1] 
The coefficients appertaining to e, x, &c. in each equation being 
added together, we have 
1. 333e+49,04 «—43,96 p+24,52 2+36,33=0 
2. 49,04e +117,4032 x+36,4579 p—9,040] z—48,2507 =0 
3. -43,96e+36,4579 x+140,2564p—25,72042—150,7903=0 
4. 24,52e—9,0401l1—25,7204 p + 180,77422—60,9190=0 
The solution of these equations give 
s= + 0",5055 * 
p= + 1,1380 
x= +0,1011 
e= — 0,0110 
The exactness of this value of z affords exceeding strong presumption, 
that the values of e, x and p, are also very exact. 
But the supposition of z being unknown has the effect of ren- 
dering the number of observations used only equivalent to a smaller 
number when z is considered as known. It is evident the greater 
the number of quantities that are to be determined from a series of 
observations, the greater is the number of observations that will be 
required to give equal exactness. Thus, if e and p only are to be 
found, a smaller number of observations will give e and p exact: 
that is, the errors of observation will have less effect than if e, p and 
& are considered unknown; and if e, p and a only are to be found, 
the results are likely to be more exact from the same observations 
than if e, p, 7, and s are to be found. 
Therefore, although four quantities have been investigated from 
the above 333 observations, yet as one of them, z, was before 
known, it is likely the result will be more exact taking this 
* Four places of decimals have been retained in the multiplication of the coefficients, 
that, as far as computation is concerned, the yalues of ¢, <, p, and z, may be exact to the 
second decimal place. 
c2 
