Rotation of Bodies uncorifined. 261 



attached. Putting, therefore, g d t for w, and d v' for ', in the 

 value of v' found above, JV* being considered as very small or 

 nothing compared with L, the mass of the vessel, which gives 



z/ = 

 we shall have 



d * = f^- 



Let d v" be the velocity with which that point of the vessel turns 

 which is distant one foot from the centre of gravity ; we shall 

 have 



d-o' : dv" :: AG : I :: D : 1, 

 and consequently 



dv' = Ddv". 

 Substituting for d v' this value, we have 



and, by integrating, 



fmr 



Let z be the arc described by the point in question during _ 

 the time / ; we shall have 



dz = v" dl, 

 and consequently 



whence, by integrating, 



'' 



Therefore, if the rope acting always perpendicularly to the 

 length of the vessel, be attached to another point /, and we call 

 zf the arc described by the same point during the same time , 

 we shall have 



