at the same Temperature. 29 
(M. T. 1876), denotes the steel bar of (M. T. 1876) and 
(M. T. 1876),, the zine ea pis the symbol for micron or 
thousandth of a millimet 
The tubes of the Bépeold base-apparatus have already been 
spoken of. A similar experiment was tried with these tubes. 
The zine bars of tube No. 1 and of tube No. 2, as well as 
° FF; then t was heated for twenty-four hours to a 
temperature between 70° and 80°, and after the heating the 
two zine and the two steel bars were again compared. ‘The 
relative lengths and expansions of the two steel and of the two 
zinc bars are given approximately by 
S’ =’, + 1518"-8 — 0%-06:, 
Z' =Z',+ 210"6 — 0”-44t, 
where ¢ is the temperature of the comparison in Fahrenheit 
degrees. The lengths designated by S’,, S’,, Z’,, Z’,, are each 
very nearly four meters, but are not the lengths used in base 
f 
bars and have been used to avoid any question of lateral . 
flexure. Temperatures were observed with three well deter- 
mined thermometers in the interior of each tube. 
In the following table it is assumed that the observed mer- 
curial temperatures are the true temperatures of the bars. The 
absolute expansions of the bars are known, and with them the 
observed difference of length of the two ‘bars is reduced to 
what it would have been if the two bars under comparison had 
had the same temperature. This is called the observed differ- 
ence of length of the two bars. ee it from the differ- 
ence of lengths of the two bars at that temperature as com- 
a from the equations given above, the residuals result. 
positive, they indicate that the sbancntian difference 
of iength of the two bars was algebraically too s 
The first column gives the date of the abiNpEtaon? the 
second es third, the mercurial temperatures of tube 1 and 
tube 2; the fourth, the residuals of the steel bars or S’,—S’, 
computed, minus S’,—S’, observed ; the fifth, the residuals for 
the zine bars or Z’, pan 7 computed, ‘minus vA ies observed. 
