Abstract: Acting on the principle of solving a particular contradiction by means of a particular method, the author applies, in this paper, the concepts of moving coordinate system and relative differentiation with respect to such a system in the discussion of some fundamental problems on the theory of meshing. Such concepts and the results obtained from them are more or less known to different authors. In the following paragraphs we show how the new method has been used and how some new results have been obtained. We analyse the limiting points of gear tooth-surfaces and thus obtain two fundamental invariants, which in this case may be called limiting functions. From these is derived the relationship between normal curvatures of conjugate tooth-surfaces at the meshing point, I. E. the induced normal curvature formula. Finally we mention some applications of the above-mentioned formula. Another feature of this paper is that the proof is entirely analytical, with no resort to intuition at all.