of movement of the various joints. DESCRIPTION OP THE APPARATUS 79 In our attempts to represent, by cbronopbotographic means, the various changes in shape and appearance of an animal’s heart, as occurring in the auricles and ventricles, we met this difficulty in its extreme form, since the red colour of the muscles and of the blood made no impression on the photographic plate. By painting the surface of the heart with a solution of Chinese white we have found it possible to take a photograph of it, and we have obtained excellent results with very short exjDosures. We need say but little about the best conditions for illuminating the contour of objects. In this respect photographers 80 MOVEMENT have acquired sucli skill that ^\■e can do no Ijetter than borrow their methods. Generally speaking, olqects should be directly illuminated, but the dark background often makes lateral illumination necessary. When this latter means is employed, the contour of certain parts of the object may be very Avell defined, but others may be too much in the shade. This can be rectified by emjfioying reflectors properly inclined. To sum up, the iDroblem of illumination must be solved in a variety of ways, but it is chiefly of importance in those rarer cases, in which artistic etfects are the chief aim. Disposition and Preparation of the Dark Field. — The breadth which one must give to the background depends uj)on the extent of the movement, the various phases of which we want to follow. The opening must correspond to the amplitude of the movement in such a way that the least possible amount of light may enter the box. In the same plane as that on which the movement is to take place, a metre scale must be fixed, and, if there is room, the chronometric dial also. Lastly, the photographic apparatus must be placed just far enough off for the sensitized surface to correspond to the limits of the background. But to regulate this, the limits of the background must be visible on the ground-glass plate, and so they should be indicated by placing on them bright-coloured strips, or other striking objects. Choice of the Objective. — When the observed move- ment is strictly confined to one plane, any sort of objective can be employed, but it must be placed at such a distance that the image on the ground-glass plate assumes the proportions required. In this case it is better to use an objective of short focal length, since it admits a larger quantity of light. Under DESCRIPTION OF THE APPARATUS 81 otlier conditions, the use of objectives of short focal length is less convenient. If the object to be photographed has any depth, it will appear at different points of its course in different perspectives, that is to say, when the observer is only a short distance off. But this difference in perspective Fig. 54.— Changes wbicb occur in the perspective of a moving animal according to the distance off at which the photographic apparatus is placed. becomes less as the observer moves further away from the object. To take an example : Suppose a bird flies “ in front of a camera, and that we observe its positions, when it is to the left of the camera, when it is exactly opposite, and when it is to right (Fig. 54). In the first case the bird will be seen from the front, in the G 82 MOVEMENT second exactly from the side, and in the tliird from behind. These differences in perspective are less appreciable if the apparatus is removed further off, and the respective images become more easy to com- pare and to measure. But by moving the camera further away the images become smaller, and hence it is necessary to use an objective of greater focal length in order to obtain large enough images. We need say no more on this subject, since text-books on photography give most exact directions. Focussing. — The object is brought into focus on the ground-glass plate in the slide (Fig. 47). The apertures of the two diaphragms must be made to coincide by turning their axes with the hand, and the image is seen through an opening situated at the back of the apparatus above the crank.* How to take the Photograph. — Just as the aperture of the box is kept within strictly necessary limits, so too is the length of the exposure reduced as much as possible. If the sensitized plate be unnecessarily exposed before or after the end of the phenomenon, the intermittent exposure of the objective will allow access to the plate of small quantities of light, which tend to cause “fogging.” This inconvenience can be avoided by placing in front of the objective a special diaphragm, of the kind which is worked by pressing an indiarubber ball with the hand. This anterior diaphragm, when shut, makes it possible to open the shutter of the dark slide, to place the apparatus in order, and prepare for the experiment, the sensitized plate being meanwhile in darkness. At the moment the phenomenon commences, the * This portion of the posterior part of the apparatus contains a special chamber adapted for photographing upon a moving film, which will be mentioned later. It is through this chamber that the image can be seen upon the ground-glass plate. DESCRIPTION OF THE APPARATUS 83 iiidiambber ball is pressed, the anterior diaphragm opens, and the process begins. As soon as the phe- nomenon is over, the anterior diaphragm is again shut, and there is time to close the dark slide without any risk of the plate being exposed to detrimental illumination. CHAPTEK VI • APPLICATIONS OP CHRONOPHOTOORAPHY TO MECHANICS Summary. — Bodies falling in air — Ballistic experiments — The resist- ance of the air to surfaces variously inclined — Applications of chronophotography to hydrodynamics — Fluid veins; changes in shape of fluid waves; intrinsic movements of fluid waves — Currents and eddies — Influence of the shape of bodies placed in currents — Oscillations and vibrations — Rolling of ships — Vibrations of metal bridges. Bodies falling’ in Air. — To determine the movement of a falling body is one of the most difficult problems in dynamics. It may be said that Galileo’s classical experiment was the origin of all experimental mechanics, for it taught us that a force could be measured by the motion it imparted to a material body. Motion which is of uniform acceleration implies the absence of resistance; but when a body falls through the air, the resistance of the latter modifies the law of motion ; it increases as the square of the A^elocity, and finally becomes equal to the force of gravity itself. At that moment the fall becomes uniform, that is to say, the resistance of the air is equal to the weight of the body. Chronophotography would be a quick and easy method of measuring the resistance offered by the air to bodies of various forms, and moving with various degrees of velocity; but experiments of this kind APPLICATIONS TO MECHANICS 85 would have to be performed in a closed space protected from every current of air. If during the night-time a vertical beam from an electric lantern were allowed to illuminate the under surface of various-shaped bodies as they fell through such a space, chrono- photographic images representing the various stages of the fall could be taken on a plate at successive intervals of time.* But in the open air the least breath of wind disturbs the progress of the moving body, and if the fall is only a short one the resistance of the air has not time to make the velocity uniform, and more especially is this the case if the object is a very light one. In the experiment referred to on page 53, an indiarubber ball of 30 grammes weight and II centimetres in diameter was the object which was allowed to fall. After a descent of two metres the diminution in acceleration hardly manifested itself. But this diminution would have been very obvious in the case of a small and light air-ball. * The Machinery Hall at the Paris Exhibition of 1889 would have lent itself admirably to experiments of this kind. Tlie objects might have been allowed to fall from the dome of this immense building into a beam of light, and side by side with this beam a chain of incandescent lamps would have done excellently as a scale of distance ; and, further, a chronometric dial with a bright needle might have served to register the time. Experiments carried out in this manner would have been very interesting from the point of view of aerial locomotion — they would have controlled and amplified the beautiful researches which are now being conducted by our colleague and friend Cailletet and by M. Colardeau at the Eiflfel Tower. One could calculate the resistance of the air for any particular velocity by allowing an object to fall until, as shown on the photographic plate, the fall became uniform, because then the resistance of the air would equal the weight of the falling object. Now, in a series of experiments, by letting the same object fall through the air, weighted with ever-increasing ballast, so that the weight increased as the following progression — 1, 2, 3, etc., it could be seen at what velocity the fall became uniform. Since the resistance of the air is always equal to the weight, one could thus calculate for an object of any particular shape the law of aerial resistance for different degrees of velocity. 86 MOVEMENT Ballistic Experiments. — Clironophotugrapliy can re- cord the path taken by projectiles which travel slowly, and can show that the behaviour of sucli bodies is in Fig. 55. — The successive positions of a projectile in respect to two axes, one vertical, the other horizontal. accordance with the shape and the character of the propelling force. When a round projectile is thrown in a horizontal direction, the course taken is obviously parabolic ; it is, liowever, affected by the resistance of the air, as will soon be shown. If the projectile de^ Fig. 56.— Stick thrown horizontally with a rotatory movement in a vertical plane. parts from the circular form ; if, for instance, it is a stick which is thrown in a vertical plane with a rota- tory motion, the images of the stick Avill be found to lie in all directions, but the centre of gravity, i.e. the middle of the stick, will folloAv a parabolic course (Fig- 56). APPLICATIONS TO MECHANICS 87 In order that the phenomenon may appear more striking, let ns unite two bodies of unequal mass by a string and throw them, giving them a twist at the same time. These two bodies (Fig- 57) Avill rotate round each other like a star and its satellite, but neither one nor the other will follow a parabolic trajectory ; but Fig. 5Y. — Movement of a system of two balls bound together by a siring. the centre of gravity of the system, Avhich they together constitute, will move exactly in that path. Now, in experiments of this kind, one can show how the resistance of the air modifies the movement of the object. Let us examine, for instance, the trajectory of a round projectile, which is thrown in a horizontal direction. Let us construct a diagram of this move- J-6 >— fj 'I f f«-Q .r 1 " -o t-c ^ ^ -< — s > — ^ / t — t 'V — V f Fig. 53. — Trajectory of a projectile in respect to two axes (negative image). ment (Fig. 58), and let us find the relationship which each position of the object bears to two axes at right angles to one another. If the resistance of the air does not interfere with the horizontal movement forward the latter should be uniformly maintained. Now, if the last section in the horizontal direction be measured 88 MOVEMENT with compasses, and compared with the earlier ones, an appreciable remission in velocity will be noticed. In the same way, if the rate of fall be measured, its degree of acceleration will be found to have diminished under the influences of aerial resistance. We have even noticed in another experiment that if an object is allowed to fall vertically and then thrown in a hori- zontal direction from the same altitude, the duration of the vertical fall is not the same in the tAvo cases. But in the second the resistance of the air has a greater retarding effect. This experimental result struck Captain Uchard, who was present at the Physiological Station when the experiment was tried. Applying this knowledge, which he believed to be neAv, to the question of the motion of artillery projectiles, he found by calculation that the resistance offered by the air to their descent was quite different, according as they were simply let fall in a vertical direction, or were provided with an initial velocity.* Resistance of the Air to Surfaces variously inclined. — The constant attempts that have been made to con- struct flying machines prove that a complete know- ledge of the action of the air on inclined planes, travelling at different velocities, and at various angles, is essential for success. Clever experimentalists have succeeded in constructing small, light machines which, when let go in the air, glide about, something after the manner of a soaring bird. The eye can hardly follow the evolutions, as they are complicated, sinuous, and combined with an ever-changing inclination of the axis of the system. A sheet of Bristol board folded length- ways so as to form an obtuse angle, elevated at the back and pointed in front, was weighted by means of a * A. Uchard, EemarJcs on the Laios of Resistance of the Air. Paris, Berger-Levrault. 1892. APPLICATIONS TO MECHANICS 89 steel needle run through the longitudinal fold. This little flying apparatus was allowed to fall in a vertical direction, and its chronophotographic trajectory taken by a series of exposures at intervals of of a second. Fig. 59 shows a reverse tracing of this trajectory, and must be read from the right-hand top corner down- wards and towards the left. This object falls at flrst vertically, with an accele- rated velocity ; but it is soon influenced by the rudder-like action of the curved portion behind, and swinging round advances in a horizontal direction, then by degrees it assumes an upward tendency. At Fig. 59,— Chronophotographic trajectory of a flying apparatus describing a sinuous curve in the air (20 images to the second). this moment the speed decreases, its axis rights itself, and becomes set in almost a vertical position. Next the axis approaches to a horizontal direction, the card takes a new plunge with the apex directed downwards, and is about to turn upside down in a new phase of accelerated velocity, only at this moment the experi- ment comes to a sudden termination. All these extraordinary evolutions, which nowadays are perfectly familiar to “aviators,” after long and patient researches, are explained by them as following the laws of Avanzini and Joessel, Avho showed that if a thin lamina of any substance were obliquely propelled DO MOVEMENT ill a Hiiicl, the conditiuns of its equilibrium were modi- fied ill accordance with the velocity of movement, and in accordance Avith the angle formed betAveen the axis of the lamina and the direction of movement. We cannot noAv dAvell upon the interpretation of these experiments, Avhich ought to be studied in a methodical manner.* It is only necessary to indicate hoAv chrono- photography may assist in researches of this kind. Applications of Chronophotography to Hydrodynamics. — The study of the movements of fluids is very difficult, and can only be accomplished by resorting to par- ticular methods. Thus Savart illuminated a fluid vein by an electric spark, and observed the changes in shape ot the drojis of fluid, as well as the distances traversed by them. Mr. Boys, ajiplying instantaneous photography to this study, obtained excellent results, in Avhich t]ie appearance of the fluid vein Avas reproduced by means of very short flashes of the electric light. In a moving mass of liquid, extremely complex phenomena occur ; changes of surface shape, and intrinsic molecular dis- placements. The phenomena can be represented in the form of chronophotographs. Let us consider the conditions represented in Fig. 50, Avhere the Abater is contained in a tank with glass sides, and is illuminated from below by sunlight reflected by a mirror situated beneath the tank, and on a level with the ground. If the AA^ater is perfectly clear, the sun- light is transmitted through it Avithout any escape in the direction of the photographic ajDparatus, except from that part of the surface AA'hich Avets the side of the glass near the observer. In this situation capillary attraction causes the formation of a concave meniscus Avhich extends all along the side of the glass. The light which traverses the Avater suffers total reflection * See The Flight of Birds, cliaix xi.v. Paris, G. Masson. 1890. APPLICATIONS TO MECHANICS 91 from the under surface of the meniscus. On the ground glass of the camera a very brilliant and fine line may be seen marking the level of the water, and which, moving with it, will imprint all the undulations of the water on the photographic negative. Any internal displacement of the water can be made visible by suspending small and brilliant objects in the water, and illuminating them by the sun’s rays. For this purpose pieces of wax and resin are mixed in the required proportion, the former being less dense than water, and the latter of greater specific gravity. From this solid material a number of small balls are moulded, and then silvered over, in the same way that pills are silvered by the chemist. These bright balls should be slightly heavier than water, so that when they are droj)ped in it they slowly sink to the bottom. If a small quantity of salt water be afterwards added, the balls gradually rise up and remain in unstable equi- librium. A paper scale, divided into centimetres, may then be gummed on to the side of the tank above the level of the fluid. This scale, which will appear in the photographs, will do very well to measure the extent of the movements which are being photographed. With such an arrangement a large number of experi- ments with liquids can be carried out. A few of them are here represented in the form of photographs. Changes in Shape of Fluid Waves. — The bright line which marks the level of the fluid shows, on shaking, variations in contour such as those afforded by vibrating strings. The ventral segments and nodes sometimes occupy fixed positions on the surface of the water, as occurs in the case of a choppy sea. Sometimes they advance with varying velocity, as in rolling breakers. A similar chopping motion can be set up in the water by plunging a solid cylinder into the tank at regular intervals, and thus imparting 92 ]\rOVEMENT regular oscillations to the water. These rliythmic movements should be in that part of the tank which is furthest removed from the point of observation. The lens of the camera should be left permanently open, so that the bright line may leave a track corresponding to all the positions assumed, but with greatest intensity where the velocity is least, that is to say, in the immediate neighbourhood of the dead points which correspond to the crests and troughs, for here, just before changing its direction, the movement is at a minimum. If one wishes to have a better appreciation of the changes in velocity during the different phases of a simple oscillation as represented by the contour of a wave, recourse must be had to chronophotography. In other words, the admission of light must be very brief, and the intervals of time perfectly regular. The successive positions of the level of the fluid will thus be obtained. These positions will be represented as curves, which will be further apart at the centre of the oscillations and closer together in the neigh- bourhood of the crests and troughs. If the rhythm of the movement is changed by gradual acceleration, another variety of “ chopping ” commences, in which the waves are shorter. In each case the profile of the wave, as it passes along in crests and troughs, takes the form of “trochoids,” a name invented by those interested in hydraulics. Waves moving onward, billows, and breakers, can be taken by chronopho- tography, so as to show the speed at which they travel, as well as the changes in size and shape which occur in them. We took a photograph of a wave by disturbing the water in the tank in the following way: — The cylinder described above was immersed in the water just to the right of the transparent part of the tank APPLICATIONS TO MECHANICS 93 in siicli a way that the cylinder itself did not appear in the photograph. The cylinder was lifted out and somewhat sharply plunged again into the liquid, and meanwhile a series of photographs was taken, repre- senting the phenomenon at the commencement of the operation. At first there was a progressive series of Fig. 60.— Chopping waves of very short period. depressions visible along the surface of the water, corresponding to the moment at which the cylinder was lifted up, and then a marked upheaval at the moment the cylinder was again plunged into the water. This upheaval travelled along with diminish- ing amplitude, more or less interrupted by smaller Fig. 61. — Advancing wave. secondary waves, which advanced with the primary one. The velocity of the wave could be estimated by measuring with a scale the distance travelled by the summit of the wave during the period of one-tenth of a second, Avhich represented the duration of the interval between each successive exposure. Progres- sive waves showed incomplete contours when the chronophotographic method was adopted, and that was because the hinder surface of the wave was the 94 MOVEMENT bost Biarkod, and soniGtiinGs iiidGGd tliG only portion visiblo.* Intrinsic Movements of Fluid Waves, — A number of tlie bright beads previously spoken of should be thrown into the tank and the water disturbed, so as to create either waves or a chopping condition. The trajectory of these beads in different parts of the Fig. 62. — Molecular movements within a simple chopping wave. waves can then be seen in the photographs, and consequently the intrinsic or molecular movements which occur in the same situations. In Fig. 62 is represented the appearance of a simple chopjiing wave as viewed from the side. Within this wave the mole- cules are seen oscillating, vertically in the ventral seg- ments, horizontally at the nodes, and obliquely in the Fig. 63. — Molecular movements within a series of chopping waves of short period. intermediate positions. To follow the phases of this movement with greater facility the waves should possess a very short period, for there the molecules may be seen describing curves, the centres of which are at the nodal points. These facts confirm the analytical studies of my colleague Boussinesq. * It seems that, owing to the advance of the wave, tlic meniscus disappears from the advancing surface of tlie wave, that is to say, from the anterior side. APPLICATIONS TO MECHANICS 95 In the case of waves which travel in an onward direction, billows, and breakers, the molecular move- ment is different. For instance, in one photograph, taken after the sudden immersion of the cylinder, the surface molecules are seen to describe parabolic arcs in planes parallel to the direction taken by the waves. The deeper they are in the fluid the less definite are the curves described, and sometimes the direction of the movement is almost in a straight line. When the cylinder is moved with a to-and-fro movement, the molecules describe curves on the surface of the fluid which are complete rings. In all such experiments, the nature of the impulse imparted to the water so modifies the character of the movement that in order to obtain exact results the force must be applied by mechanical means instead of by the hand. Currents and Eddies. — Owing to the circular form of the tank, it is possible to set up a continuous flow by means of a small screw immersed in the water. The latter, however, must be placed out of sight of the observer. The little bright beads will participate in every movement set up in the water. The chronophotographs will, at any given moment, show the successive positions of these shining bodies, which will thus serve as indices of the path taken and of the velocity acquired by the various currents set up. An obstacle, consisting of a sheet of glass, was placed in the current, making an angle of about 45° with the axis of the stream. The glass was so arranged that it touched the walls of the tank, and only presented its edge to the chronophotographic objective. A photograph was taken during a period of three seconds, and the number of images taken was forty-two to the second. On examining this photograph (Fig. 04) it was 96 MOVEMENT discovered that the various currents reached the obstacle in a more or less oblique direction, and that near the lower edge of the inclined plane the currents divided in conformity with Avanzini’s theory. At the back of the obstacle tlie behaviour of the currents was variable. The velocity of the molecules in the different Fig. 64. — Changes in velocity and in direction which occur in the liquid molecules of a current which meets an inclined plane. parts of the basin must be deduced from the distance which separates any two consecutive images. The latter are sometimes fused together in the form of a continuous trajectory, and thus demonstrate the sluggishness of the current. On the other hand, when widely separated, the intervening distances can be measured with a scale. Each interval represents of a second in time, and hence the absolute velocity Fig. 65. — Effects produced on a current by the immersion of a solid rectangular box. of the stream can be calculated. It is equally easy to determine the behaviour of the currents when they meet obstacles of different shape. For instance, if a rectangular box is placed in the stream (Fig. 65), of the same width as the tank, and provided with a glass top and bottom, the currents which meet it become deflected from their course, and pass with increasing rapidity APPLICATIONS TO MECHANICS 97 above and below. Behind the obstacle they form a number of eddies. We have also investigated the effect of a current of water coming in contact with a body of pisciform shape, that is to say, a solid body, the section of which tapers off unequally at the two extremities.* Fig. 66. — A current meeting a pisciform body at its thick end. Experiments of this kind demonstrate in the case of fish the mechanism of swimming. They might also be useful for ascertaining experimentally the shapes which offer least resistance, either in the case of bodies im- mersed in flowing water or of those moving in still Fig. 67. — A current meeting a pisciform body at its small end. water. The conditions, according to most authorities, are reversible. The extent to which eddies occur, or, in other words, the loss of energy, may be regarded as a measure of the resistance offered to bodies immersed in a current. * In order that the light might pass up through such a body, the sides were made of ebony, and the superior and inferior surfaces of celluloid — the contour of a fish being preserved throughout. The light which passed through the layers of celluloid was sufficient to illuminate the bright beads which happened to pass above the obstacle, and consequently their images appeared in the chrono- photographic negatives, and showed the paths taken by tlie various eddies. H 98 MOVEMENT Now, it can be seen that if a fish-shaped body presents its thick end to the moving water the currents track along the sides, thus minimizing the deviation of the stream (Fig. 66) ; but if the direction of the current is reversed, so that the water comes in contact with the pointed end, the water having passed the midship-frame, falls into strong eddies (Fig. 67). This experiment confirms the opinion already held, that a ‘‘ pisciform ” shape is the most favourable one that a fish could possess, since the Avater offers very little Fig. 68. — Fluid wave surmounting an obstacle. resistance to such forms as have the pointed end at the posterior extremity.* When a stream rushes violently against an opposing obstacle situated near the surface, the water rises up in a heap, and falls down on the other side in a cascade. This transient phenomenon, the details of which are not visible to the eye, can be registered in all its phases by chronophotography, and in a photograph the successive phases of the heaping up of the water, as it comes in contact Avith the obstacle, are shoAAm by the variations in the water-level, while the bright beads serve as an index of the molecular moA^ements in the depth of the basin. This brief enumeration of the applications of chronophotography for the analysis of * Ohronopliotography might, it appears to us, be applied to the study of movements in air when one wanted to find the resistance otfered by a body of particular shape to a current of greater or less velocity. For this purpose a number of light and luminous objects would have to he set floating in the air. APPLrCATIONS TO MECHANICS 99 moving fluids will suffice to demonstrate the resources of the method,* Oscillations and Vibrations. — When a pendulum swings, the suspended mass is acted upon by gravity alternately in two directions, so that the mass alter- nately presents positive and negative phases of accelera- tion, dependent, as is nowadays well known, on the continuous action of gravity. This is true also of e Fig. 69. — Jointed pendulum: an oscillation from right to left following on a half oscillation from left to right. those vibratory movements in which the elastic force of a vibrating rod takes the place of gravity in an oscillating pendulum ; but in some cases the conditions of movement are so complicated that it is difficult to foretell exactly what the oscillations will be. This * Hydraulic engineers might also perhaps have recourse to chrouo- photography when they want to prove certain points in their theories concerning waves and currents, and even when working out the effect of different kinds of propellers. This they might do by observing the movement transmitted to the molecules of the fluid by the propellers. 100 MOVEMENT liappens in the case of jointed pendulums. The alter- nating swing of our lower extremities in running and Avalking is also of this nature, for while the thigh swings from the hip joint, the leg swings from the knees, and the foot from the ankle. The movements which act and react upon one another produce very complicated results. Fig. 69 shows hoAV chronophoto- graphy can reproduce all the details. The Vibration of Flexible Rods. — A distinguished officer ill the French army occupied in studying pro- blems in ballistics, was anxious to discover whether the transverse vibrations of the barrel of a gun were Fig. To.— A^'ibrations of an elastic and wooden rod. transmitted to the extremity of the weapon. He was under the impression that, in vibrations of this kind occurring in flexible rods, they were ecpially felt along the entire length, and that even in the last segments the vibrations still occurred in the form of curves. The experiment, made by means of chronophotography, showed that this was not the case. Transverse vibra- tions imparted to a rod were represented at the terminal segments as rectilinear discursions (Fig. 70). The Rolling of Ships. — The so-called “ rolling ” of ships presents a very complicated series of problems, involving, as it does, not only the oscillations of tlie boat itself, but also the moA'ements imparted to it hy APPLICATIONS TO MECHANICS 101 the waves of a rough sea. If the characteristic move- ments of a boat in still water can be approximately calculated beforehand, those on a rough sea can only be ascertained by actual trial. Chronophotography readily lends itself to researches of this kind. Experiments with floating objects, shaped more or less like boats, show that it is easy to discover the centre or the temporary centres of the rolling. By placing a little model boat in front of a dark back- ground, and by attaching bright objects to the mast, a series of dotted lines is obtained by means of chrono- photography, each of which represents one of the successive phases of rolling, and indicates the position of the mast ; but if these dots are joined up so as to form continuous lines, and the latter are then produced until they intersect below the level of the water, the exact centre of oscillation can be determined for any particular moment, provided, of course, that the points of intersection are accurately obtained. If the floating- object be cylindrical in shape, the oscillation takes place round the axis of the cylinder, but in other forms, especially if the object is provided with a keel, the oscillation takes place round centres which are con- stantly changing. A celebrated French marine engineer assisted us in making some researches on the rolling of ships under more practical conditions ; the experiments were carried out with small models which represented the commoner types of ship. Similar researches may be carried out at the seaside ]jy fixing electric lights to the* mast-heads of boats, and by taking photographs of them during the dark- ness of night. Vibrations of Metal Bridges. — M. Deslandres * has * Deslandres, “Action of Rhythmic Shocks upon Metal Bridges,” Annales des Fonts tt Chausi^ee, Dec., 18tl2. 102 MOVEMENT just made some interesting- experiments on the re- sistance of metal bridges, by means of stylography and chronophotograf)hy. He recorded vibrations which proved that the metal arches of bridges were subject to periodic strains. The diagrams showed that, if the steps of a horse harnessed to a carriage harmonized in rhythm with the natural vibrations of the corresponding arches, the vibrations of the latter continued to increase in amplitude, until the oscillation of the bridge became thirteen times as great as when the carriage simply remained at rest on the bridge. We regret that we can do no more than simply mention this remarkable fact. We cannot here extend the applications of chrono- photography beyond the study of mechanical phe- nomena. The reader will doubtless realize for himself, from the instances already quoted, that such applica- tions are extremely numerous. CHAPTEK VII CHRONOPHOTOGRAPHY ON MOVING PLATES Principles and History of the Method Summary. — Janssen’s astronomical revolver — Muybridge’s experi- ments : luminous background — Photographic cameras arranged in series — Control of the instantaneous shutter hy electrical means— Photographic gun — Internal structure of the instrument — Method of changing the photographic plates — Principles of chronophotography on moving plates — Employment of chrono- photography — Necessity for arresting the progress of the film at the moment of exposure — Moment to choose for taking the photograph — Form and dimensions of the photographs — Regula- tion of the m;mber and dimensions of the photographs — Repro- duction, enlargement, and reduction of chronophotographs. Since the invention of pliotograpliy it has served as a means of comparing the present with the past by the lielp of authentic reproductions. In a series of portraits taken at different periods of life, anybody can see the changes wrought by time upon the features of any particular face ; an engineer can survey from afar the progress in the work of constructing a building, and a farmer the cultivation of his land. Mr. Janssen was the first who, for the purposes of science, thought of taking by automatic means a series of photographic images to represent the successive phases of a phenomenon. The honour is due to him of having inaugurated Avhat is nowadays called chrono- photography on a moving plate. It was proposed to take a series of photographs of 104 MOVEMENT the planet \eims as it passed across the sun’s disc, and tor this pui’2)ose onr learned colleague constructed his astronomical revolver. This instrument contained a circular sensitized plate, Avhich at stated interA^als rotated through a small angle, and at each turn Fig. tl.— Facsimile of the print of a photographic plate obtained with the astrono- mical revolver of the transit of the planet A^enus across the sun, Dec. 8, 18T4 (by M. Janssen). received a iieAv imj^ression on a fresh portion of the plate. The photograph (Fig. 71) which AA^as obtained by this means consisted of a series of images arranged in a circular fashion ; each image represented a neAv position CHRONOreOTOGRArHY ON MOVING PLATES 105 of the planet during the period of transit, and each was separated from its neighbour by an interval of seventy seconds. In this photograph the dark silhouette of the planet stood out in strong contrast against the white background formed by the sun’s siu-face. In the first of the series the disc representing the planet projected beyond the solar limbus, but in the third coincided with it. Mr. Janssen made the further suggestion of applying a photographic series to the study of animal locomotion.* It remained for Mr. Muybridge, of San Francisco, to discover, by means of a rather different method to that of Janssen, the analysis of equine locomotion, as well as that of man and various animals. Muybridge’s Method and Apparatus. — Mr. Stanford, formerly Governor of California, believed that the various positions of a horse in executing its different l)aces could be reproduced by means of photography. * This is how our colleague expressed himself in 1878: — “The characteristic of the revolver is that it alfords an automatic means of taking a series of photographs of the most variable and rapid pheno- mena in a sequence as rapid as may be desired, and thus opens up for investigation some of the most interesting jjroblems in tlie physiology and mechanics of walking, flying, and various other animal movements. “ A series of photographs of any particular movement, comprising the entire cycle of events, would be a most valuable means of elucida- ting the mechanism involved. In view of our present ignorance on the subject, one could imagine the interest of possessing a series of photographs representing the successive positions of a bird’s wing during the act of flight. The principal difficulty would arise from the sluggishness of our photographic plates, for images of this kind require the very shortest exposure. But, doubtless, science will over- come difficulties of this kind. “ From another point of view, the revolver may be said to present the reverse picture to that of the phenakistoscope. M. Plateau’s phenakistoscope is designed for the purpose of reproducing the effect of a movement, or of an action, by means of a series of views, which represent the component phases of the movement or action. The photographic revolver gives, on the contrary, an analytical repro- duction of the movement by representing in series its elementary phases.” — Bulletin de la Soci€t€ Francaise de Photoqraphie, Dec., 1876. 106 MOVEMENT and determined to Imve experiments made on the subject. lie was fortunate enough to secure the services of Mr. Muybridge, Avho obtained immense success in photographing different kinds of paces. A description has been given of these experiments in a work published under the auspices of Mr. Stanford, by Dr. Wellmann:* ^^^^The scene of the operations was a track which Fig. 72. — Field of operations arranged by Mr. Muybridge. On the left there is an inclined screen -which reflects the sun’s rays, and before which the horse passes. On the right there is a series of photographic cameras. Some other cameras mounted on trestles enable the operator to obtain simultaneous photographs of a horse from various points of view. passed in front of a white inclined screen, and so situated that it reflected the sunlight in the direction of the photographic apparatus (F ig. 7 2). The screen Avas marked Avith divisions at equal distances, Avhich, when reproduced in the jihotograph, served as a means of measuring the distance traversed by the horse. A series of cameras Ai as draAvn up opposite to this * The Horse in Motion, as slioicn hy Instantaneous Photography. London, Turner & Co., 1882. CHRONOPHOTOGKAPHY ON MOA'ING PLATES 107 measure the extent of the limb movements. 108 MOVEMENT tra(;k, and electric wires ^\'ere stretched across the patli at intervals. Tliese latter communicated with electro- magnets, each of Avhich held the shutter of one of the cameras tightly closed. The horse, in following the track, broke these wires one after the other, and brought about the instantaneous opening of the cor- responding shutter, each exposure allowed a photograph of the animal, in one or other of its positions, to appear on the plate. These valuable experiments settled certain points with regard to the paces of a horse in motion, about Avhich there had been, even among sj>ecialists, great divergence of opinion. Muybridge’s figures demonstrate the successive movements of the horse’s limbs, as well as the corresponding position of its body. The extent of the movement can be measured bv means of the «/ divisions marked on the screen (Fig. 73). In an album kindly presented to us by Mr. 3Iuy- bridge, one can see how all kinds of equine paces are rejDresented, as well as those of the bull, the stag, the dog, and the pig. Instantaneous silhouettes of men running, jumping, and wrestling, present certain attitudes which are very interesting from the point of view of artistic reproduction of such movements.* The Photographic Gun. — After tlie introduction of instantaneous photograp)hy, it seemed to us that the movements of a flying bird could be analyzed by this method. We therefore asked Mr. Muybridge to make use of his apparatus to study the flight of birds. He hastened to accede to this request, and when he came * In Mr. Muybridge’s first work he only used the old-fashioned wet- plate system. The discovery of the dry gelatine plate, sensitized with bromide of silver, allowed him latterly to pursue his studies under more favourable conditions, and to publish magnificent plates of animals in motion. During late years, M. Ottomar Anschiitz (of Lissa) has obtained, by Muybridge’s method, a very beautiful series of photographs showing men and animals in motion. CHRONOPPIOTOGRAPHY ON MOVING PLATES 109 Fig. 74.— The photographic gun 110 MOVEMENT to Paris, in August of 1881, lie brought us several prints of pigeons photographed in part of a second. Each of these photographs represented a number of flying pigeons in different positions, one with its wings raised, another with them in front, and another with them depressed. These positions appeared to us to coincide almost exactly with those which we had predicted from studying the mechanism of flight by the graphic method.* But beyond the fact that these photographs were not sufficiently clear, they failed in that which gave so much interest to those of the horse in motion, namely, the arrangement in a series which showed the successive attitudes and positions. This is because it is impos- sible to ajDply, in the case of a bird in free flight, the method which succeeded so well in the case of a horse, and which depended on the animal itself opening a series of photographic shutters. We determined to invent an apparatus based on the same principles as that of M. Janssen, but capable of giving a series of photographs at very short intervals of time, — of a second instead of the 70 seconds which separated the photographs of the astronomical revolver — so as to procure the successive phases of the move- ments of the wings. This instrument, gun-like in form (Fig. 74), made it possible to follow the flight of a bird by aiming at the object in the ordinary manner. The moment the trigger was pulled the sensitized plate received an impression, then moved on only to receive another, and so on, but always stopping each time that the opening of the shutter allowed the light to fall on the plate.f * “ The Graphic Method,” p. 211. t The following are the details of the construction. The barrel of the gun is a large blackened tube (Fig. 75), which contains an ordinary photographic lens. At the hindermost part, mounted firmly CHRONOPHOTOGRAniY ON MOVING PLATES 1 1 1 Fro. 75.— External appearance of the photographic gnii. 112 MOVEMENT The gelatine plates, sensitized with bromide of silver, Fig. 16. — Details of the interior of the photographic gun. on which the photographs were taken, were cut with a diamond to a circular or octagonal shape, as is shown at the butt end, is a large cylindrical breech which contains the clock- work mechanism. The axis of the breech is seen projecting at B. When the trigger is pulled the wheels begin to rotate and transmit the necessary movement to the diiferent parts of the instrument. A central axis, which revolves 12 times in a second, controls tlie move- ment of all the individual parts of the apparatus. In the first place (Fig. 76), there is an opaque metal disc provided with one small opening. This disc constitutes the shutter, and only allows the light, which passes through the objective, to gain an entrance 12 times in a second, and then only for a period of ytu second. Behind the first disc there is another provided with 12 openings whicli rotates freely on the same axis as the first, and behind these, again, there is room for the sensitized plate, which may be circular or octagonal in shajje. This fenestrated disc should rotate inter- mittently so as to come to rest 12 times in tlie second just opposite the beam of light wliich penetrates the instrument. CHEONOPHOTOGRAPHY ON MOVING PLATES 113 ill Fig. 78. In tliis photograph the successive positions of a flying gull are shown at intervals of Fig. 11. — Special box for holding the photographic plates. of a second. These little images, when enlarged by projection, furnish curious details with respect to the position of the wings, and the torsion of the remiges An eccentric, E, placed on the central axis, produces this intermit- tent rotation, by transmitting a regular to-and-fro movement to a rod which is furnished with a catch, 0. At each oscillation this catch is held by one of the teeth which form a sort of circlet round the fenes- trated disc. A special shutter, 0, etfectually prevents the light from penetrating into the instrument as soon as all twelve photographs have been taken. There are other arrangements for preventing the sensitized plate from passing, by reason of its acquired velocity, the position assigned to it by the catch, and where it should remain perfectly still during the period of illumination. A pressure button, b. Fig. 75, is brought into close contact with the plate, as soon as the latter is introduced into the gun. Under the influence of this pressure the sensitized plate sticks firmly to the posterior surface of the fenestrated disc, which is covered with india- rubber to prevent it slipping. The object is brought into focus by elongating or shortening the barrel, and thus removing or approximating the lens, and finally the process is corrected by looking with a microscope through an opening, 0, made in the breech of the gun, and obsciwing the definition on the ground glass. I 114 MOVEMENT by the resistance of the air, as is shown in Fig. 79 ; but in the majority of cases the images are too small to stand enlargement. To obtain larger images, certain authors, among others, M. Londe and General Sebert, have constructed an apparatus furnished with multiple objectives, the shutters of which open in succession. But such a Fig. V8. — Photograph of a gull during flight. Keproductlon by means of Heliogravure of a cliche obtained by means of the photographic gun. multiplication of objectives is productive of serious difficulties. Besides making the instrument very costly, especially if objectives of good quality are used, photographs are produced which, taken from different points of view, are incapable of comparison. This is not the case with photographs of small dimensions taken at a short distance. These cameras CHKONOPHOTOGEAPHY ON MOVING PLATES 115 regard, if one can use the expression, the object from different points of view. Now, these variations in perspective, although presenting few difficulties when operating from afar on objects of large size, would make the study of small objects at close quarters a matter of great difficulty,* still less would they permit one to photograph objects of microscopical size. For this reason Ave determined to employ a single objective. In order that we might simplify the instrument as much as possible, we united in a single apparatus all the accessories necessary for chronophotography on fixed or moving plates, as well as for regulating at will the frequency and duration of the exposures. Fig. 79.— Enlargement of one of the photographs obtained with the photographic gun. Principles of Chronophotography on Moving Plates. — The weak point of the photographic gun was princi- pally that the images were taken on a glass plate, the weight of which was exceedingly great. The inertia of such a mass, which continually had to be set in motion and brought to rest, necessarily limited the number of images. The maximum Avas 12 in the second, and these had to be very small, or else they would have required a disc of larger surface, and consequently of too large a mass. These difficulties may be overcome by substituting for the glass disc, a continuous film very slightly coated with gelatine and bromide of silver. This film can be made to pass automatically Avith a rectilinear move- ment across the focus of the lens, come to rest at each * See Chap. v. p. 81. 116 MOVEMENT period of exposure, and again advance witli a jerk. iV. series of photographs of fair size can be taken in this way. The size we chose was 9 centimetres square, exactly the right size to fit the enlarging camera, and by which they could be magnified to convenient propor- tions. Now, as the continuous film might be several metres in length, the number of photographs that could be taken was practically unlimited. Arrangement of the Chronophotographic Apparatus. — The necessary elements for taking successive images on a continuous film are united, as we have said, in the apparatus already known to the reader. The back part of this apparatus has a special compartment, the photographic chamber (Fig. 80), in which the sensitized film is carried. To admit light, all that is necessary is to substitute for the frame which carries the fixed plate another frame provided (Fig. 81) with an aperture, the size of which can be varied at pleasure. This is the admission shutter. At each illumination the light f- !?1 . CHKONOPHOTOGRAPHY ON MOVING PLATES 117 passes through this aperture, and forms an image on the moving film, which has previously been brought into focus. The film unrolls itself by a series of intermittent Fig. 81. — Admission shutter which is substituted for the dark slide when working with a roll of film. The size of the aperture can be regulated by the side screens E E according to the dimensions of the intended image. movements, by means of a special mechanical arrange- ment, which enables it to pass from one bobbin to another. The arrangement of these bobbins must first occupy our attention, for the possibility of loading Fio. 82. — Two metal bobbins for carrying the sensitized film. The two bobbins are placed In different positions : the letters H and B indicate respectively the upper and lower parts. or unloading in the light is dependent on their construction. The bobbins are made of metal, and two projecting ])lates are fixed to the two ends of a light cylinder. The upper of these plates is thin and the lower one 118 MOVEMENT thick. The bobbins rotate on a vertical pin which runs through their centre. A circle of little holes bored in the lower plate of the bobbin forms part of the motor mechanism. When a peg fixed in a revolving plate enters one of the holes of the other plate, the two Avill rotate together, carrying the bobbin with them. One of these bobbins serves to store the sensitized film, which is rolled round it, and Avhich is finished off at the ends by strips of opaque paper pointed at the extremities. One of these pointed ends fits into a slit made lengthways in the bobbin, and the rolling up can Fig. 83. — Showing how the film is lengthened at its two extremities by the opaque bands of paper. thus be effected. In the process of rolling, the strip of paper comes first, then the sensitized film Avhich is joined to it, and then the second strip of paper. An elastic band put round the bobbin keeps the entire roll securely fastened. This operation is executed in the dark room, but as soon as it is finished the charged bobbin can be carried into the light, for the sensitized film is protected by the coils of opaque paper. Charging the Apparatus. — On opening the photo- graphic chamber, two vertical pins may be seen (Fig. 80) ; that on the left receives the supply bobbin, the filling of Avhich has already been described, and that on the right is for the receiving bobbin — that is to say, the one Avliich will receiA^e and roll u]) the film, or CHRONOPHOTOGRAPHY ON MOVING PLATES 119 as much of it as has beeu used in taking the photo- graphs. That this may work proj)erly, the end of the strip of paper which is last wound round the supj^ly bobbin must be fixed in the slit of the receiving bobbin. The method of rolling is rej)resented in Fig. 84. The two bobbins being placed on their respective pins, the strip of paper passes through a vertical slit, and through which it keeps running, pulling the sensitized film after it. Two pressure rollers (r r. Fig. 80) are applied to the surface of the bobbins to ensure regularity in rolling and unrolling. Fig. 84,— Supply bobbin ready charged. M, the end of the paper which covers it, must be unrolled and wound round the receiving bobbin, R, in an opposite direction. We shall not describe the mechanism which produces the intermittent movement of the film. The new arrangement which we have adajited to the apparatus for making the operation more certain, and its employ- ment more easy, differs noticeably from that which we have described before.* It would be better for the beginner, instead of relying on a written description, to make a few experiments with a strip of ordinary paper in place of the sensitized film, and thus he would soon acquire proficiency in filling the bobbins, and passing them quickly into their proper chamber. * Revue Gd’n&ale des Sciences, November 1.5, 1891. 120 MOVEMENT A crank placed behind the chronophotographic apj)aratiis turns all the wheels of the instrument, as well as the circular diai^hragms. A movement, so rapid as this must necessarily be, is iDound to be continuous, for it would be impossible, as in tlie case of the photographic gun, to remit or continue the movement of such heavy bodies. The film itself comes to rest at the moment of exposure, arrested by a special mechanism which allows it to continue its movement as soon as the image has been taken. Necessity for arresting the Progress of the Film at the Moment of Exposure. — Some people have thought that, by using such a complicated apparatus as that which we have employed for arresting the movement of the film, we have given ourselves unnecessary trouble, and it has been said that for very short exposures the move- ment of the film might be neglected. It would be easy to prove by calculation that, during the period of the exposure, say yooo ^ second, the film would move enough to deprive the photographs of that clearness upon which their value depends. But it is simpler and perhaps more convincing to show by an experiment that without these periods of arrest good images are not to be obtained. By alternately suppressing and inducing an arrest of the film at the moment of exposure, we obtained a series of images which were alternately blurred and distinct. In Big. 85 two such consecutive images are shown. The different degrees of definition is so obvious that it is useless to further insist on the necessity of arresting the film during tlie period of exposure. The Moment to choose for taking the Photograph. — When the chronophotographic apparatus is pointed at the object the movements of which are to be studied, the Avheels are put in motion by turning a crank. continue taking photographs until the bobbin is exhausted. Shape and Size of the Photographs. — The shape and size of the photographs should be in conformity with the character of the subject, so as to utilize to the best advantage the surface of the film. For this purpose the opening of the admission shutter should be regulated to meet the requirements of the case, and the position of the apparatus correspondingly altered. Thus the photograph of a man in an upright position CHRONOPHOTOGRAPHY ON MOVING PLATES 121 the different parts acquire a uniform speed, but the film remains stationary until the moment when the observed phenomenon takes place. At this juncture the operator presses the trigger, the film begins to move, and the photographs are taken as long as the pressure is maintained on the trigger ; as soon as the pressure is remitted the progress of the film is arrested. The employment of this trigger makes it possible to Fig. 85. — Two successive photographs taken on a sensitized film. The image on the left is taken without arresting the onward movement of the film at the moment of e.xposure ; that on the right is taken with the film at rest. 122 MOVEMENT Fig. 86.— Sword-stroke. The series must be read from below upwards. CHRONOPHOTOGRAPHY ON MOVING PLATES 123 executing movements on the same spot should be taken on a surface the height of which is greater than its breadth ; on the other hand, two men occupied in fencing would require an opening the breadth of which is greater than the height (Fig. 86). The same is the case in taking successive photographs of a man rowing. The background of the image should be regulated by reducing the opening of the admission shutter to a greater or less degree. When the images occupy most space in the horizontal direction the camera should be turned over on its side ; the successive attitudes should then be viewed by beginning at the top and travelling downwards. Regulation of the Number and Size of the Images. — If the progress of the film is uniform, and allows, say, ten large images to be taken in the second, twenty images half the size may, if necessary, be taken in the same time, or thirty images a third of the size, and so on. To effect this, the size of the admission shutter must first be reduced to one-half or one-third of its normal size. It is important that the circular diaphragni should permit at the same time the exposures to be twice or three times as numerous. The fenestrations in the diaphragm should, therefore, have curtains which can be drawn aside or closed as required.* Reproduction, Enlargement, and Reduction of the Photographs. — The size which we have selected for chronophotographic images (9 x 9) is, as we said, precisely that adopted for the plates used for enlarging- cameras. Each photograph can be thrown on a screen, if required for public demonstration. The strip of * In the arrangement we previously adopted, the number of times the film was brought to a position of rest had to be regulated by a very delicate manoeuvre; this was dispensed witli in the new arrangement. 124 MOVEMENT Series ol photographs to sliow the successive pliuses of tlie movement of a wave. (Siniili-gravure, the photographs being reihiced to one quarter of their original size.) CHRONOPHOTOGHAPHY ON MOVING PLATES 125 film itself, or at least the series of positive images obtained from it by superposition on a similar strip, can produce a series of effects following one another in such rapid sequence that the spectator sees the move- ment reproduced in all its phases. This synthetical representation of movement will be described further on. For ordinary publication the images are reproduced by means of a special process called “ simili-gravure.” Most of the figures scattered in the text were obtained by this process. But as simili-gravure requires a special treatment of dotting, or hatching, to give the shapes of the shadows, it would be of no use for reproducing very small photographs of microscopical objects, nor for very graduated shading such as is required for the delineation of muscles. In these two cases we had recourse to impressions made with lithographer’s ink. When a long series of photo- graphs has to be reproduced, showing the successive phases of a phenomenon, plates of special size must be used, or otherwise only a small number of images can be obtained. If these photographs are reduced so as to suit the limitations of a page, they lose much of their merit and interest. This occurred in the case of Fig. 87, in Avhich eight reduced images are represented, each occupying one-fourth of the space occupied in the original plate. CHAPTER VIII HUMAN MOVEMENTS Ehom the Point of View of Kinetics Summary. — Some movements in man; the study of them hy the graphic method — Speed of different paces in man ; relationship between the frequency and length of stride — Duration of the rise and fall of the foot in walking and running — Path described by any particular part of the body during different paces; mechanical means of recording it — The study of movements in man by means of chronophotography on fixed plates; long- jumping ; high-jumping — Skilled movements, fencing, etc. — Jumping from a height — The swing of the leg in walking. Some Movements in Man. — The ancients, who positively worshipped physical exercises, only understood them from the point of view of practical experience; they 'were entirely ignorant of the functions of muscles, blit they knew how to turn out a good runner or wrestler. Later on, as anatomy revealed the structure of the human frame and the muscular system, it was the current belief that the function of an organ was dejicndent on the shape or form, and in consequence a system of physical training was established on entirely erroneous theories. Doubtless it would have been wise to have retained the traditions which were founded on practical experience, until such time as Science was in a position to impose really useful amendments. It was not till the seventeenth century that Borelli HUMAN MOVEMENTS 127 threw some light upon the mechanism of animal locomotion.* This learned Neapolitan professor applied to the case of moving creatures the same mechanical laws which had recently been discovered by Galileo, and showed that the effect of muscular force made itself felt partly on the mass of the body, and partly on another mass which was called the point of resistance, and he reduced to its simplest form the general theory of locomotion. But, to impart some accuracy to the study of human movements, it was found essential to construct instruments to measure the range, velocity, and sequence of the various phases of movement, not only in walking, but also in running, jumping, etc. The force exercised in executing these different move- ments should also have been measured ; but the necessary instruments were not in existence. Two celebrated mathematicians, the brothers Weber, realized the necessity for accurate measurements, but inefficient instruments were all they had at their disposal. A level piece of ground of known length, a watch provided with a second’s hand, and a performer was all they had to work with ; they could therefore only obtain a small number of measurements with regard to the relationship between the frequency and length of stride, of the extent of the vertical head displacements and of the various inclinations of the body, and even then these measurements had to be corrected. With the assistance of the graphic method, we deter- mined to introduce accuracy into these studies, but it was chiefly by means of chronophotography that we arrived at a scientific interpretation of the various bodily movements. Before giving the results furnished by this method, * Borelli, De Motu Animalium. 128 MOVEMENT and thereby demonstrating its importance, it would be as well to briefly sum up the results of other methods. Such a review is the more necessary, because chronophotography has nothing to do with other methods, its application only becomes of real value when mechanical methods can no longer be employed. Speed of Different Paces in Man, Eelationship between the Frequency and Length of Stride. — A man in walking or running covers at each stride a certain amount of ground, and the more steps he takes in a given time the greater is the total distance he covers. Similarly, if the stride is increased, but the number kept the same, the distance will be proportionately greater. Speed, therefore, depends on two factors : the length and frequency of the stride. Kow, the brothers Weber enunciated, as the result of their studies, that the length of stride became greater as the frequency increased ; a slow, processional step, for instance, being shorter than one executed at a greater rate. If this were the invariable law, the march of troops might be indefinitely accelerated by quickening the time of the drums or trumpets which regulated the pace. But our experiments showed that this theory of the brothers Weber was only correct uj) to a certain point, namely, until the step was so quick that it amounted to a run, and after that point was reached the rate of progression soon diminished. Our experiments were made in the following manner : — Being fully persuaded that, if one wanted to estimate exactly the average length of stride, it Avas necessary to carry out the experiments on a long track, aa'c laid out at the Physiological Station a circular and perfectly horizontal course, five hundred metres in cir- cumference ; a telegraph Avire ran all the way round the track, and the posts Avere placed at interA^als of HUMAN M()Ve?([1':nts 121) M K Fig. 8S.~ Arrangement of the odograph and of the track at the Physiological Station. 130 MOVEMENT fifty metres. Each post was provided with a little contrivance for breaking the circuit the moment the performer came abreast of the post. Within the laboratory a recording apparatus — “the fixed Odograph” — was in communication with the telegraph wires. In this apparatus a needle traced a horizontal line upon the paper which covered a revolving cylinder, and every time the performer broke the circuit, as he passed a post, the needle was displaced for a moment from its course and executed on the tracing a rectangular inflection.* As these inflections were repeated every time the performer passed a post and completed a distance of fifty metres, it followed that, at the end of a given time, the odograph had described a zigzag curve which showed the rate of progression. Time is measured on the odographic curve by referring to the horizontal divisions, which are marked along the axis of the abscissae, and are numbered 0-16, each division representing one minute. The distance travelled is measured in metres along the axes of the ordinates. So that for every point of the curve the time occupied and the space traversed may be estimated by referring to the intersections of the vertical and horizontal lines. The relationship of these two values gives the actual speed. f Instead of the staircase line (a) traced by the odograph, it is better to draw a line connecting all the angular projections on the curve ; in this way were obtained the lines o, h, d, i, which express by their variation in inclination the speed of different paces. They represent a uniform rate nhen they are rectilinear, a variable speed when they are curved. So far we only know the rate of progression with its two factors — time occupied and space traversed — at each * See, for details of tlie experiment, La Nature, 1 887. t See C. E. de VAcad^mie, November 3, 1884. HUMAN MOVEMENTS 131 point of the curve. It was important from one point of view to know the number of steps taken. F or this purpose we placed in the centre of the track a bell which rang at regular intervals, and with which the performer kept time. The intervals could be regulated by means of a pendulum, the length of which could be varied at pleasure. It was situated inside the laboratory, and could control the rate of ringing for anything between 40 and 120 strokes a minute. The number of steps per minute being thus known, one could substitute in the odographic tracing the total number of steps taken for the time occupied, and by Fig. 89. — Chart of fixed odogvapli to show paces of different velocity. dividing the distance traversed by that number, Ave could arrive at the average length of stride. It Avas from such data that Fig. 90 Avas constructed. This diagram shoAved that the length of stride increased as the step Avas quickened, that is to say, Avhen the rate Avas betAveen 40 and 75 per minute. This Avas just as the brothers Weber had shoAved ; but Avhen the rate Avas quickened beyond that point, the length of stride decreased, and finally at 85 steps per minute and onwards the total rate of progression began to diminish. That is to say, the shortening of the step became so pronounced that in spite of the increase in frequency, the total distance traversed in a gwen 132 M0VI3MENT time was markedly diminislied. These experiments, which for the most part were carried out on marching troops, have been repeated on a large number of men of A^arioiis sizes, both with and without burdens, and in the case of veterans as well as in the case of recruits. The influence of various inclines on the length of ‘T ii.inute Fig. 90.— Curves to show the rate and length of the stride. stride was also investigated,* as, too, was the shape of the shoe both with respect to the length of the sole and the height of the heel.f All these experiments on running and walking were carried out on men, some of whom carried weights, Avhile others were unburdened. Exact results have been * Experiments on different kinds of tracks were made elsewliere than at the Physiological Station by a slightly different method. A track of known length, an automatic counter of the number of steps, and a watch with a second’s hand furnished the necessary appliances. t The length of a step does not entirely depend on the degree of separation of the legs : this would be the case if, as in the legs of a compass, they only touched the ground at two points; but the length of foot must be taken into consideration when estimating the length of a step, for the foot touches the ground first with the heel, while the toe is the last part to leave the ground. Thus in estimating the total length of the stride, the length of the foot which is extended along the ground must be added to it. It follows, then, that for legs of ecpial length, those which have the smallest feet take the shortest steps, and, similarly, that a short boot will have the same shortening effect. Finally, a high heel, by curtailing the total length of foot in contact with the ground, will also detract from the length of stride. HUMAN MOVEMENTS 133 obtained without the help of photography ; moreover, the latter method, although it could give exact details of any particular, for instance, as to the length of any stride considered by itself, could not furnish the re- quired averages. Mechanical Record of Movements in Walking. — We saw in Chapter I. how the duration and sequence of the rise and fall of the foot in walking could be re- corded by mechanical means. This chronographic re- cord was effected by transmitting through the medium of pneumatic tubes the pressure of the foot on the ground to the registering tambours. We showed the result of these observations, and shall now continue the investigation. In ordinary walking on level ground one foot leaves the ground as the other reaches it. In the case of a man who carries a weight, or who walks uphill, or mounts a staircase, the foot in contact with the ground does not leave it until the other has been in contact with it for some time. There is then a period, more or less prolonged, during which both feet simultaneously rest upon the ground.* In running, the body remains suspended in air for a brief moment between two successive contacts, and this suspension lasts longer as the speed of running increases. Path described by any Particular Part of the Body during Different Paces. — So extensive are the move- ments in walking, and even more so in running, that mechanical registration of these movements becomes very difficult, and, further, they nearly always take * By siibstituting electric for pneumatic signals, M. Demeny believed that be detected, even in ordinary walking, a short period during which both feet were simultaneously on the ground, and that this period was prolonged as the pedestrian became more tired. These results would be most important if, so to speak, they provided a means of measuring fatigue. 134 MOVEMENT place ill three directions of space, and thus require simultaneous registration by three curves. Nevertheless, our late pupil and friend, Carlet,* obtained, by the geometrical combination of three curves recorded simultaneously, the actual path described by a selected point on the body of a man walking. A movement of this nature can only be represented by a solid figure. Carlet used for this purpose a piece of wire tu isted in different directions. A flat figure, even with the help of light and shade (Fig. 91), can only give a very imperfect representation of a movement of this kind. Fig. 91. — The trajectory of the pubis of a man at a walking pace. A metal wire twisted in various ways indicates the variations of this curve in re.«pect to the three directious of space. Stereoscopic images alone are capable of giving a satisfactory picture of it. Now, we said in Chapter II. how easily images of this kind might be obtained. Fig. 14 shows a trajectory very similar to that laboriously obtained by Carlet. When it is a matter of registering all the details of a man’s movements, both as regards change of position and attitude of the body and limbs, mechanical registration is out of the question. It is at this point that chronophotography comes to the rescue. The Study of Movements in Man by means of Chrono- photography on Fixed Plates. — In Chapter II. we showed how to obtain on fixed plates a series of images corresponding to the successive phases of a movement, * Carlet, “Essai Experimental sur la Locomotion dc ITIomrae,” Annales des Sciences Naturelles, 1872. HUMAN MOVEMENTS 135 aud we gave as examples dironopliotograpliic repre- sentations of walking and running. Fig. 92 shows how a long-jiimp is executed. The figures in the photograph reveal attitudes which the eyes are not accustomed to see ; they express better than language the way in which the movement is executed, and allow the ditferent phases to be followed with ease. In certain respects they correct ideas which existed on the subject of the mechanism of jumping. Take, for instance, the theory which led teachers of gymnastics to recommend their pupils to land on the toes in order to break the shock on coming in contact with the ground. Our figures show, on the contrary, that in long-jumping it is the heels Avhich first reach the ground, and that it is the flexion of the legs and thighs that breaks the shock. To sum up, chrono- photography affords the means of understanding the real characters of a movement, and is therefore of value in teaching athletic exercises. Guided by photo- graphs of this sort, it is easy to imitate the style of walking or running set by the person who serves as a model, and to reproduce his method of extending or flexing the limbs, of swinging the arms, and of bringing the feet to the ground or removing them from it. It would be much more difficult to imitate these movements by merely watching the instructor, because, especially in rapid movements, the motions are so transitory as to escape observation. In Fig. 92 the number of images is only five to the second ; this, however, is sufficient to show the series of actions which must be accomplished in executing a jump of this kind. By looking at these images in the order of execution, it is seen that the jumper acquires by a preliminary run sufficient impetus to cover a considerable distance during the period of suspension. 136 MOVEMENT i Fig. 92 —Successive phases of a long-jump. (Chronophotography on a fixed plate.) HUMAN MOVEMENTS 137 At the moment of jiimj^ing, the leg in contact with the ground is violently extended, thereby imparting a vertical impetus to the body, at the same moment the arms are thrown up, giving additional energy to the effort. The successive images show the jumper after he has left the ground, with the arms elevated in front and the legs separated ; later on, the arms drop, and the legs are brought nearer together as they become more advanced in front of the body, so that finally the heels of both feet touch the ground together, and in front of the centre of gravity of the body. A fall on the face is thus obviated. At the moment of descent the legs are flexed, so as to counteract the impetus of the body. The distance cleared is more or less extensive, according as this series of actions is skilfully or clumsily executed, and according as the jumper lands advantageously on the ground or the reverse. If he has miscalculated his speed, and his feet are not sufficiently far advanced in front of him at the moment of landing, he cannot retain his balance, but has to run forward a few steps until the impetus is checked. In the case of pole-jumping (Fig. 93), it is equally easy to follow the various stages. The jumper fixes the end of his pole in the ground, and at the same time raises himself by a vigorous extension of the legs. The combined action of the vertical and hori- zontal imjDulses imparted to the body enables it to describe an arc of a circle. In falling, the body will continue this curve, and will land just as far in advance of the point of the pole as it was behind it at starting. But a skilful jumper can avail himself of an artifice which enables him to augment his jump considerably. It consists in elongating the radius of the circle 138 MOVEMENT i Fig. 93.— Successive phases of a pole-jump. (Chionophotogrupliy on a fixed plate.) HUMAN MOVEMENTS 139 described by climbing up tlie pole at the moment it passes the vertical, and then by inclining the body until it becomes almost horizontal, that is to say, at right angles to the radius of the circle described, the jumper falls naturally on his feet at a much greater distance from the starting-point. In pole-jumping, the initial impetus is not, as in the case of long-jumping, the only force upon which the extent of the jump depends ; but this distance can be augmented by manoeuvres of the jumper, who can make use of his arms by employing the pole as a fixed point of support while he is still in the air. F or a more detailed study of movements in physical exercises, recourse must be had to those outline or geometrical photographs of which we have already given an example in the case of a man walking. A man dressed in black velvet Avith bright lines down his arms and legs produces Fig. 94 as the result of a long-jump preceded by a preliminary run. Here all the phases of the movement are arranged in close series Avith no sudden transitions, because of the great number of images (tAventy-five to the second) taken during the jump. In order to render chronophotographs of movements more instructive, these images should be taken from very strong and competent athletes ; for example, from the prize-Avinners at athletic sports. These chamj)ions Avill thus betray the secret of their success, perhaps unconsciously acquired, and Avhich they Avould doubtless be incapable of defining themselves. The same method could equally Avell be applied to the teaching of movements necessary for the execu- tion of various skilled industries. It Avould shoAv hoAV the stroke of a skilful blacksmith differed from that of a novice. It AAwld be the same in all manual per- tormances, and in all kinds of sport. MO move:ment I'ic. 94. Incomplete photographs, namely, bright lines on dark-colonrcd clothing, are received on the ii.\ed plate C'.!5 imaco.s to tlie second). Fig. 95. — Fencing. Read from below upwards. 142 MOVEMENT From a series of diagrams of the kind, we have easily l)eeii al)le to follow the successive actions of a man mounting a bicycle. The study of these figures would be an excellent preparation for any one wishing Fig. 96.— Jrniip from a height with flexion of the legs to break the fall. to learn exercises of this kind. In all trials of strength, and in fencing, certain actions occur which the eye is unable to follow and language fails to express. If an attempt is made to teach them by executing them slowly, their whole character is completely changed- HUMAN MOVEMENTS 143 Here, again, a series of photographs, taken at the rate of 10 to 20 per second, helps to explain all the details of the movement. Unfortunately, we could not represent a whole series Fig. 97. — Jump from a height with stiffened legs. of this kind in the compass of this book, and we can only give a few fragmentary examples. We have already shown in Fig. 86 three successive jikases of broad-sword-exercise. Fig. 95 similarly shows three 144 MOVEMENT instantaneous views of two men fencing; Ijoth sets of combatants represented belonged to the Italian school. Geometrical photographs sometimes elucidate ex- tremely complicated movements. Thus, in jumping from a height (Fig. 96), the position of each point of the body, in its various phases of movement, is expressed by an almost continuous curve. The axes of the long bones make the figures more or less com- plicated, revealing movements the existence of which would never have been suspected from mere ocular observation. In jumping from a height, the difference between landing gently with no shock and landing with rigid legs is clearly seen by comparing Fig. 96 with Fig. 97. The latter corresponds to the drop with > stiffened legs, namely, in which the shock is not ’ broken by flexion of the legs. ; In complicated actions, a diagram can be obtained of only one part of a movement ; for instance, in A running it may only be necessary to observe the phases ^ of oscillation of the legs — this can be done by limiting ■ HUMAN MOVEMENTS 145 the diagram to the movements of the extremities in question. Fig. 98 shows the movements of a leg in running. The sets of dotted lines show at any par- ticular moment the angle formed by each segment with the vertical, as well as the path followed by each joint. In geometrical photographs, thanks to the great number of the images, the discontinuity of the phases almost entirely disappears, and the actual path followed by each part of the body can be seen represented almost as a continuous curve. These indications are most useful in studying movement from the point of view of dynamics, for by them the velocity as well as the acceleration of the body mass can be measured. L CHAPTER IX CERTAIN MOVEMENTS IN MAN From the Point of View of Dynamics SuaiMARY. — Object of dynamics — Measurement of the forces which play a part in human locomotion — Traction dynamograph — Dynamograph for expressing the amount of pressure exercised by the feet on the ground — Comhination of the dynamograph with a method of recording movements — The laws of ballistics as applied to the mechanism of jumping — Combined employment of dynamography and chronophotography — Mechanical work done in human locomotion ; work in the vertical direction ; work in the horizontal direction; work done in maintaining the move- ment of the lower limbs during their period of suspension — Relative amount of work done during different kinds of paces — Practical applications. The movement of a solid body, and the force which produces it, are necessarily closely associated, so that knowledge of movement implies knowledge of force, and vice versa. At the same time, in practice it is easier to measure force directly by means of the dynamometer. Now, in human locomotion, the forces which are concerned are ever variable quantities, and to thoroughly understand each individual phase, a registering appa- ratus which affords a continuous record must be em- ployed. Such an apparatus is called a “ dynamometer,” and indicates by the variations in its curve the amount of force which acts upon it at any particular moment. Dynamometers are constructed on the principle that CERTAIN MOVEMENTS IN MAN 147 an elastic body is distorted in proportion to the degree of force applied. We have endeavoured to use dynamometers of uni- form pattern throughout our researches on animal movements. And for that purpose we have always employed coils of indiarubber tubing, which were more or less compressed according to the external force applied. In consequence of tliis pressure, the contained air was more or less squeezed out into the chamber of a recording tambour. The coils of tubing of which the dynamometer is formed are wound concentrically like the spring of a watch. The central end is closed, and the peri- pheral or free end communicates with the chamber of a recording tambour. The coil itself is glued on to a disc of cardboard. This instrument goes by the name of “ The spiral dynamometer.” The tube used has a very fine bore with very thick walls, so that it can resist strong pressure Avithout bursting. The distortion or com- pression is A^ery regular, so that the lever of the registering tambour is practically raised to a height proportional to the force applied.* By modifying this spiral form, Ave Avere able to con- struct a traction dynamograph (Fig. 99). The latter apparatus Avas used for measuring the force exercised by horses Avhen differently harnessed. One of the ends was securely fastened to the vehicle and the other to the swing-bar. Traction on the part of the horses tended to approximate two discs, which compressed between them the turns of the spiral coiLf The air expelled * To obtain greater accuracy the instrument may be empyrically graduated by applying a series of regularly increasing weights, and marking off on a scale the corresponding discursions of the lever. t AVe proved by these experiments that, if the traction was applied through the medium of elastic traces, the gradual distribution of the shocks thereby occasioned effected a great economy in the force 148 MOVEMENT from tlie spiral readied the registering tambour liy means of a tube. In most acts of human locomotion muscular force manifests itself in the form of pressure ; for instance, this is the case when a man extends his legs from a previous position of flexion; as the legs become ex- tended, the body mass is repelled in an opposite direc- tion, because the feet, resting on the ground, offer a fixed point of resistance. In walking or running, the foot presses on the ground Fic. 99.— Traction dynamograph. with a force equal to that Avhich is expended in moving the body, so that by measuring at any moment the pressure of the feet on the ground, we also measure the force expended on locomotion. Our spiral dynamo- graph is a useful instrument for this purpose. Lynamographic Platform for Registering the Pressure of the Feet on the Ground. — A series of spirals, similar to those previously described, are arranged on an oak platform (Fig. 100). One of these spirals is left applied, and that this economy might even amount to 26 per cent, of the total motive force (Marey, Trav. du Lahoratoire, J875). Wiist found in similar experiments a saving of 22 to 33 per cent, in the work. Eingelmann has noticed an economy in work amounting to something like 50 per cent. CEKTAIN MOVEMENTS IN MAN 149 micovered so tliat the tube of which it is made can be seen, the others are placed between cardboard discs. xVll the tubes which lead from these spirals unite in a common collecting-tube which communicates with the chamber of the recording tambour. A plate held in position by metal clips accurately covers all these Ftc. 100,— Dynamographic platform for giving a curve of foot-pressure on the ground. spirals. Such is the general structure of the dynamo- graphic platform.* When a man mounts this platform the registering lever is raised to a variable height, and remains in the same position as long as he does not move. The discursion of the lever expresses the weight of the body ; but however slightly the man may move, the * C. Tl. de I'Acadcfnie des Sciences, October 8, 1802. 150 MOVEMENT amount of vertical foot-pressure (jii tlie platform is altered in amount, and is recorded on the tracing by the lever. The following is the law which governs the variations in pressure : — All muscular actions which alter the centre of gravity of the body in such a manner as to raise it augment the foot-jpressure on the ground. All actions tending to lower the centre of gravity diminish the foot-'pressure.* The dynamograph which measures the force can be employed conjointly with an apparatus for recording the actual movement. It can be seen, then, that mechanical actions accomplished by living creatures obey general laws — amongst others those of ballistics. Now, in order to determine the phases of a move- ment, two methods may be employed, either that of mechanical registration or that of geometrical chrono- photography. Mechanical Record of a Movement. — Movements, such as we shall have to deal with, are generally too extensive to be directly recorded by means of a tracing needle. In jumping, for instance, the head may be elevated any distance between 30 and 50 centimetres in a vertical direction. This movement must be reduced to such proportions as can be regis- tered on the surface of a revolving cylinder. This reduction can be effected by means of the elastic- thread method previously described (Fig. 29). If a man stands on the platform of a dynamograph, and wears a very tight-fitting cap, the elastic thread may be fastened at one end to the cap, and at the other to a solid support by means of a clip (Fig. 101). This thread may be fixed near its uj)per end to the lever * All elfects which are produced during the performance of a movement are followed, when the movement is concluded, by counter effects in the opposite direction. Fig. 101.— Method of simultaneously recording the foot-pressure on the ground and the changes in elevation of the body during a jump. 152 MOVEMENT of a tambour. '^Pwo recording tambours register two curves on a revolving cylinder, one the curve of foot- pressure, and the otiier that of the vertical discursions of tlie head. Examination of these curves, enlarged, if necessary, shows that in all respects the laws of animal move- ments conform to general laws— in this case to the laws of ballistics. The areas of the curves which are described by the D' Fig. 102. — Superior curves; changes of height in the head during the jump. The ordinates DC and DC' are proportional to the height of the jump. Inferior curves; pressure exercised by the feet on the ground. The shaded areas show the quantity of movement communicated to the body in the two jumps. dynamographic needle express the exact equivalent of the force employed in the effort of jumping, x^nd it is found that when two such areas differ, their ratio to one another is as the square root of the height jumped. If the area of the curves be the same, no matter what be the shajie, the heights of tlie jumps must be the same. If two men of different weights jump the same height, the areas of the dynamograpliic CEETAIN MOVEMENTS IN MAN 153 curves are in proportion to the weight raised. On comparing the curve of the height jumped with that of the dynamograph, it is found that it is not the absolute initial energy of the effort which conditions the height of the jump, hut the amount or quantity of force expended, namely, the product of the force and the duration of the effort ; in other words, the area of the curve. Sometimes the lowest jumps correspond to curves which show great initial effort, hut sustained only for a brief moment. In fact, areas of different curves, which represent jumps of equal height, may be infinitely varied ; a violent and brief effort producing the same effect as one initially feeble but longer sustained. Combined Employment of Dynamography and Chrono- photography. — Mechanical registration of movement is not always feasible ; for instance, in the case of a man walking, it is difficult to register all the movements of the different parts of the limb. Chronophotography comes to the rescue, and this method can be combined with the employment of the dynamograph. Let us suppose that we want to discover with what force the foot presses on the ground during the different phases of flexion and extension of the leg, provided, of course, that the foot never leaves the ground during the period under observation. The application of the chrono- photograph combined with the dynamograph, at once suggests itself, the former recording the movements executed by the leg during half a step (Fig. 103), and the latter the degree of pressure exercised during the same period (Fig. 104). It is now necessary to establish the connection between the various chronophotographic images and the corresponding elements of the dynamograj)hic curve. For this puiq^ose we must count in Fig. 103 the number of images which correspond to the phase 154 MOVEMENT of downward pressure of the foot. 'It is found to be twelve. It is clear, then, tliat the dynamographic tracing, taken as a whole, corresponds to this total period occnjDied by the leg in its phase of downward Fig. 103. — Geometrical chronophotograph of the 'movements of the leg in walking, during the period that the foot is in contact with the ground. pressure, so we must divide the abscissa of this curve into twelve equal parts. If we draw the twelve cor- responding ordinates, each of them will express the vertical force exercised by the foot on the ground for the corresponding position of the leg. If these two sets of figures are correspondingly numbered in the tracings, comparison is greatly facilitated. One can, if so desired, dispense with the dynamo- CERTAIN MOVEMENTS IN MAN 155 graph, and measure the force expended from the data aiforded by the geometrical chronophotographs ; in short, when the body mass is known, as well as 'the position and movements of the centre of gravity. Fig. 105. — Geometrical chronopbotograpb of tbe movements executed in taking a bigb-jump. the force expended on the movement can also be calculated. Mechanical Work done by Man in Walking.^ — In view of the fact that it is possible to estimate the work done in jumping by means of geometrical chrono- 150 MOVEMENT photograplis (Fig. 105), it is easy to predict that tlie same method might be applicable in the case of various kinds of j^aces. So far j^hysicists have only calculated the amount of energy expended or gained by a man in walking along an inclined j)lane, in terms of the body weight lifted or lowered such and such a height. The first is a case of positive energy, and the second one of negative energy. The amount of energy expended in different directions is the product of the body weight and the height of lift, an amount which is expressed in kilo- grammetres. Looking at the matter in this light, progress along level ground would require no apparent expenditure of energy, and yet it is accompanied with muscular exertion and consequent fatigue. AVe thought it was j)ossible to estimate approxi- mately the mechanical energy expended in walking or running along horizontal ground by observing the movements transmitted in various directions to the body by the muscular actions involved. If the move- ments of the centre of gravity of the body could be followed in space, they would be seen to constitute a series of vertical oscillations in accordance with the movements of the feet. At the same time during each oscillation there is a certain movement of translation, sometimes at an increased and sometimes at a decreased velocity.* Another way in which energy is expended is when movements are alternately communicated to the legs, movements which gravity might account for if they were, as the brothers AA^eber believed, comparable to oscillations of a pendulum. In practice, however, these movements usually require the help of the muscles. The measurements (Fig. 106) of different movements * We ignore as unimportant the movements of the centre of gravity which occur outside the vertical plane of progression. OEETAIN MOVEMENTS IN MAN 157 of the human body and limbs in the act of walking- haA^e been obtained by means of chronophotography. Three principal elements are involved in the work which is done during the act of walking on the level. A. Vertical work. 158 MOVEMENT J). JLorizontal work. C. AVork expended on keeping np tlie oscillations of the legs during their period of snspension, A. Muscular Work done in a Vertical Direction. — The movements of the head are practically the same as those of the centre of gravity. Now, the trajectory of the head-movements is an undulating curve (Fig. 107), which periodically reaches its maximum as the foot arrives at the mid phase of contact, and similarly reaches its minimum at the mid phase of suspension.* The parallel and dotted lines (Fig. 107), which are tangents to the upper and lower limbs of this curve, afford a measure, by the distance which separates I Fig. 107. — Vertical oscillations of tb’e head when walking. them, of the extent of the vertical oscillations of the body. To measure the absolute extent of these discursions, a transparency of Fig. 107 is thrown on the screen, and enlarged by means of an optical arrangement to its actual dimensions, so that the extent of a vertical oscillation corresponds to the length of half a step measured on the ground. The work done each time the body is elevated or depressed can be estimated by multiplying the weight of the pedestrian by the vertical height which separates the dotted lines in the * On tlie other hand, in running, the maximum corresponds to the period of suspension, and the minimum to the period of contact. CERTAIN MOVEMENTS IN MAN 159 enlarged figure. So that, if the weight is 75 kilo- grams, and the amplitude of the oscillations 0*04 of a metre, each elevation of the body will represent 3 kilogrammetres of positive work, and each depres- sion the same amount of negative work. As there are two double oscillations of this kind in a completed step, the muscular work corresponding to the verti- cal oscillation will be 12 kilogrammetres for each step.* B. Muscular Work expended on Movement in a Horizontal Direction in Walking. — The velocity of the horizontal movement of the body is subject to periodic variations, and hence there must be periodic variations in the energy required, in proportion to the work executed in the different phases of foot-contact, whether this work be represented by movement or by resistance. These variations in speed are deduced from the degree of separation of the points on the trajectory, because these points are photographed at equal intervals of time, for instance, at intervals of j}q of a second. The horizontal projection of these intervals allows one to construct the velocity curve of the horizontal move- ment by taking as ordinates lengths which correspond to the distances which separate the points, that is to say, which correspond to the velocity. From the maximum and minimum velocities of the body mass, the corresponding measure of the energy expended can be deduced. The energy developed by muscles both in producing movement and in offering resistance is equal in each case to half the variation of the vital force. >So that the total sum of these two forms of energy can never exceed the * This estimate, namely, the body weight multiplied by twice the height of the vertical oscillation, is an inexact valuation, which does not really give the expenditure of muscular force : a certain portion of the energy seems to store itself up in the muscles during each period of descent, and to be liberated in the next phase of ascent. 160 MOVEMENT aiiiouut of the whole force exj)eii(Ied, that is to say, for the case in point, 2-5 kilogrammetres. C. Muscular Work done in moving each of the Lower Limbs during the Period of Suspension. — The compli- cated movements of the lower extremities correspond to those of a pair of double-jointed pendulums in unstable equilibrium : they are, however, not only acted upon by gravity, but also by muscular contractions, while the point of suspension itself moves Avith a variable motion along a curvilinear trajectory. The method employed for measuring the energy expended on these oscillations consists in measuring the moment of inertia of the lower limbs in reference to the axes of rotation, and by measuring on geo- metrical diagrams the angular velocity which they acquire. The result thus obtained is very small, 0’3 of a kilogrammetre for each step. Thus the most un- certain determination in these measurements is prac- tically a negligible qnantity, and only very slightly influences the total amount of energy expended on each step.* According to the estimates indicated above, the total amount of energy expended on a step is 9 kilogram- metres. But even the most exact measurement of the energy expended in any particular kind of pace is much less interesting than the study of the actual variations in the amount of work done as the pace is accelerated. If we calculate the total energy expended in fast running, the amount will be found to be very different from that expended on slow progression. The following are the estimates for running : — * The practical importance of an exact determination of the energy is very great; it is also most desirable that all the papers we possess on this subject at the Physiological Station should be again studied by the most approved methods. This subject is worthy of the con- sideration of the greatest mathematicians. CERTAIN MOVEMENTS IN MAN 161 kilogrammetrcs. Trauslatiou of the lower limh ... 3'4 Vertical oscillations of the body 2 3 Acceleration and remissions in velocity in the horizontal direction 18 -1 Total ... 2dT Thus the expeuditiire of energy in taking half a step on level ground varies according to the gait from 9 to 2T kilogramnietres. If account is kept of the number of steps taken in a minute in these two extreme cases, the expenditure of energy will be found to be, in slow walking 720 kilogramnietres, and in rapid running 6748 kilogrammetres, which represents about 12 kilogrammetres per second in the first case, and 112 kilogrammetres in the second.* * We knew perfectly well that walking on level gi’ound represented the expenditure of a certain amount of energy, and tried to estimate the exact amount. But that did not necessarily imply any difference of opinion between physicists and physiologists. If physicists only took account of the energy expended in walking when the road was inclined, it was because only in this case could they ascertain the exact amount of work done, namely, that required for lifting the body weight through a certain number of metres, or lowering it as the case might be. But Coulomb knew full well that both in walking and in carrying burdens the muscles developed energy and did work, but not being able to reduce this expenditure of energy to the usual formula PH, he gave it the name of “ Useful effect,” (PE), that is to say, the weight multiplied by the distance traversed. In short, the measurement of energy in walking and running on level ground demands a complete knowledge of the movements transmitted to the body and limbs as the foot is lifted from the ground. It was for physiologists to determine these movements, and as we have seen, chronophotography afforded them an excellent means of so doing. In giving the above measurements of the work performed in walking, we said that they probably represented the maximum, and that their real value was perhaps something less. This is because in alternate movements in contrary directions there may be a certain storage of energy in the organs which execute the movements, and consequently there may be a certain suppression of energy which would other- wise be expended, and consequently in the succeeding action there may be a certain amount of restitution. To make our point clear, let us take the case of an elastic ball falling on a hard surface from a certain height. Let us suppose the ball weighs 100 grams, and that it falls through a distance of one metre. As the ball reaches the ground, the action of gravity will have produced work to the M 162 MOVEMENT Relative Amount of Work done in executing Various Paces. — If the values of the different factors constituting extent of 100 grammetres. But let us go a little further. The ball in consequence will be flattened against the ground, and rebound to a certain height, 0'60 metre for instance. When the ball has reached this height, of the energy which has accrued from the eftects of gravity, only 40 grammetres have been expended, because on letting it fall down again we shall find that there are 60 grammetres of energy left. These 60 grammetres, then, were recovered by the elastic force of the ball, which had stored them up. Is there anything analogous, when at the end of a movement the antagonistic muscles tend to stop it ; and will these muscles contribute anything towards the succeeding movement in the opposite direction ? The following facts lead us to believe that there is such a restitution. When one exerts one’s self to jump and reach an object above one’s head, if the first attempt is unsuccessful, sometimes the second succeeds. Chronophotography shows that the second jump is always higher than the first. What is it that occurs in such successive acts? In the first jump, the total effort of the extensor muscles of the thighs and legs projects the body a certain height. In descending, these same muscles are contracted in order to break the fall, i.e. in order to counteract the energy generated by the body. Then these muscles are again contracted to project the body into the air a second time. Now, since the height of the second jump is greater than the first, it must be admitted that the elastic force of the muscles which arc contracted to break the fall, is added to the muscular action consciously brought into play for the second jump. Now, is this elastic force of rebound due to a physical property of the muscles, or is it due to an additional expenditure of energy? Weber demonstrated that a muscle when in action acquired, by some intimate change within its fibres, a greater elastic force, and that it was this force which produced movement. The same thing happens, then, in a living tissue as in a steam-engine, in which the elastic force of a gas is converted into work. Now, from the physiological point of view, in the second jump there was no obvious liberation of stored-up energy, but such liberation as there was must have been the result of intrinsic action accompanying all muscular contractions. If the body attained to a greater height in the second jump it was because the muscular energy was greater. We said, however, that in the first jump we exercised our muscles to the utmost extent. That is true, but it may not be by the most energetic, but by the most prolonged effort that we attained to so great a height in the second jump. It will be remembered that, in the experiments with the dynamograjih, the “area of impetus,” or the amount of movement communicated to the body, was proportional to the square root of the height jumped ; and that the height of the jump did not depend on the mere height of the dynamographic curve, because the latter only expressed the degree of effort at one particular moment ; the duration of the effort had also to be taken into consideration. For, as we mentioned, often the highest jumps corresponded to curves of the lowest amiflitude. CEETAIN MOVEMENTS IN MAN 163 the total energy expended on taking a step are com- pared, it is found that they are not equally (Fig. 108) It is necessary, then, to know whether the impetus occasioned by the muscles has not lasted longer in the second than in the first jump. In all contracting muscles, the elastic force starts at zero, and attains its maximum in a certain time. This results from the way in which the contraction is produced, namely, by a gradual summation of a series of contractions. Now, if we leave a crouching position to jump for the first time, our extensor muscles gradually contract, and these muscles will only produce their maximum effect at a more or less advanced phase of extension of the limbs. In the second jump, on the contrary, when in breaking the fall we again assume a crouching position, our extensor muscles liave already reached their maximum contracting force; and it is this maximum force which will continue to operate in raising us up again until we have left the ground. The body mass will have received the full effect of the muscular contraction during a longer period, and consequently will have received a greater “ quantity ” of movement. A familiar example will help to explain the difference which exists, as far as intensity of result is concerned, between a force gradually developed throughout the duration of a movement, and another which acts with all its intensity during the whole period of a movement. When we wish to transmit an impetus to an object by extending a finger we give it a fillip. That is to say, by holding the last phalanx of the middle finger with the thumb, and strongly contracting the extensors of the finger, we let it go like a spring at the moment the maximum degree of extension is reached. The object is thus shot away with great force. The impetus would have been very much weaker if the middle finger had previously only been bent, and wo had then suddenly extended it. In all alternating movements, the muscles work to better advantage than in simple movements. The brandishing of a weapon before striking has no other significance. Now, since the work done by a muscle is the same, whether it is merely work of resistance or work represented as motion, we believe that, if we want to estimate the work done in walking, we are justified in doubling the value of each of the component factors of the work expended in maintaining the oscillations of the body and limbs. If we said that the estimate thus obtained probably represented the maximum, it would be because the vital energy transmitted to the body in the horizontal direction, and that transmitted to the legs at each oscillation, are not totally expended on the movements, part being lost in the form of shocks imparted to the ground. Vital energy is perhaps stored up in real elastic structures of the body, such as tendons. Veterinary experts have made a special study of the energy lost by the hoofs striking the ground when a horse is travelling at a rapid pace. They maintain that the flexor of the solitary toe which consti- tutes the foot of a horse, is made to a great extent of elastic tissue. It possesses in consequence a physical property by means of which a more or less important part of the vital energy lost in falling on the feet is to some extent returned in the form of energy. Cent iiii tires 164 MOVEMENT inllueiiced by the rate of progression. Thus, during slow walking, the energy expended in vertical oscilla- tions is relatively greater than when the velocity of liorizontal translation is increased ; in rapid running, the reverse is the case. It is necessary, then, to follow through all their phases the variations which the Fio. 108 Variations in the vertical oscillations of the body in walking and in running. The rate of step varies between 40 and 130 per minute. Comparison between the curve of oscillation and that of the length of stride. component factors of the work undergo when under the influence of a gradual acceleration. In order that these variations might be clearlv un- derstood, they have been represented (Fig. 109) in a graphic form. In constructing these curves, the num- ber of steps executed in a minute has been numbered off on the abscissa. The corresponding ordinates were made proportional in length to the sum of all the factors This subject deserves re-investigation. It would be interesting to discover whether tendons in man possess this valuable property to any noticeable degree, and, if so, whether it is retained throughout life. CEETAIN MOVEMENTS IN MAN 165 of the work. Whatever was the numbei\of steps per minute, the value was marked otf on the ordinates from below upwards always in the same order. 1. The value of the work done in moving the lower extremity. 2. The value of the work done in the vertical oscih lation of the body. 3. The work done in accelerating and slowing the horizontal movement of translation. Fig. 109. — Curves of the difiFerentrelements of the work'performed iii walking and running, the rate of step varying from 40 to 145 per minute. The scale to the left of the figure indicates the number of kilogrammetres expended on each step. Each of the ordinates is composed of three separate elements, representing the value of each of the component portions of the total work. The lowest element corresponds to the work performed by the oscillations of the leg. The middle (the thick line) represents the vertical oscillations of the body. The superior one corresponds to the degree of acceleration and slowing down of the body mass. On the curves represented in Fig. 109, the different factors in the work apparently vary in an extraordinary fashion ; but these variations can easily be accounted for by certain considerations from the point of view of kinetics or dynamics.* * To quote from a communication made to the Academic des ScienccB, by M. Demeny and ourselves, November 9, 1885 : — A. Variations in Work clone in moving the Loioer Limbs. — The work 166 MOVEMENT Practical Applications. — The data afforded hy these measurements may be put to practical use, for they performed in executing tliese movements obviously increases in pro- poidion to the degree of acceleration of the rate of step ; but a fact which is at first surprising is that for the same number of steps per minute a runner expends less energy than a pedestrian. Thus, at ninety steps a minute, a man would expend in walking 1'4 kilogrmtrs in the movement of the lower extremity, while a man in running would only expend 0’5 kilogrmtrs. And yet the actual speed at which the legs move in running is greater than in the former case. This difference is because the speed at which the limbs move in reference to the body should be considered by itself in these esti- mates. Now, the speed is greater in walking than in running. Indeed, for an equal number of steps per minute, the duration of oscillation of the lower extremity is greater in proportion as the period of contact of the foot is less. The period of contact in walking occupies more than half the total time occupied in taking one ste]° In running, on the contrary, the duration of contact is always loss than half, and as the angular disijlacement of the lower extremity is practically equal in the two cases, it follows that the velocity of move- ment of the legs will be less in running, because the period of oscilla- tion will be of greater duration. A physiological result of this in- equality in the duration of oscillation of the limb in different paces is the intuitive tendency to begin running as soon as the rate of walking becomes too fast. This is one of the numberless examples of our natural instinct to expend the least possible effort in muscular actions. B. Variations in the Worlc done hy the Vertical Oscillations of the Body. — This factor in the work does not increase regularly with the rapidity of footsteps. In walking, the work rapidly inereases between 55 and 70 steps per minute and then decreases. In running, it is very great when the number of steps per minute is small, and diminishes as the rate becomes greater. This factor in the total work done depends on the weight of the body and the amplitude of the vertical oscillations. The difference in the amount of work performed in various paces bears a direct relationship to the amplitude of the above oscillations. Photographic and mechanical records of the vertical oscillations show that in walking there is a relationship between the length of stride and the amplitude of the vertical oscillations of the body, and since we have proved that the length of stride increases with the rapidity of the step up to 70 steps per minute, and then diminishes rapidly as the step is further quickened, it naturally follows that the work corresponding to these different steps varies in the same manner. In running, the work done is greater when the rate of step is slow, and then decreases indefinitely. The corresponding vertical oscilla- tions vary in the same way. The body being suspended in the air during part of the step in running is no longer constantly infiuenced by the changes in the directions taken by the limbs. Consequently, it is* the duration of the vertical oscillation which regulates the amplitude. If the rate of step is slow, the body must be elevated very high so that it may fall slowly on to the limb which comes in contact with tlie ground. CERTAIN MOVEMENTS IN MAN 167 indicate, according to the object in view, the best Avay of utilizing muscular force in walking or running : whether it be to traverse the greatest distance with the least expenditure of energy, or whether it be to cover a certain distance in the least possible time. xVttention should not only be directed to the kind of pace, running or walking, for instance, but also to the number of steps to be taken in the minute. It has already been pointed out (Fig. 109) that, in walking rapidly, from 70 steps per minute onwards, the exj)enditure of energy rapidly increases, and that in running the total energy is considerably greater when the number of steps per minute are few, but commences to diminish when the frequency of step increases, and finally again increases. There is, then, for each pace an optimum rate of steps per minute, Avhich corresponds to the point at which the velocity increases propor- tionately faster than energy is expended. There are other points to be considered in choosing a pace. Energy must not be exhausted so quickly that the muscles have not time to recover from the effects of fatigue. A long walk, in Avhich a great deal of energy has been expended, may be borne with im- punity, while rapid running would soon exhaust the muscular strength, although the total expenditure of energy may be much less. As tlie studies just described have only been made in If the rate of step is rapid, a slight extension is afforded to the oscilla- tions by the short duration assigned to it. Thus, in walking, the amplitude of the vertical oscillations of the body is related to the length of step ; it is independent of the length in running ; in fact, an inverse relationship can almost be detected. C. Variations in the Amount of Worh done in the Acceleration and Slcncing of the Horizontal Translation of the Body. — This factor in the work increases fairly regularly with the rate and length of the step. In running, it assumes considerable proportions, although the absolute variations in speed are slight. This is because the gain or loss of vital energy is in proportion to the difference of the squares of the maximum and minimum velocities of tran.slation. 168 MOVEMENT . a small number of subjects, and those generally ol' good jDhysique, the results cannot be generally applied to the average man — to a soldier, for instance. The officers in our army have taken an interest in these researches, and have furnished us with the means of repeating them on a considerable number of soldiers. The influence of the figure, the weight of the body, the uniform, and the weight carried, had all to be taken into consideration. With the co-operation of ]\I. Demeny and Lieutenant K , we carried out these researches, and our first results were reported to the Minister of War. CHAPTER X LOCOMOTION IN MAN Feom an Aetistic Point of View SuMMABY. — Influence of Photograpliy on Art — Different cliaracteristics of ancient and modern works of art — Photography catches the real attitude — Importance of representing the correct outline of muscles during different actions — Photographs taken from different points of view — Photographs taken from above — Study of the most characteristic attitudes in a movement — Importance of having a series of photographs from which to choose the most expressive attitude — Analysis of facial expression — Choice of the best method for procuring artistic results. Photogeaphy has already rendered great services to Art. Some artists openly admit it, and many more make use of it, as may readily be seen by comparing recent works with those of earlier date. It is more especially instantaneous photography that has had such an influence, because it has afforded reliable pictures of phenomena of very short duration, such, for instance, as of sea waves, or even of the attitudes of men or animals during the performance of the most rapid movements. We are not qualified to speak of Esthetics, still less to discuss the question as to whether Art has the right to represent violent actions, or whether it should restrict itself to more reposeful attitudes. In the latter, the characteristic expressions are easier to reproduce from living models ; but, as a matter of fact. 170 MOVEMENT it is incontestible that, in ancient times, as well as at the present day, artists have often represented move- ment of the most active descrij^tion, such as running or fighting. Now, if old masterpieces are compared with those of recent times, one is struck Avith this difference between them, that the modern attitudes are quieter and better jDoised, so to speak, while in ancient works of art the figures sometimes appear in positions of unstable equilibrium. Fig. 110, taken from a Greek Fig. 110.— Ocydromes or swift-runners (from a Greek vase). picture, is an example of this kind. Every one can think of some modern picture representing a similar subject. In sculpture especially, the action of running is differently represented nowadays. The sujDporting leg is generally seen vertically extended beneath the centre of gravity of the body, while the other leg is in an extreme position of elevation behind. Nature herself may fairly be appealed to in deciding between these two methods of rej)resenting the same action. Instantaneous photography is an excellent means of shoAving the actual attitudes assumed. There LOCOMOTION IN MAN 171 is no doubt about the decision. Fig. Ill, for instance, shows that a man in running assumes at certain moments positions exactly like those represented in the old masterpieces.* Fig. 111. — Instantaneous photograph of a runner : the position of the legs is the same as that of the man on the extreme left of the foregoing illustration. It is quite easy to prove that runners never appear in the positions adojited by certain modern artists, * One sometimes sees on a Greek vase a grouji of runners in tlie most curious positions. It is a perfectly familiar fact that a man in running or walking always swings the corresponding arms and legs in opposite directions. The corresponding arm and leg move, so to speak, in diagonal association. Now, on the Greek vase the arm and leg belonging to the same side are represented as moving in the same directions. Now, was this style of running, which is somewhat suggestive of the ambling of quadrupeds, really practised on the ancient race-course? or is it a mistake on the part of the decorator of the vase? This is a question we are unable to answer. Such a style of running is quite ditferent from that now practised; yet at the same time it does not appear physiologically impossible. It is certainly a question worth considering. 172 MOVEMENT wlio seem to forget that one of the characteristics of running, and even of walking, is to maintain a continuous position of unstable equilibrium. W e must not, however, spend time on these reflections, for by criticizing the details of works, which are excellent in other respects, we may expose ourselves to the warning, “Ne sutor, ultra crepidam.” We will only remark that among the infinite variety of attitudes shown by chronophotography in registering all the phases of a movement, there are certainly ) Fig. 112. — A man walking; successive positions afiforded by chronophotography on fixed plates. some which might be accepted by artists without transgressing the laws of aesthetics, and an interesting variety might be given to such representations. Thus, in Fig. 112, in which a nude figure is represented as walking, a series of attitudes is shomi, amongst which several could be introduced into a work of art ; and so with many other series of the same kind. In these pictures artists would also find a faithful expression of the action of the muscles, which show the conditions of contraction or relaxation by the degree of prominence. Now, these two opposite conditions of the muscles are closely associated witli each LOCOMOTION IN MAN 173 Fig. 113.— Chronopliotographic illustration of a runnei’. that the extension of an arm in striking, if it is to be complete, must be accompanied by the total relaxation of the flexor muscles. The latter muscles, however, come into play, if the movement of extension is to be arrested. As, for instance, in the case of a man preparing to strike, without the actual intention of delivering the blow. In the four following figures, the expression of the outstanding muscles varies according to the nature of the preceding movement, although the final attitude phase of the movement in which they take part. The standing out of muscles in action has, so to speak, an individual expression, just as is the case with the facial muscles, and if most subtle physiological know- ledge could be applied in all cases, it might be said that the modelling of a limb could not only express the action of the time being, but could suggest to a certain extent its immediate successor. Some interesting experiments of M. Demeny show 174 MOVEIMENT of tlie arm is the same. Thus Figs. 114 and 115 botli represent a semillexed arm, but in tlie first tlie outstanding biceps shows that a movement of flexion is in process of production, and in the second it is the triceps (extensor muscle) whicli stands out most Fig. 114.— Flexion of an arm. Fig. 115.— Extension of an arm. markedly, while the biceps is flattened. The attitude here represented corresponds to a phase in tlie extension of the limb. In alternating movements, the antagonistic muscles come into play. If extension of the arm is to be Fig. 116. — Alternating movements of flexion and extension. Fig. 117. — Single movement of forcible exten- sion (delivery of a blow). followed by flexion (Fig. 116), although the triceps is the muscle directly concerned in the movement, the biceps is also contracted, partly to arrest the momentum of extension and partly so as to be ready LOCOMOTION IN MAN 175 for immediate action. If the blow is delivered in a definite manner, as, for instance, a blow with the fist (Fig. 117), the moment the limb is extended the muscles have no more to do, and so relax themselves. For the purpose of sculpture the model should be viewed from different aspects. By taking chrono- photographs of a moving man from some point above his head (Fig. 118), a horizontal projection is obtained which shows the exact contour of the body. This photograph, as well as those taken from difterent angles, would doubtless be very useful to the sculptor.* Fig. 118. — Chrouophotograph of ii ruimer takeu from above, (llorizoutal projection.) Quite apart from any artistic object, it is often necessary to have recourse to various forms of modelling to represent the attitude of man, or the movements of animals, in the three dimensions of space. We have often utilized this method for determining from several photographs, taken simultaneously, the attitude of a bird’s body and wings during the act of flight. We only wish that some artist would devote his talents, * It was proposed some time ago to produce, under the name of photosculpture, a method for mechanically reproducing a model of an individual. The person was placed in the middle of a circle, on the circumference of which were arranged a row of cameras. Each of these cameras took at the same moment a photograph of the figure which was thus represented from various points of view. Each photograph was enlarged to a convenient size and transferred to a metal plate and converted into a sort of mould. On pressing some plastic material on to the plate, a rough model was obtained, absolutely exact as far as attitude was concerned, and one from which the sculptor could execute a properly finished copy. 176 MOVEMENT by the aid of such photograplis, to tlie representation Fig. 119.— Statuette made from clironophotograplis. of men in the act of running just at the moment when the feet come in contact with the ground. LOCOMOTION IN MAN 177 31. Engraiid, wishing to work on these lines, made the statuette represented in Fig. 119. The attitude is very different to those usually presented in Art ; the foot which touches the ground is well in advance of the centre of gravity, so that the choice of such an attitude perhaps creates a practical difficulty, inas- much as the figure is in unstable equilibrium. In order, however, to reconcile this with physiological knowledge, an attitude should be chosen in which the centre of gravity lies exactly over the point of support. At this moment the elevated leg is never behind the leg which supports the weight of the body, but lies directly across it. This attitude is seen in all human paces, in walking as well as in running, with this difference, that in walking the legs are much less flexed at the joints. Study of the most Characteristic Attitudes in a Move- ment.— In representing a movement, for instance, one of a man, an artist rightly attempts to reproduce a phase which is visible to the eye. It is usually the preliminary or the final phase Avhich can be best appreciated. When a machine is in motion, there are certain parts of it which are only visible when they reach their dead points, that is to say, for the brief moment when the direction of movement is changed. And this is also the case with certain movements in man. Some attitudes are maintained longer than others. Now, chronophotography on fixed plates could be used to determine these positions. They are recognizable in the photograph as the ones which have left the most intense impressions on the sensitized plate — in fact, as those wffiich have had the longest exposure. Thus in Fig. 120, which represents a fencer in the act of lunging, most of the impressions are indistinct or confused, while two of them stand out as well defined positions. The first of these is when the 178 MOVEIMENT I'lG. 120 — A sword thrust. (From ii chroiiopliotograpli on a fi.xod plato.") LOCOMOTION IN MAN 179 man is jDrepariug for his thrust, and the second is when his arm is extended to its utmost limit after he has executed the lunge. Fig. 40 was taken from two equally good photographs of a boxer.* In all possible actions, such as pulling a string, lifting a weight, turning a wheel, pushing a Avheel- barrow, etc., there are some attitudes which last longer than others, and which may be called “ positions of visibility.” f Chronophotography would determine these with the greatest precision. Importance of having a Series of Photographs from which to choose the most Expressive Attitude. — If a movement had always to be represented in its slowest phase. Art would be beggared of all originality of expression. We should then have a sort of catalogue of stereotyped attitudes, just as we have laws of anatomical proportion. Hampered by these limita- tions, the artist would lose all individuality. He ought, on the contrary, while taking Nature as his model, to make an independent choice between the objects offered to him. Among the many photographs we have obtained, some have struck us as particularly expres- sive, and we believe that they are the very ones that an artist would select. In a series of photographs that we took of a man striking a forcible blow with a stick, there was one that particularly appealed to us. At the moment of supreme effort almost every muscle in the body stood out in forcible contraction. This would not occur in a quieter action, or in a more limited movement. * These two figures were borrowed from an article on physical exercise by M. Demeny, illustrated by means of chronophotography (La Nature, October 11, 1890). t With regard to the locomotion of quadrupeds, we shall show, further, that in the horse, for instance, these phases of slow motion never occur in all the limbs at once. 180 MOVEMENT A slow aotion, such as that of a man sitting down on the ground and then stretcliing himself out in a recumbent position, would present no such general muscular contraction. Chronophotography of Facial Expression. — With the camera which we used, although it has only one objective, a subject can be photographed at a near distance, and show no alteration in perspective, how- ever long be the series of photographs. It is the only kind which, up to the present, has been capable of affording a series of photographs which shows in all their details the changes in facial exjDression, the various movements of the hands, and the different positions of the feet in walking. It would be interesting to follow in this way all the transitions between a scarcely perceptible smile and a hearty laugh, and to catch the characteristic expressions of astonishment, anger, and other emotions. The great difficulty is to find a subject caj^able of giving these various expressions in a perfectly natural manner. Most people would only produce a grin or a grimace. Clever actors would no doubt succeed better in assuming the various emotional exj)ressions ; and the method might even be useful to them in their own studies. But that which is rendered to perfection by chronophotography is the movement Avhich accompanies the act of articulation. M. Demeny has paid special attention to this extension of our method, and he has met with immense success. With strong and Avell-directed light he has shown the way the tongue moves in the articulation of consonants. His researches are of value from a phonetic point of view, and practically it ought to be of service in the teaching of deaf mutes. One ingenious method for instructing deaf mutes consists in teaching them to read the various movements of the lips in producing different 182 MOVEMENT words, and to cany on a continnoiis conversation in this way. M. Demeny was very anxious to know whether deaf mutes would he able to make out a conversation carried on by means of a series of photo- graphs. The result of his experiment was most satisfactory. The deaf mutes read from the chrono- photographs the words which had been uttered. It is unnecessary here to remark that without special teaching this novel kind of writing cannot be deciphered.* And now from an artistic point of view. AVhat is to be the outcome of this new method of reproducing the movements of speech? Painters have hitherto apparently paid no attention to the subject. In the most animated scenes, it is the general exj^ression of the features that conveys an idea of what the individuals are supposed to be saying, and the same holds good in sculpture. Eude has twice attempted to represent, if not actual words, at least a cry of imprecation or command. We wanted very much to know what sort of expres- sion a man’s features would assume when he uttered a loud exclamation. The attendant at the Physio- logical Station was the subject of our experiment. He was placed in front of the objective, and told to shout at us several times in succession at the top of his voice. The series of photographs thus obtained showed the periodical repetition of the facial expres- sion, but so curiously contracted were the muscles of expression that the appearance was rather that of an ugly grimace ; and yet simply to watch him there was nothing extraordinary in the man’s expression. The peculiarity of the photographs was due to the fact that they caught exceeding fleeting expressions of the face — movements which were really ones ]iy on moving lilms. By making use of a dark background we have obtained as many as 60 distinct images per second, k ig. 165 is an example of this kind ; the film is cut into six pieces, which are placed side by side in the illustration. The images are numbered in ordinary figures, according to the order in which they were taken. Simultaneous Photographs of the Same Bird taken Fig, 166. — Arrangement of the three dark backgrounds and the three cameras for simultaneous photography of a flying bird, as seen from three points of view. from Different Aspects. — If we want to analyze the movements of flight Avith extreme exactness, the bird must be photographed from several points of vieAv. Three cameras are usually required for this purpose, as well as three dark screens against which the object is clearly visible. The arrangement is represented in Fig. 166. AEUIAL LOCOMOTION 237 By this means we were able to obtain the attitudes of the bird in three series : from the front, from the side, and from above. The three sets of photographs Fig. leT—I hree series of images to demonstrate the corresponding positions of the bird, when taken from three different points 01 view. A, taken from above ; B, from the side ; C, obliquely from the side and front. 238 MOVEMENT were made to correspond to the same attitudes for convenience of comparison, and to show the exact position in space of the body and wings (Fig. 107). From these photographs we have been able to con- struct a series of bas-reliefs showing the successive attitudes of the bird. This kind of representation is almost the only way of illustrating the actual movement during flight, for mere ocular observation would not give the least idea. * “ We need not here repeat the analysis of these photographs, which have afforded us complete information of the movements of birds from the point of view of kinetics, and from which we have attempted to measure the amount of work performed during the act of flying by means of the degree of acceleration imparted to the body.” — See Le Vol ties Oiseaux, p. 324. CHAPTER XIV AERIAL LOCOMOTION The Flight of Insects Summary. — Frequency of the movements of insects’ wings as estimated by the sound produced in flying — Mechanical registration of the movements of the wings ; frequency among different species — Synchronous movements of the wings — Changes in inclination of the wing surface — Trajectory of an insect’s wing — Its inter- pretation— Experiments to demonstrate the direction of move- ment of the wing, and its variations in plane — The artificial insect — Theory of the flight of insects — Photography as applied to the study of insect flight — Lendenfeld’s experiments — Trajec- tory of the wing as the insect advances — Photography on moving films — Arrangement of the experiment — Different types of flying insects : Bees, flies, tipulse — Substantiation of the mechanical theory of flight. Frequency of the Movements of Insects’ Wings as es- timated by the Sound produced in Flying. — The flight of insects is accompanied by a humming sound, which is of somewhat low pitch in the larger species, and of very high pitch in some of the smaller insects, such as mosquitoes. The wings of insects may be regarded simply as vibrating wires, and hence the frequency of their movements can be calculated by the note pro- duced. But then it must be taken for granted that the four wings of an hymenopterous, or the two wings of a dipterous insect vibrate in perfect unison. In calcu- lating the frequency of the movement of the wings by this method, the following difficulty may be met with. If we listen to a fly on the wing, it will be 240 MOVEMENT noticed tliat the character of tlie sound continually changes. ]>y close attention, the sound can be dis- tinguished as of a higher pitch when the fly approaches the observer, and of lower pitch as it recedes. This suggests that there must be an alteration in the frequency of the wing vibrations. The phenomenon may, however, fairly be compared to the apparent variations in shrillness of the whistle of a moving train. As the train rushes along, the whistle seems to become shriller when it approaches, and deeper when it recedes. This acoustic phenomenon has long ago been ex- plained. However, if we hold an insect lightly in a Fig. 168. — Tbe two top lines are produced by tbe contacts of a drone’s wing on a smoked cylinder. In tbe middle are recorded tbe vibrations of a tuning-fork (250 vibrations per second) for comparison with tbe frequency of tbe wing move- ments. Below are seen tbe movements of tbe wing of a bee. pair of forceps it may be shown that when its wings vibrate the sound jiroduced is practically uniform. Mechanical Registration of the Movements of Wings in Insects. — The movements of the wings of a captive insect may be recorded directly on a revolving cylinder. If the cylinder previously be blackened with smoke the slightest touch will remove the black and expose the white paper beneath. Fig. 168 was obtained in this way, and shows several interrupted lines traced by the wing of a drone. The tracing was obtained as follows : The insect was held between a pair of forceps in such a way that the extremity of its wing only just came in contact with the surface of the cylinder, and in so AERIAL LOCOMOTION 241 doing left an interrupted track. If the wing had been forced harder against the cylinder, the mark left would have been somewhat in the form of a comma, and the frequency naturally somewhat less owing to the re- sistance due to friction. The same effect may be observed in the movements of all kinds of animals. To calculate exactly the frequency of the wing movements, the vibrations of a tuning-fork are simul- taneously recorded on the cylinder. These vibrations leave on the blackened paper an undulating line ; each vibration representing ^ o ^ second. It now only remains to count the number of marks traced by the insect’s wing on a length of paper corresponding to 250 vibrations of the tuning-fork. The number of wing movements per second is thus obtained. By this method it was calculated that in the common fly there were 330 strokes per second, in the bee 190, and in the macroglossus of cheese rennet 72. Thus obeying the general law applicable to birds, namely, the smaller the species the more rapid the movements of the wings. Synchronous Movements of the Wings, Variations in Surface Inclination. — There are other facts to be learnt from direct registration of the wing movements. Thus by holding a fly in such a position that its two Avings strike the cylinder at the same time, it will be seen that both wings impart the same number of strokes, and that the movements are absolutely synchronous. In some species of insects the upper surface of the wings is covered with fluffy hairs, while the lower surface is bare ; tracings taken from the wings of such insects show alternate variations. Fig. 169 was obtained from Macroglossus of cheese rennet, a small diurnal hawk moth which flies very rapidly and is very common in France. The insect was held in such a way that the under side of its Aving touched the cylinder. R 242 MOVEMENT N ow, ill moving to and fro, tlie wing struck the cylinder alternately with the hairy and smooth surface, which proved that the wing underwent a change in inclina- tion. This fact is important to bear in mind, for it materially elucidates the mechanism of flight. Such is the information derived from recording insect move- ment by means of mechanical methods. The attempt might be made to obtain the trajectory of the extremity of the wing by a similar means. , But the wing, moving as it does in all sorts of directions round its thoracic articulation, describes a sj)herical figure, the whole of which could not possibly Fig. 169. — Movements of the wing of Macroglossus of cheese rennet on the surface of a smoked cylinder. be traced on anything else than the inner surface of a sphere. The contact of the wing Avith the surface of the cylinder could only take place to a very small extent. Consequently another method must be em- ployed for obtaining the trajectory described in the air by the extremity of the Aving. Trajectory of the Extremity of the Wing. — Eemember- ing the fiery tracks left upon the retina when a luminous object was Avaved in front of the eyes, aac fastened a s|>angle of gold-leaf to the extremity of a Avasp’s Aving., The insect Avas then seized Avith a pair of forcej)s and held in the sun in front of a dark back- ground. We then Avatched the luminous trajectory AERIAL LOCOMOTION 243 wliich shaped itself in the form of a lemiiiscate, Jfig. 170. The hgure 8 would exactly express what we saw, and the resemblance was the more complete because, in the trajectory thus described, one of the limbs seemed Fig. 170. — Appearance of a wa.sp flying in the sun. The extremity of the wing is gilded. larger and brighter than the other. In describing this appearance we ignored, or omitted to mention the fact, that Mr. Pettigrew, in England, had noticed the same appearance in a flying insect, which gave rise on his part to claims of priority of discovery. Nevertheless, we may remark that the method of formation of the flgure described by the wing of an insect, according to ]\Ir. Pettigrew, is quite diffeient from our Pjo. 171 — The trajectory of the anterior and pos- A r>r>nrrl ^erior border of the wing of an Insect during half concepxiou. ALCOIU- an oscillation (Pettigrew). ing to the English authority, the anterior border of the wing describes one limb of the lemniscate while the inferior border de- scribes the other. In Fig. 171, which is borrowed from his work, the arrows indicate a complete reversal of the wing surface in a simple movement from left to right. 244 MOVEMENT According to our view, on the contrary, tlie extremity of the wing describes each limb of tlie lemniscate in succession, in a dual motion from left to right, and then from right to left. Meanwhile the surface of the wing is variously distorted by the resistance of the air. In Fig. 172 dotted lines indicate the direction of this distortion which could never amount to a com- plete reversal. Now, the mechanical theory which can be deduced from this optical figure depends entirely on the manner in which the wing is supposed to Fig. 112. — Trajectory of the anterior order of i -i mi-. 4 the wing during a complete oscillation UaVO CleSClTDeCl. it. AC- (Marey). The small lines which are set 2. lyr , -p <-• obliquely in various directions represent the COlCllUg tO IMT. Jrettl- inclinations of the surface of the wing. iheOVJ, the revo- lution of the wing is active and due to the contraction of muscles. According to our theory, the change in inclination of the wing is passive and brought about by the resistance of the air, for it is only the posterior part of the wing that is distorted, the anterior part being kept straight and stiff by a rigid nervure. The importance of a correct interpretation of the figm-e described by an insect’s wing is very great, because the explanation of the mechanism of flight depends upon it. We have, however, no desire to weigh the respective merits of the two theories, we only wish to enumerate the experiments by which we have demonstrated our own views. Experiments -for determining the Direction taken by the Wing in course of Movement, and Explanation of the Mechanism by which the Alteration in Inclination is effected. — The optical method, namely, that of deter- mining the movements of the wing by the impression left on our organs of sight by the gold spangle fastened AEKIAL LOCOMOTION 245 on the extremity of the wing, shows that the surface of the wing is differently inclined during the various phases of movement. Now, we have seen that the two limbs of the 8 described in this way are unequally luminous, and from this we concluded that while one of the limbs was being described, the inclination of wing must have been more favourable for the reflection of the sun by the gold spangle, and that, while the other limb was being described, the gold spangle must have had a less favourable inclination. If this is so, by altering the position of the insect, a change should be effected in the degree of reflection, and as a matter of fact this is exactly what does happen. When the Fig. 173.— Expeiiment to test the direction of movement of an insect’s wing. insect is turned through an angle of about 90°, what was before the bright limb of the 8 is now no longer conspicuous, whereas the other side, in its turn, becomes brilliantly illuminated. In this way the variations in inclination can be demonstrated. Even the angle formed by the wing with the axis of progression could be deduced from these experiments, but we shall see that, by the employment of photography, this angle varies from moment to moment. The most that one can say is that the angle is about 45°, sometimes in one direction sometimes in the other. To determine with accuracy the direction taken by 240 :uovemi-:nt tlie at (liriereiit stages of tlie trajef'tory, we ]>ro- ceeded as tollows. A small piece of cajdllary glass tubing was blackened in the smoke of a candle, so that the slightest touch on the glass was sufficient to remove the black coating and show the direction of movement in each limb of the lemniscate. This experiment was arranged as shown in the figure (173). Different points on the path of movement were tested by the smoked rod, and from the track along which the black had been removed the direction of movement was deduced. This direction is represented in the figure by means of arrows. Por the sake of comparison, we constructed an artificial insect, the wing of which consisted, as in nature, of a rigid nervure anteriorly, and a sort of flexible sail behind. We have watched this little contrivance move like a real insect, give like it a luminous trajectory shaped like a lemniscate, agitate the air behind, and by a kind of suction action aspirate air towards it in front.* Theory of Insect Flight. — The theory of insect flight may be completely explained from the preceding exjjeriments. The wing, in its to-and-fro movements, is bent in various directions by the resistance of the air. Its action is always that of an inclined plane, striking against a fluid, and utilizing that j)art of the resistance which is favourable to its onward progression. This mechanism is the same as that of a waterman’s scull,t which, as it moves backwards and forwards, is obliquely inclined in opposite directions, each time communicating an iinj)ulse to the boat. There is, however, a difference between these two * La Machine Animale, book iii., chap. ii. t Tliis refers to what is generally called “sea-sculling,” and of course has no reference to the ordinary river sculling, which requires the use of two sculls. — Translator. AERIAL LOCOMOTION 247 methods of i)ropuLsion. The scull used by the water- mau offers a rigid surface to the water, and the operator has to impart alternate rotary movements to the scull by his hand — at the same time taking care that the scull strikes the water at a favourable slant. The mechanism in the case of the insect’s wing is far simpler, the flexible membrane which constitutes the anterior part of the wing presents a rigid border, which enables the wing to incline itself at the most favourable angle. The muscles only maintain the to-and-fro movement, the resistance of the air does the rest, namely, effects those changes in surface obliquity which determine the formation of an 8-shaped trajectory by the ex- tremity of the wing. Photography as applied to the Study of Insect Flight . — The reader may, perhaps, be surprised that we have not, as yet, resorted to photography as a means of determining the trajectory of an insect’s Aving, since this is the only method of recording an accurate tracing. This is because the experiments just mentioned were carried out long before photo- graphy could be employed to study any kind of move- ment. Photography was applied by Lendenfeld * for determining the position of the wings of a dragon-fly. This author also showed how the lemniscate described by the extremity of the wing became displaced and distorted by the animal’s forward progression. The experiments of the German naturalist were made on a dragon-fly, Avhich was fixed at the end of a sort of balanced beam ; and although the animal could raise itself to a slight degree, the conditions were not such as to indicate the normal trajectory of the Aving, when the insect Avas free to fly where it liked. * Lendenfeld, Der Flug der Lihellen, Acad, der Wissenscliaften. Vienna, 1881, Heft. i. p. 289. 2^18 MOVEMENT We siicceeclecl in obtaining a ]^hotograph of tiie gilded Aving of an insect, which, though not absolutely at liberty, could fly at a comparatively high rate of speed. Photography of the Trajectory of the Wing. — The folloAving is the arrangement we adopted for our experi- ments. A wooden box one metre square and 0'25 Fig. 1T4. — Insect flying round and round in front of a dark background. metre deep, was lined throughout with black A^elvet. At the bottom of the box a central disc, supported by a footpiece, was placed in position : the periphery of the space Avas covered Avith a white material, leaving betAveen it and the central disc an annular track covered Avith black velvet (Fig. 174). It Avas round this annular AERIAL LOCOMOTION 249 track that the insect was made to fly. A needle stuck perpendicularly in the middle of the disc served as an axis for a revolving beam and its counterbalance. This beam consisted of a straw, and at the end of it was fixed a light pair of surgical forceps to hold the insect by a part of its abdomen. When thus fastened, the dragon-fly was left to its own devices. It then com- menced flying at rather a rapid rate round the track, drawing the straw after it, the movement often per- sisting for some considerable time. The gold spangle Fig. 175.— Photographic trajectory of the_vving of a dragon-fly. fastened to its wing described a trajectory which is reproduced in Fig. 175. The lemniscate described by the insect during its flight in captivity, is no longer to be seen, but in its place there is an undulating curve which presents at different stages of its course a greater or less degree of brightness, according as the inclination of the wing is favourable for the reflection of light or the reverse. Chronophotography of Insects on Moving Films. — The series of proofs which we have just given appear to us to leave no doubt as to the correctness of our views on the flight of insects. 250 MOVEMENT ]>ut altlioiig-li oiir theory may be generally true, there are still certain details which remain to be elucidated. For instance, in what way does the flight of one insect differ from that of another, and what function do the balancers subserve ? Those singular organs which from the point of view of comparative anatomy would seem to be undeveloped wings, appear to be indispensable for the flight of dipterous insects. It occurred to us that these and many problems could be solved by chronophotography, if it only enabled us to catch a momentary view of the insect’s Fig. 176. — Schematic arrangement for illuminating insects when studying their flight. wing during its flight. But one can imagine that the exposure would have to be very short to procure a well-defined photograph of an insect’s wing, when an exposure of ^oVo ^ second is too long in the case of a bird’s, although in the latter instance the movement is much less rai3id. Further, it is not improbable that with such a short exposure, the time would be insufficient to imprint a definite image on the plate. In order, then, to diminish the period of exposure the fenestrations of the rotary diaphragms must be made very small, and the light AEIilAL LOCOMOTION 251 tliat is tlirowii on tlie insect very concentrated. Fig-. 17G is a general sclieme of the arrangement we adopted. In the first place, it will be noticed that there is a parallel beam of light travelling from right to left, and directed by a heliostat towards the principal optical axis of the object-glass. This beam of light is condensed by a lens * (c) behind which the insect Fig, 177. — Chronophotographic apparatus arranged foi studying the natural flight of insects. can be seen between the points of a forceps. The condensed beam of light traverses the first lens of the object-glass, and the rays are brought to a focus at the circular diaphragms ; at the moment two fenestra- tions coincide the rays can pass through and illuminate the field of the movable film, in the middle of which a silhouetted image of the insect stands out in bold * The focal length of this lens shonkl be at least double tliat of the objective. 252 MOVEMENT contrast. were iiot very successliil in our experi- ments with all kinds of insects ; tlie method, it is true, allows of the insect being posed at will, and also allows one to obtain photographs of the attitudes of the wings as seen from different points of view, but it gives them an exaggerated appearance Ijoth as regards the extent and the rapidity of the movement. To study an insect in free flight, a cardboard box (Fig. 177) is placed in front of the object-glass, the insect is confined by means of a pane of glass Avhich just touches the condensing lens. Being introduced into this box, the insect immediately flies against the Fig. 178. — Fly crawling on a window-pane before taking to flight. glass, which previously should be placed at the focal point of the object-glass. The insect’s flight can be watched, and at the desired moment the button can be pressed which sets the film in motion. Fig. 178 was obtained in this way; it represents a fly crawling on the pane of glass and then taking flight. The exposures were extremely short, as we have previously mentioned, in order that the wings, which moved very rapidly, might be well defined. With fenestrations 2 centimetres in breadth, the actual exposure being ^ o\ja ^ second, the photographs were not distinct, at least not of the extremities of AERIAL LOCOMOTION 253 the wings. So we gradu- ally reduced the diameter of the fenestrations by drawing the metal cur- tains which regulated the size of the openings. When the openings in the two diaphragms were only 1'5 millimetre in breadth, the duration of the exposure was reduced to 25 000 ^ second, and in this case the photo- graphs obtained never failed to be absolutely distinct. An insect flying against the pane of glass must occupy a considerable amount of space in an antero - posterior direc- tion, and hence if all portions of the body are to be well defined, the object-glass must be one of considerable focal length. Now, as a mat- ter of fact, the extreme narrowness of the fenes- tration through which the light passes, and the corresponding smallness of the openings of the diaphragms give a focal length of rather more than 2 centimetres. Fig. 179.— Bee flying about in the chamber of the apparatus. 254 movement Fig. 179 shows a bee in various phases of ilight. The insect sometimes assumes almost a horizontal position, in which. case the lower part of its body is much nearer the object-glass than is its liead, and yet both ex- tremities are equally well defined in the photograph. The successive images are separated by an interval of 2^0 of a second (a long time when compared to the total time occupied by a complete wing movement, i.e. TO O of a second). xVnd hence it is useless to attempt to gain a knowledge of the successive phases of move- ment, by examining the successive photographs of a consecutive series representing an insect in flight. N’evertheless, an examination of isolated images affords information of extreme interest with regard to the mechanism of flight. We have seen that owing to the resistance of the air the expanse of wing is distorted in various dhec- tions by atmospheric resistance. Now, as the oscilla- tions during flight are executed in a horizontal plane the obliquity of the wing surface ought to diminish the apparent breadth of the wing. This ajDpearance can be seen in Fig. 180. There is here a comparison between two tipulse : the one in the act of flight, the other perfectly motionless and resting against the glass Avindow. The motionless insect maintains its Avings in a position of vertical extension, the plane is therefore at right angles to the axis of the object-glass. The breadth of the wing can be seen in its entirety ; the nervures can be counted, and the rounding off“ of the extremities of the wings is perfectly obvious. On the other hand, the flying insect moves its Avings in a horizontal direction, and owing to the resistance of the air the expanse of the wings is obliquely disposed, and only the projection of its surface can be seen in the photograph. This is why the extremity of the AERIAL LOCOMOTION 255 wing ti2)pears as if it ^^■e^e poiuted, while the other parts look much narrower than normal. The extent of the obliquity can he measured from the apparent alteration in width, for the projection of this plane with the vertical is the sine of the angle. From this it 256 MOVEMENT may be gathered that the right wing (Fig, 180, 3rd image) was inclined at an angle of about 50° with the verti- cal, say 40° with the horizontal. This inclination necessarily varies at different points of the trajectory, and must augment witli the rapidity of movement ; the ob- liquity reaching its maximum in those portions of the wing which move with the greatest velo- city, namely, to- wards the extremi- ties. The result is that the wing be- comes twisted at certain periods of the movement. The tortion which was reproduced in the case of the wings of our artificial in- sects, may be ob- served in some of the photographs, as, for instance, in the 4th image in Fig. 181. AEKIAL LOCOMOTION 257 AMieii the direction of movement varies, the inclina- tion of the plane of the wing varies also, and for a moment this plane must become vertically disposed. This may be seen in the first image of the same figure, for in this instance the wing looks exactly the same size, and has the same appearance, as in the case of the motionless insect. The balancers can be distinctly seen, and the posi- tion of these organs seems to vary according to that of the wings. Careful observation of a great number of photograjihs taken under different conditions will no doubt determine the nature of the movements of these structures. Finally, we by no means despair of being able to apply chronophotography on fixed plates to the study of insect movement, and of thus being able to obtain a sufficient number of photographs to demonstrate all the phases of the wing movement. Some of our attem]3ts have already shown that under certain conditions of illumination, the insect can be photographed as a bright object standing out against a dark background. S CHAPTER XV COMPAEATIVE LOCOMOTION Summary. — Comijarative locomotion among terrestrial mammals : the man, the horse, the elephant — Comparative locomotion among ditferent kinds of birds — Classification of different types of loco- motion— Comparative locomotion of tortoises and lizards ; frogs, toads, and tadpoles ; snakes, eels, and fish ; insects and spiders. Comparative Locomotion. — The most interesting feature of zoology is not so much the descrij^tive and systematic account of the various forms met with in the animal kingdom as the tracing of association between form and function. As comparative anatomy and physiology become more and more allied, doubtless more fundamental morphological laws will be dis- covered, and these perhaps will enable us to predict the function of any particular organ from an ana- tomical inspection. We are certainly very far from being in a position to understand this association in the case of most organs ; but the mechanical action of some of them is already so familiar that the physiological function can be explained on anatomical grounds. The form of the vertebrate skeleton, the volume and length of the muscles, and the relative dimensions of the long bones are necessarily closely associated with the kind of locomotion habitual to the animal. Inviolable mechanical laws govern this association, some of them COMPARATIVE LOCOMOTION 259 have already been enunciated, and we have no doubt that others will soon receive an accurate formulation. But to determine these laws the character of an animal’s locomotion must be as precisely defined as its anatomical structure. Chronophotography, and more particularly the diagrams which it enables us to construct, leave nothing to be desired in point of truthful expression of certain types of locomotion. A few examples will show the value of this method. Comparative Locomotion among Different Terrestrial Mammals. — A striking feature among terrestrial mam- mals is the variety of morphological form, and this is equally the case as regards their mode of locomotion. But beneath this apparent diversity, zoologists have discovered profound analogies; only to instance the most obvious of these, the lower limbs of a man evidently correspond to the hind legs of a quadruped, and all through the mammalian series some similarity may be recognized, either as regards limb or bone or muscle. Differences, indeed, exist among different species, but they are chiefly referable to inequality of development, fusion of some parts, atrophy or mal- formation of others, or to anatomical disproportion. The important point to establish is the connection between anatomical and functional variation. Now, by means of chronophotography, it is easy to trace among different species the respective movements of the different segments of the limb in walking or running. One animal supports itself on the ground by its digital extremities, another by the entire plantar surfaces of the feet. One animal will progress by means of alternate oscillations of its limbs, another by sudden extension ending in a jump. But the unaided eye cannot determine with certainty the respective parts played in these actions by the various bony segments. Chronophotography, however, shows every 260 MOVEMENT detail witli al)S()liite accuracy. Tlius tlic diaj^raius 182, 183, and 181 represent almost on tlie same scale the movements of the different segments of the lower Fig. 182. — Movements of a mai)’s leg in executing a step. limbs during the execution of half a step in the case of a man, a horse, and an elephant. These diagrams demonstrate that the same segment can execute different movements, just as it may be of different length and different shape in the three tyjies under comparison, and that the same segment may Fig. 183. — Movements of the various segments of a horse’s hind leg in executing a step. play a variable part in the flexion and extension of the limb. We can now understand why the muscles which act upon these bones present, in different species of animals, differences in length and volume, although the COMPAKATTVE LOCOMOTION 261 movement executed may be the same. It is by thus analyzing the types of locomotion proper to a large number of species that the necessary data is forth- coming for determining the association between form and function.* In returning to the study of man, the significance of individual peculiarities in the structure of the body will make itself apparent. The variation in length of the bones of the limbs, or in the develop- ment of certain muscles, so noticeable among certain races of men, connects each human type with some Fig. 184 — Movetncnts of an elephant’s hind leg in executing a step. species of animal with similar characteristics. If, for instance, the development of the gastrocnemius muscle, or extensors of the thigh, in a man suggests a resem- blance to a leaping animal, it may be concluded that this man will probably possess special aptitude for jumping, and so on. Comparative Locomotion among Birds. — We know that there are two distinct types of wing among birds, each suitable for a different kind of flight, the “ sailing ” flight and the “ rowing ” flight. Birds that sail possess narrow wings ; shorter and broader wings are peculiar to those that use them as oars. If the * See Marey, Recherches Exf^rimentales sur la MorpJiologie fles Muxclen. C. II. (le I’Acadcniie rles Sciences, September 12, 1887. 262 MOVEMENT area of wing is greatly reduced, the Ijird can fly no longer in the ordinary way through tlie air; but it can fly fairly well along the water, like penguins and birds of similar nature. This water-flight may be observed also among certain marine tortoises, the lower limbs of which resemble in shape the wings of a penguin. Turther, tortoises and birds have many anatomical resemblances. The relation between the shape of the wing and the character of flight can be traced as regards other structural details. We have already shown that the volume and shape of the muscles present differences amongst birds which use their wings as sails and those which use them as oars; in the former the muscles are short and thick, in the latter long and slender. Similar differences are to be noticed in the bones of the thorax’ which are characteristically grooved for the insertion of these muscles. The differences in flight among the 23rincipal types of birds, as far as we have been able to study them, have been demonstrated by means of chronophotography, and it is extremely probable that, by studying a great number of species by the same method, we shall find among the various types of flight, gradations and transitions parallel to those anatomical variations which have been recognized by comparative anatomists among ornithological genera and species. Classification of Different Types of Locomotion. — It is not always possible to take comparative anatomy as a guide to physiological classification. Sometimes it is the variation or functional analogy which may be most apparent, and which will assist us in discovering the zoological relationship. For this reason we have endeavoured to procure photographs of a great number of different species of animals, so as to collate the various physiological types and classify them like the COMPARATIVE LOCOMOTION 263 sections of a museum of comparative anatomy, in the hope that such a series might be able to throw some light upon the subject. The principal dilhculty in this undertaking lies not so much in the actual collection of many different species, as in the sub- jection of them to the best conditions for observation. Domestic animals or tame species can easily be dealt with, but the natural paces or movements of others can only be observed under special conditions, the nature of which can only be discovered after patient research. A frightened animal never moves about in a normal fashion, and if it is compelled to advance in a jDre- determined direction, it instinctively goes the other way. Sometimes the animal becomes scared by the bright light with which it is necessarily illuminated ; at other times it resents an abnormal support under its feet. In some cases the animal has to be brightly illu- minated against a dark background, at others it has to be silhouetted against a dark background. In all these cases a straight pathway from which it cannot diverge is essential. Being compelled to curtail the discussion of these researches, we can only give a few examples of comparative locomotion, and a brief account of the arrangements for taking the photographs. Comparative Locomotion of Tortoises and Lizards. — A water tortoise was placed in a glass aquarium and exposed to translucent illumination, just as in the case of the sea-horse described (p. 212). The animal dived and crawled about at the bottom of the aquarium, but after a time it had to rise to the surface for breath, and it was this movement of which advantage was taken. Fig. 185 shows the tortoise moving about like a quadruped in water, the successive movements of the 264 MOVEMENT four limbs being cl laract eristic of an ordinary walking pace.* Having taken breath, the tortoise returned to the bottom of the ar|uarinm by a similar mode of progression. With other species, the marine turtle, for instance, there are two distinct kinds of locomotion — firstly, that of walking, which has just been described; and, secondly, that which we have compared to flying. In this latter method of progression, the hind limbs are stretched out side by side, and are free from all movement, while the fore limbs are moved backwards and forwards in the execution of movements similar to those of the wings of a “ rowing ” bird. The progression of land tortoises apjDeared to us to A \ % Fig. 185.— Quadrupedal movements of a fresh-water tortoise in swimming to the ! surface. t I resemble ordinary walking, but not having had time to tame a specimen, we did not succeed in inducing one to walk in front of the object-glass; the animal, no doubt frightened at the noise of the apparatus, obstinately kept its limbs tucked away under its carapace. Lizards are extremely difficult to deal with. To place one under favourable conditions for observation we made use of the circular canal which was represented in Fig. 50, and designed for studying subaqueous movements. The transparent part of this canal was lighted from beneath, and the photographic apparatus was placed at a higher level, and received its images reflected from a mirror obliquely inclined at an angle * See sequence of these movements in Chap, xi , “ The Synoptic Record of Horses’ Paces.” COMPAEATIVE LOCOMOTION 265 of 45°. A lizard was placed on the glass bottom, and silhouetted on the sensitized plate. But grey or green lizards were nnable to crawl on the slippery surface of the glass ; but, on the other hand, the Gecko with its spatnlated digits could run about with ease. Tliat all j Fig. ]86. — Grey lizard. The series must be followed from right to left. I ^ these specimens might be under equally favourable i conditions for locomotion a piece of muslin was pasted on the surface of the glass. This muslin should be very transparent, and yet rough enough to admit of locomotion. Figs. 186 and 187 show the mode of pro- gression of the grey lizard and the Gecko. Taken as a whole, the paces are similar,^ but with the Gecko, * See chap. xi. Synoptic chart of the cliaracteristics of the equine trot. movemi-:n'1' 2f)() wliich lias a sliorter body, tlie track of the hind feet is very near tliat of the front. IMoreover, tlie movements are extensive, and cause a serpentine twisting of the wliole body. As tliese movements are very rapid, a great number of photograplis must be taken — about sixty per second — in order that their secpience may lie distinguished. Frogs, Toads, and Tadpoles. — In accordance with the stage of development, batrachians depend on different types of locomotion. Before the tadjiole’s legs are completely developed Fig. 188. — Locomotion of batrachians at different periods of development. it swims with its tail after the manner of a fish (Fig. 188, first row). When the tail has disappeared and the four legs are completely formed, the swimming of batrachians resembles that of man (Fig. 188, second row). The legs, which are at first widely separated, are brought suddenly together, then drawn up under the body, and finally separated again. COIMPAKATIVE LOCOMOTION C-a-aVV ^sl — Wll^Sr® ■ ^ y xj ,vV 'V-": pi* Ife'SyM Fig. 189. — Land-snake in motion. Series to be followed from left to right. 268 MOVEMENT SO as to give a fresh impetus when tliey are again suddenly approximated. Meanwhile the fore limbs are pressed against the tliorax, and appear to be quite inactive.* In the intermediate stage, when the legs are incompletely developed, and tlie tail has not yet disappeared (Fig. 188, third row), the batrachian has a mixed mode of progression. Between the hind legs, which execute the movements of swimming, the tail keeps up an incessant wriggling motion. Snakes, Eels, Fish. — Snakes Wve a slightly different method of progression according as they are on land or in water. An ordinary adder placed in the dry canal, before described, executes undulations of con- siderable amplitude (Fig. 189). As the animal moves along, the undulations pass from the anterior to the posterior end of the body, the same as in the case of the swimming eel. A water adder placed in the dry canal progresses in the same manner, as also does an eel. But when these same animals are placed in water, they swim about with an undulatory movement of less amplitude, but with far greater regularity. Fig. 190 represents an eel in the act of swimming ; the method of progression is identically the same as that of the adder, except that the movement of the tail is more accentuated. The tail of an eel is transversely flattened, and imparts a movement like that of other flsh ; the undulations of the tail are, however, more pronounced than those of the rest of the body. Among other fish the undulations of the body are less marked, although very noticeable in the case of the dog-fish, which is a long-bodied animal (Fig. 191). It is to be observed only in the tail in some species, the movements of the body being but slightly developed, as, for example, is the case with tlie Cyprinidae. * Owing to a mistake in the engraving, the order of the images has been changed in several instances on the second line of figure. COMPARATIVE LOCOMOTION 269 ®<©S|'''f! ^plfl^n^i\\\\•^\YA\\\»V^V•■• f'iiJi.-'-'. ■ < ' ' ■; »#* l^vSSsSS Ji\>VW.' v?>\v.\J «fSsf ^wvwv VV ia;«>'> r^.\\\\w c^v.v v>Sv^\v o o po bb c a a CD % 6 fe 270 movement Insects and Arachnids. — Among .six-legged insects and eight-legged araclinids tlie variations in the methods of in’ogression are entirely due to the different number of legs. In these species the separate legs of each pair act alternately, and the movements of one pair alternate with those of the next. It follows, as was carefully observed by Carlet and j\I. de 3Ioor,* Fjg. 191. — Dog-fish swimming. that among the Coleojitera, for instance (Fig. 192), the first and last appendages on the same side are in contact with the ground, while the middle one is raised. On the other side of the body the middle appendage is on the ground, and the first and last ones raised. When an insect turns round, the movements are feebler, or cease altogether, on the side towards which the animal turns. In the case of certain insects which jump as well as * De Moor (^Archives de Biolojie Liege, 1890). The author gives a very complete account of his studies made on the locomotion of insects. He describes how he obtained the track of each of the feet in different colours by coating them with different pigments; the insect, as it moved, left its track on a strip of paper. He also describes how he arranged the light so as to best observe the movements. COTtIPARATIVE L0C01\I0TI0N 271 272 MOVEMENT (T'awl wo Imvo not heoii able to ])iake out liow tlie sudden spring of tlie liind legs iselfected, but they crawl niucli in the same manner as Coleoj)- tera, as may be seen in Fig. 103, which repre- sents an orthojiterous insect. Among the arachnids (Fig. 194) the four feet of each side alternate in their movements, so that there are always two feet off and two feet on the ground, as can be seen in the case of the spider. To distinguish the feet on the ground from those which are raised we illuminated an insect from above, so that the shadow of its legs was projected on to the white surface upon which it crawled. Under these circumstances the sha- dow of each foot which was in contact with the ground extended right up to the foot itself ; on the other hand, when the foot was raised, a gap existed between the foot and its shadow. COMPAKATIVE LOCOINIOTION Fig. 195.— The walk of a scorpion. Series to be followed from left to right. 274 MOVEMENT Scorpions move very rapidly ; their progression is due to a series of sudden springs, wliicli can be pro- voked by excitation. The sequence of movements is so swift that we have found it impossible to determine their nature by means of photography (Fig. 195). All these insects moved about on glass covered witli paper or transparent muslin, and were viewed by translucent or reflected light. Their movements were directed by means of two sheets of glass, which were arranged so as to be parallel and vertical, and thus to prevent them from leaving the desired track. These few examples will suffice to show how to collect and compare from various species of animals chrono- photographs of different types of locomotion. In a collection of a great number of photographs of this kind one will find the necessary elements for the study of comparative physiology, a study which we mean to pursue. CHAPTER XVI APPLICATIONS OP CIIRONOPnOTOGRAPIIY TO EXPERIMENTAL PHYSIOLOGY Summary. — Numeroua applications of clironophotography ; it supple- ments the informfition derived from the graphic method — Study of the movements of the heart by means of the graphic method — Photography of the successive phases of cardiac action in a tortoise under conditions of artificial circulation — Variations in shape and capacity of the auricles and ventricles during a cardiac cycle — Mechanism of cardiac pulsation studied by means of clironophotography — Comparative advantages of mechanical and chronophotographic registration — Determination of the centres of movements in joints. Almost all vital functions are accompanied by move- ment ; but any attempt to investigate them is beset with extreme difficulty, for the majority of them are very complicated or very rapid. iSometimes, on the other hand, they are extremely slow and difficult to observe. The methods employed by physiologists are gene- rally devised with a view to elucidate what the unaided eye cannot discover for itself. It might reasonably be predicted that chronopho- tography might be found useful in this domain. It might show, for instance, the part played from moment to moment by the different parts of the thorax in the act of respiration. It might follow the peristaltic and the antiperistaltic contractions of the intestines through all their phases and under the various conditions which modifv the characters of these movements. In a word. 270 MOVEMENT it miglit be used in all cases in which neither ordinary observation nor the employment of the graphic method could give us any definite information. There are also many curious movements in the vegetable kingdom which can be studied by means of chronophotography, such, for instance, as the sudden retraction of the leaves and petals of the sensitive plant when touched, the gradual return of these structures to their original position, the progress of vegetable growth, the unfolding of leaves, and the blossoming of flowers. Successive photographs, taken at more or less fre- quent intervals of time, will show the various phases of these phenomena. In both kingdoms the microscope reveals deep down in the midst of living tissues movements of immense interest, for they are concerned with the fundamental principles of organic life. Of such a nature is the circulation of blood corjDuscles in the finest capillaries, and such is the movement of the zoospores in the cells of algae ; such is the slow alteration in shape of the white corpuscles of the blood, and the phenomenon of phagocytosis, etc. It would be a very interesting study to ascertain the characters of these movements bv means of photography. To give an instance of the advantages of chrono- photography as applied to an experimental problem in physiology, we will take the case of cardiac movements. This is a subject which has been exhaustively studied by means of the graphic method ; nevertheless, chrono- photography has aflbrded much new information of quite a different kind ; we will summarize the question as it stands at present. Analysis of Cardiac Movements by means of the Graphic Method. — About thirty years ago, we, together with our friend and colleague Ohauveau, suggested at APPLICATIONS TO PHYSIOLOGY 277 the Academy of Science and at the Academy of Medicine a theory of cardiac movement, based upon information derived from the graphic method. This theory, to-day universally accepted, put an end to dilferences of opinion among physiologists and physi- cians, and it has not been nnassociated with recent advances in the diagnosis of cardiac and vascular diseases. We were induced to embark on these experiments by the incomplete evidence derived from direct exami- nation regarding the nature and sequence of the extremely complicated movements, executed by the heart from moment to moment during a complete cycle of events. Our method was indirect, and consisted in register- ing the curves of pressure variations occurring in the interior of the cardiac cavities as well as outside these chambers. Our curves, properly speaking, did not explain the movements of the heart ; but, nevertheless, they enabled us to state the order and sequence of the auricular and ventricular movements from the changes in pressure which they expressed. This iuterpretation was often a very difficult task, and required a considerable number of experiments in order to verify the different points at issue. Although it was pretty evident that the maximum .of pressure in each cardiac cavity corresponded to the moments at which these cavities contracted for the expulsion of the contained blood, yet it was by no means easy to discover the significance of each variation on the cardiographic curves. Let us examine tracings which express the alterations in blood-pressure in the auricles and ventricles, and the phases of cardiac pulsation. If these figures were placed before the eyes of a physician, whom we will suppose ignorant of the physiology of 278 MOVEMENT tlio Iluart, he would derive from the curves an exaet knowledge of the blood-pressure obtaining in the cardiac chambers, and of the ever-changing force to which the exploring apparatus was exposed in its con- tact with the ve7itricular Avails. Further, he Avould notice the exact sequence of these changes : but from these curves alone he Avould gain no information con- cerning the organ which brought about these changes. It would be possible for him to picture to himself a system of pistons, pumps, and valves capable of pro- ducing similar results, but he Avould never succeed in realizing the actual shape of the heart and the altera- tion in appearance and volume Avhich the different cavities of this organ present from moment to moment. Further, as no analogous phenomenon is to be found outside the animal kingdom, the physician Avould doubtless be at a loss to understand the mechanism of the ventricular contractions, namely, the centrifugal impulse given by the organ at the moment of systole. Even physiologists must acquire some preliminary knowledge, by means of vivisection, of the shape of the heart and its peculiar movements before they can understand the real significance of a cardiogram ; but our eyes are hardly capable of following the rapid and complicated Awiations presented by a heart in motion, the shape of the various cavities Avhether being filled or emptied, the moment of distension of the blood-vessels of the heart, or the contractions of the muscular fibres, etc. As soon as we had at command a method of chrono- photography which faithfully interpreted the changes in shape and position of moving bodies, we sought to derive from this method information supplemental to that furnished by the graphic method. The folloAving experiments Avere our first attempts in that direction. Photography of the Successive Phases of Cardiac APPLICATIONS TO PHYSIOLOGY 279 Action in a Tortoise under Conditions of Artificial Cir- culation.— As we had no large animals at our disposal in which the movements of the heart were accom- panied by such strange variations in appearance, we were compelled to analyze the movements of a land tortoise’s heart by means of chronojDhotography. In order that the entire heart might be visible, we removed it from the body and placed it under con- ditions of artificial circula- tion.* Then, in order that the various parts of the cir- culatory apparatus might be confined to as narrow limits as possible, the apparatus was simplified as represented in Fig. 196. The narrow end of a glass funnel was introduced into the vena cave close up to the left auricle, and fixed there by a strong ligature. Then a glass canula was introduced into the aorta, and connected with a piece of indiarubber tubing to re- present the artery ; this tub- ing in turn was connected Fig. ise.— Heart of a tortoise under .~-i . e 1 j. 1 • conditions of artificial circulation. Wltn a piece ot glass tubing o, auricle ; u, ventricle ; a. arterial 1,, i/\xi tube; 0, outflow; s, support of the bent at an angle (^O j, tne funnel, which represents the venous • J.X, ^ „ system and its communication with opening ot the latter was auricle, directly above the glass funnel. The whole of the apparatus was placed on a solid support, and allowed to stand out in relief against a light background. * For the description of the method, see Marey, La Circulation du sang a V€lat Physiologique et dans les Maladies, p. 70, Fig. 28. Paris, G. Masson, 1881. 280 MOVEMENT Some defibriiiated bullock’s blood was p(jured into the funnel so as to fill it three parts full. After a few minutes, the blood was seen to 1111 the auricle, and theii almost immediately to be discharged into the ventriele ; the latter, in its turn, contracted and sent its contents through the tube, from which it was emptied into the funnel through the attached pipe. Instead of the weak and occasional movements executed by the heart when depleted of blood, an energetic circulation was established, and continued from six to ten hours, and sometimes even longer, the time being dependent on the season of the year. Under the influence of the heart’s activity, the blood soon assumed a veinous character, and therefore it was found essential to renew it from time to time, in order that the energy of the artificial circulation might be maintained. The photographs thus obtained can only be repre- sented as shadows, because the red colouration of the tortoise’s heart is not photogenic, and cannot, therefore, form an image by reflection, and give the configuration which is necessary for understanding the changes in form of the auricles and ventricles, which occur from moment to moment. These silhouettes, however, enable one to follow the various stages by which the blood circulates through the heart, and the tubes which communicate with the cavities of that organ. As the photograph represented in Fig. 197 has to contain several images, we re- duced as far as possible the component parts of the apparatus for carrying on the artificial circulation. The broad funnel in Fig. 196 has been replaced by a thick glass tube pointed at the end, so as to pass through the vein and gain entrance to the auricle. This constitutes the veinous reservoir. Another and finer tube, representing the artery, fits into the orifice APPLICATIONS TO PHYSIOLOGY 281 of the aorta, and curves round, so as to pour its contents into the veinons reservoir. In following the chronophotographic images which correspond to the successive phases of the cardiac cycle, the series must be read from left to right. It Avill be noticed at once that in the first position no blood is passing into the veinons reservoir through the arterial tube, the ventricle is consequently relaxed (diastole). The positions, 2, 3, 4, and 5, shoAv a jet of blood flowing into the reservoir, the ventricle is therefore Fig. 197. — Seven successive pliotograplis of a tortoise’s heart with artificial circula- tion. The series must be read from left to right. They are taken at intervals of jV of a second. In each member of the series the auricle is on the left and the ventricle on the right. From the 2nd to the 5th image the ventricular systole may be recognized by the stream of blood which pours into the venous reservoir. contracted (systole). Finally, positions 6 and 7, in which the jet of blood can no longer be seen, represents a fresh diastolic period. The same phe- nomena continue indefinitely, and pursue the same sequence of events as already described. The series of positions might, therefore, be transposed, Avith No. 1 immediately following No. 7. As for the heart, nothing but the contour can be seen, and this indicates the alternate dilatations and contractions of the auricle and ventricle. 282 MOVEMENT The auricle, wliicli commences to fill in tlie 2nd position of the series, is in process of contraction during the Otli, 7th, and 1st. Now, during the stage of auricular contraction, the ventricle may be seen gradually filling, so that in position 1, when the auricle has reached the climax of its contraction, the ventricle has attained to its maximum of repletion. The alternations between the diastolic and systolic periods of the two chambers of the heart are therefore perfect. The duration of these phases can be calculated almost exactly from the number of positions which correspond to each stage. The apparatus produced 10 images per second, and since 7 images sufficed to represent an entire cardiac cycle, the latter may be concluded to last of a second. In the same way to the systole of the ventricles may be assigned a duration of of a second, and to the diastole These primary notes on the changes in shape of the cavities of the heart will be supplemented by the following experiment. Variations in Shape and Capacity of the Auricles and Ventricles during a Cardiac Cycle. — The surface of the heart can be rendered photogenic by means of a very simjile device ; it suffices to paint it with rather a thick coat of Chinese white. The heart being rendered thus quite white, the play of light and shade displays the alterations in shape and capacity of the different cavities. If a chronophotograph be taken of such a * These measurements do not pretend to rival in exactness those derived from the graphic method, which are almost infinitely accurate. When the commencement and termination of a phenomenon is measured by means of a discontinuous series of images, there may be an error as regards both these stages. The commencement and termination may occur between two exposures of the photographic plate, and it is impossible to say exactly when they occur. APPLICATIONS TO PHYSIOLOGY Fig. 198. Oil observing the series from above downwards, the following phenomena are observed : — 1. The ventricle, v, has completed its systole, and has diminished in volume. The auricle, a, is full, en- larged, and shiny. 2. The auricle has commenced to empty itself and change its form ; its external surface is flattened, and exhibits two irregular borders and a rounded extremity, giving it a tongue- like appearance. The ventricle is beginning to enlarge. 3. The auricle has diminished in size, and the extremity is approach- ing the ventricle ; the latter is be- coming still larger. 4. The auricle is still contracting, and the ventricle is approaching its maximum of repletion. 5. The auricle has completely emptied itself, and the ventricle is diminished in volume ; its systole is commencing (at this moment the blood is being poured into the re- servoir). 6. The ventricular systole con- tinues, and the relaxed auricle com- mences to All. 7. The ventricular systole is com- pleted, the auricle is distended and shiny, and the phase represented in the first of the series is repeated. ] /) 4 % 4 V 5 V 6 V 7 V S V i 284 ^rOVEMENT lieart, which, for convenience’ sake, slionld not be obscured by complicated apparatus, it will give a series of positions which may be studied in detail. Some of the most important points learnt from examining such a series are as follows : — The cavities of the heart have each their peculiar shape, and as the blood pours in they do not assume such a rotund appearance as would be presented by a homogeneous and elastic sac, but, take on various forms, apparently conditioned by the unelastic nature of the pericardium, by which the auricles and ventricles are confined, and generally compressed. Consequently, the outer surface of these cavities appears convex, and moulded to the concavity of the pericardial sac. The adjacent sides of the chambers are flattened against one another, producing facets and more or less uneven ridges. The facets are not always equally visible : on the ventricle, for instance, only one facet can be distinctly seen just at the moment when it is uncovered by the increasing contraction of the auricle. These distinctions are gradually effaced during the systole. The ventricles then become speroidal in shape, proving that all sections of the wall contribute an equal share in the compression of the contained blood. Another fact, which such a series of photographs teaches us, is that the diastole of the ventricles coin- cides exactly with the systole of the auricles. The filling of the ventricle depends, so to speak, on the auricular systole. We recommend an examination of such a series to those who still believe in an active diastole — a sort of aspiration of the blood by the ventricles — a strange belief, not to be explained by the structure of the heart, and which the action of the auricles renders perfectly useless. Mechanism of Cardiac Pulsation studied by means of APPLICATIONS TO PHYSIOLOGY 285 Chi’onophotography. — We have already explained this phenomenon as due to the sudden hardening of the ventricles, which, although relaxed and tensionless during the stage of passive filling, become more or less spherical and hard when active contraction begins, they then actually exercise pressure on the blood which has previously distended them. • This theory alone accounts for all the phenomena which can be observed; it explains why the pulsation of the heart is 23erceptible at all points of the surface of the ventricle, it renders the fact intelligible, which appears at first paradoxical, namely, that the heart presses against the thoracic parietes, not when it expands, but when it diminishes in volume. It is not by an alteration in volume, but by an alteration in hardness, that the heart repels everything that has a tendency to compress it. The maximum degree of hardness corresponds, as we before mentioned, to the systole of the ventricles, namely, at the moment when their powerful muscular fibres compress the blood and project it into the arterial system. Such is the mechanism which causes the sudden pulse which feels like a shock to the finger, and which we call the pulsation, to suggest an analogy between it and the pulse at the wrist ; that it consists of a sudden rise in tension in the organ can be proved by touching its hardened surface with the finger. This theory becomes more intelligible if the ventricles of a large animal are held in the hand; if they are compressed by the fingers, there is a distinct sense of resistance at the moment when the surface of the heart is made tense, which intimates that the systolic contraction of the muscular fibres is in process. AVe endeavoured to render this phenomenon visible to the eye by the following experiment, in which we made use of an arrangement of this kind. The 286 MOV EM K NT apparatus, as (le[)ioted in Fig. 11)7, for carrying (jn an artificial circulation, was employed ; Init the whole of it Avas obliquely inclined and secured to a bevelled cork by means of modelling Avax. The heart. Fig. 199, AAas then placed on a horizontal stand resting on one of its surfaces, Avhile the other Avas freely exposed to vieAv, so that the pulsation might be examined. To prove our point, it must be shoAvn that, Avhen a solid body is pressed against the ventricular Avail Avitli a certain amount of force, the latter, during a condition of relaxation, is indented, and alloAvs the solid body to sink into the hollow thus formed ; and Fig. 199. — Experiment for sbowing^y'chronophotograpli3'- the mechanism of cardiac puisation. that, on the other hand, during systole, the ventricles repel this body, and efface the depression. For this purpose a small square of cork (M, image 2) is alloAved to rest on the surface of the ventricles, and a lever with a counterpoising disc is balanced on the cork. The ventricle receives an indentation from the external pressure, and the cork partially disappears within the depression, as shown in the first position of Fig. 199. This is because the diastole of the ventricles is in process of operation, as may be recognized by the absence of the jet of arterial blood. In position 2 APPLICATIONS TO PHYSIOLOGY 287 of the same figure, the ventricle is in systolic contrac- tion, which is evident by the flow of blood into the reservoir. JSTow, at this moment the entire square of cork comes into view, expelled from the depression into Avhich it had sunk when the ventricle was relaxed. Comparative Advantages of Mechanical and Chrono- photographic Registration. — To continue, these experi- ments, which constitute some of the first applications of chronophotography to experimental pfiiysiology, give additional information concerning the functions of the heart over and above that derived from ordinary cardiography. In comparing the two methods, it will be seen that they attain different ends. The one by means of variations in a curve expresses the minutest changes in blood-pressure that occur in the cardiac chambers, and indirectly this reveals the smallest details of cardiac function. But this method only appeals to the initiated ; it requires numerous control experiments so that one may fully understand the meaning of the cardiogram. The other method, strictly speaking, is the direct examination of the movements of the heart by a more subtle eye than ours, and one that is capable of grasping in a moment the sum total of the changes which take place in the different cavities of the heart. The information to be derived from this method is self-evident. The comparison of a series of consecutive images also affords an oppor- tunity of observing every visible phase of the phenomenon. It affords us no information, as does the cardiogram, concerning the energy which primarily conduces to the changes in form ; in fact, it only gives an approximate idea of the sequence of the various phases of movement, because its record is one of intermittent indications, instead of the continuous record of a curve. Nevertheless, important discoveries 288 IMOVEM EXT in the realm of physiology may l)e looked for from chronophotography. Movements which, in the case of the small heart of a tortoise, have only been sketched in outline, should be more fully studied in the case of large-sized tortoises, for the photographs would be larger and more instruc- tive. Better still to operate on the heart of large mammals, proceeding in the orthodox manner by opening the thorax and inducing artificial respiration. If the heart then be whitened as before described, and a strong beam of light directed on the organ, photo- graphs can be taken containing details not to be found when the hearts of small animals are employed. For instance, one may observe the prominence caused by arteries and veins, the muscular fasciculi, the folds of the serous membranes, and the disj)lacements of the heart within the cavity of the pericardium, etc. The effects of electrical or other excitation applied to the different points of the surface of the heart can be estimated with extreme precision. Graphic regis- tration and chronophotography give, therefore, very different kinds of information concerning the heart, but both are equally useful. Just as auscultation and percussion, though they greatly differ, nevertheless contribute with equal efficiency tov'ards the diagnosis of the physical condition and the functional adequacy of the heart. One could indefinitely multiply examples of the various applications of this new method to experi- mental physiology. We have already mentioned a few in passing; but chronophotography enables us to determine the function proper to each muscle in the act of locomotion, by observing the prominence caused by the muscle in contracting during the various phases of the movement. But if there is one question more ol>scure than APPLICATIONS TO PHYSIOLOGY 289 anotlier, it is the determination of the centres of movement of a joint. Determination of the Centres of Movement in Joints. — When two articular surfaces move on one another, the movement does not always take place round a point corresponding to the centre of curvature of the surfaces. We know, for instance, that in the case of the knee-joint the condyles of the femur simultaneously rotate and slide on the articular surfaces of the tibia, and that the condyles of the lower jaw slide in various directions in the glenoid cavity of the temporal bone, etc. It must follow, therefore, that the centre of articular movement is not indicated by the anatomical relations, but must be empirically discovered. This problem is almost identical with that which is disposed of in regard to the rolling of ships, and the same means may be employed for the experimental solution. On the cadaver the matter is simple : a hole is drilled in the condyle of the inferior maxilla, and another in the ascending process of the same bone near the lower extremity. A polished metal wire is stretched between these two points ; in the photograph it will be represented as a bright line indicating the axis of the ascending portion of the inferior maxilla. The skin of the subject is slightly blackened, and a series of photographs taken on a fixed plate while the jaw is worked up and down. The lines stand out clearly in the photograph, and cross each other at the points which represent the temporary centres of movement of the bone during its angular displacements. On the living subject the experiment is not much more difficult. A small “ planchette ” applied to the teeth of the lower jaw is kept in position by elastic bands passing under the chin. Into this “ planchette,” u 290 MOVEMENT wliicli follows all the movements of the bone, a bright metallic wire is fixed, and bent in such a manner as to correspond to the angle of the jaw ; it is cut off short at the level of the condyles. All the maxillary movements are reproduced by the wire, the upright end of which indicates by its inter- sections on the photograph the centres of articular movement. The applications of chroiiophotography for analyzing such movements as occur within the field of the micro- scope will probably be of great importance. Our efforts in this direction will be recounted in the follow- ing chapter. OHAPTEK XVII MiCKOSCOPiC CHKONOPHOTOGRAPHY ISuMMAKY. — Various movements observable witbiu the field of tbc microscope — Applications of cbronophotography to tbe study of these movements — Difficulties of the subject — Special arrange- ment of the apparatus for cbronophotography on fixed plates and on moving films — Retraction of the stalk in vorticella — Move- ment of the blood in capillary vessels — Movements of the zoo- spores in the cells of conferva — The use of the solar microscope in cbronophotography — The easy application of this method. The microscope has been found of use in all branches of natural science, and by it the observer can fathom the minutest structiu’al details of an organ, and can study in certain of their component cells movements which are the very essence of their activity. Although Harvey, by a flight of genius, concluded that arterial blood returned in some sort of way by the veins, the actual demonstration of this passage was not effected until the invention of the microscope. The whole secret was then suddenly revealed to the astonished eyes of Malpighi — the presence of corpuscles in the plasma of the blood, the capillary ramifications of the vessels which contained it, and the vagarious current which left the arteries and effected its return by way of the veins. The contraction of muscles was inexplicable until the use of the microscope revealed the existence of muscular fibres, their shortening by means of an aggregation of the component discs, and the wave 292 MOVEMENT that travelled along the length of the fibre during the act of contraction. Since that time physiologists have no longer gone astray after hypothetical “veins”; it is in the actual fibres of the muscles that they seek the origin of mechanical energy in animals. Facts accumulate — little by little the theory un- folds itself, and the moment is felt to be fast approaching when muscular contraction will be a fully explained fact. The microscope shows us in a drop of water the animate motion of a million minute organisms roaming about with curious modes of locomotion — methods which find no counterpart among the more highly developed animals. The pulsation of the heart can be seen through the transparent integuments of certain larvae ; so, too, can the contraction of the intestine, the curious phenomena connected with generation, and the slow metamorphosis of the ovum or the embryo. The chemist himself, as he watches the beautiful crystalline arborizations developing upon the micro- scopic slide, essays to interpret the laws of this mysterious architecture. All these movements, however slow or however rapid be the process, can be followed in their respective phases by means of successive photographs, no less clearly than they can be viewed under the microscope. Applications of Chronophotography to the Study of these Movements within the Field of this Microscope. — Our own instrument is the only one up till now which can be used for taking a photographic series of micro- scopical objects. Since our instrument is only pro- vided with one object-glass, the latter must be of suitable focal length for forming images on the sensitized plate of such a nature that they can be enlarged to any degree. The process of microphoto- MICROSCOPIC CHRONOPHOTOGRAPHY 293 graphy has of late years been brought to a high standard of perfection, and apparently at the present time it is only necessary to follow the rules laid down in the various treatises on the subject. In the practical application, however, difficulties arise the causes of which are not far to seek. They consist principally in the illumination of the object. Very small organisms generally move at a rate quite disproportionate to their size. Infusoria cross the field of the microscope in a moment, and execute an immense number of movements which the eye cannot follow. The vibrating cilia, for instance, which serve as locomotor appendages in many of these animalcules, vibrate with such rapidity that they are absolutely invisible, and only come into view when the animals are dead. To obtain, therefore, distinct photographs of these movements, the exposure must be extremely short. We have already learned that, to obtain photographs of the wings of an insect during flight, the exposure must be reduced to 25-000 ^ second, and that, too, under conditions of brilliant illumination ; in fact the insects were photographed in silhouette against the disc of the sun itself. For microscopic creatures, even this illumination would be altogether inadequate, in view of the extremely short exposure necessitated by the rapidity of their movements. It is no longer possible to photograph the object to actual scale, it must be enormously magnified, and this magnification entails a corresponding diminution of the light which reaches the sensitized plate. A linear magnification of 100 diameters reduces ten thousand-fold the intensity of the light dis- tributed over the plate. It is true that with powerful lenses the solar rays can be sufficiently condensed, but then the heat which 294 MOVEMENT accompanies this light would soon destroy the living creatures which move about in the preparation. The employment of vessels containing a solution of glycerine and alum has been regarded as the best means of arresting caloric rays ; it is, however, altogether in- efficient, and so we have resorted to a special arrange- ment of our own. Instead of allowing the light to shine continuously on the preparation, it was projected in an intermittent fashion, and only allowed to act for a very short duration^ generally less than yo^Q^y part of a second. By this method, no matter how great the condensa- tion of the heat, it could never inflict an injury on the creatures under observation. Chronophotography lends itself most happily to these instantaneous illuminations. It is quite sufficient to place the object under examination behind the circular diaphragms. The function of those discs from that time forward is to intercept the luminous rays, which would otherwise reach the preparation, and only to illuminate the latter during the short intervals when the fenestra- tions in the two diaphragms coincide. Big. 200 shows the principal parts of the special apparatus which is adapted to the chronophotographic camera for the analysis of microscopic movements. A wooden box with a central aperture slides into the front part of the apparatus like the frame for containing the object-glasses which has already been described. This box contains an object-glass, C, in its anterior portion for condensing the light which reaches it from the heliostat. The focus of this condenser is arranged so as to fall upon the plate _p, at the same spot at which the preparation is to be placed. During the process of focussing, the position of the plate carrier IMICEOSCOPIC CHRONOPHOTOGRAPIIY 295 is the first to be arranged, and this is carried out by means of the knob B, which controls a rack, and finally by the long rod mv, which turns a micrometer screw. The microscopic object-glass 0 is then brought to bear upon the preparation. The rays from the object then cross a square metallic F16..200. — Special apparatus adapted to cbronopholograpliy for studying the move- ments of microscopic specimens. box behind the lens, and finally traversing the wooden box, and the bellows attached, reach the ground glass of the image chamber.* From the side of the metallic box the tnbe of a microscope runs obliquely, and is provided with an ordinary eye-piece. By an arrangement invented by M. Nachet, the image can be projected either on to * For tlie (Icsciiptu.n of this chambor refer haek to p. IIG, Fig, 80, 296 MOVEMENT the ground glass or along the tube of the microscope according as desired. I.'his arrangement consists of a refracting prism, which is set in motion by the knob P. On pressing this knob, the prism is brought into play, and the image of the preparation is projected along the tube of the microscope ; on pulling the knob out, the prism is removed and the image falls directly upon the ground glass or upon the sensitized plate. As it would be impossible to search for interesting parts of the preparation from behind the apparatus by watching the image upon the ground glass, this portion of the operation is effected by looking through the eye-piece of the obliquely placed microscope. The eye-piece can be adjusted by means of a correcting lens, in such a way that the image is always in focus on the sensitive plate when it is in focus as viewed through the eye-piece. The focussing is carried out as follows, a screen of fairly thick paper is placed in front of the condenser so that the light passing through it does not heat the preparation, and at the same time the eye applied to the microscope can easily stand the illumination.* When the process of focussing is complete and the movements are ascertained to be under favourable conditions, the circular diaphragms are rotated so as to obstruct the continuous light, the screen is removed, the prism drawn away, and the camera set in order for taking a photograph. In this case, as in the other experiments described, it is as well to take some photographs on fixed plates. The moving object must be strongly illuminated in front of a dark background. For slight degrees of magnification * It would be very imprudent not to use the screen, and care should be taken that it is not removed during the process of focussing ; the blinding light which might otherwise strike the retina would be attended with grave consequences. MICROSCOPIC CHRONOPHOTOGRAPHY 297 M. Nachet has constructed a condenser in the form of a cone with a spheroidal base. This base is hollowed out in the middle for the reception of a capsule con- taining thick black varnish. If the light is thrown on the apex of this cone, it will be reflected in the form of converging rays, and illuminate the objects contained in the preparation, which consequently stand out clearly against the dark central background. But this arrangement is only applicable when the magnifying power is low, and has not up to the present produced any very interesting results. Yet we do not despair of obtaining by some other means a good series of photographs on a dark background, and with fixed plates. Chronophotography on moving plates is of far easier application, and the first object submitted by us to this method of observation was a vorticella in active movement. This species of infusoria is shaped some- thing like a funnel, and is beset with a crown of vibrating cilia. It is supported on a spirally twisted stalk which is attached by its other extremity to some vegetable fibre, and furnishes a fixed point of support. From time to time the stalk executes sudden re- tractions by approximating the turns of the spiral, and the funnel-shaped bell is suddenly brought up to the point of attachment. The stalk then lengthens out, and the spiral arrangement disappears until the following retraction. Fig. 201 shows, under a considerable degree of magnification, several of these vorticellae in the midst of a tangle of conferva filaments. To follow the movement more easily it is as well to take as a guide some fixed point such as the intersec- tion of two filaments selected from the network in the field of the microscope. For instance, in the figure 298 MOVEMENT before ns, in tlie n^jper half of the left-liaiid side, there is an irregular rectangle, and in this there are two vorticellfo of unequal size. The larger of them, or that on the left, is situated at about the same level as the other ; in the following illustrations it gradually sinks lower down in the field of the photograph, while the turns of the spiral appear more closely approximated. 1 2 Fig. 201. — Showing the movements of some vorticellae and the retraction of their spiral stalks. The series must be followed from left to right, commencing with the upper illustrations. This example is but one of the many interesting ones that could have been chosen, and, moreover, the way in which the figure is reproduced (namely, simili- gravure), necessitates, in the case of such small objects, some alteration in the images. In typography, the shaded parts have to be indicated by cross-hatching, MICROSCOPIC CHRONOPHOTOGRAPIIY 299 which causes an uncertainty of outline, and an inter- ruption of continuity. Further, in the reproduction of microscopical photo- graphs, it is always as well to have recourse to thick inks. The Movement of the Blood in Capillary Vessels. — The capillaries in the mesentery of a triton serve excellently for this purpose. A layer of the peritoneum is stretched over a piece of cork which has a hole bored through the centre, through which the light can penetrate. A fine capillary is manipulated into the centre of the field on the ground-glass plate. Outside the vessel the extravasated red and white corpuscles are motionless, but within the vessel they are hurried along in a rapid but somewhat inter- inittent stream. If the different members of a series of photographs are compared, it is quite obvious that there is some movement from the changes in arrange- ment which can be noticed among the corpuscles ; the rapidity of movement can be actually estimated by measuring the distance traversed between two successive exposures, namely, the distance traversed in part of a second. For instance, if the space traversed during five separate exposures is about 4 centimetres, say 20 centimetres per second, and the degree of magnification is about 90 diameters, the actual velocity will be a little more than 2 millimetres per second. Hence, what we call the “circulatory torrent,” though it appears very swift to the eye, is in reality a very sluggish stream. Movement of Zoospores. — In the realm of vegetable Physiology many curious movements are to be noticed ; there is one in particular which we thought would be interesting to reproduce, namely, that of the zoospores within conferva cells. These water-plants are com- posed of filaments consisting of a series of cells 300 MOVIOMENT arranged in regular rows, and capable of ramifying in different directions. Some of these cells at certain times are quite full of protoplasm, and in a photograph appear as a dark mass, limited by a transparent cellulose membrane. Later on, the cells evacuate their contents more or less completely ; they are then seen to be reduced to a transparent membrane which is indicated in a photograph as a clear outline. Concerning this phenomenon, botanists have discovered one of the most extraordinary facts in organic life. The protoplasm which at first completely fills the cells as a homo- geneous amorphous mass becomes aggregated, and breaks up into a number of portions, each of which develops at one or other extremity a pair of vibrating cilia. These units take an independent movement, but as long as they are encapsuled within the cell the move- ment is feeble. As soon, however, as part of the cell wall ruptures, the small bodies escape through the opening and swarm about outside in the water by means of their vibrating cilia. The little bodies are zoospores ; it is generally at sunrise that the escape is effected, and the movements during the first hours of freedom are very active. The movements of the zoospores may be followed throughout by observing in a series of photographs the successive positions they occupy in the mother cell. But no adequate description could be given to those, who have never watched the phenomenon, of the activity which reigns within the cell, and only ceases when all the zoospores have succeeded in effecting their escape. The Use of the Solar Microscope in Chronophoto- graphy. — The practical application of the method which has just been described presents some difficulty MICROSCOPIC CHRONOPHOTOGRAPHY 301 when it is required to observe the movements of certain infusoria as they swarm about in the field of the microscope. Hardly has the presence of these creatures within the field of the microscope been assured before they move out of range and necessitate a new adjustment of the apparatus ; for instance, they will disappear during the act of removing the iDi’ism which projects the image upon the sensitized film, or while the apparatus is being set in motion. Accurate focussing is difficult to effect because the equalization of the focus of the eye-piece and of the sensitized plate is a delicate operation. These difficulties may be surmounted by the follow- ing contrivance which seems to us to be applicable in all cases. We locate ourselves in a dark room into which the sunlight, reflected by a heliostat, can pene- trate through a hole in the shutter. The luminous rays are made to traverse a vessel containing a solution of alum, and to converge on to the preparation by means of a condenser. The image formed by the microscopic object-glass is received upon a screen. A hole is made in this screen of the same size and shape as the admission aperture, and behind this hole the chronophotographic apparatus is placed. The front part of the latter is removed and the hinder part is provided with circular diaphragms which rotate in front of the admission aperture. In this way the images of moving creatures can be seen crossing the screen, and the moment can be seized at which these images appear at the aperture ; at this moment it is clear that they must be within the field of the sensitized plate which is situated exactly behind. The knob may be pressed, and a series of photo^ graphs taken. If the image is noticed to leave the 302 MOVEMENT opening, and reappear upon the screen, the kinjb must no longer be pressed, so that tlie process of taking photographs may cease. AVhen the creatures are again noticed to be in a favourable position, the opera- tion may be continued. There are many advantages in this method; firstly, it enables the operator to focus more accurately, because he can directly gauge the definition of the image at the moment of exposure ; and, secondly, it allows him to avail himself of fugitive phenomena which would otherwise be lost, especially if it is necessary to make rather complicated arrangements before exposing the plate ; and, finally, it protects him from injurious exposure to light, in case it shpuld fall upon the retina, a danger which is threatened in other methods, because the light which is thrown by the heliostat, and con- centrated by the condenser, may by chance traverse the tube of the microscope. In this way we obtained photographs of infusoria in motion, the contraction of the internal organs of certain larv0B, the action of the limbs and prehensile appen- dages of all kinds of microscopic creatures. There even seems a possibility of discovering some curious facts as to muscular contraction from observing certain transparent larvse. This method is also well adapted for studying the crystallization of different salts. If a saline solution be concentrated by means of evaporation, crystals make their appearance. There is a sj)ecial form for each salt, and from these centres of crystallization a variety of arborizations radiate in all directions, and invade the microscopic field with unequal rapidity. The formation of these crystals can be well seen on the screen, and as soon as the edge of the crystalline development is noticed to spread over the admission aperture the photographs can be taken. Each image MICROSCOPIC CHRONOPIIOTOGEAPHY 303 shows a different phase of development. The incom- plete attempts which we have been able so far to make show that microscopic chronophotography Avoiild be capable in more practised hands than onrs of producing important results. In fact, we propose to continue this line of investigation. I CHAPTER XVIII SYNTHETIC RECONSTRUCTION OF THE ELEMENTS OF AN ANALYZED MOVEMENT Summary. — Plateau’s method; his phenakistoscope— The zootrope ; its applications to the study of horses’ paces and their relations to one another — The use of instantaneous photography in con- nection with the zootrope — Muybridge, Anschutz — Scientific apidications of Plateau’s method — Points of a good apparatus — Improvements made by different authors — Attempts at construct- ing a chronophotographic projector. Although chronophotography represents the suc- cessive attitudes of a moving object, it affords a very different picture from that which is actually seen by the eye when looking at the object itself. In each attitude the object appears to be motionless, and movements, which are successively executed, are associated in a series of images, as if they were all being executed at the same moment. The images, therefore, appeal rather to the imagina- tion than to the senses. They teach us, it is true, to observe Nature more carefully, and, perhaps, to seek in a moving animal for positions hitherto unnoticed. This education of the eye may, however, be rendered still more complete if the impression of the movement be conveyed to the eye under conditions to which it is accustomed. Such is the object of Stroboscopy, a method of immense scientific importance. The princi- ples of this method were discovered by Plateau, and SYNTHESIS OF MOVEMENT 305 they depend on the physiological property of the retina of retaining for a brief moment the impression of an image after the object which has produced it has disappeared. The duration of this retinal picture is estimated at -jIq part of a second. So that if an image is placed before our eyes ten times in a second the idea of discontinuity is lost, and the images appear to be in continual evidence. If the images shown to us are represented in the successive positions assumed by the object in motion, the impression conveyed to the eye is that of a con- tinuous movement with no intermission. Now, we have seen that not only 10, but even 20, 40, or 60 images can be produced by chronophotography per second. If the 60 photographs taken during one step of a galloping horse could be passed before the eyes at the rate of 10 per second, the duration of the whole step would be spread over a period of 6 seconds, and hence we should have a considerable time in which to observe the motion of the limbs, so hard to follow under normal conditions. In the same way a flying bird could be represented with slower wing movement, and so too with other phenomena which escape notice on account of their extreme rapidity. Inversely, when a movement is so slow as to escape observation, photographs could be taken of it at long intervals and presented to the eyes in sufficiently rapid succession to allow of the changes being clearly per- ceptible. In other cases, if the photographs are pre- sented to the eye at the same intervals as separate the successive exposures, the movement will appear as it actually took place. Such is the use of the strobo- scope. We will now show the successive developments of this method. Plateau’s Phenakistoscope. — Everybody knows the X 306 MOVEMENT ingenious toy invented by I’lateaii at the beginning of the present century, and to which he gave the name of “ Phenakistoscope.” The original form of this instrument was a play- thing which delighted us as children; it was destined, Fig. 202. — Disc of a phenakistoscope, showing the different phases of movement of a gull’s wing. however, one day, to be used for more interesting purposes. The phenakistoscope consists of the follow- ing parts, a cardboard disc perforated at equal distances round the periphery by small sHts. One side of the disc is blackened, and on the other a series of images SYNTHESIS OF MOVEMENT 307 are arranged representing men or animals in the various attitudes which correspond to the successive phases of a movement. When the disc is spun round on its axis opposite to a mirror, and the eye applied to the blackened side on a level with the revolving slits, the reflections of the various images are seen one after another corresponding to the difierent attitudes assumed by the original object; this conveys an impression of actual movement. Fig. 202 represents the disc of a phenakistoscope ; on it are arranged the successive photographs of a flying gull. If this side is made to revolve in front of a mirror and the eye be applied on a level with the slits, the gull can be seen flapping its wings. The rapidity of the movement depends on the velocity of rotation. The disc must be turned in the right direction, other- wise the images will succeed one another in the inverse order to that in which they actually occur, and the direction of movement will appear reversed. Zootropes. — The manufacture of these articles became a commercial industry, and some of them were turned out in more convenient forms ; one of them was called the “zootrope,” and consisted of a cylindrical chamber revolving on a vertical axis. Narrow upright slits were made round the brim, and inside the cylindrical wall a strip of paper was pasted on which a series of images was arranged so as to represent the successive attitudes of a man or animal in motion. If these figures were observed through the slits while the zootrope was revolving, the same impression as that caused by the phenakistoscope was produced. This contrivance, which has been adopted by many manufacturers, possesses one obvious advantage, namely, that several people arranged round the apparatus can watch the phenomenon at the same time. 308 MOVEMENT Application of the Zootrope to the Study of Horses’ Paces. — In the year 1807 we made nse of the zootrope for the purpose of representing the various paces of a horse in motion, and also for showing how the various paces differed from one another. The latter could he shown by merely altering the sequence of the move- ments of the fore and hind limbs. This was the concrete demonstration of the sequence expressed by the chronographic charts. At this time instantaneous photography had not been thought of, and so we used simple drawings to show the successive positions, our data were derived from the registered charts and from the actual foot- tracks. We chose first the simplest case, namely, the paces of an ambling horse, in which the two limbs on the same side acted simultaneously. Twelve positions were drawn on a long strip of paper, six to represent the rise of the two feet on the right-hand side, the other six to represent their period of contact on the ground, the two feet on the left-hand side were of course in the opposite phases. By arranging this strip of paper in the zootrope, the paces of an ambling horse could be easily recognized through the slits. Now, for the purpose of showing how the other paces could be derived from those of ambling, we had recourse to the following device. Vertical lines were drawn through the middle of the horses’ bodies, and square frames were constructed round the posterior halves of the figures containing the hind limbs of the animals. The squares of paper were then cut out, and the original strip of paper then remained, representing a series of positions of the fore quarters, and beliind each of these mutilated images there appeared a square hole in the paper. The strip of paper was then placed SYNTHESIS OF MOVEMENT 309 Oil another of the same size, and the liind portions of the images which had been cut away were gummed each in its proper position upon the lower strip. When this was done, the two strips taken together presented the appearance of the original slij), namely, the suc- cessive attitudes of an ambling horse during the performance of one stride. If the lower strip is moved on one place, so that the fore feet of one image are united to the hind feet of the image immediately behind it, the fore feet will be of a step in advance of the hind feet, and the whole series thus broken up will give the appearance in the zootrope of a racking pace, in which the hind limbs slightly anticipate the movements of the fore limbs. By sliding the lower strip of paper a little further forward the appearance of a walking pace is produced. Still another move in the same direction and we have a broken trot, and then again a walk. This is the concrete expression of the relations given by the chronographic chart Fig. 123. With this method persons familiar with horses’ paces can recognize each example, and realize its derivation from the others. We have been most ably seconded in these researches by M. Mathias Duval, now professor at the Faculty of Medicine and at the School of Fine Arts. This savant recognized the importance of this method for teaching complicated and rapid movements such as could otherwise only be learned at the cost of much labour by specialists. M. Zecky, professor at the School of Fine Arts at Vienna, has adopted the same method for representing horses’ paces. We still possess some very carefully drawn series which he sent us. Use of Instantaneous Photography in connection with the Zootrope. — In this method the accuracy with which the paces were represented was entirely dependent on the skill of the artist, and hence it was left for ;uo MOVEMENT photography to perfect the zootropic representation of motion. From tlie time when Mr. Muybridge succeeded in taking a photographic series of the positions assiuned by men and animals in motion, he invariably resorted to Plateau’s method for synthesizing the movements lie had analyzed. Tiie apparatus used by Mr. Muybridge was a sort of projection phenakistoscope, in which pictures of horses painted on glass discs, and copied from the author’s photographs, were placed in the focus of the projecting lantern and made to rotate. Slits made in the discs admitted light at the required moments. A consider- able audience could thus see upon the screen sil- houettes of horses moving in various directions and at various paces. Zootropes of Muybridge and Anschutz. — We have already remarked that the figures were painted. Now, one great disadvantage of Muybridge’s apparatus, and, indeed, of the zootrope itself, is that the figures are out of proportion, owing to their reduction in the transverse direction, so that the painted horses on the revolving discs have to be made longer than they , really are, so as to appear in their true proportions when thrown upon the screen. M. Anschutz prepared for the ordinary zootrope strips of pa23er covered with ]3hotogra2)hic prints of men and animals in motion. In this case the figures were distorted ; horses especially showed an appreciable diminution in length. Solid Figures in the Zootrope. — AVe also made use of the zootrojDe in studying the movements of birds wings, and for this puiqjose we resorted to a 2)articular contrivance. Instead of a strij) of 2)a})er covered with figures, we introduced into the zootrope a series of wax models jiainted in oils, and representing the bird SYNTHESIS OF MOVEMENT '311 ill all the successive phases of its wing niovemeiit. The illusion was complete, and a flying bird conld be seen flying round and round the apparatus ; sometimes flying away from the observer, sometimes across, and sometimes towards him.* Scientific Applications of Plateau’s Method. — All these applications would be simply childish if they were Fig. 203.— Zootrope, with figures of a gull in relief, and in the successive attitudes of flight. limited to the reproduction of phenomena which could be observed by the eye in the case of living creatures. They would be attended, in fact, by all the uncertainties and difficulties which embarrass the observation of the actual movement. In a bird, for instance, the wings could only be distinguished as an indistinct mass, just * This zootrope witli solid figures is still preseived at the Physio- logical Station. 312 IMOVEMKNT US tlioy appear iu nature. Hut a coiiilniiation of the zoutrupe and clironophotography has further i)ossiIhli- ties, for it enables the observer to follow movements, whieh would otherwise be impossible to examine, by slowing down the motion to any desired rate. We have already pointed out during a single stroke of the wing, which lasts 1- of a second, a series of twelve photographs can be taken at intervals of of a second. Now, these twelve photographs, which correspond to a single stroke of the wing, can be made to pass before the eye in one second. This succession is sufficiently rapid to produce an impression of continuous motion. Under these conditions, the rate of movement is reduced to one-fifth of its actual velocity, and the eye can follow it in all its phases, whereas, in a living bird, only a confused flutter of the wings can be distinguished. In the same way, by slowing down the phases of a horse’s paces by means of the zootrope, they can be more easily analyzed than by observations made directly on the animal. It is not, however, only by reason of their rapidity that some movements elude observation, sometimes their very slowness renders them inaccessible to our senses, take, for instance, the growth of animals and plants. These movements may, however, become quite visible if they are photographed at considerable inter- vals of time, and the corresponding series of images passed rapidly before the eyes by means of the zootrope. Professor Mach, of Vienna, suggests a curious line of research by means of this method. His idea is to take a number of photograjDhs of an individual at equal intervals of time, from earliest infancy until extreme old age, and then to arrange the series of images thus obtained in Plateau’s phenakistoscope. If this were done, a series of changes, which had been brought SYNTHESIS OF MOVEMENT 313 about during a period of many years, would pass before the eyes of the beholder in the course of a few seconds, and thus the stages of a man’s existence would pass in review before the gaze of the onlookers in the form of a strange and marvellous metamorphosis. This method invented by Plateau seems likely to extend our knowledge as regards all kinds of pheno- mena. But the future of the method is dependent on the possible correction which can be effected in the distortion of the images, and on the discovery of a satisfactory means of projecting a number of moving figures on a screen, so as to be visible to a large audience. And, further, it will be necessary to augment the number of successive photographs, so as to represent a performance of considerable duration. Improvements suggested by Different Makers. — So that the images might be projected without distortion, several object-glasses were arranged in a circle, and at the focus of each positive images were arranged representing the different phases of a movement. All the object-glasses were directed towards the same spot on the screen in such a way that by successively illuminating each of the positive images placed behind them, the corresponding attitudes were successively projected on the screen. To effect the successive illuminations of the slides, it has been suggested that a Drumont lamp should be made to revolve as a source of light. Images projected in this way ought to be perfect ; but the focussing of each, and the determination of the direction of the object-glasses, would be a most laborious operation. Moreover, the number of object- glasses is necessarily limited to five or six, and thus the extent of the movement periodically repeated, as the lamp completes its revolution, is necessarily very short. 314 MOVKMKNT M. Raynaud’s Praxinoscope. — Under this title, I\L Kaynancl has given to the world an extremely ingenious instrument. As in tlie ordinary zootrope, the figures are arranged within a cylinder, and are reflected by a prismatic mirror situated at the centre of the apparatus, and thence reach the eye of the observer. The con- trivance is peculiar in that the substitution of one position for another is effected without any intermediate eclipse, so that the images, owing to the constant illumination, appear exceedingly bright. By inter- posing a photographic object-glass in the path of the reflected images, M. Kaynaud has thrown them upon a screen, and magnified them to the required dimensions. Finally, by substituting for the flat circular strip of figures a long strip which winds off one roller on to another, the writer has been able to display a per- formance of considerable duration. As yet, i\I. Eaynaud has only employed figures drawn or painted by hand ; doubtless he could obtain remarkable results by substituting a series of chronophotographs. A slight defect in the apparatus is that the jdane of the pro- jected images is slightly oblique as regards the principal axis of the object-glass, this is due to the construction of the apparatus. It is thus impossible that all the parts of the images can be in focus, and hence the projection on the screen is somewhat indistinct. M. Demeny’s Photophone. — M. Demeny has employed another method for reproducing the movements of the face, the tongue, and the lips, executed during speech. My assistant at the Physiological Station has prepared on a length of film a chronophotographic series con- sisting of twenty-four portraits of a man articulating certain words. When this series of portraits was trans- ferred to the circumference of a glass disc and placed in the focus of a photographic object-glass, they were brightly illuminated from behind, and rendered visible SYNTHESIS OF IMOVEBIENT 315 for brief intervals by an arrangement of fenestrated diaphragms, as used in chronophotography. The short- ness of the exposures, and the perfect working of this apparatus, represented the images as immovable, and Fig. 204. — Demeny’s pbotophone. they appeared exactly at the same spot, in spite of the rotation of the disc upon which they were placed.* These photographs give such a perfect representation of speech that deaf mutes accustomed to read the movements of the lips have been able to recognize the words spoken by the person photographed. * This instrument was designed by BI. Domeny, and called the “Photophone” (C. R. de VAcadem'e des Sciences, July 27, 1891). 31G MOVEMENT I doubt whether it is possible to make a more perfect zootrope, and yet there are a few defects tliat one can mention. Firstly, the number of images that can be transferred to the disc is necessarily limited, unless the apparatus is of enormous size; and, secondly, since a good definition of the movements can only be obtained by very brief exposure, it follows that the amount of light given off* must be too small to produce with distinctness an enlarged projection, and this is the case even when the source of illumination is of the most powerful description. This list of the different forms of apparatuses used in the synthesis of movement is, no doubt, incomplete ; but it may serve to indicate the respective advantages and disadvantages of each system, and to serve as a guide to those who may wish to make fresh researches in the same direction. The Points of a Good Apparatus. — In apparatuses in which the figures rotate with a continuous movement the image can only be made to appear motionless by giving such a short exposure that the movement during that time is inajDpreciable. Now, the brevity of the period of illumination entails a considerable loss of light, and hence the image, when projected on a large scale, is hardly visible at all. If, on the other hand, it is necessary to produce a brilliant projection, the duration of the exposure must be as long as possible ; in that case, however, the image which is for the time being under observation must be absolutely motionless. It is obviously impossible to ensure alternate periods of rest and motion with discs or other heavy pieces of revolving apparatus. The solution of this pro- blem is the same as that which we adopted in chronophotography. The apparatus which is used for the analysis of movement is reversible, at least in SYNTHESIS OF MOVEMENT 317 principle, and might be used for their synthetic re- construction, Let us imagine that a strip of film has imprinted on it positive images, and that this strip is placed at the focus of the object-glass, and brightly illuminated from behind. If these figures are then projected on a screen as far removed from the object- glass as were the original objects, the figures will appear to actual scale. Every time the objective is exposed by the rotation of the diaphragm an image is thrown on the screen, the outlines of which are perfectly defined, because the film is arrested by compression at the moment of exposure. As a matter of fact, it is better to adopt a special contrivance for projecting moving figures. The following are the reasons which induced us to construct a new instrument, to which we have given the name, “ Chronophotographic projector.” The Chronophotographic Projector. — In a projecting apparatus the exposure should be as long as possible, and the transparency should be arrested during the whole period of its projection upon the screen. These conditions must be fulfilled if bright and clear images are required. In the case of the analyzing apparatus, the exposures, on the contrary, should be as brief as the illumination will allow. For an insect’s wing, the exposure should be no more than 23^000 of a second. Now, with such a short exposure, an image would be almost invisible if greatly enlarged by projection ; and this would still be the case even were the source of illumination very powerful. The most important point in constructing a projector is to secure as long an exposure as is possible. For instance, if ten images were taken per second, the exposure should be half or a third as long ; that is to say, for or of a second, instead of for of a second, which is the usual exposure allowed by 818 MOVEM ENT an analyziiio- a])paratus. Instead of the small fenestra- tions on the circular diaphragms, long slits should be made, occupying a third of their circumference. During this long exposure, the film should be com- pletely arrested, and for this purpose the compressor should have a particular kind of cam. To realize the nature of a movement satisfactorily, it is as well to reproduce it several times. This may easily be done by an ajDparatus fitted with revolving discs ; but, as in our apparatus, we have to use a length of film, it should be glued together at the ends, so as to produce an endless series of images continually rotating at the focus of the objective. Such a strip as this could not be introduced into the ordinary chrono- photographic apparatus. We have therefore constructed a special apparatus, in which an endless length of film containing forty or sixty figures, or even more, is allowed to pass with- out cessation under the field of the objective. The illumination, which is from behind, and consists either of the electric light or the sun itself, projects these figures upon a screen. This instrument produces very bright images, but it is noisy, and the projected figures do not appear as absolutely motionless as one could wish. Having arrived at this point in our researches, we learned that our mechanic had discovered an im- mediate solution of this problem, and by quite a different method ; we shall therefore desist from our present account pending further investigations. INDEX Advancing wave, appearance of, 93 Aerial locomotion, 226-257 Apparatus for chronophotography on moving plates, 110-112 for microscopic chronophoto- graphy, 295 for odograpby, 43-47 Arachnids, locomotion of, 270 Arts and crafts, academy of, 24 Assyrian bas-relief, 204 Astronomical revolver, 103, 104 Avanzini’s theory, 96 li Ballistics, laws of, 86 Bas-relief, Assyrian, 204 of Medynet-Abou, 201 Batrachians, locomotion of, 266 Beetle, locomotion of, 271 Blood, movements of in capillaries, 299 Bobbins for sensitized film, 117 Bodies falling in air, 84, 85 Bodies of pisciform shape, resist- ance of, 97 Borelli, 126 Borelli’s law, 226 Boussinesq, 94 Box for holding chronographic plates, 113 Boxer, positions of, 59 Bridges, vibrations of, 101, 102 C Cardiac movements, chronophoto- graphy of, 282-287 , graphic method of, 276 Carlet, 134 Centres of movement in joints, 289 Characteristic attitudes, 177 Chart of fixed odograpli, 131 of footprints, 191 Charts, chronographic, 8, 11, 12, 13, 35, 37, 39, 44, 47, 131, 132, 158, j 188, 190 I , chronophotographic, 52, 55, 79, 86, 87, 99, 140, 112, 143, 144, 154, 155, 157 of horses’ paces, 189 ' , transition from trotting ! to galloping, 189 I , walking, 1 89 , transition from galloping ; to trotting, 190 , walking to trotting, 189 Chevreul, 71 Chopping waves, 93 Chronographic charts. Sze Charts. Chronography, 3 Chronometric dial, 15-17, 51 Chronophotograph of elephant walk- I ing, 261 of flying pigeon, 233 of horse’s leg in walking, 260 of jump with flexed leg, 142 with stiffened leg, 143 of long-jump, 135-137, 140 of man’s leg in walking, 260 320 INDEX Chronophotograph of oscillations f)f 1g^, 144: of pole-jump, 137-139 of runner, 173 of sword-thrust, 178 of walking, 172 Chronophotographic apjjaratus, G7-83 , arrangement of, 116 , charging of, 118 camera, 68 charts. See Charts. enlargement, 123 focussing frame, 69 objective, 69 projection, 317 Chronophotographs, enlargement of, 123 , number of images, 1 23 , reduction of, 123 , reproduction of, 123 , shape of, 121 , size of, 121 taken from above, 175 Chronophotography applied to hydrodynamics, 90 kinetics, 126 mechanics, 84' , geometrical, 60 in sculpture, 176 , microscopic, 291-303 of avine flight, 227-230 of facial expression, 180 on fixed plates, 54-66 on moving films, 234 plates, 103-125 Comatula, locomotion of, 214 Comparative locomotion, 258-274 among birds, 26 1 terrestrial mammals, 259 Cones, 23-27 Conoids, 27 Cros and Carpenticr, 14 Curnieu, 193 Currents, 95-99 Curves of falling bodies, 52 of odograph, 131 of vertical oscillations of head, 158 of work in walking and run- ning, 164, 165 Cylinders, 23-29 D Dark background, 74 for chronophotography, 70 slide, 70 Demeny, 57, 77, 133, 168 Deslandres, 101 Drapery, 183 Drone, flight of, 240 Duck, flight of, 231 Duval, Mathias, 309 Dynamograph, traction, 157 Dynamographic platform, 148 tracings, 152 Dynamography and chronophoto- graphy, 153, Dynamometer, 149 E Eddies, 95-98 Eel, locomotion of, 217, 268, 269 Elastic thread method, 42, 150 Elephant, locomotion of, 261 Engrand, 177 Emmanuel, Maurice, 184 Expressive attitudes, 179 Fencing, photograph of, 141 Film, arrest of, at moment of ex- posure, 120 Fish, locomotion of, 268 Flexible rod, vibrations in, 101 Flight of bee, 254, 267 of drone, 240 of duck, 231 of heron, 233 of insects, 238-257 of pigeon, from above, 234 of tipulse, 254-256 Fluid waves, 91 Flying apparatus, trajectory of, 89 Focussing, 82 Frog, locomotion of, 266 G Galileo, 127 Gecko, locomotion of, 265 INDEX 321 Geometrical chronophotography, 60 of high-jump, 155 of horse, 209 of leg movement, 154 of man walking, 157 Goiftbn, 3 H Harvey, 291 Heron, flight of, 233 Heuzey, 183 Hydrodynamics, 90 Hyperboloids, 23-29 I Images, alternating, 62 , multiplication of number, 62 , separation of, 63 Influence of rate of movement, 58 Insect flight, 238-257 locomotion, 270 Instantaneous photograph of ninner. J Jansen, 103 Joints, 289 L Land- snakes, locomotion of, 267 Lever drums, 5 Lippmann’s electrometer, 49 Lizard, locomotion of, 265 Locomotion, classification of, 262 , comparative, 258-274 • , , in quadrupeds, 186-210 from artistic point of view, 169 in water, 211-225 of batrachians, 266 of comatula, 214 of eels, 216, 268, 269 of fish, 268-275 of fly, 252 of gecko, 265 Locomotion of insects, 270-274 of lizard, 265 of medusa, 216 of scorpion, 273 of sea-horse, 223 of shrimp, 225 of skate, 2 1 8 of snakes, 268 of star-fish, 223 of tortoise, 264 , types of, 226-257 Londe, 114 Long-jump, 135 M Machinery hall, 85 Macroglossus, 242 Mechanical work in walking, 155 Medusa, locomotion of, 215 Melograph, 14 Method of recording muscular con- traction, 228 Metre scale, 80 Millet, 46 Molecular movements in waves, 33-53 Movement from point of view of dynamics, 146 , graphic representation of, 35 Movements, human, 126-145 in liquids, 75-77 in vorticella, 289 of zoospores, 299 Moving bodies, trajectories of, 19-32 Muscular expression, 174 work in walking, 158, 159 Muybridge, 106, 196 Muybridge’s zootrope, 310 N Nachet, 295, 297 O Ocy dromes, 170 Odography, 43 Onimus and Martin, 59 Y 322 INDEX Orthopterous insects, locomotion of, 271 Oscillations, 99 P Paces in man, 128 , speed of, 128 , transition of, 187 Pages, 208 Paillard, Gabriel, 10 Paradoxical illumination, 30 Path described by points on the body, 133 Pellier, 10 Pendulum, jointed, 99 Perspective of moving animals, 81 Pettigrew’s theory, 243 Phenakistoscope, 305 Photographic gun, 108-113 trajectory of insect riiovement, 248 Photographs, directions for taking, 82 Photography, influence on Art, 169-180 Photophone of Demeny, 314 Physiological Station, 71 Pianist, fingering of, 12 Pigeon, flight of, 234 Planet Venus, transit of, 104 Plateau’s phenakistoscope, 305 Playfair, 2 Pole-jumping, 137 Poncelet and Morin, 40 Praxinoscope of Raynaud, 314 Pressure curves, 152 Princes Park, 71 Pulse, tracing of, 41 Q Quadrupeds, locomotion of, 186-210 R Record of movement in walking, 133 , myographic, 229 Relative amount of work in different paces, 162 Running, chronophotography of, 58 S Sea-horse, locomotion of, 222 Se'bert, locomotion of, 273 Shoes, chronographic, 7 Shrimp, locomotion of, 225 Simultaneous photography, 236 Skate, locomotion of, 218 Snakes, locomotion of, 268 Sorbonne, the, 13 Space, measurement of, 1-32 Stanford, 105 Star-fish, locomotion of, 223 Station, Physiological, 71 Stereoscopic pictures, 28, 29 Stroboscopy, 304 Synchronism of wing movement, 241 Synthesis of movement, 304-318 and chronophotography, 304- 318 T Tadpoles, locomotion of, 266 Tatin, 12 Time, 1-17 -curve, 44 , graphic record of, 1 Tipulse, flight of, 254-256 Toads, locomotion of, 266 Tortoise, locomotion of, 264 Train, chart of, 36-38 Trajectories, stereoscopic, 22 Trajectory of bird’s humerus, 229 of insect’s wing, 243 Trochoids, 92 U Uchard, 88 Useful eff'ect, 161 V Vertical foot-pressure, laws of, 150 oscillations of head in walk- ing, 107 Vibrations, 99 Vincent, 3 INDEX 323 Vincent and Goiffon, 193 Volscian bas-relief, 201 Vorticella, movement of, 298 W Walking, abnormalities, 77 Waves, photographs of, 92-95, 121 Weber brothers, 127, 131, 156 Wellmann, 106 Z Zecky, 309 Zootropes, 307, 310 Zoospores, movement of, 299 THE END. 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