74 SCIENTIFIC APPARATUS. 



means muscular effort exerted by the human frame. In this case 

 the part of the human body which is in contact with the object to 

 be moved is in a state of strain, and the force, dynamically con- 

 sidered, is of the first kind. But this state of strain is preceded 

 and followed by nervous discharges, which are accompanied by 

 the sensations of effort and of muscular strain ; a complication of 

 circumstances which does not occur in the action of inanimate 

 bodies. What is common to the two cases is, that the change of 

 momentum depends on the strain. 



Having thus explained the law of Force, which is the foundation 

 of Dynamics, we may consider the remaining laws of motion. It 

 is convenient to state them first for particles, or bodies so small 

 that we need take account only of their position. Every particle, 

 then, has a rate of change of momentum due to the position or 

 state of every other particle, whether adjoining it or distant from 

 it. These are compounded together by the law of composition of 

 velocities, and the result of the whole is the actual change of 

 momentum of the particle. This statement, and the law of Force 

 stated above, amount together to Newton's first and second laws 

 of motion. His third law is, that the change of momentum in one 

 particle, due to the position or state of another, is equal and 

 opposite to the change of momentum in the other, due to the 

 position or state of the first. 



By the help of these laws D'Alernbert showed how the motion 

 of rigid bodies, or systems of particles, might be dealt with. It 

 appears from his method that two stresses, acting on a rigid body, 

 may be equivalent, in their effect on the body as a whole, to a 

 single stress, whose direction and position will be totally inde- 

 pendent of the shape and nature of the body considered. The 

 law of combination of stresses acting on a system of particles is, in 

 fact, the same as the law of combination of velocities, so far as 

 regards the motion of the system as a whole. This beautiful but 

 somewhat complex result of Dynamics has been used in some 

 text-books as the independent foundation of Statics, under the 



