470 



SCIENCE 



[N. S. Vol. XXXVIII. No. 979 



his clock is at 9, while the hand of the sun 

 clock is at 3 ; when, as the earth moves on, A^ 

 comes opposite the sun clock (Fig. 9), he finds 

 that twelve hours have elapsed, for the hand 

 of his clock is again at 9, but the hand of the 

 sun clock has only gone from 3 to 12 ; in other 



Fig. 9 



words, nine hours have elapsed on the sun; 

 hence A^ and -B' establish the fact that twelve 

 hours on the earth are equal to nine hours on 

 the sun; that is, the sun clock runs slow in 

 the ratio of 3 to 4. 



Since the sun-men and the earth-men make 

 esaetly similar statements, each finding the 

 other slow in the ratio of 3 to 4, we must 

 logically conclude that the earth and sun 

 clocks are in reality equivalent, and establish 

 the same unit of time. 



The standard of length upon the sun seems, 

 moreover, to be different from that used upon 

 the earth (Fig. 10), but that too is true from 



riG. 10 



one view-point (one coordinate system) only; 

 the standards of length as well as of time are 

 in reality equivalent, as we will now proceed 

 to demonstrate. 



Let us remember that simultaneity is estab- 

 lished only by the clocks. 



The sun-men wish to compare their length 

 standard with the standard used upon the 

 earth. The lengths they wish to compare are 

 such that two observers are necessary, one at 

 each end of the scale. A and B decide to 

 compare their scale reading with the scale 

 reading opposite them at the same moment of 

 time. At 12 o'clock A (Fig. 10) finds zero of 

 his scale opposite zero on the earth's scale; 

 B watching his clock finds, when the hand is 

 at 12 (Fig. 11), that 60 on his scale is oppo- 



Fig. 11 



site 80 on the earth's scale. Hence A and B 

 conclude that 60 sun miles are equal to 80 

 earth miles, or that the earth mile is shorter 

 in the ratio of 3 to 4. 



The earth-men, by similar observations, 

 compare their length standard with the stand- 

 ard upon the sun. A'^, watching his clock 



Fig. 12 



(Fig. 12), finds when the hand is at 12, that 

 zero on his scale is opposite zero on the sun 

 scale. B' finds, when the hand of his clock is 

 at 12 (Fig. 13), that 60 on his earth scale is 

 opposite 80 on the sun scale. Hence they rea- 

 son that 60 earth miles are equal to 80 sun 



