DR. ANDREWS ON THE GASEOUS STATE OF MATTER. 
43o 
From Tables V. and VI. it is easy to calculate the values of a from 64° to 100° 
referred to the unit volume at 0°. These values will be found in the fourth column of 
the next table, and for comparison the values of a at the corresponding pressures from 
0° to 7°-5, and from 0° to 64°, have been taken directly from the same tables. 
Table VII. — Values of a at different temperatures. — Constant Pressure. 
JP- 
a. 
0 °- 7 °- 5 . 
0 °- 64 °. 
64 °- 100 °. 
17-09 
0-005136 
0-004747 
20-10 
0-00607 
0-005533 
0-004958 
22-26 
0-005811 
0-005223 
24-81 
0-00700 
0-006204 
0-005435 
27-69 
0-00782 
0-006737 
0-005730 
31-06 
0-00895 
0-007429 
0-006169 
34-49 
0-01097 
0-008450 
0-006574 
It has hitherto been assumed, but without direct experimental proof, that matter in 
the gaseous state will expand for every degree through which it is heated by the same 
fraction of its volume at 0°, provided the pressure remains constant. This important 
law, which is due to Gay-Lussac, is unquestionably true in the case of the perfect 
(ideal) gas ; and in the case of air and other gases which have not been liquefied, it may 
be employed for all practical purposes without sensible error. But, as far as I have 
been able to discover, no experiments have hitherto been published to determine under 
what limitations it applies to the gaseous state as that state is presented to us in nature*. 
It will be evident from a cursory inspection of Table VII. that this law does not hold 
good in the case of carbonic acid gas even at moderate pressures, and that the diver- 
gence from the law becomes greater as the pressure is increased. Thus under a 
pressure of 20 T atmospheres the coefficients of expansion, referred to the same unit, 
between 0° and 7°*5, 0° and 64°, and 64° and 100° respectively, are in the ratio of the 
numbers 
1-000, 0-911, 0-817; 
and under a pressure of 34-49 atmospheres the corresponding ratios for the same ranges 
of temperature are 
1-000, 0-770, 0-599. 
It is scarcely necessary to add that if the law of Gay-Lussac held good, the coefficients 
* Biot states, indeed, somewhat vaguely, that Gay-Lussac verified this law experimentally for air and other 
gases and found it to be strictly true ; hut the experiments themselves have never been published, and the 
methods of investigation employed by Gay-Lussac are now known to have been imperfect, so that they failed 
even to show the differences in the dilatation by heat of different gases (Biot, ‘ Traite de Physique,’ vol. i. p. 188). 
The experiments of Regxault on the comparative march of the air and carbonic acid thermometer, to which I 
shall have occasion hereafter to refer, were made by observing the change of elastic force under a constant 
volume. Regnauit states expressly that he made no corresponding experiments under constant pressure (Mem. 
de l’Acad. des Sciences, vol. xxi. pp. 168-171). 
