INSTRUMENTS USED IN ENGINEERING LABORATORIES. DAD 
of stress to which the bar is subjected, then a different value of the mean 
extension will be found for different values of the increment of load for 
which the extension is observed. 
Professor Kennedy suggested that the simple arithmetical mean of the 
observed extensions should be compared with the mean extension taken 
wut in the following way. 
Suppose six micrometer readings are taken for six equal increments of 
load. The extension is calculated for the first and fourth, the second and 
fifth, and the third and sixth, loading ; the mean of these is then taken. 
The following is a sample of this method for a single set of readings : 
1 : Micrometer Differences for Mean Extension | Mean Extension 
Load'in Tons Reading 74 Tons for 74 Tons for 24 Tons 
0 (40°41) 
a 2 
23 er 005533 
t 7s 52°17 005528 - 005553 ‘001851 
ea eee 005599 
123 60:05 
The following table contains a comparison for some of the sets 
of observations of the simple arithmetical mean of the extensions 
‘observed, and the mean calculated by the method suggested by Professor 
Kennedy : Sa 
Taste ITI.—Comparison of Mean Extension. 
Mean Extension 
Observer Bar | Loading i reel 
Arithmetical Mean} Kennedy’s Mean 
A. B.W.K. A Ist 23 00178 00182 
Be . 2nd Be ‘00177 ‘00181 
a L Ist 1} 00214 00215 
a ae 2nd a 00214 , -00216 
Hs 1 1st 22 ‘00150 “00152 
m4 6 2nd aa *0Q150 , 00151 
fi EF Ist & “OO151 00153 
Fy a 2nd 8 “00151 “00153 
W.C.U. B Ist 22 “001851 -001851 
Le Fr 2nd tA “001850, 001840 
a K { Ist 1} *002097 -002094 
od ss | 2nd a 002113 ‘002106 
. E lst 22 *0Q1546, *001537 
” ” | 2nd is 001542 “001539 
As the differences are small between the means found by. the two 
methods, compared with the variations due to other causes, the simple 
arithmetical mean has been used in the following comparisons. 
As the modulus of elasticity is usually calculated for the whole range 
of stress, it does not seem to matter which method of getting the mean 
extension is adopted. But in a case like this, where.the instrumental or 
accidental errors of single readings are obviously not inconsiderable when 
compared with the whole extension for small ranges of stress, it would 
seem that it is not desirable to take out the extensions for very small 
ranges of stress. Professor Kennedy’s method averages the error over a 
longer range of stress. 
1896, NN 
