March 13, 1879] 



NATURE 





443 



slip into our boots a bellows sole, which is connected by 

 a tube with a portable odograph. Each pace impresses 

 on the style a small movement, as does each turn of 

 the wheel of a carriage ; and if the paces be absolutely 

 equal, we may measure with certainty the distances tra- 

 velled. In walking on level ground we take steps of 

 astonishing regularity ; but if the ground rises, the step 

 gains in length ; in descents, on the contraf}', the steps 

 are shortened. There may result from this slight errors 

 in the distances traversed. Notwithstanding this, the 

 employment of this apparatus will effect a great progress; 

 it may be substituted with many advantages for the 

 pedometer, which gives, at the end of a certain time, 

 only the paces accomplished, without taking count of the 

 stoppages or the changes of rate. 



In short, when we make an experiment on a measured 

 road, if there are produced variations in the length of the 

 tracing represented by a kilometre, we conclude there- 

 from variations in the length of the pace. Such varia- 

 tions are observed under the influence of the slope of the 

 country, the nature of the soil, the boots we wear, the 

 rate of walking, or the weight carried. These studies in 

 applied physiology have, I believe, a great practical im- 

 portance, and numerous applications to the inarch of 

 troops in a campaign. 



{To be continued.) 



\J 



WILLIAM KINGDON CLIFFORD 



TT was with feelings of the deepest regret that we last 

 ■»• week recorded the sad loss the scientific world and 

 the country at large had sustained by the death, at 

 the early age of thirty-three, of one of the deepest 

 thinkers and most brilhant writers this century has 

 seen. W. K. Clifford was the eldest son of the late Mr. 

 William Clifford, J. P., of Exeter, and was born on May 4, 

 1845. Receiving his earlier education at the school of 

 Mr. Templeton of that city, he proceeded to King's Col- 

 lege, London. Here he at once gave evidence of his 

 great powers by obtaining in his first year, 1861, 

 the Junior Mathematical and Junior Classical Scholar- 

 ships, as well as the Divinity prize. In the two succeed- 

 ing years he gained the Classical and MaUiematical 

 Scholarships of the year, and in addition to the Inglis 

 Scholarship for English language an extra prize for 

 the English essay. Even at this time, whilst pursuing 

 with such success so many branches of study, he sought 

 a more genial occupation for his active mind in constantly 

 reading in the college library the higher mathematical 

 works to which he could obtain access, and towards the 

 end of his school hfe, as also during his time as an under- 

 graduate at Cambridge, he took great delight in solving 

 and propounding problems in the Educational Times. 

 While still in his eighteenth year the "Analogues of 

 Pascal's Theorem " was wTitten, and constitutes the first 

 of his papers recorded in the Royal Society Catalogue. 

 Passing from his school life, we find him entered at 

 Trinity College, Cambridge, securing a Foundation 

 Scholarship, college prizes in each academic vear, and 

 the English Declamation prize. Early in his 'career at 

 the University he read such portions of the Tripos sub- 

 jects as possessed any interest for him, and soon turned 

 his attention to the study of the original writings of 

 Sylvester, Cayley, Salmon, and some of the great Con- 

 tinental masters. In vain did his private tutor, the Rev. 

 Percival Frost, who always had the highest admiration for 

 him, and was anxious that he should attain his proper 

 place in the Mathematical Tripos, urge him to devote 

 a little more attention to examination subjects ; his mind 

 could tolerate no such restraint ; nothing but the fresh 

 and original thoughts of the greatest mathematical 

 writers could satisfy his wants 



His neglect of the examination subjects was such that 



it is said he only once wrote out a paper of bookwork 

 questions, and that under the impression that he was 

 solving problems ; many also, well qualified to judge, were 

 agreeably surprised when he obtained the position of 

 second Wrangler in the Mathematical Tripos of 1867, 

 while his success in obtaining the second Smith's prize 

 was doubtless anticipated from the wider scope for his 

 talents afforded by that examination. During this period 

 the course of his future work is clearly seen ; divinity and 

 classics, at one time so ardently studied, are laid aside, and 

 the writings of the great philosophers divide his attention 

 with the study of higher geometry. One of his longest 

 and most fully worked out papers, "Analytical Metrics,"' 

 pubUshed subsequently in the Quarterly Journal of 

 Mathematics, was written at this time, 1864. 



Of the circle of intimate friends Clifford formed at this 

 time, nothing need here be said ; two or three have gone 

 before him, the remainder have watched with the deepest 

 interest and pleasure his widening reputation and growing 

 influence, and are now left with a blank no one can fill, 

 and all bear in affectionate remembrance his ready sym- 

 pathy, delicate sense of humour, and sweetness of disposi- 

 tion. His success in the Trinity Declamation prize, and his 

 popularity in the debates at the Cambridge Union Society, 

 showed him to be a speaker of no common order, but it 

 was not until he delivered his first Friday evening lecture 

 at the Royal Institution of London, the year after he took 

 his degree, and subsequently at the Sunday Lecture 

 Society, that crowded audiences bore testimony to his 

 extraordinary power of lucid exposition. The Royal In- 

 stitution lecture, " On some of the Conditions of Mental 

 Development," delivered March 6, 1867, was the first 

 time he addressed a large public audience, which included 

 many of the leading thinkers of the time, and from that 

 day he took a recognised position amongst them. A 

 short extract from this lecture reflects the habit of his 

 mind on leaving the University, and indicates plainly 

 that the course of study pursued while an undergraduate, 

 probably by many thought misguided, was, in reality, the 

 expression of a deep inward conviction. Speaking of the 

 mind, he says, " still less must it tremble before the con- 

 ventionalism of one age, when its mission may be to 

 form the whole life of the age succeeding. No amount of 

 erudition, or technical skill, or critical power, can absolve 

 the mind from the necessity of creating, if it would grow. 

 .... The first condition of mental development, then, 

 is that the attitude of the mind should be creative, rather 

 than acquisitive;" and again, "It is quite possible for 

 conventional rules of action, and conventional habits erf" 

 thought to get such power that progress is impossible." 

 Two other Friday evening lectures were gfiven later by 

 Clifford, on "Theories of the Physical Forces," Feb. 18, 

 1870; and on " Babbage's Calculating Machines," May 

 24, 1872 ; in the latter case no pains were spared by him 

 to thoroughly master all the mechanical details of those 

 intricate machines, and for years afterAvards he would 

 occasionally discuss schemes for the completion of the 

 anal>i:ical engine. In public lecturing his greatest success 

 was probably the evening lecture at the meeting of the 

 British Association at Brighton, August, 1872, " On the 

 Aims and Instruments of Scientific Thought." Through- 

 out this lecture the key-note of so much of Clifford's most 

 powerful writing can readily be detected, as may be 

 shown by a short extract : — " If you wiU allow me to 

 define a reasonable question as one which is asked in 

 terms of ideas justified by previous experience, without 

 itself contradicting that experience, then we may say as 

 the result of our investigation, that to every reasonable 

 question there is an intelligible answer, which either we 

 or posterity may know. ... By scientific thought we 

 mean the application of past experience t o new circum- 

 stances, by means of an observed order of events. . . . 

 Remember then that it (scientific thought) is the guide of 

 action ; that the truth which it arrives at is not that which 



