34 



GEOMETRY OF MOTION. 



[64. 



The signs of O l and # 2 being taken into account, the formulae 

 of Art. 59 are now replaced by the following : 



sn 



sin J O l sin | 6 



The order of two finite rotations about parallel axes is not 

 invertible. 



Fig. 20. 



By repeating the. above construction it is evidently possible 

 to find the resultant of any number of successive rotations 

 about parallel axes, the rotations being taken in a definite 

 order. 



64. The particular case of two equal and opposite rotations 

 about parallel axes deserves special consideration. The point L 

 lies at infinity; hence, the axis of rotation being at an infinite 

 distance, the resulting motion is a translation (Art. 19). This 

 will also appear from Fig. 21 ; the first rotation, about / x , brings 



