a. and sb. [f. CO- 2 + EFFICIENT. Cf. F. coefficient sb. In senses A and B 1 often written with hyphen.]
A. adj. Cooperating to produce a result.
1665–6. Phil. Trans., I. 31. Without any other coefficient cause.
B. sb. 1. A coefficient cause; a joint agent or factor in producing an effect or result.
1708–15. in Kersey.
1721. Bailey, Coefficient, that which causes, makes or brings to pass together with another.
1755. Johnson, Coefficient, That which unites its action with the action of another.
1838. De Quincey, C. Lamb, Wks. IX. 111. Some marked originality of character in the writer becomes a co-efficient with what he says to a common result.
1865. Grote, Plato, II. xxiii. 176. Socrates will not allow such agencies to be called Causes: he says that they are only co-efficients.
2. Math. a. Algebra. A number or quantity placed (usually) before and multiplying another quantity known or unknown.
[According to Hutton, Vieta, who died in 1603, and wrote in Latin, introduced coefficiens in this sense.]
Thus in 4x2 + 2ax, 4 is the coefficient of x2, 2 of ax, and 2a of x. Coefficients are sometimes distinguished as numerical (i.e., represented by arithmetical figures) and literal (i.e., represented by algebraical letters).
1708–15. in Kersey.
1721. in Bailey.
1734. Berkeley, Analyst, § 9. Rules for obtaining the fluxions of all other products and powers; be the coefficients or the indexes what they will.
1775. De Lolme, Eng. Const., Introd. The mathematician … begins by freeing his equation from co-efficients.
1875. Todhunter, Algebra, i. 4.
1879. S. Highley, in Cassell’s Techn. Educ., IV. 292/2. I have detected an error in one of the numerical coefficients of the formula.
b. Physics. A multiplier that measures some property of a particular substance, for which it is constant, while differing for different substances.
e.g., Coefficient of friction, expansion, torsion, etc.
1829. Nat. Philos., Optics, ii. 4/2 (Usef. Knowl. Soc.). The number 1.336, which regulates the refraction of water, is called its index, or exponent, or co-efficient of refraction.
1871. B. Stewart, Heat, § 33. The co-efficient of expansion of a substance is the expansion for one degree of temperature of that quantity of the substance whose length or volume was unity at a certain standard temperature.
1879. G. Prescott, Sp. Telephone, 123. Magnetization … produces a diminution in the coefficient of elasticity in iron wire.
1879. Thomson & Tait, Nat. Phil., I. I. § 300. The relative velocity of separation after the impact…. To which we give the name Coefficient of Restitution. Note, In most modern treatises this is called a ‘coefficient of elasticity,’ which is clearly a mistake.
c. Differential coefficient: the quantity which measures the rate of change of a function of any variable with respect to that variable.
1708–15. Kersey, Coefficient of any generating Term (in Geometrical Fluctions) is the Quantity which arises by dividing that Term by the generated Quantity.
1855. Wallace, in Encycl. Brit. (ed. 8), IX. 688/2. The expression du/dx is called the first differential co-efficient of the function u, or the differential co-efficient of the first order.
1875. Todhunter, Diff. Calc., xxvii. 392.
