Page:Eddington A. Space Time and Gravitation. 1920.djvu/71

than one unit long—it has contracted on account of its motion relative to him.

Similarly $RR^{\prime }-SS^{\prime }$ is a rod of unit length at rest relatively to $S_{1}$. Overlaying $S$'s partitions we see that it occupies $R_{1}S_{1}$ at

a particular instant for $S$; and this is less than one of $S$'s partitions. Thus $S$ judges it to have contracted on account of its motion relative to him.

In the same way we can illustrate the problem of the duration of the cigar; each observer believed the other's cigar to last the longer time. Taking $LM$ (Fig. 8) to represent the duration of $S$'s cigar (two units), we see that in $S_{1}$'s reckoning it reaches over a little more than two time-partitions. Moreover it has not kept to one space-partition, i.e. it has moved. Similarly $L^{\prime }N^{\prime }$ is the duration of $S_{1}$'s cigar (two time-units for him); and it lasts a little beyond two unit-partitions in $S$'s time-reckoning. (Note, in comparing the two diagrams, $L^{\prime }$, $M^{\prime }$, $N^{\prime }$ are the same points as $L$, $M$, $N$.)

If in Fig. 4 we had taken the line $OT_{1}$ very near to $OU$, our