Important Standard Yard Measures. 53 



•except that arising from a constant difference in temperature 

 l)etween the bars depending on which occupied the North posi- 

 tion. 



The final mean from the comparisons are expressed by the 

 following equations of condition, the subscript numbers refer- 

 ring to the mean temperature of comparison, and the absolute 

 ■term being in inches. 











Computed 



0-C. 



(37)5. .4 



- (40)5.-4 



= 



+ •00018 



+ -00019 



-1x10-5 



08)49-2 



• (37)^0-. 



— 



- -00034 



- '00035 



+ 1 



(37),s., 



-(1383)^3., 



= 



+ 00176 



+ -00173 



+ 3 



(18)53-3 



- (40)53-3 



= 



- -00016 



- 00016 







<]383)5e.o 



- (18)560 



= 



- -00136 



- -00137 



+ 1 



<1383)ei.. 



- (4^).i: 



= 



- 00152 



-00153 



+ 1 



The bars are all of the same alloy, and so the coefficients of 

 thermal expansion can be assumed equal, and the equations 

 :Solved for the three unknowns: (18) — (40), (37)— (40), and 

 (1383) — (40). Giving equal weight to each equation the solu- 

 tion is — 



(18) = (40)— .00016 ins. 



(37) = (40) +.00019 ins. 



(1383) = (40)— .00153 ins. 



(37) is so badly injured that the original determination can- 

 not be used for fixing its length, while for (1383) it is almost 

 certain that some error has been made in the reductions of the 

 original comparisons. Hence only (18) and (40) remain for 

 •establishing the yard. The original comparisons give the tem- 

 peratures at which they are standard as 62.26° F. and 61.99°F. 

 respectively, from which it follows — 



Original comparison, (18) — (40)= —.00009 ins. 

 Present comparison, (18) — (40)= — .00016 ins. 



■so that a relative change of .00007 inches between the two 

 standards is indicated. This is of the order of changes shown 

 "between the similar bars which serve as Parliamentary Copies 

 (see Report by the Board of Trade (Weights and Measures), 

 1912, p. 11). To distribute this change, assume that (18) has 

 diminished by half the amount, while (40) has increased by 

 half the amount. This change of .000035 inch corresponds to 

 a change in the standard -temperature of 0.10°F. 



The final results are given in the following table: — 



