15, 16] 



MOMENTS. 



19 



in which the line L may be described is chosen, and called the posi- 

 tive sense. Describe a circle with its centre at the point where the 

 common perpendicular meets Z, with its plane at right angles to 

 L, and with the common perpendicular for radius ; the resolved 

 part of the vector at right angles to L is localised in a tangent to 

 this circle. We suppose the circle described in the sense of this 

 resolved part. Now if the sense of description of the circle and 

 the positive direction of the line L are related like the rotation 

 and translation of a right-handed screw the sign of the moment is 

 plus, if not it is minus. The rule of signs may be stated in 

 a simpler equivalent form. Imagine a watch placed in the plane 

 of the circle above described with the positive direction of the 

 line L running from the back towards the face, then if the sense 

 of the tangent to the circle is that in which the hands go round 

 the sign is , if opposite to this the sign is +. 



The student must accustom himself to the above rule of signs. It is 

 known as " the right-handed screw rule." He will be assisted by observing 

 that in the figure of a set of rectangular axes the positive senses of the axes 

 may be taken in the same way as in Articles 4 and 9, and then the 

 positive senses of rotation about them are those of a line turning in the 

 planes (y, z\ (2, x\ (x, y} from Oy towards Oz, from Oz towards Ox y and from 

 Ox towards Oy. 



Fig. 15. 



In a corner of a room, for example, let the student look towards one wall ; 

 its plane may be taken for the plane (y, z\ the wall on his left will be the 

 plane (z, x) the floor will be the plane (#, y\ If he hangs his watch on either 

 wall, or places it on the floor, so that he can see the face, the hands will go 

 round in a direction opposite to one of those shown in the diagram. An 

 ordinary screw turned so as to move in the positive direction of either axis 

 will turn round in the way shown in the diagram. 



22 



