46 FEF. E. Nipher—American Trotting Horse. 
This line is nearly coincident with the line marked A A in 
the diagram in Mr. Pickering’s paper. 
: 8 ; 
From this equation the values of ar were calculated as given 
in the fourth column of the table above. The fifth column, 
headed H, gives the time in years by which the corresponding 
time intervals dT must be increased, in order to bring Mr. 
Pickering’s values of It of the third column, into accordance 
with the values calculated from the above equation. In this 
subject to just such errors as this. If the date 1881°0 were 
made 1882°8, the value of os instead of being 0°75 would be 
0°44. 
Whatever these values of sa may be said to prove, there- 
fore, they do not prove that my results as before published 
were absurd, and they do not indicate a limiting speed of one 
mile in 25 seconds less than no time, but when qT? the 
value of s from the last equation is 98 seconds. 
esire to express my thanks to Mr. Pickering for his sug- 
gestion and his friendly criticism, as he has corrected a tendency 
whie had begun to feel, to attach too much importance to 
the numerical results reached ; but I maintain that his method, 
correctly applied, gives in general, substantially the same 
result as my own. It is not necessary to assert that this result 
is really correct, if any person feels inclined to doubt it. Ionly 
insist that the conclusion that the trotting horse will finally trot 
his mile in about the same time that the running horse will 
run, is not unwarranted-by the facts which we now know. 
Most horsemen seem to think that the limiting speed of the 
trotting horse will be somewhere near a mile in 120 seconds. 
If this were true, the differential equation could hardly be a 
linear one. The equation 
ds 
apo Vvs—L 
might, however, represent the values, L being the limiting 
