For a liquid or solid the stress does not arise entirely from molecular motions, but is due mainly to direct repulsive forces between the molecules held in proximity. These stresses must, of course, be included in the energy-tensor (which would otherwise not be conserved) just as the gaseous pressure is included. It will be shown later that if these repulsive forces are Maxwellian electrical forces they contribute nothing to~$\rho_{0}$, so that $\rho_{0}$~arises entirely from the molecules individually (probably from the electrons individually) and is independent of the circumstances of packing. Since $\rho_{0}$~is the most useful of the three quantities in theoretical investigations we shall in future call it the proper-density (or invariant density) without qualification. \Section{55.}{The force} \index{Force, covariant and contravariant components!expressed by $3$-index symbols}% By \Eq{(51.2)} the equation $(T_{\mu}^{\nu})_{\nu} = 0$ becomes \[ \frac{1}{\sqrt{-g}}\, \frac{\dd}{\dd x_{\nu}}(T_{\mu}^{\nu} \sqrt{-g}) = \{\mu\nu, \alpha\} T_{\alpha}^{\nu}. \Tag{(55.1)} \] Let us choose coordinates so that $\sqrt{-g} = 1$; then \[ \frac{\dd}{\dd x_{\nu}}T_{\mu}^{\nu} = \{\mu\nu, \alpha\} T_{\alpha}^{\nu}. \Tag{(55.2)} \] In most applications the velocity of the matter is extremely small compared with the velocity of light, so that on the right of this equation $T_{4}^{4} = \rho$ is much larger than the other components of~$T_{\alpha}^{\nu}$. As a first approximation we neglect the other components, so that \[ \frac{\dd}{\dd x_{\nu}} T_{\mu}^{\nu} = \{\mu4, 4\} \rho. \Tag{(55.3)} \] \PageSep{123} This will agree with classical mechanics~\Eq{(53.92)} if \[ -X,\ -Y,\ -Z = \{14, 4\},\ \{24, 4\},\ \{34, 4\}. \Tag{(55.4)} \] The $3$-index symbols can thus be interpreted as components of the field of force. The three quoted are the leading components which act proportionately to the mass or energy; the others, neglected in Newtonian mechanics, are evoked by the momenta and stresses which form the remaining components of the energy-tensor.