William Allen Whitworth and a Hundred Years of Probability Free

3

The sphere, referred to quadriplanar co-ordinates

.

1

,

162

–

164

.

4

Quadrilinear co-ordinates

.

1

,

193

–

203

.

5

1863

Of curves of the third order, referred to trilinear co-ordinates

.

2

,

116

–

128

and 129-135.

6

1864

On certain series

.

2

,

90

–

92

.

7

On Wilson's theorem

.

2

,

92

–

93

.

8

Arithmetical note.

2

,

172

.

9

1866

The elementary properties of chords of conic sections

.

3

,

1

–

4

.

10

Of the circle orthotomic to three given circles

.

3

,

26

–

29

.

11

Quadrilinear co-ordinates

,

3

,

71

–

82

and 173-177.

12

Of recurring series

.

3

,

117

–

121

.

13

Of the fifty-points' conicoid.

3

,

144

–

145

.

14

Pentahedral co-ordinates

.

3

,

146

–

151

.

15

Permutations and combinations

.

3

,

193

–

200

.

16

1868

Centre loci.

4

,

64

.

17

The circular points at infinity.

4

,

91

–

94

.

18

On the limiting cases of certain conics

.

4

,

148

–

151

.

19

Problems supplementary to choice and chance

.

4

,

152

–

158

and 193-200.

20

The catenary referred to three horizontal tangents

.

4

,

238

–

241

.

21

The catenary referred to an oblique tangent

.

4

,

242

–

248

.

22

1871

The nine-points' conic of any tetrastigm

.

5

,

1

–

2

.

23

A new symbol.

5

,

120

–

121

.

24

Law of force in an elliptic orbit about any point whatever.

5

,

160

–

161

.

25

1872

Chance. (New Ser.)

,

1

,

163

–

166

.

26

1873

Extension of a law of determinants. (New Ser.)

,

2

,

80

.

27

1875

Formula for a fraction approximate in value to a given surd. (New Ser.)

,

4

,

79

–

82

.

28

A regular polygon in space. (New Ser.)

,

4

,

88

–

89

.

29

1878

Sub-factorial N. (New Ser.)

,

7

,

145

–

147

.

30

1879

A theorem in combinations. (New Ser.)

,

8

,

82

–

83

.

31

Arrangements of m things of one sort and n things of another sort, under certain conditions of priority. (New Ser.)

,

8

,

105

–

114

.

32

Note on “Choice and Chance”. (New Ser.)

,

8

,

129

.

33

1880

A phenomenon of the kalendar. (New Ser.)

,

9

,

90

–

92

.

34

Educational Times

35

There are a number of references to Whitworth's “Solutions of questions” in the Educational Times, some of which were reprinted in the Messenger of Mathematics, in Jahrbuch der Fortschritte in der Mathematik, up to 1905. Many of these references cannot be positively identified without inspection of the files of the Educational Times. A few of these in the period 1868-81 are at: 3, 100–101; 9, 103-105; 10, 59; 14, 112; 34, 51; 72, 66-70.

36

Mathematical papers not listed above are:

37

1862

Determination of the trilinear equations to the axes of a conic section

.

Quart. J. Math.

,

5

,

335

–

336

.

38

1863

Note on certain remarkable properties of numbers

.

Quart. J. Math.

,

6

,

163

–

166

.

39

1870

Note additionnelle à la spirale équiange

.

Nouv. Ann. Math.

,

9

,

38

–

40

.

40

1875

Pythagorean triangles

.

Liverpool Lit. Phil. Soc. Proc.

,

29

,

237

–

249

.

41

Mathematical books are:

42

1866

Trilinear Co-ordinates and other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise

.

43

1867

Choice and Chance

.

Cambridge

:

Deighton Bell.

(2nd ed., 1870; 3rd ed., 1878;4th ed., 1886; 5th ed., 1901.)

44

1882

The Churchman's Almanac for Eight Centuries, 1201-2000, giving the Name and Date of Every Sunday

.

London

:

Well, Gardner & Co.

(

22

pp.)

45

1898

The Expectation of Parts, into which a Magnitude is divided at Random, Investigated mainly by Algebraical Methods. Suppl. to Choice and Chance

.

Cambridge

:

Deighton Bell.

(

24

pp.)

46

1906

The Law of the Wager: 16 pages from Christian Thought on Present-day Questions: Sermons on Special Occasions

(ed.

W.

Carter

).

London

:

Macmillan

, (

x + 214

pp.)

47

1948

Choice and Chance: with one thousand exercises

. Reprint of the 5th edition, 1901.

New York

:

Hafner

.

48

A list of theological works may be found in the British Museum Catalogue

.

49

Other References

50

Anscombe

F. J.

(

1948

).

The validity of comparative experiments

.

J. R. Statist. Soc. A

,

111

,

181

–

200

.

51

Barton

D. E.

and

David

F. N.

(

1956

).

Spearman's “rho” and the matching problem

.

Brit. J. Statist. Psych.

,

9

,

69

–

73

.

52

Bowley

A. L.

(

1928

).

F. Y. Edgeworth's Contributions to Mathematical Statistics

.

London

:

Royal Statistical Society

.

53

Chrystal

G.

(

1889

).

Algebra: An Elementary Text-book, Part II

.

Edinburgh

:

A. & C. Black

.

54

Eisenhart

C.

(

1965

).

Anniversaries in 1965 of interest to statisticians

.

Amer. Statistician

,

19

,

21

–

29

.

55

Garwood

F.

(

1941

).

An application of the theory of probability to the operation of vehicular-controlled traffic signals

.

J. R. Statist. Soc. Suppl.

,

7

,

65

–

77

.

56

Greenwood

M.

(

1922

).

The value of life tables in statistical research

.

J. R. Statist. Soc.

,

85

,

537

–

543

.

57

Greenwood

M.

(

1937

).

On the value of Royal Commissions in sociological research with special reference to the birth rate

.

J. R. Statist. Soc.

,

100

,

546

–

557

.

58

Irwin

J. O.

(

1955

).

A unified derivation of some well known distributions of interest in biometry and statistics

.

J. R. Statist. Soc. A

,

118

,

389

–

404

.

59

Irwin

J. O.

(

1963

).

Contribution to a discussion on fiducial probability

.

Bull. Int. Statist. Inst.

40

,

933

.

60

Keynes

J. M.

(

1921

).

A Treatise on Probability

.

London

:

Macmillan

.

61

Jeffreys

H.

(

1939

).

Theory of Probability

.

Oxford

:

Clarendon Press

.

62

Morant

G. M.

(

1921

).

Random occurrences in space and time when followed by a closed interval

.

Biometrika

,

13

,

309

–

337

.

63

Pearson

K.

(

1892

).

The Grammar of Science

.

Edinburgh

:

A. & C. Black

.

64

Pearson

K.

(

1956

).

Early Statistical Papers

.

Cambridge

:

University Press. (This is the date of publication of the collected papers.)

65

Todhunter

H.

(

1865

).

A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace

.

London

:

Macmillan

.

66

Venn

J.

(

1866

).

The Logic of Chance

.

London

:

Macmillan

. (2nd ed., 1876; 3rd ed., 1888.)

67

Quetelet

A.

(

1846

).

Lettres à S.A.R. le Duc Régnant du Saxe-Cobourg et Gotha, sur la théorie des probabilitiés, appliquée aux sciences morales et politiques

.

Brussels

:

M. Hayez

.