f ibriirD of tin Ituseum

OF

COMPARATIVE ZOOLOGY,

AT HARVARD COUECE, OAJIBRIJCE, MASS.

The gift of GU

JOURNAL

OF THE

ELISHA MITCHELL SCIENTIFIC SOCIETY,

VOLUME IX— PART FIRST.

JANUARY— JUNE:.

1892.

post-office:
CHAPEL HILL, N. C.

E. M. UZZEI.L, STEAM PRINTER AND BINDER,

RALEIGH, N. C.

1892.

OFFICERS.

1893.

PRESIDENT:

Joseph A. Hoi.mes, ...--- Chapel Hill, N. C.

FIRST VICE-PRESIDENT:
W. L- POTEAT, ------- Wake Forest, N. C.

SECOND VICE-PRESIDENT:

W. A. WITHERS, ------- Raleigh, N. C.

THIRD VICE-PRESIDENT:

J. W. Gore, -------- Chapel Hill, N. C.

SECRETARY AND TREASURER:

F. P. VENABI.E, ------- Chapel Hill, N. C.

LIBRARY AND PI.ACE OF MEETING:

CHAPEL HILL, N. C.

TABLE OF CONTEXTS.

PAGE.

Ou the Fuudamental Principles of the Differential Calculus.

\Vm. Cain 5

Remarks on the General Morphology of Sponges. H. V. Wilson 31

Record of Meetings -. 49

JOURNAL

Elisha Mitchell Scientific Society,

ON THE FUNDAMENTAL PRINCIPIvES OF THE
DIFFERENTIAL CALCULUS.

BY WILLIAM CAIN, C. E., Mem. Am. Soc. C. E.

There are probably no students of the infinitesimal cal-
culus, who have seen its varied applications, that are not
impressed with its immense scope and power, "constitut-
ing, as it undoubtedly does," says Comte, "the most loftv
thought to which the human mind has as yet attained."

It was not to be expected that a science of reasoning,
involving so many new and delicate relations between
infinitely small quantities, should appear perfect, in its
logical development, from the beginning, even with such
men as Newton and Leibnitz as its creators. For a longr
time mathematicians were more concerned in extendi nor
the usefulness of the transcendental analysis than in "rig-
orously establishing the logical bases of its operations,"
though it has given rise at all times to a great deal of con-
troversy, which has been of. great aid to those geometers
who concerned themselves particularly with establishing it
upon a logical basis. Of this number none are more
prominent than the French author, Duhamel. He pro-
ceeded by a rigorous use of "the method of limits," whose
thorough comprehension he regarded as so important that

6 JOURNAL OF THE

he devoted the first half of his Differential Calculus to its
numerous applications.

In the United States, after the appearance of Bledsoe's
"Philosophy of Mathematics" in 1867, calling especial
attention to Duhamel's elegant treatment and contrasting
it with the false logic of various other schools, there have
appeared a few good elementary books, nearly free from
errors, though sometimes showing a trace of them; thus
illustrating the tenacious grip of errors induced by early
vicious training. With these fairly good books have ap-
peared some as bad as have ever been written, from a log-
ical stand-point, as well as others, where ingenious soph-
istry has done its utmost to try and blind the student (and
possibly the author) to the false logic involved. The
English as a rule have followed in the lead of Newton,
perpetuating his error that a variable can reach its limit,
and they have occasionally introduced a number of errors
from the Leibnitz school, whose teachings still pervade most
of Germany, the place of its birth.

If the above is true as to the persistent perpetuation of
false logic in the treatment of the first principles of the
calculus, it would seem that no apology was needed for a
critical review of those first principles, particularly as no
matter what school is followed in learning the calculus the
scientific student will be sure to come across the teachings
of various schools in the applications and thus should be
prepared to take them at their true worth and modify them
in statement or otherwise when necessary.

Although a good deal of old ground is gone over, it was
essential to do so to bring out the points criticized in strong
relief The grouping of subjects is intended to be such as
to enable the beginner in the calculus to see at once its
truth and to catch on to its true spirit. The methods of
Newton and of Leibnitz, with criticism, is given in fine
print to avoid confusion, and can be omitted the first read-
ing, without detriment to the rest, if preferred.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 7

Definition of the Limit of a J ^ariable. When a variable
magnitude takes successively, values which approach more
and more that of a constant magnitude, so that the differ-
ence with this last can become and remain less than any
designated fixed magnitude of the same species, however
small, whether the variable is always above or always below
or sometimes above and sometimes below the constant, we
say that the first approaches indefinitely the second and that
the constant magnitude is the limit of the variable mag-
nitude.

More briefly, this is often stated thus: The limit of a
variable is the constant, which it indefinitely approaches
but never reaches.

Definition of an Infinitesimal. An infinitely small quan-
tity or an infinitesimal, is a finite quantity whose limit is
zero. Hence the infinitesimal approaches zero indefinitely,
but can never attain it, since zero is its "limit." As an
illustration, take two straight lines incommensurable to
each other. Mark the ends of the first line A\ B\ the
ends of the second A, B. Now as we can always find a
unit of measure that will go into A^B^ an integral num-
ber of times, apply such a unit to AB from A to C, as
many times as possible, leaving a remainder over CB less
than one of the parts. Then the ratio,

AC

A^B^

is less than the ratio of the two lines, but approaches it
indefinitely as the unit of measure decreases indefinitely,
since CB being always less than the unit, tends towards
zero but can never reach zero; hence CB is an infinitesimal
and AC approaches AB indefinitely without ever being
able to reach it. By the definition therefore, the limit of
CB is zero and the limit, of AC is AB, hence the limit
of the ratio above,

JOURNAL OF THE

AC AB

[im.

A^B^ A^B^
is what is called the incommensurable ratio, AB : A^ B^
It is assumed, of course, that the successive units of meas-
ure all exactly divide A* B\ It may happen that one of
these units applied to AB will cause the point C to lie very
near the point B, but for a smaller unit the distance CB
will be greater than before, so that the variable CB is
sometimes decreasing and then again increasing, but as it
is always less than one of the parts into which A^ B' has
been divided, it can "become and remain" less than one
of the parts or less than any finite number that may be
assigned, however small; hence zero is its limit by the
definition.

If in the ratio above we take A^ B^ as i (one foot say), we
have, limit i\C = AB from the last equation. AB and
AC can thus be regarded as incommensurable and com-
mensurable numbers respectively, and we see from the
above that an incommensurable number, as AB, is the
limit of a commensurable number as the number of parts
into which unity is divided is indefinitely increased.

The student of algebra and geometry is familiar with
many applications of the theory of limits, such ^s: limit
of (i -f- yz -f y -f i^ 4- ...)--= 2, as the number of
terms of the series is increased indefinitely; the circle is
the limit of a regular inscribed or circumscribed polygon,
as the number of sides is indefinitely increased, etc., etc.;
so that no more illustrations need be given if these are care-
fully studied in connection with the first definition given
above to show that it is complete and meets fully every
case that arises.

It may be observed, too, that although we can express
the length of a straight line or the perimeter of a polygon,
in terms of the length of a straight line, taken as a unit

ELISHA MITCHELL SCIENTIFIC SOCIETY. 9

of measure, we are confronted with the difficulty, in the
case of any curve line, that we cannot apply the unit of
measure, or any fractional part thereof, to the curve. We
can apply it, however, to the inscribed or circumscribed
polygon, and by taking the limit to which these polygons
approach indefinitely as the number of sides is increased
indefinitely, we get what is called the length of the curve.
Similarly no meaning can be attached to the expressions,
area of a curve or area of a curved surface, unless we define
them as the limit of the area of the inscribed or circum-
scribed polygon in the first case, or as the limit of the area
of the surface of the inscribed or circumscribed polyedrons
in the second case, the number of sides or faces, as the case
may be, increasing indefinitely. In the case of volumes,
too, neither the unit of measure nor any fraction of it can
be directly applied when the bounding surfaces are curved,
so that a volume must be defined as the limit of the varia-
ble volume of some inscribed or circumscribed polvedron
as the number of faces is indefinitely increased. The dif-
ficulty of measuring curved surfaces, volumes, etc., occurs
to every reflecting student, and it is strange that none of
our geometries give an\' definitions but only methods of
finding lengths, areas and volumes of curved lines, surfaces
and volumes, assuming that the student will find out in
some way what is meant by such terms.

The "Theory of Limits" will not be entered into here
as it is sufficiently exposed in many text-books. Some
strange definitions of infinity, though, appear in some
excellent books. The following is a sample: "When a
variable is conceived to have a value greater than any
assigned value, however great this assigned value may be,
the variable is said to become infinite ; such a variable is
called an infinite mtniber.'' As an "assigned value"
means some finite value, it follows from this definition that
an infinite number is only some number greater than some

lO JOURNAL OF THE

finite number, however large; in other words, an infinite
number is a finite number! If such quantities have to be
considered they should be given a different name and sym-
bol to avoid confusing these with absolute infinity. The
letter G is suggested to distinguish such finite quantities
from absolute infinity oo. We get our ideas of infinity
from space and time, for finite as are our capacities, we
cannot conceive of space or time ever ending; hence we
speak of infinite space and infinite time. However far, in
imagination, one may travel in a straight line in space, it
is impossible to conceive of ever arriving at any point
where there is not infinite space beyond. The considera-
tion of a row of figures, loooo . . . , extended without
limit, gives one an idea of an itrfinite number.
Consider the quotient,

a

= .ooooi<ir,

looooo-
where a is finite.

The number of noughts in the right member is one less
than the number of noughts in the denominator, and suc-
cessive divisions by ten show that the same law holds, no
matter how great the denominator.

If we conceive the number of noughts in the denominator
to be increased to several billion, the quotient is extremely
small, as in the right member we have the same number
of noughts less one before reaching the i ; thus as the
denominator increases indefinitely the value of the fraction
approaches zero indefinitely, and this is all that is meant

a
bv the abbreviated notation, — = o.

CO

a
Similarly it may be shown, if — = y and .r decreases

ELISHA MITCHELL SCIENTIFIC SOCIETY. II

indefinitely, that y increases indefinitely, and this is the

a
meaning of the notation — =00, which has no sense by

o
itself. Although the limit of x above is zero, the limit
of y is not infinity, since \{ y had a limit it could be made
to differ from it by as small a quantity as we wish, whereas
any finite quantity {y) will always differ from infinity by
infinity.

Thus the principle of limits, "if two variables are equal
and each approaches a limit^ their limits are equal," does
not apply, as both variables do not approach limits.

Therefore the singular forms mentioned must always be
regarded as abbreviations, having the meaning attributed
to them above and not as meaning anything in themselves.
We have an illustration of such forms in trigonometry.
Thus,

sin X

tan .r=

cos X

As X approaches 90°, sin x approaches i, cos .r, 6>, and
the left member, though always finite, increases indefi-
nitely. The latter is said to be infinite for x = 90°,
though strictly, according to the usual definition, there is
no tangent of 90°, as the moving radius produced, being
parallel to the tangent, can never intersect it. As parallel
lines are everywhere the same distance apart, they cannot
meet, however far produced, so that the statement that two
parallel lines meet at infinity is essentially false.

Similarly we can reason for all the functions that increase
indefinitely, without ever ceasing to be finite, where the
angle approaches some limit, or fixed value it can never
attain, with any meaning corresponding to the functions.
The above is still more evident when we regard the ratio
definitions first given in trigonometry, for then, there can
be no function without a right triangle can be formed and

12

JOURNAL OF THE

there is no triangle when one acute angle is either o or
90°; therefore we can only say that sin x approaches o as
its "limit" as x indefinitely diminishes, and tan x in-
creases indefinitely as x approaches 90°.

With this meaning to be given such expressions as
sin 0 = 0, tan 90 = cc , they can be safely used (and will
be used in what follows), though there is really no sine cor-
responding to 0° and no tangent for 90°.

The next subject treated will be the general one of find-
ing the limit of the ratio of two related infinitesimals,
which is the principal problem of the differential calculus.

As a special example, consider
the circular arc ABC, fig. i, of ra-
dius unity, whose length in circular
measure is 2x. Divide it into two
equal parts, x = AB = AC and
draw tangents AD and CD, inter-
secting on radius OB produced.
Call the c/wrd AB = c/iord BC = c.
Then since the radius is taken as
unity, EA = sin x and AD =r tan x.
Now by geometry we have,

AC < 2c < 2x < AD + DC;
whence, dividing by 2, we have,

sin X < r <• X < tan x.
Also since,

;=v

7./

sin X

sin X

= cos X

[im

= I

I, as

tan X tan .i*

as X indefinitely diminishes, since then, lim. cos x
cos X indefinitely approaches unity without ever attain-
ing it.

Now since c and x are always intermediate in value be-
tween sin X and tan .r, it follows that the ratio of either to
the other, or to sm x or tan .r, approaches indefinitely unity
as a limit.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 1 3

sin X sin x sin x

. • . lim. = lim. = lim. = i,

c X tan X

c c ^ X

lim. — = lim. ^ lim. ^ i ;

X tan X tan x

and it is the same for the reciprocals of the above ratios.

o
Any one of the above ratios approaches the form - indefi-

o
nitely, bnt can never attain it, as the functions cease to
exist when x = o and the ratio ceases to exist; but the con-
stant value which the ratio approaches indefinitely but
never attains {i. e.^ the limit) is at once found to be unity.
A function of x is some expression that contains x and
is designated by some letter as /J F, ... , with x in paren-
theses following. Thus /"(x), F(.r), . . . are read little f
function of x^ large F function of .f, etc. If in any func-
tion, f(x) of X, the variable x is changed throughout to
[x + h) so that the same operations are indicated for (x -f h)
as in the original function were indicated for .r, the result
is written y(.r -f h).
Thus if,

f{x) = X- cos I — I + log X,

f(x + Ji) = {x + h) ' cos I ll- log {x 4- //).

The increase in x (^= //), is called the increment of x and
is generally written in the calculus ax, so that h = ^x.
The symbol a (delta) indicates a difference, ax signifying
the difference between two states of x and the symbol ax is
regarded as an indivisible one and not composed of two
factors A and x that can ever be dissociated. Similarlv
for AjK, A^, etc., when the letters j, 5-, etc., occur in any
2

14 JOURNAL OF THE

expression. If y =/{x) and we arbitrarily change x to
(x + //) = {x -\- A-r), then y will take a new value, desig-
nated by y + A7, where aj is the increase in y due to the
increase in x.

Thus, {fy=/{x\ (i),

;/ + Aj =/{x + /i) =/{x + A:r) (2),

.V is here called the independent variable and y the de-
pendent one, since the value of y depends on that of .i-, which
we shall suppose to increase at will or independently of any
other variable in the formula.

It is important to note here that although x is generally
increased so that ax is plus, yet the new value ofy ( = j -[- Ay)
niav be either greater or less than before. In the last case
Ay will be minus. Hence, if in any case. Ay is found ulti-
mately to be minus, we shall know how to interpret the
result.

In equations (i) and (2), let x be first supposed to have a
fixed constant value, then j/ will have a corresponding con-
stant value. Subtracting (i) from (2) and dividing by a.t,
Ay /{x + ax) -/(..)
- = (3).

A V AX

We shall presently show that this expression generally
has a limit as ax approaches zero. From (2) above. Ay ap-
proaches zero indefinitely at the same time that ax does, so

o Ay

that (3) approaches indefinitely the form -, but the raho —

O AX

can never reach this form, for where Ay and ax are both
zero there is no ratio. We can however find the limif^ or

Ay /(.r-f A.r)— /(.T)
the constant value to which the ratio — =

AX Jx

tends indefinitely zvithont ever being able to reach as a
ratio^ and this limit is known as the derivative^ derived
function or differential co-efficient of the function f(x) zvith

ELISHA MITCHELL SCIENTIFIC SOCIETY. 1 5

respect to x as the independent variable. We have hitherto
supposed X to have a constant vahie, but the above method
of finding the derivative is the same whatever value of .r,
o-ivino- real values to r in o, we start from; hence the
method is perfectly general.
As an illustration let,

y=f{x)= X^ + b.

If X is changed to (.r ^ h) = {x — A.r), y will be changed
to J 4- A_>'.

. • . 7 + a;' = /(.r -^ /i) = ix -f /if -r /i.
Expanding the right member of the last equation and sub-
tracting the preceding equation from it, we have,
A>' = ^x-/i — 7,x/r -j- k^.
Dividing by /i = ax, we have,

AJ'

— = 3't" + iS'^' + ^-'^) ^-^' (4)-

A.l'

The limit to which the right member approaches indefi-
nitely is 3-1", since as a.i' diminishes indefinitely, so does
the term (3^ -f ax) ax in which A.r is a factor. Therefore
the derivative of /(.f) = x^ — ^ with respect to x is,

Aj' /(x -f A.r) — /(:t-)

lim. — = lim. = ^x^.

A.r A-i"

This limit (3.1'-) is true, no matter what value of x we
start from, and its numerical value depends upon the value
of X. It is seen to be perfectly definite and finite and to
varv from zero to plus infinity according as x changes from
zero to infinity. For a given value of x as 2, the limit
has only one value = 12. Similarly for any other value.
It is only in the case of the simpler functions that/'(.f — /i)
can be developed readily, so that the derivatives can be
easily found, but after rti/es for finding the derived func-
tions of products, powers, etc., have been deduced (as given
in elementarv treatises on the calculus) the work of finding

l6 JOURNAL OF THE

thehi by these rules is comparatively simple, however com-
plicated the functions.

A3' f{x + h) —f{x)
As lim. — , lim. , are cumbersome sym-

A.r Ji

bols it is usual to put — for them.
d.v

dy Av /(.r + //) -f{x)

. • . — = lim. — = lim. .

dx ^x h

In this expression dy is read differential of y and dx dif-
ferential of a;, and both dy and dx are to be regarded as
indivisible symbols, so that d \^ not a factor but a symbol
of operation. The differentials dy and dx are regarded as
finite quantities, whose ratio, for any value of .t, is exactly

AJ/

equal to lim. — .
c^x

Thus even for the same value of this limit, dy and dx
can be supposed to both increase or both decrease at pleas-
ure, the only restriction being that their ratio shall always
equal the value of the limit for the particular value of x
considered. There is thus great flexibility in this concep-
tion of differentials. As a rule we shall consider the dif-
ferentials as having appreciable values; in other cases it is
convenient to treat them as infinitesimals ox finite quanti-
ties whose limits are zero^ but which consequently never

dy
become zero themselves, as then the ratio — has no sig-

dx

nificance. In the same way aa' and aj are infinitesimals.
In the equation, derived from one above,
^ dy Ay

— = lim. — = 3-^^,

dx A.U

it is understood that we can clear the equation of fractions
and write.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 1 7

dy = I lim. — Idv = ^x^dx.

From this equation we see why 3.T- (in the particular

\v
example) or lim. — generally, is called a differential co-efl5-

cient.

On referring to the right member of eq. (4), w^e see that
regarded by itself^ it has no limit, since it is an essential
requisite that a variable can never reach its limit, whereas
by making A.r ^ o, the right member becomes at once yx?^
but considered in connection zcit/i the left member^ we see
that although A.r must tend towards zero indefinitely, yet
it can never be supposed zero, for then the ratio ^y -^ ^x
has no meaning. With this restriction, then, the right
member can approach 3.??- as near as we please without ever
being able to reach it; hence 3.^- is the true "limit" of
the right member when b.x is regarded as an infinitesimal
whose limit is zero.

It is evidently immaterial by what law, if any, c^x di-
minishes towards zero. We can, if we choose, suppose ^x
to diminish by taking the half of it, then the half of this
result, and so on, in which case A.r will tend indefinitely
towards zero, but can never attain it; or we can suppose
A.i' to diminish, in any arbitrary w^ay, indefinitely towards
zero without ever becoming zero. In any case the right
member as well as the left has a true limit according to the
strict definition.

It is to be observed, too, that this limit is found on the
one supposition that a.c tends towards zero, for then aji', as
a consequence, tends towards zero indefinitely without ever
beine able to reach it.

■C5

We have emphasized this point, because some of the best known Eng.
lish writers, as Todhemter, Williamson and Edwards, following the lead of

i8

JOURNAL OF THE

the great Newton, have assumed that a variable can reach its limit, so
that (4) above should "ultimately become" t,-'^-.

That Newton failed to establish a true theory of limits is shown in
Bledsoe's Philosophy of Mathematics. As it was, he made a great advance
over previous methods; but now that a correct theory of limits is so uni-
versally known, there can be no excuse for later writers in perpetuating
the same errors that seemed inevitable in ihe dawn of the infinitesimal
method. The French writers (following the lead of Duhamel), and also
some American writers, have been more logical in their development of
the infinitesimal calculus.

The problem of tangents is one which gave rise to the
differential calcnhis and needs to be carefully considered.

In fig. 2, let y z= /(x) be the equation of the curve DPS
referred to the rectangular axes x and y. Suppose we wish
to find the tangent of the angle PEX made by a tangent at
a point P of the curve with the X axis or l/ie slope of the
curve at P wdiose co-ordinates are x and y. The co-ordi-
nates of a point S to the right of P are y + aj^, x + ^x so
that, PQ = A,r, SQ = a>' and,

AJ

— = tan SPR.
A a;

This equation gives
the slope of the secant
PS which varies with
the values of A.^■ and
Aj'. If PS regarded
as a line simply, but
not a secant, is re-
volved around P, in
one position only, it
coincides with the tangent, where it touches the curve in
but one point. If it is revolved further, it cuts the curve
on the other side of P whether the curve in the vicinity of
P is convex to the X axis as drawn or concave. If the
curve is convex on one side of P and concave on the other,
the line PS will cut the curve in three points when it lies

ELISHA MITCHELL SCIENTIFIC SOCIETY. 1 9

on one side of the tangent, and in one point when it lies
on the other side of the tangent. When it coincides with
the tangent it cuts the curve in but one point.

But in all cases, it must be carefully noted, that the
secant PS as it revolves about P can approach the tangent
PT as near as we choose, but can never reach it; for then
it would cease to be a secant; hence the tangent is the lim-
iting position of the secant. Therefore as A.r (and conse-
quently Aj') diminish towards zero indefinitely, the point S
will approach the point P indefinitely and angle SPR ap-
proaches indefinitely angle TPR as its limit; whence tan
SPR approaches indefinitely tan TPR as its limit.

Therefore, taking the limit of the equation above,
Aj' dy
lim. — = — = tan TPR .... (5).
AX' dx

Hence if y ^ f {x) is the equation of the curve ^ tJie de-
rivative of f{x) with respect to x is alzvays equal to the slope
of the curve at the point (.i-, jk) considered. Thus the tan-
gent of the angle made by the tangent line of the cubic
parabola y =r .r"^ ^ b, already considered, with the axis of
.r, equals 3.1-." at the point whose abscission is x.

This value was determined above and its meaning is that
for X equal to o, ^, ^,1, etc., the slope of the curve is o,
Vi-t H^ 3' ^^^-j ^"^ ^^ increases indefinitely as .i' increases
indefinitely.

lu Edwards' DiflFerential Calculus (second edition, 1892, page 20) we
read, changing the letters to suit fig. 2, to which the theory applies:
"When S travelling along the curve, approaches indefinitely near to P,
the chord PS becomes in the limit the tangent at P." In ex. 2, page 21,
the author, in getting the final equation, again says: "When S comes to
coincide with P," etc. It is plain from these references that this most
recent English author considers a variable to actually reach its limit— a
fundamental error we have exposed above. The chord cannot reach the

tangent without ceasing to be a chord, neither can the ratio 1= slope

\x

o
of chord) reach its limit — without the ratio ceasing to exist.

o

20 JOURNAL OF THE

Let US take as another illustration the common parabola
y' = 2px.
When X increases to x + lx^ y changes to y -f- i^y

. • . yP- -f- 2y ^y + {^yf = 2/ {x + ax).
Subtracting the first equation from the second
2y Ay + {^yf = 2p A.r
a;/ 2p

A.l' 2y + A_y
As AT approaches zero, ajk tends in the same time towards
zero, a limit which neither can attain however. The right

2p
member similarly approaches indefinitely the constant —

2y
without ever being able to attain it, which is therefore its
limit by the definition. Hence slope of tangent at point

(.r, ;/) is,

A>' dy p ^ p

lini. — = — =z-z= — -yA — •
Ao; dx y ^ 2x

From this equation we see that the slope of the tangent
varies from plus or minus infinity for .t = o to plus or
minus zero for .r =: go.

^y o dy
As, lim. — r^ - ^ — ,
A.r o dx
the dy and dx would appear to replace the zeros in the

o
singular form -, which gave rise to Bishop Berkeley's wit-

o
ticism that the dy and dx were "the ghosts of the departed
quantities a^ and A.r." As we have defined them above,
dy and dx are finite quantities, of the same nature as y and
x, whose ratio is always equal to the derivative, this ratio
being variable when the derivative is variable. As y ^=/{x)
can always be represented by a locus (since for assumed
values of .r we can compute and lay off the corresponding

ELISHA MITCHELL SCIENTIFIC SOCIETY. 21

values of y) and since dy -=- dc represents the slope of the
locus at the point {:i\ j), we can represent dy and dx by the
length of certain lines. Thus in fig. 2, from the point of
tangency P, draw PR parallel to the axis of x a7iy distance
from P to R to represent dx and from the point R draw RT
parallel to the axis of y to intersection T with the tangent,
when RT will represent dy ; for then

dv Ar

— = tan TPR = lim. — ,
dx AX

as should be the case.

If we choose to make dx = a r = PQ, then dy = QI, which
is less than aj' when S is above I, for a convex curve to X,
and greater than av when j is below, or for a curve concave
to X, just to the right of P. It is only in the case where
y =/(x) is the equation of a straight line that for dx = ax
we have dy = Ay, for here Ay -^ ax represents the slope of
the line.

Other important formulas can be deduced from fig. 2.

If we call the length of the curve from some point D to
P, J, then the increment of the arc PS corresponding to
the simultaneous increment ax of x will be called as. Call
the length of the chord PS = <r.

Then we have,

PQ AX

c

AS

AS

QS Ay

c

AS

AS

COS SPQ,

sin SPQ.

c
Now we have seen before that lim. — = i, so that the

AS
3

A5

^.r

ini. — := COS TPQ

A5

dx
ds

a;/
im. — = sin TPQ
A>y

dy

ds

22 JOURNAL OF THE

A.i" \y
middle terms above approach — , — indefinitely and the

A5 A^

right members approach, as their limits, cos IPQ, sin IPQ
respectively, as A.r and consequently aj^ and a.^ approach
zero indefinitely without ever reaching it. Hence taking

A.t' dx A J dy

limits and designating lim. — by — and lim. — by — we

b.s ds
have,

^x dx

(6)

• • (7).

These equations are satisfied by representing ds by the
hypotenuse of the right triangle of which dx and dy are
the other two sides. Thus if PQ = dx and QI = dy^ then
PI = ds; but if PR = dx and RT = dy, then PT = ds.

In any case, we have the fundamental relation,
ds'' = dx'' ^ dy' (8).

It is usual to represent the derivative of y^(^') with re-
spect to X hy f^ {x).

/^y dy

.-. lim. — =/i(.r) = — .
AX dx

If we call 7e^ an infinitesimal that tends towards zero in
the same time as a.t, we can write,

-=/'(.r) + w (9),

AX

for taking the limits of both sides, we reach the preceding
equation. The variable w is indeterminate and may be
plus or minus. Clearing of fractions, we have,

Ay =/^ (x) AX -\- Zt< AX . . . . (lo).

In fig. 2, since /^ {x) ax = ax tan IPQ — IQ, we see
that the term w Jx must represent IS.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 23

Comparing the last equation with
dy =f^ (.r) dx,
obtained from an equation above, we see that when dx = A.r,
dy == Ai' — Zi'dx.
Thus we have proved analytically, when dx = A.r that
dy is never equal to aj (except when f{x) represents a
straight line) and the difference is exactly represented on
the figure by the distance IS.

Mauy of the older writers, following the lead of Leibnitz, assumed that
dy and aJ'. as well as ds and {^s, were identical when dx = A-f, and the
error is perpetuated to this day by possibly the majorit}' of the most recent
writers; thus Williamson, in his Differential Calculus (6th Ed., 1887), page
3, says, "When the increment or difference is supposed infinitely small
it is called 2i differential.''' Similarly in a recent American treatise on
the calculus by Bowser, the same definition is given.

Professor Bowser defines " consecutive values of a function or variable
as values which differ from each other by less than any assignable quan-
tity."' He then adds. "A differential has been defined as an infinitely
small increment or an infinitesimal; it may also be defined as the differ-
ence between two consecutive values of a variable or function."

As there are an infinite number of values lying between o and "any
assignable quantity," however small, it follows that such differentials are
simply quite small finite quantities.

The differentiation of a function, as y = ax- -\- b, would then pro-
ceed after the method of Leibnitz, as follows :

y := ax'^ + b.

Give to .r and y the simultaneous infinitesimal increments dx and dy,
y -^ dy = a (x -\- dx)^ -\- b.
Subtracting the first equation from the last, we have,
dy =a (2 xdx -f- dx'^).

Now from the nature of infinitesimals, it is regarded by the followers of
Leibnitz as evident that dx^ can be neglected in comparison with 2 xdx,
because the square of the infinitesimal dx is infinitely small in compari-
son with the variable itself, whence,

dy ^ 2 ax dx.

It is scarce!}' necessary to remark to the reader that, for an exact result,
we cannot make dx = o in part of an equation without making it zero
throughout; so that the equation is fundamentally wrong.

When we go to the applications to curves, however, another error is
made, of an opposite character to the first, so that by this secret compen-
sation of errors the result is finally correct. Thus a curve is regarded as
a polygon whose sides connect "consecutive points " and a tangent line

24 JOURNAL OF THE

at any point is the chord produced through this point and its " consecutive
point," so that dy -^- dx gives the slope of the tangent at the point. This
is of course wrong, but it exactly balances the other error above, for from
the last equation we find the slope, so determined for the curve j = ax"^ -\- b,
to be (2 rt-.i"), which we know to be correct by the strict method of limits.

The great French author, Lagrange, says in this connection, "In regard-
ing a curve as a polygon of an infinite number of sides, each infinitely
small, and of which the prolongation is the tangent of the curve, it is
clear that we make an erroneous supposition; but this error finds itself
corrected in the calculus by the omission which is made of infinitely small
quantities. This can be easily shown in examples, but it would be, per-
haps, difficult to give a general demonstration of it."

Bishop Berkele}-, long before Lagrange, showed this secret compensa-
tion of errors in a particular example, his endeavor being particularly to
''show hoiu error may bring forth truth, though it ca7tnot bring forth
scietice. ' '

Leibnitz, in attempting a defense of his theor}-, stated that "he treated
infinitely small quantities as i^icojnparables, and that he neglected them
in comparison with finite quantities 'like grains of sand in comparison
with the sea '; a v.ew which would have completeh- changed the nature of
his analysis by reducing it to a mere approximative calculus." See
Comte's Philosophy of Mathematics, Gillespie, p. 99.

The demonstration given above in the case ofy"(.r) = ax^ -{- b can be
made general, as follows :

From the exact equation (9) above, following the notation of Leibnitz
where dy and dx are taken as identical with AjF and A-^', we have exactly,

dy

- ==/! (.r) 4- zt>.
dx
The followers of Leibnitz, in differentiating, throw away the term w as
nothing and pretend to write exactly,

dy

- =f' i-r);
dx

but as they make another error by calling the ratio of the increments dy
and dx the slope of the curve, we thus find the latter to equal/ ^ (j), which

Ay
was assumed above to equal lim. — or the slope of the curve; so that the

AX
two errors, for au}- function, balance each other and w^e reach a correct
result.

As the truth of any result, as given by the Leibnitz method, can only
be tested, in a similar manner to the above, by comparing with a result
known to be correct by use of the method of limits, it would seem to be
inexcusable not to found the calculus upon this latter method. After-

ELISHA MITCHELL SCIENTIFIC SOCIETY. 25

wards a true "iufinitesimal method" can be easily logically deduced (as
Duhamel and others have shown) that wdll offer all the advantages and
abbreviated processes of the Leibnitz method, with none of its errors of
reasoning.

It is well to remark just here that because j' ^=/{x) can
always be represented by a locus, and since its derivative
with respect to x represents the slope of the tangent at the
point (a-, y\ it will generally be finite. It is only at the
points where the tangent is parallel or perpendicular to the
axis of X that the derivative is zero or infinity. Hence the
ratio of aj' to aa', whose limit is the slope, has generally a
finite limit.

We have studied now, with some thoroughness, the
theory of tangents and will next take up, a no less impor-
tant subject, the method of rates. When a variable changes
so that, in consecutive equal intervals of time, the incre-
ments are equal, the change is said to be uniform; other-
wise variable. For uniform change, the increment of the
function in the unit of time is called the rate. Thus in

space

the case of uniform motion, velocity = rate = .

time

For a variable change, the rate of the function at any
instant is what its increment would become in a unit of
time if at that instant the change became uniform.

In looking for an illustration to show clearly the spirit
and method of the calculus, perhaps none is more satisfac-
tory to the beginner than the consideration of falling bod-
ies in vacuo. If we call the space in feet, described by
the falling body in / seconds, s and ^ the acceleration due
to gravity, we have the relation between the space and
time, as given by numerous experiments, expressed in the
following equation,

s= Yi g i-\

26 JOURNAL OF THE

^ is a variable for different latitudes and is
slightly over 32. Take it 32 for brevity.
s = 16 t^ . . . . {11).
In the time / -j- a^ the space described would
be jr -|- ^s (see fig. 3), and by the same law,

V.

/is

'^^ (^ + A^) = 16 (/ + ^i)\

Subtracting the preceding equation and divid-
^'r ^ ing by A/,

A.9

— = 16 (2/ + A/*).
A^

This o-ives the average rate or velocity with which the
small space a^ is described.

As the rate or velocity is changing all the time, call
v^ and z'2 the least and greatest values of the velocity in de-
scribing the space a^-; then the spaces which would have
been described with uniform velocities z^,, v^ in time a/ are
z/, a/ and v^ a/, which are respectively less and greater than
the actual space /^s.

Hence z'„ — and c>^ are in ascending order of magnitude.

A/

As a/ (and a^ consequently) is diminished indefinitely, these
three quantities approach equality and the exact velocity
the body has at the beginning of the space as is given by
the constant to which they approach indefinitely but never

AS

attain. But lim. z\ = lini. v^ = limit — = velocity or

At

rate at the instant the space .? has been described (see Ed-
wards' Differential Calculus).

Hence in the particular example above, the velocity the
falling body has, at the end of / seconds, when it has de-
scribed the space s^ is,

ds AS

— = lim. — ^ 32/ (12);

dt At

ELISHA MITCHELL SCIENTIFIC SOCIETY. 27

i. e.^ the body at the end of i, 2, 3 . . , seconds is moving
with a rate of 32, 64, 96 . . , feet per second. The same
conclusion follows if we give a decrement to / in eq. (11).
Thus

[s — A-y) = l6{t — i^tf

. • . lim. — = lim. 16 (2/ — a/) ^ 32/.
a/
The average velocity in describing the space A^y just above
the point considered is 16 (2/ — a/), that below, as found
above, is 16 (2/ — a/); the true velocity lies between them
and is equal to the limit 16 (2^) of either.

The above general demonstration can be adapted to the
rate of increase of any function, n =/'(/'), which does not
change uniformly with the time, u representing a magni-
tude of any kind, as length, area, volume, etc. ; for if a//
is the actual change of the magnitude in time a/*, and
r, and r^ the least and greatest values of the rate of cJiange
of II in the interval a/, corresponding to the increments
r, a/, }\ c\t^ of the magnitude, if these rates were uniform
for the time a/, then r, a/, a// and i\ a/ are in the ascend-

^u
ing order of magnitude; also ;-,, — and i\ are in the same

a/
order. Hence, as these quantities approach equality in-
definitely as a/ tends towards zero, the limit of any one of
them is equal to the actual rate of increase of the magni-
tude u which is thus represented by lim. r„ = lim. }\^ or,

A?/ (ill
lim. — = — .
A/ dt
Thus the derivative of any function, which varies with
the time, with respect to /, gives the exact rate of increase
of the function at the instant considered.

If It and X are both functions of /, connected by the
relation ?/ ^ F (,r), then

28 JOURNAL OF THE

du

dii dt rate of change of //

dx dx rate of change of x

dt

As an illustration, find the rate at which the volume u
of a cube tends to increase in relation to the increase of an
edge X, due to a supposed continuous expansion from heat.

du
u = x^ .' . — ^ 3.i'l
dx
Therefore for x = i, 2, 3, the volume tends to increase
at a rate 3, 12, 27 times as fast as the edge increases.
Numerous examples could be given of the application of
the differential calculus to the ascertaining of relative rates,
but the above will suffice to illustrate the principle.

dii
It has been shown above that if // =zf[t)^ — represents

dl

the rate of change of ?/, if at any time /, the rate is sup-
posed to become uniform; hence die represents what the
increment of 2c would become in time di.

As time must vary uniformly, dt is always a constant^
though it is entirely arbitrary as to numerical value; hence
the differential of a variable can be defined^ as zvhat the
increment of the variable would become in any interval of
time if at the instant considered^ the change becomes uni-
form or the rate becomes constant. If 21 is a function of
several variables, then the differentials of each must be
simultaneous ones, corresponding to the same interval of
time.

Newton, in establishing his calculus of fluents and flux-
ions, conceived a curve to be traced by the motion of a
point, an area between the axis of .f, the curve and two
extreme ordinates, to be traced by the motion of a variable

ELISHA MITCHELL SCIENTIFIC SOCIETY. 29

ordinate to the curve and a solid to be generated by the
motion of an area.

As a point traces a curve DPS (fig. 2), when it reaches
the point P, it has the direction of the tangent PT at that
instant; for we can make only two suppositions: (i) the
direction coincides with that of some chord passing through
P, whether the otlier end of the chord precedes or follows
P, or (2) it coincides with the tangent; but it cannot have
the direction of a chord at the point P without leaving the
curve; hence this supposition is false, and as one must be
true, it follows that the direction of motion at P must coin-
cide with the tangent PT.

At the point P therefore, by the definition above of a
differential, the simultaneous differentials of .r, y and s are
what their increments would become, during any time, if
at P their rates of change should become constant. This
can happen only where the motion takes place uniformly
along a straight line and this line must be the tangent at
P, as that is the direction of motion at that point. The
differentials dx, dy and ds can thus be represented by PQ,
QI and PI respectively, or by PR, RT and PT, for a uni-
form increase along the tangent would correspond to a
uniform rate horizontally and vertically. This agrees with
what has hitherto been established.

The rates of increase, horizontally, vertically and along
dx dy ds

the tangent, are — , — and — respectively.
d/ dt dt

The differential of an area is found as follows: Let area
CDPA = 2/, then if A.r = dx ^= AB, du ^=ydx ; for although
A?/ = area APSB, the increase of area will not be uniform
if the upper end of the ordinate AP moves along the curve,
but it wnll be uniform if it moves uniformly along PQR;
for then equal rectangles, as APQB, will be sw^ept out by
the ordinate AP as it moves to the right, in equal times.
4

30 JOURNAL OF THE

Therefore by the definition of differential above, du ^area
APQB = ydx. This is readily proved by the method of
limits thus: Note that,

VAA- < A?^ < {y + A>') A-i-;
hence dividing- by J.r and observing that as J.i" diminishes

An
indefinitely, ( y -f aj') and hence — (which is still nearer/)

Ar
approach y indefinitely in value,
A// dii
. ' . lim. — = — = J/ . . . . (ii).
A.r dx

Similarly we can prove, by either method, that if V
represents the volume generated by CDPA revolving about
<?X, that ^V is represented by the volume generated by
APQB about OX . • . ^V = '/ dx.

Referring to eq. (ii) and fig. 2 it is seen that if for any curve u = area
CDPA can be expressed as a function of Ji% or m =y" (a-), then by the
usual notation,

Au

lim. =/i (x);

Al-
and this equals jj/ by (11).

On calling za an infinitesimal that tends towards zero in the same time
as AX, we can write,

Ati = (/' (.r) -f w) AX,
since on dividing by ax and taking the limit, we are conducted to the
preceding equation. But by the Leibnitz method the term [wax) is thrown
away, on differentiating tc =y (x), when ax and au are infinitely small,
so that Au =/'^j-Ar = ^ax.

Another error is made, however, by regarding the area au = APSB as
equal to APQB, which, combined with the preceding result, gives cor-
rectly, area APQB=jj/ax. As Leibnitz regarded du and dx, as identical
with AM and A'", when the latter were infinitely small, the}^ should replace
the latter in the above equations to express them b}' his notation.

Thus truth is again evolved from error, and it can be similarly shown
in other cases, though a general demonstration seems difficult, if not im-
possible.

The "Method of Indivisables " by which "lines were considered as
composed of points, surfaces as composed of lines and volumes as com-

ELISHA MITCHELL SCIENTIFIC SOCIETY. 3 1

posed of surfaces, has not beeu alluded to, as it is not now found in auy
text-books. It is an exploded theor\\ Cavalieri, the author, was led to
it by noticing, e. g., that in fig. 2, area APQB was never exactly equal to
area APSB; hence he made ax = 0 and regarded the area a^/ as a line
AP, so that tc = area CDPA was made up of an infinity of lines, etc.
This is analogous to the statement that a variable can reach its limit.

In conclusion, let us hope that soon, the false conceptions
concerning the fundamental principles of the calculus may
be eliminated from all text-books. The world is still
waiting for the treatise on the calculus that is simple and
clear and at the same time rio^orous in its lomc.

REMARKS ON THE GENERAL MORPHOLOGY OF
SPONGES.*

BY H. Y. WILSON.

I haYC shownt that in Esperella and Tedania the sub-
dermal caYities, canals and chambers develop as separate
lacunae in the parenchyma or mes-entoderm of the attached
sponge, subsequently becoming connected into a continu-
ous system. As regards the development of the canal sys-
tem such varying accounts are given by different authors
that were it not for the help lent by comparative anatomy
it would be quite impossible to form any idea of the fun-
damental morphology of sponges. Fortunately for the
student entering this puzzling domain comparative anatomy
has, in the hands of Haeckel, Schulze and Polejaeff, pro-
vided a stand-point from which the varying phenomena of

*These remarks were originallj' written as part of a paper on the embrj-olog-s- of
sponges, which it is expected will soon go to the press. It has not been fonnci possible
to insert in the present text the wood-cuts with which the intention was to illustrate
man J' of the facts referred to. The omission of the cuts, while it is to be regretted,
will not be found to interfere with the intelligibilitj- of the views expressed.

fXotes on the Development of Some Sponges. Journal of Morphology-, Xo). V, No. 3.

32 JOURNAL OF THE

development and structure may be viewed with at least a
partially understanding eye. It may be that an increas-
ing- accumulation of facts wnll show that Haeckel's con-
ception of the relation of the simple calcareous sponges
to the complex horny and silicious forms is not well
founded, and that Schulze's view of the parts played by
the embryonic layers in producing the adult anatomy is
not the true one. But at present it is only with the aid of
these theories that one can form any clear conception of
the sponges in general, and so provisionally at least we
are bound to accept them.

Comparative anatomy points in no undecided manner to
the phylogenetic path along which sponges have develop-
oped, and so permits us to construct a standard of ontogeny,
with which we may compare the actual development of
each species as we witness it to-day, and so be enabled to
note the amount and kind of divergence (coenogeny) ex-
hibited. That coenogeny is exhibited to a great degree in
the embryology of sponges is evident from the various
types of development described, and in the future much
may be hoped from the study of a group like this for the
understanding of the laws of development. For the pres-
ent all we can do is to accept wdiat seems the most probable
phylogeny, recording the instances of supposed coenogeny
as they are observed. Adopting this method, I have to
regard the development (?'. c.^ the later development or
metamorphosis) of Esperella and Tcdania as far removed
from the phylogenetic path. Before pointing out the fea-
tures in which the development of these sponges is so
strongly coenogenetic, it will be worth wdiile to review
briefly the evidence on which rests the current view of
sponge morphology.

Evidence from Comparative Anatomy as to Sponge Phy-
logeny. The strongest evidence offered by comparative
anatomy lies in the series of forms, passing by gradations

ELISHA MITCHELL SCIENTIFIC SOCIETY. 33

from very simple to complex types, found in the calcareous
sponges,"^' and in the little group of silicious sponges,
the Plakinidae, described by Schulze.f A comparison of
these forms goes to show that the simplest Ascon sponge
(Olynthus) must be regarded as the ancestral type of the
group, and that by the continued folding of the wall of
this simple form were produced the more complicated
sponges. Further, the exceedingly complex silicious and
horn\- sponges must be interpreted as colonies in which the
limits of the individual can in many cases no longer be
recognized.

The calcareous sponges offer a series of increasingly com-
plex forms, which Haeckel divided into Ascons, Sycons
and Leucons. HaeckePs views on the relationship of these
'forms must in great measure be accepted to-day, though in
certain respects, especially as regards the anatomy of the
Leucons, later researches (Polejaeff, /. c.) have shown that
he was not always in possession of the real facts of the case.

The simplest calcareous sponges, or i\scons, which serve
as the basis for Haeckel' s hypothetical sponge ancestor, the
Olynthus, are too familiar to call for any description. The
interesting form, Homoderma sycandra (von Lendenfeld)
may, however, be mentioned, in which the body is sur-
rounded by radial tubes, after the fashion of a Sycandra,
but with this difference: The central cavity as well as
the radial tubes is lined with collared cells. A figure of
this interesting sponge is accessible in Sollas's article on
Sponges in the Encyclopedia Brittannica, or in the Zoologi-
cal Articles by Lankester, etc., page 40.

Homoderma bridges the w^ay from the Ascon type to the
simplest Sycons, in which the radial tubes are distinct from
one another. A surface figure of such a Sycon {Sycetta

*Haeckel, Kalkspongieu. Polejaeff, Challenger Report on the Calcarea.
fF. E. Schulze, Die Placiniden, Zeit. fur Wiss. Zool. Bd. 34.

34 JOURNAL OF THE

primitiva) is given in \^osmaer. ^^~ In the majority of Sycons,
however, the radial tribes are not distinct, but are con-
nected together more or less b}' strands of mesoderm cov-
ered with ectoderm. The complicated ectodermal spaces
thus formed, which lie between the radial tubes, are known
as intercanals. Water enters the intercanals through the
openings in the surface (surface pores) and passes into the
radial canals through the openings in their walls (the primi-
tive pores — so-called chamber pores). The embryology of
the Sycons, as far as known, confirms the belief that they
are derived from the Ascons. Thus Sycandra raphanits
passes through a distinctly Ascon phase, the radial tubes
appearing later as outgrowths. The actual development
of complicated intercanals, such as those just mentioned,
has never been witnessed, but the comparison of a large
number of forms in which the connection between the
radial canals varies w^ithin wide limits makes it pretty cer-
tain that they are homologous with the simple ectodermic
spaces between the radial tubes of Sycetta. It is exceed-
ingly probable that the actual development of the compli-
cated Sycons will show that the radial tubes are in young-
stages distinct from one another, and only later become
connected together by bridges of tissue so as to form com-
plex intercanals. And so we must at present regard the
intercanals as lined with ectoderm.

'Coming now to the Leucons, we find that Polejaeff's de-
scription of the anatomy of this family accords with their
derivation from the Sycons, quite as well as did Haeckel's
more imaginative conception of the structure of these
forms. Taking one of the simplest of Polejaeff's types,
Lcncilla connexiva (PI. VI, fig. i<t, Polejaefif /. 6\), let us
compare it with a Sycon. Such a form is obviously de-
rived from a Svcon bv the eva^^i nation of the wall of the

*Vosniaer, Bronn's Klass. and Ordnvingen, Spongien, Taf. IX. .Schulze, Zeit. fur
Wiss. Zool. Bd. 31.

ELLSHA MITCHELL SCIENTIFIC SOCIETY

0:5

paragastric cavky at certain points. These evaginations
o-ive rise to numerous diverticula of the central cavitv,
which constitute efferent canals. The radial chambers are
at the same time thrown into groups, each group opening
into one of the new diverticula. The intercanals penetrate
as before between the several radial chambers, bringing
water to the chamber pores, the complexity of their arrange-
ment naturally being increased by the folding of the wall
of the paragastric cavity.

The increasing complexity in the Leucon family is
brought about by the ramification of the primitively sim-
ple efferent canals, the radial tubes growing shorter and
becoming in the most complicated types spheroidal cham-
bers quite like the flagellated chambers of the non-calcareous
sponges. In Lcucilla titer ^ for instance (Polejaeff, PI. VI,
fig. 2«), the efferent canals exhibit branching of a simple
character. But in such a form as Leucoiiia imdtiforinis
(Polejaeff", PI. VI, fig. 3^7) the ramification of the efferent
canals becomes exceedingly complex, and the radial tubes
here appear as spheroidal flagellated chambers. The inter-
canals (or afferent canals, as they are called in all sponges
but the Sycons) follow the efferent canals in all their wind-
ings, bringing water from the surface pores to the pores in
the walls of the flagellated chambers.

The chief conclusions to be drawn from this anatomical
comparison of the various forms of Sycons and Leucons
are that the afferent canals of Leucons are homologous with
the intercanals of Sycons and are lined with ectoderm;
that the flagellated chambers are homologous with the
radial tubes; that increasing complexity is brought about by
the ramification (or folding of the wall) of the efferent
canals.

The canal system of a complicated Leucon, like Leu-
conia, is essentially like that of a common silicious or
horny sponge (having flagellated chambers, afferent and

36 JOURNAL OF THE

efferent canals) except in the one respect that in the Leucon
there is a single central cavity opening by a terminal
oscuhim, while in most silicious and horny sponges there
are several orcnla leading into as many spacious efferent
cavities. But here the disposition of the calcareous sponges
to form indubitable colonies helps us out, for if we com-
pare the silicious or horny sponge with a colony of Leu-
cons instead of with a single one, we find that its deriva-
tion from such simple symmetrical forms is made easy.
We must suppose the complex non-calcareous sponge to be
a colony, in which the limits of the individuals have been
lost or obscured by the increasing thickness of the walls.
This increasing thickness would finally result in a more or
less complete fusion of the members of a colony into an
undivided mass with oscula scattered over the surface.
Each of the main efferent canals of the non-calcareous
sponge is homologous with the paragastric cavity of a sin-
gle Leucon. Both the canal and its set of branches, though,
are extremely irregular, having completely lost the sym-
metry of the ancestral type. The flagellated chambers
still bear the same relation to the efferent canals as they
did in the Leucon; /. <:'. , they are simple diverticula of the
canals. The system of afferent canals is obviously homolo-
gous with the same system in the Leucons, bearing identi-
cally the same relation as in the latter group both to the
flagellated chambers and the efferent canals. The sub-
dermal cavities (which are only modified portions of the
afferent canal system), communicating with the exterior by
numerous pores, though a late acquisition, are found in cer-
tain Leucons; e. g.^ Eilhardia Schulzei (Polejaeff, PI. IX).
In many of the Non-calcarea the colonial nature of the
sponge is indicated by the presence of elevations (oscular
tubes or papillae), bearing oscula on their summits. But
the number of oscula is not always to be taken as indicating
the number of individuals of which the sponge is com-

ELISHA MITCHELL SCIENTIFIC SOCIETY. 37

posed, for the colonies of calcareous sponges show plainly
that the budding individuals do not always develop oscula.
And on the other hand, there are certain indications in the
silicious sponges that in the adult oscula may be developed
almost anywhere. In spite of the difficulties, however, in
fixing upon the limits of the component individuals the
higher sponges are best regarded as colonies. Perhaps the
nearest approach made in other groups to the formation of
such colonies, in which the personality of the component
individual is so nearly lost, is found in corals like Maean-
drina, in which the united gastric cavities of the polyps
form continuous canals perforated at intervals by mouths.

We therefore reach the conclusion that the higher sponges
(non-calcareous) have been derived from colony-producing,
symmetrical forms, in which the evaginations of the primi-
tive paragastric cavity had already taken the form of
efferent canals and flagellated chambers; that is, from forms
allied to the existing Leucons. /Vnd we further come to
the conclusion that the subdermal cavities and afferent
canals are homologous with the intercanals of Sycons, and
hence phylogenetically, at least, are infoldings of the ecto-
derm. The whole efferent system (canals and flagellated
chambers both), on the contrary, is homologous with the
same system in the calcareous sponges, and is endodermic.

This conclusion as to the parts played by the germ layers
in producing the adult non-calcareous sponge, is the one
enunciated by Schulze in his classical paper on the
Plakinidae (p. 438). In this little family of silicious
sponges Schulze finds a genus, Plakina, the three species
of wdiich form links in a chain of increasing complexity,
showing quite as clearly as did the calcareous sponges that
the afferent system is derived from ectodermal infoldings,
and the efferent from endodermal outfoldings.

The Plakinidae are Tetractinellids. The three species
of the genus Plakina are small encrusting sponges found in

38 JOURNAL OF THE

the Mediterranean, on the under side of stones, shells, etc.
In the simplest species, P. inonolopJia^ there is a continuous
basal cavity crossed by strands of tissue. From the cavity
run more or less vertical efferent canals, which are simple
or very slightly branched, and into which open the flagel-
lated chambers. The afferent canals are spacious cavities
opening on the surface by wide mouths. The periphery
of the sponge forms a continuous rounded rim, the "ring-
wall," and the oscula, one or several, are situated here.
The surface of the sponge inside the "ringwall" is divided
up into low rounded elevations, caused by the upper ends
of the efferent canals, between which lie the wide apertures
leading into the afferent canals. Schulze was fortunately
able to observe the main features in the development of
this interesting form. There is a solid swimming larva
which settles down, forming a flat circular mass. A cen-
tral cavity appears in the mass, the lining cells becoming
columnar, and the sponge is thus transformed into a flat,
three- layered sac, the three layers being respectively ecto-
derm, mesoderm, entoderm. The flagellated chambers
appear in a single layer round the central cavity into which
they open. They are very probably formed as diverticula
of this cavity. Schulze did not follow the development
further, but a comparison of the adult with the sac-like
young form makes it pretty certain that the young form
undergoes a process of folding, which gives rise to the
efferent and afferent canals of the adult; or, in other words,
the efferent canals arise as vertical e vagi nations of the sac-
like stage. The afferent canals are consequently to be re-
garded as lined with ectoderm.

In the other two species [P. dilopha and P. trilophd) the
oscula are not situated at the periphery as in P. Dioiiolopha^
but at some distance internal to it; and the efferent canals
do not form projections on the surface as in the first species.
A comparison of the canal systems makes it evident that

ELISHA MITCHELL SCIENTIFIC SOCIETY. 39

P. dilopha has been derived from P. monolopha bv an
increase in the thickness of the mesoderm lying beneath
the surface of the sponge. The wide afferent canals of P.
mojiolopJia become transformed into the narrow afferent
canals of P. dilopha.

Plakina trilopJia goes a step farther in the direction of
complexity than does P. dilopha. It has probably been
derived from the latter species by the appearance of sec-
ondary folds in the radial efferent tubes; by the trans-
formation of the basal cavity into a system of lacunae,
owino^ to the increase in the number of the connectino^
Strands of tissue between the basal layer and the part of
the sponge containing the flagellated chambers; and by a
complication in the afferent canals in consequence of which
they do not open each by a single aperature, but by a num-
ber of small apertures the surface pores.

Schulze's conclusion that these species all lie in one line
of descent — that is, that the second species has been de-
rived from the first, and the third from the second — receives
as much support from a study of the spicules as of the
canal system, but here reference will have to be made to
the paper.

From comparative anatomy, then, we conclude the phy-
logeny of the sponges to be something as follows: The
Olynthus is the ancestor of the group. The outgrowth of
radial tubes gave rise to the Sycon type. The growth of
the mesoderm and development of new^ endodermic diverti-
cula, coupled with the metamorphosis of the radial tubes
into flagellated chambers, produced the Leucons. The
non-calcareons sponges have been derived from t\pes more
or less like the Leucons. And the conclusion with regrard
to the germ layers is that the efferent system is entirely
endodermic, and the afferent system entirely ectodermic.

Emhryological Evidence. Let us see now how far the
known facts of development support the above conclusions.

40 JOURNAL OF THE

The evidence from the calcareous sponges (Sycandra passes
through Olynthus stage) has already been given. Several
of the non-ca\cai-eo\\s sponges {Osca7^e//a /od^{ /a ris^ Reniera
filigrana^ Chalinulafertilis^ Plakina ;;^^;;/<r;A;/>/^^) run tli rough
a stage known as the rhagon (Sollas), which it is permissible
to regard as the ontogenetic representative of the Sycon type.

The rhagon of Oscarella* is a three-layed sac with a
terminal osculum. The flagellated chambers form a single
layer round the central cavity opening into it by wide
mouths, and opening on the surface by pores. Regarding
this form, as seems best, as equivalent to the Sycon type,
it will be noticed that the radial tubes of the Sycon are
coenogenetically replaced by flagellated chambers. The
rhagon of Oscarella is formed as an invaginate gastrula,
which attaches mouth down. The gastrula mouth closes
and the osculum is a new formation. The flagellated
chambers rise as true diverticula from the central cavity.
The adult Oscarella, the canal system of which is not far
removed from that of Plakina monolopha^ is very probably
formed from the rhagon, by the development in the latter
of a number of simple diverticula from the central cavity.
These diverticula are the efferent canals into which open
the flagellated chambers. The ectodermic spaces between
the efferent diverticula become the afferent canals. The
adult Oscarella, like P, nionolopha, is directly comparable
with a simple Leucon. The development of Oscarella, in
laree measures, confirms the conclusions drawn from com-
parative anatomy, and may therefore be considered as
phylogenetic.

The development of Plakina monolopha (Schulze, /. r.)
has already been described. The sac with its single layer
of flagellated chambers round a central cavity is a rhagon,
and may be taken as representing the Sycon stage. The
adult Plakina itself is the Leucon stage.

*Heider. Zur Metamorphose der Oscarella lobularis. Arb. Zool. Inst. Wien. Bd. 6.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 41

In Reniera Jiligrana^^ there is a solid swimming larva,
which after attaching acquires a central cavity with an
apical osculum. The flagellated chambers arise as diverti-
cula from this cavity. Thus in this sponge also there is a
rhagon stage. But in one matter we strike upon a coeno-
genetic modification. The afferent canals instead of being
ontogeneticall}- formed from the ectoderm, as they seem to
have been phylogenetically, are really formed from endo-
dermic diverticula, which grow outwards, meeting the sur-
face epithelium.

In Chalinula fertilist there is also a solid larva in which
a central cavity is hollowed out. But in this sponge the
flagellated chambers of the rhagon stage do not arise as
endodermic diverticula, but are formed independently from
solid groups of mesoderm cells. This origin of the flagel-
lated chambers must be regarded as coenogenetic. The
fact that the mesoderm may take upon itself the function
of forming organs ordinarily formed by the entoderm,
would seem to indicate that the two layers are of much the
same nature. This essential similarity between the tw^o
layers has always been maintained by Metschnikoff", not
only on the ground of dev^elopment, but for physiological
reasons as well. Thus in young Spongillas when the water
became bad he witnessed the entire disappearance of the
flagellated chambers, the sponge then consisting of ectoderm
and mesoderm alone. With a fresh supply of water the
chambers re-appeared. J Again, after feeding carmine in an
excessive amount to Halisarca poutica^ he found that the
canals and chambers entirely disappeared, the whole
body of the sponge inside the ectoderm consisting merely
of a mass of amoeboid cells full of carmine iibid.^ p. 272).

^Marshall. Die Ontogenic von Reniera filigrana. Zeit. fur Wiss. Zool. Bd. 37.
•Keller. Stud, uber die Organisation und die Entwicl
iss. Zool. Bd. 33.
jMetschnikoff. Spong. Stud. Zeit. fur Wiss. Zool. Bd. 32.

tKeller. Stud, uber die Organisation und die Entwick der Chalineen. Zeit. fur
Wiss. Zool. Bd. 33.

42 JOURNAL OF THE

The development of the afferent system in Chalinula was
not worked ont with certainty.

The embryology of the preceding sponges in which a
rhagon type is developed agrees pretty well with onr gen-
eral notions of sponge phylogeny. Bnt there are other
sponges, the development of which has been so excessively
modified as no longer to be of any nse as finger posts to
phylogeny, bnt which afford an excellent field for the study
of what may be called the methods of coenogeny. In
//ah'sarca Dujarc//;2n{MQtschmkoff, I. <r.), for instance, there
is a solid larva in which the canals appear as so many
separate lacunae surrounded by parenchyma (mes-entoderm)
cells. The canals only subsequently acquire a connection
with each other. In Esperia* the subdermal spaces, canals
and chambers arise separately as lacunae in the parenchyma.
The chambers are formed from aggregations of small cells
in the parenchyma, which Maas believes, on wdiat seems to
me insufficient evidence, to be ectoderm cells of the larva
that have migrated into the interior. The efferent canals,
Maas thinks, are formed from similar cells. In Esperia,
according to Yves Delage,t the chambers arise by division
of special mesoderm cells. The epithelium of the canals
comes from the larval ectoderm, which has migrated into
the interior. In Spongilla, according to the same author, J
the ectoderm cells of the larva are engulfed by mesoderm
cells and then become the lining cells of the flagellated
chambers. The observations of Delage on these points
need to be confirmed before they can be taken as the basis
for generalizations.

In vouncr Stellettas^ the subdermal cavities seem to arise

*Maas. Die Metamorphose von Ksperia Lorenzi, etc., Mith. aus dem Zool. Sta. zu
Neapel, Bd. lo, Kept. 3.
tSur le developpement des Kponges siliceuses, etc. Coinptes rendu.s. T. no.
JSur le developpement des Eponges (Spongilla fluviatili.s). Comptes rendu.s. T. 113.
gSollas. Challenger Report on Tetractinellidae, pp. XVI, XVII.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 43

as lacunae in the parenchyma. And in the external buds
of Tethya maza'^^ Selenka believes that the subdermal cavi-
ties have a similar origin.

In Spongilla, according to Gotte'^, the subdermal cavities
and canals are formed as independent lacunae in the
parenchyma, and the flagellated chambers are formed from
groups of cells, each group (and chamber 1 being produced
by the budding of a single large mesoderm cell. This
account of the development of these structures in Spongilla,
which is not very different from my own for Esperella and
Tedania, is contradicted by Maas,J who brings Spongilla
in line with the forms having a rhagon. Alaas describes
in the larva a central cavity from which the chambers arise
as diverticula, the central cavity persisting in a modified
shape as the efferent system of canals. The subdermal
spaces arise as ectodermal invaginations, from which the
afferent canals are formed as ingrowths. Thus, according
to Maas in the ontogeny of Spongilla, the whole afi'erent
system is formed from the ectoderm and the whole efferent
system from the endoderm. Ganin's earlier account§ like-
wise describes the chambers as diverticula from a main
endodermic cavity.

In the metamorphosis of a larva which probably belongs
to Myxilla, Vosmaer finds that the subdermal cavities
begin as fissures which gradually become wider, and that
the canals and chambers likewise appear as intercellular
spaces. Finally in the gemmule development of Esperella
and Tedania, I find that subdermal cavities, both sorts of
canals, and the flagellated chambers, all arise as inde-
pendent lacunae in the parenchyma.

Accepting as ancestral the development of Oscarella and

*Zeit. f. Wiss. Zool. Bd. XXXIII.

tUntersuchungen zur Entwicklungs-geschichte von Spongilla fluviatilis, 1886.
iUeber die Entwicklung des Sursswasserschwamms. Zeit. fur Wiss. Zool. Bd.
§Zur Entwicklung der Spongilla fluviatilis. Zool. Anzeiger. 1878.

44 * JOURNAL OF THE

Plakina jnonolopha^ the various coeiiogenetic modifications
which appear in other sponges may be classified as fi^llows:

1. The efferent canal system, instead of arising as a
single cavity which throws out diverticula, may be formed
as so many distinct cavities, - which subsequently unite
{Esperella^ Tedania^ Esperia lorenzi and lingua^ Halisarca
Diija rdin ii\ Myxilld) .

2. The flagellated chambers, instead of arising as endo-
dermic diverticula, may be formed from groups of mesoderm
cells {Esperella^ Tedania^ Chaliniila fertilis^ Myxilla and
probably in Esperia lorenzi and E. lingua).

3. The afferent canals, including the subdermal cavities,
instead of being formed as invaginations from the ectoderm,
arise as lacunae in the mes-entoderm {Esperella^ Tedania^
Esperia lorenzi ^lw^ lingua^ Stelletta^ Myxilla). In Reniera
filigrana they are formed as entodermic diverticula.

The coenogenetic development of the flagellated cham-
bers and efferent canals suggests, as I have said, an
essential similarity of nature in the so-called entoderm and
mesoderm of sponges. This belief, so long upheld by
Metschnikoflf, derives some of its strongest support from
this author's physiological investigations (see ante^ p. 10),
as well as from the fact first emphasized by Metschnikoff"
and Barrois, that in the most common sponge larva, /. <?. ,
the solid larva, the mesoderm and entoderm form a single
indivisible layer.

And likewise the development of the afferent system of
canals in some sponges from the ectoderm, in others from
the mes-entoderm, may possibly be taken as meaning that
even these two primary layers (the outer and the inner) are
not distinctly differentiated from each other in the sponges,
or, in other words, that the mes-entoderm is still enough
like the ectoderm to form organs ordinarily produced by
the latter laver.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 45

There is another (hypothetical) way of explaining these
phenomena, which consists in supposing that ectoderm
cells of the larva migrate into the interior, and though in-
distinguishable from the surrounding mes-entoderm cells,
alone take part in forming the afferent canals. Similarly
we ma}' suppose that in the solid mass, which constitutes
the parenchyma of Hsperella, there are two radically dis-
tinct classes of cells, one of which is potentially gifted
with the power of forming efferent canals and flagellated
chambers, while the other has not the powder, and must
remain as amoeboid mesoderm. But this is pure hypothesis.

The result of this critical examination seems to be that
the Olynthus must be regarded as the common ancestor of
sponges (Haeckel, Kalkspongien), and that the entoderm
and mesoderm are not sharply differentiated from one
another as they are in the higher animals (Metschnikoff,
Spong. Studien, p. 378).

Origin of the Olynthus. The prevalence of the solid
larva in sponges and Hydromedusse, coupled with the wide-
spread presence of intracellular digestion in the lowest
metazoa, led Metschnikoff years ago to the belief that the
solid larva represents the ancestral form of the metazoa,
while the gastrula is a coenogenetic modification. "^ To my
own mind all the facts that we know indicate that Metschni-
koff's conclusion is well founded. This hypothetical an-
cestral form is known as the Parenchymella (Phogocytella).
I may be permitted to recall its leading features as deduced
by Metschnikoff. The animal consisted of an outer layer
of flagellated cells and an inner mass of amoeboid cells.
The digestion was intracellular, the food being taken in
through intercellular openings (pores) scattered over the
surface. A central cavity having a special opening to the

*MetschnikoflF. Spongiologische Studien. Zeit. f. Wiss. Zool. Bd. 32. Metschnikoff.
Embryologische Studien au Medusen. Wien., 1886.

46 JOURNAL OF THE

exterior (osculiim) was a later acquisition, the osculnm
being in all probability one of the small apertures (pores)
especially enlarged. Even after the formation of this
cavity the division of the parenchyma into entoderm and
mesoderm was not (and is not) in the sponges a rigid
division, the primitive power of digesting food intracel-
lularly having been retained by both layers. It was only
with the appearance of the higher animals that the separa-
tion of entoderm from mesoderm became a perfect one.
(Spongiologische Studien, p. 378). This solid ancestor of
the metazoa, Metschnikoff derives from colonial forms like
Protospongia. Barrois as early as 1876* stated his belief
that the ancestor of the sponges was a solid animal, com-
posed of two layers, the outer representing the ectoderm,
the inner mass representing a parenchyma from which
have developed the entoderm and mesoderm of higher
animals (p. 78).

According to this view the early development of Plakina
(or Reniera, Chalinula, etc.) gives the first chapters in the
history of the group of sponges more faithfully than does
a form like Oscarella (or Sycandra). In the former sponges
it will be remembered there is a solid larva hollowed out
to form a three-layered sac, which then breaks open to the
exterior, forming the osculum. In the latter there is an
invaginate gastrula, which settles mouth downwards, the
gastrula mouth subsequently closing and the osculum ap-
pearing as a perforation at the upper end of the sac. In
these forms (Oscarella, Sycandra) we have to suppose that
the Parenchymella stage is skipped, the central cavity
(which properly belongs to the Olynthus stage) being pre-
cociously developed coincidently with the immigration of
the entoderm. The blastopore of the sponge gastrula, on

*Memoire sur rembryologie de quelques Eponges de la Maiiche. Ann. Sci. Nat. T. 3,
VI Ser.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 47

this view, does not represent a primitive organ (Urmiind),
but merely comes into existence owing to the special, and
highlv modified, method of forming the entoderm. We
do not, therefore, have to construe the Oscarella develop-
ment (with Heider and SoUas) as meaning that a gastrula
ancestor settled mouth downward, and that the mouth
gradually became functionless, finally closing up, while a
new series of openings, pores and osculum, were estab-
lished.

The only remaining point I wnsh to speak of is the rela-
tion of the sponges to the Coelenterates. That the two
groups have had a common ancestor in the Parenchymella
is highly probable, but the similarity between the Olynthus
and the simplest Coelenterates inclines one to go further,
and at any rate homologize the paragastric cavity of the
former with the gastric cavity of the latter. This, of
course, is done by authors like Sollas, who derive both
groups from a common gastrula ancestor. Whether the
osculum of the Olynthus is also homologous with the gas-
trula mouth, as Haeckel originally held, is a question
which needs for its answer more facts relating to the actual
use to which the osculum is put in the simplest sponges.
Sollas and Heider urge against the homology the fact that
the Coelenterate larva attaches by the pole opposite the
blastopore, while in the sponge larva the blastopore is at
the pole of attachment. But this I cannot regard as a
very strong argument, for (with Metschnikoff) I do not be-
lieve that the opening into the gastrula cavity represents a
primitive organ (mouth of an ancestor). And if it does
not, but is merely an incidental product of a particular
mode of entoderm-formation employed by the animal, it
has no bearing on the question of homology between oscu-
lum and mouth. Consequently the fact that in the attach-
ing coelenterate and sponge larvae the blastopore is at oppo-

48 JOURNAL OF THE

site poles is a curious phenomenon, but one aside from the
problem.

I doubt very much, however, if any such radical dis-
tinction can be drawn between the larvae of the two groups,
for it is. a question whether any sponge larva has a par-
ticular pole by which it must attach. Even in Sycandra,
Schulze (/. c, p. 270) records that exceptional cases occur,
which cannot be regarded as pathological, in which fixa-
tion takes place not by the gastrula mouth but on the side.
Fixation may also be delayed until the gastrula mouth has
closed and spicules have begun to appear, in which case it
is not stated by what part the larva attaches. In the solid
larvae of silicious sponges the variation is much greater.
Such larvae attach in some cases by the posterior pole, in
others by the anterior pole, and yet in others on the side.
All these variations may occur in larvae of the same species.
For instance, Maas records that in Esperia he observed
fifteen individuals attach by the posterior pole, seventy in-
dividuals by the anterior pole, and five or six on the side.
It thus appears that in the larvae of silicious sponges at any
rate there is no constant point of attachment.

University of North Carolina, November 7, 1892.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 49

RECORD OF MEETINGS.

SIXTY-SEVENTH MEETING.

Person Hall. January 19th. 1892.
President Holmes in the chair.

1. The Oyster Question. H. V. Wilson.

2. Magnetic Iron Ores of Ashe County. H. B. C. Nitze.

Report of the Secretary. One hundred and twenty-six books and pam-
phlets received and the following new exchanges:
New York Mathematical Society.
La Societe Geologique du Nord du France.

SIXTY EIGHTH MEETING.

Person H.\ll. February 9th, 1892.
Called to order by the President.

3. The Greenwood Process for the Direct Production of Caustic Soda
and Hydrochloric Acid. Chas. Baskerville.

4. The Determination of the Standards of Length. J. W. Gore.

5. Chinese Salt-making. F". P. Yenable.

6. The Plan and Limitations of the N. C. Geological Survey. J. A.
Holmes.

Report of the Secretary. Sevent3--five books and pamphlets received.
New exchange: E. M. Museum of Princeton College.

sixty-ninth meeting.

Person Hall, .\pril 12th. 1892.
Professor Gore presided.

7. Common Roads. Wm. Cain.

8. Igneous Rock Formation of North Carolina. J. A. Holmes.
New exchange: Institut Royal Grand Ducal de Luxembourg.

JOURNAL

OF THE

ELISHA MITCHELL SCIENTIFIC SOCIETY,

VOLUME IX— PART SFXOXD.

JULY— DECEMBER.

1892.

post-office:

CHAPEL HILL, N. C.

E. M. UZZELL, STEAM PRINTER AND BINDER,
RALEIGH, N. C.

1892.

OFFICERS.

1803.

presidp:nt:
Josp:ph a. H01.MES, ------ Chapel Hill, N. C.

FIRST vice-president:

W. L. PoTEAT, Wake Forest, N. C.

SECOND VICE-PRESIDENT:

W. A. Withers, ------- Raleigh, N. C.

THIRD VICE-PRESIDENT:

J. W. Gore, -------- Chapel Hill, N. C.

SECRETARY AND TREASURER:
F. P. Venable, ------- Chapel Hill, N. C.

I.IHRARV AND PLACE OF MEETING:

CHAPEL HHwL, N. C.

TABLE OF CONTENTS.

PAGE.

Statistics of the Mineral Products of North Carolina for 1S92. H. B.

C. Nitze 55

Additions to the Breeding Avi-fauna in North Carolina Since the Pub-
lication of Prof. G. F. Atkinson's Catalogue in 1S87. J. W. P.
Smith wick . 61

An Example of River Adjustment. Charles Baskerville and R. H.

Mitchell --- --- 64

Character and Distribution of Road ^Materials. J. A. Holmes 66

To Set Slope Stakes when the Surface is Steep but Slopes Uniformly.

J. M. Bandy _- 82

On the Development and a Supposed New Method of Reproduction
in the Sun-animalcule, Actinosphcrriuui Eichhornii. John M.
Stedman 83

Some Fungi of Blowing Rock, N. C. George F. Atkinson and Her-
mann Schreuk- 95

Record of Meetings 107

Report of Treasurer 108

KJ-

JUN 8 1893

JOURNAL

OF THE

Elisha Mitchell Scientific Society.

STATISTICS OF THE MINERAL PRODUCTS OF
NORTH CAROLINA FOR 1892.

BY H. B. C. NITZE.

The difficulties atteiidintr the collection of exact statis-
tics of the x'arious mineral productions are very great,
often insurmountable; and especially difficult to obtain are
those of the gold, corundum and mica mines, which form
the greater part of North Carolina's mining industry.

The following statistics have been collected from the
most reliable sources available, under the direction of the
North Carolina Geological Survey^ and although often
lacking in detail they will serve to show very nearly what
the mineral production of the State has been for the past
\'ear.

Of the metallic products gold and iron stand alone.
Under the list of non-metallic products we have iron ore,
copper ore, bituminous coal, corundum, mica, talc and
kaolin.

GOLD.

During 1892 there were fifty-six gold mines, distributed
over eighteen different counties, in operation in the State.
Of these, fifteen were placer and forty-one vein workings.

56 JOCKXAL OF THE

The total number of stamps in operation is estimated at
310, the total amount of labor at 500 men, and the total
production at $65,000.

PIG IRON.

There was but one blast furnace in active operation in the
State, namely, thatat Cranberry, Mitchell county, belongino^
to the Cranberry Iron and Coal Company. This is a small
brick stack of the following dimensions: Height 50 feet,
diameter of bosh 10 feet 2 inches, diameter of hearth
3 feet, capacity 14 to 15 tons per day. It uses the low
phosphorus magnetic ore of the Cranberry mine situated
close by, magnesian limestone from Carter county, Tenn.,
and coke from Pocahontas, W. Va.

The total output of this furnace for 1892 was 2,902
gross tons, of which 313 tons were charcoal and 2,589 tons
coke iron; the total product was valued at $52,000 at the
furnace.

The quality of this product was a special Bessemer iron,
averaging less than i.oo per cent, silicon, and less than
0.025 per cent, phosphorus. It was shipped to steel works
in Ohio and Pennsylvania.

The total production in gross tons (22,401 pounds) of the
Cranberry furnace for the past nine years is shown in the
following table:

1884.

1885.

1

1886.
1,964

1887. 1888.
3,250 2,143

1889.

1890.

1891.
3,217

1892.

388

2,5^7

2,840

2,902

FORGE IRON.

The small amount of forge iron made for pureh' local
purposes at Pasle)'s forge, in Ashe count)', is rather of
historical than commercial interest. This forge is situated
at the mouth of Helton Creek, and consists of one fire

ELISHA .MITCHELL SCIEXTIFIC SOCIETY,

57

blown b\' the water tronipe, and one hammer operated b\'
water-power. It is the only forge now in operation in the
State, and makes annnally abont twenty to thirty tons of
bar iron for local nses.

IRON ORE.

The total prodnction of iron ore dnring 1892 is esti-
mated at 23,433 gross tons, valned at $43,306.20 at the
mines. Of this amount 17,088 gross tons, valued at
$34,423.20, were shipped out of the State; the balance
w^as turned into 2,902 gross tons of pig metal.

The only two mines in operation were the Cranberry
mine in Mitchell and the Ormond mine in Gaston countv.

The Cranberry Mine^ operated b\- the Cranberry Iron
and Coal Company, produced 18,433 gross tons, valued at
$25,806.20 at the mines. Of this amount 12,088 tons,
valued at $16,923.20, were shipped to furnaces in South-
west Virginia.

The ore is a magnetite, of which the following analysis
by Mr. Porter W. Shinier shows the quality of the run of
mine:

Per Cent.

Silica 23.73

Metallic iron _ 45.90

Metallicmagaue.se .. 0.44

Alumina _-.._-. r.oi

Lime . ,_. 9.69

Magnesia - - ... 1.51

Sulphur --- ... 0.012

Phosphorus- . 0.007

The total output of the Cranberry mine in gross tons
for the past nine years is shown in the following table:

1884. 1885. 1886. 1887. 1888. , 1889. 1890. ; 18^1. I 1892.

3,998 17,839 24,106 45,032 15,705 19,819 30,290 27,628 18,433

III.

IV.

1-55

47.10

65-35

0.057

0.007

58 JOURNAL OF THE

The Onnond Minc^ situated in Ga.stoii county, on the
Charlotte & Atlanta Air Line, produced during 1892 about
5,000 tons of ore, valued at $17,500 at the mines. It
was shipped to Binninghani, Ala., and Richmond, Va. ,
for the fettling of puddling furnaces.

The ore is a mixture of hard, block hematite, or rather
turgite, porous limonite, and soft, black, powder ore,
slightly magnetic, of which the following are some repre-
sentative analyses:

I. II.

Silica 9.72 1. 51

Metallic iron 52.39 65.79

Phosphorus 0.079 0.028

I. Lump ore; analysis by N. C. Geological Survey.
II. Lump ore; analysis by Carnegie Bros. & Co., Pittsburg, Pa.

III. Limonite; analysis by C. D. Lawton.

IV. Black powder ore; analysis by Carnegie Bros. & Co.

The mine was closed down in September, 1892, on
coming into possession of the Bessemer Mining Company^
which is remodeling the plant and making preparations for
a large output in the near future.

The North Caroiina Steel and Iron Company completed
their furnace at Greensboro in June, 1892. The height of
the stack is 70 feet, diameter of bosh 16 feet, and the cal-
culated capacity 100 tons per day. The plant is fully
equipped with all modern improvements, and, together
with ore lands, town-site lands and other improvements,
represents a total investment so far of $305,000. It is now
expected to have this furnace in operation by the coming
spring, the delay of putting it in blast having been caused
by a deficiency of the neces.sary funds; and the present
low price of iron has deterred the company from
endeavoring to procure the requisite capital sooner. It
is also proposed to erect a merchant mill, machine shops,
foundry and car works during this year, the latter to have
a capacity of ten (10) freight cars a day. The principal

ELISHA MITCHELL SCIENTIFIC SOCIETY. 59

supply of ore will be obtained from the mines of the com-
pany at Ore Hill, Chatham connty, about forty miles dis-
tant. This ore is a brown hematite of very fair quality,
as shown b\- the following analyses, made in the laboratory
of the North Carolina Geological Survey:

I.

II.

III.

IV.

Silica -- ---

- 4-73

2.35

17-32

3-71

Metallic irou

- - 47.87

47-23

42.88

49-79

Sulphur

- 0.034

0.280

0.230

0.170

Phosphorus 0.069 0.139 0.106 0.038

These deposits have been partially developed during the
past year and about 700 tons of ore taken out. Besides
this source magnetic ores from the western part of the
State will be used. Limestone will be obtained from Vir-
ginia and coke from the Flat Top region in the same
State.

In Granville county some recently discovered deposits of
magnetic iron ore of good quality have been prospected
with encouraging results, but no regular mining opera-
tions have yet been started, and no ore has been shipped.

COPPER ORE.

The Blue Wing Mine in Granville county was the only
producing mine in the State during 1892. Up to October,
when the mine and concentrator closed down indefinitely,
the production of concentrates, shipped to the Orford
Copper Works, N. Y. , was valued at $15,000 (estimated).

The ore is chiefly bornite in a quartz gangue. The fol-
lowing analyses show the quality of the ore and concen-
trates:

Copper. Silver.

Per Cent. Oz. Per Ton.

Ruu of mine ore - -- 8.66 3.55

Cobbed ore -- -- 14.21 5.66

Jig concentrates 52.32 12.00

Frue vanner concentrates - -^ 36.87 12.60

6o JOURNAL OF THE

COAL.

The Egypt Coal Conipaiiy, operating- the Egypt mine in
Chatham county, shipped during 1892 6,500 tons of bitu-
minous coal, valued at $7,475. ]\Iisfortunes by fire and
water cut down the output to nearly one-half of what it
was the year preceding. The company has been engaged
in improving and increasing its plant during the past year
by the addition of three pumps underground and further
hoisting capacity. A second shaft, 8 b\- 12 feet, is being;
put down, to be used exclusively for ventilating purposes.

The following anah'sis by the North Carolina Geological
Survey represents the quality of this coal:

Moisture -- - --. 1.25

Volatile matter 33-35

Fixed carbon 4918

Ash -- 16.22

Sulphur -- - .- 1.72

Specific gravity - -- - — - ^-294

CORUNDUM.

The total corundum product for 1892 is estimated at 560
net tons. No estimate of the value can be made.

The chief producers were the Corundum Hill and
Ellijay mines in Macon, and the Hogback mines in Jack-
son county. In Iredell county some private prospecting
was carried on during the latter part of the year, two
miles west of Statesville, and several veins were located,
from which about 9,000 pounds of corundum were taken,
but no regular operations have as yet been instituted.

MICA.

During 1892 there were in operation some ten or twelve
mica mines, situated principalh- in IVIitchell and Yancey
counties. The total production of these mines is estimated

ELISHA MITCHELL SCIENTIFfC SOCIETY. 6l

at 10,000 pounds of cut mica, valued at about $35,000.
The average price of 3 by 5-inch cut mica, at the mines,
is put at $3.50 per pound.

Durino^ tlie vear three mills, manufacturing^ orround
mica from waste scraps, were in operation in Mitchell
count}-, but no estimate can be made of their output.

TALC.

The total production of prepared talc (shipments from
mills) for 1892 is estimated at 2,500 net tons, valued at
about $19,000 at the mills.

The two principal producers were The Notla Consoli-
dated Marble^ Iron and Talc Compan\\ of Cherokee, and
Messrs. Rickard and Hezvitt, of Swain county.

KAOLIN.

The total production of prepared kaolin for 1892 is esti-
mated at 3,900 net tons, valued at $31,200 at the works.

The principal producers were the works at Sylva and
Dillsboro, in Jackson count\'.

ADDITIONS TO THE BREEDING AVI-FAUNA IN
NORTH CAROLINA SINCE THE PUBLICATION
OF PROF. G. F. ATKINSON'S CATALOGUE IN
1887.

BY J. W. P. SMITH WICK.

1. Great Blue Heron [Ardea herodias). Young ones
have been seen and taken in all sections.

2. Little Blue Heron [Ardea ccFrnlae). Reported
breeding in the west by ?vlr. John S. Cairns, Buncombe
countw

62 JOURNAL OF THE

3. Red-tailed Hawk {Buteo borealis). One nest con-
tainino; two eggs was found by myself in Bertie county,
1888.

4. Broad-winged Hawk (liulco lafissiifiits). Breeds in
middle and western sections. (Brimley and Cairns).

5. American Sparrow Hawk {Falco sparDeriiis). Nests
have been found in all sections; I have noted several in
the east.

6. American Ospre>' {Pandion halicetiis carolineusis).
Have noted two nests in Bertie count\- and seen young-
ones several times; reported breeding along the larger
streams of the west by Cairns.

7. Black-billed Cuckoo {^Coccyzus erythrothahnus).
Reported breeding in Wake county by Brimley; Cairns
says that it breeds during some seasons in the mountains.

8. Belted Kingfisher [Ceryle alcyoii). I found a nest
containing seven eggs in 1889, which was placed at the
end of a burrow in a bank on the Cashie Ri\'er near its
mouth; breeds in the west. (Cairns).

9. Hair}- Woodpecker ^Dryobntes villosiis). Said to
breed in the higher mountains of the west by Cairns.

10. Yellow-bellied Sapsucker {Sphyrapiais z'an'us).
Reported breeding by Cairns in Buncombe county on
higher mountains.

11. Red-headed Woodpecker {^Melaucrpes erypJirocepJi-
aliis). Found commonly breeding in all sections.

12. Red-bellied Woodpecker {Alelancrpes caroliniis).
Rather rare breeder in all sections of the vState,

13. Chuck-wilTs-widow ^Antrostoiiius carolinensis).
Three nests, containing two eggs each, were found by
my.self in Bertie county; one in 1888 and two in 1891.

14. Night-hawk {Chordei/es virginiaujis). Found breed-
ing in the eastern section by myself.

15. Least Flycatcher {Einpidonax DiimDius). Reported
as a rare breeder in mountains bv Cairns.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 63

16. American Crow [Corviis amcricamis). Found
breeding in all sections, common.

17. Boat-tailed Grackle {Qmsatlus major). One nest
containing four eggs was taken in Plymouth from an old
elm overgrown with ivy, in 1889, by myself.

18. Towliee {Pipilo erythrotJialmus). Reported bv
Cairns as breeding in Buncombe countv.

19. Rose-breasted Grosbeak [Habia ludoviciaiia). Said
to breed on cragg\- mountains by Cairns.

20. White-bellied Swallow {TacJiycineta bicolor). Sev-
eral nests containing eggs have been taken by my cousin
(T. A. Smithwick) and myself in the last few vears.

21. Logger-head Shrike {Lanius ludoviciaims).
Reported breeding in Iredell county by McLaughlin.

22. Warbling Vireo {llreo gilvus). Reported breed-
ing along the rivers in the mountain section by Cairns.

23. Yellow-throated Vireo {Vireo Jiavifrons). I have
taken two nests in Bertie county; no others have been
recorded.

24. Mountain Solitary Vireo {l^ireo solitarius aliicola).
Found breeding in the higher mountains by Cairns.

25. White-eyed Vireo {Vireo iioveaboraceiisis). Breeds
throughout the State, common.

26. Prothonotary Warbler {Protonotaria citred). I
found one nest in 1888 in Bertie county which contained
three eggs; this is the farthest north that any nest has
been recorded on the Atlantic slope, so far, I think.

27. Worm-eating Warbler {Helmintherus veriiiivortis).
One nest was found in Bertie county by T. A. Smith wick
and one in Buncombe county by Cairns last spring; this
shows that it may breed in all portions.

28. Blue-winged Warbler {^Helmintkopliila pinus). Said
to breed in the mountains by Cairns.

29. r^Iagnolia Warbler (Dendroica maculosa). Breeds
in the west; young ones have been seen in July by Cairns.

64 JOURNAL OF THE

30. Oven-bird {Seiuriis aitrocapilliis). One nest was
found in Bertie county in 1892 by myself.

31. Hooded Warbler {Sylvania miirata). I found one
nest in' 1888, and since that time a great many nests have
been found by my cousin and myself in Bertie county.
Not reported from any other section.

32. Winter Wren [Troglodytes hienialis). Two nests
were found by Cairns on the Black mountains in the
spring- of 1892.

^2)' Golden-crowned Kinglet [Regulus satrapa).
Reported breeding on Black mountains by Cairns.

34. Olive-backed Thrush {Tiirdus iistnlatiis szvain-
sonii). One nest has been reported, it being found on
Black mountains bv Cairns.

CONTRIBrXIONS FROM GEOLOGICAL DEPARTMENT UNIVERSITY OF NORTH CAROLINA.

No. I.

AN EXAMPLE OF RIVER ADJUSTMENT.

BY CHARLES BASKERVILLE AND R. H. MITCHELL.

One could scarceh- find an example which more fully
illustrates the principles involved in determining the
courses of streams than the Jackson River in western Vir-
ginia. This is a small stream rising near Monterey, High-
land count)', flowing south-west through Bath into the
James River at Covington, Alleghany county.

The existing topography is the result of the denudation
following upon the great Permian deformation, which
gave rise to the main ranges of the Appalachians. From

ELISHA MITCHELL SCIEXTIFIC SOCIETY.

65

this upheaval dates the beginning of the history of the
riv^ers of this reeion.

Jfefertncej

I C Ckt\yhyitkyy.

II Jt/un a r*
•II Ut tion i Q r\
i(/V Loitr Co.rij9mJtrou^

yya r irt S/o f n a f

Diagram I gives a rough perspective of this immediate
region, together with a vertical section in a north-west and
south-easterly direction, just south of Warm Springs. In
the vertical section the unbroken lines represent the
geological structure of the present topography (heavy
line CD) and the dotted lines the same in Permian
time. The perspective shows the drainage consequent
upon the deformation, and combining the two, it can be
seen that the Jackson River flowed down a syncline in a
south-westerly direction on a bed of the lower carboniferous
rock. Parallel to this, and in a similar syncline on the

66 JOURNAL OF THE

same stratum with lower level, flowed now Back Creek,
formerly Meadow Fork of the Greenbrier River, West Vir-
ginia. Tributary A of Back Creek, on account of steep-
ness of slope, gnaws back, capturing headwaters of Jack-
son River by tributary A\ causing the same to have its
outlet in a north-westerly direction, thus throwing the
water-shed east (GF) between Cowpasture and Jackson
Rivers, which previously (EF) was between Jackson River
and Back Creek. The base of the syncline, then the bed
of Back Creek (Meadow Fork), was nearer base level
than base of Jackson River syncline, consequently the
softer Devonian slates were reached first by the latter.
With conditions thus changed the tributary B of Jackson
River captures in turn the headwaters (B') of Meadow Fork
(Back Creek), and the water-shed (HF) as now exists was
shifted west between Greenbrier River and Meadow Fork of
same and Back Creek. Diagram II "shows the present
flow of waters of Jackson River.

University of North Carolina. «

CHARACTER AND DISTRIBUTION OF ROAD
MATERIALS.

BY J. A. HOLMES.

In the following discussion of the character and dis-
tribution of road material in the State it is thought best
to avoid the use of technical terms as far as possible; and
the names of rocks here used are those applied by the
engineer rather than by the geologist. The character of
the materials is discussed with a view to their fitness for
use in the construction of broken-stone pavement, as used
by Macadam and Telford on the public highways.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 67

CHARACTER OF ROAD MATERIALS.

''In considering the relative fitness of the various mate-
rials," savs Byrne, "^ ''the following physical and chemical
qualities must be sought for:

" ( I ). Hardness, or that disposition of a solid which ren-
ders it difficult to displace its parts among themselves.

"(2 '. Toughness, or that quality which will endure light
but rapid blows without breaking.

"(3). Ability to withstand the destructive action of the
weather, and probablv some organic acids produced by the
decomposition of excretal matters, always present upon the
roadways in use.

"(4. The porosity, or water-absorbing capacity, is of
considerable importance. There is, perhaps, no more
potent disintegrator in nature than frost, and it may be
accepted as fact that of two rocks which are to be exposed
to frost, the one most absorbent of water will be the least
durable."

The following table shows absorptive power of a few
common stones: t

Perceutage of Water Absorbed. Percentage of Water Absorbed.

Granites ..- - -- 0.06100.155 Limestones--. 0.20 to 5.00

Marbles -. o.oStoo. 16 Sandstones - .- 0.41 to 5.48

Something of the quality and suitability of diflferent
materials for use in broken-stone pavements is shown in
the following table: 4!

Materials.

Co-efficients of Co-efficients of
Wear. Crushing.

Basalt --- - -- 12.5 to 24.2 12.1 to 16.

Porphyr}' -- -- 14.11022.9 8.3 to 16.3

Gneiss -- --- 10.3 to 19.0 13.4 to 14.8

Granite 7.3 to 18.0 7.7 to 15.8

Svenite -- -- 11. 6 to 12.7 12.4 to 13.0

Slag --- -- --- 14.5 to 15.3 7.2 to 1 1. 1

Ouartzite -_- -- 13.8 to 30.0 12.3 to 21.6

Qnartzose sandstone 14.3 to 26.2 9.9 to 16.6

Quartz ---, 12.91017.8 12.3 to 13.2

Limestone -_ - --; :6.6 to 15.7 6.5 to 13.5

^Highway Construction, p. 24. ^Ibid.. p. 26. Xlbid., p. 172.

68 JOURNAL OF THE

These ''co-efficients," showing tlie relative quality of
various road materials, were obtained by French engineers
as the result of an extended series of tests, and were found
to agree fairly well with the results arrived at by actual
observation of the wear of materials in the roads. The
co-efficient 20 is equivalent to "excellent," 10 to "suffi-
ciently good," and 5 to "bad."

Stones not Suitable as Road Material. — Before pro-
ceeding to the consideration of the stones found in North
Carolina adapted to use as road material it may be well to
consider briefly some of those that are not suited to this
purpose. In general, it may be said that all schistose and
slaty rocks, /. e., all rocks which split or break easily into
layers or flakes, should be discarded. No rock of what-
ever species which is already in the advanced stages of
decay, so as to become crumbly and soft or porous, should
be used in macadamizing roads, as the result in all such
cases will be that, under the action of the wheels and
hoofs, these materials become ground into fine powder,
which becomes mud when wet, and dust when dr\'. There
are many places, however, where a decayed granite or
gneiss rock, when highly siliceous, will make a good foun-
dation for a Macadam road, and will be found useful as a
covering on clay in the improvement of dirt roads. There
are other materials, like quartz (" white flint"), which are
hard enough, but which are quite brittle, and hence easily
crushed to powder, and which, consequently, should not
be used when better material is available. Sandstones, as
a rule, are unfit for use in macadamizing roads, as they are
easily crushed and usually porous.

Stones Suitable as Road Material. — "The materials
used for broken-stone pavements must of necessity vary
very much according to the locality. Owing to the cost
of haulage, local stone must generally be used, especially
if the traffic be onl\- moderate. If, howe\'er, the traffic is

ELISHA MITCHELL SCIENTIFIC SOCIETY. 69

]ieav\-. it will sometimes be found better and more
e<:onomical to obtain a superior material, even at a higher
cost, than the local stone; and in cases where the traffic is
verv oTeat the best material that can be obtained is the
most economical.""^ In the middle and western counties
of the State, in many places, stones now covering the cul-
tivated fields will be found satisfactory for use on the roads,
and in order to get rid of them farmers will haul and sell
them for low prices.

Stones ordinarily used in the construction of ^Macadam
and Telford roads are the following: Trap, syenite, granite,
gneiss, limestone, quartzite, gravel and sand. The first
three of these names are used here in a very general sense,
and include several species of rock which, in technical
language, would be known by other names. In general,
it mav be said that they rank in importance about in the
order named, but several of them, especially the granite,
gneiss and limestone, vary so much in quality that this
general statement is subject to modification accordingly.

The term trap, as here used, includes not only the black,
rather fine-grained, igneous rock known as diabase, which
occurs in long dykes in the sandstone basins of Deep and
Dan Rivers, but also the somewhat similar material which
is to be found in the older crystalline rock of many other
reo^ions. In this State it is often known local Iv under the
name of ''nigger-head'' rock. This rock does not usually
split well into paving blocks, but when properly broken it
is the most uniformly good material obtainable for macadam-
izing public highways, though sometimes it does not
''bind'' well.

Syenite, sometimes called Jwvjiblende granite, varies
somewhat in quality and composition. It is a widely dis-
tributed rock in the midland and western counties of

=^Byrue, Highway Construction, p.

yO JOURNAL OF THE

North Carolina, and is an excellent road material. The
v-arieties which are finer in grain, and those having the
larger proportion of the black mineral known as horn-
blende and are consequently of darker color, are best
adapted for this purpose.

Granites vary considerably, both in quality and appear-
ance, and in their value as road material. Those which
are very coarse in grain, containing large and numerous
crystals of feldspar, are, as a rule, more easily crushed and
decay more rapidly, and should not be used in road con-
struction when better materials are available. Those
which contain a large proportion of mica split and crush
more easily into thin flakes and grains, and for this reason
are also less valuable. Those varieties which are of fine
tjrain and contain an admixture of hornblende are best for
road purposes.

Gneiss^ which has the same general composition as
granite, also varies very greatly in its quality and adapta-
bility to road building. It usually has the appearance of
being somewhat laminated or bedded, and when the layers
are thin and the rock shows a tendency to split along these
layers it should be discarded for road purposes. In addi-
tion to this, the statements made above with reference to
the granites will apply also to gneiss.

Liinesione suitable for road purposes is not an abundant
rock in North Carolina, but it is found in a few of the
eastern and a few of the western counties. It is a rock
which varies very greatly in character, from the hard, fine-
grained, compact magnesium limestone, which is a most
excellent material for the Macadam and Telford roads, to
the porous, coarse and partially compact sliell-rock of
recent geological formation, which is less valuable mate-
rial. Practically all limestones when used as road material
possess one valuable qualification, that of "binding''; the
surface material which becomes ground by the action of

ELISHA MITCHELL SCIENTIFIC SOCIETY. 7 1

the wheels settles among the fragments below and consoli-
dates the entire mass. For this reason, in many cases, it
has been fonnd to be good policy to mix a considerable
quantity of limestone with some siliceous and igneous
rock, which though hard and tough does not consolidate
readily.

Gravel and Sand are not used in the construction of
stone roads as formed by Macadam and Telford, except as
an excellent foundation, for which purpose they possess a
very great value; and as a binding material, in small
quantities, they are sometimes spread over the road surface
between the layers of crushed stone. When used in this
latter connection, however, the gravel must be quite free
from round pebbles. Gravel is, however, used extensively
in the construction of what are termed gravel roads; where
there is no attempt at macadamizing the roads, but where
the gravel itself is spread uniformly over the surface of a
foundation road-bed which has been properly shaped and
drained. Gravel like that which occurs so abundantly in
many Northern States, where glaciers existed, is not found
in North Carolina. But river gravels are found in a num-
ber of our counties; and, as suggested above, in the middle
and western counties there are to be found in places decayed
siliceous granite and gneiss which, though not suited for
mixing with crushed stone in macadamizing roads, yet
will be found to serve a useful purpose as a foundation for
the broken stone on clay roads, and also as a top dressing
on clayey dirt roads.

DISTRIBUTION OF ROAD MATERIALS.

A line drawn from Gaston to Smithfield, Smithfield to
Cary, and from Cary to Wadesboro, separates the State into
two general and well-marked divisions, the eastern of
which may be called the Coastal Plain region, and the
western may be termed Piedmont and Mountain regions.

72 JOURNAL OF THE

In the Coastal Plain Region. — In the eastern counties,
except along the western border of this Coastal Plain
region at irregular intervals, we find none of the hard
crystalline rocks suitable for broken stone roads. Over
the larger part of the area we have sand, clays and loams,
the sands becoming coarser and more gravelly along the
western border and finer towards the eastern. At a num-
ber of points along some of the rivers and in some inter-
vening areas is to be found a limestone rock which will
serve a fairly good purpose in road-building.

Gravel. — The gravel along this western border can b^
used successfully in making a fairly good road-bed, and
should be used extensively where the hard crystalline rocks
cannot be obtained. It may be found at many places in
counties between the line mentioned above, extending from
Gaston to Wadesboro, and a line drawn to the east of this
from Franklin, Virginia, by way of Scotland Neck, Tar-
boro, LaGrange and Clinton, to Lumberton; and in a few
places also considerably to the east of this latter line. The
gravel is more generally distributed along the borders of
the river basins, where it occurs in extensive beds, a few
inches to twenty feet in thickness, though along the west-
ern edge of the Coastal Plain region it is often found on
the hill-toJDS and divides between the rivers.

In many places the gravel is suitable for use on the road-
bed just as it comes from the pit, containing pebbles of
the right size, from an inch down to a coarse sand, and a
small percentage of ferruginous clay, just enough to make
it pack well in the road-bed without preventing proper
drainage. In many cases, however, the proportion of clay
and loam and sand is too large and must be reduced by the
use of fine screens; and in other cases many of the pebbles
are so large that they must be separated by means of a
one-inch mesh screen, and those too large to pass through
this screen broken before thev are used.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 73

The railroads passing through this region long since dis-
covered the value of this gravel as a road material, and
have used it extensively as a ballast on their road-beds.
The small percentage of ferruginous clay soon cements the
gravel into a hard, compact mass.

Limestone. — In the south-eastern portion of this region
limestone rock and calcareous shells from the oyster and
from fossil mollusks from the marl beds constitute the only
hard materials to be found there for road construction. In
some places the limestone is fairly hard and compact, as at
Rocky Point, on the Northeast Cape Fear River, at Castle
Hayne and elsewhere, and this rock will make an excellent
road. In other places it is made up of a mass of shells
firmly cemented together, as on the Trent River, near
Newbern, and elsewhere. At many other points beds of
shells are so slightly cemented together that the material
may hardly be called a rock, as the term is ordinarily used,
and in this condition it is of less value as a road material,
but may be used for this purpose to advantage. x\ careful
search will show limestone of one of these grades to occur
in considerable quantities at many points in these eastern
counties, betw^een the Tar River and the South Carolina
line. The harder, the more compact, and finer grained
this rock, the more valuable it is as a road material; but
the loose shells from marl beds, when free from clay, and
the oyster-shells from the coast, when placed on a road
surface and ground into fine fragments by travel, will
solidify into a hard, compact road, as may be seen in the
case of the excellent ''shell road" between Wilmington
and Wrightsville, which was built of oyster-shells.

Clay and Sand. — The admixture of a small percentage
of clay or loam wnth the sand on the surface of the road-
bed wnll solidify it, and will thus very greatly improve the
character of the road; and in this connection, and only in
this connection, clay may be considered a useful road

74 JOURNAL OF THE

material. In whatever region the clay occurs in abun-
dance the road will be greatly improved by the proper
admixture of sand from an adjoining region, and by proper
drainage.

Granites and other Crystalline Rocks. — These are found
outcropping at intervals along the western border of the
Coastal Plain region, and wherever found accessible this
material should be used in the construction of roads.
Near the northern border of the State they are. found
exposed in considerable quantity; along the Roanoke River,
between Gaston and Weldon, in Northampton and Halifax
counties; near Whitaker's Station, at Rocky Mount, just
south of Wilson, and again a few miles north of Golds-
boro on the Wilmington & Weldon Railroad. Another
isolated and interesting occurrence of granite is near the
junction of Pitt, Wilson and Edgecombe counties, where
it is exposed over a tract of several acres. West of the
Wilmington & W>ldon Railroad, in the counties of Hali-
fax, Nash and Johnston, the streams have removed the
surface sands and clay in narrow strips along their borders,
and have exposed at intervals the crystalline rocks; and in
many places these rocks will be found to make good road
material. Further south-west, in Wake county, on the
Cape Fear River, and Upper Little River, in Harnett
county, and again along the banks of the Pee Dee River
and tributaries in Richmond and Anson counties, granitic
and slaty rocks occur in considerable quantities, the former
especially suitable for road material.

In considering the materials for good roads in the coun-
ties of this Coastal Plain reg^on it must also be borne in
mind that several large rivers connect this region with
ample sources of granite and other good road materials
which occur at the head of navigation on these streams
and can be cheaply transported on flats; and further, that
a number of railroads pass from the midland counties

ELISHA MITCHELL SCIENTIFIC SOCIETY. 75

where the supply is abunda-nt directly into and across the
Coastal Plain region.

Plank Roads. — As suggested above, in deep sandy regions
where timber is abundant the plank road may prove the
most economical good road that can be built for temporary
use, and some of them last six to ten years. But the great-
est objection to them lies in the fact that when the timbers
decay, whether this be at the end of four or ten years, the
road is orone; and the entire cost in labor and monev must
be repeated.

Ix THE MiDLAXD AXD PiEDMOXT CouxTiES. — Throughout
the midland and Piedmont counties of the State, w^est of
the Coastal Plain region, rocks suitable for road purposes
are abundant and widely distributed, so that no one can
claim as an excuse for bad roads that the materials are not
at hand for good roads. It will serve our present purpose
to discuss these in the order of their geographic distribu-
tion, with but little regard to their geologic relations.

Trap Rock in the Sandstone Areas. — As stated above,
sandstones possess very little value as road material, espe-
cially when broken into fragments, as is necessary in making
Macadam and Telford roads, but fortunately in this respect
the sandstones of North Carolina are quite limited in their
distribution. The larger of the two areas begins near
Oxford, in Granville county, and extends south-westward,
passing into South Carolina below Wadesboro. It has its
maximum width of about sixteen miles between Chapel
Hill and Cary, and its average width is less than ten miles.
It occupies the southern portion of Granville county, the
southern half of Durham, the western border of Wake, the
south-eastern border of Chatham, and portions of Moore,
Montgomery, x\nson and Richmond counties. The other
sandstone area is much more limited in extent.- It lies
mainly in Stokes and Rockingham counties, along the Dan
River, between Germantown and the Virginia line, a

76 JOURNAL OF THE

length of not more than thirty miles, and a maximum
width of not more than five miles.

Fortunately for the roads leading through these sand-
stone areas there is an abundance of a hard, black, tough,
fine-grained rock, known as diabase, or trap, occurring in
dykes which have broken through the sandstone and now
appear on the surface in lines of more or less rounded black
masses of rock running nearly north and south. These
dykes vary in width from a few feet to more than one hun-
dred feet, and are separated from one another by distances
varying from a few yards to two or three miles. A dozen
or more of these dykes are crossed by the wagon road
between Chapel Hill and Morrisville. Several dykes occur
at and near Durham, and the rock has been used upon
roads leading out from Durham, but unfortunately it has
not been crushed into small fragments, as should have been
done, and hence the result has not been altogether satis-
factory.

There is, probably, in both these sandstone areas a suf-
ficient amount of trap rock to properly macadamize every
prominent road that crosses them, and, after this has been
done, to furnish a top dressing for all public roads which
are likely to be macadamized in the adjacent counties.

Trap Rock in Other Areas. — Fortunately this excellent
road material is, in its occurrence, not limited to the sand-
stone regions. Dykes quite similar to tliose which abound
in the areas just described are also found extending across
the country in many of the midland and Piedmont coun-
ties, and also the region west of the Blue Ridge. Hereto-
fore this black, "nigger-head" rock, as it is frequently
called, has been regarded as a useless encumbrance of the
ground; now, in connection with the move for better roads,
it must be regarded as one of our most valuable rocks.
The city of Winston has already made extensive use of it
in macadamizintr its streets, with excellent results.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 77

77/e Eastern Granite Belts. — Granitic rocks are abun-
dant over considerable areas in the midland and Piedmont
counties, and especially in the former. One of these
important areas may be called, as a matter of convenience,
the Raleigh granite belt; which, in a general way, may be
described as enclosed by lines drawn from Gaston to Smith-
field, thence to a point midway between Raleigh and Gary,
and thence a little east of north to the Virginia line. This
belt occupies a considerable part of Wake, including the
region about Raleigh, of Franklin, and practically the
whole of Warren and Vance counties. The principal
rocks of this belt are light-colored gray, comparatively
fine-grained, granite and gneiss; on the whole a fairly good
material for road construction. The rocks vary in com-
position and in appearance at different localities, but are
fairly uniform in character over considerable areas. In
some places the black or biotite mica is largely wanting,
and the rock assumes a whitish feldspathic character; at
other points the mica becomes abundant, and the rock
assumes a dark gray color. In places the mica is so abun-
dant that the gneiss becomes somewhat schistose, or
laminated, and in this condition crushes easily, hence
should not be used on the roads. Dykes of trap rock are
occasionally met with, and these should be used in prefer-
ence to the gneiss and granite wherever accessible.

The somewhat isolated patches of granite lying east of
this belt in Halifax, Nash, Edgecombe and Wilson coun-
ties have already been referred to.

West of the Raleigh belt there is another granite area
of limited extent which occupies the extreme north-eastern
portion of Durham count}' and the larger part of Granville
county. This may be called the Oxford granite belt. The
rocks of this area resemble to some extent those of the
Raleigh belt, but there is a larger proportion of syenitic
and trap rocks, which make excellent road material.

yS JOURNAL OF THE

The Ce?itral Granite Belt. — This belt extends obliquely
across the State from near Roxboro, in Person county, to
the South Carolina line along the southern border of Meck-
lenburg. Its width varies from ten to thirty miles, and it
occupies a total area of about three thousand square miles
in the following counties: Western half of Person, including
the region about Roxboro; the south-eastern portion of
Caswell, the north-western half of Alamance, the larger
part of Guilford and Davidson, south-eastern portions of
Davie and Iredell, Lincoln and Gaston and the larger part
of Rowan, Cabarrus and Mecklenburg. In this belt
throughout its entire extent road material of most excellent
quality is abundant. The prevailing characteristic rocks
are syenite, dolerite (trap), greenstone, amphibolite, granite
and porphyry; and, as will be seen from this list, the tough
hornblende and augite rocks predominate. Dykes of trap
rock, some of them of considerable extent, are to be found
in almost every portion of the belt. So uniformly tough
and durable are these materials that one could hardly go
amiss in making selections for road construction.

The Central Slate Belt. — This region lies just east of the
central granite belt, and extends obliquely across the State
from Virginia to South Carolina. Its eastern border lies
against the Deep River sandstone basin described above
(p. 23). It varies from twenty to forty miles in width and
includes all or portions of the following counties: The east-
ern half of Person, the north-western part of Durham, the
south-eastern part of Alamance, nearly all of Orange,
Chatham, Randolph, Montgomery, Stanly and Union; the
eastern part of Davidson and Rowan, and the north-western
part of Anson. A considerable portion of this area is rich
in other mineral products, but the entire belt, as compared
with the central granite belt, is poor in road materials.
The rocks are mostly siliceous and clay slates, with a
considerable admixture of chloritic and hydromicaceous

ELISHA MITCHELL SCIENTIFIC SOCIETY. 79

schists; all of which are at best inferior for road construc-
tion. Here and there, however, trap dykes are found in
this belt; and in places the siliceous slates become some-
what massive, passing intohornstone and a quartzite, which,
when crushed, will answer fairh- well for macadamizino-
purposes. In other places the chloritic schists become
somewhat massive and tough and can be used in the same
way. In still other places, as about the State University,
and along the eastern border of Orange countv, the rock
is a fine-grained, tough syenite, accompanied by trap
dykes, and is eminently suited for road purposes; and again,
as near Hillsboro, granite occurs in a limited area. Vein
quartz ("white flint") is abundant in many parts of the
belt; and, though not usually recommended as road
material, is worthy of consideration. While, then, on the
whole the rocks of this belt are not suitable for use as road
material, yet a careful search will show the existence of a
sufficient quantity of material of .fair quality to macadam-
ize all the public roads. And should this supply ever
prove insufficient, excellent materials are to be found in
abundance in the granite belt along the western border of
this region, and in the trap dykes of the sandstone on the
eastern border.

The Gneisses and Other Rocks of the Piedmont Counties.
— West of the central granite belt as described above, and
extending back to the foot-hills of the Blue Ridge, is the
region occupied by the Piedmont counties — Rockingham,
Stokes, Forsyth, Yadkin, Surry, Wilkes, Davie, Iredell,
Alexander, Caldwell, Burke, McDowell, Rutherford, Polk,
Cleveland, Catawba, Lincoln and Gaston. The rocks of
this region resemble in many respects those of the Raleigh
granite belt. They consist of a succession of gneisses,
schists and slates, more hornblendic toward the east and
more micaceous toward the west, with here and there
masses and dykes of syenite, trap and other eruptive rocks.

8o JOURNAL OF THE

In places, avS at Mount Airy, tlie true ^ranite occurs in con-
siderable abundance. The granites and gneisses, except
where the latter tend to split into thin layers and crush,
are fairly good materials for road construction, improving
as they become finer in grain and as the percentage of horn-
blende increases; but the best material for road construc-
tion is to be found in the trap dykes and syenite ledges
which at intervals traverse this region, more especialh- its
eastern half.

The Gneisses and Other Rocks of the Mountain Counties.
— The rocks of this re^rion are not greatlv unlike those of
the Piedmont counties just described. Over much the
larger part of the area rock fairly well adapted to road con-
struction is abundant, indeed so abundant that the laborers
on the public roads in that region during the past half
century have expended the larger part of their time and
energy in endeavoring to get this rock out of the way.
Had they expended this time and energy in crushing the
rock and spreading it over a well-formed foundation, this
region would possess at the present tiuie a number of
excellent macadamized highways.

In the more northern counties — Alleghany, Ashe and
Watauga — the predominating rocks are hornblende gneiss
and slate, but massive syenites are abundant, especially
between Rich mountain in Watauga and Negro mountain
in Ashe county, and elsewhere. Further south-west, through
Mitchell, Yancey, Madison and Buncombe counties, horn-
blende schists still continue, but they are more massive,
and the gneisses predominate. These are, on the whole,
compact and sufficiently tough for use in the construction
of good Macadam roads. Aud the statement just made
concer;iing these counties is also applicable to Henderson,
Transylvania and Haywood counties, and in a measure to
Jackson, Swain and Macon counties and the eastern half
of Clay count)-, in all of whicli the supph' of good road

ELISHA MITCHELL SCIENTIFIC SOCIETY. 8l

material is ample; but in these last three counties mica
schist partially replaces the hornblende slate. In the west-
ern part of Swain, in Graham, Cherokee and the western
part of Clay county good road material is not so abundant
as in the other counties named, but nevertheless is to be
found in considerable quantities. The rocks over a con-
siderable portion of this last-named area are micaceous and
hydromicaceous in character, and are practically worthless
for the purposes of road-building, but the quartzite ledges
and beds of limestone in these counties will furnish ample
and suitable material.

In conclusion, it may be said that in the middle and
western counties of North Carolina material suitable for
macadamizing the public highways is abundant and
generally accessible. It will be the exception, rather than
the rule, that this material will have to be transported for
any considerable distance. In the eastern counties materials
suitable for this purpose are inferior in quality and only
moderately abundant in quantity, but the extensive and
intelligent use of even these materials would very greatly
improve the public roads and thereby increase the pros-
perity of the* people. And in many places where the
Macadam road is at present out of the question on account
of the lack of stone, other materials, gravel, clay, loam
and plank will be found in sufficient abundance to make
the construction of better roads practicable at reasonable
cost.

82

JOURNAL OF THE

TO SET SLOPE STAKES WHEN THE SURFACE
IS STEEP RUT SLOPES UNIFORMLY.

BY J. M. BANDY.

Let mn represent the surface of the ground. Let C repre-
sent the position of the centre peg, and let CD (=<?, the

value of which is
found from the level
notes) represent the
centre cut. The
width of the road,
BA, is b.

It is proposed to
find what engineers
designate as cuts at P, P\ S, and T.

In the direction of P, and in connection with C, one
setting of the rod determines the slope of the ground mn.
Call this slope in. Now, since the cds. of C are (^;, a), the
equation of the surface, ;;/;/, is

y = mx -T a^ (i).

The quality of the soil determines the slopes of PA P^B.
Call this slope ;;/\
equation of PA is

Then since the cds. of A are (^, o), the

m'b

y

(2).

Combining (i) and (2),. the cds. of P are known. Hence
the cut at this point is known.

Designating the cds. of P, just found, by (.1-", y^) and
the cds. of C by {x\ y^) \_=[o, a\\

CP = ^(.r^^ - x^)' + (j" -yj, (3).

Then measure this distance, CP, and fix stake at P.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 83

The equation of SA is

h

2

Substituting this value in (i), the cut S is at once
obtained. Denoting the cds. of S by (.r^\ j'^^) and the cds.
of C by (^\ y), and substituting in (3), CS is known.
Measure tWs distance, and fix stake at S.

The same course of reasoning applies in finding the cuts
at P^ and T.

The writer has found this method more expeditious than
trial and error when the surface was much inclined. The
nuinerical computations did not require as much labor as
manceuvering with the rod and level.

Since he has not seen the above method in any of the
books which have fallen under his eyes, he has been
induced to give it in the hope that it might prove useful,
as well as suggestive, to others under similar circumstances.

Trinity College. N. C.

ON THE DEVELOPMEXT AXD A SUPPOSED NEW
METHOD OF REPRODUCTION IN THE SUN-AN-
IMALCULE, ACTINOSPH.ERIUM EICHHORNIL*

BY JOHN M. STEDMAN.

Early in March my attention was called to an aquarium
which had been standing in my window during the winter,
and which contained anacharas and algae in great abundance,
but which now suddenly presented a quantity of light pink
substance on the sides of the jar. It was the appearance of
this pink-colored material among the debris of decaying
and growing algse that attracted my attention. Accord-

Atner. Soc. Microscopists, i8S8.

84 • JOURNAL OF THE

ingly a small piece- of the substance was spread out on a
slide and examined, when, to my surprise, it was found to
be composed of snn-animalculse of various sizes, among
which were other bodies, the true nature of which I did not
at first quite understand, but which on close examination
proved to be the young of the larger heliazoa. So numer-
ous, indeed, were the young heliazoa that not a single field
of the one-fifth objective and a ocular could be chosen in
which there were less than half a dozen, and usually the
number was very much greater.

Such an unusually great and rare opportunity to study
these animals could not be neglected. Fortunately they
were discovered in the morning, and by close and constant
observation for several hours their true relations to the
numerous small bodies were satisfactorily demonstrated and
proven to be different stages of the same animal.

For a description of A. Eichoniii and of its habits see
"Fresh-water Rhizopods of North America," by J. Leidy, p.
259. Plate XLI.

We will pass at once to the special subject in hand,
beginning, for convenience, with the simplest or youngest
heliazoan.

Development. — Let it not be understood that the order
in which I am now to describe the different stages of devel-
opment is the order in which I observed them. On the
contrary, what I shall first describe really came about last
in my observations, since I did not at first take the young-
est stages of this heliazoan to have any connection with
the larger heliazoa. My observations began with an
undoubted heliazoan of this species (Fig 13 of my plate),
and from that I worked both ways, but principally to the
younger. It would have been impracticable to have
watched the development of a single heliazoan from the
very youngest individual to the full-grown animal, since it
would have required not only a constant observation for a

ELISHA MITCHELL SCIENTIFIC SOCIETY. 85

much longer time than I conld spare, but would also have
needed some little care. As it was, I could watch a young
heliazoan until it had developed a few stages, and had con-
siderably lessened the near supply of food, and then I could
find another heliazoan of the same stage as the one just
discarded, but which was in more favorable circumstances
for further growth. As indicated, the number of heliazoa
was enormous, and the different stages were represented by
the score. Had I suspected these various stages to have
been wdiat they were, there would have been no trouble in
finding a complete set, for every gradation from the young-
est to the adult was present in great quantities. Fortu-
nately there were quite a number of worms — Dorylaimus
stagnalis — in the water, and their constant wriggling about
kept the heliazoa and other animals in perpetual motion,
so that they came in contact with one another, where other-
wise they would not have done so.

A far greater number of observations were made than I
shall here describe. Enough were chosen, however, to form
a complete series, and accurate drawings made of them. I
shall, therefore, describe only those observations which I
have illustrated, hoping that the series will be full enough
for our purpose.

I think it is safe to say that were this minute mass of
protoplasm which constitutes the youngest heliazoan
observed by itself for a little while, no one would mistrust,
its true nature or relations. Indeed it was only after a
long and continued observation, and that under the most
favorable circumstances, that I became convinced of its
true nature. It is nothing but a minute spherical mass of
finel\- granular and hyaline protoplasm, 14.5 21 in diameter,
with a contained nucleus and a distinct nucleolus (Fig. i).
In appearance it resembles white blood corpuscles with a
distinct and sharply defined nucleus. Later, however, a
vacuole appears in its substance, and, increasing in size.

86 JOURNAL OF THE

often becomes larger tlian the original mass of protoplasm,
so that the latter forms bnt a thin layer snrrounding it
(Figs. 2, i6, 12). In this stage a psendopodenm or ray
may be presented (Fig. 12).

Two heliazoa of the first stage were seen to come to-
gether, which, however, as in nearly all cases, was due to
the agitation of the water by the worms, and immediately
upon touching one another (Fig. 23), to fuse and run
together just as a drop of water fuses with another drop of
water. It is impossible to say which of the two was
devoured; both appeared to play an equal part, the vacuole
and nucleus of both being present, and the whole im-
mediately assuming a spherical form and appearing (Fig 3)
much like any one of the two of which it is now composed,
except that it has two vacuoles and two nuclei. In the
course of five minutes this young, two-vacuoled, heliazoan
had developed a ray, and in its interior the characteristic
axis thread could be distinctly seen (Fig. 20). The absence
or the number of rays when present in the young heliazoa
is of no special value, and varies with different individuals
of the same age, as will be seen from the figures.

Whether this fusion of two individuals of the same spe-
cies be called eating or not does not concern us, and I shall
not attempt to discuss the subject here. As a matter of fact,
however, it is not conjugation for purposes of reproduction
.or rejuvenescence, as will be seen later; and, since we have
these animals developing by this method of increase as well
as by that of an undoubted eating of other animals, it
matters not, so far as development is concerned, whether
they appropriate material so near like that of their own
bodies that it needs no change to form a part of them, or
whether the food be different and hence have to be changed
or digested before it can be so appropriated. I have ob-
served farther advanced heliazoa capture infusoria and
amoeba and surround them, and draw them into their

ELISHA MITCHELL SCIENTIFIC SOCIETY. 87

interior, where they remained to be digested; and at the
same time I have observed those same heliazoa capture
other heliazoa, and instead of drawing them into their in-
terior and surrounding them as they, did other bodies, they
would draw them in until the two heliazoa touched, when
there occurred a fusing and blending of the two animals
into one just so much larger. My only explanation is that,
as indicated, the protoplasm of the two animals is exactly
alike and hence there can be no need of digestion. Were
one of the heliazoa dead when it came in contact with
another which would otherwise have fused with it, I have
no doubt but that the dead heliazoan would be surrounded
and drawn into the interior of the live one the same as
other animals are and there digested, it being not exactly
like the protoplasm of the one which is alive. For if this
were not the case, if the dead heliazoan upon contact with
the living heliazoan were to form a part of it as the
living heliazoan did, then we should have a case where
simple contact of the living protoplasm with the same but
dead protoplasm would impart life to the dead, just as a
piece of iron which is magnetized, if brought in contact
with one which is not, will impart magnetism to it. But
it is needless to say that sucli a phenomenon of life has
never been observed.

While watching the heliazoan (Fig. 3, 20) which we
have just described as being the result of the union of two
of the youngest individuals (Fig. 2, 23), the water was
stirred by a worm, and another heliazoan, of about the same
size as the one under observation, but with three vacuoles
and no rays, was brought nearer and nearer until finally
they accidentally came in contact with one another and
immediately united (Fig. 20) and assumed a spherical form.
Presently the single ray disappeared and three more vacu-
oles made their appearance in the mass of protoplasm
together with the development of a contractile vesicle

88 JOURNAL OF THE

(Fig. 5). This individual was watched until it had
developed three rays and several more vacuoles (Fig. 6), a
process requiring about twenty-five minutes, during which
time it had eaten nothing except one of the youngest
heliazoa without a vacuole. Under the one-twelfth oil
emersion I was able to detect the axis cylinder in two of
the rays, but not without sqme doubt in the third ray.

Very near this individual (Fig. 6, 26) was another helia-
zoan of a much greater size (Fig. 25), and by touching the
cover-glass with a needle I soon brought the two so near
that the tip of one of the rays of the smaller heliazoan
touched the larger animal. Wishing to observe the result
of this contact I waited a few minutes, when it became
apparent, that the smaller individual was drawing in its
ray, which was in contact with the larger heliazon, and
was thus drawing itself towards it. The larger animal,
offering the greater resistance, did not appear to move.
Five minutes from the time the ray first touched the other
heliazoan the two had come in contact, whereupon a union
occurred and immediately the two blended into one. The
smaller animal appeared to flow into the larger and to dis-
perse itself through it in a manner which is common to
all these animals, young as well as full-grown, and which
will be described later when we reach a nearly mature
heliazoan. Before the union of these two animals they
appeared alike except in size and number of vacuoles, but
shortly after the union the granules in the protoplasm
gradually moved towards the center of the animal, where
they became more numerous, and instead of being evenly
distributed throughout the granular protoplasm now formed
a central, more granular portion with an outer, clearer,
and less granular zone. Three more rays were also
developed, and the animal presented the appearance shown
in figure 7, which, at this stage, would probably not be
mistaken for any other species. Hundreds of individuals

ELISHA MITCHELL SCIENTIFIC SOCIETY. 89

were to be found of this size and appearance, and hence it
was not necessary to watch the development of this sino^le
individual longer, as other fields promised better results.

There was almost an unlimited supph' of heliazoa inter-
mediate in size between the two whose union produced the
one just mentioned. They differed in no respect from one
another or from the two just mentioned, except a slight
difference in size, and every gradation between them was
to be found. Merely for the sake of filling up the gap
which exists in regard to size between the two individuals
whose union we just referred to, I will cite one example
out of many which I have observed. Two similar indi-
viduals, slightly larger than the smaller (Fig. 26) of the
two just united were seen to come together (Fig. 22), and,
as a result of their union, a heliazoan was produced so nearly
like the larger (Fig. 25) of the two of the former indi-
viduals, that there was practically no difference between
them.

Another field was now chosen in which were a number
of heliazoa, similar in all respects to the one representing
our last stage (Fig. 7). I had not waited long before it was
evndent that two of these animals were gradually approach-
ing one another from some cause which I was unable to
discover. When wnthin a very short distance, in fact,
almost ready to meet, there occurred a very singular move-
ment on the part of both individuals — a movement w^hich
I can hardly account for — in which there was produced a
swelling, as it were, in that part of the sphere of both
animals (Fig. 8, 9) which was just about to touch the
other, and by continued enlarging with increased rapidity
soon met one another, thus uniting the two individuals
much more quickly than they otherwise would have done.
Immediately upon touching one another the at first narrow
neck uniting them rapidly enlarged (Fig. 10), the proto-
plasm of the one flowing into the other and vice versa until

90 JOURNAL OF THE

the two animals had united into an oblong-shaped mass.
The flowing of the protoplasm from one to the other was
a most interesting sight, and could be distinctly seen,
owing to the numerous granules which it contained. Both
animals played an equal part in the union; a current of
protoplasm could be seen streaming from the first into the
second, and near it another current from the second into
the first. There were as many currents as there were
threads of denser protoplasm uniting them. Like all the
observed cases the denser and more granular portions of
the protoplasm separating the vacuoles from one another
never mixed with anything but the corresponding proto-
plasm of the individual with which it united; hence there
was no destruction of vacuoles, but merely an addition
or union, and, moreover, the peripheral layer of vacuoles
always remained on the periphery, while the central mass
of vacuoles flowed to the center of the united mass. The
heliazoan now gradually changed from the oblong or ellip-
soid shape to that of a sphere (Fig. ii), and here I left it
to seek other fields.

A nearly identical individual to the one just mentioned
was found and seen to capture by one of its rays another
but smaller heliazoan. As a result of a movement of
the water the smaller individual chanced to come in con-
tact with the tip of a ray of the larger animal and there to
unite with it, whereupon the larger heliazoan gradually
drew in its ray and the smaller creature with it. It was an
interesting sight to see this process. The ray seemed
rather to flow into the spherical mass or body of the animal,
since a stream of protoplasm was rapidly and constantly
flowing down its center into the animal, and the smaller
heliazoan was likewise flowing into the larger by this
means; but, nevertheless, the ray grew shorter and shorter
until finally the heliazoa came in contact (Fig. 13), and
then a union took place similar to the one described above,

ELISHA MITCHELL SCIENTIFIC SOCIETY. 91

except that here the flow of protoplasm appeared to be
solely from the smaller to the larger animal. Before the
animal had become entirely spherical, the denser inner
portions of the smaller heliazoan had united with that of
the larger and appeared as a swelling upon it, while the
peripheral zones of both animals had united. This ap-
peared to be such a good example of the mode of union of
the protoplasm of tw^o heliazoa that I figure it (Fig. 15).

I have observed a number of large helrazoa capture the
youngest individuals, and in all cases as soon as the young
animal touched the ray of the larger it appeared, so to
speak, to form a part of it, and would sometimes assume
an oval form and remain on the ray, looking exactly like
the little knobs of protoplasm which are frequently seen
there, except that it would be larger; and then again I
have seen them flow down the center of the ray, while the
ray itself suffered no appreciable change. In one instance,
however, which came under my observation, a moderate
sized heliazoan (Fig. 17) captured by the tip of its ray one
of the youngest individuals (Fig. 16), and while watching
to see what would happen to this young one, the ray of a
large heliazoan (Fig. 18) came in contact with the larger
of the former animals. Out of curiosity merely I watched
to see the result of this extraordinary union, and found
that the largest heliazoan drew its captured brother to itself
and united with it before the smallest individual had
touched the body of the one to which it w^as attached; the
smallest heliazoan then appeared to be fastened to a ray of
the largest animal, which, however, soon drew^ it to itself
and the two united.

Quite a different process from the one we have been dis-
cussing occurs when the heliazoan encounters food con-
sisting of other animals or plants. I have no doubt but
that the youngest heliazoan, as well as those of all stages,
are able to and generally do develope and reach maturity by

92 JOURNAL OF THE

the use of no food other than that of other animals and
plants; but there is also no doubt that this is a process re-
quiring considerable time as compared with that which
occurs when they chance to meet with their own kind,
since in the former case the food has to be digested, while
in the latter it has not. It was my good fortune to find a
large heliazoan which had just captured an infusorium and
partially surrounded it. In a few minutes the infusorium
was completely enclosed, a clear space remaining around
it, however, and gradually it was moved near the center of
the animal, where it could be seen slowly moving its cilia
in the little water which immediately surrounded it and
which separated it from the protoplasm of the heliazoan
(Fig. 19, 21). Presently an amoeba came in contact with
the heliazoan and appeared to stick to it more or less and
to constantly try to move away from it. The heliazoan
made several efforts to surround it, but the amoeba in every
case moved out before being fairly imbedded, and finally,
after several minutes of hard struggling to ascertain which
was to be victorious, the amoeba escaped. It was but a short
time, however, before another amoeba chanced to touch
the heliazoan, and this time with better success to the
heliazoan. The amoeba, as soon as it touched the helia-
zoan, spread out a little on it, and at the same time the
protoplasm of the heliazoan began to flow around and to
enclose the amoeba, which now made several efforts to
escape, but in vain, for within a few minutes a fine film of
protoplasm had surrounded it, and the amoeba was within
the heliazoan (Fig 19). A quantity of water was also en-
closed with the amoeba, and in this it exhibited consider-
able activity, even after it had been carried nearh" to the
center of the heliazoan (Fig. 21). It was not long, how-
ever, before the amoeba had assumed a globular form and
become motionless. I mention this instance in which the
heliazoa eat other animals merely to bring out the strik-

ELISHA MITCHELL SCIENTIFIC SOCIETY. 93

ing difference between the process and that observed when
they eat their own species.

Dr. Joseph Leidy* speaks of having found several glob-
ules of granular protoplasm with vacuoles and rays, and
alludes to their probable connection with this species of
heliazoa. I have reproduced in figure 24 one of his figures
of these bodies, and think that there is every reason to
believe that they are what he suspected them to be.

Reproduction. — It is not uncommon to find heliazoa in
the process of reproduction by fission; in fact, if heliazoa be
kept for any considerable length of time they are almost
certain to be found in the act of reproducing by this means.
I have observed them divide by keeping them in a watch-
glass under the microscope, and in one instance I watched
uninterruptedly the process, from an oral heliazoan before
the constriction began to appear, up to the division and
entire separation into two animals. A complete set of
drawings was made to illustrate the different steps, and I
find by referring to my notes that one of the drawings is
almost identical with figure 10, which represents the helia-
zoan in the process of union.

As regards reproduction in the heliazoa outside of the
well-known process of fission, all I can say is from a philo-
sophical stand-point, as no direct observations have been
made outside that of the finding of the young. But the
presence of young has got to be explained in some way.
From Dr. Leidy's "Fresh-water Rhizopods," p. 260, I find
that "according to Stein, Carter and other authorities, A.
Eichhornii contains many nuclei, large individuals having
a hundred or more." Whether this has any connection
with the heliazoan's having devoured individuals of its
own species and thus to have retained their nuclei, and so,
by continually adding to the number every time it captured

Fresh-water Rhizopods of North America," page 262-3.

94 JOURNAL OF THE

another heliazoan, to have finally attained the number of
one hundred, or whether it is connected with the process
of reproduction, I cannot say. It seems to me very proba-
ble that, in the fall at least, the full-grown heliazoan
becomes encysted, and that its protoplasm then divides and
subdivides, until it is converted into a mass of minute
bodies, which, when the cyst is ruptured, make their
escape into the surrounding water, and then appear as naked,
spherical masses of granular protoplasm with a nucleus.
It may be that the minute bodies acquire a covering before
they escape from the mother cyst, and that they then act
as spores, and are carried about and developed similar to
the spores of infusoria.

Of course this mode of development has never been ob-
served in the heliazoan, but it seems to me to be very
probable that it does occur, judging from the observed
young individuals, and from the fact that it occurs in
certain infusoria.

EXPLANATION OF PLATE.

All the figures were drawn from life except Fig. 24, which
is a reproduction of a figure from Dr. Leidy's work on the
Rhizopods. Fig. i, which is a heWsLzoau, Ac/z7wsp/taerm?fi
Eichhornii^ of the very youngest stage, is in nature 14.5 it
in diameter. The other figures are drawn with the same
magnification as Fig. i, and hence they all bear the same
relative size in nature as is here represented, excepting
Figs. 25 and 26, which are a little too small. I take it to
be of much more value to the reader to have the figures
drawn so as to preserve their relative size, and then to
know the natural size of one of them, than it is to have
the figures of various magnifications and know the mag-
nification of each separate figure. I do not wish it under-
stood that the figure taken from Leidy is relatively of the
same size as the other figures.

Trinity College, N. C.

'J

\ ^ /

v^^

/ /

m

\

./'^il?

:i/

^c^ Stedma.n,. Del.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 95

SOME FUXGI OF BLOWING ROCK, X. C.

BY GEORGE F. ATKINSON AND HERMANN SCHRENK.

During the month of August for the summers of 1888
and 1889 it was the good fortune of the senior author of
this paper to spend tliat time in the enjoyment of the
invigorating atmosphere and famous scenic beauty of this
point in the Western North Carolina mountains.

To the greater number of tlie readers of this Journal
Blowing Rock is not unknown. It ma\' be a matter of
interest to others to know that this now fast becoming
popular summer resort is found in Watauga count)-, and is
reached by "staging if twenty miles up the mountain
from a point, Lenoir, the northern terminus of the Ches-
ter & Lenoir Narrow Gauge Railroad, wdiich connects with
the main line of travel from the east and west at Hickory,
on the Western North Carolina Railroad.*

Even a botanist can cherish commendable curiosity, on
his first trip to the place, concerning its '' entitlements^
Upon reaching the summit near the village one is sped
through an unpretentious drive of nearly one mile when
the road curves to evade a steep hill. Here is suddenly
presented to view the grand panorama of the great John's
River valley below and the lofty peaks of the Black Moun-
tains be\ond.

When one has become disengaged from travelling para-
phernalia, and when rest and refreshments have dispelled
fatigue, there comes an irresistible desire to join others in
the pilgrimage to the ''Rock." Once there the meaning
of ''Blowing Rock" becomes apparent. The rock juts
out upon the west side of the cliff, forming a bold precipice at
the north-east of the John's River valley. The currents of
6

96 JOURNAL OF THE

air from the farther end of the valley convercre as the\' rise
at this point, favored by the cliffs at the north and east, and
on an otherwise calm day qnite a strong" breeze ^' blows"
over the rock. Throw yonr hat, walking-stick, or what-
not over the precipice and the wind brings them back to
yon. Legend has it that a despairing lover once leaped
from the side of the fair one over the rock and the crnel
winds picked him np and bronght him back to her feet! It
is proper to say, however, that when the writer visited the
spot the winds did not seem to be '\getting in their work"
properly and there was no inclination to jnmp.

Bnt legends and levity both aside. Blowing Rock is
prodigal with flowers and 'Mnnshrooms. " To one who
visits the place in Jnne the profnsion of thickets painted
with RJiododc 11 (irons and Kaluiias are a ''jo}- forever."
Later in the season "Black-eyed Snsans " wink at yon here
and there, and varions species of interesting Orchids are
freqnently met with. Eiipatoriuuis and other vigorous
growers vie with each other in their effort to hide the fences
which line the roads or cross the fields.

The great prodigality of the fleshy fungi tempted the
writer, during portions of two short months, to form the
beginning of a closer acquaintance with the Hynueiioiny-
cetes than had been gained from a general study of struc-
ture and relationships. Accordingly collections were made
of fungi chiefly in this group. Not wishing to be
encumbered with books, no efforts were made at the time
to identify the specimens. A few notes were taken on the
more evanescent characters, the specimens were then dried
and preserved for future determination.

The greater number of the Hyiuoiouiycetes were after-
ward determined b}' Mr. A. P. Morgan. Dried agarics are
very difficult of determination and it is a matter of some
interest that more than half of the .loaiicacccc were in a
recognizable condition, thouj^h some <;ienera like Cortina-
rius were complete failure:

'S.

ELISHA MITCHELL SCIENTIFIC SOCIETY. 97

One point of interest in making the collections was the
observation that quite circumscribed areas for several days
in succession would yield fresh and abundant specimens of
the same species. Near Fair View and Sunset Rock Boletus
americaniis was • abundant both seasons. A trip down
the damp slopes of Glen Burney was almost sure to be
rewarded by gorgeous TJieleplioras. Parth- down the
John's R.iver valley road, in rather open woods, several
species o{ Hydnuni would always insist on over loading one's
basket. That lovely plant, Mitreinyces lutesceiis Schwein.,
cropped out continuall\- along certain of the shad\' cla}-
road banks dripping with water. From the same situations
where there was less water, clamnn' Amanitas lifted their
heads. One point on the Valley Crucis road yielded Stro-
biloiuvces strobilaceiis. Wonder Land produced monster
clusters of Clitocybe illiidens. At one time I could have
picked more than a bushel without moving from the spot.
This plant is remarkably phosphorescent, the phosphores-
cence being confined to the InineniuuL Sometimes this
plant is taken to the hotels, and at night the guests amuse
themselves delineating various figures in the dark with the
aid of this ' ' fox-fire ' ' mushroom. Another phosphorescent
plant, Paniis stipticiis^ is common upon dead stumps, etc.
Close by the roadside at Wonder Land, also, Cyclomyccs
greenii was found. In an open field east of the Morris pas-
ture the parasol, Lepiota procera, grew in abundance, and
here and there the Ox-tongue, or beef-steak fungus, Fistii-
lina hepatica^ offered its juic}- meat. Lactarii were ever>'-
where and so the daint\- Marasniii. Marasinius capillaris
was taken, just a bit of it, from "Flat Top." Bulgaria
iuquinans, SpatJiularia vclutipes^ Leotias, were ver}- com-
mon. The Geoglossiinis were rareh' seen. Geoglossiim
Walteri was collected by ]\Iiss Etta Schafifner down in the
John's River valley near the foot of Fair View. Down in
the far depths of this valley was a profusion of the maiden's
hair fern, Adiantiim capillis-vcneris.

9^ JOURNAL OF THE

The junior author, Mr. Schrenk, a student in botany in
ni}' laboratory, has rendered valuable service in making out
the list presented below and in a careful examination of
the specimens for the purpose of verification of the identi-
fications, in order to lessen the chances of error. This has
occasioned no inconsiderable labor on his part.

In the arrangement of the list the system presented in
Saccardo's Sylloge has been mainly followed. No effort
has been made at changes in nomenclature, since it did not
seem to be called for in a bare list of no more than 254
species.

The Saccharouiyces pyriforniis and Baclerhim vertni-
forijie'^ were symbiotic organisms composing small amber-
colored grains termed ^'moss seed," "California beer
seed," used by some of the mountain people in brewing a
beer by placing the grains in water sweetened by molasses.
The grains were given me by Dr. Carter, a resident phy-
sician.

ORDER HYMENOMYCETE.'E.

FAMILY AGARICACE.^.

1. Amanita ccesarea Scop.

2. A. niuscaria Linn.

3. A. pantJierina DC.

4. A. phalloides Fr.

5. A. real tit a Fr.

6. A. soli t aria Bull.

7. A. veruus Fr.

8. Ainanitopsis vaginata (Bull.) Roz.

9. A. volvata (Pk.) Sacc.

*See Ward. The " Giiiger-beer plant," and the organisms composing it: a contribu-
tion to the study of fermentations— yeasts and bacteria. Proceedings of the Royal
Society. Vol. 50, pp. 261, 265.

ELISHA MITCHELL SCIENTIFIC SOCIETY, 99

10. Lepiota cristata Alb. et Schwein.

11. L. procera Scop.

12. Anuillaria niellea Valil.

13. Tricholoina fiih'elliim Fr.

14. T. portcntosiim Fr.

15. T. saponacenni Fr.

16. Clytocybe cyathiformis Fr.

17. C. illudens Schwein.

18. C. infiiJidibiiliformis Schaeff.

19. C. laccata Scop.

20. Colly hi a conflueiis Pers.

21. C. radicata Relli.

2 2. Mycena corticola Schuin.

23. M. galcriculata Scop.

24. M. mucor Batsch.

25. M. stipularis Fr,

26. O mpha Ha fibula ^\\\\.

27. (9. scabriiiscula Pk.

28. Pleurotits applicatiis Batsch.

29. Hygrophonis cantherelhis Schwein.

30. Lac tar ins albidiis Pk.

31. L. chrysorrJiens Fr.

32. Z. cilicioides Fr.

33. Z. cinereiis Pk.

34. Z. corriigis Pk.

35. Z. fiiliginosiis Fr.

36. A. helviis Fr.

37. Z. liysgimis Fr.

38. A, insulsus Fr.

39. Z, lignyotus Fr.

40. Z. pergamenus (Swartz) Fr,

41. Z. piper at us (Scop.) Fr.

42. Z. pyrogallus (Bull. ) Fr,

43. Z. rufesceus ]\Iorg,

44. Z. r/(/}/j (Scop.) Fr.

45. Z. subdulcis (Bull.) Fr.

lOO JOL'KXAL OF THE

46. L. siibtoiiiciitosns B. et Rav.

47. L. siihpurpurcHS Pk.

48. L. theiogaliis {V>\\\\.)V\-.
49. -A, torminosiis (Scliseff. ) Fr.

50. L. vol cm us Fr.

51. Riissitla /itrcaia (P^r^.) Fr.

52. CanlJicrcIlus aiirautiacus Fr.

53. C. cibarius Fr.

54. C. cincreus Fr.

55. C. Jioccosu s S c 1 iwe i 11 .

56. C. infiindilmlifoniiis (Scop.) Fr,

57. C. mi no?- Pk.

58. C. princeps B. et C.

59. C. zvrightii B. et C.

60. Marasmhis anomalus Pk.

61. M. archyropus (Pers.) Fr.

62. M. capillaris Morg.

63. J/, ferrugineus Berk.

64. .'!/. melanopus Morg.

65. M. pleclophylhis Mont.

66. /]/. prceacutiis Ellis.

67. .^. r^/^//.v B. et Br.

68. M. salignus Pk.

69. M. viticola B. et C.

70. Lentiuus Iccomtei Fr.

71. A. lepidciis Fr.

72. A. strigosus Fr.

73. /^<7////^- stipticus (Bull.) Fr.

74. Lenziies belulina (Linn.) Fr.

75. Z,. cookei Berk.

76. /-. cratcegi Berk.

77. Pholiota squarrosoidcs Pk.

78. Crcpidotus fulvo-toinenlosits Pk.

79. Pax i lilts Jiavidus Berk.

80. Agaricus cam pester Linn.

ELISHA MITCHELL SCIENTIFIC SOCIETY. lOI

F A:\IILY POLYPORACE-E.

8 1. Boletus aniericaiius Pk.

82. B. auriporns Pk.

83. B. badius Fr.

84. B. castaiieus Bull.

85. B. chryseuleroii Fr.

86. B. collinitus Fr.

87. B. felleus Bull.

88. B. Jiavidus Fr.

89. B. gracilis Pk.

90. B. graniilatus Linn.

91. B. leprosus Pk.

92. B. piirpui'cus Fr.

93. B. rave ne I a B. et C.

94. B. retipes B. et C.

95. B. speciosus Frost.

96. B. siihtoinentosits Linn.

97. B. variegatits Swartz.

98. Strobilomyces strobilaceus (Scop.) Berk.

99. Bolelinus decipiens (B. et C. ) Pk.
TOO. Fistnliiia Jiepatica Fr.

loi. Polyporus borealis (Wahlenb. ) Fr.

102. P. dichroiis Fr.

103. P. elegans (Bull. ) Fr.

104. P. elegans var nunimnlarius (Fr. ) Sacc.

105. P. epileiLCus Fr.

106. P. flavo-virens B. et Rav.

107. P, fiiDiosus (Pers. ) Fr.

108. P. hirsutiilus Schwein.

109. P. nivosiis Berk.

no. P. siLlphureus (Bull.) Fr.

111. Fomes applanatus (Pers.) Wallr.

112. F. earners yiees.

113. F an'/isii B^rk.

I02 JOURNAL OF THE

114. F. fiiliginosiis Fr.

115. F. salicinus (Pers.) Fr.

116. Polystictiis abietiniis Fr.

117. P. circinatus Vx.

118. P, dccipiens ^qSa^^Wl.

119. F\ Iiilcscens V^rs.

120. P. niontagnci Vx.

121. P. parvuliis Klotzsch.
12 2. P. pcrganienus Fr.

123. P. perennis (Linn.) Fr.

124. P. sanguineus (Linn.) Me)-.

125. P. toiucntosus Fr.

126. P. versicolor (Linn.) Fr.

127. Cyclomyces green ii Berk.

128. Favolus canadensis Klotzsch.

129. F. tessellatus Mont.

FAMILY HYDNACE.^.

30. Hvdnuui auran/iacuni Alb. et Schwein.

31. //. adustuni Schwein.

32. H. candidum Schmidt.

33. H. fragile Fr.

34. H. glabrescens B. et Rav.

35. H. gracile Fr.

36. H. graveolens Delast.
2)^1. H. levigatum Swartz.

38. //. pulcJierriniuni B. et C.

39. H. repandum Linn.

40. H. rufescens Pers.

41. //. squamosum Schaeff.

42. //. 30)iatum Batsch.

43. H. velutinum Fr.

44. Tremellodon gelatinosum (Scop.) Pers.

45. Raduium pallidum B. et C.

ELISHA MITCHELL SCIENTIFIC SOCIETY.

103

146

148
149

160
161
162

163

FAMILY THELEPHORE-^.

Craterellus cantherelhis (Schwein.) Fr.

C. cormicopioides (Linn.) Pers.

C. odor a tits Schwein.

Tlieh'pliora anthocepJiala Fr.

T. ccpspitulans Schwein.

T. cladojiia Schwein.

T. dissecta Lev.

T. schiveimtzii Pk.

T. sebacea Pers.

T. spectabilis Lev.

Siereitm frttshilosum (Pers.) Fr.

.S". spa dice inu Fr.

^. subpileatiini B. et C.

S. versicolor (Swartz) Fr.

Hymennchcete riibiginosa (Schr. ) Lev.

H. tab'icina (Sow.) Lev.

H. uiuhrina B. et C.

Exobsisidiiim rhododendri Cramer. On

leaves of

Rhododendron maximnni.

FAMILY CLAVARIACE.E.

164. C lav aria able tin a Pers.

165. C. cinerea Bull.

166. C. crista t a Pers.

167. C. flava Schaeff.

168. C. fitsiformis Sowerb.

169. C. gracilis Pers.

170. C. gracilliina Pk.

171. C. grisea Pers.
T72. C. petersii ^. et C.
173. C. pinophila Pk.

T74. C. tetragon a Schwein.

175. Pteriila densissima B. et C.

176. Typluila muscicola (Pers.) Fr.

I04 JOURNAL OF THE

FAMILY TREMELLACE/E.

177. Dacryomyces chrysocoina (Bull.) Till.

T78. D. in2)oluiits Schwein.

179. Gtiepinia spatJiiilaria (Schwein.) Fr.

180. Hor7)iomyces fragifonuis Cke.

ORDER GASTEROMYCETE^.

FAMILY PHALLACE^.

181. It hypha lilts impiidiais (Linn.) Fr.

FAMILY NIDULARIACE^.

182. Cyathits stercoreiis (Schwein.) De Ton.

183. C. 5/r/<2///j (Huds.) Hoifin.

184. Cnicibuliivi viilgare Tul.

FAMILY LYCOPERDACE^.

185. Mitremyces lutescens Schwein.

186. Bovista pila B. et C.

187. Lycoperdon calyptrifomiie Berk.

188. L. echinatum Pk.

189. L. gemniatum Batsch.

190. L. musconun Morg.

191. L. per latum (Pers.) Fr.

192. L. subincnrnatiim Pk.

193. L. turneri ^. et E.

194. Scleroderma lycoperdoides Schwein.

195. 6". verriicosiim (Bull.) Pers.

196. S. viilgare Horneni.

ORDER UREDINE.E.

197. Puccinia circcecc Pers. On Circcea alpina.

198. P. menthce Pers. On Labiate species.

199. P. tenuis Burrill. On Eupatorium.

ELISHA MITCHELL SCIENTIFIC SOCIETY. IO5

ORDER PHYCOMYCETE.E

FAMILY PERONOSPORACE.^.

200. Plasmopara viiicola (B. et C.) Berl. et De Ton.

ORDER PYRENOMYCETE^.

FAMILY PERISPORIACE.^.

201. MicrosphcFra alni (DC.) Winter. On Castanea
vesca and Corylus americana.

202. M. grossularicE (Wallr.) Eev. =i]/. vanbruntiana
Ger. On Sambucus canadensis.

203. M. vaccina C. & P. On Vaccinium.

204. PociosphcEra bmncinata C. & P. On Hamamelis
virginica.

205. P. oxyacaiithcF {DC.)T>. By. On Crataegus punc-
tata.

FAMILY SPH.ERIACE/E.

206. Hypoxylon petersii B. & C.

207. Daldinia vernicosa (Schwein.) Ces. et D. Not.

208. Xylaria carniformis Fr.

209. X. <:<^r;///-<^<^/;/<^ (Schwein.) Berk.

210. Ustulina vulgaris Tul.

FAMILY HYPOCREACE^.

211. Cordyceps militaj'is (L. ) Link.

212. C. ophioglossoides (Ehr.) Link.

213. Hypomyces banniiigii ^\l. On Lactarius.

214. H. lactiJiiioTiLm (Schwein.) Tul. On Lactarius
piperatus.

215. H. viridis (Alb. et Schwein.) Karst. On undeter-
mined agaric.

ORDER DISCOMYCETE.^.

FAMILY HELVELLE.F:.

216. Helvella macropiis (Pers.) Karst.

217. Mitrula hitescens B. et C.

I06 JOURNAL OF THE

2 1 8. (tC'oj^/oss///// Jiir Silt mil Pers,

219. G. IWiItrri Vi^xV.

220. Spatluilaiia veliitipcs Ckc. et Faiiow.

FAMILY PEZIZE.K.

221. Geopyxis pallidula C. et Pk.

222. Otidea oiiolica (Pers.) Fuck. ^

223. Lachnea aihoisis B. et C.

224. L. fusicarpa Ger.

225. L. Iiirta Sebum.

226. L. theleboloides Alb. et Schwein.

227. Helotiiim citriniLui (Hedw. ) Fr.

228. //. cpiphyllum (Pers.) Fr.

229. Phialea sciitiila (Pers.) Gill.

230. Chlorospleniuni ceruginosuni (CEder. ) De Not.

231. C. tortuni (Scliweiu.) Fr.

232. PJueopiza sea bras a (Cke.) Sacc.

FAMILY BULGARIE.^.

233. Lcotia cJilorocepliala Schweiu.

234. L. lubricata (Scop.) Pers.

235. OmbropJiila clavus (Alb. et Schwein.) Cke.

236. Calloj'ia xanthosiigma (Fr. ) Phil).

237. Bulgaria inquinans (Pers.) Fr.

ORDER MVXOMYCETE.^.

238. Arcyria piDiicca Pers.

239. Didyuiiuui farinaceum Schrad.

»240. D. squannilosiLDi (Alb. et Schwein. ) 'Fr.

241. Fiiligo septic a (Link) Gniel.

242. Hemiarcvria vanieyi Rex.

243. f.eoearpiis fragilis (Dicks. ) Rost.
'244. Slctnoniiis ferruginea Ehrh.

245. S. maxima Schwein.

246. Tilmadoehc nutans (Pers.) Rost.

247. Trieliia eJirysospernia (Bull.) DC.

ELISHA MITCHELL SCIENTIFIC SOCIETY. lO^

ORDER HYPHOMYCETE^.

248. /san'a fariiiosa Fr.

249. /. tenuipcs Pk.

250. Zygodes)}ius fuscus Cord a.

ORDER SPH.EROPSIDE^.

251. PJivllosticta I'iolce Desin.

ORDER MELANCONINE^.
252 Pestolozzia fnnerea var })iultiseta Desm.

ORDER SACCH.AROMYCETACE.E.

253. SaccharoDiyces pyriformis Ward.

ORDER SCHIZOMYCETACE.E.

254. BacteriiDU 7>ernii/or)fie Ward.

Botanical Department, Cornell University.
March 12, 1S93.

RECORD OF MEETINGS.

SEVENTIETH MEETING.

Gerrard Hall, September 13, 1892.
Southern Industrial Progress. Dr. William B. Phillips.

SEVENTV-FIRST MEETING.

Person Hall, October 18, 1892.

10. The Work of Science. Charles Baskerville.

11. Early Manufacture of Iron in North Carolina. H. B. C. Nitze.

12. Encystment of Earth-worms. H. V. Wilson.

13. Experiments on Halving Eggs. H. V. Wilson.

14. Effect of the Earth's Rotation on the Deflection of Streams.
Collier Cobb.

15. Note on Traps and Sandstone in the Neighborhood of Chapel Hill.
Collier Cobb.

I08 JOURNAL OF ELISHA MITCHELL SCIENTIFIC SOCIETY.
SEVENTY-SECOND MEETING.

Person Hali., November 15, 1892.

16. A New Secondary Cell. J. W. Gore.

17. Some Curious Products from the Willson Aluminum Works. F. P.
Venable.

18. On the Production of an Animal Without Any Maternal Character-
istics. H. V. Wilson.

SEVENTY-THIRD MEETING.

Person Hall, December 6, 1892.

19. Work of the N. C. Geological Survey J. A. Holmes.

20. Cerebral Localization. R. H. Whitehead.
The following officers were elected for 1893:

President --Prof. J. A. Holmes Chapel Hill.

First Vice-President Prof. H. h. Smith __- Davidson.

Second Vice-President- --Prof. J. W. Gore -- Chapel Hill.

Librarian - . . Prof. Collier Cobb Chapel Hill.

Secretary and Treasurer --Prof. F. P. VenablE Chapel Hill.

The Secretary reported 1,170 books and pamphlets received during the
year, making the total number 9,948.

Two new members were also reported: Prof. Stedman, Trinity College;
Prof. Bandy, Trinity College.

REPORT OF TREASURER FOR i8q2.

By balance from 1891 .-- .-- -_ | 40 02

By fees for 1892 64 50

By contributions . -. 100 00

By sales of Journals _- . -. 150

|2o6 02
To postage , -..

To engraving

To express — ._- .

To printing . — .-

Deficit --- - - I 15 80

$

15

65

10

82

2

75

]

[93

00

I222

22

NOV

M::M:w::M:x:M:::M::M:M::M::x:M::M::^::^::^r

JOURNAL

OF the;

Jfe|H i|ilt|lH ^tiflllifit ^0ttfl|,

-^^^1S91^^^<^

EIGHTH YEAR. F»ARX ONE.

II, 1U.

»iiKi^. ♦::♦ ♦:M:MM:.M:»i::^ * ♦: ^:.M:x^:m.;Mi3mx:M:

JOURNAL

OF THE

J^n ai%H ^mnliHt ^Dm%

-^-t^^lSQl

EIGHTH YEAR.

F>ARX SKCOND.

^i^i^^l^i^l^i^^iM'!'<^'^: ■'♦r:^'^'^^^

11.-]l^

2681 9T V.

»:♦ ♦;MM:M"M;M3#r^' ♦ ♦ '«m;m:m*^ ♦ ♦ ♦:♦ •$

JOURNAL

OF THE

Jli$|ii iii%ll ^tiintiHt %mt\\

=^t> 1 S92<5^

NINTH YEAR.

FIRST F»ART.

M..M.M-...M'W'W:'W "^ ♦ ♦ ^''W''W'''^:''W'^W'W'W''W''W

V

j'-i^ -^ 1893

l/.I^L

mm'-mmm^^^^ammm^m^^^^si^^ammi^i^^

JOURNAL

OF THE

yMp %k\t\\ ^tiinlifit ^tttil^

^:*t^ 1 892^^<^

NINTH YEAR.

SECOND F»ARX.

<•> ♦!♦ ^>

♦ ♦ > >

♦♦♦ ■ ♦♦♦ ^\ ♦♦♦ ♦♦♦'

Ti.* ^* Tk* Tfc' '^,

3 2044 106 256

■'■ V—

H^

^i..'..>fS

^^^