Differential coefficient

differential dif`fer*en"tial, a. [Cf. F. diff['e]rentiel.] 1. Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate. [1913 Webster]

For whom he produced differential favors. --Motley. [1913 Webster]

2. (Math.) Of or pertaining to a differential, or to differentials. [1913 Webster]

3. (Mech.) Relating to differences of motion or leverage; producing effects by such differences; said of mechanism. [1913 Webster]

{Differential calculus}. (Math.) See under {Calculus}.

{Differential coefficient}, the limit of the ratio of the increment of a function of a variable to the increment of the variable itself, when these increments are made indefinitely small.

{Differential coupling}, a form of slip coupling used in light machinery to regulate at pleasure the velocity of the connected shaft.

{Differential duties} (Polit. Econ.), duties which are not imposed equally upon the same products imported from different countries.

{Differential galvanometer} (Elec.), a galvanometer having two coils or circuits, usually equal, through which currents passing in opposite directions are measured by the difference of their effect upon the needle.

{Differential gearing}, a train of toothed wheels, usually an epicyclic train, so arranged as to constitute a {differential motion}.

{Differential motion}, a mechanism in which a simple differential combination produces such a change of motion or force as would, with ordinary compound arrangements, require a considerable train of parts. It is used for overcoming great resistance or producing very slow or very rapid motion.

{Differential pulley}. (Mach.) (a) A portable hoisting apparatus, the same in principle as the differential windlass. (b) A hoisting pulley to which power is applied through a differential gearing.

{Differential screw}, a compound screw by which a motion is produced equal to the difference of the motions of the component screws.

{Differential thermometer}, a thermometer usually with a U-shaped tube terminating in two air bulbs, and containing a colored liquid, used for indicating the difference between the temperatures to which the two bulbs are exposed, by the change of position of the colored fluid, in consequence of the different expansions of the air in the bulbs. A graduated scale is attached to one leg of the tube.

{Differential windlass}, or {Chinese windlass}, a windlass whose barrel has two parts of different diameters. The hoisting rope winds upon one part as it unwinds from the other, and a pulley sustaining the weight to be lifted hangs in the bight of the rope. It is an ancient example of a differential motion. [1913 Webster]