6 TWISTS AND WRENCHES. 



required to specify the screw a. The sixth or metric 

 quantity, which is called the INTENSITY OF THE WRENCH, 

 and is denoted by a", expresses the magnitude of that 

 force which, when united with a couple, constitutes the 

 entire wrench. 



The moment of the couple is the product of the inten- 

 sity of the wrench and the pitch of the screw, or in sym- 

 bols, a." pa.. 



If the pitch be positive (negative], the direction in which 

 the couple acts which forms one portion of the wrench 

 bears the same relation to the direction in which the force 

 acts which forms the other portion of the wrench as the 

 direction of a couple which would make a nut turn on an 

 ordinary right-handed [left-handed] screw bears to the 

 direction of the force parallel to the axis of the screw 

 which would give the nut the same motion if the screw 

 were frictionless. 



If the pitch be zero, the wrench reduces to a pure 

 force along a. If the pitch be infinite, then a finite 

 wrench is not possible except the intensity be zero, in 

 which case the wrench reduces to a couple in a plane 

 perpendicular to a. 



In the case of a twisting motion about a screw a the 

 rate at which the amplitude of the twist changes may be 

 called the TWIST VELOCITY and be denoted by a'. 



The following illustration may be useful : 



If the screw be conceived placed along the axis 

 around which the hands of a watch turn, and if the twist 

 be in the direction in which the hands of the watch move, 

 then, for positive pitch the translation will be from the 

 front of the watch to the back; for negative pitch the 

 translation will be from the back of the watch to the 

 front. If in this statement we interchange the words 

 positive and negative, we have the case where the direc- 

 tion of the twist is opposite to the motion of the hands. 



