20 F. BE. Nipher—Lvolution of American Trotting Horse. 
Art. Il. -—- Evolution of the American Trotting Horse; by 
RANCIS HK. NIPHER. 
[Read before the St. Louis Acad. of Science, May 7, 1883.) 
In the April number of this Journal, Professor Brewer gives 
a table of data for the number of horses capable of making or 
beating various speeds ranging from 2™ 308 to 2" 11%, for the 
series of years from 18438 to 1882. The three variables deter- 
mine a surface, having the equation 
as (s 
2 
where N represents the number of horses capable of trotting a. 
mile in s-seconds or better, and T represents the year estimated 
from any origin in time. This surface was constructed from 
the values given by Professor Brewer, and it was at once 
observed that for the lower speeds 2™ 30° and 2™ 27°, the sur- 
face was not continuous with the other speeds. The surface 
changed abruptly between the speeds 2°27 and 2:25. Thi 
abrupt change is perhaps explained by the fact that when 230 
was called a fast time, less general attention was paid to breed- 
ing trotters, so that N did not increase as rapidly as now. In — 
later years when such animals are only considered valuable as — 
roadsters and unfit for breeding for the turf, it is probable that. 
an increasing number has been lost sight of, or remain undis- 
covered in private hands. 
In plotting the values log. N and T, each of the speeds gave 
a straight line, the lines for the speeds 2°30 and 2:27 being rep- 
resented by the equation. 
log. N = 0°075 T 
while for all the higher speeds we have, very nearly at least, 
log. N=0°10 T 
where for each line, T has its origin at the intersection of the . 
line with the time axis. These lines are shown in figure 
It is evident by inspection that the values for 2°27 and 2°30 4 
are incomplete, as the lines for 2°27 and 2°25 would cross at the 
year 1880, indicating that as many horses could make 2:25 or 
better as 2°27 or better. I have therefore thought it improper 
to use the data for the speeds 2°30 and 2°27 in the subsequent. 
discussion, 
Referring now to the lines which represent the other and 
higher speeds, it will be observed that the intersection of any 
line with the time axis, determines the date when for that. 
speed, log N is zero or N is 1. In other words it gives us 
a calculated date when this speed may be supposed to have 
had its origin. To put the matter in language having no ref- 
