through Space occupied by Ether. 



195 



followed is sufficiently illustrated by the accompanying 

 Table III., which shows the whole process of calculating and 

 summing the parts for the orbit corresponding to undisturbed 

 distance '7. 



Table IV. shows the sums for the ten orbits and the products 

 of each sum multiplied by the proper value of r', to prepare 

 for the final integration, which has been performed by finding 

 the area of a representative curve drawn on conveniently 

 squared paper as described in § 6 above. The result thus 

 found is "02115. It is very satisfactory to see that, within 

 '1 per cent., this agrees with the simple sum of the widely 

 different numbers shown in col. 3 of Table IV. 



Table III. 

 Orbitr' = -7. 



Table IV. 



ds. 



ds 2 . 



dt. 



ds 2 ldt. 



■006 

 •137 

 •112 

 •077 

 •050 

 •048 

 050 

 •052 



•000036 

 •018769 

 •012544 

 •005929 

 •002500 

 ■002304 

 •002500 

 •002704 



014 



1-00 

 100 

 1-00 

 TOO 

 100 

 1-00 

 1-00 



•000257 

 •018769 

 •012514 

 ■005929 

 •002500 

 •002304 

 ■002500 

 •002704 



Sim 





•047507 









r'. 



fds-ldt. 



■T • r' .fds-idt 





 •1 

 •2 

 •3 



•4 

 •5 

 •6 



•7 

 •8 

 •9 



•0818 

 •0804 

 ■0781 

 •0769 

 •0722 

 •0670 

 •0567 

 •0475 

 •0310 

 •0114 



•ooooo 



•00080 

 •00156 

 •00231 

 •00289 

 •00335 

 •00340 

 •00332 

 •00248 

 •00102 







•02113 







§. 14. Using in (13) the conclusion of § 13, and taking 

 q = l, we find 



/c=27r.-002115 (14). 



A convenient way of explaining this result is to remark that 



(47T 1 \ 



-g- ~ (*1) 2 ] of an ideal globe 



of rigid matter of the same bulk as our atom, moving with 

 the same velocity. Looking now at the definition of k in the 

 beginning of § 12, we may put our conclusion in words, 

 thus : — The distribution of ethereal density within our ideal 

 spherical atom represented by (11) with K=100, gives rise 

 to kinetic energy of the ether within it at any instant, when the 

 atom is moving slowly through space filled with ether, equal 

 to *634 of the kinetic energy of motion with the same 

 velocity through ideal void space, of an ideal rigid globe of 



