5IO 



TRANS. ST. LOUIS ACAD. SCIENCE. 



speeds are also parallel to each other, but the two groups are not 

 parallel. 



For the first set, the lines can be represented by the equation 



log A^= ^'+0.07 5 T^ 



where A' is a function of .y, and 7" is estimated in years from any 

 arbitrarily assumed date. 

 For the second group, 



log7V^=^' +O.10 T. 



It is apparent that for the speed of 2 130 and 2 127 the values 

 of A" are too small, for the reason perhaps that in earlier years, 

 when this was called good time, less general attention was paid 

 to the breeding of trotters, while in later years, as this became a 

 common speed, a constantly increasing number of horses of this 

 grade have been used as roadsters and I'emained undiscovered in 

 private hands. 



These plotted lines are shown in Fig. i. It is clear that the 

 intersection of any one of these lines with the time axis determines 

 the date when this speed may be supposed to have originated, 

 or when A^= i, and that this determination of the date, based as 

 it is upon a number of observations running through a series of 

 years, is much more reliable than the date when some accident- 

 ally arranged trotting match revealed the fact that the horse 

 capable of making this speed had already come. 



The dates for the origin of the speeds of 2 : 13 and 2:11 cannot 

 yet be determined very accurately, and this fact is to be remem- 

 bered in considering the discussion which follows. 



The following table gives the values of s in seconds and the 

 dates for the origin of these speeds, determined as before ex- 

 plained. The third column contains the change in speed per 

 year, calculated in a well known manner from alternate differ- 

 ences in the two previous columns. 



