74 
POPULAR SCIEl^CE NEWS. 
[May, 1S90. 
A MAGIC SQUARE 5,400 YEARS OLD. 
In a very ancient Chinese work, said to 
have been written in the reign of Fo-clii, 
3500 B. C, the accompanying diagram 
occurs, under the title of Lo-chou. Al- 
though it evidently indicates some mathe- 
matical rule or formula, its exact significance 
has been the source of much speculation, 
and many theories, of more or less proba- 
bility, have been advanced to explain its 
meaning-. 
It remained for M. Lucas, a contributor to 
La Nature, to suggest a simple and reason- 
able explanation of the figure, which is 
entirely confirmed by the figure itself. He 
claims it is simply a magic square, repre- 
sented in the only way that it could be by a 
person ignorant of figures. It will be seen 
that, in whichever direction one counts the 
groups of spots and circles, whether horizon- 
tally, vertically, or diagonally, the total pro- 
duct will always be fifteen. The above 
figure, translated into Arabic numerals, 
would be written thus. 
4 
9 
2 
3 
5 
7 
8 
1 
6 
and a simple inspection of the two diagrams 
will be sufficient to convince anyone that the 
mysterious Lo-chou has no hidden mystic, or 
even mathematical meaning, but is simply the 
attempt of tome ancient student, ignorant of 
figures, to express that remarkable relation of 
numbers to each other which, under the name 
of the magic square, is a familiar source of 
amusement to every schoolboy of the present 
day. It is certainly a very curious circum- 
stance that tills arrangeinent shoidd have been 
known, not only at such an early period, but 
even before the invention of figures to express 
the numbers themselves. 
Nickel, cobalt, iron, and several other metals, 
separate very rapidly from cold sulphocyanide solu- 
tions under the influence of a weak electric current, 
according to recent experiments by E. F. Smith and 
L. K. Frankel. 
[Original in Popular Science News.] 
BRIEF STUDIES IN BIOLOGY. 
BY PROF. JAMES II. STOLLKR. 
III. 
THE EARTlIWORM. 
In the study of animals, after two or three have 
been carefully observed they should then be com- 
pared. It will, therefore, be helpful to recall Jhat 
we have thus far studied a one-celled animal, the 
amoeba, — representing the Protozoa, or first great 
division of the animal kingdom, — and a many-celled 
animal, the hydra, — representing the second sub- 
kingdom, the Coelenterata. It will be remembered 
that in the hydra the cells are arranged in two 
layers, differing somewhat from each other in their 
properties, — that is, forming tissues, — and that the 
general form of the body is that of a sack, the cav- 
ity of which serves as a stomach. It will not be 
out of the way to conceive the hydra to be an 
aggregation of amoebas in the form of a two-layered 
sack ;_, for each cell in the hydra is like an amoeba, 
— being a bit of nucleated protoplasm, — and nour- 
ishes itself and multiplies itself in just the same 
way. Only the cells are associated so that, as a 
whole, they form an animal body, and, acting in 
correlation, produce movements, etc., which, as 
belonging to the cells in toto, we regard as the life- 
phenomena of the individual animal. Now this is 
the conception we should have of any animal body, 
no matter how high in organization it may be. Its 
ultimate structural and functional units are amceba- 
like cells; these are disposed in groups possessing 
some distinctive active power dependent on the 
correlated action of the constituent cells ; these 
groups, or tissues, are organized into a body, exhib- 
iting in their united action phenomena referred to 
the animal as an individual being. 
We may now pass to a study of a representative 
of the third division of the animal kingdom, Ver- 
mes, taking for our purpose the common earth- 
worm, more familiarly known as the "fish-worm," 
and scientifically as Lumhricus agricola. The gen- 
eral features of the body, looked at from the outside, 
that require notice are : i, the elongated cylindrical 
form ; 2, the bilateral symmetry, or two-sidedness 
of the body as a whole; 3, its segmented, or ringed 
structure; 4, the presence of a head-end and a tail- 
end (though poorly differentiated) ; and 5, a dorsal 
(back) and ventral (belly) aspect to the body. 
Let it now be asked. What is the significance of 
these several bodily features of the earthworm } 
Are we able to give any explanation of them — that 
is to say, to show that they were produced by natu- 
ral causes.' As regards i, it is obvious at once that 
the form of the body is in adaptation to its manner 
of life — its habit of dwelling in burrows in the 
ground. And anyone who stops to think of the 
matter will see clearly that an adaptation to physi- 
cal surroundings, or environment, is evinced in the 
case of every species of animals. Without under- 
taking the discussion of one of the deepest questions 
of the philosophy of biology, it need only be said 
tliat it is the general opinion that adaptation has 
come about in a natural way, according to physical 
and biological laws more or less known to us. We 
shall not err if we think of the body of an animal 
as somewhat plastic, — capable of being modified by 
physical and other conditions,— and so gradually 
acquiring fitness, or adaptation, to its surroundings. 
If we admit this principle, then it is clear that the 
explanation of 2 is simply in the fact that the right 
and left sides of the body are exposed to the same 
physical conditions ; and in regard to 5, that the 
upper and lower surfaces have different physical 
contacts. 
Concerning 3, it is evident that it is a feature of a 
different nature, and does not admit of a like expla- 
nation. In regard to the ringed structure of the 
earthworm, it is to be observed — as can be shown bv 
dissection — that it relates to the internal structure of 
the body as well as the external. The constrictions 
seen in the skin on the outside are continuous with 
membranous partitions within, separating the cav- 
ity of the body into as many chambers. Moreover, 
it must be considered that in this structural feature 
the earthworm agrees with the members of the 
worm group generally, as also with other classes of 
animals — as centipedes, insects in the larval stage, 
etc. Segmentation of the body in the earthworm is 
thus not a feature peculiar — or in any sense acci- 
dental — to it, but decidedly of a generic nature. 
The explanation, therefore, is to be sought among 
the fundamental principles of morphology, or form, 
in organic nature. And the suggestion offered is 
that it is an instance of that principle of repetition 
of like parts, running through the whole range of 
plant life, and appearing in many groups of ani- 
mals. Now, among plants, part is added to part by 
process of budding; the stem buds forth branches, 
the branch twigs, and the twig leaves. Multiplica- 
tion of parts by budding is also characteristic of 
many of the lower orders of animals — as corals, 
hydroids, etc. The conclusion pointed to is that 
the rings of the earthworm represent repetition of 
like parts produced by budding. 
We have yet to consider 4; but it can only be said 
that the slight differentiation into head-end and tail- 
end seen in the earthworm is, possibly, to be as- 
cribed to the former being used more than the 
latter, occasioning a development of sensitiveness 
in the skin. Of course this does not explain why 
the anterior end hegan, to be used more than the 
posterior. We may note further, in this connection, 
that the two ends of the body are not greatly differ- 
ent in structure, and that the worm crawls about 
equally well with either end forward. But experi- 
ments show that the anterior end is more sensitive 
to touch than the posterior, and, what is much 
more significant, that it is sensiti e to light impres- 
sions. Moreover, in internal struccure the head-end 
is distinctly different from the tail-end. 
On tlie dorsal aspect of the body a dark line may 
be seen through the skin. This is the intestine, a 
part of the alimentary tube which extends through 
the body, beginning with the mouth in the first 
segment, and ending with an anal opening in the 
last. If the body of the worm be cut across, and 
the section examined, it will be seen that the ali- 
mentary tube lies within the tube formed bv the 
walls of the body, the space between being the 
body-cavity. Thus in the earthworm the alimen- 
tary, or digestive, cavity is entirely separate from the 
general cavity of the body. It will be remembered 
that in the hydra these two are united — that there is 
but one cavity, communicating with the outer world 
by the mouth alone. We see, then, the great ad- 
vance in structure of the earthworm over the hydra. 
The complete separation of the digestive tract from 
the general body-cavity is preserved in all animals, 
from the worms to mammals. 
A faint red line may also be seen through the 
skin on the dorsal side of the body. This is a 
blood-vessel, and in a large worm it m.ay readily be 
seen to pulsate. What occurs is simply the alter- 
nate expansion and contraction of the vessel, by 
which the blood is drawn in from behind and pro- 
pelled forwards. This contractile portion of the 
blood-vessel is thus analogous to the heart of the 
higher animals. 
The earthworm has a well-developed nervous s3-,s- 
tem. It consists of a double chain of ganglia lying 
on the ventral side of the body, except the most ■ 
anterior ganglion, wiiich is on the dorsal side, in 
