at dhe same Temperature. 27 
room in about twenty-four hours. Comparisons with (R, 1876) 
were made during this period and for three days or more after- 
ward. (M. T. 1876) was cooled from the ‘ertdetaanna of the 
comparing-room to about —8° F. by being placed for about 
twenty hours in a tin case surrounded by a mixture of snow 
and salt. Then it was placed in the comparing-box, allowed to 
approach the temperature of the pope room, a and compari- 
sons were made as before with (R, 1876). Temperatures of 
greatest cooling and heating were taken with maximum and 
minimum thermometers. 
rom comparisons at both high and low temperatures, the 
relative lengths and expansions of (R. 1876), (M. T. 1876) steel 
bar, and (M. T. 1876) zinc bar, are approximately known. They — 
are, (R. ee bar of (M. T. a Oe 0"-39 (-—32°); 
zine bar of (M. T. 1876)=steel bar of 
(M. T. 1876)+267" 5+10°15 (t—82), 
in which expressions ¢ is the temperature in Fahrenheit degrees. 
The residual errors have been computed with these values. 
As the temperature-range was small during the comparisons 
given in the table, slight errors in expansion values will have 
little influence on the variations in the residuals. 
In the following tables, the first column gives the date of 
comparison; the second and third give the temperatures of 
mercurial thermometers lying on the two meters; the fourth 
gives the residual errors of the comparisons. of (R. 1876) and 
steel bar of (M. 'T. 1876) in the sense computed minus observed ; 
and the fifth gives the residual errors of the comparisons of 
(R. 1876) and the zinc bar of (M. T. 1876). The section of 
these bars is 18™ by 27™™. In computing residuals the tem- 
perature of (M. T. 1876) is s taken as the temperature of both 
meters. 
From the residuals, considering only those comparisons 
forty-eight hours or more after the heating or cooling had 
ended, it is seen that the zinc bar of (M. T. 1876), when it is 
heated for twenty hours or more to a temperature of 70° F. 
and then is allowed to cool to its original temperature, 36° F., 
has a certain length; that if it is then cooled for twenty hours 
to a temperature of =§° F., and afterwards is allowed to return 
gradually to its original temperature of 36° F., it will have a 
certain other length; and that these lengths at the same 
temperature may differ by fifteen microns. Both (R. 187 6) 
and the bars of (M. T. 1376) were freely exposed to the air 
inside the comparing-box. If any large gas bi the appa- 
rent change in length of the zinc bar of (M. T. 1876) was due 
to temperature errors, the residuals of the steel pet should 
show it at least in part. 
