Marcu 22, 1901.] 
so much as it must seem to approximate, must 
apparently fit, the supposed facts of experience, 
and, on the other hand, must introduce no log- 
ical contradiction. Thus to-day the ordinary 
triply-extended space of our experience may be 
purely Bolyaian, or purely Euclidean, or purely 
Cliffordian, or purely Riemannian. 
In Manning’s ‘Non-Euclidean Geometry’ 
America has taken a step in advance of all the 
world in thus putting forth an intended, avail- 
able class-book for elementary instruction in 
this fascinating subject. 
_ The book is very gratifying to me, in that the 
method of treatment that has been taken as the 
basis of the first chapter is Saccheri’s, drawn 
from my translation, the first ever made, which 
appeared in the American Mathematical Monthly, 
beginning in June, 1894. My copy of Saccheri 
is still, so far as I am aware, the only copy on 
the Western, Continent. 
It is also matter for congratulation that so 
many of the further proofs have been taken un- 
changed from Lobachevski and Bolyai. We 
rejoice that the world will be rich now in pupils 
of those who in life had never a disciple. 
It perhaps should be noted that though the 
book says (p. 98), ‘‘ The Elliptic Geometry was 
left to be discovered by Riemann,’’ it gives only 
the simple elliptic, or single elliptic, or Clifford- 
Klein geometry. It never even mentions the 
double elliptic or spherical or Riemannian ge- 
ometry, which Killing maintains was the only 
form which ever came before Riemann’s mind. 
GEORGE BRUCE HALSTED. 
AUSTIN, TEXAS. 
Commercial Organic Analysis. By ALFRED H. 
ALLEN, F.I.C., F.C.S. Volume II., Part IL. ; 
Hydrocarbons, Petroleum, and Coal Tar 
Products, Asphalt, Phenols, and Creosotes. 
Third Edition, with revisions and additions 
by the Author and Henry LEFFMANN, M.A., 
M.D. Philadelphia, P. Blakiston’s Son 
andCo. 1900. Pp. viii-+322. Price, $3.50. 
In the revision of this volume, most of the 
notes of the second edition have been incor- 
porated in the text, the text condensed to a 
certain extent, by minor changes, and by omis- 
sions, and many valuable additions made. 
Much matter has been added in regard to the 
testing of lubricating oils and phenols, and the 
SCIENCE. 
465 
technology of acetylene. The section on 
asphalt has been largely increased. The claim 
of the preface that the nomenclature of the 
Geneva convention has been applied does not 
seem justified. Some of the analytical opera- 
tions are not described in sufficient detail, no- 
tably the method for the assay of calcium car- 
bide (page 32). The determination of sulphur 
in petroleum does not receive the attention it 
deserves, the most important method—combus- 
tion in a current of oxygen or air, and collec- 
tion of the sulphur dioxide in standard alkali— 
receiving only passing mention in the section on 
asphalt. The method for the detection of 
B-napthol ‘suggested’ by the American Asso- 
ciation of Official Agricultural Chemists was 
indeed described by the referee in his report, 
put has not yet been adopted officially by that 
body. It should be credited rather to Dr. W. 
D. Bigelow, the referee. It was considered 
necessary to call attention to these points, but 
in considering them, the general excellence of 
the revision should not be lost sight of. 
G. §S. FRAPS. 
L. M. B. C. Memoirs on Typical British Marine- 
Plants and Animals. Edited by W. A. HERD- 
MAN, D.Sc., F.R.S. V. Aleyonium by Syp- 
NEY J. Hickson, M.A., D.Sc., F.R.S. Lon- 
don, Williams & Norgate. 1901. 
A student or amateur zoologist visiting the 
sea-shore is apt to find the ordinary text-books 
of zoology somewhat too general to be of much 
service to him in unraveling the structural de- 
tails of many of the forms which attract his 
attention, and the number of forms described 
in the more special laboratory manuals being 
necessarily limited, he may find no mention 
in these of the special organism which interests 
him. ‘To meet this difficulty the Liverpool Ma- 
rine Biology Committee has undertaken the 
publication ofa series of memoirs giving detailed 
descriptions of a number of common animals 
and plants occurring in the district under in- 
vestigation by the Committee. The fifth of 
these memoirs, on Alcyoniwm by Professor Syd- 
ney J. Hickson, has just appeared, its predeces- 
sor being memoirs on Ascidia by Professor 
Herdman, on Cardium by Mr. J. Johnstone, on 
Echinus by Mr. H. C. Chadwick and on Codium 
