We find \[ \left. \begin{aligned} - 8\pi\, T_{11} &= \left(-\frac{1}{R^{2}} + \lambda\right) g_{11}\Add{,} \\ - 8\pi\, T_{22} &= \left(-\frac{1}{R^{2}} + \lambda\right) g_{22}\Add{,} \\ - 8\pi\, T_{33} &= \left(-\frac{1}{R^{2}} + \lambda\right) g_{33}\Add{,} \\ - 8\pi\, T_{44} &= \left(-\frac{3}{R^{2}} + \lambda\right) g_{44}. \end{aligned} \right\} \Tag{(69.3)} \] Since $\lambda$~is still at our disposal, the distribution of this energy-tensor is indeterminate. But it is noted that within the stellar system the speed of matter, whether of molecules or of stars, is generally small compared with the velocity of light. There is perhaps a danger of overstressing this evidence, since astronomical research seems to show that the greater the scale of our exploration the more divergent are the velocities; thus the spiral nebulae, which are perhaps the most remote objects observed, have speeds of the order $500$~km.\ per~sec.---at least ten times greater than the speeds observed in the stellar system. It seems possible that at still greater distances the velocities may increase further. However, in Einstein's solution we assume that the average velocity of the material particles is always small compared with the velocity of light; so the general features of the world correspond to \index{World!mass of}% \[ T_{11} = T_{22} = T_{33} = 0,\quad T_{44} = \rho,\quad T = \rho_{0}, \] where $\rho_{0}$~is the average density (in natural measure) of the matter in space. Hence by~\Eq{(69.3)} \[ \lambda = \frac{1}{R^{2}},\quad 8\pi\rho_{0} = \frac{2}{R^{2}}. \Tag{(69.4)} \] Accordingly if $M$~is the total mass in the universe, we have by~\Eq{(67.2)} \begin{align*} M &= 2\pi^{2} R^{2} \rho_{0} \\ &= \tfrac{1}{2}\pi R^{2}. \Tag{(69.5)} \end{align*} $R$~can scarcely be less than $10^{18}$ kilometres since the distances of some of the globular clusters exceed this. Remembering that the gravitational mass of the sun is $1.5$~kilometres, the mass of the matter in the world must be equivalent to at least a trillion suns, if Einstein's form of the world is correct. It seems natural to regard de~Sitter's and Einstein's forms as two limiting cases, the circumstances of the actual world being intermediate between them. De~Sitter's empty world is obviously intended only as a limiting case; and the presence of stars and nebulae must modify it, if only slightly, in the direction of Einstein's solution. Einstein's world containing masses far exceeding anything imagined by astronomers, might be regarded as the other extreme---a world containing as much matter as it can hold. This view denies any fundamental cleavage of the theory in regard to the two forms, regarding it as a mere accident, depending on the amount of matter which happens to have been created, whether de~Sitter's or Einstein's form is the nearer approximation to the truth. But this compromise has been strongly challenged, as we shall see. \PageSep{161}