]>Ai,i. — Contrihutiom to the Thcorj/ nj Scre/vx. 21 



If Pa is zero, the wrench is merely the force a". If 'pa is infinite, then a 

 finite wrench is possible only when a" is zero. In this case the wrench 

 rednces to a couple. 



We have now to lay down the rule for discriminating as to which of the 

 two angles 6 or 360'^ - 8, between a pair of non-intersecting vector-screws 

 shall be designated as the right-handed angle between those vector-screws. 



Let P be a point on one vector-screw a, and Qhe a. point on the other 

 vector- screw /3, such that PQ is the common perpendicular to a and /3. 

 Imagine o to receive such a right-handed rotation through an angle with 

 respect to the vector from P to Q, as shall bring the unit-vector on a to point 

 in the same direction as the unit-vector on j3, then is said to be the right- 

 handed angle between (5 and the original position of a. 



If the two vector-screws were in the same plane, the vector PQ is 

 evanescent, the construction would break down, and consequently our means 

 of discriminating between the right-handed angle and the left-handed angle 

 have vanished. 



A convenient practical rule for finding the right-handed angle between a 

 pair of vector-screws may be obtained by the hands and the dial of a watch, 

 it being observed of course that the hands are not coplanar. 



The hands are taken to be the axes of two non-intersecting vector-screws, 

 the vectors of which point outwards from the centre along the hands. The 

 hour indicated by the minute-hand (i.e., the uppermost hand) is subtracted 

 from that indicated by the hour-hand. The difference turned into angle at 

 the rate of 30° per hour is the right-handed angle between the two screws. 

 For example, if the minute-hand was at III, and the hour-hand at Y, the 

 difference is two hours, and the right-handed angle is 60°. If the minute 

 hand is at I and the hour hand at X, the difference is 9 hours, and the right- 

 handed angle is 270'. If the minute-hand is at XI and the hour-hand is 

 at II, the difference is XII + II - XI = .3^, and the right-handed angle 

 of the two screws is 90°. Finally, if the minute-hand be at XII, the hour- 

 hand itself shows the right-handed angle. 



In a figure representing a pair of vector- 

 screws parallel to the plane of the paper, the 

 analogy of the hands of a watch suggests as a 

 useful convention that the longer line OA shall 

 be above OB. Of course in this case OA and 

 0£ cannot represent the lengths of the vectors 

 on the two vector-screws, for these by hypo- " P,q j 



thesis are both unit- vectors. 



The necessity for a clear understanding as to the ilistinction between the 



