title: [Demonstration of the surface values of spheroid cell nuclei, determined in natural size order, in relation to the large and small diameters of the nuclear incision surface, as a measurement value; a further contribution to the statistics of nuclear variation].
abstract: The paper explains how the formulas for calculating the surface area of the prolate spheroid, which a nucleus resembles, can be changed by suitable substitutions into formulas based on measured diameters l and k [mm] of the nucleus approach side surface, magnified 3.000 times, and on a mixed cyclometric function dependent on the axial ratio. Their values established for distinct axial ratios are compiled in a table. The values of the mixed cyclometric function are to be calculated for any other axial ratio according to a formula based on linear interpolation. The nucleus surface Omu is obtained in the natural order of magnitude [micron2]. In case of constant axial ratio, the surface area values form a second-order arithmetic progression, and a recursion formula has been developed to check the values of its terms. In case of nuclei of spherical shape or constant small diameter k, the surface area formulas may be simplified. Numeral examples serve for explanation. For all measured-value combinations involved, a second part, which is being prepared, will contain a complete table of function values, which is referred to in the Appendix and from which the values of the natural surface areas of spheroid nuclei can be gathered.
mesh_terms: D002467:Cell Nucleus / Q000648:ultrastructure*; D006801:Humans; D007620:Karyometry / Q000379:methods; D009685:Nuclear Envelope / Q000648:ultrastructure; D013223:Statistics as Topic; D013499:Surface Properties
vernacular_title: Darstellung der in natürlicher Grössenordnung zu ermittelnden Oberflächenwerte rotationsellipsoidförmiger Zellkerne bei Abhängigkeit vom grossen und kleinen Durchmesser der Zellkernanschnittsfläche als Messgrössen, ein weiterer Beitrag zur Kernvariationsstatistik.