ON THE PREDETERMINATION OF THE SPEED OF 

 THE TROTTING HORSE. 



Fkancis E. Nipher. 



In a paper published in 1883 in the Transactions of The 

 Academy of Science of St. Louis, the writer gave a discussion 

 of numerical data covering the performance of all trotting 

 horses making public records, between the years 1843 and 

 1883. The equation which gives the speed of the best 

 horse at any date as function of the time, counted from any 

 assumed date, was then published. It was found that the 

 speed of the horse was approaching a limit, which was ap- 

 proximately that of the running horse. The limiting speed 

 indicated by the data was 1:38, or 98 seconds to the mile. 

 This was somewhat below the speed of the running horse, on 

 an oval track, and it is evident that a limit of 100 seconds to 

 the mile will also fit the observations in a very satisfactory 

 way. The equation published in 1883 was 



— ki 



s= a -}-b 



Here s is the speed, in seconds per mile, t years after any 

 assumed date. At this assumed date ^ = 0, and s =a + 6. 

 It is evident that a is the limiting speed reached in an infinite 

 time, and that b is the difference between the limiting speed, 

 and the speed at the assumed zero date. 



Mr. W. H. Pickering offered some criticisms on the method 

 of obtaining the constants in the above equation, as it ap- 

 peared in a preliminary form,* and in an appendix to the 

 paper in the Transactions, f a slightly different method was 

 employed. The constants so determined were 



- 0.0127< 



s = 98 + 43.5€ 

 or log (s— 98) =1.637 — 0.0055^, 



♦ American Journal of Science. III. 26: 20-24. July, 1883. 

 t Trans. Acad, of Science of St. Louis. Vol. IV. No. 3, pp. 514-5. 1883. 



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