312 
NATURE 
[Aug. 18, 1870 
came to the conclusion that the suspected flint Adches 
are modern fabrications, and that an ingenious and 
successful fraud had been practised by the workmen, The 
editor, however, allows M. Figuier’s versionto stand, feebly 
qualified by a note in small print, that “it should rather 
have been said that the ultimate and well-considered 
judgment of the English geologists was against the 
authenticity of the Moulin-Quignon jaw.” Why, then, 
let M. Figuier’s error be allowed to mislead the English 
public? The high antiquity of man is amply proved by 
the genuine flint Zéches, without involving the apocryphal 
Moulin-Quignon jaw, which throws a certain degree of 
doubt on the whole question. 
In 1823 Dr. Buckland advocated the theory of a great 
diluvial flood which swept over the earth, destroyed the 
extinct mammalia, and conveyed large blocks of stone 
far from their parent rock. This he shortly after with- 
drew. From that time down to the present no attempt 
has been made in England in any scientific work to ac- 
count for facts which the author could not understand, by 
the hypothesis of a deluge. The glaciers and ice-bergs 
are supposed to have transported the blocks of stone, 
and the presence of the remains of men and animals in 
caves is accounted for either by the fact of their hay- 
ing lived and died in them, or by their having been swept 
in by the action of water. Now, however, M. Figuier 
brings again the old exploded theory to the front. He 
speaks of the “cataclysm of the European deluge of the 
quaternary epoch,” as if it were an article of geological 
faith ; “the European diluvial inundation was, as we know, 
posterior to the glacial epoch, a great catastrophe, the 
tradition of which is preserved in the memory of all 
nations, marked in Europe the end of the quaternary 
epoch.” In the first place there is not the slightest proof 
to be adduced of anything of the kind having ever hap- 
pened in Europe, andin the second there is proof direct 
that it did not happen at the end of the so-called quater- 
nary epoch. And the proof direct is furnished by the 
fact that the quaternary mammalia die out one by one, 
gradually and not all at once. There is an unbroken 
sequence of animal life in Europe from the Pliocene to 
the present day. This old diluvial theory runs more 
or less throughout the first part of the book, and leads 
the author very frequently astray. There are also minor 
points which require correction. The little globular 
sponges, with a hole in the middle, washed out of the 
chalk, and found in the gravel at Amiens, which are sup- 
posed by Dr. Rigollot to have formed necklaces, are 
figured as “fossil shells.” If the author will refer to 
D’Orbigny he will find that it is figured as Coscinopora 
globularis.. That it is a protozoon and not a shell there 
can be no doubt. It is indeed hard to understand how 
the mistake could have occurred, for the arrangement 
of M. Figuier’s woodcuts is the same as that given by 
Sir Charles Lyell (“ Antiquity of Man,” p. 119) by whom it 
is rightly described. Again, why does the editor allow M. 
Figuier to call Professor Huxley “ Hippocrates Huxley,” 
Professor Vogt, “Galen Vogt,” and Sir Charles Lyell 
“ Celsus Lyell,” because the first says that the Engis skull 
might have belonged to a philosopher, the second, that it 
belonged toa degraded savage, and the third offers no 
opinion whatever? It is a piece of wit too subtle for or- 
dinary minds. The latter is certainly not a Doctor, nor 
has he written, like Celsus, on agriculture, rhetoric, or 
military affairs. The only possible point of resemblance 
between the three couples is that each was at the head of 
his own particular profession in his own time. 
The portion of the book relating to the Neolithic 
Bronze and Iron ages is much better than the earlier 
part, but it contains little or nothing of importance that 
has not been published by Sir John Lubbock. We have 
done our duty by calling attention to the leading blunders. 
The book is the work of a remarkably skilful compiler, 
and is written altogether for effect. IW Bano: 
OUR BOOK SHELF 
An Elementary Course of Plane Geometry and Mensura- 
tion. By Richard Wormell, M.A., B.Sc. Second 
Edition, revised and enlarged. Fcap. 8vo., pp. 276. 
(London: T. Murby.) 
THIS book is the work of a reformer, not so much of 
geometry, as of the mode of presenting it to the young. 
Sciences begin in practical applications, and tend by a 
universal law to become more and more abstract ; and 
the doctrine of the reforming school is that whatever the 
science may have developed into, it is necessary in teach- 
ing it to go back to practical applications, and to seek for 
a sure foundation for abstract notions in the familiar expe- 
rience of common objects. Teachers need to be inces- 
santly reminded of this necessity. In teaching physics or 
chemistry or botany it is perhaps admitted, though not 
always obeyed ; but in mathematics it is generally not ad- 
mitted ; and when admitted, it is rarely followed out to 
its logical consequences. Geometry, arithmetic, algebra, 
must alike be presented first in their applications ; and 
then alone, in most cases, can definition and soundness 
be given. In most cases, we say, because where mathe- 
matical talents of a moderately high order exist, as in the 
generality of mathematical teachers, this necessity is not 
felt. And for this reason mathematical teachers who are 
not also observant of mental- phrases, may be slow to 
believe what has just been pointed out as a necessity in 
their art. Many of them, we suspect, have a secret sym- 
pathy with the mathematician who proposed the health of 
“The prime numbers, the only branch of mathematics 
that has not been defiled by contact with the concrete.” 
The aim of Mr. Wormell’s book is to teach scientific 
geometry, the logical dependence of truths on one another 
being shown, and to make the teaching sound by giving 
familiar illustrations of all the conceptions involved, and 
applications of the result attained. The book is inter- 
spersed with examples, geometrical and arithmetical. 
Among the subjects mentioned—we turn to the index, as 
giving a good idea of the book—are star polygons, axis of 
symmetry, graduation, land-surveying, spirals and volutes, 
transmission of motion by cogs, &c. Considering what 
the aim of the writer seems to have been, the illustrations 
and applied part of the book have been well done. It is 
generally clear, moreover, and accurate in style, and is 
interesting. In form it is adapted for a school book ; and 
for certain schools it may be a success. But it fails as a 
scientific geometry intended to replace Euclid, in three 
respects ; want of clear statement of axioms and exhi- 
bition of the science as rigidly deductive ; the avoidance 
of the difficulty of incommensurables ; and a degree of 
undefinable inelegance of treatment throughout. The 
book is too long, and is too nearly scientific, to use as an 
introduction to Euclid or to any of its modern substitutes ; 
and, though it would replace them with advantage if the 
mathematical education of the student were to end with 
the reading of this book, it is not easy to see how the 
student proceeding to higher mathematics could do so 
without previously mastering another more complete 
