CTE 
EDITORIAL CoMMITTEE: S. NEwcoms, Mathematics; R. S. WooDWARD, Mechanics; E..C. PicKERING, 
Astronomy; T. C. MENDENHALL, Physics; R. H. THURSTON, Engineering; IRA REMSEN, Chemistry; 
J. LE ContE, Geology; W. M. Davis, Physiography; HENRY F. OsBoRN, Paleontology ; W. K. 
Brooks, C. HART MERRIAM, Zoology; S. H. ScuDDER, Entomology; C. E. Brssry, N. L. 
Brirron, Botany; C. S. Mrnot, Embryology, Histology; H. P. BowpircH, Physiology; 
J. S. Brutrnes, Hygiene; J. MCKEEN CATTELL, Psychology; 
J. W. Powr.L, Anthropology. 
Fray, SEPTEMBER 15, 1899. 
CONTENTS: 
The American Association for the Advancement of 
Science :-— 
The Fundamental Principles of Algebra: DR. ALEX- 
ANDER MACFARLANE.........ceccecscnecereeeeeserees 345 
Proceedings of the Botanical Club: A. D 
(SIBTETENT, ocoshososeesnosobqatbeboonosens oponounbondsequodsenous 364 
The American Microscopical Society: PROFESSOR 
IBDEIN TENE 1h) \A/ A210) -snonecpnosodasoqqdeadoosecboonds0acen) 367 
Proceedings of the Sixteenth Annual Convention of 
the Association of Official and Agricultural Chem- 
SESH mL) RAW EA ANY a VALID Weston ales se selselee)acisewlaieeiemtstsice 368 
A Card Centralblatt of Physiology: DR. WILLIAM 
ROW NSEN DUR ORTER cece scssecitccsesencesteccccsavece 370 
Scientifie Books :— 
Green on the Soluble Ferments and Fermentation : 
Dr. OscaR LOEW. Annalsof the South African 
Museum: F. A. Lucas. Bolton’s Catalogue of 
Scientific and Technical Periodicals: PROFES- 
sok J. MCKEEN CATTELL. General. Books 
TEEOGIIGL! acs ngcansaocodanscoros so enon edecOnOn SEER BEScoeaeG 373 
Scientific Journals and Articles .........+.s100ssceseereee 377 
Discussion and Correspondence :— 
The Proper Name of the Polar Bear: Dr. 
LEONHARD STEJNEGER. The Mental Effects of 
the Weather. Dr. H. HELM CLAYTON............ 377 
Notes on Physics :— 
Photography of Sound Waves ; The Hydrolysis of 
Stannie Chloride ; The Specific Heat of Solutions ; 
Magnetism and Stretch Modulus of Steel: W. 
Sep beeetess J Sonn Rucbogpoo saconogeHcasBoTEC oe doSEdc Ree auRChEG 378 
The Bacillus Icteroides as the Cause of Yellow 
TAG O GP epboboon0asboo cde Sccao neces oacOR kOe BOSROOE AE LerES 
International Congress on Tuberculosis 
Scientific eNotes|and sNewsucc cess seeenerseesecee te eoecies 
University and Educational News.........:..c0ccescesees 
MSS. intended for publication and books, etc., intended 
for review should be sent to the responsible editor, Profes- 
sor J. McKeen Cattell, Garrison-on-Hudson, N. Y. 
THE FUNDAMENTAL PRINCIPLES OF AL- 
GEBRA.* 
Tuis section of the Association, over 
which I have the honor of being called upon 
to preside, may be said to be a double sec- 
tion, for it comprises both mathematics and 
astronomy ; aSa consequence, the addresses 
which have been delivered by my predeces- 
sors fall into two distinct groups, the 
mathematical and the astronomical. Of 
the former class I have had the pleasure of 
listening to three: Professor Gibbs on 
Multiple Algebra, Professor Hyde on the 
Development of Algebra, and Professor 
Beman on a Chapter in the History of 
Mathematics. Each of these addresses was 
devoted to one feature or other of the de- 
velopment of Algebra, and the subject 
which I have chosen for to-day is another 
aspect of the same wonderful phenomenon. 
It is a subject which interests alike the 
mathematician and the philosopher, and 
indeed all thinking men, for it concerns 
the foundations of that science which is 
generally acknowledged to be the most per- 
fect creation of the human intellect. 
I propose then to review historically and 
critically the several advances which have 
been made respecting the fundamental 
principles of algebra. Here I am mindful 
of the advice which Horace gives a young 
* Address by the Vice-President and Chairman of 
Section A., Astronomy and Mathematics, of the 
American Association for the Advancement of 
Science, Columbus meeting, August, 1899. 
