THE LAW OF EEEOES OF OBSEEVATIONS. 
181 
5. If we alter the ordinate and abscissa of every point in the curve C'D' in a given 
ratio, changing the limits a, — b of the Error in the same ratio, we find the curve c'd' 
represented by 
( 3 ) 
which may be called a similar Error to (1) or C'D'. The number of observations will 
be different in the two cases, being represented by the areas of the two figures. We 
may find it convenient to suppose the number of observations the same ; if so 
will be a similar function of Error to y—$(x), the number of observations being the 
same for both, the limits of the error in (3) and (4) being ia, — ib. 
6. To find the function of Error resulting from the combination of a given Error whose 
equation is 
yi=f{x i) (5) 
{the limits being + co ) with another independent Error 
*/=<p0)> ( 6 ) 
whose limits are a , —b. 
We shall do this most clearly by help of a geometrical construction. Let the (N) 
values of the first Error be measured from A according to their signs along the indefinite 
line MR; likewise measure the (n) values of the second Error along CD, where AD=«, 
AC=5. Take any two values, AI=^, of the first, and AK=i of the second; they give 
a value x-\-x , of the compound Error, to which will correspond a point P of the plane, 
whose coordinates are x, x v The number of such points contained within the element 
mdccclxx. 2 B 
