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LECTURES TO SCIENCE TEACHERS. 



taken by such pairs of elements. It is worth while noticing 

 a few points in which the motions determined by them differs 

 from the motions of the closed pairs. First, as we have 

 already seen, the contact of the elements determining the 

 motion was surface-contact in the former case, while here it 

 takes place only along a finite number of lines. Then the 

 motions of all points in the first case were similar ; in these 

 pairs the motions of the points are not similar, but entirely 



Flo. 2. 



dissimilar, the motion of each point depending entirely upon 

 its position. Fig. 2 shows a few of the point-paths of the pair 

 of elements shown in Fig. 1. The strikingly different curves 

 obtained from one pair of elements, according to the choice 

 of the describing point, is too obvious to need further notice. 1 



1 The triangle UTQ and the three curves within it, which have M^ 

 for their centre, are point-paths. The curve -triangle and the duangle 

 shown in thicker lines will be explained further on. 



