DIAGRAMS. 



i4arenM>nu (or this imaginary system is the required diagram of relative velocities 

 of the actual system at the given instant. 



It is easy to see that the diagram gives the velocity of any one point 

 relative to any other, but cannot give the absolute velocity of any of them. 



Diagram of Acceleration. 



By the same process by which we formed the diagram of displacements 

 from the two diagrams of initial and final configuration, we may form a diagram 

 of changes of relative velocity from the two diagrams of initial and final velocities. 

 ThU diagram may be called that of total accelerations in a finite interval of time. 



By the same process by which we deduced the diagram of velocities from 

 tliat of displacements we may deduce the diagram of rates of acceleration from 

 that of total acceleration. 



We have mentioned this system of diagrams in elementary kinematics 

 because they are found to be of use especially when we have to deal with 

 material systems containing a great number of parts, as in the kinetic theory 

 of gases. The diagram of configuration then appeal's as a region of space 

 swarming with points representing molecules, and the only way in which w 

 can investigate it is by considering the number of such points in unit of 

 volume in different parts of that region, and calling this the density of the gas. 



In like manner the diagram of velocities appears as a region containing 

 (loints equal in number but distributed in a different manner, and the number 

 f ]x>inta in any given portion of the region expresses the number of molecules 

 whose velocities lie within given limits. We may speak of this as the velocity- 

 density. 



Path and Hodograph. 



When the number of bodies in the system is not so great, we may 

 construct diagrams each of which represents some property of the whole course 

 tif the motion. 



Thus if we are considering the motion of one particle relative to another, 

 the point on the diagram of configuration which corresponds to the moving 

 {article will trace out a continuous line called the path of the particle. 



On the diagram of velocity the point corresponding to the moving particle 

 will trace another continuous line called the hodograph of the particle. 



