We have to be on our guard against results of this latter kind which would only be of interest if the radius-vector were a directly measured quantity instead of a conventional coordinate. The advance of perihelion is a phenomenon of a different category. Clearly the number of years required for an eccentric orbit to make a complete revolution returning to its original position is capable of observational test, unaffected by any convention used in defining the exact length of the radius-vector. For the four inner planets the following table gives the corrections to the \index{Elements of inner planets}% \index{Mercury, perihelion of}% centennial motion of perihelion predicted by Einstein's theory: \[ \begin{array}{l@{\qquad}l@{\qquad}l} & \multicolumn{1}{c}{\delta\varpi} & \multicolumn{1}{c}{e\, \delta\varpi} \\ \text{Mercury} & +42''.9 & +8''.82 \\ \text{Venus} & +\PadTo[r]{42''}{8}.6 & +\PadTo[r]{8''}{0}.05 \\ \text{Earth} & +\PadTo[r]{42''}{3}.8 & +\PadTo[r]{8''}{0}.07 \\ \text{Mars} & +\PadTo[r]{42''}{1}.35& +\PadTo[r]{8''}{0}.13 \\ \end{array} \] The product $e\, \delta\varpi$ is a better measure of the observable effect to be looked for, and the correction is only appreciable in the case of Mercury. After applying these corrections to~$e\, \delta\varpi$, the following discrepancies between theory and observation remain in the secular changes of the elements of the inner planets, $i$~and $\Omega$ being the inclination and the longitude of the node: \[ \footnotesize \begin{array}{lrrrr} & \multicolumn{1}{c}{e\, \delta\varpi} & \multicolumn{1}{c}{\delta e} & \multicolumn{1}{c}{\sin i\, \delta\Omega} & \multicolumn{1}{c}{\delta i} \\ \text{Mercury} & -0''.58 ± 0''.29 & -0''.88 ± 0''.33 & +0''.46 ± 0''.34 & +0''.38 ± 0''.54 \\ \text{Venus} & -\PadTo[r]{0''}{0}.11 ± \PadTo[r]{0''}{0}.17 & +\PadTo[r]{0''}{0}.21 ± \PadTo[r]{0''}{0}.21 & +\PadTo[r]{0''}{0}.53 ± \PadTo[r]{0''}{0}.12 & + \PadTo[r]{0''}{0}.38 ± \PadTo[r]{0''}{0}.22 \\ \text{Earth} & \PadTo[r]{0''}{0}.00 ± \PadTo[r]{0''}{0}.09 & +\PadTo[r]{0''}{0}.02 ± \PadTo[r]{0''}{0}.07 & \PadTo{+0''.46}{\cdots} \quad \PadTo{0''.34}{\cdots} & -\PadTo[r]{0''}{0}.22 + \PadTo[r]{0''}{0}.18 \\ \text{Mars} & +\PadTo[r]{0''}{0}.51 ± \PadTo[r]{0''}{0}.23 & +\PadTo[r]{0''}{0}.29 ± \PadTo[r]{0''}{0}.18 & -\PadTo[r]{0''}{0}.11 ± \PadTo[r]{0''}{0}.15 & -\PadTo[r]{0''}{0}.01 ± \PadTo[r]{0''}{0}.13 \\ \end{array} \] \PageSep{90} The probable errors here given include errors of observation, and also errors in the theory due to uncertainty of the masses of the planets. The positive sign indicates excess of observed motion over theoretical motion\footnotemark.\footnotetext {Newcomb, \Title{Astronomical Constants}. His results have been slightly corrected by using a modern value of the constant of precession in the above table; see de~Sitter, \Title{Monthly Notices}, vol.~76, p.~728.}