434 
DE. ANDREWS ON THE GASEOUS STATE OE MATTER. 
in all these cases would have been the same, and their ratios expressed by L000. I have 
not made any comparative experiments at pressures lower than IT atmospheres; but 
there can be no doubt that, even at the ordinary pressure of the atmosphere, carbonic 
acid gas will diverge sensibly from Gay-Lussac’s law, and that its coefficient of expan- 
sion under constant pressure will change with the temperature, being less at high 
than at low temperatures. 
It follows from these observations that the coefficients of expansion in the foregoing 
tables are the average coefficients for the ranges of temperature to, which they apply. 
It would not be difficult from the experimental results to obtain an empirical formula 
wffiich would give approximately the coefficient or rate of expansion, at any tempera- 
ture and under any pressure, within the range of the experiments, so as to construct 
tables showing the expansion by heat of carbonic acid under different pressures. But 
I have refrained from doing so, as such a table would seldom be required in practice ; 
and for scientific purposes, as I have had occasion in the course of this inquiry more 
than once to observe, the results of empirical formulae are apt’ to mislead the investi- 
gator and rarely aid research. 
For the same temperature, the coefficient of expansion increases as the pressure 
augments, and more rapidly at low than at high temperatures. In the preceding tables, 
the pressures, being always referred to the unit volume at 0°, could not be carried 
beyond 3 4- 5 atmospheres. In the next table the coefficient of expansion for heat of 
carbonic acid gas, referred to the unit volume at 64°, is given at pressures ranging from 
17 to 223 atmospheres. 
Table VIII. — Values of a from 64° to 100°. — Constant Pressure. Volume at 64°=1. 
p* 
t'. 
L ' 
a. 
17-09 
63-86 
100-39 
0-06892 
0-07792 
0*003572 
20-10 
63-76 
100-37 
0-05790 
0*06567 
0-003657 
22-26 
63-79 
100-11 
0*05188 
0-05906 
0*003808 
24-81 
63 77 
100-72 
0-04614 
0*05278 
0-003892 
27-69 
63-85 
100-65 
0*04096 
0*04700 
0-004008 
31-06 
63-83 
100-64 
0-03603 
0-04158 
0*004187 
34-49 
63*65 
100-62 
0-03208 
0*03715 
0-004266 
40-54 
63*64 
100*60 
0*02665 
0*03118 
0-004596 
46-54 
63*68 
100-37 
0-02264 
0-02676 
0-004946 
