186 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1911. 
weight 12.25 instead of 12.00. Of recent years a great advance in 
the accuracy of the determinations of atomic weights has been made, 
chiefly owing to the work of Richards and his pupils, of Gray, and of 
Guye and his collaborators, and every year an international committee 
publishes a table in which the most probable numbers are given on 
the basis of the atomic weight of oxygen being taken as 16. In 
the table for 1911, of 81 elements no fewer than 43 have recorded 
atomic weights within one-tenth of a unit above or below an integral 
number. My mathematical colleague, Karl Pearson, assures me 
that the probability against such a condition being fortuitous is 
20,000 millions to one. 
The relation between the elements has, however, been approached 
from another point of view. After preliminary suggestions by 
Débereiner, Dumas, and others, John Newlands in 1862 and the 
following years arranged the elements in the numerical order of 
their atomic weights and published in the Chemical News of 1863 
what he termed his law of octaves—that every eighth element, like the 
octave of a musical note, is in some measure a repetition of its fore- 
runner. Thus, just as C on the third space is the octave of C below 
the line, so potassium, in 1863 the eighth known element numerically 
above sodium, repeats the characters of sodium, not only in its 
physical properties—color, softness, ductility, malleability, ete— 
but also in the properties of its compounds, which indeed resemble 
each other very closely. The same fundamental notion was repro- 
duced at a later date and independently by Lothar Meyer and Dmitri 
Mendeléeff; and to accentuate the recurrence of such similar ele- 
ments in periods, the expression ‘‘the periodic system of arranging 
the elements’? was applied to Newlands’s arrangement in octaves. 
As everyone knows, by help of this arrangement Mendeléeff predicted 
the existence of then unknown elements under the names of eka- 
boron, eka-aluminium, and eka-silicon, since named scandium, 
gallium, and germanium by their discoverers, Cleve, Lecoq de Bois- 
baudran, and Winckler. 
It might have been supposed that our knowledge of the elements 
was practically complete; that perhaps a few more might be dis- 
covered to fill the outstanding gaps in the periodic table. True, a 
puzzle existed and still exists in the classification of the rare earths, 
oxides of metals occurring in certain minerals; these metals have 
atomic weights between 139 and 180, and their properties preclude 
their arrangement in the columns of the periodic table. Besides 
these, the discovery of the inert gases of the atmosphere, of the 
existence of which Johnstone Stoney’s spiral curve, published in 
1888, pointed a forecast, joined the elements like sodium and potas- 
sium, strongly electro-negative, to those like fluorine and chlorine, 
highly electro-positive, by a series of bodies electrically as well as 
