103] THEOREM OF CORIOLIS. 319 



This is the expression for the component of the actual acceleration 

 of the point resolved along the instantaneous direction of the axis 



of X. We see that besides the relative acceleration ~ it contains 



terms involving the relative velocities J^> -A -=^> the angular velocities 



Gnf d t (it 



of the moving axes p, q,r and their derivatives, ^ty ~> ~ 



u>\ ut Ci/t 



A point fixed to the moving system at x, y, 8 would have the 

 accelerations 



d 



r * > 

 236) 0*0 = a - * - y (r 2 +^>) + q (rz+px), 



These may he called the components of acceleration of transportation 

 (entramemenf) or the acceleration of the moving space. They represent 

 the centripetal acceleration of the transported point. (If p, q, r are 

 constant, we have in the last two terms the ordinary expressions for 

 centripetal acceleration, whose resultant is v* divided by the distance 

 from the axis of rotation.) Beside these and the relative accelerations 

 there are terms 



T <>\n dz v d y 

 -di - r di 



These are termed the components of the compound centripetal accel- 

 eration. We accordingly have for the total acceleration 



'x, 



238) 



dt 



that is the actual acceleration of the point is the resultant of the 

 relative acceleration, the acceleration of transportation, and of the 

 compound centripetal acceleration. Accordingly we may consider the 

 axes at rest if we add to the actual forces applied forces capable of 

 producing an acceleration equal and opposite to the acceleration of 

 transportation and the compound centripetal acceleration. This is 

 known as Coriolis's theorem. 



