TWISTS AND WRENCHES. 3 



to be a straight line in space with which a definite linear 

 magnitude, termed the pitch , ts associated. 



We shall often denote a screw by a symbol, and then 

 usually by a small Greek letter. With reference to these 

 symbols, a caution maybe necessary. If, for example, a 

 screw be denoted by a, then a is not an algebraic quan- 

 tity, and cannot occur in an algebraic equation. It is a 

 symbol which denotes all that is included in the concep- 

 tion of a screw, and requires five quantities for its speci- 

 fication, because four quantities are required to determine 

 a straight line, and the pitch must be specified by a fifth. 

 It will often be convenient to denote the pitch by a sym- 

 bol, which is derived from the symbol employed to de- 

 note the screw to which the pitch belongs. The pitch of 

 a screw can be represented by appending to the letter/ 

 a suffix denoting the screw; thus, p a is the pitch of a. 

 The symbol p a represents, in fact, a certain number of 

 millimetres, or inches. 



2. Definition of the word Twist. We have now to de- 

 fine the very important use to be made of the word 

 twist. A body is said to receive a twist about a screw 

 when it is rotated about the screw, while it is at the same 

 time translated parallel to the screw, through a distance 

 equal to the product of the pitch and the circular measure 

 of the angle of rotation ; hence, 



The canonical form to which the displacement of a rigid 

 body can be reduced is a twist about a screw. 



If a body receive several twists in succession, then the 

 position finally attained could have been reached in a 

 single twist, which is called the resultant twist. 



Although we have described the twist as a compound 

 movement, yet in the present method of studying me- 

 chanics it is essential to consider the twist as one homo- 

 geneous quantity. Nor is there anything unnatural in 

 such a supposition. Everyone will admit that the rela- 



B 2 



