Page:DeSitterGravitation.djvu/12

Mar. 1911. The coefficients $$\mathrm{P, Q, R, P', Q', R'}$$ are periodic functions of $$t$$ devoid of constant terms. Consequently $$c\xi_{0},\ c\eta_{0}$$ are also periodic, and $$c\zeta_{0}$$ is constant. The point the components of whose velocity id are the non-periodic parts of $$c\xi_{0},\ c\eta_{0},\ c\zeta_{0}$$ therefore has no acceleration. If we perform a Lorentz-transformation to a new system having this point as its origin, then the mean values of $$\xi_{0},\ \eta_{0}$$ and $$\zeta_{0}$$ are zero. Thus, if we neglect the periodic terms (which are, moreover, of the second order, and would introduce into (20) only terms of the fourth order, and those multiplied by $$\mu'$$), we have—

By subtracting the second equation (20) from the first we find then—

where

If the mass of the planet is neglected we have $$\mu'=0$$, and we find—