THE NEW NATIONAL STANDAED OF LENGTH, AND ITS PEINCIPAL COPIES. 695 
inferred by the theory of probable errors from the observations of each observer taken 
separately. Thus, in the comparisons of Bronze 10 with Bronze 28, there is a discord- 
ance between the results obtained by Mr. Sheepshanks from 142 sets of observations, 
and by Mr. William Simms, junior, from 24 sets of observations, amounting (in ten- 
millionth parts of an inch) to 198; whereas the probable errors of the two determina- 
tions, deduced in the usual way from the observations of each observer separately, are 
only 15 and 26. In other words, each observer has a personal equation in the micro- 
scopic observation of the engraved lines. The existence of discordances of similar cha- 
racter between the astronomical observations of different observers has been long since 
recognized. The origin of this personal peculiarity is very obscure, but the fact seems to 
be beyond doubt. There appeared to be no proper method of treating the results but to 
take the means of the final results of the different observers, giving equal weight to each. 
“ 20. The expansions of these bars corresponding to a given change of temperature 
had been sufficiently determined in the course of the experiments ; and it was then judged 
expedient, instead of stating the difference in the length of the selected bars at the same 
temperature, to infer the difference of temperature which would cause all to represent 
the same length, by the application of which it would be possible to assign the specific 
temperature at which each bar represents precisely the length of one yard. Thus it 
was found that the length of one yard, as given by the lost Imperial Standard, is repre- 
sented vsdth no sensible uncertainty, except in the measures of the Imperial Standard 
itself, by the following bars, at the temperatures placed opposite to them : — - 
O 
Bronze 19 or No. 1, at 62-00 Faheenheit. 
Bronze 20 or No. 2, at 61-94 Faheenheit. 
Bronze 2 or No. 3, at 62-10 Faheenheit. 
Bronze 7 or No. 4, at 61-98 Faheenheit. 
Bronze 10 or No. 5, at 62-16 Faheenheit. 
Bronze 28 or No. 6, at 62-00 Faheenheit. 
‘‘21. The degrees of temperatui-e for the use of these standards are defined as pro- 
portional to the corresponding apparent increase of volume of quicksilver in the thermo- 
meter-tube ; the degree 32° representing the freezing-point of water ; and the degree 212° 
representing the temperature of steam under Laplace’s standard atmospheric pressure, 
or the atmospheric pressm-e corresponding to the following number of inches in the 
barometric reading reduced to 32° Faheenheit : — 
29-9218-1-0-0766 X cosine (2. latitude)-l-0-00000179 x height in feet above the sea; 
and the degree 62° denoting the temperature which produces in the quicksilver an appa- 
rent expansion equal to of the expansion between 32° and 212° ; and so in propor- 
tion for other degrees. 
“ 23. We propose that the bar No. 1 be adopted by the Legislature as the Paeliament- 
AEY Standaed of One Yaed ; that Nos. 2, 3, 4, 5 be adopted as Parliamentary Copies; 
and that No. 6 be retained by some officer of the Government for the comparison of 
4x2 
