SUBSTILE

, or Substilar Line, in Dialling, a right line upon which the stile or gnomon of a dial is erected, being the common section of the face of the dial and a plane perpendicular to it passing through the stile.

The angle included between this line and the stile, is called the elevation or height of the stile.

In polar, horizontal, meridional, and northern dials, the Substilar line is the meridional line, or line of 12 o'clock; or the intersection of the plane of the dial with that of the meridian.—In all declining dials, the Substile makes an angle with the hour line of 12, and this angle is called the distance of the Substile from the meridian.—In easterly and westerly dials, the substilar line is the line of 6 o'clock, or the intersection of the dial plane with the prime vertical.

SUBTANGENT of a curve, is the line TA in the axis below the tangent TB, or limited between the tangent and ordinate to the point of contact. (See the last figure above).

The tangent, subtangent, and ordinate, make a rightangled triangle.

In all paraboliform and hyperboliform figures, the Subtangent is equal to the absciss multiplied by the exponent of the power of the ordinate in the equation of the curve. Thus, in the common parabola, whose property or equation is px = y², the Subtangent is equal to 2x, double the absciss. And if ax² = y³, or | px = y^3/2, then the Subtangent is = (3/2)x. Also if a^m xⁿ = y^{m + n}, or px = y^{(m + n)/n}, the Subtangent is = ((m + n)/n)x. See Method of Tangents.