282 
central Africa; and it was likewise the home of an 
extensive and varied fauna of game and other 
edible birds. To this abundance of wild life is 
attributable the comparative facility with which 
the country was explored and settled; but no 
sooner was the settlement well advanced than 
ruthless slaughter led to the more or less com- 
plete extermination of some species, like the 
bison and the carrier-pigeon, and a vast reduction 
in the numbers of others, such as the prongbuck 
and bighorn. Fashion, sport, and other factors 
led, later on, to equal havoc among birds of many 
kinds. 
Haying permitted all this to come to pass, the 
‘country is now gradually waking up to the loss 
it has sustained, and to the remedial measures 
still possible in order to ensure the preservation 
of at least a remnant of the ancient superfiuity of 
life. In this crusade Dr. Hornaday has for many 
years been a leader, and in the volume now before 
us he reviews what has been done and what still 
remains to be accomplished in a manner worthy 
of all commendation. 
So urgent, however, is the case that the author 
calls upon all biological workers to abandon such 
comparatively unimportant matters as the de- 
scription of species and races, the protective 
coloration of eggs, etc., and to devote all their 
energies to the cause of protecting and re-habili- 
tating their country’s fauna, not only as a food- 
supply, but, in the case of insectivorous birds, as 
a protection against the ravages of insect-foes, 
which are specially severe in America. 
In his opening chapter—on the value of wild 
life—Dr. Hornaday enunciates the axiom that no 
species of wild land animal can long withstand 
systematic hunting for commercial purposes, as 
witness the destruction of the millions of the 
southern bison-herd within four years. He also 
points out that when a species has become reduced 
below a certain number it loses all recuperative 
power, and, like the heath-hen, fails to respond to 
protection. Instant action is, therefore, impera- 
tive in order to save the present remnant of the 
game-fauna, which is estimated to be only 2 per 
cent. of its former numbers. For this purpose 
“bag”-limitations have proved practically use- 
less; and the conversion of national forests into 
reserves where shooting shall be absolutely pro- 
hibited, is a sine qua non (p- 49). 
The period from 1885 to 1g00 saw the great 
boom in the plumage-trade, to check which the 
Audubon Societies were organised; other agen- 
cies, which in many cases are proving victorious, 
came into action soon after; but. the greatest 
hope for ultimate salvation is the federal law of 
1913 for the protection of migratory species, 
NO. 2376, VOL. 95] 
NATURE 

[May. 13, 1915 
which, by bringing recalcitrant States into line, 
saved the situation. Lastly came what it is hoped 
will prove the winning card in the shape of the 
Feather Bill. IRs Ibs 
FOUR DIMENSIONS, 
Geometry of Four Dimensions. By Prof. H. P. 
Manning. Pp. ix +348. (New York: The 
Macmillan Co.; London: Macmillan and Co., 
Ltd., 1914.) Price 8s. 6d. net. 
ERHAPS the main interest of this work is 
that it treats the subject in a way that is 
comparatively new, and one that is likely enough 
to be generally adopted. Until quite recently, 
most works on hypergeometry might be roughly 
divided into three classes: popular or semi- 
popular outlines, which, however stimulating or 
suggestive, have little no scientific value; 
frankly analytical disquisitions, such as those of 
Riemann, etce.; and works which, although 
couched in geometrical language, give the impres- 
sion of being, so to speak, translations of pre- 
vious analytical demonstrations. It must be ad- 
mitted, of course, that some authors (such as 
Segre) have obtained new and valuable results for 
surfaces in three dimensions by considering them 
as sections of hyper-surfaces, and have pursued 
other four-dimensional researches in a way 
which has much more the aspect of being 
purely geometrical. But since it is a psycho- 
logical fact that so far we have no true 
intuition of four-dimensional space, the infer- 
ence seems to be that these authors have become 
so familiar with the analytical arguments under- 
lying their theorems that they pass without. an 
effort to the corresponding geometrical form of 
statement; much in the same way as dualisation 
of a projective theorem becomes almost mechani- 
cal after sufficient practice. 
The method of the present work may be 
described as a logical induction based upon ex- 
plicit geometrical axioms about strictly geometri- 
cal indefinables. The primary element is the 
point; the primary undefined relation is that of a 
point P being collinear with a given segment AB. . 
From this the definition and properties of a 
straight line are deduced; thence we proceed to 
the definition of a triangle; and from this, with 
the help of Pasch’s axiom (a line meeting one 
side of a triangle and another side produced meets 
the third side), we arrive at the definition and. 
properties of the plane. 
Assuming, now, that after reaching a plane 
field of points there is. at least one point not 
belonging to that field, we can construct a tetra-. 
hedron, and, by arguments strictly analogous to 
those employed before, arrive at a three-dimen- 
or 

