INSTRUMENTS ILLUSTRATING KINEMATICS. 75 



name of the parallelogram of forces ; a singular inversion of the 

 historical order and of the methods of the great writers. 



When the result of all the circumstances surrounding a body is 

 that there is no change of momentum, the body is said to be in 

 equilibrium. In this case, if the body is at rest, it will remain so ; 

 and on this account the study of such conditions is called Statics. 

 In dealing with the statics of rigid bodies, we have only to examine 

 those cases in which the resultant of the external stresses and 

 attractions acting on the body amounts to nothing. But the most 

 important part of statics is that which finds the stresses acting in 

 the interior of bodies between contiguous parts of them ; for upon 

 this depends the determination of the requisite strength of struc- 

 tures which have to bear given loads. It is found that the way in 

 which the stress due to a given strain depends on the strain, 

 varies according to the physical nature of the body ; for bodies, 

 however, which are not crystalline or fibrous, but which have the 

 same properties in all directions, there are two quantities which, if 

 known, will enable us always to calculate the stress due to a given 

 strain. These are, the elasticity of volume, or resistance to change 

 of size ; and the rigidity, elasticity of figure, or resistance to change 

 of shape. Problems relating to the interior state of bodies are far 

 more difficult than those which regard them as rigid. Thus, if a 

 beam is supported at its two ends, it is very easy to find the 

 portion of its weight which is borne by each support; but the 

 determination of the state of stress in the interior is a problem of 

 great complexity. 



There is one theorem of kinetics which must be mentioned here. 

 If we multiply half the momentum of every particle of a body by 

 its velocity, and add all the results together, we shall get what is 

 called the kinetic energy of the body. When the body is moved 

 from one position to another, if we multiply each force acting on. 

 it whether attraction or stress by the distance moved in the 

 direction opposite to the force, and add the results, we shall get 

 what is called the work done against the forces during the change 



