Definitions for: Differential

[n] a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
[n] a quality that differentiates between similar things
[n] the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
[adj] relating to or showing a difference; "differential treatment"
[adj] (mathematics) involving or containing one or more derivatives; "differential equation"

Webster (1913) Definition: 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.

For whom he produced differential favors. --Motley.

2. (Math.) Of or pertaining to a differential, or to

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

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

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.

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

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.

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.

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.

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.

Synonyms: derivative, derived function, differential coefficient, differential gear, first derivative

See Also: bevel gear, calculation, computation, curvature, difference, figuring, pinion and crown wheel, pinion and ring gear, reckoning

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