SCIENTIFIC LIBRARY,

United States Patent Office,

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PROCEEDINGS

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MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

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VOL. XX.

Session 1880-81

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1881.

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NOTE.

The object which the Society have in view in publishing their
Proceedings is to give an immediate and succinct account of the
scientific and other business transacted at their meetings to the
members and the general public. The various communications
are supplied by the authors themselves, who are alone responsible
for the facts and reasonings contained therein.

INDEX.

Axon William E. A., M.E.S.L., F.S.S.— The Antiquity of Toughened
Glass, p. 12. Did Pascal invent the Wheelbarrow? p. 30. On
some Early Anticipations of Heliographic Signalling, p. 46. The
Literary History of Parnell’s f Hermit,’ p. 63.

Baxendell Joseph, F.E.A.S. — Ozone and the Eate of Mortality at South-
port during the nine years 1872-1880, p. 66.

Binney E. W., F.E.S., F.G.S., President.— On some Marine Fossil Shells
in the Middle Coal Measures of Lancashire, p. 18. Boulder Stones
as Grave Stones, p. 55. On some Objects of Ancient Date found
in Digging Foundations for New Buildings on land lying between
Hanging Bridge and Cateaton Street, Manchester, p. 69. On a
Eucalyptus Globulus at Douglas, Isle of Man, p. 121.

Bottomley James, B.A., D.Sc. — Colorimetry, Part VI. On a Theory
of Mixed Colours, p. 1, Additional Note on a Theory of Mixed
Colours, p. 15.

Boyd John.— On some Entomostrseea, &c„ found in Derwentwater in
September, 1879, p. 44.

Carlyle Thomas.— Four Original Letters addressed to the late Mr.
Samuel Bamford of Blackley, the Author of the c Passages in the
Life of a Eadical.’ Communicated by E. W. Binney, F.E.S.,
F.G.S., President, p. 103.

Cockle Sir James, F.E.S.— On Du Bourguet’s c Calcul ’ and on Terna-
ries, p. 119.

Darbishire, E. D., F.G.S.— On the Question of the Desirability of the
Society’s Library being handed over to the Free Eeference Library
of the Corporation, p. 64.

Dawkins Professor William Boyd, F.E.S. — On the Dates of the Intro-
duction of the Pheasant and Fallow Deer into England, p. 144.

VI

Grimshaw Harry, F.C.S. — Note on tlie Presence of Sulphur in Illumi-
nating Gas, p. 51. Note on the Presence of Arsenic in Paper
Hangings, p. 122.

Gwyther R. F., M.A. — On the Conditions of the Motion of a portion of
Fluid in the Manner of a Rigid Body, p. 29. Additions to the
paper cOn an Adaptation of the Lagrangian Form of the Equations
of Fluid Motion,’ p. 85.

Hager Herman. — List of Famines, Severe Winters, &c„ from a.d. 1100
to 1315, p. 64.

Hart Peter. — A Sulphuretted Hydrogen Apparatus, p. 96.

Johnson William H., B.Sc. — On the Relation of Electrical Resistance
to the Chemical Composition of Steel Wire, p. 125.

Joule J. P., D.C.L., LL.D., F.R.S. — Note on Sulphuric Acid produced by
Gas Lights, p. 124.

Mackereth Rev. Thomas, F.R.A.S., F.M.S. — On Gravitation, p. 77.

Mc.Coll Hugh, B.A. — On the Growth and Use of a Symbolical Language,
p. 103.

Melville James Cosmo, F.L.S. — On some Curious Forms of Fresh
Water Mollusca from Lake Tanganyika, p. 117.

Murphy Joseph John, F.G.S. — On the Addition and Multiplication of
Logical Relatives, p. 71.

Plant John, F.G.S.— On Pendant Nests of a Gregarious Moth from
Venezuela, p. 111.

R awson Robert, Assoc. I.N.A. — First Resolvents of the Quartic

Qj

if + atf + wy- X2 = 0” (*)

and the Cubic

ayB + 3 by* + 3 cyN- m — 0 (2)

p. 144.

Reynolds Professor Osborne, M.A., F.R.S. — Some further Experi-
ments on the Cohesion of Water and Mercury, p. 38.

Schorlemmer Professor Carl, F.R.S. — On the History of the Artificial
Preparation of Indigo, p. 31.

VII

Smith E. Angus, Ph.D., F.R.S.— Note on the Word Chemia, p. 15.

Smith Watson, F.C.S., and W. T. Liddle. — Some endeavours to ascer-
tain the nature of the insoluble form of Soda existing in the resi-
due left on Causticising Sodium Carbonate Solutions with Lime,
p. 20. Some endeavours to ascertain the nature of the insoluble
form of Soda existing in the residue left on Causticising Sodium
Carbonate Solutions with Lime (Part II.), p. 58.

Stewart Professor Balfour, L.L.D., F.R.S., and William Dodgson.—
Note on an attempt to analyse the recorded Diurnal Eanges of
Magnetic Declination, p. 99.

Ward Thomas,— The Land Subsidence at Northwich, p. 55.

Meetings of the Physical and Mathematical Section.— Annual,
p. 128. Ordinary, p. 77.

Meetings of the Microscopical and Natural History Section.—
Annual, p. 143. Ordinary, pp. 44, 74, 75, 110, 116.

Report of the Council, April 1881, p, 135.

ERRATA.

Page 101, line 7 from bottom, and page 102, line 7 from top, for
“ bent ” read “ beat.”

Page 104, line 1, for “ Chayne ” read “ Cheyne.”

PROCEEDINGS

OP THE

LITERARY AND PHILOSOPHICAL SOCIETY.

Ordinary Meeting, October 5th, 1880.

R Angus Smith, Ph.D., F.RS., &c., Y.P., in the Chair.

“ Colorimetry, Part VI. On a Theory of Mixed Colours,”
by James Bottomley, B. A., D.Sc. .

In some experiments which I was making on the absorp-
tion of light, I needed surfaces of different degrees of
whiteness. To obtain such surfaces I mixed black and white
powders in various proportions. They were blended by
shaking in a bottle and grinding in a mortar. In some cases
the mixture was reduced to a flat surface by pressure, in
other cases, a little water was added so as to form a paint,
and with this pieces of cardboard were covered and dried.
Although it was not necessary for my purpose that I should
quantitatively assign the degrees of whiteness in each case,
yet such a question occurred to me in the preparation of
these powders. In this matter little has, I think, been done.
Newton, in his Optics, informs us that he mixed powders of
different colours in such proportions as to form a grey, and
in later times it has been proposed to estimate the degree
of blackness of different bodies by finding the quantity of
some white powder, which, on admixture, will yield some
standard tint. But no one has I think ever considered the law
of intensity of colour when we mix a colour with white or
black. Such a question is interesting to the artist, to the
colour mixer, and to the chemist. The artist in water- colour,
if he wishes to reduce the strength of any pigment, can do
Proceedings—Lit. & Phil, Soc.—Yol, XX.—- No. L— Session 1880-L

2

so by additional water, but the painter in oil or distemper, if
he wishes to accomplish a similar object, has to mix with
some opaque white. This, then, is the matter which I first
propose to consider. A coloured powder and a white powder
are intimately blended ; what is the law of the intensity of
colour ? As a typical case, I take the mixture of black
and white, because it was such a mixture that suggested
this enquiry. In what follows I suppose the powders
to consist of indefinitely small particles, which do not exert
any chemical action on each other. Suppose that we take
a mass of some white substance, and add to it a small
quantity of some black substance ; then we shall take away
some portion of its whiteness — if w denote the whiteness
lost, and W the initial whiteness — then the remaining
whiteness would be W — w. If now we add another unit of
the black, it might at first sight appear that the remaining
whiteness would be W— 2 w, and after the addition of n units,
that the remaining whiteness would be W —nw. For some
experiments which I was making, I had prepared eight grey
tints by mixing BaS04 with carbon ; the quantity of BaS04
being 10 grms. in each case, and the carbon increasing from
0‘006 grms. to 0-048 grms. The difference in tint between the
successive mixtures seemed to diminish more rapidly than
seemed consistent with such a law of diminution of white-
ness. The difference between the seventh and eighth
mixture was almost inappreciable, but according to the
foregoing supposition, the difference between successive
pairs should be the same.

On considering the matter further, I was led to the fol-
lowing train of reasoning. If we take equal masses of
white of different intensities and to each add the same bulk
of black, then in each case the whiteness lost will be a con-
stant fraction of the initial whiteness. Suppose M to be
the mass of the white, and W0 its initial whiteness, let m
be the mass of the black. After mixing with the white it

3

will destroy some fraction of its whiteness ; let this fraction
be n. Then the remaining whiteness will be Wo - Wo n, this
we may denote by Wi, and the mass will be M+m.

Suppose we repeat the addition of the black, the propor-
tion being as before M ; m. If x denote the black to be
added, we shall have the proportion
M + m;M| \x\m

Whence

x —

(M + m)m
M

After this second mixture the whiteness will be Wi - n;
this we may denote by W2; it may also be written
Wo(l — ny by substitution for Wi, or still more briefly
W0R2 when R= (1 — n).

Let the operation be repeated a third time, the proportion
of the white mass to the black being still M ; m. After the

second mixture the mass became it ' So if x denote

M

the quantity of black to be added we shall have

(M + m)\

M

M \\x\m.

Whence

x = m +

2m2 m3
ll +M2

The mass will now become

(M + m)3
M2

If W3 denote the whiteness we shall have

W3 = W2 - W2n = W0R2(1 - n) = W0R3
If we continue the operation n times, then from the

above law, if Wn denote the remaining whiteness we shall
have W^=W0Rn.

Also the mass will be

Mn_1

I also used an independent method of reasoning. Suppose
we have a white area A, then the quantity of white light
given off in any direction, say normal, to the surface will be
proportional to A; so that if Wo denote the white light we
may write Wo=/*A. Suppose now a great number of black

4

points to fall on this surface, being equally distributed.
Then the surface will appear to the eye of a grey tint, but
grey and white are quantities of the same kind and are
therefore comparable. What we call grey being a white of
diminished intensity. Suppose a to be the area occupied
by the black points. Then A — a will be the uncovered
white area, and the quantity of white light given off by
this will be ju(A— a); moreover this quantity of white light
will appear uniformly diffused over the surface. If we
denote it by Wx we shall then have

Wi™ /i (A— a) —fxA(l — — W oR when E is written for 1 —

A A.

Now suppose a segond series of black points to fall on the

surface. It might at first sight appear that the remaining

white area would be A— 2 a; but on consideration this did

not seem necessarily the case, for manifestly it supposes

that the particles distribute themselves with some bias ;

that is, they prefer to fall upon a white surface ; but suppose

that they have no such bias, and that they will as readily

fall upon a black as upon a white surface. Now the surface

on which they fall is grey or a mixture of black and white.

So we have this question in the distribution of the second

black area (consisting of innumerable detached points), how

much falls on the black surface and how much on the

unoccupied white area ? Let p be the portion that falls on

the black surface and q the portion that falls on the white,

now what will be the ratio of p to q ? If we suppose the

second series of black points to be fairly distributed, the

portion which falls on the black surface will be to the

portion which falls on the white as the areas of those

surfaces, so that

a

q A — a

also p + q~a, ....

and the remaining white area will be A—a—q. From (1) and

•(1)

,(2)

5

(2) we have ■-^C~-=a—-q} whence q—Cl^A a\ and for the

remaining white area we have the expression

A — a— a(A~a)= A^l— 0= AR2

and the quantity of white light given off will he juAR2;
also this quantity of light will appear equally distributed
over the whole surface; hence, if W3 denote this white
light we may write W2=pAR2~WoR2.

If we allow a third series of black points to fall upon the
surface, and to be equally distributed, the remaining white
ones will be AR3, and if W3 denote the quantity of white
light

W3 = W0R3

If we suppose the operation to be repeated n times. The
expression for the remaining white light will be W0Rn.
Hence the ratio of the initial to the final whiteness would be

l

Both trains of reasoning concur in giving a similar expres-
sion for the intensity of the whiteness. In some papers
which I have contributed to this Society I have pointed out
that the law expressing the intensity of transmitted light
when we dissolve Q units of colouring matter in a trans-
parent medium, is of the form Eat cQ. Hence we have this
curious result : when the intensity of an opaque white is
diminished by mixture with an opaque black, the mathe-
matical expression for the intensity of the whiteness is of
the same form as if we had dissolved the black in a trans-
parent medium and surveyed a white area through it. In
the foregoing reasoning I have supposed the particles, after
admixture, to distribute themselves without bias. It be-
comes a question of much interest, when we mix particles of
heterogeneous matter is this always the case ? Under some
circumstances they may be brought within the sphere of

6

molecular attractions, and these may have some influence
in the distribution ; in other words, it is possible to conceive
that the particles will distribute themselves with some bias.
Here again it seems to me that so far from such speculations
on the intensity of colour of mixtures being fruitless, they
may even extend the application of colorimetry ; for while
experimental agreement with the theory would strengthen
the theory, even negation would have its value, and an
investigation into the departures from the law might lead
to interesting results, and give some insight into the opera-
tion of those molecular forces which separately elude
observation, but whose joint effect must necessarily have
some influence in determining the intensity of colour.

Some of the above reasoning applies to the case of turbid
liquids, and I was led to the conclusion that a carbon diffu-
sion would behave with regard to the extinction of light in
the same manner that it would do if the carbon were actu-
ally in solution. The only difference in the reasoning is,
that the different series of carbon points, instead of falling
on one section, are distributed through a series of circular
sections of the containing cylinder, these sections being
parallel to the external white surface. As I have shown in
another paper, the results of the experiments agree very
well with the theory. So far I have considered the intensity
of the residual whiteness when we mix black with white.
The same course of reasoning might be applied to determine
the residual colour when we mix black with any colour.
Suppose, for instance, we take a mass M of yellow and let
the initial yellow be Yo. Then, if we mix with it a mass
m of black, we shall remove some fraction of the yellow ;
let this be denoted by nYo, so that the residual yellow is
Yo(l — n), or YoR After n repetitions according to the
proportions laid down in the case of black and white, the
intensity of the residual yellow will be YoR*.

Another problem is the mixture of white with some

7

opaque colour, red for instance. Suppose we start with a
white area A, then the quantity of white light given
off normally may he denoted by juA. Suppose now a great
number of red points to fall upon this surface and to be
equally diffused, so that the eye does nob perceive detached
red and white points, but a surface uniformly tinted of a
light red colour. Let a be the area occupied by the red
points ; then the quantity of red light we may denote by
liXa, and the uncovered white area will be A ~a, and the
quantity of white light given off will be ja(A — a). Suppose
now a second series of red points to fall upon the surface,
and that they distribute themselves without bias, and also
that there is no chemical action. Then the uncovered

white area will be - ^ - and the red area will be

A (A— 4

A

Hence after the second operation the light
ju(A— a)2

given off will consist of white light

and of red

light

| A— ^ ^ - 1 or as we may write them /u AR2 and

jUiA(X— R2), where R=X— If the operation be repeated

n times the residual whiteness will become juARw and the
redness will become /u aA(X — Rw). If n becomes infinite the
whiteness vanishes and the red becomes juxA, being the red
light that would be given off if we supposed the surface to
be covered with red points only.

A method for experimentally testing the foregoing theory
relative to the intensity of the residual whiteness, after
admixture with a perfect black, would be as follows. Take
three surfaces of different degrees of whiteness (A, B, C),
due to admixture with p, q , r units of black ; look at the
surfaces through some fluid containing in solution some
soluble black substance, adjust the columns so that the
intensity of the transmitted light shall be the same.

8

Suppose first we compare A and B. Let t and t1 be the
lengths of the columns. Then

W0R^ = W0R*F (1).

Now compare B with C, whence, if 0 and 01 be the lengths
of the columns, we shall have

WoR«^ = WoRW (2)

i

From equations (1) we have R = 7

1 x ' k p — q

0l Q

and from equation (2) we have R = r

but these two values of R ought to be the same, so we
ought to have the equation.

tl—t _ 01— Q
p—q q — r

The different tints I used consisted of BaS04 and lamp
black. Tint A consisted of lamp black 0'012 grms. BaS04
10 grms. Tint B contained twice the above quantity of
lamp black to the same quantity of BaS04, and tint C
contained four times the quantity of lamp black to the
same quantity of BaS04. The absorbing medium I used
consisted of water containing a minute quantity of lamp
black in suspension. This, as I have before shown, behaves
nearly the same with regard to the absorption of light as if
the carbon were in solution.

A comparison of tint A with tint B gave R=&‘3. Tint
A compared with tint C gave R=&'346. Tint B compared
with C gave R— '4. Inasmuch as k is a fraction, these
three values of R will not differ much. The experimental
enquiry is difficult, and the following defect is likely to
have some influence on the result. The grey powders were
mixed with a few drops of water and pieces of cardboard
covered with the paint so obtained, and then dried. But if
we take an intimate mixture of two powders, and make it
into a paint with oil or water, the gravity of the two powders
being different, and the fluid medium imparting a certain
degree of mobility to the particles, there will be a tendency

9

for the lightest powder to come to the surface. I have
sometimes noticed, with regard to the tablets prepared as
above, that portions which had been rubbed seemed per-
ceptibly lighter than the undisturbed portion ; possibly this
may be due to a slight excess of carbon on the upper surface,

I also compared tint A with another consisting of 0A0G3
grams carbon to 10 grams BaS04, thus the quantity of
carbon is a considerable multipie of that contained in tint A.
The value of R got from the comparison differed considerably
from* a value of R which I got by comparing A with B. At
first I thought this was due to a failure in the theory ; after
some time it occurred to me that the conditions of my ex-
periments were not the same as the conditions of the theory.
In the theory, I had supposed that the white was mixed
with a perfect black, in the experiments the white had been
mixed with a grey.

Those surfaces which are popularly known as black, are
in reality not black but grey. If we take such a surface,
whether of black velvet or lamp black, aud hold an opaque
object before it so as to intercept a portion of the incident
light, a shadow will be found on the surface ; but it is evi-
dent that a perfect black is incapable of receiving a shadow.
Also, when I looked at a surface of lamp black through the
colorimeter (consisting of a glass cylinder covered with black
cloth, except a small aperture at the bottom) the lamp black
surface appeared grey. The formula for the intensity of the
residual whiteness, if we mix with grey, will not be the same
as if we mixed with black. The formula will have to be
altered as follows : suppose Wo the initial whiteness, after
the addition of perfect black the residual whiteness will be
W0Rra, but if the material added be grey, we must give back
a quantity of white, which will be some fraction of the
whiteness lost. Suppose p to be this fraction; also the
whiteness lost will be W0— W0R"; so the quantity of white
to be restored will be W0p(l — Rw) and the total whiteness

10

will be WoRn(l — p) + W0p. If we suppose n to become
infinite the whiteness becomes Wo p, being the whiteness or
greyness of the so-called black body. We might also have
deduced the formula as follows : take a white area
A, then the quantity of white light given off we may
denote, by g A ; now let a series of grey points to fall upon
this, let a be the area of the spots, then the quantity of
white light given off by this we may denote by fxi a, the
uncovered white area will be A — a, and the quantity of
white light given off by this will be g( A — a), therefore the
whole quantity of white light will be /^(A — a)+yia, or

juAR-P/iia if It be written for 1 - If we suppose another

series of grey points distributed over the surface, the un-
covered white area will be AR2, and the surface covered by
the grey points will be A — AR2, so that the quantity of
light will be /i AR2 -f — AR)2. If the operation be
repeated n times the expression for the residual whiteness
will be juXRn + ij}(A — ARn) which may be written in the

form juA(Rn(l — p)+p), when p—~, also g A=W0, the initial

whiteness so that the expression is equivalent to the one
previously given.

On the Theory of Engraving.

Another subject of Interest in Colorimetry is the theory of
engraving, which I think has never been considered. In
this art various shades of grey are given to white surfaces
by aggregations of lines or dots, giving rise to line, mezzo-
tint, and other varieties of engraving. If the tint be
produced by lines, it may be estimated as follows. Take a
white square area A and rule it with parallel lines. The
quantity of white light given off initially we may denote
by juA. Let b be the breadth of one of these lines and l its
length ; also suppose that then an n of these lines, then the
white area uncovered will be A — nhl. Suppose n to become

11

very great and b very small, so that we no longer have
the impression of black lines on a white surface, but see a
uniform grey surface, then the expression for its degree of

whiteness will be /x( A — nbl) or W0(l — nr) if r denote^-

Sometimes an engraver, instead of using parallel lines
only, crosses the lines (cross hatching). With a given number
of lines the tint will not be the same if he draws them all
parallel, and if half are drawn at right angles to the others.
Suppose we have 2 n lines, if drawn parallel the degree of
whiteness will be W0(l - 2 nr), but let n of these lines be
drawn perpendicular to the remaining n. Take the case of
one of these perpendiculars, it will intersect one of the first
series in a square whose area is b2, and as it is cut by n lines
the sum of these will be nb 2; the additional white area,
blotted out by this line, will be lb - nb 2, and since there are
n such lines the total area they blacken will be n(lb- nb*).
Hence the remaining white area will be A - nib - {nib - nb2,
which may be written A(1 - nr)*, since l2 = A. If Wi denote
the whiteness when the lines are parallel, and W2 when
they cross, we shall have

Wi 1 - 2nr
W2~ (l -nr)2

In both cases the lines are supposed to be so thin as to be
individually imperceptible.

Again, suppose an engraver to cover a square white area
with black circular spots which touch one another, the spots
being very numerous and individually imperceptible, so that
we receive the impression of a grey surface. If beyond this
stage he exercised his skill in diminishing the area of the
spots infinitesimally, and increasing their number, so that
they still fulfil the condition of touching, it will make no
difference in the intensity of the tint : for the area of the
spots is always the same, and equal to that of the circle that
can be inscribed in the square.

12

“ The Antiquity of Toughened Glass,” by William E. A.
Axon, M,R.S.L., F.S.S.

The toughened glass of modern times appears to have
been anticipated in imperial Rome. Inventors have never
been very well treated, but the peculiar fashion of rewarding
mechanical and scientific skill, then employed, has fortunately
found no parallel in modern days. That the secret of render-
ing glass hard had been discovered some 1800 years before
the patent of M. de la Bastie appears probable from the
following passage in the well known, work of Pancirollus.

“ If is reported, that in the time of Tiberius there was
glass found out so rarely temper’d that it might be made
ductile and flexible like paper, and also that the author of
this invention was put to death, because having repair’d at
Rome a magnificent palace that was ready to fall, and being
paid by Tiberius , and forbidden to come any more in his
sight, he having found out the way of making glass malle-
able, came again into his presence to shew his art, expecting
from the Emperor (as Dio writes) a great reward.

“ But Pliny tells us in the 26th chapter of his 36th book
that the whole shop of this artist was ruinated and demo-
lished, to prevent the lessening and bringing down th q price of
silver and gold. Some think it was done by the malice of
Tiberius, who had no kindness for virtuous and ingenious
men.

“ That which our author saith concerning this artizan, Dio
relates (in the 27th book of his history) after this manner,
who tells us that when the great Portico at Rome lean’ d dll
on one side, it was after a wonderful manner set upright
again ; for a certain Architect, (his name is not known, for
Tiberius so envy’d his art that he forbad it to be register’d)
having; so fixed the foundations as to render them immove-
able, did, by the strength and force of men and engines,
restore it again to its former posture.

“ Tiberius wondered at the thing, and so much envy’d the

13

artist, that after he had rewarded him he banished him the
City. But coming afterward again to the Prince, he threw
away a glass on purpose, and brake it, and then took it up
again and made it as whole as ever, hoping thereby to obtain
his pardon ; but he missed his aim, being presently com-
manded to be put to death.

C£ Petronius tells us that there was a certain Smith that
made Vessels of glass as strong and durable as those that
were made of gold and silver , wherefore having made a vial
of the same materials, very fine and curious, he presents it
to Tiberius. The gift is commended, the artist admir’d,
the devotion of the donor is kindly accepted.

“ And now the Smith to turn the wonder of the spectators
into astonishment and amazement and the better to recom-
mend himself to the Prince’s favour, took a glass vial and
dash’d it against the pavement with all his might, so that
if it had been brass it must needs have been broken. Caesar
did not so much wonder as fear at the fact. The Smith
took up the vial, not broken, but bruis’d a little, as if it had
been some metal in the form of glass, and afterward he
mended it with a hammer, as if it had been some tinker
cobling a piece of brass. When he had done this mira-
culous piece of work the man was puffed up into such a
conceit of himself that he presently fancy’d that he should be
snatched into heaven, and should converse with no less than
Jupiter himself, in regard he gain’d the smiles of the Empe-
rour, and had deserv’d (as he imagined) the applause of all.
But it fell out otherwise, for Ccesar enquiring whether any-
body else knew the art beside him, and being answered No,
commanded this fellow to be immediately beheaded, alledging
that if this skill and ingenuity was rewarded and encourag’d
it would bring down the price of gold and silver, and make
those metals as vile as dirt.”

In a footnote we read as to lessening the Value of Gold,
“For the use of drinking , glasses hath banish’d gold and

n

silver almost quite out of doors, and therefore the Emperour
Gallienus could not endure the sight of glass, saying, there
was nothing in the world more vile and common — ( The
History of many Memorable Things Lost which were in
use among the Ancients, by Guido Pancirollus. [English
translation.] London, 1715.)

The story of the inventive artizan was popular during the
middle ages, and is given in “ Gesta Romanorum.” Allow-
ing for the fashion of telling the tale, we appear to have
here an ancient anticipation of modern invention on the
toughened glass, which however has not yet caused that
depreciation of gold and silver, deprecated in so sanguinary
a manner by Tiberius.

15

Ordinary Meeting, October 19th, 1880.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

The following communication from Dr. R. Angus Smith,
F.R.S., was read : —

In relation to my paper on the word Chemia, Mr. Wm.
Simpson informs me that Dr. Muir, in “ Sanscrit Texts,”
vol. 5, p. 402, refers to the Rig Veda, where Kam is repre-
sented as Eros. Dr. Muir also says that Kama is distinctly
identified with Agni, the Sanscrit for fire. This gives the
word a firmer basis in the East than I found for it. He
also adds that Wilford, in “ Asiatic Researches,” identifies
Csema or Kama of India with the Chemia or Chemi of
Egypt. I shall add this to my paper, which is being
printed in full. It is one of the proofs of early connection
of Aryan and Semitic people both in language and thought ;
but this is a subject that belongs to others to speak of. I
hear of other connections with the far East in the word
Chemia, but having begun to argue this view of the case,
others may advance it. When I say begun, I merely sought
to connect old links of thought, and other old links may be
found lying about in many places.

“ Additional Note on a Theory of Mixed Opaque Colours,”
by James Bottomley, D.Sc.

At the last meeting of the Society I read a paper on a
theory of mixed opaque colours. One of the problems con-
sidered was the mixture of black with white. The prob-
lem seemed to me to have some analogy with sprinkling
small black spots on a white surface so as to yield a grey
tint. I obtained a formula Wn=WoR7i, W n denoting the
residual whiteness after n repetitions of* the operation.
Proceedings — Lit. & Phil. Soc. — Vol. XX. — No. 2. — Session 1880-1.

16

In the discussion which followed it was suggested by Mr.
Heelis that some of the spots might be superimposed on
others in the same unit. This will leave the expression for
W n unaltered in form, but will introduce a new value for

the constant. The symbol It stands for 1 — A being the

area of the white surface and a the surface occupied by the
mass of black. The problem under consideration is a physi-
cal one, and ultimately the spots will be due to the atoms
of matter ; these are finite in magnitude. Let p be the area
covered by an atom of matter, and suppose our unit of mass
to contain p atoms — let these be thrown down singly on
the surface ; then the remaining whiteness after the expen-
diture of the unit will be Wo^l - If we throw

down n units the remaining whiteness will be

Wo

(>-i)

This then will be a strict solution of the

problem, for manifestly one particle cannot be superimposed
on itself. If we keep to the same unit of mass and the

same kind of matter, we may write It for ^1 - jQ so that

the expression for the residual whiteness may be written
WoR.% being the same in form as that given before.

We may also write our first expression in the form

W^=Wo£ v a)

or if we expand the logarithm

(—a a? \n

A ZE? &c7

on a particular hypothesis a simple expression may be
obtained for the residual whiteness due to the distribution
of a given quantity of matter over a surface. Suppose j
that a can vanish and n become indefinitely great, the
first term in the index is — -Jf. Hence this multiplied by n

would tend towards the ambiguous form ° ^ ; but the limit

17

of the numerator will be the quantity of black employed,
which we may denote by b, so that the first term would

become — The second term multiplied by n may be
written in the form the limiting value of net is b, so

that this term becomes ^ ; since it contains a term which

ultimately vanishes it will disappear, so a fortiori all the
remaining terms. So that we should get as the residual
_ l

white area Ae a

This simple form of expression for the white area has been
suggested by Mr. James Heelis in a letter to me. The atomic
constitution of matter seems a bar to its perfect acceptance.
It does not seem likely that we can so divide matter as to
arrive at 0. In this, as in many problems, physical con-
ditions- place limits to mathematical generalities. Never-
theless, on account of the extreme smallness of atoms there
will be no sensible difference whether we use this formula
or the one suggested by me, which takes into account the
atomic constitution of matter, for in the term

pnp pn$

£ A -¥As-&c.

the second term of the expansion — first term x ^
This will be so small as not to be sensible, and may therefore
be neglected— and so, a fortiori, the remaining terms.. The
above remarks will apply to the mixtures of other colours
as well as black and white.

“ On some early anticipations of Heliographic Signalling,’'
by William E. A. Axon, M.RS.L.

The use of the heliograph . in war is likely to gain ground.
Nature (April 29, 1880, vol. xxi., p. 617) gives an instance
in which a message was flashed by this means as speedily
as by the electric telegraph. The following description is

18

given of the modus operandi : “ The line of communication
cannot he cut, for the simple reason that the signalling
takes place over the heads of the enemy, and the stations
required are but few and far between. A 10-inch mirror —
and this is the diameter of the ordinary field heliograph — is
capable of reflecting the sun’s rays in the form of a bright
spot, or flare, to a distance of fifty miles, the signal at this
interval being recognisable without the aid of a glass.
That is to say, two trained sappers, each provided with a
mirror, can readily speak to one another, supposing the sun
is shining, with an interval of fifty miles between them,
provided their stations are sufficiently high and no rising
ground intervene to stop the rays.

Professor Reynolds, F.R.S., said that he had been able
to get a barometer tube free from air by first washing the
tube with water, and introducing the mercury while the
tube was wet, and then leaving the tube in an inverted
position for several days. The water absorbed the air, and
floating up between the mercury and the glass left the tube
dry, full of mercury, and free from air. He hoped at the
next meeting to report some further experiments on the
suspension of mercury by its cohesion in a tube 90 inches
long.

“On some Marine Fossil Shells in the Middle Coal Mea-
sures of Lancashire.”

The President said that Mr. George Wild, of the Bardsley
Collieries, near Ashton-under- Lyne, had lately informed him
of some very interesting fossil shells having been met with
in sinking the deep pit at Ashton Moss, which has now
reached the great depth of about 800 yards.

In the Lancashire, Cheshire, Staffordshire, North Wales,
Yorkshire, and Derbyshire Lower Coal Measures it has been
long known that certain beds of marine shells of the genera

19

Nautilus Goniatites, Aviculopecten, Lingula , &c., were
met with, but they were supposed not to extend upwards
into the Middle Coal Measures. However, about ten years
since, Professor Green, M.A., F.G.S., of the Yorkshire
College of Science, then on the Geological Survey, found
some of these shells in the bed of the Tame, under the
Guide Bridge railway viaduct at Dukinfield, and he sup-
posed them to lie about 150 yards above the Big Mine of
Ashton. As no evidence of superposition could then be
obtained, doubts were entertained as to their true geologi-
cal position, some parties thinking that they might belong
to the Lower Coal Measures, and there thrown down by a
fault.

In 1861 he (the President) examined the beds and pro-
cured specimens of Nautilus, Goniatites, Discites, Aviculo-
pecten, Orthocevatites, and Posidonia, but he could find no
clear evidence of their true position in the Coal Measures,
although they certainly looked more like Middle than
Lower.

In the memoirs of the Geological Survey of Great Britain
on the country around Oldham, published in 1864, the late
Mr. Salter, A.L.S. and F.G.S., describes Professor Green’s
shells under the names Aviculopecten fibrillosus, Cleno-
donto sp. inc., Goniatites sp. inc., Nautilus prcecox, Discites
rotifer, and Discites spec. unc.

Last week he (the President) went over to the Ashton
Moss Pit, and in the spoil on the pit hill succeeded in finding
specimens of Goniatites, Posidonia, Lingula Mytiloides,
and Sanguinolites costellatus. The specimens, especially
the Goniatites, were all of small size when compared with
those generally found in the lower coal measures. Accord-
ing to Messrs. Higson, the mining engineers, the bed of
shale wherein the fossils occurred is somewhere about 130
yards above the Big Mine, thus clearly proving that there is
a bed of marine shells in the upper part of the middle coal

20

measures. It also seems probable that the bed in which the
fossils are met with at Ashton Moss pit is the same, or one
lying near to it, as that discovered by Prof. Green, above the
Big Mine of Dukinfield, and that the strata seen in the Tame
lie pretty regular between the two places, and have not
been much disturbed by faults.

“ Some endeavours to ascertain the nature of the insolu-
ble form of Soda existing in the residue left on Causticising
Sodium Carbonate with Lime/’ by Watson Smith, F.C.S.,
Assistant Lecturer on Chemistry in the Owens College, and
Mr. W. T. Liddle.

In the following are given the results of an inquiry (yet
in progress), which were obtained towards the close of
last session, in the Laboratory of Owens College, by Mr.
W. T. Liddle in conjunction with myself, and with the occa-
sional co-operation of Mr. H. Bimmer. The present inquiry
was the final step after a series of exercises in the technical
examination of some alkali products by the two gentlemen
named, kindly furnished by Messrs. Gaskell, Deakin, & Co.

Hargreaves (Chem. News, 387) and Kynaston (Chem.
Soc. J., 11, 135) have noticed the occurrence of soda in an
insoluble form in the crude soda (black ash) of the alkali
works, but they only speak of alumino-silicates and silicates
of sodium, and in these early papers mentioned don’t appear
to imagine any other insoluble compound present in which
soda may be practically lost to the manufacturer.

Dr. G. B. A. Wright published a paper (appearing in
Journ. Chem. Soc., year 1867, p. 407) in which he distinctly
shows (1) that soda in an insoluble form does exist in black
ash treated with water, in process of lixiviation, and (2) that
though it may partly exist as alumino-silicate, yet undoubt-
edly it exists in some other form, and most probably as a
double sodium calcium carbonate.

To show the importance to the soda manufacturer of this

21

loss in insoluble sodium compounds left behind in the black
ash and waste, Wright states that it forms the largest item
of the several individual losses, making up the total 2024
per cent loss out of 100 parts Na20 as salt cake occurring
in the practical conversion of salt cake to soda ash, Wright

tabulates this as follows :

Previous to lixiviation of the black ash.

XJndecomposed sodium sulphate 3*49

Insoluble sodium compounds 5*44

Vaporisation, &c., of sodium compounds 1*14

During and after lixiviation.

Soluble alkali left in vat waste 3*61

Leakage and losses in soda ash process ... 6 ‘5 6

Total loss per cent 20-24

In experiments tried with samples of black ash Wright
showed that on prolonged boiling (6 hours) with water,
the insoluble sodium compound in the black ash residue
was decomposed, and yielded a sodium salt in solution
capable of neutralising acid. On taking soda waste
and submitting this to prolonged boiling with water, only
3 -81 out of 5 ‘08 per cent of the insoluble soda, calculated as
NaaCOg, were extractible, and he considers that this differ-
ence from his experience with the black ash, is due to the
influence of the other sodium salts present on the insoluble
compound in the case of the black ash. Wright also cites
the well known fact, that on causticising sodium carbonate
solutions with quicklime, the calcium carbonate formed
retains a considerable portion of sodium in an insoluble
form, and adds, that most probably in the case of the black
ash a double sodium calcium carbonate is formed, either in
the furnace or on addition of water to the crude soda. In
further proof of this view he mentions the case of some ex-
perimental charges for black ash, in which an unusual excess

22

of limestone was used. Wright examined the resulting pro-
duct to see if more of this insoluble compound were formed,
and found there was.

Mactear (Chem. News, Feb. 2, 1872, p. 55) makes the
interesting discovery that “ oxidised alkali waste yields on
lixiviation almost all the soda contained in the waste.” The
soda thus rendered soluble occurs in the solution as sulphate.
Mactear says “The chief loss in the soda process is that
which occurs during lixiviation of the ball soda. This loss
is in part represented by the insoluble and soluble compounds
left in the waste. The former sometimes amounts to 3 or 4
per cent of the soda, and the amount is increased as the
silica and alumina of the raw materials increase.”

Wright has shown that an increase of limestone in the
black ash mixture will also increase the amount of the
insoluble soda compound.

Scheurer-Kestner (Comptes Rendus, Nov. 11, 1872) con-
firms Wright’s views. He proves conclusively that an
increase of chalk in the black ash mixture causes a propor-
tionate increase in the amount of insoluble soda compounds
left in the waste. “ The excess of chalk employed is con-
verted into lime, and when the crude soda is lixiviated with
water, the lime while becoming hydrated reacts upon the
sodium carbonate and thereby renders a portion insoluble
in water.” According to Seheurer-Kestner’s experiments,
the lime may retain even as much as from 475 to 4*95 per
cent of soda Na20.

With regard to our own experiments, we first operated
upon some samples of soda waste, with the view of deter-
mining the soluble and insoluble soda therein contained.

After titration and digestion with water of about 60°,
for an hour, a sample of waste yielded us 0*22 per cent of
alkali as Na20 soluble in water. On solution of the residue
in acid, a gravimetric determination of the residual and

23

therefore insoluble soda gave 2T8 per 'cent Na20, hence the
waste contained of total Na20 — 2*40 per cent.

Another sample analysed by Mr. ftimmer gave as
soluble Na20 — 0*31 per cent,
insoluble „ 1*91 „

Total 2*22

Wright found in an average sample of a fortnight’s soda
waste as soluble Na20 — 2*07 per cent.

insoluble „ 0*91 „

Total 2-98

In the difference noticeable between Wright’s results and
ours, as regards the insoluble soda, it is possible his own
explanation for the fact that continuous boiling with water
will extract the insoluble soda from black ash, but will not
from soda waste, may here hold good, for it will be noticed
his soda waste contains considerably more soluble sodium salt
than ours does.

We now turned our attention to the soda left behind in
the lime sludge remaining as a residue, in the process of
causticising sodium carbonate solutions. In the sludge
taken as a sample of many tons lying outside the causti-
cising plant of a works, after suitable draining, the total
Na20 extractible by water was found to be 2*62 per cent.
Calculated roughly into dry residues this would represent
3’84 per cent.

Now according to several careful analyses made some
years ago, the amount of soda existing in lime mud in the
insoluble form averages about 2J to 3 per cent on the mud.
If we add this to the above figure 2 ’63 per cent for the
soda soluble in water, we get an approximate 5 per cent of
total soda. In alkali works where black ash is made, this
soda is not lost, the mud, drained and dried as far as possi-
ble, being mixed with the black ash charges, and worked

24

into ball soda, and thus it is kept in constant circulation,
instead of being lost. The loss entailed thereby is one of
heat, and hence of fuel, in converting water into steam in
the black ash furnace.

In order to have some object to aim at, we commenced
the next step by assuming the existence of such a double
sodium calcium carbonate, as Wright believes is formed,
under the circumstances already named ; and, as the simplest
mode of representing such a compound, we took the liberty
of giving it the formula

We then made an attempt to prepare this so far hypothetical
salt. But before proceeding to this, we will just refer to
some experiments we made with the object of ascertaining
with some degree of precision under what circumstances
the insoluble sodium compound is formed.

Solutions of caustic soda and sodium carbonate were
prepared; the former had a specific gravity of T09 and con-
tained 6'52 per cent NaaO ; the latter contained 5-985 per
cent Na20.

(I.) A quantity of precipitated CaC03 was diffused in
water and boiled then with 20 c.c. of standard caustic soda
for 15 minutes. After filtering and washing till the filtrate
was no longer alkaline, it was found by titration with
normal hydrochloric acid that no soda had been retained by
the calcium carbonate.

(II.) No soda was retained either, when instead of the
precipitated CaC03, finely powdered marble was used.

(III.) A quantity of calcium carbonate (precipitated)
was now boiled for a long time with 20 c.c. of the sodium

Ca

25

carbonate solution of known strength and with the addition
of water. No soda was retained.

(IY.) The above experiment was repeated with finely
powdered marble, with like negative results.

(Y.) A quantity of milk of lime was now taken, and
boiled with 25 c.c. of the Na2C03 solution. After filtering,
washed with 500 c.c. of hot water, removed lime, filtered,
washed, evaporated to dryness, ignited, dissolved in water,
and titrated, 1-286 per cent Na20 was retained by the cal-
cium residue.

(VI.) A quantity of milk of lime taken, and to it were
added 25 c.c. of caustic soda solution with some water.
The whole was boiled for sometime — 0-05 per cent Na20 re-
tained. Some of the sodium hydrade becoming accidentally
carbonated might account for this.

This lime mud residue of (V), washed as above till the
filtrate ceased completely to react alkaline, was washed into
a flask and a current of C02 was passed through for a long
time, to endeavour to decompose this insoluble compound.
In this way only 0-078 per cent of the soda (Na20) was
extracted.

We now attempted to prepare some of the double sodium
calcium carbonate in the following manner : —

A quantity of pure sodium carbonate solution (somewhat
concentrated) was mixed with about three times its volume
of clear lime water, and this mixture was heated to boiling.
The precipitate was allowed to settle, was filtered, and
washed with hot water till the filtrate ceased to manifest
the slightest alkalinity to test paper. It was then dried in
the water bath. When the lime water was added to the
sodium carbonate solution, the precipitate of carbonate
which came down had the floccular appearance of alumina

26

freshly precipitated, but on standing for about half an hour
without heating, it became crystalline in appearance. The
dried precipitate under the microscope was distinctly crys-
talline, being apparently composed of minute rhombohedra.

In subsequent experiments we found the microscopic
appearance to vary, sometimes rhombohedra mixed with
minute prisms making their appearance.

On analysis we found that the crystalline powders (they
were only just perceptibly crystalline to the naked eye) con-
tained according to two experiments : —

CaC03 Na2C03

(5)

97-65% ... 97-90% 2-46%

It would seem probable from this that the major reaction,
so to say, is that converting sodium carbonate into hydrate,
calcium hydrate passing into pro rata carbonate, but a minor
reaction also occurs by which a small quantity of a double
carbonate is formed. It is all the more certain that such a
compound actually is formed from the fact that the precipi-
tates obtained as j nst mentioned (and this experiment has
been repeated many times) were in every case distinctly
crystalline powders; we never detected the smallest amor-
phous particle with the microscope. Now it is hard to
imagine any difficulty in removing sodium carbonate by
continued washing with boiling water in excess, from a
powder consisting of distinct crystals of calcium carbonate.
We can then best account for the presence of the alkali by
considering it as having formed itself, a crystalline and
insoluble compound with calcium carbonate, this double
crystalline carbonate being mixed in small quantity with
the superabundant calcium carbonate.

Another experiment was now tried, to prove indirectly if

27

such a double carbonate were present in the crystalline pre-
cipitated powders we obtained as already described. We
reasoned thus : “ If such a double compound exist here,
strong ignition ought to decompose it, driving off carbon
dioxide from the lime, but leaving sodium carbonate intact,”
thus

.C020Na

Ca = CaO + Na2C03 + C02

^C020Na

This experiment was tried with a small quantity of the
crystalline precipitate. It was well ignited in a platinum
crucible, and the resulting mass was treated with some
dilute alcohol, which extracted easily a quantity of the soda,
showing a strongly alkaline reaction to test paper. We
intend to repeat this experiment quantitatively, and to deter-
mine thus the amount of soda extracted.

One point becomes pretty clear by these experiments, viz.
that the materials lime and sodium carbonate in contact
with water give rise to the formation of this insoluble sodium
compound. Also that it is not a case of mere cohesive reten-
tion of soda by the lime mud, for our experiments
show that until a definite and suitable chemical reaction
between the members of the mixture sets in, no appre-
ciable amount of soda is retained, but that when such reac-
tion sets in, in the condition of nascent state and therefore
unstable equilibrium, in which the various constituents
momentarily find themselves, a major and normal reaction
takes place, and also this minor reaction to a small extent —
giving us a small yield of the insoluble sodium compound.

The experiments we have yet in view with the crystalline
precipitate prepared as mentioned, and also with ordinary
lime mud* are (1) the effect of long boiling with water to
see if thus the insoluble compound is decomposed, as with

28

Wright in the case of black-ash ; (2) boiling with water
containing certain salts in solution, such, e.g ., as sodium
sulphide. We hope by obtaining a closer knowledge, at all
events, of the properties and behaviour of this singular
compound, to find at length, peradventure, a practical and
ready means for extracting it, and thus doing a service to
the alkali manufacturer.

29

Ordinary Meeting, November 2nd, 1880.

Edward Schunck, Ph.D., F.R.S., V.P., in the Chair.

“On the Conditions of the Motion of a portion of Fluid
in the manner of a Rigid Body,” by R. F. Gwyther, M.A.

The condition that a portion of fluid may comport itself
as a rigid body, or that fluid may remain in a state of rela-
tive rest upon or within a moving solid, has not, as far as I
am aware, been mathematically investigated. We know,
however, that in certain cases, as on the surface of the earth,
the condition can be realised, or that any deviation has not
been discovered by undirected investigation.

In the case considered, the velocity at points in the fluid
must consist of a common linear velocity, and a common
angular velocity about some axis, moving or fixed. There-
fore, using the quaternion notation, the velocity must be of
the form

a = 2 + Yer,

where S is the common linear velocity, e the vector axis
of instantaneous rotation, and r the vector of any point in
the fluid.

The equation of motion is

Bto- + i vp = a (1)

P

a denoting the force acting on the element of the fluid, p
and p having the usual meanings. Under the condition
stipulated no viscosity is called into action.

If p be a function of p only, we may write

— vp = v P.

p

Substituting the required form of <r we get

S + Ver + 2Ve(2 + Ver) = a — VP (2)

Proceedings — Lit. & Phil. Soc. — Vol. XX. — No. 3. — Session 1880-1.

so

Now act upon this with V (which will not affect either 2
or e) and afterwards take the vector and scalar parts, thus :

V (Yer + 2e2? — 2eSer) = V a — V2-?
or 2e = 4e2= Va - V2P

2e = Yv« and 4e2= V2P-Sva (3)

The first of these equations gives the required condition ;
if the forces acting are conservative Yva=0, and e must be
constant in direction and magnitude —the magnitude and
pressure being connected by the second equation. The case
here considered is the general case of the possibility of a
quantity of dead water accompanying a moving solid, and
includes that of fluids in relative rest upon or within the
earth.

Considering the possibility of a fluid interior of the earth,
it must be observed that, owing to precession and nutation,
the axis of the earth is not constant in direction, and that
therefore the condition is not truly satisfied. If however
the shape of the earth gives a stable form for the fluid, the
viscosity of the fluid will tend to mitigate any departure
from the apparent rigidity, after such motion has once been
established.

Precession must also prevent the absolute rest of fluid
contained in a vessel upon the earth’s surface, and it is pos-
sible, though highly improbable, that in this way precession
might be demonstrated, as Foucault’s pendulum demon-
strates the earth’s rotation.

“Did Pascal invent the Wheelbarrow?” by William
E. A. Axon, M.R.S.L.

The recent celebrations in honour of Pascal brought up
once more a curious claim that has been advanced on his
behalf as the inventor of the wheelbarrow. The statement
has been made by Jules Janin and other writers, but the
assertion is purely traditional and has no historic basis.

81

That the wheelbarrow was known long before the days of
Pascal may be seen by anyone who will examine the curious
engravings in Georgii Agricolse de re metallica (Basilese,
1556). In this impressive folio, which may be seen at the
Manchester Public Library, there are several pictures in
which miners are represented as transporting minerals from
place to place in wheelbarrows. A writer in La Liberty states
that he pointed out this work to Janin, who replied with
characteristic indifference : “ Cela m’est bien egal, ce n’est
pas moi qui ai invente cela, je l’ai lu, j’en laisse la responsa-
bilite a ceux qui font ecrit avant moi, et n’ecrirais pas une
ligne pour le contredire.” This shows a spirit unworthy of
the true antiquary, to whom truth, even in trifles, is sacred,
and who does not readily admit the existence of trifles. A
much earlier instance of the use of the wheelbarrow can be
cited. In the mural paintings at Gaws worth in Cheshire,
discovered in 1851 and since destroyed, there was a repre-
sentation of the Doom or Last Judgment, in which one of
the demons is seen carrying a lost soul on a wheelbarrow to
the mouth of hell. In form the barrow resembles those
which are still used on the moss near Gawsworth.*

The Church is held by Mr. J. P. Earwaker to have been
erected in the fourteenth or fifteenth century. We have
thus the certain fact that the wheelbarrow was known not
only in German mines but in a remote agricultural district
of England, one hundred years before the time of Pascal.

* On the History of the artificial Preparation of Indigo,”
by Carl Schorlemmer, F.RS.

One of the most brilliant discoveries which lately has
been made is that of the synthesis of indigo, the Indian
colour, which is mentioned by Dioskorides and Pliny, as
well as by the Arabians. It was however only after the

* Historical and Antiquarian Hotes on Gaws worth Church, by Joseph
F. A. Lynch. Manchester, 1879, p. 25.

32

discovery of the sea passage to India that it became gene-
rally known in Europe ; but its use as a dye was greatly
retarded by the opposition it met with from the large vested
interests of the cultivators of woad, isatis tinctoria, the Euro-
pean indigo -plant. The English, French, and several Ger-
man governments were induced by the growers of woad to
promulgate severe enactments against it. Thus Henry IY.
of France issued an edict condemning to death anyone who
used that pernicious drug called “ devil’s food.” The em-
ployment of woad was however gradually superseded by
that of indigo, and as soon as organic chemistry had ad-
vanced far enough, chemists began to examine this import-
ant colouring matter, which was first obtained in the pure
state by O’Brien, who states in his treatise “ On Calico
Printing,” 1789, that on heating indigo the colouring matter
volatilises, forming a purple vapour, which condenses as a
blue powder, whilst the impurities of the commercial pro-
duct are left behind. Indigo-blue, or indigo tin as the pure
compound is called, was afterwards analysed by several
chemists, who found that its most simple formula is C8H6NO,
which was subsequently doubled for several reasons.

The literature of the chemistry of indigo is very large;
of the numerous researches, I can here mention only those
bearing directly on my subject.

In 1840, Fritzsche found that on distilling indigo with
potash a basic oil is produced, which he called aniline
CeHg.NHa from anil, 'by which name the Portuguese intro-
duced indigo first into Europe. The word is Arabic, and
means simply, the blue.’ In the following year he obtained
by boiling indigo with caustic soda solution and manganese
peroxide a compound which he called anthranilic acid,
and which, now known as orthamidobenzoic acid C6H4(NH2)
C02H. He also observed that by heat it is resolved into
aniline and carbon dioxide.

At about the same time Erdmann and Laurent inde-

pendently studied the action of oxidising agents on indigo
and obtained isatin, C8H6N02 which is not a colouring matter.
The further examination of this body led to most interesting
results, but as those are not directly connected with the
subject of this paper, I cannot discuss them here.

We must therefore proceed at once to 1865, when Baeyer
and Knop found that by acting on isatin in an alkaline
solution with hydrogen in the nascent state it is converted
into a j^ellow crystalline body, which they called dioxindol
C8H7N02. This is easily further reduced in an acid solution
to oxindol , C8H7NO, which forms colourless needles, and on
its vapour being passed over red-hot zinc-dust it loses its
oxygen, indol , C8H7N being formed, which is also a colourless
crystalline compound and a most interesting body, inasmuch
as it is also formed, as Nencki and Kiihne have shown,
in pancreatic digestion, and is contained in the faeces.

In 1869, Baeyer and Emmerling obtained indol from
cinnamic acid, which occurs in several plants, and can be
obtained artificially from coal-tar, as I shall show further
on. By the action of nitric acid it yields two isomeric nitro-
compounds; one of them, called orthonitro- cinnamic acid,
loses, when heated with caustic potash and iron filings,
carbon dioxide, and oxygen and indol is formed :
C8H6(N02)C02H = c8h7n + o2 + co2

The same chemists discovered, 1870, a method by which
isatin can again be reduced to indigo-blue. By heating it
with a mixture of phosphorus trichloride, acetyl chloride,
and phosphorus to 70 — 80°, they obtained a green liquid
which, when poured into water, deposited, on standing ex-
posed to the air, a blue powder containing indigotin. At the
same time a purple colouring matter was formed, which
they called indigo-purpurin.

It has been known for some time that urine, on standing,
sometimes deposits indigo-blue. Jafie, in 1870, found that
he could produce it by the subcutaneous injection of indol ;

34

and Nencki, who confirmed this observation in 1875, was
able to convert indol into indigo tin by the action of ozonised
air. But the yield is only very small, as the colouring
matter readily undergoes further oxidation.

However, the synthesis of indigo was thus completed,
because indol can he built up from its elements; but
chemists were not satisfied with it, the method being neither
a practical one nor giving any clue as to the chemical consti-
tution of indigo.

In the next year Baeyer and Caro found a very simple
and elegant method for preparing indol ; they obtained it
by passing the vapour of ethyl-aniline through a red-hot
tube :

H

CH2,

c6h5-n

CH2 - CHo

= C6H4

N

CH + 2H2

Baeyer succeeded, in 1878, in obtaining oxindol from
phenylacetic acid C6H5.CH2.C02H, which can be prepared
synthetically by different methods, and may be easily
obtained from toluol. By treating the acid with nitric acid
it is converted in the orthonitro-compound, which is easily
reduced to the corresponding amido-acid. But this, like
several other ortho-compounds, readily loses water and
yields oxindol :

CH2.CO.OH

CH2s

= c6h4v ^>co + h2o

This compound, as Baeyer and Knop had already found,
is converted by the action of nitrous acid into nitros-
oxindol. On treating this with nascent hydrogen it is
transformed into amidoxindol, and this yields on oxidation
isatin, the constitution of these bodies being expressed by
the following formulae :

Nitrosoxindol. Amidoxindol. Isatin.

CH(NO) CH(NHS) CO

c6h4< >co c6h4< >co CoH4< >co

:n!1 .Ml NH

35

I have already stated that isatin can be reduced to
indigo-blue ; Baeyer endeavoured now to find a more simple
method for effecting this. By acting with phosphorus penta-
chloride on isatin he obtained a compound which he called
isatin chloride, which nascent hydrogen converts into
indigotin.

2C8H4C1N0 + 2H2 = Ci6H10N2O2 + 2HC1.

As far back as 1869, Kekuld predicted isatin to possess
the constitution which it has been proved to have by
Baeyer’s researches, and two of Kekule’s pupils, Claisen
and Shadwell, discovered in 1879 a very simple synthetical
method for preparing it. By acting with phosphorus
chloride on orthonitro- benzoic acid C6H4(N02)C02H the
chloride, C6H4(N02)C0C1 is formed, which when heated with
silver cyanide yields the nitril, C6H4(N02)C0CN, on heating
the latter with a solution of caustic potash, it is converted
into orthonitro-phenylglyoxylic acid, C6H4(N02)C0.C02H and
this is converted by nascent hydrogen into the amido-
compound, which, like other ortho-compounds, loses water
and yields isatin.

I have now given you a sketch of the history of artificial
indigo up to 1879, when I wrote : €‘ The artificial production
of indigo has so far merely a theoretical interest; whether
the time will come when simplified methods will admit of its
manufacture on a large scale remains to be seen. But even
if not, the indigo-purpurin, which is always formed together
with the blue, may become of importance as a colouring
matter. This body, as Dr. Schunck has shown, is identical
with his indigorubin, which always occurs, but in small
quantity only, in indigo. Dr. Schunck has traced the
formation of this beautiful purple colour in Polygonum
tinctoriurm a plant used in China and Japan for the
preparation of indigo. He has cultivated it for several
years, and found that the young plants do not contain a
trace of it. It can be only obtained from plants having

36

attained an advanced stage of development. It dyes under
the same conditions as indigo tin does; but while the latter
dyes a dull dark blue, indigorubin dyes a fine purple shade.
Dr. Schunck, who is an authority on these matters, is of
opinion that if it could be obtained in quantity, it would
be a most valuable addition to the colours now in use.”*)
Since this has been written, Baeyer has succeeded in
finding a method which to all probability will soon be
employed for the manufacture of indigo-blue on a large
scale. The starting point is from cinnamic acid, which
occurs in nature, being found in Gum-benzoin, Styrax,
Balsam of Peru, and a few other aromatic bodies. These
sources would be, however, far too expensive, and the quan-
tity obtained therefrom much too small to make use
of them. Now Bertagnini found, as early as 1856, that this
acid may be obtained artifically by heating benzaldehyde, or
oil of bitter almonds, with acetyl chloride :

C6H5.CHO + CHyCOCl = C6H6.C2H2.C02H + HC1.

Since that time several processes have been found for
obtaining oil of bitter almonds from toluol and from benzoic
acid. The first point to be settled was therefore to ascer-
tain which is the cheapest and best method for preparing
this compound, as well as acetyl chloride, which is produced
by the action of phosphorus chloride on acetic acid.

W. H. Perkin, F.B.S., has discovered another synthesis of
cinnamic acid, which probably may also be of practical
value. He obtained it by boiling benzaldehyde with acetic
anhydride and sodium acetate.

By the action of nitric acid on cinnamic acid we obtain
orthonitro-cinnamic acid, C6H4(N02)C2H2C02H, which readily
combines with two atoms of bromine to form dibromnitro-
phenylpropionic acid. This compound, by the action of
alkali, is transformed into orthonitro-phenylpropiolic acid :
C6H4(N02)C2H2Br2.C02H + 2NaOH =
C6H4(N02)C2.C02H + 2NaBr + 2H20.

* ft The Bise and Development of Organic Chemistry.” Manchester,
Cornish.

37

The latter acid yields pure indigo, when its alkaline
solution is heated with a reducing agent such as grape-
sugar, indigotin being deposited in the crystalline state : —
2C9H5NO4 4- 2H2 = C16H10N2O2 + 2CO2 4- 2H20.

Besides this method Baeyer has patented some others in
which also cinnamic 'acid is used ; these processes are now
worked out by two of the greatest colour -works on the
Continent.

How far the artificial production of indigo will be a com-
mercial success remains to be seen. As far as I understand,
it is at present only intended to manufacture nitrophenyl-
propiolic acid, which, when mixed with an alkali and grape-
sugar, is printed on the cloth. By the action of steam a pure
indigo-blue is produced, which would form a most valuable
addition to the host of steam-colours which are now so
largely in use.

In conclusion I must mention another of Baeyer’s dis-
coveries which promises to be of practical value. We can
easily replace in isatin one atom of hydrogen by bromine,
the nitro-group, amido-group, &c. By subjecting these
substituted isatins to the action of phosphorus chloride they
are converted into chlorides, and these yield by treatment
with reducing agents substituted indigoes. These bodies
are all coloured, and their properties are very similar to
those of indigo. It appears not improbable that some
of them might find application in dyeing or printing,
and be prepared, not from isatin, but from substituted
cinnamic acids.

When 12 years ago the artificial madder-colours were
discovered, it was not believed that they could be produced
in sufficient quantity, nor cheap enough to compete success-
fully with . the natural colours. To-day the cultivation of
madder has almost ceased ; whether this will happen in the
case of indigo is a question which I think will soon be
solved.

38

“Some further experiments on the Cohesion of Water
and Mercury,” by Professor Osborne Reynolds, F.R.S.

Two years ago I exhibited before this Society a vertical
tube, 60 inches long and -/-6- inch in diameter, in which mer-
cury sustained itself by its internal cohesion and adhesion
to the glass to a height of 60 inches without any aid from
the pressure of the atmosphere.* This tube was subsequently
shown at the Royal Society and was submitted to inter*
mittent observation at the College until about nine months
ago when one day, on being erected, it either collapsed or
was broken by the fall of the mercury. The fracture taking
place simultaneously with the fall of the mercury, it was
impossible to say which.

This tube was of common German glass, such as is used
for chemical purposes, and as it proved insufficiently strong
I deferred further experiments until I could obtain a tube
of greater strength. This led to considerable delay, but I
have now a tube 90 inches long, in which mercury suspends
itself in a water vacuum resisting a tension or negative
pressure of three atmospheres. Although this is probably
still far short of the possible limit, a certain amount of
interest attaches to the probability that the tension in this
tube is the highest to which any fluid matter in the uni-
verse has been subjected.

Since my former communication, in working both with
the old tube and particularly with the new and longer tube,
further experience has been gained of which it is my present
object to give some account.

During the year and nine months before the old tube
broke no great change had been noticed in the water and
mercury within the tube; the former became rather cloudy
and the latter showed symptoms of a scum. These changes
were but little noticed, as they did not apparently inter-
fere with the suspension of the mercury.

* Proceedings Lit. & Phil. Soc., 1877-8, p. 155.

39

The most noticeable circumstance was that as time went
on the difficulty of getting rid of the air and getting the
tube into such a condition that its contents would sustain
themselves diminished. In the first instance it had been
only after a fortnight’s attempts that suspension was obtained.
The first successful suspension was obtained in the following
manner : a little of the water was allowed to pass up by the
side of the mercury when the tube was in an inclined po-
sition, the tube was then brought gently down so that the
water reached the top or closed end of the tube as nearly as
the air, generally a small bubble, would admit ; then further
inclined until the closed end was so low that the air bubble
and water would float up to the open end and pass out, leaving
the straight portion of the tube and part of the bend full of
mercury. The tube was then left in this position for 24 hours,
when on being erected the mercury sustained itself. It was
then again reversed and left for some days, when on being
erected not only was the mercury sustained for the 30 inches
above the barometer, but it remained suspended when the
pressure of the air on the lower end was reduced by the air
pump to one or two inches of mercury.

No other method ever proved successful with this tube.
It was always necessary to leave the tube reversed for a
longer or shorter interval.

As to what went on in this interval I changed my opinion.
At first I thought it must be that time was necessary to bring
the mercury or water into more intimate contact with the
tube, but subsequent observation convinced me that the
interval was necessary to allow the water with such air as
it contained to drain up between the mercury and the
glass — that in this way the surface of the glass was freed
from air. After arriving at this view I observed the tube
carefully to see if after it had remained some days in the
reversed position any trace of water was left. I could find
none either while the tube was full or after the mercury

40

had fallen ; but owing to the fact that there was always water
on the open end I couJdmake no such comparison with the
barometer as would show that the vacuum in the tube
Was absolutely free from vapour tension.

Having obtained from Messrs. Webb of Manchester
tubes 12 feet long, f inch external and \ inch internal
diameter, one of these tubes was closed at one end and
bent so as to leave the closed branch 7 feet 6 inches
long. The bend is a curve of about 2 inches radius, and the
two branches or limbs are not quite parallel ; they straddle
so that at 3 feet 6 inches from the bend they are 7 inches
apart. At this point the shorter or open limb was again
bent back through an angle of 160 degrees, so that when
the main tube is vertical the mouth points downwards. The
bending of so large and thick a tube was a matter of some
difficulty, but was successfully accomplished by Mr. Hay-
wood and Mr. Foster of Owens college. The tube was then
firmly fastened on to a board by Mr. Foster, and the board
pivoted on to a stand so that the tube can be turned round
in a vertical plane.

The tube being placed so that there was a slight,
downward incline all the way from the open to the closed
end, some water was introduced into the open end.
This having passed down to the closed end and filled
all the tube, mercury was introduced, which ran down, for-
cing out the water. As soon as the long limb and the bend
were full of mercury, the tube was turned into an upright
position, the mercury sinking down and forcing out the
water in the shorter limb. Having reduced the water until
it only occupied about 9 inches above the mercury, the tube
was again brought into a somewhat horizontal position, but
this time it was turned so that the mouth was downwards,
the incline being from the closed to the open end. Before
reaching that position the pressure of the air had caused
the mercury to fill the longer limb, leaving only water in

41

the shorter limb ; as the inclination continued, the mercury
and water began to change places, and the water passed up
round the bend into the longer limb ; when 5 or 6 inches of
water had passed in, the tube was erected and turned over
the other way, so that the closed end was lowest, the water
and the bubble of air running up and passing out. The
tube was then further inclined until nearly vertical, the
closed end down, and the tube was left in this position for
24 hours.

This, it will be noticed, was the process by which, after
the first trial, had proved almost invariably successful with
the former tube, and the only circumstances likely to cause
any difference in the new and old tube were the compara-
tively short time the water and mercury had been together,
and in the new tube, and the greater length, 90 inches, as
against 60 with the old tube. As regarded this latter differ-
ence, it would not effect a partial erection of the tube, so
that if the time was not an element of importance, it was to
be expected that at all events the mercury would sustain
itself until the closed end had reached a r position 60 inches
above the bend.

On examining the tube, however, after it had been stand-
ing 24 hours, it presented a very different appearance from
that usually presented by the old tube ; instead of a polished
column of mercury it was frosted with water between itself
and the glass ; it was clear that the upward draining of the -
water had been very imperfect, a great deal remaining
adhering to the glass.

On slowly erecting the tube the mercury showed no
symptom of suspension, leaving the closed end quietly as
erection proceeded.

The whole process of passing the water up the tube was
again repeated with the same result for three days.

The frosted appearance, however, gradually diminished
and on the fourth day a partial suspension was obtained.
The mercury remained up until the tube was nearly erect.

42

Having obtained so much, and as it appeared by the
turbid state of the water that the mercury was impure, the
tube was emptied, washed out several times, both with
water and a solution of nitrate of mercury, and was then
refilled as before with water and carefully purified mercury.
At first it presented much the same frosted appearance as
before, and there was no suspension.

With a view to expedite matters the board carrying the
tube was taken off its pivot and laid fiat on a table nearly
horizontal; in this position it was so adjusted that the water
and mercury both extended all along the tube. The tube
was then connected by an indiarubber tube with an air
pump, and the air pumped off until, and so long as, the
water boiled in the tube.

The board was then turned over on its edge so that the
water might come in contact with that part of the tube
which had been previously below the mercury.

Having been turned back into its first position and ad-
justed so that the closed end and long limb were slightly
lower than the rest, the pump was kept working, and the end
of the board at which was the closed end of the tube was
gently hit with the hand. At first this caused the mercury
to chatter all along the tube, and wherever the mercury
broke, a minute bubble of an air or steam showed itself ; these
passed slowly along to the open end ; until after this had
been continued for some time the chattering ceased and the
last bubble had passed out.

Keeping the closed end lowest, and without breaking the
connection with the pump, the board was replaced on the
pivot and the tube erected. The mercury remained sus-
pended until the tube was nearly erect, and this without
any assistance from the air on the open end, so that the
tension was nearly 90 inches.

The same process of tapping was then repeated, and the
tube replaced and left with the closed end downwards and

43

the air pumped off, for 24 hours. There was then no frost,
but a bright column of mercury, which on erection remained
suspended, the pump having been worked so as to remove
the last trace of air. The tube was not left standing, but was
inverted and erected for a few minutes each day for 8 da}Ts,
including this morning. When the pump was again worked,
and the tube sealed by clips on the indiarubber before bring-
ing it to the Society’s rooms — which somewhat difficult
undertaking has been accomplished by Mr. Foster, who has
assisted me throughout in these experiments. (On being
erected in the Society’s rooms the mercury remained sus-
pended for about 1 5 minutes; it then gave way with an audible
click and sank to such a level as showed that there had not
been air pressure of l-20tli of an inch on the lower end.)

This experiment shows that the cohesion of water and
mercury, and their adhesion to each other and glass, will
withstand a tension of 3 atmospheres or 90 inches of mer-
cury, being one atmosphere more than was shown by the
former tube.

But as I have been of opinion from the first that the limit
of cohesion, whatever may be that of adhesion, is a much
greater quantity, my object in making and recounting these
experiments has not been so much to prove a somewhat
higher cohesion as to throw light upon the circumstances
on which the successful suspension depends.

The fact that the frost on the glass, the imperfect draining
up of the water, and the nonsuspension of the mercury all
occur together, and may all be removed by time or by the
complete removal of the air from the glass, seems to show
that even when glass is completely wet or covered with
water there may be and generally is a considerable quantity
of air still adhering to the glass.

As regards the limit of the cohesive or adhesive strength
of water and mercury, I conceive this to be beyond any test
that can be applied by gravity. Several feet more might be

44

attained, but the difficulties increase with the length of the
tube. It has, however, occurred to me that by centrifugal
force the limit may be reached in tubes a few inches long,
and I am at present preparing some experiments for this
purpose, of which I hope soon to be able to give some
account.

MICROSCOPICAL AND NATURAL HISTORY SECTION.

October 11th, 1880.

Alfred Brothers, F.R.A.S., in the Chair.

On some Entomostraca, &c., found in Derwentwater in
September, 1879,” by Mr. John Boyd.

A new Locality for Leptodora Hyalina.

“Quite a little excitement was caused in August last year
by the announcement of the discovery of Leptodora Hyalina,
for the first time in England, in the Olton Reservoir. The
last fortnight in September I spent at Keswick, and from
the description of the places in which it has previously been
found here and on the Continent, I thought it very likely
that it might be obtained also from Lake Derwentwater ;
I therefore constructed a net of fine muslin, about two feet
long, gradually tapering to an aperture at the end; in this
aperture I inserted the neck of a wide-mouthed bottle; this
apparatus was slowly towed after a boat. The water passed
through the net, leaving all the animalcules in the bottle,
and to my delight almost the first haul brought up several
specimens of Leptodora; afterwards I got them more plenti-
fully, but found that in some parts of the lake the bottle
brought none up. They need to be looked for very carefully,
for they are so exceedingly transparent that one very easily

45

in isses seeing them. 1 1 seem s to me very probable that similar
lakes would all produce Leptodora if searched in this manner.
The ones we obtained, although not all fully grown, were all
in the mature stage, none seemed to have ova.

Besides this I got from this lake of Entomonstraca alone
nine other species, viz : —

Polyphemus Pediculus , remarkable for its enormous eye
and rapid movements.

Bosmina Longirostris , a comical fellow whose superior
antennse have the appearance of two eiephants’ trunks.

Sida Chrystallina.

Daplmella Wingii.

Alona Quadrancularis.

Chydorus Sphcericus.

Dioptomus Castor , with its enormously long antennse ;
of this we only saw one male amongst the numerous speci-
mens examined; it is easily distinguished from the female by
the thickened joints in one of its antennse.

Cyclops Quadricornis, and a beautiful variety of

Daphnia Pulex, of a greenish colour, having the carapace
terminated by a long tail-like spine. This spine is a portion
of the lower edge of the carapace, being strongly serrated.
Of these all but the last two species were new to me, as
they do not occur in any of the ponds, etc., I have examined
in this district.

Amongst the Infusoria found were Melicerta ningens,
having very large, light-coloured, fluffy pellets, very different
to the small, dark, hard bricks composing the cell of those
found about here.

Floscularia Ornata .

Uroglcna Volvox.

The lovely dark green Vorticella Chlorostigma, and
Vaginicola Valvata. In this last, which occured abundantly,
the valve was distinctly seen, closing the sheath in an
oblique direction. It is situated about one third of the

46

length down. It was very interesting to watch the
creatures push this door open as they emerged from their
tubes.

These last two species I had not found before.

Rough diagrams of each of the creatures mentioned were
exhibited by Mr. Boyd, and slides of Leptodora, Sida,
Dioptomus, and Polyphemus.

Mr. R. Ellis Cunliffe exhibited various interesting
microscopical slides.

Mr. Rogers exhibited a living specimen of an Ampullaria
from Assumoroi, River Niger, West Africa. It had remained
quite dormant for a considerable period, but was now in a
thriving condition.

The following paper was read at the meeting held on
October 19th, but only part of it printed in the last number
of Procedings : —

“ On some early Anticipations of Heliographic Signalling,”
by William E. A. Axon, M.R.S.L.

The use of the heliograph in war is likely to gain ground.
Nature (April 29, 1880, vol. xxi., p. 617) gives an instance
in which a message was flashed by this means as speedily
as by the electric telegraph. The following description is
given of the modus operandi : “The line of communication
cannot be cut, for the simple reason that the signalling
takes place over the heads of the enemy, and the stations
required are but few and far between. A 10-inch mirror—
and this is the diameter of the ordinary field heliograph — is
capable of reflecting the sun’s rays in the form of a bright
spot, or hare, to a distance of fifty miles, the signal at this

47

interval being recognisable without the aid of a glass.
That is to say, two trained sappers, each provided with a
mirror, can readily speak to one another, supposing the sun
is shining, with an interval of fifty miles between them,
provided their stations are sufficiently high and no rising
ground intervene to stop the rays.

“The- adjustment of the military heliograph is a very
simple matter. An army leaves its base, where a heliograph
station is located, and, after travelling some miles, desires
to communicate with the stay-at-homes. A hill in the
locality is chosen and a sapper ascends with his heliograph,
which is simply a stand bearing a mirror swung like the
ordinary toilet looking-glass, except that it swings horizon-
tally. It is also pivoted so as to move vertically as well.
Behind the mirror, in the very centre, a little quicksilver
had been removed, so that the sapper can go behind liis
instrument and look through a tiny hole in it towards the
station he desires to signal. Having sighted the station,
adjusting the mirror, he next proceeds to set up in front of
the heliograph a rod, and upon this rod is a movable stud.
This stud is manipulated like the foresight of a rifle, and
the sapper again standing behind his instrument, directs the
adjustments of this stud until the hole in the mirror, the
stud, and the distant station, are in a line. The heliograph
is then ready to work ; and in order to flash signals so that
they may be seen at a distance, the sapper has only to take
care that his mirror reflects the sunshine on the stud just in
front of him.”

Early in June, 1880, a writer in the Lahore Gazette called
attention to what he regards as an early instance of helio-
graphic signalling. He says : —

“ But there is a still older instance of the use of the helio-
graph indicated in a ballad as old as 1511, viz., the story of
the fight between the Great Harry and its consort under
Lord Howard, on the one side, and the Lion and the Union

48

under Sir Andrew Barton, of Scotland, on the other. Lord
Howard is represented as having met at Thames mouth a
merchantman which had been plundered by the Scotch
admiral, and the captain offered to sail back with him and
assist in the forthcoming fight if he were armed with a few
pieces of ordnance. He was also to signal to the English
admiral when he made out the enemy. The merchant
captain says :

‘ Seven pieces of ordnance
I pray your honor to lend to me,

One each side of my shipp along,

And I will lead you on the sea.

And a glass Fie set that may be seene
Whether you sayle by day or night,

And to-morrow I sweare, by nine of the clock
You shall meet Sir Andrew Barton, Knight.’

“It is clear that this glass was some sort of heliographic
signal, for the ballad goes on to say :

The merchant set my lorde a glasse
Soe well apparent in his sight,

And on the morrow by nine of the clock,

He showed him Sir Andrew Barton, Knight.

“ The real credit of the invention of the heliograph there-
fore belongs to this brave merchant captain, Henry Hunt,
and even he probably only used a common means of signal-
ling understood among all sailors four hundred years ago.”
It would not follow as a matter of course that the ballad
account of this battle must be regarded as a contemporary
narrative. The oldest text is that in the Percy Folio, and
the lines there do not refer so clearly to signalling —

if you chance Sir Andrew for to bord,
lett no man to his Topcastle goe ;

& I will give you a glasse, my Lord,

49

& then you need to fferae no Scott,

whether you sayle by day or by night ;

& to-morrow by 7 of the clocke

you shall meete with Sir Andrew Barton, Knight.

The Percy Folio is probably not earlier than the black-
letter copies of the ballad, but the text is altogether freer
from corruptions. No existing copy of Sir Andrew Barton
can claim to be older than the seventeenth century. The
possibility of using the flashing of a mirror to obtain infor-
mation from a distance is shown in the following extract
from a book of popular science of the seventeenth century :

“ If there be never so dark a room with a door or window
open, take a looking-glass in your hand, and hold it against
the sun, at a great distance from the door or window, and
moving the glass up and down, till the reflections of the
sun be upon your object, and then you may perfectly behold
anything in the room, or see to read a letter. Some un-
happy boys used to dazzle people’s eyes with a glass in this
order, as they walk the streets.” — This extract is from a
work entitled “A Rich Cabinet with variety of Inventions.”
My copy of this work is destitute of title, but it was printed
about 1670 — 80.

The “Speculum Topographicum, or the Topographicall
Glasse,” was “newly set forth by Arthur Hopton, gentleman,”
and “Printed at London by N. O. for Simon Waterson,
dwelling at the signe of the Crowne in Paules Churchyard,
1611.” At p. 183 we read the following: “To make a
glasse whereby to discerne any small thing, as to reade a
written letter a quarter or halfe a mile off. We have an
imitation of such glasses as these about London commonly
to bee sold, but they be so small that they stand one in
small steede, but amongst the writers of perspective, I have
read that if you take a glasse of the same mettall that
burning glasses be, and 16 or 17 inches broad, whose center
place directly against ye object you looke vpon, and let it not

50

incline, or hang sidewise by any meanes. Behind this glasse
set a faire looking glasse, the polished side beholding the
said burning glasse, to ye intent to receive the beames that
come through tlie^same : which done, looke in the looking
glasse, so shall you have your desire, if the burning glasse
were truely placed : for you must note whatsoeuer thing
you see through the burning glasse, that the further you
stand from the glasse, the bigger it seemeth, untill you come
to a certaine distance, and then the object seen through the
glasse doth seeme lesser and lesser, therefore care must be
had in placing the glasses, so may you see a Towne or
Castle, or any window in the same, 6 or 7 miles, or see a
man 4? or 5 miles, reade a letter in written hand a quarter
of a mile from you,” &c.

Hopton does not give the name of the writers from whom
he derived this experiment. A partial search has not been
successful in tracing it to an earlier author.

51

Ordinary Meeting, November 16th, 1880.

E. W. Binney, F.R.S., F.G.S., &c., President, in the Chair.

“ Note on the Presence of Sulphur in Illuminating Gas,”
by Harry Grimshaw, F.C.S.

That crude illuminating gas from coal contains a certain
amount of compounds of sulphur is of course a well known
fact. That even the best quality of coal gas, when purified
and made ready for consumption, contains still a certain
amount of sulphur compounds is also well, but perhaps not
generally, known.

An accidental, somewhat peculiar, but very practical
demonstration of this fact recently came under my observa-
tion, which I thought might be of some little interest to
the Society. On the interior of the glass globe surrounding
a gas jet in the hall of my house I had frequently noticed
the presence of drops of condensed liquid. The jet being
near the outer door, and the globe consequently exposed to
a rather cold current of air, I merely considered it to be
drops of water formed by the burning hydrogen of the coal
gas, and condensed on the cold surface of the glass. I
noticed however that when the glass became heated through
the turning on of a larger flame, the moisture did not, as it
ought according to all reasonable expectation, evaporate. I
was curious enough to take down the globe, wipe out a few
of the drops on slips of paper, and rinse the rest off with
water, which I preserved. Having my suspicions from the
rather oily appearance of the drop, I warmed the slips of
paper a little, and immediately obtained a very fine
reaction for sulphuric acid, by the copious blackening
and charring of the paper in those places where the liquid
had touched it. I then applied the usual chloride of barium
test, and obtained a plentiful precipitate of sulphate of
Proceedings — Lit. & Phil. Soc. — Vol. XX.— No. 4 — Session 1880-1.

52

barium from the washings of the globe ; thus showing, of
course, that the oily drops were literally nothing but toler-
ably strong oil of vitriol.

The genesis, so to speak, of these drops of sulphuric acid
is of course easily explained and pretty well understood.
The sulphur of course originally exists in the coal used for
gas making, mostly combined with iron as sulphide. In
the crude coal gas it exists as sulphuretted hydrogen (H2S),
bisulphide of carbon (CSa), and to a small extent as sulphur
dioxide (S02). The greater portion of these compounds of
sulphur are absorbed by the ammonia liquor which con-
denses from the gas itself in the scrubbers, and by the lime
and oxide of iron in the purifiers, through which the gas
passes on its way to the gasholder ; but nevertheless a suf-
ficient quantity remains in the gas to produce the effect
above described and to also produce a bright but very
objectionable green deposit of sulphate of copper on the
brass of the gaspipe above the jet I have alluded to.

The presence of the corrosive substances, sulphur dioxide
and sulphuric acid in the products of combustion of coal
gas, has always been known and always acknowledged, and
yet but little notice of their effects has been taken. It has
been said, “The quantity is so small and is disseminated
through such a bulk of other gaseous bodies.” It is as well
to see what this means. If the amount of sulphur in coal
gas is reduced to 10 grains per 100 cubic feet, it is considered
a very pure gas indeed. Manchester gas is supposed to at-
tain to this degree of purity, and is, I believe as a rule,
a better gas in this respect than that of many other towns,
For my own part I should feel inclined to think that only
a small portion of the gas made in this country uniformly
reaches this standard. However, say that the gas which I
burn in my house contains no more than 10 grains of sulphur
per 100 cubic feet. This means 100 grains, or about a
quarter of an ounce (about) per 1,000 cubic feet. I find

53

that I burn on an average, through 5 or 6 jets per evening
89,00 cubic feet per quarter. This contains 890 grains of
sulphur, which is equal to 2,670 grains of sulphuric acid
(H2S04) ; so that I turn into the atmosphere of my house,
mostly into one room, nearly 6 ounces of sulphuric acid in
three months. This is 24 ounces, or 1 j pounds per annum.
Now if I had been burning the Leeds gas, of the quality
which has recently been subjected to a good deal of criticism,
and which is stated to contain 40 grains per 100 cubic feet,
then I should be subjecting the contents of my house to the
action of 1 jibs, of vitriol per quarter, or 61bs. per annum
In many cases, certainly in those cases where the contents
of the room are most liable to damage, the above amount of
gas, namely that from 5 or 6 lights, is given off into the
atmosphere of one room.

Almost all the objects in the upper parts of a room are
susceptible to damage by the vapour of sulphuric acid. I
do not take into consideration the presence of sulphur
dioxide, for it is almost impossible that this body could
escape conversion into sulphuric acid in a very short space
of time, in the presence of oxygen, the vapour of water and
heat. Ceilings, cornices, wallpapers, pictures, with their
cords or chains, and frames, books, and so on, are all objects
which are susceptible to the corrosive action of the vapour
of sulphuric acid, and there cannot be much doubt that in a
longer or shorter time they will all suffer from the presence
of the sulphur in gas where the latter is burned in any
quantity. The great danger in the action of sulphuric acid,
in these cases is that it is a cumulative one. Its action will
be accumulative in a longer or shorter time under the fol-
lowing conditions respectively, burning the same amount of
gas in each case. In a longer time if the ventilation is very
good, and the walls of the apartment perfectly free from
any dampness. In a shorter time when these two condi-
tions are unfavourable, especially when the walls or portions

54

of them are not perfectly dry, the presence of moisture
naturally favouring the formation of sulphuric acid, and also
absorbing it when formed and assisting its action. In such
cases I have known a most rapid action upon wallpapers of
certain kinds and on organic materials where in contact
with metals, notably brass, both the metal and the organic
fibre being rapidly corroded.

Many of the objects in the upper portions of rooms to
which I ha ve alluded are replaceable, at some little expense of
course, such as the colouring of ceilings and wallpapers, and
we may make up our minds to putting up with their deteriora-
tion for the sake of the excellent light and convenience of
gas-lighting ; but to expose such objects as valuable pictures
and books to the extensive action of the products of com-
bustion of coal gas as we at present consume, is most inju-
dicious, and is, there can be little doubt, the cause of a great
deal of irreparable injury in many cases. My own opinion
is, that now that mineral and other oils for illuminating
purposes are so cheap, and lamps for their consumption are
so admirably constructed and elegant in design, there is not
the slightest reason why valuable collections of pictures and
books should be exposed to the sulphurous emanations of
coal gas.

Since writing the above I find by an abstract in the
Journal of the Chemical Society (1880, vol. ii., p. 836) that
a Mr. W. R. Nichols confirms the generally accepted view
that the deterioration of library bindings is mainly due to
the action of the sulphuric acid from coal gas, and he finds
that morocco is not so much affected as russia leather and
calf skin, and that ordinary sheep skin is attacked by this
body.

Addenda. — For methods of estimating the sulphuric acid formed
during the combustion of coal gas, and proof that suphuric acid is formed,
see Young and others. Analyst, Yol I., p. 143.; Yol. II., pp. 66, 67, 118,
133, 135, 139 ; and Yol, III., p. 201. For the effect of gas on the books
of the Libraries of the Athenseum, London, Eoyal College of Surgeons,
Portico Library, Manchester, and Literary Society, Newcastle-on-Tyne,
see Dr. Letheby’s earlier reports to the London Corporation.

55

Ordinary Meeting, December 14th, 1880.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

“ Boulder Stones as Grave Stones ”

The President said that in the numerous excavations
made in the drift deposits large boulder stones are often
met with and cause a good deal of trouble to the workmen.
They are glad to get quit of them somehow or other. Blast-
ing them with gunpowder or dynamite or burying them
near to the place where they have been found have been
generally employed. Latterly it has become the fashion to
remove them to public parks in order to preserve them ; and
fine specimens may be seen in those places at Manchester,
Salford, Oldham, and Macclesfield, where they are not only
preserved, but exposed to public attention. He (the Presi-
dent), when visiting A shton-under-Ly ne the other day,
observed another use to which boulder stones had been
applied. There in the churchyard on the Manchester Road
a greenstone boulder, instead of being buried as was for-
merly the custom, is now used as a tombstone over the
grave of a son of an alderman of that borough. This is the
first instance where he had seen a boulder stone used for
such a purpose, and it is one where they may not only be
preserved, but exhibited to the public. Over the grave of
the late Mr. Locke the Railway Engineer, in Kensal Green
Cemetery, is a block of red granite, but although plain, he
thinks it is not a boulder like the one at Ashton-under-
Lyne.

“The Land Subsidence at Northwich,” by Thomas
Ward, Esq.

Having been an eye witness of the great subsidence of
land at Northwich on December 6th, I will endeavour

Proceedings — Lit. & Phil. Soc. — Vol. XX.— No. 5— Session 1880-81,

56

to explain how it arose. The district, of which North wich
is the centre, has two beds of rock salt underneath it. The
first one, about 40 yards from the surface, is on the average
25 yards thick. Below this there is a bed of much in-
durated clay about 10 yards thick, and below this again
the bed of lower rock salt some 35 yards thick. From 1670
to 1780 all the rock salt mined was obtained from the
“ Top Rock,” as it is locally called, and the miners left too
few supporting pillars, and these not large enough, besides
working the salt out so as to leave only a comparatively
thin crust of salt as a roof. The great majority of the
mines in the Top Rock salt have fallen in wholly or
partially. Since 1780 the rock salt has been “got” from
the lower bed, and the pillars, especially of late years, have
been left much larger, the roof at the same time being much
thicker. Only from 5 to 6 yards of salt near the bottom
of the bed has been worked. As a rule the mines in the
bottom rock salt have stood firm, and where the owners
have worked to their boundaries they have allowed the
brine to run into the worked-out mines, thus converting
them into reservoirs. The quantity of rock salt mined is
small compared with the white salt manufactured. The
white salt is made from a natural brine which is found on
the surface of the “Top Rock.” It is found much cheaper to
let the water do the mining and then pump up the salt in
solution and drive off the water. The fresh water, as soon
as it reaches the rock salt, eats it away till it gets fully
saturated. This water running over the roofs of the old
“ Top Rock ” mines has in numbers of cases eaten the whole
of the salt away and opened a communication into the mine
below. The overlying clays and earths, being deprived
of their support, fall into the cavity thus opened, and a hole
is made from the surface. On December 6th this was what
occurred, and a hole or rift opened right across the course
of the Wincham Brook, the water immediately rushing

57

below. As the mines in both “Top” and “Bottom” rock
were nearly exhausted of brine, the cavities to be filled
were enormous. Directly beneath where the fall occurred,
and bordering on an old abandoned Bottom Mine, was a
rock salt mine being worked. The barrier between the two
having been on two occasions penetrated, it now gave way,
and opened a communication with 15 acres of mine having
a worked-out depth of about 18 feet. Into this mine, down
a funnel of 100 yards in length from the surface, the water
rushed with great velocity, causing the lower portion of the
brook to retrace its course and drain off a large body of
water from the Biver Weaver and an adjoining lake called
the Top of the Brook. This immense body of water,
rushing into the underground cavities, drove out the air
contained therein, and so violent was the compression of the
air that it forced its way through every portion of the con-
tiguous district that was in the least rifted or weak, show-
ing itself in violent ebullitions in all the neighbouring pits
and where the earth was fractured, causing a number of
miniature mud geysers of 10 to 12 feet in height. Much
property was seriously damaged, and a considerable piece of
land covered with water. Five sets of salt works are
stopped owing to the destruction of a road and the pipes
conveying the brine from the pumping district to the
works. The greatest sufferers by this subsidence had little
to do in causing it, and this is one of the great anomalies of
the system of obtaining salt. The property of numbers of
persons in no way connected with the salt trade is seriously
injured, and under the existing law no compensation can be
obtained.

This great subsidence is interesting from a geological
point of view, as showing the action of natural forces, and
illustrating how change of surface may occur. A counter-
part of the Old Salt Lake of Triassic times is in process of
formation.

58

“ Some endeavours to ascertain the nature of the insoluble
form of Soda existing in the residue left on Causticizing
Sodium Carbonate Solutions with Lime” (Part II.), by Wat-
son Smith, F.C.S., Assistant Lecturer on Chemistry in the
Owens College, and Mr. W. T. Liddle. Communicated by
Professor C. Schorlemmer, F.RS.

At the close of our last paper we mentioned that it was
our intention to try certain further experiments with the
crystalline precipitate obtained by mixing solutions of
sodium carbonate and lime water and warming, and also
with ordinary “ lime-mud ” from the causticizing pan of an
alkali- works, after the usual washing and draining. The
experiments we proposed to try were :

(1) The effect of ignition upon the crystalline precipitate

prepared as above, and upon the “lime-mud” of
the soda- works.

(2) The effect of long continued boiling with water.

(3) The effect of boiling with some saline solution, as for

example with sodium sulphide.

Two fresh samples of the crystalline precipitate were
now prepared, each in rather a different manner from the
other. In the first case lime water was used in slight
excess, and the sodium carbonate solution was dilute ; in the
second a strong solution of sodium carbonate was employed,
the sodium carbonate being in excess. The precipitates
obtained in both cases appeared under the microscope simi-
larly crystalline; we will call them A and B respectively.
On analysis the following results were obtained, after the
precipitates had been washed with hot water till quite free

from all soluble alkali :

A. B.

Calcium carbonate ...98*07%.: 98*11

Sodium carbonate ... 1*93% 1*88

100*00 99*99

(1) A weighed quantity of dried precipitate, previously
well washed from all soluble alkalinity, was now ignited

59

strongly for about an hour, subsequently treated with
dilute spirits of wine (water and alcohol, 5:2) filtered,
washed well, any little lime in the filtrate precipitated,
again filtered, washed, and the filtrate finally evaporated
to dryness and weighed. Thus it was found that every
trace of soda was extracted from the substance, both by ex-
amining the perfectly white sodium carbonate obtained,
qualitatively, and also the residue of calcium carbonate
with the spectroscope. The weight of Na2C03 extracted
was found to be 2*00%, closely agreeing with the amounts
determined. (See above analyses A and B.)

(2) A weighed quantity of the crystalline precipitate was
now subjected to a six-hours’ continuous boiling with water,
adding water from time to time to replace that evaporated.
By this means 17% Na2C03 was extracted, leaving about
Q‘2% Na2C03 in the residue, which the six-hours’ boiling
therefore failed to remove. The residue on spectroscopic
examination showed that soda still remained behind.
Doubtless another hour’s boiling would entirely remove it.

(3) The effect of boiling for six hours with a solution of
sodium sulphide, obtained by lixiviating the mass resulting
after fusing a mixture of ordinary salt-cake and charcoal,
showed us that by this means much less soda is extracted
than when pure water is used. The six-hours’ boiling ex-
tracted only 0‘5% Na2C03, thus leaving about 1*4% in-
soluble in the residue. The crystalline precipitates we
obtained as described were anhydrous as the analyses show.

With regard to the lime-mud , the soda insoluble in water,
and which long washing with hot water could not remove,
was found in another sample of the mud to be 2*10%
Na2C03, the amount of soluble alkali =2*62%, giving a total
content of soda as

2T0% Na2C03 insoluble
2-62% „ soluble

472%

total.

60

The water in the lime-mud was estimated by heating to
110° in a current of hydrogen till a constant weight was
obtained. Thus 34*6% of water was found, and calculating
now on dry residue , we get as

Na2C03 insoluble, 3*21%

„ soluble, 4,00%

„ total 7*21 *

(1) After first washing a weighed quantity of the lime-
mud, passing C02 to convert any lime into carbonate, and
washing again to remove soluble alkali, the residue was
ignited for an hour strongly, and then after a thorough wash-
ing with dilute alcohol, precipitation of any dissolved lime in
filtrate, determination of soda obtained, and spectroscopic
examination of residue, we found all soda was thus removed.
This result agrees with that obtained by ignition of the
precipitates we prepared. Kynaston found the same many
years ago, in some examinations of lime-sludge, and hence
we can quite confirm his results.

(2) The experiment was now tried of boiling a weighed
quantity of the mud (having first passed COa), for six hours
continuously with water, from time to time replacing what
was lost by evaporation. The whole was now filtered and
washed thoroughly, the filtrate being carefully evaporated
to dryness. The residue gave a slight soda reaction in the
flame, and was dissolved in hydrochloric acid, lime and
other bodies precipitated (a little iron and alumina with
ammonia, and the calcium as oxalate), and then this filtrate
was also evaporated to dryness. By this means it was
found that practically all the soda was extracted by the
prolonged boiling, the amount left behind being inappreci-
able.

It may now be interesting to mention that Fritzsche in
1864 (Journ. fur Prakt. Chem. 93, 339) succeeded in obtain-
ing crystals artificially of the body till then only known as
a mineral under the name of “ Gay-Lusslte” These crys-

61

tals he obtained by the action of a boiling solution of sodium
carbonate upon a smaller quantity of a solution of calcium
chloride of 1*13 spec, gr., and letting the whole stand for
some days. The analyses of these crystals showed them to
consist, as Gay-Lussite does, of CaC03, Na2C03-f5H20. On
heating with water the body is decomposed, sodium carbon-
ate being dissolved and calcium carbonate being left behind.
It was also found that the salt, when dehydrated, is more
easily and quickly decomposed by water than before dehy-
dration, and it would appear in fact as if the calcium car-
bonate and sodium carbonate were simply held together by
the water of crystallisation.

When Fritzsche came to analyse the crystalline body he
obtained, he attempted it by washing out the sodium carbon-
ate, igniting the residue of calcium carbonate, and weighing
the calcium oxide remaining after the ignition. On testing
the residue by solution in very little hydrochloric acid, a very
small evolution of carbon dioxide was observed, and this led
to further examination, resulting in the discovery of a small
quantity of sodium carbonate which had remained insoluble
with the calcium carbonate. Fritzsche promised to experi-
ment further in this new direction, but it does not appear
that he has. Nevertheless, the results he obtained show
that in two experiments the quantities of sodium carbonate
retained as insoluble in the calcium carbonate residue, after
careful washing, were, (1st) 1*8 per cent, (2nd) 2 ‘4 per cent,
thus closely agreeing with the amounts we found in our
crystalline precipitates, the analyses of which are given
above.

Of course we are aware that several speculations might
be advanced to account for the occurrence of the soda in the
calcium carbonate in the insoluble form, but it seems to us
most in accordance with the results we have obtained, with
others, to view it as combined with an equivalent propor-
tion of calcium carbonate, an insoluble compound being
formed.

62

The practical bearing of onr results would seem to be
upon (1) the “ causticizing process/’ and (2) on the “black
ash” process of the soda manufacturer. In the first case,
as already mentioned, the residual soda is kept in circula-
tion in the process, and so is not lost, the lime-mud being
drained, and used again in the black ash mixture. In some
works, however, where black ash is not made, e.g., soap
works, causticizing from soda ash, &c., an average loss of
about 7£ per cent Na2COs of the dry residue or 4*7 per cent
of the washed and well-drained mud, is sustained. In the
second case, it is evident that an adequate improvement,
by which a minimum amount of calcium carbonate is used
in the black ash mixtures, must effect an improved yield of
soda or lixiviation, a smaller retention as insoluble com-
pound in the soda-waste occurring. Wright’s results and
remarks on this head, are valuable. (See his paper, already
cited — Part I).

63

Ordinary Meeting, December 28th, 1880.

E. W. Binney, F.RS., F.G.S., President, in the Chair.

“The Literary History of Parnell’s Hermit,” by William
E. A. Axon, M.RS.L., &c.

In this paper the author traced the story of the angel
and the hermit which forms the subject of Parnell’s “Her-
mit.” Yoltaire, wTho used the same apologue, was thought
to have copied it from Parnell, but it has been used by many
others. James Plowed, Sir Philip Herbert, Dr. Henry More,
and Thomas White employed it in the seventeenth century,
and Luther Bradw^ardine and Herolt still earlier. It occurs
in Gesta Bomanorum and other similar collections of the
fourteenth century, and in various recensions of the “Yitse
Patrum.” It is also in the Koran, and had probably been
borrowed by Mahomet from a Jewish source, as a very
interesting form of it is in the Talmud.

The relations of those different versions to each other was
then discussed at some length in their connection with the
history of fiction.

General Meeting, January 11th, 1881.

E. W. Binney, F.RS., F.G.S., President, in the Chair.

Mr. Daniel Adamson, F.G.S., of the Towers, Didsbury,
was elected an Ordinary Member of the Society.

Ordinary Meeting, January 25th, 1881.

E. W. Binney, F.RS., F.G.S., President, in the Chair.

R D. Dakbishire, F.G.S., read a paper “ On the Question
Proceedings— Lit.,& Phil, Soc. — Vol. XX.— No. 6— Session 1880-81,

64

of the desirability of the Society’s Library being handed over
to the Free Reference Library of the Corporation.”

Only two of the 26 members present were in favour of Mr.
Darbishire’s proposal, and a letter from Dr. Schunck was
read also in favour ; but letters from Dr. Clay, Dr. Roscoe,
Mr. W. H. Johnson, Mr. Cottam, and Mr. Baxendell were
read against the proposal.

Ordinary Meeting, February 8th, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

Mr. Lund, F.R.C.S., exhibited a new form of mercurial
thermometer by Mr. Fraser, of Edinburgh.

Mr. S. C. Trapp and Mr. W. H. Johnson were appointed
Auditors of the Treasurer’s accounts.

Ordinary Meeting, February 22nd, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

The President reminded the members present that yes-
terday was the 100 th anniversary of the first meeting of
the Society.

Dr. Balfour Stewart, F.R.S., communicated the follow-
ing letter from Mr. Herman Hager : —

1, Derby Road, Fallowfield,
February 8^A, 1881.

Dear Dr. Stewart,

I have found in Schultz Das Hofische Leben the following
notes with regard to severe winters and famines :

1100. Very severe winter, famine, great mortality.

1111. Very severe winter, great famine and mortality.

1115. Very severe winter.

.65

1124. Great famine in England, severe winter, the Rhine

frozen over and used as a high-road.

1125. Bad harvest, in consequence famine in France from

November 1st to the next harvest, winter very
severe.

1133. Rather bad harvest.

1134. Likewise bad harvest owing to protracted drought.
1137. Unheard of drought, famine begins, -which lasts 11

years.

1142. Hard and long winter, great floods.

1144. Very bad winter, famine, harvest began August 30th

instead of July 25th.

1145. Plague and famine.

1146. Famine.

1149. Very hard winter, sea frozen 3 miles (German) out

from the coast, dearth, great famine in Austria.

1150. Very hard winter.

1151. Great famine.

1153. Saevientis hiemis insolita asperitas.

1155. Bad harvest, famine.

1159. Severe winter.

1161. Everywhere great famine.

1162. Hearth.

1167. Very severe winter.

1168. Famine.

1171. Great drought, beginning of dearth.

1172. Hearth.

1173. Unusually severe winter, much mortality.

1174. Famine.

1175. Famine in England.

1176. Famine in France.

1177. Famine and dearth.

1179. Hard winter.

1181. Great drought, dearth.

1821. Famine in Italy.

1183. Very hard winter.

1188. Bad harvest, famine, unheard of drought.

1191. Famine in Italy, much sickness in Austria.

66

1194. Famine.

1195. Famine in Austria, in France begins a famine lasting

4 years.

1196. Great famine in Germany and France, very bad harvest.

1197. Famine continued.

1202. Dearth in Italy.

1204. Famine, severe winter.

1205. Severe winter.

1206. Great famine.

1212. Famine in Upper Italy.

1216. Very severe winter in Upper Italy.

1224. Long winter, famine in Upper Italy.

1227. Great famine.

1231. Dearth.

1233. Severe winter.

1234. Severe winter in Italy.

1235. Great famine in France.

1240. Dearth.

1247. Famine.

1252. Very cold winter, rivers frozen 6 feet down, great

famine in Austria.

1253. Severe cold.

1258. Dearth all over Italy.

1261. Great dearth in Germany,

1264. Great famine in Suabia.

1270. Famine in Germany.

1271. Great dearth in Parma.

1277. Dearth in Italy, famine in Poland.

1281. Famine in Bohemia and Silesia.

1282. Famine in Poland.

1315. Terrible famine in Livonia and Esthonia.

There are many more particulars in Schultz about comets,
earthquakes, etc., but if I understood you rightly, you did not
want those for your present purpose.

Yours very truly,

HERMAN HAGER.

*r Ozone and the Hate of Mortality at Southport during the
Nine Years, 1872—1880,” by Joseph Baxexdell, F.R.A.S,
It is commonly supposed that the salubrity of a town

67

or district is indicated by the greater or less amount
of free ozone usually present in the atmosphere, and the
results of occasional comparisons of the observed amounts of
ozone with the rates of mortality have generally tended to
support this view; but in order to ascertain clearly the
nature and extent of the connection between the amount of
ozone and the rate of mortality, it is evidently necessary
that before comparison with the rate of mortality is made*
the registered results of ozone observations should be cor-
rected for the effects of the various meteorological causes
which are known to influence the observed amounts of
free atmospheric ozone. Among these causes, the velocity
of the wind is by far the most important. Other things
being the same, the greater the velocity of the wind and the
greater will be the registered amount of ozone. I therefore
calculated the mean daily velocity of the wind for the nine
years 1872 — 1880, from the observations taken with the
Eobinson anemometer mounted by Mr. Dancer at the South-
port Meteorological Observatory, and as I had found that
the variations in the recorded amounts of ozone are approxi-
mately proportional to the variations in the mean daily velo-
city of the wind, I calculated the corrections necessary to be
applied to the observed amounts of ozone to reduce them to
what they would have been had the mean velocity of the
wind been the same in every year. The data used in the
calculations, were the mean velocity of the wind for the nine
years, 266*9 miles; the mean amount of ozone for the same
period, 5*07, and the mean velocity of the wind, and mean
amount of ozone for each year.

Year.

Mean
Velocity of
the Wind

Mean
Observed
Amount of

Correction
for Velocity
of the

Corrected

Amount

of

1872

in Miles.

. 311*4 ...

Ozone.

... 5-60 ....

Wind.

.. —0-80 ...

Ozone.

... 4-80

1873

. 296-8 ...

... 5-40 ....

.. —0-54 ...

... 4-85

1874

. 294-0 ...

... 4-91 ....

.. —0-45 ...

... 4-45

1875

. 269-2 ...

... 4-21 ....

.. —0-04 ...

... 4-17

1876

. 2716 ...

... 4-51 ....

.. —0-08 ...

... 4-43

1877

,. 286-3 ...

... 6-01 ....

.. —0*41 ...

... 5-60

1878

. 242-8 ...

... 5-30 ....

.. +0-53 ...

... 5-82

1879

. 213-8 ...

... 4-96 ....

.. 4-1-23 ...

... 6-19

1880

. 2161 ...

... 4-72 ....

• • 1 • • •

.. 4-1-11 ...

... 5-83

Means, .

....266-9 ...

... 5-07 ...

... 5-13

68

It appears, therefore, from the numbers in the last column
of the above table, that when allowance is made for the
velocity of the wind, the mean amount of free ozone in a
given volume of the air in Southport— say, for instance, the
average quantity that enters into the lungs of a healthy
person during a day — was least in 1875, and greatest in
1879 ; and that in each of the five years 1872 — 1876 the
mean amount was below the average for the nine years,
while in the four years 1877 — 1880, during which consider-
able improvements in the sanitary condition of the borough
have been made, the mean amount has been much above
the average.

Comparing now the corrected annual amounts of ozone
with the death rates of the borough, we have the following
results :

Corrected

Gross

Local

Zymotic

Year.

Amount of

Death

Death

Death

Ozone.

Kate.

Rate.

Rate.

1872

480

,. 22-82 ...

... 18-06 ...

.... 206

1873

. 4-85

,. 22-03 ...

.... 3-74

1874

,. 4-45

,. 22-14 ...

... 18-42 ..

.... 3-11

1875

4-17

22-37 ...

... 19-28 ...

.... 2-64

1876

4-43

.. 2106 ...

... 17-63 ...

.... 2-82

1877

5-60

.. 19*75 ...

... 16-42 ...

.... 1-69

1878

5-82

,. 19-71 ...

... 16-35 ...

.... 2-13

1879

.. 6-19

.. 18-09 ...

... 15-48 ...

.... 0-73

1880

5-83

.. 20-73 ...

... 18-35 ..

.... 1-43

Means ,,

513

.. 20-97 ...

... 17-65 ,.

.... 2-26

An examination of the numbers in this table shows that
in the five years 1872 — 1876, when the mean amount of
ozone was always below the average for the nine years, the
gross death rate was always above the average, while in the
four years 1877—1880, when the mean amount of ozone
was always above the average, the gross death rate was
always below the average. In four of the five years of
lowest amount of ozone, the local death rate was above the
average, and in the fifth year it was almost exactly the
average ; while in three of the four years of highest amount
of ozone, the local death rate was below the average, but in
the fourth it was above. It must, however, be remarked,

69

with reference to this year, 1880, that the death rate is base'd
upon an uncertain estimate of the population, and therefore
may admit of material correction when correct returns of
the population shall have been obtained. In four of the five
years of low amounts of ozone, the zymotic death rate was
above the average, and in the fifth slightly below; and in
the four years of high amounts of ozone the rate was always
below the average.

During the five years of low amounts of ozone, the gross
death rate was 12 -8 per cent greater than in the four years of
high amounts of ozone ; the local death rate 10-9 per cent
and the zymotic death rate 92*6 per cent greater.

I have only to add that a comparison of the general re-
sults of the observations of temperature, humidity of the
air, direction of the wind, and rainfall, with the ozone results,
shows that although these elements have sometimes an
influence npon the amount of ozone during short periods,
yet that, taking a period of a year, the opposite effects
during the short periods so far neutralize each other that
the mean amount of ozone for the year is not affected by
them to any very sensible extent, so that we are fully
entitled to conclude that the corrected amounts of ozone
given above fairly represent the actual degree of purity of
the air of Southport during the last nine years, and that
variations in the actual amount of free ozone exercise a
very sensible influence upon the state of the public health.

The President exhibited to the meeting an iron key, a
leaden seal of the Duchy of Lancaster, an ancient spoon, and
a curious piece of lead with an old English alphabet on it,
all found in digging the foundations for some new buildings
on a piece of land lying between Hanging Bridge and
Cateaton Street in Manchester.

The land from Church Gates in Cateaton Street to the
river Irwell on the west slopes gently, and the underlying

70

rock is the Trias sandstone so commonly seen on the hanks
of the Irwell, covered by about 27 feet of valley sand and
gravel. It has been much changed in appearance since the
waters left it and retired to their present bed, as from the
excavations made in his land there was the course of a small
brook spanned by a bridge of two arches, now covered by
broken stones and rubbish, and connecting Cateaton Street,
along Hanging Bridge, with the site of the Cathedral.

His architect, Mr. Henry Worthington, of this city, col-
lected the specimens now on the table, and to him he was
also indebted for the sketch of the two arches, under the
most northern of which the small stream of about 18 inches
wide and 7 inches deep flows. It was in and near the bed
of this stream that the objects were found, having been
probably thrown or dropped in from the Hanging Bridge.

The seal of the Duchy appears to be of about the com-
mencement of the fifteenth century, is a casting in lead of
about 2 inches in diameter, and has a hole in it as if it had
been attached to some body by a string.

The old spoons, which are of lead, and key of iron, are of
ancient date, but their exact age it is difficult to say.

The small piece of lead, § of an inch thick, about 1 \ inches
long, by 1J inches broad, and having a slight handle of
about half an inch, has in relief on one side an ancient
alphabet, and on the other a cross. Now, Chambers, in
their Book of Days, at page 47, in giving a description of
Horn Books, say that “ they are now very rare, even the
most modern ones, and that the alphabet on them was
invariably prefaced with a cross, whence it came to be called
the Christ Cross Row, or, by corruption, Criss Cross Row, a
term which was often used instead of Horn Book. In
earlier times it is thought that a cast leaden plate, contain-
ing the alphabet in raised letters, was used for the instruction
of the youth of England, as Sir George Musgrave, of Eden
Hall, possesses two carved stones, which appear to have been

71

moulds for such a production.” In the specimen found at
Hanging Bridge, the letters are not prefaced with a cross,
hut the cross appears on the hack. However, the supposi-
tion that some of the earlier of these Criss Cross Rows were
in ancient times cast in lead has received a remarkable
confirmation by the finding of his specimen, and he hoped
some time to be able to compare his cast with the mould in
the late Sir George Musgrave’s possession. The characters
of the letters appear to be about the beginning of the
fifteenth century.

“ On the Addition and Multiplication of Logical Relatives,”
by Joseph John Murphy, F.G.S. ; communicated by the
Rev. Robert Harley, F.R.S.

In this paper the Logic of Relatives means any logical
system wherein each relation is expressed by a special literal
term. The common logic is co-extensive with so much of
the Logic of Relatives as deals with the relations of inclusion
and exclusion. These relations are expressed in the present
system by Z and N respectively, so that " A is B,” or “ A
is included in B,” is expressed by

A = ZB or B = Z~1A,

and “ A is not B,” or “ A and B exclude each other,” is
expressed by

A = AB or B = AA.

The problem of the multiplication of relatives is : — Given
the relations of any two terms to a third term, to find the
resultant relation of the first two to each other. This is
identical with the problem of syllogism ; thus, if
A = ZB and B = JfC,

where L and M are any relative terms whatever, it follows
that

A = (Z x M)C.

Prof. Pierce ( Logic of Relatives , Memoirs of the American
Academy, vol ix.) speaks of the multiplication of relatives
in this sense. But the corresponding problem of their

72

addition, so far as I am aware, is now stated for the first
time.

The problem of the addition of relatives is : — Given any
two relations subsisting between the same terms, to find the
esultant relation.

Let us, for the sake of simplification, adopt Be Morgan’s
method of working in an arbitrarily limited universe. The
simplest possible case is that of a universe of only two
individuals, exactly alike except in name, and each having
an indefinite number of names. Let the relation between
the names of the same individual be symbolised by 1, and
the relation between the names of the different individuals
by -1. Four syllogisms arise by the multiplication of
these relations, and may be expressed by the following
“ canonical equations,” all of which are true also in common
algebra.

1x1 = 1

1 x (-1)= -1
(-l)xl 1

(-l)x(-l) = l

Which are thus expressed in language :

Identical if identical is identical.

Identical if opposite is opposite.

Opposite if identical is opposite.

Opposite if opposite is identical.

By the addition of the same relatives we get the following
canonical equation,

i + (-i)=o,

which is also true in common algebra, and is the expression
for the universe under consideration, of the truth that con-
tradictory relations cannot coexist.

If, as before, we express the relation of inclusion by L ,
and the converse relation by L~\ then

L + L~' = 1.

That is to say, if A is included in B and also includes B,
then A is identical or coextensive with B,

73

If, as before, L means inclusion and N exclusion, then
L + N= 0,

that is to say, these relations are contradictory.

Relatives are either invertible or uninvertible, and either
transitive or intransitive. Using L as the symbol of relation
generally, the symbol of invertibleness is

L~l = L,

and the symbol of transitiveness is

Z2 = A

There are thus four classes of relations.

1. Transitive and invertible. To this class belong the
relations of identity, and similarity in any one respect.
The only numerical coefficient that combines these proper-
ties is unity.

2. Transitive and uninvertible. To this class belongs,
among others, the relation of inclusion. The only numerical
coefficients that combine these properties are zero and
infinity.

3. Intransitive and invertible. To this class belongs,
among others, the relation of exclusion. The only numerical
coefficient that combines these properties is negative unity.

4. Intransitive and uninvertible. To this class belong an
infinite variety of relations : — among others, partial inclusion
(some A is B). These properties are combined in all
numerical coefficients except unity, negative unity, zero,
and infinity.

74

MICROSCOPICAL AND NATURAL HISTORY SECTION.

2nd November, 1880.

Alfred Brothers, F.R.A.S., President of the Section

j

in the Chair.

Mr. E. Ward exhibited some microscopic slides containing
vegetable sections double stained.

O

Mr. Thomas Rogers exhibited specimens of Chiton sca-
bridus (Jeffreys), from Jersey, collected by Duprey. It
appears to be rare. Dr. Jeffreys thought at first that it
might have been a variety of Ch. cancellatus, but the ar-
rangement of the sculpture, and its somewhat different form,
lead him to believe it quite distinct. Mr. Duprey finds it
under stones, along with C. cancellatus, Rizzoa lactea, R
striatula, and Adeorbis sub-carinatus.

Mr. Thomas Rogers also exhibited a prepared section of
the palate of an African species of Ampullaria, which had
been shown in a living state at the last meeting of the
Section.

Prof. W. C. Williamson, F.R.S., exhibited a large mass
of one of the Nidularise from Mr. H. D. Pocliin’s estate in
North Wales. Also some slides of Ascobolus, in various
stages.

Prof. Williamson explained the bisexual reproduction of
one of the the fresh water Vaucheriee.

Dr. John Tatham, through Mr. Bailey, submitted a form
of erecting microscope designed by Mr. Stephenson, which
worked very well when used for dissecting.

Mr. T. H. Birley read a paper explantory of the process
adopted by Herr Herpell, of St. Goar, in preparing specimens
of Hymenomycetous Fungi.

75

2nd December, 1880.

R. D. Darbishire, F.G.S., Vice-President of the Section,
in the Chair.

Mr. Robert E. Cunliffe submitted a copy of the General
Introduction to the reports of the “Challenger” expedition,
and reported the progress made in the publication of some
of the reports.

Mr. Samuel Moore exhihited a parasitical Alga which
he had found at Bridlington, growing upon Griffithsia ecjui-
setifolia.

Mr. E. Ward presented ~to the Society’s cabinet a slide
containing valves of Aulacodiscus Africanus, which he had
selected from a collection placed in his hands by the Section
at the close of last session.

Mr. John Plant, F.G.S., gave an account of his dredging
experiences in Cymmeran bay, from Rhoscolyn to Aber-
ffraw, on S.W. coast of Anglesea, in the years 1874 to 1880,
and submitted a list of 191 species of marine molluscs
occurring in that locality during the period named.

January 17th, 1881.

Alfred Brothers, F.R.A.S., President of the Section, in
the Chair.

Mr. Plant, F.G.S., exhibited some remarkably large and
fine shells of the pearl oyster (Meleagrina margaritifera),
from Somerset, Australia. Also a selection of N. American
Unionidse.

?6

!

Mr. Hastings C. Dent exhibited specimens of Anastatica
hierochuntica (L.), “The ftose of Jericho/’ and read a paper
thereupon.

Mr. R D. Darbishire, F.G.S., exhibited specimens of the
rare fresh-water bivalve Mulleria lobata, from Bogota, S.
America, and explained the unique process of its growth.

Mr. Lionel E. Adams gave an account of a luminous
centipede observed by him in a garden at Maidenhead,
Bucks, probably a species of Geophilus.

Mr. Charles Bailey, F.L.S., presented to the Section a
copy of the new London catalogue of Musci and Hepaticse
known to occur in the British Islands.

77

PHYSICAL AND MATHEMATICAL SECTION,
November 9th, 1880.

E. W. Binney, F.RS., F.G.S., President of the Section,
in the Chair.

“On Gravitation,” feby the Rev. Thomas Mackereth,
F.R.A.S., F.M.S.

All life, motion, energy, and force are to ns only such as
their vehicles present them, or as they make ns conscious
of their existence. In what I am about to discuss I wish
to include whatever originates force or effort under the
name of conatus. And of conatus in any way, I venture
to assert that we can know nothing excepting as it may be
presented by and through either its assumed or sensible
vehicle. Therefore it is impossible to think of a conatus
without thinking of or assuming a vehicle or subject.
Hence, to know a conatus we must know its subject.
Again, conatus acts from within in its subject to sustain
it, and by this effort the subject can act upon other sub-
jects from without, and other subjects can react from with-
out upon it; and thus the conatus within a subject can be
brought into contact with other subjects from without to
produce an effect. Without this action and reaction exist-
ence is impossible.

Each atom in the universe according to its ability attracts
to itself every other atom of the universe. This conatus
must be within each atom, but it is the subject or vehicle
of this conatus which produces the effect of presence by
the power of attraction. Thus the subject or substance of
the atom could not subsist without the internal conatus,
and the conatus could not produce the effect of presence

78

without the substance of the atom. As regards size or
bulk, an atom is the smallest and simplest subject or vehicle
of conatus ; but I think it possible to show that there are
simple subjects of enormous extent. Before proceeding to
that part of the discussion, and for the sake of more clearly
illustrating the meaning of what I have to say, I would
observe that all the visible subjects of nature are more or
^ess compounds of conatus, that is to say, many kinds or
intensities of force and their subjects exist in one subject,
yet in that subject there is one conatus that controls the
whole, and makes out of many a unit. This all-pervading
conatus I would call the simplest, because the most univer-
sal, and therefore, relatively, a conatus and subject of enor-
mous extent. Now, every element or atom of which a tree
is composed has its own conatus and its own subject. To
suppose that these respective and differing intensities of
conatus and their subjects are annihilated during the time
that they are making up a tree is to suppose the annihila-
tion of the tree whilst it exists. But as all these various
forces make up but one subject, it is clear that there must
be one conatus that controls the whole, and which makes
all the other forces yield it service. This whole subject
now becomes the vehicle for the all-governing conatus, be-
cause in its government it makes up of all the other forces
and their subjects what we call in this illustration a tree.
And we know nothing of the all-pervading conatus of a tree
excepting as it manifests itself in the effects which its sub-
ject produces. Nor could all the conatus that make a
tree from within subsist as a tree without the reaction of
conatus from without, that is, from atmospheric air, &c#
Hence, if there be no vehicle or subject there is no conatus,
and if there be a conatus there must be a vehicle or subject
and if there be a subject there must be action and reaction.
All the subjects of nature afford an illustration of what I
have called the government of compound conatus by an alb

79

pervading simple one of enormous extent. And further, the
more a subject consists of compound forces of strong inten-
sity the more it is capable of making itself manifest to the
senses. And the less the subject of a conatus is com-
pounded, whether small or large, the less it can make itself
sensibly manifest.

The general uses of the air we breathe are well known.

O

It is equ ally a well known that the air is the vehicle of what
we call sound. Conatus acting in and through the air pro-
duces vibrations. But these vibrations are not sound until
this conatus by the vibrations of the air has affected
another subject and produced the reaction of the ear.
Then as the conatus and the subject of the ear harmonize
sound is manifest. It is plain that if the vehicle of the vi-
brations is removed sound cannot exist, or if we can conceive
of the conatus of the vibrations existing without the air, it
cannot make itself known. Further, if vibrations are made
in the air for the production of sound, and another order of
vibrations, as it were, crosses them so that a crest of one
wave coalesces with the depression of another, no sound can
be produced. But just as sound could not exist without air
so also without it this silence could not be produced. And
further, in the production of sound the law of the squares
of distance is observed, and that for a reason which I think
will shortly appear. Atmospheric air, however, is not a
simple subject, for many conatus act in it. Hence it
is a substance to that degree manifest to the senses, and
we are so far physically conscious of its existence. But if
atmospheric air be not a simple subject of enormous size,
then it may be controlled and permeated by something more
simple and more enormous.

Because the undulatory theory of light explains more of
its phenomena than the emission theory, the former has
been adopted. This undulatory theory assumes the existence
of another medium than atmospheric air called luminiferous

80

ether. Of this ether we are in no physical sense conscious,
though there are the most substantial reasons for the as-
sumption of its existence, reasons sufficiently cogent to make
its existence a fact. If we were unconscious of the undu-
latory activity of the air we should have to resort to the
assumption of such a subject and its activity to explain the
production of sound, for in every way light produces its
effects as sound does. The magnet and luminosity prove the
presence of some vehicle or subject when atmospheric air is
absent. Hence atmospheric air neither assists in the forma-
tion or the production of light, therefore the substantial
reason for assuming another medium that conatus may pro-
duce light. Light then does not exist apart from the vi-
brations of luminiferous ether, yet these vibrations do not
produce light until they are arrested by a reactionary sub-
ject. The capability of this ether, then, is to create from a
luminous force acting within it, a force of vibrations so as to
produce after reaction the effect called light. Now, it is
obvious that the capabilities of the atmospheric air cannot
produce light, nor can the capabilities of luminiferous ether
produce sound. Hence the two media must be totally
different in their constitution. But though this is so it is
equally evident that this ether pervades atmospheric air
everywhere. I have said respecting a tree that if any ot
the subordinate conatus of it should overpower the govern-
ment of the pervading one, the tree, in proportion to such
resistance and its continuance, comes to an end. And that
the vibrations of the air can be so made as to destroy the
effects of each other and so annihilate the cause of sound.
Similarly the vibrations of luminiferous ether can be made
to neutralize each other and from light to produce darkness.
And as in the vibrations of atmospheric air the law of the
squares of distances holds good, so also it obtains as strongly
if not more perfectly in luminiferous ether, for the pro-
duction of light, heat, magnetism, or electricity. But We

81

are physically unconscious of the presence of luminiferous
ether, and this must be so if it approaches nearer to a
simple subject of an enormous size, though if it be such a
subject its conatus must be more potent than atmospheric
air, and its constitution more simple.

But neither the one nor the other nor both of them com-
bined are the cause or the reason why they surround the
earth everywhere. This cause under certain modifications
may be said to originate in the earth herself. These modi-
fications I now come to discuss. The earth, according to
her density, I take to be the expression of the conatus there-
of. And the fulness of her density is the fulness of her
conatus. This conatus , like every other, acts within its
subject for its production, maintenance, and manifestation.
The subject, then, so far as the earth is considered, is the
earth’s density taken as a whole. But if we say density is
a subject we simply say that force is a subject, for where
there is no force there is no density. But if density be the
result of force then the density of a thing will be exactly
proportional to the various forces within the various atoms
of a subject to press themselves together. Hence, there will
be as many kinds of density as there are forces or intensi-
ties of conatus, and these will be manifest in their subjects
whether simple or compound. But the more compounded the
subject the more it is sensibly manifest or the more it is what
is called substance. But just as the various elements of a tree
are held together by an all-pervading conatus, so the totality
of the conatus that are in the various elements of the earth
are pervaded by a common conatus, and this common or
universal conatus is manifest in the earth herself as the
subject. This common or terrestrial conatus is exerted
within and throughout the earth for her individual preser-
vation as the subject of it. But if nature be uniform in her
mode of operation this common terrestrial and earth pre-
serving conatus must by means of its subject be able to

82

produce something beyond the subject, and this something
must reach to and affect other subjects. As conatus by
means of air affects the ear and produces sound as lumi-
nosity by means of luminiferous ether produces light on
subjects, so the preserving conatus of the earth must reach
to and affect other subjects and produce some effect.
What is this effect excepting what is called gravitation or
the power of drawing exterior things to herself? And if
this be the exterior product or conatus in contradistinction
to her own interior conatus there must be a vehicle through
which it operates. It is well known that the gravitating
power of the earth not only reaches to the moon, but to the
sun and all the planets. What is the vehicle through which
such an effect is accomplished ? It is equally well known
that all the planets have their respective gravitating
influences and so affect the earth, each other, and the sun.
But the supreme gravitating power in our system originates
in the sun.

Now, I wish it to be distinctly understood, that the
conatus or force to produce density within each member of
the solar system in the way I have described, is considered
as applying itself absolutely and solely to the maintenance
and the individuality of each planet or of the sun. From such
consideration it will follow that the maximum of this cona-
tus is found within the limit of the orb. Or, if this be not
so, then this conatus has more than one subject or vehicle,
and more than one effect, namely, more than the production
of density, which is inconsistent with the maintenance of
individuality. The region in which the gravitating power
of the sun and planets is exercised is supposed to be devoid
of density, that is, devoid of all substance or subjective
matter. Hence we arrive at the conclusion that an exterior
conatus is created by the interior conatus of the sun and
planets which has no subject or vehicle, and this happens
where there ought to be the most simple and poweiful sub-

83

ject of the most enormous extent. If this be so, nature is
most unlike herself in her greatest extent, and in her most
wonderful operation. But let us assume the existence of
such a subject. If it be of the simplest kind, as it must be,
then it can only be affected in one way, and lie utterly be-
yond the recognition of mere sense. The one way in which I
assume this universal subject or medium to be affected is the
way in which it receives and reacts on the internal conatus
of all the members of the solar system. This exterior cona-
tus will be at its maximum of receptivity and reaction in
the periphery of each orb, and at its minimum in the
boundary of the solar system. The conatus for density and
individuality reaches its greatest force in the same periphery ;
therefore it will happen that the highest result of this action
and reaction will take place. And this highest result is
what I call gravitation, which attains its maximum at the
periphery of the heavenly bodies. But I also assume that
this assumed universal medium has a conatus of its own,
independent of the produced conatus for gravitation, and
that it is a uniform, constant, all-pervading and never-
failing effort of persistence and resistance which no other,
excepting the conatus of the sun and planets, can affect.
Hence every other conatus must bow to its force and obey
its law. And I take this to be the reason why the law of
the squares of distance is found to prevail in the forces of
the air and of luminiferous ether, as well as in every part of
the solar system. That is to say, the resistance of this as-
sumed medium is equal to the squares of the distance of the
sun and planets acting upon it, and its disturbance is the
disturbance of gravitation.

In consequence of the constant and universal persistence
of this assumed conatus and its medium force of a different
kind, that is, the force which produces motion, can act uni-
formly throughout it according to its own conatus, just as our
own bodies can move about in the pressure of atmospheric

84

air, and nothing can affect the force of motion excepting
that which produces the law of gravitation, and this law
under certain circumstances the force of motion can over-
power and neutralize, as differing undulations in the air or
ether can be made to neutralize each other. Hence the
force of motion is independent of any conatus to produce
gravitation, and of course independent of gravitation itself.

85

Ordinary Meeting, March 8th, 1881.

E. W. Binney, F.RS., F.G.S., President, in the Chair.

“ Additions to the paper ‘On an adaptation of the La-
grangian form of the Equations of fluid motion’,” by R. F.
Gwyther, M.A.

With the permission of the Society I desire to add a few
results to those which I communicated to the Society in the
paper mentioned above. I treat these results as additional
to the paper rather than as a separate communication,
because the methods are identical with those used before,
and deal with the general case of fluid motion. I hope in a
subsequent paper to show how some special cases can be
treated so as to obtain simpler results, better capable of
being tested by observation.

1. If P be any scalar, so that D*P = P - (So- v P)

Then vDtP= vP- v(So-vP)

= V P — Vp v P — (S<r v ) V P — (S v P V V *

V DjP = DivP-VpVP-(SvPv)<r
and D*vP= vD*P + Vp vP + (SvPv)ff

N ow any vector h may be written l v </>i + m v 02 + n V 03
whence by applying the above we get

= D tl. V (j)i + D tm. v </>2 + Dp?.. v 03 + Vp£ + (S3 V )<r (1)

If we put S = a we get the formula of Section II. (2).

Also if l be written L^- + + N~we get

H H H

D«o = D,L.g + U(M.| + D.N.2 + LD«“ + &o.

= DtL.g + &c. -(S3v)<r (2)

because = 4^-

H d(f> i

# Notes on some Quaternion transformations. Proc. Lit. & Phil., Yol. XIX.

Proceedings— Let. & Phil, Soc.— Yol. XX.— No 7,— Session 1880*81*

86

Now V v o’ or p can be written SiH.-^ + 22H^ + 23H.!jf .

D*p = D*logH.p- (SpV)<r (3)

Imagine p also written p = H(£i v 0i + h V 02 + h V 03)

D,p = D* log H.p + H (DA- V 0i + DA* V 02 + DA. v 08) + (Sp V )<x

h r

whence D,p - Dt log H.p = - 4 DA* v 0i + DA- V 02 + DA- V 08),

or 2Dfg = DA* V 0i + &c (4)

These formulae enable us to find convenient forms for certain
expressions, giving the manner of the motion. Thus
D(Sg = SD(<r.g + S«TD1£

= S( V D,P + Vp<r + S^v <7)4 - S<7S4 V <7 by (1)

XX xi

= SvDjP.T (5)

since

S(pSo-v - <xSp v )(T = SV. Vpo- v (t = SVp<7 Vff = 0
and generally

S(pS() v -SSpv)<r = 0 (6)

whatever vector 3 may be. Again

D,^ = S;H"S(lSffV+ffSHV)ff

= StTg - 2S^.(S<7 V )<7. (7)

Also writing

i'LEtMR*NB

as in (2), we get

S3V = -(Li + M-t+N-t)

d(pi dcpz d<f> «/

M^+*&D‘+N4M

= S(DeS + Sav<7)v +SavD(by (2)
and especially

Dt'SHv =(S3v)Dt

but

Dt(Sff V ) = (Str V ) + (So- V )D<.

(8)

87

The equation (6) shows a curious theorem in the kinematics
of vortex motion, connecting the relative velocities of points
near a vortex line.

The equation may be written Sp(S«r8 v )cr = S£(S xp v )v where
we shall consider, for the moment, that p and 8 are unit
vectors — since we may divide by the product of their tensors.
The theorem may be stated thus. If 0 be any point on a
vortex line at which o- expresses the velocity, and if equal
small distances (pc) be taken in the directions of p and of
any vector 8; the velocities relative to that at O are
-a(S pv)<r and -#(S£v)<r, and are such that their compo-
nents resolved along 8 and p respectively are equal to one
another. If the vector 8 be one which moves with the
fluid (as g) we may then state the theorem of the actual
relative motions, for we could write the equation

S^D,S = S®(£-

Similarly |D*(T£)2 = S£(S3v)<r = the projection of the relative
velocity upon 8 itself; and - Va(Sa v)<r is the vector express-
ing the double of the rate at which areas are described by
the vector 8. If we operate upon this with D* we get
-VS(S5v)lV

If we project the double area found above on the plane
perpendicular to p we get

-Sp8(S8v)<r-fTp (9)

But - SP3( S3 V )(T = sa.psa V O- = SOSpV <r + SSVVpS V <7
= S^VpC) v <7 — Sc)Sp() V <7
= 0W-sspv<7

Suppose, for convenience, that p, unless when distinctly
derived from <y, stands for Up, a unit vector.

Then - SaS^V a = Sp Vpffipv <r

- - twice the rate of description of projected areas by the
vector Vp8. And we have the theorem that double the
sum of the areas described by the small vectors 8 and VUp8
is Tp(T8)2sin20, where 0 is the angle between 8 and p. It

88

must, however, be noticed that Vp£ will not move with the
fluid.

Taking § as before to be a vector moving with the fluid
and writing S = hvfa + 4v</> 2 4 hvfo we get

VtS = DA- V0i + &o. 4 VpS 4 S3v<r by (1) = - (SSv)*.

.’. the displacement at the extremity of 8 is

-"save- = i VpS 4 J(DA.' V01 + DAv^a + DAvfc)

Of these terms on the right the first denotes rotation about

an axis £ ; for the second we will write JS1. Let € be a
second vector moving with the fluid, and e1 be the vector
corresponding to S1. Then the condition that the part of
the strain corresponding to 81 may be pure is that 81 may
be self conjugate* or that SeS^SSe1.

We have S1 + VpS 4 2St)v<r = 0
e1 4 Vpe 4 2S£Vo> = 0.

S eS1 - S e2S = S3Vpe - S eVpS 4 2S(3SeV " eS3v)*

= 2S Spe 4 2S Sep = 0.

There are generally three principal axes of strain which
are at right angles ; from the equations of condition which
are V8S1 = 0 we get for these axes

DA DA DA _ D^

h ~ir k 1 y

If 8 and e represent two of these principal axes

(10)

DtS Se = SD tSe 4 S3D*e = - SeS3 V <r - S3Se V <r = SSe1 = SS'e

and since s1 is parallel to s, and S8e = 0, the principal axes
remain at right angles, and therefore remain principal
axes.

As this is important, we will give another proof of it:—

S may be written l (^v0 1 4 k2v0 2 4- zc3v0 3) where
D^ = 0 by (10), and S1 may be written
Dtl {'nV^i 4- /vW02 4
For shortness write S = l£, S1 = Dtl.£

;.d,W=vd^ + vsda

= v { (Qtvc+ ®,4)DtU - (DH.'C +

= 0.

# Hamilton’s Elements of Quaternions, III. 2—6, and passim*

89

whence we may conclude that a principal axis remains a
principal axis.

We may, therefore, now suppose that we have chosen
surfaces $ intersecting in principal axes of strain at the
points under consideration, as the surfaces to which we are
referring the circumstances of motion, and we must show
that these sets of surfaces will indicate the principal axes at
other points. We might, perhaps, conclude this from the
fact that any scalar operation of Y081 produces a zero
result ; but we will show the surfaces of reference intersect
at right angles at consecutive points.

In the case considered a = fav0i> &c. Sa/3 = Sv^iV^a = 0, <fcc.

^=s^+s“|

“ + *lS4aV^ +

= 0

with similar results for the other expressions. There is,
therefore, one and only one set of surfaces which move
with the fluid and cut everywhere orthogonally, and these
intersect in the principal axes of strain at every point.

It will be noticed that the quantity fa written above may
H /,pa\2

be shown = ^2 = , and that H2 = fa2(T«)2 = fa2fa2fa2.

When using these surfaces as those of reference ex-
pressions, such as Vp undergo considerable simplification.

If in (9) £ had been a principal axis, we should have
obtained

- = JSp^'(Vp8 + S1) = j(Vp£)2 = J(Tp)(T£)2sin20,

and as will be seen later p is one of these principal axes
only when VpD*p = 0, or when p moves parallel to itself.

2. In certain cases we may simplify considerably the ex-
pressions which we have found.

90

Thus if (Spv)<r = 0, a case which includes that of straight
parallel vortex filaments,

then "D*g = 0, and by (4) g may he written

V (pi + 12 V 02 4- l3 V 03 where = 0.

In this case by (6) we have SpS£v<7=0 or Spt>^ = 0, or the
relative motion is perpendicular to p.

Also by (7) D,(s^) = S^; =SvD,P.^; and r»,S^S = 0,
and v g moves with the fluid as g does.

A more general case, namely, when (Sp v )<r2 = 0 gives very
similar results. It may he written StrSpv <7 = 0 or Sod\o = 0,
and is the case when the tensor of the velocity is constant
along a vortex line, including the case of an ordinary vor-
tex ring.

We deduce by (6) that SpS<7V<r = 0,

and obtain

D*(So-g^ = S6g as before.

If So-Sp Vff = 0 at any point of a vortex ring, it denotes
that at that point o-2 is a maximum or a minimum.

Another case in which we get some additional simplifica-
tion is when the vortex line through any point moves
parallel to itself. In this case

VpD*p = 0 or VpSp v <r = 0

where we may omit the H or not, as we please.

Write as in (4) ^ = lx Vpi + h Vpz + h Vp8

Then because = 0,

H H

T)tl2 D^3 D ti
<3= <!= «»= < gay

v 1 ^2 ^3 v

.*. l\ — Ihi , l2 = Ik 3 , l3 = lk2 where D tk — 0
and ^ = ?(*lv^i + iaV^s + ^»V^|

2D,| = D^|^v0i + &o.} =D,log7.|.

91

we have further that S v p = 0.

T

and may deduce that = 0

To investigate another case, let us suppose that Tp in-
creases or decreases in every direction except that of p. The
condition for this is that Sp3v.p2 = 0 where £ is any vector
whatever.

But Sp SpB Vp = .Sp2c> vp — SpV.Vpc) v-p

— Sp2o v p — Sp2 v p + SpS Sp v p
= Sc)p2 v p — S^p Sp v p.

And this will not be zero for all directions of S unless p2 V p
= YpSp vp or unless Vp Vp2 = 2.pSp Vp = 0 *

This condition would have to hold if the vortex motion
existed only in an indefinitely thin filament, and was either
a maximum or a minimum at some point within it.

Another case : suppose that the surface </>i contains vortex
lines, and that Tp increases or diminishes as the surface is
crossed on either side

Then SpS v^iVp = 0.

But SpS v0iVp = Sv0iSp vp + SY.VpV0i. V.p
= Sv0]SpVp + SVpV0i. Vp
= Sv0i(Spvp- Vpvp)

= JSv«/)iVp2 =0

This condition must be satisfied at points in a vortex
sheet or at points in a thin vortex filament if it contains a
thread of fluid not affected by the vortex motion, or if the
vortex motion is a minimum within.

8. It has been shown (Section II.) that <7 may be written
V P + V v 0i + S2 V 02 + 213 v 08, but the whole portion Si v </>i
+ S2v</>2 + 23v03 will not generally contribute towards pro-
ducing rotation ; for supposing Si = ~ we may write this

cetyl

portion as vQ + S2vf + 23v fo, or generally we may write
<r = v P + £, where £ = S2 v </>2 + S3 v p8. In this we have made no

* Notes on some Quaternion transformations.

92

special choice of the surfaces 0, hut since p moves with the
fluid in such a way that if the two surfaces 02 and 03 inter-
sect in vortex lines at any time, they will continue to inter-
sect in the same lines, we may choose the surfaces 02 and
(j) 3 so as to intersect in vortex lines, and therefore put S2 = 0,

S3 = 0 and p = 2ia. Whence ■~L = 0, or, the strength of the

vortex is constant as we pass along the filament — a pro-
position generally proved by the aid of Green’s Theorem.

(TO

Also S£p = 0 and So-p = ^Sct v P = - Hs13— .

The first of these equations shows that the axis of rota-
tion is perpendicular to the part of the velocity essential to
the rotation.

4. Or we might by a proper choice of the surfaces fa ex-
press g merely as 2 iV(j>i , and since D*2 = 0, this would
remain as the proper form of o\ This form of <r expressed
as v P + 2iV0i seems that most applicable to the usual Car-
tesian notation ; comparing it with the usual form for irro-
tational motion we see that two new scalars are introduced,
connected by the two scalar equations = 0, D^i = 0.

or 2i - SiS V 0i V 2i = S V P V 2i
and ?»i-2i(vf)2 = SvPV(/)i

These two equations show very clearly that with a certain
definite system of vortex motion a definite irrotational
velocity must exist accompanying it, and that if any ex-
traneous velocity could be imposed upon the system, the
velocity must in some way be modified, and react upon the
disturbing velocity.

The fact that o- may be written as vP + ^v^i seems to
me sufficiently important to make me introduce the theorem
in Pure Mathematics on which it depends : namely, that
the ordinary differential equation P dx + Q dy + R dz consists

93

always of the sum of two parts — one immediately integrable,
the other integrable by a factor.

Let dF be the integrable part. Then

is integrable by a factor if

VdQ

ent\

dF/'dR

dP>

'dP

dQ\

\ dz "

’ dv)

dy\dx

dz )

l + &(

\dy ~

“ dz)

-<i-£M£-SM2

clF\

dy)

But this is an ordinary linear partial differential equation,
from which F can be found as a function of x y and 0 by
Lagrange’s method, and, therefore, a function F can always
be found such that P dx + Q d,y + Fdz - dF is integrable by a
factor.

5. Returning to the form of a - v P + £ we see that

D4<t = D*vP + D^.

- -S(vP + i;)v^vP + Vp£ + S£ v p by 1
= (~~t - S^Pv) VP + Vp4 + Sfvl
= (|- SvPvjvP+lv?.*

Where if K did not exist D,<r would be ^-SvPvjvP
showing that the accompanying irrotational motion is one
capable of existing by itself, while the essentially rota-
tional portion is not generally capable of so doing; and that
IV is not Dt v P(£ — 0) + D*£( v P = 0).

6. If we find the angle between the axis of rotation at
any point and at a distance x along the filament, we may
deduce a measure of the curvature of the filament, and by
taking a corresponding length on an axis perpendicular to
the osculating plane we may form a vector of curvature at
the point.

# Notes on Quaternion transformations.

94

Thus the angle between p and p-x SU pvp is a;T VpSUp v p

Tp^

whence the vector of curvature is

Tp3

in which we may substitute from the formula,

Vp2= 2V Vpp + 2(Sp v)p.

This vector will give us the curvature at any point and
also the torsional movement at that point during the mo-
tion. It however contains vp, and can only be applied in
special cases where the expressions can be simplified.

In order to express the torsional motion of a vortex line
at any point we will write Up = pi and the vector of curva-
ture as e. Then e = YpiSpiV.pi (11)

Then YeD4e will be a vector denoting the rate of torsion of
the vortex line at the point considered during the motion.

.*. YeDte = Ye{ YD^piSp! V.pi + piSpi V .D*pi)

= Spi v .piSelhpi - piSeSpi V .Ibpi.

This vector, of course, vanishes if Dfp is parallel to p ; a
case which has been considered.

The general case in which it vanishes is when

e = YD,pSpV.D,p :

in all other cases there will be a torsional flexure at each
point in the vortex line.

An expression for the radius of torsion of the vortex line
at any time could also be found, but it is more complex
than that already found, and would be of doubtful use in
any case of application. We have already introduced two
quantities Sp v p and v p for which we have found no proper
expression, and of which the second is not easily interpret-
able.

In the case considered above when Tp decreases or in-
creases in every direction round the vortex line, we have

the simpler expression that
that Sep = 0.

e =

Vp

Tp’

with the condition

95

If the vortex filament is straight we have in this case
V p = 0, which is an important condition in the case of fluid
friction. On this account we should learn in whafc cases Vp
moves with the fluid.

Writing g = livQi + l&fa + 4v</>3 as in (8), we can find that
D*Vg = ^(vDA-V^i +■ vWaV^ + V&A Vfc) “ (SVgV)o' + Aj? .Sv<r
= 2YvD,g - (Sv2 v)<r. + Sv<T.^ by (4).
and therefore the condition that gYg may move with the
fluid is that VvDJ^. = 0.

7. The general case of motion of a viscous fluid is not
capable of being simplified by the method of this paper, as
no convenient expression can in general be found for Vp.
As, however, there are cases in which simplifications can be
made, I shall consider some of these cases.

In the first case I shall suppose the fluid incompressible,
as it is convenient to take these cases separately; and also
suppose the filaments to be straight and parallel at right
angles to the plane of motion.

The equation of motion is

vDtP + DtS1v0i + Df22v02+ vV + ^Vp = 0

From this equation we will now suppose all terms of the
form v V removed, so that we remain with

D.Si V0i + D*22 V03 + ^Vp = O
But p = S3a = 23Ta . V03 = 2 V^3

when v (/>3 is now a unit vector perpendicular to the plane
of motion.

•*• Vp = Vv2.V03*

If the filament be such that Tp is a maximum or mini-
mum along it, we have shown that vp = ^ we must there-
fore have DjS = 0, or the nature of the motion is not affected
by the viscosity.

96

Next, taking the general case of such filaments, we have
always

1 + &0. +^Tp.e = 0

which shows that the vector D^. v (pi + &c. is proportional
to Tp directly and to the radius of curvature of the filament
inversely.

The only equation which we are able to obtain from this
form of equation follo ws from Sep = 0

whence = 0.

From the equation Vpvp2 = 0, we can not draw any con-
clusion as we have no convenient expression for vp2.

Turning to the terms which the elasticity of a viscous fluid

introduces, namely, ^vDJogH. and noticing that by the

equation of continuity d = H</>, where D$ = 0, we see that the
elasticity will generally give rise to vortex motion in a vis-
cous fluid ; and that the condition that it may not do so is
that H<£ may be some function of D^logH.

“ A Sulphuretted Hydrogen Apparatus,” by Peter Hart,
Esq.

When hydric sulphide is only occasionally required, and
then in small quantities, an apparatus which so furnishes it
is useful, especially when it can be used repeatedly without
washing out or replenishing. The one I have contrived
seems to me to fulfil these conditions. There have been
many invented, but they mostly require either many joints
or especially formed pieces of glass. This one can be made
by any one possessing only very small skill in fitting up
apparatus. It consists of two test tubes, the larger of one
inch internal diameter, the other of such smaller diameter
as to slide easily without friction into the larger. This

97

smaller tube is by means of the blowpipe perforated at the
bottom with a quarter-inch hole and is also provided with a
rubber stopper and a gas leading tube bent twice at right
angles. The larger tube has a piece of rubber tube two
inches in length, and of rather smaller diameter than itself,
pushed over its mouth, one inch on the tube and one inch
projecting. This completes the apparatus. To work it fill
the larger tube from one third to one half full of a mixture
of sulphuric acid and water — one part acid, three parts
water. Drop a lump of iron sulphide into the smaller tube,
insert the stopper with leading pipe firmly into this, and
thrust its lower perforated end through the rubber mouth
of the larger tube, pushing it down until it reaches the acid?
and allowing sufficient of this to enter the perforation to
cover the sulphide iron. Gas immediately commences to
be evolved and can be bubbled through the solution to be
examined. When sufficient has been obtained, raise the
upper tube until the lower end is out of the acid, the
remains of which at once drain away from the sulphide and
all action ceases, or practically so. It is only necessary to
hang up the apparatus until again needed, when, by heating
the end of the lower tube containing the acid over a Bun-
sen burner, and pushing down the upper, it commences full
action again. This can be repeated until the acid becomes
saturated, or so mucli so as to require replenishing.

Of course it need not be limited to the dimensions I have
named. A much larger upper tube might be employed,
which, combined with a suitably sized lower bottler would
furnish gas enough for a quantitative analysis. By
occasionally sinking the upper tube deeper into the acid the
stream may be fairly regulated, sufficiently so at all events
for ordinary work.

99

A letter was read from Samuel Crompton, Esq., M.D.,
&c., accompanying a fine series of photographs of distin-
guished astronomers, and of the principal astronomical
instruments of the Paris Observatory, which he had received
from x4.dmiral Mouchez, the Director of the Observatory,
and which he now sent for inspection in the belief that they
would be interesting to the members of the Society.

“ Note on an attempt to analyse the recorded Diurnal .
Ranges of Magnetic Declination,” by Balfour^ Stewart,
M.A., LL.D., F.R.S., Professor of Natural Philosophy at the
Owens College, and William Dodgson, Esq.

1. It is well known that Professor Rudolph Wolf has
endeavoured to render observations of sun spots made at
different times, and by different observers, comparable with
each other, and has thus formed a list exhibiting approxi-
mately the relative sun-spot activity for each year. This
list extends back into the seventeenth century, and is
unquestionably of much value. Nevertheless, it must be
borne in mind that we possess no sun-spot data sufficiently
accurate for a discussion, in a complete manner, of questions
relating to solar periodicity before the time when Schwabe
had finally matured his system of solar observations, which
was not until the year 1832.

We have, however, a much longer series of the diurnal
ranges of magnetic declination. Now, these are already
well known to follow very closely all the variations of sun-
spot frequency, being greatest when there are most, and
least when there are fewest spots, and it may even be
imagined that such ranges give us a better estimate of true
solar activity than that which can be derived from the
direct measurement of spotted areas.

The long-period inequalities of the diurnal range of
magnetic declination are thus, we may imagine, precisely

100

those of solar activity, so that to analyse the former is
probably equivalent to analysing the latter.

2. Our method of analysis is not new. The system
pursued by us is, in fact, that which has been pursued by
Baxendell, and probably other astronomers, with obser-
vations of variable stars, and it has already been applied by
one of us in a preliminary manner to magnetic declination
ranges (Pro. Lit. and Phil. Society, Manchester, February
24, 1880).

S. The observations at our disposal are those which have
been used by Prof. Elias Loomis in his comparison of the
mean daily range of the magnetic declination with the
extent of the black spots on the surface of the sun* These
observations are recorded as monthly means of diurnal
declination range, and we found it necessary to multiply
each by a certain factor, firstly, on account of the
well-known annual inequality of declination range, and
secondly, to bring them all to the standard of the Prague
observations. We have applied for this latter purpose pre-
cisely the same corrections as those made by Professor
Loomis.

4. The result of an analysis of these observations has
been to indicate the existence of three inequalities; two
dominant ones with periods of about 10J and 12 years,
and a subsidiary one with a period of about 16 £ years. By
these means we have been enabled to reproduce the
observed annual values of declination range with an average
difference of S9". The amount of agreement between the
observed and calculated values will be seen from a diagram
which accompanies this note. We are, however, of opinion
that the series of observed values at present obtainable is
too short to render this analysis a very accurate one. It
will certainly not bear carrying back forty or fifty years
beyond its starting poiut, which was in 1784, and it would

* American Journal of Science and Arts, Yol. L., No. CXLIX.

ioi

be very hazardous to carry it forward any considerable
length into the future. We may, however, mention that
our calculations indicate a maximum of declination range
about 1884, but not so pronounced a maximum as that of
1871,

f>. During our analysis an observation was made by us
which we think worthy of record,

It is a well-known fact that the so called eleven-yearly
oscillations of declination range are at certain times large,
and at other times small. Thus, for instance, they have
been large for the last forty years, but they were small
about the earlier part of the present century. It is clear to
us from an inspection of the observations, that a series of
large oscillations is accompanied with an exaltation of the
base line, or line denoting average efficiency, while* a series
of small oscillations is accompanied with a depression of the
same. The result is a long-period curve of the base line,
the bent period, so to speak, of the eleven-yearly inequality.

Now, a phenomenon precisely similar occurs in connexion
with shorter periods. If we take inequalities having a period
of three or four months, we find that such are alternately
well developed or of large range, and badly developed or of
small range ; and that a large range of such is accompanied
with an exaltation of the base line or line of average effi-

% 102

ciency, while a small range is accompanied with a depression
of the same. The result is a curve of the base line of which
the period is roughly speaking eleven years. May we not
therefore imagine that the so-called eleven-yearly period or,
to speak more correctly, the ten and a half and twelve-
yearly periods into which the eleven-yearly period may
perhaps be analysed, may be in reality bent periods for
shorter disturbances ? Is it not therefore possible that a
study of these shorter periods may give us information
regarding the nature of the eleven-yearly period, whether
for sun spots or declination ranges, which the small series of
actual observations is incompetent to afford ?

We beg to take this opportunity of thanking Mr. William
Stroud for the help he has given us in this investigation.

103

Ordinary Meeting, March 22nd, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

Three electric kites used by the late Mr. sturgeon were
presented to the Society by Mr. James Dancer, and the
thanks of the Society were voted to the Donor.

“On the Growth and Use of a Symbolical Language,” by
Mr. Hugh McColl, B.A. Communicated by the Rev.
Robert Harley, M.A., F.R.S.

This paper discusses in a general way the cases in which
symbols may be advantageously employed in logical and
mathematical reasoning, and endeavours, from an examina-
tion of our existing stock of symbols, to deduce some rules
or guiding principles, first, as to when new symbols should
be introduced, and secondly, as to what kinds of symbols
should be selected. It also contains a brief account of the
gradual development of the author’s own symbolic method,
as explained and set forth in his papers published in the
Proceedings of the London Mathematical Society , the
Educational Times, the Philosophical Magazine , and
Mind.

The President exhibited to the meeting four original
letters of the late Mr. Thomas Carlyle, addressed by him to
the late Mr. Samuel Bamford of Blackley, the Author of the
“Passages in the Life of a Radical.”

Proceedings— Lit. & Phil, Soc. — Vol. XX, — No. 8— Session 1880-1.

104

5, Chayne Row, Chelsea,

London, 13 April, 1843.

Dear Sir,

Will you be so good as send, by the earliest convenience
you have, two copies of your Book, Bamford’s Life of a
Radical ; addressed to “The Hon. W. B. Baring, 12, Gtj
Stanhope Street, London.” Two copies have been wanted
there for some time. Probably you have some appointed
conveyance by which your Books arrive here without
additional cost ; if so, pray use the earliest of these. Nay,
perhaps your Books are themselves procurable somewhere
in London ? That would be the shortest way of all. At
any rate the Coach or Railway remains ; and will be of no
enormous amount. Be so good as apprise me by post what
way you have adopted ; and on what day the Books may
be looked for in Stanhope Street ; — not forgetting to enclose
an account withal.

I read your Book with much interest ; with a true desire
to hear more and more of the authentic news of Middleton
and of the honest toiling men there. Many persons have a
similar desire. I would recommend you to try whether
there is not yet more to be said, perhaps, on some side of
that subject; for it belongs to an important class in these
days. A man is at airtimes entitled, or even called upon
by occasion, to speak, and write and in all fit ways utter ,
what he has himself gone thro’, and known , and got the
mastery of ; — and in truth, at bottom, there is nothing else
that any man has a right to write of. For the rest, one
principle, I think, in whatever farther you write, may be
enough to guide you : that of standing rigorously by tb e
fact, however naked it look. Fact is eternal; all Fiction is
very transitory in comparison. All men are interested in
any man if he will speak the facts of his life for them ; his
authentic experience, which corresponds, as face with face,
to that of all other sons of Adam.

105

Another humbler thing I will suggest : that it seems to me
a pity you had not your Book in the hands of some Book-
seller ; such a one could sell it for you much faster than
you yourself will. A friend of mine, for example, could not
find your Book in Liverpool at all ; and, unless he have
written to Middleton as I suggested, may still be in fruitless
search of it. The Commission charges of Booksellers are in
truth entirely exorbitant, unexampled among any other
class of sellers or salesmen in the world : but as I said once,
“if you have a waggon to drive to York, you had better pay
the tolls, however unconscionable, than try to steeple-hunt
it thither!” — This too is not to be neglected, th o’ a very
secondary side of the business.

Wishing you right good speed in all manful industry
with hand or with head or with heart,

I remain,

Yours very truly,

T. Carlyle.

P.S. What is curious enough : this Note was just folded,
but not yet sealed, when your letter was handed in to me !
Many thanks for your gift. Your remarks on Chartism are
also very welcome to me. I have now only to add that you
had better send Mr. Baring’s two copies to Mr. Ballantyne
along with the other, and request him to forward them all
to me without delay. Do not forget to enclose your account;
which will be paid thro’ the Post-Office.

T. C.

The Grange, Hampshire,

4 Septr, 1848.

My dear Sir,

Both the Nos. of your new work, which you were so kind as
send me, came safely to hand, — the last only a few days before
our leaving Chelsea for this place, whither we have come

106

to see some friends, and have a little fresh air while the
summer still lasts. I have read the two Pieces with great
pleasure, in which Mrs. C. your old acquaintance also shares :
we find the Narrative full of rough veracity ; clear, whole-
some, description of what you meant it to describe, —
namely, of an authentic phasis of Human Life ; — in which
accordingly all human creatures may take a real interest.
Withal there is a certain breezy freshness in the delinea-
tion,— as indeed in former delineations by the same hand :
a rustic honesty, a healthy manful turn of mind is nowhere
wanting, and that is a pleasant neighbour everywhere, and
to all readers and all men. On the whole, if you continue
this Work in the way you have begun, I think there is
every reason to expect a lasting favour for it, and all man-
ner of good fruit that you and your friends could have
anticipated. There are only two precepts I will bid you,
once more, always keep in mind : the first is to be brief ;
not to dwell on an object one instant after you have made
it clear to the reader, and on the whole to be select in your
objects taken for description, dwelling on each in proportion
to its likelihood to interest, omitting many in which such
likelihood is doubtful, and only bringing out the more im-
portant into prominence and detail. The second, which
indeed is still more essential, but which I need not insist
upon since I see you scrupulously observe it, is, to be exact
to the truth in all points ; never to hope to mend a fact by
polishing any corner of it off into fiction, or adding any
ornament which it had not , but to give it us always as God
gave it, — that, I suppose, will turn out to be best state it
could be in ! These two principles, I think, are the whole
law of the matter : and in fact they are the epitome of what
a sound, strong and healthy mind will, by Nature, be led to
achieve in such an enterprize ; wherefore perhaps my best
“ precept” of all were, to recommend Samuel Bamford to his

107

own Good Genius (to his own honest good sense and healthy
instincts) and bid him write or omit without misgivings
whenever that had clearly spoken ! And on the whole,
persevere and prosper : that is the wish we form for you.

We are here among high people, to whom the Passages
and other writings of yours are known : last night I was
commissioned by Lord Lansdown to ask you to send him a
copy of this new work, — or to bid Simpkin and Marshal
send it, if that can be done ; but in any way to be sure that
he gets it soon. I think perhaps you had better send it
direct yourself ; if the two Nos. are stitched together, they
will go thro’ the Post-Office for sixpence (six stamps stuck
on them) ; the address is, The Lord Marquis of Lansdown,
Lansdown House, London; — and you have only to write a
little Note (a separate Post-office Note) saying, with your
address given, that the Book is sent by my order, that you
yourself both write and sell it, and that the price is so and
so. Pray do not neglect this, however ; but set about doing
it straightway.

If yon write at any time to Chelsea, the letter finds me
after one day’s delay.

My wife bids me remember her to you and Mrs. Bamford,
whom she hopes to see again by and by; Blakely appears
to be a place very bright in her recollections.

With many good wishes, I remain
sincerely yours

T. Carlyle.

Chelsea, 9 Jan^, 1849.

My dear Sir,

Yesternight I read the Preface and the last portion of
your Autobiography. I have followed the work throughout,
as the successive instalments of it reached me by your
kindness (for which I am much obliged); and now it is

108

ended, handsomely, yet sooner than I quite expected. It
seems to me you have managed the affair very well indeed :
a manful rustic frankness runs thro’ it ; a wholesome fresh-
ness, energy, sincerity : it is very clear everywhere, very
credible ; and, to sum up many merits in one, it is singularly
memorable , and stands out in distinct visibility and con-
tinuity, in one’s mind after reading it. You will give an
innocent and profitable pleasure, I hope, to very many
persons by what you have written ; and make known, with
advantage to all parties, important forms of human life, in
quarters where they have not been known hitherto, and
much required to be known.

On the whole, however, we must not yet let you off, or
allow you to persuade yourself that you have done with us.
A vast deal more of knowledge about Lancashire operatives,
and their ways of living and thinking, their miseries and
advantages, their virtues and sins, still lies in your experi-
ence ; — and you must endeavour, by all good methods, to
get it winnowed, the chaff of it well separated from the
wheat, and to let us have the latter, as your convenience
will serve. To workers themselves you might have much
to say, in the way of admonition, encouragement, instruction,
reproof; and the Captains of Workers, the rich people, are
very willing also to listen to you, and certain of them will
believe heartily whatever true thing you tell them : this is
a combination of auditors which nobody but yourself has
such hold of at present ; and you must encourage yourself
to do with all fidelity whatever you can in that peculiar and
by no means unimportant position you occupy. “ Brevity,
sincerity,” — and in fact, all sorts of manful virtue , — will
have once more, as they everywhere in this world do, avail
you.

Since I wrote last, I have never seen Lord Lansdowne;
know not what he did with those Nos, of your Book, or

109

indeed whether he has ever yet fairly got hold of them, —
for his life all this while has been in the country, I suppose,
amid a crowd of guests, and with little leisure for considerate
reading. Pray tell me how the matter is, when you next
write. — I wish you farther to address a copy of your Book,
so soon as you have got it bound, to Lord Ashburton, whose
address I enclose : if the Book is under half a pound weight,
it will go by post if you stick sixpence worth of stamps upon
it ; above a pound and under two, it goes for a shilling’s
worth. And the Note you write must bear a cover quite
apart. With many good wishes

Yoqri s

T. Carlyle.

Chelsea, 21 April, 1849.

My dear Sir,

It will not, I fear, be of much use to try a] Bookseller
with the Poems : Poetry of all kinds is a bugbear to the
Booksellers at present, for there is no kind of Poetry that
they find the Public will buy. For my own part too, I own,
I had much rather see a sensible man, like you, put down
your real thoughts . and convictions in Prose, than occupy
yourself with fancies and imaginations such as are usually
dealt with in verse. The time is in deadly earnest ; our
life itself, in all times, is a most earnest practical matter,
and only incidentally a sportful or singing or rhyming one: —
Let S. Bamford continue to tell us in fresh truthful prose
the things he has learned about Lancashire and the world ;
that, I must say, would be my verdict too !

Lord Lansdowne has hardly come across me again at
all, — I think only once, — since he commissioned me to bid
you send your Book. In the huge whirlpool of things
great and small, which the like of him lives in, he has
doubtless let the transaction go out of his head ; and had

110

not you, according to my bargain with you, recalled the
memory of it, all had remained forgotten. I have now
communicated with his Lordship ; and probably before long
you will hear some farther account of it from him or me.

Yesterday Lord Ashburton sent me the enclosed Draft
of Twenty-five Pounds, which I was in some handsome way
to present to you as a proof of his approbation. On being
consulted, I had said there was a Public Testimonial set on
foot for your behoof some time ago ; to which, tho’ it was no
longer open to the public at large, his Lordship might still
fitly contribute whatever acknowledgment of service he
thought due to you. This Draft is the result ; — which any
Manchester Banker who knows you, or knows a responsible
man going with you to his Bank, will at once convert into
cash; — after which, pray be so good as signify that you have
received the amount, and that all is safe.

With many good wishes

Yours very sincerely

T. Carlyle.

Mr. Bamford, Blakeley.

MICROSCOPICAL AND NATURAL HISTORY SECTION.
February 14th, 1881.

Alfred Brothers, F.RA.S., President of the Section, in
the Chair.

It was determined that the Section recommend the
Parent Society to confer with the Government with a view
to obtaining a gratuitous copy of the Keports and Memoir g

Ill

now being issued in connection with the “Challenger ’
expedition.

“On Pendant Nests of a Gregarious Moth from Vene-
zuela,” by Mr. John Plant, F.G.S.

Entomologists have long been familiar with insects which
are social or gregarious either in the larva, pupa, or perfect
stages of their metamorphoses, and it appears from the
results of many recent careful investigations that although
a social instinct has been found more or less developed in
insects belonging to every order, yet it is in the Hymen-
optera that we find the highest instincts for forming and
living in communities and society. “ The bees and the ants
are a wise and perfect people” is an adage as old as historic
time.

The lepidoptera are not known to include any species
which live in entire communal life in every stage; the
caterpillars of some species will associate for feeding, such
as Clisiocampa neustria, Eriogaster lanestris, and others,
which live in a tent-like nest when in the stage of larva,
and enlarge it as necessity compels. The common silk moth,
Bombyx mori, is gregarious as a larva, and can be trained to
group their cocoons in bundles of twigs ; but these species
form no communities when in the perfect stage, they simply
pair off and are entirely independent of each other. Other
species there are which will be independent when in their
larval stage, yet will instinctively band together to con-
struct a common nest, pouch, or tent, in which they grega-
riously undergo their transformation into the stage of pupse,
again dispersing in pairs when they pass into perfect insects.
Others there are which are not known to live gregariously
either as larvae or pupae, which are yet observed flying in
extraordinary swarms as perfect butterflies and moths— so
that whilst communistic habits are displayed in one or two

of the successive stages of transformation in lepidopterous
insects, they always fall short of the complete communistic
life as seen in the bees, ants, wasps, termites, locusts, and
even gnats and mosquitoes. But for the history and details
of these marvellous creatures I would refer the student to
Kirby and Spence, Introduction to Entomology; Dr. P.
Martin Duncan, The Transformation of Insects; Sir John
Lubbock’s works on The Ants ; and the Rev. J. G. Wood,
Homes without Hands, and Insects at Home.

There are several small lepidoptera in our own country
which build nests in common, or weave some kind of case
of silk, leaves, or twigs, in which the cocoon will find shel-
ter and warmth during the season of rest. These tents and
pendulous nests are comparatively small and inconspicuous,
but they are not the less curiously made and well adapted
for the purposes they have to fulfil.

It is from the tropical forests of South America, Africa,
India, &c., that the greatest samples of gregarious nests
have been obtained, and of which I have four good exam-
ples to lay before the Section.

I have exhausted the sources of reference which are at
my command for some information about these specimens,
without having met with any description that will apply to
them. There are descriptions of various forms of pen-
dant gregarious nests of insects in the authors’ works I
have mentioned, and in other vrorks on Entomology the
general habits of moths and butterflies to gregarious habits
are amply dwelt upon — but nothing I have seen as yet
describes these curious nests.

Mr. Wood, in his Homes without Hands, page 441, figures
and describes the social nests of two species of lepidoptera,
one of which bears a fair resemblance to the specimens I
exhibit. His sample came from Mexico; it is a pendulous
nest about eight inches long, having a flask-like shape ; the

113

outside is made of a dull whitish parchment-like, hard, stiff,
and tough material, with an inside lining of softer texture.
When cut open the pupae, to the number of more than one
hundred, were seen suspended by their tails with a silken
thread round the upper part of the nest as well as to the
twig which ran from the top down the interior. The pupae
were not in any exact order — the nest had a small hole at
the bottom through which the perfect insect would escape.
All the pupae were dead and shrivelled up, but Mr. West-
wood succeeded in identifying the species after he had care-
fully softened portions of the membranous wings so as to
display the true forms of their nervures and cells — it proved
to belong to the family of the Heliconoid moths, named
Eucheira socialise

The other nest is from tropical Africa, and is the only
specimen known. It forms a large tent over the branch of
a tree. Nothing is known of the species, and it is most
probably the gregarious tent of a moth.

Humboldt describes a moth also found in Mexico— Bombyx
Modrono — which is gregarious, the larvae uniting to form a
goodish sized nest of a dense tough material and brilliant
whiteness, from the lining and cocoons of which the natives
procure a supply of silk of a soft fair quality.

The nests which I exhibit are, I believe, allied to the
species just described, but they possess some peculiar fea-
tures which he does not allude to, and which would scarcely
have escaped his notice had the nests of B. Modrono pos-
sessed them.

These nests were brought by Mr. James P. Spence with
his extensive collection of natural history objects from
Venezuela, which it will be remembered were exhibited in
the Society’s rooms December, 1872. I obtained them
when the collection was subsequently sold. As there is no
description of them in his MS. list beyond “ Nests of a cater-

114

pillar unknown/ it is not at all safe to affirm that they
came from any part of Venezuela, as he made purchases of
curiosities from travellers and agents from other parts of
South and Central America, and these may as likely as not
have come from Mexico.

The nests are somewhat irregularly pouch-shaped, and
have each been constructed from an attachment first formed
upon the bough of a tree. The length varies in each, being

six, eight, and eleven inches. The external case is evidently

made from a vegetable paste or pulp which when dry makes
a tough sort of felted cartridge paper, very light and smooth
in texture, such a material as would be made with the mas-
ticated vegetable food consumed by the caterpillars, which we
see used in the habitations of many other species of insects.

The outside of the nest is beautifully impressed with out-
lines of leaves which must have been fixed and pressed
upon the pulp when it was yet soft and adhesive. Portions
of these leaves still remain attached to the nests, and the
species can to some extent be identified. Several species of

British moths and butterflies are in the habit of enclosing the

pupa and cocoon in an extra case or nest, by drawing together
the edges of a large leaf until it completely enshrouds the
cocoon ; but the larvse which form these large tropical nests
spread out whole leaves and gum them firmly to the nest.
Probably it arises from an instinctive precaution against
enemies, for the leaves would completely hide the nest, yet
add nothing to its strength.

On cutting the nest open from end to end the interior is
seen to be closely packed with a lightish brown mass of silk
within which can be found a good number of cocoons, vary-

ing according to the size of the nest. The cocoons are

enveloped in the silk in rows of two or more, some ranged
from end to end in rows side by side, and others in irregular
files from end to end, but all very tightly packed in the

115

mass of silk. A cocoon case measures a little over an inch
long, so we can judge the perfect moth to be about the size
of the British “Oak Egger moth,” Lasiocampa Quercus,
with wings stretching about 2J inches. I have searched in
vain for a pupa sound enough to dissect ; they are all dried
up and shrivelled within the unbursted cocoons. The outer
fibres of the silk adhere fiimly to the interior of the nest,
and mixed with the silk near the end are numbers of eggs
of the moth, proving that some of the cocoons had burst and
the moth escaped.

The nest has small openings at each extremity for the
escape of the moth, and the hole where it is attached to the
bough.

I cannot detect any evidence about the nests which would
lead us to think that they are formed gradually piece by
piece over any length of time like the nests of wasps, bees,
and ants. On the other hand, they are evidently begun and
completed in a short time, when the larvae are approaching
their full growth, when instinct impels a number of them to
band together and rapidly construct a common shelter and
retreat in which to await the strange dormant stage of their
existence.

They must proceed to masticate and make a vegetable
pulp in sufficient quantity to form the covering to their
common nest, and be able to decide its capacity to hold their
whole number. The strong leaves must be applied whilst
the pulp is yet soft and sticky, and the outside completed
before a retreat is made to the interior— then the larvae
must emit each length of the silken thread, and fill the nest
to the full ; and lastly, each larva must take up its proper
rank, spin for itself a delicate cerecloth around its changing
form, and entomb itself to wait the final change which
gives it a renewed and almost seraphic life ; truly it is a
marvellous episode in the life of a gregarious caterpillar.

Upon consideration of all the features and evidences pre-
sented in my research I do not hesitate to say, that I believe
the larvae which construct these and similar nests, are the

cidse, perhaps the Bombyx Humboldt has mentioned as
being found in Mexico.

There is another specimen of a nest upon which Mr.
Spence has written a ticket, “inner layer of a nest of Grega-
rious Caterpillars, species not known.” As there is no such
lining to be found in the three nests just described, I con-
clude it must have been obtained from a different kind of
nest, though it is quite probable the nest was one made by
a gregarious moth ; it is fourteen inches long, eight inches
circumference in the middle, tapering sharply at each end,
it has been pendant like the others. The material is a thin
sort of skin of brown colour, wonderfully like some of the
common Japanese-made papers. There is no doubt of its
having been stripped without difficulty from the inside of a
stiff pendant nest, as it was held to the sides only by silken
web. This nest when complete and hanging from the bough,
would look like a long and somewhat elegant flask.

larvae of a moth belonging to the great family of Bomby-

Alfred Brothers, F.B.A.S., President of the Sectioi
in the Chair.

Mr. M. M. Hartog, B.Sc., F.L.S., exhibited a Seiss’ earner
lucida.

He also exhibited some slides illustrating the segments
organs of the Leech.

March 14th, 1881.

117

Mr. R Ellis Cunliffe brought before the Section’s
notice a copy of the first volume of the “ Challenger” ex-
pedition.

Mr. Plant, F.G.S., exhibited a glass bottle filled with
large black ants from Baltimore, U.S.A. They were all still
alive, though somewhat torpid.

Mr. James Cosmo Melvill, F.L.S., exhibited some very
curious forms of fresh water mollusca from Lake Tanganyika,
Central Africa, which had been collected in 1879-80 by Mr.
E. Coode Hore, of the Central African Mission. Mr. Edgar
A. Smith, of the Zoological Department, British Museum,
had described the new species ; and it was found necessary
to create three new genera for as many species, in the case
of Tiphobia Horei, Neothauma Tanganyicense, and Syrno-
lopsis lacustris. The first of them, T. Horei, is the most
remarkable fresh water mollusc yet discovered. It bears
more resemblance to the marine Gasteropod Murex Bran-
daris, or Tudicla spirillus, than to any fresh water genus, if
we except the strange Melaniad Io spinosa, and its allies.
The animal and operculum of Tiphobia being yet unknown,
it is placed provisionally by Mr. Smith among the Melaniadae.
Neothauma Tanganyicense is, perhaps, only a Paludina.
there are certain peculiarities about the lip, however, which
show affinity with the Melaniadge, and the texture of the
shell is not so light as most of the Paludinge. It resembles
P. umbilicata from Siam, and P. Ingallsiana from Japan.
Specimens of these and other close allies were exhibited.
Syrnolopsis lacustris, a small elongate Melaniad, with flexu-
ose lip, calls for no especial remark.

Mr. Melvill also exhibited several other shells, most of
them new species of Lake Tanganyika shells, but none of
them new genera, eg., Spatha Tanganyicensis (Smith),

118

Melania nassa (Woodward), Lithoglyphus rufofilosus (Smith),
L. zonatus (Wd.); but regretted that he had found it quite
impossible to obtain any specimens of the curious Limno
trochus of Smith, a recently-described genus containing
two species, L. Thomsoni and L. Kirkii, bearing great ex-
ternal resemblance to the Trochidse, or the Littorinoid
genus, Risella. They are shells of greater finish and granu-
lation than is usual in fresh water genera.

The great extent of this lake, or rather inland sea, is no
doubt one reason for its producing quasi-marine mollusca, and
in a short time we shall probably be startled by more curious
and undreamt-of forms. It will be difficult, however, to
eclipse the Tiphobia Horei for singularity of appearance.
There is a good plate of this species and others in the
November number of Zoological Proceedings (1880).

Errata.

Page 101, line 7 from bottom, and page 102, lme 7 from top
for “ bent” read “ beat.”

119

Ordinary Meeting, April 5th, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

“On Du Bourguet’s ‘Calcul’ and on Ternaries,” by Sir
James Cockle, F.R.S, Corresponding Member of the
Society.

1. In “Notes and Queries” for June 12, 1880 (6th S., No.
24, vol. I., pp. 469, 470), I have given a further bibliography
of Du Bourguet’s ‘Calcul’, a work on which I have already
commented (ante, vol. xix., pp. 9, 10; 181, 182).

2. Doubting Du Bourguet’s calculations, so far as they
relate to his example (6), I communicated with Mr. Robert
Rawson who, in a letter to me dated May 3rd, 1880, replied
that he found, after going over the work twice, that the
criterion of integrability for (6) becomes

and that Du Bourguet’s result is obtained by leaving out

3. Mr. Rawson’s result will be verified if in Art 9 (infra)
we put m—\-=.r and n—\.

4 . This seeming error of Du Bourguet may perhaps be
corrected by treating the x which multiplies the cube root
in the coefficient of dy (ante, vol. xix., p. 9) as a misprint for
some constant, r Tf wo cm*.

wherein u = z — y — x, and his conclusion follows. Du Bour-
guet’s theorem may be paraphrased thus, viz., “ a factor of
U (the criterion of integrability being U— 0) may yield a
solution if equated to a constant.”

the first term from the above equation.

Proceedings — Lit. & Phil, Soc. — Vol. XX.— No. 9.— Session 1880=81,

120

5. The theorem however does not cover the whole ground,
for if V be a variable function U + Y=:0 may give a solu-
tion. This is an easy deduction from (p. 116 of) a paper of
mine cited in Art. 7 {infra).

6. In my paper “On Ternary Differential Equations”
{ante, vol. xvi., pp. 66 — 68), in connection with which that
of Mr. Eawson, bearing the like title {ib., pp. 114 — 118),

should be read, ~ and ^ must be interpreted as follows, viz. :

dx dx ^ dz dy dy dz

and this being done, (3) is an equation which becomes an
identity if, in the sinister, we replace p and q by M and N
respectively, or operate vice versa on the dexter. In what
follows I recur to my paper.

7. At p. 115 of a memoir printed in the Proceedings of
the London Mathematical Society (vol X., pp. 105— -1 20) I
have in effect shown that

xdM/lv/r TT

(7)-

This numbering (7) is, and is intended to be, consecutive
to that of my paper on ternaries, and does not occur in the
memoir.

8. Subtracting (7) from (3) we get

“-^=0 (8)>

and we get this same (8) by transposing the sinister of (7)
to its dexter.

9. Comparing (3), (7), and (8), we see that IT vanishes
when 0 is eliminated by means of M =p or N = q.

10. Let z-y-x=u and M = 1 + um{ 1 + aun - bur), N = 1 4- xum ;

then ^ 4- N~ = mxum~\ M - 1) + xu^^nau71-1 - rbur~l ),

^ + = + (M ~

U = — um 4- xv?m{naun~1 — rbur~1).

121

11. When m, n, and r are positive, u = 0 is a solution of (1)
Yet the positive values of m, n, and r may be such as, while
making u = 0, to make U = ©o. This is a paradox. But U
contains the term mmm_1(M - 1)(1 - 1), which is suppressed
in the above calculation. Now, although this suppression is
in general allowable, it may (but will not necessarily) cease
to be so when the above term takes the form oo(l - 1). It
would therefore seem that X - X is not necessarily null when
X is infinite.

12. The oo(l - 1) will not occur unless one at least of the

^ be rendered infinite. The general

theorem is (not that of Du Bourguet but) this, viz., Retain
in the calculation of U all terms whatever, whether they
seem to cancel one another or not. Write the result in the
form U=Q + X(1-1). Then □ = 0, or, failing that, X = oo

(which can only arise from C~ = coor^ = oo) may yield a

.... dM -| aN
quantities and

dz

single solution.
March SO , 1881.

2, Sandringham Gardens,

Ealing, near London, W.

The President said that he had, on several occasions,
brought before the Society a notice of the Eucalyptus glo-
bulus growing near to the sea in his garden at Douglas in
the Isle of Man. It was planted in 1875, and grew about
7 feet in height annually during the three following years ;
after these its top reached higher than the wall sheltering
it, and it was exposed to the east winds from the sea, which
stopped its rapid growth. It now has attained a height of
thirty feet. During the present winter it fared pretty well
until the beginning of March, when the strong gales made
bad work with its foliage, but the tree is still alive, and he
has every hope it will rally again in the summer. It grows
about six feet above the ordinary high water mark of the
sea in Douglas Bay.

122

“Note on the Presence of Arsenic in Paper Hangings/’
by Harry Grimshaw, F.C.S.

That arsenic in various states of combination is very often
present in the colouring matter of paperhangings is a very
well ascertained fact. That it is not confined, as was at one
time generally supposed, to those papers which are coloured
green, is also pretty well understood, many chemists having
found it in papers of all shades and colours, including even
white and grey.

A case which illustrates very well this general distribu-
tion of arsenic in papers of various colours and shades, and
also illustrates one or two other interesting features in con-
nection with this subject, has been brought under my notice
by Mr. E. Le Neve Foster, F.C.S., and it will perhaps be of
some little interest to this Society. One of the two series
of specimens of wall paper which I now show you consists
of six papers of varying colours. Three greens, of different
shades, light brown, dark brown, and pink, are the tints
comprised, and all of them without exception contain
arsenic largely. The pink, which is a very light shade, con-
tains the least arsenic, and the brightest green contains the
most, though one of the brown shades contains a very large
amount. I have not determined the amount of arsenic
quantitatively, as that was not needed to condemn the
papers, but probably the pink paper contains a sufficiently
large quantity of arsenic on one square foot to poison an
adult person.

When these papers were selected from a Lancashire
manufacturer it was particularly specified that they should
be free from arsenic. The absence of this body was assured
in a positive manner, and no doubt the papers would have
been definitely guaranteed to be absolutely free from arsenic.
This assurance, however, from previous experience, was not
relied on, and the papers were qualitatively analysed for
arsenic with the result above stated.

123

The injurious effects which might have resulted, in fact
would almost certainly have resulted from papering six
rooms in a house with arsenical paperhangings, do not need
enlarging upon any more than does the almost criminal fool-
ishness of stating that such papers were free from arsenic.

The second series of six samples which I have placed
along with the six arsenical papers illustrates very con-
clusively the fact that arsenical compounds are certainly
not essential to the production of the colours required in
the decoration of paper. These second papers were obtained
from a Lond6n manufacturer to replace those which I have
described, and will be seen to be so near them in shade and
colour that in one or two cases it is difficult to perceive any
difference at all. None of the second series of papers yield
the least indication of arsenic with Marsh’s test, and there-
fore entirely justify their warranty as free from arsenic, and
were of course selected for use. We have therefore in these
six self-tinted papers and the two-patterned papers, which
I have also here, tints which alone or in combination will
serve to demonstrate that any colour almost which is desired
can be obtained without the addition of arsenic. If there
is a difference in the appearance of the arsenical and non-
arsenical colours, it is that the former are rather brighter.
This however is not altogether a merit, for wall colours may
very easily be too bright.

It is to be regretted that non-arsenical paperhangings
are at present, as a rule, somewhat dearer than the ordinary
ones, but there is not much reason to doubt that this will
be materially changed when the former are more largely
made and used than at present. The cheapness of arsenic
and its compounds is an unfortunate circumstance which
favours its adoption, but when it is more generally acknow-
ledged that the “brightness” yielded by these arsenical
colours is not at all indispensable, this cheapness will not be
an insuperable objection.

124

In papers which contain arsenic the hardness of the sur-
face and the comparative firmness with which the colour is
fixed on the paper are of course important factors in the
danger which attends their use; a paper on which the
colour is but loosely attached, though it may contain less
arsenic, will be much more dangerous than one containing
a much larger amount with the colour firmly adherent, the
minimum of danger being reached in a “ glazed” paper, or a
sized and varnished one. In any case, however, a sensible
person will prefer not to live continually surrounded by so
many square feet of arsenic-covered walls, and it is to be
hoped that the promiscuous use of arsenical paperhangings
will receive a permanent check on the completion of the
labours of the Committee of the Society of Arts, which is,
I understand, at present drafting an Act of Parliament to
regulate the application of this poisonous substance, and
endeavouring to decide upon a test to which suspected
papers may be uniformly subjected.

It is not a point to congratulate ourselves upon, that it
appears to be the opinion that the Lancashire paperhanging
manufacturers have the unenviable reputation of being
greater offenders with respect to the presence of arsenic in
papers than their fellows nearer the metropolis, and there
can be no necessity, with the local scientific and techno-
logical knowledge which is attainable, that this should be
the case.

It appears to be a moot point whether the cheaper or the
more expensive papers usually contain more arsenic, and
also in which class is it oftenest found. I hope to have an
opportunity of making a communication to the Society on
this point on a future occasion.

Dr. Joule, F.RS., said that since Mr. Grimshaw read his
paper on the sulphuric acid produced by gas lights, he had
hung two finely perforated zinc plates over one of his

125

burners. The nearest plate was 12 inches above the flame,
the other 3 inches above it. The burner was a large one,
and lighted on the average 5 hours each day. The zinc
plates were examined after three months, when it was found
that the lower one had accumulated the usual brownish
black deposit and also a furring of sulphate of zinc. The
upper plate of zinc was little affected, which leads him to
the belief that a single plate of perforated zinc of about a
foot square is sufficient to remove the greatest part of the
noxious emanations, and obviates to a great extent the ne-
cessity of a globe or chimney.

“ On the Relation of Electrical Resistance to the Chemical
Composition of Steel Wire,” by William H. Johnson, B.Sc.

I showed in a paper read before the Society in March last
year, and entitled “ On the Electrical Resistance and its Rela-
tion to the Tensile Strain and other Mechanical Properties
of Iron and Steel Wire ” that in cast steel wires drawn in the
same way but manufactured so as to contain different quan-
tities of carbon, etc., the electrical resistance increased with
the resistance to tensile strain, vide table B in the report of
my paper. — Pro. Man. Lit. & Phil. Society, No. 12, vol. XIX.

During the last year Dr. Burghardt has very carefully
analysed the identical samples of annealed steel wire whose
electrical resistance and other mechanical tests are given in
table B just mentioned. The results for all samples with the
exception of No. 6, not yet analysed, are shown in table C.

A glance at this table shows us that five of the samples
have only four elements other than iron present in quantity,
namely, — carbon in two forms combined and graphite; sili-
cone and manganese; and traces only of sulphur and phos-
phorus.

126

Now how do these elements effect the conductivity of the
steel ? Let us examine them in detail.

First, graphite carbon must be present in the steel as a
mechanical mixture, and so can scarcely exercise any in-
fluence on the conductivity. Then manganese will probably
be present in the form of an oxide, as manganese oxidises
at the high temperatures steel is cast more readily than any
of the other constituents of the steel. Now, oxide of man-
ganese can hardly be present in the steel other than as a
mechanical mixture, and thus we may disregard its influence.

There are now left combined carbon and silicon, and in
samples 1 and 2 a little sulphur or phosphorus. From ana-
logy with copper, sulphur and phosphorus should increase
the electrical resistance of iron very much. Perhaps we may
estimate in a rough way the total effect of these elements
on the conductivity by taking their sum as shown at foot of
table C. If this is correct, we are led to the interesting
result that within th e range of these experiments any increase
in the percentage of sulphur, phosphorus, carbon, and sili-
con present in a steel is accompanied by an increase in its
electrical resistance, and further, an increased electrical re-
sistance is concurrent with an increase in the resistance to
tensile strain.

The quantity of carbon, silicon, sulphur, and manganese
in the samples of steel is so very small that the most careful
analyses give results which must be regarded as approximate
rather than definite ; hence I have much diffidence in laying
these figures before you. But however much the ultimate
accuracy of these figures may be called in question, I think
we may fairly say that the electrical resistance of a piece
of iron or steel is a measure of its resistance to tensile strain
and of the amount of combined carbon, sulphur, silicon, and
phosphorus it contains.

127

Table C.

Analysis of Cast Steel Wires, Nos. 1 to 8, and Electrical Tests
as given in Table B, Pro. Man. Lit. & Phil. Soc., March, 1880.

Sample No.

1

2

3

4

5

7

8

Metallic Tron

98-980

99-070

98-870

98-880

99-030

99170

99-007

Combined Carbon

•391

•438

•270

•280

•182

•226

•268

Graphite Carbon

•040

•060

•150

•150

■130

•150

•080

plihnnn

•157

•on

•190

•1 50

•140

•080

•033

Ma.nganese

‘088

•300

•470

•410

•390

•340

•380

Sulphur

•080

•031

trace

trace

trace

trace

trace

Phosphorus

•096

trace

trace

trace

trace

trace

trace

Total

99-832

99-910

99-950

99-870

99-872

99-966

99-768

Combined Carbon, 1

Silicon, Sulphur, [■
and Phosphorus...]

•724

•479

•460

•430

•322

•306

•301

Electrical Resistance \

of annealed Steel !
Wire in Ohm’s [
per meter gramme )

2-140

1-903

1-560

1-519

1-450

1-430

1-070

Errata in Table B, Pro. Man. Lit. and Phil. Society, No.
12, Yol. XIX.

After words “ Elongation at moment of fracture,” insert
“per cent ” of original length.

128

PHYSICAL AND MATHEMATICAL SECTION.

Annual Meeting, March 29th, 1881.

E. W. Binney, F.RS., F.G.S., President of the Section,
in the Chair.

The following gentlemen were elected officers of the
Section for the ensuing year : —

JOSEPH BAXENDELL, F.R.A.S.

'®icz-$xz8xbzni8.

E. W. BINNEY, F.R.S., F.G.S.

ALFRED BROTHERS, F.R.A.S.

^xznmxzx.

JAMES BOTTOMLEY, D.Sc., F.C.S.

<§£cxetarg.

JOHN A. BENNION, F.R.A.S.

“On the Motion of Developable Cylinders,” by James
Bottomley, D.Sc., F.C.S.

I have not seen, in any works on Dynamics, the following
problem treated. A perfectly flexible surface is rolled up
so as to form a cylinder. The external edge is fixed and
the cylinder is allowed to roll down an inclined plane, under
the action of gravity, to determine the motion. As ex-
amples we may take rolls of tape or ribbon. I suppose the
lamina to have thickness, but this thickness to be indefi-

129

nitely small. Approximately the motions may be deter-
mined as follows Let a section of the cylinder be made
by a vertical plane through its centre of gravity. Take
fixed point as origin. The external forces acting on the
mass are gsina and the tension at the fixed point, these act
along the plane, which may be taken for the direction of
the axis of x; perpendicular to the plane the external forces
are— gcosct and the resistance of the plane — these acting
in the direction of the axis of y. Of the whole tension at
the fixed point a portion will be due to the unrolled part of
the cylinder in contact with the plane, also of the whole
resistance of the plane a portion will be due to the unrolled

portion. For each particle in contact with the plane
d2v

and vanishes. If then Tx denotes the tension due to the

rolling mass and It the resistance, the ordinary equations
of motion will give

(ffidC

S^a-MtfSina-Tl

a)

- Mucosa + Rj ..... ....

(2)

The summation extending to all the particles of the rolling
mass. If we suppose it to move as a rigid body these
equations may be written

Mi^ = M^sina-T:

= - Mucosa + Rj

If we take moments about the centre of the rolling cylinder
the equation will be

/ d?y d?x )

2m| \ =T^

Or, more simply, if we suppose the cylinder to move as a
rigid body,

<3>

130

Mjk2 denoting the instantaneous moment of inertia. From
(1) and (3) we have the following equation : —

+ ) - M^sina w

Also we have the following geometrical equation, since the
space x is described by a circle of variable radius : — dx - ydd .
Also the mass in contact with the plane will be bdcx where c
denotes thickness, b and d breadth and density. If we
regard the rolling portion as a circular cylinder its mass
will be bd^y2, supposing it to have the same density as the
unrolled portion. Let M be the whole mass, and B, initial
radius, thus M = 7rR2frd Since the mass is constant we
obtain the equation ^y2 = ttB,2 - cx, since y and x are the
coordinates of the centre of gravity, this equation gives a

y 2

parabola as its locus. Also Jc2 = y.

j^sina.

Hence equation (4) may be written
d2x c / dx \2 2

d#-^\dt) =

By integration we obtain

(ST = { A - | jsina(irE2 - cxf }

A denoting the constant. If this be determined by the sup-
position that the mass starts from rest, the equation may
be written as follows

cx V
7CR2J

S)2=l!sina,rR2{1-(1“®2}

1-

cx

ttRT2

or if l denotes the length of the tape

©243in©-(1_f)s}

Hence as x approaches to the value l the velocity increases
indefinitely. The whole tension at the fixed point at any
time will be

131

Mysina - ^Mxsinai | 1 +

; W

The initial tension will be ^^n._

If the external end of the tape were attached to the con-
tiguous coil so that it could not unroll, the tension at the
fixed point would be M(/sina. If the fastening suddenly
gave way, the tension would immediately alter and become
only one third of its previous value.

If we suppose the length of the tape to be infinite, then
the velocity after describing any finite space will be

v

^sina.#

If we suppose the motion to take place on a horizontal
plane, the equation of motion changes; the differential
equation now becomes

d?x _ c / dx V _ q
dP 2 ^y\dt) ~

A first integral of this equation will be
rdx V _ A

\dt) 7 rB?-CX

(1)

To determine A, suppose the mass set in motion by a
blow parallel to the plane so that the initial velocity is V,
thus A = 7tR2V2.

Substituting, integrating again, and determining the con-
stant, we have

-iH'-e-m «

To unwind the whole length of the tape, this equation
would make the time to vary as the length directly and as
the initial velocity inversely.

Equation (1) may also be written

132

!

Hence, as the mass diminishes the velocity increases, but
the kinetic energy in the direction of motion is constant

none of the energy of the blow is consumed during the
rotation of the variable cylinder ; once started it would con-
tinue of itself. In the rolled-up cylinder, there is an
amount of potential energy which may be estimated as
follows : suppose that originally we had a thin lamina rest-
ing on a flat plane ; now, the amount of work necessary to
raise a particle of weight w to the height y is wy ; and to
raise an aggregate of particles the work will be 2wy or
(/My, where y denotes the vertical height of the centre of
gravity and M the whole mass. In the rolled-up cylinder
this is stored up as potential energy ; during the motion it
assumes the kinetic form, and would of itself be sufficient
to keep up the motion on a smooth plane. In what precedes
I have supposed the centre of gravity to lie in the normal
to the plane drawn through the point of contact of the
cylinder with the plane. This would not be exactly true,
on account of the cjdinder not being perfectly circular ; there
will be an extremely small couple due to gravity tending to
produce rotation.

If in equation (2) we suppose the length of the tape to be

infinite, for the time of motion during any finite length we

shall have t = -.

v

In the above problem I have supposed the external edge
of the tape to be fixed. We may, however, have the internal
edge fixed and the external in motion, as in the following
problem. An indefinitely thin lamina is wound round a
fixed horizontal cylinder of indefinitely small cross section
to the external edge of the lamina a weight is fixed to
determine the motion of this edge. Suppose we take
moments about the fixed axis. Then the expression

and equal to its initial value. Hence it would seem that

133

for the whole mass may be divided into two parts — for the
portion that is still coiled up the angular velocity will be
the same for each particle, and equal to the angular velocity
of the body about the axis. For this portion then we shall

have the expression

d /M

dt)

For the unwound portion

the angular velocity about the axis is not the same for each
particle. At any instant y is the same for each particle,

also ^ is the same for each particle. The equation of

moments for this part will take the form

d dx f cx /T)2 2X \

dtdt i^+V))

The geometrical equations will be the same as before. The
positive direction of the axis of x is taken vertically down-
wards. Suppose w the attached weight to have n times the
mass of the tape, then the equation of motion may be
written

d dx f ny 3 cx( R2 4- By2)
dt dt\ 2 + 4 y

= cxgy + ymrBry

(Hoc •

The coefficient of — may also be written

1 /2t r2R4-cV\
4A tt ;

Writing, for brevity, this in the form F(&), the equation of
motion becomes

~F(z) + =cxgy + gmr’B?

The solution of this equation is

(S) =(^f{fM™ + n*WW(x)dX+c }

If we suppose the motion to start from rest, the constant
will be 0. Performing the integration, the result will be

dx y_ /8y_ /of~ nx3 ^

at x2\f ttR2 V

134

If we suppose the length of the tape to he infinite, the
velocity, after describing any finite space x, will be

Erratum.

Page 104, line 1, for “ Chayne ” read “ Cheyne.”

135

Annual General Meeting, April 19th, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

Report of the Council, April, 1881.

The Treasurer’s Annual Account shows that the balance
against the General Fund Account has increased from
£57 Os. 2d. on the 1st of April, 1880, to £90 Os. 7d. on the 1st
of April, 1881 ; that the balance in favour of the Natural
History Fund Account has increased from £56 10s. 5d. to
£76 5s. 8d. ; and deducting the difference between these
two sums from the Compounders’ Fund, £125, there is a
balance of £111 5s. Id. in favour of the Society on the 1st
of April, 1881, against a balance of £124 10s. 3d. on the 1st
of April, 1880.

The number of ordinary members on the roll of the Society
on the 1st of April, 1880, was 157, and one new member
has been elected ; the losses have been — defaulters, 4, resig-
nations, 7, and death, 1. The number on the roll on the 1st
instant was therefore 146.

Mr. Richard Johnson, F.C.S., the deceased member, was
born in Manchester in the year 1809, and came of an old
Lancashire family. At a comparatively early age he joined
his father and one of his brothers in business, as wire and
pin manufacturers, and under his and his brother Mr. Wm.
Johnson’s active and enterprising management, the business
grew, and soon attained a world-wide celebrity for the
manufacture of telegraph and rope wire.

Upwards of thirty years ago Mr. Johnson was elected a
fellow of this Society, and, aided by the late Dr. Grace-
Calvert, commenced a series of careful experiments on alloys
of zinc, tin, and copper in definite proportions. The results
Proceedings— Lit. & Phil, Soc.— Yol. XX.— No. 10.— Session 1880-81,

136

of these experiments were published in the British Associa-
tion Report for 1855. Mr. Johnson continued to experiment
on this subject for several years, making some of the first
experiments on the expansion of alloys by heat, their heat
conductivity, and specific gravity, see Phil. Mag., XIV.,
1857, XVIII., 1859, etc. Shortly after he invented a machine
for testing the hardness of alloys and metals generally, and
made many useful experiments.

Perhaps, however, his most important investigations were
on the chemical changes which pig iron undergoes during
its conversion into wrought iron. For more than one
hundred years previously pig iron had been converted into
wrought iron by puddling; but it was reserved for Mr.
Johnson to explain the nature of the change, by the careful
analyses he made of samples of the iron, taken at short
intervals, during the process of puddling.

These experiments are described in detail in the Phil.
Mag., XIV., 1857.

Mr. J ohnson was always very active in the cause of educa-
tion. He took a deep interest both in Owens College and
the Manchester Grammar School. To the end of his life he
remained a careful and constant reader ; by degrees he sur-
rounded himself with a large and valuable library and
picture gallery. He died on the 16th of February last, at
his residence, Kemnal Manor, Chislehurst, after a short
illness, much regretted by all who knew him.

Various proposals for the celebration of the Centenary of
the Society have been carefully considered by the Council,
but in the present state of the Society’s finances the Council
do not feel justified in recommending for adoption any
scheme involving certain, and probably considerable, ex-
pense, but which would be of very doubtful utility to the
Society.

At the request of the Committee appointed at the last
annual meeting, Dr. R. Angus Smith, F.R.S., has kindly

137

drawn up a report on the work of the Society since its
foundation, an abstract of which will be read at the annual
meeting.

The following papers and communications have been read
at the Ordinary and Sectional Meetings of the Society
during the Session

October 5th , 1880. — “ Colorimetry, Part VI.,” by James
Bottomley, B.A., D.Sc.

“The Antiquity of Toughened Glass,” by William E. A. Axon,
M.R.S.L., F.S.S.

October 11th , 1880. — “On Some Entomostracse, <fec., found in
Derwentwater in September, 1879,” by Mr. John Boyd.

October 19th , 1880.— “ On the Word Chemia,” by Dr. R. Angus
Smith, F.R.S.

“Additional Notes on a Theory of Mixed Opaque Colours,” by
James Bottomley, D.Sc.

“ On Some Early Anticipations of Heliographic Signalling,” by
William E. A. Axon, M.R.S.L.

“ On Some Marine Fossil Shells in the Middle Coal Measures
of Lancashire,” by E. W. Binney, F.R.S., F.G.S., President.

“Some Endeavours to Ascertain the Nature of the Insoluble
Form of Soda Existing in the Residue left on Causticising Sodium
Carbonate with Lime,” by Watson Smith, F.C.S., Assistant
Lecturer on Chemistry in the Owens College, and Mr. W. T.
Liddle.

November %nd, 1880.— “ On the Conditions of the Motion of a
Portion of Fluid in the Manner of a Rigid Body,” by R. F.
Gwyther, M.A.

“ Did Pascal Invent the Wheelbarrow h ” by William E. A.
Axon, M.R.S.L.

“ On the History of the Artificial Preparation of Indigo,” by
Carl Schorlemmer, F.R.S.

“Some Further Experiments on the Cohesion of Water and
Mercury,” by Professor Osborne Reynolds, F.R.S.

November 9th , 1880.—“ On Gravitation,” by the Rev. Thomas
Maekereth, F.R.A.S., F.M.S.

138

November 16th, 1880. — “Note on the Presence of Sulphur in
Illuminating Gas,” by Harry Grimshaw, F.C.S.

December 14th, , 1880. — “ Boulder Stones as Grave Stones,” by

E. W. Binney, F.R.S., F.G.S., President.

“ The Land Subsidence at Northwich,” by Thomas Ward, Esq.

“Some Endeavours to Ascertain the Nature of the Insoluble
Form of Soda existing in the Residue left on Causticising Sodium
Carbonate Solutions with Lime, Part II.,” by Watson Smith,

F. C.S., Assistant Lecturer on Chemistry in the Owens College,
and Mr. W. T. Liddle. Communicated by Professor C. Schor-
lemmer, F.R.S.

December 28th, 1880. — “The Literary History of Parnell’s
Hermit,” by William E. A. Axon, M.R.S.L.

January 25th, 1881. — “On the Question of the Desirability of
the Society’s Library being handed over to the Reference Library
of the Corporation,” by R. D. Darbishire, F.G.S.

February 14th, 1881. — “ On Pendant Nests of a Gregarious
Moth from Venezuela,” by John Plant, F.G.S.

February 22ncl, 1881.—“ List of Severe Winters and Famines,”
by Mr. Herman Hager. Communicated by Professor Balfour
Stewart, F.R.S.

“ Ozone and the Rate of Mortality at Southport during the Nine
Years, 1872-1880,” by Joseph Baxendell, F.R.A.S.

“ On Some Objects of Ancient Date found in Digging Founda-
tions for New Buildings on Land lying between Hanging Bridge
and Cateaton-street, Manchester,” by E. W. Binney, F.R.S., F.G.S.,
President.

“ On the Addition and Multiplication of Logical Relatives,” by
Joseph John Murphy, F.G.S. Communicated by the Rev. Robert
Harley, F.R.S.

March 8th, 1881.—' “Additions to the Paper ‘ On an Adaptation
of the Lagrangian Form of the Equations of Fluid Motion,’” by R.
F. Gwyther, M.A.

“A Sulphuretted Hydrogen Apparatus,” by Peter Hart, Esq.

“Note on an Attempt to Analyse the Recorded Diurnal Ranges
of Magnetic Declination,” by Balfour Stewart, M.A., LL.D., F.R.S.,
Professor of Natural Philosophy at the Owens College, and Wm.
Dodgson, Esq.

139

March 14-th , 1881.—“ On Some Curious Forms of Fresh-Water
Mollusca from Lake Tanganyika, Central Africa,” by James Cosmo
Melvill, F.L.S.

March 22nd, 1881. — “On the Growth and Use of a Symbolical
Language,” by M. Hugh Me. Coll, B.A. Communicated by the
Rev. Robert Harley, M.A., F.R.S.

Four Letters of the late Mr. Thomas Carlyle, addressed by him
to the late Mr. Samuel Bamford, of Blackley, the author of “ Pas-
sages in the Life of a Radical.” Communicated by E. W. Binney,
F.R.S., F.G.S., President.

March 29th, 1881. — “ On the Motion of Developable Cylinders,”
by James Bottomley, D.Sc., F.C.S.

April 5th, 1881. — “On Du Bourguet’s ‘Calcul’ and on Terna-
ries,” by Sir James Cockle, F.R.S., Corresponding Member of the
Society.

“ On a Eucalyptus Globulous at Douglas, Isle of Man,” by E.
W. Binney, F.R.S., F.G.S., President.

“Note on the Presence of Arsenic in Paper Hangings,” by
Harry Grimshaw, F.C.S.

“ On the Action of Sulphuric Acid from Gas Lights on a Zinc
Plate,” by J. P. Joule, D.C.L., LL.D,, F.R.S., <fcc.

“ On the Relation between the Electrical Resistance and Chemi-
cal Constitution of Steel Wire,” by William H. Johnson, B.Sc.

Several of these papers have already been printed, and
others passed by the Council for printing in the new Volume
of Memoirs.

The Council still consider it desirable to continue the
system of electing Sectional Associates, and a resolution on
the subject will be submitted to the Annual Meeting for the
approval of the Members.

The Librarian reports that the number of societies with
which we correspond is nearly the same as last year, and
that Vol. VI., 3rd Series, of our Memoirs, and Vols. 16 to
19 of the Proceedings, have been forwarded to these societies
and to all our honorary and corresponding members. In
the case of the societies the volumes were accompanied with
requests to fill up vacancies where required, and in reply we
have received many volumes to complete our sets.

»r.

MANCHESTER LITERARY AND,

Charles Bailey, Treasurer, in account with the Society,

Statement of the Accounts

1880-1. 1879-80.

1880. -— April 1. £ s. d. £ s. d. £ s. d,

To Cash in hand 124 10 3 8 10 (

1881. — March 31.

To Members’ Contributions : —

Arrears, 1877-8, 1 at £2 2s 2 2 0

„ 1878-9, 1 at £2 2s 2 2 0

„ 1879-80, 10 at £2 2s 21 0 0

New Members’ Admission Fees, 1880-1, 1 at £2 2s 2 2 0

,, Subscriptions, 1880-1, 1 at £2 2s 2 2 0

Old Members’ „ „ 130 at £2 2s 273 0 0

__ 302 8 0 343 7 (

To one Associate’s Subscription for Library, 1880-1 0 10 0

To Sectional Contributions : —

Physical and Mathematical Section, 1880-1 2 2 0

Microscopical and Natural History Section, 1879-81 ... 4 4 0

— 6 16 0 2 12 <;:

To use of Society’s Booms : —

Manchester Geological Society, to 31st March, 1880 ... 30 0 0

Manchester Scientific Students’ Association (1 meeting) 15 0

Manchester Medical Society (1 meeting) 115 0

— 33 0 0 66 5 (

To Sale of Society’s Publications 10 19 7 118 (

To Natural History Fund : —

Dividends on *1225 Gt. Western Stock 59 15 3 59 19 C

To Bank Interest, less Bank Postage, to 31st December, 1880 1 18 4 0 14 7

£539 7 5 £483 6 1

1881. — April 1. To Cash in Manchester and Salford Bank £111 5 1

11th April, 1881.

Audited and found correct,

(Signed) T. CLEMENT TRAPP.

WILLIAM H. .JOHNSON.

PHILOSOPHICAL SOCIETY.

from 1st April, 1880, to the 31st March, 1881, with a Comparative
for the Session 1879-1880.

®r.

1881 — March 31.

By Charges on Property : —

Chief Rent

Insurance against Fire

Property Tax .

Repairs, Whitewashing, &c

By House Expenditure -

Coals, Gas, Candles, and Water

Tea and Coffee at Meetings

House Duty

Cleaning, Brushes, Sundries

By Administrative Charges : —

Wages of Keeper of Rooms

Postages and Carriage of Parcels

Attendance on Sections and Societies
Stationery and Printing Circulars

By Publishing : —

Printing Memoirs

Printing Proceedings v

Wood Engraving and Lithographing. .
Editor of Memoirs and Proceedings ..

By Library : —

Binding Transactions

Binding Books for Library

Books and Periodicals

Assistant in Library

Geological Record for 18 77

Palseontographical Society for 1881
Ray Society for 1881

By Natural History Fund : —

Grant to Section for Books

By Balance

1880-1.

£ s. d. £ s. d, £

1879-80.
d. £

d.

12 12 0
12 17 6
4 5 0
2 16 10

12 13 0
12 17 6
3 10 10
0 18 2

04 li.

... 17 19

7

12 16

1

... 16 6

1

19 4

3

... 6 7

6

6 7

6

... 5 11

2

46 4

4

5 5

8

... 57 4

0

57 4

0

... 24 5

6

17 4

0

... 9 9

0

11 19

0

... 11 16

6

102 15

0

10 4

1

... 42 16

0

30 1

6

0

47 17

0

... 8 5

0

4 13

0

... 50 0

0

142 5

0

50 0

0

... 8 17

4

... 16 16 11

2 18

3

... 16 0

5

38 19

6

... 20 10

0

11 10

0

—

—

0 10

6

... 1 1

0

1 1

0

... 1 1

0

64 6
40 0

8

0

1 1

0

111 5

1

29 19 6
43 13 6
96 11 1
132 11 6

56 0 3
124 10 3

£539 7 5 £483 6 1

1880-1.

£ s. d. £ s. d.

Compounders’ Fund : —

Balance in favour of this Account, April 1st, 1881 125 0 0

Natural History Fund : —

Balance in favour of this Account, April 1st, 1880 56 10 5

Dividends as above 59 15 3

116 5 8

Less Grant for Natural History Works 40 0 0

Balance in favour of this Account, April 1st, 1881 76 5 8

„ , £201 5 8

General Fund

Balance against this Account, April 1st, 1880 57 0 2

Expenditure, 1880-1, as above 388 2 4

445 2 6

Receipts, 1880-1, as above 355 1 11

Balance against this Account, April 1st, 1881 90 0 7

Balance in favour of the Society, April 1st, 1881 £111 5 1

MANCHESTER LITERARY AKd

Charles Bailey, Treasurer, inaccount with the Soam

lilOSOFHICAL SOCIETY.

Uisawk- 8181 “ 18811 WIIH A “™ *

£ 5j

\ZZZ •>***•■<•

PJCWwPr°PBrty' 1212 0 12 18 0

±$KMI

302 8 0 M ; ,

"i :

To Sale of Society's Publications v. 10 19 7 1111

"SrilKril-S- 59 .5 3 ,11,

£539 7 6«8“

P8tessJI„JJ„.
rissifvijii ...Hi ...

pife-ii! Hi...

IHsgni Hi;..

1881.— April 1. To Cash in Manchester and Salford Banh iIU * J

11th April, 1881. Audited and found correct, ^

s.d.

rsis°f ^ "■ ** * 1881

&&iKfthia“-Ap"ii8t- 1880 . nn i

I Lcm Grant for Natural History Works l l

■ _^_SJ

1 Receipts, 1880-1, as above 855 111

2«lmce in favour of tte gocistjj April lstj 1881 £111 3 1

142

On the motion of Mr. A. Brothers, seconded by Mr. It. S.
Dale, the Report was unanimously adopted and ordered to
be printed in the Society’s Proceedings.

On the motion of Mr. J. Smith, seconded by Mr. H.
Grimshaw, it was resolved unanimously : That the system
of electing Sectional Associates be continued during the
ensuing Session.

The following gentlemen were elected Officers of the
Society and Members of the Council for the ensuing year : —

fjrmbent.

EDWARD WILLIAM BINNEY, F.R.S., F.G.S.

^ia-$rmbent0.

JAMES PRESCOTT JOULE, D.C.L., LL.D., F.R.S., F.C.S.
EDWARD SCHUNCK, Ph.D., F.R.S., F.C.S.

ROBERT ANGUS SMITH, Ph.D., F.R.S., F.C.S,

HENRY ENFIELD ROSCOE, B.A., Ph.D., F.R.S., F.C.S.

(S-emtarie*.

JOSEPH BAXENDELL, F.R.A.S.

OSBORNE REYNOLDS, M.A., F.R.S.

^xzmvxzv.

CHARLES BAILEY, F.L.S.

librarian.

FRANCIS NICHOLSON, F.Z.S.

©ther $tzmbzx& oi the Ccmnril.

REV. WILLIAM GASKELL, M.A.

ROBERT DUKINFIELD DAR BISHIRE, B.A., F.G.S.
BALFOUR STEWART, LL.D., F.R.S.

CARL SCHORLEMMER, F.R.S.

JAMES BOTTOMLEY, B.A., D.Sc., F.C.S.

WILLIAM HENRY JOHNSON, B.Sc.

Dr. R. Angus Smith, F.RS., read an abstract of his re-
port on the work of the Society since its foundation.

On the motion of Mr. C. Bailey, seconded by Mr. R. D.
Darbishire, the thanks of the Society were unanimously
voted to Dr, Smith for his report.

143

MICROSCOPICAL AND NATURAL HISTORY SECTION.

Annual Meeting, April 11th, 1881.

E. W. Binney, F.R.S., F.G.S., in the Chair.

The Annual Report was read by the Secretary, and the
Treasurer presented his Annual Statement of the financial
position of the Section, both of which were confirmed and
passed.

The following were elected officers for the ensuing year,
1881-1882:—

f xz&xbznt :

A. BROTHERS, F.R.A.S,

Dice-J) xzzxbmiz :

CHARLES BAILEY, F.L.S.

E. W. BINNEY, F.R.S., F.G.S.

R. D. DARBISHIRE, F.G.S,

cQlu%mxzx :

T. H. BIRLEY (Somerville).

gtcrrtarw# :

J. COSMO MELYILL, M.A., F.L.S.

ROBERT E. CUNLIFFE.

Cctmril :

W. C. WILLIAMSON, F.R.S.

W. BOYD DAWKINS, F.R S., F.G.S.

J. BOYD.

A. MILNES MARSHALL.

Dr. ALCOCK.

HASTINGS C. DENT.

S. MOORE.

W. E, BARRATT.

144

Professor Boyd Dawkins, F.R.S., made some remarks
with reference to the dates of the introduction of the
Pheasant and Fallow Deer into England. He stated that
there were entries of the Monks of Waltham, of allowances
to the Canons, from which it would appear that the pheasant
was known as early as A.D. 1050; and from remains found
in Roman refuse heaps it was probable that the fallow
deer was introduced during the period of the Roman
occupation of Britain.

Mr. Thos. Rogers exhibited specimens of Erinus Alpinus
from Downliam, near Clitheroe, where the plant is found in
considerable profusion, especially on the wall of the vicarage
garden, and made some remarks on the probable naturaliza-
tion of the plant in England.

The following paper was received after the Annual Gene-
ral Meeting, April 19th, 1881 : —

“ First Resolvents of the Quartic

f + af + x xy-^ = 0 (1)

and the Cubic

ay 3 + 3 by2 + 2>cy + m = 0 (2)”

By Robert Rawson, Esq., Hon. Memb. M. L. & Phil. Soc.,
Assoc. I.N.A., Mem. of the Lon. Math. Society.

1. Differentiate (1) with respect to x, xx being a function

of x and (a) being a constant.

••• (V+2a/ + ^)g + g/ = 0 (3)

Eliminate y 4 in (3) by means of (1)

Then, (6a/ + <jxlV - a2)^ = 3/^5 (4)

&X Ct X

Put, ( bay 2 + 9#i y - a*)(ly2 + my + n) = 3 y2i<~ (5)

. (XX

Equation (5) is satisfied by

(8a3 + 27 xfjl + = 0

(XX

145

(8a8 + 27»?)»t-9^ = 0

CIOC

(8a5 + 27xi)n + Zr/p = 0

CLOG

Substitute the above values of l, m, n iu
d—^ly^ + my + n

Then (8a3 + 27af)^ + 3^(2a/ - 3*# + a2) = 0

(6)

An equation, which is called the first Resolvent of the
quartic (1).

Each of the roots of this quartic is, therefore, a particular
solution of (6), and any value of y which satisfies (6) is,
therefore, a root of the quartic (1).

2. A general solution of (6) is obtained as follows : —

Let y = yx + v be a general solution (7)

where y\ is one of the roots of the quartic (1), and, v a new
variable to be determined.

Substitute the above value of y in (6) and it becomes
(8a3 + 27x\)^~ + ^ + 3^^2a(yi + vf - dx^i + v) + a2 j = 0
From which is derived

(8a3 + 27*?)^ + 3^ 1 2 av* + (4a^ - 3*,>j = 0 (8)

This equation is a well known integrable form, and, by

integrating it in the usual way, putting (8a3 + 27#?)P = 6a^
then we obtain

»(« + /|P exp. J (^-2yi)Pc&|^ = exp.y"i )p<&...(9)

using the convenient notation of Professor Cayley, viz.,
es = exp.2.

Hence the general integral, or complete primitive of (6) is

exp./'(|^-2yi)p&

V = y 1 + Y1 /-/^ — ~ r — =j—

c + J | P exp. j (^ - 2y1JPc& J dx

(10)

146

S. Equation (6) is made linear of the second order by
the assumption of

y=

8as + 27x\ du

dx1

dx

udx

(ii)

dhi

dx 2

Substitute the above value of y in (6) and we obtain

dxi
dx

. K dx i d2x i

^ dx2 f

8a3 + 27^ ( <7#

dx

+ 18a3

/ ^ \2

(^8a8 + 27^3 J w = 0 (1 2)

The general integral of (12) is, therefore, the value of (u)
determined from (11) wherein y takes the value given in
equation (10).

4. The following particular case is of some interest in the
theory of elliptic functions.

Put, X\ — -4^# + ^, and a = 6.

Substitute these values in equations (1) and (6); then
they become as follows :

'/-Qf-i(x + l)y-3 = 0 (13)

3(1 -»■ + (* + i)y + 3 = 0 (14>

The various steps in the substitution and reduction, being
simple, are omitted.

Equation (14) has been considered by Professor Cayley in
the Messenger of Mathematics, Vol. IV., pages 69, 110, and
Elliptic Functions, page 248 ; and also by Mr. Hart, in the
Messenger of Mathematics, Vol. IV., page 125.

The general solution of (14) is given by the substitution

of Xi = - 4^ + and, <z=6 in equation (10) and is as

follows :

/ x 2- l\i 2 f y\c

(—) °xp' V T-

Vidx
x 2

c +

lf\( 1 y exp. 2 f^S— l dx

3; Iw-W 3 J ijxclx I

y=y i+

(15)

5. Professor Cayley states correctly that a particular

solution of (14) is given by

y = v2x~l + 2vx* = v~2x * + 2y~b?-i (16)

where, v is a root of the quartic

v4 + 2xh3 - 2xh - x — 0 (17)

And, to obtain a general solution, he transforms (14) into a
differential equation of the second order, from which a
general solution is derived in the usual way. Such trans-
formation is obviated by the procedure of Art. 2. Of course
the elimination of v between (16) and (17) will give (13)
as follows :

y2 = (v2x~% + 2vxi)(v~2xi + 2v~1x~i)

= 2v~1x% + 2vx~% + 5

.*. y2-Q = 2v~4x$ + 2vx~% - 1

and, y4 - 6y2 = 4v~2x\ + 8v~4x% + iv2x~^ + 8vx~$ + 3

- 4 (x + y - - 4x~2xi - 8v~2x% - 4v2x~§ - 8vx~$

Then, y4 - 8y2 - 4^x + ^y -3 = 0

which agrees with (13) as it should do.

6. A root of (13) may be found by changing the inde-
pendent variable x to another independent variable 0 con-
nected with the former by a given relation. This has been
done by Professor Cayley in a particular case (see Messenger
of Mathematics, page 111.) Put y = <t>(z)

- 1 ^)W-6}- 3

.x +

If 0(,)2

m

2 z2 + 5z + 2

1 z4 + 2z2 + 2z + 1
m % fj z tj 2z2 + 5^ + 2

From which, x 2 = :

3(2 + z)
1+22

which agrees with Professor Cayley’s results.

The advantage of this transformation is questionable, as
particular values of x only can be obtained by it, except by
the solution of the quartic

z4 + 2z3 - 2 x2z - #2 = 0.

148

The selection, as it appears to me, must lie between the
above quartic and the quartic (13).

7. Differentiate (2) with respect to x, where a, b, c, m

dv

are functions of x, and put as usual = y\ &c.

. 1 o}y 3 + 3&y + 3 dy + m1 _

^ + 3 ay2, + 6by + 3c

Eliminate ys by means of (2)

(< ah 1 - bad)y2 + (ad - ca})y + ^(am1 - mal)

a?y 2 + 2aby + ac

Put (ab1 - bal)y2 + (ac1 - cad)y + \(aml - ma1)

= 0 (18)

= ( a*y 2 + 2 aby + ac)(Py 2 + Qy + R) (19)

Then (18) becomes

y1 + Vy* + Qy + R = 0 (20)

which is the first resolvent of the cubic (2).

Multiplying the right-hand side of (19), and, eliminate
y\ ys by means of (2), there results
(3 62 - 2ac)P - a6Q + a2 R = ab 1 - ba1
(36c- am) P - 2acQ + 2a6R = ac 1 - ca 1

6mP - amQ + acR = ^ (am1 - ma1) (21)

The values, therefore, of P, Q, R, which satisfies equation
(20) are to be determined from the system (21), and are as
follows

Put a — 3(362c2 - 4ac8 - 463m + 6abcm - a2m2) (22)

aP = (462m - 36c2 - acm)a1
4- 6a(c2 - bm)bx
+ 3 a(am - bc)d

+ 2a(62 - ac)ml (23)

aQ = (76cm - 6c3 - am^a1

+ 3 (36c2 - 26 2m — acm)bl
+ 3(2ac2 + abm - 362c)c1

+ (663 + a2m- 7abc)mx (24)

aR = 2m(6m - c2) a1

+ 3m(6c - am)6J
+ 6m(ac - 62)c1
4 (362c + abm - 4ac2)mx

(25)

149

Each of the three roots of (2) is a particular solution of
(20), and a solution of (20) is, therefore, a root of (2).

The above values of P, Q, R, agree with the results of
Wm. Spottiswoode, M.A., F.R.S. (See Manchester P. So-
ciety’s Memoirs, Yol. II., third series, page 230.)

The reader of Mr. Spottiswoode’s paper above referred to
must make the following corrections, viz., page 231, for
( a})2a2b read ( a})2a2d in line 10 from top; in Line 11 from top,
for Sa^ad2 read cdb\Sad2 -9bcd). Mr. Spottiswoode has
pointed out the line to be pursued to obtain the resolvent
of the second order. (See also Rev. Robert Harley’s Report
on the Theory of Differential Resolvents to the British As-
sociation for the Advancement of Science, 1873.

The problem, viz : to find the second differential resol-
vent of a general cubic is exceedingly complex and tedious ;
it was completely solved by me some three or four years ago
and the results sent to the Rev. Robert Harley, F.R.S., &c.,
in whose possession they still remain.

8. The equation (20) is soluble when c, m are constants,
and am2 = Sbcm~2c3. Hence, the root of the following

cubic is obtained by integration, viz :

(3 hem - 2c3)?/3 + 3 bm2y2 + 3 cm2y + m3 = 0.

9. When 6 = 0 then, a — - 3a(4c3 + am2)

and, aP = - acma1 + 2>a2mcl - 2 a2cm} (26)

and, aQ = - (6c3 + am2)a} + 6ac2d + a2mml (27)

and, aR = - 2 c2ma}< + Qacmc1 - ±ac2ml (28)

The further condition, c3 = Ci<xm2, where Ci is an arbitrary
constant, will cause P, R, to vanish, thereby rendering
equation (20) soluble, and determine by integration a root
of the cubic

c3y3 + 2>cxcm2y + cxm3 = 0 (29)

10. With a view of obtaining a root of a general cubic
by integration it will be necessary to examine the condi-
tions of solubility of equation (20) which are given by Abel.
(See Abel’s works, vol. 2).

150

The following may be of some use in the pursuance of
this object.

Let, (y + a)\y + b)m = pefcdx (30)

where a , b} c are functions of x, and p constant.

By taking the log. of (30) it is readily shown that
y\ - cy 2 + {wa1 + mb1 - c(a + b)}y + nba 1 + mab 1 - abc
(n + m)y + ma + nb

If m = - n, then, (y + a)n =p(y + b)nefcdx is a particular integral of

+ c£. + Ka + 6) _ al ~ h\ ,

^ n(a - b) - b) a -by

abc

bal - ah1

n(a -b) a-b

— 0...(32)

PROCEEDINGS

MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

H - f V"v ’ , jb \

O

YOL, XXI.

Session 1 88 1-82.

lyf- ?3 2-

MANCHESTER :

PRINTED BY T. SOWLER AND CO., 24, CANNON STREET.
LONDON: BALLIERE, 219, REGENT STREET.

1882.

NOTE.

The object which the Society have in view in publishing their
Proceedings is to give an immediate and succinct account of the
scientific and other business transacted at their meetings to the
members and the general public. The various communications
are supplied by the authors themselves, who are alone responsible
for the facts and reasonings contained therein.

INDEX.

Alcock Thomas, M.D. — On Frog Tadpoles, pp. 112, 135.

Axon William, E. A., M.R.S.L. — The Sea Gull in Salford, p. 11. On
the Numerical Extent of Personal Vocabularies, p. 11. On the
Pronunciation of Deaf-Mutes who have been taught to Articu-
late, p. 29. The Colour Sense and Colour Names, p. 77.

Bailey Charles, F.L.S. — On the British Species of Erythroea, p. 69.
On a Dwarf Form of Campanulata Glomerata, L., from the Isle of
Wight, p. 73. On the Isle of Wight Station for Lychnothamnus
Alopecuroides, Braun, p. 74.

Baxendell Joseph, F.B.A.S. — Notes on the Variable Stars U Canis
Minoris, V Geminorum, and U Bootis, p. 183.

Bottomley James, D.Sc., F.C.S.— On the Mean Intensity of Light that
has Passed Through Absorbing Media, p. 2. Correction of the
Formula used in Photometry by Absorption when the Medium is
not perfectly transparent, p. 5. Note on a Passage of Pollux
relating to the formation of Purple Dye, p. 40. On the Projection
of a Solid on Three Coordinate Planes, p. 188.

Cockle Sir James, F.R.S. — Note on Envelopes and Singular Solutions,
continued from vol. XVII. p. 15, p, 98.

Dent Hastings C., C.E. — Lepidoptera of the Shetland Islands, p. 126.

Gwyther R. F., M. A. — On the Failure of certain Mathematical Solutions
of the Problem of the Motion of a Solid through a Perfect Fluid,
p. 9. On Cyclic Motions in a Fluid, and the Motion of Vortex
Rings of Varying Curvature, p. 32.

Johnson William H., B.Sc. — On Professor Bjerkness’s Experiments to
Demonstrate the Analogies between Electrical and Magnetical
Phenomena and some Hydrodynamical Phenomena, p. 30. Notes
on some Experiments made in February, 1881, on the Influence of
Stress on the Electrical Resistance of Iron and Steel Wires, p. 187,

VI

Marshall Professor A. Milnes.-Oh the Larval Form of Star-fishes,
echinoids, holotharides, and crinoides, p. 57.

Melvill J. Cosmo, M.A, — On Limnothuchus Kirkii (Edgar Smith) from
Lake Tanganyika, and on a new land Mollusc, Cyclosurus Marieri
(Morelet), recently discovered by Prof. Morelet at the Mayotta
Islands, about 300 miles N.W. of Madagascar, p. 57. List of the
Phanerogams of Key West, South Florida, mostly observed there
in March, 1872, p. 101. On Cyproea Guttata (Grnel), p. 125.

Plant John, F.G-.S. — Notes on the Giant Dragon’s-blood Tree at Orotava,
p. 130.

Bawson Bobert, Assoc. I.N.A. — On Differential Besolvents, and Partial
Differential Besolvents, p. 59.

Beynolds Professor Osborne, M.A., F.B.S,. — On Drops Floating on the
Surface of Water, p. 1.

Schunck Edward, Ph.D., F.B.S. — Bemarks on the Terms used to
Denote Colour, and on the Colours of Faded Leaves, p. 43.

Sidebotham Joseph, F.B.A.S. — On the use of Aniline Colours in Water
Colour Drawings, p. 32.

Stewart Professor Balfour, LL.D., F.B.S. — A Comparison between the
Height of the Bivers Elbe and Seine and the State of the Sun’s
Surface as regards Spots, p. 93.

Thomson William, F.B.S.E. — Notes on Lead Pipes and Lead Contami-
nation, p. 84.

Ward Thomas. — On the Manufacture of Salt in Cheshire, p, 14.

Waters Arthur Wm., F.G.S., F.L.S. — Preliminary Bemarks on Ob-
servations made in Davos in the Winter 1881-82, p. 155.

Wilde Henry. — On Electro-Motor Machines for the transmission of
mechanical power by means of Electricity, p, 97.

Wills Mr. — On a Series of Preparations of Desmidiae, p. 38.

Woodward Arthur Smith. — On the Occurrence of Oxide of Manganese
(Wad) in the Yoredale Bocks of East Cheshire, p. 115.

YII

Meetings op the Physic ax and Mathematical Section. — Annual,
p. 186. Ordinary, pp. 40, 183.

Meetings of the Microscopical and Natural History Section. —

Annual, p. 134. Ordinary, pp. 36, 37, 57, 101, 125.

Report of the Council, April, 1882, p. 141.

PEOCBBDIN G S

OF THE

MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

Ordinary Meeting, October 4th, 1881.

J. P. Joule, D.C.L., LL.D., F.R.S., &c., in the Chair.

“On Drops Floating on the Surface of Water,” by Pro-
fessor Osborne Reynolds, F.R.S.

It is well known that under certain circumstances drops
of water may be seen floating on the surface for some se-
conds before they disappear. Sometimes during a shower
of rain these drops are seen on the surface of a pond, they
are also often seen at the bows of a boat when travelling
sufficiently fast to throw up a spray. Attempts have been
made to explain this phenomenon, but I am not aware of
any experiments to determine the circumstances under
which these drops are suspended. Having been deeply en-
gaged in the experimental study of the phenomena of the
surface tension of water and the effect of the scum formed
by oil or other substances, it occurred to me that the com-
parative rarity of these floating drops would be explained if
it could be shown that they required a pure surface, a sur-
face free from scum of any kind. For, owing to the high
surface tension of pure water, its surface is rarely free from
scum. The surface of stagnant water is practically never
free except when the scum is driven off by wind. But
almost any disturbance in the water, such as the motion of
the point of a stick round and round in the water, or water

Proceedings — Lit. & Phil, Soc. — Vol. XXL. — No, 1. — Session 1881-2.

2 '

splashed on the surface, will serve to drive back the scum
for a certain distance. This may be shown by scattering
some flowers of sulphur on the surface. This powder is
insoluble and produces no scum, and hence it serves ad-
mirably to show the motion of the surface and whatever
scum there may be upon it. If when the surface is so dusted
a splash be made by a stick so as to throw drops on to the
sulphured surface, at the first splash no floating drops are
produced ; but after two or three splashes in rapid succession
it will be seen that the sulphured scum has been driven
back by the falling water, leaving a patch of clear surface,
and on this drops will float in large numbers and of all
sizes. These drops are entirely confined to that portion of
the surface which is clear. The drops, either by their initial
motion or by the current of air, glide rapidly over the surface
from the point at which they are formed. When, however,
they reach the edge of the scum they disappear, apparently
somewhat gradually. I have this summer made the ex-
periment on several ponds and on various days, and I have
never found any difference. Any scum, however trans-
parent, prevented the drops, and they always floated in large
numbers when the scum was driven back in the manner
described, by the wind or any other way.

This result points to the conclusion that whatever may
be the cause of this suspension, it depends only on the sur-
face of the water being pure, and not at all on the tempera-
ture or condition of the air.

“ On the Mean Intensity of Light that has passed through
Absorbing Media,” by James Bottomley, D.Sc., F.C.S.

In colorimetric experiments the areas compared are as-
sumed to be of the same tint throughout. When, however,
we look through columns of coloured liquid at external
white surfaces, this condition will not be exactly fulfilled.

* 3

Suppose the bottom of the containing cylinder to be per-
fectly flat. Owing to the adhesion of the liquid to the
sides, and the consequent elevation there above the general
level, the colour will be more intense near the sides. This,
however, if the cylinders are of moderate radius, may be
remedied by covering the bottom with a black plate having
a small aperture in the centre ; in this way the rays coming
from the sides are cut off. But, even supposing this done,
the colour will not be exactly the same over the whole
area. Suppose an eye to be placed at A in the axis of the

cylinder, and let CH represent the section by a vertical
plane of the circular area at the bottom admitting light.
Let AE be the ray which passes through the centre ; the
path of this ray through the liquid will be EB. Let AFG
be another ray which reaches the eye ; the path of this ray
through the liquid is FG ; and as this is greater than EB,
the absorption will be greater. Hence the colour will
gradually increase in intensity as we pass from the centre

4

to the circumference. For colorimetric measurements we
take the vertical length of the column of liquid. In what
follows I propose to consider if this would lead to any
noticeable error. Our impression of colour will not be
derived from a consideration of any one point of the area,
but from a consideration of the whole area ; hence the colour
we observe is the mean colour. This, however, although
very nearly, will not be exactly the same as at the centre.
Suppose G to be the centre of a very small area, which we
may denote by ds ; then the quantity of light which passes
through this small area towards the eye we may denote by
ads. Since the area is very small, and ultimately vanishes,
we may consider GF as the path of all the rays passing
through this small area and reaching the eye. Let GF be
denoted by x ; then the intensity of the light after passing
through the liquid will be akxds , k being the coefficient of
transmission. For simplicity I shall suppose k the same for
every species of light, so that we need only consider one
term of the above form. The small element ds we may
regard as part of an elementary ring of area, 2? rrdv, where
r denotes GE. The quantity of light passing through this
ring towards the eye will be 2 y(&rkxdr. If then we inte-
grate this between limits 0 and ft, and divide by ttE2, we
shall obtain the mean intensity. This will be

~ J kxrdr - (1)

o

Let H be the elevation of the eye above the bottom of the
cylinder, and li the height of the column of fluid ; also let
ju be the index of refraction, d the angle of incidence, and d'
the angle of refraction. Then we have the relationship

sin0 = /xsin0'... (2)

r = ht an0 + (H - h) tan0' (3)

5

We may also write (1) in the form

'E,

g— wiftsecQy,^

The integration of this expression might be troublesome.
Usually 0 will be a small angle; suppose then that we
neglect the cube. From (2) and (3) we deduce with this
supposition

0 =

fir

jih + H — k

and the integral may be written in the form
9 n rn

/ €-wMl +pr*)rdr
RV

o

where p has been written for
2(fih + H - hy

we may also write it in the form

2 a

we

fR

—mh I e~

rtvphr2rdr

The integral taken betv/een the assigned limits is

1 _ q— mpKR-

a£-mh /

mR?ph\

If we expand the term e“TO^R2 and neglect terms containing
the fourth and higher powers of It, we shall obtain for the
mean intensity

ae-

2 J

If, as is usual, H be large compared with It, the mean
intensity would differ very little from the intensity of the
central ray. An examination of the term ^,Ra- will show
if a correction is necessary in any case.

“Correction of the Formula used in Photometry by Ab-
sorption when the medium is not perfectly transparent/’ by
James Bottomley, D.Sc., F.C.S.

6

Suppose we have a column of length l, containing q units
of colouring matter per unit of length, the medium being
perfectly transparent ; then the light transmitted will be
akql. Now, suppose the colouring matter, instead of being
uniformly diffused through the whole column, to be con-
fined to an extremely small section at the bottom of length
V, so that the length of the column above the section may
be still taken as l. The intensity of the transmitted light
will be the same in both cases; hence kql=kq'K

If the medium be not transparent, we may now suppose
the column of length l above the section containing the
colouring matter to be occupied by some medium that ab-
sorbs light. Let p be its coefficient of transmission. The
light incident on the bottom of the column is of intensity
qMv. After penetrating the column the intensity will be
akq'lpl ; but by what precedes, q[l'=ql ; so that the intensity
of the transmitted light corrected for absorption by the
medium will be a(kqp)\ If, then, we have two cylinders
containing q and c[ units of colouring matter per unit of
length, and columns of liquid l and we shall have the
relationship (7cqp)l=^(kqp)l'. From this equation we may
determine p in terms of k and known quantities thus :

q'V—ql
P = ki-*

In some experiments on the absorption of light by carbon
diffusions I noticed that when one diffusion was much
stronger than the other there was a slight departure from
the simple rule of colorimetry which held in other cases •
this I thought might be due to the absorption of the water
employed. The probability that this is the cause would be
increased if the value of p deduced from one experiment

7

being applied as a correction to the other experiment, gave
consistent results.

If we write p in the form kp, the formula to be used may
be written (lcpk^)l~ (kpkq,)l'. This leads to the relation

The standard solution contained 1*2 cub. c. of a strong
carbon diffusion in 500 cub. c. of water, and the length of
column was 21 ‘2. Comparing with this a solution contain-
ing 9*6 cub. c. in 500 cub. c. of water, on one occasion I
made 2*94 the equivalent column, on another occasion 2*87,
and on a third occasion 2*8. The mean of these three
results is 2 -87. Hence the corrected formula will be
(Q + 0\L14)Z = (Q' + 0*114)Z'

Q and Q' denoting the number of cubic centimetres of the
strong diffusion added to each cylinder. In the following
table I have recalculated the results given on page 197,
Yol. XIX. of the Proceedings :

A

B

C

2-02

1*92

.... 177

1*59 1-44 1-32

1-22 115 1-06

1-05

0*96

0-88

089 .....

.... 0-82

076

078

.... 0-72

0*66

A denotes length of column by experiment, B denotes
theoretical length calculated by corrected formula, C the
theoretical length deduced from uncorrected formula. It
will be noticed that the discrepancies between A and B are
less than those between A and C.

“Note on the Colour Relations of Nickel, Cobalt, and
Copper,” by James Bottomley, D.Sc., F.C.S.

8

In a paper read before the Physical and Mathematical
Section, April 13th, 1880, I referred to some experiments I
had made to obtain a soluble black, and showed the advan-
tages of such a solution in photometry, also its application
to the determination of the law of absorption of light. The
mixture used consisted of nickel, cobalt, and copper sul-
phates in acidulated water. In a paper read before the
Chemical Society, May 19th, 1881, Mr. Thomas Bayley gives
the results of some similar investigations. He also finds a
mixture of nickel, cobalt, and copper sulphate suitable.
The proportions of the metals in his solutions are :

Co. Ni. Cu.

1 1-48 2-16

The quantities of the salts used in the preparation of the
fluid referred to in my paper give the following ratios be-
tween the metals :

Co. Ni. Cu.

1 1-49 2-46

9

General Meeting, October 18th, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

Mr. Thomas Gair Ashton, B.A., of Manchester, and Mr.
Ludwig Mond, of Winnington Hall, Northwich, were elected
Ordinary Members of the Society.

Ordinary Meeting, October 18th, 1881.

E. W. Binney, F.R.S., F.G.S., President, in the Chair.

“On the Failure of certain Mathematical Solutions of the
Problem of the Motion of a Solid through a Perfect Fluid,”
by R F. Gwytheb, M.A.

Of the solutions with which I intend to deal, we may
take that by Stokes for the motion of a sphere as the type.
In his paper (Camb. Trans., vol. viii. and Reprint) Stokes
considers to what degree his solution differs from the re-
sults of experience, and discusses the origin of this diver-
gence. I propose to show that the origin is possibly of a
different nature to any there discussed. Stokes’ solution
may be stated thus : If A be the centre of the sphere, of
radius a, AX its direction of motion at time t, (r,0) the
zonal coordinates of any point in the fluid referred to AX
as axis, and if 0 be the velocity potential of the motion,

Va3

( p = const - J-^-cos0
and

~ = i~2 C^osd + ~ |(3oos20 - 1) - £;3(3cos20 + l)j (1)

giving the fluid pressure.

Proceedings— -Lit. & Phil, Soc,— Vol. XXI. — No. 2.— Session 1881-2*

10

To deduce from this the impulsive pressures due to an
impulsive change in the velocity of the sphere, we write r
for the short time of action of the impulse, multiply equation
(1) by dt and integrate from t~o to t—r. Let V' be the
final value of Y. The last term in p will contribute nothing
to the final equation, and we obtain merely

-- i$(V'-V)eoS0 (2)

O

Now, the motion in question having been produced from
rest in an infinite liquid by the motion of the sphere, the
motion is the same at every instant as that impulsively pro-
duced from rest by giving instantaneously to the sphere its
velocity Y (Thomson and Tait, vol. i., part 1, page 328.
Kirchoff, Yorlesungen, chap xix., &c.). The value of the
impulsive pressures due to the instantaneous production
of the velocity Y of the sphere, and which produces the
consequent velocities in the fluid is

7T

P

= |^-Ye°s0

(3)

7T

where—-, of course, only differs from <j> by a constant.

Now, there need be no difficulty in supposing a fluid
capable of transmitting a tension, provided this tension
tends to produce no discontinuity of motion or disruption
between near parts, as in the present case. But at the
surface of the sphere we get

- = £aVcos0.

p

and thereupon a maximum of cohesion is needed of the
order ap Y at the extreme rear of the sphere, which is double
the mean value required.* Considering the coefficient of co-
hesion as constant, all other things being alike, the velocity at

# The pressure in front, or tension behind a sphere of radius 1 foot,
started impulsively with unit of velocity in water, would be roughly
represented by that due to a slab of granite i inch thick falling through
3 inches*

11

which Stokes5 solution would fail is inversely as the radius
of the sphere, if failure can take place through want of
cohesion.*

It becomes necessary now to consider the result of such
a failure. In a perfect fluid, the consequence must be dis-
continuity, since we can not admit any minimum value of
0 and therefore of tt within the fluid. In a real fluid, on
the other hand, the possibility of the fluid under the tension
failing to exert pressure equally in all directions would
have to be considered, as intermediate between the usual
problem, and that of disruption, in either case vortex
motion would ensue behind the solid.

“The Sea Gull in Salford,55 by William E. A. Axon,
M.RS.L.

During the recent storm a sea gull ( Larus canus) which
had been injured against the telegraph wires was picked up
and cared for in the cottage at the Salford side of the Mode-
wheel. It was unable to fly, though afforded opportunities
of liberty, and appeared to be taking kindly to its new
environment.

Sea-gulls are now rare visitants in this neighbourhood, but
Mr. John Plant, F.G.S., saw two sailing over Peel Park in
the earlier part of the year.

“On the Numerical Extent of Personal Vocabularies,55 by
William E. A. Axon, M.R.S.L.

In the Bulletin of the Washington Philosophical Society,
vol. ii., app. p. ii. (Smithsonian Miscellaneous Collections, vol.
xx.) there is a paper by Prof. E. S. Holden, in which he
gives some curious estimates as to the number of words used
in speaking and writing. In order to test the matter he

* Or otherwise, consider the sphere to be brought to rest, the whole
motion of the fluid will then cease, but in order to produce rest an im-
pulsive tension of the magnitude named must be sustained at the surface
of the sphere.

12

took Webster’s Dictionary (1852), which contains 1281
pages of defined words— in all 92,488. He then examined
the relative frequency of letters as initials, as words, and
then found out the average number of words to a page.
The next process was to go over the dictionary and to count
all the words in the pages specially selected of which he had
perfect knowledge, and which he would without hesitation
employ. The result was that out of 4420 words he felt
himself to have 1599 at full command. This proportion
applied to the rest of the book would give Prof. Holden’s
vocabulary as 83,456 words.

Mr. Holden gives some other curious particulars. The
Shakspere Concordance (in which verbs and nouns
spelled alike are not discriminated) contains 24,000
words. The Concordance to Milton’s Poems contains 17,377
words. The Bible contains 7209 words, exclusive of
proper names. The Anglo-Saxon Chronicle contains about
12,000 words.

The results obtained by Prof. Holden seem to require
verification by others before we can be sure that his is an
average experience.

A friend has kindly gone over the ground for me, with the
following results

A.

pp.

1—116

Total.

1199

422

L.

pp

. 666— 670

Total.

289

157

S.

>5

974_979

455

162

G,

492—493

145

70

c.

?5

162—166

300

168

N.

1210—1211

144

50

P.

5>

790—793

300

121

H.

5)

550—554

289

165

F.

i)

462—463

144

54

W.

5)

1248—1249

145

42

M.

5)

716—717

145

68

K.

J5

638— 642

289

149

J.

?>

590—591

144

47

Y.

?)

1278

59

26

E.

380—384

289

169

Z.

}>

1281

84

11

4420

1881

My own counting reaches a somewhat higher figure than

13

Prof. Holden. Three personal vocabularies estimated in the
same manner may be thus stated : —

J. J. Alley 37,000 words.

W. E. A. Axon 35,250 „

E. S. Holden 33,500 „

It is clear, however, that such a test as that applied by
Prof. Holden is too strict. In the first place there is no
absolutely complete list of the words in the language from
which to deduce such a percentage. The existing diction-
aries vary greatly in the number of words they contain.

It has recently been stated that the number in the best

known is :

Johnson’s Dictionary, Todd’s Edition 58,000

Do. do. Latham’s Edition, estimated 63,000
Webster’s Dictionary (American), Early Edition... 70,000

The Imperial Dictionary, Former Edition 100,000

Worcester’s Dictionary (American), and Supple-
ment, recently published 11 6,000

Webster’s Dictionary (American), and Supplement,

recently published 118,000

The Imperial Dictionary, New Edition 130,000

Then there are many words which we do not use habi-
tually, but with which we aire perfectly well acquainted, and
which rise spontaneously to the lips when the fitting moment
comes. There are also many words of a technical or special
character which each individual possesses. The sportsman,
not less than the chemist, has a language of his own. Then
in the case of literary or scientific men their vocabularies
must be largely increased by the knowledge of foreign
languages, which is becoming increasingly common. For
purposes of research a man must now have some acquaint-
ance with French, Latin, German, and other languages.

The extent to which the human memory is capable of
retaining words finds its highest expression in the case of
Mezzofanti, whose remarkable linguistic powers are well
known. It is established on tolerably conclusive evidence
that he could write and speak in fifty languages. What
would be the extent of his vocabulary ?

14

General Meeting, November 1st, 1881,

Charles Bailey, F.L.S., in the Chair.

Mr. Alfred James Higgin, of Manchester, and Mr. Arthur
Greg, of Eagley, near Bolton, were elected Ordinary Mem-
bers of the Society.

Ordinary Meeting, November 1st, 1881.

Charles Bailey, F.L.S., in the Chair.

“ On the Manufacture of Salt in Cheshire,” by Thomas
Ward, Esq.

The manufacture of salt has been carried on in Cheshire
from the times of the Romans, and as the brine springs in
several places rose to the surface or nearly so in early times,
it is quite possible that the Britons may have utilised them.
We have no record of salt making during the early Saxon
times, though doubtless it existed, for in Domesday Book
we find distinct records of salt works at the three “Wiches,”
Nantwich, Middlewich, and Northwich, and a reference is
made to “ King Edwards time,” i.e. Edward the Confessor’s.
In 1182 Hugh Malbanc, in the foundation deed of Comber-
mere Abbey says, “ I grant to the same monks the fourth
part of the town of Wych and tithe of my salt and the salt
pits that are mine,” &c.

From this period till the commencement of the 16th
century the records are very scanty, but sufficient to show
that the manufacture was still carried on at the three
“Wiches.” At this period the most important salt town
was Nantwich or Wich Malbanc. Leland in his “ Itinerary”
and Camden in his “Britannia” both mention the Cheshire

15

salt manufacture, and during the 17th century references
are frequent, especially in the Philosophical Transactions of
the Royal Society. Rock salt was discovered in 1670, and
in 1721 the river Weaver was made navigable from Frods-
ham through Northwich to Winsford. After this period
the manufacture steadily but not rapidly increased until
1825, when the duty was taken off salt. Immediately a
great advance was made which continued till 1844, when
the East Indian market was opened to English salt and the
manufacture grew still more rapidly. The alkali trade
caused another rapid advance so that at the present time the
quantity manufactured is fully ten times as large as at the
commencement of the present century.

The districts of Cheshire in which salt is made are in the
valleys of the Weaver, Dane, and Wheelock, and this has
always been the case, for with the exception of a small
manufacture of salt at Droitwich for a limited time, none has
ever been made except in close proximity to these streams.
The Weaver valley is the most important, and at Winning-
ton, Anderton, Marston, Wincham, Northwich, Leftwich,
Winsford, and Nantwich salt is now being made, or has been
made in times past. Since 1847 Nantwich has ceased to
manufacture salt.

Middlewich is at the junction of the Croco with the Dane,
which latter stream is a tributary of the Weaver. In the
neighbourhood of Sandbach, at Wheelock, Lawton and the
surrounding district, salt is made. These places lie in the
Wheelock valley, a tributary of the Dane.

The Cheshire salt beds lie in the Keuper marls, though
they are not co-extensive with these marls. The red or
triassic marls of Cheshire lie in a kind of basin compared
to an elongated saucer with its longest axis lying in a nearly
north and south direction. The best known and most im-
portant beds of rock salt are about the centre of this basin
in the neighbourhoods of Northwich and Winsford. At

16

Lawton in the south-east comer of the basin beds of rock
salt have been found at a considerable height above sea
level. At Nortliwich and Winsford the rock salt lies below
the level of the sea. The Keuper marls of Cheshire are
covered by drift. The clays, gravels, and sands of the drift
are very much mixed up, and the clay is full of boulders
of granite, and various kinds of stone, many of the softer
kinds being deeply ice-marked or scratched.

In the early history of the salt trade, when but a very
small quantity of salt was made, the springs at North wich,
Middlewich, and Nantwich either gently ran away into the
rivers or rose nearly to the surface. When the rock salt
was discovered near to North wich in 1670, a strong brine
was found running upon the surface of the salt. This brine
was utilised at once, being stronger than that of the natural
springs. On the banks of the Weaver many brine wells
were sunk, and since that time all the white salt manufac-
tured has been made from the brine thus discovered. Neg-
lecting minor thin seams of salt which are met with either
above or below the main beds, we may say there are two
thick beds of rock salt known locally as Top Rock salt and
Bottom Rock salt. These two beds are separated by a layer
of marl much indurated and containing veins of salt run-
ning nearly vertically, as if occupying rifts, or cracks, or
crevices in the hardened marl. This layer is about 30 feet
thick. The first bed of rock salt, or the “ Top Rock,” is at
Northwich from 40 to 80 yards from the surface, varying
with the different surface levels and dipping from the
N.E. to S.W. The surface of this salt bed is very
irregular, being water-worn and channeled as if by minia-
ture streams. In most cases immediately before reaching
the salt a much indurated marl is found, locally termed
“ flag.” On piercing this flag brine was met with in the
first instance, and continues so to be to the present day.*'

* At Nantwich this <c flag” has been met with in a boring for brine
now being carried on.

17

Brine is formed by fresli water reaching the surface of
the salt either at the so-called outcrop or through fissures
and faults in the marl. The marl itself, when unfissured or
undisturbed, is perfectly impermeable. It is pretty certain
that the water gains admission at a higher level than the
rock salt, for the brine originally rose nearly to the surface
of the ground in some districts, and in others rose many
yards up the shaft when the “ flag” was pierced. Brine is
only met with on the surface of the Top Bock salt, which salt
averages about 25 yards in thickness in the neighbourhood of
North wich. At Winsford the Top Bock salt lies more than 60
yards from the surface, and is rather thicker than at North-
wich, though the indurated clay separating the two beds of
salt is about the same thickness. The bottom bed of rock
salt is about 35 yards thick at North wich and rather more
at Winsford. No water is ever found on this salt. The
“ Bock Head,” as it is called, is perfectly dry.

It is almost impossible to say what the area of these beds
of rock salt is. Judging, however, by the subsidence of
the land, and taking into consideration the furthest points
at which salt has been proved by shafts, I have come to the
conclusion that the Northwich beds occupy at least three
square miles, and contain in the aggregate about 900,000,000
tons — the upper bed 380,000,000, the lower 520,000,000.
The Winsford district is more difficult to determine, but,
being again guided by the distinct subsidences of the land,
there cannot be less than six miles of salt beds containing
at least 1,900,000,000 tons of salt. It is quite impossible to
estimate the quantities of rock salt in the Nantwich, Middle-
wich, and Lawton districts, as there are no mines; and only
in Lawton has the salt rock been bored through. There
are several other districts where salt must exist as is shown
by the subsiding of the land. The figures given, which •
are the merest approximations, show that practically the
salt beds are inexhaustible.

18

The first, or top rock salt, was discovered in 1670, and
very shortly after this mines were worked, hut not to any
large extent. It was not until 1721, when the river Weaver
was made navigable, that the rock salt could be largely
utilised. In the year 1732 there were sent down the Weaver
9,322 tons of rock salt. The quantity shipped down the
river increased year by year until in 1778 it reached 54,000
tons. In 1781 the bottom, or lower rock salt, was discovered,
and all new mines were sunk to it, the quality being better.
After the commencement of the present century the top
mines ceased to be worked, and now only one is known to
exist. Nearly the whole of these top mines were destroyed
by the breaking in of water or brine at the shafts. One
after another they collapsed, leaving large funnel-shaped
pits filled with water, locally known as “rock pit holes,” to
mark their position. In all the upper mines large pillars,
about 5 yards square, were left to support the roof. In the
lower mines these pillars, though originally of the same
size, are now left larger, varying from 8 to 1 2 yards square.
One or two lower mines have collapsed by the roof falling
in for want of sufficient supports. Some have been aban-
doned because of the breaking in of brine or water. Of
late years, however, when worked to the boundary of the
owner, they have been allowed to fill with brine, which is
pumped out for the manufacture of white salt. About
150,000 tons per year of rock salt are mined from the lower
portion of the salt bed, which is the purest. This is not
quite one tenth of the quantity of white salt made from brine.
Whether, however, the salt is mined as rock salt or is manu-
factured from brine, the beds of rock salt before described
furnish the whole.

The manufacture of salt from natural brine is carried on
more largely in Cheshire than in any other portion of the
world. The brine is found upon or near to the surface of the
first bed of rock salt. It is reached by the sinking of a shaft or

19

huge well, sometimes as much as 10 feet in diameter, which
is cylindered to keep out the fresh water. Till recently
there has been no great diminution in the quantity of brine.
As soon as the 'flag’ overlying the 'rock head’ was pierced
the brine rose very copiously and the most rapid pumping
only produced a slight change of level. The height of the
brine above the surface of the rock salt varied in all the
districts, but in every case was considerable, being frequently
50 yards. The level of the brine when at rest or unpumped
has fallen very considerably of late years, owing to the
enormous increase in the make of salt. At Winsford
the level in 1880 was 20 yards lower than in 1865. It is
evident that more brine is being pumped out than fresh
water getting in to make new brine to replace it. Many
shafts have been completely exhausted.

Of late years a number of old worked out mines in the lower
bed of rock salt have been used as reservoirs into which the
brine from the rock head runs night and day. These enormous
reservoirs are nearly always full, and in the majority of cases
the brine rises high up the shafts. The mines in the bottom
rock salt vary from 100 to 112 yards from the surface, and the
salt is worked out to a depth of about 15 feet. Some of
these reservoirs will hold more than 50,000,000 gallons of
brine. Every day the trade consumes more than 4,000,000
gallons in making white salt. This enormous consumption
has produced very startling results which I shall refer to
later on. The brine is pumped up by means of powerful
steam engines into reservoirs or tanks, and from these it is
distributed to the pans through pipes.

The specific gravity of fully saturated brine is about 1*2,
and it contains 26 per cent of salt. Roughly speaking, the
Cheshire brines consist of 1 part salt, 3 parts water. The
business of the salt manufacturer is to drive away the water
and to retain the salt. This is done by heat, and the rationale
of the process of making salt is extremely simple. When

brine is fully saturated there is a state of equilibrium as it
were. If we reduce the quantity of water this balance is
disturbed and a portion of the salt crystallizes out, until
the brine is again at saturation point. If we continue
driving off the water the salt continues to crystallize and
deposit. This process might go on till all the water was
expelled and all the salt crystallized ; but in the process of
manufacture this never occurs, as the pan is replenished with
brine from time to time.

During the manufacture of salt the laws regulating the
formation of salt crystals may be clearly seen. The kinds
of salt manufactured do not vary at all in their constituent
parts, but merely in the size of the crystal or “ grain,” as it
is called. To sum up the whole process in a few words, we
may say generally that the larger the crystal the less the
heat and the longer the time required to make the salt ;
the smaller the crystal, the greater the heat, and the less
time required to make the salt. Brine boils at 226° Fahren-
heit. Boiled salts are taken out of the pan two or three
times in twenty-four hours. Common salt, such as used
for soaperies, chemical works, &c., every two days. Fishery
salt remains in the pan, according to the grain, from six to
fourteen days; Bay salt, three weeks to a month. The manu-
facturer, by manipulating his brine, can make the crystal more
or less flakey, or more or less solid as he wishes, but the general
principle is not altered. Foreign ingredients, such as gela-
tinous matter, or alum, have very peculiar effects on the brine
and on the salt crystal. Bay salt is made at a temperature
of about 90° ; Fishery, from 90° to 140° according to grain.
Common salt, 170° to 180°. There is no exactitude main-
tained on this point, nor is it material, as a slight variation
in the grain makes no difference in the sale and use of the
salt.

The manufacture of salt is extremely simple, almost
rude; yet the simple plan in use for ages has been found

21

to answer best in the long run. The price of salt is so
low, and the manufacture such a bulky one, that costly and
elaborate apparatus has never been found to answer. Com-
paring the life of an ordinary open salt pan, such as is used
in the trade almost universally, with that of any of the
numberless patented pans that have been tried, it has been
found that it costs less to manufacture salt by it, and that
the pan is far easier to repair.

The pans used in the manufacture of salt are made of
wrought iron, and riveted together like boilers. Under
each pan are three or four fires, extending about five feet
from the front of the pan. The pans are set upon brickwork,
and the flues are continued under the whole length of the
pan and thence lead to the chimney. Occasionally there is
a chimney to each pan, but more often one chimney answers
for several pans, as many as 16 fires often being connected
with one chimney. The pans used for boiling the fine salts
rarely exceed 33 to 35 feet in length, or the brine could not
be kept boiling all over the pan. The surplus heat which
in the coarse salt pans would be utilised to make salt for
another 30 or 40 feet is passed under what is called the hot-
house, where the boiled salt which is made into lumps or
loaves is dried. Over this stove is a loft or storing room
where the lump salt is kept dry and warm. The quantity
of fuel consumed in making salt is very large. For making
a ton of common coarse salt about 10 cwt. of slack or other
cheap fuel is used. For making a ton of boiled salt about
13 cwt. of ‘ burgey ’ or ‘ through ? coal is used. It is found
that ordinary slack will not get up and maintain heat enough
to keep the pans boiling.

The number of pans now in existence in the various salt
districts is as follows

Winsford 638

Northwich 458 (At Droitwich 151

Middlewich 13 pans).

Sandbach 69

1178

22

The quantity of white salt manufactured annually in each
district is in round numbers : — -

Winsford 1,000,000 tons.

Northwich 600,000 ,,

Middlewich 20,000 „

Sandbach 100,000 „

1,720,000 „

The first pans used in the manufacture of salt of which
we have any record were made of lead, A sheet of lead
about J inch thick and 2 feet 8 inches square, in the case
of a pan in my possession, was obtained and bent up at the
sides, and the corners hammered together. This pan was
from 3 to 4 inches deep.* Six of these pans were usually
set over flues in a small room. The contents of these six
pans or “leads,” as they were called, formed the unit of
measurement in the salt trade when every maker was regu-
lated by laws as to quantity of brine, time of taking it,
hours of drawing salt, &c. So strict were the laws that an
officer called a “Pan cutter” was employed to see that all
the pans conformed to the standard pan. If any were larger
he was to cut them down. After a time four pans took the
place of the six, and were of equal capacity in the whole.
Dr. Jackson, about 1668, describes these four pans as made
of iron and superseding the six leaden ones. Their size, he
says, was about a yard square and about 6 inches deep, and
they held 28 gallons. In Dr. Brownrigg’s time, 1765, the
pans held 800 gallons, and Jars says the largest pans at
Northwich, in 1765, were 20 feet long by 9 or 10 wide,
holding about 1,100 gallons. Now the small pans used for
boiled salt, which are the smallest in the trade, are from
25 to 35 feet long by from 20 to 24 wide, and 15 to 18
inches deep, averaging 5,000 gallons to the pan. The pans
used for making coarse-grained salt vary from 50 to 70 feet
in length — some few being even longer than this— and about

* There is an old lead in Warrington Museum, found at Northwich.
It measures 3 feet 8 inches on greatest length, and 2 feet 8 inches in
width, being 4 inches deep. It would hold about 20 gallons at most^
The old pan in my possession, which is 25 inches square by 3 inches
deep, would only contain about 7 gallons.

23

25 feet in width, the depth being 18 inches. These would
contain over 16,000 gallons. The growth in the size of the
pan has been equalled by the growth in the manufacture of
salt, and most probably the increasing demand stimulated
the maker to increase the size of the pan.

We have no statistics showing the quantity of salt made
in early times. J udging, however, from the size of the pans
or leads, there could not be much manufactured. The pos-
session of a house containing six leads was of quite sufficient
importance to be mentioned in Domesday Book as belonging
to certain towns or villages. Many of the salt houses in
the “Wyches” belonged to noblemen, and appear to have
been used to make salt for their houses, for we read, “ There
is in Wych half a salt house to supply the Hall.” In 1605
we read in an old letter, “ There is in the said Towne
(North wich) one hundred and thirteen salt houses every
one containing four leads apeece . . . and one Four leads
which was given to the Earl of Derby ... for the portion
of his house.”

From an estimate made about 1675, by William Lord
Brereton, it would seem that about 305 tons 7 cwt. of salt
were made at North wich weekly; 107 tons 10 cwt. at
Middle wich ; and 105 tons at Nantwich. Thus, the total
Cheshire make would be about 26,927 tons per annum. The
whole of this was for the home trade. In 1732 only 5,202
tons of manufactured salt were shipped down the river
Weaver, made navigable in 1721. None of this came from
Middlewich and Nantwich, but from Winsford and North-
wich. In 1801 this had reached 142,675 tons per annum.
In 1820 we find 186,666 tons sent down the Weaver.
In 1825 the salt duty was taken off, and in 1830 the quan-
tity sent down the Weaver reached 312,012 tons in the
year, and in 1840 414,156 tons. In 1844 English salt was
allowed to be sent to the East Indies, and the result is seen
by the exports down the Weaver reaching 607,395 tons in
1850. During the next ten years the increase was not
large, but as soon as the alkali trade began to extend the
manufacture of salt increased, and in 1870 we find 991,158
tons sent down the Weaver, which reached 1,087,214 in

24

1880. It will be seen from these figures how rapidly the
salt trade has increased in the last half century. As the
Weaver is only one line of communication (though the
chief one) by which Cheshire salt leaves the county, there
being canals and railways taking large quantities, the figures
above given do not show all the trade. The following table
of salt exported from the Mersey ports — viz., Liverpool,
Euncorn, and Weston Point, which I have compiled from
the official statistics, supplied to me for the ten years ending

December 31st, 1880, will show the countries taking Cheshire
salt, and the quantities supplied to each

White Salt. Rock Salt.

Countries. Tons. Tons.

United States (North and South) 2,118,656!... 18,827

British North America 691,186!... 31,354|

West Indies and Central America 40,003!... 757!

South America 34,640 . . . 2,258f

Africa 246,429 ... 746f

East Indies < 2,552,856!.., 155

Australia and New Zealand 139,510!... 26,943

Germany 345,229 ... 1,026

Bussia 581,501f... 23,697

Norway, Sweden, Denmark, and Iceland... 197,299!... 39,636

Belgium and Holland 81,633 ... 644,471

France and South of Europe 17,699 ... 943!

England 840,285 ... 135,371

Ireland 469,310 ... 64,155

Scotland 711,229!... 19,631

Total 9,067,468 ...1,009,9734

This table is a very interesting one, but I must not dis-
cuss it, as it affords material enough for a paper in itself.
Besides the salt thus exported, we must reckon at least
500,000 tons of white salt and 30,000 tons of rock salt sent
into the interior by canal and railway yearly. During the
last three years the make of white salt, in Cheshire, cannot
have been much short of If millions of tons per annum.

It may be interesting here to speak of the price at which
salt sells at the works. In using the expression “ at the
works” it must not be understood that salt is sold delivered
at the works. The usual rule is to sell delivered at the
port of shipment, or if in the country at the place where
required ; but to avoid all complications arising out of
varying rates of carriage and freight, it is customary to sell
at a ‘ works 5 price and add on the freight or carriage. The
salt that generally regulates prices is common salt, which is

25

the cheapest and most largely used of any. Taking the
price of common salt as a standard, the other salts as a rule
vary according to the following table. When prices rule
high the difference increases, and when they rule low it is
rather less, but on the average the prices here given may be
considered the usual ones.

With common as the standard: s. d.

Butter, or unstoved boiled salt, is 1 6 per ton more.

Shoots, or broken stoved boiled salt... 3 0 „ „

Handed squares stoved salt 5s. to 6 0 „ ,,

Fishery or coarse salt (according to

quality) Is. 6d. to 5 0 „ „

Bay salt and refined table salt being made only in very
small quantities fetch prices not regulated by any other
qualities, varying from 80s. to 50s. per ton.

The following table will show the fluctuations in common
salt or the standard salt, for ten years

Average price.

Per ton.
s. d.

Highest,
s. d.

Lowest,
s. d.

1871 .....

.... 6

1 ....

..... 7

0

6

0

1872

.... 12

4 ....

..... 20

0

7

0

1873

.... 14

8 ....

..... 15

0 ....

12

0

1874

.... 10

0 ....

12

0 ....

8

0

1875

.... 8

6 ....

9

0 ....

6

6

1876

.... 6

5 ....

. ... 8

0 ....

5

0

1877

.... 5

6 ....

7

0 ....

..... 4

6

1878

.... 6

6 ....

7

0 ....

5

0

1879

.... 5

6 ....

7

0 ....

4

6

1880

.... 5

6 ....

6

6

4

6

During 1881 the price has been, on the average, only
4s. 9d. ; and stoved salts for India have ruled lower than at
any former period.

It would be interesting to point out the various kinds of
salt made, the purposes for which made, and the countries
to which sent— also to show the bearing of the salt trade
upon the general trade of the country, and more especially
upon the shipping trade of Liverpool. This, however, must
be left for another paper, if thought desirable.

The most remarkable feature in connection with the
manufacture of salt is the extensive subsidence of land, and
the great destruction of property caused by it. In mining
the rock salt in the usual way, that is by blasting and pick-
ing, an ordinary mine is formed subject to the usual mining

20

accidents of water breaking in, or the roof falling. There is
no bad gas to cause explosions. It is not accidents of this
kind that are referred to in speaking of land subsidence in
the salt districts. The whole of the manufactured salt is
literally mined by water. A constant stream of water
running over the rock salt to the pumping stations becomes
saturated with the salt that it takes up on its way. Being
pumped up, the salt is gained by the method of evaporation
before described. It is evident that in gaining the salt in
this manner, by water, no provision can be made for the
support of the roof of overlying earths, as is done by pillars
in the ordinary mine. The brine streams, or brine ‘ runs ’
as they are called, resemble brooks and rivulets into which
the waters run from all sides and drain the surface. The
course of these underground streams is marked by a corre-
sponding depression on the surface of the ground. The land
sinks more rapidly directly over the brine runs than else-
where, though there is a gradual lowering of the surface of
the rock salt generally, even out of the line of the runs—
exactly as there is a gradual lowering of the surface of the
land by the solid earths and sands carried away by the
water draining off it. The salt, however, being so much
more soluble than earths, the process is much more rapid.
In some cases the overlying earths follow the gradually wast-
ing rock salt continuously, and the subsidence on the surface
is regular and continuous; in other cases where there happens
to be a tenacious “ flag” or other stiff and solid earths, the
superincumbent mass remains suspended over the brine run
for a long time. As soon, however, as the weight of the sus-
pended mass overcomes the tenacity of the marl or flag, a
sudden sinking of the whole overlying earths takes place,
and a large hole reaching up to the surface is formed, which
in time becomes filled with water.

In recent years a number of these holes have been formed
in the neighbourhood of Winsford and North wich. In the
neighbourhood of North wich they have been formed chiefly
over old mines. Instead of the hollow being made naturally,
as near Winsford, by the ordinary brine run, it has been made
artificially by the miner. In both cases, however, the sudden

27

sinkings are directly caused by the pumping of the brine.
Whenever any sinking, whether gradual or sudden, occurs in
the neighbourhood of a brook or river, and the majority occur
in such positions, the water soon fills the hollow thus formed
and tiny lakes commence which go on increasing. The
local name for these lakes is “Flashes.” At Northwich the
“Top of the Brook,” as it is called, now covers about 100
acres. At Winsford the Top and Bottom flashes cover about
the same area, whilst both at Winsford and Northwich new
lakes are rapidly forming. Near Winsford one called the
Ocean covers about eight acres. At Marston, near North-
wich, there is one covering ten acres when the water is at its
greatest height. On Dunkirk, near to Northwich, the scene
of the great subsidence of December 6th, 1880, the hole then
formed is rapidly extending, following the course of the
Peover Brook. About two miles from Northwich, at Bil-
linge Green, away from any salt works, a subsidence has
begun and is rapidly extending, a kke having commenced
which is only about an acre in extent, though more than
100 acres show signs of subsidence. In the Winsford and
Northwich districts more than 1,000 acres in each show dis-
tinct traces of subsidence, and in both cases the towns and
buildings suffer to a most serious extent. How seriously
owners of property suffer will be seen from the statistics
given here, which I have taken from the evidence given
before a Committee of the House of Commons in May last ;

Approximate number of persons as owners injuriously

affected 418

Public Buildings damaged 11

Salt Works damaged 22

Slaughter-houses, Stables, and Out-buildings damaged 40

Warehouses, Workshops, &c., damaged 46

Public Houses damaged 56

Shops damaged 202

Houses and Cottages damaged 931

Total Buildings affected 1 308

Area of land affected (acres) 2808

The value of the property affected (exclusive of railways
and canals, which suffer seriously) in its damaged state is
estimated at £480,000. The amount of depreciation in
value is estimated at £168,500. To keep this property in

28

a good state of repair would require on the average £18,000
per annum. In this estimate, besides omitting railways and
canals, no account has been taken of the expenditure of the
Local Boards and Highway Boards in maintaining their
roads and sewers— nor yet of the county authorities in the
repair of bridges, nor of the gas and water companies in
repairs of pipes and loss of gas and water. For all this
destruction of property there is no legal remedy, and no
compensation whatever is paid.

The owners whose property suffered so severely applied
to Parliament to obtain a Bill called “ The Cheshire Salt
Districts Compensation Bill/’ The object of this Bill was to
obtain compensation from the salt manufacturers for the
damage caused by the abstraction of the salt in the form of
brine. There was no attempt made to obtain payment for
the salt taken, but merely for the damage done to the pro-
perty overlying the salt. The Bill was not obtained owing
to many serious difficulties that would arise in carrying it
out, but chiefly owing to a very ingenious line of defence
set up by Mr. De Ranee, a geologist connected with the
Ordnance Survey Department. He contended that the
enormous subsidences at Winsford were produced naturally
by the same causes that produced the Cheshire meres, and
that the Northwich subsidences were caused by bad mining.
In my opinion— based upon a far more extensive examina-
tion of these sinkings than that made by Mr. De Ranee, and
formed on the spot with the sinkings proceeding daily
before me for a number of years— Mr. De Ranee’s theories
are wholly untenable. To attribute to ordinary geological
causes, which in almost every case work slowly and con-
tinuously, the enormous subsidences of the last 50 years,
and more especially those of the last 10 years, and which
have gone on increasing in the direct ratio of the increase
in the manufacture of salt, when there is an artificial cause
at work patent to every one, tends to injure science in the
eyes of those who know the whole history of these sinkings.
The manufacture of salt in Cheshire is interesting archseo-
logically, historically, commercially, and geologically, and it
is impossible to do full justice to it in one short paper.

29

Ordinary Meeting, November 15th, 1881.

E. W. Binney, F.R.S., F.G.S., &c., President, in the Chair.

“ On the Pronunciation of Deaf-Mutes who have been
Taught to Articulate,” by William E. A .Axon, M.R.S.L.

At the meeting of the French Academy of Sciences on
the 7th, M. Felix Hdment stated that his observations had
led him to the conclusion that the deaf and dumb who have
been taught to speak, do so with the accent of the district
in which they were born, rather than with that of their
teachers or associates. This was discredited by M. Blanch-
ard, but some curious facts tending in the same direction
have already been recorded. In the “ Philosophical Tran-
sactions” (No. 312), there is the following case. About the
age of seventeen, a young man, a congenital deaf-mute, was
twice attacked by fever. “ Some weeks after recovery, he
perceived a motion of some kind in his brain, which was
very uneasy to him, and afterwards he began to hear, and,
in process of time, to understand speech. This naturally
disposed him to imitate what he heard, and to attempt to
speak. The servants were much annoyed to hear him. He
was not distinctly understood, however, for some weeks ;
but is now understood tolerably well. But what is singular,
is, that he retains the Highland accent, just as Highlanders
do who are advanced to his age before they begin to learn
the English tongue. He cannot speak any Erse or Irish,
for it was in the Lowlands he first heard and spoke.” The
curious circumstance of his possession of the Highland ac-
cent is confirmed by the testimony of similar phenomena in
Spain. “ One fact,” says Ticknor, “ I witnessed, and knew
therefore personally, which is extremely curious. Not one

Proceedings— Lit. & Phil. Soc.— Yol. XXI.— No. 3.— Session 1881-2.

30

of the pupils, of course, can ever have heard a human sound,
and all their knowledge and practice in speaking must come
from their imitation of the visible mechanical movement of
the lips, and other organs of enunciation by their teachers,
who are all Castilians, yet each speaks clearly and decidedly,
and with the accent of the province from which he comes,
so that I could instantly distinguish the Catalonians and
Biscayans and Castilians, whilst others more practised in
Spanish felt the Malagan and Andalusian tones.” — (“Life
and Journals of George Ticknor.” London, 1876, Yol. I.,
p. 196). A similar case has been mentioned to me by Mr.
J. J. Alley of Manchester. E. R became deaf and dumb at
a very early age, and did not talk until he was about seven-
teen, when he was taught articulation by Mr. Alley. He
speaks with the accent of his native county of Stafford.
These instances are cited in my paper on the Education
of the Deaf and Dumb, in the Companion to the Almanac
for 1880.

“On Professor C. A. Bjerkness’s Experiments to Demon-
strate the Analogies between Electrical and Magnetical
Phenomena and some Hydrodynamical Phenomena,” by
William H. Johnson, B.Sc.

Among the many interesting exhibits at the Paris
Electrical Exhibition, there is nothing more likely to
engage the attention of the scientific observer than the
simple apparatus and experiments of Professor Bjerkness, of
the University of Christiania.

The apparatus consists in the main of metal spheres about
one inch in diameter, and drums also an inch in diameter
with indiarubber ends. These spheres and drums communi-
cate by means of indiarubber tubes with a pair of air-pumps,
which, by an ingenious contrivance, cause the spheres to
oscillate and the drums to pulsate isochronously. If the two
air-pump pistons go in and out at the same time, the spheres

31

connected with them will oscillate concordantly. If on the
other hand one piston goes in while the other comes out,
the respective spheres connected with the air-pumps will
oscillate in opposed phase. The same will take place with
the pulsating drums.

When these spheres and drums are allowed to oscillate
and pulsate rapidly in a vessel of water, they are found to
attract each other if they vibrate in accord, and to repel each
other if the vibrations are opposed. Nor is this all, for
Professor Bjerkness, by carefully modifying his apparatus,
which has been very imperfectly described above, has been
able to imitate all the phenomena of magnetism and para-
magnetism, but always in an inverse way.

Many phenomena of statical and dynamical electricity can
also be imitated by these vibrating bodies, but likewise in
an inverse manner.

The whole subject has been investigated mathematically
by the Professor, and the Jaws which govern the attractions
and repulsions of these vibrating bodies have been shown to
be in accordance with his formulae.

General Meeting, November 29th, 1881.

R. Angus Smith, Ph.D., F.R.S., &c., in the Chair.

Mr. Richard Peacock, of Gorton Hall, Manchester, and
Mr. Edmund Salis Schwabe, of 41, George Street, Manches-
ter, were elected Ordinary Members of the Society.

32

Ordinary Meeting November 29th, 1881.

E. Angus Smith, Ph.D., F.E.S., &c., in the Chair.

The following letter from Mr. Joseph Sidebotham,
F.E.A.S., was read:

“ Some few years ago when I was at Mentone, I wrote to
yon concerning the aniline colours, so much used on the
Continent in water colour drawings. Since that time
Holman Hunt and others have called attention to the fading
of these and some other colours prepared for artists, and I
hoped the practice of making and using these colours had
ceased ; however, I find this is not the case. A friend of mine
was on his way to the South of France, and I asked him to see
if these colours were still sold and used, and he tells me they
are extensively, and sent me cakes of them ; he also sent
the enclosed sheet of the colours on drawing paper, half of
it having been exposed to the light, a fortnight, the other
half covered up. He thought that by putting gum over the
colours they might be made more permanent, and you will
see he has put a band of gum across them; the colours ex-
posed have faded in a great degree, some of them almost
disappearing. The band of gum has retarded the fading, but
the colours are even there much lighter and all the bright-
ness gone. It is most desirable that artists should entirely
give up the use of all these colours, and then the makers
would cease to supply them. When we see the sad effects
of a fortnight’s light upon them, what can we expect to see
in drawings hung on the walls of a room for a few years ? ”

“ On Cyclic Motions in a Fluid, and the Motion of a Vortex
Eing of varying Curvature,” by E. F. Gwyther, M.A.

The possible kinds of fluid motion are divided into irro»
tational, which is either cyclic or acylic, and rotational or

33

vortex motion. In treating of the motion of a perfect fluid
it is usual to consider the cases of acyclic irrotational mo-
tion and of vortex motion, considering cyclic irrotational
motion as an adjunct of the second. This appears to me to
be an improper division of the subject, which should rather
be treated in the inverse manner, since the result is that
the phenomena which are actually due to the cyclic nature
of the motion are sometimes attributed to the vortex motion.

In cyclic motion the circulation in any circuit is either
zero or constant according to the nature of the space which
the circuit encloses. If the circulation in a circuit is not
zero, the circuit either encloses a portion of space not
occupied by the fluid, or a portion of fluid, either termina-
ting afc a boundary of the fluid or bounded by a closed sur-
face, for which no velocity potential exists. Let u, v, w
denote the components of the velocity at any point in
the fluid, and f ds denote integration completely round
a closed circuit. Let J dS denote integration over any

portion of surface bounded by the circuit, of which a portion
may consist of the bounding surface of the fluid, and
let l , m, n be the direction cosines of any portion dS of
this shell. Then by a Theorem due to Stokes, the circula-
tion in the circuit may be written

/(“£ + vt + wt)ds -/(«+*»+

whence if the surface S can be drawn without passing out of
the space occupied by the fluid, and if the integral does not
vanish, £, ij, £ must have values different from zero at some
portions of the suface S. Also the integral has the same
value for all surfaces S drawn; therefore the strength of
the vortices on a]] surfaces bounded by the circuit is the
same, and if the vortex lines are capable of being cut at
right angles by a surface, is equal to the total strength of
the vortices.

If the space be polycyclic the circuit can be replaced by

34

a number of monocyclic circuits for each of which the

circulation in the circuit, or the cyclic constant, is equal to
the strength of the enclosed vortex tube upon any surface
drawn bounded by the circuit. We have therefore shown
that cyclic motion requires the space in which it exists to
be made multiply continuous either by solid boundaries or
by vortex filaments.

Cyclic motion is therefore a condition of space, and vortex
motion is a result of it. Cyclic motion can be produced by
suitable impulses applied as shown by Thomson (Yortex
Motion, Trans. Edin., R.S.), and vortex motion in a perfect
fluid can only appear as a consequence, either of cyclic or
discontinuous motions.

Since the cyclic constant can not be a function of the
time, we also infer

But from this we may not conclude that the vortex motion
is steady in the sense that it is always the same at the same
point in space. For if the circuit retained a fixed position
in space, the portion of fluid moving rotationally might
move out of it. The true conclusion is that while the core
of vortex motion remains within any circuit the strength of
the core on any shell experiences no variation with the
time, and as the circuit may at any time be replaced by a
reconcileable circuit, this theorem may be extended to all

that a circuit which embraces a core of vortex motion
moves so as to continue to embrace the same core the same
number of times. As each circuit may be diminished by
the substitution of reconcileable paths, we may apply this
to the simplest circuits embracing a core. We thus arrive
at the known properties of vortex motion accompanying
cyclic motion.

space.

Again, since

D,/(

= 0, we may conclude

85

The observed phenomena of rings, whether these be
vortex rings or material rings which make space multiply
continuous, are the effect of the cyclic motion. It is an
object of this paper to notice the motion of the ring itself
as the consequence of the cyclic motion.

The energy of a cyclic motion may be written (Lamb’s
Hydrodynamics, Art. 136)

T = 2 J J f { u{y£ - zrj) + v{zl - x£) + w(xrf- yl) j dx dy dz

and evidently depends on the size and shape of the necessary
vortex filament. To find in what way a portion contributes
to this energy by its motion, take the origin on a vortex
line, the tangent line as axis of 0, the principal normal as
axis of x, and the binormal as that of y, and consider the
part of the integral between s= —l and s=l. When we put
s3 s2 s3

x = Xl + —y = y1 + - e = s__

Xi and yi denoting the coordinates of a point in the section
of the filament in the plane of xy,
we obtain

i

Zdsda

= 4U£ J y\Cda — 4V<? J x^da

■/<*■

2U„

+V

when U and V are the mean resolved velocities of the ele-
ment.

If the core be of symmetrical section, the first two of
these integrals will vanish, and the term contributed to the
energy will contain only the velocity along the principal
normal.

The total energy will depend upon the size and shape, as
said before ; but we can conclude that if the filament be
of symmetrical section, the motion of each portion will be
along its principal normal. In the case of a straight fila-

36

ment this term would vanish, and in the case of a circle
would he the same at all points — thus agreeing with the
two cases which have been worked out.

MICROSCOPICAL AND NATURAL HISTORY SECTION.

October 10th, 1881.

Alfred Brothers, F.R.A.S., President of the Section, in
the Chair.

The President alluded to the death, in April, of Arthur
George Latham, Esq., and a vote of condolence with Mrs.
Latham was unanimously passed.

Mr. Marcus M. Hartog, B.Sc., F.L.S., made some remarks
upon damaged Indian rubber, and pointed out the ad visa-
ability of treating it with a solution of magenta. This
stains it most strongly where most damage has occurred.

Mr. J. Boyd reported upon some parasites affecting the
partridge, and the eggs were found amongst the feathers
below the beak, just where the bird was unable to touch
them. These eggs he afterwards exhibited under the micro-
scope, and also a living specimen of the parasite, which was
a species of Acarus.

Mr. Boyd also mentioned the capture by him of the 6 of
leptodora hyalina, near Keswick, distinguished by the great
length of its antennse from the 9 at a glance.

A discussion on the proportionate rarity of the 6 in the
entomostraca and copepoda then ensued.

37

November 7th, 1881.

Alfred Brothers, F.RA.S., President of the Section,
in the Chair.

A letter was read by the Secretary from Mr. Arthur
Latham, in acknowledgement of the resolution of condolence
on the death of his father, passed at the last meeting.

The following resolution passed at the council meeting of
the Parent Society on 19th April was read :

“ On the motion of Mr. R. D. Darbishire, seconded by Dr.
Joule, it was resolved that the Associates of each Section be
empowered to vote in the election of officers of the Section
with the members, and that Associates may be eligible for
the offices of the section.”

The Secretary read a communication from Mr. Side-
botham, F.L.S., relative to a supposed marine species of
alga (? fucus canaliculatus or ceranoides) which was growing
on the window of his house at Bowdon. It was about half
an inch in diameter, but was still increasing in size. It
might have originated from a spore blown by a west wind,
and nurtured by the saline breezes that blow across from
the Irish Channel through Runcorn Gap.

Mr. Hartog, B.Sc., F.L.S., made some remarks on the
result of his further investigation of the mode in which
hydra viridis swallows its food. He had found that the
endoderm cells of the tentacles possess a power of amoeboid
motion by means of which they draw themselves over the
object to be swallowed.

38

Mr. R D. Darbishire, F.G.S., exhibited Tryon’s mollusca
and the atlas of plates to Prof Hseckel’s “ Die Radiolarien,”

Mr. Wills (who was present as a visitor) exhibited an
interesting series of preparations of desmidiae, and stated
that when in Wales last year his father took a large gather-
ing of desmidiae from the stream as it flows out of the lower
of the two Capel Curig lakes. They were embedded in
mosses of the well known infusorian Ophrydium ver-
satile and also in the accompanying weeds, and it is about
some of the rarest found in this gathering that he remarked.
But first he called attention to the fact that they were found
in flowing water, not a usual situation ; on this point Ralfs
says “ They are rarely gathered in streams, being unattached,
and very minute, nevertheless, interesting species may'
occasionally be gathered where the current is so sluggish as
to permit their retaining mucus to elude its force. The
current in the case of these desmidiae certainly was the
reverse of sluggish.

In the slides shown, he pointed out many common
species, but also several rare ones, some new to England,
others new to the British Isles, and three new to science, one
of which his father had successfully demonstrated to have
been recorded for the first time last summer.

Those new to England but recorded before as Irish, Scotch,
or foreign species are :

Spondglosium pulehellum (Archer)

Tetrachastrum mucronatum (Dixon)

Cosmarium cyclicium (Lundell)

„ holmiense „

„ nymamanum (Grunow)

„ pseudo connatum (Nordstedt)

„ pseudo pyramidatum (Lundell)

„ truncatellum (Perty)

„ variolatum (Bulu)

„ globosum (Lundell)

39

Staurastrum Arctiscon (Lundell)

„ Aversum „

„ Cerastes „

„ Cristatum (Nagele) Farsets

„ longispinum (Bailey)

„ saxonicum (Reinsch)

„ paradoxum

variety longipes (Nordstedt)
„ pruigstemin (Reinsch)

Closterium cynthia (de Notaris)

„ gracile (Bretisson)

Penium nageli „

Those new to the British Isles are :
Cosmarium Holmiense variety (Lundell)

„ laeve (Nordstedt and Wittrocli)

„ nitidulum (de Fotaris)

„ pseudo nitidulum (Nordstedt)

„ praemorsum (Bretisson)
Staurastrum Brasiliense (Lundell)

„ grande „

„ inflexum (Bretisson)

„ megacan thum (Lundell)

„ pseudo porciferum (Reinsch)

„ sebalde (Reinsch)

Docidium nodosum (Bailey)

And those new to science are :

Cosmarium cambricum
Staurastrum anatinum
Cosmarium coronatum

On referring to a paper his father had written on this sub-
ject he found that no less than 150 distinct species of Des-
midiae were found at Capel Curig that summer.

The Staurastra and Cosmaria are both extremely diffi-
cult to identify, and the species ill defined, and it is often
almost impossible to name them unless you get several
aspects of the same object.

40

The way he found answered best in mounting these lovely
little plants is, after he had washed and prepared them
in the cell, to put them with a little 'plain water,
place a glass cover over them, carefully avoiding the
enclosure of any air bubbles, and having taken up any
moisture about the edge of the cell with blotting paper, to
seal them up with gold size. In some cases the colour goes,
but in others the bright green colour is retained for many
years.

In conclusion, he said there was a want among investi-
gators in this branch of microscopic work of a uniform scale
to which to make their drawings. Each man has his own
scale, and this makes the comparing of drawings, very much
more difficult than if a uniform scale, say 400 diameters were
adopted, by means of which one man might at once and
without the slightest difficulty compare his drawings with
those of other fellow- workers.

PHYSICAL AND MATHEMATICAL SECTION.
November 8th, 1881.

Joseph Baxendell, F.RA.S., President of the Section, in

the Chair.

“ Note on a Passage of Pollux relating to the formation
of Purple Dye,” by James Bottomley, D.Sc., F.C.S.

At a meeting of the Society on November 18th, 1879, I
gave a short passage from Musgrave containing a quotation
from Pollux. From this passage it was inferred that the

41

ancients were in the habit of exposing purple garments to
the sun to revive the colour. Since then I have referred
to a copy of Pollux. The passage in question does not refer
to the revival of the colour as Musgrave seems to think ; it
evidently refers to the initial action of light in generating
the colour. Moreover, in quoting the sentence, he has left
out at the end a few important words (kipoivunrojuivTiv Ik
tov avio nvpog).

The Onomasticon of Pollux is for the mosifpart a dry and
uninteresting work. As it is not likely to be very accesible
I have given the passage treating of the generation of the
colour.

JE vifjiovaiv Ifxirvpip \ef3rjn to ^rr/pa/ua to SaXamov, to $t
aljua breidav Trvpl o/JuXrtaq, y/iTai re kcu l£,av%ei kcu to ptv
%av%iZtTcu, to St Kvavavylg ytyveTCU , ro St aXXo dg aXXriv
Xpoav TpirreTai, kcu o-rc av KaSyg, irav to ^vyyevofxevov Tip
ai/LiaTi 3 tt pog Trjv avrov ypocciv fUTaxp(vvvvrai' ycuptc ^
bfJLiXovoa Trig iropijivpag r) (3a<J )ij kcu r\ aKTig avrrjv avcnrvpatvu
kcu 7r Xtuo 7 rout kcu (pcuSpOTepav rrjv avyrjv tK (poivicruo/xiviriv Ik
tov aviv Trvpog.

The Latin translator renders the passage as follows :

In fervente lebete animal marinum excoquunt, ceterum
sanguis hie, ignis viribus conceptis, diffunditur et efflorescit,
et hsec quidem ejus pars, flavum, ilia nigrum, alia vero
alium colorem induit ; et quicquid immisseris, id sanguine
commixtum, ejus colorem qualiscunque ille sit imbibit.
Tinctura vero purpura? solem amat, etenim hujus illustrata
radiis majorem lsetioremque splendorem purpureo colore
coruscantem e supero igne concipit.

Liddell and Scott give as the meanings of the word kucc-
vavyrjg dark gleaming, dusky, obscure. These seem hardly
suitable to the passage ; probably dark blue would be nearer
the meaning. The same authors also give as the meaning of
avaTTvpuevijj to make more fiery or glaring, referring to this
passage of Pollux as an example.

42

A nearly literal translation would be : — They digest the
marine animal in a caldron over the fire, and the blood
when it associates with heat liquefies and develops colour,
and part becomes yellow, part dark blue (?), and another part
changes to another colour. And whatsoever you dip in,
everything that has come in contact with the blood is changed
in colour to the colour thereof; but the purple dye rejoices
in association with the sun, and the solar beam gives it fire
and makes more intense and dazzling its splendour, which
is rendered purple by means of the fire aloft.

43

Ordinary Meeting, December 13th, 1881.

J. P. Joule, D.C.L., LL.D., F.RS,, &c., in the Chair.

“Remarks on the Terms used to denote Colour, and on
the Colours of Faded Leaves,” by Edward Schunck, Ph.D.,
F.RS.

At the recent meeting of the British Association held at
York, a paper was read by Dr. Montagu Lubbock before
the section for anatomy and physiology on “ The develop-
ment of the colour sense,” which I had the pleasure to hear.
The purpose of the author was to controvert the opinion of
those who hold that the colour sense in man was not always
what it is now, but that it has gradually been developed,
the last stages of this development having taken place
within historical times. It is supposed that the human eye
was originally only capable of distinguishing black and
white, and that the capacity of seeing the various colours of
the spectrum arose by degrees, red being the first and blue
the last colour to be discriminated. Mr. Gladstone, in a
paper published not long ago, goes so far as to say that the
ancient Greeks, having no word for blue, were blind to that
colour, and that it is only since their day that human vision
has been so far developed as to perceive the more refran-
gible end of the spectrum. The author of the paper referred
to arrived at the conclusion that there is no sufficient evi-
dence to show that the faculty of perceiving colour has been
acquired by man within historical times, a conclusion in
which Sir John Lubbock, who took part in the discussion
on the paper, entirely concurred. Whatever may have
taken place in prehistoric times, there can be little doubi, I
imagine, looking at the remains adorned with various colours
in Egypt and elsewhere, that the more civilised nations of
Proceedings— Lit. &Phil. Soc. — Vol. XXI.— No. 4. — Session 1881-2.

44

antiquity, though they had fewer pigments at their dis-
posal than we have, were quite as capable of distinguishing
colours as we are. It may indeed be asserted that so
far as appropriate arrangement of tints in dress and other
articles of daily use is concerned, no advance has been made
since the time of the ancients, but rather that we have in
this respect retrograded. Evolutionists tell us that we may
obtain a good idea of what our prehistoric ancestors were,
by observing the present state of savage and uncivilised
races, a state from which we have in the course of ages
emerged. So far, however, as the appreciation of colour is
concerned no superiority on our part can be discovered, for
whoever will, with an unprejudiced eye, compare the har-
monious combinations seen in the articles produced by the
less civilised nations of India and China, or by the natives
of America and Polynesia, with the hideous contrasts and
tasteless arrangements so often displayed in our articles of
dress and furniture, will probably incline to the opinion
that in this respect we may rather be called savages, and
that the incapacity for appreciating colour harmony inhe-
rent in the Teutonic branch of the Aryan race has not been
removed, but rather intensified by civilisation. Much has,
indeed, been done of late to promote good taste in this as in
other departments of art, though our progress has probably
been retarded by the introduction of various artificial
colouring matters, the extreme brilliancy of which acts as a
lure to the uncultivated eye.

Though much of the uncertainty which exists as to the
precise meaning of the words used by the ancients to denote
colour is of a philological kind, part of it is due, I think, to
causes which are still in operation.

1. The ancients, having no fixed scale of colour to refer to,
such as we possess in the spectrum, were unable to compare
any given tint with that which it exhibits in its highest
state of purity, whilst we, by means of the fixed standard

at our command, and with the assistance of the so-called
chromatic circles and other appliances, can determine not
only the exact position and shade of any given colour, but also
the extent to which it is degraded or rendered impure, and
though the general public very slowly adopts scientific terms
and methods, still on the whole the tendency in our days is
towards exactitude, and vague terms for objects and sensa-
tions are more and more falling into disuse.

2. In one respect the ancients must have laboured under
the same disadvantage in determining the value of colour,
as we moderns do. We very seldom see one colour
alone, but generally two or more in juxtaposition, and con-
trasted, and by contrast the effect of each colour on the
human eye is considerably modified. Complementary colours,
when seen in close proximity, heighten one another. Green
next to red will appear much brighter than when placed
close to blue. A colour of average purity will appear dull
when compared with a brighter colour of the same hue, while
it will seem, bright when seen alongside a more dingy shade,
and so on. Unless great care be taken, therefore, we are
liable to become inaccurate when describing a colour, though
on the other hand, it may be doubted whether, if the human
eye were so constructed as to see only one of the colours of
the spectrum, we should from the absence of contrast be
able to appreciate that colour correctly.

To the fact that we almost always see colours in contrast
must be ascribed the habit which men have of speaking of
“ beautiful colours.” No one who has thought on the subject
need be told thatasimple sensation cannot be strictly speaking
beautiful. It is only by combination, contrast, and harmony
of sensations that we arrive at beauty. To talk of a beauti-
ful sound, such as a single note of a musical instrument,
would be absurd ; it is only a combination of sounds that
can be called beautiful. The terms “beautiful smell/1
“beautiful taste,” would cause the most ignorant to smile,

4G

though it may be contended that a dish uniting various
flavours, or a perfume composed of well-assorted scents
might be called beautiful. We look at the spectrum thrown
on a screen, arid say it is beautiful, but it is the effect of the
various colours seen in juxtaposition, and the exquisite sha-
ding and melting of one into the other that we admire.
When we speak of- the beautiful colours of sunset, we forget
that a fine sunset is in fact a grand chromatic display. We
see the fiery red of the fleecy clouds and the deep blue of the
sky contrasted with the green of the foliage, and the brown
of the tree stems, followed by a flood of yellow light on a
cool grey ground in the heavens, while the gloom of night
is settling over the earth beneath, and the eye is pleased and
satisfied. Were we to see the sun like a ball of red-hot iron
set through a coppery sky over a sea of blood washing a
coast line of red rocks overgrown with red seaweed, it is
certain we should not speak of the beautiful colours of sun-
set. Let any one, to test what I maintain, look at any colour 3
however brilliant and pure, through a tube blackened inside,
and say whether it appears beautiful. It is the great activity
of the eye, which during our waking hours is constantly
roaming from object to object, seldom seeing the same thing
nor the same colour for more than a few consecutive mo-
ments that deceives us.

3. Much of the confusion as regards the names of colours
arises, as it has doubtless at all times arisen, from the habit,
difficult to explain, of using inexact designations, and even
applying names to colours which we know to be incorrect.
Poets, for instance, call gold red, though it is always yellow.
We speak of white wines and red wines, though in reality,
as we are well aware, they are yellow and purple, so that in
a thousand years hence it may be possible for a iiterary man
to say that we were colour-blind, our eyes having not yet
acquired the capacity to see yellow and blue, yellow appear-
ing to us colourless and purple red, and he may in support

47

of this assertion quote the line of a distinguished poet now
living who speaks of the “ costly scarlet wine/' a term which
is still more precise and emphatic than simple red. In the
course of an investigation, undertaken a short time ago with
another chemist, I found that my collaborateur and myself
never exactly agreed as to the names to be given to the
colours we saw. The series which he named blue, violet,
purple, crimson, red, orange, I called violet, purple, crimson,
red, orange, yellow, i.e., what was to his eye blue was to mine
violet ; his violet was my purple, and so on. There was no
reason to suppose that our perception of colour differed, the
difference was in my opinion simply one of terms.

The writings of ancient authors abound with instances of
the use of colour names which are seemingly incorrect.
We find in Horace (Book IV., Ode 1) the lines :

Tempestivius in domum
Paulli, purpureis ales oloribus
Comiss abere Maximi,

Si torrere jecnr quseris idoneum.

Another author says :

Purpurea sub nive terra latet
Brachia purpurea candidiora nive.

We are told by scholars that in these cases purpuereus
means bright, shining, but it still remains to be explained
why a word, which generally denotes a positive colour,
whatever that colour may have been, comes in a few in-
stances to be applied to white objects such as swans and
snow. Of course the definition of a word may be so extended
as to include any number of widely different meanings
some of these meanings being perhaps due to its mistaken
use by authors. It would probably not be difficult to find
passages in modern authors in which the word blue some-
times means green, sometimes violet. I met with a case in
point recently on reading again Goethe’s delightful auto-
biography “ Wahrheit und Pichtung.” The author, when a

48

young man, was skating on the river on a bitterly cold
winter’s day. “I had been on the ice,” says he, “since
early morning, and was therefore, when my mother later in
the day drove up to admire the scene, being only lightly
clad, almost frozen. She sat in her carriage wrapped in a red
velvet fur mantle, which, held together in front with thick
gold lace and tassels, looked magnificent. e Give me, dear
mother, your fur cloak,’ said I without much consideration,
‘ I am fearfully cold.’ She, too, did not consider long, and
the next moment I had put on the cloak, which reaching
nearly to my feet, being of a purple colour, trimmed with
sable and ornamented with gold, suited very well the brown
fur cap which I wore.” Here it is evident that Goethe calls
the same object first red, then purple, and yet Goethe was
not colour-blind ; he wrote, as every one knows, a work on
the theory of colours.

4. Part of the vagueness and uncertainty attending the
terminology of colour may be ascribed to a tendency we are
all more or less liable to, that of describing colours in figu-
rative and metaphorical terms. The habit, no doubt, arises
from the pleasure we feel in comparing two objects, both of
which are agreeable to the sense of sight. We speak of a
girl having sky-blue eyes and cherry-red lips, whereas slate-
coloured and brick-red would be more correct. How often
we hear the expression, “he turned as white as a sheet,”
whereas the human skin is never under any circumstances,
even after death, as white as a sheet. To say “ he turned
of a dirty yellowish- white,” would be nearer the truth,
though the expression might be thought somewhat in-
elegant. Poets and others speak of golden hair and silvery
locks, but human hair though it may be bright, glistening,
and so on, never reflects light in the manner peculiar to
metals. Numerous examples of the same kind will occur
to everyone. If, therefore, we meet in ancient authors with
expressions relating to colour which seem exaggerated and

49

out of place, we must make some allowance for the tendency
shown by men at all times to compare one beautiful object
with another beautiful object, or one terrific object with
another terrific object, without regard to exact literal truth.
Generally speaking, I think we may safely say that no
terms denoting colour, wherever met with, are to be con-
sidered strictly correct and appropriate unless they are
referred to some fixed and known standard. The errors
due to actual colour blindness need hardly, I think, be taken
into consideration, since the hues which the colour blind
are unable to distinguish lie so far apart as to make it
difficult for any one with normal eyes to conceive the possi-
bility of so great a defect.

The brilliant tints exhibited by the decaying foliage of
the trees in this neighbourhood in the course of the
autumn, forming a chromatic display such as those living
near manufacturing towns have few opportunities of wit-
nessing:’, have led me to think a little on the cause of the
formation of these colours and its possible connection with
chlorophyll, on the chemistry of which I have lately been
making some experiments.

The colour of the leaves of plants is a phenomenon which
is probably never quite stationary at any period of their
development. When lying rolled up in the leaf bud they
are like underground shoots and other parts of plants that
have not been exposed to light, almost white ; nevertheless
they already contain a colouring matter called etiolin, the
alcoholic solution of which is yellow and shows absorption
bands similar to those of chlorophyll. Whether this etiolin
on the leaf unfolding passes over into chlorophyll and
whether it continues to be formed during the further stages
of development is not known. All we know is that when
the leaf expands it immediately becomes green from the
formation of chlorophyll. It is, however, evident that more

50

than one colouring matter is formed after exposure of the
leaves of plants to light. The colour clue to chlorophyll
alone is probably seen in its purest state in the tender
exquisite green of the young beech leaf or blade of corn.
Other leaves, such as those of the oak, before attaining
maturity have a decidedly yellow tinge, due it is supposed
to the presence of an unusual proportion of phylloxanthin,
the yellow colouring matter always accompanying chloro-
phyll. Indeed, the lively contrast of tints seen in the
foliage of the woods in early spring, the yellowish hue of
the oak, and the pure green of the beech and larch relieving
the sombre colour of the fir tree and the yew, affords one
of the most pleasing sights of that delightful season. In
early summer the young shoots of some trees, such as the
oak, the sycamore, and the thorn, as well as the young
leaves near the summit of each shoot, are tinged of a lively
red, passing by degrees into the green of the mature leaves.
The fruit wings of the sycamore are for many weeks in the
summer similarly tinted, and the effect of the pink blush
gradually shading off into the pale green of the wing tips is
one that painters might introduce with advantage into
their pictures of still life. This red colour is said to be due
to erythrophy]l, the colouring matter formed in some leaves
in the autumn, but whether the substance is in both cases
really the same may be doubted. At the height of summer
the foliage of trees displays a uniform green tint of varying
depth, but it is probable that at this season the chlorophyll
has already undergone a change, and I suspect that the
sombre green of some leaves, such as those of the elm, in
summer, is partly due to a product of decomposition called
“modified chlorophyll,” which yields solutions of a much
less lively colour than the chlorophyll from which it is
formed.

The summer stage is succeeded by that of the autumnal
fading of foliage, a change so often observed that it needs

51

no description. With the exaggeration so often employed
when coloured objects are referred to, people frequently speak
of the multitudinous tints of autumn. In reality, however,
these colours, not counting the original green, are only four
in number, viz., yellow, brown, red, and purple, and of these
the last is a dull inconspicuous colour, while the red occurs
so seldom in our native trees as to add but little to the total
effect when our woods and plantations appear in their
autumnal clothing. It is to the passing of the original green
into yellow, and from yellow into brown, and the various
shades and tin tings so produced that the effect is in the
main due. The yellow coloration is most distinctly seen in
the chestnut and the elm. In the latter the gradual tinging
of the deep green with yellow produces a peculiarly beauti-
ful effect, and when the change is complete, and the whole
tree (to use one of those figurative expressions to which one
is so prone) is arrayed in a garb of gold, the appearance
when first seen is almost startling. Arrived at this stage
the leaves mostly fall, but retain their yellow hue for a short
time only, the colour under the influence of air and moisture
rapidly becoming brown, though they remain yellow if
quickly dried. The oak and the beech keep their leaves
after the yellow stage is passed, and the rich reddish-brown
they then exhibit forms a distinct feature in the autumnal
landscape. Young beech trees, as every one knows, remain
clothed with brown leaves during the winter, and only lose
them on the unfolding of the fresh leaves in spring.

The leaves of some of our native plants, such as the wild
cherry, the currant, the bramble, and various species of
sorrel, turn of a lively red in autumn, but this coloration
intensified to a positive scarlet is more distinctly seen in
some of the exotics which have been introduced into our
gardens, such as the Virginia creeper and the Azalea. A
mixture of red and yellow is rarely observed on the same
leaf. It is a singular circumstance that the leaves of the

52

oak and sycamore, the young shoots of which are so often
tinged of a lively red, do not turn red in fading, hut yellow,
from which it may he inferred that the process of decay in
leaves does not lead hack to the same stage at which that
of development commenced.

The autumnal purple coloration of leaves is met with in a
few native plants, notably the bryony, the privet, and the
dogwood. It imparts a dingy hue to the leaves, and is there-
fore not much noticed. I observed a case of its occurrence
last summer, which I had not previously seen mentioned.
Passing through a field of corn, which was then nearly ripe,
I saw a number of plants by the sides of the path with
blades distinctly purple. On closer observation it was
evident that in all cases where this coloration occurred the
ears of corn had been cut off before ripening, the act pro-
bably of idle passers-by, those plants which remained unin-
jured having become yellow as usual. I inferred that it
was the injury sustained by the plant, and the arrest of its
main function, that of the development of seed, that had led
to the formation of some purple substance, not seen during
the process of natural decay. I made some experiments on
this purple colouring matter, but all I can say about it is,
that it belongs to the same class as the red and yellow
colouring matters of faded leaves. I anticipated the possi-
bility of its being identical with a product of the decomposi-
tion of chlorophyll, crystallising in purple needles, which I
had discovered in the course of my investigation, but I was
disappointed in my expectation.

As regards the nature of the colouring matters to which
the various colours of faded leaves are due, opinions vary.
It is generally supposed that they are formed from chloro-
phyll by some process of decomposition, probably of oxi-
dation, and nothing can be more natural than this supposi-
tion. On exposure of the leaf to light and air, after its vital
functions have ceased, the green colour due to chlorophyll

53

gradually disappears and is succeeded by red, yellow, or
purple. Therefore, it is argued, the respective colouring
matters must be derivatives of chlorophyll. Nevertheless,
this view is open to some objection. As regards, in the
first place, the red colouring matter, since no one has suc-
ceeded in obtaining it artificially, it must be formed, if a
derivative of chlorophyll, by some process not purely chemi-
cal. I have, indeed, obtained as one of the products of
decomposition of chlorophyll a substance crystallising in
red laminae, having a semi-metaliic appearance by reflected
light, but this substance is entirely distinct from the red
colouring matter of faded leaves. The latter may easily be
procured, at least in an impure state, by extracting the
reddened leaves of the garden Azalea or the Virginia Creeper
with boiling spirits of wine, evaporating the extract at a
gentle heat, and treating the residue with water, in which
the colouring matter dissolves. The solution has a fine
crimson colour like that of red ink. The colour does not
change on the addition of such acids as exert no oxidising
action. Nitric acid gradually turns it yellow. By the
addition of alkalies, such as ammonia, its colour changes to
a yellowish-green, and it has then very much the appear-
ance of an alcoholic solution of chlorophyll, but it does not
show either before or after the addition of alkali the least
indication of absorption bands, merely a general darkening
of the more refrangible end of the spectrum. With lead
acetate it gives a grass-green precipitate. These reactions
show that the colouring matter belongs to the same class as
that of the rose and red flowers generally; but in the
present state of our knowledge regarding this class of sub-
stances, it is quite impossible to say whether any two mem-
bers belonging to the series are identical or not. One thing,
however, is certain, viz., that the red colouring matter of
faded leaves is actually formed during the process of decay ;
it does not pre-exist in the green leaf, though there can be

5 4

no doubt tliat leaves which are naturally more or less red,
such as those of the copper beech and various species of
colium, contain a ready formed red colouring matter.

As to the yellow colouring matter of faded leaves, whether
it pre-exists in the green leaf or is formed from chlorophyll
or some other leaf constituent, it is not so easy to pronounce
a decided opinion. This colouring matter, called by Berzelius
xccnthophyll , is supposed by some to be identical with
phylloxanthin, the yellow substance which, according to
Fremy and others, always accompanies the chlorophyll of
green leaves. Of its properties little is known, and that
little I find to be more or less incorrect. It is said to be
soluble in alcohol and ether, insoluble in water, to turn
green with acids, and to show a peculiar absorption spectrum
different to that of chlorophyll. These statements require
correction. It is, in fact, soluble in water, but insoluble in
ether; it does not turn green with acids,, and the absorp-
tion bands which it shows are due to an admixture of chlo-
rophyll, as a few simple experiments are sufficient to show.
Having taken some bright yellow elm leaves I extracted
them with boiling spirits of wine, and obtained a greenish-
yellow liquid, winch, after filtration, showed only the
dark absorption band in the red corresponding to band
I. of the chlorophyll spectrum. I evaporated the extract
in the water bath, and during evaporation observed a
deposit form on the sides of the dish consisting of
green fat-like masses. On adding water to the residue a
portion dissolved yielding a golden-yellow liquid, while the
fat-like masses remained undissolved. After pouring off
the liquid and washing the residue with water, the latter
was dissolved in hot alcoho], when it gave a yellowish-green
liquid which showed all the absorbtion bands of chlorophyll
distinctly. The golden-yellow watery solution on the other
hand showed no trace of absorbtion bands, merely a general
darkening of the blue end of the spectrum. Its co]our was

55

evidently due to a yellow colouring matter contained in it.
It gave an abundant yellow precipitate with lead acetate,
and a dark green precipitate with ferric chloride. It also
contained a considerable quantity of tannin, since it yielded
a thick curdy precipitate with gelatine and an abundant
deposit on the addition of a mineral acid. On again evapo-
rating the solution in the water bath some decomposition
evidently took place, for on adding water to the residue a
quantity of matter in the form of brown powder remained
undissolved. It is almost certain that it is the same pro-
cess of decomposition going on in the yellow leaf on exposure
to air and moisture that causes the colour to change to
brown. I think it probable that the process is one of oxi-
dation, and that it affects the tannin of the leaf or the solu-
tion rather than the yellow colouring matter, for it is well
known that watery solutions of tannin undergo decompo-
sition, accompanied by change of colour from light to dark,
on exposure to air, especially when the solutions are hot.
This simple experiment shows that the yellow colour of
faded elm leaves is due partly, perhaps chiefly, to a yellow
colouring matter soluble in water, partly to a yellowish
green substance consisting essentially of chlorophyll. The
former is, in my opinion, the true xanthophyll.

In order to gain, if possible, a little more insight into the
process whereby the colour of green leaves changes to
yellow, I took an alcoholic extract of fresh grass, which
was of the usual bright green colour, and exposed it in a
window to the action of the sun and air. After some days’
exposure it had undergone the well known and frequently
described transformation, i.e. the bright green colour had
changed to a greenish-yellow and the solution from being
opaque even in thin layers had become transparent in con-
sequence of the oxidation of the chlorophyll contained in it.
Now this liquid, though not quite so yellow as the alcoholic
extract of faded elm leaves, was found closely to resemble

56

the latter. On evaporating over the water bath and ad-
ding water to the residue a yellow liquid was obtained,
containing a colouring matter, the reactions of which were
similar to those of the substance from elm leaves. No tannin,
however, could be detected in the solution and this may
serve to explain the fact that blades of grass, corn, &c., do
not ultimately become brown in fading, but remain yellow.
The portion of the residue after evaporation left undissolved
by water, was green and fatty, and its solution in alcohol
showed the absorption bands due to modified chlorophyll.

These experiments leave the question of the nature and
mode of formation of xanthophyll undecided. It may be
one and the same substance in all leaves, or it may differ
according to the source whence it is derived, it may be
formed by the oxidation of chlorophyll, or it may pre-exist
in the green leaf. I am inclined to think that it exists ready
formed in the green leaf, but is not then seen on account
of the far greater tinctorial powers of the chlorophyll
present at the same time, and that it makes its appearance
only when the chlorophyll has been decomposed, the sole
trace left by the latter being the slight greenish tinge which
all faded yellow leaves show more or less. The varying
proportion of xanthophyll contained in green leaves would
explain the fact, difficult to understand if we suppose it to
be derived from chlorophyll, that some leaves assume a
deep yellow colour in fading, while others remain of a pale
yellow, and others again are almost colourless when they
fall.

I will now conclude, hoping, if I have not communicated
anything strikingly new, that I may at least have succeeded
in affording the meeting a few moments’ amusement.

Bromley, Kent,

10th December, 1881.

57

MICROSCOPICAL AND NATURAL HISTORY SECTION.

December 5th, 1881.

Alfred Brothers, F.R.A.S., President of the Section, in

the Chair.

Professor A. Milnes Marshall exhibited specimens of
the larval form of starfishes, echino'ids, holothurids, and
crinoids, and described briefly the various stages of develop-
ment, commenting on the great differences between the
larval forms and the adult in each case, and also on the
great differences between the larvae and closely allied
groups. He considered this latter feature as indicating that
the individual differences were acquired separately by each
group, whilst the general resemblance in plan was due to
inheritance, and represented the primitive ancestral forms.

The points of individual difference were in all cases
ultimately absorbed, and formed no part of the adult
animal.

The slides exhibited were prepared at the Zoological
Station, exhibited at Naples by Dr. Dohrn.

Mr. It. Ellis Cunliffe brought the 3rd vol. of the
Challenger Expedition, for inspection by the members.

Mr. J. Cosmo Melvill exhibited Limnotrochus Kirkii
(Edgar Smith), from Lake Tanganyika, which with the
newly allied and also recently described L. Thomsoni of the
same author, constitutes a new genus of Mollusca. He read
a detailed description of the genus, and pointed out its chief
characteristics, which were the trochoid shape, deep umbilicus,
and quadrangular aperture, likewise calling attention to the
unusual ornamentation of the whorls, which were remark-

58

able in a fresh water genus. Mr. Smith, from the similarity
of the operculum, which is horny and few whorled, places
the genus amongst the Littorinidse and near the genus
Echinella and Risella, which it resembles in configuration ,
It is, of course, impossible to ascertain actually the position
of the genus until the animal has been examined, but
judging from the shell alone, Mr. Melvill considered it
more approached the genus Solarium — § Philippia, agreeing
with that in the ornamented edge of the whorls, and in
the deep umbilicus, which latter is wanting throughout the
whole of the Littorinidse; with the exception of the genus
Echinella. The operculum of Limnotrochus is certainly
Littorinoid.

He also exhibited a shell of even greater interest, recently
discovered by Prof. Morelet, as a new genus, Cyclosurus,
from the Mayotte or Mayotta Islands, about 300 miles
N.W. of Madagascar, at the northern entrance to the
Mozambique Channel.

This land mollusc Cyclosurus, Mariei, (Morelet) was
recently discovered there, but few specimens have hitherto
found their way to Europe, and, although closely allied to
the genus Cyclophorus, the shell bears more resemblance to
a Dentalium, being altogether e volute with the exception
of the first two very small whorls, after which it projects
straight like a horn.

It is also conspicuous for being very minutely ribbed
longitudinally, each rib bearing a quantity of very minute
rough spines.

It was suggested by Mr. Rogers that it might be a mons-
trosity, but this can hardly be the case, as if a monstrosity,
it is that of an undescribed species, the texture being dis-
similar from any known shell, and, besides; all the specimens
that have been discovered are of a similar evolute formation.

59

Ordinary Meeting, January 10th, 1882.

J. P. Joule, D.C.L., LL.D., F.R.S, &c., in the Chair.

“On Differential Resolvents, and Partial Differential
Resolvents,” by Robert Rawson, Esq., Assoc. I.N.A., Hon.
Member of the Society.

Arts. 1 to 8 contain the first and second differentia]
resolvents of a cubic, using therein one independent vari-
able only — and, from the second differential resolvent the
usual root of the cubic is determined.

In Arts. 9 to 11 there is the first partial differential
resolvents of a general cubic, using therein two independent
variables — and, from this partial differential resolvent the
root of the general cubic is obtained.

Arts. 12 to 14 contain the first partial differential re-
solvents of a quartic, using therein three independent
variables — and, from this resolvent the root of the quartic
is determined.

1. Let f + ay + m = 0 (1)

be a cubic in which ( a ) and (m) are functions of x, a vari-
able parameter.

For convenience, y1 = a1 = ^ &c., will be used.

ax ax

Differentiate (1) with respect to x, then

^=-W=p/+Qy+R (2)

where P, Q, R are functions of (a, m) to be determined as
follows : —

- a ly - m1 = 3P«/4 + 3Qy* 4 (3R + aV )y2 + aQy + «R

Proceedings— Lit. & Phil. Soc.— Vol. XXI.— No* 5. — Session 1881-2*

60

Eliminate from this equation y 4 and ys by means of the
cubic (1), then

- a}y - m1 = 3P( - ay* — my) + 3Q( -ay-m)

+ (3R + aV)y 2 + aQy + aR
or,

(3R - (2aV)y 2 + (a1 - 3mP - 2aQ)y + m1 + aR - 3mQ = 0

To satisfy this equation it is necessary and sufficient that

3R - 2aP = 0 (3)

a} - 3mP - 2aQ = 0 (4)

m1 + aR - 3mQ = 0 (5)

From these equations the values of P, Q, R are readily
found to be

P(4a3 + 27m2) = 9 ma1 - 6am1
Q(4a3 + 27m2) = 2a2ax + 9mm1
R(4a3 + 27m2) = bama1 - ka*ml
3R = 2aP

Substitute these values in (2), then

1 9 ma1 - bam1 a _ 2 a*al + 9mm1 bama1 - 4 aW

y = 4a3 + 27m2 ' y + ~WVfhrf ' y + 4as + 27m2 ' '

Equation (6) is, therefore, the first differential resolvent of
the cubic (1).

Hence the cubic (1) is the integral of (6), and the value
of y which satisfies (6) is, then, a root of the cubic (1).

2. To find the second differential resolvent of the cubic
(1) it will be convenient to write (6) as follows : —

yx +py* - Qy + -g- = 0 (7)

where, (4a3 + 27 m*)p = bam1 - Qma1

Differentiate (7) with respect to x, then

y11 + Zpyy1 + pY - Q y1 - Qty + — ^ + ^-'= 0 (8)

From (7) there results

1 A 2 3 2apy

yy-Qy-py — 3—

= Qy2 + + mp

61

Substitute this value in (8), then

/2ap

+ 2 mp* = 0

“ + (2Q + P~)Pf + - Q>> -Q/ + ^y-+ 2f

From (7) we obtain

.(9)

9 r* 3 aP l

py = Qy--§~-y

Then (9) becomes

Op1

a o + ^

\ 3 p
4a pQ 2pcd _
3 + 3

2Q2 - Q ^jy + Imp?

(10)

But,

2 ntf - *** + M. = |(3?rep _ 2aQ + «1} _ o

3 3

Then (10) may be written

Vn - (3Q + ~ y + + 2Q2 - Q1)? = 0 . . .(11)

Eestore the values of p and Q, then

<Vy

dx*

( d Sma1 - 2am1 \dy ( aim11 - m1^11
I dx &*/4 a3 4- 27m2 Jdo? 1 2am1 - Sma1

}y=o (12)

W 4 a3 + 27m2
6 am (a1)3 - 6a(m1)3 - 6a2m1(a1)2

(2am1 - Sma1) (4a3 + 27m2

Equation (12) is, therefore, the second differential resol-
vent of the cubic (1). The value of y which satisfies (12)
is a root of the cubic (1), and, either of the three roots of
the cubic (1) is a particular solution of the differential
equation (12).

3. When ( a ) is constant, then, the first and second
differential resolvents respectively become
4a3 + 27m2 dy „ 3m 2a

dx

dx 2

- {IM

6am1
- 2am1

+ r-Ta-y+^=0

(13)

Jia3 + 27m2/ j dx 4a3 + 27 m*'V ~

4. If (m) be such as to satisfy
= 1

m1

4 a3

27

4- m2

(15)

62

• dv

then the coefficient of — in (14) is zero, and it becomes

S-I=° <l6>

The general solution of (16) is well known to be

y-(^ + (*-•)* (17)

wher Ci, c2 are arbitrary constants to be determined. Inte-
grate (15) with respect to x, then,

m 2 27 €

Hence, equation (17) is a root of the cubic

y8 + ay + |-^e“* = 0 - (19)

The values of c1} c2 are readily determined by substituting
the value of y in (17) in (19), they are as follows :

Ci—

2 a3
27

Substitute these values in (17), then

(20)

is a root of the cubic (19).

(5) The values of c* £_ in (19) can be determined by
means of a quadratic, so as to satisfy the classical cubic

y3 + ay + b = 0 (21)

This equation will coincide with (20) if

(22)

Then, e* = b-^/b* + ^

a a 2a3 -x 1 /7o 4a3 h

An ’ 27e \2 + 2\f + "27". )

Therefore,

The value of 2/ in (23) agrees with Cardan s formula.

The process of obtaining the first and second differential

63

resolvents is a direct process, and it is only fair to state that
it has been gathered entirely from the correspondence with
Sir James Cockle, F.R.S., &c., and the Rev. Robert Harley,
F.R.S., &c. ; with whom originated the important invention
of differential resolvents of algebraical equations.

I am not sure whether the results in Arts. (4) and (5)
have been published by either Sir James Cockle or Rev.
Robert Harley.

It is more than curious that Cardan’s formula should be
reached as it has been, without the slightest assumption, by
means of the second differential resolvent. And, the method
which has been adopted is, in my opinion, very suggestive
in the theory of higher algebraical equations. Especially so
when several independent variables are made use of.

6. If in (14) we put

2 am1

*/ 4a3 + 27 m2
where (r) is another function of x.

2 ar

J27

■(24)

Then,

(m1)2

27

4as + 27m2
Hence, there results by substitution

dx1 rdx dx 9 ^ ' '

which is the second differential resolvent of the cubic

e~frdx 2a3

r + ay +

27

J'rdx

.(26)

The value of (m) is found by integrating (24), and, solving
algebraically with respect to (m), to be

2a3
27 e

frdx

(27)

7. If y and z are such as to satisfy the equation

^x=ll2+^k (28>

Substitute this value of y in terms of 0 in (25), and it
becomes

r\ o 1 ( /'dry 4 r2-) .

dx + & ~ i/3 { “ ^dxi^dx) + [rdx) + 9 } (29)

64

An equation which is soluble by means of (26) and (28) for
all values of the function r.

8. Put, r = Ax2n, where (A) is constant, then
dz n(n + 1) A2 .

Tx + ^z~ /to2 + 9/3*

which is soluble by means of (81) and (82)
dy _ n

-~ + 6z + -

ydx ' x

y* + ay + Tje

A#2n+1 Ax2n+1
2^+1 2a3 2 n + 1

27 €

= 0

.(30)

.(31)

,(32)

Equation (30) coincides with the Riccatian form in one
case only, viz., when the exponent of x is zero.

This property vanquished all hopes of connecting the
solution of Riccati’s equation with the roots of a cubic in its
present form. This result was communicated to Sir James
Cockle, who kindly sent me the following neat solution
of (80).

Assume the Riccatian

Change the independent and dependent variables t and u,
for x and z, by the equations

3(2 n -i-l )t = Ahx2n+1

3Bz = A*x2nw

' x

Then the above Riccatian on reduction coincides with (30).

The solution of a general cubic by a partial differential
resolvent with two independent variables.

9. Let V3 + 3 aV2 + 3RY + 3S = 0 (33)

be a general cubic where (a) is constant and R, S functions
of x , y.

Differentiate (33) with respect to x, y respectively, then

(V2 + 2aV + B)Y + ^
dx dx

(V2 + 2aY + R)Y + ^

dy dy

v+f-o

dx

(34)

v+f=o

dy

(35)

65

From these two equations it follows that

/rf R

vdV _

fd R

,v+^'

vdY

dyj

’ dx

\dx

dx,

Idy'

Equation (34), which is a partial differential equation, is the
first partial differential resolvent of the cubic (33) together
with the conditional equation (36).

Hence it follows that the value of Y, which satisfies (34),
and satisfies also, the conditional equation (36), is a root of
the cubic (33); and, each of the roots of the cubic (33)
is a solution of the partial differential equations (34),
(35), and (36).

10. Since R, S are arbitrary functions of x, y , it remains
to determine them so as to satisfy the equations (34), (35),
and (36), when

'V = x + y + a (37)

where a, is a constant quantity.

Substitute Y as given in (37) in (36), then

/dR dRY x dS dS A /OON

K^-^)iX + y + a) + dy-dr = (> <38>

Now, if the first term of (38) is a quadratic in terms of
x, y, then, the second term must be a quadratic also. This
readily suggests the following equation, viz.

f <39>

Substitute this value in (38), and it becomes

dS dS „ 9

j3x2 + afy - a/3% (40)

The integrals of (39) and (40), are

R = fixy + C (41)

3S = fiys + (3x 3 - 3a (3xy + 3Ci (42)

where C, Ci are independent of x and y.

The values of /3, a, C are determined from (34), and are
as follows, a= - a; /3 = - 1, and C = a2.

The constant 3Ci = a3 is found by substituting Y, R, S in
the cubic (33). Hence,

Y = x + y -a (43)

is a root of the general cubic.

66

V3 + 3aY2 + 3(a2 - xy) Y - x3 - y3 - 2>axy + a3 = 0 (44)

The remaining two roots must be obtained from

V2 + (x + y + 2a) Y + x2 + y2, - xy + ax + ay + a2 = 0 (45)

11. The values of x, y in (44) can be found by a quadratic
so as to make (44) coincide with the classical cubic.

V3 + 3aV2 + 36V + c - 0 (46)

For this purpose the equations

a2 - xy = b (47)

x3 + y3 + 3 axy = a3 -c (48)

will be necessary.

From these two equations there results

. 3a& - 2a3 — c 1 — 7 —

x3 = g + ^ V (3 ab - 2a3 - cf - 4(a2 - b)3

n 3 ab — 2 a3 — c 1

ys - y/ (3ab - 2a3 - c)2 - 4(a2 - b)3

The solution of a quartic by a partial differential resol-
vent with three independent variables.

12. Let

V4 + tV2 + RV + S = 0 ,....,...(49)

be a quartic in which t, R} S are functions of the three
variables x, y , z.

Differentiate (49) with respect to x, y , z respectively, then

, . TTO o tt dt _T0 <7R TT dS .

(4Y2 + 2tV + R)-t- + -r-V2 + V + = 0

v ' ax ax ax dx

,(50)

(^+2,y+E)f+|.y^|.y+|=o (51)

(4V* + JMV + E)g + Jy» + .f.V + f = 0 (52)

From (50) and (51) ; from (51) and (52) there results

'dt 2 dR„ d8\dV
^+Tyy + Jy

dt

d R _ cZSyV

^ V + dy V +

)£-(
dV _ /dt'
dz \dz

dt y2 dR y dSWY

dx dx dx) dy‘

2 dR dS\dY

V +-T’V+ w Hr*

a, 2 dz / dy

(53)

(54)

Equation (50) is the first partial differential resolvent of
the quartic (49) together with the two conditional equa-
tions (53) and (54).

The value of V, in functions of x, y , 0, which satisfies (50),

67

and satisfies also the conditional equations (53), (54), is a
root of the quartic (49), and a root of the quartic (49) is a
solution of each of the equations 50 to 54.

13. With a view, therefore, to obtain a solution of (53),
(54), it will he necessary to try a few simple assumptions of
the forms of t, It, s, which are suggested by the equations
themselves —

Put ^ = 1; ^ = 1 ;

dy ax

dR dR _ q
dy dx

.(55)

(56)

(57)

By integrating these equations, then

t = x + y + zx

R = (y - x)z2

where z1} z2 are functions of 0 only.

The above assumption, viz. (55), necessarily implies that
S is a function of x, y only, or, = 0.

Substitute the above values in (53), (54), then

dS\aY
dx) dy

.(58)

(T,+»v+<§)s-(T‘-'v*

If, then, the roots of the quartic (49) be such as to satisfy

(60)

(61)

V* + z2V + g = °

V2-^ + l = °

These equations will satisfy (58), (59), providing

--1 — 2z

dz~Z 2

dS dS dz2

dy dx dz

\y-x)

,(62)

,(63)

Since S is a function of x, y only, then

dz

dz

dz2

-t-= -1 or,

Integrating (62) (63), we have

ZX- -z2

S = xy

68

Substitute these values in (60), (61), then

Y*-zY + x = 0 (64)

Y2 + zY + ?/ = 0 (65)

And, t = x + y - z2
R = z{x- y)

14. The values of Y in (64), (65), which satisfy (50) also,

are the roots of the quartic

V4 + (x + y - z2) V2 + z(x - y)Y + xy = 0 (66)

Equation (66) will coincide with the quartic

Y4 + aY2±6Y + c = 0 (67)

If x , y, 0 are determined from

x + y-zz = a (68)

z(x - y) = +6 (69)

(70)

These values depend upon the well known cubic

z6 + 2az4 + (a2 - 4c)z2 - 62 - 0 (80)

See Todhunter’s theory of Eqs., p. 112, 2nd ed.
Havant , Sept., 1881.

Postscript.-

which gives

-Equation (6) is made linear by the relation
4a3 4- 27m2 dz
Gand-Sma1 zdx

y=

(81)

dh d , /(4a3 + 27m2)6Wz /2am1 - SmedY'4 A

' M W-3^* j^ + 6g( + 27m* > = Q-(82)

c^2 + dx

69

General Meeting, January 24th, 1882.

E. Angus Smith, Ph.D., F.E.S., &c., in the Chair.

Mr. William Thomas Arnold, B.A., was elected an Ordi-
nary Member of the Society.

Ordinary Meeting, January 24th, 1882.

E. Angus Smith, Ph.D., F.E.S., &c., in the Chair.

“On the British species of Erythrcea,” by Chables
Bailey, F.L.S.

I exhibit to-night a full set of the species of this poly-
morphic genus, from numerous localities in Great Britain,
to show their great range of form and habit. Their nu-
merous variations appear to depend upon the greater or
lesser ramification of the stem, and of the inflorescence.

In Erythrcea pulchella, Fries, we have the single-stemmed,
one to three flowered form, an inch or an inch and a half in
height, and at the other extreme we have a repeatedly-
branched form which was at one time separated from pul-
chella as a distinct species, under the name of E. ramosissima,
Pers. When the inflorescence is spicate it is the E. tenui-
flora, Link; this form Mr. Townsend meets with near
Cowes, Isle of Wight.

Proceedings— Lit. & Phil, Soc.— Vol. XXL— No. 6.— Session 1881-2.

70

Perhaps the most variable species is the widely-distributed
E. Centaurium, Pers., as the specimens exhibited will show.
Its most usual form is that in which the stems, whether
solitary or several springing from the crown of the root,
branch in the upper third of their height, the branches
terminating in one or more dense heads. A second form,
less common than the first, bears numerous branches from
the base to the summit, its terminal cymes having a spicate
direction. A third form, which I meet with on the Lanca-
shire coast sandhills, has a solitary slender stem terminated
in its upper eighth by one to three few-flowered contracted
cymes ; the habitat in which it usually occurs is at the base
of the sandhills at the edges of the flat damp hollows in
which Erythrwa littoralis is so abundant. It varies in
height from 6 to 18 inches, and the leaves of the lower
fourth of the stem are obtuse, obovate, and at times even
spathulate. Its habit suggests its being a hybrid between
E. Centaurium and E . littoralis ; but its characters range
with E. Centaurium. At the opposite extreme is a fourth
form, also maritime, which is met with growing amongst
the grass of exposed cliffs and sea-slopes. It is a stunted
form with spreading capitate heads, whose breadth often
exceeds the entire height of the plant. Its height is usually
determined by that of the contiguous herbage, and when it
can secure the shelter of tall plants its stem elongates and
branches in the upper haif. This form is the var. capitata
of Koch, and the pseudo-latifolia of the London Catalogue.
I have not observed it away from the western coast,
although I have seen on Afton Downs, in the Isle of
Wight, plants with more contracted and fewer- flowered

71

heads, branching from the base, which must probably be
referred to this form. I have collected var. capitata on
cliffs near Porth Curnow, at the Land’s End, Cornwall ; in
Holloways and Penally Burrows, Tenby, Pembrokeshire;
and in Anglesey on the cliffs opposite the ruins of Langwfen
church, Aberffraw, and on the steep grassy slopes at the
foot of the cliffs above the South Stack Lighthouse, near
Holyhead. The plants in this latter station are identical in
habit with the single-headed specimens of E. capitata, W.,
referred to below ; they grow less than an inch in height
in the shape of little cushions for a considerable distance up
the mountain side.

The rarest of our Erythrseas is E. latifolia, Sm., a species
which, I believe, does not occur out of England, and as far
as is known is confined to the Lancashire coast. The three
specimens exhibited are from Southport, North Shore
(Liverpool), and Seaforth Common, but I am afraid that
some of these stations are built upon. I have never been
fortunate enough to find it, but it might reward a careful
search on the coast from Ainsdale in the direction of Liver-
pool.

Erythrcea littoralis , Fries, is the least variable of our
British species; its narrow spathulate leaves, strict habit,
and the peculiar orange colour of the stem and leaves in
autumn render it easy of detection. It is extremely plenti-
ful on the Lancashire coast south of Birkdale.

A well-marked species of Erythrcea, new to the British
Flora, was detected by Mr. Frederick Townsend, M.A., F.L.S.,
about two years ago, and the specimens now exhibited I
collected in July last, in the stations indicated by its dis-

72

coverer, viz : on Afton and Compton Downs, Freshwater, Isle
of Wight, It differs from all the other British species in
possessing free anthers, the filaments springing from the
base of the corolla, instead of from the throat as in all the
other forms. This species is the E. capitata, Willd. var.
splicer ocephal a, Towns., as described in the Journal of Botany
for November, 1879, p. 827; March, 1881, p. 87; and
October, 1881, p. 302; also in the Journal of the Linnean
Society, Bot., Yol. XVIII., p. 398. Like the other species
of this genus there are two extreme forms ; a luxuriant form
in which secondary axillary stalked heads arise from the
outer bracts of the primary head which they overtop; and a
dwarf form in which the axillary heads are absent. The
multi-capitate form occurs plentifully in the protection of
taller plants on Afton Down, while the uni-capitate form
grows with it on Afton Down, but is extremely frequent on
all the downs surrounding Alum Bay, and particularly on
the one which extends to the Needles.

A sixth species of Erythrsea is noted by Nyman as British
in his recently published “ Conspectus Florse Europsese,” part
III., p. 502, viz : E. diffusa , Woods. It is of diffuse ascend-
ing habit, has few flowers, and the divisions of the corolla
are as long as the tube. The lowermost leaves are elliptic
subrotund, and approximate. I do not know on what
authority it is regarded as British.

There are two other species of Erythrma whose conti-
nental distribution might almost lead to the hope of their
being detected in Britain, or at least in the Channel Islands,
since they occur on the contiguous French coasts. These
are two very distinct Mediterranean species, viz : E . spicata ,

73

Pers., where each branch ends in a long red-flowered spike ;
and E. maritima, Pers., with yellow flowers.

I have carefully examined mature seeds of all the British
species, except E. latifolia, Sm. (my specimens of which are
not in fruit), and I can detect no differences amongst them
of a specific character. The ripe seeds are of a russet brown
in all the species except E. pulchella , and in this species
they are blackish brown.

“ On a dwarf form of Campanula glomerata , L., from the
Isle of Wight,” by Charles Bailey, F.L.S.

When collecting Erythrcea capitata , Willd., var. sphceroce-
phala, Towns., in the Isle of Wight, referred to in the
preceding communication, I was greatly struck with a
diminutive Campanula which grows on the Afton Down at
Freshwater, and still more plentifully on the downs from
the Needles towards Freshwater. Its stature about Alum
Bay is no greater than that of the herbage, which is ex-
tremely short, averaging only an inch; in the more
sheltered ground opposite Freshwater it grows from one to
three inches high. It is very unlike the ordinary form of
C. glomerata, L of the limestone districts of the North of
England, which is of robust habit, frequently two feet in
height, with a long spike of clustered flowers, or a single
terminal cluster. The dwarf form of this species has
been known for nearly a hundred years, as Withering in
his “Arrangement of British Plants,” 5th Ed., Yol. II., p.
310, thus refers to specimens from the identical locality:—

“ I have gathered it when growing on a high and very
dry soil, as on the summit of Aston [ ? Afton] Down in the

74

Isle of Wight, only from one to two inches high (see PL II.
f. 8) [The 2nd plate in the 5th Edition comprises details of
the inflorescence of grasses only] when it can scarcely he
said to have a stem ; hears only one or two flowers, with
four stamens and frequently hut two summits. In the
summer of 1795 Mr. Watt brought me a series of specimens
from the Isle of Wight, from one to ten inches high, and
soon afterwards Mr. Turner informed me that on barren
limestone hills in Norfolk it grows equally diminutive;
though the blossom, as he observes, is as large as in the
largest specimens, which he has sometimes seen above two
feet high.” He also mentions amongst the localities from
which he has specimens : — “ Close to Stonehenge, on Salis-
bury plain, very diminutive. Mr. Caley.”

I am distributing, through the “ Botanical Exchange Club
of the British Isles,” under the name of var. {3. nana, the
few specimens of this dwarf form which I collected. It
differs from the typical form only in its diminutive parts,
dwarf habit, short slender stem, and heads of one to three
flowers. The colour of the corolla is paler than that of the
ordinary erect form.

“ On the Isle of Wight station for Lychnothamnus alope-
curoides, Braun,” by Charles Bailey, F.L.S.

I also exhibit another interesting Isle of Wight plant,
which had been thought to have become extinct, as it has
not been reported to have been found for several years past,
in the only British station where it is known to occur.
This plant is the Lychnothamnus alopecuroides, Braun, one
of the Charaeese, and was collected at Newtown, 14th July,

1881.

75

On the north coast of the Isle of Wight, between Cowes
and Yarmouth, is a narrow creek with numerous arms, on
whose shores many years ago a considerable trade was done
in salt, produced by evaporation in the numerous salterns
on each side of the creek. The newer method of obtaining
salt from the brine formed by the beds of rock salt in
Cheshire and other districts, has led to the abandonment of
the salt pans at Newtown, and very few are now left. Some
have been absorbed by the formation of oyster-parks on
both sides of the creek, as well as by brick-works, and
similar destruction threatens the remainder. The particular
locality in which the Lychnothamnus occurred lies a few
hundred yards north of the Coast Guard station at New-
town, and contiguous to the shores of the creek. At this
spot are the remains of three old salterns containing water
as salt (to the taste) as that of the sea, and filled with Rup-
pia spiralis, Hartm. The saltern nearest the creek is the
only one of the three which contained the Lychnothamnus,
and from it I obtained, by wading, a number of very fine
plants, many of whose stems would be from 18 to 24 inches
in length. They were greatly infested with a confer void
growth, which rendered it difficult to secure good-sized
plants.

I spent some time in a subsequent visit, exploring some
of the ramifications of the creek, but failed to find a trace of
the plant in any other station. One of the large oyster
parks on the western side of the creek was carefully, but
unsuccessfully, searched during this second visit, its nearly
empty condition affording every facility. The most likely
station for its being found on the western side of the creek

76

is at a spot where there are two old salterns, both of which
had been emptied of their vegetation a few days previously,
apparently to adapt them for duck-ponds.

FranJcenia Icevis, L., Inula crithmoides, L., and Artemisia
maritima, L., were amongst the conspicuous plants of the
same neighbourhood.

77

Ordinary Meeting, February 7th, 1882.

R,. Angus Smith, Ph.D., F.R.S., &c., in the Chair.

“The Colour Sense and Colour Names,” hy William
E. A. Axon, M.RS.L.

The recent important paper of Dr. Schunck on the terms
used to denote colour opens out the entire question — and a
very fascinating one it is — of the origin and development of
the colour sense. In the course of his opening address at
the British Association Sir John Lubbock referred to the
subject of blue .blindness, a topic which has at once a prac-
tical and an archseological interest. Mr. Gladstone, in the
course of one of his Homeric studies, made the suggestion
that the ancient Greeks were unable to distinguish blue.
As far back as 1858 Mr. Gladstone asserted “ That Homer’s
perceptions of the prismatic colours, or colours of the rain-
bow, which depend upon the decomposition of light by
refraction, and a fortiori of their compounds, were as a
general rule vague and indeterminate.” He however re-
turned to the subject in an article which appeared in the
Nineteenth Century for October, 1877. After analysing the
Homeric epithets and referring to the investigations of
Magnus and Geiger, he unequivocally adopts the suggestion
that the colour sense was comparatively imperfect in the
Homeric age. Mr. Gladstone’s general conclusion is, that
archaic man had a positive perception only of degrees of
light and darkness, and that in Homer’s time he had ad-
vanced to the imperfect discrimination of red or yellow,
but no further ; green of grass and foliage, or the blue of
the sky being never once referred to. Dr. William Pole, who
is himself colour blind, taking the instances cited by Mr.

Proceedings— Lit. & Phil. Soc.— Yol. XXL— No. 7. — Session 1881-2.

78

Gladstone from Homer, thinks that they point to the colour
blindness of the person using them. He thus summarises
his conclusions : —

"1. That Homer’s applications of colour epithets are in
many cases inconsistent with the normal ideas in regard to
them. This is the first and most general symptom of colour
blindness. 2. That this inconsistency is particularly notice-
able in the use of the expressions for red and green. This
is a further and more definite symptom, showing the pecu-
liarly defective sensations in regard to these particular
colours. 3. But that when the objects referred to are classified
in two groups according to the two colour sensations they
respectively offer to the colour blind eye, the use of the
colour epithets becomes consistent, no epithet belonging to
one group being used, except in one doubtful case, for an
object belonging to the other. This is a still more definite
symptom, pointing, as it seems to me, to the dichromic
nature of the malady.” — Nature, Oct. 31, 1878, pp. 703-4.
These results if accepted might be interpreted in two ways.
It might be, and has been contended, that the Greeks
generally were colour blind. If this be rejected, there
remains the further possibility that the Homeric colour ter-
minology was not a matter of racial but of individual
peculiarity. In fact, that although the Greeks were not
colour blind Homer might be.

Another disciple of the same school was the late Prof.
Lazarus Geiger, who tells us that blue is not used as an
epithet of the sky in the Big- Veda, the Zend-Avesta, the Old
Testament, the Homeric poems, nor in the Koran, and that
Alkindi, writing in the 9th century, is the first to speak of the
azure of the sky. Geiger also says that green is not named
in the Big-Yeda, that Aristotle speaks of the rainbow as red,
yellow, and green, that Xenophanes regarded it as purple,
reddish, and yellow, and that Democritus regarded black,
white, red and yellow as the fundamental colours, and that

79

these, with the addition of green, are now so regarded in China.
(See Geiger’s Contributions to the History of the Development
of the Human Race — London, 1880, pp. 48 et seqq.) Hence,
as the Rig-Yeda, the Zend-Avesta, the Old Testament, and
the Homeric poems contain no reference to the sky as
blue, it is argued that the peoples to whom these books
belonged were incapable of discriminating the finer shades of
colour. The weak part of such an argument is, that it may
possibly confuse mere poverty of nomenclature with defec-
tive perception. This in effect is the reply of Seydewitz
and others who are not able to accept the theory propounded
by Geiger. In the Kaffir language, although there are
more than twenty-six distinct names for the colouring and
coat of cattle, one term is used for both blue and green,
although the people who use it are perfectly well able to
tell the one from the other. If we take the savages of the
present day we see no reason to suppose that their appreci-
ation of colour is inferior to that of civilized races. On the
contrary, it is a constant source of regret to see the genuine
sesthetic qualities of aboriginal art supplanted by European
importations, often inferior both in form and colour. Dr.
Hahn, whose recent work on the Hottentot race has excited
much and deserved attention, says : — “ that the Khoikhoi
distinguished very strictly between white, black, green, red,
blue, fawn-coloured, yellow, brown, grey and dotted. Then
we have the following sub-divisions — whitish-yellow, whitish,
black-patched, black-dotted, black-shining, red-shining, with
white and red patches, chesnut-colour, reddish, green-shining,
brown-dotted, 2 words, brownish-blue (the colour of Buce-
phalus Capensis), brown-shining, like the Yipera Cornu ta.
The colour of the rainbow is always green ; only in two
cases I heard that it was considered to be red. The name
of the rainbow is tsawirub and dabitsirule. In Bible trans-
lations of missionaries we read tavi — ! hanab. This is very
incorrect, and nothing else but a verbal translation of

80

rainbow .” Mr. Grant Allen has made extensive inquiries
on this point, and his researches lead him to the supposition
“that the colour sense is as a whole absolutely identical
throughout all branches of the human race.”

The reason why colour plays so subordinate a part in the
older literature of various nations is chiefly the direct and
simple manner in which the story is related. The ideas
are concrete. The need of picturesque details does not
occur to the writer or the singer. He is speaking often
of familiar things, and feels no necessity to describe them.
If he does enter upon description, the shining and glittering
of spears and bucklers are more likely to arrest his attention
than their precise colour. Mr. A. It. Wallace says that in
the long epochs during which the colour sense was being de-
veloped the visual organs would be mainly subjected to two
groups of rays : — the green from the vegetation, and the
blue from the sky. This makes it all the more remarkable
that blue should be so largely absent from early colour
vocabularies. But much confusion has resulted from the
poverty of the colour-vocabulary. In quite recent litera-
ture we find the same objects described by the terms “blue”
and “green.”

Green, as a beautiful colour of eyes, has been celebrated
by many poets. “ Green is indeed the colour of lovers,”
says Shakspere. Drummond, Cervantes, Longfellow, and
Dante have all praised the green-eyed beauties. (There
are many communications in Notes and Queries , 6th S., vol.
I., and in the Antiquary , vol. III.) Moncrief says that the
eyes of cats were for a long time the objects of female ambi-
tion ; they could receive no praise more flattering than to
discover that they had bluish grey eyes ; that is, changing
like those of cats, or greenish as they commonly have. La
Fontaine has given Minerva such eyes,

Tout le reste entouroit la d£esse, aux yeux vers.

Marot gives green eyes to Venus,

Le premier jour que Venus, aux yeux vers.

81

The lord de Coucy, so celebrated for his ioves, acknow-
ledges in his verses that such eyes were the secret charms
that Madame de Fay el practised on him. These bluish
grey eyes are those which commonly are of a pale blue, or
sometimes of a water-colour which varies or undulates, with
different shades, in the course of the day. The green eyes
never change their shades. Diodorus Siculus tells us that
Pallas was named by the Egyptians Glaucopis, that is,
having eyes of a greenish white. And Pope’s “ blue-eyed
maid ” has been censured for being inexact ; it should be
“ eyes of a bright citron.” ( Histoire des Chats, p. 127.)
It is a custom in the East to tinge the eyes of women,
particularly those of a fair complexion, with an impalpable
powder prepared chiefly from crude antimony. It is of a
purple colour, and a Persian compares it to the violet. The
Arabian poets compare the eyelids of a fine woman bathed
in tears to violets dropping with dew.

Shakspere has

Violets dim,

But sweeter than the lids of Juno’s eyes.

Winkleman observes that “ his researches concerning the
mysterious art, said to be practised among the Greeks, of
changing blue eyes into black ones, have not succeeded to
his wish. I find it mentioned but once by Dioscorides.
Could I have cleared up this art, it would have been a
problem worthy to fix the attention of the Newtons and the
Algarottis, and have interested the fair sex by a discovery
so advantageous to their charms, especially in Germany,
where large fine blue eyes are more frequently met with
than black ones.” The same author also notices the green
eyes we have alluded to, and gives us the charming line
in which the Sieur de Coucy describes the eyes of Madame
de Fayel:

“ Et si bel ceil vert, et riant, et clair.”

(The above and other references will be found in I, Disraeli’s

82

Komances, 1801, p. 123, and in the notes to Beckford’s
Vathek.)

The value of green is an ancient belief. “Wise archi-
tects,” says Isidorus of Seville, “ do not gild the ceilings of
libraries, because the glitter might injure the eyes, and
they pave them with green marble, for that is a colour
salutary to the sight.” Calderon, in one of his fine passages,
says : —

“ La verde es color primera
Del mundo, y en quien consiste
Su hermosura.”

Mahomet had the true poetic feeling in this matter, for a
portion of his pleasures of Paradise was that the true
believers should delight themselves lying on green cushions
and beautiful carpets.

The late Mr. C. Babbage, F.B.S., whose philosophic
spirit illuminated every question he discussed, made
numerous experiments to discover the shade of colour
most suited for reading as causing the least strain to the
eye. He was then preparing his logarithmic tables,
and a “Specimen” exists in 21 volumes, printed with
different coloured inks and on variously coloured papers.
“The object of this work,” he says, “of which one single
copy only was printed, is to ascertain by experiment the
tints of the paper and colours of the inks least fatiguing to
the eye. One hundred and fifty one variously coloured
papers were chosen, and some two pages of my stereotype
Table of Logarithms were printed upon them in inks of the
following colours Light blue, dark blue, light green, dark
green, olive, yellow ; light red, dark red, purple, and black.
Each of these twenty volumes contains paper of the same
colour, numbered in the same order, and there are two
volumes printed with each kind of ink. The twenty-first
volume contains metallic printing of the same specimen
in gold, silver, and copper, upon vellum and on variously

83

coloured papers. For the same purpose about thirty-five
copies of the complete Table of Logarithms were printed
on thick drawing paper of various tints.” Where is this
wonderful and unique book now ? Yellow was the colour of
paper that had the preference, and the Table of Logarithms
was printed for the public in black ink and on a deep shade
of yellow paper. There is a review of the “ Specimens ” in
Brewster’s “ Edinburgh Journal of Science,” vol. vi. (1832),
p. 144. The writer, probably Brewster, is in favour of the
blackest ink upon the whitest paper. “ The ground of
this conclusion is that by looking through slightly coloured
media we may give to the white paper any tint we desire
without depositing a poison at the root of the ink.” I fancy
that those who can do without will be unwilling to read
with coloured spectacles.

Beturing from this digression it may be remarked that
the speculations of Geiger are by no means universally
accepted, and less so now than when they were first broached.
Dr. Krause, an earnest follower of Darwin, opposes them ;
and Sir J ohn Lubbock doubts. The matter has also been
investigated by Dr. Paul von Seydewitz, of New Orleans,
who also rejects the theory that the ancients were colour
blind. Mr. Grant Allen, whilst holding that the colour-sense
has been developed from the partiality of man’s frugivorous
ancestors for bright coloured fruit, is also a decided opponent
of the idea that this has been done within the historic
period.

In our own days the colour vocabulary is not used with
exactness. Why, then, should we suppose that the Greeks
were colour-blind because Homer appears to use the same
name for red, purple, and grey ? An exact scientific pre-
cision is not to be expected in the popular use of such terms.
The very basis, however, of Geiger’s theory is the exact
conformity of colour sense and colour terminology, and
when we see that this is notably absent in the present day

84

amongst races of a lower degree of culture, we may conclude,
until further evidence is forthcoming, that the Greeks of
old were quite as well able as their modern descendants to
appreciate the beauty of the blue sky although they had no
word by which to express their admiration.

“ Notes on Lead Pipes and Lead Contamination,” by
William Thomson, F.RS.E.

The question of the contamination of water by lead
pipes having been recently revived by Dr. Sedgewick Sander-
son’s translation of M. Belgrand’s brochure, made in
accordance with the instructions of the Commissioners of
Sewers of the City of London, I propose to bring before
the Society a few notes on the same subject which may be
of interest.

About three years ago I examined a sample of water to
ascertain whether it contained any objectionable ingredients,
and found it to be contaminated with lead to the extent of
0T97 grains per gallon. The composition of this water was
as follows : —

Grains per Gallon.

Total solid matter 7 *97 1

Organic matter, combined water, &c 1*817

Saline matter 6*154

The saline matter was composed of : —

Chlorides of Sodium and Magnesium 1*543

Sulphates of Soda and Magnesia 1*146

Sulphate of Lime 2*328

Carbonates of Lime and Magnesia and

Oxide of Iron 1*137

6*154

Free Ammonia *0028

Albuminoid Ammonia *0035

Oxygen contained in Potassium Perman-
ganate required to oxidise organic
matters, &c., acting in the cold during

three hours *028

Nitrates and N itrities absent

Total Hardness 3° *8

85

I advised that this water should not be used for drinking
purposes on account of the lead which it contained, and I
afterwards learned that one of the members of the family,
being ill and under medical treatment, suspected that there
might be something wrong with the water in question,
because she was better in health when away from her home,
and it was only after lead had been detected in the water
that lead poisoning was even suspected by the medical
attendant, and it then became evident that the patient was
suffering severely from lead poisoning, all the symptoms
being strongly marked. The gums were tinged of a bluish
shade and the fingers of both hands had become stiff and
partially paralysed.

The interesting points connected with this case are, that
whilst a number of persons were using this water only one
suffered severely from lead poisoning, although others of the
family were in indifferent health previous to, and enjoyedgood
health after, the removal of the lead pipe which conveyed
the water from the well to the house. As this lead pipe,
which was in all probability the cause of all the unhealthi-
ness of the family, had been in use for 21 years, it would
have been interesting to have known the condition of health
of the previous occupants of the same house, and if not
satisfactory, to have learned whether or no any medical man
diagnosed any of the cases as those of lead poisoning, as
there seems little doubt that those who lived in this
house must have suffered, more or less, from this cause. It
seems, unfortunately, probable that many persons may be
suffering from slow lead poisoning without the real nature
of the malady being recognised by medical men, as it was
in the case of the lady above mentioned, who by philo-
sophical reasoning and experiment salved the problem which
puzzled the doctor.

The house referred to was supplied from a well about
500 yards distant, the water passing by gravitation through

86

a one-inch lead pipe, and although this pipe had been in
use for 21 years, and the water which passed through
it contained certain proportions of sulphate and carbonate
of lime, yet the pipe had not become coated as M. Belgrand
says is the case with the lead pipe in Paris, and as is
generally supposed to be the case, but was, according to the
description of the owner of the house, as free from inside
coating when taken out as it was when put in.

I was asked to suggest a substitute for the lead pipe, and
advised the use of tin-lined lead pipe where the coating was
about l-16th to l-20th of an inch thick, because some
samples which I had obtained and examined several years
before did not in the slightest degree contaminate water
when kept in the pipe for many days. My suggestions
were carried out, and a sample of the water which had
passed through this tin-lined pipe sent to me for examination.
I found it to be contaminated with lead to a considerable
extent, and on examining some of the tin lining I found it
to contain a large proportion of lead. I sent to another
manufacturer of this tin-lined pipe for a sample. This he
sent me, and again I found that the tin lining contained a
large proportion of lead, and quickly contaminated water left
in contact with it. This I communicated to the manufac-
turer, who informed me that he could not understand how
the tin lining had become contaminated, unless it was by
its being poured down the side of a strip of lead into the
hole left in the solidified lead in the cylinder previous to
forcing it through the dies by hydraulic pressure. As I
understand this pipe is produced by pouring melted lead
into a cylinder, through the top of which an iron shape is
introduced to make a cavity in the lead of sufficient size to
hold the necessary quantity of tin; the lead is then allowed
to set; when this occurs the iron shape is withdrawn and
molten tin poured in to fill the space which the iron shape
previously occupied ; a “ die” composed of an iron tube with

87

a core dips into the tin, which remains liquid in the cavity,
whilst this outer tube forms the core of another tube
through which lead is forced, the innermost core being
prolonged, so that the tin comes in contact with and
solidifies on the interior of the lead pipe. It seemed to
me remarkable that a manufacturer who was cognisant of
the fact that tin dissolved lead should have allowed such a
device as the pouring of the tin down a strip of lead to be
employed for filling the mould.

These tin-lined lead pipes, I understand, are. used to a
large extent, and principally in making communication
between the beer in the cask and the pump on the counters
of beer retailers. Such pipes would give the idea of safety,
but it is clear that many samples of it may be of such a
nature as to contaminate beer with lead to a large extent,
as the beer contains a certain amount of free acid which
would in all probability be capable of dissolving the lead ;
and one would expect that the person who consumes the
first glass of beer from the pump in the morning would get
that which had remained over night in the pipe, and would
imbibe, therefore, a considerable quantity, depending on the
quality of tin lining, of the poisonous metal.

To test whether this was really the case, a few days ago
I got two samples of beer, drawn in the morning, from two
pumps at the same place, and examined them, and found a
considerable proportion of lead to be present in each. To
find whether it was possible to obtain tin-lined lead pipe, in
which the tin was free from lead, for making communication
between the house and well above mentioned, I obtained a
number of samples of this variety of pipe from the same
and from different manufacturers, and tested the purity of the
tin lining inside each, but failed to find one which was not
contaminated with lead, and which did not contaminate
water when left in contact with it for two or three days to
a greater or lesser extent; one or two samples, however,

88

contained very little lead, and only caused a minute trace
of contamination in the water, but the majority contained a
large percentage of lead, and polluted the water to a great
extent. Ultimately, the gentleman who occupied the house
referred to had the tin-lined lead pipe which replaced
the lead one dug up, and communication with the well esta-
blished by 500 yards of block-tin pipe; and since this change
was made, he informed me lately that his family have en-
joyed good health.

There is another kind of lead pipe manufactured called
“ tinned lead pipe,” the inside of which is covered with a
very thin coating of a white metal to afford protection
against the action of water on lead — as a matter of fact, this
coating is not tin at all. It is produced by filling the first
few inches of the ordinary lead pipe which is forced through
the dies, whilst still very hot, with molten tin, which re-
mains molten and washes the inner surface of the lead tube
as it is produced. Presumably, when a long length of pipe
has been forced through the dies, there would be little or
no tin remaining, but I was informed by a manufacturer of
this pipe that that is not the case ; on the contrary, there is
a much larger volume of tin, to use his own language, at the
end of the operation than there was at the beginning ; the
molten tin dissolves the ]ead, thus increasing in volume,
and so the coating is a mixture of lead and tin, the propor-
tion of lead in the coating being greater in those portions
of the pipe which are last forced through the die.

Some years ago, not knowing of the existence of this kind
of tinned lead pipe, I requested a plumber to make for me a
worm refrigerator with tin-lined lead pipe for the preparation
of distilled water. He did so, and to my astonishment, on
testing the distilled water which had been condensed in it,
I found it to contain a large proportion of lead. On exami-
nation of the pipe afterwards I found it to be the variety
which had been washed with tin. This coating cannot

89

therefore be regarded as a thoroughly efficient protection
against the action of water on lead, but the test was a severe

O

one, and there can be no doubt that tin-coated lead pipe is
much better adapted for use in making communication with
the water mains in large towns than the ordinary lead pipe,
whilst the cost of producing this coating, I understand,
amounts to only a few shillings per ton of pipe. To test their
respective values I placed water containing a small propor-
tion of nitrate of ammonia in two pipes of the same sizes,
the one tinned inside, the other the ordinary lead pipe.
After standing about three hours I tested the water from
each, the one from the tinned lead pipe contained only a
trace of lead, whilst that from the ordinary lead pipe con-
tained a large proportion of lead in solution. Similar
results were obtained by leaving Manchester water in the
same pipes for 18 hours.

In certain boroughs, I understand, such as Salford, Old-
ham and Southport, this tinned lead pipe is the only kind
allowed to be used for making communication with the
main, whilst in Manchester and other places ordinary lead
pipe is generally employed. I have lately observed that the
lead pipes which have been in use in Manchester for many
years contaminate water left in them over the night to a
considerable extent, but after the water has been used for a
short time during the day it is free from any appreciable
trace of lead.

I have also tested the water after remaining 18 hours in
the lead pipes in communication with the main in Salford
where the tinned pipes are employed, and although the water
was slightly contaminated with lead, it contained much less
than that found in the water which stood for the same length
of time in the ordinary lead pipes of Manchester.

It is a fact, which I have observed from my experience
during the last few years, that aerated waters are contami-
nated with lead much more often, and in many cases to a

90

much greater extent than one would expect, considering the
attention and care which is bestowed by good firms on the
manufacture of th ese articles. Lately I tested several samples
of what was termed “ pure” carbonate of potash, and “ pure”
carbonate of soda, and citric acid, which were specially
purified for use in the preparation of aerated waters, and I
found all to be contaminated with lead to a greater or less
extent. The manufacturer of these samples was apprised
of this fact, and in reply he admitted that they contained
traces of lead, but said it was impossible to obtain these
substances free from metallic contamination at anything like
reasonable cost, and he was quite satisfied that the quantity
was not objectionably large. To overcome this difficulty I
had to advise the use of the ordinary carbonate of soda,
made by Solvay’s ammonia process, as being almost as pure,
and certainly much less likely to be injurious than the
purified salt. I also advised that those salts which it is impos-
sible to obtain free from lead should be dissolved in water,
and filtered through or boiled with animal charcoal, which
has the property of removing the lead from solution. It
might here be noted that the use of charcoal filters diminishes
very much the risk of lead poisoning, as the charcoal removes
any trace of lead which the water might contain.

It was first discovered and afterwards published by the
late Dr. Crace-Oalvert and Mr. Richard Johnson in a joint
paper, that pure lead is more easily acted on by sulphuric
acid than lead containing a very small percentage of
impurities such as antimony and copper, and these results
have been repeatedly verified since. With a view to find
the effect of pure water on comparatively pure lead and on
lead to which I added f of a per cent of antimony, I
melted some of the original lead and poured some out,
which I rolled into a sheet. Antimony was added to the
remainder, and the mixture poured out and rolled into
a sheet as before; both sheets were cut to the same size and

91

placed in equal bulks of distilled water and left overnight.
In each case a fine white flocculent crystalline matter, an
oxide or salt of lead, was observed in suspension, but this
existed in considerably greater proportions in the water
containing the lead which had not been treated with anti-
mony. Thus the small quantity of antimony appears to afford
some protection against oxidation of the lead by air and
water. When the suspended matter was filtered off, only a
trace of the lead was found to be in solution in each case.

It is sometimes advisable to obtain the lead contained in
water in a contracted solution, and preferably in an acetic
acid solution if possible. I have observed frequently that
weak acetic acid dissolves no lead from the residue left on
evaporating waters which gave originally a very distinct
coloration with sulphuretted hydrogen, but on treating the
residue with strong nitric acid, evaporating off the acid
completely and again treating the residue with weak acetic
acid, the lead dissolves with apparent facility, and on evapo-
rating this acetic solution of the metal to a drop or two, it
may be obtained in a sufficiently concentrated solution for
the application of the other tests. It appears as if certain
organic matters contained in the water combine with and
render the lead insoluble in acetic acid ; these organic sub-
stances being afterwards decomposed by the nitric acid, leave
the lead in a condition in which it is soluble in acetic.

A curious case of lead poisoning lately came under my
notice and engaged the attention of a Lancashire coroner.
A woman, upon whose body the inquest was held, had
been employed in weaving cloth from yarn, which had been
dyed of a yellow colour. The colour was the ordinary
chromate of lead, and it was alleged that the dye had
caused her death by poisoning.

I examined some of this yarn, which I found to be of an
orange yellow colour due to the chromate of lead which had
been fixed in the fibre, but it was so loosely fixed that by

92

gently shaking a hank the chromate came out, forming a
cloud of yellow dust, and it was given in evidence at the
coroner's court that all or nearly all the workpeople who
had been engaged in weaving this cloth suffered more or
less from lead poisoning.

I afterwards examined some yarns containing the same
pigment colour fixed in the thread so firmly that it could
not be removed by shaking.

93

Ordinary Meeting, February 21st, 1882.

Dr. R Angus Smith, F.R S., &c., in the Chair.

Dr. Schuster, F.RS., exhibited and explained “Grants
Arithmometer.”

Ordinary Meeting, March 7th, 1882.

Dr. R Angus Smith, F.RS., &c., in the Chair.

“A Comparison between the Height of the rivers Elbe
and Seine and the state of the Sun’s Surface as regards
Spots,” by Professor Balfour Stewart, LL.D., F.RS.

1. Certain results connected with the Nile and the Thames
which were recently brought before me (see Nature , Jan.
19, 1882) have led me to think that if we suppose there is
a connexion between the state of the sun’s surface and the
heights of rivers, the nature of this connexion will probably
be best expressed by supposing that there are traces of a
double as well as of a single fluctuation in river heights
during a single sun-spot period. A. similar observation has,

Proceedings — Lit. & Phil* Soc. — Yol. XXI.—No. 8.— Session 1881-2.

94

I think, already been made with regard to the connexion
between sun-spots and rainfall.

2. To test this I have taken the heights of the rivers Elbe
and Seine as recorded by Professor Fritz, and I am indebted
to the kindness of Professor Archibald for bringing the me-
moir of Professor Fritz before me. There is a long series of
heights for both these rivers, these heights being expressed
in metres above a certain mark.

These heights have been arranged according to the sun-spot
cycle after the following method. The dates of the various
maxima of sun-spots, as given by Professor Wolf in his most
recent memoir, are taken as the starting points, or 0 and
each interval between successive maxima is divided into 12
equal parts called 1, 2, 3, 4, ... . 11, 0, no further regard
being had to the inequalities in the lengths of the various
periods. The river heights corresponding to the dates of
these various subdivisions have been obtained from Profes-
sor Fritz’s results by a simple interpolation.

3. This method will be easily understood by reference to
the following tables.

Table 1 *

HEIGHT OF THE ELBE.

Period commencing with maximum

0*5

1‘5

2-5

3-5

4-5

5-5

6-5

7-5

8-5

9-5

10-5

11 *6

1727*5

219

2-55

2-81

2-79

2*67

2*74

2-31

2-87

2*84

2-78

3*14

2-97

1738-7

3-06

3-04

3-00

2-89

2-78

2-74

3-10

3-01

2-45

2-82

3-06

2-88

1750-3

2-64

2“62

2-39

2-57

2-65

2-90

2-89

2-74

2*44

2-28

2-57

2-66

1761*5

2-52

2-50

2-53

2-84

2-95

2-62

2-45

2-45

2-60

2-60

2-76

3*19

1769-7

3-60

3*77

3-67

3-02

2-64

2-60

2-83

2-83

2-67

2-57

2-80

2-83

1778-4

2-65

2-42

2-61

3-19

2*82

2-68

2-82

2*17

2-54

2-75

2-62

2-33

1788-1

2-49

2-47

1-97

2-10

1-72

2-14

2-24

2-31

2-55

1-84

2-22

2-30

1804-2

2-92

2*95

2-60

2-28

2-04

1-88

1-63

1-83

2'15

1-82

1-78

2-06

1816-4

2-21

1-86

1-98

1*82

2-26

1-85

1-76

2-13

1-89

2-00

2-34

2-44

1829-9

2-41

2*46

2-42

1-85

1-69

1*94

1-89

1*74

1-44

1-35

1-47

1-87

1837'2

2*24.

2*20

2-33

1-91

1'98

1-58

1-91

2-34

2-21

1-99

2-04

2-04

1848-1

1-67

1-88

2-35

2-34

2-02

2-10

2*22

2-32

1-84

1-45

1-57

1-62

* It

was

intended to make the

recorded numbers correspond to

the

divisions 0, 1, 2, &c., but by an accident it was the above intervals which
were recorded. This does not affect the result obtained.

95

Table 115-

height OF THE SEINE.

Period commencing with maximum

0-5

3-5

2*5

8*5

4-5

5-5

6-5

7-5

8-5

9-5

10-5

11-5

17387

1-20

1-53

1-37

0-93

0-90

1-15

1-20

1-14

1-25

1-19

1-06

1-14

1750-3

1-21

1-82

1-08

1-13

1-09

1-02

1*72

1-32

1-32

1-11

1-37

1-27

1761-5

0*93

o-97

1-01

1-35

1-47

1-08

0-79

0-73

0-92

1-03

1-23

1-55

1769-7

1-84

1-80

1-55

1-57

1-30

1-31

1-74

1*24

1-01

1-02

1-03

1-16

1778-4

1-19

1-15

1-41

1-07

1-24

1-34

1-23

1-22

0-84

1-08

1-47

1-57

1788-1

1-10

1-34

1-19

1-64

0-92

1-19

1-21

1-00

1-46

0-82

1-67

0-83

1804-2

1-32

1-41

1-54

1-38

1-22

1-52

1-15

1-32

1-30

0-96

0-98

1-44

1816-4

2-05

1-43

1-08

1-09

1-18

0*75

1-08

1-52

0-99

0-92

1-13

1-34

1829-9

1-10

1-25

1-36

0-93

0-88

1-19

1-06

0*88

0-91

1-23

1-85

1-83

1837 '2

1-60

1-15

1-55

1-17

1-56

1-06

1-05

1-23

1-40

1-54

1-43

1-20

4. In the following table the results of tables I. and II.
for both rivers are divided into two equal parts, the various
sums for these being given in the first four columns. In
the next four these sums have been somewhat equalised by
taking their sums in threes, while in the last four columns
departures from the mean as derived from the second four
columns are given.

Table III.

HEIGHTS OF RIVERS ELBE AND SEINE.

DEPARTURES.

ELBE. SEINE. ELBE. SEINE. ELBE. SEINE.

1st 6.

2nd 6.

1st 5.

2nd 5.

1st 6
equal-
ized.

2nd 6
equal-
ized.

1st 5
equal-
ized.

2nd 5
equal-
ized.

1st 6

2nd 6.

1st 5.

2nd 5.

16-66

13*94

6-37

717

50-42

40-09

20-33

20‘39

+0-85

+3-21

+1-84

+1-67

16-90

13-82

7-27

6-58

60-57

41-41

20-06

20-47

+1-00

+4-53

+1-57

+1-75

17-01

13-65

6-42

6-72

51-21

39-77

19-74

19-51

+1-64

+2-89

+1-25

+0-79

17*30

12-30

6-05

6-21

50-82

37-66

18-47

18-69

+1-25

+0-78

-0-02

-0-03

16-51

11-71

6-00

5-76

50-09

35-50

17-95

17-68

+0-52

-1-38

-0-54

-1-04

16-28

11-49

5-90

5-71

49-19

34-85

18-58

17-02

-0-38

-2-03

+0-09

-1-70

16-40

11-65

6-68

5-55

48-75

35-81

18-23

17-21

-0-82

-1-07

-0-26

-1-51

16-07

12-67

5-65

5-95

48-01

36-40

17-67

17-56

-1-56

-0-48

-0-82

-1-16

15-54

12-08

5-34

6-06

47-41

35-20

16-42

17-48

-2-16

-1-68

-2-07

-1-24

15-80

10-45

5-43

6-47

48-29

33-95

16-93

18-59

-1-28

-2-93

-1-56

-013

16-95

11-42

6-16

7-06

49-61

34-20

18-28

19-17

+0-04

-2-68

-0-21

+0-45

16-86

12-33

6-69

6-64

50-47

37-69

19-22

20-87

+0-90

+0-81

+0‘73

+2-15

* It was intended to make the recorded numbers correspond to the
divisions 0, 1, 2, &c., hut by an accident it was the above intervals which
were recorded. This does not affect the result obtained.

96

5. The departures shown in the last columns of table III.
are exhibited graphically in the diagram which accompanies
this paper. It will be noticed that in each of the four
curves there is a river maximum shortly after the maximum
of sun-spots, and that there are also traces of a subsidiary
maximum a good deal farther on, so that the curve gives
indications of a double as well as of a single period.

In conclusion I desire to express my thanks to Mr, Henry
Stroud for assistance rendered in this investigation.

97

Mr. Wilde exhibited two electro-motor machines for
illustrating the transmission of mechanical power by means
of electricity. He remarked that soon after the discovery
of electro-magnetism numerous attempts were made to turn
the principle to account for the production of motive power.
It was soon found, however, from experiments made by
Joule and others, that the expense of motive power derived
from the voltaic battery was so great as to render its use as
a substitute for the steam engine quite impracticable, and
the subsequent production by himself and others of power-
ful electric currents by the reverse action of steam power
and electro-magnetism, had served to confirm the convictions
previously formed as to the futility of all attempts to obtain
motive power economically from voltaic electricity in sub-
stitution of the power derived from steam. Fallacies re-
specting the economic production of electro-motive power
were nevertheless more prevalent than might commonly be
supposed, as the records of the Patent Office continually
showed; and a notable instance was brought before this
Society a few years since by an eminent telegraph inventor
who endeavoured to prove that the coal consumed in fur-
nishing the power required in Manchester factories would
be more economically employed in smelting zinc to be used
in voltaic batteries for the production of motive power than
in the generation of steam for the same purpose.

While the progress of electrical science had proved most
clearly that electricity could not compete successfully with
steam in point of economy, recent experiments had shown
that it might, in some cases, be utilised as a transmitter of
motive power to points at a considerable distance from the
prime mover.

There were no doubt many circumstances in which the
method might be used with advantage, but as the trans-
mission of mechanical power by electricity was attended by
a considerable loss of the original power employed, its appli-

98

cation would only be of value where the circumstances of
locality and distance prevented connexion with the prime
mover being made by ordinary mechanical means.

Ordinary Meeting, March 21st, 1882.

Dr. R. Angus Smith, F.RS., &c., in the Chair.

“Note on Envelopes and Singular Solutions, continued
from vol. XVII. p. 15,” by Sir James Cockle, F.RS.,
F.RA.S., Corresponding Member of the Society.

6. Lagrange ( Legons , 1806, p. 178) observes that singular
values had presented themselves almost at the birth of the
calculus ; but since the theory of arbitrary constants was
scarcely known at the time, these values were not regarded
as exceptions to general rules. He adds that Euler was the
first who looked at them in this point of view, and who
gave rules for distinguishing them from ordinary integrals.

7. I shall follow Lagrange, and ascribe to Euler the first
real recognition of singularity. So far as I know there is
no proof that by a singular solution Taylor meant more
than a solution obtained by differentiation.

8. In a letter to me, dated January 15th, 1867, Mr.
Robert Rawson announced two theorems, which I give in
a footnote.* I mention this, not as claiming priority for
Mr. Rawson, but as stating his views.

* « The condition of equal roots with respect to (C) in the com-

plete primitive <p (x, yt C)=0 is a singular solution.”

“(B)” “ The condition of equal roots of <p ( x , y, p) = 0 with respect to
p, is a singular solution if it satisfies the differential equation.”

Mr. Eawson adds that the usual infinity tests are consequences of the
condition, and that if the condition does not lead to a solution of a dif-
ferential equation it is because the equation has not been derived from a

99

9. Lagrange, in fact (ib. pp. 182—183), observes that
since the derived equation Y(a) = 0 contains the condition
which renders two of the roots of F(a?, y , a) = 0 equal, conse-
quently the singular value of y gives to the last equation a
double root.

10. Lagrange also remarks (ib. p. 219), that the singular
primitive of f(x, y, y) = 0 is obtained by the aid of the two
equations /(/) = 0, f(%, y) = 0 and the elimination of y ' by
means of the proposed equation. He adds that if the two
results give the same relation between x and y that rela-
tion will be the singular primitive ; if not, it will be a sign
that the proposed equation has no such primitive.

11. But f'(y) = 0 is the condition of the equality of two
of the roots of the given differential equation, treated as an
equation in y\

12. Mr. (now Prof) Cayley long ago stated that the
singular solution is the result of the elimination of the
arbitrary constant between the primitive and its derived
equation with respect to the constant (Q. J. of Math., 1860,
vol. III., p. 36 ; see also the Messenger of Math., N. S.,

complete primitive involving an arbitrary quantity of two or more dimen-
sions or that each of the roots requires a multiplier.

I take this opportunity of observing that in a letter to me, dated
August 20th, 1862, Mr. Eawson remarks that an equation deduced from
a cubic by one differentiation can be made linear by a proper assumption.
Such a linear equation I call a first linear resolvent.

I also remark that I have verified one of the results of Mr. Eawson’ s
recent paper [ante, p. 59). We may infer from what I proved years ago
(see Phil. Mag. for May, 1861), that every cubic in y has a second linear
resolvent of the form y" +vy' + y,y— M.

Hence, slightly generalizing the process given in my Second Chapter
on Coresolvents (Q. J. of Math., vol. VI., p, 226), we get
2y" +v'2y'+ ^y—S M
or, putting ~2y—a,

a" + vd/ + ya—SM.

and M vanishes with a. Next I find
v= — ^log(r u' — uv')

and, summing again, I, after easy reductions, verify Mr. Eawson’s
logarithmic coefficient. I have not calculated p, but the process is
applicable to p.

100

1874, vol. XXXVI., p. 179). The Rev. Robert Carmichael
has given a paper on Singular Solutions (Phil. Mag., 1858,
vol, XV., p. 522), on which I need not here comment.

13. Professor Cayley has also (see Messenger of Math,
for May, 1872, p. 6; for June, 1876, p. 23), given a new
theory of the whole subject which may be stated, not per-
haps with perfect fulness, as follows : The locus represented
by the discriminant, with respect to the arbitrary constant,
of the primitive is made up of the nodal locus twice, the
cuspidal locus three times, and the envelope locus once;
and the locus represented by the discriminant with respect
to p of the differential equation is made up of the envelope
locus, cuspidal locus and tac-locus, each of them once.

14. This theory of Professor Cayley’s seems to account
thoroughly for the extraneous factors which occur in the
processes for obtaining singular solutions.

14. Take a set of circles each of which touches both axes
of rectangular coordinates and apply the Cayley theory.
The primitive is (y - c)2 + (x- c )2 = c2, the c-discriminant is
- 2xy and xy = 0 is made up of the envelope-locus once, viz.,
x = 0 appears once and y = 0 appears once. The ^-discrimi-
nant is - 2 xy(x - y )2, which is made up of the envelope-locus
once and of the tac-locus. At first sight the tac-locus seems
to occur twice. But x - y is the bisector of the right angle
at which the axes meet, and there is external contact of
non-consecutive primitives at each end of that diameter of
any one of them which when produced passes through the
origin ; and I imagine that when the parameter gradually
varies each end of such a diameter must be held to trace a
distinct tac-locus, so that (x-yY = 0 gives each tac-locus
only once. If this be so then, generally, when two non-
consecutive primitives touch a primitive not consecutive
to either of them each point of contact must be held to give
rise to a distinct tac-locus, even when the path taken by
one such point is the same as that taken by the other.

2, Sandringham Gardens, Ealing,

Near London, W., March 16th, 1882.

101

MICROSCOPICAL AND NATURAL HISTORY SECTION.

February 13th, 1882.

Alfred Brothers, F.RA.S., President of the Section,
in the Chair.

" List of the Phanerogams of Key West, South Florida,
mostly observed there in March, 1872,” by J. Cosmo
Melvill, M.A., F.L.S.

The flora of this small island is limited, and naturally, to
a great extent, maritime. In the year 1875 I recorded in
the Journal of Botany a catalogue of the Algse — it is by no
means so rich, proportionately, in flowering plants or ferns.

Key West, which is entirely of coral formation, constitutes
one of many small reefs or ‘ keys’ which extend from Bis-
cayne Bay westward to the Tortugas. Of these islets, this,
which measures some seven miles in length, by one to one
and a half in breadth, is the only one inhabited, and it is
not likely that the others would present many botanical
novelties, though but few of them have been explored. Boca
Chica, the next island, is separated at low water by only
a very narrow channel. It is densely wooded, and the
character of the vegetation is entirely the same.

The south-western portion of Key West is cultivated, and
towards the south and south-east, between the town and
the sea, there are numerous green lanes and shady natural
avenues, extending for a mile or two, which present a native
flora of much beauty, though somewhat scanty in actual
species.

The northern shores of the island are swampy, and there
are extensive mangrove flats. It is in this portion that the
original ‘ scrub 5 forest still remains, and the north-eastern
shores especially present a deserted appearance*

102

Chapman, in his Flora of the Southern States, gives some
Key West localities, mainly on the authority of the late Dr.
Blodgett, and Grisebach (Flora of the British West Indian
Islands) in his ample tables of distribution of each species,
occasionally does the same. Mr. W. T. Feay, of Savannah,
Georgia, lived for a year or more on the island, and collected
several species I did not observe. These have been added
to this list, on his authority, to make it more complete.

In the Shuttleworth Herbarium, now incorporated with
that of the British Museum, there are several specimens of
Key West plants, mostly collected by Rugel.

Owing to Key West being a town of increasing import-
ance, as it is a military as well as a naval station, and also
a calling point for all the steamers plying between New
Orleans and Cuba, it is quite probable that the whole place
may in a few years be materially changed, and by the clear-
ing away of the old original £ bush 3 the flora may undergo
complete alteration.

It will be observed that the flora is completely Carribean,
and presents hardly any connection with that of the main-
land of Florida, with the exception of that small portion
south of the ‘Everglades.’

* denotes that the plant is not originally indigenous.

PAPAYERACEiE.

1. Argemone Mexicana (L.) native, according to Chapman, and

exceedingly abundant in most places.

Crucifers.

2. Lepidium Virginicum (L.). A more slender form than the

ordinary plant. Common.

3. GakiU AEqualis (If Her). Shifting sands of the south coast,

Key west. Differs from C. Maritima (L.) in the shape of

the upper fruit joint.

Capparidaceai.

4. * Gynandropsis pentaphylla (D.C.). Occasionally in waste

places.

Capparis Jamaicensis (Jay). Rare (Mr. Feay).

103

6. Capparis Cynophallophora (L.). Occasional (Mr. Feay).

PORTULACACEiE.

7. Portulaca oleracta (L.). Everywhere, especially on paths and

clearings in the bush. Flower yellow.

8. Portulaca pilosa (L.) Rare. Flowers purple.

Malvacej:.

9. Sida rhombifolia (L.). Everywhere, in many forms.

10. Sida stipulata (Cav.) ,, „

[I did not observe S. ciliaris (Car.) and S. Lindheimeri (Gray)
noted in Chapman’s Flora, p. 55, as occurring at Key West.]

11. Abutilon crispum (Gray). Not common.

12. Hibiscus Floridanus (Shuttl).

13. Hibiscus Rosa Sinensis (L.). Escape from cultivation.

14 *Gossypium Barbadense (L.). Large shrubs occur towards the
Lighthouse, S.W. corner of Key West.

[Ayenia pusilla (W.) nat. ord. Byttneriaceae has occurred.]
Tillages.

15. Corchorus Siliquosus (L.).

Olacace^j.

16. Ximenia Americana (L.). (Mr. W. T. Feay),

AuRANTXACEiE.

Yl*Citrus Aurantium (L.), Very abundant in the S.W. quarter
of the island, though no doubt originally imported.
Meliace^:.

18 *Melia Azederach (L.). The Pride of India is planted in nearly
all villages and towns in Florida.

OxALIDACEiE.

19. Oxalis stricta (L.). Everywhere.

Z Y GOPH YLLACEiE.

20. Tribulus cistoides (L.). Superficially resembling Potentilla

anserina (L.).

[Kallstromia maxima, Torrey and Gray, was not observed, though
it has occurred at Key West].

21. Guiacum sanctum (L.). S. portion of the island, not common.

RUTACEyE.

22. Zantlioxylum Pterota (H.B. & K.). Fagara lentiscifolia (W.).

One of the most abundant shrubs of the island, but impos-
sible to preserve for herbarium purposes, as the joints of the
petiole disintegrate immediately when dry.

104

SlMARUBACEiE.

23. Simaruba glauca. (D.C.) One of the most conspicuous trees of

the island, with large and handsome pinnate leaves, and
panicles of small green flowers.

Burserace^j.

24. Bur sera gummifera. (Jay.) A large tree (Mr. F6ay).

25. Amy r is Floridanus. (Nutt.)

Anacardiace^j.

26. Rhus Metopinm . (L.) A good sized tree ; common.

VlTACEiE.

27. Vitis (Cissus) acida. L, Not uncommon in the S.W. portion

of the island. It disintegrates in drying, as Z. Pterota.
Khamnace,®.

28. Scutia ferrea. (Brong.) (Mr. W. T. Feay.) = (Condalia) (Cav.)

29. Gouania Domingensis. (L.) Common.

CELASTRACEiE.

30. Schoefferia frutescens. (Jacq.) Abundant.

31. Maytenus phyllanthoides. (Benth.) Leaves very fleshy. Com-

mon in salt marshes.

Leguminos.®.

32. Indigofer a leptosepala. (Nutt.) (Mr. W. Feay.)

33. Galactia spiciformis. (Torr and Gray.) Common.

34. Piscidia erythrina. (L.) The Jamaica Dogwood. Not common,

35. Cassia occidentals (L.). Waste places-.

36. Cassia biflora (L.).

37. *Parkinsonia aculeata (L.). Not mentioned in Chapman’s

Flora, and possibly a recent introduction, but I obtained
it from a remote quarter of the island, where was no culti-
vation. It is a remarkably elegant tree, with spikes of
orange yellow flowers.

37 a. * Tamar indus indicus (L.). Quite naturalized and common.

38. "Poinciana pulcherrima (L.). Near the town of Key West.

Now referred by most authors to the genus Caesalpinia.

39. Pithecolobium ' Unguis Cati (Benth). Very abundant by the

sea in the south portion of the island.

40. Pithecolobium Guadalupense (Desv.). Not so frequent as the

last, of which it is probably a variety.

105

41. * Acacia (Albizzia) Julibrizzin (W.). Not unfrequent, naturalized.

42 . * Acacia ( Vachellia ) Farnesiana (W.). This is almost the most

abundant shrub in the western portion of the island. Not
being mentioned in Chapman’s Flora must surely be an
error.

43. Desmanthus diffiusus (Willd). North shore of Key West.

A prostrate form.

44. Guillandina Bonducella (L.), Very abundant on sandy ground

near the South Fort. Not recorded in Chapman’s Flora,
though apparently wild.

MYRTACEiE.

45. Eugenia Monticola. (D. C.) Abundant throughout the island.

46. „ buxifolia. (Willd.) „ „ „

47. „ procera . (Poir.) „ „ „

48. Galyptranthes Chytraculia. (Swartz.) Not uncommon.

Khizophoraceje.

49. Rhizophora Mangle. (L.) Mangrove. With Avicennia oblongi-

folia on the north shore of Key West.

CoMBRETACEiE.

• VV.'v > - / >

50. Gonocarpus erecta. (Jacq). On sand by the S. shorer. Leaves

remarkably white and silky.

51. Terminalia Gatappa. (L.) Very abundant.

52. Laguncularia racemosa (Great). North shore. (Mr. W. T. Feay.)

Cactace^:.

53. Gereus monoclonos. (D. C.) Very conspicuous from its tall,

column-like stems, 10 to 12 feet high. It is used, with
Agave Americana and Opuntia polyantha, for hedges, and
the three form an impenetrable barrier.

54. Opuntia vulgaris (L.) var. polyantha. Abundant everywhere.

P ASSIFLORACEiE.

55. Passiflora angustifolia. (Sw.) Not common. (Mr. Feay.)

CuOURBITACEiE.

56. /S icy os angulatus. (L.)

. Crassulace^;.

57 *Bryophyllum calycinum. (L.) Very abundant. Not included
in Chapman’s Flora.

106

SURIANACEJE.

58. Suriana Maritima (L.). Very abundant on the south shores

of the island.

Rubiace.®.

59. Spermacoce tenuior (L.). Common in waste places.

60. Ernodea littoralis (S.W.) Not uncommon ; flowers sweet-

scented.

61. Morinda Roioc (L.).

62. Chiococca racemosa (Jacq).

63. Hamelia patens (Jacq). A very handsome shrub, with scarlet

flowers. Western shores of the Island.

64. Randia aculeata (L.). (Mr. W. T. Feay.)

65. Exostemma Caribbceum (R. & 3.). (Mr. W. T. Feay.)
[Erithalis fruticosa (L.) has been found also at Key West.]
[Guettarda elliptica (S.W.) Key West, Riigel in Herb. Shuttle-

worth, Mus. Brit.]

Composite.

66. Goelestina maritima (Torr & Gray). [Ageratum L.] South

shores of Key West. Abundant.

67. Rarthenium Hysterophorus (L.). By roadsides very abundant.

68. Iva imbricata (Walt.). Sandy shores.

69. Ambrosia Crithmifolia (D. C.). Very abundant along the

southern shores.

70. Eorrichia arbor escens (D. C.). Salt marshes, abundant.

70a. Borrichia frutescens (D.L.). Not so common as the last.

[Cosmos caudatus (Kunth.) occurs at Key West, but was not
observed.]

71. Bidens leucantha (Willd.), a common tropical weed.

72. Pluchea purpurascens (D. C.), very common.

73. * Verbesina ( Ximenesia ) encelioides (D. C.). Abundant. Not

included in Chapman’s Flora.

74. Flaveria linearis (Jay). Common.

75. Sonchus oleraceus (L.). Southern shores of Key West.

SAPOTACEiE.

76. Mimusops Sieberi (A. D. C.)„ ( = M. dissecta (R. Br.). Very

abundant. A handsome tree. South shores of Key West.
Theophrastace^:.

77. Jacquinia ar miliar is (Jacq). (Mr. W. T. F£ay).

107

Myrsinacej:.

78. Ardisia Pickeringia (Torr and Gray). A fine shrub, or small

tree, flowering conspicuously in March.

Plumbaginacejs.

79. Plumbago scandens (L.). Amongst Opuntia, in dry, 'stony

places, very abundant. Flowers white.

Bignoniace^.

80. Tecoma stans (Jussieu). Rare, flowers very large, golden

yellow.

SCROPHULARIACEiE.

81. Herpestis peduncular is { Beuth). Not uncommon, flowers small

yellow. Turns quite black in drying, in common with most
members of this family.

82. Caprariabiflora { L.). Very common. Flowers varying from

rose pink to white.

ACANTHACEvE.

83. DipteracantJms linearis (Torr and Gray.)

84. Dicliptera assurgens (Juss) = D. sexangularis (L). S.W. of

Key West, among cacti; flowers scarlet.

VERBENACEiE.

85. Priva echinata (Juss).

86. Stachytarpheta Jamaicensis . (Yahl.) Exceedingly abundant

all round the coast, the flowers bright blue in linear spikes.

87. Lippia (. Zapania ) nodiflora (Michx). Very common.

88. Lantana involucrata (L.) var. Floridana. The most frequent

shrub on the island. Chapman (Flora S. States, p. 308)
queries the colour of the corolla. It is white with a
purplish tinge in the tube.

89. Citfiarexylum villosum (L.)

90. Avicennia oblongifolia (Nutt). Common with the mangrove in

swamps.

Labiate.

91. Ocimum Campeachianum. (Mill.) Abundant, flowering in

January and February.

92. Salvia serotina (L.) Abundant.

93. Leonotis nepetcefolia. (R. Br.) Rare in the S.W. portion of

the island.

108

Boreaginace^i.

94. Cor did bullata (L.). Bare. (Mr. W. T. Feay.)

95*Cordia Sebestena (L.) Probably not native. Near the town
of Key West.

90. Ehretia Buerreria (L.). In the N. part of the island, but not
common.

97. Ehretia tomentosa (G. Don.), var. Havanensis (W.). Very

rare; one bush only observed, the central part of the
island ; not in Chapman’s Flora , though Grisebach men-
tions its occurrence.

98. Tournefortia Gnaphalodes (B. Br.). By the sea shore, very

abundant.

99. Gnaphalodes volubilis (L.). Climbing up trees in the N. por-

tion of the island.

100. Heliotropium Curassavicum (L.). Salt marshes, common.

101. Heliotropium myosotoides (Chapman).

102. Heliophytum parvijlorum (D.C.). Abundant.

CONVOLVULACEiG.

103. Pharbitis hispida (Chois.). Very abundant as a climber in

the N. portion of the island, flowers deep purple blue, very
showy.

104. Ipomoea Pes-Caprw (Sweet). Western and southern shores

of the island, very common.

105. Ipomoea sagittifolia (B.B.). (Mr. W. T. Feay.) Bare.

106. Ipomoea triloba (L.). Not frequent.

107. Ipomoea Bona nox (L.). Abundant but local, flowering in the

evening. One of the most beautiful climbing plants known,
its pure white corolla being salver-shaped, and perfectly
flat, the tube being extremely long, and pale greenish
white. The flower fades at dawn.

108. Jacquemontia violacea (Chois.). Flowers small, sky blue.

Twining over shrubs, principally Lantana, common in the
South portion of Key West.

109. Dichondra repens (Forst).

SOLANACEiE

110. Eoldnum nigrum (L.)a A small-leaved form.

109

111. Solanum verbascifolium (L.) A tall shrubby plant with heavy

leaves and white flowers. Very common in the S.W. region.

112. Solanum Bahamense (L.).

113. Solanum Blodgettii (Chapman).

114. * Solanum Lycopersicum ( L.). Tomato. Waste places.

115. Capsicum frutescens (L.). Not uncommon.

116. Physalis pubescens (L. ) ,

117. Physalis angulata (L.).

118. Lycium Carolinianum (Nichaux). Abundant in the salt

marshes.

119 . * Oestrum fastigiatum (Jacq.) Very common all round the S.W.

portion of the island. Not included in Chapman’s Flora.

120. Batura Tatula (W.). A weed.

Gentian aceas.

121. Eustoma exaltatum (Griseb). By the battery, north shore.

3 feet high, flowers very dark blue. A very beautiful plant.
APOCYN ACEiE.

122. Echites umbellata (Jacq.). Not uncommon.

123. Echites Andrewsii (Chapman). (Mr. W. T. F£ay). Bare.

124. Vinca Rosea. (L.) All round the island; in waste places

with Bicinus, Ambrosia, and Argemone Mexicana.

125. Vallesia chiocco'ides (Kunth.) = V, glabra (Cav.) Very rare ;

only one shrub observed.

126 . *T7ievetia neriifolia (Juss) = Cerbera Thevetia. (L.) Natural-

ised near the town. Exceedingly poisonous, c.f. Kingsley’s
1 At Last’ for a description.

Asclepiadee.

127. Asclepias Curassavica. (L.) Waste places.

128. Metastelma Schlectendalii. (Dec.) A twining creeper.

129. Seutera maritima. (Reich). By the salt pans. Very abun-

dant in one place only.

130. Cynoctonum scoparium. (Meyer.)

131. Sarcostemma crassifolium. (Dur.) (Mr. W. T. Feay.)

Nyctaginee.

132 *Mirabilis Jalapa. (L.) In one place towards the N. shore;

very likely an outcast from cultivation.

133, Boerhaavia viscosa. (Lag.) Common.

110

134 Pisonia aculeata . (L.) Extremely abundant, its greenish
flowers proving very attractive to insect life. The thorns
on the branches and the recurved spines of the fruit are
great impediments to comfort in the “ bush.”
Phytolaccace^j.

135. Rivina humilis (L.). Common, and striking from its scarlet

fruit.

136. * Phytolacca decandra (L.). Occasionally on waste ground.

Adv. from the Southern States of America.

Chen opodi ace^e.

137. * Chenopodum Anthelminticum (L.). Naturalized from the

States, one plant.

138. Obione arenaria (Moquin).

139. Chenopodina maritima (Moquin).

140. Salicornia ambigua (Michaux). By the salt pans, with the

preceding.

Amarantace2e.

141. Celosia panicidata ( L.). W. shore. Common.

142 . %Amarantus hybridus (L.). Adv. from U.S.A.

143 *Amarantus albus (L.). Adv. from U.S.A.

144. Amaranlus spinosus (L.).

145. Iresine vermicularis (Mogim).

146. Alternanthera Achyrantha (R. Br.).

147. Tdanthcra Floridana (Chapman).

PoLYGONACEiE.

148. Goccoloba uvifera (Jay). S. shores. Common. ‘The Sea

Grape.’

Euphorbiace^.

149. Euphorbia cyathophora (Jay) var. graminifolia (Michx.) =

E. heterophylla (L.). Abundant in many places. Easily
recognized by the uppermost leaves being deep scarlet at
the base, and bearing therefore some slight resemblance to
a small and narrow-leaved Poinsettia.

150. Euphorbia glabella (Swartz).

151. Euphorbia liypericifolia (L.). Sea shore, in sand, common.

152. Euphorbia maculata (L.). Abundant in paths and everywhere.

153. Euphorbia inceguilatera (Sond).

Ill

154. Hippomane Mancindla (L.). (Mr. W. T. Feay.)

155. A calypha corckorifolia (Willd.).

156. Croton balsamiferum (Willd.). Very common in the south

portion of the island only.

157. Aphora Blodgettii (Torrey.). (Mr. W. T. Feay.)

158 *Bicinus communis (L.). Everywhere.

Batidaoeai.

159. Batis maritima (L.) Salt marshes.

XJrTICACE/E.

160. Pilea hernarioides (Lindley). Very abundant ; a very small,

fragile plant.

Palma; .

161 *Cocos nucifera (L.). Naturalized in the northern portion of
the island ; common. The True Cocoanut Palm.
POTOMACEAl.

162. Halophila ovalis (Hook), or allied sp. Quite fresh specimens

floating in sea, after gale, 15th March, 1872.

AlismaceII

162a .Echinocarpus radiatus (L.) Around a small pond in the
interior of the Island.

Orchidacea:.

163. Epidendrum venosum (Lindley.) N. part of the island, on

trees (Mr. W. T. F4ay).

Amaryllidacea:.

164 * Agave Americana, (L.) Forming impenetrable hedges in the
N. portion of the island.

Bromeliacea:.

165. Tillandsia bulbosa (Hooker). (Mr. W. T. Feay.)

1 §§,*Ananassa sativa (Lindley). Occasionally escapes from culti-
vation.

Musacea;.

167. "' Musa sapientum. (L.) The Banana is extensively planted,

and is sometimes found apparently naturalized.

168. *2/. Paradisiaca. (L.) Ditto.

Cyperace^:.

Of this order I found 5 species of Cyperus, including
C. Confertus (S.W.) and C. fuligineus (Chapm.), the others

112

not yet determined, as they are in fragmentary condition,
and also an Eleocharis, sp. incert.

Of Graminese about 10 to 12 specimens, including Era-
grastis ciliaris (Link.) ; Panicum, 2 species ; the abundant
Dactyloctenium iEgyptiacum (Willd.) and Eleusine Indica
(Ggertn.) and Cenchrus tribuloi'des (L.). The curious creep-
ing Monanthochloe littoralis (Englemann) also occurred on
the southern sandy shores.

Only one Fern, that being Aspidium patens (Sw.), but
Mr. Fday noted Acrostichum aureum (L.) and Anemia
adiantifolia (L.) as well.

A Chara occurred plentifully in a pond toward the
south portion of the island.

Dr. Alcock read some notes on Frog Tadpoles, illustrated
by drawings. He said the life of the tadpole may be divided
into periods, each characterised by the developments which
take place in it. He described the first and second periods,
leaving the remainder to be treated of in a future paper.

The first period extends from the deposition of the ovum
to the escape of the young tadpole from the egg membrane.
In our climate this occupies about a fortnight, the first week
being spent in the segmentation of the yolk, the second in
the development of the embryo. In a mass of frog spawn,
however, the ova on the surface hatch first, and are followed
by the others in succession to the centre of the mass, so
that there is a difference of about a week between the
earliest and the latest. The structures which have been
developed when the embryo escapes from the egg are the
cerebro-spinal axis and its supporting skeleton, with the
continuation of these structures in the tail, the enclosing
body- wall, rudimentary organs of sense, the visceral arches,
the oral aperture and the cavity of the mouth, the heart,
and the blood vessels of the developing parts ; but the cavity
of the abdomen remains filled with undifferentiated yolk-

113

#

mass, and no commencement of the organs which it after-
wards contains is yet made. Two other organs, however,
have been formed, the use of which is temporary, and
confined to the second period ; these are the sucker and the
external gills, and they are already so far developed as to
be perfectly efficient when the tadpole escapes. The sucker
is at first large and single, extending across the middle line,
and it is in this condition when the animal is hatched. The
external gills, two on each side, have attained such a size as
to serve at once as organs of respiration.

The second period extends from the time of hatching to
the completion of the mouth and alimentary canal, and the
commencement of feeding ; it, like the first period, occupies
about a fortnight. The special temporary organs now in
use are the sucker, which soon divides into two, and the
external gills. The developments which take place are
those of the bronchial arches and clefts ; the internal gills ;
the eyes; the gill-chambers, formed by the opercular fold,
which begins to grow on the second day and is completed
on the fourteenth; the passages of the nostrils to the back
of the mouth, these being in connection with the internal
gills, the ciliary action of which draws water through them ;
and the suctorial, beaked mouth and coiled alimentary canal,
peculiar to the tadpole.

This second period is a continuation of the embryonic
condition ; contact with water and aquatic respiration are
necessary for further development, but rest is also required,
and the animal continues as stationary as whilst in the egg. It
is blind and helpless, and cannot feed, having no alimentary
canal. Immediately on its escape the tail is used, but only
to swim to some fixed object to wiiich it attaches itself by
its sucker, and there it remains till the close of the period,
unless forcibly detached, when it at once refixes itself.

The suckers, though efficient almost to the end of the
period, daily diminish in size and have disappeared at its

114

close. The external gills attain their full size on the second
day, after which they gradually shrink, but continue in
action about a week, soon after which what remains of them
disappears within the opercular fold. The organs which are
developed during this period are all completed at about the
same time, that is, very nearly at its close. The eyes and
nostrils progress regularly from the time of hatching, but
with regard to the internal gills and the alimentary canal,
it appears that the former are commenced first and are
probably in use about the fifth or sixth day in conjunction
with the external gills, gradually increasing in efficiency as
the latter diminish in size, but the complete apparatus for
the tadpole respiration is not perfected until the opercular
fold has joined the skin of the abdomen, leaving only a
small opening at the left side, and until, in conjunction with
the chambers thus formed, the nasal passages are opened
into the back of the mouth. The development of the
peculiar tadpole mouth and the enlargement of the abdomen,
indicating the formation of the coiled intestine, commences
only when the gill-chambers are complete, and these struc-
tures are formed and brought into use within the last
three days of the period ; during which time also the tadpole
becomes beautiful with spangles exactly resembling bits of
gold leaf embedded in the rich brown transparent skin.

115

Ordinary Meeting, April 4th, 1882.

R. Angus Smith, Ph.t)., LL.D., F.RS., &c., in the Chair.

“ On the Occurrence of Oxide of Manganese (Wad) in the
Yoredale Rocks of East Cheshire,” by Arthur Smith
Woodward, Student of Owens College. Communicated by
Dr. Charles A. Burghardt.

I. — Introduction.

One of the most noticeable geological features of the
eastern part of Cheshire is the enormous fracture forming
the boundary between the carboniferous and new red sand-
stone formations, and known as the Red Rock Fault. This
fault has a direction N.E. and S.W., and, according to the
Memoirs of the Geological Survey, extends from a little to
the N. of Stockport to Talk o’ th’ Hill, in Staffordshire, a
distance of about 80 miles. In the more northern part of
its course superficial evidence of its existence is either ex-
ceedingly scanty or entirely wanting, owing to the thickness
of the glacial drift deposits which characterise the district
through which it passes ; but as it approaches Macclesfield
there are slight indications at the surface of its presence,
and as it continues south of this town the superficial evidence
gradually becomes greater and more definite. Here there
are considerable eminences on the western side of it, con-
sisting of triassic strata not obscured by glacial drift, and
hence the fault itself becomes visible at the surface.

Between Poynton and a locality about three miles south of
Macclesfield it is bounded on its eastern side by the carboni-
ferous formations in succession, — the two lower divisions
of the coal measures being most northern, next five divisions
of the millstone grits, and below these, more to the south, the

Proceedings — Lit. & Phil* Soc.— Vol. XXI.— No. 9.— Session 1881-2.

Yoredale Rocks, — and it is in the latter rocks that the
greatest amount of disturbance has arisen from it, in conse-
quence of the fact that they are constituted not of thick,
compact masses of sandstone, but of comparatively thin
beds alternating with bands of shale. In this locality, in
and around Ratcliffe Wood, there is a large number of
sections, both natural and artificial, extending for several
hundred yards to the eastern side of the fault, and after
examining them and taking note of the dip in each case, it
is easily seen that the greatest confusion exists among the
strata; small faults are very numerous, and often prove
themselves to be great obstacles to the quarrying operations
there carried on ; and contortions of the beds, varying from
only two or three feet to several yards in extent, abound in
all directions. It is in the fissures produced by the disturb-
ance of the beds in this locality that the mineral which I
intend to describe in this paper is found.

II. — Description of Section.

The quarrying at Ratcliffe Wood is carried on chiefly in
tunnels, formed by the excavation of the beds of rock which
are best adapted for the purposes to which the stone is
applied, namely, repairing and making roads. Some months
ago the quarrymen met with a fault, which cut off the bed of
rock that they were following, and in attempting to find again
this lost stratum on the other side of the hill they opened a
section nearer to the Red Rock Fault; and it was here that I
first noticed the oxide of manganese, early in December last.

This is the nearest section to the fault now exposed in
that locality — with the exception of comparatively unim-
portant exposures in the brooks running through the wood —
and is probably not more than 30 or 40 yards from it. As
this is a very interesting section, apart from its mineral
characteristics, since it shows the effect of the force exerted
during the production of the great fault, a somewhat brief
description of it may, perhaps, be not out of place at this point,

The principal opening is about 30 feet in length and 20
feet in height, but from the other small sections around it,
many more details of the stratification can be obtained.
The direction of all these sections is nearly at right angles
to the fault, namely, E. and W.

The lowest bed exposed consists of variegated soft shale,
in small flakes (dip 59° — 10° E. of N.) ; above this is a
stratum of sandstone, 5 feet in thickness, containing
abundance of Mn02 in the many fissures which traverse it,
and it is a noticeable fact, that in the lower portion of the
section there is a larger quantity of the mineral than in the
upper portion; next is a bed of variegated soft shale, 7 feet
in thickness, in flakes, and similar in nature to the bed
underlying the sandstone previously mentioned ; the
remainder of the section consists of alternating bands of
shale and sandstone, much broken and contorted, and 14
feet thick, which gradually become more and more
bent until they reach a position nearly five feet above
the underlying bed of shale, when a stratum of sandstone, 8
inches thick, undergoes three decided bends — in one case, a
complete break. This sandstone, like all the other beds in
the section, has been shattered into small angular fragments,
and into the cracks thus formed mineral matter has been
introduced by the percolation of water. Many of the
smaller fragments have again been cemented together by
oxide of iron, as the cracks surrounding them had not
separated the adjoining portions of rock far asunder, while
the walls of the larger fissures are only coated with oxide of
iron and argillaceous matter, or, in the upper part of the
section, with oxide of manganese, and are not firmly united
together.

Above this contorted bed of sandstone, the alternating
layers of rock are similarly disturbed for a thickness of about
7 feet, when the arrangement of the beds becomes very obscure,
and a little above this the series assumes a nearly vertical dip,

118

The general appearance of the section shows that the
contortions of the series have been produced by a slip, most
probably at the time when the Red Rock Fault was formed.
This is evident not only from the disturbed beds lying
between two series, which have been very little bent, but
a]so from the peculiar appearance of the layer of shale
beneath, and the confused mass of broken sandstone above.
In the underlying shale there are two or three very thin
seams of carbonaceous matter, which are rendered rather
conspicuous by their dark colour ; these are curiously con-
torted, having been completely twisted in no less than four
places, the interior of the folds being occupied by confused
masses of variously coloured crushed shale.

III. — Occurrence and Properties of the MnCh.

The most typical specimens of oxide of manganese (wad)
are to be obtained from the fissures in the lower bed of
sandstone in the section just described. Here it occurs in
considerable quantity, and is in a very accessible place.
The walls of the cavities produced by the fissuring of the
rock are covered with a layer of the mineral, never more
than \ inch in thickness, which is not at all smooth on the
exterior, but has the appearance of soot adhering to the side
of a chimney ; this form is caused by a pellet -like structure
assumed by the substance. The layer appears to cover all
the walls of the cavities equally, not becoming perceptibly
thicker on the lower sides, and not altering in appearance
in different parts.

But the most peculiar and characteristic feature of the
wad in this sandstone is its occurrence in miniature columns,
joining the two opposite walls of the cavities, and in long
slender threads, stretching in all directions over the rough
surface of the mineral-incrustation. So far as I have been
able to ascertain, none of these columns or threads are
perfectly solid but are all pierced longitudinally by a canal,
which is often situated not quite in the centre; in some

119

cases this is so large that the surrounding oxide of man-
ganese becomes very thin and a delicate tube is formed,
while in many specimens the calibre is so small that the
perforation can only be seen on close examination. The
columns and threads are not all straight, but many are bent
in various directions and not unfrequently branched — the
axial canals in all cases being preserved throughout the
bifurcations.

These interesting structures in external appearance are
rough and dull, but cross-sections exhibit a very distinct
resinous lustre. The size of the columns is not great, their
diameter never exceeding Jth of an inch, and their length
being seldom much more than one inch ; the tubular threads
are sometimes four or five inches long, but their diameter
is very much less than that of the columns, few of them
having a section greater than -2V inch across.

To account for the formation of these columns and threads
appears, at first sight, a somewhat difficult matter, but after
carefully taking into consideration the position of the mine-
ral and the nature of its surroundings, an explanation is
afforded which has been definitely proved to be correct by
Mr. Dale, of Macclesfield.

The position which the greater part of the oxide of man-
ganese occupies is about 14 feet from the surface, a depth
to which the roots and rootlets of the surrounding wood are
able to penetrate by means of the numerous cracks in the
strata. Rootlets are to be seen in the fissures in many parts
of the section, and in those which are lined with oxide of
manganese they are especially abundant. They stretch
across the cavities, and traverse the surface of the black
mineral in all directions ; and after closely searching for
some time, it is possible to find specimens to illustrate all
stages of the conversion of these organic bodies into columns
and threads of oxide of manganese.

Many of the rootlets, probably in their first stages of de-

120

composition, have assumed a reddish or unnatural brownish
colour ; others, in a later stage, exhibit minute patches of
the black oxide studding their surface, appearing as if
affected by a black mildew ; others are almost entirely
covered with the incrusting mineral ; while, in the final
stage, the whole of the organic matter has disappeared. In
short, the rootlets are completely pseudomorphosed into
hydrated dioxide of manganese by the action of the decom-
posing plant tissue upon a solution of some manganese salt.

These facts are interesting as showing that the deposition
of oxide of manganese is still taking place, or, at least, did
take place until the section was opened. There is now
no perceptible percolating water, even in the most rainy
weather, but the mineral is at all times moist.

With regard to these oxide of manganese pseudomorphs,
it appears that very few cases of the alteration of organic mat-
ter into this mineral have been recorded. This oxide is not
mentioned in Phillips’ Mineralogy,* in the list of minerals
said to occur as petrifactions, but is referred to in the
“Erster Nachtrag zu den Pseudomorphosen,” by Blum.
Wiser has described a fossil consisting of black oxide of
manganese, which he stated, in 184 2/ f to be the first in-
stance on record of this mineral occurring in a petrifaction ;
and again, in 185 1 ,|| he mentioned a fragment of an Am-
monite from Gonzen, near Sargans (Switzerland), which was
fossilized in the same manner. Neither of these cases, how-
ever, can be regarded as quite similar to the pseudomorphism
of the rootlets, since it was not the truly organic matter
that was mineralised, but the surrounding chiefly-inorganic
shell.

The mineral itself, as found in the bed of rock in the
section at Ratcliffe Wood already described, is of a bluish-
black colour when freshly obtained, but assumes a browner

* Edit. Brooke & Miller, 1852.
f Jahrbuch fur Mineralogie, &c. || Ibid.

121

tint on exposure : its hardness is less than 1. It is easily
crushed into powder between the fingers, and has a
characteristic crispness. When heated in a closed tube
water is evolved, and under the blowpipe it is infusible.
Its streak is of a dark yellowish -brown colour.

A quantitative analysis of the mineral gave the following
as its percentage composition : —

Mn02 = 33-634
Fe203= 9-375
A1203 = 22-913
Si02= 16*815
Water = 17-237

99-974

This analysis probably does not show the exact composition
of the pure mineral, since it is almost impossible to obtain
a sufficient quantity entirely free from the surrounding
argillaceous matter.

IY. — Distribution of Mn02 in Ratcliffe Wood.

So far as I am yet aware, there is only one other spot in
Ratcliffe Wood where oxide of manganese is to be seen
occurring in the same form as the mineral in the section
previously described. This is a few hundred yards to the
east of the latter, and the deposit exhibits not only the same
peculiarities but others which render it even more in-
teresting. Here, as in the previously mentioned case, the
mineral occurs both as an incrustation and pseudomorphic
after rootlets ; but it is also in many parts covered with a
thin layer of a white, translucent, crystalline mineral — a
highly hydrated phosphate of alumina with a proportion of
silicate — which, besides, mineralizes rootlets in an analogous
manner to the oxide of manganese.

In this same section, too, there is exposed a lenticular
mass, 4ft. 6in. long and Sin. in greatest thickness, which
is black, earthy, and moist, and evolves chlorine on treat-

122

ment with hydrochloric acid. It is situated in the midst
of shales, and most of the small fissures for some distance
beneath it are filled with black oxide of manganese.

The oxide of manganese occurs in many other fissures in
and around Ratcliffe Wood, but nowhere so abundantly as
in the sections referred to. in this paper. The most widely
spread form is a thin black film, not sufficiently thick to
exhibit to the unassisted eye any pellet-like structure, as is
the case with the mineral described above. Such a film is
to be seen in some of the fissures in almost every section in
the wood, and the fact that the oxide does not occur in
larger quantities cannot be owing to the circumstance that
there are no cracks exposed so large as those in which it is
found in pellets, miniature columns, and threads, but in
consequence of its scarcity in the stratum from whence it
was derived ; for in one quarry there are two faults which
produce cavities and fissures of a much larger size, and yet
these are well filled with brown iron ore with a com-
paratively small amount of MnOa.

In the Triassic strata, on the E. side of the Red Rock
Fault, this mineral occurs not only as an infiltration-product,
but also as a part of the cementing material of certain thin
beds of the sandstone.

V. — References to Descriptions of Deposits of Hydrated

Mn02.

On referring to Bisch off’s “Chemical Geology”* an
enumeration of instances recorded before 1854 of the
occurrence of deposits of hydrated oxide of manganese is to
be found. Here no less than six cases are mentioned.

During the repair in 1840f of a water channel hewn
in the rock in the neighbourhood of Nurnberg, an immense
mass of hydrated oxide of manganese was discovered. A
spring near the Cape of Good Hope, whose waters have a
temperature of 110°F., is said to deposit in the discharge

* Yol. I., pp. 160, 161, Edit. 1854. f Journal fur prakt. Chem., Yol. 21.

123

channel a very thick incrustation of the same mineral,
extending to some distance from the spring * A mineral
spring at Carlsbad, depositing a mass resembling manganite,
has been described by Kersten. Braconnet examined and
described in 1821 f a precipitate of oxide of manganese
found in the outlets of the springs of Lnxeuil. A deposit of
the same mineral from the water in a mine at Freiberg has
been analysed by Kersten and described in the “Archives
fiir Mineralogie, &c.” (Vol. 16), and in this journal, also,
Nogerrath has given an account of the nature and occurrence
of the manganese ores in the Hundsruck, and in Soonwald,
on the left bank of the Rhine.

VI. — Associated Minerals.

The most important minerals associated with the oxide of
manganese in the strata of Ratcliffe Wood, besides the
phosphate of alumina already mentioned, are brown iron ore,
calc spar, pearl spar, iron pyrites, and zinc blende. The
brown iron ore occurs in thin incrustations, in fibrous
stalactitic masses, and in hollow spheres which have,
especially on the inner side, a very peculiar lustre. The
calcite occurs in a crystalline state in small fissures in
almost every section, and is found crystallized occasionally
in the form — JR. and the combination — J R. 16R. The
pearl spar occurs in many fissures beautifully crystallized
in the form — JR; it is tinged with oxide of iron, and the
crystal faces are bent in the characteristic manner. Iron
pyrites occurs abundantly, often perfectly crystallized ; and
zinc blende is found in small masses scattered among the
crystals of calcite and pearl spar.

VII. — Conclusion.

Oxide of manganese occurs in many places in the other
Yoredale strata of the district, but nearly always in very
small quantities. It also occurs widely spread throughout
the overlying Millstone Grits; in these strata it forms

# L’Institut, 1844. f Ann. de Chim. et de Phys., 1821.

124

dendritic markings radiating from the fissures in the rock,
and constitutes a portion of the cementing material in many
of the concretions.

In the sandstones of the coal measures, also, oxide of
manganese forms part of the cementing material in many
of the concretionary structures.

In fact, careful observations would probably show that
oxide of manganese is quite as widely distributed as oxide
of iron, the only difference being that the former mineral
generally occurs in defined patches and in comparatively
small quantities. The distributing causes seem to have
acted as universally with the one mineral as with the other,
but in the case of the manganese only small amounts were
concerned, while in the case of the iron there was an almost
unlimited supply.

125

MICROSCOPICAL AND NATURAL HISTORY SECTION.

March 13th, 1882.

Alfred Brothers, F.R.A.S., President of the Section,
in the Chair.

Mr. Theodore Sington, of Victoria Road, Rusholme, was
elected an Associate of the Section.

Mr. Marcus M. Hartog, B.Sc., F.L.S., made a communi-
cation upon Water Fleas.

“On Cyproea Guttata (Gmel.),” by J. Cosmo Melyill,
F.L.S.

This shell has been for the last two hundred or more
years esteemed as one of the most choice and rare in exist-
ence. It is strange that even in these days it is almost
unique, and in company with another shell of the same
genus (Cyproea princeps (Brod.), from the Persian Gulf), and
the far-famed Conus gloria maris (Chem.), always commands
a higher price than any other shells.

There are but three Cyproea princeps known, two of
which are in our national collection, which also boasts of
the unique C. leucodon (Brod.), while there are twelve or
thirteen of the Conus gloria maris. Allowing therefore for
the Cyproea princeps and leucodon at present to hold the
first post of honour, the Cyproea guttata, the subject of this
notice, will stand next in degree of rarity, there being but
six known, viz., the specimen now exhibited, from my
collection, one in the British Museum, two in the famous

126

collection of Miss Saul, of Bow, near London, one in the
Leyden Museum, and one, not in very good condition, in that
of Dr. Prevost, of AlenQon.

This cowry, the nearest approach to which is found in
the small and common C. erosa (L.) of Indian seas, is so
abundantly distinct from any other as to put all Darwinian
laws of evolution at defiance. It is chiefly characterized
from others of the same group in the subgenus Luponia by
being larger — 2J inches long — of lighter build, and above
all by the sulcate grooves at the base, the teeth being well
developed on both sides, and of a dark orange red, extend-
ing round the base of the shell in continuous furrows.

It is reported, but on insufficient evidence, to be a native
of China. No specimen is known by Europeans to be in
the possession of any inhabitant of that, or in fact of any
extra-European, country. There is certainly no specimen
in any collection in the United States.

It is probably an inhabitant of deep water. The shell is
very light and fragile. No specimen however in fragmen-
tary condition has been known to have been observed.

This particular specimen, which is said to be the finest of
the six in existence, I obtained through the agency of Mr.
Damon, from Mr. Hugh Owen’s collection, where it had
been located over twenty years, having previously been in
the cabinet of M. de Yerreaux.

“Lepidoptera of the Shetland Islands,” by Hastings
C. Dent, C.E.

I thought it might interest the members to see a few of
the Lepidoptera of Shetland Islands, and have brought some
which I obtained recently. In Entomologist, Nov. and Dec.,
1880, and Oct. and Dec., 1881, will be found full accounts
of these insects, so I do not purpose to do more than call
attention to two or three points.

127

Hepialus humuli var. Hethlandica. I am unfortunately unable
to show you this insect, being unable to procure specimens,
but I exhibit a plate showing some of the principal
remarkably aberrant forms of this, the common Ghost
Moth.

Hepialus velleda. Exclusively a northern insect in the British
Isles. The Shetland form is far more distinctly and
beautifully marked than the ordinary type. In the south
it is always a mountain insect, and is found in the Pyrenees
and Altai mountains.

Larentia caesiata. Abundant in the N. Counties of England. I
took it last year near the summit of Sea Fell Pike. The
Shetland form is much darker than the English or
Scotch type.

Emmelina albidata. The Hebrides form is very distinct, and has
been named var. Hebudium. The Shetland form is named
var. Thules. Both varieties vary much in the colouring
and marking.

Melanippe hastata. The English and European forms are very
similar. The Shetland form is smaller and much more
beautiful. There is a row of black spots along the centres
of the wings which are not developed in any of the typical
form. The Shetland form is an intermediate between
Melan. hastata and the Icelandic species M. hastulata.
(In Entomologist for Jan., 1881, is a beautiful var. of M.
hastulata.)

Camptogramma bilineata. The common Shell Moth. This
common moth is exceedingly variable in its markings, some
specimens being much darker than others, but I have seen
none taken in England which approach the Shetland form
in the distinct and beautiful dark tints.

Xylophasia polyodon. This is an abundant and very variable
species. I exhibit one specimen of the ordinary type of a
beautiful brown variety, taken by Mr. Melvill, at Prestwich.
But the Shetland form is distinctly black, and I have seen
an immense number of this black variety, and am informed

128

that the collector had not found one of the typical form
in the Shetland Islands.

Charoeas graminis. The Antler Moth. The only species of this
genus, very widely distributed in Central and Northern
Europe, and North Asia ; this is the insect which appeared
in such alarming abundance in the neighbourhood of
Clitheroe or Pendle Hill last year. I succeeded in rearing
from some larva I took at that time, some very light-
coloured specimens. The Shetland form is a much more
beautifully marked insect.

Mamestra furva. A local insect often confounded with commoner
species. The Shetland form is rather darker.

Anarta melanopa. In the British Isles this is exclusively a
northern insect. It will be seen that while the Scotch form
is brown , the Shetland var. is distinctly black.

I have reserved Pyrameis ( Vanessa ) Cardui , the Painted
Lady, to the last, as I wish to enter somewhat more into
detail respecting it. This is one of the three butterflies
which are alone recorded from the Shetland Islands: The

other two are P. Atalanta, and Cteenonympha Typhon, or
Davus.

Ceenonympha Typho7i, or Davus , is a north country insect,
though it is found in Ireland, but not in the Isle of Man.
It occurs on the Scotch mountains at a height of 2000ft.
above the sea level. I have taken the var. Rothliebii on
Chat Moss, and in Delamere forest. The Shetland form
does not differ from the typical C. Davus.

Pyrameis Cardui is the one of the 64 British butterflies that occurs
all over the world except in S. America. It is perhaps the
least varied of all species. I exhibit specimens from
England, Shetland, Europe, Cape of Good Hope, and India.
It is also found unchanged near Hudson’s Bay, while
P. Atalanta varies slightly at that locality.

P. Cardui and P. Atalanta are frequently found in the
same localities, and I exhibit specimens from England and

129

North America. Now, P. Cardui is found in India, but
P. Atalanta is not , but instead of it we find there is a species
which is termed P. Indica vel Callirhoe, of which I exhibit
a specimen. This insect appears to be an intermediate form
between Cardui and Atalanta. In the upper side of Indica ,
the insect is substantially Atalanta, while the lower portions
of the wings bear a resemblance to Cardui. In the under
side, the upper portions of the upper wings are similar to
Atalanta, and the lower to Cardui, and in the lower wings
the upper portion resembles Cardui, and the lower Atalanta.
It would be extremely interesting to try whether a cross
could be obtained resembling Indica, by breeding Cardui
with Atalanta for a few generations. In the free state the
Cardui and Atalanta are generally found together, yet no
intermediate is discoverable co-existent. P. Cardui is a
curious insect in the manner of its appearances. Some years
it is so exceedingly abundant as to become a pest, while
probably the next year hardly a specimen is to be found in
that locality. It is to be found near the sea coast, and in
all places up to the summits of Ben Lawers and Snowdon.

Though much has been done towards elucidating many
problems of geographical distribution, there is still much to
be explained. For instance, in the Isle of Man there are 16
of the 64 British species of butterflies. They none of them
present any difference from the English forms except one, the
Vanena Urticse, small tortoise shell. When I was in the
Isle of Man, in 1879, I to;.k a remarkably small specimen of
that insect, and on showing it to Mr. Edwin Birchall, he
informed me that this small variety is the only form of
Y. Urticae taken in the Island, and very kindly presented
me with a series.

In conclusion, I must express my best thanks to Mr.
Melvill, who most kindly placed his large collection at my
disposal to select any insects that I wished, for the purpose
of comparison with the Shetland and Hebrides forms.

ISO

“Notes on the Giant Dragon’s-blood Tree at Orotava,” by
Mr. John Plant, F.G.S.

Last August, as my friend, Mr. John Higgin, was on bis
return from the Philippines to visit old England once more,
he made a detour from Lisbon to the Canary Islands to see
the cochineal plantations as well as the physical wonders at
TenerifFe. He made a pilgrimage to Orotava, to behold for
himself the renowned patriarchal Dragon-tree, which in one
spot had survived 6000 years of mundane changes all around,
only to find every vestige of its existence swept away—
fifteen years before it had been broken down in a great gale.
A good part of it had gone for dye-wood, the chips and
fragments had been burnt, and visitors had carried off the
remainder. He offered inducements to the natives, and the
ground upon which the old tree had stood was dug into and
several pieces of the hark were found, three of which I have
now to bring before you as the very last remains of the old
giant of Orotava.

The Canary Islands were known to history in the year
1330, and the tree in 1402. In 1493 Alonzo del Lugo claimed
the islands under the Spanish authority. He relates that this
hollow Dragon-tree was in use by the Guanche Indians as a
temple for heathen rites, but that he reformed such practices
and made it into a chapel for holy mass. Other Spanish
historians and voyagers have left records of visits to Orotava
in succeeding centuries, which it is not necessary to repro-
duce here, except in the instance of Baron Von Humboldt,
who visited the Canaries in June, 1799, when on his first
journey for exploration in Central and South America.

His narrative of this visit runs : “ Although we had been
made acquainted from the narrative of many travellers with
the Dragon-tree of the garden of M. Franqui, we were not
the less struck with its enormous magnitude. We were
told that the trunk of this tree, which is mentioned in very
ancient documents, was as gigantic in the 15th century as

it is at the present time. Its height appeared to be 50 or 60
feet, its circumference, near the root, 45 feet, but Sir G.
Staunton, who was at Orotava in October, 1792, found that
at ten feet from the ground the girth of the trunk was 36
feet, which corresponds perfectly with the statement of
Borda in 1600.”

“The trunk (says Humboldt) is divided into a great
number of branches which rise in the form of a candelabrum,
and are terminated by tufts of leaves like the Agucca. The
tree still bears flowers and fruit every year. The Dracaena
presents a curious phenomenon with respect to the migration
of plants. It has never been found in a wild state in Africa ;
the East Indies is its real country. How has it been trans-
planted to Teneriffe ? Does its existence prove that at some
distant period the Guanches had connexions with other
nations originally from Asia ? ”

Humboldt gives an engraving of the famous Dragon-tree
in his “Atlas Pittoresque,” but it appears that it was supplied
from a drawing sent him by M. March ais, and that from an
earlier sketch by M. Ozone, and the result, as Piazzi Smyth
puts it, “ was a gradual growth of error and convention-
ality, as man copies from man,” and there does not exist
in any of the popular botanical works a truthful drawing of
this extraordinary floral form, which belongs to the natural
order Liliacese.

The course of the history of this Dragon-tree since the
time of Humboldt’s visit, as far as I can trace it through the
works of travellers, appears to consist of records of its
successive mutilations from frequent destructive storms and
the carrying away of pieces by visitors from every land.
In 1819 a great gale wrenched off a large arm; in 1829 a
deluge of rain fell upon the Peak and sweeping down through
Orotava, carried off nearly one half of the old hollow trunk,
and C. Piazzi Smyth records “ that certain Goths hacked an
immense piece out of the thin wall of the hollow trunk for

132

the Museum of Botany at Kew.” In place of growing larger
in later years, the old tree was rapidly collapsing, when the
Marquis of Sanzal came into possession of the Villa de
Orotava, upon whose grounds the Dragon-tree stood. The
Marquis at once put a stop to all depredation, and prohibited
any pieces of the tree from being carried off by visitors.
He further endeavoured to supply the abstracted portions
of the trunk with masonry, trying thus to give a
further chance of renewed life and vigour; for a few years
these efforts had their reward, the veteran became the lion
for all modern visitors to mount the steep and gaze at with
pleasure and wonder.

When C. Piazzi Smyth went on his astronomical inquiries
in the Canaries in 1856, twenty-six years ago, he had leisure
and opportunity for a careful examination of the old Dragon-
tree, the results of which are charmingly told in his chapter
on Dracaena Draco : “ Teneriff e, an Astronomical Experiment,
by C. Piazzi Smyth, 1858, p. 800.” Above all, he was able
to take several photographs of the old tree, as well as of
younger and more normal specimens of the Dracaena. He
describes the perilous state of the old tree from the unequal
level of the ground, and says it was nearly smothered about
the trunk with laurels, oranges, peach, and other trees, and
a rivulet — at times a torrent — flowed along its front. It
had been known by the natives as a landmark betwixt
properties adjoining for centuries. He measured it as 60 feet
high and 48 J feet circumference at that height, it was 28*8
feet circumference at the part where the branches spring
out from the trunk, and at 6 feet from the ground was 35
feet 6 inches in circumference. But he says : “ this is no
proper tree with woody substance, it is merely a vegetable.

133

an asparagus stalk of eminent slowness in growth, which
has gained for it the credit of being the oldest tree in the
world.”

When the Dragon-tree is young, the simple stems are
smooth, or marked only by shallow transverse indentations
of foot stalks of past leaves. The compound stems are
deeply corrugated longitudinally, and the trunk has an
evident tendency to divide continually as it descends.
When once a stem has branched its life seems to have de-
parted, being replaced by the lives of the several young
trees of its kind left growing on its summit, and whose
roots, entering the bark and encasing the old stem on every
side, conceal its slow withering corpse from the light of day.
Ages pass by, the young trees flourishing, die in their turn,
each producing two or more new trees mounted on their
summits, and thus presenting such a surface to the wind,
that the hollow base of the original tree would never be able,
unless artificially assisted, to support the strain, and hence
the true explanation of the hollow interior of the trunk
from the remotest times in the past to the fatal autumnal
day in 1867, when the great gale snapped asunder, for ever,
the cords of life of one of the world’s oldest inhabitants.

Mr. It. D. Darbishire, B.A., F.G.S., exhibited a fine series
of Ceylonese land and fresh-water shells, procured through
the instrumentality of Mr. M. M. Hartog, F.L.S.

The Helices were mostly of the Acavus section, which in
Ceylon reaches its highest development. Conspicuous
among these are the rare H. superba (Pfr.), H. Grevillei
(Pfr.), H. Phoenix (Pfr.), and the curious little H. Skinnerei
(Pfr.). The common H. hsemastoma (L.) was also abun-
dantly represented in many beautiful varieties, and the
curious Helix Rivolei (Pfr.) of the subgenus Polygyra was
also worthy of comment.

134

The fresh-waier shells were mostly Paludomi, which
genus is endemic to Ceylon alone.

In the discussion which ensued, Mr. Melvill said that he
possessed a specimen of a reversed Helix haemastoma,
believed by Mr. Sowerby to be the only one yet recorded in
this state.

At the meeting of the Microscopical and Natural History
Section, on the 13th February, 1882, Mr. Marcus Hartog,
referring to his remarks “ on the treatment of damaged india-
rubber with a solution of magenta,” on the 10th October,
1881, stated that Mr. William Thomson, of Manchester,
was the discoverer of the application of magenta there
recorded.

MICROSCOPICAL AND NATURAL HISTORY SECTION.

Annual Meeting, April 17th, 1882.

Alfred Brothers, F.R.A.S., President of the Section,
in the Chair.

The Secretary’s Report and the Treasurer’s Accounts
were presented and passed.

135

The following gentlemen were elected Officers for the
ensuing session 1882-1883.

J. COSMO MELVILL, M.A., F.L.S.

A. BROTHERS, F.R.A.S.

R. D. DARBISHIRE, F.G.S.

JOSEPH BAXENDELL, F.R.A.S.

®«twn«r.

MARK STIRRUP, F.G.S.

Jmntarg.

ROBT. E. CUNLIFFE.

Ccwtuil.

THOS. ALCOCK, M.D.

CHAS. BAILEY, F.L.S.

JOHN BOYD.

HASTINGS C. DENT.

MARCUS M. HARTOG, B.Sc., F.L S.

A. MILNES MARSHALL, F.L.S.

THOS. ROGERS.

W. C. WILLIAMSON, F.R.S.

Mr. Boyd remarked upon the discovery of the egg cases
of Pediculis Capitis in the crevices in an African Chief’s
head stool in the possession of a friend of his.

Mr. Plant stated that he had endeavoured to obtain
larger specimens of the Dreissena noted at the last meeting,
but without success.

Dr. Alcock concluded his notes on Frog Tadpoles by
describing the three remaining periods into which their life-
history may be divided.

The third period extends from the thirtieth to the fiftieth
day, and appears to be devoted entirely to growth, no new
developments being observed. The tadpoles swim actively,

136

feed voraciously, and grow very rapidly. During this period
water continues to he taken in through the nostrils to supply
the gills, and the opening by which it is discharged from the
gill-chamber becomes tubular, extending upwards and back-
wards, embedded in the skin until it terminates in a short
conical tube projecting from about the middle of the left
side of the body. The mouth consists of a pair of strong,
brown, homy beaks, with serrated edges, and is surrounded
by a broad expanded sheet of white fleshy membrane,
irregularly frilled and scolloped at its edges. Its inner or
front surface is furnished with long rows of small brown
teeth set upon white, apparently cartilaginous bands, so
that they resemble combs. There are three sets of these
combs on the upper and four on the lower lip. The
alimentary canal in the abdomen consists of a long simple
tube of equal diameter throughout, and about three and a
half times the length of the tadpole ; it is folded in half, and
thus doubled, is coiled round and round, filling the left half
of the abdominal cavity, and forming in its final coils the
regular flat spiral seen on removing the skin of the ventral
surface.

The fourth period extends from the fiftieth to the seventy-
fourth day. Feeding is very active, and rapid growth
continues. The developments which take place in it are
those of the limbs, with the shoulder girdle and pelvis, and
the lungs. Water no longer enters by the nostrils, but
passes through the mouth. The pair of papillae, seen on each
side at the root of the tail as early as the thirtieth day, now
begin to enlarge at their ends, become broader, and at length
divisions marking the toes appear, at the same time the knee
and ankle are indicated by bendings in the lengthening
limbs. In fifteen days both fore and hind legs may be said
to be fully formed, though the toes of the hind pair are still
without webs. The development of the fore legs within
the gill-chamber advances equally with the hind legs. At

137

the close of the period both pairs are well grown, and
the shoulder girdle and pelvis are developed. The lungs at
the same time have attained a considerable size, and are in
the form of a pair of sacculated tubes bluntly pointed at
their free end.

The fifth and last period of the aquatic life of the frog
extends from the seventy-fourth to the eighty-third day,
at which time the animal has left the water and attained
the perfect form of the adult. At the commencement of
this period it is a tadpole with a large tail, a pair of large
hind legs with webbed feet, and a pair of equally well
developed fore legs still retained within the gill-chamber.
The gills continue in action, and the opening at the left side
remains for the discharge of water. But now remarkable
changes rapidly take place The animal ceases entirely to
feed, and the alimentary canal soon becomes empty, the
large white frilled lips shrink, and the sets of small teeth
upon them degenerate and drop off, the horny beaks
disappear, the mouth widens, the lips consist of ordinary
skin, and the large fleshy bifurcated tongue of the frog is
formed. At the same time, the intestine shrinks both in
length and diameter, especially at the part which forms the
centre of the coil; soon afterwards its upper part begins to
be dilated to form the stomach, and the remainder becomes
rapidly smaller and shorter as the stomach enlarges, until it
consists of a small and slender gut, making only two or
three short turns below the stomach at the left side. The
liver at the same time enlarges, and the gall-bladder is seen,
very large and filled with dark green bile.

When these changes in the alimentary apparatus have
been partly accomplished, the forelegs are pushed out, the
action being instantaneous for each limb, sometimes the
right, sometimes the left comes out first, and the left limb
is always forced through the gill-opening, the margin of
which is torn in consequence of the size of the limb being

138

too large to pass through the natural aperture. On the
right side, the opening is usually a ragged rent in the skin,
which has become thin at that part. The immediate con-
sequence of the protension of the forelegs is to stop aquatic
respiration and throw all the work of breathing on the
lungs. The animal now remains almost constantly on the
surface, and it very soon becomes exhausted and drowns if
unable to support its mouth above water. The tail at this
time rapidly shrinks, being absorbed and used as stored-up
nutriment by the animal whilst it is unable to feed. It
remains several days in the water in this state, but when
the tail has been reduced to a brown stump of about half
an inch iong, and the changes in the alimentary canal are
completed, the animal shows an instinctive desire to climb.
Beaching the border of the pond it will make its way up a
steep or even perpendicular surface to the height of several
feet, if this be necessary, in order to climb the bank. The
remaining stump of tail serves as provision for several days
longer, after which the young frog takes small insects as
food.

It must be remarked that no special value is attached to
the exact number of days assigned to each period, for in
strictness they apply only to the particular tadpoles
examined. In order to make the successive periods agree
as nearly as possible with each other, the most advanced
tadpole was selected out of a number taken for each daily
observation, and in consequence the periods are made rather
shorter than the averages would have been. There was an
interval of twenty days between the escape of the first and
of the last frog from the water.

SOPHICAL SOCIETY OE MANCHESTER,

139

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140

List of Members and Associates, April 17th, 1882 :

IPmbfrs.

Alcock, Thomas, M.D.

Bailey, Charles, F.L.S.
Barratt, Walter Edward.
Barrow, John.

Baxendell, Joseph, F.R.A.S.
Becker, Wilfred, B.A.
Bickham, Spencer H., Jun.
Birley, Thomas Hornby.

Boyd, John.

Brogden, Henry.

Brothers, Alfred, F.R.A.S.
COTTAM, SaMDEL.

Coward, Edward.

Coward, Thomas.

Cunliffe, Robert Ellis.

Dale, John, F.C.S.

Dancer, Jno. Benjamin, F.R.A.S.
Dent, Hastings Charles.
Darbishire, R. D., B.A., F.G.S.

Dawkins, W. Boyd, F.R S., F.G.S.
Deane, W. K.

Higgin, James, F.C.S.

Hurst, Henry Alexander.
Marshall, A. Milnes, F.L.S.,
Prof, of Zoology, Owens College.
Melvill, J. Cosmo, M.A., F.L.S.
Moore, Samuel.

Morgan, J. E., M.D.

Nix, E. W., M.A,

Sidebotham, Joseph, F.R.A.S.,
F.L.S.

Smith, Robert Angus, Pli.D.,
LL.D., F.R.S., F.C.S.
Williamson, Wm. Crawford,
F.R.S., Prof. Hat. Hist., Owens
College.

Wright, William Cort.

Adams, Lionel.

Cunliffe, Peter.

Hartog, Marcus M., B.Sc., F.L.S.
Labrey, B, B.

Percival, James.

Plant, John, F.G.S.

Quinn, Edward Paul.

Rogers, Thomas.

Stirrup, Mark, F.G.S.
Sington, Theodore.
Tatham, John F. W., M.D.
Ward, Edward.

Young, Sydney.

141

Annual General Meeting, April 18th, 1882.

J. P. Joule, D.C.L,, LL.D., F.R.S., in the Chair.

Report of the Council, April, 1882.

The Treasurers Annual Account shows that the balance
against the General Fund has increased from £90 Os. 7d. on
the 1st of April, 1881, to £120 12s. 5d. on the 1st of April,
1882 ; that the balance in favour of the Natural History
Fund has diminished from £76 5s. 8d. to £35 7s. lid.; and
deducting the difference between these two sums from the
Compounders’ Fund, £125, there is a balance of £39 15s. 6d.
in favour of the Society on the 1st of April, 1882, against a
balance of £111 5s. Id. on the 1st of April, 1881.

The number of ordinary members on the roll of the
Society on the 1st of April, 1881, was 146, and 7 new
members have been elected ; the losses have been— resigna-
tions 9, and deaths 3. The number on the roll on the 1st
instant was therefore 141. The deceased members are
Mr. John Blackwall, Mr. A, G. Latham, and Mr. E. W.
Binney.

Mr. John Blackwall, F.L.S., who died May 11, 1881, was
born in Manchester in 1789, and the greater portion of his
92 years were devoted to the study of science. During his
residence at Crumpsall Old Hall he made many interesting
observations in natural history. The papers read before this
and other societies were collected into a volume entitled
“ Researches in Zoology,” which, originally published in
1834, came to a second edition in 1873. His Memoirs,
chronicled in the Royal Society’s Catalogue of Scientific
Papers, are 82 in number, and were printed between 1821
Peoceedinos— Lit. & Phil. Soc.— -Vol. XXI.— No. 10. — Session 1881-2.

142

and 1871. The most important of his works is the “ Mono-
graph on British Spiders,” published for the Bay Society
in 1861. This subject was one to which he had devoted
especial attention after his removal from Manchester to
Wales. Mr. Blackwall was for 60 years a member of this
society, and he was also one of the oldest members of the
Linnsean Society and of the British Association.

Mr. Arthur G. Latham was born December 29th, 1821,
at Everton, near Liverpool ; he joined the firm of Arbuthnot,
Ewart, and Co., and spent a great part of his early life in
India. Beturning to England, he took up his residence in
Manchester, about twenty-five years ago, since which time
he resided at Weaste Hall, Pendleton. He was instrumental
in founding the Microscopical and Natural History Section
of the Literary and Philosophical Society in conjunction with
his partner, the late Mr. Murray Gladstone, and took at all
times a lively interest in all that appertained to the Society.
He was most attached to the study of Coleoptera, both
British and foreign, and amassed a very fine collection.
Also of British Lepidoptera and birds’ eggs and shells, both
British and foreign. All these were sold at Steven’s auction
rooms in the year 1878; and latterly he directed his undi-
vided attention to microscopic researches and the study of
lichens and fungi. He died, somewhat suddenly, on April
23rd, 1881.

Edward William Binney, F.B.S., F.G.S., &c., our late
President, was born at Morton, in Nottinghamshire, in 1812,
and seems to have lost his father’s care early, but a brother
came to his help and enabled him to serve his apprentice-
ship to a solicitor in Chesterfield. Afterwards he completed
his study in London, and came to Manchester in 1836. He
was early led to the science in which he took the deepest

143

interest, and to the peculiar department of it which he never
left. His capacity for long walks gave him a great
advantage. He was tall and powerful, and he had no wish
to seek society. Indeed, he always spoke in a disparaging
manner of the usual social intercourse in the middle and
upper ranks, and delighted in rambling over the county and
mixing with the men he chanced to meet, studying their
ways and learning their observations. It was in this way
he came to take much interest in the scientifically inclined
working man, and he had a particular pride in speaking
more highly of him than of the more learned or elaborately
trained. Indeed, it was his opinion that to be a straight-
forward man and to observe well, seeing clearly what lay
before one, was the most pleasant object in life.

That he himself was fitted for clear and accurate, as well
as long-continued and patient observation, soon became
manifest, and we have a list of papers written by him and
extending over forty-two years.

He lived at Cheetham Hill (Manchester), attracted by its
sandy soil, but spent his days at his business, or in reading
at the Athenaeum, or in attending to the affairs of this
Society, in which he took a deeper interest than any
member, if we are to judge by the trouble he took in directing
its minutest details, so that for many years little was done
without his will. His attention to business was so great
that for thirty years he had not been absent from it for a
fortnight at a time.

He attended well the meetings of the British Association
for many years, and at the Geological and Palaeontological
Societies was well known as a contributor, while his studies
of the flora and wood of the coal measures have helped
greatly to make an important era in our knowledge. The
writer must leave a geologist to sum up his labour and
define his position as a scientific man. Of the 134 papers

144

mentioned there are certainly only slight notices, but some,
on the other hand, show laborious work, and have been left
unfinished.

He joined Mr. Young in beginning works for the manu-
facture of paraffin oil, adding his savings to the small
amount that was available at the time, after Mr. Young
(now Dr. Young, of Kelly) had found it necessary to have
aid in order to enlarge his establishment and begin his
Scottish Works, the supply of oil in Derbyshire having failed.
The firm was in this town called by the name of E. W. Binney
and Co. The partnership continued during the existence of
the patent, and Mr. Binney retired with a handsome sum,
which he greatly increased by his investments. He spent
a large portion of his later years at Douglas, in the Isle of
Man, where his house, Bavenscliff, gave him a fine view of
the Bay and of the sea, and was still to a great degree
sheltered.

Mr. Binney was a remarkable man. He knew many
people, but visited few, but to these few he was very
strongly attached, whilst his tenacity of purpose prevented
him from having sympathies with many, and caused him to
put many people in an attitude of opposition, without
making them enemies. In science he read very widely,
but never wrote on anything outside the first field of his
geological interest.

He had a peculiar horror, even loathing, for men who
made a display, and, although a rich man, he lived in great
simplicity. He admired great men, it is true, but his chief
love was for the poor man who gained knowledge, although
finding it difficult to gain bread. Thus he took up the case
of Samuel Bamford, the author of ‘ The Life of a Kadical/
and did not cease till he induced the Government to grant
him a sum from the Civil List. A similar kindly feeling
prompted him to great attention to Buxton the botanist,

145

the author of ‘The Botanical Guide to Manchester/ a remark-
able man, who was known to Mr. Binney only when age had
overtaken him. For many years he sat for hours daily in the
office reading. Mr. Buxton, a shoemaker but a poor man,
had never made above ten shillings a week all his life,
and he lived, of course, in a poor street. It was remark-
able, however, how fine his taste was, and how well in-
formed he was found on all subjects, an educated gentle-
man, timid and shy as a child. Mr. Binney helped him to
have his book published, and to obtain for it a fair sale.
The delicacy of his treatment of this man was remarkable
when men of great importance in the eye of society were
sent away with a growl.

His pleasure in promoting and attending meetings of the
scientific working men was great.

The small annuity obtained for Mr. Sturgeon was owing
to the persistency of Mr. Binney.

Still, a purely benevolent life was not that of Mr. Binney;
he was a man of business and a geologist. Geology had at
an early period put out of his mind much of his knowledge
of science, and his attention to the many affairs on hand
very much in later years interfered with his geology. He
has left a fine collection of geological specimens, and a for-
tune to his wife and three sons as well as three daughters.

It was his strong desire to have the rooms of the Society
retained, but enlarged ; and he intended to assist in raising
a fund of five thousand pounds for this purpose, and also for
obtaining the services of a librarian and editor. The Society
has certainly suffered by his loss in this respect, but it has
not the less suffered by the absence of his face and the full
sympathy and clear sense which he introduced into so much
of the work of the Society, although we often thought that,
liberal as he was in politics, time had made him too con-
servative of some of the forms of the Society. We learn
slowly to see the evils of rapid innovations.

146

Professor W. C. Williamson mentions as the first appear-
ance of Mr. Binney as a geologist, a paper read by him in 1835
in conjunction with John Leigh, F.B.C.S., now Medical
Officer of Health for Manchester. This paper was ‘On
Fossils found in the Bed Marl at Newtown, in the valley
of the Irk/

The earliest paper recorded seems to he in the Trans, of
the Geol. Soc.,Vol. I., p. 35, entitled a ‘Sketch of the Geology
of Manchester and its Vicinity/ It was the work of three
years, and showed in a remarkable degree the energy of the
author’s character. It was followed rapidly by others on
the coalfields of Lancashire and Cheshire, on the marine
shells of the Lancashire coalfields, and on the fossil fishes.

The enquiries which were of most interest to him were
the constitution of coal and the conditions under which it
grew. Next to these subjects came the action of glaciers
and icebergs in distributing clay and boulders over the two
counties especially in which he took interest.

A longer memoir will probably be read. At present we
may indicate his chief discoveries by the following extract :

“ Carboniferous Flora. Fart IV., 1875, pp. 98 and 99.
General Observations on Sigillaria, Anabathra, Diploxy-
lon, and Stigmaria.

“Ever since the time when the fossil plants of the coal
measures first attracted attention, Sigillaria has occupied a
chief place in the minds of botanists, for it is to be met with
in the strata near most seams of coal, in a more or less
perfect state of preservation. The trunks of this genus are
of two kinds, namely, those distinctly ribbed and furrowed
with leaf-scars on the ribs at greater or less distances, and
those with the leaf-scars contiguous, and covering the whole
surface of the trunk, both having them in a spiral arrange-
ment around the axis. Nearly one hundred species have
been described by different authors, who have made

147

numerous species out of the same trunk ; various parts of
it being in a bad or good state of preservation. No doubt,
when we are better acquainted with the true nature of the
plant, the number of species will be greatly reduced.

“ For a long time Sigillaria and Stigmaria were regarded
as distinct genera of plants, and even now, on the Continent,
some distinguished palseontologists are disposed to remain
of that opinion. In the specimens first described by me, in
the ‘Philosophical Magazine’ for 1844/ which were found in
Mr. Littler’s quarry, near St. Helens, Stigmaria was clearly
traced to the trunks of the large, irregularly ribbed and
furrowed Sigillaria, showing little, if any, traces of leaf-scars ;
but it was there distinctly stated that around these trunks
smaller trunks were found standing, which showed all the
characters of Sigillaria reniformis, with Stigmaria rootlets
in the adjoining strata, pointing in the direction of the root,
but not absolutely proved to be connected with it. On
viewing the specimens as they originally stood in the quarry
before their removal, little doubt could be entertained as to
all the trees there found having had Stigmarise for their
roots. In some specimens, however, afterwards described by
me in the ‘Philosophical Magazine’ for 1847, ser. 3, vol. xxxi.
p. 259, the connection of Stigmaria as a root, with Sigillaria
reniformis, S. alternans, and S. organum was clearly proved.”

We cannot at present enter more into an account of Mr.
Binney, but a more extended, one is expected to appear.
He spent much time at his house in the Isle of Man, and he
seems to have hurried from it, fearing illness. His death
took place on the 19th December, 1881.

Dr. Joule has presented the Society with an admirable
portrait of Mr. Binney, painted by Mr. W. H. Johnson.
It hangs on the walls of the meeting room — a characteristic
remembrance of a man who has been a friend, pleasant?
sympathetic, and wise, during an intimacy which, to a few

* ‘ Phil. Mag.5, ser. 3, vol. xxiv. p. 168 ; and 1845, vol. xxvii. p. 241, &c.

148

of us, has lasted about forty years. His family have reason to
thank him, and scientific history will not soon forget his
labours amongst vegetation of the past, illustrating calm
days in which coal grew to enrich us, or among the boulders
and till, explaining the method in which they were
deposited, making for us a pleasant and interesting land to
dwell in.

The following papers and communications have been read
at the Ordinary and Sectional Meetings of the Society,
during the Session

October Iftli, 1881. — “On Drops Floating on the Surface of
Water,” by Professor Osborne Reynolds, F.R.S.

“On the Mean Intensity of Light that has passed through
Absorbing Media,” by James Bottomley, D.Sc., F.C.S,

“ Correction of the Formula used in Photometry by Absorption
when the Medium is not perfectly transparent,” by James Bottom-
ley, D.Sc., F.C.S.

“ Note on the Colour Relations of Nickel, Cobalt, and Copper,”
by James Bottomley, D.Sc., F.C.S.

October 18th , 1881. — “On the Failure of certain Mathematical
Solutions of the Problem of the Motion of a Solid through a Perfect
Fluid,” by R. F. Gwyther, M.A.

“The Sea Gull in Salford,” by William E. A. Axon, M.R.S.L.

“ On the Numerical Extent of Personal Vocabularies,” by
William E. A. Axon, M.R.S.L.

November 1st, 1881.— '' On the Manufacture of Salt in Cheshire,”
by Thomas Ward, Esq.

November 7th, 1881 . — “On a Series of Preparations of Desmi-
diae,” by Mr. Wills.

November 8th, 1881. — “ Note on a Passage of Pollux relating
to the Formation of Purple Dye,” by James Bottomley, D.Sc., F.C.S.

November 15th, 1881. — On the Pronunciation of DeafMutes who
have been taught to Articulate,” by William E. A. Axon, M.R.S.L.

“ On Professor C. A. Bjerkness’s Experiments to Demonstrate the
Analogies between Electrical and Magnetical Phenomena and some
Hydrodynamical Phenomena,” by William H. Johnson, B.Sc.

November 29th, 1881. — “ On the Aniline Colours used in Water
Colour Drawings,” by Joseph Sidebotham, F.R.A.S., &c.

“On Cyclic Motions in a Fluid, and the Motion of a Vortex
Ring of varying Curvature,” by R. F. Gwyther, M.A.

December 5th , 1881. — “ On the larval form of star-fishes, echi-
noids, holotharids, and crinoids,” by Professor A. Milnes Marshall.

“ On Limnotruchus Kirkii (Edgar Smith) from Lake Tanganyika,
and on a new land Mollusc, Cyclosurus Marieri (Morelet), recently
discovered by Prof. Morelet at the Mayotta Islands, about 300
miles N.W. of Madagascar,” by J. Cosmo Melvil], M.A., F.L.S.

December 13th , 1881. — “Remarks on the Terms used to denote
Colour, and on the Colours of Faded Leaves,” by Edward Schunck,
Ph.D., F.R.S.

January 10th , 1882. — “ On Differential Resolvents, and Partial
Differential Resolvents,” by Robert Rawson, Esq., Assoc. I.N.A.,
Hon. Member of the Society.

January 21jth, 1882. — “On the British species of Erythroea”
by Charles Bailey, F.L.S.

“ On a dwarf form of Campanula glomerata , L., from the Isle of
Wight,” by Charles Bailey, F.L.S,

“ On the Isle of Wight Station for Lychnothamnus alopecuroides ,
Braun,” by Charles Bailey, F.L.S.

February 7th , 1882. — “ The Colour Sense and Colour Names,”
by William E. A. Axon, M.R.S.L.

“ Notes on Lead Pipes and Lead Contamination,” by William
Thomson, F.R.S.E.

February 13th , 1882. — “List of the Phanerogams of Key West,
South Florida, mostly observed there in March, 1872,” by J.
Cosmo Melvill, M.A., F.L.S. -

“ Notes on Frog Tadpoles, Part I.,” by Thomas Alcock, M.D.

150

February 14th , 1882. — “Notes on the Variable Stars U Canis
minoris, V Geminorum, and UBootis,” by Joseph Baxendell, F.R. A.S.

March 7th , 1882. — “A Comparison between the Height of the
Rivers Elbe and Seine and the State of the Sun’s Surface as regards
Spots,” by Professor Balfour Stewart, LL.D., F.R.S.

“ On Electro-Motor Machines for the transmission of mechanical
power by means of Electricity,” by Henry Wilde, Esq.

March 18th, 1882. — “ On Cyproea Guttala (Gray),” by J. Cosmo
Melvill, M.A., F.L.S.

“ Lepidoptera of the Shetland Islands,” by Hastings C. Dent, Esq.

“ Notes on the Giant Dragon’s-blood tree at Orotava, Teneriffe,”
by John Plant, F.G.S.

March 14-th, 1882. — “ Notes of some experiments made in Feb-
ruary, 1881, on the Influence of Stress on the Electrical Resistance
of Iron and Steel Wire,” by William H. Johnson, B.Sc.

“ On the Projection of a Solid on Three Co-ordinate Planes.” by
James Bottomley, D.Sc., B.A.

March 21st, 1882.~u Note on Envelopes and Singular Solutions,
continued from Vol. XVII. Proc., p. 15,” by Sir James Cockle,
F.R.S., F.R.A.S., Corresponding Member of the Society.

April 4th> 1882. — “On the Occurrence of Oxide of Manganese
(Wad) in the Yoredale Rocks of East Cheshire,” by Arthur Smith
Woodward, Student of Owens College. Communicated by Dr,
Charles A. Burghardt.

Several of these papers have been passed by the Council
for printing in the Society’s Memoirs, and will appear in
volume 8. The last paper to complete Volume 7 is now in
the printer’s hands, and the Volume will be ready for bind-
ing before the end of the present month.

The Council, at a meeting held on the 15th of November
last, resolved “ that the Memoirs of the Society be sent free
to each Member, beginning with Volume 8.”

In consequence of the ill-health and lamented death of
the President, no action has been taken by the Council in

151

reference to his proposed celebration of the Centenary of
the Society.

At a meeting of the Council, held on the 19th of April
last, it was resolved, on the motion of Mr. R D. Darbishire,
seconded by Dr. J oule, “ that the Associates of each Section
be empowered to vote in the election of Officers of the
Section with the Members, and that Associates may be
eligible for the Offices of the Section.”

The Council again consider it desirable to continue the
system of electing Sectional Associates, and a resolution on
the subject will, as usual, be submitted to the Annual
Meeting for the approval of the members.

f

m.

1881.— April i.
To Cash in hand

MANCHESTER LITERARY AND

Charles Bailey, Treasurer, in account with the Society,

Statement of the Accounts

1881-2 1880-1
£ s. d. £ s. d. £ s. d.
Ill 5 1 124 10 3

1882— March 31.

To Members’ Contributions : —

Arrears 1880-1, 1 Admission Fee 2 2 0

,, ,, II5 Subscriptions 24 3 0

Old Members’ Subscriptions, 1881-2, 121 at £2 2s 254 2 0

New Members’ ,, ,, 6 ,, 12 12 0

,, Admission Fees, 1881-2, 6 ,, 12 12 0

305 11 0 302 8 0

To one Associate’s Subscription for Library, 1881-2 0 10 0

To Sectional Contributions :

Physical and Mathematical Section, 1881-2 2 2 0

Microscopical and Natural History Section, 1881-2 ... 2 2 0

— 4 14 0 6 16 0

To use of Society’s Rooms : —

Manchester Geological Society, to 31st March, 1881 30 0 0 33 0 0

To Sale of Society’s Publications 8 10 6 10 19 7

To Natural History Fund :

Dividends on £1225 Gt. Western Stock (11 months, 1881-2) 54 18 8 59 15 3

To Bank Interest, less Bank Postage, to 31st December, 1881 2 14 4 1 18 4

£517 13 7 £539 7

1882. — April 1. To Cash in Manchester and Salford Bank

11th April, 1882.

Audited and found correct,

R. E. CUNLIFFE.
J. A. BENNION.

£39 14

CC Oi

PHILOSOPHICAL SOCIETY.

from 1st April, 1881, to the 31st March, 1882, with a Comparative
for the Session 1880-1881.

€r.

1882 — March. 31.

By Charges on Property : —

Chief Bent

Insurance against Fire

Property Tax

Repairs, Whitewashing, &c

By House Expenditure : —

Coals, Gas, Candles, and Water

»Tea and Coffee at Meetings

House Duty

Cleaning, Brushes, Sundries

By Administrative Charges : —

Wages of Keeper of Booms

Postages and Carriage of Parcels

Attendance on Sections and Societies

Stationery and Printing Circulars

Distributing Memoirs

By Publishing : — ■

Printing Memoirs ..

Printing Proceedings

Wood Engraving and Lithographing..
Editor of Memoirs and Proceedings ..

By Library : —

Binding Transactions

Binding Books for Library

Books and Periodicals

Assistant in Library

Palseontographical Society for 1882 ..
Bay Society for 1882

By Natural History Fund

Grant to Section for Books

Natural History Works

By Balance

1881-2.
£ s. d. £

1880-1.

d. £ s. d, £ s. d.

12 12 8
12 17 6
3 10 10
3 6 5

17 11

4

17

1 10

6

7

6

5

6

8

57

4

0

18 12

0

9

9

0

14

2

1

3

0

0

51

9

0

54

1

0

1 11

6

50

0

0

0

0

0

0

0

0

22

4

8

19 12

6

1

1

0

1

1

0

80

0

0

15 16

5

32 7 B
46 7 4

102 7 1
157 1 6

43*19 2

95 16 5
39 14 8

12 12 0
12 17 6
4 5 0
2 16 10

17 19 7
16 6 1
6 7 6
5 11 2

57 4 0
24 5 6
9 9 0
11 16 6

42 16 0
41 4 0
8 5 0
50 0 0

8 17 4
16 16 11
16 0 5
20 10 0
110
110

32 11 4
46 4 4

102 15 0
142 5 0

64 6 8

40 0 0
111 5 1

£517 18 7 £539 7 5

1881-2.

£ s. d. £ s. d.

Compounders’ Fund : —

Balance in favour of this Account, April 1st, 1882 125 0 0

Natural History Fund : —

Balance in favour of this Account, April 1st, 1881 76 5 8

Dividends as above 54 18 8

131 4 4

Less paid for Natural History Works 95 16 5

Balance in favour of this Account, April 1st, 1882

35 7 11

160 7 11

General Fund : —

Balance against this Account, April 1st, 1881 90 0 7

Expenditure, 1881-2, as above 382 2 6

472 3 1

Receipts, 1881-2, as above 351 9 10

Balance against this Account, April 1st, 1882 120 13 3

Balance in favour of the Society, April 1st, 1882 £39 14 8

Sr.

T:z

MANCHESTER LITERARY AND

iSSsr?o|.„.

8M March, 1881 1

’ ^SSSSSaSf^ Western Stooi (11 montA., 1881,

?:l

* b. m s. a; £ s. n\.

m iii

32 7 5 32 11

Hi 'it

rnmjMl

II! II

raSSfe:

8

15 16 2

Hill £j_l

£ B.n b. a.

125 0 0

JUJ
JS^J

35 7 11
160 7 11

£ III
HI hi

154

On the motion of Mr. A. Brothers, seconded by Mr.
J. A. Bennion, the Beport was unanimously adopted and
ordered to be printed in the Society’s Proceedings.

On the motion of Mr. William E. A. Axon, seconded by
Mr. James Smith, it was resolved unanimously: That the
system of electing Sectional Associates be continued during
the ensuing Session.

The following gentlemen were elected Officers of the
Society and Members of the Council for the ensuing year

firman!

HENRY ENFIELD ROSCOE, B.A., Ph.D., LL.D., F.R.S., F.C.S.

‘iia-flrmfont*.

JAMES PRESCOTT JOULE, D.C.L,, LL.D., F.R.S., F.C.S.

EDWARD SCHUNCK, Ph.D., F.R.S., F.C.S.

ROBERT ANGUS SMITH, Ph.D., LL.D., F.R.S., F.C.S.

REV. WILLIAM GASKELL, M.A.

<S^mtari£0.

JOSEPH BAXENDELL, F.R.A.S.

OSBORNE REYNOLDS, M.A., F.R.S.

%XZH%ViXZX,

CHARLES BAILEY, F.L.S.

librarian.

FRANCIS NICHOLSON, F.Z.S.

(Dther ef th z QLonncxl

ROBERT DUKINFIELD DARBISHIRE, B.A., F.G.S.

BALFOUR STEWART, LL.D., F.R.S.

CARL SCHORLEMMER, F.R.S.

JAMES BOTTOMLEY, B.A., D.Sc„ F.C.S.

WILLIAM HENRY JOHNSON, B.Sc.

HENRY WILDE.

On the motion of Mr. B. D. Darbishire, seconded by
Mr. Charles Bailey, it was passed unanimously : That
this Annual Meeting of the Society cannot separate without

155

acknowledging in a special manner its sense of its own pe-
culiar loss on the death of its late president Mr. Binney.
Without dwelling upon the honour conferred on it by
his own distinction as a man of science, or the support
given to all the business of the Society by his most assidu-
ous attention to its work and welfare, the members desire
to place on record the affectionate regard with which they
cherish the memory of Mr. Binney ’s constant and genial
participation in their proceedings, of his never-failing
encouragement of genuine research, and of his dignified
impersonation amongst them of faithful and successful
self-culture.

“ Preliminary Remarks on Observations made in Davos
in the Winter 1881-82,” by Arthur Wm. Waters, F.G.S.,
F.L.S.

Introduction, p. 155.— Evaporation, p. 161. — Comparison of Hygrometers :
Dry and Wet Bulb, p. 165. — Hair Hygrometer, p. 168. — Regnault’s
Hygrometer, p. 170. — Position of Instruments, p. 171. — Formula,
p. 173.— Dryness of Air we breathe, p. 175. — Wind, p. 179.— Smoke,

p. 180.

The principle of arresting disease by a residence in high
climates is now recognised by leading medical men, and has
been tried in various parts of the world, and it is very much
to be hoped for the sake of Davos that the experiment will
soon be tried in other parts of Europe, and in this immediate
neighbourhood the names of Arosa and Clavadel, besides
places in the Engadine, have been mentioned as well situated.
Everything connected with Davos is of scientific importance,
as new places should study the experience gained here.*

* Davos is a long valley with five villages — Ddrfli, Platz, Frauen-
kirch, Griaris, and Monstein. In Platz, 1,560 metres above sea level, the
experiment was first made of wintering for the cure of consumption, and
since then there have been patients in Ddrfli and a few in Frauenkirch,
but far the largest number have lived in Platz, and, therefore, when I
speak of Davos, it must frequently be understood to refer to the invalid
quarters of the valley.

156

On arriving in Davos, after an absence of 11 years, I
naturally found it much changed, and among the first
things I saw was a bank and gas-works, and then I felt the
simplicity of the Davos I had known was passed away, and
afterwards found that with that simplicity some of the
advantages of the place had also disappeared, for in the 17
years since the place was first tried it has lived a very spend-
thrift youth, and instead of a simple mountain village with
two moderate sized hotels, as I first knew it, it is now an
indifferently built small town with many of the hotels in
most unsatisfactory positions, and none have chosen as good
a one as the first hotel which was built for Swiss visitors,
and almost a climax has been reached by building a German
hospital in one of the most unfavourable places.

When I came here for the first time the number of visitors
was much larger in the summer than in the winter, whereas
it is now principally a winter resort. But this was to be
expected, for those who took an interest in it at first saw
that it had advantages in winter not possessed by other
places, whereas the summer climate is similar to a large
number of Alpine stations ; but this change from a summer
to a winter resort is a disadvantage to those who come for
the winter, for now all the hotels are full in this season,
whereas 11 years ago, when there were only two, these were
filled in the summer ; but in the winter, when the patients
are more indoors there was more space and a purer air was
breathed than is now the case, as the hotels were then only
half or a third full.

In the winter, 1870-71, there were 55 invalids with a few
friends accompanying them, whereas this winter the number
of visitors has been about 1,000, which means an addition of
considerably more than two thousand living in the valley
since I first knew it, and it is therefore now necessary to see
what the effect of this change is likely to be ; but before
going into that T may say that the Swiss issued a commis-

157

sion to see where consumption was most abundant, and to
examine the statement as to there being an immunity from
consumption at a certain height as stated by Dr. Lombard
and others. The report was edited by Dr. E. Muller.*
Nearly all the doctors applied to sent in their reports,
some few regularly during the five years which the commis-
sion sat, but although the report from Davos would have
been the most interesting in Switzerland, there is only one
line and that refers only to two years. However, from the
parallel valley of the Engadine some important reports were
sent, and since then Dr. Ludwig has published additional
particulars relating to the Engadine.")*

The results arrived at by the commission were that there
is no such thing as an immunity boundary, but that con-
sumption becomes less common as we ascend, but instead of
being found most rare in the highest villages those between
1,300—1,500 metres (4,265 — 4,921 feet) have fewer cases
than those between 1,500 — 1,800 metres (4,921 — 5,905 feet).

Dr. Hermann Weber has already in his Klimotherapiej
corrected the statement he made on the authority of others,
and as I repeated it in the pamphlet |] I wrote on Davos I
also take this earliest opportunity of correcting it, which is
all the more necessary as this does not yet seem to have
been done in what may be called the Davos literature.
However, we see from Dr. Ludwig’s figures that phthisis is
very rare in the Engadine ; and although we cannot any
longer say that the inhabitants who have never quitted the
valley of Davos have never been attacked by it, yet the
cases or case are so few (I believe it is now some time since
a case occurred) that we may say that, so far, there has been

* Die Verbreitung der Lungenschwindsucht in der Schweiz, von
E. Muller. Winterthur, 1876.

t Das Oberengadin, von Dr. J. M. Ludwig. Stuttgart, 1877.

X Ziemssen’s Allgemeine Therapie, vol. II., pt. 1.

H Klimatologische Notizen ii. den Winter im Hochgebirge, von
Arthur Wm. Waters. Basel, 1871*

158

almost immunity from this scourge for those who have never
left their native valley.

The commission, referred to, showed how much more free
agricultural and thinly populated districts were from con-
sumption, while in the higher valleys where there was a
large manufacturing population, as in the watch making
districts of the Jura, then the death-rate became considera-
ble ; and my own opinion is, that Davos, with a manufac-
turing population, would have been absolutely unhealthy,
but as this can only be a matter of personal opinion, it is
necessary to give the reasons that have led me to this
conclusion.

The position of the valley is most wonderfully favourable
for a health resort, being very wide, and well protected from
the north and east, and being so splendidly enclosed, there
is remarkably little wind in winter, but this very stillness
of the air which has made Davos unrivalled is a cause of
danger as soon as there are a large number of houses to
pour their smoke into the air, and their drainage on to the
land or into the river. We have now a very serious smoke
and drainage nuisance, and if changes are not soon made
the history of Davos will resemble that of many southern
health resorts, where favourable results have at first been
obtained, leading to exaggerated reports, upon which has
followed a rush of suitable and unsuitable cases ; then large
hotels have been built, but sanitary arrangements have
lagged behind, while instead of providing for a quiet simple
life, which is so frequently necessary for consumptive pa-
tients, the hotel keepers devoted their attention to furnishing
unsuitable amusements ; and theatres and other large build-
ings into which patients have congregated, have helped to
ruin many resorts. These are partly the reasons that the
favourite places of 20 years ago have been replaced by
newer ones. An overgrowth is more to be feared in an en-
closed valley, where there is only a very limited space, than
would be the case on the sea coast.

159

The question of drainage has received some attention
from the visitors the last two winters ; and this winter in
two little pamphlets attention was drawn to it, and also Dr.
Holland wrote to the local papers a letter which did not
receive the attention it deserved. Shortly after, this paper
intimated that the English were inclined to think too much
of drainage, because the Prince of Wales had typhoid a few
years ago, but the editor was probably unaware, or else
ignored the fact, that at the time he wrote this a petition
had just been got up entirely by Germans and Dutch, and
was signed by over two hundred visitors, with very few ex-
ceptions belonging to those nationalities. This was sent to
the central authorities of the canton in Chur, about the same
time as a petition, to the same effect, from one English hotel
with 70 signatures, and if it had been thought advisable to
make the petitions more general there would have been no
difficulty in obtaining about 400 more names. The answer
is, that certain laws relating to drainage, and which will
diminish the evils complained of, were passed May, 1881, by
the Landgemeinde. Although this law ought to have been
passed at least ten years ago, hardly anything has yet been
done towards carrying it out ; but probably the action of
the visitors will lead to this being done in the course of the
next few months.

Not very long after these petitions a letter from Mr. J.
Addington Symonds appeared in the Pall Mall Gazette ,
calling attention to an overgrowth of Davos, and pointing
out some present evils. This caused very much irritation
among some of the influential inhabitants, and at first they
were inclined to treat it all as incorrect ; but finding that
the general opinion among the visitors was that Mr. Sy-
monds was correct in the main points, their tone was very
much changed. Perhaps if this letter had remained in Mr.
Symonds’ desk for a week the irritation might have been
lessened by the modification of one or two expressions, but

160

I think that he was too good a friend to Davos to have
dealt with the facts less strongly, and in a second letter he
pointed out, that what he had written was entirely done for
the advantage of Davos, towards which he had the most
kindly feelings. Mr. Symonds’ communication was followed
by Dr. Gwillim (who had been residing here for some
months) in a letter to the Lancet , in which he supported
Mr. Symonds, saying that the drainage was in a disgraceful
condition, and probably that the results obtained in Davos
being now less satisfactory than they were at the commence-
ment must be attributed to the causes pointed out by Mr.
Symonds.

After numerous threats as to the answers which were
coming, the results were : a scurrilous one from a partially-
educated man who did not deal with the facts, but confined
himself to charging Mr. Symonds with writing merely to
forward personal and financial interests ; and afterwards an
answer signed by the Curverein, but which must be con-
sidered as an hotelkeeper’s answer, and which contained
misleading statements, especially those indicating that the
number of people living in the large hotel had not been
increased by changes made by the company owning it.

These agitations have shown that something must be done
for Davos to retain the high character that it has won, and
the hotelkeepers in consequence met tqgether and decided
to remove some of the evils, especially those caused by the
least powerful members of the community.

If public opinion makes itself felt in other years, and if
the attempt made by those who have built the theatre and
other public rooms towards what they call Concentration
des ’Kurlebens is unhesitatingly resisted, then Davos may
be saved ; but if the warnings given by those who believe
most in the principle of the climate and are its best
friends, are neglected, then it will soon be ruined, and the
judgment of the future may be that the whole thing has

161

been a gigantic fraud, and other places will suffer in conse-
quence.

As I was the first genuine Englishman to try this climate
for the winter— now twelve years ago, I feel it all the more
my duty to record the impressions made upon me now, and
as I have always been one of the most enthusiastic believers
in such climates for suitable cases, and have on both occa-
sions derived great benefit, I am anxious that warnings
given may not be neglected, but that this wonderful health-
giving treasure may be preserved to Europe for many years
and not be endangered by any who, either through igno-
rance of curative principles or zeal to become rich, are led
to overlook the true interests of the valley.

From these impressions I must pass on to the observa-
tions which I have made during the winter ; but as I have
not yet had time to put all my figures together, or revise
them, I can only refer to general results, but perhaps by so
doing I may receive some valuable hints for next winter’s
work from those who have more experience in such things
than I possess.

Evaporation.

The amount of moisture in the air is one of the most dif-
ficult questions to deal with in such a climate as Davos, and
much misunderstanding has existed concerning it. Dr.
Spengler would lay greater stress on the amount of abso-
lute moisture in the air than on the relative or percentage of
moisture, and I said ( loc . cit.) that it was not enough to con-
sider the relative moisture, but that “in my opinion the com-
parison of the weight of moisture in the air was to be recom-
mended, as in that way we could see what we were breath-
ing,” which is no doubt correct, though I should, if writing
the same thing now, express myself somewhat differently,
for the physiological action must depend more on the evapo-
ration from the body and lungs than on any other factor,
and this must be divided into two categories — firstly the

162

action on the skin, and secondly on the lungs through the
air we breathe.* I therefore considered that a series of ob-
servations on evaporation might be climatologically import-
ant from several standpoints.

The evaporation was made in a tin 27 cm. by 22 cm. by
5 cm. (nearly 9 in. by 11 in.), painted white, and hung up
by a wire in a screen 90 cm. wide by 75 cm. by 60 cm.
high, placed in the shade of a music pavilion. This pavi-
lion (27 feet diameter) was nothing more than a roof
supported by twelve pillars, thus allowing a free passage of
air, but protecting the screen from the sun during the
winter months of November, December, January, and Feb-
ruary, with the exception of a few minutes during the
last days of the month ; also during the shortest days the
sun shone for a short time between the pillars, but then the
screen was protected by cane blinds.

On the first of December there was a thaw most of the
day, and three times in the month a partial thaw. In
January there was no thaw, and until the 23rd of February
nothing more than the melting of a few drops in the warmest
part of the day, but after that the ice was mostly thawed.

The observations of value are those when the ice was not
melted, as when there was a thaw the evaporation would
neither represent that of ice nor of water, as then the tem-
perature of the water would remain at freezing point
although the air might be many degrees higher, so that
then little, or in extreme cases no evaporation might take
place.

During the months of December, January, and February,
the dew point was never above freezing ; at nine o’clock
the temperature of evaporation was also never above 32 ;
at 11 a.m. it was twice slightly above; at 1 p.m. seven

* In climatological considerations tlie amount of moisture carried off
from the lungs receives much more attention than that removed by the
skin, but as the amount removed in health, as perspiration, is greater
than that expired, both must be looked upon as of primary importance.

163

times ; at 3 p.m. fourteen times. The temperature of the
air rose more than half the days above freezing in the mid-
dle of the day, though only in a few exceptional cases above
that point in the morning. This winter has, therefore,
been an unfavourable one for my observations, as it is here
quite an exception for the air to rise so often above freezing
in the winter months. The tin of ice was weighed daily (at
11 a.m.) with a first rate beam 47 cm. long, made by Young
& Son, of London, and guaranteed to weigh 5 Kilo., and it
turned with a twentieth of a gramme.

*The evaporation from the ice inDecember was 12-24 mm.;
January 15*27 mm.; February 15-018 mm.

The smallest amount which I have had to measure in the
twenty-four hours was 0*084 mm., Dec. 13th, during which
time the temperature varied from 26*6° F. to about 19° F.,
with hardly any wind ; the largest amount with ice in the
tin all the time was 0-88 mm. on Dec. 11th, the temperature
rising to 35*7 at 11 a.m., but until about 8 a.m. the tem-
perature must have been moderately below freezing; on
the night of the 10th there was a considerable wind. Once
(Nov. 28th), with the tin full of water, the evaporation was
2*314 mm., but then the temperature was high all the time,
rising to 47° F., yet there was very little wind.

This winter has not been favourable for comparing the
evaporation of snow with that of ice, but I think the results
obtained seem to be, that when the tin is filled with snow
the evaporation is for the first day or two about 10 per cent
more than that of water, it then becomes more consolidated
and evaporation in both is about equal.

On one occasion I buried a tinful of snow up to the rim

*1 find that when there is water in the tin the temperature lags
very much behind that of the air, there being sometimes as much as
5° to 8° F. difference between the air and water. This must always be a
cause of difficulty in measuring evaporation, and therefore for comparison
the depth of water should always be the same, and perhaps the quantity
I used (viz. two inches) was too large.

164

in deep snow, exposed to the sun* from 9.15 a.m. to 3 p.m.,
the loss was 0*109 mm., or a trifle less than from the ice in
the shade during the same time, where, however, the tem-
perature was above freezing for about an hour. The loss
from the ice in the 24 hours was 0*429 mm. This form of
observation is probably worth constant repeating, and next
winter I purpose continuing the observations, with some
important modifications which experience has shown to be
advisable.

Of course the evaporation must be small when the tem-
perature is low (although somewhat accelerated here by the
low barometrical pressure). The figures for Paris and
Vienna are : —

Paris, 1875. Vienna, mean of many years.

December, 11 mm. ... 18 mm.

January, 34 mm. ... 13 mm.

In Paris, the yearly total is 776 mm. ; in London, about
650 mm.

The popular belief here is, that the evaporation in Davos is
extremely rapid under all circumstances, and this is no mere
theoretical question, for the false belief that newly built
houses dry miraculously rapidly has led to serious results,
and, probably through this error, the grave has closed over
some whose life might otherwise have been prolonged.
The south side of a house into which the powerful winter
sun pours is dried very rapidly, but the rest of the house
dries but slowly; and when here eleven years ago, I ex-
amined several houses just built, and tried to combat the
false ideas then held.

This winter a large cafd and theatre, into which very
little winter sun enters, was opened immediately upon
completion, and the results were that the larger propor-
tion of patients in the hotel to which these buildings belong
were in a few days suffering from colds, some sufficient to

* The solar radiation on the 9th as measured by a black bulb ther-
mometer in vacuo was 104° F. The day was cloudless.

165

call in medical aid, but a much larger number were only
slight cases.

The evaporation in my room in a square glass dish of the
same size as the tin out of doors, and placed on book shelves
sufficiently open for air to pass behind, gave from about
0*85 mm. to Til mm. per day, not varying much from day
to day, though, as a rule, greatest when the temperature out
of doors was coldest. Average temperature of room 55° F,
to 61° F. Dr. Volland’s figures reduced to millimeters give
a mean evaporation in the room from IT 4 mm. to 1T8 mm.
per day for the months of December, January, and February.

Comparison of Instruments : Dry and Wet Bulb.

My screen was made solely for the evaporation experi-
ments and was very open, being too open for regular
meteorological observations, as thus there was a danger of
snow being blown in laterally ; on the other hand, for the
comparison of instruments, this openness was an advantage ;
so when a Mason’s (August’s) wet and dry bulb hygrometer,
made by Casella, was offered to be lent me by Mr. Steffen,
as well as two hair hygrometers similar to those used by
the Swiss meteorological stations, offered me by Dr. Ruedi
and Mr. J. Addington Symonds,* I yielded to the temptation
and hung them up in my box, at an 18 inches lower level
than my ice tin, and by short-interval observations followed
their action in various ways through the winter.

As is well known, the difficulties in obtaining the amount
of moisture correctly with the wet and dry bulb thermo-
meters, when the temperature is below freezing, are very
great. There are difficulties which occur about the time
that the freezing point is passed which probably cannot be
got over, but I think that when the temperature is steadily
below freezing for a long time, precautions may be
taken which will lead to a greater amount of correctness

* Mr. Martini, the optician, also lent me instruments for temporary
comparison.

166

than has yet been obtained. As long as the bulb can be
supplied with water this is constantly flowing up the thread,
where it soon attains the temperature of evaporation, and
then a comparatively equal film of water is always main-
tained in the muslin surrounding the bulb, but as soon as
the temperature is below freezing the personal equation
plays a large part, for now we shall find that the covering
of the bulb is a very material point, as well as the thickness
of the ice sheet, which is no longer automaf ically arranged,
and further, the temperature of the wet bulb after an ice
sheet has been formed will vary very much from time to
time. The instructions usually given are that the bulb
should be wetted about half an hour before an observation,
but I find that in practice many observers only do this a
quarter of an hour before. I have already called attention
to this not being long enough, and although I have not
this winter obtained as striking results as I did some winters
ago, yet through some hundred of observations, in which
special attention was paid to the dew point, as that cannot
change so rapidly or irregularly as the temperature, I am
able to fully confirm what I then wrote as to a longer time
being required. This is most important in relation to the
Davos climate, because it has been charged against Davos
that it is not dry, and while the relative moisture is no
doubt greater than the popular talk about the place would
lead us to expect, yet I think that many of the figures
which have been published would make it appear moister
than is really the case.

The first observations were made by Dr. Spengler from
1867 to 1871. These were made in a metal box attached to
the side of the house, as is usually done in Switzerland, and
as I felt somewhat doubtful as to the results obtained in a
metal box so near a house, I put up, in 1870, a very large
screen consisting of an inner box with single louvres, sur-
rounded by an outer one at a distance of six inches, also

167

with single louvres, but sloping in an opposite direction.
The screen was placed about twenty feet from all buildings,
but during the winter months was, with the exception of a
short time in the day, in the shade. Rightly or wrongly, I
considered this screen was preferable for this climate to a
Stevenson’s screen, and that yet observations so made were
comparable with those made in England.

Although my times of observation were not quite the
same as those of Dr. Spengler, yet they admit of certain
comparisons being made, and we find that there apparently
was very little difference in the early morning temperature,
though my registers seem to have been a little the lowest ;
also in the middle of the day, the difference as a rule was not
great, though then mine were rather the highest.* When we
come to the moisture then the observations are more un-
satisfactory, for while the mean would not differ very much,
yet when detail examination is made we find very serious
differences, sometimes in one direction, sometimes in another,
and I have therefore in these cases compared with neigh-
bouring places, and it is clear that sometimes the error was
on my side, and sometimes on that of Dr. Spengler ; and, as
we may conclude in hygrometrical measurements that the
lower figure is the correct one, this shows that Davos is
much drier than the figures obtained by either of us would
seem to indicate. On mentioning this to Dr. Spengler, he
considered that his error would arise from the bulb having
been wetted too short a time before the observation, which
I have already shown to be a source of frequent error. The
detail comparison entirely bears this out, whereas it now
seems on similar examination that my error was in the op-
posite direction, and, therefore, although I took every pos-
* Our published monthly means are : —

Spengler.

Waters.

Difference.

November, 1870...

...— 1*39°C.

... —1*0° 0.

... 0*39.

December, 1870...,

... — 8'12°C.

... — 8'20°C.

... 0*08.

January, 1871...

...— 9-68°C.

... — 9*69°C.

... 0*01.

February, 1871...

.„ — 4-09°C.

... 0*97.

168

sible care by frequently seeing that the bulb was in order,
and no doubt Dr. Spengler was equally conscientious in his
observations, yet it does seem that we both obtained too
high a percentage of moisture

The danger of error from these sources may to a large
extent be overcome by having three thermometers, one of
which will remain the dry bulb, whereas the other two
should be kept wet, and one should have a recently formed
sheet of ice, whereas the other should have an older one to
which water has been added at least an hour before, for
though in a few cases the temperature of evaporation was
soon reached, yet as a rule this is not attained in an hour.
I intend to use such a thermometer next winter, and con-
sider that to obtain correct results this is almost a necessity,
when the temperature is below freezing. As there is little
wind here it would also be well to create a current by a
revolving fan, as is done by the Italian meteorologists.

The observations taken by Mr. Steffen since 1876 give for
the winter months a materially less percentage of moisture in
the air than Dr. Spengler obtained, and no doubt from the
causes just mentioned. Unfortunately the position of Mr.
Steffen’s house is very unfavourable for meteorological
observations, as the instruments are sheltered by the house
from the east and north winds, and a north-east wind
very frequently blows, as valley wind, where his house is
situated.

Hair Hygrometer.

Knowing the difficulty with the wet and dry bulb hygro-
meter, it becomes an important question to find out how far
hair hygrometers are available in cold weather, especially
as the Swiss meteorologists are now using them, and there-
fore I observed their action carefully to see if they would
be useful for my next winter’s work, and I soon saw from
the daily curve which they gave, compared with Mason’s,
that they were not sufficiently sensitive, and did not alter

169

rapidly enough ; so to further test their action I several
times removed one from my room to my box out of doors,
and vice versa , and then compared, to see how soon the
instrument removed corresponded with the one which had
not been recently changed, and I found that it was several
hours before the readings were similar, and further noticed
that when brought from the cold air to the warm room the
readings were much sooner reliable than when it was
removed to the cold.

As an example similar to several others, hygrometer No.
1 had, on January 7th, been out of doors for some weeks,
when I put No. 2 out from my room, at 10 a.m., when it
stood at 32*5. No. 1 stood at 66 out of doors. The course
of the two, neglecting small fractions, is shown in the fol-
lowing tables

Jan. 7th. 10 a.m.

11 a.m.

1 p.m.

3 p.m. 8th.

9 a.m.

11 a.m

1 p.m.

8 p.m.

No. 1. 66

61

50

52

73

62

51

42

No. 2. —

47

56

59

72

61

51-5

42*5

Difference . .

.-14

+ 6

+ 7

-1

-1

+ 0-5

•f 0*5

Jan. 9th.

9 a.m.

11 am.

1 p.m.

3 p.m.

Jan. 10th, 9 a.

m.

No. 1.

55

52

42

38

82

No. 2.

54

52

41*5

38

80

-1

0

-0-5

0

-2

From which we

see that in the

first

hour

it had only

risen 15 per cent, that afterwards it became too high, and
was not reliable all that day. It was, of course, a severe
test for the instrument, but as we have had as great a dif-
ference as 40 per cent out of doors in one day, any instru-
ment which changes so slowly is unsuitable for exact meteor-
ological work.

Besides this slowness of action these two hygrometers,
which I have reason to believe are first-rate instruments of
their kind, will not always give similar indications* For
instance* when

170

No. 1 showed 88, No. 2 at various times indicated *92 88 95

Do. 78 80 84

Do. 73 79 79 81

Do. 42 48 49 48

Besides these I had the loan for a short time of two other
superior instruments, made by known makers, and in each
case I found great irregularity of action. These four instru-
ments cost from 35 — 45 francs each. A short pillar gut
hygrometer was also lent me, but as these should never be.
considered as meteorological instruments (though they may
be useful in a room), comparison of their action is here un-
necessary.

In consequence of these comparisons I do not feel inclined
to place absolute reliance upon the hair hygrometer, though I
think it most useful to have one in every meteorological
box, as it may help over some points of difficulty ; for
instance, you go to take your reading and find that the ice
on the wet bulb has only partially thawed, and consequently
you know that the reading is valueless, but by now noticing
the hair hygrometer and returning in half an hour to com-
plete the observation, fairly reliable results may be obtained.

RegnauWs Hygrometer.

Towards the end of the winter I obtained from England
a Regnault’s hygrometer, but as the quicksilver of one of
the thermometers became divided on the journey, through
there being some air in the tube, I have not made as many
control observations as I otherwise should have done, but
the observations made will nevertheless enable me to form
an idea as to which formula should be used, and further, as
this is an instrument requiring considerable practice, I am
glad to have had some experience with it, as I see that here
much will depend on its being properly placed, because, as

* The last examples are given uncorrected, whereas I applied a cor-
rection to the series previously quoted, commencing Jan. 7th. Of course
it will be understood that the correction must be the addition or sub-
traction of equal arcs and not of degrees of moisture*

171

the gold cup is sometimes reduced 20 — 30 degrees* before
dew point is obtained, it is evidently necessary that it
should be protected from the wind ; but even then we may
be sure that the outside of the cup will be slightly warmer
than the inside. When this form of hygrometer has been
more used, I think that we shall better understand the
Davos climate.

Position of Instruments.

In order to obtain the relative moisture correctly, it is
of course of the utmost importance that the instruments
should be correctly placed and protected; and I have there-
fore given some attention to this question, which seems to
be one of the most difficult meteorological problems, and
is now receiving much attention from meteorologists. It
will be seen that I have on both occasions placed my screen
in the shade, and I think that I may now definitely say
that such an arrangement is necessary, for here when the
solar radiation is so intense and the movement of the air
but slight, a Stevenson’s screen, as now commonly used in
England, is warmed by the sun,-f* so that the temperature is

# On April 7th, seeing the hair hygrometer showed the air to he very
dry (under 17 per cent), I used the Regnault and found the dew point
4° F. with the air temperature 49-5° F., thus giving about 14£ per cent
of moisture. On this occasion, therefore, the temperature of the cup
was reduced 85 degrees.

f In the pamphlet to which I have already alluded, and which was
hut a youthful production, I gave my measurements of the solar radia-
tion as taken with a hlack hulh thermometer in vacuo, and I think it
well to repeat them here, because some similar observations made since
by the Rev. Mr. Redford, F.M.S., and others, for four years at the hotel
Belvedere, have found their way into a very large number of medical
publications, although they are entirely incorrect in consequence of the
radiation thermometer being placed upon the white screen, thus regis-
tering, instead of 100° F., about 120° F., and instead of 120° F, about

140—150° F. r— 1870 , r— 1871 — ,

Nov. Dec. Jan. Feb.
Mean of daily Maxima 95’IF. ... 73-9 F. ... 77'3 ... 104-3

Maxima of month 115-4F. ... 1151F. ... 117-2 ... 126-0

Mean of the Maxima of Air

Temperature, in shade 85-8 F. ... 41-9 F. 43-8 F. 32*4

172

too high, causing the readings of any hygrometrical instru-
ment to show too low a percentage of moisture. Some
observations made for three years at the Belvedere seem to
me of little value on account of being made in a Stevenson’s
screen exposed to the sun ; but on this point I do not now
wish to speak too positively, as I purpose shortly comparing
all the observations made in Davos in order to find out what
screen should be used.

It must not be forgotten that those causes which give us
so much solar radiation also bring about great terrestrial
radiation. No exact observations have yet been made here
on this subject of terrestrial radiation, and as I only had
a place very much exposed to the ravages of dogs and
children I could not place out a valuable instrument, but
put out a cheap minimum thermometer about an inch above
the snow, with the bulb painted white, because I considered
that in this way the radiation from the snow was best
tested. I had it out for about four weeks, when it was
stolen. The results were that the mean minimum from the
6th to 28th February inclusive was 5*5°Fahr., which is
about thirteen and a half degrees lower than the mean of
the minima of the shade temperature, but as the instruments
were not absolutely reliable I cannot give the exact differ-
ence. This means that on a fine day the difference between
the minimum terrestrial and maximum solar radiation is at
least 100° F.; on one occasion it was 122*8 degrees. At
nine o’clock (viz., before the sun was shining in the valley
generally) I registered — 8° Fahr. with the radiation ther-
mometer, and at the same time the temperature of the air
was 19*2° F. or a difference of 22*2 degrees. I had the
opportunity of seeing that thermometers placed, unprotected,
on the side of a house, as is so often done by those who
take “ window observations,” gave morning results fairly
parallel with these terrestrial observations, and did not give
the temperature of the air at all, and it seems that both the

173

exposed Stevenson’s screen or a metal box attached to the
side of a house, as used by the Swiss, must be very much
influenced by terrestrial radiation.*

Mr. Demmer, the intelligent proprietor of the Angieterre
Hotel, shortly before my arrival put up a Stevenson’s
screen in a provisional position, and as soon as he has com-
pleted some building and is satisfied as to the best means of
protecting the instruments, intends to make some observa-
tions. He very kindly allowed me to make some compari-
sons with the result obtained in my box, and as his instru-
ments were made by Casella and tested in Kew, and those
I was using also by Casella, they may be relied upon.

From ten observations made for the purpose, I find that
the average range in temperature from 9 a.m. to 1 p.m. is
5 degrees more than I obtained in my shaded box, and
upon one occasion the range was 9 ’2° F. more than mine.

Formula.

But even when we have got the observations correctly
taken we are by no means at the end of our difficulties, as
the different formulae used to calculate the moisture from
the dry and wet bulbs give materially different results. In
England, Glaisher’s tables, or Apjohn’s formula are mostly
used ; whereas in Germany and Switzerland tables based on
Kegnault’s formula or the formula itself are used.

In Glaisher’s tables we find under dry 36°, wet 30° F.,
relative moisture, 53 per cent at sea level, whereas Jelinekf
for the same temperatures gives 47 per cent. With a very
cold and dry air, the difference would be much larger, and
the differences of the various formulse are in some cases
increased when we give the correction for diminished baro-

# Prof. H. Wild describes a large wooden screen under wbicli the
metal boxes as used in Switzerland can be hung, and probably this would
be the most satisfactory plan for Davos. Aufstellung der Thermometer
z. Bestimm. d. wahren Lufttemp. Ak. St. Petersburg, 1878.

f Psychrom. Tafeln. fur das hundertth. Thermom. von Dr. Jelinek.
Wien, 1876.

174

metrical pressure, though by using Regnault’s or Apjohn’s
original formula the difference is not so very great.

I have, however, noticed that in some papers on high
climates presented to the London Meteorological Society,
Glaisher’s tables have been used without applying any baro-
metrical correction, whereas the tables are arranged for
England, and not for a barometrical pressure of 25 inches
without correction.

In Dr. C. Theodore Williams’ communication “On the
Winter climate of Davos,” Meteor. Journ he seems to have
taken the mean of the month’s temperature of the wet and
dry bulb,* and then by the aid of Glaisher’s tables without
barometrical correction, put down the “ relative humidity”
obtained from these figures as the month’s mean, causing in
many cases a very considerable error. For instance, he
gives Jan., 1881, from mean temperature of air at 1 p.m.
28‘9° F., mean of evaporation 24*6° F., the relative moisture
as 40, to which he refers in the text as showing how dry
the month was, whereas if he will calculate this out by
Apjohn’s formula

^ d h
96 X 30*

he will obtain COT, though if he had taken the mean of
each day’s humidity he would have obtained about 67'0 re-
lative humidity.^ It is very unfortunate that anyone of
Dr. Williams’ medical reputation, and who has written
several important things on Davos, should have given his
name to a paper where the observations are open to grave
doubts, and the calculations made as if Davos was on the
sea coast.

I have, however, found that the moisture as calculated

* These figures cannot give the mean humidity correctly, but it
must be calculated out for each day, and then the mean of these results
given.

f Mr. Muddock’s figures of observations taken by the same observers
give for Feb., 1880, temperature at 1 p.m. 36 '06° F., not 38‘4 as given by

Dr. W.

175

by Apjohn’s formula is higher than what I have obtained
with other instruments this winter. I hear that some im-
portant experiments are now being made on various hygro-
meters, and we may hope that they will result in bringing
about greater uniformity than now exists.

Dryness of Air we breathe.

Although it is necessary that the meteorological condi-
tions of the air should be studied, we must not stop there,
but must afterwards find what is the influence upon the
human organism. I formerly pointed out how much pa-
tients could be out of doors in Davos, and extended expe-
rience convinces me that they enjoy, in favourable winters,
more fresh air out of doors than in warmer resorts, as the
Riviera ; but this time I will not stop there, for what is also
very important, we can enjoy fresh air more in our rooms
than in most warm resorts. No doubt it will at first sight
seem strange that consumptive patients should sleep with
their windows open* where the temperature is 10°, 20°,
30° F., or even more, below freezing point ; but consideration
wi]l show that it is only reasonable and what we might
expect, for with the low temperature the absolute amount
of moisture, even were the air saturated, could be but small.
Now the cold air entering into the room is rapidly warmed,
and as the amount of moisture it contains is a very small
proportion of what air at the room temperature can contain,
this causes the relative moisture of the room to be very low.
I have found this winter that in my room this percentage
of the possible moisture has varied from 25° — 35° as mea-
sured with a hair hygrometer and also with a Regnault’s
condenser hygrometer. As an example, on January 15th,
at 9 a.m., the temperature of the air out of doors was 18° F,

* When I speak of the window being open I do not mean wide open,
but one large pane or the top of the window open, and this is enough to
keep the air fresh. Much wind prevents this, but fortunately this has
been very rare this winter.

176

and the relative moisture 60°, showing that the air contained
0-7 grains of moisture in a cubic foot. The total quan-
tity which air at 18° F. can contain is 1*2 grains, whereas
at 60° F., the temperature of my room, it could contain 5*8
grains; so that air entering with only 07 grains would
have only 12 relative humidity, but as there is always
evaporation going on in my room from the water basin, &c.,
and also some steam entering from the steam stove which
heats the room, the percentage of moisture is raised, and on
the occasion referred to the amount actually in my room
was 27 rel. humid.

Dr. Volland* made some observations on the amount of
moisture in the room, and he obtained much more than I
have ever found the case, but it seems to me that this is
to be accounted for by his using the wet and dry bulb
thermometers, which I find are not at all suitable for room
observations, as the stagnation of air is too great. I have
found that the temperature of the wet bulb is reduced
several degrees by the artificial current produced by waving
a newspaper in front of it.

On the Riviera di Levante I dare not sleep with an open
window, which is easily understood, because the relative
moisture being more at night than in the day, without the
temperature outside being very materially below that of the
room, we should only be breathing damp air through the
night. We now see that in Davos we are not only breath-
ing an absolutely dry air, but also nearly, or all through the
24 hours, a relatively very dry one, in fact, drier than either
on the Riviera or Egypt.

Seeing how dry the rooms really are we can easily
understand how it is that the general public should form
very exaggerated ideas as to the dryness of the place, for
even the shopkeepers when they have spoiled old stock try
to pass it off by ascribing the changes that have taken place
#Ueber Verdunstung und Insolation, von Dr. Volland. Basel, 1879.

177

to the dryness of Davos ; and many of the medical writers
on Davos have been misled in the same way, and give
examples which have nothing to do with the dryness of the
climate, for instance, the sun shining on the dark roofs or
road makes the surface on which it shines extremely warm,
and as the warm layer of air is capable of containing much
more moisture than the colder air above, the evaporation is
extremely rapid, and the roof or road is soon dried, and the
moisture rises into a colder air, in fact sometimes this
stratum of air is so much colder than that below that it
cannot contain as much moisture as exists in the warmer
air, and the banks are seen to steam, showing that the
ground is warmed by the sun, but by itself not giving any
clue as to the amount of moisture in the air. These
phenomena, or the rapid drying of ink, or cracking of furni-
ture, have often been used to illustrate the dryness of
climates, whereas they really, in such cases, only show the
difference of temperature of the room and outside air or the
warming of the ground ; but these considerations show us
that the physiological action of the dryness or dampness of
a climate is not a simple one, for as the body is warmer
than the surrounding air evaporation must take place more
rapidly from the skin than from the evaporometer, and the
difference will be more marked, cceteris paribus, when the
quantity of absolute moisture is small, that is, when the air
is cold.

In the same way cold air entering the lungs is raised to a
temperature approaching blood heat ; now this cold air may
be relatively moist, but the absolute moisture which it con-
tains is but small, so that when raised to nearly blood heat it
would be very dry, which means that it can absorb a great
deal of moisture, which will be the case, and it will carry
off a large quantity from the lungs. An example will make
this clearer. Supposing that the air breathed at the sea
level is 20° F., and contains 80 per cent of the possible

178

moisture required for saturation, this will be raised in the
lungs to something like 85° F., viz., a few degrees lower
than the blood heat; at that temperature it can contain
about ten times as much moisture as it could at 20° F.,
and will, therefore, carry off a large part of this amount
from the lungs; or to put this another way, the amount
of evaporation from the lungs will now be much the same
physically as if we breathed air of 85° F. only containing
about nine per cent relative moisture. This has already
been pointed out by Brunner, Krieger, &c. ; and Mr. Steffen,
the chemist here, published some tables, in which he re-
duced the moisture in the air to the relative of the mean
blood heat (37° Cel.), that is, he showed for each month
what per cent of the quantity which air could contain
at 37° C. was present in the atmosphere.* It seems to me
that the principle thus dealt with is undoubtedly cor-
rect, but I think that the figures require modification,
because, as pointed out by Dr. Yolland, it is taken for
granted that the air was raised to blood heat and expired
saturated, neither of which are absolutely correct. I hope
to enter more fully into this point when I have had the
opportunity of collecting more data, and seeing what has
been written on the subject.

We must not forget that the physiological feeling of cold
depends, to a large extent, upon evaporation, for perspiration
is always taking place from the surface of the body, though
we only notice it when it is abnormally great, and upon the
rapidity with which this is removed hangs to a large extent
our sensation of the air being dry or cold. We have already
seen that the evaporation from the skin is, as a rule, great
in Davos, and to this cause must, to a large extent, be
attributed our sensation of the dryness of the atmo-
sphere.

* Die Meteorologisclie Verhaltnisse von Davos von W. Steffen. Basel,
1878*

179

Wind.

The next point is the amount of wind. It has always
been maintained that there is very little wind in the valley
in winter, but as bare statements on such a subject are not
often satisfactory, I put up a Robinson’s anemometer. I
was not able to find an altogether suitable place, for on the
roof of a house we might measure the valley wind, but this
would have very little meteorological value, and none
physiologically, besides which the instrument would soon
have been clogged with smoke. I therefore decided to put
it up just over 5ft. 5in. above the ground, in a position quite
open to the north and south, but unfortunately somewhat
protected by a building (160 feet way) from the south-west
wind, of which we have had little this winter. A building
on the W.N.W. (120 feet away) did not make any difference,
as the wind in this spot never blows from that direction.
In a valley the wind often varies very much within short
distances, both in direction and force, but I think we may
say that my instrument would fairly show the force of wind
to which a patient was exposed in taking an ordinary walk.
As the value of these observations were physiological, I
noted down the movement at 9 a.m. and 3 p,m., thus getting
our winter day ; and as the valley wind rises in the after-
noon, I also observed, with a few exceptions, at 1 p.m. I
have not yet applied the correction for diminished barome-
trical pressure, but give the figures as registered, but thus
unrevised. The total movement was for—

Day. Night.

Total. From 9 to 3 : From 3 to 9 :

Miles. 6 hours. 18 hours.

November, 1881 561*69 ... — ... —

December 727*99 ... 256*14 ... 471*85

January, 1882 283*76 ... 77*95 ... 205*81

February 597*92 ... 290*95 ... 306*97

March 1656*61 ... — ... —

April (to 24th) 1439*59 ... — ... —

625*04

984*63

180

The result of the 89 days of December, January, and Feb-
ruary (during this time the ground was more or less covered
with snow when I went to my instrument at 1 p.m.), shows
that the mean rate from 9 — 1 was 0'608 miles per hour,
while from 1 to 3 p.m. it was 1-384 miles per hour; that is
to say that about one-fifth of the wind which blew in the 24
hours was between 1 to 3 p.m., and nearly all of this will be
a valley wind* ; and to return to what I before said, this
will mean that the same air may be blown backwards and
forwards two or three times over Davos, and thus there are
great dangers from any drainage carried into the river
within a few miles of the principal village.

Smoke.

There is another thing which I must mention, though not
belonging to any series of observations, but when here
before I frequently had occasion to examine the snow and
smoke microscopically, and at that time the snow really re-
mained white, and when filtered, hardly gave any deposit,
as the combustion from the stoves was very perfect and
nearly all the smoke was microscopic, consisting of small
particles, in which wood structure could often be seen, but
now all is changed, for when I filtered snow water to use it
for evaporation, the filter soon became quite black, and so
far choked up the filter as to allow the water to pass through
but very slowly.

The large amount of smoke which falls upon the snow is
to a large extent masked, because in our fine weather the
snow entirely recrystallises down to the ground, within a

* This winter has been generally still in this district of Switzerland,
that possibly there is usually more wind than this winter, but we can see
that it is as a rule but little. The ground was free of snow most of
March, and therefore the valley wind was stronger.

Out of 293 times that I went to the anemometer during the three
winter months, there was no movement at all on 208 occasions (71 per cent).

At 9 a.m. it was 16 times moving and 74 still.

At 1 p.m. do. 20 do. 59 do.

At 3 p.m. do. 44 do. 45 do.

181

few days of falling, and each night the upper crystals grow
very much through the deposit of hoar frost. In the lower
part of the valley, especially near the river, these arborescent
crystals grow to be sometimes two inches long or even more,
while on the sides of the hill they are but small. This test
as to the amount of moisture in the air shows how much
more healthy the higher positions must be. These crystals,
however, grow on the surface, so that the smoke is no
longer visible, but when a thaw comes then, in comparison
to what it was twelve years ago, it may around the village
be called black, though of course in comparison with that
in a large English town we should have to call it white.*

The Curverein, in their German answer to Mr. Symonds,
replied that what he said about the smoke could not be true,
as the snow crystals glittered, but as the English translation
in the Pall Mall was very much modified on this point, it
■would seem that a thaw in the meantime must have shown
the writers the absolute incorrectness of what they had said.f

# I should have been glad to have had some exact observations on the
amount of smoke, but I did not see the importance of this until too late*
I then wrote to my friend Professor F. Clowes, who kindly sent me
weighed filter papers, but there has not been a favourable opportunity
since. However, I sent Professor Clowes one of my larger used filter
papers, and he removed the dirt, which will be almost all smoke to a
weighed paper. I filled my tin, Feb. 20th, with 1300 grammes of snow}
which must have fallen on the 19th, and when put into the tin looked
quite clean. It was hung in my meteorological screen until the 23rd. The
dirt thus removed, and weighed by Professor Clowes in the manner,
mentioned: was 0'082 gramme.

If I had taken this snow from an area three times the size of my tin,
■which is an ample allowance, we should find that the amount of the dirt —
mostly smoke — which falls in the large Curhaus garden, amounts in a
few days to half a hundred weight. The position of the tin was nearly
due south of the large chimney, which is situated 330 feet away. More
exact observations on this point would be valuable.

f Besides the observations mentioned, I have a few temperature
measurements, made with the thermometer in the snow, or placed above
it ; and further, I have a series, from various visitors, of about 3,000
measurements of the blood temperature taken at fixed times, in order to
study the physiological action of weather. These will take some time
to work up, and will be dealt with in a separate communication.

182

There is one most important point which is sure to
receive very different judgments, and that is how the
patients are to be amused, and perhaps those who know
that various investigations give me constant employment in
my own room, may think that therefore I do not understand
its importance, whereas on the contrary I should place it
above all other medical treatment, and appreciate how
difficult it is to strike the happy mean by which people shall
be amused by taking part in amusements without these
being on so large a scale as to cause fatigue. For my own
part, I often feel that though my devotion to science causes
me sometimes to risk my health, yet from the health point
of view I am amply repaid by being enabled, in the non-
vitiated air of my own room, to ever find new interests and
never experience ennui instead of requiring to frequent
crowded salons and theatres, and breathe the second-hand
breath of 100 to 200 consumptive patients, but the work
which to me is a source of health, would to an-
other be a great danger, and so long as we are so
differently constituted, and in different stages of illness,
no rule can be laid down for relaxation. And this
leads me back to the starting point, and I wish to
lay stress on my introductory remarks being a strong
warning against the overgrowth of Davos, and do not
wish them to be interpreted into meaning that Davos
is ruined, for what is meant is that Davos must not
grow any bigger. It would perhaps be presumptuous to
say that it can never grow, for possibly in the next 10 or
20 years the great smoke producers — at the head of which
stands the Curhaus, followed by the next largest hotel in
the village — may have been taught that they have been
very uneconomical, and that there is no necessity to pour so
much smoke into the air, and also some earth system may
have solved the drainage difficulty and allow a limited
increase.

183

PHYSICAL AND MATHEMATICAL SECTION.

January 31st, 1882.

Joseph Baxendell, President of the Section, in the Chair.

Mr, W. H. Johnson, B.Sc., and Mr. William Thomson,
F.B.8.E., F.C.S., were elected members of the Section.

February 14th, 1882.

Alfred Brothers, F.R.A.S., in the Chair.

“ Notes on the Variable Stars U Canis Minoris, V Gemi-
norum, and U Bootis,” by Joseph Baxendell, F.B.A.S.

In a communication to the Section on April 13th, 1880,
I announced the discovery of three new variable stars— the
first in Canis minor, the second in Gemini, and the third in
Bootes. The observations which I have since made, though
much less numerous than I could have wished owing to
ill health and unfavourable weather, have been sufficient to
enable me to ascertain the nature and extent of the changes
of brightness and to deduce approximate elements.

U Canis Minoris.

1855-0. a = 7h. 33m. 27-5s. 2= +8° 42*9'.

A projection of the observations of this star shows that it
has a double period, but unlike the other known double-
period variables in which the sub-periods are nearly if not
quite equal, in this they are very unequal.

Proceedin 9-s—Lit . & Phil. Soc.— Yol. XXI.— No. 11.— Session 188L-2*

184

The times of four minima and three maxima have been
obtained and are as follows

Principal Minima:

1880, September 27.

1881, November 17.

Secondary Minima :

1880, January 14.

1881, March 11.

Maxima :

1880, February 24.

„ December 27.

1881, April 29.

The secondary minima give the period = 422 days.

The principal „ „ =416 „

The maxima of Feb. 24, 1880, and Apl. 29, 1881 = 430 days.
The mean period is therefore about 423 days.

The interval from the principal to the secondary minimum
is 169 days, and from the secondary to the principal mini-
mum 254 days.

The highest maximum magnitude yet observed is 8' 5,
and the lowest minimum 13 0; the range of variation being
therefore 4-5 magnitude.

V Geminorum.

1855-0. a = 7h. 15m. 2s. 3 = +13° 21-9'.

My observations of this star have yielded the times of
two maxima and two minima as follows
Maxima :

1880, February 6.

„ November 9.

Minima :

1881, March 28.

„ December 28.

185

The maxima give the period =277 days, and the minima
=275. The mean period is therefore about 276 days.

The highest observed magnitude at maximum is 8*7.
At minimum the star falls below 13*5 magnitude.

U Bootis.

1855-0. a = 14h. 47m. 37*4s. a=+18°17T'.

This variable is more regular in its changes than either
U Canis minoris or Y Geminorum, and its period much
shorter. The observed maxima and minima are as follows:—
Maxima :

1880, March 22.

„ September 15.

1881, August 31.

Minima :

1880, June 11.

1881, May 31.

It was equal to 11*5 magnitude when decreasing.

1880, May 5.

„ October 29.

1881, April 23.

„ October 14.

And equal to 11 '5 magnitude when increasing.

1880, July 22.

1881, July 4.

The mean period derived from the above data is 175*5
days ; and the mean interval from minimum to maximum
is 94-0 days; and from maximum to minimum 81*5 days.
A maximum may be expected to occur about August 17,

1882.

The highest observed magnitude at maximum is 9*15,
and the lowest at minimum 13-6, the extreme range of
variation being therefore 4*45 magnitude.

186

Mr. J. A. Bennion, B.A., F.R.A.S., read a paper “On the
Resolution into Factors of some Trigonometrical Expressions
without using imaginaries.”

Annual Meeting, March 14th, 1882.

Joseph Baxendell, President of the Section, in the Chair.

The following gentlemen were elected Officers of the
Section for the ensuing year.

3]3rcsfacnt.

JOSEPH BAXENDELL, F.R.A.S., &c.

Hicc=^icstUcnts.

J. P. JOULE, LL.D., D.C.L., F.R.S., F.C.S.

A. BROTHERS, F.R.A.S.

Suwtarg.

J. A. BENNION, B.A., F.R.A.S.
treasurer.

JAMES BOTTOMLEY, D.Sc., B.A., F.C.S.

Mr. Brothers, F.R.A.S., showed a diagram of the Baro-
metric Oscillations for the year 1881.

Mr. W. H. Johnson, B.Sc., exhibited several electric
lamps, some of which were intended for use in Collieries.

187

“ Notes of some Experiments made in February, 1881, on
the Influence of Stress on the Electrical Kesistance of Iron
and Steel Wires,” by Wm. H. Johnson, B.Sc.

A piece of piano steel wire, about 0-040 inch diameter,
was found to have a resistance of 0'418 Ohms. A heavy
longitudinal stress causing a temporary elongation of 3 /,
but not sufficient to produce any permanent strain, was
applied, and the resistance observed was 0-422 Ohms, the
temperature in both cases being the same.

If the resistance per meter gramme of the wire had been
unaltered by the stress, the observed resistance of the wire
under stress should have been 0*443 Ohms, or some 5 °/Q
more than that observed.

The resistance of hardened and tempered steel wire thus
appears to decrease 5 °/0 under stress.

Experiments were next made on hard iron wire, about
the same diameter as above, 1*774 meters long and 0*2274
Ohms resistance. Under longitudinal stress, causing a
temporary elongation of 0*33 °/0, the resistance was found to
be 0*232 Ohms. Now, if the wire had been unaltered in
resistance by stress, the observed resistance should have
been 0-229 Ohms. Thus it appears that the resistance of
hard or unannealed iron wire, unlike piano steel, is increased
by stress some 1 J %.

The figures denoting the percentage of change of resis-
tance caused by stress are of course only approximate, but
serve well to denote the direction of the change.

In both sets of experiments the iron and steel wires
returned to their original resistance when the stress was
removed.

The stress applied to the steel wire was many times that
applied to the iron wire, so it is just possible that the steel
wire under a small stress would have behaved like the iron
wire and increased in resistance. The stress applied to both

188

iron and steel wires was the highest they would hear without
permanent change of length.

The writer has long intended to continue these investi-
gations, but hitherto time has failed him, and he now only
publishes them as he sees from an abstract of the Pro.
Eoyal Society, January 26th, that Mr. H. Tomlimson, B.A.,
has been experimenting in the same direction.

Dr. Bottomley pointed out an analogy between the circle
and the logarithmic spiral, and showed how some properties
of the former curve could be derived from the latter.

“On the Projection of a Solid on Three Coordinate Planes,”
by James Bottomley, D.Sc., B.A., F.C.S.

Take a solid of any form and let sections be made by
parallel planes fixed in the solid. Let L be the longest axis
of the solid which is perpendicular to these planes. This
axis and these planes we may call the primitive axis and
the primitive planes.

Let the primitive axis make^with the axes of x, y , 0 angles
a, j3, y respectively. Consider a section whose area is Ax.
If this be projected on the plane xy the area of the projec-
tion will be A^osy. This projection we may denote by Agl.
So in like manner the projections on the other planes will
be AiCOSj3 and Aicosa, and may be denoted by 4*1* Axl.
The projections of a second area A2 will be A2cosy, A2cosj3,
A2cosa, and may be denoted by Az2, A.y2, Ax2. Let the
remaining planes be projected in the same manner. Then

by addition we shall have

Azi + Az2 + . . . Azn = cosy(Ai + Aa + . . . An) (1)

AyX + Ay2 + . . . Ayw = cos/3(A1 + Aa+ . . . An) (2)

A*! + Ax2 + • • . Axn = cosa(Ai + A2 + ... An) (3)

189

Let Z be the projection of the line L on the axis of 0; also
suppose that there are n sections. Then equation (1) may-

be written

A*i + Az2 + .. • • A zn Z _ (Ax + A2 4- . . . Aw) L

. — ooby r- —

n L n

or more briefly

4sAaAZ = ^2AAL (4)

Z Ju

Z L

when AZ and AL have been written for - and - respectively.

n n 1 J

Operating in a similar manner on equations (2) and (3) we
shall have

y2AaAY = — ^SAAL (5)

isAIAX = ~2AAL (6)

Now suppose n to become indefinitely large, then the limits
of the expressions (4), (5), (6) are

\ j\dZ^ J\dh (7)

o o

i f\dY = C^ f\dh (8)

o o

i JXAxdX = ^ j\dL (9)

o o

Now suppose a solid to be constructed whose axis is perpen-
dicular to the plane of xy and of length Z and whose
sections parallel to the same plane are Azl, A.z2, &c. Let
the volume of this solid be Yz, Let similar solids be con-
structed whose axes are Y and X. Let these be denoted by
Y y, Yx, then we shall have

(11)

(13)

Substituting these values in (7), (8), (9), we obtain
Yz COSyV

y= l 1 EH

Y^ cos/3 Y

Y “ L

V* COSaV

X = ~L~'

(14)

(15)

where Y has been written for J AdL and denotes the

volume of the primitive solid which is, of course, a constant.
Since X, Y, Z are the projections of L on the coordinate
axes we shall have

X - Lcosa
Y = Lcos/3
Z = Lcosy

Substituting in (13), (14), (15) the resulting equations will be

Y* = COS2yY

Yy = cos2/3 Y
V. = cos*aV

adding and remembering that cos2a + cos2/3 + cos2y = 1, we
obtain

Y. + V^ + V.-V

Hence if we suppose the original solid to move in any way,
the volume of each projected solid will vary, but the sum
of these volumes will be always constant and equal to the
volume of the original solid.

If the primitive axis at any time should be perpendicular
to one of the coordinate planes, then of the three quantities
V*>V„Y* two will vanish, and the remaining one will be a
solid equal and similar to the original solid.

191

As an example, consider a sphere, the diameter of which
is 2P, and let the direction angles of the primitive diameter
foe a, p>, y, and let the sphere be divided into sections per-
pendicular to this diameter. Consider one of these sections
whose radius is r, let l foe the length of the diameter inter-
cepted between this section and the lower part of the sphere,
then we shall have

The circular section projected on the plane xy will foe an
ellipse whose semi-axes are r and rcosy, the area of this
ellipse will be 7rr2cosy ; hence we have

2 is the projection of the line l on the axis of 0. Therefore

iz = Aosy

Substituting this value of l in (16) we obtain

r2 = 2Tll-P

(16)

r z

Vs = 7rCOSy / r\lz

(17)

o

r2=2R-^-- — 2-
COSy COS y

and substituting this value of r2 in (17) we obtain

P 9,’Rn.nsiv

O

In a similar manner we may obtain

r>r\c

o

o

Performing the integrations we obtain

Yz — f 7rR3COS2y

Y y = |ttR8cos2/3

Y* = |7rR3COS2a

192

By addition we get

V. + V, + V„=t*R*

or the sum of the three projections is equal to the volume
of the sphere. In this case the three component solids are
three spheroids whose semi-axes are respectively It, Rcosa,
Rcosa ; It, Itcos|3, Itcosj3 ; It, Rcos-y, Rcosy.

PROCEEDINGS

MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

VOL. XXII.

Session 1882-8 3.

vi2- 9^'3

MANCHESTER :

PRINTED BY T. SOWLER AND CO., 24, CANNON STREET.

1883.

NOTE.

The object which the Society have in view in publishing their
Proceedings is to give an immediate and succinct account of the
scientific and other business transacted at their meetings to the
members and the general public. The various communications
are supplied by the authors themselves, who are alone responsible
for the facts and reasonings contained therein.

INDEX.

Alcock Thomas, M.D. — On the Structure of the Shells of several com-
mon species of Polymorphina, p. 67.

Bailey Charles, F.L.S. — On the Occurrence of Potamogeton . Zizii, M.
and K., in Lancashire, and in Westmorland, p. 40, On the
Lancashire locality for Selinum Carvifolia, L., p. 44.

Bottomley James, B.A., D.Sc., F.C.S. — On the Formula for the Intensity
of Light transmitted through an Absorbing Medium, as deduced
from Experiments, p. 4. On the Intensity of Light that has been
transmitted through an Absorbing Medium in which the Density
of the Colouring Matter is a function of the distance traversed,
p. 7.

Boyd John. — On the Male of Argulus Foliaceous, a parasite found on
the Carp, p. 99.

Brockbank Wm., F.Gr.S. — On the Levenshulme Limestones — a Section
from Slade Lane eastwards, p. 61.

Darbishire G-. — Note upon the Mammoth Cave, p, 55.

Darbishire B. D., F.G.S. — On the animals taken in a dredging at Oban,
p, 45. .

Gwyther B. F., M.A. — On a Compound Bainbow, p. 3. A Proof of the
Addition Theorem in Elliptic Integrals, p. 81.

Joule J. P., D.C.L., LL.D., F.B.S. — Note on the Dimensions of Ships, p.
19. On a fresh determination of the freezing point in a sensitive
thermometer, p. 47. On the use of Lime as a purifier of the
products of combustion of coal gas, p. 55. On an Arrangement
for damping the small oscillations of a telescope, p. 104.

VI

Murphy Joseph John, F.G.S. — On the Transformation of a Logical
Proposition containing a Single Eelative Term, p. 36.

Eawson Eobert, Assoc. I.N.A. — On Singular Solutions of Differential
Equations, p. 35. Eemarks on Frofessor Eeynolds’ paper ‘On
Isochronous Vibrations/ p. 51.

Eetnolds Professor Osborne, M.A., F.E.S. — On an Elementary Solution
of the Dynamical Problem of Isochronous Vibrations, p. 38.

Eogers Thomas. — On a Meteorite found at Braunfels in G-ermany, p. 99.

Sandeman Archibald, M.A. — Belted Skew-Pulleys, p. 13.

Schorlemmer C., F.E.S. — On the Occurrence of Caffeine in the leaves
of Tea and Coffee grown at Kew Gardens, p. 69,

Smith E. Angus, LL.D., F.E.S — On a Vitrified Mass of Stone from
the Fort of Glen Nevis, p. 1. On the Development of Living
Germs in Water, p. 25.

Stewart Professor Balfour, LL.D., F.E.S. — Eemarks on the Simulta-
neous Variations of the Barometer recorded by the late John
Allan Broun, p. 47.

Ward H. Marshall, B.A. — On the Coffee Leaf Disease of Ceylon,
illustrated by preparations for examination under the microscope,

p. 21.

Waters Arthur Wm., F.G.S., F.L.S. — The Death-Age in Langweis
(Switzerland), p. 10. Observations made in St. Moritz in the
Winter 1882-3, p. 82.

Wilde Henry. — Note on the Vapours of Incandescent Solids, p. 49.

Williamson Professor W. C., F.E.S, — On the present state of our
knowledge of the relations between Lepidodendron, Sigillaria, and
Stigmaria, p, 32.

VII

Meetings op the Physical and Mathematical Section. — Annual,
105. Ordinary, pp. 104, 105.

Meetings op the Microscopical and Natural History Section.-

Annual, p. 100. Ordinary, pp. 32, 37, 65, 67, 99.

Eeport op the Council, April, 1883, p. 73.

PROCEEDINGS

OF THE

MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

Ordinary Meeting, October 3rd, 1882.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in the

Chair.

Dr. R. Angus Smith, F.RS., showed a vitrified mass of
stone, and gave the following description : — I went up
lately to Fort William to see Mr. Wragge, who is making
observations on the comparative amount of sunlight on the
top of Ben Nevis and on the shore at his house, after a
method advised by me, and, as usual, I amused myself with
a little archaeology. I had seen in a recent map the vitrified
Fort of Glen Nevis called by the strange name Dornadilla,
a name that is found among Boece’s Kings of Scotland, but
not hitherto applied to this fort as I supposed. I went up the
glen to refresh my view of the site, and saw the line of the
fort looking down. The glen is very grand. The fort
stands on the south looking to the precipitous sides of
Ben Nevis and down the glens both north and south. One
of its objects was evidently to watch. The name of this
fort, along with two or more of the same kind, is Dun
Deardhuil, which the Rev. Dr. Clerk, of Kilmallie, says may
mean “ The Fort of the shining eye.” This name anglicised

Proceedings— Lit. & Phil. Soc.—Yol, XXII.— No. 1.— Session 1882-3.

2

by Macpherson into Darthula is that given to the great
beauty of the western Celts* the Ulster Lady , called in Ireland
Deirdre. She was the “ Helen ” of the race, and her history
and its indirect consequences brought out the Iliad of
Ireland, but I am one of the many who cannot give an
opinion of the work. The similarity of name and the fact
that Deirdre came over to Loch Etive may have caused
people to connect these forts with her, but the fact of their
being places of security requiring also vigilance is a reason
for connecting them with the “ shining eye,” a name, too,
that may be easily supposed applicable to Deirdre. She
was vigilant and beautiful. They were vigilant, but not
beautiful. The work of the forts is rough ; shapeless and
small stones are melted together by a rude glaze. All
known to me are walled enclosures. The only one with
any very distinct connection with history or legend con-
tained a dwelling with apartments; it is described in
“ Loch Etive and the Sons of Uisnach.” The glazing or
cementing is done systematically, and instead of using
mortar. I have published elsewhere the analysis of one
piece from Loch Etive, and my youngest assistant, Mr. Frank
Scudder, has analysed the fused part of this from Glen
Nevis with the following results : —

Silica

_

Per cent.
- 68*88.

Alumina-

-

-

- 16T7.

Iron

-

-

5-33.

Lime

-

-

3-73.

Magnesia

-

3-39.

Potash -

-

1-83.

Soda

-

-

0-26.

Loss on ignition

-

092.

100-51.

The walls of some show enormous masses of vitrified matter.
One, the “ Tap o’ Noath,” in Aberdeenshire, is a remarkable

3

example, the enclosure is great, and so is the debris ; it is
on a hill, seeking however to be retired, one would think.
At St. Brieuc in Brittany, one greater still is on a flat.
There are about fifty in Scotland, two or three in Ireland,
at least one in Bohemia, more than that in France, and we
hear a whisper of one in the valley of the Euphrates and
elsewhere in Asia. Their first home is still to find. I look
to the east for them, and think that they entered Scotland
by the east. I hope no one will without good authority put
new names into maps. The first statistical account writes
Dundhairdghall, but many letters are silent in Gaelic, and
at any rate I leave that to others to explain if they think it
not simply an instance of insertion of a guttural, common to
speakers of Gaelic in many places.

Mr. R. F. Gwyther, M.A., described a compound rainbow
he had seen in Scotland last summer, in which, besides the
ordinary primary and secondary bows, a portion of a third was
seen crossing the interval between the two, and extending
a little beyond the outer border of the secondary.

Dr. Schuster, F.R.S., gave an account of some of the
results of an examination of the photographs of the solar
corona he had taken in Egypt during the eclipse of May
last

General Meeting, October 17th, 1882.

H. E. Roscoe, Pli.D., LL.D., F.R.S., &c., President, in the

Chair.

Mr. Henry Holt, of Palatine Road, Didsbury, was elected
an Ordinary Member of the Society.

4

Ordinary Meeting, October 17th, 1882.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in the

Chair.

“On the Development of Living Germs in Water,” by
Dr. R. Angus Smith, F.R.S.

An abstract of this paper will appear in a succeeding
number of the Proceedings.

Mr. William H. Johnson, B.Sc., in the absence of Mr.
Leader Williams, C.E., gave an explanation of the plans
of the proposed Manchester and Liverpool Ship Canal.

“ On the Formula for the Intensity of Light transmitted
through an Absorbing Medium, as deduced from Experi-
ment,” by James Bottomley, B.A., D.Sc.

In a former communication, an experimental method was
suggested for testing the validity of an assumed law of
intensity of light that has passed through an absorbing
medium. The method was this : take two surfaces of
different degrees of brightness, survey them through some
absorbing medium, adjust the lengths of the columns so that
the intensities shall be the same ; then, if the law of absorp-
tion be true, the intensities will again be equal if both
columns are increased by the same length. Some experi-
ments which I made gave results in agreement with the
theory. In these experiments surfaces of different degrees
of whiteness were observed through a grey solution. The
error arising from the finite extent of the surface is small,
and the mean intensity which we observe may be taken as
the intensity of the central ray.

o

But suppose we had started with no hypothesis as to
the form of the function expressing the intensity of trans-
mitted light, hut had found as an experimental result that
when the intensities are equal they remain equal when the
columns receive equal increments ; what form for the func-
tion might he deduced from such a result ?

Suppose there are two lights of initial brightness I0 and
I0' respectively, then if x and y he the lengths of the absorb-
ing columns, for the transmitted light in one case we shall
have

lx = l0<p(x) (1)

and in the other case

i y = (2)

being the unknown function which it is required to de-
termine. Since these two intensities are equal,

I0(f>(oc) = l0'<p(y) (3)

If both columns receive an equal increment, the intensities
will again be equal. Let this common increment be de-
noted by k, then :

+ k) = iMv + k) (i)

These equations will still hold if y—o, In this case the
duller surface is observed directly, and the length of the
absorbing column over the brighter surface is increased
until they are brought to the same intensity. Since when

y—o therefore ^(o) = l.

Equations (3) and (4) will become

I0<p(x) = 1/ (5)

I0(p(x + ic) = I </0(k) (6)

Expand (6) in terms of k

a**) + ^ + w*2 + &o- I;(1 + ^ + + *<=•)

Since the first terms of the expansions on each side are
equal, the equation may be written

U

fdfyx d2(f>x
V dx K + 2 dx^

+q^+&c,

0

6

Dividing both sides by k and diminishing k without limit,
the resulting equation will be

T d(f>(x) _

io~dF ""

WW

Eliminating I0 and I0' by (5)

the integral of this is

log(j)(x) = <p\o)% + c

or

<f)(x) = Qe^i°)x

when x — o <f>{x) = 1
Therefore C = 1

Also as x increases the intensity diminishes, therefore (p'(o)
must be some negative constant, let it be denoted by — m.
Then the equation becomes

< p(x ) = e~mx

and equation (1) may be written

T _ T P— mx

Hence experiment leads to the same form for the function
as the hypothetical form with which we started.

If in the above investigation we had made the length of
the column invariable, and x denoted a mass of some colour-
ing matter which undergoes no decomposition on dilution,
we might have obtained experimentally the form of the
function expressing the intensity of the light transmitted
through a column of fluid of invariable length containing a
variable quantity of colouring matter.

In the above remarks I have supposed we are dealing
with homogeneous light or with white light which has pene-
trated a medium containing soluble black in solution. To
apply the formulae generally we must prefix to them the
sign of summation.

In seeking a priori the law of transmitted light we might
have reasoned as follows, which involves less assumption

7

than Herschel’s reasoning : — Suppose we have a column of
any length, conceive it divided anywhere into two lengths*
x and y , by an imaginary plane. Let I0 he the initial
intensity of light ; after penetrating the column x we shall
have

lx = I0(j)(x).

But if light of intensity I* penetrate a column of length
y , the transmitted light will be or by substitution

1 000*00(2/)* This will be the intensity after penetrating the
whole column, since the length of the column is x+y, the
emergent light will also be expressed by I0(j)(x+y), equating
these two expressions lor the same quantity there results
<p(oc)(f)(y) = <p(x + y ).

It is well known that this functional equation is satisfied
by an exponential form.

I may also take this opportunity to correct some errors
in Colorimetry, part II., contained in vol. XIX. of the
Proceedings.

c. c.

Page 41 line 31 for 6000 read 6014.

,, „ 32 insert “nearly” before the theoretical column.

43 ,, 20 for 600 read 6000.

„ „ 23 for 6682 read 6652.

46 „ 20 for 17*9 read 9.

„ „ 22 for 5-2 read 5*1.

,, „ 26 for former read “latter” and for latter “former. n

„ „ 27 for 1600 (17+^) = 2400 x21 -2 read

1600 (21-2 + x) = 2400 x 17.

“On the Intensity of Light that has been transmitted
through an Absorbing Medium in which the Density of the
Colouring Matter is a function of the distance traversed,” by
James Bottomley, B.A., D.Sc.

In previous papers it has been supposed that the absorb-
ing matter was uniformly distributed throughout the

8

medium. In the present paper the author treats of the
intensity of light which has passed through a medium of
variable density. Such cases occur in nature, for instance,
the atmosphere increases in density as we approach the
earth, also we might have coloured glass in which the
colouring matter is not uniformly distributed, or the case of
a coloured soluble salt on which water is poured, the
colour in the immediate vicinity of the salt is most intense
and gradually fades as the distance increases. Also the
same reasoning would apply very approximately to the case
of fluids containing in suspension layers of different density
of finely divided matter, or to the case of an atmosphere
containing fine dust in suspension. For simplicity it is
supposed that we are dealing with homogeneous light, or
with white light which has passed through a grey solution.
Suppose a ray of light has penetrated a length t of a medium
which is not homogeneous and that its intensity is I when
it falls on a surface for which the coefficient of transmission
is e~m, consider a plate of thickness At and let e~[m+Am) be
the coefficient of transmission at the upper surface. Let I' be
the intensity of the light emergent from this surface. Then

^>1 e-C*H-A»»)A<

If we expand the exponentials and write A I for I' - I there
results

Al

I

i_ m2 A ft .

-mAt-v — ~ b &c.

. X + A m)2 0 .

- (m + Am) At + ^ L A t2 + &c.

Proceeding to the limit, there results

dlogl = -mdt (1)

Now suppose light to penetrate a unit length of an absorbing
medium containing q units of colouring matter, there results
the following relationship

£— m = e-M<Z

9

l u being a constant, therefore

m — fjiq

and equation (1) becomes

dlogI = - fiqdt (2)

For q we may substitute d where d denotes the density of
the colouring matter, the unit of density being that due to
the distribution of the unit mass through the unit volume.

Now suppose d to vary and to be some function of t , so that

d = (f>(t)

Let be the integral of this, so that
x(t)=Mt)dt.

Substituting in equation (2) and integrating, we get

logI=-FX(0 + c

or as it may be written

i = Ce"^(‘) (3)

To determine the constant we must know simultaneous
values of I and t. The above equation (3) is the general
equation for determining the intensity of transmitted light
when the density is an assigned function of the distance
traversed. The remainder of the paper is taken up with
special cases of this general fromula. Firstly, when the
density varies as the distance from the plane of incidence.
Secondly, when the absorbing medium is an elastic fluid
surrounding an attracting sphere, the law of attraction being
that of the inverse square. Thirdly, when the colouring
matter is so distributed as to give recurring values of the
density, taking as a particular case the relation
d = m- %sin£

m and n being constants and m greater than n, as t varies
we obtain periodic values of d. In this case the curve of
intensity is represented by a sinuous curve always situated
between two logarithmic curves and touching them alter-
nately. Finally, it is shown that the general equation may

10

be serviceable for solving inverse questions, such as what
must be the law of density in order that the intensity of
the light may be a given function of the distance traversed.
As a particular instance, the density is determined in order
that the intensity may vary as the inverse nth. power of the
distance.

“The Death-age in Langwies (Switzerland),” drawn up
by Arthur Wm. Waters, F.G.S., F.L.S.

Many visitors feeling that the growth of Davos has been
too rapid, have been anxious to see other places similarly
situated, at a high level, tried as winter resorts for con-
sumptive patients, and many competent authorities have
thought that the position of Arosa (6000 feet) at the upper
end of the Schanfigg valley was very favourable. I therefore
went over this spring to see it.

When visiting it I took the opportunity of drawing up
a table of the age at death in Langwies (4519 feet above
sea level), a village at the lower end of the Schanfigg valley.
This Schanfigg valley is parallel with the valley of Davos and
also with the Engadine, and as I some years ago published
the death age of the inhabitants of Davos (Klimatolog.
Notizen ii. Winter im Hochgebrige, Basel 1871) and Dr.
Ludwig published those of the Engadine (Das Oberengadin
von Dr. J. M. Ludwig, 1877), we have now figures for these
three neighbouring valleys.

I only used the figures since 1800 A.D., because the ages
in the last century did not seem to have been kept with
quite as much fulness as lately.

With regard to Davos I quote a second table which is the
more valuable (although only relating to a smaller number)
on account of the first table containing the register of a few
who died away from Davos.

11

There has never been a resident doctor in the whole of
the Schanfigg valley, but this summer a Swiss medical man
has gone there for twelve months on account of an invalid
wife.

The tables placed together for comparison are —

630 deaths
Langwies, from
1800-1882

(exclusive 34 still-born)

1099 deaths
Davos Valley
from

1837-1870.

271 deaths
Davos Platz
1837—1870.

590 deaths
Engadine
(Dr. Ludwig)
1861—1870
exclusive of
invalid visitors

General average
age in Europe
(Oesterlen Hand.

Med. statistik).
s p. 156, &c.

0-5

27-77

22-7

20-

22-3

25—45

5-10

3-17

3-1

3-3

2-5

10-20

3-65

4-6

4-5

3-0

5—6

20-30

4-76

6-2

3-8

4-1

5—6

30-40

5-08

5-0

5-6

5-4

6—7

40-50

7T4

6-6

8-5

7-0

. 7—8

50-60

10-16

9-4

7-8

13-1

8—9

60-70

16-98

14-9

15-5

16-

9—12

70-80

15-24

17-9

20-3

15-5

8—10

80-90

5-73

8-9

10-

10-

4—5

90-

•32

0-7

0-7

1-2

0-4— 0-6

This means that the mean age in Langwies is 48 years,
whereas in England it is 86 '92 years, and it will be noticed
that during the years of youth, viz., the most fatal time for
lung disease, the death rate is favourable, and the proportion
of those who live to a considerable age is also high.

I may take this opportunity of pointing out that although
Arosa is not yet in a position to become a winter resorb
there seems every reason to believe that in one or two years
the experiment of wintering can be made, and if successful
it will shortly be able to relieve Davos of 200 or 800 of its
surplus winter patients. At present the difficulty is the
want of a road, but Arosa is willing to contribute a reason-
able share, and no doubt Chur and other interested places
will soon be brought to contribute the rest. We must, how-
ever, remember that it is only about seven years since a road
was made from Chur to Langwies, and we must therefore

12

not much wonder that a district which is not wealthy has
not yet extended it.*

A very small hotel for summer visitors from Chur was
built about 4 years ago, and this year another small hotel is
being built and will be ready next spring, besides which the
ground is marked out for a third, so that there are already
indications that the place is likely to grow.

I have good reason to believe that the statement made by
those in the neighbourhood that Arosa is remarkably well
sheltered from wind in the winter will be found to be
correct, and as far as I can judge from the position I believe
that Arosa will be found more favourably situated than
any of the mountain resorts which have yet been tried in
winter.

St. Moritz, October, 1882.

#Each of the mountain health resorts ought, in my opinion, to be
separately and thoroughly studied, as I believe that in time we shall see
that there are marked differences, and one is suitable for one class of
patients while another may be more suitable for others, and we shall then
see that the general classification of mountain health resorts is to be placed
on a level with the remarks of a well-known German doctor, whose
works on climatic questions are often quoted, who makes a comparison of
a German watering place with Margate, Brighton, and Torquay, as if all
places on the South Coast had a similar climate.

13

Ordinary Meeting, October 31st, 1882.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in
the Chair.

“ Belted Skew Pulleys,” by Archibald Sandeman, M. A.

With that plane at right angles to the axis of a pulley
which halves the face named the Plane of the Pulley,
and with the locus of the centre of the cross section of
a belt named the Midline of the Belt; the only thing
needed for either of two pulleys to drive the other by
means of a closed belt looping them in tightly together
(art. 184 of Willis’s Mechanism) is

That the Midline of the belt leave each pulley in
the plane of the other.

The planes of the pulleys may be taken vertical and
therefore the axes horizontal. By so doing the belt is no^
drawn away by its own weight, and the axes are the more
easily set up and steadied.

If the axes be parallel to one another the planes of the
pulleys must be one and the same. Else the belt’s midline
would leave either pulley, not in, but on one side of, the
other, and therefore run off this other toward that side. Thus
with condirectionate or contradirectionate axes the midline
of the belt lies wholly in the one plane of the pulleys. This
is the simplest and commonest case of a pair of pulleys with
open or crossed belt.

Call two straight lines Skew when they are not in one
plane. And call two pulleys Skew when their axes are
skew.

Proceedings— Lit. & Phil. Soc.— Vol, XXII,— No. 2.— Session 1882-3.

14

In a projection right down
on a horizontal plane let
AiOA he the lower and
BiOB the higher of two
given horizontal skew axes
about which two pulleys of
given diameters are seve-
rally to turn in such a way
that, looking along AxOA in
the direction from A1 to A
and along BxOB in the direc-
tion from B1 to B, the rising
points are to be on the left hand of the vertical plane
through the axis and the falling points on the right.

To AxOA as axis fit a round roller or shaft or drum
A^aAdCLiAi, of the same circular cross section everywhere
throughout as the pulley which is to turn about AxOA, and
so that axa and axa may be severally the straight lines in
which a horizontal plane through AxOA cuts the drum face
to left and to right. Also to BxOB as axis fit a drum
BibibBflfaBi, of the same circular cross section as the pulley
which is to turn about BxOB, and so that bxb and ]3ij3 may
be severally the straight lines in which a horizontal plane
through BxOB cuts the face of BJiibBfifiiBi to left and to
right. Moreover let G and A be the common sections
severally of the vertical planes through ax a and bxb and
of the vertical planes through

If now the drums were
to turn round in the same
manners severally as the
pulleys which are to have
the severally same axes and
cross sections ; though all
points in the drum faces
would move in their own
and several circles at one

15

common speed, yet such only of them as lie in the straight
lines aia and bib would at any instant be moving vertically
upward and such only as lie in am and j3i/3 vertically down-
ward, and of these again only the two that lie in G would
be moving vertically upward in one straight line and only
the two that lie in A vertically downward in another.

Lay a straight edge in and along the straight line C.
Shift this straight edge both backward and forward so as
never to be taken off either drum and so as always to touch
each of the drum faces and be at right angles to the higher
axis. Let ciCc be the line
marked out by the points
where the lower drum face
is touched, and of this line
let GCi be the portion which
lies on the same side of
the plane through G per-
pendicular to the lower
axis as Cax and therefore
Gc the portion which lies
on the same side as Ca.

If then through any point
X in c-JJc two planes be
drawn perpendicular to
the axes, and therefore
cutting one another in a
vertical straight line and
the drums in a lower and
a higher vertical circle,
the straight edge when it
passes through X touches
the higher circle in some
point Y ; and a string may
be stretched, first under
the lower drum axa along

16

the lower circle toward and as far as X, next up along
the line of the straight edge as far as Y, and lastly right on
to and over the higher drum j3i b along the higher circle.
This string too, if only guided on to the lower drum axa
along the lower circle and pulled off from the higher drum
/3i b along the higher circle, may be kept always unwinding
itself off from the lower drum at X and always winding
itself on to the higher drum at

In like manner lay a straight edge in and along the
straight line A, and shift this straight edge aside both ways
so as never to be taken off either of the drums and so as
always to touch each of the drum faces and be at right
angles to the lower axis. Let SXAS be the locus of the point
where the straight edge touches the higher drum face, and
let A Si be the portion on the same side of the plane
through A perpendicular to the higher axis as Aj3i and
therefore AS the portion on the same side as a/3. If then
through any point Y in the
line Si A S two planes be drawn
perpendicular to the axes, and
therefore cutting one another
in a vertical straight line and
the drum faces in a higher
and a lower vertical circle,
the straight edge when pass-
ing through Y touches the
lower circle in some point X1} and a string may be stretched
over the higher drum (3ib along the higher circle toward
and as far as Y, down along the straight edge line as
far as Xi, and right on to and under the lower drum aid
along the lower circle. And this string, if guided on to the
higher drum ]3i6 along the higher circle and pulled off from
the lower drum axa along the lower circle, may be kept
always winding off the higher drum at Y and always
winding on the lower drum at Xi.

17

A

P CL\ iC I

LU IfJ -.v-v^V

h '

I N\;
\
X

a I W 'a

I I S',

Thus the vertical cross
planes through X fix the
circles for winding off from
aici at X and on to (3i b at
Y, and the vertical cross
planes through Y fix the
circles for winding off from
the j3i b at Y and on to axa
at Xh Still the windings off*
at X and on at Yi cannot
be windings of the same
stretched string as the wind-
ings off at Y and on at Xh unless X lie in the same circle
as X\ and F in the same circle as Fi; since by the bare
turning of a drum a stretched string can only be guided
from point to point in the same circle. That the same
stretched string therefore may so engirdle the drums as
always to wind itself off at the same fixed points X and F
and always to wind itself on at the same fixed points Xx and
Y1 it is needful and it is enough that the vertical cross
planes through X be the same as the vertical cross planes
through F. And this again happens just when the pairs
of cross planes have the very same common section, or
again just when the points X and F lie in the same
vertical straight line.

Hence through the lines &Cc and §iA§ draw vertical
cylindric surfaces. Let P be the common section of these
surfaces. Then planes drawn through the vertical straight
line P perpendicular to the axes AiOA. and BiOB are the
planes of the pulleys.

If the axis be at right angles to one another (or rather,
if from the forelook OA of the lower axis the forelook OB
of the higher axis have a bearing with a right-hand- ward
start either of once or of thrice a right angle), the lines
C\Cc and are severally the straight lines aid and j3i/3<

18

The cylindric surfaces are then nothing hut the vertical
planes through axa and (3i/3 and therefore cut one another
at right angles in the straight line P. Then too the vertical
plane through cwa not only touches the lower drum face hut,
passing through P perpendicularly to the higher axis, is
itself the plane of the higher pulley; likewise the vertical
plane through |3ij3 not only touches the higher drum face
hut, passing through P perpendicularly to the lower axis,
is the plane of the lower pulley. So then the vertical
straight line P touches each of the faces of the pulleys and
each of the midcircles. And so the millwright rule here
holds good — “ Plumh the centres of the leading off faces.”
These cases of rightangled axes are alone dealt with in
art. 185 of Willis’s Mechanism, and seemingly as if there
were no others.

In all other cases the vertical cylindric surface through
cxGc touches the vertical plane through aiCa along the vertical
straight line G and in an unbroken sheet runs away endlessly
therefrom on both sides between the parallel vertical planes
through OiCa and AiOA toward the vertical plane through
AiOA as an asymptote. Also the vertical cylindric surface
through §1 A S touches the vertical plane through (3i A j3 along
the vertical straight line A and in an unbroken sheet runs
away endlessly therefrom on both sides between the parallel
vertical planes through ]3i Aj3 and BiOB toward the vertical
plane through BiOB as an asymptote. The plate bounded by
the parallel vertical planes through aiCa and AiOA is thus
split by the vertical cylindric surface through CiCc into two
slices having for a common bounding face the vertical
cylindric surface through CiCc and for their other bounding
faces severally the vertical planes through a±Ca and AiOA.
And the plate bounded by the parallel vertical planes
through |3iAj3 and PiOP is split by the vertical cylindric
surface through Si A S into two slices having for a common
boundary the vertical cylindric surface through Si AS and

19

for their other boundaries severally the vertical planes
through ]3iAj3 and BxOB. But as each of the bounding
planes of each of these plates cuts or crosses each of the
bounding planes of the other, so likewise must each of the
plates themselves cross or cut through the other, so again
therefore must each of the slices of either plate cut across
each of the slices of the other, and so therefore lastly, must
each of the cylindric surfaces cross or cut the other. There-
fore the vertical cylindric surfaces through ciGc and
cut one another in some vertical straight line P lying within
the vertical prismatic rod which is common to the plates
bounded severally by the parallel vertical planes through
axGa and AxOA and by the parallel vertical planes through

j3i a/3 and Pi OP.

‘‘Note on the Dimensions of Ships,” by J. P. Joule,
D.C.L., LL.D, F.R.S.

I have often thought that in practising the , art of ship-
building men have too much neglected the study of the
forms of the fish which make the waters their permanent
habitation and are designed for the most part to attain the
highest degree of velocity in the pursuit of their prey.

No doubt the case of a ship partly, and that of a fish
wholly immersed, are not strictly parallel, but they offer
very many points for comparison of which we may avail
ourselves.

A fish makes use of its tail fin as the chief and nearly
sole instrument of propulsion, and in the adoption of the
screw propeller in preference to the old side wheels the
steamers of the present day have secured a great advantage
over the old forms. In the proportion of length to those of
breadth and depth, however, although there has of late
been some improvement, there would appear to be a lingering
tendency to hold by the old mistaken idea that a ship was
rather to be regarded as a wedge to cut the water than as

20

occupying the space of a wave of displacement, and so we
have ships 9, 10, or even 11 times as long as broad and
twenty times the length that they have draught. Now
knowing as we do the magnitude of the skin resistance in
ships and its smallness in the oily coats of fishes, one would
expect that the length of the latter would be greater pro-
portionally than that of the former, if ships were built in
the proper form to secure a high velocity. But what is the
fact ? — On an average of sixteen fresh water fish delineated
in Daniell I find that the extreme length inclusive of the
tail fin is 4*22 times that of the extreme depth exclusive of
the dorsal and ventral fins. The average breadth will be
perhaps J of the depth, making the proportion to length
about 1 : 8.

On an average of three species of Whale, the Narwal,
Greenland Shark, Dolphin, and the Porpoise, I find from
Scoresby and other authorities the proportion of either depth
or breadth to length, to be about 1 to 4*7, they having nearly
circular sections. Therefore it appears that while in ships
the proportion of length to width of midship immersion is in
ships as 5 : 1, that of the shark, the porpoise, or dolphin, is
not more than 1 J : 1.

Dr. Scoresby, in his e Arctic Regions,’ gives twelve
miles per hour as the utmost speed of the Whale. But
Mr. Baxendell gives it a velocity approaching 20 miles.
I had an opportunity of witnessing the wonderful swimming
powers of the porpoise during a voyage to the Clyde in the
‘Owl’ steamer on the 29th June last. About 8 a.m., the
sea being calm near the Mull of Galloway, we were beset
by a shoal of these animals which raced with the ship and
kept along side for 3 or 4 minutes with the greatest ease.
They swam in twos and threes at a foot or two distant from
one another, several approaching within ten feet of the
vessel, which was steaming at the rate of 13*4 statute miles
per hour. If such a velocity can be maintained by the

21

porpoise with its comparatively bluff figure head we may
surely expect a much higher velocity in the case of fish
more obviously designed for speed.

My son tells me that in a voyage of the ‘ Malvina ’ from
Leith to London he had observed at night two fishes of
about a yard long, which kept for a considerable time in
advance of the cutwater of the ship, being visible by their
phosphorescent light. The ship was at the time steaming
at the rate of 15*2 statute miles per hour.

The investigation of the resistance of solids moving in
fluids has been taken up theoretically by Thomson, Stokes,
Rankine, and practically by F roude, who has found that the
surface friction in long iron ships is more than 58 per cent
of the whole. Froude recognized the study of the forms of
animal life in guiding us to practical conclusions.

From the above considerations I am inclined to believe
that a length of not more than five to one of breadth would
be better than the extreme proportions of ships now in.
vogue, and that the greatest breadth should be considerably
in advance of the midship.

“On the Coffee Leaf Disease of Ceylon, illustrated by
preparations for examination under the microscope,” by
H. Marshall Ward, B.A., Fellow of Owens College.
Communicated by Prof. Osborne Reynolds, F.R.S.

Mr. Ward commenced by sketching shortly the history
of the coffee leaf disease, from its discovery in Ceylon, in
1869, to the present time, and gave some figures showing its
effect on the exports of coffee. He then proceeded to describe
the symptoms by which the disease is recognised.

The normally dark-green, laurel-like coffee leaves become
spotted with yellow blotches, which arise as pale, minute
spots on the under side, soon spreading in a centrifugal
manner, and showing through above. Each spot becomes
darker with age, and multitudes of minute yellow spores

22

make their appearance on the under side of the leaf,
forming a powder — the so called “ rust ” — on the outer sur-
face of the spot. Coloured drawings of coffee leaves thus
affected with “disease-spots” were handed round for in-
spection.

As the number of yellow spots increase, the leaf loses its
bright green colour, turns yellow, and drops off. As large
numbers of leaves thus prematurely fall from the branches,
the latter become shrivelled and brown, and the fruit drops
in all stages.

The lecturer then proceeded to describe the microscopic
details of what is seen inside a healthy leaf, and compared
it with what is found inside the yellow “ disease spots.”
The passages between the green cells of the leaf are found
to be blocked up by a fungus mycelium, consisting of short,
much-branched tubes, which send off curious sucking organs
into the cells.

As the fungus grows older, and the yellow spots, which are
the external evidence of its presence, become larger, it is
discovered that the contents of the green cells become
sucked out into the fungus. A section showing the my-
celium and its minute sucking organs was shown under the
microscope.

When a section is taken through a more advanced spot,
on which the yellow “ rust ” has formed, the origin of the
latter is seen to be as follows : certain branches of the fun-
gus grow together through the stomata of the leaf, and bud
off thousands of spores. These numerous spores form the
yellow powder or rust. An instructive section of this kind,
in which the mycelium and spores were stained blue, was
shown afterwards under the microscope.

On one spot as many as 100,000 or more of such spores
have been estimated, and 127 such spots were counted on
one pair of leaves. They are detached with the slightest
shake.

23

Mr. Ward then described the germination of the spore.
On glass or inorganic bodies the spore, after a few hours in
water, throws out a tube, which reaches a certain stage in
24 — 48 hours, and then dies. In nutritive fluids of various
kinds, also, or on the upper side of the leaf, stem, &c., no
further development was possible. On germinating the
spore in drops of water on the under side of the leaf, how-
ever, the germinal tube soon enters a stoma , and at once com-
mences to form the mycelium inside the leaf. This grows,
feeds on the cell contents, blocks up the passages, &c., and
causes the development of a yellow “ disease spot,” such as
those described.

Experiments were made which showed that the yellow
disease spot only appears where such a tube has entered the
leaf, and nowhere else on the leaf or plant, and that leaves
or plants on which no spores were sown — and therefore no
tubes entered — formed no spots. Shelter from spores is a
certain guard against disease.

It was found, as a mean of very many experiments, that
the yellow disease spot appears about 14 days after the
sowing and germination of the spore on the leaf, and that
the spores constituting the “ rust ” of such a spot commenced
to form during the third week after the sowing.

The yellow disease spot, therefore, is the outward appear-
ance produced by the fungus mycelium occupying the space
in the leaf. This mycelium blocks up the passages, robs the
cells of food substances which should have gone down to
the branches, fruit, &c., interferes with normal respiration
and other processes, and thus shortens the life of the leaf.
Since the tree thus derives so little benefit from its leaves,
it cannot bear so much fruit.

Further experiments proved that the age and condition of
the leaf, the kind of coffee, &c., have no effect on the pro-
blem of its infection ; all can be infected, though thick leaves
can support more mycelium than thin and succulent ones.

24

Mr. Ward then proceeded to show how these results of
experiments and observations in the laboratory were applied
to explain the course of events on coffee estates.

Observations demonstrated that spores are blown about
estates, reach the leaves of the coffee, are washed to the
edges and lower sides, and there germinate ; that, therefore,
all the conditions of the artificial infection are brought about
in nature. Having learnt particulars as to the periods
of growth of coffee, the time occupied in infection, experi-
ments, &c., the next step was to ascertain how far the
changes in climate, &c., account for the rise and fall in the
“ virulence of the disease” — i.e. in the quantity of leaf-
destroying fungus present at any time.

On one of a number of leaves which were carefully watched
during several months, the first spot became most evident
in the beginning of June, and on June 3rd was throwing off
spores. On June 29th there were 35 new spots forming
spores, and on July 15th appeared 12 others. On July 23rd
the leaf began to show signs of falling, and it dropped on
the 26th. In such a case, the successive generations of
mycelium appeared at such intervals as would be accounted
for if they arose from spores derived from the first spot.
No doubt the spores were shaken around, and germinated
soon after, each becoming the centre of a new spot as
described.

In a given district the weather was dry and hot during
the early period of the year, and from January to March
there were few leaves on the trees, and little or no moisture
to bring about the germination of any stray spores on them.
In April and May the wet growing season commences, many
new leaves are formed, and the few spores present germinate,
and produce disease spots in two or three weeks after ; hence,
by June, there are several “ disease spots,” each of which is
shedding spores all around at every shake. These spores,
scattered on the leaves, germinate in the rains which still

25

continue, and thus, by July or thereabouts — the process
haying gone on normally — a larger outbreak of the “ disease
spot ” occurs from the numerous new centres. During July
and August very many leaves fall, and a lull occurs until the
renewal of the growing period in September and October
produces more leaves. These, meanwhile, are having spores
scattered on their surfaces, accumulation of disease spots
continues through the next three or four weeks, and in
December, or thereabouts, the second general “attack of
disease ” has become established.

Very numerous and important experiments, published in
detail in the “ Journal of the Linnman Society,” Bot., Yol.
xix., August, 1882, could only be shortly adverted to, and
the author expressed his conviction that so bare an outline
of the results as the short time at his disposal allowed, would
not convey sufficiently clear ideas of the matter ; and, indeed,
to an audience unacquainted with the details of growth,
cultivation, &c., of coffee, and the conditions of existence in
a tropical island, it was not easy to give an intelligent
sketch in a short time, even of the salient points.

As to remedial measures, Mr. Ward expressed his satis-
faction with the energetic efforts of the Ceylon planters,
who fully recognise the importance of planting tea, cinchona,
cocoa, “ India-rubber,” and other trees which no such disease
attacks, and which, of course, screen the coffee more or less — -
an obvious mode of lessening the areas of coffee exposed to
the wind blown spores of Hemileia, and of adding new
sources of income.

The following paper was read at the Ordinary Meeting
held on the 1 7th October, 1882.

“Note on the Development of Living Germs in Water,”
by Dr. R. Angus Smith, F.B.S.

In a report on Proceedings under the Rivers Pollution

26

Prevention Act, I mention my wish to develop germs of
living things in water as a test for purity. The quotation
is from a paper printed by this Society in 1867. The results
were correct and useful, but not striking enough to attract
much attention, although I think chemists have not been
sufficiently active in using the microscope. Having long
seen its importance, I confess to having done too little with
it. In a report under the Alkali Act during the year 1873
I mention a second attempt to render the existence of
organic matter more perceptible by using the air washings
to act upon sugar, and after many trials I was disappointed ;
still I came to the conclusion “ that the air of a town influ-
ences fermentation to a certain extent.” — 10th Report, p. 43.

I neglected this development also too much, but Dr. Koch,
of Berlin, has shown us how to preserve the indications of
organic vitality by the use of gelatine. I believe he was
the first to use it. It is from Dr. Koch, at any rate, that I
learned the use of gelatine. About 2J per cent of gelatine
well heated in a little water is mixed with the water to be
tested, and the mixture forms a transparent mass which is
not movable like the water itself. When soluble or un-
observed matter develops from the organic matter of the
waters and makes itself visible in a solid and insoluble form,
it does not fall to the bottom, but each active point shows
around it the sphere of its activity, and that sphere is
observed and remains long. The gelatine preserves to us
the whole action, so far as the more striking results are
concerned, and keeps a record, for a time, both of the quality
and intensity of life in the liquid. I speak at present of
the more striking effects, which are clear and abundant,
every little centre of life making itself clear to the eye and
sometimes expanding its influence to reach both sides of
the tube. It seems to me now essential that all chemical
examinations of water should be supplemented by an
enquiry, like this of Dr. Koch’s, into the comparative

27

activity of the living organisms. How far this may go it
would he absurd to attempt to say, and I never have
much hope of a man who writes about the future of
truth ; he evidently attempts too much. I am satisfied to
bring forward such facts as I know in the present, so
that chemists may not be too late in attending to the new
ideas.

The water must not have too much gelatine in it, if so
the action is stopped. It must not have too little, if so the
gelatine becomes liquid too soon and the action of the in-
dividual centres is not observed. When a centre acts it
makes around it a sphere in some waters, and the sphere
which has the appearance of a thin vesicle is filled with
liquid. These spheres form in a day or two according to
the water, and at the bottom is a white mass containing
active bacteria chiefly. The liquid filling the spheres may
be taken out by a pipette and examined, as also the bac~
teria which lie at the bottom.

I have not examined a sufficient number of waters to
give general rules, but I hope to do so. It is an investiga-
tion which would properly belong to Professor Koch, and I
should not have touched it had I not found that it brought
into use my own enquiries as to fermentation, which were
earlier, but may now be considered only a supplement to
Dr. Koch’s. This is by the use of sugar in addition to the
gelatine. By this means a very great amount of gas is
developed and retained in the gelatine. The striking
amount of spheres and gas bubbles render the examination
of water by this method less dependent on the opinion
of the operator, and a photograph may be taken of each
specimen and the result preserved as evidence.

At the same time I know that it is necessary to examine
waters of various kinds before we make or find rules, and
this slight account is a mere beginning. I have as yet
examined no chalk water for example, but have been

28

confined chiefly to the Manchester district, hill water,
impure brook and pond water, Mersey, Irwell, and Medlock
water, and canal water. In certain specimens of Manchester
supply the spheres appear on some days very few, on other
days the amount is enormous and heavy, the whole of the
tube in which the experiment is made is filled with spheres.
At such times the water is highly impure and complained
of by the public. We have a very easy proof therefore of
the value of this test.

The photograph would be a visible report made by nature
when the water has active organisms in it. The globules do
not show themselves in strong sewer water, but the whole
mass becomes turbid and the surface of the gelatine becomes
liquid and full of life. This liquid condition gradually
increases until the whole is reached. We have therefore
two striking conditions well marked out.

A third may be said to exist, but it is often a mere
beginning of the globules. This is shown by the formation
of a small white opaque point. If this point is examined it is
seen to be full of life like the lower part of the spheres and
the fluid portion of the gelatine when this fluidity begins
on the surface.

I find, also, that the solidity or fluidity of the gelatine is
an important indication. This is known by the depth to
which a certain weight will sink in it.

I use the word bacteria at present because, although I
have observed various forms, I do not intend to investigate
the separate functions of each.

At present this mode of examining water seems to me to
be far more important than the chemical, more decided and
telling, but we cannot neglect the chemical.

An account of a few specimens is given here.

Specimen 1. — 25 cc. gelatine solution = 2 1 p.c. solid + 25
cc. distilled water 4* 5 mgms. sodium phosphate.

After 2 days a few white spots appeared.

29

After 3 days 3 or 4 small spheres appeared, containing
living bacteria.

After 4 days spheres enlarged and a deposit forming at
the bottom of them very full of bacteria.

After 6 days the surface of the jelly was beginning to
give way.

After 8 days the surface layer was liquid to the depth of
a millimetre, but the rest of the gelatine was still firm, with
no smell ; liquid layer alkaline.

Specimen 2.- — 25 cc. gelatine + 25 cc. Manchester water
4- 5 mgms. sodium phosphate.

After 1 day the tube contained a few minute specks.

After 2 days a number of minute spheres, not to be
counted, appeared, and a turbid band was formed near the
surface of the jelly, which was very rich in living bacteria.

After 3 days spheres became larger and the whole of the
gelatine was softened ; a number of air bubbles appeared
also.

After 4 days air spheres had risen to surface, bacteria
spheres disappeared, leaving the liquid jelly turbid and
smelling offensively ; liquid alkaline.

Specimen 3. — 25 cc. gelatine + 25 cc. Manchester water
+ 5 mgms. sodium phosphate after filtration through spongy
iron.

The result here resembled that of the distilled water.

25 cc. gelatine + 25 cc. Mersey water at Northenden +
5 mgms. sodium phosphate.

After 1 day a turbid band appeared near the surface and
a number of minute spots appeared.

After 2 days these spots had spheres about them.

After 3 days the surface layer was quite liquid and turbid
and a number of discs of gas appeared. Bacteria in spots
and surface liquid.

After 4 days in a somewhat similar condition, but the
surface liquid possessed a very disagreable smell.

30

Specimen 4. — 25 cc. gelatine + 25 cc. Bridgewater canal
water + 5 mgms. sodium phosphate.

After 2 days a number of spots appeared dispersed
throughout the tube.

After 3 days the tube contained one mass of small spheres
and spots.

After 4 days a number of discs of gas appeared, the sur-
face layer was becoming liquid,

Specimen 5. — 25 cc. gelatine + 25 cc. Birch pond water
+ 5 mgms. sodium phosphate.

After 1 day no alteration.

After 2 days a few specks appeared dispersed throughout
the jelly.

After 3 days a number of spots appeared and discs of gas,
surface layer of jelly becoming liquid.

A disc of gas is formed when the gelatine remains firm
and the gas struggles for freedom.

Specimen 0. — 25 cc. gelatine + 25 cc. Carlile’s pond water,
near Alexandra Park + 5 mgms. sodium phosphate.

After 1 day specks appeared dispersed throughout the
gelatine.

After 2 days numberless very minute spheres appeared.

After 4 days the spheres had increased in size.

After 7 days a number of spheres of gas appeared.

Specimen 7. — 25 cc. gelatine + 25 cc. ditch water, near
Alexandra Park + 5 mgms. sodium phosphate.

After 1 day a number of specks appeared throughout the

jetty-

After 2 days numberless spheres appeared.

After 3 days the surface of the jelly had become liquid
and turbid, the spheres were increasing in number.

After 7 days a number of spheres of gas appeared and the
whole mass was becoming liquid.

Specimen 8. — 25 cc. gelatine + 25 cc. N. Berwick water
supply + 5 mgms. sodium phosphate.

31

After 1 day the tube seemed one mass of minute specks.

After 2 days a number of minute spheres appeared and a
turbid band appeared near the surface of the gelatine.

After 3 days spheres had increased in size, a number of
discs of gas appeared.

After 4 days the spheres were disappearing, the surface
of the jelly was becoming liquid (these spheres did not leave,
a deposit).

After 8 days the surface layer was quite liquid but the
rest of the jelly was firm, and there were still left a number
of discs of gas and a number of minute spots, smell offensive

Specimen 9. — 25 cc. gelatine + 25 cc. Stockport water
supply + 5 mgms. sodium phosphate.

After 1 day a number of minute specks appeared and a
few small discs of gas.

After 2 days these discs of gas were getting larger, and
on the third day the tube was one mass of discs of gas.

After 5 days the jelly was liquid and the discs of gas
rose to the surface when shaken, smell disagreeable.

Specimen 10. — 25 cc. gelatine + 25 cc. Medlock water
-j- 5 mgms. sodium phosphate.

After 1 day a number of spots appeared dispersed through-
out the jelly.

After 2 days these spots were more decided and a distinct
turbid band appeared at the surface of the jelly.

After 3 days a number of flattened discs of gas appeared,
surface layer semi-liquid and turbid.

Specimen 11. — 25 cc. gelatine 4* 1 cc. hay infusion + 24
cc. distilled water + 5 mgms. sodium phosphate.

After 1 day the surface layer of the jelly was altering,
the layer was becoming turbid and liquid.

After 2 days the alteration was still more advanced, but
the surface layer was not yet liquid.

After 3 days the surface layer was liquid.

After 7 days a great deal of the jelly had become liquid,

32

and white specks appeared dispersed throughout the jelly.

Specimen 12. — 5 cc. gelatine + 1 cc. putrid urine -f 24
cc. distilled water -f 5 mgms. sodium phosphate.

After 1 day the surface layer was becoming turbid and
liquid.

After 2 days the alteration more advanced, surface of
jelly semi-liquid.

After 3 days the jelly at the surface was quite liquid,
turbid, and offensive.

This subject is being more fully developed under Dr.
Koch by Dr. Kozahegyi, and chemists must prepare for a
new condition of things.

MICROSCOPICAL AND NATURAL HISTORY SECTION.

Ordinary Meeting, 9th October, 1882.

James Cosmo Melvill, M.A., F.L.S., President of the
Section, in the Chair.

Dr. Hartog called the attention of members to the fauna,
especially rich in special forms of Cladocera, found at or
near the surface of deep freshwater lakes. He urged mem-
bers to use the tow net whenever they had the opportunity
on calm, fine afternoons, even at this time of year.

Professor W. C. Williamson, F.RS., made a communica-
tion respecting and exhibited a series of preparations from
the coal measures, illustrating the present state of our
knowledge of the relations between Lepidodendron, Sigilla-
ria, and Stigmaria.

S3

Commencing with a statement of Brogniart’s dictum,
that Lepidodendron was a cryptogam and Sigillaria a
gymnosperm, and showing by a sketch the appearance
which led Brogniart to found his distinction between
them, viz., the appearance in the latter of an exogenous
vascular zone externally to the non-exogenous vascular
cylinder which he found in the former genus, Professor
Williamson proceeded to show that the presence and
size of the ring of exogenous growth in the stem was
merely a question of the age of the plant examined.
Further, that the markings on the outside of the stem, sup-
posed to be diagonal in Lepidodendron and vertical in Sigil-
laria, probably depended upon differences which were not
even generic, but which might have occurred in the same
plant in different stages of growth, the Lepido dendroid con-
dition being the younger one.

Turning to Stigmaria, Professor Williamson showed
that they possessed two striking peculiarities — 1st, they
branched and subbranched dichotomously. Such branches,
however, had no share in the work of absorbing nutriment
from the soil. This function was performed by large but
delicate rootlets given off abundantly from the surface
of each root branch. 2ndly, these rootlets possessed a
single bundle of small , vessels running longitudinally
through the cortical investment. In each rootlet this
vascular bundle commenced its growth as a single vessel,
developed eccentrically within an innermost cylinder of
cortical cells, and additional vessels were added to the bundle
centripetally as the rootlet advanced in age and size until
it developed into an eccentric cluster of 40 or 50 vessels.

This peculiar arrangement is only found amongst living
plants in the Ophioglossums and Lycopods, in the latter of
which alone does the dichotomous branching of the roots
occur. It would appear, therefore, that the two features,
viz. the peculiar growth and structure of the rootlet and the

34

dichotomous ramification of the roots seen in the fossil
types, have been concentrated in these degraded living
representatives in the one root organ. Anyhow the facts
afford a strong confirmation of the Lycopodiaceous character
of the fossil Sigillaria to which these Stigmarian roots in
part belonged.

Referring to Haloma, which Binney thought was a root
of Lepidodendron, Professor Williamson exhibited a cast
of a fine specimen of Lepidodendron elegans from the Leeds
Museum, in which each Lepidodendroid branch terminated
dichotomously in a series of subdivisions, each one of which
possessed all the characteristics of a true Haloma.

Dr. Hartog, referring to the memoir recently published
by Profesor Williamson and himself in the Annates des
Sciences Naturelles, in which they criticised the opinions of
M. Renault on the relations of Lepidodendron, Stigmaria,
and Sigillaria, spoke of the part he had taken in the matter.
He also made some remarks on Professor Williamson’s inter-
pretation of his discoveries in connection with Stigmaria.

35

General Meeting, November 14th, 1882.

Edward Sciiunck, Ph.D., F.R.S., &c., Vice-President, in the

Chair.

The Rev. Brooke Herford, of Boston, U.S., was elected a
Corresponding Member of the Society; and Mr. Harry
Marshall Ward, B.A., Berkeley Fellow, Owens College, was
elected an Ordinary Member.

Ordinary Meeting, November 14th, 1882.

Edward Schunck, Ph.D., F.R.S., &c., Vice-President, in the

Chair.

“On Singular Solutions of Differential Equations,” by
Robert Rawson, Esq., Hon. Member, Assoc. I.N.A., Mem.
of the London Math. Society.

The principle employed in this paper is to impress such
forms upon the complete primitive of a differential equation
as will lead at once to its singular solution.

By this method the two theorems which produce singular
solutions, viz.., condition of equal roots of the c- equation and
of the p- equation are readily derived.

The properties also of ~=0, 0, ^~ = infinity, and

— infinity, with their limitations are shown to be

consequences of this principle.

Remarks occur on the valuable papers of Sir James Cockle,
Professor Cayley, Mr. Glaisher, and Boole’s proof of Euler’s

Proceedings— Lit. & PiiiL. Soc.— Yol. XXII.— No. 3.— Session 1882-3.

theorem to determine whether a solution of a differential
equation is singular or particular, and an attempt is made
to solve this problem without using a troublesome transfor-
mation as has been done by Boole and others.

Ordinary Meeting, November 28th, 1882.

J. P. Joule, D.C.L., LL.D., F.B.S., &c., Vice-President, in the

Chair.

“ On the Transformation of a Logical Proposition contain-
ing a Single Kelative Term,” by Joseph John Murphy,
F.G.S. Communicated by the Bev. Robert Harley, F.R.S.

Abstract.

In the system here proposed, R means any relation what-
ever, and R~l the inverse relation. The equation

X=RY

and its inverse

Y = R~1X

mean respectively that X is teacher of Y and Y is pupil of
X, without implying whether or not X has any other pupils
and Y any other teachers.

X = 1RY

and its inverse

Y=1~1R~1X

mean respectively that X is the only teacher of Y, and Y
the pupil of none but X.

If X and Y are the names of classes instead of individuals,
1X< JRY

means that every X is teacher of a Y : and its converse

ij?-1lX< Y

means that pupils of every X are included in the class Y
The proposition

1X< RIY

37

means that every X is teacher of every Y. This is a doubly
total proposition (the preceding one is singly total), and
such a proposition is inevitable, giving

1 Y< B-nx

A singly total proposition of the above form admits of the
following four equivalent forms, whereof the truth or false-
hood of each implies the truth or falsehood of all — Y signi-
fying not = teacher, and X and Y not = X and not = Y : —

1X< BY
1V~11Y<X
A'1 1X< Y
XF1Y< 0

A doubly total proposition of the above form has four pairs
of equivalent forms, as follows : —

1X< A1Y 1Y< B-nX

IVY<X_ _ 1F“1X<Y_

1 Y< I"1 F_1X 1X< l-1 FY

XFY<0 Y F_1X< 0

The concluding part of the paper treats of the application
of these principles to transitive relations, e.g. the relation of
ancestor and descendant, where the ancestor of an ancestor
is an ancestor.

Joint Ordinary Meeting of the Society, and the Microscopi
cal and Natural History Section of the Society,
December 12th, 1882.

H. E, Roscoe, Ph.D., LL.D., E.R.S., &c., President, in the

Chair.

Mr. James Heelis made some remarks upon the causes
of the movement of the old Rhone Glacier with special
reference to the power of gravity to produce such move-
ment when considered in connection with the gradient
down which the glacier has passed,

38

“On an Elementary Solution of the Dynamical Problem
of Isochronous Vibration,” by Professor Osborne Reynolds,
M.A., F.R.S.

When a heavy body is free to move in one direction,
subject only to a force which is proportional to the distance
the body has moved from some neutral position and tends to
return the body to that position, the body will, if set in
motion, vibrate about the neutral position in a period
which is independent of the magnitude of the motion.

The deduction of this theorem from the laws of motion,
although well known, is generally accomplished by the solu-
tion of a differential equation. In some text books this is
avoided by comparing the law of force on the vibrating
body with that of a component of the centrifugal force on a
revolving body; this method involves no mathematical
difficulties, but it is indirect and hides rather than removes
the dynamical difficulties. My own experience has shown
me that the mathematical difficulty or obscurity of these
methods stand very much in the way of those who are
commencing the study of practical mechanics, in which
vibration and oscillation play a part of fundamental import-
ance. It was with a view of meeting the requirements of
such students that I sought for a method involving only
Elementary Mathematics, in which the solution depended
directly on the principle of the conservation of energy.
Having succeeded in finding such a method which, although
it bears a superficial resemblance to the method of the text
books already mentioned, so far as I am aware, has not
hitherto been published, it seems that it may be useful to
publish it.

The method is to show that the vibrating body will at
all times be opposite, in a direction perpendicular to its path,
to a body revolving uniformly in a circle, having a diameter
equal to the amplitude of oscillation, with a velocity equal
to the greatest velocity of the vibrating body.

39

x 7

N. /

[^r~

Let 0 be the neutral posi-
tion of the body considered I
as a point, AOB the path de-

scribed during oscillation, let ^

p be the force on the body
when at a unit distance from

O, so that as the force varies papeffw

uniformly with the distance,
px will be the force at the
distance OP=$.

Take PN perpendicular to
OP and make PN on some scale equal px, then N will lie
on a straight line COD, and the area OPN will represent
the work U done against the force in moving from O to P
and

TT pa x op px 2 m

2 = Ip-

Let W be the weight and v the velocity of the body, then
by the conservation of energy

2g 2g w

where E is the energy of the system and v0 the velocity at
O, or substituting from equation (1)

Wvl Wv2 px2

ii=^i+T (3)

but when P is at A or B v = 0, put 0 A = a, then

2 /A\

pa =~Y (4)

and equation (3) becomes

W

— v2 = pia2 - x2) (5)

Describe a circle about 0 as centre with a radius a, and
let PN produced meet this circle in Q, and let QT the
tangent at Q meet AB in T, then the triangle QTP will be
similar to QOP and

PT PQ

TQ OQ W

40

Now suppose a point at Q moving with a velocity u such
that it keeps opposite to P.

Then the component of this velocity parallel to AB is

PT PQ

“tq~“oq2

and this is v since Q remains opposite to P.

Therefore substituting in equation (5)

W 0PQ2

guo Q2

p(c

Then since PQ3 = OQ3 — OP3 = a2 — x2 we have

W

lpct? = — u%

9

Therefore Q moved on the circle with a velocitv

(7)

V

gjo

W

which is constant. Or the motion of the vibrating body
will be such that it always keeps opposite in a direction
perpendicular to its path to a body revolving in a circle of
diameter equal to the amplitude and with the greatest
velocity of the vibrating body.

This completely defines the motion of the vibrating body
for starting from A the arc described by the vibrating after

time t is and the vibrating body will be opposite.

The time of a complete oscillation will be the time taken
to complete a revolution when

a/

P9. 9

Wt==2^

Therefore the time of oscillation is given by

/W

Vi

9-rr A / —

pg

(8)

“ On the occurrence of Potcimogeton Zizii, M. and K., in
Lancashire, and in Westmoreland,” by Chakles Bailey,
F.L.S.

41

About four years ago a new pond-weed was added to
the British flora, by Mr. Andrew Brotherston, of Kelso, who
found it growing in Cauldshiels Loch, near Melrose, Rox-
burghshire. Mertens and Koch had named the plant
Potamogeton Zizii after its first discoverer, Dr. Ziz; its
affinities are with P. lucens , P. heterophyllus, and their
allies. Though a rare plant it has a somewhat wide distri-
bution in Europe, extending from the Scandinavian pro-
vinces in the north to Bohemia and Bavaria in the south.

A description of the Cauldshiels plant, together with its
synonj^my and relationships, have been carefully worked
out in a paper by Dr. Trimen in the ‘Journal of Botany,’
No. 202, October, 1879, illustrated by a plate.

The distribution in Britain, so far as it has been recorded,
is somewhat restricted, as the published localities are in the
counties of Roxburgh and Forfar, in Scotland, and of
Anglesey, in Wales. So far, there have been no recorded
occurrences of the plant in England or Ireland, but as it is
liable to be passed over for Potamogeton lucens, it will
doubtless be found to be pretty widely distributed in the
British Isles ; indeed Mr. Arthur Bennett has already had it
sent him from several additional counties.

I have now to report its occurrence in two English
counties, namely, Lancashire and Westmoreland, and speci-
mens from both localities are being distributed, with the
plants of the current year, to the members of the Botanical
Exchange Club.

I first collected the plant on the 17th September, 1870,
close to the western shore of Derwentwater, opposite Rose-
trees, three quarters of a mile to the south of the little village
of Portinscale. On that occasion there were neither flowers
nor fruit, and I was unable to refer it to any of the
recognized British forms. It remained in my herbarium for
some years, when Mr. Arthur Bennett, F.L.S. (of Croydon),
who has paid great attention to this group of plants, was

42

good enough to examine all my British Potamogetons, and
he also was doubtful as to the proper nomenclature of the
Derwent water specimens of 1870, thinking that it might be
P. Zizii , although showing an approach to P. decipiens in
the structure of its leaves.

The uncertainty about this plant, therefore, led me to
make a careful search for fruiting specimens in Derwent-
water, during a visit in September last. The station in
which the plant was the most abundant in 1882, is in the
easternmost of two small bays which lie to the east of the
outflow of the lake. The plant grows with Scirpus lacustris,
L., in about four to six feet of water, and there are several
colonies of it. Out of some hundreds of plants examined
in situ there were but two flowering specimens, one of
which is now exhibited to the members, and the other was
sent to Mr. Arthur Bennett, who pronounced it to be
P. Zizii.

Later on, on the 22nd September, 1882, I found the same
plant growing in the greatest profusion at the northern end
of Coniston Lake, and flowering abundantly, nearly all the
plants being in flower or fruit. I had no means of ascertain-
ing the depth of the water, but in many places it would not
be less than eight or ten feet ; the longest specimen actually
gathered was six feet long. I also saw the same species
growing in Windermere, on the western side, near the new
Ferry Hotel, but I could not collect it as I was on the steam
ferry at the time.

According to the notes of Mr. Andrew Brotherston in the
Reports of the ‘Botanical Exchange Club’ for 1879, and of
the ‘Botanical Record Club’ for 1878, the plants from
Cauldshiels Loch grew in water less than one foot deep in
1878, and two feet deep in 1879 ; Mr. Brotherston’s speci-
mens of each of these two years’ growths, now exhibited for
comparison, show considerable difference in habit; the 1878
plants possess short internodes, and subsessile leaves which

43

are crowded on the stem and its branches. Those which
were collected in the same station in the year following, in
water two feet deep, have such long internodes and pedun-
cles (the latter from seven to nine inches in length) and
such distant leaves on the flowering branches, as to appear
to belong to quite a different plant. These two states of
the same plant seem to represent the two varieties figured
by Reichenbach in his “ leones Florae Germanicae et
Helveticae,” Vol. VII., tab. xxxviii. and xxxix., which are
thus characterised : —

a. validus Fieber; stem robust; lower leaves subsessile;
upper leaves shortly petiolate.

b. elongatus, M. K.; stem elongate; internodes, leaves, and
peduncles prolonged.

The only Derwentwater flowering specimens I saw were
very similar to the Cauldshiels Loch specimens of 1879, save
that they were five feet long; while all the non-flowering
specimens had short internodes in their upper portions.
The Coniston plants on the contrary had very long inter-
nodes, while their peduncles (which were very brittle)
measured from eight inches to a foot and a half in length ;
the stalk of the uppermost leaves measured from a quarter
of an inch to an inch and a half. I have therefore referred
them to the var. elongatus of Mertens and Koch, but
Mr. Bennett considers that the Coniston plant is nearer
to M. & K/s typical plant than the Derwentwater plant,
although neither is the type as found in Germany and
Sweden; but more like the French plant from the Loire.

Potdmogeton Zizii differs from P. heterophyllus in having
no floating leaves, and in its submerged leaves not being so
sessile or narrow; it differs from P. lucens in having its
stipules keeled instead of winged ; and from P nitens, and
P. decipiens in its much longer peduncles and in its leaves
not being amplexical or rounded at the base. It should
be looked for in the Cheshire and other meres in the
neighbourhood of Manchester.

44

“ On the Lincolnshire locality for Selinum Carvifolia,

L. ,” by Charles Bailey, F.L.S.

Aided by detailed indications kindly given me by Dr.
F. Arnold Lees, I paid a special visit on the 14th September,
1882, to the Lincolnshire station for the most recent addition
to our flowering plants, viz., the Selinum Carvifolia, L., an
umbelliferous plant discovered by the Rev. William Fowler,

M. A., of Lincoln, and a member of the Botanical Record Club.

Its occurrence as a British plant was first announced on

pp. 127, 128, and 156 to 161 of the 1880 Report of the
Record Club, and its first announcement was a surprise to
botanists, as it was scarcely credible that a plant of so
conspicuous a stature as from one to four feet should have
escaped the notice of so many critical eyes during the last
two centuries, and it encourages the hope that there are
other undetected native species awaiting the researches of
British botanists.

The Lincolnshire locality is situate in a sparsely-populated
portion of the county, in a somewhat woody, but very flat
district with long straight roads and drains. It is nearly
equidistant from Appleby, Scawby, and Glamford Briggs
(Brigg), Scawby and Brigg forming the base of a triangle, of
which the station for the Selinum is the apex. The locality
may be readily identified on the Ordnance map from its
contiguity to the old Ermine Street, which runs in a nearly
straight north line for thirty miles from Lincoln to the
Humber. The high road is left one mile north of the village
of Broughton, through a gate which leads into a wood by a
cart track, running due east, and opposite a lodge. In about
a hundred yards or more the track opens into a narrow
damp pasture which slopes towards a small brook flowing
eastward.

The Selinum begins to occur, in plenty, in this pasture as
soon as it is clear from the shade of the wood. Judging
by the foliage of the plant it is scattered over the small

45

area of the field, preferring its dampest portions. Very few
examples of the plant were visible on the occasion of my
visit, as the field had been recently mown, but I managed
to procure a few plants at the edges of the brook, and in the
shade of some trees. These plants were for the most part
prostrate owing to a flood just subsiding, and as they lay
tangled in the rank vegetation of the watercourse, their
winged stems afforded a more ready means of identification
by touch than anything which presented itself above the
level of the water or amidst the prostrate vegetation of the
banks. Notwithstanding the lateness of my visit, most of
the examples were found in flower, only a small proportion
possessing immature fruit.

So far as could be judged from the surroundings of the
station as seen in a single flying visit, I should not hesitate
to consider the plant as belonging to our indigenous vege-
tation, and I am quite of the opinion of Dr. Lees, given
before it was discovered the following year in Cambridge-
shire, that it will “ be found to occur elsewhere in England,
most likely in some other of the eastern counties.” (Report,
Botanical Record Club, 1880, p. 128). There does not seem
to be any ground for considering it an alien, as it is difficult
to assign a reasonable explanation for its introduction.
Further, the distribution of the plant in all countries
washed by the same seas which touch our eastern and
south-eastern coasts, is another and a very strong indication
of its English nativity.

Mr. J ohn Boyd exhibited a fine living specimen of Argu*
lus foliaceus, a parasite of the Carp.

Mr. R. D. Darbishike gave an account of dredging at
Oban in September, in company with Dr. Marshall, Mr*
Archer, and Mr. Walker, and exhibited and distributed
specimens. Without reaching deeper water than 26 fathoms

46

they had taken within a few miles of Oban a considerable
variety of animals.

Sponges : of several genera.

Hydrozoa : 1 2 larger forms, including Antennularia ra-
mosa and 2 varieties of A. antennina, and Aglaophenia pen-
natula.

Actinozoa: Adamsia palliata, large, and other forms.
Funiculina quadrangularis and Pennatula phosphorea. Of
the former several specimens were exhibited, including
one 4in. long and one 65in. long when fresh. The latter
was taken in 22 f. in Loch Nell. Except a dead one 89in.
long from the Bergen Fiord this appears to be the largest as
yet recorded specimen. It does not appear to be full grown,
being much less crowded with polypes than many of the
shorter ones. Its lower end was loaded with stiff blue mud
when taken.

Polyzoa : many kinds — not identified.

Tunicata : several characteristic forms.

Mollusca : 128 species, besides several Nudibranchs. Fine
series of Terebratula caput serpentis, Crania anomala, Pec-
ten niveus and Lima (3 species). Also Pandora obtusa,
Emarginula crassa, Trichotropis borealis and Natica heli-
coides.

Echinodermata 20, including Comatula rosacea in abun-
dance, Amphiura filiformis, Palmipes membranaceus, Brissus
ly rifer, Thy one and Sipunculus.

Annelida : a large variety.

Crustacea (podophthalmata) 17, including Munida Ron-
deletii and Eurynome aspera.

Professor A. M. Marshall, M.A., D.Sc., exhibited virgu-
laria mirabilis taken last year at Oban by the Birmingham
Natural History Society, and gave a detailed description of
the three forms of Pennatulida. He suggested the desira-
bility of the Section undertaking or taking part in similar
excursions in future years.

47

Ordinary Meeting, January 9th, 1883.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in
the Chair.

Dr. Joule said that he had, in December, 1882, made a
fresh determination of the freezing point in a sensitive ther-
mometer constructed 39 years ago. During that time the
point had risen about 1° Fahrenheit, and although now
rising very slowly, was not even yet quite stationary, having
risen -4V of a degree Fahrenheit since November, 1879.

Ordinary Meeting, January 23rd, 1883.

J. P. Joule, D.C.L., LL.D., F.R.S., &c., Vice-President, in
the Chair.

“Remarks on the Simultaneous Variations of the Baro-
meter recorded by the late John Allan Broun,” by Professor
Balfour Stewart, F.R.S.

In the Proceedings of the Royal Society for May 11th,
1876, will be found an account by Broun of simultaneous
barometric fluctuations at Singapore, Madras, and Simla,
extending over the first three months of 1845. One of
these, a maximum, was likewise shown by Broun to have
occurred nearly simultaneously on March 31st, at a great
many stations in both hemispheres.

The object of these few remarks is to ascertain, quite
apart from any theoretical considerations, whether such
apparently cosmical fluctuations have any relation to the
state of the sun with respect to spots. The spotted areas
of the solar surface corresponding to these three months
are derived from observations by Schwabe, which will be
found recorded in an appendix to the report of the Solar
Physics Committee. The unit is one millionth of the sun’s
visible hemisphere.

Peoceedings— Lit. & Phil. Soc,— Yol» XXII.— No. 4.— Session 1882-3,

48

Let us now take the epochs of the various barometrical
maxima and minima given by Broun, and record the state
of the solar surface corresponding to each epoch, and also
to the two days before and the two days after each epoch.
This is done in the following table, in which the central
number always corresponds to the barometric epoch, and
in which the numbers enclosed in brackets denote interpo-
lated sun spot values.

Table I. — Barometric Maxima.

Barometric epoch.

1845. Sun Spot Areas.

Jan.

8 ..

. (400) ..

. (470)

... 540 .,

.. 840 .

.. 180

5 J

12 ...

180 ..

. 72

... 660 .,

.. 918 .,

.. 414

Feb.

7 ..

• (0) ..

.. 12

... 30 .

.. 24 .

.. 546

jj

14 ...

. (555) ..

. 750

...(800).

.. (850).

.. 900

»

25 ...

894 ..

. 1452

... 972 .

.. (786).,

.. 600

March

7 ...

888 ..

. 360

...(255).,

.. 150 .,

.. 330

•

14 ...

(702) ..

. 816

... 648 .

.. (489).,

.. 330

))

31 ...

(0) ..

. 210

... 612 .

.. 990 .,

,. 996

Sum.

.. 3619 ...

. 4142

...4517 .

.. 5047..

.4296

Table II.-

—Barometric Minima.

Barometric

epoch.

1845.

Sun Spot Areas.

Jan.

10 ...

540 ..

. 840

... 180 .

.. 72 ..

. 660

15 ...

918 ...

. 414

... 330 .

..(246)..

.(162)

5?

31 ...

(461) ...

. 480

... (360) .

.. 240 .

.(216)

Feb.

11 ...

546 ...

■ (^3)

... 360 ..

,. (555)..

. 750

j?

21 ...

930 .

. 882

... (886) .

.. (890)..

. 894

March

4 ...

780 ...

702

... 804 .

.. 888 ..

. 360

24 ...

336 ...

. (238)

... (140).,

.. 42 ..

. 36

April

3 ...

990 ...

, 996

... 750 .,

.. 600 ..

. 540

Sum..

. 5501 ...

5005

.. 3810 ..

. 3533 ..

.3618

It will be seen from these tables that barometric maxima
appear to correspond to increasing sun spot values, while
barometric minima appear to correspond to decreasing sun
spot values ; the. observations are not, however, sufficiently
extensive to render these conclusions certain. It would, I
think, be of importance to pursue this investigation.

49

A paper was read entitled “ Jeremiah Horrox and William
Crabtree, the Observers of the Transit of Yenus in 1639,”
by Mr. John E. Bailey, F.S.A.

Mr. Bailey also exhibited the rare work of Hevelius
entitled Mercurius in Sole visits Gedani 1661 , printed at
Dantzic in 1662.

Ordinary Meeting, February 6th, 1883.

Professor Balfour Stewart, LL.D., F.RS., in the Chair.

Among the donations announced were medallion portraits
of Mr. George Walker, one of the Founders of the Society,
and Mrs. Walker, presented by the President and other
members of the Council.

On the motion of Mr. Baxendell, seconded by Mr. Bailey,
it was resolved, “ That the thanks of the Society be given
to the President and other members of the Council for the
portraits of Mr. George Walker and Mrs. Walker, presented
by them to the Society.”

“ Note on the Yapours of Incandescent Solids,” by Henry
Wilde, Esq.

It is generally admitted that the phenomena known as
Moser’s Spectral Images, which make their appearance on
polished metallic surfaces when bodies are placed very close
thereto, are attributable to the general property which solid
bodies possess of giving off vapours of their own substance
at common temperatures, and the peculiar odours emitted
by some of the less volatile metals, such as copper, when
subjected to friction or to the action of cutting tools, are
also assignable to the like cause.

The production of Moser’s images, as has been shown, is
greatly assisted by the application of heat, and it might

50

have been anticipated that at high temperatures the most
dense and refractory substances would vaporise while re-
taining their solid form.

The conditions necessary for observing the behaviour of
solids at high temperatures are well brought about in the
modern form of incandescent electric lamp. This lamp con-
sists of a bulb of glass from which the air is exhausted to
the highest degree attainable, and a filament of metal or
carbon is mounted in the bulb, and rendered incandescent
by the action of the electric current.

Platinum, from its high degree of infusibility, was con-
sidered by some the most suitable substance for the luminous
filament, and great expectations were formed, that by its
use the problem of incandescent lighting would be solved.
It was, however, found that an atmosphere of platinum
vapour was formed in the interior of the bulb, which, after
the lamp had been in action a lengthened number of hours,
condensed on the surface of the glass and formed a bright
reflecting surface like a mirror.

This property of the platinum, while affording a remark-
able illustration of the vaporisation of a dense body while
retaining its solid form, was fatal to its use as an illuminant,
as the density of the film of platinum on the surface of the
glass ultimately obstructed the greater portion of the light
from the filament itself.

Chemists, I believe, are not unanimous in opinion as to
whether elementary carbon ever passes from the solid to
the liquid form.

Some years ago, I frequently made the experiment of
concentrating upon a small pencil of carbon, two inches long
and three twentieths of an inch in diameter, an amount of
electric force sufficient to fuse a rod of platinum two feet
long and a quarter of an inch in diameter.

The light from the pencil was of intense whiteness, but
the carbon showed no signs of fusion, and rapidly diminished
in thickness by combination with the oxygen of the air.

51

The substitution of a filament of carbon for platinum has
now placed the incandescent electric light in the rank of
recognised illuminants, and when not raised to too high a
temperature the carbon filament is very durable. When,
however, a high degree of incandescence is attained, an
atmosphere of carbon vapour is formed in the interior of the
bulb which condenses on the glass and forms a dark lustrous
surface which obstructs the light in the same manner as
when a filament of platinum was employed.

The behaviour of the carbon and the platinum in each of
these lamps clearly shows that the most dense and refractory
substances in nature vaporise at high temperatures while
still retaining their solid form.

Electric lamps were exhibited by Mr. Wilde showing the
condensed platinum and carbon on the interior surfaces of
the glass bulbs.

“ Remarks on Professor Osborne Reynolds’ paper ‘ On
Isochronous Vibrations,’ ” by Robert Rawson, Esq., Hon.
Member, Assoc. I.N.A., Mem. of the London Mathematical
Society.

At the ordinary meeting, Nov. 28th, 1882, Professor
Osborne Reynolds, M.A., F.R.S., read an interesting paper
entitled “On an Elementary Solution of the Dynamical
Problem of Isochronous Vibrations.” It would seem that
the object of this paper is intended to supply a remedy for
what the author conceives to be a serious defect in our
existing elementary works on Dynamics.

Experience, it appears, has shown Professor Osborne
Reynolds that the obscurity in which the principles of
Dynamics are enveloped by means of the language and
symbols of Differential equations, “ stands very much in the
way of those who are commencing the study of practical
mechanics.”

I am not able, from my own experience, to share the views

52

of the author in respect to the charge which is thus made
against the use of differential equations in Dynamical ques-
tions ; on the contrary, I have always been led to believe
-hat it is, has been, will be, in the language of differential
equations that the principles of Dynamics have received
their greatest development and their most useful applica-
tions. Still I am greatly impressed with the truth, viz.,
that the experience and opinions of so distinguished an
authority as is Professor Osborne Reynolds on all questions
relating to the application of mathematics to the Physical
Sciences, have great weight, and will always command
careful attention.

The problem in question is, however, a simple case of
Harmonic motion, which is admirably explained and illus-
trated by:— 1. Thomson and Tait (Natural Philosophy, p.
36), 2. The late Professor Clifford (Elements of Dynamics,
p. 20), in sufficiently elementary language to suit the com-
prehension of any student of practical mechanics.

I may state here that Newton was the first to invent and
solve this interesting problem in the pages of the Principict,
and most writers on the dynamics of variable forces since
Newton’s time have copied his solution, observing that it is
exactly the case of a heavy body falling in an open shaft
through the diameter of the earth.

As Professor Osborne Reynolds has, therefore, proposed
his solution of this problem with a view of its being inserted
in our elementary treatises on Dynamics as the simplest and
best which has hitherto been given to suit the requirements
of students in practical mechanics, it may not be deemed
unnecessary, then, to examine its claims to this distinction,
and, if possible, to divest it of a few of those things which
tend to increase its complexity and thereby diminish its
usefulness.

No exception, however, can be taken either to the princi-
ples adopted, or the results derived from them, but, no

53

doubt, the diagram and the process of application of the
principles admit of greater simplicity even than that which
has been given in the paper. To this end it is necessary to
state that the principle and formula of the conservation of
energy are given by the simple dynamic of constant forces
in such wise as to be comprehended without the aid of
differential equations.

The definition of work is simple, but, the estimation of it
when the force is variable depends upon quadratures.

When, however, the force varies as the distance the esti-
mation of the work done by it is given by Moseley, Twisden,
and others by elementary mathematics, and is \ px2, using
the notation as given in the paper.

Taking, therefore, for granted a knowledge of the principle
and formula for the conservation of energy, the formula for
estimating work done by a force which varies as the dis-
tance from a given point, the resolution and decomposition
of forces — the diagram and solution of this problem, will
stand as follows.

Let 0 be the position of a body,
whose weight is (w;) and velocity (%),
moving towards A in the straight line
BOA where OA = OB. Let {p) represent
the force at a unit of distance from
O, then (px) will be the force at P,
where OP = x. Describe the circle about
O as centre with the radius OA = a, and
draw PQ perpendicular to AB meeting
the circle in Q. Put (y) the velocity of (w) at P.

Now the work done against the force {px) in moving
from O to P must be equal to the accumulated work lost by
passing from (v0) to (v). Therefore

w

= (1)

When, however, v = 0, then x = a, and the weight (w) is at
A. On this supposition (1) becomes

54

Substitute this value in (1), then

v = \]P- ' Va2 - x 2

V w v

= \Zf-pQ (2)

The velocity of ( w ) is, therefore, greatest at 0, and zero at
A and B, and will continue to oscillate between A and B so
long as the force continues to act.

It will be observed that the motion of Q is compounded
of the vertical motion of P and the horizontal motion of the
line PQ, then, by the composition of velocities

The velocity at Q = v. ^ (3)

Equation (3) shows that Q moves uniformly.

If (t) represents the periodic time, or the time of a com-
plete oscillation, then,

a\/-.t = 2arr

v w

_ / W

or, t — \ / —

* v vg

which is independent of the amplitude of oscillation.

The time of the body describing AP = the time of describing

the circular arc A-Q = /y/^.Sin

If the body when at A is slightly struck with a force at
right angles to A B it will then describe an ellipse whose
centre is 0 — this is Newton’s case of the problem.

With the above slight alteration in the diagram, the
reason for which is given above, the solution of this interest-
ing problem by Professor Osborne Reynolds is simple,
accurate, and easy to comprehend by means of elementary
mathematics.

On this ground it will no doubt recommend itself to the
favourable consideration of any writer on Elementary
Dynamics.

Thomas Alcock, M.D., exhibited and explained a series
of lithographs of his beautiful drawings illustrating the
development of the Common Frog.

55

Ordinary Meeting, February 20th, 1883.

H. E. Koscoe, Ph.D., LL.D., F.RS., &c., President, in the

Chair.

A communication from Dr. Joule, F.RS., was read, on
the use of lime as a purifier of the products of combustion
of coal gas.

The slaked lime is placed in a vessel the bottom of which,
about one foot diameter, is slightly domed and perforated
with fine holes. The vessel is suspended about six inches
above the burner. It is found that a stratum of four or five
inches of lime is sufficient to remove the acid vapours so far
as to prevent them from reddening litmus paper. The lime
seems in many respects to present important advantages
over the zinc previously recommended.

Mr. R D. Darbishire, F.G.S., read a ei Note upon the
Mammoth Cave,” by Mr. G. Darbishire.

After leaving the old “ blue grass ” formation* to the east

* “ The cultivated district of central Kentucky, commonly known as
Blue-grass District, is perhaps for its area the most beautiful rural dis-
trict in America. The surface is undulating, large areas of the original
forests have been cleared of their undergrowth, and produce a fine close
sod, and in these wood-pastures are some of the finest flocks and herds in
the world. It has happened to the writer to pass on several occasions
from this region to the richest lands of middle England, or vice versa ,
and he has always been struck by the singular likeness of the two coun-
tries. There is probably a closer resemblance between the surface of
the country, the cattle, horses, the agriculture, and even the people of
these two areas than any two equally remote regions in the world/’ —
From General Account of the Commonwealth of Kentucky (Geological
Survey), vol. II. p. xi.

Proceedings Lit. & Phil. Soc.— Vol. XXII.— No. 4— Session 1882-3,

56

and crossing the Louisville rocks, one approaches the dry
lands of the “ subcarboniferous fo rmations.”*

Here the rainfall is carried off by “ sink-holes,” and except
where important streams flow in open gorges 300 to 350
feet below the plain, the drainage is all under ground. Sink-
holes are sometimes isolated funnels in the middle of
depressions which might still hold lakes unless so drained,
and probably did so once, and sometimes are the outlets at
the bottom of dry ravines which have no mouths. The
water entering these sink-holes passes away through
cracks and caverns hollowed out of the weaker places in
the rocks. When such a cavern channel is formed near
the surface, the roof falls in at places, and a more or less
open ravine appears. At times the sink-holes, after using
an upper series of caverns for ages, have drilled down-
wards by means of the gravel and rock churning in the
bottoms of potholes till the water has found lower outlets,
and when it has eaten out on lower levels waterways
sufficient for the rainfall of the district, the upper
caverns are deserted, the muds washed in harden on the

* All this region wants the small valleys which we are accustomed to
see in any country ; but in their place the surface is covered by broad,
shallow, cup-like depressions or sink-holes, in the centre of which is a
tube leading down to the caverns below. All this region is completely
honeycombed by caverns, one level below the other, from the surface to
the plane of the stream below. In one sense this set of underground
passages may be regarded as a continuous cavern as extensive as the
ordinary branches of a stream when it, flows upon the surface. The
sink-holes answer to the smallest extremities of the branches. Some
idea of the magnitude of these underground ways may be formed from
the fact that the Mammoth Cave affords over 200 miles of chambers large
enough for the passage of man, while the county in which it occurs has
over 500 openings leading far into the earth, none being counted where
it is not possible to penetrate beyond the light of day.

57

floor, and pieces of the roof becoming detached partially fill
the unused ways with debris. As this goes on, stalactitic
and (foreseen t stalagmitic formations accumulate in these
stormless old river channels. The sign of water action in
the rocks is wonderfully preserved, and tells its tale of
stream-wear or drift-wear more faithfully than in valleys
exposed to rains, vegetation, and changes of temperature.
The unaccustomed darkness and the strange shadows cast
by the lamps of visitors give to these accumulations, masses
of debris, and water-worn roofs and walls, weird shapes
which are fancifully supposed to resemble familiar objects
above ground. Their own individualities, so different from
anything on the surface, give them a far stronger claim on
the observer s interest.

Amid slightly undulating woodlands about 325 feet above
Green River, lies a depression some 80 feet deep, and at one
place the sandstone bottom of this depression has fallen
away, exposing an opening into the “Mammoth Cave,”
whose upper and lower chambers are known to extend for
200 miles, and to communicate with further unexplored
channels.

After a descent from the open air of about 60 feet, the floor
of the “Water Cave” is reached. This has been dry as long
as it has been known. Indeed, as it is nearly 200 feet
above Green River (the drainage level in this district), the
water must for ages have been able to traverse large lower
channels.

The old deposits of mud in these upper caves have been
so saturated with saltpetre that they have been washed as
early as the war of 1812. On the theory that this saltpetre
is derived from bat-guano, acted on by the dry atmosphere

58

of the cave, a long period of inaction as a river channel must
be allowed for. The number of bats is certainly great, but
their lease of the premises during which nitre has been thus
accumulated must have been a long one.

For convenience of tourists and guides the caverns are
usually visited by wThat are called the short or the long
routes, about and 8 miles long respectively. The short
route leads for a considerable distance through the main
cave amid the workings of the saltpetre diggings. This
main cave, nearly four miles in length, has an average width
of 60 feet and a height of 40 feet above the present floor,
which is formed of debris and alluvial deposits considerably
deep over the real rock floor. Owing to peculiar causes
in this dry cave, the earth has hardened, and in places the
guide points out footprints of the oxen used by the miners
not earlier than the beginning of the century, in clay now
nearly as hard as rock. The corn-cobs used long ago are
still undecayed.

The short route leads visitors from the main cave down
by a broken opening to a lower range of caverns in the lime-
stone. These, after passing through various chambers and
galleries, lead to a series of “domes and potholes.” The
“ domes,” or portions of the potholes extending upwards, are
no doubt connected with the funnels of some slough-like
depressions in the ground above, and have supplied water to
the various levels of caverns in their turn, while the holes
having bored some 65 feet lower down, open into the pre-
sent drainage avenues below. The vertical height of these
shafts as visible at present is from 200 to 230 feet, and their
diameter about 25 feet, a size due to the cutting power of

59

the gravels in the pothole, and far in excess of anything
required by the volume of water to be removed.

On the long route, after leaving the main cave and de-
scending to the “ deserted chambers,” a second descent leads
to the third series of caves, also dry in the present age.
Presently the track sounds hollow, and at places, openings
in the floor reveal a fourth series of chambers. Descending
to these, one reaches the level of medium high-water mark
A descent of over 30 feet brought us to the water, which on
1st of November, after the protracted drought, was about
300 feet below the Hotel by my aneroid, or 24 feet above
Green River. Here then is reached a cave that is still in
use, and the roof shows that these caverns are often quite
filled with water.

After crossing several pools, the Echo River is reached,
showing a slight current on its surface. The depth of this
stream varies from 5 to 10 feet, and its width is from 20 to
200 feet, but probably the deeper parts are nearly still pools.
Rowing along this for three quarters of a mile, avenues are
next traversed which for a long distance show the mechani-
cal and chemical erosions of the water-flow, and chambers
are reached where the roofs and sides are covered with
florescent formations of gypsum, the long fibrous bunches of
crystal curving outwards from some centre, forming delicate
rosettes from 1 to G inches in diameter, and as beautiful as
flower-like sea anemones ; but, unfettered by the bonds of
species, every variety of form appears, white, yellow, or
black, and all adorned with glittering crystals.

At last, after a scramble over debris (called “ the Rocky
Mountains,”) which has piled up to a height of 200 feet above

60

the water, or a little above the top of the entrance of the
main cave, the roof is seen to change. It is above the lime-
stone, and the naked sandstone stretches from side to side.
A little further on “the Maelstrom” is reached, another
huge pothole, in which the gravels at the bottom are but
little above the present water-level, while the dome reaches
far up into the sandstone.

On the return journey, a short cut is made up what is
called “ the Corkscrew.” In reality it is a scramble up a
cleft in the rocks nearly choked by debris, the top of which
is also very near the sandstone. To give an idea of the
vastness of this underground drainage I copy from the
Guide Book a few dimensions relating to this one cave, and
be it remembered that the whole country from Bowling
Green to Mufordsville is similarly honeycombed.

The chamber called “Wright’s Botunda” is 400 feet one
way and 100 feet wide, while its height is 40 feet.

Mammoth Dome, of a similar length, has a roof of 150
feet span, in the sandstone, and its depth from the bottom
of the superincumbent sandstone to the floor is 250 feet.

61

Ordinary Meeting, March 6th, 1883.

J. P. Joule, D.C.L., LL.D., F.R.S., Ac., Vice-President,
in the Chair.

Mr. Robert E. Cunliffe and Mr. James Cosmo Melvill
were appointed Auditors of the Treasurer’s Accounts.

Mr. Wm. Brockbank, F.G.S,, referred to the paragraph
in the Daily News of the 5th, which stated that the waters
of the Rhine were so low that the freight boats had ceased
running for want of sufficient depth of water, and he
pointed out that serious difficulties might be looked for on
all the rivers which have their sources in the Alps during
the present summer.

The disastrous floods which have prevailed in these rivers
were caused by the unseasonable warm winds which blew
upon the Alps in the early part of the year, and by which
most of the snow below the permanent snow line was
melted, causing the rivers and lakes to overflow their banks
to an unprecedented extent. These snows were the reser-
voirs which stored up the summer supplies of water for the
Rhine and Danube; their exhaustion has already pro-
duced the difficulties alluded to, and which are likely to be
more serious in summer time. It is these snows also which
feed the alpine glaciers, and a shrinkage of the ice fields will
probably follow7 as summer advances.

“ On the Levenshulme Limestones — -a Section from Slade
Lane eastwards,” by W. Brockbank, F.G.S.

In making a deep sewer from Withington to Levens-
hulme, the strata had been brought to light for about two
Proceedings Lit. & Phil. Soc. — Vol. XXII. — No. 6.*— Session 1882-3.

62

miles, showing a regular sequence of red measures, commen-
cing in the new red sandstone (trias) at Withington and
passing through red clays, shales, and sandstones of the per-
mians, until the Levenshulme limestones at Slade Lane
were reached.

Mr. Swarbrick, the Surveyor to the Withington Local
Board, had made a section giving the surface of the red
measures passed through, which shows it to be much worn and
at varying depths, overlain by the lower boulder clay. A deep
sewer from Levenshulme to Cringle Brook, to join the above
sewer, has been made under the direction of Mr. Harper,
the Surveyor to the Levenshulme Local Board, whose work-
ing plan and section wrere also produced, showing the mea-
sures which were drifted through in the progress of the
works. Commencing at Cringle Brook, where the works
of the Withington sewer were met, the drift was in red
sandstone, but the limestone was soon after reached and
continued for about 750 feet. Some portions of the drift-
ing were through solid limestone rock, the beds being from
1ft. 6in. to 2ft. thick. In other places the measures were
much disturbed, a fault being marked on Mr. Harper’s plan
at one point, and a seam of ironstone Gin. thick also oc-
curred, embedded between the limestones. Bed clay was
next passed through for about 270 feet, the limestone rest-
ing upon it. The course of these works was nearly from
south to north, the drift being nearly parallel to the face of
the limestones and apparently almost upon the top of the
outcrop. A little further northwards the lower boulder
clay was entered, and shortly after the course of the sewer
turned eastwards along Albert Road, passing under the L.
and N. W. railway at Levenshulme station, and terminating
in the Manchester and Stockport road at Levenshulme.
The lower boulder clay occupied the whole of this por-
tion. Endeavours had been made to ascertain the depth of
the clay in this part of the section, but it could not be

63

ascertained. Mr. Worthington, the Engineer of the L. and
N.W. railway, under whose superintendence some large
bridges had just been erected at Levenshulme, had stated
that although a solid foundation had been sought for, no-
thing but clay had been met with to a considerable depth.
At Levenshulme Printworks, about half a mile further east-
wards, an artesian well was sunk some 'years ago, and by
the kindness of Mr. Thomas Aitken the diagram section was
now produced, showing the following measures to have been
passed through :

Section of Boring at Levenshulme Print Works.

Boulder Clay. ft. in.

Clay 32 0

Sand 3 6

Quicksand 1 0

Clay 9 6

Clay 31 0

Sand and Gravel 5 0

82 0

Trias.

Red Sandstone, very soft 12 0

Red Sandstone 83 0

Red Ruddle 8 6

Red Sandstone 24 0

Red Marl 4 0

Red Sandstone 34 4

Red Shale 0 1|

Red Sandstone 57 2

Red Marl 1 6

Red Sandstone 31 4

Red Clay 2 6

Coarse Red Sandstone with Pebbles... 39 6

Red Clay 2 6

Red Sandstone 47 2

Solid Red Rock 3 0

Red Sandstone - 17 0

Total

449 7|

64

It will be seen that the boulder clay and sands were 82
feet thick at the Levenshulme Printworks, and that the
new red sandstones continued to a depth of 450 feet, when
water was met with (of excellent quality) in the pebble beds.
Half a mile further eastwards, near Sandfold, some borings
were taken with a view to the erection of Sir Joseph Whit-
worth’s works on that site ; but although no accurate record
was kept, I have learned that clay and sand were found to
a great depth, so that no solid foundation for steam hammers
could be obtained : — thus showing that a similar depth of
clay probably prevails over a considerable area. At Sand-
fold the upper clays come upon the section, the sands being
largely developed there between the upper and the lower
clays, and producing much water. It is interesting to note
that a Roman cinerary urn was found at Sandfold, a portion
of which is in Mrs. Aitken’s possession.

The section therefore commences on the west with New
Red sandstone at Withington, and terminates westward in
the same. The fault at Slade Lane brings the Levenshulme
limestone nearly to the surface with (probably) the new red
sandstone in front of it eastwards, and the Permian mea-
sures westwards, dipping under the Trias at Withington.

The great fault which brings up the Levenshulme lime-
stone is shown in Mr. Binney’s diagram of the section from
Heaton Mersey to Goyt Hall beyond Stockport, and appears
to be the great boundary fault of the Manchester coal field,
which is seen at Collyhurst and Heaton Norris. At the
latter point it is marked on the Ordnance Survey as being a
downthrow to the east of 200 yards, but at Slade Lane it
would appear to be rather an upthrow fault to the west.
It is quite clear that the recent discoveries at Withington
and Levenshnlme will necessitate a careful resurvey of the
district, as the present maps do not show correctly the lines
of faults, nor the areas covered by the Permians, as recently
brought to light. A considerable quantity of large blocks

65

of Levenshulme limestone have been removed to the gardens
at Brockhurst, Didsbury, where they have been permanently
placed, so as to be accessible to all interested in the study
of them. They bear evidence of having formed an outcrop
of limestone for some time before they were finally covered
up by the boulder drift clays. Many of the blocks are much
weathered upon several surfaces, as if they had formed the
top of a hill, ]ike the creviced summit of a limestone crag.
Others are planed quite smooth, showing the veins of spar
as in polished marble, and have probably formed a floor, over
which the grinding force of the boulder drift passed. One
large block shows very clearly the effect of glacial action,
having well marked stride and a smoothly polished surface ;
and others are rounded and worn, as if they had been
knocked about a good deal. They thus bear evidence of
the forces to which they have been subjected, and are in-
teresting illustrations of glacial action. They also contain
many fossils.

Joint Meeting of the Microscopical and Natural History
Section and the Parent Society.

January 15th, 1883.

James Cosmo Melvill, M.A., F.L.S., President of the
Section, in the Chair.

Mr. Rogers exhibited a slide of the Lingual Palate of
Trochus Milligranus stained in nitrate of silver, and mounted
in dammar.

66

Mr. J". C. Melvill exhibited a specimen of the rare
Goliath Beetle Goliathus Druryi (Westwood), captured by
a sailor on a palm tree near the Cameroon Mountains in
Western Africa.

Mr. Charles Bailey mentioned that last summer he
had noticed the blue Pimpernel Anagallis Cerulsea growing
in the garden of the Whalley Hotel, Brooks’s Bar.

Professor A. M. Marshall gave some particulars of the
dredging excursions conducted by the Birmingham Natural
History Society, and proposed that the Section should
organise a dredging excursion during the coming summer.
After some discussion, in which Mr. B. D. Darbishire, Mr.
C. Bailey, Dr. Alcock, Mr. Melvill, and Mr. Stirrup took
part, it was resolved on the motion of Professor Marshall,
seconded by Mr. Stirrup: — “That a Committee be formed
to make enquiries and report upon the best method of
carrying out such an expedition.”

And upon the motion of Mr. Kogers, seconded by Mr. J.
Boyd : — “That the Committee be composed of Mr. J. C.
Melvill, Mr. R. D. Darbishire, Dr. Marshall, Mr. Stirrup,
Dr. Alcock, and Mr. C. Bailey.

Mr. R. D. Darbishire exhibited a series of land and
fresh-water Shells, from Budapesth, with corresponding
English species for comparison.

67

MICROSOPICAL AND NATURAL HISTORY SECTION.

12th February, 1883. -

James Cosmo Melyill, M.A., F.L.S., President of the
Section, in the Chair.

The Secretary announced the presentation to the Section
by T. R. Archer Briggs, F.L.S., of a copy of his “ Flora
of Plymouth,” and by Messrs. Melvill and Bailey of the
“Journal of Botany,” in monthly parts as issued.

Mr. J. C. Melyill exhibited a dwarf specimen of the
common Harebell Campanula Rotundifolia, having the
corolla divided into five equal lingulate segments down
to the base, found on Afton Down, Isle of Wight.

Also specimens of Calamintha Sylvatica, Blomfi, and Cam-
panula Glomerata, L., var. Nana Bailey, and of Erythrsea
Capitata, Wiild., var. Sphserocephala, Townsend, one of the
rarest British plants.

Dr. Alcock read a paper on the Structure of the Shells
of several common species of Polymorphina, and exhibited
specimens and drawings to illustrate his remarks. He
showed, by transparent specimens mounted in balsam, that
in all cases the walls of the inner chambers which have
become enclosed by later growths are to a considerable ex-
tent removed by absorption, opening out the interior into
one large cavity, and that in P. oblonga and P. gibba this
absorption is remarkably well seen.

By endeavouring to form an idea of the mode of growth
of these shells in relation to the life of the contained animal,
he had been led to doubt the distinctness of P. lactea and
P. compressa as species, the former apparently being P.
compressa in the young state ; and he could not avoid the

68

conclusion that P. oblonga is widely separated by its cha-
racters from P. lactea, the two most prominent of these
characters being the erect oblong segments all extending
to the base of the shell, and the inverted tube at the mouth.

With regard to P. Orbignii, the exhibited specimens of
which were P. gibba with the peculiar wild-grown last
chamber, he still thought his formerly expressed opinion
(Memoirs Lit. and Phil. Soc., Manchester, vol. 8, third series,
1866-67) was correct, namely, that the formation of an ir-
regular shell-covering over the external sarcode in two or
three broad arched passages with numerous tubes for the
protrusion of pseudo -podia, was due to failing power in the
animal owing to advanced age. In P. gibba the most
clearly expressed idea in the structure is strength, and
ability to resist rough usage, as is seen both in the rounded
pebble-like shape, and in the absorption of the interior walls
with redeposit of the shell-matter on the exterior ; and it
would seem that the best proof of vigour in the animal is
the regular formation of successive chambers on this globu-
lar plan ; requiring, as in other regular foraminifera, an
active contraction and collection of the external sarcode
into the correct shape and position to form each new cham-
ber; whilst neglect to do this, until a shell-covering has
formed upon it, in a shape the least capable of resisting in-
jury, can scarcely be referred to anything but enfeebled
vital power.

69

Ordinary Meeting, March 20th, 1883.

J. P. Joule, D.C.L., LL.D., F.R.S., &c., Vice-President,
in the Chair.

A discussion, commenced by Professor Reynolds, took
place on the effects of the explosion at the Local Government
Board offices, on the 15th instant.

General Meeting, April 3rd, 1883.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in
the Chair.

Mr. James Rhodes, M.R.C.S., of Glossop, was elected an
Ordinary Member of the Society.

Ordinary Meeting, April 3rd, 1883.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in
the Chair.

The President exhibited the ash of burnt diamonds, and
enlarged drawings of the same*

“ On the Occurrence of Caffeine in the leaves of Tea and
Coffee grown at Kew Gardens,” by C. Schorlemmer, F.RS.
Proceedings— Lit. & Phil. Soc.— Vol. XXII.— No. 7.— Session 1882-3.

70

Some time ago I wanted some information on the plants
containing caffeine. This interesting compound is not only
found in the seeds of Coffea arabica, but also in the fleshy
part of the berry and in the leaves. The latter are used in
Sumatra by the natives in the place of tea, and some years
ago a patent was taken out for the introduction of “ Coffee-
tea” into this country, but it has not been successful.

Caffeine also occurs in the leaves of different species or
varieties of tea ; in Paraguay-tea, consisting of the leaves
and small twigs of Ilex paraguay ensis ; and in Guarana or
Brazilian chocolate, which is obtained from the roasted seeds
of Paullinia sorbilis. It has further been found in Cola-
nuts, the seeds of Sterculia acuminata, which are extensively
used as a condiment by the natives of western and central
tropical Africa ; and likewise by the negroes in the W est
Indies and Brazil, by whom the tree has been introduced
in these countries. It is said that they promote digestion,
improve the flavour of anything eaten after them, to
counteract the effects of alcohol, and even to render half-
putrid water drinkable. Cola-nuts contain also theobromine,
which is a very interesting fact, inasmuch as this base,
which was first found in Theobroma Cacao, belonging
also to the Sterculiacece, can be easily transformed into
Caffeine.

In collecting this information I consulted, amongst other
works, “the Treasure of Botany,” edited by Bindley and
Moore, where I found the statement, that the custom of
drinking coffee originated with the Abyssinians, who
cultivated the plant from time immemorial. In Arabia it
was not introduced until the early part of the fifteenth
century; before this time the beverage made from the
leaves of the kat ( Catha edulis) was generally used, and is
still in use, possessing properties resembling those of strong
green tea, only more pleasing and agreeable. The leaves are
also chewed, and are said to have the effect of producing

71

great hilarity of spirits, and such an agreeable state of wake-
fulness, that the Arabs who chew them are able to stand
sentry all night long without feeling drowsy.

As the properties of kat resemble so much those of tea,
it appeared to me highly probable that they contain caffeine.
My friend, Mr. H. Marshall Ward, was kind enough to
apply to Professor W. T. Thistleton Dyer, F.RS., who
supplied me in the beginning of December with fresh leaves
of a plant growing in the temperate house at Kew Gardens.
He also sent me a sample from the museum. He says
“ The material in our museum is not very satisfactory, but I
enclose a portion of an authentic sample. The leaves are
different in form from those of the living plant, but I have
ascertained that in this respect they are variable.”

I first examined the fresh leaves ; not a trace of caffeine
could be found, while its presence can be easily shown in
three or four tea-leaves. The only crystalline compound
which I could extract from Catha was a kind of sugar,
apparently Mannite. The quantity was, however, too small
for identifying it.

No caffeine could be detected in the authentic sample,
but it contained common salt, showing that it must have
been in contact with sea water.

As I fully expected to find caffeine and was disappointed,
it occurred to me that possibly the leaves of tea and coffee
grown at Kew might also not contain their characteristic
principle.

Professor Dyer kindly supplied me with the fresh leaves
of several varieties and species in the middle of February.

I found caffeine in green tea (Thea viridis ) and in Assam
tea ( T . assamica).

The leaves of Cojfea arabica, which is now fruiting in
the gardens, contain it also, but much less in proportion
than tea.

72

In Coffeob laurina I found a trace, but none at all in the
large old leaves of Liberian coffee.

Caffeine and theobromine occur only in the vegetable
kingdom. They are nearly related to uric acid, guanine,
and xanthine, which are products of the material exchanges
of the animal organism. The two former can be converted
into xanthine, and this, as Professor E. Fischer has shown,
into theobromine or methylxanthine, and into caffeine or
dimethylxanthine.

As caffeine is used in medicine, it appears very probable
that in no distant time it will be manufactured from
Peruvian guano, which is the best source for guanine.

Annual General Meeting, April 17th, 1883.

H. E. Roscoe, Ph.D., LL.D., F.R.S., &c., President, in
the Chair.

The following Donations to the Funds of the Society were
announced, and the thanks of the Society voted to the Donors :

Dr. R Angus Smith, F.RS £50

Henry Wilde, Esq 100

Dr. J. P. Joule, F.RS 50

Dr. James Young, F.RS 50

Dr. H. E. Roscoe, F.RS. 50

73

Report of the Council , April , 1883.

The Treasurer’s annual statement attached to this report
shows that the balance against the General Account has
been reduced from £120 13s. 3d. — at which it stood on the
31st March, 1882— to £92 2s. lOd. on the 31st March, 1883.
But this improvement is more apparent than real, inasmuch
as an item for rental was included in the receipts immedi-
ately before the close of the financial year, while the paid
arrears of the years 1880-1 and 1881-2, included in this
year’s account, are larger than they will be in the corre-
sponding period next year. It should also be noticed that
the expenditure on account of the Library has been very
greatly reduced during the last five sessions, this year’s
amount having been £17 6s. 7d., as against £145 13s. 6d.
expended during the session of 1878-9. On the other hand,
the balance in favour of the Natural History Fund on the
31st March, 1883, stands at £55 9s. lid., as compared with
£35 7s. lid., the amount at which it stood at the corre-
sponding period twelve months previously. The balance
in favour of the Compounders’ Fund remains stationary at
£125, and this item added to the balance of £55 9s. lid. at
the credit of the Natural History Fund, less the adverse
balance of £92 2s. lOd. on the General Account, leaves a
cash balance of £88 7s. Id. in the hands of the Society’s
bankers on the 31st March, 1883.

The monetary position of the Society becomes less satis-
factory year by year, and the Treasurer has urged upon the
Council the great desirability of largely increasing the
number of members as the only sound means of bringing
the Society’s finances into a more healthy condition. The
valuable library which the Society possesses cannot be
maintained satisfactorily under a less expenditure than £80
per annum, while the state of the fabric and fittings of the

74

house will, with other heavy obligations, necessitate an out-
lay which the Society is at present unable to meet.

The number of Ordinary Members on the roll of the
Society on the 1st of April, 1882, was 141, and 2 new mem-
bers have been elected ; the losses have been, resignations
3, deaths 2. The number on the roll on the 1st instant
was therefore 138. The deceased members are Mr. H. A.
Hurst and Mr. J. G. Lynde.

Mr. James Gascoigne Lynde, M. Inst. C.E., was a native
of the south of England, and practised for many years as a
civil engineer in London as a member of the firm of Lynde
and Simpson, George Street, Westminster. In 1857 he was
appointed City Surveyor by the Manchester Corporation,
which position he retained until his resignation in March,
1879. During the long period Mr. Lynde occupied this
position he was regarded by the members of the Corporation
with the highest esteem and utmost confidence. Among
the more notable undertakings carried out under his super-
vision were the widening of Deansgate, the improvement of
the river Medlock, and the construction of the Corporation
Gasworks at Bradford Road. He prepared the plans for
laying out Alexandra Park, and, more recently, those for the
Southern Cemetery. The Queen’s Road Viaduct, the
Smedley Road Bridge crossing the river Irk, the Waterloo
Bridge which crosses the Irwell in Strangeways, the Irwell
Street Bridge in connection with the Quay Street improve-
ment, and the Prince’s Bridge which provides communication
between Manchester and Salford by way of Hampson
Street, Oldfield Road, were all constructed from his designs.
Mr. Lynde was one of the oldest members of the Institution
of Civil Engineers, having completed his 50th year of
membership ; he was a Fellow of the Geological Society of
London, and a member of the Institute of Mechanical
Engineers.

75

The following papers and communications were read at
the Ordinary and Sectional Meetings of the Society during
the Session :

October 3rd, 1882. — “On a vitrified mass of stone from the
vitrified Fort of Glen Nevis,” by Dr. R. Angus Smith, F.R.S., &c.

“ On a Compound Rainbow,” by R. F. Gwyther, M.A.

October §th, 1882. — “ On a series of preparations from the Coal
Measures illustrating the present state of our knowledge of the
relations between Lepidodendron, Sigillaria, and Stigmaria,” by
Professor W. C. Williamson, F.R.S.

October 17th, 1882.— “Note on the Development of Living
Germs in Water,” by Dr. R. Angus Smith, F.R.S.

“On the Formula for the Intensity of Light transmitted
through an Absorbing Medium, as deduced from Experiment,” by
James Bottomley, B.A., D.Sc.

“ On the Intensity of Light that has been transmitted through
an Absorbing Medium in which the Density of the Colouring Mat-
ter is a function of the distance traversed,” by James Bottomley,
B.A., D.Sc.

“The Death-age in Langweis (Switzerland),” drawn up by
Arthur W. Waters, F.G.S., F.L.S.

October 31s£, 1882.— “Belted Skew Pulleys,” by Archibald
Sandeman, M.A.

“Note on the Dimensions of Ships,” by J. P. Joule, D.C.L.,
LL.D., F.R.S.

“ On the Coffee Leaf Disease of Ceylon, illustrated by prepara-
tions for examination under the microscope,” by H. Marshall
Ward, B.A., Fellow of Owens College. Communicated by Profes-
sor Osborne Reynolds, F.R.S.

November 14 th, 1882. — “On Singular Solutions of Differential
Equations,” by Robert Rawson, Esq., Hon. Mem., Assoc.I.N.A.,
Mem. of the London Mathematical Society.

November 28 th, 1882. — “On the Transformation of a Logical
Proposition containing a Single Relative Term,” by Joseph John
Murphy, F.G.S. Communicated by the Rev. Robert Harley, F.R.S.

76

December 12 th, 1882. — “On an Elementary Solution of the
Dynamical Problem of Isochronous Vibration,” by Prof. Osborne
Reynolds, M.A., F.R.S.

“ On the Occurrence of Potamogeton Zizii , M. and K., in Lan-
cashire, and in Westmoreland,” by Charles Bailey, F.L.S.

“ On the Lincolnshire locality for S 'elinum Garvifolio, L.,” by
Charles Bailey, F.L.S.

“ On some of the Besults of a Dredging Excursion at Oban,” by
R. D. Darbishire, F.G.S.

January 9 th, 1883. — “On the Change of the Freezing Point of
a Sensitive Thermometer constructed 39 years ago,” by J. P.
Joule, D.C.L., LL.D., F.R.S., &c.

January 23rd, 1883. — “Remarks on the Simultaneous Varia-
tions of the Barometer recorded by the late John Allan Broun,”
by Professor Balfour Stewart, F.R.S.

“ Jeremiah Horrox and William Crabtree, the Observers of the
Transit of Venus in 1639,” by Mr. John E. Bailey, F.S.A.

February 3th, 1883. — “Note on the Vapours of Incandescent
Solids,” by Henry Wilde, Esq.

“ Remarks on Professor Osborne Reynolds’ paper on Isochronous
Vibrations,” by Robert Rawson, Esq., Hon. Mem., Assoc.I.N.A.,
Mem. of the London Mathematical Society.

February 1 2tli, 1883. — “ On the Structure of the Shells of seve-
ral common species of Polymorphic,” by Thomas Alcock, M.D.

February 2 §th, 1883. — “ On the use of Lime as a purifier of the
products of combustion of Coal Gas,” by J. P. Joule, D.C.L.,
LL.D., F.R.S.

11 Note on the Mammoth Cave,” by Mr. G. Darbyshire.

March 6th, 1883.— “On the low state of the waters of the
Rhine,” by Wm. Brockbank, F.G.S.

“ On the Levenshulme Limestones — a Section from Slade Lane
eastwards,” by Wm. Brockbank, F.G.S.

April 3rd, 1883.—“ On the Ash of the Diamond, by Professor
H. E. Roscoe, LL.D., F.R.S., <fcc., President.

“ On the Occurrence of Caffeine in the leaves of Tea and Coffee
grown at Kew Gardens,” by Professor C. Schorlemmer, F.R.S,

77

Several of these papers have been passed by the Council
for printing in the Society’s Memoirs, and will appear in
volume 8. In addition to volume 8, which is in progress of
formation, a Memoir, consisting of a History of the Society
since its foundation in 1781, by Dr. Angus Smith, under-
taken at the request of the Society on the occasion of its
Centenary in 1881, will appear as volume 9.

The Council again consider it desirable to continue the
system of electing Sectional Associates, and a resolution on
the subject will, as usual, be submitted to the Annual Meet-
ing for the approval of the members.

m.

MANCHESTER LITERARY AS)

Charles Bailey, Treasurer, in account with the Sociei

Statement of the Accoum

1882-3.

1883.

To Cash, in hand, 1st April, 1882 .

£ s. d.

£ s. d.
39 14 8

To Members’ Contributions : —

Arrears 1880-1, 4 Subscriptions at 42s 8 8 0

„ 1881-2, 18| „ „ 38 17 0

,, „ 1 Admission Fee ,, 2 2 0

Old Members, 1882-3, 121 Subscriptions 254 2 0

New Members, ,, 2 ,, 4 4 0

,, ,, ,, 2 Admission Fees 4 4 0

Old Member, 1883-4, 1 Subscription 2 2 0

To One Associate’s Library Subscription

313 19
0 10

To Sectional Contributions for 1882-3 : —

Physical and Mathematical Section 2 2

Microscopical and Natural History Section 2 2

To use of the Society’s Rooms : —

Geological Society to 31st March, 1882 30 0 0

„ „ „ 1883 30 0 0

To Sale of the Society’s Publications.

To Natural History Fund : —

Dividends on £1,225, Gt. Western Ry. Co.’s Stock

To Bank Interest, less Bank postages 2 14

1881-!]

£ s.l

in

5 L

305 11 j,
0 10 )

4 4

0

4 4

60 0

0

30 0

5 11

1

8 10 j]

0 5 10

59 13

9

54 18 9

2 14

7

2 14 fl

£486 12 n £517 13

• ■■■■-■"■ ' - -i

1883. — April 1. To Cash in Manchester and Salford Bank, Limited £88 7

Note. — The detailed accounts of the session 1882-3 (of which the above account is s
abstract) were audited by Mr. Robt. E. Cunliffe and Mr. J. Cosmo Melvill, on til
4th April, 1883, and have been found correct.

ILOSOPHICAL SOCIETY.

i 1st April, 1882, to the 31st March, 1883, with a Comparative
! the Session 1881-1882.

®r.

1882-3.

183 — March. 31. £ s. d. £ s. d.

Charges on Property : —

Chief Rent 12 12 2

Insurance against Fire 12 17 6

Property Tax 4 12 1

Repairs, &c 13 3

31 5 0

House Expenditure : —

Coals, Gas, Candles, and Water 15 13 1

Tea and Coffee at Meetings 15 9 6

House Duty 6 7 6

Cleaning, Brushes, &c 5 10 1

_ 43 0 2

Administrative Charges : —

Wages of Keeper of Rooms 57 4 0

Postages and Carriage of Parcels 16 19 1

Attendance on Sections and Societies 9 4 0

Stationery and Printing Circulars 10 17 6

Distributing Memoirs

Publishing : —

Printing Memoirs 75 19 3

Printing Proceedings 43 13 0

Wood Engraving and Lithographing 3 5 6

Editor of Memoirs and Proceedings 50 0 0

172 17 9

Library : —

Binding Books

Books and Periodicals 7 16 1

Assistant in Library 9 0 0

Geological Record for the Year 1878 0 10 6

Palseonto graphical Society

Ray Society

Natural History

Works on Natural History 9 16 9

Lithographing and Printing Plates of Paper

on Frog 29 15 0

Grant to Microscopical Natural History

Section

39 11 9

Balance 88 7 1

1881-2.

£ s. d. £ s. d.

12 12 8
12 17 6
3 10 10
3 6 5

17 11 4
17 1 10

6 7 6

5 6 8

— 46 7 4

57 4 0

18 12 0
9 9 0

14 2 1
3 0 0

102 7 1

51 9 0
54 1 0
1 11 6
50 0 0

157 1 6

22 4 ”8
19 12 6

"i ”i 0
110

43 19 2

15 16 5

80 0 0

95 16 5
39 14 8

£486 12 11 £517 13 7

1882-3.

£ s. d. £ s. d.

mpounders5 Fund : —

Balance in favour of this Account, April 1st, 1883 125 0 0

tural History Fund : —

Balance in favour of this Account, April 1st, 1883 35 7 11

Dividends received during Session 1882-3 59 13 9

95 1 8

Expenditure during Session 1882-3 39 11 9

Balance in favour of this Account, 31st March, 1883 55 9 11

180 9 11

ineral Fund : —

Balance against this Account, 1st April, 1882 120 13 3

Expenditure during the Session 1882-3 358 14 1

479 7 4

Receipts during the Session 1882-3 387 4 6

Balance against this Account, 31st March, 1883 92 2 10

ish at Bankers, 31st March, 1883 £88 7 1

80

On the motion of the Rev. William Marshall, seconded
by Mr. Harry Grimshaw, the Report was unanimously
adopted, and ordered to be printed in the Society’s
Proceedings.

On the motion of Mr. Alfred Brothers, seconded by
Mr. James Smith, it was resolved unanimously: —

That the system of electing Sectional Associates be con-
tinued during the ensuing Session.

The following gentlemen were elected officers of the
Society and members of the Council for the ensuing year : —

^rcstocnt.

HENRY ENFIELD ROSCOE, B.A., Ph.D., LL.D., F.R.S., F.C.S.
Hicc=iprcstocnts.

JAMES PRESCOTT JOULE, D.C.L., LL.D., F.R.S., F.C.S.
^DWARD SCHUNCK, Ph.D., F.R.S., F.C.S.

ROBERT ANGUS SMITH, Ph.D., LL.D., F.R.S., F.C.S.

Rev. WILLIAM GASKELL, M.A.

Secretaries.

JOSEPH BAXENDELL, F.R.A.S.

OSBORNE REYNOLDS, M.A., F.R.S.

treasurer.

CHARLES BAILEY, F.L.S.

'Etfcranatt.

FRANCIS NICHOLSON, F.Z.S.

0tl;cr JHcm&crs of tljc ^Council.

OBERT DUKINFIELD DARBYSHIRE, B.A., F.G.S.
BALFOUR STEWART, LL.D., F.R.S.

CARL SCHORLEMMER, F.R.S.

JAMES BOTTOMLEY, B.A., D.Sc., F.C.S.

WILLIAM HENRY JOHNSON, B.Sc,

HENRY WILDE,

81

“ A Proof of the Addition Theorem in Elliptic Integrals/’
by R F. Gwyther, M.A.

The quadriquadratic equation, symmetrical and of e\en
order

A + B(#2 + f) + 2Cxy + D ny* = 0

may be used to perform the actual addition of two elliptic
integrals of the normal form.

ft yx r b

Taking the integral / ■ „■ = / — j—r,

& b J </{ 1 -^2)(1 - Pa?) J A {x.k)

o o

we will use the above equation to obtain a substitution
giving as result an integral of the same form, and having
for its lower limit the value a.

Solve the quadriquadratic for x and y respectively
(B + D f)x + Cy=± yj - AB + (C2 - B2 - AD)^2 - B%4
(B + + Gx — J - AB + (C2 - B2 - AD)*2 - BD*4.

Now choose the constants in the equation of transformation
so that the radicals become A (g.k) and A (x.lc) respectively.
This requires

- AB = 1 ; - BD ^ k\ &c.

Also the equation connecting the variations of x and y is

dx dy

or,

(B + D*2)y + Cx
dx dy

■ + ■

(B + Dy2)* + Gy
= 0.

= 0,

A {x.k) — A {y.k)

In considering the limits of y corresponding to the given
values of x, the lower is to be a , and we will call the upper
c. This limit is to be expressed in terms of a and b.

From the solved forms of the quadratics we get
x = o ) x = b)

y~a) V = g)

Ca = + A {a.k)

Ba=l

(B + D62)c + c& = A {b.k)
with BD = - h 2.

^putting

simultaneously^

82

Hence D= -Jdb, and

(1 - BaWy = a A (b .k) + b A ( a.k )
taking the upper or lower sign throughout.

r_*_ = + =T[C

J A (x.k) J A (y.k) J

dx

A (x.k) J A (y.h) ' J A {cc.k)

o b b

and ultimately

fa dx , dx _ r

J A(x.k)~J A{x.k) J

dx

A (cc.k)

A {x.k)

ooo

aA(ii)fiA(ai)
wneie c- i_kw

according as the upper or lower sign is taken.

“Observations made in St. Moritz* in the Winter 1882-3,”
by Arthur Wm. Waters, F.G.S., F.L.S.

Knowing that the session of the Society will soon close I
hasten to put together a few of my winter observations in
order that they may be read at the closing Meeting.

Much of my time has been occupied in preparing new
instruments adapted for the climate, and therefore my
observations are few and imperfect, but I have tried to
obtain a few figures bearing upon the question of the
influence of a snow covering upon climate. This can only
be worked out after many years’ observations, but I hope that
some of the points noticed will afterwards be of considerable
use, and perhaps the most interesting are those on the tem-
perature indicated by a thermometer placed in the snow.

The thermometer used was a common one painted white
over the bulb, and which I carefully tested for the freezing
point, but some of the lower degrees may not be absolutely
correct. It was placed vertically with the bulb about 25
centimetres below the surface and with the upper part one
or two inches below the surface; and there will all through
the winter have been at least half a metre of snow between
the bulb and the earth.

# St. Moritz, the highest village in the Engadine, is 6089 feet above
the sea.

83

There are a great many difficulties about such observa-
tions, as, first, the condition of the snow is very variable,
and the thermometer must to a certain extent be influenced
by conduction. If it could be managed, the thermometer
ought to be placed horizontally ; but practically this would
be more difficult, as the condition of the snow in arranging
it would be too much disturbed for constant observations.
In order to test this, besides what I call the permanent
thermometer, I placed one about an inch below the surface
and another about a foot below; on February 22nd, for
instance, at 11.30 a.m., the one 1 inch below showed 30*8
F., the permanent one 23*7 F., and the one 1 foot below
25 F. I of course found that the upper one was much
more rapidly affected by the sun than the lower one, and
further that a thermometer placed deeper than the perma-
nent one registered higher.

Freshly fallen snow is given in the text books as melting
to one tenth of its bulk of water. I have not found quite
as much with freshly fallen snow ; but this very soon varies,
partly in consequence of pressure, but chiefly through re-
crystallization, which takes place more rapidly as soon as
the weather becomes a little warmer than usual. I have
several times measured coarse-grained r eery stall ized snow,
and found that it melts to one third of its bulk. This
change of bulk often misleads people into thinking that a
great deal has been melted, and two or three of our first
rather warmer days caused the snow to sink down several
inches without there being any melting. Nevertheless this
change of condition is of course an important factor in the
melting, as the quantity of snow which previously occupied
a larger space comes now into contact with less air, and
both the terrestrial heat and the solar can influence a greater
weight of snow.

A reference to the curves for January and March will
show that the temperature in the snow only slowly follows

84

that of the air, so that occasionally the maximum of the air
is below that of the snow, or the minimum above it.

Until the temperature in the snow at about the depth I
measured reaches freezing point, we cannot speak of any
real snow melting. The “snow melting” is often spoken of
by the natives as a season, irrespective of there being any
snow to melt; but this is a more gradual thing than is
sometimes imagined. This year from about the beginning
of March the sun cleared a few small patches on the northern
slopes. These were several times covered with fresh snow,
but soon cleared again. With the first of April the real
snow melting began, and from the first of that month until
the snow was away I always found the snow at the freezing
point. The size of the bare patches was rapidly increased,
and the water from the melting snow above ran on to them

O

and was partly evaporated ; but with the bright sun these
patches, for some time swampy or muddy, gradually became
drier. By the 12th the northern slopes were getting quite
bared, but the flat places showed little change before May ;
and the southern slopes fairly commenced to be cleared about
the 16th May.

If it were not that the increase in the amount of bared
earth is so gradual I believe that this season of the year
would be much more trying than is the case.

I made some further observations upon evaporation of ice
in the shade, using the same tin (27 cm. by 22 centimetres
X 5 cm.) as last year in Davos* hung up by wire in my
screen. The total amount of evaporation for January was
9T mm., but as I made some alterations in my screen for
other instruments I was unable to continue to weigh after
that month.

The evaporation measured in my screen, from 9 a.m. to 8

* Preliminary Eemarks on Observations made in Davos in the Winter
1881-82 by A. W. Waters, Proc. Manch. Lit. & Phil. Soc., 1882, p. 162.

85

p.m. ; on February 7tli, showed no loss.

„ 8th gain of 0*05.

„ 9 th no loss.

„ 10th evaporation of 0*50 mm.

„ 12th „ 003.

This very inconsiderable loss through the day time arises
partly from the temperature of the ice changing but slowly.
Condensation producing gain on the 8th is very instructive,
and such circumstances must be taken into consideration in
studying the climate when the glaciers had a greater extension.

I also again filled a tin (painted white) with snow, and
buried it as before in the snow so that the level of the
snow in the tin was as near as possible the same as that
surrounding it, and in this way we must find out very
approximately the amount of evaporation from the surface
of the snow covering the valley. It was placed in the sun
and measured by weighing, and the weight lost is calculated
out and expressed in the depth of water, which will mean,
as we have seen, that at least three times this depth of snow
has disappeared.

The results were : — -

Loss by evaporation — Temperature.— N Maximum,

from 9 a.m. to 3 p.m. 9 a m. 1 p.m. 3 p.m. Solar radiation.

Feb. 5th. — 0'07mm. (water)— 90C.— 3'8C.— 3*00. 37'4C. cloudless day, windy,

moderately dry.

>>

23rd.— 0-60

do.

+ 3-4

+ 2'0

+ 2-0

fairly clear, windy,
very dry.

27th. — 0*27

do.

-3-4

+ 5-2

+ 4-8

43-6

nearly cloudless, little
wind, very dry.

>5

28th.— 0-48

do.

+ 2-0

+ 2'6

+ 2-9

52-6

rather cloudy, windy,
moderately dry.

Mar. 2nd. — 0'40

do.

-42

-ri

-3-4

39-2

very little cloud,
windy, very dry.

5th.— 0-35

do.

-87

-0-8

+ 0-6

37-8

cloudless, moderate
wind,moderatelydry.

Apr

-. 2nd.— 0*27

do.

+ 2*1

+ 3‘2

+ 1*9

51-6

rather cloudy, windy,
moist.

3rd.— 0-33

do.

+ 1-3

+ 57

+ 6-4

44-6

cloudless, very little
wind, dry.

>>

4th— 0-58

do.

+ 2-3

+ 7-9

+ 6-0

47-8

almost cloudless, little
wind, dry.

5}

5th.— 0'43

do*

+ 2-6

+ 7*4

+ 8”0

44-8

cloudless, not very
windy, dry.

86

The last two days cannot be looked upon as very exact,
as the condition of the snow changed so much.

Besides these measurements made in the warmest part of
the day I found the loss from —

Feb. 5th, 9 a.m. to Feo. 7th, 9 a.m. to be OT 6 mm.

„ 22nd, 3 p.m. to Feb. 23rd, 9 a.m. to be 0-28 mm.

„ 26th, 9 a.m. to Feb. 27th, 9 a.m. to be 0’67 mm.

„ 27th, 3 p.m. to Feb. 28th, 9 a.m. to be 048 mm.

April 3rd, 3 p.m. to April 4th, 9 a.m. to be 043 mm.

„ 4th, 3 p.m. to April 5th, 9 a.m. to be 062 mm.

„ 5th, 3 p.m. to April 6th, 9 a.m. to be 043 mm.

As the snow cannot be materially warmed the evaporation
can never be very rapid from it, but this is quite different
with the earth as soon as it is uncovered, as being dark it
absorbs the heat and becomes very much warmed, causing
rapid evaporation, so that where no fresh supplies of water
are coming into the earth we may see it in a few days as dry
as mummy dust. In order to see exactly how this takes
place I propose next winter to bury a tin full of damp earth
in earth of the same temperature and moisture.

I this winter made some preparatory observations by
putting some very damp earth into my tin and burying it
in the snow in the same way as I had done when it was full
of snow, but as the tin was too large to weigh when full of
earth I was only able to partly fill it, which would
materially affect the exactness of the observation. The
earth was, of course, kept cool by the snow, whereas if it
had been surrounded by earth, it would have been warmed.

March 18th, added about 1 kilo water to about 4 kilos
very dry earth ; lost from 9 a.m. to 3 p.m. 106 mm. of water.

March 26th, lost from 9 a.m. to 3 p.m. 1T3 mm. of water.

I would specially call attention to the evaporation of the
snow during the day time, on April 2nd and 3rd, both of
which were days of genuine snow melting, and it will be

87

seen that the amount of loss by evaporation was but small.
This evidently depends upon the snow remaining at a lower
temperature than the air.

This is a most important questi >n, as one of the difficult
problems with regard to these high climates, as health
resorts, has always been what is to be done during the snow
melting, and those patients and doctors who are not fully
acquainted with the climate have not unnaturally rushed off
with the idea that the melting of two or three feet of snow
causes the air to be always laden with moisture. These
experiments, as we expected, show however that the amount
of moisture which passes into the air direct from the snow
is but small, and that the bugbear of the snow-melting is
much exaggerated. The meteorological figures taken for a
number of years in several high stations show the months
of March and April are among the driest of the year.

The experience of medical men and others who have li^ed
for many years in these climates seems to be universal that
the unpleasant and dangerous time is not, per se, when
the snow is really melting, but as soon as the ground has
become bare of snow, when people often experience feelings
of cold and chilliness to which they have been quite unac-
customed during the cold weather of the winter, and there-
fore many who live in these places do not try to rush away
at the first sign of snow melting, but rather towards the last.

Some of the days with the greatest snow melting were
this year among the pleasantest of the winter, and from the
1st April to the 6th inclusive the average relative humidity
or percentage of possible moisture was at 1 p.m. 55 per cent
(calculated by Apjohn’s formula), although the snow was
rapidly melting all day, and two of these days were almost
absolutely cloudless.

Although showing that there is not necessarily much
dampness of the air connected with the snow melting I do not

88

wish anyone to be misled into supposing that I am recom-
mending this as a favourable time of year and that there
are no disadvantages, for naturally the roads and villages
are in a dirty and unpleasant condition, and in fact the roads
have usually been dirty for a long time before the real snow
melting begins. The early melting of the roads arises partly
from the dirt on the roads, which absorbs the heat; but
besides that, any snow which is pressed down sooner be-
comes soft than snow left as it fell. The reason of this we
have seen to be that both the heat from the earth and the
sun can sooner influence it. Besides the disadvantage of
dirty roads, all the filth which has remained frozen during
the winter has to be thawed.

Another point chat must be taken into consideration is
that the snow melting is not a thing which necessarily goes
on steadily for a few days and is then finished, but, on the
other hand, as the temperature has now risen and passes
more frequently above and below freezing point, the weather
becomes more unsettled, and during the month of March
snow frequently falls — in fact, about as often as in any
month of the year ; and this also means that the sky is
more clouded. Dr. Ludwig* gives the average cloudiness
of the sky in the Oberengadine stations for ten years, and
from his figures it seems that the cloudiness, which in
January averages only 4’5 (scale 0 — 10), in February 4 *6,
increases in March to 5 ’3, and in April decreases to 4*8.
Some figures which I have prepared from other high places
fully bear this out. This is the opposite to what we find
in the neighbourhood of London (Greenwich), for from some
figures before me for a number of years we have January
7tJ, February 7‘9, March 6*4, April 5 -9.

We have so far examined the snow as removed by the
sun, but there are a] so occasionally times when a warm

* Oberengadin yon Med. Dr. J. M. Ludwig. Stuttgart, 1877.

89

south wind keeps the air warm night and day, and melts
the snow under unfavourable, cloudy, and oppressive con-
ditions, but as I have not known any real snow melting
of this kind during the last two years I am unable to give
any particulars as regards this form of melting, which is
however not so common.

As the conditions of the snow melting have been very
imperfectly understood by the majority of English doctors,
I am now trying to collect material for a more extended
study of the question, but the few facts which I have
mentioned support the views of many German and Swiss
doctors of considerable practical experience, and will, I
think, show that what must be done during the snow
melting is a question to be decided upon the individual
circumstances of each patient’s case, always however re-
membering that the majority of those who have spent a
winter in the cold of the high climates are when they go
down to the damper air of the plain sensitive to the cold,
and therefore it is better that they should not go to any
place where spring weather has not fully set in, without
being relaxing, and above all should avoid any place where
the winter snow has not been melted away four or six weeks.

It is often incorrectly supposed that any one who has
been able to bear the extreme cold of a winter in the high
climates will not feel the more moderate cold of a lower
station.

Wind.

I had last year (loc. cit. p. 179) to express my regret that
I could not find a position for my anemometer, which was
quite satisfactory to me, and I have to say the same thing
again now. As the hotel is more or less on the side of
a hill and near the highest part of the road, it was most
difficult to find a spot which was not sheltered by some
building, and in consequence I had to place my instrument
on a small mound where I think we may say it received no

90

shelter, although I have a few times seen a Jit tie more wind
on the S.E. of the hotel and also on the further rink, etc.
My object has been as far as possible to register the amount
of wind to which patients are exposed, and therefore, my
regret at having to place it on a mound, as undoubtedly
there was more wind at the top than on the level. The
position was between the hotel and the main road, so that
in going to the skating rink, or for a walk in any direction,
it was necessary to pass close by it. It also overlooked the
tennis court, causing me some anxiety lest the balls should
damage any of the instruments on the mound. It will be
seen that if it could have been three feet lower the position
would have been a very good one.

It would not be fair if I did not point out that the winter
of 1881 — 1882 was an exceptionally still one generally,
whereas this winter has not been as favourable in that
respect. •

This, however, has not been an especially windy winter,
which I was able to gather from the opinion of uninterested
parties ; and to prove this I give a comparison of the wind
taken this winter at Sils Maria, a village 7 miles S.W., and
at Bevers, 4 miles N.E. of St. Moritz, and also of Davos
Platz, in a parallel valley.

The averages for St. Moritz are for 4 — 7 years, and include
all the observations made ; for the other, places they are
from all the material which happened to be available here.
The figures are given in percentage of times that the Swiss
anemometer was not moved. This is here wrongly called
“ windstille.”

o,.n u . / Ocfc. Nov. Dec. Jan. Feb. Mar.

8 ns Maria (average

of 7— 8 years)... 63 ... 57 ... 61 60 ... 62 ... 61

1882. — ... 76 ... 77 1883. ..56 ... 63 ... 52

Bevers (average of

9 — 11 years)... ... 57 ... 59 ... 68 66 ... 56 ... 44

1882 67 ... 58 ... 73 1883. ..70 ... 51 ... 41

91

Davos (average of

Oct.

Nov.

Dec.

Jan.

Feb.

Mar.

8 — 10 years) ...

63 ..

.. 71 ..

. 74

71 ..

.. 59 .

.. 51

1882

83 ..

.. 76 ..

. 88

1883.. .81 .,

,. 69 .

.. 74

St. Moritz average. .

52 ..

,. 53 ..

. 53

57 ..

.. 45 .

.. 41

Since the Swiss anemometer in St Moritz (which however
indicated the greatest average amount of wind) was in a
very sheltered position, the figures obtained by it cannot
be directly compared with those of the neighbouring places.

The number of miles of wind registered in

November 1882, was 1965-33

December 1422-74

January 1883 1674-94

F ebruary 1556-72

March 274075

April .....2181-05

The following analysis will give an idea as to the
frequency of strong wind, and by the side of the two
months in St. Moritz I give a similar table for the month
of January, 1882, in Davos. That month was among the
stillest which has ever been known in the Alps.

The “ night ” is from 3 p.m. of the previous day to 9 a.m.,
“ morning ” 9 a.m. to 1 p.m., “ afternoon ” 1 p.m. to 3 p.m.

Average rate per hour.

Jannary, 1882.

January, 1883.

March, 1883.

Davos Platz.

St. Moritz.

St. Moritz.

Night.

Morning

Aftern.

Night

Morn.

After.

Night

Morn.

After.

3 p.m.

9 a.m.

1 p.m.

3 p.m.

9 a.m.

1 p.m.

3 p.m.

9 a.m.

1 p.m.

to

to

to

to

to

to

to

to

to

9 a.m.

1 p.m.

3 p.m.

9 a.m.

1 p.m.

3 p.m.

|9 a.m.

1 p.m.

3 p.m.

Times

Times

Times

Times

Times

Times

Times

Times

Times

No movement....

15

3

3

0

0

0

0

0

0

Less than 0’5 m.
Between

12

14

23

1

4

2

2

1

0

0-5 & l m.

2

4

3

9

6

7

4

1

1

,, 1 & 2 m.

1

5

1

12

9

7

8

3

1

,, 2 & 4 m.

2

0

7

5

6

9

9

7 .

,, 4 & 6 m.

1

2

1

2

5

4

5

6

3

,, 6 &10 m.

1

2

3

7

7

,, 10 &15 m.

1

3

3

9

Over 1pm.

...

2

92

I do not think that in real winter weather we can consider
any day as perfect when the rate is above 1 mile an hour.
This amount, of movement would hardly be felt in warm
weather, but with a very low temperature is more trying.
It is hardly necessary to remind meteorologists that if the
instrument had been placed on the top of a house the
amount registered would have been very much larger than
was the case.

Some observations made for the Swiss Meteorologiea
Society have been published to show that St. Moritz is in
the winter months warmer than Davos. It seemed strange

O

that St. Moritz, which is nearly 1,000 feet higher, should
nearly always average warmer. However, as the observa-
tions made by Messrs. Townsend and Greathead between
1868 and 1871* give a lower temperature, and as mine,*)*
taken this winter on the same spot as Mr. Greathead’s show
St. Moritz decidedly colder than Davos, I tried to find out
the reason of the results to which I referred, differing from
those obtained by Messrs. Townsend, Greathead, and my-
self. Mr. Schmidt, who formerly took the observations,
very kindly gave me every assistance in trying to find out
the cause of this discrepancy, and on two occasions took the
temperature for about a week at 1 p.m., in order that I
might compare with mine. His house is lower down in the
village, and is probably slightly warmer than the Kulm
hotel ; but the mean difference from the 22nd to the 29th

* Klimatotherapie von Dr. Hermann Weber, p. 156, ans Ziemssen’s
Allgemeine Therapie, vol. ii. pt. 1.

f A comparison with the Davos official observations taken in the Swiss
way, as published in the local paper, shows that at one p.m. in January
this year, Davos was about 2° Cent., and in March about 3|° Cent,
warmer than St. Moritz ; and further comparisons show that I have
obtained much the lower figures throughout the winter. The tempera-
ture here was, at 9 a.m. in November, — 3’4° Cent., and at 9 a.m. in
December, —6-06° Cent.

93

of January being 2 *5° Cent. (4*5° F.), and March 11th to
20th 2 9° Cent. (5*2° F.) warmer than mine, it would seem
that the difference principally arises from different screening
and placing of the instruments. The screen-box is so placed
in a corner that it will receive reflected heat from two walls
and probably the readings are too high on that account.

As I pointed out last year, the question of screening is
most difficult in such a climate, and therefore I was very
glad towards the end of the season to accept from Dr. Berry
the loan of one of the Swiss metal cylinder-screens, which
was 50 centim. high and 25 centim. in diameter.

These are usually placed just outside an upper window
and the figures to which I have referred were so taken. I
however placed it with a board below, as sometimes used by
the Swiss, and put this on a stand near to my own screen.
I then placed the lid of a large box about half a metre
away in a sloping position to the south of the thermometer
cylinder. This formed a shading root and roughly made
a protection similar to that recommended by Professor Wild.

The metal screen was entirely in the shade from 9.30 and
but little sun shone on it before that, so that the one o’clock
observation would be uninfluenced by the sun. The next
question is at what height should the thermometer be
placed. I take it that one of the objects of the screen
is to prevent terrestial radiation from the thermometer, and
that therefore the thermometer should be well protected
by the cylinder, but having seen the thermometer at the
lower level of the cylinder in one of the Swiss stations,
I placed one thermometer about one inch below the level of
the cylinder so that it would be always kept in shade by it
but be able to radiate out heat ; another one I placed near
the middle, so that it would receive any heat from the metal
if it was warmer than the air.

The upper thermometer which, as explained, was fully pro-

94

tected, was, taking the mean of 16 days, 1*28 Fahr. warmer
than the lower one, sometimes the difference being very
considerable. The lower thermometer with the bulb below
the level of the screen gave mean readings 04 Fahr. colder
than my screen, while the one in the middle of the metal
screen gave 0 9 Fahr. warmer than in my wooden one.

I also for comparison frequently hung my alcohol mini-
mum thermometer on the north side of my wooden screen
so that it was always in the shade, and this gave on an
average for 25 days a temperature of 1*7 Fahr. warmer than
inside the box. I consider that much of the difference must
be attributed to heat reflected from the snow. On one
occasion when it was 5*7 Fahr. higher than inside I swung
it for a few minutes, by which it was reduced until the two
closely approximated.

The screen which I used was large and specially adapted
for the evaporation experiments I proposed making. The
inner one was the box I used last year, 90 cm. wide by 75
cm. by 60 cm. high (see loc. cit. p. 162), but as I unfortu-
nately had no pavilion shade this year, I had to cover it
with another louvre screen and left a space of about 25
centimetres all round between these two louvre boxes. I
still think that this construction is not unsuitable for such
a climate as this, although with so much wood the thermo-
meters wi]l not indicate changes quite as rapidly as should
be the case, and further, 1 am very doubtful about the
Stevensen screen being suitable, but as the question of
screening is so important and as the conditions are so
different from those which obtain in England, I purpose
making some exact comparisons of different methods, as
perhaps some of the figures showing most variation may
have arisen from the screening being only of a provisional
character, and I do not think that the Swiss metal screen
ought to have a board at such a short distance below the

95

thermometers. No doubt when the ground is covered with
snow the height at which the instruments are placed above
it will cause differences.

Unless the instruments are satisfactorily placed, the ob-
servations with regard to moisture will be utterly unreliable.

The 9 p.m. temperature observations and also the one at
1 p.m. on the 10th of March, were taken from my rooms by
means of an electrical arrangement which I have devised,
and of which I have sent a fuller description to another
Society, but I may say that the thermometer is a spiral
metal thermometer which carries a finger. This thermo-
meter was kept in the screen with the other instruments.
I made the scale with a number of wires here uncovered,
but elsewhere insulated, wound over a piece of ebonite,
and the finger of the instrument is brought down upon
these wires by two electro-magnets, and in my room, by
a simple contrivance, I am able to tell which wire is
touched by the finger. I have also arranged a hair hygro-
meter to work in the same way, and intended to have
both instruments working this winter, but through delays
in getting the necessary material, and other causes, the
winter caught me up, and when the weather was cold
I was obliged to give up the idea of making changes *
Consequently I used the thermometer, although being short
of wire I only completed the scale to — 11 Cent., which
is the reason why on many nights when the temperature
fell below this I am unable to give any figures.

The instrument which has been used many hundreds of
times has turned out quite satisfactory, and I am sure that
the principle can be applied to almost every instrument
that carries a finger. The part of the hygrometer moved by
the hair, for which I paid a long price to an incompetent

* The instrument is only divided into | of a degree Centigrade, but
I purpose making another in a few weeks divided to to of a degree.

96

Zurich firm, was however so unsatisfactorily made that I
decided not to trouble about that instrument until I could
myself go to the town where it was manufactured and get
some changes made.

The temperature one inch above the snow was taken
with a minimum alcohol thermometer, and this is approxi-
mately terrestial radiation.

The solar radiation thermometer was only put up tem-
porarily, and was fastened with string to the large wire
netting with which I was obliged to protect my anemometer
from the children.

JANUARY,

MARCH, 1883.

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99

MICROSCOPICAL AND NATURAL HISTORY SECTION.

Ordinary Meeting, 12th March, 1883.

Alfred Brothers, F.R.A.S., Vice-President of the Society,
in the Chair.

Mr. Francis Nicholson, F.L.S., of Fountain Street,
Manchester, was elected a member of the Section.

Mr. Thomas Rogers exhibited a section, prepared and
mounted by Mr. H. Hensoldt, of a meteorite found at
Braunfels in Germany, in which were fluid cavities stated
to show under certain circumstances a slight movement of
the contents.

Mr. John Boyd read some notes on the male of Argulus
Foliaceus, a parasite found on the Carp, and exhibited
living specimens and diagrams illustrative of the anatomy
of this Entomostracan. He drew special attention to the
inaccuracy of Jurine’s description of the male organs of
generation, viz. : a penis on the last swimming leg on each
side and seminal vesicles on the corresponding joints of the
preceding pair of legs, and showed that the supposed penis
was a thumblike hook, and that each of the so-called seminal
vesicles contained a recess with a flap, into which the
corresponding thumb could be hooked. After commenting
on the extreme improbability of the generative organ being
doubled, as Jurine supposed, Mr. Boyd pointed out that the
organs in question were evidently claspers used to seize and
hold the female, just as the last pair of legs in Diaptomus is
used, and showed by a diagram that in that animal one leg

Proceedings— Lit. & Phil. Soc.— Yol. XXII.— No. 8— Session 1882-3.

100

of the last pair is abnor malty enlarged and furnished with
a hinged joint to enable it to grasp. Mr. Boyd then
explained that the real penis of Argulus was to be found in
the usual position, viz. : between the last pair of legs.

On the motion of Mr. C. Bailey, it was resolved that Mr.
Boyd’s communication be recommended to the parent Society
for publication in the Memoirs.

Annual Meeting, April 9th, 1883.

J. Cosmo Melvill, M.A., F.L.S., President of the Section,
in the Chair.

The Minutes of the last Meeting were read and confirmed.

Mr. Henry Hoyle Howorth, F.S.A., of Derby House,
Eccles, and 8, St. James’s Square, Manchester, Barrister-at-
Law, was elected a member of the Section.

The Honorary Secretary’s Report and the Honorary
Treasurer’s Report and Accounts of the Session were pre-
sented and read by the Honorary Treasurer, and after
slight alteration and the insertion of Dr. Alcock’s second
paper on the Development of the Frog, read at the Annual
Meeting, 1882, in the former.

On the motion of Mr. J. Boyd, seconded by Dr. Tatham,
it was resolved that they be received, adopted, and printed.

The President informed the meeting that the Council
recommended the abandonment for the present of the
proposed dredging excursion.

101

The following were elected officers for the ensuing
Session 1883-4 : —

Ipraibnxi :

J. COSMO MELVILL, M.A., F.L.S.

A. BEOTHEES, F.E.A.S.

E. D. DAEBISHIEE, F.G.S.

Prop. W. BOYD DAWKINS, F.E.S., F.G.S.

fasartt :

MAEK STIEEXJP, F.G.S.

:

EOBT. E. CUNLIFFE.

Council :

THOS. ALCOOK, M.D.

CI1AS. BAILEY, F.L.S.

WALTEE E. BAEEATT.

J. BOYD.

A. MILNE S MAESHALL, F.L.S.

THOS. EOGEES.

J. F. W. TATHAM, M.D.

W. C. WILLIAMSON, F.E.S.

Secretary’s Report of the Session 1882-3 of the Micro-
scopical and Natural History Section of the Manchester
Literary and Philosophical Society :

During the session the Section has met seven times, and
the Council four times. The average attendance has been

11.

Our numbers have decreased during the year. Last
session we had 32 Members and 13 Associates. Of these
we have lost by death our valued colleague Mr. H. A.
Hurst, and our Assistant Librarian Mr. B. B. Labrey, and
Messrs. E. W. Nix and J. Plant have resigned, whilst Mr.
F. Nicholson has been elected, leaving to-day 31 Members
and 11 Associates.

There have been 19 communications to the Section as

102

against 23 last session. Of these Prof. Williamson’s “ On
the present state of the knowledge of the relations between
Lepidodendron, Sigillaria, and Stigmaria,” Mr. R D. Darbi-
shire and Prof. A. M. Marshall’s “ On their dredging excur-
sion at Oban,” Dr. Alcock’s “ On the structure of the shell
of several species of Polymorphina,” and Mr. John Boyd’s
“On the male of Argulus Foliaceus,” are of special import-
ance, and the last two have been recommended to the
parent Society for publication in the Memoirs. The con-
cluding portion of Dr. Alcock’s paper on the Development
of the Tadpole, read at the Annual Meeting in April, 1882,
has also been recommended for publication.

The Sectional meeting announced for the 4th of Decem-
ber was postponed, and, on the invitation of the parent
Society, held jointly with their meeting on the 12th of that
month, and the parent Society were invited to take part in
our meeting on the 15th of January.

In November a temporary arrangement was sanctioned
enabling the authors of communications to our meetings to
have a brief note of their papers published promptly in cer-
tain local and scientific papers ; but the privilege has only
once been exercised.

In consequence of there being no distinction in the library
receiving book between books acquired by the Section and
those acquired by the parent Society, I am unable to report
the additions made by the Section to our library.

I would again venture to draw attention to the desira-
bility of members making communications supplying the
Secretary promptly with an epitome of each paper for entry
on the minutes.

A sub-committee was in January appointed to arrange,
and invitations have been sent to our Members and Asso-
ciates to take part in, a dredging expedition ; but there has
not been a sufficient response to justify its being carried out.

6th April , 1883 .

The Microscopical and Natural History Section of the Literary and Philosophical Society of Manchester

in Account with Mark Stirrup, Treasurer. Cr*

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Examined and found correct,
March 29th, 1883.

104

PHYSICAL AND MATHEMATICAL SECTION.

January 16th, 1883.

Joseph Baxendell, F.R.A.S., President of the Section, in

the Chair.

Dr. J. P. Joule, F.R.S., exhibited and explained an arrange-
ment for damping the small oscillations of a telescope.

The figure represents the object glass end of a telescope
armed with the leaden ring l. A circle of brass, r, girding
the tube, carries hooks which hold the caoutchouc bands
% i, i, thrown over the leaden ring. A similarly supported
leaden ring is placed at the eyepiece end. I have applied
rings weighing together 81bs. to a telescope tube weighing
131bs. with the result that when wind was blowing the
small oscillations were so far subdued that very satisfactory
definition of the object was obtained, which without the
rings would have been impossible.

105

Annual Meeting March 13th, 1883.

Joseph Baxendell, F.RA.S., President of the Section, in

the Chair.

The following gentlemen were elected officers of the
Section for the ensuing year:—

J. P. JOULE, D.C.L., LL.D., F.R.S., &c.

fia-frmknt# :

JOSEPH BAXENDELL, F.R.A.S.

ALFRED BROTHERS, F.R.A.S.

J. A. BENNION, B.A., F.R.A.S.

ftxmmx :

JAMES BOTTOMLEY, D.Sc., B.A., F.C.S.

April 10th, 1883.

Dr. J. P. Joule, F.R.S., President of the Section, in the Chair.

Mr. Baxendell communicated the results of a discussion
of the Measures of the Great Pyramid.

T. SOWLER AND Co., PRINTERS, CANNON STREET, MANCHESTER.

\