8o.] TWISTS. 4I 



79. It follows from the two preceding articles that a twist 

 can always be resolved into two rotations about skew axes, and 

 this can be done in an infinite number of ways. It is also easy 

 to see that two, or any number of, successive twists can be com- 

 bined into a single twist by resolving each twist into its rotation 

 and translation, and combining all rotations into a resulting 

 twist and all translations into a resulting translation ; the result- 

 ing twist combined with the resulting translation gives the 

 twist equivalent to all the given twists. 



80. For a more complete account of the geometry of motion the 

 student is referred to A. SCHOENFLIES, Geometric der Bewegung, Leipzig, 

 Teubner, 1886; and to W. SCHELL, Theorie der Bewegung und der 

 Krafte, Leipzig, Teubner, Vol. I., 1879, pp. 144-187. See also R. S. 

 BALL, Theory of screws, Dublin, Hodges, 1876; and H. GRAVELIUS, 

 Ball's theoretische Mechanik starrer Systeme, Berlin, Reimer, 1889, . 

 for the more advanced parts of the subject. Many authors treat the 

 geometry of motion in connection with Kinematics ; see the references 

 in Chapter H., in particular the works of Burmester, Resal, Villie\ 



Applications to mechanism and machinery will be found in F. 

 REULEAUX, Kinematics of machinery, edited by A. B. W. Kennedy,. 

 London, Macmillan, 1876; in J. H. COTTERILL, Applied mechanics, 

 London, Macmillan, 1884, pp. 99-134; and in ALEX. B. W. KENNEDY, 

 The mechanics of machinery, London, Macmillan, 1886. 



