ME. AIET’S ACCOrXT OF THE COXSTEHCTIOX OF 
f)76 
It seems difficult here to resist the conclusion that there is a very sensible personal 
equation. The difference between the results of different observers for the same bar 
does in every instance greatly exceed any amount of discordance which could be inferred 
as probable from the combination of probable errors. It is to be particularly remarked 
that (so far as I can trace in the observations) all the observations of any one bar Inside 
were taken by all the observers without disturbing the bar, and then all the observations 
of the same bar Outside were taken by all the observers without disturbing the bar, or 
vice versa. 
On comparing the value found for y with its probable error, it does not appear certain 
that there is any difference between results with Bar Inside and Bar Outside. 
The best way of combining the results of the different observers, with due attention 
to the circumstance that the chance-error of each observer’s result is far below their con- 
stant difference, appears to be, to take the simple arithmetical mean. Thus we obtain — 
d. 
Bronze 10= Bronze 28 — 1-66 
Bronze 19 = Bronze 28 — 0-03 
Bronze 20= Bronze 28+0'55 
Bronze 2 = Bronze 28 — O' 95 
Bronze 7 = Bronze 28 + 0T4 
In the year 1853, nearly the whole time from March to September was occupied unth 
experiments on the relative expansions of bars of several metals; Bronze 28 being in all 
cases the standard of reference. The principal part of the observations was made by 
Mr. Sheepshanks: some however were made by Mr. W. Simms, jun. I am aware that 
these observations were made with very great care, although I cannot state every parti- 
cular of the cautions which were employed. The temperatime was given by the tem- 
perature of the water in the external trough ; and I find that, when the temperature 
had been altered by pouring in hot water, &c., no observations were made until six or 
more hours after the alteration. In some cases, the trough was wrapped in blankets 
during the night. The readings of L and B. were converted mto degrees of Faheenheit 
by the Table made from the last comparisons of these thermometers. The observations 
were subsequently reduced by Mr. W. Ellis at the Boyal Observatory. . 
Each “ observation,” as before, is the mean of three comparisons ; and one revolution 
= 0‘"-003587. 
It will be sufficient to exhibit, as a specimen, the reduction of the observations of one 
bar ; and for that purpose I will take Swedish Iron B. 
Excess of Swedish Iron B above Bronze 28. 
o „ y _ 
Sum of excesses in 24 observations at mean temperature 40-972 = + 17'0053 
Sum of excesses in 28 observations at mean temperature 59-313= -j- 2-6529 
Sum of excesses in 16 observations at mean temperature 63-215= — 0-5738 
Sum of excesses in 16 observations at mean temperature 68-143= — 3-2412 
