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OF THE

LITERARY AND PHILOSOPHICAL SOCIETY

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s

MANCHESTER.

VOL. II.

Sessions 1860—61 and 1861—62.

MANCHESTEE :

PEI^ED BY THOS. SOWLER AKD SONS, ST. ANN'S SQUARE.
I^LONDON: H. BAILLI^JEE, 219, EEGENT STREET.
1862.

NOTE.

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

PROCEEDINGS

OP

THE LITERARY AND PHILOSOPHICAL
SOCIETY.

Ordinary Meeting, October 2nd, 1860.
Dr. Joule, President, in the Chair.
The President brought under the notice of the meeting a
sheet of copper, upon which, whilst under magnetic influence,
iron had been deposited electrolytically. The experiment was
made by Mr. F. H. Hobler, of London, as follows : — The
plate of copper, forming the bottom of a shallow vessel filled
with a saturated solution of sulphate of iron, was placed on
the poles of a powerful horse-shoe magnet, fixed vertically
with its poles uppermost. An iron wire, dipping into the
solution, was placed in connection with the positive electrode
of a Daniell's cell, of one pint capacity, the copper plate
being connected with the negative electrode. The deposited
iron exhibited the lines of magnetic force in the same manner
as in the case of iron filings scattered on a sheet of paper
placed over a magnet. When Mr. Hobler substituted a plate
of tinned iron for the copper, he observed indications, though
very faint ones, of the same phenomenon. On using a satu-
rated solution of sulphate of copper, Mr. Hobler observed
that the deposit was even throughout, and that no specific
position of the axes of the crystals of copper could be detected,
although they invariably formed on the outside of the two
poles. Mr. Hobler, in discussing the phenomenon, inquires
whether it is produced by the action of the magnet upon the
solution in direction of the lines of force, or whether the iron
is formed in the solution immediately above the copper plate,
and then attracted by the magnet into the direction of the
lines of force. The former suggestion appears to him to be
inconsistent with our present knowledge of the influence of
Proceedings— Lit. & Phil. Society— No. 1.— Session, 1860-61.

magnetism on chemical action ; the latter, with the theory of
electro-deposition, which supposes the coating to be formed
on the plate and not deposited, strictly speaking, thereon.

The President exhibited a slip of paper which he had received
from Professor Thomson. On the paper was printed by
photography the line indicating the various changes of atmo-
spheric electricity, which took place at the observatory of Kew
during twelve successive hours. Much interest was excited
by witnessing one of the first fruits of Professor Thomson's
beautiful instrument. The paper indicated a series of very
rapid oscillations, about one per minute, of the intensity of
atmospheric electrical force.

Mr. Henry Bowman presented the following statement
of observations on the temperature of the six summer months
ending September 30th, 1860, taken by a self-registering
thermometer at Victoria Park, Manchester : —

5

o

o

Mi

5

9

2

^1

= 1

tLi

? S aj

"' r- O

S

g

';Si

Z^

S
'3

a

3

i

§1

O V

O V

0 2 >oo

a>

S

S

c^

s

S

%

S

^

I860.

0

o

o

o

o

o

0

April

61-4

27-7

36-7

43-6

47-1

3-5

G

May

77-2

31-3

45-9

51.0

53-2

0-8

29

June

72-1

39-6

32-8

55-8

58-2

2-4

10

July

78-0

40-2

37-8

58-5

GO- 8

2.3

12

August

71-2

42-0

2[f"2

560

GO-4

4.4

1(2)

September

G6-2

31-5

3i-7

51-9

56-3

4-4

2(3)

The 6 months ]
together . . . j

78-0

27-7

50-3

53-3

56-0

2-7

12monthsend."^

ing Sept. 30, [

78-0

9-5

G8-5

46-4

48-8

t?..i,

4 (*)

1860 )

The maximum temperature in the 12 months was 78° on
July 9th.

The minimum temperature in the 12 months was 9°-5 on
December 19th.

Q) From Tables by Dr. Dalton, Society's Memoirs, Vol.
III. (new series), p. 494, and Vol VI., p. 572.

(2) The mean of August, 1799, was 55°'0.

f ) The mean of September, 1803, was 51°-7 ; 1807, 50°.l.

(^) The mean of the year 1795 was 46°-4 ; of 1799, 44°-6 ;
of 1814, 45°-4 ; and of 1815, 46°-2.

Mr. Atkinson stated that during the months of June and
August, he had observer the extraordinary rain-fall of 13
inches at Thelwell. The fall in July was not considerable.

Mr. Dyer having stated that on the morning of August
Uth, a very loud explosion was heard in the neighbourhood
of Blackfriars, London, the sky being clear at the time,
a conversation took place on the subject of fire-balls and
meteorites, in the course of which Mr. Ekman stated that
during a most violent thunderstorm, passing over a tract of
land intersected by a rapid stream, he had distinctly seen fire-
balls, the diameter of which he estimated at 2ft., projected
from the clouds down into the water. The distance of the
point where he stood, from the point at which the balls struck
the water, could not have been more than 150 to 200 yards.
The phenomenon was witnessed in Sweden many years ago.

Mr. Wild exhibited the universal or alphabet telegraph of
Professor Wheatstone, and pointed out the successive improve-
ments which had resulted in this admirable invention.

A Paper, by Arthur Cay ley, F.R.S., &c., Hon. Mem.,
was read by the Rev. T. P. Kirkman, entitled, " On the
^ faced Polyacrons, in reference to the Problem of the Enu-
meration of Polyhedra."

4

" The problem of the enumeration of the polyhedra is one
of extreme difficulty, and I am not aware that it has been dis-
cussed elsewhere than in Mr. Kirkman's valuable series of
papers on this subject in the Memoirs of this Society, and in
the Philosophical Transactions. A case of the general problem
is that of the enumeration of the polyhedra with trihedral
summits ; and Mr. Kirkman, in the earliest of his papers, viz.,
that ' On the Representation and Enumeration of Polyhedra'
(Mem. Vol. XII., pp. 47, 70, 1855), has in fact, by an
examination of the particular case, accomplished the enumera-
tion of the octahedra with trihedral summits.

" It is intended, in the present paper, to give a method for
the derivation of the triangular-faced polyacrons of a given
number of summits from those of the next inferior number of
summits, and to exemplify it by finding, in an orderly manner,
the triangular-faced polyacrons up to the octacrons ; thus, as
regards the examples, stopping at the same point as Mr.
Kirkman ; for although perfectly practicable, it would be very
tedious, and there would be no commensurate advantage to
carry them further."

At this, the first Meeting of the Session, a large number
of books, chiefly Transactions of learned Societies abroad,
were laid on the table. The Chairman congratulated the
Society on the rapid increase of its Library, which was mainly
owing to the great ability and zeal of Mr. Ekman, the
Honorary Librarian.

Quarterly Meeting, October 16th, 1860.

Dr. R. Angus Smith, Vice-President, in the Chair.

The Chairman gave a short account of his examination
of coal pyrites for arsenic. He stated that although the
knowledge of the existence of arsenic in the iron pyrites
found in coal may not be considered perfectly novel, it cer-
tainly does not seem to be known that arsenic is so widely
disseminated as to form an ordinary constituent of the coals
burnt in our towns, and chemists of celebrity have held it —
and now hold it — to be absent there. He had examined
fifteen specimens of coals in Lancashire, and found arsenic in
thirteen. He had also found it in a few^ others; but Mr. Binney
having promised a collection, properly arranged, the examina-
tion will then be made more complete. Mr. Dagald Campbell
had also lately found arsenic in coal pyrites. The Chairman
added, that this had a very direct bearing on our sanitary
knowdedge, as we must now be obliged to add arsenic to the
number of impurities in the atmosphere of our large towns.
It is true that he had not actually obtained it from the
atmosphere, but when the pyrites is burnt the arsenic burns
and is carried off along with the sulphur. One or two coal
brasses (as they are called) contained copper, a metal that is
also to some extent volatilized, as may be readily observed
wherever copper soldering takes place. Although an
extremely small amount of copper is carried up from furnaces,
it is not well entirely to ignore it. The amount of arsenic,
however, is probably not without considerable influence, and
we may probably learn the reason why some towns seem less
affected than others by the burning of coals, by examining
the amount of arsenic burnt as well as sulphur.

PiiocBEDiNGS— Lit. & Phil. Society— No. 2.— Session, 1860-61.

6

Mr. Spence said that he could confirm the remarks con-
cerning the existence of arsenic in coals, as he had burnt coal
pyrites for many years, and had always found a very decided
amount of arsenic in the sulphuric acid made from it.

Mr. Ransome called attention to the peculiar symptoms
described by Berzelius, as produced by selenium ; and he con-
sidered that some similar symptoms were produced in a
manner which might be explained if selenium were found in
coals.

A Paper was read by William Roberts, M.D., entitled,
" On the Estimation of Sugar in Diabetic Urine by the Loss
of Density after Fermentation." When a diabetic urine is
fermented with yeast, its specific gravity previously ranging
from 1030 to 1050 falls to 1009 or 1002, or even below 1000.
This result is mostly due to the destruction of the sugar it
contained, but partly also to the generation of alcohol and its
presence in the fermented product.

As the diminution of- density must be proportional to the
quantity of sugar broken up by the ferment, the amount of
loss evidently supplies a means of calculating how much
sugar any urine contains — always provided that the remaining
ingredients of the urine continue unchanged, or become
changed in some uniform ratio.

To ascertain the relation between the density lost on fer-
mentation, and the sugar destroyed, experiments were made
on the urine of diabetic patients on the following plan : —

1. The amount of sugar per 100 parts was ascertained by
the volumetrical method, with Fehling's test solution.

2. The density of the urine was taken.

3. Three or four ounces were then placed in a 12oz. phial,
with a drachm or two of German yeast, and having lightly
covered the bottle it was set aside to ferment.

4. In about twenty-four hours the fermentation was finished

and the froth dissipated. The density was then taken a
second time, and the loss calculated.

Operating in this way on a specimen of diabetic urine
sp. gr. 1038*60, the following results were obtained ; —

Sugar, per 100 parts, by the volumetrical method, 7*69.

Density before fermentation at 60° or D = 1038*60.

Density after fermentation at 60° or D' = 1005*92.

Density lost, or D — D^ = 32*68.

The relation, therefore, between the density lost and the
percentage of sugar, in this instance, was as 32*68 to 7*69, or
as 1 to 0*235. By numerous trials with diabetic urines, of
diiferent strength, it was found that the most correct pro-
portion was as 1 to 0*230. The corresponding formula,
therefore, was : —

Sugar, per 100 parts, or S == (D — DO X 0*23.

The accuracy of this method was further tested by operating
on diabetic urine diluted with known volumes of water or
non-saccharine urine, and on solutions of loaf sugar in water
and in healthy urine.

This method of estimating sugar is especially applicable
to medical practice, and the following simple and most con-
venient rule expresses the result of the analysis: —

Each degree of ' density lost ' indicates one grain of
sugar per fluid ounce of urine.

PHYSICAL AND MATHEMATICAL SECTION.

October 11th, 1360.

Some conversation took place respecting recent storms,
and the bearing of the new weather tables, given in the
Tines, on their theory, as Mr. Baxendell remarked that

8

according to these observations the wind did not blow from
the areas of greater pressure.

Mr. Baxendell called attention to certain phenomena of
solar spots recently observed by him, and stated that in
cases in which projections of the penumbra into the nucleus
occurred, the penumbra is generally increased in breadth in
that part of its circumference, and it often happens that
striations observed in the penumbra are curved, and terminate
in the points of projection into the nucleus.

A Paper was read by Thomas Carrick, '•' On the Atomic
Constitution of Water and Ice."

After briefly alluding to the nature of his own views on
the ultimate atomic constitution of terrestrial matter, and its
relations to cosmical force, the Author — guided by considera-
tions derived therefrom — proceeded to discuss the question of
the^relative specific gravities of water and ice, and arrived at
a specific gravity for ice differing by only ^^-^th part, from
the most recent and correct results of experiments.

The prominent characteristics of water and ice were also
shown to be the natural result of the disposition and relations
of the ultimate atoms.

MICROSCOPICAL SECTION.

September l7th, 1860.

A specimen of envelopes was exhibited by the Secretary,
such as were proposed to be sent to captains of vessels, in
which to preserve soundings they obtain in different parts
of the world, for this Section. The envelopes were much
approved of, and were thought likely to be productive of
future interest to the Section, and to microscopists in general.

9

Mr. Latham referred to Mr. Hepworth's method of
mounting insects in Canada balsam, and described his own
experience of the same. Mr. Latham spoke in very favour-
able terms of the facility with which slides can be washed off
and finished. He found that the balsam should be as thick
as possible, almost even to dryness ; then dissolved in chloro-
form, to a consistence only thin enough to flow easily under
the thin glass; the object having previously been mounted
by Mr. Hepworth's process, under thin glass tied on with
thread, exhausted of air, and saturated with turpentine.
After heating over a spirit-lamp the balsam sets hard almost
as soon as cool, when the slide, after cleaning with alcohol, is
ready for the cabinet. Mr. Latham exhibited several slides
thus mounted, with specimens of the gizard of a cricket, saw
fly, entire system of the silk -worm trachea, ichneumon fly,
spiracle of the silk-worm, goldfish scale, leaf of wheat showing
spiral vessels.

Mr. Lynde exhibited a fine plumatella living on the shell
of a large lymnea or water-snail.

Mr. MosLEY exhibited specimens of hydra and other
aquatic objects.

October 15th, I860.

A Circular was read, addressed to captains of vessels, with
a request that they will preserve the produce of the soundings
they make when abroad, in the envelopes sent therewith —
A Letter was read from Mr. Hayman, of Liverpool, to the
effect that circulars and envelopes have been supplied to the
captains of eight steamers belonging to Messrs. John Bibby
and Sons, in the Mediterranean trade; three of Messrs.
Mac Iver's steamers, plying between Liverpool and New

10

York; to the steamer "Armenian;" for Madeira, Sierra
Leone, Calabar, &c. ; to the " Marco Polo," and two other
vessels to Melbourne ; as well as to vessels which have gone
to Woosung in China, Bombay, Alexandria, 8ic., &c.

The Chairman made some observations in praise of the
plan, which he had no doubt would be productive of advan-
tage and add to the interest of the meetings of the Section.

It was suggested by Mr. Brothers that a special subject,
previously fixed upon, should be discussed at each meeting :
the suggestion was at once adopted. The subject for discus-
sion at the next meeting will be, '* Upon the Best Method
of Preparing and Mounting Diatoms, &c., obtained from
Soundings and other Sources." It is requested that the
Members of the Section will meanwhile obtain and communi-
cate all the information they can on the subject

Mr. Lynde exhibited a specimen of a small insect allied to
the Podura, which he found leaping about on the surface of
the water in his aquarium. Mr. Lynde had never seen a
description of such an insect, nor was it known to any of the
Members of the Section present.

Mr. Brothers exhibited the hydra viridis, &c.

A few specimens and parts of flowers obtained at the
Botanical Gardens, were exhibited by the Secretary. In
the tank of the Victoria Regia, little minute animal life could
be discovered during a short visit. A specimen of Cetochilus
was shown which was found there, as also a few diatoms not
fully examined.

11

Ordinary Meeting, October 30th, 1860.
Dr. J. P. Joule, President, in the Chair.

A Paper was read by Dr. H. E. Roscoe, entitled, " On
the Alleged Practice of Arsenic Eating in Styria."

Professor Roscoe being anxious to obtain further definite
information respecting the extraordinary statements of Von
Tschudi, quoted by Johnston in his " Chemistry of Common
Life," that persons in Styria are in the habit of regularly
taking doses of arsenious acid, varying in quantity from 2
to 5 grains daily, was supplied through the kindness of his
friend Professor Pebal, of Lemberg, with a series of letters
written by seventeen medical men of Styria, to the government
medical inspector at Gratz, concerning the alleged practice.
After reviewing the opinions of Dr, Taylor, Mr. Kesteven,
and Mr. Heisch, upon the subject, and having mentioned the
results and conclusions arrived at by those who had pre-
viously interested themselves with the subject, Mr. Roscoe
stated that all the letters received from the medical men in
Styria agree in acknowledging the general prevalence of a
belief that certain persons are in the habit of continually
taking arsenic in quantities usually supposed sufficient to
produce death. Many of the reporting medical men had no
experience of the practice; others describe certain cases of
arsenic eating which have not come under their personal
notice, but which they have been told of by trustworthy
people whose names are given ; whilst others, again, report
Proceedings— Lit. & Phil. Society— No. 3.— Session, 1860-61.

12

upon cases which they themselves have observed. Professor
Roscoe proceeded to bring forward, in the first place, evidence
bearing upon the question, — Is or is not arsenious acid, or
arsenic in any other form, well known to, and distributed
amongst the people of Styria ? He said that he had received
6 grms. of a white substance forwarded by Professor Gottlieb,
in Gratz, accompanied by a certificate from the district judge
of Knittelfeld, in Styria, stating that this substance was
brought to him by a peasant woman who told him that she
had seen her farm-labourer eating it, and that she gave it up
to justice to put a stop to so evil a practice. An accu-
rate chemical analysis showed that the substance was pure
arsenious acid. Extracts from many of the reports of the
medical men were then read, all stating that arsenious acid,
called "Hidrach" by the Styrian peasants, is well known and
widely distributed in that country. The second question
to which Mr. Roscoe sought to obtain an answer was, whether
arsenic is or is not regularly taken by persons in Styria
in quantities usually supposed to produce immediate death ?
The most narrowly examined, and therefore the most interest-
ing case of arsenic eating is one recorded by Dr. Schiifer.
In presence of Dr. Knappe, of Oberzehring, a man thirty
years of age and in robust health, eat, on the 22nd February,
1860, a piece of arsenious acid weighing 4J grains ; and, on
the 23rd, another piece weighing 5^ grains. His urine was
carefully examined and shown to contain arsenic; on the
24th he went away in his usual health. He informed Dr,
Knappe that he was in the habit of taking the above quanti-
ties three or four times each week. A number of other cases,
witnessed by the medical men themselves, of persons eating

13

arsenic, were then detailed. Dr. Holler, of Hartberg, says
that he and other persons, named in his report, guarantee that
they are together acquainted with forty persons who eat
arsenic; and Dr. Forcher, of Gratz gives a list of eleven
people in his neighbourhood who indulge in the practice.
Professor Roscoe did not think it necessary to translate the
reports in extenso ; he gave extracts containing the portions
immediately bearing upon the two questions at issue, and
deposited authentic copies of the original reports with the
Society, for the purpose of reference. He concluded that
decisive evidence had, in his opinion, been brought forward,
not only to prove that arsenic is well known and widely
distributed in Styria, but that it is likewise regularly eaten,
for what purpose he did not at the moment investigate, in
quantities usually considered sufficient to produce immediate
death. |

In the course of the conversation, after the Paper was read,
Dr. Clay mentioned instances in which large quantities of
arsenic had been prescribed for various diseases, with benefit.
It was a valuable medicine, but if taken for other purposes it
would produce most pernicious effects. It was a practice in
some parts of the country to give it to horses to improve the
sleekness of their coats.

Mr. Ran SOME confirmed the observation of Dr. Clay, and
stated that he had long ago drawn the attention of the Society
to the fact that sulphuric acid manufactured from arsenical
pyrites contained arsenic, and that this acid being employed
in the manufacture of various articles used as medicine, and
even as food, these likewise contained the poisonous ingre-
dient. He had found it even in flowers of sulphur.

14

Mr. PocHiN and Mr. Hunt remarked that the effects of
breathing the vapour of arsenious acid produced in the
smelting of ores were not so injurious as might be expected ;
occasionally, however, the workmen had to be taken off
the particular work for a short time, until the poisonous
effect which manifested itself by eruptions on the face had
disappeared.

15

Ordinary Meeting, November 13th, 1860.

Dr. Fairbairn, F.R.S., &c., Vice-President, in the Chair.

The Chairman made some obvervations respecting experi-
ments conducted in the Dukinfield Coal Pit, for the purpose
of determining the rate of increase of temperature below the
earth's surface. He stated that from these experiments a
mean increase of one degree Fahrenheit for every seventy-one
feet had been arrived at ; and he promised on a future occasion
to communicate the details of the determinations.

A Paper was read by Mr. Baxendell, F.R.A.S., entitled,
"On a System of Periodic Disturbances Atmospheric

Pressure in Europe and Northern Asia."

Whilst engaged some time ago in an investigation of the
phenomena of the general disturbances of the atmosphere, the
Author had been led to conclude that moderately accurate
determinations of the sums of the oscillations of the barometer,
for given periods, at different places on the surface of the
earth, would afford valuable information respecting the nature
of these disturbances, and, at the same time, throw additional
light upon the causes by which they are produced. Determi-
nations of the statical element of mean pressure are obviously
of very limited use in an inquiry of this kind ; but notwith-
standing the importance of the subject, meteorologists have
hitherto generally neglected to ascertain, even approximately,
the values of the dynamical element as represented by the
sums of the oscillations of the mercurial column. In none of
the many volumes of observations which issue from the public
observatories of this country and the continent has the Author
yet seen any attempt made to deduce the values of this
element.

PiiocEEDTNGS— Lit. & Phil. Society— No. 4.— Session, 1860-61.

16

Accurate absolute values of the barometric dynamical ele-
ment can, of course, be obtained for those places only where
hourly observations are made ; but as it appeared to the
Author that good comparative values would be quite sufficient
for the general purposes of his inquiry, he decided to confine
his attention, in the first instance, to oscillations derived from
observations made once a day only. By this plan the regular
diurnal oscillations are completely eliminated ; the results are
adapted for very fair comparison with each other; and a
greater number of sets of observations become available for
the purposes of the inquiry. This method has accordingly
been employed in the discussion of a very considerable number
of observations made at various places in Europe and Asia,
and a table is given showing tlie mean monthly and annual
sums of the oscillations of the barometer at seven stations in
Europe and six in Asia as derived from observations extending
over periods varying from six to fifteen years. It is, however,
remarked, with reference to the results given for Greenwich,
that as the individual observations of each day at Greenwich
are not given in the published volumes, these results are derived
from the daily means, and not from single daily observations,
as in all the other cases. Diagrams of the curves laid down
from the numbers in this table accompany the Paper. All
these curves show a principal minimum in one of the three
summer months, June, July, or August; and in many of them
there is a second minimum in one of the two winter months,
January or February. With respect to the two maxima
which occur between these minima, it is shown that the inter-
val between their summits gradually increases as we advance
from the eastern to the western stations. Thus, at Nertchinsk
(51° 19^ N., 119° 36^ E.), the first maximum occurs in the
middle of April and the second in the second week of Novem-
ber, the interval being nearly severi months; at Barnaoul
(53° 20' N., 83° 57^ E.) the first maximum takes place in
the middle of March and the second in the middle of Novem-

17

ber, the interval being eight months ; at Catherinbourg (56°
49^ N., 60° 35^ K.) the first maximum occurs in the second
week of March and the second about the second week of
December, the interval being nine months ; at Tiflis (40° 42' N.,
44° 50' E.) and at Lougan (48° 35' N., 39° 20^ E.) the inter-
val is also about nine months; at Stockholm, and also at
Milan, the first maximum occurs in the middle of February
and the second in the middle of December, the interval being
ten months; but in the British Islands there is only one
principal maximum, which occurs about the second week of
January and which appears to be formed by the union of the
first maximum of one year with the second maximum of the
year preceding, the interval between the two maxima being
twelve months. Jt is evident, therefore, that these maxima
move across the two continents in opposite directions, the
course of the first being from West to East and that of the
second from East to West.

As the apparently compound maximum of January is not
greater than either of the separate maxima, the Author con-
siders it very probable that both maxima are produced by the
same disturbing cause, such disturbing cause taking its rise
in Eastern Asia in the month of November, and gradually
moving westward until it arrives in the British Islands in
January ; then reversing its course, it returns with a diminished
velocity to the region of its origin, where it arrives in the
month of April, and afterwards rapidly disappears under the
influence of an increasing temperature, to re-appear later in
the year on the return of a low temperature.

As the times of first appearance and of final disappearance
of the disturbing cause in Eastern and Central Asia, corres-
pond very nearly with the times of the breaking up of the
monsoons in the China Sea and Indian Ocean, it is considered
very probable that the two systems of phenomena are directly
connected with and dependent upon each other.

Attention is drawn to a very decided convexity of nearly

18

all the curves in the month of October, indicating the opera-
tion of a secondary disturbing cause acting during that month
over the whole breadth of the two continents.

In concluding, the Author remarks that the first application
of the method he has employed appears to be due to Dr.
Dalton, and that the only other application of it which he has
yet met with is in IVfr. Broun's very able discussion of the
Makerstoun observations.

At the conclusion of the Paper, Mr. Robt. Worthington
expressed the high opinion which he entertained of the impor-
tance and value of the observations brought forward by Mr.
Baxendell, as forming a new step in the method of discussion
of the disturbances of atmospheric pressure in which a definite
mode of measurement was adopted. He knew, from his own
experience, how laborious such an investigation was, involving
as it did, many scores of thousands of numerical operations.
It was important to understand that the observations used
by Mr. Baxendell were those published by some recognised
meteorological institution.

The Chairman remarked that the Paper just read afforded
striking proof of the great value of the Society's library of
reference, which was fast becoming one of the most complete
in the country. Without the help of the library the collection
and arrangement of all these observations would have been
impossible ; and he strongly urged the members to assist in
rendering more effective so important a part of the Institution.

19

Ordinary Meeting, November 27th, 1860.
Dr. J. P. Joule, President, in the Chair.

A Paper by Thomas Moffat, M.D., F.G.S., F.R.A.S.,
«' On the prevalence of certain forms of disease in connection
with Hail and Snow Showers, and the Electric condition of
the Atmosphere," was communicated by Mr. Binney.

In 1852, while deducing results from the meteorological
observations of the two previous years, the Author observed
that an intimate connexion existed between falls of snow and
hail and diseases of the nervous centres, such as apoplexy,
epilepsy, paralysis, and vertigo ; and the results of eight more
years bear out the truth of the observation.

A table formed from two hundred and thirty-six cases of
the above diseases, and upwards of one thousand observations
of the electrometer, is given, showing the per centage of hail
and snow showers, the cases of diseases of the nervous centres,
and the times that the air was positive and negative with
each wind. From this table it appears that with the wind
from the N., N.E., E., and S.E. points, which the Author
calls the snow points, the per centage of hail and snow
showers is 23*2 ; of cases of apoplexy, &c., 36*7 ; of positive
electricity, 27*0; and of negative electricity, 34-1; while with
the wind from the hail points, S., S.W., W., and N.W., the
per centages are respectively 76'6, 65*7, 72*6, and 67*5, thus
showing that the number of cases of disease increases with
the frequency of hail and snow showers and the consequently
Proceedings— Lit. & Phil. Society— No. 5.— Session, 1860-61.

20

increased frequency of the alternations of positive and negative
electricity.

All observers agree that the air is negative on the approach
of great storms, and negative or alternately negative and
positive in unsettled weather, and the Author remarks that
such storms are almost invariably accompanied by convulsive
diseases, or diseases of the nervous centres in some form ; and
in support of his statement he quotes many cases from his
notes of the storms of the last twelve months, but more
particularly the succession of gales which occurred from the
21st to the 30th of October, 1859 (in one of which the
" Royal Charter" was lost), the gales of the 25th, 26th, and
27th of May last, which were accompanied with frequent hail
showers ; and those of the 24th of August and four following
days. Other forms of disease accompany such atmospheric
conditions, such as premature uterine action, epistaxis, and
diarrhoea, with vomiting and cramps ; and cases of this class
are quoted by the Author from his notes ; and he remarks
that it would then appear that negative electricity plays an
important part in the above atmospheric conditions and
morbid actions. After describing the electrical phenomena
of continued heavy rains, and of thunder storms and heavy
showers of hail and snow, the Author observes that as the
electrical tension of the clouds which produce these storms
and showers is always strong, it must have a coercive force
upon all bodies at the earth's surface ; and that as, according
to our notions of electrical action, the moment the influence
of the inducing body is removed, a re-arrangement of the
electricities in the induced body takes place, we cannot well
avoid the conclusion that during the period of induction, and

21

when the re-arrangement — the rebound — the hack stroke
occurs, some important action must take place in the organic
forces, such as the nervous and the muscular. Cases are
quoted in illustration, and the Author then remarks that
from long series of observations it would appear that there
is an intimate connexion between hail and snow showers,
-stormy weather, atmospheric electricity, and certain forms of
disease ; and he ventures to add that hail and snow are
formed under the influence of opposite electrical conditions,
and concludes by suggesting the means of putting this
opinion to the test of experiment.

MICROSCOPICAL SECTION.
November 19th, 1860.

A Letter was read from Mr. R. D. Darbishire, relative to
the deposits from the raised sea bottom found at Capell
Backen, Uddevalla, near Gottenburg, in Sweden. He
observes that " the hill side from a height of about fifty feet
above the level of the sea to that of about two hundred and
thirty feet, consists of layers of fossil shells, varying from ten
to thirty feet thick, alternating with beds of more or less
coarse gravel and clayey sand." Mr. Darbishire contributed,
for the use of the Members, a parcel of washings from shells,
and a box containing dry sieved soil for microscopical
examination.

22

A Letter was read from Mr. John Hepworth, of Crofts
Bank, describing his method of washing and mounting cal-
careous and silicious shells, dry and in balsam. Mr. Hepworth
also presented to the Members of the Section, for mounting,
a piece of injected kidney.

A Paper by Mr. J. B. Dancer, F.R.A.S., was read,
" On cleaning and preparing diatoms obtained from soundings
and other sources."

The Secretary exhibited a portion of sea weed from the
Gulf Stream, in which were found a few diatoms, remains of
entomostraca, &c., contributed by Mr. A. da S. Lima, of
London.

23

Ordinary Meeting, December llth, 1860.
Dr. J. P. Joule, President, in the Chair.

Dr. Fairbairn brought before the meeting four specimens
of Submarine Telegraphic Cable, as constructed by Messrs.
Hall and Wells. This cable has a copper wire insulated by
India rubber in the centre for the transmission of the electric
current. Outside of this are twenty longitudinal strands of
hemp steeped in pitch and cork dust, and eight steel wires
braided together with twenty-four strands of hemp saturated
with Stockholm tar. The specific gravity of the cable in sea
water is 1.4 and its weight in air 0.82 ton per mile.
The length that would break with its own weight when sus-
pended in sea water is 10,810 fathoms; its tensile strength
being 2.875 tons. Dr. Fairbairn presented an account of
experiments which had been made on the elongation of a
sample of the cable twenty feet long by the application of
different tensile forces. With a force of 4,480 lbs. there was
an elongation of half-an-inch, and after the weight had been
removed the cable was found to be permanently stretched
1^6 ths of an inch. With a force of 6,440 lbs. the cable broke
after having stretched ly^ inches.

Professor Roscoe explained the recent discoveries by
Bunsen and KirchofF of the lines in the spectrum produced by
various substances when ignited in the flame of a laboratory
lamp. He exhibited beautiful chromo-lithographic drawings
of the spectra produced by lithia and various other earths
and alkalis. Lithia, which had formerly been supposed to be
a very rare earth, was by this means proved to be one of those
most extensively distributed. Professor Roscoe stated that
Bunsen had, by this new and most delicate system of analysis,
been led to the discovery of a new metal which was present
in a mineral spring in so small a quantity that twenty tons
had to be boiled down to obtain 250 grains of the metal.
Proctbedixgs— Lit. & Phil. Society— Xo. 6.— Skssiox, 1880-6L

24

A Paper was read by the Rev. W. N. Molesworth, M. A.,
entitled, " On the Origin of Species."

The Author of the Paper stated that he was neither the
advocate nor the antagonist of Mr. Darwen's theory ; but that
he wished to point out the futility of some of the arguments
which had been made use of against it, to suggest some
additions which he thought necessary to give it completeness,
and to ask for it that it should be considered in that spirit of
philosophical calmness with which it had been proposed by its
Author.

After giving a brief sketch of Mr. Darwen^s theory, for the
purpose of keeping its more salient points before the minds of
the audience, and to enable them to follow the remarks he was
about to make on it, he pointed out the difficulties which had
given rise to it, and the classes of facts which it aimed at
explaining. He showed that, regarded as a scientific hypo-
thesis, it possessed a value which was altogether independent
of its truth or erroneousness, and that the discussion of it
would in all probability lead to important scientific results,
whatever might be the ultimate fate of the hypothesis itself.
He then proceeded to consider some of the objections which
had been made to it ; but the greater part of the Paper was
devoted to the purpose of pointing out, at considerable length,
the influence which changes in the conditions of existence
must have in producing variation. He dwelt on the distinction
between variability and a tendency to variation, showing the
former to be a quality inherent in the organised being, and
the latter to be generally a consequence of changes in its
conditions of existence; and he quoted some passages from
Darwen's work to show that in this respect the theory was
defective and required further elaboration. He concluded by
expressing his entire approval of the rule of the Society which
prohibited the consideration of the theological bearings of the
question, a rule which he regarded not merely as a regulation
of wise expediency, but as the embodiment of a great principle,

2o

namely, that the intrusion of Scriptural considerations into a
scientific discussion is as theologically wrong as it is scientifically
mischievous — that it is our duty to investigate the Creator's
viTorks with the utmost freedom in every direction, without
entertaining the slightest dread that our inquiries can ever
prejudice the moral and religious truths that are contained in
His word. He reminded the Society that truth can never
injure truth, but only error; and that we might, on this
subject, use the words which Galileo employed in replying
to objections precisely similar in their principle to some of
those which Mr. Darwen's theory has encountered. " Quin
ipsa philosophia, talibus disputationibus non nisi beneficium
recipit. Nam si vera proponit homo ingeniosus veritatisque
amans nova ad earn accepio fiet ; sin falsa, refutatione eorum
priores tanto magis stabilientur." — GalilcBisyst,cosm.^ p. 42.

An interesting discussion took place, in which Dr. Fairbairn,
Dr. Clay, Mr. Binney, Mr. Atkinson, Mr. Francis, Mr. Hull,
and others took part.

Mr. Hull, F.G.S., reviewed the geological evidence bearing
on the " Development " theory, arriving at the conclusion
that on geological grounds that theory was altogether un-
tenable. At the same time, as far as regards the permanency
of varieties, and their consequent establishment as species,
the doctrine of Mr. Darwen appeared sound up to a certain
point. The distribution of the Brachiopoda, and some other
forms, appeared to be capable of explanation on these grounds,
but Mr. Hull contended that it was impossible to account for
the first appearance of numerous highly organized groups of
animals on the hypothesis of natural selection, or any similar
theory of development.

26

PHYSICAL AND MATHEMATICAL SECTION.

November 8th, 1860.

Mr. Baxendell was elected a Vice-President of the Section,
in place of the late Mr. Long-.

Mr. Baxendell read a Paper, '« On a System of Periodic
Disturbances of Atmospheric Pressure in Europe and Northern
Asia."

[This Paper was afterwards read at the Ordinary Meeting
of the Society, on the 13th November.]— See Proceedings
No 5.]

December 6th, 1860.

Mr. George Mosley was elected Treasurer of the Section,
i n place of Mr. Baxendell.

Mr. Atkinson read a Paper, entitled " Remarks on
Abnormal Disturbances of the Barometrical Column at certain
Seasons of the Year."

Mr. Atkinson considers that all the movements in the
atmosphere of our earth, which have received the designation
of irregular^ are caused by the reflected or radiated heat of
the sun, and take place at a very moderate elevation, say
within five or six miles of the general surface level ; — and that
these apparently irregular movements or shiftings from place
to place of lighter and heavier air, causing oscillations in the
barometric column, are mainly if not wholly due to irregulari-
ties of the earth's surface. Had our earth been a globe
possessing a smooth surface of uniform texture and properties,
it seems clear that the atmosphere would have been acted

27

upon by the reflected and radiated heat of the sun, in a manner
so much in accordance with a uniform sequence of physica
effects, that the periodic movements of the gases composing-
it would have been as regular as the planetary motions them-
selves. In the northern parts of our hemisphere, it appears
by Mr. Baxendell's valuable paper, read before the General
Meeting of this Society on the 13th ult., that the barometric
oscillations are least in amount when the sun is on or near
the equator. This fact points to the inference that if the plane
of the earth's orbit had coincided with the plane of its equator
the disturbance of the barometric column would have been
comparatively small and nearly uniform throughout the year.
The coincidence of these two planes not existing, it is found,
that as the sun retreats from the equator towards the southern
tropic, the sum of the oscillations of the mercury gradually
increases for a considerable time, and then rapidly mounts up
so fast as to form a prominence in Mr. Baxendell's curves
resembling a mountain peak. This peak or summit of the
"dynamical curve" occurs above different points of its axis —
that is, at different periods of time — according to some peculi-
arity in the position — different from the latitude or the
longitude — of the locality from which the data for constructing
the curves were derived.

Speaking of the northern hemisphere, as the sun withdraws
southward from the equator, less or greater portions of the
northern part of the terraqueous surface becomes cooled down
gradually to the freezing point, according to various peculiari-
ties of substance, elevation above the sea-level, proximity to
the open ocean, or to far-inland mountain ranges, and to other
analogous causes. In similar latitudes, from the varying
conditions just mentioned, there will exist, side by side, spots
differing, or having a tendency to differ, very much in
temperature, and where consequently currents of different
density — set in motion by the constant struggle going on in
the air to attain a state of equilibrium— will cause frequent

28

fluctuations in the barometer. These disturbing causes will,
in any region, be much increased at the setting in of winter
and the commencement of hard frost ; for at this crisis a large
amount of latent heat will be liberated and will contribute its
influence to disturb the equilibrium of the air. A similar
crisis will occur at the end of winter on the breaking up of the
frost, and will necessarily be attended with similar results.
As the times of these crises appear to correspond in a remark-
able manner with the times of maximum disturbance of the
barometrical column, it seems but fair to infer that a relation
exists between the causes here stated to be in operation, at
the critical periods just named, and the periodical disturbance
of the mercury in the barometer indicated by Mr. Baxendell's
" dynamical curves." The correctness of this inference, or
the contrary, can only be established by future observation of
phenomena, and the collection of facts, many of them of a
kind seldom thought of hitherto as constituting elements for
the solution of problems in meteorology.

29

Ordinary Meeting, December 26th, 1860.

Dr. R. Angus Smith, Vice-President, in the Chair.

Ordinary Meeting, January 8th, 1861.

E. W. BiNNEY, F.R.S., F.G.S., &c., Vice-President,
in the Chair.

Mr. Ransome exhibited and explained the means of obtain-
ing a photograph, which, although appearing a confused series
of light and shade, yet, when reflected from a polished cylinder,
was a beautiful picture.

Dr. Crace Calvert brought under the notice of the
Society an interesting communication made to him by Pro-
fessor Arnaudon, of Turin, to the effect that oxalate of
ammonia completely modifies the action of yellow prussiate of
potash when mixed in solution with a salt of peroxide of iron.
Thus, if oxalate of ammonia be added to this metallic salt, it
will give no prussian blue when a solution of yellow prussiate
of potash is added ; but on the addition of an acid, prussian
blue is immediately produced. The knowledge of this fact
may be interesting to calico printers, as it will give them the
means of easily producing prussian blue on their fabrics. To
attain this desirable end, the printer will simply have to pad
his fabric through a mixture of persalt of iron and oxalate of
ammonia, dry, and print an acid where he wishes to produce
the blue.

After Dr. Calvert had made a few more remarks on this
subject, he stated that he had lately examined several varieties
Proceedings— Lit. & Phil. Society— No. 7.— Session, 1860-61.

30

of snufFs, which he had found to be more or less impregnated
with lead compounds, especially the black rappee, and he
found on further investigation that the presence of lead was
due to the corrosive action of the snuflP upon the lead foil used
for packing it. He also stated that it was his intention to
examine several other substances usually packed in lead foils,
and that he would lay the results of his observations before
the Society, as he thought it highly desirable to make the
public aware of such sources of injury and to induce manufac-
turers to adopt means to avoid inflicting this serious evil on
their consumers.

Dr. Calvert concluded by stating that he had been engaged
for the last few months in investigating the action of the
Manchester Waterworks w^ater on various kinds of leaden
pipes, and that he was arriving at such results as would show
the necessity for serious consideration on the part of the
inhabitants of this city with respect to the evils arising from
the introduction of the water into their dwellings through
leaden pipes.

Being requested by the Chairman to give his opinion.
Dr. Angus Smith said that he had never found any
Manchester water which had passed through lead pipes to be
entirely free from lead. At the same time, the quantity is in
almost all cases so small that, as far as we know, it can
produce no bad effects, and is practically equal to nothing.
There is, however, a great difficulty in knowing what is hurt-
ful ; medical men had not settled the point. Persons said to
be suffering from lead paralysis were known to have taken
water with as little as one-hundredth of a grain of oxide of
lead per gallon, whereas it was considered generally not to

31

be hurtful until it contained one-fortieth of a grain. We
have little idea of the extreme susceptibility of some persons,
and it is better to avoid lead as much as possible. Short
lead pipes may be used without fear in Manchester, especially
if the water which has stood over night be thrown away.
Long lead pipes should be avoided, and lead cisterns are
extremely dangerous, especially with soft waters, including
Manchester water. (Here, instances were given.) Soft water
dissolves lead more readily than many hard waters, and if the
hardness be due only to the earthy carbonates, the lead becomes
coated instead of beings dissolved. But if the hardness be
due to chlorides or nitrates, the water dissolves lead much
more rapidly than pure water ' (referring to what he had
written on this). He gave an instance of water from a cess-
pool obtaining, by oxidation of its impurities in a porous soil,
much nitric acid, which, along with the chlorides always
found in such cases, caused the adjacent water, when drawn up
by a lead pump, to have a very strong taste of lead salts. It is
remarkable that this water was drunk for some years, but
ultimately caused the death of two or three persons. It is a
mistake to suppose that pure water dissolves lead more than
all impure waters. Some very pure natural waters dissolve lead
simply because they contain chlorides, although in small
quantities. Such waters sometimes come from clay slates and
similar formations. As to })eaty water, it was of two kinds,
occasionally acid, with some action on lead, but in most cases
alkaline, the peaty matter not dissolving lead. Some lead pipes
were more easily affected than other. Dr. Smith gave an in-
stance of a lead pipe, nearly an inch in thickness, with holes
pierced through the sides in various places by the action of the
water; others are much more equally corroded. He had spent

32

a long time in obtaining a suitable coating for lead to protect
the water from its action, and had not quite succeeded ; but
he had given his results to a friend, who had gone further,
and, having obtained great success, patented the process.
However, he was told that no one would buy lead pipes of
the kind, as they cost half a crown per cwt. more than the
ordinary ones. People complain of evils which they refuse
to escape from. It is, however, better to avoid lead than to
avoid pure water because of its action on lead.

A Paper was read by Mr. Edward Hull, F.G.S., on

the nature and objects of Geological Surveys, with special
reference to the progress of the geological survey of Lanca-
shire and Cheshire.

After describing the various sources, both natural and
artificial, on which the geological surveyor depends for his
conclusions, and according to which he is enabled to trace the
boundaries of the formations, the author went on to observe
that, so generally is the value of such surveys recognised,
that the governments of nearly all the most civilised nations
had undertaken their support. Amongst others, France,
Belgium, Germany, Russia, the States of North America,
the British Colonies, as Canada, New Columbia, India,
Australia, and New Zealand.

The Author then explained some details regarding the maps
of Lancashire so far as they had been completed by the Geo-
logical Survey of Great Britain. Specimens of these maps,
both of the one-inch and six-inch scales, were exhibited to
the Society in the course of the evening.

33

MICROSCOPICAL SECTION

December 17th, 1860.

Letters were read from Sir Leopold Mc. Clintoek, Mr. J.
W. Read, of the Admiralty, and Dr. Wallich, who accom-
panied the former in the Bull Dog, in the late expedition to
the North Seas. Dr. Wallich kindly presented to the Section
a few copies of his pamphlet on " Life in the Deep Sea," now
circulating amongst the members.

A Letter was also read from Captain M. F. Maury, of the
U.S. Navy, promising to supply envelopes for soundings
amongst the sperm whalers and other vessels trading to the
Pacific Ocean, &c.

Specimens of incrustations from the boilers of the steamer
Edinburgh, trading from Glasgow and Liverpool to New
York ; from the steamer Rhone, from Liverpool to Venice,
Trieste, &c. ; and from the steamer Minho, from Liverpool to
Lisbon and Oporto, were received from Mr. W. A. Hayman,
of Liverpool. The incrustations are as hard as marble,
breaking with a crystalline fracture, and showing, by different
coloured strata, the crust obtained from harbours and from
the open sea. Mr. Dale stated that the component parts of
the incrustations are sulphates of lime, magnesia, &c. ; he
recommended maceration in bicarbonate of ammonia to obtain^
calcareous shells, and in weak acids or muriate of barytes to
obtain silicious shells. Various members took specimens for
examination.

34

A Letter was read from Captain Andersen, of the Cunard
steamer Canada^ from Liverpool to New York, accompanying
specimens of the soundings taken during his last voyage across
the Atlantic. Captain Andersen was kind enough to send
the soundings by post from Queenstown, by which means
they arrived just before the meeting.

Mr. W. H. Heys, of Hazel Grove, exhibited his newly
invented Kaloscope, by means of which he obtains refracted
and reflected light of different colours at the same time upon
objects under the microscope, producing beautiful effects in
some cases.

35

Quarterly Meeting, January 22nd, 1861.

Dr. J. P. Joule, President, in the Chair.

The following gentlemen were duly elected as Honorary
Members: — Wilhelm Haidinger, Director General of the
I. R. Geological Institute, Vienna, and Professor James
Joseph Sylvester, M.A., F.R.S.

As Corresponding Members: — Professor George Buckland,
of University College, Toronto, and Professor Joseph Henry,
Secretary of the Smithsonian Institute.

As Ordinary Members: — William Henry Fisher, Rev.
Thomas Buckley, M.A., Simon PincofFs, Rev. G. H.
Greville Anson, M.A., Professor R. B. Clifton, B.A., John
Shae Perring, William Radford, Thomas Alcock, M.D.,
Charles O'Neill, George Parr, jun., John Curtis, James
Bottomley, and Francis Preston.

The new rules were submitted by the Council.

It was moved by Mr. Binney, seconded by Mr. Maclure,
and resolved — " That the rules proposed by the Council be
adopted in place of those hitherto in force."

MICROSCOPICAL SECTION
January 21st, 1861.

Letters were read by the Secretary from Professor
Huxley and from Mr. W. K. Parker, respecting soundings.
Proceedings— Lit. & Phil. Society— No, 8.— Session, 1860-6L

36

Mr. Heys, of Hazel Grove, read a Paper " On the Kalo-
scope," his newly invented instrument for the use of coloured
light in the examination of objects under the microscope.
This the Author eifects by two sets of four discs each of
differently coloured glass, 21 inches in diameter, mounted on
a stand 12 inches high, one set of which is placed between
the light and the bull's eye condenser, and the other between
the light and the mirror, underneath the stage, each disc
having an independent motion, so that the light can be
transmitted through one or more of both sets at the same
time; when the object appears of the colours refracted and
reflected through the discs.

One of the important uses of the instrument is the protec-
tion of the eye from injury occasioned by the use of common
artificial light.

Many objects which do not polarise, by the kaloscope are
made to disclose the beauties of polarised light ; for instance,
the anthers of the mallow, with their pollen, when viewed by
means of red light below the stage, and at the same time
green light (the complementary colour) through the con-
denser, appear of a beautiful green colour on a red or crimson
ground.

The Author observes that some objects, viewed by
means of the kaloscope, appear in such relief that they might
be supposed to be seen through a stereoscope ; these are
anthers, jointed hairs, oil-glands, and vegetable sections in
general. The calyx of the moss-rose is alluded to, under
ordinary illumination, as a mere entanglement of fibres with
dark beads.; but by this method it is transformed into a
stereoscopic branch, with glittering glands at its extremities.

Sections of wood, spines of echini, &c., will be found as
beautiful as with the polariscope ; but, by another arrange-
ment, details are brought out not observable with the latter
instrument. A black surface being placed below the stage,
coloured light is thrown very obliquely from the mirror, and

37

the complementary colour through the condenser ; hairs on
the edges of leaves, petals, and filiments of stamens, &c., then
appear illuminated by the li ght of the condenser of one colour,
and fringed with the opposite colour on an intensely black
ground. The Author gives a list of the botanical names of
objects advantageously illuminated by this method. A single
coloured disc may be also used to advantage with white light
from the bull's eye lens. Details of structure are observable
by means of this instrument, which the Author observed are
inconspicuous without its aid, and thinks that its efficacy in
connexion with such a variety of purposes, cannot fail to
render it of value to the scientific observer.

The reading of the Paper gave much satisfaction to the
members of the Section, and it was resolved to communicate
the same to the Society, with a recommendation that it should
be printed in extenso in its Memoirs.

The Secretary read a Paper, " On Preparing Objects
found in Soundings," and described Mr. Dale's process for
disposing of the tallow by means of highly rectified benzole,
which is most effectual. The benzole (called benzine by
French chemists), being recovered, to be used again as fast as
required for a dozen filters, each with its specimen in process
at the same time, with only trifling loss from evaporation.

This Paper, and one by Mr. Dancer, on the same subject,
were ordered to be printed by the Section, for circulation
amongst its members.

Mr. Brothers presented to the Section a very old
microscope, date unknown ; he also exhibited the actinophris
eichornii, melicerta, sea weed with lipraria, &c.

Mr. Hardman, of Davyhulme, presented three mounted
specimens of the wire worm, and a number of dissecting-
needles for the use of the members ; he also exhibited a

38

mounted fly, one of the Panorpidse, which he states feeds upon
leaf-rolling caterpillars. The proboscis and feet of the insect
are peculiarly adapted for dragging its victims from their
concealment and holding them whilst extracting their juices ;
the feet being provided with combs similar to those of the
spider.

Mr. R. D. Darbyshiue presented a quantity of mud, &c.,
from the washings of shells from the raised sea bottoms at
Uddevalla in Sweden.

Mr. Dancer exhibited a new 3-inch object glass, with a
large and flat field of view ; also specimens of gold quartz
from Wales large curculia, and other objects.

Mr. Whalley exhibited some specimens of injections
obtained from Germany, which were considered the best yet
exhibited.

Mr. Latham exhibited various specimens of sand and mud
from the East Indies, portions of which were distributed
amongst the members.

39

Ordinary Meeting, February 5th, 1861.

J. C. Dyer, Esq., Vice-President, in the Chair.

Mr. John Curtis communicated his observations of the
fall of rain in the years 1860, 1859, and 1858, and compared
them with Dr. Dalton's average for 47 years, and with ^e
mean of the last 72 and 75 years. The following is a sum-
mary of the results : —

Average from 1794 to 1860 35-46 inches.

from 1786 to 1857 36-398 „

„ from 1786 to 1860 30-274 „

Dalton's from 1794 to 1840 35-5-23 „

In 1858 30-53

„ 1S69 33-09

„ 1860 36-24

Comparing the last year with 1859 it was found that

The number of rainy days in 1860 were 28 days above that in 1859.

The amount of evaporation „ vpas 092 inches below ,,

The mean temperature ,, was 3-13 degrees below „

The highest temperature in shade „ was 9 7 degrees below ,,

The lowest temperature in shade „ was 19*9 degrees below ,,

The highest temperature in sun „ was 6*0 degrees below „

The lowest temperature on grass ,, was 19*9 degrees below „

The mean of barometer „ was 0031 inches below „

The number of days of snow ,, were 8 more than „

Dr. Crace Calvert stated that in consequence of having
found lead in snuif packed in leaden cases, he had examined
tea, chicory, &c., but without discovering lead in them, which
he attributed to the protection afforded, in some instances, by
the interposition of paper between the article and the leaden
case, and in others to the absence of sufficient moisture to
promote chemical action.

Proceedings— Lit. & Phil. Society— No. 9.— Session, 1860-61.

40

One of the medals struck on the occasion of the coronation
of the present King and Queen of Sweden, presented to the
Society by the University of Christiana, excited much admi-
ration on account of the excellence of medallurgy it dis-
played.

A Paper " On the Kaloscope," by Mr. W. H. Heys, was
read by Mr. George Mosley This Paper was communi-
cated by the Microscopical Section, and an abstract will be
found in the Proceedings, No. 8, under that head.

PHYSICAL AND MATHEMATICAL SECTION.

January 31st, 1861.

Mr. Mosley read from the Gibraltar Chronicle of the 8th
instant, an abstract of meteorological observations taken at
the Royal Engineers' Observatory, Gibraltar, during the year
1860. From the results given it appeared that while the
weather in Enjrland during^ the last Summer and Autumn
had been unseasonably cold and wet, at Gibraltar, on the
contrary, it had been remarkably warm and dry. During the
six months from the 30th of April to the 1st November, the
fall of rain at Gibraltar had been only 1-237 inches, whilst at
Manchester, according to Mr. Vernon's returns, it had been
21-858 inches. It was also remarkable that the maximum
degree of humidity of the air at Gibraltar, as determined in
the usual way by the wet and dry bulb thermometers, oc-
curred on the 30th of September during the long period
of drought. The average fall of rain at Gibraltar, from
eight years' observations, is 41-2 inches, but during I860 the
amount collected in a gauge on the ground was only 34-874
inches, and in a gauge 25 feet above the ground 32-358 inches.
The mean pressure of the atmosphere for the year, at 50 feet

41

above mean water level, was 30-001 inches; the mean tem-
perature, C4°-9; and the mean dew point computed was 57°'4.

Mr. Baxendell communicated the following table of the
fall of rain at the Flosh, Cleater, near Whitehaven, during
the last three years, drawn up from observations made by
Thomas Ainsworth, Esq.. a Corresponding Member of the
Society : —

1858.

1869.

ISfiO,

January

3-435
0-4(i5
3(M)5
2-0 75
3-855

4M){)0
3 157
5-o(;7
f)-< 10
l-4()0
4-bU5

5-415
4477
4-5()7
4 017
0-400
2 5-<5
2-9:57
6-.--i;i-2
(i-^47

4-;i-25

4-737
41 -20

7-072
2-647
5-030
2-5-27
3 6h0
4-(i-22
2"2-22
6- 050
2-030
9-1-22
2-012
5-(il0

February

April

Miiv

J Ull<?

July

Auiinst

September

Oclol)er

Nnvember

December

Total

41-789

50-099

53 -^^04

Mr. Baxendell, referring to a letter by Dr. Wolf, of
Zurich, inserted in No. 1,289 of the " Astronomische Nach-
richten," on the variations in the frequency of the solar
spots, exhibited a diagram showing such frequency by the
relative len-^ths of ordiiiates laid otf from a line representing
the time. Treatiiig Dr. Wolf's data by the meti'iod of least
squares, Mr. Baxendell had deduced a mean period of I 1*086
years, the mean epoch of minimum frequency being 1732-96.

Mr. T. Hkells read a Paper " On Meteorological Ob-
servations, and Observations of the Temperature of the
Atlantic Ocean, made on runs from Liver[)ool to Gibraltar,
and from Ciibrahar to Liverpool, in September, lb(JO.'*

42

This Paper was considered by the Section worthy of being
printed in the Memoirs, and will be read at an Ordinary
Meeting of the Society.

In the course of a discussion which ensued on the red color
of the sky, often observed as an indication of approaching bad
weather, Mr. Binney mentioned that Mr. Dancer had shown
him an aurora borealis of a pale greenish white color, which,
when observed through glass upon which moisture had been
deposited, appeared red.

Mr. Baxendell mentioned that several fogs, especially
those which had occurred in the early part of the present
winter, had been observed by him to be luminous, and that
Mr. Crosse, the electrician, had found many fogs to be highly
electrical.

43

Ordinary Meeting, February 19th, 1861.
Dr. J. P. Joule, President, in the Chair.

A Paper was read by J. C. Dyer, Esq., entitled, " Brief
Notes on the Freezing, Thawing, and Evaporation of Water,
and on the Condensation of Steam, with a View to Enquire
into the Cause of those Changes."

In these Notes the Author merely aimed to place before
the Society the apparent agency of heat^ in the changes that
water undergoes in passing alternately from one to the other
of its conditions of ice, water, and steam, and vice versa ; and
that these mutations are caused, by the taking up and giving
out of heat, in its sensible or latent state, by the transitions
reciprocally from one to the other of those states. The
actual amount of the thermoraetric heat so passing from the
latent to the sensible state was given, as taken from the
common tables. On referring to the two ancient theories of
heat, the one defining it to be, "a material element, sui
generis, and pervading matter," &c. ; the other holding it to
be "no other than the motions, mechanically excited in the
minute particles of bodies," &c. — it w^as contended that, by
this latter or the " force heat theory," the melting of ice by
the action of the sun's rays could not be explained, since it
is not by their force, but by the matter of heat that enters
and becomes latent in the w^ater. The Author then sub-
mitted that the only solution, hitherto offered of the absorption
of sensible heat, in water and steam, as latent in these, and
the re-appearance of the same measure of heat, in a sensible
state, by the acts of condensation and freezing, is to be found
in the application of Dr. Black's " Latent Heat Theory."
Considering the force heat theory, as directly conflicting
with that of latent heat ; they cannot both be sustained, and
as the latter stands in elementary works as an established law
in physics, and as it affords a clear explanation of the
aqueous changes adduced ; it seems incumbent on those who
Proceedings— Lit. & Phil. Society— No. 10.— Session, 1860-61,

44

deny the entity oiheat^ to account for the alternate exhibition
and extinction of the thermometric heat, that is, in fact,
evolved and absorbed by those mutations of water.

The Author again referring to the long standing con-
trovercies concerning the essential nature of heat, stated that
more than one hundred works have been published on the
subject during the last 200 years, and yet no conclusion has
been arrived at, as to the soundness of either of the original
theories above cited, nor have any discoveries been made that
explain the agency of heat, in the mutations of water, since
the days of Bacon and Boyle, with the sole exception of
those of Dr. Black, which appear to prove its latent state in
bodies. And since we have no settled doctrine as to its
essence, we must allow that the subject is of philosophical
interest, and especially this branch of it concerning latent
heat, in defence of which these notes are offered.

The President said that some very interesting experi-
ments made by Mr. Dyer, many years ago, were in favor of
the dynamical theory of heat, which he believed to be fully
able to explain the phenomena ascribed by Black to " latent
heat."

A Paper was read by Dr. R. Angus Smith, " On the
Production and Prevention of Malaria."

The Author did not pretend to enter on the whole subject,
but to give a few observations which he considered fitted for
its illustration — Malaria has unquestionably been proved to
be caused by the decomposition of organised bodies. If so,
it must exist to some extent everywhere. By the mode of
testing the air invented by the Author, every place tried at
home and abroad was found to have some oxidizable matter
in it, although in some this was extremely small. In such
cases the matter was probably oxidized to a state in which
it would be innocuous. This oxidizable matter no doubt
rises, in a great measure, from vegetation. Vegetation does
not merely grow ; it dies. This death may be caused by

45

various circumstances, but two conditions are remarkable, one
where the agents are animals, and the other where the agents
are chemical. Animal life may act in various amounts on
vegetation in the soil, from the large vermin to the microscopic
classes. These do not prevent chemical action, on the con-
trary, it is probable that they further it exceedingly.
Decomposition goes on in the soil at various rates, and in
various ways. In a rich, highly-manured soil kept warm,
the soil will be found alkaline. Soils generally are acid.
The Author had shown in a Paper, read in 1847, that in an
alkaline, peaty district, cold weather produced acidity in a few
days. It would appear as if the acids of the mould (so
elaborately described by Mulder) were incapable of further
decomposition in the cold, and were thus retained and
increased. Our great struggle with the soil is to produce
alkalinity, or at least to diminish acidity, and where most
acids exist we use most lime. Where most alkali exists there
is a greater facility for the escape of vapours, such as we
suppose to be hurtful. So far as the vapours of putrid
substances have been examined by the Author, they have
shown indications of containing substances composed some-
what like protein, at least the carbon and nitrogen have had
relations to each other similar, or nearly identical with those
found in protein, and formed the mass of the substance.

The extreme condition of putrescence may be very readily
produced in a soil by artificial means ; the use of a little
ammonia, for example, more than vegetation will bear. The
substances putrefy until the whole becomes foetid in the
highest degree. We have then a soil rich in organic matter
and undrained. It is a swamp of the worst form if the soil be
not very poor ; worse, perhaps, than was ever seen in nature.
Such a soil would bring death everywhere. It is artificial
malaria. We can, then, produce malaria from the soil by
fostering some of its tendencies ; and we see by the rapid
acidification of soil, in colder weather, why malaria is
diminished by a lower temperature.

46

As we can imitate malaria of some kinds, so can we also
imitate the methods by which nature prevents it. The warm
alkaline soil, moistened, and washed with air and water,
becomes acid, it sends forth less volatile matter — decom-
position is stopped to a great extent, the matter is preserved.
Cold prevents the action, drainage assists oxidation by a more
active state of soil. By these modes, and others, the soil is
disinfected by nature, when these do not act sufficiently we
may use disinfecting agents. By their means decomposition
may be interrupted without fear of diminishing the power of
the plant to take up food. By the use of disinfecting agents,
Mr. Mc. Dougall had been able to feed sheep and cattle, and
retain them in health, on meadows constantly wet by irrigation
with liquid manure. The disinfectant used is from the pro-
ducts of the distillation of tar, the amount required is small.
Animal life is rapidly destroyed by it, and chemical decomposi-
tion is staid. All climates can furnish this, where coal lies or
where trees grow.

It would be possible to irrigate great districts at an extremely
small expense. The result would be as certain on a large
scale as on a small one ; and it is probable that, in some cases,
one or two applications would be sufficient, for a long period at
least. By the new state of things, destructive insects would
also be destroyed. Although, according to Dr. Mc. CuUoch,
there are many parts of our own islands infected by malaria,
most, if not all, can be cured by good attention to well-
known agricultural maxims. This new method is especially
applicable to other countries, and to more violent stages of
the disease. The Author hopes to have it tried on extensive
districts in Italy. The method arose out of an advice every-
where neglected, but still cherished as true, to disinfect
whole cities by beginning with the sewers, the origin and
reservoir of all the mischief.

The Author believes that he has shewn that decomposition,
to a most pernicious extent, is possible in soils, that this is
not a mere opinion, but a fact readily demonstrated ; but that

47

decomposition may be arrested artificially to the preservation
of health without the destruction of vegetation, and that in
these facts we have not only a surer basis in our reasonings
on the origin of malaria, but an almost certain process for its
ultimate and total extermination.

SECTION FOR STATISTICS AND SOCIOLOGY.
March 27th, 1860.

A Paper, " On Scientific Philanthropy, or the Best Means
of Promoting Social Reform," by Mr. Thomas Ballantyne,
communicated by Dr. R. A. Smith, was read.

This great problem may be thus briefly stated. A fearful
amount of moral and physical wretchedness exists in Man-
chester and the neighbourhood ; is there wisdom and energy
enough among the wealthy and intelligent classes of this city
to remove or greatly mitigate that wretchedness ; and if there
is, how can we best organize these two elements of power in
the most efficient manner ? The great point is to combine
ardent philanthropy, which gives strength of will, to scien-
tific knowledge, which gives practical insight as to the best
mode of working. Before we can hope to see a healthy and
vigorous movement for the social improvement of Manchester,
we must bring the science of our most intelligent reformers
into harmony with the warm-hearted sympathy of our self-
devoted philanthropists.

Mr. Ballantyne was of opinion that it was the peculiar
province of a Society, such as this, to illustrate the best means
of treating this most desirable object.

October 24th, 1860.

Dr. R. Angus Smith, F.R.S., read a Paper entitled,

'* Some Thoughts on the Relation of Work and Workers."

He said the want of attachment to its leaders was not found

48

in history to be the vice of the English nation. Independence
was united to attachment, preventing them from separating
without good cause. In conducting the struggle of industry,
many of the captains of industry had their commissions only
by purchase, not by merit. They had not learned their
trade. There were, in reality, no institutions where the
thorough knowledge could be gained. Such institutions as
taught portions of it were not attended. Badly educated
masters belong to the dangerous classes. The best men
rise, because talent is always before capital. Take capital
to a place and it will be lost without talent; take talent and it
will make capital.

As to the men they have a right to unite ; who will help
them if they never call out ? Pity it is that strikes represent
the ignorance of the workmen ; the best men are busy raising
their condition, not striking. The men generally, like many
of the masters, refuse to learn. They ought to combine, not
to fight, but to make themselves better workmen. It is
amazing how difficult it is to get good workmen. If masters
united with their best men, all might assist each other, and
where there is success this is really done.

The only way that workmen can rise is by intelligence ;
just as it is by intelligence only that the master can maintain
his position. Some of the best masters are men who have
accumulated property by intelligence and industry.

Intelligence in workmen causes a rise in wages, entirely
irrespective of supply and demand. Instances were given in
which there is a constant and established habit of looking to
the condition of the employed and to what he might be sup-
posed to expect. Supply and demand are generally used as
gross words that skim over great difficulties. They have
been treated as merely physical, but when moral considera-
tions enter, supply and demand alter their conditions, and the
physical laws must give way, because there are moral feelings
in men stronger than their love of gain.

49

The common notion of supply and demand relates to a cer-
tain familiar condition of things. But law changes as society
changes; new beings demand new rights; new conditions also
bring new laws. For example, our most rigorous laws relate
to property. We believe that every man has a right to what
he has obtained honestly; but in 1846 Ireland was in want,
and suddenly we found that eight millions of our money did
not belong to us, but was the property of Ireland by a higher
law than that of the police. Character always controls, some-
times despotically rules, both supply and demand.

January 15th, 1861

Mr. David Chadwick, F.S.S., read a Paper, " On the
Equitable Adjustment of Property and Income Tax, and the
Extent to which it is Practicable to Apply such Tax."

After briefly referring to the subject of taxation generally,
the mode of raising it, and the purposes to which it was
applied, and to the opinions of Adam Smith, John Stuart Mill,
Mc. Culloch, Ricardo, and others, it was held that the best
description of the principle on which all taxes should be
levied was the definition of Adam Smith : — " That all persons
should contribute to the taxes of a country in proportion to
their ability."

" That all taxes should be clearly defined, certain in
amount, and payable in a manner most convenient to the
payer."

On the general question of the advantages of direct and
indirect taxation, it was held that, direct taxation enabled
each person to know the exact amount of his individual
contribution, and would therefore afford him the best means
of judging of the necessity and justice of the national
expenditure. It was collected at a very small expense — the
total charge not exceeding 1^ per cent.

50

Indirect taxation (by customs and excise duties) was
frequently oppressive and unjust in its operation, it occasioned
vexatious delays in the transaction of business, adulterations,
and frauds. The cost of collection was from 6 to 10 per
cent ; and it was estimated that, in addition to the duties
levied in many cases, the loss to merchants and traders by
extra trouble, warehousing, waiting, and other impediments
and restrictions, involved an additional loss of from 5 to 20
per cent on the amount of duty.

Mr. Chadwick proposed to carry out the principle recog-
nised in Mr. Pitt's first income tax, and in Mr. James
Wilson's scheme, by assessing the tax on a graduated scale
as follows : —

1st. To make the tax at one uniform rate on the capitalized
value of all incomes.

2nd. To classify the various sources of income according
to their general average market value.

3rd. To assess the tax by a rate on such capitalized value,
instead of the present mode of assessing it on the annual
income.

4th. To apply, as far as practicable, the principle of the
government legacy duty tables to all fixed incomes.

5th. That the tax (on the repeal of the excise and
customs duties) should be applied to all incomes above £50
a year, and stopped by the employers out of the wages and
salaries of all persons in their service.

6th. That in lieu of the present income tax com-
missioners, there shall be in every surveyor's district, or
union of districts, a paid board of three assessors, two
elected by the inhabitants (in the first instance, by those on
the list of parliamentary electors, and subsequently by those
paying the income tax), and one by the government, with
power of appeal to the judges, in like manner as the present
appeals on assessed taxes.

51

PROPOSED NEW INCOME AND PROPERTY TAX.
Estimated uniform rate of one halfpenny in the pound on
the capitalized value of all incomes : —

CLASS.

Income
per Year.

No. of
Years
Value.

Capitalized
Value.

Income and
Property Tax, at
One Halfpenny in

the Pound on
Capitalized Value.

Labourers and Work men

Clerk

Ditto

Salesman

Attorney

Surgeon

Shopkeeper

Manufacturer

Merchant

Owner of House Property..,

,, Railway Stock
Mortgage

„ Land — Farms

,, Government Consols

„ Annuity for Life ...

„ Church Living for
Life

,, Army or Navy Ap-
pointment

,, Civil or Military
Pension

£.
60
100

300
500
600
600
400
1,000
],000

1,000

1,000
1,000
1,000
1,000

1,000

1,000

1,000

6
7
7
8
10
10

15

25
30
30
15

12

10

8

£.

300

600

1,800

3,000

4,200

4,200

3,200

10,000

10,000

15,000

25,000
30,000
30,000
15,000

12,000

10,000

8,000

b. s. a.

0 12 6

15 0

3 15 0

6 5 0

8 15 0

8 15 0
4

6 13
20 16
20 16

31

0

52 1 8

62 10 0

62 10 0

31 5 0

25 0 0

20 16 8

16 13 4

Mr. Chadwick proposed to apply this scheme by imposing
a tax sufficient to raise twenty millions, and to repeal the
following existing duties, and impose only a nominal duty, as
in the case of corn.

Customs Duty on Tea— producing £ 5,300,000

Ditto Sugar— ditto 6,000,000

Ditto Coffee— ditto 500,000

Ditto Other Articles ditto 1,800,000

Excise Duty— Paper 1,100,000

Fire Duty 1,800,000

Amount of Income Tax for 1858, at 6d.

£16,500,000
6,600,000

Total Taxes to be Repealed £23,100,000

52

NEW TAXES.

Property and Income Tax £20,000,000

Estimated saving of the cost of
collection of Customs Duties
and Charges £1,800,000

Estimated produce of new

nominal duties — same as corn

for purposes of registration... 1,300,000

3,100,000

£23,100,000

By this scheme the excessive duties on all articles of
necessity would be removed, and the only other duties
remaining would be on spirits, wine, tobacco, malt, and
hops, — corn (Is.), the stamp duties, licenses, assessed taxes,
&c., which, according to Mr. Newrnarch's schedule, would
produce the remaining forty millions.

53

MICROSCOPICAL SECTION.
February 18tli, 1861.

Letters were jread from Captain Andersen, R.M.S.
" Canada," and from Dr. Wallich, respecting the pamphlet
on " Life in the Deep Seas."

Mr. SiDEBOTHAM described his experience in mounting
desmidise, and the difficulty he found in discovering a
suitable medium for their preservation. He had tried syrup,
Goadby's fluid, and a number of other chemical preparations,
but the specimens, in course of time, were spoiled from one
cause or other ; the fluid which has best withstood the effects
of time is simple distilled water; the cells being made of gold
size and Japan black. Mr. Sidebotham exhibited desmidise,
mounted in distilled water, in the years 1842 to 1846, in
which the chlorophyll is comparatively little altered.

Professor Williamson observed that Dr. Carpenter had
mounted starfishes in glycerine, and had found the colours
were well preserved. He himself had used a mixture of
glycerine and distilled water for volvox, and had found it to
answer well.

Mr. Sidebotham also exhibited specimens of Diatomacese,
mounted in 1844. The specimens (Isthmia enervis, Bid-
dulphia, &c.) were obtained fresh, immersed in spirits of
wine to absorb the water, and mounted in balsam ; the green
colour of the cell contents is yet perfectly preserved.

Professor Williamson exhibited some scales of fish, pre-
pared by Dr. Kolliker, of W^arzburg, containing remarkable
examples of fusiform lacunae. He also pointed out how these
and other similar discoveries, to which he referred, confirmed

54

his previous conclusions in the Philosophical Transactions,
viz., that fusiform lacunse were not characteristic of reptilian
bones, as some had supposed, but that they existed in many-
fishes ; he especially referred to the salmonidse as presenting
this oblong form of bone corpuscule.

Mr. Brothers exhibited a modification of the kaloscope,
and objects to illustrate the same.

Soundings were received from the steamers " Canada,"
from New York; <« Armenian," coast of Africa; " Tagus,"
from Lisbon ; and from several vessels of war, from difi*erent
parts of the world, which were duly acknowledged. In-
crustations from the boilers of several sea-going steamers were
also presented by Mr. W. A. Hayman, of Liverpool.

55

Ordinary Meeting, March 5th, 1861.
Dr. Joule, President; in the Chair.

Mr. Joseph Sidebotham read a Paper " On the Structure
of the Luminous Eiwelope of the Sun," being a communication
to him from James Nasmyth, Esq., of Penshurst.

Mr. Nasmyth has made the discovery, that the entire
surface of the sun is composed of objects of the shape of a
willow leaf; these objects average about 1,000 miles in length,
and 100 in breadth, and cross each other in all directions,
forming a network ; the thickness of this does not appear to
be very great, as through the interstices the dark or penumbral
stratum is seen, and it is this which gives to the sun that peculiar
mottled appearance so familiar to observers. These willow
leaf-shaped objects are best seen at the edges of a solar ' spot
where they appear luminous, on a dark ground, and also com-
pose the bridges which are formed across a spot ' when it is
mending up ; the only approach to symmetrical arrangement
is in the filaments bordering the spot, and those composing
the penumbra, which appears to be a true secondary stratum
of the sun's luminous atmosphere ; here these bodies show a
tendency to a radial arrangement. Although carefully
watched for, no trace of a spiral or vortical arrangement has
been observed in these filaments; thus setting aside the
likelihood of any whirlwind-like action being an agent in the
formation of the spots, as has been conjectured to be the case.
The writer does not feel warranted at present in hazarding
any conjectures as to the nature and functions of these
remarkable willow leaf-shaped objects, but intends pursuing
the investigation of the subject this summer, and hopes to lay
the results before the British Association during their meeting
in this city. The Paper was illustrated by three beautiful
drawings. No. 1 represented one of the willow leaf-shaped
objects ; No. 2 the luminous surface of the sun as being entirely
Proceedings— Lit. & Phil. Society— No. 11.— Session, 1860-61.

56

composed of these objects ; and No. 3, a large drawing of a
solar spot as seen on the 20th of July, 1860, exhibiting the
surface of the sun composed of these objects, as also the
penumbra and the bridges across the dark portion of the spot
in which the exact shapes of these objects were to be seen most
clearly.

Mr. Sidebotham stated that the image of the sun was
examined by Mr. Nasmyth with a mirror of plane glass, set
at an angle of 45 degrees ; nearly the whole of the light and heat
of the sun passed through the glass, and the rays used were
those only reflected from its surface.

Mr. Charles O'Neill read a Paper " On Changes of
Density which take place in Rolled Copper by Hammering
and Annealing."

The results of his experiments proved that the best com-
mercial rolled copper actually lost density by hammering
instead of gaining as might have been anticipated. In the
first series of experiments, ten pieces of copper were cut from
a sheet of the thickness of i% inch, the pieces weighed from
250 to 320 grains each, their mean density was 8'879. The
pieces were then separately subjected to the action of a
powerful compressing machine, acting on the principle of the
genou, about fifty blows being given. The density of these
hammered pieces showed a mean of 8*855, being a loss of
0-024. The same pieces were annealed by being placed in
red hot sand, and cooled slowly ; when cleared from adhering
oxide, the mean density was found to be 8*884, being an
increase of 0*029 on the hammered pieces, and 0*005 on the
original pieces. A second series of experiments, made with
very great care, corroborated the first in the main points.
The pieces were from another and better sheet of copper;
ten pieces, weighing each from 420 to 520 grains, showed a
mean density of 8*898, being hammered by the same machine ;
their mean density became 8*878, showing a loss of 0*020 by

■ 57

hammering; upon annealing in a charcoal fire, the mean
density of five out of the ten pieces was 8*896, showing a gain
of 0*018 upon the hammered pieces, and a loss of 0*002
upon the original. A third series of experiments upon the
change of density in a bar of copper by successive hammerings
showed a loss of density from 8*885 to 8*867.

The Author considered there was a connexion between these
phenomena and the heat disengaged in the hammering of the
copper; he conceived it possible that the expanded state of
the copper while heated by hammering was retained, and that
the efi'ect of annealing might be to allow the molecules or
particles to recover the state in which they were in before
being disturbed by the heat produced in hammering.

PHYSICAL AND MATHEMATICAL SECTION.
February 28th, 1861.

Mr. G. V. Vernon, F.R.A.S., read a Paper, " On the
Irregular Oscillations of the Barometer at Manchester."

This Paper is an addition to one upon the same subject
brought before the Society by Mr. Baxendell, F.R.A.S.

The tables appended to it give the total amount and
number of the barometer oscillations at eight a.m., for each
month from 1849 to 1860, inclusive ; the mean daily
amount ; the monthly fall of rain, and its difference from the
average of twelve years, and Dr. Dal ton's forty-seven years'
average. For the month of August, the Author was indebted
to the kindness of Mr. John Curtis, in supplying him with baro-
meter observations, which were deficient in his own register.

The maximum amount of oscillation takes place in January,
and the minimum in July, to which may be added a second
maximum appearing to take place in October. The mean
total amount of oscillation for the year is 6 14 10 inches, and

the total number 175*5. It appears that a fall of rain, in
excess of the average, is generally accompanied by an
increase in the amount of oscillation. In the months of
February, April, May, June, July, October, and December,
a temperature below the mean for the month appears to
increase the amount of oscillation ; whilst in the remaining
months of January, March, August, September, and
November, the opposite appears to hold good. A number
of oscillations above the average appears to be accompanied
by a greater fall of rain than that accompanying a number
of oscillations below the average, in the months of January,
February, March, June, October, November, and December.
In the remaining months of April, May, July, and September,
a number of oscillations above the average appears to be
accompanied by a diminished fall of rain.

If the month of June is regarded as abnormal (which is
probable, as I have no observations for this month in 1851,
1857, 1859, and 1860), we appear to have two distinct laws,
one of which holds good in the winter months, and the other
its direct converse in the summer months. Taking the
entire year, these two laws appear very nearly to balance one
another.

Mr. Baxendell, F.R.A.S., read a Paper "On the
Irregular Oscillations of the Barometer at Lisbon."

In this Paper the Author gives the results derived from
a valuable series of barometrical observations made at Lisbon
during the twelve years 1849-60, by John Martin, M.D.,
and kindly presented by him to the Section through Mr.
Mosley. These observations were made daily at 9h. a.m.,
the barometer being permanently fixed at about fifty feet
above the mean level of the Tagus, and the readings uniformly
reduced to the temperature of 32° Fahrenheit.

From the tables which accompany the Paper it appears
that at Lisbon the maximum amount of oscillation occurs in

59

January, and the minimum in July, precisely as in the British
Islands, and therefore agreeing- with the law of disturbance
announced by the Author in a former Paper. There is a
small maximum in March, and a rather sudden and consider-
able increase of disturbance in October. The mean annual
amount of oscillation is 31*686 inches, and the mean annual
number of oscillations 156*9. The mean range and mean
duration of oscillation are both greatest in the winter, and
least in the summer months. The greatest range occurs in
January, but the greatest duration of oscillation is in Novem-
ber. It is remarkable, too, that the range is also greater in
November than in any other month except January. These
results for November are probably due to the great barometric
wave which Mr. Birt some years ago pointed out as fre-
quently occurring on or about this month.

In England the mean duration of oscillation is greater in
the summer than in the winter half of the year, and, assuming
that the breadth of a barometric wave is some function of the
time taken to complete an oscillation, it follows that at
Lisbon the areas of disturbance or breadths of the barometric
waves are greatest in the winter and least in the summer
months, whilst in England, on the contrary, they are greatest
in the summer and least in the winter months. It seems
probable, therefore, that at some intermediate latitude they
are the same in both halves of the year, and this latitude may
possibly be the nodal line separating a zone of high barometer
from one of low barometer.

Comparing the six years of greatest amount of oscillation
with the six years of least amount, it is shown that in years
when the total amount of oscillation is above the average, the
distribution of the increase in the different months is by no
means in the proportion of the numbers representing the mean
daily range of oscillation. The increase is much greater in
the winter than in the summer months, but in April and
September there is a diminution instead of an increase in the

60

amount of oscillation. The total increase for the six winter
months is 20*84 inches against 4-06 inches for the six summer
months, while the total amounts of disturbance for the
respective periods are in the ratio of 126* 1 3 to 76-44. The
Author adds, that the ratio of the amounts of increase in the
winter and summer halves of the year appears to increase
rapidly with increase of latitude ; thus at Lisbon it is as 5 to
1 ; at Brussels as 6 to 1 ; and at Stockholm as 8 J to 1.

Mr. Atkinson exhibited a Chart, showing at one view the
barometric oscillations during the present month of February,
as observed by him at Thelwall, and also the strength of the
wind, corresponding to each observed altitude of the barometer.

Mr. MosLEY read an extract from the Gibraltar Chronicle,
of the 1 1th February, 1861, giving details of a violent gale
experienced at that place, and on the coast of Morocco, on
the 9th of February. The barometer fell to 29*261, and it
oscillated violently during the gale, the mercury being jerked
up and down more than -100 inch. The range of the baro-
meter between the 26th January and 10th February, was
1*240 inches, the range for the whole year 1860 having been
only *865. The range for twenty-four hours, commencing 9th
February, at 8h. a.m., was -625 inch. The storm appears
to have been a cyclone moving on a southerly course. It
was encountered off the coast of Morocco, by the steamer
Egyptian, veering from S.E. by S.S.W. to N.W. It was
met with by the Indus mail steamer between Lisbon and
Cape St. Vincent, on Saturday, the 9th February, and blew
a hurricane from N. and N.E. It did not reach the coast of
Morocco until eight o'clock on the following morning. As
the occurrence of a cyclone on the Portuguese coast, moving
in a southerly direction, is unprecedented, this gale will be
further investigated.

61

Ordinary Meeting, April 2nd, 1861.
J. P. Joule, LL.D., President, in the Chair.
Mr. John Parry and Mr. Thomas Carrick were appointed
Auditors of the Treasurer's accounts for the present Session.

M. Durand Fardel, M.D., was elected a Corresponding
Member.

Messrs. Henry Brogden, John Thomas Hobson, Ph.D.,
William Alexander Cunningham, and George Robert Hay-
wood, were elected Ordinary Members.

Mr. T. T. Wilkinson, F.R.A.S., exhibited an Amulet,
which, having been worn by an African chief who was
captured in war about a century ago, had been recently
examined, when it was found that the centre boss of about
an inch and a half diameter contained an Arabic manuscript,
the translation of which, kindly undertaken by Professor
Theodores, is as follows : —

" In the name of God, the Merciful, the Compassionate ;
may God favor our* master Mohammad! With God (is) a
protection from Satan, the accursed ; with the perfect words
of God a protection from evil for all that He has created,
planted, and raised; with God (is) protection from the evil
eye, and the evil mouth, and the evil foe, and the evil enmity,
and the evil neighbour, and the evil neighbourhood, and the
agitations of the night, and the agitations of the day, all of
them, O Lord of Worlds ! God ! No God (exists) but He !
The Living, the Everlasting ! Neither sleep overtakes Him,
nor slumber ; His (is) what is in heaven and on earth ; which
of these can intercede with Him, unless by leave from Him ?
He knows what is before them, and what behind them ; but
they comprehend nothing of His knowledge, except in so far
as He pleases. He extended His throne over the heavens and
the earth, and on Him weighs not the watchfulness over them ;
Proceedings— Lit. & Phil. Society— No. 12.— Session, 1860-61.

62

for He is the High, the Mighty One 1 No compulsion (let
there be) in religion ! Since the right is distinct enough from
the wrong ; surely he that denies Tagoot (the idol) and believes
in Allah, has indeed laid hold on a firm handle, not subject to
being broken ; yea, God hears and knows ! * But He that
fears, on the part of the testator, an error, and thus settles
among them (the heirs) is not guilty ; for God is forgiving,
merciful. Then your hearts hardened, and were afterwards
like stones, and even harder : for among stones there are some
from which rivers flow ; and some burst asunder so that water
trickles from them ; and some of them fall down from the fear
of God ; now God is not unmindful of what you are doing.

" Or like him that came upon a city ruined to its foundation ;
he said : * Now, will God revive it after its death ? ' Then
God caused him to be dead for a hundred years; then He
raised him again, and said : ' How long didst thou continue
so ? ' he replied : ' I continued so for a day, or a part of a day.'
He said : ' No ! thou didst continue so for a hundred years ;
look but at thy food and thy drink, they are not yet decayed !
look but at thy ass ; whereby we will make of thee a sign unto
men ; now look at its bones, how we awake them, and cover
them with flesh ! ' Now, when this became clear to him, he
said : ' I know that God is all-powerful ! It is all the same,
•whether any one of you secret his words, or proclaim them ;
whether he conceal himself in night, or rove about in day-
light: there are for him attendant angels, before him and
behind him, and they watch over him by the behest of God ;
verily, God changes not towards a people, unless they have
changed what is in their souls ; but when God has decreed
evil upon a people, there is none to avert it from them, and
besides Him, there is for them no protector. * It is He that
shows you the lightning, for fear and for hope, and that piles
up the pregnant clouds. Yea, the thunder celebrates His

The places marked thus (*) arc conjectural (the text being imperfect), as suggested
by the context, which is a quotation from the Kuran.

63,

praise and the angels, through fear of Him ! He sends the
thunderbolts to strike therewith whomever He pleases, even
while they are disputing- concerning God ; indeed. He is
of immense power ! His name is Cayeeala Tacamamu
Daburim Buaburim Jawburim Masseeyayaramu. O God !
in Salvation ; if it is the will of God."

Mr. Wilkinson also laid before the meeting the following
Geometrical Theorems.

If from the angular points of any triangle, ABC, lines be
drawn making the same constant angles with the adjacent
sides, four triangles, AiBiQ, A2B2C2, A3B3C3, A4B4C1, will
be formed which possess the following properties : —

1. The triangles A,B,Ci, A.B^Co, A3B3C3, A,B,C„ are all
similar amongst themselves and to the triangle ABC.

2. If circles be described about the triangles A2C A, BoA B,
C2B C, they w^ill all pass through a common point P.

3. Circles described about the triangles A3BA, B3C B,
C^A C, will all intersect in another common point P.

4. If Oj, O2, Oo, be the centres of the circles in (2) ; and
O4, O5, Og, the centres of those in (3) ; then the triangles
OjOoOs, OiOgOg are similar to each other and to the original
triangle ABC.

5. The triangles O1O2O3, 040g06, are coaxial, sinc6 their
vertices lie two and two on the radials O Oi, O Oo, O O3 ;
they are therefore also copolar, or the intersections of their
opposite sides range in the same straight line.

6. The triangle OiOoOgziithe triangle O4O5O6; for
16 ABCx 0,Oo03=16 AB C X 0,0,0o= aH' -\-a^c'

7. If ri, ^2, r^i Ti, 7*5, re, be the radii of the circles in (2)
and (3) respectively, and R = the radius of the circle circum-
scribing ABC; then R^ = r^r.^'z = 7\r^rc.

8. Let f, g, h, be the intersections of A C3, C A,; A B3,
A Bo; CB3, BC2; then the lines A//, B/, Cg, will all
intersect in the same point P2.

.64

9. The products of the alternate sides of the circumscribed
hexagon are equal, viz : A/ Bg Ch— kg BA C/.

10. The properties in (&) and (9) hold good in the more
general case ; that is, when the angles A C A2 = B C Bg ;
C A C3 = B A B., ; A B A3 = C B Co ; and these angles may
be taken either internally or externally with respect to the
original triangle ABC.

Many other relations might be deduced from the appro-
priate diagrams; but the preceding appear to be the most
important.

A Paper was read by W. Fairbairn, LL.D., &c., " On
the Temperature of the Earth's Crust, as exhibited by Ther-
mometrical Observations obtained during the sinking of the
Deep Mine at Dukinfield."

During the prosecution of researches on the conductivity
and fusion of various substances, an opportunity occurred of
ascertaining by direct experiments, under favourable circum-
stances, the increase of temperature in the crust of the earth.
This was obtained by means of thermometers placed in bore-
holes, at various depths, during the sinking of one of the
deepest mines in England, namely, the coal mine belonging
to F. D. Astley, Esq., at Dukinfield, which has been sunk to a
depth of 700 yards.

The increase of temperature in descending, shown by these
observations, is irregular ; nor is this to be wondered at, if we
consider the difficulties of the enquiry and the sources of error
in assuming the temperature in a single bore-hole, as the mean
temperature of the stratum. At the same time it is not
probable that the temperature in the mine-shaft influenced the
results. The rate of increase has been shown in previous
experiments to be directly as the depth, and this is confirmed
by these experiments. The amount of increase is from 51° F.
to 57|°, as the depth increases from 5§ to 231 yards, or 1° in
99 feet ; but, in this case, the higher temperature is not very

65

accurately determined. From 231 to 685 yards, the tempera-
ture increases from 57J° F. to 75i°. This is a mean
increase of 1° in 76*8 feet, which does not widely differ from
the results of other observers. Walferdin and Arago found
an increase of 1° in 59 feet; at Rehme, in an Artesian well
760 yards deep, the increase was l°in 54*7 feet; De La Rive
and Marcet found an increase of 1° in 51 feet, at Geneva.
Other experiments have given 1° in 71 feet. The observa-
tions are affected by the varying conductivity of the rocks, and
by the percolation of water. The Author has exhibited upon
a diagram, in which the ordinates are depths, and the abscissse
temperatures, the results obtained between the depths of 231
and 717 yards. The strata of the mine are also shown in
section. Additional to these, the Author gives a Table of
similar results in another pit at the same colliery, taken
between the depths of 167 ^ and 467 yards, and showing an
increase of temperature of 1° in 106 feet of descent.

Assuming as an hypothesis, that the law thus found for a
depth of 790 yards, continues to operate at greater depths, we
arrive at the conclusion that at 21 miles from the surface, a
temperature of 212° would be reached, and at forty miles a
temperature of 3,000°, which we may suppose sufficient to
melt the hardest rocks. The Author then discusses the effect
of pressure and increased conductivity of the rocks in modifying
this result. If the fusing point increased 1°*3 F. for every
500 lbs. pressure, as is the case with wax, spermaceti, &c., the
depth would be increased from 40 to 65 miles before the fluid nu-
cleus would be reached; but as the same increase is not observed
with tin and barytes, the influence of pressure on the thickness
of the crust cannot yet be determined. Again, Mr. Hop-
kins has shown that the conductivity of the dense igneous
rocks is twice as great as that of the superficial sedimentary
deposits of clay, sand, chalk, &c. And these close grained
igneous rocks are those which we believe must most resemble
the strata at great depths. Now, if the conductivity of the

66

lower rocks be twice as great as that of the strata in which
the observations were made, correcting our former estimate, we
should probably have to descend 80 or 100 miles, instead of
40, to reach a temperature of 3,000°, besides the further
increase due to the influence of pressure on the fusing point.
On entirely independent data, Mr. Hopkins has been led to
conclude that the minimum thickness of the crust does not fall
short of 800 miles, in which case the superficial temperature
of the crust would have to be accounted for from some other
cause than an internal fluid nucleus.

A Paper was read by J. C. Dyer, Esq., Vice-President,
entitled " Brief Notes on the Nature and Action of Steam
in relation to Boiler Explosions."

He stated that several essays had lately appeared on
boiler explosions, wherein discordant theories and opinions
are offered on the action of steam in some anomalous
cases of explosion, and which may justify the bringing
before the Society a few established facts and prin-
ciples relating to the subject, in the hope of arriving at more
settled views concerning causes and effects in such cases than
appear to prevail at present among our most distinguished
engineers. The Author objected to the appeals made to Dr.
Dalton's theory of atoms for explaining the nature of steam as
an elastic force mechanically employed, since the law of
definite proportions of Dalton had no reference to elastic
vapours except as to the constituents of the liquors whence
they arise. He then cited the fact that water, like steam, is
an elastic body, and the pressure would therefore be of the
same nature and force above and below the water line in a
boiler ; but that explosions from fractures above or below that
line would have different effects, owing to the amount of
expansion of water and steam being so widely different when
issuing from similar apertures and under the same pressure.
Many obscure cases of explosion would be explained by the
more or less rapid generation of steam issuing under those
circumstances, as set forth in the Paper. That free space,
when suddenly and amply afforded, is to highly heated water,

67

under great pressure, nearly the same ^?>Jire is to gunpowder »
And this will account for the most destructive cases of boiler
explosions ; whilst those of a more harmless nature show that
the fractures were small at first, and then gradually extended.
He also objected to the term " superheated steam," as being
inapplicable to it in any state; because, when steam is in
contact with water, it will be of the same temperature as the
water; and if heated apart from water, the same laws of
expansion by heat apply to steam as to air, and neither can be
" superheated," though made very hot.

Again, steam can never be " mixed up with the water" in
a boiler when both are under the same statical pressure, and
the steam formed will rise into the chamber, so that the water
will always be in contact with the boiler except when steam
is drawn off. Still, in rapid escapes, it may drive out water
and become entangled therewith, as in many explosions.

It having been shown that most, if not all, explosions are
occasioned by simple steam pressure, acting on the weakest
parts at first, and thence extending more or less rapidly, it
would seem needless to seek for any other cause or force to
account for them ; yet, in some cases, the effects appear to
imply a more sudden and violent action, like that of explosive
compounds. In such instances, may they not arise from the
actual decomposition of the water by heat alone ? Although
we have high authority (cited) against this, yet the Autbor
held it rash to conclude that water could not be resolved into
its constituent gases by direct action of heat from the boiler
upon water pressed into contact with the metal plates. It
has been proved, long since, that by heat, in the most intense
form known to us — that of electricity — water is decomposed
and both of its constituent gases are liberated. Therefore,
since no evidence has been adduced to show that this does not
take place in any water when so confined and heated, the
aflfirmative may at least be possible, and seems probable, in
some instances, as before named.

However, he held it desirable that the question should, if
possible, be set at rest by experiment; and to this end a
method was suggested for putting the matter to a direct test ;

68

but he might not be able to make the experiment himself, and
hoped it might be done by some one more competent to the
task.

SECTION FOR STATISTICS AND SOCIOLOGY.
March 12th, 1861.
A Paper was read by Mr. Thos. R. Wilkinson, furnishing
statistics connected with the sale of beer and spirituous liquors,
with a view to enquire whether such sale had any effect on
the criminal returns, and how far the legislature would be
justified in a further interference with it.

The number of licensed victuallers in the United Kingdom

in 1860, was 107,024, and the number of beer sellers, 45,198.

The licensed victuallers represent interests which directly

concern £50,000,000. worth of property, and maintain

1,000,000 of people.

The revenue derived from beer and spirits in the year 1832,
was £15,000,000., or 29-41 per cent, of the whole revenue.
In 1858, this revenue amounted to £21,000,000., or 31-34
per cent, of the whole revenue. The increase of this revenue
had been 40 per cent., whilst the increase of the population
was 25 per cent.

In 1831, the amount derived from licenses for the sale of

£. £.

Beer amounted to ...273,871 And the year 1859 to... 384, 178

Spirits „ ...395,697 „ „ ...563,400

Wine „ ... 73,026 „ „ ... 88,238

£742,594 £1,035^816

An increase of 39*62 per cent.

An Act for closing public houses, from Saturday night at
Twelve o'clock, until One o'clock on Sunday, came into
operation in 1847-8.

For eight years before the passing of that Act, the annual
averao-e number ^of persons taken into custody by the Man-
chester police was 10,658, whilst after the Act was passed the
annual average was only 5,37 1 .

69

MICROSCOPICAL SECTION.
18th March, 1861.

A communication from Captain Anderson, R.M.S.
"Canada, written at sea on his homeward voyage, excited
considerable interest. He states that Dr. Wallich's pamphlet
would be communicated to the Boston Society of Natural
History by Professor Agassiz, who was particularly interested
in the Ophiocoma found at so great a depth. The Professor
is now engaged in preparing a work upon the natural history
of that class of echinoderms, which he has studied for many
years, and claims to have the finest collection of those animals
in existence, made on the coasts from Greenland and Labrador
to Mexico and round Cape Horn to California. Since the
pubHcation, in 1848, of the "Principles of Zoology," by
Agassiz and Gould (a copy of which is presented to the
Section), the Professor has ascertained that the system of
tubes and water pores, described at page 1 23, exists in all
animals which much vary their depths of water in the sea, and
in the herring they may be seen with the naked eye along
the side of the neck.

With reference to the removal of tallow from soundings,
Dr. Hayes, the Assayist for the State of Massachusets, stated
to Captain Anderson that heated turpentine, poured amongst
the soundings, will remove all the tallow with it through filter-
ing paper ; the operation should be twice repeated, and the
residue finally washed with sulphuric ether.

Dr. J. Bacon presented a copy of his Report upon the
Chemical Composition and Microscopical Characters of the
Pearl, said to have been formed in the interior of a cocoa nut
at Singapore, in the possession of Frederick Bush, Esq., and
exhibited by Dr. Winslow.*

Captain Anderson, in a very able manner, gives the outline
of a plan which has occurred to him for rendering available to

* Page 290, vol. vii., Proceedings of the Boston Society of Natural History
for 1860.

70

science the services of commanders of merchant vessels and
seamen generally, in collecting specimens of natural history
and information in natural science, whether in zoology,
ethnology, botany, or meteorology, for which they have such
facilities in all parts of the world, for the use of those scientific
institutions which may desire to join in it, and also with a
view to elevate the mercantile marine of England in the social
scale by stimulating a taste for such knowledge amongst sea-
lanng men. The consent and co-operation of shipowners will
of course be necessary, and Captain Anderson seeks the
additional influence of merchants and scientific bodies. The
subject met with the unanimous approval of the members
present; and it was resolved that the portion of Captain
Anderson's letter relating to it should be published at the
expense of the Section, for the purpose of eliciting opinions
upon the feasibility of the scheme and upon the best practical
method of carrying it into execution.

Commander M. F. Maury, U.S. navy, forwarded copy of
a letter from Lieutenant John M. Brooke, the inventor of
the Detaching Deep Sea Sounding Apparatus, and enclosing
for the Section a number of soundings from the North Pacific
Ocean, which were obtained with small twine and spherical,
weights of about 701bs., which were detached upon contact,
and left at the bottom of the ocean ; Lieutenant Brooke
observes, that " Nine consecutive casts (soundings), varying
from 2,000 to 2,900 fathoms, were made with the same piece
of twine and detaching apparatus, w-hich last weighed less
than lib." As the specific gravity of a wet flax line
is nearly that of water, a line that can he pulled down
by a weight, may be pulled up by hand, provided the weight
he detached at the bottom. One of the specimens obtained
in 3,030 fathoms, nearly three and a half miles, is the greatest
depth from which material has yet been brought up from the
ocean bed. Lieutenant Brooke sent also a few specimens
obtained by soundings in shallow waters, on the east coast of
Niphon, Japan, by him during his boat voyage from Simoda
to Hallodadi in 1855, under the orders of Commander
Rodgers, U.S. navy.

71

Mr. BiNNEY described to the Section the appearance of cer-
tain nodules found in the middle of a seam of coal, in the lower
part of the Lancashire coalfield, which contain fossil wood
associated with marine shells. Specimens of the former were
exhibited to the members, the most perfect of which was that
of Sagenaria, the old Lepidodendron elegans, in transverse,
parallel, and tangential sections. The marine shells associated
with the fossils belong to the genera Aviculopecken,
Orthoceras, Nautilus, &c.

Mr. Brothers exhibited a Section of Pearl, Isthmia
nervosa, infusoria, &c.

Mr. Wh ALLEY exhibited living DiatomaceiT from Southport.

PHYSICAL AND MATHEMATICAL SECTION.
Annual Meeting, March 28 th, 1861.
Mr. E. W. BiNNEY, F.R.S., F.G.S., &c., in the Chair.
Professor Clifton, of Owens College, was elected a
member of the Section.

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

President, Mr. Robert Worthington, F.R.A.S.

Vice-Presidents, jf/' ^"^"^^"i,^;^-^'^-^*'
iMr. BiNNEY, F.R.S., F.G.S.

Treasurer, Mr. George Mosley.

Secretary, Mr. Thomas Heelis, F.R.A.S.

A Paper was communicated* by Mr. Atkinson, from T. T.
Wilkinson, Esq., F.R.A.S., of Burnley, entitled, " Geome-
trical Theorems relating to the Triangle and its Inscribed and
Escribed Circles."

Many curious properties of these two figures have been
taken notice of by mathematicians, but the following theorems
Mr. Wilkinson looks upon as new.

1. Let A B C be any triangle, O O O2O3 be the centres
of its inscribed and escribed circles respectively; then the
twelve circles described about the component triangles of the
complete quadrilaterals O O2O1O3, OiO OsO., O OiOgO., will
pass, four and four, through ABC respectively.

72

2. The centres of the twelve circles which circumscribe the
component triangles of the three preceding quadrilaterals, lie,
two and two, in six points which are in the same circumference
ABC; and the lines Ofio, OoOg, O5O7, are each diameters
of this circle, and intersect at its centre.

3. If perpendiculars be let fall from any angle of a triangle
upon its internal and external bisectors of the other two angles,
the four points of intersection, in each case, will range in a
straight line.

4 . If A m and A w be two of these perpendiculars, the diagonals
of the rectangle Am B n bisect each other, and consequently,
the ^.raight lines in theorem 3 pass through the bisections of
tliQi sides A B, A C, B C, respectively, thus forming a triangle
*tif^ t equal to one-fourth of A B C.

^ 5. If from any point in the directrix of an ellipse there be
drawn two tangents to the curve, and if these be produced to
cut the auxihary circle upon the major axis in X and Y, then
if X Y be joined, the line X Y will pass through the centre
O of the ellipse.

6. Conversely ; if from the extremities of any diameter of
the auxiliary circle on the major axis there be drawn tangents
to the ellipse, they will intersect on the directrix.

The demonstration of some of these theorems is easy, and
of an elementary character; that of others depends upon con-
siderations which have been advanced by the Author in some
of his papers that have appeared in thQ Ladies and Gentlemen's
Diary.

Mr. G. V, Vernon, F.R.A.S., produced Manuscript
Copies of thirteen years Barometrical Observations made at
Greenwich, which had been kindly communicated by the
Astronomer Royal, showing the observations once a day for
every day instead of the daily means, and presented such
series to the Section, for which present he received its thanks.

Resolved, that the Secretary be requested to prepare and
issue a circular, applying for copies of Logs and Meteorological
Observations made at sea, and especially on board the various
mail steamers.

73

Ordinary Meeting", April 16, 1861.

Dr. J. P. Joule, President, in the Chair.

A letter having been read from Dr. Schunck, tendering-
his resignation of office as Secretary of the Society, it was
unanimously resolved, " That the Society desire to express
their regret at the resignation by Dr. Schunck of the office of
Secretary, and to offer to him their cordial thanks for the
valuable and efficient services which he has rendered to the
Society during the six years he has held the office."

Mr. E. W. BiNNEY exhibited to the meeting two specimens
of peat obtained by himself from the low mosses adjoining the
sea near Southport. One was a dull brown substance, having
an imperfect conchoidal fracture, and which burnt and smelt
like Derbyshire bitumen. This he called blazing peat.
The other was of a bright black colour, with a perfect con-
conchoidal fracture, which looked like pitch and emitted
scarcely any flame whilst burning. This he called non-
blazing peat. He said that bitumens and coals were generally
supposed to have been formed under an elevated temperature,
something analogous to the production of tar and pitch by the
distillation of wood in close vessels at a high temperature.
Now, the specimens exhibited showed that vegetable matter
could be converted in a peat bog into an inflammable bitumen
in the one case, and, in the other, into a bright substance
resembling anthracite coal, thus showing that high tempera-
ture was not absolutely requisite for the production of either
bitumens or coals from ligneous fibre.

A Paper was read by the Rev. T. P. Kirkman, M.A.,
F.R.S., entitled, "Theorems on Groups."

PaoCEEDiNGS— Lit. *S; Phil. Society— No, 13.--Session, 1860-61.

74

The following theorems form part of a Memoir presented
to the Imperial Academy of Paris, in competition for their
prize medal which was offered in 1858, to be awarded in 1860.
The subject proposed is —

" Quels peuvent etre les nombres de valeurs des fonctions
bien definies qui contiennent un nombre donne de lettres, et
comment pent on former les fonctions pour lesquelles il existe
un nombre donne de valeurs ? "

No prize has been awarded, and the report of the Referees
gives no details of the Memoirs presented. Comptes Rendus,
Mar., 1861.

The Memoir which I had the honour to present to the
Academy contains numerous results, which 1 believe to be
new, and which at least are so far important that they are
contributions, I hope, useful and pregnant, to a direct answer
to the prize question.

I may be permitted to mention what appears to me to be
more or less important, as well as new, in my results.

1. The enumeration of groups of forms already known, but
not enumerated.

2. The definition and enumeration of large classes of
groups which were before, so far as I can learn, unknown.

3. The discovery of the third and principal species of
substitutions in grouped groups.

4. The determination of the number of equivalent m-valued
functions that can be constructed on a given group ; i.e., of

functions of the same degree, of which none is among the m
values of another.

The mathematician will remark that there is a little con-
fusion of ideas in the writings of the most recent French
investigators, about the relation of groups and functions.

75

I cannot find that either Cauchy or any of his followers
have ever suspected that on the group

12 3 4 5 6

2 14 3 6 5
can be constructed any grouped group of six except this,

12 3 4 5 6

2 14 3 6 5

3 4 5 6 12

4 3 6 5 2 1

5 6 12 3 4

6 5 2 14 3

It is laid down in one of the last French contributions to
this theory (vide pages 22, 32 of " Theses presentees a la
faculte des Sciences a Paris, &c.," Paris, Mallet Bachelier,
1860), as a point apparently too plain to require demon-
stration, that there are in a grouped group two species of
substitutions, ^^ deux especes de substitutions, hien distinct esi"*

1. those whereby the elementary groups simply change
places among each other ;

2. substitutions whereby, the elementary groups being
undisturbed, displacements of letters are effected exclusively
iij their interior.

The truth is, that there is a third species of substitutions
which occurs in grouped groups more frequently than the
other two, whereby both the elementary groups are permuted
and also displacements of letters take place in their interior.

For example, there exist the three following groups con-
structed like the preceding on the partition
N=6=2-3=A«.
123456 123456 123456
214365 214 365 214365
346512 435612 345621
435621 346 5 21 436512
561243 651243 562143
652134 562134 651234
in which there are substitutions of the third species*

1^

In the theorem H which follows, I have exactly enumerated
a very large and well defined family of grouped groups, of
which only a small portion had been before detected, without
attempt at enumeration.

When the exponents in the denominator of the derivant Q
are all unity, the groups contain only substitutions of the two
first species : in other cases there are substitutions of the third
species also.

I hope that my theorems on the connection between groups
and the functions constructible on them, will be deemed of
some importance.

I remember well the embarrassment I felt in asking myself
the simple questions; 1st. What is the group to which the
3-valued function ab-\-cd belongs? 2nd. What is the general
theory of the connection between the group and the function ?

I know not where an answer can be found to these inquiries,
except in my own Memoir.

The most important addition that has been made in France
to our knowledge of this subject since the days of Cauchy, is
a Memoir in Liouville's Journal, January, 1860.

And I beg here to express my admiration of the demonstra-
tion there given of the existence of functions of jf variables,
-which have

1.2-3 • • (p''—2)
values, whenever j? is a prime number.

It appears to me that the use there made of the impossible
subindices invented by Galois, is a very high analytical
achievment.

I had succeeded in both finding and completely enumerating
these groups for yz:= 1, before I had the pleasure of reading
the demonstration of the more general theorem.

Proof of the confusion of ideas that has reigned may be
found in the Paper referred to in the " Journal of Liouville."
The corollary at page 20 is not demonstrated, neither is the
enunciation true; and there appears to be an oversight all

77

through of this principle, that in order to prove that a function
has K values, it is not enough to show that it is invariable for
a certain number of substitutions. It is required also that it
shall be proved to be variable for all other substitutions.

There is an infinite number of functions which answer the
definition of M. Mathieu, and are invariable for the substitu-
tions which he considers, which yet have not the required
number of values.

This question of groups, contrary to the very frequent
custom of the Academy for a length of years, has been with-
drawn from competition, after being proposed once only, viz.,
for 1860. I can only say that I regret this, and I wish that
the Academy had given one chance more to the improved
notation which they have done me the honour to commend.

It is to be hoped that a question which has been long under
consideration, with no great result, and which, in my humble
opinion, has somewhat been retarded by the too great generality
of Cauchy's notation of substitutions, may soon receive a satis-
factory solution.

The numerals in what follows refer to the articles of my
memoir, which has been so peacefully buried, I hope alive,
though without name or record, in the " dark unfathomed,
caves'^ of waste paper in the French Institute,

Theorems on Groups.

" Def. Let A^, A^ A,, be any arrangements of the same N
elements 1 2 3 . . N.
The operation : —

executes on A^, the substitution ^, by putting for the element

a in A^„ that which stands over a in the substitution. The

result is the permutation A/, or, what is the same thing, the

A A
product of the two substitutions, —^ .-fU in that order, where

78

(I) denotes the natural order of the elements, is the sub-
stitution — ' ."

" Def. A system of R arrangements of N elements
(1) Ai A2 • • • A,_i
is a group of k substitutions.

(1) Ai 42 . . .
(1)' (1)' (1)'

if both the products A A„ and A« A„» are substitutions of the
group, A,„ An being any pair of the group."

" Def. Let G be any group of k substitutions made with
N elements not containing the substitution P. The product
GP = (1 + Ai + A2 + • • + A,.0 P.

is a vertical column of k permutations —

P
AiP
A2P

which differs from G written in a vertical column only in the
horizontal order of entire vertical rows of elements,
GP is the derangement of G by P."

Theo. ''The derangement (GP) of G by P is the
derangement of Gby A,„P, A being any substitution of G.*'

G has ^^ different derangements; (ttN^I 2 3 • • N).

Def. '' The product PG of the same P and G is the
derived of G by P"

Theo. " The derived (P G) of G by P is the derived of
G by (P A,.)."

G has ^different derived groups (PG.)

Let P-^=:^^ ;

Def. The groups G and PGP"^ are equivalent groups
containing (I), if they be not the same group (1 Ai Ao • * A^-i),

79

Def. If PG and GP are the same group of permutations,
PG is a derived derangement of G.

(8) Theo. A. The ^ derived groups of G (including G),

Hi

are derangements of the groups G G^Ga * * G^ equivalent to
G ; and there are among these derived groups neither more
nor fewer derangements of G than of any group equivalent
to G.

(9) Cor. If the number of groups equivalent to G is

^-—^ G has has no derived derangement, except itself; and
n

every derangement of G is a group of permutations different
from every derived of G. The same thing is true of the
derangements and derived groups of every equivalent of G.

If the number of groups equivalent to G be fewer than that
of its derived groups, we know that G has derived derange-
ments.

If M be the number of groups equivalent to G, -^^^ is the

number of derived derangements of each (G^) of these equiva-
lents (including (G^) in this number), which are found among
G and its derived groups.

Each of the equivalent groups G Gi . . . G^ forms with its
derived derangements a different group (containing (1)) of

-TTT- substitutions.
M

I believe that this theorem A (8) and the corollary (9) that

follow it, are among the faits noiiveaux of my Memoir.

They lead directly to all the enumerations and extensions

following.

(10) Theorem B. The number of different groups of the
order N (1, A, A^ . . Af^-^) made with N elements, which

are N powers of one substitution, is ^ ^^~ ^, R^ being the

number of integers less than N and prime to it, unity
included.

80

I believe that this enumeration, though I think it a little
surprising, is new.

(11) Theorem C. Let N=A«+B6+Cc-}- . . + 3j,
A7B, B7C, . . FZJ, a, b, c, . . ,j being any integers
yO, and let K be the least common multiple of ABC ... J.

The number of different equivalent groups, each being K
powers of a substitution having a circular factors of the order
A (i,e, of A elemnts), b circular factors of the order
B .... 7 circular factors of the order J, is

^___ZN ^__

^^— R^ Ta-TTb • • • Trj'A^'BT' • • J^ '

where Rk is the number of integers less than K and prime to
it, including unity.

I believe that this enumeration also is a /ait nouveau : and
it is fundamental.

(16) Theorem D. If there be, among the R^_ 1 integers
less than N and prime to it, a prime root of the congruence
a;'— 1=0 (mod. N),

where ;• ^ R,y,

we can form with N elements -^-^ equivalent groups

(I Ai Ao . . . ) each of Nr substitutions, among which will be
found the N powers of a substitution of the order N.

And if there are m prime roots of this congruence of which
none is comprised among the powers of another, according to

this modulus, we can form m* -X^ ^different equivalentgroups

of the same description.

(18) Cor. With the N elements we can form ^ jf^

equivalent groups of 2 N substitutions, each comprising N
powers of one substitution, and N square roots of unity.

I believe that this theorem D, and the corollary, present
what is new.

81

(35) Theo. E. If N— 1 be any prime number, we can
form TT (N — 3) equivalent groups, each of N • (N — I) (N — 2)
substitutions.

The enumeration of these groups is, as I believe, new.

(46) Theo. F. If N > 5, it is impossible to construct a
group of N • (N— 1) (N— 2) (N— 3) substitutions, which
contain N powers of one substitution.

(53) Groups of the form G-\-RG, R G being composed
of square roots of unity,

Theo. G. Let

N=:A«+B5-l-Cc-i- • • • + J/
when A72 ; A7B7 • • 7 J, and where one at least of a 6 • *j
is 71.

Let K be the least common multiple of A B C * ' J, and
let Hk be the number of integers (unity included) less than K,
and prime to it.

There are

ttN

equivalent groups of 2 K substitutions of the form G-}-R G,
where G is the group of K powers of a substitution having a
factors of the order A, b of the order B, etc. ; and where R G
is composed of K square roots of unity. I believe that this
is new.

For example, take the partition

6=3'2=A(/.

There are 20 groups G by theor. C; and 60 groups G+RG
by thcor. G. Let G be

12 3 4 5 6 -

4 6 13 2 5

3 5 4 16 2
1?

82

We have the three equivalent groups

123456 123456 123456

4 61325 4 6132 5 4 61325

35416 2 3 54162 3 54162

124 3 65 15 432 6 164352

351426 361452 321465

4 6 3 15 2 4 2 3 16 5 4 5 3 12 6
H Hi Ho

These are equivalent groups, for we have

Hi=l 64352H16435 2=P H P"^

H2=nl 5 4 3 2 6 H 1 5 4 3 2 6c=Pi H Pf'-

Grouped Groups.
Def. A principal substitution P of a group G has the form
/P = Aa + B5 -I- Cc+ . . J/,
A-7B7 . .7 J,
which means that P has a circular factors of the order A,
b of the order B, etc. Every other substitution Q of the
group has the form

/Qr:zA,«i + BA + .. + Ji;;^

such that the first of the differences

A — Ai, a — Gi, B — Bi, 5 — ^1, . . .
which is not zero, is positive. If they be all zero, Q is also
a principal substitution.

C6. Theo. H. Let any partition of N be
N = A« -f BS + Cc + . . -f Ji ,
A7B7C. . .7Jy 1.
K being the least common multiple of A B C , . J, and such
that one at least of a b . ,j is 7 1.

Let G be any one of the W groups of K powers of a sub-
stitution constructible on this partition of N, by Theorem C,
Letpip. . . .i?«, g q ' ' -q r r , , ,r etc.

a+l rt+2 a-\-b «+&+! rt+J+3 «+6+c

be the circular factors of G of the orders ABC,', etc.
Let pi be the i^^ cyclical permutation of /?^.

83

Let tv equivalent groups be eonstructible of / substitutions
made with a+ b -\- c -\- . .j elements, of which the a elements
are consecutive in unity, the b elements consecutive, the c
elements consecutive, &c. ; and such groups (g) that every cir-
cular factor in them made of the a elements is a divisor of A,
every circular factor made out of the b elements is a divisor of
B, &c. ; and also such groups (g) that every vertical row is
composed only of the a, or only of the b, &c. elements.
Any one {g^) of these groups (g) begins by the power of a

principal substitution (P^), whose form is, by hypothesis,

/Pi = A,a, + Km, + K,a, + • • (= a)

+ B,3i + B,&, + ^A + • • (= + ^)

+ C,c, + C,e, + C3C3 + • • (= + c)

+ jji + ^-2h + ^zj\ + • • (= +y)

this being the partition of « + 6 + . . . 4- j*, in which the
equivalent groups {(g) are formed either by theo. C or by any
of those which follow.

Let M be the least common multiple of the integers—

AAA ILL A A 111 A -^ —

Ai ' A2 A3 Bi B2 • • • Ci a

whose denominators are the orders of the circular factors of the
complete group {g^)^ being Ac of the a elements. Be of the b
elements, &c.

Let the substitution Q following be formed :—
ABC HE L

Q =.

when (a /3 7 • • ^ 1/ • • • • c • • • . is) every one in turn of the
/ — 1 substitutions of the group (^^), a /3 7 ' * ' 6, being the
a elements, jj • • • • being the 6 elements, £ • • • being thee elements,
&c. ; and where the terms of the numerator are those of the
denominator in different order, so that B = ^^ if /3 = 3, &c.

84

and where the exponents of the factors /),- are anything- we please
Z A + 1, the exponents of the factors q,- are anything we
please, Z B + 1, &c., and where the same system of exponents
is employed in the denominator through all the / — I substitu-
tions Q to be formed.

The I — 1 derived groups QiG, Q^G, QjG, form with

G a grouped group of K/ substitutions, and the number of
such grouped groups constructible on the given partition of
ISIis

Rj,M wt^(A«-rr • • X EM-'r • • X . . X J-^-rr • •)

K (X K + (/— X) Kx)
where X is the number of the principal substitutions of the
group g^ when their form is

A «i (=^)

and where X =0 in every other case R/, is here the number
of integers less than K and prime to it, unity included.

The number of principal substitutions in each of the S
grouped groups is

X K + {l-X) \\^

The elementary groups (p) of these grouped groups are
groups of K substitutions ; and each group ((>) is composed

K

of a vertical column of— ^ square groups of powers of a sub-
stitution of A elements, or of a column of— ^ square groups

of powers of substitutions of B elements, &c.

These grouped groups, w'hose elements (^)) are made up of
groups of A powers, or of B powers, are grouped groups of the
first class.

(70) In theorem H we have restricted the auxiliary groups
cj of the order / to such as have no circular factors, formed
with the a elements, whose order does not divide A, etc. By
this limitation we have exactly enumerated a definite and
large class of equivalent grouped groups.

85

But, if this limitation be removed, the constructed group
of K/ substitutions is still a grouped group. But it is not easy
to give the exact enumeration without repetition of the con-
structions, when g may be any group of /, made with the
a -\-h •\- ' +7 elements. Every group of the order K/ so
formed by any group g^ whatever be the order of its circular
factors, is a grouped group, whatever be the system of expo-
nents that we employ in the denominators of Q^ Q. Q3 • • • •

(83) Grouped groups of a higher class^ of which the
elementary groups are of the order Kr, comprising r — I
derived derangements of groups of K powers of a substitw
tion. We first enunciate generalisations of theorems D and G*

Theorem J. Let

N = Aa -f B5 + Cc + • • -f Jy;
Ay 2; A y B y C y ' 7 J ; a, b, c, " j being any numbers,
and K being the least common multiple of A B C * • J.

Let X be the number of primitive roots of the congruence
x''^^l (mod. M) (r 7 2),
of which no one is comprised among the powers of another,
M being any one of the numbers A B C • J, these X roots
being such as are at the same time primitive or non-primitive
roots of the congruences

ic**^! (mod. X)
where X is each one in turn of A B C * • • J.

VVe can construct, R;r. being the number of integers (unity
included) less than K and prime to it,

Y X7r(N)

R^TT air birc ' ' ' A'' B' C ' ' 3'
different groups each of Kr substitutions, all of the form

G + e^G + e.G-f-'-f e,_i g,

where G is a group of the order K, and Gj Oo are derivants
given in terms of one of the X primitive roots. I'his theorem
J is, as I believe, a fait nouveau*
(84.) Theorem K.

86

Let N=:A-rt + B i + C c + . . + Jy,

A7B7C7..7J; K being the least common multiple
of A B C . . J, and ahc..j being any numbers.

Let E < K be any one of the numbers A B C..J;
and let E— 1 be a primitive root of the congruence

a'" ^ 1 (mod. M).
M being any one of the uumbers A B C . . J ; and such a
root that it is also a root, primitive, or not, of the congruence

x'' ^ 1 (mod. X),
X being one each in turn of the numbers A B C . . . J.

We can form by the aid of this root E — 1, on the given
partition of N, Rjc being as in theorem J,

E'^TTN _ y

R, Tra • 7rZ> • • • TTJ A« B* • • • J^ ^'

equivalent groups of Kr substitutions, e being the multiplier
of E in the partition (Aa + BZ> + . .) of N. These groups
are all of the form

G + 0iG+e2G+.. + e,_i G,
when G is any one of the W groups of theorem C*
For example, let

N=:26=:10-l-f 8-2+4-2 (E=40).

We have the primitive root 4—1 of the congruence

x',^1 (mod. 10) (Ee=4-2)
which is also a root of the congruences

x^^i (mod. 8) and
x^=^l (mod. 4).

One of theW:- ''"^^^^

R,o(«-.2)-nO-8--4-
groups G of theo. C is

1234567890 abed efg h ij hi m n ]) q =G
2345678901 bed efg h a j kli np q m
3456789012 c d efg hab hlij p q m n
4567890123 d efg hab c lijk qmnp

of 40 substitutions (1 A A" . . . A'^l)

87

We have the derived groups
3692581470 cfadgh eh jilh qpnm =01 G
&^2 o%\ 4:1 OZ fadgh ehc ilkj pnmq
9258147036 adghehcflhjinmqp

9876543210 ahcd efg h ij hi mnpq =9^ G
8765432109 bed efg ha jkli np q m
7654321098 cd efg hah hi ij p qmn

7418 5 29630 cfa dgb eh j ilk q p m 7i =QJ3[.
4.1 S 5 29 6S0 7 fadg behc ilkj pmnq
18 5 2 9 6 3 0 7 4 adgbehcflkji mnqp

which form with the group G a group of 160 substitutions.
We can form 4] diiferent such groups on this group G, with
this root 3.

I believe that this theor. K is new.
(89) Theor. L.

Let J be any group of Kr substitutions formed with N
elements on the partition

being composed of any a equivalent groups, the same or
different, formed each with A elements, of any b equivalent
groups formed each with B elements, etc. ; these equivalent

88

groups being all, either with or without repetition of their sub-
stitutions, of the order Kr.

Let F be any group ( 1 Bi Bo • • • ) of ^ substitutions formed
with

a^h^c-\- • • • 4-i
elements, in which the first a vertical rows contain only the
a elements, the h following vertical rows contain only the b
elements, etc.

Every pair of groups JF gives a grouped group of Kr/
substitutions, of which the elementary groups are the above-
named equivalent groups of K;* substitutions.

The equivalent groups of Kr substitutions which compose
J, may be any of the groups enumerated in the preceding
theorems.

It is difficult to determine how many of these groups of
K/7 substitutions can be presented as grouped groups of K/
substitutions of theor. li. But there is an enormous number
of them which cannot be so presented.

For example, take

We have the group J of Kr—Q substitutions,
123 4 56789 =J

2 31 564 897
312 645 978

213 546 879
321654987
132 465 798

We can take for the auxiliary group either
F = 12 3 orFi=l 2 3

2 3 1 2 3 1

3 12 3 12

1 3 2
3 2 1

2 1 3

89

By the first we can add to J

456 789 12 3 =Qx J

564 897 231

645 978 312

546 879 213

654 987 321

465 798 132
and 789 123 456 =Q8 J

897231456

978 312 564

879 213 546

987 321 654

798 132 465
forming a group J + Q. J + Q, J of 18 = 3 • 2 . 3 = Krl
substitutions.

By the latter we can add farther,

123789456 r^QgJ

231 897 564

312 978 645

213879546

3219 86 654

132798465

and 789456123 zzQ^J

897 564 231
978 645 312
879 546 213
987 654 321
798 465 132

and 456123789 =:Q, J

564 231 897
64531297S
546 213 879
654 321 987
465 132 798

thus completing a grouped group of 3 ♦ 2 • 6 = K/7 substi-
tutions.

c

90

Neither the group of 18 nor that of 36 can be presented as
a grouped group of K/ substitutions of theorem H, like
the following of K/ = 6 • 3 substitutions.
123 456 789 789 123 456 789 456 123
231564897 897231564 897 5 64 231
312645978 978312646 978312645
45v3 789 12 3 123 789 456 456 123 789
564897231 231897564 564231897
645978312 31297864 5 645312978

Woven Groups.

(95) " Let N - A + B.

Let G be any group of L substitutions, formed with A
elements, and G\ be any group of L^ substitutions formed with
B elements following the A in unity. We can always form
a woven group of LL^ substitutions. There is nothing to
]>revent (5 and G^ being themselves woven groups.

€. g* the two woven groups : —

12 3 4 5 and 6 7 8 9
2 3 1 4 5 7 6 8 9
31245 6798
12354 7698

2 3 15 4

3 12 5 4

will form a woven group of 24 substitutions."

Woven Grouped Groups.

(96) The grouped group J+Qi J+QJ of (89) of 3'2'3=
hrl substitutions can become a woven grouped group of
6^'3=:648 substitutions. For J can be woven into a group
of G^ thus :

123456789 123546789

123456897 123546897

123456978 123546978

123456879 123546879

123456987 123546987

123456798 123546798 &c,

91

123 564 789

123 564 897

123 564 978

123456879

123 456 987

123 456 798
Let tbis woven group of the order 6' be Jj ; then
J^+Qi Ja+QzJa is a grouped woven group of 648th order.
(99) Theorem M.

Let N=A«-i-BHCc+ . , +J;' ;

A-B B-C C-D

Let Mb be the number of groups equivalent to a group G ,
(including G^ in this number) formed with R elements, of S^
substitutions, and such that G.i shall not be equivalent to G^
even though A=r B.

Let Fr be the entire number of groups, of/,, substitutions,
that can be formed (containing unity) with r elements.

We can construct with N elements, upon the given partition
of N, and with given groups G,i G^ * * G/,

ttN • F„ F, F, ' • F, (yhYiMMMaY' • ' (Ujy
Tra' Trb • TTC" ttJ ' (^A)" (B)'^ {"^'^'f ' ' (''"J/

woven grouped groups each of

substitutions.

For example, on the partition,

10=::3 • 2 + 2-2=:Aa + BS,
where we have

M3=1 = M2 = F2,
we can form

""' , = 6300

2 • 2 • 62 • 2-
woven grouped groups, each

32 . 22 . 2 • 2 = 144 substitutions, (8^ = 3),
ot of

g2 . 2^ . 2 • 2 = 576 substitutions, (S^= 6).

92

And on the partition,

10 = 3 . -f 3' • r + 2 • 2, (M3 = 1 = M/ = M2 = FO
we can construct, if we take S3 — 6 8^3= 3 ;

ttJ^

1 • 1 • 2 • 6 • G • 2^

woven groups each of G • 3 • 2' • 1 • I • 2 — 144 substitutions,
all (iilferent groups from those above enumerated.

(1 00) If we take for each of the r groups Gn the R cyclical
permutations of 123 • • R, and write

Sji =: R, 4 ={'^r),
we obtain the group of

A" B^' C J' Tra Trb TTC ' ttJ
substitutions of which Cauchy has demonstrated the existence
in the I Xth section of his "Memoire sur les arrangements," &c.,
in the Exercises de Malhanalique et de Physique Analytique.
It is evident that the largest woven group constructible on
our partition of N is of

(ttA)'* (wBy {vCy ' ' ' Tra-Trh ire • ' ' ' —Q
substitutions. This group has no derived derangement, i. e. it

is a maximum group, and has equivalent groups, itself

included.

This theorem M is, as I believe, in that generality, new.

On the Construction of Functions.
(104) Theo. N. Let G be any group (I Ai A2 • * Al-i) of
L substitutions, made with N elements (12* • N).
Let

p _- a /3 7 . . . e

Jl — Xi X.^ X-^ X^

be the product of N different powers (7O) of the N vari-
ables a?! rcj • • • • ic ,
Let

be the sum of the N terms, obtained by performing on the
subindices of P the substitutions of G.

93

* will have -^^^ values by the permutation of the N variables,

JLi

which can be formed upon G and its ^ 1 derived groups.

And the number of different functions O, all of the same
algebraic degree, of which no one is a value of another, is the
number of groups equivalent to G.

Theo. P. Let G be any group of L substitutions.

Let

i Xl 1-^ X;i • Xy

Where

be a term such that it changes in its algebraic value by the
operation MP performed on its subindices, where MG is
any derived derangement of G, and such that no group
equivalent to G gives the same algebraic function,
$ = r, + R+- + P^

with G. The function O has — — values, which are con-

XJ

structed on G and on its — — — 1 derived groups.

Theo. Q. If two equivalent groups G and G^ of L substi-
tutions give for a certain system of exponents of XiX-z" x^ the

same algebraic function <I>i, <I>i has not ^^-^— values.

Theo. R. The number of groups equivalent to a group G
being given, and any system of exponents of Xi x-> • • Xy being-
selected, there is always an assignable number of algebraic
functions,

0 = Pi + P2+-- + P^
of the degree determined by that system, such that each

7r N
function has '--— values, and that no function is a value of

another.

1 . There are three equivalent functions, and no more, of the
6th degree, made with four letters, which have each six values.

94

2. There are three equivalent functions, and no more, of the
6th degree, made with four letters, which have three values.

3. There are two functions, and no more, of the third
degree, which have each three values.

4. There are two functions, and no more, of the second
degree, which have each two values.

5. There are six equivalent functions, and no more, of the
10th degree, made with five letters, which have each six
values.

6. There are three equivalent 6-valued functions, and no
more, of the 6th degree, made with five letters.

7. There are two 6-valued functions, and no more, of the
fourth degree, made with five letters, and these are the
simplest 6-valued functions of five letters, one of twenty,
and the other of ten term.s, of the form xr x^ x^,

8. There are six 12-valued equivalent functions, of the 10th
degree, and no more, made with five letters.

9. There are two 12-valued functions, of the fourth degree,
and no more, made with five letters.

10. There is one 12-valued function, and no more, of the
3rd degree, made with five letters.

11. There are six equivalent 24-valued functions, and no
more, of the 10th degree, made with five letters.

12. There are three equivalent 24-valued functions, and no
more, of the 6th degreee, made with five letters.

13. There is one 24-valued function, and no more, of the
4th degree, made with five letters.

14. There is one 24-valued function, and no more, of the
3rd degree, made with five letters.

15. There are ten equivalent 10-valued functions of the
10th degree, made with five letters,

16. There are six equivalent 6-valued functions, and no
more, of the 15th degree, made with six letters, each term
having five diff*erent exponents.

95

17. There are three 6-valued equivalent functions, and no
more, of the 10th degree, made with six letters, each term
having four different exponents.

18. There are two 6-valued functions, and no more, of the
7th degree, m-ade with six letters.

19. There are two 6-valued functions, and no more, of the
6th degree, made with six letters. One of these is, putting
P2'3 4 for xixlx^oh,

P223 4 -f snH 2 + 6-423 1 -f 22421 5 + 52224 6

-I- 52426 1 -I- 62223 5 + 22125 6 -1- 62325 1 + 12326 4
-I- 32122 5 + 32622 4 + 52322 6 + 2262 1 4 -|- 52622 1
-f 625*4 3 + 12425 3 + 12524 5 4- 52423 2 + 32421 2
4- 22321 6 + 5222123 + 42126 2 -f 32524 1 + 52126 3
-I- 42525 2 + 42326 5 + 32225 4 -I- 62122 3 -f 42223 6

which may be compared, as well as the preceding, with the
single 6-valued function of the lOth degree, discovered by
M. Serret, and given in his Algebre Superieure, Note viii.
This has, I think, been hitherto the French stock of 6-valued
functions, and we have repeatedly heard of it.

20. There are 45 equivalent 45-valued functions, and no
more, of the I5th degree, made with six letters.

21. There are nine, and only nine, equivalent 45-valued
functions, of eight terms, of the 10th degree, made with §ix
letters.

22. There are eighteen, and only eighteen, equivalent 45-
valued functions, each of sixteen terms, of the 1 0th degree,
made with six letters.

23. Thee are threre, and only three, equivalent 45-valued
functions, each of four terms, of the 7 th degree, made with six
letters.

24. There are seven, and only seven, 45-valued equivalent
functions, each of eight terms, of the 7th degree, made with
six letters.

25. There are seven, and only seven, 45-valued functions,
each of sixteen terms, of the 7th degree, made with six letters.

96

2G. There are 9, and only 9, 45-valued functions, each of
eight terms, of the 6th deo^ree, made with six letters.

27. There are 3, and only 3, 45-valued functions, each of
sixteen terms, of the 6th degree, made with six letters.

28. There are three, and only three, 45-valued functions,
each of 4 terms, of the 6th degree, made with six letters.

29. There are three, and only three, 45-valued fuuctions,
each of two terms, of the 6th degree, made with six letters.

30. There are two, and only two, 45-valued functions, of
four terms, each of the 4th degree, made with six letters.

31. There are three, and only three, 45-valued functions,
each of eight terms, of the 4th degree, made with six letters.

32. There is one, and only one, 45-valued function, of six-
teen terms, of the 4th degree, made with six letters.

33. There are two, and only two, 45-valued functions, each
of eight terms, of the third degree, made with six letters.

34. There are two, and only two, 45-valued functions, each
of four terms, of the 3rd degree, made with six letters.

35. There are two, and only two, 45-valued functions, of
the 2nd degree, made with six letters.

36. There are sixty 60-valued equivalent functions, and no
more, of the 15th degree, made with six letters.

37. There are thirty equivalent 60-valued functions, and np
inore, of the 10th degree, made wiih six letters.

38. There are fourteen equivalent 60-valued functions of
the 7th degree, and no more, each of twelve terms, made with
six letters.

39. There are two equivalent 60-valued functions, and no
more, each of six terms, of the 7th degree, made with six
letters.

These are
/ r= 1-^223 4 -\- 5^-P2 6 -{■ 3^GM 1 -j- 2^2 6 5 -j- 4'5n 3

4- 6^r-5 2
/= 1^223 4 + 4^Gn 5 -h 5=^3^ 1 2 + £^^5 6

-1- 63-1=2 3 -f 3^026 1

97

40. There are six equivalent 60-valued functions, and no
more, of the 6th degree, of six terms each, made with six
letters.

41. There are thirteen equivalent 60-valued functions, and
no more, each of twelve terms, of the 6 th degree, made with
six letters.

42. There are four, and only four, equivalent 60-valued
functions, each of twelve terms, of the 4th degree, made
with six letters.

43. There is one 60-valued function, and no more, of six
terms, of the 4th degree, made with six lettters.

44. There are two 60-valued functions, and no more, of
the 3rd degree, one of six and the other of twelve terms, made
with six letters.

45. There is only one 60*valued function, of the 2nd degree,
made with six letters.

None of these 60-valued functions is reducible to the pro-
duct of two functions.

All the above functions, and many others, are given in my
Memoir.

The following Paper was also read :

" On the Production of Graphite by the decomposition
of Cyanogen Compounds,'* by Dr. P. Pauli, communicated
by Professor RoscoE.

The mother liquors obtained from the evaporation of a
solution of the so-called black ash are now commercially worked
for caustic alkali.

These liquors contain the following compounds : —

1. Chiefly hydrate of soda.

2. Some quantity of carbonate of soda.

3. Several sulphur compounds of sodium, viz. : sulphide of
sodium, hyposulphite of soda, sulphite of soda, and sulphate
of soda.

98

4. Sulphide of iron held in solution by the sulphide of
sodium.

5. Chloride of sodium.

6. Several cyanogen compounds of sodium, and especially
ferrocyanide of sodium.

These liquors are evaporated down in large cast iron pots
and in order to destroy or oxidise the sulphides of sodium
and iron, as also the cyanogen compounds, an equivalent
quantity of soda-saltpetre is added. All the oxidisable
sulphur compounds, together with the small quantity of
sulphide of iron, are changed to sulphate of soda and peroxide
of iron by the nitrate of soda in the boiling liquor, at a
temperature not below 260° to 270° F. The cyanogen com-
pounds, on the other hand, are only decomposed by the nitre
as soon as the liquor begins to pass from the watery into the
dry fusion and the uncombined water of the hydrate of soda has
been driven off. When the whole mass of alkali (generally about
four tons) reaches a low red heat, a regular evolution of gas
is observed : this is evidently owing to the oxygen produced
by the decomposition of the nitrate, and to the nitrogen from
the decomposition of the cyanides ; at the same time a plen-
tiful liberation of graphite is observed, covering the whole
surface of the liquor with a bright layer of graphite. This
liberation of graphite is still more plainly seen if no nitre be
added to the liquor at first, or only so much as is sufficient to
oxidise the sulphur compounds ; but if a few pounds of nitrate
of soda be added when the water has been driven off, and
the mass is allowed to become red hot, a violent reaction takes
place, and a large quantity of graphite is set free. This
sudden liberation of graphite proves that this substance cannot
be derived from the cast iron of the pot in which the fusion is
made. So violent is the evolution of gas, that a complete
cloud of fine particles of caustic soda is carried up into the air,
rendering it almost impossible to remain in the neighbourhood
of the operation. In this way all the cyanogen compounds

93

are completely decomposed, the iron in the ferrocyanide of
sodium becomes peroxide, and this in a few hours falls to the
bottom of the pot. If the right quantity of saltpetre has
been added, a colourless mass of fused caustic soda remains,
but if too large an amount of nitre has been added, the liquor
becomes coloured deep green, owing to the formation of man-
ganate of soda. It is remarkable that, in the absence of nitrate
of soda, the cyanogen compounds act reducingly upon the
sulphide of sodium ; this is seen from the fact that a portion
of the soda lye, which gives no sulphide reaction with a lead
salt, produces a blackening after the caustic alkali has been
heated to redness.

The graphite may be skimmed off the surface of the fused
alkali, and, when washed with water and hydrochloric acid, it
appears in the form of an extremely fine bright powder. If
allowed to swim on the top of the almost red hot fused soda, the
graphite is oxidized gradually, and, after a lapse of about three
or four hours, it altogether disappears. Heated in a platinum
crucible by itself it is incombustible, but it generally contains
small particles of charcoal mixed with it, and these undergo
oxidation.

The temperature at which this evolution of graphite takes
place is a very low one, compared with that at which graphite
is liberated from cast iron, for a thin iron wire can scarcely be
brought to a visible red heat by dipping it into the fused
alkali.

From this peculiar decomposition it would appear that we
have good reason to assume, that the carbon contained in
cyanogen is present in the graphite modification ; for, if this
be not the case, how is it that the easily combustible charcoal
can withstand the oxidizing action of the saltpetre, whilst none
of the iron of the ferrocyanide of sodium is reduced to the
metallic state?

It has, besides, been lately shown by M. Caron, that the
formation of steel. /. e. the combination of iron with carbon in

100

the graphite modification, can only take place in presence of
cyanogen compounds, and that no carbon whatever is taken
up by the iron when this metal is heated with other carboni-
ferous gases. The mode of the production of graphite
noticed in this communication appears to be an intermediate
reaction between that from the carbide of iron and from the
nitride of carbon.

As in the process of cementation it is seen that the carbon
of the cyanogen is taken up by the iron without being set free,
so this reaction proves that cyanogen can be split up into its
constituent parts without either of them combining with a
third body.

Despretz asserts, that the carbonization of iron is always
preceded by a combination of this metal with nitrogen, a pro-
cess which makes it porous and more fit for the unition with
carbon. The correctness of this supposition has, however,
become rather doubtful, by Caron's recently published experi-
ments (" Comptes Rendus," No. 15 and 24, 1860).

To conclude, I beg to say some words about the formation
of native graphite ; I do not think that this body has been
formed from coal or diamond, but I rather believe it has been
separated out of carbon compounds as graphite, by processes
perhaps analagous to those above described.

101

SECTION FOR SOCIOLOGY AND STATISTICS.
April 9tb, 186 U

Mr. Arthur Ransome, M.A., M.B. Cantab., M.R.C.S.,
read a Paper " On Atmospheric Pressure and the Direction of
the Wind, in Relation to Disease, especially Hoemorrhages
and Neuralgias."

After noticing the important physiological effects of atmo-
spheric pressure upon the human body, and the influence of
changes in the degree of pressure observed by aeronauts and
mountaineers, and by others, as Vierordt, Lehmann, Junod,
Macleod, from special experiments, the Paper next treated of
the effects upon disease of the ordinary fluctuations of atmo-
spheric pressure, as shown by the barometer. Statements
made by Dr. Moffat and others upon the subject were quoted,
and from these it appeared that important effects were pro-
duced by these fluctuations upon such diseases as apoplexy,
menorrhagia, abortions, and neuralgias.

Charts were exhibited which contained records of 286 cases
of hoemorrhage, 52 of abortion, 179 of apoplexy, and 697 ot
neuralgic affections. These had been gathered from medico-
meteorological tables, published in the " Medical Association
Journal," for the years 1853, 1854, 1855.

The degrees of barometric pressure, on the days and at the
several places where the cases occurred, had also been recorded,
and reduced to the level of the sea, and a comparison between
the two series was obtained by means of curves. It was thus
found that of

Cases occurred below Cases occurred at, or

mean pressure, above, mean pressnre.

Hoemorrhage 120 166

Abortion ^3 29

Apoplexy 86 95

Neuralgic Affections 242 455

102

The largest number of cases of

Hoemorrhage (28) occurs at 30*150 inches.
„ Apoplexy (16) „ 30-200 „

„ „ Abortion (7) „ 29-900 „

„ „ Neuralgia (53) „ 30 150 „

Of Neuralgias also 51 eases occur at 30-000 inches; 50 at
30*200 inches (29*950 inches being the mean height of the
barometer.)

Other charts were exhibited, which had been drawn to
ascertain whether the extent of barometric oscillation between
two successive days, had any predisposing influence upon these
diseases — with respect to hoemorrhage, no such influence could
be traced; and neuralgias occurred much more frequently
when the fluctuations of pressure were comparatively small.

With respect to apoplexy, the enquiry was carried further,
in consequence of a statement that " of the number of cases of
apoplexy which occurred (at Hawarden) in the years 1850 and
1851, 50 per cent took place on days of decreasing reading
of the barometer, and 50 per cent on days after such reading."
Of 177 cases of apoplexy, 91 occurred with decreasing
readings, 87 with increasing readings of the barometer ; and
of the 87 cases, 44 occurred on days immediately succeeding
days of decreasing readings, 43 on days succeeding others of
increasing readings.

The sources of error from the influence of warmth or
moisture were examined, but no efl*ect was traced to these
causes, except in the case of apoplexy.

The following conclusions were drawn from the investi-
gation: 1. That a high degree of barometic pressure is

favourable to the production of neuralgias, less evidently so to
apoplexies and other hncmorrages, and that abortions are not
shown to be affected by it. 2. That increasing readings of
the barometer are as frequently accompanied by cases of these
diseases as decreasing readings. 3. That a small extent of
diurnal oscillation of the barometer seems to be favourable to

103

neuralgias, no effect from this source being traced upon
hcemorrhages.

The action of the several winds was then considered, and
statements thereon were quoted from the Medical Association
Journal* These observations did not correspond with the
results obtained by Mr. Ransome. A large proportion of
the cases of neuralgia noted were not followed^by any change
in the direction of the wind the day following ; and cases of
apoplexy, convulsions, and rheumatism were noted with the
wind from nearly every quarter. Charts were shown repre-
senting the relative frequency of attacks of neuralgia with the
wind in the several quarters. No very definite conclusion
could be drawn from these charts ; but the prevalent notion,
that easterly winds produced these affections, was to some
extent corroborated, although it was also evident, that south-
west and west winds are often accompanied by cases of these
diseases.

MICROSCOPICAL SECTION.
15th April, 1861.

A Letter was read from the West Kent Microscopical
Society, requesting specimens of the envelopes and circulars
used by this section for collecting soundings.

Mr. Beck, of London, exhibited two of his binocular
microscopes, on Mr. Wenham's principle ; also, a number of
first-class objects in various branches of microscopy. The
members were much struck with the advantages of the
binocular system, which, under low and medium powers, pre-
sents the various parts of objects in full relief; they were also

* Vol. I., p. 129.

104

pleased with the beauty of certain injected preparations, as
brought out by the binocular, such as the eyes of small ani-
mals, displaying the ckar eyeball, with lenses, cornea, and
retina; the smallest blood vessels were seen to be filled with a
bright red and transparent injected fluid — in situ — distinctly to
be traced and distinguished from each other, instead of appear-
ing as with the single microscope, a tangled mass, all in the
same plane. These instruments and objects strongly mark
the rapid advance microscopy is making in the present day.

Mr. Hardman presented a number of dissecting needles,
with turned handles, which were thankfully accepted by the
members.

Mr. Brothers exhibited Melicerta and other infusoria from
his aquaria.

105

Annual Meeting, April 30tb, 1861.

Dr. J. P. Joule, President, in the Chair.

The following gentlemen were elected members of the
Society : — As Honorary Member: Richard Roberts, M.Inst.
C.E. As Ordinary Members : William Henry Heys, Murray
Gladstone, F.R.A.S., George Venables Vernon, F.R.A.S.,
and James Parlane.

The following Report of the Council was then read by one
of the Secretaries : —

Since the last Annual Meeting the number of members has
somewhat increased. The Society contained at that time
two hundred ordinary members. Of these, five have died
and four have resigned, whilst twenty-three new members
have been elected; so that the number at present amounts to
two hundred and fourteen. Of the deceased members, the
most generally known were Mr. Isaac W. Long and Mr.
Joseph Adshead. Mr. Long was a distinguished member of
the Physical Section, and rendered valuable assistance in the
establishment of that important branch of our Society. He
was specially interested in the science of Astronomy, being a
Fellow of the Royal Astronomical Society of London. A
short account of his life appeared in the monthly notices of
that Society. Mr. Adshead's attention was chiefly directed
to subjects connected with Social Science, and his writings
were much esteemed. None of his productions were, how-
ever, published in the Memoirs of the Society. Three
honorary members and four corresponding members have
been elected.

Proceedings— Lit. & Phil, Society— No. 14. — Sessiox, 1860-61.

106

The following Papers were read during the Session of
1860-61; —

Octohsr 2ndf I860. — " On the A faced Polyacrons in reference
to the Problem of the Enumeration of Polyhedra," by Arthur
Cayley, F.R.S., &c.

October \6th, I860 — "On the Estimation of Sugar in Diabetic
Urine by the Loss of Density after Fermentation," by William
Roberts, M.D.

October 30th, I860 — " On the Alleged Practice of Arsenic Eating
in Styria," by H. E. Roscoe, Ph.D.

November ISth, I860. — "On a System of Periodic Disturbances
of Atmospheric Pressure in Europe and Northern Asia," by Joseph
Baxendell, F.R.A.S.

November 27th, I860. — " On the Prevalence of Certain Forms of
Disease, in connection with Hail and Snow Showers, and the Electric
Condition of the Atmosphere," by Thomas Moffatt, M.D., F.G.S.
Communicated by E. W. Binney, F.R.S., &c.

December Wth, I860 " On the Origin of Species," by the Rev.

W. N. Molesworth, M.A.

Januarif 8th, 1861. — " On the Nature and Objects of Geological
Surveys, with Special Reference to the Progress of the Geological
Survey of Lancashire and Cheshire," by Edward Hull, B.A., F.G.S*
Communicated by E. VV. Binney, F.R.S., &c.

February bth, 1861 " On the Kaloscope," by Mr. W. H. Heys.

Communicated by Mr. George Mosley.

February \9th, 1861 " On the Production and Prevention of

Malaria," by Dr. R. Angus Smith, F.R.S.

«' Brief Notes on the Freezing, Thawing, and Evaporation of
Water, and on the Condensation of Steam," by J. C. Dyer, Esq.

March 5th, 1861 " On the Structure of the Luminous Envelope

of the Sun," by James Nasmyth, Esq. Communicated by Mr.
Joseph Sidebotham.

" On Changed of Density which take place in Rolled Copper by
Hammering and Annealing," by Mr. Charles O'Neill.

107

April 2ndy 1861. — " Remarks on the Temperature of the Earth's
Crust, as Exhibited by Thermometrical Observations, obtained during
the Sinking of the Deep Mine at Dukinfield," by William Fairbairn,
LL.D., F.R.S., &c.

" Brief Notes on the Nature and Action of Steam in Relation
to Boiler Explosions," by J. C. Dyer, Esq.

April 2ndy 1861 " On Meteorological Observations and Ob-
servations of the Temperature of the Atlantic Ocean, made on runs
from Liverpool to Gibraltar, and from Gibraltar to Liverpool, in
September, I860," by Thomas Heelis, F.R.A.S.

" On the Irregular Oscillations of the Barometer at Lisbon," by
G. V. Vernon, F.R.A.S.

^pril \6th, 1861 " Theorems on Groups," by the Rev. T. P.

Kirkman, M.A., F.R.S.

" On the Production of Graphite by the Decomposition of
Cyanogen Compounds," by Dr. P. Pauli. Communicated by Pro-
fessor Roscoe.

Several of these have been ordered to be printed, and will
be published in the forthcoming Volume of Memoirs, which
will also contain several Papers read before various Sections.

The most important event, bearing on the interests of the
Society, which has taken place during the past year, is the
abolition of the old set of rules, which had been in force since
the year 1852, and the enactment of an entirely new code. At
the close of last Session, a Committee was appointed by the
Council, with the approval of the Society, for the purpose of
revising the old rules. This Committee met several times,
and after lengthened discussion, agreed to a draft, which was
presented to the Council and discussed by them. Another
draft, embodying most of the alterations suggested by the
Committee, was soon afterwards laid before the Council by
two of its members. Both in regard to its form and many of
its provisions, the latter was considered to be so far superior
to the previous one, that it was resolved to take it into con-
sideration at once, and lay the other aside. After being dis-

108

cussed clause by clause by the Council, it was referred, for the
purpose of final revision, to the Rev. Wm. Gaskell and Dr.
R. A. Smith, and then presented to the Society for adoption.
It will be seen, therefore, that the subject received a consider-
able amount of attention and consideration from the Council.
It was only after carefully weighing the reasons for and
against each proposed alteration, that the alteration was
finally adopted. The most important change which has been
effected, is that of altering the rate of subscription from
twenty-five shillings to two guineas per annum. The finan-
cial condition of the Society seemed to the Council to render
this change absolutely necessary. In order to prevent the
increased rate of subscription proving a bar to the less wealthy
members of the community, who might wish to join the
Society, a provision was introduced into the new rules,
allowing residents of the district, as well as non-residents, to
become honorary or corresponding members on being recom-
mended by the Council for election.

Although some dissatisfaction was expressed by several
members at the mode in which the proposed rules were
adopted, the Council consider that the course taken by them
was the only legitimate one open to them, and they trust that
as a large majority of the Society decided in favour of the new
rules, all feelings of animosity which may have arisen out of
the discussion of the subject may be laid aside, and that all the
members will cordially unite, for the purpose of increasing
the prosperity of the Society and promoting the objects for
which it was instituted.

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LIBRARIAN'S REPORT.

Since the close of last Session 677 vols., 323 parts of vols.,
and 151 pamphlets have been added to the Library ; of which
141 vols, and 22 parts of vols., by purchase, and the remainder
by exchange or donations.

The periodical publications which the Librarian is author-
ised to procure for the Library by purchase, are : —

The London, Edinburgh, and Dublin Philosophical
Magazine.

The Quarterly Journal of Pure and Applied Mathematics.

The Cavendish Society's Publications.

The Ray Society's Publications.

The Palseontographical Society's Publications.

The Annals and Magazine of Natural History.

Les Annales de Chimie et de Physique.

Le Journal de I'Ecole Polytechnique.

Poggendorff's Annalen der Physik und Chemie.

Annalen der Chemie und Pharmacie.

Journal der reinen und angewandten Mathematik.

Die Astronomischen Nachrichten.

On the motion of Mr. Mosley, seconded by Mr. B.
Joule, the Report w'as adopted.

112

The annual election of officers then took place, when the
following gentlemen were elected : —

JAMES PRESCOTT JOULE, LL.D.. F.R.S., &c.

EGBERT ANGUS SMITH, Ph.D., F.R.S., F.C.S.

EDWARD WILLIAM BINNEY, F.R.S., F.G.S.

WILLIAM FAIRBAIRN, F.R.S., Inst. Nat. Sc. Par. Corresp.

JOSEPH CHESBOROUGH DYER.

HENRY ENFIELD ROSCOE, B.A., Ph.D., F.C.S.
JOSEPH BAXENDELL, F.R.A.S.

^rcagurei\

HENRY MERE ORMEROD.

atlbrariart.

CHARLES FREDRIK EKMAN.

m tDe ^ounciK

REY. WILLIAM GASKELL, M.A.

EDWARD SCHUNCK, Ph.D., F.R.S., F.C.S.

FREDERIC GRACE CALVERT, Ph.D., F.R.S., F.C.S., &c.

JOSEPH ATKINSON RANSOME, M.R.C.S.

PETER SPENCE.

GEORGE MOSLEY.

113

PROCEEDINGS

OF

THE LITERACY AND PHILOSOPHICAL
SOCIETY.

Ordinary Meeting, October ist, 1861.
E. W. BiNNEY, F.R.S., F.G.S., Vice-President, in the

Chair.

A letter from Dr. Fairbairn, F.R.S., &c., tendering his
resig^nation of office as one of the Vice-Presidents of the
Society, having been read, it was moved by Mr. Spence,
seconded by Mr. J. A. Ransome, and unanimously resolved,
" That the Members of the Literary and Philosophical
Society express their regret that Dr. Fairbairn feels it
necessary to resign his Vice-Presidentship of the Society, and
hope he will still continue to favour them with his presence
and his valuable contributions as formerly."

Dr. Schunck, F.R.S., &c., was elected a Vice-President,
in place of Dr. Fairbairn, F.R.S.

Mr. Alfred Fryer was elected a Member of the Council,
in place of Dr. Schunck, F.R.S.

Dr. Schunck announced to the meeting that Messrs.
Spence; Roberts, Dale, and Co. ; Tennants and Co., and
others had, at his request, presented to the Society a portion
of the beautiful products which had formed part of the
interesting Exhibition in the Laboratory of Owens College
during the late Meeting of the British Association.

It was moved by Dr. Schunck, seconded by Dr. Clay,
and unanimously resolved, " That the thanks of the Society
be given to the donors of chemical products."

Proceedings— Lit. & Phil. Society— No. 1. —Session, 1861-62.

114

Mr. Baxendell, F. R. A. S., read a paper entitled
" Observations of Comet I, 1861."

Although this comet was not at any time a very conspicuous
object to the naked eye, yet some of the features which it
presented when viewed with a good telescope at the time of its
greatest brightness were sufficiently remarkable to render it an
object of peculiar interest to the astronomer; and I have
therefore thought that a brief account of the observations
made with the excellent instruments of Mr. Worthin^rton's
observatory might be acceptable to the members of this
Society.

My first observation was made on the night of May 3rd,
1861. The comet was then already visible to the naked eye
as a dull, hazy-looking star of the 4 J magnitude. At lOh.
17m. 48'7s. G.M.T. a comparison with the star Arg,
178,8 = 190,112 made with the equatorially-mounted achro-
matic of 5 inches aperture, and a dark field photographed
micrometer constructed by Mr. Dancer, gave the comet's
apparent place R.A. lOh. 5m. 27*76 Dec. 4-48° 52' 7-7".
Turning the 13-inch reflector upon the comet with powers of
81 and 196, it was found that the nebulosity was more than
20' in diameter, considerably condensed in the middle, but
without any distinct planetary or stellar nucleus. There was
a faint tapering elongation extending about a quarter of a
degree from the north following side, and stars of the 11th
and 12th magnitude were easily seen through the comet at the
distance of half a radius from its centre.

May 4th. Three comparisons with Arg. 173,122 gave the
place of the comet at 9h. 26m. l9-3s. G.M.T. R.A. 9h. 52m.
19-83S. Dec. +45° 18' 28-1".

With the 13-inch reflector the diameter of the nebulosity
constituting the head of the comet, carefully estimated by
comparison with the known diameter of the field of view, was
22'. It was much condensed in the middle, but there was
certainly no distinct stellar nucleus. The centre of greatest

115

condensation was not in the centre of the nebulosity, but
towards the north following side. The tapering elongation
of last night was now a narrow
and slightly fan-shaped tail of
21 degrees in length, but appa-
rently separated from the nebu-
losity of the head by a remark-
able and comparatively dark
interval, as shown in the sketch
which accompanies this paper.
The point of origin of this sin-
gular tail was estimated to be
from 12 to 15 minutes distant
from the centre of the head,
and its breadth at this part was
about 4i minutes, and at its
extremity about 15 minutes.
Its axis was perfectly straight,
and its brightness was greatest
at the narrow end, where it
was equal to that of the nebu-
losity of the head at two-thirds
of the radius from the centre.

May 5th. At lOh. I6m.
59*7s. G.M.T., six comparisons
with Lalandes 191G8 gave the
comet's apparent place R.A.
9h. 39m. 37-82s. Dec. + 41°
2 P 34-5".

^J'he sky to-night was not
very favourable for the obser-
vation of faint objects, but the
general features of the comet
did not appear to have under-
gone any material change. Last

COMET I, 1861,

A.S SEEN WITH Mk. WoBTBTNGTON'S

13-INCH Rkflectou, May 4ih.

116

night it occurred to me after leaving* the observatory that the
axis of the tail was not exactly in the direction of the comet's
radius vector, and to-night I found its angle of position at
13h. 35m. sidereal time to be 96*7°. At this time the
position of the sun and comet were —

The sun R.A. 42° 54'— N.P.D. 73° 33'.

The comet... R.A. 144° 50' — N.P.D. 48° 43'.
From these data we find that the angle of position of a pro-
longation of the comet's radius vector was 69'9°. The
apparent deviation of the axis of the tail was therefore 26*8° in
the direction of the comet's motion.

May 7th. At 12h. (5.M.T. the comet appeared to the
naked eye to be nearly equal to jul Leonis, and equal to, if not
brighter than, 38 Lyncis.

May 9th. Three comparisons with Lai. 17,987 gave the
comet's apparent position at 9h. 57m. 30-5s., R.A. 9h. 3m.
23-25S. Dec. + 26° 11' 26-1".

At 13h. 15m. sid. time the angle of position of the axis of
the tail was 103*2°. At this time the angle of position of the
comet's radius vector was 74*5°; the deviation therefore
amounted to 28*7°.

With the 5-inch achromatic the tail appeared to be half a
degree in lengtn ; but with the 13-inch reflector it was fully one
degree, though fainter than when last observed, and still much
less in breadth than the diameter of the head. The averag^e
diameter of the head was about 20', but the nebulosity
extended farther on the south preceding side of the point of
greatest condensation than on the north preceding or north
following sides. There was still an entire absence of any
stellar nucleus. To the naked eye the comet appeared as a
star about equal in brightness to p. Leonis.

May 14th. Notwithstanding the moonlight, the comet
was still visible to the naked eye, and in the 5-inch achromatic
with a power of 68 it was about 10' in diameter. The tail,
however, could not now be seen.

117

May 17th, lOh. 25m. The comet, though at a very low
altitude and with strong moonlight, was still very easily seen
with the 5-inch achromatic, and did not appear to have
diminished since the 14th instant. This was the last oppor-
tunity I had of observing it.

Lalandes stars Nos. 19168 and 17987 occur in Bessel's
Zones Nos. 454 and 347, and Bessel's places have been used
in making the reductions.

Mr. Baxendell, referring to the photographed mircometer
which he had alluded to in his paper, remarked that, at the
late Meeting of the British Association, Sir David Brewster
read a paper suggesting the application of photography to the
construction of micrometers for astronomical purposes, but he
did not appear to be aware that a micrometer prepared in that
way had actually been constructed and in use for some years.
The idea of employing photography for this purpose had
apparently occurred to diflferent persons, independently of each
other, but the credit of having been the first to reduce this
idea to practice belonged, Mr. Baxendell believed, to Mr.
Dancer, who, in the early part of the year 1858, furnished
him with a micrometer consisting of a system of cross lines,
neatly photographed on a small glass plate, which by a proper
adapter could readily be placed in the field of view, in a plane
perpendicular to the axis of the telescope and with the
collodion side of the plate next to the object end of the
instrument. He had since had this micrometer in constant
use for differential observations, and the results he had
obtained were quite as satisfactory as any that could be
obtained by the more elaborate and expensive reticle micro-
meters in ordinary use.

Some remarks having been made by Mr. Atkinson and
Mr. Vernon respecting the vibrations of the barometric
column which frequently take place during gales of wind

118

Mr. Fryer stated that, with a view of ascertaining whether
the barometer was subject to minute oscillations inappreciable
by the ordinary method of observing, he had placed an aneroid
barometer under the microscope, using the quarter-inch object
glass, and, by bringing one of the stricc on the surface of the
steel index into focus, he was able, by means of the micro-
meter, to observe a movement of the 20,000th of an inch.
The index a})peared to be in constant motion, but at present
he was not prepared to lay any set of observations before the
Society. Mr. Fryer also suggested, for the same purpose,
the use of a barometer filled with the oleine of olive oil, such
an instrument being free from the disturbances caused by the
watery vapour present in the water barometer and exhibiting
a greater range.

PHYSICAL AND MATHEMATICAL SECTION.

April 25th, 18G1.

Mr. MosLEY read an extract from a letter received by him
from Dr. Martin, of Lisbon, in which were enclosed a series of
meteorological observations taken at that place, from the 6tli
to the 12th February last, both inclusive.

Mr. Vernon produced a printed series of meteorological
observations made at Sydney and Paramatta, in 1857, 1858,
and 1859, which he presented to the Section.

Mr. Baxendell gave details of observations which he had
made during the last l<ow days on a large and remarkable solar

119

spot, ill which the secondary penumbra had been plainly
visible, and had been observed by him to consist of a fine net-
work of bright lines. The penumbra was strikingly striated,
and the middle of the nucleus had been occupied by a bright
spot detached from the penumbra at first, but afterwards
joined to it, as the spot began to close up, by one of the pro-
jecting spurs usually observed to occur in decaying spots.
For the purpose of the observations a trough filled with
sulphate of indigo was placed in the cone of rays coming from
the large mirror of a Newtonian reflector of seven inches
aperture, before they reached the eyepiece. The sun's image
was a deep red colour, but the definition was very good.

Professor Clifton suggested that the unusual visibility of
the secondary penumbra in this case might arise from its being
so coloured as to be rendered more visible than usual by the
use of the sulphate of indigo.

June 27th, 1861.

Mr. Baxendell read a Paper entitled " Observations of
Comet I, 1861." [This Paper was afterwards read at the
Ordinary Meeting of the Society, held on the 1st October,
1861.]

Mr. Baxendell also read a note " On a Solar Spot of
Long Duration."

At the last meeting of the Section I exhibited a sketch
made on the 24th April, 1861, of a solar spot in which the
secondary penumbra had been seen with unusual distinctness*
This spot has since twice crossed the visible disk of the sun,
and has had a term of existence considerably above the ordi-
nary average. It was first seen on the 17th of April, near

120

the eastern limb of the sun, and was then a fine spot of not
less than the 3rd magnitude, and, after undergoing many-
considerable changes of form and structure, was finally-
observed very near the western limb, on the 21st of June, as
a spot of only the 9th or UJ magnitude, and from its previous
rate of decrease it is probable that it would become entirely
extinct in four or five days afterwards. Its duration, there-
fore, would not be less than 70 days, and it thus affords a
striking instance of the fact that frequent and extensive
changes of form and structure do not necessarily tend to
produce an early extinction of a spot. Between the 20th of
April, at 5h. I3m. G. M. T., and the 15th of June, at
5h. 30m., it moved through 783*3 degrees of longitude, or at
the rate of one sideral revolution in 25*74 days. On April
20th its heliographical latitude was 14° IV N., and on June
15th 14" 2' N. These results indicate a direction and rate
of drift which agree very nearly with the results which Mr.
Carrington has obtained for other spots in and near the same
parallel of latitude.

121

Ordinary Meeting, October 15th, 1861.
Dr. J. P. Joule, President, in the Chair.
Mr. John Whalley was elected an ordinary member.

A Paper was read by G. V. Vernon, Esq., F.R.A.S.,
M.B.M.S., "On the Irregular Barometric Oscillations at
Geneva and on the Great St. Bernard, and their Relations
to the Mean Temperature and the Fall of Rain."

The object of this Paper was to deduce the effects produced
upon the irregular oscillations of the barometer by considerable
difference of elevation. The station at Geneva is the observa-
tory under Professor Plantamour, and is 1,335 feet above the
sea. The station on the St. Bernard is the Hospice, and the
observations made there are also under the direction of
Professor Plantamour; its height is 8,173 feet above the sea,
and, consequently, 6,838 feet above the Geneva station.

The maximum amount of oscillation occurs at Geneva in
January, and the minimum in August. The maximum at
the St. Bernard occurs in December, and there appears to be
two minima, one in June and the other in August.

Upon the whole, the amount of oscillation appears to
diminish as the mean temperature increases, the minimum
amount of oscillation occurring somewhat later than the
maximum temperature.

The maximum number of oscillations occurs at Geneva in
August ; and there appear to be two minima, one in February
Proceedings— Lit. & Phil. Society— No. 2.— Session, 1861-62.

122

and another in November. At the St. Bernard the maximum
number occurs in August, and a single minimum in
November.

The mean daily amount for the year at Geneva is 0.1069

inches ; annual amount, 39.0719 inches : at the St. Bernard —

daily amount, 0.0865 inches ; annual amount, 31.5941 inches.

The total annual number of oscillations is, at Geneva,

171.3; St. Bernard, 157.2.

Geneva. St. Bernard.

Six winter months 84.4 76.2

Six summer months 86.9 81.0

1848 was the year of maximum oscillation, and 1857 of
minimum oscillation.

A number of oscillations above the average at Geneva is
accompanied by a less amount of oscillation than a number of
oscillations below the average. At the St. Bernard the exact
converse of this holds good.

In January, February, and December, a temperature above
the average, at Geneva, is accompanied by a greater amount
of oscillation than when the temperature is below the average.
During the remaining months of the year the converse of this
exists. For the year, a temperature below the average is
accompanied by a larger amount of oscillation at Geneva than
when the temperature is below the average.

At the St. Bernard, a temperature above the average, in
the months of August and September, gives a larger amount
of oscillation than a temperature below the average ; during
the other months of the year the converse of this holds good.
For the year, a temperature below the average gives the
largest amount of oscillation, as at Geneva.

123

A number of oscillations in excess of the average at
Geneva, in the months of January, March, June, July,
August, and November, is accompanied by a larger amount
of oscillation than when the number is below the average;
during the rest of the year the converse holds good. For the
entire year, an increased number of oscillations is accompanied
by an increased amount of oscillation.

At the St. Bernard, a number of oscillations above the
average, in the months of January, February, March, April,
May, August, September, and November, is accompanied by
a larger amount of oscillation than when the number of oscil-
lations is below the average. In the remaining months of
the year the converse of the above holds good. The mean
of the year gives the same results as Geneva.

A rain fall above the average, at Geneva, is accompanied
by a larger amount of oscillation, in every month of the year,
than when the rain fall is below the average.

At the St. Bernard, a rain fall above the average, in the
months of February, March, May, July, August, November,
and December, is accompanied by a larger amount of oscilla-
tion than a rain fall below the average ; during the remainder
of the year the converse of this exists.

On the mean of the year, a rain fall above the average is
accompanied by a less amount of oscillation than a rain fall
below the average. This result is curious, being the direct
converse of what was obtained for Geneva.

The conclusions which may be drawn from this investiga-
tion are the following. As we ascend in the atmosphere, the
amplitude of the irregular diurnal oscillations of the barometer
diminishes, more especially in the winter months; the summer

124

months having an amount of oscillation not diflfering much
from that of less elevated stations in nearly the same geogra-
phical position.

Excessive rain fall at stations of moderate elevation appears
to be accompanied by a larger amount of oscillation than when
the rain fall is below the average. At more elevated stations
it appears as if this law was reversed, and, if found to be so,
will be a very important fact.

Temperature below the average for the season greatly
increases the amount of oscillation.

125

Ordinary Meeting, October 29 th, 1861.

• J. P. Joule, LL.D., President, in the Chair.

Professor A. D. Bache, Superintendent of the United
States Coast Survey, and Commander M. F. Maury, of the
United States Navy, were elected Corresponding Members
of the Society.

John Edward Morgan, Esq., M.B., was elected an
Ordinary Member.

Mr. Spence brought before the meeting part of a mass of
iron and copper pyrites, containing abundance of large and
well defined crystals of pure arsenious acid.

Not only are these crystals a novelty as a natural product,
but as an instance of rapid mineralisation they are interesting.
The lump was found among a cargo of small disintegrated ore
imported from Huelva, in Spain, and containing no solid
masses of large size, and the lump was merely an aggregation
of small pieces firmly agglutinated together and full of hollow
cavities, studded over with the crystals of arsenious acid ; and
from the history of the cargo of ore it is not probable that
more than twelve months has been required for their develop-
ment. Heat does not seem to have been the cause of the
metamorphosis, as there is no evidence of heat at all approach-
ing to ignition having occurred ; discoloration of the ore would
at once have been the result of this.

The ore is chiefly a sulphide of iron and copper ; but as an
arsenide of one or both of these metals exists in it, decom-
PftOCEEDiNGS— Lit. & Phil. Society— No. o.—Sessiox, 1861-62.

126

position of this latter must have taken place; the arsenic has
become oxidised, and crystals of arsenious acid are the result.

The piece of ore will be deposited in the Society's mineral
collection.

The discovery of these crystals being pure arsenious acid
was made by Mr. Bottomley, Mr. Spence's assistant in his
laboratory.

An interesting conversation followed, in which the fact was
stated that arsenic is a constituent of nearly all the artificial
manures which have superphosphate of lime as their basis;
and in connection with this a report was named of arsenic
having been found in some of the crops grown with such
manures.

Professor Roscoe exhibited the beautiful lithographic map
representing the dark lines in a portion of the solar spectrum,
lately published by Professor Kirchhoff. The lines are printed
in ink of six diiferent shades, and are of six different degrees
of thickness, so that the leading features of the spectrum can
be at once recognised. The position of the bright lines pro-
duced by the incandescent vapour of certain metals is also
given on the map, and the coincidence of many of these with
the dark Frauenhofer's lines rendered evident.

Professor Roscoe stated that the length of the drawings
when complete would amount to some twenty feet, and that to
give an idea of the scale on which the map was made, he
might remark that the distance between the two double lines
'' D" is upwards of four millimetres. These maps are as yet
only printed together with the memoir by Professor Kirchhoff,
upon the Solar Spectrum and the Spectra of the Chemical
Elements, in the Transactions of the Berlin Academy ; an
English edition will, however, shortly be published, giving a
translation of the original memoir, and containing the same
drawings of the spectrum as those exhibited, which accompany
the German text.

127

Dr. R. Angus Smith read the first part of " An Examina-
tion into the Products of the Putrefaction of Blood." He
found that 54° Fahr., or nearly so, was a marked temperature ;
that below it there was little putrefaction, but above it a large
amount, which increased as the temperature increased as far as
he tried, viz., to 72° F. The amount of gas given in twenty-
four hours, from three quarts of diluted blood, was one hundred
cubic centimetres, at 57° F. (16° Cels.), but on raising the
temperature to 72° (22^ Cels.) the amount of gas in the same
period rose to 397 C.C., or four times the amount of putre-
faction by fifteen degrees rise of temperature. When the
temperature was below 54°, no gas could be collected for
many days. A very short rise above 54° caused sufficient
pressure to allow gas to be collected. These facts were used
to illustrate climate and sudden spread of disease.

During the early period of putrefaction, the Author found
the sulphuretted hydrogen and organic matter to increase
rapidly. One hundred cubic centimetres destroyed 29 of a
solution of permanganate ; the amount then rose rapidly to
36, 40-6, 41, 60-2.

Nearly ninety-eight per cent of the gas that escaped was
found to be carbonic acid and gases with a similar action,
e.e., absorbed readily by caustic alkalies.

The gases were found to be —

Carbonic Acid. Sulphuretted Hydrogen, Residue.

82-68 17-32

85-78 14-22

89-72 10-28

95-40 ~ 4-60

96-20 3-80

96-07 1.58 2-35

96-43 2-78 0-79

97-62 0-06 2-31

97-09 1-93 1-98

. 128

The residual gas was found to consist of —

Carbonic Oxide 4*8 per cent.

Carburetted Hydrogen 2*5 ,,

Hydrogen 6*2 „

Nitrogen 86*5 ,,

100-

Where the sulphuretted hydrogen is 1*5, the sulphur is to
the carbon as 1 to 24*8.

Both the oxygen and carbon of the carbonic acid are derived
from the blood, which is therefore carried rapidly away.

The point of greatest importance was said, by the author,
to be the separation of these substances, which do not seem
to be pure gases, and which are entirely absorbed by alkalies,
and partly by acids and metallic salts. The portion absorbed
by acid salts was found to contain carbon and nitroge\i, in the
relation of 140 to 54, or as 100 to 38*5 ; but part of this was
evidently as ammonia. In albumen it exists in the relation of
100 to 28*9 The whole of the putrefactive matters were not
removed by acids or by acid salts. When the carbonic acid
and sulphuretted hydrogen are removed, the putrefactive
matters still remain. These gases, therefore, are not the only
substances to be feared.

The condition in which these putrefactive bodies exist
was then discussed. The Author believed that one of the
conditions in which solid substances were taken into the air
was in solution, the solution itself being taken up as a vesicle ;
and he instanced analogous cases, such as sulphuric acid and
zinc when hydrogen is forming. The liquid evaporates and
a concrete globule forms, leaving at last a portion of solid
matter in various states. This condition can be supposed
to occur readily in many cases, but it does not appear to be
the probable result in all cases, as he cannot readily imagine
vesicles coming through the close pores of bodies such as are

129

penetrated by these vapours. Between the actually mechanical
method of taking solid matter into the air, such as when
waves are agitated by the wind, and the purely chemical
method, such as when a liquid is transformed into a vapour
by heat, there must be many intermediate stages. These
stages are required, apparently, as we can scarcely imagine
pure gases undergoing transformation similar to bodies in a
putrefactive state ; and we are not prepared with a theory by
which diseases will be communicated without the agency of
bodies in such a state of change — one of the oldest of theories
and one promising to live long. Besides, the fact of a
substance being found capable of being absorbed by metallic
salts, and containing carbon with nitrogen in such a large
amount, leads us to believe that bodies not very far removed
from the substances decomposed are found in the vapours,
and, if not far removed, capable of undergoing transformations
so as to become farther removed, and by such transformations
exercising their special influence.

130

MICROSCOPICAL SECTION.
21st October, 1861.

Professor Williamson in the Chair.

The following gentlemen were elected members of the
Section :— Mr. Murray Gladstone, Mr. John Whalley, Mr.
William Henry Heys, Dr. William Roberts, and Dr. Thomas
Alcock.

The Secretary presented sixty specimens of soundings
received since the last Session, from the commanders of various
steamers and sailing vessels, amongst which were a number
from the South Coast of Ireland, Banks of Newfoundland,
Coast of Nantucket, U.S., North Coast of Brazil, &c. The
Secretary was requested to write a letter of thanks from the
Section to each contributor.

The Chairman remarked that these specimens deserved
the best attention of the Section, not only on account of their
intrinsic interest, but to show the contributors that their kind-
ness in preserving the soundings for the Section was fully
appreciated.

Mr. Dale offered, with the assistance of the Secretary, to
prepare the material, by separation from the tallow, &c., and
Mr. Nevill, Mr. Heys, and several other gentlemen, offered
their assistance in mounting, examination, and reporting to
the Section.

The Chairman observed that the method he employed
in the preliminary examination of similar specimens, when
freed from tallow and dried, was to stir the mass in a
vessel of water, when most of the organic forms rose to the
surface, in consequence of containing small quantities of air ;
the creamings off the top of the liquid would be found to

i

131

contain sufficient indications whether the specimens deserved
further attention.

The Secretary read a letter from Mr. Joseph Sidebotham,
accompanying a specimen and a drawing of the Aulacodiscus
formosus, showing the four projecting knobs or handles visible
upon that diatom. Mr. Sidebotham states that in all draw-
ings hitherto published, these protuberances appear like simple
elevations or bosses, nor could they be seen otherwise until
the binocular microscope revealed their true shape. Mr.
Dancer first called his attention to this peculiarity.

Mr. Crompton exhibited, and presented to the members,
specimens of capillary tubes used by him to collect and pre-
serve fluids for microscopical examination for medical purposes.
Mr. Crompton has used such tubes for more than a year, and
has preserved specimens of blood, urine, &c., which by any
other method would have spoiled. The main feature consists
in hermetically sealing the tubes after the introduction of the
fluid, by holding their ends alternately in the flame of a
candle or lamp until the glass melts, and the orifice closes;
the tubes may be about three-fourths filled by capillary
attraction or immersion, and care must be taken not to allow
the fluid to approach the hot end of the tube whilst being
sealed. The Edinburgh vaccine tubes answer the purpose
well ; they may be about three inches long, and a number of
them may be carried in a small pocket case at all times ready
to be filled. When required for examination, the tube is
broken, and the enclosed fluid placed under the microscope.

The Secretary exhibited a specimen of the compound
salt of magnesia and copper, prepared by Mr. Thomas Davies,
of Warrington. Doubts having been expressed if it were a
true compound salt, or a mere mechanical mixture, Mr. Dale,
who at the Secretary's request had prepared some of the salt,

132

undertook to report further upon it. Some forms of crystal
were exhibited, producing novel effects by polarised light.

Mr. Lynde exhibited a line specimen of copper ore, with
jasper, from Cornwall, the colours of which, when illuminated
with the Lieberkiihn, were very gorgeous.

Mr. Latham exhibited the ovary of a flea, and portions
of the skin and teeth of the dogfish.

Mr. Heys exhibited specimens, mounted specially for the
Lieberkiihn, of various seeds, hairs, and glands of plants;
the tesselated spines on the Symphytum asperrimum, or
rough comfrey, and the ruby coloured oil glands of the
origamme onites, glowing, like precious stones, with the
reflected light from above the object, were very much admired.
For certain classes of objects no illumination can compare
with that of the Lieberkiihn in the use of the binocuku-
microscope, and side lights may be obtained, to some extent
all around the object, by manipulation with the mirror.

133

Ordinary Meeting, November 12th, 1861.
Dr. R. Angus Smith, Vice-President, in the Chair.

Mr. Thomas Coward was elected an Ordinary Member.

Mr. E. W. BiNNEY said that some years since he read a
Paper before the Society, " On the Drift Deposits found
near Blackpool," which was afterwards printed in Vol X.
(new series) of the Memoirs. In the gravel at Bispham,
most probably the high level gravel of Mr. Prestwich, he
found nineteen species of shells, all identical with those now
found in the Irish Sea. He also stated that in the lowest
bed of till there found, full of scored and striated rocks, he
collected shells of the genera turritella, buccinum, nassa,
dentalium, nucula^ cardium^ and tellina. Owing to such
shells found in these deposits not having so arctic a character
as those said to be found in other till beds, it has been
supposed that they are of a more recent date than the glacial
age of Forbes, or the pleistocene of Lyell. Professor King,
of Queen's College, Galway, a geologist of high reputation,
in his Synoptical Table of British Aqueous Rock Groups, &c.,
just published, classes the Blackpool fossils with post-pleisto-
cene, as shell sands occurring just under deposits now forming
around the shores of the British Islands, and immediately
above the Devonshire raised beaches. The Blackpool gravels,
near Bispham, are as good pleistocene as can be found in any
Proceedings— Lit. & Phil. Society— No. 4.— Session, 1861-62.

134

of the high level gravels met with further inland, notwith-
standing the fossils discovered in them, which are of the same
kind, although not so numerous, as those met with in the
gravels of Bowdon, Cheshire, and the sands of Haigh,
Lancashire. He also said that the lowest bed of till seen at
Blackpool, and containing the shells previously alluded to,
had all the physical characters of the Scottish, Irish, and
North of England iceberg and glacial drift, and had been
subject to considerable elevations since its deposition.

Mr. R. D. Darbishire stated that he had lately found
under undisturbed clay at a considerable elevation on the
southerly slope of Great Orme's Head, a deposit of bones of
different mammalia intermixed with shells of mytilus, littorina,
and patella. He hoped to lay the results of further observa-
tions before the Society on a future occasion. He supposed
the deposit might be connected with the present or past
existence of some "bone cave" in the limestone rock of the
Head.

He suggested, however, that possibly the bones and shells
may have been the remnants of the cookery of former
inhabitants of the district, and referred, in illustration, to
the researches made amongst the Kjokkenmoddings on the
coasts of Denmark.

Dr. Joule, in reference to speculations on the thickness of
the earth's crust, stated that he had some time ago received a
letter from Professor Thomson, giving an account of the
progress of investigations calculated to throw light on this
interesting subject. Professor Thomson finds that the

135

equilibrium lunar tide in a solid glass globe (without mutual
gravitation) of the same size as the earth is about five feet.
Hence, from the phenomena of the actual tides of the ocean,
it follows that the earth, as a whole, is more rigid than glass.
The observations of Mallet, with experimental earthquakes,
show that the earth's crust is many times less rigid than glass.
Hence Professor Thomson infers that the earth, as a whole,
is many times more rigid than the rocks and strata on its
surface.

Dr. Grace Calvert stated that he wished to draw the
attention of the manufacturing chemists of this district to a
very simple and rapid method which had been devised by the
eminent chemist M. Pelouze, Master of the Paris Mint, for
determining the amount of sulphur existing in pyrites. He
(Dr. Calvert) was induced to do so, believing that any pro-
cess which would simplify the long and troublesome operations
now followed to ascertain the value of this mineral would be
useful to many members now present at this meeting. The
process consists in mixing intimately together one part of
pyrites, thoroughly pulverised in an agate mortar, with five
parts of carbonate of soda, seven parts of chlorate of potass,
and five parts of chloride of sodium, and placing the whole in
an iron spoon, which is gradually carried to a dull red heat.
The mass, when cold, is first washed with cold water and
then with boiling water, until the whole of the soluble matter
is removed ; and this solution is tested with a standard solution
of sulphuric acid. As 100 grains of carbonate of soda requires
92*45 of monohydrated sulphuric acid, or S O3 H O, it follows
that the quantity of soda in the carbonate of soda employed

136

will decrease in proportion to the quantity of sulphur from the
pyrites converted into sulphuric acid, which will have
neutralised a corresponding quantity of the soda in the
carbonate.

This mode of assaying is so simple, that the Author states
that he can determine, within one or one and a half per cent,
the value of a sample of pyrites, in the space of an hour's
time.

M. Pelouze also states that by employing the following
proportions of the same materials, the manufacturer can deter-
mine the amount of sulphur in burnt pyrites. Five parts of
the latter substance are mixed intimately with five parts of
pure carbonate of soda and five parts of chlorate of potash.

137

Ordinary Meeting, November 26th, 1861.

J. P. Joule, LL.D., President, in the Chair.

Mr. Joseph Sidebotham exhibited a photograph of the
contorted schists seen in the cliff near the South Stack
Lighthouse, Holyhead.

Mr. John Parry showed some photographs of fossil woods
from the South Lancashire coal field. These displayed
beautifully the structure, even to the most minute vessels.

A Paper was read by Mr. E. W. Binney, F.R.S., Vice-
President, entitled '^ Additional Observations on the Permian
Beds of South Lancashire." This was a continuation of two
previous papers read before the Society and printed in its
Memoirs.* Since that time the Author had made further
observations on the Permian strata at Heaton Norris, near
Stockport ; Medlock Vale, between Ashton and Manchester ;
Chorlton-upon-Medlock, and Ordsal, near Manchester ; and
Skillaw Clough and Bentley Brook, near Newburgh, in the
West of Lancashire.

At Heaton Norris, in the sand delf of Mr. Howard, near
the railway station, the lower new red sandstone was seen
dipping to the south-west at an angle of 25°. This was
succeeded by red and variegated marls having a similar dip
These last named strata were overlapped by the Trias, which
dips to the south-west at an angle of 12°.

* Yols. xii, and xiv. (New Series) of the Society's Memoirs.

PaocEEDiNGS— Lit. &Phil. Socibty— No. 5.— Session 1861-62.

138

At Heaton Mersey the following section was met witli :

Feet.

Trias 45

Permian — Red and variegated marls containing

limestones 1S9

Lower new red sandstone grooved. . 402

576

The Permian beds were cut off by a fault near the railway
station at Heaton Norris, first shown to me by Mr. Hull,
B.A., F.G.S., of the Geological Survey, which brought in the
Trias. This rock occupied the district between that town
and Goyt's Hall, in the Marple valley, where the lower part
of the middle coal measures was seen in nearly a vertical
position.

The Author considered that Mr. Howard's sand delf is a
likely place for ascertaining the existence of a coal field under
the town of Stockport worth working.

The next was a section made by Mr. John Wood, at Med-
lock Vale, between Waterhouses, near Ashton-under-Lyne,
and Manchester. It was as follows :

Feet In.

Drift 26 0

Trias 2S 0

Permian — Red marls, with beds of lime-
stone and five beds of gypsum 246 S
Lower new red sandstone .... 375 11
Coal measures about 90 0

761 2

What these coal measures were, whether above or under
the Bradford Four Feet Mine, it was at present impossible to
say ; but it was to be hoped that some mine would be met
with to enable us to determine the value of the great tract of
coal measures lying between Ashton-under-Lyne, Oldham,

139

Micldleton, and Manchester. Mr. Wood had done more than
any other gentleman to clear up this point, and it was to he
desired that he should meet with a good seam of coal, hoth
for his own sake and that of the puhlic.

The third section mentioned was at the sugar works of
Messrs. Fryer and Co., in Chester Street, Chorlton-on-Med-
lock, Manchester. The following beds were there met with ;

Feet.
Trias , 114

Permian... Red marls with limestones 237

Coarse red sandstone with pebbles.. 45

Coarse red sandstone . 24

Coal measures consisting of red shaly marls

and limestones (Ardwick) 126

546

The limestones in the last named strata contained speci-
mens of microconchus carhonarius and scales of palmoniscus,
which clearly proved them to be similar beds to those of the
upper coal field at Ardwick, to which they bear every resem-
blance in physical character.

The occurrence of coal measures on the south side of the
city of Manchester is quite new and of great importance,
showing that such strata at places are met with under per-
mian and trias deposits much nearer the surface than was
previously suspected, and where the upper rocks gave no
evidence of their proximity. The above bore has proved
beyond doubt that a band of coal measures lies under the
south of Chorlton-on-Medlock, and possibly extends to
Heaton Norris, being probably brought up by the great
Pendleton fault, which most likely passes through the south
of Manchester and joins the fault seen near the railway
station at Heaton Norris previously alluded to, and described
more fully in the Paper.

140

In the fourth section, at Ordsal, Messrs. Worrall found
the trias beds 460 feet in thickness without going through
them. At the bottom of the bore the water became so salt
that they discontinued the work, it being no longer fit for
dyeing and such like purposes. This is the first instance, to
the Author's knowledge, where salt water has been met with
in the trias near Manchester.

The fifth and sixth sections were at Skillaw Clough and
Bentley Brook, to the north of the Newburgh station on the
Manchester and Southport Railway. These were some time
since discovered by Mr. E. Hull, B.A., F.G.S., of the Geolo-
gical Survey, and described shortly by that gentleman in the
sheet explaining the map of the district. Further particulars
were given of the details of both sections, and an analysis of
the limestone was produced, which showed it to differ in its
chemical characters from the thin ribbon bands found in the
permian marls near Manchester, Patricroft, Astley, and Leigh,
and was very like the yellow magnesian found at Stank, in
Furness, North Lancashire. Probably it might prove to be
a different bed, and more like the great central deposit of
magnesian limestone of Yorkshire than the thin beds pre-
viously alluded to.

141

MICROSCOPICAL SECTION.
November 18, 1861.
E. W. BiNNEY, F.R.S., F.G.S., in the Chair.
Dr. Edward Stephens was elected a member of the Section.

The Secretary read a communication from Mr. Thomas
G. Rylands, of Warrington, ^' On the Classification of the
Diatomaceae." The Author desired to call attention to the
want of systematic arrangement which characterises this
favourite branch of microscopical investigation, and to the
necessity of a thorough revision of the entire classification of
the natural order. The author presented to the Section two
slides to illustrate his arguments. The predominant form
of frustules was first named by Dr. Brebisson Cocconeis Icevis.
In 1857 it was published by Mr. Roper (M. I. vol. vi. p. 22)
under the provisional name Coscinodiscus ? ovalis ; but
in consequence of finding on the valves eight to twelve
submarginal obtuse processes with tumid bases, quite distinct
from the spines or teeth which occur in the Coscinodiscese,
the Author considers this species must be placed in the genus
Eupodiscus, and may fitly be called Eupodiscus loevis. The
specimens were obtained at Llandudno, in ripples in the sand
below mid-water ; and the Paper concludes with a description
of some peculiarities connected with their sudden disap-
pearance.

Mr. John Watson read a paper "On certain Scales of
some Diurnal Lepidoptera," in which he recommends a new
and careful study of this subject. In some genera peculiar

142

scales^ called plumules, have long been known ; but examina-
tion with the binocular microscope shows that they are not
flat like the ordinary scales, but cylindrical and hollow.
They have been found only in certain genera (named in the
paper) at present, and on the males alone ; they possess
generic resemblances and specific diflerences, each species
displaying its own distinguishing variety. One of great
beauty and novelty, found only on two African butterflies,
Pieris Agathina and Pieris Chloris, was described, and some
very fine drawings of it, by Mr. Joseph Sidebotham, were
exhibited, and also other figures by him of about one hundred
species never figured before. The names and habitats of the
insects were given, and the Author pointed out the value of
these scales for the assistance of the scientific entomologist
in arranging genera and species; he then entered into the
question of their probable use as air vessels in the economy
of the insects possessing them.

The Chairman remarked that the scales of the Lepidoptera
may prove to be as valuable in determining species as the
scales of fishes.

Mr. Sidebotham alluded to the value of the binocular
microscope in defining the cylindrical form of the plumules,
and described the mode of finding them in situ, by breaking
the wing.

Mr. Watson stated that some of Mr. Sidebotham's excel-
lent drawings were taken under the eighth objective, magni-
fying 750 diameters. Mr. Watson further said that he had
examined the wings of 400 specimens of the Papilionidse,
but had not discovered any plumules in that genera ; he also
alluded to several so called species from South America, of
which no males have yet been found, others of which no
females have yet been discovered, and suggested the possi-
bility of some of these being male and female of the same
species ; to ascertain which, careful examination of the scales
might be useful.

143

Mr. Watson exhibited a number of mounted specimens of
the plumules, and four cases of the Lepidoptera from whose
wings the 98 drawings figured by Mr. Sidebotham were
taken. They were principally Pieris, Anthocaris, Thestias,
Euterpe, and Eronia; amongst the former w^ere some new
and unnamed species from Celebes, with rare specimens from
Venezuela, Quito, East and West Indies, Africa, and other
parts of the world.

Mr. Dale placed on the table a number of washed
soundings, of which several members took specimens for
examination.

Mr. Dale also reported that the sulphate of copper and
magnesia has been long known to be a compound salt. When
the magnesian salt is in excess, it has seven equivalents of
■water; and when the copper salt is in excess, it has five
equivalents of water. Mr. Dale had also made for the occa-
sion samples of the double sulphate of copper and potash,
the double sulphate of copper and ammonia, and the double
chloride of copper and ammonia, which he distributed
amongst the members. They were all beautiful polariscopic
crystals, the chloride particularly so, and each has its
characteristic form.

Mr. Linton exhibited the hairs on the Loasa Coccinea
(Chili nettle), mounted by Mr. Heys.

Mr. Dancer exhibited a specimen of the Aulacodiscus
formosus, which, in consequence of a fracture since it was
mounted, shows more distinctly the form of the projections
that Mr. Sidebotham brought under the notice of the Section
at the last meeting. These handle-shaped spines, Mr. Dancer
observed, when seen with the l-8th power and binocular
microscope, are found to project outwards from each of the
four elevations on the surface of the valve.

144

Mr. Brothers exhibited the Floscularia ornata, and a
fine group of Lacinularia socialis.

Mr. MosLEY exhibited a specimen of Amoeba^ and
described the peculiarity of its motion. He had observed
one of them rise in a straight line four-fifths of its entire
length, its internal particles appearing to force outwards a
transparent or invisible integument ; the point then fell over,
forming an arch, after which it subsided into the common
three or four-lobed form. In many specimens no vacuole
was observed ; in others, an apparent air or water space was
noticed. A portion of the one under examination appeared
to be blown outwards like a bladder, in w^hich appeared a
small animalcule making desperate efforts to escape. The
best illumination for observing the internal motion, he con-
siders to be Wenham's parabola and Lieberkiihn, with a
4- 10th objective.

145

Ordinary Meeting, December lOth, 1861.
J. P. Joule, LL.D., President, in the Chair.

Mr. Wm. K. Deane, was elected an Ordinary Member.

Mr. Baxendell made the following communication : —
A paragraph, headed '^Rain following the Discharge of
Ordnance," appears in the number of the Londoii Remeio for
November 16th, 1861. In this paragraph some new facts,
drawn from the American war, are adduced by Mr. J. C.
Lewis, in support of the view that a violent concussion of the
air by the discharge of heavy artillery has a tendency to
cause a copious precipitation of rain. Now, if we may be
allowed to regard this effect as an established fact, it seems
to me to be one of some interest in connection with the
disputed question whether, in thunderstorms, a discharge of
lightning is the cause or the consequence of the sudden
formation of a heavy shower of rain. Almost every day's
experience, in this climate at least, shows that the production
of rain is not dependent upon sudden discharges of electricity
from the clouds; and no evidence has ever been brought
forward to prove that a high degree of electrical tension in a
cloud has a tendency to prevent the resolution of the cloud
into rain. Heavy showers often fall from highly electrified
clouds without any visible discharge of electricity taking
place. "VVe are, therefore, not entitled to assume that the
sudden diminution of the electrical tension of a cloud by a
lightning discharge can have any material influence upon the
rain-forming processes going on in the cloud. As, however,
very heavy showers of rain do almost invariably follow light-
ning discharges, it seems necessary to seek some other cause
to account for them. But if we admit that a violent con-
Proceedings— Lit. & Phil. Society— No. 6.— Session 1861-62.

146

cussion of the air has a tendency to facihtate tlie conversion
of rain-forming material into actual drops of rain, then we
may well suppose that the violent concussions produced by
lightning discharges, acting on such enormous and dense
masses of rain-forming material as are usually collected in
heavy thunder clouds, are amply sufficient to produce these
sudden and heavy showers of rain.

I am aware that the eiFect of a discharge of ordnance is
usually supposed to be produced by an upward current of air
caused by the heat and the gases evolved during the com-
bustion of the gunpowder ; but as an hour's sunshine through
an opening in the clouds, especially when the sun is at a
considerable altitude, would produce a much greater effect in
heating and increasing the bulk of the air, this cannot be
received as the true explanation of the mode in which the
effect of a discharge of heavy artillery is produced.

Mr. Fairbairn stated that he had been making experi-
ments on the process of cold rolling, as applied to iron. He
had tested specimens of cold rolled iron manufactured both
by Mr. Lauth and Earl Dudley. In the former case, a black
bar from the rolls broke with 26' 173 tons per square inch, a
a similar turned bar with 27" 11 9 tons, and a cold rolled bar
of the same iron sustained 39*o88 tons. The elongations,
which may be considered as the measure of ductility, were
•200 and '220 per unit of length in the case of the ordinary
iron, and "079 in the cold rolled iron. A plate of cold rolled
iron, from Earl Dudley, sustained no less than 51*3 tons
per square inch. Endeavours were being made to apply the
invention to railway bars.

Mr. Brockbank described the Bessemer process of manu-
facturing iron and steel, and stated his belief that the
variously colored flames on the surface of newly run steel
would afford the means of detecting the presence of metals
and other bodies by the new method of spectrum analysis.

147

A Paper, entitled, " Nouveau Systeme de Communication
Telegraphique, rendant impossible toute collision de trains
sur les chemins de fer," by Professor Baulet, of Perpignan,
communicated by William Eairbairn, Esq., LL.D., &c., was
read by Professor Roscoe.

In this plan an insulated wire placed between the rails,
and divided in its middle, affords a connexion between the
instruments at the stations and others situated in the trains
themselves. The details of the arrangement could not be
understood without the drawings accompanying the Paper.

Mr. DoDWELL, the Superintendent of the Magnetic Tele-
graph, described Mr. Clark's system, which is now in full
operation between London and Rugby, and which^ he
thought, left little further to be desired.

SECTION FOE STATISTICS AND SOCIOLOGY.
November 19th, 1861.

Dr. E. A. Smith, F.R.S., &c., read a Paper, entitled,
'' Examples of Relative and Absolute Law."

The Author said that it was an easy thing to express the
most important laws that ought to rule absolute in society.
They were such as had been given in the words, ^' Love thy
neighbour as thyself, do justice, love mercy," but, when it
became needful to apply these laws to particular cases, ^ae
operations of the greatest minds were needed, and found
after all to be wanting. Quoting from a former Paper, he
said that even our ideas of property ceased to have influence
when our relation to property changed ; for example, when
millions of our fellow-creatures are dying at a distance, we
feel it scarcely right to consider that we have a right to any
luxury ; where they are dying in our own country, we feel

148

that we must still further curtail ; when we are placed in
situations where they are dying around us, all prior right
gradually vanishes. This law we acknowledge formally hy
a rise of poor-rates, according to the circumstances of the
country.

Again, to take an example from extremes, if all Britain
were in the possession of one man, who desired to send
out all the inhabitants, and hunt with a few friends only
over London and Manchester, we should no doubt refuse to
go; we should then change our ideas of property, and we
would adopt the opinions of the Fifth Monarchy men and
say, "The earth is the Lord's." If half the country were in
this state, we would still give the same answer ; but if only
a county were in this possessor's hands, we would first hesi-
tate and say, '* What county ? " If it were Middlesex, surely
not — we will allow no individual to rule so despotically on
the Thames. Lancaster also not. But when it is Suther-
land, Arran, or Skye, we then give the permission, and the
permission remains until the inhabitants become powerful
enough to say that there are rights belonging to man, as an
intellectual and moral being, on which physical rights, with-
out moral modifications, must not be allowed to trample.

This is especially the case with reference to clearances ;
they are allowed, although they would not be allowed in
densely populated counties; and they are allowed because
they are in conformity with formal law, although it is
generally thought that they are in opposition to a feeling not
yet fully expressed. It slumbers in the mind which says
that some great law is disobeyed, but on examining the law
of the land it is not found which portion is disobeyed, and it
may be that the heart is also mistaken in its feelings. It is
the business of legislators to put into words and parlia-
mentary law the great laws of justice which are written in
our hearts, and to see that all laws made for the nation are in
conformity with absolute law. All our laws are relative, or

149

nearly all; it is extremely difficult to make absolute and
relative law run together exactly parallel. Society moves
and its relations to all things move at every step ; relative
laws must therefore always be changing, whilst absolute laws
are always the same.

The same applied to the principle of free traders who
advocate local and relative conveniences as if thev were
universal and absolute laws.

150

PHYSICAL AND MATHEMATICAL SECTIOl^.
October 10th, 1861.

G. V. Vernon, Esq., F.R.A.S., was elected a Member of
the Section.

A letter from Mr. Heelis, F.E.A.S., having been read,
resigning the Secretaryship of the Section on account of the
state of his health, it was resolved unanimously, — That the
Section receive with regret the resignation, by Mr. Heelis, of
his office as Secretary, and sincerely hope that his health
may soon allow of his resumption of official connection with
them.

Mr. Vernon, F.R.A.S., read a Paper, "On the Irregular
Barometric Oscillations at Geneva and on Great St. Bernard,
and their Relations to Mean Temperature and the Fall of
Rain." [This Paper was afterwards read at the Ordinary
Meeting of the Society, held on October 15th, 1861. See
Proceedings No. 2, Session 1861-S.]

November 7th, 1861.

Professor Clifton, B.A., F.R.A.S., was elected Secretary of
the Section, in place of Mr. Heelis, resigned.

A letter from Mr. Heelis, F.R.A.S., was read, commu-
nicating the following observation of the Zodiacal Light,
recently made by him at Smyrna. " September 13th, 1861,
4h. a.m. Observed the Zodiacal light very distinctly ; the
breadth of it was not observed, but the position of the apex
was ascertained, as carefully as an eye unaccustomed to such
observations would permit, to be in a line and about midway
between Pollux and Procyon. This would give an approxi-
mate length of 75° 11'. The cluster Pra^sepe was seen
(iistinctly through the light shiniiig like a white cloud, and

151

many meteors about equal in light to the brightness of any
point in the Prsesepe, (by which I would be understood to
mean not the aggregate light of the cluster, but the light
which any part of it, if separated from the rest would appear
to have,) were seen crossing the beam of light in various
directions. The sky was quite clear, the morning just
dawning, and the horizon to seaward covered, as is usual at
that hour in summer at Smyrna with a low fog bank. Few
or no meteors were at the time of observation noticed in any
other part of the sky."

Mr. W. L. Dickinson read a Note " On the Transit of
Mercury," giving the results of his calculations for Man-
chester. In these calculations he had used the Nautical
Almanac Elements, and found that the planet would leave the
Sun's disc on the morning of the 12th instant, at 9h. 18m.
44s., Greenwich mean time, at an angle from the north point
of the Sun's disc of 24° towards the west, and from the vortex
of 1° towards the west for direct image.

Mr. Vernon, F.R.A.S., exhibited diagrams, showing the
variations of the barometer and thermometer at various
stations in England and Scotland during the storm which
occurred on the 2nd instant.

December 5th, 1861.

Murray Gladstone, Esq., F.R.A.S., was elected a Member
of the Section.

Mr. Baxendell, F.R.A.S., read a Paper " On the
Influence of the Seasons on the Rate of Decrease of the
Temperature of the Atmosphere with Increase of Height in
different Latitudes in Europe and Asia."

[This paper will be read at the Ordinary Meeting of the
Society, to be held on the 24th instant.]

152

Mr. Dickinson read a Not(3 •' On the Eclipse of the Sun.
December 31st, 1861."

This eclipse, being small compared with several that have
lately occurred, will not attract so large an amount of general
attention ; it will, however, be of considerable interest to
scientific persons, and in the hops that the members of this
Society will not consider it an unimportant phenomenon, the
following results are submitted to enable them to compare
their observations with the computed times.

Calculations for Manchester (Royal Infirmary), lat. N.
53° 29', long. W. 2° 14'.

H. M. S.

Eclipse begins, December o 1st .... 1 49 19

Greatest Phase 2 49 9

Eclipse ends S 45 29

mean time at Greenvrich.

Magnitude of the Eclipse (Sun's diameter=I) 0*413 on
the Sun's southern limb.
Angle from North Pole, of —

First contact, 143° towards the West,
Last contact, 108° towards the East.
Angle from vortex, of —

First contact, 157° towards the West,
Last contact," 80° towards the East,
for direct image.

153

Ordinary Meeting, December 24tli, 1861.
J. P. Joule, LL.D., President, in the Chair.

Mr. Brockbank exhibited some samples of steel manu-
factured by Mr. Bessemer's process. These specimens had
been bent and twisted cold, and showed a remarkable degree
of ductility. He stated that the Bessemer steel %vas one of
the most plastic and manageable of metals- — more so even
than copper. It could be bent, flanged, or twisted, either
hot or cold, without annealing, and over a considerable range
of temperature — which is not the case with ordinary steel or
copper.

A plate of 1 8 inches diameter had been forced through a
series of dies until it formed a tube 13 feet long and If inches
diameter, without any crack or ilaw.

A ring of metal could, at one heat, be hammered into a die
to form a locomotive engine chimney top.

In drilling a circular hole into a plate, continuous shavings
are formed — whereas, in copper, or Low Moor plates, or any
other metal, the shavings break into pieces iVin. long.

Thin sheets of the Bessemer soft steel can be bent back-
wards and forwards hundreds of times without a fracture, and
are almost as flexible as paper.

Mr. BiNNEY stated that many years since he had commu-
nicated to the Society a description of some markings on the
surface of the Kerridge flags. At that time he could not
satisfactorily account for them. He afterwards published, in
Vol. X (new series) of the Memoirs, a Paper on similar mark-
ings, found in the Upholland flags, near Wigan, and attri-
buted them to the burrowing of an animal similar to the
common lug worm of our coast, the arenicola piscatorum.
Proceedings— Lit. & Phil. Society—No. 7.— Session 1861-62.

154

Similar holes have since been found by Mr. Salter, F.G.S.,
in rocks of various ages^ from the Cambrian upwards, and
that distinguished palaeontologist has called them arenicolites.

The position of the Kerridge flags is, probably, one of the
best ascertained in the whole coal field. It is in the lower
division above the millstone grit. In his lower coal field he
gives two main beds of flagstones : the first or lower, the
Rochdale series, under the rough rock ; and the upper, or
Upholland or Kerridge series, above the same rock, the chief
workable beds of the lower coal field of Kochdale and other
districts, often termed the " mountain mines," lying midway
between these two flag deposits. This series of coal is now,
and has been for many years, wrought under the Kerridge
flags, so as prove beyond doubt the position of the latter.
Some discussions have lately taken place in the newspapers
at Macclesfield as to whether the Kerridge beds were per-
mian or carboniferous. No one, who ever saw permian beds,
could ever for one moment suppose Kerridge flags to belong
to those strata. It is possible that permian beds may exist in
the low district lying between Kerridge and Macclesfield, as
they have been met with at Hug Bridge on the souths and
Norbury Brook on the north, but up to this time they have
not been proved to be there.

Considerable interest has been excited by the discovery of
what were supposed to be the foot-marks of some animals on
the surface of the flags. He had been induced to make two
journies to Kerridge for the purpose of examining them.
Once he found two ripple marks pressed into one, which some-
what resembled a human foot, and which was shown to him
as the mark of one ; and at another time he was shown what
was called a track of some animal, but which was evidently
no track at all, but most probably made by running water.
Although plenty of worm holes and ripple marks are to be
found on the surface of the Kerridge flags, as yet he had seen
no tracks of animals upon them.

155

Mr. Edward Hull, B.A., called attention to instances of
glacial striations recently discovered by Mr. G. H. Morton,
at Liverpool, during a recent visit to that town in connection
with his duties on the Geological Survey. Mr. Hull was
kindly conducted by Mr. Morton to the spots where the striae
are visible. One of these is at the south, the other at the
north side of the town, and at the latter the extent of surface
exposed Js several hundred square yards. The rock-surfaces
had been protected by a thick coating of boulder clay, which
has been removed for brick-making. It is owing to the pro-
tection thus afforded to the rock that the striations are
preserved in all their original freshness. The rock belongs
to the New Ked Sandstone, and is a moderately hard reddish-
brown and yellowish building stone. There are two systems
of striae, the primary one ranging N.N.W., the secondary
nearly east and west. Of the latter, the markings are
comparatively unimportant, but are very clear and sharp.
The primary stride run in remarkably straight lines — in the
form of deep groovings and scratches, and the w^hole surface
of the sandstone is worn down to one uniform gently-sloping
plane.

It appeared evident, from the directions of the striae, that
they had been produced by icebergs coming from the north^
in all probability from the Cumberland mountains, where
glaciers are known to have existed during the period of the
boulder clay, or rather earlier. The secondary groovings
might have been produced by bergs coming from North
Wales^ but this appeared very problematical. The interest
attached to these cases of glaciation was stated to arise from
their position at so great a distance from the Cumberland
range. In the immediate neighbourhood of these mountains^
as also in that of North Wales, ice-moulded surfaces have
frequently been observed, but never before on the New Eed
Sandstone of Lancashire or Cheshire. (See Mem. Lit. and
Phil. Society, Vol. I., 3rd Series.)

156

Mr. E. W. BiNNEY referred to the existence of similar
striations ou the Carboniferous limestone of Great Ormes
Head, where the groovings were found to range northward,
or outwards from the mountains of the interior. He also
noticed the distribution of the Shap granite, blocks of which
he had lately seen on the high Silurian and Carboniferous
ranges to the south and south-east of Shap Fell.

Mr. Brockbank stated that, on the high lands of York-
shire and Derbyshire, he had observed erratic blocks which
could be traced to their northern sources.

Mr. Hull, in conclusion, stated that it had been abundantly
shown, by the collection of a large number of facts, that the
direction of the erratic blocks of the Drift period was from
north to south, so that there must have been some pre-
dominating influence in operation, either prevalent winds, or,
more probably, oceanic currents, tending to impel southward
the icebergs and rafts which were the vehicles for the
transportation of the erratic boulders and pebbles.

A Paper was read by Mr. Baxendell, F.R.A.S., ^' On
the Influence of the Seasons on the Rate of Decrease of the
Temperature of the Atmosphere with Increase of Height, in
different Latitudes of Europe and Asia."

The determination of the laws of the distribution of heat
in the different strata of the atmosphere under various
circumstances of season, locality, direction of the wind, baro-
metric pressure, &c., is one of the most important, and, at the
same time, one of the most difficult problems which can
encase the attention of the meteorologist. Notwithstanding
the labours of many able meteorologists and physicists,
several points of considerable importance to the future pro-
gress of meteorology are still involved in doubt and obscurity ;
and the necessity for further inquiries has been so generally
acknowledged, that at the late meeting of the British Asso-
ciation in this city, a grant of i>200. was renewed to defray

157

tlie expenses of balloon ascents, to be undertaken for the
purpose of obtaining additional data^ of a reliable character,
to serve as a basis for future investigations. The Author,
therefore, thought it might be worth while to submit to
the Society some results which, although confessedly im-
perfect, seem to him to indicate very clearly the existence
of a law of distribution of temperature in the higher regions
of the atmosphere in the different seasons in different lati-
tudes of Europe and Asia, which appears to have hitherto
escaped notice, and which seems likely to have an important
bearing upon many interesting questions in meteorology.

From numerous observations made at elevated stations in
Europe and India, it has been concluded, 1st, — That the
general rate of decrease of the temperature of the atmosphere
with increase of height, is least in low, and greatest in high
latitudes ; and 2nd, — That the rate of decrease is greatest in
the summer and least in the winter months. Some results,
however, which the Author obtained in the course of an
investigation of the relations which exist between falls of rain
and changes in the decrement of temperature on ascending in
the atmosphere, and of barometric pressure, in different loca-
lities, led him to doubt the general correctness of tUe second
of these conclusions, and he has therefore examined all the
observations that were accessible to him which seemed likely
to throw any light on the subject ; and from the results which
he has obtained he shows that there exists in the temperate
latitudes of Europe and Asia a belt or zone in which the
decrease of temperature, for a given ascent in the atmosphere,
is greatest in the winter months, v/hile at stations north or
south of this belt, so far at least as observations have yet been
made, the decrease is greatest in the summer months.

This belt passes over Portugal, Spain, Sicily, Southern
Italy, the Caucasian provinces, and Southern Siberia; and
at places lying within it the changes of temperature produced
by cliange of season are greater in the higher than in the

158

lower strata of the atmosphere; while, on the contrary, at
places'north or south of the belt the changes of temperature
are greatest in the lower strata. The details of the results
are given in the Paper, and all the temperatures are reduced
to Fahrenheit's scale, and the differences of elevation to
English feet.

The great changes of temperature which take place in the
higher strata of the atmosphere in the belt, indicate a less
capacity for heat and a greater degree of dryness of the air in
these strata than in the corresponding strata beyond the belt.
The Author was therefore led to conclude that the ratios of
the quantities of rain falling on the mountain and on the
plain would be less at places in the belt than in other locali -
ties ; and the results which he has given of the comparisons
of the mean annual amounts of rain-fall at different stations
fully bear out this conclusion. Comparisons are also made
of the falls of rain during the winter and summer halves of
the year ; and it is shown that at places in the belt the ratio
of the quantity falling on the mountain to that falling on the
plain is greater in the summer than in the winter half of the
year, while on the contrary, at places beyond the belt, it is
greatest in the winter half.

The Author then draws attention to some results which
appear to indicate that the annual rate of decrease of tempe-
rature, on ascending in the atmosphere, is subject to a
periodical change. Comparing Geneva and Milan with the
Great St. Bernard, the annual rate for the years 1848 — 58
exhibits, with but trifling irregularities, a gradual increase
up to the beginning of the year 1854, and afterwards a
o-radual decrease. The differences of temperature between
the two stations By well and Allenheads, in Northumberland,
at a difference of elevation of 12T3 feet, also show a progres-
sive increase from 4*14° in 1856, to 0-07° in 1860. The
Author remarks that the epoch when the rate of decrease was
at a maximum, as shown by the Geneva and Great St. Ber-

159

nard observations, corresponds exactly with the epoch of
minimum magnetic disturbance, as determined by General
Sabine from the magnetical observations made at the colonial
observatories and at Pekin ; and he shoves that there is some
probability that the period of the change in the rate of
decrease also corresponds with the period of magnetic dis-
turbance.

In concluding, the Author tenders his grateful acknow-
ledgements to Mr. Vernon^ F.E.A.S., for the valuable assist-
ance he has rendered him in procuring data, and in referring
to original publications for the purpose of clearing up doubtful
points; and he also remarks that without the means of
reference afforded by the many valuable volumes of meteoro-
logical observations now in the Society's library, it would
have been quite impossible to have undertaken an inquiry of
this nature.

160

M I C E O S C 0 P I C A L SECTION.

Meeting, December IGtli, 1861.

E. W. BiNNEY, F.R.S., F.G.S., in the Chair.

Dr. Edward Morgan was elected a member of the Section.

Dr. Wallich kindly presented to the Section for mounting
several specimens of material, from his private collection,
containing Biddulphia of various kinds, and other diatomaceae,
from Guernsey, St. Helena, &c.

Mr. Thomas H. Nevill presented to the Section eight
slides, mounted from the specimens of Soundings, No. 131,
taken in Lat. 51° 48^ N., Long. 7° 8^ W., oiF the south coast of
Ireland, in 40 fathoms, presented by Captain Moodie, of the
R.M.S.S. " Canada." Mr. Nevill reported that the specimen
contained Entosolenia Marginata, Entosolenia Squamosa,
Lagena Vulgaris, Textularia, Kotolina, Miliolina. Numerous
spines and plates of Echini ; calcareous prisms from shells,
&c., &c., all water-worn. The sand is composed of about
half calcareous and half silicious material.

Mr. Latham proposed that the subject for discussion, at
the next meeting, should be '' On the Cause of the Metallic
Lustre on the Wings of the Lepidoptera, both Diurnal and
Nocturnal," which was agreed to. Mr. Latham also reported
upon the Ovum presented at the last meeting by Mr. Leigh.
Mr. Latham presented to the Section a slide, mounted with a
portion of the elytra of the Platyomus subcostatus, from
Venezuela ; also, an oak spangle with stellate hairs.

Mr. BiNNEY exhibited mounted specimens of Fossil wood,
from Standish, near Wigan; Trigonocarpon oliviforme,
from the lower Lancashire coal bed ; and the palate of the
Psammodus porosus, from the mountain limestone, county
Armagh.

161

Mr. Joy presented mounted sections of coal from Bohemia,
showing woody fibre.

Mr. Whalley exhibited living ova of the Trout, one month
old.

Mr. Brothers exhibited a section of Agate from Siberia ;
Stentor Miilleri, &c.

SECTION FOR STATISTICS AND SOCIOLOG-Y,

December 17th, 1861.

Mr. Isaac Holden read a Paper '^ On the Effects Pro-
duced by the Character of their Residences upon the Physi-
cal and Moral Condition of the Working Classes." Mr.
Holden believed that although considerable attention had
been given to the building of cottages, sufficient progress
had not yet been made in making them comfortable and
attractive to the inmates. If this were done it would contri-
bute gi-eatly towards furthering their domestic happiness, as
they so frequently leave their homes seeking pleasure, instead
of resting after their labours, cultivating their minds, and
preparing themselves for their duties next day. The public
has already been frequently told that the accommodation was
insufficient for comfort and decency, and, he would add, also
for health.

The interest of Mr. Holden's Paper consisted in the minute
knowledge which his many facts displayed of the subject.
He particularly dwelt on the present most imperfect method
of dealing with the refuse of towns, and the great evils that
resulted from its accumulation near every house.

162

Mr. Henry Ashworth stated that a firm near Bolton
had considered it their interest to erect for their workpeople
cottages of a superior class^ mostly containing three bedrooms,
and in other respects commodious and convenient. They
were let at a rental of six per cent on the outlay, and were in
great requisition. The beneficial effects upon the social and
moral condition of the tenants was undoubted.

163

Ordinary Meeting, January 7th, 1862.

Edward Schunck, Ph.D., F.R.S., Vice-President, in

the Chair.

Prof. Dr. Johannes Gistel^of Kempten in Bavaria; Federico
Lancia di Brolo, Inspector of Studies in the University of
Palermo; and James Nasmyth, Esq., C.E., were elected
Corresponding Members of the Society.

A Paper was read by J. P. Joule, LL.D., President,
entitled, " Experiments on some Amalgams."

The weakness of the affinity which holds the constituents
of amalgams in combination seemed to the Author to oiFer
the means of studying the relationship between chemical and
mechanical force. His inquiries were extended to several
amalgams, and gave results of which the following is a
summary : —

Amalgam of iron was formed by precipitating iron on
mercury electrolytically. The solid amalgam containing the
largest quantity of mercury appeared to be a binary compound.
Iron does not appear to lose any of its magnetic virtue in
consequence of its combination with mercury. Its amalgama-
tion has the effect of making it negative with respect to iron
in the electro-chemical series. The affinity between mercury
and iron is so feeble that the amalgam is speedily decomposed
when left undisturbed, and almost immediately when agitated.
The application of a pressure of fifty tons to the square inch
drives out so much mercury as to leave only thirty per cent of
it in the resulting button.

Proceedings— Lit. & Phil. Society— No. 8.— Session 2861-62.

164

Amalgam of copper. By precipitating copper on mercury
electroly tically, a mass of crystals is gradually formed. After
a certain time the crystals begin to get fringed with pink^
indicating uncombined copper. In this state the amalgam is
found to be nearly a binary compound. On applying strong
pressure to an amalgam containing excess of mercury, the
latter is driven off, leaving a hard mass composed of equiva-
lents of the metals. If, however, the pressure be continued
for a long time, the resulting amalgam contains more than
one equivalent of copper, indicating a partial decomposition.

The Author gave an account of his experiments with
amalgams of silver, platinum, lead, zinc, and tin. In the
case of the latter amalgam, long-continued pressure drives off
nearly the whole of the mercury, indicating in a striking
manner the efficacy of mechanical means to overcome feeble
chemical affinities.

Dr. Angus Smith said, It is difficult to tell the exact limits
of chemical and mechanical action, because they flow into
each other. Let us call the attraction of surfaces a mechanical
action, as it is not to our knowledge a chemical combination.
Porous bodies exercise this to a very large extent, and yet do
not produce chemical compounds. The amount is limited on
one side by the pressure of the atmosphere. Chemical com-
pounds are too powerful to be affected by such slight forces.
Porous bodies or surfaces do not take up others in chemical
equivalents so far as we know ; the full capacity of saturation
is not satisfied, because of counteracting influences. Water
admits air very rapidly, but it is held so slightly that it is
affected by atmospheric pressure, and even seems to follow
exactly the atmospheric pressure ; but a portion is held with
such power that it is extremely difficult to remove, and is not
ever removable by the mere removal of pressure as far as we
know. The small affinity of the great mass or surface of
water is equal to a great affinity for a small amount of air.
All masses have more or less this mechanical action, but, as

\G5

in the case of porous bodies, the attraction is feeble, and not
raised into the power of a definite grasp of a given quantity-
such as an equivalent, which is the case with a powerful
affinity forming a chemical compound. Large and watery-
masses lose their water slowly by the mere force of gravitation.
Strong mechanical action rises to an equality with feeble
chemical affinity. Weak chemical affinity sinks into an
equality with mechanical action. Charcoal absorbs gases
more eagerly under pressure, but by a removal of pressure
they are still absorbed ; so that the mechanical force is greater
than the weight of the atmosphere can control. There are
many cases in which these two forces, if they be two, meet.
This of the mercury and other metal is one case. The feeble
chemical afiinity is, I suppose, overcome by the powerful
mechanical force. The alloy with sufficient chemical affinity
remains, that with a weak affinity separates. The mercury
flows off following the law of liquids ; in like cases it flows off
like water flowing slowly from a moist porous mass like wet
clay. Instances from the feeblest to the most powerful affinity
might be given, showing that only when the power reached a
definite point did the law of chemical equivalents come in.
At the same time there is a definite point where surface action
ceases under certain conditions.

These ideas have arisen partly from experiments on the
subject, which may some day be published. I believe they
explain the difficulties attending the attraction of masses
which seem occasionally to oppose the combination by atomic
weights.

A Paper was read "On the Conductibility of Heat by
Amalgams," by Dr. F. Ckace Calvert, F.R.S., and Mr.
Richard Johnson.

The method followed in the investigations described in this
Paper is the same as that detailed in their former Paper on
the conductibility of metals and alloys.

166

In the first part of their Paper the Authors treat of the
conductibility of mercury, and prove that if the source of heat
be applied at the upper part of a column of mercury, so as to
prevent any motion of the solid molecules of the mercury,
this metal becomes the worst conductor of all known metals ;
for, silver being 1000, mercury is 54.

In the second part of their Paper the Authors examine the
conductibility of the solid and semisolid amalgams prepared
in equivalent quantities of pure metals with mercury, and
they show that amalgams may be divided into two classes —
those containing an excess of equivalents of the amalgamated
metal, and those which on the contrary contain an excess of
equivalents of mercury. The first class conduct heat at the
mean rate of the two metals composing the amalgam, and in
accordance with the calculated result, as shown by the follow-
ing table.

Amalgam of Tin.

Mercury = 21-63 or 679
Tin....= 13 45 or 422

Silver = 1000

Found. Calculated. Found. Calculated.

6 Sn. Hg 10-60 15-M 332 .... 4/8

5 „ „ 10-30 15-63 323 490

4 „ „ 9-65 15-88 .... 302 .... 498

3 „ „ 9-45 16-30.... 296 571

2 „ „ .... 8-65 .... 17-19 .... 271 .... 539

Sn. Hg 5-15 18-56 161 582

„ 2 Hg 4-75 .... 19-75 .... 149 .... 619

„ 3 Ilg 4-20 20-26 .... 131 .... 635

,, 4Hg 3-95 .... 20-55 .... 124 644

„ 5 Hg 3-65 20-73 114 650

The second class, comprising those amalgams containing
an excess of mercury, conduct heat as if they contained no
other metal, although its proportions may vary from 10 to 34
per cent.

I
i

167

These interesting results were confirmed by observing
amalgams of tin, zinc, bismuth, copper, lead, and silver, and
applying the source of heat in all cases at the upper part of a
perpendicular column of the amalgam.

The third part of their Paper has reference to the conducti-
bility of mercury when mixed with two per cent of various
metals, and when the heat is applied at one end of a horizontal
column ; and they have obtained the following interesting
series of results.

Found.

Pure mercury ... . 21*63

Mercury with two
per cent of

Silver 2-30

Tin 5-65

Copper 13-19 .

Gold U-50

Bismuth 18-75

Lead 19-25

Cadmium 20-20 .

Zinc •. 21-20

Calculated.

Found.

. . 679

Calculated

.... 21-81 ..

.. 72

. . . . 684

. ... 21-43 ..

.. 177

. . . . 672

21-62 . .

.. 413

. . . . 678

21-79 ..

.. 454

. . . . 680

21-20 . .

.. 588

664

.... 21-34 ..

.. 603

.... 668

. ... 21-51 ..

.. 633

. . . ., 676

.... 21-56 ...

. . 664

676

This table shows that the greater or less conducting power
of the metal amalgamated with it has no influence in modify-
ing the conductibility of the amalgam itself; for we find that
the amalgam of bismuth (the worst conducting metal) con-
ducts heat eight times better than that of silver (the best
conductor), for

Mercury -\- 2 per cent of Bismuth 588

+ 2 „ Silver 72

They were induced to believe at the beginning of these
researches that the cause which impeded the conduction of
heat in so marked a manner in some of these amalgams was
the presence of small crystals of amalgam floating in excess

168

of mercury, as they had observed that whilst the crystallised
amalgams of silver and tin conducted heat badly, that of zinc,
which was perfectly fluid and free from crystals, conducted
heat very freely. As they pursued their researches they
found these views to be incorrect, for the amalgam of bismuth,
a very crystalline one, conducted heat with great facility.

Having observed that tin affected the fluidity of mercury
in a most remarkable manner, so that even the one hundred
thousandth part of that metal would interfere with the pro-
perty which mercury has of assuming easily a globular form,
they prepared the following series of amalgams of tin.

Silver=:1000

Found. Calculated. Found. Calculated.

Mercury 94-50+Tin 5'50 ... 4-00 ... 2M4 ... 125 ... 663
97-00-1- „ 3-00... 4-60 ...21-35... 144 ...669
98-004- „ 2-00 ... 5-65 ... 21-43 ... 177 ... 672
98-25-f ,,1-75... 5-90 ...21-45 ...185 ...673
98-50-1- „ 1-50 ...10-95 ...21-47 ...343 ...673
99-004- „ 1-00 ... 19-30 ... 21-52 ... 605 ... 675
99-50-h „ 0-50 ... 19-30 ... 21-56 ... 605 ... 675

This table proves that up to 1-75 the conductibility of
mercury remains constant, when by reducing the tin by to dth
the conductibility of the amalgam is doubled ; by further
abstracting one-third of the tin, the conductibility is again
doubled.

169

Ordinary Meeting, January 21st, 1862.

E. W. BiNNEY, F.R.S., F.G.S., Vice-President, in the Chair.

William Arthur Darbishire, Esq., B.A., was elected an
Ordinary Member of the Society.

A Communication, " On the Action of Nitrate of Sodium
on Sulphide of Sodium at Different Temperatures," by Dr.
Ph. Pauli, Union Alkali Works, St. Helens, Lancashire,
was read by Professor Roscoe.

The mother liquor obtained in the manufacture of soda
ash contains, as is well known, large quantities of sulphide
of sodium. In order to oxidise that compound, nitrate of
sodium is used. As long as the boiling point of the liquid
is betw^een 280 — 290° F., the sulphide is quietly oxidised to
sulphate, nitrite of sodium being formed.

But if the nitrate is added when the temperature of the
boiling liquid is about 310° F., a violent evolution of ammonia
takes place, according to the following equation —

2NaS + NaNO 6 + 4H0 = 2NaS04 + NaH02 + NH3

As the liquor contains a large amount of sulphide, the
quantity of ammonia is so considerable that it may prove
worth while to connect the evaporating pot with a tower
filled with coke, over which a stream of water or dilute acid
is running.

If the nitrate be added when the liquor has been heated to
a temperature much above 310°, a violent evolution of pure
nitrogen occurs.

o Na S + 4 N« NO 6 + 4 HO = 5 No SO 4 4- 4 Na O2 H + 4 N.
PfiOCEBDiNGs— Lit. & Phil. Society—No. 9.— Session 1861-62.

170

Mr. Leigh suggested that the evolution of nitrogen in
volcanic eruptions might be due to a reaction similar to that
described in Dr. Pauli's Paper.

Mr. Spence and Dr. Calvert explained the processes
employed in manufacturing caustic soda for commercial
purposes. Mr. Spence also described the beds of nitrate of
soda in Southern Peru and Northern Chili, from which
nearly all the commercial nitrate of soda is obtained.

Mr. Baxendell believed that the preservation of the
nitrate of soda in these beds had been due to the dryness of
the climate, as rain rarely falls in the region in vrhich they
are found. Had the climate been a rainy one, he believes
the deposits of nitrate of soda would long since have been
washed away.

Mr. Baxendell communicated an observation of Saturn
which he had lately made. Owing to the relative positions
of the sun and earth, with respect to the plane of the ring
of Saturn, the ring ought now to be quite invisible in
telescopes of moderate power; but on the night of the 18th
instant he had seen very distinctly a portion of the ring on
the following or east side of the planet. The telescope
used was Mr. Worthington's achromatic of five inches
aperture. He also stated that from observations made by
himself and Mr. Williamson, in 1848, he had been led to
believe that the plane of the ring was not exactly parallel
to the dark belts on the body of the planet. As several
members of the Society now possess good telescopes, it is
to be hoped they will direct their attention to this interest-
ing point, and favour the Society with the results of their
observations.

A Paper, ^^ On the Convective Equilibrium of Tempera-
ture in the Atmosphere," by Professor Wm. Thomson, LL.D.,
P.K.S., &c., was read by Dr. Joule.

171

The particles composing any fluid mass are subject to
various changing influences, in particular of pressure, vrhen-
ever tliey are moved from one situation to another. In this
way they experience changes of temperature altogether
independent of the efiects produced by the radiation or con-
duction of heat. When all the parts of a fluid are freely
interchanged and not subject to the influence of radiation
and conduction, the temperature of the fluid is said by the
Author to be in a state of convective equilibrium. The
equations of convective equilibrium in the atmosphere investi-
gated by the Author are as follows^ IT, T, and W denoting
the pressure, temperature, and mass per cubic foot of the air
at the earth's surface, and p, t, and p the same qualities of
the air at any height x,

which is the known relation between temperature and
pressure.

the deduced relation between pressure and density ; and
» dp^=z — p dx (3) ,

the hydrostatic equation, the variation of gravity at different
heights being neglected, and the weight of unit mass (lib)
being taken as unit of force. Hence by integration,

t ^ W.C ^ — 1 n

^ = 1 — 7—^ Or if, for brevity, we denote — by H,

t X k—l

— = 1 — (4)

T H ^ -^

From (4) and (1) it appears that temperature and density

1*41
would both vanish at the verv moderate height — rrxH

172

which is about 90100 feet, or between 17 and 18 miles, if
convective equilibrium existed and if the gaseous laws had
application to so low temperatures and densities. It has
always appeared to the Author to be most improbable that
there is any limit to our atmosphere ; and no one can suppose
that there is a limit at any height nearly so small as 17 or 18
miles. It is difficult to make even a plausible conjecture as
to the effects of deviations from the gaseous laws in circum-
stances of which we know so little as those of air at very low
temperatures ; but it seems certain that the other hypothesis
involved in the preceding equations is violated by actions
tending to heat the air in the higher regions. For at
moderate elevations above the surface, where we have
air following very strictly the gaseous laws, the rate of
decrease of temperature would, according to equation (4), be

•41 V T 1° /. .

be .TrfrT pel' foot, that is to say, ^ per foot, since

T

H = 26224 X 7.^1, or 1° cent per 329 feet. Now, the actual

274

decrease, according to Mr. Welsh, is 1° cent in 530 feet, or
not much more than half that according to convective
equilibrium.

It seems that radiation, instead of partially accounting
for the greater warmth of the air below, as commonly
supposed, may actually diminish the cooling effect, in going
up, which convection produces. In fact, since direct con-
duction is certainly insensible, we have only convection
and radiation to deal with, except when condensations of
moisture, &c., have to be taken into account. In fair and
cloudless weather, then, the lower and lowest air being on the
whole warmer (the lowest being of course at the same tem-
perature as the earth's surface), it is perfectly certain that
the upper air must gain heat by radiation from the lower —
and that the convective difference of temperature must be
diminished by the mutual interradiation.

173

There are difficulties connected with the radiation of air
and earth out into space, and of heat from the sun to air and
earth; but I think a full consideration of all the circum-
stances must explain the smallness of the decrease of tem-
perature which observation shows.

Dr. Joule having suggested that condensation of vapour
in upward currents of air might account, to a considerable
extent if not perfectly, for the smallness of the lowering of
temperature actually found in going up, the Author has added
the following investigation, in which the effect of condensa-
tion is taken into account.

If a quantity of air, dry or moist, is allowed to expand
from bulk v to bulk v-\-dv, it will do an amount of work
equal to pdv on the surrounding matter. Now, by the
principle established approximately by Dr. Joule, in his
experiments on air in 1844,* the change of temperature which •
the mass will experience will be almost exactly equal to what
would be produced by keeping it at constant volume, v-\-dVy
andjemoving a quantity of heat equal to the thermal equivalent

oi pdv. This is expressed by -—pdv^ if we adopt the usual

notation, J, for the dynamical equivalent of the thermal unit.
Now, if t and t-\-dt denote the primitive and the cooled tem-
peratures, so that — dt expresses the cooling effect (which is
positive, dt being negative), the bulk of the vapour, if at

ds
saturation in each case, would be v — if 5 denote the volume

of a pound of vapour at saturation at any temperature t, and

s-\-ds its volume at temperature t-\-dt. Hence if, as it will

ds
be seen is the case, v — is greater than dv, a portion equal

ds
in bulk to v — — dv of the water primitively in vapour, must

* " On the Changes of Temperature produced by the Earefaction and Con-
densation of Air," commumcated to the Eoyal Society June 20, 1844, and
published in the " Philosophical Magazine," 1845, first half year.

174

become condensed. Hence the abstraction of the heat,
~Y-pdv produces two effects; it cools the mass of air at con-
stant volume from temperature t to temperature t+df, and it

condenses a bulk

ds

— dv

of vapour. Hence, if L denote the latent heat of a cubic
foot of vapour of water at temperature f, and N the specific
heat of one pound of air in constant volume, we have

1 ds

^pdv=z'^X{—di)+L(v—~~dv,)
J \ s /

if we suppose the mass of air considered to weigh 1 lb. (with

or without the vapour, which will make but little difference

on the whole weight). Hence

dlog s

JN + JLv —

dv — dt

— dt i? + JL

ds
where, for brevity, d log s is written in place of — t log s

s

denoting the Napierian logarithm of s.

d logs .
To find L and — ^ it is necessary to know the bulk

of a pound of steam at different temperatures. Dr. Joule and
the Author demonstrated,* by experiments on air and by
dynamical reasoning, that

3 dp /^ X
7
where p denotes the pressure of vapour at saturation at the

temperature t, and — denotes the rate of the bulk of liquid

to vapour. Since — is very small, we have L = -- ^

approximately.

* On the Thermal Effects of Fluids in Motion, Part II., Theoretical Deduc-
tions, Section II., Traasactions of the Epya} Society, Jime, 1851.

175

It was shown also in the same Paper, that the density of
saturated vapour was to be obtained more accurately from
this equation, and Eegnault's experiments on the latent heat
of a stated weight of vapour, than from any direct experi-
ments on the density of vapour made up to that time. This
conclusion has been verified by the recent experiments of
Messrs. Fairbairn and Tate. With the assistance of some
excellent tables in Rankine's " Steam Engine and other
Prime Movers," calculated on these principles, the Author
has obtained the following results :■ —

lit

Volume of 1 lb. of

Dynamical
value of latent

onnte
1 of bulk
1 vapour
.. of any
ed
iture.

Augmentation of

Elevation
from earth's

S 2?j

air at pressure

beat of 1 lb.

■■gS^sai

volume of 1 lb. of

surface re-

|1^

2,117 lb. per

of saturated

moist air required to

quired to cool

square foot.

vapour.

cool it 1» cent.

moist air by

Pr

dimi
of sat
per]

te

1" cent.

d log s

dv

dx

<-273 7

V.

J L

-dt

-dt

-dt

0°

12-38 cubic ft.

249 ft. lbs.

•0698

•1905 of a cubic ft.

499 feet.

5

12*61

348

•0671

•2150

551

10

12-83

481

•0644

•2434

611

15

13.06

655

•0617

•2753

678

20

13-29

881

•0592

•3096

751

25

13-52

1171

•0569

-3455

827

30

13-74

1538

•0546

•3800

900

35

13-97

1999

•0524

•3950

932

The last column of this table, headed ___ -, is calculated
from the column headed __ , by the following formula : t—

dx

—dt

P

(^+t)

which shows the height, dx, that must be reached to get a
lowering of temperature, — dt, when air saturated with
moisture ascends. The pressure, jo, is taken as 2117 lbs. per

V

square foot ; and the value of -— , which is the name for the

t

176

diiFerent temperatures, is - -. The results, for tempe-
ratures from 0° to 35° cent, are exhibited in the last column
of the table. For the temperatures 0°, 5°, and 10°, they
agree very well with the height in which Mr, Welsh found a
lowering of temperature of 1° cent; and we may conclude
that at the times and places of his observations the lowering
of temperature upwards was nearly the same as that which
air saturated with moisture would experience in ascending.

It is to be remarked that, except when the air is saturated,
and when, therefore, an ascending current will always keep
forming cloud, the effect of vapour of water, however near
saturation, will be scarcely sensible on the cooling effect of
expansion. Hence the law of convective equilibrium of
temperature in upward or downward currents of cloudless air
must agree very closely with that investigated above, and
must give a variation of 1° cent in not much more or less
than 330 feet.

It appears, therefore, that the explanation suggested by
Dr. Joule is correct ; and that the condensation of vapour in
ascending air is the chief cause of the cooling effect being so
much less than that which would be experienced by dry air.

The following extract of a Letter from Professor W.
Thomson, LL.D., &c., to the President, was also read : —

"About two years ago I wrote to you that a metal bar,
insulated so as to be moveable about an axis perpendicular to
the plane of a metal ring made up half of copper and half of
zinc, the two halves being soldered together, turns from the
zinc towards the copper when vitreously electrified, and from
the copper towards the zinc when resinously electrified.

" If the copper half and the zinc half of the ring are insu-
lated from one another, and if they are connected by means
of wires with two pieces of one metal maintained at any stated
difference of potential by proper apparatus for dividing the

177

electro-motive force of the two plates of a Daniell's element
into 100 parts, from 60 to 70 of those parts are required to
reduce the zinc half ring and the copper half ring to such
a state that the moveable bar remains at rest whether it is
electrified vitreously or resinously.

'•' If the copper half ring is oxydised by heat, the amount
of electro-motive force then required to neutralise the two
halves is much increased. If, after oxydising the copper one
day by heat, I leave the apparatus till the next day, the effect
is generally diminished, though something of it still remains.
After again heating the copper by laying it for some time on
a redhot iron heater and alloAving it to cool, I found the effect
almost exactly 100 parts. I have no doubt that by making
the coat of oxyde very complete and thick enough, and by
cleaning the zinc perfectly, I shall be able to get considerably
above the electro -motive force of a single Daniell's element.
I remembered perfectly Avhat you told me a long time ago
about heating the coppers of a battery and getting a strong
effect, for some time equal to that of the Daniell's cell, when
I tried the effect of oxydising the copper plate by heat.

'^I believe there are also electrical effects of heat itself; so
that if one half of a ring of one metal is hot and the other is
cold, the needle will show a difference according as it is
charged positively or negatively.

^^ For nearly two years I have felt quite sure that the proper
explanation of voltaic action in the common voltaic arrange-
ment is very near Volta's, which fell into discredit because
Volta or his followers neglected the principle of conservation
of force. I now think it quite certain that two metals dipped
in one electrolytic liquid will (when polarisation is done away
with) reduce two dry pieces of the same metals, when con-
nected each to each by metallic arcs, to the same potential.

" There cannot be a doubt that the whole thing is simply
chemical action at a distance. Zinc and copper connected
by a metallic arc attract one another from any distance.

■ 178

Sd do platinum plates coated with oxygen and hydrogen
i:espectively. I can now tell the amount of the force, and
calculate how great a proportion of chemical affinity is used
up electrolytically, before two such discs come within to-o uth
of an inch of one another, or any less distance down to a limit
within which molecular heterogeneousness becomes sensible.
This of course will give a definite limit for the sizes of atoms,
or rathei*, as I do not believe in atoms, for the dimensions of
molecular structures."

179

Ordinary Meeting, February 4:th, 1862.
J. P. Joule, LL.D., F.R.S., President, in the Chair.,

Mr. BiNNEY said that soon after the death of Professor
Eaton Hodgkinson^ F.R.S., one of the former Presidents of
the Society, and a man of science, of whom not only this
Society, hut the city of Manchester, has good reason to be
proud, a few of his friends and admirers gave a commission
to Mr. Slater, the sculptor, of London, to execute a bust of
the deceased, to be presented to this Society. As his valuable
memoirs, which gave to the world the formulae for solid and
hollow pillars of cast iron, now the basis of calculation on all
structures of that metal, were printed in our Transactions, it
was thought that the Hall of the Literary and Philosophical
Society of Manchester was the fittest place for the bust of
their discoverer.

The following gentlemen, viz., our worthy President,
J. P. Joule, LL.D., F.R.S., E. Schunck, F.R.S., James
Hey wood, F.R.S., John Hawkshaw, C.E., F.K.S., Joseph
Whitworth, F.R.S., R. P. Greg, F.G.S., Thomas Turner,
F.R.C.S., G. R. Stephenson, C.E., Robert Rawson, and E. W.
Binney, F.R.S., present the bust to the Society. In doing
so it would not be necessary for him to allude to the great
talents.and many virtues of the deceased, as his friend Mr.
Robert Rawson was now eng*aged in writing a Memoir, to
be communicated to the Society; but he could not omit
reading a letter which showed how the present President
of the British Association for the Advancement of Science
hailed the election of Mr. Hodgkinson as the successor of the
late Dr. Holme to the chair of this Society. It was as follows :
— ^' Chester and Holyhead Railway Company, Conway,
Peoceedings— Lit. & Phil. Society— No. 10.— Session 1861-62.

180

June 28, 1848. My Dear Sir, — I cannot resist the tempta-
tion to congratulate you on your election to the Presidency
of the Manchester Philosophical Society. I think the mem-
bers have used a sound discretion in the selection, and I am
heartily glad, after all our squabbles, to find you in a position
to which you are justly entitled. I am yours faithfully,
W. Fairbairn. To Eaton Hodgkinson, Esq."

The bust forms a companion to one of another distinguished
member of this Society, the late Dr. William Henry, F.R.S.,
and both as a likeness and a work of art does the sculptor
credit.

On the motion of Mr. Spence; seconded by Dr. R.Angus
Smith, it was resolved unanimously : — '' That the thanks of
the Society be given to the donors of the bust of the late
Professor Eaton Hodgkinson, F.R.S."

Mr. Spence brought under the notice of the Society a
ball of the dried leaves and stems of a plant imported from
the West Coast of Africa, in the Kingdom of Dahomey.
This plant, which grows spontaneously in great abundance,
is used by the natives in dying cloth, to which it is said to
give a good but not very permanent blue colour.

The parties who have imported these leaves are Messrs.
Burnet and Thwaites, of Manchester, and they state that
two years ago the sample had been examined without any
result. About two months ago, Mr. Spence gave Dr. E.
Schunck, F.R.S., a portion of them, he kindly undertaking
to see whether they contained indigo. Circumstances pre-
vented Dr. Schunck, until very lately, from entering upon
the investigation, and the importers being anxious as to the
matter, Mr. Spence, assisted by Mr. Bottomley, undertook
the investigation, and at once found that the plant contained
indigo perfectly formed, and which was easily extracted by
the usual modes of deoxidisation and solution, the indigo
being then precipitated pure and of a beautiful deep coppery

181

shade. The only question now was as to its containing indigo
in quantity sufficient to render the importation profitable.
The solution of this question being partly one of chemical
manufacture, has been undertaken by Mr. R. Rumney, who
is to operate on a large quantity so as to get results of
commercial value.

Mr. Spence was chiefly induced to bring this subject before
the Society from the fact that a new source of indigo at the
present time would be a matter of great importance to trade,
the growth of the article in India being from peculiar causes
rather on the decline.

Dr. ScHUNCK corroborated Mr. Spence's statements so far
as that he had found indigo fully formed existing in the
specimens submitted to him ; he had not had time as yet to
ascertain what quantity of that body they contained.

Mr. MosLEY stated that it had been known for some time
that the indigo plant grows wild in many parts of the West
Coast of Africa ; he believed it would be of great importance
at present if a new source of indigo could be found, as the
Indian manufacture seemed to be declining. He believed the
manufacture had been attempted in Africa, but had not
succeeded.

The Rev. Robert Harley, F.R.A.S., communicated to
the Society the following statement on the Theory of the
Transcendental Solution of Algebraic Equations : —

Certain published Papers of Mr. Cockle, as well as some
private communications from that mathematician to myself,
have led me of late to study the theory of equations under a
new and interesting aspect.

Lety (y, ^) = 0 be an algebraic equation of the nth. degree
in y, and such that its roots ^/i, ^/o? • • • ^,i ^'^'^ ^^^ functions of
a single parameter x. From this equation we may deduce a
linear diiferential equation of the (ji — l)tli order which it
is proposed to call *' the differential resolvent," The 7i roots

182

<^^ / Cy? ^) = ^i ^^^ therefore also aii)^ linear function of
those roots must satisfy the differential equation. But it is
known [see my Paper '^ on the Theory of Quintics," published
in the Quarterly Journal of Pure and Ajyplied Mathematics^
Vol. III. p. 34o] that each of the constituents of the roots of
an equation is a linear function of those roots. Consequently
each of the constituents of y must satisfy the differential
resolvent, these constituents being in fact so many particular
integrals of that equation. It follows that every particular
integral is a linear function of the constituents, for otherwise
there would be more than {n — 1) independent integrals,
which is impossible, seeing that the resolvent equation is
only of the {ii — l)th order. Hence the solution of the
differential resolvent, that is, its complete integration so as
to evolve ?/, or the several constituents of ?/, in terms of x,
will give the required solution (algebraic, trigonometric, or
transcendental) of the equation in y.

Of the two trinomial forms, suggested by Mr. Cockle, to
which it is known that any equation of a degree lower than
the sixth can be reduced by the process of Tschirnhausen or
Mr. Jerrard, I have selected the following

if^ny -\-{n — \)x=0 =f{y, ^)
because it has, when :2;=: 1, two equal roots, and therefore
affords some good verifications, and also because it leads, as
I shall show in certain researches which I hope shortly to
publish in detail, to some remarkably simple expressions.
At present I content myself with placing on record the
following results : —

In general, the first differential coefficient ~j is equal to

— I . —1— . { y^-' + xy^^-' + - • + x^^-'y—{n~ 1)
n I — x"~^ {

which gives immediately for the quadratic (n=2) the
differential resolvent

2(l-x)^4-^/"l = 0...(l)

183

and which also enables us with ease to calculate the resolvent
for the cubic {?i =. 3), viz.

Results (1) and (3) were first calculated by a different process
by Mr. Cockle, The following are now published for the
■first time. For the biquadratic {n — 4) the differential
resolvent is

• 2=(:-.,g-...3v3-..43.|+5, = 0...(3)

And for the quintic (n = 5) the resolvent is

— 3.5^M7.r^H-3.7-lly=:0...(4)
ax

The Boolian form of (3) is

("-|)("-t)(^-t) 3. „ ,, ■

^ D(D— 1)(D — 2) *" ^

d e

where D is the differential symbol — , and £ =j:.

" do

I notice also tlie following remarkable relations among the

' differential coefficients for the general case, viz.,

+ 3(/i — l)(?i-!-2)(2n+l)y

— (2;i.-l)(3?2'4-3?i — 8):^

dx

The investigations on this subject^ which I intend to
publish shortly, embrace a curious and anomalous result in

184

the theory of quadratics, a new and simple method of
deducing the arbitrary constants that occur in the integration
of the resolvents, together with the actual calculation of the
foregoing diiferential equations and some interesting formulae
of verification, by which the correctness of those equations
may be ascertained. Such formulae play a somewhat con-
spicuous part in the general scheme, for, if the differential
resolvents be employed as tests of existing theories of differ-
ential equations, it is of the utmost importance that their
accuracy should be placed beyond dispute. Notwithstanding
the complexity of the calculations by which I have arrived
at them, the differential resolvents for quartics and quintics
are, it will be noticed, of a remarkably simple form. It is
proper to mention that a large portion of the calculation of
that for the quintic was performed independently by Mr.
Cockle, and that on comparing results and making one or
two corrections, I found that his calculations coincided (so
far as they went, for they only extended to the determination
of the differential coefficients) with my own.

A Paper was read '' On the Causes of Sickness and Mor-
tality in the Manufacturing Towns of the North- West of
England," by Dr. C. J. Shearman, of Sheffield, communi-
cated by Dr. R. Angus Smith, F.R.S.

Previously to any examination of the disturbing causes of
vitality, the proportion of age to the whole population should
be ascertained for town and country districts ; for under all
circumstances, favourable or otherwise, age of an individual
determines to a great extent the kind of sickness and the
consequent mortality. In the towns of this part of England
there are up to 15 years of age less, from 15 to 55 7no7'e, from
55 upwards less than in the adjacent country. Hence one
of two evils results — either that towns kill young people
and old fast — or middle age is imported.

As to the feeding of town population, an average of 6 per

185

cent is imported from purely country districts of those under
20 years of age ; and of 26 per cent over 20 years. This
constitution of replenishment of towns, associated with what
is subsequently shown, large mortality at early ages, leads to
the view that considerable drafts from the country from 15
years upwards are made by towns, and which latter are
responsible for their health.

With the exception of infantile diseases, those of 1 5 to 55
years of age are the most fatal, and towns present a large
field for the operation of disease at that age.

The diseases of infancy and childhood are in a great degree
infectious. Hence density of population would be considered
a great element of mischief at those periods ; but smallpox,
scarlet fever, and some others, more infectious than others,
present a less increase of mortality than measles over that of
the country. The same law will apply to fever, influenza,
and others at a later age — density and infection do not obey
the same law of proportionate increase: neither will Dr.
Farr's formula, for mortality increasing according to a certain
root of the density, apply to provincial towns.

Imprudent and early marriage, and inebriety have a certain
value in the production of town mortality, but only to a
slight extent, especially as to the former ; the latter evil is
not productive of so great an increase in the direct disease
consequent upon it as materially to elevate town mortality
over that of the country.

Atmospheric causes, those from malarious mischief, in this
Paper are not entered upon to any extent : they have a
variable value, which is balanced to a great extent by the
higher rate of income and consequent improvement of
sustenance.

The centralising system of this century is in itself not,
therefore, it would appear, a great bane to the country ; and
yet towns kill considerably greater numbers of people than
the country. There is an element of destruction which

186

sanitary movements have overshadowed — viz. '' The special
influence of occupation."

In this abstract, to simplify as much as possible, the town
population is divided into groups : one-fifth consists of certain
occupations not peculiar to towns, but common to the present
state of society, viz., out-door heavy occupations. This class
is amenable to the worst influence of town life, and without
the advantage of high wages and consequent choice of abode
and addenda to the necessities of life — its mortality in towns
is yet only 17*5 in the 1,000, the lowest mortality of the
kingdom being 15 in the 1,000. The other four-fifths consists
mainly of the skilled operative and commercial and profes-
sional classes. The mortality of this section is caused by the
skilled workers, and mostly so when constrained position is
requisite. One main object of the paper is to draw attention
to this special element of town mortality, the alteration in
the normal proportion of respiration to circulation of the
blood appearing to be the turning point from health to disease.
This portion of the subject cannot be entered into without
considerable detail, given in the Paper itself. One point
appears to be prominent, viz., that in the endeavour to venti-
late, cleanse, drain, and distribute our town population, the
necessary employment to earn a livelihood in towns has carried
with it the seeds of disease and death, and escaped to a great
extent the notice of those able and philanthropic people who
have devoted their energies to the best mode of increasing
the health and prosperity of their fellow-labourers.

187

MICROSCOPICAL SECTION.

January 21st, 1862.

Professor Willi amson. President of the Section^
in the Chair.

Mr. William K. Deane was elected a Member of the
Section.

A letter was read from Mr. H. A. Hurst, late of Calcutta,
making a donation to the Section of his entire collection of
mounte 1 microscopical objects, consisting of upwards of four
hundred specimens ; they comprise 90 slides of diatomacese ;
100 of algse, mostly marine ; about 30 different kinds of
starches, and the remainder an assortment of Desmidiae,
preparations of insects, bone sections, and a variety of other
objects.

Mr. Hurst also presented a collection of specimens of
Asiatic woods, in small blocks, obtained from the Horti-
Agricultural Society of India at Calcutta. They consist of
98 specimens from Arracan ; 76 from Upper Assam ; 6 from
Central India; 8 from the coast of Tenasserin ; and 13 from
Chittagong; 201 specimens of woods in all, most of them
with the native names.

Capt. Penrice, of the ship ''Pegasus'' from Shanghae,
forwarded to the Section a number of soundings taken during
his last voyage, amongst which may be noted one each from
the mouth of the Yang-tse-Kiang river in China, coast of
Borneo, Java ; and a portion of mud, rich in foraminiferse,
from the anchor fluke, at Gaspar Island,

188

The Se(;retaiiy laid on tho tabic sixty specimens of sound-
ings, which had been freed from the tallow *' arming" in
two evenings after business hours, at Mr. Dale's laboratory,
by Mr. Dale, Mr. Dancer, and himself, assisted by Mr-
liichard Dale. The system adopted is that described in Mr.
Moslcy's Paper, read to this Section on 21st January, 1861,
publislied in the Quarterly Journal of Microscopical Science,
vol. 1st, new series, p. 14-3, and is found to answer better than
any other method yet made known.

Professor Williamson presented fourteen specimens of
dredgings, supposed to be from the mouths of the Ganges.

A communication from Mr. A. G. Latham was read, upon
the subject named for the evening's discussion, " On the
cause of ihe metallic lustre on the wings of the Lepidoptera,
both diurnal and nocturnal.

Mr. Latham believes that the metallic lustre may be
simply referred to the pres(!nce of a pigment in the substance
of the wing, in some cases light-absorbing, and in others light-
reflecting ; all the scales seem equally adapted for reflecting
the prismatic colours, consisting of three distinct membranous
films, covered with minute irregularities. Mr. Latham sent
to be exhibited a number of slides for illustration.

A communication was read from Mr. Dancer, in which he
referred to a paper, read by Sir D. Ikewster at the last
meeting of the British Association, containing the following
remarks by Professor Dove : —

" In every case where a surface appeared lustrous there was
" always a transparent, or transparent reflecting stratum of
"much intensity, through which we see another body; it is
" therefore externally reflected light in combination with
" internally reflected or dispersed light, whose combined action
" produced the idea of lustre. * * This effect we see
" produced when many watch glasses are placed in a heap, or

189

'* when a plate of transparent mica or talc, when heated red
'^hot, is separated into multitudes of thin layers, each of
"which, of inconceivable thinness, is found to he highly
" transparent, while the entire plate assumes the lustre of a
" plate of silver."

Mr. Dancer sent for exhibition several pieces of talc, which
in places, by the action of the blowpipe, had been heated to
redness ; the films were thereby separated, and the raised or
blistered portion gave a metallic lustre like silver.

Mr. W. C. Unwin believed that the metallic lustre was due
not to pigment but to the reflection of light from internal
surfaces of the scales through the transparent outer layer.
The light so reflected appeared to be modified in two ways —
by the ribs or striae ; it was dispersed by them so that the
scales were lustrous at various angles, and it was also in some
cases coloured by interference caused by them. Iridescence
appeared to be also produced in some scales by the thinness
of the laminae through which the light was refracted causing
interference. Mr. Unwin exhibited a number of specimens
to illustrate his arguments.

Mr. Dale referred to beautifully coloured films which
arise upon various chemical solutions, the metallic brilliancy
of which may arise from similar causes.

Mr. Sidebotham observed that the metallic appearance
was not due to any colouring matter in the scales, as chemical
agents, which destroy the coloured scales, have no eflect
whatever on these metallic ones ; he also mentioned a curious
polarizing effect produced by crossing the metallic scales of
Plusia bractea.

Mr. Sidebotham exhibited the metallic scales from Plusia
orichalcea, Plusia bractea, Plusia festucae, Plusia concha, &c.,
illustrative of his remarks.

It was ultimately resolved that the discussion should be
adjourned so as to enable the proposer of the subject, and other
gentlemen not present, to express their views.

190

Mr. SiDEBOTHAM also exhibited a new finder for hi^h
powers. It consists of squares formed by crossing lines, one
hundredth of an inch apart, enclosing progressive numbers,
executed by photography. He promised to prepare a number
for the use of the members, all to be exactly alike

Mr. Joy exhibited a nose-piece, made for him nearly two
years ago, consisting of a diaphragm plate, under which are
screwed four objectives of different powers ; the centreing is
so true, that he can use the three-inch as a finder for the J or
even |-inch power. Several members of the Section have
nose-pieces made upon the same principle.

Mr. Linton and Mr. Watson exhibited the tuft scales on
the upper wing of the Peronea Cristana and others.

191

Ordinary Meeting, February 18th, 1862.

J. P. Joule, LL.D., F.R.S., President, in the Chair.

Henry Ashworth, Esq., The Oaks, Bolton, and Thomas
Clarke, M.D., Wilmslow, were elected Ordinary Members of
the Society.

Mr. Dyer made some remarks relative to the first invention
of the electric telegraph, and read the following extract from
Arthur Young's " Travels in France " (2nd edition), London,
1794, which proved that electricity had been employed at
that early date for the purpose of transmitting intelligence.

" In the evening to Mons, Lomond, a very ingenious and
inventive mechanic, who has made an improvement in the
jenny for spinning cotton. Common machines are said to
make too hard a thread for certain fabrics, but this forms it
loose and spongy. In electricity he has made a remarkable
discovery. You write two or three words on a paper; he
takes it with him into a room, and turns a machine enclosed
in a cylindrical case, at the top of which is an electrometer, a
small fine pith ball : a wire connects with a similar cylinder
and electrometer in a distant apartment, and his wife by
remarking the corresponding motions of the ball, writes down
the words they indicate, from which it appears that he has
formed an alphabet of motions. As the length of the wire
makes no difference in the effect, a correspondence might be
carried on at any distance ; within and without a beseiged
town for instance, or for a purpose much more worthy, and a
thousand times more harmless, between two lovers prohibited
Proceedings— Lit. & Phil. Society—No. U.— Session 1861-62.

192

or prevented from any better connection. Whatever the use
may be, the invention is beautiful. Mons. Lomond has many
other curious machines, all the entire work of his own hands.
Mechanical invention seems to be in him a natural propensity."

A Paper was read " On the Present State of Meteorology,"
by Mr. Thomas Hopkins, M.B.M.S.

In this paper the Author represented that certain recent
meteorological writers had abandoned the Hadleian theory, —
of winds being caused by the ascent of sun-heated air in the
tropical regions, and its passage through the upper atmo-
spheric space, to descend in the polar regions, and return to
the tropics. It was shown that great eiforts had been made
in different countries to discover the causes of those atmo-
spheric disturbances which often take place, withdut much
uniformity in the conclusions arrived at. From extensive
researches made by American observers, Commander Maury
had attempted to prove that near to each tropic there was the
crest of a large atmospheric wave, from which air flowed
down towards the equator on one side, and towards the pole
on the other ; and that light air ascended from the surface in
both the polar regions. Numerous English registrations have
been placed in the hands of Admiral Fitzroy, who has not,
like Commander Maury, promulgated a new hypothesis, but
has exhibited what he considers the general action of cyclonic
storms in middle latitudes ; this is, however, opposed to the
Hadleian theory. Sir J. F. Herschel, in his elaborate work
" On Meteorology," omits to notice the disturbing influence
of the liberated heat of condensing vapour on the gases ; but
he also abandons the old theory of winds, and attributes them
to ihe action of aqueous vapour in a new form. It is con-
tended by the writer, that the great cause of atmospheric
disturbance is to be found in the local heating of gases by the
liberated heat of condensing vapour. It is then pointed out
that the term " atmospheric wave " is founded on a false

193

analogy, and leads the mind in a wrong direction. To speak
of storms coming /ro^Ti a certain. quarter also misleads, as the
cause of storms is to be found in the part towards which the
wind blows. In conclusion it was suggested that aeronauts,
when ascending into the higher regions to ascertain the state
of the atmosphere in those regions, should, in addition to the
ordinary instruments, use a wet bulb thermometer in con-
junction with a dry one, in order that the hygrometrical state
of the upper regions may be ascertained.*

A Paper was read entitled " Note on a Differential
Equation," by Arthur Cayley, Esq., F.R.S.

The investigation was suggested by Mr. Harley's remarks
on the Theory of the Transcendental Solution of Algebraical
Equations, communicated to the Society at the meeting of
the 4th February last.

The equation y—u-\-a\f' (which is used instead of Mr.
Harley's equation if — ny-\-{ii — 1) a;=0) gives by Lagrange's
theorem an expression for y in the form of an infinite series,
and by means of his series it is shown that y satisfies the
differential equation

(imY denotes as usual the factorial m (m — I) . . (m — v+l) J .
It is remarked that the equation may be written in the
form

and the law of the coefficients is obtained.

* Mr. Welsh employed the wet bulb thermometer in his balloon ascents.— Phil.
Trans., 1853. Pt 3.— Ed.

194

PHYSICAL AND MATHEMATICAL SECTION.

January 16th, 1862.

The following returns of the rain-fall for 1861 were com-
municated to the Section.

Old Trafford, Manchester.

By a. V. Veenon, F.R.A.S.

Eeceiving surface of guage, 3 feet above the ground.

1861.

January

February

March

April

May

June

July

August

September

October

November

December

Year

Difference

'

from

Days

Difference

Fall of

Dr. Dal ton's

on which

from

Rain.

47 years'

Rain fell in

12 years'

Average.

1861.

Average.

In.

In.

0-388

—1-869

10

—10-1

2-522

+0-079

17

-- 0-6

4143

- -1-835

25

- -11-0

2-426

4-0-312

10

— 3-5

0-734

—1-712

10

— 31

2-412

—0-279

17

-- 2-3

3-646

—0-060

25

-- 8-7

2-232

—1-231

15

...

4-050

+0-858

19

+ 5-8

1-230

—2-524

16

— 2-3

3-878

+0-156

20

+ 4-4

2-066 .

—1-371

15

— 31

29-727

—5-796

199

The rainfall in 1861 was 6*803 inches below the fall of
1860, the fall in that year being 36-530 inches.

Kain fell upon 36 more days in 1860 than in 1861.

The months in which the rain-fall was the heaviest, viz.,
March, July, September, and November, were accompanied
by an amount of barometric oscillation above the average.

195

Thelwall, near Warrington.
By John Atkinson, F.Q-.S. *

January 0-264

February 2"7ll

Marcli 4-276

April 1-710

May 0-705

June 2-673

July 3-596

August I 2-440

September ' 3*436

October

November

December

1-463
3-665
1-986

Days

of
Eain.

28-925

4
13
25
10
10
17
24
18
19
16
20
15

191

Days on which

half an inch

or upwards fell.

8th, 21st.

2nd, 20th, 31st.

2ncl.

2l8t.

11th.

2nd, 22nd.
5th, 14th.

5th, 25th.
6th.

Station, 96 feet above the mean level of the sea. GTauge, 18 inches above
the ground.

The Flosh, Cleator, near Whitehaven.

By Thos. Ainswoeth, Esq.

Inches.

Days of Rain.

4 years' Mean.

January... .
February .
March . . . .

April

May

June

July

August ....
September .

October

November ,
December ,

3-107
4-442
6-492
0-765
1-340
4-142
5-260
7-377
4-832
3052
8-780
4-517

18
17
28
10
12
16
22
24
21
18
23
26

In.
4-922
3-008
4-923
2-471
2-314
3-396
3-605
5-879
4-694
5-777
4-232
4-728

54-106

235

49-949

196

February 6th, 1862.

The following returns of the rain-fall for 1861 were com-
municated to the Section.

Sale, near Man

CHESTER.

By John Curtis, Esq.

Fall.

No. of Days.

January

February

March

0-480
2-120
4-100

11

17

22

April

May

June

1-580
0-860
2-230

8

8

18

July

August

September

October

4-020
2-440
4-070
1-140

28
20
21
10

November

3-490

22

December

1-750

13

Year

28-580

198

LoNGSiGHT, Manchester.

By J. Casaetelli, Esq.

Fall.

No. of Days.

0-260

4

2-660

14

5-260

19

1-290

4

0-650

6

2-120

18

3-890

24

1-870

11

3-950

19

1-430

10

3-910

18

2040

14

January

February . . ,

March

April

May

June

July

August ,

September . . ,

October

November ..
December ..

Year

29-330

161

97

Mr. Vernon, F.R.A.S., read a Paper ''On the Direction
of the Wind at Manchester during the Years 1849 to 1861,
at 8h. a.m."

The prevailing winds in the various months are as
follows : —

Month,

Most Prevalent
Winds.

Le^Bt Prevalent
Winds.

January

s.w.
s.w.
s.w.

N.E.
KE.

S.W.
S.W.

s.w.
s.w.
s.w.

s.w.
s.w.

N., I^.E.
]S\, W.
N.
]^.
N.
N.
E.
E.
N.
N.
IN".
N.

February

March

April . . . .

May

June

July

August

September

October

November

December

The mean order of frequency of each wind is as follows : —

S.W.

= 91-5

days

per

N.W.

= 560

do.

N.E.

= 48-6

do.

W.

= 420

do.

S.

= 40-T

do.

S.E.

= 38-7

do.

E.

= 30-3

do.

N.

= 16-3

do.

When these figures are referred to the four principal
points only, we have

N = 68-6; E. = 74-0; S. = 105-8; W. = 1158;

showing a gradual increase towards the W. The mean
3'early direction appears to be exactly S.W.

When the directions of the wind are found for each season
of the year, we arrive at the following facts : —

In the winter months, the S.W". wind predominates.

198

In the spring, the N.E. and S.W. predominate, and are
nearly equal : the N.E. wind blows upon more days this
quarter than any other.

In the summer quarter the S.W. wind prevails, and next
comes the N.W. which has a greater prevalence this quarter
than in any of the other quarters.

In the autumn the S.W. is the prevailing wind, next
comes W., N.E., and N.W., which are nearly equal : the
N.W. wind is at its minimum amount in this quarter.

When the winds are referred to the the four principal
points only, we find the very marked prevalence of S. winds
in winter : this wind occurring to a much greater extent in
winter than in any other season. The E. winds of spring
become also very prominent when the above method is
adopted. With summer comes the great excess of W. winds,
and diminution of E. winds. Autumn brings an increase
of N. and E. winds, and a falling off of W. and S. winds.

399

*(D)

Ordinary Meeting, March 4tb, .1862.
J. P. Joule, LL.D., F.R.S., President, in the Chair.

The Rev. Robert Harley, F.R.A.S.^ made the following
statement : —

I am induced by the interest and attention excited by my
communication on the Theory of the Transcendental Solution
of Algebraic Equations (see pp. 181 — 184 of the current
volume of the Proceedings) to offer to the Society some
supplementary observations on the subject.

The Boolian or symbolical form of the differential resolvent
for the equation

is, in general, (D denoting as usual the differential symbol
fl 0

^^, and £ being written for the independent variable x,)
where

D (D— 1) (D— 2) . . . (D— w+2)
The quadratic equation

is an exception ; for, in this case the sum of the roots (S?/) is
not, as in the other cases, equal to zero, and therefore the
differential resolvent must contain a term independent of y.
In fact, for this equation, the symbolical form of the resolvent
is

p-4. 1 .

PaOCEEDINGS-LlT. & PhIL. SOCIETY -No. 12.— SESSION 1861-62.

200

the sinister member of wliiclij it will be observed, coincides
with

when in this formula we make ?2=2.

It is noteworthy that the fractions

2n—l 3w— 2 4w— 3 n^—n-\-\
J ..*

n n n n

which occur in <^ (D), are in arithmetical progression, the

common difference being .

The form given at the foot of page 183 for the fourth dif-
ferential coefficients may be simplified and brought into
striking symmetric relation with the other forms by the
elimination of x. In fact, writing

n—\
for X, and reducing these results

+4(«— 2) (2«—l )!/■-•
+(„_2)(„_3)} {'^}

The relations among the differential coefficients may also be
exhibited under the following forms, viz.

^^ = ;.>"-« |3(.^+l)(2n+l)/

—2 (2w-l) {Zn\^)xy

+ (2.-1) (3.-1) .^}{^}

I think it important also to notice a transformation of the
differential resolvent for the biquadratic similar to that which

201

is known to lead directly to the solution of the cubic resol-
vent. If we change the independent variable by assuming

X-=:

we are conducted to the equation

Sin t dv' dt^

sm «f ^ ^ dt

the complete integration of which will of course give the roots
of the biquadratic.

In reference to the symbolical form of the biquadratic
resolvent given in my last communication to the Society,
Dr. Boole, in a letter to myself, under date Feb. 25th, 1862,
(of which he kindly permits me to make this use), remarks,
^' I see how it could be solved by a definite integral; but that
is not what we want, I presume. If it do not admit of
resolution or reduction to forms recognized as primary in my
theory, it must itself be considered as a new primary form,
and then it constitutes a real addition to the theory of
diiFerential equations. So also," he adds, "for the quintic
resolvent, which no doubt is a new form. If you have my
Finite Differences, I would ask you to look at the conclusion
of Chapter IX. I certainly thought that I had found all the
primary forms for binomial equations, but it now seems that
I had not." These remarks, from one who has contributed so
largely to the theory of differential equations, will no doubt
be read with pleasure by all who are interested in the pro-
gress of Algebra or the cultivation of the Calculus. It will,
certainly, as Dr. Boole in a more recent letter to me (dated
March 1st) observes, "Be a remarkable result if it should
ultimately prove that the primary forms of integrable, linear,
differential equations, stand in some close connexion with the
solvable forms of algebraic equations,"

202

Mr. Harley also laid before the Society the following
communication from Mr. Cockle, dated Temple, February,
1862.

The theorem which I gave in my first paper, '' On Tran-
scendental and Algebraic Solution," in the Philosophical
Magazine for May, 1861, viz., that the solution of an
algebraic equation of the n-th degree, whereof the coefficients
are functions of one parameter, depends upon that of a linear
differential equation of the (n — 1) th order, may be applied
to any algebraic equation whatever, without any preliminary
modification of its coefiicients. And the simplest, or nearly
the simplest, form of the general process indicated in my
second paper (^' Supplementary Paper," Philoso2yhical Maga-
zine for February, 1862) wdth the above title is, as I have
pointed out to Mr. Harley, obtained by treating all the
coefficients as constant and multiplying the last into a para-
meter X, which is to be treated as the independent variable.
Thus, given the quadratic

fJ^hy^cz=:0,
we deduce, successively, from

the following relations :—

dy

c

c {2y-\-h)

dx

- 2yJrh
___ 2cy
4.CX — Ir' ~

— Acx—b' '
he

dx

- 4cx-^b''
I,

/ =

C \/Acx—b^

2"

In this expression x is to be made equal to unity, and the
arbitrary constant C determined by substituting for y in the
given quadratic, or by processes which will, I hope, soon be
explained by Mr. Harley. For the general sextic I should
be disposed to deal with the form (attainable by Mr. Jerrard's
process, by vanishing groups, or by Mr. Sylvester's method)^

203

transform it into

t/J^Zey^—QyJrgx^%
and proceed as before. Or we might start at once with

y^J^Sey^—^yJr^x^Q,
and regard x as the independent variable, and e as constant.

The simplicity and beauty of the results obtained by Mr.
Harley in the case of trinomial biquadratics and quintics
suggested to me the following investigation, which I think I
communicated to him some months ago. Let
J'V , dry

r being taken from 0 to n, and A being constants. Then 7i
particular integrals are obtained from the formula

by giving to m the values 0, 1, 2,, ,n, successively; z being
taken from 0 to go , and zi being defined by

where

P=:2 A^ TT,. (m-\-zn),

The symbol tt here introduced is such that
^J=l (^_i) (1—2). .(/— r+1)
is its defining relation.

Mr. Egbert Eawson, Honorary Member, read the First
Part of a Memoir of the late Professor Eaton Hodgkinson,
F.R.S. Thanks having been given to Mr. Rawson, on the
motion of Mr. Binney, seconded by Dr. Smith,

The Rev. Mr. Kiukman said, " It is no ordinary renown
that the late Professor Hodgkinson secured to himself, and
for ever will reflect on Manchester. It is a great thing to
outstrip one's cotemporaries in commercial competition, and
to accumulate fairly-gathered wealth ; it is a great thing to

204

win university distinctions, and to grow old in the plenitude
of college dignities ; it is a great thing to wear civic honour,
and to enjoy, for any good reason, a social celebrity ; but
Hodgkinson aspired to more. He thirsted for enduring and
world-wide fame, and he has won it. How few are there of
the young men of this ardent and crowded Lancashire, even
of those who may achieve what are esteemed the greatest
successes of life, who will find, when their hair is grey, that
their names are printed year by year as seals of science in the
industrial manuals of all civilized nations ! Hodgkinson
diminished instead of increasing his little patrimony, in the
search of truth equally abstruse and beneficent; but this
proud memory he has left behind him — that, go where you
will in any clime of earth, if you meet a man fit to give
counsel about constructions, and to take the command of
labour, he will have in his breast pocket a little book, in
which many of the most precious oracles and most pregnant
formulae are stamped with the great name of Hodgkinson.
And this is fame — fame that will grow higher and speak
louder, as the world grows happier and wiser. For ages and
for ao-es the discoveries of Hodgkinson will economize
millions of treasure to the governments and the nations of the
globe, and prevent the destruction of innumerable lives."

A Paper by Professor W. Thomson, LL.D., F.R.S.,
Honorary Member, was read, entitled "Observations on
Atmospheric Electricity."

I find that atmospheric electricity is generally negative
within doors, and almost always sensible to my divided
rin"- reflecting electrometer. I use a spirit lamp, on an
insulated stand a few feet from walls, floor, or ceiling of my
lecture room, and connect it by a fine wire with the insulated
half rinp- of the electrometer. A decided negative efl'ect is
o-enerally found, which shows a potential to be produced in
the conductors connected with the flame, negative relatively

205

to the earth by a difference amounting to several times the
difference of potentials (or electro motive force) between two
wires of one metal connected with the tw^o plates of a single
element of Daniell's. I have tested that the spirit lamp
ofives no idio-electric effect amountini]^ to so much as the
effect of a single cell. The electric effect observed is there-
fore not due to thermal or chemical action in the flame. It
cannot be due to contact electrifications of metallic or other
bodies in conductive communication with the walls, floor, or
ceiling, because the potentials of such must always fall short
of the difference of potentials produced by a single cell. I
have taken care to distinguish the observed natural effect
from anything that can be produced by electrical operations
for lecture or laboratory purposes. Thus I observe generally
in the morning before any electrical operations have been
performed, and find ordinarily results quite similar to those
observed on the Monday mornings when the electrical
machine has not been turned since the previous Friday.
The effect, when there has been no artificial disturbance,
has ahvays been found negative, except two or three times^
since the middle of November ; but trustworthy observations
have not been made on more than a quarter of the number
of days.

A few turns of the electrical machine, with a spirit
lamp on its prime conductor, or a slightly charged Leyden
phial, with its inside coating positive put in connection with
an insulated spirit lamp, is enough to reverse the common
negative indication. Another very striking way in which
this may be done is to put a negatively charged Leyden
phial below an uninsulated flame (a common gas burner,
for instance). The flame, becoming positively electrified by
induction, keeps throwing off, by the dynamic power of its
burning, portions of its own gaseous matter, and does not
allow them to be electrically attracted down to the Leyden
phial, but forces them to rise. These, on cooling, become.

206

like common air, excellent non-conductors,* and^ mixing
with the air of the room, give a preponderance of positive
influence to the testing insulated iiame (that is to say,
render the air potential positive at the place occupied by this
flame).

Half an hour, or often much more, elapses after such
an operation, before the natural negatively electrified air
becomes again paramount in its influence on the testing
flame.

That either positive or negative electricity may be carried,
even through narrow passages, by air, I have tested by
turning an electric machine, with a spirit lamp on its prime
conductor, for a short time in a room separated from the
lecture room by an oblique passage about two yards long,
and then stopping the machine and extinguishing the lamp,
so as to send a limited quantity of positive electricity into
the air of that room. When the lecture room window was
kept open, and the door leading to the adjoining room shut,
the testing spirit lamp showed the natural negative. When
the window was closed, and a small chink (an inch or less
wide) opened of the door, the indication quickly became
positive. If the door was then shut, and the window again
opened, the natural effect was slowly recovered. A current
of air, to feed the lecture room fire, was found entering by
either door or window when the other was shut. This
alternate positive and negative electric ventilation may be

* I find that steam from a kettle boiling briskly on a common fire is an
excellent insidator. I allow it to blow for a quarter of an hour or more
against an insulated electrified conductor, without discovering that it has any
effect on the retention of the charge. The electricity of the steam itself, m
such circumstances, as is to be expected from Faraday's investigation, is not
considerable. Common au* loses nearly all its resisting power at some tem-
perature between that of boihng water and red hot iron, and conducts
continuously (not, as I believe, is generally supposed to be the case, by
disruption) as glass does, at some temperature below the boihng point, with
so groat case as to discharge any common insulated conductor almost com-
pletely in a few seconds.

207

repeated many times without renewing the positive elec-
tricity of the adjoining room by turning the machine afresh.

The out of doors air potential, as tested by a portable
electrometer in an open place, or even by a water dropping
nozle outside, two or three feet from the walls of the lecture
room, was generally on these occasions positive, and the
earth's surface itself, therefore, of course, negative; — the
common fair weather condition, which I am forced to con-
clude is due to a paramount influence of positive electricity
in higher regions of the air, notwithstanding the negative
electricity of the air in the lower stratum near the earth's
surface.

On the two or three occasions when the in-door atmo-
spheric electricity was found positive, and, therefore, the
surface of the floor, walls, and ceiling negative, the potential
outside was certainly positive, and the earth's surface out of
doors negative, as usual in fair weather.

208

SECTION FOR STATISTICS AND SOCIOLOaY.

February 11th, 1862.

Dr. Angus Smith, F.E.S., in the Chair.

Mr. David Chadwick, F.S.S., read a paper "On the
Responsibilities of Trustees in regard to Charity and other
Public Funds."

Mr. Chadwick considered the great importance of this
question, in regard both to its social and statistical bearings,
well worth the earnest consideration of the Section.

He referred to the rule of law that the Sovereign, as
parens patricB, is the guardian of all charities, and the
Attorney-General, at the relation of an informant, may file
an information in the Court of Chancery, to restore any
abused or dilapidated foundations ; and also to the various
acts in relation to charitable trusts, and to the powers and
duties of the charity commissioners.

Mr. Chadwick then referred to the duties of trustees in
relation to public hospitals, schools, religious endowments,
sick, burial, and trade societies; savings banks, charities
distributed in money, food, and clothing, &c. And he held
that, in consequence of the legislature not requiring all
trustees to " give an account of their stewardship " in a
clear, open, and satisfactory manner, many charities had
been lost, and many had been seriously impaired.

Reference was made to some of the principal charities of
Manchester and Salford, and the mode of their management
by trustees, and of their distribution; and it was strongly
recommended that the trustees, as well as the distributors ,^

209

should in all cases publish an account of their income and
disbursements; that whenever trustees released^ renewed^ or
sold charity property^ the particulars should be duly reported
and published with the annual statement of accounts. This
is in some cases done^ but is not in all.

Where the property was in land and held in leases, and
renewed by trustees, it was very important that the terms of
the renewal of all such leases should be published.

Mr. Ghadwick quoted the instance of the " Accounts of
the Queen i?i regard to Her Duchy of Lancaster^'' as a good
instance of a published account of trustees^ represented by
the Duchy Court, in which the rent, terms, and conditions
of each tenant are set forth.

Mr. Chadwick also called attention to the account required
to be kept by all joint-stock companies, as a good step in the
right direction.

He recommended publicity in every way as the first and
main condition, an exact form of accounts, an annual report
of proceedings, and the acknowledgment of the principle by
public trustees as part of their duties and responsibilities of
^^ public accountahility r

210

MICEOSCOPICAL SECTION.

February 17th, 1862.

Professor Williamson, F.R.S., President of the Section,
in the Chair.

Soundings were acknowledged from Captain W. B. Hall,
of the P. and O. S. S. " Tagus;' taken off Ushant, Coast of
France, and from Captain J. R. Husband, ship "Florence
Nightingale,^^ taken off the Coasts of Patagonia and Tierra
del Fuego.

Professor Williamson called the attention of the section
to the new rotifer (Cephalosiphon Limnias), recently dis-
covered by Mr. H. J. Slack, in a pond at Hampstead, and an
account of which appeared in No. 1 of the Intellectual
Observer of the present month. Attention was specially
directed to the fact, that the animal only possesses one of
those organs that have been designated "respiratory tubes,"
'^calcars," and "tactile organs;" whereas, the Floscularian
Rotifera, when furnished with them, have two. It remains
to be ascertained from a study of the embryo, whether this is
the typical condition in the Cephalosiphon, or whether there
were primarily two, the missing one having been suppressed
during the development of the embryo, as sometimes occurs
amongst higher animals.

The Secretary read a Paper, by Mr. Thomas Davies of
Warrington, on Crystallisation.

Mr. Davies treats more particularly upon some of the
double salts, which show beautiful combinations of form and

211

colour by polarised light ; and upon his method of obtaining
determinate flower-like forms, surrounded by a film of the
uncrystalised salt. The novelty of the author's system, con-
sists in the following particulars : — he makes a nearly
saturated solution, say of the double sulphate of copper and
magnesia; he dries rapidly a portion on a glass slide, allowing
it to become so hot as to fuse the salt in its water of crystali-
sation; there then remains an amorphous film on the hot
glass. On allowing the slide to cool slowly, the particles of
the salt will absorb moisture from the atmosphere, and begin
to re-arrange themselves on the glass, commencing from
points. " If then placed under the microscope," says the
the Author, 'Sve shall see points starting up here and there,
" and from those centres, the crystals may be watched as they
" burst into blossom, and spread their petals on the plate."
Starting points may be made at pleasure by touching the
film with a fine needle, to enable the moisture to get under
it ; but this treatment renders the centres imperfect. If
allowed to go on, the crystals would slowly cover the plate,
or if breathed upon, they form immediately ; whereas, if it
is desired to preserve the flower-like forms on a plain ground,
as soon as they are large enough, development is suspended,
by again applying gentle heat ; the crystals are then covered
with balsam and thin glass, to be finished off" as usual. The
balsam must cover the edges of the film, or moisture will
probably get under it, and crystallisation go creeping on.

Many crystals which produce similar forms, cannot be
preserved in balsam ; in the hyposulphite of soda they are
very fine, and the Author is endeavouring to preserve them
in castor oil.

Mr. SiDEBOTHAM referred to the vegetable forms produced
by Mr. Petschler, with bichromate of potash in gelatine,
exhibited at the British Association Microscopical Soiree.
Since then flower-like shapes had been obtained from nitrate
of silver amongst the ramifications of the bichromate ; as it

212

is an interesting subject, he should endeavour to bring it
before the next meeting.

The discussion *'0n the cause of metallic lustre upon the
wings of the Lepidoptera" was resumed. Mr. Latham
stated that he saw no reason to alter the views he had ex-
pressed ; but since the last meeting Mr. Watson had called
his attention to an article in the *^Annales des Sciences
Naturelles" for February, 1835, by Bernard Dechamps, "Sur
les Ailes des Lepidopteres/' which contains much information
upon the scales and the cause of their brilliance; he (Mr.
Latham) had translated and printed extracts from the paper ;
copies were handed round to the members present, and may
be had (gratis) at the Society's rooms, or from the Secretary
of the Microscopical Section.

A Paper was read by Dr. Thomas Alcock *' On the
Tongues of Mollusca."

The Author remarked upon the great variety and beauty
of these objects, and pointed out their scientific value as a
help in the classification of shells. On investigation the
tongues were shown to arrange themselves into four groups,
according to the pattern or type of the lingual dentition, and
these groups were stated to correspond with four of the orders
established by Cuvier, on the characters of the breathing
organs. The four orders illustrated ■were the Pectinibran-
chiata, the Scutibranchiata, the Cyclobranchiata, and the
Pulmonata; and he believed that, on the evidence of the
teeth, it will be necessary to re-establish the order Cyclo-
branchiata as distinct, instead of including jt in the
Scutibranchiata, as is done by our latest authorities.

The Author had examined many specimens of Buccinum
undatum of both sexes, a series of which were exhibited to
prove that the number of points on the central teeth in this

213

species varies from five to seven, but without reference to sex.
The very close agreement both in the lingual teeth and in the
general internal anatomy of Fusus and Buccinum was men-
tioned, and a doubt was expressed as|to the propriety of their
wide separation in our present systems of classification. The
association of Fusus with Murex, and of Purpura with
Buccinum, was also commented upon, and shown by the
evidence of the tongues, as well as the general anatomy of
the animals, to be clearly incorrect.

In conclusion, some remarks were made on the method
used by the Author, of extracting the tongues from the
difi'erent kinds of mollusca, illustrated by specimens, some
of which were many times longer than the bodies of the
animals, being coiled up near the neck, and brought forward
as the teeth are worn away. The Paper was illustrated by
beautifully executed drawings of the difi'erent types^ and a
series of dissected animals.

Professor Williamson asked the Author if he proposed to
include the Chitons in the order Cyclobranchiata.

Dr. Alcock was satisfied the Chitons ought not to be so
placed; but, judging from the general character of their
teeth, he thought they might possibly remain with the
Scutibranchiata, or perhaps it would be necessary to establish
a new order expressly for them.

Professor Williamson was glad to learn that this was the
result of Dr. Alcock's observations ; for the animals certainly
appeared very distinct, and the Chitons, which he remarked
have the form of a gigantic woodlouse, were evidently not
Cyclobranchiata, as they have a separate gill down each side
of the body.

On adjourning to the microscopes. Dr. Alcock exhibited
mounted specimens of tongues from thirty different species of
Gasteropoda, with the shells from which they were extracted.
One of the lingual ribands was two and a half inches long.

214

Mr. Latham exhibited scales from the wings of the
Catarrhactes Papua, a Penguin from the Falkland Islands,
which appear to be intermediate between feathers and
scales.

Mr. Edward Lund exhibited two forms of stands for
holding a microscope, condenser, lamp, &c. ; one in the form
of a tray fixed on four castors, to run upon an ordinary-
table, and the other a small round turn-table, thirty inches
high and fifteen inches diameter. The lamps were for
parafiin oil^ fitting into wooden cups secured to the stands.

215

Ordinary Meeting, March 18th, 1862.
J. C. Dyer, Esq., Vice-President, in the Chair.

The following communication from Sir John F. W.
Herschel, Bart., M.A., D.C.L., F.R.S., &c.. Honorary
Member of the Society, was read by Mr. Baxendell: —

In the report of the Ordinary Meeting of the Literary and
Philosophical Society for February 18, 1862, I find an
abstract of a paper " On the Present State of Meteorology,"
by Mr. T. Hopkins, M.B.M.S., in which he is reported to
state that in my recent work on Meteorology I ''^omit to
notice the disturbing influence of the liberated heat of con-
densing vapour on the gases," and also that in that work I
" abandon the old theory of winds " (meaning, I presume
from the context, the Hadleian theory,) *' and attribute them
to the action of aqueous vapour in a new form."

With regard to the former of these two statements I beg
to refer to Art. 5o of that work, where, alluding to the con-
densation of the vapour in the atmosphere, it is remarked
that " in every case, such condensation is accompanied with
a mitigation of cold at the point where it actuallij takes place. ^^
What effect beyond this the condensation of vapour can pro-
duce on the gases I am at a loss to understand. It can in
no case give rise to an actual elevation of temperature above
that of the mixture of air and vapour which may be intro-
duced into any mass of cold air and which may thereby effect
a partial condensation. It can only act in mitigation of the
chilling effect of such admixture on the introduced portion
which would arise were the vapour not condensed. Inasmuch,
however, as its condensation and precipitation as rain
diminishes joro tanto the total barometric pressure, and there-
fore allows both air and vapour to flow in from other quarters ,
Proceedings— Lit. & Phil. Society— No. 13.— Session 1861-^62.

21G

such condensation may, and no doubt does aid in producing
atmospheric movements. See Meteor. ^ Arts. 165^ 171.

But as respects the statement that I abandon the Hadleian
theory of the winds, I can only say that nothing is farther
from my thoughts, and that I must protest against any such
mode of expressing my views. It is true that in describing
the modus oj^eraildi in which the sun's heat, acting on the
equatorial regions of the earth, ocean, and air, produces that
ascentional movement and overflow of the atmosphere which
is what Hadley assumes as the primum mobile of his theory,
I have {MeleoroL, Arts. 54, ^^, 58) brought expressly and
prominently into view the very considerable share Avhich the
generation and ascent of vapour has in producing that result,
but without ignoring or in any way unduly depreciating the
effect of the rarefaction of the air itself. On the contrary, it
is expressly said (Art. 55), " The general effect" (of the two
causes) '^ is similar, and as the sun cannot generate vapour
without at the same time heating the air, it is impossible to
separate their dynamical effects. Whether the air go forth
from its place proprio motu or be jostled out of it by the
introduction of a lighter medium, the local relief of pressure
is equally produced." When Hadley wrote, the distinction
between air and vapoi.r was not recognised. He took the
atmosphere en masse and attributed to it an ascentional move-
ment due to the heat of the sun, by the process of " rarefac-
tion;" and this, so worded, remains true, although such
rarefaction be a more complex process than he understood it
to be.

The displacement of air by vapour, the disturbance of
statical equilibrium, and the dynamical effects consequent
thereon, are no new principles in meteorology. They have
been strongly insisted on, and, if I may venture to say so,
rather over insisted on, and with a premature air of reduction
to computative precision, by Daniell in his Meteorological
Essays, and perhaps hardly enough insisted on in my work

217

on Meteorology which has given occasion to Mr. Hopkins's
remarks. I would take this opportunity, however, to call
the attention of meteorologists to the very extraordinary and
abnormal features of the last two years as strongly illustrative
of the important part this element of meteorological dynamics
has been playing in their production. The great outbreak
of the solar spots occurred in the year 1859 with unusual
suddenness, and on the 1st of September in that year pheno-
mena were exhibited in its photosphere indicative of a most
remarkable state of excitement, accompanied with magnetic
and auroral disturbances of unprecedented intensity and
duration. This occurred as the sun was passing southward
across the equator, and from the accounts received from
Australia, the southern summer of that year 1859-60 appears
to have been one of very unusual heat. The quantity of
vapour thrown into the atmosphere during that^summer from
the southern ocean would seem not yet to have been got rid
of, and to have given rise to diversions of the aerial currents
both of air and vapour from their normal courses which have
not even yet subsided into their regular and habitual train.
I throw out this, however, rather as a suggestion which I
consider worthy of further examination by the light of
meteorological records and returns collected on a very large
scale, than as having myself arrived at any definite concep-
tion of the actual steps of the process that has been going
forward.

Mr. Baxendell, in illustration of the remarks in the latter
part of Sir John Herschel's communication, read the follovv -
ing extract of a letter dated at sea, near Ceylon, January
30th, 1862, which he had received from Mr. Thomas Heelis,
F.R.A.S., who sailed from England for Calcutta on the 18th
of November last : —

"We have had very peculiar and unsatisfactory trade
winds ; we ran down inside of Madeira and the Cape de

218

Verde Islands, and had the north-east trade almost the whole
way down at E.S.E. Our south-east trade, which we picked
up in the Bight of Benin, came out at S.S.W., hut we
afterwards on going to the S.W. got it in its proper direction.
We were on the skirts of three cyclones between the Cape
and Amsterdam Island ; and there have been within the last
week evident indications from the set of a heavy swell that
another cyclone is now running down to the Mauritius.
The result is, that although we have had trade wind clouds,
we have had no S.E. trades in the Indian Ocean, and we are
now, and have for some days been in the N.W. monsoon, and
have been nearly boiled by its warm damp atmosphere. The
Captain has told me that for days since leaving the Cape he
has not known what to make of the weather, and his
experience of these seas (which is great) has only served to
puzzle him. This leads me directly to a point which bears
strongly upon the theory of hurricanes, and which I want
you to put in train. All old seamen agree that the trade
winds are variable in force and direction. I should be glad
if Mr. Mosley, or some one who is from time to time in
communication with Capt. Maury, would try to get him to
discuss his collection of above 500,000 trade wind observations
in order of time, as this question bears directly upon that of
which I have spoken to you, viz., the perturbations, so to
speak, of the hurricane orbits of the West Indies, by which
their tracks sometimes pass over St. Domingo and sometimes
do not."

Dr. Joule made a communication " On the Probable
Cause of Electrical Storms."

The very close correspondence between the theoretical rate
of cooling in ascending, and the actual, indicates a rapid
transmission of the atmosphere from above to below, and
vice versa, continually going on. We may believe that
during thunderstorms this interchange goes on with much

219

greater than ordinary rapidity. At a considerable distance
from the thundercloud, where the atmosphere is free from
cloud, the air descends, acquiring temperature according to
the law of couvective equilibrium in dry air. The air then
traverses the ground towards the region where the storm is
raging, acquiring moisture as it proceeds, but probably
without much diminution of temperature, on account of
the heated ground making up for the cold of evaporation.
Arrived under the thundercloud, the air rises, losing tempera-
ture, but at a diminished rate, owing to the condensation of
its vapour to form part of the immense cumulus cloud which
overcasts the sky on these occasions. The upward current of
air carries the cloud and incipient rain drops upwards, but
presently, in consequence of the increased capacity of the mass
from the presence of a large quantity of water, the refrigera-
tion of the air, in consequence of its dilatation, will be so far
diminished as to prevent the condensation of fresh vapour,
and ultimately to redissolve the upper portion of the cloud.
This phenomenon, which has been noticed by Rankine in the
cylinder of the steam engine, will account for the defined
outline of the upper edges of cumulus clouds. The upward
current no doubt extends occasionally to regions below the
freezing temperature. If cloud be carried with it, snow
or hail will be formed, which, if sufficiently abundant,
will pass through the cloud and fall to the ground before
it is melted. Now, the dry cold air in which the snow
and hail are formed is a perfect insulator. Ice has also
been proved, by Achard, of Berlin, to be a non-conductor
and an electric. Even water, in friction against an insulator,
is known from the experiments of Armstrong, explained by
himself and Faraday, to be able to produce powerful electric
effects, and this fact has been suggested by Faraday to
explain powerful electric effects in the atmosphere. Sturgeon
has noted the remarkable development of electricity by hail
showers. Few heaw thunderstorms occur without the fall

'220

of hail. Hail, whether in summer or winter, is almost, if
not invariably, accompanied with lightning. In the presence
of these facts, it seems not unreasonable to consider the
formation of hail as essential to great electrical storms;
although, as has been pointed out by Professor Thomson,
very considerable electrical effects might be expected from
the negatively charged air on the surface of the earth being
drawn up into columns, and although, as the same
philosopher has observed, every shower of rain gives the
phenomena of a thunderstorm in miniature. The physical
action of insulators and electrics in mutual friction must
certainly produce very marked effects on the grand scale of
nature. If we suppose that the falling hail is electrified by the
air it meets, the electrification of the cloud into which the
hail falls might thus be constantly increased until the balance
between it and the inductively electrified earth is restored by
a flash of lightning. If the hail is negatively electrified
by the dry air with which it comes in contact, the latter
will float off charged with positive electricity, which may
account for the normal positive condition of the atmosphere
in serene weather, as well as the electrification of the upper
strata evidenced by the aurora borealis. The friction of
wind has been supposed by Herschel to contribute to the
intense electrification of the cloud which overhangs volcanoes
during eruption.

Dr. Thomas Alcock read a Paper " On the Tongues of
Mollusca." [An abstract of this Paper will be found in the
report of the Microscopical Section, Proceedings No. 12.]

Dr. Grace Calvert stated that one of the difficulties
which Dr. Alcock had encountered in his extensive and
laborious researches, namely, that of preserving his specimens
from putrefaction, would be overcome by the use of a saturated
solution of pure carbolic acid, taking care that a small excess
of this powerful antiseptic should also remain at the bottom of

221

the vessel in which the anatomical preparations were pre-
served. His authority was Dr. De Morgan, of the Middlesex
Hospital, who stated to him a few days since that he had
succeeded by that means in preserving classes of animals
which all other means had failed in preserving, namely,
Molluscae, Zoophytes, and Acalephse.

Dr. Calvert also read a Paper " On the Employment of
Galvanized Iron for Armour-plated Ships."

The Author stated that no doubt many gentlemen present
were acquainted with the fact that he had been for some
time past engaged in ascertaining the chemical composition
of various woods employed and susceptible of being employed
in the navy. On a recent visit to one of the dockyards he
found that while the armour-plates were fixed against a layer
of teak, the ribs of the ship were of oak, and that the iron
bolts which were to fasten the plates were to pass through
the oak ribs. It occurred to him that the inconvenience
which would probably result from the action of the oak upon
the iron might be obviatfed by substituting galvanized iron
bolts for those now in use, and he therefore instituted a series
of experiments, the results of which he had great pleasure in
laying before the meeting.

The first series of experiments consisted in having driven
through large pieces of oak, bolts and screws of iron and
galvanized iron prepared by his friends, Messrs. Richard John-
son and Brother, of Dale-street, Manchester, which were then
immersed in soft and sea water for the last three months. The
results clearly showed, first, that the friction did not remove
the zinc from the galvanized iron ; secondly, that the oak and
galvanized bolts were unchanged ; whilst in the case of the
iron bolts, they were much rusted, and the pieces of oak had
become quite black by the formation of tannate and gallate
of peroxide of iron. During the experiments the waters were
changed every week, and those containing the galvanized iron

222

appeared unchanged, whilst in the case of the iron, they had
a dark blue-black appearance, owing to the formation of
gallate and tannate of iron.

In order to ascertain the comparative action of soft and
salt water upon iron and galvanized iron when in contact
with oak under identical circumstances, he made the following
series of experiments.

Plates of galvanized iron having 18 inches of surface lost
during three months the following weights: —

SOFT WATER. SEA WATER.

Plate No. 1 . . . . 0.10 grains.

„ No. 2.... 0.11 „

„ No. 3 0.095 grains.

„ No. 4 0.090 „

Similar plates of iron lost during the same time : —

SOFT WATER. SEA WATER.

Plate No. 1 1.28 grains.

No. 2.... 1.52 „

99

„ No. 3 2.40 grains.

„ No. 4 2.38 „

There can therefore be no doubt that galvanized iron offers
great advantages, the action of water on it being less than a
tenth of the same action on ordinary iron. As there is no
doubt that iron when galvanized is in the most favourable
electrical condition to resist the action of oxygen, being in
an electro-negative condition, it follows that in all probability
the use of galvanized iron would be very advantageous in
armour-plated and other iron ships. The Author hoped
that Government and other large ship builders would avail
themselves of this suggestion, and make experiments on a
large scale to verify the results he had obtained.

223

PHYSICAL AND MATHEMATICAL SECTION.
February 27th, 1862.

Mr. Baxendell, F.R.A.S., read a Paper " On the Relations
between the Decrement of Temperature on Ascending in the
Atmosphere and other Meteorological Elements."

According to the theory which attributes the production of
Avinds and storms to upward currents of air, caused by the
heat liberated during the condensation of aqueous vapour
into clouds and rain, the rate of decrease of temperature on
ascending in the atmosphere ought to be less in rainy than
in fair weather ; and the reasonings and calculations of Dr.
Wm. Thomson, in his valuable Paper '' On the Convective
Equilibrium of Temperature in the Atmosphere," lately read
to the Society, point to the same conclusion ; but in a Paper
entitled "Remarks on the Theory of Rain," read to the Section
on the 29th of March, 1860, the Author gave some results
derived from a discussion of the Greenwich and Oxford obser-
vations, which seemed to militate against this theory, and
reference was made to the fact stated by Ksemtz and others,
that the diminution of temperature on ascending in the
atmosphere is more rapid in rainy than in fine weather. It
appears, however, that this fact is not generally admitted by
meteorologists, as the observations from which it is derived
were mostly of a desultory nature, and continued for only
short periods of time. The Author, therefore, thought that
a discussion of the monthly results of the observations made
during the years 1848-58, at Geneva and on the Great St.
Bernard, given by Mr. Vernon in his valuable Paper " On
the Irregular Barometric Oscillations " at those places,
might throw some light on the subject, and, at the same
time, serve to indicate the relations which exist between the
decrement of temperature and other meteorological elements,
a branch of meteorology which has hitherto been almost
entirely neglected.

Tables are given, containing the comparisons of the

224

monthly differences of temperature between the two stations,
with the mean temperature, rain-fall, amount of barometric
oscillation, and height of the barometer.'

The final results derived from these comparisons may be
stated as follows : —

1 . On the average of the year a decrement of temperature
below the mean is accompanied by a rain-fall and amount of
barometric oscillation helow the mean, and by a mean tem-
perature and barometric pressure ahove the mean.

2. A decrement of temperature above the mean is accom-
panied by a rain-fall and amount of barometric oscillation
above the mean, and by a mean temperature and barometric
pressure helow the mean.

3. A decrement of temperature above the mean for the
season is due to a cooling of the higher strata of the atmo-
sphere, and not to a heating of the lower strata.

4. The production of rain is attended with a diminution of
the general temperature of the atmosphere, the diminution
being greater in the higher than in the lower strata. This
result, therefore, agrees with that which the Author had
previously derived from a discussion of the Greenwich and
Oxford observations ; and it indicates clearly the influence of
a cooling agency sufficiently powerful to neutralise completely
the effects of the heat supposed to be liberated during the
condensation of aqueous vapour into rain.

The Author remarks that from the relations established by
this investigation it may be concluded that in a mass of air
moving from a higher to a lower latitude and acquiring an
increase of temperature, the change of temperature is more
rapid in the lower than in the higher strata ; while on the
contrary, in a mass moving from a low to a high latitude and
losing heat, the change is most rapid in the upper strata. It
also seems probable that one of the essential conditions in the
formation of a rotatory or cyclonic storm is a greater diff'er-
ence of temperature than usual between the successive strata
of the atmosphere at the point where the storm originates.

225

Ordinary Meeting, April 1st, 1862.
J. P. Joule, LL.D., F.E-.S., President, in the Chair.

Mr. David Joy was elected an Ordinary Member of the
Society.

Mr. Frederick N. Dyer and Mr. Samuel Cottam were
appointed Auditors of the Treasurer's accounts for the present
Session.

A letter from Dr. Fairbairn, F.R.S., was read, enclosing
a dried specimen of a fibrous bulb which he had received
from Mr. James Niven, of Jeffrey's Bay, Human's Dorp
District, Cape of Good Hope. In a letter, dated 17th
February, 1863, Mr. Niven says, ^^I enclose a leaf and some
of the fibre of a very fibrous wild bulb, very plentiful in this
country, and, if of any commercial value, a large quantity in
the leaf could be exported annually. The sample is not a fair
one, as the bulb is not matured at this season, and has only its
outermost leaf dry. I think the fibre is stronger in the
matured bulb. I do not know its botanical name. In the
Dutch of the country it is called Maager-man boll (Slender-
man bulb), probably from its tall and slender flower stem,
which sometimes attains the height of six feet. The bulb
resembles an onion."

Mr. BiNNEY, after examining the specimen, said that it
had always appeared to him most strange for a large manu-
facturing town like Manchester to be without a museum, in
which should be deposited all the new raw products, whether
of animal, vegetable, or mineral origin, that were from tim.e
to time discovered. At the present time, when public atten-
tion was directed to the supply of cotton, the want of such a
collection was peculiarly felt. If the Chamber of Commerce
Proceedings— Lit. & Phil. Society— No. 14.— Session 1861—62.

226

and the merchants woukl use their influence in collecting
specimens, and the town provide a museum for their reception,
this Society might appoint committees of scientific men to
report on the uses for which such products were best suited,
and the result of their labours might be published. Up to this
time commerce had not sought the aid of natural history and
chemistry to the extent which it might have done. For a
commencement the Natural History Society would probably
aiford the use of a room, in which the specimens could be
exhibited.

Mr. Alfred Fryer stated that he had recently been
making a series of experiments with the oxyhydrogen light,
with a view to determine what substance made incandescent
produced the greatest amount of light. He operated on
various salts of calcium, magnesium, strontium, barium, and
also upon some other substances. The best results were
obtained from magnesium. The sulphate of magnesia, when
baked, yielded a bright light, but was decomposed by the
heat ; and the sulphurous acid escaping was very unpleasant.
Calcined magnesia succeeded the best of all ; but when the
powder was used, the gases blew it away. When the powder
was mixed with water, and afterwards dried, the cake was
friable ; and when the dry powder was pressed in a mould
by means of hydraulic pressure, the cake split up into laminse
when subjected to the gases. After many experiments with
the materials in different proportions, it was found that
sulphate of lime one part, and calcined magnesia two parts,
mixed with water and modelled into a cake and dried,
produced the best results. This, however, is not all that
could be desired, as in time the cake becomes cracked and
fissured by the gas. The illuminating power is to that of
lime, pressure and volume of gas being equal, as 54 is to 27.
The experiments have been conducted with oxygen and
the coal gas supplied to Manchester. The jet used is a form

227

supplied by Mr. Dancer, a jet of oxygen being surrounded by
an annular jet of the coal gas. Mr. Dancer has further
improved the jet by allowing the oxygen pipe to project
beyond the hydrogen, and by not contracting the aperture of
the hydrogen pipe.

Mr. Alfred Fryer exhibited the light which he had
explained, and the effect produced was very striking.

Professor Roscoe read the following communication, by
Professor Clifton and himself, entitled, '^ On the Effect of
Increased Temperature upon the Nature of the Light Emitted
by the Vapour of certain Metals or Metallic Compounds."

In a letter communicated to the Philosophical 3Iagazine
for January last, we stated that in examining, with Steinheil's
form of Kirchhoff and Bunsen's apparatus, the spectra pro-
duced by passing the induction spark over beads of the
chlorides and carbonates of lithium and strontium, we had
observed an apparent coincidence between the blue lithium
line, which is seen only when the vapour of this metal is
intensely heated, and the common blue strontium line called
Sr §. Y/e further stated that on investigating the subject
more narrowly by the application of several prisms and a
magnifying power of 40, we came to the conclusion that the
lithium blue line was somewhat more refrangible than the
strontium 8, but that two other more refrangible lines were
observed to be coincident in both spectra. Having con-
structed a much more perfect instrument than we at that
time possessed, we are now able to express a definite opinion
ou the subject, and beg to lay a short notice of our observa-
tions before the Society. Our instrument is in all essential
respects similar to the magnificent apparatus employed by
Kirchhoff in his recent investigations on the solar spectrum
and the spectra of the chemical elements. It consists of a
horizontal plane cast iron plate, upon which three of Steinheil's
Munich prisms, each having a refracting angle of 60°, are

228

placed; and of two tubes fixed into the plate, one being a
telescope having a magnifying power of 40, moveable with a
slow-motion screw about a vertical axis placed in the centre
of the plate, and the other being a tube carrying at one end
the slit, furnished with micrometer screw^ through which the
beam of light passed, and at the other end an object-glass
for the purpose of rendering the rays parallel. The luminous
vapours of the metals under examination were obtained by
placing a bead of the chloride or other salt of the metal on a
platinum wire, between two platinum electrodes, from which
the spark of a powerful induction coil could be passed. In
order to obtain a more intense, and therefore a hotter spark
than can be got from the coil alone, the coatings of a Ley den
jar were placed in connection with electrodes of the secondary
current respectively. When this arrangement was carefully
adjusted, the two yellow sodium lines were observed to be
separated by an apparent interval of two millimetres, as
seen at the least distance of distinct vision.

The position of the blue line, or rather blue band of
lithium, was then determined with reference to the fixed
reflecting scale of Steinheil's instrument, by volatilising the
carbonate of lithium in the first place on a platinum wire
between platinum electrodes, and secondly on a copper wire
between copper electrodes. A bead of pure chloride of
strontium was then placed on new platinum and copper wires
between two new platinum and copper electrodes, and the
position of the blue line Sr S read off upon the same fixed
scale ; a difference of one division on the scale was seen to
exist between the positions of the two lines, the lithium line
being the more refrangible. The salts of the two metals
were then placed between the poles at the same time, and
both the blue lines were simultaneously seen, separated by a
space about equal to that separating the two sodium lines.
When experimenting with this complete instrument, we were
unable to observe any other blue lines in the pure lithium

229

spectrum than the one above referred to ; we have, however,
noticed the formation of four new violet lines in the intense
strontium spectrum, and we nov\^ believe that the other two
lithium hues mentioned in our letter to the Philosophical
Magazine are caused by the presence of the most minute
trace of strontium floating in the atmosphere, and derived
from a previous experiment. We have convinced ourselves
by numerous observations that the currents of air caused by
the rapid passage of the electric spark between the electrodes
are sufficient to carry over to a second set of electrodes
placed at the distance of a few inches, a very perceptible
quantity of the materials undergoing volatilisation. The
greatest precautions must hence be taken when the spectra
of two metals have to be compared ; and no separate observa-
tions of the two spectra can be relied upon, unless one is
made a considerable space of time after the other, and unless
all the electrodes which have been once used are exchanged
for new ones.

Kirchhoff, in his interesting Memoir on the Solar Spectrum
and the Spectra of the Chemical Elements,* noticed in the
case of the Calcium spectrum, that bright lines which were
invisible at the temperature of the coal gas flame became
visible when the temperature of the incandescent vapour
reached that of the intense electric spark.

We have confirmed this observation of Kirchhofl''s, and
have extended it, inasmuch as we, in the first place, have
noticed that a similar change occurs in the spectra of
Strontium and Barium ; and, in the second place, that not
only nevf lines appear at the high temperature of the intense
spark, bat that the broad hands characteristic of the metal or
metallic compound at the low temperature of the flame or
weak spark, totally disappear at the higher temperature.
The new bright lines which supply the part of the broad

* KirclihoiF on the Solar Spectrum, &c. Translated by H. E. Eoscoe.
JVIacMillanj Camljriclge. 1862.

230

bands are generally not coincident with any part of the band,
sometimes being less and sometimes more refrangible. Thus
the broad band in the flame-spectrum of calcium named Ca [5,
is replaced in the spectrum of the intense calcium-spark by
five fine green lines, all of which are less refrangible than
any part of the band Ca /3 ; whilst in place of the red or
orange band Ca a, three more refrangible red or orange lines
are seen. The total disappearance in the spark of a well
defined yellow band seen in the calcium spectrum at the
low^er temperature, was strikingly evident. We have assured
ourselves by repeated observations that, in like manner, the
broad bands produced in the flame-spectra of strontium and
barium compounds, and especially Sr a, Sr /3, Sr y, Ba a,
Ba /B, Ba y, Ba S, Ba ^, Ba rj, disappear entirely in the spectra
of the intense spark, and that new bright non-coincident lines
appear. The blue Sr S line does not alter either in intensity
or in position with the alterations of temperature thus
effected, but, as has already been stated, four new violet
lines appear in the spectrum of strontium at the higher
ten^perature.

If, in the present incomplete condition of this most
interesting branch of inquiry w^e may be allowed to express
an opinion as to the possible cause of the phenomenon of the
disappearance of the broad bands and the production of the
bright lines, we would suggest, that at the lower temperature
of the flame or weak spark, the spectrum observed is pro-
duced by the glowing vapour of some conipound, probably
the oxide, of the difficultly reducible metal ; whereas, at the
enormously high temperature of the intense electric spark
these compounds are split u}), and thus the true spectrum of
the metal is obtained.

In conclusion, we may add that in none of the spectra of
the more easily reducible alkaline metals (potassium, sodium,
lithium) can any deviation or disappearance of the maxima of
light be noticed on change of temperature.

231

A Paper was read, entitled, ' Notes on Calorific
Phenomena," by J. C. Dyee, Esq., ^ .P.

The Author states that the essences of matter, their
number and their forms, are only known to us by their
observed properties and mutations ; that conflicting theories
on physics arise from the various interpretations given to the
same phenomena ; and if unable to reconcile such differences,
further inquiry, with that view, may not be improper, whilst
the laws of nature rest on debateable grounds. That
practically matter, in its aggregate, is found to consist of two
sorts or classes — the " ponderable" and the "imponderable" —
gravity and elasticity serving to distinguish their respective
inherent properties. That as no tests of weight or measure
can apply to the latter, its mutations and action on other
bodies are the sole means we have of forming any judgment
concerning its agency in the laboratory of nature. That the
calorific element, or heat, is assumed to be the o/ie ^^ sole
imponderable element which pervades matter and space
throughout the universe," and it constitutes the elastic forces
reacting upon and halancmg the gravitating forces in all other
bodies. This elemental state of heat must be taken as distinct
from its other tlwee states of sensible, radiating, and specific
heat, commonly recognised. That elemental heat is acted
upon by mechanical and chemical forces, and the changes
which it undergoes from the one to the other conditions of
heat, give rise to atmospherical phenomena, known as
electrical, magnetic, and optical ; as also to the entire range
of meteorological changes, as set forth in the Paper. That
by the mechanical forces of the earth's motion in its orbit
and diurnal rotation, acting upon the elemental medium, its
equilibrium is disturbed and motions generated which afford
rational explanations of the luminous and ordinary electrical
and magnetical conditions of the atmosphere, as indicated by
their respective meteors. That by the action of chemical
forces, great mutations of heat are continually going on ; for

232

example, the heat which on a vast scale ahoimds in vapour,
is given out as clouds are formed, and accounts for the
positive and negative electricity ; and also, when redundant,
for lightning from thunder clouds. As much heat is evolved
above the clouds, where cold prevails, it must become
elemental or neutral there, and justifies the inference that it
is identical with the electric fluid, as above said. That
electricity and magnetism are but diverse actions of one
element has been proved, and their action on matter proves
their materiality. The mechanical and chemical action of
light proves its materiality also ; and that light and heat are
identical has been clearly established. The plurality of
imponderable elements is, therefore, disproved by the fact
that the mutations of the one element fully account for all of
the phenomena attributed to several. The gravitating and
elastic properties of matter constitute their statical and
moving forces, for ever balancing each other. The former of
these forces would consolidate the material universe *' with
lightning speed," but for the reaction of the latter force.
There is no reason wliy the force of gravity should be
measured by the established laws of falling bodies, except
that experiment has shown the velocities actually attained by
them in vacuo. But this vacuum is the absence of air only^
not that of the " elastic medium ;" and it is this that holds
the poise of matter throughout illimitable space.

233

MICEOSCOPICAL SECTIOIS'.

March 17th, 1862.

E. W. BiNNEY, Esq., F.R.S., F.G.S., in the Chah-.

Twelve specimens of soundings were received from Captain
George Randall, of the barque " Brazil," taken on the north
coast of Brazil; also five specimens from Captain George
Murray, of the ship '^ Finzel," taken off Robin Island, Table
Bay ; coasts of Sumatra, Java, and St. Helena.

Mr. H. A. Hurst made a donation of eight slides of
diatomaceee of various kinds ; also specimens of fibre from
the Bombax, or East Indian Cotton Tree, and the fibre of
the Asclepias Syriacus from Bengal. Some conversation
arose upon the adaptation of these fibres as substitutes for
cotton, but, although fine and silky, there is not sufficient
strength in the staple to render them fit for manufacturing
purposes.

Mr. Blandford presented, through Mr. Hurst, a number
of specimens of the tongues of mollusca from Burmah, upon
which Dr. Thomas Alcock reported that there Avere four
species, two being fresh water, Melania variabilis ; a species
of Paludomus; and two land shells, different species of
Cyclophorus.

Cyclophorus belongs to a section of the order Pulmonata,
distinguished by having an operculum or door to the mouth
of the shell, and by having a type of teeth similar to that of
the Pectinibranchiata. Cyclostoma elegans is a British
representative of the same group.

Mr. Cheetham exhibited a prism, which he uses to
illuminate objects under the microscope with the variously

234

coloured lights of the spectrum in succession, instead of
ordinary light. He finds that details of structure are more
distinctly brought out by some of the colours than others ;
the blue and green rays are also very pleasant to work with,
and easily varied by throwing the required part of the
spectrum on the mirror below the stage.

Mr. SiDEBOTHAM brought before the notice of the meeting
Mr. Petschler's process for producing vegetable forms with
crystals of bichromate of potash in gelatine, which was
discovered by him in the preparation of glass plates for
photographical purposes, and exhibited at the Microscopical
Soiree given to the British Association at the last meeting.
Specimens on large glass plates were handed round, which,
when magnified, aptly represent mosses, ferns, and algae, in
beautiful ramifications, which vary in many ways, dependent
upon the strength of the solution, temperature, state of the
atmosphere, and other causes. Mr. Sidebotham called
especial attention to the peculiarity of the form of crystallisa-
tion, and to the fact that an inorganic salt, in contact
with organic matter, should produce vegetable forms.

The Secretary then read a Paper by Mr. Petschler,
describing the plates and the process.

Glass plates, Nos. 1, 2, and 3, were coated with collodion,
on the surface of which a hot mixture of gelatine and
bichromate of potash had been poured, then allowed to cool
and to dry spontaneously. In a few hours the crystals began
to form and ramify themselves over the plate. The mixture
was composed of three parts of gelatine and water twenty
grains to the ounce, to one part of a saturated solution of
bichromate of potash.

Plate No. 4, the same mixture spread hot without
collodion. On a corner of the plate the crystals liavc been
dissolved out Avith water, showing skeleton traces in the
gelatine left behind.

23fl

l*l;ilf No. .'* i'i rovrx'd vvilli ri)ll<Mli<)n .mil ji ifJnliuii <»('
lM('.liroin;il<; vvif.liotil, (^cliiliiic

l*l;t,(,<! No. i'l Willi (ii'fil, r,ov<!H<l Willi IIm' iiii-Jiik- .hhI iImii
Willi j.'lydTiMc, hill, no <i yMliillruil loii lool; |»l.i<c. 1 1, vvn«
IIkii <Iiii(| Willi .Jroii" liciil, I'cl.ilnM- iiiid I»h hi om.ilr poiiird
<»v<'i' liol, jiikI IJkii iill(>\v<<l ((» < I yiliillnM'.

\*\.iU' No. '■/ ))r<-|);iir.l ;ri No. -1, willi [m-LiIiih' iiinl
l)i< liioin;il<- vvillioiil < oliodion. Alhi lln- cryfiliilii vv<'l'<<

f"onri('<|, (lie jj.ilc vv;ri di))|)< d imIo u. c.oIiiIioii of iiiliul'' of
Hilv< r, wlnrli < li;iii;'(;«l lli<- ■■,:t\\ inio IIk- k <I « In omitlc ol oiJvn',
iliMoluM*: in vv;il,<r, l)iil, f.oliiMf: in li y |»o nlplii If ol hodif,
JiiMinoniJi, tv,(;. In on': «'OMi<i I, In- nyt.l.il'! \v<r<' ditsfiol v<r<l
(Mil, l( ;iviii;', iIk ir <;(i;hl,M ill I.Ih) |j;<!|jil.iin?.

I'lilf No. /' '.vaM pi'<'p;ii'fM| M", I,'*/, Mii'l .'», I»y r,oll(>'lioii iiiid
1,1k: niixidic, iIImI ;iri( I lli«- loiin;ilion oi llic <iy<iliili rlnin;'/-'!
into I'll ' Jii'i/n.il': '»! ;;ilv<:r fi'i No. 7.

I*l;il«' N'>. *.), j>i 'ji-ii''! ;i''. N'r ^», Willi f'lyiniii- 'ln< il willi
^r<;;jl, ln:;il,, IIk/i <:o,iI''1 Willi Mi' nii/'.lui'- .ui'l liciliil willi

nilTMf,<; ofhilv*;/' uH No. 7.

TIk; jm'';iI, v;ui<l,y .ui'l \n ''uly <A' iIk ;' I'/i inss hi ( i ytil,(i.lM c-oiild
Willi 'liffi'iilly 1)1- ii'j»ir';«nl« 'I liy 'l»(i,winp/fj.

'I'll': Aullioi 1)1 II' v ■: lliiil. II') ':ll» llli'tdl ' 'mdIhimIioIi l.d'.Ctt
j)l;i':<; li' l.wc JI III': ;:;dl, .ui'l l,li'' f" lnlin«-> hot IIj:.I iIi' I. ill"!'
fU'X'i i'Atii\t\y UH ;i, ni<'liinn. 'Ili' !'/d;ilin'-, wli'/i imn , icUuHf.
u, (:';rl;iin 'juimlily <>\ ni';i!d,in'', wli/<;lj i'-. lii voin-'il/l'; l'> 'ly'^.dil
IJHatJ'/n ; hnl. wli';n tli' mol'din'- !•. drivn off l»y li<;il , iJic
crynUiW'iiiid'ion tn Murip' n'l' d

In III': <:()Ur:<: ui l,li'; c^n v';r'i;i.l ion win' li ';n;ii'd, lli«
(/'//AJliMAN r<:f'<;rr';d I'i III': i;iinilj''l lonn i/i v/lii'di til'! f,Ji|f«
of h'/fn<; ffM:(,fi,hi w';/': fo'in'l nnlin.iily, in u^jtU-, h\id<', Htid
»;vn li;ij» i';';l-., v/li' »': iJi': 'i/.i'l'; 'd in;in;/;in<j»<} WU« r/<-'jM"nl.ly
f'^iin'l I'i li;i,V(; «,««urri<;d f;i/nil;o ihimti.

My. M<t?,l,U,V pm</^ii^i',nU'(\ Uj.jI, i.Ii'; ;n l>'in;^,r;<;/<t lornr^. mrlil.
p<jrh/'j.|>;i iii'h<i i'nmi Ukj i,':nijii.y 'd tli': f.oliiUo/), f/ /i/i iIim
r(;>*i«tanc<; <d' Um,- {/<;l;<.f,in<; f.o .'iII'av of cry^f.M.lli«Jil.Ioii in Ui'!

236

usual rhombic form, and possibly to the subtle electrical or
galvanic action supposed to be excited during crystallisation.
Some years ago he had obtained from solution of bichromate
of potash, tree-like forms with spreading branches and pendent
rhomboids, which under the polariscope appeared like a tree
with gems of rich colours for fruit.

Mr. MosLEY exhibited an edition of Baker's work on the
Microscope (London, 1785), with many engravings of
vegetable forms in crystals of manna, salts of antimony,
copper, &c.

Mr. Brotheks exhibited a drawing of a small animal he
found leaping on the surface of the water in his aquarium,
supposed to be identical with the species of Podura found
last year by Mr. Lynde.

237

Ordinary Meeting, April loth, 1863.
E. W. BiNNEY, F.R.S., F.G.S., Vice-President, in the Chair.

The Rev. Robert Hahley, F.R.A.S., Correspondini?
Member of the Society, made the following communication
^^ On the Theory of the Transcendental Solution of Algebraic
Equations."

In my iirst communication to the Society on the Theory
of the Transcendental Solution of Algebraic Equations (see
pp. 181-184 of the current volume of the Proceedings), there
is a statement to the effect that any linear function of the
roots oi f{y,x) — 0 must satisfy the differential resolvent.
This statement requires, I find, some slight modification.

The differential resolvent for the 71-\g equation in y may
be written as below : —

*(.)=£a+x.£i...+x„.2+x,._„+x,.=o.

Now, if Y be a linear function of the roots and of the form

in which a^y «i, cio, •••«,» are arbitrary constants, it is easy
to show that

$(Y) = rtoX,_i + (l— ai-i-«2-..+«„)X„

the sinister member of which equation vanishes when «o=0
and X„ = 0. So that the true theorem is — Any 1iomoge7ieons
linear function of the roots will satisfy the differential
resolvent provided that such resolvent is also homogeneous.

But further, whatever may be the form of the resolvent, it
is satisfied by any of the constituents of the roots. For we
know by Lagrange's theory that those constituents are
severally of the form

PnocBEDiKcs— Lit. & Phil. Society— No. 15.— Session 18G1-62.

238

or what is the same thing

u) denoting, as usual, an unreal nth root of unity. And if
we put

we shall have

Y=(i + «,)2/, + (i + <.^)y....+(i + «-••>„
and

$(Y)=:0,

which establishes the proposition. It hence appears that the
argument in which the statement above amended occurs,
does not require any further modification.

The general form of the differential resolvent for the 9i~ic
equation

y"—ny + (^^ — 1)^ = 0
given in my last communication to the Society (see pp. 199-201
of the Proceedings)^ may be deduced from Mr. Cayley's equa-
tion (p. 193, ibid) —

r <^n"-^ V n d 2w— 1-1"-^ „_,

L duA -^ Lw—l du n — ij -^

by simply writing - and ^^ in place of a and u re-
spectively. But I think it right to mention that the form
was suggested to me by induction from the particular cases,
w=3, w=4, ??=5. In fact, I found by direct calculation that
the several symbolical forms of the differential resolvents are
as follow, viz. : — For the cubic the resolvent is

{^-i)(p-l).

D(D-l)

e^^=:0;

239
for the quartic, it is

(^-i)(p-^)(p-'!) ,,

^ D(D — 1)(D— 2) ^ ^~-^'

and for the quintic, it is

^ D(D — 1)(D— 2)(D— 3) ^ ^-^'

which are all comprehended under the general form given
on page 199. The induction, though incomplete, is yet
sufficiently wide for the purposes of the present theory, inas-
much as, when 7i is greater than 5, the given n-ic equation
cannot in general be reduced to the trinomial form with which
we are now working. But Mr. Cayley's brilliant piece of
analysis, of which an abstract is given on page 193, enables
us, as we have seen, to establish the theorem in all its
generality.

I noticed in my last commuhication the exceptional case
n=z2. The following remarks on the same subject by Mr.
Cayley will be read with interest. I had taken the liberty
of calling his attention to the form of the resolvent for
the quadratic, and replying in a letter to me, under date
25th February, 1862, he says, "I ought to have seen,
and after writing the note on the Differential Equation did,
in fact, see from your paper that n=2 is an exceptional
case : the d priori reason is, that for the equation

we have (not as in the general case yi -}- t/z 'h <&c. = 0) but
^1+^2=0. Hence for n=:2, the differential equation cannot
be of the form

for if so, its solution, which would be of the form y=:CY,

240

could not by any determination of C give each of the roots
y—yi, y—y2' The differential equation must have a term
independent of y, and the solution is

2/=yi+C (1-yO
which in virtue of y^-^yo—2, is

=y,+(2-C) (1-y,)

and gives y^ or y.^ as 0=0 or C=f2."

Mr. W. H. L. Russell, of Shepperton, Chertsey, has
favoured me with the following elegant solution of the
quartic resolvent obtained by the aid of definite integrals.
( 5 2 1 /17 5\ /14 2\ yll _lx X

5^ = A L , 4 ' 4 ' ~i 3 . VT'i j VT'i AT'~4 j,^, ,
I ^ "T" 3 • 2 • 1 "^ (6 • 3) (5 • 2) 4 • 1) ^ /

/ 9 6 3 y21 9\/18 6\/15 3\

+bJ i'i'i^3^vT'iAr;AT'4>>^

I ^ ^ 4 • 3 • 2 ^ (7-4) (6-3) (5-2) ^

/ 13 10 7 /^25 13x/^22 lO-v >^19 7>^ s

^Qx' T'T'i 3 . vT'TyVT'Tyl^T'i) e. .

(1+5 43''^ "l8~^ ) (7^1) WW '

=A I . 10485763:^ t f' f' ^ ^' ^^'^ (1—^)^ (l^^F (1— m^)^ <^t^ dw dz
( 8197r=^ 0 0 0 ' \—vzivx^

4-Ba; f'f'f' ^^ '^^ ^"^ (1—^)^ (l-~;s)^"(l--w)^ <^y d% dw
"^ 0 0 0 l~-t;2z^a;3

4-Ca;- f'f'f' ^^ ^' ^^ (1—^)^ ^—^ {\—v^ dv dz dw
^ 0 0 0 \—vzivx'

In this solution x is assumed less than unity. An inter-
esting paper by Mr. Russell, on the Theory of Definite
Integrals, will be found in the ^^ Philosophical Transactions'*
for 1854, pp. 157-178.

Dr. Boole has also pointed out to me a method of solving
the quartic resolvent, which does not, however, essentially
differ from the above. And Mr. Russell remarks that a

241

similar process is applicable to the more general resolvent.
But what is wanted is a solution Avithout the aid of definite
integration.

Sir John F. W. Herschel^ in a letter to me under date
March 15th, 186^, referring to the closing remark in my last
communication, calls attention to a paper of his in the
^^Philosophical Transactions" for 1814, "On various Points
of Analysis/' "§ IV. On Equations of the First Degree," and
also to a paper of his in the "Memoirs of the Analytical
Society" of Cambridge, 1813, "On Equations of Differences,"
in which there is something, Sir John Herschel thinks^ tend-
ing to confirm the opinion that the primary forms of inte-
grable linear differential equations stand in close connexion
with the solvable forms of algebraic equations. In the latter
paper, however. Sir John Herschel informs me that he wishes
to "repudiate all that occurs from page 100 to page 105, as
founded on a mistake." I need hardly add that the writings
of so distinguished a member of our Society shall receive, as
they deserve, my most careful attention. I hope soon to
return to the subject.

Dr. R. Angus Smith, F.R.S., read a Paper entitled
"On the Putrefaction of Blood, No. 2." The following
is an abstract.

When I first began to examine the products of the putre-
faction of blood, it was merely with the object of ascer-
taining the nature of the gases, and of ascertaining whether
any matter in them exists in a so-called organic condition,
and, if so, in what quantity. I have ascertained the nature
of the gases. So far as I see, however, I have added no new
one, but I believe that for the first time I have given the
proportionate amount of each.

I have also decided on a simple and certain method of
collecting some organic substances from the gases, namely,
the use of caustic potash, ^vhich I find superior to acid salts.

242

Other methods also I have found promising, hut I have heen
compelled to give up the inquiry, at least for a long time, on
account of the extremely nauseous emanations which pene-
trated every room in the laboratory, and were, no doubt,
waiting for a favourable opportunity of changing into deadly
poisons. These, by proper arrangements, might be avoided.
I mentioned formerly that the temperature of 54° Fahr., or
12° C, was a very marked one in favoring putrefaction. I
now find that on to 120° Fahr., (49° C,) at least, the process,
if it ceases, may be set in motion by raising the temperature.
After that point it is difficult to induce putrefaction. I give
here a specimen of the

PROGRESS OF THE DECOMPOSITION.

Gases Absorbed. Not absorbed,

Nov. 9 88-65 11-85

„ 12 91-32 .... 8-68

„ 13 91-56 8-44

14 95-90 4-10

15 96-04 3-96

18 98-26 1-74

19 98-50 1-50

20 98-95 .... 1-05

After the decomposition had proceeded to such an extent
that it was difficult to obtain even a few bubbles more, the
gases existed in the following proportion : —

Carbonic acid 97.09

Sulphuretted hydrogen 1-93

Hydrogen. , . ..^ 0*18042

Carbonic oxide 0-13968

Marsh gas 0-07295

Nitrogen 2-51715

100.
A trace of a compound of cyanogen was found, and a
small amount of phosphorus was obtained in the acid

243

solution. Ammonia was found in considerable quantities.
These substances exist along with the gases, and arc all
I have hitherto determined.

Other experiments gave me much more hydrogen , and I
am prepared for a considerable variation in the amount of
the several gases. The nitrogen came to a minimum when-
ever the decomposition became slov/. This might be in-
terpreted in two ways— first, by the absence of air to
continue the process ; and second, by absence of the nitrogen
from the decomposed albuminoids. I do not see from my
experiments a sufficient proof of the elimination of nitrogen.
The amount was in a state of constant decrease, suggesting
a gradual removal of atmospheric air.

I mentioned that by passing the gas through lead and
other metallic salts, only a small amount of organic matter
was collected ; but by passing it through caustic potash the
amount was considerable. A flocculent matter fell, but the
chief amount remained in solution. The solution was boiled
down, and, when heated, a perfectly fresh odour of soup
was spread through the room ; everything offensive had been
removed, and the smell was for the first time very agreeable,
Here we find that the substances sought for are decomposed
by the very means which we take to retain them. But in
this experiment we see a demonstration that substances of
an organic nature pass over with the gases. When strong
sulphuric acid was added to the potash solution there was an
abundant black precipitate of carbon and carbonaceous
matter. More than enough for an analysis had been made.
There was a fatty odour from it when sulphuric* acid was
added, leading me to think of Chevreul's remarks on a
similar occasion.

As these compounds were not retained by acid salts, but by
alkalies, I concluded that they were acids ; but on allowing
some of the solution to stand for a few hours, I ^vas surprised
to find that the organic matter had almost disappeared.

244

We see clearly how difFerently the organic substances act
from carbonic acid. I took home a small piece of cotton wool
through which the gas had passed for some days. My inten-
tion was to examine it with the microscope. Less than a
grain of this cotton was taken out of the tube in which it
was enclosed, but so thoroughly did the room become offen-
sive that some friends, not aware of my pursuits, were much
annoyed.

This is one of those many facts which lead to the conclusion
that the amount of carbonic acid is entirely incapable of
showing the true condition of an atmosphere unless we esti-
mate that gas at once on its formation, as then it is mixed
with organic matter. If, however, we allow even a short
time to pass, a separation takes place, the carbonic acid dif-
fuses and the organic matter clings to substances to be
gradually given off: the tendencies of the two are entirely
different, and the separation begins at once.

When the gases were previously passed through charcoal,
it was difficult to obtain a trace of organic matter.

I imagine that I see my way now to a very satisfactory and
comparatively easy investigation, although for tlie time I
must leave it to others.

245

Annual Meeting, April 29th, 1862.

J. P. JouLE^ LL.D., F.R.S.j President, in the Chair.

Mr. Andrew Knowles was elected an Ordinary Member of
the Society.

A Paper was read " On Non-Modular Groups," by the Rev.
T. P. KiRKMAN, A.M., F.R.S., and Hon. Mem. of the Literary
and Philosoj)hical Societies of Manchester and Liverpool.

From the seven triads which exhaust the duads of seven
elements, 157 261 372 413 524 ^^h 746, we can write
twenty-one triads containing each a capital and two small
figures, thus : —

157 571 715 261 612 126 372 723 237, &c.

We can collect the triplets of these triads which contain the
same small letter, thus, the order of two small figures being
indifferent : —

EllRATUM.

Page 245, line 6 from bottom, for "every vertical" read
" everv first vertical."

^.>^ v»vy« «"-! **ii AO-x ^it JL^O iSiO J.:iO S(5iO

413 143 134 524 314 254 536 356 356 536

where every triad and every vertical row containing three
figures is one of the seven fundamental triads. We have thus
formed twenty-eight triplets of triads, and have exhausted
3'7-4 of the 21*10 couplets possible with the 21 triads, 157,
571, &c.

PaooEBDiNGS— Lit. & Pjijl. Society— No. 16.— Session 1861—62.

244

We see clearly how differently the organic substances act
from carbonic acid. I took home a small piece of cotton wool
through which the gas had passed for some days. My inten-
tion was to examine it with the microscope. Less than a
grain of this cotton was taken out of the tube in which it
was enclosed, but so thoroughly did the room become offen-
sive that some friends, not aware of my pursuits, were much
annoyed.

This is one of those many facts which lead to the conclusion
that the amount of carbonic acid is entirely incapable of
showing the true condition of an atmosphere unless we esti-
mate that gas at once on its formation, as then it is mixed
with. organic matter. If, however, we allow even a short
time to pass, a separation takes place, the carbonic acid dif-
fuses and the organic matter clings to substances to be
gradually given off: the tendencies of the two are entirely
different, and the separation begins at once.

When the gases were previously passed through charcoal,
it was difficult to obtain a trace of organic matter.

I imaarine that I see mv wav now to a verv satisfactorv and

245

Annual Meeting, April 29th, 1862.

J. P. Joule, LL.D., F.R.S., President, in the Chair.

Mr. Andrew Knowles was elected an Ordinary Member of
the Society.

A Paper was read '^ On Non-Modular Groups," by the Rev.
T. P. KiRKMAN, A.M., F.R.S., and Hon. Mem. of the Literary
and Philosophical Societies of Manchester and Liverpool.

From the seven triads which exhaust the duads of seven
elements, 157 261 372 413 524 635 746, we can write
twenty-one triads containing each a capital and two small
figures, thus : —

157 571 715 261 612 126 372 723 237, &c.

We can collect the triplets of these triads which contain the
same small letter, thus, the order of two small figures being
indifierent : —

157 157 517 517 571 571 751 751
327 237 327 237 431 341 431 341
467 647 647 467 261 621 621 261

175 175 715 715 372 372 732 732 273 273
365 635 365 425 452 612 542 612 653 563
425 245 245 635 162 542 162 452 143 413

(A)

723 723 674 674 764 764 746 746 476 476
653 563 254 314 254 314 126 216 126 216
413 143 134 524 314 254 536 356 356 536

where every triad and every vertical row containing three
figures is one of the seven fundamental triads. We have thus
formed twenty-eight triplets of triads, and have exhausted
3-7'4 of the 2M0 couplets possible with the 21 triads, 157,
571, &c.

Pboceedings— Lit. & Phtl. Society— Xo. 16.— Session 1861—62.

*i46

We can next form a quadruplet upon each of the 2\ triads
thus : —

on (157), 517 on (524), 254 on (563), 653
126 517 517

751 452 365

134; 563; 524;

(B)

on (715), 732 on (134), 126 on (261), 126 on (612), 126
517 341 237; 635

746 157 621- 261

157; 431; 245; 647

In the first of these, 157 126 134 are three triads which
have the same capital, and 157 517 751 are the three triads
which have the same figures ; &c.

The twenty-one quadruplets thus formed exhaust the 21 '6
duads not formed in the 28 triplets, so that we have once
and once only employed every duad possible with the 21
triads 157 571, &c., in these 21 quadruplets and 28 triplets.

We may interpret the three triads 157 126 134 as the
three substitutions

16435 2 7, 124376 5, 163472 5,
which obviously determine each other, having all three
elements undisturbed, and all being of the second order.
We have thus twenty-one similar substitutions, each defined
by a distinct triad.

The first of the above written triplets and quadruplets are
found to be

1643 5 27 1462537

6235417 1243765

2154 3 67 13 26547

16 3 4 7 2 5,

of which the former are the didymous radicals of ^,=6153427

of the third order, and the latter are those of ^4=1362745 of

the fourth order, where ^/=(157), which determines the

247

quadruplet, is permutable with all its four triads. Vide
art. 76 of my memoir 0)i the Theory of Groups and many-
valued functions^ in the volume of the Memoirs of this Society
for 1861.

It is thus proved that every pair AB or BA of the 21
square roots of unity determined by the 21 triads have for
their product either one of 2*28 substitutions of the third
order, or one of 2*21 substitutions of the fourth order, or one
of the 21 radicals.

The values of the triplets possible with the 21 radicals
have next to be discussed. Some of them will be, and some
will not be, reducible to a couplet. Let {AB} denote any
triplet or quadruplet of the 28+21 above formed, in which
the couplet AB (consecutive or not) appears among the
didymous radicals. The condition that a triplet ABC should
be reducible to a couplet is any one of the following : —
1° That A be permutable either with B or with C,
2« That {BC} contain A' permutable with A,
3« That {AB} contain C permutable with C,
4° That {AC} contain D^ permutable with CBC=D,
for ABC=A*C-CBC=ACD. D is equidistant with B from C
in {AC}. Every one A of the 21 radicals has four per-
mutables, which are those of the quadruplet (A).

It is easily proved, or can be seen by inspection when the
quadruplets are all written, that any irredudible triplet PQR
in which QR=^3 of the third order, is identical in value with
ABC where BC=:0i of the fourth order. Hence every irre-
ducible triplet is of the form of A(BC),=A •517-126=:
A-1462537-l243765=zA 1426735. It can be proved or seen
by inspection of triplets and quadruplets (A), (B), that the
only values of A which render this ABC irreducible are the
eight following—

372, 273, 425, 245, 356, 635, 467, 647.
The circular factors of (BC)i are 2 4 6 3, 7 5, 1. None of

248

the eight triads has 1, none of them has both 7 and 5.
Hence none of them has a transposition which fractures
either of the circles 2 4 6 8, 7 5. Consequently the effect of
any one of the eight is to unite the circles of (BC)4 into one ;
that is A(BC)4 irreducible is always a substitution of the
seventh order. It is easily demonstrated that if A^A.^ be any
two of the eight values of A^ A^BC can be no power of
AaBC. Hence there are not less than eight substitutions of
the seventh order, no one of which is a power of another :
that is, there are 8-6r substitutions of the seventh order.

The number of irreducible triplets is eight times that of
the substitutions of the fourth order, written each under four
forms, BC=CD=DE=EB in terms of the didymous radicals
BCDE. That is, there are 8-2-21'4 irreducible triplets.
This must be divisible by 4*8"6r, because each of the sub-
stitutions ABC of the seventh order is formed with four
values of BC ; consequently r=l or r—7, the latter of which
is easily seen to be inadmissible.

It is thus proved that there are in reality 48 different irre-
ducible triplets, and so many substitutions of the seventh
order. We demonstrate easily that every quadruplet ABCD
is reducible to a triplet ; hence every quintuplet ABCDE, &c.,
is reducible to a triplet. And we thus prove that the 21 similar
radicals form with their products a group of

28-23-|-21-24-f2M2+8-67+li=7'6-4
substitutions.

The equivalent groups will have each 48 substitutions of
the seventh order, The number of these substitutions is
6'5'4:'S'2'. Hence if each be r times found in the equivalents,

r6-5-4-3'2

1 have shown, ill the iMeinoir above quoted, that two groups
of 7*6*4 can hs formed to contain the powers of ^3345671 ; and
the same thing is deducible from the fact that we might have

249

begun above with one other only system of seven cyclical
triads, exhausting the duads in seven. Hence r=2, and
there are thirty equivalent groups of 7'6*4. And as

we see by the corollary to my theorem A (art. 9^ '^ Theory of
Groups/' Sec), that the group has no derived derangement,
i. e., it is maximum.

Take next the 66 triads : -—

12436 12590 15738 235^7 267i.5 2748o 340,9 39^46 46^27 5702« eOfir^

1093„ 17^60 I6O28 20au 249g« 28O35 37826 45769 4806« 590^8 68^13

13^25 128-« I4O57 29067 2O849 34658 35O16 458i2 469io 59rzi7 780i9

18956 1564^ 13679 236„„ 27«39 3ao78 3795o 45^30 56870 6798« 78«45

la489 138^0 17924 239i8 25cr68 347i« 3589« 48937 56903 67O34 89a,2

which exhaust the duads of eleven elements 12 '"' oa three
times, and which^ disregarding the subindices, fulfil the con-
dition, that if ahc, abd, abe, be three triads, cde is a fourth.
These 55 triads are formed by a simple cyclical kind of pro-
cess from the triad 128. The subindex under 124 shows
that 361, o62 and o64 are triads of the system.

Each of the 55 triads determines a sextuplet. We form

on (347«i), on (68«i3), on (I9O3,), ou (325^7), on (a5268), on (I2590),

13«23

13a25

13a2,3

13a25

13^25

13«25

67034

6798,

46940

24780

66870

29067

14fl?89

13840

300578

56923

2495«

45842

23547

25aes

12590

3474«

68043

1903„

17a6o

13679

39^46

28O35

5072„

26745

48937;

4086^;

780ig;

45769;

26849;

59048;

-.vhich are all the sextuplets containing ISao^. The first,
third, and fifth of (347)ai are the three containing al ; the
second, fourth, and sixth are the three whose subindices are
the circle 34, 47, 73 ; and so on of the rest. The remaining

250

12 triads not combined with ISa in the above sextuplets
form with it six quintuplets thus : —

13^52

IScfo,

Sal,,

Sal,,

laSo,

1«32.5

89a2o

46fl27

89156

4OI5;

463^8

79350

450^,3

59«n

241o3

281:«

29381

263,„

27^39

20a,,

5713S

561 '1

503i6

583,9

60^95

78a«

6OI32

791,,

78360

403^

where the subindices form circles of five duads^ and every
triad of a quintuplet has the same final figure.

We have combined ISa with all the other 54 triads, and
in the same way we can form 66 quintuplets and 55 sextuplets
which shall once and once only exhaust the duads of the
bo triads.

We interpret the triad ISa,, as the substitution of the
second order,

(13«25)=1 5 37284609 «,
which has ISa undisturbed, and whose four transpositions
are the subindices 25, 47, 68, 90, of ISa, 251, 253, 25a.

The triads of the sextuplet (147„i) are found to be the
didymous radicals of a substitution As of the sixth order,
whose third power is ^6^=147«2, which is permutable with the
six triads of (147„i). The quintuplets are sets of didymous
radicals of substitutions of the fifth order, having circles of
five subindices.

Thus every pair AB of the 55 triads is either ^6 ^3 ^5 or
one of the 55 triads. It remains to examine the triplets
ABC.

We easily prove that every irreducible triplet can be
written as A(BC)6, when (BC)g is of the sixth order. The
renditions that A should make A(BC)6 reducible are those
above given in the like case. And we can demonstrate,
either a 2)riori, or by inspection of the quintuplets and sextu-
plets, that the only values of A Avhich make

(A(BG)e=:) A {1U,,'Q1%,\

irreducible are the twelve following: — 1243e, 30^78, 78^^.5, 460^2^,
15738, 27(730, 140,;, 361,9, 1792^, 39^46, 138^0, 54a3o-

251

The substitution ISayr,' GlOu is

1537284609«-a943867520 l=a 073684259 1=:6>,
whose circular factors are 209568, 437, a \.

It can be demonstrated, either a priori, or by simple in-
spection of the above table of the 55 triads, that none of the
twelve just written transposes a consecutive pair of the circle
2 0 9 5 6 8, i.e., none has a transposition which fractures
that circle into one of five and another of one. And as each
of the twelve has one element of each of the three circles
undisturbed, it must have for one of its four transpositions a
non-consecutive pair of the circle 2 0 9 5 6 8, while the other
three transpositions will of necessity \iQ junctures of the four
resulting circles into one circle of eleven.

Theor. A transposition of tioo letters of any circle always
fractures that circle into ttco : a transposition of elements of
txoo circles always unites those circles into one.

From this follow many important theorems on substitu-
tions. Hence we deduce easily, as above for substitutions of
the seventh order, that there are 12*1 Or substitutions of the
eleventh order, represented by 12 * 2 ' 55 • 6 triplets A(B0)6,
each substitution by at least six different triplets having the
same A. Hence r-=\ or r=ll, of which the former only is
the true value ; and there are 120 substitutions of the
eleventh order. We prove readily that no quadruplet A B C D
is irreducible ; hence no quintuplet, &c. And the 55 substi-
tutions of the second order, 15 7, 5 T 1, &c., form with their
products a group of

6 6 • 45-1-55 • 26 -f 55 • 23 -V 55 • I2 -f- 12 • lOn -j- Ij = 11 • 10 • 6
substitutions. This group is maximum, and has 9*8"T*5'4*3'2
equivalents.

We thus find that, in the discussion and construction of
these hitherto difficult groups, we can dispense with con-
gruences, and with the still more formidable apparatus of
imaginary subindices, which MM. Betti and Mathieu have
so skilfully handled.

252

The groups of 7 ' 6 * 4 and 11 '10 '6, which I think ought
to be called the groups of Galois, will always be remarkable
as being among the earliest discovered and the most diificult
to construct. They appear to be a complete family of them-
selves. One is indeed strongly tempted to believe in the
existence of other non-modular groups of ^{n-\-l)n(ji — 1) for
higher prime values of n=2p-\rl, p being prime, since they
exist for 7i=z5, nzrzl^ and 7i=:ll, But the non-existence of a
similar group for n=:2S may be easily proved, in half an
hour's labour, by the method pointed out in the 94th article
of my Memoir on Groups above quoted. It suffices to write
four vertical rows of the powers to be examined. Instead of
" As there are N values of /*," I should have written in that
section, ^^ As there are N — 1 values 7 0 of A.'* And in the
last line of page 383, art. 90, the word principal ought to
be substituted for onfy. The latter is correct, if N=:S^-fl,
where p is prime. This does not affect the reasoning. The
groups E and E^ should be represented thus —
{234567890a}ii { 3 6 9 1 4 70 2 5 S^jg {3 8 1 9 5 0 7246a}3

X{6084715293«}2 {6 518934720 43 =E,
{2345 6 7 89 0a}n {3 6 9 1 4 7 0 2 5 8a}g {l 8 43 9 0 72 5 G^ja

x{l 537284609 a}o {O 8 3 2 7 5 6 4 1 9 rtjg rrEi,
of which the observations there following are true, except
that *^non-" should be written before modular in the next
line, p. 390 ; as also in the third line of page 374.

Triads can be formed with 23 elements to exhaust the
duads of 23 six times, by perpetual additions of unity to all
the elements following : —

1-2-4, 1-2-6, 1-2-8, 1-2-9, 1-211, 1-2'12, 1-3-6, l-3'7,
1-3-10, l'3-ll, 1-3-12, 1-4-8, 1-4-10, 1-4-11, 1-4-12,
1-5-10, 1-5-11, 1-5-13, 1-6-12, 1-6-13, 1*6-14, 1-7-15.

I have a simple tactical method of forming many such
systems for all imme numbers, depending on the theory of
difference circles, which requires the solution of no equation
or congruence.

253

It is easy to demonstrate and construct, by a method
similar to the foregoing, all M. Mathieu's non-modular
groups of (N' + 1)N'(N* — 1), N being any prime number,
without taking for granted any other group, and without
having recourse to congruences ; but I do not think it worth
the while to pursue the inquiry, as this method of combina-
tions is certainly less general, although the separate cases may
thus be made to appear more simple, than the methods which
have been already given. The theory of combinations appears
likely to owe more than it can contribute to that of groups.

Two theorems are worth recording in combinations, which
I owe to the study of groups.

Eleven quintuplets can he formed to exhaust tioice the duads
of eleven elements. This can be done by continual additions
of 1 1 1 1 1 either to 1 S 3 5 8, or to 1 2 3 T « («=10).

When N is any prime number^ W- elements can he thrown
into JN(N-i-l) {^—X)'plets, N+1 1^-plets, and iN(N--l)
(^■\-\)-plets, so as once and 07ice only to exhaust the duads
of N^ elements.

This is proved by the systems of didymous radicals in the
groups of (N+1)N(N — 1), when N is prime. All the triplets
of these radicals are easily shown to be reducible to duads.

In the Memoir of which the above is an abstract, this method,
of combinations independent of equations, will be applied to
other groups, superior and inferior to those here treated,

The following Report of the Council was then read by
one of the Secretaries : —

In presenting the Annual Report, the Council congratulate
the members on the improved condition of the Society,
especially as regards its financial position. The balance in
the Treasurer's hands, as seen in his Report annexed,
was on March 31st, 1861, £58. Ss. ; whilst on March 31st
last, it amounted to £M8. 6s. 7d. ; and this in spite of

B

254

necessarily heavy expenditure incurred in the printing
of the Proceedings and of the volume I., 3rd series,
of Memoirs, which is now ready for distribution. This
improvement is mainly owing to the fact that the members
have almost unanimously supported the Council in their
proposal to raise the subscription to £%. 2s. per annum, as
the only available means of enabling the Society successfully
to carry out its objects. The number of ordinary members
on the books last year was 207 ; it is now 204. Since the
last Annual Meeting seven members have resigned, eight
new members have been elected, and four ordinary members
have died, viz., Professor Eaton Plodgkinson, F.R.S.; Dr.
M. Satterthwaite ; Mr. Absolam Watkin; and Mr. George
Woodhead.

Professor Hodgkinson's high scientific eminence as an
experimentalist and as the founder of the principles of
many branches of mechanical science, is now universally
acknowledged ; and the members will be proud to recollect
that our illustrious townsman was for 41 years connected
with the Society, and that it was through the medium of our
Memoirs that the greater part of Hodgkinson's important
researches were made known.

The following is the list of Papers published by Professor
Hodgkinson in the Society's Memoirs : —

(1) Vol. iv., 2nd series, p. 225. — " On the Transverse Strain and
Strength of Materials," read March 22nd, 1822.

(2) Vol. v., second series, p. 354. — " On the Forms of the Cate-
nary in Suspension Bridges," read February 8th, 1828.

(3.) Vol. v., second series, p. 384. — " On the Chain Bridge at
Broughton," read February 8th, 1828.

(4) Vol. v., second series, p. 398. — "A few Remarks on the
Menai Bridge," read December 12th, 1828.

(5) Vol. v., second series, p. 407. — " On the Strength and best
■ Formes of Iron Beams," read April 2nd, 1830.

(6) Vol. vii., second series. — ^ " On the Measure of Moving
Force," read April 30th, 1844.

255

The Council congratulate the members on the possession
of the life-like bust of the late Professor Hodgkinson^ which,
thanks to the liberality of a. few gentlemen, now adorns our
rooms; and they also notice that Mr. Eobert Rawson is
engaged in preparing a valuable Memoir of our deeply
lamented friend, the first half of which has already been
read before the Society.

Of the Honorary and Corresponding Members, the Council
have to notice the deaths of the celebrated French philosopher,
M. Biot, and Dr. Peter Barlow, F.R.S.

Notwithstanding the natural claims which the late very
successful meeting of the British Association for the Advance-
ment of Science, in Manchester, made upon the scientific
resources of our town, it is gratifying to observe no falling
ofi* either in the quality or quantity of the original communi-
cations presented to the Society during the past Session.

The following is the list of Papers and Communications
laid before the Society in the Session 1861-62: —

October Ut, 1861.— •" Observations of Comet I, 1861," by J.
BaxendeU, F.R.A.S.

October 15th, 1861. — " On the Irregular Barometric Oscillations
at Geneva and on the Great St. Bernard, and their relations to the
Mean Temperatme and the Fall of Rain," by G. V. Vernon,
F.II.A.S.

October 29th, 1861.—" On the Putrefaction of Blood," No. 1, by
Dr. B. Angus Smith, F.R.S.

November 26th, 1861. — " Additional Observations on the Per-
mian Beds of South Lancashire," by E. W. Binney, F.R.S., &c.

" On certain Scales of some Diurnal Lepidoptera," by Mr. John
Watson.

December loth, IS61. — " Nouveau Systeme de Communication
Telegraphique, rendant impossible toute collision de trains sur les
chemins de fer," by Professor Baulet, of Persignan, communicated
by W. Fairbairn, LL.D., &c.

256

December 2ith, 1861. — " On the Influence of the seasons on the
Rate of Decrease of the Temperature of the Atmosphere with the
Increase of Height in different Latitudes of Eui'ope and Asia," by
J. Baxendell, F.R.A.S<

January 1th, 1862. — "Experiments on some Amalgams," by the
President, J. P. Joule, LL.D., &c.

" On the Conductibility of Heat by Amalgams," by Dr. F. Grace
Calvert and Mr. Richard Johnson.

January 2\st, 1862. — " On the Action of Nitrate of Sodium on
Sulphide of Sodium at different Temperatures," by Dr. Ph. Pauli,
communicated by Professor Roscoe.

" On the Convective Equilibrium of Temperature in the Atmo-
sphere," by Professor William Thomson, LL.D., &c.

February 4M, 1862. — "On the Theory of the Transcendental
Solution of Algebraic Equations," No. 1, by the Rev. Robert
Harley, F.R.A.S.

" On the Causes of Sickness and Mortality in the Manufacturing
Towns of the North-West of England," by Dr. C. J. Shearman,
communicated by Dr R. Angus Smith.

February 18M, 1862. — "Note on a Differential Equation," by
A. Cayley, F.R.S.

" On the Present State of Meteorology." by T. Hopkins,
M.B.M.S.

March 4th, 1862. — " On the Direction of the Wind at Manchester
during the years 1849-61, at 8h. a.m.," by G. V. Vernon, F.R.A.S.

" On the Theory of the Transcendental Solution of Algebraic
Equations," No. 2, by the Rev. Robert Harley, F.R.A.S.

"Memoir of the late Professor Eaton Hodgkinson, F.R.S. , &c..
Part 1st," by Robert Rawson, Honorary Member of the Society.

" Observations on Atmospheric Electricity," by Professor Wm.
Thomson, LL.D., &c.

March 18th, 1862. — "On the Probable Cause of Electrical
Storms," by the President, J. P. Joule, LL.D,, &c.

" On the Tongues of Mollusca," by Dr. Thomas Alcock.

" On the Employment of Galvanised Iron for Armour-plated
Ships," by Dr. F. Grace Calvert, F.R.S.

257

Api'l Isf, 1862. — " On the Effect of Increased Temperature upon
the nature of the Light emitted by the Vapour of certain Metals or
Metaliia Compounds," by Professors Clifton and Roscoe.

" Notes on Calorific Phenomena," by J. C. Dyer, V.P.

April 15th, 1862.—" On the Theory of the Transcendental
Solution of Algebraic Equations," No. 3, by the Rev. Robert
Harley, F.R.A.S.

" On the Putrefaction of Blood, No. 2, by Dr. R. Angus Smith,
F.R.S.

" On the Relations between the Decrement of Temperature on
ascending in the Atmosphere, and other Meteorological Elements,"
by J. Baxendell, F.R.A.S.

April 29th, 1862. — "On Non-Modular Groups," by the Rev.
T. P. Kirkman, A.M., F.R.S., &c.

The Council have decided to print several of the above
Papers in the next volume of the Memoirs.

The Report of the Librarian shows that a very large
increase has this year taken place in the stock of valuable
scientific books of reference in the Library. The Society is
now (through the umvearied exertions of the Librarian) in
regular communication and exchanging publications with all
the most important academies and learned societies throughout
the world; and a scientific library of reference is being
gradually collected, the importance of which, especially
to those engaged in scientific research, cannot be over
estimated. Li order to complete the sets of the series of
Transactions, the current and future numbers of which are
obtained in exchange for the Society's Memoirs, a much
larger sum of money is requisite than the ordinary income
of the Society can supply. A sum of £85. Ts., being the
balances due to the subscribers of the British Association
local fund, has been kindly placed by them in the hands of
the Treasurer, for the purpose of assisting our Librarian to
carry out this important work.

258

In conclusion, the Council report with satisfaction the
increased activity and usefulness of the Sections, as shown
by their published Proceedings.

LIBRARIAN'S REPORT.

Since the close of last Session 564 vols., 608 parts of vols.,
and 206 pamphlets, have been added to the Library; of
which 176 vols., 64 parts of vols.^ and 4 pamphlets, by
purchase, and the remainder by exchange or donations.

The periodical publications which the Librarian is
authorised to procure for the Library, by purchase, are : —

The London, Edinburgh, and Dublin Philosophical Magazine.

The Quarterly Journal of Pure and Applied Mathematics.

The Cavendish Society's Publications.

The Ray Society's Publications.

The Pala3ontographical Society's Publications.

The Annals and Magazine of Natural History.

Les Annales de Chimie et de Physique.

Le Journal de I'Ecole Poly technique.

Poggendorff's Annalen der Physik imd Chemie.

Annalen der Chemie und Pharmacie.

Journal der reinen und angewandten Mathematik.

Der Astronomische Nachrichten.

On the motion of Mr. J. W. Maclure, seconded by Mr.
G. V. Vernon, the Report was unanimously adopted.

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260

The following Gentlemen were Elected Officers of the
Society for the ensuing Session : —

EDWARD WILLIAM BINNEY, F.R.S., F.a.S.

EGBERT ANaUS SMITH, Ph.D., F.R.8., F.C.S.

JAMES PRESCOTT JOULE, LL.D., F.R.S., F.C.S., &c.

EDWARD SCHUNCK, Ph.D., F.R.S., F.C.S.

JOSEPH CHESBOROUG-H DYER.

Secretaries.

HENRY ENFIELD ROSCOE, B.A., Ph.D., F.C.S.

JOSEPH BAXENDELL, F.R.A.S.

treasurer.
HENRY MERE ORMEROD.

librarian.
CHARLES FREDRIK EKMAN.

m ti^e eCoimcil.

REY. WILLIAM GASKELL, M.A.

aEORaE MOSLEY.

JOSEPH ATKINSON RANSOME, F.R.C.S., F.S.A.

FREDERIC CRACE CALVERT, Ph.D., F.R.S., &c.

PETER SPENCE, F.S.A.

ALFRED FRYER.

261

M I C it O H C O I' I C A L :i I, (J 'I I o .\ .

Aj>jil :tl\.\i, IHC'ji.

Jv w. lijNNKY, i\J^s., !'•.(;. s., iji \.\ii- (:ii:.,ir.

(Joiil.) llxiljojjs vv<^J'; ;i,f;l'.jj'>vvl':(l;_M:(J fVojn (';(,jjf;iin .i;irri<'H
(/'l.'i.rkf;, of l\i<: lji|> " lii;j}il,jiijj^' ," roji'ii^l.JjjM (jf ;j, mjxm;!-
rrion of" j/jij<1, iVoin iloh.son'H li-'iy, A ij--t,);i,li;i, ; ;i H|)rif:Jm<;ri
of" ]''ijf;iis jr,iX:uiH, or ^^ulf" wo<;f], from i\i(t Sar^uHMO Sf;;«., and
h;ujfi, ^<:., f'rorii ;i. Hfjuuffiuj^ off" t,}j^; hfjiitJj <:oahf- of Irf:Iari(l.
(j;i.p1,;i,iij (Joij1,';iif.<;, of 1,1j*; J'o) tuf^uf-'HO HtO';i.rri';r '* liij',jl,;ujia,"
f'orward(;fl a Houudi/j^ takf;n Im;Uv<:':jj ^'.-ipo (/;i.rv<i«;ijo .'uj*! Ujo
Hcrllnr^ JHlauds, off 1,}j«- (Joa--,!. of i'o/l.iif^aJ.

I*rofV;HHor (Jaja'KJj.'j j>ro:,<:nt.O'fJ t'j the rncrnlj^^rn of t,}jr;
S<-*cfj"oij a ijiiiiif>f:r- of boU,l<:s con lii.iiiin;^ r:;i,rhr>ljf acid i/j
f;ry*if,alH, for iIjo jjurpoif^ of «;Xjjf:rirrio-n1 in^^ iijjon il •, ulilif.y as
a proHorval.ivo fluid i'oj- rninro.ifjopjoal o}>j<;f;tH, as vv<:Jl an for
Hpocirnf.'rjs of nat.tjral fjist.ory.

Mr. 'I'jfOMAs I). 'J'oA ]■;, of Janiaira., pr''-:';n1<;d, ihrou^^fj
ProfoHHor Calvori, Hjj(;r:jn'jf;n ', of lJia.f,orfjao<;a.. from KJn^^st,o/J
Ifarbour ; polJo-n of a Wc-.i Indian lily; a, jjort.ion of a. jjlajj-
l.ain ]f:af, vviUj Uvo rrjou/jlo-d hlido-h of iIj'; sam<;, •Jjowinj^
co'IIh, rapliidf.";, ^o. Mr. 'i'oas*- also sf.-nf dravviri^^s arjd
d(jHcrij>t.ion of a. Kof.iffrr, fouiid uporj (Jonfo'rva, at, Jarrjaira,
which ]'; rjof krjovvn fo any of t.lio rnomljo-rn j>n;HC'nt.. Jt,
conHJHtH of an oval f^o'ly or outor f:a,' o of a. hrowninfi colour
Trf'r,'. of arj irjf;}i in I'rn^it.h ; frojn near om: rnd < A' i\i<t fjval is
protruded a trans jiarent jicck or contractile body, furnislicd
wlicn fjrotrudcd vvitfi four liairs or i't-.c.lc.t'"..^ a. lip, and a. kind
of opc-rculurrj, arou/jd vvhiclj Mr. 'i'oasc- r<:coj_MiJscd tlj(;
prcsc-ncc of cilia l^y thr- current of water, f;ut he fajled \()
discover tlie cilia for warjtof rJefinin^ powc-r in liis rrjicroscope.

262

There is not sufficient detail either in the description or
the drawings to be of much use to the microscopist, but
further information has been written for.

Mr. Brothers presented to the Section photographs of
the four drawings by Dr. Alcock, illustrating his Paper on
the Tongues of the Mollusca.

Mr. SiDEBOTiiAM exhibited a drawing of an undescribed
species of Zygnema, found by Mr. Watson and himself, at
Southport, in brackish water. It exhibited no appearance
of conjugation, and the spores were like balls covered with
spines, which when released from the cells move rapidly
through the water like vol vox.

Mr. MosLEY reported upon the specimen of the outer
coating of a bulb, received through Dr. Fairbairn from Mr.
Niven, of Jeffrey's Bay, Cape of Good Hope.

On examination with the microscope, he found that the
leaf is about rio of an inch in thickness ; that between the
outer and the inner cuticle a number of tubes or vessels run
longitudinally through the structure of the leaf; and that
these tubes are composed of very delicate fibres, coiled up so
as to form spiral vessels. On breaking the leaf, the fibres
may be uncoiled and drawn out to an almost indefinite ex-
tent. From the thicker middle portion Mr. Mosley had
drawn out fibres to the extent of 18 to 20 inches without
breaking; they arc beautifully fine, but are in his opinion
too weak and delicate, as well as too long, to be used as a
substitute for cotton. He considers it possible some applica-
tion may be found for the fibre if a sufficient sample were
sent for experimental trials. Desirous of knowing the
botanical history of the plant, lie wrote to Sir W. J. Hooker,
director of the Royal Gardens at Kew ; but it was not
possible to classify the plant with certainty from a specimen

263

so imporfect. Sir William observed that in all probability it
is one of tbe Amaryllidaceaej and possibly of the genus
Buphane.

Mr. Mosley also exhibited the leaf of a species of Digitalis,
brought by Mr. Hurst from the Hazaree-bagh, Bengal, upon
the surface of which the poison glands are closely set in
groups of four glands, placed in a lozenge form.

Mr. Nevill exhibited a new form of microscope, by
Matthews, of London, for field use or class instruction,
which can be used with either transmitted or reflected light.

Mr. Nevill proposed that the subject for discussion at the
next meeting should be, ^' On the Motion of the Naviculae,"
which was agreed to.

^DEMY

OF SC^

^

INDEX.

AiNSWOETH Thos. — Eainfall at Wliitcliaren, p. 41, p. 195.
Alcock Tnos.j M.D. — Tongues of Mollusca, p. 212.
Anderson Capt., E.M.S. Canada. — Letter from, p. 69.
Atkinson J. — Eainfall at TbelwaU, p. 3, p. 195. Abnormal Disturbances of
tbe Barometric Column, p. 26.

Ballantyne T. — Scientific Pbilantbropy, p. 47.

Batjlet Professor. — Telegraphic Communication, p. 147.

Baxendell J., F.E.A.S., Hon. Sec. — Phenomena of Solar Spots, p. 8, p. 41.
System of Periodic Disturbances of Atmospheric Pressure in Europe
and Northern Asia, p. 15. Eain near Whitehaven, p. 41. Luminous
Fogs, p. 42. Oscillations of the Barometer at Lisbon, p. 58. Observa-
tions of Comet I., 1861, p. 114. Eemarkable Solar Spot, p. 118, 119.
Eain after Discharge of Artillery, p. 145. Influence of Seasons on
Bate of Decrease of Temperature of Atmosphere on Ascending, p. 156.
Observation of Saturn, p. 170. Eelations between Decrement of
Temperature on Ascending in the Atmosphere and other Meteorological
Elements, p. 223.

Beck. — ^Binocular Microscope, p. 103.

BiNNEY E. W., E.E.S., P.a.S., V.P.— jSTodules in Coal, p. 71. Peat from
Mosses near Southport, p. 73. Drift Deposits near Blackpool, p. 133.
Observations on the Permian Beds of South Lancashire, p. 137.
Markings on the Kerridge Flags, p. 153. Want of a Museum for Eaw
Products, in Manchester, p. 225.

Bowman Heney. — Temperature at "Victoria Park, p. 2.

Beockbank. — Bessemer Process, p. 146, j). 153.

Cal^t:et F. Crace, Ph.D., F.E.S.— Lead in Snuff, p. 30. Lead in Water,
X3. 30. Sulphur in Pyrites, p. 135. Conductibihty of Amalgams,
p. 165. Gralvanised Iron for Armour-plated Ships, p. 221.

Caerick T. — Atomic Constitution of Water and Ice, p. 8.

Casartelli J.— Eainfall at Longsight, p. 196.

Cayley Arthur, F.E.S., &c., Hon. Mem.— The A faced Polyacrons in
Eeference to the Enumeration of Polyhedra, p. 3. On a Differential
Equation, p. 193.

Chadwiok D., F.S.S. — Property and Income Tax, p. 49. Eesponsibihties of
Trustees, p. 208.

266

Clipton Professor, M.A., F.K.A.S.— Influence of Temperature on the Nature
of the Light Emitted by the Vapours of Incandescent Metals, p. 227.

Cockle James, M.A., F.R.A.S.— Transcendental and Algebraic Solution,
p. 202.

Curtis John.— Kainfall in Manchester, p. 39. Eainfall at Sale, p. 196.

Danceb J. B., F.R.A.S. — Photographed Micrometer, p. 117.

Darbishiee R. D.— Deposits of Fossil Shells at Capell Backen, p. 21.

Deposit of Bones at Grt. Orme's Head, p. 134.
Daties Thos. — On Crystallisation, p. 210.
Dyer J. C, V.P. — Explosion at Blackfriars, ]). 3. Notes on Freezing and

Evaporation, &c., p. 43. Action of Steam in Boiler Explosions, p. 66.

Invention of the Electric Telegraph, p. 191. On Calorific Phenomena,

p. 231.

Ekman C. F., Hon. Librarian. — Fire Balls seen in Sweden, p. 3. Increase
of the Library, p. 4, p. 257.

Fairbairn W., LL.D., F.E.S., V.P. —Temperature in Dukinfield Coal Pit,
p. 15. Temperature of the Earth's Crust, p. 64. Cold RoUing of
Iron, p. 146. Fibrous Bulb, p. 225.

Fryer Alfred. — Vibration of the Barometric Column, p. 118. Oxyhydrogen
Light, p. 226.

Harley Eev. Robert, F.R.A.S. — Transcendental Solution of Algebraic

Equations, p. 181, p. 199, p. 237.
Heelis T., F.R.A.S. — Observations of the Zodiacal Light at Smyrna, p. 150,

Abnormal Trade "Winds, p. 217.
Hepworth John. — Method of Washing and Moimting Shells, p. 22.
Heeschel Sir John F. W., D.C.L., F.R.S., Hon. Mem.— His Meteorology,

p. 215. Effect of Solar Spots on Aerial Currents, p. 217.
Heys W. H. — Description of the Kaloscope, p. 36.

Hobler F. H. — Influence of Magnetism on Electro Chemical Deposition, p. 1,
HoDGKiNSON Prof. E., F.R.S., The late. — Presentation of a Bust of, p. 179.
Holden Isaac. — Residences of Working Classes, p. 161.
Hopkins Tnos., M.B.M.S-. — Present State of Meteorology, p. 192.
Hull Edwd., B.A., F.G-.S. — Theory of Development of Species, p. 25. Nature

and Objects of Geological Surveys, p. 32. Glacial Striations near

Liverpool, p. 155.

Johnson R. — Conductibility of Amalgams, p. 165.

Joule J. P., LL.D., F.R.S., P.— Experiments on Amalgams, p. 163.

Depression of Temperature on Ascending in the Atmosphere, p. 173.

Cause of Electrical Storms, p. 218.

267

KiEKMAN Eer. T. P., M.A., F.R.S.— Theorems on G-roups, p. 73, On Non-
Modular Groups, p. 245.

Latham A. Or. — Hepworth's Method of Mounting Insects, p. 9. Wings of
Lepidoptera, p. 188, p. 212.

Matjet M. F., Commander U.S. Navy. Deep Sea Soundmg, p. 70.

MoLESWOETH Eev. W. N., M.A. — Origin of Species, p. 24.

Moffat Thos., M.D., F.G-.S. — On Disease in Connection with HaU and

Snow Showers, p. 19.
MoSLEY G.— Envelopes for Soundings, p. 8. Meteorology of Gibraltar, p. 40.

Hurricane at Gibraltar, p. 60. Report on a Fibrous Bulb, p. 262.

Nasmtth James. — Structure of the Luminous Envelope of the Sun, p. 55.

O'Neill Chaeles. — Density of Rolled Copper after Hammermg and
Annealing, p. 56.

Pauli Dr. P.— Production of Graphite, p. 97. Action of Nitrate of Soda on

Sulphide of Sodium, p. 169.
Petschlee Mr. — Crystals in Vegetable Forms, p. 234.

Ransome J. A. — Seleniimi in Coal, p. 6. Arsenic in Sulphur, p. 13.

Ransome Aethue, M.A., M.B., M.R.C.S.— Atmospheric Pressure and Direc-
tion of Wind in Relation to Disease, p. 101.

Rawson Robeet, Hon. Mem.— Memoir of the late Professor E. Hodgkinson,
p. 203.

Robeets W., M.D.— Estimation of Sugar in Diabetic Urine, p. 6.

RoscoE H. E., Ph.D., &c., Hon. Sec— Arsenic Eatmg in Styria, p. 11. Lines
of the Spectrum, p. 23, p. 126. Effect of Temperature on the Light
Emitted by the Vapour of Incandescent Metals, p. 227.

Rylands T. G.— Classification of the Diatomace®, p. 141.

ScHXJXCK E., Ph.D., F.R.S., V.P.— New Source of Indigo, p. 181.
SHEAEMAif Dr. C. J.— Causes of Mortality in Manufacturing Towns, p. 184.
Sidebotham Joseph.— Drawings of Insects, p. 142, p. 262.
Smith R. Aicgus, Ph.D., F.R.S., &c., V.P.— Arsenic in Coal Pyrites, p. 5.

Arsenic in the Atmosphere, p. 5. Lead in Manchester Water, p. 30.

Production and Prevention of Malaria, p. 44. Relation of Work and

Workers, p. 47. Products of Putrefaction of Blood, p. 127, p. 241.

Examples of Relative and Absolute Law, p. 147. Limits of Chemical

and Mechanical Action, p. 164.

268

Spence Petee. — Arsenic in coal, p. 6. Arseiiious Acid in Pyrites, p. 125.
New Source of Indigo, p. 180.

Thomson Professor W., LL.D., &c., Hon. Mem. — Photographic Eegistering

Atmospheric Electrometer, p. 2. Equilibrium Lunar Tide, p. 135.

Convective Equilibrium of Temperature in the Atmosphere, p. 170.

Explanation of Voltaic Action, p. 177. Observations on Atmospheric

Electricity, p. 204.
ToASE T. D.— New Kotifer, p. 261.

Tebnon GI-. v., F.E.A.S. — Oscillations of the Barometer, p. 57. Ditto in
Connection with mean Temperature and Rainfall, p. 121, p. 194. Wind
at Manchester, p. 197.

Watson John. — Scales of some Diurnal Lepidoptera, p. 141.

Wilkinson T. T., F.E.A.S. —Manuscript in an Amulet, p. 61. Geometrical

Theorems, p. 63, p. 71.
Wilkinson T. E. — Sale of Spirituous Liquors, p. 68.
Williamson Prof. W. C, F.E.S.— New Eotifer, p. 210.

JReports of the Council^ April 30, 1861, p. 105 ; April 29, 1862, p. 263.

PRINTED BY THOS, BOWLER AND SONS, ST. ANN'S SQUARE,