ROTATIONS. 



33 



dQ will be found in magnitude and direction as the diagonal of 

 the parallelogram whose adjacent sides are dQ^ and dO^ just as 

 in the case of translations (Art. 46). The importance of this 

 proposition will appear later (Art. 276). 



It is to be noticed that, in the case of infinitesimal rotations, 

 the order of succession in which they take place is obviously 

 indifferent; they can therefore be imagined to take place 

 :simultaneously. 



63. Parallel Axes. The composition of two successive rota- 

 tions about parallel axes is not essentially different from the 

 composition of rotations about two intersecting axes. The 



trihedral //^ of Fig. 17, formed by the given axes./!, / 2 , and 

 the resulting axis /, becomes now a triangular prism, and the 

 spherical construction is replaced by a construction in a plane at 

 right angles to the axes. Fig. 19 shows this construction for 

 the case of two rotations having the same sense (0 1 and # 2 

 being of the same sign) ; Fig. 20 illustrates the case of two 

 opposite rotations. The letters have the same meaning as in 

 Fig. 17. 



PART I 3 



