(Association française pour l'avancement des sciences. 7th session. Paris. Meeting of 28 August 1878.)
After having indicated that the idea of this study came from the communication made, two years ago, at the Congress of Clermont-Ferrand, by M. Edouard Lucas, on the geometry of weaving from fabric with rectilinear threads, M. Tchébichef set out general principles for determining the curves along which one can cut different pieces of material to make a well-adjusted sheath serving to envelop a body of any form.
Taking as a point of departure the principal observation that in the deformation of fabric one can consider, in the first approximation, the change of the angles formed by the warp threads and the weft threads, without taking account of the lengthening of the threads, he gave formulas which allow the determination of the outline of two, three, or four pieces of fabric to cover the surface of a sphere, with any desired accuracy. M. Tchébichef presented in this section a rubber ball covered by fabric, of which two pieces had been cut following his instructions; he observed that the problem would be essentially different if one replaced the fabric by a skin. Besides the proposed formulas, M. Tchébichef also gave a method to follow for the juxtaposition of pieces for sewing.
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In accordance with the will of Tchebychef, the study "On the cut of clothes" found in his papers will not be published, because the manuscript did not bear the inscription: "publish."