6 GEOMETRY OF MOTION. [12. 



through the centre makes with any fixed line through the centre 

 in the plane. 



12. We have seen that a translation as well as a rotation is 

 measured by a single algebraical quantity, the translation by a 

 distance, the rotation by an angle. This is the reason why 

 such motions may be called linear or of one dimension. The 

 two fundamental forms of motion, translation and rotation, are 

 thus seen to correspond to the two fundamental magnitudes of 

 metrical geometry, viz. distance and angle. 



It is to be noticed that both for translations in the same 

 direction and for rotations about the same axis the resultant 

 displacement is found by algebraic addition of the components, 

 not only when the components are consecutive motions, but even 

 when they are simultaneous. Thus we may imagine a point P 

 displaced by the amount P^P^ along a straight line while this 

 line itself is moved along in its own direction by an amount 

 Q^Qv The resultant displacement of P is the algebraic sum 



13. Translations being measured by distances or lengths, 

 and rotations by angles, we need in mechanics a unit of length 

 and a unit of angle. 



The two most important systems of measurement are the 

 C. G. S. (i.e. centimetre-gramme-second) system, and the F. P. S. 

 (i.e. foot-pound-second) system. The former is frequently 

 called the scientific system ; it is based on the international 

 or metric system of weights and measures. The F. P. S., or 

 British system, is still used in England and the United States 

 almost universally in engineering practice.* 



14. The unit of length in the C. G. S. system is the centimetre 

 (cm.), -i.e. YOU of the metre. The original standard metre is a 



* For fuller information on all questions relating to standards and units see 

 J. D. EVERETT, Illustrations of the C- G-. S. svsten: of units with tables of physical 

 constants; London, Macmillan, 1891. 



