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DIFFERENTIAL, a. An epithet applied to an infinitely small quantity, so small as to be less than any assignable quantity. This is called a differential quantity. The differential method is applied to the doctrine of infinitesimals, or infinitely small quantities, called the arithmetic of fluxions. It consists in descending from whole quantities to their infinitely small differences, and comparing them. Hence it is called the differential calculus, or analysis of infinitesimals.
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. Of or pertaining to a
differential, or to differentials.
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.)
An increment, usually an indefinitely small one,
which is given to a variable quantity.
* 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. 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.
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.
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