OBSERVATIONS OF CHANGE OF POSITION 25 



along paths which do not resemble that of the body as a whole. 

 In other words, a rotation of the body may have taken place in 

 addition to a translation, and it is at once recognisable that the 

 essential of rotation is the possession of parts. That is rotation 

 cannot exist unless a body possesses parts, and it cannot be 

 observed unless we distinguish parts. If a sphere of perfectly 

 even and similarly coloured surface were rotating we should 

 be unaware except by touch. To become aware, marks upon 

 the surface would be needed, from which rough measurements 

 could be made by eyesight. In the case of an irregular-shaped 

 body, rotation is easily observed. By making a hole in a body 

 and placing it on the various wires representing paths, illus- 

 trations of rotation may be given and its meaning made clear. 

 Combinations of rotation with the various kinds of translation 

 may also be shown. With this arrangement we find that a 

 given body is capable of ten modes of motion with regard to 

 three given planes, viz., the five which we have shown a point to 

 be capable of exhibiting, together with five others derived from 

 a combination of these with rotary movement. If we are not 

 limited to special planes for purposes of measurement, we are 

 able to arrange all kinds of motion into six classes, namely : 



1. Displacement in a straight line. 



2. Displacement in a plane curve. 



3. Displacement in a non-planar curve. 



4. Displacement in a straight line with rotation, or rotation 

 alone. 



5. Displacement in a plane curve with rotation. 



6. Displacement in a non-planar curve with rotation. 



All these classes should be illustrated not only with single 

 bodies, but with systems of separate bodies, joined together by 

 wires, and so forming a rigid system, that is, a system which 

 does not undergo any internal displacements. In reality the 

 parts of any rigid solid form such a system. If a system 

 undergoes change of shape, if, for example, the wires connect- 

 ing the various parts of the system used as a model were to 

 shorten or lengthen while other displacements are taking place, 

 it is easy to see how very complicated the path of any member 

 of the system may be. 



