then the totality of the intersecting points will be called a cross section of the filament. At any point P of such across-section, we can introduce by means of a Lorentz transformation a system of reference (_x′_, _y_, _z′_ _t_), so that according to this ∂Θ/∂_x′_ = 0, ∂Θ/∂_y′_ = 0, ∂Θ/∂_z′_ = 0, ∂Θ/∂_t′_ > 0. The direction of the uniquely determined _t′_—axis in question here is known as the upper normal of the cross-section at the point P and the value of _d_J = ∫∫∫ _dx′ dy′ dz′_ for the surrounding points of P on the cross-section is known as the elementary contents (Inhalts-element) of the cross-section. In this sense R₀ is to be regarded as the cross-section normal to the _t_ axis of the filament at the point _t_ = _t₀_, and the volume of the body R₀ is to be regarded as the contents of the cross-section. If we allow R₀ to converge to a point, we come to the conception of an infinitely thin space-time filament. In such a case, a space-time line will be thought of as a principal line and by the term ‘Proper-time’ of the filament will be understood the ‘Proper-time’ which is laid along this principal line; under the term normal cross-section of the filament, we shall understand the cross-section upon the space which is normal to the principal line through P. We shall now formulate the principle of conservation of mass. To every space R at a time _t_, belongs a positive quantity—the mass at R at the time _t_. If R converges to a point (_x_, _y_, _z_, _t_), then the quotient of this mass, and the volume of R approaches a limit μ(_x_, _y_, _z_, _t_), which is known as the mass-density at the space-time point (_x_, _y_, _z_, _t_). The principle of conservation of mass says—that for an infinitely thin space-time filament, the product μ_d_J, where μ = mass-density at the point (_x_, _y_, _z_, _t_) of the filament (_i.e._, the principal line of the filament), _d_J = contents of the cross-section normal to the _t_ axis, and passing through (_x_, _y_, _z_, _t_), is constant along the whole filament. Now the contents _d_J_{n} of the normal cross-section of the filament which is laid through (_x_, _y_, _z_, _t_) is (4) _d_J_{n} = (1/√(1 - _u²_))_d_J = -_i_ω₄ _d_J = (_dt_/_d_τ)_d_J. and the function ν = μ/-_i_ω₄ = μ√(1 - _u²_)) = μ(∂τ/∂_t_. (5) may be defined as the rest-mass density at the position (_x_ _y_ _z_ _t_). Then the principle of conservation of mass can be formulated in this manner:— _For an infinitely thin space-time filament, the product of the rest-mass density and the contents of the normal cross-section is constant along the whole filament._