SCIENCE 
EvITORIAL COMMITTEE: S. NEwcomsB, Mathematics; R. S. WoopDWARD, Mechanics; E. C. PICKERING 
Astronomy; T. C. MENDENHALL, Physics; R: H. THURSTON, Engineering; IRA REMSEN, Chemistry; 
J. LE ContTE, Geology; W. M. DAvis, Physiography; O. C. MaRsuH, Paleontology; W. K. 
BROOKS, C. HART MERRIAM, Zoology; S. H. SCUDDER, Entomology; N. L. BRITTON, 
Botany; HENRY F’.. OSBORN, General Biology; H. P. Bowpitcu, Physiology; 
J.S. BILLINGS, Hygiene ; J. MCKEEN CATTELL, Psychology ; 
DANIEL G. BRINTON, J. W. POWELL, Anthropology. 
Fripay, Aueust 27, 1897. 
CONTENTS: 
The American Association for the Advancement of 
Science :— 
A Chapter in the History of Mathematics: W. W. 
TBYEINIUAIF coosasenoso00cqonacnosesqoonoboSsenaDSncH60e00n003000 297 
Eimer’s Evolution of Butterflies: M. VON LINDEN, 
CHARTEES| Sr VOUN OT seassesscen anes nec coeeececce rae 308 
Progress of Professor Kitasato’s Institute for Infec- 
tious Diseases at Tokio: A. NAKAGAWA.......... 313 
Ninth Annual Meeting of the Association of Economic 
Entomologists: A. H. KIRKLAND................+ 315 
Current Notes on Anthropology :— 
The Ancient Slavonie Type; The Language of the 
Mams: D. G. BRINTON............000esc0eeeeeceeeeees 1 
Notes on Inorganic Chemistry: J. L. H o 
Scientific Notes and News.........0ceceeeseceeeeeee: sneseeee 
University and Educational News. ...........ssseceesesees 
Discussion and Correspondence :— 
Meteorological Observations during an Atlantic 
Voyage: R. DEC. WARD ..........0.seceeeeeeeeeeeeee 324 
Scientific Literature :— 
Kingsley’s Travels in West Africa: WiLLIAM 
LIBBEY. The Microscope and Microscopical Meth- 
ods: HENRY BALDWIN WARD. Pearson on 
The Chances of Death and other Studies in Evolu- 
tion: J. MCKEEN CATTELL............000:000sseeeeee 325 
Scientific Journals :— 
The American Chemical Journal: J. ELLIorTT 
(CATIETEI ESS soGanbodoonneconadodaccnacocaaaaoGeadsQadaqesceodaeccd 331 
MSS. intended for publication and books, ete., intended 
for review should be sent to the responsible editor, Prof. J. 
McKeen Cattell, Garrison-on-Hudson, N. Y. 
AMERICAN ASSOCIATION FOR THE ADV ANCE- 
MENT OF SCIENCE. 
A CHAPTER IN THE HISTORY OF MATHE- 
MATICS.* 
On the 10th of March, 1897, a hundred 
years after its original presentation, the 
Royal Academy of Sciences and Letters of 
* Address by the Vice-President before Section A, 
Mathematics and Astronomy. 
Denmark published a French translation 
of a memoir by Caspar Wessel, entitled 
Om Direktionens analytiske Betegning, et For- 
sdg, anvendt fornemmelig til plane og sphae- 
riske Polygoners Oplosning, or an Hssay on 
the Analytic Representation of Direction, 
with Applications in Particular to the De- 
termination of Plane and Spherical Poly- 
gons. 
This paper, which deals with the geomet- 
ric representation of imaginary quantities ; 
which was read and printed several years 
before the famous essay of Argand and con- 
tains fully as exact a treatment of the sub- 
ject, lay buried for nearly a century until 
attention was again drawn to it in 1895 by 
a thesis of S. D. Christensen upon the de- 
velopment of mathematics in Denmark and 
Norway in the eighteenth century. 
Inasmuch as this memoir of Wessel’s is 
still comparatively unknown, I have thought 
that it would not be uninteresting at this 
time to present a sketch of the development 
of the geometric treatment of the imagi- 
nary, particularly in the latter part of the 
eighteenth century and the first part of the 
nineteenth. 
We find thesquare root of anegative quan- 
tity appearing for the first time in the Stere- 
ometria of Heron of Alexandria, 100 B. C. 
After having given a correct formula for the 
determination of the volume of a frustum of 
a pyramid with square base and applied it 
successfully to the case where the side of 
