126 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



librium will not be destroyed — 1, if we imagine the single points 

 of the system in their present position to be rigidly united to 

 each other ; and 2, if we then remove the forces which the points 

 exert upon each other. From this however it follows further : 

 If the forces which two material points exert upon each other be 

 brought into equilibrium by the action of exterior forces, the 

 equilibrium must continue, when, instead of the mutual forces of 

 the points, a rigid connexion between them is substituted. Forces, 

 however, which are applied to two points of a rigid right line can 

 only be in equilibrium when they lie in this line and are equal 

 and opposite. It follows therefore for the forces of the points 

 themselves, which are equal and opposed to the exterior ones, 

 that they must act in the direction of the line of connexion, and 

 hence must be either attractive or repulsive. 



The preceding propositions may be collected together as 

 follows : — 



1 . Whenever natural bodies act upon each other by attractive 

 or repulsive forces, which are independent of time and velocity, 

 the sum of their vires vivce and tensions must be constant ; the 

 maximum quantity of work which can be obtained is therefore a 

 limited quantity. 



2. If, on the contrary, natural bodies are possessed of forces 

 which depend upon time and velocity, or which act in other 

 directions than the lines which unite each two separate material 

 points, for example, rotatory forces, then combinations of such 

 bodies would be possible in which force might be either lost or 

 gained ad infinitum, 



3. In the case of the equilibrium of a system of bodies under 

 the operation of central forces, the exterior and the interior 

 forces must, each system for itself, be in equilibrium, if we sup- 

 pose that the bodies of the system cannot be displaced, the whole 

 system only being moveable in regard to bodies which lie with- 

 out it. A rigid system of such bodies can therefore never be set 

 in motion by the action of its interior forces, but only by the 

 operation of exterior forces. If, however, other than central 

 forces had an existence, rigid combinations of natural bodies 

 might be formed which could move of themselves without needing 

 any relation whatever to other bodies. 



