angle through which each single turning takes place be given. This angle we must therefore look at more closely.
Kotation about the centre extends through the angle P P l = <f) r It will help us in our examination of the matter if we suppose the line M M v which is equal to 1 0, and which is so placed that /. 1 M = <f) v the point M coinciding with 0, to be rigidly connected with PQ. Then in the first turning the line
Fig. is.
M M v turning about 0, will take the position 1} and at the same time P Q (with which it is rigidly connected) will be moved as before into the position P l Q I} so that so far as the determination of the motion is concerned, M M l may replace PQ. If we repeat the whole process for the rotation about O v by joining the line M 1 M 2 (=0 1 2 ) to M M l in such a way that when M^ coincides with O lt the angle 2 1 M 2 is equal to < 2 , we can again replace the figure P Q by M 1 M 2 , or rather by the polygon MM^M^ In this way a second polygon, M M l M 2 M s , can be found, which by the consecutive turnings of its corners about the corresponding
