SEPTEMBER 21, 1899] 
AMERICAN ASSOCIATION FOR THE 
ADVANCEMENT OF SCIENCE. 
AS already notified, the forty-eighth meeting of the American 
Association for the Advancement of Science was held at 
Columbus, Ohio, on August 19-26 Dr. W. O. Thompson, 
President of the Ohio State University, welcomed the Associ- 
ation on behalf of the University, and Dr. Edward Orton, the 
President, in expressing the thanks of the Association, briefly 
referred to some of the scientific advances of the present century. 
The address of Prof. F. W. Putnam, the retiring President 
of the Association, was printed in NAruRE of September 7, and 
the following are extracts from some of the addresses delivered 
by the Presidents of the Sections. 
THE FUNDAMENTAL PRINCIPLES OF ALGEBRA, 
In his address to the Section of Mathematics and Astronomy, 
Prof. Alexander Macfarlane reviewed historically and critically 
the several advances which have been made in the present cen- 
tury respecting the fundamental principles of algebra. The 
conclusion reached, after a statement and criticism of algebraic 
symbols, operations and laws, is as follows :— 
If the elements of a sum or a product are independent of 
order, then the written order of the terms is indifferent, and the 
product of two such sums is the sum of the partial products ; but 
when the elements of a sum or of a product have a real order, 
then the written order of the elements must be preserved, though 
the manner of their association may be indifferent, and a power 
of a binomial is then different from a product. This applies 
whether the sum or product occurs simply, or as the index of 
a base. 
Descartes wedded algebra to geometry ; formalism tends to 
divorce them. The progress of mathematics within the century 
has been from formalism towards realism ; and in the coming 
century, it may be predicted, symbolism will more and more 
give place to notation, conventions to principles, and loose ex- 
tensions to rigorous generalisations. 
THE FIELD OF EXPERIMENTAL RESEARCH. 
Prof. Elihu Thomson described to the Section of Physics a few 
of the recent developments of physical science, and pointed out 
that physical research by experimental methods is both a broad- 
ening and a narrowing field. There are many gaps yet to be 
filled, data to be accumulated, measurements to be made with 
great precision, but the limits within which experimental work 
can be done are becoming, at the same time, more and more 
defined. In most fields of research progress in the future will 
depend in an increasing degree upon the possession, by the in- 
vestigator, of an appreciation of small details and magnitudes, 
together with a refined skill in manipulation or construction of 
apparatus. He must be ready to guide the trained mechanic, and 
be able himself to administer those finishing touches which often 
mark the difference between success and failure. 
In conclusion, Prof. Thomson remarked that his endeavours 
had been to indicate in his address directions in which the field 
of experiment may be extended, and to emphasise the fact that 
research must be carried on by extension of limits, necessitating 
more liberal endowment of research laboratories. The physicist 
must avail himself of the powers and energies set in play in the 
larger industrial enterprises, and finally the field of possible ex- 
ploration in physics by experimental methods has its natural 
boundaries, outside of which our advances in knowledge must 
be derived from a study of celestial bodies. 
The riddle of gravitation is yet to be solved. This all-per- 
meating force must be connected with other forces and other 
properties of matter. It will be a delicate task, indeed, for the 
total attraction between very large masses closely adjacent, aside 
from the earth’s attraction, is very small. 
Scientific facts are of little value in themselves. Their signi- 
ficance is their bearing upon other facts, enabling us to generalise 
and so to discover principles, just as the accurate measurement 
of the position of a star may be without value in itself, but in 
relation to other similar measurements of other stars may become 
the means of discovering their proper motions. We refine our 
instruments ; we render more trustworthy our means of observ- 
ation; we extend our range of experimental inquiry, and thus 
lay the foundation for the future work, with the full knowledge 
that, although our researches cannot extend beyond certain 
limits, the field itself is, even within those limits, inexhaustible. 
NO. 1560, VOL. 60] 
NATURE 
| 
THE DEFINITION OF THE ELEMENT. 
Prof. F. P. Venable briefly discussed the nature of the 
elements in his address to the Section of Chemistry. He passed 
in review some of the evidence which leads to the belief that the 
so-called elementary atoms are but compounds of an intimate 
peculiar nature, the dissociation of which has not yet been ac- 
complished. Referring to the conclusions to which investigations 
lead, it was remarked that the hypothesis that the elements are 
built up of two or more common constituents has a larger 
number of supporters, and would seem more plausible than 
Graham’s hypothesis. Some have supposed one such primal 
element by the condensation or polymerisation of which the 
others were formed. Others have adopted the supposition of 
two elements. 
There are many practical difficulties in the way of these sup- 
positions ; the lack of uniformity in the differences between the 
atomic weights, the sudden change of electro-chemical character, 
and the impossibility, so far, of discovering any law underlying 
the gradation in the properties of the elements with the increase 
of atomic weights, are some of the difficulties. In comparing 
these two hypotheses, that of Graham seems very improbable. 
It is possible to think of valency as dependent upon the character 
of the motion of the atom, but one cannot well conceive of a 
similar dependence of atomic weight and all the other properties. 
There remains, then, the hypothesis of primal elements by the 
combination of which our elements have been formed. These 
molecules are probably distinguished from the ordinary mole- 
cules by the actual contact and absolute union of the component 
atoms without the intervention of ether. 
Since these elemental molecules cannot as yet be divided, the 
name atom may be retained for them, but the idea of simplicity 
and homogeneity no longer belongs to them. The definition of 
an element as a body made up of similar atoms is equally lack- 
ing in fidelity to latest thought and belief, but chemists would 
scarcely consent to change it, and, indeed, it may well be re- 
tained, provided the modified meaning is given to the word 
atom. But, after all, an element is best defined by means of its 
properties. It is by close study of these that ‘its elemental 
nature is decided, and through them it is tested. Complete 
reliance can no longer be placed upon the balance and the 
supposed atomic weight. 
THE DEVONIAN SYSTEM OF CANADA, 
Mr. J. F. Whiteaves’s address to the Section of Geology and 
Geography was upon the present state of knowledge of the 
Devonian rocks of Canada, from a palontologist’s point of 
view. In accordance with long usage in Canada, the line of 
demarcation between the Silurian and Devonian systems was 
drawn at the base of the Oriskany sandstone. The information 
that has so far been gained about the Devonian rocks of Canada 
was considered in geographical order, from east to west, under 
the three following heads, viz. (1) The Maritime Provinces 
and Quebec; (2) Ontario and Keewatin; and (3) Manitoba 
and the North-west Territories. 
The present state of our knowledge of the Devonian rocks of 
the whole Dominion, from a purely palzeontological standpoint, 
was thus briefly summarised :—We now possess a fairly satis- 
factory knowledge of the fossils of the Devonian rocks of 
Ontario, and of the relations which these rocks bear to the 
typical section in the State of New York. The fossil plants of 
the Gaspé sandstones have been described and figured by Sir 
William Dawson, and the remarkable assemblages of fossil 
fishes from the Upper Devonian of Scaumenac Bay and Lower 
Devonian near Campbellton have been worked out somewhat 
exhaustively, the earlier collections in Canada, and the later 
ones by the best ichthyological authorities in London and Edin- 
burgh. We have now some idea of the fossil fauna of the 
Manitoba Devonian, and have added materially to our know- 
ledge of the fossils of the Devonian rocks of the Athabasca and 
Mackenzie River districts. But, on the other hand, our know- 
ledge of the organic remains of the Devonian of Nova Scotia is 
still in its infancy, and it would seem that the plant-bearing beds 
near St. John, N.B., which have so long been regarded as 
Devonian, may possibly be Carboniferous. In the Rocky 
Mountain region of Alberta we have not always succeeded in 
distinguishing Devonian rocks from Carboniferous, and we have 
yet to obtain a much fuller knowledge than we now possess of 
the Devonian fossils of Keewatin and the area to the south-west 
of James Bay. 
