Jan. 8, 1885] 



NA TURE 



225 



gular mixture of town and country folk, and of sedentary 

 and active professions among the persons measured, but 

 I have not yet verified this surmise.) Per-centiles were 

 then drawn to the curve corresponding to abscissa? that 

 were respectively 5 per cent., 10 per cent., 20 per cent., 

 Sec, of the length of the base line. As the length of the 

 base-line was 275, these per-centiles stood at the gradua- 

 tions i3°"8, 27°'5, 55° - o, &c. Their values, as read off on 

 the sectional paper, are those which I have given in the 

 Table. 



It will be understood after a little reflection that the 

 9th r.ink in a row of 10, the 90th rank in a row of 100, 

 and the 900th rank in a row of 1000, are not identical, 

 and that none of them are identical with the 90th per- 

 centile. There must always be the difference of one half- 

 place between the post which each person occupies in a 

 row of n individuals, numbered from 1 to n, and that of 

 the corresponding graduations of the base on which they 

 stand, and which bear the same nominal value, because 

 the graduations are numbered from o to » and begin at a 

 point one half-place short of the first man, and end at one 

 half-place beyond the last man. Consequently the gradu- 

 ations corresponding to the posts of the 9th, 90th, and 

 900th man in the above example, refer to the distance 

 of those posts from the beginning at o of their several base 

 lines, and those distances are related to the lengths of the 

 base lines in the proportions of S'5 : 10, S9"5: ioo,and899'5 : 

 1000, which when reckoned in per-cents of the several 

 base lines are 85, 89'5, and 89^95 respectively. The larger 

 the number of places in the series, the more insignificant 

 does this half-place become. Moreover, the intrusion of 

 each fresh observation into the series separates its neigh- 

 bours by almost double that amount, and propagates a 

 disturbance that reaches to either end, though it is 

 diminished to almost nothing by the time it has arrived 

 there. We may therefore ignore the existence of this 

 theoretically troublesome half-place in our ordinary- 

 statistical work. 



There is aJatent source of error that might affect such 

 statistics as these, as well as many others that are drawn 

 up in the usual way, which has not, so far as I know, 

 been recognised, and deserves attention. It is due to 

 uncertainty as to the precise meaning of such headings as 

 30-, 31-, &c. If the measurements, no matter whether 

 they were made carefully or carelessly, are read off from 

 the instruments with great nicety, then a reading such as 

 30^99 would fall in the column 30-, and the mean of all 

 the entries in such a column might fairly be referred to a 

 mean value of 305. 



But if the instruments are roughly read, say, to the 

 nearest half inch, the reading of a real instrumental 

 value of 30^99, and even that of a real value of 3076, would 

 both be entered in the column 31-. The column 30- 

 would then contain measurements whose real instrumental 

 values ranged between 29 75 and 3075, and the column 

 31 would contain those that ranged between 3075 and 

 3175 ; consequently, the means of all the entries in those 

 columns respectively should be referred, not to 30^5 and 

 31 *5, but to 30^25 and to 31 '25. An error of a quarter of 

 an inch in the final results might easily be occasioned by 

 the neglect to note the degree of minuteness with which 

 the instruments were read, and I strongly suspect that 

 many statistical tables are affected by this generally un- 

 recognised cause of error. The measurements at my 

 laboratory were read to the nearest tenth of an inch and 

 to a fraction of a pound, so I can afford to disregard this 

 consideration. There was, however, a slight bias in 

 favour of entering round numbers, which should have 

 been, but were not (because I neglected to give the neces- 

 sary instructions), rateably divided between the columns 

 on either side. 



A fuller description of the results of the measurements 

 at the laboratory will appear next February or March in 

 the forthcoming number of the Journal of the Anthro- 



pological Institute, at which place the original data will 

 ultimately be deposited. 



Francis Galton 



NOTES 



It having become known to some' of the friends of the late 

 Mr. Henry Watts, the well-known chemist, whose death 

 occurred very suddenly on the 30th of last June, that his 

 widow and family are in very straitened circumstances, an 

 informal meeting was recently held at the Royal Institution. 

 Those present resolved to form themselves into a committee, 

 with power to add to their number, in order to collect a fund 

 for the benefit of Mrs. Watts and those of her children who are 

 not of an age to provide for their own support. Dr. Atkinson 

 consented to act as secretary, and Dr. Perkin, President of the 

 Chemical Society, as treasurer. Among the names on the com- 

 mittee are those of Sir F. A. Abel, Prof. H. E. Armstrong, 

 Mr. William Crookes, Dr. Warren De La Rue, Prof. James 

 Dewar, Prof. G. C. Foster, Dr. J. H. Gladstone, Prof. A. G. 

 V. Harcourt, Dr. Hugo Midler, Dr. William Odling, Dr. W. 

 H. Perkin, Dr. B. W. Richardson, Prof. W. Chandler Roberts, 

 Sir H. E. Roscoe, Dr. W. J. Russell and Prof. A. W. 

 Williamson. Mr. Watts's public labours for the advancement 

 of chemical science may be said to have begun with the transla- 

 tion of Gmelin's " Handbook of Chemistry," the admirable 

 English edition of which was prepared and edited for the 

 Cavendish Society by him. This work occupies eighteen large 

 octavo volumes, of which the first appeared in 1849, and the 

 last in 1871. A work scarcely, if at all, inferior to this in 

 magnitude, and one which has perhaps been of even greater 

 service to English chemists, both scientific and industrial, is 

 Watts's great "Dictionary of Chemistry," which appeared from 

 1863 to 1881, in eight volumes, containing altogether nearly 

 9700 pages. Mr. Watts also edited and largely added to the 

 second volume of the late Prof. Graham's "Elements of 

 Chemistry," published in 1858 ; he prepared several editions of 

 Fownes's well-known "Manual of Chemistry," which he almost 

 entirely re-wrote and made into virtually a new work ; and in 

 conjunction with Mr. Ronalds and Dr. Richardson, he prepared 

 for Messrs. Bailliere an elaborate treatise on chemical tech- 

 nology. Up to the time of his death, and for about thirty years 

 previously, Mr. Watts was editor of the Journal of the Chemical 

 Society, and in this capacity, as well as in that of librarian to 

 the Chemical Society, he became personally known to and 

 gained the friendship of very many among the Fellows of the 

 Society. But although Mr. Watts's life was one of unremitting 

 labour, the money return for his work was barely sufficient to 

 enable him to provide for the daily wants of a delicate wife and 

 a numerous family. It was not possible for him to provide for 

 their future needs. But if he could not leave behind him 

 pecuniary resources, he accumulated esteem and affection among 

 all who knew him, which, it is confidently hoped, will prove a 

 valuable legacy for those who were dependent on him. The 

 facts of the case show that there is great need of whatever 

 practical proof of their regard for him and appreciation of his 

 labours Mr. Watts's friend =, and English chemists generally, 

 may be willing to make. For many years Mrs. Watts has been 

 in ill-health, so that she cannot do anything for her own support 

 and thai of her family. One son is a permanent invalid, and 

 the four youngest children have still to be educated. A consider- 

 able expenditure is therefore unavoidable for a good many years 

 to come, if the children are to have a fair chance of a start in 

 life. A considerable sum has already been promised in the way 

 of subscriptions, but much more will have to be done in order 

 that any substantial benefit may accrue to Mrs. Watts and her 

 young family. Subscriptions will be received and acknowledged 



