80 LECTURES TO SCIENCE TEACHERS. 



block. If the block be pressed on one side as it slides, it at 

 once moves sideways, and can only be kept in a straight path 

 if directly the pressure is exerted on the one side an equal 

 and opposite force (or a force which has a resultant with the 

 first in the direction of motion), be caused to act upon it on 

 the other. If, on the other hand, the block be made to slide 

 between accurately fitting grooves (like a guide-block in a 

 machine), inclined at the same angle as the plane, and like 

 it fixed, the block may be pressed sideways or in any other 

 direction, but no alteration in its motion can take place ; the 

 motion is "constrained," it can occur only in the one 

 direction permitted by the guiding grooves. In the one 

 case the external force has to be balanced by another 

 external force, in the other the balancing force is molecular, 

 i.e. is a stress and not an external force, and comes at once 

 into play the instant the disturbing force is exerted. The 

 geometric forms which are used in this way to constrain or 

 render determinate the motions in machines are very various, 

 and are chosen in reference to the particular motion required. 

 If every point in a body be required to move in a circle 

 about some fixed axis, a portion of the body is made in the 

 form of a solid of revolution about that axis, and this is 

 caused to " work in " another similar solid ; the two form- 

 ing the familiar pin and eye. If all points of a body be 

 required to move in parallel straight lines we get similarly 

 for guiding forms a pair of prisms of arbitrary cross- section ; 

 a slot and block. If every point of a body be required to 

 move in a helix of the same pitch we use a pair of screws 

 of that pitch, one solid and one open, for constraining the 

 motion ; a screw and nut. 



The general condition common to these very simple forms 

 is that in each case the path of every point in the moving body 

 is absolutely determined at every instant, that is to say, the 

 change of position of the moving body is absolutely 

 determinate. 



The geometric name for these mutually constraining bodies 

 is envelopes, and each one is said to envelope the other. We 

 shall call them (kinematic) elements, and the combination of 

 two of them we shall call a pair of elements. 



Those we have mentioned are special and very familiar and 

 important cases of pairs of elements, which are of great 

 simplicity. They have the common property of surface 



