W. H. Pickering—American Trotting Horse. 879 
first differences of the first column, by those of the second, 
directly. By so doing the figures in the third column will 
read 59, 55, 54, 46, 55, 35, 75. This method does not smooth 
own the curve at all, ‘but shows it with all its original irregu- 
larities. Plotting now a curve with these figures as ordinates, 
and the corresponding values of s as abscissae, we get the 
following fig 
These results could evidently be represented by a curve. 
And they show what mine did, as y I think in an exaggerated 
8 
Way, the increasing value of a nalts the last few years. 
Mr, Nipher, however, prefers to represent them by a straight 
line. This line N is shown upon the plate, calculated from his 
Values of aand b. Fo llowing him in this respect, two lines of 
my own A and B are also given. Now there are two metl hods 
by which we may determine ap ser oes ately the accuracy with 
which a line represents a series oO observations. Fi Irst, that 
While the line coincides as ak yas possible with on points 
observed, the algebraic sum of the ordinates should be zero; 
and second, that the sum of the squares of the ordinates should 
be reduced to a minimum. Making these calculations we ob- 
tain the following results : 
Sum of the ordinates ......... ee (2 
Sum of the squares..... ...--.-. 
