314 Dr. F. Galton. An Examination into the 



vatious is good enough to certify their general trustworthiness. 

 As regards the pinnacle it is a different matter, and is one which 

 when beginning work, as I did, on the 1892 entries only, was very 

 perplexing. However, by persevering with the other years it became 

 increasingly plain that the pinnacle was a false maximum ; in 1896 

 it was certain that the true maximum la^v well within the portion of 

 the curve included in the diagram. The explanation of the pinnacle 

 then became obvious ; it was that the tolerance granted to those 

 horses who failed by only a little to qualify themselves, was extended 

 considerably beyond the quarter second for which I was prepared.* 

 The cases of 2' 30*0" were few ; they do not appear in the diagram, 

 but their addition would be quite insufficient to remove the difficulty. 

 If the pinnacle were distributed among two adjacent columns outside 

 and to the left of the diagram it would smooth away the incongruity, 

 so I suspect that cases of " under 2' 32" and down to 2' 30" " are 

 habitually rated at a trifle less than 2' 30". Consequently I had no- 

 hesitation in wholly disregarding the entries that helped to make the 

 pinnacle, namely, the whole of those contained in the first column to 

 the left in every one of the diagrams. The course thereupon became 

 clear and straightforward . When fixing upon the mean for each year, 

 I was somewhat biassed by the entries in the adjacent years ; simi- 

 larly as to the probable error. Now that the curves are drawn I see 

 that somewhat better fits might have been made, but they are close 

 enough to show the existence of a. fair amount of correspondence 

 between the observed values and those calculated according to the 

 law of normal frequency. It is near enough to remove hesitation in 

 working with the arithmetic mean. 



* {Jan. 20. — I hare since learnt that the conditions of timing are too rigorous lo 

 justify this inference ; also that the very numerous efforts simply to secure a 

 standard record, and thenceforward to cease training, may be a chief cause of the 

 pinnacle.] 



