diˈmensionless, a.
[f. as prec. + -less.]
1. a. Without dimension or physical extension. b. Of no (appreciable) magnitude; extremely minute. c. Without dimensions: see dimension 3 a.
| 1667 Milton P.L. xi. 17 To Heav'n thir prayers Flew up..in they pass'd Dimentionless through Heav'nly dores. 1752 Warburton Wks. (1811) IX. ii. 34 As the Earth is but a point compared to the orb of Saturn, so the orb of Saturn itself grows dimensionless when compared to that vast extent of space which the stellar-solar Systems possess. 1825 Coleridge Aids Refl. App. C. (1858) I. 394 If we assume the time as excluded, the line vanishes, and we leave space dimensionless. 1890 J. H. Stirling Gifford Lect. viii. 150 With our scales and weights..and measuring-rods, we do but deceive ourselves: what is, is dimensionless: the truth is not in time; space is all too short for a ladder to the Throne. |
d. Of a physical quantity or its unit: having no dimensions (dimension n. 3 c); of the nature of a pure number or ratio, and therefore having a value independent of the choice of units for other quantities.
| 1904 Proc. Inst. Mech. Engineers 248, K is a dimensionless quantity approximating to unity, and the working formula becomes V = K√(2P/ρ). 1914 Physical Rev. 2nd Ser. IV. 345 The coefficients of a complete equation are dimensionless numbers, i.e. if the quantities Q are measured by an absolute system of units, the coefficients of the equation do not depend on the sizes of the fundamental units but only on the fixed interrelations of the units which characterize the system and differentiate it from any other absolute system. 1970 Nature 28 Nov. 889/2 It would..be incorrect to say: ‘the molecular weight of protein X is 25,000 daltons’, for the dalton is a unit of mass, and molecular weight is dimensionless. |
2. Measureless, immense, boundless, vast.
| 1813 Hogg in New Monthly Mag. (1836) XLVI. 446 Here, in these almost dimensionless regions, nature is seen on a large scale. a 1839 Galt Demon of Destiny iii. (1840) 28 As if man were not but an atom thing In the dimensionless, the Universe. |