n.; pl. Differentiæ [ L. See Difference. ] 1. (Logic) The formal or distinguishing part of the essence of a species, by which it is distinguished from other members of its genus; the characteristic attribute of a species; specific difference; as, a proper definition must have both genus and differentia. [ 1913 Webster +PJC ]

2. the set of characteristics distinguishing an entity from related entities. [ PJC ]

adj. 1. (Math.) possessing a differential coefficient or derivative; -- of a mathematical expression. [ WordNet 1.5 ]

2. capable of being perceived as different; as, differentiable species. [ WordNet 1.5 ]

n. 1. (Math.) An increment, usually an indefinitely small one, which is given to a variable quantity. [ 1913 Webster ]

☞ 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 ]

a. [ Cf. F. différentiel. ] 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 ]

adv. In the way of differentiation. [ 1913 Webster ]

v. t. 1. To distinguish or mark by a specific difference; to effect a difference in, as regards classification; to develop differential characteristics in; to specialize; to desynonymize. [ 1913 Webster ]

The word then was differentiated into the two forms then and than. Earle. [ 1913 Webster ]

Two or more of the forms assumed by the same original word become differentiated in signification. Dr. Murray. [ 1913 Webster ]

2. To express the specific difference of; to describe the properties of (a thing) whereby it is differenced from another of the same class; to discriminate. Earle. [ 1913 Webster ]

3. (Math.) To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation. [ 1913 Webster ]

v. i. (Biol.) To acquire a distinct and separate character. Huxley. [ 1913 Webster ]

adj. 1. made different (especially in the course of development) or shown to be different; as, the differentiated markings of butterflies; the regionally differentiated results. Opposite of undifferentiated. [ WordNet 1.5 ]

2. (Biol.) exhibiting biological specialization; adapted during development to a specific function or environment; as, differentiated cells. [ WordNet 1.5 ]

n. 1. The act of differentiating. [ 1913 Webster ]

Further investigation of the Sanskrit may lead to differentiation of the meaning of such of these roots as are real roots. J. Peile. [ 1913 Webster ]

2. (Logic) The act of distinguishing or describing a thing, by giving its different, or specific difference; exact definition or determination. [ 1913 Webster ]

3. (Biol.) The gradual formation or production of organs or parts by a process of evolution or development, as when the seed develops the root and the stem, the initial stem develops the leaf, branches, and flower buds; or in animal life, when the germ evolves the digestive and other organs and members, or when the animals as they advance in organization acquire special organs for specific purposes. [ 1913 Webster ]

4. (Metaph.) The supposed act or tendency in being of every kind, whether organic or inorganic, to assume or produce a more complex structure or functions. [ 1913 Webster ]

n. One who, or that which, differentiates. [ 1913 Webster ]