* 
as before, has utilised the opportunities presented in the interest 
of science. Captain Giraud surveyed a large portion of the so- 
called “volcanic region” of the Atlantic Ocean, finding the 
water very deep in that vicinity. Specimens brought up from 
the bottom appeared to be of undoubted volcanic origin. The 
Casella-Miller deep-sea thermometer was used on one occasion 
at a depth of 2,040 fathoms, two miles north of the equator, in 
longitude 22° 16’ west, and indicated a temperature of 35° F., at 
1,000 fathoms 38°, and at the surface $1°, the air being 80°. 
During the voyage from the Canary Islands to Rio the tempe- 
rature at uniform depths was found to vary only about two 
degrees. 
THE Iron-Steel Institute conclude their meeting at Willis’s 
Rooms to-day. 
Prizes for papers on the ‘‘ Elyan Courses” of Cornwall, are 
offered by Mr. J. A. Phillips, F.C.S., to the present and former 
pupils of the Miners’ Association of Cornwall and Devon. The 
papers and illustrative specimens are to be deposited with Mr. 
J. H. Collins, F.G.S,, Hon, Assistant Secretary of the Miners’ 
Association, Polytechnic Hall, Falmouth, on or before Sept. 1, 
1873. The author of the best paper will be entitled to a prize 
(in books, selected by himself) of the value of 57. A second 
prize, also in books, of the value of 3/., will be given to the 
author of the paper next in order of merit. 
WE have received the first number of a new American journal, 
started last month, Zhe Sanitarian, edited by Dr. A. N. Bell, 
of New York. It aims at presenting the results of the various 
inquiries which have been, and which hereafter may be made, 
for the preservation of health and the expectations of human 
life, so as to make them most advantageous to the public and to 
the medical profession. Among the most important articles is 
one by the editor, on ‘‘ The New York Quarantine Establish- 
ment,” which is illustrated with two maps, This is preceded by 
one on ‘‘Infant Mortality, with suggestions for improving the 
condition of Foundlings ;” and followed by another on ‘* The 
necessity of Re-Vaccination.” We strongly recommend this ex- 
cellently conducted journal to those interested in sanitary 
science. 
AMONG the rarer and more interesting remains found in the 
mounds of the west of America, are plates of mica cut into 
different shapes, and evidently preserved as objects of great 
rarity and value; and, in the absence of this mineral in the 
Mississippi Valley, the question has frequently arisen whence 
the material could have been derived. A recent communication 
from Prof. W. C. Kerr, the State Geologist of North Carolina, 
tends to throw some light on this subject, and to open an inte- 
resting chapter in regard to the American prehistoric man. The 
work of collecting mica is at present carried on upon the largest 
scale in the high and rugged region between the Black Mountain, 
the Roanoke, and the head waters of the Nolachuchy, principally 
in Mitchell County, North Carolina, The region in question 
_ has long been known for the existence of numerous open works 
and tunnels, which, at first sight, were supposed to have been 
made in the search for silver or some other valuable metal. 
Prof. Kerr, in his capacity of State Geologist, was led to investi- 
gate this question, and very soon found, in every instance, that 
the excavations referred to were much older than the earliest 
discovery of the country by the Spaniards, and that in all cases 
they were found in ledges of coarse granite, which contained 
nothing but large patches of mica. Prof. Kerr has been satisfied 
for some time that in these mines we have the work of the 
* contemporaries of the mound-builders, and the localities whence 
they derived the mica. What use they made of it we cannot 
say ; but it is suggested that it may have served the purpose of 
mirrors, or possibly have been used as windows, as well as for 
NATURE 
ormament, The number and size of these mines is remarkable, 
some of the open cuts being more than too ft. in diameter, and 
20 ft. or 30 fi. in depth, even after the caving in and filling up of > 
centuries of weathering. The tunnels often extend inwards several 
yards, but are said to be too small for a man of ordinary size to 
work in, These show distinct marks ofthe tool in the granitic 
wall, as if made by a chisel-shaped instrument about an jinch 
broad. Numerous plates of mica are found in these tunnels and ex- 
cayations, some of them trimmed to particular shapes. These facts 
open up a new chapter in the history of the American aborigines, — 
illustrating the character of the commerce carried on at a very 
remote period, and showing the magnitude of the operations, 
and the extended period of time over which they must have been 
prosecuted, to enable a people furnished with nothing better than 
wooden and stone tools to produce excavations of so great 
magnitude, 
Sirius, a journal of popular astronomy published at Leipzig 
and Vienna, contains, in its fourth number for this year, a lec- 
ture by Prof. Oppolzer, on ‘‘ The Importance of Astronomy in 
connection with Ancient History,” the continuation ofan article 
on ‘‘ Copernicus and his Anniversary,” one of a series of articles 
on the ‘‘ Topography of the Heavens,” the present treating of 
the constellation Gem ini, besidesa few notes, 
THE additions to the Zoological Society’s Gardens during the 
last week include a Ring-necked Parakeet (Paleornis torquata) 
from India, presented by Mr. W. E. Johnson; a long-eared 
Owl (Otus vulgaris) feom Europe, presented by Dr. Bree; a 
Wood Owl (Syrnium aluce), presented by Mr. H. W. L. Browne 5 
a Chinese Harrier (Circus spilonotus) ; a grey Eagle Owl (Budbo 
cinereus) and a Bosman’s Potto (Perodicticus potto) from W.- 
Africa; a horned Tragopan (Ceriornis satyra) from the Hima- 
layas ; a black-tailed Hawfinch (Coccothraustes melanurus) from 
Japan ; two crested Buntings (JZelophus melanicterus) ; two red- 
eared Bulbuls (Pycxonotus jocosus), and a red-vented Bulbul 
(P. hemorrhous) from India; a red-headed Bunting (Zmberiza 
rutila), and a yellow-browed Bunting (Z. chrysophrys) from 
Japan; a black Tanager (Zachyphonus melaleucus) from S$. 
America, purchased; two Emus (Dromeus nove-hollandia) 
from Australia, deposited; a great Kangaroo (Macropus gigan- 
zeus), and a Derbian Wallaby (Halmaturus derbianus), bom 
in the gardens. } 
ON THE HYPOTHESES WHICH LIE AT” 
THE BASES OF GEOMETRY* ; 
Plan of the Investigation 
I T is known that geometry assumes, as things given, both the 
notion of space and the first principles of constructions in 
space. She gives definitions of them which are merely nominal, 
while the true determinations appear in the form of axioms. 
The relation of these assumptions remains consequently in dark- ~ 
ness ; we neither perceive whether and how far their connection 
is necessary, nor, @ friori, whether it is possible. ‘ 
From Euclid to Legendre (to name the most famous of modern 
reforming geometers) this darkness was cleared up neither by ma- 
thematicians nor by such philosophers as concerned themselves 
with it. The reason of this is doubtless that the general notion of 
multiply extended magnitudes (in which space-magnitudes are 
included) remained entirely unworked. I have in the first place, 
therefore, set myself the task of constructing the notion of a 
multiply extended magnitude out of general notions of magni- 
tude. It will follow from this that a multiply extended magni- 
tude is capable of different measure-relations, and consequently 
that space is only a particular case of a triply extended magni- 
tude. But hence flows as a necessary consequence that the pro- 
positions of geometry cannot be derived from general notions of 
magnitude, but that the properties which distinguish space from 
other conceivable triply extended magnitudes are only to be 
_“ By Bernhard Riemann. (Translated by Prof.W. K, Clifford, from vol. 
xiii. of the Gottingen Abhandlungen.) 
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