20 Proceedings of the Royal Irish Acadenuj. 



scalar a' which may be either positive or negative, and which is termed the 

 twist velocity of the motion. 



The instantaneous twisting motion is formed by compounding (1) a 

 motion of rotation, and (2) a motion of translation. 



(1) The motion of rotation is right-handed or left-handed about the 

 vector on the vector-screw, according as a is positive or negative. In this 

 we see the advantage of the vector-screw over the screw. Had it not been 

 for the vector, we should have had no means of indicating the direction of the 

 rotation in the specification of the twist. 



The angular velocity of this rotation is a radians per imit of time. 

 (2) The motion of translation is in the same direction as the vector, or iu 

 the opposite direction according as a'^J^ is positive or negative. 



If a be the angular velocity with which a changes, then the numerical 

 value of the velocity of translation is 



To show how the employment of the vector-screw enables all possible 

 conditions of tlic twisting motion to be specified, we observe that 



If Pa> and a > 0, the rotation is right-handed, and the translation is 

 with the vector. 



If y>. < and a > 0, the rotation is right-handed, and the translation is 

 against the vector. 



If ;). > and a < 0, the rotation is left-handed, and the translation is 

 against the vector. 



If /', < and u <. 0, the rotation is left-handed, and the translation is 

 with the vector. 



The statement that a couple is right-handed about a vector implies not only 



(1) That tlie vector is normal to the plane of the couple, 

 but also 



(2) That the couple tends to give a body a right-handed rotation about 

 that vect<:>r. 



A wrench may Ije completely specified by a vector-screw a (of pilch p^), 

 and a scalar a", which is termed the Intensity of the Wrench. The wrench 

 is produced by the combination of (1) a force, and (2) a couple. 



(1) The intensity of the force is a" units of force, and its tendency is 

 with the vector or against the vector, according as a" is positive or negative. 



(2) The couple is to be right-handed or left-handed about the vector, 

 according as a"p. is positive or negative. 



The numerical value of the moment of the couple is 



