o be verified. No general rule was found until M. Van
der Waals first enunciated a primary law, viz., that if the pressure,
the volume, and the temperature are estimated by taking as units the
critical quantities, the constants special to each body disappear in
the characteristic equation, which thus becomes the same for all
fluids.

The words corresponding states thus take a perfectly precise
signification. Corresponding states are those for which the numerical
values of the pressure, volume, and temperature, expressed by taking
as units the values corresponding to the critical point, are equal;
and, in corresponding states any two fluids have exactly the same
properties.

M. Natanson, and subsequently P. Curie and M. Meslin, have shown by
various considerations that the same result may be arrived at by
choosing units which correspond to any corresponding states; it has
also been shown that the theorem of corresponding states in no way
implies the exactitude of Van der Waals' formula. In reality, this is
simply due to the fact that the characteristic equation only contains
three constants.

The philosophical importance and the practical interest of the
discovery nevertheless remain considerable. As was to be expected,
numbers of experimenters have sought whether these consequences are
duly verified in reality. M. Amagat, particularly, has made use for
this purpose of a most original and simple method. He remarks that, in
all its generality, the law may be translated thus: If the isothermal
diagrams of two substances be drawn to the same scale, taking as unit
of volume and of pressure the values of the critical constants, the
two diagrams should coincide; that is to say, their superposition
should present the aspect of one diagram appertaining to a single
substance. Further, if we possess the diagrams of two bodies drawn to
any scales and referable to any units whatever, as the changes of
units mean changes in the scale of the axes, we ought to make one of
the diagrams similar to the other by lengthening or shortening it in
the direction of one of the axes. M. Amagat then photographs two
isothermal diagrams, leaving one fixed, but arranging the other so
that it may be free to turn round each axis of the co-ordinates; and
by projecting, by means of a magic lantern, the second on the first,
he arrives in certain cases at an almost complete coincidence.

This mechanical means of proof thus dispenses with laborious
ca