214 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1911, 
These two run partly parallel with one another; but a deviation 
in the parallelism appears, which is full of suggestiveness: The 
peaks of the curves representing oxides shift distinctly to the right 
of the curve representing chlorides as the atomic weight increases. 
Lithium marks a maximum with both curves, but the oxygen curve 
lags greatly at the succeeding peaks, having its maximum with lan- 
thanum at the atomic weight 139,! and shifting over as far as lead 
above 200. This simple fact standing alone would perhaps mean 
but little, but other similar facts seem to point im the same direction. 
For example, the property of electro-positiveness, exhibited by the 
alkali metals, instead of reappearing in copper, has been carried over 
with diminished intensity to zinc; and finally, among the higher 
atomic weights the cusp has deserted mercury (the analogue of zinc) 
and gone as far afield as thallium. Clearly the rate of progression 
which determines electro-positiveness has a longer “wave-length” 
than that which determines valence, if we may describe the perio- 
dicity of these zigzag curves as waves. Again, the tendency toward 
low melting point unquestionably likewise progresses with a longer 
“wave length” than most of the other properties. In the first 
complete period, nitrogen, oxygen, fluorine, and neon all have very 
low melting points. At each recurrence of these groups with higher 
atomic weights the melting point rises, whereas with each recurrence 
of the immediately following alkali metals the melting point falls. 
By the time antimony is reached, this analogue of nitrogen has a 
melting point as high as 900° absolute, whereas the next alkali metal 
has the lowest melting point of all these metals. Clearly the prop- 
erty of melting has shifted toward the right. Other examples of a 
similar kind have been pointed out by others, for example, the well- 
known displacement from strict periodicity of argon, cobalt, and 
tellurium all point to an unequal rate of progression in isolated cases. 
Thus, this phenomenon seems to be a general one; the various prop- 
erties of material seem to oscillate with varying rhythms as the 
atomic weights increase. The variation is so great that one may 
almost suspect not only varying rhythms but also rhythms repre- 
sented by different types of mathematical functions. 
These facts suggest a possible reason for the great irregularity of 
the last part of the periodic table. May it not be that the nature 
1 The essential data for discovering this generalization, namely, the heats of oxidation of the metals having 
great affinity for oxygen, are as follows: Lithium, 72; sodium, 50; magnesium, 72; potassium, 43; calcium 
76; rubidium, 42; strontium, 71; cesium, 41; barium, 67, and lanthanum, 74. These values correspomd 
with gram-equivalents, that is, combination with 8 grams of oxygen, and are expressed in kilogram- 
calories. The typical oxide is always meant. The figures rest chiefly upon the recent work of Rengade. 
de Forerand and Guntz. References to most of the papers are to be found in Abegg’s ‘“‘ Handbuch der 
anorganischen Chemie.’”’? The work of Guntz is published in Compt. rend., 1903, vol. 136,p. 1071; 1905, vol. 
140, p.863; Bull. Soc. chim., 1906 (iii), vol. 35,p.503. ‘The work on lanthanum was done by Matignon, Ann. 
Chim. Phys., 1906 (viii), vol.8, p.426. The heat of oxidation of beryllium is not accurately known, but 
since the oxide may be decomposed by magnesium at high temperatures, the value is very probably less 
than 70 calories per gram-equivalent. 
