The classical work of Andrews was not very wide.  Andrews did not go much beyond pressures close to the normal and ordinary temperatures.  Of late years several very interesting and peculiar cases have been examined by MM.  Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and other physicists.  Sir W. Ramsay and Mr S. Young have made known the isothermal diagrams[6] of a certain number of liquid bodies at the ordinary temperature.  They have thus been able, while keeping to somewhat restricted limits of temperature and pressure, to touch upon the most important questions, since they found themselves in the region of the saturation curve and of the critical point.

[Footnote 6:  By isothermal diagram is meant the pattern or complex formed when the isothermal lines are arranged in curves of which the pressure is the ordinate and the volume the abscissa.—­ED.]

But the most complete and systematic body of researches is due to M. Amagat, who undertook the study of a certain number of bodies, some liquid and some gaseous, extending the scope of his experiments so as to embrace the different phases of the phenomena and to compare together, not only the results relating to the same bodies, but also those concerning different bodies which happen to be in the same conditions of temperature and pressure, but in very different conditions as regards their critical points.

From the experimental point of view, M. Amagat has been able, with extreme skill, to conquer the most serious difficulties.  He has managed to measure with precision pressures amounting to 3000 atmospheres, and also the very small volumes then occupied by the fluid mass under consideration.  This last measurement, which necessitates numerous corrections, is the most delicate part of the operation.  These researches have dealt with a certain number of different bodies.  Those relating to carbonic acid and ethylene take in the critical point.  Others, on hydrogen and nitrogen, for instance, are very extended.  Others, again, such as the study of the compressibility of water, have a special interest, on account of the peculiar properties of this substance.  M. Amagat, by a very concise discussion of the experiments, has also been able to definitely establish the laws of compressibility and dilatation of fluids under constant pressure, and to determine the value of the various coefficients as well as their variations.  It ought to be possible to condense all these results into a single formula representing the volume, the temperature, and the pressure.  Rankin and, subsequently, Recknagel, and then Hirn, formerly proposed formulas of that kind; but the most famous, the one which first appeared to contain in a satisfactory manner all the facts which experiments brought to light and led to the production of many others, was the celebrated equation of Van der Waals.