Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference., Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference., Differential 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., Calculus Cal"cu*lus, n.; pl. Calculi. [L, calculus. See Calculate, and Calcule.] 1. (Med.) Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc. 2. (Math.) A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation. Barycentric calculus, a method of treating geometry by defining a point as the center of gravity of certain other points to which co["e]fficients or weights are ascribed. Calculus of functions, that branch of mathematics which treats of the forms of functions that shall satisfy given conditions. Calculus of operations, that branch of mathematical logic that treats of all operations that satisfy given conditions. Calculus of probabilities, the science that treats of the computation of the probabilities of events, or the application of numbers to chance. Calculus of variations, a branch of mathematics in which the laws of dependence which bind the variable quantities together are themselves subject to change. Differential calculus, a method of investigating mathematical questions by using the ratio of certain indefinitely small quantities called differentials. The problems are primarily of this form: to find how the change in some variable quantity alters at each instant the value of a quantity dependent upon it. Exponential calculus, that part of algebra which treats of exponents. Imaginary calculus, a method of investigating the relations of real or imaginary quantities by the use of the imaginary symbols and quantities of algebra. Integral calculus, a method which in the reverse of the differential, the primary object of which is to learn from the known ratio of the indefinitely small changes of two or more magnitudes, the relation of the magnitudes themselves, or, in other words, from having the differential of an algebraic expression to find the expression itself., Galvanometer Gal`va*nom"e*ter, n. [Galvanic + -meter: cf. F. galvanom[`e]tre.] (Elec.) An instrument or apparatus for measuring the intensity of an electric current, usually by the deflection of a magnetic needle. Differential galvanometer. See under Differental, a. Sine galvanometer, Cosine galvanometer, Tangent galvanometer (Elec.), a galvanometer in which the sine, cosine, or tangent respectively, of the angle through which the needle is deflected, is proportional to the strength of the current passed through the instrument., Differentially Dif`fer*en"tial*ly, adv. In the way of differentiation., Differentiate Dif`fer*en"ti*ate, v. i. (Biol.) To acquire a distinct and separate character. --Huxley., Differentiate 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., Differentiation 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., Differentiator Dif`fer*en"ti*a`tor, n. One who, or that which, differentiates., Differently Dif"fer*ent*ly, adv. In a different manner; variously., Indifferent In*dif"fer*ent, adv. To a moderate degree; passably; tolerably. [Obs.] ``News indifferent good.' --Shak., Indifferentist In*dif"fer*ent*ist, n. One governed by indifferentism., Differential 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., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Differential 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., Undifferentiated Un*dif`fer*en"ti*a`ted, a. Not differentiated; specifically (Biol.), homogenous, or nearly so; -- said especially of young or embryonic tissues which have not yet undergone differentiation (see Differentiation, 3), that is, which show no visible separation into their different structural parts.
Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference., Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference., Differential 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., Calculus Cal"cu*lus, n.; pl. Calculi. [L, calculus. See Calculate, and Calcule.] 1. (Med.) Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc. 2. (Math.) A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation. Barycentric calculus, a method of treating geometry by defining a point as the center of gravity of certain other points to which co["e]fficients or weights are ascribed. Calculus of functions, that branch of mathematics which treats of the forms of functions that shall satisfy given conditions. Calculus of operations, that branch of mathematical logic that treats of all operations that satisfy given conditions. Calculus of probabilities, the science that treats of the computation of the probabilities of events, or the application of numbers to chance. Calculus of variations, a branch of mathematics in which the laws of dependence which bind the variable quantities together are themselves subject to change. Differential calculus, a method of investigating mathematical questions by using the ratio of certain indefinitely small quantities called differentials. The problems are primarily of this form: to find how the change in some variable quantity alters at each instant the value of a quantity dependent upon it. Exponential calculus, that part of algebra which treats of exponents. Imaginary calculus, a method of investigating the relations of real or imaginary quantities by the use of the imaginary symbols and quantities of algebra. Integral calculus, a method which in the reverse of the differential, the primary object of which is to learn from the known ratio of the indefinitely small changes of two or more magnitudes, the relation of the magnitudes themselves, or, in other words, from having the differential of an algebraic expression to find the expression itself., Galvanometer Gal`va*nom"e*ter, n. [Galvanic + -meter: cf. F. galvanom[`e]tre.] (Elec.) An instrument or apparatus for measuring the intensity of an electric current, usually by the deflection of a magnetic needle. Differential galvanometer. See under Differental, a. Sine galvanometer, Cosine galvanometer, Tangent galvanometer (Elec.), a galvanometer in which the sine, cosine, or tangent respectively, of the angle through which the needle is deflected, is proportional to the strength of the current passed through the instrument., Differentially Dif`fer*en"tial*ly, adv. In the way of differentiation., Differentiate Dif`fer*en"ti*ate, v. i. (Biol.) To acquire a distinct and separate character. --Huxley., Differentiate 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., Differentiation 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., Differentiator Dif`fer*en"ti*a`tor, n. One who, or that which, differentiates., Differently Dif"fer*ent*ly, adv. In a different manner; variously., Indifferent In*dif"fer*ent, adv. To a moderate degree; passably; tolerably. [Obs.] ``News indifferent good.' --Shak., Indifferentist In*dif"fer*ent*ist, n. One governed by indifferentism., Differential 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., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Differential 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., Undifferentiated Un*dif`fer*en"ti*a`ted, a. Not differentiated; specifically (Biol.), homogenous, or nearly so; -- said especially of young or embryonic tissues which have not yet undergone differentiation (see Differentiation, 3), that is, which show no visible separation into their different structural parts.
Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference., Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference., Differential 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., Calculus Cal"cu*lus, n.; pl. Calculi. [L, calculus. See Calculate, and Calcule.] 1. (Med.) Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc. 2. (Math.) A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation. Barycentric calculus, a method of treating geometry by defining a point as the center of gravity of certain other points to which co["e]fficients or weights are ascribed. Calculus of functions, that branch of mathematics which treats of the forms of functions that shall satisfy given conditions. Calculus of operations, that branch of mathematical logic that treats of all operations that satisfy given conditions. Calculus of probabilities, the science that treats of the computation of the probabilities of events, or the application of numbers to chance. Calculus of variations, a branch of mathematics in which the laws of dependence which bind the variable quantities together are themselves subject to change. Differential calculus, a method of investigating mathematical questions by using the ratio of certain indefinitely small quantities called differentials. The problems are primarily of this form: to find how the change in some variable quantity alters at each instant the value of a quantity dependent upon it. Exponential calculus, that part of algebra which treats of exponents. Imaginary calculus, a method of investigating the relations of real or imaginary quantities by the use of the imaginary symbols and quantities of algebra. Integral calculus, a method which in the reverse of the differential, the primary object of which is to learn from the known ratio of the indefinitely small changes of two or more magnitudes, the relation of the magnitudes themselves, or, in other words, from having the differential of an algebraic expression to find the expression itself., Galvanometer Gal`va*nom"e*ter, n. [Galvanic + -meter: cf. F. galvanom[`e]tre.] (Elec.) An instrument or apparatus for measuring the intensity of an electric current, usually by the deflection of a magnetic needle. Differential galvanometer. See under Differental, a. Sine galvanometer, Cosine galvanometer, Tangent galvanometer (Elec.), a galvanometer in which the sine, cosine, or tangent respectively, of the angle through which the needle is deflected, is proportional to the strength of the current passed through the instrument., Differentially Dif`fer*en"tial*ly, adv. In the way of differentiation., Differentiate Dif`fer*en"ti*ate, v. i. (Biol.) To acquire a distinct and separate character. --Huxley., Differentiate 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., Differentiation 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., Differentiator Dif`fer*en"ti*a`tor, n. One who, or that which, differentiates., Indifferentist In*dif"fer*ent*ist, n. One governed by indifferentism., Differential 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., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Partial Par"tial, a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.] 1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.' --T. Burnet. 2. Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial. Ye have been partial in the law. --Mal. ii. 9. 3. Having a predelection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.' --Pope. Not partial to an ostentatious display. --Sir W. Scott. 4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant. Partial fractions (Alg.), fractions whose sum equals a given fraction. Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone., Differential 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., Undifferentiated Un*dif`fer*en"ti*a`ted, a. Not differentiated; specifically (Biol.), homogenous, or nearly so; -- said especially of young or embryonic tissues which have not yet undergone differentiation (see Differentiation, 3), that is, which show no visible separation into their different structural parts.
Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference.
Differentia Dif`fer*en"ti*a, n.; pl. Differenti[ae]. [L. See Difference.] (Logic) The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference.
Differential 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.
Calculus Cal"cu*lus, n.; pl. Calculi. [L, calculus. See Calculate, and Calcule.] 1. (Med.) Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc. 2. (Math.) A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation. Barycentric calculus, a method of treating geometry by defining a point as the center of gravity of certain other points to which co["e]fficients or weights are ascribed. Calculus of functions, that branch of mathematics which treats of the forms of functions that shall satisfy given conditions. Calculus of operations, that branch of mathematical logic that treats of all operations that satisfy given conditions. Calculus of probabilities, the science that treats of the computation of the probabilities of events, or the application of numbers to chance. Calculus of variations, a branch of mathematics in which the laws of dependence which bind the variable quantities together are themselves subject to change. Differential calculus, a method of investigating mathematical questions by using the ratio of certain indefinitely small quantities called differentials. The problems are primarily of this form: to find how the change in some variable quantity alters at each instant the value of a quantity dependent upon it. Exponential calculus, that part of algebra which treats of exponents. Imaginary calculus, a method of investigating the relations of real or imaginary quantities by the use of the imaginary symbols and quantities of algebra. Integral calculus, a method which in the reverse of the differential, the primary object of which is to learn from the known ratio of the indefinitely small changes of two or more magnitudes, the relation of the magnitudes themselves, or, in other words, from having the differential of an algebraic expression to find the expression itself.