LET P, Q, R,… be consecutive generating lines of a skew surface, and on these take points p′, p; q′, q; r′, r… such that pq′, qr′… are the shortest distances between P and Q, Q and R, &c. Then for the generating line P, the ratio of the inclination of the lines P, Q to the distance pq′ is said to be “the torsion,” the angle q′pq is said to be the deviation, and the ratio of the inclination of the planes Qpq′ and Qqr′ to the inclination of P and Q is said to be the “skew curvature.” And similarly for any other generating line; so that the torsion and deviation depend on the position of the consecutive line, and the skew curvature on the position of the two consecutive lines. The curve pqr… is said to be the minimum distance curve [or curve of strictionj. {When the skew surface degenerates into a developable surface, the torsion is infinite, the deviation a right angle, the skew curvature proportional to the curvature of the principal section, i.e. it is the distance of a point from the edge of regression, multiplied into the reciprocal of the radius of curvature, a product which is evidently constant along a generating line. Also the curve of minimum distance becomes the edge of regression.} A skew surface, considered independently of its position in space, is determined when for each generating line we know the torsion, deviation, and skew curvature.