Differential \Dif`fer*en"tial\, n.
   1. (Math.) An increment, usually an indefinitely small one,
      which is given to a variable quantity.
      [1913 Webster]

   Note: According to the more modern writers upon the
         differential and integral calculus, if two or more
         quantities are dependent on each other, and subject to
         increments of value, their differentials need not be
         small, but are any quantities whose ratios to each
         other are the limits to which the ratios of the
         increments approximate, as these increments are reduced
         nearer and nearer to zero.
         [1913 Webster]

   2. A small difference in rates which competing railroad
      lines, in establishing a common tariff, allow one of their
      number to make, in order to get a fair share of the
      business. The lower rate is called a differential rate.
      Differentials are also sometimes granted to cities.
      [1913 Webster]

   3. (Elec.)
      (a) One of two coils of conducting wire so related to one
          another or to a magnet or armature common to both,
          that one coil produces polar action contrary to that
          of the other.
      (b) A form of conductor used for dividing and distributing
          the current to a series of electric lamps so as to
          maintain equal action in all. --Knight.
          [1913 Webster]

   Partial differential (Math.), the differential of a
      function of two or more variables, when only one of the
      variables receives an increment.

   Total differential (Math.), the differential of a function
      of two or more variables, when each of the variables
      receives an increment. The total differential of the
      function is the sum of all the partial differentials.
      [1913 Webster]