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MEMOIRS OF THE MANCHESTER
LITERARY AND
PHILOSOPHICAL SOCIETY.

MEMOIRS
MANCHESTER

LITERARY AND PHILOSOPHICAL soorey, /

—_—_—_—_

THIRD SERIES.

—

a+

LONDON: H. BAILLIERE, 20 Krve Wittram Street,
W.C.; anp 290 Broapway, New York.

PARIS: J. BAILLIERE, Rupr Haurereviire.

1882.

«
ALERE ? FLAMMAM.

>——__

PRINTED BY TAYLOR AND FRANCIS,
RED LION COURT, FLEET STREET.

CONTENTS.

ARTICLE PAGE
I.—On the Internal Cohesion of Liquids and the Suspension
of a Column of Mercury to a height more than double
that of the Barometer. By Professor OsBornE Reyno.ps,

GED Dseecoee ne censnasenen se alonevere secs tasenetadidetiecens descecesenc: I

II.—On the Oombinations of Aurin with Mineral Acids, By
R. S. Daz, B.A., and O. Scuortemmemr, F.RB.S. ............ 19

III.—On the Estimation of Small Excesses of Weight by the
Balance from the Time of Vibration and the angular
Deflection of the Beam. By J. H. Poyntine, B.A., B.Sc. 23

IV.—On Siliceous Fossilization—Part II. By J. B. Hannay,
F.R.S.E., F.C.S., Assistant Lecturer on Chemistry in the
Dryens Colores. taweceneMeaens cesesskbagsnpvcvahwsaversevatce en 31

V.—On the Mean Temperatures of the Winters of the last

Twenty-nine Years, By the Rev. THomas Mackeretn,
PODER in Cis mrks kat ha wants sdpaaelainlaasuvavsdanwdiecsacaseko> aie 34.

ViI.—Colorimetrical Experiments.—Part II. By James Bor-
TOMIEMy eibyeeay EN NG-, SUIS. ect. oceans o0a hs shina da oneguase-s 38

VII.—List of Leguminose’ observed growing near the Egyptian
Seashore, West of Rosetta, 1875 to 1877. By H. A.
Rueer and? A. URTOURNBU Re. ys6 sons tcis> sas sctce sxesdetecias Vas 53

VIII.—On Colorimetry.—Part III. By James Borromtey, B.A.,
TD Spee A OU Sa ma reer ney poets Sa ee He mi Sere rae Ss gi a 66

IX.—On the Origin of the Word “Chemistry.” By Carr
SOHGRURMIMBR RS ij se0is05svicus catensen concencec ainsanteh sys 75

al CONTENTS.

ARTICLE i PAGE
X.—Note on the Identity of the Spectra obtained from the
different Allotropic Forms of Carbon. By Axruur
Scuustrr, Ph.D., F.R.S., and H. E. Roscon, LL.D.,

PRES Ee fe cei cicctelteaeisiansinnsneecteaside vee eiedeiet on catverer feeee trae 80

XI.—On the Anal Respiration of the Copepoda. By Marcus M.
Harrog, MAA. BSc: BaGiS.).-cssdeaGesckeesacitocweeseeeeceeee $3

XTI.—The Radiograph. By D. Winstantey, F.R.A.S. ............ 86

XITI.—On an Extension of the ordinary Logic, connecting it with
the Logic of Relatives. By Joszen Jonn Murrny, F.G.S.
Communicated by the Rev. Robert Haruny, F.R.S....... go

XIV.—The Word “ Chemia” or ‘‘ Chemistry.” By R. Ancus Surruy,
PhD se BRS 5 Gee 28. oe arctans cc dav ade oeanase eae ae oe

XV.—Notes on a Bore through Triassic and Permian Strata,
lately made at Openshaw. By E. W. Binney, V-P.,
HRS Ci oneeeee see a Vvuag adiiela Sue wee awola Melaka RG ROC eee EEE 126

XVIL—On an Adaptation of the Lagrangian Form of the
Equations of Fluid-Motion.—Part I. By R. F. Gwy-
THUR yp DAL bs Wi daeheecnsa erence ee oeeeeee _ aa’ ceu sig ee Cee 130

XVIL.—The Literary History of Parnell’s ‘ Hermit. By Winutam
By A. Axon, MIR: Sil, Ger syeae ition s eincencea ne tech ee eeeeeeee 144

XVIII. —On the Long-period Inequality in Rainfall, By Baxrour
Stewart, LL.D., F.R.S., Professor of Natural Philosophy
at the Owens College, Manchester..................seeseeeneees 161

XIX.—On a Form of representing the Velocity at any Point of an
Incompressible Fluid under Conservative Forces. By R,

FB. Gwytumr; MOA, csc ssscdsascatccsesus taameskeccorsonaeeeneetees 169
XX.—Notes on some Quaternion Transformations. By R. F.

Gwenn WMESAU ater canaaise tneeets oetemcacacteats "rsa scams oe eee 174.

XXI.—Colorimetry.—Part IV. By James Borromuzy, D.Sc. ...... 177

XXITI.—Colorimetry—Part V. On the Absorption of Light by
Turbid Solutions. By James Borromuny, D.Sc. ......... 187

XXITIT.—On the Conditions of the Motion of a Portion of - Fluid
in the Manner of a Rigid Body. By R. F. Gwyrunr,
MA. cojcevcsinniee s tas a acleneon valegnne torte cn iets Tate idee ee eRe eames 199

CONTENTS. Vil

ARTICLE PAGE
XXTV.—On the Addition and Multiplication of Logical Relatives,
By Josrrn Joun Murpny, F.G.8. Commumicated by the
REV MOBERT TEARDE Ys) He kusn) iss eon broaden cece cveceasiuocecen 201

XXV.—On the Growth and Use of a Symbolical Language. By
Hvueu M‘Cort, Esq., B.A. Communicated by the Rev.
Rosert Harzey, E-.R.S,.......... Secdiscog seen eenee SSicononvece 225

XXVI.—On a Chemical Investigation of Japanese Laquor, or Urushi.
By Mr. Sapamvu Isuimatsvu, late of Tokio University.
Communicated by Professor Roscoz, Pn.D., F.BS. ...... 249

ERRATA.

Vor. VI.

262, 3, for 3°2 read 2°2.
264, 2, for1§ read 50.
Vou. VII.

41, 20, for 5955 read 5935.

—, 31, for 6000, under O, read 6014.

—, 32, before theoretical quantity insert nearly.

43, 23, for 6682 read 6651.

46, 20, for 17'5 read 9.

—, 22, for 52 read 5't.

—, 26, for latter read former, and for former read latter.

—, 27, for 1600(17-+x)=2400 X 21'2 read 1600(21'2+2)=2400 X 17.
189, 5, for Sax read Zak"

—, 18, for Qe = Q'y read Qt ~ Qi’

NOTE.

T’ _ Authors of the several Papers contained in this
Volume are themselves accountable for all the statements
and reasonings which they have offered. In these par-
ticulars the Society must not be considered as in any way

responsible.

MEMOTRS

OF THE

MANCHESTER

LITERARY AND PHILOSOPHICAL SOCIETY.

I. On the Internal Cohesion of Liquids and the Suspension
of a Column of Mercury to a height more than double
that of the Barometer. By Prof. OsBorNE REYNoLDs,
E.RS.

Read April 16th, 1878.

Introduction.

Tur ease with which, under ordinary circumstances, the
different portions of liquid may be separated, is a fact of
such general observation that the inability of liquids like
water to offer any considerable resistance to rupture
appears to have been tacitly accepted as an axiom. Inno
work on Hydrostatics does it appear that the possibility
of water existing in a state of tension is so much as con-
sidered; and suction is always described as being solely
attributable to the pressure of the atmosphere.
SER. III. VOL. VII. fyy B

F

2 PROF. OSBORNE REYNOLDS ON THE

The limit, of 32 feet or thereabouts, to the height to
which water can be raised by suction in the common pump,
and the sinking of the mercury in the barometer-tube
(leaving the Torricellian vacuum above) until the column is
at most only 31 inches (sufficient to balance the highest
pressure of the atmosphere) , are phenomena so well known
as to be almost household words with us. It is not, there-
fore, without some fear of encountering simple incredulity
that I venture to state

The Object of this Communication.

In the first place my purpose is to show that certain
facts, already fully established, afford grounds for believing
that almost all liquids, and particularly mercury and water,
are capable of offering resistance to rupture commensurate
with the resistance offered by solid materials. In the
second place, I have to describe certain experimental
results which, as far as they go, completely verify these
conclusions and subvert the general ideas previously men-
tioned as to the limits to the height to which mercury can
be suspended in a tube, or water raised by suction. And,
in conclusion, I shall endeavour to explain the nature of
the circumstances which have resulted in the practicak
limits to these phenomena.

The Separation of Liquids is not caused by Rupture.

Although the smallness of the force generally requisite
to separate a mass of liquid into parts leads to the suppo-
sition that the parts of the liquid have but little coherence,
it may be seen on close examination that this supposition
is not altogether legitimate; for such separation of a
liquid as we ordinarily observe takes place at the surface
of the liquid, is caused by an indentation or running-in o
the surface, and not by an internal rupture or simultaneous

INTERNAL COHESION OF LIQUIDS. as

separation over any considerable area. Thus when we see
a stream of liquid break up to drops, the drops separate
gradually by the contraction of the necks joining them, as
shown in fig. 1, and not suddenly as in fig. 2. And the
ease with which portions of a liquid may be separated by
the forcing or drawing in of the surface affords no ground

Fig. 1. Fig. 2.

| |

for assuming that the liquid is without coherence, any
more than does the ease with which we may cut a piece of
string, cloth, or metal with sharp shears, or even tear some
of these bodies by beginning at an edge, prove that they
are without strength to resist great force when these are
applied uniformly so as to call forth the resistance of all
the parts of the body simultaneously. It is true that under
certain circumstances we observe the internal rupture
of liquid—whenever bubbles are formed, as when water
is boiled; but under these circumstances we have no
means of estimating the forces which cause the internal
rupture: they are molecular in their action ; and, for all
we know, they may be very considerable. Having thus
pointed out that the ease of separation of the parts of a
mass of liquid does not even imply a want of cohesion on
the part of the liquid, I shall now point out that we have
in common phenomena
B 2

4, PROF. OSBORNE REYNOLDS ON THE

Evidence of Considerable Cohesion.

These are, for the most part, what are considered minor
phenomena ; they are confined to the surface of the Bie
and are included under what is called “ capillarity,”

‘ surface-tension.” :

The phenomena of capillarity or surface-tension have
recently attracted a great deal of attention ; and many im-
portant facts concerning them have been clearly elucidated,
some of which bear directly on my present subject.

Of the phenomena I may instance the suspension of
drops of water, the rising of water up small tubes, the
tendency of bubbles to contract, and the spherical form
assumed by small fragments of mercury.

These phenomena and others are found to be explained
by the fact that the surface of these liquids is always under
a slight but constant tension, as if enclosed in a thin
elastic membrane.

No satisfactory explanation as to the cause of this sur-
face-tension has, I believe, been as yet found ; but the fact
itself is proved beyond all question. It is a molecular
phenomenon ; and in order to offer any explanation as to
its cause, it would be necessary to adopt some hypothesis
respecting the molecular constitution of the liquid. Such
an explanation making the surface-tension to arise from
the cohesion of the molecules of the liquid is, I believe,
possible; but this is beside my present purpose, which will
be completely served by showing that

The Surface-tension proves the existence of Cohesion.

To prove this requires no molecular hypothesis; but,
before proceeding, it may be well to define clearly the
term cohesion.

Cohesion in a liquid is here to be understood as a

INTERNAL COHESION OF LIQUIDS. 5

property which enables the fluid to resist any tendency
to cause internal separation of its parts—any tendency
to draw it asunder ; or, more definitely, it is the property
which enables a liquid to resist a tension or negative
pressure.

Let us suppose a mass of liquid without internal cohesion.
Then any external action tending to enlarge the capacity
within the bounding surface of the liquid would at once
cause the interior of the liquid to open, and a hollow would
be formed within the liquid without any resistance on the
part of the liquid. Such a condition is inconsistent with
surface-tension; for the tension of the surface of the
internal hollow would tend to contract the hollow; and
since the interior of the hollow is supposed to be empty,
there could be no resistance to the tendency of the surface
to contract, such as that offered by the pressure of the gas
within an ordinary bubble. Hence any force that might,
under the circumstances, balance the surface-tension and
keep open the hollow must be supplied by the suction or
cohesion of the liquid outside.—Q. E. D.

Again, the intensity of the cohesion is determined by the
intensity of the surface-tension and the smallness of the least
possible opening over the surface of which tension exists.

So far as has yet been determined by experiment, it
has been found that the surface-tension is independent of
the curvature of the surface—is constant for the same liquid.
Assuming that ‘this is the case, it follows that the intensity
of the force necessary to keep a spherical bubble or opening
from contracting (whether this force arises from the pres-
sure of the gas within the bubble or the cohesive traction
of the liquid without the opening) is equal to twice the
intensity of the surface-tension divided by the radius of
the sphere. Hence the cohesive tension must be equal to
twice the surface-tension of the liquid divided by the diame-

6 PROF. OSBORNE REYNOLDS ON THE

ter of the smallest opening for which the surface-tension
exists.—Q. E. D.

It immediately follows from the foregoing proposition,
that no matter how small the surface-tension may be, if
it is finite even when the opening is infinitely small,
then the cohesion of the liquid must be infinitely great.
For, if the liquid were continuous in its origin, the opening
must always be infinitely small; and hence to cause such
an opening would require infinite tension.

That the cohesion is infinitely great is not probable, to
say the least. Hence it is improbable that the surface-
tension remains finite when the opening becomes infinitely
small. As has already been stated, it has been found that
the surface-tension is constant, or nearly so, under ordi-
nary circumstances ; but it has never been measured for
bubbles of very small diameter, and there appears to be
every probability that, when the size of the bubble comes
to be of the same order of small quantity as the dimensions
of a molecule, the surface-tension must diminish rapidly
with the size of the bubble. .

If this is the case, then we have a limit to the cohesion,
although it is probably very great for most liquids, some-
thing like the cohesion of solid matter of the same kind.
That is to say, it is probable that it would require nearly
as great intensity of stress to rupture fluid as it would to
rupture solid mercury, or as great tension to rupture
water as to rupture ice.

The Effect of Vapour.

Nothing has yet been said about the effect of the
pressure of vapour within the bubbles in balancing the
surface-tension. It may, however, be shown that this can
be of no moment. Even supposing that the tension of the
vapour within the opening of the liquid were equal to the

INTERNAL COHESION OF LIQUIDS. 7

tension due to the temperature under ordinary circum-
stances, this would be inappreciable. So that, unless the
tension of vapour within small openings were much greater
than that in larger openings for the same temperature, its
effect might be neglected ; and so far from this being the
case, Sir William Thomson has shown that the pressure of
the vapour within a bubble at any particular temperature
diminishes with the size of the opening. Hence it is clear
that this vapour can have no effect on the result—a con-
clusion verified by the now well-known fact that water
may be raised to a temperature high above 212° without
passing into steam.

Experimental Verification necessary.

This line of reasoning has been apparent to me now for
several years. I find notes on some of the principal points
which I made in 1873 ; and for several years I have pointed
out the conclusions arrived at as regards the probable
cohesion of water to the students in the engineering class
at Owens College. I have, however, hitherto refrained
from publishing my views, because I had no definite
experimental results to appeal to in confirmation of them.
Experimental indications of such a cohesive force were not
wanting, but they were not definite. And although me-
thods of making definite experiments have often occupied
my thoughts, certain difficulties, which turn out to have
been somewhat imaginary, kept me from trying the expe-
rimeuts.

It had always appeared to me that, in order to subject
the interior of a liquid mass to tension, it would be neces-
sary to, as it were, hold the surface of the liquid at all
points to prevent its contracting. To accomplish this, it
was necessary to have the liquid in a vessel, to the surface
of which the liquid would adhere as water adheres to glass.

8 PROF. OSBORNE REYNOLDS ON THE

The experiment which I had conceived would have been
equivalent to a vertical glass tube more than 32 feet long,
closed at the upper end and open at the lower, so that when
the tube was full of water the column would be higher than
the pressure of the atmosphere would maintain, and hence
could only be maintained by the cohesion of the water.
The difficulty of such an experiment, however, appeared to
be great. It was clear that if mercury could be substituted
for water this difficulty would be much reduced ; but then
mercury does not readily adhere to glass, and the ordinary
method of making barometers seemed to disprove the pos-
sibility of making it adhere.

It was only on the 2nd of this month that an accidental
phenomenon at once afforded me the experimental proof
for which I had been looking.

First Experiments.

The phenomenon was observed in a mercurial vacuum-
gauge (a siphon gauge which admitted a column of mer-
cury 31 inches long). Before the mercury was introduced
the tube had been wetted with sulphuric acid, a few drops
of which covered the mercury on both ends of the column.

The gauge had been in coustant use as a vacuum-gauge
for three weeks ; and, probably owing to the action of the
acid on the mercury, a little gas had been generated between
the mercury and the closed end of the tube, sufficient to
cause the column to sink to 27% when the barometer stood
at 29. To get rid of this air, the tube was removed from its
situation and placed in such a position that the bubble of
air passed along the tube and escaped, the open end of the
tube being entirely,free. Before the tube was tilted in this
way, the unbalanced column was 273 inches long. When
tilted, the mercury ran back right up to the end of the tube
as the bubble of air passed out. On erecting the tube

INTERNAL COHESION OF LIQUIDS. 9

again, the mercury remained up to the end of the tube,
except about one eighth of an inch, which was filled with
sulphuric acid. The unbalanced column of mercury was
therefore 31 inches long. At first the full significance of
this phenomenon was not recognized ; but in order to as-
certain that the tube was cleared of air, it was moved gently
up and down to see if the mercury clicked, as it usually
does when the tube is free from air, but the mercury did
not move in the tube. The rapidity of the oscillation was
thereupon increased until it became a violent shake, and,
as the mercury still remained firm, it was clear that some
very powerful force was holding it in its place. The tube
being in a vertical position, was then left in order that the
barometer might be consulted. This was standing at 29
inches. After a few seconds, when the gauge was again
examined, the column no longer reached the end of the
tube, but stood at 29 inches. As it was singular that the
mercury should have quietly settled down after having re-
sisted such violent shaking, the tube was again inclined
until the mercury and acid came, apparently, up to the end
of the tube; but this time on the erection of the tube the
mercury at once settled down. That is to say, it settled
down gradually as the tube was erected. At first what
appeared to be a very small bubble opened in the sulphuric
acid; and this enlarged as the top of the tube was raised.
On again inclining the tube until it was horizontal, and
examining it closely, a minute bubble could be seen in the
acid, and it was this bubble which expanded as the tube was
erected, and so allowed the mercury to descend. To get
rid of this bubble, the tube was turned down so as to allow
the bubble to pass along the tube ; but, owing to its small
size, it did not pass many inches along the tube before
it became fixed between the mercury and the glass. When
the bubble came to a standstill at about six inches from the

10 PROF. OSBORNE REYNOLDS ON THE

end of the tube, the gauge was again erected ; the bubble
immediately began to move back, but so slowly that it was
some seconds before it entered the region of no pressure.
During this interval the mercury remained up to the end
of the tube; but the bubble, as soon it neared the top of
the tube, expanded and rapidly rose to the top of the tube,
leaving the column at 29 inches. This operation having
been repeated several times, it became quite evident that it
was this small bubble which, either by rising up the tube
or being generated at the top, had caused the mercury in
the first instance to sink. As the bubble would not pass
out by itself, the tube was tilted so as to allow a larger
bubble of air to enter; and having been left standing for
about twelve hours to allow the small bubble to unite with
the larger one, it was again tilted so as to allow the air to
pass out. When this was done the mercury again remained.
firmly against the end of the tube and did not descend
when violently shaken. The open end of the tube was then
connected with an air-pump and exhausted until the pres-
sure within it fell to about four inches of mercury. This
operation occupied some seconds; but all this time the
mercury did not move from the end of the tube; but
eventually the column opened near the bottom of the tube
and a large bubble appeared, which rose up the tube, the
the mercury falling past the opening. That the breaking
of the column so near the bottom of the tube was owing
to the presence at that point of a small bubble of air was
almost proved by the fact that, on readmitting the air to
the open end of the tube and inclining the tube to see
if it was free from air, there was found a minute bubble
which played exactly the same part as the small bubble
which had been previously examined.

At the instant previous to the rupture of the column at
the bottom of the tube, there must at the top of the tube

INTERNAL COHESION OF LIQUIDS. 11

have been an unbalanced tension or negative pressure equal
to 27 inches of mercury ; and this tension did not break the
continuity of the column. Hence I had a proof that the
cohesion within the mercury and the sulphuric acid as well
as the adhesion of the sulphuric acid to the mercury and
the glass is sufficient to resist this very considerable tension.

Further Experiments.

In the hope of improving the experiments, another gauge
was constructed, the tube being 3, of an inch in internal
diameter and 35 incheshigh. Into this tube mercury and
sulphuric acid were introduced, as in the first tube. But
on trying to get rid of the small bubbles of air, it was
found impossible to do so, as bubbles were continually
generated. Hence it appeared that the three weeks during
which the mercury and sulphuric acid in the first tube had
remained in contact had had an important influence on the
result. Failing in this attempt, it occurred to me to try if
water would answer the purpose as well as sulphuric acid.
Having in my possession an old vacuum-gauge with a
column three inches long, which had originally been wetted
with sulphuric acid, but into which a considerable quantity
of water had accidentally been introduced, I carefully
allowed all the air to escape, and then applied a mercurial
air-pump to the open end of the gauge, and exhausted as
far asthe pump would draw. The mercury did not descend.
As I could apply no further tension, I shook the gauge up
and down; but still the mercury remained unmoved. I
then tapped the gauge smartly on the side; the mercury
then fell three inches, until it was level. Having succeeded
so far, I extracted the mercury and sulphuric acid from the
35-inch gauge and introduced some water without washing
the tube, and, having boiled the water in the tube, again
introduced the mercury.

12 PROF. OSBORNE REYNOLDS ON THE

Having extracted all the air, I found no difficulty in
making the gauge to stand up to the 35 inches without any
immediate tendency to fall. On applying the air-pump to
the open end the mercury several times remained up until
the exhaustion had proceeded so far that when it fell it fell
from 22 to 28 inches, and when the rupture took place it
was accompanied by a loud click. I could not on that
occasion get the mercury to withstand complete exhaustion ;
but after leaving the gauge with the mercury suspended.
for 24 hours at 35 inches, I was able to exhaust the open
end of the tube as far as the pump would draw, without
bringing the mercury down; so that I had a column of
35 inches of mercury suspended by the cohesion of the
liquids. —

There was no reason to suppose that this was the limit
or anywhere near the limit. It was clearly possible to
suspend a longer column ; but as the length of the column
increased so would the difficulty of getting rid of the dis-
turbing causes, and I determined to rest satisfied with the
35 inches ; but in order to see if this could be maintained,
I obtained a gauge 60 inches long, which would leave
30 inches above the pressure of the atmosphere.

The difficulty of getting rid of the air in this tube suffi-
ciently to allow of the mercury standing 60 inches was
very considerable. Before filling the tube it was rinsed
out with concentrated sulphuric acid, then twice washed
with distilled water, and then water put in and boiled in
the tube. Then sufficient mercury was introduced to fill
the long leg and the bend, so that the column, when com-
plete, was 59 inches long, the barometer being at 29°5.

After the tube had been tilted several times so as to
allow the air to pass out, the mercury would be suspended
as the tube was slowly reerected, until it had attamed an
elevation of 40, 50, or sometimes the full height of 60 inches

INTERNAL COHESION OF LIQUIDS. 13

(as shown in fig. 3), but only for a few seconds. When
the mercury fell, if the column broke anywhere near the
top of the tube, it gave way with a loud click. But this
was by no means always the case. The mercury would
sometimes separate nearly 30 inches down the tube; and

Fig. 3. Fig. 4.

1

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od

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then the appearance of the upper portion falling was very
singular: the upper portion of the column remained
intact ; and a stream of mercury fell from its under surface,
as shown in fig. 4, breaking up into globules as it came
into contact with the lower portion, with a loud rattling
noise. I was unable to get the column in the tube thus filled

14. PROF. OSBORNE REYNOLDS ON THE

to maintain itself for more than twenty or thirty seconds,
which failure was clearly due to the presence of air; for
after the mercury had fallen a small quantity of air was
always found to collect above it. Sometimes, when on
inclining the tube the liquid again reached the top, the
bubble which remained was so small as to be scarcely
visible, although subject to no pressure other than the
surface-tension ; but its presence always became apparent
instantly on erecting the tube. In no case was it possible,
after the mercury had once fallen, to get it to remain up to
any considerable height above that due to the pressure of
the atmosphere until the bubble of air collected had been
allowed to pass out.

The tube was then again emptied, washed, and filled
with glycerine. This behaved much in the same manner
as the water; but the difficulty of getting rid of the air
was greater.

Similar results were obtained when very dilute ammonia-
liquid was tried.

The tube was then again carefully washed, first with
water, and then several times with concentrated sulphuric
acid. The mercury was subjected to nitric acid, washed
and dried, and then filtered into a bottle of sulphuric acid,
from which it was poured into the tube, some acid passing
in with the mercury. When first introduced into the
tube a few small bubbles could be seen rising between the
mercury and the tube and passing up through the sulphu-
ric acid into the vacuum above ; but after it had stood for
five or six hours no bubbles were perceived, the surface of
the mercury against the tube being perfectly clear ; never-
theless, on erecting the tube, the mercury would not rise
above the height of the barometer, and air was always found
to have collected above the mercury. Water was then
introduced so as to dilute the acid ; then the mercury was

INTERNAL COHESION OF LIQUIDS. 15

suspended as before, for a few seconds only. The tube was
then placed in a position with the closed end lowest, so that
the air and water might ascend towards the end and pass
out ; and after being in this position for some hours, when
it was again erected the column remained intact.

It was thereupon again lowered and left to drain for
forty-eight hours. On being again erected, the mercury
was still suspended. The tube has since been carried ina
more or less horizontal position some three miles to the
Society’s rooms in order that I might exhibit this pheno-
menon. If it has not been affected by the shaking, you
will see a suspended column of mercury some fifty-nine
inches high, or twenty-nine inches above the height due to
the atmosphere*,

Conclusion.

The difficulty of obtaining a column of mercury thirty
inches above the pressure of the atmosphere does not, I
think, prove that the limit of the cohesive power of the
liquid has been arrived at, or even the limit of the adhesive
power of the water for glass and mercury, but simply
shows that, although imperceptible, there are still bubbles
of air in the liquid between the mercury and the glass
which will not readily pass out.

It seems to me to be probable that, with sufficient care,
or by using apparatus more suitable to the purpose, much
greater heights might be attained. But however this may
be, we have proof that mercury and water will, by their
cohesion, resist a tension of at least one atmosphere, or
that the common pump would, if the water were free from

* At the Meeting not only did the mercury remain suspended when the
tube was erect, but on the pressure of the atmosphere being removed with
an air-pump it still remained suspended, although the tension at the top of
the tube was nearly equal to two atmospheres,

\

16 PROF. OSBORNE REYNOLDS ON THE

air, raise water by suction to a height of more than sixty
feet. At first sight it cannot but appear remarkable that
such a fact should for so long have escaped notice; but a
little consideration removes the difficulty.

Water is almost always more or less saturated with air,
which separates into bubbles as soon as the pressure is
relieved ; and in the common pump a single minute bubble
would be sufficient to cause the column to break and
prevent it being raised to a greater height than that due
to the pressure of the atmosphere.

In the case of barometers it is the custom to fill the tubes
full and boil the mercury, so as to get rid of the air; but
the column falls to the usual height not by the rupture of
the mercury, but by the separation of the mercury from
the glass, for which it has but little adhesion. Whether
the ordinary method of boiling the mercury really disen-
gages all the air is, | think, an open question. In vacuum-
gauges of small diameter it is not uncommonly found that
the mercury sticks to the glass until the pressure has fallen
considerably below what is represented by the height of
the mercury, so that on the gauge being shaken the mer-
cury falls with a sudden drop. Although it does not seem
to have attracted any special notice, this phenomenon is
clearly due to the same cause as that which I have found
capable of maintaining thirty inches of mercury suspended
in a comparatively large tube.

Tt would seem then that, although the facts which I now
bring before the Society have little bearing on the prac-
tical limits to the height of the column of mercury in the
barometer or the column of water in the common pump,
they show that these limits are owing to the presence of
air or some other minor disturbing cause, and are not, as
seems to have been hitherto supposed, owing to the want
of cohesion of the liquid. And it seems to me that the

INTERNAL COHESION OF LIQUIDS. Liv

cohesion now found to exist occupies an important as well
interesting place in the properties of liquids.

Apprnnix (26th April).—Previous Notices of the
Cohesion of Liquids.

Besides the hanging of mercury in small gauges, another
phenomenon, which has long been known, shows a small
degree of cohesion in water; that is, that water will rise
up small tubes by capillary attraction as well in the receiver
of an air-pump as in air at the ordinary pressure. This
fact was shown before the Royal Society by Robert Hooke.

Prof. Maxwell, in his ‘ Treatise on the Theory of Heat,’
p- 259, after commenting on the fact that water has been
raised to a temperature of 356° F., without boiling, re-
marks :—‘ Hence the cohesion of water must be able to
support 132 lbs. weight on the square inch,” from which
it would appear that he recognizes cohesion as a property
of water, and considers that the possibility of raising the
temperature above the boiling-point is evidence of such
cohesion ; but I am not aware that he has anywhere given
his reasons for such a conclusion.

I am indebted to Dr. Bottomley for reference to a paper
in the Ann. de Chim. et de Phys. (3) xvi. 167, by M. F.
Donny, in which M. Donny gives an account of experi-
ments in which he found that columns of sulphuric acid
could be suspended in vacuo to a height of 1°3 métre
(about 50 inches), showing a tension of about 7 inches of
mercury, care having been taken first to remove all the air
from the acid. M. Donny further describes experiments
made with water in exhausted tubes, in which he showed
the effect of cohesion by shaking the tube. M. Donny
does not, however, appear to have thought of the plan
which I adopted of making mercury adhere to the tubes by
wetting them with sulphuric acid or water. Not being

SER. III. VOL. VII. c

18 ON THE INTERNAL COHESION OF LIQUIDS.

able to use mercury, the tensions which he obtained were
comparatively small; and although he seems to have con-
sidered that greater tensions might be obtained, he mentions
one or two atmospheres as probably possible. It would
therefore appear that he had not conceived the possibility
of the cohesion of liquids being comparable with that of
solids.

M. Donny appears to have been influenced in adopting
this limit to his idea of cohesion by a passage from Laplace,
‘Mécanique Céleste,” Supplément au X° livre, p. 3, which
he quotes.

Laplace, who was the first to investigate systematically
the phenomena of capillary attraction, proceeded on the
hypothesis that the molecules of a liquid exercise attraction
for each other at insensible distances only; and from this
assumed attraction he deduces the surface-phenomena.
The entire passage quoted by M. Donny is too long to
introduce here; but the gist of it is comprised in the fol-
lowing extract :—

“ Son expression analitique est composée de dhe termes :
le premier, beaucoup plus grand que le second, exprime
Paction de la masse terminée par une surface plane ; et je
pense que de ce terme dependent la suspension du mercure
dans un tube du barométre a une hauteur deux ou trois fois
plus grande que celle qui est due a la pression de V atmosphere,
le pouvoir réfringent de corps diaphanes, la cohésion, et gé-
néralement les affinités chimiques.”

Laplace here speaks of the suspension of mercury to 60
or gO inches as if it were a well-known phenomenon; but
I cannot find any reference to experiments, or, indeed, any
further mention of the phenomenon in his memoir.

I did not refer to Laplace in the first instance, although
I knew well that it is to him we are indebted for the theory
of surface-tension almost in the form now accepted, because

MESSRS. DALE AND SCHORLEMMER ON AURIN. 19

I wished to avoid all reference to molecular hypothesis, and
particularly the molecular attractions assumed by Laplace,
lest it might in any way appear as if the conclusion that
continuous liquids are as capable of resisting tension as
solids (at which I arrived simply from considering the phe-
nomena of surface-tension) were based on such assumptions.
I was not aware, however, that Laplace had at all inferred
or attempted to apply his theory to prove the ability of
liquids to resist great tensions; nor do I find, on again
reading his memoir, that he anywhere, with the exception
of the almost casual reference quoted above, treats of such
a property of liquids. His purpose appears to have been
solely to explain the phenomena of capillarity. It appears
obvious, moreover, that his lne of reasonmg must have
forced upon his notice the conclusion that, according to his
hypothesis, liquids ought to possess the property of very
great cohesion; so that from the extremely slight notice
which he has accorded to this property, one can only infer
that he was not completely convinced of its existence.

II. On the Combinations of Aurin with Mineral Acids.
By R. S. Dats, B.A., and C. Scuortemmer, F.R.S. ,

Read December roth, 1878.

In our last communication* we stated that by the action
of acetyl chloride on aurin we obtained a colourless crys-

* Proc. Lit. and Phil. Soc. 1878, p. 141.
Gz

20 MESSRS. DALE AND SCHORLEMMER ON THE

talline compound, which we intended to examine more
closely. We have since found that this body is identical
with a compound which Griabe and Caro* obtained by the
direct union of aurin and acetic anhydride and having the
formula C,,H,,0, +C,H.O,.

We also mentioned that the purification of this substance
was found to be beset with several difficulties. The cause
of this was found out after some trouble; but at the same
time we were rewarded by the discovery of a series of re-
markable bodies, consisting of combinations of aurin with
mineral acids.

These salts, as we may call them, are beautiful bodies,
crystallizing exceedingly well ; and although some of them
are decomposed by water, they are very stable in dry air.
To their discovery we were led by the following ob-
servations.

On heating aurin with glacial acetic acid and acetyl
chloride, the crystals lose at once their steel-blue lustre
and assume a pale red colour. To obtain the compound
thus formed in a pure state, acetyl chloride was added to
a saturated solution of aurin in acetic acid. The liquid
assumed at once a much lighter colour; and soon pale red
needle-shaped crystals having a diamond lustre separated
out. On recrystallizing these repeatedly from alcohol, we
obtained oblong six-sided plates, which, as analysis showed
were pure aurin,

On treating the original crystals with ee they became
dull and brownish red, the solution containing acetic and
hydrochloric acids. It therefore seemed not improbable
that an additive product of aurin and acetyl chloride had
been formed, containing, however, also acetic acid, as a
superficial examination showed that the liquid contained,
to one molecule of hydrochloric acid, much more than one

* Ber. deutsch. chem. Ges, xi. p. 1122.

COMBINATIONS OF AURIN WITH MINERAL ACIDS. 21

molecule of acetic acid. We therefore tried to obtain an
analogous benzoyl compound, and to determine in it,
after decomposition with water, the relative quantities of
hydrochloric and benzoic acids.

On adding benzoyl chloride to a hot solution of aurin in
acetic acid, similar crystals as before were obtained, which,
after being dried on filter-paper in dry air, were decom-
posed by water; but only hydrochloric and acetic acids went
into solution, and on heating the product with water or
alkalies but a mere trace of benzoic acid could be detected.

These facts, coupled with the observation that the bright-
red needles formed (as we stated in our former paper)
by crystallizing aurin from hot aqueous hydrochloric acid
retain the latter obstinately, led us to the conclusion
that this acid forms a definite compound with aurin.

Such a body could be formed under the above conditions,
as our glacial acetic acid contained a little water. More-
over Mr. Charles Lowe had informed us that the splendid
specimen of aurin which he exhibited at Paris was obtained
in the following way. The crude but crystalline aurin
which is obtained by heating pure phenol with sulphuric
and oxalic acids was dissolved in alcohol, and some strong
hydrochloric acid added, by which a crystalline precipitate
was formed, crystallizing from hot acetic acid in beautiful
red, glistening, flat needles. He was kind enough to give
us a sample; and on examining it we found that water
acted upon it in the same way as on our crystals.

In order to prepare a pure compound for analysis, a hot
solution of aurin in acetic acid was saturated with hydro-
chloric acid gas. The colour of the liquid changed into a
light yellowish red ; and soon the compound separated out
in glistening needles, which, even when perfectly dry, smell
strongly of acetic acid. When exposed to the air, they
soon assume a steel-blue lustre and gradually crumble into

22 _ MESSRS. DALE AND SCHORLEMMER ON THE

a reddish brown crystalline powder. The same properties
are shown by the crystals obtained from acetyl chloride
and those obtained from Mr. Lowe. When heated to 110°
in a current of dry air, they gradually lose all the acetic
acid (which plays the part of water of crystallization) and
assume a dull red colour.

On passing hydrochloric acid gas into an alcoholic so-
lution of aurin, similar but smaller needles are formed,
containing alcohol, which is given off at 100°; the dullred
residue can, like the preceding one, be heated to 190° ina
current of dry air without losing hydrochloric acid, which
only begins to escape at 200°

Analysis of these adda showed that the dried sub-
stance consists of C,,H,,O,,HCl, while the crystals obtained
from an acetic-acid solution have the composition C,,H,,0,,
HCl+ 2C,H,0,, and those from alcohol 2C,,H,,O,,HC1+
3C,H,0.

When sulphuric acid is added to a hot alcoholic solution
of aurin, small red needles are formed on cooling, which
consist of (C,,H,,0,),SO,H,+alcohol. Under the same
conditions an acetic-acid solution yields fine prismatic
crystals, or flat very glistening needles, which are an acid
sulphate, its formula being C,,H,,0,,80,H,+ acetic acid.

We have also prepared a nitrate (which is readily formed
and crystallizes well), but have not analyzed it yet.

In our first communication to the Chemical Society we
described a compound of aurin and sulphur dioxide, which
is easily obtained in bright-red crystals by passing sulphur
dioxide into a saturated alcoholic solution of aur. Our
former observation, that this body contains water but no
alcohol, we found confirmed. On heating it decomposition
easily takes place, pure aurin being left behind; but it ap-
pears to be quite stable when exposed to the air ; and even
on heating it with water, no sulphur dioxide is given off;

ON THE ESTIMATION OF SMALL EXCESSES OF WEIGHT. 23

but a drop of sulphuric acid added to the mixture is suffi-
cient to evolve the gas abundantly. Aurin sulphite has
the composition (C,,H,,0,),S50,H,+4H,0.

As we have already showed, aurin forms very charac-
teristic compounds with the acid sulphites of the alkali-
metals, which, in accordance with the newly established
formula of aurin, must now be written as follows :—

Cy, HO, sO KH;
C030, Nall;
C,H. ,.0.;50,(N EL) A,

We have also found that rosolic acid, or the next higher
homologue of aurin, forms compounds with mineral acids
which crystallize well. Being, therefore, a base like aurin,
we think its name ought to be altered; and as it has only
been obtained from rosaniline, we propose for it the name
rosaurin.

III. On the Estimation of Small Excesses of Weight by the
Balance from the Time of Vibration and the angular
Deflection of the Beam. By J. H. Poyntine, B.A.,
B.Se.

Read December roth, 1878.

Wuite working last year on an experiment to determine
the mean density of the earth by the balance, I had to
measure such an exceedingly small difference of weight
that I could not at that time estimate it by means of a rider,

24. MR. J. H. POYNTING ON THE

but was obliged to adopt the method described in this paper.
Stated generally, it consists in treating the balance as a
pendulum. Knowing the nature of the pendulum (that is
its moment of inertia) and its time of vibration, we can
calculate what force acting at the end of one arm of the
beam will produce a given angular deflexion. It is, in fact,
an application to the common balance of the method which
has always been used with the torsion-balance when it has
been necessary to calculate the forces measured in absolute
measure. I cannot find any record of a previous applica-
tion of the method ; and as it might be of use in very
delicate weighings or in verifying the small weights in a
laboratory, I have thought it worth while to give a full
account of it.

When small quantities of the second order are neglected
and the oscillations are of the first order, it will easily be
found that the equation of motion of the beam of the
balance is

(air + 2) + (aPh-+Mgh)O—ap, fake
where MI*=moment of inertia of beam about central
knife-edge,
M=mass of beam,
a=half length of beam,
P=weight of either pan and the mass in it,
h=distance of line joining terminal knife-edges
_ below the central knife-edge,
k=distance of centre of gravity of beam below
central knife-edge.
p=small excess in one pan.
§=angular deflection in circular measure pro-
duced by p, .

g =gravity.

ESTIMATION OF SMALL EXCESSES OF WEIGHT. 25

If 6=6, we have the position of equilibrium given by

aL ca i
Ty aRn a ake HOO Ra PREETI)

The semiperiodic time is

Ve 2
MIt +. 2Pa

\/ 2Ph4Mgk (3)

(—"

From equations (2) and (3) we can eliminate 2Ph + Mgh,
obtaining

__,MgI*+2Pa* 6 )
—-/s ey Bee f . . . . (4)

From this expression it appears that, if we know the
moment of inertia of the beam, its length, and the weight
at each end, we can find the excess p from the time of
vibration and deflection.

The results given in this paper were obtained with a
16-inch chemical balance by Oertling. The exact length
of the half beam (a) measured by a dividing-engine is
20°2484 centimetres.

To find the Moment of Inertia MI* of the Beam.—The
simplest way theoretically would appear to be this. Find
the times of vibration ¢,, ¢,, and the deflections 6,, 6,, due
to the same excess p with two different loads P,, P, in each

pan. Equating the values of p given for the two by
equation (4) we have

MgI*+2P,a*_ 0,¢,?
MglI*+2P,a* 6,t,”’

an equation which will give Mgl* in terms of known
quantities ; but on trial it was found that a very small

26 MR. J. H. POYNTING ON THE

proportional error in the observed time made a large error
in the value of MglI?; and the following method, that
usually adopted in magnetic observations, was employed in
preference. A stirrup was suspended by a platinum wire,
and its time of vibration (¢,) against the force of torsion
(w) of the wire was observed. The moment of inertia of
the stirrup being S, we have

The time of vibration (¢,) was then observed when a cylin-
drical brass bar of known moment of inertia (B) was in-
serted in the stirrup. We now have

a
t,*>=—(S+B).
618).

The bar was then removed and the balance-beam inserted
in its place; and the time of vibration (¢,) gives

2 ase 2
— (S+ MI’).
From these three equations, eliminating S and yw, we obtain
B(t,*—t,”)

Wor? ea
nank ese

Now Bg was calculated from the weight and dimensions
of the bar.to be 6332°83 (in centimetres and grammes).
The observed times were ¢,=3°6792', ¢,=4°495°, #,=
7°1483°%. From these values we find

Mgl’=35651°6%

* To this a small correction should be added if the adjusting-bob is not in
its lowest position, This amounts to 7°6 for each turn of the screw, and may
therefore in general be neglected.

ESTIMATION OF SMALL EXCESSES OF WEIGHT. 27

To measure §.—The angle of deflection was measured by
the number of divisions of the scale which the pointer
moved over, As the length of the pointer is 32°1006 cen-
timetres, while 20 divisions of the scale measure 2°5658
centimetres, a tenth of a division, in terms of which the
deflexion was measured, corresponds to an angle of
0°0003996°. The oscillations were observed from a distance
of six or eight feet by a telescope. The resting-point (i. e.
the point where the balance would be in equilibrium) was
found in the usual way by observing three successive
extremities of two swings and taking the mean of the
second and the mean of the first and third. Five deter-
minations of the resting-point were usually made with the
excess to be measured alternately added and removed.
From these five, three values of the deflection (x) due to
the excess were calculated in a manner which will be seen
from the example below.

Lhe Time of Vibration —This was found from several
determinations of the time of ten oscillations. The method
will be seen from the example. No correction was needed
for the resistance of the air as long as the vibrations did
not exceed two divisions of the scale. When, however,
they were much more than that, the time of vibration was
found to increase with the are. As the time of vibration
frequently changes slightly, probably through variations
of temperature, it was usually observed before and after
the determination of the defiection (7) and the mean of the
two taken as the true time.

The following example of the determination of the value
of a centigramme rider by placing it halfway along the
beam will sufficiently explain the details of the method.

28 MR. J. H. POYNTING ON THE

Time of Vibration at Commencement.

«. & | Observed time of | , & | Observed time of
o-2 |passage of pointer}! ©-3 | passage of pointer | Time of 10
= = | through resting- 2 & | through resting- | vibrations.
7 point, Is point.
Pointer apparently moving from left to right.
h m. 38. lek hy AEE 8.
° LY) ts) 36 10 Tis L748 127
2 TT 1G) Vr tz Li, 2s ows 127
4 It 16 26°5 14 It 18 33°5 127
6 Il 16 52 16 tr 13" 59 127
Mean value of 10 vibrations ...............0ecee0e 127
Pointer apparently moving from right to left.
I II 35 49 II Il 17 56 127°
3 Ir 16 14 13 Ir 18 21 127
5 II 16 39°5 15 ir 18 46 12675
7 TG PPG 17 Il 9 I1°5 126°5
Mean value of 10 vibrations..............0.s2s2.06- 126°75

Mean of means= 126°875 ; ¢,=12°6875°.

Determination of Deflexion nu.

Excess Extremities | Resting- Mean of preceding | Deflection
weight of oseillation.| point. EBs) SUPERS gol he
‘ resting-points. excess.
109
Added ...... 96 102°5
109
93
Removed 40 66°25 102°25 36
92
152
Added ...... 53 102 66°75 Binal
150
80
Removed ... 55 67°25 102°5 35°25
79
147
Added ...... 60 103
145

Mean value of n= 35°83.

ESTIMATION OF SMALL EXCESSES OF WEIGHT. 29

Time of Vibration at end.

«. & | Observed time of! . ¢ | Observed time of
©-2 | passageof pointer! ©-= | passage of pointer Time of ro
is = | through resting- | .° & | through resting- | vibrations.
= point. = point,
Pointer apparently moving from left to right.
Bethan a? beens s.
° II 26 19 10 Tl Zoe 27 128
2 ry 26 4ass 12 Thon 653 128 5
4 EI 27. tO 14 11 29 18 128
6 ED 27a es 16 Il 29 44 128°5
Mean value of 10 vibrations...,.............s00005 128°25
Pointer apparently moving from right to left.
I Ir 26 32°5 II Ir 28 39 126°5
3 11 26 58 13 II 29 § 127
5 II 27 23:5 15 EE, £20) 40'S 127
7 11 27 49 17 Ir 29 56°5 127°5
Mean value of 10 vibrations ................0eeeeee 127

Mean of means=127'625; ¢,=12°7625.

Remembering that one tenth of a division of the scale
is an angle of ‘0003996° in circular measure, formula (4),
expressed in milligrammes, becomes

=o: 20906 (Mol? 2
p= 7 3098 +2Pa’),

In our present example*

n= 35°83,
t= "th = rags,

* For this, as for several other cases, I removed the pans and hung the
weights directly by fine wires from the suspending-pieces. By this means
the resistance of the air was yery much diminished,

30 ON THE ESTIMATION OF SMALL EXCESSES OF WEIGHT.

Mgl-— 505m,
2Pa*=94704,

p=5'724 milligrammes.

The length of time occupied in this determination was
not quite a quarter of an hour.

The following table contains a series of results which I

have obtained of the weight of two centigramme riders,
the first of which was accidentally destroyed after the

conclusion of the fourth determination.

As the rider was

always placed at division 5 on the beam, the values given
in the table are double those actually obtained.

No. of
experi-
ment.

519769

MgI2 +2Pa*
145364
309356

130355

130355

130355

130355

130355

130355

4.54405

tin
seconds.

Weight of

mn, |rider in mil-

ligrammes.
13°458 9°78
254g | 10°05
19°12 3) 3)
34°71 10°47

36°6 pepe ®
35°5 11°35
35°83 11°45
35°5 ieee
36°37 ave

22°08 see

Mean yalue.

‘ g'96 milli-
grammes,

+ 11°35 ©milli-
grammes.

MR. J. B. HANNAY ON SILICEOUS FOSSILIZATION. 31

IV. On Siliceous Fossilization.—Part II. By J.B. Hannay,
F.R.S.E., F.C.S8., Assistant Lecturer on Chemistry in
the Owens College.

Read March 18th, 1879.

In a former paper it was shown, by chemical and optical
means, that the fossil siliceous rods Hyalonema Smithii
were identical in constitution with those from modern
sponges, and that the curious nodulized appearance of some
of the rods was due, not to the original form of the rods,
but to certain physical and chemical changes which have
passed over them since they were deposited where they
were found. It was also shown that of the three forms of
silica, transparent, gelatinous, and opaque, the first and
second were easily acted upon and retained the original
structure of the organic silica, whereas the last was in the
truly mineral form and had lost every trace of organic
structure, and was not easily acted upon by chemical
means. Mr. John Young, I’.G.S., having kindly supplied
me with several specimens of the fossils from the limestone
quarry at Kilwinning, which are very different from those
I previously examined, and which throw more light on the
changes which siliceous fossils may undergo, I beg to give
an account of them to the Society. One piece of limestone
simply contained (instead of rods) a number of cylindrical
holes where the rods had lain. In fig. 1, which isa wood-
cut from a photograph, are seen these cylindrical holes,
which plainly show that the rods have been dissolved away.
The solvent must have been a strong calcareous or other
alkaline solution, as the calcareous fossils are not in the

32 MR. J. B. HANNAY ON SILICEOUS FOSSILIZATION.

least disfigured. In fig. 2 we see a beautifully preserved
sample of Fenestella; and we know that a very slight
solvent action would have destroyed the structure of these
delicate organisms. From other internal evidence, such as
little shells and diatomacee, it is clear that the calcareous

portion of this limestone has not been at any time dissolved

to any extent ; and yet such an obdurate substance as silica
has been completely removed. Then, as to the cause of its
removal. The solution was no doubt highly calcareous ;
but we know that highly calcareous water may run over
quartz crystals for a very long period without having the
slightest effect upon the faces. I think that fig. 3 will

MR. J. B. HANNAY ON SILICEOUS FOSSILIZATION. 33

explain how the rods came to be so easily dissolved. This
is a photograph of a hollow where a rod has lain which still
contains some rounded nodules of silica. It will be seen
from my former paper that these nodules are anhydrous
inorganic silica, crystallizing out of the hydrated silica
after the rod has undergone a little dehydration since it
was alive. Now here we see the whole rod dissolved except
such portions as were entirely mineralized, if I may use
such a term; so that the reason the silica rods were so
easily dissolved by the calcareous solution was because
the silica of which they were composed was in a hy-
drated easily soluble form. Thus the existence of those
nodules which had before puzzled naturalists now gives us
the clue to the state of the rods at the time of solution.
Fig. 4 will still further elucidate this subject. Here it will
be seen we have a large number of rods partially dissolved.
I have examined, by the means given in my former paper,
above twenty, samples of these partially dissolved rods,
and I have not found one sample containing water ; so that
again we see the whole of the thoroughly mineralized
silica is left behind, and those portions which were very
probably hydrated dissolved. I say very probably; for we
see that the solvent action has gone on in a very irregular
manner, andin a manner which could not be accounted for
on any circulation-hypothesis, but just in such a manner
as would be caused by the irregular manner in which the
rods get mineralized.

It might be expected that, since the rods were so neatly
and perfectly dissolved out, the spaces might get filled up
with carbonate of lime and reproduce the silica rod as a
calcareous fossil; but, although I have examined some
hundreds of these fossils, I have not found one case of this
nature. The only case I have found even approaching
to this is, that when the centre of the rod is dissolved it is

SER. III. VOL. VII. D

34 REV. T. MACKERETH ON THE MEAN TEMPERATURES

sometimes, as in fig. 5, filled in with carbonate of lime. I
have noticed that when carbonate of lime is deposited
in the cavity where the rod lay it is highly crystalline, and
could never be mistaken for any thing organic. Fig. 6 is
from a photograph showing the carbonate of lime in the
silica-centre.

As the above remarks border on a subject which has
been discussed very extensively, I may be allowed to point
out that they settle one half of the discussion, namely that
silica may be dissolved in presence of calcareous fossils ;
but the other half, namely whether or not the spaces so
left may be filled up with carbonate of lime so as to look
like fossils, is still an open question.

V. On the Mean Temperatures of the Winters of the last

Twenty-nine Years. By the Rev. THomas Macke-
RETH, F.R.A.S. &c.

Read before the Physical and Mathematical Section,
February 25th, 1879.

Ir may be considered somewhat premature to institute a
comparison of the mean temperatures of the last twenty-
nine years when the colder of the extremes of the winter
months has not yet been entered upon, viz. the month of
March. In a meteorological sense winter may be consi-
dered as including five months of the year, viz. November,
December, January, February, and March. But January,

OF THE LAST TWENTY-NINE WINTERS, 35

so far as low temperature is concerned, is the pivotal
mouth of the winter, and March has a mean temperature
slightly below that of November. The difference is so
small, only about 0%7 Fahr., that in comparing the mean
temperature of winters, the mean temperature of these two
months may be practically neglected. The mean tempe-
ratures deduced from my own observations extend over
only 17 or 18 years; but the late G. V. Vernon, Esq.,
F.R.A.S., was kind enough to furnish me with the weekly
temperatures he had deduced from the year 1850 onwards
till 1861, when I began to make my own observations and
deductions. That the mean temperatures here presented
may have a common basis, I have calculated them upon
the weekly mean temperatures of the last 29 years, which,
of course, include those of the late Mr. Vernon.

The results are as follows for the winters extending
from the first week of December in one year to the last
completed week in February of the year following :—

Winter of Mean temperature. Winter of Mean temperature.

° °
LSGO—E 55. sc ccseans 40°3, TSO5-O). yaseecesne=s 41'9
EXGE—2 | sen addesenes 39°8 ESGO— 7 valsccnecses 39°9
WOS2—4)- acevecteseae 39°9 ES O7 Si. snee thoes 40°0
WSS GHA. cecscccecece he Ye} DOUG —Oiancacceers -crs 43°6
BOGA— Bw eacscdacp sd 351 E8609), cedaseavsas 3771
DS5C—O vecssecases's 37°3 PS7OmI esse skvcens 35°6
BORG 7 Scivdeceane 37°9 WOVE — 2 en cedesat see 40°3
POE7—O. > scecsadeceos 39°4 WB72—9) css acsaen acs 39°2
MORO—G) cevesnaccees 410 aA ON cian dconn ieee 40°6
1859-60 ..........4. 354 DOTA E NN eke se cee 38°6
BE GO=w devisscaeate 36°4 TS75—-O © se ecicicwses 38°8
VON oe ae cametenens 39°3 TO YO—F «25. seasove 42°3
TOO2—3. i \cecsenaaacis 419 BOG7—O)") Seach sedi 39°6
1 ES Se tere hor pry 37°9 ES78—9). ijsvccusaees 314.
SOAS Eoeoe faye 36°6

From the above table of winter mean temperatures it

D2

86 REV. T. MACKERETH ON THE MEAN TEMPERATURES

will be seen that the coldest winters of the last 29 years
were in 1854-55, 1859-60, 1870-71, and in 1878-79, and
that the present winter is colder than the coldest of the
preceding, viz. 1854-55, by 3°7 or 12 per cent. The mean
temperature of the winter months for 29 years is 38772
And whilst the winter of 1854-55 was 3°°6 or a little over
g per cent. below the average winter-temperature, the
present winter is 7°°3 or Ig per cent. below the average.

The accompanying diagram sets forth the ratio of all the
winters from 1850-51 :—

Igs5a-1
1855-6
[860-1
1865-6
i870-1
1875-6
1878-9 -

TEE RPS eeE eee. meer 1
SO
eles fee Fela | —\\- SaRERER
Se REP Geese
PT tt A TT oe

BBE SSe tee —

Pt eee

EEC Bil

eed | Spears pasha do.) oe ead eb le leeds]
SEER GEEL LCE eo

Bs]
SSS00SSS0055e0 “5/RG80e=—cnm

489 | aa
TNCISST PTL
MEAN BEERS EERE EEC EEE Ere ey
BEE PPE EEE EEE Ere ona8

eS BE aS Ol

v1 i oeoes eee See SaReReEH
EERE He PTW INIZINETA
St

OF THE LAST TWENTY-NINE WINTERS. 37

Here it will be seen that five years elapsed between the
cold winters of 1854-55 and 1859-60, but that six years
elapsed between the cold winters of 1864-65 and 1870-71,
and that eight years elapsed between the present cold
winter and the previous one of 1870-71. Itisnow known
that the sun-spot period is irregular and not so nearly an
interval of ten, eleven, or twelve years, as was imagined.
The minimum of the sun-spot period happened about two
years ago; but it is still at a minimum, and very seldom
have spots been seen on his disk during the past year.
Whether these cold winters are traceable to this solar in-
activity or not, the present coincidence is very striking.

In the same diagram I have presented the ratios of the
mean summer temperatures of the last eighteen years.
These ranges are included in the weekly mean tempera-
tures of June, July, and August, and will be seen to be
far less than the ranges of the winter mean temperatures.
This, perhaps, may be accounted for by the relative dif-
ference of the amount of atmospheric vapour existing in
the air in the two opposite seasons of the year. In the
winter season the ratio of atmospheric vapour reaches 87
per cent., whilst in the summer season it reaches only
about 75 per cent. But whether this is so or not, thereis
the fact. Here it will be seen that between the hot sum-
mer of 1861 and the still hotter one of 1868 there is an
interval of seven years; since then the coming summer
will make an interval of eleven years. In the interval of
seven years there was only one summer with the tempe-
rature slightly above the average, 1865; all the other
summers of this interval were mostly far below the average;
but in the eleven years’ interval all the summers, with only
two exceptions, have eithtr been above, or equal to the
average summer temperature. The ratios of the summer
and winter temperatures have not the slightest relationship

388 DR. JAMES BOTTOMLEY’S

to each other. Hence it is impossible to form any idea
from the temperature of a winter what kind of summer
temperature may follow.

I have shown on the same diagram the mean tempera-
ture of each year from 1861-1878. The mean of allis 48°.
The ratios of their differences are extremely small, so small,
indeed, as to be of no practical value; for between the
coldest year and the warmest of the last seventeen years
there is a difference of only 2°-9, and the mean difference
of temperature of all these years amounts to only 03.
These differences do not, from the data I have, seem to
observe any definite rule.

VI. Colorimetrical Experiments.—Part II.
By James Borromuey, B.A., D.Sc., F.C.S.

Read before the Physical and Mathematical Section,
April 22nd, 1879.

In a short note which I read before this Society (vol. xv.
p- 63) I proposed to measure quantities of colouring-
matter in solution, using the formula g¢=gq'¢' in the calcu-
lation, g and gq! denoting quantities of colouring-matter,
t and ?' lengths of columns of coloured fluid, the colour-
ing-matters being dissolved in equal volumes of water.
Last session I gave the results of some experiments which
IT had obtained two years previously. Lately I have made
some further experiments, which I give in this paper, along

COLORIMETRICAL EXPERIMENTS. 39

with some additional remarks on colorimetry. In my last
paper I took -ooor gram as the unit of measurement.
For comparison I have retained it in this, although the
quantities used can no longer be considered as traces. The
colouring-matter used was ammonio-sulphate of copper..
A solution was made by dissolving 10 grams of crystallized
sulphate of copper in a mixture of 200 cubic centimetres
of water and 50 cub. c. of ammonia. Mixtures of various
degrees of intensity were made by taking portions of this
solution and mixing with water so as to make up
500 cub. c. As in my last paper, A denotes the amount
of the colouring-salt present, B the length of the column
of fluid, and C the amount of the colouring-salt thence
derived by calculation.

Standard solution 4000 in 500 cub. c. of water, depth of
disk 8°3 :—

A B C
6000 43 7721,

a result considerably remote from the correct value. Also
when the disk was placed inside the solution at the depth
given by theory, it seemed too dark. Next, a comparison
was made by looking through the cylinders at external
white surfaces; standard solution 4000 in 500 cub. c. of
water, length of column 8°4 :—

A B Cc
6000 51 6588.

Thus the result is considerably different from the real
value. Also both experiments concur in giving too high a
value. The theoretical depths, moreover, were tried with
external surfaces, and seemed slightly too great. My next
experiments were made with solutions containing 2400 and
1600 of sulphate of copper. The disk being inside, the

40 DR. JAMES BOTTOMLEY’S

results were as follows; standard solution 1600 in 500
cub. ¢., depth of disk 8-3 :—

A B 1)
2400 5°6 2371.

The number under B was the result of seven trials.
The value under C is a fair approximation to the real value.
I also tried external surfaces with these solutions; stand-
ard solution 1600 in 500 cub. c., length of column 8°4 :—

A : B Cc
2400 62 2161

Somewhat further from the correct value than we might
expect. I also tried the theoretical length of column ;
with external disks it appeared a little too light. The
results obtained with the last standard solution are incon-
sistent with the results obtained with the first. In the
latter case the results are too low, while previously they
were toohigh. Errors of observation arising from imperfect
perception of colour, from imperfection of instruments and.
unfavourable conditions of light (for many of the experi-
ments were made during the winter months, sometimes on
gloomy unfavourable days) would, no doubt, contribute to
this result ; yet, allowing for all these, there seemed to be
some other cause. In my last paper I mentioned that an
ammoniacal solution of copper, when largely diluted,
became turbid, and that to carry out the experiment an
additional quantity of ammonia was necessary. This small
quantity was added at hazard, as I did not think it would
have any influence on the result. It seemed to me after-
wards to be a point worth examining in connexion with
the above experiments. Two solutions were made, each
containing 5 cub. c. of the previously mentioned copper-
solution with 245 cub. c. of water. The solutions were

COLORIMETRICAL EXPERIMENTS. 41

placed in similar cylinders: to one of the cylinders more
ammonia was added ; it appeared perceptibly darker than
the other. Hence it appears that the excess of ammonia
has some influence on the result. I presume that ammo-
nio-sulphate of copper has a tendency to be decomposed
by water, and that some change is effected even before it
becomes obyiously marked by the formation of a turbidity ;
moreover it seems likely that the excess of ammonia has
the power to counteract this property of water and to
restore the original compound. ‘Two solutions were made,
the bulk of each being 545 cub. c.,—one containing 4000
of copper sulphate along with an additional 20 cub. ec. of
ammonia, the other containing 6000 of copper sulphate
with 30 cub. c. of additional ammonia. The comparisons
were made in new cylinders graduated to millimetres. An
experiment with white surfaces external gave the following
results ; standard solution 4000 in 545 cub. c. of water,
length of column 23 centimetres :—

A B 6)
6000 15°5 5955

Thus the result is very near the real quantity. I also took
shorter lengths of the standard solution, namely 18, 13, and
8 centims.; the corresponding lengths of the other solution
were 12°4, 8°5, and 5‘3 centims. Reduced to 23 centims.
of the standard, the lengths would be 15°8, 15, and 15:2,
numbers not far removed from 15°5, which was got by ob-
servation. lIrepeated the experiment with fresh solutions,
the bulk of the liquid being 500 cub. c.; standard solution
4000 in 500 cub. c., length of column 21°2 :—

A B Cc

6000 I4'I 6000

The number under B is the theoretical quantity, and was

42 DR. JAMES BOTTOMLEY’S

the mean result of four trials. Also with shorter columns
of the standard liquid, namely 15°2, 10°2, and 5°2 centims.,
the corresponding lengths of the stronger liquid gave similar
tints. At the same time lengths differing a little from the
theoretical would also satisfy. With these solutions I also
tried an experiment with disks inside; standard solution
same as last :—

A B C
6000 12°3 6894.

The number under B was the mean of 15 trials; thus
the result with disks inside was not so good as with disks
outside. Also 14‘1 centims., the theoretical depth, when
tried, seemed slightly too dark with disks imside. I re-
peated the experiment with a solution containing 2400,
using one containing 1600 as a standard. In preparing
these solutions, to the stronger I added 12 additional cub.
c. of ammonia, and to the weaker 8. With external white
surfaces the results were as follows; standard solution
1600 in 500 cub. ec. of water, length of column 212 cen-
tims. :—

A B (8)
2400 13'8 24.58

The number under B was the result of fifteen trials.
Thus we get a good approximation to the real quantity.
With disks inside the results were as follows; standard
solution same as last :— ,

A B O

24.00 12 2824.

The number under B was the mean of twelve trials. The
value got with disks inside is not so good as with disks
outside. Also the theoretical depth 14°1 centims., when
tried, seemed to be slightly too great. From the foregoing

COLORIMETRICAL EXPERIMENTS. 43

experiments it would appear that with considerable ad-
ditions of ammonia the results with disks outside were much
improved. Why the results were not equally good with
disks inside may, I think, be accounted for, and will be
considered further on. I also compared the solution con-
tainmg 4000 with the one containing 1600; standard
solution 1600 in 500 cub. c., length of column 21°2 :—

A B O
4000 8 4240

The number under B was the mean of eight trials. The
theoretical length was 8-5. With the standard solution on
the left hand this length seemed to give asimilar tint ; but
with standard solution on right it seemed a little darker.
And now I remarked for the first time, or, if I had previ-
ously remarked it, had not thought it worthy of notice,
that even an apparently so trivial circumstance as altering
the positions of the cylinders from right to left had a per-
ceptible influence in the determination of colour. I after-
wards made some experiments to test this. Next I com-
pared solutions containing 1600 and 600; standard so-
lution 1600 in 500 cub. c., length of column 21°2 :—

A B Cc
6000 ce 6682

The number under B was the mean of eight trials. The
result is not so satisfactory as the others. I also tried
these solutions with white surfaces inside; standard so-
lution same as last :—

A B 0)
6000 3°9 8697

—a widely remote result, and much further from the real
value than with disks outside ; also a disk placed in the so-
lution at the depth assigned by calculation seemed too dark.

44, DR. JAMES BOTTOMLEY’S

It seemed possible to me that a more satisfactory result
than this experiment had yielded might be obtained. The
excesses of ammonia used in the experiments were nearly
proportional to the quantities of sulphate of copper in so-
lution; but if we regard water as an agent whose tendency
is to diminish the intensity of the colour, and ammonia as
an agent whose tendency is to restore the colour, it would
seem reasonable that the ammonia should be proportional
to the water. The difference of the excesses of ammonia
in the last two solutions was large, being 22 cub.c. I
prepared fresh solutions, one containing 4 cub. c. of the
copper-solution with 30 cub. c. of additional ammonia and
sufficient water to make 500 cub. c. The other solution
contained 15 cub. c. of the copper-solution with 30 cub. c.
‘of additional ammonia, and sufficient water to make 500
cub. c. The quantities of the copper-solution taken should
correspond to 1600 and 6000 of copper-sulphate. To guard
against imperfect measurements from the burette, I also
weighed the solutions: the 4 cubic centimetres weighed
39854 grams; and the 15 cubic centimetres weighed 14°99
grams. The ratio of the volumes is 3°75, and the ratio of
the weights is 3°761; so that the error of measurement
would be but small.

With disks outside, the results of experiments were as
follows ; standard solution 1600 in 500 cub. c. of water,
length of column 21°2 :—

mas B O
6000 bee 5653

The number under B was the result of eight trials; also
the standard solution was on the left hand. With the
standard solution on the right the results were :—

A B Cc
6000 54 6283

COLORIMETRICAL EXPERIMENTS. 45.

The number under B was the mean result of eight trials.
In one case the value got by experiment is too high, and
in the other too low. The theoretical lengthis 5°65; and
5°4 is not very farfromit. When I actually tried a column
of the theoretical length, it seemed to give the required tint
when the standard solution was on the left; when the
standard solution ‘was on the right it seemed a little darker.
The mean of the two values previously obtained is 5968,
which is near to the real value.

From the above experiments it seems that, when excesses
of ammonia are added, very fair approximations may be
obtained by colorimetry to the quantity of copper-sulphate
in solution, the white surfaces being external ; also that
with white surfaces internal the results are more remote.
In my last paper I stated that, when there was much dif-
ference between the standard solution and the one to be
compared with it, the discrepancies when internal disks
were used were considerable. Then I was using very small
quantities of colouring-matter. From these experiments,
where the colours were intense and the quantities of
colouring-matter used considerable, a similar conclusion
follows. The reason for this is not far to seek, and it also
suggests a correction that must be applied to the formula
when the white surfaces are inside. A white disk inside a
column of coloured liquid looks darker in colour than a
white disk outside placed a few inches below a column of
the same length. This may be tried by looking through
different columns, or through the same column, and having
inside a white disk of smaller diameter than the cylinder ;
the inside disk will then appear surrounded by a rim of
lighter colour. When the disk is internal, it is evident
that the light which illuminates it has previously passed
through the solution, so that we are looking not at a white
disk, but at a coloured disk, through a coloured solution.

46 DR. JAMES BOTTOMLEY’S

Some allowance must be made in the calculation for this
coloration of the disk. The formula gt=q’/' is applicable
to the case in which the surfaces are outside; to adapt this
formula to the case when the disks are inside, suppose z to
be the length of the column of fluid which would cause the
difference in colour between an external and an internal
surface, then the formula would be g(¢+a)=q' (t'+2).

To find the value of z experimentally, I took a solution
containing 2400, and sunk asmall disk in it until the side
and outside colour seemed the same: for the outside the
length of column was 22°5, for the inside 17°7, this being
the mean of eight trials. The difference is 4°38. With a
solution containing 1600, a white surface outside, with
length of column 21°2, seemed to give the same colour as
white surface inside with length of column 16°2; the
difference is 5. I also tried to get the value by the follow-
ing combination :—A solution was taken containing 2400
with disk inside, and compared with a solution containing
1600 with a disk outside. ‘Length of column in latter case
was 21°'2; in the former case a column 17‘5 seemed to give
a similar colour. From the formula g (f+) =q/'t' the re-
sulting value of z would be 5°2. JT also tried the following
combination :—Solution containing 2400 and disk outside
was compared with solution containing 1600 with disk
inside. The mean of eight trials gave length of column 17
in the latter case, equivalent to 21°2 in the former; from
the formula 1600 (174+) =2400 x 21°2, the resulting value
of xis 4°3. Finally, we get for the approximate value of a,
taking the mean of the four determinations, z=4°8. The
experimental determination is not easy ; but the value ob-
tained gives better results when we use it in the formula.
For instance, on a former occasion, with disks inside, when
a solution containing 1600 and length of column 21°2 was
used as a standard, and there was compared with it a so-

COLORIMETRICAL EXPERIMENTS, 47

lution containing 2400, the length of column was 12;
from the uncorrected formula the result is 2824; from
the formula

g'(12+4°8) =1600(21'2+ 4°8)
the resulting value of g is 2476, which is not far from the
proper value.

When the fluids compared differ much in strength, the
value of the correction will probably vary. It will be
better not to have the difference large, whether the disks
be external or internal ; for when the differences are large,
any errors in the determination of the lengths of the
columns have a greater effect on the calculated result.

I also tried to make a rough estimate of the length of
the cylinder which might be covered without any percep-
tible darkening of the disk. JI found that a black cloth
cover investing the cylinder, might be drawn down until it
was about 3°5 or 3°2 centims. from the disk ; this would
vary with the dimensions of the window and the relations
of the cylinder toit. Also the length given is less than the
value of x previously deduced : but it ought to be so; for
the light from a vertical window to illuminate a horizontal
disk must pass obliquely through the solution. It would
also follow that parts of the disk more remote from the
window are darker than parts nearer; hence, if the cylin-
ders are of moderate radius, either the disks should be small
and should be kept with their centres moving along the
axes of the cylinders, or, in the case of larger disks, the de-
termination of colour should be made by a comparison of
similar parts of the disks.

In the estimation of colour, it is also not a matter of
indifference, when we are given any tint as a limit, how
we approach that limit. Suppose we have two cylinders, «
and $8, full of coloured liquid, that in « being the darker.

48 DR. JAMES BOTTOMLEY’S

Now pour out from « until the colour seems the same as
in 8; before reaching the theoretical division sight will fail
to discern any difference of colour. Now, if we proceed
cautiously, as we approach the limit there will be a natural
hesitation and tendency to stop; and it seems likely that in
most cases, in obedience to that feeling, we shall stop with
a column a little too long. Nowsuppose we start with the
cylinder « empty and pour fluid into it; as we again ap-
proach the limit cautiously we shall again have a tendency
to stop, and, inasmuch as before reaching the limit we pass
through tints which we cannot distinguish from it, we are
likely to take a column of fluid too short. In my own
case I have noticed this on several occasions. For example,
in trying to estimate a particular colour, the mean of seven
trials made by pouring out from the cylinder gave 14°1 as
the length of the column, the mean of seven trials made by
pouring into the cylinder gave 13°7 as the length; and with
disks inside, the mean of six trials made by moving the disk
from below upwards gave 12°5 as the length of column,
while moving from above downwards the mean of six ex-
periments gave 11°7. In trying to estimate a colour, it
seems to me that it would be well to approach the limit by
both ways, and then take the mean of the results.

In a previous part of this paper I stated that altering
the position of the cylinders made a little difference in my
perception of colour. I made some experiments to try
this. I took a solution containing 2400, and poured from
the cylinder on the right hand into the cylinder on the left
hand; the columns ought to be equal. The mean of nine
trials gave length of column on right hand 11:2, length of
column on left hand 10°61. In these experiments the
judgment was made using both eyes. I next tried using
one eye only. With the right eye the results were, length
of column on right hand 10°86, length of column on left

COLORIMETRICAL EXPERIMENTS. 49

hand 11°09; these numbers were the mean of nine trials.
With the left eye alone the results were, right-hand cylin-
der 10°78, left-hand 11'o1, being the mean of nine trials.
Thus, using one eye only, the results are nearly the same in
both cases; they also tend to made the right hand a little
less, thus reversing the case of two eyes. These experiments
were made in aroom with asmall window facing the south.
I afterwards repeated the experiments, using two eyes, in
another room having a window of larger dimensions and
facing the north. A solution was used containing 1600 ;
the mean of nine trials gave, right-hand cylinder 11°16,
left-hand 10°55, nearly the same results as I got before.
Why I should have this tendency to make one column a
little longer than the other I do not know; possibly it may
be some peculiarity of vision confined to myself. In the
course of my experiments I have also noticed the following
curious phenomenon, and this repeatedly, when working
with solutions coloured with bichromate of potash and with
ammonio-sulphate of copper :—Look steadily with one eye
(say, the right) through the solution at a white surface, after
the lapse of about a minute suddenly turn the head so as
bring the left eye close over the cylinder ; then the colour
will seem more intense than it did with the right. Having
looked with the left eye for about a minute, bring again
the right eye suddenly close over the cylinder, and the
colour will seem more intense than it did with the left, and
so on alternately. It would seem as if the first impressions
of colour on the eye were the stronger, and as if there were
a gradual and imperceptible decrease in intensity. Per-
haps alterations in the aperture of the pupil may contribute
to this.

Another matter for consideration in colorimetry is the
nature of the incident light. On some occasions we have
the light from a blue sky; on other occasions the sky is

SER. III. VOL. VII. E

50 DR. JAMES BOTTOMLEY’S

invested with clouds of various depths of grey, or sometimes
tinged by the sun with a variety of tints, from yellow to
red ; while the light of the sun itself is frequently yellow
or orange. All these variations of light are likely to have
some influence on our judgment of colour, especially when
the tints to be compared are light. Of the disturbing in-
fluence of colour in the incident light any one may convince
himself by comparing yellows on a morning when the sky
is enveloped in a yellow fog. In some experiments which
I made with bichromate of potash during such fogs I found
it much more difficult to decide at what depth equality of
colour was effected ; the disk in the stronger solution could
be moved through a very considerable range without any
change of colour being perceived. A similar result
happened when I hung up yellow screens and tried to
make determinations of colour behind them; also when
looking at light-yellow external surfaces, differences in the
lengths of the columns failed to give any differences in tint,
although when looking at white external surfaces they did
so. But in quantitative determinations of matter by co-
lorimetry, the excellence of the results require sensible
variations in colour when we alter slightly the length of
the column; hence, when the incident light is tinged with
the colour we wish to determine, the advantage of the
method is diminished. Such a consequence may also be
deduced from the formula which I obtamed in my last
paper. For suppose white light to consist of yellow, blue,
and red (as far as the reasoning is concerned, we might
have considered it also composed of green, red, and violet,
as some physicists do). Let I denote the incident white
light, and B, Y, R the intensities of blue, yellow, and red
necessary to produce white light, so that we may write

I=B+Y+R;

COLORIMETRICAL EXPERIMENTS. 5]

let there be two solutions containing g and gq! of yellow
colouring-matter, and let ¢ and ¢' be the corresponding
lengths of columns; then the intensity of the light trans-
mitted through one cylinder will be

(1 —mgt) ¥ + (1—m,gt)R+ (1—m,g2)B ;

m denoting the amount of yellow light absorbed by a unit-
layer, and m, the amounts of red and blue absorbed by a
unit layer. Also the light transmitted by the other cylin-
der will be

(1—mea't')¥ + (1—m,q't') R+ (1—m,q't') B.

Since both cylinders are of the same colour, these expres-
sions will be equal. m will be less than m, because the
transmitted light is yellow. Let m=m,—p; then we
shall have

I(1—m,gt) +pgtY=1(1—m,g't) +pg''¥, (A)

the expression on the right hand denoting the light trans-
mitted through one cylinder, and the expression on the
left hand denoting the light transmitted through the other
cylinder. Each expression consists of two terms. The term
of the form I(1—m,gt) denotes the white light transmitted;
the term of the form pgtY denotes the excess of yellow:
this term we may call the effective yellow; for it is the
only portion which produces the sensation of colour. Now
suppose the light, before passing through the cylinder, to
pass through a yellow screen; suppose the composition of
the incident light, after transmission through the screen,
to be
eX +p,B+,,R,

p being greater than p,, say p=p,+7, so that the compo-
sition of the light may be written

pL+rY,
E2

52 DR. JAMES BOTTOMLEY’S

rY being the effective yellow after passing through the
screen. After using the screen, the left-hand expression
of (A) would become

Ip,(1—m,qt) + Yr—Yrm,qt+p,qtYp.

Since gt=gq't', if we substitute g/t! for gt in the last ex-
pression, we shall get the light transmitted by the other
cylinder after using a screen ; hence, if the columns be ad-
justed so as to produce equality of colour with white light,
they will still be in adjustment if the light should become
tinged with yellow.

Let y, and y, denote the effective yellows in one of the
cylinders with white incident light and with yellow light ;
then we shall have

yi=ugXt,
y,.= Yr—Yrm,qt+ Yp,ugt.

Now suppose the length of the column of coloured liquid
to be altered a little so as to become ¢+0¢; let dy, and by,
denote the alterations in the effective yellow in each case,
then

oy.= (Yp,ug—Yrm,q)ot,

dy, = Ypgit.

Hence

. oy, —oy, = — {Yrm,q+ ug (1—p,)}dt.

Therefore 6y, is less than 6y,; that is to say, we shall not
see so much difference of colour for a given alteration of
depth when the light is tinged with yellow as when it is
white; therefore the sensibility of the method is diminished.
This may be put in another way. When the incident

LIST OF EGYPTIAN LEGUMINOSZ, 53

light is tinged yellow, the expression for the effective yellow
after transmission through the cylinder is

Mie Yqt(rm, ra PK) 7

Suppose the term in brackets to vanish, then the expression
for the effective yellow becomes Yr, which is independent
of the quantity of colouring-matter and of the length of
the column.

VII. List of Leguminose observed growing near the Egyp-
tian Seashore, West of Rosetta, 1875 to 1877. By
H. A. Hurst andA. Lerournevx.

Read before the Microscopical and Natural-History Section,
April 7th, 1879.

[Mar. indicates that the plant is said to grow in Marocco by John Ball,
Esq., in his “Spicilegium Flore Maroccanex,” Journal Linnean Society,
1878. Lx. Exs. shows that the species is represented in the ‘ Plantze Mgyp-
tiacee auspice A. Letourneux lecte,’ under the number given.]

Argyrolobium uniflorum, Decaisn. Jaub. et Spach; Lx.
Exs. 41.

Sinai; Southern Palestine; Libanotic Syria; Tunis ;
Southern Algeria.— Boiss.

The occurrence of this plant in Northern Egypt was, I
believe, first ascertained by H. H. Calvert, H.B.M. Vice-
Consul at Alexandria.

Representative of a Cape genus, it is most dificult of

5A MESSRS. H. A. HURST AND A. LETOURNEUX’S

detection on the sands of the desert, though, when once
seen, more easily found. While looking for it, I walked
over many specimens, till, when accidentally kneeling on
the ground, it attracted my attention.

A, Linneanum = Cytisus argenteus, L., of the northern
shores of the Mediterranean, may be known to most of us ;
but the other species of this Cape genus are seldom seen,
except in large collections.

Lupinus termis, Forsk.
Arabicé Termis.

Generally cultivated in Egypt} but notwithstanding
Boissier’s remark “ spontaneous in sandy places,” I cannot
say I have seen it so. Its seeds are edible, which is
rather an exception in this genus. They are sown on
the muddy banks of the receding Nile broadcast without
being covered. The bitter seed becomes sweet during
germination, owing to the transformation of its starch into
sugar. In this state of germination the seeds have been
an article of consumption among all the nations at one
time or other subdued by the Arabs.

L.——?

Near Mex 1 found among some barley a fragment which
was probably LZ. digitatus, Forsk., but too imperfect to
identify.

Genista retam, Forskohl.

G. monosperma B. rigidula, D.C. Prodr.
Retama retum, Boissier, F. O.; Forsk.; Lx. Hxs. 40; et auctores.

The representative in Eastern Africa of G. monosperma

LIST OF EGYPTIAN LEGUMINOSA. 55

of Western Africa, so well known in our gardens. Of this
plant, the first discoverer, Forskohl, says :—‘‘It is the
emblem of all that is most miserable in life. Its roots are
eaten only by those who can find no other food. It is
found in arid sterile deserts destitute of shade. Its branches
are few, thin, and scattered.””’ Thrown into the fire, it
burns with a loud crackling noise; and seems to be the
plant named in Psalm 120, v. 4, as Juniper (Refem). If
so, it is interesting, as bearing on the Darwinian theory,
to find a plant which has retained its name so long, what-
ever modifications may, unknown to us, have taken place
in its structure.

Syria ; North-eastern Africa.

The plant found about Alexandria is called Retama Du-
ri@i in Letourneux’s ‘ Second Century,’ no. 186; but must
be Forskohl’s plant.

Hooker and Ball, in their ‘Tour in Marocco,’ say,
speaking of G. monosperma :—“ There is something sad in
the meagre and drooping aspect of the plant, that brings to
mind those dismal mourning trinkets wherein a lock of
hair is made to form the effigy of a Weeping Willow.”

Bentham and Hooker retain Retama, a genus of Bois-
sier’s, among the Geniste (p. 482).

Ball, ‘Spicilegium Flore Maroccane,’ p. 398, remarks
of G. monosperma, Lam. :—“ fugit loca arida saxosa,” the
reverse of Forskohl’s plant. Are these two the same species
under different conditions of life ?

Syria; North-eastern Africa.

Ononis vaginalis, Vahl, i. p. 53; Lx. Exs. 42.
=O. kotschyana, Fenzl.

= Q. Cherleri, Forsk., non L.

56 MESSRS. H. A. HURST AND A. LETOURNEUX’S

= 0. vestita, Viv. Lib.

An interesting and well-marked species, well seen about
Ramlé.

Antilebanon (Gazll.); Graciosa; Lancerotta (Canary
Island) ; Cyrene (Boiss.).

O. reclinata, L.

Canary Islands; Southern Europe; Northern Africa ;
Cairo; Grecian Islands; Abyssinia; Syria; Palestine ;
Arabia Petrea.

O. serrata, Forsk.

This species has often been confused with O. diffusa, to
which it is closely allied.

Canary Islands ; northern and southern shores of the
Mediterranean ; Arabia Petrzea ; Southern Persia.

O. sicula, Guss.

Only found by me to the westward of Alexandria. —
Southern Spain; Sicily; Northern Africa; Arabia
Petra; Palmyra; Aleppo ; Southern Persia.

O. mitissima, L.
Rare.
Madeira; Canary Islands; shores of the Mediterranean;

Palestine; Mesopotamia.
These four last species occur in Algeria and Marocco

(Munby & J. Ball).

LIST OF EGYPTIAN LEGUMINOS&. 57

Trigonella fenum-grecum, L.

- Trigonella fanum-grecum is a plant which, in former
days, was much esteemed. We only know it in England
as a condiment to mix with mouldy hay.

Native name Helva. The scent very peculiar; said to
be used as a condiment in Thorley’s Food for Cattle.

In cultivated ground.

I doubt whether this be indigenous. In fact it is so
generally cultivated in the East that it would be difficult
to say where it is truly spontaneous.

Mediterranean basin; Abyssinia.

T. hamosa, L.; Lx. Exs. 43.
Egypt ; Tropical Nubia.

T. laciniata, L.; Lx. Exs. 45.

The plant found about Alexandria, chiefly about Gabari,
is the var. @. subsessilis, = T. arguta, Vis., = T. nilotica,
Presl.”

The typical 7’. laciniata is found near Cairo.

T. maritima, Delile ; et var. 8. dura.
T. dura, Vis.

Sardinia; Sicily; Tunis ; Lower Egypt; Joppa.

The luxuriant forms of the typical 7. maritima, grown
near irrigated land, differ so widely from the var. B. dura
that it is difficult to believe they are the same species ; but
there seems little doubt of this being the case.

58 MESSRS. H. A. HURST AND A. LETOURNEUX’S

T. anguina, Forsk.; Lx. Exs. 46.

Occurs in the vicinity of Alexandria on irrigated land,
but is not common. It is more frequent near Cairo.

Canary Islands; Algerian Sahara; Tunis; Babylonia,
near Mohammera (Noé). 7

T. occulta, Del. ; Lx. Exs. 44.

T. stellata, of Forsk., is indicated by friends as growing
in this district; but I have no specimens: I think it
possible it may be a form of 7. hamosa. .

None of the above species is named by Mr. Ball as
growing in Marocco.

Medicago marina, L. Mar.
M. littoralis, Rhode. Mar.

M. tribuloides, Desr. Mar.

Mr. Ball seems quite correct in holding that these two
are distinct species, although that close observer Lowe
has joined them.

M. denticulata, Willd.
M. apiculata, Willd.
M. maculata, Willd. Mar.
M. laciniata, All. Mayr.
M. orbicularis, All. Mar.

M. lupulina, L.

LIST OF EGYPTIAN LEGUMINOSA. 59

M. corenata, Lam.
M. minima, Lam. var. longiseta.
Trifolium angustifolium, L. Mar.

T. bicorne, Forsk.

Probably T. resupinatum, L.

If 7. bicorne, Forsk., be really 7. resupinatum, L., it is
the var. 8. minus, Fl. Orient. ii. p. 137, distinguished as
“ caulibus tenuioribus szepe abbreviatis, foliolis minoribus,
pedunculis gracilioribus, folio spe brevioribus (semper,
Hurst), capitulis minoribus, dentibus labii superioris calycis
fructiferi brevioribus, calycis parte inflata minus elongata,”
and not the var. «. majus of Boissier,” caulibus robustiori-
bus, pedunculis folio longioribus, floribus majoribus.”
This, Will. and Lan. say, is the 7. suaveolens of Willd. ;
but I am inclined to think the Egyptian plant is a
distinct species from that ; therefore Forskohl’s T. becorne
should stand as such.

T. fragiferum, L. Mar.
T. tomentosum, L.; Lx. Exs. 187. Mar.
T. nigrescens, Viv.
T. alexandrinum, L.

T. formosum, Urv.

Rare. Aspecies of the Chronosemium section was found
by Mr. Letourneux ; but the specimens were mislaid.

Melilotus sulcata, Desf. .Mar.

60 MESSRS. H. A. HURST AND A. LETOURNEUX’S

M. messanensis, L.
M. elegans, Salzm.
M. parviflora, Desf., =indica, All. Mar.

Hymenocarpus nummularius, DC. ; Lx. Exs. 47.

Medicago ctrcinata, var. 8, Willd.

Boissier only gives this plant as growing in Egypt and
Southern Persia.

Lotus argenteus, Del. ; Lx. Exs. 184.
L. edulis, LL. Mar.
LL. creticuss L. Mar.
L. cystisoides, DC. Mar.
L. corniculatus, L.
L. tenuifolius, Rchb.
L. pusillus, Viv. Fl. Lib.

With the following :—

L. pusillus, var. 8B. major, = L. halophilus, et L. Aucheri,
Boiss. ; pedunculus biflorus vel rarius 3—4-florus.

This latter plant may be considered a good type of a
variety. In a dry season only the type can be found;
while in a season with an excess of wet, such as1876—7 the
variety 8 predominates on the very same ground.

Sicily; Attica; Syria; eastern part of Northern Africa;

LIST OF EGYPTIAN LEGUMINOSA. 61

Grecian Islands; Arabia Petrzea; Southern Persia, at
Buschir.

L. cystisoides, L.; Kotschy, pl. Mgypt. exs. no. 949.
Lotus creticus, B. cytisoides, Boiss. F. O. p. 165.

L. creticus, L. ; Rehb. Icon. t. 134.
Var. «. genuinus, Boiss. F. O. p. 165.

See Prod. Flore Hispanice of Willkomm and Lange,
Pp. 341, for a good discrimination of these two species or,
varieties. They both occur around Alexandria.

L. ornithopodioides, L.

Scorpiurus subvillosa, L. Mar.
S. sulcata occurs more in the interior; but I have not
seen it in this district.

Tetragonolobus palestinus, Boiss ; Lx. Exs. 185.

Sesbania egyptiaca, Pers. Syn. ii. 316; Lx. Exs. 57.
Alschynomene sesban, L. Roxb.

AB. indica, Burm.

Coronilla sesban, Willd., Rheede.

Plains from the Himalayas to Ceylon and Siam, ascend-
ing to 4000 feet in the north-west ; cosmopolitan in tropics
of the Old World (J. G. Baker, F. I.) ; Senegal ; Nubia;
Afghanistan and Eastern India (Boiss. F. O.).

This plant reminds one of the genus Coronilla, under
which it is placed by Willd. Boissier, in his ‘ Flora Ori-
entalis,’ asks whether it is really spontaneous in Egypt—a
question I must echo. I never saw it looking truly wild.
It has probably been introduced from India in very ancient

62 MESSRS. H. A. HURST AND A. LETOURNEUX’S

times, and is, perhaps, the most easily recognized plant in
old Prosper Alpinus’s work.

Astragalus hispidulus, DC. ; Lx. Exs. 51.
A. annularis, Forsk. ; Lx. Exs. 52.
A. beticus, L. Mar.

A. hamosus, L.; Lx. Exs. 189. Mar.
A. hamosus, var. legumine majore, Lx. Exs. 188.

A. hamosus, var. legumine dorso profundius suleato,
Lx. Eixs. 49.

These three forms appear worthy of further examination.
The latter may be distinct.

A, trimesiris.
A. mareoticus, Del.
A. tribuloides, Delile ; Lx. Exs. 48.
A. radiatus, Ehrenb.
A. peregrinus, Vahl; Lx. Exs. 53.

A, alexandrinus, Bois. Diag. ser. 1, ix. p. 74; Lx. Exs. 54.

A peculiar and distinct-looking plant, though allied to
A. platyraphis, Fisch.

A common plant from Alexandria to Aboukir; also found
in Arabia Petrzea, Palestine (on the Jordan, near Damascus),
and Tunis.

LIST OF EGYPTIAN LEGUMINOS&. 63

A. trigonus, DC.; Lx. Exs. 55.

A. trigonus is the sole representative in this northern
district of the woody Astragali of which further south so
many species occur. They and the Acacias are the sources
of our supplies of gum.

Hippocrepis cornigera, Boiss. ; Lx. Exs. 56.

H., divarieata, Hochst. MSS.

Its older name is H. bicontorta, Loisel. Fl. Gall.

It hardly seems correct for Boissier to substitute his
own name for an older one, even on his own ground
(nomen antiquius sed improprium).

Northern parts of Eastern Africa; Arabia Petrza;
Ramleh, Syria; Southern Persia, at Abuschir.

H, unisiliquosa, L.

Basin of the Mediterranean ; Portugal and Spain.

H, multisiliquosa, L.

Southern Europe; Northern Africa.
Both the above species are commoner to the west than
the east of Alexandria.

H. biflora, Spreng.; Mex.
Onobrychis crista-galli, Lam. Mar.
O. Gertneriana, Boiss.

Alhaji maurorum, DC.; Lx. Exs. 58.

Hedysarum athaji, Linn.
Manna hebraica, Don.
A, mannifera, Desy.

The Camel’s Thorn, found from Songaria to Greece and

64 MESSRS. H. A. HURST AND A. LETOURNEUX’S

Nubia. Plains of North-western India, Upper Ganges and
Concan, ascending to 3000 feet on the Kishangunga (J. G.
Baker, F. In.).

Vicia sativa, L. Mar.

V. lutea, L., var. hirta, Boissier. Mar.

V. hirta, Balbi et auct.

V. angustifolia, Roth. Mar.

V. angustifolia, var. a. albiflora, Boiss.
V. calcarata, Desf.
V. gracilis, Loisel.

Cicer arietinum, L.

Widely cultivated, but origin unknown.

Cicer arietinum is eaten fresh as well as dry, like peas ;
in the latter state often with the bulbs of Cyperus esculen-
tus, when it is called by the natives ‘‘ Habb el aziz u humus.”
The word Cicer has attained a melancholy celebrity,
as being that by the pronunciation of which the French
origin of many of the victims of the Sicilian Vespers was
detected. It was the test-word the pronunciation of which
decided their life or death.

Ervum lens, L.

Cultivated and escapes.
E. ervilia, L.
Lathyrus aphaca, L. Mar.

L. sativus, L. Mar.

LIST OF EGYPTIAN LEGUMINOSE. 65

LL. cicera, li. Mar.
L. hirsutus, L.

L. marmoratus, Boiss. et Bl.

Indicated in the F. O. as found near Alexandria by
Cadet.

Pisum arvense, Li.

Parkinsonia aculeata, L.

A native of Tropical America, is subspontaneous in the
grounds of the Gabari palace.

Acacia nilotica, Del.

Apparently indigenous and much cultivated on banks
of canals ; is probably a native of Nubia.

Albizzia lebbek, L., sub Mimosa.

Acacia lebhek, Willd. ; DC.
Cassia planisiliqua, Burm.

Much planted in squares and along roads, but not a
native.

Ad inquirendum :—

Lotonotis.
Coronilla.
Psoralea.

Biserrula.

SER. III, VOL. VII. ¥

66 DR. JAMES BOTTOMLEY ON COLORIMETRY.

VIII. On Colorimetry.—Part ITI.
By James Borromtey, B.A., D.Sc., F.C.S.

Read before the Physical and Mathematical Section,
October 14th, 1879.

In this paper I give the results of some further experi-
ments to test the accuracy of the assumption that, when
light is transmitted through transparent coloured solutions,
the length of the column multiplied by the quantity of
colouring-matter is constant if the colour is constant. In
a communication which I made to the Society in April of
this year, I gave the results of some experiments with
ammonio-sulphate of copper, which appeared to indicate a
failure of the law; but the failure was traceable to the
decomposition of the salt by water, and better results were
obtained when a suitable menstruum was employed. I
was wishful to obtain some colouring-matter which might
be diluted with water without decomposition ; it occurred
to me that caramel would be a suitable body. I prepared
some caramel by heating loaf sugar. The resulting dark
brown vitreous mass dissolved entirely in water. In, these
experiments I also wished to see if the law would hold
when one quantity was a considerable multiple of the
other; also the quantities used are no longer mere traces.
In order to avoid an ambiguous result from any difference
in sensibility to colour of the two eyes, in making the de-
terminations I used one eye only. The cylinders used in
these and previous experiments were not specially made for
colorimetric purposes. At the bottom they were curved a

DR. JAMES BOTTOMLEY ON COLORIMETRY. 67

little inwards. Measurements were taken from the summit
of the curve. When in such cylinders we have short
columns of fluid, the depth not being uniform, the colour
is not uniform over the whole area as we look through the
cylinder at an external white surface. Manifestly the
colour at the sides is more intense than at the middle ; but
for purposes of comparison we must restrict our attention
to the middle. It is not easy to confine attention to a
limited portion of a coloured area, so as to receive no im-
pression from the remainder of the area, without some
provision. Hence it is necessary to limit the field of view
at the bottom of the cylinder. This was done either by
placing small porcelain disks on a black ground and holding
the cylinder so that its axis passed through the centre of
the disk, or, still better, by covering the bottom of the
cylinder with a black external plate having a small hole
(about a quarter of an inch diameter) in its centre. With
such a provision, columns seemed in some cases to satisfy
the experiment which otherwise would have given the im-
pression of too dark a colour. In these experiments I
used a method for determining colours indicated in my last
paper, regarding the proper colour as the mean of two sets
of determinations, one set giving too great and the other
too small values. Thus the determination of colour has
some analogy with the method used by old geometers for
determining areas bounded by curved lines ; considering
them as the limits of internal and external polygons. In
these experiments A denotes the number of cubic centi-
metres of caramel solution mixed with water, B the length
of the column, and C the number of cubic centimetres
thence derived by calculation. In one experiment the mean
of four trials for the greater limit gave 2°83 cm. ; and the
mean of four trials for the smaller limit gave 2°65. Hence
the result will be as follows (standard solution contains
F2

68 DR. JAMES BOTTOMLEY ON COLORIMETRY.

10 cub. c. of caramel in 500 cub. c. of water, length of
column 21*2 cm.):—

A B C
80 2°74 77°4

The above result was obtained by using the right eye
alone. I made another series of determinations, using the
left eye alone. For the greater limit the mean of four
trials was 2°85; and for the smaller limit the mean of four
trials gave 2°58. Hence the result will be as follows
(standard solution same as last) :—

A B C

80 275 732
I next made some experiments with stronger solutions.
For the greater limit the mean of four trials gave 2°78, and
the mean of four trials for the smaller limit 2°68. Hence
the results were as follows (standard solution 40 cub. e.
of caramel solution im 500 cub. c. of water; length of
column 21'2; observations made with right eye only) :—

A B Oa

320 DFS 310°6
I also compared a solution containing 320 cub. c. with
another solution containing 10 cub. c.: the theoretical
length was 0°65 cm.; a column between 0°6 and 0°7 would ©
satisfy ; but the meniscus rendered the exact determination
difficult. I also made a further experiment with the
solution containing 40 cub. c.; one determination for the
greater limit gave 5°7, and one determination for the
smaller gave 5. Hence the results are as follows
(standard solution 10 cub. c.in 500 cubic c. of water,
length of column 21°2 cm., observations made with right
eye) :—

A B C

40 5°35 39°6

DR. JAMES BOTTOMLEY ON COLORIMETRY. 69

Thus the result is very near.

The solutions of caramel ought not to be kept many days.
After the lapse of twelve days some of the solutions were
turbid and unfit for comparison, owing to the development
of vegetable organisms. It seems very probable that even
with large differences between the lengths of the columns
and with larger quantities of colouring-matter the relation
gt=constant is valid when the colour is constant. But
suppose the colour to vary, what will be the connexion
between the quantity of colouring-matter, the length of
the column, and the intensity of colour? If g denote the
quantity of colouring-matter per unit of length, and ¢ the
total length, we have the relation gt=c if the colour be
constant ; but if the colour vary, ¢ will be a function of
the transmitted light. Hence

e=f (1)

if T denote the transmitted light, therefore gt=f (T), or, as
we may write it, T=¢(gt), the probable form of this func-
tion may be obtained as follows :—Suppose we have two
perfectly transparent cylinders of unit area and a fluid of
such a nature that, if in any portion of it we dissolve some
colouring-matter, on further addition of the fluid no
decomposition takes place. Suppose we have a standard
solution containing one unit of colouring-matter per unit
of volume. If the colouring-matter remain constant in
quantity, then the intensity of the light will be a function
of the length of the column of fluid only, say y(t); and if
the length of the column of fluid remains constant, the
intensity of light will be a function of the quantity of
colouring-matter only, say $(g). Suppose now that into
the cylinders (which we may distinguish as A and B) we
pour a unit length of the standard fluid ; then the light trans-
mitted will be the same in both ; hence we shall have T=

70 DR. JAMES BOTTOMLEY ON COLORIMETRY.

(1)=¢(1). Dissolvein A another unit of the colouring-
matter, and make the column of the standard solution two
units long in B; the colour will remain the same; hence
we have (2) =¢(2). If we dissolved three units in A and
made B three units long, we should again find y(3)=(3),
and generally y(n)=¢(n). If, then, we know w(n), we
shall obtain ¢(n). For the intensity of light transmitted
through a column 2 units long, Sir John Herschel has
given an expression (to which I have referred in a previous
paper) of the form

Sak"

k being the intensity of light passing through a unit thick-
ness, a the intensity of the incident light, and the summa-
tion having reference to the composite nature of light.
This formula is given by Herschel in the ‘ Encyclopedia
Metropolitana,’ also in an article on the absorption of light
by coloured media in the ‘Transactions of the Royal
Society of Edinburgh.” In neither of these works do I
find the experimental confirmation of the formula. It
appears to have been obtained a priori. If we assume its
accuracy we shall obtain for d(n) the expression ak”, if we
suppose we are dealing with homogeneous light; if we
substitute g for we shall obtain ak? for the intensity of
light which has passed through a unit length containing ¢
units of colouring-matter. We may now suppose the
length to vary: for two units of length the expression will
be a(k?)* for three a(k?)? and for ¢ units a(k?)’. Finally,

if we suppose that there are various kinds of light, we have
ae

as a probable expression for the intensity of light passing
through a column ¢ units long and containing g units of
colouring-matter per unit of length. I think that in many

DR. JAMES BOTTOMLEY ON COLORIMETRY. 71

cases where the relation gt=constant fails, it may be
traced to some decomposition having taken place, or to
some change effected by light. For example, I commenced
some experiments with ferricyanide of potassium; but as it
did not prove a suitable salt for making experiments
without some special precautions with regard to the action
of light, I discontinued them. As I am not aware that
any one has particularly noticed this darkening, a few re-_
marks may be interesting. A standard solution was pre-
pared containing 0°8 gram in 500 cub.c. In the afternoon
having occasion to use this standard for comparison with
another, the result was not satisfactory, owing to its trans-
parency not being so perfect as when freshly made. On
the following morning I made a fresh standard solution
of the same composition ; it differed from the old in being
more transparent, and I thought that it had more of a
greenish tint. This new solution being left on the table
before the window, after a time became of diminished
transparency ; also on looking down into the cylinder a
very faint red cloudiness was perceptible. _ I also compared
a solution containing 3°2 grams in 500 cub. c. which had
been freshly prepared with a solution containing 6°4 grams
in 500 cub. c.; this solution had been prepared on the
previous day and had, been exposed to light during that
interval. I found the length of the column indicated by
theory decidedly too great; it occurred to me that the
discrepancy was due to some action of light on the ferri-
cyanide. About six o’clock in the afternoon I again com-
pared these solutions ; the theoretical length gave a colour
which was still too dark, but the disparity of colour was
not so marked as at first. The comparison was also dis-
turbed a little by the slightly diminished transparency of
the weaker solution.

I now prepared a fresh solution, contaming 6°4 grams

72 “DR, JAMES BOTTOMLEY ON COLORIMETRY.

in 500 cub. c., thinking that when we work with solutions
which vary gradually in colour we are apt to forget the
initial condition. This new solution seemed quite different:
from the old one of the same strength. The latter was
much darker and browner. So great was the difference
that 9‘ cm. of the old seemed as dark as 22°5 of the new.
To find whether the darkening was due to the action of
light or to some intrinsic cause, I divided the newly made
solution into two equal columns. One [ left on the table
before the window ; the other I kept in a cylinder which
was closely invested with black cloth. After the lapse of
six hours [compared them. The one exposed was so much
darker that 5 cm. of the exposed solution gave a tint as
deep as 10°9 cm. of the unexposed. This observation was
made on the Saturday. On midday of the following
Monday, when I again compared them, the darkening had
evidently increased ; for 3 cm. of the exposed solution gave
a tint about as dark as that furnished by 10°9 cm. of the
unexposed.

Wishing to ascertain whether keeping in the date would
reverse the action of light, on Saturday, May 24th, I took
a solution containing 6°4 grams in 500 cub. c., the solu-
tion having been prepared three days previously and
darkened by exposure during that interval to light. The
containing cylinder was closely invested with black cloth
and kept ina dark closet. On the morning of the following
Monday I thought that it appeared not quite so dark asat
first; and on the evening of the same day I thought it a
little lighter than in the morning. After keeping it in the
dark for a week I found that it had become much lighter ;
and on June 4th, when I examined it again, it seemed
nearly as light as a freshly prepared solution; there was,
however, a minute quantity of precipitate.

From these results it is evident that in some cases

DR. JAMES BOTTOMLEY ON COLORIMETRY. 73

special provision must be made to avoid needless exposure
to light in quantitative determinations by colorimetry, or
in studying the laws of the absorption of light passing
through coloured solutions.

I also made some experiments with chromate of potash.
This I thought a stable salt suitable for experiments.
Nevertheless some of the results were not satisfactory when
one cylinder contained a solution which was several times
stronger than the other. For instance, a standard solution
was made containing 0°8 gram in 500 cub. c. of water.
Another solution compared with this gave the following
results :—

A B 6)
6°4 3°7 4°5865

A repetition of the experiment gave nearly the same result
namely 3°6 for the length of the column.
It occurred to me that possibly, when potassic chromate

3

is diluted, there may be liberated a minute quantity of
chromic acid, which would increase its absorbent power ;
this might be inferred from the greatly increased absorbent
power imparted to the bichromate by the additional mole-
cule of CrO,. I therefore took the cylinder containing the
standard solution used in the last experiment, and divided
its contents into two equal columns: to one I added a few
drops of ammonia ; this column became slightly but per-
ceptibly lighter than the other, so that I have little doubt
some change had been effected in the constitution of the
dissolved salt. The hypothesis of the liberation of a little
chromic acid is, I think, strengthened by the fact that a
solution of the salt is of a deeper yellow than the undis-
solved salt. J think that probably a trace of carbonic acid
in the water had liberated a little chromic acid.

To try what the effect of the addition of a little weak

74: DR. JAMES BOTTOMLEY ON COLORIMETRY.

acid would be, I took a solution containing 1°6 gram in
500 cub. c. and divided it into two equal parts. To one I
added a little extremely dilute sulphuric acid. The colour
of this portion became decidedly deeper than that of the
other. I also tried what would be the effect of the addi-
tion of a little ammonia to a strong solution; so I divided
the solution containing 6°4 grms. in 500 cub. c. into two
equal portions. One I treated with ammonia: this I
thought a little lighter than the other; but the difference
was very slight. This, however, we might expect ; for any
small change of intensity would be less noticeable in a
strong solution than in a dilute one.

I now made some fresh experiments with Grama of
potash, a little ammonia being added to both columns.
The mean of four trials gave for the greater limit 3°35 ;
and the mean of four trials gave for the smaller limit 2°18.
Hence the result will be as follows (standard solution 0°8
gram in 500 cub. c. of water; length of column 22°5):—

A B Cc
6"400 2°77 ; 6:498

In this experiment I used the right eye. The theoretical
length is 2°81; and the above result is therefore a near
approximation. |

With the same solutions, on the following day (June
26th) the results were not so favourable; the mean of
eight trials gave 2°57 cm. as the length of the equivalent
column, the left eye beimg used in the determinations.
On the next day (June 27th) I repeated the experiments
with these solutions, using the right eye; the mean of
four trials gave 2°3._ To each solution I added 5 cub. c.
of ammonia, and repeated the experiment ; the mean of
four trials gave 2°13 as the result. These differences of
results are probably due to some internal changes in the
coloured fluids.

ON THE ORIGIN OF THE WORD CHEMISTRY. 75

I may also take this opportunity to correct two numeri-
cal errors in the sixth volume of the Society’s Memoirs.
Page 262, line 3, for 3°2 read 2°2; and on page 264, line 2,
for 15 read 50.

IX. On the Origin of the Word “Chemistry.”
By Caru Scnortemmer, F.R.S.

Read November 18th, 1879.

CHEMISTRY as a science is first mentioned* by Julius
Maternus Firmicus, a native of Sicily, and procurator under
Constantine the Great. He wrote, about a.p. 336, a work
on Astrology, which has been preserved only in a defective
state, and is commonly known by the name of ‘ Mathesis.’

In this work he states that by observing the position of
the moon, in respect to certain heavenly bodies or con-
stellations, at the hour when a child is born, its future
inclinations can be predicted. He continues :— Et si
fuerit haec domus Mercuri, astronomiam. Si Veneris,
cantilenas et laetitiam. Si Martis, opus armorum et
instrumentorum. Si Jovis, divinum cultum et scientiam
in lege. Si Saturni, scientiam alchimiae. Si Solis, pro-
videntiam in quadripedibus. Si in Cancro domus sua,
scientiam dabit omnium quae exeunt de aqua’’y.

Other editions of this work have also “scientia alchi-
miae”{; but Vossius informs us that in the manuscripts it

* Kopp, Beitrage zur Geschichte der Chemie, p. 43.

+ Julius Firmicus de nativitatibus. Ed. Simon Bevilaqua: Venice, 1497.

¢ Ed. Aldus Manutius, Venice, 1499; Ed. Nicolaus Brucknerus, Bile,
1533-

76 ; MR: C. SCHORLEMMER ON THE

is “ chimie ” *,- He says :—‘“‘Alchimiz scientiam nominat
Firmicus, lib. iii. cap. xv. Ita quidem editum ab Aldo, sed
in chirographis est chimize.”’

Athanasius Kircher also states that the manuscript in
the library of the Vatican has “ chymiz,” and not “al-
chymiz ”’}.

Firmicus does not give any explanation of this term.
However, another writer, who probably lived at the same
time, if not earlier, explains it. Zosimus, the Panopolite,
according to Georgios Synkellos, a writer of the ninth
century, states that ynuwela (or yupeia, as some manu-
scripts have) meant the art of making gold or silvert.

The curious passage in which the word occurs is the
following :—

“The sacred Scriptures inform us that there exists a
tribe of genii who make use of women. Hermes mentions
this circumstance in his Physics ; and almost every writing
(Adyos), whether sacred (pavepos) or apocryphal, states
the same thing. The ancient and divine Scriptures inform
us that the angels, captivated by women, taught them all
the operations of nature. Offence being taken at this,
they remained out of heaven, because they had taught
mankind all manner of evil, and things which could not
be advantageous to their souls. The Scriptures inform
us that the giants sprang from their embraces. Chema is
the first of their traditions respecting these arts. The
book itself they called Chema; hence the art is called
Chemia.”

It is not difficult to trace the origin of this myth. We
find it first in Genesis, chap. vi.: “And it came to pass,
when men began to multiply on the face of the earth, and

* Htymologicon lingue latins: Amsterdam, 1695.
t Kopp, op. cit. p. 9.
t Thomson’s History of Chemistry, p. 5.

ORIGIN OF THE WORD CHEMISTRY. Ve

daughters were born unto them, that the sons of God saw
the daughters of men that they were fair, and they took
them wives of all which they chose.

“There were giants in the earth in those days; and
also after that, when the sons of God came in unto the
daughters of men, and they bare children to them, the
same became mighty men, which were of old, men of
renown.”

Alluding to this, later writers state that the fallen angels
taught women all the secrets of nature*. That one of
these is the art of making gold and silver, however, is first
mentioned by Zosimus. Other Greek writers use the
word Chemia or Chymia in the same sense; in print we
find it first in the Lexicon of Suidas, who lived in the
eleventh century, and defines ynueta as “the preparation
of gold and silver.”

All the earlier Greek writers who mention this word
were in close connexion with the university of Alexandria ;
from this it has been inferred that the artificial preparation
of the noble metals was first attempted in Egypt.

That country was conquered by the Arabians in 640.
Here they made undoubtedly their first acquaintance with
chemical science ; they prefixed their article to the Greek
name, and thus introduced the terms Alchemy, Alchimy,
or Alchymy.

The origin and meaning of these terms have often been
discussed. Plutarch states that the old name of Egypt
was ynula, that it was so called on account of its black
soil, and that the same word designated the black of the
eye. From this the conclusion has been drawn that
chemistry originally meant the science of Egypt, or, the
black of the eye being the symbol of darkness and mystery,
that chemistry was the secret or black art. But alchemy

* Kopp, op. cit. p. 4.

78 MR. C. SCHORLEMMER ON THE

has never been called the black art, a name which was
exclusively reserved for magic or necromancy.

It has also been stated that the name was derived from
the Arabic kema, to hide; while others have maintained
that the founder of our science was Cham or Ham, the
son of Noah, or an Egyptian king with the name of Chem-
mis. It has further been suggested that the name of the
science was derived from yéwo (to melt), or from yupos
(juice or liquid).

To this it has been objected that the original spelling
was ynwela and not yupela, which, although Hermann
Kopp, the great historian of chemistry, inclines to this
view, has not yet been proved satisfactorily. Humboldt
believes that the latter word got into some manuscripts by
a mistake of the transcriber, and continues :—-“Alchimy
commenced with the metals and their oxides, and not with
the juice of plants.” This objection, however, cannot be
maintained at all, because vegetable juices, or, at least,
substances designated by their names, are mentioned by
the older alchemists as the most potent substance by which
transmutations could be effected *.

Some time ago my friend Professor Theodores called my
attention to an interesting paper on this subject, published
by Professor Gildemeister +, m which he maintains the
derivation of the word chemistry from yuuos. According
to him kimiyd in Arabic does not originally have an
abstract meaning, and is the name, not of a science, but
of a body by which, or rather by a substance obtained
from which, the transmutation of metals is effected; it is
synonymous with iksiv. Alchemy, as a science, was called
the preparation of kimiyd or ikstr, also the science of the
preparation of kémiyd, or, more shortly, science of kimiyd.

* Kopp, op. cit. p. 76.
+ Zeitsch. deutsch. morgenland. Ges. xxx, p. 634.

ORIGIN OF THE WORD CHEMISTRY. 79

In the Arabie Lexicon (QAmis) al-iksir is explained by
al-kimiyd, and the latter again by the former, or by any
medium which, applied to a metal, transports it into the
sphere of the sun or the moon, i. e. converts it into gold
or silver.

Even to this day the word is used in the concrete sense ;
Kotschy* relates that the pasha of Nicosia talked much
of flowers, chiefly kimia, a plant having the property of
converting metals into gold.

The later writers, however, called the science shortly
al-kimiyd, and retained the term al-iksir (elixir) for the
transmuting medium or the philosopher’s stone. This
latter word is identical with Enpiov, as the writers of the
Alexandrine school called the philosopher’s stone+; while
the same name was employed by the physicians for a
healing powder used for sprinkling over wounds, 7. e. a
desiccative powder (from &npds, dry)t.

Now the correlate to dry is moist or liquid, yuuos; and
from this is derived yupela, a moist substance corresponding
to AvHeta, a material formed of AéOos, or Kepapeta, the
occupation with cépayos.

Ibn Khaldtin, who lived in the 14th century, says that
from the philosopher’s stone a liquid or a powder might
be prepared called ikstr, which, when thrown on molten
copper converted it into silver, and molten silver into gold.
In opposition to its etymology the word is here used for a
liquid, because at that time kiémiyd no longer meant the
transmuting substance, but the science of transmutation ;
and this explains why today we may understand by “elixir”
a liquid.

* Petermann’s Geog. Mitth. viii. p. 294.

t Kopp. op. cit. p. 209.

} Zosimus calls the substance by which copper is tinged yellow or con-

verted into brass 7d did ris Oov9ias Enptoyv, a powder prepared by means of
tutia ; now tutia (zinc oxide) is still today used in medicine as a desiccative.

80 DRS. SCHUSTER AND ROSCOE ON

We also find that the philosopher’s stone is often called
“the red tincture,’ from tinguo (to moisten).

It appears therefore very probable that the name of our
science is derived from yuuwos; and the proper spelling
would therefore be Chymistry, as the ‘Times’ newspaper
for a long time insisted. As, however, this derivation
has not yet been proved quite satisfactorily, the time-
honoured term Chemistry will remain in use, and, I think,
be retained even if it should be shown that yupeta was the
original spelling.

X. Note on the Identity of the Spectra obtained from the
different Allotropic Forms of Carbon. By ArtHuR
Scuuster, Ph.D., F.R.S., and H. E. Roscoz, LL.D.,
P.R.S.

Read December 2nd, 1879.

SPECTRUM analysis serves as our most delicate test of the
chemical constituents of a substance. Hence it appeared
not uninteresting carefully to examine the nature of the
spectra obtained by the combustion of natural graphite
and of diamond in a vacuum of pure oxygen, and to
compare the spectra thus obtained with the well-known
spectrum of carbonic oxide obtained from charcoal. The
preparation of such an oxygen-vacuum which shall yield
an oxygen spectrum exhibiting no other lines than those
of oxygen is a matter of considerable difficulty. The
slightest trace of any impurity containing carbon produces
the spectrum of carbonic oxide. For this reason the use
of caoutchouc tubing and of greased stopcocks must
altogether be avoided, and thus the experimental diffi-
culties are considerably enhanced.

ALLOTROPIC FORMS OF CARBON. 81

In order to obtain a spectrum of pure oxygen entirely
free from the lines of carbonic oxide, a necessary prelimi-
nary condition of our experiment, the following arrange-
ment was made. The figure exhibits
the form of the tube employed. The
part from A to 5B consists of an
ordinary Pliicker’s tube. At the
lower end of this a piece of hard
glass tubing (d) was sealed. Before
the experiment, the requisite quan-
tity of permanganate of potash or
oxide of mercury was brought into
this, to serve as the source of the
oxygen, and then the tube was sealed
at the lower end.

The other end of the Pliicker’s
tube was closed by a ground-glass
stopper (S), through the sides of
which two stout platinum wires (pp)
were fused, and these were joined
together within the tube by a spiral
of fine platinum wire (e), into which
the graphite or the diamond was
placed. To prevent leakage be-
tween the ground sides of the stopper
and those of the tube a drop of
mercury, rendered less fluid by the
immersion in it of a bit of tin foil,
was introduced into the joint. The
tube was placed in connexion with
the air-pump by means of a side
tube sealed on at (C). For this
purpose a Sprengel pump was used,

to which the side tube was herme-
SER: III. VOL. VII. G

82 ON ALLOTROPIC FORMS OF CARBON.

tically sealed. In this way, and in this way only, was it
found possible to obtain a pure spectrum of oxygen.
After the connexion with the pump had been made, the
whole tube was exhausted, and then the substance con-
tained in the hard glass tube was heated. The oxygen
which is given off was then removed by the pump, the
tube filled a second time with oxygen, this again removed,
and this process repeated over and over again, until at last
no other lines but those of oxygen are seen when the
spark from an induction-coil passes between the electrodes
(g and h).

When this stage had been reached, and when especially
no trace of the carbonic oxide bands could be seen in the
tube, the platinum spiral (e) containing either the diamond
or the graphite was rendered incandescent by means of an
electric current.

The spiral contained sometimes a piece of natural
graphite, sometimes a Cape diamond; but the result was
the same in the two cases. As soon as the platinum
spiral had been sufficiently heated, a channelled-space
spectrum appeared in the capillary part of the tube. This
channelled-space spectrum was carefully compared with
the spectrum of carbonic oxide obtained from charcoal
and found to be identical with it. No band or line could
be seen in the tubes thus prepared which was not also
seen in a tube containing carbonic oxide. The spectrum
which appears when a Leyden jar is introduced into the
circuit is different ; but here also we found that every line
was due either to oxygen or to carbon. ‘Two lines were
seen in the green and greenish yellow which are not con-
tained in any map of the spectrum of carbon or of oxygen,
lines which had not been seen in a great many oxygen
tubes prepared and examined by one of us. But it was
found on further investigation that these are really

oe nites ee ee

ON THE ANAL RESPIRATION OF THE COPEPODA. 83

oxygen lines, which only appeared at very high tempera-
tures. The capillary portion of the tubes we used was
much shorter than that in the ordinary Pliicker’s tubes,
and this accounts for the temperature of the incandescence
being higher than usual. As one of the lines is near
the unknown aurora line, its wave-length was determined
and found to be 5591, showing it to be decidedly less
refrangible than the aurora line.

The experiment was repeated in four different tubes
and many times in each tube; but whether graphite or
diamond was employed, no line was seen which was net
also obtained in a tube of the same dimensions containing
carbonic oxide.

XI. On the Anal Respiration of the Copepoda.
By Marcus M. Harroe, M.A., B.Sc., F.L.S.

Read December 16, 1879.

In a note on Cyclops read at the British Association I
pointed out that its respiration was exclusively anal. I
have now made out the same in Canthocamptus (fam.
Harpacticide) and Diaptomus (fam. Calanide). In all
three the mechanism is the same; at regular intervals,
after the backward sway of the intestine, the anal valves
open for an instant and then close, giving just time for
a slight indraught of water after the opening, a slight
expulsion at the close. The necessary pressure to confine

the animal seems to interfere somewhat with these move-
G2

84 MR. M. M. HARTOG ON THE ANAL

ments, sometimes stopping them if excessive; hence I
refrain from noting with illusory exactness the intervals
between each respiratory movement.

It is to be noticed that the rectum contains, as a rule,
liquid only, the bolus of feeces remaining in it but a short
time. By endosmose the liquid in the rectum will tend
to be at the same condition of gaseous saturation as the
body fluid around it, kept constantly agitated by the
backwérd-and-forward sway of the stomach. During
the short interval that the anus is open an approach to
gaseous equilibrium with the external water takes place,
even despite the very slight movement of the water (shown
by the little change of place undergone by suspended
indigo or carmine particles). In the absence of any other
suitable respiratory apparatus, no one can hesitate as to
the function of the action I have described.

In the Nauplius larvee of Cyclops and Diaptomus the
working is slightly different. The rectum is a_sub-
spherical muscular sac, which at regular intervals contracts
so as to leave a linear cavity (along the long axis of the
animal), and immediately dilates, sucking up the water
from without.

An anal respiration, such as that of Cyclops, is found
widely among Crustacea—even those which have well-
developed gills like Astacus, which is one of the highest
forms. It has been demonstrated in Phyllopoda and
Cladocera, and is here probably the exclusive mode im
Leptodora, as shown by Weismann. That it is therefore
primitive, and should be expected to occur in the primitive
or at least very generalized group of the Copepoda, is an
obvious deduction. Hence I anticipate that the homeo-
morphic Zoea larve of the Decapoda will prove to have
this same mode of respiration.

If there be any connexion between Rotifers and Nau-

RESPIRATION OF THE COPEPODA. 85

plius, it is easy to make out the origin of the arrangement
in the latter. The ciliated funnels and lateral canals of
the former can only be of service when there is a thin
unchitinized anterior surface through which water can
transude into the celom: by the extension of chitiniza-
tion over the whole surface these organs lose their func-
tion and abort, while tbe cloacal “contractile vesicle”
takes on an inspiratory as well as an expiratory function,
and becomes more or less confounded with the,rectum,
from which probably, even in Rotifers, it takes origin.

Here must be noticed the wide diffusion of anal respira-
tion in aquatic insect larve (alternate inspiration and
expiration by the pumping movements of the rectum).
This would point to a common origin with Crustacea.

A list of the groups in which anal respiration is made
out may be added.

VERMES:

Rotifera.
Gephyrea.
Oligochzta Limicola.

EcHINODERMATA:
Holothuroidea.

ARTHROPODA:

Crustacea (general).
Insecta (most aquatic larve).

86 MR. D. WINSTANLEY ON THE RADIOGRAPH.

XII. The Radiograph. By D. Winstan.ey, F.R.A.S.

Read January 13th, 1880,

I nave described already one of the several arrangements
which I have devised for the automatic registration of the
solar radiance*. The instrument in question places a lead
pencil on a sheet of paper and writes down therewith
when and for how long the sun may chance to shine, but it
makes no record of the intensity of his rays. I will now
ask your attention to the description of another and much
more perfect apparatus, one which continuously records
the intensity of thermal radiation to which it is exposed.
This instrument I have called the “ radiograph.” It con-
sists essentially as follows :—A differential thermometer of
which the stem is circularly curved is mounted concentri-
cally upon a wheel of brass in a groove cut with that
object for its end. This wheel is supported with its plane
in a perpendicular position by a knife-edge of hardened
steel, which passes through its geometric centre and rests
on agate planes. The tube of the thermometer is partly
filled with mercury (preferably through half its curve), and,
for the reason given in my description of the simple sun-
shine-recorder, to which I have alluded, a little sulphuric
acid is introduced as well. If we now arrange it that the
centre of gravity of the solid portion of the system here
described shall be below the surface of the planes on which
it turns (and the apparatus is provided with adjustments
by means of which the point in question can be moved) it
is clear that the arrangement may be made to swing in
* Proceedings of Manchester Lit. and Phil. Soc., Noy. 18th, 1879.

MR. D. WINSTANLEY ON THE RADIOGRAPH. 87

pendulous oscillations, notwithstanding the presence of
the liquids it contains; for these remain substantially at
rest whilst the tube which holds them does, in fact, slide
over them (and with very little friction too) in swinging
to and fro through arcs of the circle of which its parts
are curves. Both bulbs of the thermometer are closed.
It is obvious therefore that the tension of the air or gas
which they contain will be uninfluenced by the barometric
variations of the outer air, the temperature of which latter
being experienced equally in each bulb will also leave the
equilibrium of the apparatus undisturbed. When, how-
ever, one bulb is more heated than the other, the air con-
tained therein will press more strongly on the heavy
liquid piston in the tube and wheel the swinging portion
of the system round until a fresh position of equilibrium
is gained, and this will be (providing that the centre of
gravity of the system has previously been made coincident
with the point on which it turns) when the tension of the
gases is equal in both bulbs. In fact, in so far as now
described, the instrument is a differential thermometer,
and is that alone—differing in this from Leslie’s, that it is
a solid and accessible portion of the thing which moves
and not the liquid it contains. When, however, one of the
bulbs is blackened and the other one is silvered or left
clear, the apparatus becomes a “radiometer” in the
proper meaning of the term*—that is to say, a measurer of
the thermal radiance to which it is exposed and the inten-
sity of which it indicates by variations in the angular posi-
tions of a needle prolonged from one or other of the radii
of the wheel.

It is only needful now so to arrange it that this needle

* The “radiometer” of Crookes should in its simple form have been
called a ‘‘ radioscope,” as it merely makes visible the effects of radiance, but
does not measure their amount.

88 MR. D. WINSTANLEY ON THE RADIOGRAPH.

shall make a tracing of its curves on a cylinder driven by
clockwork at an even speed, and the “‘ radiograph” is
complete.

Concerning the actual instrument I use, its wheel is
--2 inches in diameter, and the weight thereof a trifle
more than two pounds. The other portions of the appa-
ratus are of the same dimensional proportions as are indi-
cated in the sketch. Of course some delicate method of
recording has to be employed, and I have thus far used
the smoked-paper process so much adopted in the obser-
vatories of France. In this way the “ radiograms”’ which
illustrate this paper were obtained.

When using the instrument to record the radiance of
the sun, I have hitherto exposed it in a box of copper sur-
mounted by a dome of glass into which the bulbs of the
thermometer project. The line which joins them is in the
plane of the meridian of the place and the black bulb to
the north. The box itself is supported, at an elevation of
four feet or thereabouts, upon a stand of wood, the legs of
which are fimly embedded in the ground. The stand
itself is located at the extremity of a garden which over-
looks a valley and the sea. A small window in the box
permits the movements of the train to be seen and the
promptness with which the apparatus acts to be observed.
If a cloud “no bigger than a man’s hand,” and “ light
as a feather” in its texture, floats before the sun, and
occupies but three or four seconds in its transit, its pre-
sence, the duration of its passage, and the degree of
thermal obscuration it effects are at once set down.

The cylinder of the radiograph passes over a space of
875 of an inch per hour, a somewhat open range; but, as
will be seen on reference to the tracings, the needle often
moves for some considerable distance in both directions
along the same thin line, thereby showing a practical

MR. D. WINSTANLEY ON THE RADIOGRAPH. 89

if
| -
AAW (| MAS

90 MR. JOSEPH JOHN MURPHY ON AN

instantaneity of action under very ordinary thermal
changes in the radiance from the sky. The influence of
the sun’s rays at daybreak is almost always shown, for
some minutes at any rate, before the sun is seen, and
occasionally, it would seem, even for hours before his time
to rise.

It is not, however, now my purpose to dwell upon the
interesting changes which take place in the intensity of
the thermal radiance from the sky, my present object
being to describe an instrument by means of which they
may be recorded or observed. Doubtless in several of its
details the “radiograph”? may be improved, notably in
the condition of its bulbs, and it would unquestionably be
better if it computed for itself the areas included by its
curves. This, I dare say, I shall presently enable it to do.
Meanwhile, as a recorder of the duration and intensity of
radiant heat, the instrument, so far as I have seen, is the
only one whose readings are uninfluenced by the tempera-
ture or the pressure of the air.

XIII. On an Extension of the ordinary Logic, connecting
it with the Logic of Relatives. By JosrrH Jonn
Mourruy, F.G.S. Communicated by the Rev. Roprerr

Harzey, F.R.S.

Read October 7th, 1879.

—

Tux present paper has been suggested by the section on
Elementary Relatives in Prof. Pierce’s “ Description of a

EXTENSION OF THE ORDINARY LOGIC. 91

Notation for the Logic of Relatives,” extracted from the
Memoirs of the American Academy, vol. ix.

In applying algebraic notation to the ordinary logic, in
however extended and generalized a form, the terms
denote objects and classes of objects; there is no need of
terms denoting relations between these ; and the ordinary
logic, as generalized and extended by Boole and Jevons,
has consequently been called the logic of absolute terms.
Nevertheless all logic belongs to the logic of relatives.
The logic of relatives is related to the ordinary logic, not
as relative is related to absolute, but as the entire science
is related to its simplest part. It is im accordance with
all analogies drawn from the history of science, that the
simplest part of a science should thus be studied alone and
brought to comparative perfection, before any one suspects
that its problems are not isolated, but constitute only the
simplest part of an infinitely wider subject.

From the present point of view, the old logic is defined
as that part of logical science which deals with the rela-
tions of inclusion and exclusion.

In order to exhibit inclusion as a particular case of re-
lation, we shall need a symbol for it. De Morgan uses L
as the symbol of relation generally, and I propose to use
L in this sense, keeping the Roman capitals for absolute
terms.

Combination in logic is analogous, though not closely
so, to multiplication (see Boole and Jevons, passim).
What is the corresponding mathematical analogue of
logical relation? The Rev. Robert Harley maintains that
it is function generally (see the British Association Trans-
actions, 1866 and 1870); and I have no doubt he is
right. But within the very limited scope of the present
inquiry it will not be misleading if we treat relation as
analogous, though not closely so, to ratio, and the sym-

92 ; MR. JOSEPH JOHN MURPHY ON AN

bols of relation, consequently, as analogous to numerical
coefficients.

In mathematics, if any one of the following four equa-
tions is true, the rest are true :—

A
B SUs — 3 (
ATE > isl; A.

The same is true in logic if A and B are understood to be
the names of any two individuals or classes, LZ the relation
of A to B, and Z—' the inverse relation of B to A. Let
L, for instance, be the relation of teacher, then the fore-
going equations are thus interpreted :—

The relation of A to B is A is the teacher of B.
that of teacher.
The relation of B to A is B is the pupil of A.

that of pupil.

The equivalence of these four forms has the same kind
of self-evidence as the principle of identity and contra-
diction.

It is to be observed that we use the copula = with the
meaning of the word is, without raising the question
whether there may not be many individuals standing in
the relation LZ to B, and many standing in the relation
L-to A. Ifit is required that the equation

A=LB
shall mean that A is the only teacher of B, then the as-
sertion that A is one of the teachers, or a teacher of B,
without implying whether B has other teachers or not,
will be expressed by

A AEB,
and its converse by

B=BL "A.

EXTENSION OF THE ORDINARY LOGIC. 93
If A and B are both pupils of M, their relation is that
of fellow pupils of M. This relation is expressed by
IM
LM’
equivalent in arithmetic to
(LM)’,
which expression we shall adopt. In arithmetic, every
term with zero index has the value of unity, so that if

A :
== (EM)
we may eliminate, or drop, M, and write >
A fe}
BT :

In logic we may eliminate in the same way ; that is to
say, if A and B are fellow pupils of M, they are fellow
pupils. But it is not true in logic that all terms with
zero index have the same value; and from

Baa:
we cannot infer that
A
ES (ZM)°.

We may drop at pleasure the absolute term M, but we
cannot insert or substitute a term, nor can we drop the
relative term LZ. ‘This is analogous to the rule that in the
logic of absolute terms, if
A=ABC,
it follows that
A=AB and A=AC.
But though we can thus drop a factor we cannot insert or

substitute one; from
A=AB.

94, MR. JOSEPH JOHN MURPHY ON AN ~

we cannot infer either
A=ABC,
or

A=AC.

But though in logic a relative term with zero index is
not necessarily equal to unity, yet every such term has
two important properties which belong to unity and are
not combined in any other number—namely, that it is
equal to its own reciprocal, and equal to its own second
power. Thus if

A= PB,
it follows that
B=L°A.

That is to say, if Ais a fellow pupil of B, then Bisa
fellow pupil of A. And if

A=L°M and M=L°B

it follows that
A (0S) ss.

That is to say, if A is a fellow pupil of B and B of C,
then A is a fellow pupil of C. This inference is a syl-
logism, the middle term, M, being eliminated. It must
be observed that its validity depends on the relation of
fellow pupils being understood in relation to the same
teacher throughout. With this convention, the axiom
that “fellow pupils of the same teacher are fellow pupils
of each other” has the same self-evidence as the axiom
that “ equals of the same thing are equals of each other ;”
and both are cases of Jevons’s principle of the substitution
of similars, that “what is true of any thing is true of its
like.”

We now proceed to apply these principles to the old
logic. The proposition of the old logic, “all A is B,” is

EXTENSION OF THE ORDINARY LOGIC. 95

expressed in our system by “ A is included in B.” Using
Las the symbol of inclusion, we write it

A=ZLB.

Its converse is “ B is included in A ;” and this we express
by

B= La
In the old logic,
All A is B
becomes, by conversion,
Some B is A.

But this is an inadequate and indeed an inaccurate ac-
count of the subject, because, when reconverted,

Some B is A
becomes only
Some A is B;

so that by reconversion we do not get back the original
proposition, which by any satisfactory theory of conversion
we ought to do.
We postulate that
Ewe

This is not true of all relations, but it is true of many,
and among others of inclusion. When asserted of that
relation, it means that if A is included in M, and M in B,
then A is included in B; or, more briefly, the enclosure
of an enclosure is an enclosure. This is the expression in
our system of the canon of the old “ syllogism in Barbara.”
And conversely,
(Ly =L";

that is to say, the includent of an includent is an in-
cludent. These words, enclosure and includent, will be
found useful.

96 MR. JOSEPH JOHN MURPHY ON AN

From the premises

A=L[-™, Bes Ne
we can, as has been shown, infer that
Naa Se Seana
La Vie (L M) 2

whence
Nba Sula
If LZ means inclusion, then the meaning of the syllogism
is as follows :—

A is an includent of M ;

B is an includent of M ;

therefore A is a co-includent with B of M;
or A is a co-includent with B.

This is no more than the old logic would express by the
following :— |
Mis A;
Mis B;
therefore some A is B.
But if the premises are the converse of these, as follows—
A=IM, B=LM,

the conclusion will be
A=L°B;
that is to say, A is a co-enclosure with B—a conclusion
not recognized in the old logic; yet it is valid, and may be
important. Let H, for instance, mean Irishmen, W the
Duke of Wellington, and P Lord Palmerston; then from
the premises
W=LH8, P=LE,
we have the conclusion
P=(LE)W=L°W;

EXTENSION OF THE ORDINARY LOGIC. 97

that is to say, Lord Palmerston was a fellow Irishman, and
therefore a fellow countryman, of the Duke of Wellington.

As we have seen, out of the relation of inclusion three
others arise. We express the four as follows :—

A=LB, A is an enclosure of B.
Ja fee me lo A is an includent of B.
ah be A is a co-enclosure of B.

A=(L-")°B, A is a co-includent of B.

It must be remembered that when we speak of co-inclusion
or co-includence, we mean, throughout, inclusion in the
same includent, or includence of the same enclosure.
This is different from the usage of the common logic.
Where the old logicians say

| Some A is M,

Some B is M,

we express this by

=(li-"2)?,, » er =A and M are co-includents of P ;

lod Sl >

ua Lies) SNC aa 8 and M are co-includents of Q,

where P and Q are or may be different ; and from these
premises no conclusion can be drawn.

By combining the four forms of proposition stated
above, we get sixteen syllogisms, which constitute as
many syllogistic canons. Fourteen of these are conclu-
sive; that is to say, in fourteen cases the relations ex-
pressed in the two premises combine in the conclusion into
a simple relation, which is always of the same kind with
one of the four forms given in the premises ; in the re-
maining two cases they do not socombine. These sixteen
are given in the following tabular statement. As the
equations

D=L and (LF = Ee

SER, III, VOL. VII. H

98 MR. JOSEPH JOHN MURPHY ON AN

are not generally true of numbers, the conclusions of
these syllogisms are not all true in arithmetic, except
when L has the value of unity, of which the interpretation
is that the enclosure is co-extensive with its includent.
Those conclusive forms are doubly underlined which are
true in arithmetic for all values of Z; those are singly
underlined which are true in arithmetic only when L has
the value of unity; and the inconclusive ones are not
underlined. It will be seen that eight out of the sixteen
are doubly underlined.

iM Doel gt Taba

Da bf pl em OS On Wl? Wissel?

Boy ee Lip gee 02 Dem be

4. LL ")P=h 12, (1° L) = Ee
5. L-.L=(L-")° 13. -(L-)°. L=(L~)

On ha ia 4. (b>). Lt=L

7 ED. DP=L7 1s. (L7)°. L°=(L-")°. Le

Bis at. (a7)? se (Eee) 16. Ci)? . (is) oe

The truth and the applicability of the fundamental
equation of this system, namely

i

do not depend on the interpretation of Z as inclusion ;
this equation is merely the expression of the transitiveness

EXTENSION OF THE ORDINARY LOGIC. 99

of the relation; and if LZ is understood to mean any
transitive relation whatever, all the syllogisms as stated
above remain true, but with changed interpretations.
Let L, for instance, mean cause, then Z—' will mean effect,
L° concause (to use a good though obsolete word), and
(L-")° co-effect ; and let us assume that the cause of a
cause is a cause; or let

‘mean superior,
Le winterior,

I >» co-superior,
(i*)> 5 _e0-imienior ;

with either of these interpretations of our symbols, all

the sixteen syllogisms will remain true.

The interpretations of the foregoing sixteen equations

are as follows :—

CONN DN sey eS it

©

‘10.

Enclosure of enclosure is enclosure.
Enclosure of includent is co-enclosure.
Enclosure of co-enclosure is co-enclosure.
Enclosure of co-includent is enclosure.

Tncludent of enclosure is co-includent.
Includent of includent is includent.
Includent of co-enclosure is includent.
Includent of co-includent is co-includent.

Co-enclosure of enclosure is enclosure.
Co-enclosure of includent is co-enclosure.
Co-enclosure of co-enclosure is co-enclosure.
Co-enclosure of co-includent constitutes no relation.

. Co-includent of enclosure is co-includent.

Co-includent of includent is includent.
Co-ineludent of co-enclosure constitutes no relation.

. Co-includent of co-includent is co-includent.

H 2

100 ON AN EXTENSION OF THE ORDINARY LOGIC.

We have now to speak of the relation of exclusion,
which is expressed in the common logic by

A is not B;
whereof the inverse is
B is not A.

If we use N as the symbol of exclusion, the above pro-
position will be expressed by

ANB,
and

i

This relation is thus seen to be invertible; or, to express
it symbolically,
: N- ral J N,

an equation which is true of two numbers, namely 1 and
—1. Further, N is not equal to its own second power;
so that it combines these two characters, which are united in
negative unity and not in any other number, that it is not
equal to its own square, and is equal to its own reciprocal.
Consequently the following equations are true im arith-
metic as well as in logic,—N meaning in logic excludent,
and in arithmetic negative unity; N° meaning in logic
co-excludent, and in arithmetic unity, lke any other
term with zero index :—

IN N= Nee NON C= Ne
N° NING UNO RaIN CNC
The following are the logical interpretations :—
Excludent of excludent Excludent of co-excludent
is co-excludent. is excludent.
Co-excludent of excludent Co-excludent of excludent
is excludent. is co-excludent.

In this system, when we speak of exclusion and co-

ON THE WORD “ CHEMIA ” OR “ CHEMISTRY.” 101

exclusion, we imply that it is the same thing which is
excluded.

The foregoing logical equations will be equally true if
we interpret NV to mean “not related to, either as cause
or as effect,” or “ out of relation with.”

I believe I have in this paper shown an unexpectedly
direct transition from the common logic to the logic of
relatives.

XIV. The Word “ Chemia” or “ Chemistry.”
By R. Aneus Samira, Ph.D., F.R.S., &c.

Read March 23rd, 1880.

Tue meaning of the word “chemistry”’ has been discussed by
several writers recently, as well as by many in early times.
The observations made by Professor Schorlemmer and the
paper by Mr. Mactear (one at the Literary and Philosophical
Society of Manchester, and the other in Glasgow) have
caused me to return to the subject, which I had at various
times thought of. I have always considered the book of
Borrichius ‘De Ortu et_Progressu Chemiz’ (on the rise and
progress of chemistry) to have given the right direction of
thought ; and the Greek manuscripts on the subject, at least
on the sacred art, point so strongly to Egypt by the use of
the words Isis and Osiris as symbols of their mysteries
that there seemed little room for doubt.

I shall begin as if all my readers were acquainted with
the history from the 4th or 5th century according to the

102 DR. R. ANGUS SMITH ON THE

work ‘ Geschichte der Chemie, by Prof. Kopp—who must
be regarded as the writer of the most complete history,
although every one who wished to obtain the fullest know-
ledge would read also Hoefer’s ‘ Histoire de la Chimie.’

If Firmicus used the word chemia for “chemistry” so early
as the fourth century, it is clearly not an Arabic word.
We find in the ‘ Beitrige zur Geschichte der Chemie,’ by
Prof. Kopp, that it is a word not well defined by him,
although from later (still not much later) writers we find
that it refers in the same century to gold or metals. Later
still, possibly not also at a very early time, the transforming
of metals was the absorbing idea. The use of the word
went also, as we know, towards the meaning “elixir of life.”
The known tract by Democritus speaks of many chemical
subjects, whilst metals and purple dyeing are said to have
been treated by him in works not extant; and he is, by
legend at least, said to have learnt the wisdom of the Egyp-
tians as well as of the further Hast. We may take Kopp’s
period for him as being correct, viz. the fourth century.
Everywhere, as we go back, we have our eyes turned to
Egypt or Assyria.

The reason, however, for connecting Chemistry and
Egypt can have no sound relation whatever to Plutarch’s
assertion that Egypt was called Chem because of the black
soil. Neither has it to do with the “ black art,” as Dr.
Schorlemmer truly remarks—a name never connected with
chemistry, although we must remember that some (and one
may say many) individuals have combined in themselves
the magician and the chemist. The expression “black art ”
is not of extreme antiquity, so faras | know. I wasstrongly
inclined to doubt the accuracy of Plutarch, although I have
not been in Egypt, and to say that the soil is not black, and —
to think that the people were meant to be alluded to. I have
some of the mud of the Nile, brought me by a friend ; and as

WORD ‘‘ CHEMIA ” oR “ CHEMISTRY.” 103

that covers the whole of Egypt, I thought myself justified.
Besides, from the drawings of Egypt, which are very
numerous, we obtain no idea of blackness. However, I
find that Brugsch’s wonderfully interesting book ‘ Egypt
under the Pharoahs’* puts the expression in a form which
is very clear, as well as convincing up to a certain point.
He says that “on countless occasions the King is mentioned
in the inscriptions as the ‘lord of the black country and of
the red,” thus distinguishing the fertile land from the
desert. He also adds “that the Egyptians designated
themselves simply as the people of the black land, and that
the inscriptions, so far as we know, have handed down to
us no other appellation as the distinctive name of the
Egyptian people” (vol.i. p. 10). We must conclude then,
I would say, that ham does not always mean “ black,” but
sometimes simply “ dark *” in comparison with the sand.
Information like this, confirming (although with some
modification) opinions drawn from the earliest times, leads
us into difficulties in arriving at the real meaning of
“chemistry.” It is certainly true that the name of an art
might be derived from a country ; we have an instance in
the word “ japan,” used for a varnish or lacquer of a
superior kind; and that the name of objects made in a
country may take the name of the country itself, we have
a proof in the word “ china,” used for porcelain. So people
finding an art coming from Egypt, and having no native
name at hand for it, might have given it the name of the
country ; but so many things came to the north of the
Mediterranean from that country on the Nile that it was
most certainly not the habit of Greeks and Romans to adopt
such a mode of speech, as it would have produced great
confusion. Of course we might add that one name at least

* A History of Egypt under the Pharoahs, derived entirely from the
Monuments. By Brugsch-Bey. (Murray: 1879.)

104 DR. R. ANGUS SMITH ON THE

might be taken from the name of the country, one promi-
nent art for example. This is fair ; but where was chemistry
such a prominent art or branch of thought or practice
that it should be so honoured as to receive the name of
this wonderful country ? :

Whilst, then, we are driven by the earlier arguments to
look to Egypt as a source of the art, we are repelled from
the belief that the name of the art came from the name
given to Egypt as a whole; and we are prevented also from
believing that any word signifying “black earth” has turned
itself round to mean the science of chemistry, although
transformations as great are by no means uncommon, or
we might rather say are the rule, in all languages.

I lately came upon a new line of thought, which pleased
me much. The Hebrew word MOM) (Hema or Khema) means
“heat ;” and in one dictionary the meaning of “ poison”
is also given. This seemed to suit perfectly. But Pro-
fessor Theodores tells me that when the word is used in
the Bible in connexion with serpents it means, more
correctly, their violence than their poison ; and this is con-
nected with heat and glow. Now, if there is any natural
action more connected with chemistry than another, it is
that which arises from heat; and it is especially the case
whenever metals are extracted from their ores or much
manipulated. In all probability the first use of chemistry
was for obtaining metals from their ores. But we do not
require to keep to the furnace-work only, in order to
obtain a good idea of the early chemistry. The Egyptians
were chemists in the practice of pharmacy to a very large
extent; that is, we know that they made preparations
from plants for the cure of diseases and wounds, and that
they made very effective preparations for disinfection.
They divided gold finely enough for stuffing teeth; but
I suppose it must have been used as leaf; at least they

worp “ CHEMIA”’ OR “ CHEMISTRY.” 105

could make it fine. They seem also to have dissolved
metals for marking-ink, showing that they used acids.
As to distillation (which used to be thought such a late
invention) the oil of cedar, used by the embalmers and
mentioned by Herodotus, points distinctly to that process.
Soda was used; and it was made caustic by lime, as Pliny
tells us, and exported to Gaul. This is a peculiarly che-
mical process.

Judging from these facts, is it possible for us to consider
that the arts employing all these operations, for each of
which heat was used, could possibly have escaped having
aname? Prof. Kopp does not, so far as I see, feel sure
that a name existed early ; and others have had similar
doubts, as we have seen, whilst there has been a strong
inclination to derive the word from some simple object or
fact. Such an origin for a word is probably more usual in
the history of language than any other; and it is not to
be expected that the difference between abstract and
concrete words should have received much consideration
in Egypt, although not unknown, since we can point to a
distinct recognition of it. There is a manuscript which is
considered by Dr. Birch to have come from 1100 B.c., which
has the following title :—‘ Principle of Arriving at the
Knowledge of Quantities, and of Solving all Secrets which
are in the Nature of Things.” It is arithmetical and geo-
metrical. This I have obtained from Mahaffy’s ‘ Prolego-
mena of Ancient History;’? but I understand that we may
soon expect much more information on such points from
manuscripts now under examination. The medical treatises,
as well as the anatomical, show abundant abstract thinking

From these considerations I see no difficulty in supposing
that the Egyptians used one word to designate the strange
phenomena produced in substances by means of heat. If
we consider the operations of a laboratory, we find it re-

106 DR. R. ANGUS SMITH ON THE

markable that heat comes into nearly all of them, and heat
to a large extent: there are exceptions, especially those
peculiarly modern actions producing changes in solutions.
It is an old saying that bodies do not act but when dis-
solved; and in order to dissolve them, fuse them, or make
them liquid, it is seldom that heat to a very sensible amount
does not take part in the process.

Did not some old Egyptian see some one working with
furnaces at the mines of Midian, at Akita, east of Coptos, or
any places between the Nile and the Red Sea, bringing out
lead and silver, and collecting small amounts of gold at the
bottom of a crucible? and did he not speculate on the
wonderful things produced by heat in the chief towns in
Chem of the Thebaid? When he went over to Ramses or
to Heliopolis, we can suppose him following his studies
among the physicians, who had most certainly laboratories
in which they boiled their plants and roots and seeds.
They could not boil without vessels in which to boil them;
and wood or charcoal fires under the vessels were necessary ;
and that there were roofs to cover the workers is most pro-
bable, if not certain, whilst men would stand and watch the
processes. These are chemical operations; and there is a
similarity in the appearance to an outsider amongst them
all. If, too, we include the dissolving of metals and the
boiling down of soda solutions, the idea is widened. And we
can suppose the same inquirer going to a dye-house at Tini,
on the west of the Nile, and observing the cloth treated with
different mordants plunged into the boiling dye solution,
perhaps madder, and coming out of various colours, even
when only one colour was used. Itseems to me, then, not
likely that such a class of artisans and professional men
would be without a comprehensive name for their labours.
A name which did emerge out of darkness into near places
is known to be “ chemia ;” and this is the word so much

WORD “ CHEMIA”’ oR “ CHEMISTRY.” 107

criticised. If we can prove it to be associated with or to
mean ‘‘ heat,” it is more nearly associated with such arts
than any we know. But the people who obtained the word
in Europe did not obtain the arts, except in a very imperfect
manner; and thus, when the meaning was sought, it was
given also in that imperfect manner which ignorant people
are driven to. Thus many have imagined that it referred
only to gold-making ; but we are not called upon to take
their definition of the word, as no early writer has considered
the subject from a wide view.

I say, when the word came out of darkness ; with this I
mean that when it came to be used in the West, it came
with all its connexions traced to Egypt. Nay, the first
reputed writer on subjects distinctly chemical comes from
Egypt. It may be said that we are not sure of his history ;
still it is also true that he has no claim to come from any
other place, and there seems no reason to deny the con-
nexion. I refer to Zosimus. He might be enough, had we
no other writings having a frequent reference to Egypt ; and
although these may in some (not quite in all) cases have been’
written in Christian periods, there seems no reason to
suppose that the writers were mistaken in attributing the
origin of the ideas to Egypt. The Egyptian system was
slowly broken up, and traces ofits knowledge were scattered
in miserable fragments among writers, although artisans
may, in a traditional way peculiar to themselves, have
retained many useful inventions.

While this is a fair view of a possible case, I do not
think it probable that the word came directly from “heat”
by one act of the mind of any Egyptian or other man.
It came, as many words do, by a tortuous route, but
keeping, as it were, in view its true origin by a constant
association with things and places connected with heat.

It appeared to me that the Hebrew was not the

108 DR. R. ANGUS SMITH ON THE

language from which to find the root of the word; but it
was necessary to work out the idea begun; and for this
reason I took the opportunity of the nearness and friendliness
of Professor Theodores, from whom also I sought guidance
in going into other languages of the Hast. .

Having been satisfied that Ham, “black” and “secret,”
could have no useful meaning as applied to chemistry, I
decided to search if my new idea of chemistry as an agent
or art depending on heat was well founded, knowing next
to nothing of Hebrew, although three brothers who knew
more or less of Eastern languages gave me once a taste for
it; I found that the word which I may write Hama meant
not only heat but the sun. Knowing also that the vowels
in the word were, under certain circumstances, changeable,
it was not difficult to reach Hem; and we may say that
every one knows that the name of Egypt is Ham, or Khem,
or Khemi.

I then went to Prof. Theodores, fearing to trust myself in
the maze of Hebrew etymologies; and he gave, as the mean-
ing of the most important derivative of Ham, ‘‘burnt black,”
and quoted from Littré’s Dictionary under the word Chimie,
p. 76, ‘‘ Cham, Kem, Khemi is a name often read on the
hieroglyphic monuments; it signifies properly ‘black earth,’
and is the name of Kgypt.” It seems to me that the
meaning of an important derivative being “‘ burnt black ”
is a most valuable step in advance. This seems the proper
mode of connecting the word with heat. We canscarcely
imagine the word black bemg the root of the word sun;
but we can easily imagine the word heat being so; and the
heat, burning, leads us readily to black.

Prof. Theodores says, “ DOM (cognate in character to
om‘) means to be hot, to heat; from it are derived the
nouns Ham-mah, ‘heat,’ also ‘sun,’ the receptacle of heat.
Another noun is Hema, ‘fiery anger.’ This latter form

worp “‘ CHEMIA” OR “‘ CHEMISTRY.” 109

occurs in Deuteronomy, xxxii. 24, in connexion with the
names of snakes or some such animals.”

“The fundamental meaning of the Arabic root Hamma
is also ‘to be hot ;’ but this verb has been made to serve
for ‘ to decree,’ ‘to be black,’ ‘to have a fever.’” After
giving a number of derivatives, he says, “ Many of the
above words (Hummums, for instance) have been adopted
over all Asia by non-Semitics no less than Semitics.” He
considers the root to be Egyptian.

Prof. Theodores says that, “if Kimia be an Arabic word,
the attempt to graft it on hot or black is futile.” This
being from grammatical considerations, I take it as decisive,
as I will not venture on transcribing the Arabic vocables
which the Professor so easily jots down. “ Bochart says
that Chimia was first mentioned by Firmicus.” ‘The
word Chimia is not of legitimate Arabic formation. The
Arabian lexicographers are unable to arrange it under a
verbal root ; they merely explain what Kimia can do, not
how the word originated. Therefore Freitag, in the fourth
volume of his large Lexicon, explains the word, but calls
it aforeignimportation. Bochart’s notion to derive it from
Kama, ‘to conceal,’ because it was an occult science, is
no revelation: No adept gives such a title to his own
profession.”

“«The Arabians took the word as the Romans and Greeks
had done before, where they found it, viz. in Egypt, the
Greek inhabitants of which, at the time of the Moham-
medan conquest, called that science by a name closely re-
sembling that by which it was known in Europe, although
it was of old Egyptian, Hamite origin. The Arabians
made its acquaintance in the form of ynyeva or ynia.
This sound they transcribed in Semitic characters, putting
the > for the Greek x. That this was an orthodox practice,
the Talmud incidentally but fully proves. In the treatise

110 DR. R. ANGUS SMITH ON THE

‘ Kerithuth’ (or excision) of the Babylonian Talmuds, folio
5 6, the following occurs:—‘ The anointing of a king is in
the form of a diadem, the anointing of a priest in the form
of a Greek ki (3).? Now a Greek ki is y, consequently
Semitic K was considered the equivalent of Greek y, and
xnucia or xnwia ought to be writtten as it is written,
nypD, kimia.” ‘‘Egyptiay etymology, then, ought to be
consulted. It is not probable, although it is possible, that
the Egyptians named it from their country; fornatives donot
think of naming a produce of their own, whether abstract
or concrete, after their own country ; foreigners do that for
them. Then the Egyptian term must have been chosen
for the connexion between the science of Xnpia and the
idea of heat” (blackness) ; “ but,” he adds, “I have not
succeeded in discovering an express declaration to the effect
that chemistry is called so because it deals with fire or
heat.”
- Thus far Professor Theodores has confirmed my idea,
and with learning that I could not muster.

He also adds :—“ As in Semitic, so in Egyptian, ‘black’

3

is a derived meaning ;” and I am glad to have this autho-
rity for altogether throwing aside the word “ black” as
connected with chemistry.

Prof. Theodores came to the conclusion that,.although
the word was found in Semitic, it was of Hamitic origin ;
and he agreed with me that it was needful to go a step
onwards or to the side, and adds,“ Bunsen, in his large work
‘Die Stellung Aegyptens in der Weltgeschichte,’ vol. v.
sect. 2, in the Etymological Table, mserts :—‘ Hem, or
‘hem, sieden, glihen, = Hebrew ham. As ‘h is related to s,
the Egyptian Sém has the same value, and with this the
Teutonic Sommer. Sommer has some connexion through
Sun, Sonne.’ This is in Bunsen.” ,

By this reasoning we are fairly removed from the Arabic,

WORD “CHEMIA” OR “ CHEMISTRY.” 111

and partly from the Hebrew, and are in Egypt. However,
it did not seem to me well to stop there. We cannot tell
the true connexion of Egypt with Assyria and with the
old Accadians ; and we know that magic was highly culti-
vated in the East by the latter people. It was necessary,
therefore, to seek in that direction; and I wrote to Dr.
Birch, as it seemed to me impossible to obtain this infor-
mation direct without some knowledge of the language ;
but perhaps the late dictionaries and other aids might have
served me so far.

Dr. Birch’s letter is very explicit so far as Assyrian and
Egyptian are concerned. He says:—‘‘The word for ‘heat’
in Assyrian is Hhamamu or Khamamu. In Egyptian we
have Khemt, ‘fire,’ ‘to warm.?” Then he gives “ Qam,
‘Egypt,’ or ‘the black land, gam meaning in Egyptian
‘black.’ ”

I then went to Prof. Sayce’s ‘ Vocabulary of Assyrian
and Accadian,’ under the guidance of Mr. Harry G. Rylands,
of the Biblical Archeological Society ; but we got nothing
out of the Accadian : the words out of the Assyrian, how-
ever, are interesting :—

Samsu, the sun.
Samu, the heavens.
Samas, the sun-god.
Khamamu, heat,
Khammu.

Khamsa, fire.
Khamdu, light.

Here, then, seems the true origin of the word. The
meaning is intelligible, worthy of the people and worthy
of the science. The question, however, again occurs, Was
it Egyptian or Assyrian? ‘The reasons for believing the
primitive not to have originated in Egypt may stand ; but

ie DR. R. ANGUS SMITH ON THE

we must learn, I suppose, whether a Semitic people took
the word to Egypt and gave it that Hamitic cast which
Prof. Theodores remarks. It seems, however, to be allowed
by later writers that some at least of the Egyptians came at
an early period from Asia, although they seem to have been
much mixed during their time of power.

The connexion of the Egyptian with the Semitic lan-
guages has been long believed; and Brugsch-Bey is very
strong in his belief against its African origin. He says
(vol. i. p. 3):—“The Egyptian language, which has been
preserved on the monuments of the oldest time, as well as in
the late Christian manuscripts of the Copts (the successors
of the Pharoahs), shows in no way any trace of a derivation
and descent fron the African families of speech. On the
contrary, the primitive roots and the essential elements of
the Egyptian grammar point to such an intimate connexion
with the Indo-Germanic and Semitic languages, that it is
almost impossible to mistake the close relations which for-
merly prevailed between the Egyptians and the races called
Indo-Germanic and Semitic.”

In Upper Egypt, as we find from the same author, there
was a city called Tini, now entirely out of existence, but
once giving the title of Princes of Tini to the highest
functionaries of the blood royal. From this place the first
of all Egyptian kings was descended, namely Mena or
Menes. In the time of the Romans it was known only
from its dyers in purple. This town is mentioned here
because of its arts; but it serves my argument chiefly
because we find almost opposite to it, in the district of
Chem, the town of Chemmis mentioned in Herodotus.
This town had as chief deity Chem or Khim, who was the
representative of the heat of the sun and the transmuter of
death into life as we may say, as well as the producer of
the fruits of the earth. This name was translated by the

WORD “ CHEMIA” oR “ CHEMISTRY.” 113

Greeks into Pan from some supposed similarity of charac-
teristics. This Greek and Roman habit of translating or
giving equivalents for names has caused a great deal of
confusion.

We have seen that Zosimus was one of the earliest
chemists ; and he is called Panopolites, a citizen of Pano-
polis. If the Greeks had not translated the name, he
would have been called Zosimus of Chemmis, or Zosimus
the Chemmite (the chemist); and then probably no one
would have disputed the meaning. And here he stands
before us with his description of metals and of distillation,
and with drawings of his alembics, and what appears as a
crucible with fire under it.

I have said that I believed the origin of the word to be
“heat ;” but it is not necessary that it should have taken
the leap at once. It is probable that the name came
directly from the town of Chemmis or the district of Chem,
whilst the name of the town came from the god Khem, the
representative of solar heat. The common people would
think of the town, the more scientific of the character or
quality.

Herodotus tells us of two places in Egypt called Chem-
mis; the second is a floating island in Lower Egypt, at Buto.
It is one of the wonders that people here would not believe
until a similar one was found in England, although there
were several on the Thrasimenian lake not far north of
Rome, and also on the Tarquinian.

The mysterious word Jmouth, which is connected with
chemistry, Pan, and Asculapius, has been said to be an
Egyptian word for “ chemistry ;” but if we look at Khem,
we have a clue to Jmouth also. Khem, in the widest sense
as the producer, ‘‘ was the father of his own father ;” and
Mauth was the abstract idea of mother, who consequently
proceeded from herself (this from Wilkinson); or, the

SER, III. VOL. VII. I

114 DR. R. ANGUS SMITH ON THE

goddess with the sun’s disk had a son Imhotep (in Greek
Imuthes), the Asculapius of the Egyptian mythology: this
again connects with the sun and with medicine, a branch of
chemistry. Here nothing appears to me to be forced, but
all comes in naturally. All the chemical allusions to
“Tmuth” may be seen in Kopp’s work (Beitriige, &c.)
alluded to. I do not here attempt to collect the
remains of chemical history at any pot, but to lead up
to the view which I wish to illustrate.

We see, then, that the word Khem has no trifling
meaning, but relates to the principle in nature which,
even now, in the latest of times, we look on as the great
promotor of all life both on the earth and beyond it. It
goes directly to the sun and coincides with our own ideas
on the subject. It goes also'to’mental emotion and to
violence, as we saw inthe rage of the serpent. It includes
internal action, but excludes the glory of the sun, which is
represented by the sun-god Ra, translated by the Greeks
into Apollo. Still the qualities are mixed. The floating
island Chemmis had a temple on it dedicated to Apollo,
according to Herodotus. Had he mistaken the heat-god
of the chemists and the farmers for the god of light, the
glorious Apollo? The difficulty of separating the two is
probably the real cause of the mixture of qualities in Chem.

Thus far it seems natural that “chemistry” should come
from Khemi, and from the town Chemmis in Khemi,
the spot where the god Khem ruled, and that the earliest
of chemical writers, or, at least, one of them, and the best-
known of the earliest, should have come out of Chemmis,
and the name of the art or science (as it may, to some
extent, be considered) should have been preserved as
“chemia.” It seems so far to have been connected with
metals, distillation, dyemg, and medicine even in the
earliest ages.

WORD “ CHEMIA” OR “ CHEMISTRY.” 115

We may go a little further, namely into the hills east of
Coptos, and see where chemistry was practised by the
workmen. Probably Coptos was another place devoted to
Chem, or, rather, in a district of Chem. Chem was the
“Jand of Coptos ;” and we learn that there was a road
from Coptos to the Red Sea among the mountains where
the valley of Hammamat is, and where the Egyptians
obtained stones for building as well as gold- and silver-ore.
I suppose the word “ Hammamat” to have also to do with
heat (I am told that it sounds as if an Arabic inflexion); and
if the ores were treated near or at the mines, there would
be no wonder. The heat of the district would perhaps
suffice to give the name—although there are many hot
places east and west of Egypt, and the probability rather
is that the Arabic form has merely grown out of the old
Egyptian, the root being the same.

The god Chem is called “the master of the tribes
which inhabit this valley,” and “ the lord protector of the
mountain ;” and Brugsch-Bey also tells us that the traveller
said his prayers to him, and cut out “in tablet and holy
characters his reverence for the god.”

We learn in the rock-inscription of Hammamat that the
Arabian desert and the coast adjoining it was called the
“Jand of the gods ;” and to this the valley led.

As an incident in connexion with this, it is interesting
to read of a journey made by king Seti to see the mines
in the fourteenth century B.c. :—-“ After he had mounted
up many miles, he made a halt to take counsel with himself
and to come to a conclusion upon the information he had
received, that the want of water made the road almost im-
passable, and that travellers by it died of thirst in the hot
season of the year.”

From the monuments we learn, still following Brugsch-
Bey :—“ He had the well bored for them. Such a thing

12

a
116 DR. R. ANGUS SMITH ON THE

was never done before by any except him the king. Ye
gods of the well, assure to him your length of life, smce
he has made for us the road to travel upon, and has opened
what lay shut there before us, and the way has become
good. Now the gold can be carried up, as the king and
lord has seen. All the living generation and those which
shall be hereafter will pray for an eternal remembrance of
him,” &e.

In another place a great deal of water is spoken of as
being found. The well mentioned, although 120 cubits
deep, had dried up; but Ramses the second again bored
other wells at the instigation of the Prince of Cush, “‘ who
said that the land was accursed for want of water.” At
this time water appeared at 12 cubits depth; brooks were
formed ; and fishermen from the islands came, enjoyed
themselves, and sailed on the water. Whether this water
was used for washing the ores, or not, I do not see
mentioned *.

It is difficult to stop adding near relationships to things
chemical in the land of Egypt; but one I must add. It
certainly seems strange that the Egyptian name for Her-
mopolis should be Khimunu, as if also related to Khem;
and it brings to mind the name of Hermes, the thrice great
and of Egyptian fame, among the alchemists an authority
for final appeal.

We have passed to Egypt and touched on Assyria,
finding there the same word. There may be reason to
believe that this word is originally from Asia; and it may
have come from its centre: at any rate it has connexions
there. We find the word Kem there with the same chief
meaning, “heat.””? I was very much inclined to think that
Aryaus or Semites coming from the north called Egypt
hot; but the idea of blackness has possessed so many

* Brugsch, vol. ii. p. 83.

WORD ‘‘ CHEMIA ” OR “ CHEMISTRY.” 1

people that I suppose it is not to be neglected. If the
land was not black, I was inclined to say that the people
were black and had gradually been driven out. But it
may be too far to go back. The land must have differed
in early times. There cannot be metallurgy without heat;
and for that we must have fuel. Have Egypt and Midian
made a desert of themselves in part and of much of their
surroundings by burning up their forests? Civilization of
a high character without fuel is impossible in any country
known to us. Want of wood has made much of the ancient
world desolate, and keeps it so now; and the world has
much to thank the Germans for in teaching the cultivation
of forests. Without this care Germany would have had
no position as a great power.

In Egypt wood, and therefore fires, must have been a
scarce thing for ages; people have lived on uncooked
food ; civilization has been essentially stagnant for want
of fuel. There is no wonder that an idea arose that
heat could do any thing. Did it not warm the earth which
even the Nile could not make fertile alone? and did it not
bring gold and silver, iron and brass out of stones? It
turned rosin into strange oils; and it brought strange
liquids, essences, and medicines with wonderful virtue out
of vegetation. Wonderful drinks were prepared ; and are
we to be astonished if one of them was also connected with
Kemi, that appeared to renew man’s life and make him
stronger and wiser? We have seen that Hama became (in
an apparently wonderful philological manner, however
simple when explained) a relative to Soma and Summer and
the Sun which warms up all nature ; and it is fair to go to
Old Indian words to seek for new analogies. There is the
liquid Soma, which is “ pressed out of the Asclepias acida,
making an intoxicating drink, used by the gods to
strengthen them in their fight with demons” (see ‘ Indo-

118 DR. R. ANGUS SMITH ON THE

germanische Chrestomathie,’ written by H. Ebel, A. Les-
kien, Johannes Schmidt, and August Schleicher: Weimar,
1869).

Tn Colebrooke’s Essays we find that “ sacrifices with fire”
are connected with ‘‘ the drinking of the milky juice of the
moon-plant or acid Asclepias*, and furnish abundant
occasion for numerous prayers adapted to the many stages
of these religious rites.”

This milkiness does not favour the idea of distillation ;
but as there are treatises on the preparation of the juice,
I dare say the usual plan may beknown. A good deal has
been written on the plant, I believe. Indra and other
subordinate deities are made to say, “We have drunk of
the juice of the Soma and are become immortal, we have
attained effulgence, we have learnt divine truths. How
can afoeharm us? How can age affect the immortality
_ of a deathless being ?”

If, however, we inquire what is the quality of this drink
Soma, we get into some difficulties. At least, chemical
books give us most unsatisfactory information. We are
there informed that the juice is milky and contains a
crystalline substance called asclepiadine and asclepion,
bitter, purgative, and emetic. Now such a drink is not
that which the gods would be supposed to drink to
strengthen themselves against demons.

From one of the Asclepiads (Pseudosarsa or Hemidesmus
indicus) a substance was obtained called Indian sarsaparilla.
Dr. Ashburner introduced it from India as improving the
general health, “plumpness and clearness and strength ;
succeeding to emaciation, muddiness, and debility.” The
Asclepiads are also said, in Pereira’s ‘Materia Medica,’ to
possess stimulating properties. I cannot give more of the
properties of this plant; and I think that the mode in which

* Soma-lata, Asclepias acida or Cynanchum viminale

WORD “‘ CHEMIA” OR “‘ CHEMISTRY.” 119

chemists have treated it in analysis has prevented its
fermentation ; or, rather, they have extracted one peculiar
principle and left the rest unknown. From other works
I learn that there are various characters to the juices of
the various Asclepiads.

In speaking of Old Indian or Sanskrit, I am quite aware
that it is the chief of a family of languages different from
the Semitic; but I have already shown what Brugsch has
said of their relations; and we could confidently reason
from the ready way in which some inventions pass from
nation to nation, keeping their original names.

But we must attend a little more to this drink Soma.
We have seen that Kemi goes readily into Chem and into
Hem or Ham, and that S becomes a substitute for H; and
this must be borne in mind.

In the Sanskrit we have the words Soma and Kami curi-—
ously connected—the first meaning the celebrated drink
that strengthens the hearts of the secondary gods as well
as of men and makes them immortal, whilst the second,
Kami, is the vessel into which it flows*. Whether this
means flowing from the plant or not I do not learn.

Again, we find it mentioned, by the authors quoted, as
found in old Bactrian in Haoma, the name of a plant from
which a sacred drink was prepared, also of the genius of
the same, as if it alluded to Chem also. To this, however,
is added that it comes from the root Hu, “to press out,”
“to prepare.” This I bring in, not as strengthening the
argument, but as necessary to remember ; for, by pushing
the inquiry further, it may be found that the preparing
was a mode of warming up; but this is more likely to
be a mere fancy.

In the East we also find Kama-deva as Cupid; and Mr.
William Simpson sends me the following from his stores :—

* Schleicher’s ‘ Indogermanische Chrestomathie.’

120 DR. R. ANGUS SMITH ON THE

“ Muir, in ‘Sanscrit Texts, vol. v. p. 402, refers to the
‘Rig-Veda,’ x. 129, 4, where Kama is identified with the
idea of "Epos as the. first of all the gods, according to
Hesiod. Dr. Muir also refers to the ‘ Atharva- Veda,’ ii.
21, 4, where he says kama is distinctly identified with agnt,
the Sanscrit for ‘fire.’ In the Asiatic researches, in an
article by Wilford, in which he identifies the cama or kama
of India with the chemia or chemi of Egypt, he says, ‘ It
has been conjectured that the more modern Greeks formed
the word chemia from this name of Egypt, whence they
derived their first knowledge of Chemistry.’ Gesenius
points out the similarity of the Sanscrit kam with. the
Hebrew.”’

Thus Chem is connected with heat from Africa to India,
and in a secondary way with an “ elixir of life,’ whilst gra-
dually it has been made to mean that science which does so
many wonders by means of heat, having reference both to
the effects in external nature and the analogous influence
in the temper of man and the lower animals.

We have followed the words far, and everywhere have
come upon “heat ;” and we find that there were many
chemical operations used in Egypt which required heat,
but that the word did not consolidate itself so as to mean
a science in Egypt; at least it did not appear to have done
so to the earliest writer who is known to have used the
word with somewhat of our meaning. Firmicus was not a
man to understand a science ; besides he was an astrologer,
and the age in which he wrote was one in which the world
was getting into confusion ; he could only hear whispers of
truths in nature. The discussion on his position in Kopp’s
book isinteresting. We see also, under the names Zosimus
and Democritus, that all of these men had a limited,
merely practical and unscientific view of things, behind
even what we may suppose to have existed under the very

—— —

WworD “ CHEMIA” oR “ CHEMISTRY.” 121

orderly method in which knowledge was arranged in Egypt.
As to the secrets, we know well that the Egyptians had
power enough to keep them ; and even when they tried to
convey knowledge, we, after’a couple of thousand years,
find it a very difficult thing to read any of their writing,
and he who can read a few lines is looked on by us as a very
learned man.

It seems, then, clear that chemistry came out of the
darkness with its name connected with metals in the fourth
century; and in the works of Zosimus we find distillation
treated of side by side with metals, he and Synesius and
Democritus looking to Egypt as the land where all was
to be learnt. This I need not prove, but refer to Kopp’s
‘History of Chemistry,’ and to Hoefer, and to Olaus Bor-
richius, whose writings all must consult. In Zosimus we
have metals, “ furnaces, and apparatus” spoken of; and he
came from Panopolis; he is sometimes called also of Alex-
andria. Until the contrary be proved wise, we seem obliged
to start clear from him as from a landmark of the ending
of the period of Egyptian secrecy, although we learn too
little from him.

These facts enable us to trace the idea of chemistry as it
gradually consolidated itself :—going back in time to early
Egypt, where the word was used for ‘‘ heat ” in various re-
lations; going into Syria and Palestine, where the word
was also used for “ heat,’”’ and for “ rage ” or mental heat,
and for violence caused by intoxication ; moving onwards
to the Assyrians, who. also had the word as meaning heat ;
and following it into Bactria and India, where it associ-
ated itself with intoxicating liquors as well as with heat, and
where we find the vessels called kamu, as if in imitation
of the vessels for heat or the crucibles which must have
existed in Egypt.

A chief intoxicating liquor of Asia still retains the name;

122 DR. R. ANGUS SMITH ON THE

and koumiss comes from the horse-feeding plains to Russia
and the West. I do not know the history of the word ;
but the likeness is remarkable, and the character likewise.

People may say that I have imagined something ; but it
is easy to find out what is imagined and what isnot. The
statements or facts are not deniable ; one can only deny
the connexions which have been made.

I am going, however, to add a little which may be less
certain to some minds. Certain people are called very
reliable—those who never reason, but merely collect facts :
they are safe, but never go far; we could not learn much
if we had only our touch instead of eyesight. Let us spe-
culate alittle. When we look for “the elixir of life” among
early alchemists, we find the introduction of silver and
mercury into its preparation; and I will not inquire who
was the earliest who did this; but if we go far enough
back in point of space and time, we find the “ elixir of life ””
to have been an intoxicating liquid. The long time of pre-
paration, the wandering search after a proper heat (which
in some cases, at least, was quite that of fermentation), and
the confused ideas of distillation put into bombastie words
among the alchemists lead me to suppose that they had tra-
ditions of the preparation which were lost as to clearness,
whilst they point towards the formation and distillation of
alcohol. In the far Hast the precious liquid is simply an
intoxicating one; the peculiarity of the Asclepias found
by chemists exists to a small extent only, and did not show
itself with sufficient prominence to be noticed in the Kast.

This confused idea of early men, who, when they were
excited by drunkenness, fancied themselves elevated above
common life, and imagined that if they could obtain enough
of the liquid the elevation would last for ever, passed
readily into the notion of an elixir; and we see that the
gods themselves used it. This idea kept its place even in

worp “ CHEMIA” oR “ CHEMISTRY.” 123

Palestine; and we have in the Bible itself (Judges, chap. ix.
verse 13):— The vine said, Should I leave my wine, which
cheereth God and man?” evidently a quotation not unfa-
miliar to the people of the time.

Whilst, then, it is certain that an intoxicating liquid was
an elixir vite of the East, and hama was a word used for
the heat of intoxication among a Semitic people, we
move onwards to Zosimus teaching chemistry and distil-
lation, and uniting the operations of metallic chemistry
and vegetable. The Arabs, naturally more eastern, with
other Asiatics, gave more study to the elixir, as if holding
the tradition of the Soma. However, there is an old drink
mentioned among the Egyptians which partook of the
qualities of the elixir, and in the preparation of which they
used honey, a ready former of alcohol.

And after all, some may say, Was the Elixir of Life,
after which so many earnest men have striven, nothing but
alcohol, mere brandy and whiskey? I fear it really was,
and that the memory of the past was adelusion. This idea
has been held by others. We have the same idea still; and
the name is retained in the words aqua vite, which mean
simply the elixir or water of life. The elixir is, according
to some, a “ pure water.” We have the delusion ready
formed, and greedily preserve it among our population.
Men still believe brandy to be life-giving, whereas many
others know that for every benefit it confers it gives seven
curses. Still it is made by heat, it produces heat, it is kemi.

There have been many such delusions : respecting opium
there is acommon one; tea itself has been said to cure all
diseases ; and that concerning alcohol is one of our oldest
and most persistent.

The idea that gold was made by a liquid seems to have
arisen from the properties of mercury. Throw it among >
the sand, stir it about, then heat it strongly, and you will

124. DR. R. ANGUS SMITH ON THE

obtain gold if there was gold in the sand ; and thus mercury
came to be associated with gold. It works wonders ; but
this, also, is done by means of kemi (heat).

Take simple honey and add it to some plants, let it
stand, and then apply heat. ‘The tree of the philosophers
is extracted or drawn off in three; but the wine thereof is
not perfected till at length thirty be completed.”

«This is not water in its form, but fire, containing in a
strong and pure vessel the ascending waters, lest the
spirits should fly away from the bodies ; for by this means
they are made tinging and permanent or fixed’ “ Look
into the sweetness of sugar, which is one kind of sweet
juice, and into the sweetness of honey, which is yet more
intense and inward. Except you make the bodies spiritual
and impalpable, you know not how to purify ixir or to
proceed in the work.” These isolated sentences from the
so-called Hermes point to fire and distillation; and I might
end with a saying quoted from Van Helmont * :—‘ Let
him who would learn buy coals and fire.”

AppENpvUM I.

It appears, then, that I go on a very different track from
that followed by Prof. Gildemeister and Prof. Schorlemmer.
T leave the Arabs as too late to have an opinion; and J can
easily imagine how a Pacha’s mind could mix all the un-
certain ideas together and form some notion of a plant
called kimia which changed base metals into gold. I
consider the connexion with “ moisture”? (yupos) far-fetched,
and had never any confidence in it. If, however, yupos
were considered rather in connexion with “ pouring,” it
would have more probability ; but then the original is yéo,
“T pour,” and the v is found only in compounds.

* T have not the original beside me.

WORD “ CHEMIA” oR “ CHEMISTRY.” 125

Apprenpvum II.

There is another derivation of the word “ chemistry,”
mentioned by Mr. James Mactear, F.C.S. I have only
received a few lines on the subject, an abridgment of a
paper read at the Philosophical Society of Glasgow. In
this it is said that Mr. Mactear traces the history of
chemistry through the medical science of Greece, Persia,
&c., and the word itself to kham, an Arabic word of
Sanskrit origin meaning “five,” or rather its compound
khamis meaning “ the fifth,’—adding, “ As is well known,
the ancient Hindoos recognized five elements—water, fire,
earth, air, and ether, the latter being the principle or
type of active force or motion which caused the changes
in the condition of the elementary types or their combi-
nations. From a consideration of these and other facts, he
derived the title of the science from al khamis, ‘ the fifth,’
meaning the science of force or change. No more perfect
descriptive title could be found for it in our present enlight-
ened age.”

The scientific division of the elements is found in the
atomical philosophy of Canade, where ether comes in as
the fifth existence, “infinite, one, and eternal.” In the
Sankhya philosophy the first is a diffused etherial fluid oc-
cupying space. The further account of it and its power of
influencing the other elements will, I dare say, be published
by Mr. Mactear. I can refer at present those who are in-
terested in the question to the ‘ Essays on the Religion
and Philosophy of the Hindus,’ by the late H.T.Colebrooke,
a standard authority.

It cannot be agreed to give the Arabs more than the
form of the word, or the a/ in alchemy; they are there-
fore left out,—unless the word “ fifth ” can be taken further
back and shown in any Sanskrit dialect to have a connexion

126 MR. E. W. BINNEY ON THE TRIASSIC AND

with philosophy except as a mere enumeration. Indeed,
we see that in the Sankhya philosophy ether cqmes first ;
but of more importance is the fact that we have no proof
of the chemical arts being well known in India ; and there
is no historic indication of their existence connected with
a system of philosophy. This is very conclusive, because
Indian philosophy is well preserved : itis full of speculation
and subtle abstraction ; but it is not experimental; and
from experiment must have arisen the great power which
is in the hand of the chemist, the science of chemia.

The connexion between the “ elixir of life” ‘and aqua
vite is by no means new, although the mode of approaching
it here may be so.

XV. Notes on a Bore through Triassic and Permian Strata,
lately made at Openshaw. By HE. W. Binney, V.P.,
F.R.S., &c.

Read February toth, 1880.

For many years attention has been given by local geolo-
gists to the district lying between the Manchester coal-
field and that of Aston-under-Lyne and Oldham. The
first authors that treated on it were probably Messrs.
Conybeare and Phillips, in their ‘ Outlines, published in
1822. Mr. James Heywood, F.R.S., in a paper published
in vol. vi. (2nd series) of the Society’s ‘ Memoirs,’ also
noticed it. In a communication of my own, published in
the first volume of the ‘Transactions of the Manchester
Geological Society,’ a horizontal section is given of the

PERMIAN STRATA OF OPENSHAW. 127

country between Manchester and Waterhouses, showing
one great fault as then known. Afterwards, in vol. xii.
(2nd series) of our ‘ Memoirs,’ evidence is given of another
fault at Medlock Vale, and lately, in part vi. vol. xv. of
the ‘ Transactions of the Manchester Geological Society,’
Messrs. Bradbury and Atherton have shown a third fault
at Openshaw. As the district is thickly covered by drift
deposits, and few natural sections are exposed, we have to
wait till evidence is afforded by borings and sinkings. In
several papers by me, printed in the ‘ Memoirs,’ information
has been given as it was met with; and as Mr. John
Bradbury’s boring is one of the most valuable, I wish to
add it to my other communications on the subject, in
order to make them more complete.

Mr. Bradbury’s labours have shown the Permian sand-
stone, the one so well exposed at Vauxhall, in our city, to
be of greater thickness than hitherto proved in the
district ; and as this deposit isa most formidable difficulty
in sinking to the underlying coal seams, it is desirable
that all information respecting it should be given to the
public.

The bore was made near to the Ashton canal in Open-
shaw, and adjoming the boundary of that township with
Clayton. According to Messrs. Bradbury and Atherton
it was as follows :—

feet,
PIECEMEAL inca aninsia son cacdn cpcsnneat seas secon onusia+pedenqucack ae 36
SIA, CL OUHLO-DEGS) | covcudanssnyn's cu ddsustecvvcassseneansovaevoaseswag 46
Permian marls, containing beds of limestone, one of which
was 1 ft. 4 in. in thickness, and nodules of gypsum. In
the lower parts of the marls and limestones were shells
of Schizodus obscurus, Gervillia antiqua, &C. ........0000008 200
MUP LOMICTALG ponte w dion teove eds ive ttnandsocdvceisccdercevsecatsdacretend 3
PEER BANCSLONON fad sie acs staves Vartan vadnaseoscoaand saad Queen reheee 752
Upper Coal Measures, containg 12 beds of Ardwick Limestone,
one of which is 5 ft. in thickness..............cesccssceeseneas 263

128 MR. E. W. BINNEY ON THE TRIASSIC AND

The dip of the Permian strata was about 1 in 8, fal
that of the Upper Coal Measures 1 in 3, to the 8.S.W.
The strata found resemble those at Medlock Vale, except

that the Permian sandstone has increased from 420 to 752

feet in thickness. I have estimated that rock under Man-
chester at 400 feet; but its entire thickness has never to
my knowledge been proved. In Chester Street, Chorlton-
upon-Medlock, at the sugar-works of Messrs. Fryer & Co.,
on the south side of the fault which runs from N.W. to
S.E. between that place and the late Mr. Green’s dye-
works in Brook Street, the Permian marls and conglome-
rate bed, increased to 260 feet im thickness, were found
resting on upper Coal Measures containing the Spirorbis-
limestone similar to that at Ardwick, without any trace of
the Permian sandstone. Similar results have been found
at the borings and sinking of the Seedley print-works and
the Patricroft colliery ; and very lately Dr. Perri informed
me that the same occurred in a sinking at Plank-lane
Colliery, near Leigh.

All the facts hitherto observed appear to show that the
Permian sandstone is found of great thickness under the
district lying between the Manchester coalfield and that of
Ashton-under-Lyne and Oldham, while to the south of
Manchester, under the Trias, it is replaced by the con-
glomerate of increased thickness. The former rock has
probably never been deposited ; nevertheless the fact of its
general absence is of great importance to all parties who
may sink for coal under the Trias.

At the present time the Permian strata of the N.W. of
England and the S.W. of Scotland, so far as my knowledge
extends, are represented in Lancashire in the following
descending order :—

1. Upper Permian sandstone of Moat, Shawk, St. Bees,
and Furness Abbey; absent in South Lancashire, unless

etc terthinets,

PERMIAN STRATA OF OPENSHAW. 129

there is a representative of it in the Knowsley Quarry,
near Prescot.

2. Magnesian marls with limestones and gypsum, con-
taining Schizodus obscurus, Gervillia antigua, and other
characteristic fossils.

3. Conglomerate.

4. Permian sandstone of Vauxhall, Manchester.

5. Lower Permian sandstone of Whitehaven and Astley,
by many English geologists taken to be unconformable
Coal Measures, but in Germany termed Lower Roth-
hegende.

The old Magnesian Limestone formation, as described
by Professors Sedgwick and King, and my friend Mr. J.
W. Kirby, in the East and N.E. of England under the
four first-named divisions, was pretty plain, although the
line of demarcation between the Brotherton limestone and
the Trias was not so easy to make out in all places. In
the N.W. of England, and adjoining Scotland, the St.-
Bees sandstone, a rock of about 1000 feet thickness,
cannot be traced passing distinctly upwards into the Trias,
although doubtless it does somewhere betwixt Carlisle and
the Solway ; but in the valley of the Irk at Manchester
the beds Nos. 4, 3, and 2 are seen lying on each other,
apparently passing into the overlying Trias, all the three
rocks dipping at the same angle and in the same direction.

Near Manchester the occurrence of Permian fossils has
enabled us to fix the position of the red sandstones and
marls of the Trias and Permian beds; but after leaving
Barrow Mouth, near Whitehaven, and traversing the
country by Maryport, Carlisle, and Longtown to Cano-
bie, as yet no fossil organic remains have been met
with to help us, and we have to trust chiefly to super-
position to separate the two formations. All who have
investigated these formations know the difficulty of

SER. IIl. VOL. VII. K

130 MR. GWYTHER ON THE LAGRANGIAN FORM OF

determining a Permian from a Triassic sandstone by
external characters.

In some places in Lancashire the Coal Measures are
covered by Triassic beds without the occurrence of the
intermediate Permian beds; but near Manchester the latter
are generally met with either as the upper deposits, the
marls and the conglomerate (Nos. 2 and 3) most frequently
together, or with all the three beds of the series.

XVI. On an Adaptation of the Lagrangian Form of the
Equations of Fluid-Motion—Part I. By R. F.
GwytHer, M.A.

Read April 20th, 1880.

1

Tue object of the Lagrangian form of equation is to follow
the motion of a particular element; and although the
Eulerian forms suit the general purposes of fluid-motion
best, there are certain cases, as that of vortex motion in a
perfect fluid (which may be termed steadily progressive),
where the course of an element may be investigated with
advantage.

For this purpose I propose investigating the course of a
fluid element, defined by means of surfaces moving with
the fluid, and expressing the results as far as possible in
terms of the parts of the element.

This method leads to a more general integral form than
that of Weber, and finally exhibits some of the known
properties of fluid-motion in a novel manner*.

* A similar method with the ordinary coordinates has previously (Q. J.

of Math. Feb. 1880) been used by Mr. Hill to obtain some similar results,
which will be referred to later.

THE EQUATIONS OF FLUID-MOTION. 131

If ¢ be a scalar function of the position of a point in
the fluid, its total differential after time 8¢ is D,gét; and if
D,p=0, the property of the point of which ¢ is the analy-
tical expression is unchanged during the motion. Now
let p= be the equation to a surface all points on which
enjoy the same property; such a surface will, if Ds=o,
move with the fluid.

The number of independent surfaces of this kind which
can pass through any point, or the number of independent
integrals of the equation D,@=0, is three, or the dimensions
of the space considered; for the Jacobian of a higher
number would vanish.

The position of a point in the fluid in motion may be
represented in terms of the three independent sets of
surfaces $,=,, $,="., ?;=";, Where #,, »,, and pm, are
parameters.

I have avoided the use of theorems and terms such as
those of “ circulation,” as I think they are apt sometimes
to override and hide the more important facts which their
discoverers intended them to express; and I have en-
deavoured to bring the fundamental properties to the
surface.

Imagine an element of the fluid separated from the rest
of the fluid by the surfaces which we shall denote by

Pers Pas bs, By + bu,, be, + Ou, and bb; + Ojt,.

We will investigate expressions for the parts of this ele-
ment.

First, V?,, V2, V¢; represent vectors in the directions
of the normals to the three surfaces, such that if h,, ,, h,
stand for their tensors, the thicknesses of the element will

F ou, 8 D :
be given by te and 2 respectively.
3

Mj uae
The directions of the edges are given by VV¢.V9;=4,
2K

132 MR. GWYTHER ON THE LAGRANGIAN FORM OF
say, and the similar quantities 8 and y, so that

VBy= —SV6:V0.V6s + VP:= HV6., say:

The length of an edge will be given by the thickness
divided by the cosine of the angle between the correspond-
ing normal and the edge. Thus length of the edge a is

oe, A,Ta oy, Ta
h, Sy¥¢,a ELA?

and the vector edge is

Oe,
Tart 5 e A 5 ° 5 (1)

whence the area of the face ¢, is

ORT h,
H? : TVBy = H Ou. 0u,,

and the vector of the face

Oy. .0 um,
H

Ver os

From either (1) or (2) we may get volume of element

0,0. Op Oy, P p20
= hye A)

The condition of continuity is therefore that D,(dH-) =
o, where d denotes the density ; and this condition in an
incompressible fluid becomes D;H=o. Generally d=H¢
where D,g=o.

Before proceeding to investigate any forms for co, the
velocity, we will find some expressions from the action of
D, on the expressions just found.

‘Remembering that

—Soy,

THE EQUATIONS OF FLUID-MOTION. 133

we see that

Dvy=vD:4+ A(Scy)

symbolically, where A is the same operator as vy, but acts

on the ¢ only.
Thus

d
Diye=yDe+A (Seve) =yDe +Vv9S7, VP

dco do

FE ieee cement ra)

since
V=Vv? 106 4 16 @
'd@, “do, do,
[These other two forms of v7 will also be used,
—Hy=Vv¢,SVF.V6;V + VP:5V9;V,V + V9;9V8,00V

or

=aSV9,V7 + PSV¢.V +7S8¢,V,

since v is in form a vector. |
Let us first apply these results to Sy¢,v¢.v¢, or —H;

therefore

—D,H=SD.v@,. 79.09; +8V9,D:7 2-79; +SV¢,7¢.D:V9,
da da da
or

I
y DHl=Sye=—- HD.( 5) A. oan

or is evidently rate of compression per unit of volume.
If, again, we act similarly on « or V¥¢.V¢,,

134 MR. GWYTHER ON THE LAGRANGIAN FORM OF

De=V ie Le
o
+ S an VVG.V9, sf S ae do, aa

ds g do de
ENA do, Vo.8— S70 rei

dco
See ee

therefore
d
pi De+D, H¢ = ie,
or
a do
a ance wa ee er
whence we obtain
dco

PUL a Me ae
V7=VP, do, VP de, he ie
=vp.D.i+ve.D.% +79;D; F. ae)

Now

S 2
Ver + VE + VE, = imeem ee)

o ues + 7¢.8+17;7)
/ t :

of which the vector part is seen to vanish and the scalar

becomes — 3, whence

V9, Diz & +-7e.DA is V9Der Wo =—DV.7q —pve,F

—D:V¢; =

THE EQUATIONS OF PLUID-MOTION. 135
and
HV Vo=V(«D:V$,+P8D:VG.+vD:V;). - (8)

Of these (7) gives the more convenient form, from
which we obtain

HVVc=VV¢,DiVVP,V9;+ ke.
=VvV¢,VD.V¢.V4;+ VVP,VV4.D:V9,+ &e.;
and applying to each of these expressions the formula
VaV By=ySe8—pSay,
we obtain
ves{Sv¢,Dive.—Sve.Dive,} + &e.
+ D:V,{SV9,7¢.—SV¢,ve.} + &e.
=V91SV¢,D:7 ¢,-SV4,D:V¢.} +&e.+ &e.,
whence
SV¢.D:V¢,=Sv¢,D:V¢., &c.,
if the motion is irrotational. Also expressing
Vyo=lethBt+lhy,
we find, by operating with SV¢, on €ach side,
—H,=Sy¢,v9.D.8 +8v¢9,V9;,Diy
=8(yD.8—BDyy)

therefore
sftp 88 phy
L=8( 7 Di Defy)
and
—presS%¥p28_fp:72
Di,=8{ 2 p25 vii

iD. }= S( (Vv¢, Vv) Dio

=S{tape? tr a H

136 MR. GWYTHER ON THE LAGRANGIAN FORM OF

This form enables us to express in a general way the cri-
terion that the vortex motion may exist in the form which
it will be seen to take in a perfect fluid. Taking the two
other similar quantities, and equating each to zero, we get
VVD.c=0 or Di of the form vP; and, conversely, if
Vv D,c=0, then DJ=o

This notation also enables us to give a verbal expression
for Vvc. Thus: let PQR lie on a line of intersection of
two surfaces ¢, and ¢,, and let them be distinguished by

) :
Pir Pr jee and ¢,— Ps Then the vector difference ot
the velocities at Q and R is op and resolving parallel

to the face ¢, of the element, having P for centre, these
differential velocities on the parallel faces ¢,, we get

dco

5¢,V TE

do
== fi See
volume x \ ie! Vey

and similarly for the other faces. Therefore volume
x Vvo = resultant differential velocity and Vyc =
mean resultant differential velocity per unit of volume,
as the result of three shears and rotations. And by a
similar method we may find the force due to viscosity,
arising in consequence of the motion noticed above, upon

THE EQUATIONS OF FLUID-MOTION. 137

the faces ¢,, being due to the rate of change of the differ-
ential velocities just found. It will plainly be proportional

to volume x Vig VVO)VE.

EE:

The equation of motion is, on the generally adopted
theory,

DotvV+ wa VSVo+ 7 V'o=0,. « (1)
where V represents what would be written, in Cartesian,

= ( (X8x+ Y8y + Z8z) + (2 F

and therefore assumes each of these quantities perfect dif-
ferentials , and therefore g a function of p only.

We will first take po.

In any case o can evidently be written in terms of the
normals to the three surfaces ¢, determining the point at
which a is the velocity. Thus

o=K,V¢,+ K.V¢.+K,V¢,.
On the previous assumptions K,, K,, and K, must be of a
definite form, which we proceed to find thus :-—

Deo=D-K,V79,+K,D:7¢,+ ce.

de ds

=(D.K,+K, ae 0+ KS Ve.
d
+KS7. V¢,) Ve, +ke. + he.
da
= (DK, +8o a V¢,+&e.+ &e.

=D.K,V9,+DK,v9,+DK,v9,+2V (2), + (2)

138 MR. GWYTHER ON THE LAGRANGIAN FORM OF

whence the required form of the functions K,, K,, K, is
given by :

dP! dP! dP!
»)K= dg,? DK,= de,’ , D:K,= dg,’
or
dP dP dP
K,=— +%,, K,= + .,, K, AE )
d$, de, ae .

where P is a scalar, and D;}=o; .*. = is a scalar function
of 0,9. ¢; only, and o takes the form

VP+E,VOi+2:V02 42,79 - - - (4)
Proceeding to find V Vc, from this we get
Vyo=V (V=,V4, +V>:V¢2+ V>;V9;)

=(3- i )a+k&e. 4+&e.

=>,a4+ 3,843.9, say, 1. i ae
where D;==0, whence, if the motion is irrotational,

the >’s can be included in the VP under the above
hypotheses.

> = B bia
Also V Vo may be written HS, 5 TH2.F BS 23H

and since eee &c. denote the edges of the element, the

: HS
components of Vyo are — ys * &c. times the correspond-

I

ing edge; and if the fluid is incompressible this ratio
remains unaltered in time; and the manner of variation,
if the fluid is compressible, is dicated by the formula.
Also since D;2=0, if Vy is ever=o it always was and
will be = o, and the strength of the section of the vortex

* Conf. Mr. Hill’s paper “On some Properties of the Equations of Hy-
drodynamics,” Q. J. of Math. Feb. 1880.

oe |

THE EQUATIONS OF FLUID-MOTION. 139

on the surface ¢, is gee, V7 9,>,a=5pu,6y,>, and is con-

stant in all time.

If we compare the form of c here obtained with that
assumed by Helmholtz, we find that his form is not suffi-
ciently general, since he writes £,V¢,+2.V¢.+=2;V¢,
=VYo, where » is a vector with the condition Syw=o.
That is, he includes two undetermined quantities instead
of three, and does not express in a distinct form the essen-
tial condition (namely D,{ =o) affecting them.

The quantities = are in no way dependent on finite
forces which are acting (under the hypothesis) , but entirely
on the initial conditions (boundary conditions not now
being entertained).

Unless the density be a function of the pressure only,
the relations just proved will certainly not hold; for then

Dio +VV +yp=0,
and
Ey en Eb eae Jee
DK, + 75(\ A SS ich:
dP

<p = dg,

+2,
where =,=/(¢,, %., ¢,, and ¢), in which case the fluid-
pressures will of themselves cause vortex motion.

This seems to be a quite possible condition in a gas
rapidly heated or expanded.

Now turning to the terms containing wv and imagining d
a function of p only, and remembering that wu is independ-
ent of d, then
I
H

SVo= DH==Dd= D, log d

140 MR. GWYTHER ON THE LAGRANGIAN FORM OF

will not necessarily be a function of d only, since D,d is
not necessarily nor even generally so. Hence the con-
clusions we draw above will not generally hold good for

: : ¢ I
viscous fluids, even in the cases where V*o—0 or av ca

v Q, where Q is ascalar. But if the fluid is incompres-
sible, in either of these latter cases the theorems hold good.

Norr.—Since writing the above I have seen a paper by
M. Bresse, “ Fonction des vitesses, extension des théorémes
de Lagrange au cas d’un fluide imparfait” (‘ Comptes
Rendus,’ March 8, 1880), in which he seeks to show that,
if o=VP at any time, it will remain so throughout the
motion. In the investigation, however, the author follows

Navier in taking = as an absolute constant of the fluid.

This, of course, will not lead to correct results for a gas,
at any rate; and I think his result must be wrong for any
liquid, even incompressible, as it would follow that vortex
motion could not be generated, owing to the fluid-friction,
if, for instance, it started from rest.

I should explain the defect in his reasoning thus :—
Writing e@ for VVYo, and considering d constant, the
equation affecting ¢ is

Det (Sev )o+5V7e=0, or Vy Dis +5 V*e=0,

from which M. Bresse concludes that, if @ is at any time
zero, it remains so. Now this seems to require that, fora
small value of eg, y*e should not take a value of an infi-
nitely greater order. It has been shown by Maxwell, that

if @ be a vector function of any point, ae represents

the difference between the value of @ at that point and its

THE EQUATIONS QF FLUID-MOTION. 141

mean value over a small sphere of radius r about the point ;
and therefore I conceive that we cannot conclude from
the above equation that vortex motion may not arise in
lines or surfaces, but merely that it could not appear in a
solid form, a form of the existence of which we have no
evidence. The true criterion would be found by equating
to zero the expressions found above.

Although I conceive that the theorem is not proven for
the case which M. Bresse considers (where mu “ may have
any value other than zero),” I think that if wis sufficiently
small a proof may be given. For if « were zero the pro-
position is true, and the terms owing to which it departs
from the truth will appear with mu as a factor, and may
therefore be omitted from the term »% Ve; and under this
hypothesis, if «7 *e is ever zero it will continue so, and the
proposition is completed.

fie

Considering how the portion =,V¢,+>.V¢.+ 2, V4; of
the velocity can be impulsively generated, we see that the
initial equation of motion will take the form

ram Ty

where T is the infinitely small time during which the im-
pulsive force ) acts, and p is the impulsive fluid-pressure.
Now generally there will be no impulsive forces acting
bodily on the fluid. But the velocity will be generated by
the impulsive pressures only ; and therefore, if o does not
satisfy Vyo=o, it must be on account of one of two
reasons: either during the impulse d does not follow the
law of dependence on p, which is highly probable; or p is
discontinuous, so that the form Vp is an improper form.

14.2 MR. GWYTHER ON THE LAGRANGIAN FORM OF

DWis

The velocity can also be written in a form of simple ap-
pearance, thus,

*

fa— fg—f,, a

since
D.¢, =¢,— (Sov $:) =9,

whence

Dio= = Dea Dee —De,7

—(¢.4 eae Shee ~)e-

But

d Gs
(ScvV)= =O:95 + Org + Pigg 5

. do=—D9p,4 De, Dp,

and the condition for steady motion is D.g=o, showing a
close resemblance in form between the velocity in this case
and the rotation in a perfect fluid *.

We may at any time, by elimination of ¢, find two sur-
faces of the nature @ for which o= o; and since in steady
motion D,p=o, the property will continue in the surface,
Taking the two such surfaces for @, and @,, they will act as
fixed boundaries, their intersections will be the stream-
lines, and the form of o will be

o=— Fa. * Oo. halle A agiete aattamteay

* [Note that ?, is the flux through the side ¢, of the element of the fluid
under consideration, and remains unaltered if the motion issteady. If also
Syo=o, @, has properties similar to those of ¥,.|

THE EQUATIONS OF FLUID-MOTION. 143

In spite of the simplicity of this form, it does not appear
to yield a convenient form of condition affecting Dc, nor
for Vyo. The following property, however, can be
deduced.

In a perfect fluid under conservative forces we must
have (Scv)o of the form VP. But

(Scv)o=V = +VoVvoc;

“. VoVVc=VQ, say,

or
—0,3,79.+9,>,V?,=VQ,
whence
dQoa
dpe
and site and ae become o when acted on by D,, whence
dp, dp,

Q is a function of ¢, and 9, only. The existence of this
surface Q, on which both stream-lines and vortex-lines lie,
is dependent on the existence of vortex motion ; but if the
surface exists we may take it in place of the surface @, to
indicate the stream-lines; and then we get

=e
and
0.2,= I,
or
zy I
— - 9
Py

and the rotation would be given by

Vve-3,Vveva+ ~ Vv ve, . * .Q)

144, MR. WILLIAM E. A. AXON ON THE

_ Steady vortex motion will, I think, generally occur in
cases allied to the surfaces of discontinuity investigated
by Helmholtz; and the surface Q will then be such a
surface.

XVII. The Literary History of Parnell’s < Hermit.’
By Witu1am EH. A. Axon, M.R.S.L., &e.

Read December 28th, 1880.

AutHoucH Parnell’s poem of the ‘ Hermit’ can no longer
be considered what Mitford declared it to be, “ one of the
most popular in our language,” it still holds a certain and
assured place in English literature. But, apart from
its interest as a piece of English verse that has been a
favourite with several generations, the ‘ Hermit’ demands
attention as one link in a curious chain of the history
of fiction.

The readers of Voltaire are never likely to forget his
romance of ‘ Zadig ;’? and one of the most striking passages
in that remarkable work is the tweutieth chapter, in which
Zadig travels in company with an angel disguised as an
hermit who steals a gold cup from a dispenser of ostenta-
tious hospitality to give it to a miserly curmudgeon, burns
down the house of a man who has received them with true
liberality, and drowns the nephew of a widow lady by whom
they had been most honourably entertained. These seem-
ingly unjust and atrocious actions are all justified by the

LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’ 145

wider view of the supernatural being who has read the
book of fate and can foresce their real effect. The transfer
of the cup is to reform the pride of the one and to excite
the generosity of the other. Beneath the ruins of his
wrecked mansion the good man finds a greater treasure to
recompense his loss. The widow mourns the innocent
youth of one who, if he had lived another year, would
have been her murderer. Thus does the hermit vindicate
the dark and mysterious ways of Providence to man.

Some of the critics, vain in the possession of a little
learning, remarked that Voltaire’s apologue was not ori-
ginal, but copied from Parnell. It is quite possible that
such was the case; though Fréron might have remembered
that Antoinette Bourignon, the mystic, had employed the
same fable*. Parnell, although he does not make any avowal
of his indebtedness to any previous author, would hardly
have cared or dared to claim credit for the invention of
the story. He found the fable ready to his hand; he saw
that it formed good material for poetry ; and accordingly
he made the best use of it that he could in the poem which,
more than any thing else, has kept his memory from
oblivion. Pope says that Parnell found the story in
Howell’s ‘ Letters, a very curious book which was first
printed in 1645. Pope pronounced Parnell’s poem very
good. “The story,” he says, “was written originally in
Spanish, whence probably Howell had translated it into
prose and inserted it in one of his‘ letters.? Addison hked
the scheme, and was not disinclined to come into it”? +i:@
this supposed Spanish original we have no other testimony.

* Mitford has pointed this out in his < Life of Parnell,’ p. 61, where he
quotes from W. Harte these two lines :-—

“ Antonia, who the Hermit’s story fram’d,
A tale to prosemen known, by versemen famed.”

She was born in 1616, and died in 1680.
+ Goldsmith’s ‘ Life of Parnell.’

SER. III. VOL. VII. L

146 MR. WILLIAM BE, A. AXON ON THE

James Howell found the story in Sir Percy Herbert’s
‘ Certaine Conceptions or Considerations upon the Strange
Change of People’s Dispositions and Actions in these latter
times,’ a work “directed to his Sonne” and printed in the
year 1652*. Yet Howell’s ‘ Letters’ were printed two
years earlier, as Beloe has pointed out+. But as this
apologue is the sixth letter in the fourth volume, it may
have been added in a later issue.

It is also used by Henry More, the Platonist, in his
‘Divine Dialogues,’ which were published in 1668. The
«¢ Eremite and the Angel ”’ is in the second dialogue, chap.
xxiv., and follows very closely that given in the ‘ Gesta Ro-
manorum,’ to which we shall presently refer. This coin-
cidence was pointed out by Mr. 8S. Whyte at the close of
the last century { More’s version is as follows :—

‘‘ A certain Eremite having conceived great jealousies
touching the due administration of Dive Providence in
external occurrences in the world, in this anxiety of mind
was resolved to leave his cell and travel abroad to see with
his own eyes how things went abroad in the world. He
had not gone half a day’s journey, but a young man over-
tcok him and joyn’d company with him and insinuated
himself so far into the Hremite’s affection, that he thought
himself very happy in that he had got so agreeable a com-
panion. Wherefore resolving to take their fortunes
together, they always lodged in the same‘house. Some
few days’ travels had overpast before the Eremite took
notice of any thing remarkable. But at last he observed
that his fellow-traveller, with whom he had contracted so
intimate a friendship, in an house where they were extra-

* Lowndes, Bib. Man. (Bohn), p. 1049. Dunlop’s ‘History of Fiction,”
4th edit. (1876) p. 290.

t Beloe, ‘ Anecdotes of Literature,’ vol. vi. (1812) p. 324. He gives the
story in full from Herbert.

t ‘Miscellanea Nova,’ by 8. and E. A. Whyte, (Dublin, 1300) p. 145.

ee

LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’ 147

ordinary well treated, stole away a gilt cup from the gen-
tleman of the house and carried it away with him. The
Eremite was very much astonished with what he saw done
by so fair and agreeable a person as he conceived him to
be ; but thought not yet fit to speak to him or seem to take
notice of it. And therefore they travel fairly on together
as aforetimes, till night forced them to seek lodging. But
they light upon such an house as had a very unhospitable
owner, who shut them out unto the outward court and
exposed them all night to the injury of the open weather,
which chanced then to be very rainy; but the Eremite’s
fellow-traveller unexpectedly compensated his host’s ill-
entertainment with no meaner reward than the gilt cup he
had carried away from the former place, thrusting it in at
the window when they departed. This the Eremite thought
was very pretty, and that it was not covetousness but
humour that made him take it away from its first owner.
The next night where they lodged they were treated again
with a deal of kindness and civility: but the Eremite
observed with horrour that his fellow-traveller for an ill
requital strangled privately a young child of their so cour-
teous host in the cradle. This perplext the mind of the
poor Eremite very much; but in sadness and patience
forbearing to speak, he travelled another day’s journey
with the young man, and at evening took up in a place
where they were more made of than anywhere hitherto.
And because the way they had to travel next morning was
not so easie to find, the master of the house commanded
one of the servants to go part of the way to direct them ;
whom, while they were passing over a stone bridge, the
Eremite’s fellow-traveller caught suddenly betwixt the legs
and pitched him headlong from off the bridge into the
river and drowned him. Here the Eremite could have no
longer patience, but flew bitterly upon his fellow-traveller
L2

148 MR. WILLIAM E. A. AXON ON THE

for those barbarous actions, and renounced all friendship
with him, and would travel with him no longer nor keep
him company. Whereupon the young man smiling at the
honest zeal of the Eremite, and putting off his mortal
disguise, appeared as he was, in the form and lustre of an
angel of God, and told him he was sent to ease his mind
of the great anxiety it was encumbered with touching the
Divine Providence. ‘In which,’ said he, ‘nothing can
occur more perplexing and paradoxical than what you have
been offended at since we two travelled together. But yet
I will demonstrate to you,’ said he, ‘ that all that I have
done is very just and right. For, as for that first man
from whom I took the gilded cup, it was a real compen-
sation indeed of his hospitality ; that cup being so forcible
an occasion of the good man’s distempering himself and of
hazarding his health and life, which would be a great loss
to his poor neighbours, he being of so good and charitable
anature. But I put it into the window of that harsh and
unhospitable man that used us so ill, not as a booty to him,
but as a plague and a scourge to him, and for an ease to
his oppressed neighbours, that he may fall into intemper-
ance, disease, and death itself. For I knew very well that
there was that enchantment in this cup, that they that
had it would be thus bewitched with it. As for that civil
person whose child I strangled in the cradle, it was in great
mercy to him and no real hurt to the child, who is now

with God. . But if that child had lived, whereas this gen-
- tleman had been piously, charitably, and devotedly given,
his mind, I saw, would have unavoidably sunk into the
love of the world, out of love to his child, he having had
none before, and doting so hugely on it; and therefore I
took away this momentary life from the body of the child,
that the soul of the father might live for ever. And for
this last act, which you so much abhor, it was the most

LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’ 149

faithful piece of gratitude I could do to one that had used
us so humanely and kindly as that gentleman did. For
this man, who, by the appointment of his master, was so
— officious to us as to show us the way, intended this very
night ensuing to let in a company of rogues into his master’s
house to rob him of all that he had, if not to murder him
and his family.’ And having said thus, he vanished. But
the poor Eremite, transported with joy and amazement,
lift up his hands and eyes to heaven and gave glory to God
who had thus unexpectedly delivered him from any farther
anxiety touching the ways of Providence, and thus returned
with cheerfulness to his forsaken cell and spent the residue
of his days there in piety and peace.”

Indeed, in the seventeenth century it had become a
commonplace with which theologians might “ point a moral
or adorn a tale.’ Thus Thomas White, a Puritan divine,
writing in 1658, says :—

“There is a famous story of Providence in Bradwardine
to this purpose :—A certain Hermit that was much tempted
and was much unsatisfied concerning the providence of
God, resolved to journey from place to place till he
met with some that could satisfie him. An Angel in the
shape of a mau joyned himself with him as he was journey-
ing, telling him that’ he was sent from God to satisfie him
in his doubts of providence. The first night they lodged
at the house of a very holy man, and spent their time in
discourses of heaven and praises of God, and were enter-
tained with a great deal of freedom and joy. In the
morning when they departed the Angel took with him a
great cup of gold. The next night they came to the house
of another holy man who made them very welcome and
exceedingly rejoyced in their society and discourse; the
Angel notwithstanding, at his departure, kill’d an infant
in the cradle, which was his only son, being many years

150 MR. WILLIAM E. A. AXON ON THE

before childless, and therefore was a very fond father of
this child. The third night they came to another house
where they had like free entertainment as before. The
master of the family had a steward whom he highly prized,
and told them how happy he accounted himself in having
such a faithful servant. Next morning he sent this his
steward with them part of their way to direct them therein :
as they were going over a bridge the Angel flung the
steward into the river and drowned him. The last night
they came to a very wicked man’s house, where they had
very untoward entertainment; yet the angel next morning
gave him the cup of gold. All this being done, the Angel
asked the Hermit whether he understood those things.
He answered his doubts of Providence were increased, not
resolved ; for he could not understand why he should deal
so hardly with those holy men who received them with so
much love and joy, and yet give such a gift to that wicked
man who used them so unworthily. The angel said, ‘I
will now expound these things unto you. ‘The first house
where we came the master of it was a holy man, yet
drinking in that cup every morning, it bemg too large, it
did somewhat unfit him for holy duties, though not so
much that others or himself did perceive it; so I took it
away, since it is better for him to loose the cup of gold
than his temperance. The master of the family where we
lay the second night was a man given much to prayer and
meditation, and spent much time in holy duties,and was very
liberal to the poor, all the while he was childless; but as
soon as he had a son he grew so fond of it, spent so much
time in playing with it that he exceedingly neglected his
former holy exercise and gave but little to the poor, thinking
he could never lay up enough for his childe; therefore I
have taken the infant to Heaven and left him to serve God
better upon Earth. The steward whom IJ did drown had

LITERARY HISTORY OF PARNELL’S © HERMIT.’ 15]

plotted to kill his master the night following. And as for
that wicked man to whom I gave the cup of gold, he was
to have nothing in the other world, I gave him something
in this which, notwithstanding, will prove a snare to him,
for he will be more intemperate ; and let him which is
filthy be more filthy.” The truth of this story I affirm
not ; but the moral is very good ; for it shows that God is
an indulgent father to the saints when he most afflicts
them, and that when he sets the wicked on high ‘he sets
them also in slippery places, and their prosperity is their
ruine.’—Prov. 1. 327’*.

The caution of the worthy divine is to be commended in
declining to affirm the literal truth of this narrative.

White, it will be noticed, gives Bradwardine as the
authority for this apologue. This may be conjectured
to be the author who was styled the Doctor profundus
and whose ‘ Causa Dei contra Pelagium’ was a work of
weight and fame in the fourteenth century+. He was an
Archbishop of Canterbury, who was born in 1290 or
earlier, and died in 1349, of the plague. We can thus trace
the legend in England to the early part of the fourteenth
century.

In Germany it was used by Luther and by Joh. Herolt f,
whose ‘ Sermones de Tempore’ were printed at Nuremberg
in 1496.

In the thirteenth century it is found in several forms.
From M. Gaston Paris § we learn that it is in the sermons

* White's (Th.) ‘Treatise of the Power of Godliness,’ 1658, pp. 376-379.

+t Hook's ‘ Lives of the Archbishops of Canterbury,’ vol. iv. (1865) p. 80.

t Mitford’s ‘ Life of Parnell, prefixed to the Aldine edition of that poet.

§ “L’Ange et l'Ermite, étude sur une légende religieuse, par Gaston
Paris, lue dans la séance publique annuelle de l’Académie des Inscriptions,
12 Nov. 1880,” Journal Officiel, 16 Noy. 1880. The present paper was in
progress before the appearance of the “ étude” of M. Paris, All special in-
debtedness to his work has been carefully acknowledged.

P52. MR. WILLIAM E. A. AXON ON THE

of Jacques de Vitri, who died in 1240, and in the ‘ Scala
Coeli’ of Jean le Jeune, who wrote about the commence-
ment of the fourteenth century. “This beautiful apologue,”
observes Mr. Thomas Wright, ‘‘is of frequent occurrence
in old MSS., and differs considerably in different copies.”
He has printed a Latin version from the Harleian MSS. of
the thirteenth or fourteenth century*. The great collec-
tion of stories known as the ‘ Gesta Romanorum,’ there is
reason to suppose, was compiled in England about the close
of the thirteenth century for the use of preachers. It has
been a storehouse for the poets and dramatists also; but
its original intention was to provide the ecclesiastics with
something wherewith to enliven their dry theological dis-
courses. The story of the Hermit and the Angel is the
eightieth of this collection ; and an abstract of it is given
by Warton +. i

The story is found in a French conte, published in 1823,
by Méon, who found it added to some of the manuscripts
of the ‘ Vie des Péres,’ to which it did not originally belong.
In this poem we have the incidents of a cup stolen from
one host and given to another, of the servant drowned, of
the infant strangled, and of an abbey burned down that
the monks might once more be poor and pious. By a
process of natural selection Voltaire has omitted one of
the murders, and Parnell has left out the conflagration.
From this it may be doubted whether the witty French-
man was indebted to the English poet or to one of the
earlier texts. This has also been commented upon by
Dunlopt. ;

The story is also in some of the recensions of the ‘ Vitz

* «Latin Stories, edited by T. Wright, 1842, pp. ro and 247.

t+ Warton, Hist. of English Poetry, edited by Hazlitt (1871), vol. i. p. 256.

t Dunlop, ‘ History of Fiction, 4th edit. 1876, p. 289. _Wright’s ‘ Latin
Stories, 1842, p. 101.

LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’ 153

Patrum.’ One of these, in the ‘ Bibliotheque Mazarine,”
which has been published by M. E. du Méril, is regarded
by M. Gaston Paris as the origin of the medizval
variants. In this manuscript of the fourteenth century
the actors in the story are all hermits or ecclesiastics,
but the incidents, with the exception of the fire, are the
same.

Goldsmith, writing of Parnell’s ‘ Hermit,’ says that he
had been told that the fable was an Arabian invention.
In effect it is m the Koran, where Moses is said to have
met a nameless prophet whom the commentators style Al-
Khedr :—

« And Moses said unto him, ‘ Shall I follow thee that
thou mayest teach me part of that which thou hast been
taught for a direction unto me?’ He answered, ‘ Verily
thou canst not bear with me: for how canst thou patiently
suffer those things the knowledge whereof thou dost not
comprehend ?”? Moses replied, ‘ Thou shalt find me patient
if God please, neither will I be disobedient unto thee in
any thing,’ He said, ‘If thou follow me, therefore, ask
me not concerning any thing until I shall declare the
meaning thereof unto thee.’ So they both went on by
the sea-shore, until they went up into a ship; and he made
a hole therein. And Moses said unto him, ‘ Hast thou
made a hole therein that thou mightest drown those who
are on board? Now hast thou done a strange thing.’ He
answered, ‘ Did I not tell thee thou couldest not bear with
me?’ Moses said, ‘ Rebuke me not, because I did forget,
and impose not on me a difficulty in what I commanded.’
Wherefore they left the ship and proceeded until they met
with a youth ; and he slew him. Moses said, ‘ Hast thou
slain an innocent person without his having killed another ?
Now hast thou committed an unjust action.” He answered,
‘ Did I not tell thee that thou couldest not bear with me?’

154 MR. WILLIAM E. A. AXON ON THE

Moses said, ‘ If I ask thee concerning any thing hereafter,
suffer me not to accompany thee. Now hast thou received
an excuse from me.’ They went forwards, therefore, until
they came to the inhabitants of a certain city: and they
asked food of the inhabitants thereof; but they refused to
receive them. And they found therein a wall which was
ready to fall down; and he set it upright. Whereupon
Moses said unto him, ‘If thou wouldest, thou mightest
have received a reward for it.’ He answered, ‘ This shall
be a separation between me and thee: but I will first
declare unto thee the signification of that which thou
couldest not bear with patience. The vessel belonged to
certain poor men who did their business in the sea; and I
was minded to render it unserviceable because there was a
king behind them who took every sound ship by force.
As to the youth, his parents were true believers, and we
feared lest he, being an unbeliever, should oblige them to
suffer his perverseness and ingratitude: wherefore we
desired that their "Lord might give them a more righteous
child in exchange for him, and one more affectionate
towards them. And the wall belonged to two orphan
youths in the city, and,in it was a treasure hidden which
belonged to them ; and their father was a righteous man:
and thy Lord was pleased that they should attain their
full age, and take forth their treasure, through the mercy
of thy Lord. And I did not what thou hast seen of my
own will, but by God’s direction. This is the inter-
pretation of that which thou couldest not bear with
patience ’” *.

This is the oldest literary form of Parnell’s ‘ Hermit.’
It may well be supposed that the Arabian Prophet borrowed
the beautiful legend, as he did many other things, from a

* Koran, Sale’s translation, chap. xviii. Dunlop’s ‘ History of Fiction,’

p. 292.

LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’ 155

Jewish source. The Talmud may, in its present form, be
later than the Koran; but it embodies the traditions of a
race who have always clung to the sacred memories of
their literature and their religion. The form in which we
find it in this vast encyclopedia of Hebrew learning is very
different from those already given :—

- “Rabbi Jochanan, the son of Levi, fasted and prayed to
the Lord that he might be permitted to gaze on the angel
Elijah, he who had ascended alive to heaven. God granted
his prayer; and in the semblance of aman Elijah appeared
before him.

“Let me journey with thee in thy travels through the
world, prayed the Rabbi to Elijah ; ‘ Let me observe thy
doings, and gain in wisdom and understanding.’

“ « Nay, answered Elijah ; ‘my actions thou couldst not
understand ; my doings would trouble thee, being beyond
thy comprehension.’

*« But still the Rabbi entreated. ‘I will neither trouble
nor question thee,’ he said; ‘ only let me accompany thee
on thy way.’

“Come then,’ said Elijah; ‘but let thy tongue be
mute. With thy first question, thy first expression of
astonishment, we must part company.’

“So the two journeyed through the world together,
They approached the house of a poor man whose only
treasure and means of support was a cow. As they came
near, the man and his wife hastened to meet them, begged
them to enter their cot and eat and drink of the best they
could afford, and to pass the night under their roof. This
they did, receiving every attention from their poor but
hospitable host and hostess. In the morning Elijah rose
up early and prayed to God, and when he had finished his
prayer, behold the cow belonging to the poor people
dropped dead.

156 MR. WILLIAM E. A. AXON ON THE

“Then the travellers continued on their journey.

“Much was Rabbi Jochanan perplexed. ‘Not only
did we neglect to pay them for their hospitality and
generous services, but his cow we have killed ;’ and he
said to Elijah, ‘ Why didst thou kill the cow of this good

3

man who

«<< Peace !’? interrupted Elijah ; ‘ hear, see, and be silent !
If I answer thy questions we must part.’ And they con-
tinued on their way together.

“Towards evening they arrived at a large and imposing
mansion, the residence of a haughty and wealthy man. They
were coldly received ; a piece of bread and a glass of water
were placed before them, but the master of the house did
not welcome or speak to them, and they remained there
during the night unnoticed. In the morning Elijah re-
marked that a wall of the house required repairing, and
sending for a carpenter, he himself paid the money for
the repair as a return, he said, for the hospitality they had
received.

« Again was Rabbi Jochanan filled with wonder; but
he said naught, and they proceeded on their journey.

“ As the shades of night were falling, they entered a
city which contained a large and imposing synagogue. As
it was the time of the evening service, they entered and
were much pleased with the rich adornments, the velvet
cushions, and gilded curves of the interior. After the
completion of the service, Elijah arose and called out
aloud, ‘ Who is here willing to feed and lodge two poor
men this night?’. None answered, and no respect was
shown to the travelling stranger. In the morning, how-
ever, Elijah reentered the synagogue, and, shaking its
members by the hands, he said, ‘I hope that you may all
become presidents.’

“Next evening the two entered another city, when

LITERARY HISTORY OF PARNELL’s ‘ HERMIT.’ 157

the Shamas (sexton) of the synagogue came to meet
them, and notifying the members of his congregation of
the coming of two strangers, the best hotel of the place
was opened to them, and all vied in showing them attention
and honour.

“In the morning, on parting with them, Elijah said,
‘May the Lord appoint over you but one president.’

“ Jochanan could resist his curiosity no longer. ‘ Tell
me,’ said he to Elijah, ‘ tell me the meaning of all these
actions which I have witnessed. To those who have
treated us coldly thou hast uttered good wishes ; to those
who have been gracious to us thou hast made no suitable
return. Even though we must part, I pray thee explain
to me the meaning of thy acts.’

« ¢ Listen,’ said Elijah, ‘and Jearn to trust in God, even
though thou canst not understand His ways. We first
entered the house of the poor man who treated us kindly.
Know that it had been decreed that on that very day his
wife should die. I prayed unto the Lord that the cow
might prove a redemption for her; God granted my prayers,
and the woman was preserved unto her husband. The
rich man whom next we called up, treated us coldly, and
I repaired his wall. I repaired it without a new founda-
tion, without digging to the old one. Had he repaired it
himself, he would have dug and thus discovered a treasure
which lies there buried, but which is now for ever lost to
him. To the members of the synagogue who were inhos-
pitable, I said, ‘May you all be presidents,’ and where
many rule there can be no peace ; but to the others I said,
‘May you have but one president;’ with one leader no
misunderstanding may arise. Now, if thou seest the
wicked prospering, be not envious; if thou seest the
righteous in poverty and trouble, be not provoked or
doubtful of God’s justice. The Lord is righteous, His

158 MR. WILLIAM E. A. AXON ON THE

judgments all are true; His eyes note all mankind, and
none can say, ‘ What dost thou?’ ”

“ With these words Elijah disappeared, and Jochanan
was left alone ”’*.

There is another story illustrating the same moral.
“‘ Moses sees a warrior come to a fountain, by whose side
he leaves a sack of gold, which was taken away by a
shepherd. An old man, bending beneath a heavy burden,
then came to the fountain, when the horseman returned
and accused him of having purloined the sack of gold.
In spite of his protestations of innocence the warrior drew
his sword and slew the old man. Whilst Moses is filled
with horror at the sight, the voice of God explains to
him that the old man had murdered the father of the
warrior, that the money really belonged to the shepherd,
although he was unaware of it, and that the warrior lost
because he had acquired it without right and used it only
for evil purposes” f.

This has also found its way into the ‘ Gesta Romanorum”
and similar collections.

We have thus traced Parnell’s ‘Hermit’ as far back
as is at present possible. Whether it was the in-
vention of a Jewish poet or borrowed by a Hebrew
moralist from some still earlier source it is impossible
to say.

That the Prophet of Islam learned it from some of the
Arabian Jews is very probable ; but the manner in which
it entered Europe and the mode in which it became in-
corporated with the ecclesiastical literature of the middle
ages are not known; though M. Paris has conjectured that

* «The Talmud,’ by H. Polano, (London, n. d.) p. 313. Baring-Gould’s
‘Legends of Old-Testament Characters,’ vol. ti. (1871) p. 113.
t Baring-Gould’s ‘ Legends of Old-Testament Characters,’ vol. ii. (1871)

p-s023,

LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’ 159

it may have come from Egypt, where adherents of the
three faiths of Judaism, Islam, and Christianity existed
side by side. In corroboration of this, the simplest form
of the European story has for its characters the hermits
of the Thebaid.

The apologue commended itself not only to a crowd of
churchmen and divines, but to a poet like Parnell, a fanatic
like Antoimette Bourignon, and a doubter like Voltaire.
Sometimes it assumes the form of a very practical homily
upon everyday life, and at others is bounded by the
narrow limits of the artificial virtues of ecclesiasticism ; but
in each case the motive is the same. All versions of the
legend seek to vindicate the moral order of the universe
by an explanation of the seeming contradiction of parti-
cular stances.

The problems of life are essentially the same in all ages.
“*T have been young,” says the Psalmist, “and now am old ;
yet have I not seen the righteous forsaken, nor his seed
begging their bread.” There are many, however, both in
ancient and modern days, who have not been so fortunate,
and who have looked out upon a world where the righteous,
to all earthly appearance, were forsaken. They have seen
the tyrant triumphant whilst none dared to comfort the
slave. They have seen Vice seated on the throne and
Virtue dying in the dungeon. They have seen sorrow and
evil in a thousand forms.

The existence of evil is alike the moral and physical
riddle of the universe. Notwithstanding all man’s efforts
the sphinx has not relaxed the rigidity of her features,
which still proclaim her the keeper of the unsolved
mystery. This beautiful Hebrew apologue is one of
the many efforts to reconcile the conception of an all-
good and all-wise ruler of the universe with the existence
of Wrong clothed in purple and fine linen, and of Right

160 ON THE LITERARY HISTORY OF PARNELL’S ‘ HERMIT.’

that eats the bread of sorrow and drinks the water of
affliction.

There is a subtler problem which the story leaves un-
touched. It deals only with the surface of things.
Beautiful as it is, it embodies the judgment of a primitive
people who see only the concrete aspects of life. With
them the blessings of God take visible shape in worldly
possessions, in flocks and herds, in gold and silver, in men-
servants and maidservants. The real touchstone, how-
ever, is internal, and not external.

‘‘ He that has light within his own clear breast
May sit i’ the centre and enjoy bright day ;
But he that hides a dark soul and foul thoughts
Benighted walks under the mid-day sun;
Himself is his own dungeon.

Into this sphere of thought the old fabulist enters not.
He is content to give dramatic force to that which Pope
has expressed in didactic form :—

“ All Nature is but art unknown to thee;
All chance, direction which thou canst not see ;
All discord, harmony not understood ;
All partial evil, universal good ;
And spite of pride, in erring reason’s spite,
One truth is clear, whatever is is right.

ON THE LONG-PERIOD INEQUALITY IN RAINFALL. 16]

XVIII. On the Long-period Inequality in Rainfall. By
Batrour Stewart, LL.D., F.R.S., Professor of Na-
tural Philosophy at the Owens College, Manchester.

Read February 24th, 1880.

1. If it be true that there is a variation in the power of
the sun depending ou the state of his surface, this varia-
tion might naturally be expected to make itself apparent
through a corresponding change in the rainfall of the
earth; so that when the sun is most powerful there ought
to be the greatest rainfall. ny

2. While the connexion indicated above is that which
most readily occurs to the mind, yet the difficulty of
ascertaining the facts of the case in a manner bearing the
smallest approach to completeness is so great as to be at
present insuperable.

There is first of all an intense reference to locality in
rainfall, so that the rainfall at one place may differ greatly
from that at another place in its near neighbourhood.
Again, there are probably, in addition to possible secular
inequalities, very great oscillations in the yearly rainfall at
any one place, or accidental variations, as we may term
them in our ignorance of their cause.

Thirdly, it is in comparatively few places, and those
places chosen without the smallest reference to this par-
ticular problem, that we have any thing like a trustworthy
account of the rainfall throughout a considerable number
of years.

SER. IIL. VOL. VII. M

162 PROF. B. STEWART ON THE LONG-PERIOD

Fourthly, we have no information of any importance
with respect to the rainfall at sea.

3. Besides the formidable catalogue of difficulties now
mentioned, we ought to bear in mind the following con-

siderations. The convection currents of the earth are
regulated by two things, one of which is constant, while
the other may be variable. The constant element is the
velocity of rotation of the earth on its axis, while the
element of possible variability is the power of the sun.
Hence it follows that, if the sun be variable, it will cause
a variation in the direction as well as in the intensity of
the earth’s convection currents, on the principle which
tells us that the resultant of two forces, one constant
and the other variable, must vary both in magnitude and

, direction.

Now, if it be true that we have a long-period variation,
not merely of the intensity, but also of the distribution of
the earth’s convection currents, and if we bear in mind
the intensely local reference in rainfall, it would be too
much to expect that the rainfall inequality should exhibit
the same years of maximum and minimum at all
places. It is even conceivable that some places might
exhibit a maximum while others showed a minimum,
while others, again, might exhibit a double instead of a
single period.

4. It appears to me that, if we bear in mind these con-
siderations, it will not answer to add together the rainfall
of a few selected stations as they stand, with the view of
determining by this means whether there be a long-period
inequality in the rainfall of the whole Karth. We are not
yet in a position to reply experimentally to this question.
It does not, however, follow that nothing can be done.
Dr. Meldrum and others appear to have achieved good
preliminary work in the direction of indicating the exist-

INEQUALITY IN RAINFALL, 163

ence of a rainfall-inequality depending upon the state of
the sun. Dr. Meldrum began by pointing out that in a
good many places there is a greater rainfall during years
of maximum than during years of minimum sun-spots,
and that this phenomenon repeats itself from one solar
cycle to another. Again, Governor Rawson has pointed
out the existence of certain localities where the rainfall-
inequality appears to be of a precisely opposite character,
while Dr. Hunter has showed the practical importance of
the investigation with reference to certain tropical stations.
The subject has likewise been discussed by Smyth, Stone,
and others.

5. The question has arisen whether it might be possible
to throw any light on this problem by the method of
detecting unknown inequalities, proposed by Mr. Dodgson
and myself (see ‘ Proceedings’ of the Royal Society,
May 29, 1879). The essence of this method consists in a
way by which we may numerically estimate the indica-
tions of an inequality. Let us suppose for instance that,
in ignorance of the diurnal range of temperature, we try
to find whether there be a temperature-inequality of 24
hours or whether there be not rather one of 26 hours. We
should begin by taking a large number of hourly readings
of temperature; and we should group these into two series,
the one containing 24 numbers in each horizontal row,
and the other 26. We should thus have 24 vertical
columns from the one series and 26 from the other; and
we should take the mean of each vertical column of each
series as well as the mean of the whole.

Now it would.speedily be found that an inequality was
indicated by the 24-hourly series and none by that of 26
hours. For in the first series the mean of the vertical
column representing observations at 5 a.m. would be
greatly less than the mean of the whole, while the mean

M 2

164. PROF. B. STEWART ON THE LONG-PERIOD

of the column representing observations at 2 p.m. would
be much higher than the mean of the whole. On the
other hand, in the 26-hourly series, provided it were suffi-
ciently extensive, we should perceive no such differences.
Thus, in the 24-hourly series the differences of the means
of the various vertical columns from the mean of the
whole would be much greater than in the 26-hourly series;
and the mean amount of these differences might be taken
to form a numerical criterion of the presence or absence
of an inequality.

6. This method, therefore, applied to the subject in
hand, might be expected to reveal the presence or absence
of inequalities in rainfall, provided we have observations
sufficient for the purpose. It is clear that the successful
application of this method does not require a previous
knowledge of the exact form of the inequality. Whether
a maximum rainfall occurs at epochs of maximum or at
epochs of minimum sun-spot frequency, whether there
be only one rainfall maximum corresponding to the solar
period, or two, or even three, is a matter of no con-
sequence as far as this method is concerned. All that is
necessary is that the rainfall should always be similarly
affected by similar states of the sun. Here, however, we
must bear in mind that this method of detecting inequa-
lities by summing up and averaging the departures from
the mean caused by the inequality, likewise sums up and
averages the accidental fluctuations. Now these accidental
fluctuations are particularly large for rainfall; and it is
therefore desirable to lessen their disturbing effect as
much as possible. This can only be done by confining
ourselves to long series of observations, in which the
accidental fluctuations may be supposed to counteract each
other to a great extent, while the long-period fluctuations
will remain behind.

INEQUALITY IN RAINFALL. 165

7. Through the kindness of Mr. Whipple, Director of
the Kew Observatory, I have received copies of those
catalogues of rainfall which he has himself made use of in
a paper which was recently communicated to the Royal
Society (January 8, 1880). Of these Paris, Padua, Eng-
land, and Milan form the most extensive series, that of
Paris embracing 161 years, Padua 154, England (Symons’s
Table) 140, Milan 115. Mr. Whipple has likewise
furnished materials by which the labour of applying the
process in hand to these series will be much abridged ; and
he has kindly allowed me to make use of these. I will
therefore apply the process to these four stations.

8. Let us begin by grouping the Paris yearly values "
into series of 8. We thus obtain the following final num-
bers expressed in centimetres—51°4,47°5, 45°7, 48°7, 51°I,
49°8, 46°5, 47°2, the mean being 48°5. From these we
obtain the following series of differences :—

+2'9, —1°0, —2°8, +0'2, +2°6, +1°3, —2°0, —1°3.

In order to diminish the effect of accidental fluctuations,
let us equalize this series of differences by taking the mean
of each two. We thus obtain—

+0°8, 4+-1'0, —I°9, —1°3, +1°4, +1°9, —0'4, —1°7.

If we now add these together, without respect of sign, and
divide by their number (8), we obtain 1°3 as the mean
departure from the mean of the whole ; and bringing this
into a proportional shape by dividing it by the mean rain-
fall (48°5), we obtain een 8 per cent.

g. These explanations will enable the reader at once to
perceive the principle of construction of the following

Table :—

166 PROF. B. STEWART ON THE LONG-PERIOD

Proportional Rainfall-inequality, as exhibited by series
of years.

Eight Nine Ten Eleven Twelve Thirteen Fourteen

years. years. years. years. years. years. years.
English rainfall,

2°63

Symons’sCata- Avi APR TAG) GIS 1°69 2°57

logue ....:...:
IPAMIS aise nsesen tenes PANS Heyy OG gfe) 2°57, 3508
PACU siec eee oleslan same 177 iO? ee O27 oD 2162) ee Rrac
Milan .......scties.. i2 322 3176 178 41g 3°78 =. 2°49

We ought to give the English, the Paris, and the Padua
observations a somewhat higher weight than those of
Milan, as the former embrace a longer period. This will
be done sufficiently well by giving the first three sets
weights of 3 each and the Milan set a weight of 2. If we
perform this operation and then take the mean, we obtain
as under :—

Hight Nine Ten Eleven Twelve Thirteen Fourteen

years. years. years. years. years. years. years.
Mean of the four

stations,weight- 215 4:00 2:09 1°94 3°52 2°81 2°92
ed as above

A maximum corresponding to nine years, and a still greater
one, corresponding to twelve years, are thus exhibited, each

, of these being recorded at three stations out of four.

The proportional numbers indicated are not large; but
it must be remembered that it is the mean difference for
all the years that is given, and that the maximum and
minimum rainfall will represent differences above and
below the mean which will each be about double the num-
bers recorded above.

10. Regarding the rainfall-values as representing the
meteorological result of the sun’s action, let us now com-
pare these with declination-range values, which may be
taken to represent the sun’s magnetic effect. Professor
Loomis has compiled (American Journal of Science and

INEQUALITY IN RAINFALL. 167

Arts, 2nd ser. vol. 1. p. 153) what seems to be a very good
Table, exhibiting a set of yearly values of magnetic decli-
nation-range extending, with slight breaks, from 1777 to
1868.

Let us take this Table and treat it precisely as we have
treated the rainfall, except that it does not seem necessary
to make any attempt at equalization such as that made in
article 8.

[ We thus obtain the following result :—

Proportional Declination-range Inequality, as exhibited by
series of years.

Eight Nine Ten Eleven Twelve Thirteen Fourteen
years. years. years. years. years. years. years.
Prague, or re-
duced to Pra-+ 3°37 3°39 10°07 4°66 9°33 4°09 4°98
gue eecceescccce
Here we have decided maxima corresponding to ten
, and twelve years. The result is thus not unlike that
which has been derived from rainfall-observations, where
the maxima correspond to nine and twelve years ; indeed
we could hardly expect a more perfect correspondence
between the two, bearmg in mind the limited amount of
observations which we have for determining inequalities of

long periods.

Note added on March 6th.

I take this opportunity of saying a few words on what I
imagine to be the proper line of policy that should be
pursued in this research.

(1) There are manifestly two stages in the investigation.
In the first place we wish to ascertain whether there is any
connexion between the state of the sun’s surface (as
revealed by spots) and the meteorology of the earth; and

168 ON THE LONG-PERIOD INEQUALITY IN RAINFALL.

in the second place we wish to find the nature and laws of
this connexion should it be proved to exist.

(2) If the various meteorological elements at the va-
rious stations of the earth are found to present the same
periodic inequalities as those which characterize sun-spots,
this must be taken as decisive in favour of a connexion of
some sort between the two, quite irrespective of the exact
form of the inequalities. Nor will this evidence be invali-
dated if an inequality at one station should be different in
form from that at another.

(3) Assuming the probability (from the evidence already
brought forward) of such a connexion, the most natural
hypothesis is that which supposes that the sun has inequa-
lities which affect his radiating-power. Hence it is of
great importance (as proposed by Professor Stokes and
others) to ascertain by judicious actinometrical experi-
ments whether the heating effect of the sun’s rays be in
reality variable. |

(4) In absence of actinometrical results, we have
grounds for believing that the magnetic activity of the
sun is greatest at epochs of maximum sun-spots; and it
seems most natural that the meteorological activity of our
luminary should be greatest when his magnetical activity
is greatest.

From the reasoning of the paper to which this note is
added we may conclude that there is no evidence which
can be deduced from rainfall against this hypothesis.

(5) But while there is considerable preliminary evidence
in favour of a variability in the heating-power of the sun,
and while this is constantly accumulating, we must not
deem it impossible that the sun affects the earth in some
other way.

There is ground for supposing that the moon affects
both the magnetism and meteorology of the earth in a way

VELOCITY OF A FLUID UNDER CONSERVATIVE FORCES. 169

which we do not at present understand ; and it is possible
that the sun may have a similar influence.

Since writing the above, I have learned that Mr. Baxen-
dell made use of the method of mean departures described
in this communication in one of a remarkable series of
papers which he presented to this Society on March 8th,
1864. But I have no reason for supposing that he was
aware of the peculiar characteristics of the method de-
vised by Mr. Dodgson and myself, in virtue of which we
can, with comparatively little trouble, ascertain the exact
periods of inequalities which are crowded very near to-
gether in the time-scale.

XIX. On a Form of representing the Velocity at any
Point of an Incompressible Fluid under Conservative
Forces. By R. F. Gwyruer, M.A.

Read February 24th, 1880.

1. The velocity at any point of a fluid may be repre-
sented in other forms than the usual velocity potential or
the vector potential of Helmholtz.

The form c= v¢ corresponds to the case when Sa6r is
a complete differential without a factor; let us imagine it
to be made a complete differential by a factor—that is, o
to be of the form

o=k Vv,

or to be a combination of the two, thus,

C= Varn seh tame fete) (hs)

170 MR. R. F. GWYTHER ON THE VELOCITY OF

2. First let us consider the circumstances accompanying
the forms. If Scé7 is integrable by a factor, the condition
- Sov o=o, or Sop=0,—
that is, the axes of vortex-motion perpendicular to the
lines of flow, a case satisfying the conditions of parallel
cylindrical vortices and vortex rings.

If c—V ¢ be integrable by a factor, the condition is

S(¢—v¢) Vv (*—-V¢) =9,
or S(c— V ¢)p=o0.

From this scalar equation ¢ could be found ; and we
may consider c=y¢+hkyy as a general form of expres-
sion for the velocity at any point.

3. The kinematical condition that o must satisfy is the
“ equation of continuity,’ which if the fluid is incompres-
sible takes the form

Svyo=0;
or
| V O+tkV bt+SVivwso; . . =. . (a)
and the angular velocity at any poimt in the fluid is

given by
2p=VVEVV. 2s fo

The form taken by the equation of motion, when this
expression is submitted for o, will now be found ; for
Do=—V (v +2)
may be written
D(vetiyy=—v(V+2),
or

Day + Dive +kDiyy= —a(v ~ *).

Now Div=V.- DAD, where A acts only. on the o in
D, or d;— (Soy) ; therefore

A FLUID UNDER CONSERVATIVE FORCES. bog) |

D;« Vb+KD:. Vv=V7 -Didpt+kV - Dear
+A{(Scv)G+k(Sov7)}

=V -Ddtkyv .Dab+i vo’,
and, finally, the equation of motion is

SVD6+Dk.VP+kV Dap thVor= -V(V+ -).

Now this equation is equivalent to three scalar equa-
tions; and if we make in it the substitutions D,A=o,
Dyrr=o, we reduce it to a single equation and solvable ;
for then

o2
vDip= —v(V +24 =),
or
o2

a tn LER oes =
Did= ¥ m Pee ONY) O,

where VY ‘Oo is independent of the position and may be
included in the @¢ on solution.

Putting for D.¢, ¢—(Scv)¢, and substituting for o
we get

é—(ag)—-iSy gyy=—V—2_Wet ive”

or

2g— (V9)? +R(yp)?=—2V—, . pont anew)

In support of the substitutions D,sA=o and Dab=o I
should state

(1) That such surfaces can be found from the differential
equation.

(2) That only three scalar equations have been used in
determining o so as to satisfy the equation of motion.

(3) That as the intersections of such surfaces, if they
exist, are to move with the fluid, it is not unnatural to

172 MR. R. F. GWYTHER ON THE VELOCITY OF

make the trial of the possibility ; and a fourth we shall see
later.

[It may not be out of place to notice that from the
equation

o— (Soy)o=y(V+2),
m
which may be written
es Digs
o—2V.cp= v(V at ett );
we may by operating with SV get the equation
4p?—2Svpc=y’P,
2
where P stands for V + £ + ae r
TS oe?

an equation I have never seen stated. |

4. In order to interpret as far as possible the expres-
sions here introduced, we take first the last two con-
ditions, which express that the surfaces & and yw move
with the fluid so as always to contain the same fluid-
elements ; and, referring to the expression for the angular
velocity, we see that they intersect in the vortex-lines.

It would be well to determine these surfaces more fully.
We have as yet treated them as distinct. However, the
surfaces k and coincide or do not exist where vortex-
motion does not exist ; for then V. VAVy=0 at all points,
and the normals to the surfaces at all points are parallel ;
whence the surfaces k= const. and y= const. coincide
except at points where vortex-motion exists. In order,
therefore, to apply this method to the solution of rotational
motion of a fluid, we should consider kyy an additive term,
and take for k and yf values such as to make the surfaces
k= const. and y= const. move with the rotational fluid,
and always intersect in vortex-lines, while the term Ad
would be taken to satisfy the general irrotational motion. —

A FLUID UNDER CONSERVATIVE FORCES. Ifo

5. To investigate the energy within a surface drawn
within a fluid we get, by continually using a modification
of Green’s Theorem and omitting Thomson’s correction,

—2T ={o"dv={8 (Ad thy) odv=|Soygdv + \Skoyydv
= —[Syoddv + [SopvdS—|Sykowdv + {SkyovdS
= —|Syo($ +h) dv—\Spykodv +\8 ($+ kp)ovdS
=—[Syvkodv+|S(p+kpovdS;. . . . . (VY)
where v stands for the unit normal to the surface, and
where the last term vanishes if there is no flow across the
bounding surface.

We may then use the equation of continuity to give
other forms to the volume integral. Thus

Syvlo=ypSvk(yo +kvyp)
=V8 (vivb—ky*p—Byp),
forms which will allow us to use Green’s theorem again.

From the rate of change of the circulation in a closed
circuit moving with the fluid we get

DScdr=o, where dr is an element
of the circuit, or

JSDirdr + {Sod . Der=[SD,odr + \Sodo=o.

The second is zero over every closed circuit. In order
that the first may be so we must have VV .Dio=o, or
referring to

VivDé.vrtviv.Dap}=o, . . . (VI)

a further justification for our assumption.
The simplest way of finding D,p is as follows:—We have
seen that

Do=o—(S vy) c= —2Vop—hyo?.

174 MR. R. F. GWYTHER ON SOME
Operate upon this with Vv, then
VyD,o=p—2VyVop=p-— (Soy)p + (Spv)o
=Dp+ (Spv)e.

But, from the circulation, VV Dic=0 ;

Dio —(Spw)e.) 2052), Vale)
The value in terms of & and ¥ is not so simple as to
deserve notice.

The geometry of the motion is not easily explained,
owing to the fact that ¢ is not the third surface satisfying
Dé(v)=0; also & and w will not generally be independent,
as the condition for irrotational motion is that they should
touch at the points of intersection.

XX. Notes on some Quaternion Transformations.
By R. F. Gwyrner, M.A.

Read February 24th, 1880.

Tuer following theorems are frequently required in phy-
sical problems, especially in the motion of fluids.

I.

If + denote the vector of any poimt and yV Hamilton’s
operator, and if p and o are any vector functions of 7,
then

V (pc) =Vpo—pvot2(Spv)c.. . . . {1)
More generally, if p and o be any vectors depending on
the scalars a, b, c, &c., and if «, 8, y, &c. be any vectors

QUATERNION TRANSFORMATIONS. 175

whatever, and if ad,+6d,+yd.+ &c. =D (where d, de-
notes differentiation with regard to a, &c.), then

D(pc) =Dp.c—pDao+2(SpD)c.
For
ad,(po)=ad,p.c+ap.d,o

=ad,p.c—pa.d,o+2(Spad,)o,
since
ap + pa=2Spa.

If we now form the similar quantities for Bd,, &c., and
add the respective sides of the equation thus formed,

. D(pc) =Dp.c—pDo+2(SpD)c.. . . (IL)

But 7 may be written ae+08+ cy, where a, B, y are rect-
angular unit vectors. D in this case becomes identical
with V7, and the preceding form may be deduced.

The more general form is occasionally useful.

From I. we may, by taking scalar and vector parts, get

SV (¢o)=8 . vpo—S pyas) does) &) GD
Vv (pc) =Vvpo—Vevot2(Spy)o,. - (IV.)
whence we may deduce by putting p=o

Vye—2)..Vivo.c+2(SovVio. .... (V.)

We may also deduce from (1) expressions for Vv (Vpc)
and V (Spc).
Thus V (Veo) =2V (po—ap)

=S.ypo—S.pyot (SpVjo—(Soy)p+Svp.c—Syo.p,

and

V (Spc) =V .Vvp.c—VpVvyo+ (SpV)o+ (Sov )p.

176 ON SOME QUARTERNION TRANSFORMATIONS.

These forms simplify still further when in fluid-motion o
is the velocity at any point, and Vyo=2p gives the rota-
tion at that point, in which case Syp =o.

We have then

Vv (Veo) = (Sev)o— (Sov)p—Sve-p,
Sv(Vpo) =S . vpo— 5p",
and
V (Sea) = Vvpo + (Spy)e + (Sov)e.

Again, Helmholtz’s notation for the form of o gives
o=V($+), where ¢ is a scalar and Syw=o; and these
formulz are applicable in the reduction of the equations.

A slight adaptation of this method enables us to prove
that, if p and g are quaternion functions of 7, we should
have

V(pq)=Veg+ Kpvg+2(Spv)¢. - - (VI)

II.

These results are very useful in obtaiing modified
forms of Green’s theorem.
The general form of the theorem is

[Syyrdv=|Swr . ds,

where vf is a single-valued vector function in simply con-
nected space, dv an element of volume, ds of its bounding
surface, and v the unit vector normal to ds drawn

outwards.
Casz I. Let ~=V(po).
Then by (V)
Syv=Sypo—Spve,
and we get

{Sypodo—(Spyodv=[SVpo.vds=[Spovds. . (VIE)

DR. JAMES BOTTOMLEY ON COLORIMETRY. Lay

Case IT. Let y=¢o, where ¢ is a scalar.
Then

Vr=v¢.o+¢Vo,
and

[Svdeo.dv+([Syo.pdv=[pSovds. . . . (VIIL)

Stokes’s theorem can be made by similar treatment to
give varied forms, both more and less simple.

XXI. Colorimetry.—Part IV.
By James Bortromtey, D.Sc.

Read before the Physical and Mathematical Section, April 13th, 1880.

—

On the Colour-relations of Nickel and Cobalt.

For some experiments which I was making in colorimetry
I wished to obtain a solution which would absorb all the
kinds of light in the same ratio, so that whatever sort of
light we started with, after penetration through such a
solution, it would remain the same in character, the only
variation being a change in intensity. Hence through
such solutions white surfaces would appear grey of various
shades, verging towards blackness as the length of the
column increased. Such a fluid we might call a soluble
black. I am not aware of any single fluid that fulfils the
above conditions. It might be said, Why not use ink ? but
such specimens of ink as I have examined are bluish or
violet on copious dilution. Moreover the colour alters
SER. II. VOL. VII. N

178 DR. JAMES BOTTOMLEY ON COLORIMETRY.

with the degree of oxidation ; also it seems to be colouring-
matter in suspension rather than in solution. I had some
hopes of succeeding by mixing solutions of nickel and cobalt
salts. On reference to the ‘ Philosophical Magazine,’
vol. vi. p.15, I find that the colour-relations of nickel and
cobalt had been studied by Mr. Thomas Bayley with a view
to the quantitative determination of these metals founded
upon the complementary character of their colours. He
states, ‘‘ The fact will have been observed by chemists that
solutions of nickel and cobalt salts are so far complemen-
tary in colour that when they are mixed together the re-
sulting liquid, if moderately dilute, is hardly to be distin-
guished from pure water.” After considering the nature
of the absorption-spectra of ‘nickel and cobalt salts, he
states, “If the spectra were exactly complementary, on
superimposing the nickel spectrum upon the cobalt spec-
trum the dark part on the one would cover exactly the
light part on the other. This, however, though nearly the
case, is not exactly so...... this is why the solution obtained
by mixing strong solutions of nickel and cobalt is not grey,
but reddish brown in colour.” Some experiments which
I made seemed to confirm the opinion of Mr. Bayley. The
nickel solutions contaimed 0-05 grm. of NiSO, per cub.
c.; and the cobalt solution contained 0:05 grm. CoSO, per
cub. c. A mixture consisting of 50 cub. c. of cobalt so-
lution with 100 cub. ec. of nickel solution, contained in a
white porcelain basin, seemed to be a grey tinted with
pink in the shallower parts, and having the tendency to
pass into a yellowish tint as the depth increased. I now
poured the fluid into a tall glass cylinder covered externally
with black cloth except a circular aperture of 8 millim.
diameter at the bottom. When I looked through the
column of fluid at a white surface, the colour was decided,
resembling somewhat the pigment known as yellow ochre.

DR. JAMES BOTTOMLEY ON COLORIMETRY. 179

Also with a less proportion of cobalt to nickel, namely 20
cub. c. of cobalt solution to 50 cub. ce. of nickel solution,
I still obtained a tint in which yellow seemed to predomi-
nate. Had I employed solutions so dilute that no colour
was perceptible in the mixture, this would not strictly
imply that the colours were complementary, but that the
resulting tint was too feeble to produce the impression of
colour ; and if we filled a long tube with such a dilute so-
lution the colour might again become manifest. More-
over my aim was not to mix two coloured solutions so as
to obtain a fluid which exercised no perceptible absorption
of light, but to obtain a fluid which would exercise a con-
siderable absorption subject to a certain condition. The
following cousideration seemed to me to render it hopeless
to obtain a soluble black by nickel and cobalt only. A
solution of cobalt when dilute is pink; but if we look through
a considerable thickness or through a concentrated solution,
the pink shows a tendency to pass into a scarlet. This
shows that as the quantity of the salt increases, the ratio
of the yellow to the red increases. The colour of the
undissolved salt is brownish red; and the colour of the
solution seems to approximate towards this as the concen-
tration increases. Hence the colour of a solution of cobalt
alters not only in intensity, but also in kind, as the amount
of the salt is increased. On the other hand, the green of
a solution of nickel varies in intensity, but does not seem
to vary in character, at least in any marked manner, as the
quantity of the salt increases. In order that it should be
generally complementary in character to cobalt, any in-
constancy in the ratio of the red to the yellow of the latter
would require a corresponding variation in the ratio of
the yellow to the blue in the former, and the tint ought
to pass from an emerald-green to a bluish green. As this
does not seem to be the case, it would follow that even if
N2

180 DR. JAMES BOTTOMLEY ON COLORIMETRY.

we mixed nickel and cobalt so as to obtain a perfect grey
for a column of a definite length, a column longer or shorter
than this would still retain some colour. My experiments
seemed to indicate a deficiency of blue in the mixture; and
this I thought might be supplemented by another salt. So
I tried the addition of sulphate of copper. After some trials
I got a solution containing in 1000 cub. c. 7°275 grms.
NiSO,, 4°868 grmsCoSO,, and 11°468 CuSO, : the solutions
also contained 30 cub. c. of strong sulphuric acid; this I
added to guard against any possible formation of subsalts
on copious dilution. This solution seemed nearer to what
I wanted than a solution of nickel and cobalt only. It did
not, however, appear wholly free from colour ; and possibly
a variation of the quantities might have given a better
result ; also the tint seemed to vary somewhat with the
nature and intensity of the incident light. When in the
failing light of approaching evening I held the containing
bottle against the grey sky, I thought that there remained
a somewhat pinkish tint, whilst in the colorimeter, when
looking at an external white surface through a column
sufficiently long to produce a perceptible absorption, I
thought the solution had a bluish tint. When viewed
against gaslight, it gave a greenish tint. Within the range
of coloured fluids in chemistry there may be some which,
if combined, would yield a mixture absorbing all colours in
the same ratio, so as to be truly asoluble black. The pre-
paration of such a fluid would be an interesting problem in
physics. It seems to me that we might also have such
fluids which, on spectral analysis, would show not an
absorption of all colours in the same ratio, but would be
resolved into a violet and yellow, or an orange and blue,
or red and green, or some other combination of colours of
a complementary character.

DR. JAMES BOTTOMLEY ON COLORIMETRY. 18]

Remarks on the Formule for the Intensity of Light that
has passed through absorbing media, and on a Method of
Experimental Verification.

In my last paper on colorimetry I pointed out that the
function which expresses the connexion of the intensity of
light with the quantity of colouring-matter is of the same
form as the function expressing the relationship of the
intensity and the length of the absorbing column; and if we
accept Herschel’s formula Sak‘ for the latter relationship,
then an expression of the form Ya«® must be taken to ex-
press the former relationship. The connexion of these two
may be shown more directly than I indicated in my last
paper. If we grant one of the laws, the other may be
deduced from it as a corollary. Take, for instance, the law
as given by Herschel,

T=a,k,f+a,k,'+ &e.

Now it is manifest that, if g be the quantity of colouring-
matter per unit of length, we may write the above formula

t t
T=a,k,27+a,k,27+ &e.

I I I
For k,7, k,7, k,7, &c. substitute new constants ,, 2, K;, &e.
Then we may write

T= Dan.

Since g denotes the quantity of colouring-matter per unit
of length and ¢ the total length, we shall have

Q=¢,

182 DR. JAMES BOTTOMLEY ON COLORIMETRY.

where Q denotes the whole quantity of colouring-matter ;
so that we finally deduce

T= dar®.

As the basis of a method of colorimetry, I took the re-
lationship that the length of the column was inversely as
the quantity of colouring-matter present when the colour
was made constant. It may be readily shown to be a

consequence of the laws stated above. Suppose C to be
the constant colour, then

C= Sake.

The form of the equation shows that C is the sum of a
number of constants C,, C,, C,, &c., such that

= » Ot
C, an ak, 2D

Wo t
C,=a,k",

Ci =a,k”;
whence we obtain
log “ = qt log k,,

I

and by addition we obtain

DR. JAMES BOTTOMLEY ON COLORIMETRY. 183

log = +log 2 + &c.=qt(log k, +log k,+&c.),

jog (Ca

DoD eeeeee <i

or gt= i ”“_=constant.
log(h,ka.cssee k,)

In my last paper I stated that the law of absorption of
light given by Herschel appears to have been obtained a
priori ; I have not found in his memoirs any experimental
confirmation of it. The form of the expression has a some-
what formidable appearance, inasmuch as it involves the
measurements of infinite varieties of light. But suppose
that in the formula Sak’, & is the same for every species of
light ; then we may write T=*a or T=#'L, if I denote the
incident light. In such a case the emergent light will be
of the same nature as the incident light, and will differ only
in intensity. Suppose the incident light to be white, the
emergent light will be a white of less intensity—that is,
will be a grey approaching to blackness as the length of
the column increases. A fluid medium affecting white
light in this way we might call a soluble black ; and my
aim in seeking to obtain such a fluid was to apply it to the
confirmation of the law. In a previous note I stated that
I had tried to obtain such a body. What I got was not
wholly satisfactory; but I thought that with it I might
obtain some approximate results. The solution I used
consisted of 500 cub. c. of the previously mentioned fluid
with 500 cub. ec. of distilled water.

The mode in which I proposed to operate was as follows.
Take two white lights of different intensities, say W, and
W.,, and look at them through the liquid. Suppose the
lengths of the columns when equality of intensity is ob-
tained to be ¢/, and ¢,, then

W k= Wh.

184. DR. JAMES BOTTOMLEY ON COLORIMETRY.

Suppose we alter the lengths of the columns, and in a
second experiment we find

Wk =W.E? ;

by cross multiplication and elimination of the common
factor W,W, we obtain

Jets fol'2 = ft a fet's

or, as we may write it,

fistte—fites,

Then taking the logarithms of both sides and dividing by
log k we get finally

t,47¢,=t,40,.

In this way I proposed to test the law.

I took as standard tints a smooth surface of BaSO, and
another of BaSO,, and carbon in the proportion of 10 grms.
of BaSO, to 0006 grm. of carbon; these materials were
intimately mixed, and the powder reduced by pressure to
a flat surface. The colorimeters used were glass cylinders
covered externally with black cloth, the circular apertures
at the bottom admitting light being 8 mm. in diameter.

One experiment gave the following results. Length of
column 22°2 c., standard tint W,(BaSO,). I now attempted
to get the same intensity when looking through the second
cylinder at tint W, (BaSO,+carbon). The mean of two
trials gave 14°8 c. as the equivalent column. Hence we
have the following results :—

Whe — W,k48.

DR. JAMES BOTTOMLEY ON COLORIMETRY. 185

I now made the length of the column over W, 13 centim.
The equivalent column over W, was, as the mean of two
trials, 7°5. Hence

W,k3=W,K75.

From these experiments we get as the sum of ¢, and @’, 29°7,
and the sum of ¢', and ¢, 27°8.
A second experiment gave

WELW kos,
W ke = WA hrs545.
Here ¢, +7, =28'45, and ¢,+/',=28°76.
A third experiment gave
Wir aee = W. K106s,
W ki43= WAFS,

Here ¢, + ¢/,=25°3, and @’, + ¢, =24'93.
A fourth experiment gave the following results :—

W,k222= Wk" ;
W, ki? Who?

Here ¢,+?',=28°4, and ¢',+¢,=27°4.
A fifth experiment gave

W Kes? = W,k'%6s,
W,k37= W,k885,

Here we have ¢,+?/,=31'95, and /, +¢,= 0°35.
It seems to me that the above results are as favourable

186 DR. JAMES BOTTOMLEY ON COLORIMETRY.

as might be expected, considering the difficulties of the
inquiry ; and even if all external circumstances necessary
for the successful completion of such experiments had
existed, there would yet remain the difficulty of deciding
about the equality of two grey tints. In such matters it
is difficult to say where judgment ends and fancy begins.

That any discrepancies might be due to such a cause
was shown by the following experiments :—I took the two
cylinders and poured from oue into the other with the in-
tention of obtaining the same tint in both. In one trial I
could not very clearly distinguish a column 16°4 centim.
long from one 14°6 centim. long; and in a second trial a
column 16°2 centim. long seemed to give the same tint as
a column 14°6 centim. long. In the above experiments
I used one eye only, namely the right one.

I also made the following experiments :—I took as the
standard of intensity W seen through a column 12°5 cen-
tim. long. On a former occasion I had made 6:2 as the
equivalent column to be used with W,. On the present
occasion I thought 6°5 centim. gave a nearer result; so I
took the column at this length. Now, if the law of absorp-
tion of light be true, if we increase both columns by the
same quantity, the intensities should again correspond.
So I added 4 centim. to each, making one column 16°5
and the other 10'2. I thought that the tints were the
same. I now made one column 20’5 and the other 14°2.
Again I thought the tints were the same. Finally I made
one column 24°5 and the other 18:2. The tints seemed
again to correspond.

ON THE ABSORPTION OF LIGHT BY TURBID SOLUTIONS. 187

XXII. Colorimetry.—Part V. Onthe Absorption of Light
by Turbid Solutions. By James Borromury, D.Sc.

Read before the Physical and Mathematical Section, April 27th, 1880.

Mepia containing colouring-matter may be divided into
two classes, transparent and turbid. It might be consi-
dered that in their behaviour with regard to light they
were wholly dissimilar. But the question arises, Is not the
difference between transparency and turbidity one of degree?
Experience in the laboratory brings under our notice cases
where matter is so finely divided as not to be separable
from fluids by filtration, and showing but slight tendency
to settle as a precipitate ; and in some cases we have liquids
which are apparently transparent, and yet are considered
to hold solid matter in suspension. May not such examples
be intermediate between solutions and cases where ex-
tremely fine particles are uniformly diffused through some
transparent medium? If, then, we consider the passage
from transparency to turbidity a continuous one, and if
for a transparent fluid we have established some law of ab-
sorption of light, may not the same law be applicable to a
turbid solution? The subject seemed to me interesting
both as a scientific inquiry and on account of its application
to quantitative analysis.

Suppose we have diffused through a liquid some finely
divided solid matter; the action of such a turbid solution
on light will be twofold : it disperses light and it absorbs
light. By reason of the first action we are made aware of
the colour of the turbidity ; by reason of the second any

188 DR. JAMES BOTTOMLEY ON THE ABSORPTION

object seen through tke liquid seems of diminished dis-
tinctness.

As a typical case take carbon diffused through water. In
a paper which I read at the last Meeting of the Physical
and Mathematical Section I alluded to some attempts to
obtain a soluble black in order to make some experiments
on the absorption of light. To assist my judgment as to
the appearance which such a liquid should present, I had
a cylinder containing a little carbon diffused through water.
Weak diffusions of carbon in the colorimeter gave the same
appearance when I looked at external white surfaces as I
should have expected a liquid containing a soluble black in
solution to give under the same conditions. A diffusion
of carbon both disperses light and absorbs light. The
dispersion gives rise to a greyish tint, due to the light
coming from the innumerable particles of carbon. Owing
to the absorption a white surface seen through the column
of liquid seems of diminished whiteness. Hence, under
ordinary circumstances the light which comes to the eye
has a twofold origin, part being transmitted light and part
dispersed light. My first object was to dissociate these
two phenomena. I therefore used cylinders which were
covered with black cloth, admitting light by circular aper-
tures at the bottom, 8 millim. in diameter. In this way
the dispersed light was almost wholly cut off. In some
cases a feebly nebulous light could be seen around the
apertures ; but it was very slight and did not interfere with
experiments to determine the absorptive properties. With
any attempt to explain by physical optics the analogy of
the absorption of light by solutions and diffusions I have
nothing to do; but, on the supposition that there was con-
tinuity, I was led to expect that a function of the same
form would express the intensity of the transmitted light in
both cases. Also, independently of such considerations, it

OF LIGHT BY TURBID SOLUTIONS. 189

seemed probable, from reflection upon the mode of distri-
bution of the particles throughout the mass of fluid, that
the function would be the same as for transparent solutions.
In the latter case both experiment and reasoning from
first principles concur in giving a formula Sak! for the in-
tensity of light passing through a column ¢ units long. As
I have pointed out in another paper, this implies an ex-
pression of the form Yax®, denoting the connexion between
_ the transmitted light and the quantity of colouring-matter.
Therefore we might expect a similar expression to hold in
the case of diffusions (the term seems to me more conve-
nient than to speak of turbid solutions). Ifsuch be the
case, one consequence will be that, if we have two cylinders
containing in equal bulks of water Q and Q! of solid
matter in suspension, if we adjust the columns so as to
obtain the same intensity of light when we regard an
external white surface, then the lengths of the columns
will fulfil the condition Q¢t=Q’?’.

The carbon that I used was lamp-black recaleined in a
covered platinum crucible. After being so treated’ it
seemed blacker than it did before. Of this 0:417 grain
was ground up in a mortar with 10 drops of a solution of
gum. ‘The contents of the mortar were then rinsed out
with water and diffused by shaking through 500 cub. ec. of
water. This was poured into a cylinder; the length of
the column was 22°5 centimetres. After the lapse of 24
hours I drew off by a pipette the upper portion; the
column so removed was 15°8 centim. long. This carbon
diffusion contained so much solid matter that I found it
inconveniently strong for experiments; so, as occasion
required, I made weaker diffusions, containing in 250 cub.
€. 5, 10, 20, or 40 of the stronger diffusion. Of these
weaker liquids portions were taken and mixed with water
so as to yield a bulk of 500 cub. c. I stated above that

190 DR. JAMES BOTTOMLEY ON THE ABSORPTION

the carbon was ground up with 10 drops of gum, so as to
yield a smooth, thick consistence. The amount of dry gum
would be very small; nevertheless it had a remarkable
effect in increasing the adhesion of the carbon to the water.
When I had shaken up carbon alone with water it had
sensibly subsided after the lapse of a few hours. After the
addition of so small a quantity of gum the tendency to
deposit is much diminished. The following are the details
of some experiments. The strength of the carbon diffusion
is given in terms of the number of cub. c. of the strong
carbon diffusion in 500; cub. c. of water. The external
white surface was a sheet of white paper. In all cases I
have used the right eye only. The number under A de-
denotes the mean of two trials got by pouring into the
cylinder, and therefore likely to yield too low results. B
denotes the mean of two trials got by pouring out of the
cylinder, and therefore likely to give too high results. C
denotes the mean of A and B. D denotes the length
required by theory.

Standard-diffusion 1:2 cub. c. in 500 cub. ec. of water,
length of column 21°2.

Exp. I.—Comparison-diffusion contaims 1°8 cub. ¢. in
500 cub. e.

A B C D
14°35 16°35 15°35 14°13

A second. trial gave

A B Cc D
12°65 14°65 13°65 14°13
Exp. I1.—Comparison-diffusion contains 2°4 cub. ec. in
500 cub. ec.
A Tag C D

10°6 11°25 10°93 10°6

OF LIGHT BY TURBID SOLUTIONS. 19]

Exp. I1I.—Comparison-diffusion contains 3'0 cub. ¢c. in
500 cub. ec.

A B Cc D
3°4. 9°25 8°83 3°48

Exp. 1V.—Comparison-diffusion contains 3°6 cub. c. in
500 cub. ec.

A B Cc D
6°85 7°6 GB) 7°07

Exp. V.—Comparison-diffusion contains 4'2 cub. c. in
500 cub. c.

A B Cc D
5°6 6"1 5°85 6°06

Exp. VI.—Comparison-diffusion contains 4°8 cub. c. in
500 cub. é.

A B C D
5 5°55 5°32 Sys

Exp. VII.—Comparison-diffusion contains 5°4 cub. c. in
500 cub. e. )

A B Oo D
4° 4°5 4°3 4°71

On another occasion I got a nearer result, as follows :—

A B C D
4°7 4°95 4°82 4°71

Exp. VIII.—Comparison-diffusion contains 6 cub. ec. in
500 cub. ec.

A B O D
4°13 4°58 4°36 4°24

192 DR. JAMES BOTTOMLEY ON THE ABSORPTION

Exp. IX.—Comparison-diffusion contains 6°6 cub. c. in
500 cub. e.

A B oO D
3°98 4°25 411 3°85

Exp. X.—Comparison-diffusion contains 7°2 cub. c. in
500 cub. e.

A B C D
3°48 3°75 3°61 3°53

Exp. XI.—Comparison-diffusion contains 7°8 cub. c. im
500 cub. ec.

A B Cc D
3°23 3°45 3°34 3°26

Exp. XII.—Comparison-diffusion contains 8°4 cub. ec. in

500 cub. ec. ,
A B C D
3°03 3°45 3°24 3°03

Exp. XIII.—Comparison-diffusion contains g cub. c. in
500 cub. ec.
B C | D
2"9 3 2°95 2°82
Exp. XI V.—Comparison-diffusion contains 9°6 cub. e.
in 500 cub. c.

A B 16) D
2°33 3°05 2°94. 2°65

Exp. X V.—Comparison-diffusion contains 14°4 cub. ec.
in 500 cub. c.
A B C D
1°98 2°08 2°03 1°77

OF LIGHT BY TURBID SOLUTIONS. 193

Exp. XVI.--Comparison-diffusion contains 19‘2 cub. c.
in 500 cub. ec.
A B C D
1°6 1°58 1°59 1°32
Many of the above numbers are close approximations.
I also tried columns of the lengths given by theory in all
experiments, except in the ninth, where by an oversight I
neglected to do so. The tints so obtained were in every
case satisfactory until I reached Experiment XIV. In
this and in the succeeding experiments I thought that
columns of the theoretical lengths gave tints slightly lighter
than the standard diffusion. On some occasions I have
wavered in my opinion that the theoretical column gave
too light a tint in the fourteenth experiment. At another
time I got the following result :—
Exp. X VII.—Comparison-diffusion contains 9°6 cub. c.
in 500 cub. ec.
A B C D
2°83 2°95 2°87 2°65
Here again the number under C is a little greater than
that under D. I afterwards repeated the experiment with
this variation—that the standard diffusion was contained
in the comparison-cylinder and the comparison-diffusion
in the standard cylinder.
Exp. X VIII.—Standard diffusion contains 1°2 cub. ec. in
500 cub. c.; length of column 22°6.
Comparison-diffusion contains ‘6 cub. c. in 500 cub. c.

A B 10) D
2°85 3°07 2°96 2°82

On another occasion I got :—

A B 18) D
2°85 3°15 3°0 2°82
SER. III. VOL. VII. Q

194 DR. JAMES BOTTOMLEY ON THE ABSORPTION

Here again there still remains a tendency to make the
column a little longer than the theoretical.

I repeated the experiments in which the strength of the
comparison-diffusion is several times a multiple of the
strength of the standard diffusion. The strength of the
standard diffusion was the same as in the previous experi-
ments ; and the length of the column was 21:2.

Exp. XIX.—Comparison-diffusion contains 9°6 cub. ec.
in 500 cub. c.

A B C D
2°63 2°98 2°8 2°65

When I actually tried the theoretical column I thought
that the tint was, perhaps, slightly lighter.

Exp. XX.—Comparison-diffusion contains 14°4 cub. c.
in 500 cub. c.

A B C D
1'9 2°15 2°02 177
The tint given by the theoretical column I thought slightly
lighter.
Exp. XXI.—Comparison-diffusion contains 19°2 cub. e.
im 500 cub. c.

A B C D
1°55 1°63 1°59 1°32
The tint given by the theoretical column I thought slightly
lighter.
Exp. XXIJ.—Comparison-diffusion contains 24°0 cub. c.
in 500 cub. c.

A B C D

Ils 13 1°22 1°06

The tint given by the theoretical column I thought slightly
lighter, but hardly distinguishable.

OF LIGHT BY TURBID SOLUTIONS. 195

Exp. XXIII.—Comparison-diffusion contains 28°8 eub.
c. in 500 cub. c.

A B C D

1'o Vl 1°05 0°88

The tint given by the theoretical column 1 thought slightly
lighter.

Exp. XXIV.—Comparison-diffusion contains 3 3°6 cub.c.
in 500 cub. c.

A B Cc D
0°83 o'9 0°89 0°76

The tint given by the theoretical column I thought slightly
lighter.

Exp. XX V.—Comparison-diffusion contains 38°4 cub. c.
in 500 cub. c.

A B 10) D
0°73 0°83 0°78 0°66

The tint given by the theoretical column I thought slightly
lighter ; they were, however, very nearly the same.

This second series of experiments confirms the result of
the first series, that there is a slight departure from the
rule when the strength of one diffusion is several times a
multiple of the other. Both series show a tendency to
make the column in the comparison-cylinder slightly too
long. We must not hastily conclude that in these cases
the theory is not applicable. It seems to me that we should
expect such a result ; for the medium is not perfectly trans-
parent,and in one cylinder we have a column of this medium
(water) several times a multiple of the length of the column
inthe other. This would require some slight compensation.
In these experiments I have taken the lower level of the
meniscus as the proper reading. In some of the stronger

02

196 DR. JAMES BOTTOMLEY ON THE ABSORPTION

diffusions it was a little difficult to determine this exactly.
On the whole I think that the above experiments are
favourable to the assumption that for a column of fluid
containing finely divided carbon in suspension the relation-
ship Q¢= constant holds, if the intensity of the transmitted
light remain constant. If we represent the above results
graphically, and take as the theoretical curve the rectan-
gular hyperbola «y= 25°44, it will be seen that the results
of the experiments do not depart far from the curve.

In a paper read at the last Meeting of the Section I
suggested a method for testing the assumed laws of the
absorption of light. I have also applied the same reasoning
and method of experiment to carbon diffusions. In one
series of experiments I took a diffusion containing 1°934
cub. c. in 500 cub. c. The standard shades of grey used
were:—one consisting of 10 grms. BaSO, and 0-012 of lamp-
black (this I denote byWa); the other consisted of 10 grms.
of BaSO, and 0048 of lamp-black (this I denote by Wb).
The materials were well incorporated by shaking and
grinding. To the powder I then added a little water, so as
to obtain a mixture of suitable consistence to be used as
a paint. This was applied by a brush to pieces of cardboard,
so as to obtain uniform surfaces. These surfaces were then
dried. The colorimeters employed were the same as in the
last experiments. I looked at Wb through a column 3 cm.
long. I held the other cylinder over Wa, and endeavoured
to get the same tint. The mean of two columns, one
probably a little too long and the other probably a little too
short, gave 8:2 as the proper length; soI made the column
of this length; I thought that the tints were thesame. Now,
if the law hold with regard to turbid soluticns, if we increase
both columns by the same length the tints will again
correspond. I took 4 cm..as the common increment ; the
lengths of the columns were made 7 and 12°2; I thought the

OF LIGHT BY TURBID SOLUTIONS. 197

resulting tints equal. The lengths of the columns were
made 11 and 162; I thought they were about equal, pos-
sibly Wa slightly lighter. My impression varied a little
with the illumination of the surfaces. The lengths of the
columus were now made 15 and 20°2; the tints seemed
about equal, possibly Wa slightly lighter. The difference,
if any, must be small, as is shown by the following experi-
ment. ‘Taking Wb seen through a column 15 cm. long
as the standard tint, I endeavoured to get the same tint
with Wa seen through the other cylinder. For the lower
limit I got 19°9 cm., and for the upper limit 21 cm.; the
mean of these is 20°45, not far removed from 20°2. After-
wards I thought a column of this length satisfied. I now
made the lengths of the colmmns 1g and 24'2; I thought
that the tints again corresponded.
Some experiments of a similar nature were made witha
stronger diffusion, it contained 3°747 cub. c. in 500 cub. ec.
The tints of grey used were the same as in the last experi-
ments. The standard tint at the commencement was Wb
seen through a column 4 em. long. ‘To get a similar tint
with Wa one determination for the upper limit gave 6'5,
and one determination for the lower limit gave 6:1. The
mean of these is 6°3._ A column of this length seemed to
satisfy. The common increment is 3 cm. The columns
were made 7 and g*3 cm. long; the tints seemed to
correspond. The columns were made 10 and 12°3 cm.
long ; the tints again seemed to correspond. The columns
were made 13 and 1573 cm. long; the tints seemed
again to correspond. Finally the columns were made 16
and 18:3 cm. long. The tints again corresponded. In
the last two experiments the greys obtained were very
deep. I also made the following experiment :—I took
two grey tints: one consisted of 10 grms. BaSO, and
0042 grm. of lamp-black; the other consisted of 10

198 THE ABSORPTION OF LIGHT BY TURBID SOLUTIONS. |

grms. BaSO, and 0'4003 grm. of lamp-black. These
greys were made into a paint by the addition of a little
water, and pieces of cardboard covered with them. They
were then dried. These we may denote by W,and Weg. I
looked at W, through a column 4°1 cm. long, and en-
deayoured to get a similar tint with W, under the other
cylinder. For the upper limit the column was 6°95 cm.
long, and for the lower limit 6:2 cm. long. The mean is
6°57 cm. I next altered the length of the column over Wz,
to 11°75. In the other cylinder for the upper limit the
column was 14°9 cm., and for the lower limit 14°8; the
mean is 14°85. Hence we have .

W,K41= W,K°s7,
W,KI'75 = W,K1485,
By cross multiplication and elimination of W,, Wg, .
K4i1K 435 — K6s7K* 1°75
Theory requires the sums of the indices to be equal.
The sum on the right hand is 18:32, and on the left

18°95. The difference is, I think, not greater than what
might be due to errors of observation.

ON THE CONDITIONS OF FLUID-MOTION. 199

XXII. On the Conditions of the Motion of a Portion of
Fluid in the Manner of a Rigid Body. By R. F.
GwyrtuHer, M.A.

Read November 2nd, 1880.

Tue condition that a portion of fluid may comport itself
as a rigid body, or that fluid may remain in a state of re-
lative rest upon or within a moving solid, has not, as far as
IT am aware, been mathematically investigated, We know,
however, that in certain cases, as on the surface of the
earth, the condition can be realized, 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

o=>+ Ver,

where = is the common linear velocity, ¢ the vector-axis of
instantaneous rotation, and + the vector of any point in
the fluid.

The equation of motion is

I esd
Hse NA eee SNTOey aah aye r(x)

a denoting the force acting on the element of the fluid, p

and g having the usual meanings. Under the condition

stipulated no force due to viscosity is called into action.
If @ be a function of p only, we may write

I
—-Vov=VP.
g

200 ON THE CONDITIONS OF FLUID-MOTION.
Substituting the required form of c, we get
S$ Ver+2Ve(> + Ver)—a— VP... - sae)

Now act upon this with Vv (which will not affect either >
or €), and afterwards take the vector and scalar parts, thus

V (Ver + 2677 — 2eSer) = Va— VP,
or
2e— 4 = Va-—V'P;
therefore
2e=VVva, and 4¢=Vy*P—Sva.. . (3)

The first of these equations gives the required condition ;
if the forces acting are conservative, VyYa=o, 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. |

ADDITION ETC. OF LOGICAL RELATIVES. 20]

XXIV. On the Addition and Multiplication of Logical
Relatives. By Josrrpu Jonn Mureny, F.G.S. Com-
municated by the Rev. Roperr Harzey, F.R.S.

Read January 25th, 1881.

In every science, and most of all perhaps in Logic, it is
desirable to begin at the beginning. In order the more
effectually to do so, I shall avail myself of the method
introduced, I believe, by De Morgan, of working in an
arbitrarily limited universe.

The simplest possible case is that of a universe contain-
ing only two individuals, exactly alike but with different
names, A and X. Lach of these is the logical negative of
the other: whatever is not A is X, and conversely. Let
A have also the names B, C, &c., and let X have also the
names Y, Z, &c. We call the names of individuals and
classes absolute terms. Let the relation between identical
names be indicated by 1, and that between contrary
names by —1. Both of these relatives are invertible ;
that is to say, each is its own reciprocal, and, if used as a
multiplier, may be transposed to the other side of an
equation without change. Thus,

if A=aB, then B=1A,
and
if A= —1X, then X=—1A.
But, as we shall see, in another equally important respect
their properties differ.
These two relatives form the following four syllogistic
combinations :—

202 MR. JOSEPH JOHN MURPHY ON ADDITION

Am, A=—I1xX,
Bac, Xs Ve
A=1C; A=—IY;
A=1B, A=—1X,
B=—1X, X= — 1B,
A=—1X; A= 1b:

These syllogisms may, however, be more compendiously
expressed by means of canonical equations, using the
relative terms only, thus :—

IxXi=1; (—1)xI=—I1;
Ix (—1)=-—1; (—1)x —-I=I.

These equations are also true in common algebra. Their
logical interpretations are :—

Identical of identical is Negative of identical is
identical ; negative ;

Identical of negative is Negative of negative is
negative. identical.

Thus 1 is equal to its own second power, indicating that
identity is a ¢ransitive relation; —1 is not equal to its
own second power, indicating that the relation of the logical
negative is intransitive.

In investigating this simplest possible case, we have now
considered the formulz of conversion and syllogism, which
are generally regarded as coextensive with the whole of
elementary logic. But there is in the logic of relatives a
third operation, which appears to be related to addition as
syllogism is to multiplication*. The syllogistic formule

* My logical reading has been by no means extensive; and I am quite

prepared to find that my ideas have been anticipated ; but, so far as I know,
what I have written on the addition of relatives is original.

AND MULTIPLICATION OF LOGICAL RELATIVES. 203

given above show how syllogism is analogous to multipli-
cation: if the relative terms are numerical coefficients, the
process is multiplication ; if they are logical relatives, it is
syllogism. The problem of syllogism may be thus stated :—
Given the relations of two terms to a third, to find the
resultant relation of the first two to each other. The
problem of what I propose to call the addition of relatives
is this :—Given two relations between two terms, to find
their resultant.
In the case before us the solution is as follows :—

1+(—1)=0.

This is true both in common algebra and in logic; its logical
interpretation is that these two relations cannot coexist;
and it is the expression of the law of contradiction within
the limits of the present case.

As a further illustration of the relation between the ad-
dition and the multiplication of logical relatives, let L
signify the relation of teacher and M that of brother ;
then

A=(Z+M)B
means that A is a teacher and a brother of B; while
A=(Lx M)B

means that A is a teacher of a brother of B.
The order of addition is a matter of indifference, that is
to say

L+M=M+L,

whatever the meaning assigned to L and M. This, as we
shall see, is not generally true of the multiplication of

204. MR. JOSEPH JOHN MURPHY ON ADDITION

relatives. But the most important law of the addition of
relatives is that

RES OSI

whatever relative Z may be. The same is true of the ad-
dition of absolute terms in the logical systems of Jevons,
MacColl, and Pierce.

So far as I see, we have exhausted the subject of the
formal relations between the terms in the simplest possible
universe. The possible interpretations, however, are not
confined to those given above; the relative 1 may mean
agreement in possessing or not possessing any character
whatever, and —1 the corresponding difference. Let the
universe, for instance, be a village of one street; let A, B,
C, &c. be the houses on one side of the street, and X, Y,
Z, &c. the houses on the other side; let 1 be the relation
between any two houses on the same side, and —1 the
relation between any two houses on opposite sides; then
the interpretation of the four syllogistic forms will be :—

Same side with same side Opposite of same side is
is same side ; opposite ; ,

Same side with opposite Opposite of opposite is
is opposite. same side.

Now let us imitate the order of nature, and evolve the
more complex out of the simpler. The first step we have
to take in the direction of greater complexity consists in
presenting a case exactly similar to the last, except that
the sides of the street which constitutes our universe are
distinguished as north and south. The relations now
arising cannot be expressed by numerical coefficients ; so
let us use L (Li being the symbol used by De Morgan for
relation in general) to indicate the relation of any house

AND MULTIPLICATION OF LOGICAL RELATIVES. 205

on the north side to any house on the south side, and Z-'
for the inverse relation *.

In the system here expounded the ruce for logical con-
version is simply to transpose the relative term, changing
the sign of its index. ‘This is also valid in common algebra.
When a relative is equal to its own reciprocal, it is not
necessary to change the sign of the index, though to do so
would not be erroneous.

Two other relations arise out of Z and Z7'. The fol-
lowing syllogistic reasoning is valid in common algebra for
all values of Z :—

‘ ae
B=LX or X=L-'B,
A=L~x L"'B,
=:

and it is also valid in logic, with this interpretation :—

A is north of X ;
B is north of X;
A is fellow-northern of B.

The following is equally valid :—

Das FEISS:
y=L"A or A= Ly,
ail Daan ae) bi) fs

= (L")%y,

* The use of the negative index to signify inverse relation is, I believe,
the only mathematical expression introduced by De Morgan into logic. The
use of the zero index was first, so far as I am aware, introduced into logic in
my paper “ On an Extension of the ordinary Logic, connecting it with the
Logic of Relatives,” in the ‘Memoirs of the Manchester Literary and Phi-
losophical Society,’ Session 1879-80 (supra, pp. 90-101).

206 MR. JOSEPH JOHN MURPHY ON ADDITION

with the interpretation

X is south of A,
Y is south of A,
X is fellow-southern of Y.

And, generally, if any two terms stand in any relation L to
a third term, they stand in the relation L° to each other.

The canonical equations of the two foregoing syllogisms
are the following :—

DL Sie Ee
and °

Lx L=(L-).

We here see that logical multiplication is not neces-
sarily commutative; that is to say, the product may, as
in this case, be changed by changing the order of the
factors.

In logic, as in common algebra, every term with zero
index is transitive,

(L°) 2 — Ee;
and invertible,
(L°) —I = iE?

properties which are combined in no other terms.

Every relative term with zero index signifies identity or
exact similarity in some respect. Equality means exact
similarity of magnitude ; and the axiom that “ equals of
equals are equal” is a particular case of the more general
truth expressed by

(L°) 2 _ LS

where Z means any relation whatever.

AND MULTIPLICATION OF LOGICAL RELATIVES. 207

From the four relatives

L or north, L° or fellow-northern,
L- or south, (Z-")° or fellow-southern,

we obtain sixteen syllogisms, as set forth in the following
table, which is a multiplication table, and is arranged as
such. (In what follows we shall speak of logical premises
as factors and logical conclusions as products.) The mul-
tipliers, corresponding to the minors of the ordinary logic,
occupy the left-hand column; the multiplicands, corre-
sponding to the majors of the ordinary logic, occupy the
top line; any product is found on the line with the mul-
tiplier and under the multiplicand *. It will be observed
that in half the places the product is zero; this imdicates
that in the universe and with the relatives under conside-
ration such products do not exist. In the other eight
places the products are what we may call affirmative
results.

75 Le (L-*)° L-1
i; Po or og cise L bale L°
Le Eis iy ie 1° Lert) i: ne
ee 0 ihe g We Tia) alae ae Fe
a? Gene [4 pS a See

The interpretations of these syllogisms are the follow-
ing +; A, B, and C being houses on the north side of the

* We owe to De Morgan the improvement of writing the minor premise
of a syllogism before instead of after the major.
+ This table is the same as that given on p. 45 of Prof. Pierce's ‘‘ Notation

208

MR. JOSEPH JOHN MURPHY ON ADDITION

street, X, Y, and Z houses on the south side, and no others
existing in the universe under consideration :—

I.
2.

II.

15.

16.

A is north of X;
A is north of X ;

. A is north of X;

. A is north of X;

. Ais fellow-northern

of B;

. Ais fellow-northern

of B;

. Ais fellow-northern

of B;

. Ais fellow-northern

of B;

. X is fellow-southern

of Y;

. is fellow-southern

of Y;
X is fellow-southern
of Y;

. Xis fellow-southern

of Y;

. X is south of A;

. X is south of A;

X is south of A;

X is south of A;

X is north of W ;

X is fellow-northern
of W;

X is fellow-southern
of Y;

X is south of B;

€

B is north of X;

B is fellow-northern
of C;

B is fellow-southern
of W;

B is south of W;

Y is north of W;

Y is fellow-northern
of W ;

Y is fellow-southern
of Z;

Y is south of A;

A is north of Y ;

A is fellow-northern
of B;

A is fellow-southern
of W;

A is south of W ;

There is no W.
There is no W.

A is north of Y.

A is fellow-northern
of B.

A is north of X.

A is fellow-northern
of C.

There is no W.

There is no W.

There is no W.
There is no W.
X is fellow-southern

of Z.
X is south of A.

X is fellow-southern
of Y.

X is south of B.

There is no W.

There is no W.

In the eight cases where the results are affirmative, they

are true of all relatives whatever; their truth is inde- -
pendent of the meaning assigned to L; and they are also

for the Logic of Relatives” (Memoirs of the American Academy, vol. ix.),

but with a different notation.

have shown that there is a yet simpler case.

He calls these elementary relatives; but I

AND MULTIPLICATION OF LOGICAL RELATIVES. 209

true in arithmetic for all numerical values of Z. In the
eight remaining cases the results depend on the properties
of the relative L and the constitution of the universe.
When our logical universe is the actual universe and of
indefinite extent, and when the relative is neither transitive
nor invertible—that is to say, when neither of the equations

P=L and L-'=L

is true—the eight syllogisms which here have zero pro-
ducts become inconclusive ; that is to say, none of the
products are of the same form with any of the factors. In
arithmetic there is nothing analogous to an inconclusive
syllogism, because every number is a factor of every other
number.

Let us now suppose the universe to be of indefinite
extent, and the relative Z, and of course also its reciprocal
I~", to be transitive, the table will then be as follows. It
will be seen that two of the places for products are blank;
this indicates that the syllogisms are inconclusive.

L thes (Gx)2 L-

L Bice: L z ea a Gi jaa a
a Le ner L caus L° 7 8 L° ie
hin5° 9 (L-1)° 10 i II ener 12 jue

L-* i 9 Ce Si ™ (z-1° RG iy one

These syllogisms are true if we assign any transitive
meaning whatever to L, such as greater, smaller, above,
below, before, or after. Let us, for instance, convene that
the cause of a cause is a cause; and let Z mean cause,

SER. III. VOL. VII. P

210 MR. JOSEPH JOHN MURPHY ON ADDITION

then Z-" will mean effect, Z° concause (to use a good
though obsolete word), and (Z7*)° coeffect, and all the
syllogisms in the foregoing table will be true.

But its most important application is to that part of the
ordinary logic which deals with the relation of inclusion”.
Using L as the symbol for inclusion, the old “ syllogism
in Barbara,”

Aus B,

B is C,

Ais C,
becomes

A=LB,

B=,

A=f7C;

= LC,

or, in language,

A is included in B,
B is included in C,
A is included in C,

of which syllogism the canonical equation is
f= Ls

which we may express in language by saying that the en-

closure of an enclosure is an enclosure. And, conversely,
(L-*) 2 D Bat 3

or the includent of an includent is an includent.

L° in this notation means coenclosure, or enclosure in

* The problems of the ordinary logic are generally stated as dealing with
the relations of inclusion and exclusion ; but they may easily be generalized
so as to deal with coexistence and non-coexistence.

AND MULTIPLICATION OF LOGICAL RELATIVES. 211

the same includent ; and (Z~')° means coincludent, or
includence of the same enclosure. When A and B are co-
includents, the old logic would say merely “some A is B;”
but these expressions are not equivalent. As we shall see
further on, I propose for “some A is B” to say “Aand B
are participants of each other.” Every pair of coincludents
are participants ; and every pair of participants are coin-
cludents ; but we say that coincludents are coincludents
of the common part or enclosure, and participants are par-
ticipants of each other. It must also be remembered that
every relative with zero index is used transitively, so that
when we speak of coinclusion or coincludence we mean,
throughout, inclusion in the same includent, or includence
of the same enclosure.

With Z meaning inclusion, the interpretations of these
sixteen canonical equations are as follows :—

Enclosure of enclosure is enclosure.
. Enclosure of coenclosure is coenclosure.
. Enclosure of coincludent is enclosure.
. Enclosure of includent is coenclosure.

is

2

3

4

5. Coenclosure of enclosure is enclosure.

6. Coenclosure of coenclosure is coenclosure.

7. Coenclosure of coincludent constitutes no relation.
8

. Coenclosure of includent is coenclosure.

g. Coincludent of enclosure is coincludent.
10. Coincludent of coenclosure constitutes no relation.
11. Coincludent of coincludent is comeludent.
12. Coincludent of includent is includent.

13. Includent of enclosure is coincludent.
14. Includent of coenclosure is includent.
15. Includent of coincludent is coincludent.
16. Includent of includent is includent.

212 MR. JOSEPH JOHN MURPHY ON ADDITION

When we interpret Z as inclusion, there is a double re-
lation between L and L-': they are not only inverse or
reciprocal to each other, but also contrapositive. The
contrapositive of the relation between any two terms is
defined as the relation between the negatives of those terms.
Thus, writing 4 and b for the logical negatives of A and B
(that is to say, whatever is not A, and whatever is not B),
if any one of the following four propositions is true, the
rest are true :—

We now go on to that part of the old logic which deals
with the relation of exclusion.

When A is not B, I propose to say that A and B are
excludents of each other; and to use N as the symbol of
exclusion.

If A=NB, then B=NA;
that is to say, N is an invertible relative, or
Nit SNE

But it is intransitive, or not equal to its own second power
—excludent of excludent is not excludent.

Let us use M as the symbol of the contrapositive re-
lation to N, so that if either of the following two propo-
sitions is true the other is true:—

A=NB; a=Mb.

That is to say, if nothing is both A and B, then every thing
is either not-A or not-B. In other words, if A and B are

AND MULTIPLICATION OF LOGICAL RELATIVES. 213

excludents, then not-A and not-B are alternatives. Simi-
larly, the truth of either of the following implies the truth
of the other :—

A=MB; a=Nb.

That is to say, if every thing is either A or B, then nothing
is both not-A and not-B ; and conversely *.

M, like N, is invertible and is not transitive. Every
invertible relative has this property, that its second power
is equal to its zero power. This follows from the definition
that when two terms stand in the same relation to a third,
they stand to each other in the zero power of the same
relative. Thus

A=NB,
BoNG
A=N-C=N°C,

whereof the canonical equation is

N* = N° -
and similarly
Nis,

That is to say,

Excludent of excludent is coexcludent.
Alternative of alternative is coalternative.

This combination of properties—equal to its own reci-
procal and not equal to its own second power—exists in
negative unity and in no other number.

* The introduction of this relation, which I call alternation, into logic is
due to De Morgan. What I call an alternative he calls a complement.

214 MR. JOSEPH JOHN MURPHY ON ADDITION

We have now these four relations :—

A=LB, or Ais included in B;

A=T-"B, or A includes B;

A=NB, or Nothing is both A and B;
A=MB, or Every thing is either A or B. ©

These are expressed in Boole’s and Jevons’s systems by the
following :-—
A=AB, or Ab=o
AB=B, or aB=0;
A=Ad, or AB=o;
a=aB, or ab=o.

If we multiply these four relatives into each other, ex-
changing the places of N and M in the column of multi-
pliers, we obtain the symmetrical result shown in the
following Table. The products / and /—' ought properly
to be omitted from this table, and the squares containing
them left blank, because these products are not of the same
form with any of the factors; but they are inserted in
order to facilitate comparison with the larger table further

on. Asweshall see, / is the denial of L,and /— of L-';
that is to say,

A=/B means some A is not B,
and

A=/-'B means some B is not A.

L L-: N M
Cee | ee eae ae
Ts ‘(Ey Dae 1 M
ae ae | ee ae
es eran rg

AND MULTIPLICATION OF LOGICAL RELATIVES. 215

We have next to consider the addition of these rela-
tives. In what follows, U means coextension with the
universe, and U~* membership of the universe wherewith
the other absolute term is coextensive ; 1, as before, means
identity, and — 1 the logical] negative, or the relation be-
tween A and whatever is not A. Six pairs from the four
terms are added together, as follows :-—

(ee FS ii 2. N+M =—-1.
3. N+L =o. 4. N+L-"*=0.
Ne Foe U)—*, Shey ee Dat UE

These canonical equations may be called syllogisms,
because they give the resultant of two propositions ; but
they are not syllogisms in the technical sense, because
they do not eliminate any middle term. ‘Their interpre-
tations are as follows :—

1. A is included in B; ©
A includes B ;
A and B are identical.

2. Nothing is both A and B;
Every thing is either A or B;
A and B are the negatives of each other.

3. Nothing is both A and B;
A is included in B;
One or both of the premises must be untrue.

4. Nothing is both A and B;
A includes B ;
One or both of the premises must be untrue.

5. Every thing is either A or B;
A is included in B ;
A is a member of the universe wherewith B is coex-
tensive.

216 MR. JOSEPH JOHN MURPHY ON ADDITION

6. Every thing is either A or B ;
A includes B ;
A is coextensive with the universe whereof B is a
member.

We return to the multiplication of relatives. If we
multiply these four relatives by the logical negative, and
inversely, we get the following eight canonical equations,
where it will be seen that the inverse order of multipli-
cation gives the contrapositive result.

1. (-1)xL =M. 5. L .x(= yeas
2. (—1)xLIt=N. 6. L-'x (—1)=M.
2h, (Sa) UN ae 7N x(— p=
4. (—-1)xM =L 8. M x(—1)=L".

That is to say :—

1. Negative of enclosure is alternative.
2. Negative of includent is excludent.
3. Negative of excludent is includent..
4. Negative of alternative is enclosure.

. Enclosure of negative is excludent.
. Includent of negative is alternative.
. Excludent of negative is enclosure.
. Alternative of negative is includent.

conwr OM

We have seen that in two important properties N and
M are analogous to negative unity. If we call —1, N,
and M negative terms, and Z and L-' positive ones, we
shall see that the foregoing equations conform to the rule

that like signs by multiplication produce +, and unlike
signs —.

AND MULTIPLICATION OF LOGICAL RELATIVES. 217

By adding these four relatives to unity and to negative
unity, we obtain the eight following canonical equations.
It will be remembered that, as 1 is the symbol of identity,
the following equation is true,

A=1A,

whatever be the meaning of A.

tga Ja 5. -1+L =0
re 6. —1+L-"=0
3. 1+ N =o. 7, —-I+N =-1
4. 1+M =U+U. 8. —1+M =-I1

These are to be interpreted as follows, in syllogistic
form :—

r. A is identical with B ;
A is included in B ;
A and B are identical.

2. A is identical with B ;
A includes B ;
A and B are identical.

3. A is identical with B;
Nothing is both A and B;
One or both of the premises must be untrue.
4. A is identical with B ;
Every thing is either A or B;
Every thing is both A and B.
5. A and B are the negatives of each other ;
A is included in B;
One or both of the premises must be untrue.
6. A and B are the negatives of each other ;
A includes B ;
One or both of the premises must be untrue.

218 MR. JOSEPH JOHN MURPHY ON ADDITION

7. A and B are the negatives of each other;
Nothing is both A and B;
A and B are the negatives of each other.

8. A and B are the negatives of each other ;
Every thing is either A or B;
A and B are the negatives of each other.

It will be observed that if we add Z or L-* to 1, the
sum is 1, and if we add N or M to —1, the sum is —1.
As L and L~* are positive and N and WM negative, this
may be compared with the equation in-the logic of ab-
solute terms in the systems of Jevons, MacColl, and Pierce,

A+AB=A;

that is to say, if we add a part to the whole we do not
increase the whole. This is expressed by the equation
already given,

It will be observed also that of the above eight equations,
the sum of three is zero, of two unity, of two negative
unity, and of one

U+U-",

indicating that the A and the B of the equation are each
of them a member of a universe wherewith the other is
coextensive; in other words, both A and B are co-
extensive with the universe. To give an instance of the
reasoning :—

Inertia and gravity are coextensive.
There is nothing which has neither inertia nor gravity.
Every thing has both inertia and gravity.

AND MULTIPLICATION OF LOGICAL RELATIVES. 219

These eight equations work out less symmetrically than
we might have expected; but their asymmetry may,
perhaps, point to some principle which I do not now see.

Every syllogism has its reciprocal. This is found by
substituting for the factors their reciprocals, and writing
them in reversed order. Thus, if Z and M be any two
relatives, the syllogism

Lx M
has for its reciprocal
Ms he
that is to say
Che) a SO
This is also true in arithmetic ; but in arithmetic we do
not need to reverse the position of the factors, as this has
no effect.

Every relative term has its corresponding denial; and
these we propose to write as follows :—

LE, or enclosure, is denied by i, or indifferent ;

L-*, or includent, 3 /-*, or indeterminant ;
N, or excludent, sy nm, oY participant ;
M, oralternative, _,, m, or inessential*.

The following is a fuller statement of the same :—

1, A=ZB; or A is B.
Denied by
2. A=/B; or some A is not B.

* These verbal expressions are, I think, more self-explaining than De
Morgan’s equivalent ones.

220 MR. JOSEPH JOHN MURPHY ON ADDITION

220A a Bs om is iA.
Denied by
4. A=/-'B; or some B is not A.

5. A=NB; or no Ais B; or no Bis A.
Denied by
6. A=nB; or some A is B; or some B is A.

7. A=MB,;; or every thing is either A or B.
Denied by
8. A=mB ; or something is neither A nor B.

Each of these eight relatives has its form with zero
index, making altogether sixteen terms, which combine
into 256 syllogisms; but of these only 76 are conclusive.
They are set forth in the following table. As before, the
multipliers are in the left-hand column, and the multi-
plicands in the top line. The terms are so arranged,
that if the table be folded by the middle either vertically
or horizontally, each of the four terms

L L-? N MM

will rest on the term denying it; and each of the four
terms

pe (L —! ) fe) N (e) M °
will rest respectively on

LP (A n m°.

t)
The numbers in the top left-hand corner of each square
are those of the multiplier and the multiplicand which
form the product in that square; and the numbers in the
bottom right-hand corner are those of the multiplier and

————

a a |

—— : ee a Fs = = = ———— — “— _ [To face page 290,
Teasers Goenciostre Gonaud t In tad t. 2; & a a || 9. Io, Ir f I ~
e cs 5 Ms igh c ut ent, Pxcludent. Coexcludent. Coalternative. Alternative. | — Tuessential, Coinessential Copartici Boe ae 4p 15: 16,
A , (Z>y2; 16 N. No. Mo, M. | = aE . part eB Participant. Indeterminant. | Coindeterminant, Coindifferent, Indi :
| a | eet : a | mM, n°, Fr. T1, (ere RB ferent,
= SS ———— ————— =| . P A
1] 1|2 | mA ae. ——— ——
ened | f 1/3 14 1/5 1/6 1|7 18 1\9 1|10 1[rr 112 1\13 | w=
I. re. ° = 114 1 :
| L 77 iH [T° N yo a =o 3 x [15 1\16
al alg a eye i,
3l4 l4 s\4 Sa 7/4 8\4 914 10/4 114 “alls 16) . Enclosure. 1,
j — + 14/4 T5\4 13/4
2\I 22
I 23 2/4 25 26 2\7 2/8 29 2|10 2[rr 2\12 2\r Ee es
2. Coenclosure. % Ie re 3 2\14 2|15 2\16
IB, :
| , T°,
42 2\2 3\2 1\2 5|2 6\2 7\2 8\2 9l2 ro|2 11\2 12)2 6 Coonclosure. 2.
= Let 16|2 14/2 15l2 y)2
1) ix 3[2 313 314 || als 3/6 3|7 318 : : |
3\9 310 I 2 ee)
3. Coincludent. aay Gap ae 7 SU alr 3ln3 3lt4 3lr5 4\16
(f°. ne (I=),
| alr 2\3 3{3 1/3 513 63 713 3| Coincludent,
| 3 9/3 10|3 11| 3
i ‘ 3 12)3 16{3 14)3 153 133
4x 4\2 4/3 4 45 6 8
ee : : \¢ ; 4 4\7 4| alo 4|ro aint aj 413 alg are 4h
. : =r — = = = =
ae (I>) i (Z>) r- Z Me M a - ie i fips,
al3 2|r F Are A 6lr Tneludent. 4,
I) | : alll s |! 5| a aE alt rolr ur 12|1 16|x 14lr 15|1 141
5|t 5\2 5|3 s\4 sls 5|6 5\7 58 slo 5|10 glu 5|r2 5|13 sta dks : dhe
5. ea fax i N No N L ma
NG JN, Wxeludent. 5.
| .
4'5 2\5 3|5 1/5 515 6ls 7\5 8\5 9ls 105 115 12|5 16|5 1415 15|5 13/5
61 6\2 63 6/4 6\5 66 6\7 6/8 6\9 6|10 6\11 6\12 6\13 6|14. 6\15 [16
6. gasenaen: Ne N Ne Ne,
Cooxeludent. 6,
4\6 2\6 3|6 1/6 5|6 6|6 7\6 8/6 9/6 10|6 11/6 12|6 16|6 14/6 15/6 1316 |
= Ses = = =o |
|
7X 72 73 7/4 |) als 7/6 77 7/8 a) 7\10 7|rt 7|12 7|13 714 715 706
7. COE, Me Mo M i Me,
WO. Conlternative, 7. «
4/7 2\7 3i7 1(7 | 5|7 6\7 a7 8\7 9l7 10|7 117 12\7 16|7 14{7 15|7 14/7
Bir ‘8h2 8/3 8l4 8|5 86 8\7 88 8) 810 Sar S|12 | sir3 shr4 sir 8116
9 5
8. Alternative. a = M,
I e
, M. Mu Al Mo g Alternative. 8
4\8 2|8 3/8 1/8 | 5|8 6|8 78 8/8 9/8 108 11/8 12|8 168 14|8 15/8 13/8
i 9\ 9|2 9l3 al, ols 9/6 9l7 9/8 9l9 9|10 olaa glt2 9113 glt4 glts 9/16 ss ee
9. Inessential. \ewZ pf AP a | m, Tnessential. 9.
mM.
419 219 319 19 s\9 6\9 719 it) 99 109 11\9 12/9 16/9 14/9 15/0 13/9
10|r 102 To|3 10|4 105 106 1ol7 10/8 1o|9 1o|10 pees rola elt pel reus Tein ~
: i oo ae ‘i me,
a vageneen sie Gio m me Coinessential. 10.
is |
4lro 2|10) 3\r0 1|10 5|x0 6|10) 7|10) 8|10 g|10 To|To) 11|10 12|10 HOPE) 4lt0) tslt0 rg|10
i| is eee)
|
|
tat r1|2 11/3 13\4 115 116 11|7 118 |11\9 11|10 ibe 1i[12 11|13 ri|14 mils 1116 bb
e _ Z n°,
II. Copatiicipants ne ne n | Coparticipant, 1.
n°.
qn 2|r1| 3] 111 he 6\r1x 7|ux Slr g|tx ro[rx ri[11 1a|rr 16|11 14)rt 1511 1311
7 . 5 a
| | 12|16 I}
12\1 12|2 12)3 124 12/5 126 12\7 12|8 12|9 12|10 12|11 12|12 jr2lr3 12\14 rafts \16 | .
12. Participant. FA | Ao T n n° | Participant. 12.
n.
| 15|12 13|12
Ayal Aka Aa - x|12 5[r2 6|12 (12 8|r2 gl12 1o|12 11|12 12121) ntpes a _ ee = ane
= = k: = = = —— == = = ; ae |
|rqlr 13/14 13/15 x3i16
13|1 13 [2 1313 1314 1315 1316 1317 1318 1319 13/10 kale r3l12 ue ; [-1) tat
13. Indeterminant. Fos ee CON | Indeterminant. 13.
a 6 16|16 14116 AG 76
4\16 2|16 3|16 1|16 5 [16 616) 7\16 8|16 9|16 10|16 11|16) 12|I : |
= |
- 16 |
ra4lts 14/1 Z
‘ 14)2 t4lz 143 14/4 14\5 14/6 14l7 14(8 1419 14]10 14lir X4lr2 ralt3 fale a (61)? Co-
14. Ooindetermi- 710 T (me indeterminant. 14.
di mr
nant. ((-")°, a) 16|14 14{14| 15|t4 1314
4\r4| 2\14| 3|14| 1|14 5|t4 6\14 7/14 8|14 9|14) To|14) rr|14 12|14) : - =
= 15|16
15|14 15\15 =
15|1 15|2 15/3 15|4 15|5 15/6 15|7 15/8 15/9 15|r0 rs|t1 15|12 513 s| an i 8
15. Coindifferent. pe . a Coindifferent. 15.
7, 15|15 13)15
6 14|15
4\rs 2|r5 3)i5 3|15 5|45 6|15 7t5 8|15 girs ro|15 11|15 1a|15 sate _--——
eae ee els |
||] = 6\16
; 6\1 16|15 Y =
16|1 16|2 16|3 16|4. 16|5 16|6 16|7 16|8 \ 16/9 1610 16)11 16|12 16|13 r6lr4 S Fe ie ,
16. Indifferent. 7 a : e t meee “>
Zi : vale 15]13 13/13
| 8h | 16l13
4ir3 2113 313 1113 5|r3 6|13 713 i 3 9/13 10|13 11\13 12|13 EEE
_ ; et (2, Ie, Z,
. J MM. Wi Be i 7°, 5 aay 5 iE Coindifferent--- Indifferent.
ii} DP, (I>), I, N, Ne; TS, 4 5 Pitan Ds #0) i Coindeterminant. |
Enclosure. Coenclosure. Coincludent. Tneludent. Excludent. See Coalternatiye. Aas: zee aes EAE Participant. pe 3 14. ce 16. 1
‘ \ ae : : : 7. , b hb : } 12. ;
I 3 4e 5 an
* \

,
a
; :
R ‘ f
;
ogee
ore
|
¥ Ly
' a ‘
i 1 7
™ eh,
, :
1 v y
Hs
J
‘ fe
! a
i
4
f
a
‘
; «:
4 were ‘
ye i
4
We i
J i
ish ~ 2
: 4 ‘
Ma
, ‘i
, °
{ ‘
° A
: i

i
;
t
1

fi

AND MULTIPLICATION OF LOGICAL RELATI VES. 221

the multiplicand of the reciprocal syllogism. Of course,
when any syllogism is inconclusive, its reciprocal is in-
conclusive, and conversely. The vacant squares, as before,
indicate inconclusive syllogisms.

It will be seen that the entire table is divided into six-
teen squares of sixteen syllogisms each. The top left-hand
square is the same as that on page 209. The bottom right-
hand square is the same as that on page 207, except
that the syllogisms which there have zero products are
here inconclusive.

In interpreting those syllogisms which contain factors
with zero index, it must be remembered that when we
deal with inclusion and coinclusion, exclusion and co-
exclusion, &c., the unexpressed middle term is understood
to be always the same; that is to say, it is the same thing
which is included or excluded. For instance, the syllogism

Nx N°=N.

_A and B are excludents of each other,
B and C are coexcludents of A,
A and C are excludents of each other.

The analogy of all terms with zero index to unity fails
without this convention. But we adhere to this only as
between a term and its own zero power, not as between
one term and the zero power of another. This will
explain the only unsymmetrical or anomalous-looking
results in the table. We have seen (page 211) that
coincludents [(Z-')°] of any third term are participants
[nv] of each other. Consequently

(Ds") ox mma 7 x ("ois

222 MR. JOSEPH JOHN MURPHY ON ADDITION

that is to say, coincludent of participant is coparticipant,
and conversely. But the syllogisms

L-"*x n° and n° x L-*

are inconclusive, because the factors, having different
letters, are not understood as referring to the same unex-
pressed middle term.

Considered exclusively with respect to their logical form,
there are four classes of relatives. All of them have
representatives i this table.

1. Every relative of the first class is transitive, or equal
to its own second power—and invertible, or equal to its
own reciprocal. The only numerical coefficient which
unites these two properties is unity. ‘To this class belong
all terms with zero index.

2. Every relative of the second class is transitive, but
notinvertible. The only numerical coefficients which unite
these two properties are zero and its reciprocal infinity.
To this class belong Z and L-'.

3. Every relative of the third class is not transitive, but
is invertible. The only numerical coefficient which unites
these two properties is negative unity. To this class belong
N and M, with their denials 7 and m.

4. Every relative of the fourth class is neither transitive
nor invertible. These properties are united in all nume-
rical coefficients whatever except unity, zero, infinity, and
negative unity. To this class belong / and /-".

The denial of a relative of the first class belongs to the
third class (e. g. “ equal” is denied by “ unequal ”’).

The denial of a relative of the second class belongs either
to the second class (e. g. “‘ greater than ”’ is denied by “no
greater than ”’) or to the fourth (e. g. “ enclosure ” or “A
is B ” is denied by “ indifferent” or “ some A is not B”).

AND MULTIPLICATION OF LOGICAL RELATIVES. 223

The denial of a relative of the third class belongs

either to the first class (e. g. “unequal” is denied by
“equal”’) or to the third (e.g. ‘‘excludent” or “no A
is B” is denied by “ participant ” or “ some A is B”’).
- The denial of a relative of the fourth class belongs
either to the second class (e. g. “ indifferent ” is denied
by “enclosure,” as above) or to the fourth class (e. g.
“teacher” is denied by ‘‘ not teacher ”’).

Of our sixteen terms, the old logic recognizes only four,
namely

L or inclusion, N or exclusion,
n or partial inclusion, / or partial exclusion ;

and these are respectively equivalent to the well-known
forms of proposition

A, EK,
Lie O.

All our syllogisms are in the fourth figure, having the
minor premise first, and the middle term second in the
minor and first in the major.

Of course there is an endless number of relations
belonging to each of our four classes. Logicians, how-
ever, are right in treating inclusion and exclusion as
the fundamental relations of the science. Inclusion and
exclusion (£ and N) belong respectively to the second
and third classes of relatives; and it is worth while to
remark that the two fundamental relations of geometry,
namely direction and distance, belong to the same. That
is to say, direction is transitive but not invertible. The
following syllogism is valid :—

224 ADDITION ETC. OF LOGICAL RELATIVES.

A is north of B;
B is north of C;
A is north of C.

But if A is north of B, B is not north of A. Distance, on
the contrary, is invertible but not transitive: if A is a
mile from B, B is a mile from A ; but from the premises

A is a mile from B,
B is a mile from C,

we can only infer that A and C are equidistant by a mile
from B. Perhaps these relations may hereafter lead to
the establishment of some connexion between logic and
geometry analogous to that which Boole and his continu-
ators have shown to exist between logic and arithmetical
algebra.

Note added while correcting proof.—On seeing the abs-
tract of this paper, Prof. Pierce wrote to me that my
addition of relative terms is, in all but notation, the same
as his internal multiplication of the same. This is quite
true. See his paper in the ‘ Algebra and Logic,’ reprinted
from the ‘ American Journal of Mathematics,’ vol. iii.

ON THE GROWTH AND USE OF A SYMBOLICAL LANGUAGE. 225

XXV. On the Growth and Use of a Symbolical Language.
By Hvuen M‘Cort, Esq., B.A. Communicated by
the Rev. Roserr Hartey, F.R.S.

Read March 22nd, 1881.

In an article on “Symbolical Reasoning,” in a recent
number of ‘ Mind’ (No. 17, Jan. 1880), I have described
the relation between symbolicaF reasoning and ordinary
verbal reasoning as analogous to that between machine
labour and ordinary manual labour. To trace this analogy
through all its various points of resemblance would take
too long; but there is one point which deserves some
notice, as it bears more especially upon the present
subject.

For what kinds of operations are machines usually
invented? A little reflection will show that one common
and prominent characteristic of such operations is same-
ness ; we employ machines to perform operations which
have to be frequently repeated, and repeated in the same
unvarying manner. Sewing-machines, knitting-machines,
reaping-machines, and, in fact, the great generality of
machines, however widely they may differ in other respects,
resemble each other in this.

For what kinds of expressions and relations, mathe-
matical or logical, do we usually invent symbols? We
shall find, as before, that the common characteristic of
such expressions and relations is sameness—that they are
expressions and relations which have to be repeated fre-

SER. 1II. VOL. VII. Q

226 H. M‘COLL ON THE GROWTH AND

quently. When any complex expression or relation is
perceived to have a tendency to recur again and again, we
economize thought, time, and space if we denote this
expression or relation by some simple, suggestive, and
easily formed symbol which we may always recognize as
doing duty for its more complex equivalent.

The representive symbols thus invented combine after-
wards among themselves into new expressions and rela-
tions of more or less complexity, and give birth, in their
turn, when the necessity or convenience arises, to fresh
representative symbols, whose abbreviating power bears, on
an average, the same ratio to that of the symbols they dis-
place, as the abbreviating power of the latter bears to that
of their immediate progenitors. In strict conformity with
this law of symbolical growth the science of mathematics
has gradually attained its present wonderful power within
the limits of its application ; and in strict conformity with
the same law, the science of logic, which is now evidently
entering on quite a new phase of existence, will probably
before long, and within much wider limits of application,
surpass the achievements of mathematical science itself.

Now it is clear that the power and progress of any
symbolical language must depend very largely upon the
judgment exercised, first, as to whether, in any proposed
case, a new symbol is really required, or would on the
whole be useful, and, secondly (supposing the need of a
new symbol to be admitted), as to the kind of symbol that
should be selected. With regard to the first point, we
must remember that the introduction of a fresh symbol is
always accompanied by the disadvantage that it adds a
fresh item to the load which the memory has to carry,
and it is only when its advantages more than outweigh
this very serious drawback that it should be admitted as a
permanent addition to the existing vocabulary. Can we

USE OF A SYMBOLICAL LANGUAGE. 227

‘discover any general principles or rules which should
guide us in this important matter of admission or rejec-
tion? Let us examine a few of the symbols which we
now possess, and see whether any such rules can be
discovered.

The ratio which the circumference of a circle has to its
diameter, namely, 3°14159 &c., is one that occurs fre-
quently, and for this reason mathematicians express it by
a single arbitrary symbol 7. The ratio which the diagonal
of a square has to its side, namely, 1°41421 &c., is another
ratio which also occurs frequently, and yet mathemati-
cians do not express this by any single arbitrary symbol,
nor would any mathematician think the introduction of
such a symbol desirable. Why is this? The answer is
obvious: the latter ratio may be expressed, without any
fresh definition or explanation, by avery brief and simple
combination of existing symbols, namely by the combi-
nation 4/2; while we know of no brief and easily formed
combination of existing symbols, requiring no fresh defi-
nition, which would accurately and unambiguously express
the former ratio.

From these and other analogous examples we may safely
assume as one guiding principle, that some conventional
symbol of abbreviation should be used as a substitute for
any expression that has a tendency to recur frequently,
provided that no suitable combination of existing symbols
(i.e. a combination short, simple, and requiring no fresh
definition or explanation) can be found to replace it.

The next point is, as a rule, more important and also
less easily decided. It is this :—Granting the necessity for
some new symbol of abbreviation, what kind of symbol
should be selected ?

In the case of the symbol z, to which we have already
alluded, this question of suitable selection is, it is true, of

Q2

228 H. M‘COLL ON THE GROWTH AND

secondary importance ; almost any arbitrary symbol of
easy formation would have done just as well; but this is
an exception to the general rule. Consider the symbol a”,
which has been invented as an abbreviation for the pro-
duct of n equal factors, each equal to a; that is, a? for aa,
a for aaa, and so on. If the first of these products,
namely aa, were the only one that had a tendency to
recur, we may be quite sure that mathematicians would
remain satisfied with it in its original form, and would
never have accepted the innovation a* as its equivalent.
But since aaa, aaaa, &c. have also the same tendency of
frequent recurrence, the appropriateness of the symbol
selected is evident : the numerical index reminds us of the
number of equal factors; and we are at once provided
with a more effective notation for considermg the pro-
perties and relations of all expressions that are products of
equal factors, as, for instance, in the binomial theorem.

Let us now examine the raison d’étre of that remark-
able class of symbols which were invented at a more
advanced stage of the science (by whom I know not), and
which give such a wonderful sweep and power to sym-
bolical language generally, logical as well as mathematical ;
I refer to that class of symbols of which f(z) may be taken
as a specimen. This symbol denotes any complex expres-
sion whatever (mathematical or logical) that contains the
simpler expression 2, 7n any relation whatever, as one of its
constituents. What was the special need which this symbol
was invented to supply ?

We have often to consider what an expression would
become if one of its constituents were taken away and a
fresh constituent put into its place, just as people some-
times speculate as to what would be the effect upon a
ministerial policy if a certain member of the cabinet were
to resign and a certain other person appointed in his place.

USE OF A SYMBOLICAL LANGUAGE. 229

If f(z) denote the expression of which # is a constituent,
then f(a) will denote the new expression which is formed
by substituting a for z. To take a simple case, let /(z)

denote the algebraical expression <a +a+5; then f(2)
will denote a +2-+5, and will be equal to 13; f(o) will
denote = +0+5, and will be equal to 7; f(7—5) will

6
denote ae and will be equal to
6

=——+2; and so on.
8—2

The last symbol f(v—5) warns us of a danger to be
carefully guarded against in the introduction of fresh
symbols, namely the danger of ambiguity. The meaning
here attached to it might in certain cases be confounded
with an older and commoner meaning ; for the symbol
f(w—5) also denotes the product of the two factors f and
x—5. How is this danger of ambiguity to be guarded
against? We might, it is true, guard against it by
adopting, instead of f, a totally new symbol of some
unwonted shape; but this is a course to be avoided if
possible. Strange-looking symbols somehow offend the
eye; and we do not take to them kindly, even when they
are of simple and easy formation. Provided we can avoid.
ambiguity, it is generally better to intrust an old symbol
with new duties than to employ the services of a perfect
stranger. In the case just considered, and in many
analogous cases, the context will be quite sufficient to pre-
vent us from confounding one meaning with another, just
as in ordinary discourse we run no risk of confounding
the meanings of the word air in the two statements—
‘He assumed an air of authority,’ and “ He resolved the

230 H. M‘COLL ON THE GROWTH AND

air into its component gases.” In the special case of
f(e—5) no ambiguity exists when the letter fis used in
no other sense throughout the investigation on which we
happen to be engaged; and when it is used in another
sense, all risk of confusion is obviated by simply em-
ploying instead of f, in the expressions f(z), f(z—5), &c.,
some other symbolic letter, such as ¢.

We may recapitulate the results so far arrived at
thus :—

1, Anew symbol, or an old symbol with a new meaning,
to be accepted as a permanent addition to the existing
stock, should represent an expression or relation that
tends to occur frequently, and that cannot be logically
expressed by any short combination of existing symbols. —

2. Provided we can avoid ambiguity, it is better to
employ an old symbol in a new sense than to invent a
totally new symbol.

3. The symbol chosen should be of short and easy
formation and lead to symbolic expressions of simple and
symmetrical forms.

The illustrations hitherto given have heen borrowed
from mathematics, because these are more familiar to the
general reader than any that could have been taken from
symbolical logic; yet the latter is im every respect the
simpler science of the two,—simpler in the conceptions*

* That the conceptions which underlie the very elements of symbolical
mathematics are by no means easy to grasp will be admitted by any one
who has attempted to explain to beginners the real logical meaning of the
“ Rule of Signs” in multiplication and division of ordinary algebra. This
difficulty meets the tyro on the very threshold of the science. When he has
advanced a few steps further, he is confronted with a symbolical paradox
which it has taxed the ingenuity of the subtlest mathematical intellects to
explain, and of which no rational explanation whatever was given until
within very recent times; I allude to the useful and important yet per-

plexing symbol Y —1.

USE OF A SYMBOLICAL LANGUAGE. 231

represented by symbols, simpler in the smallness of the
number of symbols employed, and simpler in the mecha-
nical operations that have to be performed. In claiming
this advantage for logic over mathematics, I speak solely
of that scheme of symbolical logic which I, rightly or
wrongly, consider the simplest and most effective, namely
the scheme which I have explained and illustrated in
‘Mind,’ in the ‘ Proceedings ’ of the London Mathematical
Society, in the ‘ Educational Times,’ and in the ‘ Philo-
sophical Magazine.’ According to this scheme the whole
and sole duty of the logician is to investigate the relations
in which statements (i.e. assertions and denials) stand
towards each other. For all practical reasoning-purposes
a statement may be defined as anything that conveys directly
through a bodily sense (as the eye or ear) any information
(true or false) to the mind. In this sense a nod or a
shake of the head is a perfectly intelligible statement.
The Union-Jack fluttering from the mast of a ship con-
veys as clear and definite information as the words “This
is a British ship” shouted through the captain’s speaking-
trumpet; and therefore the flag is as much a statement
in the logical sense as the words ; and, like the words, it
may (as we know by experience) be a true or a false
statement. |

Logic, then, being concerned with statements, the
analogy of ordinary algebra suggests the propriety
of denoting simple statements by single letters, and
the relations in which statements stand to each other
either by the relative positions of the statement-letters,
or by separate and distinct symbols. Therefore a very
important inquiry in laying the foundation of a prac-
tical symbolical calculus for solving logical problems is
this :—What are the characteristics and relations which
most frequently distinguish or connect the statements of

2028 H. M‘COLL ON THE GROWTH AND

an argument? Foremost among distinctions we shall find
that of truth and falsehood. All intelligible statements
may be divided into two great classes, the ¢rue and the
false. Every statement must belong to one or other of
these two classes, though we may not always know to which.
If it were not for this element of uncertainty, reasoning
would be purposeless, and logic would have no raison d’étre.
This uncertainty (sometimes real, and sometimes only
hypothetical) suggests the convenience of dividing the
statements of any argument upon which we happen to be
engaged into three distinct classes, the admittedly true, the
admittedly false, and the doubtful. Borrowing a hint from
mathematical probability, we may denote any statement
belonging to the first class by the symbol 1, and any
statement belonging to the second class by 0, while any
doubtful statement (whether the doubt be real or hypo-
thetical) may be denoted by any symbol we choose except
these. Now, generally speaking, in the course of any
consistent argument or investigation the boundaries of
these three classes will be found to be gradually changing ;
the first two classes, the admittedly true and the admit-
tedly false, though never encroaching upon each other’s
ground, will both constantly encroach won the ground of
the third, the doubtful.

Statements may also, independently of their truth or
falsehood, be divided into two distinct classes, namely
assertions and denials. Every assertion either claims or
has already obtained admission into the class denoted by
the symbol 1; while its denial contests its right to this
symbol, which it claims for itself, and seeks to brand it,
as an impostor, with the symbol o. As long as these two
claimants belong to the class of doubtful statements, all
that we can say about them is, that the one (either the
assertion or its denial) must be true, and the other false.

USE OF A SYMBOLICAL LANGUAGE. 233

The denial of any assertion may be conveniently de-
noted by an accent, thus :—Let 2 denote the statement,
“He is in England;” then 2! will denote “ He is not
in England.”

The statements hitherto spoken of are simple or ele-
mentary statements—that is, statements represented each
by a single letter, or a single letter and an accent. Any
statement that requires more than one letter to express it
may be called a complex statement. The principal rela-
tions by virtue of which simple statements combine into
complex ones are three—namely, conjunction, disjunction,
and implication, corresponding respectively to the three
conjunctions and, or, if. The first relation is generally
symbolized (like multiplication in ordinary algebra) by
simple juxtaposition, and occasionally, though never
necessarily, by the symbol x; the second (like addition in
ordinary algebra) by the symbol +; and the third by the
symbol :, as in the following examples :—

Let # denote the statement ‘ He will go to Paris ;” and
let y denote the statement “I shall go to York.” Then
ay denotes the compound statement “ He will go to Paris
and 1 shall go to York ;” the symbol #+y denotes the
disjunctive statement ‘‘ He will go to Paris or I shall go
to York ;” and x: y denotes the implication “ Jf he goes
to Paris I shall go to York.”

A compound statement, as adc, claims the symbol 1 for
every one of its factors; a disjunctive statement, as
a+b-+c, claims the symbol 1 for one at least of its terms ;
and the implicational statement a: claims the symbol 1
for the consequent b, provided the antecedent a is entitled
to it, but neither claims nor disclaims it for 6 if a is not
entitled to it.

Brackets are used when necessary to collect the different
elements of a complex statement, and so prevent any uncer-

234 H. M‘COLL ON THE GROWTH AND

tainty respecting to what complex statement any element or
relational symbol belongs. Thus, the compound statement
a(b+c), formed by the two factors a and 6+¢, is a very
different statement from the disjunctive statement ab+ce,
formed by the two terms ad and c. So, again, is (a: 6+c)!,
the denial of the whole implicational complex statement
a:b+c, avery different statement from a:b+c', m which
_the symbol of denial affects only the element ce.

Reciprocal implications—that is, compound implications
of the form (a : 6) (6; @)—occur so frequently that a symbol
of abbreviation is convenient. Borrowing again from the
existent mathematical stock, we may use* either :: or =.
Thus, either the symbol a::6 or the symbol a=4 may be
taken as an abbreviation for the reciprocal implication
(a:6)(b: a).

The symbol f(#) has been already considered, and is
employed in logic in the same sense as in mathematics ;
that is to say, it denotes any statement whatever that con-
taims w as one of its constituents; but the symbol /'(z#),
for which no logical meaning analogous to its mathematical
one is likely to turn up, may be conveniently employed as
an abbreviation for {f(«)}!.

These are the only symbols that need be employed in
the system of symbolical logic which I advocate, and they
are amply sufficient not only for the complete solution of
any logical problem that I have ever seen solved by any

* To avoid the employment of brackets and repetition as much as pos-
sible, it will be convenient to use both, with this distinction, that the symbols
: and :: should be coordinate (7. ¢. of equal reach in regard to the state-
ments affected by them), but both subordinate (é. e. of inferior reach) to the
symbol =. Thus, a:b+¢::d+e:f::g is an abbreviation for the complex
statement

(a:b+c)(b+e::d+e)(d+e:f)\(f:: 9),

while a@:64+c=d+e:f::g is au abbreviation for

(a: b4+c)=(d+e:f::9).

USE OF A SYMBOLICAL LANGUAGE. 235

other method, but also for the complete solution of many
problems which, I think, it would be difficult to solve by
any other method with which I am at present acquainted.

The rules which I have proposed for observance in
introducing new symbols are, I believe, sound, and I have
followed them myself to to the best of my ability. As the
science advances, other symbols will, no doubt, become
necessary ; but they should be introduced slowly, and not
till their utility is made clearly manifest.

My statement in ‘ Mind, that though a: 6 implies
a' +6, it is not equivalent to it, has been called in ques-
tion, my critics maintaining that there is no real difference
between the conditional statement “If a@ is true, 6 is
true,” and the disjunctive statement “ Hither a is false or
bis true.” Now, I admit at once that, in the ordinary
language of life, disjunctive statements are often made
which convey, and are intended to convey, a conditional
meaning, and, further, that the example which I gave in
illustration, namely ‘‘He will either discontinue his
extravagance, or he will be ruimed,” is one of them.
Many statements, however, are made in common life
which are tacitly understood to convey a stronger meaning
than logically and literally belongs to them. Take, for
instance, the well-known expression, ‘ He will never set
the Thames on fire.” In its literal sense this very harm-
less-sounding statement does not commit one to much ; it
may, with equal safety, be applied to the cleverest man
living and to the most incapable idiot. What the practical
reasoner would be concerned with in making use of any
evidence conveyed to him in such terms would be the
intended meaning of the speaker; and if his argument
should be of such a nature as to necessitate the employ-
ment of symbols, the symbol for the statement should
denote its intended and not its literal meaning. The real

236 H. M‘COLL ON THE GROWTH AND

question in dispute is this, does the conditional statement
“Tf ais true bis true,” as I define and symbolize it, con-
vey a2 meaning in any way different from the disjunctive
statement “ Hither a is false or 0 is true,” as I define and
symbolize it ? .

My argument in ‘ Mind’ was, that since the denial of
the first, namely ‘‘a may be true without 6 being so,”
conveys less information than “a is true and 0 is false,”
which is the denial of the second, the conditional disjunc-
tive statements of which these are the respective denials
cannot be equivalent. As the non-equivalence of the
denials, however, is much more evident than that of the
affirmative statements, it will be well worth while to give,
if possible, a more direct proof of the non-equivalence of
the latter. |

As it can easily be shown that a:b is equivalent to
1:a'+46, the question may be narrowed to this, is the
implication 1:a,in which e denotes a!+6, equivalent to
the simple affirmation a? It seems to me that 1: and «
differ in pretty much the same way as the statement “ It
is well-known that tin is heavier than zinc,’ and the
simpler affirmation ‘‘ Tin is heavier than zinc ;” that is to
say, the former implies the latter, but is not implied in it.
The statement 1 :, in addition to claiming the symbol 1
for itself, asserts that its protégé « has fairly made good
its right to it; whereas « only claims this symbol on its
own account. The symbol (1: «)’, which is the denial of
I:a, may be read, “is not necessarily true ;” whereas a,
the denial of a, is much stronger, and asserts positively that
ais false. It follows from the law of logic called contra-
position that the denial of the weaker (or implied) state-
ment is stronger than and implies the denial of the stronger
(or implying) statement.

The disjunctive statements of ordinary language may be

USE OF A SYMBOLICAL LANGUAGE. 237

divided into conditional disjunctives and unconditional (or
pure) disjunctives—-the former being those already referred
to as conditional in meaning though disjunctive in form.
Among these may be classed the famous disjunctive of
Edward I., “ By God, sir Earl, you shall either go or
hang ” (symbolically, 9+), the meaning of which is evi-
dently, ‘If you won’t go, I will have you hanged.” The
king, by a not uncommon trick of speech, used the weaker
statement in order to express a stronger meaning. ‘The
earl, in his reply, “ By God, sir king, I shall neither go
nor hang” (g''), secures emphasis of a more direct kind
by flatly denying even the king’s weak disjunctive, stead
of the much stronger conditional statement which would
more logically, though less emphatically, express the king’s
real meaning. The denial of “If you won’t go, I will
have you hanged,” would be the very mild assertion, “ I
may refuse to go without your having me hanged,” a mode
of speech which would not at all have suited the temper of
Ear! Bigod.

As an instance of a simple unconditional disjunctive, we
may take the statement, “‘ We shall either go to Brighton
or Hastings this summer.” ‘There appears to me to be a
fundamental difference between the class of disjunctives of
which this is a type, and the conditional class of disjunctives
previously illustrated. At the same time it must be ad-
mitted that in common language, just as statements which
are conditional in meaning are often expressed in a disjunc-
tive form, so real disjunctives unconditional in meaning are
often expressed in a conditional form. The last example,
for instance, “ We shall either go to Brighton or to Hastings
this summer,” might, according to usage and without any
perceptible difference of meaning, be expressed as “ If we
don’t go to Brighton this summer, we shall go to Hast-
ings,” or in the same words with Brighton aud Hastings

238 H. M‘COLL ON THE GROWTH AND

interchanged. The fact, however, that conditionals and dis-
junctives are frequently confounded in ordinary untechni-
cal language, is no reason why they should be so in formal or
symbolical logic. Even if I have not succeeded in satis-
factorily proving that a: 6 and a’+ 5 are not synonymous,
it is safest, I think, to adopt my view in actual practice.
Let it be observed that the hypothesis of non-equivalence
commits one to less, and therefore involves less risk to the
inferred conclusions. My critics admit with me that
(a: 6): (a’! +6) 1s a correct formula; but they would also add
the formula a’+: (a: 6), the validity of which I deny. If
I am wrong, I am open to the charge of seeking to deprive
logic of a new formula which might possibly prove useful,
but whose utility has yet to be proved. If my opponents
are wrong, they are open to the graver charge of seeking
to introduce an erroneous formula, which not only can
render no service in reasoning, but might even seriously
endanger our conclusions.

As this article is an attempt to explain and illustrate
the laws which necessitate the growth, and the principles
which determine the form, of a symbolical language, I
hope it will not be considered either irrelevant or egotis-
tical, if I give a brief account of the development of my
own method. By “my own method” I mean simply the
method which I discovered (including those features which
it has in common with the prior methods of others), as
well as those characteristics which are peculiar to itself.
What these are I leave to others to decide. The question
is certainly irrelevant to the expressed object of this
article ; and its discussion would only provoke the natural
impatience of the reader. I only mention this at all in
order to explain that I use the possessive pronoun my
merely as a convenient abbreviation, and in a sense which
cannot possibly give offence to any of my fellow workers.

USE OF A SYMBOLICAL LANGUAGE. 239

As I stated in my third paper in the ‘ Proceedings’ of
the London Mathematical Society, my method originated
in a question in probability proposed in the ‘ Educational
Times’ for June 1871*. The question (as I understood
it) may be thus generalized :—“ Given that the variables
2, y, 2 are each taken at random between given limits,
what is the chance that an assigned function of these
variables, say ¢(z, y, 2), will be real and positive? When
I began to solve the problem I found that, in addition to
the particular event whose chance was required, I should
have to consider the relations in which this event stood
towards several other events on which it more or less
depended. It struck me that it would help the memory
and facilitate the reasoning, if I registered the various
events spoken of in regular numerical order in a table of
reference. The event whose chance had to be found
resolved itself into a concurrence of two distinct but not
independent events 1 and 2; and J denoted the chance (or
probability) of this concurrence by the symbol p(1.2).
The compound event 1.2 implied the occurrence of a
third event 3, which it was necessary also to take into
account ; I had therefore to replace p(1 .2) by p(1.2. 3).
But the consideration of 1.2.3 could not be separated
from the consideration of a fourth event 4, m conjunction
with which it might happen, but not necessarily ; and the
probability of the concurrence 1.2.3 depended mate-
rially upon whether it happened in conjunction with this
fourth event or withoutit. Denoting the non-occurrence of
this fourth event by the symbol : 4, I thus had the equation
w(i.2.3)=—p(I .2.3.4)=p(1.2.3:4). Proceeding in
this way, but ina somewhat groping’ and tentative manner,

* The subject of probability was one which I had recently taken up at the
request of Mr. J. C. Miller, the mathematical editor of the ‘ Educational
Times,’ who felt great interest in it himself, and strongly recommended it
as “an unworked vein in which I should find many treasures.”

240 H. M‘COLL ON THE GROWTH AND

I finally resolved the problem into a form which brought
it within the reach of the integral calculus; in other
words, I had somehow determined the limits of integration,
though I hardly knew how. I applied the same method
successfully to two or three other problems in the ‘ Edu-
cational Times,’ but without being able to make any mate-
rial improvement in it. Whilst occupied with these
researches, the editor of the ‘ Educational Times’ sent me
a very neat and simple geometrical solution by Mr. G. 8.
Carr of the very problem which had given me so much
trouble. This so discouraged me (in the belief that I was
only wasting my time) that I threw up the whole subject in
disgust, and determined for the future to eschew all
mathematics that did not fall within the very narrow limits
of my requirements as a teacher.

When, six years afterwards, I broke my resolution and
again took up the subject of probability, my mind natu-
rally reverted to the old abandoned method;- and it then
struck me that, with all its defects, it had one important
merit, namely independence of geometrical diagrams, and —
that, consequently, it would be well worth my while to
apply myself patiently to the task of removing its defects
and developing it, if possible, into something better.

My first step was to drop the letter p (for probability),
which I thought might, without ambiguity be left under-
stood; so that, for instance, 1.2.3 should replace
p(1.2.3) as an abbreviation for “ the probability of the
event 1.2.3.” My next step was to use letters instead
of numbers, as ABC instead of 1 . 2 . 3, and an accent to de-
note non-occurrence, as ABC! instead of 1.2:3. But at
this point a difficulty presented itself: how was ABC, the
chance of the compound event ABC, to be distinguished
from ABC, the product of the chances A, B, C? for the
chance of the compound event would not generally be the

USE OF A SYMBOLICAL LANGUAGE. 241

product of the chances of the separate events. To guard
against this risk of confusion I decided to use capitals, as
ABC, when the chance of the whole compound event was
meant, and small italic letters, abc, when the product of
the separate chances a, 6, c was meant. Thus, though the
chances A, B, C were separately equal to a, b, c, the
symbol ABC would not (except in the case of independent
events) be equivalent to the symbolade. The equivalence
of A(B+C) and AB+AC, and of similar expressions, I
discovered before I introduced letters instead of numbers.
So far, I had made no real advance : the substitution of
a literal for a numerical notation improved perhaps the
appearance of the method; but it did not affect it practi-
cally. In applying the method to such questions as
required the integral calculus it still remained a tentative
method; I still groped my way towards conclusions in
particular cases without the help of any general rules of
procedure. At last I was struck by the fact that the
events registered im my tables, and whose chances were
denoted by the letters, were all of the form z>z2,, 7,>2z,
Br, >2Ly YY Y2>Ys Y2.>Y;,, &e., and had all reference to
the limits of the different variables. This suggested the
idea of a partial return to the original numerical notation
and classifying the events according to the variable spoken
of. I denoted the event and also the chance of the event
z>x, by z,, the event z,>2 and its chance by z,, and
so on for #,, #4, #3, 23) Yx) Yv, &e. This was a very impor-
tant step so far as my method related to integration limits ;
and after this its development in this direction was com-
paratively rapid—too much so for me to remember very
accurately its different stages. Still, I looked upon the
method as essentially and inseparably connected with pro-
bability ; and even when I had decided that it would be
more convenient and less confusing to let my symbols de-
SER. lII. VOL. VII. | R

24.2 H. M‘COLL ON THE GROWTH AND

note logical statements rather than mathematical chances,
I could not for some time turn to any account the inde-
pendence of mathematics which I had thus secured for the
method. The notion of the mutual exclusiveness of events
(or statements) connected by the sign + clung to the
method up to a very late period; in fact, I was in the very
act of writing my first article “On Symbolical Reasoning”’
for the ‘ Educational Times,’ when the needlessness of this
restriction occurred to me. I had written down my defi-
nitions of the equations ABC=1 and ABC=o in the fol-
lowing words :—

The equation ABC =1 asserts that all the three statements are true; the
equation ABC=o asserts that all the three statements are ot true, 7. é. that
at least one of the three is false ;

and I had to consider suitable definitions of the equations
A+B+C=1 and A+B+C=o. It was quite evident
that the equation A+B+C=o, whether the statements
A, B, C were mutually exclusive or not, must assert that
all the three statements are false; and the very words used
in the previous definitions of ABC=1 and ABC=o
suggested that, as a symmetrical complement of this, the
equation A+B+C=r1 should assert that all the three
statements are not false, z.e. that at least one of the three
is true. The only question to decide was whether the rule
of multiplication, (A+B)(C+D)=AC+AD+BC+BD,
would still hold good. A very little consideration showed
that it would ; so, though the method was correct, so far
as it went, on either supposition, I judged it wiser to leave
room for possible future development by adopting the
wider rather than the narrower hypothesis for its basis.
Finding myself thus, at the end of my investigation, on
logical instead of mathematical ground, I naturally began
to study the relation in which my method stood towards

USE OF A SYMBOLICAL LANGUAGE. 243

the ordinary logic, and especially towards the syllogism.
The only book on logic that I possessed was Prof. Bain’s
work ; and to this I turned. The resemblance which my
method bore to Boole’s, as therein described, of course
struck me at once; but Boole’s treatment of the syllogism
was more likely to put me on the wrong track than to
help me. As my most elementary symbols denoted state-
ments, not necessarily connected with quantity at all, I
could not see how the syllogism, with its ever recurring
all, some, none, could be brought within the reach of my
method. The Cartesian system of analytical geometry at
last supplied the desiderated hint as to the proper mode of
procedure. In this system, as every mathematician
knows, one single point is spoken of in every equation, but
with the understanding that it is a representative point,
and that the equational statement made respecting it is
also true respecting every other point in the locus ex-
pressed by this equational statement.

The symbol :, which I had already begun to use as an
occasionally convenient abbreviation for the word “ im-
plies,”’ now became almost imperative. Syllogistic rea-
soning is strictly restricted to classification. The state-
ment “ All X is Y ” is equivalent to the conditional state-
ment “If any thing belongs to the class X, it must also
belong to the class Y.” Speaking then of something
originally unclassed, if z denote the statement “ It belongs
to the class X,” and if y denote the statement “It belongs
to the class Y,” then the implicational statement 7: y
(or x implies y) will be equivalent to the syllogistic state-
ment ‘ All X is Y.”

It was evident after this that 2:7! would be the proper
symbolical expression for “No X is Y;” but, strange to
say, the discovery of the suitable symbolic expressions for
“Some X is Y”’ and “some X is not Y” caused me no

R 2

244. H. M‘COLL ON THE GROWTH AND

small trouble, even though I had previously more thai
once wondered under what circumstances the symbol
(@:y)' would be required. For a long time I did not
recognize this (wv: y)' as the equivalent (in classication) of
«Some X is not Y,” and (w:y)’ as the equivalent of
“Some X is Y.” In my second communication to the
Mathematical Society I used the symbol v: zy to denote
“Some X is Y;” and it was only when I had read the
very just objection made by one of the referees to my
introduction of the arbitary and possibly non-existent
class V that it suddenly flashed upon me that the true
symbolical expression for “Some X is Y” should be
(x:y')', the denial of the implication z:y', and that the
true symbolical expression for “ Some X is not Y” should
be (a: y)!', the denial of x: y.

~The next new symbol which I introduced into my
symbolic system was the symbol z,, to express the chance
of x being true on the assumption that ais true. The cir-
cumstances which suggested this symbol to me are curious
and instructive. My first idea was to use the symbol z,
to denote the chance of # being true, the suffix c being
merely suggestive of the word chance and not denoting a
statement. In fact, this was the notation which originally
formed the basis of my fourth paper, “‘ On the Calculus of
Equivalent Statements,” when it was first communicated
to the London Mathematical Society. While this paper
was in the hands of the referees, I was occupied with a
problem proposed to me by Mr. C. J. Monro, and
involving among other things the consideration of a
chance (vz),, which I at first considered as equal to
x,(a:2),, being under the idea that, since x: z expressed
the conditional statement “If 2 is true z is true,” (w: 2),

would be the proper symbol to express the chance that if
x is true z is true. On reflexion I discovered that this,

USE OF A SYMBOLICAL LANGUAGE. 245

plausible as it sounded, would lead to inconsistency of
notation. For, since x:z is equivalent to 2z!:2', con-
sistency of notation required that (x: z) should denote
the same chance as (z!:2’)-; and, as I had interpreted the
symbols, this would not be the case. The chance that z is
true, on the assumption that x is true, is not generally
equal to the chance that x is false on the assumption that
zis false. I was thus forced to the conclusion that I had
put a wrong interpretation on the symbols (a@:z), and
(z': 2')., which must be equivalent, and that neither of
them, therefore, was the proper symbol for the chance
which I wished to express. It became necessary, therefore,
since there did not appear to be sufficient data for logi-
cally inferring a correct expression for this chance, to
invent a new and arbitrary symbol for it; and then the
important question presented itself as to what that symbol
should be. It must, if possible, be brief and easily
formed; it must be formed, at least partly, of the symbols
# and z; and yet it must be some unambiguous combination
of those symbols—that is to say, a combination which
should convey no other meaning either by definition or by
implication.. Out of several symbols that offered them-
selves as candidates for the important post to be filled, I
at last selected the symbol z, as the one most likely to
perform effectively the duties required of it.

The symbol z, being thus fairly installed, I was struck
by the resemblance between it in some respects and the
symbol z,. Both expressed the chance of the truth of z,
though on generally different assumptions; and, what was
more remarkable, some of the formule which I had ob-
tained involving the constant suffix c, as

(2+ B)-=a.+B.—(#B)c,

were also true when for ¢ I substituted the variable suffix

246 H. M‘COLL ON THE GROWTH AND

a. This suggested the propriety of considering c too as a
statement, instead of a mere arbitrary abbreviation for “ the
chance of the truth of,” and it soon became evident what
that statement must be. The constant suffix c, like the
variable suffix 7, must denote a statement taken for
granted ; but, unlike the variable 2, it must denote a
statement whose truth is taken for granted always—that is,
throughout the whole of an investigation. In other words,
the suffix c must be an exact equivalent for the logical
symbol I.

This, however, necessitated other symbolical changes,
As long as the suffix c did not denote a statement, I was at
liberty to use this letter in conjunction with the letters a
and 6 in other positions as a statement; so that c, (like a,
and 6.) would simply denote the chance of the truth of the
statement ¢c, and its value might vary from o to 1; but
with the new meaning of the suffix ¢, we should always
have c.=1. It thus became expedient to leave c at liberty
to discharge other functions in company with its old com-
rades a and 4, and to intrust the duty of denoting univer-
sally admitted statements to some letter whose services in
other capacities could be more easily spared. I decided,
after some hesitation, on the Greek letter ¢, which is easily
formed, pleasing to the eye, and not often wanted. It
may be asked, why was I not satisfied with the symbol 1,
which already denoted an admitted statement? My
answer is, first, that I thought this numeral would not look
well in frequent companionship with Jiferal suffixes; and,
next, that I thought it better to reserve it, in company
with other numerals, for distinguishing statements of the
same class or series, as @,, @,, @, &c., which, though different
statements, will generally be found to have some common
factor or characteristic a.

Having thus decided that « should denote a statement

USE OF A SYMBOLICAL LANGUAGE, 247

of acknowledged truth, that x, should denote the chance
of the truth of x2 on the assumption that a is true, and
that therefore 7, mnst simply denote the chance that & is
true, with no assumption beyond the understood data of the
problem, it soon became evident that this notation would
express many of the laws of probability in neat and compact
formule, and also that it would contribute towards pre-
cisicn of reasoning from its constant reference, by means
of its suffixes, to the assumptions on which any argument
in probability rested. It is well known that of all mathe-
matical subjects probability is the one in which mistakes
are most apt to be made; and these mistakes are usually
the result of correct reasoning based upon unperceived
false assumptions. These assumptions, for the most part,
would be readily seen to be false, if they were only
expressed; a notation therefore that actually forces them
on the attention must be considered as possessing one very
important advantage in that fact alone.

As this new scheme of probability-notation quite super-
seded that which formed the basis of the paper which had
been already submitted to the referees of the Mathema-
tical Society, these gentlemen naturally declined (on the
scheme being communicated to them through the Honorary
Secretary, Mr. Tucker) to pronounce any opinion either
upon the original paper or on the proposed alterations, till
the whole was recast and rewritten. When this was done,
and the paper again submitted to them, they advised its
publication.

In my former paper in ‘ Mind,’ “On Symbolical Rea-
soning,” I referred to the analogy between the relation
connecting antecedent and consequent in logic and that
connecting subject and predicate in grammar. Would it
be presumptuous to suggest as a probable hypothesis that
this analogy is more than a mere coincidence, and that it

248 ON THE GROWTH AND USE OF A SYMBOLICAL LANGUAGE.

really points to an original identity? It does not seem

unreasonable to suppose that in the very early stage of
human speech, each separate word represented a complete

statement and conveyed its own independent information.

On this supposition, the growth of vocal language would

proceed according to laws im some respects analogous to

those which shape the development of a language of
symbols. Our abstract nouns, for mstance, seem to be’
nothing but abbreviations for original statements. Take

the compact and well-known saying, “ Unity is strength.”

What is this but an abbreviation for the conditional state-
ment, ‘“‘ If a company be wnited, they will be strong’? or,

as it may be otherwise expressed, “If the statement

symbolized by the abbreviation unity for ‘They are

united’ be applicable to a company of persons, so will

also the statement symbolized by the abbreviation strength

for ‘ They are strong.’ ”

But here I must stop. Speculations as to the primeval
forms of human speech do not come fairly within the
limits prescribed by the title of this article ; and further
discussion of the subject in this direction would therefore
be irrelevant.

A CHEMICAL INVESTIGATION OF JAPANESE LAQUOR. 249

XXVI. On a Chemical Investigation of Japanese Laquor,
or Urushi. By Mr. Savama Isuruatsv, late of Tokio
University. Communicated by Professor Roscoz,
Ph.D., F.R.S.

Read February 18th, 1879.

Tux Japanese have a peculiar juice of a plant with which
they manufacture their beautiful cabinets and boxes so
celebrated all over the world, that, now, those articles
varnished in imitation of those which are finished with
this juice are termed japanned articles. However, as far
as I am aware of, no attempt has yet been made to analyze
the substance, and none seem to know what it is.

During a few months last year I ventured to undertake
the examination of this body, so as to afford some clue to
those who will have the opportunity of examining this
substance in future more fully and perfectly with ample
time.

Urushi and its Cultivation*.

Japanese laquor is nothing but a sap of a certain kind of
tree called Rhus vernicifera, and commonly termed laquor-
tree, and growing chiefly between the North latitudes 23°
and 38°, ‘The plantation of this tree constitutes one of
the most important parts in the agriculture of certain
districts of the Empire, and in all the laquor-producing

* This description is partly derived from a popular account of the urushi
manufacture published for the use of Japanese primary schools. A similar

statement has been already translated into French by M. Ory, and published
in 1875 by the French Asiatic Society.

250 MR. SADAMA ISHIMATSU ON A CHEMICAL

provinces was protected in the time of feudal government,
just as the production of tea and mulberry-tree are pro-
tected now by the local government assisted by special
officers for this purpose.

As to the mode of planting, there are two different
ways :—In the first case, some time at the end of autumn
or beginning of winter the seeds from grown trees are
collected and ground in a mortar called “usu,” by means
of a “rine,” which plays the same office as the pestle to
the mortar; then they are well stirred and washed in the
solution of caustic lye which they obtain, in a way much
the same thing as lixiviation, from ash of common wood.
They are next put into a rice-straw bag and soaked under
water, or, still better, under the urine of horses, until
the next spring, when, at or about the 2nd of May, the mass
is taken out of the water or urine, and then well spread over
the previously well tilled and prepared ground specially for
this purpose. Then in time the small plants will germinate.

That of the second method is conducted by digging the
roots of old trees; several pieces of roots are cut off by
means of a knife; and these are then directly put under
ground until the germs come out, and are afterwards trans-
ferred to any desired place. The process is much simpler ;
but it is said that the trees obtained from this source are
much more liable to wither or die out from external causes
than the first one ; therefore it is always preferable to adopt
the first method where it is in any way practicable.

After the plants have attained sufficient height, they are
usually planted in the hill-sides, corners of farms, plains, on
river-banks, or on any other vacant places where the land-
tax is light. Urushi-tree or laquor-tree is chiefly cultivated
in the provinces Yamato, Bee, Oshu, Yechigo, Yechizen,
Kai, Shiusha, &c.

In about four to five years the tree grows large enough

INVESTIGATION OF JAPANESE LAQUOR. 251

to be tapped without any injury to the tree itself; and after
three or four years more, in the districts where from its
seeds the manufacture of candles is not carried out, it is cut
down, and from the entire tree the whole of the “ urushi”’
is extracted ; hence we never meet with any large trees in
these districts. In the provinces of Aidsu and Youezawa,
where the manufacture of candles from its seeds is the
principal production, the trees themselves are never cut, and
cutting them was prohibited by the authorities in feudal
times, so that even nowadays many trees are as high as 30-

35 feet.

How to obtain the Juice “ Urushi.”

The tapping of the juice is conducted from the end of
April to the end of November. For this purpose a num-
ber of incisions are made in the bark, which just reach
the wood; the sap immediately runs out, which, coming in
contact with air, is blackened on the surface, and forms in
time a hard crust.

These incisions are made at first about 36 centimetres
distant from one another, on the alternate sides of the
trunk ; and the sap is collected by means of a bamboo or
iron spatula.

After about four days new incisions are made above and
below the former cuttings, and the sap is collected by a
spatula as before. Similar operations are conducted until
the end of the due season, when the whole tree is
covered with a number of cuttings, and (in the districts
where only sap is obtained and candles are not manufac-
tured from its seeds) is cut down. The branches from
trees which are cut down: are made into pieces of about
2°5 feet, and made into fagots, and soaked under water
from ten to twenty days; they are then taken out, and the
incisions are made by means of a certain kind of knife, and
the juice is collected. This is the way by which juice is

252 MR. SADAMA ISHIMATSU ON A CHEMICAL

obtained from branches; and the juice obtained in this
way becomes very hard on drying, being mostly used for
priming, and is known as “ shesime-urushi.”

The quality of urushi depends upon the season in which
it is tapped and also on the condition of climate and nature
of soil, as well as the care taken for its cultivation—the
juice that is tapped just at the beginning of the season and
towards the last being of much inferior quality ; that just
obtained at the middle is considered the best. The raw
product is a slightly sticky liquid having a dirty grey
colour, and always covered with a black crust where it
comes in contact with the atmosphere.

This juice is then put into a large tub, where it is
allowed to stand for some time; then, in time, finer and
better quality and inferior and worse ones separate out
into two layers. It is then separated by means of decan-
tation. The superior quality is stirred in the open air in
sunlight, as you may see in some parts of the city of Tokio,
for the purpose of allowing a certain excess of water to
evaporate, after which it assumes a brilliant dark brown
or nearly black colour; but in thin layers it is almost
transparent. The further operations which the juice under-
- goes before it is ready for use are as follows :—It is first
of all filtered through a strong porous paper called “ yo-
shino gami,” and then mixed with the kind of colouring-
matter with which it is desired to tint the juice.

It is a great pity that white cannot be laquored with the
juice ; but it is said that in the province of Noto, ata place
called ‘‘ Washima,” white is laquored; but the process is
kept unknown, and is rather doubtful.

Various trees produce more or less the same kind of sap.
There is one kind of tree called hazé or hagi, belonging
also to the Rhus family, which has almost exactly the same
appearance as laquor-tree; and one cannot distinguish the

INVESTIGATION OF JAPANESE LAQUOR. 253

two ataglance. This tree grows more largely in warmer
climates than in cold ; therefore this tree abounds in the
south of the Empire, being one of the great agricultural
products, candles being manufactured from its seeds like
from those of laquor. lLaquor-tree, on the contrary, is
mostly found in colder climates.

These conditions made me suppose that the laquor-tree
and hagé or hagi tree were originally one and the same
tree, but changed somewhat in property by change of
climate, soil, or cultivation. We have many instances of
plants being changed in character by the change of place.
It is the actual case in Japan that a certain kind of tree
called “ youdsu,” which in warm climates produces a
fruit which has a very pleasant fragrance, when carried up
to the north is changed to another kind of tree called
“< gédsu,” which is in all its outward appearance exactly
similar to youdsu, but produces an entirely different kind
of fruit. A plant called “nasu,”’ which is, I think, the
same thing as the English egg-plant, produces in the south
of Japan a fruit which is quite long, but when carried to the
north produces only round-oval-shaped fruit. It is also
the case that a cane-sugar plant which grows in the West
Indies, when brought to America forms no seed which is
capable of producing another plant. Again, hagé or hagi
produces also a poisonous gas, the effect of which is exactly
the same as laquor, but rather less in power; and, further-
more, this tree produces a small quantity of laquor, but
the quantity is too small to be profitably extracted.

Chemical Investigation.

During a few months I have had the opportunity of ex-
amining roughly into the nature of “ urushi” in the labo-
ratory of Tokio University.

The specimen of “ urushi ” which I haye examined was

254, MR, SADAMA ISHIMATSU ON A CHEMICAL

obtained from Kuyemon Nakamuraya, in Tokio, a large
urushi-keeper.

It is amilky juice of a pale grey colour ; and the Japanese
call it “ ash-colour,” from its colour resembling so much
that of ash. It gives out a certain kind of volatile acid,
poisonous in its property, and some persons are seriously
attacked by it, producing great swellings on the face
especially, and even the whole body where the acid
comes in contact. During my examination in the labora-
tory, one day one of the apparatus-keepers came in and
was violently attacked by it, producing ugly swellings all
over his face. He told me at the time it was exceedingly
itchy, and by using the solution of acetate of lead, chloride
of potash, and carbonate of soda, was said to have recovered
from this suffering within a week.

The poison that is evolved from urushi acts only on
certain persons. I had to work with it for many days, yet
never had any attack of the kind nor felt any uneasiness
by it.

Urushi being heavier than water, sinks to the bottom;
and under this condition oxidation does not take place ; so
the colour remains unaltered, and the mass remains soft
as long as it may be kept in this way.

It has a sweetish characteristic smell and has an irri-
tating taste. It burns with a very luminous flame, evolv-
ing dense black smoke like oil of turpentine. Itis soluble
in absolute alcohol, ether, benzol, &c. to a great extent,
leaving behind a blackish grey residue, in which gum was
found.

Urushi, on exposure to the atmosphere, rapidly loses its
weight, and at the same time blackens on its surface,
forming in time a hard crust—although this loss is dif-
ferent in different specimens, varying in the specimens I
have examined from 25 to 35 per cent.

— —

~

INVESTIGATION OF JAPANESE LAQUOR. 255

When the laquor is exposed to sunlight in an atmosphere
of carbonic acid in hermetically closed flasks, the blacking
does not take place; and, to my surprise, I found a great
deal of moisture collected on the sides of the flask. The
loss of weight in the air is almost, if not entirely due to
the escape of water with a minute quantity of carbonic
acid, which may be formed by the oxidation of some
organic compound existing im the laquor. The attempt
has been made to estimate the relative amount of carbonic
acid and water, yet it was not successful at the time, being
too difficult, and it must be left open to future investigation.

The laquor is a substance which is very difficult to dry ;
and the way by which the Japanese artists dry the laquored
articles is this :—Those who perform these operations have
a square wooden box of various sizes according to the
amount of work they do, the insides of which are furnished
with shelves to hold the laquored articles; and the boxes
are provided with doors. In order to do this, the inside
is moistened with spray of water, and then laquored articles
are introduced and the door closed. It is a well known
fact to the artist that the removal of air, dry air, or heating
it are the great checks to the drying of the laquor. It is
usually the case to dry a paste like gum arabic or dextrin,
to place it in a current of air, dry air, or heat it; but in
the case of the laquor the reverse is the case. This seems
strange, but it is really the fact. I have inquired of many
artists, they all say the same. This is then true, as we
cannot deny the fact; and there must be some reason or
other for it being so.

According to my opinion, the following is the probable
explanation of it, if not really the true one. If we expose
the laquored articles in the current of air, dry air, or heat
it, then only the surface is dried and forms a crust—a wall
as it were ; and this impervious crust prevents the volatile

256 MR. SADAMA ISHIMATSU ON A CHEMICAL

matter, as water &c., to escape ; it is thus prevented from
drying any further. However, in case of moist air, the
drying takes place much more slowly, so the volatile matters
which are contained in the interior have sufficient time to
escape, and the complete drying takes place. In winter
the laquor dries with much more difficulty than in summer
time ; and in the “rainy season ”’ especially it dries very
quickly, probably due to the dampness of the atmosphere
for the above reason. It is also said that “ urushi” dries
much quicker by the addition of a small quantity of alco-
hol or camphor.

Fused with caustic potash just at the temperature at
which potash fuses, then treated with water and filtered,
on addition of a little dilute H,SO, to neutralize the alkali
no precipitate was obtained.

The blackening of the laquor in the air is by many
supposed to be due to the combined action of light and air ;
but this was proved to be erroneous. First, I made a
square box which has a. well-fitted sliding cover, and the
inside of which was made perfectly black, so that no light
is admitted to enter; in it a small quantity of fresh laquor
on a piece of paper was put in at night in the dark ; and on
looking the next morning it was observed that the surface
of the laquor was covered with a perfectly black wall,
proving that it is not due to the light.

Second, the bottle in which I kept my laquor more than
three months during my examination was exposed to the
incident light of the laboratory ; then the surface of the
laquor in the bottle turned perfectly black, while those
portions which were in contact with the sides of the bottle,
which receives as much light as if there were not any glass
sides before it, was not at all blackened.

This phenomenon is just complementary to the first one,
that the blacking in the atmosphere is, in all probability,

INVESTIGATION OF JAPANESE LAQUOR. 257

due to the oxygen of the air, but not to the light alone nor
to the combined action of air and light (as might have been
supposed).

The laquor when distilled with water gives a colourless
distillate which is slightly acid to test-paper. The attempt
has been undertaken to examine this acid, but not success-
fully, on account of too minute a quantity of the acid that
is evolved.

The distillation by itself and in a current of steam were
tried; but the results in both cases were the same as the
first one. Then, lastly, distilled with a small quantity of
dilute H,SO, into the solution of acetate of lead; but
scarcely any precipitate was obtained.

The laquor mixes with any kind of fixed oil in all pro-
portions ; hence the oil is often added as an adulteration ;
but sometimes a very small quantity is added purposely to
make the laquor more mobile.

The specimen of urushi which I obtained in my labora-
tory for examination consisted of the following three sub-

stances :-—
1s Il.
Part soluble in absolute alcohol............... 58:24 58°23
MANETS eee ea a's tcc anid gs pais dacatlouscauareavisceeseessies 6°34 6°30
LE SEIU Re eke SRR aR ar eee ane ee a ase 2°24 2°30
Moisture and other volatile matter ......... 33°18 33°17
100°0 100°

As I have mentioned already, the laquor loses its weight
rapidly when exposed to the atmosphere : for the determi-
nation I weighed out samples each time from a well-stop-
pered bottle and determined by difference.

Then this was treated with absolute alcohol, and the
filtrate evaporated to small bulk, and dried at 100° C. until
the weight remains constant. This is put down as “ part
soluble in absolute alcohol ” in the above analysis.

SER. III. VOL. VII. s

258 MR. SADAMA ISHIMATSU ON A CHEMICAL

The residue was treated then with hot water, and the
filtrate evaporated to dryness, and dried at 100° C., and
put down as gum.

The residue after gum has been dissolved out is now
dried on aweighed filter, and, after drying at 100°C., weighed
and put down as residue. .

Moisture and other volatile matters are, of course, de-
termined by the difference.

The examination of the amount of soluble part in alco-
hol after the laquor has been exposed for some 20 or 30
days in the sunlight, shows that the soluble portion in-
creased up to 72°82 per cent. This lost 25 p.c. water and
other volatile matter on exposure, the difference being
therefore 58°3 p.c., which is nearly equal to, and practically
the same as the analysis given in the preceding page.
From this we see that there is no material change in the
amount of soluble.

Now a perfectly dried laquor, after being finely semen
and dried at 100° C., was analyzed, and gave the following
result :—

Part soluble in alcohol ............... 18°07 per ceut
Gaur crosiecntenc ee etek ne unceremeree SOR mess
SIGUE te eeecame de onc dt oboetsesioceeet 78230) og,
I00°O

It occurs to me, from this analysis, that the laquor on
perfectly drying, alcohol as well as water has greater diffi-
culty to get access to the dried powder than to the undried
laquor, although the laquor itself may not have undergone
any change.

Now urushi consists of three principal bodies :—a portion
soluble in alcohol ; gum; and residue. In addition to these,
although it contains water and volatile matter, yet they
are not strictly constituents.

INVESTIGATION OF JAPANESE LAQUOR. 259

1. Residue is, I think, nothing more than a mixture of
the bark, cellulose, dusts, &e.

2. Gum is soluble in cold as well as hot water. It has
no smell, almost no taste, yellowish or rather brownish
colour, uncrystalline mass. It is insoluble in alcohol.
On subjecting this substance to organic combustion, I got
the following percentage amounts of oxygen, hydrogen,
and carbon :—

I. i
WALDO ooiticesesecesionac 41°20 41°43
Pivdrogen!’ <)-nssc-.cm 00 6°51 6°58
Oey ON en es cent geese 52°29 51°99
100° 100'0

The formula calculated from I. is C,,H,,0,,, and from
II. C,,H,,;0,,. But I think this is near enough to conclude
it to be the same substance as ordinary gum.

3. Part soluble in alcohol seems to be the principal part,
and has a smell like original laquor, but it never dries up
in the ordinary way. It is brownish black, slightly sticky
to the touch. When treated with potash solution it forms
a bluish-black precipitate ; but nothing is obtained on ad-
dition of dilute H,SO, to the filtrate.

When boiled with HCl acid it merely forms an elastic
mass while hot, something like that when heated sulphur
is allowed to drop into cold water.

When boiled with nitric acid, nitrous fumes were given
off and the mass gradually became yellow, and finally a
beautiful orange-coloured mass was obtained. This mass
was washed several times with hot water and then treated
with absolute alcohol ; the mass was to a greater extent
soluble, leaving behind still some quantity of a yellowish
mass. (This may be the part that has not been yet sufli-
ciently acted upon by the acid.)

260 MR. SADAMA ISHIMATSU ON A CHEMICAL

_ This alcoholic extract is precipitated by either acetate
of lead or nitrate of silver as a beautiful yellow mass. I
took a quantity of this alcoholic extract and precipitated
by means of acetate of lead; and the precipitate was
thoroughly washed with absolute alcohol, and then decom-
posed by dilute sulphuric acid ; we cannot decompose the |
lead-salt with sulphuretted hydrogen (which may be better),
as the acid is altogether destroyed by some reducing action
of sulphuretted hydrogen or other ; and then the acid was
again dissolved in absolute alcohol : thus it was separated
from the sulphate of lead.

Now this alcoholic solution was again precipitated by
means of acetate of lead, and after drying partially in the
air-bath, was transferred under the receiver of an air-pump
and dried over H,SO,. This lead-salt explodes when
heated. The amount of lead was estimated by igniting
the salt with HNO,, as PbO; and also the mass was sub-
jected to organic combustion. Nitrogen determined by
Dumas’s method.

The following numbers were obtained as the result :—

ie Ii. Mean.

@arbonyey.rnce2es: 26°77 27°10 26°93

Hydrogen ...... 4°10 4°12 4°11

NOs eee ek: 18°60 18°28 18°44

POC seven Penaeus 4741 47°43 47°42
Oxygen............ 3°12 3°07 31
100°0

The formula calculated from these results is
Cri... (NOs); Ppos
Now, replacmg PbO, by (OH), and (NO,), by H,, we

CPi ky OF:

have

INVESTIGATION OF JAPANESE LAQUOR. 261

Now I prepared the silver salt of this substance, and
obtained 18°5 per cent. silver, the formula from which
does not correspond at al] with the above ; and therefore
silver salt seems to give no help as to the formula for this
acid.

As such was the case, I took alcoholic extract of
original laquor and precipitated it with acetate of lead,
and, after thoroughly washing, dried it at too’. The lead
was estimated as before, and then subjected to organic
combustion.

As J had but limited time, only the following two results
were experimentally obtained :—

ls II. Mean.
Oarbon. on .-s-c2: 49°84 51°06 50°45
Hydrogen ...... 5°81 5°60 5°705
Oxyren..5J-0. 00: 40°30 39°84. 40°O7
BDO oisnecscanes 3°50 4:05 3°775
100°0

Roughly, when a formula is calculated from the above
analysis, substituting (HO), for PbO,, we have very nearly
Ort. .O;,

In concluding my paper, I must say that I do not
satisfy myself at all with the analysis, inasmuch as the
two different salts do not agree. But I thought it might
be interesting to some of you from the fact that, as far
as I am aware of, this is the first analysis of the kind

attempted.

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THE COUNCIL

OF THE

MANCHESTER
LITERARY AND PHILOSOPHICAL SOCIETY.

Aprit 19, 1882.

President.
HENRY ENFIELD ROSCOE, B.A., LL.D., Pu.D., ERS. B.C.S.

CWice-Brestvents.
JAMES PRESCOTT JOULE, D.C.L., LL.D., F.RBS., F.CS.,
Hon. Mem. O.P.S., ere.
EDWARD SCHUNCK, Pu.D., E.R.S., F.C:S.
ROBERT ANGUS SMITH, Pu.D., F-.R.S., F.C.S.
Rev. WILLIAM GASKELL, M.A.

Secretaries.

JOSEPH BAXENDELL, F.R.A.S., Corr. Mem. Roy. Puys.-Hcon.
Soc. Kontespere, anp Acap. Sc. Lit. PALERMO.
OSBORNE REYNOLDS, M.A., F.R.S., Proressor or ENGINEERING,
Owens CoLuEaeE.

. Creasurer.
CHARLES BAILEY, F.LS.

Librarian.
FRANOIS NICHOLSON, F.Z:S.

Other MHMembers of the Council.

ROBERT DUKINFIELD DARBISHIRE, B.A.,, F.G.8.
BALFOUR STEWART, LL.D., F.R.S.
CARL SCHORLEMMER, F.R:S.
JAMES BOTTOMLEY, D.Sc., F.C.S.
WILLIAM HENRY JOHNSON, B.Sc.
HENRY WILDE.

HONORARY MEMBERS.

DATE OF ELECTION.

1847, Apr.20. Adams, John Couch, F.R.S., F.R.A.S., F.C.P.S.,

1843, Apr.

* 1860, Apr.

1859, Jan.

1866, Oct.

1868, Apr.

1844, Apr.
1869, Mar.
1843, Feb.

1853, Apr.
1848, Jan.

ish

ive

25.

30.

28.

30.

9.

7.

19.
25.

Lowndsean Prof. of Astron. and Geom. in the Univ.
of Cambridge. The Observatory, Cambridge.

Airy, Sir George Biddell, K.C.B., M.A., D.C.L., F.R.S.,
Astronomer Royal, V.P.R.A.S., Hon. Mem. R.S.E.,
R.LA., M.C:P.S., &c. The Royal Observatory, Green-
wich, London, SL.

Bunsen, Robert Wilhelm, Ph.D., For. Mem. R.S.,
Prof. of Chemistry at the Univ. of Heidelberg.
Heidelberg.

Cayley, Arthur, M.A., F.R.S., F.R.A.S. Garden
House, Cambridge.

Clifton, Robert Bellamy, M.A., F.R.S., F.R.A.S.,
Professor of Natural Philosophy, Oxford. New
Museum, Oxford.

Darwin, Charles) M.A., F.RBS., FE.G.S., F.L.S.
Bromley, Kent.

Dumas, Jean Baptiste, Gr. Off. Legion of Honour,
For. Mem. R.S., Mem. Imper. Instit. France, &e.
42 Rue Grenelle, St. Germain, Paris.

Frankland, Edward, Ph.D., F.R.S., Prof. of Chemistry
in the Royal Schcol of Mines, Mem. Inst. Imp.
(Acad, Sci.) Par.,&c. The Yews, Reigate Hill, Ret-
gate.

‘Frisiani, nobile Paolo, Prof., late Astron. at the Ob-

_ serv. of Brera, Milan, Mem. Imper. Roy. Instit. of
Lombardy, Milan, and Ital. Soc. Se. Milan,

Hartnup, John, F.R.A.S. Observatory, Liverpool.
Hind, John Russell, F.R.S., F.R.A.S., Superintendent
of the Nautical Almanack.

3

DATE OF ELECTION.

1866, Jan. 23.

1869, Jan. 12.

1872, Apr. 80.

1852, Oct. 16.

1844, Apr. 30.

1851, Apr. 29.

1866, Jan, 23.
1866, Jan. 23.

1849, Jan. 23.

1844, Apr. 30.

1872, Apr. 30.
1869, Dec. 14.

1851, Apr. 29.

1861, Jan. 22.

Hofmann, A. W., LL.D., Ph.D., F.R.S., F.C.S., Ord.
Leg. Hon, S™ Lazar. et Maurit. Ital. Eq., &c.
10 Dorotheenstrasse, Berlin.

Huggins, William, F.R.S., F.R.A.S.
Hill, Brixton, London, S.W.

Huxley, Thomas Henry, LL.D. (Edin.), Ph.D., F.B.S.,
Professor of Natural History in the Royal School
of Mines, South Kensington Museum, F.G.S:, F.Z.8.,
F.L.S., &e. School of Mines, South Kensington
Museum, S.W., and 4 Marlborough-place, Abbey-
road, N.W.

Upper Tulse

Kirkman, Rey. Thomas Penyngton, M.A., F.R.S.
Croft Rectory, near Warrington.

Owen, Richard, M.D., LL.D., F.R.S., F.L.S., F.G.8.,
V.P.Z.S., Director of the Nat. Hist. Department,
British Museum, Hon. F.R.C.S. Ireland, Hon.
M.R.S.E., For. Assoc. Imper. Instit. France, &c.
British Museum, London, W.C.

Playfair, Rt. Hon. Lyon, C.B., Ph.D., F.R.S., F.G.S.,
M.P., F.C.S., &e. 68 Onslow-gardens, London, S.W.

Prestwich, Joseph, F.R.S., F.G.S. Shoreham, near
Sevenoaks,

Ramsay, Sir Andrew Crombie, F.R.S., F.G.S,, Director
of the Geological Survey of Great Britain, Professor
of Geology, Royal School of Mines, &e. Geological
Survey Office, Jermyn-street, London, S.W,

Rawson, Robert. Havant, Hants.

Sabine, General Sir Edward, R.A., D.C.L., F.R.S.,
F.R.A.S., Hon. Mem. C.P.8., Chev. of the Prussian
Order “ Pour le Mérite.” 13 <Ashley-place, West-
minster, London, S.W.

Sachs, Julius, Ph.D. Prague.

Sorby, Henry Clifton, F.R.S., F.G.S., &e. Broomfield,
Sheffield.

Stokes, George Gabriel, M.A., D.C.L., Sec. R.S., Lu-
casian Professor of Mathem. Univ. Cambridge,
F.C.P.S., &e. Lensfield Cottage, Cambridge.

Sylvester, James Joseph, M.A., F.R.S., Professor of
Mathematics. Johns Hopkins University, Baltimore.

A

DATE OF ELECTION.

1868, Apr. 28. Tait, Peter Guthrie, M.A., F.R.S.E., &c. Professor of
Natural Philosophy, Edinburgh.

1851, Apr. 22. Thomson, Sir William, M.A., D.C.L., LL.D., F.B.SS.
L. and E., For. Assoc. Imper. Instit. France, Prof.
of Nat. Philos. Univ. Glasgow. 2 College, Glasgow.

1872, Apr. 30. Trécul, A., Member of the Institute of France. Paris.

1868, Apr. 28. Tyndall, John, LL.D., F.R.S., F.C.S., Professor of
Natural Philosophy in the Royal Institution and
Royal School of Mines. Royal Institution, London,
W.

CORRESPONDING MEMBERS.

1860, Apr. 17. Ainsworth, Thomas. Cleator Mills, near Egremont,
Whitehaven.

1861, Jan. 22. Buckland, George, Professor, University College,
Toronto. Toronto,

1867, Feb.
1870, Mar.

ox

Cialdi, Alessandro, Commander, &c. Rome.
Cockle, The Hon. Sir James, M.A., F.R.S., F.R.A.S.,
F.C.P.S. Sandringham-gardens, Ealing.

od

1866, Jan. 23, De Caligny, Anatole, Marquis, Corresp. Mem. Acadd.
Sc. Turin and Caen, Soce. Agr. Lyons, Sci. Cher-
bourg, Liége, &c.
1861, Apr. 2. Durand-Fardel, Max, M.D., Chev. of the Legion of
Honour, &c. 386 Rue de Lille, Paris.

1849, Apr.17. Girardin, J., Off. Legion of Honour, Corr. Mem. Im-
per. Instit. France, &c. Lille.

1850, Apr. 30. Harley, Rev. Robert, F.R.S.,F.R.A.S. College Place,
Huddersfield.

1862, Jan. 7. Lancia di Brolo, Federico, Duc., Inspector of Studies,
&e. Palermo.

1859, Jan. 25. Le Jolis, Auguste-Francois, Ph.D., Archiviste per-
pétuel and late President of the Imper. Soc. Nat.
Sc. Cherbourg, &c. Cherbourg.

5

DATE OF ELECTION.

1857, Jan. 27.
1862, Jan. 7.

1869, Jan. 12.

1867, Feb. 5.

1834, Jan, 24.

1881, Jan. 11.
1861, Jan. 22.

1873, Jan. 7.
1870, Dec. 13.
1861, Jan. 22.

1882, Jan. 24.
1837, Aug. 11.
1881, Noy. 1.
1874, Nov. 3.

1865, Nov. 15.
1824, Jan. 23.
1876, Noy. 28.
1867, Noy. 12.

1858, Jan. 26.

Lowe, Edward Joseph, F.R.S., F.R.AS., F.GS.,
Mem. Brit. Met. Soc.,&ce. Nottingham.

Nasmyth, James, C.E., F.R.A.S., &c. Penshurst, Tun-
bridge.

Saint Venant, Barré de, Ingénieur en chef des Ponts
et Chaussées, Corr. Soc. Sci. de Lille et de l’Acad.
Romaine des Nuovi Lincei, &e.

Schonfeld, Edward, Ph.D., Director of the Mannheim
Observatory.

Watson, Henry Hough. Bolton, Lancashire.

ORDINARY MEMBERS.

Adamson, Daniel, F.G.S. The Towers, Didsbury.

Alcock, Thomas, M.D., Extr. L.R.C.P. Lond.,
M.R.C.S. Engl, L.S.A. Oakfield, Ashton-on-
Mersey.

Allman, Julius. 2 Victoria-street.

Angell, John. Manchester Grammar School.

Anson, Ven. Archd. George Henry Greville, M.A.
Birch Rectory, Rusholme.

Arnold, William Thomas, M.A. Plymouth Grove.

Ashton, Thomas. 36 Charlotte-street.

Ashton, Thomas Gair, B.A. 36 Charlotte-street.

Axon, William E. A., M.R.S.L., F.S.I. Fern Bank,
1 Bowker-street, Higher Broughton. :

Bailey, Charles, F.L.S. Ashjield, College-road, Whalley
Range.

Barbour, Robert. 18 Aytoun-street.

Barratt, Walter Edward. Kersal, Higher Broughton.

Barrow, John. 38 Edensor-place, Dickinson-road,
Rusholme.

Baxendell, Joseph, F.R.A.S., Corr. Mem. Roy. Phys.
Econ. Soc. Kénigsberg, and Acad. Se. & Lit.
Palermo. 14 Liverpool-road, Birkdale, Southport.

6

DATE OF ELECTION.

1847, Jan. 26. Bazley, Sir Thomas, Bart. Stow-on-the- Wold, Glou-

1877, Nov.

1878, Nov.

1847, Jan.

1870, Nov.

1868, Dee.
1876, Apr.

1861, Jan.

1839, Oct.

1875, Nov.

1855, Apr.

1861, Apr.

1844, Jan.

1860, Jan.
1846, Jan.

1872, Nov.

1874, Dec.

1842, Jan.

1854, Apr.

1841, Apr.

1858, Jan.
1859, Jan.

1861, Nov.

1848, Jan.

1876, Apr.
1861, Apr.

1854, Feb.

1871, Nov.

27.
26.
26.
15.

15.
18.

22.

. Coward, Thomas.

cestershire.

Becker, Wilfred, B.A.
Cross-street.

Bedson, Peter Philips, D.Se.

Bell, William. 51 King-street.

Boonen John A.,B.A., F.R.A.S. Barr Hill Mount,
Bolton-road, eepieton.

Bickham, Spencer H.,jun. Endsleigh, Alderley Edge.

Birley, Thomas Hornby. Somerville, Pendleton, near
Manchester.

Bottomley, James, D.Se, B.A., F.C.S. 7 Irwell-
terrace, Lower Broughton.

Bowman, Henry. Brooklands,
Reigate, London.

4 Commercial Buildings,

Owens College.

Brockham Green,

Boyd, John. 58 Parsonage-road, Withington.
Brockbank, William, F.G.S. Prince’s Chambers,
26 Pall Mail.

Brogden, Henry, F.G.S. Hale Lodge, Altrincham.

Brooks, William Cunliffe, M.A., M.P. Bank, 92
King-street.

Brothers, Alfred, F.R.A.S. 14 St.-Ann’s-square.

Browne, Henry, M.D., M.A., M.R.C.S. Engl. Wood-
hey, Heaton Mersey.

Burghardt, Charles Anthony, Ph.D. 110 King-street.

Carrick, Joseph. Prince’s Chambers, 26 Pall Mail.

Charlewood, Henry. 1 S¢. James’s-square.

Christie, Richard Copley, M.A., Prof. Hist. Owens
College. 2 St. James’s-square.

Clay, Charles, M.D., Extr. L.R.C.P. London, L.R.C.S.
Edin. 101 Piccadilly.

Cottam, Samuel, F.R.A.S. 6 Essex-street.

Coward, Edward. Heaton Mersey, near Manchester.

Bowdon.

Crowther, Joseph Stretch. Endslergh, Alderley Edge.

Cunliffe, Robert Ellis. 18 Vine-grove, Pendleton.

Cunningham, William Alexander. -Auchenheath Cot-
tage, Lesmahagow, by Lanark.

Dale, John, F.C.S. Cornbrook Chemical Works,
Chester-road.

Dale, Richard Samuel, B.A. Cornbrook Chemical
Works, Chester-road. F

‘i

DATE OF ELECTION.

1842, Apr. 19.
1853, Apr. 19.

1878, Nov. 26.
1869, Noy. 2.

1861, Dec. 10.
1879, Mar. 18.

1840, Jan. 21.

1881, Noy.

iz
1874, Noy. 3.
9

1875, Feb.

1878, Apr. 30.
1862, Nov. 4.
1839, Jan. 22.
1873, Dec. 16.
1828, Oct. 31.
1868, Nov. 17.
1838, Apr. 26,

1864, Mar. 22.

1881, Noy. 1.

1851, Apr. 29.
1846, Jan. 27.

1873, Dec. 2.
1857, Jan. 27.
1855, Jan. 25.

1872, Feb. 6.
1870, Nov. 1.
1878, Noy. 26.
1848, Apr. 18.

Dancer, John Benjamin, F.R.A.S. 41 Cross-street.

Darbishire, Robert Dukinfield, B.A., F.G.S. 26
George-street.

Davis, Joseph. Lngineer’s Office, Lancashire and
Yorkshire Railway, Hunt’s Bank.

Dawkins, William Boyd, M.A., F.R.S. Museum,
Owens College.

Deane, William King. 25 George-street.

Dent, Hastings Charles. City Surveyor’s Offices,
Town Hail.

Gaskell, Rey. William, M.A. 46 Plymouth Grove.

Greg, Arthur. Zagley, near Bolton.

Grimshaw, Harry, F.C.S. Thornton View, Clayton.

Gwyther, R. F., M.A., Lecturer on Mathematics,
‘Owens College. Owens College.

Harland, William Dugdale, F.C.S, 25 Acomb-street,
Greenheys. ;

Hart, Peter. 192 London-road.

Hawkshaw, Sir John, F.R.S., F.G.S., Mem. Inst.
C.E. 33 Great George-street, Westminster, London,
S.W.

Heelis, James. 71 Princess-street.

Henry, William Charles, M.D., F.R.S.
street, Lower Mosley-street.

Herford, Rey. Brooke. Arlington-street Church, Bos-
ton, U.S.

Heywood, James, F.R.S., F.G.S., F.S.A. 26 Ken-
sington-Palace- Gardens, London, W.

Heywood, Oliver. Bank, St. Ann’s-street.

Higgin, Alfred James. 22 Little Peter-street, Gay-
thorn.

Higgin, James, Little Peter-street, Gaythorn.

Holden, James Platt. 56 Johnson-street, Smedley
Lane, Cheetham Hill.

Howorth, Henry H., F.S.A. Derby House, Eccles.

Hunt, Edward, B.A., F.C.S. 42 Quay-street, Salford.

Hurst, Henry Alexander. The Albany, Liverpool.

1l ast-

Jewsbury, Sidney. 39 Princess-street.

Johnson, William H., B.Sc. 26 Lever-street.

Jones, Francis, F.R.S.E., F.C.S.. Grammar School.

Joule, Benjamin St. John Baptist. 12 Wardle-road,
Sale,

8

DATE OF ELECTION. 7

1842, Jan, 25.

1852, Jan,

1863, Dec.
1857, Jan.

1870, Apr.
1850, Apr. 30.

1859, Jan.

1866, Noy. 13.
1859, Jan.
1875, Jan.

1879, Dec. 2.

1873, Nov. 4.

1864, Noy. 1.

1873, Mar. 18.

1879, Dec. 30.

1881, Oct. 18.
1877, Nov. 27.

1861, Oct. 29. .

1850, Jan. 24,
1873, Mar. 4.

1862, Dec. 30.

1861, Jan. 22.

1844, Apr. 30.

27,
1862, Apr. 29.

15.
1850, Apr. 30.
ON fs

19.

25.

25.
26.

Joule, James Prescott, D.C.L., LL.D., F.R.S., F.C.S.,
Hon. Mem. C.P.S., and Inst. Eng. Scot., Corr. Mem.
Inst. Fr. (Acad. Se.) Paris, and Roy. Acad. Se.
Turin. 12 Wardle-road, Sale.

Kennedy, John Lawson. 47 Mosley-street.
Knowles, Andrew. High Bank, Pendlebury.

Leake, Robert, M.P. 75 Princess-street.

Leese, Joseph. Fallowfield.

Longridge, Robert Bentink. Yew-Tree House, Tabley,
Knutsford.

Lowe, Charles. 43 Piccadilly.

Lund, Edward, F.R.C.S. Eng., L.S.A.
street. :
Lynde, James Gascoigne, M. Inst. C.E., F.GS.

32 St. Ann’s-street.

22 St. John’s-

McDougall, Arthur. City Flour Mills, Poland-street.

Maclure, John William, F.R.G.S. Cross-street.

Mann, John Dixon, Licentiate of the King and Queen’s
College of Physicians, Ireland; and M.R.C.S. Eng.
16 St. John-street.

Marshall, Alfred Milnes, M.A., D.Sc., Professor of
Zoology, Owens College. Owens College.

Marshall, Rev. William, B.A. 81 High-street, Chorl-
ton-on-Medlock,

Mather, William. Iron Works, Deal-street, Brown-
street, Salford.

Melvill, James Cosmo, M.A., F.L.S. Kersal Cottage,
Prestwich. .

Millar, John Bell, B.E., Assistant Lecturer in Engi-
neering, Owens College. Owens College.

Mond, Ludwig. Wéinnington Hall, Northwich.

Moore, Samuel. 25 Dover-street, Chorlton-on-Medlock.

Morgan, John Edward, M.B., M.A., M.R.C.P. Lond.,
F.R. Med. and Chir. S. 1 S¢. Peter’s-square.

Newall, Henry. Hare Hill, Littleborough.
Nicholson, Francis, F.Z.S. 62 Fountain-street.

Ogden, Samuel. 10 Mosley-street West.

O’Neill, Charles, F.C.S., Corr. Mem, Ind. Soc, Mul-
house. 72 Denmark-road,

Ormerod, Henry Mere. 5 Clarence-street.

9

DATE OF ELECTION.

1861, Apr.

1876, Noy

1881, Nov.

1874, Jan.

1854, Jan.

1861, Jan.

1854, Feb.
1859, Apr.

1869, Noy.

1880, Mar.

1860, Jan.
1864, Dec.

1822, Jan.
1868, Jan.

1851, Apr.
1870, Dec.

1842, Jan.

1873, Nov

30.
. 28.
29.
15.

24,

1881, Nov. 29.

1852, Apr.

1838, Jan.

1876, Nov.
1844, Apr.

1859, Jan.

1851, Apr.

1870, Nov.

1863, Oct.

6.

Parlane, James. Rusholme.

Parry, Thomas. Grafton-place, Ashton-under-Lyne.

Peacock, Richard. Gorton Hall, Manchester.

Pennington, Rooke, LL.B., F.G.S. Mavwdsley-street,
Bolton.

Pochin, Henry Davis.
SW.

Barn Elms, Barnes, Surrey,

Radford, William. 1 Princess-street.

Ramsbottom, John. Fern Hill, Alderley Edge.

Ransome, Arthur, M.A., M.D. Cantab., M.R.C.S.
1 St. Peter’s-square.

Reynolds, Osborne, M.A., F.R.S., Professor of En-
gineering, Owens College. Owens College.

Roberts, Lloyd, M.D. Kersal Towers, Higher Broughton.

Roberts, William, M.D., B.A., F.R.S., M.R.C.P. Lond.
89 Mosley-street.

Robinson, John.
street.

Robinson, Samuel. Blackbrook Cottage, Wilmslow.

Roscoe, Henry Enfield, B.A., LL.D. F.R.S., F.C.S.,
Professor of Chemistry, Owens College. Owens
College.

Atlas Works, Great Bridgewater-

Sandeman, Archibald, M.A. Tulloch, near Perth.

Schorlemmer, Carl, F.R.S., F.C.S. Owens College.

Schunck, Edward, Ph.D., F.R.S., F.C.S. Oaklands,
Kersal.

Schuster, Arthur, Ph.D., F.R.S. Owens College.

Schwabe, Edmund Salis, B.A. 41 George-street.

Sidebotham, Joseph, F.R.A.S. The Beeches, Bowdon.

Smith, George Samuel Fereday, M.A., F.G.S. Grove

_ House, Tunbridge Wells.

Smith, James. 35 Cleveland-road, Crumpsall.

Smith, Robert Angus, Ph.D., LL.D., F.RS., F.C.8.,
Corr. Mem. Royal Bavarian Soc. 22 Devonshire-
street, All Saints.

Sowler, Thomas. 24 Cannon-street.

Spence, Peter, F.C.S., M.S.A. Alum Works, Newton
Heath,

Stewart, Balfour, LL.D., F.R.S., Professor of Natural
Philosophy, Owens College. Owens College.

Stretton, Bartholomew JBridyewater-place, High-
street,

10

DATE OF ELECTION.

1873, Apr. 15, Thomson, William, F.R.S.E., F.C.S. Royal Institu-
tion.
1860, Apr. 17. Trapp, Samuel Clement. 88 Mosley-street.

1879, Dec. 30. Ward, Thomas. Brookfield House, Northwich.

1878, Nov.18. Waters, Arthur William, F.G.S. Woodbrook, Alderley
Edge.

1874, Dec. 15. Watson, Morrison, M.D., Professor of Descriptive
Anatomy, Owens College. Linda Villa, Heald-
road, Bowdon.

1874, Jan. 27. Watts, John, Ph.D. 23 Strutt-street.

1857, Jan. 27. Webb, Thomas George. Glass Works, Kirby-street,
Ancoats.

1858, Jan. 26. Whitehead, James, M.D., M.R.C.P. Lond., F.R.C.S.
Engl., L.S.A., M.R.LA., Corr. Mem. Soe, Nat. Phil.
Dresden, Med. Chir. Soc. Zurich, and Obst. Soc.
Edin., Mem. Obst. Soc. Lond. 87 Mosley-street.

1839, Jan. 22. Whitworth, Sir Joseph, Bart., F.R.S. Chorlton-street,
Portland-street.

1859, Jan. 25. Wilde, Henry. Mill-street, Ancoats.

1859, Apr. 19. Wilkinson, Thomas Read. Manchester and Salford
Bank, Mosley-street.

1874, Nov. 3. sy Tienes) William Carleton, F.C.S. Oils College.

1851, Apr. 29. Williamson, William Crawford, F.R.S., Professor of
Nat. Hist., Anat., and Pig dal, Owens College,
M.R.C.S. Engl., L.S.A. Egerton-road, Fallowfield.

1836, Jan. 22. Wood, William Rayner. Singleton Lodge, near
Manchester.

1860, Apr. 17. Woolley, George Stephen. 69 Market-street.

1863, Nov.17, Worthington, Samuel Barton, C.H. 12 York-place,
Oxford-street.

1865, Feb. 21. Worthington, Thomas. 110 King-street.

1864, Nov. 1. Wright, William Cort, F.C.S, Oakfield, Poynton,
Cheshire.

N.B.—Of the above list the following have compounded for their
subscriptions, and are therefore Life Members:—

Brogden, Henry.

Johnson, William H., B.Sc.

Sandeman, Archibald, M.A.

Smith, Robert Angus, Ph.D., LL.D.,F.R.S..

Printed by TAYLOR and Francis, Red Lion Court, Fleet Street.
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