70 OUTLINES OF NATURAL PHILOSOPHY. 



with the sum of the forces, if they are all in the 

 same direction, and with their difference, if they 

 are in opposite directions. 



127. When there is an equilibrium in the lever, 

 if each force be multiplied into the velocity which 

 the point of its application would have, reduced to 

 the direction of that force, if motion were to take 

 place, the sum of all the products so formed is equal 

 to nothing. 



a. Forces that act in opposite directions are here ac- 

 counted positive and negative. This is always to 

 be understood when the sums of forces or of momen- 

 ta are said to be equal to nothing. 



b. This property of the lever is common to all the 

 mechanical powers, and, indeed, to all machines 

 whatsoever. It is known by the name of the prin- 

 ciple of Virtual Velocities, and consists in this, that 

 if the equilibrium of a machine be disturbed, by a 

 quantity indefinitely small, and if the velocity of 

 each force be multiplied into its quantity, the sum 

 of these products, reckoning the forces which are 

 in opposite directions, positive and negative with 

 respect to one another, will be equal to nothing. 

 This principle was suggested by BERNOTJILLI, and 

 is of great use in mechanical investigations. It 

 admits of a general, though indirect, demonstra- 

 tion. 



The velocities compared, being not actual, but such 



as would take place if a certain event, the subver- 



2 sion 



