J 4 



NATURE 



[May I, 1896 



in the middle ; III. is unmistakable. It must,' however, 

 be understood, that although the values are given to the 

 second place of decimals both in the tables and in this 

 diagram, I do not enter more than one decimal on the 

 dice. The use of the second decimal is to make multi- 

 plication more accurate, when a series is wanted in which 

 each term has a larger probable error than i. 



I. II. III. 



In calculating Table I., n was taken as 48. This gives 

 24 positive and 24 negative values in pairs, but I do not 

 enter^the signs on the dice, only the 24 values, leaving 

 the signs to be afterwards determined by a throw of die 

 III. It will be observed that the difference between the 

 adjacent values in Table I. is small at first, and does not 

 exceed 0*2 until the last three entries are reached. These, 

 which are included in brackets, differ so widely as to 

 require exceptional treatment. I therefore calculated 

 Table II. on the principle of dividing that portion of the 

 curve of distribution to which those entries apply, into 

 24 equal parts and entering the value of the ordinate at 

 the middle of each of those parts in that table. More- 

 over, instead of entering the three bracketed values on 

 die I, I leave blanks. Then whenever die I. is tossed 

 and a blank is turned up, I know that I have to toss die 

 II., and to enter the value shown by it. 



The precise process I follow is to put 2 or 3 of dice I. 

 into a small waste-paper basket, to toss and shake them, 

 to take them out and arrange them on a table side by side 

 in a row, squarely in front of me, but by the sense of 

 touch alone. Then for the first time looking at them, to 

 write down the values that front the eye. If, however, 

 one of the blank spaces fronts me, I leave a blank space 

 in the entries. Having obtained as many values as I want 

 from die I., I fill up the blank spaces by the help of die II. 



Lastly, the signs have to be added. Now as 24 = 16 -}- 8 

 = 2* -f 2^ it follows that 16 of the edges of die III. may 

 be inscribed with sequences of 4 signs in every possible 

 combination, and the remaining 8 with sequences of 3 

 signs. Then when die III. is thrown, the several entries 

 along its front edge, which are 4 or 3 in number as the 

 case may be, are inserted in an equal number of successive 

 lines, so as to stand before the values already obtained 

 from the other dice. 



The most eff"ective equipment seems to be 3 of die I., 

 2 of die II., I of die III., making 6 dice in all. 



Values for Die I. 



0*03 ... 0-51 ... 104 ... 178 



o-ii ... 059 ... 1-14 ... 195 



o'i9 ... 067 ... 125 ... 215 



0-27 ... 076 ... 1-37 ... (2-40) 



0-35 - 085 - 1-50 ... (275) 



0-43 ... 094 ... 163 ... (3-60) 



Values f 07- Die J I. 



2-29 ... 251 ... 277 ... 325 



2-32 ... 255 ... 283 ... 3-36 



2-35 ... 259 ... 290 ... 3-49 



2-39 ... 264 ... 298 ... 365 



2-43 ... 268 ... 306 ... 4-00 



2-47 ... 272 ... 3-15 ... 4-55 

 Values for Die III. 



■¥ + + + -l----f- - - + + +--I- 



Francis Galton, 



THE ROYAL SOCIETY SELECTED 

 CANDIDA TES. 



'X*HE following fifteen candidates were selected oi» 

 -*■ Thursday last (April 24) by the Council of the 

 Royal Society to be recommended for election into the 

 Society. The ballot will take place on June 5, at 4 p.m. 

 We print with the name of each candidate the statement 

 of his qualifications. 



Sir Benjamin Baker, Mem Inst. C.E., 



Hon. Mem. of the American Society of Mechanical Engineers, 

 and of the Society of Engineers. Hon. Mem. of the Manchester 

 Lit. and Phil. .Soc. Has been engaged as an Engineer during 

 the last twenty- five years, in the design and construction of many 

 important works at home and abroad, including the Forth 

 Bridge, and has carried out numerous investigations relating to- 

 the strength of materials and of engineering structures generally, 

 and has contributed papers thereon to various Scientific Societies, 

 viz., Proc. Inst. Civil Eng., Trans. Amer. Soc. Mech. Eng.,^ 

 Brit. Assoc. Reports, &c. Author of " A Theoretical Investi- 

 gation into the Most Advantageous System of Constructing 

 Bridges of Great Span," upon which plan the Forth Bridge and 

 six of the largest bridges in the world have been built. 



Robert Holford Macdowall Bosanquet, M.A.^ 



Fellow of St. John's College, Oxford. Barrister. Long and 

 successful devotion to scientihc inquiry, as shown hy the following 

 list of papers, and the printed copies sent herewith for the use of 

 the Council : — " On an Experimental Determination of the 

 Relation between the Energy and Apparent Intensity of Sounds 

 of Different Pitch " {Phil. A^rt^., xliv., 381-387) ; " On Just 

 Intonation in Music ; with a Description of a New Instrument 

 for the Easy Control of all Systems of Tuning other than the 

 Ordinary Equal Temperament" (Roy. Soc. Proc, xxi. , 131-132); 

 "Note on the Measure of Intensity on the Theories of Light 

 and Sound" [Phil. Mag., xlv., 215-218) ; "The Theory of the 

 Division of the Octave, and the Practical Treatment of the 

 Musical Systems thus obtained" (Roy. Soc. Proc, xxiii., 

 390-408) ; On the Polarization of the Light of the Si^y " {Phil. 

 Mag., 1., 497-520) ; " On a New Form of Polariscope and its 

 Application to the Observation of the Sky" (/%«'/. Mag.,\\., 

 20-28) ; "On the Hindoo Division of the Octave, with some 

 Additions to the Theory of Systems of the Higher Orders" 

 (Roy. Soc. Proc, xxv., 540-541, xxvi., 372-384) ; "On the 

 Relation between the Notes of Open and Stopped Pipes " 

 {Phil. Mag., vi., 63-66); "On the Present State of Experi- 

 mental Acoustics" {ibid., viii., 290-305); " Notes on Practical 

 Electricity" (zY'iV., xiv., 241-258); " On a Uniform Rotation 

 Machine, and on the Theory of Electromagnetic Tuning Forks" 

 (Roy. Soc. Proc, xxxiv., 7445-447) ; "On Magneto-motive 

 Force" {Phil. Mag., xv., 205-217); "On Permanent Mag- 

 netism" («^zV/., 257-259, 309-316); "On Self-regulating Dynanno- 

 electric Machines" {ibid., 275-296) ; " On a Standard Tension 

 Galvanometer" {ibid., xvii., 27-30); "On a Determination of 

 the Horizontal Component of the Earth's Magnetism at Oxford" 

 (t'^^zV., 438-447) ; " On Electro-Magnets," No. I. {ibid., 531-536) ; 

 No. II., "On the Magnetic Permeability of Iron and Steel, 

 with a new Theory of Magnetism" {ibid., xix. , 73-94) ; No. 

 III., "Iron and Steel: a New Theory of Magnetism" {ibid., 

 333-340) ; No. IV., " Cast Iron, Charcoal Iron, and Malleable 

 Cast Iron" {ibid., xx., 318-323) ; "Permanent Magnets," No. 

 I. {ibid., xviii., 142-153), No. II., "On Magnetic Decay ' (i(5/^., 

 xix., 57-59) ; "On the Supposed Repulsion between Magnetic 

 Lines of Force" {ibid., 494-495). With a further list of twenty- 

 seven papers. 



Samuel Hawkesley Burbury, M.A., 



Barrister-at-Law. Formerly Fellow of St. John's College, Cam- 

 bridge. Second Classic, and Chancellor's Medallist, and fifteenth 

 Wrangler in the year 1854. Has done much work in Mathe- 

 matical Physics, espeially in the theories of Electricity and 

 Magnetism and the Kinetic Theory of Gases. Joint author of 

 Watson and Burbury's "Generalized Co-ordinates"; also of 

 Watson and Burbury's "Electricity: Part 1. Electrostatics." 

 Author of sundry papers on physical science ; for example, the 

 following : Paper in Phil. Mag., January 1876, " On the Second 



