F. E.. Nipher—Evolution of American Trotting Horse. 23 
where e is the Naperian base, and where A is the value of 
Us—L) at any arbitrary zero in time, T being,estimated in 
years from the same zero. The following table contains the 
common logarithms of s—L for the corresponding -dates, and 
these two variables are also plotted in figure 2. 
Year, s—L | log (s—L) T (s—L) cale. diff. 
1854:0 53 1724 =~ 66 527 —0'3 
1857°4 51 1°706 26 50°8 —0-2 
1861-0 49 1:690 + 10 48°9 —01 
1864:7 47 1672 + 47 47-0 0-0 
1869-0 45 1°653 + 9:0 44°8 —01 
1872°6 43 1°633 126 43°1 +01 
1878-3 41 1°613 +183 40°5 —0°5 
1881-0 39 1591 21°0 39°3 +03 
2. 
1850 1860 1870 1880 Year. 
_ds : log (S—L) 
aT ++... eee Ar ae 
— ape 
0°6 
0°5 
0-4 1°65 
1:60 
133 135 137 139 141 143. «*# 
Estimating T from the year 1860 and taking common log- 
hegiane we obtain, by graphical methods, from the plotted 
ine 
* Jog (s—L)=1°694—0-0047T (5) 
Substituting in this equation the values of T, and re-calculating 
the values of s--I as given in the fifth column of the table, it 
48 seen that the greatest difference between the calculated and 
observed values of s, for any date of the table is half a second, 
which corresponds to an error of about a year in the date for a 
given speed. The differences in the final column show that a 
readjustment of the constants in eq. (5) would make the agree- 
ment better, but at present it is hardly worth the trouble, as 
the values would not be materially changed. 
By making s—L=1 in (5) we have » 
1°694—0°0047T=0 
or T=860 which is the number of years after 1860 when the. 
