70 Trans. Acad. Sci. of St. Louis. 



where t is measured in years from 1860. According to 

 this equation the speed of the trotting horse in 1903 

 would be obtained by making t = 43. The value so com- 

 puted is s = 123.1 or two minutes and three seconds per mile 

 (2:03). 



The date when the two-minute horse will appear is found 

 by making s = 120. The corresponding value of t is 54. 

 The date is therefore 1860 + 54=1914. These two results 

 do not at present seem very far from the mark. 



If in the above equation s be made 180, the date when the 

 three-minute horse appeared is found to correspond to ^ = 

 — 50. The date is 1810. As a matter of fact the date when 

 the three-minute horse appeared was, as I am informed, 1818, 

 in response to a bet of a thousand dollars that no such horse 

 could be produced. 



Nearly all of the fast trotters belong to a few families. A 

 very large per cent, have descended from Rysdyk's Haynhle- 

 toniati, foaled 1849, and Mamhrino Chief, foaled 1844, both 

 of whom were descended from the thoroughbred Mamhrino. 

 It would therefore be unreasonable to expect a very close agree- 

 ment between observed speeds, of a century ago, and those 

 computed from the above formula. 



If in the equation, s be made 99, the time when the horse 

 will have reached within one second of his limiting speed, is 

 found to be 298 vears after 1860. 



The data from which the above equation was deduced were 

 published in the American Journal of Science for April, 1883, 

 by Professor Brewer, of Yale. The data covered all known 

 official trotting records between the dates 1843 and 1883. 

 From 1854 to the present time the speed of the trotter has 

 increased from s = 145 to s = 123. This is a change of 22 

 seconds in the time of trottino^ a mile. Accordino; to the 

 equation as shown above, it will take 255 years, or until the 

 year 2158 to change the speed by 24 seconds more. In all 

 time thereafter, the speed will be practically constant, as the 

 «peed of the running horse is now. 



In 1892 when JSfancy Hanks lowered the trotting record, 

 the writer applied the above equation to her standard track 



