DIAGRAMS. 649 



sections through different planes, to specify the form of objects having three 

 dimensions. 



In such systems of diagrams we have to indicate that a point in one 

 diagram corresponds to a point in another diagram. This is generally done by 

 marking the corresponding points in the different diagrams with the same letter. 

 If the diagrams are drawn on the same piece of paper we may indicate 

 corresponding points by drawing a line from one to the other, taking care 

 that this line of correspondence is so drawn that it cannot be mistaken for 

 a real line in either diagram. 



In the stereoscope the two diagrams, by the combined use of which the 

 form of bodies in three dimensions is recognized, are projections of the bodies 

 taken from two points so near each other that, by viewing the two diagrams 

 simultaneously, one with each eye, we identify the corresponding points intuitively. 



The method in which we simultaneously contemplate two figures, and 

 recognize a correspondence between certain points in the one figure and certain 

 points in the other, is one of the most powerful and fertile methods hitherto 

 known in science. Thus in pure geometry the theories of similar, reciprocal, 

 and inverse figures have led to many extensions of the science. It is sometimes 

 spoken of as the method or principle of Duality. 



DIAGRAMS IN KINEMATICS. 



The study of the motion of a material system is much assisted by the 

 use of a series of diagrams representing the configuration, displacement, and 

 acceleration of the parts of the system. 



Diagram of Configuration. 



In considering a material system it is often convenient to suppose that 



we have a record of its position at any given instant in the form of a diagram 

 of configuration. 



The position of any particle of the system is defined by drawing a straight 



line or vector from the origin, or point of reference, to the given particle. 



The position of the particle with respect to the origin is determined by the 

 magnitude and direction of this vector. 



VOL. n. 82 



