260 Dynamics. 



If the distance GZ or D = ; that is, if the direction of the 

 impulse passes through the centre of gravity G, the velocity of 

 rotation ?/ = 0, the velocities u' and v are equal to each other 



and to , as indeed they ought to be, according to article 



288. The velocity u' being determined, if it be compounded 

 with the velocity El, which has suffered no alteration, we shall 

 have the absolute velocity of JV, and its direction after collision. 



If the body L were in motion before collision, we should de- 

 compose the velocity of JV before collision into two others, one of 

 which should be equal and parallel to that of L ; this would 

 contribute nothing to the impulse, and we should employ the 

 second as we have employed the velocity according to EQ, con- 

 sidering the body L as at rest. 



If we compare the value found above for t/, with that which 

 363. we before found for the velocity of rotation, by attending to the 

 difference in the import of r in the two cases, we shall be able to 

 determine the difference between the velocity of rotation which 

 belongs to a free body, and that belonging to one which admits 

 only of a rotation about a determinate point or axis. 



381. From the value which we have found for i/, the veloc- 

 ity of rotation, may be deduced a method for determining by 

 experiment the value ofjffiiJrS and the position of the centre of 

 gravity in a body of any figure whatever. We shall apply to a 

 vessel what we have to say upon this subject. 



Let us suppose, that, by means of a weight JV and a rope at- 

 tached near the stern, the vessel is drawn in a direction perpen- 

 dicular to its length, the weight being small compared with the 

 whole weight of the vessel. Let this weight pass, for instance, 

 Fig 187 over the pulley P. The velocity of the vessel during the exper- 

 iment, (which should continue only for a very short time, as a 

 minute or half a minute) will be so small as to make it unneces- 

 sary to take account of the resistance of the water. 



The action of gravity communicates to ^V, in the instant d /, 

 the velocity g d t (g being the velocity acquired in a second o 

 time), and produces in the vessel an infinitely small velocity of 

 rotation, which I shall call dv f for the point A where the rope is 



