GB622684A - An instrument for describing conic sections - Google Patents

Abstract

622,684. -Calculating-apparatus. GRABOWSKI, W. T. Oct. 31, 1946, No. 32412. [Class 106 (i)] [Also in Group XX] A computor for use with an instrument for drawing conic sections (see Group XX), comprises a base-plate 51 marked with a rectangular mesh having a uniformly graduated scale of ordinates Ah and an exactly similar scale of abscissµ B and with an arc of a circle concentric with the origin O and having a radius equal to the full length of the scales Ah and B. An arm 52 is pivoted to the base-plate 51 at the origin O and is marked with a scale of graduation Ae divided in the same way as scales Ah and B. The arc of the circle is graduated with two scales of angles we and wh such that we=tan<SP>-1</SP> (sin #) and wh=tan<SP>-1</SP> (1/sin #), where 0 is the angle which the arm 52, when set at the graduation we or wh on the arc, makes, with the scale B. The drawing instrument is set according to the values of two variables w and d, where 1 tan w=e, for an ellipse or tan w=- for a e hyperbola, e being the eccentricity of the conic section to be drawn and d=ep, where p is the distance of the focus from that directrix for that conic. The angle w for an ellipse may be read off from the appropriate scale we on the are by setting the arm 52 so that it intersects the arc at a point whose ordinate is e, or, alternatively, where a and b the values of the major and minor semi-axes are known by setting the arm 52 so that the graduation on scale Ae indicating the given value of a has as its abscissa the given value of b, whereby sin 6 will equal #a<SP>2</SP>-b<SP>2</SP>/a which equals e. Similarly, since d=ep=b<SP>2</SP>/a =b cos # d may be found by finding the abscissa on scale B of the point on the scale Ae on the arm whose value is b. Similar methods may be used to determine the values of w and d for setting up the drawing instrument to describe hyperbolµ.