214 



NATURE 



[yuly 6, 1876 



other than those desired in the mechanism are prevented." 

 When one of the mechanical forces of nature, such as 

 that of falling water, moving air, or expanding steam, is 

 applied to one of the movable links in such a manner as 

 to cause it to change its position, mechanical work is 

 performed accompanied by certain determinate motions, 

 and the whole is called a machine. The relative motion 

 of two bodies in a plane is next considered, and the con- 

 ceptions of the instantaneous centre and of centroids 



Fig 3. 



introduced. At each instant of the motion in a plane of 

 one body with respect to another considered as fixed, the 

 motion can be accurately represented by a rotation in the 

 plane about a fixed point, which, however, in each suc- 

 ceeding instant may occupy a dififerent position ; this point 

 is called the instantaneous centre, and the positions it 

 occupies in successive instants trace the centroid. Space 

 will not permit us to 'show the formation of the reciprocal 

 centroid, or how the motion of the moving body can be 

 represented at each instant by the rolling on one another 

 of the centroids, and the motion of any points connected 

 rigidly with the moving body determined when the 

 centroids are known, but the example given as illus- 

 trating the determination of relative motion from the 

 known centroids will speak for itself. The centroids 

 given are a circle and straight line which roll on each 

 other. All points rigidly connected with the circle 



Fig. 4. 



describe trochoids, the line being regarded as fixed ; all 

 points rigidly connected with the straight line describe 

 involutes, the circle being considered fixed, aad all these 

 paths are determinate, and can be constructed if the 

 position of the moving point with respect to the moving 

 element, circle or line, and the centroids, the line and 

 circle are given. 



From motion in a plane and the determination of 

 centroids. we pass to motion in space. If the position 



of three points in a rigid body not in the same straight 

 line are known, the position of any other point in it may 

 be determined from them, and if the three points are 

 fixed in space the body is also fixed. Thus, to determine 

 the relative motion of two rigid bodies in space, we have 

 only to consider the motion of two triangles fixed one in 

 each of them ; or the motion of one triangle fixed in the 

 moving body with respect to the other reduced to rest. 

 The change of position of the moving triangle may take 

 place in many ways, but it may in every case be effected 

 by its translation parallel to itself in a line joining the 

 old and new positions of one of its angular points, and 

 then by a rotation about an axis through the new position 

 of that angular point. Thus any change of position of 

 a rigid body may be effected by a simple translation and 

 a simple translation about an axis. The simplest case is 

 when the translation takes place along a line parallel to 

 the axis of rotation, when, if the change of position of 

 the moving body be taken indefinitely small, the instan- 

 taneous axes of rotation along which sliding simulta- 

 neously takes place become indefinitely near each other ; 

 the motion is then a simple twist. 



" Consider a pair of bodies having conical rolling, in 

 which both cones have a motion of translation in space. 

 The rotation then takes place through the conical rolling, 

 and the sliding through the translation of the pair ot 

 bodies." Next " consider the consecutive positions of the 

 axes as forming a pair of ruled surfaces, one for each 

 body, so that the motion is reduced to the rolling of the 

 two ruled surfaces upon each other with a simultaneous 

 endlong sliding upon each other of the generators which 

 are in contact. The surfaces of these solids being the 

 loci of the axes, are called axoids. Thus all relative 

 motions of two bodies may be considered as the twisting 

 or rolling of ruled surfaces or axoids." The ruled sur- 

 faces roll on each other without sliding, when all the 

 axes meet in a point as in a pair of cones or a cone and 

 cylinder ; also when the point of intersection is at any 

 infinite distance, as in the case of two cylinders with 

 parallel axes. These are, however, only particular and 

 more obvious cases of the general condition of rolling 

 without sliding, viz., that the two ruled surfaces are deve- 

 lopable on each other. 



APPARATUS FOR REGISTERING ANIMAL 

 MOVEMENTS^ 



'T'HE registering apparatus which have enabled us to carry so 

 far the investigation of the functions in living animals are 

 applicable to the analysis of movements of every kind in health 

 and in disease. It is to this important application that I desire 

 to draw your attention at the present time. 



Most of the movements whose various phases we have to esti- 

 mate must be transmitted to a distance, preserving at the same 

 time all their characteristics. It is by the medium of the air 

 that this transmission is effected, and its principle is as follows : — 



Upon the organ (muscle, artery, heart) whose movements are 

 to be investigated an apparatus called the exploring drum is 

 applied. It is a small metal basin closed by a caoutchouc mem- 

 brane, and communicating by a longer or shorter tube with a 

 similar drum, upon the membrane of which is supported a re- 

 cording lever. The pen with which the extremity of this lever 

 is provided inscribes the curve of the movement impressed on 

 the membrane of the first drum on a cylinder covered with 

 smoked paper and turning on a horizontal axis. 



I. Let us at once apply the process of analysis to the muscular 

 movements of man. For this purpose we may either grasp the 

 muscles of the ball of the thumb between the flattened jaws of 

 the pincers which I show you, or apply to the fleshy substance 

 of any muscle an exploring drum, the knob of which rests upon 

 the muscle. When by means of electricity we cause a contraction 

 or tetanus of the muscle to be studied, the curve of the contrac- 

 tion or that of the tetanus is recorded at a distance upon the 

 revolving cylinder. 



This apparatus shows the thickening which a muscle undergoes 



» Paper read in the Biological Section at the Loan Collection Conferences, 

 by Pro£ Marey. 



