∫∫∫∫ lor ν[=ω] dx dy dz dt,
the integration being extended over the whole range of the sichel, and (comp. (67), § 12)
lor ν[=ω] = (∂νω₁/∂x₁) + (∂νω₂/∂x₂) + (∂νω₃/∂x₃) + (∂νω₄/∂x₄).
If the sichel reduces to a point, then the differential equation
lor ν[=ω] = 0, (6)
which is the condition of continuity
(∂μux/∂x) + (∂μuy/∂y) + (∂μuz/∂z) + (∂μ/∂t) = 0.
Further let us form the integral
N = ∫ ∫∫∫ ν dx dy dz dt (7)
extending over the whole range of the space-time sichel. We shall decompose the sichel into elementary space-time filaments, and every one of these filaments in small elements dτ of its proper-time, which are however large compared to the linear dimensions of the normal cross-section; let us assume that the mass of such a filament νdJn = dm and write τ⁰, τl for the ‘Proper-time’ of the upper and lower boundary of the sichel.