322 Prof. A. S. Eddington on Astronomical 



in the instantaneous radial and transverse directions are given 

 by the usual formula for rotating axes, viz. 



dli x a, dh 2.A h 



Tt' 6 ^ ~di +eh - 



Equating these io the corresponding forces ( — F, 0), we 

 have 



d 



, (inr ) — mrO 2 = — F, | 



j(iur0) + mr0 = 0. J 







The second of these is equivalent to 







so that 



mr 2 = constant = M/t, 



* a J> 





where M is the mass at rest. 



Then 



. MA r Mh dr ^ . du 



mr — - - - = — =- -^ = — M/i-7^. 



r 2 # r 2 ^(9 </0 



(•■ 



■i) 



Also >?ir# = M//m. 







(2) 



Hence, dividing the first equation of (2) by 6, 

 -Mh^-Mhu = -F/0 



-m mr2 - 



Whence, finally, 



# + W'M 2,! w 



This differs from (1) by having the factor m/M. instead 

 of M/m. It is easily seen that the change will just 

 reverse the sign of all the perturbations predicted ; but this 

 correction makes no essential difference in the application 

 to astronomy, since we have only to make a corresponding- 

 reversal of direction of the sun's motion through the sether. 



There is another way of looking at the correction. We 

 may try to think in terms of mass instead of momentum ; 

 but in that case we have to distinguish between the longi- 

 tudinal and transverse mass : the latter is the same as our m. 

 When a transverse force acts on a particle, the magnitude of 

 the velocity does not change, and hence dm/dt is zero ; but 

 it is not zero for a longitudinal force. The transverse mass 

 therefore corresponds to dm/dt = ; and the neglect of dm/dt 



