TIME AND MOTION 69 



rated by unit time (absolute) . If the three beads 

 start together and move with different veloci- 

 ties, QA, QB and QC would represent their 

 space-time paths. The relative velocity of two 

 beads is measured by the length of their sepa- 

 ration at the end of unit time. This separation 

 is AB for the first and second beads, BC for the 

 second and third, and AC for the first and 

 third ; but AC is the sum of AB and BC. 



So also it may be proved from the postulates 

 that there is no limit to possible velocities, for 

 we mav have one body at rest and another body 

 moving northward from it at the rate of one 

 mile per second. But by the fourth postulate we 

 can consider the second body at rest, and there- 

 fore we can have a third body moving north- 

 ward from it at the rate of one mile per second, 

 and so on wdthout limit. Hence by the previous 

 theorem we may find a body moving from the 

 first as many miles per second as we please. 



Let us next consider some consequences of 

 postulates 2 and 3. If in constructing Figure 11 

 we had started our diagram three minutes ear- 

 lier and we had reckoned our distances from an 

 object two feet to the left of the knot O, we 

 might have obtained a more extensive map. But 

 the part which is shown in the figure would have 



