418 Dr. C. V. Burton on the Sun s Motion 



a memoir which is about to appear as vol. Hi. pt. ii. of the 

 Harvard Annals*. 



3. Let the origin of coordinates coincide always with the 

 sun's centre, the coordinate axes being in directions fixed in 

 space. At any time t let the coordinates of Jupiter's satel- 

 lite I. be (./, ?/, 2') and those of the earth (#, y, z) ; let the 

 velocity of the sun with respect to the aether have components 

 (a, b, c) in the directions of the coordinate axes, the assump- 

 tion being made that this velocity does not vary sensibty 

 within the period covered by the observations considered. 



4. Let an eclipse of satellite I. be observed at time t' '; then 

 the eclipse actually occurred at some previous time t = t f — t, 

 when the coordinates of the satellite were 



U-ifl+hy, y'-{b+y')T, z'-(c + i')r}; . (1) 



the axes of reference being here understood to have the 

 same position in the cether as our heliocentric axes have at 

 time t. In the interval of time t, therefore, light has 

 travelled through the aether from (1) to a point whose co- 

 ordinates, referred to the same axes, are (a, ?/, c). It may 

 be provisionally assumed that « + #', 1> + y, e + ~' are small 

 compared with V, the velocity of light ; the distance between 

 (1) and («r, y, z) is then approximately 



r+ T -{^a + k') + V {b + y') + ^c + z')}; . . (2) 

 where 

 £ V , f =»-«', y-y', z-z', and r'= („_«')■ + (y_yjt+(«_«')t (3 ) 



5. Since (2) has to be equated to Yt, each observation 

 furnishes an equation of the form 



Vt - r-r/r . {£ (a + i') + v [b + if) + f (c + z ')} = ; 



or, remembering that rjr is very approximately equal to V, 



t(a + y)+ v (l + y') + !;(c+z')-Y(YT-r)=Q. . (4) 



Now (#', y', 'z') is the resultant of Jupiter's orbital velocity 

 and of the velocity of satellite 1. in its orbit around the 

 planet. At the time of an eclipse it may amount, perhaps, 

 to 22 kilom. per second, which is about half the smallest 

 possible estimate of the probable error in the most favourably 

 conditioned velocity-component (a) [see (11) below]. More- 

 over, the error introduced into a, b, or e by neglecting 



* Since tliis note was written Prof. Sampson lias favoured me with 

 some advance sheets of his work, wherein are tabulated just those 

 residual errors from which the Sun's velocity has to be computed. 



