VOLUME VARIATION OF BOTTLED FOODS. 11 
glass given in literature, and is found to be sufficiently accurate for 
use in this bulletin. The volumes equivalent to the variations in 
overweight as given in Table 1 are computed by this factor and tabu- 
lated in Table 9 (page 20) under the heading " Individual bottles," 
opposite the various capacities given in Table 2. These are calculated 
maximum variations computed in this bulletin, on which further 
computations are based in Tables 4 and 6. 
The blower is continually cautioned to " work as close to the weight 
specified as possible." Since those bottles which are outside the per- 
mitted variations in weight may be rejected, the blower will attempt 
to have them occur as seldom as possible. As a result of following 
this caution and attempting to keep within the limit, the weights of 
the bottles will be distributed in accordance with the normal law of 
errors. For example, if the blower intends to deliver a bottle weigh- 
ing 8 ounces, most of his bottles will weigh close to 8 ounces and only 
a few will be over or under by large amounts. Their average weight 
will approximate 8 ounces and there will be about as many over as 
under weight. The allowable variations stated in Table 1 would 
probably occur very few times in the course of a day's work. These 
are the primary conditions for distribution according to the normal 
law of errors. In accordance with the principles of the law of errors, 
the variation of the average of the representative sample, which has 
the same chance of occurrence as the variation of an individual bottle, 
is equivalent to the individual variation divided by the square root of 
the number of bottles in the sample (3). In making observations of 
this type, it has been found that at least 50 bottles should be meas- 
ured in order that the results may be accurately representative. The 
calculated maximum variation in the volume of a representative sam- 
ple has been computed according to this rule and included in Table 
9 under the column "Average of representative sample." 
Data to show the possibilities of meeting these variations of the 
average volume are not presented in this bulletin. Studies of a simi- 
lar nature (4) on other products have shown that variations com- 
puted by this method are within the range of commercial possibilities. 
In the calculations of the maximum variations in Table 9 the assump- 
tion has been made that the bottler is able to limit his variations in 
filling to any desired degree. The figures chosen for the calculations 
are the weight variations allowed to hand blowers.^ Machine-blown 
bottles are more uniform in weight and also in capacity. Since the 
majority of the bottles are blown by machine, this calculated maxi- 
mum variation is" representative of the variations in the volume of 
bottle foods when they are packed under the specific good commer- 
cial practice conditions outlined, which require that the bottler give 
special attention to his methods of filling. Data are presented to 
show the possibilities of meeting the calculated maximum variations. 
