## Dr W F Sheppard's papers

**William Fleetwood Sheppard**'s papers are listed in

*Proc. Roy. Soc. Edinburgh*

**56**(1935-36), 279-282. We give a version below:

On the calculation of the most probable values of frequency constants for data arranged according to equal divisions of a scale."

*Proc. Lond. Math. Soc.,*vol. xxix, 1897, pp. 353-38o.

"On the geometrical treatment of the 'normal curve' of statistics, with especial reference to correlation and to the theory of error."

*Proc. Roy. Soc. London,*vol. lxii, 1898, pp. 171-173.

"On the relations between Bernoulli's and Euler's numbers."

*Quart. Journ. Math.,*vol. xxx, 1898, pp. 18-46.

"On the application of the theory of error to cases of normal distribution and normal correlation."

*Phil. Trans.,*vol. cxcii A, 1899, pp. 101-167.

"On the statistical rejection of extreme variations."

*Proc. Lond. Math. Soc.,*vol. xxxi, 1899, pp. 70-99.

"On the calculation of differential coefficients from tables involving differences, with an interpolation formula."

*Nature,*vol. lx, 1899, pp. 390-391.

"On the tabulation of certain frequency distributions."

*Phil. Mag.,*vol. 1, 1900, pp. 393-398.

"Central difference formulae."

*Proc. Lond. Math. Soc.,*vol. xxxi, 1899, pp. 449-488.

"A method for extending the accuracy of certain mathematical tables."

*Ibid.,*pp. 423-448.

"Some quadrature formulae."

*Proc. Lond. Math. Soc.,*vol. xxxii, 1900, pp. 258-277.

"On the calculation of ++ expression in normal correlation."

*Trans. Camb. Phil. Soc.,*1900, pp. 23-68.

"Quadrature formulae and curve-fitting." Incorporated in "On the systematic fitting of curves," by Karl Pearson,

*Biometrika,*vol. i, 1902, pp. 273-279.

"Table of the probability integral."

*Biometrika,*vol. ii, pp. 174-190.

"On the accuracy of interpolation by finite differences. I."

*Proc. Lond. Math. Soc.,*vol. iv, 1906, pp. 320-341.

"Table of deviates of the normal curve."

*Biometrika,*vol. v, 1907, pp. 405-406.

"The calculation of the moments of a frequency distribution."

*Biometrika,*vol. v, 1907, pp. 450-459.

"Quadrature formulae in relation to moments." Math. Gaz., vol. iv, 1908, pp. 325-326.

"The accuracy of interpolation by finite differences. II."

*Proc. Lond. Math. Soc.,*vol. x, 1912, pp. 139-172.

"The power-sum formula and the Bernoullian function."

*Math. Gaz.,*vol. vi, 1912, pp. 332-336.

"Summation of the coefficients of some terminating hypergeometric series."

*Proc. Lond. Math. Soc.,*vol. x, 1912, pp. 469-478.

"Calculation of the moments of an abrupt frequency distribution."

*Proc. Fifth Intern. Congr. Math.,*vol. ii, 1912, pp. 414-426.

"Reduction of errors by means of negligible differences."

*Ibid.,*pp. 348-384.

"The power-sum formula and the Bernoullian function. III. The Euler-Maclaurin formula."

*Math. Gaz.,*vol. vii, 1914, pp. 100-104.

"Factorial moments in terms of sums and differences."

*Proc. Lond. Math. Soc.,*vol. xiii, 1914, pp. 81-96.

"Fitting of polynomials by method of least squares. (Solutions in terms of differences and sums.)"

*Ibid.,*pp. 97-108.

"Graduation by reduction of mean square of error Part I,"

*Journ. Inst. Act.,*vol. xlviii, 1914, pp. 171-184,

"Graduation by reduction of mean square of error Part II,"

*Ibid.,*vol. xlviii, 1914, pp. 390-412.

"Graduation by reduction of mean square of error Part III,"

*Ibid.,*vol. xlix, 1915, pp. 148-157.

"Central difference interpolation formulae."

*Journ. Inst. Act.,*vol. 1, 1916, pp. 88-99.

"Reduction of error by linear compounding."

*Proc. Roy. Soc.,*Vol. xcviii, 1921, pp. 64-66.

"Reciprocal correspondence of differences and sums."

*Proc. Lond. Math. Soc.,*vol. xxi, 1923, pp. 291-305.

"Reduction of error by linear compounding."

*Phil. Trans.,*vol. ccxxi A, 1921, pp. 199-327.

"Extended meaning of conjugate sets."

*Proc. Lond. Math. Soc.,*vol. xx, 1922, Pp. 222-224.

*From Determinant to Tensor.*Oxford. Clarendon Press, 1923. 127 pp.

"Interpolation with least mean square of error."

*Proc. Intern. Congr. Math. Toronto,*1924, pp. 821-830.

"The fit of a formula for discrepant observations."

*Phil. Trans.,*vol. ccxxviii A, 1927, pp. 115-150.

"Interpolation by means of given differences. (Central Difference Notation.)" Proc. Edin. Math. Soc., Vol. iii2, 1933, pp. 1-5.

Article on "Interpolation" in

*Ency. Brit.,*11th Ed., 1910.

Various papers and lectures on probability, statistics, arithmetic, etc., to the Math. Assoc., in

*Math. Gaz., T.F.A.,*etc.