6 BULLETIN 897, U. S. DEPARTMENT OF AGRICULTURE. 
fore, is defined for the purpose of this bulletin as that error in the 
weight of the finished package which has approximately the same 
probability of occurrence as each of the constituent errors. 
As illustrations of the method of calculation, two examples, one of 
net weighing (3-pound packages) and one of gross and tare weighing 
(75-pound packages), are worked out in detail. The results on pack- 
ages of other sizes are given in Tables 5 and 6. Such combinations 
of constituent errors as will result in the maximum error have been 
chosen. 
3-POUND PACKAGES. 
The specifications of good commercial practice require that a 
3-pound package shall be weighed net on an even-arm scale of not 
more than 15 pounds capacity and carrying a 1-pound beam gradu- 
ated to one-fourth ounce, and that the poise of this scale shall be set 
to within one-fourth of a minimum graduation, and that no error 
ereater than one-half of the sensibility reciprocal be made in estimat- 
ing the exact balance. Then the maximum constituent errors intro- 
duced, as read from the tolerance tables and specifications, are: 
a. “‘On parts requiring the employment of removable 
weichts’ (Cok 2, abled) for 2)pounds*:4---25----- zs or 0.062 ounce. 
b. ‘On beam or reading face” (Col. 3, Table 1) for 1 
pound 3.22 ate. Sy oe Rise Sage ties ei aay bee zs or 0.062 ounce. 
c. Counterpoise weights times ratio of scale, 2 pounds 
times ((Labled) a. ck een eet ee eee 15 grains or 0.034 ounce. 
d. One-fourth of a minimum graduation (4 of + ounce)... zs or 0.062 ounce. 
e. One-half of the sensibility reciprocal (Table 2) for 15 
pounds-G of ounce) = 22 eee a ae ae eee + or 0.250 ounce. 
For all practical purposes errors a, 6, c, and d have approximately 
the same probability of occurrence, which is quite small, since they 
are the maximum tolerances allowable, and may be either plus 
or minus in any particular scale. Consequently, the law of pro- 
pagation of errors may be applied, and v (a)? + (6)? + (ce)? + @)? rep-_ 
resents the calculated maximum constant error introduced into every 
package by a scale, the error of which is just within the tolerance 
after the most inaccurate attempt permitted has been made to set it 
on the proper graduation. = 
Error e is variable for every package, and is directly additive to the 
calculated maximum constant error. Then the calculated maximum 
error on any single package will be— 
(0.062)? + (0.062)? + (0.034)? + (0.062)? + (0.250) or 0.363 ounce. 
According to the laws of errors the error on the average of a 
Variable Error 
vn 
nis the number selected. In this case the resulting error has the same 
probability of occurrence as the variable error. Error é is the maxi- 
random selection from a total distribution is » where 

