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 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.
Dif`fer*en"tial, n. 1. (Math.) 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.
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.
Dif`fer*en"tial*ly (?), adv. In the way of differentiation.
Dif`fer*en"ti*ate (?), 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.
The word then was differentiated into the two forms then and than.
Earle.
Two or more of the forms assumed by the same original word become differentiated in signification.
Dr. Murray.
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.
3. (Math.) To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.
Dif`fer*en"ti*ate, v. i. (Biol.) To acquire a distinct and separate character. Huxley.
Dif`fer*en`ti*a"tion (?), n. 1. The act of differentiating.
Further investigation of the Sanskrit may lead to differentiation of the meaning of such of these roots as are real roots.
J. Peile.
2. (Logic) The act of distinguishing or describing a thing, by giving its different, or specific difference; exact definition or determination.
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.
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.
Dif`fer*en"ti*a`tor (?), n. One who, or that which, differentiates.
Dif"fer*ent*ly (?), adv. In a different manner; variously.
Dif"fer*ing*ly, adv. In a differing or different manner. Boyle.
Dif"fi*cile (?), a. [L. difficilis: cf. F. difficile. See Difficult.] Difficult; hard to manage; stubborn. [Obs.] -- Dif"fi*cile*ness, n. [Obs.] Bacon.
Dif`fi*cil"i*tate (?), v. t. To make difficult. [Obs.] W. Montagu.
Dif"fi*cult (?), a. [From Difficulty.] 1. Hard to do or to make; beset with difficulty; attended with labor, trouble, or pains; not easy; arduous.
Difficult implies the notion that considerable mental effort or skill is required, or that obstacles are to be overcome which call for sagacity and skill in the agent; as, a difficult task; hard work is not always difficult work; a difficult operation in surgery; a difficult passage in an author.
There is not the strength or courage left me to venture into the wide, strange, and difficult world, alone.
Hawthorne.
2. Hard to manage or to please; not easily wrought upon; austere; stubborn; as, a difficult person.
Syn. -- Arduous; painful; crabbed; perplexed; laborious; unaccommodating; troublesome. See Arduous.
Dif"fi*cult, v. t. To render difficult; to impede; to perplex. [R.] Sir W. Temple.
Dif"fi*cult*ate (?), v. t. To render difficult; to difficilitate. [Obs.] Cotgrave.
Dif"fi*cult*ly, adv. With difficulty. Cowper.
Dif"fi*cult*ness, n. Difficulty. [R.] Golding.
Dif"fi*cul*ty (?), n.; pl. Difficulties (#). [L. difficultas, fr. difficilis difficult; dif- = dis- + facilis easy: cf. F. difficulté. See Facile.] 1. The state of being difficult, or hard to do; hardness; arduousness; -- opposed to easiness or facility; as, the difficulty of a task or enterprise; a work of difficulty.
Not being able to promote them [the interests of life] on account of the difficulty of the region.
James Byrne.
2. Something difficult; a thing hard to do or to understand; that which occasions labor or perplexity, and requires skill and perseverance to overcome, solve, or achieve; a hard enterprise; an obstacle; an impediment; as, the difficulties of a science; difficulties in theology.
They lie under some difficulties by reason of the emperor's displeasure.
Addison.