| 释义 |
‖ modulus|ˈmɒdjʊləs|
Pl. moduli |ˈmɒdjʊlaɪ|, moduluses.
[L.: see module.]
†1. Arch. = module n. 4. Obs.
1563Shute Archit. C j, A Modulus, or half the thicknes of the pillor.
2. Math.
a. A number by which Napierian logarithms must be multiplied in order to obtain the corresponding logarithms in another system (usually that with base 10).
[1722R. Cotes Harm. Mensur. 4 Pro diversa magnitudine quantitatis assumptae M, quae adeo vocetur Systematis Modulus.] 1753Chambers Cycl. Supp. s.v. Logarithm, The line oe is what Mr. Cotes calls the modulus of the system. 1798Hutton Course Math. (1828) II. 306 Multiply the result by the modulus of the system of logarithms. 1897Chambers' Math. Tables (ed. Pryde) 454 Modulus of common logarithms = M = 0·4342944819.
b. A constant multiplier, coefficient, or parameter involved in a given function of a variable.
For the specific applications see Greenhill Elliptic Functions (1892) 4, 53, and Forsyth Theory of Functions (1893) 377.
1843MacCullagh in Proc. R. Irish Acad. II. 448 The given plane may be called a directive plane, and the constant ratio may be termed the modulus. 1865Brande & Cox Dict. Sci., etc. I. 768 Any trigonometrical function of ϕ is termed an elliptic function, having the argument u and modulus k. 1873Maxwell Electr. & Magn. (1881) I. 217 We may call k and k′ the two complementary moduli of the confocal system. a1883H. J. S. Smith Collect. Math. Papers (1894) II. 570 Geometrical Construction of the Transformed Modulus by means of the Modular Curve.
c. A measure of a quantity which depends upon two or more other quantities. In recent use chiefly, the absolute value of a complex quantity.
1845De Morgan Calculus of Functions in Encycl. Metrop. II. 375/1 By the modulus of α (x, y) we mean the function α (x, x) considered as of a single subject. The moduli of the sum, difference, product, &c. of two functions are the sum, difference, &c. of the moduli. 1846Cayley Coll. Math. Papers I. 238 The square of the secant of the semi-angle of resultant rotation will be the modulus of the rotation. 1891Hobson Trigonom. 255 The modulus of the sum of a number of complex quantities is less than, or equal to, the sum of their moduli.
d. Theory of Numbers. A number in respect of which other numbers are congruent. [Introduced in this sense by Gauss in Disquisitiones Arithmeticae (1801) i. 1.]
1845Encycl. Metrop. I. 642/2 Numbers of the same form with respect to any modulus, are all those which can be represented by the same formula. Thus, 13, 17, 21, &c. are all of the form 4n + 1; and 19, 25, 31, &c. of the form 6n + 1; 4 and 6 being the moduli. 1888C. Smith Treat. Algebra xxviii. 487 If two numbers a and b leave the same remainder when divided by a third number c, they are said to be congruent with respect to the modulus c. 1892G. B. Mathews Theory Numbers 7. 1949 [see mod prep.]. 1967J. E. Shockley Introd. Number Theory iii. 48 Corollary 6.2 furnishes the most efficient method for solving several systems of congruences when the same sets of moduli appear in each system.
3. Physics and Mech. A constant indicating the relation between the amount of a physical effect and that of the force producing it.
modulus of elasticity: originally applied by Young to the quantity by means of which the amount of longitudinal extension or contraction of a bar of a given material, and the amount of the tension or pressure causing it, may be stated in terms of each other. Now used in a wider sense (see quot. 1877).
1807T. Young Lect. Philos. xiii. I. 137 According to this analogy, we may express the elasticity of any substance by the weight of a certain column of the same substance, which may be denominated the modulus of its elasticity. Ibid. II. 66 It may be shown that every small change of form is propagated along an extended chord with a velocity equal to that of a heavy body falling through a height equal to half the length of a portion of the chord, of which the weight is equivalent to a force producing the tension, and which may be called the modulus of the tension. 1824Tredgold Strength Cast Iron 251 The measure of the power of a body to resist impulsion, that is, the modulus of resilience. 1843Moseley Mech. Princ. Engin. 162 The modulus of a machine..is the relation between the work constantly done upon it by the moving power, and that constantly yielded at the working points [etc.]. 1846Mallet in Trans. R. Irish Acad. (1848) XXI. 93 If we take the modulus of elasticity for the following rocks from the preceding table, and, comparing these with the modulus of cast iron, suppose the time of wave transit in each to be proportionate roughly to the square roots of their respective moduli, we get the following table of results. 1877Sir W. Thomson in Encycl. Brit. VII. 804 Moduluses of Elasticity. A modulus of elasticity is the number obtained by dividing the number expressing a stress by the number expressing the strain which it produces... An isotropic solid has two principal moduluses—a modulus of compression and a rigidity.
4. A unit of payment (see quot.).
1882Cambr. Stat., Trin. Coll. (1883) 590 The Council shall fix for the year the amount being not more than..250l. to be called a modulus. And there shall be paid to each Fellow..his proper dividend fixed as hereinafter mentioned by reference to the amount of the modulus. There shall be paid to the Master seven moduli, and to each of the Chaplains and to the Librarian one half of a modulus.
5. gen. A norm or standard. Cf. module 3. rare.
1864Reader 30 Apr. 544/3 He sometimes deviates from the strict modulus of the sonnet. |