326.] BODY WITH FIXED POINT. 



Multiplying these expressions by the mass m of the particle 

 situated at the point (x, y, z), we have the components of the 

 effective force of this particle. 



325. To form the equations of motion (4), Art. 223, and (6), 

 Art. 224, for our case, we must reduce the system of the 

 effective forces to its resultant and resulting couple ; or, what 

 amounts to the same thing, we must form the sums occurring 

 in the left-hand members of these equations. 



The summation of the components of the effective forces 

 throughout the body gives, as usual, 



^mx MX, ^ my My, ^mz = Mz, 



where x, y, ~z are the components of the acceleration of the 

 centroid. The resultant is therefore equal to the effective force 

 of the centroid, the whole mass M of the body being regarded 

 as concentrated at this point. 



To make the body free, the reaction A of the fixed point 

 should be introduced. Denoting its components by A x , A y , A gt 

 those of the resultant R of the external forces by R x , R y , R g , the 

 equations (4), Art. 223, assume the form 



(2) 



The left-hand members evidently vanish if the origin be the 

 centroid. The equations (2) can serve to determine the press- 

 ure A on the fixed point in magnitude and direction. 



326. To form the moment ^m(y'z-zy) of the effective forces 

 about the axis of x, we have to multiply the second of the 

 expressions (i) by z, and subtract the product from the third 

 multiplied by y ; then multiply the difference by m, and sum 

 throughout the body. 



Performing this operation first on the last two terms which 

 were shown in Part L, Art. 302, to be due to the angular 

 acceleration, we find 



PART III 12 



