164 Prof. A. S. Eddington on Astronomical 



of perihelion, e the eccentricity, and d represents change in 

 a century. 



edm. de. 



Mercury -f 8' 24 + 0-29 -0'88 x 6'33 



Venus -0-06 + 0-17 + 0-21 + 0-21 



Earth + O07 + 0-09 + 0-02 + 0*07 



Mars +0-64 + 0-23 +0-29 + 0-18 



It may be desirable to explain why we use edm instead of 

 simply the centennial motion of perihelion dm. In a circular 

 orbit m is indeterminate, and when the eccentricity is small 

 the direction of the apse line is difficult to determine with 

 accuracy. Multiplying dm by e, we obtain a quantity which 

 can be observed with the same degree of accuracy whatever 

 may be the eccentricity. In fact, edm measures a distortion 

 of the orbit of the same nature but at right angles to that 

 indicated by de; and it will be seen from the table that for 

 each planet de and edm have been found with nearly the 

 same probable error. They are actually rectangular com- 

 ponents of a vector (like dr and rd6 in polar coordinates). 



After the perihelion of Mercury, the next largest dis- 

 cordance (in comparison with the probable error) is in the 

 perihelion of Mars ; but this can scarcely be considered 

 a genuine discordance, since the theory of errors predicts a 

 residual of about this size among eight residuals. However, 

 Lodge's theory gives complete agreement for the perihelia 

 of Mercury and Mars. We have to examine whether it can 

 accomplish this without spoiling the agreement of theory and 

 observation for the other six elements. 



It is clear that the initial chances of success are less 

 favourable to Lodge's than to Einstein's theory. The latter 

 makes no theoretical change in the eccentricities, so that the 

 agreement of these with observation is automatically pre- 

 served ; but Lodge's theory predicts changes usually of the 

 same order as in edm, and it could only be by a particular 

 arrangement of the orbits that a discrepancy could be avoided. 

 Secondly, his theory (besides less important differences*) 

 has edm where Einstein has dm. Now, for Venus and the 

 Earth, whose orbits are nearly circular (unlike Mercury and 

 Mars), Einstein is saved, because his rather large corrections 

 dm have to be multiplied by the small factor e ; on Lodge's 

 theory we have no such opportunity of escape. In fact, 



* A further difference is that Einstein has v 1 instead of v in his co- 

 efficient, so that the effect for the outer planets diminishes more rapidly. 



