OcroBER 20, 1899.] 
of Bolyai Farkas, interesting as proving 
that in 1804 Gauss was still under the spell 
of Euclid. 
Then is to follow the Latin text of the 
immortal Appendix with a German trans- 
lation. Next comes in German translation 
selections from the ‘ Tentamen.’ The book 
concludes with the geometric part of 
‘Kurzer Grundriss,’ the only one of the 
Bolyai’s works printed originally in Ger- 
man. This volume is nearly published and 
may be expected in a few weeks. The 
volume undertaken by Engel has just ap- 
peared (1899). It is a German translation 
of Lobachévski’s first published paper 
(1829), ‘On*the Principles of Geometry,’ 
and also of his greatest work, ‘ New Ele- 
ments of Geometry, with Complete Theory 
of Parallels.’ Only from the ‘New Ele- 
ments’ can any adequate idea be obtained 
of the height, the breadth, the depth of 
Lobachévski’s achievement in the new uni- 
verse of his own creation. 
Of equal importance is the fact that En- 
gel’s book gives to the world at last a com- 
plete, available text-book of non-Euclidean 
geometry. There is no other to compare 
with it. 
For the history of non-Euclidean geom- 
etry we have the admirable Chapter X., of 
Loria’s pregnant work, ‘ I] passato ed il 
presente delle principali teorie geome- 
triche.’ This chapter cites about 80 au- 
thors, mostly of writings devoted to non- 
Huclidean geometry. 
In my own ‘ Bibliography of hyper-space 
and non- Euclidean geometry,’ in the Ameri- 
can Journal of Mathematics (1878), I gave 81 
authors and 174 titles. This, when re- 
printed in the Collected Works of Lo- 
bachévski (Kazan, 1886), gives 124 authors 
and 272 titles. 
Roberto Bonola has just given in the Bol- 
lettino di Bibliografia e Storia della Scienze 
Matematiche (1899), an exceedingly rich 
and valuable ‘ Bibliografia sui Fondamenti 
SCIENCE. 
507 
della Geometria in relazione alla Geometria 
Non-Euclidea,’ in which he gives 353 
titles. 
This extraordinary output of human 
thought has henceforth to be reckoned 
with. Hereafter no one may neglect it 
who attempts to treat of fundamentals in 
geometry or philosophy. 
GEORGE Bruce HALstTep. 
AUSTIN, TEXAS, Aug. 14, 1899. 
BOTANY AT THE COLUMBUS MEETING OF 
THE AMERICAN ASSOCIATION FOR THE 
ADVANCEMENT OF SCIENCE. 
Secrion ‘G’ was attended by a large 
number of Botanists and the meeting was 
in every way pleasurable and _ profitable. 
On Monday afternoon Charles R. Barnes 
gave the vice-presidential address in Botan- 
ical Hall of the Ohio State University, to 
a large and appreciative audience. His 
theme was the ‘ Progress and Problems in 
Vegetable Physiology,’ and the address has 
been published in full in Scrence. 
During each of the succeeding four days, 
two sessions were held and thirty-three 
papers were read and discussed. Wednes- 
day was made a Memorial Day to Sullivant 
and Lesquereux ; the exercises are described 
below by Mrs. Britton. 
Among the items of business transacted 
by Section ‘G’ may be mentioned that 
which related to the publication of the card 
index of American Botany, and an expres- 
sion of high appreciation of the appoint- 
ment of an eminent physiological chemist 
in the Division of Vegetable Pathology and 
Physiology, United States Department of 
Agriculture. 
The authors of papers and an outline of 
the more important points are herewith 
presented : 
‘The Fertilization of Albugo bliti,’ by F. 
L. Stevens, Chicago, Ill. 
The paper presented the results of two 
year’s research on the development of the 
