56 THE PRINCIPAL SCREWS OF INERTIA. 



a are fll , &c., a 6 , the twist velocity about u) m may also be 

 represented by d'a m ( 36), whence 



If we multiply this equation by/ m 2 a m , add the six equa- 

 tions found by giving m all values from i to 6, and re- 

 member that a and X are reciprocal, we have ( 39,) 



whence a 7 is determined. 



This expression shows that the twist velocity pro- 

 duced by an impulsive wrench on a given rigid body 

 constrained to twist about a given screw, varies directly 

 as the product of the virtual coefficient of the two screws 

 and the intensity of the impulsive wrench, and inversely 

 as the square of ^ . 



6 1 . The Kinetic Energy acquired by an Impulse can be 

 easily found by 59 ; for, from the last equation, 



hence the kinetic energy produced by the action of an 

 impulsive wrench on a body constrained to twist about 

 a given screw varies directly as the product of the square 

 of the virtual coefficient of the two screws and the square 

 of the intensity of the impulsive wrench, and inversely 

 as* the square of u a . 



62. Free Body. We shall now express the kinetic 

 energy communicated by the impulsive wrench on rj to 

 the body when perfectly free. The component on u) m of 

 intensity rj'j\ m imparts a kinetic energy equal to 



