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IOWA ACADEMY OF SCIENCES. 
quantity of the fundamental matter included in each. The 
properties of an element are then dependent upon the distribu- 
tion of matter in three-fold space in its atoms, and are func- 
tions of the three space coordinates. The properties cannot, 
therefore, be completely expressed by a one-fold or a two-fold 
diagram. A three -fold diagram on such a plan implies a far 
fuller knowledge of the atoms than we can hope to gain for a 
long time, and for the present we must be content with approx- 
imations. 
Mendeleeff’s diagram is based on two units — atomic weight, 
which is proportional to mass; and valence, which is a rough 
indication of the distribution of the matter of an atom in space. 
Lothar Meyer takes for the units in his diagram atomic weight 
and atomic volume. The latter is a different measure of the 
distribution of the matter of an atom in space. If to either of 
these diagrams be added a third coordinate indicative in a dif- 
ferent manner of some essential feature of the distribution of 
the matter of an atom in space, the curve in space thus found 
will be a still closer approximate to the true and complete three- 
fold diagram. The third coordinate must represent some prop- 
erty which is constant under known conditions for all elements. 
Valence is too variable. The atomic weight is the only known 
property of atoms which is strictly constant. Atomic volume, 
considered as the inverse of the density of the solid element, is 
slightly variable. If the density could be taken at absolute 
zero we should have the volume under more uniform conditions. 
Wherever the coefficient of expansion of an element is known, 
its volume at absolute zero may be approximately calculated. 
I have done this in the case of a few elements, and find that its 
general result is to smooth out the irregularities on Meyer’s 
curve. If, instead of atomic volume, the cube root of the vol- 
ume is taken, so as to make the coordinate refer to atomic 
diameter, the curve shows a much more even distribution of 
atoms than it shows when drawn in the ordinary way. 
For a third coordinate the force of attraction between atoms 
of the same kind seems to be the best property we can find at 
present. In solids this force is represented by tenacity; in 
liquids it is proportioned to surface tension, and in gases it is 
proportional to the heat energy required to move the atoms so 
far apart that they can no longer cohere, that is to say, to the 
critical temperature of gas. 
