512 



TRANS. ST. LOUIS ACAD. SCIENCE. 



The constants B and C are best determined by taking the lo- 

 garithms of (^-91) for the various values of 5, and plotting 

 them on the time axis. These values are given in the following 

 table : 



The constants are determined by well known graphical meth- 

 ods, and it is thus found that the observations are represented by 

 the equation 



log (5-91) = 1.703 - o-oo ^' - (5) 

 where the logarithms are common, and T is estimated in years 

 from 1S60. Substituting in (4) the values of T for the dates of 

 the above table, the values of s and their differences from the ob- 

 served values of s have been determined and are given in the 

 final column. These differences are seen to be greatest for the 

 later dates, where the possible errors are known to be greatest ; 

 but the error in s even here corresponds to an error of only a 

 year in date, which is certainly within the error of observation. 



From (5) it is easy to determine the date when the horse will 

 have reached within one second of the limiting speed. Making 

 s= 92, this value of 2" turns out to be 370 years. By the close 

 of the present century the time of trotting a mile will be reduced 

 to 2 :04, and the time of 2 : 00 will be reached in the year 191 2. 

 But they indicate that the trotting-horse will finally be able to 

 make his mile in a time not differing materially from the time 

 of the running-horse, which is at present about 100 seconds. 

 Whether or not the trotting-horse will finally beat the running- 

 horse, as the present results seem to indicate, it is perhaps not 

 possible to decide at present with the insufficient data at our 

 command. A weighty consideration is found in the fact that a 

 well trained trotter carries his body more steadily, or with less of 

 rise and fall, than the racer, and this may possibly result to the 



