F 
JANUARY 29, 1914] 
three separate places. On one occasion they were 
found among matted masses of the Polyzoan, Bower- 
bankia, on another in a pocket occurring in a pendu- 
lous colony of Botryllus, and on another occasion 
they may have been in the same situation as the last, | 
or they may possibly—but not probably—have been 
present in the mantle cavity of the Botryllus colony. 
On obtaining these free-living Amcebz I started a 
culture of them in petri dishes, and also a culture of 
Amcebe from sponges. The former culture is now 
in a healthy condition, and there has been a large 
increase in the number of individuals. The culture 
from sponges begun on December 10 yielded an in- 
creasing number of Amcebz, until on December 24 
there were numerous specimens all over the bottom 
of the dish. About December 30 this culture began 
to decline, the Amoebz becoming replaced by Ciliates, 
so that at present only occasional specimens can be 
found even by careful hunting. The food of the 
Ameoebz in these cultures was probably bacteria, but 
occasionally algal inclusions were to be observed, and 
in one case an included diatom was almost certainly 
a Nitzschia, a culture of which I added to the 
Amcebe, 
During the progress of these cultures no dividing 
Amcebz were seen, although they were looked for, 
but a few days after starting the cultures a large 
number of small Amcoebz were noticed. These small 
ones undoubtedly grew larger, as the progress of the 
cultures showed. And indeed various sizes of these 
Ameebz from about 30” by 12 to 80, by 40 were 
obtained, both from sponges and the free-living habi- 
tats mentioned above. Unfortunately in my former 
letter I gave the size only of what I considered to 
be the adult form, and have thus misled Prof. Dendy 
into the error of supposing that they are too large to 
be the germ-cells of the sponge. The mature oocytes 
of Sycons are about 35, in diameter, when stained 
and mounted, whereas a large, living Amoeba in a 
spherical condition, measured about .45 » in diameter, 
but even allowing for shrinkage of the oocyte, it is 
probable that it would be somewhat smaller in the 
living state than a large Amoeba. Moreover, as Mr. 
Bidder has pointed out, the adult Amcebz are too 
large to be the metamorphosed collar-cells of the 
sponges, and it may be added so. also are probably 
even the smallest ones. 
Indeed, the identity of the free-living Amoebe and 
those obtained from sponges as indicated by their 
general characters and their similar behaviour under 
culture, apart from the fact of the ingestion of 
diatoms, is sufficient to establish these animals as 
independent organisms. 
It is an interesting fact that the largest forms of 
these Amoebe when flowing quickly can travel their 
own length in about 40 seconds. One specimen was 
observed to travel nearly six times its length in a little 
more than seven minutes, making various stops and 
meanderings on the way. | J. H. Orton. 
The Marine Biological Laboratory, 
The Hoe, Plymouth. 
Projective Geometry. 
Are not the references to the ‘‘ epidemic of projective 
geometries" in a note in Nature of January 1 (p. 510) 
somewhat unfair ? 
It is complained that they ‘“‘may teach pupils to 
copy out nroofs of stereotyped bookwork.’’ The best 
of the treatises contain an excellent selection of 
problems calculated to give the student a firm grasp 
of fundamental geometrical ideas. As for “ problems 
in mechanics involving a conic, cycloid, or catenary,”’ 
the geometry required is usually closely connected 
with the calculus, and is to be found in text-books 
on that subject. 
NO. 2309, VOL. 92] 
NATURE 
607 
Without doubt the calculus is the most important 
branch of mathematics, and should come as early as 
possible, but to those who are interested in the 
geometry of conics the powerful methods of projec- 
tion and reciprocation form a natural and attractive 
sequel to the usual elementary course on the straight 
line and circle. H. Praceio. 
University College, Nottingham, January 1. 
I aGREE with Mr. Piaggio that projective geometry 
is a pleasant and suitable subject of study for arts 
students, especially women, who are reading for 
honours with a view of entering the teaching pro- 
fession. But for such students a single text-book 
written by an eminent pure mathematician would be 
better than the present array of books, the authors 
of many of which have not added much to our know- 
ledge of mathematical Science. 
forgets that thesearts candidates are not the students 
who want their ealculus so early; indeed, they 
flourished ‘and prospered. as well thirty, years ago, | 
taking their ¢alculus:late,.as to-day,. perhaps better. 
Further, Mr: Piaggio- 
It is for the science student who combines. pure’ 
mathematics with mechanics, physics, and chemistry! 
that the early calculus-is most needed. The geo- 
metrical properties of space involved.in the study of 
physical problems are almost invariably essentially 
metric, and a course in. projective geometry will 
appear to such a candidate as a blind-alley, affording* 
very little outlook. Although I liked the subject 
myself, I cannot remember a single outside problem 
to which I could apply my knowledge of it. 
other hand, the geometrical properties of conics and 
On the’ 
other curves are constantly involved in applications. 
to mathematical physics, where their significance can 
only be. properly understood when the curves have 
been studied from first principles. .Mr. Piaggio con- 
siders that this geometry is contained in text-books: 
on the calculus, but the treatment in these, books— 
especially in the case of the conic—is quite inadequate, 
and, moreover, is almost invariably too analytical. 
The old dividing line between geometrical and 
analytical conics was, of course, a mistake, but its 
abolition has led to the failure of students to study 
these curves from first principles, with the result that 
the metric geometry of curves, especially conics, is 
neglected, and students of physics get into the diffi- 
culties mentioned in my note. Now it will be found 
that the authors of many of these text-books run 
down the study of geometrical conics, and propose 
these projective methods as a substitute, and my 
object is to point out that so far as my experience 
goes this substitution leaves the student of mathe- 
matics combined with physics much worse prepared 
than he was before. 
A former pupil, now a lecturer, once brought me 
a proof that the path of a certain particle (I believe 
an electron) was a cycloid. He had worked it out 
analytically ; but I pointed out that the result followed 
immediately from first principles. 
By all means let projective geometry be taught, but 
let its place be beyond the dividing point at which 
students of pure mathematics and of physics branch 
off in different directions. There is plenty of other 
work which is now crowded out of the course common 
to all candidates, which possesses pressing and urgent 
claims for inclusion therein. 
THe WRITER OF THE NOTE. 
Zonal Structure in Colloids. 
THE notice of Prof. Kiister’s work on zoning in 
colloids in Nature of January 8 suggests to me that 
such an influence is often manifest in our concretionary 
formations. : 
In 1912 Prof. S. Leduc, after seeing some of my 
