# Earliest Known Uses of Some of the Words of Mathematics (Y)

**Y-AXIS**.

*Axis of y*appears in "On the Attractions of Homogeneous Ellipsoids" by James Ivory,

*Philosophical Transactions of the Royal Society of London,*Vol. 99. (1809), pp. 345-372. [JSTOR].

*Y-axis*is found in 1855 in

*The Gurley Manual of Surveying Instruments*: "In place of the ordinary axis of the telescopoe represnted in our engraving, we sometimes make one resembling the Y axis of the English Theodolite." (Google print search)

**Y-COORDINATE.**See

*x-coordinate.*

**Y-INTERCEPT.**Isaac Todhunter refers to "the intercept on the axis of

*y*" in the 7th ed. of

*A Treatise on Plane Co-ordinate Geometry*(1881).

*y-intercept*is found in 1904 in

*The Elements of Analytic Geometry*by Percey Franklyn Smith and Arthur Sullivan Gale: "(d)

*Y*-intercept = 5 and slope = 3." [Google print search]

**YATES'S CORRECTION.**In the 5

^{th}edition (1934) of his

*Statistical Methods for Research Workers*R. A. Fisher put a section on "Yates' Correction for Continuity" into the chapter on χ

^{2}. The section was based on F. Yates's "Contingency Tables Involving Small Numbers and the χ

^{2}Test,"

*Supplement to Journal of the Royal Statistical Society*,

**1**, 217-235 [John Aldrich].

See the entry on

*Fisher's exact test*.

The term

**YOUDEN SQUARE**was used by R. A. Fisher in his "The Mathematics of Experimentation,"

*Nature*,

**142**, (1938), 442-443. "Youden squares" featured prominently in Fisher's

*Statistical Tables for Biological Agricultural and Medical Research*(with F. Yates), from the second edition (1943) onwards; the sixth edition is available on the web. The reference is to W. J. Youden "Use of Incomplete Block Replications in Estimating Tobacco-Mosaic Virus," Contributions

*Boyce Thompson Institute*,

**9**, (1937), 41-48. (David (2001))

**YOUNG'S CRITERION**for the convergence of a Fourier series. The criterion was given by W. H. Young in his "On the convergence of the derived series of Fourier series,"

*Proceedings of the London Mathematical Society,*

**17**, (1916), 195–236. The phrase "Young's criterion" appears in N. Wiener "Tauberian Theorems,"

*Annals of Mathematics*,

**33**, (1932), p. 1. See the

*Encyclopedia of Mathematics*entry.

**YOUNG'S THEOREM**on the equality of mixed partial derivatives. See CLAIRAUT'S THEOREM, SCHWARZ' THEOREM & YOUNG'S THEOREM.

**YULE PARADOX**or

**YULE-SIMPSON PARADOX.**See SIMPSON's PARADOX.

The

**YULE PROCESS.**The term appears in W. Feller

*Introduction to Probability Theory and its Applications, volume one*(1950, p. 369) where it is used to refer to an example of a pure birth process.

The reference is to G. Udny Yule's "A Mathematical Theory of Evolution, Based on the Conclusions of Dr. J. C. Willis, FRS "Philosophical Transactions of the Royal Society of London, Ser. B, Vol. 213, (1924), 21-87.

The

**YULE-WALKER EQUATIONS**relate the parameters of the AUTOREGRESSIVE PROCESS to its SERIAL CORRELATIONS. A

*JSTOR*found the term in Maurice G. Kendall "The Estimation of Parameters in Linear Autoregressive Time Series,"

*Econometrica*,

**17**, Supplement: Report of the Washington Meeting. (1949), 44-57.

The references are to G. Udny Yule's "On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers" Philosophical Transactions of the Royal Society of London, Ser. A, Vol. 226, (1927), pp. 267-298 and to Sir Gilbert Walker's "On Periodicity in Series of Related Terms," Proceedings of the Royal Society of London, Ser. A, Vol. 131, (1931), pp. 518-532. Gilbert Walker, a Cambridge applied mathematician, became head of the Indian Meterological Service and is best remembered today for his early study of El Niño. (See R. W. Katz "Sir Gilbert Walker and a Connection Between El Nino and Statistics,"

*Statistical Science, 17, (2002), pp. 97-112*.)