22 FE. Nipher—Evolution of American Trotting Horse. 
s date. aT 
145 1854°0 
143 1857°4 0°57 
141 1861°0 0°55 
139 1864-7 0°50 
137 1869-0 0°50 
135 1872°6 0°43 
133 1878°3 0°48 
y3) 1881°0 
On plotting the values of S and s, we get a somewhat irreg- 
ular series of points which, Coa are represented fairly well 
by the equation 
OF b 1 
This line is shown in figure 2. It will be observed that the 
two points, which are farthest from the line, correspond to a 
speeds 2-11 and 2°13. 
The values of the constants in equation (1) are déterminadl 
by well known graphical methods to be 
a= 1°289 
b=0°014 : 
. It is evident that the condition giving the limiting speed is 
<7=0. This condition in (1) gives the maximum speed to 
which the American trotting horse will constantly approximate 
but never reach. is speed is a mile in 92 seconds or 1°32. 
_ Equation (1) can be put into the form 
ds : Gi 
aera a 
where L is the limiting speed or >. 
This equation admits hi direct integration as follows: 
Sz ds i rf 
_ or performing the ere operations 
Us—L)=U(s,—L)+6T,-sT 
or putting the absolute term equal to A 
i(s—L)=A—0T fo (Oe 
or finally for the primitive function 
s=L+e4"T , (4) : 
gee 
nee . Ee 
Solan SES ETERS ES RS GP al pea tna ea RRA as Tuer lei eae 
