英语词汇“method of dimensions”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

c. [ < French dimension (J. B. J. Fourier Théorie anal. de la Chaleur (1822) ii. §ix. 154).] The power to which any one of the fundamental quantities or units is raised in the expression defining a derived quantity or unit in terms of them; also (in plural), all the fundamental quantities in such an expression, each raised to its appropriate power, which together show how the unit of the derived quantity depends on the fundamental units; method of dimensions, dimensional analysis. The ‘fundamental quantities’ are usually taken to be mass, length, and time, with the addition of one or more other quantities in certain cases (such as electrical and magnetic phenomena).

ΚΠ

1864 Rep. Brit. Assoc. 1863 132 The value of a force is directly proportional to a length and a mass, but inversely proportional to the square of a time. This is expressed by saying that the dimensions of a force are LM/T².

1877 Ld. Rayleigh Theory of Sound I. iii. 47 From the necessity of a complete enumeration of all the quantities on which the required result may depend, the method of dimensions is somewhat dangerous.

1878 A. Freeman tr. J. B. J. Fourier Anal. Theory Heat ii. 128 Every undetermined magnitude or constant has one dimension proper to itself, and..the terms of one and the same equation could not be compared, if they had not the same exponent of dimension. We have introduced this consideration..in order to make our definitions more exact, and to serve to verify the analysis.

1878 A. Freeman tr. J. B. J. Fourier Anal. Theory Heat ii. 129 The dimensions of x, t, v with respect to the unit of time are 0, 1, 0, and those of K, h, c are −1, −1, 0.

1911 Encycl. Brit. XXVII. 736/2 Velocity is of +1 dimension in length and −1 dimension in time.

1925 London, Edinb. & Dublin Philos. Mag. 6th Ser. 50 32 The dimensions of the viscosity, η, are ML⁻¹T⁻¹, of the density, ρ, ML⁻³, whilst σ/σ′ is of no dimensions.

1925 London, Edinb. & Dublin Philos. Mag. 6th Ser. 50 31 Much information can be obtained concerning F by means of the method of dimensions.

1933 A. W. Porter (title) The method of dimensions.

1960 McGraw-Hill Encycl. Sci. & Technol. IV. 197/2 Quantities with the same dimensions can be expressed in the same units.

1964 H. S. Hvistendahl Engin. Units i. 7 For example, in the case of force, the term ‘dimensions’ is now generally understood to mean LMT⁻², and not merely 1, 1, −2.

1969 L. Young Syst. Units Electr. & Magn. i. 7 Area has dimensions of length squared; denoting ‘dimensions of’ by square brackets, we write [A] = [L]².

1970 Nature 29 Aug. 935/2 In SI units the constant μ₀ = 4π × 10⁻⁷ is indispensable in many formulae, if the dimensions are to balance.

单词	method of dimensions
释义	> as lemmas method of dimensions c. [ < French dimension (J. B. J. Fourier Théorie anal. de la Chaleur (1822) ii. §ix. 154).] The power to which any one of the fundamental quantities or units is raised in the expression defining a derived quantity or unit in terms of them; also (in plural), all the fundamental quantities in such an expression, each raised to its appropriate power, which together show how the unit of the derived quantity depends on the fundamental units; method of dimensions, dimensional analysis. The ‘fundamental quantities’ are usually taken to be mass, length, and time, with the addition of one or more other quantities in certain cases (such as electrical and magnetic phenomena). ΚΠ 1864 Rep. Brit. Assoc. 1863 132 The value of a force is directly proportional to a length and a mass, but inversely proportional to the square of a time. This is expressed by saying that the dimensions of a force are LM/T². 1877 Ld. Rayleigh Theory of Sound I. iii. 47 From the necessity of a complete enumeration of all the quantities on which the required result may depend, the method of dimensions is somewhat dangerous. 1878 A. Freeman tr. J. B. J. Fourier Anal. Theory Heat ii. 128 Every undetermined magnitude or constant has one dimension proper to itself, and..the terms of one and the same equation could not be compared, if they had not the same exponent of dimension. We have introduced this consideration..in order to make our definitions more exact, and to serve to verify the analysis. 1878 A. Freeman tr. J. B. J. Fourier Anal. Theory Heat ii. 129 The dimensions of x, t, v with respect to the unit of time are 0, 1, 0, and those of K, h, c are −1, −1, 0. 1911 Encycl. Brit. XXVII. 736/2 Velocity is of +1 dimension in length and −1 dimension in time. 1925 London, Edinb. & Dublin Philos. Mag. 6th Ser. 50 32 The dimensions of the viscosity, η, are ML⁻¹T⁻¹, of the density, ρ, ML⁻³, whilst σ/σ′ is of no dimensions. 1925 London, Edinb. & Dublin Philos. Mag. 6th Ser. 50 31 Much information can be obtained concerning F by means of the method of dimensions. 1933 A. W. Porter (title) The method of dimensions. 1960 McGraw-Hill Encycl. Sci. & Technol. IV. 197/2 Quantities with the same dimensions can be expressed in the same units. 1964 H. S. Hvistendahl Engin. Units i. 7 For example, in the case of force, the term ‘dimensions’ is now generally understood to mean LMT⁻², and not merely 1, 1, −2. 1969 L. Young Syst. Units Electr. & Magn. i. 7 Area has dimensions of length squared; denoting ‘dimensions of’ by square brackets, we write [A] = [L]². 1970 Nature 29 Aug. 935/2 In SI units the constant μ₀ = 4π × 10⁻⁷ is indispensable in many formulae, if the dimensions are to balance. extracted from dimensionn. < as lemmas
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> as lemmas