312 



Dr. F. Galton. An Examination into ilie 



same on the average as that of two horses each having the speed of 

 2' 20", or will it be something altogether different? In short, is the 

 arithmetical the most appropriate mean or not ? It would be a 

 strong presumption in the affirmative, if the relative frequency of 

 the various speeds should correspond approximately with those 

 determined by the normal law of frequency, because if they do so 

 they would fall into line with numerous anthropometric and other 

 measures which have been often discussed, and which, when treated 

 by methods in which the arithmetic mean was employed, have 

 yielded results that accord with observed facts. Whether the 

 speeds do or do not occur with the normal frequency had therefore 

 to be ascertained. So my inquiry had two objects : first, did the 

 run of the observations suggest a tolerably smooth curve ? Secondly,, 

 was that curve a tolerable approach to the curve of normal fre- 

 quency ? 



The investigation was troublesome and tedious. It was necessary 

 to pick out from a large collection the names of those stallions, 

 geldings, and mares (all three being equally efficient trotters), whose 

 records had been made in the year under consideration, and who also 

 had arrived at maturity, that is, who were not less than five years 

 old, and therefore had had time to show their full powers. Had 

 younger horses been included, the frequency of the slower records 

 would have been much increased. Assisted by a friend, the 

 appropriate entries were underlined in the printed volumes, then 

 one of us read them out, and the other ticked them down in the 

 appropriate column of a page ruled for the purpose. Finally the 

 marks in each column were counted. In this way 5705 extracts 

 were made from the entries for the years 1892-96 ; they were not 

 subsequently verified, so some few omissions are probable. Anyhow 

 they form a fair and large sample, and are quite sufficient for the 

 present purpose. 



The discussion of this material resulted in rather bulky tables, 

 which it is needless to reproduce here, because their contents are 

 given in an adequate and much simpler manner by the accompanying 

 diagrams. The successive columns in the table are represented in 

 the diagrams by imaginary columns that stand on corresponding- 

 bases. They run as follows : — The first column, counting from the left, 

 contains the percentage value of all observations recorded as 2' 29*0", 

 29i", 29i", or 291"; that is of all under 30 down to 29 inclusive 

 (the minutes being here omitted for brevity). The second column 

 referred to 28-0", 28J", 28J", and 2S|", and so on with the rest. Con- 

 sequently the dot in the diagram which indicates the percentage 

 number of observations, according to the side scale, stands in the 

 middle of its own imaginary column. For example, that of the 

 2' 28" set stands vertically above the point that lies half way 



