THE NEW NATIONAL STANDAED OP LENGTH, AND ITS PEINCIPAL COPIES. 675 
Hence the value of is — 1’78 with a probable error or 0 ‘’- 088 . 
The expressions for x\o, x^e, found from solution of the equations, contain six 
terms each, multiplying e,, 62, ^43, ^u, ^51, «52- The expression for y contains fifty-four 
such terms. In each of these cases, the probable value of each term is to be set down 
separately (not combined ■with the others by numerical addition or subtraction), the 
square of each value is to be formed, the sum of the squares is to be taken, and the 
square root of that sum will be the 'probable error of the quantity under treatment. In 
this manner, the Results included in the following Table are formed : — 
Abstract of results. 
Apparent increase in measure of referred 1 
bar, when the referee is outside J 
Probable 
Error 
e 1 
^ 1 0-018. 
Excesses of the Lengths of Bars above Length of Bronze 28. 
Name of Bar. 
Observer. 
Excess. 
Probable Error. 
^2 
X4 
^6 
^8 
^10 
^36 
^’38 
3^40 
X^2 
a^-14 
3^46 
Bronze 10 
Sheepshanks., 
Henderson ., 
Dunkin 
Simms 
W. Simms, jun. 
De la Rue 
r 
Bronze 19 
Sheepshanks.. 
Henderson .. 
Dunkin 
Simms 
W. Simms, jun. 
De la Rue 
Bronze 20 
Bronze 2 
Bronze 7 
Sheepshanks. 
H enderson . 
Simms 
W. Simms, Jun. 
De la Rue 
Sheepshanks.. 
Henderson .. 
W. Simms, jun. 
De la Rue 
Sheepshanks.. 
W. Simms, jun. 
d. 
— 1-28 
- 1*78 
-1-41 
-1-39 
-1-83 
- 1-66 
+ 0-17 
— 0-03 
— 0-20 
+ 0-29 
— 0-41 
— 0-01 
+ 0-31 
+ 0-50 
+ 0-46 
+ 0-83 
+ 0-63 
-0-.36 
- 0-78 
-1-90 
-0-74 
+ 1-15 
-0-72 
d. 
0-042 
-088 
-101 
•079 
•074 
•117 
•069 
•123 
•123 
•097 
•138 
•138 
•074 
•123 
•097 
•138 
•159 
•067 
•087 
•138 
•195 
•055 
•104 
Excess of the Length of Bar above Length of Bronze 7 - 
Xso 1 
Bronze 10 < 
Henderson 
— 1-29 
•123 
^.50 / 
Dunkin 
—2*01 
•123 
Excess of the Length of Bar above Length of Bronze 28 through the intermediation 
of Bronze 10. 
x ^— x ^^ 1 
Bronze 7 < 
Henderson 
-0-49 
•150 
Xq — X^i) j 
Dunkin 
+ 0-60 
•159 
