262 Dynamics. 



2/wra ' 

 calling jy the distance IG ; whence we have 



z : z' : : D : ZK : : JIG : IG ; 

 and hence 



Alg.224. 



z z' : z : : AG IG or 



Now if after each experiment we measure, as may easily be 

 done in several ways, the angles of rotation, that is, the num- 

 ber of degrees contained in the arcs z, z 1 respectively, we may 

 substitute these numbers instead of the arcs z, z', in the propor- 

 tion ; and since the distance Jil is known, we readily obtain .4G, 

 that is, the position of the centre of gravity. 



The value of JIG or D being determined, we calculate the 



294. * length of the arc z which has 1 for radius, and of which the 



number of degrees is known ; then, since JV is known, and g is 



271. equal to 32,2 feet; if we take care to observe the number of 



seconds which elapse up to the instant at which the number of 



degrees in z is counted, we shall know every thing except f m r 2 



in the equation 



gWDt* 



but this equation gives 



fmr* = 



whence we obtain the value of j*m r 2 , which it would be very 

 troublesome to obtain by a particular calculation of the differ- 

 ent parts of the vessel. 



382. When a body L of any figure whatever, having received 

 ' an impulse in a direction HZ, not passing through the centre of 

 gravity, takes the two motions of which we have spoken, it is ea- 

 sy to see, that for an instant it may be regarded as having but 

 one single motion, namely, a motion of rotation about a fixed 

 point or axis F, which according to the figure of the body, and 

 also the distance GZ at which the impulse passes from G, may 

 be situated either within or without the body. For if, while the 



