44-] SCREW MOTION. 23 



TT, and finding the intersection of the perpendicular bisectors of 

 these projections. This intersection is evidently a point of the 

 central axis, and a perpendicular through it to the plane TT will 

 give the central axis in position. 



43. In the case of continuous motion there exists a central 

 axis for every position of the body; but its position both in 

 space and in the body in general varies in the course of the 

 motion. The central axis at any moment is therefore called in 

 this case the instantaneous axis. 



44. The straight lines of space which during the progress of 

 the motion become instantaneous axes for the infinitely small 

 twists of the body form a ruled surface. Similarly, the lines of 

 the moving body which in the course of the motion come to 

 coincide with these axes generate another ruled surface. In 

 .any given position of the body these two surfaces are in contact 

 along a line (the instantaneous axis) which is a generator in 

 each of the two surfaces. The body has an infinitely small 

 rotation about this line and at the same time slides along this 

 line through an infinitely small distance. 



Thus the continuous motion of a rigid body in the most general 

 -case can be regarded as consisting of the combined rolling and 

 sliding of one ruled surface over another. 



