. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . ents, we find r = ^^ ^-^ . Hence by geometrical construction the radius and centre of the osculating circle may be found thus ;—let P Q be perpendicular to the tangent at P, and produced to meet a 1592 FUEL. perpendicular to the directrix at T, the intercept PQ is the radius, and Q the centre of theosculating circle ; for P M : P T : : T M : P Q, by the similar triangles M P T, R P Q. To find the evolute of the Anti-friction Curve.—Let the co-ordinates of t
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . ents, we find r = ^^ ^-^ . Hence by geometrical construction the radius and centre of the osculating circle may be found thus ;—let P Q be perpendicular to the tangent at P, and produced to meet a 1592 FUEL. perpendicular to the directrix at T, the intercept PQ is the radius, and Q the centre of theosculating circle ; for P M : P T : : T M : P Q, by the similar triangles M P T, R P Q. To find the evolute of the Anti-friction Curve.—Let the co-ordinates of the centre of the osculatingcircle be x^, y^. By substituting in the general formulae for the values of these the particular values of the differential coefficients, the results are t/^ and x^ = X -{• a (¿/,2 _ a^f Vx Eliminating x c\,\^ Ï1 + w - «)* ]. and y by means of these equations, and that of the curve, the result is x^ which is the equation of the evolute. The evolute of the anti-friction curve of Schiele is thereforea catenary, whose parameter is a = A B, Fig. 3083, whose vertex is at B, and whose axis is A Y. If a string P G applied to a catenary G B, have its extremity P at the vertex B, and be wound off,its extremity P will describe the anti-friction curve, in the examination of which mathematicianshave blundered much. FRICTION AL GEARING. Fb., Engrenage de frottement; Gee., Frictionscheihen ; Ital.,Euote ad attrito ; Span., Organo de trasmisión de movimiento sin fricción. See Geaking. FUEL. Fe., Combustible ; Gee., Brennmaterial ; Ital., Combustibile ; Span., Combustible. Great quantities of combustible substances, of immense importance in metallurgy and thevarious arts, are found in the bosom of the earth. They are evidently produced by the decom-position of vegetables which grew in the vicinity, or the debris of vegetables carried down by mosses exhibit, though on a smaller scale, an example of this formation ; as they consist ofinnum
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