Memoirs of the Literary and Philosophical Society of Manchester

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“MEMOIRS

OF THE

LITERARY

‘AND

- PHILOSOPHICAL SOCIETY

OF

SMlanchester,
SECOND SERIES.

VOLUME II.

GOL LL DLL

PRINTED FOR
R. BICKERSTAFF, ESSEX-STREET, STRAND, LONDON,
by

RUSSELL AND ALLEN, MANCHESTER,

1813.

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A LIST OF THE MEMBERS.

OP LL LD PE L

* Mr. Thomas Henry, F. R. S.

&e. &e. °

* Edward Holme, M. D.
* William Henry, M. D. F.R..S. &c.

* Mr. John Dalton.
. * Mr, Peter Ewart.

* Rey. William Johns.
* Mr. J. A. Ransome.

President.

Vice-Presidents.

t Secretaries.

* Nathaniel Heywood, Esq. Treasurer.
* Mr. William Cririe, Librarian.

Mr. James Ainsworth.
Mr. Thomas Ainsworth.
Mr. Thomas Atkinson.
Mr. Thomas Barrett.
Mr. Charles Barrett.

’ Mr. H. H. Birley.

* Mr. B. H. Bright.

Mr. William Brigham, jun.

Mr. Laurence Buchan.
Mr. William Bayliff.

Mr. John Chippendale.

* Mr. Peter Clare.

Mr. John Close.

Mr. William Clowes.
Mr. John Craig.

Mr. James Darbishire, jun.
Mr. Jacob Davis.

Mr. John Ditchfeld, jun.
Mr. Benjamin Dockray.
Mr. David Dockray.

Mr. John Douglas.

Mr. George Duckworth.

Mr. Joseph Eveleigh.

* Mr. William Finch.

Mr. Samuel Greg.

Rev. John Grundy.

Henry Hardie, M. D.

Mr. William Harrison.

Mr. T. F. Hatfield.
“Mr. B, A. Heywood.

Mr. Samuel Hibbert, jun.

Mr. Robert Hibbert.

Mr. Thomas Holland.

Mr. Thomas Houghton.

Mr. David Holt.

Mr. Thomas Hoyle, jun.

John, Hull, M. D.

Mr. John Hyde.

Mr. John Jackson.

Mr. Charles Jackson.

Mr. Roger Jackson.

* Thomas Jarrold, M. D.

Mr, Samuel Kay.

Mr, John Kennedys

iv. LIST OF MEMBERS.

Mr. G. A. Lee. Mr. Thomas Robinson.

Mr. James MConnell. Mr. T. H. Robinson.

Mr. Charles M‘Niven. Mr. John Rothwell. .

Mr. Samuel Marsland. Mr. Richard Rushforth.

Mr. Joseph Mayer. Mr. Damien Runten.

Mr. Samuel Moxon. Mr. John Sharpe.

Mr. Benjamin Naylor. Mr. John Taylor.

George Phillips, Esq. M. P. Mr. Arthur Bourne White.
Mr. Robert Philips. William Winstanley, M. D.
Mr. Robert Peel. Mr. Gilbert Winter.

* Rev. J. G. Robberds. * Mr. George William Wood.
N. B. Those marked (*) are of the Committee of Papers.

PLL LL

CORRESPONDING MEMBERS.

Mr. Acton, Ipswich.

Dr. Astbury, Newcastle-under-Line.

Lieutenant James Bayley, of the Honourable East Tudia
Company’s service.

William Butterworth Bayley, Esq. Calcutta.

George Bew, M. D. Kendal.

Dewhurst Bilsborrow, M. D. Derby.

Mr. John Burns, Glasgow.

D. Campbell, M. D. Lancaster.

Mr. John Dawson, Sedbergh.

Mr. James Denholm, Glasgow.

Henry Dewar, M. D. Lassoddie, Fifeshire.

Mr. Thomas Falconer, A. M. C.C, C, Oxford.

Mr. Fontana, Surgeon, Member of the Asiatic Society.

George Smith Gibbes, M. D, Bath.

A. B. Granyille, M. D.

Mr. John Gough, Kendal.

James Greene, Esq.

LIST OF MEMBERS. Vs

Mr. Edward Greene.

Rev. Johnson Grant, A. B.

J. Hamilton, M. D. Ipswich.

Rev. G. J. Hamilton.

Henry Holland, M. D.

John Haworth, M. D.

Thomas Hull, M. D. Beverley.

John Johnstone, M. D.

William Lambe, M. D.

Mr. R. Lyall, Paisley.

Mr. Wilson Lowry.

John Lyon, M. D. Liverpool.

James Mease, M. D. Philadelphia.

Edward Percival, M. D. Dublin.

P. Roget, M. D. London.

Alexander N. Scherer, M. D. Weimar,

Mr. Helenus Scott, Bombay. +

Richard Taunton, M. D.

Charles Taylor, M. D. Secretary to the Society for the
Encouragement of Arts, &c.

Mr. James Thomson.

John Thomson, M. D. Halifax.

Rev. Robert Uvedale, A. B. Trinity College, aintiitiaes

Dr. Waterhouse, Cambridge, New England.

Mr. Thomas Willis, London.

Mr. C. H, Wilkinson, London.

Mr. Kinder Wood, Oldham.

POL LDL

HONORARY MEMBERS.

John Aikin, M. D.

Sir Joseph Banks, Bart. P. R. S. &zc. &c.
M. Berthollet, Paris.
Sir Richard Clayton, Bart,

Vie LIST OF MEMBERS.

Edwood Chorley, M. D.

Sir Humphry Davy, LL. D. F. R.S. &c.

Edward Hussey Delaval, Esq. F. B.S. &e.

Lt. Colonel Drinkwater.

John Jamieson, D. D.

Edward Jenner, M.D. F.R.S.

Rey. William Magee, B. D. Fellow of Trinity College,
Dublin.

William Falconer, M. D. F. R. S.

Rev. Thomas Gisborne, A. M.

Charles Hatchett, Esq. F. R. S.

John Haygarth, M. B. F. R.S.

Mr. William Hey, F. R. S.

Mr. George Hibbert. ,

John Coakley Lettsom, M. D. F. R. S. &c.

Mr. Patrick Mac Morland,

Thomas Marsham, Esq.

Sir George Onesiphorus Paul, Bart.

George Pearson, M. D. F. R.S.

Rev. John Radcliffe, A. M. Brazen-nose-College, Oxford.

William Roscoe, Esq.

Benjamin Count Rumford.

Benjamin Rush, M. D. &c. Philadelphia.

James Edward Smith, M. D. F. R. S. &e.

Smithson Tennant, Esq. F, R.S. &e.

Rev. William Turner, Newcastle-upon-Tyne.

Professor A, G. Werner, Freyberg.

William Wright, M. D. F. R. S, &e.

Arthur Young, Esq. F. R. S.

CONTENTS.

PLP LD PL

An Account of some Experiments to ascertain whe-
ther the Force of Steam be in proportion to the genera-
ting heat. By John Sharpe, Esq. sevsssessssvesvecvereoee

On Respiration and Animal Heat. By John

Dalton.escssccccreccccccccvescccvvcccsssesoosessssoseseentseese

An Inquiry into the Principles by which the import-
ance of Foreign Commerce ought to be estimated. By
Menry Dewar, Df. D.....--.-- pebeovons vaved@berepancesieede

Remarks on the Use and Origin of Figurative Lan-
guage. By the Rev. William Johns, «.sssesseee vrreevers

On the Measure of Moving Force. By Mr. Peter

Ewart. cover eceesscsesceeescepesesceseseeseesessrsenereeenserees

Account of a Remarkable effect produced by a
Stroke of Lightning ; ina Letter addressed to Thomas
Henry, Esg. F.R.S. &c. from Matthew Nicholson,
Esq., with Remarks on the same. By Mr, Henry, «+

Theorems had Problems intended to elucidate the
Mechanical principle called Vis Viva. By Mr. Jobn

Gough...orsecscereseresversenccsvevessogeravsnescsesepasesceres

On the Theories of the Excitement of Galvanic
Electricity. By William Henry, M.D. F. B.S. &e,

Page

15

45

74:

105

259

270

293

Vill. CONTENTS.

Page
Cursory Remarks on the Mineral Substance, called

tn Derbyshire, Rotten-Stone. By William Martin,
F. L. &. Oeianwwas cdwelhn We ska moet sea ve Radetdadaucachsnassnes 313

On National Character. By Thomas Jarrold,

mM. D. SOPOT H EEE REET OOEEES ESE HET OH ONE HEHE TERETE OEOSEE SEES SEED 328

Observations on the Ebbing and Flowing Well at
Giggleswick in the West-riding of Yorkshire; with a
theory of Rectprocatimg Fountains. By Mr. Jobn
Gough. Ina Letter to Drs Holmesecesecerrsseecsereerees 354

Description of an Eudiometer, and of other Appa-
raius employed in Experiments on the Gases. By
W. Henry, M. D. F, R. S. RECuaeseescnnsenvecvuswasudens’ 384

4 Memoir on the Uric Acid. By W. Henry,
M, D. B. R. S; &e. SOTSOT SCRE SEH EHH TFETEM SHER ORETHEEH EEE EEE 391

A Demonstration of Lawson’s Geometrical Theorems. -
By the late Rev. Charles Wildbore. Communicated by
Mr. Mabbott to Mr. Ewart, and by him to the Society. 414

Remarks on the Summer Birds of Passage, and on
Migration in general. By Mr. John Gough. Com-
municated by Dr. Holme. csscsssescescceseecevececesessers 403

ERRATA. :

Page 28 line 24, for 30, read .30.
76 line 18, for columen, read presidium.
92 line 22, for verb, substantive, read verb-substantive.
101 line 2, at theend, insert “of Language.”
123 line 19, for “‘ direction AB,” read “ direction AD.”
213 line 9, read “If D bea comparatively soft non-elastic body.”
For other Errata between pages 116 and 215, see page 258.

1

MEMOIRS ~

of the

LITERARY & PHILOSOPHICAL SOCIETY
of

SManchester.
nv ARRARARR
AN
ACCOUNT of sone EXPERIMENTS,

TO ASCERTAIN WHETHER THE FORCE OF STEAM BE
IN PROPORTION TO THE GENERATING HEAT.

By JOHN SHARPE, Esq.
(Read February 7, 1806.) '

—=ALQTITS

I BEG leave to submit to the Society, an
account of some experiments for ascertaining
the quantity of latent heat contained in steam
at different temperatures. Having lately had
an opportunity of observing some steam-en-
gines worked by steam of a high temperature,
and being told that they were attended with a
saving of fuel, I was led to inquire the cause.
There are some mechanical contrivances in
the construction of the engines that lessen the
consumption of fuel; but it seemed a question
worth investigation, whether there was any
A

2 Experiments on the

specific difference between the constitution of
steam at a high temperature, and that pro-
duced at the common boiling point. Every
body knows, that water, in the open air, boils
at 212 degrees of Fahrenheit; but in a Papin’s
digester, or closed vessel, or under the pres-
sure of a column of mercury, it may be heated
very considerably above 212° without boiling
at all. In the exhausted receiver of an air-
pump it boils much below 212°, the boiling
point in this and all the other cases depending
- upon the superincumbent pressure.—So that
water always begins to boil in the open air
when the elasticity or force of the steam be-
comes equal, or a little more than equal, to
the pressure of the atmosphere. The force of
steam, therefore, of the temperature of 212°,
is equal to the weight of the atmosphere, or
to a column of niercury of about 30 inches
high. But this force is very rapidly increased
by increasing the temperature ;—so that if
steam, in contact with water, is heated to
about 40° above the boiling pomt, the force
is doubled, and it becomes capable of sustain-
ing a column of mercury of 60 inches: and
if the temperature is raised about 55° still
higher, or to 307°, the steam is then equal to
four atmospheres, or 120 inches of mercury.
I make these statements from the table that

wrtyy =

Force of Steam. 3

accompanies Mr. Dalton’s interesting Paper
on this subject, in the 5th vol. of the Society’s
Memoirs!” In a valuable Essay on the article
“ Steam,” published in the 17th vol. of the
Encyclopedia Brit. and in the account of
Mr. Betancourt’s experiments on the same
subject, the force of steam over water is stated
to increase in a still greater ratio with respect
to the temperature; but I rely on Mr. Dalton’s
table, which seems to have been constructed
with great accuracy. When I first began to
consider this subject, the question that natur-
ally occurred to me, was, How does this com-
paratively small addition of temperature pro-
duce so remarkable an increase of force? I
could find no satisfactory answer to this ques-
tion in the papers that had been published ; nor
did the information I obtained from such of my
friends, as were most conversant with the sub-
ject, supply the defect. I was told, that Mr.
Watt had made experiments; but could not
learn the nature of them, or the precise results.
It was supposed, however, that, as steam over
water increased in temperature, it continued
to combine with a greater quantity of heat
than what was indicated by the mere increase
of temperature ;—so that steam of double the
force of the atmosphere probably contained
twice as much heat, in the same bulk, as
A 2

-4 Experiments on. the

steam at fhe common boiling temperature. I
take for granted it will be remembexed, that
the steam which rises from boiling water ine
dicates the same degree of heat to the ther-
mometer as the water does, viz. 212°; but
that it, in fact, contains about 940° of latent
heat, not appreciable by the thermometer ;—-
so, that if steam, which is double the force of
the atmosphere, had combined with a propox-
tionate quantity of heat, it must necessarily
contain. upwards of 1800° of heat more than
what. would be indicated by the thermometer,
at least, if we consider the latter steam of
the same density as the former.

I proceed to an explanation of the experi-
ments.

First Class of Experimenis.

IT procured a small oblong cast-iron boiler,
capable of holding about two gallons of water,
into which was fitted a thermometer, gradu-
ated considerably above the boiling pot;
also two stop cocks, with joints and screws to
connect with different sorts of apparatus.—
Underneath was fixed a trough to contain
spirits of wine, the lid perforated. with two
rows, of six holes each, for the cotton wicks,
Being desirous of keeping the heat as equal

Force of Steam. 5

as possible, I fixed upon spirits of wine, because
the wicks want no snufling. There wasasmall
pipe communicating with the trough, for re-
gulating the supply of spirit of wine. I found —
it howevera very difficult matter, from various
causes, to keep the heat constantly equal.

_ My first object was to try if the water
would heat through the different degrees of
temperature in equal times. For this purpose
I made several experiments with the boiler,
sometimes half and sometimes two-thirds fulk
of water, and all the wicks lighted. In order
to saye time, I generally put hot water into
the boiler, and let it stand till the iron was —
heated equally throughout, and then began
the experiment, the water usually standing at
120° or upwards. It is unnecessary to go
through the detail of these experiments; but
the result is, that water heats through the
several degrees of ihe thermometer nearly in
equal times; and when in a closed vessel, the
same rule holds good, as well above the boil-
“ing point as below it. It may be proper to
state the result of one experiment more parti-
cularly :—the water was heated from 140° to
280°. in the space of 45 minutes and 31 se-
conds, all the 12 lights being kept burning,
and the time in rising through every 10° was
noted. It rose the first 10° in 3 minutes and

6 Experiments on the

50 seconds, and the last 10° in 3 minutes and
52 seconds, which was the longest period.—’
The shortest time of passing through 10° was
2 minutes and 37 seconds. In most of the
experiments, however, a little more time
elapsed, as the temperature increased; but
this seems to be accounted for by the greater
rapidity with which the boiler cools, as its
temperature increases beyond that of the sur-
rounding atmosphere, and perhaps also by the
lesser rapidity with which it heats, as the
temperature approaches nearer to that of the
lamps. I conceive however that it may be taken
as a reasonable approximation to the truth that,
by an equal and uniform application of the
same quantity of heat, water will rise through
the several degrees of the thermometer in
equal times, and that to a temperature consi-
derably above the boiling point, if confined in
a close vessel. It appears, from the above
experiments, that the temperature rises equally
with the expenditure of the fuel, or nearly so,
and it was before shewn, that the force of the
steam increases in a much more rapid degree ;
but it is to be remembered, that the process is
here carried on in a close vessel, and no steam
escapes during the experiment, which I shall.
advert to more particularly by and by.

Force of Steam.

~—)}

Second Class of Experiments.

I filled the refrigeratory of a still, contain-
ing exactly 300 ounce measures, with water,
and noted the temperature. To the worm I
fixed a flexible metal tube, which was screwed
at the other end to one of the stop cocks of
the boiler. I sent over steam from the boiler
at different degrees of temperature, usually
fillimg a6 ounce measure with the distilled
water, and then trying the temperature of the
water im the refrigeratory again, I observed
how many degrees the 6 ounces of steam had
raised the 300 ounces of water. 'The general
result of these experiments is, that steam sent
over at the common boiling temperature, or
within a few degrees above it, gives out as
much latent heat as steam sent over at a much
higher temperature, and most probably at any
higher temperature whatever. The following
is a more particular statement of the two last
experiments I made for this purpose.

The refrigeratory was filled with 300 ounce
measures of water at 55°. The thermometer
in the boiler was then standing at 276°, and
the stop cock being turned as little as possible,
the steam was let into the worm; when 7
ounce measures of condensed water had come

8 Experiments on the

over, the cock was stopped, and the tempera-
ture of the water in the refrigeratory accu-
rately noted, and found to be 81°, being raised
26° by the 7 ounces of steam. During the
experiment, the thermometer in the boiler felt
from 276° to 274°, making the medium 275°
for the sensible heat of the steam which passed
through the worm. Had this steam contained
no latent heat, it would have raised the tem-
perature of the water in the refrigeratory only
5° anda small fraction; but it did, in fact,
raise it 26°, and the result in figures gives
920° for the latent heat of the steam. If the
latent heat of steam above the boiling point in-
creased in proportion to its elasticity or force,
the above experiment ought to have indi-
cated considerably more than 2000° latent
heat ; but it will necessarily be remarked, that
the quantity djd not amount to the 940° con-
tained in steam at the common boiling tem-
perature, according to the authority of Mr.
Watt. This difference, however, is easily ac-
counted for by a sinall portion of heat, neces-
sarily given out during the experiment from
the metal tube which conducted the steam
from the boiler into the worm, and another
small portion from the surface of the water in
the refrigeratory. In order to remove any doubt
im this respect, I repeated the experiment in
. i

Force of Steam. 9

the same apparatus with the water reduced to
the common boiling point. Having renewed
the water in the refrigeratory, and ascertained
its temperature at 53°, the thermometer in
the boiler standing at 212°, the steam was let
into the worm till 6 ounces had come over.
During the experiment, the thermometer in
the boiler fluctuated between 212° and 215°.
I estimated the medium, taking the whole
experiment together, at 213°. When the 6
ounces of condensed water had come over, the
temperature of the refrigeratory was carefully _
ascertained to be 74°, having been raised
21° by 6 ounces of steam at 213°. Making
the calculation as before, the result gives 910°
of latent heat, leaving a difference of 10° in
the latent heat between this and the former
experiment, which is as near as it is possible
to come in experiments of this description,
and with this sort of apparatus. Some of- the
former experiments had given the difference
in favour of steam, at the common boiling
temperature. I conceive, therefore, it may
be safely concluded, that there is as much
latent heat in a given weight of steam, raised ©
from common boiling water, as in that of a
much higher temperature; and that, when
once steam is saturated with the specific quan-
tity of heat necessary to its formation, all
B

10 Experiments on the

further accession of heat is appreciable by the
thermometer.

In attending to the progress of the preced-
ing experiments, I observed that when the
steam was let off from the boiler, at a high
temperature, it passed into the worm with
great rapidity, and more water was condensed
in the same space of time than when the
steam was sent over at the common boiling
temperature. Also, when the steam at high
temperature was suffered to pass freely through
the stop-cock, the thermometer in the boiler
began to sink with considerable rapidity.—
From these circumstances, it is evident, that
the steam of high temperatures is more dense
than that which proceeds from common boil-
ing water; that a greater quantity of it is
compressed into a less space ; and the increase
of force, occasioned by the increase of tem-
perature, no doubt proceeds chiefly, if not
wholly, from this increased density of the
steam, by new generation, and not at. all
from any additional combination of the pre-
viously existing steam with latent heat. It is
a well-known law, with respect to atmospheric
air, that doubling the pressure, doubles the
density ; but whether this law holds good with
respect to steam (so that double the quantity
compressed into the same space is requisite to

Force of Steam. 1

produce double the effect) I have not yet
made any direct experiment to determine.*
In stating the latent heat of steam to be
uniformly the same at all temperatures, it must
be understood, with reference to the quantity
of water converted from the fluid to the gase-
ous state, and not to the quantity of space
occupied by the steam, as the actual quantity
of heat increases progressively with the den-
sity. In order to obtain steam of any given
density, a specific temperature corresponding
with that density is also necessary ; aud with-
out that temperature the steam cannot exist.
If it be required to produce steam equal to
two atmospheres, that can only be done by
raising it from water at the temperature of
252°, or thereabouts; and if an additional
weight or pressure is put upon the steam so
raised, or if the temperature is lowered a few
degrees, and the pressure of two atmospheres
continues, in either case it will be immediately
condensed into water again, although the
temperature still continues several degrees
above the common boiling point. The fol-
lowing experiment will shew this:—Take a
barometer tube, hermetically sealed at one

* This seems to have been proved by Gay Lussac.
An. de Chimie, Vol. 43. 1802. or Nicholson’s Journal,
Vol. 3. p. 267.

B 2

12 _ Experiments on the

end, bend up three or four inches of the sealed
end in the form of a syphon, introduce a drop
or two of water into the tube, and upon that,
a few inches ef mercury; bring the mercury
close up to the sealed end of the tube, so as to
exclude all the air; and after letting the tube
rest a little, a small portion of the water will
ascend to the top of the mercury at the sealed
end; let the mercury in the open leg be a few
inches above the level of the closed end. If this
tube is put into boiling water, and continued
there ever so long, the small drop of water
above the mercury will never expand into
steam, because it has not only te act against
the weight of the atmosphere, but also the co-
lumn of mercury ; and the temperature of com-
mon boiling water is notsufficient to constitute
steam of an adequate force for that purpose ;
but if the tube is put into heated mercury,
and kept there till the temperature rises to
the proper point for overcoming the pressure,
(for which see Mr. Dalton’s table) the water
will then be converted inte steam, and occupy
a certain portion ef the tube, lifting up the
column of mercury. If, before the tempera-
ture is further advanced, more mercury 1s
poured into the tube, so as to increase the
pressure of the column a few inches, the steam
will be immediately condensed into water

Force of Steam. 13

again, and will remain so until the tempera-
ture is still further increased to the necessary
point specified in the table.

JOHN SHARPE,
January, 1806. ‘

I have subjoined the following Note, received from Mr.
Darron, which, I apprehend, will require no apology.
Oct. 1810:

There are but three opinions, which can be entertained as
at all probable on the subject of the force of steam, in con-
tact with water, in high temperatures. Ist. Steam, over
water of 252°, may be of the same density as that over watex
of 212°, and the great increase of force may arise from the
increase of temperature solely. In this case, the application
of steam for mechanical purposes would be much more econo-
mical, in regard to expenditure of fuel, at a high temperature.
2d. Steam, over water of 252°, may be of the same density
as that over water of 212°, and the great increase of force
may arise from its having combined with double the quantity
of latent heat (as it has been called.) In this case, there
would be no advantage in using high temperatures, except
that less water would be requisite ; and the precediug ex-
periments on distillation would have abundantly manifested
the truth of the supposition, by giving a much greater in-
crease of temperature in the water condensing the steam of
high temperature than in that condensing the lower. The
experiments, therefore, shew the fallacy: of this supposition.
3d. Steam, over water of 252°, may be of double density,
compared with that over water of 212°,"and the increase of

4

14 Experiments on the Force of Steam.

force may arise from the increase of density: in this case,
it would be indifferent as to the expenditure of fuel at
what temperature steam was used, because the quantity of
latent heat would be as the force, or as the density : and in
the distillation of water, the increase of temperature in the
receiver, arising from the latent heat, would be as the weight
of water distilled, without regard to the temperature of the
steam.

Now, though the preceding experiments do not absolutely
decide between the first and third supposition, all analogy
and experience are in favour of the latter. Steam on this
principle will agree in expansion with all other elastic fluids,
The experiments of Gay Lussac, as well as my own, on the
steam of ether, water, &c. are conformable to it; and the
expansion of vapoury air and dry air by heat are found to
be exactly the same, provided the vapoury air be com-
pletely cut off from the acquisition of any more vapour,

The result of one of the experiments deserves particular
notice; I mean that in which it was found the temperature
of the water in the boiler increased in direct proportion to
the time of heating. One would certainly have expected
the water to heat most quickly at first, and more slowly as
the temperature advanced. Ido not doubt the accuracy of
the experiment; but I explain it by supposing the common
thermometric scale inaccurate; the degrees of the mercu-
rial scale are progressively too small as they ascend. See
my New System of Chemistry, page 14.

ON

RESPIRATION

AND

ANIMAL HEAT.

By JOHN DALTON.

(Read March a1, 1806.)

wwe

Ir is not my design, in the present Essay,
to give a history of early opinions respecting
the uses of Respiration, and the causes of
Animal Heat. I intend to confine my obser-
vations to such authors as have written on
these subjects within the last thirty years; a
period in which so many discoveries respecting
heat and elastic fluids have been made, as to
enable modern physiologists to give a much
more rational account of that important ani-
mal function, Respiration, than their prede-
cessors could do.

Priestley and Scheele discovered that oxygen
was consumed during respiration, or the quan-
tity of oxygenous gas inhaled was greater
than that exhaled. Black and Lavoisier found
that a considerable portion of the air expired

16 On Respiration and Animal Heat.

consisted of carbonic acid gas; this fact, when
joined to the former, led to the discovery of
the true cause of animal heat, or that excess
of temperature which warm-blooded animals
possess, above the temperature of the sur-
rounding atmosphere.

The striking analogy which the effects of
respiration have to those of the combustion of
charcoal, could not long escape the observa-
tion of Lavoisier and others. In both cases,
charcoal, in a fixed or melastic state, combines
with oxygen, and produces carbonic acid gas.
In combustion, a great quantity of heat is
liberated, so as to raise the temperature of
surroundmg bodies to an intense degree; in
respiration, however, little or no increase of
temperature is observed, if we except the air
itself, which is inspired cold and expired
warm. This want of complete resemblance
in the chemical effects of combustion and re-
spiration, for a time, obstructed the progress
of this branch of physiology. It was perceived
that the quantity of carbonic acid produced
by respiration, had it been obtained from the
combustion of charcoal, would have evolved
heat sufficient to preserve the temperature of
the body; but the heat so evolved, if applied
to the lungs of an animal, must be injurious,
if not fatal. The body of a living animal is

On Respiration and Animal Heat. 17

subject to a continual expenditure of heat
from the action of the surrounding atmo-
sphere; it must therefore have a continual
supply; an adequate supply appears to be
provided by the continual combustion of ihe
charcoal of the blood in the lungs; but how
is so large a quantity of heat applied to so
delicate a viscus as the lung's, without injuring
it, and even without raising its temperature ? ~

It is to Dr. Crawford we are indebted for
the complete solution of this difficult ques-
tion; his admirable work on animal heat and
combustion will be a lasting monument of his
‘superiority to all his cotemporaries in this
walk of science.

The essential characteristics of Dr. Craw-
ford’s theory of animal heat are two; namely,

Ist. That the specific heat of carbonic
acid gas is less than that of oxygenous gas
and of atmospheric air.

2d. That the specific heat of blood drawn
from an artery, is greater than the cote
heat of that drawn from a vein.

The former of these facts, indeed, might
be inferred a priori from Lavoisier’s experi-
ments on the combustion of charcoal; but it
. was first proved experimentally by Dr. Craw-

ford. The latter was, for aught that appears,
c

18 On Respiration and Animal Heat.

never so much as conjectured by any one prior
to him.

According to this theory, the acquisitior
and distribution of animal heat is obvious =
In respiration, heat is abstracted from the at-
mospheric air, or more properly, from the
oxygenous part of it inspired, in consequence
of the chemical union of elements; this heat
is imparted to the blood without materially
affecting its temperature, and is, during the
course of circulation, given out to the rest of
the body, im proportion as the blood changes
from its arterial to its venous constitution.

Most, if not all, philosophers who have at-
tended to this subject since, have adopted the
two fundamental positions above laid down,
which have never, E believe, been controverted
by any one; and, whilst they continue to be
admitted, it would be in vain to frame any
other theory in order to account for animal
heat.

» Notwithstanding this general agreement as
to the source of animal heat, there are still
various opinions respecting the mode of
those chemical changes that take place in
the air and in the blood in consequence of
respiration. Before we can animadvert upon
these, it will be necessary to premise, that the
air of the atmosphere inspired consists of

On Respiration and Animal Heal. 1%

azotic gas, oxygenous gas, aqueous vapour,
and a very small quantity, almost inappreci-
able, of carbonic acid gas; that the air ez-
ptred consists of azotic gas nearly the same as
before, oxygenous gas diminished in quan-
tity; and carbonic acid and aqueous vapour,
both considerably increased in quantity; the
temperature ef the expired ‘air, as is well
known, is in most instances much superior to
that of the inspired air.

Lavoisier and Crawford, followed by many
respectable writers, seem to maintain, that the
basis of carburetted hydrogen gas transpires
through the thin membranes of the lungs, from
the blood, where, meeting with the oxygenous
gas of the atmosphere, a chemical union of
the carbone and hydrogen with the oxygen
takes place, forming carbonic acid and aque-
ous vapour; at the same moment, part of the
heat of the oxygenous gas is given out, which,
according to Crawford, enters the blood of
increased capacity for heat, and consequently
does not materially increase its temperature.
This heat is again given out during the circu-
lation, as has been observed, in order to sup-
ply the waste from the body.

In order to establish this explanation, it is
necessary to shew, that the oxygen disappear-
ing is just sufficient to form the carbonic acid

c 2

20 On Respiration and Animal Heat.

and the aqueous’ vapour. Upon a careful —
examination of the facts, however, the results
do not form a true equation; the quantity of
aqueous vapour exhaled is undoubtedly greater
than can be accounted for as above; the ex-
cess of vapour is\supplied, we may suppose,
by the natural exudation of moisture through
the thin membranes of the lungs.

In the Annales de Chimie for 1791, about
three years after the 2d Edit. of Dr. Craw-
ford’s book, we ‘find a memoir by Hassen-
fratz on the subject of animal heat.—In the
course of the memoir, M. de la Grange is
introduced as objecting to Crawford’s theory,
because it supposes all the heat to be given
out in the lungs, which, he thinks, would be
in danger of consuming them; he finds it ex-
pedient, therefore, to invent another theory,
as he conceives, in which the heat may be
gradually given out, during the course of the
circulation, to all the parts of the body.—It
is scarcely possible for any one, who under-
stands the doctrine of Crawford, to read the
observations of La Grange, and his commen-
tator, Hassenfratz, without smiling at their
palpable ignorance of the doctrine under
their review. The distinguishing feature of
Crawford’s theory is, that of the greater capa-
city of arterial blood for heat, than of venous

On Respiration and Animal Heat. 21

blood, by which the large quantity of heat
can be received ito the lungs without at all
raising their temperature. This object is pre-
cisely what La Grange and Hassenfratz have
had in view by their new theory; notwith-
standing their pretended objections, they, in
reality, adopt the very same principles which
Crawford. had the merit to discover.
_ The change they propose to make is this;
the oxygen inspired, instead of entering im-
mediately into combination with the carbone
and hydrogen, as Crawford supposes, enters
first of all into the blood, without depositing
mauch of its heat; during the circulation, this
oxygen gradually combines with the carbone
and hydrogen, forming carbonic acid and water,
and giving out heat in consequence, till the
blood, on its return again to.the lungs, throws
out the carbonic acid and water, and receives
a fresh supply of oxygen. Every one must _
see, that these positions are necessarily depen-
dent on the two essential characters of Craw-
ford’s theory; namely, that of carbonic acid
having a less capacity for heat than oxygenous
gas, and that of arterial blood having a greater
capacity for heat than venous blood.

instead, therefore, of pulling down the
mgenious edifice erected by Crawford, and
building another in its place, as they imagine;

22 On Respiration and Animal Heat.

the whole change effected consistsin removing
the cornice, and substituting another in its
place. We must now enquire in which state
the edifice presents the most symmetrical ap-
pearance.
According to La Grange and Hassenfratz,
oxygen enters the blood in the lungs. How
does it enter? By mechanical or chemical
means? Not by mechanical; for then azote
would enter four times more copiously, owing
to its greater density. It must enter by che-
mical means.—How does the blood attract
oxygen through the membrane of sensible
thickness which separates them? Granting
the fact, how does the elastic fluid enter into
combination with a liquid, without depositing
its heat in the lungs, a circumstance so much
to be guarded against on this hypothesis ?—If
the heat be given out to the blood in the
lungs, there will be none left to be extricated
during the circulation in order to form carbo-
nic acid. Passing by all those difficulties, how
is the carbonic acid to escape through the
membranes of the lungs ito the air cells?
Not by chemical means, for there is no agent
to attract it; mechanical means nrust be used ;

simple pores will not effect the business, be-

cause air might enter as well as escape; there
must then be air pores with valves opening

On Respiration and Animal Heat. 23

outwards so as to permit the escape, but
bar the entrance of any gas. These pores, I
am afraid, would be so constantly filled with
liquid, that it would obstruct, if not altogether
destroy, their proper function.

The whole scheme is evidently attended
with insuperable difficulties. But it will be
urged, that the blood has a known affinity for
oxygen; witness the florid colour which it
always assumes in oxygenous gas. True; but
does this prove that oxygen has combined
with the blood, and entered into that liquid,
or does it prove that some particles of the
blood have combined with oxygen, and made
their escape from the surface of the liquid,
which assumes a vermullion hue after their de-
parture? I apprehend this question has not
yet been determined: Mr. Davy informs us
(Researches, page 381,) that venous blood,
agitated with atmospheric air and oxygenous
gas, assumed the vermillion colour at its sur-
face ; “but no perceptible absorption had taken
place.” —Here then we have a change of co-
lour without sensible absorption when the
blood is in contact with the gas; is it pro-
bable then that an absorption will take place
when the blood is separated from the gas by
a membrane of considerable thickness ?

24 On Respiration and Animal Heat.

It is somewhat remarkable, that this sup-
posed amendment of Crawford’s theory should
have been so generally adopted. The authors
of it evidently did not understand the prin-
ciples they were attempting to refute; their
objections to them may be applied with equal
force against their own principles; they ob-
tain the very same end by means much less
probable : yet the physiological writers of this
country have almost universally embraced their
innovation upon the original system. I can-
not ascribe this to any other cause than that
unwarrantable neglect of cultivating the doc-
trine which instructs us respecting the capa-
cities of various hodies for heat. Having
now given my own views of the present
state of the theory of Respiration and Animal
Heat, I shall proceed to make a few observa-
tions upon the facts and experience relative
to this subject, since the time of Crawford.
~ Davy, Henderson and Pfaff have almost
established the fact, that a small portion of
azotic gas disappears by respiration; this es-
caped the notice of Lavoisier and Crawford,
who seemed to have concluded, that oxygen-
ous gas was the only part of the atmosphere
changed by breathing. Whatever other use
may be-attached to the fixation of azote in

On Respiration and Animal Heat. 285

the system, one is evident, namely, its con«
tributing to the support of temperature in the
same way as oxygen does,

Since the late improvements in Eudiometry,
attempts have been made to determine with
greater precision, the changes effected by re«
spiration:in the elastic fluids. It is obviously
of im»vortance to learn the precise quantities of
oxygenous gas inspired and expired, together
_ with the quantities of carbonic acid, and aque-
eus vapour expelled from the lungs. With
respect to oxygen and carbonic acid, my own
experience concurs with that of the generality
who have carefully investigated the subject ;
more in bulk of oxygenous gas is consumed
than that of carbonic acid generated; the
former appears to be about 5 per cent. upon
all the gas inspired; the latter about 4 per
cent. upon all the gas expired. It is very
desirable, but at the same time very difficult,
to determine the ratio more exactly. It ought
to be observed too, that the quantities above
specified are the medium for each one natural
expiration; if the gas at the first moment of
expiration be caught, it will be feund to con-
tain about 3 per cent. acid, and to have lost 4
of oxygen ; but if the last portion be examined,
it usually contains 5 of acid, and wants 6 or
more of oxygen; by taking the last gas of a

D

26 On Respiration and Animal Heat.

forced expiration, I find it to contain 6 per
cent. of acid, and to have lost nearly 8 per
cent of oxygen.

By frequent trials, I find the quantity of
ar taken in at each natural inspiration by
me, is about a pint, wine measure, or nearly
30 cubic inches. This quantity is consider-
ably less than some authors state it, and more
than others. It is probable, that different
subjects exhibit a difference in this respect ;
but it can scarcely be so great as is represent-
ed. I find, too, that in a state of quiescence,
I take 20 inspirations in a minute. This
gives 500 cubic feet of atmosphericair inspired
in a day, =46,5lbs. troy, of which 105 is
oxygenous gas, and 25 of this enters into new
combinations. This will be found to weigh
45120 grains=2,6lbs. troy.—By a full forced
inspiration, my lungs can contain about 7

pints or 200 cubic inches of air, which can be
expelled again by a forced expiration; the
quantity still remaining in the lungs, after
such expiration, is not easily to be determined ;
it cannot however be much, and it is of little
consequence to know it exactly. It appears
then, that after an ordinary expiration, my
lungs still contain 3 pints of air; and that
after an ordinary inspiration there is still reom
left for 3 pints more.

On Respiration and Animal Heat. 27

The quantity of carbonic acid gas expired
ina day may be calculated thus: the whole
quantity of gases expired in a day being as
stated above =46,5lbs. troy, and 4 per cent.
or +, of this in bulk, being carbonic acid,
we have +£:5=1,86lbs.; but carbonic acid
being 13 times the weight of an equal bulk
of common air, we have 2,8 lbs. troy for the
weight of carbonic acid gas expired in a day.

There is a considerable diversity in different
authors, and even in the same author at dif-
ferent times, respecting the quantity of car-
bonic acid, obtained by respiration. Lavoi
sier, in his first memoir in 1789, and Davy,
nearly coincide with the results I have given
above from my own experience. Afterwards,
it seems, that Lavoisier made the quantity
much less, not one half of the above. I can-
not conceive what could induce him to rate
it solow. On the other hand, Dr. Menzies —
estimates the quantity nearly 4lbs. troy;
which, I think, must be above the medium
for men in general. .

The quantity of aqueous vapour exhaled
from the lungs in a day has been variously
estimated ; and a greater uncertainty respect-
ing it subsists at this moment, than respecting
any other product of respiration. Dr. Hales,
by experiment, found that 20 oz. per day were

D2

28 On Respiration and Animal Heat.

expired ; Dr. Menzies found 6 oz.; Mr. Aber-
nethy, 90z.. Lavoisier, partly by experiment,
and partly by theory, in one of his memoirs,
estimates the water exhaled from the lungs
daily at 28 0z.; but im some instances, he
estimates more, in others, less.

This diversity of results amongst the earlier
physiologists was not to be wondered at; but
it is somewhat surprizing, that after the re-
cent discoveries on the nature of steam or
aqueous vapour, any material uncertainty
should still remain respecting the quantity of
water exhaled from the lungs in a given time.
Nothing is more obvious and easy than to eal-
culate, @ priori, the precise quantity of aque-
ous vapour in a given quantity of air expelled
from the lungs. At the temperature of 98°,
the utmost force of aqueous vapour is nearly
equal to 14 inches of mercury, as appears from
Tables of various authors.* The force of
aqueous vapour existing in the atmosphere is
various; but the medium quantity in this cli-
mate may be estimated at 30 of an inch of
mercury, due to the temperature of 44°. (See
Memoirs, vol. 1. second series, page 243.)

New it is certain that the air in the small

* See Memoirs, vol. 5, page 560, Bettancourt’s Exe
periments in-Encycl. Brit. or Hutton’s Math, Dic. &c.,

Ou Respiration and Animal Heat, 29

yamifications of the air-vessels of the lungs,
surrounded by moist membranes, must, in a
moment, be nearly saturated with vapour; we
shall have, therefore, an increase of the force
of vapour from that inspired, .30 to that ex-
pired of 1,74 inches of mercury, being an
increase of 1,44 inch, But by reason of the
less specific gravity of vapour than air, in pro-
portion as 7 to 10, vapour of the above force
will only be equal in weight to air of 1 inch
of force. Hence the weight of aqueous vapour
exhaled at any time must be nearly equal to
3, of the weight of the whole mass of elastic
fluids expired. We have then +£:5 =1,55 lbs.
troy for the weight of aqueous vapour expired
in a day, on the supposition that 464 lbs. of
air, &c. are expired, and that the air so ex-
pired is saturated with vapour, or contains as
much as any gas can do in the temperature.
The real quantity expired can not exceed that
stated above; nor is it probable that it can
fall much short of it.

It is worthy of remark, that Dr. Hales, who
was one of the earliest to investigate the
quantity of water exhaled, should have ap-
proximated nearest to the truth; and that he
should rather have exceeded the truth in con-
sequence of his alkali extracting, not only
the additional vapour acquired in the lungs,

30 On Respiration and Animal Heat.

but a portion of what was previously in the
air. . .

‘We may now deduce one conclusion, which
indeed Lavoisier was fully aware of, that the
oxygen which disappears during respiration,
is not adequate to the formation of the carbo-
nic acid and the water exhaled. It is only 3
of the requisite quantity. He conceives only
a part of the water is formed in the lungs by
the union of oxygen with hydrogen from the
blood, while the rest transpires ready formed,
through the membranes of the blood-vessels,
and is vapourized by the heat.

This indeed is the most difficult part of the
subject. I am inclined to think, that no water
is formed in the lungs by the union of oxygen
with hydrogen; but that the whole quantity
exhaled is an exudation from the blood,
through the membranes of the lungs, which
are thereby constantly kept moist.—It is in-
consistent with the simplicity of the laws of
nature to employ two causes when one is ade-
quate to the effect. There is another way
by which the difficulty may seem to be ob-
viated ; that is, by supposing that all the water
exhaled is formed in the lungs by direct com-
bination of its elements, but that the carbonie
aeid is formed from carbonic oxide, which has
previously one half of the oxygen necessary for

I

On Respiration and Animal Heat. $1

the acid. On thissupposition, the oxygen would
be sufficient for both; and we must consider a
triple compound of carbone, hydrogen, and.
oxygen, to transude through the lungs, which is

' to be converted ito carbonic acid and water.

This explanation would not differ essentially
from that given by Lavoisier and Crawford ;
which supposes that nothing enters the blood
in respiration ; but that the combustible mat-
ter unites with oxygen on the surface of the
lungs. The position seems to require that
whenever carbonic acid is generated in the
lungs, a certain portion of water must be
generated at the same time; I doubt whether
this is consistent with facts. It is well known
a person may, for some time, breathe with
impunity, air containing more aqueous vapour
than that ordinarily expired; yet carbonic
acid continues to be formed nearly as usual.
I have been for 10 minutes in a stove where
the temperature was 140°, and where the
vapour inspired was more abundant than that
expired ; yet the air expired at the conclusion
of that time contained 3 per cent. of carbonic
acid, and had lost 4 per cent. of oxygen,
nearly as usual; and no superabundance of
vapour was perceived on the lungs. Having
made some comparative trials upon air that
has been breathed, and air in which charcoal

82 On Respiration and Animal Heat

has burned out, I am almost convinced that
the changes effected by these processes are
the same; and consequently am inclined to
believe that all the oxygen, which disappears
im the Inng’s, goes to form the carbonic acid
produced, whilst the heat liberated enters the
blood for the purpose of preserving the tem-
perature of the body.

But it will be said, there is more oxygen
spent than is requisite for the carbonic acid ;
what then becomes of the surplus ? In answer
to this I would observe, that the fact stated
in the objection must first be ascertained.—
According to Lavoisier, whose results have
been since corroborated by those of Clement
and Desorme, 28 parts of charcoal, by weight,
unite with 72 of oxygen, to form carbonic
acid; in this case, a given volume of carbonic
acid contains almost exactly the hke volume
of oxygenous gas; whence the objection would
have validity. But Crawford, (page 343)
finds 20 of charcoal unite to 80 of oxygen
to form carbonic acid; in this case, 4 mea-
sures of carbonic acid will be found to con-
tain 4,68 measures of oxygenous gas, or 6
contains 7 nearly; and the proportion will
come very near to that observed as the effect
of respiration; the difference is so small as
may easily be attributed to imaccuracies, even
in the present improved state of Hudiometry.

( 33 )

APPENDIX.

(Read November 16, 1810.)

A

As considerable time has elapsed since this
paper was read (in 1806), and several im-
portant memoirs have been published on sub-«
jects nearly related to the present, the commit-
tee has given me leave to make such addition-
al observations as may be judged expedient.

At the time of writing the preceding me-
moir, I had not seen a judicious collection of
facts and observations on respiration, by Dr.
Bostock, published in 1804. From a careful
comparison of the results of physiologists, at
that period, he draws, amongst others, the
following conclusions:

1. Air loses near 4 per cent. in bulk of
oxygen by being once respired; a man con-
sumes about 2lbs. 8oz. in 24 hours, or 26
cubic feet.

2. The carbonic acid generated by. res-
piration, is 82 for 100 oxygen in volume;
and consequently, from the known constitu-
tion of carbonic acid, it cannot contain all
the oxygen which disappears. The weight

E

es >
34. On Respiration tnd Animal Heat.

of carbonic acid formed in 24 hours is about
3 lbs. which are equal to 22 cubic feet.

3. A quantity of aqueous vapour, the
amount of which is still undetermined, is
emitted from the lung's.

In July, 1806, after. the preceding paper
had been read, [I instituted a series of experi-
ments on respiration, and on the combustion
of charcoal, oil, &c. by the results of which
I became convinced, that the changes made
in common air, by the combustion of char-
coal, and by respiration, are the same. I
find the following note made on the 4th of
July :—“ The result of all these experiments
is, that breathed gas and gas in which chare
coal has been burnt, are the same in regard to
acid and oxygen, and that the acid is either
equal to, or rather less than, the oxygen in its
composition.” Since that time, I have made
no more experiments relative to the subject.
The substance of this note was soon after
communicated to Dr. Thomson, who publish-
ed it in the 3d Edition of his Chemistry, 1807,
and corroborated it by the results of some
subsequent experiments of his own. Though
it had appeared from the experiments of

Crawford, Menzies, and Davy, that the car-.

honie acid produced. in. respiration was equal,
or nearly. equal, to the oxygen consumed (in

On Respiration-and Animal’ Heat: 35

bulk); yet it was most commonly supposed,
that the experiments of Lavoisier were more
to be depended upon. At least, the above con-
clusions of Dr. Bostock, and the account which
Mr. Murray has given m his Chemistry, 1807,
seem to warrant the observation. The last
gentleman adopts the proportion’ of 84 ‘aia
for 100 oxygen in respiration.) © 9%

In the Phil. Transac. for 1807, aaani
‘Allen and Pepys have given a very excellent
paper on the quantity of carbone in carbonic
acid, and on the nature of the diamond. (See
also Nicholson’s Journal, vol. 19, 1808.)
These authors, to all appearance, indisputs
ably confirm the results of Lavoisier, in re>
gard to the constitution of carbonic ‘acid;
namely, that it is a compound of 28° parts of
carbone by weight, and 72 of oxygen, or very
nearly so; and that carbonic acid contains
just its own bulk of oxygen.

The Phil. Transac. for 1808» (or Nichol-
son’s Journal, vol. 22.) contain’a very labori-
ous, and apparently, accurate series of experi-
ments on respiration, by Messrs. Allen and
Pepys. After a great number of experiments,
made under advantageous circumstances, with
the experience of previous enquiries before
them, and with improved methods of analysis,

‘EV 2

Pi
36 On Respiration and Animal Heat.

they deduce a number of important. results.
The first and the principal one is, that the quan-
tity of carbonic acid gas emitted is exactly equal,
bulk for bulk, to the oxygen consumed. This
is the same conclusion as I had obtained ; it
amounts almost to a demonstration, that the
oxygen which disappears is spent wholly in
the formation of carbonic acid; though it is
possible to conceive that one half of the oxy-
gen unites to carbonic oxide, from the lungs,
and the other half to hydrogen, from the same
source, thereby forming both carbonic acid
and water, agreeable to the notion of Lavoi-
sier and Crawford. 'This last position, how-
ever, appears to me highly improbable. The
authors do not produce any decisive experi-
ments, nor give an opinion, respecting the
question, whether the oxygen combines im-
mediately with the carbone presented to it, as
supposed by Crawford, or, on the other hand,
the oxygen combines with the blood, and in
the process of circulation, carbonic acid is
formed, which is given out in the lungs, as
La Grange and Hassenfratz would have it.
Messrs. Allen and Pepys estimate the carbonic
acid emitted in a day by a middle-sized man,
to be about 3ilbs. troy. They establish a
fact, that before was doubtful, viz. that in
ordinary respiration no material absorption or

On Respiration and Animal Heat. 37

evolution of azote takes place; and another,
that no carbonic oxide is ever found in re-
spired gas. |

In a series of experiments on respiration,
published in the Phil. Transac. 1809, by the
same gentlemen, (see also: Nicholson’s Jour-
nal, vol. 25.) several, curious and interesting
results are obtained,. Among them are some
to the following purport; 1.,That when pure
oxygen is respired, a portion of it is missing
at the end of the experiment, and its place
supplied. by a corresponding quantity of azote.
2. That a mixture of 78 hydrogen and 22
oxygen may be inspired for an hour or more;
it tends to produce sleep ; at the end, a defi-
ciency of hydrogen and corresponding increase
of azote are obseryed, more than can be as-
cribed to the uncertain capacity of the lungs.
3. That the lungs of a middle-sized man con-
tain more than 100 cubic inches of air, after
death.

From these results, it should seem, that
any air which can be respired would lose a
portion in the process, and acquire an equal
portion of azote; this may, perhaps, be occa-
sioned by the blood parting with the common
air, which it contains mechanically; that is,
in the same way that water and other liquids
gontain it, and receiving a portion of the

A,

38 On Respiration and Animal Heat.

other gas, agreeably to the principle of pres
sure established by Dr. Henry. But the
quantity of gases thus interchanged was too
large in some of the instances to admit of
this explanation, ‘unless there was some inac-
curacy in the experiment.

The. above accurate deyeriendeidilatiies

not yet published any enquiry concerning the -

quantity of steam or aqueous vapour produced
by respiration.’ ‘If they should think the the-
oretical determination in the preceding pages
insufficient, namely, 141b. im a day per man, it
is to be hoped they will endeavour to ascer-
tain the facts expermentally, being well qua-
tified for the purpose. and having an apparatus
superior to most or all of their predecessors in
this department of science.

From these additional remarks, it with be
understood, that the leading principles of
Crawford’s theory of animal heat remain yet
in nearly the same state in which he left. them.
Several of his ‘subordinate facts have been
either corrected or ascertained with greater
precision ; for instance, the proportion of ecar-
bone and oxygen in carbonic acid, which he
deduces as 1:4, has been found as 1: 2,6;
the change made in respiring common air has
been found to resemble that made by burning
eharcoal rather than wax; the quantity of the

On Respiration and Animal Heat 39

aqueous vapour expired has been shewn and
its source explained in a way contrary to his
view:: But that arterial blood has a greater
capacity for heat than venous blood, that, oxy-
gen gas has a greater. capacity for heat than
carbonic acid gas, the two great pillars on
which his theory is supported, remain un-
touched ; indeed his results in regard to these
points are so plausible, and. his whole theory
so beautiful, that one would feel a regret in
having to question the accuracy of his prin-
ciples.

—_—

On ihe gradual Deterioration of the Almo-
sphere, by Respiration and Combustion.

IT is now upwards of 20 years since Dr.
Priestley published an Essay, “ On the Res-
toration of air infected with Animal Respira-
tion and Putrefaction, by Vegetation.”* After
remarking that candles will bura only a cer-
tain time, and animals live ‘only a certain
time, in a giyen volume of atmospheric air
the air being rendered noxious by those pro-
cesses, he adds, “I do not know that any

\ * Experiments and Observations payee vol 3, page
« 25u. JOS DO i9'S4 J
4

“40 On Respiration and Animal Heat.

“ methods have been discovered of rendering
“it fit for breathing again. It is evident, -
“ however, that there must be some provision
“in nature for this purpose, as well as for
“that of rendering the air fit for sustaining
“ flame ; for without it the whole mass of the
“atmosphere would, in time, become unfit
“ for the purpose of animal life; and yet there
“is no reason to think that it is at present at all
“ less fit forrespiration than it has ever been.”
In the sequel, he concludes, from certain ex-
periments on vegetation, that it is one of the
processes employed by nature for the great
purpose of restoring the atmosphere to a fit
state for the support of respiration and com-
bustion. How far this conclusion is correct,
namely, that the growing of vegetables ab-
stracts the carbonic acid from air, I have had
no opportunity to observe. But the necessity
of this, or some other process, for the pur-
pose, has, I believe, been generally adopted
by the later writers on this subject. No one,
that I know of, has undertaken to calculate
the quantity of carbonic acid, which is pro-
bably thrown into the atmosphere in any
given time, in order to compare it with the
whole quantity of the atmosphere. Now, if
we state the diameter of the earth to be 8000
miles, and the circumference 25000, in round

On Respiration and Animal Heat. 41

numbers, the area of the earth will be 200
millions of square milés: calculating the weight
of the atmosphere at the rate of 15 lbs. upon a
square inch; for such a number of miles we
obtain 12 trillions of lbs. avoirdupoise ;—cal-
culating also the quantity of carbonic acid
which 1000 millions of men; (the supposed:

_ population of the earth) would expire in the

space of 6000 years, at 3 lbs. per day, we
shall find it to be 6 thousand billions of lbs:
or just... part of the whole atmosphere :
now, supposing this doubled, to allow for the
quantity of acid which may be supposed to be
generated by combustion, we shall then have
«cso part of the atmosphere to be carbonic
acid, which agrees with experiments as to the
quantity now actually found in it; There is
not therefore any necessity to believe from the
phenomena, that means are used by nature for
the restoration of the purity of the atmo-
sphere.*

* Since this paper was sent to press; I have had ati op
portunity of making a few comparative experiments, the
results of which deserve notice. Hearing of a young per-
son living upon simple diets; and taking no fermented
liquors; who feels cold very sensibly, so as to require
warmer clothing, and who is obliged to avail himself of
artificial heat, more than others; I was desirous to learm

sy

42 On Respiration and Animal Heat.

how far the above circumstances might be connected with
the function of respiration. We found that each of us
breathed at an average 20 times in a minute, but that the
quantity of air which he expired each time, was only two
thirds of that which I expired. The capacities of our
lungs appeared to be in the same ratio of 2 to 3; for, the
whole quantities of air which each of us could expel from
our lungs, both after a natural and forced inspiration, were
as nearly as we could determine in that ratio. The quality
of the air expired by us was found to be the same, both in
the natural and foreed expirations; in the former case the
air contained 43 per cent. of carbonie acid, and 16 of
oxygen, and in the latter, 7 carbonic acid, and 13 or 14
oxygen. The size of our persons is nearly the same. The
experiments were made in August, in a temperature of 60°,
Now if the quantity of heat generated, or more properly
speaking, acquired by the animal system, be in direct pro-
portion ta the carbonic acid expired from the lungs, as all
experience would seem to warrant from its evolation, the
above results are consistent therewith, 2nd the facts admit
of a satisfactory explanation.

a

Ihave Just seen a paper in the Philosophical Transactions
for the present year (1811), by Mr. Brodie, containing
some facts affecting the theory of animal heat. It is en-
titled “ Physivlogical Researches respecting the Influence
ef the Brain on the Action of the Heart, and on the Ges
neration of Animal Heat.” There is an important addi-
tion to it in a subsequent paper of the same author.
From his experiments the author deduces the following
conclusions:

“1. The influence of the brain is net directly necessary
to the action of the heart.

On Respiration and Animal Heat. 43

«2, When the brain is injured or removed, the action of
the heart ceases only because respiration is under its in-
fluence, and if under these circumstances respiration is
artificially produced, the circulation will still continue.

«3, When the influence of the brain is cut off, the secre-
tion of urine appears to cease, and nv heat is generated ;
notwithstanding the functions of respiration and the circu-
lation of the blood continue to be performed, and the usual
changes in the appearance of the blood are produced in the
lungs.

“4, When the air respired is colder than the natural
temperature of the animal, the effect of respiration is not
to generate, but to diminish animal heat.”

Mr. Brodie seems to doubt from the above conclusions,
and from sundry observations in the paper, whether
respiration is the source of animal heat. But it seems
premature to draw conclusions respecting the source or
acquisition of animal heat from experiments relating to
its evolution; the two functions by which these processes
are carried on may be variously affected in sueh extra-
ordinary circumstances as those above alluded to, and there
may not be that mutual and correspondent action which
takes place when the animal is in full possession of all its
vital energies. It should appear from the last experiment
(though the results are not ascertained with the requisite
accuracy) that the acquisition of heat goes on in some
degree ; for carbonic acid is generated ; but the secretion
of heat, like that of urine, is totally suspended. {t is
somewhat remarkable, that in all the experiments previous
to this, in which a comparison of the venous and arterial
blood was made, (the Ist, 2d, 3d, 5th and 6th) the blood in
the arteries was seen of a florid red, and that in the veins
of a dark colour ; but in the 9th experiment, when oxygen
gas was inspired, and the production of carboiric acid ob-

served, “the blood in the arteries was very little more florid
EF 2

44 On Respiration and Animal Heat.

than that in the veins.” Query, does this mean that the

blood in the arteries approached to that in ‘the veins in

colour; or vice versa ; or neither of these, but that they

mutually approached to each other in colour? Upon the

whole the production of carbonic acid from oxygen and car-

bone without the evolution of heat (sensible or otherwise),

in the animal system or any where else, would be a

phenomenon so extraordinary in chemistry, that very direct

and precise evidence of the fact must be adduced, beforg |
it could be generally admitted,

(45°)

AN INQUIRY

Into the Principles by which the Importance
of Foreign Commerce ought to be estimated.

By HENRY DEWAR, M.D,
(Read April 1, 1808.)
(RRS

‘Tue science of Political Giconomy, being
connected with the best of all social senti-
ments, that of a rational philanthropy, and
comprehending an extensive range of inquiry,
characterised by a delicate mutual dependence
among its various parts, and consequently
affording excellent scope for patient investi-
gation, I hope we shall be agreeably employed
in directing our conversation for this evening
to one of the most interesting problems which
this science affords. While we contemplate
with unpleasant sensations some prominent
features in the present state of Europe, we
must, as friends to science, derive some little
consolation from the light which modern dis-
cussions are likely to throw on some of the
most important questions of political ceconomy.
This is, in some measure, the consequence of

4G On the Importance of

the interest which the gloomy features of the
age have procured for them. Amidst the un-
certainty under which we labour, regarding
the future fate of the civilized world, we may
cherish the most confident assurance that the
improvements made in this science never can
be lost, and that they cannot fail to produce
beneficial effects on the management of the
great concerns of every civil community.
The present imperfect state of some branches
of the science gives occasional room for party
debates ; but it is to be hoped that the time is
not far distant when the subject will ve so fully
explained, and information on it so generally
diffused, that the opinions of every statesman
who weuld maintai any portion of character
with the public, must be sound and precise.
When this takes place, the merits of every
proposed regulation will be at once apparent.
Crude experiments will no longer be resorted
to, and the public supplies will be levied in
such a manner as will best obviate all oppres-
sion and inconvenience.

My present intention is to offer a few re-
yoarks on the j:rinciples by which we ought te
estimate the importance of foreign commerce.
For the sake of bemg clearly understood, I
shall consider separately its influence on

A

Foreign Commerce. A?

wealth, on population, on happiness, and on
national power.

In estimating its influence on wealth, it will
be necessary to observe a strict uniformity in
the meaning which we attach to that word.
Mr. Spence, the author of the ingenious
pamphlet entitled “Britain independent of
Commerce,” has involved the argument in
much confusion, by attaching no precise
meaning to the term wealth. For, though he
sets out with a formal definition of it, we
find him in the course of his reasonings,
sometimes considering wealth as consisting in
every thing that man, as molded by habit,
esteems valuable ; and, at other times, restrict-
ing it to those articles which man would value
if his taste were always correct. At present, I
shall use the term in the first of these accepta-
tions, that is, as including those commedities
which man actually values, and for which he
is willing to part with some other valued
' article in exchange. The meaning of the
term value we shall restrict in the same man-
ner; we shall consider the value of every
commodity as fixed by the quantity of any
other that will be given in exchange for it.

While we adhere to these definitions, it is
susceptible of complete demonstration that
foreign commerce increases the wealth of

48 On the Imporiance of

every nation that enjoys it. If one coiintry,
which abounds in the comiodities of rice and
silk, exchanges part of these for the wheat
and flax of another, both countries must be
enriched, because each sets a higher value on
the articles which it receives than on the
quantity of its own produce which it gives in
exchange. On this account, these articles aré
able to bear the expence of carriage, and after
this expence is added to their price, they still
are objects of demand, While other things
are equal, the increase of wealth must bear a
regular proportion to this species of com-
merce, as in each country there is an increase
of the overplus value of imported articles
above that of articles exported.

This conclusion, however, only applies to
the influence of foreign commerce on wealth
in that limited acceptation in which it is here
taken. The importation of a drug for the
purpose of ruinous intoxication, is equally
conducive to wealth with the first article of
necessity and comfort... A quantity of poison,
purchased ‘by a nation of assassins in ex-
change for grain, contributes as much to the
increase of wealth as the most useful produce
of nature or of arts)

This being the case, the influence of foreign
commerce on wealth, affords: a. very partial.

- t ‘aT ~

Foreign Commerce. 49

view of its merits. We shall now consider its
influence on population.

Population depends on the abundance of
food, and the facility with which it is generally
procured. The abundance of food must en-
tirely depend on two circumstances, the state
of agriculture, and the extent of the importa-
tion of foreign articles of sustenance. The

- state of agriculture includes not merely the

degree of improvement in agricultural know-
ledge, but also the kind of culture which the
soil receives. Land employed in rearing ani-
mal food, supports a much smaller number of
individuals than land employed in raising
corn: potatoe fields are much more productive
than either. In order to understand this sub-
ject, it is necessary to inquire into the radical
causes which determine the mode in which the
ground will be cultivated. This is wholly
regulated by the pleasure of the proprietors of
land. Landed property differs from property
of other kinds im this leading circumstance,
that it has the original command of the whole
overplus of produce and of human labour,
above that which is necessary for the sus-
tenance of the proprietors themselves. If the
chief amf¥ftion of landed proprietors is to
possess extensive pleasure grounds, deer parks,
‘ G

ms ~

|

50 On the Importance of

and hunting forests, a large quantity of tlie
surface of the earth must be appropriated to
their enjoyment, without the intermediate step
of population. If on the other hand they hold
such pleasures in contempt, and only study the
most effectual measures for increasing the
number of their servants and dependents, or
if they consume such articles of commerce as
require much human labour for their manu-
facture, and little or no land for the production
of the raw materials, their wants will operate
as a certain cause of the most productive
agriculture.* ‘This process has no direct de-
pendence on the state of improvement of other
arts. When the state of manufactures is low,
the wealth of a country is proportionally in-
significant ; but if the manufactured commo-
dities are in demand among landed proprietors
or their dependents, every cause that promotes
the cultivation of the ground, and the popula-
tion of the country, exists in full activity.
When manufactures are highly improved, and
internal commerce regular and brisk, society
becomes wealthier, but the rate of population

» * If we could suppose the views of landed proprietors te
be perfectly harmonious, formed on principles of inde-
pendence, and directed by sagacity, they would effectually
regulate both the degree and the kind of population that
would exist in every country.

Foreign Commerce. 5k

is not different. The proprietor of land still
possesses the original command of human
labour. The capital and credit of the mer-
chant reduce the employment of this labour to
a system. By. thus rendering it more pro-
ductive, he adds to the conveniences of the
landed proprietor, and he himself is also fur-
nished with the luxuries of life. An increase
takes place in the proportion of persons who
live in affluence ; but none in the sum total of
population.

Mr. Spence errs in considering commerce
as a necessary spur to agriculture. In a
country destitute of commerce, the passion of
men of influence for increasing the number of
their vassals, would produce the same effect.
This principle formerly supported tillage in
some districts ef our country from which it is
now excluded, Formerly a chieftain was as
well satisfied when his brave hordes supported.
themselves amidst inaccessible mountains as
when they subsisted on the produce of the
open plain. Now, land will yield no profit in
grain, unless manufactures are brought to its
neighbourhood, or means found to convey its
produce toa distance. On this account, under
such circumstances, grain is not raised: We
thus find, that the commercial spirit has had a
G2

52 On the Importance of

discouraging influence on some branches of
agriculture ; and we formerly showed, that,
where men are regulated by motives of luxury,
those who aim at the enlargement of their
fortune, by the improvement of land, will have
equally powerful motives in the lowest, as in
the highest state of commerce. If it is said
that commerce improves land, by enabling
merchants to accumulate profits which are
often expended in agricultural improvements,
it should be recollected that this effect of
commerce is extremely limited; and that the
same efiect would be produced by habits of
virtuous parsimony, or by a regular system of
credit, established on landed security.

It sometimes happens that an improvement
in the useful arts threatens to injure popula-
tion. When new machinery is invented
which supersedes the greater part of the labour
employed in a particular branch of manufac-
ture, many elderly persons, who are unable to
change their mode of employment, are re-
duced to indigence; and even the active
Jabourer is unemployed for a time. ‘The latter
however, is certain of finding employment in
a short time im some other department. The
reason of this is, that the article of manufac-
ture prepared by means of the improved ma-
chinery, is reduced in price ; and the persons

Foreign Commerce. 53

who consumed it, whether landed proprietors
or their servants, or manufacturers, have it
now in their power to purchase some other
article with the overplus of their income.
The manufacturer and the merchant, per-
petually watching the state of the market,
observe what particular article comes into
demand, and direct their labourers accord-
ingly. If the article thus extended in its sale
requires no additional extent of land for the
production of the raw material, the change
produces no ultimate effect on population: if
otherwise, population is diminished.

These considerations enable us to form a
ready estimate of the influence of foreign com-
merce on population. ‘The theorem on this
subject may be reduced within very narrow
bounds. Whenever an article manufactured
for the foreign market requires for the pro-
duction of the raw material a portion of our
own soil, which is capable of producing food,
the tendency of foreign commerce is to dimi-
nish our population, except in so far as it is
compensated by an equivalent importation of
the necessaries of life. Where an article is
‘manufactured for the foreign market, from
foreign raw materials, or where the materials
are procured. from subterranean mines, from
the sea, from land incapable of producing

54 On the Importance of

human food, or from a substance which other-
wise would exist as mere refuse, foreign com-
merce cannot possibly injure population; and
if it procures an importation of food, in return
for the export now mentioned, its effect must
be to'extend it. This effect is most likely to
take place where a nation that enjoys a free
trade excels its neighbours in the ingenuity
and industry of its manufacturers, because a -
given quantity of goods is produced by a share
of exertion comparatively moderate, and pro-
cures a liberal return in the produce of other
countries. If a trade, under such circum-
stances, is sufficiently long continued, a part of
the return will be given in the form of food, or
other articles of necessity, for the support of an
additional population.

A mere increase of population, however, is
not one of the most hberal objects of political
ceconomy ; and, when it is procured at the
expence of a large portion of misery, it is to
be sincerely regretted. ‘To add to the hap-
piness of a people, is far more desirable than
to swell their numbers. If the increase of
happiness could be praved to be the invariable
consequence of the extension of foreign com-
merce, that would be the best possible reason
for setting a high value on it. There is no
doubt that its tendency is in general favourable

$

Foreign Commerce. 55

to immediate gratification, as it affords a
choice of pleasures. It ought therefore to be
highly conducive to happiness, and cannot, in
fact, be the cause of misery among a people,
except in consequence of some perversion of
their taste. When any perversion of this sort
is general, any event that would deprive a
country of their favourite gratifications, would.
certainly prove a blessing, however much it
might diminish the wealth or the sum total
of exchangeable value. Mr. Spence, however,
is unfortunate in selecting the importation of
wine and foreign spirits into Great Britain, as
an instance of this sort. If the importation
of these articles were prohibited, the imme-
diate consequence would be, that those who
now send their native produce abroad, to pay
for these luxuries, would convert more of their
own grain into intoxicating liquors. The
same scope would thus be afforded for hurtful
excess. When we enquire into principles of
conduct, we should presume, that men, when
well informed, will make a prudent choice.
In an enquiring age, we should suppose, that
they will become practically enlightened by
the influence of moral research. On this
principle, we should pronounce foreign com-
merce to be favourable to the happiness of a
country. At the same time, we must not
; 1

ae

«

56 On the Importance of

forget that national happiness is far more
‘powerfully affected by circumstances totally
independent of it. It depends so much on
the degree in which a nation enjoys freedom
of principle, political equity, and social order,
on the general diffusion of the comforts of
life, the prevalence of virtuous habits, mode-
rated desires, kind affections, and cultivated
manners, that, in comparison, the effects of
foreign commerce almost entirely disappear.
Foreign commerce, in its present state, is
attended with some causes of unhappiness,
which it is to be hoped are not inseparable
from it: The unhealthiness of various pro-
cesses: for preparing goods for the foreign
market, is a very important subject, and: has
been frequently adverted to. The moraleffect
of trade, in general, on the human character,
ought also to be seriously considered. It is
the error of some to extol it discriminately
as the cause of industry, and to hail its-profits .
as the rewards of merit. It ought to be
remembered, that its profits are often equally
fortuitous with the sums acquired by gaming,
or by lottery. ‘They are not indeed so per-
nicious in their tendency, because they have a
connection, though somewhat loose, with in-
dustry. But the chances of high success on
the one hand, and the risks of failure on the

Foreign Commerce. 57

other, tend to give a vague character to the
hopes of the trader, and generate a spirit of
adventure which often leads to disappoint-
ment. An industry of a steadier and happier
kind would be produced, if a constant atten-
tion to business were attended with a slower
augmentation of fortune, exempt from all
risk of disappointment. The mind, in that
case, no longer injured by excessive passions,
would be invited to relish life, by the uniform
encouragement which it would afford.—
Perhaps the state of commerce may, at a
future period, be in this, point of view im-
proved. The frivolous caprice of fashion
among the rich, may give place to a taste for
more steady enjoyments; and thus a more
uniform demand for the products of the useful
arts may be created. An improvement may
also take place in commercial sagacity, which
will enable the merchant more easily to foresee
the fluctuations of the market, and prevent
the derangement occasioned by unexpected
changes. |

Let us now consider the influence of foreign
commerce on national power. ‘This part of
the subject is at present peculiarly interesting,
as the posture of the affairs of Europe threatens
_to bring the principle to the test of experience,
H

58 On the Importance of

in the case of Great Bram. We are
threatened with the total loss of our foreign
commerce: and, if our power depends on it,
the accomplishment of the threatening will
involve the destruction, not only of all that
from political habits we reckon dear, as an
independent nation, but of the more substan-
tial blessings of domestic peace and security.
It is therefore highly interesting for us to
know in what degree our power can be sup-
ported by our own native resources.

The power of a nation depends chiefly on
the defensible state of its territory, the extent
of its population, the facility with which that
population can be called into the public ser-
vice, and its degree of knowledge and dex-
terity in the art of war. Some of these
circumstances have evidently no dependence

‘on foreign trade: in others, its influence is,

in the present state of our knowledge, some-
what problematical. The argument has very
properly been made principally to rest on the
influence which it possesses in enabling us,
through the medium of an extended taxation,
to call out our population into the public
service. Some have asserted that foreign
commerce is a separate source of revenue ;
others that it is merely a more circuitous
method of taxing the produce of land and

Foreign Commerce. 59

domestic labour. As illustrations of these
two different modes of thinking, we quote
the opimions of Mr. Spence, and those of the
critic who replies to him in the Edinburgh
Review.

Mr. Spence pronounces it absurd to consider
any branch of our commerce as deriving im-
portance from the duties which are levied
on it. All such duties, according to him, are
finally paid by the consumers of the articles
on which they are laid, and these consumers
are equally able to pay the sums they
advance, whether they consume such articles
or not. If the present consumers of tea and
wine, for example, were to drink nothing but
water, they would possess not only the same,
but a considerably greater, power of contri-
buting taxes for the exigencies of the state.

To this the reviewer replies, that the appe-
tite which men have for the luxuries on which
the taxes are laid, is the sole cause of the pro-
duction both of the luxuries themselves, and
of the taxes which they bear: and, therefore,
if the incitement is withheld, industry and
production must infallibly languish. That it
is not enough for the Chancellor of the Exche-
quer to recommend to the people to leave off
tea and wine, that they may be better able to

H2

60 On the Importance of

pay taxes, and make voluntary contributions,
unless he has power to persuade them to take
as much pleasure in earning money for the
‘service of the state, as in consuming these
luxuries. ue

- There are two modes of attempting to
produce a political effect through the medium
of public discussion. Some direct their doc-
trmes entirely to the candour of statesmen,
and consider the existing habits of the com-
munity at large as facts which must be taken
as they are found, without depending on the
possibility of moulding them to particular
purposes. Others address the mass of society
as consisting of persons, who, when once in-
formed of their interests, may be roused to
patriotic feelings sufficient to make them
cheerfully submit to great privations. It is
not necessary to determine whether statesmen
or the rest of the inhabitants of this country,
exhibit the greatest patriotism and self-denial,
or which of the two classes is most slavishly
tied down by immediate appetite, and by the
homage demanded by the caprice of fashion.
But the prevalence of public virtue in either
class of persons, would certainly promote it
in the other. Where a nation is universally
‘ patriotic, there exists the greatest spur to
patriotism among statesmen ; and, on the other

Foreign Commerce. @L

hand, if the leading men in government show
a disinterested patriotism, the people, con-
ceiving their interests lodged in safe hands,
will feel the best encouragement to cherish a
spirit truly patriotic. An improyement in the
sentiments of each is most likely to advance,
by their going hand in hand. Political writers
should address their doctrines to both alike.
It is injudicious to impress the one with an
opinion of the untractableness of the other.
If it is difficult to excite among the inhabi-
tants of this country an interest in its fate
fully adequate to make them submit to priva-
tions as well as to hazards, this certainly pro-
ceeds from some unfortunate want of mutual
confidence and of cordial co-operation, rather
than from any invincible attachment to imme-
diate ease and pleasure, and no such principle
ought to be adopted as a fundamental position
by writers who are endeavouring to unite
their countrymen by enlightening their minds,
In this point, the reviewer appears to be de-
ficient. He is also chargeable with some
inaccuracy in estimating the operation of the
love of luxury, even supposing it to continue
as predominant as it now is.

That sentiments of disinterested patriotism
must be fully exerted before the government
can avail itself of their existence, is so far

62 On the Importance of

just ; but in the illustration which the reviewer
subjoins, he shows himself in some measure
aware of the reply to which the application of
that argument was open. He adds, “ Nor do
we think that Mr. Spence will succeed in
convincing the people of England to go
without wine, and to hoard Birmingham ma-
nufactures.” This also may be true: but it
only shows that the taste of consumers may
not take that turn which a particular author
might recommend. It cannot probably be
directed, and its changes may not be easily
foreseen. But there is one principle in human
nature to which it is of the utmost importance
for us to attend; that as long as a spirit for
active labour exists in the country, and as long
as that spirit is encouraged by a love of luxury
among the rich, those of the latter, who are
deprived of the opportunity of purchasing one
luxury, will find some means of spending their
superfluous income ; and these means will call
into a different field of exertion, the labour of
those persons who were employed in importing
luxuries from abroad, or in preparing manu-
factures to pay for them in the foreign market.
The most serious disadvantage that arises,
consists in the temporary embarrassment pro-
duced by the sudden change given to the great
machme of commerce, and the uncertainty

Foreign Commerce. 63

which, in the first instance prevails, respecting
the direction which general consumption may
take. It is the business of the financier to
discover, as soon as possible, to what particular
quarter the consumption is directed, and from
whence the revenue may be advantageously
raised. It is vain to object, that the destruc-
tion of foreign commerce leaves no super-
fluous income, and only deprives of their in-
come those persons who were engaged in it.
We must bear in mind, that what we call in-
come, is applicable to national defence only
in so far as it gives the possessor a hold on the
Jabour of the community. As long as the
labourers exist, and the produce of the ground
can be commanded by persons living in the
country, their labour will be called forth,
and the same scope will remain for all that
taxation which is subservient to military ob-
jects. The wealth of the country, according
to the definition formerly given of it, must be
diminished ; and the prices of many articles of
consumption may fall. A diminution of the
amount of the taxes consequently takes place :
but this must be attended with a reduction in
the price of those articles by which the public
service is supported. The expenditure and
the revenue still bear the same mutual pro-
portion.

64 On the Inportance of

These doctrines will apply to every case
in which the navy and army consume the pro-
duce of our own country: and if it be consi-
dered that our own country produces the most
essential articles, and that our colonial pos-
sessions furnish a variety: of those which we
usually procured from other quarters, it will be
found that we possess, in an ample degree,
the means of maintaming our fleets and armies,
independently of foreign commerce. Some
apprehensions which were once entertained
regarding the possibility of procuring naval
stores, when cut off from the commerce of the
continent, seem now to have vanished, in con-
sequence of the inquiries that have been made

4

ou the subject.
We shall therefore pass from financial con-

siderations to another topic highly worthy of
attention, namely, the reply which Mr. Spence.
has given to those who consider foreign com-
merce as an indispensible nursery for seamen.
It seems perfectly clear, that, whatever has
been the origin of our naval power, its dura-
tion is independent of a commercial naviga-
tion, because young men can be trained on
“board ships of war to every naval operation,
with even greater advantage than in merchant
vessels. This is an argument to which no
rational reply has yet been given.
1

Foreign Commerce. 65

I hope that no apology is necessary for
having dwelt so much on the subject of war.
That ambition, whether of individuals or of
nations, from which it most frequently arises,
is a mean and a vicious sentiment. But the
strictest system of self-defence is the only
species of war to which I have directed any
portion of your attention ; and independently
even of this, we may consider the points now
adverted to, as affording a profitable subject
for discussion, which have, in some instances,
been too much overlooked; and in others,
subjected to too hasty decision.

66 On the Importance of

i a oie cg, UD RN TE

In a Letter t to the Pr nee and Mawbees of
nF the Literary Y and Philosophical Societ, ty yo
Manchester.

ylirabmoqobs (Read October 4, 1811.)
» (GENTLEMEN,
Gite a 1 had the agit of reading the

preceding observations in your hearing, some
further discussions on the subject have been

presented to the public. Considerable addi- -

tional light has been thrown on it m Mr.
Chalmers’s inquiry into the nature and extent
of national resources. The observations of
that author might produce an extensive effect
on the general mind, if they were luminously
prosecuted in detail, and patiently defended
from common objections.

A second pamphlet also has been published
by Mr. Spence, in which he has not corrected
his opinions so carefully as might have been
expected ; and his errors have met with point-
ed reprobation in another article devoted to

the subject in the Edinburgh Review.

a

' Foreign Commerce. 67

The author of that article, however, has
made assertions which require to be carefully
weighed before we can give them our assent.
He, no doubt, justly accuses Mr. Spence of
assuming erroneous data for the foundation
of his reasonings; but he is not successful in
refuting his leadig conclusion, that Britain
is independent of commerce. If we wish to
estimate the truth of that conclusion, and the
degree of importance that ought to be attached
to it, we must beware of mistaking the point
at issue, by allowing the meaning of the word
independence to be insensibly shifted. We
must enquire what was the common impres-
sion on the subject previous to the discussion,
and what is the result to which that discussion
has led.

The fixed and almost universal impression
was, that the moment foreign commerce is.
shut up, the, power of Britain must be an-
nihilated. 'This apprehension has certainly
been removed. The loss of foreign commerce
is indeed acknowledged to be productive of.
privations and sacrifices; but these by no
means amount to national ruin. A nation un-
willing to submit to sacrifices, is always pro-
nounced unworthy of independence. Every
war implies sacrifices to which we are not

12

68 On the Importance of

subjected during peace. The hardships,
dangers, and losses, inseparable from military
service, need not be recounted ; but no defini-
tion of national independence has ever yet
been received, which implies that this inde-
pendence is lost as soon as a nation is obliged
to go to war. An attachment to the cause
in which the soldier perishes, often consoles the
affliction of surviving friends. In the same
manner, if we resign our foreign commerce
in an honourable cause, the immediate suffer-
ers, if their patriotism is ardent, will receive,
in the general advantages secured to their
country, some consolation for their personal
distresses ; and the nation at large may, with-
out any want of sympathy for the disappointed
merchant, reckon such evils necessary for the
public interest. The merits of every parti-
cular case are a fair subject of inquiry: but
they are foreign to the present argument.
It may however be laid down as a very mode-
rate assumption, that the losses of the mer-
chant ought to be as easily. consoled, as the
calamity often sustained in the death of valued
friends.

The disadvantages arising from the loss
of foreign commerce, do not bear so close an
analogy to the common calamities of war, as
they do to evils of much inferior magnitude.

Foreign Commerce. 69

They resemble those which have sometimes
resulted from extensive commercial specula-
tions turning unfortunately out. Private losses
of the same kind arise even from occurrences
which are productive of essential gain to the
country. Working people are put to as much
inconvenience by the change of fashion in a
particular luxury, or even by the invention of
machinery which supersedes a portion of their
labour, as they are by the decay of foreign
commerce. They are equally obliged in each
of these cases to enter on a species of labour
to which their habits are not adapted. When
peace is concluded, and foreign commerce
restored, it is not unlikely that this restoration
will bring with it inconveniences exactly
similar to those which follow its temporary
departure..

The alarms of merchants and manufactu-
rers are not confined to such occurrences as
the loss of foreign connections, but are some-
times loudly heard when changes are appre-
hended which are undoubtedly beneficial to
the public. Of this sort was the alarm taken
by the woollen manufacturers of Yorkshire,
when it was proposed to give greater freedom
to the trade and manufactures of Ireland:
With the same justice might the proprietors
of West Indian plantations deprecate the

70 On the Importance of

taking of any sugar islands from the enemy,
as an event that must overstock the market
of sugar.

Some consolations, of a commercial nature,
mentioned by Mr. Spence, are greatly under-
rated by the reviewer. When the large
manufacturing establishments by which the
foreign market was supplied are reduced, a
part of them is acknowledged to be retained.
That part is not sufficiently proved to be con-
temptible, because in a comparative point of
view, we may attach to it the epithet puny. It
serves the purposes of our own consumption,
and it gives employment to a part of the
labouring population. Nor when establish-
ments altogether new are formed at home to
supply us with articles which we formerly
procured at a lower rate from abroad, ought
their awkwardness and the inferiority of their
' produce to be treated with unqualified con-
tempt : especially when we consider, that lately
the general impression was, that the loss of
foreign commerce brought along with it the
ruin of every commercial and manufacturing
establishment ; and that no ability could exist
of forming any new establishment, even the
most insignificant. The inferiority of the
article may imply no sacrifice which is not
compensated by the advantages. which the

Foreign Commerce. 71

insulation of our interests secures to the
country. Even this change in the direction
of industry, has in itself a chance of securing
some permanent advantages. Foreign ma-
nufactures may, in some instances, owe their
advantages to their previous establishment.
The removal of a manufacture to another
local situation, is, in general, a process too
tedious and expensive to be prudently under-
taken by private individuals. This circum-
stance often prevents the establishment of
manufactures which might ultimately prove
beneficial. On this principle, it is probable
that manufactures might, in a case of neces-
sity, be introduced, in which no individuals
would otherwise have had the hardiness to
engage. Qur exclusion from the foreign
market, would thus ultimately add to our per-
manent domestic resources. But it is most
important of all. to recollect, that such
establishments will exactly suffice to give

employment to that part of the labouring

population which the reduction of our former
manufacturing establishments throws idle.
The merits of this whole question, and of
some others closely.connected with it,, deserve
a more full discussion than has yet been given
to them. When we have been, emancipated
from the slavery of unfounded apprehensions,

12 On the Importance of

we ought not to be insensible to the hard-
ships which really attach to the loss of foreign
commerce. There is, no doubt, room for
devising expedients by which the pressure of
these might be considerably alleviated.

Much improvement may also be made in
the art of disseminating more widely those
principles of political ceconomy which are
established on sound reasoning.’ Those literati
who have ready access to the press, and leisure
for instructing the public, should spare no
exertion to combat error in all the channels in
which it flows. No periodical publication,
however trifling, should be suffered to soothe
the prejudices of the ill-informed, without an
offer being made to exhibit the antidote along
with the poison. The difficulty of convincing
the public of truths which they have not
been in the habit of believing, should not
give rise to elegiac lamentations, rude re-
proaches, or contemptuous neglect, but be
viewed as a fact which furnishes a motive to
patient exertion, and which, when minutely
studied in its various aspects, will suggest the
means of conveying truth more successfully.
Great care ought to be taken to avoid con-
founding those questions which are agitated
by the political parties of the day, with any
particular argument with which such questions

1

Foreign Commerce. 73

are not necessarily connected. Those who
believe that all existing misfortunes have
arisen from mismanagement on the part of
government, should, whenever it. is. possible,
proceed on the same data with those who
believe that the wisdom of government has
averted the most dreadful calamities, and se-
cured to us all the advantages which we
enjoy. The questions of parties are often in-
deed highly important; but by avoiding their
influence, where it is not strictly legitimate,
we shall render our discussions the more can-
did, and make some advances, in giving to
such questions a greater simplicity. When
political adversaries are mutually deprived of
their fallacious arguments, they will come to
a better understanding on the remaining points
of difference ; and if their spirit is manly, they
will make gradual and cordial approaches,
The triumph of reason is equally grateful to
an ingenuous man, when his own fallacies are
refuted, as when those of his antagonist are
exposed.
I have the honour to be,
Gentlemen,
Your obedient and humble servant,

seneth * t Mie

Lassoddie, by Kelty-bridge, \
12th Jan. 1811.
K

es (7) ine

REMARKS

* ON THE USE AND ORIGIN OF

FIGURATIVE LANGUAGE.

- BY THE REV. WILLIAM JOHNS.
(Read October 21, 1808.)

Quanquam hoc videtur fortasse cuipiam durius, tamen
audeamus imitari Stoicos, qui studiose exquirant, unde —
verba sunt ducta.—CicERo.

A CORRECT notion of the origin and
use of Figurative Language will greatly assist
us in discovering the principles according to
which language has been formed and im-
proved. ‘Though much light has been thrown
on the subject of the formation of language
by modern critics, and especially by Mr. Horne
Tooke, yet I cannot help being of opinion
that room is left for further discoveries ; and
under this impression, I offer the following
theory to the candid consideration of the
society.

This essay has a two-fold object, and natu-
rally divides itself into two parts; but, as far
as relates to my present purpose, the first is
only subservient to the second.

On Figurative Language. 75

The first shews the nature and use of figu-
rative language; the second traces it to its
source, and deduces from it some properties
of language hitherto, I believe, but little
known. — fo; o4R /
-L. The nature of figure is generally un-
derstood, and‘ has been ‘critically explamed
by writers: on rhetori¢,) both ancient and
modern: © Figure is a: change of words,
éither from their original meaning,’ or from
their most usual and commonly received ac-
ceptation.. This change, according to the
different circumstances under which it was
used, was denominated by the ancient writers
on oratory, (whom the moderns have copied)
tropus, figura, metaphora, translatio, and
many others; all which terms imply a change
in the use of certain words in a discourse, and
a turning of them from what may be called
their original and proper meaning. Thus
when we say, that the Roman empire flourish-
ed under Augustus, that splendid victories
were gained, and that the arts were culti-
vated—the words flourished, splendid, and
cultivated, ave obviously metaphorical, being
transferred from their proper acceptation to
one that is merely analogical, and one only
of real or fancied resemblance.

yu

76 On Figurative Language.

Of the different: sorts of words into which
speech has been usually divided, the substan-
tive, the adjective and the verb—and. likewise
the adverb, when derived from any of these
three, are obviously capable of suffering the
foregoing transformation. Of the other parts
of speech we at present affirm nothing: | It
is scarcely necessary here to exhibit instances
of each, as language, whether prose or verse,
luxuriantly abounds in them--indeed much
more so than is generally imagined... A few
promiscuous examples; nevertheless, may not
be deemed improper.

Patet isti janua letho.—Virc.
Dulcia \inquimus arva.—Zd.
Corydon ardebat Alexim.—Id.
O et columen et dulce decus meum.—Hor.
Tu, cum te de curriculo petitionis deflexisses, &c.
3 Cic. pro Muren.
Sed himen; Servi, quam te securim putas tyecisse petition:
tute, &e, oxi Id.
Smit with the love of sacred song.—Miutt.
The full blazing sun,
Which now sat high in his meridian tower.—Id.
And the moon
Riding i in her highest noon. —Ia.
Now jis the winter of our discontent,
Made glorious summer ‘by this sun 1 of York,
Andall the clouds that lowerel ‘pon Bur house,
In the deep bosoin of the ocean buried. —SuakEsPEARE.

On Figurative Language. 77

- II. This part of my subject being suffi-
ciently explained for my present purpose, I
shall now proceed to shew for what reasons
and under what circumstances metaphorical
or figurative language originated ; what pur-
poses it serves; and how, in the progress of
language from infancy to maturity, words
assume, renounce, and re-assume a figurative
meaning.

The most judicious critics truly ascribe the
origin. of figurative language to necessity.
This is expressly stated by Ciceroin his book
de Oratore. . |

_“Tertias ille. modus. transferrendi verbi
late patet, quem necessitas genuit, inopia
coacta et angustiis.”—Zibd. III. 55,

We use figurative language, according to
Quinctilian, “aut quia necesse est, aut quia
significantius est, aut quia decentius.” In
explaining the case of necessity, he adds;
“Necessitate rustici dicunt yemmam in yiti-
bus; quid enim dicerent aliud? et. sitire
segetes, et, fructus laborare. Necessitate nos,
durum hominem, aut asperum. Non enim
_ proprium erat quod daremus his affectionibus
nomen.” —Lib. VIII. Cap. VI.

Dr. Blair has expressed nearly the same
sentiments in his Lectures on Rhetoric:
‘Tropes of this kind abound in all languages,

78 On Figurative Language.

and are plainly owing to the want of proper
words.” He errs, however, in’ my opinion;
in adding soon after, “that necessity is not
the principal source of' this form of speech;
but that tropes have! arisen more frequently,
and spread themselves wider from the influ-
ence’ which imagination possesses over lan-
guage.” This indeed may he true in rézard
to those figurative expressions for which
proper ones might readily be found, which
spring only from a wanton search after analo-
gies, and which add neither force nor justtiess
to a sentiment ; but it can by no means be
true concerning those tropés of which the great
body of a language consists, and without the
assistance of which we can scarcely utter a —
sentencé. It will appear too, front the man-
ner in ‘which I shall endeavour to trace the rise
and origin of figurative diction, that we do
not owe much of it to the influence of imagi-
nation, but that the want of proper words of
sufficient force and significance, has obliged
men to supply the deficiency in the best
manner they were able.

I regard the appropriating of distinct names
to sensible objects as the first step in the
formation of language; and, therefore, I con-
sider nouns as the basis of the whole super-
structure. Without nouns there cannot, in —

4

On Figurative Language. “79

the nature of thing's, be any communication of
ideas. External objects are the only things
with which the senses can be impressed ; they
‘are the. first things with which men could
‘become acquainted, and they must be regarded
as the primary objects of knowledge and
attention: The invention of those elements
of speech, which grammarians have denomi-
nated nouns, was at once the most obvious and
the most necessary. "I shall therefore consider
‘myself authorized to assume it as a fact, that
the appropriation of articulate sounds to spe-
cify different sensible objects, is the ground-
owork of all language..
_» Dr. Blair, however, is of opinion, “ that
- those exclamations, which by grammarians
are called interjections, uttered in a strong
and passionate manner, were beyond doubt
the elements of speech.” But after these
inarticulate cries, he gives the next place to
nouns. — Bi
If by interjections Dr. Blair meant onty
inarticulate cries, we observe, that they are
not to be deemed any legitimate part of
language; but if those broken fragments of
speech be meant, to which grammarians may
-have sometimes given the appellation of in-
terjections, it is sufficiently evident that these

80 On Figurative Language,

must be posterior to those words from which
they are derived.

But though nouns compose the primary and
most necessary part of language, men would
soon discover, that it is absolutely impossible
to denote every individual object by a distinct
name. This indeed is a task of such extent
and difficulty, that the life and faculties ‘of
man are not equal toit. Necessity, therefore,
drove men to devise some means to accomplish
the end of mutual communication, without
attempting a hopeless labour. .
One of these contrivances, and one of very
extensive application, is transferring the name
of an object already known in language to an
unnamed object ; in doing which, men were
guided by analogies more or less obvious,
more or less remote. Upon this principle,
death would be called sleep ; a governor, head;
ignorance, darkness ; knowledge, light, &c.
Remote as we are from the original formation
of languages, there are but a few mstances
comparatively in which we can trace the
names of objects to their primary source, be-
cause the analogy followed has no certain or
determinate laws or restrictions, and because
the disuse of most words in their primary sig-
nification has been of so long continuance, that
scarcely any trace or vestige is left to form a

On Figurative Language. $1

elue ; yet the number of instances is sufficient
to verify the fact, and fully to shew the nature
ef the modification which imnumerable words
must have undergone.

Generally in all eine in, the English,
atleast, in its present state, men do not abso-
lutely invent new names (as quinbus, flestrin,
in. the yoyage to Lilliput) to denote new
objects or things, but,.either compound old
ones, or use old names in. a new or transferred
meaning. ‘Thus at the inyention of the ma-
chine which turns a spit, it was called jack, in
compliment to the former operator... The
contrivance to change the level of a vessel in
a canal is called 4 lock; from its confining the
vessel, by an analogy rather remote. When
_ an artificer in wood-work confines his object
to one species of labour, e.g. making carts or
wheels, he is denominated cartwright or wheel-
aright. There are other compositions in the
danguage, in great numbers, less apparent, but
not less real: asin the words Godhead, good-
ness, saimtship, gaily, preferment,. and others;
the latter syllable was originally .a. word or
part of a word, in composition with God,
good, &c. There would have been many more
contrivances of this nature in our language, if
it had not borrowed so copiously from other

82 On Figurative Language.

languages, in which such contrivances had
already taken place.

The names, and expressions, which have
been applied to the mind, its faculties and
operations, are transferred from external ob-
jects and the corporeal senses, Spirit means
mind or breath. Were I sufficiently ac-
quainted with the Anglo-Saxon, I do not
doubt but mind and soul might be accounted
for in the same manner. Who does not at
once see the transferred use of the words
action, passion, affection, understanding, per-
ception, recollection, and many more, when
used in reference to the mind? What is more
common than to say, I see, I take you, I assent,
L consent, I refuse, I reject, &c. &c.? Though
we cannot, at this distance, ascend to the
‘primary objects to which these words were ap-
plied, we can, at least, retrace them so far as
to prove our object—that after men had pro-
ceeded toa certain extent to give names to
‘sensible objects, their next step was to apply
these names figuratively to other objects,
according to a certain analogy, real or sup-
posed,

All intellectual ideas are expressed by the
names of sensible objects, from a supposed
analogy or resemblance, the best the circum-
stances of the case were supposed to admit of.

or

On Figurative Language 83

Thus a connection, in a long process of reason-
ing, is called a link in the chain of reasoning.
But not only the words link and chain are
obviously used in a transferred sense, but
likewise connection and process, (which seem-
ingly express intellectual, as aptly as sensible
ideas) are in the same predicament, because
they are traced at once to cunnecto, to tie
together ; and procedo, to yo forward. Rea-
son, too, 1 am confident, is a word of the same
stamp, though I cannot now recur to what
grammarians call its etymon, 7. e. its true or
proper meaning. Suppose, however, we allow
the word reason to mean, in its proper accepta-
tion, a faculty of the mind, yet, in the progress
of language, it becomes to be used in a trans-
ferred meaning, in several instances. By a
process, to be hereafter explained, it becomes
averb, I reason. It stands not only for the
act, but also for the thing acted or done, i.e.
the thing reasoned, the conclusion. It stands
likewise for cause or motive, as in the following

expressions: “ the sea arose by reason of 2

great wind ;” and, “ they received the men by

reason of their victuals.” It may sustain

other meanings; but it is not my object to
comprize them all. |

In the language of rude and savage nations,

the number of words, in a proper sense,
L2

84 On Ragheraie Language.

(extra ‘pgjaram) is small; but words used
figuratively, or ih a transferred ‘sense, are
endléss. With them, war is a fire, fire and
sword, a tempest, the red axe, according to the
view which they dre analogically led to take
Of it; peace is an olive-bianch ; ‘mourning is
sackcloth and ashes ; a dwelling or‘ habitation
js a seat; and so in’ instances almost iniu-
merable, if they were diligently sought.
Poverty of language necessarily requires the
\iseOf figuiative speech. ‘Ft will consequently
be found, that, in the progress of all languages,
in proportion as sensible objects are destitute
of names, figurative, or borrowed names, will
be used. "Though we are greatly removed
at’ present from this state of language, yet
Some traces of it may still be discovered, and
‘something analogous to it is still used. The
word | cation is used ‘for a law or Pule, and,
With an ithmaterial difference in the spelling,
for a large gun ; house is both a building and
@ family. "The ‘words place, post, rank, and
‘many ‘others, tedidus to enumerate, have the
Satie Vaiiéty-of ‘signification. “If lihguage is
hidw tinder the necessity of — recourse to
sly Awkwatd’eXpedients, we ‘nay well ima-
wine that that necessity was much more oe
‘ina Pider State.

‘Men, however, tiust havé cvstitiitly: endehi-

On Figurative Language. 85

youred to free language from these shackles.
From the:evident inconvenience and confusion
arising from a multiplicity of objects bemg
denoted by one name, facility and clearness of
conimunication required that they should, as
speedily as: possible, appropriate distinct names
to every individual object, as far as practi-
cable. Thus, if the word knave meant prima-
vily a labouring man ora servant, but cane
gradually to sigmfy a man basely dishonest,
from the prevailing character of that.class of
people in: fornzer times, this would clearly be a
transfered er figurative meaning; and if the
word. kxave happened in time to be entirely
discontmued in its primary or proper meaning,
the figurative one would appear and»come to
be cdnsidered as its: proper meaning. © For
which reason, every word thus appropriated,
became, as it) were, divested of ats figurative
imeanmg, and had a proper character of its
own ;°so thatit could not be applied to any
other ‘ebject, not even to that for which it
originally: stood, without again-sustaining a
figurative: character. -Knave, in the sense of
servant; is 2Ow an improper meaning, and the
transferred ‘sense of 'a vtan buscly dishonest,
must be regarded as its pr on extr afigurative
acceptation. | ,

To exemplify this: By another’ instanicé : : If

86 On Figurative Language:

we suppose that the word paz in Latin, ori-
ginally, in its proper sense, meant agreement,
and peace in a figurative one, from the circum-
stance that an agreement precedes peace ; but
that, in process of tune, another word, pactum,
came to be used for agreement, and pax was
confined to the meaning peace ; we imagine it
will be readily granted, that paar again
becomes figurative, when it is made to denote
any thing besides a termination of hostilities,
even if it were made to express that very idea
which it was originally used to convey.

We asserted above, that the first language
of men must have been nouns, or the names
of sensible objects,* because without these no
verbal communication can be attempted, or
even imagined. It is certainly possible for the
communication of ideas to be carried on by
means of nouns oply, when duly assisted by
the gestures and actions of the persons speak-
ing, and by indicial references, i.e. the.
pointing to different objects remarkable for
the quality or action meant to be expressed.
It is a circumstance of frequent occurrence
among rude or savage tribes, to have recourse
to actions significant of the meaning intended.

* Gen. ii. 20. And Adam gave names to all cattle, and te
the fowl of the air, and to every beast of the field.

On Figurative Language. 87

Thus the expression of burying the axe, used
among the American Indians, for making
peace, may be regarded as a sort of historical
_record of the circumstance being at some
former period actually transacted. We have
an account of something very similar to this
in the writings of the Jewish prophets.

But such a mode of communication is ex-
tremely imperfect and deficient, and could be
but of short continuance. Necessity plainly
‘required, that words should be used under
the character which distinguish verbs and
adjectives as parts of language. No commu-
nication, purely verbal, can possibly take place
without the use of adjectives and verbs, in
addition to nouns, or the names of things.

Here, then, a most important question im-
mediately oecurs—W hat is the origin of these
words? Did men absolutely invent names,
de novo, for qualities and actions? For in-
stance, when the word. fly, for the action of
flying, was first used as a verb, was it a verb
in its first utterance, and at the same time an
entirely new word, or was it the appropriation,
in a certain way, and according to certain prin-
ciples, of the name of the insect fly, to express
the action which it very frequently performs?
To me, the latter appears to have been the
¢ase, in all instances, in the formation of verbs ;

3

88 On Figurative Language,

and, consequently, every verb, as fay asiregards
its origin, is to. be considered, as’ a moun, ina
figuative or transferred, sense, It may,
indeed, be termied its, proper sense, as. soon as
its use a8 2 noun Js discontinued,;, or. when it is
accompanied with, circumstances plainly cha-
racteristie of a verb, (which cireustances are
hereafies tobe specified); but Jd ¢annot help
regarding all verbs m/ their origin, as nowns
m a transferred or. transformed sense. |.
Indeed, not only verbs, but all. words, under
whatsoever: division: of; the;-parts. .ef | speech
they may be classed,: were m:their original or
primitive state, the names of sensible objects..
| Whea weave occasion to.express amy new
or very untsual action, we never coin a new
word,’ properly .speaking, (as quinbus or
flestrin, as before) but we cither apply to some
existing noun the ¢oncomitants of verbs, as
at' snows, J: water, to place, they murmured,
&c.; or we add to nouns fragments of verbs
previously in use, as electrify, from scxrpv and
fio; scandalize, fron 'scandal:and %, a terni-
nation borrowed from the Greek.) 5
It is ‘a eurious speculation: to sinvestigate
what was.the actuabprocess in the distribution
‘and translation ‘of nouns into the other parts of
speech, i: e, into verbs, adjectives, pronouns,
and ‘prepositions: as to the adverb, it is

On Figurative Language. 89

included in the rest, A clear insight into the
nature and genius of language, will, I am
persuaded, détermine in favour of the hy-
pothesis, that all the grammatical divisions of
speech are, in thei origin, resolvable into
modifications of nouns.

A noun is converted into a verb, so as to
answer every practical purpose, whenever by
means of gesture, by peculiar utterance or
intonation, or by position in a sentence, it is
made to communicate the notion of motion or
action.

I beg leave to introduce here a short extract”
from Mr. Jones’s excellent Greek Grammar:
In explaining the origin of verbs, he says,
(page 132. 2d edit.) “We acquire the idea
of action, by reflecting on ourselves, or ob-
serving others, in certain circumstances; and
‘the most simple way which nature could at
dirst.suggest of expressing these ideas, was to
combine the name of the person or thing
which acts, with the person or thing
acted upon. Thus, om, and eye joined and
abbreviated, is ow; and this term would be
sufficient to express I drink wine, though
originally it meant only wine J; association
‘supplying to the speaker and the person
addressed, the intermediate notion of
drinking.”

; M

90 On Figurative Language.

From this explanation of the origin of
verbs, he draws the following conclusion :
“ Verbs were originally the names of things,
and received their character as verbs from
association.” (p. 133.) What Mr, Jones calls
association, 1 call translation, or change of
meaning, because it appears to me to approach
as near as possible to what the rhetoricians
have so denominated.

It is scarcely necessary to exemplify how
actions can be indicated by gestures; for who
can be ignorant of the inder, &{3>; of the
sign of silence, the finger on the lip, &c.? Ina
poor language it is well known how much
gesture assists communication.

If m the primitive state of a language a
person wished to inform another that a certain
man (Thomas) had escaped him, (John) by
running or starting swiftly from him, he
would, probably, for this purpose, select the
name of some well-known animal, remark-
able for the habitual practice of the action he
wished to express—we will suppose a fly—
and with appropriate gestures, express himself
thus: Thomas fly John. This is probably a
true history of the origin of the English verb
to fly. Thus, by peculiarity of utterance, or
greater intonation of voice, the name of any
object would be made to represent the action

On Figurative Language. 91

or property for which it was most remark-
able.

_ Lastly, it is easy to imagine how position
would change a noun into a verb, because it is
now practised very extensively in our own
language ; as is well exemplified in the follow-
ing expressions: Flag the floor; floor the
house; John, load the horse. Here flag,
floor, load, are verbs, merely by the position,
assisted, perhaps, by the utterance and into-
nation of voice. Sometimes it is not easy to
determine whether a word is a noun or a verb,
as in the sentence, “ Jol is prone to love.” —
But I forbear to produce examples.

Adjectives were originally formed from
nouns, in nearly the same manner as verbs.
A word closely joined to another in position
and utterance, would signify the addition of
its own most prominent attributes or proper-
ties. When, for instance, it was necessary to
call any man strong, or swift, the name of the
animals most distinguished for those qualities,
was joined to his name. Thus lion-man,
would obviously enough express the notion
of a bold, strong, and courageous man; and
swvallow—or swift man, signify a man that
can move with great rapidity. The adjec-
tiving * of nouns to nouns, in this manner, is

* A word used by Horne Tooke.
mM 2

92 On Figurative Language.

of extensive use in English, as in the follow-
ing expressions, and numerous other similar
ones: sea-water, dragon-fly, master-key, day-
light, &c. &e. Mr. Horne Tooke has very
fully explained this part of the subject.

The consideration of prepositions and con-
junctions, I think, may be safely omitted, as
the author just mentioned has demonstratively
proved them to be the fragments of other
parts of speech, especially of verbs, the de-
velopement of which has been already at-
tempted in this essay. I do not however
judge it amiss to add the following attestation
of Mr. Kirwan, to the truth of the theory :

The celebrated Mr. Horne Tooke, in a
very subtle and ingenious work, has shewn
that even those particles that denote the rela-
tion of objects, or of sentences, with each
other, originated from circumstances apparent
to the senses.” —Kirwan’s Logic, v. 1. p. 12.

In regard to the verb, substantive, and the
pronouns, I do not well see how they can be
traced to their sources, by the methodof the
formation of language now proposed ; nor
indeed am I acquainted with any satisfactory
theory of their formation. This, however, is
by no means sufficient to overpower the evi-
dence which has been adduced. It is only
a negative kind of objection. At best it is

On Figurative Language. 93

only an argument ex ignorantia. No one, I
suppose, will presume to say, that the pro-
nouns, and verb substantive, were at a certain
stage, in every language, coined by a council
of philologers, entirely de novo, from the
chaotic mass of unformed sounds. This
surely is wholly inadmissible. Their formation
according to the method here supposed, is as
probable as any other, if not more so. They
are words, which in comparison with the other
words of which speech is composed, are ex-
ceedingly few in number, and for that reason,
though abundantly useful, are the least neces-
sary for abridging the process of communi-
cation, and perhaps were of late invention.
By the same process, by which proper names
became appellatives, might names of very
frequent use, as nominatives to verbs, become
pronouns. Hence, it appears to me highly
_ probable, that pronouns are nothing but frag-
ments of some names or words of very fre-
quent recurrence, which men _ gradually
learned to substitute for the proper names of
the persons or things frequently repeated, and
by which they obviated a very evident and
awkward inconvenience.

If it be admitted, conformably to the theory
above stated, that the first language of men
was nouns, or the names of sensible objects,

94 On Figurative Language. cs

or in other words, that nouns form the ele-
ments of all language, and that these names,
appropriated to sensible objects, were trans-
lated, (to use the Latin term) not only to
signify other sensible objects of similar pro-
perties or form, but likewise to. express quali-
ties, actions, &c. as already pointed out, it
must follow of course, that all nouns, except
those used in a proper meaning, (0. e. ori-
ginally appropriated to sensible objects) that
all adjectives and verbs, without exception,
and, consequently, all the words derived from
them, are to be viewed originally as figurative
language; for the very essence of figurative
language consists in changing words from
their originally proper meaning.

As the purposes of communication thus
required words to be constantly used in a
figurative sense, 7. e. either as figurative nouns,
or as adjectives and verbs, it would happen in
various instances, from different causes,* that.
words came to be disused in a literal meaning,
and only the figurative use to be continued.
From the time of this change, their commenly
received meaning must be regarded as the
proper one, and every other meaning, even

Ss?
that in which they were originally used, as

* Those causes, whatever they be, which effect the con-
stant flux of language.

On Figurative Language 95

figurative. This might be exemplified in
numerous instances, but the selection of a few
will perhaps sufficiently explain my position.

The expression, I understand you, in its
originally literal meaning, is disused, and that
should be considered as its proper meaning
in which it is commonly used; and if any
person should now use it in the sense of
L bear you, or I stand under you, it would
plainly be considered as metaphorical.

The word extravagant, must once, in its
proper meaning, have signified smandering
beyond the ordinary, or allowed limits. But
having been long disused in this sense, its
proper meaning now is, wasteful and immo-
deraie in expence, &c. When, therefore, we
say of a man that he is an extravagant liver,
or extravagant eater, we use the word ina
proper meaning ; but we should express our-
selves in a manner highly figurative, however
agreeably to the originally unfigurative mean-
ing of the word, if we said that a prisoner is
extravagant when he breaks his prison ; that
a river is extravagant when it overflows its
banks*; or a horse if he broke from his
pasture.

*

———_ Vagus et sinistra
Labitur ripa (Jove non probante) uxorius amnis.—Hor.

é

56 On Figurative Language.

The analogies by which words may be
transferred from a proper meaning to 2
figurative one, are, in general, so obvious,
that there is no difficulty m applying a word
to a new meaning, nor in understanding the
application. Words, thus affected, are con-
stantly used by the speaker, and equally well
tinderstood by his hearers. In many; perhaps
in most instances, the analogies are so obvious,
that we are not aware, except by reflecting on
the subject, that the words used are diverted
from their proper extra-figurative signification.
Thus, for example, the expressions go on,
stop, though in their proper meaning they ap-
pear to be applicable to some kind of motion,
e.g. walking ; yet they are as readily applied
to the action of speaking, reading, writing, and
a variety of other actions, and are as easily
understood.

This is the natural, and indeed ‘the ne-
cessary progress of the creation of words m
the formation of a language. Were new
sounds ‘to be embodied on-every fresh occa-
sion, were it allowable on no emergency to
| adapt an old'word to anew meaning, language
would immediately become more unwieldy
than the armour of Goliah. As speech is now
managed, a speaker has no occasion to be at
a loss for the want of a word to express his

2

we

On Figurative Language. 97

ideas, because he has the choice of analogies
to an indefinite degree; and he is aware that
the person or persons whom he addresses, are
in the daily habit of deciphering the meaning
of words by such analogies, and that he is in
much greater danger of proving deficient in
invention, than his auditors in comprehension.
This habit of developmg the meaning of
figurative speech, we do not possess in any
great perfection, except in our vernacular
tongue ; or, at least, it is perfect, or otherwise,
in proportion to our acquaintance with any
particular language. And hence the fact is
easily accounted for, that, in the early progress
of learning any language, we are frequently
unable, by the mere help of a dictionary,
satisfactorily to develope the meaning of an
author. In every language, for various rea-
sons, the mode of metaphorizing, or using
figurative language, is, in a greater or less
degree, characteristic and peculiar. And
hence likewise arises the difficulty of using a
foreign dialect with propriety, either in dis-
course or writing, because We are in continual
danger of departing from the idiomatical mode
of metaphorizing customary in that dialect.
The evidence of the above theory, if it may
aspire to be so denominated, appears more or
N

98 On Figurative Language.

less as.we advance in developing and explain-
ing it; and if its reasonableness have. not
already appeared, it will be to little purpose
to seek for accessory or collateral — proofs.
The writer, however, would justly be charge-
able with want of respect to this society, if
not, of deference to his own opinion, if he
omitted some additional remarks which seem
further to. confirm what he has advanced.
Most. writers on rhetoric have been suffi-
ciently aware of the manner in which words
assume a metaphorical attitude, as may be in-
ferred from. the short extracts which were
introduced at the commencement. In con-
firmation, of which change of words from a
proper to a metaphorical meaning, the follow-
ing sentence may be quoted from Quintilian’s
Oratorical Institutes: “‘ Verborum vero figure
et mutate sunt semper, et utcunque valuit
consuetudo, mutantur. Itaque si antiquum
sermonem nostro comparemus, pene jam
quicquid Joquimur, figura est.”* There is a
passage in Dr. Blair’s Lectures on Rhetoric +
which seems still nearer to coincide with what
has been suggested in the foregoing pages.
“ In every language,” says he, “ there. are a
multitude of words, which, though they were
figurative in their first application to certain

* Quiatil. B. UX. c. IIT.—Gizson. + Lect. XIV.

On Figurative Language. 99

objects, yet by long use, lose that figurative
power wholly, and come to be considered as
simple or literal expressions.”

These authors, however, do not seem to
have been aware, that words, universally,
except those originally appropriated to

‘sensible objects, were sometime, and at

some given point in the progress of language,
figurative; that by common and exclusive
application to certain objects, figurative words

- become proper, and that they become again
- liable to the same laws of figurative applica-

tion to which words are liable in their origin-
ally proper state.
That this however is actually the case, may

be further shewn by an appeal to the progress

and state of those languages which are best
known. We shall discover that a great pro-
portion of every language consists of words,
which, however they may be regarded now,
were once metaphorical. Let us examine
whatever author we please, in prose or verse,
we shall not fail to be convinced of this fact.
I shall here beg leave to introduce a few in-
stances, merely by way of example.

Spirit, signifying breath, or life, or spiritual
existence, is only the word spiritus, wind, used -

metaphorically. Its appropriation, however,,

N2

100 On Figurative Language.

to that meaning, is so common, that it may be,
and is generally, deemed extrafigurative.
Ache was originally an exclamation expressive
of pain; by metaphorical transformation, it
came, in process of time, to signify pain itself:
The verb to bite, besides its common or proper
meaning, has a metaphorical one in the follow-
ing not uncommon expression, the biter is bit.
It formerly likewise had another metaphorical
meaning, still preserved in the compound
back-bite, which sigmifies to speak ill of a man
behind his back.

If we but open a system of geography,
and read but the definitions, we shall imme-
diately discover the method of metaphorizing
which I have been endeavouring to explain.
An isthmus is a neck or tongue of land, which
joins a peninsula to a continent. A gulf or
bay is an am of the sea which runs or stretches
into the land. A cape is a point or nose of
land which stretches out into the sea. In these
definitions, the use of the words neck, tongue,
jos, arm,. runs, nose, stretches, sufficiently
corroborates the foregoing obse’ vations.

It is generally acknowledged that the Greek
language is one of the most copious with
which we are acquainted, and yet it is well
known that its primitives are comparatively
very few. 'These two facts, seemingly incon-

On Figurative Language. 101

sistent, are in some measure accounted for by
the scheme of the formation and progress
above developed, and especially by the theory
of metaphorizing proposed. These, together
with the great facility of composition which
this language enjoys in an indefinite degree,
will sufficiently account for its wonderful
copiousness. |

The languages of barbarous nations, and
their modes of speech, as represented to us
in the fragments which are occasionally given |
by travellers and navigators, tend greatly to
corroborate the foregoing observations. These
fragments, however, it is not in my power
at present to collect, and I only refer to them
in general as sources of proof with which few
scholars can be unacquainted.

The imyvention of hieroglyphic writing,
which took place at a very remote period,
affords a further proof and illustration of the
foregoimg remarks. The symbol which stood
for any object, it is highly probable was only
a picture of the name which in spoken lan-
guage, by a metaphor, represented that object.
Thus, if imprudence was expressed in hiero-
glyphic writing by the picture of a fly, for
what other reason could it be, than because
imprudence was expressed metaphorically in

102 On Figurative Language.

oral language by the name of that little
animal ?

Words deriving their origin from a meta-
phorical source, are, without doubt, much
more numerous than we are generally aware
of. The names of all qualities and properties
were, when first applied to express those
qualities, used. in a figurative meaning ; and
to this class must be added all the names of
ideas which are denominated intellectual, as
has been stated in the foregoing pages. The
words round, square, hard, soft, high, low,
and all similar ones, it is highly probable,
(not to use stronger language) are of this
description; but the words affection, passion,
understanding, spirit, inspiration, perception,
invention, motive, habit, with many hundred
others, are so evidently in this predicament,
that no reasonable doubt can be entertained on
the subject.

Language is in a state of constant flux.
Words, in the progress of speech, are continu-
ally undergoing various and important changes.
These changes are beautifully described in
Horace’s Art of Poetry:

Ut silvis folia privos mutantur ia annos,
Prima cadunt ; ita verborum vetus interit <etas,
Et juvenum ritu florent modo nata vigentque.

On Figurative Language. 103

Mortalia cuncta peribunt ;
Nedum sermonum stet honos, et gratia vivax:
Multa renascentur que jam cecidere, cadentque,
Quz nunc sunt in honore vocabula.

As the knowledge of things is acquired
through the medium of words, it becomes
highly necessary for us to become acquainted
with the mamner in which, in the progress
of the developement of human reason, words
have been applied to things, how they become
the means of communicating thoughts and
trains of ideas, and in what manner the
structure of human speech has been built
from the time of laying the first rough stone
at the foundation, to the completion of an
useful and ornamental edifice. Our know-
ledge of words can by no means be deemed
perfect, except we are acquainted with their
various modifications and changes. | Though
we actually learn a language and the different
meanings of words in a manner very different
from this—and that too in a manner fully
adequate to all the useful purposes of life—
yet in attempting to reduce language to its
primary elements, and words to their original
sources, we must be able clearly to see the
whole course of their progress, their various
windings and deflections, their compositions

1

104 On Figurative Language.

and divisions, and, in a word, every mode in
which they have been affected.

How imperfect the foregoing attempt is, in
proportion to the importance and difficulty of
the subject, I am fully sensible. 'The exam-
ples for illustration in many cases, perhaps in
most, will not, I am afraid, be deemed very
fortunate. Researches into etymology have
been almost entirely overlooked: to pursue
them, indeed, was not by any means my prin-
cipal object. Fewer authors have been con-
sulted, or referred to, than is perhaps con-
sistent: with the importance of the subject, or
the respect which I owe to this society. But
these, and other imperfections, some of which,
perhaps would have been precluded had my
leisure and opportunities been more adequate
for the subject than they are, I have no doubt
the candour of the society will overlook. »

(105 »)

ON THE
MEASURE

‘MOVING FORCE.
BY MR. PETER EWART.

(Read Nov. 18, 1808.)
CWS

Ix the theory of mechanics, forces ate,
understood to be mathematical quantities,
capable of being measured and compared with
as much certainty as lines, or surfaces, or any
other mathematical quantities. Respecting
the principles, however, of this measurement _
and comparison, various doctrines have been
held. A controversy on this subject, after
having been long and warmly agitated by
learned men in different parts of Murope, ap-
pears, about seventy years ago, to have gradu-.
ally subsided ;* and since that Fe dade it has been
the eta opinion with mathematicians,

* Dr. Reid says, «it was dropt rather than ended, to the
no small discredit of mathematics, which bath always bozsted
of a degree of evidence inconsistent with debates that can ..
be brought to no issue.” Essay on Quantity. — Philosophical

Transactions, 1748,
oO

106 On the Measure of

that the argument respecting the measure of
the force of a body im motion, was merely
a dispute about terms, and that, though the
force in question may be variously estimated,
according to circumstances, it is most natu-
rally and consistently expressed by the product
arising from the mass being multiplied into its
velocity.

Although scientific men have, for more
than half a century, been generally satisfied
on this question, it must nevertheless be
acknowledged that considerable difficulties
have occurred in the practical application of
their measure of force; and, it is remarkable,
that the measure which they have rejected,
appears to have been first suggested to Hooke
and Huygens, by their practical observations
on the motion of pendulums, and was after-
wards adopted by Smeaton, as a rule for the
great operations in which he had so much
experience.

It is much to be regretted that theory should
appear to be at variance with practice, or that
any ambiguity should remain on a question of
such general application in mechanics.

{t has often been asserted, indeed, that
practical operations need not be affected by
differences of opinion about the measure of

force ; for, there being no disputed facts, the
A

Moving Force. 107

mere scientific explanation of the phenomena,
it is said, can be of little importance to prac-
tical men.

On this point, however, Mr. Smeaton’s ob-
servations merit particular attention. He
says, in reference to mistaken notions about
the measure of force, “that not only himself
and other practical artists, but also some of the
most approved writers, had been liable to fall
into errors, in applying the doctrines of force
to practical mechanics, by sometimes forget-
ing or neglecting the due regard which ought
to be had to collateral circumstances. Some
of these errors are not only very considerable
in themselves, but also of great consequence to
the public, as they tend greatly to mislead the
practical artist in works that occur daily, and
which require very great sums in_ their
execution.” *

Notwithstanding Mr. Smeaton’s excellent
experiments and observations on this subject,
exhibiting much want of agreement between
the theory usually given, and the practical
results, the mechanical principles of force
continue to be treated nearly as before; and,
I believe, we are not without recent instances
of errors similar to those which he has noticed.

* Philosophical Transactions, vol. 66. part 2d, p. 452.
Q 2

‘108 On the Measure of

/

Mr. Atwood, in his Treatise on the rectili-
near motion and rotation of, Bodies, bestowed
considerable attention on Mr. Smeaton’s ex-
perinmients and conclusions... He also observes,
‘that Emerson, and other authors of merit,
‘have been led into considerable errors, “by
supposing the momentum of bodies, to be as
the quantity, of matter into the velocity.*, In
that he agrees with Mr. Smeaton;. but he
afterwards concludes, that neither of the mea-
sures of force are capable of general applica-
tion, and that for one class. of the effects of
force, we have no proper measure,

After discussing various examples, of. force,
he proceeds as follows: ‘ But the truth is, the
principle’ (of permanent quantity) obtains not
according to either of the measures, except in
particular cases, which may be demonstrated
as the other properties of forces are from the
general laws or axioms.

“In the rectilinear motion of bodies, ac-
celerated from quiescence, or retarded until
they ave at fest, the permanency of any given
quantity of motion is demonstrated from the
axioms, whether that motion be estimated by
one measure or the other.

“In bodies which revolve round fixed axes,

* Treatise on Rectilinear and Rotatory Motion. Pre-
face, p. 10.

_ Moving Force. 109

the. principle obtains, without exception, when
the, momentum is measured by the quantity of
‘matter, into the square, of the velocity, but
fails when. measured by the quantity of matter
into the velocity,;.a given quantity of motion
thus estimated. being alterable in any assigned
ratio. hat )

., “In the communication of motion to bodies
by collision, when the direction of the stroke
passes through ths centre of gravity, the prin-
ciple in, question holds universally, according
to the measure of the mass into its velocity,
but fails when the momenta are estimated by
the, mass into the square of .the velocity, in
every case, except when both bodies are per-
fectly, elastic, or one perfectly elastic, and the
other perfectly hard.

és Lastly, when motion is communicated to
bodies by impact, the direction,,ef which
passes not through the centres of gravity, the
quantity of motion communicated, whether
_ estimated, by one measure or the other, pre-
serves neither equality nor any constant pro-
portion to the quantity of motion impressed.”*

These conclusions appear to be rather para-
doxical, but they are. neither new nor jun-
common.

* Treatise on Rectil. and Rotat. Motion, p. 366—368,

110 On the Measure of

It is true they have not been usually’ stated
in the same terms: but I believe the same
inferences strictly follow from the reasoning of
many other good writers on this subject. If
forces be mathematical quantities, we may
reasonably enquire how it is that they are so
indeterminate in relative magnitude ?

If two given lines, angles, surfaces, or
solids be equal, they are equal in whatever
manner they may be applied, or however they
may be measured. But if we have two given
bodies, moving with velocities inversely as their
masses, their forces, it would appear, are
either equal or unequal, according as they
may be classed under one or other of the
above subdivisions of mechanical phenomena.

If the forces of two given bodies in motion
are either equal or unequal, according to the
purpose ‘to which they may be applied, it
would’ be very desirable to have a complete
and accurate classification of all the pheno-
mena of force, exhibiting the variations to
which they may be subject ; and we are so far
indebted to Mr. Atwood, that he is, I believe,
the only author who has attempted to make
such anarrangement. But his arrangement is
not complete, for he has omitted to include
in it many important practical applications of
force ; such, for example, as the raising of a

Moving Force. 1i1

body to a given height, where it is to be left
at rest ;—the driving of piles ;—the overcoming
of friction ;—the grinding of corn ;—the ham-
mering and rolling of metals; and various
other applications of force of a similar kind.

Mr. Atwood appears, however, to have been
aware that the doctrines of force, as they are
usually treated, could not be of much service
in practice; for, a little farther on he observes,
“It is not probable, that the theory of motion,
however incontestible its principles may be,
can afford much assistance to the practical
mechanic; and there appears as little room to
imagine, that any errors or misconceptions
which may have been propagated concerning
the effects of forces considered in a theoretical
view, have at all impeded the due construction
of useful machines, such as are impelled by
the force of wind or water, by springs or any |
other kind of motive power. Machines of
this sort, owe their origin and improvement to
other sources: it is from long experience of
repeated trials, errors, deliberations, correc-
tions, continued through the lives of individu-
als, and by successive generations of them,
that sciences, strictly called practical, derive
their gradual advancement from feeble and
aukward beginnings, to their most perfect
state of excellence.”*

* Treatise on Rectil, and Rotat. Motion, p. 381

112 On the Measure of

But he has, in this instance, I apprehend,’
pressed his’ argument rather too far ; and he is
1, quite at variance with Mr. Smeaton, whio has
_-—- pointed out many inconsistencies in theoretical.

conclusions, which ‘have been carried’ into
practice with most injurious effects. *

It cannot be doubted, that i ingenious men,
of rare natural endowments, have, without
any scientific aid, accomplished wonders in’
the invention and improvement of machinery.

But how can it be supposed that these men
could have derived no assistance from a clear
- and sound knowledge of the principles of

es a

* See Philosophical Transactions, vol. 66, part 2d. p. 452,
&c. and the following note, ps 454. “ Belidore (Arch. Hydr.)
greatly prefers the application of water to an, undershot
mill, instead of overshot; and attempts to demonstrate,

that water, applied undershot, will do six times more exe-
ae ug ition than the same applied overshot. See vol. 1. p. 286.
ThileDe saguliers,endeavouring to invalidate w bat had been
: . I s088 by Belidore, and greatly preferring an overshot
. to an undershot, says, (Annotations on Lecture 12. vol. 2.
p- 532.) that from his own experience, “ a well-made over-
shot mill, ground as much corn in the same time, with ten
times less water ;” so that betwixt Belidore and Desaguliers,
here. is a difference of no less than 60 to 1.—Smeaton.

Each of these authors has been considered by many as -
the best authority for practical. men ; and their various in-
consistent rules have often been adopted, in the construction
of expensive machines, in this country, as well as on the
continent,

<i

Moving Force. 113

“mechanics? Every new combination pre-

‘sented to their minds must have involved them

in new and repeated labours to ascertain its
effects ; and these labours must have frequently
terminated in a conviction that their time and
pains had been wasted in examining old facts
under new appearances. Such disappoint-

ments have sometimes served indeed rather to

stimulate than to damp their zeal for making
farther discoveries. But if a good theory in
physical science be understood to comprehend
a distinct arrangement of what is known on
the subject; or if it furnish the means of ap-
plying the experience of one case so as to
determine the result of another of the same
kind, but different in degree, or under different
circumstances; it cannot be questioned that
such information must tend to shorten’ the
labours, and smooth the path of the ingenious
inventor ; and still more valuable must it be to
those whose task it is to distinguish the curious

from the useful, and to carry into execution

the real but not the fanciful improvements.
Neither does it appear that Mr. Atwood is
supported in his opinion, by the history of
useful discoveries in mechanics. If Huygens
and Hooke had not been scientific as well as
ingenious men, we might possibly have been
P

il4 On the Measure of

still ignorant of the properties of the balance
regulated by springs. If Smeaton had not
availed himself of just. theory, as well as ex-
periment, we might still have had to learn the

"principles by which we must be guided in

applying water to the best advantage as a
moving power. If a clear and strong under-
standing, and a mind richly stored with
scientific attainments, had not been combined.
with wonderful fertility of invention, in the
justly celebrated improver of the steam-
engine; incalculable labour might still have
been wasted in performing operations which
are now accomplished with as much ease and
regularity as the gentle motions of a time-
piece.

But if it were even granted, that all these
distinguished men might have attained their
objects without the aid of theory ; it must still
be acknowledged, that to those who have to _
follow their steps, and to apply their inventions
and improvements to various purposes, under
various circumstances, it must be of essential
importance to be free from perplexity in the
principles by which they must be governed ;

_ and it is under this impression that L have been

induced to state to this society some of the
difficulties which have occurred to myself, in
common, I believe, with many other practical

Moving Force. 115

men, in the application of the prevailing doc-
trines of moving forces; in the hopes that
others, better qualified for the task, may be
prevailed upon to reconsider the subject, and
remove the obscurities in which some. parts of
it appear to be involved.

{ shall first briefly describe some particular
cases where these difficulties occur, divesting
them as much as possible of all complicated
circumstances; and I shall be careful to state
such facts only as will be readily admitted by
any one moderately acquainted with the sub-
ject. Iwill then quote, from approved writers
on mechanics, such observations as appear to
have been given in explanation of the points
in question, accompanied with some remarks
which they seem to require; and I shall con-
clude, by venturing to offer some farther
explanations, which appear to me to be capable
of general application in mechanics.

‘ Examples of Force producing Motion in
* Bodies from a State of Rest.

1. If two balls, A and B, (figure 1.) whose
masses are as 1 to 4, be suspended like pendu-
lums; and if they be set in motion by two
equal weights, C and D, acting on them by
means of the bent levers, E and F, whose

P2

116 * On the Measure of

fulera are fixed, and whose perpendicular
arms are equal, but the length of the hori-
zontal arm of F’,. twice the length of the cor-
responding arm of E. If C descends through
the space S, D will descend through an equal
space in the same time; and by these equat
forces in equal times, A will have acquired

exactly twice the velocity of B. Now if

these effects are to be measured by the products
of the masses into their velocities, D produces
twice the effect of C, although their forces are
precisely equal.

In this and the following cases, the mass of
the lever, &c. is supposed to be indefinitely
small, when compared with that of the ball
which it moves.

2. If we suppose two balls, m and n, (fig. 2.)
whose masses are as 1 to 2, to be suspended as
in the last case, and put in motion by the
pressure of the atmosphere on the pistons
P and Q acting upon mand n, by means of the
levers GL and AB; A F being equal to BF,.
but G H=2 HI, and the area of the cylinder
E twice that of C ; supposing these cylinders
and the fulcra F and H to be immoveable,
and the.space under each pistonto bea vacuum.
Then E and C will move through equal spaces

in equal times, and m will acquire just twice:
the velocity of n.

Moving Force. iti

Here the force of P is twice that of Q, but
the effects of these forces, if estimated by the
product of each mass into its velocity, are equal.

3. In treating of rotatory motion ;—in find-
ing, for example, the centre of gyration of a
mass revolving about a fixed point, the rotatory
force of each particle is universally understood. ,
to be as the square of its distance from that
point, or as the square of its velocity. Ifa
body, A, (fig. 3.) be made to revolve about
the centre C, bya force acting at P; four times
that force, applied at the same point, P, will
be required to make a body, B, equal to A,
placed at twice the distance of A from C,
revolve with the same angular velocity, that
is, with twice the absolute velocity of A. Hf
both the bodies be disengaged from C, they
will each ‘continue to move with the same
velocity as before, but in rectilinear directions;
and then the force of B is said to be only
twice that of A. But it is not alledged that
A can gain, or B lose force, by the mere cir-
cumstance of being disengaged from C. How
then is this change in their relative forces

- to be accounted for ?

4. Let the lengths of the arms AF, FB,
(fig. 4.) of the balance beam, A B, be in the
proportion of 1 to 2, and let the weight of the
ball, m, be to that of n, as2tol. If they

or V\

118 On the Measure of

vibrate about the fixed fulcrum F, the quantity
of motion of m, will be equal to the quantity of
motion of n. Let CD be another balance
beam, and let CG and GD be each equal to
AF, and the weights of o and p be each
equal to that of m, and let A and C move with
equal velocities. If the quantity of motion
of m be equal to that of », the quantity of
‘motion of p must also be equal to that of n;
a 1 the sum of the quantities of motion of

9 and p must be equal to the sum of the

quantities of motion of m and x. But let
both beams be at rest, and let the pressure of
2 be applied for a given time to C, to generate
velocity in o and p; a pressure of 3 will be
required to be applied to A for an equal time,
and through an equal space, to generate an
equal velocity inm. The generating forces,
therefore, are as 2 to 3, although the quan-
tities of motion generated by these forces are
equal.

5. Let G (fig. 5.) be the centre of gravity
of two bodies, A and B, connected by an
elastic rod, at rest, but free to move in any
direction ; and let a given quantity of motion
be communicated at any point, D, ina direc-
tion at right angles to the rod, Mr. Vince has
demonstrated that the velocity of G will be

_ the same wherever the motion is communi-

Moving Force. 119

cated ;* that is, if a given force be applied,
or quantity of motion communicated at G, a
progressive motion of the mass, without any
rotatory motion, will be the result; but if the
same force be applied at any other point D,we
shall have the same progressive motion, and
a rotatory motion besides.

Is that rotatory motion produced without
force?

Examples of Motion destroyed, and of
. Motion transferred from one Body to
another.

*

G6. If the weight of the ball, A, (fig. 6.) be
to that of B, as 2 to 1, and if they move in op-
posite directions with velocities reciprocally as
their weights, and strike at the same instant
the ends of the spring, S. If the strength of
the spring be such, that the balls shall be at
rest when its ends. are brought to meet; they
will meet at E, DE being equal to 2CE.
Here the effect produced is the compression of
the spring. But though the quantity of motion
of A is equal to that of B, the portion of the
effect, produced by A, is less than that which is
produced by B.

If we substitute.for B a ball equal in weight

* Philosophical Transactions, vol. 70. p, 551,
1

Reo 7 On the Measure of 4 RE ene

and velocity to A, the ends of the spring will
not be brought to meet by the action of the —
balls. In that case, when the balls are at rest,
the distance between the ends of the spring
will be to C D, as 1.1 to 6 nearly.
7. Ifanon-elastic mass, A, (fig. 7.) moving
with a given velocity, strike an equal non-
elastic mass, B, at rest in free space; both
balls will move on together, with half the
velocity of A. Upon the principle of the
moving forces being as the quantities of mo-
tion, and the quantities of motion as the masses
into their velocities ; it is held that the moving
force of A is equal to that of Aand B, moving
together with half the original velocity of A.
If the ball B, have a spring attached to
it, furnished with a toothed catch C, to retain
the spring in the form to which it may be
compressed ; it will then represent a perfectly
non-elastic body. Let A strike the spring and
compress it to E, and let A and B move on
together, with half the original velocity of A.
Let the spring be then removed in its com-
pressed state, and placed between two other
balls, C and D, equal in their masses to A and
B, and at rest in free space; let the catch C,
be then disengaged ; the spring will resume its
original shape, and the balls, C and D, will
: each move off with half the original velocity

Moving Force. 121

of A; and we shall then have three masses
besides A, each equal to A, moving with half
the original velocity of A, and all of them
deriving their motion from the original force
of A.

8. Let A (fig. 8.) be a non-elastic soft mass,
uniformly penetrable by the cylinder c; that
is, the tenacity of the parts of A shall be such,
that c shall meet with the same resistance at
every point of its progress. Let A move with
the velocity v, in the direction AB, against
an immoveable obstacle, and be brought to
rest by forcing the length EF of the cylinder
into the ball. ‘That penetration of c¢ is, in this
instance, the whole effect produced by the
force of the motion of A. Let the operation
be repeated, but instead of an immoveable
obstacle, let B be a mass equal to A, in free
space, but not penetrable by c: then the cy-
linder will be forced into A a depth equal only
to EF, and when the side of A has arrived
opposite to H, the side of B will have arrived
opposite to I, (as represented at No. 2.) and
the velocity of both balls will be iv.

If we repeat the experiment with a ball of
half the weight, and twice the velocity of A,
striking B in free space, the effects will be very
different. We must then have a longer cylin-

Q

122 On the Measure of

der; for the length of it forced into the bail
will be —3 EF, and the velocity of both balls
after collision will be $v. It is not easy to un-
derstand how these last effects can be produced.
by a force no greater than the first.

9. It is argued that the mass into the velo-
city must, be the proper measure of the force of
a body in motion, because the sum of the pro-
ducts of the various masses of any system of
bodies into their respective velocities, is always
the same in the same direction, unless acted
upon by some external force. In other words,
because the motion of the centre of gravity of
any system of bodies cannot be changed or
disturbed by any action of those bodies upon
each other.

If two equal non-elastic balls A and B,
whose common centre of gravity is G, (fig. 9.)
move with the velocities and in the direc-
tions AC and BC, oblique to each other,
they will meet at C, and after collision they
will move on together with the velocity and
in the direction GC. If the product of the
mass into the velocity in the same direction
be taken as the measure of the moving force,
we have in the motion of these bodies, equal
effects of force before and after collision.
But it is obvious, that to produce the separate
motions of A and B before collision, much

= ’
al

Moving Force. 123,

greater force must be required than to produce
the motion of their joimt mass.

10. If two elastic equal balls E and F,
(fig 10: ) mov ing with the respective velocities
AC and’ ‘AB, at right angles to each other,
strike at the sameiastant a third elastic ball
A, equal to E or F; E and F will be brought
to rest, and A will move off with the velocity
and ‘in the direction AD. In this case, the
whole amount of the forces of E and F must have
been communicated to A; but the velocity
acquired by A is less than the sum of the velo-
cities of E and F.

(1. if the directions of E and F be not at
right angles, (as in fig. 11. ) the result will be
as follows: produce AB, and draw the per-
pendicular DG. After the str oke, the velocity

2AB x AD
of A in the direction A B, will be ~ AB LAG»

and E and F will each: continue to move in
AB x BG*
B+ AG.

In his case, as in all alias the velocity and
the direction of the centre of gravity of the
system is, no doubt, the same before and after

their fir st directions with the Vv elocity 3a AG a

* If BAC be an obtuse ‘angle, the same solution applies,
enly 2 aad F rebound instead of proceeding forward.
Q2

124 On the Measure of

collision. But that is only one feature of the
case. If we examine all the results after col-
lision, we shall find that the motion of A is not
the same as it would have been if it had been
struck by a mass equal to E+F, having the
same velocity as the common centre of gravity
of E and F before collision. If, however, we
reckon the forces as the masses into the squares
of their absolute velocities, we shall (if they be
‘perfectly elastic) always find that whatever
force is lost by the striking balls, is gained by
that which is struck.

12. Let four equal balls A, B, D, E, (fig.12.)
revolve about their common centre of gravity,
C. Let A and B be connected by a rod of no
sensible inertia, and D and E by a similar
rod, but unconnected with A and B. Let the
distance of the centres of gyration of A and B
be twice that of D and E, and let D and E
make two revolutions while A and B make
one. Ifthe balls and rods be elastic, and the
velocity of each ball 10, and if the rod con-
necting A and B be struck by the balls D and
E at their centre of gyration, the velocity of
A and B after the stroke will be 14, and that
of Dand E will be 2. If the balls and rods be
non-elastic, the velocity of A and B after the
stroke will be 12, and that of D and E, 6.

4

Moving Force. 125

In the first case, the sum of the products of
the masses into the squares of their respective
velocities, is the same before and after collision ;
but in the second case, that sum is less after
than before collision ; and it must, I presume,
be admitted, that the rotatory force in that case
is diminished by the collision.

13. If an iron prism AB, (fig. 13.) move-
able on a fixt centre at A, be let fall on a piece
of soft clay C, the greatest impression might be
expected to be made when the clay is placed
under P, the centre of percussion of the prism.
But if the experiment be made, the impression
will be found to be the same, whether the clay
be placed at C, D, or E, or at any other dis-
tance from the centre of motion.

14. Let two equal elastic balls A and B,
(fig. 14.) be connected by an elastic rod, and
be at rest in free space, and Jet G be their com-
mon centre of gravity. If another elastic ball C,
whose mass is equal to the joint masses of A,
B, and the rod, moving with the velocity
v in the direction C G at right angles to the
rod, strike it at G; C will be brought to rest,
and G will move off with the velocity v, in the
direction CG. But if we repeat the experi-
ment, applying the force of D instead of C,
the mass of D being equal to that of A or Band
half the rod ; and its velocity equal 2 v, striking

126 On the Measure of

A at its centre of gyration around the point, G,
the result will be as follows : D will be brought
to rest, G will move off as before with the
velocity v, and A and B will have a rotatory
motion about G, with the velocity v at their
centres of gyration. In both instances, the
striking forces, if measured by the masses into
their velocities are the same; and as the strik-
ing balls are in both instances brought to rest,

they must have communicated exactly their.

whole force to the mass which was struck.
The results, however, are far from being equal.
If the force of D be no greater than that of C,
we shall have the rotatory motion produced
without force, although we have no reason to
suppose that the rotatory can be produced
with less force than the rectilinear motion.

St

In order to avoid unnecessary calculations
or analyses, I have stated these cases in the
most simple forms I could devise. Iam aware
that there are many who think they may be

easily solved in the usual way, and that some .

of the cases will be considered as trivial para-
doxes. But if we examine the explanations
which have been given of similar cases, we
shall find that there is considerable diversity of
opinion about the principles by which they are
to be explained ; and that some of the solutions

_-

4
{
5
|
\

Moving Force. 127

are not quite so obvious as, at first sight, they
appear to be.

Before we enter upon the examination of
these particular cases, it may be proper to
observe, in addition to what has been already
noticed ; that, in respect to the general ques-
tion, or in respect to the existence even of any
question at all on this subject, some of the best
recent authorities are the most difficult to be
reconciled with each other.

Few authors, in our language, on the prin-
ciples of mechanics, have been more generally
read and referred to than Emerson. From
the great analytical skill of this author, one
would have expected something decisive on
the long pending question concerning the
measure of moving force; but he seems to take
for granted, that the measure is the mass into
the velocity or the momentum, for he scarcel y
condescends to mention the other, and after a
few observations, dismisses it in the following
laconic manner :—“ It seems to be a neces-
sary property of the vis viva, that the resist-
ance is uniform. But there are infinite cases
where this does not happen; and in such cases,
this law of the vis viva must fail. And since it
fails in so many cases, and is so obscure in
itself, it ought to be weeded out, and not to
pass for a principle in mechanics.”’*

* Emerson’s Principles of Mechanics, p. 20.

128 On the Measure of

Mr. Atwood, however, has shewn that Mr.
Emerson himself has been led into error, by
neglecting this very principle which he pro-
poses to weed out. In reference to a particu-
lar problem, he says, “ In Emerson’s Fluxions,
p- 177,* there is this problem: 'The radii of a
wheel and axle are given in the proportion of
b:a; aweight w acting by means of a line on
the circumference of the wheel, elevates a
weight y suspended from a line which goes
round the axle; it is required to assign the
quantity y, when y x into its velocity gene-
rated in a given time, is the greatest possible.”

«In the solution, the author supposes the
momentum of bodies to be as the quantity of
matter into the velocity generated; and ac-
cording to the usual doctrine of momentum,
assumes it as an universal truth, that if a force
acts on any different quantities of matter for a
given time, it will always generate the same
moment, estimated by the quantity of matter
into the velocity. From this reasoning
he deduces the weight sought, Ya 2-1 x2

b+ hsb
when its true value is y=wxX ery gee Ts
(page 249.) agreeing with the former only in
the extreme case when b=a, that is, when the
yadius of the wheel is equal to that of the

axle.” +
* 2d Edit. + On Rectilineal Motion, Preface, p. x.

Moving Force. 129

Mr. Smeaton, at the commencement of the
description of his experiments on water-wheels,
says—‘ The word power, as used in practical
mechanics, I apprehend to signify the exertion
of strength, gravitation, impulse, or pressure,
so as to produce motion.’”’* And near the end
of his “ Experimental Examination,’ we have
the following conclusion :—

“ It therefore directly follows, conformably
to what has been deduced from the experi-
- ments, that the mechanic power that must of
necessity be employed in giving different de-
grees of velocity to the same body, must be as
the square of that velocity.” And in the next
page he observes, “It seems, therefore, that
without taking in the collateral circumstances
both of time and space, the terms quantity of
motion, momentum, and force of bodies in
motion, are absolutely indefinite; and that
they cannot be so easily, distinctly, and funda-
_ mentally compared, as by having recourse to
the common measure, viz. mechanic power.” +

M. De Prony, however, gives a different
conclusion, as follows: “ I] y a eu des disputes
trés vives parmi les mathématiciens pour sayoir
si on devoit faire la force d’un corps en mouve-
ment proportionelle a la vitesse ou au quarré

* Philos. Trans. 1795, p. 105. 4 Ibid, 1776, p. 473.
]
R

130 ' On the Measure of

de la vitesse: il est bien aisé, d’aprés tout ce
qui précede, de réduire la question a un énoncé
raisonnable qui en suggérera sur-le-champ la
solution. Le mot force ne désignant qu'une
cause dont la nature est inconnue, et dont les
effets sont les seules choses que nous puissions
mesurer, il est clair qui par ce mot mesure de
la force, on ne peut entendre que celle d’un de
ses éffets; or ces effets pouvant se considérer
sous différents aspects, chacun comporte une
espece de mesure particuliere et conforme a sa
nature. Cela posé, si l’on considere l’effet de
la force comme consistant dans la destruction
d’une certaine somme d’obstacles ou de quan-
tités de mouvement, cette somme est propor-
tionnelle a la simple vitesse. Si on ne considere

point leffet de la force relativement a la .

somme des obstacles vaincus, mais relativement
a leur nombre, ce nombre sera proportionnelle
au quarré de la vitesse lorsque tous les obstacles
seront égaux.* .

* What is here meant by the sum and the number of
obstacles, is not very obvious, That explanation has, how-
ever, been adopted by various other authors. Jt appears to
have originated with D’Alembert, who states it thus: “ Done
dans l’équilibre le produit de la masse par la vitesse, ou ce
qui est la méme chose, la quantité de mouvement, peut
représenter la force. Tout le monde convient aussi que
dens le mouvement retardé, le nombre des obstacles vaincus
est comme le quarré de la vitesse ; ensorte qu’un cerps qui a

’
f

Moving Force. #3

‘Qn voit par-la que la fameuse question des
forces vives n’est qu’une dispute de mots qui
n’auroit jamais subsisté si l’on avoit voulu
s’entendre, c’est a dire analyser et definir.’’+

fermé un ressort, par example, avec une certaine vitesse,
pourra avec une vitesse double fermer, ou tout a la fois, ou
successivement, non pas deux, mais quatre ressorts sem-
blables au premiere, neuf avec une vitesse triple, & ainsi
du reste.”———“ I faut avouer cependant, que Popinion de
ceux qui regardent la force comme le produit de la masse
par la vitesse, peut avoir lieu non-seulement dans le cas de
Véquilibre ; mais aussi dans celui du mouvement retardé,
si dans ce dernier cas on mesure la force, non par la quantité
absolue des obstacles, mais par la somme des resistances de
ces mémes obstacles. Car on ne sauroit douter que cette
somme de résistances ne soit proportionnelle a la quantité
de mouvement, puisque, de l’aveu de tout le monde, la
quantité de mouvement qui le corps perd 4 chaque instant,
est proportionnelle au produit de la resistance par la durée
infinement petite de l’instant, & que la somme de ces
produits est évidemment la résistance totale: Toute la
difficulté se reduit done a savoir si on doit mesurer la force
par la quantité absolue des obstacles, ou par la somme de
leurs résistances. _ Il paroitroit plus naturel de mesurer la
force de cette dernier maniere, &c.”* — But it should be
remarked, that although equal quantities of motion are lost
‘in equal times, it is not universally acknowledged that these
equal times denote equai quantities of force, or equal
quantities of resistance. That indeed is the very question.
at issue.

* Traité de Dynamique Discours Prelim.p.20 et 21..
+ Arch. Hydr. p. 24.
R2

a
132 On the Measure of

- Qn the other hand, Dr. Milner, of Cam-
bridge, holds, “ that it is plain, that if any one
contends for the equality of action and re-
_ action, and explains those terms by the change
_ produced in the absolute forces of bodies, the
dispute is not merely verbal.”* And again,
he says, “some writers have considered this
question as entirely verbal, and have affected
to treat the advocates on both sides with the
greatest contempt. Such persons save them-
selves a great deal of trouble, and have the
credit of seeing farther into the controversy
than others; but after all, I am afraid the
practical mechanic will receive little intorma-
tion or security from such speculations.” +
Dr. Wollaston’s opinion is, that “the con-
ception of a quantity dependent on the continu-
ance of a given vis motria for a certain time
may have its use, when correctly applied, in
certain philosophical considerations ;. but the
idea of a quantity resulting from the. same
force exerted through a determinate space is
of greater practical utility, as it occurs daily
in. the usual occupations of men.’{ And
he concludes his lecture on the Force
of Percussion thus: “In short, whether we

* Philosophical Trans, 1778, p. 377." + Ibid p. $78.
t Philos, Trans. 1806; p. 15.

Moving Force. 133

ave considering the sources of extended exer-
tion or of accumulated energy, whether we
compare the accumulated forces themselves by
their gradual or by their sudden effects, the
idea of mechanic force in practice is always
the same, and is proportional to the space
through which any moving force is exerted or
overcome, or to the square of the velocity of a
body in which such force is accumulated.”
This conclusion coincides nearly with Mr.
Smeaton’s, but still it remains to be explained
how two given quantities of foree may, con-
sistently, be considered as equal to each other
for philosophical purposes, but unequal for all
practical purposes.

The Edinburgh reviewers of Dr. Wollaston’s
lecture, adopt a different doctrine. In refer-
ence to the first passage quoted above, they
say, “ Now, with the judgment here given as
to the respective utility of the two measures of
the force of moving bodies, we cannot entirely
agree ; though we differ from Dr. Wollaston
with considerable diffidence; and the more,
that his opmion is supported by one of the
greatest authorities in practical mechanics of
which this or any other country can boast—
the late Mr. Smeaton.”* And after some

_ | * Edinb. Review, vol. 12, p. 122, .

134 On the Measure of

remarks on supposed errors of Mr. Smeaton, —
which I shall have occasion to refer to again,
they say, “ 'T'o whatever cause, therefore, the
imperfection of the theory of the machines
moved by water is to be ascribed, it is not to
any thing that would be corrected by the
introduction of a measure of force different
from that which is commonly in use.”* At
the beginning, however, of the same article, |
they give the following opinion: “It is no
longer doubted that this force (of percussion)
may, with perfect truth, be considered as
proportional, either to the quantity of matter
multiplied into the velocity, or to the quantity
of matter multiplied into the square of the
velocity, according to the nature of the effect
which it is destined to produce.” +

On the subject of forces, M. Laplace ex-
presses. himself as follows: “La force peut
étre exprimée par une infinité de fonctions de
la vitesse, qui n’impliquent point contradiction.
Iln’y en a point, par exemple, a la supposer
proportionnelle au carré de la vitesse.” t After
stating a hypothetical example of force, where
the results would be different from those of
experience, but where the square of the velo-

* Edin. Rev. vol. 12, p. 126. + Ibid. p. 120.
£ Systeme du Monde, 3d edit. Livy. III. ch. 2, p. 141.

Moving Force. 135

city is taken in a sense quite different from
that in which it appears to have been under-
stood by every other author I have had an
opportunity of consulting, he proceeds :—

_ Parmi toutes les fonctions mathématiquement

possibles, examinons quelle est celle de la na-

”

ture.
various effects of force he concludes, “ Voila

And after reasoning at some length on

donc deux lois du mouvement, savoir, la lois
d’inertie et celle de la force proportionnelle a
la vitesse, qui sont données par l’observation.
Elles sont les plus naturelles et les plus simples
que l’on puisse imaginer, et. sans doute, elles
dérivent de la nature meme de la matiére ;
mais: cette nature étant inconnue, ces lois ne
sont: pour nous, que des faits observés, les

seuls, au ai Bs la mécanique emprounte

de l’expérience.’’*

It appears then to be the opinion of this dis-
tinguished philosopher, that, although it may
be mathematically possible for the force of a
body in motion to be-proportional to the square
of its velocity, yet such a principle is incon-
sistent with the phenomena of nature; but
that the law of imertia, and the law of force
proportional to the velocity, are the most natu-
tural and the most simple principles imagin-
able, that they are derived from the very

* Systéme du Monde, p. 144.

136 On the Measure of

nature of matter, and that they are the only
facts which the science of mechanics borrows
from experience.

It may be proper to observe here, that M.
Laplace adopts as first principles, only the two
first of Sir Isaac Newton’s laws of motion.

It is surprising that so many different opini-
ons on this subject should still be held, and it
is not easy to understand how so many good
reasoners have, from the same data, drawn
conclusions so much at variance with each
other.

Fifty years ago, M. D’Alembert, speaking
of the science of mechanics, observed, “that
“En général, on a été plus occupé jusqu’a
présent 4 augmenter l’édifice qu’a en’ éclainer
Ventrée; et on a -pensé ‘principalement: a
l’élever, sans donner a sés fondemens toute Ja
solidité ‘convenable.’’*

No one will deny, that, during the last fifty
years, great advances have been made in
the application of mechanical principles to the
investigation of the motions of the heavenly
bodics. But as far as these principles have
been adapted to practical uses, may not) M.
D’ Alembert’s observation be with seme justice
applied to the present state of mechanical
science? or may it not be said, that, not only

* Tyaité de Dynamique, Discours prelim. p. 4.

Moving Force. 137

the entrance, but the interior of the structure
is not very conveniently arranged for the occu-
pations of life?

But there is another observation of M.
D’ Alembert, which has, on the present occa-

sion, still stronger claims on my attention.

He says, “mais il semble que la plipart de
ceux qui ont traité la question de la mesure
des forces, ayent craint de la traiter en peu de
mots.”

Although the censure be severe, it may be
just, and [I shall endeavour to profit by it.
Some repetitions, however, in discussions of
this kind, are unavoidable. .

In the observations which I have made, as
well as in those which I have still to make on
various passages in some of the best authors

_on mechanics, I hope to escape the charge of

being in any degree disrespectful towards
them. Iam sensible that any remarks having
that tendency would ill become me, and could
be of no availin my argument. Anxious as I
am to state distinctly the reasoning and the
conclusions which appear to me to be ob-
jectionable, I am not less anxious to state them
fairly and respectfully. I am well aware of
the disadvantages under which I labour ; the
general prejudice against this subject being so
strong, that a great national institution has
$

138 On the Measure of

absolutely proscribed the discussion of it.*
That circumstance, however, enhances the
value of the indulgence, of which I now avail
myself, in submitting it to the considera ation of
this society.

Proceeding now to the consideration of the
particular cases which I have described, I
may observe, that the first two cases (p. 115.)
comprehend, I believe, the chief points at issue,
as far as they relate to force producing rectili-
near motion by the intervention of levers or
wheels, and to motion produced about fixed
axes.

That the forces of C and D in the first case
are equal, cannot, I think, be questioned ; and
it is not less obvious that their effects, if esti-
mated by the masses into the squares of their
velocities, are also equal.

In the second case, the force of P is twice
that of Q, and the effects of these forces, if ,
measured by the masses into the squares of
their velocities, are respectively in the same
proportion.

Mr. Atwood (as we have already noticed at
page 109) admits, that the measure composed
of the mass into the square of its velocity

* The French National Institute has, I understand, pro-
hibited the reception of all dissertations on the measure
of force,

Moving Force. 139

obtains in all cases of rotatory motion about
fixed axes; and that the measure composed of
the mass into its velocity, when applied to the
same cases, fails ; “a given quantity of motion
thus estimated, being alterable in any assigned
ratio.”

But authors on mechanics generally concur
in the following conclusion: that “a distinc-
tion is always to be made between the actions
of bodies when at liberty, and when they
revolve about a centre or axis. In the first
case, the motion lost is always equal to the
motion communicated m an opposite direc-
tion: m the second, the motion lost is to be
encreased or diminished in the ratio of the
levers before it will be equal to the motion
communicated.”’*

We do not find, however, that the absolute
forces, or their effectt$_can be encreased or
diminished by any alteration in the lengths of
the levers. For if the arm H G, for example,
be extended to any assumed length, the same
velocity will still be produced in m by the
motion of P through the same space. It is
true the velocity will not be produced in the
same time ; but the result will be the same, in
whatever time, or by whatever complication of
levers or wheels, it may be produced.

* Dr. Milner. Philos. Trans. 1776, pe 371.
$2

140 On the Measure of

The converse of this case is stated by Dr.
Wollaston, as follows: “ It may be of use also
to consider another application of the same
energy, and to shew more generally that the
same quantity of total effect would be the con-
sequence not only of direct action of bodies
upon each other, but also of their indirect
action through the medium of any mechanical
advantage or disadvantage ; although the time
of action might by that means be encreased
or decreased in any desired proportion. For
instance, if the body supposed to be in motion
were to act by means of a lever upon a spring
placed at a certain distance from the centre of
motion, the retarding force opposed to it
would be inversely as the distance of the body
from the centre; and since the space through
which the body would move to lose its whole
velocity would be re lly as the retarding
force, the angular motion of the lever and
space through which the spring must bend,
would be the same, at whatever point of the
lever the body acted.”* Practical men are
much beholden to Dr. Wollaston. He is, I
believe, the only author, professedly on the
theoretical principles of mechanics, who has
written decidedly in support of Mr. Smeaton’s

* Philos. Trans. 1806, p. 21.

<_<

Moving Force. 141

conclusions, and we have only to regret that
he has not pursued the subject farther.

If the amount of the force could be encreased
or diminished by any variation of the length of
the lever, we might expect to find its measure
to be of that indefinite kind which might be
estimated by the product of the mass into any
function of its velocity. Such a conclusion,
however, is quite inconsistent with experience ;
for under every variation of the proportions
of the lever, the effect, if measured by the mass
into the square of its velocity, is uniformly
found to be in proportion to the moving force
by which it is produced; if that force be
measured by the pressure multiplied into the
space through which it acts. But if we
multiply the mass into any other. function than
the square of its velocity, no such general cor-
respondence between the force and its effects
is to be found.

Mr. Smeaton has well illustrated this prin-
ciple by many valuable experiments on the
more complicated cases of the action of water
on mill-wheels, and on force generating: rota-
tory motion in masses of matter about fixed
axes. *

The Edinburgh reviewers of Dr. Wollaston’s
lecture on the force of percussion, have urged

* See Philos. Trans. for 1759 and 1776,
1

142 On the Measure of

some strong objections against Mr. Smeaton’s
conclusions. I would willingly excuse myself
from venturing to controvert any thing in a
criticism written with so much candour and
ability; but some of the arguments it contains
are. pressed so powerfully against the applica-
tion of the square of the velocity of a body
in motion as the measure of its force, that
they must, I apprehend, be answered before
that measure can be consistently defended.

In the first place, it is argued, that the
principle which Mr. Smeaton understood to be
confirmed by the result of all his experiments,
“is in fact abandoned by him at the very
outset of ‘his investigation, in consequence of
having included the time in the measure of the
effect.”* Now, I do not see how this supposed
contradiction in Mr. Smeaton’s reasoning can
possibly be maintained. 'The measure of me-
chanical power adopted by him, consists of the
pressure multiplied into the space through
which it acts. In cases where the pressure
moves through equal spaces in equal times, it
can make no difference whether the time or the
space be taken as an element of the mechanical
power ; and when, in such cases, Mr. Smeaton
takes either of these, it does not follow that
he abandons the other.

* Edinb. Review, vol. 12, p. 123.

| Moving Foree. 143

He does not say that the consideration of
the time is necessarily excluded, he only says
it is not necessarily included in the estimation
of mechanical power; and he has (at the
_ conclusion of the passage referred to by the
reviewers) taken care to discriminate ‘the par-
ticular cases in which the time may or may
not be so taken into consideration. He says,
“ but nofe all this, (relating to the quantity of
power expended in raising a known weight
with a uniform velocity to a known height) is
to be understood in the case of slow or equable
motions of the body raised ; for in quick, ac-
celerated, or retarded motion, the vis inertia,
of the body moved will make a variation.’’*

He might indeed, consistently with his
‘principles, have excluded altogether the con-
sideration of the time in which any mechanical
effect is produced. For, according to these
principles, the same quantity of mechanical
power is required to raise a given weight to a
given height, in whatever time it may be
effected, or whether the motion be equable
or not, provided that the velocity of the weight
at the beginning and the end of the operation

be the same.t Accordingly he says, “from

n

* Philosophical Trans, 1759, p. 106.

t It is, I presume, hardly necessary to say, that when the
motion of the weight is so quick as to make the resistance of

144 On the Measure of

the whole of what has been investigated, it
therefore appears, that time, properly speaking,
has nothing to do with the production of me-
chanical effects, otherwise than as, by equally
flowing, it becomes a commen measure ; so
that whatever mechanical effect is found to be
produced in.a given time, the uniform con-
tinuanee of the same mechanical power will,
in a double time, produce two such effects, or
twice that effect. A mechanical power, there-
fore, properly speaking, is measured by the
whole of the mechanical effect produced, whe-
ther that effect is produced in a greater or
lesser time.”’* From the context, it is obvious,
that by “ the uniform continuance of the same
mechanical power,” he means a continuance of
an uniform pressure moving through equal
spaces in equal times, and he considers that to
be a perfect uniformity of action.

It should be observed, that, a weight raised
to a given height, and velocity generated in a
given mass, are two very different effects of
mechanical power; but the measure, com-
posed of the pressure into the space through
which it acts, applies equally to both of them.

the air, or any other medium through which it moves, con-
siderable, other effects besides the mere raising of the
weight, must be taken into the account.

* Philos. Trans. 1776, p. 473.

Moving Force: 145

When velocity is generated, the mass into the
square of the velocity is always in the ratio of
the pressure into the space ; but when a weight
is raised with an uniform velocity toa given
height, it has never, I believe, been contended
by any one, that the absolute quantity of
mechanical power necessary to produce that
effect, or the ascensional force, as it was deno-
minated by Huygens, must be as the square of
the velocity with which the weight rises.
Such a conclusion would indeed be quite in
contradiction to the principle of the me-
chanical force being as the square of the
velocity generated.

Mr. Smeaton’s meaning will appear still
more distinctly, perhaps, if we attend to the
particular case he was treating of in the pas-
sage objected to by the reviewers. His object
was to ascertain the mechanical power of a
given quantity of water moving with a given
velocity. In order to do this, he constructs an
apparatus by which it may be determined to
what perpendicular height. a known weight
may be raised with an uniform velocity by the
action of that given quantity of water ; and he
considers the product of the weight multiplied.
into the height to which it is raised; or, in
other words, the pressure into the space
through which it acts, as. the proper measure

T

146 “On the Measure of

of the effect produced. The current of ‘thie
water being uniform, he first ascértains (by
means of a ‘punip which supplies it) the quan-
tity which passes in one minute, and ‘then he
makes various experiments to ascertain the
greatest effect that can be produced hy that
quantity, by merely multiplying, after every
experiment, the weight into the height to
which it is raised in a mintite. ‘Now the time
of one ‘minite is taken merely because it is
known that a certain quantity of ‘water passes
m that time—the effect which is to be esti-
mated, being produced in the same ‘time.
But the time is by no means a ‘necessary
element in the estimation of the effect ; for the
height to which a weight is raised by any other
given quantity of the running water, may
easily be determined without reference to the
time, and the result will be the same as when
the time is considered. “Let p, for example,
represent the power, that is, a given quantity
of water moving with a given velocity, and’e
the effect, or the product of the weight imto the

height to which it is raised by that power, —

without any reference to the time in which it is
raised. “Let p’ be any other quantity of water
moving (for the sake of simplicity) with the
saine velocity, and e’ its effect. Now, if the
power be equally well applied in both cases,

Moving Force. 147

and if we have adopted a proper measure
in estimating the effect, we shall have

— It is obvious that this equation will

constantly be found by Mr. Smeaton’s method,
and we must therefore conclude that he has
adopted the proper measure of the force.

But Mr. Smeaton’s reasoning is farther ob-
jected to as follows: “ His second general
maxim is, that the expence of water being the
same, the effect will be nearly as the height of
the effective head, or (as it is expressed in -
maxim third) as the square of the velocity of
the water. This conclusion seems, at first
sight, quite in favour of the theory of mechani-
cal force, as laid down by our author, and the
other supporters of the vis viva; and yet we
shall presently find, that it 1s perfectly con-
formable to the other theory, ‘and to those
reasonings of Desaguliers and Maclaurin,
which Mr. Smeaton has censured, as leading
to conclusions altogether wide of the truth.”

«“ Let c be the velocity of the stream, v that
of the wheel, A the area of the part of the
float-board immersed in the water, g the velo-
city which a heavy body acquires in one
second when falling freely. Then c—v will
be the relative velocity of the stream and the
wheel,or the velocity withwhich the water strikes
the wheel; andif we take /, a fourth proportional

T2

148 On the Measure of

to g*, (e—v)* and 39, h will be the height from
which a body must fall to acquire the velocity
c—v, and will be=“—**. Wherefore, by a

proposition, well known in Hydraulics, the
circumference of the wheel is urged by the
weight of a column of water, of which the
section is A, and the height on and of

which the solidity is therefore Ax oon

&
Thus far the inyestigation is applicable to all
undershot wheels, and to all hydraulic engines
of a similar construction.” *

Now, before we proceed to the remainder
of this demonstration,t which is grounded
upon the supposed certainty of this last con-
clusion, let us see how far this theory agrees
with the results of Mr. Smeaton’s experiments.

Let w represent the weight of the column,
the solidity of which is expressed by A x —?)® ee

The value of w in Mr. Smeaton’s ee
is easily found; and he has furnished data by
which we can determine nearly the pressure
by which the circumference of the wheel is
urged. Let p represent that pressure; then,
if the experiments agree with the theory, we

* Edinb. Review, vol. 12, p. 124.

+ Namely, that the maximum effect must be produced ;

when v=3e, and that it is proportional to c?.

a i a i i i li i)

Moving Force. 149

should always have p=w. But we shall look
in vain to the results of Mr. Smeaton’s experi-
ments for this equation. I subjoin the com-
parative values of p and w, calculated from
Mr. Smeaton’s first table of eight experi-
ments :*

Exper. !. p = 2.3w
2. p= 2.370
3. p = 2.15
A. p = 2.22m
5. p = 2.16
6. p = 2.11v
7. p= 2.0lv
8. p= 1.85w

And in the 27th Ex. p. 115, we have p = 2.7.

‘If these results be correctly stated, Mr.
Smeaton might truly say, that he “found these
matters to come out in the experiments, very

* If Mr. Smeaton’s reduction of his 5th Experiment,
page 112, be compared with the table page 110, it will
appear, that he has omitted to include in the quantities set
down in the table, the weight of the scale, pulley, and
counter-weight. In finding the value of p, I have, in each
experiment, taken twice the weight of the scale and pulley,
added to the counter-weight, to be equal te 1.37 Ib. which
will be near enough for the purpose of comparisen.

It should be observed also, that if the table had been
made out in the same way, the fourth experiment would
have given the maximum effect.

150 On the Measure of

different from the opinions and calculations
of authors of the first reputation.”*

It is true, Mr. Smeaton’s maxims agree
with some of the results brought out by the
common theory. His maxims, however, are
by no means the most important conclusions
which he has drawn from the results of his
experiments; neither can 1 agree with the re-
viewers in supposing that he considered these
maxims to be inconsistent with the common
theory. Ifit were admitted, according to the
theory, that the pressure at the circumference
of the wheel is always as Ax(c—w)” we can
hardly suppose Mr. Smeaton to have been so lit-
tle acquainted with the principles of calculation
as-not to have been aware that the maximum
effect must. consequently be as Axc*. The
principle of the ws viva agrees still more
remarkably with the common theory in cases
of rotatory motion generated about fixed axes,
as I have already observed at page 117. But,
although the rotatory force of a body in motion
is, according to the common theory, as the
square of its velocity, [do not see why that
agreement with the principle of the vis viva
should be brought as an objection against it.
The chief object in discussion is to ascertain

* Philos. Trans. 1776, p. 457.

Moving Foree. 151

upon which principle the most consistent
explanation of the facts is to be obtamed m
cases where the two measures disagree.

It appears to me that Mr. Smeaton’s four
maxims on undershot water-wheels may all be
comprehended in one, expressed thus : That in
cases where the maximum effect is produced, tt
is nearly as the quantity of water multiplied
by the effective head.* But the theory is
founded on the supposition that in all cases the
pressure at the circumference of the wheel is
as (c+v)*, and if it were so, the maximum
effect would, no doubt, be produced when
v=tc. Bythe mere inspection, however, ‘of
the results which I have stated above, it will be
seen that the pressure at the circumference of
the wheel is not as (c—v)* and therefore, the
maximum effect cannot be produced when
the wheel moves with one-third of the velocity
of the water.

‘I have to regret that I cannot ‘at present
refer to M. Bossut’s experiments on water-
wheels. It is observed, however, by M.du Buat,
that according to these experiments, the maxi-
mum ‘effect was produced when the velocity of
the wheel was 4 that of the water, which corre-

* Tt should be observed,’ that the maximum effect was
not always produced at the same relative velocity.

152 On the Measure of

sponds very nearly with Mr. Smeaton’s con«
clusions. ) rH0td

From that result, M. du Buat concludes that
the pressure at the circumference of the wheel
is as (c—v)**. After highly commending the
experiments and observations of M. Bossut,
M. du Buat continues: “ Nous avouons néan-
moins, a regret, que, quelque nombreuses et
variées qu’elles soient, elles ne sont pas encore
suffisantes pour étre applicables a tous les cas.
Ce ne sera qu’aprés en avoir fait de nouvelles
sur le méme plan, et en avoir rapporté les
résultats a quelque loi d’approximation simple,
telle que celle que nous avons exposée, qu’on
pourra. espérer de donner des régles pratiques
propres a guider les artisans auxquels ces
sortes de constructions sont abandonées.’’t
This observation well merits the attention of
every writer on theories of hydraulics, ,Whe-
ther we contemplate the number and diversity
of the theories which have been proposed,
or the still greater number of facts which ap-
pear to be beyond the reach of mathematical
explanations, it must, I apprehend, be obvious,
that approximation by experiment is all that
can, in the present state of the science, be
reasonably expected in the comparison or esti-
mation of hydraulic forces; and we have a

* Principes d’hydraul. yol. 2. p. 356. + Ibid, p. 360.
2

“Moving Force. — 153

convincing proof of the great caution with
ewhich such approximations should be sought,
in the mistake into which this ingenious, per-
severing, and skilful experimenter has himself
been led, by attempting to generalize too far
the results of some of his experiments—I
allude to his peculiar theory of non-pressures.
After very reasonably concluding, that, in
cases where water is descending, as it were
upon an inclined plane, the bottom of the
channel does not sustain the whole weight of
the water, he extends that principle as follows :
“Si, par une cause quelconque, une colonne
duide comprise dans un fluide indéfini, ou
contenue dans des parois solides, vient a se
mouvoir avec une vitesse donnée, la pression
quelle exercoit latéralemeut avant son mouve-
ment contre le fluide ambiant, ou centre la
paroi solide, sera dimimuée de toute celle qui
est. due a la vitesse avec laquelle elle se
meut.”* Now this doctrine is obviously
untenable. For, when water is moving upon
a horizontal plane, we cannot doubt that the
plane must support the whole weight of the
water. It is never supposed that.a ball loses
a part.of its weight by rolling upon a hori-
zontal plane, excepiing indeed the amount of

* Principes @hydraul. vol. 2. p. 175.
. UD .

154 On the Measure of |

its centrifugal-force from the centre of the
earth; but that exception does not apply to
the case in question, for the centrifugal force,
whatever it is, must, according to M. du Buat’s
theory, be added to the non-pressure. In con-
firmation of his theory of non-pressures, M. du
Buat observes, “ Qu’ayant fait mouvoir, 4 une
certaine profendeur, dans une eau stagnante,
un tube vertical ouvert par les deux bouts,
dont le supérieur étoit hors de l'eau, le fluide
s'est maintenue dans le tube, plus bas que la
superficie du réservoir, d'une quantité a~peu-
pres égale a Ja hauteur die a la vitesse avec
laquelle il étoit mu.”* But he has omitted to
take into consideration the cohesion or the
lateral action of the particles of the water
upon each other, which has since been so well
observed by M.Venturi; from whose experi-
ments, and from those of Dr. Matthew
Young,t made under the receiver of an air-
pump, we may safely conclude, that, were it
not for the pressure of the atmosphere, and
the cohesion of the particles, there could be no
depression in the tube as observed by M. du
Buat; and, had he been aware of these cir-
eumstances, he surely would never have
reasoned as he has done on the subject of

* Principes dhydraul. Vol. 2. p. 156.
+ Irish Philos. Trans. vol. 7. p. 63.

Moving Force. 155

non-pressures. But to return to the subject
of water-wheels.

It has been attempted to be theoretically
demonstrated by M. de Borda, and afterwards
by Mr. Waring, of America, that the force of
the water against the wheel is not proportional
to the square of the velocity with which it
strikes the wheel, but that it is in the simple
ratio of that velocity ; and that the maximum
effect is therefore produced when the velocity
of the wheel is half that of the stream.

M. de Borda, in reference to the labours
of others, says, “ On ne considéroit qu’une
seule palette contre laquelle on cherchoit
Ja force du choc du fluide ;---mais il falloit
observer que dans le mouvement dont ils’agit,
Yaction du l'eau ne s’exerce pas contre une
palette isolée, mais contre plusieures palettes
A la fois, et que ces palettes fermant tout le
passage du petit canal et étant au fluide la
vitesse qu’il a de plus qu’elles, la quantité du
mouvement perdu par ce fluide, et par conse-
quent le choc qu’éprouvent les palettes, n’est
plus proportionnelle au carré de la difference
des vitesses du fluide et des palettes, mais
seulement a la difference de ces vitesses.”’*

* Memoires de l’Acad. Paris, 1767, p. 274.
U2

156 On the Measure of

- Mr. Waring’s demonstration is: as follows :
“Tf the relative velocity of a fluid against a
siigle plane be’ variéd, either by the motion of
the plane, or of the fluid from a given aperture,
or both, then, the number of particles acting
on the plane in a given time, and likewise the
momentum of each particle, being respectively
as the relative velocity, the force on. both these
accounts, must be-in the duplicate ratio of the
relative velocity, agreeably to the common
theory, with respect to this single plane ; but,
the number of these planes, or parts of the
wheel acted on in a given time, will be as the
velocity of the, wheel, or inversely as the rela-
tive velocity; therefore the moving force of
the wheel must be in the simple direct ratio of
the relative velocity,” and, consequently, the
maximum effect must be produced when the
velocity of the wheel is half that of the
water.*

. But this kind. of demonstration cannot, I
think, be very satisfactory. It leads, I appre-
hend, to this conclusion, that we may double
the power of any undershot water-wheel,
(whatever may be its velocity) by merely
doubling the number of its floats or planes
acted upon by the w ater. Mr. Smeaton, how-

ae

* Ameriezn Philos, Trans. vol. S$. p. 146,

ww

Moving Force. 157

ever, found, that no such advantage was to be
gained by that: means.* :

It must be acknowledged, that the cele-.
brated experiments of D’ Alembert, Condorcet,
and Bossut, furnished results in confirmation of
the common theory. But these were made
under particular circumstances; they did not
comprehend a sufficient variety of depths and
velocities to afford satisfactory conclusions as
to the general question, and various deduc-
tions, of rather an arbitrary kind, were made
from the actual pressure before the result which
agreed with the theory was brought out.

On the other hand, we have many experi-
ments which are quite at variance with the
theory. We may, in particular, refer to those
of Don Juan and M. du Buat. ‘The former
exposed to a current of water, moving with
the velocity of two English feet in a second, a
plane of one: square foot, immersed one foot
under the surface, and found that it supported
a weight of 152 lb. which is nearly four times
the weight it should have supported, according
to the theory.t M. du Buat exposed to a
current, having the velocity of three French
feet in a second, a plane of one square foot,

* Philos. Trans. 1759, p. 124.
+ De Prony Arch. Hydr. p. 304,

158 On the Measure of

immersed three inches under the surface, and
found that it supported a weight of 19.45 liv,
which, by the theory, should have been
only 8.75 liv.* | M. de Prony attempts to ac-
count for the results obtained by Don Juan,
by the additional pressure occasioned by the
surface of the water over the plane being raised
higher than the general level of the current.
That circumstance, however, can account for
a small part only of the difference. -M. du
Buat explains his experiments by his theory
of non-pressures, which I have already shown
to be fallacious.

M. du Buat has diowmriberd other experiments
which are considered by some to accord better
with the theory.t ‘They were made upon insu-
lated veins of water, spouting from the per-
pendicular side of a vessel against a surface
not greater than the section of the vein; and
from their results he draws the following
conclusions: “ Il résulte des expériences qui
précédent, que le choc d’une colonne ou d’une
veine fluide contre une surface de méme
étendue & directe, est sensiblement égal au
produit de cette surface, par la hauteur die 4
la vitesse. L/intensité du choe dépend néan-
moins en partie de la liberté plus au moins

* Priucipes d’hydraul. yol. 2. p, 218. et Ibid, p. 142, &e,

Moving Force. 159

grande que les filets ont de se dévier aux
approches de cette surface; mais si la veine
rencontre une surface plus grande qu'elle, qui
Yoblige & changer en entier la direction de
tous ses filets, la vitesse perdue, étant par 1a
augmentée, la resistance devient beaucoup
plus grande.’’*

But in these experiments, a part only of the
vein strikes the surface opposed to it, and the
force of that part appears to be equal to the
force assigned by the theory to the whole vein.

Of all theoretical propositions, that which
was first demonstrated by Daniel Bernoulli
in his Hydrodynamics, page 290, and after-
wards more fully by the same author, in the
Comment. Petropol. vol. 8. page 120, appears
to be the most applicable to Mr. Smeaton’s
cases, and comes the nearest to his results.
It is, that, when the force of an insulated vein
of water is directed perpendicularly against
a plane indefinitely large, its pressure against
the plane is equal to the weight of a column of
water, of which the base is equal to the area
of the section of the vein, and the height
equal to twice the height due to the velocity
of the vein. But the circumstances of this
case are not quite the same as those of Mr.
Smeaton, and he found the pressure against

* Principes d@’hydrau!, rol. 2. p. 150.

160 On the Measure of

the plane to be still greater than the weight of
a column of twice the height due to the rela-
tive velocity of the water and the wheel.

The most important conclusions drawn by
Mr. Smeaton from his experiments are (as I
have already noticed) not in his maxims ; but
they are to be found, I apprehend, in the two
following observations, which I shall quote in
his own words : .

1. “It is somewhat remarkable,” he says,
“that though the velocity of the wheel in
relation to the water turns out greater than +
of the velocity of the water, yet the impulse of
the water, in the case of a maximum, is more
than double of what is assigned by the
-theory.* . hae eas

2. “ We have seen before, in our observa-

tions upon the effects of undershot wheels, that
the general ratio of the power to the effect,
when greatest, was 3:1; the effect, therefore,
of overshot wheels, under the same circwn-
stances of quantity and fall, is at a medium
double that of undershot: and as a conse-
“quence thereof, that non-elastic bodies, when
acting by their impulse or collision, communi-
cate only a part of their original power ; the
other part being spent in changing their figure
in consequence of the stroke.” t

= Philos. Trans. 1759, p. 113. + Ibid, 1759, p. 130.
3

Moving Force. 161

It was chiefly in this last consideration that
he found the prevailing theory to be defective ;
for, according to that theory, as it is applied
in explaining the collision of bodies, there can
be no force spent in producing change of
figure: and it is very remarkable, that no
succeeding writer has, as far as I can learn,
paid any attention to this circumstance.

However much Mr. Smeaton’s valuable ob-
servations may have been disregarded by
authors, they have not been lost to practical
men. Before the publication of the paper
which I have been endeavouring to defend,
several mills had been constructed under Mr.
Smeaton’s direction, in which his chief object
was to apply the water so that less of its force
should be expended in producing change of
figure, and consequently more of its force be
communicated to the wheel. Although he had
obtained by his experiments results which
were “more than double of what is assigned
by the theory,” yet by comparing the effective
with the real head, he found that nearly'
half the power was, in many instances, spent
in producing a change of figure in the water,
before it reached the wheel; and still finding
(as stated above in the second observation)
that more than half of what remained of the

x

162 On. the Measure of

power was sjfent in the same way, by the
manner in which it acted upon the wheel; he
determined to apply the water, in all cases, so
that it should act more by its weight, and less
by its impulse; and the advantage gained by
that improved construction was found to be
fully equal to his expectations. It was
afterwards so generally adopted and improved
upon by himself and by other engineers in this
country, that although undershot water-wheels
were, about fifty years ago, the most prevalent,
they are now rarely to be met with; and
wherever the economy of power is an object,
no new ones are made. So that all the points
in question, as far as they relate to undershot
water-wheels, although highly important at
the time when Mr. Smeaton wrote his first
paper, are now become matters of mere spe-

culative curiosity, and, in this country at least, |

they can no longer be of any practical use.
The question, however, respecting that part
of the power which is expended in producing
a change of figure, is highly interesting in
other points of view, and we shall have occa-
sion to consider it more fully when we come
to examine the Gth, 7th, 8th, 9th, 12th, and
13th cases.

Dr. Milner, in allusion to Mr. Smeaton’s
‘yemarks on the theory, observes that, “ It is
1

Moving Force. 163

acknowledged, that the experiments which
have been made to determine the effects of
wind and water-mills do not agree with the
computations of mathematicians; but this is
no objection to the principles here maintained.
Writers generally propose such examples with
a view rather of illustrating the methods of
calculation by algebra and fluxions, than of
making any useful improvements in practice.
They suppose the particles of the water to
move in straight lines, and to strike the
machine with a certain velocity ; and after
that to have no more effect. As such suppo-
sitions are evidently inconsistent with the
known properties of a fluid, we are not at.a
loss to account for a difference between expe-
riment and theory ; and therefore it should
seem unreasonable to assert, that certain
authors of reputation have neglected the col-
lateral circumstances of time, space, or velocity
in the resolution of these problems, unless we
are able to point out such omissions.”* But if
the theory be applicable to speculative objects
only, why are its conclusions laid down as rules
to be adopted in practice? Mr. Smeaton
objected to the practical application of the
theory by the distinguished authors which he
quoted, because they omitted to take into

* Philos. Trans. 1778, p. 371.
x 2

164 On the Measure of

consideration circumstances which render that
application inconsistent, as Dr. Milner ac-
knowledges, with the facts. When a stream
of water strikes a plane opposed to it, a small
number only of the particles of the water touch
the plane, and unless we suppose these parti-
cles to be pressed forward by the water which
is behind them, the actual pressure exerted
against the plane cannot be accounted for,
But that action of the water is not considered
in the prevailing theory; and it is omitted
even in the corrected theory which has been
proposed by M. de Borda and Mr. Waring ;—
| they appear not to have considered, that when
the number of planes acted upon are increased,
the quantity of water acting upon each plane
is deereased in the same proportion ; neither
are the number of planes acted on in a given
time “inversely as the relative velocity,” as
stated by Mr, Waring. at

The Edinburgh reviewers, object to Mr.
Smeaton’s opinions, upon more general
grounds, at pages 126—7—8, and continu-
ing to reason as if he had understood the
consideration of the time to be necessarily
excluded in all estimations of force, they traly
and eloquently observe, that “in most in-
stances, time is a very material element in the
estimation of an effect, or an event of any

Moving Force. 165

kind; and is, of all our resources, that which
it most behoyes us to economize.”’*

Now, I apprehend, it is obvious, from the
whole of Mr. Smeaton’s reasoning on this
subject, that he was perfectly aware, that, in
most cases of moving force, if the pressure, the
time, and the manner of its acting be given, the
effects may be found. He observed, however,
(as in the two first cases) that the effects were
not always in proportion to the pressure and
the time of its acting, But he found, that if
the pressure and the space through which it
acts (or when variable, the fluent of the
pressure into the space) be given, the effects
may always be determined, without reference
to the manner, or the time, in which they may
be produced; and finding the total amount of
the effects to be, in all cases in proportion to
the product of ‘the pressure multiplied by the

_ space through which it acts, whatever may be

the time or the manner of its acting, he con-

_ siders that product to be the principle capable

of the most general application, and conse-
quently adopts it as the proper measure of
mechanical force.

_ With regard to the proper economy of time,
I have always understood that Mr. Smeaton
was fully sensible of its value, and most ex-
emplary in his punctual attention to it, in all

* Edinburgh Review, vol. 12. p. 128.

used in that sense, has no reference to th

1

166 On the Measure of’

its various bearings. We can form no notion
of velocity, without taking time as an element
of it.—As far as it relates, however, to me-
chanical power, time would come under his—
consideration chiefly in the following manner.
If, for example, the object before him was to
apply, to the best advantage, a given stream —
of water in producing a mechanical effect, he
would first ascertain the quantity of water _
passing in any given time, and the height of
its fall. He would next inform himself whe-
ther the effect to be produced should be con-:
tinuous or intermitting in its duration. If con-
tinuous, he would construct his machine of such
dimensions as to receive and apply the power
of the stream uniformly and constantly from _
hour to hour, and from day to day. But if it
were required to produce an intermitting ef-
fect, he would construct his machine of larger
dimensions, in order to avail himself of the |
quantity of water which might be treacveeidae aa
during the time that no effect ‘was required to
be produced; and he would take care to
arrange and proportion the whole, so that no
more people than necessary should be em-
ployed in attending it. In the latter case, rl
machine would be said to lie: tore powerful
than in the former: but the word power,

Moving Force. 167

measure of the effect when compared with the
: force by which it is produced. The machine,
without the moving force, has no power; and
; , when we speak of the greater or less power of
_amaachine, we only mean to say that we make
yy use of a larger or smaller instrument to convey
the moving force. If we have to let off the
% __ water from a reservoir, we know that it will be
Rte emptied in less time through a large -aperture,
or channel, than through a small one; and just
i‘ so we know, that bya large and strong ma-
chine, a given quantity of moving force may
be conveyed in less time than by a small and
weak one. But if the whole, or any deter-
___- Minate portion of the moving force be properly
o applied, the whole, or proportionate effect,
must nevertheless be the same, whatever may
__ be the portion of time oceupied in the opera-
| tion. | And the same principle holds good in
the application of the elastic force of steam, or
of any other moving force, to produce a me-
chanical effect.
a In jection, however, to this, the reviewers
observe as follows :—
__ “When it is said, for example, that a bushel
‘of good coals will give to a steam-engine the
wer required to grind eleven bushels of
eat, this must always imply a rate of burn-
ing included within certain limits ; for the fuel

168 On the Measure of

might be applied so slowly that the steam
generated would not be of strength sufficient.
to work the mill; or it might he made to turn
so fast, that very little effect would be pro-
duced. In the same way, when Mr. Smeaton
says, if 1000 tons of water be let out on an
overshot wheel, and descend through twenty
feet, it will grind the same quantity of corn, at
whatever rate it be expended,* the extreme
cases of very great slowness, or very great
rapidity, must surely be excepted. But if the
extreme cases must be excepted, it is a proof
that, even in the intermediate cases, the effect
is not constant or invariable in its magnitude,
though the differences may be inconsiderable ;
this, at least, is what one would be disposed to
infer from that continuity in the variation of

causes and effects, to which there is, perhaps, —

no exception, either among the works. of
nature or of art.” ¢

‘
To these objections it may be replied, that —

however slow or quick the combustion o the
coals may be, if they be effectually burnt, the
full quantity of heat must be given out. Ff
the heat be allowed to escape without being
communicated to the water; or, if after being —
communicated to the water the pressure of the

* Philos. Trans. 1776, p. 474. i
+ Edinburgh Review, vol, 12, p, 129. sam)

Moving Force. 169

steam be not wholly applied in producing the
intended effect, the loss must be owing to
_ practical imperfections in the construction of
the apparatus. Such imperfections must exist,
more or less, in every apparatus, and they will,

‘no doubt, be greatest in extreme cases. But
although the whole heat, or the whole force,
can, in practice, never be completely transferred
from one given object to another, yet there
can be no doubt of the real existence of both
the heat and the force in their full quantities ;
and we can form no idea of the portion of time
being limited in which the one must be evolved
or the other transferred.

A water-wheel may be made to move with a
ei so great, that almost the whole pressure
of gravity shall be employed in generating
motion in the water; or it may be made to
move so slow as to require a wheel of such
magnitude to hold the water, that almost the
whole of the force shall be exhausted in gene-
~ rating motion in the wheel, and in overcoming
the friction of the machine; but the whole
moving force is, nevertheless, in both cases
exerted, and it is immaterial to the principle
of its proper measure, whether it be applied in
generating motion in the water, or in the
machine,—in overcoming friction, or in pro-
ducing any other known effect of moving force.

Y

170 On the Measure of

If it appear that I have insisted too much on
this part of my subject, it should be recollected
that many of the objections which I have been
endeavouring to meet, apply not only to the

particular cases under consideration, ie

generally to the. whole question at issue.
must acknowledge too, that I have felt more
than ordinary solicitude that the experience
‘and the conclusions of one who has long been
looked up to, in this country, as the father of

civil engineers, should be duly appreciated.
But it is not necessary, I apprehend, to resort
to complicated cases for the purpose of examin-
ing the points in question. If the two first
cases which I have stated, were once distinctly
explained and agreed upon, no difficulty would

remain in explaining their various and multi- —

plied applications in machinery.

Although these cases comprehend much of
what relates, in this question, to rotatory mo-
tion, the three following cases apply more
particularly to that branch of the subject.

In rotatory motion, it is universally admitted,
that four times the force is necessary to generate
the same angular velocity, or twice the abso-
lute velocity, in the same body placed at twice
the distance from the centre of motion; and
it is but reasonable to enquire why we must
have one measure for rotatory, and another for

\

Moving Force. 171,

rectilinear force. That inconsistency (stated
in case 3d) is overlooked in the usual demon-
strations respecting rotatory motion; it is
nevertheless one of considerable importance,
and it requires explanation. I have already
endeavoured to show (p. 139.) that the expla-
nation, which refers us to the properties of the
lever, is by no means sufficient. If, however,
the product of the mass into the square of its
velocity, be taken as the proper measure of
the force of a body in motion, the explanation
is obvious. | .
The case of the balance beams (case 4th.)
has been adduced by many authors in proof of
the moving forces being as the masses multi-
plied into their velocities. There is no doubt
that after they have been put in motion, the
weights will balance each other the same as
when they were at rest ; but the question is,
whether or not the motion of x can be gene-
rated by a moving force no greater than that
which generates the motion of m? If these
two quantities of motion can be generated by
equal forces, the same forces should generate
equal quantities of motion in o and p; bat
equal pressures applied to A and C will not
produce, in equal times, equal quantities of
motion in the respective weights. - Mr. Emer-
son, by neglecting this circumstance, appears
x2

172 On the Measure of

to have been led into the error pointed out by
Mr. Atwood, which I have quoted at page 128.
But if the weights were attached to, instead
of being suspended from the ends of the
beams, the case would then be one of pure
rotatory motion; and would have been in-
cluded in the 56th prop. of Emerson’s. Princi-
ples of Mechanics, where it is demonstrated,
that unequal quantities of motion are produced

by equal forces in equal times, and where

the individual forces are made out to be as
the revolving masses into the squares of their
velocities. If he had applied the same prin-
ciples to the solution of the problem quoted
above from his Treatise on Fluxions, he
would, no ‘doubt, have brought out the true,
instead of an erroneous result.

In his 56th prop. the forces are understood,
in the usual way, to be modified by the proper-
ties of the lever, and then their relations to

each other, and to the squares of the velocities
generated, are made out. But it is the pres-
sure only that is modified according to its
distance from the centre of motion. The
product of the pressure into the space through
which it acts, remains the same, whether it be
taken at the point where the force acts on the
Jever, or where the lever acts on the body

which is moved. ‘The force of a body in.

3

cee ee ee Se Oe

Cat

Moving Force. 175

motion cannot be considered greater or less
according to the manner in which it has been
produced, and when we see a body in motion,
if its mass and velocity be given, we never ask
by what kind of lever it has been produced in
order that we may judge of its force.

The case of a balance beam was noticed
by Sir Isaac Newton, near the end of his
scholium to the laws of motion ; but it is not
clear that he considered that case in the same
light in which it has since been. taken by
Desaguliers and other authors, to prove that
the moving forces of the weights are not as the
squares of their velocities. It may, I appre-
hend, with greater consistency, be inferred,
that he noticed that case merely to show, that
the pressures of the weights balance each
other when they are in motion, the same as
when they are at rest. It will be seen, when
we come to examine the 14th case, that Sir
Isaac Newton did not consider quantities of
motion to be in all cases in the ratio of the
forces by which they are produced.

The 5th case belongs to that class of the
effects of force which are considered by Mr.
Atwood to be disproportionate to the forces by
which they are produced, which ever way
they may be estimated, whether by the mass
into its velocity, or by the mass ‘into the

174 On the Measure of

square of its velocity. However strange this
opinion may appear, it is perfectly correct
as far.as it is applied to the measure of force
composed of the pressure and the time of
its acting; for according to that measure, the
quantity of force communicated will be always
the same, whether.it be applied at G, D, or at
any other point in AB. The progressive
velocity generated m G, will, no doubt, be
the same, at whichever of these points the force
is communicated ; that is, the product of the
mass into its velocity in the same direction
will, in this case, as in all others, be as the
product of the pressure into the time of its
acting; and according to that measure, the
whole effect of the force communicated is
found in the progressive motion of the mass,
the rotatory motion appearing to be produced
without force. ‘The explanation most com-
monly given of this inconsistency, is, that the
rotatory motion consisting of equal quantities
of motion in opposite directions, balances
itself; but can it be shown that equal quanti-
ties of motion in opposite directions may be
produced without force? ‘Such is not the
doctrine of Sir Isaac Newton; he certainly
understood rotatory motion, as well as rectili-
near motion, to be a measureable effect of
force.—M. de Prony attempts to explain ‘this

Moving Force. 175

difficulty,,in the application of the prevailing
~ measure of moving force, as follows: “ Puisque
nous savons que lorsque la résultante des
quantités de mouvement imprimées passe par
le centre de gravité d’un corps, ce corps,
abandonné a l’action dés moteurs, n’a aucun
mouvement de rotation, il faut en concluré que
le mouvement de rotation n’a lieu que lorsque
la -résultante des quantités de mouvement im-
primées. passe hors du centre de gravité.
Ensuite, comme le mouvement de ce centre
est le méme, soit que la resultante y passe ou
n’y, passe pas, c’est done autour du point ou il
est placé que se fait la rotation, quand il y en
a, puisque ce point est le seul qui ne participe
pas a cette rotation. I! suit de la que le
mouvement de translation est absoluement
indépendant du mouvement de rotation, puis-
quw’il est indépendant de la cause qui le produit,
savoir, la direction de la résultante par un
autre point que le centre de gravité.”*

But how can these two motions be inde-
pendent of each other, when they are both
produced by the same force? 'The pressure
can neither be inereased nor diminished with-
out encreasing or dimimishing, at the same
time, the rotatory as well as the progressive
motion; and if we attend to the space through
which the pressure acts, we shall have no

* Arch, Hydr, p. 176. .

176 On the Measure of

difficulty in finding what part of the whole

moving force is expended in producing the
progressive, and what in ee the rota-
tory motion.

Let E be the centre of gyration of Aand B
around G. Draw GF, DH and EI perpen-
diculars to AB. On ET take two points K
andI,sothatEK:KI::GE:G@D. Through
K draw K F parallel to A B, and through F

and I draw MN. Then if we take GF to

represent the progressive velocity produced in

G by any force acting at D, K I will represent.

the rotatory velocity produced in E in the same
time; DH will be the whole space through
which the pressure has acted ; D L will repre-
sent that portion of the moving or mechanical
force which has produced the progressive

velocity ; and LH that portion which has_

produced the rotatory velocity, and we shall
have GF?: KI?::DL:LH. These results
are so well known, that it would be superfluous
in me to give a demonstration of them here.
The same relations of the moving force to the
effects, and of the effects to each other, take
place whether the force be communicated by
impulse or by gradual pressure. For, however
sudden the impulse may be, a determinate
space must be deseribed by the pressure during
its action, and if the pressure be uniform, that
space, however small it may be, must consist

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Ls ZEEE Aen TOR

Moving Force: 177

of two parts, as described in the figure, having
the ratio to each other of GF*:KI*. If the
pressure be not uniform, the fluent of the
pressure into the space will bear the same re-
lation which DH bears to the sum of the
products of the masses into the squares of their
velocities.

I am quite at a loss to understand why Mr;
Atwood excluded this case from those in which
the moving force may be estimated by the
products of the.masses into the squares of their
velocities. If, in cases of rotatory motion
about fixed axes, that principle “ obtains,” as
he observes, “ without exception,” there can,
I think, be no exception to its application in
cases of this description.

- Having gone through the examples of force
producing motion from a state of rest, we come
now to the examination of cases where motion
is destroyed, or where it is transferred from
one body to another.

It was a favorite doctrine with the Cartesians,
and it was maintained also, though upon quite
different. principles, by Leibnitz, and John
Bernoulli, that motion could not be lost; for
the same quantity of motion, or of force, it
was said, must be always preserved in the
world. A similar doctrine, applied to explain

Zs

178 On the Measure of

the collision of soft bodies, has been supperted
by authors of later date; and if it were ad-
mitted that we have no indication of the lo’s
ef force unless motion be lost in the centre of
gravity of the system in which the force acts,
it might truly be said that no force can be lost.

It has never been questioned that motion
may be generated, accelerated, or retarded, in
a variety of ways, and there appears to be no
good reason for supposing that it may not be
destroyed as well as generated.

It was Sir Isaac Newtoun’s opinion that
motion may be lost, and he has given many
familiar examples of the manner in which it is:
fost. ‘It may be tried,” he says, “ by letting
two equal pendulums fall against one another
from equal heights. If the pendulums be of °
lead, or soft clay, they will lose all, or almost.
all, their motion.”* In the same way the:
motion of A and B (case 6th.) is lost when
the spring is compressed. 'This case has-been
so often brought forward, and so much has
been said about it, on both sides of the ques-
tion, that it may appear strange that I should
produce it again.—I shalt endeavour to confine
my observations upon it in a small compass.

It is very generally understood, and it has:
been received almost as an axiom,. that if two

* Horsley’s Newton, vol. 4. p. 259.
y 2

Moving Force. 179

bodies meet and destroy each other’s motion,
their quantities of motion, and their respective
forces, must therefore be equal.—Dr. Reid has
given a better enunciation of this proposition.
He says, “ If two bodies meet directly with a
shock, which mutually destroys their motion,
without producing any other sensible effect, it
may be fairly concluded that they meet with
equal force.”* Now this is a fair reference to
experiment, and, in the case under considera-
tion, we certainly have a measurable, “ sensible
effect” in the compression of the spring, which
cannot be produced without force. But al-
though the ends of the spring meet at bh,
(fig. 6.) it is still held by many that that effect
is produced equally by A and B. If the forces
of A and B are really equal, we should have
the same effect produced when we substitute
for B another ball equal in weight and velocity
to A. But the same effect cannot be produced
by that means; and if the real effects be ex-
amined, we shall always find that the spring is
less compressed (as measured by the pressure
into the space) by A than by B in the ratio
of 1 to 2.
It is true the common centre of gravity of

* Essay on Quantity--Philos. Trans. 1748, p. 515.
— £2

180 ‘On the Measure of

A and B remains undisturbed ; but is it neces-
sary that we should confine our attention solely
to that centre of gravity ?—If we find that
the motion of a body. cannot be destroyed
without producing certain measurable effects
of force, and if we find these effects to bear an
unvarying relation in quantity to the motion
destroyed, there surely can be no inconsistency
in taking the amount of these effects for the
measure of the force of the moving body.

~ I confess I have never been able to under-
stand M. D’Alembert’s distinction between the
sum and the number of the obstacles over-
come.* If the obstacles be equal to each
other, it can make no difference whether their
sum or their number be taken as the measure
of the force. If they be unequal, the sum of
their separate amounts must surely be the abso-
lute quantity of resistance overcome, and the
proper measure of the force by which it is
overcome. ‘To say that the quantities of re-
sistance during infinitely small instants of time
must be equal to each other, is assuming a most
unreasonable postulatum.—The difficulty can-
not be removed by taking insensible, instead
of sensible portions of time; for we have no
reason to suppose that the pressure into the :
space approaches nearer to equality in infi-

* See page 131.

Moving Force. 181

nitely small, than in palpably large portions
of time.

This compression of the spring is compre-
hended by Mr. Smeaton under the term
change of figure; and he has shown, by some
well-chosen experiments, that when a non
elastic yielding body, moving with a given
velocity, strikes directly another equal body at
rest, exactly half the force of the striking body
is expended in producing change of figure.*.

The facts exhibited in the 7th case are
similar to those which Mr. Smeaton has de-
scribed as the results of his experiments.—
According to the theory, the whole force of A
(fig. 7.) before collision, is to be found in the
motion of A and B after collision. But if that
be admitted, we must suppose the spring to
have been compressed without force :—yet we
have no more reason to suppose that the spring
can be compressed without force, than that a
body can be put in motion without force ; and
the amount of the force which has been ex-
pended in compressing the spring, is ascer-
tained by its effects in producing motion in
C and D; and although these balls move in
opposite directions, it cannot be supposed that
their motion can be produced without force.

. Experiments on Collision—Philos, Trans. 1782,

182 On the Measure of

In this explanation, however, of the action
of the spring on C and D, Mr. Maclaurin
understood a material inconsistency to be in-
volved, which he stated in a treatise that
obtained the prize of the Royal Academy of
Sciences at Paris, in 1724.* Mr. Maclaurin
supposes two equal bodies like C and D, with
the compressed spring between them, te be
situated in a space E FGH, which, together
with the balls, “ meves uniformly in the direc-
tion CD with the velocity as 1; and that the
spring impresses on the equal bodies C and D
equal velocities, in opposite directions, that are
each as 1. Then the absolute velocity of D
(which was as 1) will be now as 2; and accord-
ing to the new doctrine, its force as 4: whereas
the absolute velocity and the force of C (which
was as 1) will be now destroyed ; so that the
action of the spring adds to D a force as 3,
and subducts from the equal body € a force as
Jonly ; and yet it seems manifest, that the

‘actions of the springs, on these equal bodies
ought to be equal; (and M. Bernoulli ex-
pressly owns them to be so): that is, equal
actions of the same springs upon equal bodies

* The “ Discours sur le mouvement” of John Bernoulli
avas offered for the same prize, but was rejected, the
preference being given to the treatises of Maclaurin and
Maziere.

Moving Force. 183

would produce very unequal effects, the one
being triple of the other according to the new
doctrine; than which hardly any thing more
absurd can be advanced in philosophy or
mechanics.’’*
This argument of Mr. Maclaurin has al-
ways been considered as the most ingenious
and the strongest objectiom that has been
brought against the principle of the vis viva,
But we have the following remarks upon it
from Dr. Milner: “ I shall only just observe,
that if M. Bernoulli expressly owns, that
springs, interposed between. two bodies in a
space, which is carried uniformly in the direc-
tion in which tke springs act, will always
generate equal forces in the bodies according
to his own: definition of the term, he talks
more inconsistently than I have observed him
to do: on the contrary, if I could find that he
has answered this famous argument. (which
Dr. Jurin proposed. over again in the Philo-
sophical Transactions, volume XLII. with a
conditional promise of embracing the Leib-
nitzian doctrine) by simply saying, that springs
he considers as moving forces, or, when the
bodies are equal, as accelerating forces ; and
that their actions are equal, when in equal

* Account of Sir Isaae Newton’s Discoveries, book 2.
chaps 2.

184 Oni the Measuré of

times they generate equal velocities, but not
necessarily equal forces in the equal bodies;
should not make the least scraple to own that
I thought his reasoning solid and conclusive,
and his distinctions a full answer to every
objection of that sort.” To this, Dr. Milner
has added the following note: ‘No doubt
Mr. Maclaurin refers to the following passage
of Bernoulli—La force du choc, ou de l’action
des cor'ps les uns sur les autres; depend unique-
ment de leurs vitesses respectives; or il est
visibles que les vitesses respectives des corps
ne changent pas avant le choc, soit que le plan
ou Pespace qui les contient soit sans mouve-
ment, soit quil se mouve uniformement,
suivant, une direction donnée, les vitesse re-
spectives seront donc encore les mémes apres
le choc. This quotation puts the matter be-
yond dispute. It is plain, Bernoulli, though
he makes use of the word aetion, is’ only
speaking of the motion lost or communicated,
and the relative velocities of the bodies: there
is not the most distant hint at the change in
their absolute forces.”

“In addition to this, I would, with great.
deference, observe, that by the term equal
actions of the spring, as used above by Mr.
Maclaurin, equal pressures only are meant :
but M. Bernoulli held that the motion of a

Moving Force. 185

body cannot be produced by mere pressure.
Unless the pressure act through some portion
of space, no motion can be produced ; and if,
together with the pressure, we take into con-
sideration the space through which the pres-
sure acts, we shall find that, while the motion
of C has been transferred to D, the whole
force of the spring has also been communi-
cated to D. This will become more chvious in
examining the 8thcase. It should be observed
too, that when Mr. Maclaurin sets out with
supposing the bodies to be in motion, and the
spring to be in a compressed state, he refers
to a previous application of force, of which he
takes no farther notice, although a part of
this previous force is.afterwards expended, or
given out, in producing the changes which he
describes.

It is true our researches must be limited
chiefly to relative motion—Of absolute motion
we know but little. But is not the motion of
the space EF GH with the velocity as 1,
relative motion with regard to some supposed
point, as much as the final motion of D is
relative motion?

if the compressed spring be disengaged
while the bodies are at rest, the motion of the
bodies is acknowledged to be produced by
the -force of the spring: but when the space

Aa

186 On the Measure of

EFGH and the bodies are supposed to be
put in motion before the spring is disengaged,
there is, according to the prevailing theory,
no motion produced by the spring.—There is
merely a transfer of motion from C to D, and
we have only the same motion after, that we
had before, the action of the spring.—Is there
not some inconsistency in supposing the spring
to produce motion in one case but none in the
other ?

If instead of the mnequal pressure of a spring,
an uniform pressure be applied, as in the 8th
case, the various quantities of mechanical
force expended at different periods of the ope~
ration, will, be more distinctly shown : for,
the pressure being constant, each portion of
space through which it acts will express the
quantity of mechanical power which has been
‘expended in that space.

Tn its passage through a space =EH=3 EF
(Fig. 8) an uniform resistance has. been
opposed to A, which would bring it to rest in
a space = EF. When it has arrived opposite
to Hit has therefore lost. half its velocity ;
and B having arrived opposite to I by the
action of an equal. pressure through a, space

= FL=i HF, has acquired the velocity ss
. and ‘KG, 2 ee E Y, will i hati a So

3

Moving Force. 187 |

the depth of the penetration of c into A. Now |
if A be a nonelastic soft mass, of ‘clay for
example, we know that it cannot be pene- »
trated without foree; nor have we any reason
to suppose that the force which hasbeen ex-
pended in producing the penetration, can ever
be restored. We therefore cannot expect to
find in the motion of A and B after collision,
the same quantity of force which they had
before collision: If, however, the pressure
into the space through which it acts, be taken.
as the measure of the force, we’ shall find,
that a compound effect, has been produced by
A in its passage through the space = EH,
that only 4 of the force which A has lost has
been communicated to B, and that the other 3 of
that force has been spent in producing a change
of figure in A. These proportions are obvious
from the mere inspection of the diagram. We
may suppose A to be a much harder substance
than clay, so that the space represented by
EF may be very small; but the pressure being
proportionally greater, the product of the
pressure into the space will still be the same,
however small the penetration may be.

Any explanation, however, which takes
into consideration the force which is expended
in producing a change of figure, is strongly

Aa2

188 On the Measure of

~ objected to by all those who hold that the pro-
duct of the mass into its velocity is the proper
measure of the force of.a body in motion.
They contend that‘ all the experiments
which are usually brought to determine the
impressions made upon soft bodies, as snow,
clay, &c. are absolutely unfit for the purpose.”
That “ the circumstances, which take place
in the production of these effects, are such as
-we can never discover.” And that ‘ ‘the
directions in which the particles recede, the
velocities. they acquire, their mutual actions
upon one another, and lastly, the time, in
which these effects are performed, are all
beyond the reach of computation,” *

To this it may be replied, that if only the
pressure and the space through which it has
acted be determined, it would be quite super-
fluous to enter into any farther computation
cof the cireumstances above enumerated, in
order to estimate the quantity of mechanical
force expended in producing the impression.
For, whatever may have been the relative
directions, velocities or mutual actions of the
particles during the time that the impression
was making, no internal motion remains after
the impression is completed; and the force

* D:. Milner. Philos, Trans, 1778. p. 353.

Moving Force. 189

can have been spent in no other way than in
compressing the particles together, or in over-
coming their tenacity. To take a familiar
example.—If a quantity of corn is to be
ground, a considerable quantity of motion
must, no doubt, be produced before that can
be effected ;—but after it is ground, there is
no more motion in the flour than there was in
the corn before it was ground, and the whole
force employed must have been expended in
overcoming the tenacity or cohesion of the
particles of the corn.

In answer to the very common objection,
that the quantity of force expended in pro-
ducing an effect of this kind, cannot be
precisely ascertained, it may be observed, that
in real practice, such quantities of force are
estimated with quite as much precision as the
force necessary to generate a given velocity in
a given mass,—in projecting a cannon ball, for
example.—The application and measurement
of mechanical force producing changes of
figure are indeed the chief occupations of
practical men, in the construction and ma-
nagement of machinery.

The force spent in producing change of
figure in the collision of bodies, was noticed
by John Bernoulli in his dissertation De vera

es

notiope virlim vivarum, as follows. “ Si

190 On the Measure of

corpora non sunt perfecte elastica, aliqua pars
Viriwm vivarum, que periisse videtur, consu-
mitur in Compressione corporum, quando per-
fecte se non restituunt; a’ quo autem nunc
abstrahimus, concipientes, compressionem
illam esse similem compressioni elastri, quod
post tensionem factam impediretur ab aliquo
retinaculo, quo minus se rursus dilatare posset,
et sic non redderet, sed in se retineret vim
vivam, quam a corpore incurrente accepisset :
unde nihil viriuni periret, etsi periisse vide-
retur.” *

From this passage, and from various other
passages in his works, relating to the doctrine
** de conservatione virium vivarum,” it ap-
pears, that Bernoulli thought it necessary to
maintain that no force could be lost, and that
even in the collision of nonelastic bodies he
considered the change of figure to be such,
that the force which had been expended in
producing it might be recovered by the resto-
ration of the figure, or by. some other means.
Why he considered it incumbent upon him to
maintain such opinions, or upon what founda-
tion he understood them to rest, it is hard to
gay. Experience furnishes us with nothing
which can justify the conclusion that the force

* Bernoulli’s works, Vol. iii. p. 243.

Moving Force. 19}

spent in producing change of figure in non-
elastic bodies, can ever be restored.

_I believe Mr. Smeaton was. the first who
subjected to actual admeasurement. the force
spent in producing change of figure in the
collision of non-elastic bodies.* He appears to
have been led to this investigation, not by
curiosity merely, but by a conviction of the
insufficiency of the prevailing doctrines of
forces to account for the facts which were _
constantly presented to him in. his ordinary
occupations, and particularly, as I have before
observed, in the action of water on water
wheels. It is very remarkable, that while
Mr. Smeaton’s other dissertations . on. the
principles of moving force, haye met with
considerable attention abroad as well as at
home, this last treatise on the collision of
bodies, (which he himself considered a most
important one, as containing the best confir-
mation of his former conclusions) has been.
almost totally neglected by all succeeding
writers. It is impossible for me to. do justice
to it by giving an abstract of it; but I would
earnestly recommend the entire treatise to the
attention of all those who.take an interest in
investigations of this kind.

«With regard to the collision of bodies. which
are supposed to be perfectly hard as well as
an # Philos. Trans. 1782,

192 On the Measure of

nonelastic, Mr. Smeaton understood a contra-
diction to be involved in the very supposition
of the existence of such bodies. It has never
been contended that any such are to be found
in nature. But it is very generally argued,
with Mr. Maclaurin, that “ there is the same
objection [of non-existence] against admitting
and treating of bodies of a perfect elasticity.*”
fn reply to this I would observe that, the
objection does not appear to be of the same
weight against perfectly elastic, as against
perfectly non-elastic hard bodies. For, we
have substances which approach very nearly
to perfect elasticity ; but we can find no sub-
stance of which the qualities approach to
hardness and non-elasticity united. In gene-
ral the elasticity encreases as the hardness
encreases, and no substance has ever been pro-
duced that can be called hard, without posses-
sing, at the same time, great clasticity. _

It does not appear that the possible exist-
ence of a perfectly hard non-elastic body was_
obvious to the first discoverers of the laws of
percussion. Huygens appears to have under-
stood a hard body to be one that is perfectly
elastic. His 6th law of percussion is as fol-
lows, “ Summa productorum factorum a mole
eujuslibet corporis dwi ducta in quadratum

* Account of S:r Isaac Newton’s discoveries, p. 93.

Moving Force. 193

suze eeleritatis, eadem semper est ante et post
eccursum eorum.’’ *

M. Laplace considers that “ Ce principe”’
de la conservation des forces vives “ n’a lien
que dans les cas, ou les mouvemens des corps
changent par des nuances insensibles. Si les
mouvemens éprouvent des changemens brus-

-ques, la force vive est diminuée d’une quantite

que l’on determinera de cette maniére ;”———f
and taking it for granted, in the usual way, that
where the change of motion. is sudden, the
bodies must be non-elastic, he investigates the
motions which are known to result from the
collision of non-elastic soft bodies. But that
conclusion is not justified by experience; for
the characters of elasticity are often the most
apparent where the changes of motion are, as
far as we can judge, the most sudden.
The supposition of the possible existence of

a perfectly hard body, appears to involve
another inconsistency which I will endeavour
to state in a few words.—The resistance, or
pressure, against c (fig. 8) being encreased,
and the depth of its penetration being dimi-
nished, in proportion as the hardness of A is
increased, it follows, that if, by supposing A
to be perfectly hard, the depth of the pene-

* Phil, Trans. 1669. p- 928. . :

+ Méchanique céleste, vol. 4. p. 52.
Bb

194 On the Measure of

tration be reduced to nothing, the pressure —
must be increased to infinity. That is, the
pressure must be infinitely great to communi-
cate even the smallest finite quantity of motion.
But I believe the “ law of continuity ” is not.
so much objected to now. as it was formerly,
and few will be disposed to contend that a
body may, from a state of rest, arrive at. any)
given velocity, without passing through the.
intermediate degrees of velocity, between that
and rest; and consequently, few will now
contend for the possible existence of a per-
fectly hard substance.

- If instead of a non-elastic soft substance,.
we suppose A to be a hollow sphere filled with
a dense elastic fluid, and ¢ to pass through a
hole im the side of the sphere so as to move
without friction, and be uniformly pressed
outwards by the fluid; A will then ee
a perfectly elactic body.

It may be proper to observe, that although
we suppose c'to make no penetration into B,
we do not suppose B to be perfectly hard.
We only suppose it to be so much harder than
A, that the penetration , shall be very. smal
when compared with the penetration into A.
If we were to suppose A and B to yield equally
to c, the same explanation of the phenomena,
as when A only is supposed to be penetrated,

Moving Force. 195

will strictly apply; only the diagram would
be a little more complicated.

Let us now suppose the first part of the
operation in the collision of A against B, to
be the same as already described im the case
of a soft body, and supposing them to be in
the situation as represented at No. 2, let us
observe what must follow.—When A has ar-
rived opposite to F, as represented at No. 3,
e will have returned to its original place with
respect to A, and B will have arrived oppo-
site to G (FG being = EF), A will be at
rest, and B will have acquired the full velo-
city v.—Now it is obvious, that if A had not
moved on from its position No. 2, ¢ would in
this last part of the operation, have acted upon
B only till it arrived opposite to L (FL being
=+4EF), and its final velocity would have

been only V2v7%. But A having moved on
to its place No. 3, ¢ will have acted on B till
it has arrived opposite to G; and the force
which has been lost by A in its passage
through the space = HF, as well as the force
of ¢ through a space = HK, has been com-
municated to B. In other words,—the force
which, in the first part of the operation, had
been expended in producing the change of
figure, has, in the last part of the operation,
' been reproduced by the expansion of the
Bb2

‘4
196 On the Measure of

figure to its original state, and has, together
with the remaining force of A, been commu-
nicated to B. If this explanation be applied
to the change of motion produced in C and D
Fig. 7, as referred to at page 185, it must be
obvious, I think, that when C is brought to
rest, the force which it has lost, and the force
of the spring, have both been communicated
to D. “

In the collision of unequal masses, the dis-
tribution of the force is rather more compli-
eated. Let M (fig. 15) be immoveable and
filled with a dense elastic fluid so that N, mov- .
ing with the velocity v and meeting with an
uniform resistance, would be brought to rest
by driving the cylinder C up to O. Then if
we suppose M, = 2N; to be in free space,
and if we divide O P, = OR, into nine equal
parts, and make OS=2:OR, it will be
obvious, that when N has arrived at S’ its
velocity will be = and M will at the same
time have arrived.at 2’ and will have acquired
the velocity =, and the penetration of C into
M will be 2 OR.—In this part of the operation
then, N has (on the principles adopted in ex-
plaining the last case) lost, or rather given out,
£ of its force; of the effects of which 3 are
found in the acquired motion of M and $ in

1

Moving Force. 197

the change of figure of M, In the next stage
of the operation N will have arrived at O’ and
be at rest ; M will have arrived at 4.5, and will

have acquired the velocity = And lastly when

M has arrived at 8’ it will have acquired the ve-
locity 2. v, and N will have moved back to S”
and will have re-acquired the velocity > and
the balls will be at the same distance that they
' were at first when N struck C.—In explaining
these facts by the common theory, it is ad-
mitted that N has communicated to M a
greater quantity of motion than it had; that
inconsistency, however, is supposed to be re-
moved by saying, that the motion of N being
in the contrary direction, it must be deducted
from the motion of M, and the remainder will
be equal to the original motion of N. But
we know that a body cannot be put in motion,
in any direction, without force, and as the
final motion of N, as well as that of M, must
have been derived from the original force of
N ; it appears that the motion of N should be
added to, instead of being deducted from,
the motion of M, before we can properly
compare the effects with the force by which
they have been produced.—tf N had remain-
ed at rest at O’, M would have been acted
upon by C till it arrived at 9’, and the whole

#

198 On the Measure of

original force of N would have been found in
the motion of M, which would finally have

acquired the velocity ' = .

This, last explanation is given by Dr.
Wollaston as.follows. ‘ But there is one
view,” he observes “in which the compara-
tive forces of impact of different bodies was
not examined by Smeaton, and it may be
worth while to shew that when the whole ~
energy of a body A is employed without loss —
in giving velocity to a second body B, the
impetus which B receives is in all cases equal
to that of A, and the force transferred to B,
or by it to a third body C, (if also communi-
cated without loss and duly estimated as a
mechanic force,) is always equal to that from
which it originated.

«« As the simplest case of entire transfer, the
body A may be supposed to act upon Bin a
direct line through the medium of a light
spring, so contrived that the spring is pre-
vented by a ratchet from returning in the
direction towards A, but expands again en-
tirely in the direction towards B, and by that
means exerts the whole force which had. been
wound up by the action of A, in giving motion
to B alone.’’*

* Philos, Trans. 1806. p. 19.

Moving. Force. 199,

In the explanations which I have offered of
the phenomena which occur in the collision of
bodies, I have supposed all the changes of
motion and of figure to be gradual, not, in-
stantaneous; and it may be objected to, these
explanations that they cannot be applied to
cases of instantaneous impact. But I believe
it is now generally admitted, as I have already,
obsetved, that impact cannot be perfectly in-
stantaneous,—that some small but finite portion
- of time must pass during the operation;* and
if this be so, the changes of motion must
occupy also some portion of space.—Now,
if we suppose that portion of space to be.
magnified by means of lenses, we cannot doubt
that we should see_all the changes of figure,. as
wellas of motion, distinctly. in their order,
_the same as they actually appear when they,
are gradually produced in extended, spaces,

applied to the changes which take place im
. the smallest as well as in the largest spaces.

The 9th case is stated, merely to.show, that.
we cannot form a just, estimate of the forces of
bodies in, motion by. attending: solely to, the
quantity of motion, of their common centre of
gravity; and that, in eases of composition of
motion, wherever there is a loss. of mechanical

* See Hutton’s Dict. art. Force, vol. 1. pz 496.

200 On the Measure of

force in any direction, there must be a corre-
sponding change of figure, which may always
be estimated upon the principles adopted in
the preceding cases.
In the 10th case, the quantity of motion of
A (fig. 10) after collision is the same as that
of the common centre of gravity of EK and F
before collision. But the whole forces of EK
and F are not exhibited in the quantity of
motion of their common centre of gravity.—
The motion of A, however, is the whole effect
produced, and if we estimate its force by its
mass into its velocity, we cannot account for
the total loss of the forces of E and F; but if
we estimate all the’ forces by the masses into
the squares of their separate velocities, the
agreement between the forces and their joint
effect is obvious. gi

I have already adverted (page 134) to a
statement of a case of composition of motion
made by M. Laplace, in which a hypothetical
relation of the force of a body in motion to the
square of its velocity is adopted, and where
the supposed effects would be quite at variance
with those of experience. It will perhaps
be better understood with a reference to this
10th case. |

- M. Waplace says, “ La force peut étre

Moving Force. 201

exprimée par une infinité de fonctions de la
vitesse, qui n’ impliquent pas contradiction:
Il n’y ena point, par exemple, a la supposer
proportionnelle au carré de la vitesse: Dans
eette hypothése, il est facile de déterminer le
mouvement d’un point solicité par un nombre
quelconque de forces, dont les vitesses sont
connues; car si Yon prend sur les directions
de ces forces, A partir de leur point de con-
curs, de droites pour représenter leurs vites-
ses; et si l'on détermine sur ce mémes diree-
tions, én partant du méme point, de nouvelles
droites qui soient entre elles, comme les
carrés des premiéres ; ces droites pourront
_représenter les forces elles-mémes. En les
composant ensuite par ce qi précéde, on aura
la direction de la résultante, ainsi que la
droite qui Pexprime, et qui sera au carré de
la vitesse correspondante, comme la droite
qui représente une des forces composantes,
est au carré de sa vitesse. On voit par la,
comment on peut déterminer le mouvement,
d’un point, quelle que soit la fonction de la
yitesse qui exprime la force.””*

Now if AB (fig. 10th) be produced to G,
and AC to H, making AH: AC*: : AG:
AB?*, and if we complete the rectangle, and

* Systéme du Monde, p: 141.
ec

302 On the Measure of -

draw the diagonal AIT; we shall have 2
diagram of the construction described above
by M. Laplace ; and, if I understand him
right, he concludes, that if the forces of E
and F are respectively as the squares of their
velocities, AI must be the resulting direction
of A, and the square of its velocity must be

to Al as AB*: AG. If, by the force of a |

body in motion being as the square of its
velocity, it were meant, that the pressure
exerted in bringing it to rest in a given time
must be as the square of its velocity, the
result must no doubt be such as M. Laplace
describes. I cannot find, however, that this
meaning has ever been applied to the prin-
ciple in question. Such a hypothesis could
not be entertained, indeed for a moment,
without setting aside the incontrovertible ex-
planations and conelusions of Galileo. In
answer to the objection implied, in the reason-
ing of M. Laplace, against the force being

as the square of the velocity, I can only ©

repeat, what I have already so often repeated,
that it is not the pressure exerted in a given
time, but the pressure exerted through a given
space, that is understood to be universally as
the mass into the square of its velocity; and

I may add that there is nothing hypothetical.

in this conclusion.—Being derived from an

~——

a ee

. Moving Force. ~ 203

induction of facts,.it must stand or fall with
the facts on which it is grounded.

In the next case, where the angle BAC
(fig. 11) is not a right angle, the results after
collision are, in two respects, different from
the last. Ev and F are not at rest after col-
lision ; and the quantity of motion of A is not
the same as that of the common centre of
gravity of E and F before collision.* This
case, or rather the converse of it in a less
simple form, was first explained by Jokn
Bernoulli in. the eleventh chapter of his
“« Discours sur le Mouvement,’ and the
solution which I have given (page 123) will
be found to agree with his. In his twelfth
chapter, however, he extends his solution to
the case where a ball D (fig. 16) strikes any
number of pairs of balls,—the balls in each
pair being equal and at equal distances from
the line of direction of the striking ball.— But
that solution, as it has been justly observed by
Mr. Robins, “ will be true only when the
same time is taken up in communicating

* In describing this case at page 123, I have omitted to
state that E and F are supposed.to move with equal veloci-
ties; but it will be obvious from the figare and from the
results which are given, that it was so understood,
1 CaQad

204 On the Measure of

motion to all the balls,’ * and that cannot
take place unless a peculiar modification of
the elasticity be adapted to the respective
masses and positions of each pair of bails at.
their points of contact; and even then the
results will not always be as they are laid
down by M. Bernoulli. His solution :there-
fore was not, what he i WO it to be, a
general one.

Cases of this description appear to have
been imperfectly understood at the time when
M. Bernoulli wrote. In the “ Histoire de
¥/Academie Royale” of Paris, for the year
1721, p. 84, the following case is’ stated.
Two equal bails moving with equal velocities
are supposed, as in the 11th case, to strike at
the same instant a third ball at rest ; and the
directions AC and AB of the striking balls E
and Fare supposed to be such that we shall
have AC or AB=2 AH. That is, that the
absolute velocity of E or F, before they strike —
A, shall be equal to twice the velocity of
their common centre of gravity.—And it is
concluded that AD will represent the velocity
of A after the stroke.

It appears also that some of the most ob-

* Robins’ Tracts, vol. 2. p. 186.

Moving Force. 205

vious effects of elusticity in the ‘collision
of bodies were as much misapprehended then
as the motion of the bodies after collision. In |
the same department of the valuable work last
quoted, for the year 1728, the same subject
(sur la force des corps en mouvement) is
resumed, and at page 77 there is the follow-
ing statement. f

“ Un corps, quia une vitesse a parcourir
d’un mouvement uniforme 1 pied en | minute,
parcourra 2 pieds en 2 minutes, une infinité
de pieds en une infinité égale de minutes; ila _
en soi de quoi se mouvoir éternellement,
quoique sa force soit finie, il faut seulement
qu'il ne rencontre point d’obstacles. Je sup-
pose cette force telle que quand il se sera mu
pendant 1 minute, todjours appliqué 4 un
ressort qu’il fermera a la fin, et dont la base,
qui répond al’ouverture qu’il aura etié d’abord,
ait été de 1 pied, cette force soit entiérement
-consumée, et je suppose ensuite qu’au lieu de
ce ressort on lui en donne a fermer deux
‘consécutifs égaux a celui-la. I] ne peut. les
fermer sans les appliquer tous deux l’un contre
l'autre, sans réduire a rien leur base commune
double de la premiere, c’est~a-dire, sans
parcourir un espace de 2 pieds. Or cet
espace, il ne le peut parcourir qu’en 2 minutes,
7 “

206 On the Measure of

donc dans la premiere minute il ne peut avoir
fermé qu’ a de mi chacun des deux ressorts, et
a la fin de la seconde il les aura entiérement
fermés tous deux, et sa force sera consumée.”

Mr. Maclaurin has given, in his Treatise
of Fluxions, page 431, some ingenious solu-
tions of the problem where two or more bodies
at rest are struck at the same instant by ano-
ther body moving with a given velocity ina
given direction. It is remarkable, however,
that the consideration of the time was. omitted
by him in the same way that it was omitted by
M. Bernoulli; although the oversight of the
latter had been pointed out by Mr. Robins
fourteen years before Mr. Maclaurin published
his solutions; which appear to be defective
also in the following respect. . The resulting
motions are first given on the supposition that
the bodies are hard and non-elastic, and from
these results are deduced the motions which are
supposed to result from the collision of elastic
bodies.—But M. D’Alembert has shown that,
in all cases where the bodies which are struck
are not. equal to each other, and similarly
situated with respect to the direction of the
striking body, the supposition of hard. bodies
leads to erroneous results. with respect to

Moving Force. 207

elastic ones,* and it is. remarkable that the
cases selected by Mr. Maclaurin are all of +
that description.

Far be it from me to say that the oversights
of that excellent philosopher and profound
mathematician, or that the omissions er over-
sights of any of the distinguished men to
whose works [ have referred, are of much
importance when compared with the nume-
~ rous benefits which they have rendered to
science. I only wish to show that the prin-
ciple, which appears to me to be capable of
general and correct application, has been
condemned on insufficient grounds; and the
circumstance of such a man as Maclaurin
having been led to erroneous conclusions by
reasoning from the supposed action of hard
bodies, affords the hest argument for rejecting |
that doctrine. .

M. D’Alembert appears to have been fully
sensible of the difficulties which attend the
solution of problems of this description; and
from his general reasoning respecting them,
as well as from the demonstrations of some of
them which he has given, it is obyious that, ~
without considering the pressure and the space
through which it acts, as well as the time of
its acting, during the process, if I may so

* Traité de Dynamique, p, 234—5.

208 On the Measure of

call it, of collision; the resulting velocities
and directions of the bodies, after collision,
cannot be determined. .

‘have selected the case which I have stated,
(as I have selected all the rest,) as being the
most simple of its kind; and the solution
which I have offered is also simple; being
derived from examining the pressures and the
spaces through which they act in producing:
the motion of A.

The 12th example is stated for the purpose
of showing that, in cases where quantity of
motion in one direction forms no part of the
subject to be considered, there is in the colli-
sion of non-elastic bodies a positive loss of
force, in whatever way it may be reckoned,
and if that loss be estimated by examining the
pressures and the spaces through which they
act, a change of figure, corresponding to the
force which has been expended, will be found.

The 13th case was propesed to me by my
friend Mr. Dalton, to whose candid encou-
ragement I have been much indebted in the
prosecution of this enquiry. It is stated in
order to show that the same effect is produced
by the same force, whether it act by gradual
pressure or by sudden percussion.—lf the
piece of clay be placed so near to A as to
touch the prism when it begins to fall, the

Moving Force. 209

whole impression will be produced by gradual
pressure. —In estimating the force in this case;
a practical man thinks of nothing but the
quantity of mechanical force—or the pressure
into the space—necessary to raise the prism
to the given height; and as the same quantity
of force will always raise it-to the same height;
he concludes'that the same effect must always
be produced by its fall, although the times
in which these equal effects are produced
may be very different. If instead of a piece
of clay, we place a much harder substance—
a block of iron for example—under the
prism, we shall have an impression produced
on the prism as well as on the block; and,
unless the centre of motion be ofa very: per-
manent kind, we shall, when the block is
placed near to A, have a change of figtire in
that centre also. But still if all these changes
of figure could be accurately measured, by the
pressure and the space expended in producing
each of them, their sum would be equal to the
whole change of figure produced on the clay,
or'on any other comparatively soft substance,
placed under P. There are many very com=
plicated cases of this kind,—such as the biam=
mering and rolling of metals, which may, I
apprehend, be all distinctly sc: al upon
the same principles.
pd

210 On the Measure of

In the {4th Case the same effects are pro-
duced by percussion, which, in the 5th case,
are produced by gradual pressure through
sensible spaces; and we must either admit
that the moving force of D (fig. 14) is greater
than that of C, or conclude that the rotatory
motion is produced without force. It may be
said that there is in both cases only the same
quantity of motion in one direction.—I must
observe however, that Sir Isaac Newton
understood the swm of the motions of the two
bodies to‘include the rotatory as well as the
progressive motion. ‘“ If two globes,” he
says, “ joined by a slender rod, revolve about
their common centre of gravity with an uni-
form motion, while that centre moves on
uniformly in a right line drawn in the plane
of their circular motion, the sum of the mo-
tions of the two globes, as often as the globes
are in the right line described by their common
centre of gravity, will be bigger than the sum
of their motions, when they are in a line
perpendicular to that line.” * On this passage
we have the following note from Dr. Horsley.
«« The contrary seems to be true; that the
sum of the motions will be greatest, when the
rod connecting the revolving bodies is perpen-
dicular to the right line, along which the

* Horsiey’s Newton, yol. 4, p. 258.
2

Moving Force. 211

common centre of gravity is moved. But in
either way the different quantity of that sum
of motion, in these two positions of the rod,
equally makes for our author’s assertion. Of
which perhaps there is yet a more striking
proof in the prodigious generation of motion
by the collision of elastic bodies in certain
arrangements, vid. Huygens De motu corpo-
rum ex percussione.” But this is obviously
an oversight of the learned editor; for, if he had
bestowed a little more consideration on the
case as it is distinctly stated hy the illustrious
author, he would not, we must presume, have
given a commentary so much at variance
with the text—When A is perpendicular
over B, B is at rest, and A only is in motion
with the velocity 2v. The whole quantity of
motion, when the balls are in that position, is
therefore expressed in the usual way by
AX2v. But when AB is in a horizontal
position, the common centre of gravity of A
and B is moving horizontally with the velocity
v, and each ball is moving round that centre
with the same velocity v. The sum of the
motions, when in that position, must therefore
be A+B.v+A.v+B.v ; and I think, it
cannot admit of a doubt that Sir Isaac New-
ton understood the case in that light, But
although the motion is exhibited in such vari-
pd2 +

212 On the Measure of

ous quantities according to the positions of the
rod; it cannot be questioned that the quantity |
of force must remain the same, under all
positions of the rod—While the motion con-—
tinues uniform there certainly can be no vari-
ation of the force. Yt appears, therefore, (as
I have before observed p. 173) that Sir Isaac
Newton understood, that unequal quantities of
motion might be derived from the same quan-
tity of force. It must be acknowledged that,
from some expressions of Sir Isaac Newton,
in alluding to this and some other cases, it
might appear—if these expressions are taken
individually without reference to his eeneral
doctrines, that he supposed a variation of
force to take place in this case. That suppo-
sition has been noticed by M. Bernoulli with a
degree of unfortunate asperity peculiar to
himself, and very inconsistent, it must be con-
fessed, with the character by which philoso-
phical discussions ought to be distinguished,
From the context, however, it is obvious,
that Sir Isaac Newton could not mean the
casual expressions in question to be strictly
apphed as relating to variation of force in the
cases which he mentions. For, if they canbe
so applied, they must be indiscriminately ap~
plied to cases which have no resemblance to

each other, The force which is expended in
: «

Moving Force. 213

overcoming the cohesion of pitch,* for exam-
ple, can never be seriously compared with
any supposed change of force in the case un-
der consideration.—Yet, according to Mr.
Bernoulli's acceptation, Sir Isaac Newton
must have meant that there was in both cases
the same kind of variation of force.

If D be a non-elastic body, we shall then
indeed have a variation of the force similar to
that which takes place in the motion of the
pitch.—A portion of the force will be expend-
ed in producing change of figure, and the
results after collision will exhibit four distinct
effects of moving force, namely, a change in
the progressive motion of D, a change of
figure in D, a progressive motion in G, and a
rotatory motion in A and B. For, D will
move on with the velocity a and its figure
will be changed, G will move on with the

= v e.
velocity =» and A and B will revolve around

G with the velocity a That is, one fourth

of the original force of D will remain
with it after collisionx—one half will have
been expended in changing the figure of jieo
one eighth will have produced the progressive
motion of G,—and one eighth, the rotatory
motion of Aand B. But if these effects must

* See Horsley’s Newton, vol. 4, p. 259,

214 On the Measure of

be estimated by the product of the mass into
its progressive velocity, the change of figure,
as well as the rotatory motion, must be left
wholly unaccounted for.

If the more complicated cases of this des-
cription, where the force is neither communi-
cated in the directions of the centres of gravity
nor in those of the centres of gyration, be
examined on the same principles by which E
have attempted to explain the fifth case and
the case before us, it will be found, that the
force expended in producing change of figure,
added to that which is exhibited in the
motion of the bodies after collision, will
always be equal to the original force of the
striking body.

Having stated, more fully perhaps than is
consistent with the due limits of a paper of
this kind, various opinions and explanations
relating to the examples of force which I have
offered to the consideration of this society; I
wish to observe, that the terms, pressure,—
foree,—moving force,—momentum, &c. are
used, by different authors, and sometimes
even by the same author, with various mean-

Moving Force. 215

ings. It is probable therefore that I may
not have understood them, in all instances, in
their proper, or even in their intended mean-
ing.* I have been careful however to give, in
most cases, the authors’ own words; and in
all cases I have given such references that
any mistakes of that kind may be easily de-
tected by those who are disposed to examine
the subject.

That great misunderstandings respecting
the subject under consideration have arisen
from the various senses in which the terms
have been taken, must be acknowledged.
But it cannot, I think, be reasonably con-
tended that the whole has been merely a dis-
pute about words.

Soon after it had been shown by Huygens
that the “ascensional force” of a body im
motion is as the square of ‘its velocity ; that

* Since page 150 was printed, I have noticed that the fol-
lowing passage (line 17) “that the maximum effect must
consequently be as AXc*” should be corrected thus ‘that
the maximum effect of a given quantity of water must con-
sequently be as c?.” I wish to observe also, that although
the reviewers admit that there is a great difference between
* the theoretical conclusions and the acknowledged results
of experience, they appear to consider the theory to be
unexceptionable. To that I could reply only by stating at
some length the difficulties which attend the application
of the theory to practices

.

816 On the Measure of

principle was extended and brought forward
in a manner very unfavorable to its general
reception. It was adduced by Leibnitz* as an
argument against Des Cartes; and afterwards

_by Bernoullit and others, as a principle which

must supplant or supersede some of the lead-
ing doctrines of the Newtonian philosophy.
Great opposition was naturally excited by
these last pretensions ; and, as it invariably is
the case in intemperate controversies, the ad-
vocates on both sides were led into many in«
consistencies. It soon became quite a party
question, and the prejudices against one side
became so strong, that if any one ventured to
consider the absolute force of a body in motion
to be as the square of its velocity, he was
pitied or condemned, as if he had lapsed into
a dangerous heresy. It is to be regretted that
these prejudices, if such they are, are not yet
entirely removed. For myself I must ac
knowledge, it is a matter of some concern
to me, that in consequence of the explanations
which 1 have thought it necessary to adopt in
endeavouring to understand this subject, I
have, by some of my very good mathematical
friends, whose favorable disposition it is my
wish to conciliate, been considered more in
the light of a perverse schismatic than in that

* Act. Erud. Lipsiz 1686. p. 161. + Works vol. ili.

Moving Force. 217

of a patient enquirer; and I entreat that the
too great length of this, I fear tedious, dis-
cussion may be ascribed to my desire to merit
the latter rather than the former appellation.

I cannot help thinking that if this rejected
_ principle had been first produced, not in oppo-
- sition to, but as, what I believe it really is,
an extension of the Newtonian doctrines of
force, it would have been zealously cultivated
and might have proved highly interesting to
mathematicians, as well as of essential service
to practical men, in explaining those variations
of force, to the useful application of which
their operations are chiefly directed.

If we wish to trace the history of this mea-
sure of force to its origin, we must go back to
Galileo. It was first demonstrated by him
that the spaces described by heavy bodies,
from the beginning of their descent, are as
the squares of the times, and as the squares of
the velocities acquired in those spaces ; and he
first distinctly explained all the phenomena
of the motions of bodies uniformly accelerated
or retarded by constant forces, in their simple
and likewise in their compound actions. The
law of continuity appears also to have origin-
ated with him.—It is most extraordinary that
both Mr. Robins and Mr. Maclaurin have

Ee

218 On the Measure of

spoken of this law with great disapprobation,*
and that although it had been distinctly
stated by Galileo, nearly a hundred years
before the time they wrate against it, they
considered it as a new and a visionary doc-
trine produced by Leibnitz or his followers,
for the purpose of controverting the argu-
ments which had been produced in support of
the supposed collisions of hard bodies. Galileo
appears to have been fully sensible of the
importance of the law of continuity, and to
have been aware also of the objections which
might probably be brought against it. In his
first dialogue he supposes a difficulty to arise
in the mind of one of the speakers, who states
it thus ‘ Id est, quod non satis capio, cur
necesse sit, ut mobile quietem deserens, et
motum inclinatione naturali subiens, omnes
transeat gradus precedentis tarditatis, qui
inter quemcunque certum velocitatis gradum,
et statum quietis interjecti sunt: To which
the following remarkable answer is given,
‘“ Non dixi, nec ausim dicere, nature ac
Deo impossibile esse, velocitatem illam quam
dicis, immediaté conferre: sed hoc affirmo,
quod id natura de facto non prestet. Si vero
prestaret, ea operatio nature cursum exce-

* Robins’ tracts, p. 174-5.

Maclaurin’s Account of
Sir Isaac Newton’s discoveries, p. 923.

1

Moving Force. 219

deret, ac proinde miraculosa foret.” * This
short but comprehensive argument contains
every thing that can be urged in support of
any of the principles which are termed laws
of nature; and it is not easy to understand
upon what grounds of experience or analogy
this principle of continuity has ever been
rejected.

The laws of uniformly accelerated or re-
tarded motions having been demonstrated by
Galileo, the same principle was extended by
Newton to motions produced by varying
forces, where the acceleration or retardation
cannot be uniform; and in the 39th prop. of
the first book of the principia, it is demon-
strated, that when a body is urged in one
direction by a varying force, the square of
the velocity which it has acquired in any
given space, measured from the beginning of
its motion, will be as the curvilinear area
which is formed by the aggregate of the
increments of the space drawn into right
lines denoting the pressures exerted. at each
increment.

As far therefore as the measure of force,
which is composed of the pressure into the
space through which it acts, can be applied to

* Dialogus de Systemate Mundi. Lugdani 1641, p. 11.

This was first published at Florence in 1632.
Ee2

220 - On the Measure of

the estimation of the forces of moving bodies,
itis, properly speaking, the doctrine of Galileo
and of Newton. PA

But we have seen that the same principle
has been still farther extended, and applied to
explain the phenomena of force producing
changes of figure in masses of matter.

No indications of force are more constantly
presented to our notice than those which con-
sist of mechanical changes of figure.—The
fabrication of every thing that is useful or
convenient to us is accomplished chiefly by
the application of mechanical force to pro-
duce change of figure. The grinding of
corn, the expressing of oil from seed, the
sawing of timber, the hammering and rolling
of metals, the driving of piles,—are all ex-
amples of moving force producing changes of
figure; and although, in all these cases the
effects produced are of a complicated kind, yet
the moving forces by which they are produced
may be estimated with tolerable’ precision.
The force expended in driving piles into the
earth,. has been.examined by many mathema-
ticians. In this case, the whole force of a
body m motion is supposed to be expended in
driving the pile, and this quantity of force is
understood to be as the height from which the
body falls, or as the square of its velocity.

Moving Force. 221

But there appears to be a material inconsis-
tency in this application of the prevailing
theory. For, there is in fact no difference in
kind between this case and the 8th case which
we have before examined; although in that
case there is, according to the theory, no force
expended in driving the cylinder into the ball
of clay. I do not see how this inconsistency
can possibly be removed, but by adopting
Mr. Sméaton’s explanation of the collision of
non-elastic bodies.

I am aware that many object to the compa-
rison of changes of figure with changes of
motion, as effects of force. Our knowledge
ef both, however, appears to be acquired by
the same means.—They are both produced by
pressure acting through some portion of space;
and there appears to be no difficulty in esti-
mating the forces by which they are produced
' hy the same measure.

Of all the various terms that have been
adopted in explaining the phenomena which
we have been examming, none has been so
uniformly used with the same meaning as the
word pressure. All our notions of force
appear to be derived from pressure, as it is
perceived by the sense of touch. By balancing
and comparing all other pressures with that of
gravity, we obtain a common measure of

222 On the Measure of

pressure. Although pressures are balanced by
pressures relatively at rest, under an almost
infinite variety of circumstances; their most
intricate combinations are distinctly explained
and estimated by the application of a small
number of general principles; and upon that
subject no difference of opinion exists.

If pressure be applied to a mass of matter
at rest, but free to move in any direction, the
mass is put in motion. But that motion of
the mass implies motion of the pressure ; for
unless the pressure follow and act upon the
mass through some portion of space, no motion
can be produced.’ If it be clear that the
motion of a mass of matter must be produced
by the action of pressure through a portion of
space, it is not less obvious that the mecha-
nical compression, or the mechanical separa-
tion, of the parts of a mass of matter, must be
produced by the same means; and when we
speak of the resistance of inertia in one case,
or of that of repulsion or cohesion in the other,
we only mean that the exertion of pressure
through some portion of space is necessary to
overcome the resistance in either case. Al-
though we suppose the resistance in the differ-
ent cases to proceed from different causes, we
find no difference in the means by which the
vesistance is to be overcome; and by taking

a

Moving Force. 223

the pressure conjointly with the space through
which it acts, we obtain a common measure
for this description of force.

When we speak, therefore, of the force by
which the motion, or the change of figure, of
a mass of matter is produced, we mean some-
thing more than simple pressure balanced by
pressure, relatively at rest. In the latter case
we have to consider only the pressures as they
are balanced by each other, without any
reference to motion. But in the former case
no effect can be produced unless the pressure
act through some portion of space.—If the
pressure be increased in the same ratio that
the space through which it acts is diminished,
or vice versa, the same effect will still be
produced. The space, therefore, compensates
for the pressure, and the pressure for the
space ; and when taken together, they consti-
tute a determinate measurable quantity of
moving force, capable of producing effects of
various kinds, but in determinate quantities
which are always proportional to the moving
forces by which they are produced.

The term force is often indiscriminately
used to signify simple pressure, as well as to
denote the compound quantity of force by
which the motion of a body is produced.—
The “ force of gravity” for example, (mean-

*!

224 _ On the Measure of

ing quiescent pressure), and the “force of a
body in motion,” are very ‘common expres-
sions.—But these two descriptions of force
are as different in kind, as lines are different
from surfaces, or surfaces from solids; and
they have been distinguished by various
authors by different terms. From the follow-
ing proposition it appears that Galileo apphed
the same meaning to impetus which was after-
wards applied by Huygens to ascensional
force. “ Mobile grave descendendo acquirit
eum impetum, qui illi ad eandem altitudinem
reducendo sufficiat.”’ *

Leibnitz and his followers adopted the dis-
tinctive terms, vis mortua and vis viva. Dr.
Wollaston prefers impetus to vis viva, but he
sometimes uses energy in the same sense. The
Edinburgh reviewers approve of Dr. Wollas-
ton’s application of the term impetus; but
they propose to apply the same meaning to
energy which is applied by Sir Isaac Newton
to vis impressa, namely the pressure multiplied
into the time of its action.

Mr. Smeaton uses the term mechanic power
to express the product of the pressure into the
space through which it acts, or the product
af the mass into the square of its velocity.

~ * Dialo, de Syst. Mund. p. 12.

SS oe

ee a

See

Moving Foree: 225

In his definition of power (which I have
quoted at page 129) he refers only to its
effects in producing motion. But we havé
seen that he understands the same measure to
be the proper one, whether the force be ex-
pended in producing motion or change of
ficure, and he concludes that the effects of
force “ cannot be so easily, distinctly, and
fundamentally compared, as by having’ re-
course to the common meastire; viz. mechanic
power.” *

If this principle be capable of such general
application, it is desirable that it should be
denoted by a distinct term, in order to
obviate ambiguity or misapprehension. The
compound term moving force has been com-
monly applied, Ly various authors, to signify
the action of moving pressure, as distinouished
from qiiiescent pressure ; and from its general
use in this acceptation, I have been induced to
adopt it.

It is sometinies indeed used for motive force,
or the pressure uncembined with time or with
the space through which it acts. But the two
terms need not be confounded, and if moving
force were defined to be “ moving pressure
producing change of velocity; or change of
figure in masses’ of matter,” it could not be

* Philos. Trans, 1776, p. 4730
Rf

226 On the Measure of

easily misunderstood. For, if the moving
force be estimated by the changes which it
produces, the space through which the pres-
sure acts, as well as the pressure, must be
taken into the account. In the above defini-
tion it is necessary to adopt the expression
“ change of velocity’? in preference to
“ change of motion;” because change of
direction is included in, change of motion;
and change of direction cannot be estimated
by tlie pressure combined with the space with-
out reference to the time. The centripetal
force which retains a body in a circular orbit,
is similar to quiescent pressure ;—the pressure
at the centre moves through no space, and
therefore there is no change of velocity ; but
if the revolving body approach or recede from
the centre, any given space, the pressure
moves through the same portion of space, and
a corresponding change of velocity is produced.
Excepting change of direction, however, the
above definition and measure of moving force
apply to every case of moving pressure of
which we have any experience.

The pressure taken together with the time
of its direct action, bears a constant relation
to an important class of the phenomena of
moving force producing motion in masses of —
matter. . But when the pressure is applied

Moving Force. 227

indirectly by levers, or other means, or when

a change of figure is produced, the velocity

of the pressure being different from that of

the mass which is moved, this relation is no -
longer preserved. In cases of that description,

the sum of the changes produced by the mov-

ing force, is not in any constant ratio to the

time of its action. If this statement be cor-

rect, the relation between the effects of a mov-

ing force and the time of its action cannot be

reduced to a general formula—It can only be

considered as an individual character, or

property of one class of the phenomena of
moving force,—a property of great impor-

tance no doubt, but still not a general pro-_
perty. The duration therefore of a moving
force cannot be taken generally as an element
in the estimation of its quantity.

If we attempt to estimate some moving
forces by their duration, and others by the
spaces through which the pressure acts,—
according to particular circumstances which
may appear to be more favorable to the appli-
cation of one measure than the other; we
cannot avoid the inconsistency of sometimes
concluding that a given quantity of moving
force may be considered greater or less,
according to the nature of the effect it is
intended to produce.

Ff 2

228 On the Measure of

This principle of moving force may perhaps
be illustrated in some degree, by comparing
the phenomena of force with those of heat.—
‘Metals and fluids having been observed to
expand and contract according as their tempe-
rature is increased or diminished, it was for a
long time understood that temperature was the
measure of heat. After it had been proved
by Dr. Black that bodies of equal tempera-
tures contain unequal quantities of heat, it
was no longer eontended that temperature
eould be taken generally as the measure of
heat. Yet temperature is a most important
property of heat, and in cases where the tem-
perature and the heat increase and diminish in
the same ratio, the temperature may be used
as the measure of the heat.—In cases of mov-
ing force, where the space described by a
constant pressure, and its duration increase
in the same ratio, the duration may be taken
as the measure of the moving force.—Of abso-
lute motion or of absolute heat, we know
little—our researches are chiefly directed to
relative heat and to relative motion.—In the
estimation of deflecting forces, the duration
becomes an important element.—In investi-
gating the phenomena of liquefaction and
evaporation, temperature becomes an essential
consideration, Yet there appears to be no more

Moving Force, 229

yeason for taking duration as the general
measure of moving force, than for taking
temperature as the general measure of heat.

It has been shown (page 187) that if a
given non-elastic body, moving with a given
velocity, strike an equal non-elastic body at
rest in free space, half the moving force of
the striking hody is expended in producing
change of figure; and in the same manner it
has been shown (page 197) that, when the
mass of the striking body is half that of the
body which is struck, two thirds of the moving
force of the striking body is expended in
producing change of figure.

Upon the same principles, the following
general theorem is easily made out.—If any
non-elastic mass A strike another non-elastic
mass B at rest in free space, (the direction’ of
the stroke passing through the centres of gra-
vity of A and B,) the original moving force
of A will be to that part of it which is
expended in producing change of figure, as
A+B: B, and to the remaining moving force
of A and B after collision, as A+B: A. *

* The following isa demonstration of this. Let v= the

oa the velocit
re a e velocity
of A and B after collision. The moving force before

collision will be Av?, and that after collision

velocity of A before collision; then

230 On the, Measure of

The practical application of this principle
is exemplified in a variety of imstances.—In
driving piles—if the weight of the ram be very
- small in proportion to that of the pile, a great
part of its moving force is expended in bruis-
ing the pile, and the progress of the pile into
_ the earth is very small. The heavier the ram
is in proportion to the pile, the greater is the
progress of the pile, by the application of the
same quantity of moving force.—On the other
hand, if the object be to produce a change of
figure in the substance which is struck, in
hammering iron for example, if the anvil be
light in proportion to the hammer, the intend-
ed effect is not produced in the same degree
as when the anvil, or the mass which is struck,
is heavy in proportion to the hammer which
strikes it. *

If a non-elastic body strike a non-elastic

<—,07. But these two quantities are as

den
ies shea) ASE"
] Fear hence it appears that the fractional part of the

moving force found in the motion of the bodies after colli-

sion is , consequently the part which is spent in pro-

A+B
ducing change of figure is remy

* Examples of moving force similar to these are referred
to by Mr. Leslie, in his excellent work on heat, p. 128,

He explains them however on different principles.

Moving Force. 231

machine moving with a uniform velocity (such
as the float of an undershot water-wheel) the
maximum effect of moving force will be com-
municated to the wheel when the part of it
which is struck moves with half the east
of the body which strikes it.

Let A (fig. 17) be a non-elastic soft mass,
uniforgnly penetrable by the cylinder c, and
moving in the direction AB with such a velo-
city v that it would be brought to rest by
driving the cylinder up to F against an im-
moveable obstacle—If instead of an immove-
able obstacle, we suppose B to be the float of
a water-wheel moving with an uniform velo-
city =4v, and to be struck by c at F; in
that case when B has moved through a space
FH=EF, A will have arrived at G, EG
being =3 EF, and will have lost half its
velocity. In this operation 4 of the moving
force of A has been expended in changing the
figure of A, 4+ remains with it when moving
on with the same velocity as B, and the
remaining 4+ has been expended in pressing B
through the space FH, and it is easily de-

monstrable that if the velocity of B be either

greater or less than $ v, it will be pressed by

c through a space less than FH. And whether

A be uniformly penetrable by ¢ or not, the

same relative velocity of A and B is required
9

~.

232 On the Measure of

in order that the greatest possible quantity of
the moving force of A shall be transferred
to B.*—It would be too much to say that this
explanation may be applied to the action of |
water on a water-wheel, but it is remarkable
that these conclusions agree very nearly with
the results of Mr. Smeaton’s experiments.
(See page 160).

The expenditure of moving force in over=
coming the cohesion of the particles of fluids
is always exhibited under very complicated

* To mathematical readers it may perhaps be acceptable
to have the problem in a more general form.

Problem. Given two non-elastic bodies; A and B, such
that A, moving with a given velocity, 2, shall overtake B;
moving with a variable velocity, 2, in the same right line ;
itis required to-find 2, such that the increase of moving
force found in the motion of B after the stroke may be a
maximum.

Solution. Let y= the velocity of B after the stroke.

By mechanics, =y; and per question, By? —Bx?=

Av+Bxr
A+B $
maximum, That is, B. ae) —Bxr? = maximum.
Reduced, 2 Boa—(A+-2B)x7= maximum.

In fluxions 2Box—(A+2B)2xz—=o, or Bo=(A+2B)s,

B
& Snaant te

Cor. 1. If B be indefinitely greater than A,’ thien its velo-
city after the stroke will be the same as before, & r==10,
which is the case in the text.

Cor. 2. If B=A, then #=!0.

Cor. 3. If A’be indefinitely greater than B, then r=o.

Moving Force. 233

circumstances ; but the amount of it may in
© sone instances be estimated with considerable
exactness. When a jet of water issues from
an orifice of a particular construction, it has
very nearly the same velocity which a body
‘would acquire in falling freely through a
height equal to the depth of the orifice under
the Famaetties of the water.—In that case there-
fore, a very small part only of the moving force
is expended in changing the figure of the
water before it reaches the most contracted
part of the orifice.—But if the orifice be con-
structed so that any separation of the particles
of the water from each other takes place,
although they may be brought together again
and completely fill the most contracted part of
the orifice, yet there is invariably a consider-
able loss of moving force. In other words, a
portion of the moving force is expended in
producing this separation of the particles of
the water; and that portion may be estimated
by deducting from the whole moving force
‘which the water would acquire in falling
freely through the height of the head, that
portion of moving force which is found to
remain with the water after it has issued.
The following important proposition re-
‘lating to this subject, is laid down by Daniel
Bernoulli in his Hydrodynamics, page 278.
Gg

234 On the Measure of

If a jet of water I (fig. 18) issue from the
side of a vessel.A, with the. velocity. which a
body would acquire in falling: freely from the
_ surface B to C, he says the repulsion. of the
water in the opposite direction to the e jet. will
be equal to the weight of a column of ‘water,
of which the base is equal to the section of
the contracted vein, and. the height, equal: to
2 BC. det inna
This question respecting the ‘amount. of
what has been termed the “reaction of the
effluent. water,’ derives additional interest
from the circumstance of its having particu-
larly engaged the attention of Sir Isaac
Newton, and from his having given a solution
of the problem in the first edition of the
“Principia,” which he materially altered i in the
succeeding editions. In the first edition (book
2d, prop. 37) he infers, that the reaction 1s
equal to the weight of a column of water cof
which the base is equal to the area of the
orifice, and the height equal to that of the
surface of the water above the orifice. In, the
succeeding editions, the subject i is more fully
discussed. in the 36th prop. of the second
book, where he infers (cor. 4.) that, when the
area of the surface B is indefinitely large

compared with that of the orifice, the reaction.

is, what it was afterwards in a different manner

Moving Force. 235

demoustrated to be by D. Bernoulli. Sir Isaac
Newton further observes, that he found, by
admeasurement, the area of the orifice in a
thin plate to be to that of the section of the
contracted vein, at the point of its greatest
contraction, in the ratio of y 2:1 nearly.
He takes the re-action, therefore, to be greater
than what he understood it to‘be when he pub-
lished the first edition, in the ratio of v2: 1
nearly. He refers, however, more to experi-

ment than to theory for a solution of this

question; ‘and many valuable experiments
have since been made on effluent water; yet ©
I cannot find that the results of any direct
experiments have been published which go to
determine the precise amount of this re-action.

Sir Isaac Newton suggested (Principia,
first edit. p. 332) a method by which the
reaction may be easily measured. If the
yessel be suspended like a pendulum, he —
observes, it will recede from the perpendicular
in the opposite direction to the jet.—I have
made some experiments on a vessel suspended
in that manner, and in order to ascertain the
reaction as accurately as possible, I made use
of a balance-beam furnished with a perpendi-
cular arm’ of the same length as the horizontal
arms, as represented | at fig. 18. The scales
were exactly balanced, and the end of the rod

@g2

~ 236, . On the Measure of

D made just to touch the side of the vessel...
—The. orifice. was then opened, and the ~
water in the vessel was kept uniformly at
the .same height. by’ a. stream falling
gently on the plate E. The scale F having
been raised by the reaction of the jet,
weights were put into it till it was brought:
exactly to the position in which it was before
the orifice was opened, The diameter of the
vessel was 7 inches, and the height BC ex-
actly 3 feet. I tried orifices of various dia-
meters from .85,to .7 of an inch. Their
exact diameters were ascertained by a micro-
meter, and the time carefully observed in .
which 30 Ibs. of water were discharged through
each orifice.

When the orifice was made ina thin plate
(3's of an inch in thickness), [ found the re- —
action to be greater than Sir Isaac Newton’s
first conclusion, in the ratio of 1.14 to 1.
There was some variation in the results of the
experiments. The greatest reaction, however,
was as 1.16 to 1, and the least as 1.09 to 1,
which fall far short, of Sir Isaac Newton’s last
inference. The velocity of the water at the
orifice (ascertained by observing the time in
which 30 lbs. were discharged) was less than
that which a body would acquire in falling
freely from B to C, in the ratio of .6 to 1.

Moving Force. 237

I.found no constant ratio to subsist between

the diameter of the contracted: vein and that '

of. the orifice ;. and observing. considerable
opacity. in the jet at, the, contracted vein, I

~

concluded it to be divided ‘into.a number of —

different. filaments, and I gave up all hopes of
ascertaining the) actual-area of the section of
the stream at that place by measuring its
diameter... After repeated trials I found that
when the water issued through a contracted

hole, of the shape represented at G, the jet

was quite transparent, and the ‘reaction
(taking the mean of 12 experiments with 4
different orifices) was less than the weight of a
column of water of twice the height of the head
and diameter of the smallest part of the hole,
in the ratio of .865 to 1. The least reaction
was as .85 to 1, and the greatest as .88 to 1.
By measuring the quantity of water delivered
in a given time, I found the velocity of the
jet, at the smallest part of the orifice, to be less
than that which a body would acquire in
falling freely from B to C,in the ratio of
94 to1. The highest ratio was as .95 to 1,
and the lowest .89 to 1.*

* Although these experiments were made since this
paper was read before the Socicty, I have taken the liberty
to insert the results, because they afford a good illustration
of the principle which I have endeavoured to support.

238 On the Measure of

From thése results’ it ‘appears, that when
the contracted vein is not opaque, ‘and when’ '
its -vélocity is nearly equal to that whichis due |»
tothe head, the reaction is'nearly equal to’
what it was concluded to be by Sir Isaac
Newton and M.D. Bernoulli ; and the great
apparent difference between Sir Isaac Newton’s ~
first and second conclusions arises from his
haviig been misled by some experiments to
which he alludes: He says—“ Per experi- |
menta vero constat, quod’ quantitas aque, |
que, per foramen circulare in fundo vasis
factum, dato tempore effluit, ea sit, que cum —
velocitate preedicta,” [viz. the velocity due to
the head] “non per foramen illud, sed per
foramen circulare, cujus diametrum est ad
diametrum foraminis illius ut 21 ad 25,
eodem tempore effluere debet.”* We
must presume, however, that he refers to ex-
periments made by others ; for if he had made
them himself, he would, no doubt, have arrived
at. the same results which have since been so
well established by various authors, and he
would have stated the above ratio to be as
19.5 to 25 nearly.

But his demonstration of the reaction re-
quires that the velocity at the contracted vein
shall be equal to that which is due to the head.

* Principia, edit. 2. lib. 2. prop. 36.

\, Moving Force.) (239

:, Now. that, velocity cannot) be determined by
_, measuring the imperfectly contracted vein in
eases, of water apesttings none a hole in a
. thin Phlates:(: one
We may safely ‘afeed infos ‘tet in euch
| cases, the velocity. is, considerably, less, than
what i is due to the, head. For, the jet being
| opaque, some moving force must be expended
in . Separating the particles from each other,
and the distance to which the jet from such an
orifice i is projected on a horizontal plane, con-
firms. that. inference, The, demonstration,
therefore, of, the. reaction can be properly ap-
plied . to such. cases only as, those, where the
_ water, issuing through a tube properly, con-
tracted, acquires the velocity nearly which .
is. due to the head, and in. those cases the
experimental results agree, as I have stated,
remarkably well with the demonstration. a
These results agree also with the explana-
tions which have been given of moving force.
If we suppose the velocity of the jet to, be
equal to that which is due. to the -head,; and
the vessel to move uniformly in the opposite
direction cD with the same, velocity ;. the
water will be at rest asitissues: ., ©, |.)
Let a represent. the area of, the. ieaaliies
: ‘section. of the orifice. "Then ; while the vessel
has moyed ‘through a space =2 BC, a quantity

(240 On the Measure of

of waterirepresented by @X2BC has descénded

. from B torC, and has: been’ brought’ to’ rest.

. But the: reaction is =axX2BC, and this

multiplied by 2BC, the space through which

‘ithas acted, gives ax2 BC} for the amount
of the moving force’ produced, which’ js ex-

2 actly the quantity of moving force necessary

>to 'raise the column ax 2 BC to the height BC,

and to projéct it with the velocity 2BC. ‘For,
“a moving force =ax2BCX BC ‘will raise that

“golumn from © to B; and an equal moving
force will generate the velocity 2BCit in the same

i]

‘column, therefore 2ux2BCx BC=ax2BC\

is the whole moving force necessary to restore

that column to the” place and condition in

which it was before it began to descend ; and

as no moving ‘force has been ekpended in
producing dnttige of figure, that quantity of
moving force must be‘ found in the reaction
of the water through the space which the
vessel has moved’ while the water descended
and was brought to rest.

Upon the same principle an easy and simple
explanation may -be given, I apprehend, of
the action of the hydraulic machine called
Barker’s mill. Let AB (fig..19) be the per-_
pendicular tube, and BC the horizontal arm ;
let v express, in feet per second, the rotatory
velocity of the arm at the orifice C, and let the

Yaag > —

_“e

“Moving Force. 241

water be supposed to issue with the velocity
due to the pressure. Put g—16,, feet.

If BC be a cylindrical tube, and if g repre-
sent the quantity of water it contains from B
to C, the centrifugal ie upon a section

of the arm at C, will be NUR? 5 and what-
4¢ BC

ever the length BC may bes the diameter
remaining the same, g being as BC, the
centrifugal pressure at C will always be as
0? ; and it will be equal to the pressure of a
Beapeorticaler column of water whose height in

feet 1 al Then if h express in feet the hei ght
AB of the water in the vertical tube, ht

will be the whole pressure at ‘C ; and if a eda

in feet the area of the most contracted section
) a

4p :) will express the

reaction, which being multiplied by v, the

space through which it acts in a second, gives

of the orifice, 2a (it

a”
2av\ h+—~q, ) for the total moving force of

5 ;
the arm in a second. But a part of this
moving force is expended in producing the
rotatory motion of the water, and in raising it

to the height. For, if we suppose a

perpendicular tube CP. to: rise from the arm

at C, the surface of the water in that tube

Hh

242 On the Measure of

~ would stand at P, PR being if. Now if
instead of letting the water escape at C, it
be allowed to flow over the perpendicular tube
at P, and fill another similar perpendicular
tube adjoining it, and issue from an orifice at
the bottom of that tube, the effect must be
the same as if it issued at C, and a moving
force must be expended at C, sufficient to
generate the velocity v, in the water which
passes, and also to raise it from R to P.

The pressure at C being equal to the
weight of a column of water whose height is

ht, (that is =AB+PR), the velocity

. 5 . . .
with which the water issues will be

“ps Ge) or V4gh+v*. Let V ex-
press that velocity, then aV will express the

quantity. of water which passes in a second ;
v* . .
and 2aV dg will express the moving force

necessary to generate the velocity v, in that
quantity of water, and to raise it from R to P.
That quantity of moving force being deducted
from the total moving force of the arm, leaves

Vv 2 2
2av (i £59) -- chit Ps for the effective

moving force of the arm in a second.

Moving Force. 243

That this is the effective moving force, may
be shownealso in another manner, as follows :
The absolute velocity of the water after it

has left the machine will be V—v, and (V—v)?
ree

will be the head which would produce ‘that
velocity ; which being multiplied by aV, the
quantity of water delivered in a second, gives’
a V (Y—)* for the moving force which re-

4g
mains with the water after it has left the

machine.
If that be deducted from aVh, the whole

moving force of the water, there will remain

i=
aVh— aV ———_ Wah
force, which wn be found to be equal to

¢ ou) prowl yg oft dh.
2av ht ap —2a agt e effective mov-

for the effective moving

ing force stated above.

The theory of this machine has occasionally
occupied the attention of many distinguished
mathematicians, and M. Euler has given two
elaborate treatises on its principles in the
memoirs of the Berlin Academy for 1750,
p- 311, and for 1751, p. 271. His demonstra-
tions relating to this subject are very compli-

Hh2

244 On the Measure of

cated, and they do not appear to have been
adopted by succeeding authors. —

Mr. Waring, of America, has given quite a
different Diente) which has been approved of
by several good writers on hydraulics. He
concludes that the greatest effect will be pro-
duced when the velocity of the orifice is half
that of the issuing water; and that this effect
will be nearly the same as that of a well-con-
structed undershot water-wheel.*

The explanation which I have offered of
the action of the water on this machine is
different from any other that I have had an
opportunity of consulting. I offer it, there-
fore, merely as an attempt to solve an intri-
~ cate problem. —

If it were possible for the water to issue
with the velocity due to the pressure, it is
“obvious, if my explanation be right, that
although a very large proportion of the moving
force of the water may be communicated to
' the machine, moving with a moderate velocity,
the maximum of effect can only be obtained
by an infinite velocity. But when the water
issues with a velocity which is less than what

is due to the pressure, as must always be the —

* American Philos. Trans. yol. 3, p. 191 and 192.

Moving Force. 245

case in practice, the velocity at which the
maximum of effect is produced, may be found
as follows. It should first be ascertained by
experiment how near the issuing velocity can
be brought to that which is due to the pres-"
sure. From the experiments which I have
made, I have been Jed to conclude that no
greater issuing velocity can possibly be ob-
tained from a machine of this kind than what
is due to .8 of the pressure. If this conclusion
be correct, it follows that, whatever may be
the issuing velocity of the water, a moving
force, equal to 7 of the moving force which is
necessary to generate that velocity in the
water, when falling freely, is expended in
. producing change of figure ; that is, in forcing
the water through the tubes and through the
or ifice C ; and if the velocity of the machine
be such that PC=5AB, the i issuing velocity
will be equal to the velocity of the orifice, and
the whole moving force of the water in
descending from A to B will be expended ia
producing change of figure. )
For, the head due to V, the issuing velocity,
will in this case be PR, which is also the head
due to v, the velocity of the orifice. We shall
therefore have V=v ; and if CP represent the
total moying force necessary to raise the

4A

246 On the Measure of

water from C to P,,CR=AB will represent
that part of it which is expended in producing
change of figure. The greatest velocity,
therefore, that the orifice, when the machine
meets with no resistance, can acquire, will be
VERE.

When the velocity of the orifice is less than
that, V will be greater than v; and V—v, the
absolute velocity of the water after it has left
the machine, will be V.8 (4gh4v7)—v. The_
head or the moving force expended in produc-
ing that velocity will be v.8 (4gh+v* )—v)

| 4g

- The moving force expended in produc-

ing change of figure will be a(t ‘ )

Now when the sum of these two quantities, or
pei Mery wee
v8 (Agh+v* )—v) +a( mt) is a mi-

ag ;

nimum, we shall find v=/2gh(y¥5—1)=

6.3056vV 7 for the velocity of the orifice when

the machine produces a maximum of effect ;

and in that case the above sum becomes
=.4472h.

~ We shall therefore have h—.4472h=.5528h

for the maximum of effect, supposing / te

Moving Force. 247

represent the whole mioving force of a given
quantity of water descending from A to B. This
effect is considerably greater than that which
the same quantity of water would produce if
applied to an undershot water-wheel, but less
than that which it would produce if properly
applied to an overshot water-wheel.
Respecting the maximum of effect produced
by machines, I wish to observe, that in the
actual construction of machines it is necessary
to aim at a maximum quite different from
that which is usually proposed in books on the
theory of mechanics. 'This will perhaps be
best explained by examining the simple case
where a given weight P, (fig. 20) connected
with another W, by a string passing over the
pulley F, descends vertically and raises W,
without, friction, from the horizontal line AC
along the inclined plane AB. If we make
AB: BC::2W:P, W will be raised to B in
the least time ;* and upon this principle, the
maximum of effect in machines is usually de-
monstrated in theory. In practice, however,
the object is not merely to raise W to B
in the least time, but to raise it with the
least expenditure of moving force. When

* If the ascent be made in the least possible time, W
must ascend not along the plane AB, but along a concave
surface AGB.

248 On the Measure of

it is raised in the least time, P > must’
descend ‘through a space =AB, but when
it is raised with the least moving force,
P descends through a space =1AB only.
For, if we make BD=ZAB, and let W ascend:
along any concave surface DEB, of which
BD is the ehord, it will be raised to B by
the descent of P through a space =BD, and
it will be at rest when it arrives. at B. This
is so obvious, that it would be superfluous to
give a demonstration of it. 1t appears then,
that ‘twice the quantity of moving force which
is absolutely necessary to raise W to B, must
be expended if it is to be raised by P im the
least time. To determine the curve by which
W will ascend from D to B in the least time,
is an intricate’ problem, and I do not know
that it has ever Leen solved ; but a practical
approximation to it in any particular case may
be easily found. A well constructed steam-
engine for raising water exhibits in’ every
stroke a practical example of the same pro-
blem. At the commencement of the stroke,
a very great pressure of steam is thrown upon |
the piston, and this pressure is gradually
diminished, so that at the end of the stroke
there is a considerable preponderance in the
opposite direction. In consequence of this

x OK A

Moving Force. 249 |

regulated pressure of the steam, the motion
of the machine resembles the uniform vibra-
tions of a pendulum, and the moving force
of the steam is applied to the greatest ad-
vantage.

By proceeding on the principle that when
W is raised to B in the least time, the maxi-
mum of effect is produced, many erroneous
conclusions have been drawn respecting the
proper construction of machines. It is laid
down for example, on this principle, that “ In
an overshot water-wheel, the machine will be
in its greatest perfection, when the diameter
of the wheel is two-thirds of the height of the
water above the lowest point of the wheel.”’*
But it is very well known that there would
be lost, by that construction, nearly one-third
of the moving force of the water, which is
saved by making the wheel one-half larger in
diameter, and by making its velocity much
less than what is required by the above rule.

It should be borne in mind, that the me-
chanical effects produced by means of ma-
chines, consist, almost invariably, of changes
of figure. Even when a given mass is raised with
an uniform velocity to a given height, a change
of figure only is produced. For, if the mass

* Gregory’s Mechanics, vol. J, p. 447.
Ki

250 On the Measure of

were pressed to the earth by the elastic force
of a spring instead of the force of gravity, we
should not hesitate to, say, that, a mechanical
changé of figure is preduced when it is raised.
Changes of figure of this kind being easily
estimated, the raising of a given. weight toa
given height, has Jong been adopted | asa cons
venient common measure for almost-every kind
of, moving force. If the ‘rule, - quoted above,
for. the construction, of an_ overshot water-
wheel, had, been tried by this IDSA Grn Hs
fallacy would have. been apparent. .

Dr. Wollaston has described a case. lt adi
lision. and change of. figure, which has been
understood to prove, | that the force of a body
in motion may. be properly estimated either
by the duration of its action, or by, the space
through which it acts, according to the par-
ticular views which may be taken of the
phenomena, Cc (fig. 21) is supposed to be a
ball of clay, or any other soft and wholly
inelastic substance, suspended at rest, but free
to move in any direction with the slightest
impulse ; the two pegs, O and P, to be similar.
and equal in every respect, and to meet with
uniform and equal resistance in penetrating
C; the weight of A to be double that of B,
ane velocity of A moving in the direction AC,
to be half that of B, moving in the opposite

ee"

‘Moving Force.” 251

direction BC, and’ A’and B ‘to strike their
respective pegs at the'same ‘instant. The
result will be as follows.’ C will remain un-
moved, A and B will be brought to rest in the
same time, and the peg P will be found to
have penetrated C twice as far as it has been
penetrated by O. This case appears to me to
admit of the same explanation as some’ of
those which we have already examined. It is
considered by many, however, to show dis-
tinctly, that the forces of A and B are equal.
If we confine our attention solely to the cir-
cumstance of C remaining at rest, we must
no doubt conclude, that the opposite forces of
A and B are equal; but if we attend to all the
results of the experiment, we cannot con-
sistently, draw that conclusion. It has often
been asserted by the advocates on both sides of
this question, that we can judge of forces only
by their effects ; yet it has been contended by
M. D’Alembert,* and by many other gcod
writers on dynamics, that the estimation of
forces by their total effects, involves a meta-
physical question which ought not to be mixed
with experimental investigations of physical
facts. -It may be safely. affirmed, however,
that nothing can be more strictly grounded upon

_* Traité de Dynamique, Disc. Prélim. p. 22.
\ £UZ

252 On the Measure of

experiment, than conclusions derived from the
examination of mechanical changes of figure.
This term, as has been already observed,
includes every change of figure which requires
moving force, or pressure acting through some
portion of space, to produce it. Whether
it be the repulsion or the cohesion of the inte-
grant parts of bodies, or the ‘attraction of
masses to each other, that is to be overcome,
mechanical change of figure is produced ; and
we have seen, in various cases which have
been examined, the uniform relation whick
subsists between determinable quantities of
change of figure and the moving forces by
which they are produced. We find by expe-
rience, that when a body in motion is retarded
or brought to rest, either a change of figure is
produced, or a quantity of moving force, equal
to that which the body has parted with, is
communicated to some other body or system
of bodies. It has been supposed, indeed, that
A and B, in the case stated, may be brought to
_ rest without any change of figure being produc-
ed. That supposition, however, is contradicted
by universal experience, and in point of fact
we may, with as much consistency, suppose
that a body may be put in motion without
force, as that two bodies moving in opposite
directions may destroy each other’s motion

Moving Force. 253

without producing change of figure. It ap-
pears then, that if any metaphysical consi-
deration has been improperly mixed with
this question, it is the supposed possible ex-
istence of perfectly hard non-elastic substances.
But unless we have actual proof of the
existence of such substances, we can have no
evidence derived from experience to justify
the inference, that Aand B may be brought to
rest without producing change of figure.
When a physical experiment of any kind is
made, it is generally understood, that unless
all the results be collected and examined,
erroneous conclusions may be formed. If
an experimenter reject some of the results
which he obtains, on the supposition, that
sometimes they may not occur, although
in fact they constantly occur in deter-
minate quantities, he cannot reasonably
demand assent to general conclusions drawn
from so partial an examination of the facts.
If this reasoning be well founded, we can-
not reject the consideration of the changes of
figure produced by A and B; and if we have
no experience of a mechanical change of
figure being produced without moving force,
nor of bodies destroying each other’s motion
without producing mechanical change of
figure, we cannot, in the case before us con-
4

254 On the Measure of

sistently. do otherwise than estimate the abso-
lute forces of A and B by the respective
changes of figure produced by each.

I shall now conclude my observations ‘with
a simple application of the principle which I
have endeavoured to support, to the resolution
of compound moving forces.

If we suppose BAC (fig. 22) to be aright
angle, and three strings, AB, AC, and AF,
in the same plane, to be united at A; the
strings AB and AC to be prolonged to a
length indefinitely great, when compared with
the diagram, and the end of each of the
three strings to pass over a vertical pulley.
If the parallelogram be completed, and if
three weights m, n, and 0, which are to each
other as AD, AB, and AC respectively, be
suspended by the respective strings AE, AB,
and AC, they will balance each other, and the
strings will coincide in direction with the dia-
gonal and sides of the parallelogram. If the
weights be set in motion, by taking from m an
indefinitely small part of its weight, n and o will
descend, raising m, and the point of junction
of the strings will move in the direction AD.
When that point has arrived at D, the weight
m will have ascended -a space equal to AD, n
will have descended a space equal to AB, and
o will have descended a_ space equal to AC.

VOSS

Moving’ Forces 255

The quantity of moving force therefore, is, on
one side m.AD, balanced on the other side by
n.-AB+o.AC ; the moving force of each string
being as the weight suspended to it multiplied
into the space, through which it has moved.
So that in this case, where the parallelogram
is right angled, the moving forces m the dif:
ferent directions are as the squares of the
diagonal and the respective sides of the
parallelogram. x

When BAC is not a right ol let sp
parallelogram be completed, and the weights
suspended as hefore, and draw DF and DG
(fig. 23) perpendiculars to AB and AC. «If
the weights be set in motion, the point of
junction of the strings will move in the direc-
tion AD, and when that point has arrived at
D, the. weights m, n, and o, will have moved
through the spaces AD, AF, and AG re-
spectively. The moving force, therefore, is
on one side m.AD balanced by nw. AF'+0.AG
on the other side ; or the moving forces in the
different directions are réspectively as the
square of AD, the rectangle AB. AF, and
the rectangle AC.AG.

This conclusion, however, involves the ge0-
metrical proposition, that the square of AD i is
equal to the sum of the rectangles AB. AF
and AC. AG, a property of the triangle which

256 _On the Measure of

is demonstrated in the first prop. of the fourth
book of Pappus; and that prop. unfolds, as he
observes, a general principle, including the
properties demonstrated in the 1.47, and VI. 31,
of Euclid. For the following concise demon-
stration, [am indebted to my friend Dr. Roget.
Draw BH and CI petpendiculars to AD.
Then the triangles ABH and ADF being
similar, AB: AD:: AH: AF. Also ACT and
ADG being similar, AC:AD :: AI(=HD):AG,
from these proportions we obtain the following
equations AB.AF=AD.AH and AC.AG=
AD.FID, which being added together, give
AB.AF+AC.AG=AD.AH+AD. HD=AD.
(AH+HD)=AD>.*

Various other interesting and useful exam-
ples might be given of the application of the
measure of moving force, which consists of the
pressure multiplied into the space through
which it acts; but I believe I have already
exceeded the proper limits of a dissertation of
this kind, and doubtful as I must be of the
favourable reception of the reasoning which I
have adopted, I am more disposed to curtail
than to lengthen it.

By way of recapitulation, however, I Irish
briefly to observe, that we appear to derive all

* The same proposition is demonstrated in the IL. 19. of
Professor Leslie’s Elements of Geometry.

gg tI emake e~

It Serene \

OP ta

Moving Force. 257

our notions of force from pressure as it is per-
ceived by the sense of touch, and that in all
cases where neither the velocity nor the figure

' of the body pressed is changed by the pres-

sure, we have only simple pressure balanced by
pressure, the various combinations of which
have long ago been explained and demon-
strated in the most satisfactory manner.

But in all cases where either the velocity or
the figure of the body pressed is changed by
the pressure, we have examples of moving
force, which may be properly represented by
a rectangle; of which the pressure forms one
side, and the space, through which it acts, the
other side: and however various and compli-
cated the changes of velocity and of figure may
appear, they must all be derived from deter-
minate quantities of moving foree. We may
have changes of rectilineal velocity in various
directions, changes of rotatory velocity, and
changes of figure, all produced at the same
time by a given quantity of moving force;
and it is certainly a desirable object to deter-
mine what portion of that quantity has been
expended in producing each of these different
effects. I have endeavoured to show that all
these changes may be distinctly explained and
estimated, by examining the pressure and the
space through which it acts in producing them.

Kk

258 On the Measure of Moving Force.

In objecting to the opinions of many eminent
‘writers on mechanics, I have ventured much.
Although this has not been done inconsider-
ately, Iam sensible there are in the arrange-
ment of my arguments some faults, and others
which have escaped my observation, will no
doubt occur to the reader. But if my endea-
vours to make this essay more free from im-
perfections than it is, had been successful, it
would still be unreasonable to expect it to
obtain more attention than has been paid to
the arguments of the illustrious men who have
preceded me in the same track of investiga-
tion. If I have succeeded so far only as
to show, that the prevailing doctrines of
force, especially in their application to practi-
cal purposes, involve some difficulties which
are unexplained ; and if I have offered any
inducement to men of science to reexamine
this question, my chief object will in a great
measure be accomplished.

_ Errata.

Page Line.

116 27 for “ EandC,” read “ P and Q”

121 21 for“ and when,” read “and, if FH and #1 be
taken each =1EF, when”

123 15 after “ right angles” insert “ and if AC=AB”

150 17 for effect, &c.” read “effect of a given quantity
of water must consequently be as c?”

176 12 for “ force acting at,” read “ pressure ‘acting
through a small space at’

176 14 for “ DH will he,” read “and if DH represent”

215 ~— 8 of the Note, for “‘ theory” xead “ theoretical mea-
sure of force.”

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( 259 ) .

Account of a remarkable KrFECT produced by
A STROKE OF LIGHTNING;

In a Letter addressed to Thomas Henry, Esq.
F.R.S. &c. President of the Literary and
Philosophical Society, from Matthew Nichol-
son, Esq. With Remarks on the same, by
Mr. Henry.

(Read October 20, 1809.)
ee
Liverpool, 12th Sept. 1809.

Dear Sir,

I have complied with your request in

the best way I could, by soliciting and re-
ceiving Mr, Chadwick’s assistance in the
description of the Thunder-storm which hap-
_ pened at his house; and which description
I mean herein to inclose—leaving it to you,
Sir, to make what use of it you think proper.

I am, dear Sir,
Your obliged humble servant,

MattHew NICHOLSON.

Kk2

260 Remarkable Effect of a

Some Lacis respecting a Thunder-siorm at
the house of Mr. Elias Chadwick, of Svin-
ton, in the parish of Eceles, and county of
Lancaster, on Sunday the 6th of August,
1809—reported from: information. commu-
nicated upon the spot, and stnce extended
and revised, by Mr. Chadwick himself—Ath
September, 1809.

Me. CHADWICK’s house is situated five
miles from Manchester, between the roads
leading from thence to Wigan and to Bolton,
upon the elevated range of country which lies
to the right of the river Irwell. The near
prospects from the house are ‘towatds the
South-west, over the Worsley ‘coal-district,
and the flat country bounded by the rivers
Trwell and Mersey below Manchéster. A
considerable part of this scene consists of @
bog called Chat-moss. If the ‘house itself be
not over coal, it. is probably owing ‘to some
derangement of the strata, for coal is procured
at different depths through the neighbourhood
in almost every direction.

The plan (plate 3, fig.2) may give some idea
of the buildings, where BCDE is the scite of a
coal-vault with its open entrance at F, and of a

1

ns ee

Thunder: Storm. 261

water-cistern over it. The building for these
purposes was made of bricks, with a lime-
cement, which holds water. Its foundation,
and the bottom of the vault, were about one
foot below ground. The walls, three feet
thick, were about twelve feet high, strengthen-
ed by bond-timbers. The top and bottom of
the cistern, and all its walls, were covered with
large flags. The whole was about eighteen
feet long, eight feet. broad, and eleven feet
high. above ground; and there was in the
vault at the time about one ton of coal.

_ About half past, twelve at noon, after re-
peated peals of distant and approaching thun-
der in the lower country, the heavens became
suddenly enveloped in thick darkness; and it
was thought prudent to open all the windows
and doors of ihe house, as the best preparation —
for receiving the expected storm. No sooner:
was this done, than a tremendous explosion
occurred ; the effect of which was the re-
moval of the outside wall of the described
eistern, from its upright position shewn. by
the sketch G, (fig. 3) into the inclined position,
intended to be represented in the sketches H
and K, as it now stands, with its coping
entire, among the shattered fragments of the
end-walls, It may be necessary, as the
sketches are not perfectly correct, to say, that

262 Remarkable Effect of a

the end of the outside-wall next the entrance
to the vault was removed about nine feet, the
other end only about four feet.

Mr. and Mrs. Chadwick were standing in
the passage L. Mr, Chadwick was suddenly
turned half round ; but neither of them were
injured, A young man of seventeen years
old, also received the shock unhurt, and was
the first to communicate the astonishing event,
which had occurred out of doors ; for he alone,
standing in the stable about twenty-four feet
distant, saw the cistern wall remove from its
place, which it did, not instantaneously, but
gradually. Two young trees at twelve feet
distance appear untouched. The bond-timbers
of the cistern were forced by the shock to a
greater distance than the brick-work, and
were apparently scorched. That part of the
building, which was removed and is yet stand-
ing, contains about seven ‘thousand. bricks.
The wall seems to have been lifted from its
foundations. The weight of the works, re-
moved and thrown down, is probably not
over-rated at twenty-six tons, inclusive of the
flags and mortar. Some water was in the
cistern, but the quantity is unknown. No
metals, excepting slender spout-brackets, were
near the place, and. these were not even dis-
turbed.. A leaden pipe for conveying the

Thunder Storm. 263

water into the adjoining kitchens, had also
sustained no injury. Immediately after the
explosion, rain fell ina torrent, deluging for
a moment every thing around; and fora few
minutes the air in the nearer parts of the
house was offensively smoky and sulphureous.

Such were some of the circumstances and
effects attending an event, in itself awful ; and
perhaps, unequalled in the records of this part
of the world.

ass RAN ——$

REMARKS

On the Foregoing Narrative,
BY MR. HENRY.

THE very extraordinary circumstances,
attending the storm described by Mr.
NICHOLSON, called to my recollection an
account of a thunder-storm near Coldstream,
in Scotland, related by Mr. Brydone, in a
letter to Sur- Joseph Banks, which is inserted
in, the 77th volume of the Philosophical
Transactions. Of the leading facts, detailed
in that communication, the following is a
brief abstract.

The storm of thunder and lightning, alluded
to, happened on the 19th of July, 1785. In

964 Remarks on the

the early part of it, the interval of time,
between the flashes and the arrival of the
sound, was so considerable, as to allay all ap-
prehensions of danger in Mr. Brydone and his
family, who were watching the progress of the
tempest. Suddenly, however, they were
alarmed by a loud report, for which they
were not prepared by any immediately pre-
ceding flash. It resembled the firing of seve-
ral muskets, rapidly succeeding each other,
and was not followed by a rumbling noise like
the other claps. After this, the clouds began
to disperse without any subsequent disturbance.

At this moment, and at a small distance
from the place where Mr. Brydone and his
companions were observing the tempest,
James Lauder, who had just crossed the
Tweed, sitting on the fore-part of his cart,
and had nearly gained the summit of an ascent
about 70 feet above the bed of the river, was
suddenly killed by an electric discharge, toge-
ther with the two horses which he was driving.
Part of the iron work of the wheels was
found, on examination, to be in a state of
incipient fusion, and the wood connected with
it was shattered and dispersed; but though
the heat had’ affected the metal thus strongly,
there were no marks of combustion on the
timber. About four feet and a half behind

Foregoing Narrative. 265

each wheel of the cart, was a circular hole in
the ground, about 20 inches diameter.. The
earth and small stones seemed as if they had
been torn up by the violent strokes of a pick-
axe, and were thrown on each side of the
road. On pushing back the cart, in the same
track it had described, to the spot where the
acgident had happened, the marks of fusion
‘on the wheels were found to correspond with
the centres of the holes in the ground. Yet
another cart, which was following at the dis-
tance of about 24 yards lower down the hill,
was not injured ; the driver, though he had
his companion full in view and was stunned
by the report, perceived no flash; nor was he
aware of any unusual sensation.

From the above and other circumstances, it
appears probable that the electric fluid,
which occasioned the disaster, did not proceed
directly from an impending cloud, but was
discharged from the earth. The manner in
which this might happen, has been explained
by an ingenious theory of EaRL STANHOPE,*
of which the following is a sammary outline.

Let ABC (plate 3, fig. 1) represent a cloud
of several miles in length, one end only of
which approaches the earth within striking
distance at G. Let another cloud DEF be

* Philos. Trans. vol, 77.
cy |

266 Remarks on the

imagined. to extend beneath the former, and a
portion of it at E to be nearly within strik-
ing distance of the road at LM, where the
two carts may be supposed to have been pass-
ing. Both clouds may be assumed to be
positively electrified. When the upper cloud
discharges itself violently into the earth at G,
the electricity of the lower cloud, hitherto
condensed by the contiguity of the upper one,
will rush at DA to restore the equilibrium in
the latter. The electricity of the earth at
LM, which had hitherto remained quiescent,
though condensed by the electrical atmo-
sphere of the lower cloud, being now freed
from the superincumbent elastic pressure, will
issue, with great force, into the contiguous
cloud DEF, destroying or greatly injuring
the imperfect conductors through which it
passes. This mode of action of the electric
fluid, Earl Stanhope has denominated the
returning stroke. ‘It accounts,” his Lordship
has observed, “for the loud report of thunder
that was unaccompanied by lightning at L or
at M. The report must be loud from its
being near; but no lightning could be per-
ceived at L or M by reason of the thick
thunder cloud DEF being situated immedi-
ately between the spectator at M and DA, the
place between the two clouds where the
lightning was.”

Pees
ond:

described by M

R

tts ba ore the

Foregoing Narrative. 267

The foregoing narrative and ingenious
theory may tend to explain, in some degree,
the extraordinary event at Swinton. In both
instances, the thunder and lightning, which
were observed previously to the great explo-
sions, were distant. In the Scotch storm,
though distant lightning had been visible, ne
- flash was perceived at the place where Lauder,
the driver of the cart, was killed ; nor does it
appear that any flash attended the destructive
explosion at Swinton. The great darkness at
the latter place renders it probable that, ac-
cording to the hypothesis, there were distinct
clouds at different altitudes. It can scarcely
be doubted that the electrical current passed
from the earth to Lauder’s cart ; nor can we
imagine that such a mass of brick and stone
work, asformed the cistern at Mr. Chadwick’s,
could have been lifted and moved from its
foundation either by a main or lateral stroke.
A proof, indeed, that it was not, is, that the
wall was left upright with its coping entire.
Mr. Chadwick, who was standing in the
house, was turned half round, which motion
was probably caused by the action of the
electric fluid on his feet. In the same storm,
by which Lauder was destroyed, shocks were
felt in several places in the vicinity, but were
not immediately preceded by lightning. A

L12

268 Remarks on the

little before the fatal accident, a tremulous
motion of the earth was perceived by a re-
spectable witness ; and a man in a hayfield,
who was thrown down, complained of having
received a violent blow on the soles of his feet.
In one respect, the circumstances at the two
places were dissimilar. No rain succeeded
the explosion in Scotland, where there had
been a long continued drought ; but the storm
at Swinton was followed by a very heavy
shower ; and the four days immediately pre-
ceding the storm had been showery.

From a meteorological journal, kept by
Mr. Hanson, house-surgeon of the Manchester
Lying-in Hospital, it appears that there were
four remarkable changes in the pressure of the
atmosphere, from the second to the eleventh
of August. On the evening of the sixth,
there was much distant thunder and lightning.
On that day, the barometrical column was
much augmented, and indicated the greatest
variation in the space of twenty-four hours.
The range of the thermometer, on the same
day, was from 68.5° to 55°; and the wind,
from the 4th to the 8th inclusive, was west.
On the 10th we had one of the most tremen-
dous thunder storms ever experienced in this
part. of the country ; and, during the whole
month, the most violent and fatal tempests
raged in almost every part of the kingdom.

Foregoing Narrative. 269

The quantity of rain, that fell at Man-
chester during the month of August, 1809,
amounted, according to Mr. Hanson’s journal,
to 3.875 inches ; and at Malton in Yorkshire,
by Mr. Stockton’s register, it reached the
enormous quantity of 9.7 inches. At Bingley,
in the West-Riding of that county, it is stated
at 4.96 inches. It would add greatly to the
value of meteorological registers, if they were
made to include the variations in the electrical
state of the atmosphere; and from a com-
parison of these changes with the tables of
diseases, kept by medical practitioners in the
same situations, it is not improbable that
valuable inferences might be drawn, especially
respecting the cause of the prevailing epi-
demics. \

Connected with the present subject, it may
be remarked, that the temperature of the
atmosphere during the last summer, though the
season was distinguished by numerous and
awful storms, has been unusually low. On
the 10th of August, the day so remarkable for
the violence and permanence of the thunder
storm, it did not exceed 68°, and the mean
heat of the day was only 55°.88,

( 270 )

THEOREMS anp PROBLEMS,

INTENDED

To elucidate the mechanical principle called
VIS VIVA.

BY MR. JOHN GOUGH.
(Communicated by Dr. Houme.)

swe

DEFINITIONS.

1. Force is an abstract term comprising
motive force, retarding force, resistance, and
the vis viva of mathematicians on the con-
tinent.

2. Motive force is any force, that increases
the motion of a body on which it acts.

3. Retarding force is any force that dimi-
nishes the motion of a body subjected to its
influence.

A. Resistance is a force constantly exerted
by a body, when affected by pressure or
percussion, to preserve its figure unchanged.

5. Quantity of resistance is the whole force
thus exerted by a body, while its figure is
undergoing a certain change.

6. Vis viva is the whole force opposed by
a body in motion, to a retarding force which
impedes its progress : and, conversely, it is the

1

wen. —

On the Vis viva. 271

whole force accumulated in a body by the
action of any motive force, which puts that
body into motion.

Axioms, or Maxims derived from universal
Experience.

1. Forces are magnitudes, consequently two
forces of the same kind have a ratio the one
to the other.

2. If two bodies, which are equal and alike
in all respects, move with equal velocities ;
their vires vive are also equal.

3. A motive or retarding force is equal to
a force, which, by acting in a contrary direc-
tion, would preserve the body, thus acted on, in
a state of uniform motion or rest.

4. The vis viva of a body is equal to the
quantity of resistance, which it is able to
overcome.

THEOREMS,

THeorem I. If two bodies, A and B,
move with equal velocities, their vires vive
will be directly as their masses or quantities
of matter; that is, put F=vis viva of A;
f = vis viva of B; a= massof A; b = mass
of B; and we have as F:f:: a: 6. vi

For let ¢ be a mass which measures aand 6b,
and let g be its vis viva when it moves with

9272 Theorems and Problems

the velocity common to Aand B. Now F
and f are magnitudes by az. Ist: therefore
they may be divided into equal parts, as well
as the masses a and b to which they belong:
but a and 6 have been divided into masses,
each of which is equal to ¢; and each of
these masses moves with the velocity common.
to A and B; therefore g denotes the vis viva
of each of them by axiom 2d. Hence it fol-
lows that a and F are equimultiples of ¢ and
g, aand F being divided into an equal number
of parts; for the same reason 6 and / are
equimultiples of the same magnitudes; con-
sequently as F: f:: a:b by Euclid V. 4.
Q. E. D.

Coroxtiary 1. If two bodies be acted on,
for the same or equal intervals of time, by
motive or retarding forces, which are as their
masses ; the vires vive acquired or lost by
them are also as their masses, or as the
momenta acquired or lost by them. For the
accelerative forces are equal in this case by
dynamics, and the times being equal, the
vélocities are equal; therefore as F': f:: a:6
by the proposition: But when the velocities
are equal, the momenta are as the masses:
Hence as F: f:: M:m.

Cor. 2. Bodies, which ascend or descend
for equal times near ihe surface of the earth,

On the Vis viva. 273

acquire or lose quantities of the wis viva,
which are as the momenta acquired or lost by
them in equal intervals of time, because the
motive force of gravity is as the matter on
which it acts.

Turorem II. Suppose two mediums,
whose powers of resistance, P and p, act
uniformly, to be penetrated by any mechani-
cal means whatever, to the depths S and s:
Put R and r for the quantities of resistance
surmounted in penetrating them; and we
have as R:r:: PS: ps.

‘For since P and p are magnitudes by ax. 1,
they may be represented by right lines:
Assume the right line AC, (plate 4, fig. 1) in
which take CB, making AC: CB::P:p;
also make CE perpendicular to AC ; in which
take CT—S and CV=s; also let CE measure
both CT and CV: complete the parallelograms
CT Aa, CVBb, and draw EG parallel to AC,
meeting Aa in G, and Bb in H: lastly divide
the lines CV, CT, by means of the common
measure CE into the equal parts CE, EL, IV,
VL and LT.

In the first place, let P=p; then CA=CB;
let n= quantity of resistance required to pene-
trate the medium having the resistance p,
from C to E, by def. 5; and the same quan-
tity will be again demanded to carry the work

Mm

274. Theorems and Problems

on from E to I, as wellas from I toV : Hence
y and CV are equimultiples of n and CE;
therefore as n:r:: CE: CV:: rectangle
Cii: rectangle BV: let g= quantity of re-
sistance which would penetrate the same me-
dium through the space CT; and we shall
have for the same reason, as n:q:: rectangle
CH: rectangle BT. Now let P be greater
than p; and AC will be greater than BC.

In this case, the force required to penetrate
the medium whose resistance =p, through the
space CE, will be to that required to penetrate
that whose resistance =P, through the same
space, as BC to CA, by def. 5.; that is, the
quantities of resistance of the two mediums
will be in the same ratio, by axiom 4. Hence
by equimultipies g: R:: rectangle BT: rec-
tangle Ca; but as qg:r:: rectangle BT: rec-
tangle Cb; consequently as R:r:: rectangle
Ca: rectangle Cb:: PS: ps. Q.E.D.

Cor. 1. When FP is constant, R has a con-
stant ratio to PS; but when p is variable,
y has a constant ratio to ps, by prime and ulti-
mate ratios; hence as R:r:: PS: ps.

Cor. 2. As F': f:: R: r, by axiom 4; hence
as F': f:: PS: ps, Pand p bemg invariable;
but if p be variable, we have as F': f:: PS:
ps; that is, F has a constant ratio to PS;

On the Vis viva. 275

and this is true whether P is a motive or re-
tarding force, by def. 6.

Cor. 3. If gravity be the motive force, and
a, b, the masses acted on, it will be money:
aS: bs; for itis as P: p::a:b in this case.

Cor. 4. If the vitoestis of the bodies be
equal, we shall have by theor. 1.as F: f::a:6;
hence by cor. 2. asa: b:: PS: ps, and p-equal
bPS~as; therefore if gravity be the motive
force acting on the body whose mass =a, we
have P=a; and p—bS~s, or the weight of a
body which is equal to the resistance opposed
to the given body whose mass =b, by the
medium, which it penetrates ; this follows front
the 3d axiom.

Tuerorem III, Put u« ui v for the velo-
cities of the bodies a@ and 5b, and we have as
F :f :: au’: bv* universally.

Case 1. Let P and p be constant forces,
and it will be by cor. 2. theor. 2. as F: f::
PS: ps; but as PS: ps:: au*:bv*, Emer-
sons’s Mechanics, prop. 6; hence as F': f:;
au”: bv’.

Case 2. Let one of the forces P and p be
variable, namely, p; then by cor. 2. theor. 2.
as F: f::PS:ps; but ps is in constant
proportion to bux, by Emerson’s Fluxions,
(sect. 3, prob. 2, Ist edit. ); thereforethe fluent,
or f,is in constant proportion to 6 v* ; moreover

Mm2

276 Theorems and Problems

PS or F is in constant proportion to au,
Mechanics, Prop. 6; hence. as F: f:: au? ;
bv*. Q.E.D.

Cor. 1. As PS: ps::au?:by?.

Cor. 2. Let gravity be the motive force
acting on a, then P=a 3 also put c=16,3, feet,
and we have w=32+ feet=2c, and it will be,
by cor. f, as ac *ps::4ac*: bv*; hence
Acps=bv’.

Cor. 3. If P=p, we have F's f:: S:s::u:v.
For F:f:: PSips::8:5:: au*>:bv*; but
au=bv, Mechanics, prop. 4th; therefore as
Fifi::Sis::usv:: 6:a@; and this corollary
is true when the force P or Pp is variable; for
in this case it will be as Fi f >: Siaiss eats
bv»,

Cor. 4. If m be the momentum of b, f will

. . 2
be in constant proportion to ” or to mv;
b

hence if b be one of a system of bodies in
motion, its vis viva will be affirmative in all
cases ; because m? is affirmative, and the signs
of m and v are always alike.

Tuerorem IV. If a, b, d, &ec. be the
masses of any number of bodies moving with
the velocities u, V, v, &c. which they have
acquired by the uniform action of the motive
forces P, p, gq, &c. in passing through the
spaces S, s, t, &e,; we have 4 ex (PSt+pst+
@t Ke. )=au? +bV2+d v2, &e, .

On the Vis viva. Q277

For 4c P S=au’?;4cps=bV*;4cqt=dv’,
by cor. 2. theor. 3.; hence, by addition, 4 cx
(PS+pstqt, &e.)=au?> t+bV*t+dv’*, &e.
Q.E.D.

Cor. 1. If g be the sum of the vires vive of
the bodies, whose masses are a, b,d, &c.g
will have a constant proportion to au*+bV* +4
dv’, &c.

Cor. 2. Let n—a+b+d, Kc. r= its velocity
when g denotes its vis viva, and we have by
cor. 1. nz?=au?+bV?+d v’, &c. ; hence 7—
pate MATT Rs

ScnHotium. It appears from the last
corollary, that a system of bodies in motion
has an assignable quantity of vis viva, even
when the momentum of it, or the motion of its
centre of gravity is equal to nothing.

TrErorEM V. Let P, Q, R, &c. (plate 4,
fig. 2) be a system of bodies in motion, whose
common centre of gravity is G, moving in
absolute space, in the direction Gg: put y=
the velocity of G in Gg; u= the velocity,
with which P approaches to, or recedes from
G in the relative space P,Q, R; V the same
‘Kind of velocity in respect of Q, and v in re-
spect of R; and let a, 6, d, denote the masses
of P,Q, and R: then the vis viva of the sys-
tem will be as (a+b4d).y*+tau*+bV*+dv*.

278 Theorems and Problems

For each of the bodies P, Q, R, moves in
absolute space, namely, in the direction Gg,
with the velocity y, common to them all;
consequently the sum of their vires vive in
this direction is as (a+b+d) y*, by cor. 1.
theor. 4. But the vires vive of P, Q, R, in
the relative space PQR are respectively as
au*, bV* and dv’ by theor.3 ; hence the sum
total of these forces is as (a4)4d). y*+au? +
bV*+d v’, cor. 1. theor. 4. Q.E.D.

Cor. 1. If P, Q, and R be at rest in the
relative space PQR, they move only in abso-
lute space with the velocity y; that is the vis
viva of the system is equal to that of its centre
of gravity; because u=V=v=o; and the
figure of the system undergoes no change;
because P, Q, and R preserve their relative
positions unaltered. |

Cor. 2. But if u, V, and v be real quanti-
ties, the vis viva of the system exceeds that of
its centre of gravity, by the theorem. For
the same reason, the bodies P, Q, and R are
not at rest in the relative space QRP; that is
the figure of the system is undergoing a
change ; consequently if P, Q, and R react
upon each other from any cause whatever, the
foregoing excess of vis viva will be exerted to
overcome this reaction; which will continue

On the Vis viva. 279

until a quantity of resistance has been sur-
mounted equivalent to the excess in question,
by axiom 4,; at which time the figure of the
system will become permanent by the last
corollary; if no new disturbing force inter-
vene.

Cor. 3. The excess of vis viva, pointed out
above, is exerted altogether in the relative
space PQR ; consequently the mutual reaction
of the parts of a system can not alter the vis
viva of its centre of gravity ; therefore the
same cause does not change the momentum
of this point by cor. 4. theor. 3 ; which agrees
perfectly with the common dynamics.

Scuorium. In estimating the change of
figure, produced in a system by the reaction of
its parts, we may consider the centre of gravity
to be at rest, and take notice only of the velo-
cities of the constituent parts relative to the
centre of gravity; in which case we shall
have, au4bV+dv=o.

Turorem VI. Let APE, BQH, (plate
4, fig. 3) be two bodies, which meet in E;
put k= their relative velocity, and a, 6 for the
masses of APE, BQE respectively ; and the
quantity of vis viva exerted on the system

APQB, to change its figure, will be as - - .

a

For let G be the centre of gravity of the
1

280 Theorems hua Problems

system ; put wand v forthe absolute velocities of
APE and B@E respectively; then the vis viva
of the system is as au*+bv* by theor. 4; but
the velocity of et by dynamics, where

the sign, connecting the terms of the nume-
rator, is affirmative when the bodies APE,
B@E move in the same direction, and nega-
tive when they move in contrary directions;
a* u* + 2aubo +570”,
a+b
by theor. 3; but the excess of au*+bv* com-
pared with this expression is as the vis viva
which acts on the figure of the system by cor.

2. theor. 5; which excess =a b* (“+ 242 +07)
a+b ;

now the vis viva of G is as

now when the bodies move in the same direc-
tion u—v=k and when they move in contrary
directions wtv=k; therefore the excess in

question —“2", Q. E.D.
a+b

Cor. 1. The momenta of the bodies APE,
BQE are equal, in the relative space APQB ;
because they add nothing to the momentum of
the centre of gravity G; therefore the vis viva
of APE before concussion is to the vis viva of
BQE, as the velocity of the former, to that of
the latter, or inversely as their masses, by
cor. 4. theor. 3: moreover the velocities of

APE, B@E are respectively equal to
ok asd
a+b a-+-b°

On the Vis viva. 2$1

Cor. 2. Let P and Q be the centres of gra-
vity of the bodies, when they come into con-
tact at E; p and q their centres of gravity, when
they are at rest in the space PABQ by Cor.
2, Theor. 5; then as action and reaction
are equal at EK, GE will be constant in all
cases ; because G and the space PABQ move
with equal velocities ; and from the nature of
the centre of gravity it will be as PG: pg::
QG:qg. Now let the bodies APE, BQE
be homogeneous and pliant ; and it is evident,
that one of the points P or Q moves faster than
G; from whence it follows that pg and gq are
less than PG and GQ; i. e. the points P and @
approach each other and the common centre
of gravity G, while the mutual reaction of
the bodies is exerted to reduce the vis viva of
the system to that of its centre of gravity.
Let us suppose in the next place APE to be
an indefinitely hard body, and BQE to be
soft; then APE will suffer no change of
figure; PG (or PE+EG) will be constant ;
that is, pg=PG; therefore qg=QG and
pg=PQ, in which case the body BQE under-
goes all the change. Lastly, if both the
bodies be infinitely hard, neither will suffer
any change; and PQ will remain invariable:
but a force situated in @ will act equally on
their respective centres of gravity in the,

Nn

282 Theorems and Problems

directions GP and GQ thereby giving to each
body equal quantities of motion in opposite.
directions... In this, imaginary case, then, the.
whole force of APE, and BQE acts in. the,
character of momentum ; consequently ; the
vires, vive of bodies. arise from the. soft,
and pliant, texture of all. substances with,
which men are acquainted. ‘This observation
affords a. clear distinction of momentum, and.
vis viva: the former is a force, which. one
body. exerts on another to change its motion,
in absolute space; but, the latter is employed
in overcoming the continued reaction of resist,
ing mediums, and in Lage the Pana of
soft and elastic bodies. ;

Cor. 3. Let P, Q, R, sci (plate 4, fig. A)
be the centres of gravity of three . or, more
bodies situated in the right line PR ;,im which.
some or all of them move so as to bring all of
them. into contact ; moreover let a, b, d,, &e.
be the masses of P, Q, R, &c; &. the relative
velocity of P and Q;' + that.of P and R;
n that of Q and R; é= the. mass. of the sys-
tem =at+b+i, &c: LI say the quantity of vis
viva exerted on the system to change its figure,
is as the sum of the rectangles of each.pair of
bodies drawn into the square of their relative.
velocity directly, and.inversely as the mass ¢5

or it isas S004 ae" x ee bdn*. For let u,V, v;
t

On the Vis viva. 283

&e, denote the absolute velocities of P, Q, R,
&e, and proceed as in nga RET of
the theorem. |

Txurorem VII. saat APE: dial BQE,
(ithe 4, fig. 3), be two homogeneous and
elastic bodies in motion, which meet at: E;
put’ Fand f for the quanitities of vis viva which
are exerted during the streke, on APE and
B pe to change their figures, and let their
masses be denoted by a and 6; and it will be q
as F: fi: b: a; that is, these quantities of
vis viva will be inversely as = quantities of
matter on which they a cme
For, ‘since the bodies APE and BQE
are homogencous, their powers of resistance
are “equal ; “therefore the point BH, and their
common centre of gravity G, are at rest in
the relative space AP QB, by cor. 2. theor.
6; and the motion of AP EH, as well as that
of BQE, is opposed by a force acting at G
in the contrary directions GP and GQ, by
mechanics, prop. 44. cor. 4; hence we have
as Pp: Qq: 2b: 4, “by cor. 3. theor. 3 ; but
ary Te Pe Qq, by cor. 2. theor 2;
because the resisting powers are equal in both
directions ; therefore as I’: f:: b: a. Q.E.D.
| Cor. 1. The vis viva, exerted on an elas-
tic body , does not become inactive by chang-
ing the figure of that body. On the contrary

n2

284 Theorems and Problems

the force remains accumulated in the matter,
constantly ready to restore its original shape ;
that is, the vis viva infused into a body of this
description acts on the cohesion of its consti-
tuent particles. Let g= the vis viva thus
infused ; d= the mass, which receives it; t=
the intensity of its action or its effect ona

given part of d; and ¢ is as 43 and g as td.

Cor. 2. We have, by the theorem, as
Fif::b:a; but by cor. 1. as Fi f::aT
;bt; hence as 7’: 1::b* : a*; that is, the
intensity of the vis viva accumulated, by
collision, in APE, is to the same power in
BQE; asthe square of the mass of BQE,
to the square of the mass of APE, hence it
happens, that when two homogeneous elastic
bodies of very different magnitudes strike each
other, the Jess is broken while the greater
remains uninjured: because the smaller body
receives the greater quantity of vis viva in a
less portion of matter.

Cor. 3. The theorem is equally applicable
to homogeneous bodies which are soft and
ductile; now by the demonstration of the
theorem, as F: f::Pp:Qq; that is, the
vis viva exerted to change the figure of a body
is as the space through which its centre of
gravity is compelled to move by that effort.

On ihe Vis viva. 285

MECHANICAL PROBLEMS;

The solutions of which depend for the most
pari on the preceding theorems.

Prosiem I. Ifa cube, whose height =
inch, and weight =1 pound, move with the
velocity acquired by falling freely through
193 inches, and strike with one of its faces
an indefinite mass of soft matter, which it
penetrates to the depth of 7-72 inches before
its velocity is destroyed: required a weight
which is equal to the resistance of the matter
to the face of the cube ?

Sotutrion. We have in cor. 4, theor. 2.

a=1=6b; S193; s=7: = 3 hence p or

the required weight, equal 4S. 5 __ 95 itys)
s

$
Q.E.L.

Progiem If. Ifa sphere, and cube equal
to its circumscribing cube, move with equal
velocities, and fall upon an indefinite bed of
matter, having an uniform resistance, in such
a manner that the cube strikes the bed with
one of its faces, and sinks m inches perpendi-
cularly into it: what is the perpendicular
depth to which the sphere will sink; supposing
the bodies to be homogeneous, and neglecting
the action of gravity ?

286 Theorems and Problems

Sotution. Put d= the diameter of the
sphere and height of the cube; j=314159, Ke;
also let F, f, R and r denote the quantities,
which they represent in theor. 2. Then the
masses of the cube and sphere are as d? to
= or as 6 toj; therefore as Fi: f'::6: 7,
by theor. 1; but as F:'f:: Rs 7, by ax. 4.
hence as 6:7:: R:r; ‘but R is as nd, the

matter removed by the cube; therefore as.

6 Ht YY n d*: int = the matter removed by

the sphere. Now if J ae be less than? 2 or

“half the sphere, the depression made by the
globe is a segment less than a hemisphere, the
perpendicular height of which is =; ; but if
jn 4* be greater than ie that is, if m be
6

greater than Ly the depression made by the
globe is a cylindrical pit, having a hemispheri-
cal bottom, the perpendicular height of which
is $21". Q EL.

Prositem UI. Lect AOB and aob,
(plate 4, fig. 5.) be two levers, revolving
with the angular velocities C and ¢ about the
‘points O and o; and let two material points,
whose masses are B and b revolve with the
levers; these things being supposed, let two
forces F’and f act for an instant at the points A

On the Vis viva. 287

and a, so as to disturb the:angular velocities of
B and 6, denoted by C and c; it is required to
find, by the doctrine of the vis viva, what ratio
the fluxion of C has to the fluxion of ¢?

Sorution. Let Band 6 move through the
arcs B E and be, with the absolute velocities
uand v, while the forces F and f are acting
at the points A:anda; let P and p be two
forces which would produce the same changes
of motion in the material points B and b, by
ing at the distances OB and ob, which are
produced by F and f at the distances O A and

a; put d4=OA; D=OB; a=oa; d=ob.
By the laws of circular motion, we have as
D*. C* :.d*. c* >: u*:v?; and by fluxions,
as D*.Co:d?.ce::ua: vy; but by theor. 3.
as PiBE :.p.be:: B.D*C Cb. d* ec ;
now as BE:be::D.C:d.c;._ hence
as P.D:p.d::B.D’*c:6.d*c; but as
ere d::A.F:a.f; therefore as

a

CVesee tr. VET.

Cor. 1. If Fand/ be constant forces acting
at A and aon B and 8, it will be as C:c:

AI od '
Cs. go} : pe +} : also, if and f be va-
riable, but have the constant ratio of om to 2,

it will be as @: @:' 744, &.
, a Bip ora

§ ‘

288 Theorems and Problems

Cor. 2. If C=c, in the prob. or C=c in
cor. l, weshall have, as A F:a f:: BD* :bd’.

Cor. 3. Hence if A F=a f, then BD*=
b d*; that is, the vires vive of Band b are
equal, and B:b::d*: D*::v* su’.

Cor. 4. Consequently when A F=a/fy if
Band b be so placed, as to receive equal
angular velocities from the forces F and /;
they also acquire equal quantities of vis viva
at the same time. !

Pros. IY. Let it be required to find the
centre of gyration of a system of material
particles b, 1, k, (plate 4, fig. 5,) revolving
about a given point 0, in consequence of a
force f, acting at a, perpendicular to the arm
ao, of the compound lever ob kia?

SoxuTion. Assume O as a centre of
rotation ; and let OB represent the radius of
wyration to the system bh1; make AO=a 0;
and let the force F=f, act at A, perpendicu-
lar to AO; then F.AO is in constant pro-
portion to O Br. (6+4+/), by cor. 1, prob. 3,
and the definition of the centre of gyration.
Now f, acting at a is, divided into as many
parts as there are particles 6, k and J; let p,
gandr, be these parts; p.a0o, g.a0 and
r.ao, are as bXbo', kXko* and bx/o*, by
cor. 2, prob. 3; therefore asp.a0:b.bo0*::
f.ao:b.botk.k ot]. 10°; but p.ao:

On the Vis viva. 289

b.bo? :: F.AO:OB?. (b+k+1), ibid;

hence O B* . (b+k+/)=b.bo0° th. ho*tl,

1o?, and BO = | (Libor tt- bolt fo") Q.ELL.
al bk-I

Cor. 1. The centre of gyration of a system

b, k, I, is also the centre of its vis viva ;
that is, if a material point, B, whose mass
=b+k+l, &c. revolve round the centre O at
the distance O B with the angular velocity of
the system 5}, k, l, the vis viva of B is equal
to the vires vive of the particles, 6, k, 1, &c.
i by cor. 4, prob. 3, or theor. 4.

Cor. 2. Ifo, the centre of rotation, coin-
cide with the centre of gravity of 6, k, J, the
system has no momentum, (mechanics,
prop. 50); but it has a quantity of vis viva
equal to that of B, by the last corollary ;
hence if the parts of a system move amongst
themselves, it has a quantity of vis viva by
this cor. and theor. 4, whatever may be the
state of the centre of gravity.

Cor. 3. Let G be the centre of gravity of
the system b, k, 1; jom oG, in which pro-
duced, take o R=O B, the radius of gyration
to the point o; also make G r= the radius of
gyration to the point G; puto R=R, 0 G=g,
G r=r, then g?+7r°=R’, by mechanics ; but the
system revolves with equal angular velocities
about the points o and G; therefore the abso-
lute velocity of R may be resolved into the

00

290 Theorems and Problems

absolute velocities of G andr, consequently
the vis viva of the point R may be resolved
into the vires vive of the points G and r; be-
cause the quantities of matter, supposed to
move with these three points, are equal. |
Propitem V._ Required the centre of
oscillation of the system 6, 7 and k? ti
Soxrution. Let OS (plate 4, fig. 5,) be
the length of a simple pendulum, which
vibrates through similar arcs in equal times
with the system b, & and J, vibrating upon
the point 0; and let the matter in the point S
be equal to ‘all the matter in b, k and 1; make
os=OS8; and s is the centre of oscillation
required. Now to find the length of OS or
os, we are to consider that the matter in the
system acts by its weight at G perpendicular
to the horizon to give the point R a certain
angular velocity ; and the matter in the pen-
dulum acts at S in the same direction to give
GS the same angular velocity ; therefore put
O S=s; and we have as g:s:: R?:s* by
cors. 1 and 2, prob, 3; henceasg: BR: is 8.
9.E.T. : 3

Cor. 1, R*=gs.

Cor. 2. If the system b, &, and J, revolve
about the point 0; put t= the time of revolu-
tion, m= the matter in b, k andl: and the

m Zs

m R*
vis viva of the system | is as™—, or as ~.
¢2 t
ae

2

———seerercerr

i

On the Vis viva: 29%

for, the velocity of the point R or the centre

of gyration, is as R; therefore the vis viva of
t

7 P} 2 : yi :
the same centre is as le by theor. 3;
’ & zt

m R?,

therefore the vis vita of the system is as ——-
t

cor. 1, prob. 4, or as ae by the last
corollary. . !
Proriem VI. Let there be two cylinders
A and B of the same ductile matter whose
diameters are a and 0, and heights ¢ and d,
respectively ; aud let these cylinders be drawn
out ia length until. their diameters become

and 4. what is the ratio of the forces

ae ?
m nN

F and f, required to produce these changes ?

-Soxurron. When the cylinders have
been drawn as directed in the problem, the
length of A= m*c; length of B= n* d; and
the heights of their centres of gravity above
the plane, on which they stand, are as their
lengths, or as m2 eto n?d; but the. heights
of the centres of gravity of A and B above the
same plane were as ¢ to din their first. shape;
therefore the spaces through which their
centres of gravity move, while their figures are
changing, are as (m*—1) .¢ to (n?—1) a3
consequently as Fi f+: (m*—1) . ¢:
(n?—1). d, by cor. 3; theor. 7; where the
diameters .a, and b, are not found in the

proportion, Q.E.L.

292 Theorems and Problems, sc.

Examrre. Let A and B be two wires,
the first 5, and the latter 3 inches long; and

let A be drawn to one tenth, and B to one

fourth of its original diameter; and we have
Fi: f'::99X5:15x3::11: 1.

Prospitem VII. If a brittle ball A be
broken by falling with the velocity uv, on a
‘Jarger ball B of the same matter; with what
velocity v, must B strike another ball C
larger than itself, to be broken in like man-
ner ?

Sotvution. Put a, 6 and c= the masses
of A, B and C; then a= the vis viva
exerted to change the figure of the system
A and B, by theor. 6; and the quantity
bar pity to change the figure of it is as

aes = by cor. 1, theor. 6, and theor. 3; for
a
the same reason, the force employed to change

the figure of B when -it falls upon C, is as
b c? vo?
(b-+-¢)?
and B must be equal; because they produce

equal effects ; but the intensity is.as the vis viva
directly and mass ce by cor: 1, theor.7;

therefore apache 3 hence as c. (atb)
(@Fb* ora
1b. (b+e) ::u:v. Q.EI

Cor. If € be iudedinitely great, it will
beasatd:b::u:v

: now the intensities of these forces in A

» Lage, 292. Plate.

*
i}
\
‘
;
>
.
Ca
’
, .
‘
t
iM
~
“
'
‘
4
N
.

( 293 )

ON THE
‘ THEORIES

OF THE

EXCITEMENT
GALVANIC ELECTRICITY ;

BY

WILLIAM HENRY, M.D.F.R.S, &c.

~<<<@>>>-

| Severat theories have been framed to
account for the origin of the electricity, which
is excited by the Galvanic pile, and by simi-
lar arrangements. Of these, the first in the
order of time was proposed by the distin-
guished philosopher* to whom we are in-
debted for some of the earliest, and therefore
the most difficult, steps in this department of
science. The hypothesis was suggested by a
fact, which may be considered, indeed, as
fundamental to it. It had been observed by
Mr. Bennett, so long ago as the year 1788,
and afterwards confirmed by Volta himself,
that electricity is excited by the simple appo-
sition of different kinds of metals. The best
way of exhibiting this fact is to take two discs
or plates, the one of copper, the other of zinc;

* Signor Volta, in Nicholson’s Journal, 8yo. i. 1335,

294 On the Theories of the

to apply them to each other, for an instant,
by their flat faces, and afterward, separating
them dexterously, to bring them into contact
with the electrometer. The instrument indi-
cates, by the divergence of ifs gold leaves,
what kind of electricity each of the plates has
acquired ; which proves to be positive in the
zinc plate, and negative in the copper one.
To explain the phenomena, in the experi-

ment which has been just described, it has
been supposed by Volta, that, during the
contact of the plates, a movement of the elec-
tric fluid takes place from one plate to the
other; and that the zinc acquires just as much
as the copper has lost. The metals, therefore,
he denominates motors of electricity, and the
process itself electromotion, the latter of which
terms has been adopted by Mr. Davy. From
subsequent experiments, Volta ascertained
that the metals stand to each other, in this-
respect, in the -following order; it being
understood that the first gives up electricity
to the second; the second to the third; the
third to the fourth; and so on:

Silver,.

Copper,

Tron,

Tin,

Lead,

Zinc.

Excitement of Galvanic Electricity. 295

It is to this transference of electricity, that
Volta ascribes the whole of the phenomena,
exhibited by Galvanic combinations. Ac-
cording to his view, the interposed fluids act
entirely by their power of conducting electri-
city, and not at all by any chemical property.
The effect of a series of Galvanic plates, or
of a Galvanic pile, he believes to be nothing
more than the sum total of the effects of seve-
ral similar couples or pairs. Why the evolved
electricity is determined to one end of the
series, and exists there in its greatest force, I
shall attempt to explain by the following
illustrations, :

If a plate of zinc be brought into contact,
on both sides, with a plate of copper, it may
be considered as acted upon, in opposite
directions, by equal forces, which destroy each
other. No alteration, therefore, takes place
in its state of electricity ; nor does any change
happen, even when we substitute, for one of
the copper plates, a third metal; on account
of the trifling difference between the electro-
motive powers of bodies of this class. But
liquids, possessing this power in only a very
small degree, may be brought into contact -
with one of the zinc surfaces, without impair-
img the electromotive effect ; and acting merely
as conductors, they convey the excited elsctri-

296 On the Theories of the

city from the zinc plate, across the contigu-
ous cell, to the next copper plate.

Let us imagine, then, a series of copper
and zinc plates, arranged in pairs for any
number of repetitions; (See the Diagram in
plate 5, fig. 1,) with cells between each pair for
the purpose of containing a fluid. Before
these cells are filled, every copper plate will,
according to the hypothesis, be in the state of
negative, and every zinc plate in that of posi-
tive electricity. Let us farther suppose the
natural quantity of electricity in each copper
and zinc plate, before they are brought into
apposition, to be denoted by gq, and that,
when the electricity has passed from the cop-
per to the zine, the ratio of the quantities in
each may be as 1: 2.* Let now the cells be
filled with a idineais fluid; every pair of
contiguous plates of copper and zine will still
maintain their relative proportions of electri-
city, viz. as 1: m. But, by reason of the
conducting power of the fluid, the electricities
of the first zinc and second copper plates will
be equalized; as, in succession, will be also
those of the zinc plate 2, and copper plate 3,
&e. Now in order to find the relative quan-'

* For the algebraical expression of this theory, which,
in the paper as originally read, I had stated in common
numbers, I am indebted to my friend Mr. Dalton.

Excitement of Galvanie Electricity. 297

tities of electricity in the several pairs of plates,
when an equilibrium in the arrangement is
effected, if m equal the number of pairs of
plates, then 2nq= the total quantity of elec-
tricity in all of them taken together. Let 2 =
the quantity of electricity in the first eopper
plate of the series ; then, by hypothesis, mz =
that of the contiguous or first zine plate; also
mx =the quantity in the second copper plate
{by reason of the conducting fluid); but
1: m::mx:m’*x = the quantity in the second
zinc plate. In lke manner the quantities in
the successive copper and zine plates may be
found, and will constitute this series ;

1 2 8 4 n
Copper plates, x, ma, m*x, mix, &c.....ma"™

Zinc plates, mz, m?x, mix, m*a, &e.....m2"
Hence it appears that the quantities of elec-
tricity in the successive plates of copper or of
zine form a geometrical progression, the ratio
of which is m. Also the total quantities of
electricity in the successive pairs of plates
form a series in geometrical progression, as

ander.
Pairs of pl. 1 2 3 4
Quant. of El. 1-m.xla.1-- m.x,m?.1-+-m.alm3,1--m.xl&e.

From the above theory of Galvanic action
it necessarily follows, that if the effect ofa
pile be in proportion to the difference in the

298 On the Theories of the

electricities of the first and last plates of the
series, a pile of 50 pairs will not be exaetly
half so energetic as one of 100 pairs, but some-
what less; because the differences in the terms
of a geometrical series increase as the terms
increase. But, in the present instance, there
is great reason to apprehend that the ratio of
1 to m is very nearly that of equality. If so,
the geometrical series for a moderate number
of terms, will scarcely differ from an arith-
metical one. ‘This accords very nearly with
experience ; for it has been determined by _
Volta, that if a combination of 20 pairs of
plates produce a given effect on the electro-
meter, a series of 40 will produce double the
effect ; one of 60 triple, and so on. At the
same time it is probable that the electric
intensity of the plates, composing each pair,
relatively to one another, continues unaltered,
notwithstanding the change in their absolute
quantities of electricity.

When a connection is established between
the two extremitics of a series like the above,
for example between the third zinc plate, or its
contiguous cell, and the first copper plate, the
opposite electricities tend to an equilibrium.
The third pair loses a share of its electricity,
which is gained by the first; and the intermedi-
ate pair, being placed between opposite forces

Excitement of Galvanic Electricity. 299

of perhaps equal amount, remains in equilibrio.
Hence, in every Galvanic arrangement, there
must be a pair of plates at or near the centre
“an the natural state of electricity. A commu-
nication, between the two extremities of a
pile would therefore reduce it to a state of
permanent inaction, if there did not still exist
some cause, capable of disturbing the equili-
brium. On the hypothesis of Volta, this can
be nothing else than the property of electro-
motion in the metallic plates, which has been
described as the primary cause of all the phe-
nomena. .

This theory, on first view, appears suffici-
ently to explain the facts on electrical prin-
ciples, without the interference of chemical
action. Consistently with the hypothesis,
different fluids, when made parts of Voltaic
arrangements, produce effects more or less
energetic, as they are more or less active in
conducting electricity; the only property,
according to Volta, that can be considered as
influencing their efficiency in the pile. There
are several facts, however, which, if not
absolutely irreconcileable with the hypothesis,
are certainly not at all explained by it. Why,
for instance, it may be asked, when pure
water forms a part of the arrangement, is the

Pp2

300 On the Theories of the

action of the pile suspended by placing it im
an exhausted receiver, or in any of those gases:
that are incapable of supporting oxidation?
Why is its efficiency increased by an atmo-
sphere of oxygen gas, or by. adding, to the
water in the cells, several fluids, in a propor-
tion not sufficient to change materially its
conducting power? Why is the nitric acid,
though a worse conductor of ‘electricity than
the sulphuric, more active m promoting the
energy of the apparatus? Why is the power
of these combinations proportional to the dis-
position of one of the metals composing them
to be oxidized by the interposed fluid? These
facts undoubtedly suggest that, in some way
or other, the chemical agency of the fluids
employed is essential to the sustained activity
of the pile. The principle has even been con-
- ceded by some distinguished electricians, who
have attempted to explain it in different ways.

To account for the effect of the interposed
fluids, Mr. Cuthbertson has suggested a
theory, which is both ingenious and suffici-
ently feasible.* With Volta, he assumes: the
electromotive change in the metals to be the
first in the order of phenomena. And when
(he observes) the copper has given, andthe

* Nicholson’s Journal 8vo. ii. 287.

Excitement of Galvanic Electricity. 301

zine has received, all. the electricity,, which
their mutual powers require, if any menstruum
be presented, which is capable of effecting a
change in the metallic property of the two
bodies, a change in their electrical states must,
at the same time, happen. Bat as tlie altera-
tion of metallic property is only superficial,
the change of electrical condition will, also,
be only at the surface; and the interior; part
of the zine plate, retaining its. property of
resistance, the electric fluid, evolved at its
surface, will necessarily be propelled forwards,
through the menstruum, to the next copper
plate of the series. This, however, can only
happen in a progressive manner, because the
fluid is but an imperfect conductor, a condi-
tion indispensible to the maintenance of any
Galvanic intensity.

* The explanation of Mr. Cuthbertson... is
unquestionably a valuable supplement to the
theory of Volta, in-as much as it takes into
account the efficiency of chemical menstrua.
These, consistently with his view, will evolve
electricity the more. freely, in proportion as
they destroy more rapidly the metallic pro-
perty of the plates of zinc. The hypothesis,
however, is defective, because it fails to
account for some of the phenomena ;—why,
for example, the action of the menstruum is

302 On the Theories of the

chiefly, if not entirely, exerted in oxidizing,
and dissolving the zinc plates; and why the
evolution of hydrogen gas, or of nitrous gas,
occurs chiefly at the copper surfaces. |
An hypothesis, originally suggested by
Fabroni, and reversing those which have been
already stated, has been adopted sy several
eminent philosophers in our own country. It
assumes the oxidation of the metals composing
galvanic arrangements to be the cause, and
not the effect, of the evolution of electricity.
In the solution of a metal (it bas been observ-
ed by Dr. Wollaston) * it would appear that
electricity is evolved by the action of the acid
upon the metal ; and, in cases where hydro-
gen is disengaged, that this evolution is re-
quired to convert the hydrogen into gas.
When a piece of zinc and another of silver are
immersed in very dilute sulphuric acid, the
zinc is dissolved and yields hydrogen gas;
the silver, having no power of decomposing
water, is not acted upon. But as soon as the
‘two metaJs, placed under the diluted acid, are
made to touch, hydrogen gas arises also from
the surface of the silver. In this case, it is
added, we have no reason to suppose that the
contact of the silver imparts any new power;
but merely that it serves as a conductor of

® Phil, Trans.

Excitement of Galvanic Electricity. 303

electricity, and thereby occasions the forma-
tion of hydrogen gas.

The chemical theory of the Galvanic pile,
though already suggested in general terms,
may be considered however, as having been a
mere outline, till Dr. Bostock undertook to
give it greater distinctness and consistency.*
To the extended hypothesis, which he has
proposed, it is necessary to admit, as a ground
work, the three following postulates; Istly,
that the electric fluid is always liberated or
generated, when a metal or other oxidizable
substance unites with oxygen; 2dly, that the
electric fluid has a strong attraction for hydro-
gen; and 3dly, that when the electric fluid,
in passing along a chain of conductors, leaves
an oxidizable substance, to be conveyed
through water, it combines with hydrogen,
from which it is again disengaged when it
returns to the oxidizable conductor.

To the efficiency of the pile, two circum-
stances, it is observed by Dr. Bostock, are
essential ; that the electric fluid be disengaged ;
and that it be confined and carried forward in
one direction, so as to be concentrated at the
end of the apparatus. The first object is ful-
filled by the oxidizement of the zinc; the
second, Dr. Bostock supposes, is effected by

* Nicholson’s Journal 8yo, iii, 9.

304 On. the Theories of the.

the union of the evolved electricity. with
nascent hydrogen, and by the attraction of
the next copper plate for electricity, At the
surface of this plate, the hydrogen and elec-
tricity are supposed to separate ; the hydrogen
to be disengaged in the state of gas, and the
electricity to be conveyed onwards to the next
zinc plate. Here, being in some degree
accumulated, it is extricated in larger quan-
tity, and in a more concentrated form, than
before. By a repetition of the same train of
operations, the electric fluid continues to
accumulate in each successive pair; until, by
a sufficient extension of the arrangement, it
may be made to exist at the zine end of the
pile in any assignable degree of force.

.. The hypothesis of Dr. Bostock agrees, then,
with that advanced by Mr. Cuthbertson, in
pointing out the more oxidable metal as the
source of the electricity, which is put in action
by Galvanic arrangements. It goes farther,
however, and defines that change, which Mr.
Cuthbertson was satisfied with terming, in
general language, “ a loss of metallic pro-
perty,” to be the process of oxidation ; and it
adds also the important and necessary expla-
nation of the transmission of hydrogen across
the fluid of the cells, and the appearance of
hydrogen gas at pe surface of the copper

Excitement of Galvanic Electricity. 305

plates. In these respects, it is certainly more
adequate to account for the phenomena. It
is chiefly objectionable, in as much as the
data, on which it is founded, are altogether
gratuitous. For what other evidence have
we, than those very phenomena of the pile,
which the theory is brought to explain, that
electricity ts evolved by the oxidation of me-
tals, or that hydrogen is capable of forming,
with the electric fluid, a combination so little
energetic, as to be destroyed by the mere
approach of a conducting body? The theory
is imperfect, also, in taking no account of
that. change in the relative quantity of
electricity in two metallic plates, which,
according to the observations of Bennett and
Volta; must necessarily happen when their
surfaces are put in apposition.

The discoveries of Mr. Davy, respecting
the chemical agencies of the electric fluid,
have:led him to a theory of the Galvanic pile,
intended to reconcile, in some degree, the
hypothesis of Volta with that of the philoso-
phers of our own country. It is admitted, by
this acute reasoner, that the action of the men-
struum, contained in the cells, is absolutely
essential to the activity of Galvanic arrange-
ments; and that .the two circumstances even
bear a proportion to each other. Notwith-

aq

306 On the Theories of the

standing this concession, he’ is disposed te
consider the movement of electricity which -
takes place on the contact of two metals, as
the cause originally disturbing the equilibrium ;
andthe chemical changes as secondary, and
chiefly as efficient in restoring the balance.
For example, in a pile of copper, zinc and
solution of muriate of soda, in its condition of
electrical activity, the communicating plates
of copper and zine are in opposite electrical
states. And solution of muriate of soda being
composed of two series of elements, possessing
contrary electrical energies, the negative
oxygen and acid are attracted by the zinc;
and the positive hydrogen and alkali by the
copper. An equilibrium is thus produced, |
but only for an instant ; for muriate of zinc is
formed and hydrogen is disengaged. The
positive energy of the zinc plates, and the
negative energy of the copper ones, are con-
sequently again exerted; and thus the precess
of electromotion continues, as long as the
‘chemical changes are capable of being car-
ried on. . ee
The most obvious objection, which presents
itself against the theory of Mr. Davy, is, that
‘if the chemical agents, forming part of #
Galvanic arrangement, be merely effectual in
restoring the electric equilibrium, no adequate

Excitement of Galvanic Electricity. 807

source is’ assigned of that electricity which
gives energy to the apparatus. In other
words we perceive, in such a process, nothing
more than a constant disturbance of the
balance of electricity by the action of the
plates, and an immediate renewal of it by
the agency of the chemical fluids. Accord-
ing to the hypothesis, the production and
annihilation of Galvanie energy are carried
on in a circle, leaving unexplained that im-
mense evolution of electricity, which is ma-
nifested by the most striking effects, both in
oceasioning the combustion of bodies, and in
disuniting. the most refractory compounds.

© On the whole, the electromotive power of
the plates, and the chemical agency of the
interposed fluids, appear to be the only circum-
stances, that can be brought to explain the
efficiency of the Galvanic pile. To decide
which is to be considered as the cause, and
which as the effect, is a difficulty not peculiar
to this case, but common to every other, where
two events, that are invariably connected, are
not distinguished by an appreciable interval of
time. The most defensible view of the subject
however, seems to me to be that, which attri-
butes the primary excitement of electricity to
the chemical changes. But it may be ques-
tioned whether the whole of the effect arises

aq?

308 On the Theories of the

from the oxidizement of the more oxidahble
metal; and whether it is not essential to the
activity of the pile that one at least of the
elements of the interposed fluids should be
incapable of entering mto union with the
negative metal. For example, ina pile com-
posed of zinc, copper, and solution of muriate
of soda, the oxygen of the water and the
muriatic acid, both of which are negative as
to their electrical state, are attracted by the
zine, and have their electricities destroyed.
But the hydrogen and alkali, having no-
affinity for copper, except what arises from a
difference of electrical habitude, deposit upon.
that meta] a part of their electricity. The
electromotive power of the plates now becomes
efficient, and determines the current to one
end of the apparatus, in the manner already
described in a former part of this essay.
Another series of Galvanic phenomena, the
explanation of which is attended with some
difficulty, are the decompositions that take
place in imperfect conductors, forming an
interrupted circuit between the two extremi-
ties of the arrangement. When two wires,
for example, which are inserted into the oppo-
site ends of a tube containing distilled water,
are connected with the extremities of the pile,
the positive wire, if of an oxidable metal,
8

‘

Excitement of Galvanic Electricity. 809

becomes oxidized, but if of a non-oxidable
metal, oxygen gas is evolved from it, whilst,
in both cases, a stream of hydrogen gas pro-
ceeds from the negative wire. Why, it may
be asked, do the elements of water, thus dis-
united, arrange themselves at a distance from
each other? If the particle of water, which
has been decomposed, be imagined to have
been in contact with the extremity of the
positive wire, the hydrogen must have been
transmitted in an invisible state to the nega-
tive wire: But if the decomposed water were
in contact with the negative pole, then the
oxygen must have passed imperceptibly to the
positive wire.

These appearances have been explained by
Dr. Bostock on the same hypothesis, by which
he has accounted for the phenomena of the
pile. The electric fluid, he imagines, enters
the water by the positive wire, and is there
instrumental either in oxidizing the metal or
in forming oxygen gas. In either case, the
decomposition of the water must furnish hy-
drogen, which, uniting with the electric fluid,
is carried invisibly to the negative pole, the —
attraction of which for electricity again occa-
sions the separation of hydrogen, and _ its
appearance in a gaseous state. This theory,
however, is liable to some objections,

310 © On the Theories of the

“It explains the decomposition of those
bodies only, which contain hydrogen as one
of their elements. And though it has been
ably contended by Mr. Sylvester, that the
presence of water is, in every case, essential
to Galvanic decompositions, yet the fact does
not appear to be sufficiently established. Even
if it were ‘verified, the agency of moisture
might be supposed to consist in its giving that
peculiar interrupted transmission, on. which the
efficacy of Galvanic electricity in disuniting
the elements of bodies seems much to depend.
2. If the postulate of Dr. Bostock be
. granted, that electricity is evolved by oxida-
tion, we shall be entitled to assume the reverse
as equally true, viz. that electricity is absorb-
ed when oxygen passes to the state of gas.
In cases, where the positive wire is of an
oxidable metal, the phenomena accord suffi-
ciently with the theory ; for by its oxidation,
electricity may be supposed to be liberated,
and to form the: required combination with
hydrogen. But when the positive wire is of a
non-oxidable metal, oxygen gas is disen-
gaged ; and in the production of this gas the
electric fluid might be expected to act, instead
of being employed in carrying mpretaen te
the negative wire.
The same class of phenomena has been

Excitement of Galvanic Electricity. 31%

explained by Mr. Davy on a different theory.
According to his view, bodies, which are
capable of entering into chemical union, are
invariably in opposite electrical states, oxygen
for example is negative and hydrogen positive.
From the known laws of electrical attraction
and repulsion, it will follow that oxygen will
be attracted by positive and repelled by nega-
tive surfaces, and the contrary process will
happen with respect to hydrogen. It 1s easy
then to conceive that these opposite attractions
may produce the decomposition of water. ‘To
explain the locomotion of its elements, we
may imagine a chain of particles of water,
extending from the point P to the point N,
fig. 2, and consisting each of an atom of
oxygen united to an atom of hydrogen. In
fig. 2, the combination is represented as undis-
turbed, and the chain as consisting of six
atoms of water. But when the attractive
force of the point P for oxygen, and N for
hydrogen, begin to act, an atom of oxygen and
another of hydrogen are removed, as shewn -
by fig. 3, and new combinations happen be-
tween the remaining atoms; the second of
oxygen uniting with the first of hydrogen,
and so on. ‘The terminating atoms being
supposed to be removed, a new change will
follow similar to the first, and thus the process

312 On the Theories of the, ec.

will continue to be carried on, not only wher
the chain of particles is a short one, but when
‘it extends to a very considerable length.
‘The theory of Mr. Davy, which FE have
thus attempted to illustrate, derives probability
from its being founded on a general property
of bodies (their different electrical energies)
‘which appears to be established experiment-
ally, as far at least as experiment can be ap-
plied to so delicate a subject. It has’ the
advantage also of explaining a number of
facts, chiefly arising out of his owm researches,
which scarcely admit of beg brought: under
any former generalization. ‘Thus: the invisi-
ble transference of an element to a considerable
distance, even through fluids having a strong
affinity for it, (of sulphuric acid for example
through liquid ammonia) which is inexplicable
on'any antecedént theory, is sufficiently ext
plained by this. The ingenious’ speculation
of Dr. Bostock limited the carrying power
of electricity to its action on hydrogen, a
defect not imputable to him, but tothe state
of the science at’ the time when he wrote.
Since that period, the discoveries of Mr. Davy —
have been unfolded by a train of experimentand
induction which is probably not surpassed: by
any thing in the history of the physical sciences,
and which will forta a’ durable monument of
the genius and industry of their author,

P 312 Platz. 5.

( 313)

CURSORY REMARKS

a

’ ON THE
MINERAL SUBSTANCE

Called, in Derbyshire,

ROTTEN-STON EL.*
"
WILLIAM MARTIN, F.L.S. &c.
COMMUNICATED BY J. HULL, M. D, F.L. S.

(Read December 28, 1810.)

— > Ose

Me. KIRWAN in his “ Elements of
Mineralogy,” (vol. i. p. 203.) states, that
Tripoli is often of pseudo-volcanic and some-
times, perhaps, of genuine volcanic origin ;—
he adds, however, that “ it also frequently
arises from the decomposition or disintegra- |
tion of other stones.” The latter observation
appears to apply strictly to our Derbyshire
Rotten-stone, which is usually considered by
mineralugists as a variety of Tripoli, origi-
nating from some unknown decomposed stone
of the argillaceous kind. 'That the substance
producing otten-stone is, however, in its

. 4
* Cariosus Anglorum, Gmel. Linn. Syst. Nat. p. 146.—
Tripoli. Kirwan. El. Miner. p. 202,
Rr

314 Cursory Remarks on

primary state, a calcareous and not an argil-
laceous stone, can only be doubted, I think,
by those, who have not had an opportunity of
examining this fossil in its native repository.
Indeed, I feel little hesitation in affirming,
that the phenomena, attendant on the sub-
stance in question, strongly support the origi-
nal idea of the late ingenious Mr. Whitehurst,
“who, from personal and extensive observation,
was led to conclude, that the parent rock of
the Derbyshire Rotten-stone was black mar-
ble,* or some other variety of our dark-co-
loured lime-stones.

It is some years back, since I availed myself
of a favourable opportunity, that occurred, of
examining the Rotten-stone pits on Bakewell
Moor ;f and which, 1 understand, are only
opened at particular periods—that is, every
third or fourth year, according to the demand,
which may then prevail for the fossil as an
article of traftic. On looking over the memo-
randu, made at the time of visiting these pits,
I find they differ, in some trifling respects,

-* Vide Whiteburst’s “ Inquiry into the original state
and formation of the Earth.”
’ + Rotten-stone also occurs at Wardlow Mire; and, as
Iam informed, at Ashford and some other parts of the
county: but I am not acquainted with the local circum.
stances with which it is attended in those places.

Rotten-Stone. 315

from Mr. Whitehurst’s account. of the mode,
in which Rotten-stone is procured, the appear-
ances it exhibits as a mineral deposit, &c.
and, as no late author that I am acquainted
with has entered into any detail on these sub-
jects, the following brief statement may not
be unacceptable to those, who are interested in
geological inquiries.

1. The Rotten-stone, found on Bakewell”
Moor, is deposited on a limestone, which seem-
ingly belongsto the first or uppermost stratum i

2, It occurs in different parts of the moor;
frequently on the surface of the limestone,
immediately under the vegetable mould; but
is procured in the greatest quantity in a long,
or somewhat trough-shaped hollow, intersected
by several broad irregular fissures, which are
filled up with small fragments of limestone—
the gravel-like debris (rubble) of the traversed
stratum.t

3. In these fissures the Rotten-stone occurs
at the depth of a few inches below the surface,
and from that to ten or fifteen feet.{

A. It is procured in two distinct states.—In
one, the Rotten-stone when dry has an indu-
rated, and sometimes even a stony consist-

* Vide Note A.

+ Vide Note B.

t Vide Note C.
Rr2

B16 Cursory Remarks on

ence; texture, earthy; fracture, sometimes
imperfectly conchoidal; at other times slaty;
hardness, from that of chalk to that, which
does but just yield to the scraping of the knife
(3—6. Kirwan.); feels smooth, sometimes
rather greasy—never so meagre as the foreign
tripoli ; does not. crumble soon in water ;
eflervesces slightly with acids; sp. gr. 2,3,
Lis colour is usually between a brownish grey
and isahella-yellow.—The other variety occurs
in a loose or pulverulent form ; feels meagre ;
rarely effervesces with acids; sp. gr. 2,2; its
colour ight yellowish-grey.

5. The kard Rotten-stone (as the indurated
kind is called by the Rotten-stone geééers)
occurs in detached, nodular lumps, dispersed
through the rubble above noticed ;—the soft,*
as a spongy earth or mud, either coating the
more indurated variety, or deposited, in con-
siderable quantities, under the debris, on the
surface of the limestone rock.

6. Water, from the upper part of the moor,
is constantly draining through the loose mate-
rials, which fill the hollows and fissures of the
rotten-stone tract.

7. In this mineral depot are found, with the
Rotten-stone, fragments of chert; fragments
of a calcareous stone in every possible state,

* Vide Note D.

4¢

- wit

wn ee

‘Rotten-Stone. 317

intermediate between Rotten-stone and per-
fect limestone; Rotten-sione mith nuclei of

solid black limestone; Ke. &c.

8. The calcareous stone, which forms, in
these instances, the central parts of the nodu-
lar lumps of Rotten-stone, has the eziernal
characters of the black limestone or marble,
found at Ashford-in-the-waters, &c. but dif-
fers, somewhat, in its internal properties,’
from any stratum of limestone yet discovered
in Derbyshire.

9. Marine reliquia are sometimes found in
the hard Rotten-stone ; and these are gene-
rally such as have been observed to be most
frequent in the black marble ; viz. Entomoli-
thus Derbiensis, Conchyliolithus Breynii, &e.
(v. Pet. Derb. T. 45, 39, &c.)

Such are the principal phenomena, which
were noted during my examination of the
depot of Rotten-stone near Bakewell.—The
conclusions, to which this examination led, have
been already alluded to; namely, that Rotten-
stone is produced by the disintegration of a
particular variety of limestone, probably a
black marble ; and that, consequently, authors
are incorrect in considering the original sub-
stance of this fossil to have been an argillace-
ous stone.

It will here, however, be asked—how is

318 Cursory Remarks on

the production of this particular substance
from another, chemically as well as externally
distinct, to be accounted for? and, if Rotten-
stone be actually the result of a certain change
in black marble or limestone, why is it not
found in every situation, where such rock
occurs? 'To answer these questions satisfac-
torily will perhaps be impossible ;—to answer
them, however, in any way, without having
recourse to the reciprocal transmutation of
what have hitherto been considered, as simple,
elementary parts in mineral compositions,*
we must first recur, it is evident, to the nature
of the constituent matter of the original rock,
as well as of the substance, which the disin-
tegration of such rock has been presumed to
produce.

Limestones, it is well known, are composed
principally of an indurated calcareous carbo-
nate ;—Rottenstone, according to the following
analyses, of alumine in a loose or earthy form,
and with its constituent particles in a very
minute state of division—But we must remem-

* The transmutation of silex into lime, or that of lime
into silex or alumine, however strongly contended fur by
some modern Geologists, most assuredly ought not to be
assumed in apy attempt to account for the phenomena of
the mineral kingdom, till supported by stronger facts than
those on which it rests at present.

Rotten-Stone, 319

ber, that many other principles enter into the
composition of most limestones besides carbo-
nate of lime; as alumine, silex, bitumen, and
sometimes magnesia ;—and that Rotten-stone
contains, besides alumine, silex, bitumen or
carbon, and frequently iron and calcareous
earth;—and that the comparative proportions
of these component parts differ greatly in the

different varieties both

Rottenstone.

of Limestone and

Our analysis of Rotten-stone has afforded

the following results.

1 Very hard Rotten-stone, ap- ||

proaching Black Limestone in
external appearance.

Alumine ........- hesesene td
Silexisiiieescse Sera eS
Carbonate of Lime..... . 14

Oxide of [ron .........0.. 2
Inflammable matter and
FOSS) 5c/seesses Shaeeea! it

_-

100 |

3. Hard Rotten-stone, but less ,

indurated than specimen 2,
colour nearly similar.

Alumine ...... she pwacsnney Oe |

Bile daedancbachdevedepeseeskyiic: |
Carbonate of Lime...... 5.
Oxide of Iron.......00--. O-|

{inflammable matter and |
SA GOW; aay csGewassel Ve |
|

100 |

2, Another specimen of the hard
variety, but of a light brown
colour.

Alumitietest.isccecsesecaas (GO

eeGeresen 2
Carbonate of Lime...... 10
Oxide of Iron.........006 1
Inflammable matter and

Silexteceacssnsesess

JOSS? escnctecocedacansiiam
100

4. Soft Rotten-stune, i.e. witha
texture much more loose or ear-
thy than in the other specimens.
Alumine See 7g

waccsnece,, ©

BLES ae te hlannes
Carbonate of Lime...... 0

Oxiderol Uran...deseoscan nD
Inflammable matter and
loss

@ereereeresestseee g*

100

* It should be observed that the “ loss,” in these ana«

$20 Cursory Remarks on

If we compare the foregoing analysis with
those, which mineralogists have given us of
limestones, we shall find, that the chief differ-
ence (in a chemical point of view) between
Rotten-stone and certain varieties of limestone,
exists in the larger proportion of alumine,
which the former of these substances contains,
and its comparative, or, in some instances, its
total want of the carbonate of lime. The
particular varieties of limestone now alluded
to are thosé, which Mr. Kirwan has denomi-
nated argilliferous marlites, on account of
their holding a large proportion of argill
(alumine) in their composition. (v. E. Min.
v. 1. p. 99.)—Some of -these stones, though

lysis, never exceeded 1,5;—hence the proportion of
“ inflammable matter” may be stated as varying from 5,5.
to 7,5. At the time of making my experiments on Rot-
ten-stone, the principal object in view was to ascertain the
predominating earth in its composition, and not determin-
ing the nature of the inflammable matter, it was placed with
the loss ;—there can be little doubt, however, of its being
carbon. Silex was found in all the specimens examined.
Carbonate of Lime only in the harder varieties, and not
constantly in those. Two or three specimens analysed, in
‘all external respects similar to No. 5, were without it.
Oxide of Iron was only present in the harderRotten-stones.—
The actual constituents, therefore, of genuine or perfect
Rotten-stone (that is, Rotten-stone in which the disinte-
gration of the original substance is complete) may be
stated to be alumine, silex and inflammable matter (carbon? )

Rotten-Stone. 321

affording lime, contain 30 per ct. of alumine,
together with small quantities of silex, iron,

‘&e :—and our Derbyshire black marble, or

limestone, undoubtedly belongs to this class.—
The greatest quantity of this stone 1s quarried
at Ashford-in-the-waters; and, as the quarry
is situated at no great distance from the depot
of Rotten-stone, and affords an excelient
example of this formation, I shall here des-
cribe the state, in which it is found, and some
of its principal varieties. It occurs in beds,
which vary in thickness, from a few inches to
two or three feet, with interposed seams
(semistrata) of black, bituminous shale and
clay. The substance of these beds, though
throughout of the same general aspect, and
constantly burning to lime, more or less pure,
differs greatly in the proportion of its consti-
tuent parts, as well as somewhat in its exter-
nal characters. The limestone of those beds,
immediately worked as marble, is of a deep
greyish-black, which, on the stones being
polished, becomes perfect, or dark-black * :—

* Its colour must be ascribed to the bitumen or carbon,
which it contains, as it becomes perfectly white, when
caleined, and also acquires a white, or ash-coloured, crust,

on exposure to the weather. In mauy instances I have

found the crust of a considerable thickness and become
perfect Rotten-stone. And there is no doubt but in walls,
ss

322 Cursory Remarks on

texture. close, fine-earthy : fracture slaty,
passing into the imperfectly conchoidal * :
hardness from 6 to 7 (Kirwan. p. 38.) : emits
a fetid or rather urinous smell when scraped,
but ina much less degree than the following
varieties ; contains, according to the specimen
examined, about 18 per ct. of alumine, with
small proportions + of silex, iron, and inflam-

mable matter.

The next variety of limestone, it will be
proper to notice, is one rejected by the work-

which are sometimes built of black marble, and in other
exposed situations, this would frequently be the case, if a
further decay of the stones were not prevented by a timely
and friendly covering of lichens aud mosses. I have ob-
served, however, that pieces of polished marble, though
equally exposed with those in the unpolished state, do not
so soon acquire a white crust—Polishing, by filling up the
minute interstices, induces a greater degree of external
hardness of the stone and prevents for a longer time the
decomposition of the surface.

* By fracture, is here meant the general presto cop or
form, which the broken surface of the fossil presents : by
texture, the grain, or form and disposition of the particles,
observable throughout the surface of the fracture.

+ In no instance did the proportion of silex exceed
4 per ct. or that of the iron 14. As the experiments,
however, which gave these results, were not repeated on
each variety of stone, we do not give these proportions as
those, which analysis hereafter may find to be correct.—
The pruportion of alumine, in each instance, we believe,
will be found to be near the truth.

Ses *

+

Rotten- Stone. 323

men at Ashford, as being less fit for their
purpose than that I have just described—It
appears to be too soft to receive a lasting
polish, and its colour, though black, is much
less deep than in the foregoing variety, fre-
quently verging on brownish-black :—texture
earthy: fracture slaty : hardness 6: gives out
a very fetid smell on being scraped. One
specimen of this stone contained, according
to the experiments made on it, 66 carbonate
of lime; 24 alumine ; 1,2 oxide of iron; 1,5
silex ; and 7 inflammable matter. Anotler
specimen of this stone, however, from the
same bed, yielded only 19 alumine.

A third strongly marked variety of lime-
stone, found with the foregoing, has the follow-
ing characters: colour black, or brownish-
black : texture splintery, with disseminated,
shining, spar-like particles ; these frequently
exhibit the minute parts of organic remains:
fracture slaty : hardness 7: emits a very fetid
odour, when scraped or rubbed. “’I'he speci-
men analyzed gave 8 per ct. alumine, and 4
silex, with 7 inflammable matter, but little or
no trace of iron.

It must now be observed, that, along with
these three described varieties of limestone,
several others occur, which, in their eaternal
characters, exhibit various gradations between

ss2

324 Cursory Remarks on

the black-marble and the. bituminous shale,
that separates the calcareous beds; and that
the whole formation of these limestone stratula
_ appears to graduate, or to pass by an almost
insensible transition, into the great stratum of
shale, under which the limestone of Derby-
shire, for the most part, dips.

It is evident, from the above remarks on
the black-limestone formation, that among its
numerous beds the original of Rotten-stone
probably exists ; and, though the result of my
own experiments and observations certainly
does not warrant the conclusion, that it has
yet been detected as a native rock or stratum,
there seems little doubt, but that a more care-
fal examination, than what my leisure when at
Ashford permitted me to make, may hereafter
determine the stone in this state. The variety
of black limestone already described, as hold-
ing, sometimes, 24 per ct. of alumine, un-
doubtedly comes near in external characters
to the central nodules of marble, which, it
has been observed, occur frequently as nuclet
to the fragments of hard Rotten-stone,
(v. p. 317.) and which, there is every reason to
conclude, are remaining portions of the
original calcareous rock. Still, however, this
rock appears to have differed essentially from
the hmestone, with which we are now com-

Rotten-Stone. 325

paring it:—Ist. in being a somewhat softer
stone. 2d. in containing a much larger pro-
portion of inflammable matter—and, lastly,
in holding, at least, 30 per ct. of alumine.*
It may here, perhaps, be objected, that a stone,
holding even 30 per ct. of alumine, can never
be presumed to give by its decomposition a
substance, containing more than double such
proportion of the material—especially as this
substance is evidently not composed (in cer-
tain instances at least) of the travelled, and
at length deposited, particles of the origmal
stone ; but actually exhibits the matter (in
part) of the original stone itself under its pri-
mitive structure, and merely deprived of one
of the constituent principles.—For this really
seems to be the state, in which the greater part
of the indurated Rotten-stone occurs. To this
objection, I can only, at present, oppose, as
probable, the supposition, that, during the
formation of hard Rotten-stone, while losing
the calcareous particles, a gradual and consi-
derable contraction took place in the remain-
ing matter ; and that this was effected without
destroying the slaty structure, where it pre-
viously existed, in the primary stone.t By

* Allthe specimens I have examined have given some-
thing more than the proportion of alumine here stated.
+ A nearer approximation of the aluminous particles to

326 Cursory Remarks on

this assumed contraction in the substance of
Rotten-stone, it is evident, we may readily
account for the greater proportion of alumine
it exhibits, on comparing a given quantity of
it, with an equal one of limestone.—But it
will probably be advanced, that the hypothe-
sis eventually supports more than we wish to
prove; as, admitting the contraction of the
matter forming Rotten-stone, any limestone
holding a small quantity of alumine may be

each other may easily be supposed, as a natural conse-
quence of the removal of the calcareous matter ; but, that
the structure of the original stone should remain, after this
loss of matter, will not, perhaps, be as easily supposed or
admitted.—However, as the ingredients of black lime-
stones, &c. exist (it is probable) merely in the state of
mixture, the extraction of any one of these constituent
parts will certainly be less liable to destroy the general
structure of the stone, than if the process had to act on
principles chemically united.

We have here considered the structure, or fracture of
hard Rotten-stone to be immediately derived, generally
speaking, from that of the original limestone ; but in some
instances, particularly where the slaty structure is present, -
it is rather, perhaps, the consequence of the contraction
contended for, than the remains of any particular disposition
of particles, which existed in the primary fossil.—We have,
not unfrequently, observed the slaty structure in hard
Rotten-stone, where no vestige of it appeared in the
enclosed nuclei of limestone; though it must be observed,
that these nuclei, in every other respect, were perfectly
similar to those, in which such structure was very evident.

. "(aaa

Rotien-Stone. §27

the original stone.—The local circumstances,
however, attendant on Rotten-stone must
prevent such a supposition from being adopt-
ed.—aAll limestones, it is true, are liable to
decomposition ; and the black seem to be more
subject to this process * than the lighter.

N. B. It is to be regretted that this paper
was left in an unfinished state, owing to the
death of the ingenious author, and that several
of the notes, referred to, have not been disco-
vered amongst his manuscripts, though these
have been examined with very great care and
attention.

* Vide Note.

( 328)

NATIONAL CHARACTER.

BY THOMAS JARROLD, M. D.
(Bead January 25, 1811.)

rwe

Ons of the great uses of history is the
display it makes of the character of man.
Actions, without their corresponding and con-
necting circumstances, are robbed of much of
their interest, by being thus.deprived of their
character. ‘The motives which lead to an
action, the mode of its execution, and its influ-
ence, are all necessary to be known, in order
to its character being appreciated; and it is
the office of the historian to place these in a
conspicuous point of view.—Although history
is the only true and legitimate source from
whence a knowledge of the national character
can be derived, it is but seldom appealed to
for that purpose ; on the contrary, the customs
of a people are erroneously made the founda-
tion of their character. Captain Cook’s ac-
count of the islanders he visited, is deemed

On National Character. $29

sufficient data to form an estimate of their
characters from; thus national prejudices are
engendered and kept in existance.

A fair appeal to history might cause our
pity, but not our contempt of any
people; but by forming an opinion of the
character of other nations by their customs,
we feed our vanity till it usurps the place of
the understanding, and that which has but
little relation to character is made the basis of
it. For, most national customs have their
origin in utility, not in disposition, or in pre-
conceived opinions. A Russian drinks rancid
oil, and we infer that he is one of the most
brutish and uncivilized of all the human
race; we are disgusted at his conduct; but
the climate of Russia requires the inhabitants
to use strong and nutritious diet; and no
article is so much so as oil. Our own pea-
santry would use oil, were they to reside in
Russia, on account of its utility. The Hot-
tentots anoint themselves with grease and oil;
the utility of the custom is apparent, from the
defence it gives from insects. The imhabi-
tants of the South Sea Islands lacerate their
"persons; an ancient Britain daubed himself
with paint; each had a reference to the same
object, utility. To terrify an enemy, or to
conciliate a friend, have ever been the leading

Tt :

330 On National Character.

objects in directing the mode of dress and
other attentions to the person.

In general, the customs formed during the
age of barbarism are continued. through suc-
cessive generations, modified by circumstan-
ces; but to the custom itself the people are in-
separably attached. It is wrong to call it cha-
racter; it is habit, to which the. people’ are.
attached.. When Ferdinand attempted to assi-
milate, the dress and customs of the Spaniards
to those of the French, the people revolted from
his government. What character can be given
to the transaction, but that of a fondness for
national customs, common to every people ?
and also, when Peter of Russia ordered his sub-
jects to be shaved; although his people loved
him as their father, they were unwilling to
submit. to this supposed degradation, this
yielding up an ancient custom. What hap-
pened in Scotland when the Highlanders were
required to change their dress, is familiarly
known to most of us. With such evidence
before us, and much more might be adduced,
we may infer that. national customs are well
calculated to keep up national distinctions,
and even national animosities; but they do
not express the character. The same dignity
of office commands equal homage, whatever
‘the costume of that office may be. A Mo-

On National Character. 331

hawk chief is not less honored than an Eng-
lish magistrate. ;

Were there an universal standard of
taste, the customs of a people might be
scrutinized by its laws; but even taste
does not govern character; this last rises
above and is independent of those things over
which taste has any influence. Objects of taste,
when applied to character, are what the cor-
nice is to a building ; they beautify; but if the
people of every country hastily and on insuffi-
cient grounds estimate the character of others,
the subject has not been overlooked, or neg-
lected, but has exercised the talents of men of
yast capacities. Voltaire gives the subject the
title of the Philosophy of History; Lord
Kaimes, Montesquieu, and Adam Smith,
have aided the enquiry ; and every historian
and political economist, have made national
character a leading object of their researches :
among whom, Hnme holds a conspicuous
place.

Every one conversant with the writ-
ings of these philosophers, will recollect
that they derive national character from reli-
gious opinions, civil government, and the
state of industry, The subject may be
branched into many particulars; but they all
resolve themselves into these three points;

Tt2

832 On National Character.

in my apprehension, these assigned causes are
only consequences. Let us examine the sub-
ject. Religion, they say, forms a prominent
feature in the character of every people:
granted, But religion, having the same
object of worship, assimilates its followers ; it
by no means diversifies their character, how-
ever remote their residence; its tendency is
to make of one family all nations of the earth; —
it creates no new principle, nor calls into
exercise any new passion; the spirit of devo-
tion is the spirit of filial affection; that act of
the mind towards the supreme Being is worship,
which exercised towards a parent, is honour
and reverence.

But it may be said, that religious prin-
ciples are acted on only as they are under-
stood, and that persons of different capa-
cities can only understand in proportion to
their capacities. This is placing the
difference of character not in religion but in
the capacities of individuals, which is shifting
the ground ; but admitting the objection, what
does it prove ? It proves that the resemblance
is incomplete; not that the bent of character .
produced by religious principles is diversified.

If the pure worship of God be the same in its
principle and tendency wherever the worship-
per may live, so is its counterpart, superstition.

The negroes of Africa, the philosophers of

On National Character. 333°

Athens, the abstemious Bramin, the licenti-
ous Turk, vary in the forms of worship ; but the
spirit of their religion is the same. They all
seek to purchase heaven through the agency
ef a priest. Should a negro become a maho-
metan, he might change his dress, and perhaps
his dinner hour, but the man would be the
same; he would not be under the influence of
any new motive; he would change his agent,
not his character. The question is narrowed to
a point; is superstition in its nature the same
every where? If so, it must infuse the same
spirit and produce the same character. An
army is divided into regiments, as the world
is into kingdoms; each regiment is known by
its dress, its hours of exercise, its peculiar
habits and customs ; but the character of the
regiment is not formed by these fortuitous
circumstances. The whole army is led by
one general and inspired by one spirit, and
the spirit of an army is its character, A nation
may worship an ox, ora hero, the sun or a
saint, without the slightest shade of difference
of character being produced. Let us suppose
the same people worshipping these deities in
succession; could we in that case discover by
the character of the people, which of the
deities they were worshipping ?

But if national character be not the effect of
religious sentiments, is it not decided by the

334 On. National Character.

form of civil government ? At a period but
little removed from the present, the spirit of the
laws, and even the form of worship of all the
great states of the continent of Europe were
the same. But these strong conspiring causes
did not produce an uniformity of character.
The French were gay, the Germans grave,
the Spaniards dignified, the Portuguese mean,
and the Italians base; we must therefore look
for some other cause of this contrariety of cha-
racter.

Small states, by being less secure, are
supposed to be mean, cringing and national ;
and large states, feeling their security, to be
oppressive and violent. Should this remark
be admitted ‘as correct, it by no means relieves
the subject of its difficulties ; because there is
not a similarity of character in states of the
same size, although under the same laws, and
observing the same form of religious worship.
But before we pursue the subject further, let
us consider the extent of the influence ps in-
dustry on character.

In nations, as well as in individuals, in-
dustry appears to be the effect of a previ-
ously acquired character, not the origin of
it. Rude and uncivilised people are never
industrious; industry is the effect, not ‘the
cause, of civilization. Industry © supposes
energy, frugality, and security ; it supposes a

On National Character. 335

fixed government, and a firm individual cha-
racter. Industry is the wealth of a state and
its security. It gives a perpetuity and an im-
pulse to all our blessings. _When once in
motion it rolls forward, and, like the ocean,
surmounts and overwhelms every obstacle.
But it is not self-moving ; it receives its im-
pulse from wants that are felt, and is an evi-
dence of the state of civilization; but. it does
not create that state. When we see a luxu-
riant tree, we attribute its luxuriance to a
rich soil and a skilful gardener. In like man-
ner, industry may be attributed to intelligence
in the people, and wisdom in the government.

Besides the causes that have been mentioned,
climate is commonly considered as having a
powerful influence on the character of a peo-
ple; but a mere glance at history will refute
theidea. Men of every character reside in every
climate; in the east, the Malays are as brave,
and the Chinese as ingenious, as the people
of any country. The inhabitants of St. Vin-
cent were courageous to a proverb; and the
people of Mexico astonished their discoverers
by their attainments in useful knowledge.
Climate affects a stranger, but to a native
every climate is agreeable, and admits of the
developement of his mental energy and corpo-
real strength. There is no imperfection in the
creation = God, but there would he if man

One,
| 2
336 On National Character.

was only adapted to one climate; if another
situation changed his character and lessened
his consequence.

Should a different plan be adopted, and
in place of examining each assigned cause
of national character the whole were taken
collectively, still we should be as much
embarrassed as in ascribing to family eha-
racter its precise origin; for, nations conti-
guous to each other, the genius of whose laws
and whose religion are the same, are not
similar in the leading features of their charac-
ter: witness, the French and the Spaniards,
the Malays, and other nations of India, the
original inhabitants of St. Domingo, and of
St. Vincent. As we therefore are not able
to form a correct estimate of the character of
a people by a knowledge of their laws, their
religion, or their climate, let us appeal to
history.

History is the record of the actions of men;
the motives which led to these actions, and
the mode of their performance constitute their
character; if we were to select a nation, say
our own, as an example, and after carefully
scratinising the conduct of the preceding
generation, were to state the character of
that generation; it is highly probable that
the opinion so formed would be correct. If

On National Character. 337

we were in like manner to unfold the trans-
actions of each succeeding generation, and
assign to them their respective characters, it
would be evident on comparing them toge-
ther, that all along the character of the na-
tion was the same, only new circumstances
occasioned new expressions of it. If we even
turn back to the period of which Tacitus and
Czesar were the historians, and compare the
Germans and French of those days, with the
Germans and French of the present, we shall
discern the same people ; and if we take a wider
scope, and place before us the maxims of alk
the rude and barbarous nations that we are
made acquainted with, we shall be able to di-
vide them into classes, and to form an estimate
of their present and future character.. For
instance, it is a maxim of most. barbarous
nations, that theft, and what is always con-
nected with it, lying, are honourable. With
other nations, truth and honesty are sanc-
tioned. In the first class we may place the
Spartans, the Romans, the Scythians, with
all their descendants ; and thus we embrace
nearly the whole of Europe. In the other
elass we may place many nations of Africa,
perhaps some tribes of America, the Chi-
nese, and the Laplanders. Parke bears ample
testimony to the kindness, the integrity, and
Uu

$38 On National Character.

truth of some African nations. A mother
bewailing the loss of her son, found conso=:
lation in reflecting that he never told a lie;
no, never. Do we not receive Negroes into
our families in’ full confidence of their, ho-
nesty ? We'could not receive a Tartar im the
same manner.. Dr. Franklin relates that some
Indians, noticing the fraud and deception
practised by the white people, asked if they
had had no mothers to instruct them; evi-
dently implying the office of those of their
nation. When referring to the page of his-
tory we learn that nations of the first class,
when their wants increase beyond their power
to supply them, by the robbery of strangers
enlarge their views, and that which was called
theft is now called war; and he who was the.
leader of a gang of banditti, is now called
general, There is no instance of a nation
who in their days of barbarism were great
thieves, that did not afterwards make good
soldiers. On the other hand those nations
whose maxims inculcate honesty, are, at every
period of their history, seekers of peace..
They do not want courage when forced to
exercise it; but they endeavour to avoid. the
occasion of its being called forth. Hence the
Chinese built their wall. Other instances
might be advanced to shew how ‘far the

On National Character. 389

maxims adopted by a people influenced their
character.; but the present is sufficient for our
purpose. One general remark it may. how-
ever not be improper to make: the maxims
adopted by a people carry us Leyond the pe-
riod of their authentic history, and are there-
fore entitled to much consideration, because
they have not their origin, and cannot be en-
forced by religion or civil government; but
they are opinions and voluntarily received by
the people, and are an expression of their dis-
position and character. Heuce it appears much
safer to argue from the maxims than from any
enactment of the legislature, or from any
custom that may be followed, and yet they
have been almost wholly neglected by en-
quirers into national character. But with all
the aid: that can be obtained from history,
assisted by the early maxims of a people, the
subject, is still) involved in difficulty; for,
there. is a striking contrast of character in
nations under similar circumstances at. the
remotest period of their histery. To remove
this difficulty we must go baek to the period
when a nation consisted of a small number,
and was hut as one family; and such a period
many nations have known.. Thus circum-
stanced, the father, the patriarch of the fa-
amily, would inculcate-his principles and infuse
Uu2

340 On National Character.

his spirit; and hence it is probable the diver-
sified characters of nations have arisen.

Here a most important practical question
arises; it has been stated that a nation so_
pertinaciously adheres to its early received
maxis, and so uniformly pursues its first
principles in conduct, that the same character
ever presents itself. Hence some infer that
a child of rude and uncivilized parents, taken
from them at its birth, and brought up in the
family of an intelligent, well bred European,
would both in manners and in mental refine-~
ment appear as one of the family. The ques-
tion to solve is this; would that consequence
follow? I presume not. Education, I wil-
lingly allow, refines, exalts and assimilates
mankind; but no number of the most ap-
proved and excellent schoolmasters, would be
able to elevate a nation of savages to the
rank even of Swedes or Germans in one ge-
neration. I do not know that history affords
us a precise example of this fact; but there
are several which approach towards it, besides
many decisive individual cases. Every colony
of civilized persons settling among barbarians
may be considered as a colony of school-
masters ; but in what instance has a rapid
civilization followed? ‘The ancient Germans
lived almost under the walls of Rome, and

On National Character. 341

raust have felt their own inferiority. Know-
ledge, which had elevated the Romans, was
in its practical effects exhibited to the Ger-
mans; but they were scarcely if at all im-
proved by it. America has been peopled by
Europeans more than two centuries; but the
aborigines have not received the instruction

that was offered to them, and that still conti-
nues to be held out. Besides these general
facts, many attempts have been made to edu-
cate individuals born of uncivilized parents;
but no good effect has been produced. The
Dutch carried this plan to a considerable ex-
tent in attempting to train up young Hot-
tentois in European manners; but the first
opportunity that has presented, they gladly
threw off their dress, and all the benefits
civilization held forth to them, for the filth,
the danger, and the wretchedness. of their
former state. The Americans have trained
up young Indians in their principal cities ; but
they. have gone back again to their tribes,
filled-with contempt at the manners of Huro-
peans. The African society also with the
most laudable intention educated many negro
children in England ; and if Tam not misin-
formed, they ran to a certain level in the
acquisition of knowledge, and there be-
came stationary. There was a point, far

342 On National Character.

‘below that which European children readily
gain, beyond which they could not go. But
it is unnecessary to multiply instances; for,
there is not a barbarous nation with which
Europeans are acquainted, one or more of
whose youths have not been trained up and
educated with much care in European senti-
ments and manners: but in every instance
without producing a change of disposition.
The wilderness and the desert, the tomahawk
and the scalping knife, have presented allure-
ments which they could not resist. All they
possessed they gladly abandoned ; all they
had been taught to anticipate, they without
hesitation relinquished, and pressed from the
crowded city, where all they received was
forced upon them, to mix with those who
knew no law but their inclination, and whose
inclinations were regulated by no principle,
but was the mere expression of the passions.
Was there only a solitary instance upon re-
cord of a child of savage parents, fostered
with the utmost care and kindness ina’ civi-
lized family, being impatient of restraint and
hearing of the manners of its parents, endea-
voured to imitate them; the subject would not
be entitled to consideration. But when every
one so circumstanced has resisted civilization,
the disposition cannot depend on capricious-

On National Character. 343

ness, but must have its: origin in the nature
and constitution of man,

~ When a pheasant, a wild duck, ashare, or
any other undomesticated animal, is attempted
to be brought into that state, the effort fails ;
no person has so tamed a pheasant that it will
not, when liberty is given, fly away and not
return again; yet the domestication of that
species of animals is very practicable. But
in order to illustrate the various stages of this
process, it may be advisable to select an
animal with which we are more familiar. The
duck is of this description. It will be granted
that wild and tame ducks are of the same
species, and differ in no other respect, than
that one is domesticated and the other not.
In what therefore does domestication consist?
It is not in being familiarised to the presence
of man; for many have been familiarised
without being domesticated. It is a dispo-
sition, not a habit; an act of the affections,
not the restraint of discipline. A tyger do-
mesticated would be as harmless as a cat;
and a cat undomesticated would be as fierce
as a tyger. There is no natural propensity
in any animal to domesticate. The whole is
an effect produced by circumstances. It fol-
lows therefore, that there must be a physical
change produced on the animal; far from

344 ~ On National Character.

being alarmed at the presence of man, and
untractable, it is attached to his person, and
submits to his discipline. As a change. of
disposition, of constitutional feeling is pro-
duced, how is it effected? Let us illustrate
the subject by an instance: suppose a pair of
wild ducks to be the subject of domestication ;
they are confined to a yard or a pond, and
habituated to the presence of their owner, by
whom they are fed and caressed. After a
length of time they lose part of their wild-
ness; in this state a nest is formed, and a due
number of eggs are laid for a brood of young;
but the mother duck is not permitted to sit
upon them; they are taken from her and put
under a most domestic hen ; when the eggs
are hatched the hen is unceasing in her
attention, informing the young by tones, well
understood by them, that they are in safety.
But notwithstanding this, the wildness. of their
nature predominates, and they shun the pre-
sence of man, and if not prevented, as soon
as they could fly, would take wing and leave
the place where they had been brought up.
But we will suppose they do not obtain an
opportunity to escape, but remain confined to
the poultry yard; they are evidently wild, but
yet they are not so much so as the old. ones
that produced the eggs, from which they were

On National Character. 345

hatched. The discipline and counsel, if 1 may
be allowed theterm, of the hen have ina measure
softened and ‘corrected their disposition; and
being regularly -visited without being injured,
has also had its effect in lessening their terror at
the sight of man. Asthe summer approaches
these also bring forth eggs, which -in like
manner with the former, are placed under
some very tame and familiar hen, and are
hatched in due season. The young, like
their progenitors, are wild and untractable ;
but the hen exercises ber influence and au-
thority ; she persuades, and threatens, and
some further impression is made ; they are
not quite so fearful of man as the last brood,
but still are eager to escape, and among wild
ducks would be as though they had been
hatched among them. By pursuing the same
plan a few generations more, the object ainred
at is obtained; wildness no longer exists ; for,
a radical change has been effected, not only
in the habits, Lut in the disposition of the
animal. The young as soon as hatched are
now tame; they require no discipline, no
restraint; the building in which they were
brought up is their home, and to it they re-
turn.as the night approaches. So great is the
change produced by domestication, that it has
the semblance. of adding to the world a new
Xx

$46 On National Character.

race of animals ; the dog that by nature is
fierce, like the wolf, becomes the companion
and guardian of man; the propensities of the
animal have acquired a new bias.

Now what takes place in an animal on its
being domesticated, is I apprehend a full
illustration of the constitutional, or in other
terms, the physical change which passes upon
a nation in its progress from the barbarous to
the civilized state of society. Perhaps no
subject which comes before the political eco-
nomist is so important as this; and there is
no one which he has so entirely overlooked and
neglected. It would be very satisfactory to
me to enter fully into the subject, and by an
appeal to history, to establish the sentiment
advanced; but the rules of the society prevent
my taking more than a glance of the subject
at present.

* A nation in a state of barbarism, remains
age after age, without any variation in their
manners, or any improvement whatever, un-
less some circumstance arises to compel a
change. The circumstance which in every
instance has been instrumental to this purpose
is, an increase of population. The rivers and
the forest have not afforded a sufticiency of
food, in consequence ot which agriculture, in
a rude manner, is commenced ; and tribes

On National Character. 347

which had been wandering now become sta-
tionary. The seed their hands had planted
requires their presence to protect it.* Thus
an important point is gained, and a new era
commences; the wives and children are in
greater safety; consequently the families be-
come larger and require an increase of in-
dustry to provide the means of subsistence.
The effort this requires enlarges the ideas and
encreases the knowledge of the people; and,
after a succession of generations, their habits
and their constitutional propensities change ;
they no longer delight in the practices their
ancestors were attached to; having passed

* Mr. Malthus in his work on population, asserts that
when the population of a state has encreased beyond the
existing means of subsistence, the superabundant part must
be removed ; he appears not to have taken into his considera-
tion the possibility of a change of system, and the effect that
change may have on the produce of the soil, and on the
fecundity of the people; but especially he does not appre=
hend that an increased population is the great agent for the
civilization of mankiud; no people have ever increased in ci-
vilization in consequence of wealth, abundance, and a thin
population, but as the effect of an increase of industry, and in-
dustry is the creature of want, supposed or real. There is
not enough, and therefore individuals labour to obtain more ;
and by this effort their mental energies are roused, and they
goforward. Ihave no hesitation in stating that there is no
progress in civilization, but what is compelled by the very
circumstance which Mr, Malthus lays down as the founda.
tion of human misery, an increasing population.

Xx2

“348 On National Character.

from the savage to the agricultural state of
society, they are how passing on to the next
step of ‘their progress, the imitative state.
Every change here’ noticed has been effected
by the natural consequence of’ an increase of
population, as the history of the world bears
ample testimony ; indeed every pagé records
the fact, that progress in civilization and in
population correspond, and are cause and
effect. Ascertain the one, and a correct ae
ment may be formed of the other.”

Let me here call the disciples’ of Mr.
Malthus to a consideration of this subject,
and to a candid enquiry whether what that
gentleman has held forth to the world as its
great curse, is not its greatest political bles-
sing. 'That there is fixed in the nature and
constitution of man a check by which the
unlimited increase of the species is prevented
is readily acknowledged ; civilization is that
check. If we banish war, famine and pesti-
lence (and it is in the power of man so to
do,) and let population roll forward with its
utmost speed, the efiect will be. to dignify
man by the expansion of his faculties. But
as this takes place he becomes less of the
animal, and the average number of children
to a marriage sink: if they are five at a given
period, .alittle increase of population and its -

On National Character. 349

consequent civilization, sinks the: number to
four. Such is the testimony of ‘the registers of
nations, and not that disheartening sentiment
Mr. Malthus makes them speak.
We have conducted the human race from
the: agricultural to the imitative stage of ci-
vilization ; let us view him im that situation.
In the purely agricultural state the faculties
of man are dull, and it is difficult to excite
an interest in any’ new pursuit. They are
agticulturalists merely to procure the means
of: stibsistence, having no relish for mental
pursuits. -But when they have burst this
barrier, they see with delight what nations
moré civilized have effected, and they strive
' to imitate! them; and’ it is at this stage of
civilization, that the imitative powers of man
are by far the strongest. It is now that
nations’ undertake those stupendous works
which ‘astonish future generations. ‘There is
little envy among them; for, there is no
invention. They are pleased because they
can imitate, and thus claim a connection with
those to whom they look with admiration and
“respect. If at the lowest link of the chain
we place the New Hollander, and designate
him’ by the name of savage, if at the next
advance we find the Otaheitean, and many
‘tribes of Americans, people whose business it

350 On National Character.

is to procure the means of subsistence, and
to injure their neighbours; we come next
to the point at which the human faculties
begin to unfold, and the man to appear ;
when the malignant passions, which he had
nursed in a state of barbarism, now. give
way, and he begins to seek for rank and
consequence among civilized nations... In
this stage of civilization are the Russians, the
Negroes, the Mexicans and the Peruvians.

Dr. Clarke in his account of the Russians,
lately published, describes their imitative
powers as most astonishingly great. A paint-
ing of the most exquisite art, they copy with
so much accuracy, that even with a good judge
it passes for the original ; and this capacity ”
for imitation embraces every object, whether
of the most exquisite or of the rudest struc-
ture ; but they invent nothing. Many. Rus-
sian youths have been instructed by the best
masters in their own nation, and in foreign
universities; but there has never yet been a
book written by a Russian, worth translating
into another language, or the smallest im-
provement made by them in any art or sci-
ence. Their judgment is weak; give them a
written description, and they would not com-
prehend it ; but place before them a model,
and they will without hesitation undertake to

On National Character. “35k

copy it. A little below the Russians are the
Africans, a people so ill treated by their bre-
thren of mankind, that they have been kept
back from civilization. Their population has
been lessened by European baseness, and thus
their progress has been stopped; but still they
are advanced to the imitative stage ; and it
is because they imitate well that they are
bought as slaves, and that they are made.
domestics. The aborigines of America were
not in general advanced far enough in civili-
zation to be made useful to their conquerors ;
they could not be made to work, in other
words to imitate, and therefore negroes were
bought with money to supply their place. A
slave has no inducement to exercise the talent
he possesses: but that the negroes possess the
imitative talent will not be denied ; when
introduced into our families they speedily
catch our manners; in our West India Islands
they are good artisans; but at St. Domingo
their real state of civilization is best appre-
ciated. With respect to the Mexicans and
Peruvians, history furnishes ample testimony
of their being advanced to the first siaye of
civilized nations. Arrived at that full and
overflowing state of population, which re-
quires a new system in obtaining the means
of subsistence. Mungo Capac, a man in

352 On National. Character.

many respects like the father of our country,
the great king Alfred, was placed among
them; he ‘taught them the arts of civilized
life ; and the whole nation at once imitated
them, so that when the Spanish ships arrived
on their coast, drawings of them were made
and sent by post to Mexico. But the history
of that period is knéwn to you, Gentlemen,
In referring to it you have only to ask the
question, whether that people were not as far
advanced in civilization as the Russians are
now, and whether their civilization was not
of the same description; whether it did not
‘consist in imitation. When a nation has
remained several generations in this degree
of refinement, and the population again
presses forward, further advances are made.
The mind becomes stronger as it is more
exercised, till step after step the highest, and
the best state of man is attained. The limits
of anessay, do not admit of a full discussion
of the subject, or it might be shewn that
every nation that has attained to a high
degree of civilization, has passed through the
gradations that have been mentioned.

I must also call the society to a farther
consideration than the limits of this paper
will admit, of the physical change which civi-
lization produces on its subject; a change

1

On National Character. 353

only to be effected by many generations, but
which when once accomplished is permanent;
so that a nation, when it has attained a degree
of civilization, never loses it ; it becomes
part of the constitution, I may say, of the
nature of the man; in the same way as
domestication becomes part of the nature or
constitution of an animal. A people may
become stationary; they may become igno-
rant ; but they never a second time become
savages.

Yy

QE BbA GM ot

OBSERVATIONS
EBBING AND. FLOWING WELL,
| At cs eH in the West Riding of Yorkshire,

‘WITH Ke THEORY OF

RECIPROCATING FOUNTAINS;

‘BY Mr. JOHN GOUGH.

IN A LETTER TO DR. HOLME.

(Read October 4th. 1811.)
>? O<<— .

SIR, Middleshaw, near Kendal, July 22, 1811.

I ADDRESSED a letter to you on recipro-
cating fountains, in February 1806); which
you did me the honour to lay before the
Literary and Philosophical Society of Man-
chester, on the seventeenth of October fol-
lowing. Certain additional facts relating to
the subject have come to my knowledge since
that time; the importance of which has in-
duced me to supersede my former communi-
cation by a corrected essay on these singular
phenomena.

When a theory happens to be formed from
the comparison of a few facts only, future
observations frequently perplex it with diffi-

Observations, &c. 355

culties, which are not easily surmounted. It
is not necessary to seek for examples to cor-
roborate the preceding assertion; for, in all
probability, most philosophers will be able to
establish the truth of it, by incidents which
are preserved in the private histories of their
own speculations. In my opinion, however,
_ the writers on Hydraulics furnish a striking
instance of the fact inthe machinery, which
they commonly employ for the’ purpose of
explaining ‘the causes of reciprocating foun-
tains, or of ebbing and flowing wells as they
are called in vulgar language.

Springs of this description may be reckoned
amongst the rare productions of nature; the
infrequency of which leads me ‘to conclude,
that but few thinking men have had an oppor-
tunity of observing a number of them with
attention, and of comparing their operations ;
for it is certain, that by far the greatest part
of the world knows nothing of the subject,
except by report. This want of ocular infor-
mation, in all probability, has obliged specu-
lative writers to rest content with the few
facts, which are to be found in books; and
Iam only acquainted with the following nar-
ratives, which can be said to throw any light
on the curious properties of reciprocating
fountains. The first that I shall mention,

Yy2

856 Observations on an _

came from the pen of the younger Pliny ;
who flourished as a statesman and a man of
letters in the time of Trajan. The account
may be found in the concluding letter of the
fourth book of his epistles ; and the following
is an attempt to give it in my own language,
as I have no translation of the work in my
possession.

Puiny to Licinius. “I am going to pre-
“‘ sent you with a description of a natural cu-
“ riosity in the neighbourhood of my country
‘¢ house, in hopes that it will prove an interest-
“‘ ing speculation to a person of your extraor-
“ dinary attainments. A spring rises on the side
“ of a mountain, and runs along a rocky chan-
“ nel into an artificial basin placed in a summer-
“house, where it is for some time detained, and
‘¢ then falls into the Larian Lake. This foun-
“ tain possesses a surprising property; for it
“ flows and ebbs thrice a day, observing a
“‘ stated law of increase and decrease. This
“ singular circumstance, may be observed with
“ ease, and is calculated to amuse the specta-
“tor. You may sit in the apartment, make a
“ slight repast, and drink of the water of the .
‘‘ fountain ; which is deliciously cool. In the
“ mean time the reciprocating motion of the
“ spring proceeds equally, and. in a manner
‘‘ which is easily ascertained, by placing a

Ebbing and Flowing Well. 357

‘ring, or any other small object, upon a dry
* part of the basin. The water will rise
* gradualiy to the mark, and afterwards cover
“it. The fountain will, at length subside, so
‘« as to leave the object dry ; and will be after-
“ wards seen to retire slowly. If you pro-
“long your stay, these alternate motions will
“be repeated two or three times. Is this
‘* singular appearance occasioned by air act-
“img upon the outlet of the fountain; so as
“to obstruct the current, when it enters by
“the mouth of this channel, and, after its
“escape to allow the water to issue more
“freely? We know this to be the case
“« with bottles, and all kind of yessels,, which
“have narrow necks: for when they are
*« placed in a position proper for discharging
‘‘ their contents, the resistance of the air
“ makes them guggle, and the liquor issues
“from them in an interrupted stream. Or,
“does this fountain partake of the nature of
“the ocean? Is its current retarded at one
“time, and accelerated at another by the
“causes, which give rise to the flux and
‘“‘ reflux of the sea ? Rivers we know are
“driven back, when they fall into the sea
“ against the wind and tide. May not some
“ cause, in like manner, periodically obstruct
“ the discharge of this fountain ? Or, are we

358 Observations on an

“to suppose, that the subterranean veins of
“the fountain have a certain capacity ; and
“that while they are recruiting their ex-
*“ hausted stores, the stream is small and
“languid; but becomes stronger and more
«abundant, when these reservoirs are reple-
“ nished? Or is there a secret and unknown
“contrivance of a stop acting on the prin-
“ciple of a balance; which accelerates the
“efflux of the fountain while it empties itself,
and diminishes the current, while it is
“ filling ?”’

The two last suppositions are’ obscurely
expressed in the original; the latter of them
however seems to have suggested the hypo-
thesis of a rocking stone; which acting on
the principle of a valve, alternately opens
and shuts the out-let of the spring; and my
translation is made to favour this conjecture.
The elder Pliny also mentions the same foun-
tain, and ascribes to it a very remarkable and
unaccountable difference ; for he asserts, that it
ebbs and flows regularly in the space of an
hour. Hist. Nat. Lib. IL. Cap. etii.. We are
surprised to find the uncle and nephew, both
intelligent and observing men, vary so widely
in the statement of an obvious fact. ‘Their
disagreement however does not contradict the
regularity of the spring’s operations ; which is

Ebbing and Flowing Well. 359

a consideration of importance, in the natural
history of reciprocating fountains. As for the
question of accuracy, it has been decided in
the uncle’s favour by Catanaeus, the learned
commentator on the epistles of the nephew;
who says, the fountain continued to recipro-
cate in his time, that the neighbours called
it Pliny’s well, and that it answered to the
description given of it, by the elder writer of
that name. After all, future observations may
prove, both these anthors to be in the right.
Perhaps. it will be found, that wet weather
accelerates the reciprucations of the spring,
by increasing its discharges ; while a dry sea-
son diminishes the efflux of water, and makes
the fountain ‘more dilatory in its operations,
The preceding conjecture is countenanced by
the reciprocating spring at Giggleswick; for
it ebbs and flows most frequently after copious
rains; but the depth of the well shews. the
greatest variations, when the efflux is but
small.

The elder Pliny also takes notice of another
reciprocating spring, and gives the following
short. character of it with bis usual brevity.
“The fountain of Jupiter, in Dodona, ex-
“ tinguishes lighted tapers like any other cold:
“‘ water ; but if a taper be, first extinguished,;
“and then brought to the surface of the welly

360 Observations on an

“it takes fire again. This fountain is called
“ ANATIATOMENOS that is, the Loiterer ; be-
“cause it is empty at noon; but beginning
“to increase after mid-day, it overflows in
“the middle of the night, and then subsides
“again gradually.” Hist. Nav. lib. I.
cap. ciil. |

A third extraordinary fountain of this kind
is mentioned by various modern authors. It
is said to be in Paderborn a district of
Westphalia, and to go by the name of
Bolder-born, or the boisterous brook. This
is an appellation which it deserves; for after
flowing twenty-four hours, it ceases for six
hours; at the end of which period, it returns
with a great noise and force sufficient to turn
three mills, situated near its visible source.
The operations of this fountain are differently
described in the Philosophical Transactions,
where it is said to lose itself twice in twenty-
four hours ; coming always after six hours
back again. -Lowthorp’s abridgment, Vol. II.
Page 305.

The prevailing opinion, respecting the na-
ture of reciprocating fountains, appears to
be derived from the three preceding instances ;
at least, Iam not acquainted with any other
topographical account, which can be said to
favour the notion on rational, or even on pro-

1

Ebbing and Flowing Well. 361

bable principles. This theory may be found
in many popular works on natural philosophy ;
and it is easily explained by the hydraulic
machine called Tantalus’s Cup. This instru-
ment consists of a vessel furnished with a
siphon, which may be attached to it in differ-
ent ways. To avoid the necessity of a dia-
gram, we will suppose the bottom of the
vessel to be perforated, and the longer leg of
the siphon to pass through the hole, being
firmly cemented ina position, which places
the highest point of the bend within the
vessel, and half an inch or an inch below
the brim, and at the same time keeps the
open or lower end of the shorter leg at a
small distance from the cup’s bottom. Water
flows through a tube in an uniform stream
into the cup; where it is collected for want
of egress, and entering the siphon at the open
end of the shorter leg, it rises gradually to
the bend or highest point.’ The subsequent
rise of the water in the cup, forces the cor
lumn in the ascending leg of the siphon, to
pass over into the descending or longer
branch; upon which this instrument begins
to act, not in the manner of a simple tube,
but in its proper character. Now the draft
of the siphon is made to exceed the opposite
stream or supply of water; in consequence
Zz

362 -. Observations on an

of which contrivance the cup is emptied again
sooner or later; at this moment the action

of the siphon is suspended, until the cup is.

replenished by the constant current. In this
manner the water will be seen rising and
falling alternately in the cup, which will be
full and empty, or nearly so, by turns. Si-
milar vicissitudes will also take place in the
siphon; for it wilkrun, so long as its shorter
leg is in the water, and then stop, until the
highest point of the bend is again conor by
the contents of the cup.

The transition is easily made from ‘Tan-
talus’s cup to a fountain, which reciprocates
periodically ; for we have only to suppose a
secret reservoir to be formed in the bowels of
a mountain on the principles of this instru-
ment, and the following appearances will take
place in the visible well, which receives the
water from the natural siphon. Ist. So soon
as the surface of the pool in the subterranean
reservoir, rises above the bend of the siphon,
this canal will begin to act; and its discharge
will be greater at that moment than at any
other period; because the power of a siphon
is greatest, when the distance, betwixt the
bend and the surface of the water in the basin,
is least. 2d. 'This abundant influx into the
external well will make it rise; in conse-

Ebbing and Floming Weil. 363

quence of which the efflux will continue to
encrease at the outlet, so long as the water
continues to accumulate in the visible basin.
3d. Now the discharge from the outlet, which
becomes more copious every moment, being
contrary to the influx from the siphon, which
grows gradually weaker, the surface of the
well will cease to rise so soon as these opposite
powers are equal in their effects ; and the
flow will be at the full in this instant. 4th.
The well cannot rembin stationary, for any
length of time, at its highest elevation; be-
cause the vigour of the siphon being perpe-
tually on the decline, all the water discharged
by it will rua off through the outlet, toge-
ther with part of that, which had been pre-
viously accumulated in the visible fountain,
during the time of the flow. Sth. Hence it
is evident, that the well will begin to subside,
the moment it becomes stationary ; after
which it will persevere in a retrograde motion,
until the siphon shall have emptied the sub-
terranean reservoir. 6th. If no veins of
water discharge themselves into the visible
basin, besides the siphon which runs periodi-
cally, the spring is called, an INTERMITTING
fountain. The Bolderborn is of this kind,
for it remains dry while the secret reservoir is
filling, and flows while the siphon is in action.
Zz 2

864 Observations on an

7th. But if the spring receives other supplies
in addition to the intermitting current, it is
called a RECIPROCATING fountain; because
the stream that issues from the outlet of the
visible basin is permanent, though it varies in
quantity ; on this account the well ebbs and
flows alternately, but never runs itself dry.
All the fountains, which will be mentioned in
the sequel, are of this kind; and Pliny’s well,
near Coma, appears to possess the same cha-
racter from his description of it. 6th. The
fluctuations of an ebbing and flowing well,
which is fed by a siphon, will remain invari-
able, so long as the stream, that falls into the
subterranean reservoir continues to be uni-
form. But these external and visible opera-
tions of the well, are so far under the mflu-
ence of the current last mentioned, that they
will evidently suffer a temporary suspension,
so often as the influx into the concealed cistern
amounts to a certain quantity’in a certain
time ; for the siphon is but a secondary agent
in producing the phenomena of ‘reciprocation,
its business being to empty the subterranean
basin, so often as it is replenished. Now the
time of filling this magazine of water will be
the shortest, when the influx into it is most
abundant, and the contrary, consequently an
increased discharge into the subterranean re-

Ebbing and Flowing Well. 865

servoir, will diminish the intervals of the
siphon’s inactivity, and prolong the periods
of its action. It follows from these premises,
that when the influx becomes equal to the
feeblest effort of the siphon, the quantity of
water thrown into the concealed basin, will
exactly counterbalance the quantity which is
drawn off by the crooked canal; and the
external weil will assume the character of a
common fountain under these circumstances.

I have now explained the principles, on
which the common theory of reciprocating
springs is founded; and the necessary conse-
quences of the theory are stated in the eight
preceding propositions. This has been done,
to shew with what ease a natural apparatus on
the construction of 'Tantalus’s cup elucidates
the appearances, which have been ascribed by
writers to the fountains of Dodona, Coma,
and Paderborn. The operations of these
springs are happily illustrated by the instru-
ment in question; on which account I do not
hesitate to pronounce the theory to be a good
one, so far as it relates to these fountains
alone; provided they are faithfully described.
The simplicity of the preceding explanation
and its coincidence, with the narratives of the
two Pliny’s, as well as the history of the in-
constant brook in.Westphalia, disposed me to

366 Observations on an

admit the common theory, and to imagine it
to be equally applicable to reciprocating foun-
tains in general; until an instance occurred
to my notice, which proved that, fluctuating
fountains do not universally exhibit the perio-
dical operations which are described by the
writers. already quoted. I made a visit to
Giggleswick Well in the autumn of 1796;
which taught me to value this once favourite
theory not so highly, and in particular to dis-
pute the universality of its application. The
causes of these doubts will be easily perceived
from the following description of the well and
its operations. .

This spring lies at the foot of Giggleswick
Scar, which is a hill of limestone in the
West Riding of Yorkshire. 'The water dis-
charged by it, falls immediately into a stone
trough; in the front of which are. two holes
near the bottom; these are the outlets of two
streams, that flow constantly from the arti-
ficial cistern. An oblong notch is also cut in
the same side of the trough; which extends
from the brim of it, nearly to the level of the
two holes already mentioned. 'This aperture
is intended to shew the fluctuations of the
well: for the water subsides in it, when the
stream issuing from the rock becomes lan-
guid; on the contrary the surface of the

Ebbing and Flowing Weil. 367

water rises again in the notch, so soon as the
influx into the trough begins to be more co-
pious. The reciprocations of the spring are
easily observed by this contrivance ; and they
‘appear to be very irregular both in respect
of duration and magnitude. For the interval
of time betwixt any two succeeding flows, is
sometimes greater, and at other times less,
than a similar interval which the observer
may happen to take for his standard of com-
parison. The rise of the water in the cis-
tern, during the time of the well’s flowing, is
also equally uncertain; for it varies from one
inch, to nine or ten inches, in the course of
a few reciprocations. It is necessary to re-
mark on the present occasion, that the spring
discharges bubbles of air, more or less’ copi-
ously into the trough; these appear in the
greatest abundance at the commencement of
a flow, and cease during the ebb, or at least
issue from the rock very sparingly at that
time. In fact the appearance and disappear-
ance of these bubbles, are circumstances
equally inconstant with the rise and fall of the
water. .

The irregularities exhibited by the ebbing
and flowing weli, during my short visit, di-
minished the respect which I formerly had for
the popular theory, more especially when consi-

368 Observations on an

dered asa general explanation of reciprocat-
ing springs. This change of opinion was
suggested by the caprices of the well; which
were too many and too singular to be

ascribed to the uniform operations of a single.

siphon, as we have seen already; and the
accidental combination of several siphons in

one fountain, is a conjecture too improbable

in itself to demand a serious discussion. My
suspicions respecting the accuracy of the
principle were not a little increased, by the
following descriptions of two reciprocating
fountains. Weeding Well in Derbyshire,
appears to be more fickle and uncertain in
its reciprocations, than the well at Giggles-
wick. Dr. Plot describes this -remarkable
fountain, at page 48 of his history of Staf-
fordshire, where he reports it to be very un-
certain in its motions, ebbing and flowing
sometimes thrice in an hour, and at other
times not oftener than once in a month: he
also quotes the following character of it, to
the same import, from a Latin poem by
Mr. Hobbs.

“ Fons hic temporibus nec tollitur (ut Mare) certis 5
4¢ Mstibus his nullam prefigit Ephemeris horam.”

The following account of a reciprocating
fountain is extracted from an article in the
second volume of Lowthorp’s abridgement,

7 1

Ebbing and Flowing Well. 369

page 305; in which care has been taken to
preserve the facts recorded by the author,
Dr. W. Oliver, in language more concise than
his own.. “ Lay Well, near Torbay, is about
“ six feet long, five feet broad, and near six
“ inches deep ; it ebbs and flows very visibly;
“and many times inan hour. The recipro-
‘cations succeed each other more rapidly
«« when the well is full, than they do when it
“jis low. When once the fountain began to
“flow, it performed its flux and reflux in
“little more than a minute’s time; but the
“Doctor observed it to stand sometimes two
‘‘ or three minutes at its lowest ebb; so that
“it ebbed and flowed about 16 times in an
« hour, by his watch. So soon as the water
“began to rise in the well, he saw a great
“* number of bubbles ascend from the bottom ;
“ but when the water began to fall, the bub-
“bling ceased immediately. The Doctor
«« measured the distance betwixt the high and
«low water marks, not on a perpendicular
«line but on aslope, and found it exceeded
** 5 inches.” :

The three preceding instances of irregular
reciprocation undoubtedly diminishes the im-
portance of the popular theory, by proving
that it is not of universal application; as it
only explains the constitution of those foun-

3A

$70 Observations on an

tains, which ebb and flow periodically. The
Bolderborn of Westphalia, may be reason-
ably pronounced to be of this description; as
for the fountain of Jnpiter in Dodona, we
know too little of it to judge of its true cha-
racter; and it is not improbable but future
observations will add Pliny’s Well to the class
of irregular reciprocators.

It may be reasonably supposed, that since
I have endeavoured to confine the esta-
blished theory of reciprocation to one or
two springs at most, a new explanation will
be offered on my part, comprehending the
phenomena of those wells, which ebb and
flow according to no certain rule. Before
I make this attempt, it will be proper to
give a more circumstantial account of the
appearances exhibited by the well at Gig-
gleswick, than has hitherto been published.
I neglected, when in the country, to pre-
serve a correct register of its fluctuations,
and committed no other observations to wri-
ting, except those which appear in a former
part of this essay. This omission, however,
has been fully supplied by Mr. John Swainston,
of Kendal; to whom I formerly communi-
cated my imperfect remarks on this well, re-
questing him at the same time to note down
a series of its operations, at some copvenient

,

Ebbing and Flowing Weil. 371

opportunity. This request was complied with
by my friend; who has digested his observa-
tions in the following table, which merits the
esteem of the naturalist, as being a faithful
history of this singular fountain.

Observations made on Giggleswick Well, August
20th, 1804, from 3 to nearly 6 P. M.

On first coming to the Well it continued flowing near ten minutes, and
then as in the Table,
No. of | Time in ppatiaey No.of | Time |

inches |Ebbing in'at Ebb in| inches jin flowing Stationary at flow in
ebbed, minutes. | minutes | Flowed jin minutes}, minutes,

‘BE | 4 TE 49 2 iF
| 1 Tho F 7 :
= coed — z — =
2
or |.420)) 3 gr | 4 2 a
1 3 — |: — 2
5r |} 3h | —.] 7 1 1
eS — 1 — — —
3 2 “oa 4 5 A Bason f inch short
of full,
Ginridie: RiaiihsieeekoT= Ghh la 1 on
6f 3 none }| 6 1 2}
61 3 St gz 13 13 full
9 42 Qt 9 2 2
gz 4 5i gt 33 li x
Zz Z 3 — _ ——
Zz Zz
1 — | 3 —|-—- —
5 QL none 63 1} Left it fowing over.

Mr. Swainston has favoured me with the
following explanatory remarks; which per-
haps will throw some additional light on the
history and properties of Giggleswick Well.
In the two observations marked with crosses,

3A 2

872 Observations on an

the water flowed slowly for the. first 3 or 4
inches, and then rose very quickly, until the
cistern was full; the same appearance took
place not unfrequently in the course of his
remarks. Where the blanks are in the co-
lumns marked stationary at ebb, the water
flowed again instantaneously; but there are
some inaccuracies in this part of the table;
for Mr. Swainston was interrupted more than
once by travellers stopping to let their horses
drink. The term stationary at ebb, signifies
that the surface of the water in the cistern
was stationary at its lowest elevation ; at
which time the discharge from the trough was
commonly confined to the two holes near the
bottom of. it.

I have now stated all the facts in my pos-
session, that relate to reciprocating springs.
The fountains, which have been described,
are six in number, of these the inconstant
brook in Westphalia, appears to require the
agency of a siphon to account for its opera-
tions. The characters as ascribed to Pliny’s
Well, and the well in Dodona, are very am-
biguous and unsatisfactory : but the operations
of the three remaining springs, and more espe-
cially the register of Giggleswick Well, per-
plex the hypothesis of a siphon with insuperable

2

Ebbing and Flowing Well. = 873

difficulties; which a superficial inspection of
the table will discover to the reader.

The theory, which I shall now propose for the
explanation of irregular reciprocating springs,
was suggested by an accidental observation;
which occurred to Mr. Swainston, whom I
have mentioned above. This Gentleman, who
is a manufacturer of Morocco-leather, has a
contrivance in his works, for the purpose of
fillin@ a boiler of a particular construction
with water. This apparatus consists of a tub,
which is elevated considerably above the
boiler. The water is conveyed from a pump
along a trough into this vessel; from which it
runs immediately into the upper extremity of
an inverted siphon, which is cemented into a
hole in the bottom. This compound tube
consists of three branches or legs; the first
descends perpendicularly beneath the tub,
and is the longest of the three; the second
ascends again and carries the water, which
‘comes into it from the first, to a convenient
height above the brim of the boiler; the third
is a descending leg, which performs the office
of a nozle, that is, it discharges the water
from this crooked canal into the boiler. Mr.
Swainston observed by accident, that when
the workmen were filling the vessel last men-
tioned, the water reciprocated in the tub, the

374 Observations on an

surface of it rising and falling alternately in
a manner which he could not explain, by sup
posing some slight irregularity in the manage-
ment of the pump. When the appearance
was more carefully examined, he found a
corresponding variation in the efflux at the
nozle; for when the water was rising in the
tub, the stream was perceptibly weaker at
this outlet, than it was during the ebb or fall
of the water in the vessel last mentioned.
He farther observed, that when the water in
the boiler rose high enough to cover the end or
nozle of the siphon, bubbles of air were seen
ascending from this orifice, during the ebb
in the tub, or at least during the former part
of it; but that they did not appear during the
flow, or whilst the water was accumulating
in the tub. The fluctuations here described,
were far from being regular, either in magni-
tude or duration; for the water rose much
higher in the tub at one time, than it did
‘at another ; and the intervals betwixt flow
and flow, or ebb and ebb, were very unequal.
In fact the appearances seen in this vessel
imitated the caprices and singularities of Gig~ —
gleswick Well in a natural and. surprising
manner.

The exact coincidence of the effects, pro-
duced by an artificial apparatus, and a noted

Ebbing and Flowing Well. 375

reciprocating fountain, will naturally turn the
attention of the curious to inquire into the
cause of the irregular motions, which Mr.
Swainston observed in his reservoir. The cir-
cumstance on which these fluctuations de-
pended, -is easily understood; for, seeing the
inverted siphon discharged bubbles of air
occasionally into the boiler, it is manifest that
this subtle fluid entered the tube, mixed with
the water, or in other words in the state of
foam. Now it is well known, that the bub-
bles, constituting this frothy substance burst,
‘and the air separates from the water, when
the agitation ceases ; by which the compound
was produced. Such a separation would take
place unavoidably in the siphon; because a
current flowing in a tube moves on smoothly,
or without interruption which is the cause
of agitation. The process here described,
discovers the nature of the phenomena which
are exhibited by Mr. Swainston’s vessel; for
the air, which separates from the water in the
siphon, is collected in some part of that tube,
most probably in a bend connecting two adja-
cent legs; where it forms a bubble or mass,
large enough to produce a considerable ob-
struction in the current, by contracting the
area of the pipe. The water will evidently
rise in the tub, so long as its efflux is inter-

-

376 Observations on an

rupted by this obstruction; but the action of
the stream in the siphon will push the mass
of air from place to place in its own direction
until it shall be discharged at the nosle. The
removal of this impediment will restore the
stream to its full vigour ; upon which the
water will begin to subside in the tub; and
it will continue to do so, until the surface
arrives at its proper level; unless a second
collection of air happens to be formed in the
mean time. We have now investigated the
nature of the reciprocation, observable in Mr.
Swainston’s apparatus, it proceeds entirely
from the obstruction of air bubbles, lodged
in the crooked canal; the formation of which
depends on causes that act in a fortuitous or
irregular manner ; consequently the recipro-
cation which results from their united opera-
tions will prove to be equally uncertain and
variable.

Should the preceding theory of an ebbing
and flowing vessel receive the reader’s appro-
bation, he will be disposed to think, that Pliny
discovered the true nature of reciprocating
fountains, when he compared the fluctuations
of these springs to the interrupted and irre-
gular stream, which issues from a bottle. In
fact, only one circumstance seems wanting
to render his explanation of the phenomenon

Ebbing and Flowing Well. 377

complete; he has not informed his friend
Licinius, how he supposes the air gets into
the subterranean channel, which supplies his
well with water. Perhaps this omission was
the effect of design, rather than of negli-
gence ; for many philosophers in Pliny’s time
held the singular opinion, that the earth pos-
sesses the faculty of respiration like animals ;
in consequence of which it inhales and expires
air through the crannies and caverns, which
extend to its surface. Supposing Licinius
to be of this way of thinking, Pliny had no
reason to tell this ingenious and learned man,
that he imagined the outlet of the fountain
had a communication under ground, with one
of these spiracles of the globe. Be this as
it may, the notion is too absurd to be mert-
tioned in the present improved state of Na-
tural Philosophy, in any other light than as
a curious document of the puerile conceits
with which the philosophers of ancient times
amused their hearers. Ln the foregoing
attempt to’ complete the theory, I have
had recourse toa well known phenomenon;
water is beaten into foam by being agitated ;
which was the case with Mr. Swainston’s
vessel, because a strong current fell into it
from the pump. There is, however, one
objection still remaining, which deserves to
3B

378 Observations on an.

be considered: the levity of foam, compared
with the superior weight of water, may lead
some persons to suspect, that this light sub-
stance will not mix with water, but will float
‘on the surface of the reservoir, in which it
is formed. Supposing this suspicion to be
well-founded for the sake of argument, we
must allow the foregoing theory of recipro- |
cating vessels to be defective in a very essen-
tial point; because if foam cannot sink, the
air, that proceeds from it, cannot find its
way into the tubes or siphons, which convey
the water from such vessels. Being unwil-
ling to leave this objection unanswered, I
resolved to put the truth of this principle to
the test of direct experiment; which was
done in the following simple manner. A
small bell glass, being first filled with water,
was inverted in six quarts of the same fluid,
contained ina small tub. Things being thus
prepared, the contents of the open vessel
were agitated briskly; and the air which
entered the water, found its way into the
inverted glass, the upper part of which it
occupied. The water of the tub was agitated
by the motion of a whisk, or a bundle of
slender twigs; it was sometimes taken up
in a pitcher, and returned into the vessel
quickly, from the height of a foot or more:

Ebbing and Flowing Weil. 379

both methods proved successful, but the
fexmer appeared to introduce air into the
glass with more expedition than the latter did ;
the difference here mentioned, may however
depend entirely upon management and acci-
dental circumstances. The experiment which
I have now related, shews the foregoing
objection to be of no moment; consequently
the present theory of irregular reciprocation
may be pronounced to stand upon a safe foun-
dation, and unexceptionable principles.

The observations which have been made
on Mr. Swainston’s accidental discovery, ren-
der an elaborate inquiry into the constitution
of Giggleswick Well unnecessary. Nature
may he easily supposed to have produced an
apparatus in the side of the hill, possessing
the mechanical properties of the reciprocating
tub, and all the phenomena will follow ;
which are so remarkable in this fountain.
Let us imagine a reservoir to be -concealed
from view under the rocks; into which the
stream of a subterranean brook falls, and
beats part of its contents into foam by agi-
tation. Let this cavity be connected with
the external or visible basin, by a narrow
serpentine chink concealed in the interposing
strata; and the reader must perceive without
farther explanation, that this conduit will
3B2

880 Observations on an

perform the part of the inverted Siphon al-
ready described, and exhibit the operations
as well as the irregularities of the fountain
in question. The same internal structure
may be supposed to exist in Lay Well, near
Torbay; but something is required im addi-
tion to this simple apparatus to account for
‘the casual reciprocation of Weeding Well,
in Derbyshire: It is not a difficult. task
to accommodate the theory to the description
of this spring; but when we consider how
imperfect such descriptions are commonly
found to be, it appears more advisable to
pass over this fountain in silence; until some
accurate observer shall present the public
with a correct and minute history of. its
operations. |

All parties allow, that reciprocating foun-
tains flow from pools of water, concealed
under ground; on which account it will not
be very foreign to the tepic of the present
essay, if I conclude it with a few remarks on
the structure and formation of caverns, I
have visited many caves in this part of Eng-
land; all of which are situated in the strata
of calcareous hills. They also appear to have
been once filled with an argillaceous stone,
of a less durable nature than the surrounding
limestone. This supposition is corroborated

Ebbing and Flowing Weil. 38h

by the following fact; masses of clay, mixed
with gravel, are found scattered up and down
these hollows; and as they are lodged in
chinks from which they cannot be easily re-
moved by water, I suppose them to be the
remains of extensive beds, which formerly
occupied these recesses in the calcareous strata.
This argillaceous matter, which choaked up
the natural vaults of our limestone hills in
early ages, has been gradually worn away by
a simple, but powerful agent. The rains
which have fallen from the remotest times,
constantly find their way through the chinks
of the limestone ; thus subterranean brooks
were formed, which attacked the soft argil-
laceous matter, situated under the harder co-
vering of limestone. This perishable sub-—
stance was first softened by the water; and
afterwards broken down by the currents;
which washed away the clay and gravel. In
consequence of this alteration, the incumbent
rocks of limestone were left to rely on them-
selves ; such therefore fell down, as were not
supported by mutual pressure; while the rest
still remain suspended in the roof and sides
of the caverns, being locked together like the
stones of an arch, The agents, which were
formerly employed in the excavation of those
subterranean chambers, remain in many in-

382 Observations on an

stances to the present day; for almost every
cavern is the place of union to a number of
secret brooks, which enter it in different di-
rections, some of them being perennial, but
others depend on the weather. |The impetu-
osity of these currents is very apparent in
some caverns, which are filled with water in
wet seasons; for the bottoms of them are
covered with large masses of stone; the edges
and, angles of which are worn away, like
those of a pebble, that has been rolled im the
channel of a rapid river.

I have already remarked that the caves of |
the North of England are commonly found
in calcareous strata. This circumstance may
be traced to natural causes; for the rain water
descends with great ease through the vertical
fissures of these rocks; which generally rest
upon a base of gray schist, and in some places
on a soft argillaceous substance of a lamf-
nated texture. This base is not uniformly
flat: for it swells occasionally into lumps’ or
hillocks ; some of which appear above the
surrounding limestone. Such of these hillocks
as were originally situated under one, or a
number of subterranean brooks formed in the
calcareous strata, have been washed away
long ago; and the caverns, which remain ‘at
present, shew the extent and form of these

eee

Ebbing and Flowing Weil. 383

demolished eminences. The recesses, thus
produced, frequently contain pools of water;
and if the presence of a grotto be necessary to
a reciprocating fountain, perhaps few places
are more. likely to produce one, than the
neighbourhood of Giggleswick. For the
country abounds with ‘caves, and also with
subterranean brooks ; one of which is heard
very distinctly through the rocks which cover
it, ata place where it sounds lke a stream
falling into an extensive chamber.

Having now finished my remarks. on reci-
procating fountains, I have only to recom-
mend them to your attention. Should the
essay appear to deserve the notice of your
Literary and Philosophical Society, your
kindness in presenting it to that learned
body, will confer an additional favour upon

Your’s, &c.

JOHN GOUGH.

( 384)

DESCRIPTION |

OF AN

EUDIOMETER,

And of other Apparatus employed in Expe-
riments on the Gases,

BY W. HENRY, M.D. F,R.S. &c.

(Read Nov. 11, 1811.)

CWARS

CHEMICAL instruments have generally,
by their progressive improvement, been ren-
dered more complicated and expensive ; but
the one, which I am about to describe, if it
has any merit, is recommended by greater
simplicity and economy, than those which
have hitherto been applied to the same pur-
pose. While it possesses these advantages,
I am not aware that it is liable to objection
from any sources of inaccuracy, that do not
equally exist in all other eudiometers.

In its construction, it most nearly resem-
bles, and indeed was originally suggested by,
one which was invented, several years ago, by
Professor Hope of Edinburgh. His appa-
ratus consists of a tube sealed at one end,
which holds precisely a cubic inch, and is

j

Description of an Eudidmeter. . 385

accurately graduated into 100 equal parts.
This tube is fitted by grinding into the
neck of a bottle, capable of holding two or
three ounce measures of water, and having,
near the bottom, another opening or neck,
which is occasionally closed by a glass stop-
per. The bottle being filled with the eudio-
metric liquid, the tube containing the gas
under examination is next put into its place;
and. on inverting the apparatus, the gas
ascends into the bottle, where it is briskly
agitated in contact with the liquor. An ab-
sorption takes place ; and, to supply this, the
stopper is taken out ander water, which
rushes into the bottle. The agitation, and
opening of the stopper, are renewed alter-
nately till no farther diminution is produced
in the gas. |

To this instrument, though very simple and
ingenious, there are several objections: For
Ist. by the absorption of. part of the gas, the
remainder becomes of less density, and is,
therefore, iess easily taken up by the liquid.
2dly. By the repeated admission of water,
the eudiometric liquor becomes much weaker
towards the close of the process, when its
unimpaired strength is most wanted. 3rdly.
If any defect exists in the joints of the vessel,

ac

386 Description of an Eudiometer.

_ the external air rushes into the instrument to
supply the vacuum. 7

All these objections, it occurred to me,
after using the apparatus two or three times,
might be obviated by substituting a bottle of
caoutchouc or elastic gum, the sides of which,
by collapsing as the absorption goes on, must’
place the included gas under an uniform de-
gree of pressure during the whole experi-
ment.* As a neck to the elastic bottle, for

* Tt would be unjust to Mr. Pepys, who has benefited
chemical science by the invention of a variety of, useful
apparatus, not to state that he published the first account
of an instrament, in which a bottle of elastic gum is used
for containing the eudiometric liquid. (Phil. Trans. 1807.)
As in his apparatus, however, the liquid is injected from
the elastic bottle into the graduated tube, no contrivance
was necessary for facilitating the return of the gas from the
former into the latter; and his eudiometer, therefore, is
adapted only for those liquids, which, like the solution of
nitrous gas in sulphate of iron, act by a very moderate
degree of agitation. The liquid, which I prefer, on ac-
count of the greater cheapness and facility of making it, is
prepared by boiling a little quicklime, sulphur, and water,
together ina Florence flask, decanting the clear fluid, and
shaking it strongly in a bottle about three-fourths filled
with it. To effect the absorption of oxygen gas by this
liquid, especially towards the last, when it bears a smatl
proportiog to any other gas with which it is mixed, brisk
and long continued agitation is necessary.

‘ =

Description of an Eudiometer. 387

the purpose of receiving a graduated tube not
differing from that of Dr. Hope, I employ
a piece of tube of about + an inch diameter,
and about one inch long. Into one end of this, f
the graduated tube is accurately fitted by
grinding; and the other end is made some-
what funnel-shaped as shewn by Plate VI.
fig. 3. 6. The outer surface of the wider tube
being previously ground, to destroy its smooth-
ness, the neck of the elastic bottle is firmly tied
upon it, care being taken to bring the folds of
string so low, that no space may he left for
the lodgment of air between the bottle and
the tube. ;
The apparatus is used in a similar way to
that of Dr. Hope, the gas being measured
from time to time to ascertain when the ab-
sorption ceases. The only difficulty, which
is likely to be experienced, and which a little
practice will overcome, is to return the whole
of the gas from the bottle into the tube. Be-
fore measuring the residuary gas, it is proper
to remove the graduated tube from its attach-
ment, either under water or mercury ; for:
otherwise the elasticity of the sides of the
bottle increases a little its apparent quantity.
-In most cases, the graduated tube may
be cylindrical as shewn by fig. 5; but when
- 302 |

388 Description of an Eudiometer.

the residue of gas is expected to be very
small, I employ a tube the sealed end of
which is drawn out toa narrower diameter,
so as to admit of more minute divisions (see
fig. 6.) On the contrary, when only a small
portion of gas is expected to be absorbed,
the tube may be narrowest at the open end.

To satisfy myself of the adequacy of this
instrument to its purpose, I compared the
analysis of artificial mixtures of oxygen and
nitrogen gases, by its means, with that effected
by nitrous gas used in Mr. Dalton’s mode ;
by phosphorus ; and by detonation with hy-
drogen. The results, in order to avoid all
‘bias in favour, of any of the processes, were
registered by Mr. H. Creighton, (to whom I
am indebted for the annexed drawing) and
when compared after the experiments were
finished, they did not differ from each other
more than 54, of the whole mixture.

In graduating tubes for eudiometry or any
other purpose, I have long been in the habit —
of using a contrivance, which renders the
operation greatly quicker, and insures perfect
accuracy.’ It consists of a tube (Plate. VI.
fig. 7.) open at both ends, and not more than
.08 of an inch in diameter. ‘This is carefully
divided into equal parts, which may be en-

ee ——_ se

‘Description of an Eudiometer. 389>*

tirely arbitrary; but those, which I employ,
are each ten grains of mercury at 60° Faht.
the whole tube containing 100 grains. It is
some trouble to divide this tube; but, when
once prepared, any number may, by its means,
be easily graduated. The successive portions
of mercury, used in dividing wider tubes, are
measured by this, into which they are drawn,
either by plunging it into a jar filled to suffi-
cient height with that fluid, or by the action
of the mouth. .
_ The two figures in the plate, which remain

to be described (fig. 1. and 2.) represent an
apparatus, which I have found extremely
useful for submitting various gases to the long
continued action of electricity. The platina
wires, for conveying the electric fluid, are
inclosed in two short pieces of almost capil-
lary tube 6 c, which are sealed round them,
and then ground away so as to expose merely
the points atd d. These tubes are hermeti-
cally sealed into the small globe at 6 c, so
that the points of the wires may be at a
proper striking distance. The vessel may be
filled with gas over mercury, and closed by
the stopper g, fig. 2, or the elongated stopper
¢, fig. 1. But if it is desirable entirely to

390 Description of an Eudiometer.

exclude mercury, some small globules of
which always remain in the globe when filled
over that fluid, a metal cap may be cemented
upon the neck of the vessel (fig. 1.) which,
after exhausting it by the air pump, may be
filled with gas from a receiver furnished with
a proper stop-cock. An apparatus of this
kind was used in the experiments on muviatic
and oxymuriatic acids, which I have de-
scribed in the Philosophical Transactions for
1812; and may be advantageously applied to
other purposes.

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A MEMOIR

ON THE

URIC ACID,

BY WILLIAM HENRY, M. D. F. BR. S. &c. *

(Read Nov. 29, 1811.)

SECT. I.

History of Discoveries respecting the Uric Acid.

TWN

"T'HovGH the properties of the Uric Acid
have not been well understood, until the last
thirty-five years, yet it appears from the wri-
tings of some of the earlier chemists, that
they had made very near approaches to the
discovery of its real nature.

Van Helmont, by the destructive distilla-
tion of an urivary calculus, obtained what he
calls a foetid spirit, a yellow crystalline mass,
and an oily product, all resembling the sub-

stances which may be obtained by a similar

* The principal part of this essay was published in my
inaugural dissertation at Edinburgh in 1807; but having
‘since repeated most of the experiments, I have corrected
some of the results, and added those of new ones,

392 A Memoir on the Uric Acid.

treatment of the dry extract of urine.(a)
Hoffman, having placed a fragment of a stone
from the kidney upon a red hot coal, found
that it emitted a smell of ‘volatile alkali, and
left a portion of charcoal, which was perfectly
tasteless. He ascertained, also, that the same
substance was very sparingly soluble in water,
and not at all in sulphuric or muriatic acids
at common temperatures ; but that hot nitric
acid acted upon it, and gave a solution, which
was not precipitated by carbonate of pot-ash.
Hence he concluded, with reason, that con-
cretions of this kind donot consist of calca-
reous earth.(b) Slare, in order to shew that
the stone of the bladder is not tartar, sub-
mitted it to destructive distillation, and ob-
tained oil, volatile alkali, and a brown and
bitter salt. ‘A coal remained, which was
nearly consumed by burning it with free ac-
cess of air.(c) Dr. Hales, in addition to the
same condensible products, collected. a large
quantity of permanent gas, amounting to 516
cubical inches, from a quarter of a cubical
inch of the stone. He denies the power of
dissolving calculus, not only to the sulphuric
acid, but to alkaline salts ; evidently in con-

(a) De Lithiasi, cap. v. § 9. Amst. 1648.

(b) Obs. Phys. et Chem. lib. ii. obs. 25. Genev. 1748.

(c) Lowthorp’s Abridgment of the Phil. Trans. iii. 179.
2

Ea

aa

egal ©

A Memoir on the Uric Acid. 393

sequence of his having employed the mild,
instead of the caustic alkalis. Nitric acid,
however, he found to act on the stone with an
effervescence, which he shews to be owing to
the formation of a permanent gas.(d)

No further examination appears to have
been made of this substance for nearly half a
century ; for it was not till the year 1776, that
Scheele published the excellent essay, which
contains the first accurate history of its che-
mical properties.(e) With Hoffman and
Hales, he found the matter of calculus * to
be soluble in nitric acid ; and he added the
observation, that by evaporating the solution
to dryness, a red mass is obtained, which
imparts its peculiar colour to the skin and
other animal substances. This property is of
importance, inasmuch as it distinguishes the
body in question from all others. Scheele,
also, first pointed out its title to be ranked.
among acids, in consequence of its reddening
the infusion of turnsole.. He determined,
moreover, that the acid, which he had found

(d) Hales’s Heemastatics 1727, p. 190.

(e) Scheele’s Essays, Essay IX.

* It is necessary to remark that this applies to one spe-
cies of calculus only ; and that there are several kinds, dif-
fering not only in external appearance but in chemical
composition.

3D

394. A Memoir on the Urie Acid.

in urinary calculi, is not merely a product of
disease, but is constantly present in the urine,
even in its most healthy condition.* Some-
times, from urine which had been voided a
few hours, he observed it to be deposited in
small crystals ; or, when the separation did
not take place spontaneously, he found that
it might be produced by evaporating the
urine to one fourth, or one third of its bulk.
Bergman confirmed the experiments of
Scheele,(f) and their united authority was
deemed sufficient by the framers of the
French nomenclature, (g) to entitle the newly
discovered substance to a distinct place among
the acids. Having been originally obtained
from the stone of the bladder, they derived the
name of Lithic Acid, from the Greek word
aidos, lapis.

* The uric acid was till lately supposed to be peculiar to
he urine of the human species. (Ann. de Chim. xvi. 166.)
Mr. Brande, however, has found it in the urine of the
camel, but not in that of other animals that feed chiefly
on vegetables. (Phil. Trans. 1806, p. 373.) And Dr.
Wollaston bas found that it forms a considerable part of
the urine of birds, which is voided along with their dung,
especially of such as aie carnivorous. (Phil. Trans. 1810.
p- 229.)

(f) Act, Stockh. an. 1776, Opusc. Phys. et Chem.

viv. 387, f

(g) Methode de Nomenclature, 1787.

-

| A Memoir on the Urie Acid. 895

The next series of experiments on the lithic
acid, were published by Mr. Higgins of
Dublin; (h) and these were soon afterwards
followed by the researches of the late Dr.
Austin. (ij) The mode of investigation,
adopted by both these philosophers, was
chiefly that of destructive distillation. Little,
therefore, was added to our knowledge of the
subject, except the discovery, by Mr. Hig-
gins, that nitrate of ammonia is produced by
the action of nitric acid on this variety of
calculus; and a more accurate .examination,
by Dr. Austin, of the permanently elastic
fluids. .

In the year 1793, Mr. Murray Forbes, in
an ingenious treatise on Gravel and Gout, (/)
pointed out a mode of separating the lithic
acid from urine, which has the merit of great
simplicity and efficacy. It consists in adding
diluted sulphuric acid, to recently voided
urine (in the proportion of about 20 drops of
the former, tohalf a pint of the latter,) and
in allowing the mixture to stand about 24
hours. At the expiration of that time, small

(h) Compar. View of the Phlogistic & Antiphlog.
Theories, p. 283.
(i) Treatise on the Origin and component parts of the
Stone of the urinary bladder, 1791.
(k) Published in 8yo. at London, 1793.
3 D2

396 A Memoir on the Uric Acid.

crystals are found adhering to the sides of the
~ vessel, which may be collected and purified
by washing them with cold water. The in-
vention of this process, since described by
Dr, Egan in the Transactions of the Irish
Academy, (/) is, indeed, to be attributed to
Link, who first made it known in his Disser-
tation, published at Gottingen, in 1788, (m)
Beside the peculiar variety of calculus which
consists chiefly of uric acid, Dr. Wollaston,
in the Philosophical Transactions for 1797,
described several other well characterized spe--
cies ; and proved that the concretions, which
are found in the joints of gouty persons, con-
sist of lithic acid united with soda. Dr.
Pearson, in the following year, was led by a
long and laborious investigation of the pro-
perties of the lithic acid, to a conclusion re-
specting its nature different from that of
Scheele and Bergman ; for its properties, he
conceived, agree better with those of an oxide
than of an acid, and he proposed, therefore,
to call it the uric ovide.(n) His memoir
. incited Fourcroy and Vanquelin to repeat and
extend the experiments of Scheele, whose

(l) Vol.x. p.-256.

(m) H. F. Link Commentatio de Analysi Urine et
Origine Calculi.

(m) Phil. Trans. 1798;

A Memoir on the Uric Acid. 397

original conclusions they fully verified. (0)
They concede, however, to Dr. Pearson the
propriety of using the ‘specific name uric ;
and this term has since been generally re-
ceived by chemical philosophers. My own
experiments, it will presently appear, fully
confirm the propriety of ranking it in the class
of acids.

SECT. II.
On the Chemical Properties of the Uric Acid.

THE following account of the properties of
the Uric Acid, is to be understood as applica-
ble to it in a pure state. To obtain it in
‘sufficient quantity, I have generally had re-
course to that variety of urinary calculus,
which is chiefly composed of uric acid. Con-
cretions of this sort may readily be distin-
guished by their external characters. They
are of various sizes, from that of a horsebean
to that of a large egg. Their shape is gene-
rally a flattened oval; and, when broken or
divided by a saw, they exhibit generally a
radiated structure, and have acentral nucleus
of more compact texture and greater hard-
ness than the rest of the stone. Their colour

fo) Ann. de Chim, xxvii. 225. Fourcroy’s Systeme,
tom. ¥. 4to. p, 515,
1

398 A Memoir on the Uric Acid.

is various, from pale straw yellow to deep
brown, sometimes with an intermixture of
red; and the divided surfaces bear consider-
able resemblance to wood. ‘To separate the
uric acid from the other substances with
which it is mixed, the calculus, finely pow-
dered, is to be dissolved in a heated solution
of pure potash. The solution is to be poured
into a quantity of diluted muriatic acid, which ~
is more than sufficient to saturate the alcali;
and the precipitate is to be repeatedly washed
with a large quantity of distilled water. In
order to remove any adhering portion of mu-
riatic acid, a little carbonate of ammonia,
may also be added to the first washings.
After edulcoration, it may be dried in a tem-
perature not exceeding 212° Faht.

1. In this state, the uric acid has the form
of white shining plates, somewhat resembling
those of the acid of borax, but considerably
smaller. It is perfectly soft to the touch, and
entirely destitute of taste and smell.

2. When added in powder to the infusion
of litmus, it changes the blue colour of that
liquid to red, but less distinctly than the mi-
neral and most of the vegetable acids.

3. Four ounce measures of boiling distilled
water take. up about 1.4 grain, and. of this
about half a grain separates again on cooling.

A Memoir on the Uric Acid. 399

According to Dr. Pearson, the acid is soluble
in only 800 times its weight of water; and
Scheele states the quantity required at still
less, viz. 300 parts. It is to be observed, how-
ever, that Scheele employed, for his expe-
riments, only the pulverized calculus, and
not the purified acid.

4. The watery solution reddens the infusion
of litmus, but produces no change on the
solution of alkaline carbonates. .

5. When a small portion of the dry acid
is heated on a bit of window glass with a few
drops of nitric acid, and the mixture is eva-
porated to dryness, the residuum has a beau-
tiful red colour. The addition of a few drops
of water greatly increases its intensity ; and
occasions it to resemble that of carmine. This
colour is communicated to the skin, to wood,
nd to other animal and vegetable substances.
It is also soluble in water, and the solution
has the hue of an acidulated infusion of rose
leaves; but soon loses it and becomes limpid,
even when secured from the access of air. The
colour is destroyed by all acids, and by pure
alkalis; and is not restored again by any che-
mical agent which I have employed with this
view. Fourcroy (p) ascribes this charac-

(p) Systéme, 4to. V. 516.

400 A Memoir on the Uric Acid.

teristic property (of affording a red colour
with nitric acid) to the admixture of urea,
and denies it to the pure uric acid. I have
satisfied myself, however, that it belongs even
most remarkably to the purified acid, and that
it cannot by any process be obtained from
urea.

6. The watery solution of uric acid does
not produce any change in the solutions of
earths or metals in acids.

7. The dry acid is not at all acted upon by
the solutions of the alkaline carbonates, or
sub-carbonates. Even digestion with them,
for several hours, occasions no greater loss of
weight, than would be produced by a quan-
tity of water equal to that of the solution.
This fact I determined by repeated expe-
riments, both on account of its influence on
medical practice ; and because, though test»
fied by every preceding writer, it has lately
been denied by Dr. Egan.(q) It suggests
the necessity of administering alkalis in a
pure state, whenever they are given with the
view of dissolving a stone, which is already
formed in any of the urinary passages.

8. The watery solution of uric acid does
not decompose soap ; but when the dry acid

(q) Irish Transactions x. 289.

A Memoir on the Urie Acid. 401

is digested with a solution of that substance,
the oil is detached, and a ‘liquid results,
which bears much resemblance to an emul-
sion. Ten grains of uric acid, digested with
30 grains of soap, and four ounce measures of
distilled water, at a temperature of 180°
Faht., were dissolved, except a small portion,
estimated at most at half a grain. It appears,
therefore, that soap may be expected to exert
2 solvent action on those uric acid conéretions,
which are lodged in the urinary passages.

» 9. The compounds of sulphur and sulphu-
retted hydrogen with alkalis are decomposed,
when heated with uric acid,

- 10. The uric acid is not dissolved, when
digested with a solution of prussiate of
potash.

11. It is not acted upon by any acid, ex-'
cept by those which, at the same time, effect
its decomposition, viz. the sulphuric, nitric,,
and oxymuriatic, the agency of which will
be described, after detailing the properties
that belong to the acid in its entire state.

12. The uric acid is rapidly dissolved. by
heated solutions of pure potash and pure soda,
but less readily by that of ammonia. An
ounce measure of liquid potash, of the spe-
cific gravity 1108, dissolves about 60 grains
of the acid. The solution has a strongly.

3 E

402 A Memoir on the Uric Acid.

alkaline taste, and is decomposed by all
acids. Even the carbonic acid and» the
alkaline carbonates occasion a white preci-
pitate from it. The nature of this precipitate
differs, however, according to the circum-
stances under which it has taken place. If
‘the alkaline solution be poured) into diluted
muriatic, sulphuric, or any other strong acid;
or if these acids be employed in any: way,
provided their quantity exceeds what is ne-
cessary to saturate the alkali, uric acid is
precipitated in a pure state. But if the
precipitating acid, on the contrary, be gra-
dually added to the alkaline solution, and. in
a quantity insufficient for its saturation,’ the
precipitate is, either wholly or in part, an
insoluble compound of uric acid and alkali.
This saturated compound of uric acid. and
alkali is alone thrown down by solution of |
carbonate of ammonia, and by carbonic
acid.* The alkaline solution may, therefore,
be regarded as consisting of a neutral com-
pound of uric acid and alkali, dissolved by
an excess of the latter substance... To obtain
the saturated compound, we may either, di-
rectly combine the uric acid with the alkali,

* This fact escaped the observation of Scheele, whose

sagacity and accuracy on most occasions are singulatly
conspicuous, “See ‘his 9th Essay, § 4.

A Memoir on the Uric Acid. A038

jn such proportions as mutually saturate each
other; or we may adopt the easier method of
forming a solution of urie acid, by an’ excess
‘of alkali, and then precipitating by carbo-
‘nate of ammonia, and edulcorating’ the’ sedi-
ment. The latter process answers best, when
we employ potash or soda; but to obtain
saturated compounds of uric acid with am-
monia, baryta, strontita, lime, magnesia, or
alumine, I have generally had recourse to the
former method. In whatever mode these
‘compounds are prepared, they are termed
‘Urates.

/ SECT. UT.
Urates.

Tuovueu I have examined the properties
of each individual urate with great/attention,
yet they do not appear to me sufficiently
important, to entitle each of them to a sepa-
rate history. It will, therefore, be sufficient
“to state those properties, which are common
to the whole of this genus of salts.

1. The urates are all perfectly insipid, and,
when moist, are scarcely distinguishable from
the uric acid itself. In the act of drying,
however, they shrink somewhat like alumine,
and form hard masses.

SE 2

-A04 dA Memoir on the Urie Acid.

2. ‘They are all permanent, or undergo no

change, by exposure to the atmosphere,
_ 8, Though more soluble than the uric acid
itself, yet they are universally difficult of so-
lution, even by hot water. Of urate of pot-
ash, an ounce of boiling water takes up about
a grain. This is the most soluble; and the
rest succeed it in the following order, urates
of soda, haryta, strontita, lime, amRAABIA>
magnesia, and alumine,

4. They are decomposed by a red batt
and. after being burnt with access of air, the
base remains in the state of a carbonate, ex-
cepting when we employ the urate of ammo-
nia.* After being’ thus decomposed, the
quantity of alkali, which has saturated the
acid, proves to be extremely small. The
urates of potash and soda, after the destruc-
tion of their acid in this way, leave only
about one eighth their weight of the respee-
tive subcarbonates. of those ‘alkalis., . Also,
ten grains of uric acid, dissolved, by potash
or soda, and precipitated by carbonate of am-
monia, give from 9, to, bO grains of dry urate.
This, fact shews, Ist. That the uric acid

* Mr. Forbes, who composed the urates of magnesia and
alumine, and. investigated their properties, remarks that
after evaporation to dryness, they emit volatile alkali ata
degree of heat not very considerable. (On Gout, &e, p. 15.)

A Memoir on the Urie Acid. 405

contains a small portion of water, which it
loses either wholly, or in part by combining
with the alkalis; and 2dly.. That the quantity
of alkali required. for einem is exces-
sively small.

5. When to a watery solution of any of the

-urates, we add the sulphuric, nitric, muriatic,
-or any other acid, except the ‘prussie or car-
bonic, the uric acid is precipitated, from the
‘more soluble urates immediately, and from
the less soluble after some interval of time.
-. 6, Solutions of the alkaline urates are de-
composed by the muriates, nitrates, and
acetates of baryta, strontita, lime, magnesia,
and alumina, but least readily by those of
magnesia.

7. They are also precipitated by the bee
tions of all metals, except that of gold. The
precipitate by solutions of iron has a tinge of
red, and that by solutions of copper a green-
ish hue; but all the other precipitates are
white, and extremely difficult of solution. |

8. The saturated urates are mostly soluble
by an excess of fheir respective alkaline or
‘earthy bases.. Those of ammonia, magnesia,
and alumine, are exceptions.

From a consideration of the properties
which have been already described, as be-
longing to the peculiar substance, which

‘406 ©AMenoir on the Uric Acid.

forms the chief ingredient; of urinary calculi,
there can be little room’ for doubt about refer-
‘ing it to the class of acids. |
Ist. Because’ it’ reddens the infisiots of
litmus. It must be acknowledged: that Dr.
‘Pearson has ‘given a contrary statement ; (7)
but his result was probably obtained, by em-
ploying a substance which had been precipi-
tated by a deficiency «of acid. In that case,
he must necessarily have operated not: on uric
acid, but on a saturated. urate: so . closely
resembling the acid, as not to be distinguish-
able .by external. properties. . It), may, be
alledged, indeed, that the uric, acid, which I
employed, might retain a portion of, the ma-
rine acid used for its precipitation; but this
is not at all probable, since it was well edul-
corated. by carbonate of ammonia. . Besides,
the powdered stone itself produces the same
effect; and certainly not from any mixture of
super-phosphate of. lime, for, which, relying
on the authority of Brugnatelli, (s), I have in
vain sought in several specimens. of | uric
caleuli. | . move
2dly. Because it dhecpepliibes as Dr. Daew-

Cr) Phil. Trans. 1798.
(s) Ann, de Chim. xxv. 53.

A Memoir on the Uric Acid, 407

son admits, the compounds of alkalis with
sulphur, and with sulphuretted hydrogen.

3dly. Because it detaches the oil from soap.
That Dr. Pearson did not obtain this result,
may be ascribed to his having used either a
saturated urate, or an insufficient quantity of
uric acid; for itis well known that even the
stronger acids, added in too small a propor-
tion to solution of soap, scarcely effect any
change in it. To produce this change with
urie acid, it is essential that it should be
added in powder and in due quantity, and
that its action be assisted by heat.

Athly. An unequivocal test of the acidity.
of this substance is, that it forms with the
alkalis and earths, chemical compounds, in.
which the qualities, that belonged to them,
when separate, are no longer apparent. . To.
the evidence of all these properties, it cannot
be sufficient to object the want of sourness
to the taste, a quality which is equally defici-
ent in the prussic acid.. We may safely,
therefore, consider the body in question as en-
titled to be ranked in the same class of chemi-
cal compounds; but its acid power is extremely
feeble, as is proved by the very small proportion
of alkali which it is capable of neutralizing.

408 A Memoir on the Uric Acid.

_ SECT. IV.

Decomposition of the Uric Acid by other
Acids. —

On this subject I have no additions to
make to the facts which have been stated by
other chemists, whose testimony, so far as I
have examined it, I have found to be per-
fectly correct.

1. Concentrated sulphuric acid and uri¢
acid, when heated together, are mutually
decomposed; and sulphureous and carbonic
acid gases are obtained. (7)

2. The mutual destruction of the nitric
and uric acids, was first determined by Berg-
_ man, who observed that the red stain, left
after heating the two acids together, was
itself scarcely acid. The action of these
acids on each other has since been farther
investigated by Mr. Higgins,(u) and Dr.
Pearson. (x) The latter chemist, by repeat~
edly distilling nitric acid, from the same por-
tion of uric acid, effected its entire decom-
position. The nitric acid, yielding its oxygew
to the carbon of the animal acid, formed

(t) Scheele, Essay IX. § 1. Ms

(u) On Phlogiston, p. 299.
(x) Phil. Trans. 1798.

A Memoir on the Uric Acid. 409

carbonic acid ; while its nitrogen, with the
hydrogen of the uric acid, formed carbonic
acid; and this, uniting with a portion of un-
decomposed nitric acid, composed nitrate of
ammonia.

3. The oxymuriatic acid, according to the
same chemist, also generates ammonia with
uric acid ; and the volatile alkali remains com-
bined with muriatic acid, the muriate of am-
monia being the only substance which he
obtained. — Fourcroy,’ however, asserts that in
addition to this product, he obtained acidu-
Jous oxalate of ammonia, and the muriatic
and malic acids in an uncombined state: and
Brugnatelli observed the formation of oxalic
acid.

SECT.’ V.
Destructive Distillation of the Uric Acid. —

THe distillation of the uric acid per se,
with a view both to the condensible and: per-
manently elastic products, has been performed
by Scheele, by Mr. Higgins, by Dr. Austin,
and by Dr. Pearson, whose statements do not
essentially differ from each other. The re-
sults are carburetted hydrogen and. carbonic
acid gases; prussic acid ; carbonate of am-
monia; and an acid sublimate of peculiar
properties. It is also commonly stated that

3F

410 A Memoir on the Uric Acid.

a portion of the uric acid is volatilized unal-
tered; but this L have never been able to —
observe, and I believe that volatility is not
one of its properties. Using a succession of
receivers, and taking the products at various
periods, I have remarked them to be formed
in the following order, Ist. A very minute
portion of water, not exceeding a drop or
two from 100 grains of the acid, impregnated
with carbonate of ammonia; then concrete
carbonate of ammonia; next prussic acid);
and afterward the peculiar sublimate of
Scheele, in the proportion of about one fourth
the calculus employed. In the retort there
remains about 4 the weight of charcoal.

The nature of this sublimate not having
been sufficiently examined, I investigated its
properties with considerable aitention. Scheele
believed it to resemble the succinic acid; but
Dr. Pearson thought that its qualities are
rather analogous to those of benzoic acid.
The experiments, which I have made, lead
me to infer that. it contains neither of those
acids; but that it is composed’ of ammonia
united with an acid swt generis. Its properties
are the following:

1. It has a yellow colour, a cooling bitter
taste not mixed with that of any acid, but
strongly flavoured with an animal empyreuma.

A Memoir on the Uric Acid. All

2. It readily dissolves in water, even at
common temperatures, and in alcohol. It is
soluble, also, in alkaline solutions, but 1s not
precipitated by acids; thus evincing a marked
difference from the uric acid and its com-
pounds. |

3. It is volatile, and, by repeated sublima-
tions, is greatly improved in freedom from
colour.

4. Its watery solution reddens the infusion
of litmus, but a single drop of solution of
ammonia destroys this property in a consi-
derable quantity of the solution, thus proving
that the acid is only slightly in excess.

5. When the watery solution of the subli-
mate is slowly evaporated, it shoots into
crystals. The shape of these is not well
defined, owing to their mixture with a portion
of resinous matter, resulting from the oxyge-
' nizement of an essential oil, which the sub+
limate always contains. Repeated crystal-
lizations do not. entirely purify the salt,
though they render it much whiter, nor do
they deprive it of its excess of acid.

6. When the crystals are added to solu-
tion of pure potash, they emit a smell of
ammonia.

7. They do not, after being evaporated to

3F 2

A12 A Memoir on the Uric Acid.

dryness in mixture with nitric acid, give a
red stain as the uric acid does when similarly
treated. :

8. The watery solution does not, like the
alkaline urates, decompose neutral salts with
earthy bases.

9. It has no action on salts with base of
copper, iron, gold, platina, tin, or mercury.
It differs, therefore, from succinate of am-
monia, which precipitates solutions of iron
and tin; and from the alkaline urates, which
decompose all metallic salts, except that of
gold. The solution of the sublimate agrees,
however, with succinate of ammonia, in
throwing down, from nitrates of silver and
mercury and from acetite of lead, a white pre-
cipitate, which is soluble by an excess of nitric
or acetic acids.

10. It differs from benzoate of ammonia,
in not being precipitated by muriatic acid,
which instantly separates benzoic acid from
the latter salt. The precipitates, also, from
metallic solutions by benzoate of ammonia,
are not re-dissolved by nitric or acetic acid.

These properties sufficiently shew that the
acid ingredient of the sublimate is not either
the succinic or benzoic, but one distinguished
by a peculiar set of properties.

A Memoir on the Uric Acid. AIS

Dr. Austin has proved that the sublimate
itself may he decomposed by the action of
heat, and may be resolved into ammonia,
azotic gas, and prussic acid. Her has ascer-
tained, also, that when heated with nitric
acid it affords carbonic acid and_ nitrogen
gases. As to the nature of its components,
it agrees in general with the uric acid, from
the disunion of whose elements, and their
re-combination in a new manner, it undoubt-
edly results. Both substances contain oxy-
gen, hydrogen, carbon, and nitrogen, but in
different proportions, which I am not at pre-
sent able to assign. It is only, indeed, of
late, that the improved instruments and me-
thods of analysis, invented by Gay Lussac
and Thenard,* have enabled us to determine
minutely the composition of animal and vege-
table substances ; and I have not yet been
able to furnish myself with the apparatus,
which is necessary to the successful prose-
eution of this branch of the enquiry.

* Recherches Physico-Chimiques, Tom. ii.

( 414 )

A DEMONSTRATION

oF
LAWSON’S

GEOMETRICAL THEOREMS: ©
BY THE LATE REV. CHARLES WILDBORE;
Communicated by Mr. Dlabbott to Mr. Ewart, and by him to the Society.
(Presented January 10, 1812.)
rww ~

To Peter Ewart, Esq.

Dear Sir,

J REQUEST you to present the inclosed
manuscript to the Literary and Philosophical
Society. It contains solutions, by that very
able mathematician, the late Rev. Charles
Wildbore, to all the sixty theorems in the
well known pamphlet entitled, “ A Disserta-
tion on the Geometrical ‘Analysis of the An-
cients, with a collection of theorems and
problems, without solutions, for the exercise
of young students; 1774.” These theorems
have all been elegantly demonstrated before,
in Leyburn’s Mathematical Repository. But
I esteem the following train of solutions to be
a very curious specimen of investigation, and
a proper exemplification of the method, which
the ingenious author of the theorems recom-

Lawson's Geometrical Theorems. 415

mends, of inventing and deriving one geome-
trical property from another, to an almost
endless variety. I have sent you herewith a
copy of the Pamphlet containing the theorems,
as it may be thought necessary they should
accompany the solutions. It is well under-
stood that the author of the “ Dissertation”
was the late Rev. John Lawson, B. D.

I remain your’s truly,

J. MABBOTT.

Manchester, Jan. 8, 1812,

Sse SE

Mr. Wildbore’s Demonstration of Lawson's
Theorems, &c,

The author at page 18, of his Pamphlet on -
the Analysis of the Antients, very justly ob-
serves, that in the resolution of problems there
is often need of a previous preparation, a kind
of mental contrivance and construction, in
order to form a connexion between the data
and guesita. And I would not have it con-
cealed that herein consists the great difficulty
of this branch of science. Nor do I know
any advice so proper to give’ the admirers of
these rational amusements, as to endeavour
to attain a facility of investigating or invent-

416.» A Demonstration of

ing one: geometrical property from another.
Itis for: their assistance herein, and not from
any supposed.excellence of the solutions above
(though most of them are different from
those of the original authors themselves, ) that
I have taken the trouble to run through, and
investigate the 60 Theorems. I believe 1
may safely say that any person that will take
the trouble to follow me herein, will find it
worth his while, and may in a short time,
from hence find out many times this number
of theorems of like nature, and equally cu-
rious with these. And as this may possibly
fall into the hands of some more learned readers,
I would wish them to think, whether or no
this may not possibly be a specimen of a me-
thod of investigation similar to that of the
Ancients, which has been a desideratum ever
since the Saracens burnt the library at Alex-_
andria in Egypt.

Diacram 1.—(Plate IX.)

Draw ED the perpendicular of the isosceles
triangle BEC, and:AH through the vertex,
parallel to the base; from any ‘point A in
which, draw lines through the extremes of the
base and perpendicular, viz. AC, AB, AD ;
and through D, the extreme of the perpen-
dicular, a line ad libitum, cutting AB in F,

1

Lawson's Geometrical Theorems. 417

AC inG, AH in H;; and bisect DH in
n. Then because the triangles DGC, AGH
are similar, DC : AH: : DG: GH; and
because BFD, AFH are similar, BD = DC
:AH:: FD: FH. Therefore by equality
of ratio DG: GH: : FD: FH. Which is 3
the third Proposition.

Join EF, EG cutting BC in k and 1],
through G draw Gi |jto EH cutting ED in
o and EF in i; then by reason of the pa-
rallel lines, AH : EH :: BD: Dk:: DC:
Dl, and because BD = DC, .. Dk = DI;
consequently ED bisects the 2 FEG, and
EF: EG:: FD: DG. Which is the fifth 5
Proposition. .

Let fall Fm perp. to ED produced ; then

LAWSON’S

GEOMETRICAL THEOREMS.

ad

PROP. I.

r a right line AB be bisected in E, and two points C and
D taken therein such that AC : CB :: AD: DB; then
I say the rectangle DC E = the rectangle ACB.

The converse of this proposition is also true, which is
this.

If a right line A B be bisected in E, and two points C
and D taken therein such that DCE = ACB; then I say

AC: CB:: AD: DB.

Pror. IL, If in AB the diameter of a circle two aes

3G

418 A Demonstration of

because FD : DG: : FH: GH, therefore
Dm’: Do : : Em: Eo, and FE: EG::
FD:DG::FE: Ei. Therefore if in any
line Emo, be taken two points D E such,
that Dm : Do: : Em: Eo, and m F,oG be
drawn perp. to Em, and through the point
D, be drawn any line to meet mF, oG in F
and G,and EF, EG be joined; then FE :

6 EG::FD : DG, and FE: EG:: FE:
Ei. Which is the sixth Proposition.

Since Gi is bisected by the perp. Do, .-.
Di= DG;; and because » DEH is right, .°.
En is equal to nH, and parallel to iD ; be-
cause iG is parallel to KH, therefore the
lines FG, FH. are similarly divided in the

—--

Cand D be assumed such that AC: CB:: AD: DB, and
from D an indefinite perpendicular to the same diameter as
L Dbe erected, and through C any line be drawn to cut
the same in E, andthe circle in F and G; I say FC:
CG:: FE: EG.

The converse of this proposition is also true, which is. .
this.

If any right line as L D be drawn perpendicular to the
diameter A B of any circle and meets the same in D, and
if from a point in the same diameter, as C, any line be
drawn to meet the same perpendicular in E, and the circle
in F andG, so that FC: CG: : FE: EG; Isay that AC:
CB:: AD; DB.

Prop. III, Let there be a triangle A BC, whose base
BC is bisected in D, and through the vertex Aa line A E

Lawson's Geometrical Theorems. 419

points D and n, or Fn: FH: : FD: FG. 1
Which is the first Proposition.

On the centre n, describe the semi-circle
DEH, join FE, cutting the circle again
in h, erect Gg perp. to FH, cutting FE
in g, and the circle in T ; then since
FG : FD: : FH: Fn, therefore by divi-
sion, FG: FD: :GH: Dn = Hh, and
FG :GH:: DG: Gn, or DG.GH =
FG . Gn, but DG .GH = TG’, therefore
FG . Gn = TG’; consequently the points
F, T, n are in a semi-circle, and FT a tan-
gent tothe circle DEH. Which is the 15
Jifteenth Proposition.

Produce EG, hG till they cut the circle

drawn parallel to BC, and any line drawn through D to
meet A B, AC, AE in F, G, H; thenIsay GD: DF::
GH: HF,

Prop. IV. If in AB the diameter of a circle two points
C and D be taken such that AC: CB: : AD: DB, and
through the point D any line be drawn to meet the circle
in E and F, and CE, CF be joined; then I say EC : CF
:: ED: DF.

Pror. V. If the base BC of a triangle be bisected in D,
and through the vertex A a parallel thereto be drawn, and
from D a perpendicular to BC be drawn to meet the pa-
rallel in E, and through D any line be drawn to meet AB,
AC in F and G, and EF, EG be joined; then I say EF :
EG: : FD: DG.

Psor. VI. If in the line AB be taken two points C and

3G2

420 A Demonstration of

again in h’, EH’, and TG to T’; join FT’,
which must be equal to FT, and join EE,
cutting FH in f; then because the angle
hEh’ = hE‘h’, and EhE’ = El’£,, therefore
WwhE’ = EE‘, hE’ = bE, bh’ ’ = hE; also
because hGE = hGH’, ... Gh = Gh’, GE
= GE’; but GT — GT’, therefore KE’, as
also hh’, is parallel to T'T’; and because
FhE is a right line, .-. Fh’E’is aright line
and the triangles TGH, T’GEH’ equal and
similar, and therefore gEG, g’H’G are so;
consequently the angle EGg = H’Gg’ =
hGg, and gE : hg: : EG: Gh= Gh’::
Ef : hq: : EE’: hh’:: FE: FH. Hence
if in DH the diameter of a circle, two

Dsuch that AC: CB: : AD: DB, and AE, BF be drawn
perpendicular to AB, and through the point C be drawn
any line to meet AE, BF in G and H, and DG, DH be
joined; then I say that DG: DH: : GC: CH.

Prop. VII. Hin the diameter of a circle AB be taken
any point C, and CDE be drawn meeting the circle in D
and E, and DF be perpendicular to AB meeting it in F, and
the circle again in G, and EG be joined meeting AB in H;
I say that AC: CB: : AH: HB.

Also, as the converse, that if in the diameter AB two
points be taken as C and H such that AC: CB :: AH: HB,
and from the points C and H two lines CE, HE be inflected
to any point of the circumference E meeting the same
again in D and G; when DG is drawn, it will be perpen-
dicular to AB.

Lawson's Geometrical Theorems. 42\

points F and G be assumed, such that
FD: FH:: DG: GH, and from Gan
indefinite perp. be erected, and through
F any line be drawn to cut the same in g,
and the circle in h and HE, then Fh: FE: :
hg: gE. Which is the second Proposition. 2
Also EF: Fh’:: EG : Gy = Gh. Which
is the fourth Proposition. A
Also if in the diameter of a circle, any
point F be taken, and FhE be drawn
meeting the circle in h and E, and hq be
perpendicular to DH meeting it in q, and
the circle again in h’ and Eh’ be joined |
meeting DH inG;then FD: FH:: D@ 7
:GH. Which is the seventh Proposition.

Prop. VIII. If in the diameter of a circle AB two
points C and H be taken such that AC: CB: : AH: HB,
and from the points C and H be inflected to any point of
the circumference E two lines CE, HE meeting the same
again in D and G; I say that EC:CD:: EH: HG,

Prop. IX. If in AB the diameter of a circle be taken
any point C, and CD be drawn meeting the circumference
in D and E, and from the point D be drawn DF perpen-
dicular to CD, which meets the diameter AB in F and the
circumference in G, then I say that DC: CE: ; DF : FG.

Prop. X. If in AB the diameter of acircle two points
Cand D be taken such that AC: CB:: AD: DB, and
through the centre E a perpendicular to AB be drawn, and
from C a line be drawn to meet the same in F, and if
through D any line DG be drawn to meet the circle in G

422 A Demonstration of

Again, if in the diameter of a circle
DH, two points F, G be taken such that
FD:FH:: DG : GH, and from the
points F and G, be inflected to any point
of the circumference E, two lines FE,
GE meeting the same again in h and bh’.

8 Then Fh: FE:: Gh’: EG. Which is
the eighth Proposition.

Perpendicular to FE, draw Ee, cutting
the diameter in c, and the circlein e ; then
the angle EcF = FEf = FgG, and heE
= h’H’E = FE; .-. h’ e is parallel to FH,

9 and Fh = Fh’: FE : : Gh’: EG: :ce
Ec. Which is the ninth Proposition.

and H, and from the point G be drawn GK the same side
of DG as F is of the diameter AB to make the angle DGK
equal to the angle CFE, and let the line GK meet the cirche
in L and the line CF in M; then I say that GM : ML::
GD: DH.

Prop. XI. If from any point C in the diameter of a
circle produced a perpendicular be raised and from any
point D in the same a line be drawn to cut the circle in E
and F; then I say the rectangle EDF is equal to the rect-
angle ACB together with the square of CD.

Prov. XII. If from any point C in the diameter of a
circle produced a perpendicular be raised and thereon CD
be taken whose square is equal the rectangle ACB, and CE
be put equal CD, and from any point in DE as H a line
be drawn to cut the cirele in Fand G; then I say twice the

Lawson’s Geometrical Theorems 423

Diacram II.

Perpendicular to n the center, or any
other point of the Diameter DH, erect
ng, and make the » gf'n — FEG; then
Fon = GEe ; produce F¢ till it meets He
in m; then ¢F'n = heh’ — hnF'; therefore
Fm is parallel to he, and lG: GE:: Fh:
FE ::em: Em. Which is Proposition 10
tenth, part 1st.

Also if through the point h, any line
hL be drawn to the circle, and at G the
zg¢GM be made equal to LhE, the points
M, G, g, hare ina circle, therefore the

rectangle FHG is equal to the sum of the squares of HD
and HE.

Prop. XIII. If in AB the diameter of a circle two
points C and D be so taken that, C being without, and D
either within or without the circle, the square of CD be
equal to the rectangle ACB, and from C a perpendicular
to AB erected, and any line drawn through D to cut the
same in G and the circle in E and F ; then I say the square
of GD will be equal to the rectangle EGF.

The converse is also true, which is this.

If GC he perpendicular to AB the diameter of a circle
and meets it without the circle in C, and if from Ga line
be drawn to cut the circle in E and F, and the diameter
either within or without in D, and the square of GD be

424 A Demonstration of

angle hMg = the supplement of hGg, and
consequently of hE’E ; therefore hLE =
hMeg, Mg parallel to LE, andhM: ML: :
he :gE::Gh’:EG:: Fh: FE. Which
is Proposition tenth, part 2d. ;
At F erect a perpendicular to FH,
produce Hh till it meets it in 3, and join
Dh; then the z DhH being right, F, 3,
h, D are in a circle; therefore Hh . H3 =
FH. DH—FH’?—FD.FH —H3*—H.
th; .*. Hy. 9h — He’— FH’ + FD. FH
1 =Fy 4+ FD .FH. Which is the eleventh
Proposition.
If Fd’ = Fa = Fq = FT, then 32= Fq
+ F3, ad’ = Fq — Fa, 3a* + ad — 2Fq*

equal to the rectangle EGF; then I say the square of CD
will be equal to the rectangle ACB.

Prop. XIV. Things remaining as inthe last proposition,
if the perpendiculars Eg an@ FH be.demitted ; then I say
that the rectangle gCH is equal to the square of CD.

Prop. XV. If from C any point in the diameter of a
circle AB produced a tangent be drawn, and from the
point of contact Da perpendicular to the diameter DE be
demitted; then I say that AC :CB:: AE: EB.

Or conversely thus :

If in AB the diameter of a circle be taken two points C
and E such that AC: CB:: AE: EB, and from Ea per-—
pendicular ED raised, and CD ate then I say CD
touches the circle in D.

Or thus:

Lawson's Geometrical Theorems. 425

+ 2F3? = 2q? = 2FD. FH + 2F3* =
2H3.sh. Hence if from any point F in
the diam. of a circle produced, a perpen-
dicular be raised, and thereon F’d be taken
whose square is equal to the rectangle
DFH, and Fa be put equal to F’d and
from any point in ’d.a as 3a line be drawn

to cut the circle in any two points as:h
and Hi, then twice the rectangle h3H is
equal to the sum of the squares of sd 12
and ja. «Which is the twelfth Proposition.

If 3s be drawn through q cutting the
circle in r and s, themthe rectangle =:res

= hoyH = (by the last) *q*. Which is the 13
thirteenth Proposition. |

If in AB the diameter of a circle produced. a point C be
taken, and therefrom a tangent as CD be drawn, and in the
diameter a point E be taken such that AC: CB: : AE :
EB ; then I say ED being drawn will be perpendicular to
‘the diameter AB.

Prop. XVI. Let AB be any chord in a circle and CD
another cutting the former in E, CB being jomed, from D
draw DF parallel to CB to meet AB in F; I say that the
rectangle AEF is equal to the square of DE.

Prop. XVII. It ABC be a iriangle inscribed in a circle
whose sides CA and CB are equal, and the rectangle CBD
Equal to the square of AB, and let AE be any line cutting
CB in Fand the circle again in E, and from E let a parallel
to AB be drawi to meet CB in G; then I say that the
rectangle OFG : BF?-::. CG: BD. ’

3H

A426. A Demonstration of

Let fall the perpendicular sw, rv, then
Fv: Fq:: ar: 3q:: (by the last) oq : as
::Fq: Fw; therefore the rectangle vVFw
14 =Fq’*. Which is the fourteenth Propo-
sition. .
Through the points H and T describe
a circle cutting HF, TF produced in x
and y, then the angle DIF = DHT =
xyF'; consequently xy is parallel to DT.
If therefore xH be any chord in» a circle,
and yT another, cutting the former in F,
xy being joined, from T draw TD pa-
rallel to xy to meet xH in D, then the
16 rectangle HFD = FT’. Which is the
sixteenth Proposition. .

Prop. XVIII. Let ABC be a triangle inscribed in a
circle, whose sides AB and AC are equal, and from A any
line be drawn meeting the circle again in D and BC in E;
I say that the rectangle DAE is equal to the square of AB.

Prop. XIX. Things remaining as in the last propo-
sition, if lines touching the circle in A and C be drawn to
meet in F, and FD be drawn cutting BC in G; I say that
the rectangle BCG is equal to the square of CE,

Prop. XX. Let ABC be a triangle inscribed in a circle
whose sides AB and AC are equal, and let AD be parallel
to BC, and taking any point therein D, let the rectangle
under AD and P be equal to the square of ABor AC, and
from the points A and D let the lines AE, DE be inflected
to any point E in the circle, meeting BC in F and G; I
say the rectangle under FG and P = the rectangle BFC. .

Lawson's Geometrical Theorems 427

Join TH, T’H and from T’ set off T’7B
so that T'l’* = the rectangle H'T’B, and
let TE be any line cutting T’H in A, and
the circle again EK’ and from HE’ let a pa-
rallel to T'T’ be drawn to meet T’H in »,
then (by the ast) AE’* = Ay. AH and
the As AvE’, AHE’ and consequently
AT’T similar, as also K’H, THE’, there-
fore as AK’? — Ay. AH: AT’ : : E’'H?
: TT’; butyH : KH::E’H: TH, .:. F'H?
=—7H.TH: TT? = T'B.TH:: 7H:
T’B; consequently HA. Ay: AT’? : : YH: 17
TB. Which is the seventeenth Proposition.

Let Hh cut TT’ ini, then GH: TH: :
TH : DH and GH : iH::hH: DH;

Prop. XXI. If in AB the diameter of a circle be taken
two points C and D such that AC:CB:: AD: DB, and
D be within the circle, and DE be perpendicular to AB
meeting the circle in E and F, and if through C any line
be drawn meeting the circle in G and H, andthe line DE
in K, and GL touch the circle in G, and meet DE in L;
then I say the rectangle LDK is equal to the “na
of DE.

Prop. XXII. If in AB the diameter of a circle be
taken two points C and Dsuch that AC: CB:: AD: DB,
and D be without the circle, and DE be perpendicular to
AB, and through C be drawn any line meeting the circle
in G and H, and the line DE in K, and GL touch the
circle in G, and meet DE in L; then I say the rectangle
LDK is equal to the rectangle ADB,

oH 2

428 A Demonstration of

18 therefore TH? =iH .bH. Whieh is the
eighteenth Proposition.

_ Or describing the semi-circle that passes
through F, T, », cutting FE int, we have
Fo: FT:: FT: oe and FG : Fg : : Ft ;,
Fo; «. FT? = - Ft. — ¥ Pro-
position 18.

Join d t cutting TT’ in z, aT souidbinig
the circle in T being first drawn, then Fd
= dT the angle dFT = FTT’, the trian-
gles FdT, TFT’ equiangular, and Fd:
FT: : FT : TT’; therefore Fd . TT’ =FG
-Fn— Fe. Feand Fd: Ft :: Fg: TT
:: ag: gt, zg. TT’ = Fg. gt = (because
T,t, T’, Fare ma circle) Tg.gT’= Tg.

Prov. XXIII. If AB be the diameter of a circle and
CD perpendicular thereto meeting it in C, and from the
points A and B be inflected AE, BE to any point E in
the circumference, meeting CD in F and G; I say the
rectangle GCF is equal to the rectangle ACB.

Prop. XXIV. In AB the diameter of a circle let two
points C and D be taken such that AC; CB: : AD: DB,
and the point D be within the circle, and DE be perpendi-
cular to AB, meeting the circumference in E and F, and
Jet through C any line be drawn meeting the same inG
and H, and from the points G and H let GN, HN be in-
flected to any point in the same N, andlet them meet DE
in M and L; [I say the rectangle LDM is equal to the
square of DE. :

Prop. XXV. Let AB he the diameter of a circle and

Eawson’s Geometrical Theorems. 429

(TT’ — Tg), consequently zg ..'TT’ +
Tg? =Tg.TT’ and Tg? = TT. Tz. 19
Which is the nineteenth Proposition.

If the line Fo be taken of any length,
so that the rectangle under Fo and a givem
line P may be equal to F’T* and ot cut
TT in Zz, then FE? = FO. P = (by the
18th) Fg . Ft, hence Fo: Ft: : Fg: P::
wg: gt; therefore P . vg = Fg. gt =
Teg. gT’. Whichis the twentieth Pro- 20
position.

Let E® perpendicular to nE meet GT
produced in x, then because the 2s 4En,
xGn are right, 4, E,n, Gare in a circle
whose diameter is an, therefore the angle

CD perpendicolar to the same meeting the circumference
in Cand D, «and let E be the centre, and from C and D
let CF, DF be inflected to any point F in the circumfer-
ence meeting the diameter AB in G and H; I say the
rectangle GEH is equal to the square of the radius AE.
_ Prop. XXVI. In ABthe diameter of a circle let two
points C and D be taken such that AC: CB: : AD: DB,
and let D be without the circle, and DE perpendicular to
BD, through the point C let any line be drawn meeting
the circumference in F and G, and from the points F and
G let FH and GH be inflected to any point H in the cir-
cumference. meeting DE in K and L; J say the rectangle
KDL is equal to the rectangle ADB.

Prop. XXVII. In AB the diameter of a circle let be
taken the point C, and CD be perpendicular to AB, meet-

430 A Demonstration of

mE — ,GE= GEE’ = GHE= thE,
therefore 2n bisects the angle hnE, and be-
cause nh = nH, therefore ht = tH is per-
pendicular to na, therefore the same circle
passes through h, and ha = Ea is perpendi-
cularto hn, and Ge .e*=hg .gH =Teg.

gTY, add Gg* and Gg . GAa=Tg. gT’

21 + Gg? = TG*. Which is Proposition
21st. both cases.

Dracram III.

Through h’ draw EK cutting the per-
pendicular through F in K, and produce
FE’ till it cuts it in 1, then the triangles

ing the circumference in Dand N, in CD let be taken
two points E and F on the same side of C with D such
that the rectangle ECF may be equal to the square of CD,
and from the points E and F let EG, FG be inflected to
any point Gin the circumference, meeting the same in H
and K, and let HK when drawn meet the diameter AB. in
L; then I say that AL: LB: : AC : CB.

Prove. XXVIII. In AB the diameter of a circle pro-
duced let be taken the point C, and CD be perpendicular

to AB, and therein be taken two points E and F on differ- -

ent sides of C such that the rectangle ECF, may be equal
to the rectangle ACB, and from the points E and F let
EG, FG be inflected to any point G in the circle, meeting
the samie in H and K, and Jet HK when drawn meet

———_

Lawson's Geometrical Theorems.. 431

Eh’, F’K, Gh’e’ are similar as also Ghg, .
and the points G, h, 4, E are in a circle,
the triangle ,agE, and consequently LIE is
similar to hgG, and consequently to Fh’K,
therefore FK : Fh’: : FE : Fl and FK .
Fl= Fh .FE=FD.FH. Which is the
twenty-second Proposition.

Produce hD to y, then by similar trian-
gles FD: Fy: : Fo : FH. Which is the 23
twenty-third Proposition. .

| From hand E to any point N in the
_circle, let lines be inflected cutting G in
k and L, then because the angle ENh =
EE‘ = LGh the points h, L, N, G are
ina circle, consequently Lk .kG@ =kh .

22

the diameter AB in L; then I say that AL: LB:: |
AC : CB.

Prop. XXIX. Let AB touch a circle in B, and any
line AE be drawn equal to AB, and likewise from A let
any line be drawn to cut the circle in C and D, and let
EC, ED be drawn meeting the circle again in F and G;
then FG being drawn will be parallel to AE.

Prop. XXX. Let AB touch a circle in B, and
therein be taken two points E and F on the same side of
A such that the rectangle EAF may be equal to the square
of AB, and from A let any line be drawn meeting the
circle in C and D, and EC, FD be drawn meeting the
circle again in G and H; then GH being drawn will be
parallel to AB,

Prop. XXXI. Let AB touch a circle ia B, and any

/

432 A Demonstration of

kN = Tk. kT’ = TG* ~Gk?; therefore

24 TG? = Gk> + Lk . Gk = LG . Gk.
Which is the twenty-fourth Proposition.
Since (by the first) Fn: FH:: FD:
FG::Fn:Ho::FD: DG:: Fn—FD:
25 Hn —DG or Fn: Hn: : Hn: Gn. Which
is the twenty-fifth Proposition. .
Produce ET, ET’ till they cut the per-
pendicular in A and fF; then the 2 TFA =
FFT’ and the angle ATF made with the
tangent is equal to the angle T'T’E in the
segment — AFE, therefore the triangles
a TE, FFT’ are similar, therefore FT:
FY’ = FT :: FT: F4, and ¥72 . FA

line AE be drawn and therein be taken two points Eand F
on the same side of A such that the rectangle EAF
may be equal to the square of AB, and from A any line be
drawn to meet the circle in C and D, and EC, FD be
drawn meeting the circle again in G and H; GH being
drawn will be parallel to AE,

Prov. XXXII, Through any point A within a circle
jJeta line be drawn meeting it in Band E, and therein two
points F and G be taken such on different sides of A that
the rectangle FAG may be equal to the rectangle BAE,
and through A any line be drawn meeting the circle in
C and D, and FC, GD being drawn to meet the circle
again in H and K; then HK being drawn will be parallel
to AB. :

Prop, XXXIII. Let AB ‘be a line without a circle,

1

Lawson's Geometrical Theorems. 433

= FD.FH. Which is the twenty-sixth 26
Proposition.

The 28th is the converse of this, viz. if
FY .Fa = FD. FH then DG: GH:: 27
FD: FH. And the 27th of the 24th. 28

If Fa — FT and aH, ah be drawn cut-
ting the circle in p and o, then since Fh :
Fa: : Fa: FE, the triangles Fha, FaH
are equiangular, therefore the zFha =
Fak, also ao: ap :: aE : ah; therefore
the ‘triangles aop, ahE are equiangular,

Z apo= ahE; .-. opE = Fha= Fak; .«.
op is parallel toaF. Which is Proposi- 29
tion 29th.

The 30th is very evident from the 30
printed figure, for since AE . AF = AB?
= AC . AD, the points C, D, E, F are in
a circle, therefore the external angle ACE
= EFD and = DHG;; .-. EFD being =

and from A and B two lines be drawn to touch the circle
in C and D, and let the square of AB be equal to the sum
of the squares of AC and BD, and from A any line be
drawn to meet the circle in E and F, and BE, BF he drawn
meeting the circle again in G and H; the points A, G, H,
will be in aright line.

Prop. XXXIV. Let AB meet a circle in C and D, and
A be without and B within the same, and let the rectangle
CAD be equal to the square of AB together with the rect-
angle CBD, and through A any line be drawn meeting the

$i

434 A Demonstration of

DHG, GH is parallel to AB. Take FY
= Fl, then F’ . FK = FT? = FD . FH
— Fq . FN, two lines FN’, KN’ being in-
‘flected to any point N’ in the circle cut-
ting it ing and T’, draw Iq cutting the
circle again in T, then the points K q
N’ are in a circle because Fl’, FK = Fq.
. FN’, therefore the angle Fl’q = FN’K
= q TT’. consequently 'T'T’ is parallel to
FK. Hence if ET touch a circle in T,
and any line l’F be drawn, and therein be
taken two points I’ and K on the same side
of F such that the rectangle /FK may be
equal to the square of FT, and from F
any line be drawn to meet the circle in q
and N’, and lq, KN’ be drawn meeting
the circle again in T and T’, TT’ being

31 drawn will be parallel to ’'F. Which 1s
Proposition the 31st.

circle in E and F, and BE, BF be drawn meeting the circle
againin Gand H; then the points A, G, H, are in a right
line.

Prop. XXXV. From the extremes of AB let two lines
AC, BD be drawn to touch a circle in Cand D, and in AB
let a point E be taken onthe same side of A with B such
that the rectangle BAE may be equal to the square of AC,
and also in AB another point F on the same side of B with

‘E suchthat the rectangle EBF may be equal to the square
of BD, and through A any line be drawn meeting the
1

Lawson's Geometrical Theorems. 435

(The 32d is evident from the printed 32
figure, because FA. AG = DA. AC, F,
D, G, C are in acircle ; therefore 2FCA
= DGA = DKH, and KH parallel to
BG.) If R be taken so that RK . Kl — the
square of a tangent to the circle from K,
then R, I’, T’, N’ are ina circle; through
K draw Kq cutting the circle again in s,
then R, Il’, q,s are ina circle, and Z’IqK
= l’Rs, but ’qK — sqT = T'T’s, therefore
YRs = TT's and R, s, TF’ are in a right
line. Hence if from the extremes of FK
two lines be drawn to touch a circle, and
in FK let a point I’ be taken on the same
side of F with K such that the rectangle
KEV may be equal to the square of FT
the tangent from F, and also in FK ano-
ther point R on the same side of K with I,
such that the rectangle KR may be equal

circle in G and H, and BG, BH be drawn meeting the
circle again in K and L; thenthe points L, K, F, are ina
right line.

Prop. XXXVI. If from A the vertex of a triangle
_ ABC be drawn AD to any point D in the base, and DE
be drawn parallel to AC, and DF to AB; I say the sum
of the rectangles BAE, CAF will be equal to the square of
AD together with the rectangle BDC.

Prop, XXXVII. Let A and B be two points in the
diameter of a circle whose centre is C, and let the

312

436 _A Demonstration of :

to the square of a tangent from R to the
circle, and through F any line be drawn
meeting the circle in q and N’, and Kq,
KN be drawn meeting the circle again in
s and 'T’, then the points s, T’, R, are in

35 a right line. Which is the thirty-fifth
Proposition.

Diacram IV.

In the preceding Diagrams it is shewn |
that 3H. 2h which is the square of a tan-
gent from 3 to the circle is = F2> + FD.
FH (Prop. 11.) = F8* + F3. Fy (Prop.
23.) == Ba. ay 3 also yo. yE = yh * yD (be-
cause in the preceding Diagrams, F, 3, h,
D are in a circle) = the square of a tan-
gent from , to the circle; therefore 24 x
(F3 + Fy) = 37? = the sum of their squares.

rectangle ACB be equal to the square of the semidiameter ;
bisect ABin D, and raise the perpendicular DM; from the
point A draw AF to any point F in the circumference,
and FE perpendicular to DM; then I say that the square
of AF is equal to twice the rectangle contained by AC+
and FE, ;
Prop. XXXVIJI. If any regular figure be circum-
scribed about a circle, and from any point within the figure
there be drawn perpendiculars to all the sides of the figure 5
the sum of the perpendiculars will be equal to the mul-

Lawson's Geometrical Theorems. 487

Hence we have a ready way of finding
two such points 3, y in the perpendicular
that 3y7 may = the sum of the squares of
the tangents from these points to the cir-
cle. Let 3, yin Diagram 4, be two such
points, and from y, let a line be drawn
meeting the circle in any two points E’
and H’, then 3H’, aK’ being drawn meeting
the circle againin hand D’, because 3H’.
dh = SF’ . 3 = 9D’. 3E’; therefore F, h, H’, y
are in a circle, as also F', D’, E’, v; therefore
the 2 FyH = 2D’F = 3dbP, therefore 3, h,
D’, F are in a circle, and 73D’“h = 3Fh =
3H’y, also FD’y = F2h; consequently the
three angles 2D’h, 3D’F’, yDF at the point
D’ being respectively equal to. 3Fh, shF,
Fh, those of the triangle Feb, their sum
must be equal to two right angles, and

tiple of the semidiameter of the circle by the number of the
sides of the figure,

Prop. XXXIX. Let there be any number of right
lines intersecting in a point, and making all the angles about
the point equal, and let any circle pass through the same
point; Isay the circumference thereof will be divided by
the intersecting lines into as many equal parts as there are
lines.

Prop. XL. If there be two triangles ABC, DEF,
~ which have one angle A in one equal to one angle D in the

438 A Demonstration of

33 consequently y, D’, h are in a right line.
Which is the thirty-third Proposition.
Also because °D’h—?Fh=,D’W’ — »FH
therefore Fh, FE’ make equal angles with
dy and EE’ is perpendicular to the diameter
DH, and parallel to TT’; draw FD’ cut-
ting T'T’ in G’, and the circle in N, then
FD’. FN = FT? = FG? + GT? =FG*
4 GG’ +TG@. GT =FG" +DG’.
GN. Therefore T'T’ is the locus of all
points G’ dividing lines intercepted be-
tween F and the periphery so that FD’.
FN — GF’ + DG’. GN. From E and
h through G’ draw lines meeting the circle
again in S and R, and describe as in the
2d Diagram, the circle FTnT’ cutting
FN inl. Then because FG’. G1=TG’.
G'T’, and this = SG’. G’E = hG@’ . GR,
therefore the points F, 1,8, E are in a

other, and another angle B in the first equal to the sum of
the angles D and E in the second; then shall the sides AC’
BC, DE, EF be proportional.

Prop. XLI. The square of the line bisecting the ver-
tical angle of any triangle is a mean proportional between
the differences of the squares of each side including that
angle, and the square of the adjacent segment of the base
made thereby.

Prop. XLII. If from the same point two tangents be
drawn to a circle, and a line be drawn joining the points

Lawson's Geometrical Theorems. 489

circle, and the angles FIE — FSE. Also
DG .GN + FG? ~ (TG. GT’) G1.
F@’ +. FG =F@’. FlI= FD’. FN =Fh
. FE, therefore h, G’, 1, E are in a circle,
consequently the angle HhR = ESR, and
the sum of the angles EhR. FIE is equal
to two right ones, therefore the sum of
their equals ESR, ESF must be equal to
two right, and F, S, R ina right line.
Which is the thirty-fourth Proposition.

Dracram V.

' To any point g” in TT’ from the center
ndrawn g’n, perpendicular to which thro’
g’ draw ba cutting the two tangents in a
and b ; then the angles at 'T and g’ being
right, the points g’, a, 'T’, n are in a circle,
and the angle nag’ = nT'g’ =nI’g’; again

34

of contact, and another line to be intercepted between the

tangents cut the foregoing which joins the point of contact,

so as to be bisected in the point of intersection; then I say

that the part of that line which is a chord of the circle will

also be bisected by the same point.

And, conversely, if the chord cutting the Jine joining

the points of contact be bisected by the point of intersec-

tion; then the continuation of the same to meet the tan-

gents will also be bisected by the same point.

Prop. XLII. If from one of the equal angles of an

440 A Demonstration of

42

the angles at 9’ and T’ being right, the
points g’, 'T’, b, n are ina circle, and the
Znbg’ = n'T’g’, consequently nbg’ = nag’
and ng” bisects both ab and the chord of
the circle. Which is the a ae
Proposition.

Let fall TC david dicdtin to T’n then
by similar triangles TG =iTT’: Tn: :
TC : TT, therefore Tn. T’C— £TT”.

_ Which is the forty-third Proposition.

If any diameter AB be drawn to this
circle, and TA, T’B be drawn intersect-
ing in O, through which drawing OF
intersecting AB in P and producing BT,
AT’ till they intersect in H; then because
BA. is a diameter, the angles at T and
T’ are right, and the points T, O, T’, H
inacircle; .. the 2THT’ = TOB =the
complement of TBO; but because F'T' is

i

isosceles triangle a perpendicular be drawn to the opposite
side; then Isay that the rectangle contained under that
side and it’s segment intercepted by the perpendicular and
the base is equal to half the square of the base.

Prop. XLIV. If ina line AB two points C and D be
taken; then I say that

AB-+ AD x BC + BC* = 2ABC + BCD.
And moreover that ACV. DEES

.

AB+AD X CD-+- CD* = 2ADC + BCD.

—-

Oe fan ee Pl

Lawson's Geometrical Theorems. 441

a tangent, the TBO in the segment is

= FTG, consequently THT’ = TFG =
TFG, therefore F'T’ being = FT, and
the angle TF'I’ double THT’ F must be
the centre of the circle TOT’H, conse-
quently the diameter HO passes through
F. Also since the 2OHT’ = OTT’ =
OBA = the complement of PAH, the
ZHPA isright. Which is the forty-ninth 49
Proposition.

Moreover FE’? : FT? = FE.Fh’: : FE’:
Fl: : (by Prop. 15.) E’g’ : g’h’, therefore
FE”? : FT” :: H’g’: g’h’. Which is the 56
JSifty-sixth Proposition.

Diacram VI.

Having described a circle about the
triangle BAC, and produced AD till it
cuts in G, draw DF’, ED parallel to AB,

Prop. XLV. If from the vertical angle of any triangle
two lines be drawn to make equal angles with the sides
containing it, and to cut the base; then I say that the
square of one side is to the square of the other side asthe
rectangle under the segments of the base contiguous to the
first side is tothe rectangle under the segments contiguous
to the other side.

Prop. XLVI... If in AB the diameter of a semicircle
any point C be taken, and from thence any line as CD

3K

442 A Demonstration of

AC respectively, and then another cir-
ele through G, F, C cutting AG in b,
and jom LF, GC. Then the zAFL =
AGC, ALF = ACG = the supplement
of ABG, therefore ABG = DLF, and
ADF — BAG by construction ; conse-
quently the triangles DLF, ABG are
similar, and AG: BA:: DF ~ AE: DL
and AG: AC: : AF; AL; but DL + AL
— AD, therefore BA. AE + CA. AF
~ AG. (DL+ AL) = AG .AD=GD.

36 AD + AD? = BD. DC + AD*. Which
is Proposition 36.

Dracram VII.

The construction being as in the Propo-
sition, through B draw BF, join FC,
make EH = EF, and join AH; then by
liypothesis AC: FC: : FC: BC, there-

drawn to meet the circumference in D, anda perpendicalar
DE be demitted; then I say that the square of the line
AC is equal to the square of the line CD together with the
rectangle under the sum of the distances of C from A and
C from Band the line AE, when C is taken in the diameter
AC produced; but equal to the square of CD together
with the rectangle under the difference of the distances of
C from A and'C from Band the same line AE, when vain is
taken in the diameter itself.

Lawson's Geometrical Theorems. 443

fore the 7 F BC = AFC, CFB = FAC

= HFA, but the -AHF — BFH — FBC

= AFC, therefore HAF = FCA, and the
triangles HFA, FCA similar, conse-
quently HF = 2EF: AF:; AF : AC, 37
Which is the thirty-seventh Proposition.

Moreover, the two triangles AFC, AFB
have the angle A common, and the angle
AFC = FBC = A + AFB, and taking
FI = BF, the angle AIF=FBC = AFC,
therefore AC: FC: : AF: FI = FB::
(drawing GK parallel to FB) AG : GK. 40
Which is Proposition Av.

As to the two intermediate Propositions
viz. the 38th and 39th; since the double
area of any regular polygon is = the con-
tinual product of the radius of the in-
scribed circle, the number of sides and.
the length of one side; and if it be di-
vided into triangles equinumerous with

Prop. XLVIJI. If ‘from one angle A ofa rectangle
ABCD a line be drawn to cut the two opposite sides BC,
DC, the former in F, and the latter produce in E; then I
say that the rectangle EAF is equal to the sum of the rect
angles EDC, CBF. ;

Prop. XLVI. If a rectangle be inscribed in a right-
angled triangle, so that one of its angles coincide with the
angle of the triangle; then I say that the rectangle under
the segments of the hypothenuse is equal to the sum of

3K 2

AAA A Demonstration of

the sides, the sum of their double Areas,

must be equal to the product of the sum

of their perpendiculars and the side of

the polygon. Therefore the radius x

number of sides = the sum of the perpen-
38 diculars. Which is Proposition 38.

And since equal arches of the same

circle subtend equal angles as well at the '
39 circumference as centre, therefore the

39th. Proposition is manifest.

meee oy FD B,

Because AD + DB = AB, therefore
AD + BC =CD + AB, and AB + AD

+ BC =2AB + CD, consequently (AB

+ AD) .CB + CB* = 2ABC + BCD.
Also AB + CD + AD=2AD + BC,

therefore (AB + AD). CD + CD? =
44 2ADC + BCD. Which is Proposi-
tion 44.

the rectangles under the segments of the sides about the
right angle made by this inscription.

Pror. XLIX. If from the same point C two tangents
be drawn to a semicircle whose diameter is AB, and if the
extremes of the diameter and the points of contact be
joined, either cross-ways by two lines intersecting in F, or
other-ways by two lines intersecting in H; then I say that
CF or HC produced to meet the diamater AB will be per-
pendicular to the-same.

Lawson’s Geometrical Theorems. 445

Againif AB: AD:: AD: DB, mul-
tiplying by AB, AB* : AB .AD:: AB.
AD : AB’. DB. Which is Proposi- 51
tion 51.

Also AB? : AD? :: AB.: DB, and by
composition AB* + AD*: AD* = AB.
DB:: AB + DB: DB, and multiplying
the consequents AB. DB and DB by AD,
and dividing them by DB, we have AB*
4+ AD: AB. AD:: AB + DB: AD. 52
Which is Proposition 52. For it is evident
that this holds whether AB be equal to
AD + DB or not.

Diacram VIII.

The rectangle under the difference of
two lines or quantities, and the difference
of two other lines or quantities is easily
shewn to be — the sum of the rectangles

Ee nnn aaa

Prop. L. If in a semicircle whose diameter is AB the
chord of 60°. equal to the radius be inscribed and from the
center E a perpendicular drawn thereto and produced to
meet the circumference in F; then I say that AF, EF, BF
are continual proportionals.

Prov. LL If a line be cut in extreme and mean pro-
portion; then I say that the square of the whole, the rect-
angle under the whole and the greater segment, and the

446 4 Demonstration of

41

under the two greater and two less, minus

the sum of the rectangles under each of —

the greater and each of the less, There-
fore (AC*—AF* ) x(CB*—FB?) — AC*
. CB’ + AF’. FB*— AC’, FB* —CB?
. AF*. But CF bisects the angle ACB,
consequently CF? = AC. CB —AF. FB,
AC .FB= AF .CB, and AC*. FB* +
CB? . AF = 2AC* . FB* = 2AC . FB.
AF. CB, therefore the quantity above =
AC* . CB* + AF? . FB*— 2AC.CB..
AF. FB= the square of AC. CB—
AF. FB, and consequently = CF* x CF” ;
therefore AC? — AF* : CF’: : CF* : CB
— FB*. Which is Proposition 41.

If upon CF produced be taken E so
that BE = BF, then the angle BEF —
BFE = AFC, and the angles at C being
equal, the two triangles ACF, BCE are

rectangle under the whole and Ashe lesser segments are con-
tinual proportionals.

Prop. Lil. If three lines are continual proportionals :
the sum of the squares of the mean and the greater ex-
treme is to the rectangle contained under the same, as the
sum of the extremes is to the mean,

Prop. LIU. In every right-angled triangle, as the
hypothenuse is to the sum of the sides about the right

eee

——

4

Lawson's Geometrical Theorems. AA47

similar, consequently EB =FB:CE:: 5

AF: CF. Whiehis Proposition 58.:
Having taken CFL = CBF, it will be
CB: CF: : CF: CL, andthe angle
CLF being = CFB, ALF must be =
AFC, and the triangles ALF, AFC

similar ; therefore AC: AF ::AF : AL. 59°

Which is Proposition 59,

If the cireumscribng circle be rion
about the triangle ACB, and HL be
drawn. parallel to AB to eut it m H and
L’, and CH, Cl be joined cutting the
base in M and N, and making equal
angles ACH, BCL with the sides; then
the rectangle AMB = CMH, and CNL’
‘= ANB, but CM: CN : : MH: NU’
therefore CM*: CN*:: CM. MH; CN.

NL’:: AMB: ANB. Which is Propo- 45

sition 45.

[4

angle, sois the said sum, to the sum of the hypothenuse

and twice the perpendicolar from the right angle.

Prov. LIV. If aright line AD be any-ways cut in B,
and from thence a perpendicular BE erected equal to a
mean proportional between the whole AD and the part AB,
aud a circle be drawn through the points A, D, E, and
from A perpendicular be erected to meet the circumference
in F; them Lsay that AF, AB, BE, AD are four continual

proportionals,

448 A Demonstration of

Diracram IX.

Since EC? = DC* — DE’; .-. AC*

= AK*?+ 2AE. EC + EC*= AE’? +

AE .EC + AE .BC+ AE. EB+

EC?— AE. AC + AE. BC+ DE’ +

EC?= DC: + AE.(AC+BC). Also

AC” — AE? + 2AE x EC’ + EC7= AE

.AC’+ AE. EB — AE. CB EC?

AE x (AC’— C’B) + DE*+ EC* =DC*

46 + AE x (AC’— C’B). Which is Propo-
sition the 46th.

DraGrRaM X.

Having through the given rectangle
ABCD drawn AE meeting DC produced
in E, and cutting BC in F, let fall BL
perpendicular thereto. Then by similar

Pror. LV. In every right-angled triangle, as the differ-
ence between the hypothenuse and one side is to the differ-
ence between the same side and its adjacent segment, so‘is
the same side to the same segment. :

Pror. LVI. If HC bea tangent toa circle meeting the
diameter DB produced in H, and from the point of contact
Ca perpendicular CK to that diameter be drawn, and like-
wise a line from H cutting the circle in Fand G, and the
perpendicular CK in I, and F be the nearest point to H;

1

Lawson’s Geometrical Theorems. 449

triangles EA: ED:: AB = DC: AL,
and HA: AD = BC :: BF: LF’; conse-
quently the rectangle EDC + rectangle
CBF — EA x (AL + LF) = EA. AP.
Which is Proposition 47.

Draw FK parallel to DE, then FE :
CE :: KF = CD = AB: AL, and FE:
CF: : BF: “oe therefore FE x (AL +
LF) = x AF = ECD + CFB
(DKA). or: is Proposition 48.

Also AF : AB + BF :: AB+ BF:
AL+BL+ BL+ LF ~ AF + 2BL.
Which is Proposition 53.

And AF — BF: BF — LF:: BF:
LF, because AF : BF: : BF : LF. Pro-
position the 5ath.

Diacram XI.

if CB — AE = EB = CE, and CF
= FB, then the angle FCB = FBC, and

47

53

55

NS Fe

then I say that the square of HF is to the square of the

tangent HC as FI to IG.

Prop. LVH. If one side AC of an equilateral triangle
ABC be produced to Eso that CE may be equal to AC, and
from A a perpendicular to AC raised, and from E a line
drawn through the vertex B to meet the perpendicular in
D; then I say that BD-is equal to the radius of the circle

which circumseribes the triangle.
3L

450 _ A Demonstration of

— FAR = AFE, and the triangles CFB,
AEF similar, consequently AF’: AE=
50 CB: : CB: BF. Which is Proposi-
tion 50.
If CG be drawn perpendicular to EB
and EL parallel to CG cutting AC in L;
then because the angle FEB = CAB, AC
is parallel to EF, consequently LE = co
57 — EO = BO. Which is Proposition
the 57th.

Dracram XII.

Erect DC perpendicular to the centre
D of the semi-circle ACB; join AC, CB,
which produce till it meets a parallel FE
to CD in F, that cuts the semi-circle in
H and AC in G; then because AE = GE,
and FE = EB, and AE. EB = HE’
60 = FE. GE, therefore GE : HE: : HE:
FE. Which is Proposition the 60th.

——_—

Prop. LVIII. If BD bisect the vertical angle B of a
triangle ABC and meet the base in D, and if with either
of the other angular points A or C as center and the adja-
cent segment of the base as radius a circle be described to
cut BD again in E; then I say that BE isto BD as that seg-
ment used as a radius is to the other.

Prop. LIX. If BD bisect the vertical angle B of the

Lawson's Geometrical Theorems. ‘451

Upon HE produced as a diameter de-
scribe a semi-circle through H and A
meeting it in K, then EK: AE = GE: :
AE=GE:HE::HE: FE; take ME
‘= EK, and parallel thereto NG = HE,
and OE = NG; then NG: ME: : FE:
GE, and by division NG: MO: : FE:
FG, and MO: FG::NG=HE: FE:-:
GE ~ NO :HE=NG, or MO: NO::
FG: NG, therefore the triangles FGN,
MON are similar, and the angle NMO=
NFE, consequently the points E, M, N,
Fareinacircle. And conversely when
these points are in a circle, and FE :
NG: NG: GH, take EO = NG, and the
triangles NOM, NGF are similar; there-
fore F@ :OM:: NG: NO=GE :: by
hypothesis FE : NG, and NG — OE:
OM :: FE: FG, and by division NG:
ME:: FE: GE, or FE: NG:: GE:
ME, consequently FE : NG: : NG:

triangle ABC, and if on BA or BC from B be put a third
proportional to the other side and the bisecting line; then
Isay the rectangle under that side on which it is put and
its remainder when the third proportional is taken from it
is equal to the square of the adjacent segment of the base
made by the bisecting line. i. e. BCE==CD?, or BAE
"== AB?,
3L2

A52 A Demonstration of

GE::GE:ME, or ME, GE, NG, FE
54 are four continual. proportionals. Which
as the 54th Proposition. ‘

Its converse is here also proved. And
likewise the following, viz. FE being di-
vided by the 60th Proposition, so that
GE : EH:: EH: FE, if EL be. taken
= AE = GE, a circle drawn through the
points A, H, L will cut FE produced in K
so that EK, GE, HE, FE, are four con-
tinual proportionals.

Prop. LX. If an isoseeles triangle be inscribed in a semi-
circle and one of the equal sides produced, and if from any
point Ein a diametera perpendicular thereto be drawn to
cut the side, the circle, and the side produced in the points
G, H and F respectively ; then I say that EG, EHand EF
are continual proportionals.

Llate7.p452,

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bn Mand

REMARKS

ON THE

SUMMER BIRDS OF PASSAGE,

AND ON

MIGRATION IN GENERAL.
BY MR. JOHN GOUGH.
COMMUNICATED BY DR. HOLME.

_ (Read March 20, 1812.)
TW
Sin, Middleshaw, Feb. 21, 1812.

THE following Essay appears to me to
contain some new ideas relating to the natural
history of periodical birds, Should you en-
tertain the same opinion after perusing the
paper, the communication of it to the Lite-
rary and Philosophical Society of Manchester,
will oblige,

Yours, &e.

JOHN GOUGH.
To Dr. Holme.

Peruars no phenomenon in the history of
animated nature has engaged the attention of |
men of observation, in all ages and countries |

454 Remarks on the

‘so generally, as the regular appearance of
those birds which visit the northern climates
in spring, and disappear as regularly at the
approach of winter. » But though many facts
have been collected, relating to the manners
of these singular birds, by the industry of
naturalists, their history still remains involved
- in much obscurity and perplexed with difficul-
ties; many of which in wy opinion arise from
a negligent or an injudicious arrangement of
the facts already ascertained. Philosophers
have been induced by this oversight, to take
partial views of the subject ; and to entertain
very discordant notions respecting the winter
retreat of the birds in question. All parties,
however, are unavimous in concluding, that
the regularity of their visits in spring is inti-
mately connected with the apparent motion
of the sun betwixt the tropics, whose northern
declination is increasing at the time of their
appearance, and consequently the temperature
of the northern hemisphere is also advancing
towards the heat of summer in every latitude.
The Philosophers, who have undertaken to
discuss this curious question in natural history,
agree then, in ascribing the alternate appear-
ance and disappearance of the swallow tribe,
the cuckoo, the wryneck, and a majority of
the British warblers, to the vicissitudes of

Summer Birds of Passage. 455

temperature, which are annually experienced,
wm this country, in common with all other
places at a distance from the equator. But
their unanimity ends here; and, at this point,
they split into two parties, who view the
subject in very different lights. I intend to
state the opinions of each in succession, be-
ginning with those philosophers, who ap-
pear to me to have the less degree of proba-
bility in their favour; or, to speak more pro-
perly, whose notions cannot be defended on
their own principles, when these are carefully
examined. ©

Pliny is the oldest naturalist that I recol-
lect, who maintains, that the swallow tribe,
and many other birds, with whose winter
quarters he was unacquainted, retire to ea-
verns at the end of autumn, where they lie
in a torpid state until the return of spring.
Many moderns have embraced this idea; and
they conclude from a familiar analogy, that
the sun, after making certain advances to-
wards the north, recalls these sleepers from a
lethargic state, to active existence, in the
same manner, that he breaks the winter slum-
bers of the bat, the field-mouse, and the
hedge-hog ; as well as of various reptiles, and
insects inhabiting the temperate, and frigid
zones, ‘This idea is captivating on account

456 Remarks on the

of its simplicity; and I, for one, would not
refuse to adopt it, if the accuracy of the
analogy were but fairly established. But as
this appears to be an impossible task, I shall
proceed immediately to state my objections to
the supposed constitutional connexion of the
birds under consideration, and the animals
with which they are compared.

Those quadrupeds, reptiles, and inseets,
which pass the winter in a state of imsensibi-
lity ; may be recalled to sensation and action
at pleasure, by the application of a gentle
degree of warmth. This constitutional sin-
gularity of these animals, has induced philo-
sophers to conclude unanimously, that the
return of the sun in spring rouses them from
a torpid condition, at a time when the bene-
fits of the season are ready for their enjoy-
ment. 'There is another circumstance, which
gives something more than plausibility to
the supposition when it is properly under-
derstood. For the animals im question take
ap their winter quarters, some of them in
subterranean habitations, a little below the
surface of the soil: others lodge in the cre-
vices of walls or rocks; and a few, such as
frogs, female toads, and water newts, bury
themselves in the mud of shallow ponds.
These retreats are all of them but slightly

1

Summer Birds of Passage. 457

covered by a thin stratum of earth, ora sheet
of water of a moderate depth; in conse-
quence of which, they are warmed in due
season by the rays of the sun, after he has
entered the northern half of the ecliptic.
The preceding assertion, is not a plausible
conjecture built upon probabilities; but a
fact, which has been determined by. experi-
ment; for the Rev. Dr. Hales, in the course
of his experimental enquiries into the process
of vegetation, discovered that a thermometer,
the bulb of which was buried 16 inches below
the earth’s surface, stood at 25° of his scale
in September, at 16° in October, and at 10°
in November during a severe frost; from
which point it ascended again slowly, and
reached 23° in the beginning of April (old
style). Now the latter part of September
and the whole of October is the season in
which the bat, the hedgehog, the shrew, the
toad, and the frog are seen but seldom, and
finally disappear. ‘The same animals all leave
their retreats and are observed abroad again
in the time betwixt the vernal equinox and
the middle of April; which circumstance
makes the preceding theory agree very well
with the variations of temperature, that take
place in the winter habitations of those ani-
3M

458 Remarks on the

mals, which are actually known to pass the
cold season in a torpid condition.

After making the foregoing remarks on
-torpidity, I come to certain facts, which are
far from favouring the supposed analogy of
those animals which are known to be lethar-
gic in winter, and our summer visitors of the
feathered tribe. Birds of this description
are very numerous in this part of the world
at the time of their disappearance ; from
which circumstance it is reasonable to con-
clude, that if they take up their winter abode
near the surface of the earth, they would be
frequently found in the cold season; which
is the case with bats, field-mice, and hedge-
hogs. Though discoveries of this kind are
mentioned by various authors, the uncom-
monness of the circumstance obliges the
advocates of torpidity to dispose of the pe-
riodical birds during winter, in places which
are inaccessible to men, such as the vaults of
profound caverns or the bottoms of deep
lakes. My objections to this opinion, are
derived from certain facts respecting the tem-
perature of places situated at great depths ©
below the surface of the land and water.

Every place on the globe has an invariable
temperature peculiar to itself, which cannot be

Summer Birds of Passage. 459

found at less than 80 feet below the external
soil. Mr. Boyle kept a thermometer for a
year, in a cave which was situate under a
roof of earth 80 feet in thickness; and found,
that the liquor in the instrument remained
stationary all the time. In compliance with
my, request, the late Dr. Withering made a
similar experiment on a well 84 feet deep,
at Edgbaston near Birmingham, the tempe-
rature of which was found to be 49° in every
month of the year 1798. Pits or wells of
a less depth give more or less annual varia-
tion of temperature, according to the distance
to which they penetrate the superficial strata
of the earth, A remarkable singularity,
however, is observable in experiments made
on pits of a moderate depth. I kept a
monthly account of the temperature of a
well, for the Years 1795 and 1798, the
perpendicular depth of which was 20 feet;
and the annual variation of its temperature
fell a little short of 4°. But the following
circumstance deserves to be carefully re-
marked on the present occasion. ‘The tem-
perature of the ground, at the distance of
20 feet from the surface, is at the highest in
October, when a thermometer exposed to the
atmosphere makes the monthly mean coincide
with that of the year: on the contrary, the
3 M2

460 Remarks on the

subterranean temperature does not arrive at a
minimum before the end of March; which is
three months later than the coldest weather
above ground.

The facts just stated throw much light on
the subject of the present essay, by pointing
out the reason which determines animals of
known lethargic habits to form their winter
retreats near the surface of the ground.
This choice exposes them, according to the
experiments of Dr. Hales, to a variable tem-
perature, which ‘sinks slowly at first, and
keeps them benumbed by a sleepy torpor ;
but after the rigours of winter are past, the
hiding places of these slumberers are gradu-
ally warmed by the returning sun, which
reanimates their torpid limbs, and _ recalls
them from their secret dens, at the proper
moment for ther appearance above ground.
Had the hedgeliog, the field-mouse, &ce.
made a contrary choice, and retired to ca-
verns 80 feet deep, all the benefit they could
have derived froth an invariable temperature,
would have consisted, in the certainty) of not
being frozen; for the same. degree of cold -
which disposes them to sleep im autumn,
would evidently perpetuate. their slumbers
in these situations; unless we suppose them te
be roused to action by the calls of hunger;

Summer Birds of Passage. 461

which is a precarious and treacherous cause.
For the sense of want would not fail in many
instances to invite these animals to certain
death in the midst of frost and snow, at an
earlier season than the commencement of
spring, If we suppose our known sleepers,
or any other animals suspected of torpid
habits, to retire to a depth less than 80 feet,
but to a distance from the surface which is
sufficient to conceal them, in damp and dreary
grottos, from human observation; the suppo-
sition will not remove the difficulty. For the
time when our periodical quadrupeds, birds,
and reptiles disappear, coincides with the
maximum of temperature in such places, and
they are seen abroad again when the same
temperature is at the lowest.

Very few arguments will be now required
to demonstrate the impessibility of the ana-
logy which is supposed to connect the pe-
riodical birds of summer, and the sleeping
animals of winter. It is sufficient barely to
iémark; that the former are’ never found
slumbering with the latter, near the sur-
face of the earth; and deep caverns are
proved to be unfit for the reception of
any creature in the torpid season. Con-
sequently the birds in question, desert the

A462 ' Remarks on the

temperate zones at the approach of winter,
to seek a better climate in lower latitudes.

The migration of our summer visitors being
established upon authentic facts, I intend to
proceed in the next place, to give a theory of
their annual motions derived from natural
causes. All the birds constituting the migrat-
ing’ tribe feed upon insects, which disappear
and become torpid, either in a perfect state
or under the form of embryos, soon after the
autumnal equinox. This circumstance re-
fuses the animals under consideration a far-
ther supply of proper aliment in the higher
latitudes. They are therefore compelled by
tke apprehension of starving, to use their
wings and retire southwards into more ge-
nial climates, where the rigours of winter do
not lock up the sources of their natural food.
The manners of the winter birds of passage
favour the last conclusion; for the jack-snipe,
the red-wing, the woodcock, and the fieldfare,
with some other species, quit the frosty re-
gions of the north at the approach of cold
weather, and spend the winter in the more
temperate parts of Europe. But the return
of spring admonishes them when to leave
these countries; and they retire generally be-
fore the end of April, to pass the breeding
season on the confines of the arctic circle.

Summer Birds of Passage. 463

The twite (Fringilla montium) breeds on the -
hills of Yorkshire and Westmoreland, but
does not remain all the year in its summer
habitation. For twites congregate in mul-
titudes about the beginning of October and
disappear; but large flocks of them are
seen at that time, or not long after, in the
south of England. 'Thus are the two retreats
of this migrating finch pretty well ascertained.
But the same cannot be generally affirmed of
those birds which retire from Britain in au-
tumn. ‘The swallow, however, is now known
to winter in different parts of Africa; and, in
all probability, fature observers will discover
the southern retreats of the other migrating
species partly on the same continent, and
partly in the warmer countries of Europe or
in the corresponding districts of Asia. The
last opinion must be received as a conjecture,
but it has the recommendation of being pro-
bable; because those birds which return
hither about the time of the vernal equinox,
may be expected to pick up a livelihood near
home during the preceding months, without
accompanying the swallow to the mouth of the
Seneyal, in the 16th degree of north latitude.
Finally we may conclude, apparently with
safety, that no bird retires in autumn farther
from its summer residence than necessity

464 ‘ Remarks on the

requires; and that its winter abode is fixed
by the article of food, which depends on the
temperature of the place, and the appetite of
the visitor.

After making the foregoing imperfect re-
marks on the southern retreats of the migrat-
ing tribe, I come in course to the cause
which invites these wanderers northward, to
spend the summer in higher latitudes. No
sooner has the sun touched the tropic of Capri-
corn, than he begins to lessen his southern
declination, and to shine more directly upon
the -opposite hemisphere: every latitude of
which experiences his animating influence in
succession, commencing with the parts con-
tiguous to the torrid zone, and proceeding
gradually to the frozen regions within the
arctic circle. The adyances of spring towards
the north, keep pace with the diffusion of
solar heat over the northern half of the globe:
For the same plants flower much earlier im
low than in high latitudes; and we may
safely conclude that the same lethargic ani-
mals, especially the same flies and other in-
sects, will observe the like rule in quitting
their winter quarters ; and will appear abroad
in Italy much sooner than in Britain. The
following comparative facts may serve to elu-
cidate the slow progress of spring from the

1

Summer Birds of Passage. 4G5

south to the north. Iam sorry, that the ob-
servations are chiefly confined to the vege-
table kingdom. The table, however, contains
a remark, which is of importance to the pre-
sent subject. For it traces the nightingale,
afeeble bird of passage, through 22° of north
latitude ; by assigning the times of its appear-
ance on three distant parallels. Now it has
been shewn, that the periodic birds do not
remain torpid through winter, in those coun-
tries which they frequeut in summer; conse-
quently, we may infer with safety, that the
nightingale travels leisurely towards the arctic
circle during the vernal months, after leaving
its winter retreat. which is unknown. In
this long journey, this bird passes from one
degree of latitude to another, as the advances
of spring prepare the successive climates of
the northern hemisphere for its reception, by
warming the ground, and calling the insects
of each country progressively into active
existence,

Remarks on the

466

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OL [ady} PL -qagycc oy “eso1omat suowsuy;

CT ABP Zs Your G ‘q2,J/'FSussiore N-opnasd snssta1VN

eT pady L ‘qoagyccc yp uanadaa wntosne7y

196 6G II} 9G oF F WIP SH oBF “4el} SS oLE “I]

jesdq, {yepusy uoyeIGg ‘suauiy omen

~~ ‘sapnpyyy quaiaffip ur squnjg auivs
ay fo bursonoyf fo oun, ayy fq uaays buudy fo ssatboug YT,

Summer Birds of Passage. 467

This deliberate manner of travelling re-
lieves the theory of migration from one of its
principal difficulties. For this supposition
makes an easy task of along journey to-those
birds of passage which are not remarkable for
agility and power of wing; such as the red-
start, the yellowwren, the nightingale, and
other species. These wandering birds are not
required by the theory, to fly with the greatest
expedition through 40 or 50 degrees of lati-
tude, from their winter quarters to their sum-
mer haunts. On the contrary, one of them
has been proved to move slowly from one
station to another, as the sun advances in his
return towards the tropic of Cancer. The
winter labours of the jack-snipe, which is re-
markable for its inactive habits, confirm the
foregoing supposition. For this bird quits the
northern regions early in autumn; and, in
spite of its natural feebleness and indolence,
makes a shift to travel over the greatest part of
Europe in the cold season. 'The woodcock also,
after leaving the same summer retreats makes
a similar journey, and passes over into Africa.

I shall now proceed to give a few points
in the vernal course of the chimney swal-
low (Hirundo rustica,) which is known to
tvavel in the spring from Senegal, in lati-
tude 16° north, to Drontkeim, in latitude 64°

3N2

468 Remarks on the

north. This bird appears in the neighbour-
hood of Senegal on the 6th of October; and
has been seen as Jate as February in the same
country. It is said to arrive at Athens, in lat.
37° 25’, on the 18th of February; at Rome,
in lat. 41° 45’, on the 22d of the same month;
at Piacenza, in lat. 45°, March 20th, A. D.
1738; at Tzaritzin, in lat. 48°30’, April 4th;
in the late spring of 1793, at Catsfield, Jat.

, April 14th, from a mean of twenty ob-
servations; at Stratton, lat. 52° 45’, April Sth,
from a mean of twenty observations; at Ken-
dal, lat. 54° 20’, April 17th, from a mean of
twenty-three observations ; at Upsal, lat. 59°
30’, May 9th, from one observation.

This route of the swallow towards the arctic
circle, shews that the bird does not rely on its
agility, and loiter in the torrid zone longer
than is necessary. Onthe contrary, it travels
slowly from climate to climate, until the sun
isin 17 or 18 degrees of northern declination,
and spring has made considerable advances in
the ungenial climate of Sweden. One ano-
maly occurs in the vernal progress of the
swallow, which deserves the attention of the
naturalist, because the circumstance when
properly understood, shews how attentive the
bird is to the local causes, which retard the

spring in certain districts. The swallow ap-

Summer Birds of Passage. 469

‘pears upon an average, six days earlier at
Stratton in lat. 52° 45’, than at Catsfield in
lat. 51°. There is little or no doubt that this
apparent exception to the present theory arises
from some circumstances which retard the
increase of the vernal temperature at Catsfield ;
and make the spring advance more quickly at
Stratton. As I am unacquainted with the
situations of both places, it will be proper to
state a few facts, which shew how powerfully
causes of this sort influence the excursions of
migrating birds. Ist. The bank | martin,
(Hirundo riparia) is commonly seen at the
mouth of the river Kent six or seven days
before it arrives at Kendal; though the dis-
tance does not exceed five or six miles. But
the town lies near the mountains; and the
air is colder in that part of the valley than at
the head of the estuary. 2d. I have fre-
quently heard the redstart, the yellow-wren,
and the white-throat singing in the gardens
at Kendal, two or three days prior to their
arrival at Middleshaw. 1 attribute this differ-
ence to the same cause; for Middleshaw lies
200 feet higher than the town, being distant
from it three miles to the south east. Lastly,
the chimney-swallow was seen at Kendal on
the 24th of April, A. D. 1808; but did not

make its appearance at Settle, before the first
9

470 Remarks on the t

of May. The latter town lies south of east
thirty miles from the former, in a moun-
tainous district not far from the source of the
Ribble.

The preceding instances, with other facts
of a similar nature, shew how absolutely the
motions of the birds under consideration, are
regulated inthe vernal months by local causes
affecting local temperature; and the principal
object of the present Essay may be called an
attempt to demonstrate, that the same leading
eause, naturally connected with the article of
food, compels them to traverse the temperate
zone, Wholly or in part, twice in the course
of the year. When the phanomena of mi-
gration are considered in this way, winter
and summer birds of passage become rela-
tive terms belonging to the place of obser-)
vation. For instance, the twite inhabits the
southern parts of Britain during the cold
months, but returns to the hills of Yorkshire
in spring; and if we may judge from the op-
posite climates of the torrid and frigid zones,
the former will have no visitors but in winter,
and the latter none excepting in summer,
The intermediate space on the surface of the
globe is the chief scene of their operations.
It is here that the temperature of the atmo-
sphere undergoes great variations, but never

Summer Birds of Passage. ATL

arrives at extremes; in consequence of which,
every wanderer of the feathered tribe has the
power of selecting a suoimer residence in the
temperate zone which is agreeable to its
feelings and appetite. The different kinds of
these birds can naturally subsist in places
where the spring has made less or greater
advances ; for the redstart precedes the swal-
low, and the swallow precedes the cuckoo.
This is the reason why the different species
travel in distinct parties, resembling the le~-
gions of a numerous army marching in the
same direction; the whole body being in mo-
tion together alternately to the north and
south. I shall close the Essay with a table
exhibiting the order of this procession in
Westmoreland. The first column contains
the names; the second gives the times of
migrating northwards, which is when the
winter birds depart, and the summmer visi-
tors arrive ; the third gives ‘the times of
migrating southwards, that is, when the sum-
mer birds depart, and the winter visitors
arrive. .

Birds.

Anas Cy guus..csssseeee
Fringilla montium......
Anas Anser ceoeseeees as
Numenius Arquata......
Tringa Vanellus....+0-
Motacilla flava ...+++0. ‘
Sylvia Hippolais ......
Motacilla Boarula .....-
Scolopax rusticola ......
Hirundo riparia s...s0++
Turdus pilariseessseeeeees

Sylvia Pheenicurus ... }

Sylvia Trochilus......+«.
Hirundo rustica .+. ieee
Tringa hypoleucos
Sylvia Sylviella.........
Cuculus Canoruses+eresee
Hirundo urbica .....+e0
Sylvia rubicola «sess
Charadrius Morinellus
Sylvia cinerea
Hirundo Apus ssseseees
Sylvia sylvicola.....0.+-
Sylvia hortensis ...+e++0.
Sylvia salicaria ...... ves

Migrate

——<—$$5
; : TTR

North.

March 1
March 8

March 10
March 13
March 21
March 26

April 14

April 15
April 17
April 22
April 26
April 27
April 29

in exposed
situations

Sunmer Birds of Passage.

TABLE.

South.
Jan. or Feb. }In hard frosts
October4 4.
September 10
September 9

October 24 —

October 14

Octeber 18

‘ October 3

September 25

A.D. 1793

August 18

( 478 )

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(478)

INDEX.

—>>O<e-

A

Aun and PEPYS, Messrs. their results on respira-
tion, &c. 35. et segs

Animal Heat, how acquired, 17—Dr. Crawrorn’s theory
of, stated, ibid.—is less in proportion as the carbonic
acid evolved in respiration is less, 42.

Aqueous vapour, see steam.

Atmosphere, gradual deterioration of, considered, 39—quan-
tity of carbonic acid in it estimated—this quantity is
not less than known natural operations would produce
in 6000 years, 41.

Arwoop, Mr. conceives the measure of force to be, in
rotatory motion as the mass into the square of the velo-
city, in rectilinear motion as the mass into the velocity,
—and that in mixed cases there is no measure, 108, 109.

B

Barker’s mill, explanation of its principles, 240.

Bernovtut, M. Daniel, his proposition on bydrodynamcis,
159—important proposition on the force of effluent
water, 234,

———--——, M. John, his observation on the change of
figure in bodies by collision, 190.

Birds, see Summer-Birds.

Bostock, Dr. his theory of galvanic electricity, 303.

Bropiz, Mr. on animal heat, 42.

INDEX, 479

co

Carbonic acid gas, quantity of, expired ina day = 2.8 Ibs.
troy, 27—or = 33 lbs, 36—quantity of, in the atmo-

_ sphere, is in all probability gradually increasing, 41.

Change of figure, one great object of the application of
mechanical force; various instances of, 220—Change
of motion, the other great object of mechanical force,
221—formule for estimating the moving force expended
in each, 230, .

Collision, various cases of considered, 120, 121 POO SM abe
&c. 250.

Crawrorp, Dr. his theory of animal heat stated, 17—it
continues uncontroverted, 38.

D

D’AemsBert, M. on the measure of force, 130, 131, 136,
137, 180—on the case of one elastic body striking two

others, 206, 207,

Dattoy, Mr, John, on respiration and animal heat, 15,

Davy Sir Humphry, his theory of galvanic electricity,
305.

De Borpa, M. argues that the force of water against a
wheel is as the relative velocity, 155—his omission, 164,

De Prony, M. observes there are various measures of force,
130—asserts the dispute about the vis viva is merely
verbal, 131—his explanation of mixed motion, 175.

Dewar, Henry, M. D. on foreign commerce, 45,

Du Buat, M. on water wheels, &c. 151,157, 158—his
theory of non-pressures controverted, 154,

E

Ebbing and flowing well, observations on one, at Giggles-
wick, 354 e¢ seq.—table of observations on, 371,
Edinburgh Reviewers are of opinion that the force of a

480 INDEX.

body in motion is either as the matter into the velocity
or into the square of the velocity, according to the effect
intended to be produced, 134—object to Mr. SmeaTon’s
opinions, 164.

Emerson, Mr. undervalues the principle of the vis viva,

~ 127—has fallen into an error in his fluxions by neglect-
ing that principle, 128.

Eudiometer, description of one, and of other apparatus,
384,

Ewart, Mr. Peter, on the measure of moving force, 105.

F

Figurative Language, on the origin and use of, 74—the
result of necessity, 77.

Flowering of Plants, in different latitudes, times of, 466.

Force, in mechanics, has two significations, the one denoting
pressure simply, the other pressure multiplied by space ;
this last denominated moving force; they differ as a line
differs from a surface, &c. 224.

Foreign Commerce, its importance, 45—in some cases in-
creases in others diminishes population, 53, 54—when
favourable to happiness, 55—its influence on the power
of a nation, 57 et seq.

G

GauiLEo M. the first author of the doctrine of the vis viva,
and of the Law of continuity, ascribed to Leisnitz, &c.
217, et seq.

Galvanic electricity, theories on the excitement of, 293—
quantities of electricity in the successive plates constitute
a geometrical progression, 297-——approaching an arith-
metical, 208—chemical agency necessary to the action
of the pile, 300. ;

Giggleswick, in Yorkshire, observations on the ebbing and
flowing well of, 354, ¢¢ seq.

Gover Mr. John, on the ois viva, 270—on an ebbing

INDEX. 48}

and flowing well, 354—his remarks on the summer birds
of passage and on migration, 453.

H
Hassenrratz and La Grance, their objections to Craw-
Forp’s theory of animal heat considered, 20.
Henry, Mr. Thomas, his remarks. on a thunder storm, 263.
Henry, William, M.D. on galvanic electricity, 293—his
description of an eudiometer, &c. 384—on uric acid, 391.
Horstey, Dr. his mistake in a comment on Newton, 210.
J
Jarrotp, Thomas, M. D. his essay on national character,
328. ;
Jouns, Rev. William, of the origin of + figurative lan-

guage, 74,
L

La Ptact, M. thinks that moving force may be measured
by any power of the velocity, 134, 200—supposes the
collision of elastic bodies to be performed in time, and
that of inelastic bodies to be instantaneous, 193.

Law of continuity, in the communication of motion de-
fended, 194, et seq. and 199—originated with Gate,
217—opposed by Rosins and Mactaurin, ibid.—sup-
ported by Leisnirz and his followers.

Lawson’s geometrical theorems demonstrated, 414, et seq.

Lightning, remarkable effect of, 259, et seq.

M

Mactaurin, Mr. his celebrated argument against the vis
viva, 182 ~—<supposes there may be perfectly hard non-
elastic bodies, 192
cases of collision, 206———opposes the law of continuity,
217.

Mattuus, Mr. remark on his principles, 347, 348.

Martin, Mr. William, on rotten-stone, 313.

Measure of moving force, great practical importance of,
112 ~is the pressure multiplied by the space, 223, &c.

3P

his defective solution of certain

482 INDEX.

Maximum effect of machines, some new observations upon,
247, et seqg.—erroneous conclusions respecting it, 249.
Mechanic power, -a phrase adopted by Mr. Smeaton to sig»

nify moving force, that is, the pressure into the space,
or the mass into the square of the velocity, 224.
Mechanical Problems solved, 285, et seq.
Micrvier of birds, remarks on, 453—1table of the times
f, 472,
Myuwes, Dr. observes the question of the vis viva is not
merely verbal, 132
riments, 163

his remark on SMEATON’s expe-

his remarks on Mactaurin’s ingenious
proposition, 183. —

Moving force, on the measure of, 105, et seq.—reasons for
adopting the: phrase, 225—— definition of it, ibid.
is quite distinct from motive force, chid.—tules for esti-
mating the quantity of it expended in producing motion
and in producing change of figure, 229, et seq.—four
distinct effects of moving force produced in one instance,
213.

i N

National character, essay on, 328.

Newron, Sir Isaac, his doubtful proposition of two globes
revolving around their common centre of gravity which
moves in a straight line, considered and explained,
210, et seq. on the reaction of effluent water, 234.

Nicnotson, Mr. Matthew, his account of athunderstorm, 259.

Nouns the basis of language, 78—verbs derived from them,
88 adjectives also derived from them, 91.

O

Oxygenous gas consumed in respiration in a day, 2.6 lbs.

troy, 26.

P
Plants, time of flowering in different latitudes, 466.

Pressure in mechanics one of the two elements of moving
force, 223,

2

INDEX. 483

Pronouns, conjectures concerning the origin of, 93.
R
Reaction of effuent water, original experiments on, 235, et seg,
_ Rew Dr. his remark on the controversy concerning the
measure of moving force, 105'——his definition of equal
moving forces, 179.
Resolution of compound moving forces explained, 254, et seq.
Respiration on, 15—bow it affects atmospheric air, 25
quantity of air inspired each time equal to 30 cubie

inches—number of inspirations in a minute, 20, &c.
26—makes the same changes in air as the combustion of
charcoal, 34.

Rotten-stone, cursory remarks on, 313—is found on Bake-
well-moor, Derbyshire, 314—supposed to be derived
from black marble, 317 analysis of, 319.

Ss

Suarrs, Mr. John, his experiments on the force of steam
compared with its heat, 1, e¢ seq.

Smeaton Mr, on mistaken notions about the measure of
force, 107—his definition of power in mechanics—is
proportional to the square of the velocity generated, 129
—or to the pressure multiplied by the space through
which it acts, 142, 224—-his remarkable result with
water-wheels in which the maximum effect. far exceeded
that by the common theory, 160—important conclusion
thereupon, 2bid—demonstrates that half the force of a
body in motion is expended in certain circumstances in
producing a change of figure, 181.

Summer birds of passage, remarks on, 453—etables of the
times of their migration.

Space, in mechanics, one of the two elements of moving
force, 223.

Stanuore, Earl, his theory of the returning stroke applied,
266.

Steam, latent heat of, nearly the same at all temperatures
in a given weight, 7, 8 and. 9—is equal to 920°, g;

484 INDEX.

Steam, Or aqueous vapour, exhaled from the lungs in a
day, equal to 1.55 Ib., 29reasons for supposing it not
formed from its ultimate elements in the lungs, 31.

’ T }

Theorems and Problems, on the vis viva, 270, et Seq-

Thunder-storm, remarkable effect of, 259, et seq.

Time, in mechanics, not a necessary element of the mea-
sure of moving force, 227.

Uric acid, memoir on, 391—chemical properties of»397,
et seq.—urates, 403—reasons for classing it amongst
acids, 406, 407—-decomposition of by other acids, 498—
destructive distillation of, 409. ;

Vv ;

Vince, Mr. his proposition on the communication of force,
118. :

Vis impressa, a phrase used by Newron,, for pressure mul-
tiplied by time, 224.

Vis viva, a phrase used by Lersntrz, &c. for moving force,
or pressure multiplied by space—and vis mortua for pres
sure simply, 224.

» principles of, elucidated, 270, et seq.

——

a i

Water, heats through the several Dido of the thermo-
meter, nearly in equal times, 5.

Wanrine, Mr. argues the force of water against a wheel is
as the relative velocity, 156—his omission, 164.

Wealth defined—is increased by foreign commerce, 47.

Wirppore, Rev. Charles, his demonstration of Lawson’s
theorems, 414, ef seq.

Wo xtaston, Dr. concludes the measure of mechanic force
to be as'the square of the velocity, 133—his explanation
of a case where the whole force is transferred from one
body to another, 198—his particular case of collision
considered, 250, et seq.

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Russell & Allen, Printers, Manehester.

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