62 SCIENTIFIC APPARATUS. 



before any other part of the science of motion, namely, by 

 Archimedes, who proved that when a lever with unequal arms is 

 balanced by weights at the ends of it, these weights are inversely 

 proportional to the arms. But no real progress could be made in 

 determining the conditions of rest, until the laws of actual motion 

 had been studied. 



Translation Returning, then, to the description of motion, or 

 Bodies. Kinematics, we must first of all classify the different 

 changes of position, of size, and of shape, with which we have to 

 deal. We call a body rigid when it changes only its position, and 

 not its size or shape, during the time in which we consider it. It 

 is probable that every actual body is constantly undergoing slight 

 changes of size and shape, even when we cannot perceive them 

 but in Kinematics, as in most other matters, there is a great conve- 

 nience in talking about only one thing at a time. So we first of all 

 investigate changes of position on the assumption that there are 

 no changes of size and shape ; or, in technical phrase, we treat of 

 the motion of rigid bodies. Here an important distinction is made 

 between motion in which the body merely travels from one place 

 to another, and motion in which it also turns round. Thus the 

 wheels of a locomotive engine not only travel along the line, but 

 are constantly turning round ; while the coupling-bar which joins 

 t\vo wheels on the same side remains always horizontal, though its 

 changes of position are considerably complicated. A change of 

 place in which there is no rotation is called a translation. In a 

 rotation the different parts of the body are moving different ways, 

 but in a translation all parts move in the same way. Consequently, 

 in describing a translation we need only specify the motion of any 

 one particle of the moving body ; where by a particle is meant a 

 piece of matter so small that there is no need to take account of 

 the differences between its parts, which may therefore be treated 

 for purposes of calculation as a point. 



We are thus brought down to the very simple problem of 

 describing the motion of a point. Of this there are certain cases 



