ii^^^fr

V'-A

•>-*

-:, -X

«d3

L—

January 1828.

jg$S^£G^fl^lffiKS^

v?a

fig

Published the First Day of every Month. — Pnce 2s. 6d.

U

THE

Eg

PHILOSOPHICAL MAGAZINE

§S

AND

ga

pi

ANNALS OF PHILOSOPHY:

COMPREHENDING

ga

KS

THE VARIOUS BRANCHES OF SCIENCE, THE LIBERAL

US

AND FINE ARTS, AGRICULTURE, MANUFACTURES,

AND COMMERCE.

teg:;

NEW SERIES.

KjS

No 13.— JANUARY 1828.

Wn

WITH A PLATE,

fi^

Illustrative of Dr. Prout's Paper on the Ultimate Composition of
Simple Alimentary Substances.

gS

t.Sw

■ —

BY

»H

RICHARD TAYLOR, F.S.A. F.L.S. M. Astr. S. &c.

gg

r ,x

AND

RICHARD PHILLIPS, F.R.S. L. & E. F.L.S. &c.

gg

9

p jy

K^

ALlRI JL FLAMMAM.

1*8

ey

iJRj

gS

Kg

^n^*

§3

Kg

lanOon :

PRINTED BY AND FOR RICHARD TAYLOR, RED LION COURT, FLEET STREET :

*tm

rH

And sold by Baldwin and Cradock ; Longman, Rees, Orme, Brown, and
Green; Cadell; Sherwood, Gilbert, and Piper; Simpkin and Marshall;
Underwood ; W. Phillips ; Harding; Highley : — and by Adam Black, Edin-
burgh ; Smith and Son, Glasgow ; and Hodges and M'Arthur, Dublin.

gS

BaS/?^8Q$^

TO CORRESPONDENTS.

Mr. Nixon's Communication has been received, and will appear in our
next. — Q. Q. will hear from us in a few days.

We have to acknowledge the receipt of Mr. Haworth's paper, which
we also hope to insert.

Professor Thomson's Letter on the Mutual Decomposition of Sulphate
of Zinc and Chromate of Potash came too late for our present Number,
but will appear in our next.

*#* The Editors request that all Communications intendedfor immediate
insertion may he sent to the care of Mr. Richard Taylor, Printing Office,
Red Lion Court, Fleet Street, London, at furthest by the 15th day of the
month, or they mil be too late to appear in the ensuing Number.

RICHARD COWLING TAYLOR,

Land and Geological Surveyor and Estate Agent,

7, WILMINGTON SQUARE, LONDON:

BY whom Surveys for Lines of Canals, Railways, Turnpike Roads,
Parishes, &c. Geological Surveys, Plans and Sections, with Illustrative
Drawings from personal Observation, and Models of Mineral Pro-
perty and Districts, are executed.

Specimens of such Models, Drawings, Sections, and Maps of extensive
Districts in various Counties, may be inspected at his Office.

THE REV. H. R. BOWLES,

QUEEN STREET, YARMOUTH, NORFOLK,

ECEIVES as Boarders a small number of YOUNG GENTLEMEN,
who are carefully instructed in the Latin and Greek Languages ;
strict Attention being paid to the niceties of Grammatical Construction
and Prosody.

The Hebrew is taught if , desired.

While a thorough knowledge of the Classics is afforded them, by a
judicious Distribution of Studies, the Pupils are made well acquainted
with the Mathematics; and at the same time, due Attention is paid to the
Formation of a correct and elegant English style.

Pupils intended for the learned Professions are prepared for the English
or Scotch Universities.

The Modern Languages are taught in the School. Music and Draw-
ing by approved Masters.

To encourage habitual affection and confidence between himself and
his Pupils has always been a principal object in Mr. Bowtles's plan of
Education, from a belief that this is the 'only means of securing their
Moral and Intellectual Improvement.

Terms: Forty Guineas per Annum. — Parlour Boarders, Fifty Guineas.
—Entrance One Guinea.

A Quarter's Notice to be given, or a Quarter's Board paid, previous
to the Removal of a Pupil.

R

February 1828.

Published the First Day of every Month, — Price 2s, 6d.

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY:

COMPREHENDING

g THE VARIOUS BRANCHES OF SCIENCE, THE LIBERAL
AND FINE ARTS, AGRICULTURE, MANUFACTURES,
AND COMMERCE.

NEW SERIES.
N° 14.— FEBRUARY 1828.

WITH TWO ENGRAVINGS :

I. Illustrative of Dr. Prout's Paper on the Ultimate Composition of

Simple Alimentary Substances.

II. Illustrative of Mr. Nixon's Paper on the Hills of the Penine Chain.

BY

RICHARD TAYLOR, F.S.A. F.L.S. M. Astr. S. &c.

AND

RICHARD PHILLIPS, F.R.S.L. &E. F.L.S. &c.

AbKRB ft FLAMMAM

tontion :

PRINTED BY AND FOR RICHARD TAYLOR, RED LION COURT, TLEET STREET:

And sold by Baldwin and Cradock ; Longman, Rees, Orme, Brown, and
Green; Cadell; Sherwood, Gilbert, and Piper; Simpkin and Marshall;
Underwood ; W. Phillips ; Harding; Highley : — and by Adam Black, Edin-
burgh ; Smith and Son, Glasgow : and Hodges and M'Arthur, Dublin.

TO CORRESPONDENTS.

Mr. E. Giddy's Communication on the Climate of Penzance, and
Mr. Marshall's Meteorological Summary from Kendal, will appear in
our next.

Mr. Brayley's paper on the T&hettik also in our next.

*#* The Editors request that all Communications intended/or immediate
insertion may be sent to the care of Mr, Richard Taylor, Printing Office,
Red Lion Court, Fleet Street, London, at furthest by the 15th day of the
month, or they mil be too late to appear in the ensuing Number.

AN ELEGANT PRESENT FOR YOUTH.
Just published in 12mo, price 12.?.

ORNITHOLOGIA; or, The Birds; a Poem in Two Parts ; with an
Introduction to their Natural History, and copious Notes, in which
are described about One Thousand Birds, and the most interesting and
recently observed Facts concerning them ; the whole forming a Compre-
hensive Manual of the Science of Ornithology. By JAMES JENNINGS.
Embellished with two picturesque and highly finished Engravings on Wood,
by Hughes, from original designs; and also accurate delineations of the
Golden Eagle and the Condor.

" They whisper truths in Reason's ear,
If human pride will stoop to hear." — Lord Ers/cine.

" This is at once a curious, instructive, and amusing work." — Literary
Gazette.

" We cannot conclude this notice of Ornithologia without paying our
due meed of praise to its scientific details, as well as to the amiable spirit
of philanthropy that pervades both poetry and prose." — Netv Lit. Gazette.

" A very interesting volume — the poem, which forms the ground-work,
affords a favourable specimen of the author's genius in this branch of com-
position."— Atlas.

" We can promise those who look into Ornithologia a most pleasant
and profitable employment. For youth especially, we know not a more
clear or attractive book." — Sunday Monitor. — See also Literary Chronicle,
Taunton Courier, &c.

London: Poole and Edwards, 12, Ave Maria Lane.

NEW EXCISE REGULATION ACT.

Just Published, Price Is. 6d.

AN ABSTRACT OF THE EXCISE GENERAL REGULATION
ACT. 7 and 8 GEO. I Vv Cap. 53. Intituled " An Act to Conso-
lidate and Amend the Laws relating to the Collection and Management
of the Revenue of Excise throughout Great Britain and Ireland." To
commence on the 5th of January 1828.

Printed from an Abstract used by the Officers of Excise. With a eo-
pious Index.

London : Printed and sold by Richard Taylor, Red Lion Court, Fleet
Street; sold also by Simpkin and Marshall, Stationers' Court; and by
R. B. Bate, Mathematical Instrument Maker to the Honourable Board
of Excise, 17, Poultry.

March 1828.

Published the First Day of every Month. — Price 2s. 6d.

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY:

COMPREHENDING

THE VARIOUS BRANCHES OF SCIENCE, THE LIBERAL

AND FINE ARTS, AGRICULTURE, MANUFACTURES,

AND COMMERCE.

NEW SERIES.

N° 15.— M ARCH 1828.

BY

RICHARD TAYLOR, F.S.A. F.L.S. M.Astr.S. &c.

AND

RICHARD PHILLIPS, F.R.S. L. & E. F.L.S. &c.

ES

lonflon ;

PRINTED BY AND FOR RICHARD TAYLOR, RED LION COURT, FLEET STREET :

And sold by Baldwin and Cradock ; Longman, Rees, Orme, Brown, and
Green; Cadell; Sherwood, Gilbert, and Piper; Simpkin and Marshall;
Underwood; W.Phillips; Harding; Highley: — and by Adam Black, Edin-
burgh ; Smith and Son, Glasgow : and Hodges and M* Arthur, Dublin.

m

TO CORRESPONDENTS.

Mr. J. Phillips's Paper on the Geology of the Vale of Pickering has
been received, and will meet with early attention.
Mr. Tredgold's Theory of the Resistance of Fluids, in our next.
Dr. Forster's Journal of the Flowering of Spring Plants, in our next.
Mr. Ma gcou gh's Paper has been received.

*#* The Editors request that all Communications intendedjbr immediate
insertion may be sent to the care of Mr. Richard Taylor, Printing Office,
Bed Lion Court, Fleet Street, London, at furthest by the 1 5th day of the
month, or they will be too late to appear in the ensuing Number.

This Day is published, Price 3s. 6d.

A POPULAR EXPOSITION of the EFFECT of FORCES applied
to DRAUGHT ; with Illustrations of the Principles of Action, and
Tables of the Performance of Horses and Locomotive Engines on Rail-
ways and an Appendix containing the Results of some Experiments on
Friction.

By DAVID RANKINE, Esq.

London: printed for Longman, Rees, Orme, Brown, and Green;
Oliver and Boyd, Edinburgh ; and John Smith and Son, Glasgow.

This Day is published, in 2 vols. 8vo. Price 21s. boards,

SYSTEMATIC MORALITY ; or, a Treatise on the THEORY and
PRACTICE of HUMAN DUTY, on the Grounds of Natural Re-
ligion.

By WILLIAM JEVONS.

Printed for R. Hunter, 72, St. Paul's Churchyard.

" We can safely recommend it as containing a valuable fund of practi-
cal good sense, which few can study with the attention it deserves with-
out being made both wiser and better."

" We doubt whether there exists in any other work a statement of the
evidence in favour of a future state, as derived from the light of nature,
which can be compared with it for intrinsic [force, or for elegance and
beauty of illustration." — Monthly Repository.

PHILOSOPHICAL INSTRUMENTS.

A DESCRIPTIVE Catalogue of the Optical, Mathematical, Philoso-
-£*- phical, and Chemical Instruments and Apparatus, constructed and
sold by Watkins and Hill j may be had, (price One Shilling,) at their es-
tablishment, 5, Charing Cross, London.

Vol. 3.

April 1828,

No. 16,

Published the First Day of every Month, — Price 2s. 6d.

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY:

COMPREHENDING

THE VARIOUS BRANCHES OF SCIENCE, THE LIBERAL

AND FINE ARTS, AGRICULTURE, MANUFACTURES,

AND COMMERCE.

NEW SERIES.

N° 16.— APRIL 1828.

WITH TWO ENGRAVINGS :

I. Illustrative of Mr. John Phillips's Remarks on the Geology of

the North Side of the Vale of Pickering, Yorkshire.

II. Illustrative of Mr. Tredgold's Theory of the Resistance of Fluids.

BY
RICHARD TAYLOR, F.S.A. F.L.S. M. Astr.S. &c.

AND

RICHARD PHILLIPS, F.R.S. L. & E. F.L.S. &c.

ALi&I O. flam Mam

Lontron :

PRINTED BY AND FOR RICHARD TAYLOR, RED LION COURT, FLEET STREET !

And sold by Baldwin and Cradock ; Longman, Rees, Orme, Brown, and
Green; Cadell; Sherwood, Gilbert, and Piper; Simpkin and Marshall;
Underwood; W.Phillips; Harding; Highley: — and by Adara Black, Edin-
burgh ; Smith and Son, Glasgow : and Hodges and M' Arthur, Dublin.

TO CORRESPONDENTS.
Mr. Galbraith's Paper in our next.

*#* The Editors request that all Communications intended for immediate
insertion may be sent to the care of Mr, Richard Taylor ; Printing Office,
Red Lion Court, Fleet Street, London, at furthest by the 1 5th day of the
month, or they mill be too late to appear in the ensuing Number.

PHILOSOPHICAL MAGAZINE.

A FEW Complete Sets of the PHILOSOPHICAL MAGAZINE,
in 68 volumes ; recording the Improvements which have been effected
in the various Departments of Science, from its Commencement in 1798
to the Conclusion of the First Series in ] 826, may be had at the Printer's,
at Half Price.

Vol. 3.

May 1828

-

No. 17.

K2^^^

m

P«

blished the First Day of every Month.

— Price 2s. 6d.

THE

PHILOSOPHICAL MAGAZINE

aw

K^

AND

gS

kJ

ANNALS OF PHILOSOPHY:

gS

COMPREHENDING

§5^3

Km

THE VARIOUS BRANCHES OF SCIENCE, THE LIBERAL

gS

AND FINE ARTS, AGRICULTURE, MANUFACTURES,

Kg

Si

AND COMMERCE.

gH

gS

p jy

NEW SERIES.

Dm

N°17.— MAY 1828.

gs

Kg

WITH AN ENGRAVING,

gg

Eg

Illustra
RIC

tive of Dr. Weber's Paper on Savart's E
the Undulations of Sound.

(cperiments on
\str. S. &c.

gS
gS

BY

MARD TAYLOR, F.S.A. F.L.S. M. j

RI

AND

CHARD PHILLIPS, F.R.S. L. & E. F.L.S. &c.

m9

£j3

Bl

ALkRZ 1 FLAM MAM

g^

JLJoj

gS

Rk

^1^9*

#88

K^

LonDon :

PRINTED BY AND FOR RICHARD TAYLOR, RED LION COURT, FLEET STREET :

gja

Kg

And sold by Baldwin and Cradock ; Longman, Rees, Orme, Brown, and
Green; Cadell; Sherwood, Gilbert, and Piper; Simpkin and Marshall;
Underwood ; W. Phillips ; Harding; Highley : — and by Adam Black, Edin-
burgh ; Smith and Son, Glasgow : and Hodges and M* Arthur, Dublin.

g3

ic^l

M5E

x&ff^£^£^:£^£

Wui

M

mMSw^

TO CORRESPONDENTS.

The Paper " On Single and Erect Vision," in our next Number.
Mr. Martin's « Geological Memoir on a Part of Western Sussex
has been received, and will be noticed in our next.

*** The Editors request that all Communications intendedfor immediate
insertion may be sent to the care of Mr. Richard Taylor, Printing Office,
Red Lion Court, Fleet Street, London, at furthest by the 1 5ih day of the
month, or they mil be too late to appear in the ensuing Number.

PHILOSOPHICAL MAGAZINE.

A FEW Complete Sets of the PHILOSOPHICAL MAGAZINE,
in 68 volumes ; recording the Improvements which have been effected
in the various Departments of Science, from its Commencement in 1798
to the Conclusion of the First Series in 1826, may be had at the Printer's,
at Half Price.

Vol. 3. June 1828

No. 18.

Published the First Day of every Month. — Price 2s, 6d.

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY:

COMPREHENDING

THE VARIOUS BRANCHES OF SCIENCE, THE LIBERAL p
AND FINE ARTS, AGRICULTURE, MANUFACTURES,
AND COMMERCE.

NEW SERIES.

NM8.-JUNE 1828.

WITH A PLATE,

Illustrative of Mr. R.Walker's Paper on the artificial Production
of Cold.

BY

RICHARD TAYLOR, F.S.A. F.L.S. M. Astr. S. &c.

AND

RICHARD PHILLIPS, F.R.S. L. & E. F.L.S. &c.

JLonDon ;

PRINTED BY AND FOR RICHARD TAYLOR, RED LION COURT, FLEET STREET !

And sold by Baldwin and Cradock ; Longman, Rees, Orme, Brown, and
Green; Cadell; Sherwood, Gilbert, and Piper; Simpkin and Marshall;
Underwood ; W. Phillips ; Harding; Highley : — and by Adam Black, Edin-
burgh j Smith and Son, Glasgow : and Hodges and M* Arthur, Dublin.

TO CORRESPONDENTS.

We omitted to mention, in our last notice to Correspondents, that
Mr. Kingston's promised communications, On the geology of the Bovev
district, would be very acceptable.

The Review of Mr. Martin's Geological Memoir was prepared for in-
sertion in the present Number ; but the length to which the Proceeding
of Learned Societies have extended, has compelled us to defer it till oSr

next Number.

%* The Editors request that all Communications intended/or immediate
insertion may be sent to the care of Mr. Richard Taylor, Printing Office,
Bed Lion Court, Fleet Street, London, at furthest by the 15th day of the
month, or they mil be too late to appear in the ensuing Number.

PHILOSOPHICAL MAGAZINE.

A FEW Complete Sets of the PHILOSOPHICAL MAGAZINE,
- u m 68.voIu™es J recording the Improvements which have been effected
in the various Departments of Science, from its Commencement in 1798

*? !5ei£on.CluS10n of the First Series in ] 826, may be had at the Printer's,
at Halt Price.

On the 1st of May was published, in 8vo. No. I. (to be continued every
I wo Months, alternately with the Gardener's Magazine) Price
3s. 6d. of '

HPHE MAGAZINE of NATURAL HISTORY, and JOURNAL

MEtIoROLOgI/ B°TANY' MINERAL°GY,' GEOLOGY™ 4

Conducted by J. C. LOUDON, F.L.S. H.S. &c.

The different Departments edited by Gentlemen eminent in each. The
Drawings of Botany and Conchology, by Sowerby;-of Animals, by
Brandon"" ' 7 ktrUtt: and the Engravings on Wood by

The objects of this work are-To record every new fact belonging to
the subject; to render every part of the subject interesting to the amateur

ZJT' al/faMer; 1° tad -0n the reader hy Agrees from the more
elementary details to higher views and discussions; and to translate the
Technical terms, and Latin or Greek words used in Natural History, as
they occur, and to give the derivation and accentuation of all systematic
names. J

Printed for Longman, Rees, Orme, Brown, and Green, London.

This Day is published, in 4to Price 1/. in boards, illustrated with a Map

and Three Sectional Plates,

A GEOLOGICAL MEMOIR on a Part of WESTERN SUSSEX-

2ch^SS3T UP°n Cha,k"BasiDS> the Weald DTdati-,

By P. J. MARTIN.
»&M&i?^?*M*> Port.and-place; aad a.i

THE

PHILOSOPHICAL MAGAZINE,

OR

ANNALS

OF

CHEMISTRY, MATHEMATICS, ASTRONOMY,

NATURAL HISTORY, AND

GENERAL SCIENCE.

BY

RICHARD TAYLOR, F.S.A. F.L.S. M.Astr.S.&c.

AND

RICHARD PHILLIPS, F.R.S. L.&E. F.L.S. &c.

" Nee aranearum sane textus idee- melior quia ex se fila gignunt, nee noster
vilior quia ex alienis libamus ut apes." Just. Lips. Monti. Polti. lib. i. cap. 1.

VOL. III.

NEW AND UNITED SERIES OF THE PHILOSOPHICAL MAGAZINE
AND ANNALS OF PHILOSOPHY.

JANUARY- JUNE, 1828.

' v

LONDON:

PRINTED BY RICHARD TAYLOR, RED LION COURT, FLEET STREET :

AND SOLD BY LONGMAN, REES, ORME, BROWN, AND GREEN; CADELL ; BALDWIN,

AND CRADOCK; SHERWOOD, GILBERT, AND PIPER} SIMPKIN

AND MARSHALL; UNDERWOOD; W. PHILLIPS; HARDING ;

HIGHLEY, LONDON : — AND BY ADAM BLACK,

EDINBURGH ; SMITH AND SON, GLASGOW ;

AND HODGES AND M'ARIHUR,

DUBLIN.

TABLE OF CONTENTS.

NUMBER XIII.— JANUARY.

Page
Mr. Ivory on the Theory of Capillary Action, and the Depres-
sion of the Mercury in the Tubes of Barometers 1

Mr. Nixon on the Heights of some of the principal Beds of

Ingleborough Hill and Moughton Fell, Yorkshire 11

Mr. Bakewell on the Thermal Waters of the Alps 14

Mr. Herapath on the Integration of Linear Differential Equa-
tions having Constant Coefficients and last Term any Func-
tion of the Indeterminate Quantity x 19

Mr. Riddle on the Occultation of jS Scorpii, September 25,

1827 26

Mr. Teschemacher on the Crystalline Form of some Salts 27

Mr. Bevan's Remarks on Mr. J. Taylor's Rain-gauge 29

Reply to F.R.S.L.'s Remarks on Compound Interest SO

Dr. Prout on the ultimate Composition of simple alimentary
Substances ; with some preliminary Remarks on the Analysis

of organized Bodies in general (continued) ... 31

New Books: — Mr. Farey's Treatise on the Steam-Engine. ... 40
Proceedings of the Royal Society, President's Anniversary Ad-
dress 46—64

■ Astronomical Society 64

Zoological Society 68

Isopyre, a new Mineral Species 70

Osmelite, a new Mineral Species — Hydrosilicite, a new Mineral

Species / 71

Russian Platina Sand 72

New Phenomena of Vapour observed by Clement Desormes —

Rev. S. E. D wight's Notice of a Fire- Ball 74

Dr. Forster on the Aurora Borealis of 26th September 75

New Patents 76

Scientific Books, &c 77

Meteorological Observations 78

by ]yjr> Howard near London,

Mr. Giddy at Penzance, Dr. Burney at Gosport, and Mr.
Veall at Boston 80

NUMBER XIV.— FEBRUARY.

Dr. Thomson on the mutual Decomposition of Sulphate of Zinc
and Chromate of Potash : . 81

Mr. Nixon on the Measurement by Trigonometry of the Heights
of the principal Hills in the Vicinity of Dent, Hawes, and
Sedbergh, in Yorkshire {continued) 82

On Mr. Herapath's Method for the Integration of Linear Equa-
tions with constant Coefficients 96

On the Error imputed by Mr. Herapath to Lagrange in his

Method of integrating Linear Differential Equations 97

Dr.

IV CONTENTS.

Page

Dr. Prout on the ultimate Composition of simple Alimentary
Substances ; with some preliminary Remarks on the Analysis

of organized Bodies in general 98

Mr. R. Phillips on the Means, of ascertaining the Purity of Sul-
phate of Quina Ill

Mr. Main on the Phenomena of Water-spouts 114

Mr. Gray on the Nursing Pouch or Chamber of the Chama con-

camerata of Gmelin 117

Dr. Roget on an Apparent Violation of the Law of Continuity. ] 18
Prof. Hunefeld on the Titaniferous Iron-slag of Konigshutte in
Upper Silesia, and on the Probability of its containing Tan-

talium 121

New Books : — Philosophical Transactions for 1827. Part II.
Transactions of the Linnaean Society of London. Vol. 15th.
Part II. — Memoirs of the x\stronomical Society. Vol. 3rd.

Part 1 126—127

Proceedings of the Royal Society 128

Linnaean Society 130

w Geological Society 132

Astronomical Society 136

Royal Geological Society of Cornwall 138

Royal Academy of Sciences of Paris .... 139

Mr. Faraday on the Fluidity of Sulphur and Phosphorus at

Common Temperatures 144

Elementary Nature of Bromine— Quantity of Bromine in Sea

Water 145

Sale of Bromine — Preparation of lodous Acid — New Borate
of Soda — Analysis of a Salivary Concretion— Haidingerite,

a new Mineral Species 146

M. Sdrullas's Bromide of Selenium 147

Electricity of Gases and the Atmosphere 148

Rose-coloured Petrosilex from Sahlbergh in Sweden — Nontro-

nite, a new Mineral 149

Analysis of some Vegetable Products 150

New Chloride of Manganese — On the Power of Water and

Bromine in conducting Electricity 151

Effects of Heat upon Sulphur— Peroxide of Barium 152

On certain Habitudes of Sepias — Notice of an Error in Gal-

braith's Mathematical Tables and Formulae 153

Errors in Hutton's Log. Tables (Fifth Edition) — Crystalliza-
tion of Phosphorus — Chemical Examination on Ancient In-
struments, &c. — London Institution 154

New Patents 155

Meteorological Observations 157

by Mr. Howard near London,

Mr. Giddy at Penzance, Dr. Burney at Gosport, and Mr.
Veall at Boston 160

NUMBER XV.— MARCH.

Mr. Gilbert on the Regular or Platonic Solids 161

Mr.

CONTENTS. V

Page
Mr. Ivory on the Ellipticity of the Earth as deduced from Ex-
periments with the Pendulum 165

Mr. Giddy on the Climate of Penzance, Cornwall — Meteoro-
logical Results of the Temperature, Wind and Weather de-
duced from diurnal Observations made at Penzance for 21
Years ; (the Thermometrical Observations made at 8 a.m.
and 2 p.m.) to which are added the Maxima, Minima, and
Media of the Register Thermometer for 7 Years, with the

Inches of Rain fallen during that Period 173

Mr. Haworth's Description of New Succulent Plants . . . 183

On the supposed Subsidence of the German Ocean 188

Mr. Nixon on the Measurement by Trigonometry of the Heights
of the principal Hills in the Vicinity of Dent, Hawes, and

Sedbergh, in Yorkshire 189

Dr. Roget on an Apparent Violation of the Law of Continuity. 203
Mr. Ivory's Additional Discussion respecting the Ellipticity of
the Earth as determined by Experiments made with the Pen-
dulum 206

Mr. Herapath's Failure of Lagrange's Method of integrating

Linear with Constant Coefficients 210

Mr. Bicheno on Systems and Methods in Natural History

{continued) 1 213

New Books : — Tredgold on the Steam-Engine — Young's Ele-
ments of Geometry, with Notes 21 9 — 222

Proceedings of the Linnaean Society 223

Geological Society 225

Astronomical Society ^27

— at the Friday Evening Meetings of the Royal In-
stitution of Great Britain 229

Analysis of some Alloys of Bismuth 230

Examination of Copper — On Efflorescence 231

Native Platina— Manufacture of Ultramarine 232

Heat given out during Combustion — Inflammable Gas arising
after boring for Salt— Inflammable Gas from Salt Mines em-
ployed for producing Light — Natural Gas Lights at Fredonea 233
Iodine in Cadmium — Analysis of the Green Iron Ore and
Arseniate of Lead — Mr. Robotham's Geometrical Problem —

Scientific Books 234

New Patents — Meteorological Summary for the Year 1827 . . 236

Meteorological Observations 237

■ by Mr*. Giddy at Penzance, Dr.

Burney at Gosport, and Mr. Veall at Boston 240

NUMBER XVI.— APRIL.

Mr. Ivory's Letter to the Editors relating to the Ellipticity of
the Earth as deduced from Experiments with the Pendulum 241

Mr. J. Phillips's Remarks on the Geology of the North Side of

the Vale of Pickering 243

Mr.

Vi CONTENTS.

Page
Mr. Tredgold's New Theory of the Resistance of Fluids, com-
pared with the best Experiments. 249

a(3on Mr. Herapath's Second Attack on Lagrange's Method 262
Mr. Bicheno on Systems and Methods in Natural History . . . 265
Dr. Brandes's Examination of a gelatinous Substance found in
a damp Meadow ; — as a Contribution to the Knowledge of

the Meteors called Shooting- Stars 271

Lieut.-Col. Miller's Description of a Percussion Rifle, igniting

by a Spring instead of a Lock 277

Mr. Younge's Account of an improved Form of Apparatus for
exhibiting M. Clement Desormes's Experiments on Currents

of Air, &c 282

Mr. Bracy Clark on the Insect called Oistros by the Ancients,
and of the true Species intended by them under this Appel-
lation: in reply to the Observations ofW. S. MacLeay, Esq,
and the French Naturalists. To which is added, A Descrip-
tion of a new Species of Cuterebra 283

New Books: — Bakewell's Introduction to Geology 289

Proceedings of the Linnaean Society 290

■i Geological Society 291

1 at the Friday Evening Meetings of the Royal In-
stitution of Great Britain . . 304?

Royal Academy of Sciences of Paris. . . . 305

Obituary :— Sir J. E. Smith 307

Analysis of Alcohol, iEther, &c 309

New Patents 311

Meteorological Journal for 1827, kept at Gosport, Hants. By

Dr.Burney 312

Observations , 317

made at the Garden of the Hor-
ticultural Society at Chiswick, near London ; by Mr. Giddy
at Penzance, Dr. Bumey at Gosport, and Mr. Veall at Boston 320

NUMBER XVII.— MAY.

Mr. Galbraith on the Ellipticity of the Earth, as deduced from
Experiments with the Pendulum ; and on the Formulae em-
ployed for obtaining it .... . 321

Account of a Paper by Prof. Gauss, intitled " Disquisitiones

f enemies circa Superficies Curvas:" communicated to the
Loyal Society of Gdttingen on the 8th of October 1827 . . 331
Dr. Weber on Savart's Experiments on the Motions of medi-
ately agitated Membranes 336

Supplement : — On the Employment of a resounding Mem-
brane for the Observation of the Interference of the

Undulations of Sound 342

Mr. Ivory on the Figure of the Earth, as deduced from Mea-
surements of different Portions of the Meridian 343

Dr.Wackenroder's Mineralogical and Chemical Examination of

the Diopside of Fassa in the Tyrol 349

Lieut.-

CONTENTS. vii

Page

Lieut.-Col. Miller's Description of a Shell, exploding by Per-
cussion when trod upon 358

Mr. Kingston's Account of the Iron-Mine at Haytor, in De-
vonshire 359

Mr. Mageough's Account of a new Method of mounting Ther-
mometers 365

New Books : — Horsfield's Descriptive Catalogue of the Lepi-
dopterous Insects in the Museum of the East India Com-
pany— Haworth's Lepidoptera Britannica 368 — 370

Proceedings of the Royal Society 370

Linnaean Society 374

, Astronomical Society 377

at the Friday Evening Meetings of the Royal In-
stitution of Great Britain— Obituary : — Sir J. E. Smith 391

New Minerals 397

Meteorological Observations 398

made at the Garden of the Hor-
ticultural Society at Chiswick, near London ; by Mr. Giddy
at Penzance, Dr. Burriey atGosport, and Mr. Veall at Boston. 400

NUMBER XVIII.- JUNE.

Mr. Walker on the Artificial Production of Cold 40 1

On the Causes of Single and Erect Vision 406

Mr. Ewart on the Reaction of EffluentWater, and on the Maxi-
mum Effect of Machines. With Notes relating to the Theory

of Barker's Mill ; by Mr. Ivory 416

Mr. ivory on the Figure of the Earth, as deduced from Mea-
surements of the Meridian 431

M. Fayolle on the characteristic Equation of Curve-surfaces

capable of being evolved in a Plane 436

Proceedings of the Royal Society 436

, Linnaean Society 440

. Geological Society '. 441

. 1 — Astronomical Society 451

at the Friday Evening Meetings of the Members

of the Royal Institution 456

Origin of Trap Rocks 458

Analyses of Tourmalines 460

Prof. Stromeyer's New Method of separating Manganese from
Lime and Magnesia — Singular Action of Phosphoric Acid

on Albumen 462

List of Earthquakes which occurred in 1827 — Red Rain sup-
posed to arise from Butterflies 463

Weather in Paris — MM. Dumas and Boullay's Analysis of

Alcohol, Mther, &c 465

Test of the Presence of Ammonia — New Patents 466

Scientific Books — Meteorological Observations * 467

Meteoro-

Vlll v CONTENTS.

Page

Meteorological Observations made at the Garden of the Horti-
cultural Society at Chiswick, near London ; by Mr. Giddy at
Penzance, Dr. Burney at Gosport, and Mr.Veall at Boston. . 469

Index 470

PLATES.

I. and II. Engravings illustrative of Dr. Prout's Paper on the Ultimate
Composition of Simple Alimentary Substances.

III. An Engraving illustrative of Mr. Nixon's Paper on the Hills of the

Penine Chain. i

IV. An Engraving illustrative of Mr. John Phillips's Remarks on the

Geology of the North Side of the Vale of Pickering, Yorkshire.

V. An Engraving illustrative of Mr. Tredgold's Theory of the Resistance

of Fluids.

VI. An Engraving illustrative of Dr. Weber's Paper on Savart's Experi-

ments on the Undulations of Sound.

VII. An Engraving illustrative of Mr. R.Walker's Paper on the Artificial

Production af Cold.

Erratum.

P. 363, line 10 from bottom :for " Irregular masses of siliceous matter that
have obviously invested, either wholly or partially, crystals of iron-ore.
Iron-pyrites, quartz or garnet, are of frequent occurrence" — read u Irre-
gular masses of siliceous matter that have obviously invested, either
wholly or partially, crystals of iron-ore, iron-pyrites, quartz \>r garnet,
are"&c.

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY.

[NEW SERIES.]

JANUARY 1828.

I. On the Theory of Capillary Action, and the Depression of
the Mercury in the Tubes of Barometers, By J. Ivory, Esq.
M.A. F.R.S.*

r|1HE elevation and depression of liquids in capillary tubes,
-*- that is, tubes of a very small bore resembling a hair, has
long occupied the attention of natural philosophers. If we
would acquire a precise notion of the present state of this
branch of science, we must consider it in two separate points
of view. In the first place we are in possession of a mathe-
matical theory which quadrates exactly with the phenomena ;
but, in the second place, when we direct our attention to the
physical foundation of this theory, we find as many opinions
as there are different inquirers, and no one account is entirely
free from difficulties. My present intention is to make some
observations on the first part of the subject, without touching
at all on the second, which is reserved for future discussion.

The mathematical theory of the capillary phaenomena is
not complicated, being derived from two independent princi-
ples. The first of these is the fact, that the surface of the same
liquid always makes the same angle with the surfaces of solids
immersed in it, when the matter of the solids is the same.
In the case of glass and water, and generally whenever a solid
is wetted by a liquid, the two surfaces touch one another, or
make an infinitely small angle. In glass and mercury, the
two surfaces are inclined to one another in an angle of about
42°.

* Communicated by the Author.

New Series. Vol. 3. No. 13. Jan. 1828. B The

2 Mr. Ivory on the Theoiy of Capillary Action, and

The second principle is the equation of the curve surface of
the liquid under the influence of the capillary force. When
a liquid is elevated above the general level by capillary action,
the surface is always concave upward ; on the contrary, it is
always convex upward, when the liquid is depressed below
the level. In either case, the distance of any point in the curve
surface from the level, is proportional to the sum of the cur-
vatures estimated in any two directions at right angles to
one another. To speak more precisely, let a normal be drawn
to the curve surface at any point; make two planes per-
pendicular to one another, pass by the normal and inter-
sect the curve surface ; put R and R/ for the radii of curva-
ture of the two sections, and y for the distance of the point
from the general level ; the equation of the surface in the ca-
pillary space is,

/3 being a quantity to be determined by experiment. It is a
property well known to mathematicians, that the sum of the
curvatures is always the same, provided the two sections be at
right angles to one another.

A little reflection will show that the two principles we have
mentioned fully ascertain every circumstance relating to the
capillary phaenomena. The equation determines the position
of every point in the curve surface above or below the general
level ; and the other principle limits the extent of the same
surface in the capillary space, by making known the inclina-
tion of its extreme boundary to the surface of the immersed
solid.

It is evident that the equation cannot be verified by direct
observation. It was first suggested by the resemblance of the
surface of liquids under capillary action to the class of elastic
curves treated of in geometry. In reality, there seems to be
no circumstance accompanying the greater or less elevation
or depression, except a variation of curvature ; so that the at-
tention of the inquirer is naturally directed to examine the re-
lation of these two things. There is no other way of proving
that the equation accords with nature, but by comparing the
mathematical deductions from it with the results obtained by
careful and accurate experiments. The most general classi-
fication of the capillary phaenomena we owe to Dr. Jurin, who
makes the quantity of the displaced fluid, which is the proper
measure of the capillary force, proportional in all cases to the
length of the line of common section of the surfaces of the
fluid and solid immersed in it. I do not here allude to the
physical cause assigned by Dr. Jurin, which will not bear ex-
amination ;

the Depression of the Mercury in the Tubes of Barometers. 3

amination ; but to the law of the phenomena, considered as
a general fact allowed to be consonant to experience. Now
one of the most curious points in Laplace's theory of capillary
action % is a demonstration, deduced from the equation of the
curve surface, which proves that the volume of elevated fluid,
or the space made void by the capillary force in the case of a
depression, is proportional to the interior periphery of any
cylindrical or prismatic tube immersed in the fluid. And it is
correct to affirm generally, that what is called Dr. Jurin's
theory, is no other than a mathematical consequence flowing
from the two principles we have laid down.

There is one set of facts very proper to bring the exact
agreement of the mathematical theory with nature to a severe
trial. We allude to the depression of the mercury in the tubes
of barometers of various diameters. The accuracy requisite
in modern philosophical pursuits has drawn the attention of
experimentalists to determine the quantity of the depression,
in order to derive the true height of the mercury, from the
observed height. In tubes from about one tenth of an inch in
diameter, to seven or eight tenths, the convex curvature of
the surface and the depression are found to vary very quickly
and notably ; and the comparison of the theory with such a
series of connected experiments, cannot but furnish a delicate
test of its exactness. Here, however, a difficulty occurs. The
mathematical determination of the depression is a problem of
great difficulty, which does not yield to the methods of inves-
tigation usually employed by analysts, and which has not yet
been solved in a satisfactory manner. The remainder of this
article is an attempt to overcome this difficulty.

I put y for the vertical ordinate of a point in the convex
surface of the mercury, or the distance below the general level ;
r for the distance of the same point from the axis of the tube ;
and z for the sine of the inclination of the vertical section of
the curve surface to r, or to the horizon : according to what

ll V

is taught in geometry, — is the radius of curvature of the
vertical section ; and — , the radius of curvature of the sec-

z

tion at right angles to the vertical section : and hence we ob-
tain from the principles laid down,

d z z Q9

-d7 + T = *Py>

dy _ i

dr " /tl^'

* Suppl. a la Theorie de V Action Capillaire, p. 10.

B 2 4-/3* being

4 Mr. Ivory on the Theory of Capillary Action, and

4|39 being a quantity to be found by experiment in tubes of
any given matter.

In the glass tubes of which barometers are made, 4 /32 is
very nearly equal to 496, and j3 to 7 ; and the value of z at the
surface of such tubes, or the sine of the inclination of the mer-
cury to the horizon, may be taken equal to 0*735. These
numbers, which are very convenient, accord nearly with the
results of the best experiments, or at least approach to them
within the limits of the errors to which all such experimental
determinations are liable.

Instead of the curve surface actually formed in the tube, I
shall now consider another similar surface, of which the linear
dimensions are increased fourteen times, or in the proportion
of 2/3 to 1. If ?/ represent the vertical ordinate of this new
curve, and y stand for 2/3r, we shall have these equations, viz.

dz z

dy z_

Exterminate y, and put t = -^- = /3r; then

, ddz dz z 4*

~dF~ + Tdt """ ~F ~ ^73^"

It may be proper to observe here, that the depression is the
value of the vertical ordinate, when % and x vanish together,

in which case also — = -r-. Hence the depression is equal
to — or — ,— , that is, to ■»-■ or -^-, when z and t are both

x dx t dt'

evanescent.

Next assume, z = qt cfa d \

c being the base of Napier's logarithms, and q a constant
quantity, which is no other than the depression. Substitute
the values of z and its fluxions in the last equation, leaving
untouched the radical on the right-hand side ; then,

dt

dt V 1 - z*

In the foregoing operations z and co are considered as func-
tions of t : but I shall now suppose that z is a function of /,
and co a function of the independent variables z and t. In the

last equation we must therefore write -£ + ~ • -^ for

at

the Depression of the Mercury in the Tubes of Barometers. 5

-£- ; which being done, and the value of -— - substituted, we
shall get this equation in partial fluxions, viz.

a . da da z a da 4 , *

dz dz t t ' dt y^/l—z* * '

to which we must join the value of ~^-9 viz.
I next write the equation (1) in this manner,

1 d . a z3 da t d.alz* 4

t z*dz dt 2zdz .V i_JK2

and assume, co = § + Az2 + Bz4 + &c.

§, A, B, &c. being functions of t. Substitute this value of co,
and expand the radical on the right-hand side of the equa-
tion ; then, by equating the coefficients of the like powers of
z, we shall get,

&c.
These equations give us,

* = *-4 +&c.

A = T-T +&c.

&c.

There is another consequence of the first of the equations (3)
which it is necessary to notice. Put

then we readily derive from the equation mentioned,
— i 3 dx -i,.y

and by integrating in a series, without introducing any arbi-
trary constants, which the present purpose does not require,
we shall get,

' Oi *<* a "I" 2». 32. 4a. 5 "*" ^C*

If

6 Mr. Ivory on the Theory of Capillary Action, and

If Z be the diameter of the tube, then t = /3r = -£- . Z, and
Z8 = 12*25 Z8: thus we have,

A= 1 + 6-125 Z2

+ 1 2-505 14

+ 12-756 /6

+ 7*819 18 (A)

+ 3-193 110

+ 0-931 Z12

+ &c.
In all tubes a few terms of this series will give the value of A.
with sufficient exactness.

Substitute the value of co that has been found in the equa-
tion (2); then

The quantities g, A, B, &c. evidently vanish when t is equal
to zero ; let us then inquire what are their values when t is
infinitely great When t is infinite, the equation ( 1 ) becomes
simply,

d.efiz* 4

Izdz

Vi

. 2 // 2-2 a/ l-*a

hence, co = - ,

or . = 2 + ^ + 1£ + &c.

Thus it appears that while t increases from zero to be infi-
nitely great, g, A, B, &c. increase from zero to the finite quan-
tities 2, £, F7¥, &c. The terms in the values of w, and of -^ 9

which are omitted, do not, therefore, affect the approximation
except in a very limited degree. The same conclusion may
be obtained another way; namely, by solving the equations (3)
in serieses of the descending powers of t. If this be done,

the parts of g, A, B, &c. independent of — , will agree with

the values above assigned.

Put 2 a for the value of w, or of — ^-, when t is infinite ;

7 zdt

then,

a = = i + __ + _ + &c.

Subtract ag from both sides of the equation before found, then,
JjL - ag = -J- - (a-1) g + Az9 + Bz4 + &c. :

and,

the Depression of the Mercury in the Tubes of Barometers. 7
and, by making,

B' = B"i^ = l^-|^ + &c.

we get, ^j - aq = -i- + A'z9 + B'z4 + &c.

The left side of this equation is equal to zero when t is in-
finite ; for a g then becomes 2 a. From this it follows that
A', B', &c. are evanescent both when t is equal to zero and
when it is infinite. The terms on the right side, except the
first, do not therefore increase indefinitely, but always remain
inconsiderable.

dz da

Assume,

az ff

then,

z3 B

2 = <r + — + &c.

a = 1 + ^ + TST + &c-

then, by dividing all the terms of the foregoing equation by a,
and introducing j for z9 we shall get,

.T dtt ds fedt

Next Put> Tdl - § " TIT '•' °" = 5C,/ = *•*

Let a' stand for the same function of s that a is of cr, or of
As: then, making,

A"=A'=-|^-^+&c.

B" = B' + 41=-l4i-wiS + ^

we shall get,

— = — . \ — + A" A2. 53 + B"A4.54 + &c.

sdt a { t

The fraction — must next be reduced to a series of they

a

powers of s. Now,

and,

8 Mr. Ivory on the Theory of Capillary Action, and
and, by division,

— =1 -tF.s*-tV.f-ka

a

P - S=l - — 4- — f + &c
^ - St ~ 8 + 96 l + **C'

_ 7» + a*«-9 _*_ _41_ 3 , &c

r m 128* 8 + 384 ^ K

The series for — must next be substituted, and, after having
multiplied and reduced, we shall get,

^i = -L + A'"s2 + B"V + &c.

sdt t

A'''=A''x* -P = -^+ £ + &c.

B'"=B"x4-P'-A"a2.P; = -^t + -^-^ + &c.

The principle of all this analysis lies in this, That, the left
side of the equation being equal to zero when t is infinite, all
the terms on the right side except the first must be evanescent
both when t is zero and when it is infinite. These terms,
therefore, remain always inconsiderable, _ and of no value ex-
cept in some tubes of small diameter. In order to exhibit the
equation in the most simple form possible, I finally put,

a! d s du

s u '

U = S + ^g" + &C.

s=u- — -&c:
and, by introducing u for s,

^- = — + A*u2 + B1^4 + &c.

udt t

A" -A" =-£+£ + &*

We must now integrate, and for this purpose write the last
equation in this manner,

XL

AiV XtV

= — a3+ 4-^ + &c.:

dt t t

then assume, ^- = q + Q w3 + Q' u5 &c

q being

the Depression of the Mercury in the Tubes of Barometers. 9

q being a constant, and Q, Q' &c. functions of t. By differen-
tiating,

d —
' t dQ « dQ! ,

d* d* d<

+ -^-(3Qms + 5Q'M5 + &c.)

war v

Substitute the value of — ~ , and equate the coefficients of the
two equal quantities, then

d.Qfi AiV

&dt t

and hence, Q = -^ + -^- + &c.

These coefficients being known, we have the value of the con-
stant q, which it is most convenient to arrange according to
the'powers of t, viz.

U , / tt3 W5 \

S, = T-<Cl8 + We)

1 Km

T 1024/

It has already been noticed that the depression is the value of
— when x and t are both evanescent. But it is obvious that

the vanishing fractions, — -, -, — have all the same limit :

wherefore q is the depression. It does not however belong
to the surface of the mercury in the tube, but to a surface
increased fourteen times in its linear dimensions. To get
the real depression we must therefore divide by 2/3. Now

t = |3r = — l9 and f = 12*25 I2 ; and we thus obtain the fol-
lowing formula for the real depression,

U ,/ M3 M5 \

* "" 49/ \ 192 + 1024/

V 2304 T 4096 )

The symbol u stands for a known function of s ; but in prac-
tice it will be most convenient to have q expressed immediately
New Series. Vol. 3. No. 13. Jan. 1828. C in

10 Mr. Ivory on the Theory of Capillary Action^ $c.

in terms of s. The necessary operations being performed, we
finally obtain,

_ 1 / jl _5f_ 119s7 393 s9\

2 — "497 V + 16 + 256 T 12288 + 65536 /

1 x v 192 T 512 y

The term multiplied by I3 being omitted, as it does not affect
the value of a in the fifth decimal place. In order to find s,
we must compute <r, for which purpose we readily obtain this
series,

_ jL *5 35 z> 137 & « .

r "" 16 128 12288 98304 +

and * being 0*735, we get <r = 0*70805. Then

•70805

A being computed by the formula (A).

As the diameter I decreases, s approaches indefinitely to cr,
and u to z ; so that, for tubes of an extremely small bore, the
depression is,

z -015

q~~ 49* ~ I
On the other hand, the diameter of the tube increasing, s de-
creases very rapidly ; and when the diameter is half an inch,
or greater, all the powers of s are inconsiderable, and we have
simply,

- s - '70805 _ -Q1445

? ~~ 49 1 49 i ' >. ~~ 1 . *

The first term of q in the formula (B) being the expansion of
a known function, it may be continued to any degree of ap-
proximation ; but the terms set down are sufficient even for
very small tubes. Suppose I = fa thus A = 1*01539, s =
•69736, and

Next, let I = i, then A = 1*5460, 5 = *1997, and
•1997

I have subjoined a Table of the depressions in tubes of va-
rious bores, and have added the experimental determinations
published by Lord Charles Cavendish ; by which it will be
seen that the agreement of the theory with experiment is very
satisfactory.

Depression

Mr. Nixon on the Heights of the Ingleton Fells. 1 1
Depression of the Mercury in the Tubes of Barometers.

Diameter.

Depression,
inches

Observed by

inches.

Ld. Cavendish.

0-05

0-29490

•10

•14026

0140

•15

•08628

•092

•20

•05811

•067

•25

•04077

•050

•30

•02919

•036

•35

•02110

•025

•40

•01534

•015

•45

•01117

•50

•008 15*

•007

•60

•00431*

•005

•70

•00228

•80

•00119

Dec. 14, 1827.

J. Ivory.

II. Heights of some of the principal Beds of Ingleborough Hill
and Moughton Fell, Yorkshire. By John Nixon, Esq.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
TN the xith volume of the Annals of Philosophy, I pro-
* posed to the geologist the measurement, by one barome-
ter only, of the heights and dip of strata known to be nearly
horizontal, and furnished at the same time the requisite in-
structions and tables. From, the numerous measurements of
this description made by me in different parts of the north-
west of Yorkshire, I beg to transmit you a selection of such
as may serve to determine the thicknesses and dip of the prin-
cipal beds of Ingleborough Hill and Moughton Fell.

Having carefully measured by trigonometry the heights of
the summits and other elevated parts of the hills, as well as of
different places at their bases, barometrical observations were

* In the Supplement to the Encyclopaedia, Article Fluids, there is an
arithmetical blunder in each of these numbers, as will appear by having
recourse to the formula. I was obliged to notice this point on a former
occasion, in order to stop the triumph of an antagonist, who has stuck to
my skirts for a period of at least six years, and who seems to have great
confidence in the efficacy of the adage, If one way will not do, another will.

C 2 regularly

12 Mr. Nixon on the Heights of some of the principal

regularly made in the course of the day at the lowest and
highest of the trigonometrical stations within reach, in order
to ascertain and correct the error of the measurements by
the barometer. When the station at the base could not con^
veniently be revisited, the observation at the superior one, to-
gether with their difference of altitude, served to determine the
fall or rise of the barometer.

The following list, comprising the chief beds of the Ingle-
ton Fells, is arranged conformably to their order of superposi-
tion.

A 1. Various beds of grits; Yorkshire paving grits (very si-
liceous), micaceous sandstones (flagstones and roofing
slates) with beds of shale, bearing on some hills three
seams of coal.
2. Very rough millstone grit (240 feet thick on Pen-y-gent).

B. The top lime of the Ingleton Fells and the upper part

of Wharfdale. It is of very variable thickness, and
contains lead in Dod and Settron Fells.

C. 1. A thick bed of various shales with grits and flagstone

beds interstratified. It contains a seam of coal on
Noughtberry hill at the Garsdale, King's-cross, and
pits.

2. Various beds of paving grits, flagstone beds, and shales.

In the lower half of this section are two or three very
thin beds of limestone.

3. Yorkshire paving grit and shale.

D. 1. Limestone shale containing beds of Dent black marble.

2. Gray limestone without shale, &c. Lead has been found

in this bed south-west of the summit of Ingleborough,
and is at present procured on the north-west side of
the hill.

3. (In some places) a very thin bed of clayshale containing

a slender seam of coal.

E. Grauwacke, (clayslate, &c?)

Heights of different points of these sections, ninth their bearings
and distances from the summit of Ingleborough.

A. 1 & 2. Height of the station on the loftiest point of Ingle-

borough, 2374 feet above the Irish Sea.

B. Height of the upper surface of the top lime on the sum-

mit of Simon Fell (part of Ingleborough) one mile
E.N.E., 2125 feet

C. 1. Height of the under surface of the top lime (at a spring)

half mile E.S.E., 2062 feet; — (at a spring dividing
Simon Fell from Ingleborough) half mile E.N.E.,
2061 feet;— (on Simon Fell) li mile E.N. E., 2035

feet.

Beds of Ingleborough Hill and Moughton Fell, Yorkshire. 13

feet. Height of some quarries of grit slate, £ mile S.,
2090 feet;— (on Simon Fell, east side), l£ mile E. by
N., 1968 feet.

C. 2. Height of the upper surface of a thin (15 to 20 feet) bed

of limestone on Simon Fell, If mile E., 1608 feet.
Height of another bed of limestone near the last, 1479
feet.
3. Quarry of thin grit slate, If mile E., 1427 feet.

D. 1. Height of the upper surface of the Dent marble bed,

1 J mile S. by W. (in the direction of Newby), 1467
feet;— 1£ mile S. by E., 1368 feet;— 1* mile S.S.E.,
1395 feet;— (on Simon Fell) Jf mile E.S.E., 1350
feet ; — (near Selside) 2 miles E., 1 270 feet ; — (on Park
Fell, part of Simon Fell,) 2 J miles N.E., 1166 feet.

E. Height of the grauwacke (in the, Ribble under New-

Inn Bridge near Harton), 4 J miles E.S.E., 740 feet; —
(near the blue slate quarries at the south-east end of
Moughton Fell) 4j miles S.E., 1116 feet. (This is
the loftiest point of the denuded grauwacke.) At
Hunterstyle (near Cromack) 3 miles S.E., 1047 feet;
— (under the huge grauwacke boulders near Austwick)
3| miles S.S.E., 705 feet; — (in Claphambeck, a patch
a little below the recently discovered cave in the lime-
stone,) 3 miles S. by E., about 600 feet; — (in the Greta,
3 miles above Ingleton,) 1 J mile N.W., about 750 feet.

Dip of the beds above the grauwacke. — A comparison of the
heights of C. 1. and especially of D. 1. to the south and north
of the station on Ingleborough, indicates the dip of these beds
to be northerly. Near Newby the height of D. 1. is 1467
feet; and on Park Fell, 3§ miles to the N.E. 1166 feet. A
fall of 300 feet in a distance of 19,360 feet is equal to a dip
of 0° 53' 16"; but as the line of maximum depression is pro-
bably more to the north, its angular value will exceed 1°. —
(At the marble quarries east of Dent and N.N.E. of the sta-
tion, the height of this bed was found to be 1030 feet#.)

Dip of the grauwacke beds. — In the Greta, 80° N.E. ; — at
Hunterstyle, and at the south-east end of Moughton Fell,
45° S. by E. ; — on Swartmoor, 80° northerly.

Thicknesses of the beds. — A. 2. and perhaps a portion of 1.
about 234 feet on Ingleborough.

B. The top lime is about 80 feet thick on Ingleborough
and Simon Fell.

* Visually estimated the dip appears to be most rapid to the south of
the summits of Ingleborough and Whernside.

C. On

14? Mr. Bakewell on the Thermal Waters of the Alps.

C. On Ingleborough, Simon Fell, and Park Fell, about 700
feet thick.

D. As the upper surface of the grauwacke, &c. apparently
diversified with hill and dale previous to the deposition of the
superincumbent beds, is not a regular plane, the thickness of
this section must vary in conformity. In some parts of Wharf-
dale it is very probably upwards of 1200 feet in thickness.

I have the honour to be, Gentlemen,
Your most obedient servant,
Leeds, Dec. 8, 1827. John NlXON.

III. On the Thermal Waters of the Alps. By R. Bakewell, Esq.

To the Editors of the Philosophical Magazine and Annals.

Gentlemen,

Yl^HEN we approach a range of lofty mountains, like that
J " of the Pennine Alps, and observe the calcareous strata
on the outer part of the range, bent and contorted in various
directions ; when we further observe beds of limestone and
puddingstone alternating and placed in an elevated position,
as we advance to the central part of the range ; and that the
beds of granite in the central part are frequently vertical ; we
feel assured that their present contorted or vertical position
is not the original one. The opinions of geologists have been
much divided respecting the cause or causes that have elevated
mountains and given a vertical position to beds that once
formed the bottom of the ocean. Those who maintain that sub-
terranean heat has expanded and broken the solid crust of
the globe, and has raised from vast depths the ancient bed of
the ocean, appeal to a cause that is known to exist, and which
seems sufficient to explain most of the various appearances
which alpine regions present.

In opposition to this theory, it is asserted that there are no
remaining vestiges of the action of subterranean fire in the
Alps ; — but this I am convinced is erroneous. It is true that
from near the source of the Rhone, to the foot of the Little
St. Bernard, there does not occur any known rock of a vol-
canic character, with the doubtful exception of some rocks in
the valley of Sass, and in the Valorsine. I have examined
various parts of this range on the northern side of the highest
mountains in the Alps, along a line of one hundred and twenty
miles ; and though I could discover no indications of the ac-
tion of subterranean heat in the rocks themselves, I was greatly
surprised to observe, the numerous thermal springs that are

abundantly

Mr. Bakewell on the Thermal Waters of the Alps. 15

abundantly gushing out at the feet of the primary mountains,
near the junction of the mica-slate, or the dark schist passing
into mica-slate with the lowest calcareous beds of that vast
series of limestone strata, which forms the outer ranges of the
Alps. Numerous as these hot springs are on the northern
side of the Alps, and not un frequent on the southern side also,
it appeared to me remarkable, that they had hitherto been re-
garded as isolated phenomena ; and their geological position
had not been noticed. It is true, some of the warm springs in
the Valais and in Savoy had been long known and visited,
but the greater number have been discovered since Saussure
published his Voyages dans lesAlpes; and it appears probable,
that they would every where be found near the junction of the
primary and secondary rocks, were it not for eboulements that
have covered them with a heap of ruins, or that torrents from
the glaciers have mixed with them, and reduced their tem-
perature. Since I visited Savoy in 1821 and 1822, another
considerable warm spring has been discovered near the village
of Chamouni, at the foot of a glacier; and in 1820 several
thermal springs were discovered in that branch of the Alps
which extends to Grenoble.

I shall here briefly enumerate the principal known thermal
waters in the Pennine Alps, and add some observations and
inferences, which I trust will be acceptable to several of your
readers.

Naters in theHaut Valais. — The warm spring rises under
a rock of mica-slate on the north side of the Rhone. The tem-
perature when I visited the place was 86° Fahrenheit, but it
is variable from the intermixture with surface-water. At the
time of the great earthquake of Lisbon in 1755, the mountain
above the spring, I was informed, opened and threw out a con-
siderable quantity of hot water.

Leuk in the Haut Valais^ — situated in a deep gorge on the
northern side of the Rhone. There are twelve springs, varying
in temperature from 1 1 7° to 1 26°. These springs have been
long known, and are visited by patients from various parts of
Europe.

The Valley of Bagnes in the Bas Valais. — The warm
springs in this valley were buried under a heap of debris from
the fall of part of a mountain, which destroyed the baths, the
village of Bagnes and one hundred and twenty inhabitants in
the year 1545. The name of the valley is obviously derived
from the baths. The temperature of the water unknown.

Chamouni. — The thermal waters at this place have been
discovered since I visited Chamouni in 1821. I have received
no account of the temperature; baths have recently been

erected.

16 Mr.Bakewell on the Thermal Waters of the Alps.

erected. The situation is near the junction of mica-slate with
the lowest beds of secondary limestone.

St. Gervaise, — situated on a deep gorge on the north-east
side of Mont Blanc. The thermal water rises near the junction
of mica-slate and limestone. The temperature 94° to 98°.
This spring was discovered about the year 1806 : it is very co-
pious. Baths have recently been erected, and are much fre-
quented.

Aix les Bains in Savoy; the temperature from 1 12° to 117°.
The thermal waters rise in great abundance from two springs
situated at the foot of a lotty calcareous mountain, and are
near the bottom of the great calcareous formation that forms
the outer range of the Alps : there are also numerous hot
springs in the vicinity, which the Sardinian government will
not allow to be opened. Of the mode of douching at these
baths, I have given a particular account in the first volume
of my Travels in Savoy, Switzerland, and Auvergne. The
thermal waters of Aix were well known to the Romans.

Moutiers in the Tarentaise.< — The thermal waters rise in
great abundance from the bottom of a nearly perpendicular
mass of limestone. From the position of this rock, and its
connection with those on the opposite side of the valley, in
which the hot springs rise, I have no doubt that it is the lowest
calcareous bed in that part of the Alps; but its junction with
mica or talcose slate is not here seen. The thermal waters
of Moutiers contain about two per cent of saline matter, chiefly
common salt. The process of extracting it, I have described
in the Philosophical Magazine, vol. lxiii. p. 86.

Brida in the Tarentaise, — The thermal waters of Brida were
noticed in the ancient records of Savoy, but they were covered
during a sudden inundation of the valley, and their situation
was concealed for many years. In the summer of 1819, an-
other inundation, occasioned by the breaking down of the side
of a glacier, laid open the spring again. The rock from which
the spring rises, is a greenish talcose slate passing into mica-
slate: it is in junction with limestone. The temperature of
the water is from 93° to 97° Fahrenheit. The geological po-
sition of this spring is more obvious than that of any of the
other thermal waters which I visited, being situated close to the
steep bank of the river Doron, where both the rocks are laid
bare. There are some warm springs on the opposite bank of
the river which rise in .limestone ; but the temperature is lower,
owing to an intermixture with common water.

Saute de Pucelle, or Virgin's Leap. — There is a very
copious thermal spring rising from the bottom of a perpendi-
cular rock near the Isere, between the town of Moutiers and

St. Maurice

Mr. Bakewell on the Thermal Waters of the Alps. 17

St. Maurice at the foot of the Little St. Bernard ; but owing to
the difficulty of access to it, I did not visit it, to ascertain its
temperature.

Beside the above thermal waters in the Pennine Alps, va-
rious thermal springs were discovered in the adjacent Alps,
near Grenoble, in the year 1 820 : and it seems probable, that
a series of these springs might be found, were proper search
made, extending westward to the thermal waters of the Py-
renees ; for in this line we should approach the southern bor-
der of the volcanic district of France. On the Italian side of
the Pennine Alps there are also thermal waters : the warm
baths of Cormayeur and of St. Didier are situated almost im-
mediately under the southern escarpment of Mont Blanc. I
was prevented by the weather from examining the geological
position of these springs : their temperature is stated to be 94>°
of Fahrenheit *.

The inference that may be drawn from the geological posi-
tion of these thermal waters near the junction of the calcareous
beds with mica-slate, or the dark schist which passes into mica-
slate, is, that the waters do not rise from the upper strata, but
spring out of the lower or primary rocks ; and as they break
out near the feet of the highest range of the Alps, that extend
from the northern side of the Simplon through the Valais
-and Savoy into France, we may with much probability infer,
that these mountains are situated over or near to one com-
mon source of heat, by the agency of which they were ori-
ginally elevated, and their beds placed in a position nearly
vertical. This inference is in some degree supported by the
well attested fact, that the districts where the hot springs are
situated are subject to great and frequent convulsions, parti-
cularly in the upper valley of the Rhone. In the year 1755
and 1756, at Brieg, Naters, and Leuk, the ground was agi-
tated by earthquakes every day from the 1st to the 27th of
February ; some of the shocks were so violent, that the
steeples of the churches were thrown down, the walls split,
and many houses rendered uninhabitable : many of the
springs were dried up, and the waters of the Rhone were ob-
served to boil. At three different times the inhabitants aban-
doned their houses and fled for safety into the fields. It has
been before mentioned, that the mountain above the warm
spring at Naters opened during the time of the great earth-
quake at Lisbon, and threw out hot water ; at the same period

* Nearly all the thermal waters in the Alps emit sulphureous vapours,
and are slightly saline, except the waters of Leuk, which have the highest
temperature, and are inodorous and free from saline impregnation.

New Series. Vol. 3. No. 13. Jan. 1828. D the

18 Mr. Bakewell on the Thermal Waters of the Alps.

the warm saline springs at Moutiers ceased to flow for forty-
eight hours. When the water returned, the quantity was
said to be increased, and the saline impregnation was weaker.
Former and more formidable agitations of the earth are re-
corded in the Haut Valais, particularly in the district where
the principal hot springs are situated. The last earthquake of
consequence in the Valais took place in January 1 803.

I am informed that several of the retired valleys on the
Italian side of the Alps, at the foot of the central chain, are
subject to earthquakes, during which the ground has opened
or sunk down in various parts, though these effects have been
too local to excite attention at a distance. From these facts
it seems as reasonable to infer that the thermal waters of the
Alps owe their high temperature to subterranean fire, as that
the hot springs in countries that have formerly been volcanic,
derive their warmth from an internal unextinguished, but
quiescent source of heat. No person who has attentively ex-
amined the lofty granitic plain to the west of Clermont Fer-
rand in France, and observed the granite in various parts
pierced through by ancient volcanos that have poured cur-
rents of lava over its surface, or seen other parts where the
granite itself has been changed by its contiguity to subter-
ranean fire, or upheaved and intermixed with volcanic rocks ; —
no one, I say, who has observed this, can doubt that the hot
springs of Mont Dor and Vichy derive their high tempera-
ture from a source of heat situated beneath the granite moun-
tains, though ages have passed away since the volcanos of that
country have been in an active state : and the only proof of
the present existence of subterranean fire in Auvergne, is to
be found in the hot springs themselves*. Nor can any ade-
quate reason be assigned for attributing the high temperature
of the thermal waters in the Alps, to any other cause than to a
source of subterranean fire under these mountains, — a cause
which is sufficient also to have produced their original eleva-
tion. It is however proper to state, that in some of the moun-

* I visited the extinct volcanos of Auvergne in the spring of 1822; and
in 1823 I published an account of my observations in the second volume
of my Travels, accompanied with cuts, and a section and outline of the
country near Clermont, which, as far as I know, was the first attempt to
render in this manner the structure of this volcanic district intelligible to
the general reader. I discovered the bones of large mammalia in the fresh-
water limestone under the volcanic tufa of Mount Gergovia, — a fact at that
time unknown to Messrs. Brongniart, Cordier, and Brochant, to whom I
mentioned it on my return through Paris. I was therefore surprised to
see it intimated in the Quarterly Review for October 1827, that Dr.
Daubeny and Mr. Scrope were the only Englishmen who had given an
account of the extinct volcanoes in France.

tains

Mr. Herapath on the Integration of Differential Equations, 19

tains of the Alps the temperature may be slightly increased by
a cause hitherto unnoticed. In the upper part of the secondary
formations covering the granite, there are beds of gypsum,
and this gypsum is anhydrous ; but when exposed to air and
moisture, it combines with water, and passes to the state of
common gypsum : and during this combination we may sup-
pose heat to be evolved, but the process must be extremely
slow, and the heat evolved must be totally inadequate to raise
the temperature of powerful streams to 1 26°. Saussure found
the temperature of the water in the lower part of the salt
mines of Bex, which are situated in the vicinity of gypsum,
to be four degrees of Reaumur higher than the mean tempe-
rature of the earth. It is not improbable, though Saussure
was not aware of the circumstance, that this small increase of
temperature in the mines of Bex might be partly owing to the
combination of water with gypsum : however, an increase of
temperature it is well known, is observed in deep mines, far
removed from the gypsum formation.

In reply to what I have advanced respecting the thermal
waters in the Pennine Alps, it may be said that few thermal
springs have been yet discovered in the northern range of the
Alps which form the Bernese Oberland ; but the difference in
the geological structure of the two ranges will, I conceive, be
sufficient to explain why hot springs are more rare in the lat-
ter, than in the southern range. Most of the highest moun-
tains in the Bernese Alps are covered with secondary strata ;
and the valleys are chiefly excavated in these strata, or in enor-
mous beds of sandstone and conglomerate, that form a thick
intervening mass between the surface and the primary rocks,
sufficient to obstruct the rise of thermal waters ; for it has be-
fore been stated, that all the thermal waters in the Pennine
Alps issue from the primary rocks, or near their junction with
the lowest calcareous strata,

Hampstead, Dec. 8, 1827. Robert Bake well.

IV. On the Integration of Linear Differential Equations having
Constant Coefficients and last Term any Function of the In-
determinate Quantity x. By John Herapath, Esq,

[Concluded from vol. ii. p. 425.]

Y^E shall now proceed to a few exemplifications of the
J * formulae.
Ex, 1. Suppose n = 2 then (17) becomes

y = er"{c1+fe(r-r')x{c+fXe-r*

D 2 the

20 Mr. Herapath on the Integration

the same as we have given in vol. ii. p. 420 ; for A = — r— r,
by the well-known property of equations.
Ex. 2. Putting n = 3 our (17) gives

■$m*»\ c>+ />'-'* { Cl+fe^-ri)x{ c+pie-" (19)

just as we should have it from (6) by putting for A its value
— r •— r, — r2 and for r,, which is aToot of the reduced qua-
dratic from the equivalent cubic, rl — r found by (16). The
solution however here given, exhibits to advantage the great
superiority of our general investigation. Had we been con-
tented with the process of successive eduction at first adopted,
it would have been almost impossible to develop the simple
and elegant law which reigns in the exponents.

Ex. 3. To carry on the reduction of the general formulae
to differentials of the 4th, 5th, &c. orders would be super-
fluous, the application being so very obvious. Let us there-
fore suppose that any two of the roots in (19) as rt and r2 are
equal. In this case because dx} dx~, are understood as factors
respectively to ctn c, (19) is

(r-r )x
r x . tjc , ce v 2y

or v = cae* + cxxe * + — — -r- »

supposing X = 0.

Ex. 4. Let us now imagine that all three roots are equal.
Our (19) under these circumstances, it is evident gives

rx . rx . cx*e . rx AY „—rx

y = c2erx -f ckxerx -f — - — + e J *&e ,

or when X = 0

y = c2erx + clxerx + \cx2erx>

in which as before all three arbitrary constants appear. We
have therefore the solutions directly with the full complement
of arbitrary constants without any of the refined artifices with
which D'Alembert found it necessary to aid the half-guessed
imperfect solutions of Lagrange.

Demonstration of the Completeness of the preceding general

Solution.
Because the roots r, r, , r2, r3, . . . will admit of a great
number of combinations of their differences, besides those we
have assumed, it may reasonably be imagined that our general
formula (17) or (18) not containing the whole, cannot be com-
plete. Our attention will, therefore, now be directed to the
consideration of this point. The formula most convenient for

this

of Linear Differential Equations, 21

this object is (18), which is precisely the same as (17) but un-
der a different form.

Now that part of (18) which consists of the sums of the ex-
ponentials clearly remains the same, whatever commutation
takes place in the order of the roots : we must therefore apply
our attention to the part affected with the successive integral
signs. Taking the lowest integral sign, and integrating by
parts,

/,-»x---r"Jx+2- + ^- + -£+.-..

of which the general term is

z+1

Hence employing the sign <y— to signify produces, gives, &c.

r +]

And because the part under the integral sign is of the same
form as before, the general term of the quantity will be

— r,rr ,2s -^

6 «+i *+i- Therefore
ri r

J J ru*+1r«+I

Pursuing the same course we at length have

(r — r )x

xr r> Cr — r )x /» —rx

e n~l/e n-2n-i ....Je X

<T

*+l *+l x+1
r . ri ..../ n— 1

taking no notice of the algebraic sign. This may be regarded
as the general term of the last number, and hence as the in-
dex of the form it assumes when all the integrations have been
executed. But this term wrould manifestly have the same value
and form in whatever order the roots r, rl9 r2, . . . be taken;
and therefore the member itself would have the same value
and form, and consequently the solution we have given com-
prehends all the varieties which can arise from the different
arrangements that may be given to the roots, and is therefore
the complete solution.

Failure of Lagrange's Method.

Having established the accuracy and completeness of our
own method, we will now transfer our attention to that pro-
posed

22 Mr. Herapath on the Integration

posed by Lagrange, which has been received and relied on as
correct by the scientific world for nearly half a century. That
we may treat this method with perfect justice and fairness,
we propose to work out as directed the identical example
with which it is in all the works of the present day illustrated,
and then show its absurdity by direct differentiation. The
equation usually taken is one of the third order,

d3y + Ad2y + Bdy + Qy = X. (20)

Suppose erx, er*x, e*2*, or yl9 y2f y3be the three partial solu-
tions when X = 0 ; then if we take

y = perx +p1eTlX + p2er*x or = py, + p,y2+p2y3

p, pl , p2 being instead of arbitrary constants arbitrary func-
tions of x, these arbitrary functions may, it is conceived, be
subjected to certain restrictions, and yet satisfy the conditions
of (20). For instance in the value of dy in

dy=pdy, + pxdy2 + p2dy3+ytdp + y2dpl -ty3dp2

the first three terms are the same as would result if p, px , p29
were constant coefficients ; and Lagrange therefore assumes
that he may put

y, dp + y2 dp, + y3 dp2 = 0
as one condition for determining the functions p9 px , p29 which
leaves dy = p dy, + p, dy2 + p2 dy3

This being a second time differentiated becomes

d2y = pd2yt +pld*yi + p2d% + dyxdp + dy2dp, + dy3dpi

which for similar reasons Lagrange again decomposes into

d2y = pdzy, + pxd*y2 + p2d*y39

and dy, dp + dyzdpt + dy3dp2 = 0

Differentiating once more we have

d3y=pd?yv + pvd3y2 + p2d3y3 + d2y, dp + d2y2dpx + d%dp2

Substituting the several values of y9 dy9 d2y9 d3y for these
quantities in the proposed equation there results

p {d3yf + k#yx + Bdy, + Cyx}

+ Pi Kj/2 + Ad*y2 + Bdy2 + Cy,}

+ p, {d3y3 + Ad2y3 + Bdy3 + Cy3}

+ cPy,dp + (PyAPi + d*y3dp2 = X

But because the parts multiplied by p, px , p2 are assumed

to

of Linear Differential Equations. 23

to satisfy each, the equation proposed deprived of its last term
X they separately vanish, and leave

d?yxdp + d2y2dpx + d2y3 dp2 = X which, together with
dyxdp + dy2dpx + dy3dp2 = 0
and Vidp+y2dpt + y3dp2 = 0

furnishes three several equations from which two of the quan-
tities dp, dpx , dp2 may be eliminated, and the value of the
third p9 pt , p2 be obtained by a simple integration. And this
performed with the others will afford us the values of p, pt9
p2 ; and of course, according to Lagrange, the complete solu-
tion of the differential equation.

In order to investigate this with every possible regard to
generality, let as before r, r, , r2 be the roots of the equivalent
algebraic equation

r3 + Ar2 + Br + C = 0;
and let yx = erx, y2 = er,x, y3 = er%x

which give dyx = rerx, dy2 m rxeriX9 dy3 = rier2X
and d2yl = r2erx, d2y2 = r2er<x, d% = r*er*x

Hence the three equations give

r2erxdp + r*er**dpt + r2er*xdp2 = X

rerx dp + r1eriXdpl + r2er'2Xdp2 = 0

erxdp + er>xdPl + er*xdp2 = 0
from which eliminating dp2 we obtain

(f-rr*) erxdp + (r?-rxr2) er*x dp, = X
{r-r2)er*dp +(rl-r1)er*xdpl = 0
and then eliminating dpx from these

(r2—rr2—rrx + rxr2)erxdp = X

c+/Xe-rx

or P == •

r r^—rr2—rrl-\-rlr2

In the same way the other coefficients pl9 p2 are found; but
as this one will answer our present purpose, we shall not trou-
ble ourselves to determine them. From this coefficient we
obtain,

pyx = acerx + aerx f^e~rx
putting a for the numeral reciprocal. This is one value that
must satisfy the proposed equation. Now in this value r

being

24? Mr. Herapath on the Integration

being a root of the equivalent algebraic equation, the part

acerx must vanish when the successive differentials of the
value are taken and respectively multiplied by A, B, C to an-
swer the conditions of the given differential.

Therefore the part aeTXJ Xe~rx must also satisfy the dif-
ferential, that is

Caerx/Xe-rx= CaerxfXe-rx

Bd.aerxfXe-rx = BarerxfXe-rx + BaX

Ad*.aerxfXe-rx=Aar*erxfXe-rx+AarX + AadX

d?.aerx/Xe-rx= at*erx ' fXe~rx + ar2 X + ard X + ad2X
or (r2 + Ar + B) aX + (r + A) adX + ad2X = X

the other four terms vanishing in consequence of r being a
root. Putting for A its value = — r — r, — rti and for B its
value =rrI + rr2 + rtr2 according to the theory of algebraic
equations, and restoring the value of a, the above equation
becomes

r^X — (r, + r2)dX + d2X = {f—rr2 — rrx -f rxr2) X
or d*X - (r, + rJdX -(r2 - rr.-rr,) X = 0

a linear equation of the second order with respect to X. This

equation therefore limits X to a particular form (namely ebx
b being determined from b2 — (r, + r2) b = r2 — r?\ — rrx)y
whereas it ought to remain indefinite. Consequently the so-
lution which^ requires this limitation cannot be a solution to
the equation proposed having X unlimited.

In looking round for the cause of Lagrange's failure we
perceive that it must arise from the limitations which his equa-
tions of condition introduce. He assumes that the functions
p, px , p2 are arbitrary, and hence thinks the limitations he has
given them will not affect the accuracy of the solution. If,

however, we consider that erx is not a solution of the equation
proposed, but of this equation deprived of its term X, it is ob-
vious that the functional factor p has certain conditions to
fulfil, namely, to render the solution erx of

d3y + Adzy + Bdy + C y = 0
a solution of the equation

d3y + Ad*y + Bdy + Cy = X
and if at the same time we consider that the difference be-
tween the solutions of the former and latter equation depends

entirely

of Linear Differential Equations. 25

entirely on the influence of the quantity X, it is clear that p
which transforms one solution into the other must also de-
pend on X, and for this reason cannot be arbitrary. Con-
sequently the very first assumption of Lagrange is erroneous,
and the arguments which he founds on this assumption pro-
ductive of error. It is most extraordinary that mathemati-
cians have for upwards, I believe, of half a century suffered this
to pass unobserved and uncorrected ; and, as if to crown their
conduct with absurdity, have actually praised Lagrange's me-
thod as the most perfect and general that could be given.

Verification of our own Solution.

The simple manner in which we have, step by step, deduced
our general formula of solution cannot, we presume, leave a
doubt as to its truth. But since we have shown the failure of
Lagrange's method by differentiating one of his examples, it
is but fair that we should apply the same test to a similar ex-
ample given by our own method.

It is obvious by (12) and (16) that

— xR x(r — r )

dXt = Xt_ie <~2 =Xf_xe n-2 n-1

and in the equation just above (17), that

xr

Therefore putting n = 3 we have

dy=r2er*xX3 + er>xX2

d*y=r2er*X, -f (r2 + r^e^X, + erx X

^=;Y^X3 + (raH^^

If we multiply these values ofd2y, dy, y by A(= — r2— r, — r),
B ( = i\rt + r.zr + r, r), C (= r2r, r) respectively, it is clear,
r2 being a root of the equivalent algebraic equation, that
the sum of the left-hand column will = 0. It is also obvious
from the value of A, that the two terms which constitute the
third column = 0. But the numeral part of the second co-
lumn, putting for A and B their values, is plainly

r* + rirl + r* — {r2 + rt) . (r2 + rx + r) + r2?\ + rzr 4- r,r=0

So that all the terms vanish except X, and leave X = X as it
should be.

We might here develop some other properties of our so-
lution, both as it regards integration and even the doctrine of
algebraic equations; and we might show how to extend a
similar method to linear equations having variable coefficients ;
but these things we think it better to reserve for another op-

New Series. Vol. 3. No* 13. Jan. 1828. E por-

26 Mr. Riddle on the Occultation of $ Scorpii.

portunity, more especially as we contemplate investigating the
latter subject on much more general principles than we have
employed in that of which we nave been treating.

, John Herapath.

Errata in the preceding part of this paper, printed in the last Number of
the Philosophical Magazine and Annals.

Page 424, last line, for R*_2 read Rt_2

425, in (16) for r + Rt + R2 read r + R + R, + R2

425,in(18)for exrn"1 read e*r n-l

V. On the Occultation of ft Scorpii, September 25, 1827. By
E. Riddle, Esq.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
rT,HE double star |9 Scorpii has been occulted almost every
■*• lunation during the present year ; but only the occupa-
tions in May, July, and September, occurred at such times as
admitted of their being seen in this country. I happened to
see that which took place on September 25th, at about six
o'clock in the evening; and as it was not seen by any other
person that I have met with, and was attended by some cir-
cumstances which I believe were unexpected, it seems desire-
able to ascertain, if possible, whether it was witnessed by any
one else in this neighbourhood, and to what extent the phe-
nomena differed from those which I observed.

Perhaps the insertion of this notice in the Philosophical Ma-
gazine may elicit a communication on the subject from some
gentleman who observed it with means superior to mine, as I
had merely a 30-inch achromatic, with a power of about 80.

The stars are about 14" apart, the smaller one the more
northerly; and though the elements of the occultations of both
stars are given in the Nautical Almanac, and both marked
there as visible at Greenwich, where I observed, which was in
lat. 51° 28' 53" N., long. 8" W., and about 120 feet below the
level of the axis of the transit instrument, at the Royal Obser-
vatory, the larger star was not occulted at all. When I first
turned the telescope on the moon, I saw both the stars very
distinctly, a little to the eastward of the southern enlightened
horn. The smaller one vanished behind the dark limb, a lit-
tle before it reached the horn. I expected every instant as the
laro-er one approached the enlightened edge, that it would be
occulted by some of the luminous protuberances near the horn;
but it glided steadily along, appearing in my telescope, nearly
if not quite in contact with the enlightened limb. It never

was

Mr. Teschemacher on the Crystalline Form of some Salts, 27

was invisible,- I never lost sight of it, till I saw both it and the
smaller one quite clear of the moon.

But the larger one was so nearly occulted here, that it must
have been quite so at a very small distance to the north-east-
ward ; and it would be curious, and not quite useless as con-
nected with the question of lunar parallax, if it should be
found that the occultation was observed where the star's ap-
parent path was an accurate tangent to the moon's limb.
I am, Gentlemen, yours, &c.

Greenwich Hospital, Dec. 10, 1827. E. RlDDLE.

VI. On the Crystalline Form of some Salts. By Mr.
E. F. Teschemacher.

To the Editors of the Philosophical Magazine and Annals.

Gentlemen,

{OBSERVING a paper in your Journal of December last,
^^ on some new double chromates, I beg to remark, that
during an investigation which I made last winter, of some of
the combinations of chromic acid with the different metals, I
met with the same salts ; and by an examination of their cry-
stallographical character arrived at the same results as Mr.
Henry Stokes, with regard to the combinations of sulphate
of nickel and sulphate of zinc with chromate of potash, which,
as they have not been before described, it may be interesting
to detail.

Struck with the similarity in form of the crystals deposited
by the solution containing nickel with some crystals of sul-
phate of nickel and potash given to me by Mr. H. J. Brooke,
and described by him in the Annals of Philosophy, New Series,
for December 1823; I subjected some very brilliant crystals
of this new salt to an examination by Dr. Wollaston's reflec-
tive goniometer, which gave the following measurements.
— Primitive form an oblique rhombic prism.

V

p

i
M !
\ ;

Sulphate of Nickel and
Potash.

P on M or M' 102° 15'
P on eoxe*. 15* 32
M on M' . . 109 10

Chromo-sulphate of Nickel
and Potash.

P on M or M' 101° 37'
P on e ... 154 30
M on M' . . 107 37

A small difference in the meeting of the angles of these two salts

E 2 will

28 Mr. Teschemacher on the Crystalline Form of some Salts.

will be observed. From this similarity of form I concluded
this new salt to be a sulphate of nickel and potash combined
with a small quantity of chromic acid, which is now further
confirmed by comparing the analysis of the former salt made
by Mr. Cooper, and inserted also in the same paper of Mr.
H.J.Brooke, with that of the new salt made by Mr. Stokes.

Sulphate of Nickel and Potash.
Sulphuric acid . . 18*95
Oxide of nickel . 8*77

Potash 10-24

Water 12-04

50-

Chromo-sulphate of Nickel and Potash.
Sulphuric acid . . 18*260
Oxide of nickel . 8-200

Potash 9-862

Water 12-700

Chromic acid . . 0-978

50-

Primitive form of both, an oblique rhombic prism.
Chromo-sulphate of Zinc and Potash. Sulphate of Zinc and Potash.

P on M .... 101° 4-7' P on M . . . 102° 20'

P on e 154 31 M on M' . . 108 40

M on M' . . . . 108 45

This latter salt, the sulphate of zinc and potash, I formed
by adding pure potash to a solution of sulphate of zinc, sepa-
rating the precipitate, and allowing the clear solution still
containing oxide of zinc to crystallize. Not having made the
analysis of this latter salt, I am unable to compare it with
the analysis of the chromo-sulphate of potash and zinc as
given by Mr. Stokes.

These are further instances in which the combination of
minute quantities of matter vary the measure of the angles of
crystals, and which show the value of Dr.Wollaston's gonio-
meter in immediately detecting their existence.

I take this opportunity of sending you the measurements of
the crystals of two other substances, which I am not aware have
been previously given.

Hematin.

Primitive form a square prism.

1\

Pon M .
MonM'

Moni.
M on cx .

c2 .

c3 .

90°

90
135

122 10'
118 15
116 15

M

¥

This substance was found in the interior of a piece of log-
wood ready formed in a crystalline mass; I merely dissolved

the

Mr. Bevan's Remarks on Mr. J. Taylor's Rain-gauge. 29

the crystalline part in spirit of wine and obtained the hematin
in regular crystals.

Tartrate of Strontian. Primitive form an oblique rhombic prism.

P on M .... 92° 35'

M on M' . . . . 125 20

This salt was formed by adding a solution of tartrate of
potash to one of nitrate of strontian.

On platina wire with borax before the blowpipe the chrorao-
sulphate of nickel and potash gives a transparent light brown
glass ; the chromo-sulphate of zinc and potash a transparent
yellowish-green one. Yours, &c.

Bamsbury Park, Dec. 10, 1827- E. F. TESCHEMACHER.

VII. Remarks on Mr. J. Taylor's Rain-gauge. By B. Be van, Esq.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
¥N the last Number of your Magazine, at page 406, is a de-
* scription of a rain-gauge by Mr. J. Taylor, in which a re-
ference is made to my selt-registering gauges, as described in
a former Number *.

From the tenor of the paper, it may be supposed that the
gauge invented by Mr. Taylor was an improvement upon
mine. Now setting aside as far as may be, a partiality for our
own inventions, I am not able to see in what respect it can
be denominated a registering instrument : it may serve, and
doubtless will, to point out the total quantity collected in the
intervals of inspection, and so will the old simple floating in-
dex ; but neither of them will show the time of commencement,
the duration, and the rate of raining, for each shower, — which
was effected by my gauges for some years : and although it
was necessary to wmd up the clock, and replace the paper on
the cylinder once a week, it could not be considered any very
objectionable trouble, considering the information it afforded ;
the whole operation might possibly occupy about five minutes,
and as this occurred but once a week, it was not quite equal
to the proportion of one minute per day.

I am aware, that to a gauge, such as is described by Mr.
Taylor, additional apparatus might be applied, so as to ren-
der it a proper registering instrument ; but at present it does
not seem to possess any great superiority to the common float-
ing gauges.

* See Philosophical Magazine and Annals, vol. ii. p. 74.

The

30 Reply to F.R.S.L.'s Remarks on Compound Interest.

The metals used by me in the construction of the receiver
and conducting tubes, were, plate iron and tin, painted, to
prevent oxidation ; and they were found to last several years.
The above remarks are not intended to discourage im-
provements in such instruments, but to prevent an erroneous
impression upon your readers.

I am, Gentlemen,

Your obedient servant,
Leighton, Dec. 10, 1827. B. Bevan.

[We think that Mr. Taylor's expressions can hardly be
considered as intending to propose his instrument to super-
sede Mr. Bevan' s, or to be an improvement upon it.

He describes his object as indeed a different one, which
may suit others as well as himself, and which is simply to
have a rain-gauge which will record quantities between periods
of observation, — if the term registering be objected to, — and
without the care or management of persons skilled in such
matters.

Mr. Taylor seems to us to acknowledge the merits of Mr.
Bevan' s instrument, and does not appear to have thought of
any rivalry between the two inventions. — Edit.]

VIII. Reply to F.R.S. L.'s Remarks on Compound Interest.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,

YOUR correspondent F. R. S. L. in his " Remarks on the
Principle of Com pound Interest," seems to have bewildered
himself sadly in his attempt to defend Dr. Young's paper on
that subject ; nor is it in my power to extricate him out of the
labyrinth. " It is," he says, " lawful to receive ^%jl. each
day that 100/. is in the hands of the borrower, but at the end
of the year it is only lawful to receive 51. for the use of the
100/. without any interest on the interest." — All this is true
if the interest is payable yearly; but if it is made payable at
shorter intervals, what law restrains the lender from improving
that interest during each interval, like any other part of his
capital ? The borrower pays only at the rate of 51. per cent ;
nor does the lender improve his money at a higher rate, the
advantage in his favour arising only from the more frequent
opportunity of adding the interest to his capital. From the
nature of compound interest, it is evident that the value of an
annuity payable at shorter intervals than one year must vary
less and less from the value of the same annuity payable

yearly,

Dr. Prout on simple Alimentary Substances. 31

yearly, as the term is lengthened ; so that the values of the
perpetuity in both cases must differ from each other by less
than any assignable quantity, and therefore must be equal,
agreeable to Dr. Price's theorems, and so far prove the cor-
rectness of his solution : but this plain and obvious truth ap-
pears to F.R.S.L. to be a revolting paradox ; nor is it to be won-
dered at, considering his method of reasoning on the subject.

In attempting to prove that Dr. Price employs two differ-
ent rates of interest in his method of computing, it is observed,
that "the discount on ten shillings, receivable at a certain
moment as a payment of the half yearly annuity, is greater in
the computation than the discount on ten shillings receivable
at the same moment as half an annual payment."

Now as the present value often shillings, or a moiety of \l.
to be received at the end of six months, and the present value
often shillings to be received at the same time as the half-
yearly payment of the annuity, are expressed by the same
fraction j5.j^, it would, I believe, puzzle any person, however
well acquainted with the subject, to produce different results
in this case.

At the conclusion of your Correspondent's remarks, Mr.
Morgan's documents respecting the probabilities of human
life are said to be " greatly calculated to encourage the po-
pular delusion of the improved healthiness and greater lon-
gevity of the people of this kingdom." Had he indeed as-
serted, as Dr. Young states in his paper in the Philosophi-
cal Transactions, that only one in 1500 died in the year
among the members of the Equitable Society, this accusation
would have been just ; but I should be glad to know in what
part of his works has Mr. Morgan been so absurd ? In the
Nosological Table at the end of his Treatise on Annuities he
represents the number of deaths in each year to be in the
proportion of 1930 to 151,754, or as 1 to 78 nearly. By
what rule in arithmetic these numbers are made to be in the
proportion of 1 to 1500, I shall not stop to inquire.

F.R.S.

IX. On the ultimate Composition of simple alimentary Sub-
stances ; with some preliminary Remarks on the Analysis of
organized Bodies in general. By William Prout, M.D.
F.R.S.* [With two Engravings.]

T^HE present being the first of several communications on
x the same subject which I hope to have the honour of lay-

* From the Philosophical Transactions, for 1827, Part ii.

ing

32 Dr. Prout on the ultimate Composition

ing before the Royal Society, a few observations on the origin
and object of the whole series may not be deemed irrelevant.

Many years ago I published an anonymous paper, contain-
ing some views, at that time new, connected with the doctrines
of chemical proportions*. Though this paper, for reasons
which need not be here stated, was drawn up and published
in a very hasty and imperfect manner, it attracted some no-
tice : and the views therein advanced gradually gained ground,
and at present appear.to be generally admitted in this countryf.
When this paper was published, it was my intention to have
pursued the subject further, but I soon found my progress ob-
structed by insuperable difficulties. The first and chief of
these was the want of accurate data; and the infinity of ob-
jects comprehended by chemistry prevented the hope of ac-
quiring, by individual exertion, however unremitting, a suffi-
ciency for the establishment of general laws. Professional
duties still further limited my exertions, and at length obliged
me to relinquish chemistry in general, and confine my atten-
tion solely to the chemistry of organized substances ; a sub-
ject that has occupied the greater portion of my leisure hours
for the last ten or twelve years.

Organic chemistry is confessedly one of the most difficult
departments of the science ; and though much has been done,
and more attempted on the subject, it is yet in a very imper-
fect and unsatisfactory state; and it must be frankly admitted
that physiology and pathology have derived less advantage
from this most promising and really powerful of the auxiliary
sciences, than might have been expected. To explain this
perhaps would not be difficult; but as the explanation would
be misplaced here, I shall merely observe, that, dissatisfied
with the old modes of inquiry, I determined to attempt a
different one, and keeping in view the notions I had origi-
nally formed respecting chemical combinations, proposed to
myself to investigate the modes in which the three or four
elementary substances entering into the composition of orga-
nized bodies are associated, so as to constitute the infinite
variety occurring in nature.

With these views my first object was to determine the ex-
act composition of the most simple and best defined organic
compounds, such as sugar, and the vegetable acids ; a point
that had been several times before attempted, but, as it ap-

* Annals of Philosophy, vi. 321 , and vii. 1 1 ] . (O. S.) The object of the
second Paper was simply to correct some oversights in the first.

f Dr. Thomson's Chemistry, and his attempt to establish the first prin-
ciples of chemistry by experiment. Also, Dr. Henry and Mr. Brande's
Elements of Chemistry, &c.

peared

of simple alimentary Substances, tyc. S3

peared to me, without complete success. About the same
time also albumen and other animal products, as urea, lithic
acid, &c. were examined with similar views. The subject of
digestion, however, had for a long time occupied my particular
attention ; and by degrees I had come to the conclusion, that
the principal alimentary matters employed by man, and the
more perfect animals, might be reduced to three great classes,
namely, the saccharine, the oily, and the albuminous : hence,
it was determined to investigate these in the first place, and
their exact composition being ascertained, to inquire after-
wards into the changes induced in them by the action of the
stomach and other organs during the subsequent processes of
assimilation. In conformity with this plan, the object of the
present communication is the consideration of the first class
or family above mentioned, namely, the saccharine.

Preliminary observations on the analysis of organized substances.

Vegetable substances contain at least two elements, hydro-
gen and carbon ; and most generally three, hydrogen, carbon,
and oxygen. Animal substances are still more complicated ;
and besides the above three, usually involve a fourth element,
namely, azote, to which they appear to owe many of their pe-
culiar properties. These general facts have been known ever
since the elements themselves have been recognized as distinct
principles, though the determination of the exact proportions
in which they enter into any particular substance, has always
proved a most difficult problem. To enumerate all that has
been done on this subject would be loss of time ; and it need
only be mentioned, that all idea of separating the different
elements from one another, so as to obtain them per se, has
been long since abandoned, if indeed it was ever entertained;
and the general principle on which the analysis of organic
products has been usually conducted, has been to obtain their
elements in the form of binary compounds, either by destruc-
tive distillation, as was formerly practised ; or by combining
the elements with some other element with which they pos-
sessed the property of forming definite binary compounds,
from the quantity and known composition of which, those of
the original elements might be readily obtained by calcula-
tion. For this latter purpose oxygen has been the principle
usually employed, which, as is well known, forms water with
hydrogen, and carbonic acid gas with carbon; two compounds
not only as well understood as any in chemistry, but likewise,
from their physical properties, well adapted for the purpose.
When azote is involved, other means must be adopted, which
will be fully considered hereafter.

New Series.Yol 3. No. 13. Jan. 1828. F The

34 Dr. Prout on the ultimate Composition

The modes in which chemists have attempted to combine
oxygen with the hydrogen and carbon of vegetable substances
have differed very considerably. The illustrious Lavoisier
attempted their union by burning the substance at once in
oxygen gas, a method subsequently followed by Saussure and
others. Afterwards the metallic oxides were employed for
the purpose ; and Berzelius in particular informs us, that so
early as 1807 he had tried the oxide of lead, but did not suc-
ceed with it*. In 1811, Gay Lussac and Thenard published
the analysis of different organic substances made by means of
the chlorate of potash ; and, considering the nature of the ap-
paratus they employed, they obtained admirable approximate
results f. Berzelius, in 1814, published an elaborate paper
on the subject of vegetable analysis, in which he likewise em-
ployed the chlorate of potash, but in quite a different manner;
and to this celebrated chemist I believe we are indebted for
the improvement subsequently adopted by most of his suc-
cessors, of introducing the mixture of the substance to be
analysed, and the oxide, into a narrow tube, and submitting
the different portions of it to heat in succession. The results
of Berzelius were in general more accurate than those of his
predecessors, especially as far as related to the quantity of
carbon, but his method was not well adapted for determining
the proportion of hydrogen J. In 1816, Gay Lussac seems to
have thought of employing the oxide of copper for the pur-
poses of analysis §, the introduction of which undoubtedly
constituted one of the greatest improvements hitherto made in
organic analysis ; and the use of which has continued to the
present time, and will perhaps never be entirely superseded.
The oxide of copper has however some disadvantages, which
it is one object of the present remarks to point out ; another
is, to propose a form of apparatus free from most of the ob-
jections to which those hitherto in use have been more or less
liable.

There are two methods of arriving at the quantity of water
formed during the combustion of an organized substance ;
either actually to collect and weigh it, as Berzelius did, or to
estimate the quantity by the loss of weight sustained by the
tube after the combustion. The latter in general is the best
method, and was that adopted by me from the first : it has
since been followed by Dr. Ure, and others ||. Whichever
method is adopted, it obviously becomes necessary that no

* Annals of Philosophy, iv. 403. t Recherches Physico-chimiques, ii. 265.
% Annals of Philosophy, iv. 323. § Annates de Chimie, xevi. 306.
|| Phil. Trans. 1822. p. 457-

extraneous

of simple alimentary Substances, fyc. 35

extraneous water be present ; but all pulverulent substances,
and oxide of copper among the rest, are more or less hygro-
metric, and rapidly attract moisture from the atmosphere.
This circumstance seems to have struck the French chemists,
and it occurred to me at a very early period. Dr. Ure, how-
ever, was the first who published a method of obviating this
difficulty ; and his method, if this were the only difficulty to
contend with, is capable of considerable precision. But there
is another, and perhaps still more troublesome property, pos-
sessed by the oxide of copper, in common with many other
powders, namely, that of condensing air as well as water * ;
and these two difficulties, taken together in conjunction with
another mentioned in a note below, render great precision
almost out of the question f. To conquer these, every means

* See Saussure's paper on the absorption of the gases by different bo-
dies. Annals of Philosophy, vi. 241. Also Gilbert's Annalen der Phi/sick,
xlvii. 112.

f As I am unwilling that so much labour should be lost, particularly as
it may be of some use to other inquirers, I have thrown into the form of a
note a few of the principal circumstances connected with the inquiry men-
tioned in the text. In my earlier experiments, tubes of iron, copper, &c.
were employed instead of glass, and charcoal instead of spirits, as the me-
dium of heat ; and during this period most of the modifications of apparatus
which have been since proposed as novelties or improvements, were tried
and rejected. I first took the hint of employing a spirit lamp from Mr.
Porrett, and was certainly among the first that did so employ it. Various
forms of lamps were tried, but at length I was induced to relinquish the
use of the horizontal apparatus for the vertical onea; and this, I have no
hesitation in saying, is by far the best form of apparatus hitherto proposed
for the substances to which it is adapted ; nor would any other have been
required by me, at least, had it not been for the properties of the oxide of
copper alluded to in the text, which render this and all other forms of ap-
paratus depending on the employment alone of that substance perfectly
useless when great accuracy is required. It has been objected to the lamp,
that the heat produced by it is not sufficient ; but this is a mistake ,• at
least I have never met with any substance that resisted its action, provided
the oxide of copper was well shaken up in the tube, or, if necessary, taken
out of the tube and retriturated, and afterwards exposed to heat a second
time, one or other of which ought to be done in all instances, whatever be
the medium of heat employed j for no ordinary heat will induce the oxide
to part with its oxygen to a combustible substance at some distance off, and
not immediately in contact with itself. A great heat is also attended with
some disadvantages, and among others, that of causing the oxide to adhere
together in hard and solid masses, which thus beeomes more difficult to be
removed from the tube, and much less adapted for future experiments. In
general, organized bodies are more difficult of combustion, and require more
heat than crystallized ones. The lamp described in the text I have only
recently employed, and it answers the purpose in all respects better than
any I have yet seen.

With respect to the sources of error above mentioned, it was found that

* Described in the Annals of Philosophy, xv. 190 (O. S.) ; and more com-
pletely in Dr. Henry's Chemistry, ii. 167, ninth edition.

F 2 that

36 Dr. Prout on the ultimate Composition

that could be thought of, as likely to succeed, were tried, but
without effect, and I was obliged to relinquish the matter in
despair, and endeavour to contrive some other mode of ana-
lysis that should be free from these difficulties altogether.
After a good deal of consideration I was induced to adopt a
method which had occurred to me long before, but which I
had never put in execution. This method is very simple, and
founded on the following well known principles.

When an organic product containing three elements, hy-
drogen, carbon, and oxygen, is burnt in oxygen gas, one "of
three things must happen. 1. The original bulk of the oxygen
gas may remain the same, in which case the hydrogen and oxy-
gen in the substance must exist in it in the same proportions in
which they exist in water ; (for it is well known that oxygen
gas by being converted into carbonic acid gas is not altered in
its bulk) : or, 2. The original bulk of the oxygen may be in-
creased, in which case the oxygen must exist in the substance
in a greater proportion than it exists in water; or 3. The
original bulk of the oxygen gas may be diminished, in which
case the hydrogen must predominate.

Hence it is obvious, that in the first of these cases the com-
position of a substance may be determined by simply ascfer-

200 grs. of the oxide of copper, recently ignited, gained, after ten or fifteen
minutes, exposure to the air, a quantity varying from '02 to *05 gr. one
half of which, or even more, was acquired before it became cold; that
is to say, before it had cooled down to 100°, considerably above which point
it began to acquire weight. Of the increase of weight above mentioned, it
was found that about j, or £, (for the proportion varied from causes that I
could not discover,) was due to the condensation of air, the rest was due to
moisture. The oxide I employed was perfectly pure, and prepared by ex-
posing metallic copper to heat. Dr. Ure states, " that 1 00 grs. of the oxide
prepared from the nitrate of copper exposed to a red heat merely till the
vapours of nitric acid were expelled, absorbed in the ordinary state of the
atmosphere from '1 to '2 gr. in the space of an hour or two, and about half
that quantity in a very few minutes."

In determining the quantity of water formed by the oxide of copper in the
usual manner, there is yet another difficulty to contend with, to which we
have alluded above, and which we shall here briefly notice. It has been
stated that complete combustion seldom or never takes place during one
exposure to heat, and that in many cases the oxide ought to be removed
from the tube and retriturated. Now it was found, almost invariably, that
during the second exposure to heat, the tube, instead of losing additional
weight, actually became heavier, sometimes to the amount of *03 gr. though
often much less than this. I was a good deal puzzled to account for this
anomaly at first, but believe that it arose chiefly from the reoxydation of
the partially reduced oxide, by the air of the atmosphere.

Since this paper was read before the Royal Society, I have observed one
or two other singular facts connected with this subject, which will be no-
ticed when we come to speak of the analysis of substances containing
azote.

taining

of simple alimentary Substances, fyc. 37

taining the quantity of carbonic acid gas yielded by a known
quantity of it ; while in the other two, the same can be readily
ascertained by means of the same data, and by noting the
excess or diminution of the original bulk of the oxygen gas
employed. Such are the simple and universally admitted
principles on which the following method of analysis is founded;
the only novelty in which, therefore, is the form of the appa-
ratus ; and of this it is hoped the following summary sketch,
and annexed figures, will convey every requisite information.
Fig. 1. Plate I. represents a front view or elevation of the
whole apparatus in the act of being employed. A B is a plat-
form, two feet square, surrounded by a ledge about 2 J inches
high, for preserving any mercury that may chance to fall about,
and furnished with four adjusting screws (of which two, C C,
are sectional views), by means of which it may be placed per-
fectly horizontal. Into this platform, in the manner repre-
sented, are fixed perpendicularly four square pillars, DE,DE,
about four feet and a half high, at the top of which is placed
another small platform, F F, about four inches wide, and which
may be fixed or removed at pleasure by means of the brass
pins ab, ab. II are glass tubes graduated with the utmost
care to hundredths of a cubic inch, and which are cemented
at bottom into semicircular iron tubes inclosed in the blocks
K K (as represented by the dotted lines). These iron tubes
project a little below the wood at the lower part, where they
are furnished with iron stop-cocks, S S, for drawing off the
mercury when it may be necessary. Into the other end of these
semicircular tubes are likewise cemented the glass tubes L L
(of smaller dimensions, and a little longer than the tubes 1 1),
and forming with them, when taken together, inverted syphons.
Thersmaller tubes, L L, are represented as surmounted by fun-
nels, R R, furnished with stop-cocks, the object of which is to
permit the mercury to flow into them with any velocity that
may be required. On the tops of the larger tubes, 1 1, are ce-
mented the vertical stop-cocks, M M, of which fig. 2. Plate II.
is a sectional view on a larger scale, and which renders the
construction so obvious, that perhaps no further remark is
necessary, than merely stating that the cup, a, is filled with
oil, and that the plug, b, which is square at the upper part,
and adapted to a key, is furnished with a shoulder, on which
the screw-cap, c, rests, and by means of which it may be
tightened at pleasure*. On

* These syphons are fixed together independently of the general
frame-work, and may be removed at pleasure by taking out the pins
c d, cd, and ef, ef. This admits of their being replaced by others of
different sizes. Those of a larger size have balls near the top, as repre-
sented

38 Dr. Prout on the ultimate Composition

On the platform, F F, (fig. 1.) is a thin piece of wood, capa-
ble of being raised or depressed at pleasure, by means of the
screws, OO; on this the lamp Q is placed, which may thus be
placed at any distance that may be required from the tube, P.
Fig. 3. is an enlarged view of this lamp: it consists of two
reservoirs, d e, for holding the spirit, connected together by
means of the tube, f, into which are placed, at the distance
from one another of about £ of an inch, a number of vertical
burners, g g, &c. about T^ of an inch in diameter, and f inch
long, and made as thin as possible, with the view of preventing
the conduction of the heat. These burners are each furnished
with a few threads of cotton, and are bent a little alternately
like the teeth of a saw, in order that their flame may envelope
the tube, P, (fig. 1.) more completely, h is a cover for the wick
of the lamp when not in use. The tube, P, (fig. 1.) is of green
or bottle glass, moderately stout, and about £ of an inch in-
ternal diameter. It is fixed between the horizontal parts of
the vertical cocks, M M, so as to be perfectly air-tight; and
when required, the whole, or any part of it, may be heated
by means of the lamp, Q, at the pleasure of the operator.

When the apparatus is to be employed, both the syphon
gasometers, I L, I L, are to be filled with quicksilver, and a
small green glass retort, containing the requisite quantity of
chlorate of potash, (and which had been previously heated so
as to completely expel the common air, and to fill it with
oxygen gas,) is to be attached to one of the cocks, as repre-
sented in fig. 4, by means of a caoutchouc tube. Heat is then
to be applied, and any quantity of oxygen gas that may be re-
quired, introduced into the tube, I. After the whole has ac-
quired the temperature of the atmosphere, the exact quantity
of the gas is to be accurately noticed, as well as the state of
the barometer and thermometer at the same time. The tube,
P, containing the substance to be analysed, is then to be firmly
fixed between the cocks, M M,# and subjected to heat, during
which the oxygen gas is to be transferred from one syphon to
another, through the red hot tube, with any velocity that may
be required, and which may be regulated by means of one of

the

sented by the dotted lines, and may contain as much as 20 cubic inches of
gas. It much facilitates the process of determining the exact quantity of
gas contained in the apparatus, to have both legs of the syphon graduated,
which may be easily done so as to obviate the effects of capillary attraction
when the tubes are not both of the same calibre.

* I have tried various modes of connecting the tube so as to insure its
being air-tight. Caoutchouc answers very well ; but the best substance I
have hitherto employed are slips of thin moistened hogs' bladder, tied on
very tightly with fine dry twine. The twine is then to be moistened also,
and the whole kept in this state till the end of the experiment.

of simple alimentary Substances, Sfc. 39

the stop-cocks of the funnels, R R, and the stop-cock, S, of
the opposite syphon.

Such is a general view of the apparatus, and the principles
of its operation : but perhaps a few practical remarks on some
of the circumstances to be attended to during its employment,
may not be deemed superfluous.

The substance to be analysed may be placed in a small tray
made of platina foil, and introduced alone into the tube P,
and gradually submitted to the action of heat and oxygen gas ;
but this does not answer well with organic compounds, as a por-
tion of them is apt to escape combustion. Another method is
to mix the substance with pure siliceous sand, and to retain
the mixture in the centre of the tube by means of asbestos.
But this method often fails, except there be about an inch of
the oxide of copper at each end of the tube, which must be
kept red hot during the experiment, and in this case it suc-
ceeds completely with many substances. Another method,
and that which the most generally succeeds, is to mix the sub-
stance with peroxide of copper, to heat these together in the
tube in the first place, and afterwards to open the other stop-
cock and send the oxygen gas through the ignited and par-
tially reduced oxide, by means of which it again becomes
peroxidized ; and any portion of the substance that had es-
caped complete combustion in the first part of the experiment,
is now completely burnt. This last method is also that em-
ployed when it is required to determine the quantity of carbonic
acid gas yielded by a given quantity of any substance ; only
in this case, of course, oxygen gas is not required, and the
contents of the tube P, must be taken out and well triturated,
and subjected to heat a second time. If it should be required
to analyse the gas formed, one method of removing it from
the tube I, is represented at fig. 5; and others will readily
occur to the practical chemist.

The following are some of the advantages of this apparatus,
and mode of analysing organic compounds. In the first and
chief place, there is nothing to be apprehended from moisture.
Whether the substance to be analysed be naturally a hydrate,
or in whatever state it may be with respect to water, the results
will not be affected ; and the great problem, whether the hy-
drogen and oxygen exist in the substance in the proportions
in which they form water, or whether the hydrogen or oxygen
predominates, will be equally satisfactorily solved, and that
(of course within certain limits), independently of the weight
of the substance operated on*. When however it is the ob-
ject

* It is to be observed, that, throughout the experiments, great care is

taken

40 Notices respecting New Books,

ject to ascertain the quantities of carbonic acid gas and water
yielded by a substance, it is, of course, necessary to operate
on a known weight ; but this being once determined, there is
no fear, as in the common methods, of exposing the substance
to the atmosphere as long as may be necessary. The hy-
grometric properties of the oxide of copper, as well as its
property of condensing air, are also completely neutralized ;
for the whole, at the end of the experiment, being left pre-
cisely in the same state as it was at the commencement, the
same condensation of course must take place, and any little
differences that may exist are rendered quite unimportant
from the bulk of oxygen gas operated on, which of course
should, in all instances, be considerably greater than that of
the carbonic acid gas formed. Another advantage of this
method is, that more perfect combustion is insured by it than
by any other that I am acquainted with. There is also no
trouble of collecting or estimating the quantity of water, — a
part of the common process attended with much trouble, and
liable to innumerable accidental errors besides those already
mentioned, and which there is no method of obviating or ap-
preciating : here, on the contrary, the results are obtained in
an obvious and permanent form, and, from the ease with
which they are thus verified, comparatively very little subject
to error.

It need scarcely be stated, that the form and principles of
this apparatus render it well adapted for many other chemical
operations besides the analysis of organized substances. Such,
for example, as the reduction of oxides by hydrogen, and a
variety of others that will readily occur to the practical
chemist.

[To be continued.]

X. Notices respecting New Books.

Account of a New Work, entitled, A Treatise on the Steam-Engine;
Historical, Practical, and Descriptive. By John Farey, Engineer.
London. Published by Longman, Rees, and Co. in 4to. Price Five
Guineas.

CONSIDERING the great extension which has been given to all
branches of our national manufactures, by the application of
steam power to expedite laborious operations, it is surprising that
no competent engineer has hitherto undertaken to publish on this

taken that the gases are saturated with moisture: the errors from this cause
are thus rendered definite, and are easily corrected by tables calculated for
the purpose from the most accurate data, and which will be given in a sub-
sequent communication.

subject,

Notices respecting New Books. 41

subject, in a detailed manner, to be instructive to men of business and
practitioners. It is evident, from the repeated instances of dreadful
explosions, failures, and misapplications of capital, which have hap-
pened (even recently), that engineers as a body are not yet suffi-
ciently informed on this branch of their art. Whilst on the other
hand, the continued success of the best engineers proves that real
skill does exist amongst them, and may be expected to be attainable
by others, with study and proper instruction.

As a means of such instruction, the present work cannot fail to pro-
duce public good.

The importance of a scientific guide to students and young prac-
titioners cannot require to be pointed out. Merchants, manufac
turers, and men of business, who must call in the aid of engineers to
construct engines and apply steam power for them, may easily gather
as much knowledge from such a work as will enable them to dis-
tinguish between those who are competent to execute what is re-
quired, and others who will be likely to lead them into similar errors
to those by which so many have suffered. And it will be a most im-
portant aid to practical engineers, in directing those studies by which
they may render themselves competent to execute what they under-
take.

At present, many who are well acquainted with the mechanical
structure of steam-engines, and are even accustomed to make them
in established forms which they have copied from others, have only very
imperfect and even incorrect notions of their operations when in use ;
they are in the condition in which a physician would be who had only
studied the anatomical structure of dead animals, without much know-
ledge of the physiology and pathology of their living functions. Such
engineers often succeed very well in their ordinary business, and ac-
quire a reputation which their knowledge will scarcely bear out, when
they are required to depart from their established models, and make
such modifications of their parts as is necessary for applying steam
power to new purposes.

To obtain these useful results from a publication, it must be com-
posed with great care by a practitioner of competent knowledge and
experience $ for a self-sufficient guide in an unknown road would be
worse than no guide at all : and but little could be expected from
literary men, who can have no other acquaintance with the subject
than what they may acquire in collecting information from others,
merely for the purposes of publication.

Mere descriptions of steam-engines will not prove of any very great
utility, even if accurate, and however they may be elucidated by draw-
ings of such extent as can be added to any publication : for to general
readers such descriptions will prove tediously minute, and to practical
men they will afford no information which is not already habitually
imprinted in their memory. To form an instructive guide, the de-
scriptive part must be accompanied by accurate statements of the actual
and relative magnitudes of all the parts, and of the quantities of mat-
ter and of action that each part is required to possess, together with
such a complete development of the principles on which their opera-

New Series. Vol. 3. No. 13. Jan. 1828. G tions

42 Notices respecting New Books.

tions depend, as can only be obtained from a very long and intimate
acquaintance with the subject, and a natural habit of observation exer-
cised in an extensive field.

Mr. Farey has been long known as one of those who possess the
knowledge required for such an undertaking 5 and the great length of
time which has elapsed since this work was first promised to the pub-
lic, must have given ample time for its execution in a careful manner.

We have not had time to give this volume the examination that
the subject demands, but the objects and general tenor of it may be
gathered from the following extracts from the Preface.

" The object of the present treatise is to give a historical, practical,
and descriptive account of the steam-engine, and its application to
useful purposes.

" The historical part is intended to form a complete account of the
invention, from its first origin, to its present state of perfection, from
which the statesman and political economist may observe the influence
that the adoption of steam power has exercised upon our national
prosperity and advancement, during a century past, and may form
an opinion of the future advantages to be expected from more ex-
tended applications of the same principles.

M The practical and descriptive part is intended to form a course of
instruction for professional students, in the practice and principles of
making and using steam-engines. At present, such students are left
to form and digest their own crude and imperfect observations ; and
for want of a scientific guide, their conclusions are liable to be tinc-
tured with many erroneous notions and false assumptions. The same
part is also intended to form a manual, which, by the aid of tables and
theorems for calculation, will facilitate the practice of experienced
professional engineers ; and will tend to perfect the practice of those
engineers and others, who require to employ steam-engines, and
apply them to various purposes ; but who do not possess a complete
knowledge of their construction, and therefore require information,
which it has hitherto been difficult to attain. The principles of me-
chanical and chemical action, upon which the ooeration of steam-
engines depends, and the application of those principles to practice,
will be also embodied in this part.

" Another part will contain a record and brief explanation of all the
speculative projects which have been proposed for the improvement
of steam-engines ; so as to exhibit to mechanical inventors the various
ideas which have been suggested for that object : the instruction that
they may obtain from other parts of the work, together with the hi-
story of the circumstances from which the great points of invention
have originated, may enable them to make some further improve-
ments.

" To attain these objects is not an easy task ; for it is only in the
course of an active professional practice, that sufficient information is
to be obtained ; and all competent engineers are too much engaged
to find leisure for a literary occupation. The author could not have
undertaken such a work, if he had not formed the plan, and collected
materials for its execution, at his first entrance into business j and

Notices respect i?ig New Books. 43

as it became known that he had such an object in view, he has con-
tinually received contributions of information from other engineers,
who wished to promote the undertaking j and, with very few excep-
tions, this feeling has been general in the profession. In this way
the author became personally acquainted with two great authorities
in this branch of mechanics, the late Mr. Watt and Mr. Woolf, and
received from them a full knowledge of the origin and progress of their
respective inventions, and of the principles which they followed in ap-
plying those inventions to useful practice.

•' At the commencement of his professional studies in the years 1805
and 1806, the author felt the want of a guide of this kind j and after
carefully studying Dr. Robison's article in the Encyclopaedia Briton-
nica, and M. Prony's Architecture Hydraulique, and finding them in-
sufficient for that purpose, he determined to preserve notes of all the
observations and investigations, by which he should acquire his own
knowledge of the construction and principles of operation in steam-
engines and other machines, and their various applications ; in the
expectation that at some future period a useful publication might be
formed from those materials. Professional avocations have long since
occupied all the time which might have been devoted to such an ob-
ject, but it has never been abandoned j and if the sale of the present
work should prove sufficient to induce the publishers to undertake
others of a similar nature, the author has an accumulation of notes,
which in the course of years he may find time to arrange in a corre-
sponding form with the present work.

" In the year 1815, the author drew up a descriptive article on the
steam-engine for Dr. Rees' Cyclopadia ; but the plan of that work,
and the limited number of engravings, rendered it necessary to avoid
details, which must constitute the great value of a practical treatise.
Since the publication of that article in 1816, the want of a correct
manual has been still more felt, from the great and increasing ex-
tension of the use of steam power, and the author was advised by his
friends in the profession to resume his original project j this he under-
took to do in 1820, and the bulk of the historical part was written,
and, most of the plates were engraved by the late Mr. Lowry, in the
next year ; but the author being obliged to reside at a distance from
London, by engagements which left no leisure for this object, the
impression has been carried on at intervals, and the publication of
the first volume has been unavoidably protracted until the present
time.

" To instruct students, it is necessary to state such elementary pro-
positions in mechanics, as have a direct application to the subject of
steam-engines j for this purpose a series of definitions are given in
an Introduction to the present volume. These definitions have been
formed from a full examination of the works of the best writers on
the theory of mechanics, viz., Belidor, Emerson, Smeaton, Hutton,
Banks, Gregory, Robison, Young, and others. The author has en-
deavoured to preserve their modes of reasoning, and the mathemati-
cal accuracy of their conclusions, without employing the language of

G 2 geometrical

44 Notices respecting New Books,

geometrical or algebraical analysis ; but all quantities are represented
in numbers, and their proportions established by the ordinary pro-
cesses of arithmetic : this plan has been adopted, in order to render
the principles very apparent to those who are not accustomed to any
other mode of calculus. This part of the work is intended to give
practical men an exact knowledge of the true principles upon which
their operations ought to be conducted ; and other parts, to show the
means of applying those principles to their daily practice, in the con-
struction and use of steam-engines.

" To readers who are conversant with mathematical investigations,
the mode of stating the propositions will appear to leave them with-
out sufficient demonstration ; but the principles which it is intended
to explain and define (rather than to demonstrate) have been so well
established in mathematical evidence, as to leave no doubt of their
truth j and such readers may be referred to the mathematical writers
whose principles have been adopted.

" Dr. Gregory's Treatise of Mechanics, in 2 volumes, 8vo., contains
the best collection of mathematical investigations j and the fullest
and clearest exposition of the principles will be found in Dr. Young's
Course of Lectures on Natural Philosophy, in 2 volumes, 4to. j also
Dr. Robison's articles on Mechanical Philosophy, in the Encyclopae-
dia Britannica, reprinted by Dr. Brewster, in 4 volumes, 8vo. To the
young student, a previous mathematical course is strongly recom-
mended : the best guides are, Martin's System of Mathematical In-
stitutions, in 2 volumes, 8vo.j Dr. Hutton's Course, in 3 volumes,
8vo. j and Dr. Gregory's Mathematics for Practical Men.

" One great object of the present work is to furnish practical engi-
neers with a series of rules for calculating all proportions and quan-
tities, which can be required to be known for the construction and
use of steam-engines : these rules have been deduced from very nu-
merous observations made upon steam-engines and mills of all kinds
and of all magnitudes. In each case the observations have been very
carefully compared, and assorted in series, according to the similarity
of circumstances, and then such formulae deduced from them, as
would give results corresponding equally well with all parts of the
series. The construction of these various formulae has been a work
of great labour, of which very little appears, because only the results
of the investigations are retained in the form of an arithmetical rule.
The greater part of these rules have been formed by the author for
his own use, in professional practice ; and having undergone the test
of continual application during a course of several years, and re-
ceived frequent corrections, he is justified in claiming some confidence
iu their accuracy.

"The principles which regulate the proportions of the different quan-
tities which are to be computed by each rule, are stated in the most
concise terms which could be chosen, without using algebraical sub-
stitutions j these have been avoided throughout the work, because
the methods of algebra and fluxions are only necessary to investigate
the formulae, wherebv computations may be performed in numbers,

by

Notices respecting New Books. 45

by the processes of ordinary arithmetic j and it is sufficient for prac-
tical use, to have rules which will give the required results.

" The method of performing each calculation by the sliding-rule is
added, and will tend to facilitate the computations. This valuable
instrument was introduced into considerable use amongst engineers
by Mr. Watt, and only requires a good collection of formulae to be-
come of universal application. The author hopes that what he has
done will contribute to extend the use of that excellent mode of com-
putation amongst the profession.

" The history of the invention of the steam-engine and its applica-
tion, is divided into chapters. — The first of which contains an account
of the various projects and attempts which were made, during the
seventeenth century, to obtain a moving power from fire ; and a de-
scription of the first working engine which was invented by Mr. Sa-
very for raising water, but it never came into extensive use.

"The second chapter is on the invention, principle, and construction
of the fire-engine of Newcomen, which was the first engine brought
into important use, and it is still very extensively employed. This
subject is treated at length, and rules are laid down for the propor-
tions of its parts.

" The third chapter is on the various applications of Newcomen's
invention, which were made during the first half-century after its
invention.

"The fourth chapter is on the introduction of cast-iron into the con-
struction of machinery, and the application of the fire-engine to the
manufacture of iron.

. "The fifth chapter is a history of the origin and progress of Mr.
Watt's invention of his first steam-engine for pumping water ; with
an account of that engine, and of the rules which he established for
the proportions of its parts.

" The sixth chapter gives an account of the first application of the
steam-engine to give continuous circular motion to mills j with a
complete description of the principle, operation, and structure of
Mr. Watt's rotative engine for that purpose ; and the dimensions of
several standard engines made by himself, which have been in use for
years, and which perform as well as any modern engines which
depend upon the same application of steam.

" The seventh chapter is a treatise on the construction and use of
the sliding-rule, and its application to the purposes of calculations
relative to steam-engines.

" The eighth chapter is a collection of rules for calculating the pro-
portions and dimensions for all parts of Mr. Watt's rotative steam-
engines.

" The ninth chapter is in continuation of the history of the invention
of the steam-engine, and describes those modifications in the form of
Mr. Watt's engine which were proposed and executed by his co-
temporaries.

"The present volume concludes at that part of the history of the in-
vention of the steam-engine, when it had been brought to such a de-
gree

46 Royal Society,

gree of perfection that all its principles of action were fully developed
and realized in practice ; and, although the art of constructing these
machines has been very greatly improved since Mr. Watt's time,
and their applications widely extended, no important inventions
have been established in practice, except high-pressure engines, and
particularly those of Mr. Woolf, which are still used in the same
form as he first made them. — The remainder of the subject will con-
sist of technical descriptions of the structure of such steam-engines
as are now in use, and as they are made by the best engineers j this,
with their applications to various purposes, and the principles which
should be followed in making such applications, will form the subject
of another volume."

XL Proceedings of Learned Societies.

ROYAL SOCIETY.

Nov. 15. — T^R» KIDD and Dr. Richardson were respec-
*-* tively admitted Fellows of the Society.

The Croonian Lecture, by Sir E. Home, Bart. V.P. was
read, entitled, " On the muscles peculiar to organs of sense in
particular quadrupeds and fishes."

The author selected for the subjects of this lecture the pecu-
liarities in the muscular structure of the tongue of the Xariffa
or Camelopardalis Giraffa, an inhabitant of Soudan in Africa;
and a muscle belonging to the eye of the Cobitis anableps, a
fish inhabiting the rivers of Surinam, and called by the natives
" the four-eyed fish."

The tongue of the Giraffa, besides being an organ of taste,
has many properties of the elephant's proboscis. The latter is
incapable of elongation it is true, while the former may be ex-
tended to seventeen inches in length. The author observes, that
some mechanism must exist by which this elongation can be
performed, but that an opportunity of examination after death
would be requisite to decide on its nature. The tongue of rein-
deer offers the same analogy, which however he has not been
able to trace for want of time. The chameleon can dart out
its tongue to the extent of twelve inches, and, for this purpose,
as well as to direct its motion, it has a conical bone inclosed in
a muscular tube, the fibres of which are circular, and aid
by their pressure to make the bone slide forwards. The
Xariffa wants the receptacle for water, which the camel and
dromedary possess, it being needless for it as it lives on
succulent plants ; neither has it the padded hoof to fit it
for travelling in sand, but two toes defended by a horny co-
vering,

Royal Society. 47

vering, to enable it to climb rocky ground without stumbling.
Its long neck consists of only seven bones, being the same
number that occurs in the human skeleton. The tongue is
every where smooth and slightly adhesive ; it is spotted, but
the spots are not raised. Its favourite food is the Acacia tree,
of that species now called Acacia Xariffa : it has a pleasant
flavour both boiled and raw, and its twigs are succulent. The
tongue being much exposed to the sun, has a black rete mu-
cosum, to prevent blistering. Drawings, by Mr. Cross, ex-
hibit the mode in which it lays hold of the branches of trees.
It drinks milk, first rinsing out its mouth with a portion, and
rejecting that so employed. It chews the cud, its body being
then recumbent and its head and neck erect*

The organ of vision of the Cobitis anableps is very remark-
able. The specimens examined by the author were furnished
by Dr. Muttlebury, of Bath. He first exposes the errors of
Artedi and his followers, in their description of this animal ;
and states, that the cornea being removed, the iris is exposed,
having an appearance of two pupils; but on more accurate ex-
amination this effect is seen to arise from two lateral project-
ing portions, folding over each other in the middle, thus di-
viding the aperture into two. They do not however unite;
and in some specimens they leave the pupil entire, only very
narrow in the middle, forming an oval, broad above and nar-
row below ; usually, however, they leave two distinct aper-
tures. The crystalline, instead of being spherical, is not even
circular, having a small projection at the lower edge, directly
behind the smaller aperture. When examined in the micro-
scope, a small bundle of muscular fibres is seen coming from
the capsules of the vitreous humour in the lower part, and en-
tering that of the crystalline just at the disc where the smaller
curve joins the large one, the action of which is to bring the
lower mammary process of the lens downwards and backwards
into the centre of the lower apertures in the iris; thus con-
stituting a complete organ for vision at near distances, inde-
pendent of the part of the lens opposed to that large aperture,
which is destined for more distant objects.

The author regards this structure as destined to a similar
purpose with that of the marsupium in birds, viz. to obviate
a difficulty arising from a want of motion in one direction in
the eye-ball. He considers that by its means also, the fish,
when lying with its eye-ball above the surface of the water,
may enjoy distinct vision both in air and water by the motions
of the crystalline and eye-ball, combined with the adapting
power of the two apertures of the iris to a circular form.

A paper was read, entitled, H Experiments to determine the

difference

48 Royal Society.

difference in length of the seconds' pendulum in London and
Paris ; by Capt. E. Sabine, Roy. Art., F.R.S."

The author commences this paper by a brief statement of
the existing state of the determinations of standards of length
in the two countries ; and he observes that an attempt made by
M. Arago in 1817 and 1818, to bring into immediate com-
parison the standards of the two countries, proved inconclu-
sive, from the rates of the pendulums not having been obtained
with sufficient exactness. The author having obtained from
His Grace the Master- General of the Ordnance a general leave
of absence from his military duties, so long as he could be use-
fully employed in scientific pursuits, conceived he could in no
way better satisfy the condition than in carrying into effect this
purpose. Accordingly, being provided with two pendulums, —
one made by M. Schumacher, another the property of the Board
of Longitude, — he set out for Paris, whither the pendulums were
forwarded to him. The comparison was made in Paris at the
Royal Observatory, in the Salle de la Meridienne, on the spot
in which M. Biot's measurement had been made, and every
proper facility and assistance was afforded him. The coinci-
dence clock was compared every twelfth hour by M. Mathieu,
with the transit clock of the Observatory. On the 27th of April,
the weather having set in mild and steady, the experiments
were begun. The results are stated in the tbrm of appended
tables, of which a detailed account is given.

Each of the pendulums, when not used in observing co-
incidences, was employed in determining its rate by a journey-
man-clock or counter, — amethod used by Messrs. Freycinet and
Duperrey ; but which the author thinks inferior to that of co-
incidences, though capable of giving good results. The par-
ticulars of these are given in two of the tables. From all the
experiments in conjunction, it appears that the numbers of
vibrations performed in a mean solar day at Paris (reduced
as usual) by the two pendulums, were respectively 85922*06
and 85933-83.

The pendulums and apparatus were reconveyed to London,
early in September, by water ; and the rates again determined
at Mr. Browne's house in Portland-place, by means of that
gentleman's excellent clocks and transit observations made by
Capt. Sabine. The precautions used are fully detailed ; and
the observations, which are also appended in a tabular form,
the author being assisted by M. Quetelet, of Brussels. They
give as a final result 85933*29 and 85945*85 for the numbers
of vibrations respectively made by each in a mean solar day,
similarly reduced for London.

As a final result of the whole operation, the author regards

" 12s*00

Royal Society, 49

12**00 as the acceleration of the seconds' pendulum in passing
from Paris tQ London. The same acceleration deduced from
a comparison of M. Biot's and Capt. Kater's direct measure-
ments of the seconds' pendulum, in Paris and in London,
comes out 1 1 s,76 ; or conversely, the length of the seconds' pen-
dulum observed by the former in London transferred to Paris,
by an assumed retardation of 12 s, gives a length differing from
M. Biot's by 0in'00023. Borda's agrees within 0in'00079 with
M. Biot's ; and Capt. Kater's, so transferred, holds very nearly
a mean between the two, but approaches rather nearer to
Biot's than to Borda's.

Nov. 22. — W. A. Mackinnon, Esq. was admitted a Fellow
of the Society.

A paper was read, entitled, " On a peculiarity in the struc-
ture of the ductus communis choledochus and of the pancreatic
duct in man; by John Davy, M.D. F.R.S."

The peculiarity noticed by the author, consists of a valvular
apparatus formed by delicate angular processes of the mucous
coat of the lower part of the ductus communis choledochus and
of the pancreatic duct; which he detected by slitting open
these tubes under water, and washing off the adhering mucus.
The effect of this structure is to prevent any retrograde mo-
tion in the fluids conducted by these tubes : and although a
very delicate probe may be made to descend through the ducts
with facility, its passage in the opposite direction is arrested
by the sacculi which are formed by the processes of the inner
membrane. This structure is not met with either in the sheep
or in the ox, in which animals there is no junction of the bi-
liary and pancreatic ducts.

Another paper by Dr. Davy was read, entitled, H Observa-
tions on the action of the mineral acids on copper, under dif-
ferent circumstances."

In prosecuting the researches into the slow operation of
electro-chemical agency on the alloys of copper, which was
the subject of his former paper published in the Philosophical
Transactions, the author was induced to examine the action
of the mineral acids on copper, under different circumstances.
When atmospheric air was excluded, dilute sulphuric acid,
into which a bar of polished copper was immersed, had dis-
solved at the end of three months only a very minute quan-
tity of that metal, and the bar was slightly tarnished with the
black oxide of copper. A similar result was obtained with
dilute muriatic acid ; but dilute nitric acid dissolved a larger
portion of the metal, and the bar was encrusted with black
oxide. When the vessels in which similar experiments were
made, were covered only with glass, so as to retard evapora-

New Series. Vol. 3. No. 13. Jan. 1828. H tion

50 Royal Society.

tion but not to exclude the air, at the end of eight months
the sulphuric acid was found saturated with copper, and the
bar covered with a thin crust of black oxide. With nitric
acid there was also a considerable deposition of protoxide of
copper on the bar, together with a little crystallized sub-
nitrate, and a very minute quantity of metallic copper. With
the muriatic acid, depositions similar to those with the nitric
acid took place, the submuriate being very abundant, and cry-
stallizing as in the native specimens of this mineral from Peru.

The author considers the complicated results produced by
the presence of atmospheric air as referrible to electro-che-
mical action, arising from the reaction upon each other of
the combinations formed.

A paper was likewise read, entitled, " On the structure of
the knee-joint in the Echidna setosa and the Ornithorhynchus
paradoxus; by G.Knox, M.D.F.R.S. E., communicated by
Sir James MacGregor, F.R.S."

After a short review of the labours of comparative anato-
mists on the animals which are the subject of this memoir, the
author describes a peculiarity of structure which was discover-
ed by his brother in the knee-joint of the Echidna, consisting
of an extension of the ligamentum- adiposum, or re-duplica-
tion of the synovial membrane transversely across the whole
joint, dividing it into two cavities which have no distinct com-
munication with each other. The articular surfaces of the up-
per cavity are the patella and the anterior portions of the con-
dyles of the os femoris, while the lower are formed by the in-
ferior and superior surfaces of these condyles, the upper sur-
face of the tibia, and the semi-lunar cartilages. In the Orni-
thorhynchus paradoxus, the double fold of the synovial mem-
brane extends only half-way across the joint, thus constituting
an intermediate link of gradation between the Echidna and
Man, in whom the ligamentum adiposum is wholly within the
joint.

Nov. 30.— At the Anniversary Meeting of the Royal So-
ciety on St. Andrew's day, — after the names had been read of
all Members deceased in the preceding year, and before the
Medals were delivered, Mr. Davies Gilbert (President,) ad-
dressed the Society to the following effect :

Among the names now read, that of His Royal Highness
the Duke of York demands our first attention.

We have in common with the whole nation to deplore the
loss of an illustrious personage, who has rendered most es-
sential services to his country by discharging the duties of a

high

Royal Society. 51

high military office during a period more arduous than any
other in the modern history of Europe. But on topics so re-
mote from our habitual pursuits it would be useless for me to
dilate. Justice is done to His Royal Highness by the high
station which his memory holds in the opinion and in the esti-
mation of the public.

We have also to lament the loss of two of our Fellows, con-
nected with the Society in the relation of Vice Presidents —
the Earl of Morton, and the Bishop of Carlisle.

The first, — in addition to his own merits possessing a strong
hereditary claim to our regards, as the descendant of Lord
Morton who presided over the Society about sixty years ago,
— assisted in our labours'; and contributed his aid, with Lord
Macklesfield and other distinguished persons, in 1 752, to as-
similate our Style or Calendar to that used by the continental
nations of Europe. To the individual of whom death has now
deprived us, we owe much gratitude for his uninterrupted
countenance and attention during a long series of years : and
in the Transactions for 1821 will be found a communication,
by Lord Morton, of a curious fact in physiology.

Dr. Samuel Goodenough, late bishop of Carlisle, has ever
sustained the character of a sound and elegant scholar. En-
trusted with the education of distinguished personages, and
having qualified them for the first situations in the state, he
fairly and honourably ascended to the summit of ecclesiastical
preferment. To classical and theological learning, Dr. Good-
enough added a very intimate knowledge of natural history,
as is manifested by a communication to the Linnean Society,
where his labours have thrown a steady light over an exten-
sive genus of aquatic plants, left by all former botanists in ob-
scurity and confusion. The memory of Dr. Goodenough will
long be cherished with affection and with esteem by all who
had the honour of his acquaintance either in his public or in
his private life.

If it were usual to advert in a particular manner to each
Member of whom the Society has been deprived within the
last year, there has not been read perhaps the name of a
single person, on whom one might not dilate with a melan-
choly pleasure and satisfaction. — Mr. Canning, pre-eminent
throughout the world ; The Bishop of Winchester, senior
Wrangler of his year, and tutor to Mr. Pitt; Mr. Cline;
The Marquis of Hastings ; The Duke of Gordon; — all men of
literature or science. But as these and other individuals have
not been connected in any peculiar relation to the Society, nor
shared in its labours, we have only to mention them with re-

H 2 " gret.

52 Royal Society.

gret. — Colonel Beaufoy may be considered an exception. That
gentleman is well known to have devoted his time and attention
to practical astronomy ; and having confined himself to certain
departments, in these he is said to have greatly excelled. His
observations of stars occulted by the moon, and of eclipses
of Jupiter's satellites, are believed to form the most complete
series any where to be found ; and such observations are very
essential for completing the theories of these respective bodies.
— And here it is not irrelevant to mention, that, by the libera-
lity of his son, (professionally engaged in other pursuits and in
other countries,) the instruments so well used by Col. Beaufoy
are now bestowed on the Astronomical Society.

Two Fellows of the Society demand, however, our special
notice — The Rev. Abram Robertson, and The Rev. John
Hellins.

Dr. Robertson first appeared in the town of Oxford as a
practitioner of medicine : but his abilities and mathematical
attainments soon attracted notice. He was induced to be-
come a member of the University ; was admitted into orders ;
received a chaplainship of Christ Church ; and became lec-
turer in geometry, first to the College, and afterwards to the
University. In due course Dr. Robertson became professor
of mathematics, and finally astronomer at the RadclifFe Ob-
servatory. We have in our Transactions various proofs of
Dr. Robertson's diligence and abilities. Two papers "On a
demonstration of the laws given by Sir Isaac Newton for ex-
panding a binomial." This expansion, justly esteemed of the
utmost importance as the foundation of every other, and as
developing the whole system of fluxions, has received various
elaborate demonstrations, the great author having simply con-
tented himself with the annunciation. Among those of the same
date none are more clear or satisfactory than the one given by
Dr. Robertson : nor does it detract from his merit, that sub-
sequently others have been devised in the general expansion of
functions, more concise, and perhaps more immediately urgent
of conviction on the mind. We have a third paper " On
the precession of the equinoxes." A fourth, showing " A di-
rect method of computing the excentric from the mean ano-
maly." And a fifth, demonstrating "A theorem in spherical
trigonometry, given by the late Dr. Maskelyne." But the
great work of Dr. Robertson is his Treatise on Conic Sec-
tions;— following the geometric method of Apollonius among
the ancients, and of Hamilton in our own times, by deriving
all the properties from the cone itself. As an academic book
for the instruction of young men this may well be stated as too

extensive,

Royal Society. 53

extensive, and requiring more time than can now be allotted
to any one branch of mathematical science. As a monumerit
to the author's fame, it promises to remain for ages.

The Rev. John Hellins was one of those extraordinary men,
who, deprived of early advantages, have elevated themselves
by the force of genius and of industry to a level above most
persons blessed with regular education. Mr. Hellins at one
time computed for the Nautical Almanac. He afterwards
assisted at Greenwich. And what is now perhaps almost un-
known, he furnished the late Mr. Windham with all the calcu-
lations and tables on which that gentleman brought forward
his new military system, as minister of war, in 1806. Mr.
Hellins applied himself with great industry to some of the
most useful branches of pure mathematics. No less than nine
communications appear in our Transactions, " On the sum-
mation of series." — " On the conversion of slowly-converging
series into others of swifter convergency." — " On their appli-
cation to computing of logarithms, and to the rectifying of
circular arcs." — " On the roots of equations." And in 1798,
" On a method of computing with increased facility the plane-
tary perturbations:" for the last he was honoured with your
Copley medal. Retired to a small living in Northampton-
shire, Mr. Hellins became a pattern of philosophic calmness
and content

Far from the madding crowd's ignoble strife,
His sober wishes never learn'd to stray.

He seems to have said

Curtatis decimis, modicoque beatus agello,
Vitam secrete in rure quietus agam.

I have known Mr. Hellins above forty years, and I can testify
to his virtues. It once happened that, through the late Dr.
Maskelyne, I had nearly obtained for him the Observatory at
Dublin. The failure cannot however be lamented, since
Brinkley was appointed in his stead.

Although death has deprived us of several eminent persons
at home ; yet undoubtedly the greatest loss to science must be
sought for this year in our foreign list. We find there the
names of Bode, of Volta, and of La Place.

Professor Bode is known to every one by his magnificent
Caelestial Atlas in twenty large plates, containing 17,000 stars
laid down and catalogued with a degree of accuracy unknown
to former times ; and with an elegance and beauty that may
never be excelled. This book appeared about thirty years
ago ; and the author is said to have employed himself up to
very recent times in the cultivation of his favourite science,

and

54? Royal Society.

and in giving to the public some books explanatory of the ele-
ments, and others more profound ; but all in a language little
known in this country. He has now departed this life full of
years, and with a reputation commensurate with his age.

Professor Volta has enjoyed the rare and enviable felicity
of founding a new science. Mr. Galvani had indeed observed
the extraordinary effects of peculiarly modified electricity, in
exciting the nerves and muscles of frogs : but misled by the
physiological hypothesis of a nervous fluid acting interme-
diately between the sentient principle and the material frame,
he hastily concluded that the nervous fluid was now within his
reach ; and the appearances were denominated Animal Elec-
tricity. Nor can we perhaps justly blame Galvani for the
generalization that he had formed. Volta himself adopted it
for some time, as appears from his paper communicated in
1 793 : but further experience convinced him that the whole
might be explained by electricity chemically produced ; and
this opinion has been satisfactorily demonstrated by the in-
vention of his pile. Mr. Volta communicated a paper to the
Royal Society as early as the year 1782, "On a method of
detecting minute quantities of electricity." In 1791 he was
elected a Fellow on the Foreign list. And in 1793 Mr. Volta
transmitted to the Royal Society, through Mr. Cavallo, the
account of Mr. Galvani' s discoveries and of his own ; which
obtained for him the reward of your Copley medal. And in
1800 the Transactions were again enriched by a paper from
Mr. Volta " On the electricity excited by mere contact." —
To pursue the history of Voltaic or chemical electricity any
further, would be to detail the successful labours of our own
countrymen. Here the pile has been modified into the much
more convenient and efficient form of the plates and trough
which, in the hands of Sir Humphry Davy, have produced
effects equally astonishing and important: and enlarged by
the gentleman who now sits on my left hand*, the plates have
exhibited such energies as were previously not even contem-
plated. Galvani has not affixed his name to the science of which
he is in a great degree the parent, and which has continued
to exercise his genius up to the extremity of a long life : but
he has had the satisfaction of witnessing the continually in-
creasing brightness of a flame first kindled by himself, and
which he has never ceased to fan.

I now approach La Place. But it cannot be expected that
I should give more than a very slight sketch of this extra-
ordinary man.

La Place appears to have commenced his illustrious career
* Mr. Children.

in

Royal Society. 55

in consort with a philosopher distinguished by the sagacity
which enabled him to seize the clues leading to all the recesses
of modern chemistry, by the indefatigable industry and acumen
exerted in exploring every chamber of the labyrinth, and by
the unfortunate period in which his lot was cast: a period
devoted to an unrestrained action of the worst passions of the
human heart, — which could have alone arrested, by a violent
death, the progress of Lavoisier. Deprived of his friend and
associate in chemical pursuits, La Place appears to have de-
voted the whole energies of his powerful mind to a science the
most abstruse and difficult, but the most sublime of all that are
placed within the reach of human intellect. Astronomy, so
far as two bodies were alone concerned, had attained absolute
perfection by the discoveries of Kepler and by the demon-
strations of Newton.

The elliptic orbits, areas proportional to the times, and the
squares of the periods, as the distances cubed, left nothing to
be desired. But when the regular motion of a heavenly body
round its primary is disturbed by a third, the circumstances
are widely different. Sir Isaac Newton had indeed sufficiently
shown that the principles of gravity and inertia were adequate
to solving the problems of three bodies : but in a field so
vast, the exertions of no one man, not even those of Newton,
were sufficient for its entire cultivation. The labour of others,
— of Bernouilli, of Clairaut, of Euler, of Mayer, of La Place,
were required in aid ; but still pursuing the system and plan
dictated by their great master.

To describe the first important discovery of La Place, it
will be necessary to premise some particulars. The problem
of three bodies requires, From the momentary direction and
intensity of the disturbing force, expressed in the generality
applicable to all parts of the orbits, to infer the effects pro-
duced (through the medium of integration) in any finite time.
It is probable that no effort of the human intellect could
ever have attained this object, but for the expedient of im-
puting to the orbit a physical existence, and consequently a
liability to variation in all its parts. The larger axis equal to
twice the mean distance, the lesser axis indicative of the ex-
centricity, the line of the apsides, and the inclination of the
orbit and the nodes in respect to the orbit of the disturbing
body. All these variations are expressed by expansions the
most elaborate and complicated. But La Place has the glory of
discovering, that after including every term of the expansion
which involves the second powers of the excentricities, the
larger axes, and consequently the mean distances, remain un-
changed. All the larger terms in expanded series indicative of

perturbations

56 Royal Society.

perturbations re-establish themselves in short intervals: but
others of less magnitude are extended by the peculiar form of
their coefficients through periods extremely long. Those mea-
sure what had previously been termed secular equations, sup-
posed to vary as the squares of their distances from some as-
sumed epoch. Since the Mechanique Celeste has enlightened
the world, empirical equations have disappeared ; and others
corresponding with the true principles of rotary movements
have assumed their place. Among these, as similar in their
nature, may be included the two great equations of Jupiter
and Saturn, each corresponding to the attractive power of the
other planet, as is ascertained by the periods and distances of
their satellites.

Descending to the peculiar system of our earth, La Place has
deduced from gravity all the complicated inequalities of the
lunar movements, and some of these involving the distance of
the sun in comparison with that of the moon. The solar pa-
rallax has been derived from the lunar, with a degree of
accuracy greater than can probably be obtained from obser-
vations on Mars, or even from that rare phenomenon, a
transit of Venus.

Arrived at the earth itself, this illustrious philosopher has
investigated with peculiar care the precession of the equinoxes,
— an element of the utmost importance in all astronomical re-
searches, caused partly by a displacement of the ecliptic from
planetary attraction ; but in a much greater degree by the
attraction of the sun and moon on the oblate figure of the
earth : the compression entered therefore as a main ingredient
into these inquiries, to be considered under every probable
variation of internal densities. The theory of compression has
been perfected by La Place : but data were still wanting to re-
concile all the anomalies caused by depositions or formations
dependent on causes, to us, apparently fortuitous. These
data, we hope, are either now attained, or at the least brought
within our reach, by the ingenuity and perseverance of a gen-
tleman who hears me *, in adapting to practical use the re-
ciprocating property in pendulums between the axis of sus-
pension and the centre of oscillation ; a property long known,
but never before applied. And by the unhoped-for accuracy
recently attained in geodetical operations, by the use of mea-
sures possessing within themselves the power of adjustment
for heat and cold, under the care of that distinguished indivi-
dual who is at this moment conducting the trigonometrical
survey of Ireland f.

* Capt. Kater. f Col. Colby.

The

Royal Society. 57

The attention of our great philosopher was by a natural pro-
gress carried on to a consideration of the tides, which ex-
hibit phaenomena in apparent direct opposition to their cause ;
and which remained utterly incapable of solution till the dis-
coveries of Newton disclosed the powers of centrifugal and
centripetal forces. La Place, in the investigation of this most
interesting, curious, and important problem, has not only taken
into account the declinations and parallaxes of both the great
luminaries, but also the oscillations of fluids in transmitting
motion as connected with their depths. And hence he has
been enabled to form a probable conjecture respecting the
depths of our great oceans. From investigating the laws of
Nature as displayed by the heavenly bodies, La Place de-
scended to a subject not less difficult or intricate, — the action
of particles on each other in capillary attraction, and in the
transmission of sound. And in a separate work he has ex-
hausted, by the most ingenious expedients, a subject scarcely
less profound than either of the former, — the doctrine of pro-
babilities. I do not notice separate memoirs and communi-
cations to Societies, most of which are embodied in his subse-
quent works. He is said to have contemplated a rigorous
mathematical survey of the atomic theory, as developed by
definite proportions. But the fate common to humanity has
interposed. La Place has lived sufficiently long for his own
fame : but no extension of his life would have satisfied the
expectation or the demands of science. The time is not ar-
rived, nor can I presume to assign to this extraordinary man
his rank among those that are no more. Yet, speaking from
this place and on this occasion, I will say, that Newton holds,
and ever must hold, the highest station in the fane of philo-
sophical renown. That to him

Non viget quicquam simile aut secundum.

But although the second niche must remain unoccupied, yet
one approximating to that of Newton will hereafter become
the elevated station of La Place.

On delivering the Royal Medal for Sir Humphry Davy.

It is with feelings the most gratifying to myself, that I now
approach to the award of a Royal medal to Sir Humphry
Davy ; and I esteem it a most fortunate occurrence, that this
award should have taken place during the short period of my
having to discharge the duties attached to the office of Pre-
sident ; having witnessed the whole progress of Sir Hum-
phry Davy's advancement in science and in reputation, from
his first attempts in his native town, to vary some of Dr. Priest-

New Series. Vol. 3. No. 13. Jan. 1828. I ley's

58 • Royal Society.

ley's experiments on the extrication of oxygen from marine
vegetables, to the point of eminence which we all know him
to have reached.

It is not necessary for me more than to advert to his dis-
covery of nitrous oxide ; to his investigation of the action of
light on gases ; on the nature of heat ; to his successful dis-
crimination of proximate vegetable elements ; nor to his most
scientific, ingenious, and useful invention, the safety-lamp, — an
invention reasoned out from its principles, with all the accu-
racy and precision of mathematical deduction.

The particular series of discoveries for which the Royal
medal has been awarded, are those which develop the relation
between electricity and chemistry.

Soon after Sir Humphry Davy had been seated at the
Royal Institution by an invitation from Count Rumford, an
invitation founded on his first production, — A paper on the
nature of heat, — our late President began his experiments and
investigations on electric chemistry : a most powerful Voltaic
apparatus was fortunately placed at his disposal ; and in his
hands electric chemistry soon became the most important
branch of practical science: important from its immediate
energies and powers; but much more so from the general
laws of nature, which it has laid open to our view.

A new acidifying principle, or supporter of combustion, was
discovered, possessing the same negative electric properties as
oxygen. Muriatic acid disclosed its real composition. The
oxymuriates were transferred to their proper class. The
alkalies were reduced into metals ; and the earths were proved
to be similar oxides. But in the progress of these experi-
ments a discovery was made, surpassing all the wonders attri-
buted to alchemy. Three basins were arranged in a straight
line, each containing water, and to the middle basin some
neutral salt was added. The three were connected by moist-
ened syphons of asbestos : the opposite piles of a Voltaic bat-
tery were then applied to the extreme vessels ; and in a short
time the neutral salt disappeared from the middle basin, and
its constituent parts were found separated ; the acid attracted
to the positive pile of the battery, the alkali to the negative.
This astonishing result, followed up by other experiments,
led to the conclusion that chemical energies may be increased,
diminished, or even inverted, by the superinduction of electric
powers homogeneous with or dissimilar from their own. This
metastasis in the hands of physiological inquirers promises to
conduct them to discoveries of the utmost importance in the
functions of life. I flatter myself that it is now actually in
such hands.

The

Royal Society. 59

The principle of varying or modifying chemical energies
by those of electricity has been applied by the invention, in a
manner the most philosophical, and on a scale the most ex-
tensive.

The copper sheathing of ships and vessels had been found
to corrode in the short period of a single voyage, being con-
verted into an oxide through the medium of some acid, or at
least of a decompounded substance, occupying the negative
extremity of the electric scale. The copper must therefore be
positive in respect to tbe body decomposed or attracted. A
reference was made by the Government to the Royal Society,
with the hope of discovering some remedy for this most serious
evil. Grounded on a perfect knowledge of chemical and of
electric powers, it immediately occurred to the illustrious dis-
coverer of their relations one to the other, that if a substance
more positive than copper, and in contact with it, could be
exposed to the corroding action, that the copper would, by
induction, be rendered less positive, and therefore indisposed
to combine with any other negative body.

Experiments the most satisfactory were then made on a
small scale ; and in consequence of their success, plates of
zinc, and afterwards of iron, were applied to ships' bows ; and
the copper has been fully and completely protected. The
theory and the experiments have been confirmed in the most
ample manner. A defect has indeed occurred in practice, from
the over success of protection. The induction of negative
powers to the copper has gone too far ; they have caused it to
act on the compounds in an opposite direction, by attracting
to itself the earths and alkalies, thus affording attachments to
the marine vegetables which the copper was intended to pre-
vent. This appears to me, however, susceptible of a cure.
I am sufficiently advanced in years to remember the American-
revolution war. Ships were then first sheathed with copper :
they were preserved clean from weeds, nor was the copper
corroded : but the ships were fastened together by iron bolts,
and these, to the utter astonishment of every one, decayed; and
the ships became unable to sustain the ordinary straining in
gales of wind. For some time the effect could not be traced
to its cause, for galvanism was then unknown; but at last
bolts made of bronze were substituted for those of iron, and
immediately the copper failed. When the theory has therefore
been modified by experience on the principle of these empiric
trials during the American war, I cannot hesitate in predicting
complete practical success ; with full glory to the illustrious in-
dividual who deduced the practice from theory, and with ample

I 2 advantage

60 Royal Society.

advantage to all those who may then bring the practice into
beneficial use.

Sir Humphry Davy having last year communicated a pa-
per to the Society in continuation of his former inductions and
generalization on chemical and electric energies, there cannot
be a doubt but that the only obstacle against his then re-
ceiving a Royal medal, on the first occasion that the Society
had it to bestow, was his occupying this chair. That obsta-
cle, unhappily for science, no longer exists ; and the Royal
Society take this earliest opportunity of testifying their high
estimation of these talents and of these labours which all Eu-
rope admires. We trust and hope, although our late President
has been induced by medical advice to retire from the agitation
of active public stations, that his most valuable life will be long
spared ; and that energies of mind may still be displayed to
this Society and to the civilized world, equal to those which
have heretofore rendered immortal the name of Davy.

On delivering the Medal for M. Struve.

In no science has progressive dilatation and expansion
been equally manifested as in astronomy. Limited at first to
observing the phases of the moon; to conjecturing the re-
turn of eclipses after certain periods; to arranging religious
festivals, or the times for agricultural labour by the heliacal
rising and setting of stars, — it has ultimately extended to
these stars themselves.

A most eminent individual of our own times may be consi-
dered as the parent of sidereal astronomy. The late Sir Wil-
liam Herschel, having doubted the extent of the solar system,
leapt boldly beyond its comparatively narrow bounds, and
laid open to our view suns mutually revolving round each
other at distances from whence the orbit of the earth can
subtend no more than a physical point. The same piercing
eye distinguished between clustered stars, and spaces shining
from collections of nebulous matter, destined perhaps in the
course of ages to condense into a more solid form. These
sublime pursuits are now actively continued, I am most happy
to say, in our own country by a son worthy of such a father,
and by a gentleman who, uniting energy, ability, and perse-
verance, allows no one to run before him in whatever he un-
dertakes #.

The same subject is also investigating on the continent of
Europe, with the attention and assiduity that it so well de-

* Mr. South.

serves,

Royal Society, 6 1

serves, especially by M. Struve, director of the Observatory
at Dorpat. Having obtained the use of a powerful refracting
telescope, this indefatigable astronomer has, in the short space
of four years, alone and unassisted, produced this work, — A
Catalogue of Double and Multiple Stars, to the amount of
3063 stars, " Catalogus Novus Stellarum Duplicium et Multi-
plicium" — all laid down with an accuracy commensurate to
the great labour and attention bestowed on them. The Royal
Society have not hesitated in marking with their highest ap-
probation such labour, such attention, and such ability, dis-
played by an individual who has thus established strong claims
for gratitude on the astronomical world, and from a continued
exertion of whose energies much more may with confidence
be expected.

On delivering the Copley Medal to Dr. William Prout.

The science of chemistry, like that of astronomy, may
reckon its different periods and distinct elevations. The de-
composition of neutral salts; the discovery of gases; the de-
composition of water ; the application of voltaic energies, by
the skilful hands of our late President ; the atomic theory,
with definite proportions. But nature is inexhaustible, and
much more remains to be done. Although the ultimate ele-
ments of animal and vegetable substances are known to be
few; yet their proximate elements, produced by unions of the
former in different proportions and in different manners, con-
tinue indefinite. Besides the amylaceous, the saccharine, and
twenty other principles widely diffused through the vegetable
kingdom, there remain the essential oils and specific secretions;
each resolvable into the few ultimate elements, and so readily
changing the Proteus-like appearance of their proximate forms,
as to baffle all but the most delicate and refined attempts to
investigate their real properties and discriminating qualities,
— qualities induced through the agency of life, and perhaps
involving substances not subservient to the laws of gravity
and inertia; the essential attributes of ordinary matter.

Much progress has indeed been made in separating parti-
cular substances from their combinations with others, to the
great improvement of pharmacy and medicine.

But the Royal Society have viewed with peculiar satisfaction
a new and accurate mode of analysis described by Dr. Prout,
and founded on the most evident and simple principles ; pro-
mising not merely to disentangle any one particular combina-
tion, but to afford an insight into all the products created by
living chemistry. They have hastened, therefore, to stamp
with the highest mark of their approbation, as well the mode

of

62 Royal Society.

of analysis itself, as the specimens of what, in the hands of
Dr. Prout, it has already performed: and not doubting, but
that by the exertion of such talents, such ingenuity, and such
labour, their satisfaction will from year to year be continually
increased.

On delivering the Copley Medal to Lieutenant Henry Foster.

Of all the accidental discoveries ever made by man, the
most unexpected and extraordinary, as well as most useful
in its consequences, appears to have been the magnetic needle.
No one could have thought it within the range of possibi-
lity to devise any plan, by means of which a ship in the midst
of a wide ocean, surrounded with perfect darkness, and tossed
by the winds and by the waves, might yet be able to ascertain
its course with the same certainty as in open day, and under
circumstances the most favourable. Yet the simple experi-
ment of a child floating a magnetized needle on a cork, directly
led to this important discovery. The variation must, without
doubt, have been immediately observed. Columbus is said
to have first noticed, and with astonishment and dismay, that
the variation increased as he proceeded on his great voyage of
discovery towards the West. Magnetism, a subject at once
so curious and so useful, was attended to with such care, that
the secular change of variation in the same place did not long
escape notice. The dip was early known ; and more than a
century ago observations were made on the daily change of
direction, and on a supposed relation which it bore to the ap-
pearance of northern lights, and to other natural phaenomena.
Nor were theories wanting : — some utterly gratuitous, as that
conjectured by the celebrated Dr. Halley, who supposed arbi-
trary points of attraction, and an internal earth or revolving
nucleus. Other theories, although given by less eminent men,
appear to be more conformable to trie true principles of gene-
ralizing by induction; as that quoted by Mr. Foster, from
Derham in his Physico-theology. But the accuracy of modern
experiment was wanting. The method of counting vibrations
to ascertain intensity had not then occurred ; nor were instru-
ments, in all probability, to be procured that were accurately
made, or of much delicacy of motion. In recent times, and
by a member of this Society *, we have seen the local attraction
of ships compensated on the most scientific principles ; terres-
trial direction neutralized ; and the line of action, at least of
diurnal variation, ascertained.

And we have seen phaenomena little less astonishing than

* Mr. Barlow.

the

Royal Society. 63

the one displayed by the original discovery of magnetism itself,
in the connection that it bears to electricity and in the induc-
tion from rotary motion. It was important, however, that
experiments should be repeated in different places, and espe-
cially in those which are most difficult of access, but situated
near to the magnetic pole.

Lieutenant Henry Foster, well known to this Society by
the cooperation he afforded to Captain Basil Hall in deter-
mining the number of vibrations made by an invariable pen-
dulum near the equator, and at several other stations ; having
shared in the dangers of Captain Parry's second voyage,
eagerly seized the opportunity afforded by a winter residence
at Port Bowen, on the eastern side of Prince Regent's Inlet, in
lat. 73° 14/, to ascertain the rate of an invariable pendulum,
to conduct an elaborate course of experiments on magnet-
ism ; and in addition to these, observations on refraction.

One is utterly astonished at the magnitude of these labours,
and at the accuracy and care with which they were conducted,
(as is manifest from internal evidence,) in a situation where
comfort and ease were unattainable, and where peculiar dif-
ficulties presented themselves at every step. It is impossible
for me to give an abstract of Mr. Foster's most ample and
detailed communication : I must refer every scientific inquirer
to the paper itself. Among its important contents are : — The
amount and times of daily variation attributable of course to
the sun, but including in one series the action apparently
caused by the moon. — The line on which a needle being di-
rected the daily variation ceases. — A refutation of the supposed
connection between tremors of the needle and aurora borealis.
— The amount and times of daily variation in the dip ; with
a deduction from thence, according to the known law of the
cosines, to the periodical change in horizontal intensity. — And
a legitimate conclusion from all these facts, that the magnetic
axis of the earth may probably describe a small curve, com-
pounded of circles attributable to the sun and moon, of two
or three minutes' radius round its mean place, which will solve
the change of dip, of diurnal variation and of horizontal inten-
sity ; and may account for the secular variation in a manner
similar to that which explains the precession of the equinox.

The Royal Society are of opinion that they do no more
than strict justice, in awarding their Copley medal to the au-
thor of these observations and deductions ; and not without a
hope that by so doing, public attention may be more strongly
drawn towards an officer possessing such abilities, energies,
and preseverance #.

* Never were expectations more speedily or more amply gratified ; tot

on

64 Astronomical Society.

After the delivery of the Medals, the Society proceeded
to the election of a Council and Officers for the year ensuing ;
when on examining the lists, the following was found to be
the state of the ballot :

Members of the old Council to continue. — Davies Gilbert,
Esq. M.P. Capt. Francis Beaufort, R.N. ; John George
Children, Esq. ; Sir Humphry Davy, Bart. ; John F. W.
Herschel, Esq. M.A.; Sir Everard Home, Bart. V.P. ;
Capt. Henry Kater, V.P.; John Pond, Esq. A.R. ; William
Prout, M.D.; William Hyde Wollaston, M.D. V.P.; Thomas
Young, M.D. Foreign Sec.

Members of the Society chosen into the Council. — Francis
Baily, Esq.; The Rev. William Buckland, D.D. ; Charles
Lord Colchester; John Wilson Croker, Esq.; William Henry
Fitton, M.D. ; The Rev. Edmund Goodenough, D.D. ; John
Guillemard, Esq. ; John Ayrton Paris, M.D. ; Peter Mark
Roget, M.D. ; Capt. Edward Sabine, Roy. Art.

Officers for the ensuing year :

President: Davies Gilbert, Esq. M.P. — Treasurer: Capt.
Henry Kater. — Secretaries : Peter Mark Roget, M.D.; Capt.
Edw. Sabine.

ASTRONOMICAL SOCIETY.

Nov. 9. — Mr. Baily presented a paper " On the right ascension
of y Cassiopecc." As this paper is a short one, and of an interesting
nature we shall give it nearly in the words of the author:

" On comparing the Catalogue of Stars, recently published by
this Society, with the Catalogue of 100 principal fixed stars given
by Mr. Pond, at the end of the Nautical Almanac for 1829, 1 was
struck (he says) with the considerable difference which appears in
the JR of y Cassiopea? : Mr. Pond making the JR of that star up-
wards of one second (in time) more than the Catalogue printed by
this Society. At first I imagined that some error might have crept
into the calculations of the Society's Catalogue, notwithstanding
they were made by two computers, independent of each other, and
afterwards revised by our indefatigable secretary, Mr. Stratford.
I therefore, for my own satisfaction, went through the whole com-
putations myself, and was pleased to find that there was not the
slightest difference in the results. I next reduced the whole of the
observations of that star made by Mr. Pond at the Royal Observa-
tory at Greenwich, and found them to agree very nearly with the
result, deduced by Mr. Taylor, who makes the mean of 10 ob-
servations to be = 0h 46m 13s,23 reduced to Jan*. 1, 1825: whereas
the Society's Catalogue gives only 0h 46m 12s,13 on January 1,
1825 ; being a difference, as already stated, of 1%1. Bradley has

on the very clay that the medal was delivered, His Royal Highness the
Lord High Admiral was graciously pleased to advance Mr. Foster to the
situation of a commander, and to assign him a ship for a voyage of scientific
investigations in the Southern hemisphere.

5 observa-

Astronomical Society, 65

5 observations of this star, and Piazzi has 46. It is scarcely possi-
ble that Bradley should be in error one second of time : and still
less probable that the mean of 46 observations by Piazzi should be
erroneous to such an amount. The result of Bradley's observations
(after allowing for the effect of precession) differs 8",5 in space
from those made by Piazzi : which quantity, divided by 45 (or the
interval of years between the two observers), will make the annual
proper motion of the star, if it really have any, about 0",19 in
space. But, this is not confirmed by the recent observations of
Mr. Pond j and we must look elsewhere for a solution of the diffi-
culty. That the position of a star of the third magnitude should
be so undecided at the present day that its Ai cannot be satisfac-
torily depended on, to a second of time, does not speak much in
favour of modern astronomy ; and shows us that a great deal still
remains to be done towards establishing the fundamental parts of
the science. * * * Amongst other suggestions I have imagined that it
might arise from a typographical error; and, in fact, if we sup-
pose a misprint of 10'' in the /R of y Cassiopece in Piazzi's Cata-
logue, that is, if we read iR=ll° 11' 17",6 instead of 11° 11' 7",6,
the whole difficulty will vanish, and the results of the observations
of Bradley, Piazzi, and Pond, will agree to the greatest exactness.
But, we are scarcely warranted in making such an alteration with-
out a reference to the original observations. Some suspicion how-
ever is excited that the printing is not strictly correct, from the
circumstance that Piazzi considers the annual proper motion in
JR, as deduced from Bradley's observations, to be = 0 ; which
would agree with the amended reading as here suggested : but
which does not accord at all with the present reading in the Cata-
logue, since the annual proper motion is, as I have already ob-
served, in such case = — 0',19.

" Before I close these remarks, I would observe that there are also
differences in the JR. of three other principal stars (besides that of
|3 Scorpii, which is acknowledged to be an error in the Greenwich
Catalogue) to which I am desirous of calling the attention of the
Society j and for which I can, by no means, account. These are
£ Ursce Majoris and (5 Cephei (both stars of the third magnitude)
and c Draconis, a star of the fifth magnitude. The two last differ,
as in the case of y Cassiopece, above a second in time from the Ca-
talogue of Mr. Pond : but £ Ursce Majoris differs as much as 1*,4.
The case of this last star is the more remarkable, since the obser-
vations of Bradley and Piazzi correspond with wonderful exact-
ness ; there being a difference of only one second, in space, between
them, after a lapse of 45 years : whereas from the time of Piazzi to
the year 1825, a period of only 25 years, there appears, from Mr.
Pond's observations, to be a difference of upwards of 20".

" The whole of the computations relative to the positions of
these stars, I have frequently repeated, and can assure the Society
that there is no error in the results as printed in their Catalogue.
Time only, and further observations, can clear up these apparent
difficulties."

New Series. Vol. 3. No. 13. Jan. 1828. K A paper

66 Astronomical Society.

A paper was read " On double object-glasses ; by M. Littrow."

The first part of this communication is devoted to the derivation
of the equations expressing the conditions proposed by Mr. Her-
schel for the destruction of the aberration of sphericity in a thin
double object-glass, by the ordinary processes in use among the
German geometricians for such investigations. The author states
himself to have entered on this investigation with a view to disse-
minate a knowledge of the theory alluded to in his own country ;
but being induced thereby to resume some former investigations of
his own, he takes the opportunity to communicate to the Society
his own principal results.

Taking for granted the well-known expression of Euler for the
aberration of a lens of two surfaces, and developing it in descending
powers of the distance of the radiant point from the lens, he obtains
expressions, from which, by proper management, and substitution
of similar quantities for a second lens, he derives the two final equa-
tions (A) and (z) demonstrated by Mr. Herschel. He then pro-
ceeds to the main object of his paper. This may be briefly stated
to be the embodying of the relations expressive of the refraction
of a ray through any four spherical surfaces, however situated,
(provided they have a common axis), in trigonometrical equations,
in which no quantity is regarded as small, and of course nothing
neglected. These equations are in themselves sufficiently simple
when undeveloped, and in that state may very readily be applied
to determine whether any proposed construction of an object-glass
really does satisfy the essential geometrical conditions of a perfect
telescope, by producing a rigorous union of different coloured rays,
and rays incident on different parts of the object-glass. Accordingly
the author instances their application to a construction recently
proposed by a German optician, as of peculiar excellence. In this
construction the indices of refraction of the crown and flint lenses
being respectively 1*53 and 1*60, and their dispersive ratio 0*25, the
thickness of the crown lens 0-01 , that of the flint 0, and the lenses
being supposed in contact, the radii of the surfaces are

For the crown 1st surface (convex) 0*69281

2nd surface (convex) 2-255319

For the flint 1st surface (concave) 1-543030

2nd surface (concave) 5*768005
Substituting these data in his equations he finds that they satisfy
sufficiently well the conditions of achromaticity, but that they are
very far from being entitled to the same encomium when the sphe-
rical aberration is considered.

But when the question is inverted, and the problem is, not to try
whether a proposed construction be good or not, but, a priori, to
determine what is best, the equations in question, though simple
enough in their trigonometrical form, become complicated by the
algebraic developments their direct analytical resolution necessi-
tates. Now the essence of M. Littrow's proposed method is to do
away with all this development, so far as it tends to produce com-
plication ; and after preparing the equations in the most convenient
manner the case will allow, to substitute for their direct algebraical,

Astronomical Society. 67

an indirect numerical, solution, by the well known and ready method
of trial and error, a method perfectly correct in theory as well as
easy in practice.

M. Littrow exemplifies this theory by applying it to that parti-
cular case when the indeterminate problem is limited by the condi-
tion of Kliigel, viz. that the refractions at the first two surfaces
shall be as small as possible, in which case the first or crown lens is
in fact wholly given, and it only remains to determine the radii of
the flint. He takes into consideration the thickness of the former,
but not the latter, lens, and neglects also their distance inter se.
As a numerical instance, he supposes the indices of refraction 1*53
and 1*58, the dispersive ratio l,and the thickness of the crown lens
one hundredth part of its focal length, when, by applying the pro-
cess described, he finds the following radii :

Crown lens. . 1st surface (convex) 0*186823

2nd surface (convex) 0*608170

Flint lens . . 1 st surface (concave) 0*407996

2nd surface (concave) 0*445808

Focal length of the compound lens ;= 1 ; aperture 0*06495
M. Littrow, however, is by no means of opinion that the condi-
tion of minimum refraction here assumed is the best, or in any way
essential to a good object-glass ; only it facilitates calculation. He
regards it as more advisable to aim at increase of aperture, and for
this purpose to assume the first or crown lens equiconvex, which
he affirms to be the condition requisite for the attainment of that
end. He therefore explains his method of proceeding in this case,
and applies it to the same numerical data with those last mentioned,
which give for the final results :

Crown lens (equiconvex) Radius of each surface. ... 1*06
Flint lens (biconcave) Radius of 1st surface .... 1*04394

of 2nd surface 3*296512

Focal length 3*702231
Aperture. . . . 0*09973 x focal length
or nearly Tv of the focal length, being a much larger proportional
aperture than it has been usual hitherto to give to achromatic
telescopes.

The author concludes by stating the reason of his entering into
these investigations : viz. an application made to him by an artist of
Vienna.

A paper was also read from M. Slawinsky, containing the fol-
lowing observations, made at Wilna. (Longitude l1' 4im 12* East
of Greenwich).

1. Eclipses of Jupiter s Satellites.
Sidereal time.
. 4b 0m23s,7 good observation.
8 51 51 ,9 very good.
10 44 25 good enough.
12 29 38 ,7 very good.

15 31 56 ,1 middling.

16 46 0 ,1 middling.
16 I 14,9 a little doubtful.

, 16 46 15 ,2 passable.

K2 2. Oceu

1825. Jan. 17

Im.

1

Mar. 22

Em.

2

Apr. 23

Em.

1

May 5

Em.

1

1826. May 8

Em.

1

June 2

Em.

2

1827. Mar. 18

Im.

1

Apr. 18

Im.

1

68

Zoological Society*

2. Occultations.

Sidereal time.

1825. Apr. 1

T • S Im. 10h8,n55%2 very precise.
e i.eoms. • • • * Em. 11 15 14 ,2 a little doubtful

23

Star (mag. 8-9) Im. 1 1 22 29 exact.

1826. Feb. 15

208 Tauri Im. 6 55 58 ,8 good.

16

Saturn

1st ansa ^ r 3 11 58 ,8 ^

1st limb Urn.? 3 12 8 ,8 I good.

2nd ansa ) <-3 14 48,3 3

1827. Mar. 18

A Librae Im. 17 4 55 ,9 good enough.

ZOOLOGICAL SOCIETY.

We extract from an Address delivered by Mr. Children at the An-
niversary Meeting of the Zoological Club of the Linnaean Society, on
the 29th November last, the following outline of the progress and
present prospects of this new, but flourishing, Society.

* From this short sketch of what has passed under our immediate
observation within these walls in the course of the last twelve months,
I turn to what has been doing in another quarter, to which we all
look with an interest and anxiety commensurate with the importance
attached to the growth and progress of that young but promising
child of British energy and science, the Zoological Society. It is a
glorious feature in the philosophical character of Great Britain, that
whilst in foreign countries, Science owes most of her success to the
fostering care of Royal patronage, or the protection of executive
power, — here, with faint exceptions, ' few and far between,' she relies
on her own resources ; and, unlike the creeping parasite, raises her
head in independent dignity by the individual exertions of her disin-
terested cultivators, who, loving her for herself, seek only to accele-
rate her progress, and establish her empire in the human mind on
the firm basis of immutable truth. To such an origin the Zoological
Society may proudly assert its claim y — not one shilling has been
drawn from the public purse for its support : and could it condescend
to ask such aid, I for one would raise my voice against the humiliating
petition — Absiste precando, viribus indubitare tuis. But it has not so
forgot its dignity ; it has relied solely on the liberal ardour of an en-
lightened people, and it will still rely on it j— nor will it rely in vain.
The spirit of its immortal Founder has gone forth, and will not fail to
light up in every heart capable of exalted feelings, some portion of
that fire which animated his own ; some wish, some sacred hope of
treading, with however unequal steps, in the path he has so zealously
marked out for them. In saying that not one shilling has been drawn
from the public purse for the support of the Zoological Society, I
must not be understood as meaning to imply that therefore its wel-
fare is a subject of indifference to the gracious Monarch who wields
the sceptre of these kingdoms, or the enlightened individuals whom,
in his wisdom, he has summoned to his councils. That the very re-
verse is the fact, has already been confirmed by the exertion of Royal
munificence in favour of the Society, and by its having at its head one

of

Zoologic wl Society. 69

of His Majesty's principal officers i of state — a man, whose qualities of
head and heart have rarely been equalled, never surpassed j and of
whom both the Society and the B ritish nation may honestly be proud.
Such a Monarch and such a Minis ter will never be backward to further
the interests of Science, when paramount claims shall happily cease to
divert the current of national treasure into other channels, and when
increasing prosperity shall relax the strict bands of public ceconomy,
by which their natural impulses are at present checked and circum-
scribed. If proof be wanting to support this assertion, we need only
turn our eyes a short space northward, for indisputable evidence of the
inclination of His Majesty's Government to further the views of the
Zoological Society : and it is peculiarly gratifying to me to inform
you, that in addition to the ground already allotted for the gardens
and vivaria, final arrangements haive been very recently completed,
for the grant of the lake and its islands in the Regent's Park, for the
purposes of breeding, rearing, and preserving water-fowl and other
aquatic animals j and for a plot of ground for the erection of suitable
offices and farm-yards, for breeding- and domesticating poultry, &c.
The right of entree has also been granted to the Members of the Zoo-
logical Society, to the walks and ornamental grounds on the West
side of the Regent's Park next to the lake 3 — all, privileges of essential
importance to the Society, and gratifying proofs of the interest that
His Majesty's Government takes in its welfare.

" As an accurate and sufficiently minute account of the valuable
additions that have lately been made to the Society's Menagerie and
Museum appears in the last Number of the " Zoological Journal," it
would be superfluous to dwell on them in this place. I shall there-
fere merely state, that among the latter, stands conspicuous the ex-
tensive collection of its lamented founder, the late Sir Thomas Stam-
ford Raffles, particularly rich in those rare animals, only lately known
to science, from the eastern islands 5 as the male and female Probos-
cis Monkey (Simia jiasica, Linn.) — a new species nearly allied to it, —
the Malay Bear (Helarctos Malay anm, Horsf.) y different species of
Tupaia, and of the other new genera Mydaus, Ictides, Gymnura, &c.
The Birds include most of the splendid species of Sumatra, particu-
larly the gallinaceous fowls. Various new and interesting species are
also found among the Fishes, Reptiles, Insects, and Zoophytes.
Various other valuable animals have been added by the members" and
friends of the Society : but the most conspicuous of the late acquisi-
tions is a fine specimen of the Ostrich, graciously presented by His
Majesty. In the menagerie and gardens nearly two hundred living
animals are exhibited in suitable paddocks, dens, and aviaries j as
two beautiful Llamas, from the Duke of Bedford and Mr. Robert
Barclay y a Leopard, the gift of Lord Auckland ; Kangaroos, a Rus-
sian Bear, Ratel, Ichneumons, &c. &c. j besides a pair of Emus,
Eagles, Cranes, Gulls, Gannets, Corvorants ; various Gallinaceous
Birds, and many others.

" The number of Members, whose names are inscribed in the books
of the Zoological Society, amounts this day to 685."

XII. /«-

[ 70 ]

XII. Intelligence and Miscellaneous Articles.

ISOPYllE, A NEW MINERAL SPECIES.

THE following account of this mineral by W. Haidinger, Esq.
F.R.S. E. &c. as well as the four following notices, we copy
from the last number of Professor Jameson's Journal.

1. Description.— Regular forms not observed. Very pure masses
of considerable size, often nearly two inches in every direction, oc-
cur imbedded in granite.

Cleavage none. Fracture conchoidal ; highly perfect, where the
mineral is pure ; of lower degrees of perfection, where there are
foreign admixtures in it.

Lustre vitreous, often considerable. Colour grayish-black and
velvet-black, occasionally dotted with red, as in the heliotrope.
Streak pale greenish-gray.

Opake, or very faintly translucent on the thinnest edges, with a
dark liver-brown tint.

Brittle. Slight action on the magnetic needle.

Hardness =5'5. . .6*0. Specific gravity =2*912.

2. Observations. — Several specimens of the species of isopyre are
preserved in the cabinet of Mr. Allan. Some of them are quite
pure, and have no rock attached to them ; others are imbedded in
a kind of granite, chiefly consisting of quartz, crystals of which
often penetrate the dark-coloured mass of the isopyre. Someof the
specimens were procured by Mr. Allan three years ago, on a journey
through Cornwall, in which I had the pleasure of accompanying
him, from a miner in St. Just; others were given to Mr. Allan by
Mr. Joseph Carne of Penzance, whose collection of minerals is par-
ticularly rich in the products of the western districts of Cornwall.
The west of Cornwall is certainly the native country of the isopyre,
but I am unable at present more accurately to indicate its locality,
as I then considered the substance actually to be, what it was called,
black opal, and, as such, much less interesting than it proved on
more attentive examination, and omitted to take a note of the ex-
act locality.

The resemblance of the isopyre to obsidian, or to what might be
supposed to be the appearance of opal, when of a black colour, is
very ^considerable; only the lustre of isopyre is less bright and
glassy than that of obsidian. It is also very much like certain va-
rieties of iron slag, and in fact it would be difficult to suspect the
mineral not to be a product of the same kind of fusion which we are
capable of producing in our own furnaces, if it were not associated
with crystals of quartz, or did not contain, as in one of Mr. Allan's
specimens, small imbedded crystals of tin-ore and of tourmaline.
In allusion to this appearance, and also on account of the perfect
similarity of a globule melted before the blowpipe, with the frag-
ment employed in the experiment, I propose the trivial name of
Isopyre, for designating the mineral, from wo; (equal) and iru§ (fire).
The similarity of properties is even preserved in regard to mag-
netism,

Intelligence and Miscellaneous Articles. 71

netism, the globule obtained by exposing a fragment of the mineral
to the blast of the blowpipe being magnetic, as well as the fragment
itself, and even in a higher degree.

From the description given * of the Tachylite of Breithaupt, this
mineral should much resemble the isopyre. Its specific gravity is
much lower, being only 2*5. . . 52*54, so as to preclude the possibility
of their belonging to the same species. It occurs in basalt and
wacke at Saesebuehl, near GofHtingen, likewise only massive.

Dr. Turner has analysed the isopyre, and finds its composition to
be Silica 47*09

Alumina 13*91

Peroxide of iron 20*07

Lime 1543

Peroxide of copper. . ] *94

98*44

OSMELITE, A NEW MINERAL SPECIES.

Professor Breithaupt, of Freyberg, gives the following account
of this substance :

The name of this mineral is derived from ocrpj (smell) and \iQo$
(stone). Its characters are as follows : Colour grayish-white, which
passes into a tint between smoke and yellowish -gray. Planes, which
have been exposed to the weather, have their colour changed into
dark hair-brown. It consists of thin prismatic concretions, either
scopiformly or stellularly arranged, and these again collected into
coarse granular concretions, forming massive portions. Cleavage
visible only in one direction, owing to the thinness of the prismatic
concretions, which indeed pass into fibrous. Its form is conjectured
to be rhomboidal ; is strongly translucent : it feels rather greasy : its
hardness, owing to the fibrous structure, is difficult to determine. It
appears, however, from some trials on the file, to be intermediate
between that of fluor-spar and apatite. Specific gravity =2*792
to 2*833.

It gives out, in the common temperature of a room, a distinct
clayey smell, which is increased by breathing on it, or when brought
from a warm to a cold place. In the mouth it tastes like clay, and
appears as if it would dissolve like clay, although no change takes
place.

This species is distinguished from the zeolites by its greater spe-
cific gravity. It approaches to tabular spar in hardness and specific
gravity, but in no other characters.

It occurs superimposed on calcareous spar, mixed with datolite,
— in veins in trachyte, in a hill at Niederkirchen, near Wolfstein,
on the Rhine.

HYDROSILICITE, — A NEW MINERAL SPECIES.

Dr. Kuh, in his inaugural discourse, entitled " De Hydrosilicite,
novafossilium specie, Berlin, 1826," informs us, that he found, in the

* Leonhard, 2d edit. p. 781.

serpentine

72 Intelligence and Misc ellaneous Articles.

serpentine of Frankenberg in Silesh i, along with chrysoprase, opal,
and pimelite, a mineral which he na mes Hydrosilicite. It is white,
without lustre, feels greasy, translincent, fracture even, soft, does
not adhere to the tongue, amorphou s, and appears to be almost en-
tirely composed of pure silica and v/ater.

RUSSIAN PLATI NA-SAND.

Professor Bjeithaupt has given the annexed mineralogical ex-
amination of this substance.

I was favoured by M. Schwetzau vrith a quantity of the platina-
sand, washed out of the sand of Nijr.iotaguilsk, in the government
of Perme, in Siberia. Of this Siberian sand there are two kinds :
the one is ferriferous, and contains platina; the other, which is
purer and more quartzy, afforded principally remarkably fine wash-
gold.

The platina-sand, even at first glance , appears composed of grains
of different kinds. I separated, by the eye, the following minerals :
1. Plaiina. 2. Gold. 3. Irid-osmine. 4. Silver -white Jlat grains.
5. Iserine, or magnetic iron-sand.

The grains, from their appearance, oould not have rolled far, and
must have been found at no great distance from the place of their
origin, for many of them are very sharp-edged, or even bristled
with points.

1. Platina- grains. — I attempted to separate these from the iserine
grains, by means of the magnet ; but was surprised to find that not
only the iserine, but also many of the platina-grains, adhered to it.
I found that some of the platina-grains were magnetic, others not :
hence these two kinds are probably varieties of two distinct species.

First species : Common Platina. — It is the same with the platina
brought from America by Humboldt, and possesses the following
characters :

Colour platina-gray, which is different from steel-gray. On con-
cave places there is observed a yellowish appearance. — The grains
are angular and bristled, seldom blunt-edged ; the crystals are hex-
ahedral, and grouped, as in silver-glance. Hardness =70*— 8*5*.
Is perfectly malleable. Specific gravity 17*001 — 17*608. A large
American specimen in the Wernerian cabinet was 16*914. It is
well known that the native platina is always lighter than that pre-
pared by chemical means.

Second species : Ferruginous Platina. — The colour is platina-
grai/, but darker than in the preceding species. In hollows in the
specimens, the surface is tarnished, from dark brown to black, as
in meteoric iron. The grains and crystals have the same forms as
in the former species. — Hardness =8*0—8*5. Malleable, but not
so completely so as in the first species. Specific gravity 14*666
— 15*790. It is magnetic, and in some grains not only repels, but
also attracts. It is distinguished from the former species by lower

* Scale of hardness here used is that of Breithaupt, in his Mineralogy,
7 m that of glassy actynolite, 8 = that of adularia, 9 m quartz.

specific

Intelligence and Miscellaneous Articles. 73

r>

specific gravity, less perfect malleability, and its affording, by che-
mical trials, a considerable portion of iron.

2. Gold. — I found few grains of gold in the platina-sand : these
were partly gold-yellow, partly grayish- yellow. Is Werner's grayish-
yellow gold, gold combined with platina ?

3. Irid-osmin. — This species, which is a compound of iridium
and osmium, presents the following characters :

The colour is not steel-gray, as is generally believed, but a mid-
dle colour between whitish lead-gray and common lead-gray. It
occurs crystallized in low hexagonal prisms, which have an axoto-
mous cleavage. Hardness =8-0—8-75. Is imperfectly malleable.
Specific gravity = 17*969-18-571.

It would be desirable to have iridium and osmium again examined.
Iridium will probably be found to possess a higher specific gravity
than platina, and probably belong to the tessular system. The os-
mium, on the contrary, appears to belong to the electro-negative
metals, which possess a hexagonal crystallization, such as arsenic,
tellurium, and antimony.

4. Silver-white fiat grains. — They appear to be palladium.
Concluding Remark. — In the portion of platina-sand I examined,

the large half was ferruginous platina, the smaller common or true
platina. The remaining grains composed about ^th part of the
whole.

In the Phil. Mag. and Annals for November, we gave a notice of
Professor Ossann's having discovered various new metals in the
Uralean platina. From the following account, by the same Pro-
fessor, it appears that there are several varieties of it.

The platina, from ore of the Urals, is more varied in character
than that found in America. — I have already been enabled to di-
stinguish four different sorts, and I am told there are still more.
One of the kinds, that which is most abundant, is sold at the mint
in Petersburg. It consists of grains of different descriptions. Small
grains can be separated by means of the magnet, resembling the
magnetic grains in the platina of Brazil. The other grains are partly
of* a lighter and darker lead-gray colour, and about a line in diame-
ter,— partly of a gold -yellow colour; and some are small, flattisb,
and shining metallic. In the following analysis I used the bluish-
gray coloured grains. The following results were obtained in so-
luble matter :

Palladium 1-64-

Rhodium 11-07

Platina 80-87

Copper 2-05

Iron 2-30

Sulphur 0-79

Trace of Iridium.

Residuum 0-11

98-83
Poggendorf's Journal.

New Series. Vol. 3. No. 13. Jan. 1828. L new

74 Intelligence and Miscellaneous Articles.

NEW PHENOMENA OF VAPOUR OBSERVED BY CLEMENT
DESORMES.

This philosopher communicated, on the 4th of December, to the
Royal Academy of Sciences, some singular results relative to steam.
" When compressed in a boiler, and issuing in a violent and hissing
jet, through an orifice made in a pretty large plate, if a flat disk of
metal be presented to it, at a little distance from the orifice, the
disk is strongly repelled 3 but if it be brought near and placed against
the plate, as' if to close the orifice, although the steam issues on all
sides like artificial fire-works, and presses against the disk more,
than before, not only is the disk not driven away, but it adheres to
the plate even when the jet is directed downwards. It remains
suspended in opposition to its gravity, and can be detached only by
force. The same result takes place in an experiment with the wind
which issues from the large bellows of a furnace."

NOTICE OF A FIRE-BALL: — BY THE REV. S. E. DWIGHT.

This meteor appeared on Saturday evening, March 21, 1813, a
little before ten o'clock. The sky was extensively overcast, yet the
covering was every where thin : and in the North where the meteor
appeared, in various tracts of considerable extent, the stars were in
full view. I was standing on a platform on the north side of the
house, where I could survey the whole tract of sky over which the
meteor passed. When the light first broke upon me, I was looking
eastward, and for a moment supposed it to be a flash of very vivid
lightning j but from its continuance was led almost instantly to look
to the, luminary whence it proceeded. The following are the observa-
tions which 1 made at the time with regard to it.

1 . The meteor, when I first saw it, was about 35° above the horizon -,
and from the course of the fence near which 1 stood, I judged its di-
rection, at that time, to be about N. 20° E.

2. Its figure was nearly that of an ellipse, with the ends in a slight
degree sharpened or angular.

3. The length of the transverse diameter appeared to be about
equal to the apparent diameter of the moon when on the meridian -,
■and that of the conjugate, about three-fourths of the transverse.

4. The colour of the body resembled that of the moon, but was evi-
dently more yellow.

5. A trail of light was formed behind it of considerable length,
perhaps of ten or twelve degrees. It was broadest near the body,
and decreased in breadth very slowly for about two-fifths of its
length ; after which it was an uniform stripe of light, about as wide as
the apparent diameter of the planet Venus. The direction of the
tail was coincident with that of the transverse diameter.

6. The ball was much more luminous than the tail, so that the end
of the ball connected with the tail was scarcely less distinct in its
form than the opposite end.

7. The illumination was so powerful, that all the objects around

me

Intelligence and Miscellaneous Articles. 75

me cast distinct shadows, though less strongly marked than when the
moon is at the full.

8. Numerous sparks, of the apparent size of the smaller stars, but
much more brilliant, were continually issuing from the ball of the
meteor, and after descending a little distance, soon disappeared.

9. The length of time, in which the body was visible, was about
eight, or possibly ten seconds.

1 0. A short time before its disappearance, — say one or two seconds,
— three much larger sparks, or luminous fragments, were thrown from
the body at the same moment. Two of these were apparently as
large as the planet Venus ; the third was still larger. These three
were the last pieces which I saw leave the body. Their paths were
at first nearly parallel with that of the meteor, yet beneath it. From
this direction, however, they all deviated constantly and rapidly in
parabolic curves, until they seemed falling perpendicularly towards
the earth. Each fragment became less and less distinct, until it dis-
appeared. The largest of the three continued visible until it was
within about 20 degrees of the horizon.

11. The meteor itself disappeared as suddenly as if, in one indivi-
sible moment, it had passed into a medium absolutely opaque, or as if,
at a given moment, it had left the atmosphere ; but a few moments
afterwards there was a distinct and somewhat extensive illumination
over that part of the sky for about a second, as if the light of the de-
parting luminary had been reflected from some unknown surface to
the earth.

12. When the meteor disappeared, it was about 30° above the ho-
rizon, and, as I judged from the course of the fence, in the direction
of N. 45° E., or 25° eastward of the place where 1 first saw it. I con-
cluded that the direction of its path was probably from W. by S. to E.
by N. It was obviously going from me ; its path making an angle
with the optic axis of about 60°.

13. Not less than eight minutes, nor more than ten, after the dis-
appearance of the meteor, there was a report very loud and heavy,
accompanied with a very sensible jar. Though mistaken for thunder
by those who did not see the meteor, it did not much resemble either
thunder or the report of a cannon j but was louder, shorter and
sharper than either, and was followed by no perceptible echo.

14. A friend of mine, who was in Berlin at the time, about 23 miles
due N. of New Haven, saw the meteor distinctly, but made no par-
ticular observations concerning it. His estimate of it accorded ge-
nerally with mine, but it appeared to him larger, more elevated, and
somewhat more to the East in its apparent place. — 1 could not learn
that the fragments which fell from it were discovered. — Silliman's
Journal, vol. xiii. p. 35.

ON THE AURORA BOREALIS OF 26TH SEPT.: BY DR. FORSTER.

Boreham, Nov. 25,1827.
Having seen the remarkable aurora which occurred on the 26th of
September last, slightly mentioned in several of the journals, but no
where accurately described, I send you the following brief notes on

L 2 this

76 New Patents.

this remarkable phenomenon, which 1 made during its continuance,
through the night of the 25th, as it was seen by me and by others
from the neighbourhood of Chelmsford in Essex. — I was passing the
night at Boreham, and about nine o'clock P.M. I first noticed a very
remarkable light in the North, the sky became intensely red in the
N.N.E. and N., and afterwards very light all over the northern hemi-
sphere. Clouds, however, soon obscured it for a time, and I returned
to the house. At midnight on looking out of window, towards New
Hall, I noticed the sky to be remarkably luminous, and on going out
perceived every object as clearly as on a bright moonlight night. In
the North the most brilliant streams of light shot up into the zenith
from the horizon, generally in irregular diverging radii, whose centre
appeared to be at nearly N.N.W. by N. ; but other streamers of white
light in other directions becoming alternately brilliant and faint ap-
peared, while in E.N.E. and N.E. the whole sky seemed of a bright
yellowish light : the red colour which I perceived at nine o'clock had
quite disappeared, and the white light continued to prevail till it was
lost in the day-light of the following morning. It is recorded that on
two former occasions, one about twenty years since, and the other
early in the eighteenth century, bright auroras happened on the same
day ; namely, 25 th of September. I should like to have authenticated
particulars of this fact, as it would establish a most remarkable co-
incidence of dates with the occurrence of this rare and beautiful phe-
nomenon.

With regard to the aurora of the last 25th of September above de-
scribed, I may observe, that 1 never saw distant objects so clearly on
the brightest moonlight night as I did on that occasion at midnight j
but its light more resembled that of the break of day than of the
moon, and hence the name of Aurora has not unaptly been applied
to this meteor. T. Forster.

LIST OF NEW PATENTS.

To R. Wheeler, of High Wycomb, for improvements on refrigera-
tors for cooling fluids. — Dated the 22nd of November 1827. — 6" months
allowed to enrol specification.

To W. J. Dowding, of Poulshot, Wiltshire, for improvements in
machinery for rollering wool from the carding-engine. — 22nd of No-
vember.—2 months.

To J.Roberts, of Wood-street, Cheapside, and G.Upton, of Queen-
street, Cheapside, for improvements on Argand and other lamps. —
24th of November. — 6 months.

To J. A. Fulton, of Lawrence Pountney-lane, Cannon-street, Lon-
don, for a process of preparing or bleaching pepper. — 26th of Novem-
ber.— 6 months.

To J. Apsey, of John-street, Waterloo-road, Lambeth, for an im-
provement in machinery to be used as a substitute for the crank. —
27th of November. — 2 months.

To J. Jenour, jun., of Brighton-street, Pancras, for his cartridge
or case, and method of more advantageously inclosing therein shot or
other missiles for loading fire-arms. — 28th of November.— 6 months.

To

Scientific Books, tyc. 77

•To T. Bon nor, of Monkwearmouth Shore, Durham, merchant, for
improvements on safety-lamps. — 4th of December. — 6 months.

To W. Fawcett, of Liverpool, and M. Clarke, of Jamaica, for im-
proved apparatus for the better manufacture of sugar from the canes.
— 4th of December. — 6 months.

SCIENTIFIC BOOKS, &C.

A small work, entitled " The Circle of the Seasons," has just been
published by Mr. T. Hookham, of Bond-street, in which the average
day of flowering of most of our common garden plants throughout the
year is noticed, under its respective day; and a short account of other
phenomena is added, with some popular observations on the weather,
&c. &c. The work is in one small volume 12mo., and intended for
a daily companion to the popular botanist out of doors.

Polariscope, — an instrument for observing some of the most inter-
esting phenomena of polarized light. Made and sold by W. Cary,
Strand. The principle of this instrument was, we believe, first dis-
covered and described by Biot, and its form we observe is nearly the
same as one which has been described by Herschel. We conceive
that Mr. Cary has rendered an acceptable service to science by ma-
king these instruments for sale, as it will place the important and in-
teresting subject of polarized light within the reach of a greater num-
ber of inquirers than would otherwise have had an opportunity of
studying it.

A Tabular View of Volcanic Phaenomena, comprising a list of
the burning mountains that have been noticed at any time since
the commencement of historical records, &c. &c. By Charles Dau-
beny, M.D.F.R.S. Professor of Chemistry in the University of Ox-
ford. This is an extremely useful accompaniment to the author's work
on Volcanos. It consists of three parts : 1st, A list of the countries
in which volcanos occur ; 2ndly, A chronological list of volcanic
phaenomena j 3rdly, A view of the comparative heights of volcanic
mountains. The just estimation in which Dr. Daubeny's work is
held, is of itself a sufficient recommendation of the present tabular
view, which in addition to the information already mentioned, con-
tains an account of the geological nature of the various volcanic
mountains.

A new weekly Medical Journal, under the title of " The London
Medical Gazette," being a journal of medicine and collateral sciences,
was published on Saturday, December 8.

A short series of Popular Lectures on the Steam-engine, by Dr.
Lardner, Professor of Natural Philosophy in the new University, is
announced for publication in a few days. The author professes to
have stripped the subject of all its technicalities, and to have presented
it in such a form that readers totally unacquainted with mechanical
science may readily comprehend the construction and operation of
the steam-engine, as well as the most interesting circumstances con-
nected with the history of its invention and progressive improvement.

METEORO-

78 Meteorological Observations for November 1827.

METEOROLOGICAL OBSERVATIONS FOR NOVEMBER 1827-

Gosport. — Numerical Results for the Month.
Barora. Max. 30-40 Nov. 5. Wind N W.—Min. 29-28. Nov. 29. Wind N.W.
Range of the mercury 1-12.

Mean barometrical pressure for the month . 29-964

for the lunar period ending the 18th instant .... . . 29*872

for 14 days with the moon in North declination . . . 30*057

for 15 days with the moon in South declination . . . .. 29*687

Spaces described by the rising and falling of the mercury . . . 6-790
Greatest variation in 24 hours 0-730. — Number of changes 19.
Therm. Max. 62° Nov. 13. Wind N.— Min. 27° Nov. 22. Wind N.
Range 35°.— Mean temp.of exter. air 48°-42. For 30 days with 0 in n\ 50*60
Max. var. in 24 hours 19°-00— Mean temp, of spring water at 8 A.M. 54°-82

De Luc's Whalebone Hygrometer.

Greatest humidity of the air on five different days 100°

Greatest dryness of the air in the afternoon of the 2nd ; ... 51

Range of the index 49

Mean at 2 P.M. 70°-0— Mean at 8 A.M. 79°-2— Mean at 8 P.M. 81-2

of three observations each day at 8, 2, and 8 o'clock . . 76-8

Evaporation for the month 0-70 inch.

Rain near ground 1-835 inch.— Rain 23 feet high 1-690 inch.

Prevailing Wind N.W.

Summary of the Weather.
A clear sky, 1 \ ; fine, with various modifications of clouds, 9 *, an over-
cast sky without rain, 14 ; foggy 1£; rain, 4. — Total 30 days.

Clouds.
Cirrus. Cirrocumulus. Cirrostratus. Stratus. Cumulus. Cumulostr. Nimbus.
15 10 27 1 15 19 12

Scale of the prevailing Winds.
N. N.E. E. S.E. S. S.W. W. N.W. Days.
6 3i 3 2 4 1 2£ 8 30

General Observations. — This month has been calm and dry, excepting four
or five days, and very mild for the season till the 20th ; afterward it was
mostly cold, foggy, and an extremely damp air.

At 20 minutes part 8 p.m. on the 4th instant, two coloured paraselenes
appeared, one on each side of, and 22° 39' distant from, the moon's centre,
as determined by the star marked / (Iota) in the left heel of the constella-
tion Auriga, which star was conspicuous through, and apparently centered
in the paraselena on the northern side of the moon. These mock- moons
were formed in a turbid-looking broad band of cirrostratus as it slowly passed
the moon's horizontal rays.

In the afternoon of the 9th there was a curious appearance of nascent
cumuli in a long connected range between Gosport and Portsdown Hill ;
they had the appearance of whitish columns of steam moving eastward
near the surface of the earth with a gentle wind from N.W.

On the 11th, 18th, 19th, 25th, and 26th, the index of the hygrometer
advanced to the extreme moisture point, or 100 degrees, the whalebone on
these days being expanded to its utmost extent, by the deposition of dew
and thick haze thereon. The dew deposited in the rain-gauge in the nights
of the 17th and 18th amounted to four hundredth of an inch in depth.

From 11 till 12 p.m. on the 18th, a faint aurora borealis appeared in the
horizon between the N.W. by N. and N. by E. points. A mild lemon-
coloured

Meteorological Observations for November 1827. 79

coloured light, and the segment which it described above the horizon, in-
dicated the phenomenon, whose altitude did not exceed five degrees ; nor
was it accompanied by any perceptible coruscations during the hour of
observation.

In the mornings of the 22nd and 23rd the ice lay pretty thick on the
ground, and icy efflorescences appeared on the inside of the glass windows
(being the first time this autumn), which were succeeded by a frosty haze on
the latter day, and a light shower of snow in the evening. This was the
earliest fall of snow observed here during the last twelve years. Several
showers of snow also fell in Northumberland on the 21st, and much more
fell between London and Manchester on the 22nd and 23rd.

The mean temperature of the atmosphere for November varies con-
siderably in different years, sometimes to ten or twelve degrees. Sudden
changes from a temperate air to several degrees below the freezing point,
as was the case the latter part of this month, are found so powerful on
some delicate constitutions, as to cause a general languor and a painful
sensation of the flesh, which are mostly experienced at the setting in of
piercing northerly and easterly winds immediately after mild currents of
air from the opposite points of the compass. By some attention to this sub-
ject, it may be ascertained that colds and their calamitous train of con-
sequences at the close of autumn and beginning of winter are more fre-
quently produced by sitting in wet clothes and shoes, or in a brisk current
of air when warm ; or 'by going out of a hot room for any length of time
in the dewy or foggy night air, — circumstances which seldom fail in obstruct-
ing the insensible perspiration of the body, than by a uniform decrease of
temperature, however low, with the precaution of wearing suitable winter
clothing.

The atmospheric and meteoric phenomena that have come within our
observations this month, are two paraselence, three lunar halos, an aurora
borealis, two meteors, lightning in the evening of the 8th, and three gales
of wind, two from the South, and one from the West.

REMARKS.

London.— Nov. 1. Fine day : some rain in the evening. 2, 3. Fine.
4. Foggy morning : fine day. 5. Cloudy. 6. Fine. 7, 8. Cloudy. 9. Drizzly.

10. Cloudy. 11, 12. Fine. 13 — 15. Cloudy. 16. Rainy. * 17. Cloudy.
18. Foggy morning. 19. Cloudy. 20. Gloomy: cloudy. 21. An extraor-
dinarily high tide this morning about 4 o'clock, doing very considerable
damage: day fine. 22. Fine : a fall of snow about 4 p.m. covering the ground
generally. 23. Cloudy : clear night. 24. A considerable fall of snow during
the night. 25. Gloomy : calm : a gradual thaw. 26. Gloomy. 27. Fine.
28. White frost : fine, having rain in the night. 29. Fine. 30. Cloudy.

Penzance.— Nov. 1, 2. Fair. 3 — 5. Fair : showers. 6 — 9. Misty. 10. Fair.

11. Fair: rain. 12. Fair. 13, 14. Misty. 15— 17. Rain. 18. Fair.
19,20. Clear. 21. Fair: hail-showers. 22. Hail-showers. 23. Rain.
24. Showers. 25. Misty. 26. Fair. 27, 28. Rain. 29. Fair. 30. Misty.
— Rain-gauge ground level.

Boston. — Nov. 1. Fine. 2. Stormy. 3, 4. Cloudy. 5. Fine. 6. Rain.
7. Cloudy : rain, a.m. 8, 9. Cloudy. 10 — 12. Fine. 13, 14. Cloudy.
15. Foggy. 16, 17. Cloudy. 18. Cloudy: rain a.m. 19, 20. Cloudy.
21, 22. Fine : plenty of ice for the first time this season. 23, 24. Fine : snow,
p.m. 25, 26. Cloudy. 27. Foggy. 28. Fine. 29. Rain. 30. Cloudy.

RESULTS.

Winds, N.2:NE. l:E.l: SE. 3: SW. 2 : W.3: NW. 13: var.l.

London. — Barometer : Mean height for the month 30-154inch.

Thermometer : Mean height for the month 43°

Evaporation '83 inch.

Rain 1-32.

Meteor o-

V

'3

isog

; t : : :^^ : : : : : :^^ : :t :::::::::: »p :

!

1

dsog

:::::::-§:: :§88# :::::::§:: :2 :£

:::::: :oo : : :9co-<*9 :::::: : oi : : :<p : .-•

10
?

r— <

"5

zuaj

o . . .ICO o „ . .o .

• rf . . .0010 VO • • .CO *

ip**,90'*«*'-'r^'''Tf'

6 6 6 6 ^

IO

CO

•<

Ico . . . tj< . co . c* . . .rfoocoe* O . co

paorj:9 :::9:9:9:::7,t'9'7,:::::::::;:^o:7'

CO

i

u

o

*

h

•dsoo

' • o : :o : :o : : •<* : ;<& • • © • : m : : »n • • to • • in
: rj * "T1 • • t» • «9 • -9 • ^t1 • • 9 • • 9 - «o: .9
0

O

6

CO

op

•paoq

£: * .* tfi

c

E

C

•»sog

> P ffi a; > — < u — — ' .^ — ? i» -jj — u — > — • -— — ■ '• > £ S — ■ . i ^ ~

zzrr,|S«l,1,,s'5c'li!|J««11Jt3!j(,?i>;>i>;lll8I«ww«

11

•dsoQ

^ l^l![Hi Si '^^*"*'*^.^:**;*M;,!|^ *t&

1

•ZU3J

ii** * ► ^ s i ^i j s' ^ s * s « m g s e g i i - g ^

§

5

•pucj

iiiiiiii»iiii»iii*iiiiii*ii*i*

8

a>
S
5

8

JSOJf lOrf-^r-rfiO'^'^^Tt^incou^Tj'rf'^'^'^r^T^coC* <N CM (T) C5 rf CO rf ■'t

CO

1

W

i

o
Q)

to
O

O

i

CM

g

1

OjtO l>00 OaOU50M>!X)Tt(Sn(N^,Ot^r|<HTl'WOQ0>Ofl0--'CH0

■M

o
u

a

c3
N

s

£

>0«0^000>(N(NHO\0^'-l>(NiOt^'<tOOMv5aOO(Or«00000\

CO
CO

9
0

iDif>iniomioio»mcioicin>fi>o>0'^inioio»OTj<^'ioTjtoLnioiomtn

0
10

^

c
o

a

i

0*

i

0

i

H

■a

<U
V

s

o
5

n

Id

!>-00<Nt^iOt>0<OOtoiCTf<(OVOCO^OOOOO'r}<iOtnoOOt>.00

ipTfro^t^^^r^^in^t^t^ifciy ■•TfixQpr^Qp toLf3>pr^9i9i9'7i«N
^(^i^^iC^^o^^c^qnc^^iO^o^^^^^^i 6i^o>^<^6iO%6i6io^o\

C4C^C^C^C*C<C<CNC>IOlO»c^C<0«C^C*CSC<C«C^0«C<C^C^C101O»C<rN<N

0
«o

g

s

c

1

o

a

00
(N
61
CM

M

2

noo>nO'*xMoe)Ot^(siOTf<S'*ot^'*(Mis»t>-^o"o-OQ0

666666666i666666i6\6i66666>6i6i66666i6i
coco(T30cocorO<OOicocococococ^c^c<cocococo<Nr^oicocococo(NC^

O

■jr

6

CO

o
o

c

1
N

c
ft

2

O00«inOO^O(NO(XI(N<OO'tOOO'tO*0tOi|(0TfO<NOO'1l
OC^O^C^cp9C0t^99^^9^^^0^9^9g^>pc»90^7<>p•p'rt,
66i666666i6>i666666i6i6i6i6666i6sio>66o6i6><yi

0

CM

=:
Q

1

-

lOOO»'OO>O(MtO(NOCO<ll(StOOOXO00O^O^(S«O't(S

66666666^^666666i6i6>6 6 6o66>6>66666\<^

cocorOOCOCOCOCN CN nnncocow 0« <N COCOCOCOCO<N C* cococococn CN

|co

IS

1
1

1

s

1

e

0
T3

c
o

a

2

^ocico^co<N9999^c^^vp*oo^fNOcp^a>apopcN^w»p»p<?1
6\6666o6666666 eio^OMX) 65666><Ji6>6oo^o\6>
C?cococococccocococoocococ>i <N c< <N nrocnM(N CN CN coc^coc^ C* <N

CM

3
1

— <^<o6o<oot^oou,5-H^t^ooo>^oor^t^oooooiotomqM^

0CNO^^^O<N^^^C0C0CN^(D>CN^7tC0cp^O<^^^iprN*0ip

666666666666666,i6xi66©6666666666\6>

10
6

CO

«4-

c

a
1

c

| O « • ■ ■ «

ll

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY,

[NEW SERIES.]

FEBRUARY 1828.

XIII. On the mutual Decomposition of Sulphate of Zinc and
Chromate of Potash. By T. Thomson, M.D. F.R.S. L. # E.

Professor of Chemistry in the University of Glasgow.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
TN the last Number of your Journal (for December 1827) I
* observed a paper by Mr. Henry Stokes " On some new
double chromates." The three compound salts which he de-
scribes as double chromates, in fact contain merely a small
quantity of chromate of potash, or rather of chromic acid in a
state of mechanical mixture. They are the three salts which
I have described in my First Principles of Chemistry, vol. ii.
under the names of Potash-sulphate of zinc, p. 435,
Potash-sulphate of nickel, p. 434,
Potash-sulphate of copper, p. 436,
as any one may satisfy himself by comparing my descriptions
and analyses of these salts with those of Mr. Stokes.

I shall take this opportunity of rectifying the account which
I have given of chromate of zinc in my First Principles of
Chemistry, vol. ii. p. 357. The salt which I describe as a
chromate of zinc is in reality a dichromate of zinc, for it con-
tains exactly twice as much oxide of zinc as I have assigned
it. This mistake I discovered soon after the publication of
my First Principles. And it induced me to examine carefully,
what takes place when solutions of sulphate of zinc and chro-
mate of potash are mixed in the atomic proportions. The re-
sult is curious, and will be sufficiently understood by the fol-
lowing statement. If we mix together solutions containing

16 atoms chromate of potash = 200

16 atoms sulphate of zinc = 164 364.

New Series. Vol. 3. No. 14. Feb. 1828. M There

82 Dr. Thomson on the Decomposition of Sulphate ofZinc> fyc.

There will be deposited

6 atoms dichromate of zinc .. =102

By carefully concentrating the mother liquor we
obtain 1st, 5 atoms bichromate of potash... s 95

2nd, 4 atoms potash-sulphate of zinc = 85

3rd, 6 atoms sulphate of potash = 66

4th, 1 atom bisulphate of potash. ... = 16

Total 364

All these salts are conceived to be anhydrous, merely to sim-
plify the numbers.

The practical chemist will easily understand how I pro-
ceeded. 1 evaporated the liquid as carefully as possible, pick-
ing out the crystals as they formed, and examining them. I
easily recognized bichromate of potash, potash-sulphate of
zinc, and sulphate of potash, by their forms. I did not perceive
any crystals of bisulphate of potash, I merely inferred the for-
mation of this salt from the impossibility of accounting in any
other way for the formation of the other four salts from the
atoms which I had mixed, unless the formation of that salt
also be admitted. The reader will not suppose that I suc-
ceeded in separating the whole of these four salts from each
other, I merely endeavoured to determine the nature of all
the salts formed. The rest was the result of an obvious cal-
culation.

From Mr. Stokes's experiments it would appear that similar
salts are formed when sulphate of nickel or sulphate of copper
is mixed with chromate of potash in the atomic proportions.
This I have not hitherto had occasion to investigate. But it
will probably turn out that my chromate of nickel and chro-
mate of copper are in fact, dichromates. This I shall endea-
vour to ascertain os soon as I have leisure.

I am, &c.

Dec. 14, 1827. Thomas Thomson.

XIV. On the Measurement by Trigonometry of the Heights of
the principal Hills in the Vicinity of Dent, Halves, and Sed-
bergh, in Yorkshire. By John Nixon, Esq.*

HPHREE years ago I commenced, and in the course of the
-■- present summer I succeeded in completing, the trigono-
metrical measurement of the heights of a group of hills of the
Penine chain. Different observers have generally furnished
from similar operations results so extremely discordant, that

* Communicated by the Author.

it

Mr. Nixon on the Heights of the Hills of Dent, fyc. Yorkshire. 83

it becomes necessary, in order to inspire confidence, to give
every needful particular respecting the bases, signals, instru-
ments, and methods of calculation.

Bases. — From the third volume of the Trigonometrical Sur-
vey of England and Wales, are extracted the following di-
stances between stations, &c. placed on hills forming part of
the above group.

Ingleborough to the Calf 77,615 feet.

Ditto Shunnor Fell . . 82,397

Ditto Pen-y-gent Rock 32,124

Ditto Whernside . . . 22,435

Shunnor Fell to the Calf 59,487

On the Calf were found the stakes which had supported the
theodolite used in the Ordnance Survey. Shunnor Fell was
not visited, but the signal now on its summit has most pro-
bably been erected over the proper station-mark. In the centre
of the pile of stones yet remaining on the highest point of
Whernside, there stood some years ago a signal-staff' known
to have been erected by Colonel Mudge's party. The rock
on Pen-y-gent now cut up, and forming part of the boundary
wall of Horton, was not situated exactly on the summit of the
fell. The station on Ingleborough could not be satisfactorily
identified, but the highest point of the mountain corresponds
very nearly with it in its bearing and distance from the old
hut, as given in the account of the survey. Assuming as a
base for the calculations the distance of the summit of Ingle-
borough to that of Pen-y-gent, which we shall call 32, 1 60 feet,
the errors of such of the distances as are comparable with those
of the Ordnance Survey will be ;

Ingleborough to the Calf +32 feet.

Ditto Shunnor Fell . . — 22

Ditto Whernside . . . + 6

Shunnor Fell to the Calf +18

Signals. — Where stones were at hand, small towers five to
eight feet high with bases six to nine feet in diameter were
erected. When the summit of the hill was destitute of rocks,
the (pyramidal) signals wrere formed of large sods. These
signals were invariably placed on the loftiest point of the hill,
determined in doubtful cases by resorting to a well-adjusted
twelve-inch telescopic level.

Description of the Theodolite. — With the exception of a few
observations made by a common four-inch theodolite, the ho-
rizontal angles were measured by a six-inch theodolite, con-
structed in the autumn of 1 826, by Mr. P. Lealand, London.

M 2 The

84 Mr. Nixon on the Measurement by Trigonometry of the

The excellent twenty-inch telescope of this instrument is fur-
nished with cylindrical rings, a delicate spirit-level, and very
fine adjustable (steel ?) cross-wires. — It is supported in the
Ys of a cradle (common to theodolites of this description)
having a horizontal axis four inches in length. A clamp and
tangent screw, fitted to one of the supports of this axis, serve
to give a slow vertical motion to the telescope*. The lower
of the six-inch horizontal circles is divided (on silver) into
thirds of a degree, capable of being read off to half-minutes by
means of the two opposite verniers of the upper circle and a
pair of double magnifiers. The latter are very conveniently
fixed to a ring moveable about the rim of the under circle.
The upper circle is also provided with a clamp and tangent
screw for slow horizontal motion, and has a couple of spirit-
levels placed at right-angles to each other, which with the
four screws of the parallel plates enable the observer to render
the plane of contact of the two circles parallel to the horizon.
On the upper parallel plate is fixed a third clamp and tangent
screw, intended, no doubt, to bring the cross-wires of the te-
lescope, the circles being clamped together, with some parti-
cular degree coincident with the zero of one of the verniers,
exactly on the observed object.

When the ground at the station proved impenetrable, heavy
stones were piled against the feet of the tripod (set up with its
legs at an angle of 45° to the horizon), in such a manner as to
render it fixed and inflexible. The summit of the hill being
swampy, the legs (set up more erect) were forced below the
surface of the turf to some depth, and large stones were heaped
on the ground immediately under the centre of the instru-
ment f.

Either of the levels of the upper circle being brought ex-
actly over any two of the screws of the parallel plates, the lat-
ter served to place its bubble at the mark. The circle being
then moved half round, one half of the deviation of the bubble
from its mark was corrected by the two screws, and the other
by the adjusting nuts of the level. The level at right angles
having undergone a similar verification and correction, the
plane of contact of the two circles would consequently be ren-
dered parallel to the horizon J. The intersection of the cross-

* The instrument has no vertical arch.

f Noughtberry Hill excepted, the ground at the theodolite-stations
proved hard and firm.

\ The correctness of this adjustment was confirmed when the upper
circle could be moved quite round without displacing the bubble of the
level of the telescope, previously brought to its mark.

wires

.Heights of the principal Hills of Dent, fyc. Yorkshire. 85

wires of the telescope (or line of collimation) was known to
be parallel to the cylindrical rings encircling its tube, when
the telescope could be made to revolve in its Ys without
causing the point of intersection to deviate from the distant
well-defined object which it had bisected. After this adjust-
ment, the line of collimation, provided the artist had made the
axis of the cradle parallel to the plane of contact of the two
circles, and the Ys at right angles to that axis, would neces-
sarily move in a vertical plane. As the remote signals could
not be distinctly seen on interposing the horizontal wire of the
telescope, the following method of observation with the verti-
cal wire only was resorted to. The point of intersection of the
wires being made to accurately bisect an object at a moderate
distance, one wire was rendered perfectly vertical by turning
the telescope to the right or left within its Ys, until either
extremity of the wire, on elevating or depressing the telescope,
would also pass through the middle of the object observed.
Thus adjusted, it would evidently be superfluous to bisect
constantly with any particular point of the vertical wire. To
guard, however, against the possibility of the wire not being
perfectly straight, a point, visually estimated to be equi-distant,
from some particular particle of dust, &c. adhering to it, and
the point of intersection by the other wire, was invariably
brought on the signal. {

The graduations being numbered from 0° to 360°, it follows,
that the readings from the one vernier should differ exactly
1 80° from those given by the opposite one ; or it will prove either
that the vertical axis does not coincide with the centre of the
divided circle, or that the divisions of the latter are incorrect.
As both sources of error may exist, it will be proper to re-
gister for calculation the mean of the two readings. The or-
der of numeration of the graduations being from left to right,
the angle between any two of the observed signals is imme-
diately found from a similar register, being equal, either to the
difference of their respective readings, or to 360° minus that
difference, according as it falls short of, or exceeds 1 80°.

The description of the instrument and its adjustments has
been so ample, that the mode of observing with it will be too
evident to require pointing out. It may, however, be needful
to remark, that notwithstanding the length of the vertical axis,
which is nearly four inches, it was found that a variation in
the degree of force with which the two circles were clamped,
caused a sensible deviation in the direction of the line of col-
limation ; a source of error which it was endeavoured to ob-
viate by always applying the utmost force to the clamp. Having
Completed single observations of the whole of the signals, it

would,

86 Mr. Nixon on the Measurement by Trigonometry of the

would, without doubt, have materially increased their accuracy
to have repeated them (circumstances permitting) with the
telescope reversed in position ; but such was the inconvenient
situation of the tangent screw of the upper circle, as to render
the method impracticable*. To make a second set of obser-
vations with the telescope in its original position was the only
alternative.

As data for the reduction of the observations to the centre
of the base of the signal, the telescope was pointed so as to
bisect the latter, and the reading of the verniers in addition
to the distance of the centre of the circles to that of the signal
registered in the usual manner. In order to comprehend the
nature of the reduction, let S in the annexed figure represent

. o

the centre of the signal, T that of the divided circle, U the
prolongation of the straight line passing through S and T, and
O the object observed. Make TO' parallel to SO ; then, as
the angle USO equals that of UTO', the angle USO must
exceed the observed angle UTO by the angle OTO', equal
to SOT. It is -also clear that the observed angle, whether
acute or obtuse, to the left or right of the line UST, will al-
ways be in defect. To calculate the angle SOT we have
given the angle STO, the side ST, and (approximative^) that
of SO. Then, as the graduations of the circle are numbered
from left to right, the angle at T between U (or S) and an
object O to the right, will be equal to the reading of O minus
that of U ; and we must add the angle of correction SOT to
O, in order to make the registered readings coincide with those
of another theodolite placed over S, the reading for U being
alike by the two instruments. When the object (P) is to
the left of the line UST, it will form with it at T an angle
* I have since discovered that, by unfixing the clamp on the upper pa-
rallel plate, the circles might have been moved half-round in azimuth.

equal

Heights of the principal Hills of Dent, fyc. Yorkshire. 87

equal to U minus P, and the correction must be applied to P
with the negative sign, in order to make USP greater than
UTP by the angle of correction SPT. These corrections
being applied to the readings for the different signals, we
form a new register, whence we can immediately find by sub-
traction (as before) the angular distance of any two of the sig-
nals as observed from S in lieu of T.

On referring to the distances of some of the more remote
signals from the theodolite-stations as measured from different
bases, discrepancies, amounting'in some instances to upwards
of 100 feet, will be remarked. These differences were occa-
sioned in a great measure by the signals having a diameter
too inconsiderable for the distance, so that the vertical wire
in lieu of bisecting, appeared to efface them *. The formula
adopted for obtaining a proper mean of such of the different
measurements of a distance as were remarkably discordant,
requires to be explained.

In order to find the distance between the point e and the
inaccessible object a, measure from e in different directions

any number of bases, as ABC, and observe at the two ex-
tremities of every base the inclination of that base to a line
passing through the point of observation in the direction of
the inaccessible object. With these data we shall be able to
calculate from each base an independent measure of the re-
quired distance ;— but supposing the observations to have been
subject to a small uncertainty, limited, for instance, to one
minute, required the probable error of each of the respective
calculated dist'dnces ?

By trigonometry, 180° minus the sum of the angles taken at
the ends of any* one of the basjes will be equal to the subtense
of that base at a. Then if we restrict ourselves in our calcu-

* At a distance of 60,000 feet a tower 6 feet in diameter appears under

an angle of only 21". *

"O lations

88 Mr. Nixon on the Measurement by Trigonometry of the

lations to the use of logarithms, treating them in the notation
as natural numbers, F (or the distance required) will be equal
to the sum of the base and sine of the angle opposite F, minus
sine of the angle subtended at a by the base. — Here we may
observe that tne value of the angle at e affects the calculation
merely as it serves to determine that of the unobserved an-
gle a.

Admitting that one only, as well as both of the angles de9
may have been inaccurately observed, the subjoined list will
include every possible arrangement of the angular errors to^-
gether with the consequent alteration of the correct value of
the unobserved angle a :

I. Make the error of d -f 1', and e + 1'; whence a = — 2';
II. +1 0 -1;

III. 0 +1 -1;

IV. +i-i o.
As the log. sines increase from 0° to S0°, and diminish from

90° to 180°, it will be necessary to divide our investigations
into two classes.

Class I. — The angles at a and d being both acute. Call a!
the difference of the log. sine of a and the log. sine of a + 1'
(or of a— 1'); and d1 the corresponding difference of d and
d + V (or of d and d — 1'). Then as the correct length of F
has been shown to be equal to A 4- sin d — sin a, its value
with an arrangement of the angular errors as given in No. I.

will become

=■ A -f sin d + S — sin a — 2 a'<; or simply
= F + d' + 2 a' ; whence x or the lineal error required will
be = d1 + 2 a'. For the whole class of the angular errors the
values of x will be as follows :

I. .r...= d! + 2a'

II d' + a'

III a'

IV d\

Hence the probable error of calculation will be equal to the

mean of the above four quantities, or to a1 -\ — — .

Class II. — When a is obtuse. Selecting No. I. of the ar-
rangement of the possible errors of observation, the calculated
length of F becomes

B + sine? -f dP— sin a + 2an; whence x will be equal to
d'oo 2 a', and its value for the complete arrangement of errors,
I. . . x = d'cv>2a'

II d'ooa'

III a'

IV d':

Consequently

Heights of the principal Hills of Dent, fyc. Yorkshire. 89

Consequently when either a or d are obtuse, the mean error
of calculation will be

a! — — , when a1 is greater than d! \

— 7—5 when d! is greater than twice a1;

—p — , when d! is greater than a! but less than ZaK

x as thus expressed is the logarithm of the natural number
by which we must multiply the correct distance, in order to
obtain its value as affected by the mean of the possible errors
of observation arranged conformable to our list. Consequently
if we call 1 the correct distance, then will the error of mea-
surement be equal to this natural number minus 1. Now if
the distance as derived from one base A shall be liable to an
error of 10 feet, and the same distance, as deduced from an-
other base B, be uncertain to 20 feet, then must the claim to
accuracy of A exceed that of B in the reciprocal ratio of 10
to 20 or as 10 to 5.

When we have given P, F", P" or the required distance as
calculated from the same number of bases, together with the
reciprocals of x — 1 corresponding to the respective bases,
which call tf, x", •*•"', the correct value of F may be considered
as equal to

x 4- x" + *'" '

In practice it will be most convenient to take out the log. dif-
ference for 1' of the sines of the angles d and e, noting them
+ or — according as the angle is acute or obtuse. A type
of calculation is subjoined.

Base A; Noughtberry Hill to Ingleborough . . 44106 feet,
B Ditto Dod Fell .... 19347

A. Noughtberry 62° 19' 8"

Ingleborough 55 26 53 log. diff. of 1'= 4- 0-0000870=*/',
Berkin ( 62 13 59) 4- 0*0000665 = a!.

B. Noughtberry 145° 40' 35"

Dod Fell 23 30 40 log.diff.of l'=e 4-0-0002904=^,
Berkin (10 48 45) ...... 4-0*0006610=0'.

Berkin to Noughtberry Hill by base A . . 41053 feet.
Ditto Ditto B . . 41142

Arithmetical mean 41097*5

x for the base A will be a' + — , =0*00
New Series. Vol. 3. No. 14. Feb. 1828. N of

The value of x for the base A will be a' 4- -^, =0*0001 317,

90 Mr. Nixon on the Measurement by Trigonometry of the

of which the natural number minus 1 is -000303 ; and the re-
ciprocal of the latter 330033.

The value of x for the base B will be a! + —-, = 0-0008788,

of which the natural number minus 1 is 002026, and the re-
ciprocal of the latter 49358.
The corrected distance will therefore be equal to

41053 x 330033' + 4H42 x 493581

= 41064-5 feet.

330033 + 49358

"We might now proceed to investigate what proportion of
the difference of 180°, and the sum of the three observed an-
gles of a triangle should be assigned to each angle, were not
the differences in the present survey, as appears from the fol-
lowing list, too trivial to require such nicety of correction.

No. 1. -0' 40"

2. -f 0 19

3. -0 17

4. -0 35

No. 5. -2' 35"

6. +1 18

7. -1 37

8. -0 12

No.

9. + 1' 54"
10. -0 6

Mean difference 57" or 19" per angle.

In the succeeding register of the observations, the second
column contains the reading from the nearest vernier; the
third column that from the opposite one, suppressing the de-
grees. The two next columns give the minutes and seconds
of the corresponding readings for the second set of observa-

tions.

At Bod Fell

Lovely Seat 265° 5'
Shunnor Fell 248 46
Noughtberry Hill 182 42

Berk in
Bow Fell
Pen-y-gent
Whernside
Colm

Blea Moor
Ingleborough
Wildboar Fell
Cam Fell
Cotter Fell*
The Signal

159
191
66
138
151
139
110
215
116
232
354

30''

6' 0"

5' 0"

5' 45"

30

47 0

46 0

46 30

0

42 0

42 0

41 30

15

11 0

11 0

10 30

30

1 30

1 0

1 0

0

40 30

41 0

40 30

30

51 0

51 0

50 45

30

36 0

36 30

36 0

0

57 15

58 15

57 15

45

40 0

41 0

40 30

0

20 30

20 0

20 30

30

36 30

....

....

0

20 0

....

....

0

6 feet

distant

11
1

41
51
36
58
40
20
37
20
0

At Whernside.

Colm
The Calf

241° 15' 30"
277 42 30

15' 30"l
42 30

Reduction

to Centre.

-0'

34"

-0

28

-0

10

+0

6

-0

9

+0

32

+0

20

+0

10

+0

30

+0

24

-0

15

+ 1

42

-0

19

0'

0"

+0

10

* There was no signal on this hill.

Bow

Heights of the principal Hills q/De?it, Sfc. Yorkshire. 91

Reduction

303° 26' 30"
336 56 18
343 17 30
34-8 2 30
358 40 15

15 39 15
308 30 30

70 57 30
119 53 0
189 56 0
241 0 0

26' 30"
55 30
17 0

2

10

$8
81

56 30
52 30
b5 30
4*5 feet distant.

At Pen-y-gent.

Bow Fell
Shunnor Fell
Noughtberry
Lovely Seat
Whaw Fell
Dod Fell
Wildboar Fell
Pen-y-gent
Ingleborough
Graygreth
The Signal

Whernside
Ingleborough
Colm
Dod Fell
Bow Fell
Noughtberry
Wildboar Fell
Blea Moor
Shunnor Fell
Lovely Seat
The Signal

Berkin
Colm
The Calf
Whernside
Pen-y-gent
Dod Fell
Noughtberry
Blea Moor
Graygreth
Bow Fell
Lovely Seat
Shunnor Fell
The Signal

Dod Fell

Pen-y-gent

Ingleborough

* On the point of making the second set of observations one of ihe feet
of the tripod was disturbed. f Rubm Chavucmorus.

N 2 Blea

85° 49' 30"

49' 0"

51' 30"#

50' 30"

54 5 30

5 0

6 30

6 30

83 22 0

21 30

23 30

22 30

138 21 30

21 30

23 0

22 30

108 53 30

53 0

55 0

54 0

117 9 0

8 30

10 30

10 0

119 28 0

27 0

29 0

29 0

101 38 0

37 30

39 0

3*7 30

139 28 30

28 30

29 30

27 30

147 38 0

37 30

38 30

38 30

265 49 0

4 feet

distant.

At Ingleborough Hill.

3° 52' 0"

52' 0"

51' 30"

51' 30"

14 9 30

10 0

9 30

9 30

20 27 0

27 0

36 23 0

22 30

23 0

22 30

135 44 0

44 0

44 0

44 30

83 59 30

60 0

58 30

59 0

59 19 0

19 30

19 0

19 30

60 21 30

21 30

22 0

21 0

350 32 30

32 30

38 30 30

30 30

72 36 30

36 30

63 59 30

60 0

(Fell misty)

230 30 0

9 feet

distant.

At Noughtberry\ Hill.

224° 17' 0"

16' 30"|

267 5 0

5 30

307 38 30

38 0 J

to Centre.

+ 0' 25"

+ 0

14

+ 0

36

+ 0

14

+ 0

41

+o

19

+ 0

15

-0

4

-0

36

-0

41

0'

0"

+ 0

14

■4-0

1

-0

18

-0

5

-0

9

-0

5

-0

6

-0

9

-0

10

+ o'

31"

+ 0

47

+ 0

12

+o

21

-0

57J

— 0

23

-0

6

-0

11

+ 1

9

+o

7

-0

9

-0

5

+ 0/29"

+ 0

24

+ 0

26

92 Mr. Nixon on the Measurement by Trigonometry of the

Reduction
to Centre.

Blea Moor 305°47' 30" 47' 0" + 1' 14"

Whernside 328 5 0 5 15 .., -fO 38

Colm 354 36 30 36 0 +0 15

Berkin 9 58 0 57 30 +0 4

The Calf 56 12 15 11 45 -0 15

Bow Fell 60 7 30 7 0 -0 42

Wildboar Fell 92 14 30 13 30 -0 30

Cotter Fell 112 29 0 28 30 -0 27

Shunnor Fell 137 37 30 36 30 -0 28

Lovely Seat 155 53 0 53 0 —0 21

Whaw Fell 282 38 0 37 30 +2 43

The Signal 197 30 0 6 feet distant.

The angles at the following stations were measured by a
four-inch theodolite (much out of repair) reading off to one
minute. The graduations were numbered precisely as those
of the six-inch theodolite.

At Whaw Fell

At Ryssell,

Dod Fell

291° 30'

0"

Blea Moor

305° 56'

0"

Noughtberry

192 42

0

Bow Fell

200 24

0

Blea Moor

54 32

0

Whaw Fell

285 17

0

Whernside

73 33

0

Cam Fell

328 40

0

Bow Fell

160 58

0

At Bear's

Head,

Ryssell

135 30

0

Dod Fell

167° 49' 30"

Snays Fell
Bear's Head

291 58
274 20

0
0

Noughtberry
Whaw Fell

205 33
189 56

30
30

Ten End

265 14

0

At Blea Moor.

Dod Fell

26° 6'

0"

At Ten End,

Cam Fell

42 28

0

Bear's Head

267° 16'

0"

Snays Fell

14 28

0

Cam Fell

22 30

0

Whaw Fell

349 0

0

Blea Moor

47 58

0

At Colm,
Whernside 235° 52'

0"

Whaw Fell
Noughtberry

57 41

80 8

0
0

Ingleborough

272 17

0

Graygreth

313 19

0

Calculation oj

^the Distances,

.

Feet.

Feet.

Ingleborough to Pen-y-gent 32160

Ingleborough 76*°23' 55"

44098

Pen-y-gent 6c

I 3 9

48082

Noughtberry 40 32 56

Ingleborough 99° 20' 18" 22441
Pen-y-gent 31 44 16 42096
Whernside 48 55 26

Ingleborough 22 56 55
Whernside 136 35 9
Noughtberry 20 27 56

44111
25026

Pen-y-gcnt

Heights of the principal Hills of Dent > $c. Yorkshire. 93

Feet.
Pen-y-gent 31°19' 46" 48086

Whernside 87 39 35 25023

Noughtberry 61 0 39

Ingleborough 51 44 24 46068
Pen-y-gent 84 15 49 36354

Dod * 43 59 47

Ingleborough 47 33 58 46068
Whernside 104 13 24 35095
Dod 28 10 38

Wbernside 55 18 4 35096

Pen-v-gent 52 31 45 36356

Dod" 72 10 11

Mean Distances.
Ingleborough to Noughtberry... 44 105

Ingleborough to Dod Fell 46068

Pen-y-gent to Noughtberry 48084

Pen-y-gent to Dod Fell ..36355

Whernside to Noughtberry 25024

Whernside to Dod Fell 35095

Pen-y-gent 21° 12' 2" 48091

Dod v 115 59 59 19350

Noughtberry 42 47 59

Ingleborough 24 39 5 44110
Dod 72 0 6 19345

Noughtberry 83 20 49

Whernside 32 21 7 25031

Dod 43 50 20 19339

Noughtberry 103 48 33

Mean distance of Dod ) 1QS4^

to Noughtberry 3

Ingleborough 38 51 57 77647
Noughtberry 108 33 4 51393
Calf 32 34 69

Whernside 65 35 11 56420

Noughtberry 88 6 0 51404
Calf 26 18 49

Mean distance of the Calf > r 1 oQQ

to Noughtberry S —owyo

The Calf to Pen-y-gent 95894

Ingleborough 121 ° 32' 46" 32250
Pen-y-gent 29 16 18 56210

Colm 29 10 56

Ingleborough 22 12 42 32283
Whernside 121 23 21 14296
Colm 36 23 57

Feet.
Ingleborough 69° 48' 28" 32267
Dod 40 55 27 46230

Colm 69 16 5

Ingleborough 45 8 45 32260
Noughtberry 46 57 49 31288
Colm 87 53 26

Pen-y-gent 54 59 25 56230

Dod 84 55 8 46237

Colm 40 5 27

Pen-y-gent 33 46 57 56222

Noughtberry 87 30 51 31291
Colm 58 42 12

Whernside 102 2 21 14284
Noughtberry 26 30 45 31294
Colm 51 26 54

Whernside 134 23 26 14276
Dod 12 45 1 46221

Colm 32 51 33

Dod 31 5 17 46268

Noughtberry 130 19 16 31335
Colm 18 35 27

Mean Distances.

Ingleborough to Colm 32265

Pen-y-gent 56221

Whernside 14285

Noughtberry 31302

Dod 46239

Ingleborough 45° 49' 27" 23444
Whernside 70 2 55 17888

Graygreth 64 7 38

Ingleborough 23 36 45 23439
Colm 41 2 0 14301

Graygreth 115 21 15

Whernside 51 20 26 17890

Colm - 77 27 0 1431 1

Graygreth 51 12 34

Mean Distances.

Ingleborough to Graygreth 23442

Whernside 17889

Ingleborough 65°26'53" 44141
Noughtberry 62 19 8 41053
Berkin 62 13 59

Ingleborough 80 6 36 44157
Dod 48 30 4 58080

Berkin 51 23 20

Dod

94 Mr. Nixon on the Measurement by Trigonometry of the

Dod

Noughtberry

Beikin

23°30' 40"
145 40 35
10 48 45

Feet.

58182
41142

Corrected mean Distances.

lngleborough to Berkin 44149

Dod 58092

Noughtberry 41065

lngleborough 97° 12' 33" 55981
Pen-y-gent 54 47 42 67971

Bow Fell 27 59 45

lngleborough 20 48 32 55981
Noughtberry 1 12 27 52 21520
Bow Fell 46 43 36

Dod

Noughtberry
Wildboar Fell

32° 38' 18"
132 3 44
15 17 58

Feet.
54436
39545

lngleborough

Dod

Bow Fell

Pen-y-gent
Whernside
Bow Fell

Pen-y-gent
Dod
Bow Fell

Whernside
Noughtberry
Bow Fell

Whernside
Dod
Bow Fell

45 28 15
80 20 8

54 11 37

23 3 40
127 30 1
29 26 19

29 28 1

124 19 49

26 12 10

39 50 56
92 0 48
48 8 16

72 12 1
52 9 42

55 38 17

55998
40495

67951
33550

67993
40503

33580
21530

33576
40480

Mean Distances.
lngleborough to Bow Fell .

Pen-y-gent

Whernside

Noughtberry

Dod Fell

Pen-y-gent 33° 38' 2"

Whernside 122 25 56
Wildboar Fell 23 56 2

Pen-y-gent 18 53 39

Dod ' 148 38 43
Wildboar Fell 12 27 38

Whernside 67 7 56
Dod 76 28 40

Wildboar Fell 36 23 24

Whernside
Noughtberry
Wildboar Fell

34 46 51
124 7 45
21 5 24

.55987
.67972
.33568
.21525
.40493

87582
57475

87672
54561

575 16
54506

57566
39670

Corrected mean Distances.
Whernside to Wildboar Fell ...57522

Dod 54494

Pen-y-gent 87613

Noughtberry 39616

lngleborough 71° 43' 30"
Pen-y-gent 85 22 15

Shunnor Fell 22 54 15

lngleborough

Whernside

Shunnor

27 36 34

142 56 2

9 27 24

lngleborough 19 59 12
Dod 138 5 4

Shunnor 21 55 44

Pen-y-gent
Whernside
Shunnor

Pen-y-gent

Noughtberry

Shunnor

Whernside

Dod

Shunnor

53 38 13
94 0 49
32 20 58

22 19 0

129 29 7

28 11 53

38 42 49
109 54 38
31 22 33

82363
78465

82326
63300

82407
42163

78480
63352

78541
38643

63377
42158

Noughtberry 86 40 32 38619
Dod 66 4 20 42180
Shunnor 27 15 8

Corrected mean Distances.

lngleborough to Shunnor 82375

Pen-y-gent 78500

Whernside 63359

Noughtberry 38628

Dod 42168

lngleborough 63° 6' 49" 80969
Pen-y-gent 93 31 51 72354

Lovely Seat 23 21 20

lngleborough 13 \7 12 80899
Noughtberry 151 46 2 39303
Lovely Seat 14 56 46

lngleborough 11 22 31 81008
Dod Feb* 154 24 2 36978

Lovely Seat 14 13 27

Pen-y-gent

Heights of the principal Hills of De?it, $c. Yorkshire. 95

Feet.

Feet.

Pen-y-gent

61 °47' 49"

72300

Whernside

16° 58'

8"

20434

Whernside

82 54 27

64213

Dod

20 58 52

16655

Lovely Seat

35 17 44

Whaw Fell

142 3

0

Pen-y-gent

30 28 36

72316

Mean Distances.

Noughtberry
Lovely Seat

111 13 0

38 18 24

39345

Noughtberry to Whaw Fell...
Whernside

... 7598
..20426

Whernside

27 36 27

64188

Dod

..16668

Dod Fell
Lovely Seat

126 13 6
26 10 27

368/0

Shunnor Fell

..45068

Lovely Seat...

..44290

Bow Fell

..27603

Dod Fell

82 23 18

36873

Ingleborough

..37356

Noughtberry
Lovely Seat

68 24 35
29 12 7

39305

Blea Moor ....

.. 9371

Berkin

..41407

d mean Distances.

0 Lovely Seat... 80959

Colm

..29836

Correcte

Pen-y-gent ...

..40818

Ingleborough 1

J o~ " ••■

Whernside ...

..64200

Blea Moor

16°22'

0"

14348

Pen-y-gent ...

..72321

Dod

23 19 29

10211

Noughtberry

..39320

Cam Fell

140 18 31

Dod

..36887

Blea Moor

53 28

0

14343

Noughtberry

111°48'56"

46333

Whaw Fell

85 52

0

11555

Dod

49 38 0

56456

Cam Fell

40 40

0

Cotter Fell

18 33 4

Whaw Fell

122 36

0

7618

Pen-y-gent to Cotter Fell ....

..92115

Blea Moor

25 28

0

14926

Snays Fell

31 56

0

Ingleborough

75°21'51"

28252

Pen-y-gent

47 31 48

37058

Whaw Fell

72 33

0

19821

Blea Moor

57 6 21

Noughtberry
Ten End

85 0

22 27

0

0

18981

Ingleborough

23 37 33

28250

Dod

29 17 13

23144

Whaw Fell

63 24

0

19829

Blea Moor

127 5 14

Cam Fell
Ten End

81 25
35 11

0
0

17931

Pen-y-gent

15 31 27

37063

Noughtberry

38 42 50

15860

Whaw Fell

81 39

0

27998

Blea Moor

125 45 43

Noughtberry
Bear's Head

82 44
15 37

0

0

27925

Pen-y-gent

36 43 55

37056

Dod

73 16 54

23140

Whaw Fell

17 8

0

28011

Blea Moor

69 59 11

Dod Fell
Bear's Head

140 45
22 7

0

0

13042

Dod

42 43 31

23149

Noughtberry

81 31 15

15880

Mean Distances.

Blea Moor

55 45 14

Ten End to Whaw Fell

...19825

in Distances.

Bear's Head .

...28004

Me<

Ingleborough

to Blea Moor .

..28251

Whaw Fell

80° 58'

0"

26028

Pen-y-gent ...

Blea Moor

78 23

0

26243

Dod

..23144

Ryssell

20 39

0

Noughtberry

..15870

Whaw Fell

25 28

0

25984

Whernside

15° 22' 57"

20418

Bow Fell

69 39

0

11916

Noughtberry

45 25 17

7604

Ryssell

84 53

0

Whaw Fell

119 11 46

Mean distance of Whaw

}•••

..26006

Noughtberry

58 23 14

7593

Fell to Ryssell

Dod

22 49 16

16671

Whaw Fell

98 47 30

[Tol

be continued.]

XV. On

[ 96 ]

XV. On Mr. Herapath's Method/or the Integration of Linear
Equations with constant Coefficients,

T^HE integration of linear equations with constant coeffi-
■*• cients engaged the attention of analysts very early in the
progress of the Integral Calculus. The subject has been treated
of so often and so ably, that we can hardly expect any addi-
tion to our knowledge of it either new in principle, or very
interesting in the details. It would not therefore have been
necessary to notice particularly the communications of Mr.
Herapath published in the last two Numbers of this Journal,
if he had not fallen into an inadvertence respecting Lagrange's
investigation, of which it seems proper to advise the public.

In pp. 22, 23, of the last Number of this Journal, Mr. He-
rapath applies Lagrange's process to the equation,

dx3

+ AS + Bif + c3' = x.

The calculation is given at length in Lacroix's Treatise on the
'Integral Calculus, 2nd edit. vol. ii. pp. 326, 327. If r, rv r%
stand for the roots of the equation

I* + Ar2 + Br + C = 0,
the complete integral is as follows, viz.

erx(c+f*e-rxdx)

y a- 1 .

Y r—rt . r—r2

er'*(C,+/Xg-^rf*>)
rl — r.rl—r.z

r.2 — r.r2 — rt

Of these three parts Mr. Herapath has calculated only the
first, which he says must separately satisfy the proposed equa-
tion. Now in this assertion, of which no proof is given, lies
his mistake. If every part had contained only one root, it
might have been rightly inferred that it must separately satisfy
the differential equation ; but, as the case stands, there is no
ground for the assertion. If Mr. Herapath will substitute the
two remaining parts of the integral in the differential equation,
in like manner as he has substituted the first part, he will find,
on collecting the three results, that there is no failure in La-
grange's method.

«/3.

XVI. On

[ 97 ]

XVI. On the Error imputed by Mr. Herapath to Lagrange
in his Method of integrating Linear Differential Equations.
By A Correspondent*

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
XTOUR Correspondent Mr. Herapath has endeavoured to
A prove that Lagrange has fallen into an error in his in*-
tegration of linear differential equations, and expresses his sur-
prise that mathematicians have for upwards of half a century
suffered this to pass unobserved. Skilful mathematicians will
not take Mr. Herapath' s word for his bold assertion without
examination, and will then easily detect the fallacy of his rea-
soning : but as your readers are not all of them mathemati-
cians of competent knowledge, it will perhaps not be useless
to point out Mr. Herapath* s error.

Mr. H. has deduced the following equation (page 24?.)

{f + Ar + B) aX + {r + A) adX + ad2X = X

a being : = ; -77 ;

This equation is quite incomplete. Mr. H. having employed
that part of y which depends on the root r, only; all the terms
arising from those parts of y which depend on r, and r2 are
left out. A and B involve the three roots equally, and their
values may be substituted in the above terms on the left-hand
side of the equation as Mr. H. does, and we obtain for them
the following

r^aX — (rt + r2)adX -f ad2X

Call a\ a" the values corresponding to a for the two other

roots r., rq, so that a1 == .— r and a"= «*%

(r, -r) (rx-r2) (r2-r) (r2-rt)

The terms which are, consequently, to be added to make
Mr. H.'s equation complete will be

r r2a'X - (r + r2) a! dX +a'd2X

rrxa"X — (r+ rx)a"dX + a" dlX, and the aggregate
of all terms will give this equation :

(r.r^+rr^' + rr.a'OX-Un + rJa + ^ + ^y + Cr-frXJ^X
+ (fl + a'-f a»)^X^X.
It will now be easily seen that a + a! -f #"= 0,
(rt + rjfl + (r + r2) a' + (r + rx) a"= 0 and
rx r2 a + r r.2 a' + r r, a" = 1 and that, consequently, the equa-
tion becomes X = X, as it ought to be. This is the same

New Series. Vol. 3. No. 14. Feb. 1828. O proof

98 Dr. Prout on the ultimate Composition

proof of the correctness of Lagrange's solution that Mr. He-
rapath employs to establish the truth of his own.
I am, Gentlemen,

Your obedient servant,
4, Pancras-Lane. F. R. S.

XVII. On the ultimate Composition of simple Alimentary Sub-
stances ; with some preliminary Remarks on the Analysis of
organized Bodies in general. By William Prout, M.D.
F.R.S.

[Concluded from page 40.]

Of the Saccharine principle.

T N the following observations, the word Sugar, is used in its
•*■ ordinary acceptation; but the extended sense in which
the term saccharine principle is employed, requires a few re-
marks.

Messrs. Gay Lussac and Thenard were induced to con-
clude, from their experiments on organized products, that
when the hydrogen and oxygen of a substance exist in it in
the proportions in which they form water, the substance is
neither acid nor alkaline, as in sugar, starch, gum, &c. ; that
when the oxygen exceeds this proportion, the substance pos-
sesses acid properties ; that when it is less, an oily or resinous
character*. These conclusions are true to a certain extent,
but by no means universally so, as will be shown hereafter.
I shall however adopt this general distribution of organized
substances so far, as to confine my attention at present to those
substances in which the first peculiarity above mentioned
exists ; and as sugar, on account of its crystalline form, ap-
pears to constitute the most perfect and definite of these sub-
stances, I have thought it best entitled to give a name to the
whole class, or family, and hence have included, under the
term saccharine principle, all those substances, whatever their
sensible properties may be, into the composition of which the
hydrogen and oxygen enter in the proportions in which they
form water. Now it will be found, that the substances thus
constituted may generally be employed as aliments ; and as
they are chiefly derived from the vegetable kingdom, they
may be considered as representing vegetable aliments, pro-
perly so called ; hence, saccharine principle and vegetable ali-
ment may be regarded as synonymous terms, and they will be
so employed throughout the present inquiry.

* Recherches P/iysico-chimiques, ii. 321.

As

of simple alimentary Substances, fyc. 99

As a subject of general interest to chemists, as well as of
considerable importance in the present inquiry, I shall also
attempt to investigate the composition of a few of the com-
pounds of the saccharine principle with oxygen, or what are
usually denominated the vegetable acids.

Of Sugars.

Many analyses of sugar have been published by different
chemists, no two of which agree with each other. These dis-
crepances have doubtless arisen from various causes, though
one cause has probably been some real or accidental difference
in the composition of the sugars employed*. How many
distinct varieties of sugar exist I do not pretend to know, but
there are at least two, (independently of the sugar of milk,
manna, &c. which belong to another series,) and probably
there are several others ; and it is to the mixture or combination
of these in different proportions, and the frequent presence of
foreign bodies, that a good deal of the confusion respecting
the composition of sugar has undoubtedly risen.

Cane Sugar. — The strongest and most perfect sugar that I
am acquainted with, is sugar candy carefully prepared from
cane sugar. This, purified by repeated crystallizations from
water and alcohol, and deprived of the little hygrometric

* Some years ago I published an analysis of sugar, in which the propor-
tions of carbon to water were stated to be to one another as 40 : 60. I was
not aware at that time of the differences existing among sugars, and the
results given were founded on the analysis of a specimen of remarkably fine
looking sugar candy, a quantity of which I had purchased and kept by me
for several years for the purposes of experiment8. At length my stock be-
came exhausted, and I was surprised to find on analysing other specimens,
that they in general contained upwards of one per cent, more of carbon
than what I had before examined. This induced me to recur to the notes
of my former experiments, but I could detect no material error in them ;
and though I readily admit that the apparatus I then employed was much
less susceptible of accuracy than what I now use, I cannot help thinking
that the candy itself was partly in fault, and that it was prepared from an
imperfect sugar, probably from the East Indies.

There was also another circumstance which contributed to mislead me,
not only in this but in all my other results, viz. an inaccuracy in the weight
usually assigned to atmospheric air, at least as regarded my weights. I have
long suspected the perfect accuracy of this datum as settled fifty years ago by
Sir G. Shuckburgh, and have been accustomed for some time past to make
an allowance for it ; but I was not aware till recently of its exact amount,
when I was induced to undertake a series of experiments on the subject,
which I hope shortly to lay before the public.

a See Annals of Philosophy, iv. 424 (N. S.) I do not distinctly remem-
ber whether, at the time this paper was published, some of the original
sugar candy existed or not, but I had then only made one or two experi-
ments on the sugar of commerce.

O 2 moisture

100 Dr. Prout on the 'ultimate Composition

moisture that usually adheres to it by exposure for some time
to a temperature of 212°, was found to be composed of

Carbon 4-2*85

Water 57*15

Now, all the finest and purest specimens of loaf sugar of
commerce that I have yet examined, give, when similarly
treated, precisely the same results. They may therefore be
considered as identical in their composition with sugar candy*.
Cane sugar appears to undergo no change whatever at the
temperature of boiling water ; but at about 300° it begins to
melt, and assume the form of a dark-brown liquid. In one
experiment, after exposure to this temperature for seven hours,
it lost *6 per cent, only of its weight, but its properties seem
to have been permanently injured. Berzelius however has
shown that, on being combined with lead, sugar parts with
about 5*3 per cent, of water without undergoing decomposi-
tion ; for he has likewise shown that it may be obtained again
from the lead in its original state. This saccharate of lead I
have several times formed, and once by accident I obtained it
iu the state of beautiful crystals.

Sugar of Honey. — The lowestf well-defined sugar that I
have yet examined, was first obtained from Narbonne honey,
by means of a process formerly pointed out by me for obtain-
ing diabetic sugar in a state of purity J. This, deprived of
its hygrometric moisture by being placed under a receiver
with sulphuric acid for several days, was found to consist of

Carbon 36*36

Water 63*63

This sugar in the ordinary state of the atmosphere usually
contains more water than indicated by this analysis ; that is
to say, generally about 64*7 per cent. On the other hand,
on exposure to a temperature considerably below that of boil-
ing water, it rapidly loses about 3 per cent, of water, and be-
gins to assume the fluid form : kept at the temperature of
boiling water for 30 hours, it lost in one experiment upwards

* Dr. Ure states that he has found sugar to contain upwards of 43 per
cent, of carbon ; but no such specimen has occurred to me, though 1 by
no means deny its existence. Indeed I have hitherto met with no sugar
as it occurs in commerce, yielding more than 42*5 per cent, of carbon, and
frequently it contains considerably less than this.

f In commerce, these imperfect sugars are denominated weak or low
sugars, which last epithet is here employed in this sense.

J Med. Chirurg. Trans, viii. 537. I have little doubt that honey con-
tains a still lower sugar, and which is incapable in this country (at least
during a great part of the year), of assuming the solid form. This is pro-
bably the liquid sugar of Proust.

of

of simple alimentary Substances, fyc.

101

of 10 per cent, of its original weight, became of a deep brown
colour, and seemed to be partially decomposed *.

Sugar prepared from starch evidently belongs to this va-
riety, as is sufficiently indicated both by its sensible properties
and composition. The same is true in general of diabetic
sugar, and probably also of the sugar of grapes, figs, fyc When
pure, all the varieties of this sugar are beautifully white, cry-
stallize in spherules, and are permanent under the ordinary
circumstances of the atmosphere.

Between these two extremes, sugars occur of almost every
grade, as the following table will show.

Carbon.

Water.

Pure sugar candy .....

42-85

57-15

Impure-f sugar candy . . .

41-5 to 42-5

58*5 to 57*5

East India sugar candy (v)

41-9

58-1

English refined sugar . . .

41-5 to 42-5

58-5 to 57-5

East India refined sugar (v)

42-2

57*8

Maple sugar (v)

42 1

57*9

Beet-root sugar (u) ....

42-1

57-9

East India moist sugar (v)
Sugar of diabetic urine . .

40-88

59-12

36 to 40 ?

64 to 60 ?

Sugar of Narbonne honey

36*36

63-63

Sugar from starch .....

36*2

63-8

On some of these it may be necessary to make a few re-
marks. The sugar candies of the shops frequently contain
minute quantities of foreign fixed bodies, such as lime, &c,
as well as others of a destructible character. Both the spe-
cimens of India sugar candy I examined were obviously im-
pure to the eye, being of a brown colour and deliquescent ;
they contained, among other things, traces of potash. The
East India refined sugar was perfectly white, but rather soft
and friable, and it did not possess the fine and brilliant grain

* I observed that after this sugar had been cautiously melted it might
be preserved in the state of a transparent fluid, if placed in a perfectly dry
atmosphere, as under the receiver of an air-pump with sulphuric acid; but
that in a few hours after exposure to the air, it began to grow opaque and
assume the crystalline form, by attracting moisture. Is not this precisely
analogous to the deterioration which is known to take place in the sugars
of commerce? See Mr. Daniell on this subject in the Royal Institution
Journal, vol. xxxii. Dr. Ure supposes that this deterioration depends on
the absorption of oxygen ; but I have hitherto met with no sugar contain-
ing an excess of oxygen.

t In these results fixed bodies only have been allowed for, and those
marked (i>), as occurring in commerce, are probably subject to slight varia-
tions in their composition.

of

102 Dr. Prout on the ultimate Composition

of the best refined sugars of commerce. For a specimen of
the maple sugar I was indebted to Mr. Faraday; this, when
I received it, was very impure and deliquescent, but by treat-
ing it by the process above alluded to, a portion was separated
that differed but little in its appearance from cane sugar. The
beet-root sugar was made and refined in France; it was per-
fectly white, but rather soft and fine in the grain. The East
India moist sugar was of a very low kind, and known in com-
merce by the name of Burdwan sugar; it was deprived of its
hygrometric moisture before analysis by exposure to sulphuric
acid under a receiver. The diabetic sugar was prepared as
above ; the results given were obtained many years ago, and
I have had no opportunity of repeating the analysis with the
present apparatus ; I believe however that diabetic sugars in
general belong to the honey variety. The sugar of starch was
prepared by myself in the usual manner.

Of Amylaceous Principles.

Before we proceed to consider the analysis of amylaceous
bodies, a few remarks on the nature of these and similar sub-
stances may not be deemed improper. It has been known
from the very infancy of chemistry, that all organized bodies,
besides the elements of which they are essentially composed,
contain minute quantities of different foreign bodies, such as
the earthy and alkaline salts, iron, &c. These have been usually
considered as mere mechanical mixtures accidentally present ;
but I can by no means subscribe to this opinion. Indeed, much
attention to this subject for many years past has satisfied me
that they perform the most important functions ; in short, that
organization cannot take place without them. This point will
be more fully investigated hereafter : at present it is sufficient
merely to observe, that many of those remarkable changes
which crystallized bodies undergo on becoming organized, are
more apparent than real ; that is to say, their chemical com-
position frequently remains essentially the same ; and the only
points of difference that can be traced, is the presence of a little
more or less of water, or the intimate mixture of a minute
portion of some foreign fixed body. There is no term at {pre-
sent employed which expresses this condition of bodies, and
hence, to avoid circumlocution, I have provisionally adopted
the term merorganized*, (ftsgo; pars vel partim,) meaning to
imply by it that bodies on passing into this state become partly,
or to a certain extent, organized. Thus starch I consider as
merorganized sugar, the two substances having, as we shall see

* I am indebted to my friend Mr. Lunn for this term.

„^ presently,

of simple alimentary Substances, $c. 103

presently, the same essential composition, but the starch dif-
fering from the sugar by containing minute portions of other
matters, which, we may presume, prevent its constituent par-
ticles from arranging themselves in the crystalline form, and
thus cause it to assume totally different sensible properties*.

Wheat Starch. — The most perfect form of the amylaceous
principle is undoubtedly that derived from wheat. This has
been analysed by different chemists with very different results.
MM. Gay Lussac and Thenard state that they found it to con-
tain as much as 43'55 per cent, of carbon ; while Dr.Ure in-
forms us that he only found 38*55 per cent. The following
observations will sufficiently explain these differences.

A very fine specimen of wheat starch, which had been pre-
pared expressly at my desire without the addition of the co-
louring matter commonly added to the starch of commerce,
and which had been kept in a dry situation for many months,
was found, in the ordinary columnar form in which it usually
occurs, (abstracting foreign matters,) to consist of

Carbon 37*5

Water 62-5

One hundred parts of the same specimen reduced to a state
of fine powder, and subjected to a temperature between 200°
and 212°, for the space of twenty hours f, lost, m a mean of

* When this subject first occupied my attention many years ago, I was
at a loss to form any notion of the modus operandi of these minute admix-
tures of foreign bodies, except the mechanical one mentioned in the text,
viz. that they operated by being interposed, as it were, among the essential
elements of bodies, and thus by weakening or modifying their natural affi-
nities. But the admirable paper, published by Mr. Herschel, in the Philo-
sophical Transactions for 1824, " On certain motions produced in fluid con-
ductors when transmitting the electric current," appeared to throw an en-
tire new light on the subject. The facts brought forward in this paper are of
the most important kind, and seem to me to be evidently connected with a
principle of a more general character, which when completely developed,
will lead to the most unexpected results. " That such minute proportions
of extraneous matter," says Mr. H. " should be found capable of commu-
nicating sensible mechanical motions and properties of a definite character
to the body they are mixed with, is perhaps one of the most extraordinary
facts that has yet appeared in chemistry. When we see energies so intense
exerted by the ordinary forms of matter, we may reasonably ask what
evidence we have for the imponderability of any of the powerful agents to
which so large apart of the activity of material bodies seem to belong?"

Any substance may be supposed capable of performing the part of a mer-
organizing body ; but, in a certain point of view, ivater appears to consti-
tute the first and chief, at least in organized substances.

1 1 have reason to believe from other experiments that six or eight hours,
or even less, of steady exposure to the boiling temperature, will sometimes
reduce both starch and arrow root, and even gum, to this state of desicca-
tion.

two

104 Dr. Prout on the ultimate Composition

two experiments, 12*5 parts, and on being analysed in this
state gave Carbon 42*8

Water 57'2

which very nearly coincides with what by calculation it ought
to have given, on the supposition that the loss of weight was
owing to the escape of water, a circumstance indeed of which
there could have been little doubt. Starch however in this
state still retains water, a portion of which may be separated
by subjecting it to higher temperatures. Thus, after having
been exposed as above for twenty-four hours to the tempera-
ture of 212°. on being further submitted to a temperature be-
tween 300° and 350° for six hours longer, it lost 2*3 per cent,
more, and analysed in this state gave very nearly

Carbon 44

Water 56

It had now acquired a slight yellow colour, and seemed to
have suffered some change in its properties ; hence, this is pro-
bably nearly the utmost quantity of water that starch is ca-
pable of parting with, short of decomposition.

Arrow root. — This is another variety of the amylaceous prin-
ciple, of which, like sugar, there seems to be a great variety.
The specimen on which the following experiments were made
was remarkably fine, and free from adventitious matters. It
had been kept in the same drawer with the starch before men-
tioned, and under precisely similar circumstances of the at-
mosphere was found to consist of (abstracting foreign matters)

Carbon 36*4

Water 63*6.

One hundred parts, in the above state, exposed for twenty
hours to a temperature between 200° and 212°, lost fifteen
parts. Hence its composition, when thus dried, was very
nearly the same as that of wheat starch similarly exsiccated ;
or it consisted of Carbon 42-8

Water 57*2.

On being subjected to the full temperature of 212° for six
hours longer it lost 3'2 per cent, more, and was then reduced
to a state similar to that of starch dried between 300° and
350°, or it consisted very nearly of

Carbon 44*4

Water 55'6

When subjected to the temperature of 300° and 350° for six
hours longer, it lost 1 '38 per cent, more of its weight, but be-
came of a deeper yellow colour than starch similarly exposed,
and consequently showed greater marks of decomposition.
Hence, this form of the amylaceous principle, like the sugar
of honey before mentioned, seems to part with the whole of

the

of simple alimentary Substances, fyc. 105

the water not essential to its composition at the temperature of
212°, or even perhaps below this point if exposed for a period
sufficiently long.

It may not be deemed superfluous to notice here very
briefly two or three circumstances resulting from the above
analyses, which, though their importance may not be seen at
present, should be constantly borne in mind, as they will en-
able us hereafter to throw light on many points connected
with organization, which otherwise would be inexplicable.

In the first place, the identity of composition between the
sugar of honey and arrow root, under the ordinary circum-
stances of the atmosphere, seems to show that the differences
among the varieties of the amylaceous principles are precisely
analogous to those existing among sugars, or in other words,
that there are low starches as well as low sugars. Whether
arrow root be the lowest that exists, I am unable to say ; but
I have met with none lower ; and have reason to believe that
the greater portion of the other varieties of the amylaceous
principle known to exist, like the varieties of sugars above
given, are intermediate in their composition between arrow
root and wheat starch. The same remarks apply to other
merorganized principles.

In the second place, the identity of composition between
wheat starch and cane sugar, and between the sugar of honey
and arrow root above mentioned, seems to show that, though
merorganized bodies are not actually capable of assuming the
crystalline form, yet that the original tendency among their
essential elements to combine in certain proportions (and per-
haps to assume certain forms) still continues to operate, though
in a mitigated degree, and thus to exert, as it were, a feeble
nisus, or endeavour toward the maintenance of certain definite
modes of existence.

Thirdly, and lastly, crystallized bodies usually part with
their water of crystallation with difficulty, and when they do, it
is commonly per saltum, or in definite quantities. Meror-
ganized bodies, on the other hand, retain water so feebly at
all points, that within certain limits this fluid may be readily
separated, or made to combine with them in every proportion.
And this appears to be true, not only with respect to water,
but with other substances capable of combining with meror-
ganized bodies. It may be remarked also in general, that low
varieties of principles resemble merorganized bodies in these
and some other respects ; thus, they usually part readily with
all the water not essential to their composition at the tempera-
ture of 212°, or even less (provided they be submitted to it

New Series. Vol. 3. No. 14. Feb. 1828. P long

106 Dr. Prout on the ultimate Composition

long enough,) above which point they rapidly undergo decom-
position, &c.

Lignin, or the Woody Fibre.
Messrs. Gay Lussac and Thenard first showed that the hy-
drogen and oxygen in this principle exist in it in the propor-
tions in which they form water, a result fully confirmed by
my experiments. The variety of forms in which lignin occurs
in different woods is so great, that an examination of them all
would be quite out of the question ; I therefore selected two,
viz. the woods of the Box and Willow, which appeared to pre-
sent the greatest contrast ; the one being among the densest,
the other the lightest of the woods. These were both treated
exactly in the same manner ; that is to say, they were first re-
duced to the form of a coarse powder by rasping, then well
pulverized in a Wedgwood mortar, and afterwards sifted.
Being by these means reduced to the form of impalpable pow-
ders, they were boiled in repeated portions of distilled water
till that fluid came off unchanged : a tedious process, requir-
ing several days to accomplish perfectly. After this they were
similarly treated with alcohol, and finally again with distilled
water. They were now exposed to the atmosphere, when in
a dry and favourable state; and when they ceased to lose
weight were submitted to analysis, and found to consist of
(abstracting foreign matters)

Box. Willow.

Carbon 42*7 42-6

Water 57*3 57-4-

A known weight of each was then exposed for twenty- four
hours to a temperature of 212°, and afterwards for six hours
longer (by means of an oil bath) to a temperature between
300° and 350° ; and at the end of this time they were found
to have lost, per cent.

Box. Willow.
14-6 14*4
Analysed in this state of desiccation, they were found to con-
sist of Carbon 50*0 49*8

Water 50'0 50*2

showing that the loss of weight arose from the escape of water.
These latter results nearly agree with those of MM. Gay
Lussac and Thenard, as obtained from the analyses of the
woods of the Oak and Beech, and seem to show beyond a doubt,
that the composition of all of them is similar, or that they con-
sist of equal weights of carbon and water ; to which simple
analogy this important principle probably owes its stability.
Lignin undoubtedly exists in many other forms besides the

woody

of simple Alimentary Substances, fyc. 107

woody fibre ; indeed it appears to constitute the skeleton or
ground work on which most organic processes in the vegeta-
ble kingdom are carried on. To illustrate its properties as
an aliment, the only point of view in which we have to consi-
der it here, I shall briefly quote the experiments of Professor
Autenrieth, of Tubingen, who showed some years ago, that
by proper management this principle might be rendered ca-
pable of forming bread. The following was the method he
employed for this purpose. In the first place, every thing that
was soluble in water was removed by frequent maceration and
boiling. The wood was then reduced to a minute state of di-
vision ; that is to say, not merely into fine fibres, but actual
powder; and after being repeatedly subjected to the heat of
an oven, was ground in the usual manner of corn. Wood thus
prepared, according to the author, acquires the smell and taste
of corn flour. It is however never quite white, but always of
a yellowish colour. It also agrees with corn flour in this re-
spect, that it does not ferment without the addition of leaven,
and in this case sour leaven of corn flour is found to answer
best. With this it makes a perfectly uniform and spongy
bread ; and when it is thoroughly baked, and has much crust,
it has a much better taste of bread than what in times of scar-
city is prepared from the bran and husks of corn. Wood
flour also, boiled in water, forms a thick tough trembling jelly,
like that of wheat starch, and which is very nutritious*.

It may be remarked that all the preceding principles are
capable of being converted into oxalic acid by the action of
the nitric acid, and into sugar by the action of dilute sulphuric
acid.

Acetic Acid, or Vinegar*

This principle seems to have been more or less used as an
aliment, either by accident or design, in every age and country.
There have been various analyses of it published, by different
chemists ; but it is singular, that although some of them have
given its exact composition, no one seems to have been struck
with the most remarkable peculiarity of its composition f, viz.

* See the Edinburgh Magazine for November 1817, p. 313, where an
account is also given of the Lapland mode of making bread from the bark
of trees, as described by Von Buch. It is not improbable that during the
above processes the lignin combines with water, and forms an artificial
starch. ;

f Berzelius, in his paper On the definite proportions, in which the ele-
ments of organic nature are combined, assigns to vinegar this composition.
See Annals of Philosophy, v. 174 (O.S.) Dr. Thomson also, in the last
edition of his Chemistry, gives the same composition ; though in his more
recent work he has assigned to it another proportion of hydrogen.

P 2 that

108 Dr. Prout on the ultimate Composition

that the hydrogen and oxygen exist in it in the proportions in
which they form water. Some experiments which I made
many years ago appeared to render this probable; but from the
difficulties attending the analysis of this acid, and the uncer-
tainty arising from the properties of the oxide of copper formerly
stated, I was unable to satisfy myself completely on the sub-
ject. On repeatedly burning, however, a very fine specimen
of the acetate of copper, in a given bulk of oxygen gas, with
the apparatus described at the commencement of this paper,
it was found that the volume of the gas underwent no change,
and hence, that the above opinion was correct.

Acetic acid, freed from non-essential water, I find to be com-
posed of Carbon 47 '05

Water 52*95

results which almost exactly agree with those of other che-
mists.

Sugar of Milk.

The sugar of milk employed in these experiments was pre-
pared by myself in the usual manner, and rendered as pure as
possible by repeated crystallizations. It was then freed from
its hygrometric moisture by confinement under a receiver with
sulphuric acid, and was found to consist of

Carbon 4-0

Water 60

results almost exactly agreeing with those of Berzelius.

Manna Sugar. — The saccharine principle existing in manna
has been long known to possess peculiar properties. That
employed in the following analysis was separated by means of
alcohol in the manner commonly described in chemical books,
and was obtained in a state of perfect purity by repeated cry-
stallizations from that fluid. It was then dried at 212°, and
in this state was found to consist of

Carbon 38*7

Water 61*3

results very different from those of M. Theodore de Saussure*.
This sugar seems to part with hygrometric water only at the
temperature of boiling water; but a few degrees above this
point it begins to suffer decomposition, and at 250° it assumes,
without melting, the form of a brown powder, and acquires a
strong empyreumatic odour.

Gum Arabic. — A very fine specimen of gum arabic reduced
to powder, and analysed as it existed under the ordinary cir-

* See Bibliotheque Britannique, 1814; also Annals of Philosophy, vi. 424.

cumstances

of simple alimentary Substances, fyc. 109

cumstances of the atmosphere, was found (abstracting foreign
matters) to consist of

Carbon 36*3

Water 63*7

One hundred parts of the same gum, exposed to a tempera-
ture between 200° and 212°, for upwards of twenty hours, lost
12*4 parts. Hence its composition thus dried would be nearly

Carbon 41*4

Water 58.6

results confirmed almost exactly by actual analysis.

The same gum, further exposed to a temperature between
300° and 350° for six hours longer, assumed a deep brown
colour, and seemed to have suffered decomposition, though it
lost in weight only 2*6 per cent. more. Hence, gum probably
parts with the whole of the water not essential to its composi-
tion at the temperature of 212°, provided it be exposed for a
sufficient time to this degree of heat.

Substances belonging to this series appear in general to be
of a weak or low kind, though they are probably very numer-
ous. They may be readily distinguished by being converted
into saclactic acid by the action of nitric acid.

The vegetable Acids.
Oxalic Acid. — Many years ago I ascertained that this acid
in the crystallized state consists of

Carbon 19*04

Water 42-85

Oxygen 38*11

a composition assigned to it long since by other chemists, and
now I believe generally admitted, except by Dr. Thomson,
who informs us that he has met with a specimen containing as
much as half its weight of water*. I have examined a great
many specimens with the view of verifying this result, but
hitherto have not been successful.

Citric Acid. — This and all the following acids, except the
malic, were analysed at the same period as the oxalic acid
above mentioned, and the results have been recently verified.
I find the crystals of citric acid to consist of

Carbon 34*28

Water 42*85

Oxygen .... 22*87
This composition has been approached very nearly by se-
veral chemists ; but no one, so far as I know, has given it ex-
actly.

* Attempt to establish the first principles of chemistry by experiment,
ii. 103.

Tartaric

1 10 Dr. Prout on simple Alimentary Substances.

Tartaric Acid in crystals is composed of

Carbon 32*0

Water 36*0

Oxygen .... 32*0
a composition assigned to it by Dr. Thomson in his work just
quoted.

Malic Acid. — I am not acquainted with any analysis of malic
acid except that of M. Vauquelin*, which has not, I believe,
obtained much confidence among chemists, chiefly on account
of the large proportion of hydrogen which he assigns to it.
The acid I employed was obtained from the berries of the
mountain ash by a process very similar to that of Mr. Dono-
van. It was not analysed per se, but in combination with
lead, with lime, and with copper, and was found, abstracting
water not essential to its composition, to consist of

Carbon 40*68

Water 45*76

Oxygen 13*56

This acid, in many points of view, may be regarded as one
of the most interesting and important of all the vegetable
acids.

Saclactic Acid. — The unexpected composition of this acid in-
duced me to investigate its properties more fully than I had
otherwise intended. What I first employed was obtained
from the sugar of milk, and hence was tolerably pure, though
not perhaps completely so. Latterly, I have preferred that
prepared from gum, which, though exceedingly impure as
first obtained, may be easily and completely purified by the
following simple process.

Add ammonia in slight excess to the impure acid, and af-
terwards as much boiling distilled water as will dissolve the
saclactate formed. Filter the solution while boiling hot, and
then evaporate it very slowly nearly to dryness. The saclac-
tate of ammonia will be separated in the form of crystals,
which are to be washed with cold distilled water till they be-
come quite white and pure. They are now to be again dis-
solved in distilled water, and the boiling saturated solution
permitted to drop from a filter into cold diluted nitric acid.
This latter of course decomposes the saclactate, and precipi-
tates the saclactic acid in a state of perfect purity. Thus ob-
tained, this acid was found to consist of
Carbon . . . . 33*33

Water 44*44

Oxygen .... 22*22

* Ann. de Chimie et de Physique, torn. vi. 337.

results

Mr. R. Phillips on the Purity of Sulphate of Quina. ill

results differing a little from those of other chemists, who pro-
bably did not take the necessary pains to obtain this acid in a

perfectly pure state.

In conclusion, I wish to observe, that I purposely abstain
at present from making any further observations on the pre-
ceding results than those already given. I do this for several
reasons : in the first place, such observations will appear with
greater effect, when the whole of the facts in my possession
are laid before the public ; and secondly, I consider that data
which lead to such important conclusions as these appear to
do, cannot be too firmly established ; I therefore, in the mean
time, earnestly invite chemists in general to repeat them, and
thus either to confirm them, or point out their errors ; and
for the sake of those who may be inclined to take this trouble,
I shall close this part of the subject with the following re-
marks: 1. The multiples of hydrogen, carbon, and oxygen,
are assumed in the preceding calculations as 1 : 6 : 8. 2. The
results given are, on all essential points, the means of many
experiments, the differences among which are either inappre-
ciable, or at most vary from *01 to *03 of a cubic inch in
from 5 to 8 cubic inches of carbonic acid or oxygen gas ; the
greatest differences in general being, for obvious reasons, found
among merorganized bodies ; and hence the analyses of these
are usually stated to the first decimal figure only. 3. As rules
to be observed, I would say, that a single result should never
be registered, nor a single calculation made, till the operator
has made himself complete master of his apparatus, and care-
fully studied the nature of the substance to be analysed ; for
different substances often require very different management :
that two or three results should never be relied on ; the mi-
nute quantities here sought can be only obtained, like those
of astronomy, by repeated observations : and lastly, the ut-
most care should be taken that the substances operated on be
pure, a point of greater importance, and frequently of more
difficult accomplishment than any other, and one that has
caused me more trouble than all the rest put together.

XVIII. On the Means of ascertaining the Purity of Sulphate
of Quina. By R. Phillips, F.R.S. L. % E. $c.

HPHE great demand which has arisen for this important me-
A dicine, and the high price at which it is necessarily sold,
have excited some, who are careless as to the means by which
they acquire gain, to sophisticate it in a vast number of ways,-
and by every means which talent misapplied could suggest. .

Having

112 Mr. R. Phillips on the Means of ascertaining

Having repeatedly of late been requested to examine va-
rious samples of sulphate of quina, I thought it might be use-
ful to state the several modes which may be employed for that
purpose: and I make the present communication with the
greater confidence, because I have received the very able as-
sistance of my friend Mr. John T. Barry, of Lombard-street, to
whose chemical skill, and the opportunity of frequently apply-
ing it, I am indebted for the greater number of hints and facts
detailed in this paper.

Pure sulphate of quina has the form of minute fibrous cry-
stals, it is inodorous, and its taste is bitter. If certain vegeta-
ble products, such as starch or sugar, be mechanically mixed
with it, they may possibly be observed by merely inspecting
the preparation with a glass.

1st. If the sulphate of quina be mixed with a considerable
proportion of foreign matter, it may probably be detected by
dissolving the salt in question in about three hundred times
its weight of water, — say one grain in about five fluid drams
of boiling distilled water. On cooling, pure sulphate of quina
will be deposited in feathery crystals in twenty-four hours, if
there be no adulteration.

2dly. As indirect, but as good collateral evidence, the taste
of sulphate of quina of known good quality may be compared
with that of another sample. Thus when pure, a grain of
sulphate of quina will render nearly a pound and a half of
water, or 10,500 grains, sensibly bitter.

3rdly. The alkalies either pure or their carbonates, if but
slightly in excess, always occasion precipitation at ordinary
temperatures in a solution of sulphate of quina containing only
l-1000dth of its weight, or less than one grain in two fluid
ounces of water.

4thly. A solution of tannin occasions a very sensible pre-
cipitate in an aqueous solution of sulphate of quina, containing
only l-10,000dth of its weight of the salt, provided there be
no acid in excess. Kino is that form of tannin which best
answers the purpose. It is however to be observed, that the
salts of morphia, cinchonia, strychnia, &c. are similarly af-
fected by tannin ; but they are not likely to be mixed with
sulphate of quina.

5thly. Sulphate of quina suspected to contain sugar, gum,
or other substances soluble in cold water, may be tried by di-
gesting the same portion of the salt in small and successive
portions of water to saturation. If the sulphate of quina be
pure, and the solutions all properly saturated, they will have
the same taste and specific gravity ; and similar portions will
yield by evaporation equal quantities of solid residuum.

6thly.

the Purity of the Sulphate of Quina. 113

6thly. A repetition of the above process, substituting alco-
hol for water, answers for extracting resin and some other
substances, because sulphate of quina is soluble in alcohol to
only a limited extent.

7thly. If a white substance insoluble in cold water be found
in the sulphate of quina, heat the mixture to about 170° of
Fahrenheit. This will render starch soluble, and its presence
may be determined by the addition of an aqueous solution of
iodine, which will immediately occasion a blue colour, and
eventually a blue precipitate. The iodine should be added in
very small quantity.

8thly. Sulphate of quina has been adulterated with ammo-
niacal salts. These are rendered obvious by adding a little
of the suspected salt to a solution of potash. If any ammo-
niacal salt be present, ammoniacal gas will be readily detected,
either by the smell, or by holding over the mixture a piece of
turmeric paper, or a bit of glass moistened with acetic acid.

9thly. To ascertain whether sulphate of quina contains any
earthy salts, such as sulphate of magnesia or sulphate of lime ;
burn a portion of it in a silver or platina crucible, or even in
a clean tobacco-pipe. Any earthy salt, or any matter inde-
structible by heat, will of course remain in the vessel.

lOthly. To ascertain that the sulphate of quina contains
the proper quantity of sulphuri cacid and quina, dissolve a'little
in pure muriatic or nitric acid, and add a solution of muriate
or nitrate of barytes: 60 parts should give about 17'3 to
17*4 of sulphate of barytes; or the method may be varied
without the trouble of drying the precipitate. Dissolve 60
grains of sulphate of quina in water slightly acidulated with
muriatic or nitric acid ; add a solution of lo grains of nitrate
of barytes, and separate the precipitated sulphate of barytes
by filtering. If nitrate of barytes be now added to the clear
solution, it should still occasion slight precipitation, for 60 of
sulphate of quina contain 5*8 gr. of sulphuric acid, equiva-
lent to 19*1 of nitrate of barytes.

This test is only to determine that there is no crystallized
vegetable matter uncombined with sulphuric acid in the sul-
phate of quina ; the detection of earthy or alkaline sulphates
has already been provided for.

llthly. Sulphate of quina should lose not more than from
8 to 10 per cent of water by being heated till deprived of its
water of crystallization. Mr. Barry informs me that he once
examined a sample which contained more than 40 per cent of
water in excess diffused through it.

New Series. Vol. 3. No. 14. Feb. 1828. Q XIX. On

[ 1U ]

XIX. 0?i the Phenomena of Water-spouts. By Mr. James

Main*.
TN sailing from Madras to China, the usual course is through
* the Straits of Malacca and Sincapore. On the passage
from Pulo-penang (i. e. the Island of areca-nut trees) to Ma-
lacca, the prospect from the ship was interesting : to the right,
the thinly inhabited island of Sumatra was distinctly seen co-
vered by impervious jungle, with lofty and thickly growing
woods, even to the water's edge. To the left, the kingdoms of
Quida, Malay, and Siam, on the continent of Asia, presented
the same aspect ; but, unlike many parts of the torrid zone,
beautifully verdant and refreshing to the eye which had just
left the sultry atmosphere and comparatively thinly planted
coast of Coromandel. During the passage through those
scenes, the navigation was tedious, and the weather uncom-
monly unsettled ; the heat of the air was generally from 75 to
85 by Fahrenheit's thermometer. Occasional and insufferably
hot gleams of sunshine, raised from the sea ; and especially
from the wood-covered and damp surface of the adjacent lands,
a most copious evaporation ; surcharging the air, and suddenly
forming vast accumulations of clouds, all highly charged with
electricity. In all directions lightning descended, followed by
heavy and impetuous rain. The surrounding air and clouds
converging to the spaces thus left unoccupied, generated va-
rious and contrary currents of air, wheeling the clouds in vio-
lent commotion ; partial tornados were consequently created :
these by their vertiginous course affected the adjacent and sur-
rounding vapours, drawing them into the vortices ; the grosser
parts of this whirling body of vapour naturally inclined to the
centre of the tornado, and there coalescing, formed the aqueous
column called a water-spout.

The first appearance of this phaenomenon is the lower end
of the column impending from the base of a dark cloud in the
shape of an inverted cone, in a somewhat waved direction,
descending gradually to the sea or earth. When it happens to
descend on the former, it is plainly discernible that a consider-
able body of air below and around the spout partakes of its
dinetical motion ; because the water is violently agitated there-
with for a considerable time before the point of the cone reaches
the surface ; and during its approach, a cylindrical body of thick
spray of much greater diameter than the spout, is seen raised
from the waves, and appears to meet it in its descent ; and when
in collision, the agitation is extreme. The contact continues
for ten or twenty minutes, according to the size of the spout ;

* Communicated by the Author.

and

Mr. Main on the Phenomena of Waterspouts. 1 IS

and when exhausted, the lower end becomes broken, less de-
fined, and shrinking as it were upwards, disappears as it began.

Some travellers have reported, that water-spouts rise out of
the sea; having observed them, perhaps, only when the spout
had descended and was in contact with the surface ; or it might
happen, that in such a case the tornado might be first generated
below ; and before the clouds were acted on, a column of spray
would be seen to rise and approach the clouds, before a co-
lumn of water is formed in them of sufficient density to de-
scend. Similar appearances are sometimes seen on shore, when
columns of dust, or, as the writer has often witnessed, even
cocks of hay are carried up into the air by whirlwinds to a
great height.

So frequent were these meteorous appearances during this
part of the voyage, that on one occasion (when in sight of
" The Rabbit and Coney," two small islands in the Straits, well
known to navigators), no less than five water-spouts were seen
from the ship at the same instant ! some of which were falling
on the land, and others on the sea ; — the nearest to the ship
being computed to be at the distance of five miles. The writer,
who attentively observed these phaenomena, used an excellent
perspective glass, and on one occasion had an opportunity of
seeing one while the sun shone upon it (about 7 a.m.), which
appeared to be tubular ; as the sun's rays were reflected in a
double parallel stripe along that part of the spout on which
they shone, viz. one stripe reflected from the exterior side next
the sun, and another less bright from the interior surface (as
was supposed) of the opposite side. This, however, is only a
surmise ; but from similar motions of fluids which may be seen
at any time, there may be reason for supposing that the spout
is not solid : for instance, if a hole be made in the bottom of
any vessel, and plugged up with the end of a stick ; let the
vessel be filled with water and the plug withdrawn, the water
in escaping through the aperture soon assumes a circular or
rather a spiral motion, the descending column draws, or more
properly speaking, admits after it an inverted cone of air,
reaching from the surface of the water to the hole at which it
escapes.

The idea of preventing the approach (for these phaenomena
are seldom stationary) of a water-spout upon a ship (which
might produce dreadful consequences), by discharging great
guns towards it, is reasonable ; and if it did not approach too
rapidly, no doubt would be effectual ; because the concussion
from the gun would counteract and break the sweeping cur-
rent of the tornado, and thereby dissipate the motion-em-
bodied fluid, and of course prevent its effects.

Q 2 Many

116 Mr. Main on the Phenomena of Waterspouts.

Many ideas occur to the beholder of such " elemental
strife." Moses hath told us, that soon after the creation " there
went up a mist from the earth, which watered the whole face
of the ground ;" and this necessary alternation of the ascent
and descent of the element of water has continued ever since.
The aspiring agency of heat, both from the earth and from
that daily borrowed of the sun, is apparently the cause of the
ascent of humidity ; yet without the assistance of some other
no less powerful agent, it is difficult to account for all the
phaenomena connected with the ascent and descent thereof.
For though most copious between the tropics, and in our sum-
mer months, the lowest degree of temperature even within
the arctic circle does not materially check evaporation, and the
assumption by aqueous vapour of an invisible state in the at-
mosphere takes place as well in winter as summer. We find
when the atmosphere is most fully charged with aqueous vapour,
and has its temperature above the dew point, and consequently
not a cloud to be seen ; when almost all of it is exhaled from
the surface of the earth ; when vegetables and even animals
languish, — the barometer is high : but when this sustaining
power becomes diminished or withdrawn, a change takes place,
a sensible precipitation of moisture (erroneously called dew) is
felt, the air becomes turbid, clouds are formed, lightning is
seen, thunder heard, and rain descends. The barometer, eased
of its burden, sinks to the point of rain, or snow, or storm ;
and to this succeeds " a showery time, " which continues till
the atmosphere is again charged with that power which keeps
its vapour in solution, and restores its transparency. Is elec-
tricity this agent?

These meteorous changes, so interesting to mankind, al-
ways suggest and force upon us the wish to obtain an efficient
weather-glass ; such an one as would be affected by the exist-
ence and motions of those powers which cause the changes in
the atmosphere which are out of the reach of our perceptions.
Perhaps an electrometer which would indicate the quantity,
but especially the character and direction of that subtile fluid
{if such an instrument could be constructed), would be of the
greatest service in foreshowing the changes of the weather.

The above description and remarks are from actual obser-
vation. No reference has been made to any book, or other
authority on the subject; and whether the writer has been de-
ceived by appearances, and been led to erroneous conclusions
as to the cause of them, must be left to the judgement of the
reader.

6, Union Row, Chelsea,

April 21, 1827. XX. On

[ 117 ]

XX. On the Nursing Pouch or Chamber of the Chama concame-
rata ofGmelin. By John Edw. Gray, £59. F.G.S. fyc.*

WALCHin the 12th volume of the Naturforscher Journal,
of Berlin, described and figured (t. \.f. 7.) a very cu-
rious shell, which Chemnitz has since named Chama con-
camerata. It has been considered as very rare ; but having
lately been brought to this country in considerable abundance,
— through the kindness of Mr. Pratt, of Bath, I have been en-
abled to examine several specimens which had the dried ani-
mal in them : and as the formation of the cavity, which is itself
an anomalous structure in Mollusca, and the use to which it
appears to be applied by the animal, has not hitherto been
described, I shall proceed briefly to describe them.

The cavity is formed by a folding-in of the middle of each
of the valves; and this folding-in does not appear to take place
till the shell has arrived at the middle period of its growth.
It is marked externally by a groove formed by the coming to-
gether of the sides of the fold ; the parietes of the cavity are
thin, and marked with the same lines of growth as the valves
themselves; the cavities or folds of both the valves are exactly
opposite, and when the valves are closed, they meet so as to
form a nearly closed chamber, which, although in the internal
cavity of the shell, is completely external to the animal; and the
contents of the cavity, like when the head is in a double night-
cap, are on the outside of the shell. Indeed, the manner in
which the cavity is formed may be easily understood by fold-
ing a piece of paper to the shape.

The chamber appears to be used by the animal as a nursing
pouch to contain its eggs ; for in all the specimens which I have
seen, the cavity of each of the valves contained a group of
oval, crumpled, pellucid bodies, adhering together, which, when
they were soaked in water under the glass of a microscope, di-
lated, became semi-transparent, regularly oval, and had all
the appearance of the eggs of bivalve Mollusca ; but they are
rather large for the size of the shell.

This is indeed a remarkable anomaly; for most Conchiferce,
as was described by Lister, aerate their eggs in their gills,
and then emit them into the water to the protection of Nature.
Some freshwater species, as the Cyclades, indeed, appear to
keep them in the concave part of their shell, so as to be vivi-
parous. I do not know of any instance but the above, where
a pouch appears to have been formed for their protection; and
what is more remarkable, the other species of the genus Car-
dita, to which Lamarck has referred this shell, are un-
doubtedly destitute of any thing of the kind.

* Communicated by the Author.

XXI. On

[ H8 ]

XXI. On an Apparent Violation of the Law of Continuity.
By P. M. Roget, ilf.Z). F.R.S.*

FT cannot fail to strike every philosophical observer of na-
■■• ture, that the greater number of changes which take place
in the universe are effected only in a gradual manner ; that
each event is connected by insensible differences, both with
the one which immediately precedes, and the one which im-
mediately follows it; and that we may hence infer that the
whole series of mutations which constitute any observed
change, is perfectly uninterrupted and continuous. With re-
gard to those changes which appear at first sight to be more
suddenly effected, a careful analysis of the whole of the pheno-
mena, and a more minute subdivision of the time during which
they occur, will enable us to perceive the operations of the same
general principle of successive and intermediate gradation of
condition necessarily existing between opposite states of being.
Thus, the apparently sudden impulse communicated to a ball
by the explosion of gunpowder is, in reality, as much the re-
sult of a gradual communication of motion, during which the
ball passes successively, though with great rapidity, through
every intermediate degree of velocity, as in the case of the
slowest increase of motion, which it might acquire by the con-
stant operations of the greatest accelerating force. It was by
extending these views to a variety of subjects of physical sci-
ence, that Leibnitz was led to the conclusion, that the same
principle pervaded every department of nature, and that the
Law of Continuity^ as he called it, was the law of the universe.
Natura non operatur per saltum was his motto ; implying that
every thing that is executed in nature is done by indefinitely
small degrees. Boscovich has assumed this principle as the
foundation of his ingenious and profound theory of natural
philosophy, and deduced from it a variety of important corol-
laries and conclusions. The law of continuity, says that phi-
losopher, consists in this, that any quantity, whilst passing
from one magnitude to another, must pass through all the in-
termediate magnitudes of the same kind : or, according to the
law of continuity, all changes in nature are produced by in-
sensible and infinitely small degrees ; so that no body can in
any case pass from motion to rest, or from rest to motion,
without passing through all possible intermediate degrees of
motion*

* From the Scientific Gazette, Nos. 19 and 20, for November 5 and 12,
1825. — As this work has long since been discontinued, and was of confined
circulation, we think Dr. Roget's interesting paper will be acceptable to the
readers of the Philosophical Magazine. — Edit.

The

Dr. Roget on a Violation of the Law of Continuity. 119

The simpler illustrations of this law are obvious, and must
readily occur to those who seek for them ; but it is important
to familiarize the mind to them, with a view of preparing our-
selves for the inquiry to what extent the principle admits of
being carried, and whether it be really, as it is pretended, a uni-
versal law. It appears to obtain without exception in all those
physical changes of situations, qualities, and conditions, which
are connected with one another by their mathematical rela-
tions. All the forces and powers of nature vary by a con-
tinuous gradation from one period of time to another, or un-
dergo differences of degree at different parts of space, without
suffering any abrupt transition at any one point. Continuity
is an attribute common to the law of gravitation, which acts
at a distance, as well as to the laws of the corpuscular forces,
of which the sphere of operation is limited to insensible di-
stances, and which give rise to the phaenomena of cohesion, of
elasticity, and of all chemical combinations and decomposi-
tions. It belongs equally to the forces concerned in the phae-
nomena of electricity and of magnetism. As the law of each
of these forces may be expressed by some mathematical func-
tion of the distance at which they operate, so the same con-
tinuity must continue to pervade and characterize all the ef-
fects which can result from them, either when exerted singly,
or in combination. The motions of bodies may in every case
be regarded as the aggregate of the motions of every one of
their particles ; and the motions of any single particle, as well
as of an aggregate of par tides, produced by a continuous force,
must be itself continuous, not only with regard to augmenta-
tions or diminutions of velocity, momentum, mechanical force,
&c, but also with regard to the spaces they traverse, and the
lines they describe in space. No deflection from a perfectly
rectilineous course can take place but by infinitely small de-
grees ; or, to express it in geometrical language, the line of
motion cannot pass into any curve, of which that line is not
the tangent at the point where the change of direction begins;
far less, therefore, can a motion in one right line, suddenly
pass into a motion in another right line, which forms any angle
whatsoever with it. All angular motions are therefore ex-
cluded by the law of continuity, according to which abrupt
transitions, either of velocity or direction, are physical impos-
sibilities. The apparent violations of this law in the effects of
the collision of elastic bodies, or their reflection after impinge-
ing on hard surfaces, and even the phaenomena of the refrac-
tion and reflection of the rays of light, are shown by Bosco-
vich to be really all in perfect conformity with the law of con-
tinuity.

Not

120 Dr/Roget on a Violation of the Laiso of Continuity.

Not content with establishing the universality of this law by
induction, Boscovich has endeavoured to prove it by other
arguments, of a still more positive nature, derived from abs-
tract considerations. This universality, he says, arises ne-
cessarily from the very nature of continuity. The limit which
joins the precedent and the consequent of any thing is com-
mon to both, and is therefore indivisible. Thus, a superficies
separating two solids has no thickness, and is that in which a
transition from the one to the other occurs ; a line, dividing
two portions of a continued superficies, has no breadth ; a
point, discriminating two segments of a continued line, has no
dimension of any kind. So it is with regard to time: for the
limit of two consecutive portions is common to both and in-
divisible; and as every change of a variable quantity from one
magnitude to another must be made in time, so every change
must participate in the continuity of time. But to every mo-
ment of time, a certain magnitude of the variable quantity cor-
responds, and the limit of two moments of time is common
and indivisible ; therefore the limits of two magnitudes, corre-
sponding to these two moments, must, in like manner, be com-
mon and indivisible. Moreover, it is impossible for any quan-
tity to have two magnitudes at the same time, and when con-
tinually varying, that it shall have the same magnitude at dif-
ferent times ; much more impossible, therefore, that in the li-
mit of two moments of time it shall have two magnitudes, the
one course pending to the precedent, and the other to the
consequent moment; or shall not have gone through the in-
termediate magnitudes in the intermediate moments of time.
For the same reason, a body cannot have two velocities at the
same time, and therefore cannot have two velocities in the li-
mit common to two moments of time ; and when continually
changing its velocity, cannot have the same velocity in different
moments of time, but must go through all the intermediate ve-
locities in the intermediate moments of time. Hence, then,
in passing from the magnitude 8 to the magnitude 12, the
variable quantity passes through the magnitudes 9, 10, 11.
The increase or diminution of temperature, for example, goes
on gradually ; the mercury in the thermometer rises or falls
progressively, passing through every intermediate degree from
one point of the scale to another. Now as this reasoning is
unaffected by any considerations of the hardness, softness,
elasticity, or other physical property of bodies, the universality
of the law, as resulting from the nature of continuity, is a
truth independent of such considerations. From these argu-
ments, which I have given as stated by his able expositor
Professor Robison, Boscovich has concluded that the law of

continuity

Prof. Hiinefeld on Titaniferous Iron-slag. 121

continuity is essentially universal, and that a breach of it is
metaphysically, as well as physically, impossible.

The severest test to which the validity of this mode of rea-
soning can be put, is to apply it to the pure mathematical re-
lations of space and quantity, to which, if the law of continuity
have any necessary existence in the nature of things, it ought
to apply with the greatest rigour. We find, accordingly, that
all the changes of magnitude in those quantities of which the
value is dependent on that of certain other quantities, accom-
pany corresponding changes in these latter quantities, in a
manner strictly conformable with the law of continuity.
[To be continued.]

XXII. On the Titaniferous Iron-slag of Kbnigshiitte in Upper-
Silesia, and on the Probability of its containing Tantalium.
By Prof Hunefeld, of Greifsvoalde* .

A LTHOUGH the investigations of Wollaston, Walchner,
•*** Rose, Du Menil, Cordier, Vauquelin, Peschier, Berzelius,
Zinken, Schrader, Karsten, and others, have shown that tita-
nium is widely distributed, it has been nowhere found in great
quantities. Wollaston found it in 1822 in the slag of the great
iron-works at Merthyr Tydvil in Wales, in regular pale cop-
per-coloured cubes f ; and Walchner found the same in the slag
of the pea-iron-ore of the High-furnace of Kandern in Baden J;
and Karsten, before this, in those of the Konigshutte§. Kar-
sten's observation has been but rarely mentioned, and has
been especially neglected by Berzelius. It seems to me that it
is particularly calculated to extend our knowledge of titanium
(at least for the German chemists) ; and this has induced me
to give an account of the titaniferous slag of the Konigshu tte,
which I examined in 1824 at Breslau. I must however pre-
mise, that I had then no opportunity of combining the investi-
gation, as to quantity, with that as to the nature of the sub-
stances.

The slag containing titanium, which was given to me for
examination by my friend M. Miiller, was thickly covered
and filled with pale copper-coloured cubes of titanium ; and
I found that Dr. Wollaston' s description was applicable to
them in all respects. Peschier, it is well known, has declared
it to be titanate of iron, of which, however, too little proof has
been offered for it to be admitted as a fact ||.

* From Schweigger's Jahrbuch, N. S. Band xx. p. 332.
f See Philosophical Magazine, vol. lxii. p. 18. and lxiii. p. 15.
X Ibid. vol. lxvi. p. 124. § Karsten's Archiv. iii. 524.

|| Walchner has declared himself decidedly against this opinion, and
New Series. Vol. 3. No. 14. Feb. 1828. R A por-

122 Prof. Hiinefeld on the Tituniferons

A portion of the slag was digested in aqua regia : the greater
part of it was dissolved, with evolution of sulphuretted hydro-
gen gas, whilst a considerable number of the small cubes of
titanium remained undissolved, having a perfect metallic lustre.
But besides these, there remained in the residuum a blackish
powder, containing grains and minute laminae, nearly of the
colour of silver, and having a metallic lustre, to which I shall
return in the sequel. Another portion of the slag was ignited
with nitre, in order to oxidate the titanium. The melted mass
dissolved in water gave a beautiful green solution, which, when
exposed to the air, soon assumed first a deep red, and then
a dark violet colour, and at last lost all colour *, whilst por-
tions of the protoxides of manganese and iron were deposited.
Subsequently, this deposit (marked a) and the sides of the
vessel became covered with fine crystalline iridescent laminae
and needles, probably titanate of potash precipitated by the
substances having attracted carbonic acid from the air.

The residuum of the dissolved mass in the porcelain crucible
was washed and dried, by which it assumed the colour of iron-
rust. It was partly dissolved in muriatic acid, and thereby
gave a solution of iron, and left a blackish powder (b). The
filtered strongly alkaline re-acting liquid was evaporated, and
mixed with nitric acid (c). After standing somewhat longer,
il gave crystals of nitre, and then others of an indistinct form.
They were mostly white, somewhat opalescent, not easily solu-
ble grains of salt, cracking and decrepitating between the
teeth, and which, with salt of phosphorus, were melted before
the blowpipe into a clear bead, which within the flame re-
ceived no colour, either by itself or mixed with tin. The so-
lution was rendered somewhat turbid by caustic ammonia, and
white flakes were deposited. Boiled and dissolved with pot-
ash, and acidulated with muriatic acid, infusion of galls pre-
cipitated it of a dark yellow ; but hydrosulphuret of potash and
ferroprussiate of iron gave no precipitate ; which leads me to
suppose that those grains of salt were tantalate of potash.

The fluid c had the following properties. With an alcoholic
infusion of galls, a yellowish-orange precipitate was formed,
which was dissolved on being heated ; and when it was con-
centrated, it gave a brown liquid, which remained clear on

shown that the iron between the laminae of the cubes of pure titanium had
been mechanically interposed ; whence (like Wollaston) he also explains its
magnetism.

* The cracks of the crucible contained a beautiful orange-red efflorescence
in needles, which were not examined. Were they manganesate of potash,
or sulphuret of titanium with sulphuret of potassium ? (Vid. Berz. Jahresber.
v. 134.)

cooling.

lron~slag of Kbnigshutte, in Upper Silesia. 123

cooling. Sulpho-cyanate of potash dissolved in alcohol pro-
duced a red colour; with a greater addition, a dark rose colour ;
but with impure sulpho-cyanate of potash (still containing ferro-
prussiate of potash), a greenish white precipitate; with the
ferroprussiate of potash itself a dark grass green precipitate,
which was in part dissolved in the remaining liquid, giving it
the same colour ; and it was also dissolved by nitric acid. This
last solution turned gradually brownish green *. Another so-
lution made with muriatic acid, gave, by contact with a cylin-
der of zinc, the usual indications of titanium.

The black powder b was digested in aqua regia, which ex-
tracted the iron and manganese, leaving however a consider-
able proportion of a black powder, which under the burnisher
gave an iron-gray streak of a metallic lustre, became inflamed
even before it arrived at a red heat, and yielded a whitish sub-
stance, which, with a few deviations, bore the characters of
tantalic acid. These deviations were probably produced by a
small portion of manganese, which was indicated in the trial
by the blowpipe.

I subsequently obtained, through the friend above men-
tioned, a larger quantity of slag containing titanium. It had
a still greater quantity of large and small regular cubes of
titanium, which were affixed on the outside as well as to the
inner cavities of the slag. They had nearly all the same regu-
lar form and the rose copper colour, except a few very small
groups, which tended somewhat to an orange tint, and had
but a faint brilliancy (sulphuret of titanium ?). But besides
these visible crystallizations of titanium, the slag had some
other interesting substances upon it.

1. Granules of metal melted into it of the shape of beans
or spheres, weighing from two to thirty grains.

2. Cavities of different sizes, the sides of which, when filed,
had a fine lustre as of steel.

3. Several grains of metal as it were sprinkled in the slag, of
a globular or oblong shape, with a metallic lustre, and a colour
between that of silver and that of tin. In their chemical pro-
perties they resembled the small lustrous metallic leaves which
have been mentioned above; they scratched glass, gave a
shining powder, and seemed therefore to be tantalium, such
as we have found it hitherto described.

4. Melted grains of metal, partly globular, with a tint ver-
ging upon the colour of brass.

5. Portions of melted blag, of a dark rose red nearly. They

* See Pfaff's Neue Versuche uber das Vcrhalten der Titans'dure gegen ver-
schiedene rcagentien (New Experiments on the Habitudes of Titanic Acid
with different re-agents); Jahrb. b. xv. p. 372; and Pfaff's Analyt. Chem.
b. ii. p. 523.

R2 all

124 Prof. Hunefeld on the Titaniferons

all showed, on being filed, a fine metallic lustre, were very
hard and tough, but not malleable, some scratching glass di-
stinctly, others but feebly.

No. 1. — The metallic granule was attracted by the magnet,
showed, when filed, a bright steel-lustre, which continued in
the air ; it was very hard, not ductile, but after many blows
with a hammer, flew into several pieces, and showed a fine-
grained fracture. These fragments could not be melted even
in the most intense flame of the blow-pipe ; they only became
slightly diminished in lustre. Treated with muriatic acid,
they yielded odorous hydrogen ; the muriatic acid dissolved
iron, the granule turned black, and after a longer digestion
crumbled into a black dust. In aqua regia, a little more was
dissolved ; about five-sixths remained, which, when washed
and polished with a glass stick, gave a streak of a metallic
lustre similar to molybdena. When moistened, it gave a
smell of hydrogen gas, such as is given by manganese. Thus
it remains undecided whether this quality belongs to a small
residuum of manganese, which however is probably the case,
since the black powder treated with salt of phosphorus yielded
a pearl of a faint amethyst colour, whilst otherwise nearly
the whole covered the pearl of salt of phosphorus with a me-
tallic pellicle ; and this result remained unchanged on the ex-
periment being continued. Treated with soda and borax, no
other re-action took place but that of the salt being covered
with a metallic pellicle, which remained unchanged even after
the pearl had been repeatedly touched with solution of caustic
potash, and a scrap of tin added to it. If, however, the granule
of slag had not been sufficiently treated with aqua regia, the
black metallic powder gave a blueish green substance with
soda, with salt of phosphorus, a yellowish brown pearl in the
external flame, a greenish one becoming clear on cooling in
the inner flame, and which therefore contained iron and man-
ganese.

After several experiments made with the black powder, I
could perceive, at least in this manner, no indication of tita-
nium ; but another granule, also treated with aqua regia, left
undissolved small rose copper coloured crystals of titanium.
Another piece of a melted granule in the titaniferous slag gave
on the filed surface visible particles of titanium, as it were
sprinkled among it. The granule just described could be filed
like the other portions described in what follows, adhering a
little to the file.

No. 2. — These parts proved to be almost entirely the same
as the former, but were a little harder, and yielded more of
the black metallic powder.

No. 3. — They scarcely lost any thing in aqua regia, preserved

their

Iron-slag of Kmiigshiitte, in Upper Silesia. 125

their lustre, and did not crumble. Similar granules remained
behind in another experiment with the same solvent, scratched
glass, and when beaten and broken with a hammer, made red
hot with caustic potash, and treated with the blowpipe appara-
tus as well as with humid re-agents, did not give any indications
of titanium. A portion, however, having been melted with pot-
ash, and acidulated with nitric acid, the solution remained for
several days exposed to the air, and being afterwards filtered,
was by means of a solution of galls precipitated rather abun-
dantly, of a dirty orange colour; whilst hydrosulphuret of pot-
ash produced a scarcely perceptible turbidity (tantaliumP).

No. 4. — The brass colour was only superficial, the mass un-
derneath almost entirely resembling Nos. 2 and 3.

No. 5. — The dark rose red, yellowish, and metallic colour of
these pieces extended deeper in the last-mentioned portions ;
they evidently contained titanium, were more difficultly filed,
were magnetic, and might contain a mixture of iron and tita-
nium on the surface, one of tantalium and iron, and some ti-
tanium itself further in.

The black powder obtained from the portion of slag of the
other mass, was ignited with carbonate of soda; the mass,
which when cold appeared white with blueish green margins,
was dissolved in water, in which the green colour, which is
the property of manganese, disappeared. A white, somewhat
loose and flaky powder was precipitated. The remaining fluid,
mixed with muriatic acid, when treated with oxalate and ferro-
prussiate of potash, gave a yellowish red precipitate, small in
quantity. The fluid, when exposed to the atmosphere, turned
to a fine grass-green, without the least deposit of cyanuret of
iron ; it was not acid. An infusion of galls produced a dirty
yellowish white precipitate, which after some time became
grayish white, and subsequently yellowish green. Sulpho-
cyanate of potash produced a reddish deposit. Neither the
solution nor the precipitate gave any indications of titanium
on being treated with salt of phosphorus ; nor even after a
short contact with a cylinder of zinc, tin or iron, muriatic acid
having first been added to the solution. But on mixing an-
other portion of the dissolved mass with nitric acid, drying it
and treating it with salt of phosphorus and tin before the blow-
pipe, I obtained, by adding a little oxide of iron, a glass of a
hyacinth colour, which by a greater addition of the evaporated
solution, turned to a violet blue, and became almost transpa-
rent.

On comparing these experiments with the slag, with the
known chemical properties of the substances, it is evident that
they contained not only an abundance of titanium (as has been

shown

1 26 Notices respecti?ig New Books.

shown before by Karsten), but probably also tantalium. As
both these metals are so scarce, especially tantalium^ I have
thought it of use to call the public attention to this slag.

It is not improbable but that the titanium originated by re-
duction from prototitanate of iron and manganese, and the
tantalium from the tantalates of the same bases (tantalite). It
would be a very meritorious performance, and highly important
to the geology of Silesia, if any one would institute a strict ex-
amination ol the iron ore which yielded this slag, as well as of
its locality, and the process of smelting it undergoes. 'Perhaps
by so doing some pure tantalium, or combinations of that
metal, as well as of titanium (and perhaps wolfram), may be
found in larger or smaller quantities. It need scarcely be
mentioned, that titanium is found in the Riesengebirge of Si-
lesia, especially in the Iser (Iserin) in the shape of nigrin.

XXIII. Notices respecting New Books.

THE following are the Contents of those Parts lately published,
of the Philosophical Transactions, and of those of the Linnean
and Astronomical Societies :

Philosophical Transactions for 1827. — Part 11.

On a new form of the differential thermometer, with some of its
applications. By William Ritchie, A.M. — On the structure and use
of the submaxillary odoriferous gland in the genus Crocodilus. By
Thomas Bell, Esq.— On the permeability of transparent screens of
extreme tenuity by radiant heat. By William Ritchie, A.M. — On the
derangement of certain transit instruments by the effects of tempera-
ture. By Robert Woodhouse, A.M. — On some of the compounds of
chromium. By Thomas Thomson, M.D. — Rules and principles for
determining the dispersive ratio of glass j and for computing the
radii of curvature for achromatic object-glasses, submitted to the
test of experiment. By Peter Barlow, Esq. — On the change in the
plumage of some hen -pheasants. By William Yarrell, Esq. — On the
secondary deflections produced in a magnetized needle by an iron
shell in consequence of an unequal distribution of magnetism in its
two branches. First noticed by Captain J. P. Wilson. By Peter
Barlow, Esq.— On the difference of meridians of the royal observa-
tories of Greenwich and Paris. By Thomas Henderson, Esq.— On
some observations on#the effects of dividing the nerves of the lungs,
and subjecting the latter to the influence of voltaic electricity. By
A. P.W.Philip, M.D. — On the effects produced upon the air cells of
the lungs when the pulmonary circulation is too much increased.
By Sir Everard Home, Bart.— Theory of the diurnal variation of the
magnetic needle, illustrated by experiments. By S. H. Christie, Esq.
M.A. — On the ultimate composition of simple alimentary substances ;

with

Notices respecting New Books. 127

with some preliminary remarks on the analysis of organized bodies in
general. By William Prout, M.D.

Presents received by the Royal Society : — Meteorological Journal.

Transactions of the Linnean Society of London. — Vol. 15th. Part II.

Some account of a collection of cryptogamic plants from the Ionian
Islands. By Robert Kaye Greville, LL.D. — Description of a new
genus belonging to the natural family of plants called Scrophularince.
By Mr. David Don, Libr. L.S. — On Boswellia and certain Indian Te-
rebinthacece. By Henry Thomas Colebrooke, Esq. — The natural hi-
story of Oiketicus, a new and singular genus of Lepidoptera. By the
Rev. Lansdown Guilding, B.A. — Observations on the tracheae of
birds ; with descriptions and representations of several not hitherto
figured. By William Yarrell, Esq. — On two new genera of land
tortoises. By Thomas Bell, Esq. — Of the insect called Oistros by
the ancients, and of the true species intended by them under this
appellation : in reply to the observations of W. S. MacLeay, Esq.,
and the French naturalists. To which is added, a description of a
new species of Cuterebra. By Bracy Clark. — A review of the genus
Combretum. By Mr. George Don. — Description of a new genus of
plants belonging to the order Nymphceacece i in a letter to H. T. Cole-
brooke, Esq. By Nath. Wallich, M.D. — Observations and experi-
ments, made with a view to ascertain the means by which the spiders
that produce gossamer effect their aerial excursions. By John Black-
wall, Esq. — Descriptions of two quadrupeds inhabiting the South of
Africa, about the Cape of Good Hope. By Andrew Smith, M.D. —
An account of a pair of hinder hands of an orang otang, deposited in
the collection of the Trinity- House, Hull. By John Harwood, M.D. —
On systems and methods in natural history. By J. E. Bicheno, Esq.,
Sec. L.S. — An account of a new species of Pin us, native of Califor-
nia. By David Douglas. — Remarks on the Antilope Chickara : in two
letters addressed to the Secretary. By Robert Hills, Esq. — Extracts
from the minute-book of the Linnean Society, &c. &c.

Memoirs of the Astronomical Society, Vol. 3rd. Part I.

Observations made in the Island of Cuba. By the late Don Jose*
Joaquin de Ferrer, of Cadiz, member of the Phil. Acad. Boston. Com-
prehending, 1. Observations of the comet of 1807, with the determi-
nation of the elements of its orbit j 2. Observations of the lunar
eclipse, Nov. 14, 1807 j 3. Observations of the comet of 1813, with
the determination of the elements of its orbit, together with remarks
on its magnitude, and that of the comet of 1811 ; 4. Observations,
and computations of the elliptic orbit, of the comet of 1811 . — On the
longitude of Port Bowen, by the method of moon-culminating stars.
By Lieut. H. Foster, R.N. — Approximate places and descriptions of
295 new double and triple stars, discovered in the course of a series
of observations with a 20-feet reflecting telescope : together with some
observations of double stars previously known. By J. F. W. Herschel,
Esq. Pres. — Notice respecting some errors common to many tables
of logarithms. By Charles Babbage, Esq., For. Sec. — Astronomical

observations

128 Royal Society.

observations made at Bushey Heatli (north latitude 51° 37' 44",3 j
west longitude, in time, from Greenwich 0h lm 208,93), in the
years 1825 and 1826. By Colonel Mark Beaufoy : comprehending,
1 . Transits of the moon and moon-culminating stars ; 2. Occupations
of stars by the moon ; 3. Lunar eclipses j 4. Eclipses of Jupiter's sa-
tellites.— On a new application of the method of determining the time
by observations of two stars when in the same vertical, to the case of
Polaris, when so situated with respect to any other circumpolar star
in the course of its diurnal revolution below the pole. By Dr. Tiarks.
— On the passage of the comet of Bootes over the disc of the sun on
the 18th of November 1826. In a letter from M. Gambart to J. F.
W. Herschel, Esq. Pres. — On a new period of eclipses. By James
Utting, Esq. — On an appearance, hitherto unnoticed, in the nebula
of Orion. By John Pond, Esq., Astronomer Royal. — Notice of a comet
discovered by M. Flaugergues at Viviers, March 29th, 1826. Ex-
tracted from a letter from M. Flaugergues to F. Baily, Esq., Pres. —
Astronomical observations : I. Observations taken at Stargard, and
the Paramatta observatory, New South Wales, in the years 1 825 and
1826. By Dr. Rumker. 1. Of the great comet of 1825 j 2. Of the
comet in Leo in 1825 ; 3. Of the lunar eclipse in May 1826 — of an
occultation during the eclipse — and of Mars near the opposition in
1826. II. Observations of the solar eclipse in November 1826, taken
at Bushey Heath. By Lieut. George Beaufoy, R.N. III. Observa-
tions of a comet in Eridanus, and of Ceres, Pallas and Vesta, near
their oppositions in the year 1 826, taken at Padua. By Professor San-
tini. IV. Observations of the eclipses of Jupiter's satellites, taken at
the Madras observatory, in the years 1817 — 1825. By John Golding-
ham, Esq. V. Observations taken at Calcutta in the year 1822 j and
an extract of a letter from Major J. A. Hodgson to Dr. Gregory.

1. Of the transit of Mercury over the sun's disc in November, 1822 $

2. Of occultations of stars by the moon ; 3. Extract of a letter rela-
tive to the mode adopted for determining the times of the observations
of Jupiter's satellites, recorded at p. 440, vol. ii. of the Mem. Ast.
Soc. — Report of the council of the society to the seventh annual ge-
neral meeting. — Address delivered at a special general meeting of the
Astronomical Society of London, on April 11, 1827, &c.

XXIV. Proceedings of Learned Societies.

ROYAL SOCIETY.

Dec. 6, 1827.— ^HOMAS Henry Hall, Esq., and William Phillips,
JL Esq., were admitted into the Society.

A paper was read, entitled, " On the Corrections in the Elements
of Delambre's Solar Tables, required by the Observations made at
the Roval Observatory at Greenwich ; by G. B. Airy, Esq., M.A.,
Lucasian Professor of Mathematics in the University of Cambridge,
communicated by J. F. W. Herschel, Esq."

The author was desired by the Board of Longitude to examine the
discordancies between the right ascension of the sun, as observed at

Greenwich

Royal Society. 129

Greenwich since the erection of the new transit instrument, and as
computed by the solar tables of Delambre, which are used in the
computation of the Nautical Almanac, with a view to the discovery of
the errors in the elements of those tables. The result of the compa-
rison at first indicated the necessity of a correction of the epochs of the
sun's longitude, and of the longitude of the perigee, and perhaps also
of the equation of the centre. But upon pursuing the examination
through a series of years, it became manifest that some other source of
irregularity existed, and that this could be no other than an erroneous
estimate of the masses of some of the planets, especially of Venus
and of Mars. A more critical examination snowed that there was
also an error in the assigned mass of the moon. It was found necessary
in these investigations to take into account an error which occurred in
the tables with regard to the secular motion. It results from the au-
thor's researches that the epochs for 181 6, and those for 1821 to 1825,
ought to be increased respectively by 4",734 and 5",0(jl j that of the
perigee increased by 46",3, and the greatest equation of the centre
diminished by 0",84 j the mass of Venus should be reduced in the
proportion nearly of 9 to 8, and that of Mars nearly in the proportion
of 22 to 15. On a comparison of these results with those which have
been derived from an examination of some of Dr. Maskelyne's ob-
servations as given by Burckhardt in the Connaissance des Terns for
1816, they are found on the whole to agree in the most satisfactory
manner.

Dec. 13. — A paper was read, entitled, " On the measurement of
high temperatures -, by James Prinsep, Esq., Assay Master of the
Mint at Benares, communicated by P. M. Roget, M.D. Sec. R.S."

In the commencement of this paper the author describes the many
abortive endeavours of former experimenters to obtain instruments for
the accurate admeasurement of high temperatures, and afterwards
describes several attempts of his own to effect this very desirable ob-
ject. In the course of his inquiries a remarkable fact presented it-
self in the change which occurred in an index constructed on the
compensation-principle, and formed by two slips of meta^ the one
of silver, the other of gold, originally quite pure, and united without
any alloy. In the course of a few years, although it had never been
subjected to a very high temperature, the surface of the gold became
converted into an alloy of silver, the impregnation extending gra-
dually to a considerable depth in the gold, and destroying the sensibi-
lity of the instrument to changes of temperature.

After trying various plans, he gave the preference to the one
founded on the following principles : namely, that the fusing points
of the pure metals are fixed and determinate ; that those of silver,
gold, and platina, comprehend a very extensive range of tempera-
ture ; and that between these three fixed points in the scale, as
many intermediate ones as may be required, may be obtained by
alloying the three metals together in different proportions. When
such a series of alloys has been once prepared, the heat of any
furnace may be expressed by the alloy of least fusibility which it is
capable of melting. The determinations afforded by a pyrometer
New Series. Vol. 3. No. U. Feb. 1828. S of

1 30 Linnaan Society.

of this kind will, independently of their precision, have the advan-
tage of being identifiable at all times and in all countries ; the small-
ness of the apparatus is an additional recommendation, nothing
more being necessary than a little cupel, containing in separate cells
the requisite number of pyrometric alloys, each of the size of a pin's
head. The specimens melted in one experiment need only to be
flattened under the hammer in order to be again ready for use. For
the purpose of concisely registering the results, the author employs a
simple decimal method of notation, which at once expresses the na-
ture of the alloy, and its correspondence with the scale of temperature.
As the distance between the points of fusion of silver and of gold
is not considerable, the author divides this distance on the scale into
ten degrees ; obtaining measures of each by a successive addition
of 10 per cent of gold to the silver, the fusion of which, when pure,
marks the point of zero, while that of gold is reckoned at 10 degrees.
From the point of fusion of pure platina to that of pure gold, the au-
thor assumes 100 degrees, adding to the alloy which is to measure
each in succession, one per cent of platina. The author then enters
into a detailed account of the method he employed for ensuring accu-
racy in the formation of the requisite series of alloys, and of various
experiments undertaken to ascertain their fitness as measures of high
temperatures. The. remainder of the paper contains the recital of the
author's attempts to determine, by means of an apparatus connected
with an air-'tftermometer, the relation which the fusing point of pure
silver bears to the ordinary thermometric scale.

A paper was likewise read, entitled, " On Alimentary Substances ;
by Sir George Smith Gibbes, M.D. F.R.S."

After a few remarks on the very scanty assistance which physio-
logy and pathology have yet derive^ from the chemistry of orga-
nized substances, notwithstanding the great improvements which
have been lately introduced in the methods of analytical research, the
author maintains the proposition, that all alimentary substances,
whether belonging to the animal or vegetable kingdoms, retain some
principles originally the result of vitality, which they communicate to
other bodies, and thus constitute their food. He considers the ap-
pearances of the infusory animalcula, and more especially of the
Monas Termo, during the decomposition of alimentary substances as
favouring this hypothesis. In support of this argument, he adduces
experiments by Dr. Ingenhouz, himself, and others, from which he
infers that these animalcula perform some definite function during
the growth of vegetables.

From the circumstance of chloride of lime preventing the deve-
lopment both of vegetation and of infusory animalcula, the author
infers that these animalcula are instrumental in the production and
growth of plants.

LINNJEAN SOCIETY.

Dec. 4. — Read a paper " On the Locomotive Power of the Snail,
by Mr. James Main." The author describes as the species which
have chiefly come under his notice the following ; — Limax maximus:

ater :

Linruean Society. 181

ater : lichenivora ; rufus ; mutabilis : tenax : and agrestis. The belly
of the snail being perfectly smooth, there are no appendages to do
the office of feet 5 and the whole of the body moves at once, and not
in parts successively. By placing the animal on a piece of glass,
Mr. Main was enabled to observe a muscular motion ; but this, in-
stead of being from head to tail, was directly the reverse, so that the
animal's motion cannot be caused by impulses in the direction of its
progress. He gives, in conclusion, two conjectures as to the cause
of the animal's motion j namely, 1st, that the body is moved forward
by the retromissive discharge of slime, which being emitted simul-
taneously from every part of the under surface, he conceives may ex-
ercise a force adequate to the propelling of the animal s — or 2ndly,
from its power of forming its lower surface into segments of circles
along the whole of its length j and thus by assuming a vertical ver-
micular action on the plane of the sustaining surface, impelling the
body forward by alternate contraction and expansion.

As dry air deprives the animal of motion, Mr. Main is inclined to
consider the first surmise the more probable.

Read an extract from a letter from Dr. Rigby to Mr.R. Taylor, dated
Berlin, on the ova of the Hirudo medlcinalis •" with some specimens.

Read also "An account of Margarodes, a new genus of insects
found in ihe neighbourhood of Ants' Nests ; by the Rev. Lansdown
Guilding, B.A., F.L.S. &c." Mr. Guilding, after quoting Dr. Nugent
(Geol. Trans, vol. v. p. 463), who states that the ground pearl (im-
properly supposed to be fossil) is found in prodigious quantity in the
furrows of the land in Antigua when newly turned up, and suggests
that it may be the production of an insect, informs us that he has
succeeded, by watching some that he preserved in moist marl, in de-
tecting the insect which issued from them. He conceives it to be a
parasite on the ants, whose formidable numbers in the dry islands,
they are calculated to keep down. The entire want of a mouth is
remarkable in this new insect, the food being absorbed by tubes in
the fore claws. It also possesses the extraordinary power of throw-
ing out long filaments, when in dry situations, supposed to be for
preserving itself by obtaining moisture. Its scales effervesce and
disappear in nitric and muriatic acid ; sulphuric turns them black 3
and vinegar slowly decomposes them. In flame they burn like horn.
Mr. G. is uncertain at present what station is to be assigned to this
insect.

Dec. 18. — Three new species of Land Tortoise were exhibited by
Mr. Bell : — Testudo pardalis, actinodes. and tentoria, descriptions of
which are given in the number of the Zoological Journal just pub-
lished.

Read a portion of Dr. Hamilton's " Commentary on the Hortus
Malaharicus"

Jan. 15, 1828. — Some specimens of lanthince were exhibited by
L. W. Dillwyn, Esq., washed ashore in July last in Oxwick bay near
Swansea, many of them picked up alive and yielding a beautiful
dye. Specimens of the Medusa Vellela and M. Navicula were found
with them.

S 2 Read

132 Geological Society.

Read " Descriptions of three new species of Plants, natives of
New Granada, by M. Gondot, Professor of Botany at Bogota : the
plants are,

1 . Sessea corymbjfiora foliis obovatis attenuatisque, floribus corym-
bosis. — In woods near Bogota.

2. Cinchona Muzonensis foliis ovato-oblongis acutis basi attenuatis,
stipulis revolutis, panicula brachiata, corollis albis, limbo imberbi.
— In great forests near the city of Muzo.

3. A plant of a Genus nearly akin to Theobroma, from which it
differs chiefly in habit, in the form of the calyx, and the structure of
the stamens. Monadelphia Dodecandria. Bu'ttneriocce, Brown. "Ar-
buscula foliis digitatis, quinatis." — Forests near Muzo. Called by the
inhabitants the Cacao Montaras or Symoron. The poor people mix
the fruit with the cultivated cacao.

GEOLOGICAL SOCIETY.

Dec. 7. — John Braddich, Esq. of Boughton -Mount near Maidstone j
G. VV. Featherstonhaugh, Esq. of Duanesburgh, New York ; Arthur
Kett Barclay, Esq. of Grosvenor Place ; and Lord Francis Leveson
Gower, of Albemarle Street, were elected Fellows of the Society.

A paper was read, " On the Geology of Quebec and its Vicinitv,
by J. T. Bigsby, M.D. F.L.S. G.S." &c. &c.

The author, who acknowledges the assistance he has derived from
the manuscripts of Lieut. Skene, R. E., first describes the tract, on
the eastern termination of which the city of Quebec is situated, as an
oblong ridge of about seven miles and a half in length, and in aver-
age width about one mile and a half; subsiding on the north-west
by steep and rocky slopes, into rich meadows j whilst on the south-
east it advances in the form of cliffs towards the northern bank of
the St. Lawrence.

Various rivers traverse the district above mentioned, nearly from
north to south, of which the most considerable are the St. Charles
and the Montmorenci. On the southern bank of the St. Lawrence,
Point Levi is the most conspicuous promontory ; and to the west of
it the country is intersected by several streams running from south to
north.

Diluvium. — The districts above mentioned are partially covered
with boulders of gneiss, granite, syenite, and labrador felspar 5 the
greatest quantities of which are found on and near Cape Diamond,
Point Levi, and Point Montmorenci j whilst occasional deposits of
clay, gravel, and sand, including organic remains, the author supposes
to be of diluvial origin, — and not produced by the operation of any
existing watercourses.

The rocks of this region repose upon each other in the following
descending order: — 1st. A slaty series, composed of shale and grau-
wacke, occasionally passing into a brown limestone, and alternating
with calcareous conglomerate in beds, some of which are charged
with fossils. — 2nd. A conchiferous brown and black limestone some-
times based upon a calcareous conglomerate. — 3rd. Gneiss. The
author's chief reason for considering the slaty-6eries as superior to the

limestone,

Geological Society. 133

limestone, is, that the latter is in some situations in immediate con-
tact with gneiss ; while in others it passes into beds of the first series
above mentioned j of which the conglomerates contain organic re-
mains derived from the conchiferous limestone.

1 . The slaty-series occupies the whole of the southern shore of the
St. Lawrence, the Island of Orleans, and a considerable portion of the
north bank of the river, including the ridge upon which Quebec is
placed. In that neighbourhood the mass of the deposit consists of a
black and brown slaty limestone, inclined at high angles, in some
instances nearly vertical j and alternating with semi-crystalline lime-
stone, and various conglomerates. The limestone contains several
varieties of crystallized carbonate of lime, intermixed with quartz
crystals, and occasionally traversed by seams of bituminous matter.
Near Cape- Rouge, and on the plains of Abraham and Kilgraston,
some of the strata consist of red and greenish clay-slate. In the cal-
careous conglomerates, organic remains are mixed with fragments of
clay-slate, and the beds alternate with compact gray limestone and
quartzose layers. Between Quebec and Cape-Rouge, boulders of
primary rocks, and fragments of compact grauwacke, are buried deep
in the red schist.

The channels of the various streams east and west of Quebec, afford
instructive sections, which, according to the author, prove these slaty
deposits to be more recent than the conchiferous limestone.

On the south side of the river St. Lawrence, the slaty limestone of
Quebec is no longer seen, but several new beds of conglomerate pre-
sent themselves ; one of the lowest of which contains trilobites, en-
crinites, corallines, and other fossils associated with vegetable impres-
sions, probably fuci and amansice. In the schistose beds near the
mouth of the Etchemin are thin seams of coal ; and at the village of
St. Henry the slate is so compact as to be used for hones.

2. The horizontal conchiferous limestone occupies a zone from
two to three miles in breadth, on the north of the slaty tract, and
included between the slate and a mountainous range of gneiss. It is
exposed in the beds of all the rivers which flow southwards into the
St. Lawrence, and its characters are well developed at the falls of the
Montmorenci and the St. Charles, and at the quarries of Beaufort. The
organic remains consist of several species of trilobites, orthocerae,
terebratulae, encrinites, ammonites, &c. On the Montmorenci the
beds are from eighteen inches to two feet in thickness, nearly hori-
zontal, and of a blackish -brown colour j in one situation they pass
into a subjacent calcareous conglomerate, whilst in other places the
limestone itself contains large blue nodules, and reposes immediately
upon gneiss. At Beaufort-quarries, ledges of fetid limestone alter-
nate with calcareo-bituminous shale, containing organic remains
similar to those noticed on the Montmorenci.

From the characters and fossils of the limestone above described,
the author regards it as the same with the calcaire intermediaire of
D'Aubuisson, or the equivalent of the " Carboniferous-limestone" of
English geologists.

Dec. 21.

134 Geological Society.

Dec. 21. — Henry Holland Stutzer, Esq. River-Terrace, Islington,
was elected a Fellow of the Society.

The reading was begun of a paper tf On a group of Slate- Rocks
in Yorkshire, between the rivers Lune and Wharfe, from near Kirby
Lonsdale to near Malham, by John Phillips, Hon. Mem. of the Leeds
and Yorkshire Philosophical Societies."

1828. Jan. 4. — John Murray, Esq. Jun. of Albemarle Street 5
Henry Tuffnell, Esq. of Chris tchurch, Oxford 5 The Right Hon.
Viscount Cole, of Christchurch, Oxford j R. C. Fergusson, Esq.
M.P., of Craigdarroch, Dumfriesshire, and of Great Cumberland
Street j John Phillips, Esq. of York, Hon. Mem. of the Yorkshire,
Leeds, and Hull Philosophical Societies ; and John Gurdon, Esq. of
Assington Hall, Suffolk, — were elected Fellows of the Society.

The reading of Mr. Phillips's paper begun at the last meeting, was
concluded.

The object of this paper is to describe the geological structure and
relations of a group of rocks which the author characterizes as " aber-
rant from the slate district of Cumberland," and extending about
fifteen miles towards the east under the summits of Greygarth, Ingle-
borough, and Pen-y-gent, — a tract remarkable for the variety and sin-
gularity of its geological appearances, among which the proofs of
dislocation are peculiarly striking and important.

To this description a sketch is premised of the slate-series of the
Lakes of Westmorland and Cumberland, where the rocks are grouped
in three principal divisions, the lowest consisting of dark soft slate
much contorted, with fine-grained gneiss beneath it passing into
granite. The second division occupies a country of very different
aspect from that of the slate. The mountain-ranges being marked by
abrupt precipices, as at Helvellyn, Langdale Pikes, and the Lakes of
Ulswater, &c. and composed of brecciated argillaceous rocks contain-
ing calcareous spar, green-earth, and calcedony, with greenstone and
other forms of trap. On the south of this chain is a tract of transi-
tion limestone, containing caryophyllia, products, spiriferae, and other
fossils ; and this is covered by a third zone of slate, the most recent
rock of the country, usually divisible into rhomboidal blocks, of which
two principal varieties are observable, alternating with each other; the
one homogeneous and fissile, and containing organic remains spa-
ringly distributed, of the genera trigonia, pecten, gryphea, turritella
terebratulaj — the other more granular and micaceous. This forma-
tion is in some cases succeeded by red conglomerate, but more com-
monly by mountain-limestone, the lowest beds of which contain nu-
merous pebbles of slate and quartz ; and above the limestone are the
carboniferous rocks, including the millstone grit and the upper coal-
measures. The highest strata known in the country, consist of the
new red sandstone, placed in an unconformable position above the
coal formation.

The tract, which is the more immediate object of this paper, extends
from the valley of the Lune in an easterly direction, to that of the
Wharfe. Along its middle, from Casterton Fells to a few miles east

of

Geological Society, 135

of the Ribble, ranges an almost continuous line of argillaceous rocks,
generally fissile, and belonging to the third division of slates above
mentioned. This tract is bounded on the north by the elevated strata
that support the summits of Greygarth and Pen-y-gent ; and on the
south (in consequence of great dislocations) by millstone grit and the
coal measures. If the rivers Lune and Wharfe are included, no fewer
than nine streams cross the district from north to south, and exhibit
very distinctly the structure and relations of the rocks 5 the greater
number of the streams cutting through the limestone and millstone
grit, exposing the subjacent slate, and finally passing off on the de-
pressed strata of the coal measures. The author describes in detail,
the phenomena presented in these several sections, and illustrates his
observations by sectional views and sketches.

The structure of the country is very well displayed in the course of
the Kibble, where the slate first appears on the north, beneath paral-
lel bands of limestone ; while on the south, the carboniferous
strata, of which the northern portion is horizontal, decline at a high
angle, thus indicating a vertical dislocation of about four hundred
feet. Besides this fault on the southern verge of the slate, another
still more important one may be traced in a parallel direction across
the valley of Ribbles-dale, and over Malham Moor 5 by which, strata
have been brought into opposition, that in their original place were
separated by a thickness of more than five hundred feet. Various
facts are stated by the author in proof of this derangement, and de-
scriptive of the phenomena produced by it.

The author subjoins to his descriptions some remarks on the strati-
fication of slate, and on the difficulty of discriminating between the
planes of general stratification, or dip, and those of the cleavage ef-
fected by a blow, — the latter of which are often disposed at consider-
able angles to those of the dip. He is disposed to think, that in, the
fissile granular varieties of slate approaching to sandstone, the laminae
of cleavage may really be those of deposition j since the surfaces are
frequently coated with mica, and the fossil remains are in a disposition
parallel to them. Besides this more general cleavage, however, the
slate is also traversed by other planes, oblique to those of cleavage,
and less conspicuous, to which the quarry-men give the name of
" Bate." The direction of these planes, though nearly alike in limited
spaces, is found to vary considerably in different portions of the same
tract ; and even the better-defined planes of the ordinary cleavage are
seldom parallel to each other throughout any great extent of country.

A collection of fossil vegetables, chiefly from the Jarrow and Fell-
ing collieries in the Northumberland and Durham coal-field, pre-
sented to the Society by William Hutton, Esq. of Newcastle-upon-
Tyne, with drawings describing the plants according to the system of
M. A. Brongniart, was accompanied with some remarks by the donor,
comprised in a catalogue. — The collection consists of Calamites, Sigil-
laria, Sagenaria, Stigmaria, Filices, Sphsenophyllum, Asterophyllum,
&c. j also several specimens of undescribed confervae, leaves, stems,
&c.

A notice was read on the occurrence of "Chlorophseite" in basaltic

dykes

136 Astronomical Society.

dykes in Northumberland ; and of carbonate of strontian in the lead
measures at Fallowfield near Hexham, by William Hutton, Esq. of
Newcastle-upon-Tyne.

The author discovered "Chlorophaeite" in a basaltic dyke near the
river Coquet, about two miles N.E. of Felton, in the form of small
nodules, which upon fracture exhibit the changes of colour and ap-
pearance mentioned by Dr. MacCulloch, who first found this mineral
in the Isle of Rum. This substance has also been observed by the
author at Coaley Hill near Newcastle, in the steatitic or earthy form,
and but rarely crystallized.

ASTRONOMICAL SOCIETY.

Dec. 14. — Aletter was read from Maj. Hodgson the Surveyor- General
of India, dated from Calcutta, April 18, 1827, accompanied by two
copious lists of astronomical observations. The first contained a series
of transits of the moon and some of the principal fixed stars, as ob-
served at his own house (situated 5 seconds in time, east of the
Flag-staff of Fort William) from November 18, 1826 to March 20,
1827, both inclusive. The observations are above 300 in number:
and the stars observed are not those which are usually denominated
moon-culminating stars, but consist of some of the principal stars
only ; and many of these situated occasionally at very considerable
distances from the moon in declination. In fact, the list of moon-
culminating stars has never yet been computed early enough to en-
able it to be sent to such distant places in sufficient time for the ob-
servations. It is therefore to be feared that correspondent observa-
tions of many of the stars observed by Major Hodgson may not be
found at the observatories in Europe. The results of the transits are
regularly computed by Major Hodgson, agreeably to a printed form,
where every step of the process is minutely laid down, and of which
he has forwarded to the Society two examples. It is Major Hodgson's
intention to continue his observations for one whole year at least,
and to transmit them to the Society, together with the daily compu-
tations showing the results. The instrument employed was a 3 1-inch
transit by Dollond ; but he is in expectation of a more powerful one
shortly from England. The second list contained a series of upwards
of 200 observations of the eclipses of Jupiter's satellites taken by gen-
tlemen in the civil service, and by officers of the Bengal army, at dif-
ferent times and at different places. The dates extend from July 18,
1795 to April 1 1, 1827 : and the names of the observers are given,
together with the length, the aperture, and the magnifying power, of
the telescope employed. Major Hodgson states that he shall trans-
mit several others as soon as he can collect them : for (he observes)
" observations of this kind have been of much use in determining
geographical positions in this widely extended country ; and the pro-
bability of obtaining correspondent observations through the medium
of the Astronomical Society, will excite travellers and surveyors to
take advantage of all opportunities of making observations of the
eclipses of the satellites of Jupiter, and of the culmination of the moon
and stars."

A paper

Astronomical Society. 137

A paper was also read, entitled " On the computation of the geo-
centric places of the planets for ephemerides :" by J. F. Littrow.

The usual mode of computing the geocentric places of the planets
for ephemerides consists in instituting a first computation of their
heliocentric positions, which are then reduced to geocentric by well
known formulae. To avoid the very laborious calculations entailed
by this process, Prof. Gauss devised a method much more expeditious,
and which gives at once the geocentric right ascensions and declina-
tions, as well as the distance of the planet from the earth, in terms of
the co-ordinates of the earth and planets at the instant of observation.
The equations expressive of these relations are stated by M. Littrow,
and are extremely simple. By them, the right ascension (a), the de-
clination (o), and mutual distance (§ ) are given directly as follows :

tan a =

X + *

tan o = — cos a

X-f-*

(I)

t

z + *

sin 3

X, Y, Z being the co-ordinates of the earth, and x, y, z of the planet.

Now it is obvious, that if we neglect the perturbations (on which
neglect it will be observed the application of this method mainly de-
pends), all these co-ordinates are, ultimately, functions respectively of
the mean longitudes of the earth and planet, and their values may
therefore be tabulated as such ; and the tables, once constructed, will
last till the secular variations of the elements of the planetary orbits
shall have so changed them as to produce an error surpassing that
which can be tolerated in an ephemeris. — These tables once com-
puted, the foregoing equations reduce the annual computations to the
utmost brevity. The only point then to consider is the construction
of the tables themselves.

The expressions of the co-ordinates in terms of the mean longitude
are made to depend on the true longitude as the independent variable,
by means of six constant quantities for each planet. These are, 1st,
the respective inclinations of the plane of the planet's orbit to the
solstitial and equinoctial colures and the earth's equator ; and, 2ndly,
the plane angles made by the line of intersection of the planet's orbit,
and the ecliptic respectively with its line of intersection with the sol-
stitial and equinoctial colures and equator. The author states the
method of computing these constants from the known elements of
the orbit, and gives their actual numerical values for all the planets
with their secular variations. — These once known, and the true lon-
gitude, as a preliminary step, computed for every mean longitude, he
states the equations by which the co-ordinates are formed from them
for every given value of the longitudes ; and, finally, embodies the
whole result of his computations in a table stating their values for each
of the planets, and for intervals of 4° for Mercury and Venus, 3° for
Mars, 2° for Jupiter, Saturn, and Uranus, and for each day in the year
for the Sun.

New Series. Vol. 3. No. 14. Feb. 1828. T The

1 38 Royal Geological Society of Cornwall.

The publication of the 1st Part of the 3rd Volume of the Memoirs
of the Society, was announced by the President.

At the conclusion of the business of the evening, An instrument
contrived by Mr. Henry Atkinson, of Newcastle-upon-Tyne, to illus-
trate some of the phenomena of rotation, was submitted to the in-
spection of the members, by Mr. Riddle. —It consists of a flat circular
disk, through the centre of which passes a small endless screw, having
a cup in one of its extremities. When the cup is below the centre of
gravity, and set on a point on which the disk (inclined to the horizon)
is made to rotate in its own plane, the whole rotating plane per-
forms at the same time, a slow revolution round the perpendicular to
the horizon, which passes through the point of rotation ; and the re-
volution of the plane is in the same direction as the rotation. When
the point of rotation is above the centre of gravity, the plane moves
slowly round in a direction contrary to that of rotation, affording an
apt illustration of precession. When the point of rotation is in the
centre of gravity, the position of the revolving plane continues per-
manent.

ROYAL GEOLOGICAL SOCIETY OF CORNWALL.

At a special meeting of this Society, assembled for the express
purpose, the following Address of Congratulation was unanimously
adopted.

To Davies Gilbert, Esq. M.P. fyc. &>c.

Sir, — At the last annual meeting of this Society, over which you
have presided from its first institution, and which is so deeply in-
debted, in its origin and advancement, to your zeal and ability, we
ventured to express a hope that your continued exertions, and sue
cessful labours in the wider fields of philosophy and science, might
be crowned with honour in a higher sphere, by your being elected
to the office of President of the Royal Society of London.

It is gratifying to us to see that our wishes are fulfilled ; and we
most sincerely congratulate you on being chosen to fill that chair,
which having been the seat of Newton, may be deemed the throne
of intellectual eminence.

That two of our countrymen, natives of this remote province, al-
most of the same spot, should have been raised in succession to the
dignity of this station, is to us a source of pleasure and of pride.

As members of this Society, we rejoice at an appointment which
forms for us, though at an humble distance, a connecting link with
the most renowned Society of our country, and brings us within
the influence of its notice and support j for although your enlarged
mind will lead you equally to protect and encourage every branch
of science and knowledge, since they all mutually assist each other,
blending their various colours into one ray of intellectual light ;
yet we shall indulge the feeling, that Geology has, as it were, a
filial claim upon your regard, and will experience that kind and
fostering care which may fairly be asked for a science, now only in
its infancy.

While

Royal Academy of Sciences of Paris. 139

While we request you to accept our congratulations, we deeply
Jament the occasion of our illustrious townsman's resignation.

Be pleased, Sir, to take an early opportunity of conveying to Sir
Humpnry Davy our condolence on his illness, and our sincere wishes
for his restoration to perfect health, and to the exercise of those
faculties which he has employed to the noblest purposes — the en-
largement of the boundaries of human knowledge, and the gaining
for his name the most enviable kind of immortality (such is his own
estimate) "that which is connected with the gratitude and blessing
of his fellow-creatures."

May the enjoyment of health enable you, Sir, to continue for
many years in the discharge of the high situation in which you
have been so honourably placed, with happiness to yourself, with
satisfaction to your associates, and with benefit to the world.

(By order of the Royal Geological Society of Cornwall,)

Joseph Carne, Treasurer,

Penzance, Dec. 22, 1827. Chairman of the Meeting.

ROYAL ACADEMY OF SCIENCES OF PARIS.

May 28. — The following are the titles of the works or manu-
scripts received by the Academy at this sitting : — Description of
a new steam-apparatus for boats ; by M. Tourasse. — New facts
relative to the therapeutic employment of the Pyrothonide, by
M. Rauque. — Notice respecting comets ; by M. Courbon, surgeon.
— New notice on the bursting of steam-boilers; by M. Tabareau.
— New theory of the phenomena of vision; by M. Plagge.

M. Delessert read a letter from M. Brunei on the subject of the
accident which happened at the Thames Tunnel. — M. Thenard, on
the part of the Commissioners, read a favourable account of the me-
moir by M. Isidore Boullay. — M. Bonastre had presented a me-
moir On the compounds of the oil of cloves and of pimento with
the alkalies, and several salifiable bases. The principal fact con-
tained in this memoir is, that these oils, which do not redden litmus,
combine nevertheless with salifiable bases ; but M. Chevreul, re-
porter of the Academy, stated, that this fact not being accompanied
with the necessary details and precision, is devoid of the interest
which it may hereafter possess. M. Bonastre was recommended to
continue his researches.

June 4 — The Minister of the Interior communicated the edict
of the King, by which the nomination of M. Cassini, jun., as a
free academician, is confirmed. — M. Girard presented a notice re-
specting hydraulic mortars, made with fossil argillaceous sands. —
M. Dulong, in the name of the Commission, made a report relating
to the compression of liquids. — M. Cordier read the first part of a
memoir On the temperature of the interior of the earth. — M. Bon-
nard read a memoir On the regularity of the geognostic facts which
exist in the territory of Arkose in the East of France.

June 11 — At this, which was a public sitting, M. Cuvier read
An historical eulogium respecting M. Halle. — M. Dupin read Sta-
tistical researches respecting the canals of the north and south of

T 3 France.

140 Royal Academy of Sciences of Paris.

France. — M. Cuvier read An historical eulogium respecting M. Cor-
visart; and M. Cordier, a memoir On the temperature of the earth.

June 18. — The following are the titles of the memoirs or manu-
script works presented to the Academy: — Notice respecting two
mussels and a toad, which were taken alive from a well which had
been filled up for one hundred and fifty years ; by Dr. Quenin, mayor
of Orgon. — A sealed packet, containing An account of a new process
for breaking calculi ; by M. Cazenave. — A sealed packet, containing
New chemical researches ; by MM.Quesneville and Julia fontenelle.
— Description of a method by which boats may go up rivers alone
and without expense or danger ; by M. Anatasi. — Design for a new
pump for fire-engines ; by M. Stolz. — New considerations respecting
the boilers of steam-engines ; by M. Tabareau. — On certain organs
of the Hymenoptera, Diptera, ike. ; by Mi Robineau-Desvoydi. —
Researches respecting the vibration of several sonorous bodies, and
particularly elastic cords; by M. Cagniard de la Tour. — Notice
respecting the extinct volcanoes of the South of France, the erup-
tions of which occurred since the deposition of the second fresh-
water formation; by M. Marcel de Serres. — On the elementary
principles relating to the division of territories. — The Minister of
the Interior announced his having sent the Academy a collection
of the fossil bones found in the grottoes of Osselles. — M. Geofrroy-
Saint-Hilaire sent from Montelimart several particulars which he
had collected respecting the scientific establishments of the South
of France.— M. Blainville, in the name of the Commission, read An
account of an extremely curious memoir, by MM. Raspail and
Robineau-Desvoydi, but which appears to require new researches.
— M. Brochant gave a favourable account of the new memoir by
M. Bonnard On the territory of Arkose. — M. Constant Prevost
read a memoir, entitled An examination of the geological question,
" Whether the continents which we inhabit have been repeatedly
covered by the ocean ?"

June 25. — MM. Raspail and Robineau-Desvoydi announce that
they possess myriads of Alcyonellce, and sent a packet of them. —
M. Lacroix gave a favourable account of M.Denaix'swork, entitled
A methodical comparative geographical essay. — M. Cuvier read a
memoir On the Scarus of the ancients. — M. Berthier read A notice
of four memoirs which he presented to the Academy on some new
mineral species. — M. Roger communicated some results which he
had obtained respecting the height of Mont-Blanc. — M. Raspail
read a memoir, entitled A physiological analysis of the Spongilla
friabilis of Linnaeus.

The Academy decided that the place vacant by the death of
M. Ramond should be supplied.

July 2. — M. Pons, of Florence, informed the Academy that he
had discovered on the 20th of June, a small comet, invisible to the
naked eye, in the constellation of Cassiopccia; and according to a
letter from Marseilles, M. Gambart also observed it at 2 o'clock in
the morning of the 21 st of June. — M. Beudant reported, in the
name of the Commissioners, very favourably with respect to four

memoirs

Royal Academy of Sciences of Paris. 141

memoirs which M. Berthier had presented to the Academy at one
of its late sittings. — M. Prevost read an extract from a new me-
moir on geology.

July 9. — The Minister of the Marine forwarded Observations on
various subjects, which had been sent to him from New Holland, by
M. Durville. — M. Rembielinski presented a memoir, entitled De-
scription des conrbes prod act ionelles. — M. Velpeau read a memoir,
entitled R6cherch.es stir Vceuf humain. — M. Serullas read a memoir
already noticed in the Annates. — M. Cordier, in the name of a Com-
mission, gave a favourable account of the memoir lately read by
M. Prevost. — The Commission for the presentation of candidates
for the place of Foreign Associate, vacant by the death of Volta, was
composed of MM. Arago, Fourier, Legendre, Cuvier, Thenard,and
Desfontaines. — A secret Committee of the Section of Mineralogy
presented the following list of candidates for the place vacant by
the death of M. Ramond : MM. Bonnard, Berthier, and Constant
Prevost.

July 1 6. — The lamented death of M. Fresnel was announced to the
Academy. — M. Keller, engineer in the Marine, requested permission
to deposit a sealed packet. — M. Boucharlat also sent a sealed
packet, containing the results of his experiments upon ammonia,
and an analysis of a memoir On the possibility of considering am-
monia as an hydracid as well as an alkali. — M. Cuvier reported re-
specting the fossil bones found in the cavern of Oisselles near Be-
sancon. — M. Berthier was elected a member of the Academy —
M. Andreossy presented an historical notice of the giraffe. — M.
Turpin read a memoir On the structure and reproduction of the
truffle compared with those of the toadstool.

July 23. — M. Arago communicated several new experiments on
bromine, by M. Aug. de la Rive.— M. Cordier finished the reading
of his paper On the temperature of the earth. — M. Turpin con-
cluded his memoir On the reproduction of the truffle. — M. Du-
trochet communicated some observations on Endosmosis and Exos-
tosis.

July 30. — M. Roger sent the Elements of the calculation by which
he determined the height of Mont-Blanc — M. Thenard, in the
name of a Commission, reported that the manuscripts of M. Rei-
neck, who died at Ancennis, contained nothing worthy of being
printed: the examination was made at the request of the Minister
of the Interior. — M. Collard de Martigny communicated an an-
nouncement of the principal consequences deduced from his re-
searches into the alterations produced in the quantity and composi-
tion of the blood and lymph, by complete abstinence from liquid
and solid food. — M. Binet read a memoir On the determination of
the orbits of planets and comets. — MM. Robiquet and Colin read
a second memoir on madder. — M. Savart presented a new memoir
On the vibrations of solid bodies. — At a secret sitting, the
President, in the name of the Commission of the 9th of July, pre-
sented the following candidates for the vacant place of Foreign As-
sociate. In the first rank, Dr. Thomas Young, of London ; and af-
terwards,

142 Royal Academy of Sciences of Paris.

terwards, in alphabetical order, MM. Bessel, of Kcenigsberg ; Blu-
menbach, of Gottingen ; Robert Brown, of London ; Leopold de
Buch, of Berlin; Dalton, of Manchester; Gibers, of Bremen;
GErsted, of Copenhagen ; Plana, of Turin ; and Soemmering, of
Frankfort.

Aug. 6.— The following memoirs were received at this sitting :—
On the use of chloride of lime in disinfecting the air in which silk-
worms are kept, by M. Bonafous j On the propagation of heat in
a triangular prism, by M. Ostrogratzki ; On an artificial nose from
the skin of the forehead, by M. Delpech; On the motion of fluids
in the atmosphere, by M. Le Chevallier.— Dr. Young was elected
Foreign Associate of the Academy. — M. Geoffroy-Saint-Hilaire
presented the head of a young giraffe, in which it was seen that
the bony nucleus of the horn in the young animal is separated from
the forehead by a distinct suture. There were read a memoir On
some electrical phenomena produced by the pressure and cleavage
of crystals, by M. Becquerel ; On the compression of gases, by
M. Despretz; On a new theory of sonorous vibrations, by M.
Cagniard-Latour ; On the operation for the artificial pupil, by M.
Faure. — M. Molard gave a favourable account of tachygraphy, and
of the tachy type, invented by M. Conti.

Aug. 13. — Titles of memoirs received ; — Memoir in continuation
of the history of quina, cinchonia and kinic acid, by M. Henry ;
Remarks on the weight and dimensions proper for the sails of ma-
chines in order to produce the desired effects, by M. Landormy ; A
third notice on the motion of fluids, by M. Le Chevallier ; Memoir
on two cases of luxation of the cervical vertebrae with compression of
the spinal marrow, by M. Barny. — M. Chevreul read a notice On
the discovery of phocenic acid in the alkanet. — M. Lisfranc read
a memoir On rhynoplastie, and presented an individual who had
successfully undergone the operation. — M. Geoffroy-Saint-Hilaire
communicated Some observations on a polydactyl horse, with toes
separated by membranes. — M. Savart read a memoir On vibrations.
The Academy received at this sitting two verbal reports : one by
M. Freycinet, On M. Balbi's ethnographical atlas ; the other by
M. Silvestre, on M. Francceur's work On the teaching of linear
drawing.

Aug. 20. — The ordonnance of the King confirming the nomination
of M. Berthier was received. — A letter from M. Pons announced
the discovery of a new comet. — M. Fossombroni communicated a
report respecting the Caesarean operation lately performed in a
hospital at Florence. — Titles of memoirs received: Researches and
observations upon false consecutive aneurism, by M. Breschet;
Discoveries on the treatment of scrofulous affections, and a process
for healing fistula in ano (a sealed packet), by M. Deygallieres ;
New observations on yellow fever, by M. Leymerie. — M. Cassini, in
the name of a Commission, gave a favourable account of M. Turpin's
researches on the reproduction of truffles. — M. Pouillet read a
memoir On electro-magnetism. — M. Chabrier read An extract of
some new observations on the progressive motion of animals.

Aug.

Royal Academy of Sciences of Paris, 143

Aug. 27. — The Academy received a memoir from M. Madelaine
On steam engines. — M. Chevreul gave a very unfavourable account
of a new process, proposed by M. Ratieuville, for dyeing wool of a
blue colour. — The following papers were also read : Researches on
the determination of the series which represent the functions given
in one part only of their extent, by M. Brisson ; A memoir on
the dyeing of woollen with prussian blue, by M. Raymond ; A me-
moir on the formation of sulphuric aether, by MM. Dumas and
Boullay ; Researches on the human ovum, by M. Velpeau. —
M. Frederic Cuvier gave a favourable verbal account of the Baron
Gerando's work On the education of the deaf and dumb.

Sept. 3. — The Minister of the Interior transmitted the ordonnance
of the King, by which the nomination of Dr. Young was confirmed.
— -M. Deygalieres sent two Observations on scrofulous diseases,
cured according to the principles of his new method. — M. Tournal,
junior, of Narbonne, announced the discovery of caverns containing
fossil bones, near that city. — M. Lalanne presented an instrument
which he names secateur per spectif. — Mr. Perkins read a memoir On
new high-pressure machines. — M. Dumeril gave an account of the
researches of M. Velpeau on the human ovum. — M. Chevreul,. in
the name of the Commission, made a favourable report respecting
the memoirs of M. Serullas. — M. Blainville began the reading of a
report on the work of M. Jacobson On the reproduction of bivalves.
— M.Parseval presented a memoir On the integration of linear equa-
tions.— M. Cauchy read a memoir On the determination of the series
of Lagrange, and the conditions of convergence.

Sept. 10. — M. Rambur, a physician of the department of Inare
and Loire, sent a description of a monstrous child which had two
bodies and only one head. — M. Blainville made a verbal communi-
cation respecting the organization of a species of Terebratula.—
M. Navier read the report respecting M. Clement's memoir On the
escape of elastic fluids and safety valves, &c. — MM. Julia Fonte-
nelle and Poisson read a notice respecting a new kind of paper
made from liquorice. — M. Boisduval read a memoir On the mono-
graph of the tribe Zyneides.

Sept. 17- — M. Raspail announced that he had discovered in the
subterraneous logs of typha, a fecula possessing very peculiar cha-
racters, which he details — M. Milne Edwards deposited a sealed
packet. — M. Haldat sent two memoirs, one On diffraction, and the
other On magnetism in motion. — The following memoirs were read:
On the general system of the internal navigation of France, by
M. Brisson ; A second memoir, by M. Cauchy, On the application of
the calculus of residuums to physico-mathematical questions;
Researches into the vertebral organization of the lower order of
animals, by M. Robineau Desvoidy. — On the magnetic action
exerted in all bodies by the influence of a very powerful magnet,
by M. Becquerel.

Sept. 24. — M. Gendrin, a physician, sent some researches into
the heat of hot springs. — M. Mozembas, of Bordeaux, sent a me-
moir On the means of constructing lightning conductors with ceco-

nomy.

14-4? Intelligence and Miscellaneous Articles.

nomy. — M. Tournal sent a second letter On the caverns containing
fossil bones, which he had discovered. — M. Ilaspail read a memoir
On the Alcyoneilcc of marshes. — M. Gerard, in the name of a Com-
mission, gave a favourable account of the last memoir by M. Vicat.
— M. Dugez read a memoir On a monstrous conformation in the
heart of a new-born infant. — M. Chevreul gave a detailed account
of the recent labours of MM. llobiquet and Colin On the colouring
matters of madder. — M.Villermet read a memoir entitled, Statistique
des conceptions. — M. Velpeau communicated new researches On the
human ovum.

Jan. 7, 1 828. — Mr. Ivory was nominated a correspondent, in the
section of Geometry.

XXV. Intelligence and Miscellaneous Articles.

ON THE FLUIDITY OF SULPHUR AND PHOSPHORUS AT
COMMON TEMPERATURES : BY MR. FARADAY.

I PUBLISHED some time ago a short account of an instance of
the existence of fluid sulphur at common temperatures • and
though I thought the fact curious, I did not esteem it of such import-
ance as to put more than my initials to the account. I have just
learned through the Bulletin Universal for September, p. 178, that
Signor Bellani had observed the same fact in 1813, and published it
in the Giornale di Fisica, vol. vi. (Old Series.) I also learn, by the
same means, that M. Bellani complains of the manner in which facts
and theories, which have been published by him, are afterwards given
by others as new discoveries ; and though I find myself classed with
Gay-Lussac, Sir H. Davy, Daniell, Bostock, &c. in having thus erred,
1 shall not rest satisfied without making restitution, — for M. Bellani,
in this instance, certainly deserves it at my hand.

Not being able to obtain access to the original journal, I shall quote
M. Bellani's very curious experiments from the Bulletin, in which they
appear to be fully described. " The property which water possesses,
of retaining its fluid state, when in tranquillity, at 10° or \5° below
its freezing point, is well known : phosphorus behaves in the same
manner ; sometimes its fluidity may be retained at 13° (centigrade ?)
for a minute, an hour, or even many days. What is singular is, that,
though water cooled below its freezing point, congeals easily upon
slight internal movement, however communicated, phosphorus, on the
contrary, sometimes retains i;s liquid state even at 3°, even though
it be. shaken in a tube or poured upon cold water. But as soon as it
has acquired the lowest temperature which it can bear without solidi-
fying, the moment it is touched with a body at the same temperature,
it solidifies "so quickly, that the touching body cannot penetrate its
mass. If the smallest morsel of phosphorus is put in contact with a
liquefied portion, the latter infallibly solidifies, though it be only a
single degree below the limit of temperature necessary j — this does
not alwavs happen when the bodv touching is heterogeneous.

" Sulphur

Intelligence and Miscellaneous Articles, 145

" Sulphur presented the same phenomena as phosphorus ; frag-
ments of sulphur always produced the crystallization of cold fluid por-
tions. Having withdrawn the bulb of a thermometer which had been
plunged into sulphur at 120°, it came out covered with small gobules
of sulphur, which remained fluid at 60° j and having touched these
One after another with a thread of glass, they became solid : although
several seemed in contact, yet it required that each should be touched
separately. A drop of sulphur, which was made to move on the bulb
of a thermometer, by turning the instrument in a horizontal position,
did not congeal until nearly at 30° j and some drops were retained
fluid at 15° i. e. 75° of Reaumur below the ordinary point of lique-
faction."— Quarterly Journal, Jan. 1828, p. 469.

ELEMENTARY NATURE OF BROMINE.

Iodine colours a solution of starch blue, bromine renders a similar
solution orange colour. M. A. de la Rive added a few drops, of bro-
mine to a solution of starch coloured blue by iodine, and obtained a
compound which gave two distinct colours with starch — one brown,
the other yellow j the difference of colour corresponding with the two
bromides of iodine described by M. Balard. These compounds of
iodine and bromine, dissolved in a solution of starch, were subjected
to the voltaic pile : immediately the yellow solution became blue
about the negative pole and orange about the positive pole, indicating
the separation and places of the iodine and bromine. Thus the small-
est quantity of iodine may be discovered in bromine ; but when the
experiment was resorted to, to prove whether the idea thrown out,
that bromine was a compound of chlorine and iodine, was founded in
fact or not, it gave no such indication, and a solution of bromine in
starch electrified for a long time together, gave no appearance of iodine.
Hence M. de la Rive concludes, that bromine contains no iodine, but
is an element analogous to iodine and chlorine. When bromine and
iodine are combined, the former passes to the positive pole, and is
consequently more negative than the latter j which accords with the
observation of M. Balard, that it should occupy a place between chlo-
rine and iodine. According to the Bulletin Universel, when the
letter to M. Arago, containing an account of the facts above referred
to, was read to the Academy of Sciences, that body decided that the
assertion of M. Dumas, that bromine was a compound of chlorine and
iodine, should be considered as retracted, and that it should be so
entered upon the proces-verbal of the sitting. — Ibid,, p. 466.

QUANTITY OF BROMINE IN SEA WATER.

One hundred pounds of sea water, taken up at Trieste, treated by
chlorine, ether, &c. according to M. Balard's process, produced five
grains of bromide of sodium, or 3*278 grains of bromine. It would
appear, that in the sea water of Trieste, the bromine is unaccompanied
by any iodine j and the same is the case, according to M. Hermbstadt
with the waters of the Dead Sea. In the water of the Mediterranean,
on the contrary, iodine always appears with the bromine. — Ibid.y.466.

New Series. Vol. 3. No. 14. Feb. 1828. U sale

146 Intelligence and Miscellaneous Articles,

SALE OF BROMINE.

The discoverer of bromine, M. Balard, has been enabled, by his im-
provements, to prepare that peculiar body in quantities sufficient to
permit its sale. It may be obtained at his shop, Rue Argenterie at
Montpellier, or at M. Quesneville's manufactory of chemical sub-
stances, at Paris. The price is four francs the gros (about 60 grains),
fourteen francs the half ounce, and twenty-three francs the ounce. —
Ibid.

PREPARATION OF IODOUS ACID.

M. Pleischl says that, in preparing this acid, three parts of chlorate
of potash with one of iodine are to be used, and not equal parts, ac-
cording to M. Sementini j and also that it is indispensable to cool the
receiver considerably during the whole operation. — Ibid.

NEW BORATE OF SODA.

M. Payen lately presented to the Society of Pharmacy a new borate
of soda, which will advantageously be substituted for calcined borax.
It crystallizes in regular octahedrons, is harder than common borax,
and is almost as sonorous as cast iron : its fracture is vitreous, and
rather undulated. When immersed in water, the crystals become
opake, and retain their opacity in dry air.

This borate differs but little from common borax, except in contain-
ing less water of crystallization. It is more convenient for soldering
copper than common borax, because it does not swell so much. —
Journal de Pharmacie, Dec. 1827. p. 624.

ANALYSIS OF A SALIVARY CONCRETION.

This concretion was analysed by M. Lecanu : it weighed 0'45
gramme, its form was oval and slightly rough in the surface : when
broken it presented two distinct layers j the central one was hard,
compact, and of a gray colour -, the outer one was friable and per-
fectly white. It yielded by analysis :

Phosphate of lime 75

Carbonate of lime '20

Animal matter and loss 5

100
This salivary concretion differs, then, in its composition from those
previously analysed by MM. Wollaston, Laugier, and Henry jun. j —
from the first, by the presence of carbonate of lime j from the second,
by the absence of carbonate of magnesia ; and from the third, by the
absence of carbonate and phosphate of magnesia and common salt.
It contains the same principles as the salivary concretions of the horse,
elephant, and cow, analysed by M. Lassaigne. — Ibid. p. 626.

HAIDINGERITE, A NEW MINERAL SPECIES.

This substance, so called in honour of M. Haidinger, is an ore of
antimony which is found near Chazelles in Auvergne. The ore was

rejected,

Intelligence and Miscellaneous Articles, 147

rejected, because it yields metal of so bad quality that manufacturers
could not use it. A portion of the ore was sent to M. Berthier, who
gives the following account of it. Haidingerite has not yet been met
with in regular forms, but some cavities exhibit rudiments of prismatic
crystals, having the appearance of those of common sulphuret of anti-
mony : this new mineral occurs generally in confused laminated
masses, mixed with quartz, white ferruginous carbonate of lime, and
cubic pyrites. Its colour is iron gray, and its surface is frequently
covered with iridescent tints. It has generally less splendour than
sulphuret of antimony, without any shade of blue. It does not obey
the magnet. It has not been procured in pieces sufficiently pure to
admit of its specific gravity being ascertained. It readily melts be-
fore the blowpipe, and is quickly acted upon by cold muriatic acid,
and gives out pure sulphuretted hydrogen gas, and is totally dissolved,
except some pyrites and quartz • no sulphur is deposited.

By analvsis • — taken the mean of several experiments, it yielded

Sulphur 28-3

Antimony 48*3

Iron 14*9

Zinc 00-3

Sulphuret of Iron 03*2

Quartz 032

98*2
or independently of the gangue, it consists of

Sulphur .... 30*3 or Sulphuret of Antimony 71*5

Antimony . . 52'0 Protosulphuret of Iron .... 25*5

Iron 16-0 Sulphuret of Zinc 005

Zinc 00*3

975

98-6
Ann. de Chim. e.t de Phys. torn. xxxv. p. 351.
The above affords an excellent illustration of the complex views of
foreign chemists with respect to atomic composition. M. Berthier
considers it as composed of
18 atoms of Sulphur, or 4 atoms of Sulphuret of Antimony.

4 atoms of Antimony, 3 atoms of Protosulphuret of Iron.

3 atoms of Iron.

Adopting the simpler views generally entertained in this country,
the mineral in question is constituted of
3 atoms of Sulphur or 2 atoms of Sulphuret of Antimony 120
2 atoms of Antimony I atom of Protosulphuret of Iron 44

1 atom of Iron

164
— Edit.

BROMIDE OF SELENIUM*. — BY M. SERULLAS.

Selenium combines with bromine in several proportions ; but five
parts of the former and one part of the latter appear to form the most
intimate compound. To obtain bromide of selenium, the latter in

U 2 powder

148 Intelligence and Miscellaneous Articles.

powder is to be put into a moderately large tube, and the bromine is
to be poured upon it. Combination takes place rapidly with a noise
similar to that produced by immersing red-hot iron in water j much
heat is given out, and the mixture becomes instantaneously solid :
the compound has a red brown colour, similar to that of iodide of
phosphorus ; and some parts are yellowish like chloride of iodine ; it
gives out vapour when exposed to the air, which has an odour similar
to that of chloride of sulphur. It is entirely soluble in water, except
some particles of selenium, which precipitate. The filtered solution
is colourless when there is no uncombined bromine -, it is strongly
acid, and consists of selenic and hydrobromic acids. The solution when
saturated by potash, gives, by evaporation, a crystallized mixture of
seleniate and hydrobromate : on the addition of muriatic acid, either
before or after saturation with potash, the selenium is precipitated in
particles of a fine red colour.

When a bar of iron or zinc is kept immersed in the solution of
bromide of selenium, rapid action occurs, and especially with the
zinc j hydrogen gas is abundantly evolved, and the metallic bar is
covered with selenium, which adheres in the same manner as one
metal precipitated by another j by agitation the selenium is detached,
and bubbles of hydrogen gas, which had also been retained, are given
out. The selenium being separated by filtration, the hydro-bromate
of zinc may be decomposed by carbonate of potash, by which car-
bonate of zinc is precipitated and hydro-bromate of potash remains in
solution. This action of zinc or iron, in the solution of bromide of
selenium, is similar to that which occurs when either of these metals
is put into a mixture of selenic and muriatic acids ; the selenium is
deoxidized, and hydrogen evolved by the decomposition of water.
Is the whole of the hydrogen evolved, or is part of it employed in re-
ducing the selenic acid ? Or is there, as with the metals, a voltaic cir-
cuit formed ? A slight smell of decayed cabbage is perceptible, which
is one of the characteristics of oxide of selenium. When bromide of
selenium is strongly heated, a portion of it sublimes, and assumes a
yellow appearance, the remainder is decomposed into bromine and
selenium. — Ibid. p. 349.

ELECTRICITY OF GASES AND THE ATMOSPHERE.

M. Pouillet concludes from numerous experiments : 1st, That
gases give out electricity, when they combine together, or when they
unite with solid or fluid bodies ; and in these combinations, oxygen
always gives out positive electricity, and the combustible body, what-
ever it may be, gives out negative electricity ; and reciprocally, when
a compound is decomposed, each of the elements then requiring the
electricity which it had given out, is in the opposite state of electricity.
This reciprocity shows in what consists the difference of the nascent
state of a body from its ultimate condition.

2ndly. The action of vegetables upon the oxygen of the air is one
of the most permanent and powerful causes of atmospheric electricity ;
and when it is considered on one hand that a gramme (about 15*5
grains) of charcoal, in becoming carbonic acid, gives out sufficient

electricity

. Intelligence and Miscellaneous, Articles. 1 4,9

electricity to charge a Leyden jar; and on the other hand, that the
charcoal which is contained in vegetables does not give out less elec-
tricity than charcoal which burns freely, one may conclude, says
M. Pouillet, as my direct experiments tend to prove, that over a suri
face of vegetation 100 metres square, more electricity is produced in
a day, than is necessary to charge the strongest electrical battery. —
Ibid. p. 420.

ROSE-COLOURED PETROS1LEX FROM SAHLBERGH IN SWEDEN.

M. Berthier has analysed this substance. Its characters are, that it
is compact, homogeneous ; its fracture is very fine-grained, waxy ; its
colour is deep flesh red ; it is very translucent, and capable of receiv-
ing a fine polish. By the blowpipe it melts into a white enamel;
but it is much less fusible than felspar. When it is calcined in a
strong white heat, it does not soften, nor does it alter in colour or
appearance. When strongly heated in a charcoal crucible in a por-
celain furnace, its angles are rounded, it becomes milk-white, and re-
sembles chalcedony. It loses only about l-200dth of its weight in
this high temperature — a loss which is to be attributed to hygrometric
moisture. It yielded by analysis

Silica*. 79*5

Alumina 12*2 >

Soda 06-0

Magnesia 01*1

Oxide of iron 00*5

993

Ibid. t. xxxvi. p. 22.

NONTRONITE, A NEW MINERAL.

This mineral occurs in the arrondissement of Nontron, in the
northern part of the department de la Dordogne, which contains a
mine of manganese of considerable importance, near the village of
Saint Pardoux, in heaps of which this mineral was found. This sub-
stance is disseminated throughout the ore in kidney-shaped masses,
which are usually very^mall, and are rarely as large as the fist. This
mineral is compact, of a straw or canary yellow colour, with a shade
of green; its fracture is uneven : it is opake, unctuous to the touch,
and very tender ; its consistence is that of clay, and it is easily
scratched with the nail ; it takes a fine polish, and assumes a resinous
lustre by being rubbed with very soft bodies. It flattens and becomes
lumpy under the pestle, and is not reduced to powder ; it has not the
argillaceous smell, nor any action upon the magnet. When immersed
in Water it immediately disengages numerous bubbles of air ; it be-
comes translucent on the edges without softening or losing its form,
as clays do ; and if after some hours it is taken from the water and
weighed, after being well wiped, it is found to have gained about
1-1 0th of its weight of water. When heated in a glass tube it loses
water at a low temperature, and becomes of a dirty red colour. When
strongly calcined in a crucible, it assumes a similar appearance, and

its

1 50 Intelligence and Miscellaneous Articles,

its weight is diminished 19 to 21 percent. After calcination it is
sensibly magnetic.

Muriatic acid acts very readily upon it j the solution does not con-
tain the smallest trace either of manganese, protoxide of iron, or of
alkali : it contains peroxide of iron, alumina, and magnesia j the in-
soluble portion is gelatinous, and is composed of silica, soluble in the
alkaline solutions, and sometimes mixed with a small quantity of
clay, when the mineral has not been picked with sufficient care.
By analysis this substance yielded

Silica 44-

Peroxide of Iron 29*

Alumina 3*6

Magnesia 2*1

Water 187

Clay 1-2

986 Ibid, p. 22.

ANALYSIS OF SOME VEGETABLE PRODUCTS.

M. F. Marcet has analysed some vegetable bodies : the method
employed was that proposed by M. Gay-Lussac of using peroxide of
copper. Common starch yielded

Carbon 437

Oxygen 497

Hydrogen 6 6

100-
Roasted starch gave

Carbon 357

Oxygen 58*1

Hydrogen 6'2

100-
It appears therefore that roasted starch contains much more oxygen
and less carbon than common starch. Hordein is the name given by
Proust to a substance separated from barley flour. It yielded

Carbon 44'2

Oxygen 47*6

Hydrogen 6*4

Azote 1 *8

100-
M. Marcet remarks that some chemists have considered this sub-
stance as a modification of starch, and others as analogous to saw-
dust. Dr. Thomson appears to regard it as of the same nature as the
parenchyma of the potato : this latter substance gave M. Marcet

Carbon 37'4

Oxygen 58'6

Hydrogen 4*

100- It

Intelligence and Miscellaneous Articles, I5t

It appears therefore that hordein differs very materially from this sub-
stance as well as from saw-dust, of which the analysis is thus given
by MM. Gay-Lussac and Thenard :

Carbon 52*

Oxygen 42*4

Hydrogen 5*6

100-
M. Marcet therefore considers hordein a peculiar substance, but
most resembling starch. The azote which it contains may, he thinks,
be derived from the presence of gluten.

The following are the results of M. Marcet's analysis of gluten
and yeast :

Gluten. Yeast.

Carbon 557 30*5

Oxygen 22-0 57*4

Hydrogen .... 7 '8 4-5

Azote 14-5 7*6,

100- 100- Ibid. p. 27.

NEW CHLORIDE OF MANGANESE.

M.Dumas obtained this compound by putting a solution of man-
ganesic acid into contact with sulphuric acid and fused common salt.
Water and the new chloride are formed ; the former is retained by
the acid, the latter volatilizes in a gaseous form, with a greenish tint,
and when passed into a tube cooled to 5° or 4° of Fahrenheit, it con-
denses into a liquid of a brownish-green colour. The most simple
process appears to be to form a common green chameleon, to convert
it into red chameleon by sulphuric acid, and to evaporate the solution,
which will give a residue consisting of sulphate and manganesate of
potash. This mixture acted upon by concentrated sulphuric acid
produces the solution of manganesic acid, into which the common salt
is to be thrown in small pieces until the vapours which rise are co-
lourless j the latter effect is a sign that all the manganesic acid is
decomposed, and that muriatic acid only is produced. This chloride
of manganese corresponds in proportions to the manganesic acid $ it
is readily formed and examined, but not easily preserved. An ana-
logous compound is obtained when a fluoride is used instead of the
chloride, but a sufficient quantity for examination has not yet been
procurable. — Ibid, xxxvi. 81.

ON THE POWER OF WATER AND BROMINE IN CONDUCTING
ELECTRICITY.

M. de la Rive found, as had been previously ascertained by M.
Balard, that pure dry bromine did not conduct the electricity of a
voltaic battery, consisting of sixty pairs of plates very strongly charged,
a delicate galvanometer being the test. A similar experiment was then
made with pure water contained in a glass capsule, and communi-
cated

152 Intelligence and Miscellaneous Articles.

cated with the battery and galvanometer by platina wires j and the
deviation of the needle was scarcely sensible. A few drops of bro-
mine were then added to the water, which soon imparted a yellow
colour to the water } being now included in the voltaic circuit, the
galvanometer needle was deviated 70°, and an abundant disengage-
ment of gas took place from the platina wires. There were oxygen
and hydrogen in the usual proportions, showing that water only had
been decomposed. From these experiments it results, that a body
which conducts voltaic electricity very imperfectly, namely, pure water,
may be rendered a good conductor by holding in solution a very mi-
nute quantity of a perfectly non-conducting substance, namely, bro-
mine : the same fact occurs with iodine, and iodine and water. -

Ibid. xxxv. p. 161.

EFFECTS OF HEAT UPON SULPHUR.

According to M. Dumas fused sulphur begins to crystallize between
226° and 228° 3 between 230° and 284° it is as liquid as a clear var-
nish, and of an amber colour j at about 320a it begins to thicken, and
acquire a red colour j on increasing the heat, it becomes so thick,
that it will not pour. This effect is most marked between 428° and
572° j the colour is then a red brown : from 572° to the boiling point
it becomes thinner, but never so fluid as at 24-8° 5 the deep red brown
colour continues till it boils. When the most fluid sulphur is sud-
denly cooled, it becomes brittle 3 but the thickened sulphur similarly
treated, remains soft, and more soft as the temperature has been
higher. Thus at 230° the sulphur was very liquid and yellow 3 and
cooled suddenly by immersion in water, it became yellow and very
friable 3 at 374° it was thick, and of an orange colour 3 but by cooling
became at first soft and transparent, but soon friable and of the or-
dinary appearance : at 428° it was red and viscid 3 and when cooled,
soft, transparent, and of an amber colour 3 at the boiling it was deep
brown red colour 3 and when cooled very soft, transparent, and of a red
brown colour. It is not necessary, as is sometimes stated, to heat
the sulphur a long time to produce this effect 3 all depends upon tem-
perature. The only precaution necessary is, to have abundance of
water, and divide the sulphur into small drops or portions, that the
cooling may be rapid. If it be poured in a mass, the interior cools
slowly, and acquires the ordinary hard state. When the experiment
is well made at 446°, the sulphur may be drawn into threads as fine
as a hair, and many feet in length.

Ibid, xxxvi. p. 83.

PEROXIDE OF BARIUM.

M. Quesneville recommends the following process for preparing
this compound. — Put nitrate of barytes into a coated earthenware re-
tort, to which a tube is to be attached, for the purpose of conveying
the liberated gases to a water-trough. The heat is to be continued
until pure oxygen gas comes over, and the operation is then to be
stopped. The peroxide of barium thus obtained falls to pieces in wa-
ter without producing heat 3 when boiled in water, oxygen gas is evol-
ved,

Litelligence and Miscellaneous Articles. 153

ved, and by a strong heat it is reduced to protoxide. Sulphuric acid
evolves no nitric acid, nor does nitric acid produce nitric oxide when
mixed with it. The protoxide of barium evidently becomes peroxide
by combining with the nascent oxygen of the decomposed nitric acid.

.Ibid xxxvi. p. 108.

ON CERTAIN HABITUDES OF SEPIiE.

Portsmouth, Aug. 15, 1827.
Gentlemen, — A fisherman this morning brought me a large bunch
of the eggs of the Sepia, or common cuttle-fish, fastened to a sea weed.
The young were alive in the fluid contained in the membranaceous
coverings, and their motions could be readily seen by removing the
outer or dark membrane. As I wished to preserve them for a specimen
to be added to a long series of bottles containing the natural history,
anatomy, &c. of this fish, which I have presented to the museum of
the Portsmouth Institution (the eggs being larger than any 1 had be-
fore obtained), I laid the specimen on a mahogany table while I
prepared some spirit. On returning in a few minutes, I found the
young Sepiae had (with one exception) burst the membranes near the
stem-like process, and were swimming about in the fluid which escaped
during the time of my removing them by means of a broad spatula
into a glass of salt water. I was surprised by the amazing strength
with which these minute fish (not bigger than a large pea) ejected a
current of water, followed by the dark-coloured fluid peculiar to
them, through an extent of at least half a yard, and with such force
as to be quite unpleasant to the face. I have deemed it worth while
to notice these facts, as it is uncommon to obtain the eggs at the state
of perfection, even here on the sea coast. The little creatures lived
in my window for several hours, exhibiting all the voracious propen-
sities of the full-grown ones. I am, &c,

Henry Slight, Surgeon,
Librarian to the Portsmouth Institution.

NOTICE OF AN ERROR IN GALBRAITH'S MATHEMATICAL
TABLES AND FORMULAE.

In the practical problems, at page 1 67, for computing the deflection
of beams, fixed at one end and loaded at the other with any given
weigtu, an erroneous rule is copied from Mr. Barlow's Treatise on
the Strength of Timber. When errors of this nature are circulated
in books of such general practical utility, it becomes an important
although an ungracious duty, to point them out.

The rule should be —

Multiply the tabular value of E by the breadth, and cube of the
depth, both in inches.

Multiply also the cube of the length in inches, by the given weight,
and that product again by 16.

Divide the latter product by the former for the deflection sought.

N.B. The tabular value of E is four times the weight in pounds of
the modulus of elasticity. B. Bevan.

New Series. Vol. 2. No. 14. Feb. 1828. X errors

154 Intelligence and Miscellaneous Articles.

ERRORS IN HUTTON's LOG. TABLES (FIFTH EDITION).

*

For Log. Tang, of 0° 44' 13"— 8*1 193361 read 8-109 &c.

14 -8-1194998 read 8'109 &c.

15 -8-1196634 read 8-109 Arc.

16 -8-1198269 read 8*109 &c.

17 -8-1199904 read 8-109 &c.

J. Nixon.

CRYSTALLIZATION OF PHOSPHORUS.

By the fusion and careful refrigeration of a large quantity of phos-
phorus, M. Frantween has obtained very fine crystals of an octahedral
form, and as large as a cherry-stone.

CHEMICAL EXAMINATION ON ANCIENT INSTRUMENTS, &C.

M. Vauquelin has analysed a poignard blade, formed entirely of
copper; a mirror found to consist of 85 parts of copper, 14 tin, and
1 of iron per cent ; and a blue colour found in a tomb, gave by
analysis, silica 70, lime 9, oxide of copper 15, oxide of iron 1, soda
and potash 4. A blue colour similar to this both in tint and com-
position, was found in the bottom of a furnace in which copper had
been fused at Romilly. — Bull. Univ. A. vii. 264.

LONDON INSTITUTION.

Encouraged by the success of the Royal Institution, the managers
of the London Institution propose, during the present season, to try
an experiment which they trust will prove acceptable to the proprie-
tors.

The library and theatre of the London Institution will be prepared
during eight evenings for a soiree or converzatione, to which pro-
prietors and their friends will be admitted under certain regulations.
Coffee and tea will be supplied in the library, where it is intended to
introduce all new scientific inventions or discoveries, that can be ex-
hibited by models or drawings. New literary works, original draw-
ings, and scarce books, will constitute another source of interest and
information. This plan will be attended with the advantage of intro-
ducing learned foreigners and men of science to a complete view of
the establishment, and to a social conversation with its managers and
proprietors. At some period during the evening an adjournment will
take place to the Theatre, where it is intended to give a short dis-
course or lecture, either honorary or professional, on any new ma-
chinery, or on any chemical, philosophical, or literary novelty that
may be considered by the managers to deserve the attention of the
Institution.

The following is a notice of the series of lectures for the season, to
be delivered in the Theatre of this Institution: —

Course I. — On the motive forces of the arts : illustrated by models
of machines, steam-engines, &c. ; by Norton Webster, Esq. To
commence on Monday, the 4th of February, at seven o'clock in the
evening.

Course

New Patents: 155

Course II. — On the phenomena and history of igneous meteors
and meteorites : illustrated by a series of transparent paintings of
meteors, and an extensive collection of meteorites ; by E. W. Bray-
ley, jun. Esq. A.L.S. To commence on Saturday, the 9th of Febru-
ary, at one o'clock in the afternoon.

Course III. — On music, particularly as to vocal music (illustrated
by voices), by Samuel Wesley, Esq. To commence on Tuesday, the
4th of March, at one o'clock in the afternoon.

Course IV. — On poetry and the drama in general, and on Milton
and Shakspeare in particular, by John Thelwall, Esq. To commence
on Thursday, the 6th of March, at seven o'clock in the evening.

LIST OF NEW PATENTS.

To R. W. Winfield, of Birmingham, for his improvements in tubes
or rods produced by a new method of manufacturing and in the con-
struction only, and for manufacturing the same, with various other
improvements, into parts of bedsteads and other articles. — Dated the
4th of December 1827. — 6 months allowed to enrol specifications.

To J. Meadon, of Millbrook near Southampton, for improvements
on wheels for carriages. — 4th of December. — 6 months.

To S. Wilkinson, of Holbeck, Yorkshire, for improvements in
mangles. — 4th of December. — 6 months.

To Maurice de Jough, of Warrington, cotton-spinner, for improve-
ments in machines adapted for spinning, doubling, twisting, roving,
or preparing cotton, &c. — 4th of December. — 6 months.

To T. Tyndall, of Birmingham, for improvements in the manufac-
ture of buttons, and in the machinery for manufacturing the same :
communicated from abroad.— 4th of December. — 6 months.

To D. Ledsam and W. Jones, of Birmingham, for improvements in
machinery for cutting sprigs, brads, and nails. — 4th of December. —
6 months.

To J. Robinson, of Merchants -row, Limehouse, for an improve-
ment in the manufacture of brushes of certain descriptions, and in
the manufacture of a material and the application thereof to the manu-
facture of brushes and other purposes.— 4 th of December. — 6 months.

To Paul Steenstrup, of Basing-lane, London, esquire, for im-
provements in machinery for propelling vessels, and other purposes.
— 1 1th of December. — 6 months.

To J. H. Sadler, of Hoxton, Middlesex, for improvements in power-
looms. — 13th of December. — 6 months.

To R. Rewcastle, of Newcastle-upon-Tyne, for an improved method
of ballasting ships or vessels.— 13th of December. — 6 months.
To R. Stein, of Regent-street, Oxford-street, for an improvement

in applying heat to the purpose of distillation 13th of'December. —

6 months.

To F. B. Geithner, of Birmingham, for improvements on castors for
furniture, &c— 13th of December — 6 months.

To H. Peto, of Little Britain, for an apparatus for generating power.
— 13th of December. — 6 months.
t.»;l To

156 New Patents.

To J. A. Berrollas, of Nelson-street, City-road, for a method of
winding up a pocket watch, or clock, without a key, which he calls
" Berrollas's keyless watch or clock ;" and also a certain improvement
to be applied to his late invented detached alarum watch. — 13th of
December. — 2 months.

To Lieut. A. M. Skene, of Jermyn-street, for an improvement in
propelling vessels, and for working under-shot water-mills. — 13th of
December. — 6 months.

To J. L. Stevens, of Plymouth, for a new method of propelling
vessels by the aid of steam or other means, and for its application to
other purposes. — 18th of December — 6 months.

To T. Tyndall, of Birmingham, for improvements in the machinery
for making nails, brads, and screws : communicated from abroad.—
18th of December. — 6 months.

To J. George, of Chancery-lane, esquire, barrister-at-law, for his
invention for preserving decked ships or vessels, so as to render them
less liable to dry-rot, and for preserving goods on board such ships
and vessels from damage by heat. — 18th of December. — 6 months.

To T. S. Holland, of the city of London, esquire, for combinations
of machinery for generating and communicating power and motion,
applicable to propelling of fixed machinery, as also floating bodies,
carriages, and other locomotive machines. — 19th of December. —
6 months.

To W. Harland, M.D., of Scarborough, for improvements in appa-
ratus for propelling locomotive carriages, which improvements are also
applicable to other useful purposes. — 21st of December. — 6 months.

To C. A. Furguston, of Mill Wall, in the parish of All Saints, Pop-
lar, mast-maker, and J. Falconer Atlee, of Prospect-place, Deptford,
for their improvements in the construction of made masts. — 22nd of
December. — 6 months.

Tq W. Hale, of Colchester, for his improvements in machinery for
propelling vessels. — 27th of December. — 6 months.

To W. Gossage, of Leamington Priors, Warwickshire, for improve-
ments in the construction of cocks for the passage of fluids.-— 2nd of
January, 1828. — 6 months.

To T. Botfield, of Hopton Court, Salop, for improvements in making
iron, or in the method or methods of smelting and making of iron. —
2nd of January. — 4 months.

To J. Hall, jun., of Ordsall near Manchester, for improvements in
dyeing piece-goods by machinery. — 2nd of January.—- 2 months. ,

To J. CI. Daniell, of Stoke, Wilts, for improvements in dressing
cloths, and in the machinery applicable for that purpose. — 2nd of
January. — 6 months.

To W. Morley, of Nottingham, for improvements in and additions
to machinery now in use for making lace or net. — 9th of January. —
6 months.

To J. A. Hunt Grubbe, of Stanton Saint Bernard, Wilts, clerk, for
a transmitting heat wall for the ripening of fruit. — 9th of January. —
6 months.

To J. Gilbertson, of Hertford, for an improvement in the construc-
tion

Meteorological Observations for December 1827. 157

tion of furnaces, by which they consume their own smoke. — 15th of
January. — 2 months.

To C. Hooper, of Spring Gardens, in the parish of Marston Bigott,
Somersetshire, for an improved machine for shearing and cropping
woollen and other cloths. — 15th of January. — 2 months.

To J. Evans the younger, of Moreton Mills, near Wallingford,
Berks, for improvements on steam engines.— 15th of January.— 6 mom

To J. Blades, of Clapham, Surrey, for an improvement in the water-
proof stiffening for hats : communicated from abroad. — 15th of Janu-
ary.— 6 months.

To W. Newton, of Chuncery-lane, for an improved surgical chair-
bed with various appendages. — 15th of January. — 6 months.

To G. D. Harris, of Field-place, near Stroud, Gloucestershire, for
improvements in dressing and preparing woollen yarns, and in clean-
sing, dressing, and finishing woollen cloths, &c. and in the apparatus
for performing the same. — 15th of January. — 6 months.

To J. Falconer Atlee, of Prospect-place, Deptford, for improvements
on bands or hoops for securing made and other masts, bowsprits and
yards, and applicable toother purposes. — 15th of January. — G months.

To W. Erskine Cochrane, esquire, of Regent-street, for improve-
ments in certain apparatus for cooling, and other purposes. — 15th of
January. — 6 months.

To J. Taylor Beale, of Church-lane, Whitechapel, and G. Richard-
son Porter, of Old Broad-street, for their new mode of communicating
heat for various purposes. — 19th of January.— 6 months.

To W. Percivall, of Knightsbridge, for improvements in the con-
struction and application of shoes without nails to the feet of horses
and certain other animals. — 19th of January. — 6 months.

To G. Jackson, of Saint Andrew, Dublin, for improvements in ma-
chinery for propelling boats and other vessels, which improvements
are also applicable to water-wheels and other purposes. — 19th of
January. — 6 months.

METEOROLOGICAL OBSERVATIONS FOR DECEMBER 1827.
Gosport. — Numerical Results for the Month.
Barom. Max. 30-58 Dec. 28. Wind NE.— Min. 29-07. Dec. 1. Wind W.
Range of the mercury 1-51.

Mean barometrical pressure for the month 29-810

for the lunar period ending the 18th instant 29*763

for 15 days with the moon in North declination . . . 29*693

for 15 days with the moon in South declination .... 29*834

Spaces described by the rising and falling of the mercury . . . 8-900
Greatest variation in 24 hours 0-560.— Number of changes 26.
Therm. Max. 57° Dec. 5. Wind W.— Min. 31° Dec. 29. Wind N.
Range 26°.— Mean temp.of exter. air 47°*82. For 30 days with 0 in $ 47*50
Max. var. in 24 hours 17°*00— Mean temp, of spring water at 8 A.M. 53°-87

De Luc's Whalebone Hygrometer.

Greatest humidity of the air on nine different days 100°

Greatest dryness of the air in the afternoon of the 6th ; . . . 55

Range of the index 45

Mean

158 Meteorological Observations for December 1827.

Mean at 2 P.M. 78°-2— Mean at 8 A.M. 83°-0— Mean at 8 P.M. 85-5

of three observations each day at 8, 2, and 8 o'clock . . . 82*2

Evaporation for the month 0«60 inch.

Rain near ground 5*625 inch.— Rain 23 feet high 5-115 inch.

Prevailing Wind S.W.

Summary of the Weather,
A clear sky, 3 ; fine, with various modifications of clouds, 9 ; an over-
cast sky without rain, 7h i foggy 2 ; rain, 9$.— Total 31 days.

Clouds.
Cirrus. Cirrocumulus. Cirrostratus. Stratus. Cumulus. Cumulostr. Nimbus.
15 8 28 0 14 12 23

Scale of the prevailing Winds.
N. N.E. E. S.E. S. S.W. W. N.W. Days,
li i 1 1 4 10£ 8 4| 31

General Observations. — The weather to the 24th inclusive was remark-
ably mild for the season, but windy and wet, five inches and a quarter of
rain having fallen ; and on several days before the winter solstice it was
remarkably dark, from there being no opening in the prevailing strata of
clouds to admit the passage of the solar rays.

Early in the morning of the 12th there was a thick fog, which gave out
a very strong sulphurous smell : the 29th was also distinguished by a cold
dense fog throughout the day and night.

The last spring tides were high in Portsmouth harbour, and along the
southern coast, also at Liverpool, and along the western coast, in conse-
quence of so great a fall of rain, with accompanying south and south-west
gales. The highest spring tide was a few minutes before 12 p.m. on the 18th,
although it was the first after the change of the moon. The rain on the
18th, 19th, and 20th continued fifty hours without intermission.

On the 21st and 22nd, thunder storms, with lightning and hail, were ex-
perienced in several places in Hampshire.

On the 25th a parhelion appeared at mid-day on the western side of the
sun, when the cirrocumulus and attenuated cirrostratus clouds were beauti-
fully tinged with faint prismatic colours thirty degrees distant from the
sun's centre.

The maximum temperature of the external air occurred in the nights of
the 3rd, 7th, 9th, 13th, 15th, 17th, 21st and 23rd, instead of in the days.
These frequent occurrences rendered the circumstance remarkable and de-
serving an explanation. It seems to be influenced by the sun's position in
the zodiac at this time of the year ; the temperature of the ground at and
near the surface; and the inosculation of the sea air with that over the
land in the evening, just before the coming on of rain from the western
side of our meridian. 1st. The sun's meridional altitude in this latitude in
December varies from 16 to 17| degrees, and from so great an obliquity
of his rays, or so small an angle, that from this altitude they make with
the horizon, only three or four degrees of thermometrical heat are pro-
duced near the earth's surface, more than the temperature of the ground.
2ndly. The temperature of the atmosphere in a wet December like the
present, depends very much on the temperature of the ground, and the
quality of the prevailing vapours, which, if humid and accompanied with
mild currents of air, then the temperatures of the ground and air are
found to coincide nearly. 3rdly. If under these circumstances of tempera-
ture and condensing state of the lower medium of the atmosphere, the
sea air should unite with the land air on the approach of rain after sunset,
on any day in December or January on which the temperature of the air

has

Meteorological Observations for December 1827. 159

has been rather low, there is a great probability, from the sea air being
warmer than the land air, that the maximum temperature will happen in
the night instead of in the day.

Long solar lights and shades were very conspicuous half an hour before
sunset on the 30th, and moved round the sun, in a westerly direction, like
the spokes of a large wheel in slow motion. This singular appearance was
no doubt caused by a brisk wind blowing against the eastern side of a
hemispherical cumulus cloud (on whose dense surface the sun's horizontal
rays had previously impinged and were reflected) so as to give it a revolving
motion.

These reflected rays repeatedly varied in length, perhaps from the un-
even surface of the cloud. A short time before they disappeared, they
were nearly equidistant, their angular distance from each other in at least
a semicircle, was about twelve degrees ; and each of the horizontal rays
reflected to a distance of nearly sixty degrees. The sun being near the
horizon, the lower rays could scarcely be traced: but the phenomenon
certainly exhibited a grand and gratifying appearance.

The mean temperature of the external air this month, is h\ degrees
higher than the mean of December for the last twelve years, and is also for
that period unprecedented.

The atmospheric and meteoric phenomena that have come within our
observations this month, are one parhelion, one large lunar halo in the
night of the 26th, which set with the moon ; four meteors, one rainbow ;
lightning and thunder in the night of the 20th ; and fourteen gales of wind,
or days on which they have prevailed ; namely, one from the East, three
from the South, seven from South-west, and three from the West.

REMARKS.

London.— Dec. 1. Cloudy. 2. Drizzly. 3. Fine. 4. Cloudy: drizzly.
5. Cloudy. 6. Fine. 7. Stormy night. 8, 9. Fine. 10. Rain : drizzly.
1 1. Foggy morning : rainy night. 12. Cloudy : rain at night. 13. Cloudy :
foggy morning. 14. Rainy. 1 5. Cloudy : rainy night. 16. Fine morning :
heavy shower at 3 p.m. 1 7. Cloudy. 1 8. Rain : boisterous night. 1 9. Rainy.
20. Fine. 21, 22. Cloudy. 23. Fine. 24. Rain. 25 — 27. Fine. 28. Fine
day : foggy night. 29. Gloomy : dense fog all day. 30. Fine. 31. Fine :
rain at night.

Penzance.— Dec. 1, 2. Showers. 3. Fair. 4, 5. Misty. 6. Clear. 7. Clear,
fair : rain at night. 8. Clear. 9. Misty : rain. 10. Rain. 1 1, 12. Rain :
fair. 13. Clear. 14. Rain: fair. 15. Rain. 16. Clear : hail-showers.
1 7. Fair : rain. 18, l9.Rain. 20. Hail-showers. 2l,22.Rain. 23. Fine:
rain. 24. Rain : fair. 25. Clear. 26. Fair. 27. Clear. 28. Fair. 29 —
31. Clear. — Rain-gauge ground level.

Boston. — Dec. 1. Cloudy : rain early a.m. 2. Rain. 3. Cloudy. 4. Cloudy :
rain early a.m. 5. Fine. 6. Stormy. 7— 9. Fine. 10. Cloudy. 11. Fine:
rain p.m. 1 2. Misty : rain at night. 13. Cloudy: rain early a.m. 14. Rain:
rain early a.m. 15—17. Fine. 18. Cloudy: rain p.m. 19. Cloudy.
20— 21. Fine. 22. Fine : rain p.m. 23. Fine. 24. Cloudy. 25. Fine:
rain a.m. 26. Cloudy. 27— 29. Fine. 30. Cloudy. 31. Fine.

RESULTS.

Winds, NE. 1 : SE. 4: SW. 14 : W. 3 : NW. 9.

London. — Barometer: Mean height for the month S0'0S8inch.

Thermometer : Mean height for the month 44«274

Rain 3-60

Evaporation , 1*24 inch.

Meteoro-

-

•jsog

^--r :::::: :rt?r9 :::?:::?:??:::::
6 ........ •••...::

•dsoQ

o o O OOOOOOO ©lOOOOOO© O o
• • c?\ :o • o :<or-^c^c<cor^Tj< ; r^r^»o o« co t^ro>-< ; • • • co • <^

: :© :o :«n : 9 ogo s« ~ i^~ :9'?'^'r^99? : : : 19 : co
6 ,"

lO

•ZU3J

.O . . »o . . .0 . . . to © . tr> . © to 010

. C>» Tf • • • Tj« . . . CO © • © .O W • •• • iio X

•10 (0'*,ap,,,i>»p*^H*ip9 10 >p

6 -* 6 ^6 i 66 6li>-

•ptHrj

,tocr«roc5 .0 . . <o £Otoej 0 0 <n 00 con* ^oooo m

.-.009 :9 ; ;9op« 9 ^too 0 con jono^ —>

O

a*

>

•dsoj)

• • to : : © : : i£ : ; © j : »o : ? :to-:;to:.no:*»o« • »r>
::©::-«.. 9 .. -p .. 0 .::©::©::©::©:: ©

6

6

•paoq

:::::::::: 7* ::::::::::::: ^ ::::: <p

t3

c

•isog

.J| *• .• £ * £| £ g:|| & & £ i £ £ .. tf .• k- jg .- J | S || c

•dsog

* i *** * 1 s" &' - s ■» « s' * i i £ £ £ i 1 * i£*.ii 1 1 .1 i* I

•ZU3J

til *i" i'd ki t :t $ i ^iiiiiii i i t * * * * i i# \

•puoq

tit* *i i *" S * i i ? & i i £ * * * i * * £ £ * £ £ £ « «

1
1

I

■fcrfg

•jsog

»p »p ip ip 10 10 in to

^^TtlOlOTt"CO^C^lO^TtTf^^^OUOtOTtC*5^-rtLO'^''^,-^'Cv5CO<v5CO

o
a
<«
o
0

i

^^!2,0£i^^^^^C<C^^tOtOCT1t^C^*OCNCOCr)lOO'OTf(NiO--OVD

ro

y

c
m

c

1

2,!£210.19,l£2i2,!ii,^^CN 2 9 to-^r^c^c^cooi 'rf^c^ ^*co 00 00 <o to r-

O

3

tOtOtOiOi0^^iotOin»0^iO»OiOiOtOt0^ioK^tOU^tOtOiO§>?>SS

>o

a

o

QC
CN

i

1

^^©lOTj'Tjio^irjinin'^rtinifjTtioinin'^ri'tninTf'^ininTj'f'jTi'rt

s

Si

S

o

-

o J?

si

■toxooor^Tfioioocoocioiooioo^oiN^'icoornorfio

iO^C^C^^tpt^C»»p7<O>9Oc^fN7*VptOO9C^C^rJ'«p30OOC0'-^OtO

2 2£'2'2'2,?2'<^^c° c^6>cb 6\cV«c>ia\c>i6^<6>cb cVi6m6>6 6 6 6 6 <5>

c

o

E

O

O

£

9 — ivpap 91QP 900 <o cococpipcptpvp 0 t^tptpco^fap t^cpTtcpipTt^H v©

o\ cs <y\ &\ 0*1 <?\ c> 3\<y\&\d>cr\G\c\<y\<y<iC> &\c\cr\0^&\0\o^c> 6 6 6 6 6 cS>

0

CI

-

■"^•lO O (N00 TtoiOVO OVOCSTf-rflO rft^CN -i^OX O fO^tlOO»^O00 C^t^t>-
»n csao 9iO>— (N 91QOVO Ttcpio 10 0 cy> «t ' ex) 0 ipio ipo CTiro-^'TyioTfCNcX'
2^2,S^S*S,2,2.S'2^^S,<^,C^,<:^C^,<^10 cViOicVia^o^o cri6 6 6 6 6 6 6>

X

6

c

S3
N

c
Pi

OtOTfOOO-*OOO«WOT*OClOC«(STfC)OT)'OOC00t(0^
CS<0t>Cp990CC»OC<C^CNipcpip^9^^rf^ipc»I^CSC0C0OC^

o^o^osos 0 6 c^c^6\c^c^6^ctncticVic^6 c^c^cViONcVicyicyio 6 6 6 6 6 6>

c:

OO5I00OO»OOlOlOOiOO(OO(O'<t©(N(NceOlO'fOr)<O(0«O

<p«o^cp97'9coi^cp(Ncp^yr^9^9^7f>pvo«p9>i9<^«ptp^O'7*
c^icyichc^o 6 0 o^o^o^^oso^G^o^o^o 0*1 os &\ £t\ o\ O) 0 6 6 6 6 6 6 6\
c<csc<eso<ococsc^c^c*cic^c^c<c*coc*cic*e<csc<c^

O

6

1

. o

►J

3

-H-Hioom>oin-*acy5c*5»Mioaooin»noo--«»a)^XT)no
<Ncocyi9i--.-. 99cp^o^vp^cpcx)9cpi^t>.(ovp99»ppp^.»p— i>

ONcy>c^o>6 6 0 6 ososososcsosososo oso^os cV> 6> 6 6 6 6 6 6 6 6 c?s
wc«esc*cococococ*c*cscNc^e<c*c^cocsc^c*fNC*coco

CN

M

I
1

--<oin»0'i,Tfrico-HM^ot*oxc^c^ooi^iocj\o\(N(N(N-HH-1QOTji
99<^h ^- -^"Tr-- T'spvo r^r^-coco 00^90000 1^9 0 ip<ooc»ao t^to —
^6\^666666c^6^»^^cyi666cji6NcV6666666666
c^^cinncoconnc<wc<«^c<nnoo)(N(Nr'5nconncocoP3c<;n

5

6

CI

iDays of
Month,
1827.

rtOco^ko«h«xaiOHor5T)"ici«tNxciOrtc<n^io(o t^cc cyio -1

1

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY.

[NEW SERIES.]

MARCH 1828.

XXVI. On the Regular or Platonic Solids. By Davies
Gilbert, F.R.S. fyc.

To Mr. Richard Taylor.
Sir,
T^HE following trifle, extracted from my memorandum-book
A of many years standing, may perhaps (as a mere curiosity)
be favoured with a place in your Journal. It exhibits an easy
method of deriving these bodies from a modern discovery in
spherics ; and it illustrates the extreme generalization attached
to algebraic expressions.

Montucla and other writers on mathematics, attribute to
Albert Girard, about the year 1629, the discovery of this very
curious property of the sphere : — That if the whole surface of
the sphere, or what may be considered as its subtense from
the centre, be represented by eight right angles ; then will the
subtense from the centre of any figure, on the surface of the
sphere bounded by arches of great circles, equal the excess of
the spherical angles above the plane angles formed by the
chords of the sides. A discovery applied in recent times with
great advantage to all geodetical operations conducted on an
extensive scale.

Now as three planes at the least must meet at each solid
angle, or point of every solid ; it is obvious that no regular
equal and similar planes of any figures exceeding the pentagon
in number of sides, can possibly meet in one point or solid
angle. Thus the angle between two sides of an hexagon
being 1^ right angle, three of these would make up 4 right
angles, and consequently the sides would expand themselves

NewSei'ies. Vol. 3. No. 15. March 1828. Y into

1 62 Mr. Davies Gilbert on the Regular or Platonic Solids.

into one plane. The same would take place with four squares
and with six equilateral triangles.

The solid angles or points of all solids bounded by regular
equal and similar sides, must then consist either of three, four,
or five equilateral triangles. Of three squares or tetragons,
or of three pentagons. And consequently the number of these
finite bodies cannot exceed five.

That five such actually exist, is thus proved.

When three equilateral triangles meet in a point, the three
equal spherical angles must, to complete space, amount each
to one-third of four right angles, or to 120°. The three an-
gles therefore of each spherical triangle will equal four right
angles, or be two right angles above the two right angles of a
plane triangle. The solid angle therefore at the centre of
each spherical triangle will subtend one quarter part of the
surface of the sphere, and the solid must be a tetraedron.

If four equilateral triangles meet at a point, the angle of
each spherical triangle must, for the same reason, be in this
case a right one. Consequently, the three angles of each sphe-
rical triangle will equal three right angles, or be one right angle
in excess of the three angles of a plane triangle. The solid
angle therefore, at the centre of each spherical triangle, will
subtend one-eighth part of the surface of the sphere, and the
solid must be an octaedron.

If five equilateral triangles meet in a point, the angle of each
spherical triangle must be one-fifth of four right angles, or
72°; that is, four-fifths of one right angle : the three angles of
each spherical triangle will amount, therefore, to two right
angles and two-fifths of a right angle, exceeding the two right
angles of a plane triangle by two-fifths of a right angle, or 36°,
being the twentieth part of eight right angles ; the solid angle
therefore at the centre of each spherical triangle is one-twen-
tieth part of the spherical surface, and the solid must be the
icosaedron.

If three squares or tetragons meet in a point, each spherical
angle must be 1 J right angle, and the four spherical angles of
the tetragon will amount to 5% right angles, exceeding (2rc— 4)
right angles, or the four right angles of a plane tetragon by
1 J right angle, or by one-sixth of eight right angles : the solid
must therefore be the hexaedron or cube.

If three pentagons meet in a point, each spherical angle
must be lj right angle, as in the last instance; and the five
spherical angles of the pentagon will be 6§ right angles, ex-
ceeding the (2n — 4) right angles of the plane pentagon by f ds
of a right angle, or by y^th of eight right angles. The solid
must therefore be the dodecaedron.

The

Mr. Da vies Gilbert on the Regular or Platonic Solids. 163

The same results may be obtained analytically in a manner
exhibiting the extensive generality of algebraic language.

Let x = the number of regular similar and equal planes
bounding the solid body.
y = the number of sides in each plane.
z = the number of planes, and consequently of spheri-
cal angles, meeting at each point.

Then "g ang es = the solid angle subtended by each side of
the solid from the centre of the sphere.

But since all the spherical angles meeting at any point of
the solid must in every instance equal four right angles to fill

space ; each spherical angle will be equal to — — g- — ^rf-r and

all the spherical angles of a side of the solid = ~- x 4 right

angles. But the plane angles of each side of the solid =
(2j/ — 4) right angles. Consequently, the excess of the sphe-
rical angles above the plane angles = (4^- — 2y + 4) right

angles. And this equals the solid angle subtended by each
side of the solid from the centre of the sphere. Consequently,

(4 ~ — c2y + 4) right angle = rlg * ang es . 8 z = 4 #3/ —

2xyz + 4 xz, and x = _ . ., ? — •

Now it is obvious, from the nature of the quantities repre-
sented by x, y, and z, that they must in all cases be integral

and positive. But since x = - — — ~ — r — . The denominator

r 2y-K2-y).z

<2y _}. (2 — y) must be also affirmative. To ascertain therefore
the limit which y cannot exceed without making the expres-
sion negative, put 2y + (2 — y) ,z = 0. Then y= 2 -\ .

If z were infinite y = 2 and it attains its next integral

value;

when z = 6 y = 3;

when z — 5 y = 3 ;

when 2 = 4 y may be 4 ;

when z = 3 y may be 6 ;

when z = 2 y at its maximum infinite: therefore

any finite number may be taken
for it.
If z less than 2, the highest value of y is negative.

Y2 If

164 Mr. Davies Gilbert on the Regular or Platonic Solids.
If therefore z — any number from infinity to 2.

y may be 2. Indicating that the sphere is divided
into any number of parts by great cir-
cles (meridians) passing through the
same two poles.

z = 6 y at its maximum 3, x infinite. Hence the
sphere may be covered by an infinite number
of equilateral triangles meeting with 6 angles
at each point.

% = 5, y at its maximum = 3 x = 20. Hence the
sphere may be covered by 20 equilateral tri-
angles meeting 5 in a point.

% = 4, y at its maximum = 4, x infinite. Hence the
sphere maybe covered by an infinite of squares
or tetragons meeting 4 in a point.

y = 3, x = 8. Hence the sphere may be co-
vered by 8 equilateral triangles meeting 3 in
a point.

* = 3, y at its maximum = 6, x infinite. Hence the
sphere may be covered by an infinite number
of hexagons meeting 3 in a point.

y = 5, x = 12. The spheres may therefore be
covered by 12 pentagons meeting 3 in a
point.

y = 4 . x = 6. The sphere may therefore be
covered by 6 squares or tetragons meeting
3 in a point.

y = 3, .r = 4. The sphere may therefore be
covered by 4 equilateral triangles meeting
3 in a point.

z = 2 ^ at its maximum infinite x any number what-
ever. Appearing to indicate that a sphere
being divided by a mathematical plane into
two equal parts, may have that plane bounded
by any regular polygon, when 2 angles only
will meet in a point.

y = 2 The plane appears to contract itself into a right
line.

The

Mr. Ivory on the Ellipticity of the Earth. 165

The quantities may be arranged in the following manner :

x = 4

3/= 3

2 = 3

x = 6

y = 4

2=3

x = 8

3/=3

2 = 4

x = 12

3/ = 5

2 = 3

x = 20

3/ = 3

z = 5

j: infinite

J/ = 3

2=6

7/ = 4

2 = 4

y = e

2=3

x any number whatever

> 3/ = 2,

2 = the same number as x.

XXVII. On the Ellipticity of the Earth as deduced from Ex-
periments with the Pendulum. By J. Ivory, M.A. F.R.S*

TN the Conn, des Terns 1830, lately published, there is a no-
•*■ tice of experiments made with an invariable pendulum, by
M. Duperrey, in the course of a voyage round the world. The
places of observation are not numerous, and one only, namely,
Toulon, is a new station. But, in the present state of this in-
quiry, no less instruction is to be reaped from the repetition
of the experiments at the old stations, than from the extension
of our knowledge by new observations. If we could com-
pare the lengths of the pendulum determined by different ob-
servers on the same spot, the errors to which such experi-
ments are liable would become known, and we should be able
to estimate the degree of precision with which the figure of
the earth can be investigated by this mode of experimenting.
An attentive examination of all that has been accomplished in
this research will clearly prove that the high expectations of
accuracy which were at first entertained from it, have not been
realized in practice. It is remarkable that the pendulum-ex-
periments within 30° of the equator are very irregular ; while
in higher latitudes, if we except Drontheim, the results ob-
tained are not chargeable with inconsistency in any great de-
gree. Two causes only can be imagined in order to account
for the irregularity near the equator : either the experiments
must be erroneous, or gravity must be very unequally distri-
buted in that quarter of the globe f.

* Communicated by the Author.

f Captain Sabine's experiments have lately appeared in this Journal,
corrected from an error in estimating the divisions of the level of his re-
peating circle. The corrections are excessively trifling, so much so that it
seemed hardly worth while to call the attention of the public to the cir-
cumstance, as the experiments must be considered as remaining in statu quo.
That very great irregularity prevails in these experiments, and indeed in
all those made near the equator, is a fact that all will allow ; but the cause
has not been ascertained in a satisfactory manner.

The

166 Mr. Ivory on the Ellipticity of the Earth

The pendulum which beats seconds at Paris, at the tempe-
rature of 1 5° Cent., being represented by unit, M. Duperrey
has determined the relative lengths, at the same temperature
and at the level of the sea, at the five following stations :

Toulon

Isle of Ascension
Isle of France. .
Port Jackson . .
Falkland Islands

Latitude.

43° 7' 20" N.
7 55 48 S.
20 9 23
33 51 40
51 31 44

Relative Length.

0-99950585
0-99729881
0-99789022
0-99871430
1-00025995

Adopting 39-12929 for the length of the pendulum at Paris
in English inches, at the temperature 62° Fahr., the fol-
lowing table shows the lengths of the pendulums at the sta-
tions of M. Duperrey, in English measure, at the standard
temperature, and likewise the errors according to my formula
published in this Journal for October 1826.

Observed
Pendulum.

Computed
Pendulum.

Excess of
Calculation.

Toulon

Port Jackson . .
Isle of France . .
Ascension ....
Falkland Islands

39*10996
39-07899
39-04674
39*02360
39*13945

39-11071
39*07637
39-03643
39-01566
39-13940

+ •00075
—•00261
—•01031
-•00796
-•00005

The pendulums in this table at Ascension and the Isle of
France coincide very nearly with the lengths previously de-
termined by Captain Sabine and M. de Freycinet. From
some cause or other, they are both anomalous, and they are
treated as such by M. de Freycinet and M. Duperrey, being
left out in computing the ellipticity which they adopt. But
the other three pendulums fall within the limits laid down in
this Journal for October 1826, and increase the number of
instances that come under my formula to 31, out of 40 the
total number of experiments that have been made. My for-
mula was originally constructed from 26 experiments; and
all the pendulums since determined by M. de Freycinet, Mr.
Foster, and M. Duperrey, agree with it within the prescribed
limits, except in the three instances of the islands of Mowi,
Guam, and the Isle of France, which are greatly irregular
and irreconcileable with the other experiments. It is there-
fore very probable that the mean ellipticity of the earth will
ultimately be found to approach very near ^^ as deduced
from my formula.

' At

as deduced from Experiments with the Pendulum. 167

At Port Jackson the pendulum determined by M. Duperrey
is less than the length found by M. de Freycinet, and ap-
proaches nearer to the pendulum at Paramatta, to which it
ought to be very nearly equal : and this proves the justness of
the remarks I made relative to this point at pp. 351, 352, of
this Journal for November 1826.

Comparing the results obtained by M. Duperrey and M. de
Freycinet at the same stations and on the same spot, the pen-
dulum of the former observer at the Falkland Islands is longer
than that of the latter by '00233 ; and, at Port Jackson and
the Isle of France, the pendulums of the former are respec-
tively less than those of the latter by -00145 and -00095. We
may therefore conclude, that such experiments are liable to
an error amounting from *002 to -003 in the length of the pen-
dulum, or from two to three vibrations in a mean solar day.
We are sure that the error may amount to the quantity men-
tioned ; but it may be much greater. At Ascension the dif-
ference between the pendulums of Captain Sabine and M. Du-
perrey is very small.

In deducing the ellipticity of the earth, M. Duperrey com-
bines his own experiments with M. de Freycinet's, exclusively
of those made by other observers. The results he obtains
vary between the limits ^-^ and ^q. Upon the whole he
concludes that the two hemispheres of the earth are similar,
and he fixes definitively upon ^^ or ^n, as the ellipticity
common to both. But on examining the calculations of M. Du-
perrey, it will be found that the ellipticity he adopts, depends
entirely on the equatorial pendulum determined by M. de
Freycinet at Rawak. If we suppose that the pendulum at
Rawak errs in excess, which is very probable, and diminish
its length by correcting the possible error, the ellipticities
will come out of less quantity in all the combinations in which
they were before equal to ^F or ^^. Wherefore, although
M. Duperrey finds five combinations of his experiments in
which the ellipticity is ff ^s or 2"io » vet> wnether its real value
be equal to either of those numbers, or to a less fraction, will
depend entirely upon the error that may exist in the pendu-
lum at Rawak. Captain Sabine has deduced the same ellipti-
city, viz. 2^, by many combinations of his own experiments
and those made in England and France ; and I have already
remarked that this uniformity of result is occasioned by the
pendulums at the Islands of Ascension and St. Thomas, which
enter into all the computations. If these two stations be left
out in any, or in all, the combinations, the ellipticity will no
longer be the same as before, but a less fraction. The ar-
riving at the same result by a multiplicity of arithmetical ope-
rations

168 Mr. Ivory on the Ellipticity of the Earth

rations is in reality a play of calculation caused by one common
datum, or several common data; and therefore it does not
furnish independent proofs in favour of the number in question.
There must, in all probability, be some error in the pen-
dulum at Rawak ; and we know that the two pendulums of
Captain Sabine are anomalous, involving an irregularity much
greater than usually occurs in such experiments ; from which
considerations we must conclude that the evidence for the el-
lipticity 2^ rests but on slender foundations.

It is reasonable to think that every new set of experiments
with the pendulum should be joined to the stock we already
possess, in order to add to the number of unexceptionable ex-
periments, and to correct such as are of doubtful authority.
By proceeding in this manner our data for obtaining an exact
knowledge of the figure of the earth and of the distribution of
gravity on its surface, would continually increase and improve
in accuracy ; and, by applying proper methods of calculation,
we might hope to bring this great question to a satisfactory
solution. But if every new set is to be taken by itself, we
may, by making arbitrary combinations of the experiments, be
led into great error, and to entertain speculations that have
little foundation in nature.

The number of experiments made with the pendulum by
good observers at present amounts to 40, contained in the
subsequent table ; but of these, six, placed last in the table, are
-decidedly anomalous, and must be separated from the rest.
In setting aside these six experiments I do not now proceed on
my own opinion ; I follow the example of M. de Freycinet
and M. Duperrey. There remains 34 experiments which may
be compared together; and we have now to inquire, What
mode of calculation must be adopted in order to obtain a re-
sult entitled to the greatest confidence the case will admit of.
On reflection it will appear that we cannot expect to attain
what we wish for by the method of the least squares as usually
applied, nor by the modification of that method I used in
this Journal for October 1826. These more direct methods
are useful in bringing out a first approximation ; but it seems
necessary to correct the approximate elements thus obtained
by the methods used with success in so many problems of
astronomy. It is on these principles that the following inves-
tigation is conducted.

If we put 39+ I for the pendulum in English inches at any
station ; K for the latitude ; and 39 + A for the equatorial pen-
dulum; we shall have this equation,

A+/sin2A = 8 + f, (1)

e being

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY.

[NEW SERIES.]

MARCH 1828.

XXVI. On the Regular or Platonic Solids. By Da vies
Gilbert, F.R.S. $c.

To Mr. Richard Taylor.
Sir,
HPHE following trifle, extracted from my memorandum-book
* of many years standing, may perhaps (as a mere curiosity)
be favoured with a place in your Journal. It exhibits an easy
method of deriving these bodies from a modern discovery in
spherics ; and it illustrates the extreme generalization attached
to algebraic expressions.

Montucla and other writers on mathematics, attribute to
Albert Girard, about the year 1629, the discovery of this very
curious property of the sphere : — That if the whole surface of
the sphere, or what may be considered as its subtense from
the centre, be represented by eight right angles ; then will the
subtense from the centre of any figure, on the surface of the
sphere bounded by arches of great circles, equal the excess of
the spherical angles above the plane angles formed by the
chords of the sides. A discovery applied in recent times with
great advantage to all geodetical operations conducted on an
extensive scale.

Now as three planes at the least must meet at each solid
angle, or point of every solid ; it is obvious that no regular
equal and similar planes of any figures exceeding the pentagon
in number of sides, can possibly meet in one point or solid
angle. Thus the angle between two sides of an hexagon
being l£ right angle, three of these would make up 4 right
angles, and consequently the sides would expand themselves

New Series. Vol. 3. No. 15. March 1828. Y into

162 Mr. Davies Gilbert on the Regular or Platonic Solids.

into one plane. The same would take place with four squares
and with six equilateral triangles.

The solid angles or points of all solids bounded by regular
equal and similar sides, must then consist either of three, four,
or five equilateral triangles. Of three squares or tetragons,
or of three pentagons. And consequendy the number of these
finite bodies cannot exceed five.

That five such actually exist, is thus proved.

When three equilateral triangles meet in a point, the three
equal spherical angles must, to complete space, amount each
to one-third of four right angles, or to 120°. The three an-
gles therefore of each spherical triangle will equal four right
angles, or be two right angles above the two right angles of a
plane triangle. The solid angle therefore at the centre of
each spherical triangle will subtend one quarter part of the
surface of the sphere, and the solid must be a tetraedron.

If four equilateral triangles meet at a point, the angle of
each spherical triangle must, for the same reason, be in this
case a right one. Consequently, the three angles of each sphe-
rical triangle will equal three right angles, or be one right angle
in excess of the three angles of a plane triangle. The solid
angle therefore, at the centre of each spherical triangle, will
subtend one-eighth part of the surface of the sphere, and the
solid must be an octaedron.

If five equilateral triangles meet in a point, the angle of each
spherical triangle must be one-fifth of four right angles, or
72°; that is, four-fifths of one right angle : the three angles of
each spherical triangle will amount, therefore, to two right
angles and two-fifths of aright angle, exceeding the two right
angles of a plane triangle by two-fifths of a right angle, or 36°,
being the twentieth part of eight right angles ; the solid angle
therefore at the centre of each spherical triangle is one-twen-
tieth part of the spherical surface, and the solid must be the
icosaedron.

If three squares or tetragons meet in a point, each spherical
angle must be 1 J right angle, and the four spherical angles of
the tetragon will amount to 5^ right angles, exceeding (2n— 4)
right angles, or the four right angles of a plane tetragon by
l£ right angle, or by one-sixth of eight right angles : the solid
must therefore be the hexaedron or cube.

If three pentagons meet in a point, each spherical angle
must be 1^ right angle, as in the last instance; and the five
spherical angles of the pentagon will be 6§ right angles, ex-
ceeding the (2n — 4) right angles of the plane pentagon by f ds
of a right angle, or by T^th of eight right angles. The solid
must therefore be the dodecaedron.

The

Mr. Davies Gilbert on the Regular or Platonic Solids. 163

The same results may be obtained analytically in a manner
exhibiting the extensive generality of algebraic language.

Let x m the number of regular similar and equal planes
bounding the solid body.
y = the number of sides in each plane.
z = the number of planes, and consequently of spheri-
cal angles, meeting at each point.

Then "gl jnges — the solid angle subtended by each side of
the solid from the centre of the sphere.

But since all the spherical angles meeting at any point of
the solid must in every instance equal four right angles to fill

space; each spherical angle will be equal to — — — -2L- and

all the spherical angles of a side of the solid = — x 4 right

angles. But the plane angles of each side of the solid =
(2y — 4) right angles. Consequently, the excess of the sphe-
rical angles above the plane angles = (4— — 2y + 4) right

angles. And this equals the solid angle subtended by each
side of the solid from the centre of the sphere. Consequently,

(4 f- — cly + 4) right angle = nght ang es . 8 z = 4 xy —

2xyz f 4xz, and x = ^1,),, '

Now it is obvious, from the nature of the quantities repre-
sented by x, y, and z> that they must in all cases be integral

and positive. But since x = - — — <- — r— . The denominato1"

2y + (2 — y) must be also affirmative. To ascertain therefore
the limit which y cannot exceed without making the expres-
sion negative, put 2y + (2 — y) . z = 0. Then 3/= 2 H .

If z were infinite y = 2 and it attains its next integral

value;

when z = 6 y = 3;

when 2 = 5 y = 3;

when z = 4 y may be 4 ;

when z = 3 y may be 6 ;

when z = 2 y at its maximum infinite: therefore

any finite number may be taken
for it.
If z less than 2, the highest value of y is negative.

Y2 If

1 6* Mr. Davies Gilbert on the Regular or Platonic Solids.
If therefore z = any number from infinity to 2.

y may be 2. Indicating that the sphere is divided
into any number of parts by great cir-
cles (meridians) passing through the
same two poles.

% = 6 y at its maximum 3, x infinite. Hence the
sphere may be covered by an infinite number
of equilateral triangles meeting with 6 angles
at each point.

z = 5, y at its maximum = 3 x = 20. Hence the
sphere may be covered by 20 equilateral tri-
angles meeting 5 in a point.

z = 4, 3/ at its maximum = 4, .r infinite. Hence the
sphere maybe covered by an infinite of squares
or tetragons meeting 4 in a point.
y = 3, x — 8. Hence the sphere may be co-
vered by 8 equilateral triangles meeting 3 in
a point.

z = 3, ^ at its maximum = 69 x infinite. Hence the
sphere may be covered by an infinite number
of hexagons meeting 3 in a point.

y = 5, x =z 12. The spheres may therefore be
covered by 12 pentagons meeting 3 in a
point.

y = 4 . x = 6. The sphere may therefore be
covered by 6 squares or tetragons meeting
3 in a point.

y = 3, j; = 4. The sphere may therefore be
covered by 4 equilateral triangles meeting
3 in a point.

* = 2 y at its maximum infinite x any number what-
ever. Appearing to indicate that a sphere
being divided by a mathematical plane into
two equal parts, may have that plane bounded
by any regular polygon, when 2 angles only
will meet in a point.

y = 2 The plane appears to contract itself into a right
line.

The

Mr. Ivory on the Ellipticity of the Earth. 165

The quantities may be arranged in the following manner :

x = 4

j/= 3

2 = 3

x = 6

*/ = *

z = 3

# = 8

3/ = ^

z = 4

x = 12

3/ = 5

z = 3

.r = 20

</= 3

z = 5

.r infinite

3/ = 3

z = 6

y = 4

z = 4

j/= 6

z = 3 i

x any number whatever

, 3/ = 2,

z = the same number as x.

XXVII. On the Ellipticity of the Earth as deduced from. Ex-
periments with the Pendulum. By J. Ivory, M.A. F.R.S.*

TN the Conn, des Terns 1830, lately published, there is a no-
-*- tice of experiments made with an invariable pendulum, by
M. Duperrey, in the course of a voyage round the world. The
places of observation are not numerous, and one only, namely,
Toulon, is a new station. But, in the present state of this in-
quiry, no less instruction is to be reaped from the repetition
of the experiments at the old stations, than from the extension
of our knowledge by new observations. If we could com-
pare the lengths of the pendulum determined by different ob-
servers on the same spot, the errors to which such experi-
ments are liable would become known, and we should be able
to estimate the degree of precision with which the figure of
the earth can be investigated by this mode of experimenting.
An attentive examination of all that has been accomplished in
this research will clearly prove that the high expectations of
accuracy which were at first entertained from it, have not been
realized in practice. It is remarkable that the pendulum-ex-
periments within 30° of the equator are very irregular ; while
in higher latitudes, if we except Drontheim, the results ob-
tained are not chargeable with inconsistency in any great de-
gree. Two causes only can be imagined in order to account
for the irregularity near the equator : either the experiments
must be erroneous, or gravity must be very unequally distri-
buted in that quarter of the globe f.

* Communicated by the Author.

f Captain Sabine's experiments have lately appeared in this Journal,
corrected from an error in estimating the divisions of the level of his re-
peating circle. The corrections are excessively trifling, so much so that it
seemed hardly worth while to call the attention of the public to the cir-
cumstance, as the experiments must be considered as remaining in statu quo.
That very great irregularity prevails in these experiments, and indeed in
all those made near the equator, is a fact that all will allow ; but the cause
has not been ascertained in a satisfactory manner.

The

166

Mr. Ivory on the Elliptic ity of the Earth

The pendulum which beats seconds at Paris, at the tempe-
rature of 1 5° Cent., being represented by unit, M. Duperrey
has determined the relative lengths, at the same temperature
and at the level of the sea, at the five following stations :

Latitude.

Relative Length.

Toulon 43° 7' 20" N.

Isle of Ascension ! 7 !)5 48 S.
Isle of France. .20 9 23
Port Jackson . . j 33 51 40
Falkland Islands i 51 31 44

0-99950585
0-99729881
0-99789022
0-99871430
1-00025995

Adopting 39*12929 for the length of the pendulum at Paris
in English inches, at the temperature 62° Fahr., the fol-
lowing table shows the lengths of the pendulums at the sta-
tions of M. Duperrey, in English measure, at the standard
temperature, and likewise the errors according to my formula
published in this Journal for October 1826.

Observed
Pendulum.

Computed
Pendulum.

Excess of
Calculation.

Toulon

Port Jackson . .
Isle of France . .
Ascension ....
Falkland Islands

39-10996
39-07899
39-04674
39*02360
39-13945

39-11071
39*07637
39-03643
39-01566
39-13940

+ •00075

— •00261

— •01031

— •00796

— •00005

The pendulums in this table at Ascension and the Isle of
France coincide very nearly with the lengths previously de-
termined by Captain Sabine and M. de Freycinet, From
some cause or other, they are both anomalous, and they are
treated as such by M. de Freycinet and M. Duperrey, being
left out in computing the ellipticity which they adopt. But
the other three pendulums fall within the limits laid down in
this Journal for October 1826, and increase the number of
instances that come under my formula to 31, out of 40 the
total number of experiments that have been made. My for-
mula was originally constructed from 26 experiments; and
all the pendulums since determined by M. de Freycinet, Mr.
Foster, and M. Duperrey, agree with it within the prescribed
limits, except in the three instances of the islands of Mowi,
Guam, and the Isle of France, which are greatly irregular
and irreconcileable with the other experiments. It is there-
fore very probable that the mean ellipticity of the earth will
ultimately be found to approach very near 7£n, as deduced
from my. formula.

At

as deduced from Experiments with the Pendulum. 167

At Port Jackson the pendulum determined by M. Duperrey
is less than the length found by M. de Freycinet, and ap-
proaches nearer to the pendulum at Paramatta, to which it
ought to be very nearly equal : and this proves the justness of
the remarks I made relative to this point at pp. 351, 352, of
this Journal for November 1826.

Comparing the results obtained by M. Duperrey and M. de
Freycinet at the same stations and on the same spot, the pen-
dulum of the former observer at the Falkland Islands is longer
than that of the latter by '00233 ; and, at Port Jackson and
the Isle of France, the pendulums of the former are respec-
tively less than those of the latter by '00145 and '00095. We
may therefore conclude, that such experiments are liable to
an error amounting from '002 to '003 in the length of the pen-
dulum, or from two to three vibrations in a mean solar day.
We are sure that the error may amount to the quantity men-
tioned ; but it may be much greater. At Ascension the dif-
ference between the pendulums of Captain Sabine and M. Du-
perrey is very small.

In deducing the ellipticity of the earth, M. Duperrey com-
bines his own experiments with M. de Freycinet's, exclusively
of those made by other observers. The results he obtains
vary between the limits ffa and ^o* Upon the whole he
concludes that the two hemispheres of the earth are similar,
and he fixes definitively upon g|^ or ^m as the ellipticity
common to both. But on examining the calculations of M. Du-
perrey, it will be found that the ellipticity he adopts, depends
entirely on the equatorial pendulum determined by M. de
Freycinet at Rawak. If we suppose that the pendulum at
Rawak errs in excess, which is very probable, and diminish
its length by correcting the possible error, the ellipticities
will come out of less quantity in all the combinations in which
they were before equal to ^fa or y^j, Wherefore, although
M. Duperrey finds five combinations of his experiments in
which the ellipticity is 7 fa or -gfa ; yet, whether its real value
be equal to either of those numbers, or to a less fraction, will
depend entirely upon the error that may exist in the pendu-
lum at Rawak. Captain Sabine has deduced the same ellipti-
city, viz. -sin* Dy many combinations of his own experiments
and those made in England and France ; and I have already
remarked that this uniformity of result is occasioned by the
pendulums at the Islands of Ascension and St. Thomas, which
enter into all the computations. If these two stations be left
out in any, or in all, the combinations, the ellipticity will no
longer be the same as before, but a less fraction. The ar-
riving at the same result by a multiplicity of arithmetical ope-
rations

1 68 Mr. Ivory on the Ellipticity of the Earth

rations is in reality a play of calculation caused by one common
datum, or several common data; and therefore it does not
furnish independent proofs in favour of the number in question.
There must, in all probability, be some error in the pen-
dulum at Rawak ; and we know that the two pendulums of
Captain Sabine are anomalous, involving an irregularity much
greater than usually occurs in such experiments ; from which
considerations we must conclude that the evidence for the el-
lipticity 2^s rests Dut on slender foundations.

It is reasonable to think that every new set of experiments
with the pendulum should be joined to the stock we already
possess, in order to add to the number of unexceptionable ex-
periments, and to correct such as are of doubtful authority.
By proceeding in this manner our data for obtaining an exact
knowledge of the figure of the earth and of the distribution of
gravity on its surface, would continually increase and improve
in accuracy ; and, by applying proper methods of calculation,
we might hope to bring this great question to a satisfactory
solution. But if every new set is to be taken by itself, we
may, by making arbitrary combinations of the experiments, be
led into great error, and to entertain speculations that have
little foundation in nature.

The number of experiments made with the pendulum by
good observers at present amounts to 40, contained in the
subsequent table ; but of these, six, placed last in the table, are
decidedly anomalous, and must be separated from the rest.
In setting aside these six experiments I do not now proceed on
my own opinion ; I follow the example of M. de Freycinet
and M. Duperrey. There remains 34. experiments which may
be compared together; and we have now to inquire, What
mode of calculation must be adopted in order to obtain a re-
sult entitled to the greatest confidence the case will admit of.
On reflection it will appear that we cannot expect to attain
what we wish for by the method of the least squares as usually
applied, nor by the modification of that method I used in
this Journal for October 1826. These more direct methods
are useful in bringing out a first approximation ; but it seems
necessary to correct the approximate elements thus obtained
by the methods used with success in so many problems of
astronomy. It is on these principles that the following inves-
tigation is conducted.

If we put 39 + I for the pendulum in English inches at any
station ; A for the latitude ; and 39 + A for the equatorial pen-
dulum ; we shall have this equation,

A+/sin2A = & + *, (1)

e being

as deduced from Experiments with the Pendulum, 169

e being the error of observation, and^a quantity which is the
same at all points of the earth's surface. The equation (1)
being general, if we add all the like equations at the 34 sta-
tions we propose to include in our investigation, we shall get

34 A + fX (sin2 K) =. 2 (8) + 2 (e).

Now I have found,

2 (sin2 A) = 15*9316,
2(8) = 3-72872;

and hence by dividing all the terms by 34, we get,

A + -4686/= -10966, (2)

neglecting the term containing e9 which must be very small,
both because the errors must in some degree compensate one
another, and on account of the great divisor 34. The equa-
tion (2) must be very exact, provided we take care not to en-
hance its error by introducing small divisors.

Again, when the ellipticity is ^F, we havey = -202 nearly,
as appears from the calculations of Captain Sabine ; and, when
the ellipticity is tof^/ is nearly -208, according to my formula
in this Journal for October 1826. The mean is -205, which
cannot err from the true value of f more than + -003. Now
it is evident that this small error will not affect the product
jfsin2 X near the equator, and so long as sin2 \ is less than 0*2.
I have therefore computed the values of A by means of the
formula, A = 8 — f sin2 A,

on the supposition that fz=. -205, for all the stations in the
table where sin2 K is less than 0-2, as follows:

A

Maranham -01173

Bahia -01398

Rio Janeiro -01264

Trinidad -01188

Madras -01289

San Bias -01066

6)-07378(-01230, mean of 6.

Rawak -01479

Sierra Leone... -01550
Jamaica -01560

9)-11967('01330, mean of 9.

The inequality of the several values of A is very remarkable ;
in particular the three stations placed last, greatly exceed the
mean of the first six. But whatever be the cause of the irre-
gularity, it cannot arise from the approximate value assigned
New Series. Vol. 3. No. 15. March 1828. Z to

170 Mr. Ivory on the Ellipticitij of the Earth

to f. The mean of the nine stations must be an approxima-
tion sufficient for our present purpose. Let -01330 be sub-
stituted for A in the equation (2), then/ = '2057, which will
serve for a first value of f. Now put

a m -01330, A = a + s,

b = -2057 / = b + t,

s and t being the corrections of the approximate quantities :
then since A and f must satisfy the equation (2), and a and
b likewise satisfy the same equation, we get,

s + -4686 t = 0.

The formula (2) is one of the equations of the method of

the least squares applied to all the 34- experiments ; and in

order to find the other equation of the same method, let all

the terms of equation (1) be multiplied by the coefficient of

f: then,

A sin2 A +/sin4 A = 8 sin2 A + <? sin2 A;

by substituting the values of A and^J

5 sin2 A -f- t sin4 A = sin2 A (8 — a— b sin2 a) + e sin2 A :

and the sum of the like equations for all the 34 stations will
be the equation sought, viz.

5 2 (sin2 A) + t 2 (sin4 A) = 2 . (sin2 A (h-a — b sin2 A)),

the term containing e being neglected. Now,

2 (sin2 A) = 15-9316,

2 (sin* A) = 10-4381;
wherefore,

15-93165 + 10-4381 t = 2 . (sin2 A (£-«-£ sin2 A)) :

and, by a former equation,

15-9316 5+ 7-4654 r = 0;
consequently,

2-973 t = 2 . (sin2 A (%-a-b sin2 A)).

The sum on the right-hand side consists of thirty-four terms,
which must be separately calculated by substituting for % and
sin2 A their values at the several stations. The computation
being made, and all the results combined according to their
respective signs, I have found

2-973 t= - -00061.
Hence, t = — -00020 ; s = — -4686 t = + -00009 ;
/ = -2055, A = -01339.

If

as deduced from Experiments with the Pendulum. 171

If therefore / = 39 -f &, be the length of the pendulum at
the latitude A, we have this general formula, viz.

/ = 39-01339 + -2055 sin2*,

•2055 i

ellipticity = -00865

39-01339

= -00338 =

2955

Stations.

Latitude.

Observed
Pendulum.

Computed
Pendulum.

Excess of
Calculation.

Observers.

inches.

inches.

Falklandlslands

51°31'44"S.

39-13945

39-13935

—00010

Duperrey.

Ca. Good Hope

33 55 15

39-07817

39-0/739

—00078

Freycinet.

Port Jackson...

33 51 40

39-07899

39-07719

—00180

Duperrey.

Paramatta

33 48 43

39-07622

39-07702

+ -00080

Sir T.Brisbane.

Rio Janeiro

22 55 22

39-04374

39-04457

+•00083

Hall and Foster.

Bahia

12 59 21

39-02433

39-02377

—00056

Sabine.

Maranham

2 31 43

39-01213

39-01379

-f -00 166

Sabine.

Rawak

0 1 34

39-01479
39-01997

39-01339

—00140

Freycinet.
Sabine.

Sierra Leone ...

8 29 58 N.

39-01787

—00210

Trinidad

10 38 56

39-01888

39-02041

+•00153

Sabine.

Madras

13 4 9

39-02338

39-02390

+ -00052

Goldingham.
Sabine.

Jamaica

17 56 7

39-03503

39-03288

—00215

San Bias

21 32 24

39-03829

39-04109

+- 00280

Hall and Foster.

Formentera. ...

38 39 56

39-09424

39-09361

—00063

Biot.

New York

40 42 43

39-10120

39-10081

—00039

Sabine.

Toulon

43 7 20

39-10996

39-10941

—00055

Duperrey.

Figeac

44 36 45

39-11322

39-11476

+•00154

Biot.

Bourdeaux

44 50 26

39-11303

39-11557

+ -00254

Biot.

Clermont

45 46 48

39-11809

39-11893

+•00084

Biot.

Paris

48 50 14

39-12929

39-12929

+.00056

Biot.

Dunnose

50 37 24

39-13614

39-13618

+ -00004

Kater.

Dunkirk

51 2 10

39-13773

39-13762

—000 H

Biot.

London

51 31 8

52 12 55

39-13929
39-14250

39-13932
39-14174

+ -00003
— 00076

Kater.
Kater.

Arbury Hill ....

Clifton

53 27 43
55 48 41
57 40 59

39-14600
39-15554
39-16159

39-14605
39-15454
39-16016

+ -00005

—00100

—00143

Kater.
Kater.
Kater.

Leith

Portsoy

Stockholm

59 20 34

39-16541

39-16546

+ -00005

Suanberg.

Unst

60 45 28
63 25 54

39-17146
39-17456

39-16985
39-17778

—00161
+ -00322

Kater.
Sabine.

Drontheim

Hammerfest ...

70 40 5

39-19476

39-19636

+•00161

Sabine.

Port Bo wen ...

73 13 39

39-20347

39-20177

— 00170

Foster.

Greenland

74 39 19

39-20328

39-20428

+•00100

Sabine.

Spitzbergen ...

79 49 58

39-21464

39-21248

—00216

Sabine.

Ascension

7 55 48 S.

39-02385

39-01730

—00655

Sabine & Duperrey.

Isle of France .

20 9 40

39-04721

39-03780

—00941

Freycinet & Dupy.

St.Thomas

0 24 41 N.

39-02074

39-01339

—00735

Sabine.

Galapagos

0 32 19

39-01717

39-01341

—00376

Hall.

Guam

13 27 51

39-03023

39-02453

—00570

Freycinet.

Mowi

20 52 7

39-04737

39-03946

—00791

Freycinet.

Z2

This

172 Mr. Ivory on the Ellipticity of the Earth

This table shows the errors of the formula. The greatest
error is at Drontheim, and it is nearly as much with the ellip-
ticity ?^F. The next greatest error is at San Bias ; but this
would be considerably diminished by adopting the length
found by Captain Foster, viz. 39*03881, instead of the mean
of the lengths found by that gentleman and Captain Hall,
which stands in the table. The excess at Galapagos is little
greater than the defect at Drontheim ; and as we know that
the former pendulum was determined in unfavourable cir-
cumstances, the experiment seems to be sufficiently well re-
presented by the formula. We may therefore affirm that, if
we adopt Captain Foster's pendulum at San Bias, the formula
represents 35 experiments out of 40, within the limits of the
probable errors : for the difference between the observed and
the calculated lengths is less than what would arise from an
error of 2 vibrations in a mean solar day, except at Sierra
Leone, Jamaica, San Bias, Bourdeaux, and Spitzbergen, where
the error is 2| vibrations ; and at Drontheim and Galapagos,
where it amounts to 3 \ and 4 vibrations. But at the five ano-
malous stations, the errors are between 6 and 10 vibrations in
a day.

Without laying any stress on the mode of investigation we
have here followed, it cannot, I think, be denied that the el-
lipticity Q-gjj represents the observations much better than
2^; it ought therefore to be adopted until another shall be
found, if it be possible, that will represent the same observa-
tions still better, or until future experimental researches shall
have corrected and enlarged our present knowledge on this
subject. What other reason can be alleged for preferring one
ellipticity to another ?

But if the experiments can be represented within the limits
of the probable errors, what becomes of the splendid specula-
tion about local attraction, which connects the apparent in-
equality of gravity with the variation of the soil. It is evident
that we can have no measure of the excess or defect of gravity
caused by the attraction of the adjacent matter, if the errors
of observation be sufficient to account for the irregularity in
the length of the pendulum. This theory too is quite uncer-
tain, so long as there remains any doubt about the exact quan-
tity of the ellipticity. At Maranham and Trinidad, Captain
Sabine makes the observed pendulums gain upon the calcu-
lated ones upwards of 4 vibrations in a mean solar day; in
my table the acceleration is only 1^, which may be attributed
to the inaccuracy of experiment. According to the same gen-
tleman,

as deduced from Experiments with the Pendulum, 1 73

tleman, the observed pendulum at Spitzbergen falls short of
the calculated one 3 \ vibrations in a day ; — in my table the de-
fect is only 2{. The density of the matter near the surface of
the earth, varying at the different stations of the pendulum,
must in some degree influence the time of vibration : but the
speculation is premature ; and there is good reason to think,
at least in far the greater number of cases, that the effect in
question will never be separated from the unavoidable errors of
observation.

What has just been said will not, however, apply to the five
anomalous experiments, all of which show an excess of gravity
far surpassing the ordinary measure of experimental error.
Besides, at two of the stations the pendulums have been veri-
fied by two independent experiments varying little in the re-
sults. It is remarkable that in all the five cases, and at Gala-
pagos, there is an excess of gravity; and, according to my
table, there is a like excess, though much less in quantity, at
Rawak, Sierra Leone, and Jamaica. On the other hand, there
appears to be a defect of gravity at Maranham, Trinidad, and
San Bias. Thus there are nine instances of excess, and only
three of defect ; and we may suspect that there is some cause
of error, different from local attraction, tending to make these
tropical pendulums longer than they should be. At the Isle
of France, the excess of gravity is no less than 10 vibrations
a day; yet this is a small island, surrounded on all sides by an
extensive sea; and we might infer, a priori, that a pendulum
placed upon it very little above the level of the sea, instead of
being accelerated, would be retarded by the great defect of
density in the waters of the ocean. But the purpose of this
paper is to deduce from the experiments the consequences that
necessarily flow from them by a strict investigation ; and I
shall refrain from entering into the region of conjecture and
opinion.

Feb. 11, 1828. J. Ivory.

XXVIII. The Climate of Penzance, Cornwall. — Meteorologi-
cal Residts of the Temperature, Wind and Weather deduced
from diurnal Observations made at Penzance for 21 Years:
{the Thermometrical Observations made at 8 a.m. and 2 p.m.)
to which are added the Maxima, Minima, and Media of the
Register Thermometer for 7 Years, with the Inches of Rain
fallen during that Period. By Edward Collins Giddy,
Curator of the Cabinet of the Royal Geological Society of
Cornwall.

January

174

Meteorological Results of Observations made

<

Si

F

Q

CO N O « (fi N N» O ff) O W O » K5 N(fi 00 CC O h
PHr-(r-*r-( ,_ir-lr-lCMi-«r-l,-lCMrH ^H CM

*

00

1

W5(^Qt)»0^(HHK»0(»K5(»HWH&«HlNa)N

HHHH(J)&t5>HHrt ,_,,-<,_ _ CM CM -I r-H

1

cm

CO

aoo^aoooaoa>aoaoooo^aoaoooo^aoaoaoo,>ooaoao

CO
OS

o5

C

H3

55

0-^l>.i-Hif3COiO'*"*i>,cy305QOCO>-<COC£>r-iTt«i-irH

0>

£

1— < I— 1

£

tO

o

W2

a0«C£>l>.fl5NN(NOH^^Tt(i0O(^05Cn'0CQH

r-4 i— I i— < i— 1

1

CO

CM

1— 1

CO

HHO»on^'t^coaj©(£>^^^'*o^o(No

CO

00

1©

02

Hp-llNNNm^COCOHr-KfHHtO^MCOCDHGl

co

CO

to

W

occocoooi-io^ooor-iocMeoooTficioco

r- 1 l-H

w

fOn>OOOrtiOO(fiC<JOH(»HrtC<5NOHOO

55

CM

t©

*

c^^ooo^OrtHoopjn^^iH^HrtOH

fe

CO

s

o

|

c
1

*©0©©i©0©©i©0©»©iO©»0©©OiO©©
tOr^WiO^t^tO^CMcS^O^OOI^T^iWI^^^tCo^aO1

e

es
6

»©

»©

*U!H

MC«eOO<-*CC«COMGtTjHWeOCOWCOWMeO'*M

•uij\[

t©
CM

•xbjve

to©-«*<tO"'*l''tfCMCMt©t©toao*oto<McocMaot©tO'<*t

iQif5'fli'5»OU5«5"5>OK5i/50'0>fliO>C"5«5"5iO»0

•XBH

00
*©

><

NCDO>Oi-(^pj'1Hi5«iN00O5©H(^M'*ir5t£)N

©©©r-lr^rH^Hi-Hr^^r-tr-I^HCMCMCMCMCMCMCMCM

QOOOaOQOQOQOQOGOQOGOQOaOQOGOQOQOQOCOQOGOOO

>5

la

S
1

Q

G^r-tr-l<Mr-1i-lr-lr-<i-(i-Hl-t i— 4i— 4i— *•— li^-lr— iC^ti— 1

Q

tO
CO

S

is

O^GOC^©Tf<£>(MaOaoaOO}COC©Tt<tOt©*>»''tfi'^aoai

0>

is

i©

CO
CO

o <s

MnM«cocowcowwn«wP5coco«wn««

O c3

35-9

*©
t©

C

-1

►

*

£

£

H(£c*HGOOOOWQO(^WC£l'<l,C£iOHOt£iNi*N

*

*©

CM

*

^H^OO^^rtO«^HQ0WNlN^N«H00

*

o
o

CO

©tOtO*>.*©'<*<MCMC0Tt<CMCOt©CM©CM»©C0C0CMCO

co

o

CO

^^pHio^Mncon^^^N^tsNHOco©©

CO

o

CO

W

CO

"5hcCi«^hW"5«K5I5«I5<cO^K5©hh©©M

ft 1— t

w

CO

W

CM©-<*<Tt<|>.CM*>»C©©CM»-HCMi-ii©Tt<r-4C©C©C©O0Tt<

w

to

tO

(O^cOtO^^WiCOHOOKNCO^COQONN^

i©
as

z

HHHWH^«Oi^(NNW©H©^MW©^W

fc

to

I©

g

o

e
2

©'©©©^^©i©*©©*©©*©©©^^^©©©*©

C?2 2 dTE?2? lf£:2 c© j^c^T^© *© »© © «?«o co tjT

a

1

©

CO

COO<WH6JMWN(NncOWMG^MM«lMGO<

•utfl[

o>

•XBW

iCiOiOiOiO»f3kO«5«5>CiOiC"5>C»C«5ir}U5iCiCiC

•xbh

to
1©

E

■

o2a°'HG<C1'*lCCfiN00,?)OH<NW'1,"5CCN

•SJB3A

**2

;-

at Penzance, in Cornwall, for 21 Years.

h4

1— <

01

<

B

■a
13

Q

HcctooiOHO-f^cooitnconciococoooo

b

Q

CO

o

*

OiN^OOOOiO(£iOOS<HT((TjtNQOO^NrtOO

1

CM

*8

ooooooooooooooooooooo

c rt

o

CO

to

1

"51
aJ.S

*

3

"^■-•a50^co"^irt<co<»Tt<eocoi-ia>i-"CO"«**o^cooM>»

i—l i— 1

*

fc

*>•

o

£

W©*<N©*©*(N^^©©*.^Q*»0.-<CO©*»0»Ot>»l>.aO

>

CO

*

CO

'»fl«OOC£>00<»00(HOHGin»0»0^^(N'<l<N

CO

CO

CO

NCOO'tMOH^rt^rtNiQOH^^ionOrt

«?

f-H

W

CO

ir)T(tH(fi»cQOT)irj*wooo:m'*H^,w,*'-,(^s^o

w

CO

CO

W

rtHH«C0C0».'JN(O^(0C)0iN©(N"5O«5HW

w

S

lOHNNWHNOtO^O^HW^^tn^flOrtH

00

fc

©u3<^r-H.^I>.C©COCO^OCOi-iCOCO©C>©*CO©CO©*

fc

S

o

a

a
2

OOOiOOK5iOiO"50K5K5K50>'5iOO'OiOOfl

o^ta tc h h cS h n e? o o h 't n co o1 m o «5 e? h

1

•uij\[

COCOC0C0C0COC0''^,'^,C0COC0'^'',tf,'^l "^ "^ "^ ^ "^ ^

*UIK

CO

•xb^

CO CO kOCOCOCOCOCOCOCOCOCOCOCOCOCO iO CO CO CO CO

•xbjvt

00
CO

CO

E

1

5

000000000000000000000000000000000000000000

•sibsX ig

o

a

5

•

>»

S

CM
CO

1

^*>»i>»©*a>.t>.rHCS*—tcoaoco©c>i>»''t|coaoi>.aoao

i— t HHH(Si- If— 1 (S i- 1 i— 1 r-l i— < i— 1 r— 1 i—l

1

c -

COCSCOWWCOWtOMCOCOWCOWCOCOWMWCOO

CO

in

c

h3
CL -S

is

PS

k

fc

■^i-nfJt^r-iTjHOONOiOXO 05(0 N N iO GO (J< ■* to

55

O

£

»-i©©C©»Or-<C0©*Tt<©*<MQ0C0COO'>COCO»O'^e0a0

►

a>

«3

OONt0 0)N^Q0MOW5^5<i(ir5Ot>»C0^Hrt

*
co

CO

CO

(NN0tO«OW©^r-iTPWW^(N»0©'fGlt£)i-t

CO

W

CO

«^H05H»OrtCOe<0^(SOHiOT)(500iO^^

w

co

00
CO

«

^©^Q<^ii50-fOU50<rtCOeOrHH(3<0»i5^©

W

*>•

W

•— • i— <

w

55

<7>

B

N©©oo<tc(o©©ioionHHO<G<>o^HWN

5?

o

HO

a

o

3

H

g

8

©©*©©i©©©iOi©©*0©iO©©©©©tO©*0
(5? S? (5 N 00 Tl? fl? S? rt i(j 00 N 00 CO © ©"cfi N 0O (£ »

s
2

©

*«!Jtt

©O^Ot>.Q0 00©a0G<S<iXl®©©-*C0(£)(»Q0t0

wneococoo^oiKiwwcowoico^Ttteocowcoco

•uijv[

00

•XBJ\[

*^©«H©e<a(5<to(»©H(£no^s)©^K5

iO»OCO*©COCOCO*©CO*©CO*©<OCO»©»©*OCOCOCO*0

XBW

CO

i

2

.2

©©©>-h-<--h>-h.-i^.-Hi-i,-<,-.0*&*©*C}*©*©$G*©*

QOQOQOOOQOQOQOQOOOOOOOQOQOQOaOQOQOQOODOOaO

•sat?aX

[

176

Meteorological Results of Observations made

p

S

9

Q

CO
CO

CO 1© CJ5 l^» "^ C75 t""» 'f h 00 h QO t^» QO C7) O M W M ^ ^

1

as

1— 1

ooooooooooooooooooooo

o £

O CO

o

CO

to

C

Bu'J

*

B

ft

WiHOoo^xo^OiOjpioota^HWPjn^ao^

CO

£

1— 1

►

GO

*

Tf«Tti|>.iO1-iTFC0C©C©i-H<S*C©''<*<Q*©G*©'<tlC0©C0

CO

00

to

~\ ©~

t©

CO

i"«O(HKrH^(OTj<<£lCr)He0OHTt<O>l5lflHH

CO

W

CO

<J«W^OOG)O^^H(NOH^0000(£>MlNCiC0

m

CO

tO

w

O^HOHi.'JNNirjHTfNH'tiOniOW^N©

w

to

(HHnco^HH^coH^o^eiioooNto^tc

»©

»©

B

^sjtnoN^^aH oiD^toNTjH^to w«rtrt

*

S

o
S

E
S
XI

H

s
«
9

©I0©©©©i©i0©i0»©i0©©i0©x0ir5»0»©©
COtOtOtOtOtOtOtOtOtOtOtOtOtD iQ tO uO to tO tO tO

a

1

Jo

&?

to
to

•uijvt

^WiC^rt^KOtSNtNOOCDHOXHiC^OOKl
I0i0-*t,i©i©i©i0*0>0i0i0t0i0»0»©t0t0i0v0»0>©

•uiJVT

•XBJV[

o^iow^^^^^tacoN^aoNoo^oio©©

•xbh

o

CO

>*

N00O5© M^C0'*u:tCib.CCa5©f-iGtM't>OC£)N

©0©,-l^,-lr-lr-l.-lr-ll-l.-lP-l©*C^G*©*©3!(S*G*G*

GOcoaoaoaocoGCcoaocccocccococococoaocccoco

JOJ

9

P

^GDP5C0Mt>.^(X>iOt>.kO,<t>C^CO^Q0?£iiOC©^

S'

00
CO

0)

is

rt<c©Qoao©"<t|io»otO'<i'<toi>.toi>»iocy>c©i©to*oJ>»

^Hi-H Q$ ,— | ,— 4 i— 1 i— 1 i— 1 r-l r- 1 r— 1 i— Ir-ti— < f— 1

1

C «

z-3

CO

i— t

to

o s6

WWCOMCOWCOMCOMMCOMMCOCOPSCOrtWCO

c

is

pj.9

* I , % S 1 - • ■ « «% * fc * * ' S ' * *: *■ 1- g: 4: ■ S i

13

pu.S

BQ

(NH>OrHCOC£)'*>flGlHiCMif5'^CO©Mt©,^u:c©

f— (

*

CO

£

eOHMHMONKtC^iflM^OO^ThM^^N

£

!>.

CO

iOhiOiO©i-"C5^M«51'1'«»0©GIOhW©(0

CO

CO
GO

CO

5000©^N<HC?5tX©l(^COW(«^N»CMt>.©'*
I— 1 1— 1 r- 1

co

to

CO

"JN"5©^hiOS«^hCOO^^iON«h^h^

CO

to

w

1— ( i-H

w

GO

OOOOH(£iriM©neO«5t£)SlCOH^NTfHK

o

&

»o»-if-HaocoF-i<^^HO^^io(3<'*i-Hp-H'«^i-H'^Tt"i-HO

%

to

I
g

I

a

9

»0©»O»0i©»Oi©©il0iO©©*0© «©*©©©©©©

to" co at(f c£oo coco d<o iJoc^o^c^tocc^GOt^cTaSio

>10>';oi"OiflK5UiOi/5iOifliOiOi'J>'5iO!0'0''5

1
a>

»©

CO

i©

•uijv[

Wf-f'tO©t5'*(N(N'* OOOCOCOMIN^OON^)

•utflr

©^

^

•xsj\[

0^i-«0^C©©<OQ0a0^-*Q0'«**O'*0*^C75O©*t>«i-HC0

»->»*>.*— to *>. r>. to to *>. to to ^. *->. t^. to to *>•*>. to *^. to

XBM

<*

■a
E
?

NOOOjO^eiCO^ifl^NQOCTjOfH^W^^tCN

OOOrHHHHHHHHHrt(3<S(&(6<0(5<0)5<

QOcoooooaooxooooooooooooooooMxaxooco

•SJBDi

1

at Penzance, in Cornwall, for 21 Years.

Ill

1

p

s

00

CO

H

o
u

<

1

HXQOcoHiooDoaj^icoNo^oioQonoiKS

iH ^HrH^H ,-1 ^-1 ©* ©* .-« i-H ©* r-« ,-1 r-t

"35

c©

Si -8-

cococococococococococococococococococococo

OS.

o «
ZT3

"5

c©

•1

IB

Ph*.S

CL.5

25

coc©a>— iaoc©»©©»©co*>»cocococo©*co<©a>t>.<©

l-H f— I

00

>

(—1 1— 1

*

c©

co

1 <© o> "* c© t>. ©* io't>. Oicoco^uocri^t^ax^cKuo©*

CO

t>.

CO

1 (JlTtt^io^tOrttOHrttOO^^KIS^OO^rt

1 »

1 "^
1 <©

CO

-^Oi-i^-toccooooi-iOT^o^i-ir^ot^t^G^^

w

co

o
wo

w

ooo©^»-tTt<»-iP-«-«!t<»oi-ia>©i-«oop-<i-Hco©ii-i

W

r-4

o

%

n-ioM^aco.Htoo'tH^ic^co^niNHn

fc

00

S
o

S
c
5

$

s

i5

iO©iOOiOi©iO©©©©©©©©©©©»©»©©
<©C©C©C©C©C©C©C©C©C©C©C©C©e©<©C©C©C©C©C©C©

c

C3

i

»o
c©

•«iw

•n!K

o

•xbj^;

i>«..i>.i>»t>.t-.i>.i>»j>.^»i>.i>.t>.i>»t>.t>»i>»c© t>. i>. i>» c©

"XBJ\[

OS

E

©©©i-l»-li-lr-li-lp-Hp-li-4r-li-l©l©*©*Q*©*©lQl©*

000000000000000000000000000000000000000000

•saBaX xs

►-3

3

1

9

b

p

«5OIN'*iflONOOWN0<N^1-i05HX05(3'lO

b1

Q

o

-4->

I

«a^05NCO^"*HO)Xa5<J)Tt*050G<OMe)05H

,-( ^ _ _ ,_ ^h — 1 r-t f-H ©* ©* r-1 r-l

3

►

o C3

MCOCOCOWMMCOtOMCOCOMCOCOWCOCOW CO* CO

CO

fe

fc

COiOO>Tt«C©C©QO.-i©©CO*OC©UO<X>t>.tX>Tt<f-«QO©*

*

fc

CO
~CO_

£

NG<H»OIN-*C£>S<rHXH(£)»0"5NCiNiO©«N

£ '

co

I-H P-H F— 1

1

to

o

co

>OiNrtW«G<^X«^«5W^NW«(S^H©©

CO

OS

HiC^^OCO^^^HCOO^-t^^FH^WiOTt*

C4

CO

0^

c©

H

^HCOOtOWHHtOHOJOO^HHOCO^^rt

H

00

(^^iQOCO^OOOlOOOiOi-tCOOOrft^G^CO

5a

"crT

fc

hONC0^hW*>0«h0C}NN(£iC0N>0WG<h

55

S

o

1

9

a

1

Oi©i©OOOOOOt©OO^C© ^ ^ ^® ^ ^ "2>

t© c© c© c© c© c© c© c© c© c© c© c© c© c© c© c© c© c© t© c© c©

c

1

c©

•UIfl[

xaico^toco^xn'tcooNOfnco^oo.ox

10*©*0»©»©100*0*0*0»0*0»©C©10»0»©5©<©^©,10

*UIH

CO

>©

H

•XB^[

«J©'*^tOCO'*tO'*'^,<J*XX^>-ii-t©--<,<f»0(N

•XBJV[

00

NXOiOHNCO^iOtCNXOiOHWW^iQtON

0©©r-trHn.-l,-ii-l.-li-l.-li-lO*©*G*Cn©*0*©*©*
000000000000000000000000000000000000000000

•&reaX

IS

3$

»s

er?es.

Vol. 3. No. 15. March 1828. 2 A

ITS

Meteorological Results of Observations made

C*

W

CO
O
H
O
O

la

S

1

b

Q

©*rHO**-«^r-H^O*.-lr-H©*.-lr-lp^.-l.-<r-< i-H G*

£ i

©

CO
CO

1

HNCOWMOOK>HC5NOOOU5b.(»©ff)(C^N^

1

G*

CO

O A

COCOCOWCOWCOMCOWMCOWWWCOCOCOWWCO

° &

O «S

tO
CO

C

CO

!

CO

"^Mcow^OT^ZM^^^^ca^^^^^cQ

fc'J

*

^tOHiflMaoujtON^^HOCO^HrltON^iO

£
fc

G*
CO

£

(£)COON^'*NO<?0'*0»0^'<f©WiHiOHCOifl

i

CO

CO

r— 1 «— 1

co

to

r-l

W

CO

r- 1 p-(

CO

CO

05

H |

06<>OiOOO!£iT(<e<0«05a)HNOOHOHHO

w

to

H |
* 1

»ooocoi-toOi-iTj*f-i»o^HCO'-ii-io»-i®t©t©eo

CO

* 1

n^owoioeooo^NH^isifjwosfJOrt

fe

1

B

a

1

1

irjiOO>OiO»o»000000»00>0»00000»0

?0 o" CO "f 00 rp pf CO iO CO o"^'^MiO'*'<ti'iOCIOQO>C

c
i

to
to

»o

*a!M

(NtO"5XO(^t>»(N'tl^©C500»CC£)l>.'*i5<C£iO"5

•uji\[

CO

•xbjv[

OOOCfiiCrt<t>.00(3<iOOOOO"500©lT(H(^^Tj*iO^'^
CO CD CO CO CO CO CO CO CO CO to CO CO CO CO "O CO CO CO CO CO

•XBJ\[

00
VO

g

6h

NOOOJOH^M^iOiXiNOOOOH^fO^iOtON

OOOHHrtHHHHHHH(H8<(S8l(S^S<«

000000000000000000000000000000000000000000

•siBaX 15

08

W

CO

COiCCCOOt-iNQOOX^COCON^rtNOiOCON

£

5

CO

1

o rt
£*0

T*«i©Tt«tr5000iCOG*-<G*aOt^.-«t<COC©aiCOaO©l>.CO

1

to

g*

©©©©©©©©ooooooo©©©©©©

•MMWMMCCWMCOWCOCOWCOMCCMCOCOKlM

©

CO
CO

£

Z

1

HN>-itOCO^CO'>!|<«NS<iC&<'«}tN(N«£ieO'*'tN

1 CO

©

£

©i-ikC©©CO»©"— i ^ Nf- (COi— i iflCC ^ i- 1 «J »occ ■*

£

00

CO

t>.Tt<^TtiG^COr^COQOrti©<»©4->»-<fi— i !>. G* CO CO CO »0

l-H

*

CO

00

9>

93

wwoiownn^'tw^ioioocoH^HOOHH

CO

©

CO

M

CO

© »-h •'f CO ■* <— i <X N ^ r- iiCMNNGtOOnoOMOOm

CO

©

H

©CO©"*COCOt>»»Otr5CO^G*COCO©C©kO»-tr-<iO»0

w

©

»io«on--irHeOHtoeoH©^H©f^o©^Hto

1— 1

to

K

CDCO©»©i-iaOCO©©G*i-iTj<COC©i-HG*r-tCOG*G*r-i

fe

©

CO

s

o

■

c

1

©O»0©©»0©0©©00©©©0©©©©©

N^o^®©ftrtOr^n©r©rrreo"o?o?o?o?rt'*covdv

_^0_tO tOiOCOCOCDCOCOCOCDCOCOtrjcotatovOCOCOCD

a

§

q

r3:

©
©

CO

•*f,G*00G*Ort<0"}©r;*C^©G*00Q0'<tl<>»©0'H>»C©C0

*n!I\[

g*

•XBW

oooo"*G*©G*o6ao-<t<oo©G*"<*i©r-<ooj>.aoG*©ao
coco *>• t>» *>» i>. co vo t>.co l>»*>»l>»*>.t>»COCOCO *>» l>»C©

•XBJV[

t>»QOCi©i-«G<COTt4ir5«o*>»aOO,i©f-iO<CO'«*tir5«oi>»

©©©<-l,-4r-t,-l,-H,-i,-|l-.,-|,-lG*G*G*G<G*G*G*G*
000000000000000000000000000000000000000000

•SJB9
JO

£ IS

at Penzance, in Cornwall, for 21 Years.

179

w

o

w
0

■

1

acfi«Oriifl>Ortioxt>.HH05<^^rtict£io

b
Q

CO

ao

CO

3 -

ZT3

MWC5C0CCWCOWWCOWCOMWWCOWWWWW

o e8

^•9

iO
CO

B

pj.S

*p

is

ft

£
K

i— ( i— ( i— 1 f-1 r-H

25

CO

£

»0"5»0«0^>CN'>tr4W(N(^t>.G<COCOlNtO»C"5

i— 1 i— 1 r-\ i— 1

£

CO

co

WH«OOCOOMCOHKHN"*t>.«)COG<MNW*N

CO

*>.

CO

C0rtOHO«^K5OK5KJ6(C<5H*OG<OH(Srt

CO

3

CO

MNOrt^'WWJWOOlONOCON^OeOiOi-i^

w

CO

iO

W

O^O-^OO-fC^i-iCHr-tCOi-ii-HOOp-ipHOOO

w

25

O(£)O^irjC0CDHC0(HiO(£HOt>OtC©OINWrH

25

ft

nNcSrt^Hn^otHHiowHOHMweoojo

25

©

iO

EJ

o
S

H

1

iOiOOOOOiO^OOOO»0 »0 "O © © © iO © © O

8

©

CO

•uifl[

0*<^COCO©*©*COCO©*COCOCO©*©*COO*'*COCOCOTt<

•uijvt

0*

•XBJ\[

©Tj*rt<CO^"<tf',l*00©*-<tiaOaOCOCOiacO-'t|l>»COaO'*tl

'XBJtf

00

a

5

t»acft©iH(5<W'*»occt>.cioai©H(^«'*icc£n>

©©©r-IP-lrl^r-tp-l.-.r-.rHP-lC^O^^O^C^^O*. (5^

QOQOOOOOQOQOQOGOQOQOQOQOQDQOQOCOQOQOQOQPQO

•SJB3iC 15
JOJ

erf
W

CQ

s

►
o
ft

8

i

8

>-HCO'-i©,i©CO^iH0>>©^0©a>©*CiaO©CO'0*^.C>

b

Q

0*

Ol-'J'CJHOrrcOHOtOriOHOOrtlNO^irjCOi-i

o3

CO
*0
CO

OS.

o OS

©©©©©©©©©©©©©©©©©©©©©

25 •«

©

CO
CO

0?

S

■a

4

*

©ii5 0C5iM»OXO)»0»N^OiW©M^HQ<iHN

25 '

1*

£

ustorHwoo^oir-iH^oi^ccoai^tooiio^

t

©

00

co

ifJCOi-i©l>.^©^C^Tj<cC©QO(^kOCy5©^5QOCOp-i©

CO

©

CO

©Si©rt©NCO«(NH XtOMKNOONii©©^

CO

IR

W

CO

NN^H©»0^(^rtC<5>HN©»0'*©©^OHW

w

CO

»o

W

N^(60(HeOX5H05S«©KH^©©^©000

1 «

W

25

iOrtN^eO(CHU5^tfiHOyjX©l-irtO(NN'*

25

H©H©b.©©H!5»HHN«^l-IHO^lOO

*

5r

1
8

©00©©©»0©©©©©©©©kOiC©»OiC©

c

s
*

©

©©CCCO00ert©COC>*CO©a0'«*a0p-<0*©*'«t'a0CO©

•»!W

00

•XBJ^

^co^^aoc©<^coc^^ao©*ooao©Qoaoaot>.coco

XBJtf

CO

*

I
ft

t>»aocj>©.-<©*cO'«<*<»riCor>*aoa>©.-H©*cO'<*»ocot>»

©©©l-Ht-l.-H.-IP-r-l.-H.-i,-!,--.©*©*©*©*©*©*©*©*

xxxxxxxxxxxxxxxxxxxxx

I 15

L..

2 A 2

180 Meteorological Results of Observations made

u
6

A
1

6

sXsp a\iq

>-< QONONCOOCONCONtfi
COG^CO-'tCO'^TiHCOCOCOG*©*

SABp AJQ

*
<*

CO

sXup ^a^Y

sXBp }9jVY

stop jo
aoquin^

i-lCO—lOi-HOr-l^-lOr-lOi-'

CO lOCOCOCOCOCOCOCOCOCOCO

sjCbp jo
jaqurn^

©
CO

SA*Bp

WCO "3 CO CO — i tJ< CO CO *"» ao CT5

S^Bp
XuiBTI

CO

co

UIBJ
IBtUBJ

M^ao^iotoaoNONO

UIBI

SA*Bp A^SIJ\[

©*coco»o<-t"^©Q*coco<x>c£>

sXBp Xjsij^;

G*

sA*Bp

A*A\OUg

t>.00000000000

SABp

A.YYOllg

*>.

SJ3MOqS
AlOUg

©i-iOOOOOOOO^-iCOCO

SJ3M.oqs

AiOUg

CO

saaMoqs
IPH

G* ©* 0< ©* hN'*

SJLOAVOqS

©
©

SA*Bp

XjaMoqg

C0©*rf<a0r-i<£>O**CD00©i0
G«G<HrtH r-t i-i i-H CO CO CO

S^Bp

A\iaA\oqvj

co

0*

SiBAVOqS
JBIWBJ

i-i©*t>»GOQ*©*aaocoa>co"*

C£>iOCO<X>l>»l>»C£>QOGOI>»aOQO

saOAvoqs

JBpjBJ

ao
*>.

ao

VI

C

pUIAV

SuijiBAaij

fcajfcz; £ 25 ;z; 3 fc fc ;z;

pUIAi
§UqiBA3J^

21

£
a

>0 C) CT> *>• *>•!>. >0 00 CO CTi J>. CO

*

*

£

©

«2

i>.©*o<oao<o^H.-'C7iCi©.-<

03

W

as

CO
00

03

C}coaococo*^©*©©co'*i>»

J>. CO CO C?> !>. CO CO lOI.^OikJO iti

CO
GO

w

COt^O-f^t^OO*^-*^ iijus
CO"*t>»l>.QOC£)Tt<Tt<OiOiOTti

1 ©

CTSCOCTit^t^iO^tfSiOCOt^W

00

fc

iOC0»Ot>.C£)C75t>.a0C£>»O^iO H

<*

i

o
S

6

Bipaj\[

O'OOl'SiijuhqioOio'oO

co »o *-C-T qo . ©TifT ■* © *o oSco

'f'<t'*iO»CC£)(£)COtOkC'*,f

uinipaj\[

BUIIU}I\[

O->CO00©<©*iOC0©©*W00G*

uinui;uij\[ I 2?

cuurojQ

coaocoooTti©Tfo,i'*aoG*oo

lOtf3CO«OI>»0000l>.t>»COCO»O

uintuix«j\[ | ^

sq}UOj\[

A £ S <! S 4 ^ < » O 21 a

53 g

O 4*

at Penzance, in Cornwall, for 21 Years.

181

n

c

3

"*' CU

3 J

o o o © © o ©

CO Tt< "^ CO © CO CO

to gi ct>co oo co rH

FH ©^ r-T Tf rH © ©T

■

1

©

G^

©

»o

L

6

s

o

0)

Q

O iO to © »o © ©
© -tf Oi l>» 00 © 00
tO to G* "f Gl tJ< iO
OSG? CD CO tO Tpt^

B

c

tO

©

Gl

si
IS

tO © to © © © ©

co" ^ to *C oo gi oo

iO co to to iO CO "5

T3

s

*

©

in to to © »o © ©

t-C© CO 00 to © c£
^* ^V Hfl '^ ^^ iO '^

T3

B

tO
CO

•niH

Tf* *0 ^* "^ "^ "^ ^*

•Ulfl[

©

CO 00 © G* CTiCO ©
CO G* -* CO G* CO Tfi

•uih

00
Gl

•xbh

*>. 00 CO © »C © rH

COKCONN00N

•xbk

©

Q0

co -^ »o WCO 00 tO

iO >o to to to to to

•x«H

00
tO

fe-
te

.5 <* '

tO © © to "5 © iO
00 r^ |>. ~ 00 © pH
CO CO *>» ^ © CO CO
CO f-T Gl pf "* © tO

■
it

a

M

©

to

G^

£

B
cu

>
o

O to to © © © to
*>. to © i-i Gt 00 CO

tO 1^ CO CO to "^ CO

VI

E

M

CJ

a

M

tO

©

CO
CO

CO

si

.2 g

o 0)

$

§

tO» »0 © © © © ©
© to to CO iO "£" gT

«5 iO iO "5 iO »0 "5

1

a

©

CO

O © to tO to © to

^© 00 © Nto" ©
to to •* IO TjH "ft1 io

T3
i

©

•uijvi

© Gl ■* 00 00 00 ©
rf rft t£_CO "* CO "*

•inW

00
CO

© OJ 00 CO to rt< CO

•* CO CO CO CO CO CO

•°IH | co

•xbjvt

Gl OJ © Gl *>» ft CO
CO CO !>.!>. CO WCO

•xbh

G*

© 00 00 00 l>»CO CO
CO to to to to to tO

•XBH

©

CO

<

.9 «

11

03 —

© © © © lO © ©
© 00 00 © © r-i CO

CO CO or>co © — ' CO

■
o

s
)— (

»o

CO

gT

u."

0)

o

•*«

CJ

o

o tO © to © © to
NHritOOl^O
W CO G^ O^ © 00 r-^
tO tO 00 to to G? CO

CO
(V

a

M

tO

Ci

Gl

CO

SI

© © © © © to ©

© CO t-C to 00 © 00

>o ^ -* ^ <* iC >*

00

© iO to © © © to

tjT co~ i-T rjT -^ co" tj5"

to to to to to to to

1

tO

to

•uijv[

t>.CO 00 CO CO CO CO

CO CO CO CO CO CO CO

•uij\[

CO
CO

i-h CO 1>» C7i 00 CO Gl
•^ -rf CO CO CO "^ ^

•ufM

CO

*XBJ\[

t »C O0©t>.r1 Fl

CO CO n"5 CO CO CO CO

*XBJ\[

CO

t^ CO "^ ^ to to CO
CO CO CO CO CO CO CO

•XBH

to

CO

fj=

p

to © to © © © "5
OOO^hhCO
0* 00 Gl^CO CO G^
rlT Gl CO to CO Gl to

H

B

B
s

iO
CO

Gl

.n

a

-i-j
o-

O to to to © to ©
Gl CO "* CO CO .-h Gl

tO 00 CO rH|^ CO 00

^ i— t CO ^ Gl Tt< Gl

CO

1

a

©

CO

©

Gl

si

"So S

cu o»

£?=

•3

K)»0000>00
CO CT) co" to co" CO tC

6

iO

CO

iO © to to to © ©
©" C3? tC f-T OO © cc
CO to to to to CO to

©
00
tO

•«!JV[

>* Oi to Gl to tJH Gl

CO CO CO CO CO CO CO

•uih

Gi

CO

C75 tO CO © CO CO 00

^^ ^^ Tt^ TjH -"^H ^H ^H

•uim

©

.Ypr,T 1 CO 00 to Gl fH CO CO

xx*iM 1 io «: io to co w >o

•XBftT

CO

CO

Gl 00 t>. 00 Gl © 00
l>-CO CO CO *->. !>. CO

•XBH

Gl

C3
3
J-
-Q
CD

•§■§

OOU500W50
Gl -<* CO 00 © C75 ©
»0 ^ CT> Gl^l>» Gl^CO
© Gf CO CO G?"T i-T

CO

6

o

c

©
©

00
Gf
Gt

M
3

3

© © to © © to to

i>. © oo © -rt" i— i co

rf Gl © CO >-• r-i 00
"^ ©Is tC Gl CO Gl GT

CO

B

9

a

l-H

to

Gl

ii

bC £

1

lO U3 © © HO © ©

r-Tio co ccTio t-Coo

■^ "^ ^f "^h "^ ^ CO

3

S

to

© © to © © © ©

CO" r-n" CS9 r-T Gl CO" o9
CO CO to CO CO CO to

1

tO
CO

•uift[

G* CO Oi ^ "5CON
CO CO G* CO CO CO G*

•"!M 1 &

tO 00 00 CTJ Gl Gl ©
tO "* ■* "* to tO tO

•uih

00

*xbj\t

Gt "* G< 00 t^-CO ^

Li iO ^O O u"S iO iO

:**rt 1 s

CO t>» 00 Gl CO CO ©

•xbh

b

05
3
C

4

O "5 »o »o «5 «: o

Oi^J CO g CO © "*
t>T o? oo ^ CO CO "<f

en
B

o

B

»o

Gt

00

CO
G^

"3

©©©©©©©
CO *>• CO 00 i-h ■<*< to
CO © © f-H^CO Gl Gl

r-^ o9 co co © f-T gT

CO

cu

o

s

©

©
Gl

fe S

2 o
.2 S
bO C
ST a>

T3

© © © »o © © ©
io rjT o^ ti? »o i-H gT

■^ ^ CO ^ ^ ^ ^

©

CO

tO ©<©©©© to

© -^ <3^ p-T co -«f p-T

CO CO to CO CO CO CO

T3

©

CO

'*w

CO "^ t-^ © G* CO -^

G* CO G* CO CO Gt G<

*UII\!

G<

f-h Gl o> © C?5 Gl Gl
to to -^ to "^ »o to

•«iw 1 S?

•xnH

tf5 © -^f "^ ^5 »0 Tf"

iO >0 ifl "5 >C i(^ KJ

•xbjv[

iO

to

hhOh^KJM
!>. t->. t>. Ir^ 00 !>.!>.

*X«H | GO

•siua^

h S* CO Tf i(5 (O N
G< G* Gt G) Gt G* G*
00 00 00 00 00 00 00

r-i Gl CO ^ tO.CO t^
Gl Gl Gl Gl Gl Gl Gl
00 00 00 00 00 00 00

182 Meteorological Results made at Penzance, in Comwall,for 2 1 Years.

Annual Results for

7 Years.

o

2

Register
Thermometer

Rain in
inches

Years

Register
Thermometer

Inches

of rain

fallen in

each year

Wet

days

Dry»
days

Max.

Min.

Med.

Max.

Min.

Med.

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

55

58
66
67

72
80
84
77
72
65
60
58

24

27
32
33
38
40
49
48
40
37
33
28

43,0
44,5
46,5
48,5
54,0
59,0
61,0
61,5
58,0
54,5
49,0
46,5

26,825
22,800
27,135
12,735
21,450
15,020
20,740
24,475
24,060
39,295
36,305
42,075

1821

1822
1823
1824
1825
1826
1827

73

78
70
72
84
80
73

26

28
27
30
29
26
24

52,5
53,0
51,0
51,5
52,0
53,5
51,5

46,020
41,875
57,455
51,470
38,950
32,240
44,905

186

172
196
225
161
114
188

179
193
169
141
204
251
177

Max.
of 7
years

Min.

of 7
years

Med.
of 7

years

Inches
of rain
fallen in
7 years

Med.
of the
Max.

Med.
of the
Min.

Med.
of 7
years

Average

quantity

ofrainfor

7 years

Aver-
age wet
daysfor
7 years

Aver-
age dry
daysfor
7 years

84

24

52,0

312,915

75,5

27,1

52,0

44,702

177,3

187,5

The thermometers I use are two double registers, — one made
by Newman, and the other by Cary, — which are placed in a
north-eastern aspect, in such a manner as not to be acted
upon by reflected heat.

My rain-gauge is placed in my garden at the level of the
ground, entirely free from the influence of buildings or trees.
The gauge is exactly six inches diameter at the edge of the
brass rim at the top. The basin is made of pewter c2\ inches
deep. The tube attached to the basin is three inches long,
tapered to about £th of an inch at the point. The measure is a
glass cylinder graduated to a quarter of an inch of water, or
1 784T«o grains, nearly 1 784*796 grains.

Penzance, Jan. 18th, 1828.

Edwakd C. Giddy.

* Dry days are those on which no fall whatever takes place, — not the
slightest shower.

XXIX. Description

[ 183 ]

XXIX. Description of New Succulent Plants. By A. H. Ha*-
worth, Esq. F.L.S. SfC.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
TJAVING finished another new Decade, viz. the eleventh,
■*■ -t of new Succulent Plants, which may now commence a se-
cond century of them, I lose no time in forwarding it to you,
as under ; hoping it may soon find a place in your very useful
Annals.

The Decade contains, as usual, a regular and scientific dis-
tribution and description of ten distinct species of Succulent
Plants ; all, as far as my long experience enables me to deter-
mine, perfectly new and unrecorded. And no less than eight
of these fine plants are from our old and most productive
source, the Cape of Good Hope ; where Mr. Bowie, detected
them, and succeeded in transmitting them to the royal gardens
of Kew, where they are now flourishing, and where the de-
scriptions were made from the living plants.

Of the native countries of the two remaining plants which
constitute the Decade, I am not quite so certain. But if they
are not both from North America, one of them at least, viz.
the Yucca, is probably from thence, as the greater part of its
noble genus has been found there.

I remain, Gentlemen, yours, &c.

Chelsea, Sept. 1827. A. H. Haworth.

Decas undecima Plantarum Novarum Succulentarum.
Classis et Ordo. Pentandria Pentagynia.

Genus, Sedum Auctorum.
Sectio, * Acutifolia Nob.
viridulum. S. (small green) foliis suberectis lineari-subulatis
1. viridibus uno latere submucronulatis.

Nova species, ex horto Chelseiano, communicante
amico Dom. Anderson.

Obs. Patriam nescio, nisi Europaeam seu America-
nam, vix Asiaticam. Sub dio cum affinibus viget.

Obs. Sedo virenti affine ; et S. recurvato Willd. si-
millimum, at foliis paulo majoribus planioribus viri-
dioribus, et sine dubio obtusioribus, potiusve ad apicem
quasi a latere inferiore oblique truncatis. Minus est
quam Sedo anopetalo, atque viridius.

Genus,

184 Mr. Haworth's Description of new Succulent Plants.

Genus, Curtogyne Nob. in Revis. PL Succ. p. 8.
undosa. C. (reflexing-leaved) foliis ovato-linguiformibus cris-

2. pis, ramulorum florentium retroflexis.

Habitat ad Caput Bonae Spei, ubi in locis natalibus
invenit amicus Dom. Bowie, misitque ad regium hor-
tum Kewensem.

Floret Aug. G. H. ^ .

Obs. Simillima Crassula? albce Sims in Bot. Mag.
at major, floribus ut in ilia. Subpedalis ramosa, ramis
florentibus, calamo saepe crassioribus, et terram ver-
sus decumbentibus, apicibus assurgentibus. Folia
arete amplexicaulia decussata numerosa viridia : infra
flores imbricatim retroflexa, atque in aere aperto saepe
rufo-cincta: in ramis junioribus longiora magisque cris-
patim undosa, et saepe sesquiunguicularia. Etiam si-
mulat Crassulam undosam Nob. at major, magisque
undosa : sed post id locarem.

Obs. Squamula ordinaria ad lentem quadratim
truncata retusa pallida at cerina. Styli interne (len-
ds ope) cultrati et puberulo-ciliati.

Classis et Ordo. Pentandria Pentagynia.

Purgosea* (TuuGOSEANob. in Revis. Succ. p. 14.)

Crassula Thunb.
Inflorescentia spicato-thyrsoidea. Corolla 5-petala,
petalis basi laeviter imbricantibus, infra apicem mu-
cronulatis. Gcrmina intiis plana, extus gibba, squa-
mulis ordinariis emarginatis.

Sectio, Lingu^folia, foliis lorato-linguaeformibus
subacutis crassis.

pertusula. P. (small impress-dotted) foliis lanceolatis recur-

3. vulis supra subimpresso-punctatis ; bracteis summis
cordatis integris, scapo paniculato.

Habitat ad Cap. B. Sp. ubi invenit Dom. Bowie.

Florebat in regio horto Kewensi, Oct., Nov., &c.
A.D. 1824. G. H. %.

Obs. T. pertusce simillima, at plus duplo minor.
Folia radicalia subbiuncialia 4-5 lineas lata crassa pal-
lide viridia, rubro saepe inferne smTusa, minute cartila-
gineo-serrulata ; ad lentem parceque (florendi tempore)
impresso-punctata : (nee incurva semicylindracea im-
presso-punctata 4-5-uncialia, 9 lineas lata, ut in T.per-
tusd.) Scapus inferne longe ramosus, ramis simplicibus,
vix puberulus. Bractea? numerosissimae usque ad

* A voce vv^yosy Turns : wrongly printed Turgosea, in Revis. Succ.

30 paria,

Mr. Haworth's Description of new Succulent Plants. 185

30 paria, cordato-lanceolatae expansae internodiis lon-
giores ; imae remotae, superiores pedetentim magis ap-
proximate. Flores pauciores in singulo fasciculo quam
in C. pertusa, pedunculo saepe longiore. Corolla nivea
petalis erectis sed ultra medium revoluto-recurvis. Styli
basi collecti erecti, superne recurvo-patentes breves
pallide virides, stigmate (per lentem) hemisphaerico
limpido sive albo.

Obs. The specific character of C. pertusa will now
require to be altered as follows : — Foliis lorato-acumi-
natis incurvis semicylindraceis, bracteis superioribus
ovato-lanceolatis cartilagineo-serrulatis adscendenti-
bus ; scapo thyrsiformi.

Obs. T. pertusa is my ancient Aloe pertusa, taken
from Commeline (Vide Revis. PI. Succ. 15 & 201,
A.D. 1821); and it is also Crassula corymbulosa of the
same work, p. 10, (described from a bad and dead spe-
cimen) ; and likewise Crassula corymbulosa of Link's
HorU Berl. A.D. 1821.

Classis et Ordo. Decandria Pentagynia.

Genus, Cotyledon Auctorum.

Sectio, * Latifolia.

cuneiformis. C. (short, wedge-leaved) brevicaulis : ramosa :

4. foliis confertis obovato-cuneatis mucronatis subfarinoso-
albis.

Habitat ad Cap. B. Sp. ubi invenit Dom. Bowie,
ante ann. 1824.

Obs. Caudex brevis fruticosus valde ramosus. Folia
subinde (per culturam) virescent, sed saepe farinoso-
alba. C. crassifolice Nob. similis, at multoties humilior.
Flores non vidi.

Sectio nova, Villosul^.

interjecta. C. (fleshy-stemmed) foliis anguste oblongis acutis

5. inflexo- canal iculatis ; caudice brevi valido.

Habitat ad Cap. B. Sp. Dom. Bowie. G. H. ^ .

Flores non vidi.

Obs. Caudex teres adhuc 4-uncialis, tuberoso-ra-
mosus carnosus. Folia incurva crassa carnosa glau-
cescente-cinerea triuncialia, quinque lineaslata; subtus
convexa, basi semiteretia, sine carina, C. spuria proxi-
ma, sed altior,yb/z7s brevioribus crassioribus angustio-
ribus, magisque canaliculars, et sine dubio incurvis,
nee recurvis. In C. spuria, folia 4-5 uncias longa pe-
Nem Series. Vol. 3. No. 15. March 1828. 2 B tiolo

186 Mr. Haworth's Description of new Succulent Plants.

tiolo desinentia, 9 lineas lata recurva, et spatulato-lan-
ceolata. Viget in regio horto Kewensi, sed fiores non
vidi.

Classis et Ordo. Hexandria Monogynia.

Genus, Yucca Auctorum, et Nob. in Suppl. PI. Succ.
31, charactere novo ampliori.

Sectio, * * Filifer^; Nob. in loco.

puberula. Y. (pubescent, thready) acaulis: foliis lorato-lan-

6. ceolatis patentibus glaucis ; fibris marginalibus pauculis
fulvis : ramulis florigeris dense puberulis.

Habitat forte cum caeteris affinibus in America Sep-
tentrionali. Communicavit florentem mense Augusti
A.D. 1827, amicus Dom. Sweet, Horti Britannici;
Geraniacearum ; Cistinearum ; Flora Australasia? Ico-
num, Sj-c. Sf-c. utilissimus Auctor.

Obs. In sectione Filifer^e inter Yuccam glaucescen-
tem Nob. et Y. recurvam Salisb. Pa fad. Lond. 31.
speciem hanc conspicuam pro certo locarem. Folia
inflexo-concavula, deorsum ad costam magis magisque
incrassescentia. Sc'apus affinium quadripedalis ramosus
corymbosus, inferne magis bracteolatus ; jloribus laevi-
bus ovato-globulosis, pendulis lacteis. Petala lanceo-
lata, interiora longiora, fere duplo, atque quam aliis
latiora.

Obs. I believe Mr. Sweet received the fine plant
above described, in bloom, from Mr. Millar's nursery
at Bristol, the day before he brought it to me : and we
may soon expect a figure of it in his beautiful Hardy
Flower Garden.

Genus, Haworthia Duval in Cat. PI. Succ. in
Horto Alenponio, A.D. 1809.

Sectio, Margaritiferje.
clariperla. H. (small, bright- pearled) foliis subulato-acutis

7. undique praeclari-perlatis, perlis subtiis majoribus.

Habitat ad Cap. B. Sp. Etiam viget apud amicum
Dom. Hitchin, Nordovici, qui nuper viventem com-
municavit.

Obs. Inter H attenuatam et H.fasciatam apparet ;
priorem valde simulat sed minorem, perlis longe pul-
chrioribus et clarioribus, et subtus ssepe fasciatim
serialibus ; foliis longe brevioribus sive minus attenu-
atis. Forte H. fasciata? magis affinis, praecipue in
magnitudine. Fiores ut in affinibus. Ab H. attenuatd

distinguitur,

Mr. Ha worth's Description of new Succulent Plants. 187

distinguitur, perlis undique magis extantibus pulchri-
oribus; et ab H.fasciatd, foliis undique (nee infra
solum) perlatis.

Classis et Ordo. Dodecandria Trigynia.

Genus, Euphorbia Auctorum.

Sectio, Florispin^ Nob.

pentagona. E. (Cape, 5-angled) erecto-decumbens : dodran-

8. talis: spinis subsemuncialibus.

Habitat ad Cap. B. Sp. ubi invenit Dona. Bowie,
ante ann. 1825. G. H. $ .

Obs. Caudex adhuc pentagonus, diametro semun-
ciali, superne glaucescens, sulcis validis, et concinne
lineola exarata impressis. Spina adhuc trilineares ul-
traque, florigerae ut in Euphorbia enneagond Nob. cui
simillima, et ante id locarem.

Obs. Caudices in horto caldario, decumbentes at
grossi, apicibus assurgentibus, spinis citius marcescen-
tibus; et postea decidentibus affinium more. Flores
affinium, sed perfectos non examinavi.

Classis et Ordo. Dodecandria Monogynia.
Rulingia Ehrhart. Portulacca Linn.

intermedia. R. (thready, intermediate) foliis densissime nu-

9. merosis expansis planis, extus convexis ; apice retuso-
deltoidibus ; filamentis axillaribus tortilibus fulvis.

Habitat ad Cap. B. Sp. ubi invenit Dom. Bowie,
circa ann. 1823. G. H. ^ .

Obs. R. polyphylla Nob. in Suppl. PI. Succ. p. 63.
simillima, at duplo plusve minor, seu angustior, sed for-
tasse elatior. Etiam simulat R.Jilamentosam Nob. at
latior, foliis numerosioribus confertioribus pallidiori-
bus, pilis axillaribus fulvicantibus, nee albis.

Obs. Surculi saepius simplices subtrilineares, diame-
tro semunciali, incompte piliferi. Folia arachnoideo-
incompta, sordida, sive fusco- seu rufo-viridia. Flores
affinium.

Classis et Ordo. Syngenesia Polygamia Necessaria.
Genus, Cineraria Auctorum.

vestita. C. (cottony) subacaulis: lanato-vestita : foliis multi-

10. fariis subtereti-spatulescentibus planiusculis.

Obs. Caudex crassus, 2-3-uncialis, ramulis e terra
pullulantibus et demum caespitose crescentibus.

2 B 2 Folia

188 On the supposed Subsidence of the German Ocean.

Folia 3-4-uncialia varianter depresso-teretiuscula suc-
culenta, niveo laevi atque nitenti tomento, uti cau-
dices eleganter vestita, Kleinii tomentosi Nob. exacto
more, cui forsan ob multifaria folia affinis, sed non re-
sinosa ut in ilia. Foliorum majorum apices saepe plus
minus impressi potius quam planatim-spatulescentes.
Flores non vidi, sed secundum Dom. Bowie, corym-
bosi, et ut in Cineraria.

Obs. Cinerariam cacalioidem cui forsan simillima
appareat proxima.
P.S. — The Epiphyllum truncatum Nob. Sup. PL Succ. p. 85.
has, since that publication appeared, been figured on t. 696.
of the Botanical Register; and my friend Mr. Hood, about
the end of November last sent me, from his fine collection at
South Lambeth, a specimen, in bloom, of this beautiful plant.
And the following is a description of its remarkable flower :

Flos in medio apicis ramulorum terminalis, solitarius triun-
cialis subincurvulus elegantissimus, tubo cum germine subrect-
angulatim curvato. Germen nudum virescens truncatim
semunciale, subpyriforme, utroque carinulato, seu linea pro-
tuberante. Corollce tubus proprius satis crassus roseus ni-
tens, distanter petalino-squamosus ; et basi, calyculatus cum
foliolis reflexis oblongo-ovatis omnino corallinis coccineis, sed
inferne violascentibus. Petala propria^ numerosa, ringenti-
reflexa, calycinis foliolis valde similia. Stamina numerosa col-
lecta capillacea nitentia alba, apicem versus incur vula, peta-
lisque parum humiliora. Antherce (in nostro exemplo) ele-
gantes stramineae, sed exiguae; et (fortasse per Novembris
frigorem) sine fcecundante farina.

XXX. On the supposed Subsidence of the German Ocean.
By A Correspondent.

XT AVING only just met with No. 9, of Vol. II., for last
-*-•* September, of the Philosophical Magazine, it may be
useless, probably, (from the disputed point having been
settled,) to recommend that the following experiment should
be tried, in order to decide the hypothesis of Mr. Robberds,
on the former level of the German Ocean, viz. : A surveyor
should be employed to take an exact level from high water
mark of the present day — not the very highest tides, but a
mean spot of spring-tides — up to the furthest spot recorded
in Domesday, where a salina was situated, and then measure
down to the marine deposition, which, according to Mr. Rob-
berds, is found under an alluvial deposit. One composed of

fresh

Mr. Nixon on the Heights of the Hills of Dent, Sfc. Yorkshire. 189

fresh water arid marine shells intermixed. This deposit* may
naturally be allowed to mark the highest tide of those days. And
if it is found that the present level of high water is below the more
ancient one in the valleys, it is proved at once that the ocean has
receded at that particular district ; but if the levels are found to
be nearly the same, it will be proved that the sea has been ex-
cluded, and thus set the question completely at rest : at present
I lean towards the latter opinion, from circumstances in some
degree similar on the Kentish coast near Hythe. The sea was
known to have come much nearer the hills formerly, than it now
does ; but the level of the Military Canal proves that the level
of high water has not decreased, and that the change has taken
place by the formation, by the ocean, of natural barriers of
shingle, over which it very rarely flows, and even then in such
small quantities as to be harmless ; whilst the lower parts of
Romney Marsh are liable to inundations to a great extent when-
ever a breach is made in Dymchurch, or the other walls :
thus adding proof that the sea has not decreased on this coast,
but is kept out by natural and artificial boundaries.

It would add to the proofs, if the mean of the low water
level was also carried on, and the bottom of the ancient sandy
deposit bored to, and measured.

Sittingbourne, Feb. 4, 1828. , J. ,

XXXI. On the Measurement by Trigonometry of the Heights of

the principal Hills in the Vicinity of Dent, Hawes, and Sed-

bergh, in Yorkshire. By John Nixon, Esq.
[Concluded from p. 95.]
rj^HE vertical angles were measured by the horizon-sector,
■"* described in the Philosophical Magazine, vol. lix. p. 130.

At Noughtberry Hill the instrument stood upon a large
square board screwed firmly to the tripod of the larger theo-
dolite, and at Pen-y-gent it was placed upon the well-built
wall crossing the summit of the hill ; but at the other stations
a flag firmly fixed upon the signal-tower reduced to an alti-
tude of about four feet, formed the rude yet incomparable
stand.

Formerly the minute error of adjustment of the levels, which
was found to vary with the temperature, was ascertained when
on the point of setting out for the station, and a register of the
thermometer kept contemporary with the observations. To
this plan two objections existed : the error of adjustment might

* 1 mean the upper surface of the one Mr. Robberds mentions, in speak-
ing of the soil of the meadows and marshes ; as " the lowest bed of their
soil is sand in which marine shells are found."

have

190 Mr. Nixon on the Measurement by Trigonometry of the

have varied on the route ; and the thermometer would rarely
indicate the precise temperature of the levels, necessarily ex-
posed on bright days during a pair of observations alternately
to the sun and the shade of the instrument. Some time ago
the original levels were replaced by two superior ones (by
Dollond), with tubes so nearly cylindrical as to require little
or no correction for temperature*. To avoid the other source
of error, when the instrument had acquired at the station
the temperature of the air, the telescope was placed with-
in its Ys at a slight angle of elevation f. The left index being
then levelled and the angle of elevation read off, the telescope
was inverted, and the right index similarly levelled and read off.
The telescope was subsequently taken out of the Ys, and re-
versed in position, when the indices were once more levelled
and read off. With the levels correctly adjusted, the angle of
inclination would be the same by the four readings ; or if the
sum of the two angles read off before the telescope was reversed,
equalled that of the two succeeding measurements, a compen-
sation of error would exist ; otherwise one-fourth of their dif-
ference would give the mean error of the levels, additive to,
or subtractive from angles of elevation, according as the second
pair of readings exceeded or fell short of the first pair. Thus
at Dod Fell the readings were :

Left index and level ... 3' 30"; reversed ... 4' 15"
Right 3 45 3 50

Sums 7 15 8 5

Difference 0 50

Hence 12"\5 (= -^-) is the mean error of the levels additive
to the elevations. The inclination of the telescope, as given
by the left level, is 3' 52"-5; by the right one, 3' 47"*5 ; of
which the minute difference may arise from errors of division
and reading off. When the temperature had varied consi-
derably in the course of the observations, the verification of
the adjustment was repeated on their termination, and the mean
of the two values registered as the proper correction.

In addition to this variable error is the constant one arising
from an inequality in the size of the cylindrical rings ; the one
at the object end of the telescope exceeding the other by a
quantity which affects the elevations with an error of at least

* The bubbles are displaced one-eighth of an inch for a change of incli-
nation of 5", the angle to which the graduations (having a radius of about
15 inches) are read off.

f Had there been no risk of mistaking an elevation for a depression in
the readings with the telescope reversed, it might have been preferable to
have placed the telescope in a horizontal position.

Heights of the principal Hills of Dent, Sfc. Yorkshire. 191

— 11". As the observed refractions come out negative for
terrestrial arcs not exceeding 5', it is to be suspected that this
error, especially as it was determined by a method liable to
some objection, may have been undervalued. In the beginning
of the year, the graduated arcs (which had become bent from
improper packing) were repaired, and the divisions renewed.
At the same time, fine cross lines were substituted for the de-
licate filament extended diagonally from the original vertical
wire to the horizontal one ; an alteration which may account
in part for the refractions alluded to appearing negative ; — the
horizontal line being probably depressed, in order to avoid
the other extreme, some little below the summit of the ob-
served hill.

With regard to the adjustment of the cross lines, although
the line of collimation should in strictness be parallel to the
plane of the graduated arcs, as well as to the axis of the tubes
of the levels, it would nevertheless require a very gross error
in this respect to affect elevations or depressions not exceeding
3°. As the sector is fitted up with two divided arcs (one on
each side of the tube), each furnished with a moveable index
carrying a spirit-level, the one used with the telescope erect,
and the other with it inverted, — it becomes superfluous to ren-
der the line of collimation strictly parallel to the cylindrical
rings ; for the half sum of the readings by the two indices, when
corrected for the error of the levels and cylindrical rings, is
evidently the true angle. The transverse levels were adjusted
by bringing their bubbles to the marks (by means of the nuts),
whilst the planes of the arcs appeared to be parallel to a fine
plumb-line suspended nearly in contact with them.

As a preface to the regis-
ter of the observations it may
be useful to point out the re-
quisite corrections, and al-
lude to the errors and un-
certainties to which they are
liable.

Admitting the earth to be
a sphere, the difference of
altitude or level of any two
points on its surface ED will
be equal to their difference
of distance fom C the centre
of the earth, where the ver-
tical of D meets that of E.
Through E, perpendicular
to its vertical EC, draw the horizontal line EH ; and per-
pendicular

192 Mr. Nixon on the Measurement by Trigonometry of the

pendicular to DC, draw through D the corresponding hori-
zontal line DH'. The angle formed at E or D by the meet-
ing of a straight line passing through any point, and a hori-
zontal line situated in the same vertical plane, is termed the
elevation or depression of that point, according as it lies
above or below the horizontal line: thus the angles HED,
H'DE are both depressions. To find by trigonometry the
difference of altitude of DE, no more data are required than
the lineal distance EE' or DD', and the depressions HED,
H'DE; or, simply, either of them, provided we have also
given the terrestrial arc E'VE, or angle E'CE. Through C
draw a line perpendicular to the chord of equal altitude or
level E'E, which line, from the properties of the circle, will
bisect the contained arc (at V). Make EC parallel to VC,
whence VCE or half the arc will be equal to CEO. As
HEC and E'EC are both right angles, the horizontal line
EH will be elevated above the chord of level E'E by the angle
HEE' = CEC'= half arc. It is also similarly demonstrable
that the horizontal line DH' must be elevated above the chord
of level DD' by the half arc DCV' = VCE, and that the angle
D'DE, as the chords DD', EE' are parallel, will be equal to
DEE' the angular difference of level. The depression at the
upper station will consequently exceed the angular difference of
level by the half arc, and the elevation at the lower station will
be equally in defect; whence the depression must exceed the
elevation by the contained arc, and half their sum will be equal
to the angle DEE'. When both angles are depressions, that
at the upper station (or larger one) is the half arc plus DEE',
and the other is the half arc minus DEE', so that their sum
equals that of the half arcs, and half their difference the angle
DEE'. With this angle, the distance EE', and the angle
E'DE ( = 90° plus half arc*), we get the side E'D or difference
of altitude. When one only of the angles is given, the dif-
ference of the half arc and the. depression (considered as an
elevation when the former exceeds the latter), or the elevation
increased by the half arc, will give the angular difference of
level f.

Error of Collimation. — When the cylindrical rings of a
telescopic-level are unequal in diameter, the line of collimation,
supposed to be horizontal, describes, in a revolution in azi-
muth, the sides of a cone, erect or inverted, according as the
line passes below or above the true horizon to which the axis

* In the calculations, E'DE has been considered as a right angle.

f In latitude 54° the log. of the mean value of the half arc in seconds
may be found by subtracting the constant logarithm 2*308227 from the
log. of the distance in feet

of

Heights of the principal Hills of Dent, $c. Yorkshire, 193

of the cone will be perpendicular. This constant error might
be ascertained, were there no refraction, by reciprocal obser-
vations of the elevations and depressions. Let d e denote the
true depression and elevation; d1 e9, their values affected by
the error of collimation y9 and a the contained arc ; then, as it

has been shown that (e + a) = d, consequently 1 =

~ J "-^- will be equal to the error of collimation, to
be added to the observed depressions, and — — - the er-
ror subtractive. When both angles dT> are depressions, their
sum, it has been demonstrated, will equal the contained arc ;

hence - 9 or ° „— — will give the error of colli-

2 2

mation ; the depressions being observed in excess in the former
case, and in defect in the latter.

When the line of gravity, disturbed by local attraction, is
not in the direction of the centre of the earth, the line of col-
limation supposed to be horizontal, describes in its revolution
a plane inclined to the true horizon at an angle equal to the
deflection, and cutting it at right angles to the direction of the
disturbing cause. The elevations must therefore be in defect
in the direction of the attraction, and in excess in the op-
posite quarter of the horizon by a quantity equal to the incli-
nation of the planes to each other ; but in the direction of
their intersection the error of collimation will be null. When
the deflection ( g ) as measured on the vertical plane passing
through two stations, is the same at both and in one direction
(or parallel), the elevation and corresponding depression will

be equally in excess or defect, and Lzil_ Jf — £ wiU exceed

~^~ by gl but should the deflections be in opposite direc-
tions (or inclined to each other), a compensation of error takes
place, (d'fg2+(g~— being equal to ^—-. Admitting the line

of gravity to be disturbed at one station only, LjL|£_jL1 w\\\
differ from ~J~ e by — .

2 f 2

Refraction. — In the general state of the atmosphere the ele-
vations may be considered as increased, and the depressions
equally diminished by a constant ratio of the contained arc (a).
In this case, if d and e represent, as before, the true de-
pression and elevation, their values d! and e1 as affected by

New Series. Vol. 3. No. 15. March 1828. 2 C the

194 Mr. Nixon on the Measurement by Trigonometry of the.
the (positive) refraction r9 will be d — r and e + r. Hence
(e -fa) -rf^ or a'- J: — ^ wjji De tne refraction * ; but the an-
gular difference of level maybe obtained without previously
ascertaining the refraction or having given the contained arc,

DEE' being equal to —^ — , or to -^- — .

When the instrument, from some imperfection in its con-
struction, gives the elevations in excess or defect by an un-
known but constant quantity y, then will e* be equal, in the
former case, to (e + y -f- r), and d! to (d — y — r); but in the
latter case we shall have e1 = (e — y + r) and d'= (d + y — r) ;

whence — — , or — ^— , will be the correct angular difference

of levelf, and 2 , or <L^i_Z — * the refraction plus, or

minus the constant error of the instrument, according as the
elevations are in excess or defect J. Were the refraction a
constant ratio of the arc, its value, unaffected by the instru-
mental error, might be determined from reciprocal observation
on arcs differing in extent. Let (r ± y) be the observed re-
fraction for the arc a, and (V + y) that for the (much) greater
arc a! ; then (r' ± y) — (r ± y) will be the true refraction for
the arc («' — «).

Unfortunately for the accuracy of trigonometrical measure-
ments, it will frequently occur, especially on low grounds with
a cloudless sky in the spring, that a thin stratum of air in con-

* When the observations are not reduced to the ground, the refraction,
calling h the angle subtended by the sum of the heights of the eye at the

two stations, will be — , or 2 ■— .

d' 4- e
f When the height of the eye is the same at both stations — - — , or

<f— d7

— , will still give at once the angular difference of level /; for

a h. , C

whence d -f- «' = 2 / ;
and

or -£- + r — v / = D' ; whence d' - D'= 2/.

2^2

J When y is known, and the observations are not reduced to the ground,
the refraction will be equal to

(a + h + e' ± 2y) - <£ (a + h + 1y) - (<f + DO
2 , or to — 2 .

tact

Heights of the principal Hills of Dent, fyc. Yorkshire. 195

tact with the ground at the station is rarer in the heat of the day
than the stratum immediately above it, and denser in the morn-
ing and evening, than comports with the natural constitution
of the atmosphere. The refraction varies in consequence from

~ + x in the morning to x, its amount about noon,

and reverts in the evening to the first expression of its value.
Hence the refraction on similar days is perpetually changing,

and becomes a constant ratio of the arc (—} only twice in

the day ; viz. in the middle of the forenoon and afternoon, when
x or the maximum increment or decrement of the regular re-
fraction resulting from the passage of the ray through the dis-
turbed stratum of air, becomes 0. In such a condition of the
atmosphere it would evidently be impossible to ascertain the
correct angle for calculation from even contemporary reciprocal
observations, unless x and its horary variations should have
the same value at the same time at both stations.

On a careful consideration of the errors to which the determi-
nation of the angular difference of level is liable, we cannot but
admit that the least objectionable method of measuring the
difference of altitude of two hills is to make the requisite ob-
servations at an intermediate station. When the latter is equi-
distant from the former, so complete a compensation of errors
(that arising from local attraction excepted) is effected, that it
becomes superfluous to be acquainted with the error of colli-
mation (from whatever cause arising), or even the refraction,
although variable to a small amount, provided the two obser-
vations were nearly contemporary. But if we suppose the two
hills AB, and the intermediate station S, to be in a line and
equal in altitude, and admit the plumb-line to be drawn 10"
towards A, then shall we make A lower, and B higher than S

by about — * 1S ncc, and B will be calculated to be higher

than A by twice this quantity. As it may frequently be im-
practicable to have an equidistant station, we must select two
(or more) places ST, so situated that the distances S A + TA
may be nearly equal to SB + TB. In this latter case the error
of collimation and the refraction should certainly be known
approximatively; but great errors may be committed in this re-
spect without materially affecting the difference of altitude of
the two hills. When SA is more nearly equal to SB than
TA is to TB, the difference of level is probably more cor-
rectly determined from S than from T, unless S A + SB should
greatly exceed TA + TB. Hence the following correction :

2 C 2 Let

196 Mr. Nixon on the Measurement by Trigonometry of the

(CAi on -v

— y |-SAcv)SB), and g

the reciprocal of ( — - h TA cv> TB) : then if //' repre-
sent the difference of altitude calculated from the observations
at S and T, the correct value may be considered as equal to

•* 8 . The heights of two or more hills having been simi-
larly determined, it may be useful, in the event of being sta-
tioned on one of them, to observe the elevation or depression
of the others, with a view to learn the actual refraction. On
such occasions it is requisite to have given the instrumental
and adjustment errors. Adopting this method, the following
refractions were obtained : Arc Rep,

Gt.Whernside as observed from Pen-y-gent . 8' 50" + 4"*5

DodFell .. 10 24 +25

Noughtberry 13 34? +28

Pendle Hill Noughtberry 24. 42 + 1 -30

The refractions deduced from the reciprocal observations
are given below: Arc Refll

Between Whaw Fell and Noughtberry .... 1' 14"+ 6"

Dod Fell and Noughtberry 3 10+ 9

Whaw Fell and Whernside 3 21 — 18

Ingleborough and Whernside .... 3 41 — 9
Noughtberry and Whernside .... 4 6 + 2
Ingleborough and Pen-y-gent .... 5 16 — 6

Dod Fell and Whernside 5 45 + 4

Pen-y-gent and Whernside 6 54 + 1 1

Noughtberry and Ingleborough ...714+ 3*5

Dod Fell and Ingleborough 7 31 — 7*5

Noughtberry and Pen-y-gent .... 7 53 + 16*5
Mean arc 5'"6: Mean refr. + 1".

As the refraction resulting from observations made some
years ago by the same instrument ^on numerous arcs, several
of which were "of considerable extent, appeared to be about
1-1 8th of the arc, the refraction adopted in the calculations,
when not determinable from reciprocal observations, has been
1-1 8th minus the constant quantity 18". In addition to the
elevations being observed in defect after the substitution of
the cross lines for the filament, two other causes may be as-
signed for the smallness of the refraction ; — the ray, as the hills
were lofty and differed little in elevation, would be confined
to a stratum of rare air; and the observations were made (a
little too early in the year) about the warmest part of the day,

when

Heights of the principal Hills of Dent, tyc. Yorkshire. 197

when the variable part of the refraction is at its negative maxi-
mum*. The refraction between Noughtberry Hill and the
much lower hill Pendle, comes out, it is true, very considerable
(1-16*5); but as the day on which the observations were made
was of extraordinary clearness, which is generally attributed
to the rate of decrement of temperature in the atmosphere be-
ing much less than wanted, the refraction would in consequence
exceed its mean value.

The register of the observations will require explanation. —
The first column gives the time at each observation ; the se-
cond, the name of the hill of which the ground at the summit
(Pen-y-gent excepted) was observed ; the third, its elevation E
or depression D as read off on the left index ; the fourth, the
half difference of the corresponding reading by the right in-
dex + the constant error of the instrument and the variable
one of the levels, forming together what is termed the error
of collimation, additive to, or subtractive from the given read-
ing according to* its prefixed sign. (Were the graduations
perfect and the adjustments of the cross lines and levels un-
affected by variation of temperature, the error of collimation
should be a constant quantity.) The last column contains the
difference of level of the ground at the station (Pen-y-gent
excepted) and the summit of the observed hill, the latter being
higher or lower than the station according as the difference is
marked H or L.

At Whaw Fell.

Height of Eye 3-5 feet.

Sept.l5,llh 0™

Noughtberry H ill

1824. 11 5

Lovely Seat

11 10

Ten End

11 20

Bear's Head

11 30

Dod Fell

11 40

Ingleborough

13 0

Ingleborough

Mar. 29,15 25

Ingleborough

1825. 15 50

Ingleborough

15 10

Bow Fell

15 40

Bow Fell

Sept. 15, 11 45

Shunnor Fell

1824. 12 50

Shunnor Fell

12 0

Whernside

12 10

Berkin

13 25

Pen-y-gent, Wall

2° 46' 20" E.

-19"

0 25 40

-11-5

0 12 5

- 9

0 20 0

-11-5

1 11 25

— 4

0 46 32

-17-5

0 46 30

-16-5

0 45 45

+ 16

0 45 50

+ 11

0 45 30

+ 9-5

0 45 20

+ 21

0 35 30

— 9

0 35 25

- 6'5

1 35 20

-14

0 10 25

-16-5

0 34 40

-14

Feet.
372-6H.
377-1
82-4
184-0
356-8

537-9

388*8

V513-7

579-4
165-6
451-2

* The mornings were generally slightly frosty.

Height

198 Mr. Nixon on the Measurement by Trigonomet?y of the

Height of Eye 3-5 feet.
Blea Moor 0°29' 35"D.
Snays Fell 0 25 30

0 4 20

Ryssell

+ 6»-5
+ 11-5
-16

Feet.
74-8 L.
51-5
10-7

Sept.l5,llh35m

1824. 15 30
Mar.29,15 15

1825.

As the minute error of the levels was unregistered, the
greater part of the observations serve merely to verify those
made at the other stations. The refraction, although the Jila-
tnent was made use of, it was found necessary to consider as
1--18 minus 18".

At Ingleborough,

Height of Eye 4 feet.

Feet.

Junel7, 10h30m

Shunnor Fell |0° 7; 10"D.| + 10"

27-2L.

1822. 13 10

Lovely Seat [0 12 45 1 + 15
(Call the refraction for the above l-18th.)

162-8

July 2,

Colm

0 16 30

-21-5

122-6

1827.

Berkin

0 33 30

-22

376-5

NoughtberryHill 0 17 32

-22

170-5

Dod Fell 0 18 28

-22

186-2

Graygreth 0 49 2

-22-5

314-3

Blea Moor 118 5

-25-5

614-9

Pen-y-gent, Wall \0 13 35

-37

91-7

Bow Fell (dim)
Whernside

0 14 20

-37

148-4

|0 3 20 E.

+ 22

41-2H.

At Whernside.

Height of Eye 4 feet.

Feet.

July 4, 12h 55m

Wildboar Fell i0°10' 15" D.

- 2"

92-0L.

1827. 13 0

The Calf 0 16 32-5

+ 6

196-9

13 5

Bow Fell

0 22 40

+ 5-5

1 191-7

July 6. 14 10

Bow Fell

0 22 56

- 8

12 20

Colm

0 41 35

+ 1

1 163-3

July 4. 13 10

Colm

0 41 22-5

+ 12

13 50

Graygreth

1 10 35

+ 3-5

I 356*2

July 6. 12 30

Graygreth

1 11 10

-14

f \J\J\i *d

13 10

Shunnor

0 8 50

-12-5

)

14 40

Shunnor

0 8 52

-10

V 64-2

July 4. 13 45

Shunnor

0 8 30

+ 2

J

13 37

NoughtberryHill

0 30 52-5

+ 14-5

1 209-0

July 6. 12 45

Noughtber ry Hill

0 31 35

- 9

13 15

Lovely Seat
Dod Fell

0 15 50

- 2-5

197*6

12 40

0 25 20

- 7'5

224-7

12 0

Pen-y-gent, Wall

0 14 33

-15-5

131-0

12 5
12 35

Ingleborough
Whaw Fell

0 9 7-5

1 40 27-5

-11
- 4

41-2
582-2

At

Heights of the principal Hills of Dent, fyc, Yorkshire. 199

July 5, 15h35m
1827. 15 45

15 25

16 5
16 10
16 13
15 0
15 20

15
15

16

4

8

15

15 12
15 16
15 40
15 50

15 55

16 0

At Noughtberry Hill.

Height of Eye 4 feet.

Great Whernside
Pendle Hill
Dod Fell
Berkin
Whaw Fell
Blea Moor
The Calf
Lovely Seat
Bow Fell
Wildboar Fell
Wildboar Fell
Cotter Fell
Shunnor Fell
Pen-y-gent, Wall
Ingleborough
Whernside
Colm

Feet,

0° 2' 5"D.

- 1"

0 19 48

-15

0 5 5

- 4-5

16-lL.

0 20 50

0

205-7

2 50 55

-15

371-6

1 38 45

+ 6

445-6

0 3 22-5

- 1

14-5H

0 3 7-5

- 7-5

5-7

0 0 43 E.

4- 3-5

20-5

0 6 35
0 6 52

4-13-5
4- 3

\ 119-6

0 5 5

4- 1

122-4

0 9 6

4-10

143-0

10 1 30

4- 1

76-6

0 9 20

4- 5

170-5

0 26 25

4- 6

209-0

10 2 12*5

4- 6

48-4

At Pen-y-gent.
Height of Eye above the Wall 9 inches.

July 11, llh35ra
1827. 14 50

11 55

12 30
14 5

13 40

13 55

11 50

12 10
12 16
12 35

12 45

14 55

13 45

14 35

14 30
14 40

Ingleborough
Ingleborough
Whernside
Wildboar Fell
Wildboar Fell
Cotter Fell
Shunnor Fell
Colm
Bow Fell
Noughtberry Hill
Blea Moor
The Calf
The Calf
Lovely Seat
Penhill(Wens-

leydale)
Great Whernside
Great Whernside

}

0°

0

0_

0

0

0

0

0

0

0

0

0

0

0

0

0

0

6' 52" E.

6 50

7 17

4 52-5D,

5 5

5 37-5
3 12-5

6 20

8 12

9 6
51 27-5

9 12-5
9 25
8 52-5

27 5

2 43
2 48

4-
4- 7
4- 5

u

8-5

- 6
-11
-21
-12

- 4-5
-12
4- 6

- 8

- 1

- 9-5

- 8

-13

-11
-15

Feet.
91 -7 H.
131-0

47-6

47-8
69-1

}

30-OL.
53-7
76-6
520-2

53-5

65-9

At

200 Mr. Nixon on the Measurement by Trigonometry of the

AtDodFell

Height of Ey

Aug.25

,15h35m

Great Whernside

1827.

13 40

Wildboar Fell

13 55

Cotter Fell

14 5

Shunnor Fell

14 25
14 40

Noughtberry Hill
Colm

14 45

Whernside

15 5

Ingleborough
Pen-y-gent, Wall

15 20

14 15
14 20

Lovely Seat
Bow Fell

14 35

Berkin

15 10

Blea Moor

15 30

Penhill(Wens- >
leydale) $

e 4 feet.

0° 1' 15" E.
3 55

40
10
20
40

18 28
9 15
5 15

0 1 25 D.
0 0 35

0 16 7

1 6 40

0 25 0

Feet.

+ 16"

+ 20

139'OH

+ 20

142-6

+ 22

162-1

+ 22-5

16-1

+ 18-5

66-4

+ 20-5

224-7

+ 26

186*2

+ 23-5

95-0

-23-5

24-9

-22

39-5

-20-5

186-2L.

-21

429-2

-16

Calculation of the mean differences of Level of the Stations,

Whernside above Ingleborough.

Feet.
By reciprocal observation 41-2
By obs. from Pen-y-gent 39-3

— Noughtberry 38*5

Dod 38-5

Ar. mean 39*4 ; cor. mean 39*8

Ingleborough above Pen-y-
gent^ Wall.
By reciprocal obs. 91*7

By obs. from Whernside 89*8

Noughtberry93*9

Dod 91-2

Arithm. and corr. mean 91*7

Ingleborough above Nought-
berry Hill.
By reciprocal obs. 170*5

By obs. from Whernside 167*8

Pen-y-gent 168-3

Dod Fell 170-1

Ar. mean 169*2; cor.mean 168*9

Ingleborough above Dod Fell.
Feet.
By reciprocal obs. 186*2

By obs. from Whernside 183*5

Noughtberry 186*6

Pen-y-gent 186*7

Ar.mean 185*8; cor. meanl 85*7

Whernside above Pen-y-
gent.
By reciprocal obs. 131*0

By obs. from Inglebro'. 1 32*9

Dod Fell 129*7

Noughtberry 1 32*4

Ar. mean 131*5; cor.mean 131*4

Whernside above Nought-
berry Hill.
By reciprocal obs. 209*0

By obs. from Inglebro' 211*7

Pen-y-gent207*6

Dod Fell 208*6

Ar.mean209*2; cor.mean209*l
Whernside

Heights of the Hills of Dent, 8?c. in Yorkshire. 201

Wiernside above Dod Fell j Noughtberry Hill above Dod

Feet. I Fell Feet.

By reciprocal observation 24* 7 By reciprocal observation 16*1

Byobs. from Inglebro' 227*4 By obs. from Ingleboroughl 5*7

Noughtberry225*l — Whernside 1 5*7

Pen-y-gent 226*0 _ Pen-y-gent 18-4

Ar.mean225*8; cor.mean225*6 Ar. mean 16*5 ; cor. mean 16*3

Pen-y-gent, Wall, above Dod

Fell.
By obs. from Dod Fell 95*0

Ingleborough94*5

Whernside 93*7

Noughtberry 92-7

Ar. mean 94*0; cor. mean 94*1

Heights of the Stations above the Irish Sea at low water.

Feet.
Ingleborough* ......... 2374*6

Whernside . 2414*4 Feet.

Pen-y-gent, Wall 2283*0 (ground 2277*0).

Noughtberry Hill 2205*5

Dod Fellf 2188*9

Calculation of the Height of Whaw Fell.

Feet.
By obs. from Noughtberry Hill ... 1833*9

-J Whernside 1832*2 Feet.

Cor.meanl833*6

By obs. at Whaw Fell of Whernside 1835*0

Inglebro' 1836*7

. Pent-y-gent 1831*8

Noughtberry 1832*9

Dod Fell 1832*1

Cor. meanl 833*4

Height of Whaw Fell 1833*5

In the following table are given for each hill its height as
determined from the stations at the head of the column ; — the
claims to accuracy of the different values of the altitude being
considered in the calculation of the mean to be reciprocally as

* See Phil. Mag. for 1823.

f Observations made some years from hills chiefly in Wharfdale, gave,
Whernside 2412; Pen-y-gent, Wall 2281*4; Dod Fell 2189*8 feet.
New Series. Vol. 3. No. 15. Mar. 1828. 2 D the

202 Mr. Nixon on the Hills of Dent, fyc.in Yorkshire.

the distance of the station to the hill. The last column con-
tains the heights deduced from the observations at Whaw Fell.

Hills.

Height by Ob-
servation
from Whern-
side.

ep

O
C

I

c

c
5
be
>-,

c

b

o

O

Q

*£

O) i — i

C

*-> s

O cJ

Height by

Observations

from Whaw

Fell.

Shunnor Fell
Cotter Fell ...
Wildboar Fell
Colm

Feet.

2350-2

2322-4
2251-1
2222-7
2217*5
2216-8
2058-2

Feet.

2347*4

2252-0
2226-2

2211-8
2060-3

1998-1
1759-7

Feet.

2352-1
2330-8
2330-6
22530
2229.3
2229-6
2217*1

1762-8

Feet.

2348-5
2327*9
2325-1
2253-9
2226-0
2220-0
2211-2

1999-8
1759-9

Feet.

2351-0
2331-5
2329*0
2255-3
2228-4

2213-8
2002-7

1759-7

Feet.

2349-8
2329-7
2326-3
2252-4
2226-1
2221-3
2214-0
2059-2

2000-0
1760-3

Feet.

2347-2

2222-3

2210-6

2017-5
1999-1
1915*9
1822-8
1782-0
1758-7

Bow Fell

The Calf

Lovely Seat...
Graygreth ...
Bear's Head
Berkin

Ten End

Ryssell

Snays Fell ...
Blea Moor ...

Mean error...

-1-5

-0-9

+ 3-2

-0-8

+ 1-6

-2-7

Mean distance

43,892

49,632

73,462

36,051

44,745

32,930

At the Bear's Head the apparent elevation of Dod Fell,
measured by the 4-inch theodolite, was 43' 18", whence the
altitude of the former would be 2021 feet. At Ten End the
Bear's Head was elevated 40' 97, giving 191 1 feet for the height
of Ten End. The heights of Ryssell and Snays Fell are as
yet unconfirmed.

When the mean error of a number of Heights determined
from any particular station is considerable, it would appear to
argue that the altitude of the station had been assumed in ex-
cess or defect according to the sign and by the amount of the
error. But if the mean distance of the several hills to the
station should greatly exceed the mean of their distances to
the other stations, the error, as in the case of Pen-y-gent, may
with greater probability be attributed to a false estimate of the

refraction. Had we made use of —q minus a smaller quantity

than 18", the discrepancies would have disappeared.

On

Dr. Roget on a Violation of the Law of Continuity. 203

On another occasion I shall beg to add the results of a few
barometrical measurements, and furnish some geological no-
tices.
Leeds, Dec. 26, 1827. John Nixon.

XXXII. On an Apparent Violation of the Law of Continuity.
By P. M. Roget, M.D. F.R.S*

[Concluded from p. 121.]

nPHE severest test to which the validity of this mode of
T reasoning can be put, is to apply it to the purely mathe-
matical relations of space and quantity, to which, if the law
of continuity have any necessary existence in the nature of
things, it ought to apply with the greatest rigour. We find,
accordingly, that all the changes of magnitude in those quan-
tities of which the value is dependent on that of certain other
quantities, accompany corresponding changes in these latter
quantities in a manner strictly conformable with the law of
continuity. The same exact correspondence also obtains
with regard to the geometric relations of space, such as lines,
angles, surfaces and volumes. Thus, all the trigonometrical
lines which are functions of the arcs of circles, undergo regu-
lar and continuous changes, corresponding to the regular and
continuous increase or diminution of the arcs to which they
are related. Some, as the sine and cosine, pass from every
intermediate magnitude between nothing and a certain limit,
which they do not exceed, but to which, when the arc in-
creases uniformly, their last approximations are made with
extreme slowness. Arrived at that limit, they again begin to
decrease ; but at first with extreme slowness, like bodies that
are set in motion, from a state of rest, by the action of a
moving force. Their progress of diminution is by degrees
accelerated ; and is again retarded only when they are pre-
paring, as it were, to undergo some other change. By the
time they arrive at any of their states, either of maximum or
minimum, their rate or velocities of increase or diminution
have gradually been extinguished, and reduced to nothing.
Some of these lines, as the tangent for example, have no li-

* The former portion of this article was inadvertently reprinted in our
last Number, without having been previously submitted to the author; in
consequence of which, several inaccuracies in the original (now noticed in
p. 20b*,) were left uncorrected ; and the division having been made in an im-
proper place, the last paragraph of the former portion is here repeated. —
Edit.

mits

204 Dr. Roget on a Violation of the Law of Continuity.

mits to their increase of magnitude, and pass through every
possible linear dimension from nothing to infinity, while esti-
mated in one certain direction, characterized by the positive
sign. From positive infinity, the transition is made at once
to negative infinity, and the subsequent changes consequent
upon the further enlargement of the arc, consist in the gra-
dual diminution of the negative tangent; that is, of the line
estimated in a direction opposite to that which was assumed
as the measure of the original, or positive tangent. This ne-
gative tangent passes again, by the continuation of the same
process, into the primitive tangent, after having been again
reduced to nothing.

By considering, in like manner, the generation and the
course of curves of every kind, whether produced by the in-
tersection of lines, moving according to certain laws, or of
points whose motions are limited to certain conditions with
relation to other lines or curves, we shall find that the same
law of continuity obtains, both with respect to the changes of
magnitude and the changes of direction. No mathematical
quantity changes from positive to negative, or from negative
to positive, without either becoming infinite, or being reduced
to nothing ; and it passes through every possible intermediate
degree of magnitude, in its progress from the one to the other.
The change from increase to diminution, or the reverse, is
never abruptly made ; but is always effected by a transition
through a condition of momentary quiescence, which is the
limit of opposite kinds of changes, and at which instant no
actual change takes place.

Such being the universal law which is observed by lines
generated according to any given geometric conditions, we
should naturally be led, from analogy, to expect that the mo-
tions of points, having certain geometric relations to given
curves, would also be governed by the same law. Let us
take, for example, a small portion of any curve. This portion
will have, what is termed, a certain radius of curvature, and
the furthest extremity of this radius will be the centre of cur-
vature. In proportion as the curvature is diminished, this
radius will increase in length ; and the centre of curvature
will be removed to a greater distance. Its motion during this
gradual change will be along a right line, perpendicular to
the tangent of the curve at the point of contact. As the curve
in the change we are supposing it to undergo, approaches
more and more to a straight line, the centre will recede with
great rapidity ; till at length, when all curvature is lost, it
may be regarded as removed to an infinite distance ; and at

this

Dr. Roget on a Violation of the Law of Continuity. 205

this precise moment it is indifferent whether we consider it
as existing on the one side or the other of the tangent, with
which the curve has now coalesced. But we may suppose
the same power, whatever it be, which has effected this gra-
dual change of curvature, to continue its operation still fur-
ther. A curvature in the opposite direction will now take
place, and the centre of this curvature will be found on the
opposite side to that in which it had at first been situated.
Its motion, in proportion as the curve continues to follow the
same uniform progress of change, will approach the line from
a distance infinitely negative. All these successive changes
of position in the centre of curvature are perfectly similar to
those of the extremity of the tangent, during the increase of
the arc of a circle from nothing to the entire circumference
of the circle ; and are, in both cases, perfectly accordant with
the law of geometric continuity.

A case, however, has occurred to me, in which this appa-
rently universal and necessary law seems to be directly vio-
lated. Let the ellipse ADBE be the curve which is to be sub-
jected to the operation of the cause, tending, as in the former
instance, to diminish its curvature ; and let us trace the
successive changes which will ,

thereby be occasioned in the
position of the two foci, F, f.
A compressing force, for ex-
ample, is applied in the direc-
tion of the transverse diame-
ter, AC, BC ; or, what will
produce the same effect, a P-j
stretching force is applied in
the direction of the conju-
gate, or shortest diameter,
CD, CE. By the action of
either of these forces, the
form of the ellipse will be
brought nearer to that of a
circle, till it at length becomes a perfect circle, represented by
the dotted circumference. But it assumes this form only for
an instant, being merely the passage to another series of
ellipses, which, taking their rise from this circle, at first differ
but insensibly from it ; but afterwards gradually assume every
possible degree of compression, until they are ultimately re-
duced to a straight line at right angles with the transverse
diameter of the first set of ellipses. The former represent
circles that are elongated, the latter circles that are compressed

in

206 Mr. Ivory's additional Discussion

in one particular direction ; the two pass into each other by
a continuous series, of which the perfect circle is merely a term
of transition.

Let us now attend to the changes of position in the foci,
corresponding to these transitions. During the gradual change
of the first ellipse into the circle, the foci F, f, move along
the diameter AB, approach nearer and nearer to the centre
of the figure C, until they both coalesce in the centre. In
the next series of changes, we find them again separating
from each other ; but instead of moving in the same line as
before, we observe them starting off, each in a new direction,
CP and CO, precisely at right angles to their former lines of
motion, AC and BC ; and this change of direction is made
abruptly, per solium, and by an angular motion. Are not
these changes direct violations of the law of continuity ?

As the question which I have now proposed may be thought
deserving the attention of such of your philosophical readers
as are stimulated by the appearance of paradox to renewed
investigation; and as the attempts to solve it may give occa-
sion to the exercise of ingenuity, I shall abstain from suggest-
ing the considerations which might, perhaps, enable us to
explain this apparent anomaly, consistently with the univer-
sality of the law of continuity.
Bernard-street, Russell-square, P. M. RoGET.

November 1, 1825.

Errata in the last Number.

Page 118 line 23, for " operations," read " operation."

— 118 — 23, for " greatest," read " gentlest."

1 19 — 3, for " to," read " with."

119 — 32, for " rectilineous," read " rectilineal."

120 — 26, for " course pending," read " corresponding."

XXXIII. Additional Discussion respecting the Ellipticity of
the Earth as determined by Experiments made with the Pen-
dulum. By J. Ivory, Esq. M.A. F.R.S*
N deducing the figure of the earth from the observed
lengths of the pendulum, I have always thought it neces-
sary to leave out a few of the experiments that were incon-
sistent with the rest. The inconsistency is proved by com-
paring the pendulums on the same parallel, or nearly on the
same parallel; in which latter case a small correction must be
made for the difference of latitude. It is evident that, if the

I

Communicated by the Author.

pendulums

respecting the Ellipticity of the Earth, 207

pendulums when thus compared are excessively irregular, we
never can deduce from them, by any mode of investigation
whatever, any conclusion respecting the figure of the earth,
in which much confidence can be placed. On this ground I
always rejected such of the experiments as were irreconcile-
able with the rest ; and I thought this proceeding the more
justifiable, both because the experiments set aside were al-
ways very few in comparison of the whole number, and be-
cause those that remained were brought within the compass
of inequality to be expected in experimental quantities. The
results obtained on this principle, are already before the
public, and therefore need not be particularly mentioned.
My present intention is to solve the problem, by taking in all
the 40 experiments we at present possess, in the expectation,
that by this means some light will be thrown on this subject,
although my former mode of solution still appears to be
founded on sound principles.

In order to abridge, I shall begin with laying down the
general formulas of the mode of solution I follow. Put 39 + 5
for the pendulum in English inches at any station ; A, for the
latitude; 39+ A, for the equatorial pendulum; and/ for the
difference between the pendulums at the pole and the equator:
then A +/sin«A = 8.

Further, let G = 2 (&),

H = I (sin2 a),
K = 2 (sin4 A),
the sums being extended to all the stations of which the
number is n : then, by taking the sum of all the like equa-
tions at the n stations, we get,

±+"f=l (A)

Next, a being an approximate value of A, find an approxi-
mate value of / namely b, by substituting a for A in Equat.
(A) ; or, if b be an approximate value of / find, by means of
the same equation, a corresponding value of A , namely a :
then, if we put, A = a + 5

we shall have, 5 + 5T = 0. (B)

Again : Multiply all the terms of the first equation by the
coefficient of f: then

A sin2 A + /sin4 A = 8 sin2 A ;
and, by substituting the values of A and/

$ sin2 A + t sin4 A = sin2 A (8 — a — b sin8 A) ;

and,

208 Mr. Ivory's additional Discussion

and, by adding the like equations at all the stations,
Hs + Kt = 2 (sin2A(8 — a — &sin0~A));
and, by exterminating s,

(K - S!) t = 2 (sin2 A (8 - a - b sin2 A)). (C)

If sin2 X had exactly the same value at all the stations, the
coefficient of t in this last formula would be evanescent. In
reality this can never be the case : but if all the stations were
in higher latitudes than 45°, the coefficient would be so small
that a minute variation in the sum on the right-hand side,
would produce a great alteration in the values of s and t;
and, considering the uncertainty of the experimental errors,
the problem would be in a great degree indeterminate. Were
we in possession of no other experiments than those north of
Formentera, the figure of the earth would be very ill deter-
mined ; because all the pendulums might be sufficiently well
represented at the same time that the equatorial pendulum is
made to undergo considerable variations. The practical so-
lution of this problem requires many accurate experiments
between the tropics for finding the exact length of the equa-
torial pendulum; and likewise many experiments from the
tropics to the poles for ascertaining the value of the other
element,/ with the requisite precision.

Now taking all the 40 experiments in the table of my
former paper, I have found,

G = 3*91529
H = 16*25069
K = 10-47158:

hence, n being 40, by equat. (A)

A + -40627/ = -09788.
In order to find an approximate value of A, the six ano-
malous experiments must be reduced to the equator on the
same supposition as before ; namely, f — -205 : Then

A

Galapagos -01717

Ascension -01995

St. Thomas -02073

Guam -01912

Mowi -02136

Isle of France '02277 I

Sum ......... -12110

9 equatorial values of A in my former paper -11967 mean

15)":24077(-01605
By

respecting the Ellipticity of the Earth. 209

By substituting '01605 for A in the foregoing equation, we
get y= '2014. We now have,

a = -01605, A m a + s,

b = -2014, f = b + r:

and the equations (B) and (C) will give us,
5 + -40627 t = 0
3-869 t = (sin* A (8 — a - b sin2 X)).

Computing now the sum on the right-hand side of the last
equation, which sum consists of 40 terms, we shall find,

3-869 t = + '00307 ;
wherefore, r = -f -00079; s = — -00032;
/= -2022; A = '01573:

And we hence obtain this general formula for the length of
the pendulum, viz. I - 39-01573 + '2022 sin» A,

•2022 I

ellipticity = -00865 - ^^ = -00346 =^.

This result coincides almost exactly with what Captain Sa-
bine has deduced from his experiments. We have next to
examine, how the formula agrees with the phaenomena. Be-
ginning with the six anomalous stations, there is still an ex-
cess of gravity at them all, as will appear by the following
errors which must be applied to the observed pendulums to
make them equal to the calculated lengths ; viz.

errors. errors.

Galapagos . — -00144
St. Thomas - -00500
Ascension.. — -00427

Guam —'00355

Mowi — 00599

Isle of France —'00746.

The error at Galapagos is now very small, and, in all pro-
bability, smaller than the actual error of observation. At the
other five stations the excesses of gravity are still great ; and,
with respect to the like errors in my table, they appear to be
reduced nearly in the proportion of 3 to 4. But if some ad-
vantage be gained at the anomalous stations, there is a disad-
vantage at all the other stations within 50° of the equator on
either side. Within these limits all the observed pendulums
are uniformly short of the calculated ones, except at Port
Jackson and Jamaica, where there is a very small difference
of an opposite kind, which may be neglected ; and even, with
respect to these two stations, there is great reason to think
that the observed pendulums are both too long. Nor are
the deficiencies trifling, as will appear by the following list of
New Series. Vol. 3. No. 15. March 1828. 2 E errors,

210 Mr. Herapath on the Failure of Lagrange's

errors, which must be applied to the observed pendulums to
make them equal to the calculated lengths :

errors.

errors.

Paramatta. + '00212

Madras . . .

. + -00269

Rio Janeiro + -00266

San Bias . .

+ -004.18

Bahia. + '00161

Figeac

+ -00224.

Maranham . + -00399

Bourdeaux

+ -00323

Rawak + -00094

Clermont . ,

+ -00148

Trinidad . . + '00376

Paris ....

+ -00103

About 50° of latitude all the formulas very nearly agree with
one another, and with observation. In receding more from
the equator, the pendulums are shorter in the formula we are
considering, than in the others; but the effect of this is not very
perceptible except at the highest latitudes. At Port Bowen
and Spitzbergen, the errors are — -00239 and — -00302.

It appears then that, by lengthening the equatorial pendu-
lum, we approach a little nearer to the anomalous experi-
ments, and recede from all the rest within 50° of the equator.
The foregoing investigation proves that all the 40 observed
pendulums can never be represented, without great discre-
pancies, by any one ellipticity. In my last formula all the
pendulums, except the five anomalous ones, are placed on
one and the same surface within the limits of the errors of
observation. But no one pendulum within 50° of the equator
answers to its proper place in the surface of which the ellip-
ticity is =gj This surface is merely an imaginary mean, the

offspring of calculation. It can have nothing to do with what
is called local attraction : for it makes an excess of gravity at
five particular stations, and, as far as experience enables us
to pronounce, a defect of gravity every where else within the
limits mentioned.
Feb. 14. J. Ivory.

XXXIV. Failure of Lagrange's Method of integrating Linear
with Constant Coefficients*. By John Herapath, Esq.f

TF we suppose the roots r, rtf r2 of the equation
r3 + Ar2 + Br + C = 0

* It should have been mentioned in my last paper,that the constants in
(18) are not precisely the same as in (17), except the first two. In the other
terms several factors in the denominators were suppressed and understood
in the constants, for brevity and ease of printing.

f Communicated by the Author.

to

Method of integrating Linear with Constant Coefficients, 211

to be all equal, the three equations of condition, p. 23, which
are asserted, p. 96, to give the " complete integral " of

S- + A^ + B^ + Cj, = X (a)

by Lagrange's method will become

r2erx{dp + dp, + dp,} = X
dp + dp, + dp2 =0
dp + dpx -f dpi = 0,

giving obviously X =0. That is, the equations of condition,
which are said to furnish the " complete integral " of (a), and
which therefore ought to give all cases of the integral without
limiting the value of X, fix in the above instance the value of
this indefinite function to zero.

Any candid mind would not need a more decided proof of
absurdity in the principles of Lagrange's method than the
above ; but as some may think it dealing a little too summarily
with a process which has obtained so much celebrity, and may
prefer an instance of failure in result to a theoretical exposi-
tion of absurdity in principle, I submit the following, taken
not from any investigation of mine, but copied from a pro-
fessed advocate of Lagrange in the last Number of this vo-
lume. We are informed, p. 96, that the " complete integral"
of (a) is

« y _ erx{e+fXe-rsdx}
" r—r. . r—r

1 2

gr'x{cl+/X«-r'*d*} b)

r-r1.r1-ra

er*X{c2+fXe-r2Xd*}.„

Now this being the " complete integral," must give the
value of y whatever values be assigned to r, r„ r, and X.
Putting for simplicity X = 0, and then supposing r = r, the
above equation becomes

i r2x

rx c—cx ce

f " Ox(r-rc) ^ (r-«jR

that is, the value of y is infinite unless the arbitrary constants
c, c, are equal, or certain functions of r, rx. But c, cx being
in the strict sense of the word " arbitrary constants," are not
necessarily functions of x or r,r,; and therefore the infinite
value of y remains. We however know from other principles
that y may be finite.

E2 Lest

212 Mr. Herapath on the Failure of Lagrange's Method, Sfc.

Lest it be supposed that the failure of Lagrange's method
may be remedied by putting the pretended " complete inte-
gral " under the form of our (17), so as to take away the zero
divisors, and thus bring out the complete solution : I shall now
examine this point. For the sake of simplicity I will take an
equation of the second order only, the lowest to which La-
grange's method can be fairly applied ; and which from its
having but two roots, and therefore but one difference between
them, is peculiarly adapted to exhibit perspicuously the justice
or injustice of our observations.

If r, rx be the roots of the equivalent algebraic equation, the
" complete integral " is

rx r.x . rx f^r —rx . r, x /*■«■ — r, x ,

_ ce —c,e ' -fg ./ Xe dx—e ' J Xe l dx

Jr r —rl

And if we put X = 0

cerx-c,eriX rtx f (r-rx)x , rx/%(ri-r>J

y = —ce ' J eK dx -f cte J eK ' dx

AT r-rx

must be the " complete integral " of

dx* dx ^

But when r = r, the latter expression for the " complete in-
tegral " is

y = (c + c^xe**
which is evidently not the " complete integral," were it only
that c + cx makes but one arbitrary constant. The integral
by our formula (17) is

y = {cx + cx] erx
in which two arbitrary constants appear.

J. Herapath.

P.S. Since writing the above, I have examined with more
attention Lagrange's method, and I find that the solution (b\
which is professed to be taken from Lacroix's great work, as
the " complete integral " by Lagrange's method, is not strictly
the integral which this method gives. The result of La-
grange's contains less of absurdity than the above, but never-
theless fails to give the complete solution. I have not found
where Lagrange published his method, nor what examples of
it he gave. If that of Lacroix be one, it is a curious circum-
stance that he should fail both in method and deduction.

XXXV. On

[ 213 ]

XXXV. On Systems and Methods in Natural History, By

J. E. Bi cheno, Esq., F.R.S., Sec. L.S., $c* ' * ^]

J PROPOSE to myself on the present occasion to make
some observations on Systems and Methods in Natural
History; a subject of great importance at all times, but more
especially so at present, when new views of arrangement and
nomenclature are proposed, and to some extent adopted. Let
me not be understood, however, in the general observations
which follow, to be opposed to any particular system; my ob-
ject being to discuss the first principles of arrangement, and
to leave others to judge how far they are applicable to the views
adopted by any individual systematist.

It has appeared to me that the difficulties of the subject
have not been duly appreciated ; and the time cannot be un-
profitably occupied, if I accomplish no more than to enable us
to estimate them. It might even be suspected, from the readi-
ness with which new systems are adopted, that they have a
peculiar attraction for ardent minds ; as it has not unfrequently
happened that young naturalists have found themselves pre-
maturely embarrassed in a subject, which of all others requires
not only an extensive acquaintance with the operations of the
human mind, but long experience and various practice. The
line of argument I propose to employ, must necessarily be
somewhat abstract; yet I hope I shall be borne with, since
the practical naturalist could make no accumulations to his
science, and all his particulars would stand unconnected and
discrepant throughout, without the aid of abstract reasoning.
Besides, I am anxious to engage the attention of persons ac-
customed to turn their observations to the operations of the
human mind, and to the instruments which it employs to per-
form its labours; feeling assured that, by obtaining the co-
operation of this class of philosophers, we shall have great
light thrown upon our subject ; and that it will be one means
ot attracting the notice of those who delight in a large and li-
beral treatment of science. While they impart to us a philo-
sophical solidity, in which I am apprehensive we are wanting,
we may hope to communicate to them a reciprocal benefit, in
some of those graces and charms to be derived from the study
of Nature, and in which perhaps they may be deficient.

Without undervaluing the study of species, upon which a
great deal of our knowledge is built, it cannot be denied that
naturalists in general have been too often content with assign-
ing them names, and a place in the systems they have adopted ;

* From the Transactions of the Linnean Society, vol. xv. Part ii. p. 471.

and

214 Mr. Bicheno on Systems and Methods

and this they have done without having an ulterior view to
their structure and functions, and the relations subsisting
amongst them. Much less have they kept in view the end of
generalizing the particulars they are accumulating ; but they
continue to heap together a " rudis indigestaque moles" until
they are actually overwhelmed by their materials. To build
up science skilfully, the combination should go on with the
collecting, or the superstructure will exhibit neither use nor
beauty.

Mr. Roscoe has clearly illustrated,'the comparative merits of
the artificial and natural arrangements in Botany in a former
volume of the Transactions * ; and has satisfactorily proved,
in my estimation, that however admirable and comprehensive
the system of Jussieu may be, yet it ought not to supersede the
use of the Linnaean arrangement. The two great masters of
botanical science propose different ends, and ought not to be
regarded as rivals. The President of this Society has also
constantly pressed upon the attention of the student the same
important fact.

In some respects it is not to be regretted that the absolute
sway which the name of Linnaeus has had among English na-
turalists is somewhat abated : for although authority is an ex-
tremely useful bond of union, and has in this instance esta-
blished among us a nomenclature which nothing short of ho-
mage to the founder could probably have made current, yet it
has brought with it the ordinary evils attendant upon great
names. The range of the pupil has been limited by that of
the master ; and it has been considered a species of hetero-
doxy to dissent from the established opinions. The danger
to be now apprehended is, that those who adopt other arrange-
ments will forget the advantages to be derived from what is
old, in their love of that which is new.

In addition to the remarks made by Mr. Roscoe and the
President, I would beg leave to suggest to those who adopt
new systems, — and in adopting them think it advisable to break
up the old orders and genera into many new ones, — that the
artificial and natural systems aim at two very distinct objects,
which are in some measure incompatible with each other. The
one is to make us acquainted with individuals : and the other,
founded upon an acquaintance with individuals, to combine
them according to their characters, so as to abridge the la-
bour of reasoning, and to enable us to ascend from particular
to general truths.

In order to assist us in these investigations, we employ cer-
tain words in a peculiar sense. Thus the word Species, when
* Trans. Linn. Soc. vol. xi. p. 50.

used

in Natural History. 2J5

used by naturalists, has a more confined signification than the
same word when employed in scholastic language. We have
agreed that a species shall be that distinct form originally so
created, and producing by certain laws of generation others
like itself: whereas all that logicians have meant, is a number
of objects bearing a certain resemblance to one another, and
on that account denominated by a single appellation, which
may be employed to express any one of them. This term is
the creature of art, to help us up the first step of generaliza-
tion. By its assistance we propose to reason upon all the in-
dividuals conforming to the law we have laid down, as safely as
we can do of any one of them. There is this inconvenience at-
tending the use of it by naturalists, that it assumes as a fact, that
which in the present state of science is in many cases a fit sub-
ject of inquiry; namely, that species, according to our definition,
do exist throughout nature. It is too convenient a term to be
dispensed with, even as an assumption ; only care should be
taken that we do not accept the abstract term for the fact.

It might, for instance, be proposed as a legitimate question,
whether the species of some familiar genera, such as Rosa,
Rubus, Saxifraga, do not run into one another by impercepti-
ble shades, unappreciable by human sense, in the same man-
ner as certain genera melt and intermingle their characters, so
as to render it impossible to circumscribe them. Indeed, the
extent to which species-making has been carried in modern
times, almost leads to this conclusion. Visible and palpable
distinctions are in many cases no longer relied on ; and there
are many acute naturalists, who, without bringing the subject
to the test of experiment, are content to rely on those empi-
rical characters, which can only be perceived by long and fa-
miliar experience, and cannot be described by words. The
truth is, that all sensible objects have characters which leave
impressions upon the mind, without our being capable of em-
bodying them in language. We are all aware of this when
we speak of tastes, and tints, and the countenances of our
friends. Every-body perceives them, yet nobody can com-
municate to his neighbour his perception of their differences.
Thus botanists speak of certain species of plants differing in
appearance, habit, touch, &c. ; by which they often mean that
they have some indescribable peculiarities about them, which
point them out to the practised observer as distinct. A great
number of such species may be detected in every modern Flora
of a well investigated country ; but whether they deserve to be
ranked among those which are capable of definition, is a ques-
tion of great doubt : — that the practice is an inconvenience,
none will deny ; and if it be much longer continued, will in-
volve

216 Mr. Bicheno on Systems and Methods

volve in inextricable difficulty all our well known species, make
us dependent upon empirical and traditional evidence for our
acquaintance with them, and render it impossible to derive in-
struction from books. In such cases the assumed law ought
to be brought to the test of experiment, or the species should
be rejected.

Many of our cultivated plants also tend to invalidate the
law. Who can refer our cerealia and esculent vegetables, in
many instances, to their true types ? and how few of our old
flowers are there, of which the astutest botanist can trace the
origin ! Domesticated animals afford a still more striking
example ; and man himself furnishes the most difficult pro-
blem of all.

These remarks and examples are, I apprehend, sufficient to
show how difficult it is to adopt the term in its strict accepta-
tion ; and that however precisely the naturalist has attempted
to employ it, he has not succeeded to the extent he has pro-
posed ; and that it can only be taken as correct in a vague
and general sense, and as a convenient abstraction to relieve
him at the first step from the necessity of becoming acquainted
with every individual.

The next term of importance to the naturalist upon which
the accuracy of his reasoning depends, is that division of his
system which he denominates a Genus, This is an assemblage
of individuals agreeing also in some common characters ; but,
unlike the word species, it is not previously defined. Thus
much indeed has been thought requisite; that in botany these
common characters should be taken from the parts of fructi-
fication, and in zoology from such parts as are indicative of
structure and habits. " A genus should furnish a character,
not a character form a genus." We are not here, as in the
word species, precluded from inquiry by a previous definition.
Though both words are terms of generalization, there is the
same difference between them, as instruments of reasoning, as
between a definition and a proposition in geometry.

The species includes all the characters which are in the
genus, and those likewise which distinguish that species from
others belonging to the same genus ; and the more divisions
we make, as order, family, class, it is intended that the names
of the lower should become still the more comprehensive in
their signification, but the less extensive in their application
to individuals. Naturalists by this invention, which is not
exclusively their own, have it in their power to contemplate
and reason upon these separate characters, with all their conse-
quences, as if they existed independently of species ; as by the
use of the word species they are enabled to look at their pe-
culiar

in Natural History. 217

culiar attributes independently of individuals. This faculty
of the mind, which is one of the most curious that belongs to
it, has given rise in all languages to a multitude of words of
the same kind as the names of genera in Natural History ;
words, which do not express individual existences, but are
abstractions of qualities and characters belonging to them *.

All general reasoning in morality, law, politics, and even
mathematics, depends for its accuracy upon the proper use of
generic and other abstract terms. In mathematics they admit
of exact (or I would rather say more exact) previous defini-
tion; and hence arises the accuracy of deductions the most
recondite and remote in that science. In the other sciences,
which are of a speculative and contingent nature, these terms
are employed not with the same precision, but seem to be the
result of our necessities, borrowed from sensible objects and
analogy, and frequently indeed from accidental coincidences.
They derive their force rather from the character of the mind
that employs them, than from any exact definition they may
have received ; and it seems impossible to make men use such
words in a common acceptation. Hence it is, I apprehend, that
knowledge of a speculative kind so soon finds its limits; and
where at its outset it has promised such glorious results to
mankind, as long as it floated in general propositions, the same
subject eludes the grasp of the human faculties when it is at-
tempted to be reduced to exactness, and leaves something al-
ways to be desired. We are constantly approximating to the
truth, yet never reaching it.

It is sometimes asserted, but not correctly, that Natural
History, by the aid of its terms, partakes of the nature of ma-
thematical truth; or that it lies intermediate between that
science and speculative knowledge. The situation of the na-
turalist is rather this. He finds himself placed amidst an in-
finite number of unknown particulars ; and in order to facili-
tate an acquaintance with them, he at once, without regarding
individuals with much minuteness, throws together a number
of them, which he calls a species, according to an assumed
hypothesis. These he attempts again to combine by certain
external characters, and calls them a genus. By these means
he is enabled to contemplate and treat of them, without being
utterly bewildered in the labyrinth of unarranged individuals.
Classification is his^filum Ariudneum. It was but imperfectly
understood by the ancients ; and has enabled the moderns to
arrive at conclusions with much more expedition than they,

* I would avoid here, and leave the question to be decided by the
reader, after he has consulted Locke and Berkeley, whether we have got
ideas corresponding to these abstract terms, or whether they are mere
signs, like #, yy and z, in algebra.

New Series. Vol. 3. No. 14. March 1828. 2 F and

218 Mr. Bicheno on Systems and Methods in Natural History.

and with equal safety. It does that at once which is constantly
going on in ordinary language, — the modifications of it to ex-
press the classes of external objects. The invention of new
terms suited to express new ideas in an abridged and com-
pressed form, is a slow process, and in most cases is the re-
sult of convenience. There is no convention to attain the ob-
ject, because nobody can arrest the subtile means that are
employed. But the naturalist being without terms, or at most
with so few that they are within his power, attempts to anti-
cipate the slow process usually working in language, and forms
at once his instruments of reasoning; and systems and me-
thods can be regarded as no further useful, than as they are
assimilated to the ordinary process of abridging the labour of
thought adopted by mankind in other subjects of a like nature.
Naturalists err greatly who imagine they are employing
terms possessing some new and distinct properties ; whereas all
they can do is to hold the subjects of natural history together in
a loose manner by the use of the words species, genus, order, and
class; thus presenting certain characters to the mind as se-
parate objects of contemplation by means of abstract terms, of
a similar though somewhat more precise import than those
which are employed by the rest of mankind in treating general
subjects. A stricter use may be made of these words by na-
turalists than by metaphysicians, because the business of the
one is to examine characters and qualities more nicely than
the subjects entertained by the other will admit of. Never-
theless, the one cannot employ these abstractions as instru-
ments of reasoning in a different sense from the other. There
is no magic about them in the hands of a naturalist more than
there is in any of the thousand general terms in the mouths of
the vulgar. " Rose " and " Grass " were generic names be-
fore the flood, and will continue to be so in spite of systems
and methods. The naturalist has attempted only to carry
this necessary operation of the mind somewhat further and
with more precision, and has thus exposed himself to errors,
which the vulgar have escaped. Thus, although there are but
two modes of reasoning ; namely, by the use of words expres-
sive of an individual and its attributes, or by general words
indicative of an aggregation of individuals with their common
attributes ; yet naturalists have used their terms in a different
sense, and have invented additional ones, such as order, tribe,
cohort, family, class, by which they attempt to express with
more accuracy larger generalizations than they would do by
employing a generic term, and as if they could settle the re-
lative rank of the different groups whose existence they have
assumed. Whereas the truth is, that in many instances a
class may be equivalent to an order or a genus. These dif-
ferent

Tredgold on the Steam-Engine. 2 1 9

ferent gradations, thus strictly aimed at, are gratuitous assump-
tions with which Nature has nothing to do; and which fre-
quently lead to the establishment of fake hypotheses.
[To be continued.]

XXXVI. Notices respecting New Books.

The Steam - Engine : comprising an Account of its Invention and Pro-
gressive Improvement, with an Investigation of its Principles and the
Proportions of its Parts for Efficiency and Strength ; detailing its
Application to Navigation, Mining, impelling Machinery, Sfc. with
20 Plates and numerous Wood-cuts. By Thomas Tredgold,
Civil Engineer, Member of the List, of Civ. En. fyc. Price 21. 2s.
4to. Jos. Taylor.

A BRIEF analysis of the contents of this valuable work will give
our readers some idea of its utilitj', as well as of the immense
degree of labour necessary to collect, arrange, and reduce to their
elementary principles, the various phaenomena concerned in that
master-piece of human contrivance, the Steam-engine. In so doing,
we propose to follow, in some degree, the author's statement of its
contents in his Preface j with the addition of many particulars he
has not noticed in that short summary.

The work is in sections. The first contains a short history of
the invention and improvement of the steam-engine, the inventors
being noticed in the order of "the dates of their first essays, com-
mencing with the Marquis of Worcester, and closing with Woolf
and Oliver Evans : a short sketch is added of the rapid progress of
the application of steam power ; and the section concludes with the
remark " that the whole tends to prove that the steam-engine, in
the highest state of perfection it has yet attained, is entirely of
British origin. The remark extends to the discovery of physical
principles, as well as of mechanical combinations. No new princi-
ple, nor no new combination of principles, has yet been derived from
a foreign source, the most perfect of foreign steam-engines being
professedly copied from British ones, and not unfrequently manu-
factured by British workmen."

The second section treats of the nature and properties of steam,
its elastic force, expansive force, and motion ; first stating the ge-
neral principles of the equilibrium of heat, the phaenomena attend-
ing a change of state, and a comparison of the best experiments on
the quantity of heat required to convert bodies into vapour or steam,
with the necessary formula for the comparison. The elastic force
is next considered, with the principles which guided the author in
his choice of a formula for a case where empirical means are neces-
sarily employed: and here we remark for the first time a formula for
the expansion and expansive force of water, free from the objec-
tion of becoming negative in either high or low temperatures. The
connection between the boiling point of sea-water and the force of
its steam is treated, and a simple formula for the force of vapours
is shown to apply to those from various fluids, wtfh the necessary

2F2 correction

22Q Notices respecting New Books.

correction of the constants. — The mechanical power of compressed
gases is examined ; and it is inferred,that the steam of water possesses
greater advantages for use in an engine, than the vapour of any other
liquid. — Rules are next given to find the volume the steam of a
given quantity of water occupies at a given force and temperature ;
the laws of the mixture of steam and air, as in the air-pump of an
engine; and the laws of the motion of steam in the passages, &c. of
engines, with the loss by cooling ; and a curious inquiry respecting
the temperature of condensation which affords the maximum of
useful effect in the old atmospheric engines ; illustrated by a re-
ference to Mr. Watt's experiments, with a model of one. The sec-
tion concludes with the investigation of the formula for the escape
of steam at safety-valves.

The third section is on the generation and condensation of steam,
and the apparatus required j first treating of combustion and com-
bustibles, with an extensive table to show the relation between the
heat afforded by bodies, and that which their constituent elements
would give : then the conditions favourable to the process of com-
bustion are considered, and the quantity of the gaseous products,
with rules for the supply of air, and size of chimneys. The relation
between the surface of boiler to be exposed to heat, and the quan-
tity of steam to be generated ; and of the capacity of the boiler to
the effective power of the engine, are also exhibited, and compared
with practice ; and then rules given to fulfil the essential conditions.
The different species of boilers, fire-places, safety-valves, and other
apparatus, are then described ; and the section closes with the prin-
ciples of condensation, the quantity of water required to produce
it, and a tabular view of the methods that may be used, referring
to the dates of the first use of them in the steam-engine.

The fourth section commences with a popular illustration of the
nature and modes of obtaining- the power of steam, and their relative
advantages 5 next, proceeding to show how to calculate the utmost
effect steam can possibly afford to produce rectilinear motion ; and
afterwards its effect in rotary engines, — showing the loss of effect in
the latter to be constant, and in some cases very considerable. The
modes of applying the power of steam are classified, with their com-
binations ; and then the laws which determine the relations of the
parts for cylinder engines, so as to afford a maximum of useful effect
with a given quantity of steam ; the capacity of the air-pump, and
the power lost in working it.

The fifth section treats of the proportions, power and constructions
of noncondensing engines, usually called high-pressure engines,
showing the causes of loss of power, and the means of estimating the
quantity of loss ; the best proportion for cutting off the stroke when
the steam acts expansively -, and the theory of combined cylinder ex-
pansive engines.

The sixth section treats of condensing engines. After a general
view of their nature, and a classification of the methods of construc-
tion, the proportions, causes of "loss, and the power of the atmo-
spheric engine are investigated j and also in its combination with a

separate

Tredgold on the Steam- Engine. 221

separate condenser. The steam-pressure engines of Boulton and
Watt, both single and double, is next considered, with the construc-
tion of them either for expansive action, or not, and all the causes of
loss of power, and the proportions of the parts in detail j also the
combined engines of Hornblower and Woolf are treated of in a simi-
lar manner.

The seventh section is occupied by the construction of the parts
common to most engines j as valves, slides, pistons ; with the mode
of estimating their friction, methods of moving valves, &c. cranks,
parallel motion apparatus, and practical rules for the strength of the
parts of engines, with the conditions necessary for safety in boilers,
and the mode of estimating the effect of irregular expansion on the
strength of boilers of cast-iron, — closing with the methods of joining
the parts of engines together.

The eighth section is on equalizing the action, regulating the
power to the effect, measuring the quantity of useful effect, and ma-
naging the working of engines j describing, with investigation when
required, the fly and counterweight to equalize the action, the throttle
valve, Field's valve, #ie conical pendulum, the regulator and the ca-
taract to regulate the power j and the gauges, indicator, and counter,
to show the state of the parts, and how by friction the useful effect
of any engine may be measured at a trifling expense j and lastly,
the circumstances to be chiefly attended to in working the engine.

The ninth section is on the application of the steam-engine to va-
rious purposes -, first, generally to raising water, then its particular
cases, as the drainage of mines, the supply of towns, with a table of
the supply to towns in ancient and modern times ; secondly, to im-
pelling machinery for manufacturing purposes j thirdly, its applica-
tion to agricultural purposes 5 and lastly, its application to steam car-
riages.

The tenth section is on steam navigation, treating of the longitu-
dinal and lateral stability of vessels, and the resistance of vessels ; in
the latter inquiry a new theoiy of resistance is adopted, which ap-
pears to give results nearly according with practice. The various
modes of propelling vessels are noticed, and those by water-screws
and paddle-wheels are investigated, and the modifications pointed
out ; then the strength of vessels, the power of sails and of currents,
and their combination with steam power, followed by the necessaiy
rules for arranging the proportions, power, and effect of vessels, and
a tabular view of the vessels, executed at different times by the best
manufacturers in this country.

These multifarious inquiries are followed by an extensive table of
the properties of steam, and two tables of the proportions of engines
for different powers, with the expenditure of water and fuel each re-
quires. The letter-press is illustrated by wood-cuts in the pages, and
the whole by twenty plates, each having its description opposite to
it; and a copious index, and a full table of contents, renders reference
to particulars easy ; and, as a whole, this most useful work presents
that combination of science with practice, which perhaps no one, ex-
cept a person having the experience of a workman, as well as an

extensive

222 % Notices respecting New Books.

extensive knowledge of science, could have written, — and such we
know to be the case with the author*.

The Elements of Geometry, with Notes. By J . R. Young.

The great excellence of Euclid is well known to consist in the
completeness and perfect accuracy, as well as the general sim-
plicity and elegance of his demonstrations, admitting no assumption,
no step in the process of his reasoning that has not been previously
established, and at the same time, with this requisite, usually adopt-
ing the shortest course for arriving at his conclusion. It is not, how-
ever, pretended that this admirable work, so long and so deservedly
received as the text-book for instruction, is absolutely free from de-
fects. Even the very rigour of his proofs is sometimes the source of
so much intricacy and abstruseness, especially in the equally difficult
and important branch of the mathematics, the doctrine of propor-
tions, as to form a serious and discouraging obstacle fcto the progress
of the learner. The want of success in every attempt hitherto made
to lessen this difficulty, might seem to render the task hopeless. The
aim of Mr. Young, however, in the work before us, has been, with-
out impairing the completeness and satisfactory nature of his de-
monstrations, to contract and facilitate the labour of the student as
much as possible by simplicity and conciseness, and also to add to
the extent and accuracy of his geometrical knowledge. Nor do we
hesitate to recommend his treatise, not certainly as superseding the
use of Euclid, but as a useful auxiliary to that great work. His ob-
servations on the theory of parallel lines j his demonstration of the
converse of every proposition where this is possible, and showing its
failure, where it is not ; the labour he has bestowed on the doctrine
of proportions, as well as his corrections of many errors of preceding
geometers, and supplying their defects, together with his minute
attention to accuracy throughout, — may be justly considered as ren-
dering his performance valuable, especially to the learner.

The notes are numerous, and most of them important. Among the
various errors and defects of modern geometers detected and cor-
rected in them, one instance especially is singular, and deserves to
be noticed. Mr. Thomas Simpson, in his Elements of Geometry, has
substituted in the place of the seventh proposition of Euclid's sixth
book, one which Mr. Young has proved to be absolutely false. This
is the more remarkable, as, though the work in which it occurs has
been in the hands of geometers more than seventy years, this error
has hitherto escaped detection. Even Dr. Robert Sirnsou, the edi-
tor of Euclid, though entertaining no very friendly feeling towards
his contemporary, suffered it to pass unnoticed. A similar error oc-
curs also in Mr. Leslie's Geometry, Prop. xiv. B. vi. last edition.

As the celebrated propositions of Euclid, (B. i. Prop. 47.) the
discovery of which is attributed to Pythagoras, admits of various de-
monstrations, Mr. Young has given three j the last of which in the
notes is concise and simple, though that inserted in the text instead
of Euclid's, is inferior to the latter, not only in elegance but in sim-
plicity also.

* His first Essay was a paper in the 46th vol. of the Phil. Mag. p. 15.

The

Linncean Society. 223

The first eight books of this work now published treat of lines si-
tuated in the same plane. The second Part, as announced by the
author, will contain the geometry of planes and solids ; with an Ap-
pendix, and Notes on the Symmetrical Polyedrons of Legendre.

XXXVII. Proceedings of Learned Societies.

LINN^EAN SOCIETY.

Feb. 5. — T> EAD some account of the Botany of the provinces lately
AV ceded by the Burmese to the Honourable the East India
Company ; with a description of two new genera of plants : in a letter
to H.T. Colebrooke, Esq., F.R.S. & L.S. &c. By Nathaniel Wallich,
M.D.F.L.S. F.RS. E. &c. Superintendent of the Botanic Garden at
Calcutta. The author states that his botanical treasures are most ex-
tensive 3 the number of species having long ago surpassed 2000; and
that he has never seen any vegetable production equal to his Am-
herstia nobilis when in full bloom. It surpasses all the Indian plants.

Amherstia. Diadelphia Decandria — Nat. Ord. Leguminosse. The
flowers of this splendid tree are disposed in pyramidal pendulous clus-
ters 2 feet long, and 10 inches broad at the base. Leaves \\ foot
long, with 8 or 10 pair of oblong pointed pinnae, which are from 8
to 10 inches long, and of a peculiarly delicate glaucous hue. The
racemes are scarlet. The petals are furnished at the apex with a
broad yellow spot, having a tubular calyx : and the genus is evidently
allied to Heterostemon of Desfontaines.

Dr. Wallich has at length found the Varnish-tree of the Burmese,
which he constitutes a new genus, and calls it Melanorrhcea ; Poly-
andria Monogyniaj Anacardise, Brown. — Also another singular plant,
which he calls Phytocrene gigantea, allied to Araliacese. The trunk is
as thick as a man's thigh, and when divided affords a large quantity
of a limpid, tasteless, and very wholesome water.

Feb. 19. — Read a description of a curious Fungus belonging to the
Gastromycous order, found nearWrexham by J.T. Bowman, Esq. F.L.S.
on decaying oak branches stript of bark. In its earliest stages it is
globular : afterwards, from the expansion of the filaments, the spo-
rules are exposed, and the sporangium becomes rugged and broken ;
from the ripening of the seeds the peridium bursts, and the filaments
being set at liberty acquire first a horizontal and then a more erect
position, resembling the branches of a palm-tree.

At the above meetings were also read some portions of a paper by
J. E. Bicheno, Esq. F.R.S. Sec. L.S. entitled "Remarks on the Flora
of Great Britain, as connected with Geography and Geology."

The Author in this paper, instead of attempting to connect plants
with particular temperatures, as most authors who have treated the
subject have done before, endeavours to show the relation which ve-
getables have to Geographical and Geological structure. He regards
England as the most favourable place to commence such remarks,
because of the intimate knowledge we have of its stratification, and
also of the stations of all our plants.

In order to assist our inquiries he thinks it necessary to reject all

those

224 Limuean Society. .

those species the introduction of which may be traced to artificial
causes, regarding those alone as indigenous which are coeval with the
soil. Agriculture, Medicine, and even Religion, have each swelled
our list. Coronopus didyma is not found in England but at ports,
and seems to be a particularly migratory species. It may be found,
he says, in almost every latitude where ships frequent j — at Lisbon,
Madeira, Rio Janeiro, the Cape, Sydney. He thinks the same dis-
position may be witnessed in many of the Cruciferae, and adduces as
instances, Sisymbrium Irio, and Thlaspi campestre. Whether the cause
of such phenomena is to be sought for in the structure of the seed,
or in the pabulum necessary to the growth of the plant, remains to
be determined. The Blatta orientalis (common Cock-roach), and
the Norway Rat, which has eaten up the old Black Rat, are instances
from the animal world, showing a similar tendency.

In order to ascertain whether a species be indigenous, it is of im-
portance to ascertain upon what stratum, or in what places, it ter-
minates its range. Many southern plants he finds terminate their
northern range upon old walls, such as Sisymbrium Irio and tenuifo-
lium, Dianthus Caryophyllus, Teucrium Chamccdrys, &c. Others
again abounding in the south, finish their course by attaching them-
selves to some of the warmer strata, as to mountain limestone, or
new red sand-stone. Hutchinsia petrcea grows in the Olive country
so abundantly that it is gathered as a salad. With us it finds only
a few localities, and those always on mountain limestone. Campa-
nula patuta finds its most northern accommodation in England on
the new red sand-stone. It has one other station with us on chalk,
which is its place in Brittany.

The sea-coast also carries many plants further north, than inland
situations can do. The Common Privet for instance, though so abun-
dant in the south on the chalk and gravels, becomes rarer as we
proceed to the north. In Scotland it affects the coast, and in Sweden
is wholly confined to it. On the other hand, plants which belong to
a more northern latitude and to more primitive countries, do not
terminate their southern range on our warmer and richer soils. The
author suspects Daphne Mezereum not to be English, because it is
found only on the more recent strata.

The stratum producing the greatest number of rare plants with us
is the mountain limestone ; and although but a small portion of this
rock should appear above the surface surrounded by other rocks of a
different structure, it seems to have caught the rarer species. The
district of Gower, Brean Down, St. Vincent's Rocks, Orme's Head*
are examples.

Next to mountain limestone the Bury sand seems to be a fa-
vourite station of unusual productions. Veronica triphyllos and verna,
Vicia lathyroides, Tillcea muscosa, Scleranthus perennis, &c. &c. grow
there.

The richest soils are the least productive of rare species. Slaty
countries, excepting the highest elevations, are also singularly de-
ficient.

Many of our promontories are remarkable for the rarities they pro-
duce

.Geological Society. 225

duce. Erica vagans terminates its northern range on the serpentine
of the Lizard ; Draba aizoides, in Gower.

The author then proposed to consider the vegetation which is pro-
duced by the different strata, commencing with the eastern side of
the kingdom, or with the most recent deposits.

The diluvial soil of the Fens, which is composed of decayed vege-
tables resting on clay, is, when left to nature, soon covered with
grasses, to the exclusion of every other plant. Scarcely a single rare
species is to be found on it. The water in such soils, on the con-
trary, abounds in rarities. Stratiotes aloides, Arundo calamagrostis,
Teucrium Scordium, Lactuca Scariola, Senecio paludosus, &c. &c. are
of this number. The author remarked, that the first of these species,
though wild in Berkshire, had not been observed to flower there.
Arundo calamagrostis he regards as peculiarly a Fen plant with us,
and that the localities assigned to it elsewhere belong to A. epigejos.
This locality appears to be on its most southern limit. The most re-
markable feature of Fen vegetation is the luxuriance and quantity of
Cruciferae.

Whatever phenomena geologists may discover to induce them to
regard the Bury sand as the same with that of Bagshot-heath, the
author remarks that their vegetable productions do not correspond ;
and though he does not assert that we ought to find a similar vegeta-
tion on strata of the like nature, yet it so frequently occurs that the
rarer plants correspond where strata are alike, that he regards such
differences as worth noticing.

The rare plants of the Bury sand are peculiar to itself, while the
Bagshot sand is remarkably deficient in uncommon species j the only
one of notoriety, he has remarked, being Agrostis setacea, which is
abundant, and which may be traced upon the sands and gravels of
the plastic clay, through Dorsetshire, Hampshire, Surrey, and even
to the Commons in the neighbourhood of London, where its range
terminates.

GEOLOGICAL SOCIETY.

Feb. 1. — The reading of Professor Sedgwick and Mr. Murchison's
paper, begun at the last meeting, was concluded.

This paper consists of three divisions : 1st. A brief outline of the
general structure of the Isle of Arran. 2d. An account of the section
on the N.E. coast of the island. 3d. Concluding remarks explanatory
of the probable causes, and geological epochs of the several phe-
nomena. In the 1st division, the authors, considering that the sub-
ject has been amply elucidated by Jameson, MacCulloch, and Hen-
drick, confine themselves to such details as are necessary to make
their subsequent description intelligible. In the 2d part, the strata
on the N.E. coast are described in great detail, for the purpose of
comparison with the corresponding members of the English Series $
from whence it appears, that a succession of formations, analogous to
the old red sandstone, carboniferous series, and new red sandstone,
are exhibited twice over, in an anticlinal section.

New Series. Vol. 3. No. 15. March 1828. 2 G The

g$| . Geological Society.

The mineralogical centre of this section is at North Sannox, and
the lower red conglomerate is there seen in several situations, rising
to the height of about 1 000 feet above the sea. 1 . This formation is
supposed to be identified with the old red sandstone ; from its lowest
members graduating into grauwacke ; from its containing concretionary
limestone not distinguishable from the cornstone of Herefordshire ;
and its being regularly overlaid by the carboniferous series. 2. The
middle deposit of the section is clearly referable to the carboniferous
series, by its mineralogical structure, by the organic remains in the
calcareous beds, which are identical with those of the mountain-
limestone ; by its containing seams of coal, which have been worked ;
and by the plants in the shale being of the same species with many
of those most abundant in the coal-measures of England. 3. The
superior sandstone and conglomerate are of enormous thickness, rising
into lofty and precipitous hills upon the coast. These are referred to
the new red sandstone, from their position and internal characters ;
and this classification is confirmed particularly by the structure of the
sandstone on the southern coasts of the island. This formation differs
however from the new red sandstone of England, not only in being
conformable to the beds on which it rests, but also by graduating into
the superior parts of the carboniferous order.

In conclusion, the authors endeavour to show, that the great dis-
locations of the secondary deposits have been produced by an up-
heaving of the granite ; and they state, in corroboration of this
opinion, that where the breaks .in the strata are greatest, there the
granite makes the nearest approaches to them. It is further attempted
to be proved, that the granite could not have been in a perfectly fluid
state at the period of its elevation, from the fact of its existence in
the form of mural and serrated precipices on the flanks of the se-
condary strata j being in this respect prominently distinguished from
the trap of the southern regions of the island, which has, in number-
less places, not only penetrated, but overflowed upon the new red
sandstone.

Feb. 15.— The Anniversary Meeting of the Society was held this
day ; and the following Fellows were elected Officers and Council for
the year ensuing : — President : William Henry Fitton, M.D. : Vice
Presidents: Arthur Aikin, Esq. F.L.S.; Rev. W.Buckland, D.D. F.R.S.
Professor of Mineralogy and Geology in the University of Oxford ;
Charles Lyell, Esq. F.R.S. & L.S. j Rev. A. Sedgwick, F.R.S. Wood-
wardian Prof. Camb. — Secretaries: W. J. Broderip, Esq. F.L.S. j
R. I. Murchison, Esq. F.R.S. & L.S.— Foreign Secretary: Henry
Heuland, Esq. — Treasurer: John Taylor, Esq. F.R.S. — Council:
J. E. Bicheno, Esq. Sec. L.S. ; John Bostock, M.D. F.R.S.; Rev.
W. D. Conybeare, F.R.S; John Crawfurd, Esq. F.R.S.; Michael
Faraday, Esq. F.R.S.; Davies Gilbert, Esq. M.P. Pres. R.S. ;
G. B. Greenough, Esq. F.R.S ; J. F. W. Herschel, Esq. Sec. R.S. ;
Leonard ' Horner, Esq. F.R.S. ; Ashhurst Majendie, Esq. F.R.S. ;
Rev. J. H. Randolph 5 N. A. Vigors, Esq. F.R.S. ; Sir R. R. Vvvyan,
Bart. M.P.; Henry Warburton, Esq. M.P. F.R.S.

ASTRONOMICAL

Astronomical Society. 227

ASTRONOMICAL SOCIETY OF LONDON.

Jan. 11, 1828. — There was read a paper entitled "Third Series of
Observations with a 20-feet reflecting telescope ; — containing a Ca-
talogue of 384 new double and multiple stars, completing a first
thousand of those objects detected in sweeps with that instrument j —
together with Observations of some previously known." By J. F. W.
Herschel, Esq., President of the Society.

This paper, as its title imports, is a continuation of the two papers
previously communicated by the author on the same subject. The
field of discovery in this department of astronomy, though narrowed
by the great work recently published by Professor Struve, the author
considers as not yet exhausted; since, on an average of the part of
the heavens swept by him, not above one in four, of double stars
sufficiently remarkable to attract attention in sweeping, have been
catalogued by the eminent astronomer last named : not to mention
the vast number of interesting close double stars, below the 9th
magnitude, which a minuter examination than the nature of his
sweeps permits would no doubt produce. The double stars of this
Catalogue, he observes, are considerably more select than those of his
two former ones; those whose distance exceeds 32" being (except in
particular cases) excluded, and the limit of distance being narrowed
according to the faintness of the component stars.

The author prefaces his Catalogue with a comparison of the mag-
nitudes habitually assigned to the stars by himself and Professor'
Struve j from which it appears that on the average, his magnitudes
have a denomination about one unit lower than those of that astro-
nomer ; — a star (for example) which M. Struve would call of the 9th
magnitude, being, in Mr. Herschel's nomenclature, of the 10th. The
limit of vision in the Dorpat telescope, he presumes to lie about his
average 14th magnitude, though such a determination must neces-
sarily be liable to some latitude. This conclusion he deduces from
a series of instances, in which small companions have been seen by
him attached to large stars, within the limits of Professor Struve's
4th class, which have escaped the notice of the latter.

The author then states the principle on which he estimates magni-
tudes below the 6th, which is that of continual bisection of the light;
and he cites some experiments, by which it appears that the light of
an average star of the 1st magnitude is at least lf)0 times that of the
6th. He then adduces a series of observations of a considerable
number of the closer stars, of M. Struve's Catalogue, by which it
appears that the Slough telescope easily defines with its ordinary
sweeping power, the generality of M. Struve's stars of the 1st class,
and many of those marked by him as vicince, and even pervicince ; but
those which have the epithet vicinissimce, he has not yet succeeded
in separating with the highest power (240) usually applied, — which
indeed was to be expected. In lieu of M. Struve's classification of
double stars, which he considers as enlarging beyond due limits the
number of those of the 1st class, he proposes the following system,
which in fact very nearly approximates to that originally followed by
Sir William Herschel.

2 G 2 Class

22S Astronomical Society.

p. | r close 0" and below 1"

1 not close 1 and below 2

Class II 2 and below 4

Class III 4 and below 8

Class IV 8 and below 16

Class V 16 and below 32

Class VI 32 and below 64

So that the limit of distance of stars of the nth class shall be 2" x 1".

The author then subjoins a list of stars common to his two former
Catalogues, and to that of Professor Struve, 86 in number ; after
which he proceeds to describe some singular phenomena observed in
the course of his examination of these objects, which explain certain
discrepancies between the results of observations of their angles of
position on different nights, and which tend to throw light on some
obscure points in the theory of vision. He considers it as rendered
very probable, by some of the facts adduced, that time is required for
light to make an impression on the retina, as well as for the impres-
sion made to wear off j and that this time is the less, the brighter the
object ; and explains by this principle a remarkable degree of unstea-
diness and fluctuation observed in the limb of the planet Mars, while
small stars in the field remained perfectly tranquil, as well as certain
other curious phenomena.

He then adds some observations on the contrasted colours so fre-
quently observed in double stars, and regards them as (at least) in
many cases referable to the laws of vision -, in virtue of which, a strong
light having an excess of the less refrangible rays, will cause a feebler
one, in which no such excess exists, to appear of the complementary
hue ; instances of which, in artificial lights, are adduced. He notices
especiallv the extremely intense red colour of a star of the 8th mag-
nitude, R. A. 4h 41". N.P.D. 61° 47' (1828.)

These prefatory remarks are terminated by some observations of
the 5th star in trapezio nebula Ononis, pointed out by M. Struve.
The author adducevS evidence, which he considers as satisfactory, that
no such star existed in that situation on the 13th March, 1826. It
was observed, however, by M. Struve, to be conspicuous on the 1 1th
Nov. of that year. It is now readily seen in the Slough telescope ,
and at the time of drawing up the present paper, it was so bright as
not to be overlooked with the most ordinary degree of attention. He
considers it therefore, if not as a new star, at least as a variable
one of very singular character.

The Catalogue, which follows, is arranged in all respects like the
preceding ones published in the Memoirs of this Society, and is fol-
lowed by a list of about 200 double stars, for the most part found in
the same sweeps with the others ; but which, occurring in M. Struve's
Catalogue, cannot now be regarded as new double stars. Their ob-
served places and estimated angles of position, distances, and mag-
nitudes, are however given, in order to afford ground of comparison
between the two Catalogues, of which comparison the Tesults are
stated.

PROCEEDINGS

Royal Institution of Great Britain. 229

PROCEEDINGS AT THE FRIDAY EVENING MEETINGS OF ,THE
ROYAL INSTITUTION OF GREAT BRITAIN.

Jan. 25. — The Members of this Institution commenced their meet-
ings for the season, on this evening j Mr. Brande occupied the place
at the lecture table, and gave an account of the discovery of the
three most important vegeto -alkalies, Morphia, Cinchonia, and Qui-
nia ; also of their properties, the best methods of preparing them, the
methods of detecting impurities in them 5 illustrating the whole by
reference to experiments and specimens.

At the close of the evening he paid a just tribute to the memory of
Mr. Daniel Moore, who, a firm friend to the Institution during his
life, left it a thousand pounds at his death.

A quantity of the new element bromine was laid upon the library
tables, with specimens of Brazilian manufactures, &c. &c.

Feb. 1 . — An experimental illustration and explanation of the cu-
rious phenomena produced in certain circumstances by a current of
air, steam, water, or of any other fluid, was given in the lecture
room, by Mr. Faraday. The phaenomena were first brought to the
notice of scientific men by M. Clement, and consists, as our readers
well know, in the apparent adhesion of a flat disc against an aper-
ture in a plane surface, out of which the stream of fluid is passing. —
Make a smooth round hole about the eighth of an inch in diameter,
through the middle of a large sound bung, cut one of the flat sur-
faces of the bung smooth with a sharp knife, stick three or four
pins upright into that surface, equidistant from each other, and about
three quarters of an inch each from the central hole ; and then drop
between them a disc of paper or card one inch and a half in diameter,
so as to lie loosely between the pins over the hole. No effort to blow
tbe paper off by forcing air or the breath through the hole in the
bung, will succeed j but the stronger the current, the more forcibly
will the paper be pressed up against it. Mr. Faraday gave the same
explanation of the effect as that given by M. Clement. He stated it
to be a pure effect of the momentum of thd air between the disc and
the cork, and to have no necessary connection with the lateral cur-
rents of air which move on to join a stream passing in one direction :
—these lateral currents were cut off in some of the experiments, and
still the effect remained unabated. He equally denied the effects of
friction as having any thing to do with the effect.

Numerous objects of interest were placed upon the library tables,
amongst which were several from Ashantee, and especially the scull
of an Ashantee slain in the battle of Aug. 1824, which had two oc-
cipital bones.

Feb. 8. — Mr. Ainger gave an illustrated account of the origin of
Grecian architecture, and of the principles acknowledged in modern
times as derived from it, and then applied those principles to cer-
tain parts of St. Paul's cathedral ; at the same time strongly repro-
bating the species of tyranny which has resulted from judging a
building of one kind by the rules and the taste which have been
formed upon others altogether of a different nature.

Presents,

'ISO Intelligence and Miscellaneous Articles.

'to

Presents, curious specimens, and new machinery were laid upon
the library tables as usual.

Feb. 15. — The subject of the evening was Resonance, or the reci-
procation of musical sounds. It was explained and illustrated by
Mr. Faraday ; but he stated that his information was obtained from
Mr. Wheatstone, to whom belonged also the new matter brought
forward.

The vibration of one string when another in unison with it was
struck, was referred to as an illustration of the nature of reciproca-
tion. The honour of this discovery was given to Messrs. Noble and
Pigott, pupils of Dr. Wallace. Reciprocation by undulations com-
municated through the air, or through solid bodies, was then illus-
trated, and the nature of stringed instruments explained.

After this, followed matter of a more original nature. It was stated
that columns of air could reciprocate to vibrating bodies, when their
vibrations could accord with those of the latter j in illustration of
which, a flute was made to speak, simply by approaching a vibrating
tuning-fork to its embouchoir. Other columns of air were also made
to produce intense sound by reciprocating with tuning-forks which
were themselves inaudible. An elementary model of an instrument
to be constructed upon this principle was also exhibited.

Some musical instruments were then referred to, which had been
brought by Sir Stamford Raffles from Java, and which had been lent
to the Institution by Lady Raffles, for the evening's illustrations.
They consisted of plates of sonorous metal, suspended by their nodal
points over pipes of bamboo adjusted to reciprocate to the lowest
note produced when the plate was struck. When the apertures of
the tubes were covered, and the plates made to sound, the ordinary
tones were produced j but upon removing the cover, the air in the
tubes instantly reciprocated to the lower notes, and a series of fine
rich sounds were produced. This instrument is called the Gender.

A further illustration of the reciprocation of sound was then given
on the guimbardor Jews-harp, the different tones of which are found
to depend upon the circumstance, that columns of air reciprocate not
only when they vibrate in equal times with the original phonic, but also
when their vibrations are any multiple of those of the phonic. This
fact was illustrated by a syringa, and also by the beautiful perfor-
mance of M. Eulenstein on the Jews-harp.

Some illustrations of the resonance of the columns of air in the
cavities of the ear were then given, — and the subject concluded.

In the library were several beautiful engravings, by Robinson,
Turrell, and others.- A new perspective instrument by Mr. Turrell,
called a Perspectograph, &c. Sec.

XXXVIII. Intelligence and Miscellaneous Articles.

ANALYSIS OF SOME ALLOYS OF BISMUTH.

MLaugier has analysed several of these compounds. To analyse
• an alloy of bismuth and lead, he dissolves it completely in dilute
nitric acid, and then pours into the solution'one of carbonate of am-
monia,

Intelligence and Miscellaneous Articles. 231

monia, which at first precipitates both oxides in the state of carbon-
ate j and when added in excess, redissolves the carbonate of bismuth.
The carbonate of lead is to be washed in the filter with a solution of
carbonate of ammonia, in order to dissolve any adhering carbonate of
bismuth ; the washing is to be finished with warm water, in order to
dissolve all the carbonate of ammonia used in the washing.

The alkaline liquor containing the oxide of bismuth, is to be satu-
rated by an acid, and then ammonia is to be added in excess ; all the
oxide of bismuth is precipitated, and after washing on a filter it is to
be dried and weighed.

There is another method, which is perhaps more simple, but not so
exact. — Boil the alkaline liquor and evaporate to diyness, wash it
and filter in order to collect the oxide of bismuth. But this method is
inconvenient, because the oxide of bismuth adheres to the vessel in
which the solution is evaporated.

An alloy of equal weights of lead and bismuth gave by analysis
49*1 of the former metal, and 496 of the latter j the loss being 1*3
per cent. The nitrate of lead and oxide of bismuth separated by this
process were both pure.

The fusible compound of 8 parts bismuth, 5 lead, and 3 tin, ana-
lysed with nitric acid, left the oxide of tin on the filter : the oxides of
bismuth and lead were separated as above directed j 16 parts yielded
bismuth 7*98, lead 4*95, tin 3 5 the loss of the operation amounting
to .It, of the whole. — Ann. de Chim. xxxvi. p. 333.

EXAMINATION OF COPPER.

Some samples of copper which 1 examined some time since, con-
tained a small portion of silver, without any other impurity which I
could detect : lately, some other samples have been put into my hands,
in order to determine the cause of their being complained of. The
copper was dissolved in dilute nitric acid, used in excess j it contained
no lead, and upon the addition of muriatic acid to a very dilute solu-
tion, slight precipitation took place, which I at first imagined was oc-
casioned, as in the former case, by the presence of silver. I happen-
ed, however, to remember a fact mentioned in conversation some
years since, and which 1 have never met with in any chemical work, —
That a solution of bismuth so dilute or so acid that water would oc-
casion no precipitation in it, is decomposed by the addition of com-
mon salt or muriatic acid ; and this I found to be the case in the pre-
sent instance : the precipitate was small in quantity, not amounting
to one per cent for the copper employed, and it differed from chloride
of silver in very readily passing through filtering paper. I found it
necessary, in order to determine its quantity, to supersaturate with
ammonia, by which the oxide of copper was dissolved, and the oxide
of bismuth precipitated. R. P.

ON EFFLORESCENCE.

The following observations are by M. Gay Lussac. Many salts
when exposed to the air, are well known to effloresce j that is, they fall
to powder and lose their water of crystallization j and it is generally

supposed

232 Intelligence and. Miscellaneous Articles.

supposed that salts after efflorescence are perfectly anhydrous.
Having been long convinced that this opinion is not correct, I have
made some experiments upon the principal salts which are efflorescent
in a high degree. Crystallized sulphate of soda, exposed to the air even
when it is not very dry, readily loses all its water of crystallization.
Phosphate of soda becomes readily opake without losing its form.
After three months' exposure to the air, it contained on the 18th of
July, 7*4 of the 1 2 proportions of water, which it contains in its usual
state. Reduced to powder, and thinly spread upon paper, it con-
tained on the 26th of July 5*65 proportions of water; — again exposed
to the air during a hot and dry period, it contained on the 31st of
July only 5*65 proportions ; — afterwards exposed till the 2 1st of Oc-
tober, the weather having become colder and more damp, it was found
to contain 72 proportions of water : some phosphate which had been
calcined, absorbed in five days' exposure to the air, nearly half a pro-
portion of water.

Carbonate of soda behaves on exposure very much as the phos-
phate : it becomes opake, loses much water without altering its form -y
but I have never found it anhydrous after exposure.

It results from these observations, that some salts completely lose
their water of crystallization by efflorescence j but that others retain
variable quantities, according to the hygrometric state of the air. I
do not assert, however, that the water may not remain in definite pro-
portions j it merely appears that in the phosphate and carbonate of
soda, which retains a proportion of water of a certain number, — the
seventh for example, — differs but little from that which unites the pro-
portion, immediately above or below. — Ann. de Chim. xxxvi. 335.

NATIVE PLATINA.

A piece of native platina, weighing about 64 grains, has recently
been found in the Russian mines at Hijne-Taguilski. Its shape was
round, its surface granulated, and in some places it bore a metallic
lustre. Its specific gravity being only 16, it must contain the various
alloys met with in platina. It is singular that this specimen was met
with in digging an argillaceous stratum. — Monthly Mag. Feb. 1828.

MANUFACTURE OF ULTRAMARINE.

M. Gay Lussac announced to the Academy that M. Tunel, inspec-
tor of gunpowder and saltpetre, had succeeded in the direct formation
of ultramarine, and that what he obtains by his process is finer and
more brilliant than the natural colour. It was by following the ana-
lysis made by M. Clement Desormes, that the inventor accomplished
this desirable object. M. Tunel has already been able to supply the
public with ultramarine at 25 francs the ounce j the colour having hi-
therto been sold for 50 or 60 francs the ounce. He hopes that he
shall be able to sell it at a still more moderate price. M. Tunel has
thought proper to keep his process secret for a certain time. — Le
Globe, Fev.9, 1828.

HEAT

Intelligence and Miscellaneous Articles. 233

HEAT GIVEN OUT DURING COMBUSTION.

M.Despretz read at the Academy of Sciences, on the 15th and 22d
of October last, a memoir on the heat given out during combustion.
By means of a new method of observation, he found that hydrogen is
the body, of which a given weight gives out most heat, and the me-
tals least. The result will be opposite if we refer the results to the
same weight of oxygen. It is remarkable that carbon, which in burn-
ing does not alter the volume of oxygen gas, produces three-fifths of
the heat developed by the metals, iron, zinc, and tin, which reduce
the oxygen to the solid state. Hence it is in the act of combination
that we must seek for the principal cause of the development of heat,
and not in the approach of particles.

In his second memoir, M. Despretz has shown that the quantity of
heat developed by a certain quantity of a body which burns without
changing the volume of the gas, is the same, whatever be the density
of the gas. — Le Globe.

INFLAMMABLE GAS ARISING AFTER BORING FOR SALT.

In boring for salt at Rocky Hill, in Ohio, about a mile and a half
from Lake Erie, after proceeding to the depth of 197 feet, the auger
fell, and salt water spouted out for several hours. After the exhaus-
tion of this water, great volumes of inflammable air issued through
the aperture for a long time, and formed a cloud ; and by ignition,
occasioned by the fire in the shops of the workmen, consumed and
destroyed every thing in the vicinity. — Transactions of the Philoso-
phical Society of New York.

INFLAMMABLE GAS FROM SALT MINES EMPLOYED FOR PRO-
DUCING, LIGHT.

In the salt mine of Gottesgabe at Rheine, in the county of Teck-
lenbourg, there has issued for sixty years from one of the pits, (which
has on this account been called the Pit of the Wind,) a continued cur-
rent of inflammable gas. The same gas is produced in other parts of
the mines. M. Roeders, the inspector of the salt mines, has used this
gas for two years, not only as a light, but as fuel for all the purposes
of cookery. He collects it in pits that are no longer worked, and
conveys it in tubes to the house. It, burns with a white and brilliant
flame. Its density is about 0*66. It contains only traces of carbonic
acid and sulphuretted hydrogen, and therefore should consist of car-
bonated hydrogen and olefiant gas. — Brewster's Journal, Jan. 1828.

NATURAL GAS LIGHTS AT FREDONEA.

This village, on the shores of Lake Erie, is lighted every night by
inflammable gas from the burning springs, as they are called, in its
vicinity. Captain Hall has visited this village, and will no doubt give
us a good account of it on his return. — Ibid.

New Series, Vol. 3. No. 15. March 1828. 2 H iodine

234

Intelligence and Miscellaneous Articles.

IODINE IN CADMIUM.

Iodine is found in the great zinc foundry at Konigshute in Upper
Silesia, in the cadmium which accompanies the zinc ores. — Ibid.

ANALYSIS OF THE GREEN IRON ORE AND ARSENIATE OF LEAD.

According to Dr. Karsten, a variety of this ore from the Hollester
mines near Siegen, in Rhein Prussia, consists of

Oxide of iron 63*450

Phosphoric acid 27*717

Water 8*560

99*727
And according to the same authority, a variety of arseniate of lead
from Herrhausen near Siegen, in Rhein Prussia, consists of

Oxide of lead 6997

Muriatic acid 0*81

Arsenic acid 29*22

10000
The results of this analysis are not accordant with those obtained by
Dr. Wohler. — Voggendorff's Annalen, vol. iv. p. 161.

GEOMETRICAL PROBLEM. BY MR. J. ROBOTHAM.

Required, a square equal in area to the space comprised between
the arcs [AB, DC, and EF, DC,] of two
concentric circles, and two parallel right
lines, tangents to the interior circle. The
area of the exterior circle being double that
of the interior.

Let ABFE, and d C v D be the two con-
centric circles. Bisect the quadrant ao f a\
by the line o B. Then by the nature of the
problem, the area aB d e = d e o = e o C.
To each of these equals add the area e BC,
then will the area of the space a BC d =
the area of the triangle oBC. And since
o a — oB, the square, described on oa, viz. aofb = 4 times the
area of the triangle o BC =the space AB, DC, and EF, DC. Which
may be seen by drawingthe diagonal af.

SCIENTIFIC BOOKS.

Just Published.
The 19th Number of Leybourn's Mathematical Repository ; con-
taining twenty mathematical questions, and their answers, selected
from an extensive correspondence. — Horse Arithmetics, by Mr.
Horner. — On Porisms, by Mr. Galloway. — On Central Forces, by
the Rev. Mr. Bromhead. — On Equations, by the Rev. Mr. Hawkes.

—On

Scientific Books, dye. 235

— On Attraction, by Ch. Fred. Gauss.— Solutions to a curious Pro-
blem, by Mr. Lecbmutz. — Cambridge Problems, 1821 — 1826.
Together with a set of twenty questions, to be answered in Number
XXI.

A Manual of Natural and Experimental Philosophy, beautifully il-
lustrated, has just been published by C. F. Partington, and dedicated
to the London Institution. It is well calculated to assist those who
attend the Lectures, and not less so to give those who cannot attend
a vast mass of useful information.

Observations on the Cruelty of employing Climbing-boys in sweep-
ing Chimneys: and on the Practicability of effectually Cleansing
Flues by Mechanical Means. With Extracts from the Evidence be-
fore the House of Commons : &c. &c.

Flora Londinensis. Nos. 35 and 36 of the New Series. — These
Numbers, containing Twelve rare and highly interesting British
Plants, complete the new edition of this splendid Work, which con-
tains upwards of 650 accurate Delineations of Indigenous Plants.

A Manual of Electro-Dynamics, chiefly translated from the Manual
d'Electricite Dynamique j or, A Treatise on the Mutual Action of
Electric Conductors and Magnets of J. F. Demonferrand j with
Notes, &c. &c. by James Cumming, M.A. 8vo.

Reports of Medical Cases, selected with a view of illustrating the
Symptoms and Cure of Diseases by a reference to Morbid Anatomy j
embracing Dropsy, Inflammation of the Lungs, Phthisis, and Fever.
By Richard Bright, M.D. RR.S. &c. 4to. with 16 coloured plates.

Popular Lectures on the Steam Engine, in which its Construction
and Operation are familiarly explained ; with an Historical Sketch of
its Invention and Progressive Improvement. By the Rev. Dionysius
Lardner, LL.D. 12mo.

Preparingfor Publication.

Capt. John Ross, K. S. R. N., is about to publish a Treatise on
Steam Navigation, Illustrated with Plates, comprehending a History
of the Steam-Engine, its Principles, an Explanation of the Terms, and
an Account and Examination of the Improvements applicable to Naval
Purposes. — A Complete System of Naval Tactics peculiar to Steam
Navigation as applicable to Naval Warfare and Commerce, including
a comparison of this System with all others. — The Effects of such a
System in National Defence. — Rules and Regulations calculated to
prevent Accidents by Explosion and Collision. — An Alphabetical Ar-
rangement of Technical Terms used in Steam Navigation j and a
Chronological Table of the Progress of the Steam Engine, from the
most ancient period of its invention. — The Description and Use of
the Royal Clarence Sextant, an Instrument recently invented by the
Author, and highly useful in Steam Navigation, for ascertaining the
exact distance of Ships from Land, or any object in view: with Tables
applying the principle to a Common Sextant.

An Essay on the Application of Mathematical Analvsis to the

2 H 2 Theories

236 New Patents.— State of the Barometer, fyc. for 1827.

Theories of Electricity and Magnetism.— This Essay will comrnehce
with an Exposition of the General Principles common to both The-
ories j which will be followed by particular Applications of them to
many cases not hitherto submitted to Calculation.

In the course of the present month will be published by W. Wood,
428 Strand, the 4th and concluding Part of Haworth's Lepidoptera
Britannica, with a complete Index to all the species.

Also, the second edition of Wood's Index Testaceologicus, or Cata-
logue of English and Foreign Shells, illustrated with 2300 Figures.

LIST OF NEW PATENTS.

To J. Weiss, of the Strand, for improvements on instruments
for bleeding horses and other animals.— Dated the 26th of January
1828. — 6 months allowed to enrol specification.

To Augustus Applegath, of Crayford, Kent, for his improve-
ments in block printing. — 26th of January. — 4? months.

To Donald Currie, of Regent-street, "esquire, for a method of
preserving grain and other vegetable and animal substances and
liquids. Communicated from abroad.— 31st of January.— 6 months.

Summary, for the Year 1827, of the State of the Barometer,
Thermometer, fyc. in Kendal. By S. Marshall, Esq.

Barometer.

Thermometer.

Quantity

No. of

Preva-

1827-

of Rain
in Inches.

rainy
Days.

lent
Winds.

Max.

Min.

Mean.

Max.

0
49

Min.

Mean.

January

3008

28-89

29-61

0
9

34°59

8-630

14

SW.

February

30-40

28-89

29-51

53

14

33-92

2-698

5

N.

March

30-03

28-40

29-36

56

23

42-93

8-676

22

SW.

April

3013

29-42

29-77

70

30

47-23

2-553

14

SW.

May

2994

29-10

29-56

69

32

52-87

3-483

15

w.

June

3014

29-27

29-69

74

45

56-98

4-264

17

W.&SW-

July

3015

29-39

29-79

74

42

59-01

3-170

15

W.

August

30-18

2910

29-81

68

46

56-61

5-214

12

NW.

Septemb.

30-20

29-14

29-78

68

41

55-55

3-329

16

SW.

• October

30-18

28-92

29-54

63

34

51*95

3-009

17

SW.

Noverab.

3005

2909

29-78

55

21

42-30

2-615

9

w.

Decemb.

30-46

28-57

29-47

54

24

42-53

10-365

23

SW.

Average

29-63

48-03

58-006

179

In comparing the preceding summary with that for 1826, it ap-
pears that the barometer has not reached the altitude which it then
attained, 3078, and the mean height for the year is one tenth of an
inch less. The heat of the summer months has not equalled that of
1826, the greatest being 74° ; whilst in 1826 the maximum was 85°,
and the mean 47°'8I. The superior mean temperature for 1827
may be accounted for by the weather's being more uniformly mild.
From 26th of April to 21st of November, (or a period of nearly seven
months) the thermometer was never so low as the freezing point ;
and from the former date to the end of the year, there have been but

eleven

Meteorological Observations for January 1 828. 337

eleven days of frost. We have had thirty-two wet days more in this
year than in 1826, and the quantity of rain is greater by 14*926
inches. The writer of these remarks has carefully registered obser-
vations on the weather in this town for upwards of five years. He
subjoins a summary from 1823 to 1827, both years included. From
observations made by the late John Gough, and by John Dalton of
Manchester, he inferred the mean annual quantity of rain for Kendal
was 51*8 inches. The average for the five years alluded to, will be
found to be 57*310 inches. The difference may arise from two causes :
— one, the difference of altitude in the places where the observations
were made, above the level of the sea ; but though that does not
exceed many yards, yet even so small a difference will affect the
amount of the mean in a series of years. The observations from
which the former mean was calculated, were taken from twenty dif-
ferent years, though not twenty successive years. Assuming all the
observations to be equally correct, the mean deduced from the twenty-
years is most likely to be the correct one. There are few places
where rain-gauges are kept, that have so great a quantity of rain as
at Kendal, though it is probable that in many places there are more
rainy days within the same period. From a number of observations
now in my possession, the annual mean quantity of rain which falls
in England, may be stated at 352 inches.

Years.

Mean of

Mean of

Inches of

No. of

Prevalent

Barometer.

Thermometer.

Rain.

Rainy Days.

Winds.

1822

62-726

1823

2956

4500

62-749

198

1824

29-76

46-88

62-762

187

SW.

1825

2964

4749

59-973

169

sw.

1826

2973

47-81

43060

147

SW.

1827

29-63

48-03

58-006

179

sw.

Mean

29-66

47-04

57310

176

sw.

METEOROLOGICAL OBSERVATIONS FOR JANUARY 1828.

Gosport. — Numerical Results Jor the Month,

Barom. Max. 30-40 Jan. 27. WindN.W.— Min.29-17 Jan. 13. Wind S.W.
Range of the mercury 1-23.

Mean barometrical pressure for the month 29-895

Spaces described by the rising and falling of the mercury 6-740

Greatest variation in 24 hours 0-530. — Number of changes 22.
Therm. Max. 56° Jan. 18 and 25. Wind SW.— Min. 29° Jan. 9. Wind NE.
Range 27°. — Mean temp.of exter. air 44°-95. For 31 days with © in v?44-05
Max. var. in 24 hours 17°-00 — Mean temp, of spring water at 8 A.M. 52°-57

De Luc's Whalebone Hygrometer.

Greatest humidity of the air several times during the month 100°

Greatest dryness of the air in the afternoon of the 27th 63

Range of the index 37

Mean at 2 P.M. 80°-8— Mean at 8 A.M. 87°-4— Mean at 8 P.M. 89-8

of three observations each day at 8, 2, and 8 o'clock 86'0

Evaporation for the month 0-60 inch.

Rain

238 Meteorological Observations for January 1828.

Rain near ground (5-710 inch.— Rain 23 feet high 6*135 inch.
Prevaling Wind S.W.

Summary of the Weather.

A clear sky, 2; fine, with various modifications of clouds, 9; an over-
cast sky without rain, 11£ ; foggy 1; rain, 7a- — Total 31 days.

Clouds.

Cirrus. Cirrocumulus. Cirrostratus. Stratus. Cumulus. Cumulostr. Nimbus.

16 8 30 1 8 9 19

Scale of the prevailing Winds.
N. N.E. E. S.E. S. S.W. . W. N.W. Days.
h H 3£ 6 4 7 4 2£ 31

General Observations. — The first part of this month to the 17th was very
wet, and generally stormy, 6*385 inches of rain having fallen here ; the lat-
ter part was dry, with a humid atmosphere. From the 2nd of December
last to the 17th instant, upwards of a perpendicular foot of rain fell here,
and during that period heavy rain frequently fell throughout England, but
chiefly along the southern shores ; also along the shores of Ireland and Scot-
land, in consequence of the S.W. winds and gales having prevailed two-
thirds of the time, and having often been crossed by upper winds : the re-
sult was an overflowing of the rivers, and a general inundation of the low
lands. Even the level roads and lands near the hilly districts in Hampshire,
and the adjoining counties, lay under water several days about the middle
of the month, which rendered them impassable to foot-passengers.

On the 1st instant, 1*89 inch of rain fell between the hours of 8 a.m. and
6 p.m., accompanied with a brisk gale from the S.E. in the morning, and a
very hard gale from the North throughout the afternoon and night. That
depth of rain in so short a time is with us unprecedented ; but nearly the
same depth fell here in 24 hours on the 29th of August 1821. — A more
violent gale and rain in the afternoon, (as the latter frequently came down
in torrents), have seldom been experienced : and in consequence of the
then highly saturated state of the ground, the level roads and fields about
the town and neighbourhood lay under water several hours, and carriages
were prevented from travelling in the roads till the rush of water from the
higher ground had subsided. On the morning of the 5th, icy efflorescences
appeared on the inside of the glass windows ; and at mid-day a bright par-
helion was observed on the eastern side of the sun, 22£ degrees distant
from his centre, From the 6th to the 10th the atmosphere presented a
snowy appearance, and on the latter day one inch and a half of snow fell
here, with a gale from the North-east. Early in the afternoon of the 11th
a thick fog came on, but was soon dispersed by a change of wind to
the West ; and from a sudden rise of temperature the ice and snow were
dissolved in four or five hours. While the thaw was thus rapidly going
on, and immediately after the fog cleared away, a dense stratus, two or
three feet in height from the ground, formed in the town and its vicinity,
which viewed an hour before sunset from a height of twenty feet, had an
unusually whitish appearance, like smoke from a tobacco-pipe. It was no
doubt produced so suddenly, by the heat from the ground communicating
with the lower atmosphere, whose temperature was only 40 degrees; while
the heat of the ground, which had been kept down by the ice and snow,
was 13 degrees higher. A wet fog prevailed throughout the day of the
12th: its temperature on the ground at 9 a.m. was 40 degrees; at three
feet high, 43 degrees ; and at nine and twelve feet high, 46 degrees. At

midnight

Meteorological Observations for January 1828. 239

midnight vivid lightning appeared in the W.S.W. horizon, preceded by
two winds crossing each other, the upper one from that point, and the
lower one from the South-east. Several black thunder-clouds also ap-
peared at the same time at a great distance to the westward, which, with
a rapid fall of the quicksilver in the barometer, indicated an approaching
storm. The thunder-storm and hurricane are said to have come on at
Plymouth soon after midnight, and to have lasted three hours with in-
creasing violence, so that not only the ships and vessels at that port re-
ceived considerable damage, but those in the Atlantic Ocean, over which
the hurricane came, as since ascertained. At 4 o'clock the following
morning a very heavy gale from the S.W. was felt here, accompanied with
heavy rain, vivid lightning, and long peals of thunder, from half-past five
till half-past six : and in three hours afterward the storm was very awful
at Dover, and severely felt in the Straits ; so that it was more or less vio-
lent along the whole southern coast. It is remarkable that the morning
tide here, and at Plymouth, on this occasion, was very nearly as high as
any of the following spring tides, notwithstanding it was a neap tide.

The mean temperature of the external air this month is unprecedentedly
high; indeed the mean of March in several preceding years was much
lower, and it certainly felt more like a spring than a winter month, which
has been verified in some measure by the unusual appearance of spring
flowers. This may be justly attributed to three co-operating circumstances,
viz. the prevalence of warm winds, as may be seen by the above scale ; the
wet state of the ground, and the consequent humidity of the contiguous
air; and the uncommonly high temperature of the ground, from there
having been but little frost this winter to diminish its heat. The maximum
temperature of the air has occurred four times by night instead of in the
day.

The atmospheric and meteoric phenomena that have come within our
observations this month, are two parhelia, one lunar halo, two 'meteors,
and eleven gales of wind, or davs on which they have prevailed ; namely,
one from the North, five from the North-east, two from the South-east,
and three from South-west.

REMARKS.

London.— Jan. 1. Fair. 2. Foggy. 3. Fair. 4. Rain. 5. Snow.
6— 9. Cloudy. lO.Fine. 11. Snow. 12. Fog. 13— 15. Cloudy. 16. Snow.

17, l8.Rain. 19— 21. Fine. 22. Cloudy. 23.Fine. 24. Cloudy. 25.Rain.
27. Fine. 28. Foggy, 29. Rain. 30, ,31. Fine.

Penzance. — Jan. 1. Heavy rain : fair. 2. Fair. 3. Rain : hail-showers.
4. Hail-showers. 5. Fair : rain. 6. Clear. 7. Rain : blowing strong. 8. Fair.
9. Fair: rain. 10. Rain. 11. Clear. 12. Cloudy: rain: stormy at night.
13. Rain. 14. Cloudy : rain. 15. Rain. 16. Clear: rain. 17. Rain.

18. Rain : clear. 19. Fair. 20, 21, Clear. 22. Cloudy : clear. 23. Clear :
misty. 24. Rain. 25. Rain : clear. 26. Clear : 27,28. Fair. 29, 30. Clear.
31. Rain. — Rain-gauge ground level.

Boston. — Jan. 1. Rain. 2. Fine: rain p.m. 3. Fine. 4. Fine: rain p.Ar.
5 — 8. Cloudy. 9. Cloudy: snow p.m. 10. Fine. 11. Snow. 12. Fine:
rain early a.m. 13. Rain. 14. Cloudy: rain p.m. 15, 16. Cloudy.
17. Rain and stormy. 18. Rain. 19 — 23. Fine. 24. Cloudy : rain a.m.
25— 28. Fine. 29. Cloudy. 30. Fine. 31. Cloudy.

Owing to the Discontinuance of Mr. Howard's Observations, our Meteoro-
logical Table has some deficiencies, which we hope to supply in our next.

Meteor o-

•isog

CI -* .

6 6 :

'O

r^-oo o in

C5 in 7« O

O O mo O O

dsOQ

5 :?i :
© 6

oocminooo

CO © 00 ^ ~ -* CO CO

s !

in . . o in o o o o

o* • • ic oo ( o oo o cn

i^ • • (N 00 T* ^ -tf <N

6 h66666

b im
-* m
o ht
6 lr-

puo^j

dsoQ

: o o
6

puoi

I b s £ >• *• > s . .as.-s s . . .a.aa.as.. . a a a .
•>sog hi I s £1.1 w "ll^l w w w1 ^11 *11 * * *1 1 1 •

dso°U tf I - i i* " " *-" s b£ 3 g «" 8 1 1 £ i| *i i *i «;« H

•zuaj » > j* £ fe «t w J,* w w fe £ £ ^ £. <* > > t te > fe te St > £ & «5 £ £ £

•pu°t g * •&* * a

» * ^ % ? & % > >

«J 03 03 03

*•£*>

„„ ,JL0|C0<o co^oot^^t^inv©c<»coON^6iuo©>r^i>coao«©cooOi^oo<©c* © -*

*?SOg[ |T}<CO-'*COC0C0C0COrO— • <N OrJ<C^CO<v5cn'*rt<'*TtTtT^r3«rtrJ<'^CO-^^J,'^<

3 15 C0"tfCOCOCOC0COC0C< COT}«T*TtfCOO^U3^^rf^Tr^TfTfTf?OTj»'«tfTfTtr>|

<N — 00 <©

g mm

OHO(NOiONaHOi>(NOcniOi^(NTtioT*io(o-(na(MO(N'to
TfTtrf ^Tt coco rf in in ^-^ in in in in in >n in in in -n in in in in in in >n

Si-ilSSi'^.^ocJ ooooinmmfN ^oo ©oooioooit^t>t^iciOTtirnot^

ooooo»nininm^c^^c^QOt^c^csj^mTticninocNoicJ--Hooocooci
inTtin^^^^-^^ioioin^^^mininminminuoininin^inininin

c .£ ^in-<*co<=*cococooNao<o<Nooin.--aooNOc^
o g co^cococococococicico-TfcocococoTi"^^

Q

oooTfin^oooifl^otOMot^ooioio
rfininTi<cocncocccnco'^-^'"rti^,co'^,inin«n

CQ oo

(NClOt^iOt^iOOeit^OfliOWOit^OiOOiOMXXSiOOrf^lO-iOCO

si in© on<n ^^^oo^^Ttcooirpini^-o r^r^r^inc^oo r^t^co onoo r^in
on On On On on on on on on on on on oo on on onOn©nonononononononononononono>
c^c*c*c*cNC*c<CNic^c*oie<c<JC*e*c^cNc^cNc^c^cNeNoic^c^

<© — oioaioonooTt*

CNC'N'7<<NCO<N>7'ONON

onononon^^^onononononononononon© o b b b b b © b o b © on on
c»c*cic^<>i<NC*c*c*c>ioic<c*c*c<oic<cocococococococococococoa}c^

c^coinooNoocoino^t|ooco(NO<oin'*(Noo--<oininoNooooi>.ino

U5O0 t^OO *pi>-Op QpOl^ipt^^ipt^^ON-HlNiaiN^nip-inTfco-HOCi
ONONON<^©NONONONONONONONONONGNONONb © O © © © © © © © O © C5 CT\

O^ONONONONONONONONONONONONONONONONONb b c b o o b O O O <~> 6>CN
CI O CIO OJ (M d CM <N Ol Ol C< CN (N <N d CM <N <OCOCOCOCOCOCOCOCOCOCOCNCN

jlOOOOOOOpcT)00 0 000(M'*OiOOO<NOOOinOt^OO<0

g Up C30 op r^r^t-»»nt^r^>n7t^p in>nininr-~9 o *~ *-< --. oi m oi cn ^<cn 9000
s 6>on^on^on<^onononononononononono b b b b o o b b o b b o on

*!c*C*C*C*CIC*C*C><CIC^<^C*C*CNC<e<C^COCOCOC0^

S

§ 2

T3

o^otNn-HTtmt^tNN'-inO'-oon^orr)
OTtoioipop r^a>r^ipr)iLOTtTto>ociO'-<
On ON On On on On on On on on On on on on on On on b b
C^(^C4C*C<C<CN<NOI010ICNCNC>IClOIOIC0CO

ibNO^ONONONONONONONONONONONONb b
d<NdC*dO«C*d<NC«C>J<NCJ(NCOCO

o

• THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY.

[NEW SERIES.]

APRIL 1828.

XXXIX. A Letter to the Editors relating to the Ellipticity of
the Earth as deduced from Experiments with the Pendulum.
By J. Ivory, M.A. F.R.S.

Gentlemen,
T N examining the calculations in the articles relative to the
«■ ellipticity of the earth, inserted in the last Number of this
Journal, I have detected a small arithmetical error, which, al-
though of little moment, it may be proper to correct. The
equation at the bottom of p. 1 70, viz.

2-973 t= --00061,
should be, 2*973 t = — -00033:

consequently, t = — -00011, s == -f 00005,

/=-2056, A= -01335;

and the formula for the length of the pendulum,

I = 39-01335 + -2056 sin2 A.
But the error just corrected is so small as not to affect either
the reasoning deduced from the formula at the top of p. 171,
or any of the results obtained by it.

It is directed in p. 207, that the two approximate quantities
a and b, be so taken as to satisfy equation (A) : but it is ob-
vious that, although this be convenient, it is not necessary in
the method of computation I have followed. Nothing more
is required than that a and b nearly satisfy equation (A) ; in
which case the right-hand side of equation (B), will not be
equal to zero, but to a small known quantity positive or ne-
gative,— a circumstance which makes no essential difference in
finding the corrections 5 and t.

From the calculations which have been made, we may infer
New Series. Vol. 3. No. 16. April 1828. 2 I that

24-2 Mr. Ivory's Lette?- relating to the Ellipticity of the

that no great confidence can be placed in the ellipticity de-
duced from any partial combination of the experiments with
the pendulum : for we have found that there is considerable
uncertainty in the value of that element, even when we avail
ourselves of all the experiments we at present possess. This
matter will be placed in a clear light by setting before the
reader, the values of A, or of the excess of the pendulum at
the equator above 39 inches, which we have obtained by ta-
king different means of the tropical experiments, viz.
A

•01230^ C 6 experiments.

•01330 > mean of < 9

•01605 J (.15

The true value of the equatorial pendulum is therefore very
uncertain. If we take the first mean of six tropical experi-
ments, and neglect the other nine, we shall obtain, by com-
bining the 31 remaining experiments, a formula for the length
of the pendulum coinciding very nearly with that published in
this Journal for October 1826, the ellipticity being about 7^n.
The other two means are the bases of the calculations in the
two papers inserted in the last Number of this Journal. A strict
scrutiny of the experiments would perhaps bear us out in
adopting ^-^ as the ellipticity that best agreed with the bulk
of them ; but any ellipticity between ^-^ and ^^ will repre-
sent sufficiently well 34 out of the 40 experiments in our pos-
session. The ellipticity ^-gdoes not represent with much ac-
curacy, either the six anomalous experiments, or the remain-
ing 34; and in the present state of our knowledge, we may
consider it a thing nearly demonstrated, that this value is too
great.

What is most remarkable in the experiments with the pen-
dulum, is their excessive irregularity near the equator. This
is well illustrated by the four values of A following, which are
experimental quantities, not the results of calculation, viz.

Longitude. A

Maranham 44°21' W. -01173

Rawak 131 1 E. -01479

Galapagos 90 0 W. '01717

St. Thomas 6 45 E. -02074

The longitudes are set down, as all the stations are so near
the equator, that they may be reckoned upon it. If the same
irregularity shall be found to prevail upon all the parallels, it
must be acknowledged that the figure of the earth, deduced
from such incoherent data, will lose much of the interest and
utility, which are usually attached to it. But no such irregu-
larity

Earth as deducedfrom Experiments witkthe Pendulum. M£

larity has hitherto been experienced beyond the tropics; and
even between the tropics there are only a few stations at
which so great an excess of gravity has been observed as ex-
cludes them from belonging to the same surface as the other
experiments. I apprehend it cannot be said at present that
the great anomalies alluded to, are so well ascertained as to
render any further inquiry unnecessary in regard to their ex-
act quantity, or to the causes which produce them : and the
determination of these points in preference to any other, seems
to claim the attention of the experimenter ; because it must
fix in a great degree the complexion of the whole theory.
Can we hope to determine an elliptical surface that will re-
present ail the experiments within the limits of the probable
errors of observation ? Or, must we be content with a mean
elliptical figure liable to great discrepancies ? These seem at
present to be the most interesting questions in this research.
The least attention to the position of the anomalous stations
on the surface of the globe, will prove how fruitless it would
be, to suppose that the experiments can be better represented
by a figure different from the elliptical spheroid. Far less can
we expect, in the present state of our knowledge, to attain any
useful purpose by pushing the theoretical solution of the figure
of the earth to quantities of the second order ; because the
corrections thus introduced must be ultimately determined by
the experiments themselves, the uncertainties of which greatly
surpass the quantities to be found.

I remain, Gentlemen,

Your obedient servant,
March 12, 1828. J. Ivory.

XL. Remarks on the Geology of the North Side of the Vale
of Pickering. By John Phillips, F.G.S., Keeper of the
Museum of the Yorkshire Philosophical Society*

[With an Engraving.]
HPHE principal object of this communication is to explain
• some of the peculiar appearances which are exhibited
along the southern edge of the oolitic hills which margin the
Vale of Pickering from Seamer to Helmsley.

My attention was first drawn to a part of this country by a
visit to Kirkdale Cave, in company with Mr. Salmond and
Mr. Smith, in March 1824. In August of the same year I had
further opportunity of examining with the aid of a barometer,
the whole line during my walk from York to Scarborough.

* Read to the Yorkshire Philosophical Society, Jan. 1, 1828; and com-
municated by the Author.

2 I 2 In

244 Mr. J. Phillips's Remarks on the Geology

In September 1825, I again traversed the line from Craike
by Wass Bank to Helmsley; in September 1826, the Rev.
W, V. Vernon and myself twice observed with attention the
country about Ebberston and Snainton; and in October 1827,
I very carefully reviewed with a barometer in my hand the
whole line from Scarborough to Brandsby.

The roads from Craike and Brandsby to Helmsley, and from
Helmsley to Scarborough, are lines remarkably well adapted
for inquiring into the stratification of the country in question,
and slight deviations to the right and left are easily made.

Some results of these several investigations I now beg to sub-
mit to the consideration of the Society.

Four strata or formations as usually enumerated, are seen
along the north side of the Vale of Pickering.
Kimmeridge clay.
Coralline oolite.
Calcareous grit.
Oxford clay.
Of these the Kimmeridge clay, coralline oolite, and calca-
reous grit, may be considered as well identified by imbedded
fossils with the strata bearing those names in the midland and
southern parts of England. The Oxford clay is defined by its
position between the well identified calcareous grit and Kel-
loways rock, and contains besides some ammonites which lo-
cally serve to characterize it.

Kimmeridge Clay, — It was in 1824 that I first had the plea-
sure of finding in the Kimmeridge clay, where it had been ex-
posed by cutting the road at the east end of Kirby Moorside,
plenty of characteristic pieces of Ostrea deltoidea, a fossil which
Mr. Smith and myself had always considered to mark this
stratum. The clay here is thin, contains minute layers of brown
and white sandy lumps, in the upper part of which lies an am-
monite like A. jplicomphalus (Min. Conch.), and covers brown
sandy stone incumbent on coralline oolite. The clay rises to
the north, and forms the little insular hills which have recently
afforded new examples of Ostrea deltoidea. From Kirby to
Sinnington it retires to the south of the road, but beyond Sin-
nington forms a hill nearly a hundred and twenty feet high
above the stream which there exposes the uppermost beds of
the oolitic series beneath. From this point its course is wholly
on the south of the road, but so much concealed by the allu-
vial and diluvial covering, that it would be a difficult matter to
represent it on a map with even tolerable accuracy. It is seen
on the coast at intervals from Filey to the Speeton Cliffs ; but
Ostrea deltoidea has never yet been found there. Unless at
"about one mile east of Helmsley, the Kimmeridge clay lies

wholly

of the North Side of the Vale of Pickering, 24? 5

wholly to the south of the road from Kirby Moorside to Sprox-
ton, one mile south of Helmsley. In this clay hill I found no
opportunity of searching for fossils, but about a mile further
west, where the road crosses a low insulated woody hill, I had
the satisfaction of finding, in a broken clay bank, a layer of
Ostrea deltoidea in tolerable perfection. This is the fifth ex-
ample within my own knowledge of this remarkable fossil be-
ing found in the Kimmeridge clay of Yorkshire. Its true po-
sition here, as at Heddington and other places in the south of
England, is very near the top of the oolitic formation which
lies beneath ; and I have no doubt it would be found in several
other places, and in greater plenty, if it were carefully sought
after. From the hill above mentioned, the Kimmeridge clay
turns away toward Malton, and accompanies the eastern
boundary of the coralline oolite.

The Oolitic Rocks rise from out of the Vale of Pickering
to the north and to the west. Every one accustomed to prac-
tical geological investigation will at once recognize in the long
slopes from Hambleton and Oswaldkirk, the Terrace of Rie-
vaulx, and the sides of Newton dale, the characters of regular
declination. There has been a general mistake respecting the
order of succession of the members of the coralline oolite
series in this tract of country. It has been generally believed
that the uppermost beds of the series are coralline or shelly
limestone, such as is seen in the quarries near Scarborough
and Malton. But in truth, these oolitic beds are separated
from the Kimmeridge clay by a considerable thickness of
sandy calcareous and ferruginous beds, containing some fossils
analogous to those which lie in the calcareous grit beneath the
oolite.

This fact is evident on either the Gilling or Coxwold road
to Helmsley. Oswaldkirk bank on the former road shows
oolite under a considerable covering of brown sandstone, which
continuing beyond Grange is twice covered by detached hills
of Kimmeridge clay, but never once exposes the subjacent oolite
till we descend to the town of Helmsley (see Plate V. section A).
On the Coxwold road, after ascending nearly the whole height
of the romantic Wass Bank, we notice the Oxford clay, sur-
mounted by mural precipices of calcareous grit, and at the brow
of the hill a quarry of coralline oolite covered by a hundred
feet of brown and yellow sandstone. This forms the poor
heathy moors to the north-west, and continuing N.E. towards
Helmsley, presents to that town an escarpment on the declining
side which exposes the coralline oolite (see section B).

Here then we first find indications of a denudation of a very
interesting character : a denudation on the dipping edge of the

strata

246 Mr. J. Phillips's Remarks oh the Geology

strata which has produced here and there escarpments looking
toward the formations which cover their continuous slopes.
This principle will, I am satisfied, be admitted by all who care-
fully consider the facts ; and it avoids the impropriety of sup-
posing a dislocation without evidence. According as the de-
nudation has extended more or less toward the "rise" of the
strata, more or fewer beds of the oolitic series are exposed :
where the denudation has produced the greatest effect, the
lowest stratum exposed is Oxford clay.

A similar escarpment is found on the Rievaulx road from
Helmsley as on the Oswaldkirk road; but long slopes of co-
ralline oolite and brown sandstone over it cross the road to
Bladlam. Hence to the valley of Kirkdale the same brown
stone lies on all the higher parts of the road, and in a soft con-
dition covers the oolite in the quarry at the famous cave. A
mean of three measures very carefully made in 1824, gave me
thirty-one feet for the height of the cave above the bed of the
stream. (The statement of eighty feet in Dr. Buckland's ac-
count is probably a typographical error.) Nearly fifty feet of
oolite are here exposed, and there are about twenty feet of
sand and sandstone above. The brown stone continues be-
low Manor-dale to Kirby Moorside, where it is covered by
Kimmeridge clay.

In the stream which flows through the heathy common on
the road from Kirby Moorside to Sinnington, geologists may
observe in a very satisfactory manner the relation of this sand-
stone to the coralline oolite. The road-bridge over the stream
stands on irregular sandstone layers, containing a few frag-
mented shells. Rising toward the north at a greater angle
than the slope of the valley, fresh beds are exposed in succes-
sion as we proceed, and at length below six feet of yellow sand
we find the uppermost very solid bed of oolite full of Turri-
tellce, Melanin, spines of Cidaris and Trigonia costata, as at
Helmsley. A few beds lower lies a coarse variety of Ostrea
gregaria ? (Min. Conch.) At about half a mile from the road
these observations may be repeated in the large limestone
quarries, where the remarkable turbiniferous bed covers the
other calcareous layers. Some Turritellce also occur in the
lower beds of the rock, which occupies the whole stream and
sides of the valley, being covered by the heathy cap of sand-
stones. In the bank of the stream at Sinnington these sand-
stone beds are again exposed dipping south, and afford some
fossils extremely similar to those which accompany the lower
calcareous grit; particularly ammonites and pectines. Be-
yond Sinnington, the road crosses a hill of Kimmeridge clay
one hundred and twelve feet above the stream; then descend-
ing

of the North Side of the Vale of Pickering. 247'

ing almost as many feet, it continues by Wretton and Aislaby
on the long slopes of the same sandstone series to Pickering.

It thus appears that from Helmsley to Pickering the effects
of denudation on the dipping edge of the oolitic series are
scarcely at all observable ; the beds declining regularly, and
almost without interruption, into the Vale of Pickering. The
denudation of Helmsley appears to be connected with the for-
mation of the valleys about that town ; but from Pickering east-
ward, a more extensive operation of similar causes has pro-
duced a long range of escarpments crossing the direction of
the little existing valleys, but parallel to the general line of the,
great Yale of Pickering.

The valley descending to the south by the town of Picker-
ing, presents good opportunities of observation. The strata
on the western side are much lower than on the eastern, and
slope south into the Vale of Pickering, without presenting any
escarpment. On the eastern side calcareous grit is quarried
beneath the limestone, a thin covering of the upper sandstones
mixed with clay lies above that rock, and the whole series,
sloping south into the Vale of Pickering, has been subjected to
denudation parallel to the range and on the declining side.
The effect of this denudation becomes extremely evident as
we proceed further toward Scarborough. Before reaching the
village of Thornton we cross a hill which appears to me to be
formed of the Oxford clay. At Allerston, springs issue from
the top of it, beneath the calcareous grit which is found on all
the little risings to Ebberston, while the clay fills the valleys.
At Ebberston, as at Allerston, springs issue from beneath the
calcareous grit, and flow southward over the Oxford clay, in
which stratum Mr. Vernon and myself found Mya. V-scripta,
and a peculiar ammonite as at Scarborough (see section C).
At Parson's Houses, between Ebberston and Allerston, a well
was sunk twenty-one yards through the clay of Ebberston to a
brown freestone rock, which I suppose to be Kelloways stone.

Above the line of springs at Ebberston, calcareous grit in
its usual characters with calcedonized ammonites occupies a
good height in the hill, and is surmounted as usual by the
coralline oolite, here full of Ostrece in the lower part, and of
Melanice and TurriteLlce at the top. This escarpment, showing
calcareous grit and coralline oolite, is very distinct above and
north of the village of Snainton ; and I think may be traced,
though less evidently, by Brompton and Wykeham to the old
Tower at West Ayton. After this, the long slopes of calcareous
grit, descending from Falsgrave Moor and Oliver's Mount, are
covered by parallel beds of oolite at Seamer, sloping down into
the Vale of Pickering without any denudated edge.

Between

24-8 Mr. J. Phillips on the Geology of the Vale of Pickering.

Between these sloping beds of the oolitic range as they con-
tinue to Filey Brig, and the projection of chalk from Hunman-
by, the Vale of Pickering is much narrowed; and where it opens
into the sea exposes such a vast quantity of diluvium as to
cover almost all the beds of oolite, and effectually to hide the
junction of this series with the Kimmeridge clay. This stra-
tum is seen irregularly in the cliffs peeping out from under its
huge load of diluvium, and at length near Speeton is exposed in
very decided characters, lying immediately beneath the chalk.

I have no doubt that an impartial examination of this line
of country will lead to the adoption of my opinion, that the
pseudo-escarpments of the oolitic rocks on the north side of
the Vale of Pickering are caused by denudation nearly parallel
to their ranges, and that no general dislocation is at all con-
cerned in the appearances. Even a new zigzag fault would
add nothing to the explanation, the facts remain just as before :
sometimes the dip of the strata is uninterrupted till the Kim-
meridge clay, as at Sproxton and Kirby Moorside, lies on the
oolitic rocks; in other cases the declining surface is interrupted,
and a pseudo-escarpment results, exhibiting coralline oolite
alone as at Helmsley, or calcareous grit beneath it as at Pick-
ering, or even Oxford clay beneath that as at Ebberston.
The strata re-commence no doubt on the south of this last
place; but they are not seen, because from the breadth of the
denudation the opposite edges are sunk much below the ge-
neral level of the vale, and covered by diluvial and alluvial
accumulations. These accumulations prevent the Kimmeridge
clay from being seen in the flat central part of the vale ; but
on its southern side where the ground rises to the Wolds this
stratum maybe very well traced. (See Plate IV. section D.)

The inferences from these results connect themselves closely
with general views on denudation and diluvial action, but it
seems improper to enter into a discussion of them on such an
insulated example. This is not the only instance which may
be brought forward when the details have been more carefully
studied. Till then, I must content myself with referring to the
accompanying sections in illustration of these remarks, and
have only further to observe that they were all drawn on the
spot. — One general explanation will apply to them all :
Plate V. 1. White chalk.

2. Red chalk.

3. Kimmeridge clay.

4. Upper calcareous grit.

5. Coralline oolite.

6. Lower calcareous grit.

7. Oxford clay.

8. Kelloways

Mr. Tredgold on a new Theory of the Resistance of Fluids. .249

8. Kelloways rock, which appears on the northern edge
of the oolitic lulls, but is not seen at the surface
in the Vale of Pickering.
Dec. 1827.

XLI. A new Theory of the Resistance of Fluids, compared with
the best Experiments, By Mr. Thomas Tredgold, CVw7
Engineer; Hon. M. Inst. Civ. En., and of the Liter, and Phil.
Society of Newcastle-upon-Tyne.*

[With an Engraving.]

1. HPHE following is an account of some inquiries respecting
f- the resistance of fluids, which were undertaken to en-
able me. to render more effectual assistance to those who con-
sult me on subjects where an accurate knowledge of this re-
sistance is of importance : a further motive to proceed in the
research was the extensive application of which it is susceptible
among the wants of a commercial nation. With a like sense of
its utility it was long ago remarked by Dubuat, " that to de-
termine the resistance which a body in motion experiences
in a fluid at rest, is one of the most important problems of
general mechanics;" and since that time it has acquired still
greater interest, in consequence of the application of a new
species of power to propel vessels at sea.

2. Since I commenced the investigation, the French Aca-
demy of Sciences have offered a premium for the best series
of experiments on the resistance of fluids* ; and certainly a good
series of experiments under a great variation of conditions would
be valuable ; but when they are not made for the express pur-
pose of determining particular truths, or data, they become of
little value in assisting the progress of scientific investigation.
The object of an experiment, like that of an equation, is the
determination of something unknown; the same principles ap-
ply to both cases. The fine discoveries which made chemistry
a science, resulted from experiment conducted by the methodi-
cal system of the mathematicians, though not in the same tech-
nical form.

I have felt the defects of the miscellaneous system of experi-
ment, in attempting to correct and confirm my own inquiries ;
but have compared them with the best I am acquainted with.

3. When a body is moved forward in a fluid, the parts of
the fluid before the body must be displaced ; the force required
to produce this effect is the measure of the direct resistance.

* Read to the Lit. and Phil. Society of Newcastle-upon-Tyne ; and com-
municated by the Author.

New Series. Vol. 3. No. 16. April 1828. 2 K 4. The

250 Mr. Tredgold on a new Theory of the Resistance

4. The vacancy left by the motion of the body is filled by
the motion of the fluid ; but, with a loss of the force necessary
to maintain an equilibrium among the parts of the fluid, equi-
valent to the force producing this motion in the fluid. The
increase of resistance from this cause has been termed the
minus pressure of the fluid.

5. The sum of the direct resistance, and that due to the de-
ficiency of equilibrium, called the minus pressure, is the total
resistance when the friction is neglected.

6. If fluids were devoid of friction they would be perfectly
elastic, differing only in the degree of compression produced
by a given force ; hence, in considering the effect of collision
on a fluid, it must be esteemed an elastic body. The coherence
and friction of natural fluids render their elasticity in a slight
degree imperfect, but not sufficiently so to interfere with the
application of rules founded on its perfect elasticity in most
of the cases occurring in practice. The total want of elasti-
city is incompatible with the very nature of a fluid.

7. If a body moving with an uniform velocity in a straight line
AB, Plate IV. fig. 1 . impinge on a filament of a fluid in which
it moves, with a part of its surface inclined in any manner to the
direction of the motion, the fluid will be reflected, and the di-
rection of the resultant of the impingeing and reflecting forces
will be perpendicular to the surface, and equal to the pressure
of a column of the fluid capable of producing the actual ve-
locity of the body. For the fluid being elastic, the restoration
of figure produces the reflecting force, and the force in a di-
rection perpendicular to the surface is only half that which
would arise from the collision of a non-elastic body.

•8. Of the direct Resistance. — Let v be the difference between
the velocity of the fluid and that of the body, when estimated
in the direction of the motion ; g = the space described in a
second by the velocity due to the force of gravity in vacuo =
32£ feet ; a = the angle the portion of the surface, on which
the filament of fluid strikes, makes with the direction of the
motion: and h = the height of the column of fluid equal to
the direct resistance. The velocity of the body is to that of
the surface in a direction perpendicular to itself; or in the di-
rection of the resultant as v : v sin a ; and "n = the co-

lumn of fluid whose weight would be equivalent to the per-
pendicular pressure. This pressure reduced to the direction

of the motion is h = v *"— , the forces perpendicular to the

direction of the motion being supposed to mutually balance
one another.

9. Of

of Fluids, compared with the best Experiments. c25\

9. Of the Minus Pressure. — It is obvious, from the property
of figures having parallel sides, that the quantity of fluid re-
quired to fill the vacancy left behind the body when it moves,
is a constant quantity, whatever be the form of the body ; there-
fore the deficiency of pressure will vary only with the velocity
the fluid must acquire to follow the retiring surface. But if
c be the angle that surface makes with the direction of the
motion, the velocity will be v sin c ; consequently, the motion
of the fluid being established, the resistance from the defi-

ciency will be — .

Combining the two resistances, we have the height of the

column = -v"— f2 sin3 a + sin 2 c) + F = H ; where F is the

4g N

friction. When the body is a cube or a cylinder, with the
ends perpendicular to the direction of the motion, the angles

become 90°, and neglecting the friction ~ — = H.

The height due to the resistance being to the height due to
the velocity as 3 : 2.

10. If the height of a column that would balance the fric-
tion be x feet, and H be the height producing the motion, then

H — <r= -— (2 sin3ff + sin2c); or x=H — (2 sin3 a + sin2c).

4g v 4g v

Assuming that the friction varies as the square of the velo-
city, and as the surface of the body; and putting f— the
height of a column of water whose weight is equal to the fric-
tion of one foot of surface when the velocity is one foot per

f
second ; then — will be the height when distributed over

the whole section of the moving body, when 5 is the area
of that section ; therefore, if Ip be the area of the surface,

s

11. There is also the friction of the fluid itself to be consi-
dered when the velocity is considerable ; and without being
able to assign a satisfactory reason for it, if we consider the
length to be increased by a quantity Aw, where A is a coeffi-
cient depending on the nature of the fluid, the result agrees
nearly with experiment, and the value of x including this effect

is fp&U -f- Av) , ,

x = * s ; and consequently,

Before attempting to determine the constant quantities from
2 K 2 experi-

252 Mr. Tredgold on a new Theory of the Resistance

experiment, it will be useful to consider the different cases
corresponding to the experiments to be compared.

12. If a plane of given area, and equal thickness, be set at dif-
ferent angles to the direction of the motion, the resistance will

be expressed by -^- j2(sin2a-{-cos2fl)+ sin a + cosfl? = H

when the effect of friction is neglected. (See Plate IV. fig. 3.)
When the thickness is inconsiderable, the effect of the edge

may be neglected, and then — (2sin2tf -f sin a) = H.

13. In the case of a parallelepiped, with a wedge-formed
prow attached, we have sin c = 1 ; ^see fig. 2.) and,

— (2sin3« + 1) = H.
4g v

Including the friction £ (2 sin 3 a + 1 + ffift *?•»«) ) = H.

The same equations will apply when a cylinder terminates at
one end in a cone.

14. The resistances of curved surfaces may also be com-
puted: for example, let it be the resistance of a sphere; — put
p =• 3*14159, and y = the variable radius of the base, and
2pyy = the fluxion of its area. Then the figure being a circle,
and x the abscissa measured on the direction of the body's

motion (fig. 4.) — — = sin a ; and yy = (r—x) x; consequently,

; — *. — 3. -v

2pv2l 2r — xx r—xx I « fl

4rV— -+ -7T-J=Hx2W
The fluents are,

2p«>«Cg(rS-(r-«)0 H-(r-x)* y _

And, when x = r,

4g \ 5 2 / 4g r 4g

The resistance of a sphere is to the resistance of a cylinder
of the same diameter as 1*3 : 3, or as 1 : 2*308 ; or as *433 : 1.

15. If a cylinder have a hemispherical end or prow, then
sin c becomes unity, and substituting this value of it in the
equation we have,

16. And, if the motion be reversed, or the flat end go for-
ward, t* / 1 \ 2-5 «« _

17. Ac-

of Fluids, compared with the best Experiments. 253

17. According to this investigation we have therefore the
following order of resistance.

A cylinder with flat ends 3 or 1*00

A cylinder with the hind part a hemisphere 2*5 or 0-833

A cylinder with the fore part a hemisphere 1 *8 or 0*60

A sphere 1*3 or 0-4.33

These ratios are likely to be altered a little by the effect of
friction ; and if the cylinder be reduced in length till it becomes
a thin plate (fig. 9. and 10.), a still greater alteration is caused
by the interference of the two motions of the fluid. The ef-
fect is easily observed by moving differently-formed bodies in
water.

18. When a cylinder moves in a direction perpendicular to
its axis (fig. 7. and 8.), making d its length, we have 2di =

the fluxion of its area, and — = sin a ■= sin c; hence,

r 7

The fluents are, when z is the arc of the curve,

Idv* /3r*z—{r-x). (3r*y + 2y») 2 r*-2 (r-x)3-3y« (r— x) v.

4g \ 4^ * 3^ /

= Hx2rfi.

In this form the equation applies to the curved ends of
canal boats having flat bottoms, the curves being usually por-
tions of circles ; and an approximate equation in the following
form is easily applied.

Let mr = half the breadth of the boat, r being the radius
of curvature; then

2rfu* f 3 z-r (1 -m) . (3-4m) V 2^ r(2-2(l-m) ( ( 1 - m)* + 3^) ? _

Ag i 4 + 3 3

(2dHi'. In the ordinary boats m ='125, and therefore,

Ag > 4 /

From these equations I have been enabled to compare some
experiments made by Mr. Bevan on the power required to
draw canal boats ; which will be detailed after treating of the
friction of bodies moving in fluids.

When a perfect cylinder is the form of the body, then r -=.x
and p = 3*14159 7-, we have,

3p j 2 \ 1-8448 v*

4g \ 8 + 3 /

H.

Ag

19. 'Of the Friction of Fluids* — A series of experiments on

the

254- Mr. Tredgold on a neiv Theory of the Resistance

the friction of water were made by CoLBeaufoy *, from whence
it appears that the friction of water is very nearly as the square
of the velocity ; and about -0032 pounds for one foot of surface
moving at the rate of one foot per second. It is somewhat
greater than this in slow motions ; most likely from the effect
of cohesion being sensible in small velocities. The experiments
made by the Society for the Improvement of Naval Archi-
tecture do not appear to be so nearly in the ratio of the square
of the velocity, but at the velocity of four nautical miles per
hour the resistance is exactly -0032 pounds (see Dr. Young's
Nat. Phil. ii. p. 229). The head of water equivalent to this

resistance is ~?- = 0-0000512 =/

20. If the resistance from the friction of the fluid itself be
neglected, the general equation for water will be

0c 2sin3a + sin * c 0-0000512 pi ) TT

*\ 12*76 + s— * =H>*

or, — ~g (2 sin3 a + sin* c + 0*0066 J&XmlJL

When sin a = sin c = sin 90°, the resistance from friction

v I
is to the resistance from pressure as 3 : 0-0066 - — .

21. The value of the coefficient A, for water is of very little
use, neither are there good experiments for determining it ; in
the resistance of air, however, it becomes of importance. The
equation for air, when the length of the body may be neg-
lected, is

;l( sin3 a + sin* c + M±UL) | H.

And if n be the resistance of the body compared with a
plane of equal section when the friction is neglected, the re-
sistance of the plane being unity, the best experiments give
4>gfA = 0-000000332 n. The results of experiments, how-
ever, differ considerably ; and it is difficult to fix on a datum
which it never was their object to determine.

22. Comparison with Experiments. — The experiments of
Bossut f were made with a parallelepiped four feet in length,
two feet in breadth, and two feet draught of water. It was
first tried alone, and afterwards with wedge-shaped prows of
different degrees of acuteness (see fig.2.); the time of describing
ninety-six feet was observed, when the velocity had become
uniform, except in the experiments with the most acute angles

* Dr. Thomson's Annals of Philosophy, vol. vi. p. 281, 1815.
f Traite J? Hydrodynamique, torn. ii. p. 394 -411.

in

of Fluids, compared with the best Experiments. 255

in which the time of describing seventy-two feet was observed.
Five trials were made with each change of form, except with
the most acute prows, which were tried only thrice, and in the
latter the results were not so regular as the others. The fol-
lowing table contains the mean resistances as Bossut has col-
lected them, the resistance of the parallelepiped being denoted
by 10000.

The equation applying to this case is t^tv 2 sin3 a -f- 1 +

128-76

0*0066

f — l8i^ J ; and neglecting the difference be-
tween the measures, the resistance must be 10000 when sin
a = l, consequently 0*3285 f 2 sin3 a -fl-f '0445 (s-h ^-)^
is the expression for other angles.

Angle with

Resistance

Resistance b)

r Calculation.

Old Theory

the Direc-
tion of the

collected
from Ob-

neglecting

without

with

Motion.

servation.

friction.

friction.

1 I 1C IIU11 •

90°

10000

10000

10000

10000

84

9893

9891

9893

9890

78

9578

9571

9578

9568

72

9084

9067

9083

9045

66

8446

8417

8442

8346

60

7710

7663

7700

7500

54

6925

6863

6913

6545

48

6148

6068

6131

5523

42

5433

5330

5407

4478

36

4800

4687

4777

3455

30

4404

4170

4272

2500

24

4240

3781

3897

1654

18

4142

3530

3662

955

12

4063

3393

3552

432

6

3999

6341

3578

109

The numbers in the fourth column ought to represent the
resistances ; and as the difference between these and Bossut's
mean results are not greater than the differences among the
trials with the same form, in any case we may, I think, con-

* See Bossut's Hydrodynamique. torn. ii. p. 411, or Robison's Mechani-
cal Philosophy, vol. ii. p. 295. Vince's Hydrostatics, sect. iii. Dr. Hut-
ton's Course of Mathematics for the Military Academy, vol. ii. Problem xix.
p. 353.

elude

256 Mr. Tredgold on a new Theory of the Resistance

elude that the formula is sufficiently uear for any practical
purpose, as far as this species of body is concerned.

23. Some experiments were made in a very different man-
ner by Mr. Vince*, and besides being chiefly made with thin
planes, they were made by a rotary machine, which rendered
it necessary to determine the centre of resistance. This he
has done inaccurately ; but neglecting its effect on the results,
the experiments give the ratio of the height due to the resist-
ance to be to the height due to the velocity as 3 : 2. This is
the same as the ratio we have derived from theory (Art. 9.).

The experiments with a thin plane set at different angles

may be compared with the equation — (2 sin2 a + sin fl) = H;
(Art. 12.) which making the resistance at 90° equal 1000, will

vary as lOOO (2 sin * a + sin a)

3 -

Angle with

Ratio by

Ratio by

Differences.

the Direction.

Experiment.

Calculation.

90°

1000

1000

0

80

963

975

+ 12

70

915

902

-13

60

820

788

— 32

50

660

646

-14

40

506

4?9

-17

30

330

333

+ 3

20

157

192

-h35

10

48

78

-f30

Mr. Vince also tried the resistance of hemispheres moving
in water; with the base foremost, and with the spherical side
foremost, the ratio was 8339 to 3400. The resistance of a
cylinder of the same diameter he found to be 7998; hence
making the latter unity we have By experiment ; Cylinder 1 ;
base of hemisphere 1*05 ; round side *427.
By calculation ; Cylinder 1 ; base of hem. *835, round side *6.

24. The experiments of Dubuatf on the pressure of water
on bodies moving in it tend to confirm the relation of 2 to 1
between the direct and minus pressure of a column capable of
generating the velocity. He has shown that the pressure is
different on different parts of a plane surface, and this we might
expect ; but the whole effect is not altered by the distribution

* Phil. Trans. Abrid., vol. xviii. p. 250.

f Principes (V ' Hydraulique, torn. ii. partie 3.

of

of Fluids, compared with the best Experiments. '257

of the resisting forces, which will vary in proportion to the
facility with which the fluid can escape by reflection from the
different parts of the surface.

25. The experiments made by the Society for the Improve-
ment of Naval Architecture*, differ considerably from others,
but they are most readily compared in a tabular form. The
resistances were taken at a velocity of five nautical miles per
hour, which is equivalent to 8*35 feet per second.

Form of the Body.

Thin square plane

Cube

Thin round plane

Cylinder

Cylinder and hemispherical end

The same reversed

Cylinder terminating in a he-1

misphere at both ends J

Sphere

Resistance
by Experi-
ment.

Pounds.
80-76
79-34.
80-64
74*69
56-04
22-28

18-53

25-24

Ration

1-08
1-07
1-08
1-00
•75
•30

•25

•34

Calculated
Resistance.

Pounds.
100-7
100-7
100-7
100-7
83-9
60-4

43-6

43-6

I have no doubt that there is an error somewhere in the
mode of trial which gave the resistance stated in the account
of these experiments, for they do not agree with others.

26. Col. Beaufoy made some experiments on the resistance
of water, which appear to have been conducted in a similar
manner. He found the resistance of a square foot, moving at
the rate of one foot per second, to be 1 -2949 pound ; according
to my mode of calculation, it should be 1-45 pound.

27. Borda, from an experiment made in sea-water, makes
the resistance of a foot of surface If pound Fr., at a velocity
of about one foot per second; and Bouguer, as quoted by
Robison, makes the resistance 1-44 pound Fr. My mode of
calculation gives 1*785 pound Fr. for the resistance of sea-
water, to a surface one foot square moving at the rate of one
foot (French) per second.

28. Mr. Bevan has given me an account of some trials he
made to ascertain the resistance of a canal boat on the Grand
Junction Canal. The length of the boat was 69*57 feet; its
width, 6-83 feet ; floating depth in the water, 0*89 foot ; weight,
9 1 tons ; radius of curvature four times the breadth ; and the
area of surface in contact with the water, 540 feet. (See fig. 7.)

* Buchanan on Propelling Vessels by Steam. 1816.
New Series. Vol. 3. No. 16. April 1828. 2 L The

258 Mr. Tredgold'on a ?iew Theory of the Resistance

The equation rendered applicable to this case is

v* (-242 d (3 z — 1*1629 r) -f 0-0032 ^? I) = the resistance in

pounds ; and as d = '89 ; z = 13 8 ; r = 27*32, and p I = 540,

it becomes 3*79 if = the resistance in pounds.

Velocity in

Resistance

Calculated

Feet per

in Pounds by

Second.

Experiment.

Feet.

Pounds.

Pounds.

1-31

6-1

6-49

1-98

14

14-8

2-93

28

32-5

4-3

56

70-0

Considering the complex form, the resistance is expressed very
well by the equation, and quite as nearly as a general rule
could be expected to give it ; and every one is aware of the
advantage of being able to anticipate practical effects so nearly.
29. The most important experiments on the resistance of
air appear to be those conducted by Dr. Hutton*, for the
improvement of the theory and practice of Gunnery. In or-
der to ascertain the effect of giving different inclinations to the
same surface, he fixed a rectangular plane 32 inches in areas
at different angles to the direction of its motion ; the velocity
was twelve feet per second.

Angles with

Resistance

the Direc-

by

Resistance.

Difference.

tion.

Experiment.

90°

1000

1000

0

80

994

975

-19

70

957

902

-55

60

868

788

-80

50

724

646

-78

40

533

489

-44

30

331

333

+ 2

20

158

192

+ 34

10

52

78

+ 26

5

19

34

+ 15

The resistance of the plane when set at an angle of 90° and
moving at the rate of twelve feet per second, was 0*841 ounce.
By my mode of calculation it comes out 0*896 ounce. In an-
other set of trials with a triangular plane, the resistance cor-

* Tracts, vol. iii. p. 202.

responding

of Fluids, compared with the best Experiments, 259

responding to the same area and velocity was '846 ounce. The
mode adopted by Dr. Hutton to reduce for the edge of the
plane is not quite correct, as it obviously has an unequal ef-
fect at the different angles. (Art. 12.)

30. In comparing the resistance of bodies of different forms,
Dr. Hutton obtained the following ratios :

Cone.
Angle 25° 42'.

Sphere.

Cylinder.

Hemisphere.

Convex
side.

Base.

Vertex.

Base.

Ratio by Ex- 1
periment J
By Calculation

126
•44
•388

291
1*02
•729

124
•435
•434

285
1-00
1-00

119
•42
•6

288
1-01
•833

It will be remarked, that in air as in water, the hemisphere
with the convex side foremost differs most widely from the
result of calculation. The sphere is very near, and the near
coincidence of the actual resistance, as well as the ratio, is
worthy of notice.

The resistance of a ball two inches in diameter was found
by experiment to be -163 ounce at a velocity of twenty-five
feet per second. By calculation I find its resistance '1655
ounce at that velocity, — a difference of only -£j in excess.

31. Col. Beaufoy* made some experiments on the resistance
of air on bodies of different shapes, and published a table of
the resistances. When the area of the base is one superficial foot
the force is in ounces ; and taking the line corresponding to a
velocity of twelve feet per second, I have added the numbers
my mode of computation give in these cases. %

Cone.
Angle 45°.

Thin
Plane.

Cylinder.

Wedge.
Angle 45°.

Vertex.

Base.

Vertex.

Base.

Resistance by >
Experiment $

Calculated 1
Resistance J

Differences...

3-61

2-294
1-316

4-586

3-36
1-226

4-834

4-032
•802

4-668

4-032
•636

3-005

2-294
•711

4'69

3-36
1-33

In these comparisons the calculated numbers are in defect,
and the ratios are not very different.

32. Returning to Dr. Hutton's experiments f, I must next

* Annals of Philosophy for 1815, vol. vi. p. 277.
• t Tracts, vol. Hi. p. 230, where the tentative formula of Dr. Hutton are
given. 2 L 2 show

260 Mr. Tredgold on a new Theory of the Resistance

show how far the formula will apply to great variation of ve-
locity.

The equation for a spherical ball reduced to the form ap-
plicable to this case is

£0<

3 +

1*3 x 0-000000332 x 4 v

)=H;

and since a cubic foot of air weighs 1*2 ounce at the mean
temperature and pressure, and the area of the section of the
ball is d? x -7854 feet, it becomes

i)^1/. , 0-000001328 v \ .

— (1 + -. ) = the resistance in ounces.

Velocity in

Feet per

Second.

Resistance to a Ball two Inches

Diameter in Ounces.

By Experi-
ment.

By Theory, neg-
lecting Friction.

By Theory,
with Friction.

5

0-006

•0066

•00661

10

0*026

•02647

•026478

15

0*058

•0595

•05977

20

0-103

•106

•10664

25

0*163

•166

•16725

30

0-237

•238

•24016

40

0-427

•425

•43012

50

0-676

'665

•675

100

2-78

2-647.

2-727

200

11-34

10-6

11-24

300

25-8

23-8

25-96

400

46-5

42-5

47-62

500

74-4

66'5

76-5

600

110-4

96-0

113-28

700

156-0

130-0

157-44

800

212-0

171-

211-96 '

900

280-3

215-

273-32

1000

362-1

265-00

345-

1100

456*9

321-

427-48

1200

564*1.

383-

521-24

1300

683*3

450-

625-76 •

1400

811-5

520-

739-52

1500

947*1

595'

865'

1600

1086-9

680-

1007*68

1700

1228-4

769-

1162-

1800

1368-6

860-

1326-56

1900

1505-7

960-

1508-72

2000

1637*8

1060-00

1700*

In this series of comparisons there are only two places in
which the difference amounts to y1^ ; and the one is in excess, the
other in defect ; and if the resistances were represented by the

ordinates

of Fluids, compared with the best Experiments. 261

ordinates of two curves, these curves would cross five times at
unequal distances in the range.

Explanation of the Plate.

Fig. 1. A body moving in the direction AB. The collision
and line of reaction of a filament of the fluid from the oblique
surface of its fore-part are indicated by faint lines, with dotted
lines to represent the composition and reduction of the forces.
The motion of the fluid after the body is also shown by lines
of a light tint. The dotted rectangle is equal to the oblique
parallelogram, but the motion of the fluid is less as the obli-
quity increases.

Fig. 2. Represents the plan of the body used by the French
Academicians in their experiments ; the head was altered to
different angles, but the form of the after-part remained the
same in all their experiments.

Fig. 3. is to show the effect of moving a plane surface in a
fluid when placed obliquely in respect to the direction of its
motion ; and it is obvious that the edge of the plane must have
a sensible effect on both the direct and minus-pressure.

Fig. 4. 5. and 6. are, a sphere ; a cylinder, with the after- part
a hemisphere ; and a cylinder with the fore-part a hemisphere ;
having the characters used for calculation annexed to their
respective lines.

From the flat end of fig. 5. the stroke and reaction being
in the same direction, the fluid cannot move laterally till the
central pressure so far exceed that on the more remote parts as
to cause the proper quantity of lateral motion ; or till a portion
of the fluid accumulates before the body : but the portion ac-
cumulated being a fluid, the forces must produce the same effect
as if each filament were struck and reflected by the solid plane.

Fig. 7. The plan of a body formed by segments of circles,
with the characters annexed to the lines. When the radius is
half the breadth, the form becomes a prism terminating in semi-
cylinders at the ends (as fig. 8).

Fig. 9. and 10. are to show how the two motions of the fluid
interfere when the fore- and after-part are separated by a thin
edge only. In the hemisphere (fig. 9.), the resistance is in-
creased by the fluid displaced by the fore-part preventing the
fluid from following behind the body. In fig. 10. the reflected
fluid from the fore-part in some degree facilitates the motion
of the following fluid.

It will be evident to any one who examines the preceding
paper, that it must have cost me a great deal of labour ; and
in consequence I was desirous of presenting it to the Royal
Society. But finding that I must sacrifice all claim to new

theoretical

262 On Mr. Herapath's Second Attack

theoretical investigation in order to secure its appearance in the
Transactions of that Society, I chose in preference to send it to
Newcastle, and to take this most respectable channel for pre-
senting it to the public, knowing that it will be extensively cir-
culated among men of science, as well as that in these days it
does not require the aid of authority to support the cause of
truth ; while, recollecting the state of hydrodynamical science
as it appears in books written for the use of University stu-
dents, we know that when authority has not truth to propa-
gate, it does not hesitate to teach that which is known to be
erroneous.

Having opened a new path in this difficult subject of the
motion of fluids, it was not in my nature to stand still ; the ef-
flux of fluids, the impulse on bodies placed in a moving fluid,
and various other inquiries followed. These, as my health per-
mils, will be presented to the world. Thomas Tredgold.

XLII. On Mr. Herapath's Second Attack on Lagrange's

Method.
[" AGRANGE's method still charged with failure ! In re-
-*-i turning to this subject it was incumbent on Mr. Herapath,
as a man of an ingenuous mind, to acknowledge the mistake he
has already committed ; of which he says not a word, although
it was so clearly pointed out to him. Who, that felt the spirit
of Science within him, could bear the thought of having made
a charge of failure in consequence of a mistake of his own,
without hastening to apologize to his living readers, and to the
illustrious dead from whose fame he had detracted ! The former
argument, which was to overturn Lagrange's method, origi-
nated in the erroneous notion that every one of the three parts
of the integral considered, must separately satisfy the diffe-
rential equation ; whereas it is the aggregate of all the three
parts which satisfies that equation*. The matter is so very

* At the bottom of p. 23, of this Journal for January, Mr. Herapath
gives the value of/?, which he has computed. Taking this value, it is ob-
vious that his p yu is the same with the first part of the integral in p. 96 of
this Journal for February. The other two parts of the same integral are
of course identical with p{y2 and p.2y^t all the parts being derived from
one another by interchanging the roots. Mr. Herapath's expression of y,
viz. pyx -f- p{y2 -f Piya is therefore the very same with the integral in
p. 96 of this Journal for February. This being established, however surpris-
ing it may appear, yet we must infer, from what he says of the integral just
mentioned, and from the very confident postscript to his article, that he is
not acquainted with what he has himself computed. The truth is, that care
was taken not to change his expressions in the slightest degree. God knows
what would have been the consequence, if, in explaining this gentleman's
mistakes, any one had presumed to alter one tittle of his formulas !

plain,

on Lagrange's Method. 263

plain, that it is not easy to account for the mistake; unless
indeed his last article help us to a solution of the difficulty.

He is now puzzled how to deduce the case of equal roots
from the usual form of the complete fluent. There is some
confusion in what he writes, arising from his not distinguish-
ing between the mathematical definition of the complete inte-
gral, and a property belonging to it. An algebraic expres-
sion which satisfies the differential equation, and contains the
requisite number of arbitrary constants, is the complete in-
tegral ; and it possesses the property of comprehending every
possible case, by varying the arbitrary quantities. It is cer-
tain that Mr. Herapath's integral of the third order, when we
take in all its three parts, does satisfy the differential equa-
tion * ; it also contains three arbitrary constants ; it is there-
fore the complete integral : but notwithstanding, he contends
that it is not general ; for he makes it fail, particularly in the
case of equal roots. Now this proceeds, not from a failure in
any method or in any doctrine, but from a failure in Mr. He-
rapath, who does not reason correctly in adapting the general
expression to the particular case.

Let us take his own example, p. 212, of the last Number of
this Journal, viz.

= cerx-cter*x+erx/Xe -rxdx-er*x/Xe-r*X dx
" r — r,

When the two roots are real and unequal, or when they are
imaginary, there is no difficulty; but the puzzle is, what must
be done when the roots are equal, for then the integral is in-
finite. For the sake of simplicity, let rx — r = co, then r, m
r -f cy; also put ct = c + hoo: then, by substitution,

erx + »x(c + hu+SXe-rx-"'xdX)-erx(c+fXe-rxdx)
y - _

This is only another form of the complete integral, the arbi-
trary constants being c and h; but it has the advantage of
bringing out the correct value of y when the roots are equal,

or co = 0. If we substitute the expansions of eax and e~ ax9
we shall obtain, supposing co = 0,

y = erx (ji -f- ex + xfe~~r*X.dx —fe~ "Xxd*);

b\xt^ xfe" *Kdx — fe Xxdx =fdxfe~ Hdx;

wherefore, y = e r xyh + c x 4- fd xfe ~~r x X d xj9

* See the calculation in this Journal for February last, p. 97.

which

264 On Mr. Herapath's Second Attack on Lagrange's Method.

which is the complete integral in its simplest form when the
roots are equal. If we suppose X = 0, then,

y — erx(h + c <r).
Thus, when we follow a proper method, it appears that the
complete integral comprehends all the subordinate cases;
which proves the incorrectness of Mr. Herapath's views.
, Nothing more was intended by the notice inserted in this
Journal for February last, p. 96, but to correct Mr. Herapath's
mistake about Lagrange's method. It may now be proper to
inform him that there is nothing new in his papers. Euler
has integrated the equation of the third order in his Calculus
Integrates, torn. ii. sect. ii. cap. 3. prob. 149; and at the be-
ginning of the scholium to the problem, he observes : ". In
genere autem, nulla integralium reductione adhibita, integrale
nostrae equationis ita exprimi potest ;" and he then sets down
the very same expression of y which is contained in Mr. He-
rapath's equation 19. Euler's words contain the exact de-
scription of Mr. Herapath's method, which finds the integral
by successive integrations without attempting to reduce it to
the form best adapted for use. In prob. 151. of the same chap-
ter, Euler exhibits the unreduced integral of any order inde-
finitely, being the very same with Mr. Herapath's equation 17,
and therefore containing the sum and substance of that gentle-
man's doctrine. Lastly, in prob. 152. cor. 4. it is observed
that this form of the fluent is free from the difficulty about
the equal roots, on account of the absence of zero divisors.
These accumulated proofs show that there is nothing new in
Mr. Herapath's papers, except the extraordinary mistakes they
contain.

The history of this problem ; the real difficulties attending
it; the slips that were at first made by geometers of the highest
eminence about the case of equal roots ; the correction of these
slips, and the artifices by which the solution has been com-
pleted ; — all these are points about which it is fair to presume
that Mr. Herapath is at present not well informed.

Some apology is due to the readers of this Journal, for the
length of these remarks ; but it seemed proper to explain the
matter pretty fully ; for, unless the writer of this article has
been misinformed, Mr. Herapath's solution of this problem
has, not much to the credit of British science, been blazed
abroad as a great discovery. I now withdraw from any further
intermeddling in this trite subject *. n

XLIII. On

* It is probable that his Postscript relates to this frivolous point, viz.
whether the arbitrary constant in p is to be written with the same deno-
minator

[ 265 ]

XLIII. On Systems and Methods in Natural History, fty
J. E. Bicheno, Esq., F.R.S., Sec. L.S., fyc.

[Concluded from p. 219.]
TT was the opinion of Linnaeus, and continues to be the opi-
* nion of some of his disciples, that genera are actually founded
in nature as much as species. " Naturae opus semper est
species et genus." Phil.Bot. § 162. "Genus omne est na-
turale, in primordio tale creatum, hinc pro lubitu et secundum
cujuscunque theoriam non proterve discindendum aut conglu-
tinandum." lb. § 159. So the excellent and elegant author of
the " Introduction to Physiological and Systematic Botany,"
says, " A genus comprehends one or more species so essen-
tially different in formation, # nature, and often many adventi-
tious qualities from other plants, as to constitute a distinct fa-
mily or kind no less permanent, and founded in the immu-
table laws of the creation, than the different species of such a
genus. Thus in the animal kingdom a horse, ass, and zebra,
lorm three species of a very distinct genus, marked not only
by its general habit or aspect, its uses and qualities, but also
by essential characters in its teeth, hoofs, and internal con-
stitution." It was the circumscribing these insulated assem-
blages of species that Linnaeus regarded as the business of the
accomplished naturalist.

Those therefore who use the word genus in the Linnaean
sense, do not employ it with the same meaning as those who
regard genera as merely conventional, and subject to be broken
down to suit convenience. The latter would do well to enl-
ploy some other term, else one great object will be lost at
which we are aiming ; — the keeping together under some one
common head those small assemblages of species which in
some instances are so obvious, and so important in enabling
us to comprehend and discourse of the scheme of nature.

Whether such insulated groupings really exist, it is for the
naturalist to determine, and this can be only inferred from a
very extensive knowledge ; but as long as we are witnesses to

minator as the variable part, as he has himself written it; or without the
denominator. Write it how he will, the same egregious blunder still re-
mains ; namely, his supposing that every part of the integral must separately
satisfy the differential equation. His Postscript is not clear ; but two things
may be gathered from it: one, that he is possessed of a method for mea-
suring the degrees of absurdity ; the other, that he is not well assured
what is, or what is not, Lagrange's method, although he has, twice in this
Journal, accused it of failure. The truth is, that all his arguments are di-
rected, not peculiarly against Lagrange's method, but against the complete
integral, reduced to its simplest form, by whatever method it may have been
obtained. , . -

New Series. Vol. 3. No. 16. April 1828. 2 M such

266 Mr. Bicheno on Systems and Methods

such striking modifications of form as we discover in the genus
Erica, Rosa, Eriocaidon, &c, among plants, and in Vesper-
tilio, Strix, Scarabaeus, &c, among animals, it would be the
height of folly to give up a term so expressive and at the same
time so useful, or to transfer its received meaning to some
other word which has not been used in the same sense.

As the success of the systematist depends so materially upon
the proper use of these abstractions, I shall now proceed to
show some distinctions which it is necessary to keep in view
while we employ them. We aim, as I said before, at two di-
stinct objects by the use of systems : we use the artificial for
becoming acquainted with individuals, and the natural as the
means of combining them, and enabling the student to com-
prehend and speak of the general truths relating to nature by
a knowledge of a few particulars.

Division and separation is the end of the artificial system : —
to establish agreements is the end of the natural. In one case
we reason a priori; in the other a posteriori. The one is a
descending, the other an ascending series. Linnaeus under-
stood this distinction when he remarked, " Ordines naturales
valent de natura plantarum; artificiales in diagnosi planta-
rum." — " Cavendo in imitando naturam filum Ariadneum
amittamus." Nevertheless it has appeared to me that many
modern naturalists have not adopted these truths ; and that it
is the prevalent error of the day to attempt to generalize where
they ought to analyse; while their arrangements, called na-
tural, are almost all of them framed with a view to distinguish.
Let me not be supposed by these remarks to wish to exclude
from the natural system every attempt at diagnosis ; for it is
obvious, that as the business of the naturalist is to study all
the characters, he can no more neglect differences than he can
agreements. I only wish to point out the two dissimilar ob-
jects we have in view, that they may not be confounded.

M. Decandolle, for instance, whose labours as a systematist
are invaluable, seems to overlook this distinction. In his
Regni Vegetabilis Sy sterna Naturale, he starts from things the
least known, to reason on things best known. He begins
his comprehensive work with a predicate of the stars; and,
proceeding downwards to minerals, comes to plants. Here
he employs a series of terms expressive of a natural gradation
from the highest to the lowest group, attempting fresh com-
binations at every stage, and making a place for every thing.
Thus he has class, sub- class, cohort, order, tribe, genus, section,
species. The extraordinary number of these combinations di-
minishes their value as a work of natural arrangement. It is
a difficulty of sufficient amount to establish a few well marked ;

and

in Natural History. 267

and when they are so multiplied, it may be suspected that
many of them are arbitrary and artificial. This attempt at
breaking down good orders and genera into many subordinate
and loosely defined groups, and encumbering them with names,
involves the subject in obscurity, and may well be questioned
as contrary to his main design of presenting those compre-
hensive views which are afforded by a natural system.

Mr. Brown has adopted a different mode in his Prodromus.
He has attempted to combine no further than his knowledge
wrould warrant, not even employing the terms class or order as
the names of his groups. As his object is chiefly synthesis, he
keeps his diagnostic characters apart, thus leaving the mind
less embarrassed when it is in pursuit of analysis. It must be
admitted indeed, that his work cannot be employed with any
success by the inexperienced, or even by those who have oc-
cupied themselves only in searching for species ; but to have
made it subservient to this purpose, would have been to have
rendered it less beautiful and complete as a work of synthesis.
His aphorisms and remarks not being reduced to exact me-
thod, " are," as Lord Bacon expresses it, " still in their growth,
increasing in bulk and substance."

Now wherever the object of the systematist is to enable his
reader to discover species, it is necessary to define at every
step ; and where natural characters do' not present themselves,
we must adopt artificial ones. For this purpose large classes
are formed, many of which are necessarily artificial. These
again are broken up into orders, mostly of an artificial cha-
racter; and thus the naturalist is led step by step from more
comprehensive definitions to less, from class to order, from
order to genus, and from genus to species. In this descend-
ing series it will be observed that the essential feature is the
facility that is afforded for definition. Hence the Linnaean
system of botany has succeeded so well, because its author se-
lected chiefly as the ground of his arrangement the number
and proportion of parts most obvious and least liable to vary.
His classes and orders are avowedly so many assumptions,
which practice has shown to be convenient; but when we come to
genera, the artificial system falls in with the natural, as Linnaeus
framed their characters upon resemblances founded in nature.

Now in the natural system this machinery of terms cannot
be employed in the same manner. It is an ascending series
from the less to the greater predicate. From genera we pro-
ceed upwards to orders, and orders we combine into classes.
We become more and more general in our characters, instead
of more and more definite. Here indeed we ought not to sa-
crifice, as in the artificial scheme, to convenience ; and break

2 M 2 up

268 Mr. Bicheno on Systems and Methods

up well-defined genera and orders because they contain a large
number of species. If we find a large genus, for instance, as
Erica, agreeing in some well-marked characters of structure,
form, station, and properties, it appears contrary to the end
proposed by the natural system, to divide and subdivide the
species into small groups, and to give each of these the same
value as is now possessed by the whole. This is frittering away
characters which are essential to the use of a genus, and de-
stroying our power over it when we proceed to generalise.
The value of generic terms consists essentially in the distinct
conceptions we have of them ; but if we go on to multiply them,
as is at present the fashion, we render it as impossible to cir-
cumscribe them, as it is to parcel out the colours of the rain-
bow; and instead of making Natural History familiar and
popular, it will require the compass of a man's life to master
the terms we employ. If indeed the object be to analyse, di-
vision may be very convenient, because the inquirer may be
otherwise bewildered in the multitude of particulars. It does
not follow from hence that the student of the natural system
may not avail himself of subordinate groups by whatever cha-
racters they may furnish; only the giving them equivalent
names, and making them co-ordinate, is destructive, as it ap-
pears to me, of his system as a means of general reasoning.

In no department of natural history are the inconveniences
arising out of this confusion of analysis and synthesis more felt
than in Entomology. The multitude of species , included in
this kingdom of nature is so great, that it requires the most
skilful arrangement to enable the student to determine them :
yet it is unquestionably the worst furnished with assistance in
this way; — a defect which may be attributed chiefly, I appre-
hend, to the attempt which both we and our continental neigh-
bours have made to combine the natural with the artificial
system. We have aimed at analysis and synthesis at the same
time. A comprehensive acquaintance with this infinitely varied
tribe can alone enable us to synthesise with safety ; and a long
period must elapse before we can hope to embrace within our
synthesis the whole of the insect world.

In the large views taken by means of the natural system,
our business will for ever be the labour of separating what we
shall know from that which is unknown. The profoundest
knowledge will at last be but a fragment. Some groups of
nature are so closely related, that they have been observed
from time immemorial. " Whatsoever parteth the hoof and
is cloven-footed, and cheweth the cud," comprehends a group
of animals so obviously connected, that they must have re-
ceived a generic appellation from the remotest period. As

knowledge

in Natural History. 269

knowledge has increased, more and more families have been
separated : still there is always a remainder of unknown things.
Take any natural system, and see if this is not the case.
Linnaeus in his " Fragments of a Natural Method " professes
only to separate from the mass those groups which he saw
clearly. Again, his definition of vegetables indicates the same
truth : " Vegetabilia comprehendunt Familias septem, Fungos,
Algas, Muscos, Filices, Gramina, Palmas" and then, to in-
clude the remainder, he adds, " et Plantas" defining the last
thus, " Plantae dicuntur reliquae, quae priores intrare nequeunt.
familias." Phil. Bot. § 78. Take up Jussieu's Genera Plan-
tarnm : and besides his " Plantae incertae sedis," see how he
is obliged to dispose at the end of many orders his M Genera
affinia," and " Genera nondum satis determinata." This is
true inductive philosophy; yet the same author may be sus-
pected of departing from this mode of investigation when he
attempts to edge in his remainder under artificial or sweeping
characters, as he has done in Eleagni and Junci, and when,
falling in with this modern innovation, he invents a multitude
of new orders to embrace every known species of plant.

The mammiferous animals are arranged with more ease ac-
cording to a natural system, in consequence of their number
being comparatively small, and their forms strongly marked.
Nevertheless the system of M. Cuvier, in the Regne Animal,
clearly shows the vain attempt of finding a place for every
thing. Nothing can be more satisfactory and beautiful than
many of his orders and divisions; yet see how he is compelled
to change his ground when he comes to the Packydermata,
and to huddle together species very remotely connected. His
birds also exemplify the same fact, where his order Passeres is
made to include all that his other orders will not hold. " Son
caractere semble d'abord purement negatif, car il embrasse
tous les oiseaux qui ne sont ni nageurs, ni echassiers, ni grim-
peurs, ni rapaces, ni gallinaces." Thus it contains the War-
blers, the Shrikes, the Goatsuckers, the Crows, the Creepers ;
birds of the most dissimilar habits, and living upon the most
dissimilar food. The Chough is separated widely from the
Corvi, and Anthus from Alanda. Now this is what we might
expect from the nature of the subject ; only it is desirable that
the remainder of unknown things should be distinctly avowed,
and not reduced to an exact place in the natural system.
Jussieu's was the most philosophic mode, which was to place
this residue at the end. Linnaeus too was very correct when
he pronounced his natural orders to be a " Fragment;" and
those persons who imagine it to be necessary or advantageous
to find a place for every thing, and to divide and split for the

purpose

2.70 Mr. Bicheno on Systems and Methods in Natural History.

purpose of making such places, appear to lose sight of the
chief object of the natural system, and to destroy its utility as
an instrument of general reasoning.

The French writers in general are prone to combine in their
systems the very distinct objects of individualizing and genera-
lizing. They are for ever subdividing where the great aim
should be to combine, and thus they detract from the utility
of their arrangements for either purpose. It is they who have
countenanced the use of sub-classes, cohorts, tribes, stirpes, sub-
genera, and sub-species ; and they also are the great contribu-
tors to the minute division of genera. Strictly speaking, in the
natural system we should employ but few terms of the kind
alluded to, and those of loose application. For instance, the
word sort or group would as correctly express any natural as-
semblage of species, as sub-class, race, tribe, cohort, or stirps ,-
for what do we know of the relative value of the groups at-
tempted to be pointed out by these expressions ? And how
can we say they are not co-ordinate or commensurate with
each other? The great division of cotyledonous plants may,
for aught we know, be only equivalent to the order of Grasses ;
and a genus in some cases seems as distinct as any class, as
Parnassia and Linncea among plants, and the Ornithorhynchus
and Hippopotamus among animals. Indeed in the recent work
of M. Latreille, Families Naturelles du JRegne Animal, he has
arranged the monotrematous animals in a class by themselves,
and has made two orders ; in one case, consisting of a single
species, the Ornithorhynchus paradoxus, and in the other, of
two other species before considered as belonging to that genus.
Thus it is, as M. Cuvier remarks, that these animals set at
naught all our classification by their osteology and mode of
bringing forth.

The adoption of these numerous terms, intended to express
fixed ideas, must be looked on with suspicion. The terms
species and genus are too well established by custom, and are
so clearly the result of convenience, and moreover conform so
closely to the ordinary use of these words, that their utility
cannot be questioned ; but those numerous subdivisions cur-
rent among our neighbours, and sensibly increasing among
ourselves, may well be doubted as unphilosophical language.
To each of them is attempted to be assigned a definite value
beforehand, and an impracticable degree of precision; and
we deceive ourselves by fancying that we can deal with these
delicate and fleeting instruments of thought differently from
the rest of the world. But are we to attempt to fetter nature
by our systems and terms? " Books should follow sciences,
not sciences books," says the immortal Bacon ; yet the adop-
tion

Dr. Brandes's Examinatioji of a gelatinous Substance, fyc. 271

tion of systems and technical expressions, which have received
their definition beforehand, cannot be employed without the
danger of perpetuating false hypotheses, and an apprehension
on the part of the ignorant, that these inventions give us some
power over nature not belonging to ordinary language.

The more correct mode would be to exclude from the na-
tural method most of these terms, and to employ in their place
some convertible words'of looser import, as indeed M. Cuvier
has to some extent done ; such for instance, as group, section,
division, to express those larger assemblages of approximations
to assigned forms, which are rather predicated than proved ;
and in many cases to point them out by mere signs, such as
are used in printing. Thus, for instance, the word section,
or any similar word, might be employed to express the plants
severally comprehended in the order Graminea?, the class
Composite?, and the division Monocotyledones ; and where the
characters are less definite, the plants pointed at might be
assembled under a simple asterisk.

One chief recommendation of the natural system over the
artificial, is the liberty which it leaves to the mind. The one
shuts it in to the narrowest scope of observation, while the
other suffers it to range in search of all the properties belong-
ing to created beings ; their functions, their structure, relations
and resemblances, affinities and analogies. It is speculative
and general truth that the natural system enables us to pur-
sue ; and this will never submit to be bound by any fetters
which the art of man can invent. Books after all are but a
rude mode of holding knowledge together ; and language but
an imperfect vehicle to convey with precision the just relations
of things. At best it bears the image of the earthy, while
things themselves bear the image of the heavenly.

XLIV. Examination of a gelatinous Substance found in a damp
Meadow; — as a Contribution to the Knowledge of the Meteors
called Shooting-Stars. By Dr. R. Brandes*.

"Il/fY friend Dr. Buchner communicated some time ago (in
-*-*-*- Kastner's Archiv. v. 182), a treatise on the substance of
the meteors called Shooting-Stars, which Kastner has desig-
nated by the name of star-jelly. This substance, found in a
damp meadow, was of a gelatinous appearance, and was sup-
posed by Dr. Schultes to be Tremella nostoc. M. Buchner,
however, having examined it, was of a different opinion, not
having been able to discover in it any trace of an organic tissue.

* From Schweigger's Jahrbuch der Chemie, N. R. Band xix. p. 389.

Indeed

272 Dr. Brandes's Examination of a gelatinous Substance

Indeed he does not decide whether its origin was terrestrial
or not; yet he asserts that this substance could be neither a
plant nor an animal, (at least not an entire one,) but perhaps
the produce of an animal, an excretion resembling gum$ mu«-
cus, &c. ; and although he does not deny the possibility of such
a body having descended from the atmosphere, he does not
think it very probable. Nay, he does not much object even to
the comparison of this slimy substance with the manna of the
Israelites, which fell from heaven ;-^he thinks at least that this
slimy mass might be as nourishing as oysters. However in-
clined I may feel to agree with my respected friend on the
first two points ; viz. that this mass might originate from the
excretion of an animal, or a gelatinous meteor, the idea of com-
paring it with the manna of the Israelites seems to me un-
tenable, there being too great a difference between both the
nature of the substances and the places in which they have
been found. I was much inclined to ascribe to the substance
in question an atmospheric origin, in consequence of the want
of organic structure, which M. Buchner ascribes to the mass
he examined ; in consequence also of the account given by
R. Graves of a fiery meteor which had fallen in Massa-
chusetts, in the United States, in a spot where the following
morning a gelatinous substance was found*; in consequence,
moreover, of my own observations on the existence of atoms
of azotized substances in the atmosphere, at least in rain-water,
(Jahrb. 1826, iii. 253); and ultimately from the account fre-
quently repeated to me by a soldier of the contingent of
Lippe, who had fought in the Peninsula, of his having fre-
quently noticed in Spain, while on duty during cold nights,
stars to shoot, and perceived in the morning in damp places,
where he thought them to have fallen, white gelatinous masses,
which were soon decomposed ; an opinion which I also men-
tioned in my treatise on Rain-water.

M. Schwabe, an apothecary at Dessau, published some
time after a treatise on the same subject (Kastner's Arc/iiv. vii.
p. 428), on his having had an opportunity of examining a sub-
stance which had been found in a damp meadow, which was
likewise gelatinous and of a green colour. Mr. S. recog-
nised this mass distinctly asNostoc commune Vauch. (Tremella
?iostoc, Linn.), having discovered in it through the microscope
the structure of this singular nostoc: As this mass agreed not
only in its external form and place of discovery with that of
Buchner, but also in its chemical composition, Mr. S. thought
himself justified in assuming that both this substance and that

* Gilbert's Annalen, Ixxi. 314.

of

found in a damp Meadow. 273

of Buchner were of the same nature ; since, qwing to its pecu-
liar texture, Mr. B. might have overlooked its organic struc-
ture. But on comparing more closely the descriptions given
by the two naturalists of the substances observed by them,
we discover several other differences, besides the one that
Mr. Schwabe discovered, — a distinct organic structure ; while
Mr. Buchner saw none. The substance examined by Mr. S.
was of a greenish colour; that of Mr. B. white, like swelled
tragacanth. The former on being burned emitted, not an
animal smell, but one quite peculiar, resembling burning con-
ferva, rivularice, and chcetophorce, and yielded a shining coal,
which preserved the skinny form of the pieces employed ; and
being reduced to ashes, left a residuum of silica, with carbonate,
muriate, and sulphate of potash, with traces of phosphate of
lime and oxide of iron ; but Buchner' s substance, on being
heated, swelled considerably, diffusing at the same time a strong
animal smoke ; caught fire at last, and left a coal that could
not be reduced to ashes, and which contained carbonate of
soda and phosphate of lime. However similar Mr. S. may
consider his substance to that of Mr. B., the facts here stated
seem to invalidate his conclusion as to their identity. I feel,
therefore, great pleasure in being able to communicate an ex-
amination which I had an opportunity of making last autumn,
and which may perhaps throw some light on the point in
question.

A friend and fellow-townsman of mine, who has a large
meadow near our city, which, lying in the lower part of our
salt-valley, has been drained in a slight degree by dint of great
labour, and the grass in it improved by the application of salt
and ashes, for manure, found in this very meadow a gela-
tinous substance, and was told by a labourer that he had fre-
quently seen similar ones there ; a circumstance which had
escaped my friend and me, though both often passing through
it.

My friend having brought me this substance for exami-
nation, my mind immediately reverted to that examined by
Mr. Buchner; and perceiving even outwardly several differences
between them, I undertook a close examination of it, as fol-
lows.

The substance was of a very clear white colour, represent-
ing a strongly swelled mass, which Mr. B. very properly com-
pares to swelled tragacanth ; its bulk might be about 2 \ cubic
inches. On a closer view, I perceived that in several places
it was covered with a very fine white skin, which seemed to
have burst in the centre only ; in such parts the inside had
protruded in the shape of a very bulky gelatinous mass. The

New Series. Vol. 3. No. 16. April 1828. 2 N bursting

27* Dr. Brandes's Examination of a gelatinous Substance

bursting of the skin had undoubtedly been produced by the
swelling of the mass on account of the moisture it had ab-
sorbed from the meadow, a tension which the thin mem-
branous covering could not resist. In such parts too the mem-
brane was so concealed by the jelly that it could scarcely be
perceived. Nor had the jelly here any distinct form, or any
traces of organization. But wherever the mass had remained
entire, and although swelled was still inclosed, it showed a ver-
micular appearance of the thickness of a quill and thicker ;
whilst in those places where the membrane had burst, the in-
side projected in lumps of three-quarters of an inch in thickness.
This vermicular appearance presented several small slightly
indented divisions, and had entirely the figure of an intestine ;
the back was marked by a tender vessel of a darkish-brown
colour, which spread with fine veins towards the front, losing
themselves about the middle in small blackish points. By this
vessel the back of the mass was entirely contracted, and much
extended towards the surface, just like an intestine.

In a dry place the substance gradually shrunk, soon lost its
white colour, turned to a brownish yellow hue, became very
tough, so that it could be drawn into threads like glue, and
dried at last into a horny mass.

Burned in a crucible of platinum it swelled, became gra-
dually black, emitted a strong animal smell, like singed wool,
and left 1*2 of grayish white ashes, which were scarcely af-
fected by water for some time, but at length gave a slightly
alkaline solution. In nitric acid the ashes were completely
dissolved, and ammonia gave a precipitate of phosphate of
lime.

Twenty grains of this substance were desiccated on a water-
bath. It became hard and tough; and its weight was re-
duced to four grains. Moistened with water, it in a short time
re-assumed its former size and white colour.

One hundred grains of the substance were boiled in three
ounces of water ; by this it swelled into a tremulous jelly, which
was so bulky that it had thickened almost all the water ; for
the whole being deposited on a loose clean linen cloth, it con-
gealed upon it ; and after several hours but little of the liquid
had oozed out, which was rendered turbid by protonitrate of
mercury and acetate of lead, but not by superacetate of lead.
A little of the substance was shaken with alcohol ; this acted
but little, but separated from it some of the water, and on its
bulk being diminished, it likewise lost its transparency.

A solution of ammonia acted but slightly, whether in the
cold or by heat ; but a solution of caustic potash affected it
perceptibly even while cold, and entirely absorbed it when

heated :

found in a damp Meadow, 275

heated : neutralized by any acid, the substance was again pre-
cipitated. The sulphuric, nitric, and muriatic acids also acted
upon it while cold, and entirely dissolved it by heat. The
nitric acid turned somewhat yellow, the sulphuric acid brown;
the muriatic acid remained colourless.

From these experiments it is evident that this substance did
not resemble albumen, but essentially agreed with jelly, and re-
sembled the slime of springs. It consisted of

Gelatinous substance 18*8

Animal ditto traces

Phosphate of lime and phosphate of soda, with V

an organic acidity J

Water 800

100-0

What now is the origin of this substance ?

The evident existence of an organic structure will not al-
low any opinion of its being of an atmospheric formation, but
shows on the contrary that its origin must be terrestrial and
of an animal kind. Its striking resemblance to an intestine,
led me at first to suppose that it might have been the intestine
of a bird ; but its containing a smooth jelly, and being inclosed
in so fine a membrane, compared with the tougher skin of any
intestine, which could not have swelled to the degree mentioned,
the want of the usual contents of an intestine, &c. left ultimately
no room for such a supposition. But the chemical resem-
blance of this substance to the spawn of frogs, led me to the
idea of its being perhaps the spawn of some animal. It could
not be that of a frog, but it might be the swelled spawn of a
snail, such as are frequently found in damp meadows ; as the
Limax vufus, agrestis, stagnalis, fyc. I compared the descrip-
tions given in this respect in Cuvier's Comparative Anatomy ;
in Oken's Natural History, iii. chap. i. p. 309 ; in the same
author's Natural History for Schools, p. 668 ; in Goldfuss'
Hanbuch der Zoologie, i. p. 661, and other works; — in all of
which, however, I found little information respecting the object
of my research ; viz. the spawn of snails. Oken, in his Natural
History for Schools, however, remarks, when speaking of Li-
max stagnalis, that " its spawn was a small gelatinous cylin-
der, of one inch in length and one line in thickness, containing
a dozen small yellow eggs ; that these rows of eggs generally
adhere to some aquatic plants, and at the end of a fortnight
or three weeks the young snail crept out of it." Oken further
mentions in his Natural History, concerning the limaces :
" The excremental canal of the sexual bladder is short, ends
in the vagina close to the ovarium, much longer as it should

2 N 2 seem,

276 Dr. Brandes's Examination of a gelatinous Substance, tyc.

seem, in proportion to the penis, and the ovarium connects
with it before it enters the vagina. There is, therefore, no
doubt that this bladder forms a portion of the female parts,
and furnishes perhaps the gelatinous substance for the eggs,
especially as this bladder is found in all snails. Their con-
tents, however is solid, soft like pomatum, and red-brown,
which has led to the erroneous supposition of its being pur-
ple." (Compare also Cuvier on the same subject.) Although
the egg-sticks of the Umax, as mentioned, are very small, it is
yet possible to suppose our substance to have been the spawn
of a Liimax rufus, or some other species, since its great bulk
chiefly arose from water, — a reason too why its solid contents,
compared with its volume, were so small, and those of the water
so great ; and I was enabled, as we have seen in the experi-
ment with boiling water, to swell it to its actual extent. This
supposition was further confirmed, on my finding in a portion
of the substance which I had placed in a small cup before the
window of my study for a few days, a little naked snail (limax)o$
about a quarter of an inch long. I think, therefore, I may po-
sitively assert that the white gelatinous substances which are
occasionally found in damp meadows, and frequently pro-
nounced to be the substance of shooting- stars, are not of at-
mospheric origin, but consist of the spawn of the above-men-
tioned snails, which, although small in its natural state, and
therefore remaining unobserved, assumes, in damp places, by
absorbing water, the large bulk and white gelatinous appear-
ance, necessarily attracting the attention of persons who find
them in their way ; and finally, that its being found only in
damp places is owing to the very nature of this spawn.

I doubt whether the real substance of a shooting-star has
ever been found. Whoever has observed these meteors, must
be convinced that one could not so readily notice the spot
where they seem to fall in the darkness of night, as to be able
to find out the supposed substance, and as it were be able to
say that he has a fallen star in his hand. Before this can be
clearly shown, it may yet have to be proved whether any opi-
nion can be formed as to the nature of shooting-stars. Even
the observation of the above-mentioned American meteor seems
subject to doubt ; and it is still a question whether the produce
of a fiery meteor could be a gelatinous mass ?

Our knowledge of meteors is indeed much increased by the
inquiries of Professor Brandes of Breslaw ; but still the nature
of the substance seems to be enveloped in doubt.

It now only remains for me to consider the apparent dif-
ferences which seem to exist between the observations of
Messrs. Buchner and Schwabe, and my own ; which may be

satisfactorily

Col. Miller's Description of a Percussion Rifle, fyc. 277

satisfactorily done in consequence of the precision with which
those gentlemen have written their accounts.

The substances they have respectively examined offer, as
I have stated above, qualities so different in their nature, as to
ascribe to each a different origin ; so that I cannot agree with
Mr. S. in supposing the substance examined by him to be of
the same kind as Mr. B.'s, while I readily admit that the sub-
stance he has investigated was a real tremella. Mr. B.'s sub-
stance, on the contrary, fully agrees with that examined by me.
Their chemical contents are quite the same ; and the only es-
sential difference between them seems to be, that the substance
examined by him no longer exhibited any organic structure ;
whilst that observed by me still bore the evident traces of an
animal production. But if we consider that this snail-spawn
had lost all appearance of organic structure wherever the mem-
brane had burst, and especially when it was much swelled with
water, I suppose that Mr. B. found this substance so swelled,
that it had burst the membrane in every part, so as to cover
and obliterate the organic structure entirely. That the mass
examined by Mr. B. was actually very much swelled, appears
from the fact, that he found only 40*4 of solid substance; whilst
the one examined by me still had 20*0. If then the identity of
the two cannot be doubted, we must at once ascribe the same
origin to both, — that of being the spawn of a snail. — Thus I
think I have explained the nature of the substance called star-
jelly, and have had the satisfaction of reconciling the differences
between the observations of Messrs. B. and S. ; having shown
that the observations of both these meritorious naturalists were
correct, but that the substances were entirely different in their
nature.

XLV. Description of a Percussion Rifle, igniting by a Spring
instead of a Loch By Lieut.-Col, Miller, F.R.S.*

nnHE stock of this rifle is made either of iron or bronze f,
-■• hollow in the centre, and the barrel is made to screw into
it at the breech. The spring acts horizontally, and is screwed
to a plate, fixed to the left side of the small of the stock. A
cross piece is attached to the fore part of the spring, which
passes through the stock behind the breech, and projects a
little on the left side. In the cross piece there is a notch, and
a button at the end of it ; — the trigger moves upon a pivot in
the upper part of the stock, and is pressed forward by a spring
behind it. The piece is cocked by grasping the small of the

* Communicated by the Author. f As manufactured by Nock.

stock

278 Col. Miller's Description of a Percussion Rifle,

stock with the fingers of the right hand, and pressing the thumb
against the button of the spring until the notch comes oppo-
site the trigger. The cap is then put on the nipple, and the
spring let down upon it, by again placing the thumb against
the button, and pulling the trigger with the middle finger. In
that position the spring is allowed to remain, until the piece
is about to be used, when it is again cocked and fired off. Fig. 1.
represents a side view of the gun ; and fig. 2. the action of the
spring. A piece of leather is put round the small of the stock,
to make it more pleasant to the touch ; and a box placed be-
hind it, for holding caps and patches. The power of the spring
may be increased or diminished at pleasure, by turning the
screw.

This contrivance, it is conceived, produces fire more instan-
taneously than a common lock, from its having no friction. It
is also less liable to get out of order ; and a gun can be con-
structed on this principle, at about half the expense of that
now generally in use.

A rifle of this construction was tried at Woolwich in August
last, of which the following is the result.

Woolwich, August 1, 1827.
Report of the experiment carried on this day with a per-
cussion rifle, igniting by a spring instead of a lock, proposed
by Col. Miller. The rifle was fired by Col. Miller, and at
the ranges of 400 and 100 yards, proposed by himself. The
powder used was Curtis and Harvey's, brought by Col. Miller.
The target was one of 9 feet, of two boards each an inch thick.

Target at 400 yards, balls 28 to the pound.

Round 1. charge 1 drachm; grazed 100 yards short.

2. 100 yards short.

5. 20 yards short.

4. 1 20 yards short.

5. . 30 yards short.

6. — — 1£ drachm; 30 yards short.

7. • over all.

8. struck target 4 feet 7 inches

right of bull's eye, 1 foot 9 inches
under; ball penetrated 1 inch,
and lodged in target.

9. grazed 20 yards short ; struck

target, and dropped ; ball made
an impression half its own dia-
meter in depth.
10. grazed 28 yards short.

Round

igniting by a Spring instead of a Lock.

279

CIS

a

o

•5

~-
I

c
o

c
a

o

c

'§0
'u

o

JS

.S
a,

a>

^2

^

n

n

g
.2

u
<1

s

Si

E

^~Y

*

280 Col. Miller's Description of a Percussion Rifle,

Round 11. charge 1 J drachm; over.

12. . grazed about 60 yards short.

13. grazed twice, and struck target.

14. over.

15. grazed about 20 yards short,

struck target, and dropped ; ball
made an impression half its own
diameter in depth.

16. grazed about 80 yards short;

struck target, and dropped ; ball
made an impression one-fourth
its own diameter in depth.

17. over.

18. grazed 20 yards short.

19. grazed to the right of target.

20. grazed 3 yards short.

Target at 100 yards distance.

Round 1. charge J drachm, through target (hung fire a little)

21 inches above, 7 left of bull's

eye.
2. ■ through, ^ inch under, If left of

bull's eye.
3. through, 9 inches under, 3 right

of bull's eye.
4. through, If inch under, If left

of bull's eye.
5. through, 9 inches under, 5 left

of bull's eye.
6. ■ through, 6 inches under, 8 left

of bull's eye.

Penetrations of Col. Miller's rifle compared with the Govern-
ment rifle, through elm boards, each \ an inch thick, steeped
in water, and placed in a frame f of an inch apart from each
other, at the distance of 60 feet.

Col. Miller with his own rifle, and Government powder.
Weight of rifle, 7 lbs. 10 oz. ; length of barrel 23 inches.

Round 1. charge 1 drachm, flashed once, barrel just washed;
through 7 boards, struck 8 smartly.

2. 6 split the 7th.

3. 6

4. 6 struck 7th.

5. ,. , g struck 7th slightly.

Col.

igniting by a Spring instead of a Loch, 28 1

Col. Miller, with his own powder.

Round 1. charge 1 drachm (Not taken, struck near a former

shot).
2. , . through 7 boards, struck 8th

slightly.

3. (The same as the first).

4«. through 7 boards.

5. 6 boards, struck 7th

slightly.

Government rifle with Government rifle powder.

Weight of rifle 9£ lbs. ; length of barrel 30 inches ; balls 20

to the pound.
Round 1. charge 3 \ drachms (4? drachms including priming)
thr6ugh 8 boards, just touched the 9th.

2. 8 boards, split the 9th.

3. 8 boards, splintered the 9th.

4. 8 boards, splintered the 9th.

5. 8 boards, splintered the 9th.

6. 8 boards, split the 9th.

Col. Miller's rifle, 28 balls to the pound.

Round 1. charge \\ drachm, through 7 boards, struck the 8 th.
2. 1 \ through 6 boards, struck the 7th.

Government rifle, 20 balls to the pound.

Round 1. charge 1 drachm, through 5 boards, struck the 6th.

2. 1 \ « 5 boards, struck the 6th.

3. \\ 6 boards, struck the 7th.

Here ends the Report. — From the preceding experiments,
the great superiority of percussion over the flint-lock is very
apparent, as the penetration of the percussion rifle is not very
much inferior to that of the flint-lock, with a much heavier
ball, and four times the quantity of powder. The penetration
of the percussion rifle also does not appear to be increased
by increasing the charge beyond a drachm ; which tends to
prove, if any proof were wanting, that moderate charges are
the best, and that heavy ones only tend to destroy arms, and
an unnecessary expenditure of ammunition, without producing
any corresponding effect.

New Series. Vol. S. No. 16. April 1828. 2 O XLVI. Ac_

[ 282 ]

XL VI. Account of an improved Form of Apparatus for exhi-
biting M. Clement Desormes's Experiments on Currents of
Air, Sfc. By Robert Younge, Esq.*

HPHIS improvement consists in the application of moveable
* pins on the plate, which enable the operator to vary the
size of his discs ; and it is presumed involves the explanation
of these phenomena. The form of the glass tube permits the
effect to be very distinctly seen, particularly when the current
is powerful, the edge of the plate being on a level with the
sight.

AB is a bent glass tube about six inches long ; C is a circular
copper plate, having a tube of the same metal attached under-
neath, which receives the end of the glass tube B.

D are upright moveable pins f, passing through holes in
the plate, which are represented in the circular drawing. At
E the plate is perforated, to form a communication between
the upper side of the plate and the glass tube J.

By commencing with a large disc, and gradually reducing
its diameter, we may perceive corresponding alterations in the
force of the resistance which it offers ; and by striking circles
of different diameters round the central opening, and leaving
three or more smaller holes in each circle for inserting the
pins, we may easily apply discs of any diameter ; and when
these bear a certain proportion to the diameter of the central
opening, they are invariably blown off.

In No. 2. of the Journal of Science, p. 473, it is observed,
" If the issue for the vapour be turned towards the earth,
and the disc consequently tend to fall, as well by its own
weight, as by the pressure of the vapour, still it will not de-
scend." Might not the amount of this counter-attraction, or
overcoming of gravity, be pretty accurately estimated by the
application of a series of discs, of different weights, varying
according to the diameter of the opening, and weighted in pro-
portion to the power of the current ?

* Communicated by the Author.

\ The sole use of these pins is to keep the discs over the central opening.
X This apparatus was exhibited at the last meeting of the Sheffield Li-
terary and Philosophical Society.

XL VII. Of

[ 283 ]

XLVII. Of the Insect called Oistros by the Ancients, and of
the true Species intended by them under this Appellation : in
reply to the Observations of W. S. MacLeay, Esq., and the
French Naturalists. To which is added \ A Description of a
new Species o/*Cuterebra. By Bracy Clark, F.L.S., and
Foreign Member of the Royal Academy of Sciences of Paris.*

TN the 14th volume of the Transactions of the Linnean So-
-*■ ciety, is a communication written by my friend W. S. Mac-
Leay, Esq., intended to prove that the fly, intitled Oistros by
the ancients, was not the insect so named by Linnaeus, but that
it probably belonged to the present Linnean genus Tabanus,

Being of a contrary opinion, I am led once more to address
this learned Society, to lay before them the grounds on which
it is founded, that naturalists may not incautiously and too
hastily adopt the above conclusion, and that they may avoid
the confusion which change of names and counter changes al-
ways produce in science. I am also led to this undertaking
in order to vindicate Linnaeus himself, our great master, and
such distinguished naturalists as Vallisneri and Reaumur, with
whose views on this subject I wholly concur. Nor is the justi-
fication of myself wanting as a motive to induce me to re-ex-
amine the subject, having formerly sent to this Society a dis-
sertation of some extent on the genus CEstnis, unfolding some
curious discoveries in the characters and natural habits of this
singular race of insects f .

Disputations about the meaning of the ancients, and iden-
tifying their descriptions with the modern species of natural
history, would perhaps, in a general way, be better avoided in
the valuable volumes of this Society, as leading to much de-
sultory and unsatisfactory discussion : practical subjects and
didactic facts would perhaps better maintain their reputation.
As, however, the Society have in this instance already ad-
mitted the discussion, it is but fair and just to allow the reply
in the same channel, that the impression, if erroneous, may be
removed.

W.S.MacLeay, in the paper alluded to, insists that the o'icrTgo$
of the ancients, and the Brize or Breeze of the old English
poets, is not the CEstrus of the moderns ; and he infers this
from the anatomical characters which some of the ancient au-
thors have left us of their insect. Now, besides the anatomi-
cal descriptions to be found in the works of philosophers, there
is another mode of identifying the insect ; and that is, by the

* From the Transactions of the Linnean Society, vol. xv. Part ii. p. 402.
f Published in the 3rd volume of the Society's Transactions.

2 0 2 description

284 Mr. Bracy Clark on the Insect

description of the effects it produces upon cattle, and which
are so singular, that they have afforded incidents to most
rural poets, ancient and modern : and the truth seems to be,
that the poets in describing these effects have been true to
nature ; while the philosophers, being presented with a wrong
insect, have only involved the subject in error.

That it is an Italian insect we have the authority of Valli-
sneri of Padua, who appears to have been the first naturalist
who bred the true (Estrus Bovis from the grubs found in the
backs of the cattle ; and for the first time, as far as we possess
any record of the subject, saw with certainty the identical ob-
ject that created so much commotion among them. He ap-
plied correctly enough the passages of the ancients which he
thought had allusion to this insect. Reaumur followed Valli-
sneri in these researches, and bred with great difficulty one
imperfect specimen of the true Oestrus Bovis. Linnaeus next
followed ; but not having ever seen the insect, and not daring
to describe from figures merely, or the descriptions of others,
he took the large Horse Bot for it, — -the CEstrus Equi of my
enumeration. This error is continued through all the editions
of the Systema Naturce, intending all the while, and referring
to Vallisneri and Reaumur for, the true CEstrus Bovis. Thus,
like some of the ancients, he also described a spotted-winged
insect for the (Estrus Bovis ,• whereas the true insect has per-
fectly spotless wings. The true fly cannot be caught in the
act of oviposition, from the violent running of the cattle, and
the terror they are in at the approach of their enemy.

This makes it more than probable, nay, almost certain, that
if Aristotle, iElian or Pliny described an insect with spotted
wings, or with a trunk or proboscis, &c, they knew nothing
about the true CE. Bovis, and had been deceived as to the real
object of their research. It was indeed much more easy for
them to have been presented with one of the numerous host
of flies that infest the backs of cattle and lodge on them, than
the true CE. Bovis. Their fly may have been a Tabanus or an
Asilus, a Conops, or a Culex, or any other with spotted wings ;
for as the true fly cannot be caught in the act of oviposition, it
was next to impossible they should have discovered, or been
made acquainted with, the true object of such disturbance.
Indeed, during these commotions it would be dangerous to
approach the cattle, or to remove any thing from their back ;
and if an insect was caught under any other circumstance,
how could it be known that it was the genuine cause of this
agitation r

It is in vain now to inquire what precise fly these ancient
philosophers might have been presented with, as their testi-
monies

tailed Oistros by the Ancients. 285

monies are various, and militate against each other ; but none
are descriptive of the true fly, which we now fully know.
Surely such a conclusion is more natural and just, than to sup-
pose these conflicting descriptions true, and that the poets and
common observers were false witnesses.

I now proceed to give what Virgil says respecting the name
of it among the ancients, and the tumult it occasions ; and of
which no sweat-sucking Tabanus, Conops, or modern Asilus,
can in any way be the cause.

*' Est lucos Silari circa, ilicibusque virentem
Plurimus Alburnum volitans, cui nomen Asilo
Romanum est, (Estron Graii vertere vocantes :
Asper, acerba sorians : quo tota exterrita sylvis
Diffugiunt armenta, furit mugitibus iEther
Concussus, sylvaeque, et sicci ripa Tanagri."

Georg. lib. iii. v. 146.

From this admirable description, it is clearly manifest that
Asilus was the Roman name for the fly which agitates the
cattle ; and it is equally clear that (Estros was the Greek name
for it

Not much weight is due to the observation, that Homer's
insect was not the modern CEstrus, because he mentions the
spring as the season of its appearance, since he also adds, in
the same line, ore r ^oltol (xotxpol nshovTcti, " when the days are
long ;" nor that Shakespeare did not use the word Brize for
the same insect, merely because he has assigned its appear-
ance to the month of June, when it more often appears now
in July. Indeed the alteration of style will account for this
difference. But the same poet uses the word in another place,
where the allusion is too distinct to be mistaken :

" The herd hath more annoyance by the Brize,
Than by the Tiger." Troilus and Cressida.

And again in an old Play, quoted by Archdeacon Nares in his
Glossary, the following use of the word occurs,

" I will put the Brize in 's tail, shall set him gadding presently."

Now if MacLeay or Latreille, who entertains a similar opi-
nion, had ever been as much among cattle on the heaths, as
my pursuits have led me, they would have long since obtained
a practical acquaintance with the effects produced by these in-
sects, and would not have been led to suppose that the Tabani,
Conopses, or Culices, were the object of poetic description, or
have made any mistake between the effects of one and the
other. When the Tabani and Conopses have come and set-
tled in great numbers on the back and sides of the animal, he
would, as I have often witnessed, scarcely regard them. A

toss

286 Mr. Bracy Clark on the Insect

toss of the head, perhaps, towards the part, if they sucked a
little too vigorously ; or, if they were still more importunate,
a lash of the tail, was in general all the notice he would con-
descend to take of them. But if an (Estrus approached, the
consternation was indescribable, and the agitation most re-
markable ; and the object attacked, however lazily he might
be disposed from the heat of the weather, or a full belly, would
become suddenly as agile as a young deer, and canter away,
holding out his tail, and running with a sort of undulatory
movement of the back (thereby endeavouring, perhaps, to dis-
appoint the touch and designs of his enemy), till he had ob-
tained his accustomed retreat in the water, or the fly had
quitted him, —

Tossing the foam

They scorn the keeper's voice, and scour the plain,
Through all the bright serenity of noon ;
While from their labouring breasts a hollow moan
Proceeding, runs, low-bellowing, round the hills. — Thomson.

Assuredly no Tabanus can produce any effects like these. Un-
able to account for this extraordinary agitation, I had formerly
given way to the notion of some very painful infliction by the
(Estrus : but I am now led to question this opinion, inasmuch
as I can discover no instrument by which this effect can be
produced. The shrill sharp sound, which Virgil describes,
was, I dare say, not stated without some real ground ; and a
friend of mine actually informed me, that he was standing in a
farm-yard one day near some cattle, when one of these flies
entered and approached them, and that he distinctly heard
this shrill sound. In confirmation of this account we may re-
mark, that the wing-scale, covering the halteres, which has
been supposed by Keller to be the organ of sound, is particu-
larly large in this insect; but further than this we dare not
assert, but leave the point for future investigation. We know
from Linnaeus's own account, that the (Estrus Tarandi, or
Rein-deer Bot, very similar in all respects to the (E. Bovis,
makes no sound while depositing its egg ; which again brings
me into doubt upon this matter.

We next have to observe, in confirmation of the peculiar
effects of these insects upon the animals they infest, that those
of the (Estrus of the Rein-deer, are equally singular and re-
markable ; and this fact we have from the indefatigable re-
searches of our immortal leader, Linnaeus himself. He says,
speaking of the (E. Tarandi, in his Lapland Tour, that as he
was in bed early one morning, he perceived a very ungrateful
smell, and when day-light appeared, " there were standing

about

called Oistros by the Ancients. 287

about the cot a thousand of these Rein-deer, driven by old
men, boys, dogs, and women, who milked these animals.
They appeared to be under the apprehension of some invisi-
ble attack : the animals carried their heads aloft, their ears
pricked up and extended, beating the ground, and kicking in
the air with their feet, as though by enchantment. Then for
a while they would be quiet ; then, again, they were seen most
furious, and this with so general and regular a movement, that
no army would have surpassed their exercises in uniformity."

Linnaeus further states, in the Lachesis Lapponica, respect-
ing the effects produced by this sort of (Estrus, that in passing
afterwards into the Lapland alps he observed a Rein-deer,
which was loaded with his own package, frequently to stop
short and become perfectly quiet and motionless as a pillar of
stone, or one suddenly struck with catalepsy ; the head held
straight out, the ears upright, the eyes fixed ; nor could he by
any ill treatment be induced to proceed ; but in a little while
he would again resume his march. Where, I would ask, is
the Tabanus, or Conops, that could produce effects like these ?
or what naturalist, at all acquainted with the operations of
Nature herself, could confound the dissimilar effects produced
by these several insects ?

Linnaeus further says, that in the Rein-deer fly he saw the
egg held out " like a white mustard-seed" at the end of the
abdomen, which, if true, fully confirms the supposition that
there can be no infliction.

The (Est? us hcemorrhoidalis and (Estrus Ovis, in performing
their office of ovi-deposit, are also equally irritating and pecu-
liar, as I have shown in the paper above alluded to, in the 3rd
volume of the Society's Transactions.

I avail myself of this opportunity in conclusion, to state, in
addition to my former remarks on this genus, that it appears
to me, as there is no aculeus or weapon of infliction at the end
of the abdomen of the female of the (Estrus Bovis, that the egg
is simply thrust down among the hair, till it meets the skin,
and that then it is affixed to it by a glutinous liquor secreted
at the same time ; and that the egg being hatched, the young
grub insinuates itself into, and finally through the skin, form-
ing an abscess beneath it. In a somewhat similar manner it
is that the ichneumon flies deposit their eggs on the sides of
living caterpillars of the Lepidoptera, and hatching, perforate
their skins, and entering within, live on the parenchyma or
pulp of their bodies till matured and fully grown, when they
make their way out again and change to the chrysalis.

I may also remark of the (Estri, that they appear to be

wonderfully

28 S Mr. B racy Clark on a new Species of Cuter ebr a. ,

wonderfully kept from such an increase as would be fatal to
the animals they feed upon, by the difficulties and imminent
hazards they are exposed to in the act of depositing their eggs.
The teeth of the horse must destroy, one should imagine, nine-
tenths of the CE. Equi, ktzmorrhoidalis, and salutiferus. The
(Estri seem however, in the hands of Providence, to make a
double recompense for the sufferings they occasion ; first, by
keeping the animals on the alert during hot weather, when
they would be often too idly disposed for their welfare; while
the few larvae which succeed in getting into their bodies, ap-
pear to benefit them by their local irritations, stimulating the
stomach to a quicker digestion of their watery food, and di-
verting diseases by their counter irritations of the skin and
frontal cavities, — thus producing the effect of issues or vesica-
tories, which are powerful remedies in relieving and in pre-
venting diseases.

I apprehend that I have now sufficiently shown that the
(Estrus of the ancients could have been no Tabamis, and that
it is clear Olivier, who appears to have originated this notion,
and who was followed by Latreille, was mistaken.

A very extensive enumeration of this genus is seen in a late
ingenious publication, the Systematische Beschrcibung of J. W.
Meigen. It is however in some instances not correct ; for on
carefully examining the (Estrus lineatus of this writer, intro-
duced from Villers, it would appear to be that stumbling-
block of systematists in entomology, the CE. Bovis of my enu-
meration*, and not of Linnaeus, as he states, who, as we have
repeatedly said, described the CE. Equi for this species. The
(E. pictus of this author, beautifully figured by Curtis in the
British Entomology, no. xxvi. 1. 106, 1 rather suspect to be the
faucial bot of the Stagf.

As the species of the new genus Cuterebra were taken for
(Estri till I separated them, and are closely allied to them in
their habits, I have ventured at the close of this paper to com-
municate to the Society a new and undescribed species lately
received from America, along with some other insects sent me
by my nephew, Joseph Clark, from the Illinois.

* The lines on the thorax, and the figure of Villers, undoubtedly con-
firm it. Meigen's CE. Bovis is the CE. Bovis of my enumeration, under
which this should have come as a synonym.

f I may here observe, that a few days since, in visiting the British Mu-
suem, I was shown the insect Dr. Leach has called CEstrus Clarkii, and
find it only a variety, and scarcely that, of the CEstrus veterinus of my
enumeration.

Cut-

Notices respecting New Books. 289

CUTEREBRA F0NT1NELLA.

C. thorace atro, lateribus albis ; abdomine violaceo, ultimis
segmentis albis, nigro-punctatis.

White-tailed Cuterebra, or Blue Rabbit Fly.

Habitat in Illinoe Americae Septentrionalis, cuniculos infestans.

Descr. Cuterebra Cuniculi dimidio minor; atra, subcylin-
drica, cum capite parum latior. Frons insuper atra et
circa oculos lucida, infra albida, pilosa, utrinque puncto
elevato atro. Oculi picei. Thorax insuper ater, late per
medium et ad latera pilosus, albus, punctis tribus nigris
utrinque notatus. Alee obscure nigro-fuscae, sulcis valde
puculatae et rugosae, corpore longiores ; ad basin squa-
mula foliacea erecta, magna : tympanum halterem tegens
magnum, convexum, marginatum. Abdomen breve, atrum,
lucidum, superne violaceo resplendens; segmentis duo-
bus postremis hirtis, albidis, punctisque variis atris eleva-
tis, glabris. Anus utrinque quasi forcipe prehensorio
armatus. Pedes atri.

XLVIII. Notices respecting New Books,

An Introduction to Geology: comprising the Elements of the Science
in its present advanced State, and all the recent Discoveries. By
Robert B a kewell. The Third Edition, entirely recomposedt
and greatly enlarged. With new Plates, Cuts, fyc. Octavo, pp. 540.

THE readers of the Philosophical Magazine, may probably
remember, that after the first edition of Mr. Bakewell's In-
troduction to Geology appeared in 1813, the late Mr. John Farey,
a practical geologist and accurate observer, published a very co-
pious analysis of the work, in several Numbers of the Magazine, (see
vol. xli. and vol. xlii.*) A second enlarged edition of the Introduc-
tion to Geology was soon after published ; and it was translated into
German by Mr. Fred. Muller, of Friburg. The work has now been
several years out of print, and has been frequently called for. We
shall extract from the author's Preface a brief account of what has
been done in the third edition, in order to present a distinct view

* Mr. Farey opposed with some warmth, the parts of Mr. Bakewell's
work which were at* variance with his own opinions on the Geology of
Derbyshire; but he concludes his strictures with the following remarks:
" I beg however distinctly to state, that I have yet perused no systematic
work on Geology, which I think entitled to a general and careful reading,
in any degree compared with Mr. Robert Bakewell's ' Introduction to Geo-
logy > and which I sincerely wish may be read and studied by hundreds
of persons, with no* less care and attention, than I have bestowed upon
it. Because I can assure them that it contains more facts concerning our
planet, and fewer absurdities and whimsical assertions and theories, than
any of the numerous systematic works which have preceded it, in our own
language, or I believe in any other." — Phil. Mag. vol. xlii. p. 246.

New Series. Vol. 3. No. 16. April 1828. 2 P of

290 Limuean Society.

of the progress of geology, and the important discoveries that have
recently been made.

u The causes which have retarded the publication of a third edi-
tion it is unnecessary to mention : the delay has, I trust, been fa-
vourable to its appearance in a very improved state ; as 1 have been
collecting materials for it, during several years, having visited al-
most every situation of much geological interest in our own island,
from the Land's End in Cornwall, to the Grampian Mountains in
Scotland ; and passed part of three years in examining the geology
of Savoy, Switzerland, and France. There is scarcely a rock-for-
mation described in the present volume, that I have not examined
in its native situation, and compared with the descriptions of former
geologists. I have also had opportunities of examining the collec-
tions, and of profiting by the communications, of some of the most
eminent geologists on the Continent.

" While engaged in these pursuits, I have not been inattentive
to the labours of other observers. So numerous and interesting are
the discoveries made in geology during the last ten years, that in
order to present a concise view of the science in its present ad-
vanced state, the * Introduction to Geology' has been recomposed,
and all the chapters are greatly enlarged.

" The following new Chapters have been added : — Chap. n. On
Fossil Organic Remains. Chap. iv. On the Principles of Stratifica-
tion. Chap. x. A Retrospective View of Geological Facts. Chap.
xviii. On the Destruction of Mountains ; and on the Bones of Land
Quadrupeds, found in Diluvial Depositions and in Caverns. Chap,
xix. On the Formation of Valleys ; and on Deluges and Denuda-
tions.—The Plates are new, except Plate iv. and part of Plate vn."

" In the course of the present work, I have frequently attempted
to elucidate the geology of England, by comparisons with situa-
tions I have examined on the Continent, in order to connect the
geology of our own island, with that of France, Switzerland, and
Savoy.

" By comprising the numerous facts and observations contained
in the present volume, within the limits of an elementary work, from
the desire to be concise,- I may have run the risk of becoming ob-
scure: this I have studiously endeavoured to avoid; my chief aim
being to present the reader with a system of geology, which shall
explain geological phenomena in a clear and intelligible manner,
and as free from technical obscurity as the nature of the subject
would admit. In order that the price may not exceed that of the
last edition, this work is printed in a smaller type."

XLIX. Proceedings of Learned Societies.

LINN^EAN society.

March 4. A COMMUNICATIONfrom the Rev. Leonard Jenyns,
-£Jl M.A. F.L.S. was read, On the distinctive characters
of two British species of Plecotus Geoff, supposed to have been con-
founded under the name of Long- eared Bat.

A new

Geological Society. 291

A new Bat found adhering to the bark of a pollard willow, and
which the author names brevimanus, is discriminated in this Me-
moir from the auritus, which together with barbastellus make up
Geoffroy's subgenus Plecotus of the Vespertilionidae.

Spec. Char. P. brevimanus, Lesser long-eared Bat, " vellere
supra rufo-fusco, subtus albescente ; auriculis oblongis, capite haud
duplo longioribus; trago ovato-lanceolato ; cauda antibrachium
longitudine aequanti, apice acuto."

The difference in absolute size, in the relative proportions of the
parts, in the colour, and in the apparent habits, seem to require the
making it a distinct species.

March 18. — The chair having been taken by A. B. Lambert, Esq.
V.P., Edward Forster, Esq. the Treasurer of the Society, communi-
cated to the meeting the afflicting tidings which had arrived during
the day, of the decease of Sir James Edward Smith, their eminent
and much-beloved President, — an office to which he had been ap-
pointedby the annual and unanimous choice of the Society from its
first establishment in 1788, till his death. The Society immediately
adjourned.

GEOLOGICAL SOCIETY.

Feb. 15. — This day being the Anniversary, after the election of
Officers and Council, as noticed in our last Number, a Report from
the Auditors and Council was read and approved j after which the fol-
lowing Address was delivered from the chair by W. H. Fitton, M.D.
F.R.S. &c the President of the Society.

Gentlemen of the Geological Society.
You have just received from your Council a report on the condition of
your finances j with a statement of the accessions to your number du-
ring the past year, and of the measures adopted for advancing the wel-
fare of the Institution. It remains for me to lay before you a few
remarks on the branch of knowledge which the Geological Society
is intended to promote : and what I shall offer upon this subject will
be confined, in a great measure, to the state of Geology in this coun-
try ; since neither have my opportunities of acquiring information
during the past year enabled me to give, nor does my duty appear
to call for, a more extended view j— though such periodical reports in
other hands, and on more suitable occasions, have been frequently
attended with advantage.

We have had since our last Anniversary to regret the loss of one of
our foreign members. Mr. Brocchi, whose death, according to the
accounts we have received, took place in Egypt, whither he had been
invited to discharge the duties of a mining Engineer, is distinguished
in the recent scientific history of Italy by numerous contributions to
the Geology of that country ; — and his principal work "On the Fossil
Conchology of the Subapennine Hills," abounds in valuable obser-
vations, and in proofs of accuracy and acuteness in the comparison
of the fossil and existing species. His talents, however, were not
merely those of an observer $ — his general views were always wide

2 P 2 and

292 Geological Society,

and philosophic ; and the style of his writings is considered by com-
petent judges as remarkable for its purity and good taste. But those
only, who have had the pleasure of being personally acquainted
with Mr. Brocchi, could appreciate his patriotism and philanthropy,
the variety of his acquirements, and the spirit and eloquence which
rendered his conversation more than commonly instructive.

The printed " Proceedings" of the Society, and the portion of the
Transactions published within the year, are the best records of our
contributions to geological science during that period : and the vo-
lume now in progress will, I trust, be found to have contributed in
no small degree to the advancement of inductive Geology. New
monsters, it is true, have not been brought to light from the depths of
our strata ; nor has Zoology been enriched with new genera, by such
rare coincidences of genius and good fortune as distinguish the last
volume of our Transactions : but the Geology of England has been
illustrated by various memoirs, on tracts not previously examined ;
and by more exact and extended researches on portions of our strata,
the general relations of which had been before determined. Cor-
rect data have thus been recorded, to which inquirers in other coun-
tries may refer, for the purpose of comparison with their own.

I have to congratulate you upon the progress which has been
made in the Trigonometrical survey of Ireland -} a wrork designed
with all the skill of modern science, and committed for the execution
to such hands, and with such instruments, as to leave no doubt of the
result. Maps alone, such as this survey will produce, are an acqui-
sition of the first importance to our inquiries ; since they form one of
the chief and indispensable instruments of geological research : — but
with these, in the present case, will be connected a series of obser-
vations more strictly geological, which cannot fail to throw great light
upon the structure and composition of the country to which the ope-
rations extend. The Tract, which I now show you, has been drawn
up by one of the principal officers engaged in the Irish survey*, and
lithographized for the use of the subordinate surveyors j and it con-
tains so clear and able a system of instruction for their guidance, il-
lustrated by sectional sketches, as greatly to facilitate the task of
geological investigation. The surveyors will thus accumulate a series
of specimens, the precise places of which will have been recorded in
maps upon a very large scale, — on which also the heights above the
sea will be determined, in points almost innumerable j while sections
are taken in well chosen situations, for the purpose of illustrating
more effectually the order of the strata. The ultimate results of ope-
rations so well combined, must be equally honourable to those who
are engaged in this vast work, and fertile in various and substantial
advantage to physical science.

But while the survey of Ireland is in progress, it is to be hoped that
that of England will not cease to advance ; and that no great delay
will take place in the publication of the maps which have been actu-
ally prepared by the Ordnance. To geologists who have travelled in
England, I need not mention the benefits that our science has derived
* Captain Pringle, of the Royal Engineers.

from

Geological Society. 293

from the maps already engraved ■ nor dwell upon the misery of plung-
ing, from a tract that we have traversed with the advantage of this
guide, into regions where the survey leaves us, lost, as it were, and
bewildered from the want of such assistance. The sheets of the Ord-
nance Survey which I now lay before you, represent a portion of the
midland counties, coloured geologically by a gentleman whose activity
and accuracy of research have made him minutely acquainted with
the stratification of the district around him* j and the maps thus co-
loured, are probably as complete specimens of geological illustration
as ever have been produced. The knowledge of this observer extends
with equal precision several miles to the north of the tract here re-
presented j but these sheets, you perceive, are bounded by a right
line ; — and beyond that line it has not been in his power to extend his
colours, because no good map of the adjacent district is in existence.
In this instance therefore, and no doubt in numberless other cases,
the want of adequate maps may cause the final and irreparable loss
of much geological information : And when it is considered, that
Geology is but one of many departments of useful inquiry, to which
good maps administer,— how much they contribute to the advancement
of commerce, and to the comforts and conveniences of life, — it will
be unnecessary to urge the enlightened and public spirited persons,
to whose hands this great undertaking is committed, to finish with as
much promptitude as possible what has been so admirably begun.

The effective establishment in this country of a society for the
cultivation of Zoology, — a source of just gratification to all who are
interested in the progress of Natural History, — is an event connected
very intimately with the advancement of our subject : for to the
Geologist it is of great importance to obtain facility of access to
cabinets and to living specimens, in elucidation of fossil remains ;
and to have the privilege of appealing, in doubtful cases, to compe-
tent authorities, in what relates to the animal kingdom. But the
connection of Zoology with our science, is a field too wide to be dis-
cussed upon the present occasion ; nor would my own acquaintance
with the subject justify my dwelling upon it.

The numerous provincial institutions, which have been recently
established for the promotion of useful knowledge, will also materially
contribute to the diffusion of a taste for Geology j and will throw
new light upon the structure and productions of their respective dis-
tricts.

I wish that it had been in my power to speak with equal gratifica-
tion, of the relation in which our subject stands to another principal
department of Natural History j but the fossil remains of the vege-
table kingdom do not appear to occupy, at present, a just share of the
attention of Botanists in England : and hence it has happened, that
of the numerous and interesting specimens of fossil plants continu-
ally brought to light from our strata, especially within the coal dis-
tricts, the greater part has been sent for illustration to those na-
turalists on the continent, whose publications upon this branch of
inquiry, are so creditably known to science. Ought we not then
* Mr. Lonsdale of Bath.

to

294 Geological Society.

to imitate the example of those, for whose labours we have so much
reason to be grateful; and to reflect, that — if the botanical charac-
ters of fossil specimens be obscure, and the investigation of them at
present unsatisfactory, — the subject is still comparatively new, and
the difficulties such as perseverance and the multiplication of speci-
mens must every day diminish : whilst the views to be derived from
the connection of vegetable remains with geology, are scarcely infe-
rior in interest to those already disclosed by the fossil remains of
animals ? The distribution of plants upon the former surfaces of the
globe, — its relation to the epochs of geological deposition, — the varia-
tions it may have undergone from change of climate, either by alter-
ation of internal temperature, or of elevation above the sea ; — the
former existence of vegetation in the more complex forms, in tracts
where scarcely any traces of it exist at present, — are subjects which
give rise to some of the most important general questions connected
with the history of the globe ; — and that require for theif due con-
sideration such an acquaintance with the characters of fossil vegetable
remains, as none but the most skilful and experienced botanists
can be expected to possess.

On the Geology of foreign countries, the last year has not been
unproductive. A valuable paper on the structure of Jamaica, has
been published in our Transactions, by one of the most skilful of our
practical observers. We have received a very important contribution
of specimens from Captain Franklin and Dr. Richardson, under whose
direction the expedition to the northern coast of America has been
conducted with so much ability and success -, — and a memoir by the
latter, on the structure and components of those regions, will soon
be read at one of our meetings. Captain Parry also, and Captain
Foster, have presented us with a valuable collection of specimens from
Spitzbergen, obtained during their late expedition to the north.
Captain King, who has enriched our cabinets with specimens from
the coasts of Australia, and done so much for other departments
of natural history, has recently sent home a collection of rocks
obtained during the earlier part of his survey in the Straits of Magel-
lan ; and further collections, accompanied with new information, may
still be expected from the same indefatigable observer. We have rea-
son also to hope that Geology will not be neglected during the expe-
ditions soon about to sail, — of Captain Boteler, for the survey of the
western coast of Africa, and of Captain Foster, for the purpose
of determining the longitude of important stations on the shores of
the Atlantic.

There is the greater reason to rejoice in the contributions thus
given, or to be expected, from the Naval department of the public
service, since it has not unfrequently been the reproach of this
country, that — possessing colonies, which have dispersed the natives
of Britain in every region of the habitable globe, and commerce, that
maintains continual intercourse with them,— the benefits conferred
by England on the natural history of distant countries, have fallen
very far short of what the intelligence and activity of our national
character might have afforded. Let us hope, however, that brighter

days

Geological Society, 295

days are opening upon us j and that those who are employed in the
various departments of our foreign service, will universally feel, that
where such frequent opportunities of advancing useful knowledge are
likely to occur, an acquaintance with branches of science not imme-
diately essential to professional duty, is strictly accordant with the
dignity of the naval and military character.

Among the donations of foreign specimens to our cabinets, there is
one of very peculiar interest ; — the rich collection of fossil bones and
shells presented to us by Mr. Crawfurd from Ava : which has the
greater value, as it is one of the first collections of this description,
that has made its way into England from our extensive empire in
the East, or the adjoining territories. These specimens afford some
very striking novelties, both to the Geologist and Zoologist j an ac-
count of which, I trust, will soon be laid before you by competent
describers.

The last year has produced some valuable publications on the Geo-
logy of Volcanoes, which, though not emanating immediately from this
Society, are the work of our own members. We are indebted to Dr.
Daubeny for a judicious volume, in which he has combined what had
been previously published on volcanoes, with much valuable obser-
vation of his own. The productions of Mr. Scrope, though his
speculative views are not free from objection, are full of originality
and talent. — To that especially, which describes the extraordinary
volcanic region in the centre of France, illustrated with such effect as
to render the task of comparison with other districts easy and inviting,
I should have had pleasure in alluding more fully ; if an eloquent ac-
count of it, in one of our leading journals, were not familiar to us
all * : and this, also I believe I do not err in ascribing to an active
member of our Institution.

In the speculative department of Geology, nothing has been of
late more remarkable, with reference to its history in this country,
than the universal adoption of a modified Volcanic theory, and the
complete subsidence, or almost oblivion, of the Wernerian and
Neptunian hypotheses ; — so that what, but a few years since, it
was by some considered as hardihood to propose in the form of con-
jecture, seems now to be established nearly with the evidence of fact.
It is no longer denied, that volcanic power has been active during all
the revolutions which the surface of the globe has undergone, and has
probably been itself the cause of many of them j — and that our continents
have not merely been shaken by some mighty subterraneous force,
but that strata, originally horizontal, have thus been raised, shattered,
and contorted, and traversed, perhaps repeatedly, by veins of fluid mat-
ter j — operations which have produced phenomena, so nearly resem-
bling those of recent volcanic agency, that to have so long disputed the
identity of their cause, is one of the most remarkable proofs in the an-
nals of philosophic history, of the power of hypothesis in distorting or
concealing truth. Whatever, therefore, be the fate of the Huttonian
theory in general, it must be admitted, that many of its leading pro-
* Quarterly Review, Vol. xxxv. page 447, &c.

positions

296 Geological Society.

positions have been confirmed in a manner which the inventor could
not have foreseen.

The most striking modern support of these correcter views, is due
to Von Buch and Humboldt, and to the facts and inferences derived
by Dr. MacCulloch from the country which gave birth to Hutton,
and to his illustrator, Mr. Playfair, and in which were made the expe-
riments of Sir James Hall. More recently, a series of facts observed
by Professor Henslow, in the Isle of Anglesea*, has proved, in the most
satisfactory manner, the connection of veins of trap with very high tem-
perature 5 since the change produced upon the strata, through which
the substances now occupying the veins were injected, has approached
so nearly to fluidity, as to admit of their crystallization, in forms differ-
ent from any which the components of the rocks, if they had not been
thus acted on, would have afforded. Sir Humphry Davy's experiments
on the fluids contained within cavities in crystals f, are another strik-
ing and unexpected confirmation of Hutton's views : and our own
Transactions, besides various incidental pieces of evidence derived
from this country, supply the testimony of an unprejudiced witness to
an earthquake on the coast of Chili J, which brings almost before the
eyes of the reader, the movement and permanent elevation of the land.

Having alluded to Mr. Playfair's support of the volcanic theory, it
would be unjust to the memory of that distinguished man, not to
mention, that his geological writings have had, indirectly, an effect in
accelerating the progress of our subject, the benefit of which we expe-
rience at this moment, and probably shall long continue to feel j and
which, perhaps, outweighs in value the partial success of the specula-
tions for which he so strenuously contended. He clothed our sub-
ject with the dignity of an eloquence most happily adapted to phi-
losophic inquiry, and redeemed the geologist from association with
that class of naturalists who lose sight of general laws, and are
occupied incessantly with details j — placing him, where he ought
to stand, beside the mathematician, the astronomer, and the che-
mist -, and permanently raising our science into an elevated depart-
ment of inductive inquiry. His mild and tolerant character threw an
assuaging influence upon the waves of a controversy, which in his
time considerations entirely foreign to science had exasperated into
unusual violence : and if, fortunately, there is no longer any trace of
this asperity, the change must, in a great degree, be ascribed to the
tone of Mr. Playfair's writings, enforced by the manly and consistent
tenour of his blameless life.

I cannot, for your sake, regret that the presence of some of those
who have had a large share in the foundation of this Institution, pro-
hibits my alluding to their continued and unremitting efforts in sup-
port of it. — And the same cause prevents my dwelling on the effects
produced, at both our Universities, by the geological instructions de-
livered there ; which have given to the subject an impulse perhaps

* Transactions of the Cambridge Philosophical Society, vol. i. page 406.

f Philosophical Transactions, 1822, page 367, &c.

j Geological Transactions, second series, vol. i. page 413.

without

Geological Society. 297

without example in the history of those institutions, and gone far to
render natural science a permanent department of general education.

But there is one of our number, whom professional and domestic
occupations retain so much in a remote quarter of the country, that
we have seldom the gratification of his presence amongst us, though
his writings are in all our hands • and it is a duty, — not to Mr. Cony-
beare, but to the subject, and to ourselves, — to say, that among the
more recent causes which have accelerated the progress of Geology in
England, the publication of the " Outlines of England and Wales,"
by him and Mr. Phillips, has had an effect, to which nothing since
the institution of this Society, and the diffusion of the geological maps
of England, can be compared. It is with peculiar pleasure that this
statement can be made in this place j since a large proportion of that
work has been derived from our own Transactions, and the authors
have long been distinguished members of our Society. Of course
their publication is not free from defects and inequalities, — inevitable
perhaps in a first edition, composed for the greater part during its
progress through the press : — but, regarding it as the first general
sketch of a country so complex as our own, it may be said without
fear of contradiction, that no equal portion of the earth's surface has
ever been more ably illustrated 5 — nor any geological work produced,,
which bears more strongly impressed upon it the stamp of original
talent for natural science.

The object, however, of our Institution, to adopt the language of
the charter, is " to investigate the mineral structure of the Earth j" —
not to confine ourselves to the British Islands only, (and even they
are best illustrated by comparison,) but to extend our researches if
possible, to every part of the globe ; — to record the geological phe-
nomena of the most distant countries, as well as of our own, — and from
the whole, derive the laws that have regulated the structure of this
planet, and still influence the changes which are in progress upon it.
It is our good fortune, and the fact is intimately connected with
the commercial wealth of our countiy, that it affords a greater
variety of strata and of geological appearances, than most other por-
tions of the civilized world of such limited extent ; while the range
and variety of our coasts unveil the geological anatomy of England,
with an obviousness and convincing facility to the observer, that have
greatly accelerated our inquiries. The Geology of England, therefore, —
which, with a view only to commercial advantage, and to the com-
forts and conveniences of life, would have well deserved all the labour
that has been bestowed upon it, — acquires a new and more dignified
interest, when we reflect that this island is in a great measure an
epitome of the globe j and that the observer, who makes himself fa-
miliar with our strata, and the fossil remains which they include,
has not only prepared himself for similar inquiries in other quarters,
but is already, as it were, acquainted by anticipation with what
he must expect to find there. If, therefore, I were called upon
to state in what manner those who have leisure, health, and talent
for such inquiries, can most effectually advance the bounds of our
science, and increase the reputation which England has begun to ac-
New Series. Vol. 3. No. 16. April 1828. 2 Q quire

298 Geological Society,

quire in this department of natural knowledge, — I should say, that it
would be, — First, by rendering themselves accurately familiar with the
geological phenomena of our own country; and then, — by taking
abroad with them the knowledge thus acquired, and comparing the
phenomena with those of distant regions; since it is only from the
multiplication of such comparisons, that sound general views can
be derived.

But even within the British Islands, there still are tracts, and of no
small extent, which are comparatively, and a great part of them abso-
lutely, unknown. More than one half of Ireland is in this condition : for
the publications of Conybeare and Buckland, Stephens, Weaver, Grif-
fith, and Dr.Berger, comprehend nearly all that has been done in that
country. But this subject, as I have already mentioned, has passed into
such hands, as will, no doubt, accomplish every thing that can be
desired.

In the North and North-west of England, the labours of Otley*,
Smith, Professor Sedgwick, and some other inquirers, have already
ascertained the principal relations of one of the most important dis-
tricts ; but very little has yet been published upon it. And on the
mountainous tracts in Wales, the ancient and very interesting essay
of Owen f, and the valuable papers of Mr. Aikin and Professor
Henslow, with that of Mr. De la Beche on Pembrokeshire, and of
Mr. Martin on the Coal Basin of Glamorganshire %, — a tract on which
Mr. Conybeare is occupied at present, comprehend nearly every
thing that deserves to be mentioned here.

In Scotland also, notwithstanding the graphic and copious illus-
trations of Dr. MacCulloch, and the mineralogicai skill and perse-
verance of other eminent naturalists who have applied themselves to
the Geology of their native country, — no geological map has yet ap-
peared ; and a great part of that rich and varied region remains to be
explored. But the Society will have pleasure in observing, in the last
portion of their Transactions §, that an effective comparison of the
more recent strata of Scotland with our English formations has
already begun. The memoir of Mr. Murchison on the Brora Coal-
field is an excellent specimen of what may be effected in this de-
partment of inquiry ; and a paper produced at the last meeting by
the joint labours of Professor Sedgwick and Mr. Murchison, leaves no
doubt that the remaining memoirs which are to be expected from
those gentlemen, will throw great light on the comparative geology
of that distant portion of our island.

The value, however, of the researches and identification at Brora,
goes much further than the mere comparison of a remote tract, with

* The work here referred to, is a brief but valuable notice, * On the
succession of rocks in the district of the Lakes," published in the Lonsdale
Magazine, or Provincial Repository, for October 1820:—- Vol. I. No. x.
pp. 433, &c.

f Dated in 1570:— See Cambrian Register, for 1796, and Geol. Trans.
N. S. Vol. I. page 312.

X Philosophical Transactions, 1806. page 342.

§ Second Series, vol. ii. p. 293.

the

Geological Society. 299

the stratification of England : they confirm a suggestion of Dr. Buck-
land and Mr. Lyell, that the coal formation of that neighbourhood
was in reality the equivalent of a portion of our Oolitic strata ; and
demonstrate the remarkable fact, that the same fossils which in En-
gland occur in oolitic limestone, exist there in strata of quartzose sand-
stone and of shale ! The whole series indeed, of the phenomena
developed by recent examination in Scotland and the north of En-
gland, gives rise to the most interesting speculations on the questions
of geological identity, and of the relative value in geology of mine-
ralogical and zoological characters, — which has been so ably treated
by Brongniart and other continental writers: — questions, which it is
necessary to keep continually in view, and that acquire fresh interest
and importance in proportion as we extend our researches to the re-
moter districts of the world.

To those amongst us who are confined to England, the most use-
ful task perhaps would be, when we have mastered the general re-
lations of our series, to take up some one portion of the subject, —
a group of strata, or even a single stratum, or any one of the num-
berless questions connected with their zoological and mineralogical
relations, — and to publish in the form of Monographs the results of
our inquiries. For it may be stated with confidence, that there
is not any one of our strata, however familiarly it may be supposed
to be already known, that would not, if thus treated, reward the
most elaborate and minute examination.

But those who are deprived of the privilege of travelling even in
England, must not suppose that they can be of no service as geo-
logists ; or if they belong to our body, that they are thus released
from their obligation to be active in our cause : and there are two
descriptions of persons, — the resident clergy, and members of the
medical profession in the country, — to whom what I am about to
say may be more particularly deserving of attention. Such persons,
if they have not yet acquired a taste for natural science, can hardly
conceive the interest which the face of the country in their vicinity
would gain, however unpromising it may appear, by their having such
inquiries before them ; how much the monotony of life in a remote
or thinly inhabited district would thus be relieved y nor how much
benefit they might confer on the natural history of their coun-
try. Even of those who have made some progress in geological
studies, many, I apprehend, are prevented from investigating atten-
tively the tracts where they reside, or from communicating their know-
ledge, by a belief that the Geology of England itself is sufficiently
known already ; and that the district, with the phenomena of which
they are themselves familiar, would have no interest or novelty for
the world at large : — whereas it may be asserted (and it were easy to
produce examples from modern researches in some of the counties
near London), that there is no district that will not furnish sufficient
interest and novelty to an attentive inquirer, not merely to repay his
own exertions, but to instruct the most learned, and enlarge the
bounds of our science.

To landed proprietors also, it can hardly be known, without some

2 Q 2 tinge

300 Geological Society.

tinge of geological information, how nearly our subject is connected
with Agriculture, — with an acquaintance with the nature and correc-
tives of the soil, the supply of water, and facility of effectual drainage,
and numberless facts essential to the perfection of rural ceconomy; the
discovery and supply of stone, for building and the construction of
roads, the choice of the line of roads and of canals, and the facility
of their execution. All these are but a few of the topics that
come strictly within the province of the geologist : and which are so
essential to the prosperous management of landed property, that a
geological map may perhaps with truth be considered as not less
necessary to the country gentleman, than the topographical plan of
his estates.

I am fully aware, that much of what I have just said is obvious j —
and even familiar, to the greater part of those who hear me : — But my
object is to be useful ; and I believe that some of those whom these
remarks are likely to reach, are not sufficiently acquainted with the
practical advantages derivable from our pursuits ; — and that others are
unconscious of the means within their own power for advancing them.
I shall conclude, Gentlemen, by congratulating you on the good
feeling by which the proceedings of this Society have always been cha-
racterized ; and on the self-command that renders both agreeable and
instructive the conversations, (I will not call them discussions— much
less debates,) with which it is now our practice to follow up the reading
of memoirs at our table ; and which have given to our evening
meetings a character more like that of social intercourse in a private
circle, than of the formal proceedings of a public body. This practice,
I know, has been a subject of doubt, to many who wish well to our
institution, and do not undervalue the personal character and dispo-
sition of our members. But, so long as our conversations are car-
ried on with the urbanity by which they have hitherto been dis-
tinguished,— while it is the wish of those who share in them to
give or to receive information, and not to shine, — and the object is
not victory but truth,— there seems to be no reason to apprehend any
very serious injury from the continuance of our geological warfare.

There is still another train of thought connected with our meet-
ings, on which I confess I have sometimes delighted to dwell. The
spirit in which they have been conducted has been so kind, — so little
tainted with, or rather so perfectly free from, any admixture of the
leaven with which from interest or ambition most of the pur-
suits of life are embittered j — and our duties here have been asso-
ciated with so many offices of cordiality and friendship j — that when,
in after life, the cares and chances of the world may have dispersed
those whom I have now the happiness to see around me, I am fond to
believe that the remembrance of these evenings will be called to mind
with pleasure i — And I feel confident, that, as many of us already de-
rive the chief part of our enjoyments from the friendships to which
congenial pursuits have led, the Geological Society will continue to
be no less effective, in the production of warm personal attachment,
and of manly and ingenuous intercourse among its members, than
it has been, in maintaining an active and energetic spirit of research.

March 7. —

Geological Society. 301

March 7. — A Paper was read ". On the Geological Relations and
Internal Structure of the Magnesian Limestone, and the lower por-
tions of the New Red Sandstone series, in their range through Not-
tinghamshire, Derbyshire, Vorkshire, and Durham." — By the Rev. A.
Sedgwick, M.A. F.R.S. V.P.G.S. &c.

A sketch of the subjects contained in this paper was laid before
the Society in 1826 (Nov. 17) : — They were resumed in a more sy-
stematic and detailed form during two meetings in 1827} and are
now terminated by the observations read at the present meeting.

The contents of the Memoir are presented in the following order :

Part I. — J 1 . Introduction. — The new red sandstone is considered
as one great complex formation, interposed between the coal measures
and the lias ; — with two calcareous formations subordinate to it,
one in the lower part of the series (the magnesian limestone), and
another in the upper part (the muschel-kalkstein) . The lower of the
two calcareous formations is considered in detail -, the upper has not
yet been discovered among the British secondary deposits.

§ 2. External characters of the country through which the Magne-
sian Limestone ranges. — The form of the western escarpment is de-
scribed, and is supposed to exhibit proofs of great denudations j and
the general character of the soils resting upon the formation is no-
ticed.

§ 3. General distribution of the formation. — The range of the es-
carpment is given in great detail ; some errors of the geological
maps are corrected; and in describing the eastern boundary, the
enormous masses of diluvium in the county of Durham are briefly
noticed.

§ 4. Outliers. — Sixteen outliers from the western escarpment are
described ; the most southern of which is at Conisborough. In addi-
tion to these, there are eight detached patches of magnesian lime-
stone on the line of bearing, which are not considered as outliers.
The most remarkable of these are seen in the range through Yorkshire.

§ 5. Relations of the Magnesian Limestone to a succession of Coal
Measures. — In a general point of view these formations must be
unconformable, because the overlying beds are extended far beyond
the limits of the productive parts of the carboniferous order : and
the fact is also proved by actual sections in several parts of York-
shire and Durham. At the same time there are continuous tracts of
country where the want of conformity does not appear, and where
the overlying beds seem almost to graduate into the coal measures.
Several details are given respecting ancient coal works, in which, in
more than one hundred places, the coal had been extracted by shafts
sunk through the magnesian limestone: and it is asserted that the
quality of the coal is never injured by the presence of the overlying
formations. Such injury is not only contrary to fact, but seems to
be a physical impossibility.

§ 6. On the Faults affecting the Magnesian Limestone and Coal
strata, Trap dykes, #c. — Examples are given of some great faults
which traverse both the carboniferous and the superior formations :
but it is remarked that many of the dislocations of the lower order of

rocks

302 Geological Society.

rocks do not affect the upper. Respecting the age of the trap dykes
of the coal-fields, it is not possible to determine their epoch in com-
parison of the magnesian limestone, where they range up to the es-
carpment j and of such dykes there are only two examples ; one of
which does, and the other does not, pass through the beds of the
overlying series.

Part II. — Internal Structure and great Subdivisions of the Magne-
sian Limestone. — Considered as a subordinate part of the new red
sandstone series, this formation admits of five natural subdivisions,
each of which is described in a separate section.

§ 1. Lower Red-sandstone, or Rothe-todte-liegende. — In Yorkshire
this appears generally in the form of a coarse siliceous sandstone, of
a reddish tinge. It is associated with incoherent sand, red micaceous
shale, and sometimes with variegated marls. In Durham it is
generally represented by a yellowish and nearly incoherent sand. In
some places it cannot be distinguished from the gritstone beds of the
coal measures : but as it commences in the edge of Derbyshire, and
is almost co-extensive with the magnesian limestone as far as the
mouth of the Tyne,. it must on the whole be unconformable to the
inferior order. It is, however, of very unequal thickness, and its
upper beds are not always parallel to the strata of limestone which
rest upon it. In Durham, being of loose texture and pervious to
water, it throws the greatest difficulties in the way of mining opera-
tions carried on within the limits of the limestone.

§ 2. (a). Variegated Marls, with irregular Beds of Compact and of
Shell Limestone. — This deposit is not either of great extent or thick-
ness, and is confined to a small part of the escarpment in Notting-
hamshire and Derbyshire. It is supposed to be contemporaneous
with the following subdivision :

§ 2. (b). Marl-slate, and Compact Limestone. — This is much m e
extensively developed than the preceding formation ; and though by
no means coextensive with the yellow limestone, derives importance
from its constancy of position and from its fossils. Several locali-
ties in the county of Durham are described ; and among the beds
of marl-slate of East Thickley, &c, two or three species of fern have
been discovered ; and seven or eight species of fish, four of which
at least seem to be identical with fish of the Copper-slate.

§ 3. Great central deposit of Yellow Limestone.— It is subdivided
into the following modifications, each of which is described in detail.
( 1 ) Dolomite, a simple crystalline rock. — (a) Arenaceous dolomite,
coarse, nearly incoherent, often in minute rhombs. — (b) Small-
grained dolomite. Many quarries of this variety are described as
existing on the back of the deposit, and extending from the neigh-
bourhood of Mansfield to Bramham Moor. The crystalline beds pass
into others of mechanical structure, and in some extreme cases con-
tain 20 or 30 per cent of siliceous sand. — (2) Compact magnesian
limestone. — (3) Laminated. — (4) Earthy. — (5) Masses of irregular
concretionary structure. — (C) Beds or concretionary masses of cry-
stalline limestone without magnesia. Examples of these are derived
from quarries near Ripon, Knaresborough, and Newton Kyme, &c.

i!
Geological Society. 30$

— (7) Brecciated structure. This modification abounds on the coast
of Durham. — (8) Small concretionary structure. — (a) Irregular. —
(b) Regular or oolitic. — (9) Large globular concretionary structure.
— Of this, four principal modifications are described with minute de-
tail. All these several subdivisions of structure are supposed to have
been produced by great internal movements, after the mechanical
deposition of the formation.

§ 4. Lower Red Marl and Gypsum. — This extends from the
edge of Nottinghamshire to the banks of the Wharf; thins off at the
two extremities ; attains its greatest thickness (perhaps nearly 100
feet) on the right bunk of the Ain ; — but has not been discovered in
Durham or the northern parts of Yorkshire.

§ 5. Upper thin-bedded Gray Limestone. — Near Ferry Bridge this
contains very little magnesia. In other places it contains subordi-
nate dolomitic beds. It commences at Carlton near Worksop, and
ranges without interruption to the left bank of the Wharf. Further
north it reappears in several places, under a modified form : and the
highest beds on the coast of Durham may perhaps be referred to it ;
but the classifications are made obscure by the absence of the lower
red marl.

§ 6. Great Subdivisions of the new red Sandstone which are supe-
rior to the dolomitic series. — In Nottinghamshue these consist of two
principal deposits.* — (a) Upper red sandstone. — (b) Upper red marl
and gypsum. — The same subdivisions may be traced near the mouth
of the Tees. In the central parts of Yorkshire they are obscured by
diluvium.

By way of conclusion, — the deposits described in § 1 and § 2, are
supposed to be the equivalents of the rothe-todte-liegende, the kupfer
schiefer, and zechstein. — The ore described in § 3, 4, and 5, are in
like manner supposed to be the equivalents of the rauchwacke, asche,
foliated stink stein, breccias, and gypsum, which compose the upper
part of the Thuringerwald system. The coincidence, in order, mi-
neralogical character, and organic remains, seems to be nearly per-
fect. In like manner the two divisions described in § 6. are taken
as the respective , equivalents of the bunter sandstein and keuper j
and, the enormously thick deposits between the coal measures and
the lias, with the exception of the muschel-kalkstein, are thus found
to admit of the same natural subdivisions in England and in central
Germany. Finally, the author speculates about the origin of the do-
lomitic deposits, and adopts in part the theory which derives them
from the mechanical destruction of the rocks of the carboniferous
order. He states however two facts ( 1st, the greater abundance of
magnesia than could have been supplied by the dolomites of the
carboniferous limestone ; 2ndly, the fact that some beds contain a
greater proportion of magnesia than is found in true dolomites),
which seem to imply that the waters of the ocean had a power of
separating carbonate of magnesia from the preexisting rocks, in a
manner which is not explained by the mere mechanical hypothesis.
Whatever may have been the origin of the whole system j its extent,
regular subdivisions, and characteristic organic remains, seem to

prove,

304 Royal Institution of Great Britain.

prove, that it originated in the long continued and consistent ope-
ration of powerful causes, acting simultaneously in distant parts of
the earth.

PROCEEDINGS AT THE FRIDAY EVENING MEETINGS OF THE
ROYAL INSTITUTION OF GREAT BRITAIN.

Feb. 22. — The progress of printing by machines, from the im-
provement of the press by Lord Stanhope, to the present time, was
briefly traced by Mr. Cowper, who at the same time illustrated the
various inventions by drawings, models, arid many of the working
parts of the present machines : after which a more particular account
was given of the machines invented by Mr. Kcenig and perfected by
himself and Mr.Applegath*, and of the one recently erected at The
Times newspaper office. The extraordinary speed of this machine
is such, that 4000 impressions on one side can betaken in one hour.
The disposition of the form, inking apparatus, paper rollers, and
conveying tapes, were explained upon models and sections.

The library contained a variety of interesting objects, and espe-
cially several productions of the fine arts.

Feb. 29.—Mr. S. Solly, jun. gave an illustrated account of the
analogies and differences between the skeletons of man and birds.
The accordance between the skeletons was first pointed out, and
that of man referred to as a standard ; and then the departures and
differences in different animals, with the effects thereby produced,
were explained.

March 7. — Supplementary remarks on the subject of February
JSth, — i. e. the reciprocation of sound, — were given by Mr. Faraday.
New cases of reciprocation were adduced, and illustrated ; especially
of one column of air by another, and of beats and chords by co-
lumns of air. The formation of the grave harmonic was referred
to, and cases of its reciprocation mentioned : and the theory before
laid down relative to the Jews-harp, experimentally proved by an
apparatus consisting of a column of air in a tube which could be
lengthened or shortened at pleasure, and before which a Jews-
harp was firmly fixed and made to vibrate. This apparatus gave
all the sounds which could be produced by the mouth, at the same
time that the columns reciprocating to the tongue of the instrument
could be measured.

Presents : Works of art, specimens of paper prepared in France
from straw, and other objects, were laid upon the library table.

March 14. — Mr. Turrell, the engraver, gave an account of the
latest improvements in etching upon steel. He illustrated the pro-
cesses of laying a ground etching, rebiting, &c. ; of ascertaining
whether the plates were in a proper state ; of preparing peculiar
menstruums for biting in steel, and many others which constitute
the latest improvements of the arts. He showed the application
of etching upon steel to the manufacture of graving tools, which

* We believe that all printing-machines which have hitherto been pro-
duced since Mr. Koenig's original invention, have been varied applications
and combinations of his principles. — Edit.

could

Royal Academy of Sciences of Paris. 305

could be manufactured only in an inferior manner by any other
process ; and concluded by explaining the principles and use of a
new instrument invented by him, and called a Perspectograph.

Amongst the objects in the library was a very large specimen of
native silver from Mexico.

ROYAL ACADEMY OF SCIENCES OF PARIS.

Oct. 1. 1827. — M. Julia Fontenelle exhibited a well preserved
head of an inhabitant of New Holland. — M. Latreille gave a very
favourable account of the monograph, presented by M. Bois-Duval,
of the tribe of Zygenides, of the order Lepidoptera. — M. Geoffroy-
Saint-Hilaire, made a very favourable report respecting a notice of
a monstrous child, by M. Rambur, physician at Ingrandes. — M. Po-
isson read a memoir on sonorous bodies; and M. Cauchy stated that
he had made similar researches. — MM. Milne Edwards and Audoin
presented anatomical researches on the nervous system of the Crus-
tacea. M. Cagniard de Latour communicated the results of several
new experiments which he had made respecting the vibration of so-
norous bodies.

Oct. 8. — M. Tournal communicated some details respecting the fos-
sil bones of the caverns of the department of the Aude. — Dr. Thomas
Young thanked the Academy for having recently elected him a Fo-
reign Associate. — M. Rousseau, of Coucy-le-Chateau, sent a memoir
on the improvement of forceps. — M. Parseval sent a supplement to
his last Memoir on Analysis. — M. de Senne communicated a work
on the operation of tracheotomy. — M. Magendie gave a favourable
account of M. Breschet's memoir on false consecutive aneurism of
the heart, and true aneurism of the arteries. — M. Mirbel made a fa-
vourable verbal report on the botanical part of M. Freycinet's Voyage
edited by M. Gaudichaud. — M. Frederic Cuvier read an extract of a
work on the development of the bristles of the hedgehog. — M. Cag-
niard continued his communication respecting his researches on so-
norous vibrations.

Oct. 15.— M. Julia Fontenelle sent a sealed packet. — M. Delafuge
presented a manuscript entitled : Nouvelle Jerusalem apocalyptique.
— M. Joseph Anastasi sent a memoir On practical mechanics. — The
Academy afterwards heard ; A memoir by M. Binet on the solution
of indeterminate equations of the first degree. — Researches by M. Des-
pretz On the heat disengaged during combustion. — A memoir by M.
Gasparin, On European climates. — Researches by M.Desvoidy on the
vertebral organization of the Crustacea, the arachnida, and insects. —
And a work by M. Delpech on the resection of the inferior maxillary
bone.

Oct. 22. — M. Champie sent a manuscript containing some new pro-
positions in geometry. — M. Serullas announced that he had formed a
bromide of arsenic. — M. Cordier gave a very favourable verbal ac-
count of the Geological Essay on the Environs of Issoire, published
by MM. Devese and Bouillet. — M. Lacroix, in the name of the
commission, read an analysis of M. Binet's memoir On the determi-
nation of the orbit of comets, which was not approved of. — M. Savart

New Series. Vol. 3. No. 16. April 1828. 2 R read

306 Royal Academy of Sciences of Paris.

read an extract of a memoir On the elasticity from bodies. — M.Despretz
communicated some new experiments on the heat disengaged by-
combustion. — M. Cagniard de Latour presented the continuation of
his experiments on what he terms les chocs solides des cordes. — The
Academy decided that M. Fresnel's place should be filled up.

Oct. 29. — M. Coste, captain in the artillery, announced the for-
warding of a work containing several mechanical experiments. —
M. Fossard sent a manuscript entitled : Utility de Vhorlogerie. — The
Academy heard a favourable account given by M. Mirbel, of M.
Despreaux's work, entitled Essai sar les Lamenaires des cotes de la
Normandie ; and a report by M. Cordier on the researches made
by M. Marcel de Serres on the extinct volcanoes of the South of
France. — The Academy decided that the place vacant by the death
of M. Laplace should not be filled up. — M. Payen read a notice re-
lating to a new crystallized borate of soda, and its employment in
the arts. — The Section of Physics afterwards presented, in a secret
committee, the following candidates for the vacant place : MM. Sa-
vart 5 Becquerel ; Cagniard de Latour, Pouillet, Despretz.

Nov. 5. — M. Berniersent a memoir on the means of descending
to the bottom of water. — The Academy proceeded to a scrutiny of
the ballot for the election of a member: of 49 votes, M. Savart had
29, M. Cagniard de Latour 9, M. Pouillet 6, M. Despretz 5.— M.
Cordier gave an account of the memoir on thermal waters, presented
by M. Gendrin. It results from this memoir, as might be expected,
and has been already proved, that thermal waters and common water
cool in the same manner. The contrary opinion, however widely
spread, is therefore a prejudice. — M. Cauchy communicated some
new fundamental propositions on the calculus of remainders. — M.
Adolphus Brongniart read a memoir containing new observations
on the spermatic granules of vegetables. — M. Girard stated that the
memoir lately presented by M. Anastasi was unworthy of any ex-
amination.— M. Raspail communicated observations on the motion
of the tentacula of the vorticella.

Nov. 12. — M. Marcel de Serres sent from Montpellier a sketch of
a geognostic map of the department de PHerault. — M. deFreycinet
read a letter from M. Gaymard, dated New Zealand, containing
several details respecting the voyage of the Astrolabe. — M. Girard
read a memoir respecting some standards of the ancient Egyptian
cubit, lately discovered. — M. Boyer read a favourable account of the
memoirs presented by M. Faure respecting the iris and artificial pu-
pils.— M. Barry, physician of Limoges, sent a memoir concerning
two cases of luxation of the cervical vertebrae with compression of the
spinal marrow, which he stated he had reduced : The commissioners
named by the Academy did not approve of it. — M. Coquebert gave a
verbal account of the new Anwltsde Sciences naturelles, published at
the Havana by M. Ramon de la Sagra. — M. Delpech read a notice
respecting his labours relating to Rhinoplastie.

Nov. 19.- -The President of the Council of Ministers informed the
Academy, that a marble bust of M. Laplace would be executed for the
Library of the Institute. — M. Jomard presented engravings of four

measures

Obituary :— Sir J. E. Smith. 307

measures of the Egyptian cubit. — M. Dupetit-Thouars gave a verbal
report respecting the work, entitled Disposition mkhodique des
mousses; by M. Walker Arnott. — M. Bouillaud read Experimental
researches on the functions of the posterior portion of the brain. —
M. Willerme read the remainder of his Memoir on the distribution
of conceptions and births, in relation to the seasons. — M. Serullas
read Experiments on the iodide of antimony, and laid upon the
table some observations relating to the bromide of bismuth.

Nov. 26. — The Minister of the Interior sent a Notice of M.
D'Hombres-Firmas respecting the fossil bones found in the environs
of Alais. — M. Saint- Hilaire deposited the manuscript of a new
work which he proposed to publish under the title of Flore et Pom-
mone francaises. — M. Damoiseau, in the name of a Commission, gave
an unfavourable account of the chronological tables by the Abbe La-
chevre.- — M. Le Gendre verbally announced the recent ingenious la-
bours of M. Jacobi of Konigsberg. This geometer has greatly per-
fected the important theory of elliptical functions. — M. Dupin, in the
name of a Commission, read the first part of a report respecting M.
Brisson's Essay on the general system of French navigation. — M.
Cagniard de Latour read some New experimental and theoretical
researches on the properties of sound.

December 3. — MM. Gauthier de Claubry et Person requested that
a sealed note which they had deposited, should be given to the Com-
missioners, who were to give an account of the Memoir on madder by
MM. Robiquet and Collin— M. Malbouche announced that he had
successfully practised the method for the cure of stammering, invented
by Mrs. Leigh of New York. — At his request two Commissioners
named by the Academy were to attend the experiments. — At the re-
quest of the Academy of Inscriptions, two members of the Academy
of Sciences were added to the Commission named by them, for exa-^
mining the Egyptian cubits lately discovered. — M. Dumeril, in the
name of a commission, reported respecting M. Chabrier's Memoir on
the progressive motion of man and animals. — M. Gay-Lussac made a
verbal report upon a pamphlet by M. Burridge, On the improvement
of civil architecture. — M. Biot read a memoir On the figure of the
earth.

OBITUARY : — SIR J. E. SMITH.

. On Monday, the 1 7th of March, died at his house in Surrey Street,
Norwich, his native city, aged 68, Sir James Edward Smith, M.D.
F.R.S. Member of the Academies of Stockholm, Upsal, Turin, Lisbon,
Philadelphia, New York, &c. &c. the Imperial Acad. Naturae Curio-
sorum, and the Royal Academy of Sciences at Paris, Hon. Mem. of
the Horticultural Society ; and President of the Linnasan Society,
which office he had held from the first establishment of the Society
in 1788.

Of this eminent Naturalist and most excellent and amiable man,
as time does not permit us in our present Number to give such a no-
tice as is due to his station and his merits, we must fulfill that duty at
a future time. We shall now only add, that he had laboured nearly

2R2 up

S08 Obituary :•— Sir J. E. Smith.

up to the day of his decease (though often impeded by sickness), with
unabated zeal and success in the advancement of his favourite science ;
the fourth volume of his "English Flora" having been published but
a few days before his death. The former volumes of this masterly
work have been noticed by us on their publication *. At the close
of the volume which has just appeared, are the following remarks,
which will now be read with melancholy interest by the friends
and admirers of the much lamented author.

u Several circumstances have caused a long delay in the publica-
tion of the present volume, which, if their recurrence should not be
prevented, may render the completion of the work, according to its
original plan, very precarious* In the mean while, the number of
volumes originally proposed is now finished, and the first twenty-
three Classes are completed, as well as the first Order of the twenty-
fourth, Cryptogamia Filices, the only one that required more study
and emendation than it has hitherto received.

" Of the remaining Orders, the Musci have been detailed in the
Latin Flora Brltannica and Compendium of the author, as well as in
his English Botany ; and by other well-known writers, in two editions
of the Muscologia Britannica, and the Muscologice Hibernicce Spicile-
gium. The monograph of Dr. Hooker on British Jungermannice,
which, with their allies, constitute the next Order to the Musci, diffuses
a new light over the whole of that Order. The works of Mr. Dawson
Turner on Fuci, and of Mr. Dillwyn on Conferva?, have gone far to
exhaust the species of those tribes ; an application of scientific prin-
ciples to the settlement of their genera being all that is wanting. The
Lichen family, under the controul of the great Acharius, assumes the
dignity of an entire and well-arranged Order. The Fungi, better
discriminated by Withering than by most popular writers, and well
explained by the figures of the excellent and lamented Sowerby, are,
in their minutest details, exquisitely illustrated by the Cryptogamic
Flora of the ingenious Dr. Greville, and the accurate publications of
Mr. Purton. These, marshalled by the aid of the learned Persoon
and others, might possibly have proved less obscure than heretofore.
This tribe indeed leads the botanist to the end of his clue, and leaves
him in palpable darkness, where even Dillenius was bewildered.

f* All these subjects, if not yet brought into perfect daylight, might
well, by the help of those brilliant northern lights, Acharius, Fries, and
Agardh, have been made more accessible to the student, and more
instructive to systematic botanists, by one long accustomed to their
contemplation in the wild scenes of Nature, and not unfurnished with
remarks of his own. If our bodily powers could keep pace with our
mental acquirements, the student of half a century would not shrink
from the delightful task of being still a teacher ; nor does he resign
the hope of affording some future assistance to his fellow-labourers,
though for the present, "a change of study," to use the expression of
a great French writer, may be requisite j\ by way of relaxation and
epose."

* See Phil. Mag. vol. Ixvii. p. 60.

L. Jfh

[ 309 ]
L. Intelligence and Miscellaneous Articles.

ANALYSIS OF ALCOHOL, .ETHER, ETC.

MESSRS. Dumas and Boullay have recently analysed alcohol,
and several sethereal preparations. The alcohol used was re-
peatedly rectified from chloride of calcium ■ its sp. gr. was 0*7925
at 64° Fahr.; it boiled at 169° at a medium pressure.

The analysis of alcohol agrees, the authors remark, with that de-
duced by M. Gay-Lussac, from the density of its vapour. The
following are the results of the experiments compared with those of
calculation.

Experiment. Calculation.

Carbon 52-37 52-28

Hydrogen 13-31 13-02

Oxygen 34-61 34-70

] 00-29 100-00

Sulphuric aether was obtained perfectly free from alcohol by recti-
fication from chloride of calcium, until the operation produced no
alteration in its properties. Its sp. gr. was 0-713 at 68° Fahr. ; it
boiled at 93° Fahr. at a medium pressure. The experimental re-
sults compared with those of calculation were as follow:

Experiment. Calculation.

Carbon 65*05 64-96

Hydrogen 13*85 13*47

Oxygen 21-24 21-57

100*14 100-00

There is a slight excess of hydrogen, but the authors consider sul-
phuric aether as consisting of a volume of olefiant gas and half a
volume of the vapour of water.

The oil of wine examined was separated from pure aether by distil"
lation : as it is not volatilized at a very low temperature, it remains
almost entirely in the retort ; a part is then distilled and afterwards
rectified from chloride of calcium and a little potash. Its sp. gr.
is 0-9174. It was found to consist of

By Experiment. By Calculation.

Carbon 88-36 ' 88*80 88*94

Hydrogen . : 1 1 -64 1 1 -20 11 -06

100*00 100*00 100*00

Oil of wine is therefore a carburet of hydrogen, differing in the pro-
portion of its constituents from all the previously known carburets.
The calculated result is obtained by supposing it to be formed of
four volumes of the vapour of carbon with three volumes of hydro-
gen gas. The authors observe that this composition necessarily re-
sults from the kind of reaction which gives rise to the formation of
oil of wine, as elucidated by other experiments.

Sulphovinic

$10 Intelligence and Miscellaneous Articles.

Sulphovinic acid was analysed in combination with barytes.
The results are thus stated :

Sulphate of barytes 53-30 54-00

Sulphurous acid 14-65 14-85

Carbon 11-32 10-33

Hydrogen 1-46 1-39

Water 19-31 20-

100-04 1C0-57

The composition of the oily matter, brought to 100, would give

Carbon 88-37

Hydrogen 11-63

100-00
It is therefore oil of wine. This being admitted, the sulphovinate
of barytes is represented by an atom of hyposulphate, two atoms
of oil of wine, and five of water ; or

By Experiment. By Calculation.

Hyposulphate of barytes 68-40 67-37

Oilofwine 12-25 12-27

Water 19-65 20-36

100-30 100-00

The authors then show that similar results are obtained by analy-
sing the sulphovinates of copper and lead.

The authors consider the theory of authentication as rendered ex-
tremely simple by these analyses: the acid and the alcohol are di-
vided into two parts, one of which produces oil of wine and hypo-
sulphuric acid, and occasions the formation of a certain quantity of
water; and the other portion of acid and alcohol furnishes by their
action weakened acid and aether. It will be seen, according to this
process (say the authors), what would be the nature of the action
of peroxide of manganese or chromic acid in the formation of aether.
They would lose a portion of their oxygen to form water and oil of
wine, thus presenting the formation of hyposulphuric acid. M. Gay-
Lussachas in fact stated that this acid is not produced in these kinds
of reaction. The formation of hyposulphuric acid is not then ne-
cessarily connected with that of aether • it is also difficult to believe
that the production of oil of wine is necessary to that of aether, the
reactions producing them seeming so independent. If it be ad-
mitted, as stated by M. Desfosses, that fluoboric acid gives aether
without oil of wine, it seems at least that the necessity is not ge-
neral ; and the authors conclude that the two phaenomena have no-
thing in common. — Annales de Chimie et de Physique,- Nov. 18ii7.

I shall probably offer some observations upon the paper from
which the above is extracted in the next Number of the Annals,
more especially with respect to the notice taken of the experiments
of Mr. Faraday and Mr. Hennell. In the mean time I cannot help
regretting the great use (if that term can be properly applied) which
MM. Dumas and Boullay have made of symbols to represent che-
mical

New Patents. SJ.1

mical compounds. Can they, or can any body, believe that the fol-
lowing is a very intelligible mode of describing bisulphovinate of
lead?

fb + i*S + 8H2 C« + 3HH = Vb +• 2S* + 4H3 C4 + 5HH.

R. P.

LIST OF NEW PATENTS.

To W. Nairn, of Dane-street, Edinburgh, for his improved me-
thod of propelling vessels through, or on the water by the aid of
steam, or other mechanical force. — Dated the 5th of February 1828.
— 6 months allowed to enrol specification.

To C. Hitch, of Ware, Hertfordshire, for his improved wall for
building — 21st of February. — 2 months.

To G. Dickinson, of Buckland Mill, near Dover, for his improve-
ments in making paper by machinery. — 21st of February. — 4mon.

To Angelo Benedetto Ventura, of Cirencester-place, Fitzroy-
square, for his improvements on the harp, lute, and Spanish guitar.
—21st of February. — 6 months.

To T. Otway, of Walsall, for an expedient for stopping horses
when running away. — 21st of February.— 2 months.

To D. Bentley, of Pendleton, Lancashire, for an improved me-
thod and machinery for bleaching and finishing linen or cotton yarn
and goods. — 21st of February.— 6 months.

To W. Brunton, of Leadenhall-street, for improvements on fur-
naces for the calcination, sublimation, or evaporation of ores, metals,
&c. — 21st of February. — 2 months.

To J. Levers, of Nottingham, for improvements in the manufac-
ture of bobbin net-lace. — 3rd of March. — 4 months.

To W. Pownall, of Manchester, for improvements in making
healds for weaving. — 6th of March. — 4 months.

To B. H. Brook, of Huddersfield, for improvements in the con-
struction and setting of ovens or retorts for carbonizing coal for gas-
works.— 6th of March. — 6 months.

To Lieut. W. Roger, of Norfolk-street, Strand, for improvements
on anchors. — 13th of March.— 6 months.

To R. G. Jones, of Brewer-street, Golden-square, for a method,
communicated from abroad, of ornamenting china and other com-
positions, which he denominates Lethophanic, translucid, or opaque
china. — 13th of March.— 2 months.

To G. Scholefield, of Leeds, mechanic, for improvements in or
additions to looms for weaving woollen, linen, «&c— 13th of March.
— 6 months.

To N. Gough, of Salford, Manchester, for an improved method
of propelling carriages or vessels by steam, &c. — 20th of March. —
6 months.

To S. Clegg, of Chapel Walks, Liverpool, for improvements in
steam-engines, and steam-boilers and generators. — 20th of March.
— 6 months.

Results

4

<3

%3

iS

1

»

3
B

Q

I'd 8
%v Bipai\[

Oo»-.ooo(^cpip»p»p9<^>p
•rtib .- ob 6 •— »h -^ i>- ^ —• «h
t^«c i^<or^<ovo<©i©ooaoao

1*

*KV 8
*b Bipajvr

-7«cp^pip-iocp^t<OQp<S9

c-^tvb 6ico 6 ob ob ^^tihidi^

r-»^ovo*o*o to to to <o t^t^oo

I\fd 5
%u Bipaj\[

i>»9 t^ip.-* rj<t>.vp <p c» © c«
o icvo to to to 'o ■** to <o t~ t-^

00

6.

to

•xapui aqjjo

38uBa UB3J\[

oc* co<Nvoc*votx<oo^o^to

10

'U!M

0ooto-*f<Nco<or^aooo^-* to

°Tj«^trt -<^COCOCO cert TfioiO

CO
CO

*XBft[

uO OM^OO o%oo <y»oo o c o o

0
0

•jajB^ Suudg
jo 'duiax uBaj\[

Qv© -^tpi^cicpopcpcit^cipap
^< 6 6*6i6^c«TJ,totb,'b,cb

CI

5

u

s

I

5

B
|

1

"So

8

3

•M*<I 8
;b Bipaj\[

<0 00>T)H CO OM^ to <N t^O

°ob6tbobcbobc»6dwobob
no-^Ttinio©^ to to "S"**

o\

1— I

10

17 8
*b Bipajfl

Qvo oo r^ ^r r-^op 9 rt tp oi op r*.

^cbOoo&oib-^ow'oib

CO

10

%v Bipaj\[

(O-HCOr^OOC^rttNt^tOOrH
o-Ti^TH^ipcNopipc^rpcoop

•0

sinoq tz, ui

UBA *£) '

OOO -- "^d — ^i^nrt- OM>-

10
CM

•aSuBu

UB3J\[

CO^C*COCOCO<N<NO<COCO<N

UO
CO

•Bipaj\[

0<N<Ot^— tOCOOOr>-<©<N<N

919 9 9 nt^o tor^io^oo
cob6i>.^-ivb6»bci 6 10 ob r»

COCO'Tt,iOtoiO<OVO<0 icrff

uo

to

'»!!

°(N -< C0C0rt"<tftO"<f^rc0C« CO

3!

•XBJ\[

- .'tioooc^ino^cococfh
°to to <o r~- •>• t>- ao i^r^'o^o to

O

00

S

i

a

n

•JVLM8
?b Bipaj\[

coxin m^oioaiOo^cociH
goo 9r-9i>. 9 9 9 91^.900

l-H 61 0> 6> 6> 6> 61 6 O 61 0> 61 6>
CI<M<NC«CIOIC0C0<N<N<N<N

1

29900 29-903

jb Bipa^

iOoo-H-rj<crioo?N'*oc^^^
jjoo 9 C^ "^ t~^ 9 T1 *? <?''^9V'QP

»— i 6> 6> 61 6> 61 61 6 O 6> 61 61 61
<N<M<NCN<NOICOCOCI<NC*<N

IT 8
ye Bipaj\[

00t^>-H^<NCri0000<NI>-O'^

(NtNO>OOiOOO»«iOH

pop 9 1^9 ^9-^ 9 9.(^900

HH ^ 0*i O*! O^ OlO^O 0 Oi o> O^ O^i
d<N<NO<<N<NCOCOC/ICJC»<S

o^
00
6»

•sjnoqf-5 ui

UOpBIJB^

?sa^Bajt£)

looo^cor^cio^ovooocovo
cJ r^rto>cotoco-**co*<T«oi>.to

h666666666666

5f
6

•paquDsap
saoBdg

.(SN'J^^X(S«CO>aO

^ 1^ 10 ^ ^ »b ^ ^ -^ to r>.vb do

0

CO

•saSuBq^
•aSuBy

<S^HCO^H'-*<NCI<NCO-H~<N

SOM^tOGOOOt^OOO<Np-<iO

to

2

1

S

cop o^h-OM^osiH 9 9^900

^OiO^^O^OiO O 61 Ot C^i 61

0
0

a

^ON-yi^taN^^ooo 0 r^co r~
• c* Ttr^^t9<or^cpip9C»9

0<rM<N(N(NO«010<0<<NCI(N

0^
ob

1

(OrfOOOmnCHTfOOOO
•CN^COtN^CO-rfTtCOrp-rpip

£666666666606
C3COCOCOCOCOCOCOCOCOOCO

00

to
6

CO

•StpilOI\r

'LZSI

• «• »I T >» 2 >> fcc +; «j bf J

<

Meteorological Summary for 1827. — Hampshire.

3 IS

•03J <S0q3UJ Ul UIB^J

o o »c o »o © to ©

©<N'<*'-*CN(0'-'<©

to tO lO to
CO CO CO d

ooooano

COTf-^ >0

CM

—•©CO-<C'»'-''-'CN

'saqouj ut uopBjodBAg

OOiOW5iCOOW5>fliOOO
r-~O^OCp99t>apqp CO t>-o

©
9

9

fi

a
§

£

•s

1
I

\iapuni(j.

jo : -h «s -. oi • ^ |

©

'•Sujmq^n

\\r* I CO fH -« .-< <M CM ^< ^ |

CO

•sjo3jaj\[

orrrN-^o^i^o^t'O'HCM^

*©

•SAvoqurey

^2 :- 1

t^

•SO[BfJ JBUn'J

h |CfW ; |h (

- i*~ 1

d

•sopH aupg

\ ^* C^ CO "tf ^ CI

_co : : |

: : rsi '. i

©

CO

•BipqjBj

\ \ <© <N tON

: : °^ : I

00

Bqoqmy

•sabq

jo aaqunitf rK»o£

hqohOhOhhOhO-
co c coo^ncoonroco^

>o

CO

•33J *UIB}J

■^C^i0^t<OiOCO^fOtOrt<^

iO

•iCSSoj

: : ; . . .: <n ~ <m 1

00

•A^g 1SBDI8AO uy

•ItOI -Hi?)

3

1— 1

•spno|3 qjiM 'jibj

a
.5

c

•Xjjs JB3p v

tj* ■*? co -rt* co -tf <© ioocih co

iO

«5

3
. ^O

U

o

1/3

S3

.2

1
eg

"1

•snquii^j

<3^oo<N"tfaoto©coaooo<Nco

1

o
W

•sn^Bj^so[nuin3

^h cN*-CIC«CIC<C«-i~p-«

©

1 c?

4sn|nuiti3

o

-

iO-^CTM>-C«tOQ0iOTS<fMiO-^
_^f_„h<>I<n1<njCIC<CI*hph

•sniB-ng

: : : ^ : : ,"H J'*3i**< ■* j

o

•StHBJ?SOJJ|3

COCMCOCIClCICIOCJCOCICi

(M
CO
CO

•sn^nuinoojji^

CMOoaW'-^ciowoa)

i— i

•saui3

oooo-«ooi>c-H(X)(Ninirt

— • d— >CM^C»CI-<<M-<~

00

©

CN

■

s
<|

•5
1

1

•sXbq
jo asquint jbioj.

CO CI COCOCOCOCOOCOCOCOCO

to
*©

CO

r>saAV-qyo^

HkS -fc* -W M|<S

<OfNC^^tCO<©CM'!f'*rN00^

to

-1S3A\

H« M|H win

-!(*

0 <N <N CJ CI 00

•^sa^-q^nog

-oii-iIh h|c» HO h|c»

eoco©-<©co-HT},oi©,-«©

o

oo

•qjnos

M|C*

^^hco^co co co ■<* -tf •<* -tf

5

CO

•}SBg;-q}nog

*}SBg;

rp :coco CJ — hio^h

Ho
CN

•^SB^-qwoj^

^OCOCNVOCOiOcNt^OO^CO

s

"WOK

inc<^rCHp.^a)ci(sio-

00
CO

2

tfiuary . .
ebruary
'arch . . .

pril

ay . .
ine . . . .

ugust . .
ptember
ctober . .
ovember
ecember

5c7

. - —

►^^s^^aofcQ

AJn» ^rzW. Vol. 3. No. 16. April 1828. 2 S

914 Meteorological Summary for 1 827. — Hampshire .

ANNUAL RESULTS FOR 1827.

Barometer. Inches.

Greatest pressure of the atmosphere, Dec. 28th. Wind N.E. 30-580
Least ditto i. ditto March 4th. Wind S.W. 28*790

Range of the quicksilver 1*790

Annual mean pressure of the atmosphere 29-900

Mean pressure for 190 days with the moon in North decl. 29-872

for 164 days with the moon in South decl. 29-927

Annual mean pressure at 8 o'clock A.M 29-899

at 2 o'clock P.M 29-900

. at 8 o'clock P.M 29-903

Greatest range of the quicksilver in March and December 1-510

Least range of ditto in June 0-690

Greatest annual variation in 24 hours in March 0-940

Least of the greatest variations in 24 hours in June 0*320

Aggregate of the spaces described by the rising and falling

of the quicksilver 73*000

Number of changes 266*

Self-registering Day and Night Thermometer. Degrees

Greatest thermometrical heat, July 7th and 8th, Wind N. 80

cold, February 16th, Wind E 14

Range of the thermometer between the extremes 66

Annual mean temperature of the external air 52*57

. of do. at 8 A.M 51*43

of do. at 8 P.M 51*19

. of do. at 2 P.M 57*54

Greatest range in February 42*00

Least of the monthly ranges in September 24*00

Annual mean range 31*25

Greatest monthly variation in 24 hours in July 25*00

Least of the greatest variations in 24 hours in December . . 17*00

Annual mean temperature of spring water at 8 o'clock A.M. 52*46

De Luc's Whalebone Hygrometer.

Greatest humidity of the atmosphere, several times in Degrees.

November and December 100

Greatest dryness of ditto, May 1 3th 33

Range of the index between the extremes 67

Annual mean state of the hygrometer at. 8 o'clock A.M.. . 67*5

at 8 o'clock P.M. . \ 71*2

. at 2 o'clock P.M. . . 59*8

■ r- at 8, 2, and 8 o'clock 66*2

Greatest mean monthly humidity of the atmosphere in Dec. 82*2
— — — dryness of ditto in August 56*2

Position

Meteorological Summary for 1827. — Hampshire. 315

Position of the Winds. Days.

From North to North-east*. 38

North-east to East 6U

East to South-east 24?|

South-east to South 26

South to South-west 34|

South-west to West 80§

West to North-west 46

North-west to North 54

365

Clouds , agreeably to the Nomenclature, or the Number of Days on
•which each Modification has appeared.

Cirrus 208

Cirrocumulus. . 122

Cirrostratus . . . 332

Stratus 10

Days. Days.

Cumulus 240

Cumulostratus . . . 230
Nimbus 190

General State of the Weather. Days.

A transparent atmosphere without clouds 45

Fair, with various modifications of clouds ..... 149£

An overcast sky without rain 103

Foggy 8

Rain, hail, sleet and snow 59A

■365

Atmospheric Phcenomena. No.
Parhelia, or mock- suns on the sides of the true sun 18

Paraselenae, or mock-moons * 3

Solar halos 30

Lunar halos 12

Rainbows t 17

Meteors of various sizes 66

Lightning, days on which it happened 13

Thunder, ditto ditto . . 10

Evaporation. Inches.

Greatest monthly quantity in August 3-85

Least monthly quantity in December 0*60

Total amount for the year 25*00

Rain.

Greatest monthly depth in December 5*625

Least monthly depth in February 0*820

Total amount near the ground for the year 29*965

Total amount near 23 feet high for ditto 27*635

The instruments are the same, and were placed in the same si-
tuations as described in the February Number of this work, in the
Results of the Meteorological Journal for Hampshire, for 1826.

Barometrical Pressure. — The mean pressure of the atmo-

2 S 2 sphere

316 Meteorological Summary for 1827. — Hampshire.

sphere on the mercurial column this year, is T§-^ of an inch lower
than that of last year, and -^^ of an inch higher than the mean of
the last twelve years. The yearly maximum pressure is not high,
nor the minimum comparatively low.

The aggregate of the spaces described by the alternate rising
and falling of the quicksilver, is 14*59 inches greater than in 1826.

The number of changes in the Barometer this year, viz. 266, co-
incides with that of 1826 and 1816, and is only four short of the
annual average for the last twelve years. Although the aggregate
of the spaces differs very much in different years, yet the yearly
number of changes is pretty uniform ; and the average time of each
change during the last twelve years, is 32J hours nearly. The
annual uniformity of these changes, as influenced by the varying
weight of the atmosphere on the column of quicksilver, might have
first suggested to meteorologists the idea of the existence of atmo-
spherical tides, as chiefly effected by the moon's attractive force on
the spheroidal mass of the earth's atmosphere. But these changes
not happening regularly, compared with the regularity of the tides
of the ocean in connection with the moon's motion, as sometimes
they are quick and at other times very slow, at least near the earth's
surface, a train of imperceptible effects, besides the moon's sup-
posed attraction, should therefore be taken into consideration to
account fairly for the atmospherical tides, as the diurnal action of
the sun's calorific rays upon the atmosphere ; the ascending heat
from the earth in the spring and summer months ; the rarefaction
of the atmosphere, particularly under the sun's vertical rays and
about the equator ; the consequent perturbations of the air, and
dispersion of dry and moist winds, according to their position, to
every known place on the earth ; and the influence of the seasons
upon the constitution of the atmosphere in every climate without
the tropics of Cancer and Capricorn.

Temperature. — In the temperature of the atmosphere we ge-
nerally feel more interest than in the pressure, from the effects it
often produces in us when too much exposed to the extremes of
either cold or heat. The heat we sustain beyond the temperature
of the ground, is the effect of the solar rays on the earth and sur-
rounding atmosphere, while the earth moves in that part of its orbit
which coincides with the northern signs of the ecliptic ; for while it
moves through the space occupied by the southern signs, the mean
temperature of the atmosphere in this latitude is almost invariably
below the mean temperature of the ground, and especially during
the time it moves through Capricornus, Aquarius, and Pisces. How-
ever, in respect to the temperature connected with the seasons, it
is sometimes reversed for three or four weeks in the spring or au-
tumn. A deviation of this sort occurred last February, the mean
temperature of that month being 2| degrees below the mean of
January. Two other deviations also occurred in 1826, as explained
in our Meteorological Summary for Hampshire that year.

The mean temperature of the external air this year is about a
degree below that of last ; but it is nearly three quarters of a de-
gree higher than the mean of the preceding twelve years.

The

Meteorological Observations for February 1828. 317

The mean temperature of spring water at 8 A.M. is only -rW of
a degree less than the mean temperature of the external air, which
seems to prove that the additional thermometrical heat near the
ground in the summer, is balanced by the decrease of temperature
in the opposite season, when the sun's diurnal arc with us is much
shorter, and his rays more oblique.

The difference between the annual mean temperature of the air
as taken daily at 8 A.M. and 8 P.M. is only «24?, or a quarter of
a degree.

Wind. — The scale of the prevailing winds this year deviates very
little from that of last. High winds prevailed in January, February,
March, April, October, and December ; but in the other months
the winds were comparatively light. The number of strong gales,
or the days on which they have prevailed this year, is as in the fol-
lowing scale : ■

N.

N.E.

E.

S.E.

s.

s.w.

w.

N.W.

Gales.

10

11

3

3

8

39

8

7

89

Here the number from the S.W. is remarkable, as usual. The
weather in January and February was cold ; and in March, Sep-
tember, October, and December it was wet, but rather dry in the
other eight months.

The amount of evaporation this year is considerably under the
depth of rain, from the atmosphere near the ground having been
more than usually humid in the summer months.

METEOROLOGICAL OBSERVATIONS FOR FEBRUARY 1828.

Gosport. — Numerical Results for the Month.

Barom.Max.30-44Feb.3. Wind N. W.— Min. 28-90 Feb. 21. Wind S.E.
Range of the index 1*54.

Mean barometrical pressure for the month 29*763

Spaces described by the rising and falling of the mercury 6*250

Greatest variation in 24 hours 0-570. — Number of changes 1 7.
Therm. Max. 61° Feb. 26. Wind SW.— Min. 28° Feb. 12. Wind N.
Range 33°. — Mean temp.of exter. air 45°-74. For 30 clays with © in £Z 45*32
Max. var. in 24 hours 17°-00— Mean temp, of spring water at 8 A.M. 51°-56

De Luc's Whalebone Hygrometer.

Greatest humidity of the air in the afternoon of the 25th 100°

Greatest dryness of the air in the afternoons of the 3rd & 15th ... 59

Range of the index 41

Mean at 2 P.M. 71°*6— Mean at 8 A.M. 82°-l— Mean at 8 P.M. 81-8

of three observations each day at 8, 2, and 8 o'clock 78*5

Evaporation for the month 0-75 inch.

Rain near ground 1-515 inch.— Rain 23 feet high 1-395 inch.

Prevailing Wind S.E.

Sum-

318 Meteorological Observations J or February 1828.

Summary of the Weather.

A clear sky, 2; fine, with various modifications of clouds, 9£ j an over-
cast" sky without rain, 12| ; foggy $ ; rain, 4^.— Total 29 days.

Clouds.

Cirrus. Cirrocumulus. Cirrostratus. Stratus. Cumulus. Cumulostr. Nimbus

14 8 29 1 10 17 20

Scale of the prevailing Winds.

N. N.E. E. S.E. S. S.W. W. N.W. Days.
5 21726 4 2 29

General Observations. — This month has been calm and generally mild,
and although it has rained more or less on seventeen different days, yet the
amount at the ground is very little more than one and a half inch in depth ;
therefore it has generally been light.

From the 10th to the 18th instant, the weather was rather cold • and on
the 11th and 12th, sleet and granulous snow fell. In the morning of the
14th it snowed three hours, and the depth was about 2£ inches, which dis-
solved in this neighbourhood in two hours with a temperature from 37 to
41 degrees in the shade. In the evening of that day about 20 minutes
before 7 o'clock, a very large meteor, in the form of a cone on its side,
passed over towards the S.E. It appeared very low, perhaps not above
200 feet from the ground : its light was glaring for five or six seconds of
time, and nearly the colour of the moon's reflected light, and its train
sparkling. It passed through an apparent space of about 60 degrees before
it disappeared behind some houses, and was seen by many persons in the
town and vicinity.

In the evening of the 15th, a short time before Venus set, a mild light
reflected in the atmosphere from that planet eastward, was distinctly traced
to the first star of Ariesy marked y, a distance at that time of 34 degrees.

The maximum temperature of the external air occurred in the nights of
the 3rd, 13th, and 24th. The maximum temperature of the present month
is remarkable, it being four degrees higher than in any February for the
last twelve years. It occurred on the 26th, and appeared to have been in-
fluenced after light rain, by two warm winds crossing at right angles from
the S.E. and S.W., and a dense body of cumulostratus clouds with some at-
tenuated parts, sufficient to admit the calorific rays to the earth's surface,
which acted powerfully on the exterior thermometer. The mean tempe-
rature of the month is very high for the season. Much has been said in
conversation on the mildness of the last winter, viz. December, January,
and February, which in this latitude are understood and very generally
taken as the three winter months ; and it certainly has been the mildest
during the last thirteen years. The mean temperature of these months for
the last thirteen years, is 41*38 degrees ; and for the last three months 46*16
degrees; therefore, the mean of the last winter is 4f degrees higher than
the mean of that period. The next mildest winter occurred in the years
1821-2, the mean temperature of which was 45*56 degrees, that is three-
fifths of a degree lower than the mean of the last winter. The spring has
commenced, and the trees are progressively breaking into buds.

The atmospheric and meteoric phcenomena that have come within our
observations this month, are one lunar and two solar halos, two meteors,
one rainbow, and two gales of wind, one from the South-east, the other
from South-west.

REMARKS.

Meteorological Observations Jo?' February 1828. 319

REMARKS.

London.— Feb. 1. Fine. 2. Very fine. 3. Fine. 4. Slight fog : cloudy.
5. Cloudy. 6. Slight rain : cloudy. 7. Cloudy: rain at night. 8. Fine.
9. Hazy, with showers. lO.Clear and cold. 11. Snowy: cloudy. 12. Cloudy.
13.Fine. 14. Cloudy, with sleet. 15.Fine. 16, 17. Very fine. -.18. Cloudy,
with showers. 19— 21. Fine. 22. Cloudy. 23. Showery. 24, 25.Cloudy.
26. Rain in morning : cloudy. 27. Fine. 28. Slight fog : fine. 29. Slight
fog: cloudy.

Boston. — Feb. 1, 2. Fine. 3. Fine : rain a.m. 4. Cloudy : rain a.m. and
p.m. 5. Cloudy. 6. Cloudy : rain early a.m. 7- Dense fog: rain early a.m.
8. Fine: rain at night. 9. Cloudy: rain at night. 10, ] l. Cloudy. 12. Snow.
13. Cloudy. 14. Stormy: heavy fall of snow. 15 — 17.J^loudy. 18. Fine:
rain p.m. 1 9. Cloudy. 20. Fine : rain p.m.
rain a.m. 24. Cloudy. 25. Cloudy : rain a.m.
29. Cloudy.

Penzance. — Feb. 1. Clear: rain at night.
4. Rain. 5. Misty: rain. 6. Fair : misty.

clear. 9. Clear. 10. Fair : rain; 11. Hail-showers. 12. Fair: rain.
1 3. Clear : rain at night. 14. Fair : hail and rain. 15. Clear. 1 6. Clear :
fair. 17. Fair: rain. 18. Showers. 19. Fair: showers. 20, 21, Fair :
rain. 22. Fair: showers. 23. Clear : hail-showers. 24, 25. Rain. 26. Misty:
fair. 27. Fair. 28. Clear. 29. Clear : fair. —Rain-gauge ground level.

21, 22. Fine. 23. Cloudy :
26, 27. Cloudy. 28. Foggy.

2. Misty : clear.
7. Rain : clear.

3. Clear.
8. Misty:

We give the following to supply the deficiencies in our last Number in the
Meteorological Register for January.

London.

Barometer.

Thermometer.

9 A.M.

10 P.M.

Max.

Min.

Jan. 20

30-13

30-18

53

43

21

30-13

30-11

50

45

22

30-00

30-13

46

40

23

30-18

30-24

52

44

24

30-23

30.23

52

48

25

30-20

30-01

54

42

26

30-15

30-23

51

47

27

30-24

30-31

53

37

28

30-31

30-25

47

42

29

30-08

30-06

50

40

30

29-98

29-90

47

40

31

29-90

29-86

49

43

We are enabled in the present Number to supply the place of Mr. How-
ard's observations, by extracts from the accurate Register kept by Mr.
W. B. Booth, at the Garden of the Horticultural Society at Chiswick,
near London ; with which we trust we shall be favoured monthly.

Meteor o-

'isog
•dsog
•zuaj

TP CN

^ ; cm

O to

o o
6
o ©

0 £0

01 o

6 6

• — — < o • • 00

: o o -i : : ^

o o o o ©

o o

O 00

".OOP . ICO

6 6 6

mooookooomio

— CN CN ONU0 h CN CO 00

o o o o -

.©inmmiooooo^o
^r^r .ooo>><Nvoir5<oiot^.eioi

iori '09p^7tc<99^H

6 6 6666666666

pacKj

I : : : : : o c* : o :

dso9

ess . . 8 ; s a . .s . e >■ a 8 ; a a . e s fe- s s s >•
1 1 s.mjl'g w "1 *1 *H * si 11 Si 1 1 1
' -2 *i 2 3 « * * £ g s" * *

11
II

i ^

.22 I
p i

11

•jsog
dso£)

> £ £ > £ $ w j,j ^ « as* j5* ^

ZU3J

k fe fc st fc £ > > 'i « £ w w * |t B " £ £ » « i £ £ * * £

p«ot *- * *- *- £ g * 1 | * g » i *ia * « s * «• * i * i * i i

% *

I«V Q f5 "P *P "P P P *PP "PPT5 P

•'°<C OIOhO) t^QO t^O\nC<6w6nO<NTj'C?>0'-H C«d\»0'H(0^0

.2 t^t-» O "** 00 IT^OO iTlO <© 00 *© ON© VO iO CN <© l>-00 lO — i CN ^O to ON00 "tfCO
«g ^rf ->tTt rf r* rf -tf CO CO CO CO CN •>* CO CO -^ CO CO CO •»* ^i4 ■<* CO ■** -^ ■<* t* ^«

U0O ^f-rfCOCOO ONNChX©0)X>0»CiO © 00 CO CN Tp^ftOCN r-i

toioto>otoiou^io^^^^^^'^"^f,^,,^,'*toiOTfTpLointo>r5uo>.o

c .3 cnot^>oiooonTfoa)tNOM^coint^-(NC«)oainooiooQO-H

O -5S COCOCO^Tf^rtCOC0COC^0^C^C^C*(NCNC0CO^CO'^COTj<rt'-^-^cO'^t

*a _
c

c

pq

COtOI>-t^COOC^OOtor^CO'OCOtOVOiOOlOCN<MiOiOOCO'^,tO(MO

-^p <o om^^o in •<* to cp ip cn t^qp ipnipt'N on op op 1^0 -^p co to <© op oo
666666666©non6on6ononon6oooooooo on 6 6 6 6 6 on
cncncncncncncncncncncncncncncncncncncncncncncncncncncncncn

(NiOaO-^COOO^CNOO — «<©©<©»-ntOa0©<©ONON©©'<1,COC000<MTp©

&©ocN^gNopi^m9cpgNON^9i^mcNCN9gNgNCN t^-op ON9 CN CN

6 6 6 6 6 66on666i66666on6i©n6oooo oso^oscio 6 6

CNCOCOCOCOCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCOCOCO

oX.^cN^og^^«9^90cpco9cpco<Ng^9»pGp<»9i^cpcN

6 6 6 6 6 6 on 6 6 on on 6> 6 666i66non6noo on on on ©n 6 6 6 6
cococococococncncncncncncocncncncncncncncncncncncncncococo

Tl'0"TJiO«<»00»W«lOTflOlOtOCOO'*OHOO*0000

6^cpcN^ONa5^t^vpvpcNgN^t^ocNCNcNap i^qc cn t^ r^ op on cn cp
66 6 6 6 6666n6n6n6n656v6i6on6nonooooqo on 6n on on 6 6 6
cnc0cocococncnencnc»c«c<cnc*cncnc<c*enc*c*dcncnc<cncnc0c0

•0©©0<©©00©00©CN©©

o\cNyi,c^r->9qpo1r^opr^99
616666666616600
CNCOCOCOCOCOCNCNCNCNCNCOCO'

00 CO
O CN

6 6

COCO

00 O
VC ON

cn »■«
6 6

coco

r-ao — vo "*

CM coin
•rfCOCN

tOON-p

6616
d ci co

(OQO 10

O CN

o «o

TfCO

66

(M CN

Q0 00
CN O

66

CN CN

0 -h 00
l>-t^CO

9 rpop

01 ON ON
CN CN CN

00 o ^ CO CO

66666

CN CO CO CO CO

0 goo

Ms

co omdoo t^

•^l>.coco»0

— < on cn t^ao

»O00 -< £-"*

moo cn on -^

O t« >PO> CN

6 6 6 6 6

CO CO CO CO CO

V_ r^ CO "3* to o 'r~ X ON o

CO t^OUN-
ON© <N COCO

66666

CN CO CO CO CO

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY.

[NEW SERIES.]

MAY 1828.

LI. On the Ellipticity of the Earthy as deduced from Experi-
ments with the Pendulum ; and on the Formula employed for
obtaining it. By William Galbraith, Esq. A.M.*

HPHE number of accurate experiments made with the pen-
-"- dulum to determine the figure of the earth, is now consi-
derable, and the discussion of them has been somewhat exten-
sive. From these it appears that discrepancies in the length
of the pendulum by experiment in a given latitude may be
considerable, amounting to above 0*005 of an inch, arising
from the unequal action of the strata immediately under the
station, for which no allowance can be easily made. From
these considerations, it is evident combinations of pendulum
experiments may be employed to bring out any required ellipti-
city, at least within certain limits, unless a judicious selection
be made of those placed under analogous circumstances. To
obviate these, the mean of a number of experiments in the same
latitude, but in very different longitudes, distributed as regu-
larly as conveniently can be, over the same parallel, should be
chosen, comprehending, if possible, every variety of geologi-
cal basis. From this method of proceeding, local irregularities
would be so far counteracted as to bring out results somewhat
satisfactory; and until this is accomplished, perhaps other arti-
fices may be advantageously employed to obviate as far as pos-
sible these unavoidable and troublesome incongruities. Among
other considerations, perhaps a basis of a certain specific gra-
vity might be chosen as a standard ; and by comparing the
lengths of the pendulum on various bases of different specific
gravities, an approximate rule might perhaps be obtained by
which, with considerable exactness, the lengths of the pendu-

* Communicated by the Author.
New Series. Vol. 3. No. 17. May 1828. 2 T lums

322 Mr. Galbraith on the Figure of the Earth.

lums on different bases might be reduced to the same. Taking
ordinary alluvial formations for the standard density, of which
the specific gravity may be about 2-5, — and by experiments
made on subsoils of light sand, gravel, or clay, combined with
those made on sandstone, basalt, schistus and granite,in the same
latitude, and thence finding what effect these have in varying
the length of the pendulum, — an approximate value of that ef-
fect may be pretty well estimated ; whence a rule may be ob-
tained, to reduce them all to the standard density, so far as re-
lates to the exterior crust of the earth. These, combined with
the form of the substratum and other peculiarities, of which
several instances may be seen in Captain Sabine's work on the
Figure of the Earth, would give the means of obtaining pretty
accurately the medium length of the pendulum in any given
latitude. Thus it may be inferred, that a variation of the spe-
cific gravity from 2 to 3 at the surface, and continued for
some distance towards the centre, would give a variation of
the length of the pendulum amounting to about 0*01 of an
inch. Consequently, if 2*5 were taken for the standard spe-
cific gravity at the surface, and the lengths reduced to this,
they may be increased or diminished about 0*005 of an inch,
— a quantity sufficient to reconcile the most discordant of the
pendulum experiments. These reductions, no doubt, should
be applied to those experiments only which are likely to be
employed to determine the figure of the earth, in order to ob-
viate the discordancies from local irregularities ; while the ac-
tual lengths from observation applied to other purposes, — such
as our standards of weights and measures obtained at a par-
ticular spot, — ought to be allowed to remain as they are. In-
deed, in an extensive series of experiments, the several correc-
tions for the height, shape, specific gravity, &c. of the station,
should be all placed in their respective columns beside the
original lengths, to be employed or omitted, as might appear
advisable, according to the purposes for which they are wanted.
No doubt, with regard to these corrections, a good deal is left
to the accuracy and judgement of the observer; and in some
of them great precision cannot be attained ; but in most cases
a probable approximation only, which, although not perfectly
accurate, will at least tend to give the mean ellipticity more
truly than when they are neglected. — Having stated these pre-
liminaries, our attention may now be directed to the formula;
for obtaining the ellipticity.

It appears from our ordinary treatises on the Figure of the
Earth, supposing it to differ little from a sphere, that the cen-
trifugal force which acts in opposition to gravity, decreases from
the equator to the pole as the square of the cosine of the la-
titude ;

Mr. Galbraith on the Figure of the Earth, 323

titude; and consequently the diminution of gravity from this
cause, in proceeding from the pole to the equator, will also be as
the square of the cosine of the latitude. But the square of the
sine increases as the square of the cosine diminishes ; therefore
the increase of gravity in proceeding from the equator to the
pole, will be as the square of the sine of the observed latitude
nearly. A little consideration will readily show, however, that
this is correct, on the supposition of the earth being a perfect
sphere, and is only an approximation not far from the truth in
the case where the compression is small. The centrifugal force,
therefore, is strictly proportional to the ordinate to the polar
axis which involves the compression, — the very thing we are in
quest of. Now as this is supposed to be the unknown quantity,
it must be assumed equal to about ^j, what it is already known
to be nearly; we may infer that the centrifugal force decreases
as the square of the sine of the reduced latitude exactly. The
difference arising from these two suppositions is undoubtedly
small ; but in very nice disquisitions, minute quantities ought
not to be entirely disregarded.

The length of the pendulum is as the force of gravity; and
it has generally been inferred, from suppositions not far from
the truth, that the length of the pendulum from the equator to
the pole, increases as the square of the sine of the latitude.
The latitude hitherto used is that derived directly from obser-
vation, supposing the plumb-line to hang perpendicularly to
the surface, or to the tangent plane to that surface, at the place
of observation. Now there is no doubt that, from the equili-
brium of the fluid part of the earth, the direction of gravity at
the surface is exactly, or very nearly, in this vertical line. But
the force of gravity at any point on the surface of a spheroid
is (Schubert, Astronomie Physique, vol. iii. § 125.) inversely
proportional to the radius of the spheroid, or the line drawn
from the place of observation on the surface to the centre.
This is conformable to experience ; for it is known that the
length of the pendulum, independently of centrifugal force, in-
creases as we proceed from the equator to the pole where it is
nearest the centre ; and consequently, on that very account, its
length there is greatest. I am well aware that the length of
the pendulum has, so far as I know, always been affirmed to
increase from the equator to the pole, nearly as the square of
the sine of the observed latitude ; though from what I have al-
ready advanced, it appears that it increases as the square of
the sine of the reduced latitude, the compression being assumed
by estimation, as has already been observed.

" For in an oblate spheroid (Plavfair's Outlines of Natural
Philosophy, vol. ii. § 296.) differing little from a sphere, if

2 T 2 h be

324* Mr. Galbraith on the Figure of the Earth.

b be the polar semiaxis, b + c the radius of the equator, $ the
angle which a line drawn from the centre to a given point on
the surface makes with the axis of the spheroid, and f the force
with which the given point is attracted by the spheroid ; then it
has been shown by M. Chastellot, (in the French translation of
Newton's Principia, torn. ii. Paris edition of 1756, § xxxvii.
coroll. I. page 236, 237.) that

/=— 0+-5T- IS sln 0 W

But if X be the latitude, and 0 the angle of the vertical with
the radius, commonly called the reduction of the latitude, and
therefore $ = A. — - 0, or the reduced latitude, then

there will result

/= '%(* + f * * i^in'(X-fl)) (2)"

This expression for the attraction, shows that the gravitating
force in proceeding from the equator to the pole, increases as
the square of the sine of the reduced latitude. From similar
principles, and the considerations formerly advanced, it fol-
lows that the increase of the force of gravity depending upon
the diminution of the centrifugal force, also increases as the
square of the sine of the reduced latitude. On combining these,
the absolute increase of the length of the pendulum from the
equator to the pole, is proportional to the square of the sine of
the reduced latitude, not of the observed latitude. I advance this
conclusion with diffidence, and with all due deference to those
who have preceded me, and am fully aware of the authority of
such names as those of Clairaut and Laplace : but I think my
conclusion is founded in truth ; and if it be so, it cannot be
shaken by the authority of any name, however great. No doubt
the difference between the square of the sine of the observed
and reduced latitude is not great; since at its maximum at 45°,
supposing the ellipticity to be about 7£n, making the reduction
11' 29" only, the square of the sine of the observed latitude,
or 45°, is 0*5, and the square of the sine of the reduced latitude,
or 44° 48' 31", is 0-4966596. Now if the excess of the polar
above the equatorial pendulum amount to 0*208 of an inch,
then 0*208 (0-5—0-4966596) = 0*000695 of an inch, the quan-
tity that the computed pendulum at the observed latitude of
45° would be too great : and hence, when the lengths of the
experimental and computed pendulums are compared in the
usual hypothesis, a disagreement at this parallel will always
occur, which may very easily be imputed to a wrong cause ;

such

Mr. Galbraith on the Figure of the Earth. 325

such as an error in the experimental results, a protuberance
of the earth at that latitude, a diminution of density, &c. This
has occurred to me from some of my own computations, as
well as from those of others which I have seen, but which
seem to disappear when the proper (the reduced) latitude is
employed. In order to obtain correct results, the formulae
should possess all the accuracy which can be given them. For
this purpose I have elsewhere reconsidered the usual method
of obtaining the compression, and made some slight cor-
rection.

If <p denote the centrifugal force at the equator, r the radius
of the equator, t the time of rotation of the earth about its axis,

and I the length of the pendulum, then <p = ( (1)

V~2/ l
and consequently the ratio of the centrifugal force to gravity

will be expressed by r~- = \ yi = q (2)

If the most accurate values of these quantities be introduced,
q will be found to be 0*003455 = g 6 , somewhat less

than -Tj-, that usually employed. Now if t denote the ellip-

ticity, p a certain coefficient to be found from an investigation
of the conditions of equilibrium of a spheroid, y the excess of
the polar above the equatorial pendulum, and % the length of
the equatorial pendulum, then

e = —tL -fc (3)

Since by considerations derived from the case of a homo-
geneous spheroid, which may be supposed very nearly appli-
cable to the case of the earth, the value of j?is 2*4?91516, in-
stead of 2*5, that commonly adopted ; whence it follows that

6 = 0-0086082-^- (4)

This formula will, I believe, give the ellipticity as nearly cor-
rect as the necessary data required in the substitutions can
be depended on.

As we have not as yet a sufficient variety of experiments in
different longitudes under the same parallel, affected by the
various irregularities tending to destroy each other, neither
have we sufficient data to reduce them to a substratum of a
given density, as formerly proposed; it remains to employ the
only method left, which may perhaps effect nearly the same
thing. This consists in reducing as many lengths of the pen-
dulum as possible to the same point which are very near it, by

the

326 Mr. Galbraith on the Figure of the Earth.

the usual formula, which, from their proximity, cannot intro-
duce any considerable error, as none are selected for this pur-
pose whose latitude differs more than about 5° on each side of
it, from that to which they are reduced. As an equal number
was generally chosen on each side of it too, any small error
in the formula of reduction which was used, or Al = + 0*208
(sin2 A" — sin2 A'), will be by that means counteracted.

No doubt objections may be urged against this mode of
procedure ; but it is perhaps the best under the present cir-
cumstances of the problem which can be employed, as the
most accurate method of distributing the observations regu-
larly over the quadrantal arc of the meridian. Now a series
of observations distributed regularly over the meridian is of
considerable importance to determine the exact ellipticity, even
when the method of the least squares is employed ; for in this
case also a preponderance of observations at any latitude has
its effect in obtaining the compression. — Having now assigned
the reasons for adopting the methods we have chosen, it re-
mains to apply them to a collection of all the experiments
which could with confidence be employed. These are prin-
cipally the series of Captain Kater, M. Biot, Captain Sabine,
M. Freycinet, M. Duperrey, together with a few more from
Sir Thomas Brisbane, Captain Hall, and perhaps one or two
others.

Places.

Rawak

Sumatra

St. Thomas

Galapagos

Maranham

Ascension (D.)
Ascension (S.)
Sierra Leone...

Trinidad

Bahia

Madras

Guam

Jamaica

Isle of France..
Isle of Mowi ...

San Bias

RioJaneiro(H.)

Latitude.

1'

1
24
32
31
55

7 .55

8 29
10 38

12 59

13 4
13 27
17 56
20 9

20 52

21 32

22 55

34" S.
49 N
41 N.
19 N
43 S,
9 S,
48 S.
28 N,
56 N

21 S.
9N

51 N.

7N
56 S.

7N
24 N,

22 S.

Experi-
mental
Pendulum.

39*01482
39-01812
39-02074
39-01717
39-01214
39-02364
39-02410
39-01624
39-01884
39-02223
39-02338
39-03023
39-03144
39-04769
39-04737
39*03828
39-04374

Reduced
Pendulum
to Latitude.

Length.

0° 0'

0"

39-01650

5 0

0

39*01877

10 0

0

39-02090

15 0

0

39*02913

20 0

0

39*03856

25 0

0

39-05167

Rio

Mr. Galbraith' on the

Figure of the

Earth

327

Experi-

Reduced

Places.

Latitude.

mental
Pendulum.

Pendulum
to Latitude.

Length.

Rio Janeiro (F.)

22° 55' 13" S.

39*04371

30°

0'

0"

39*06492

P.Jackson (B.)

33 51 34 S.

39*07724

P.Jackson (D.)

33 51 39 S.

39-07897

35

0

0

39-08166

Formentera. ...

38 39 56 N.

39*09424

New York

40 42 43 N.

39-10168

40

0

0

39*09908

Toulon

43 7 9 N.

39-11038

Fi^eac

44 36 45 N.
44 50 26 N.

39-11322
39*11303

45

0

0

39-11585

Bordeaux

Clermont

45 46 48 N.

39*11812

Paris

48 50 14 N.
50 37 24 N.

39-12929
39-13614

50

0

0

39-13329

Shanklin

Dunkirk

51 2 10 N.

39*13773

London

51 31 8 N.
51 31 44 S.

39*13929
39-13966

Falkland i.(D.)

Falkland I. (F.)

51 35 18 S.

39-13720

Arbury Hill ...

52 12 55 N.

39-14250

55

0

0

39-15163

Clifton

53 27 43 N.

39-14600

Leith (Biot.)

55 58 37 N.

39-15547

Leith (Kater.)

55 58 41 N.

39-15554

Portsoy (Kater.)

57 40 59 N.

39-16159

60

0

0

39-16772

Stockholm

59 20 34 N.

39-16541

Unst (Biot.)

60 45 25 N.

39-17181

Unst (Kater.)

60 45 28 N.

39-17146

65

0

0

39-18213

Drontheim (S.)

63 25 54 N.

39-17456

Hare Isle

70 26 17 N.

39-19840

Hammerfest ...

70 40 5 N.

39-19519

70

0

0

39*19553

Greenland

74 32 19 N.

39-20335

Melville Isle ...

74 47 12 N.

39-20700

75

0

0

39*20600

Spitzbergen. ...

79 49 58 N.

39-21469

A

A—

&.

Pendulum.

0°

0° 0'

0"

39-01650

5

4 58

1

39*01877

10

9 56

5

39*02090

15

14 54

17

39-02913

20

19 52

38

39-03856

25

24 51

14

39-05167

30

29 50

5

39-06492

35

34 49

14

39*08166

40

39 48

42

39-09908

45

44 48

31

39*11585

2-0*0000000#=E
2—0-0074963 j/=Ei
•2— 0-029 7652 y- E2
s-0-0661582 j/ = E3
2— 0-1156039<z/=E4
■z— 0-1766568t/=E5
2-0*2475060 t/=E6
z-0-3260503 j/=E7
•2—0-40994073/= E8
2-0-4966596 j/=E9

50

A

x-£

50°

49° 48' 41"

55

54 49 12

60

59 50 3

65

64 51 11

70

69 52 36

75

74 54 15

328 Mr. Galbraith on the Figure of the Earth.

Pendulum.

3943329-2-0-5835803 j/=E10
39-15163— 2-0*6680546 j/=En
39-16772— z— 0-7474900 */=E12
39-18213-*— 0*8194250j/=E13
39*19553— z-0-8816350 2/=El4
39*20600-2-0*9321740j/=E15

Whence z = 39*098334 — 0-4067622 y (A)

Again,

0-0000000 — 0-0000000 z — O'OOOOOOOj/ = E

0-2924964— 0-0074963^— 0-0000562 j/=Ei

1-1614649-0-0297652 ■* — 0*0008860#=E2

2-5820970-0-0661582 2— 0*0043769^= E3

4*5130098-0*1156039 2— 0*0133643 ?/=E4

6*8987431— 0*1766568 2-0*0302076 */=E5

9*6688209— 0*2475060 2-0*061 2592 j/=E6

12-7425870— 0-3260503 2— 0-1063088 ?/=E7

16*0283042— 0-4099407 2— 0-16805143/=E8

19-4272624-0-4966596 2-0*2466707 j/=E9

22-8374171 -0-5835803 2-0-3405660 j/=Eio

26-1554265— 0-6680546 2-0-44629703/=En

29-2774790-0-747490O2-0-5587402j/=E12

32-1068169-0-8194250 2-0*6714573<2/=E13

34*5561511— 0*8816350 2— 0*7772800 j/=E]4

36*5468138 — 0*9321740 2— 0*8689486 j/=E15

Whence z = 39-1498536 — 0-6598551 y (B)

Equating (A) and (B) there will result

y = 0-20348 and z = 39*015576

therefore 2- — 0*0052153, and

z

E = 0-0086082 - 0*0052153 = 0*003393 =5 ^y*.

Adopting the formula for the length of the pendulum, or
I = 2 + y sin3 (A — 0), the lengths of the pendulum by com-
putation may be compared with the foregoing means derived
from experiment.

* As there is some reason to believe that several of the pendulums near
the equator are too great ; if the first three of those above be rejected, then
the ellipticity will be -y^.. Indeed, I have for some time been induced to
consider -^fay to be that which must ultimately be generally adopted.

Lat.

Mr. Galbraith on the Figure of the Earth,

329

Lat.

Reduced

Experi-

Pendulum

Deviations

Latitude.

mental

computed by

of

>

x—i:

Pendulum.

y xsin2(X— 6).

Formula.

0°

0° 0' 0"

39-01650

39-01558

- 0-00092 = E

h

4 58 1

39*01877

39*01710

-0'00167 = Ei

10

9 56 5

39-02090

39-02163

+ 0-00073 = E2

15

14 54 17

39-02913

39-02904

- 0-00009 = E3

20

19 52 38

39-03856

39-03910

+ 0-00054 = E4

25

24 51 14

39-05167

39-05152

-0'00015 = E5

30

29 50 5

39-06492

39*06594

+ 0-00102 = E6

35

34 49 14

39-08166

39*08192

+ 0-00036 = E7

40

39 48 42

39-09908

39-09899

-0-00009 = E8

45

44 48 31

39-11585

39*11664

+ 0-00079 = E9

50

49 48 41

39-13329

39*13432

+ 0-00103 = E10

55

54 49 12

39*15163

39-15151

— 0-00012 = En

60

59 50 3

39-16772

39*16767

— 0-00005 = E19

65

64 51 11

39-18213

39-18231

+ 0-00018 = E13

70

69 52 36

39-19553

39*19497

-0-00056 = E14

75

74 54 15

39-20600

39-20525

- 0-00075 = E15

80

79 56 4

39-21284

85

84 58 0

39-21749

90

90 0 0

39-21906

From a review of the whole, it appears that the ellipticity is
somewhat greater than it has generally been supposed, though
the difference is not very great. It seems also probable that
the discordancies of the results derived from the formula for
computing the length of the pendulum are not very consider-
able, and are so irregular that no general protuberance, or
uncommon diminution of the force of gravity, is any where
likely to follow from the observations by the pendulum.

The only doubt that remains, is perhaps the effect of com-
bining the lengths of the pendulum on stations of very differ-
ent specific gravities, where a preponderance of dense or light
materials is likely to prevail.

It is to be feared that the lengths of the pendulum near the
equator are rather in excess, as the stations have been, generally
speaking, on bases of considerable density; and by this means
rendering the equatorial pendulum too great, the excess of the
polar above the equatorial pendulum too small, and conse-
quently the compression too great ; though more numerous
experiments near that circle are still wanting to decide this
point in an unexceptionable manner.

It is to be expected, that some light may be thrown on the
New Series. Vol. 3. No. 17. May 1828. 2 U exact

330 Mr. Galbraith on the Figure of the Earth.

exact quantity of compression by the various arcs on the me-
ridian, and the parallels now executing throughout Europe;
though I am inclined to believe, that measurements of arcs of
the meridian near the equator, and as close to the poles as
convenient, will be more decisive. In the execution of these,
however, care should be taken to select proper portions of the
meridian under uniformity of geological character. Some of
the extensive plains in the North of Russia and in South
America, appear to me to be the most eligible ; though I have
seen Spitzbergen recommended, from the facility it affords of
executing the necessary operations. Yet for these very rea-
sons I am disposed to think that from its irregular and broken
character, by extensive Jiords, as they are called, running
amongst the islands, it is to be feared that very irregular lo-
cal attractions will be found to prevail ; so that each series of
zenith distances would be something like the Schihallien ex-
periment; and the irregularities thence produced, would rather
tend to throw a doubt over the true compression, than to point
out the proper quantity.

Edinburgh, April 1827*. WlLLIAM GALBRAITH.

P.S. In the foregoing remarks, it will be seen that I have
endeavoured to introduce a few small corrections into the usual
formulae for obtaining the ellipticity, which may perhaps be
thought by some, to be too minute to deserve much attention
in the present state of the problem, as being much within the
probable errors of observation. For instance, instead of taking
the ratio of the centrifugal force to gravity at the equator at
2 i^ I have adopted g iy . nearly, as it ought to be ; and for the
coefficient | = 2*5, it is assumed at about 2*49. These, no
doubt, appear trifling ; but nevertheless their adoption reduces
the constant 0*00865 to 0*00861, and this small modification
diminishes the ellipticity in an equal degree. I have also pre-
ferred the reduced latitudes to the apparent, or those got di-
rectly from observation ; and this removes an irregularity which
at one time I was persuaded occurred in the elliptical figure
of the earth ; namely, a protuberance at about the parallel of
45° N., which I am now disposed to attribute to a slight error
in the approximate formula usually employed. It has also
been thought advisable to apply the method of the least squares
with caution. I am perfectly aware that this method is the
best that can possibly be applied in many cases ; but that there
may be particular instances where, by employing it without
discrimination, it may, from the manner in which it must be
employed, be the means of leading to more erroneous conclu-
* So in the MS.— Edit.

sions

Account of Prof. Gauss's " Disquisitiones generates, &c" 331

sions than by a selection of the most decisive observations.
As this subject has, since the first part of these remarks was
written, been treated of by Mr. Ivory, in a late Number of the
Phil. Mag., much more ably than I could pretend to, it will
be unnecessary for me to say any thing more at present upon
the subject.
Edinburgh, March 12, 1828. W. G.

LII. Account of a Paper by Prof. Gauss, intitled " Disquisi-
tiones generales circa Superficies Curvas :" communicated
to the Royal Society of Gbttingen on the 8th of October
1827*.
A LTHOUGH geometricians have much occupied them-
-**• selves with general investigations on curve surfaces, the
results of which form a considerable portion of the higher de-
partment of geometry, this subject is so far from being ex-
hausted, that it may be safely asserted that as yet a small part
only of a most fertile field of inquiry has been cultivated. The
author has already endeavoured some years ago to take a new
view of this subject in the solution of the problem : To find all
representations of a given surface on another surface, in which
the smallest parts shall remain similar. The object of the
present paper is to open new views, and to unfold a portion of
the new truths which are thereby rendered accessible. We
shall explain as much as can be rendered intelligible without
entering too deeply into the subject ; but we must remark, that
the new definitions as well as the theorems, in order to be ge-
neralized, will require some restrictions and qualifications
which must be omitted in this place.

In investigations which involve a variety of directions of
straight lines in space, it is advantageous to designate these
directions by those points on the surface of an invariable sphere
at which the radii drawn parallel to the same, terminate : the
radius and centre of this auxiliary sphere are entirely arbi-
trary ; for the latter, the unity of linear dimension may be
chosen. This proceeding agrees, in fact, with the one con-
stantly used in astronomy, where all directions are referred to
a fictitious celestial sphere of an infinite radius. Spherical tri-
gonometry, and some other theorems to which the author
has added one of frequent application, are then employed for
solving the various problems that present themselves by a

* From the Gottinguche gelehrte Anzcigen. — This abstract is probably
from the pen of the distinguished Author.

2 U 2 comparison

332 Account of Prof. Gauss's Paper intitled

comparison of the different directions which occur. If the
directions of lines normal to the curve surface, drawn from
every point of the same, be designated by the points of the
sphere, corresponding to them according to the proceeding
above explained, so that each point of the curve surface has
its corresponding point on the auxiliary sphere, then, generally
speaking, every line on the curve surface will have a corre-
sponding one on the auxiliary sphere, and every portion of
surface of the former will have its corresponding portion on
the latter. The smaller the deviation of a part is from a plane,
the smaller will be the corresponding part of the sphere ; and
it is therefore a very natural proceeding to employ, as mea-
sure of the total curvature, the area of the corresponding por-
tion of the sphere. The author, accordingly, calls this area
the entire curvature of the corresponding portion of curve sur-
face. Besides this quantity, the position of the part comes into
consideration, which, independently of the relation of magni-
tude, may be a similar or a reversed one : these two cases may
be distinguished by the positive or negative sign being put
before the expression of the total curvature. This distinction,
however, has only a definite signification, so far as the figures
are assumed to be on definite sides of the surfaces : the author
assumes them in the sphere on the exterior, and in the curve
surface on that side on which the normal line is supposed to
be erected ; and it follows that the positive sign belongs to con-
vex-convex and to concave-concave surfaces (which are not
essentially different), and the negative sign to concave-convex
ones. If the portion of the curve surface in question consists
of parts dissimilar in this respect, further specifications be-
come necessary, which must here be passed over.

The comparison of the areas of the portion of the curve
surface and its corresponding portion of the auxiliary sphere,
leads to a new notion (in the same manner as the comparison
of volume and mass produces the notion of density). The
author calls measure of curvature in any point of the curve
surface, the value of the fraction whose denominator is the
area of an infinitely small part of the curve surface at this
point ; and the numerator the area of the corresponding part of
the auxiliary sphere, or the entire curvature of the element.
It is clear that in the sense of the author, entire curvature and
measure of curvature are in curve surfaces analogous to what
in curve lines is respectively called amplitude and curvature ;
he doubted of the propriety of transferring to curve surfaces
the latter expressions, which, though sanctioned by use, are
not very appropriate terms. It is however of less consequence

how

" Disquisitiones generales circa Superficies Curvas." 333

how these new notions are denominated, than to justify their
introduction by remarkable and useful theorems to which they
give rise.

The solution of the problem : To find the measure of curva-
ture in each point of a curve surface, — presents itself under
various forms, according to the manner in which the nature of
the curve superficies is given. The simplest manner is, the
points in space being expressed by three rectangular co-ordi-
nates x, y, z, to represent the one co-ordinate as a function of
the two others : in this case the expression which is obtained
for the measure of curvature is the simplest. This leads at
the same time to a remarkable connection between this mea-
sure of curvature and the curvatures of those curves which are
produced by the intersection of the curve surface by planes
perpendicular to it. It is well known that Euler has first de-
monstrated, that two of the intersecting planes, which are like-
wise at right angles to each other, have the property, — that to
the one belongs the smallest, to the other the greatest radius
of curvature ; or rather, that in them the extreme curvatures
occur. Now it results from the expression for the measure of
curvature just alluded to, that this becomes equal to a fraction
whose numerator is unity, and the denominator the product of
the two extreme radii of curvature.

The expression for the measure of curvature becomes less
simple when the nature of the curve surface is given by an
equation between <r, y, z ; and the former still more compli-
cated, when the surface is represented by x, y, z being given as
functions of two new variable quantities p, q. In the latter
case the expression contains fifteen elements ; viz. the par-
tial differential quotients of the first and second order of x, y, z
for p and q : but it is less important in itself, than by its being
the transition to another expression, which forms one of the
most remarkable propositions of this theory. In that manner
of representing the nature of the curve surface, the general ex-
pression for any linear element of the same, or for \/(dxz -f
dy* + dz2) assumes this form: \Z(E,dx2 +2¥dx ,dy +Gdy2);
where E, F, G become functions of p and q ; the above-men-
tioned new expression for the measure of curvature contains
only these quantities, together with their partial differential
quotients of the first and second order. It is evident, there-
fore, that for determining the measure of curvature, the ge-
neral expression of a linear element only is required, and not
the expressions for the co-ordinates x9 y, z themselves. An
immediate consequence of this is the following remarkable
theorem : If a curve surface or a portion of the same can be
evolved on another plane, the measure of curvature remains

unchanged

334 Account of Prof. Gauss's Paper intitled

unchanged in every point after the evolution. From this fol-
lows, as a particular case ; that in a curve surface which can
be evolved in a plane, the measure of curvature is always =0.
From this is immediately derived the characteristic equation
of the surfaces capable of being evolved in a plane; namely,
if * be regarded as a function of y and x

ddz ddz / ddz

dx* dy*

(adz \* __
~dx~d~y) ~ '

an equation which, indeed, has long been known, but in the
author's opinion has never yet been rigorously demonstrated.

These propositions lead to a new view of the theory of curve
surfaces, and open a wide uncultivated field of investigation.
If surfaces be considered not as bounds of bodies, but as bodies
one dimension of which is evanescent, and at the same time flexi-
ble but not expansible, it will be conceived that two essentially
different classes of relations must be distinguished, — those
which suppose a definite shape of surface in space, and those
which are independent of the various shapes which the surface
is capable of assuming. It is of the latter that the author
treats ; and it appears by what has been observed above, that
the measure of curvature is one of them: but it will easily be
seen that the consideration of the figures which can be de-
scribed on the surface, their angles, their areas and entire cur-
vature, the connection of the points by shortest lines, &c. be-
long to this class. All these investigations must proceed from
this, That the nature of the curve surface is given by the ex-
pression of an indefinite linear element of this form \/(JZdp2-h
ZFdp.dq + Gdq*).

The author has inserted in the present paper a part of the
investigations on this subject, which have engaged him during
several years, confining himself to such as are not too remote
from the point where his labours began, and which may serve
as general auxiliaries for numerous further investigations. In
this notice we must be still shorter, and be content to give
only as a specimen the following theorems. — If on a curve sur-
face, a system of an infinity of shortest lines, all of equal length,
proceed from one point, the line passing through their ex-
treme points is at right angles to every one of them. If from
every point of any line on a curve surface, shortest lines of equal
length and at right angles to that line are drawn, — all these
lines are likewise at right angles to that line which connects
their other extreme points. Both these theorems, the second
of which may be considered as a generalization of the first, are
demonstrated analytically, as well as by simple geometrical
considerations. The excess of the sum of the angles of a tri-
angle

w Disquisitiones generales circa Superficies Curvas." 335

angle formed by shortest lines above two right angles, is equal
to the entire curvature of the triangle. It is here supposed,,
that the unity of angles is the one whose corresponding arc
equals the radius (57° 17' 45"); and that for the entire curva-
ture, which is a portion of the surface of the auxiliary sphere,
the area of a square whose side is the radius of the auxiliary
sphere is considered as unity. This important theorem may
evidently be thus expressed : The excess of the angles of a
triangle formed by shortest lines above two right angles : eight
right angles : : the portion of the auxiliary sphere corre-
sponding to that triangle : the whole surface of the auxiliary
sphere. Generally the excess of the angles of a polygon of
n sides, all shortest lines, above 2n — 4 right angles, is equal
to the entire curvature of the polygon.

The general investigations contained in the paper are finally
applied to the theory of triangles formed by shortest lines.
We shall mention only a few of the principal theorems of this
theory. If a, b, c be the sides of such a triangle (which are
considered as quantities of the first order), A, B, C the oppo-
site angles, a, (3, y the measures of curvature in the angular
points, <r the area of the triangle ; then \ (a -f /3 + y) <r will
be the excess of the sum A + B + C above two right angles
down to quantities of the fourth order. With the same ac-
curacy the angles of a plane rectilinear triangle, the sides of
which are a, b, c, will be

A - TV (2a + J9 + y) or

c-TV(« + /3 + 2y)<r

It is clear, that the latter theorem is a generalization of a well
known proposition first given by Legendre, by which, omit-
ting the quantities of the fourth order, the angles of the recti-
linear triangle are obtained by diminishing the angles of the
spherical one by one-third of the spherical excess. For sur-
faces which are not spherical, unequal reductions must be ap-
plied to the angles, and, generally speaking, the unequal part
is a quantity of the third order : if, however, the whole surface
deviates but little from the spherical form, it involves besides
a factor of the same order with the deviation from the spheri-
cal form. It is, undoubtedly, important for the theory of geo-
detical operations, to be able to calculate the inequalities of
these reductions, and to obtain thereby the full conviction that
they are to be considered as insensible for all measurable tri-
angles on the surface of the earth. Thus it is found, that in
the largest triangle in the measurement conducted by the au-
thor,

336 Dr. Weber on Savart' s Experiments on the

thor, the greatest side of which is nearly fifteen (German) geo-
graphical miles, and in which the excess of the sum of the
three angles above two right ones is nearly fifteen seconds, the
three reductions of the angles to angles of a rectilinear trian-
gle are 4"'951 13, 4"*95104., 4"*95131. The author has, how-
ever, likewise calculated the terms of the fourth order wanting
in the above expressions, which assume for the sphere a very
simple form ; but in measurable triangles on the surface of the
earth they are quite insensible; and, in the above example, they
would have diminished the first reduction by only two unities
in the fifth decimal place, and have increased the third reduc-
tion by the same amount.

LIU. On Savart's Experiments on the Motions of mediately
agitated Membranes. By Dr. Wm. Weber, Academical
Teacher at Halle*.

[With an Engraving.]

" Tj^ROM the manner just stated of the division of mem-
-*- branes into vibrating divisions," says Savart, in the Ann.
deChim. ctdePhys. (1826. torn, xxxii. p. 385.) " it is evident
that the acoustic figures called by Chladni distortions, form
the transition between a variety of figures of sound which are
not distorted (in which may be reckoned several tones of the
flageolet). As Chladni has only observed the distortions of
figures of sound which are nearest the undistorted figures
(which he considers as fundamental figures), and as he fixed
the number of vibrations merely by the ear, which does not
admit of sufficient accuracy, he might justly assert that the
tone in the distortion of the figures of sound is the same as in
the fundamental figures. But in the tables accompanying his
Traite aV Acoustique, we find distortions of figures of sound
to which belong semitones, a whole tone, and even one-third
higher than when the figure of sound has what is termed the
fundamental form." The difference between Chladni and
Savart, according to these observations of the latter, is, that
Chladni asserts that there is in sounding plates no transition
from one tone of the flageolet to another ; whilst SaVart says
that by a repetition of experiments, he has discovered this
transition.

Savart justly says, that nothing in nature appears isolated.
He has actually shown in this treatise, as well as in some
former ones, an extraordinary number of transitions of one
kind of vibration into the other, in almost all bodies used for
musical purposes. Elut it is also a universal rule of nature,

* From Schweigger's Jahrbuch dor Chemie, &c, N.R. Band xx. p. 176.

that

Motions of mediately agitated Membranes. 337

that the transitions of the different phenomena do not show
themselves when these phaenomena appear most regularly and
forcibly, but only when they become indistinct and indefinite.
Now the sounding vibrations (which Chladni always considers
by themselves) are constantly the most uniform and the most vio-
lent vibrations. There is, therefore, probably, a transition from
a sounding vibration, through a series which do not produce
sound (such as are less distinct and precise) standing vibra-
tions, to a very different sounding vibration ; but there is no
transition from a sounding vibration through nothing but
sounding vibrations to a quite different sounding vibration (pro-
ducing a much higher or much deeper tone). However, Savart
is perfectly right in affirming that many of the distortions of
the figures of sound observed by Chladni are the beginnings
of the transition of one kind of vibration to another, and that
in these distortions, even the number of vibrations, whilst the
tone is becoming weaker and beginning to cease, is a little al-
tered. But if a vibrating body gives a distinct tone, it is in a
very uniform and violent vibration, which is only possible when
the number of its vibrating divisions is strictly fixed, and the
sum of the motions is in all as equal as possible, in which case the
height of the tone {the velocity of the vibrations) is unchangeable,
as it depends as much on the elasticity and form of the membrane,
as the velocity of the vibrations of a pendulum of a given length
on gravitation. This rule, laid down by Chladni, has thrown
an extraordinary light and intelligibility on all acoustic phae-
nomena.

In order, therefore, to render what has been said still more
intelligible ; and in consequence of there being several simi-
larities in the motions of membranes observed by Savart, with
the vibrations of sounding elastic plates; and finally, as it is
now generally necessary to find out by experiment as closely as
possible the extension of small vibrations on visible bodies ; — I
shall here communicate from the 32nd volume of the Ann. de
Chimie et de Physique, the phaenomena discovered by Savart.

Savart examined the lines upon which the sand remains in
its place on mediately agitated bodies.

If an equally-stretched square rectangular or triangular
membrane is mediately and regularly agitated, grains of sand
scattered over it are thrown off from equally large and regu-
larly-bounded divisions of those membranes, but are collected
on the limits of these divisions nearly in the same manner as
they are on the sounding plates.

Savart wished to cause the stretched membranes to vibrate
mediately and with the utmost uniformity, and thereby to de-
termine at his pleasure, the quicker or slower result of the

New Series. Vol. 3. No. 17. May 1828. 2 X agitations,

338 Dr. Weber on Savart's Experiments on the

agitations, and to become perfectly acquainted with its velo-
city. How could these objects be better attained than by the
sounding vibration of an organ-pipe, a bell, or disk, before
which the membrane was expanded, so that every vibration
transmitted by the air of those sounding bodies necessarily
agitated the membrane ?

In this manner he made the following double series of ex-
periments. Once he held the extended membrane before
an organ-pipe, which he was enabled by means of a stopper to
lengthen or shorten at will, by which means the same mem-
brane was successively agitated by very various rapid concus-
sions. In the second place, he stretched a membrane of a very
hygrometrical substance, viz. of paper, and made it gradually
imbibe an increasing quantity of aqueous vapour. In this
manner he was enabled to agitate a membrane of very different
degrees of elasticity by constantly equally-quick concussions,
ex. gr. by means of a sounding plate or bell held before it.

The membranes thus mediately agitated show, according to
Savart's observations, the following similarity to sounding
plates :

1. In mediately agitated membranes vibrating divisions are
formed, which are separated by quiescent or slightly moved
lines, as in the sounding plates.

2. These quiescent fines may undergo such distortions as
Chladni has observed in the sounding plates. On the other
hand, there are the following differences between the motions of
mediately agitated membranes and sounding plates. First, In
mediately agitated membranes the divisions near the edge are
as great as those within, whilst in sounding plates the divisions
near the border are not half so great. Secondly, In mediately
agitated membranes the different distortions of the quiescent lines
are produced by the different width of the agitating undulations^
(i.e. by different high tones of the organ-pipe placed before the
membrane,) whilst the observation in the sounding plates, as is
generally known, is, — that when the quiescent lines are some-
what distorted, the breadth of the waves of the undulation pro-
ceeding from the plate is either not altered at all, or very im-
perceptibly, which may be easily known from the height of
the tone.

If we hold a square membrane, the elasticity of which is
not changed, before the opening of an organ-pipe provided
with a stopper and made to vibrate, we may effect by means
of the stopper the circumstance that the sand thrown off" from
the divisions represented in Plate VI. fig. 1. No. 1. remain
only on the boundary line. If the tone of the organ-pipe be-
comes a trifle higher, the form of this boundary line upon

which

Motions of mediately agitated Membranes. 339

which the sand remains, varies as in No. 2 ; and becomes, as the
tone of the organ-pipe gets still higher, as in No. 3, 4, 5, 6,
where the boundary lines merely consist of four parallel lines.
In this manner the boundary lines which at first intersected
each other at right angles, are changed into parallel lines.
This transmutation may also be effected as represented at fig.
2, 3, 4, 5, 6, 7.

In the same manner four parallel nodes may pass into two
parallels which have towards the former a perpendicular po-
sition, as shown at fig. 8 ; or four parallel nodes may change
into four others intersected by two more perpendicularly, as
shown in fig. 9. Other remarkable changes of the position
and number of these boundary lines with increasing velocity
of the agitating concussions, are seen in fig. 10, 11, 12, 13.

From these experiments it may be seen that there is a possi-
bility of several transitions of one and the same sand-figure to
another; as for instance, fig. 10. and fig. 11. The question is,
what is it that produces any particular transition? Savart
mentions a criterion by which, from the first alteration of the
figure, it may be foretold what transition will ensue. He says:

First. On proceeding from a figure of nodes intersecting each
other at right angles, the character of the following changes
depends on the magnitude of the vertical angle on the points of
intersection separate from one another. This is very apparent
in the comparison of fig. 10. with fig. 11. which both form
transitions of four parallels, from two other lines normally
crossed, into six parallel lines.

Secondly. If, on the contrary, we have at first only parallel
nodes, we may say that the character of the following changes
depends on the difference of the curves which these lines may
receive, which is distinctly seen from the. same figures (10. and
11.), if one begins backwards (from No. 5, 4.); for in fig. 10.
the nodes curve inward, whilst in fig. 11. they curve outward.
The transitions are particularly remarkable when the lines
form two curves outward, and one inward, or vice versa; or
when they form three curves outward, and two inward, &c.
of which fig. 12. and fig. 13. furnish remarkable instances.

Circular and triangular membranes produce analogous phe-
nomena. On a circular membrane, three diametrical lines
may in this manner be produced, and these may be gradually
again changed into one diameter and one circular line (fig. 14.).
Moreover, on a circular membrane five diametrical lines may
be produced and gradually changed into five parallels, as
shown in fig. 15; and these five parallels may again be trans-
formed into one diametral and two circular lines.

Very narrow long rectangular strips show similar phamo-
2X2 mena.

340 Dr. Weber on Savart' s Experiments on the

mena. Thus the fundamental lines, where the sand keeps its
position, may have the form fig. 16. No. 1. As the tone be-
comes deeper, all these lines approach the end B, so that the
interval An, and n n\ and n' nl!, become larger ; but n" finally
advances to B, so that the membrane has only two lines left.
Another change is shown in fig. 17.

Savart has formed the hypothesis, that the membrane agi-
tated by the undulations of the air is also in a standing and
sounding vibration ; that from this sounding membrane waves
of sound are proceeding exactly of the breadth of those which
arrive at it : that he therefore knew the breadth of the waves
of sound proceeding from the membrane, from knowing the
breadth of those which arrive at it. From these hypotheses
it is inferred, that the modes of vibration produced by various
flageolet sounds are gradually transfused into one another by
an uninterrupted series of intermediate tones. What now
may be said of sounding membranes, says Savart, is probably
also the case with sounding elastic plates. But according to
Chladni's account, it is not so with sounding plates. Savart
thinks that Chladni has been mistaken in his observations.
(See the beginning of this paper.) But in all the experi-
ments I have hitherto made, I have always found Chladni's
observations confirmed. But should Savart find a different
result, it would be desirable that he should exactly point out
the material, form, and thickness of the plate with which he
made his experiments, as well as the manner of his having
fastened the plate and made it vibrate, in order that the ex-
periment may be repeated *.

These discoveries of Savart merely concern the extension of
small oscillations in form bodies, in membranes; as there is no
question here about sounding bodies, nay not even of rever-
berating bodies, as one may be convinced by the ear, but only
as to vibrations and soundless motions, which however show
much similarity to the motions of reverberating and even
sounding bodies.

I had a small wooden square'frame made, which measured in
the hollow six Paris-inches in length and breadth. Upon this
I glued a sheet of wet English letter-paper (wove paper, with-
out any wire-marks), which was perfectly free from thin places
or other defects, and glued upon this paper small laths, so that
it was equally stretched, and its edge everywhere immoveable.

* Chladni has investigated, in his Acoustics, Leipzig, 1802. § 114. p. 131.
a particular case, in which with a similar fundamental figure, but which once
has received a curve outward, and at another time inward, several tones
are produced, and has proved that here too no transition from one flageo-
let^tone to another, through an uninterrupted series of tones, is manifested.

Such

Motions of mediately agitated Membranes. 341

Such a paper will sound even on any one pushing against the
frame or gently blowing upon it. If one strewed upon this
paper held horizontally some grains of coarse sand, and held
a bell of a watch or a small disk of glass over the paper, ex. gr.
near a corner, making it sound by means of a violin-bow, the
sand began to move, and collected in those lines described by
Savart.

In these experiments I found : —

1. That here also in the mediately agitated membranes an
actual intersection of the reposing lines nowhere takes place,
as Oerstedt and Strehlke have observed in sounding plates.

2. That the deepening or heightening of the tone of the
organ-pipe, and the change of elasticity by the wetting of
the membrane, are not the only means whereby the nodes in
mediately agitated membranes became curved ; but that this
curving of the nodes might also be produced by trifling cir-
cumstances ; by bringing, for instance, a sounding bell some-
times near a corner and sometimes near the centre of the square
membrane.

3. That, as I have stated before, no trace of self-sounding
or reverberation of the paper is to be observed. At the meeting
of the Society for the Investigation of Nature, at Halle, on the
14-th of July in the present year (1827), I repeated these ex-
periments, and convinced the assembled members of it, espe-
cially the editors of this Journal.

I consider therefore the careful separation of the sounding
reverberating vibrations from those slight motions of the bodies
that do not sound or reverberate (which may certainly be very
similar to the former), and which I have indicated in this arti-
cle, as necessary ; since great confusion is introduced by the
interference of the latter with the laws of motion of sounding
disks and reverberating bodies.

It has been shown in the Doctrine of Undulation, published
by my brother and myself, how sounding and reverberating
vibrations, figures of sound and figures of vibration, should be
distinguished ; and how it results from this, that Savart's and
Chladni's experiments do not contradict each other*: but we
must also distinguish between these vibrations and vibrations
without any acoustic effect, which latter may also unite the scat-
tered sand into nodes. We have further shown, in the work
just quoted, that the sounding vibration is always of the class
of the standing vibrations, with which all small motions of all
bodies seem to terminate. From the circumstance that in all
these small motions of bodies left to themselves, at last a cer-
tain balance and uniformity manifest themselves ; and that this
* Vide Jahrbuch, 18%.

uniform

342 Dr. Weber on the Interference of Sound.

uniform fin at vibration is, in fact, the standing vibration, it
may be explained why standing vibrations, and especially the
sounding, are most independent of the first vibration — of the
excitement of the tone; and also why Chladni's figures of sound
are likewise very independent of it. The reverberating vibra-
tion consists of the first intersection of the waves just excited,
and may in many instances coincide with the sounding vibra-
tion ; for which reason also the reverberating figures are often
represented like the figures of sound, (see Savart's former
treatises). One recognizes, however, the figures of reverbera-
tion by a great dependence on the original agitation, ex.gr. on
the direction in which the sounding body is moved. Finally,
it is evident, that vibrations without any acoustic effect may at
times be of the same nature as the sounding and reverberating
vibrations ; for all standing vibrations, for instance such as are
so weak as not to act upon the organs of hearing, belong to
this class.

Supplement to the foregoing Paper. On the Employment of

a resounding Membrane for the Observation of the Interference
of the Undulations of Sound*.

I have stated in an Essay on Savart's Experiment with me-
diately agitated Membranes, (Seep. 340, 341.) that in these
membranes we observe neither an original sound nor a re-
sonance, when an organ-pipe, a bell, a swinging disk, or any
other longitudinally or transversely swinging body of a flat
surface is held before the membrane. I have however suc-
ceeded in making such a membrane resound by simply hold-
ing a tuning-fork before it, so that one prong was held close
to it, parallel with the diagonal line of the square frame. The
sound of a tuning-fork by itself is but slightly heard, or not
at all, at a little distance. But on bringing it in the manner
described towards the membrane, without touching it, the
sound is heard distinctly ; while it is perceived that it pro-
ceeds, not from the fork, but from the membrane.

(With the help of such a resounding membrane I have been
enabled to observe the phenomena of the action of the undu-
lations of sound, the description and investigation of which has
appeared in the Jahrbuch, 1826. iii. p. 385 to 430.)

The sounding of the membrane is in fact very distinct, when
the outside of a prong is turned towards it. It is equally di-
stinct when the two prongs are brought near at an equal di-
stance ; but on turning the tuning-fork gradually from the first
position into the second, we come to a point where the sounding

* From Schweiggcr's Jakrbuch, Band xx. p. 247.

of

Mr. Ivory on the Figure of the Earth. 343

of the membrane suddenly ceases almost entirely ; but on the
fork being turned further, it immediately reappears. If we
distinguish in the prongs of the tuning-fork three different
surfaces; viz. 1. front and back surfaces; 2. side surfaces;
3. end surfaces ; we observe this disappearance of sound at
every transition from a front surface to a side one, and vice
verm: again, in every transition from a front surface to an
end one, and vice versa; but no cessation of sound is per-
ceived in the transition from a side surface to an end one, and
vice versa. These phaenomena are not distinctly audible when
there is any noise, for which reason the experiments will be
best made at night.

The following differences in these phaenomena from those
mentioned in the treatise alluded, to (in the Jahrbuch 1826,
iii. p. 385) are remarkable: 1. That the membrane is a plane
extending far beyond the tuning-fork, and that every point of
it can be agitated with equal facility, whilst the reciprocating
inclosed column of air had only one narrow opening, and
could only resound when the undulations of sound penetrated
through this aperture ; 2. That the membrane did not reci-
procate, and nevertheless showed these phaenomena, whilst
with a column of air not reciprocating, at least if it be narrow,
nothing can be observed.

LI V. On the Figure of the Earth, as deducedfrom Measurements
of different Portions of the Meridian. By J. Ivory, M.Af
F.R.S*
TJ AVING examined the figure of the earth as deduced from
•■--*• experiments with the pendulum, we are naturally led to
consider the same question as it depends upon the measure-
ments that have been made, of different portions of the meri-
dian. If this interesting inquiry be placed within the reach
of the human understanding, and be accessible to our industry,
the two views of it must be consistent ; and, by instituting a
comparison between them, we may both learn what is already
sufficiently well ascertained, and be directed in our future at-
tempts to the most important points that still remain uncer-
tain.

Let a denote the equatorial radius of the earth ; e the ec-
centricity of the elliptical meridian ; <p an arc of the meridian
reckoned from the equator ; and X the latitude of the extre-
mity of $ : then

(1— e*rinax)4

* Communicated by the Author.

If

344 Mr. Ivory on the Figure ofthe'Earih, as deduced from

If we now put */ 1 *- e% « 1 — •«, then e will be the compression
or the ellipticity; arid we shall have,

a(l-t)*.dk
(l_(2s_82) sin*\)4

By expanding this formula and integrating as usual, rejecting
the cube and higher powers of e, we shall get,

f = «• l^-£(i + Tsin2A) + sS(^ +-M- sin*A)}'

And, if p denote an arc of the meridian between the latitudes
V and X ; then

<p = a . { A- A'-£ (j±^ + -| (sin 2 A - sin 2 V))

Further, let n = A — A'
m = x + A'
^ = 57°-2957795

A = f\

then, $ = A . | w — s (~ + ~ p sin n cos w) (A)

+ 8\-Tq + Tg" i7 sm n cos w cos 2w) \ *

In this formula A is the length of 1° on the earth's equator;
and n and the coefficients of g and e2, are reckoned in degrees.
There has been so much discussion about the merits of the
different portions of the meridian that have been determined
trigonometrically, and their character is so well known, that
it would be superfluous to say any thing on that subject here.
The following table, which is taken from a paper by Professor
Airy, in the Phil. Trans, for 1 826, contains the five arcs which
unquestionably deserve the preference, both as they are the
longest that have been measured, and likewise on account of the
excellent instruments employed, and the great care taken in
executing all the operations. But even of these there is one,
namely the Swedish arc, measured by Svuanberg, to which
some objections are made ; because it makes the length of a
degree in latitude 66° 20', more than 200 toises less than it
had been found to be by Maupertuis and the French Acade-
micians who accompanied him. I shall therefore leave out
this arc in determining the elements of the elliptical figure of
the earth ; but, these elements being found by means of the
other four arcs, we may then apply them to the case omitted,

both

• Measurements of different Portions of the Meridian. 345

both as some test of their own exactness, and likewise in or-
der to judge what real ground there is for objecting to the
Swedish measurement.

Country.

A

x'

P

fathoms.

Peru

-0° 2' 31"

8 9 38-39
38 39 56*11
50 37 5-27

3° 4' 32"
18 3 23-6
51 2 9-2
53 27 29-89

188510
598630
751567
172751

India

France

England

Sweden

65 31 30-27

67 8 49-55

98870

Applying now the data of the four first measurements in the
table to the formula (A), the four equations following will be
obtained,

188510= A (3-11750- 6-2261. g+ 3-095. e*)
598630 =A (9-89589-18-1985.6+ 6-163. e8) ,R>
751567 =A(12-37030- 6-2811 .«- 10*266. e2) W
172751 =A (2-84017- 0-3844. s- 2-166. e2).

It is known that e is not much different from ^^, and cer-

e=-^r -M;

We may therefore assume,

300 '

tainly does' not surpass T^.
j_

job * " ' ~ 90000
the correction t being a small fraction which we are sure is
less than 3^. The foregoing equations will now become, by
substitution,

188510= A (3-09678- 6-206 t)
598630= A (9-83530- 18*157/0
751567 =A(12-34925- 6*350*)
172751 =A (2-83887- 0*399*).
In order to find a first approximate value of A, I add the
four equations, neglecting the terms containing t : thus

1711458 = 28:1202. A; A = 60862.

Next, put D =60862, A = D (1 + s) ; then, by substituting
in the four last equations, we shall get,

= '3-097 5- 6-206*

1

D

i)
33

= 9-835 s -18*157*

- ^ = 1 2-349 s- 6-350*

- ~-v= 2-839 5- 0-399*.
New Series. Vol. 3. No. 17. May 1828.

2Y

These

346 Mr. Ivory on the Figure of the Earth, as deducedfrom

These equations are next to be reduced to two, the number of
the unknown quantities, by employing the method of the least
squares : thus

_ il^i - 267*234 5 - 277-342*

+ ——■ = 277-342 s - 408-673 t.

And, by solving these equations,

Ds = — 6; A = D+ Ds - 60856

t = _ -00009, . = 3l0Q + t = -00324 = Jj.

Returning now to the original equations (B), and substituting
the values of A and e, we shall obtain the errors, E(,), E(2),
E(3), E(4), or the quantities that must be added to the given
measurements on the left sides of the equations, in order to
make both sides exactly equal ; as follows,

E(,) = - 20, E2) = + 10, E(3) = - 7, E4) = + 13.

The greatest error is in the Peruvian arc, which appears to
be too great, as has generally been surmised. But the small-
ness of the errors proves the consistency of the different mea-
surements ; and shows that the four portions of the meridian,
although very remote from one another, belong to one and
the same elliptical spheroid.

If we now substitute the data of the Swedish measurement
in the formula (A), we shall get,

98870 + E(3) = A (1-622022 + 0*8378 . ft - 0'022 . s2) :

and, by substituting the values of A and s, it will appear that
the error E(3) = + 5. This measurement is therefore very
consistent with the other four ; and, as it seems liable to no
just objection, it adds to the evidence in favour of the ellipti-
cal elements that have been found.

The degree of the meridian bisected by the parallel of 45°, is
111115 metres at zero of the thermometer. This result is dedu-
ced from the actual measurement of the meridional arc between
the parallels of Greenwich and Formentera, and is indepen-
dent of any assumption about the figure of the earth. To re-
duce this length to fathoms at the temperature of 62° of Fahr.,

oq. ^7070

it must be multiplied by — — — , which gives 60758 fathoms.

Now, if we put A = 45° -f£, X' = 45 — J, we shall have, in
he formula (A), n = 1°, m = 90°, and the length of the de-
gree having its middle point in latitude 45°, wtfl be,

A(,-^-i-,);

or,

Measurements of different Portions of the Meridian. 347

or, in numbers 60856 (1— -001629) = 60757 fathoms, which
is only one fathom less than the observed quantity.

There is also another measurement with which we may
compare the elliptical elements that have been found. A por-
tion of the parallel to the equator in latitude 45° 43' 12", little
short of 13° in amplitude, has been measured, and the most
probable length of 1° of longitude on that parallel has been
fixed at 77865m,75#. The large arc was measured in six
portions, the difference of longitude between the extremities
of every portion .being ascertained by means of signals made
by exploding gunpowder. If we compare the six degrees,
deduced from the several partial arcs, it must be allowed that
their differences are great and irregular f. There must there-
fore be considerable uncertainty in the arithmetical mean of
such irregular quantities; which mean is only three metres
less than the most probable value, of a degree. The length of
a degree deduced from the four partial arcs contained within
the territory of France, which together exceed 7° of longi-
tude, is 77885m,75, or 20 metres more than the length de-
duced from the whole arc of about 13° %. It is to be observed
that the errors of longitude at the intermediate stations accu-
mulate as the arc is extended ; so that there is not the same
advantage in measuring a large arc of the parallel, as in the
case of the meridian ; for, in one instance, the total amplitude
is affected by the sum of the errors at all the intermediate
stations ; whereas, in the other, it is affected only by the errors
of the two extreme latitudes. If we further add that a great
length of the parallel answers to a minute portion of time ; in
so much that an error of a single second in the amplitude of
the large arc, would produce a variation of no small magni-
tude in the mean degree of longitude ; it must be evident that
in point of accuracy, we cannot repose the same confidence in
a degree of the parallel measured in the manner described, as
we can in a degree of the meridian deduced from an arc of
nearly the same amplitude.

The radius of the parallel to the equator at the latitude A,
or the perpendicular drawn to the polar axis, will be found,
by the properties of the ellipse, equal to

a cos X a cos A

And if this expression be expanded and multiplied by — , we
shall have the length of a degree of the parallel equal to

a. * i i i ' <> * . •/ 3 sin 4 A. sin f *. \ 1

A cos X < 1 -f e sin2 A + s ( — -z 3 — ) { •

* Conn, dcs Terns 1829, p. 291. t Ibid. p. 290. J Ibid. p. 293.

2 Y 2 . Now,

348 Mr. Ivory on the Figure of the Earth,

Now, put A — 45° 43' 12", and a degree of longitude at that
latitude, will be equal

42487*8 x(l +-001661)= 42557*4 fathoms.

But 77865m-75 reduced to fathoms at 62° of Fahr. is equal to
42578*2 fathoms, which is 20 fathoms more than the calcu-
lated quantity. If this discrepancy appear very great, we shall
only remark, that it is very small in comparison of the differ-
ences of the degrees deduced from the partial arcs, and that
it supposes not quite so much as 1"J of time, for the sum of
all the accumulated errors in the amplitude of the large arc.
Unless we possessed some means of estimating with tolerable
exactness the error really existing in the degree of the parallel,
the discrepancy we have found can hardly be deemed suffi-
cient to throw any doubt upon the elliptical elements which
agree so well with all the most exact measurements that have
been made on the earth's surface.

If the earth be really an elliptical spheroid, there can be
little doubt that the ellipticity must be very nearly what we
have found it to be. But the solution of the problem would
be greatly improved, and the results obtained would be more
exact and more certain, if the measurement of the meridian
in England were extended as far north as possible. An arc
of 8° or 10° north of Dunnose, would be the most valuable
addition that in the present state of this research can be made
to the data for determining the figure of the earth. Another
very profitable addition would be the extension of the Indian
arc, already the largest we have except the French measure-
ment; and more especially if it could be extended southward
nearer the equator. Supposing the difference between A and
A' to be small, it will readily appear that the coefficient of s in
the formula (A) will be equal to zero, or so small as to render
the term insensible, when

Cos (A + A') = - £ and A + A' = 109° 28'.
Thus if, by means of the formula mentioned, we compute
the expression of the length of an arc extending northward
from Dunnose about a degree beyond Portsoy, to latitude
58° 55' 30", it will be found that the length of this large arc
is almost independent of the ellipticity e, and equal to an arc
of the equator. The reason is that, in latitude 54° 44', the
radius of curvature of the meridian is equal to the radius of
the equator, and the degree of the meridian having its middle
point in that latitude is equal to A , that is, to a degree of
the equator. Thus the length of the portion of the meridian
contained between the extreme north and south points of Bri-
tain depends chiefly on A> and very little on the other ele-
ment

Dr.Wackenroder's Examination of the Diopside qfFassa. 349

ment s ; at the equator, the compression e has greater influ-
ence on the length of a meridional arc, than at any other po-
sition on the surface of the globe ; and it follows that two arcs
of considerable extent, in the situations mentioned, combined
with other good measurements in our possession, must lead
to a very exact determination of the elliptical elements of the
figure of the earth. One remark it seems important to add;
namely, that the ellipticity cannot be determined with any
precision by combining different degrees of the meridian mea-
sured in England ; because the element sought has little in-
fluence on the lengths of such degrees. And this observation
may be extended to all latitudes within 15° or 20° of 54° 44'
on either side; within which limits the ellipticity contributes
only an inconsiderable share to the length of a meridional arc.
And what has now been said will serve to explain the discre-
pancy of the ellipticities deduced by combining different de-
grees of the meridian within the boundaries of England and
France ; and likewise the great variation between the quantities
so obtained, and what is found by the comparison of remote
degrees. These observations may be illustrated by examining
the equations (B). In the English and Swedish measurements,
the coefficients of i are small, and have opposite signs. The
coefficients of the same quantity are nearly equal in the French
and Peruvian arcs, although the former has more than four
times the length of the latter. In the Indian and French
measurements, the coefficients are as 3 to 1, while the arcs
themselves are as 3 to 4 ; and this shows how important it is,
for the exact determination of the ellipticity, to have a large
arc near the equator.

April 12, 1828. J. Ivory.

LV. Mineralogical and Chemical Examination of the Diopside
of Fassa in the Tyrol, By Dr. H. Wackenroder, Pro-
fessor of Chemistry at Gottingen*.

A MONG the various new minerals discovered by Bonvoi-
•f~ sin-j- during a journey through Piedmont, there were two
which this mineralogist considered as distinct species of mi-
nerals ; and he called them, after the places in which they were
found, Mussite and Alalite. According to an account given
by Tonnellier %, Haiiy found in the crystalline form of these
two minerals such a degree of conformity as induced him to

* Communicated by the Author.

t Journ. de Vhys. par Delametherie, torn. Ixii. p. 418, 423.

% Journ, des Mines, torn. xx. p. 65.

consider

350 Dr.Wackenroder's Mineralogical and Chemical

consider them to be one and the same mineral, and which, from
its peculiar crystallographic characters, he presented as a par-
ticular species, of the name of Diopside*, Soon afterwards,
however, Haiiy himself published a memoir, in which, after a
further investigation of this mineral, he proved, from crystal-
lographical reasons, that diopside coincides with pyroxene f.
He also found diopside to agree with pyroxene in its physical
characters f.

Having found the specific gravity of themussite to be 3*2374,
that of the alalite 3*31, and that of pyroxene from Vesuvius
3*3578, he says that the specific gravity of diopside lies within
the limits of that of pyroxene, as indeed the remaining external
characters of the mineral substances hitherto considered to
belong to pyroxene, sometimes differed more from each other
than from diopside. ,

Other mineralogists have grouped diopside, according to
their different views of the systematic arrangement of mine-
rals, with different species, comprehended under augite or py-
roxene. Thus Hausmann§ enumerates diopside among the
formation of the malacolites in the pentaklasite substance;
Leonhard || quotes it as a variety of augite ; Mohs % refers it,
together with the coccolite, fassaite, augite, sahlite, baika-
lite, malacolite, &c. to the paratomous augite-spar, &c. In-
dependent of these well-known classifications of diopside in
the different mineralogical systems, it must form, in a system
founded on the relation of the external characters to the che-
mical composition of the minerals, one of the divisions which,
inconsequence of the experiments made on the substituted con-
stituents, must now be made in the species of pyroxene and
augite. It is in consequence of this that, according to the latest
system of Counsellor Hausmann, the diopside is, considered as
an augitic substance, and as represented by the formula

CS2 + MS9.

To this formation also belongs the diopside which I lately
bought of a dealer under the name of Diopside qfFassa, and
which I subjected to a strict examination, as we do not possess,
to my knowledge, either a chemical analysis or a detailed de-
scription of the diopside of the valley of Fassa.

* Journ. des Mines, torn. xx.

f u Sur l'Analogie du Diopside avec le Pyroxene;'' in the Ann. du Mus.
dllist. Nat. torn. xi. p. 77. Journ. des Mines, torn, xxiii. p. 145.
X Journ. des Mines, torn, xxiii. p. 154, 156.
§ Hanbuch dcr Mineralogie. Band ii. p. 694.
|| In his Hanbuch der Oryktognosie. New edit. p. 50.3.
f In his Grundrus dcr Mineralogie. 2d vol. p. 306.

I. Miner alo-

Examination of the Diopside of Fassa in the Tyrol. 351

I. Mineralogical and Chemical Examination of the Diopside of
the Valley of Fassa.
This diopside, in the state I received it, consisted of single
loose crystals, which appeared to have been attached. They
usually are a couple of inches long, and are mostly compressed,
so as to appear flat. They are generally free from extraneous
substances, and I saw only a few crystals covered on their
surface with laminae of chlorite. But they are found more
frequently covered with a gray tarnish or bloom resembling
iron, which is especially perceptible near the ends, and seems
to have at times come out from the mineral itself, in which
case it also seems more intimately connected with it.

I am indebted to the obliging kindness of my respected
teacher Counsellor Hausmann, for the following crystallo-
graphical communication on the diopside of the valley of
Fassa.

" The crystals of diopside, usually broken at the ends, pre-
sent themselves most frequently as rectangular prisms, the
greater sides of which are more or less striated longitudinally,
whilst the other sides are either smooth or slightly striated.

" The appearance of planes replacing the lateral edges ex-
plains the nature of the surface of these rectangular prisms.
For the planes agreeing with the planes E of the prism of au-
gite, which, according to Haiiy, are respectively inclined at
92° 18' and 87° 42', the narrower planes of the sides which
form with the replacing planes an angle of 136° 9', present
themselves as the planes B', and the broad ones as the planes B.
" Sometimes the planes BB' 3 (f) appear perfectly formed,
making with each other angles of 141° 44?' and 38° 16'. A
disposition to the formation of these planes is distinctly dis-
covered in the deep striation of the planes B.
" The observed combinations are :

2 B'. 2 B

2 B'. 2 B. 4 E.

2B'. 4BB'3.

2 B'. 2 B. 4 BB'3

2 B\ 4 E. 4 BB'3.
" The respective inclinations of these planes are, the angles
given by Haiiy being taken as the basis,

B' - B = 90° 0'

B' - E = 186 9

B - E = 133 51

B' - /= 109 8

B - /= 160 52

E - /= 152 59

/ - / = 141 44

Sometimes

352 Dr.Wackenroder's Mineralogical and Chemical

" Sometimes a combination of several individual crystals is
seen. One end of the crystals is always fractured, while the
other often shows a tendency to a summit.

" Besides the marked cleavages of E', those of B' and B are
also perceptible. Besides the cleavages, we perceive fissures ;
also transverse fissures, which are sometimes irregular and
sometimes corresponding to the planes D'."

The fracture of diopside is imperfectly conchoidal and splin-
tery. The angular pieces which are detached from it are fre-
quently tabular and prismatic.

Its colour is a pistachio-green or olive, but sometimes runs
in the same prism from greenish white to colourless.

The crystals are usually translucent only, sometimes trans-
parent. Small detached laminae can always be seen through,
and are slightly coloured. The fissures in the interior of the
crystals sometimes produce a play of colours.

I have not been able to perceive a double refraction in these
crystals. The external planes as well as the cleavage-planes
show a glassy and pearly lustre. It scratches fluor spar, and is
scratched by felspar.

According to Brewster, diopside will show signs of electri-
city ; but neither by heating nor by rubbing it, have I been
able to discover any electricity in this variety. As little does
this diopside act on the magnet. Its specific gravity, at 59°
Fahr. is = 3*299. A piece strongly striated not belonging
to the purest portion, gave at the same temperature a specific
gravity of 3*296 ; and one almost white, covered at one end with
the above-mentioned bloom, a specific gravity of 3*277. Heated
in a platinum spoon, the diopside of Fassa loses its peculiar
green colour, but suffers no further change.

In the flame of the blowpipe, sharp splinters of it are rounded
at the edges, but by means only of a very strong heat ; while
thick pieces only become of a dirty green colour. With borax
it is dissolved very slowly and without colouring the bead.

Carbonate of soda at a red heat dissolves it with ebullition,
and gives a bead of a reddish colour. Phosphate of soda
mixed with the mineral in powder, and melted before the
blowpipe, yields a dark yellowish bead. On charcoal with
nitre it yields a greenish mass, which by further heating as-
sumes a dirty reddish colour. Concentrated sulphuric acid,
muriatic acid, or nitric acid, does not dissolve the diopside.

II. Preliminary analytical Experiments.

A certain quantity of pulverized diopside ignited with thrice
the quantity of carbonate of soda freed from water, gave a
half-melted mass, which was dissolved in water and muriatic

acid.

Examination of the Diopside of Fassa in the Tyrol. 353

acid. The solution having been evaporated to dryness, and
the residuum digested with water and muriatic acid, a large
quantity of silica remained undissolved.

Carbonate of soda precipitated from the solution when cold
some oxide of iron with a few traces of alumina ; but oxalate
of potash precipitated much oxalate of lime, which was partly
ignited and partly mixed with caustic ammonia. A very small
quantity of deutoxide of manganese was found mixed with the
lime. After this, carbonate of magnesia together with a little
manganese was precipitated, by means of carbonate of soda,
from the hot solution ; and subsequently, by means of triple
phosphate of soda and ammonia, a considerable quantity of
magnesia.

Again, about 2*0 grammes of pulverized diopside were fused
with carbonate of soda and l-6th of its weight of nitre. Water
gave with the melted mass a greenish solution, which soon
completely lost its colour in the air ; and on being tested for
the chromic, fluoric, phosphoric and boracic acids, no trace
of either was perceptible.

III. Analysis for the Proportions of the Constituents.

a. 2' 502 grammes of select and very pure pieces of diopside
dried on a hot iron plate, were exposed for three quarters of an
hour to a red heat. But the mineral was unaltered in appear-
ance and weight, except that its colour turned nearer bottle
green.

b, 2*503 grammes of the diopside finely powdered, were inti-
mately mixed with thrice their weight of carbonate of soda freed
from water and exposed for half an hour to a moderate red
heat The fused mass was dissolved in a moderate quantity of
water, placed in an evaporating-dish, and diluted with as much
muriatic acid as was necessary to effect a perfect solution. By
the evaporation to dryness of the yellowish solution, and by
digesting the residuum (which was of the same colour) in water
and some muriatic acid, pure white silica was obtained, weigh-
ing, after having been dried and heated, 1*3581 gramme. It
was completely dissolved in a solution of caustic potash, as well
as in a concentrated solution of carbonate of soda assisted by
heat ; and after having stood for some time, only a few unim-
portant flakes were deposited from this solution. A part of it
only was dissolved in caustic ammonia, but the remainder was
entirely taken up by carbonate of soda. It will be worthy of
a distinct investigation to ascertain the cause of this pheno-
menon *.

* Dr. C.F. B. Karsten has also mentioned the facility with which silica is
dissolved in caustic ammonia. See Poggendorff 's Annalen, Band vi. p. 357.

New Series. Vol. 3. No. 17. May 1828. 2 Z c. The

354- Dr. Wackenroder's Mineralogical and Chemical

c. The solution having been copiously diluted, was mixed
first, in the cold, with carbonate, and then with bicarbonate of
soda, in order to separate the oxide of iron and alumina. The
precipitate was then slightly heated, and again dissolved in
concentrated muriatic acid. There remained a small quantity of
silica, which after having been heated, weighed 0*002 gramme,
and remained unaffected even after a continued digestion in
sulphuric acid.

d. The solution of iron in (c) was abundantly mixed with
caustic potash, and the precipitated hydrate of iron separated
and slightly heated. The 0*0701 gramme of pure oxide of iron
calculated for protoxide, in which state the iron evidently exists
in the mineral, give 0*6029 gramme of protoxide, if the equiva-
lents of the two oxides bear the proportion to each other of
39 to 35.

e. Carbonate of ammonia, with heat, precipitated from the
solution (d)9 which had been saturated with muriatic acid, the
alumina contained in the mineral ; which, after the burning of
the filtre that had been used to separate it, and after deduct-
ing the ashes of the latter, consisted of no more than 0*005
gramme.

f. In order to separate the manganese from the liquid (e)
which had been treated with carbonate of soda, I made use of
the method lately pointed out by Counsellor Stromeyer*. Ac-
cordingly the solution, in consequence of the small quantity
of manganese it contained, was first reduced by boiling to a
smaller bulk, saturated with chlorine gas, and then mixed
with as much neutral carbonate of soda as was necessary to
precipitate the deutoxide of manganese, and render the solution
colourless. The precipitate having been dried off for forty-
eight hours, and then collected on a filtre and heated, amounted
to 0*0027 gramme of deutoxide of manganese, which, according
to the equivalents, 39*17 for the deutoxide, and 36*5 for the
oxide, indicate 0*0025 gramme of the latter, it being requisite
to assume that the manganese is in this state of oxidation in
the mineral.

g. The solution having been again concentrated by boiling,
it was mixed with as much oxalate of potash as was necessary
to precipitate the lime ; and the precipitate separated as soon
as possible by filtering, its separation having been promoted
by a small addition of oxalic acid. The oxalate of lime ob-
tained was made red hot, in order to destroy its acid,
again dissolved in nitric acid ; and the solution mixed with
caustic ammonia freed from carbonic acid, gave a slight pre-

* Gotting. Gelehrte Anzeigen. St. 158. October 1827.

cipitate.

Examination qfthe.DiopsideofFassa in the Tyrol. 355

cipitate. This when made red-hot amounted to 0*0024 gramme,
and consisted of deutoxide of manganese, which reduced to
oxide, according to the proportion of these two oxides as-
sumed above, is equal to 0*0022 gramme of oxide of man-
ganese.

The reason of this small quantity of manganese yet being
found, is the facility with which, on its being separated from so-
lutions by means of chlorine, a small portion of it is redissolved,
when the precipitate is left in contact with the fluid beyond
the time necessary for its formation, during which a little mu-
riatic acid may be produced.

k. The nitric solution of Jime was now, while boiling, mixed
with caustic ammonia and carbonate of ammonia. The pre-
cipitated carbonate of lime gave, after heating, 0*6064 gramme
of pure caustic lime, which was completely soluble in greatly
diluted nitric acid, and with little effervescence.

As in precipitating the lime with carbonate of ammonia,
especially without a sufficient addition of caustic ammo-
nia, small quantities may easily be left suspended, and the
carbonate of lime not being quite insoluble in the water used
for washing it ; — the solution having been much boiled down,
was again tested with oxalate of potash, and by means of it a
little more oxalate of lime was precipitated, but which, when
made red-hot, yielded only 0*0150 gramme of caustic lime.
Consequently the entire quantity of pure lime separated amounts
to 06064. + 0*01 50 = 0*6214 gramme.

i. In order to separate the magnesia from the solution
(g),the former was acidulated with muriatic acid, concentrated
by boiling, and mixed with phosphate of soda and caustic
ammonia. At the expiration of about twenty-four hours the
crystalline deposit was collected and heated : it weighed 1*1790
gramme.

After a second similar treatment, rendered necessary by the
easy solubility of the substance in a large quantity of water,
even if the latter should be mixed with some caustic ammonia,
which may perhaps itself promote the solubility by the access
of carbonic acid from the atmosphere, — another precipitate was
obtained weighing, after being heated, 0*0582 gramme. Con-
sequently the whole of the phosphate of magnesia obtained
amounts to 1*2372 gramme ; in which, if 100 parts of this salt,
heated, indicate 37 parts of magnesia*, 0*4577 gramme of
the earth are contained.

* See the above-mentioned Essay of M. Stromeyer.

2 Z 2 Conse-

356 Dr.Wackenroder's Mineralogical and Chemical

Consequently, 2*503 grammes of the diopside of Fassa are
composed of

Silica (b) 1-3581 \

(c) 0*0020/ J Jb01gramme'

Lime (h) 0*6214

Magnesia (i) 0*4577

Protoxide of iron (d) 0*0629

Oxide of manganese . . (f) 0*0025 \ ft.nai7

(g) 0*0022 |uuu*'

Alumina ,.(e) 0*0050

•xygen.

?7*07")
6*94 VU-i
7*28 J
0*54)
0*05 > 0*1
0*09 )

2*5118 grammes.
Accordingly, 100 parts of this diopside contain,

Oxygen.

Silica 54*154 27*

Lime 24*740 6*94

Magnesia 18*222

Protoxide of iron .... 2*504

Oxide of manganese .. 0*183 0*05 } 0*68

Alumina 0*195

100*001
If as the essential constituents of the diopside we take only
silica, lime and magnesia, the composition of this mineral
is to be expressed by two single bisilicates of lime and magnesia.
But this expression presupposes 2*74 per cent more silica than
the analysis has furnished; which difference, however, will be
reduced by one per cent, if we assume in the magnesia 38*71
per cent of oxygen ; consequently assume in the quantity of
magnesia found 7*05 parts of oxygen, instead of putting 20 as
its equivalent, as we have done in conformity with Gmelin's
latest Handbuch der Chemze, whose statement of equivalents
has been followed throughout in this calculation.

If we wish yet to take into consideration, that, if the pro-
portion of magnesia should be diminished by so much as was
precipitated in the analysis («), but the omission of which may
have been assumed by chemists for the calculation of the cal-
cined magnesia, the magnesia first obtained would then con-
tain very nearly as much oxygen as the lime: we have ex-
actly such quantities of the principal constituents of the diop-
side, that the latter may be exactly expressed, in a chemical
point of view, by the symbols,

(CaO + 2S*0) + (MgO + 2S* O) ;

and in a mineralogical one by

CS2+MS2.

The

Examination of the Diopside of Fassa in the Tyrol. 357

The composition of the mussite indeed, according to Lau-
gier*, differs considerably from that of our diopside : we might,
however, presume that this difference partly arises from the
less perfect state of chemistry with respect to those substances
in Laugier's time. It is possible, too, that the same circum-
stance has produced the smaller difference from the composi-
tion of our mineral which appears in the analysis of the ma-
lacolite or sahlite examined by Vauquelin f.

Among the other existing analyses of minerals referred to
pyroxene or augite, according to which other formations of
augite-substance are proved, we must consider, with respect
to the diopside of Fassa, several examinations made by Von
Trolle Wachtmeister Hisinger, Von Bonsdorf, and H. Rose.
From the comparison of the results of these analyses enume-
rated in the well-known treatise of Professor Rose, " On the
Pyroxene J," with those of the analyses just-mentioned of Lau-
gier and Vauquelin, and with those obtained by me on the
composition of the diopside of Fassa, for which purpose I have
prepared the following table ; it seems that all the minerals
thus examined, may be referred to the diopside, and their com-
position expressed by the formula CS3-f MS2.

Mag-
nesia.

Oxide

Ox. of

Alu-
mina.

Loss

Analyses.

Silica.

Lime.

of
Iron.

Man-

ganese.

by

Heat.

Total.

Laugier. — Mussite of Piedmont

57-5

16-5

18-25

6 with

98-25

Von Trolle Wachtmeister. — }

ox. ma.

White malacolite from the >

57-40

23-10

16-74

0-20

0-43

...

97-87

TafelTjotten, in Norway... )

protox.

H. Rose. — Yellowish malaco- 5

lite from Langbanshyttan >

55-32

23-01

16-99

2-16

1-59

...

...

99-07

in Warmland )

Hisinger. — Malacolite from )

Langbanshyttan in Warm- >

land )

H. Rose. — Greenish sahlite \
from Sahla $

54-18

22-72

17-81

2-18

1-45

...

1-20

99-54

54-86

23-57

16-49

4-44

0-42

0-21

...

99-99

Von Bonsdorf. — Perfectly )

protox.

white malacolite fromTam- >

54-83

24-76

18-55

0-99

0-28

0-32

99-73

mare in Finland )

H. Rose. — White malacolite ^
from Orrajerwi in Finland )

5464

24-94

18-00

1-08

200

...

100-66

H. Wackenroder. — Diopside \
from Fassa in the Tyrol ... \

54-154

24-740

18-222

2-505

mang-
0-183

0-198

...

100-001

Vauquelin. — Malacolite or \
sahlite S

53-00

20-00

1900

protox.
4-00

with ox.
mangan.

300

...

99-00

* Ann. du Mus. d'Hist. Nat. torn. xi. p. 153.

JHaiiy, Traite de Mincralogie, 1st edit. vol. iv. p. 382.
Schweigger's Journ.f. Chem. u. Phys. Band xxxv. p. 86. &c.

LVI. De-

[ 358 ]

LVL Description of a Shell, exploding by Percussion when

trod upon. By Lieut. -Col. Miller, F.R.S.*
'T'HIS is a very simple contrivance, and will easily be un-
-■" derstood from the figure. A spring is attached to the
upper part of the shell, which produces ignition by falling on
a copper cap ; and a support is placed under the spring, moving
on a hinge, with a handle attached to the support ; so that by
treading on the handle, the support is withdrawn, the spring
falls, and explosion follows. The sides of the shell must be
of equal thickness, for the better splintering; and as an oval
form will be the most convenient for fixing the spring. The
following construction is given :

Length of shell 8 inches.

Breadth of ditto 5*5

Depth of ditto 5

Length of chamber 6

Width of ditto 3*5

Height of ditto 3

Length of spring 6

Fall of ditto 1

Length of handle from 10 to 30.

Vertical section of shell when cocked, taken lengthwise.

Shells of this description, it is conceived, might be made to
perform the duty of sentinels on many occasions, by giving
notice of the approach of an enemy, and presenting a con-
siderable obstacle to his advance by their explosion. They
might accordingly be used with advantage in the ditches of

Communicated by the Author.

fortresses,

Mr. Kingston on the Iron Mine at Hay tor, Devon. 359

fortresses, before breaches, and to defend bridges and passes,
wherever an enemy is likely to attempt a surprise. They
might also be placed around field works likely to be at-
tempted by assault. They would require to be sunk a little
in the ground, so that the splinters of one might not derange
those near to it, and covered lightly over to protect them from
wet, and also to conceal their position from an enemy.

This principle might also be applied to the firing of artil-
lery by percussion ; more particularly at sea, where the roll of
the vessel presents so great an obstacle to accuracy of fire. In
that case, the vent of the gun would require to be placed a
little on one side, to be clear of the line of sight, and a hole
drilled through the spring opposite the vent, to allow the flash
from it to escape. The support of the spring would, of course,
be pulled away by a string, so that the man who laid the gun
might also fire it.

LVIL Account of 'the Iron Mine at Hay tor, in Devonshire. By
J. T. Kingston, Esq.

To the Editors of the Philosophical Magazine and Annals.

Gentlemen,

A MINERAL production discovered at the Haytor Iron
■**■ Mine having formed the subject of two or three papers
in your valuable Journal *, you may perhaps consider a de-
scription of the mine itself not unworthy of occupying a page
or two of your next Number ; especially as it is, at least to
the best of my knowledge, the only one of the kind hitherto
discovered in this island, and as such, of some importance in
a geological as well as in an ceconomical point of view f.

The lode, to the depth at present explored, is a very regu-
larly stratified one, of oxidulated iron ore and argillaceous
schist, in alternate beds ; and is situated on the edge of the
granite district, near the base of the Haytor rocks. The hill,
on the brow of which, near the centre, it crops out, is imme-
diately incumbent on the granite ; its principal slope is gra-
dual and towards the East, the sides having a more precipi-
tous descent to the North and South. It consists chiefly of
micaceous passing into clay schist, and of trapf (provincially

* See Phil. Mag. and Annals, N.S. vol. i. p. 38, 40, 43.

\ Some particulars of the vein of ore worked in this mine, will be found
in Mr. W. Phillips's paper on Haytorite, which is the first of the communi-
cations just referred-to. — Edit.

\ Mr.W- Phillips, we observe, has stated that this substance appears to
be siliceous schist. — Edit.

termed

360 Mr. Kingston's Account of the Iron Mine

termed Ironstone) of a compact basaltic texture, and great spe-
cific gravity ; and mostly containing a proportion of iron-ore,
which occasionally runs in distinct threads and patches through
small portions of it The lode occurs in the clay schist, and
the direction of its strata is nearly North-west and South-
east, underlying to the North-east at an angle of 22° or 23°
only for the first few feet from the surface ; but below this the
dip is very regular at an angle of 45°. It happens to be si-
tuated in two distinct estates, which a road, intersecting the
lode near the centre, divides ; and having hitherto been worked
separately, a complete wall from the surface to the depth ex-
plored, has been left, of which the following is an accurate
section and measurement; the measurement is taken at the
depth indicated by the dotted line, which is also the direction
of the level driven from the back of the lode.

Thickness of Beds.

No.

Ore.

Schist.

1

ift oin-

2

Qft. gin.

3

.1 3

4

1 3

5

1 3

6

2 0

7

0 6

8

2 6

9

8 0

10

3 6

11

2 0

12

1 3

13

0 6

14

1 0

15

1 6

16 feet ore.
1 2 feet schist.

26 feet whole width of lode.

By

at Hay tor ^ in Devonshire, 361

By this it will be seen, that the central bed is of iron-ore,
and considerably the largest ; whilst the other alternating beds
of schist and ore are disposed above and below it in a tole-
rably regular relative proportion. The schist having a ten-
dency to contract in width, as the depth increases, and the ore
to approximate each way towards the central bed, into which,
the obvious probability is, that the other beds, at a greater
depth, run ; but whether this is the case, or whether, if they
do so, the central bed is proportionally increased, must of
course remain uncertain, until a level is driven, which I un-
derstand it is proposed to drive from the northern ravine, and
which would cut the lode at about 150 feet perpendicularly
below the surface. Permanent springs rise at the depth of a few
feet, the water from which is carried off by a syphon bent over
the northern slope of the hill. A level driven from the back of
the lode, at the depth of about 20 feet from the surface, through
schist, in a south-west direction, intersected, about 30 feet from
its commencement, another small bed of ore, about 3J feet in
width, in which a large proportion of iron-pyrites is dissemi-
nated, the dip being the same as that of the principal lode, with
which, however, it does not seem to be connected ; the latter
being included in a well-defined manner, within the limits
pointed out by the above section, from which the width will
be seen to be about 28 feet. The length, of course, is not ca-
pable of being so accurately defined : from the part where the
section was taken on the western side, the traces are observa-
ble on to the granite, a distance of 230 yards, which they do
not enter, but are conformable along its edge for some distance
in a northerly direction ; and on the eastern or lower side,
it has been traced for the distance of 250 yards, down to a
compact stratum of trap*, blended with garnet and actinolite,
against which the traces appear to have been hove in a zigzag
curved manner, and to dip under it. The length however of
the beds containing ore of a quality available for smelting, does
not (at least to the depth at present excavated) exceed 150
yards.

The surface along the whole line of the lode, as well as on
each side of it, is apparently regular and undisturbed, and con-
sists of a loose head of flat schistose stones and fragments,
and the earthy mould arising from their decomposition, to the
depth of five or six feet. In this head, at either end, along the
line of the lode, bunches of manganese contaminated by iron
occur. Near the central part of the lode an old sinking was
discovered to the depth of 42 feet on one single bed of the

* See former note on this substance.— Edit.
Ncxq Series. Vol. 3. No. 17. May 1828. 3 A ore.

26V Mr. Kingston's Account of the Iron-Mine

ore. There remain no records in the neighbourhood, as to
when or for what purpose this excavation was made ; but the
probability is, that it was mistaken for tin, old stream-works
for obtaining which abound in the neighbourhood. Only a
small portion (if any) appears to have been carried off; as the
chief part was left in heaps, and strewed on the surface to the
extent of two or three acres immediately round, and which in
fact led to the discovery of the mine, and remained unaccounted
for some time after.

The chief part of the ore is of a compact texture, but por-
tions of it, especially on approaching the surface, are coarsely
granular ; more or less perfectly formed crystals, loosely ag-
gregated, are also frequent. The per-centage of iron it con-
tains varies from 40 to 70 (the average probably of what has
hitherto been worked yielding in the large way about 50); some
of the richer specimens are actively magnetic; when pulve-
rized, the ore is brownish black, and passively magnetic. It
occurs also mixed with sulphur and with arsenic, in coarsely
granular masses. Spathose carbonate of iron and also iron-
pyrites are met with ; the latter, either in decomposing granular
concretions, radiated, in more or less perfect cubic crystals,
and in small spangles disseminated through the coarser gra-
nular ore. Copper-pyrites and arsenical pyrites also occur,
the former very sparingly.

The other mineral specimens discovered in the faults and
cavities of the lode, and in the loose head immediately above
it, having excited considerable local attention, I shall (with
your permission) give as complete an enumeration of them as
I am able, though a minute and lengthy description would be
equally tedious and unnecessary ; as they are chiefly aqueous
depositions of siliceous and aluminous matter, coloured by the
oxides of iron and manganese, and do not essentially differ from
other formations of the same kind of frequent occurrence in other
mining districts ; for as to the statement, that precious gems,
&c. had been discovered there, that being now admitted to
have originated in a mistake, no further notice need be taken
of it.

Quartz — Occurs in a granular form, in corroded amorphous
masses, in thin plates crossing each other at right angles (cel-
lular quartz), stalactitic and crystallized. The crystals are all
secondary, and mostly hexagonal prisms, terminated by an
hexagonal pyramid ; the faces generally unequal. In some
the pyramid is nearly triangular, the alternate angles being
deeply replaced by planes. In some the edges, either of the
prism, or pyramid, or both, are bevelled ; occasionally very
regular prisms, terminated by a pyramid at each end, are met

with,

at Haytor, in Devonshire, 36S

with, and in some specimens the prism is so shortened that
the pyramids appear to be nearly joined base to base. Co-
lumnar hexagonal prisms of opaque quartz are of frequent
occurrence, forming the nucleus, round which the other cry-
stals are often clustered, or stalactitic chalcedony deposited.
Of the transparent crystals, some are colourless ; of the rest,
the colours are ferruginous (this most common), clear topaz
yellow, dark red passing into black ; smoky brown (cairngorm) ;
various shades of purple, violet, or rose-pink (amethystine
quartz), and bright ruby red : these last are minute and very
perfectly formed crystals, lining cellular quartz. The finest
specimens of the amethystine quartz occur (very sparingly) in
geodes, in the loose head; the rest are found clustered in
rounded, reniform, or radiated masses, lining cavities, and in-
vesting and invested by chalcedony.

Flint — In amorphous masses, and passing into chalcedony,
&c; the colours mostly ferruginous, or brownish black.

Chalcedony — Passing into and also investing crystallized
quartz ; stalactitic (this occasionally incloses distinct globules
of water), mamillated, botryoidal, and lenticular. The prevail-
ing colours, various shades of ferruginous brown passing al-
most into black ; but occasionally, specimens are met with of
clear yellow ; pure milk-white, passing into pearly and trans-
lucent white ; caerulean, passing into peach-colour, and light
gray ; and fine plum-colour (the last from a bunch of manga-
nese). Frequently two or three successive coatings, some-
times of the same, sometimes of distinct colours, invest each
other, between each of which a thin lining of clay is often in-
terposed ; some of the white and caerulean varieties are hydro-
phanous; others have a very delicate coating of aluminous
matter, which causes their colour to deepen considerably on
the application of moisture. Pseudo-morphous crystals of this
substance also occur, formed within cavities from which other
crystallized substances have been by some natural cause, (pro-
bably solution,) removed. Irregular masses of siliceous mat-
ter that have obviously invested, either wholly or partially, cry-
stals of iron-ore. Iron-pyrites, quartz or garnet, are of frequent
occurrence. I have specimens of the substance in moulds of
this kind, and conceive that much of (if not all) the Haytorite
(as those crystals have been named) is referable to some of the
different forms of the above substances, and is chalcedonic
matter filling the said cavities by stalagmitic deposition ; some
of the faces of the crystals are very splendent, others rough ;
in some of the crystals all are rough : the fracture is different
from that of a true crystal, nor have I ever succeeded in ob-
taining a regular cleavage ; the crystals are of various sizes ;

3 A 2 the

364 Mr. Kingston's Account ofthe Iron-Mine at Haytor.

the sides of the planes in some exceeding an inch, in others
scarcely l-8th of an inch. They are mostly found in a matrix
of ferruginous clay, in juxta-position with massive chalcedony,
quartz, and specular iron.

Semi-opal — Mostly in irregularly rounded nodules, invested
by indurated clay (lithomarga). The colours, various shades
of blue, green, or yellow, occasionally all passing into each
other in the same specimen, or forming distinct stripes. It
also frequently alternates in stripes with the indurated clay.

Garnet — Massive, blended with actinolite, &c. in the lode,
and especially at the eastern end ; and crystallized, mostly in
rhomboidal dodecahedrons, and their modifications. The co-
lours, various shades of yellowish or reddish brown, passing
into black minute crystals, occur (rarely) on the surface of the
ore under glassy actinolite. Most of the crystals are coarse,
and of inferior size.

Actinolite — Intimately blended with the ore, in amorphous
masses, and in distinctly radiated clusters, the radii from l-8th
of an inch to an inch in length : the colours varying from a
light to a very dark green. A thin variety, with a vitreous
lustre, occurs sparingly on the surface ofthe ore. Actinolite
is very abundant, and gives a greenish hue to a large portion
of the ore. It is most prevalent in the upper and under beds,
and seems to increase with the depth.

Some fine cabinet-specimens of all the above species have
been found ; an interesting series of which (the most complete
I believe that has been formed) is in the possession of Shirley
Woolmer, Esq. of Exeter.

The ore, when melted, produces iron of a very tough and
superior description, as I have myself proved by some experi-
ments. It is also stated, on good authority, to be capable of
conversion into excellent steel ; but the purpose to which it
has hitherto been applied is that of mixing with the argillaceous
ironstone ofthe Welch coal-measures, to improve its quality;
for which, I understand, it is preferable to the hematitic ores
of Lancashire ; and this, I should suppose, will be the pur-
pose that it will ultimately be found most practically available
for; as its distance from proper fuel (the Bovey coal, situated
within three or four miles of it, from some late experiments
that have been made, giving very little hope of being efficient
for the purpose of smelting, and the Dartmoor peat being at
too great a distance) would probably be an effectual obstacle
to the erection of any works in the neighbourhood, even sup-
posing a less limited quantity of ore to exist, than at present
appears to be the case. But this is a part of the subject on
which I am incompetent to treat, and it is besides foreign to the

object

Mr. Mageough's Method of mounting Thermometers. 365

object of this communication, which is to illustrate a small
portion of a district, that in the circle of a few miles (taking the
large clay-deposit of Bovey-heath as a centre) is perhaps, in a
geological point of view, one of the most interesting districts in
the kingdom. And I propose (in conjunction with J. G. Croker,
Esq. of Bovey Xracey? wno nas f°r many years paid great
local attention to the subject), if consistent with the plan of
your Journal, to make it the medium of two or three commu-
nications (accompanied by sections, &c), pointing out carefully
the different strata, their extent and junction, and the lodes,
as far as explored, that occur in them. To this gentleman, as
well as to Mr. Petherick the superintendent of the iron-mine,
I am indebted for much valuable assistance in drawing up the
present paper. I remain, Gentlemen,

Your most obedient servant,
Ilsington, Devon, April 9, 1828. J. T. Kingston.

LVIII. Account of a new Method of mounting Thermometers.
By Mr. W. Mageough.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,
T I ''HE following is an account of a method of mounting the
-*• thermometer-tube, in order to make it applicable to pur-
poses for which, as fltted-up at present, it could not be used.

This method has not, that I know o£ been hitherto prac-
tised in making thermometers ; but about two years since, the
same principle was successfully applied to barometers.

Mounted in this manner, the tube may be made of earthen-
ware or metal, as well as of glass ; it may contain metals or
other substances which will expand by heat; and by a little
management be introduced into, and made to indicate degrees
of temperature, that would speedily destroy thermometers of
the ordinary construction. The present account relates only
to tubes of glass, such as are generally used for making ther-
mometers, without any other condition, than that the size be
adapted to the purpose proposed to be effected by the instru-
ment. If large enough, it will move with sufficient force to give
notice when the apartment where it is placed attains a given
temperature, by touching a light lever connected with the sort
of alarum-machinery often put into the cheapest clocks. Or, a
prepared paper maybe made to pass over a hair-pencil, charged
with a liquid not liable to dry or freeze, which pencil, by means
of a simple addition to the hour-movement of a common clock,

will

366 Mr. Mageough's Method of mounting Thermometers.

will trace on the paper all the changes in temperature occur-
ring through twelve or twenty-four hours.

But, where nothing more is required, the highest and lowest
degrees of temperature happening in a given time may be
registered by the assistance of a couple ol fine slips of light
wood, or two bristles, poised on axles, the ends being brought
over the circular scale so as to come in contact with a catch
fixed on the tube.

Let AB, fig. 1. represent a thermometer tube, containing
the mercury, and being marked at the boiling and freezing

c\\

points. Such tubes are easily obtained at the opticians. Let
C be the centre of gravity when the mercury is at the freezing,
and c the centre of gravity when it is raised to the boiling-
point; S is the place of an axle fixed across the tube, and
resting in two hooks or rings, one of which is represented in
the figure at the termination of the wire PS. Suppose the
point S to be in a perpendicular to the axis of the tube, erected
at the point c ; then it is clear that when the mercury rises to
the boiling-mark, the centre of gravity moves into c, this point
will therefore get into the perpendicular to the horizon under
S, and put the tube AB into the horizontal position, as shown
in the figure. Again, when the mercury sinks to the freezing-
mark, the centre of gravity coming into C will cause that point
to get into the perpendicular under S, and put the tube into
the position A'B': the arch A A' through which the end of the

tube

Mr. Mageough's Method of mounting Thermometers. 367

tube has moved, measuring an angle equal to 90° less by the
angle cCS.

If the arch AS and the tube be graduated, the correspond-
ing divisions are easily noted as the mercury rises or sinks,
and the divisions can be marked on the former at leisure.

Because in the tubes commonly to be obtained, the distance
cS, of the point of suspension above the axis of the tube, must
be very small, the adjustment is rendered comparatively easy,
by making the axle of a piece of thin steel wire bent in the
form of fig. 2, the inner part of the curve being as nearly as

possible half the circumference of the tube ; the curve being
underneath, the axle is fastened to the tube by a thread wound
four or five times round both, and they may be secured from
slipping by a drop or two of varnish. Now it is evident that
by increasing or diminishing the distance between the points
of support or bearing hooks, the centre of gravity c will be
more or less sunk below the points of suspension S, and the
distance c S will be obtained without the trouble of filing. A
knife-edge is however undoubtedly preferable to the wire.

To find the centres of gravity on the tube, it is only neces-
sary to sling it in a horizontal position, by means of a thread
fastened to it at each end, and put over a pin : then a plumb-
line, hung from the same pin, will cross the tube at the centre
of gravity, the place of which should be marked on the glass
by a file or diamond. The arch VPV may be of pasteboard,
wood, or metal, and should be attached to the wires SP. At
P is a loop or ring by which the instrument is suspended.

If the figure of the tube be altered, and the bulb contain
spirits of wine in the upper part and mercury in the lower, it
is evident the distance between the centres of gravity at any
two temperatures, and consequently the power of the instru-
ment, will be much increased. The shading in the subjoined
figure shows the portion of the bulb and tube to be occupied
by the quicksilver when the temperature is low.

Fig. 3.

It may be added that thermometers of this construction might
perhaps advantageously accompany wheel-barometers in large
apartments or halls. I am, Gentlemen, &c.

Feb. 23, 1828. W. Mageough.

LIX. 2Vb-

[ 368 ]

LIX. Notices respecting New Books.

Part I. of a Descriptive Catalogue of the Lepidopterous Insects con-
tained in the Museum of the Honourable East-India Company, Il-
lustrated by Coloured Figures of New Species and of the Meta-
morphosis of Indian Lepidoptera, with Introductory Observations
on a General Arrangement of this Order of Insects. — By Thomas
Horsfield, M.D. F.R.S. L.S. & G.S. Member of the Royal-
Asiatic, and Zoological Societies of London, and of the Imperial
Academy Naturce Curiosorum ; Corresponding Member of the
Academy of Natural Sciences of Philadelphia, and of the Histo-
rical Society qf Pennsylvania, fyc. To be completed in Six Parts.

THE subjects which this work will bring before the public are
arranged in the Museum of the Honourable East-India Com-
pany. They consist principally of a general series of Lepidopte-
rous insects from the island of Java, accompanied by an exten-
sive set of drawings representing their metamorphosis, the history
of which is detailed in the Introduction. To this will be added
various subjects contained chiefly in a collection of insects from
Ceylon, presented by M. Jionville, and in a smaller miscellaneous
collection from continental India, presented by Claude Russell,
Esq., the brother of Dr. Patrick Russell. It is likewise the author's
intention to include such additions as may be made from time to
time to the Museum during the progress of his work, from the ter-
ritories of the Honourable Company in the Eastern World.

The work will be published in royal quarto, and will consist of
six parts, each containing about eighty pages of letter-press; the
distribution of the subjects being the following :

Part I. Introduction : detailing the outline of a general
arrangement of Lepidopterous insects according to their
metamorphosis. Description of the First Tribe, or of the Le-
pidoptera Diurna. Stirps the Jirst, with Vermiform
Larvje. Genera Polyommatus and Lyccena.
Part II. Conclusion of the Vermiform Stirps. Second Stirps
of Lepidoptera Diurna with Chilogn athiform or Iuli-
form Larvae. Third Stirps with Chilopodiform or
Scolopendriform Larv^:. Fourth Stirps with Thysa-

NURIFORM LARV-ffi.

Part III. Fifth Stirps of Lepidoptera Diurna, with Anoplu-
riform Larv^.

Second Tribe of Lepidoptera or Sphingidje.
Part IV. Third Tribe or Bombycid^e.
Part V. Fourth Tribe or Noctuid^e.
Part VI. Fifth Tribe or Phaljenida.
Each part will be illustrated by four plates consisting of highly
finished engravings by artists of eminence. Three of these will be
coloured with accuracy and elegance ; the fourth^ more elaborate
as an engraving, will be gi/en plain.

The first plate is devoted to the illustration of new species, and
such subjects will be preferred as are typical of the groups defined

in

Notices respecting New Books. 369

in the progress of the work: they will be arranged, as far as pos-
sible, according to their affinities. For the second plate, those sub-
jects will be chiefly selected which form types of genera ; and they
will, in most cases, be accompanied by dissections. On the third
and fourth plates the history of the metamorphosis will be eluci-
dated, and they will likewise contain additional generic illustra-
tions and dissections.

As to the plan of the descriptive part, a very concise outline can
only be given in this place. The arrangement proposed to be fol-
lowed, and the constitution of the higher divisions, namely of tribes
and stirpes, are explained in the Introduction. These are defined
from a review of the whole order : but the sections indicated either
in the stirpes or in the genera are provisional only, as they are re-
gulated by the extent of the collection. A detailed generic cha-
racter is given in the Latin language ; this is followed immediately
by a somewhat amplified description in English. Every species is
distinguished by the generic and specific name at length. This is
followed by a Latin description, in technical language, intended to
exhibit a concise but accurate delineation, sufficiently minute to
afford the means of precise discrimination from all other species.
In the English description of new species the object is to give a
full history of the external character in all its details. It is not
consistent with Dr. Horsfield's present plan to give specific cha-
racters according to the Linnaean models : these belong, in his opi-
nion, to works in which a general comparison of species contained
in extensive collections, enables the writer to define the characters
with a precision and confidence which cannot be obtained in the
examination of a merely local collection.

The detailed specific descriptions will be followed, in most cases,
by a series of miscellaneous observations. In these it is the au-
thor's chief object to illustrate the history of those. individuals
which he has traced through their various stages of existence, and
of which the collection contains representations in their larva and
pupa states. The arrangement projected for this work being
founded primarily on the metamorphosis of the insects of this
order, this part of the subject will be found to have an important
bearing on the whole. These observations will also afford the ne-
cessary explanations of the figures contained in the third and
fourth plates, and they will lead to the detail of the remarks made
on the food of the larvae, the season of the year when found, their
abundance or scarcity, and to such other peculiarities as may have
been noticed in Java. Under this head, he will also give an ac-
count of the state of the collection regarding the materials from
which the descriptions have been made, with the view to illustrate
many doubtful or imperfectly known species. The public or private
collections in the British metropolis, in which the species described
may have been observed, will also be indicated ; and finally their
range through other parts of India : and in the whole of these mis-
cellaneous observations, as well as in the generic and specific de-

New Series. Vol. 3. No. 17. May 1828. 3 B scriptions,

S70 Royal Society,

scriptions, a principal object will be to render the work generally
useful and interesting to the British naturalist.

The parts will follow each other with every degree of expedition
consistent with the preservation of the style of publication in which
the work has been commenced. Those preparatory arrangements
which are inseparable from every undertaking of this nature have
in some measure retarded the first part, but the publishers are en-
abled to engage, with every prospect of success, a regular conti-
nuation of the work : accordingly they announce the appearance of
the second part early in July next, of the third, at the commence-
ment of the ensuing year, and of the remaining parts at intervals
of six months. According to this plan, the whole will be completed
within three years from the commencement.

Lepidoptera Britannica ; sistens Digestionem novam Insectorum Le-
pidopterorum quce in Magna Britannia reperiuntur, larvarum pa-
bulo, temporeque pascendi ; expansione alarum ; mensibusque vo-
landi ; synonymis atque locis observationibusque variis. Autore
A. H. Haworth, Linn. Soc. Lond. Soc, fyc. fyc.

We congratulate the admirers of British Entomology on the long
expected appearance of Part IV. of Mr. Haworth's Lepidoptera
Britannica, which is at last completed.

This comprehensive and valuable work consists of 609 closely
printed octavo pages, and 36 of Preface, and has been divided into
four parts ; to the first of which was appended above 200 similar
pages, called Miscellanea Naturalia.

Complete new-wrought descriptions and synonymies of all the
known British Lepidoptera are given throughout in Latin ; together
with occasional observations in English, respecting their pecu-
liarities, size, food, times and places of appearance, &c.

The First Part, which was published by the author in 1803, con-
tains the Papilionidce, Sphingidce, and Bombycidcc. After this, the
work languished for want of encouragement, till the beginning of
1809, when the Second Part was published. It contains the He-
piali, Lithosice, Palcarice, Noctuadce, Phalcenadce, &c.

The Third Part appeared in 1811. It contains the Pyralid<z,
Tortricidce, &c. And the Fourth Part, which has just been pub-
lished, completes the arduous and useful undertaking of its inde-
fatigable author. It contains the Tineadce, &c. ; and concludes the
work with a complete Index of all the genera and species of Lepi-
doptera described ; about 1450 in number.

LX. Proceedings of Learned Societies.

ROYAL SOCIETY.

Feb. 21 & 28 F) EAD An account of the accident to the packet-

AV ship the New York, from lightning. By T.
Stewart Traill, M.D. of Liverpool. Communicated by Henry
Brougham, Esq. M.P. F.R.S.

The

Royal Society. 371

The ship which met with the accident of which the effects are
the subject of this communication, was the American packet the
New York, of 526 tons, commanded by Captain Bennet. She
sailed from New York for Liverpool, on the 16th of last April ; and
on the morning of the 19th was struck by lightning, which shattered
the main royal mast, and gliding down the iron chain main-top-sail
tie, burst the iron bands on the main-mast head. It was thence
conducted by the iron main-top-sail sheets, to the iron work of
the pumps. It then entered between decks, demolishing the bulk-
heads that formed the store-room, in its way to a small leaden cis-
tern : whence it was conducted, by a leaden pipe, through the star-
board side of the ship, where it started three five-inch planks, ten
feet in length, at the lower part of the bends. Many other parts of
the ship, not in the direct line of its passage, were also shattered,
apparently from the effects of a lateral explosion ; several doors
and partitions were thrown down, a large mirror in the cabin was
shivered into small fragments, and a piano-forte was thrown down,
its top blown off and broken in pieces. The loudness of the ex-
plosion was appalling and spread universal consternation. A sul-
phureous smoke, which had issued with a bluish flame from the
hatches, filled the cabins ; and at first inspired alarm, lest the cargo
in the hold, consisting chiefly of cotton and turpentine, had taken
fire ; but on clearing the main hatch, it was soon ascertained that
no danger from fire existed. The ship however had sprung a leak
which made four inches of water every hour, but which on washing
the pumps was found to be under command, and would not prevent
her proceeding on her voyage to England.

When the first terror created by the accident had somewhat sub-
sided, it was found that none of the passengers or crew had sus-
tained any injury. The chief mate was sleeping in the birth op-
posite to the main hatch, near the spot where the lightning entered
the store-room, the lock of which was forcibly driven into his cabin :
but he was not himself affected by the shock, and a quantity of
gunpowder which was kept under (lis bed was fortunately not ig-
nited by the lightning. An ewer and a basin placed on a stand over a
child's bed were thrown down by the explosion, but the child had
escaped unhurt. A remarkable effect was however produced on an
elderly gentleman, who for the last five years had not been able to
walk half-a-mile at a time : terrified by the crash, he forgot his debi-
lity, and springing from his bed, rushed on deck with singular quick-
ness and agility. He has retained, ever since the event, the power
over the muscles of his limbs, derived from this sudden emotion.

The threatening aspect of the heavens, the appearance of numer-
ous water-spouts on the surface of the sea, and other electrical in-
dications, gave rise to apprehensions of further danger, and induced
the captain to put up the conductor with which he was provided,
but which had not been previously applied. It was made of iron
links eighteen inches long, connected by iron rings one inch in dia-
meter ; and was furnished at the top with an iron rod four feet long
and half an inch in diameter, tapering to a fine point. This rod was
fixed so as to rise three feet above the main royal mast head ; and

3 B 2 the

372 Royal Society.

the chain was made to descend along the back-stay, and below was
kept at a distance of ten feet from the starboard bulwarks by a light
wooden outrigger, or spar. Its whole length was 145 feet, of
which about nine feet of its lower part descended into the sea.
The wisdom of adopting this precaution was soon apparent, for in
the course of the same morning the ship was struck by a second
explosion, which is stated by the unanimous testimony of all on
board to have far exceeded in violence the first. It melted a great
part of the conductor, producing a vivid combustion of many of the
links, which burned like so many tapers ; and descending into the
sea, darted off to a considerable distance along the surface of the
waves. The resistance to its passage was so great as to cause the
ship to recoil with a sudden and violent shock, so as to throw down
several of the crew. The melted iron of the conductor fell in large
drops on the deck, which although already strewed with hailstones
that had previously fallen, intermixed with rain, was set fire to in
many places by the ignited metal. No damage, however, was done
to the masts or rigging, not the least injury to any of the crew, with
the exception of a carpenter, who being at work with an iron auger
in his hand, received a smart shock through the wrists, which oc-
casioned a livid tumour which was still visible six weeks after the ac-
cident.

Soon after the arrival of the vessel in Liverpool, she was docked
in order to ascertain what damage she had sustained. Some of her
planks were found to have started, but her timbers were uninjured.
Every instrument made of steel, — such as the carpenter's tools, and
the knives and forks ; and also those made of soft iron, even to the
very nails in every part of the ship, — had been rendered permanently
magnetic. All the watches and chronometers were either stopped
or rendered useless, by the magnetism imparted to the balance-
wheels and other parts of their works that were made of steel. Con-
trary to what usually happens from shocks of artificial electricity,
the lightning had given a strong northern polarity to the upper part
of the conductor. Many parts of the iron-work indeed had ac-
quired the magnetism corresponding to their position with respect
to the magnetic direction ; but in others no relation of this kind
could be traced. Great changes were produced on the magnetism
of the compass needles, in many of which were formed several
sets of poles, and their indications could therefore no longer be
relied on.

The circumstances attending the accident which is the subject of
this paper, are considered by the author as strongly confirming the
value of conductors to ships in obviating the destructive effects of
lightning. From the inquiries he has made, he is led to the belief
that injuries from lightning at sea are much more frequent than is
generally imagined. One source of increased danger of late years
is to be found in the greater proportion of metal, and particularly
of iron, which is employed in the rigging ; more especially as the
metallic masses are there nearly insulated, or connected only by
very imperfect conductors. In the instance before us, it is in the
highest degree probable, that if the New York had been without

the

.' Royal Society. 373

the protection of the conductor, she must inevitably have been de-
stroyed by the second tremendous explosion, which, thus guarded,
she sustained without the slightest injury. The author remarks
that copper is a better material for such a conductor than iron, from
its being less liable either to fusion or corrosion: and also that a
rod is, from its continuity, a better form of conductor than a chain.
In the case of ships, however, the greater convenience of a chain,
arising from its flexibility, will generally insure it the preference.
The author recommends, that, instead of carrying the conductor
through the decks to the keel, as suggested by Mr. Harris, the
lower end of the chain should be kept at a distance from the sides
of the ship, by means of a light outrigger, or spar, as was done in
the New York.

March 20. — Read a paper On the Phenomena of Volcanoes ; by
Sir H. Davy, Bart. F.R.S.

In a paper on the decomposition of the earths, published in the
Phil. Trans, for 1812, the author offered it as a conjecture, that the
metals of the alkalies and earths might exist in the interior of the
globe ; and on being exposed to the action of air and water, give
rise to volcanic fires, and to the production of lavas, by the slow
cooling of which basaltic and other crystalline rocks might subse-
quently be formed. Vesuvius, from local circumstances, presents
peculiar advantages for investigating the truth of this hypothesis ;
and of these the author availed himself during his residence at
Naples, in the months of December 1819, and of January and Fe-
bruary 1820. A small eruption had taken place a few days before
he visited the mountain, and a stream of lava was then flowing with
considerable activity from an aperture in the mountain a little below
the crater, which was throwing up showers of red-hot stones every
two or three minutes. On its issuing from the mountain, it was
perfectly fluid, and nearly white hot : its surface appeared to be in
violent agitation from the bursting of numerous bubbles, which
emitted clouds of white smoke. There was no appearance of vivid
ignition in the lava when it was raised and poured out by an iron
ladle. A portion was thrown into a glass bottle, which was then
closed with a ground stopper, and, on examining the air in the
bottle some time afterwards, it was found not to have lost any of
its oxygen. Nitre thrown upon the surface of the lava did not
produce such an increase of ignition as would have attended the
presence of combustible matter. The gas disengaged from the lava
proved on examination, to be common air.

When the white vapours were condensed on a cold tin plate, the
deposit was found to consist of very pure common salt ; and the
vapours themselves contained nine per cent of oxygen, the rest
being azote, without any notable proportion of carbonic acid or
sulphureous acid gases ; although the fumes of the latter of these
gases were exceedingly pungent in the smoke from the crater of
the volcano. On another occasion, the author examined the saline
incrustations in the rocks near the ancient bocca of Vesuvius ; and
found them to consist principally of common salt, with some chlo-
ride of iron, a little sulphate of soda, and a still smaller quantity of

sulphate

374 Limiiean Society.

sulphate or muriate of potassa, with a minute portion Of oxide of
copper. In one instance, in which the crystals had a purplish tint, a
trace of muriate of cobalt was detected. From the observations
made by the author at different periods, he concludes that the dense
white smoke which rose in immense columns from the stream of
lava, and which reflected the morning and evening light of the
purest tints of red and orange, was produced by the sajts which
were sublimed with the steam. It presented a striking contrast to
the black smoke arising from the crater, which was loaded with
earthy particles, and which in the night was highly luminous at
the moment of the explosion. The phenomena observed by the
author afford a sufficient refutation of all the ancient hypotheses, in
which volcanic fires were ascribed to such chemical causes as the
combustion of mineral coal, or the action of sulphur upon iron ;
and are perfectly consistent with the supposition of their depending
upon the oxidation of the metals of the earths upon an extensive
scale, in immense subterranean cavities, to which water or atmo-
spheric air may occasionally have access. The subterranean thun-
der heard at great distances under Vesuvius, prior to an eruption,
indicates the vast extent of these cavities ; and the existence of a
subterranean communication between the Solfatarra and Vesuvius,
is established by the fact that whenever the latter is in an active
state, the former is comparatively tranquil. In confirmation of
these views, the author remarks, that almost all the volcanoes of
considerable magnitude in the old world, are in the vicinity of the
sea : and in those where the sea is more distant, as in the volcanoes
of South America, the water may be supplied from great subter-
ranean lakes ; for Humboldt states that some of them throw up
quantities of fish. The author acknowledges, however, that the
hypothesis of the nucleus of the globe being composed of matter
liquefied by heat, offers a still more simple solution of the phaeno-
mena of volcanic fires.

LTNNiEAN SOCIETY.

April 1. — Lord Stanley in the chair.

His Lordship opened the meeting of the Society by adverting,
with much feeling, to the great loss which had been sustained by the
country and by the world, and more especially by the Society, in
the death of its illustrious and beloved President Sir James Edward
Smith, who from its first establishment, in which he had taken an
active part, had been called upon to preside over it by the annual and
unanimous votes of its members, and had greatly contributed to
place the Society in the distinguished rank which it had attained, by
his great talents, indefatigable industry, sound judgement, and en-
larged views as a naturalist ; — by the high estimation in which he had
long been held by men of science all over the world ; by the excel-
lence of those valuable and accurate works in which he had done so
much to promote and improve the study of natural history ; and espe-
cially by the qualities of his heart, mind, and temper, for which his
memory would long be revered by those who had enjoyed the happi-
ness of his friendship. — He could not forbear expressing what he

felt

Linn&an Society. 375

felt on the present occasion, especially with reference to the par-
ticular moment of his loss, — at a time when those considerations of
religious distinction were about to be removed, which had seemed
to have a tendency to deprive those who, like this excellent and dis-
tinguished man, differed from the established religion, of the rank
in society due to their talents or their worth*.

His Lordship expressed his anxiety that whatever choice might be
made by the Society to fill the vacancy in its Chair, should be such
as would contribute to its prosperity, however impossible it might
be adequately to supply the loss which it had now so much to re-
gret.

Lord Stanley then adverting to the last volume of the English
Flora, which had been received from Sir James Smith but a few
days before his death, and was among the presents on the table,
related that, showing it to a friend, he had exclaimed, " This is
the close of my labours." — As its distinguished author was now
removed from the possibility of receiving the customary vote of
thanks, His Lordship concluded, by proposing that the grateful
feelings of the Society might be expressed to Lady Smith for this
last gift of their revered President.

A portion of Dr. F. Hamilton's Commentary on the Hortus Mala-
baricus, Part V., was then read.

April 15. — Read a letter addressed to the Secretary, from Charles
Lucien Buonaparte, Prince of Musignano, F.M,L.S., dated on board
the Delaware, near Gibraltar, March 20th, 1828, containing the fol-
lowing notice relative to the migration of certain birds. — " A few days
ago, being 500 miles from the coasts of Portugal, 400 from those of
Africa &c, we were agreeably surprised by the appearance of a few
swallows, Hirundo urbica and rustica. This, however extraordinary,
might have been explained by an easterly gale, which had cut off the
swallows migrating from the Main to Madeira, only 200 miles distant
from us ; — but what was my surprise on observing several small
warblers hopping about the deck and rigging ! These poor little
strangers, exhausted as they were, were soon caught and brought to
me. The following short list is that of the species.

"1. Sylvia trochilus. — 2. Sylvia erithacus (tethys, Temminck). —
3. Sylvia suecica, or rather a similar species, which I have already
received from Egypt and Barbary. — 4. A species new for Europe and
perhaps even a nondescript, having the plumage of an Anthus, and
which I think belongs (as Sylvia cisticola and others) to the hitherto
African genus Malurus. This, however, must rest undecided, my
specimen missing its tail, which was pulled ofFby the sailor who caught
the bird."

A communication was likewise read to the Society from J. Morgan,
Esq. F.L.S., relative to the structure of the mammary organs of the
Kangaroo, in which a detailed account was given of a recent dissection

* Alluding to the proceedings for the abolition of the sacramental test,
— Sir James Smith having been a member of the congregation of Unitarian
dissenters at Norwich.

of

376 Linncean Society.

of these parts, both in the virgin and in the impregnated animal ; to-
gether with the author's opinions respecting the physiology of certain
structures which have been hitherto unnoticed, and of others which
have been incorrectly or imperfectly described by former investigators
of this interesting branch of natural science.

The author first pointed out the anatomical peculiarities which he
had discovered in a dissection of the pouch and mammae of a young
and unimpregnated kangaroo ; by which it appears, that, in the virgin
state, the two upper nipples only are found to be developed, and that
beneath each of these a minute circular aperture, resembling in ap-
pearance the mouth of a follicle, occupies the exact situation in which
the lower teat is known to exist in the adult impregnated animal. —
The mammae are described as consisting of double glandular struc-
tures on each side ; they are situated directly behind the follicular
openings already mentioned, and are closely confined to the posterior
surface of the integuments. Each double mamma is formed by an
upper and smaller gland, which is attached by its excretory ducts to
the already developed nipple, and by a second and larger glandular
substance from which no excretory duct could be traced. The folli-
cular apertures which occupy in the pouch the situation of the lower
teats, form the external openings of cylindrical membranous canals
which lie imbedded in the substance of the larger and lower mam-
mary glands. Each of these membranous canals or tubes is about
three-fourths of an inch in length, and extends through nearly the
whole diameter of the larger gland which encloses it ; the interior of
the tube is lined by cuticle, and the internal extremity is terminated
by a rounded papilla which projects into its cavity.

In these papillae the author found a perfect miniature resemblance
to the extremities of the lower teats in the adult animal, which teats
he considers to be formed, during the first gestation, by the complete
eversion of the membranous canals, and the consequent projection of
their papillary terminations. He further states, that by artificially
everting the parts, two perfect teats are produced in the precise situa-
tion of those which are found in after life. It has been however as-
certained that this extraordinary change occurs only during the first
gestation, since after being once developed the teat remains perma-
nently formed and projected.

Having thus described the condition of the mammary glands and
the development of the lower teats in the virgin animal, the author
gave a particular account of his dissection of an adult female, which
at the time of death was suckling a young one nearly half-grown.
In this we are informed that the panniculus carnosus which covers
the anterior surface of the belly is of extraordinary thickness, and
composed principally of perpendicular muscular fibres, which in their
course from the thorax downwards surround the mouth of the pouch
to which they form a sphincter muscle, and that a fasciculus of its
fibres descending over the symphysis pubis is inserted into the sphinc-
ter muscle of the cloaca ; so that the contraction of this part of the
panniculus carnosus would powerfully operate in approximating the
external aperture of the vagina with the mouth of the pouch.

On

Linnaan Society.— -Astronomical Society, 377

On removing the panniculus carnosus a pair of muscles (Of which
the attachments and uses have been hitherto incorrectly described) are
brought into view. Each of these muscles is of a triangular shape,
being attached by a narrow origin to the posterior part of the pelvis ;
and expanding in its course, is continued transversely round the lower
part of the belly, before the abdominal muscles, and immediately
above the brim of the pelvis. Each of these triangular muscles en-
closes, between an anterior and posterior layer of its fibres, the mam-
mary gland, and the two muscles afterwards cross the fore part of the
abdomen to unite in front of the linea alba. By this union a perfect
muscular girdle is formed, by the contraction of which the mammae
are compressed against that part of the abdomen in which the mar-
supial bones lie imbedded.

The conclusion of this paper, containing further particulars of the
dissection of the mammary organs as well as of the muscles attached
to the marsupial bones of the adult and impregnated animal, together
with the author's opinion respecting their physiology, remains to be
read at a future meeting.

ASTRONOMICAL SOCIETY.

Feb. 8. — This day being the Anniversary, Dr. O. G. Gregory, one
of the Secretaries, read the following Report of the Council to the
Eighth Annual General Meeting.

Your Council are happy in being able to commence this, their
Eighth Report, with a general expression of congratulation on the
progress of the Society, and on the prospects of increased and in-
creasing utility, which a view of its actual state and resources, and a
consideration of the events of the year now closed, in their minds
appear to justify. They trust, too, that a review of these events will at
the same time justify the confidence reposed in them, by showing that
they have not been neglectful of the opportunities which have offered
of advancing in various ways the objects and interests of the, Society.

One of the first acts of the Council of the year elapsed, was to
enter into an arrangement with Mr. Taylor, the printer to the Society;
and who is also one of the editors of the Philosophical Magazine, for
the publication of a series of monthly notices of its Proceedings,
and for the supply of a sufficient number of copies of them, in suc-
cession, for distribution among the members. The convenience and
advantages of this plan have been sufficiently proved by the trial which
has been given it, and it will of course be continued. The public is
hereby brought more immediately into contact with the Society — the
labours of its contributors are canvassed and discussed, while the in-
terest of the author in his subject is yet warm, and when the inter-
change of ideas respecting it is most beneficial, not only to the pub-
lic, but to the author himself, whose views may, and probably in
many instances will, be enlarged or corrected by such intercourse.
An authentic and at the same time public record is, as it were, opened,
of the papers read, and the outlines of their contents rendered matter
of history -} — thus affording ready means of establishing the claims of

New Series. Vol. 3. No. 17. May 1828. 3 C authors

378 Astronomical Society,

authors to priority of discovery, so far at least as priority of public
communication can be regarded as evidence in questions of that na-
ture. The same arrangement offers the further advantage of relieving
the Council from all difficulty in the disposal of matter of merely tem-
porary interest ; such as notices of phenomena, ephemerides of the
smaller planets, comets, &c. which require speedy circulation, and do
not need to be formally enrolled in the Memoirs ; and it may occasion-
ally happen, that the matter of more regular communications may so
far be condensed into the monthly abstract, as to dispense with a
second publication in the Memoirs — to the material relief of the funds
of the Society.

The same consideration of the advantages derived from the speedy
publication of communications read to the Society, has induced the
Council to adopt the principle of sending immediately to press all
papers which, on passing through the prescribed formalities, shall be
deemed of a nature for publication in their Memoirs j and although
objections have been considered to exist against the separate pub-
lication of each particular memoir, the division of their volumes into
smaller parts can be attended with no inconvenience. Acting on
this principle, the Council have directed the publication of Part I.
Vol. 3. of the Memoirs, including all papers (regarded by them as
suitable for printing in the body of the Memoirs) read during the
interval elapsed from the last publication. This Part is now,
accordingly, before the public, and furnishes satisfactory proofs of
the zeal, diligence, and talents, both of our Home Members and our
Associates.

It is not merely, however, in communicating to the world the ob-
servations of their members, but also in causing observations to be
made, and in lending every assistance in their power to those meri-
torious and public-spirited individuals, who, actuated only by an
earnest desire to render available their leisure and talents in the
cause of science, are willing to undertake the task of regular obser-
vation,— that a Society like this can render service to science. The
munificent act of a private individual, has happily placed this par-
ticular line of utility more directly than heretofore in the power of
the Society ; and its members have not been slow in availing them-
selves of its advantages, and applying them to effective use. — Among
the great and lamented losses which the Society has sustained in the
course of the last year, is that of the late Colonel Mark Beaufoy ; the
latter days of whose existence we recollect with a melancholy plea-
sure to have been cheered and gratified by the highest mark of this
Society's approbation, in the award of their medal for his Astronomical
Observations. His son, Lieut. George Beaufoy, has, with the utmost
liberality, placed his deceased father's astronomical instruments in
the possession of this Society. They consist of

One 4-feet Transit, by the late Mr. Cary, Strand.

One Altitude and Azimuth Circle, by the same.

One Clock, adjusted to mean Solar time.

One Clock, adjusted to Sidereal time.
Your Council conceive, that the opportunity fortunately placed be-
fore

Astronomical Society. 379

fore them, by Lieut. Beaufoy's recent election as a member of this
Society, of marking their sense of this liberal and public-spirited con-
duct on his part, by a high and complimentary distinction, ought not
to be neglected. They have therefore thought it adviseable to re-
commend to the Society to elect him a member for life.

The Council wish to observe, with respect to the measure so re-
commended, that though it may seem equivalent to the acknowledge-
ment of a class of members similar to that, which in the constitutions
of some scientific bodies are deemed honorary members, — yet they
are rather desirous to avoid the establishment of purely complimentary
distinctions, and to mark by it, in this and any future case which may
occur, the Society's sense of some distinct benefit accruing to itself
or to astronomical science, through the individual so distinguished,
which could not be properly acknowledged otherwise : — thus leaving
every future case to rest on its own individual merits, as if it were the
first of its kind.

The surest criterion of the utility of a donation is its immediate and
effective practical application. That of Lieut. Beaufoy was scarcely
announced to the Council, when an application was made to them by
one of our members, Captain Smyth, R.N. (justly distinguished for
his knowledge of the resources of practical astronomy), for their loan,
which was immediately accorded j and the Council have the high
satisfaction of being able to announce to you, that the instruments in
question are at this moment (with the exception of one of the clocks)
mounted in the best manner, in a regular observatory established by
Captain Smyth, at his residence at Bedford, for their express recep-
tion, and already in actual use in celestial observation. The Council,
though not unaware of the general nature of Captain Smyth's astro-
nomical views, purposely forbear from publicly stating at present the
course of observations in which he purposes to engage ; being desirous
to leave his meritorious exertions as far unfettered as possible by any
public pledge — and trusting rather to his high character and well-
known zeal, talent, and activity, than to any express stipulation, that
the means thus placed in his hands will be exerted for the advance-
ment of astronomical science.

Actuated by a similar desire to promote, as far as our means will
admit, the great objects of astronomical inquiry in all its branches, the
Council have ordered two invariable pendulums of iron and of cop-
per, on a construction somewhat different from those hitherto em-
ployed, to be consigned to Captain Foster, for the purpose of inves-
tigating the possible effects of the earth's magnetism in various geo-
graphical positions, in these delicate researches, in the course of his
approaching scientific voyage j an enterprise which honourably cha-
racterizes the enlightened views of Government, and from which a
rich harvest of important results may be anticipated.

From the report of the Finance Committee it appears that the funds
of the Society continue in a flourishing state, notwithstanding the
heavy demands for computation and printing during the last year.
This extraordinary expenditure has principally arisen from the great
expense incurred in publishing the Catalogue of the principal fixed

3 C 2 stars.

380 Astronomical Society.

stars, alluded to in the last Report, and which appears to have met
the approbation of every astronomer. But the Council are happy to
state, that this disbursement has been followed by a corresponding
spirit of zeal and liberality on the part of several of the members,
who, by entering into a subscription, have enabled the Council to de-
fray nearly the whole expense of that useful and valuable work, with-
out intrenching on the ordinary funds of the Society. And it may be
mentioned, as a proof of the liberal spirit which animated those mem-
bers, that the sum of 320 1, was subscribed, within a few hours, towards
the expense of publishing the Catalogue above alluded to.

The Council cannot too earnestly impress on the attention of the
members, the necessity of encouraging the sale of the Memoirs as
much as possible : since it is only by a quick return, arising from
such sale, that they can expect to continue the publication, from year
to year, without a serious diminution of the funds of the Society.

Among the accessions to our home list of members, in the year
elapsed, the Council have to record, with all those sentiments of re-
spect which his illustrious rank so peculiarly inspires, the name of
His Royal Highness the Lord High Admiral : and they trust that this
accession, so honourable in itself, and so gratifying to the Society,
will be attended with the most beneficial results to the science which
this Society was formed to promote, and which is so intimately con-
nected in its practical application with the department over which
His Royal Highness presides. Our home list has been further in-
creased by the accession of fourteen new members, and our foreign,
by that of one associate.

Among the losses sustained by death, the Society has to lament, in
addition to Colonel Beaufoy, that of its most illustrious associate
Laplace : and on our home lisl, of the Rev. Lewis Evans j His Grace
the Duke of Gordon j our amiable and excellent trustee, Mr. Daniel
Moore (whose loss will be felt far beyond the limits of this body by
many, as the privation of a benefactor, in whose ears the calls of dis-
tress never sounded in vain) ; Mr. W. M. Mosely j and Mr. J. Sanders.

Mr. Mosely, in addition to a competent knowledge of various sci-
ences, had turned much of his attention, in the latter part of his life,
to astronomy. He possessed several valuable instruments, and is
said to have left behind him a series of observations of transits and
north polar distances, and some measures of double stars confirmatory
of their changes.

Mr. Evans also possessed instruments of considerable merit, and
for several years employed himself as a skilful and successful ob-
server.

It will not be expected that any sketch should here be attempted
of the labours of M. de Laplace. No history of his scientific life, of
the origin and development of his views, adequate to the occasion,
could be comprised in such limits as those of this Report : and the
general nature of the more important results of his researches is al-
ready so well known, and so incorporated with the intellectual hi-
story of the last half century, that it constitutes a portion of the know-
ledge of every well informed man. During the long period of fifty-five

years,

Astronomical Society. 381

years, from the date of his first considerable mathematical production
on the integration of equations of differences, in the Turin Memoirs
in 1/72, to almost the moment of his death, his march was in the
van of intellect 5 and the highest point of scientific attainment to
which the age had reached, was uniformly marked by his progress.
His whole career was a succession of brilliant and profound disco-
veries, where every great step in the theoretical departments of ana-
lytical science was sure to be attended with a corresponding advance
in its practical application j and every difficulty which occurred in
applying his principles to the sublime problems of physical astronomy,
served only to give rise to new methods, and create more powerful
engines of mathematical inquiry j a rare combination, — of which Ar-
chimedes and Newton had afforded the only previous examples, — of
a philosophical spirit of the first rank wielding all those unbounded re-
sources of abstract science, which a few extraordinary men of a diffe-
rent turn may have perhaps possessed in an equal or superior degree,
but which only attain their highest value when exerted from the van-
tage-ground of a mind at home in every department of experimental
philosophy, impressed with the fullest sense of the importance of
practical application, and familiar with all the means of disentan-
gling principles from natural phenomena. Laplace also afforded a
conspicuous instance of that union of gentle and amiable social qua-
lities, which is one of the best characteristics of the highest order of
genius — as indicating a mind secure of its rank. No pretension — no
assumption — nothing dictatorial in science or offensive in taste,
marked his mild and modest deportment. They, who have heard
his sublimest views propounded with the diffidence of a youth seek-
ing information ; they, whose early scientific attempts have been en-
couraged, and whose maturer efforts were assisted and directed by
his talents, — will long retain a penetrating sense of this estimable
feature of his character.

The only one of the prize questions proposed at the instance of the
Council in February 1824, the period of which remained unexpired
during the year elapsed, is that relating to the development of the
differential equations of the lunar theory, and the improvement of the
lunar tables. No answer has been received to this question ; and the
proposed period has now expired. The Council have not thought it
adviseable either to prolong this period, or to propose any new ques-
tions for the present or future years : but, should subsequent re-
searches either afford complete solutions of any of those questions, or
material elucidations of their peculiar difficulties, future Councils will
not fail to bear in mind the importance that attached to their subjects
in the minds of former ones, and recommend to the Society the ac-
cordance of such marks of their approbation as the degree of progress
made in them may appear to demand.

Two medals have been awarded this year by the Council. One
to Sir Thomas Macdougal Brisbane for the inestimable benefit
conferred by him on astronomical science, in the establishment of his
observatory at Paramatta in New South Wales, and for the valuable
and important series of observations made there by himself, and under

his

382 Astronomical Society.

his directions, during his residence as governor of that colony. The
other to Mr. James Dunlop, for his disinterested and indefatigable
pursuit of astronomical researches, subsequent to the departure of
Sir T. M. Brisbane from the colony of New South Wales, whereby
he has added, in a most material degree, to our knowledge of the
nebula? of the southern hemisphere.

These medals will be delivered to these gentlemen respectivelv,
or to their proxies, by the President, before the Society proceed to
the business of election of the officers for the ensuing year.

The Council cannot conclude this Report, without an earnest ex-
hortation to the members of the Society, collectively and individu-
ally, to cooperate by their active exertions in the great cause for
which the Institution exists. They entreat them to remember that
every one who possesses an instrument, whose claims rise even not
above a humble mediocrity, has it in his power to chalk out for him-
self a useful and honourable line of occupation for leisure hours, in
which his labour shall be really valuable, if duly registered : that those
who possess good instruments, have a field absolutely boundless for
their exertions. To such they would hold out the brilliant examples
of many other of the members and associates of this Society, — of a
Bessel, a Struve, — as showing what may be accomplished by perse-
vering industry, and how little reason there is to apprehend the fail-
ure of matter for their researches. They would strongly impress on
the minds of all observers, however, whether private or public, the
daily increasing necessity which exists for the reduction of their ob-
servations when made, and for the employment for that purpose of a
uniform system of corrections adopted by common consent : and
that, not when the work of many years shall have accumulated on
hand, till it shall have become overwhelming ; but regularly, year
by year — nay, month by month, while the immediate interest of the
observations retains its freshness in the memory, and while their
actual value can be checked, and the means of further refinement
suggested and attained. The extreme facility afforded for these re-
ductions by the Catalogue published by this Society, leaves no excuse
for their neglect, when stars contained in it are observed ; and it is
most earnestly to be hoped, that no departure in other cases, from
the coefficients there used, will take place.

The Council would also strongly draw the attention of the mem-
bers of the Society to the high importance, both for nautical and as-
tronomical science, of observations of occultations, eclipses of the
sun, and satellites of Jupiter, moon-culminating stars, and even
ordinary lunar distances well and carefully observed on land, at fixed
stations, such as observatories, and at all remarkable points in di-
stant countries, where opportunities may offer. The Society will feel
its utility most materially increased by the communication of such
observations, if carefully made. No class of individuals have so fre-
quent and available opportunities for such observations, as naval
officers, nor to any is the object of such direct utility. — It is gratify-
ing to know, that the requisite scientific attainments for such re-
searches are already widely diffused among them, and daily becoming

more

Astronomical Society, 383

more so ; and it is cheering to indulge the pleasing reflection, that the
calls thus made upon them will not be unavailing.

(The President then addressed the meeting on the subject of the
award of the Medals, as follows : — )

Gentlemen, — In pursuance of the1 award of your Council, which
you have just heard, I have now to call your attention to the subject
of the honorary marks of this Society's approbation, which it is part
of our business at this meeting to bestow. The selection of objects
on which such distinction may most deservingly and most usefully
be conferred, has been, in this instance, of much interest and some
difficulty, — not from a paucity of claims, but from their variety and
magnitude. On all sides, both abroad and at home, the spirit of
Astronomical research and discovery has been diligently alive. The
great work which has been commenced on the Continent, for the de-
termination of the places of all the stars of our hemisphere in zones,
has been continued with a patient ardour to which no words can do
justice. — The heavens have been ransacked for double stars j and
the results of the search, developing a most rich and unlooked-for
harvest of striking discoveries, being the first fruits of the great te-
lescope of Fraunhofer, have been consigned to immortality, in a
work which does honour to its age and nation, and which has already
been brilliantly rewarded in another quarter. The ingenuity of one
of our own countrymen, has placed new, simple and powerful means
in the hands of observers, for verifying the stability of their instru-
ments, and determining their fluctuations. And in every quarter,
to go no further in this detail, an activity worthy of the high ends
and dignity of our science, has been remarkably displayed. Among
so many important labours, however, some of which are yet awaiting
their final completion, or receiving the last touches of their authors,
the attention of your Council has been fixed, by the imposing mass
of valuable observations which has emanated during a series of years,
from the Observatory at Paramatta, established ,by the late governor
of the colony of New South Wales, Sir Thomas Macdougal Brisbane,
one of our Vice-Presidents, long distinguished among us by his ar-
dent love of Astronomy, and an intimate familiarity both with its
theory and practice.

Nothing can be more interesting in the eyes of an European as-
tronomer, especially to those who*se field of research, like our own,
is limited by a considerable northern latitude, — than the southern
hemisphere, where a new heaven, as well as a new earth, is offered
to his speculations ; and where the distance, the novelty, and the
grandeur of the scenes thus laid open to human inquiry, lend a cha-
racter almost romantic to their pursuit.

A celestial surface equal to a fourth part of the whole area of the
heavens, which is here for ever concealed from our sight, or whose
extreme borders at least, if visible, are only feebly seen through the
smoky vapours of our horizon, — affords to our antipodes the splendid
prospect of constellations different from ours, and excelling them in
brilliancy and richness. The vivid beauty of the Southern Cross has

been

384 Astronomical Society.

been sung by poets, and celebrated by the pen of the most accom-
plished of civilized travellers ; and the shadowy lustre of the Magel-
lanic clouds, has supplied imagery for the dim and doubtful mythology
of the most barbarous nations upon earth. But it is the task of the
Astronomer to open up these treasures of the southern sky, and dis-
play to mankind their secret and intimate relations. Apart, however,
from speculative considerations, a perfect knowledge of the astronomy
of the southern hemisphere is becoming daily an object of greater prac-
tical interest, now that civilization and intercourse are rapidly spread-
ing through those distant regions, — that our own colonies are rising
into importance, — and that the vast countries of South America are
gradually assuming a station in the list of nations, corresponding
with their extent and natural advantages. It is no longer possible to
remain content with the limited and inaccurate knowledge we have
hitherto possessed of southern stars, now that we have a new geo-
graphy to create, and latitudes and longitudes without end, to de-
termine by their aid. The advantages too, to be obtained, even for
the perfect and refined astronomy of the north, by placing nearly a
diameter of the globe, between the stations of observatories, and
taking up the objects common to both hemispheres, in a point of
view, and under circumstances so every way opposite to those which
exist here, have been strongly pointed out by a venerable and illus-
trious member of this Society, in an elaborate paper published in its
Memoirs, and would alone suffice to justify a high degree of interest,
as due to every well conducted series of observations from that
quarter. The observations of H alley at St. Helena, had made known
the places of a moderate number of the brighter southern stars ; but
the only catalogue of any extent and accuracy, which existed pre-
vious to the establishment of the observatories of the Cape and Pa-
ramatta, was that of Lacaille, who spent three years at the Cape of
Good Hope, and the Isles of France and Bourbon ; and, though with
very inadequate instrumental means, yet, by dint of the most inde-
fatigable industry, succeeded in observing and registering upwards
of 10,000 stars. But by far the greater part of these observations
have never been reduced; a selection only from them of 1942 of
the principal ones, not amounting to a fifth of their whole number,
having been formed into a catalogue, and published by this merito-
rious astronomer. It must be admitted, however, that the degree of
accuracy stated by Lacaille himself to have been probably attained
by him, is hardly such as to make us now very deeply regret their
want of reduction, especially as the observations themselves are
printed with every requisite for that purpose, when required. Still,
however, from his method of observing, which was with a fixed te-
lescope and rhomboidal network, his observations have what may be
termed a dormant value, as they most probably give correct differ-
ences for each night's work ; and when a catalogue of standard
southern stars shall be completed, Lacaille's observations will be-
come available, by regarding these as zero points, and referring all
the rest to them.

Such was nearly, with little improvement, the state of the astro-
nomy

Astronomical Society. 385

nomy of the southern hemisphere, when Sir Thomas Brisbane was
appointed governor of the Colony of New South Wales. The inten-
tion of our Government to found an observatory on the largest scale,
at the Cape of Good Hope, was, indeed, already fixed ; and the ob-
server, a member of this Society, supplied with instruments sufficient
for the purpose of constructing a preliminary catalogue, occupied
himself with the necessary observations, while awaiting the arrival
of those ultimately destined to adorn that establishment, and the
building of his observatory. The approximate catalogue so con-
structed and reduced, containing all the southern stars observed by
Lacaille, down to the 5th magnitude, is already printed by the Royal
Society in their Transactions.

Sir Thomas Brisbane's attachment to Astronomy had ever been a
prevailing principle of his mind, and one which even amidst the dis-
tractions of a military life of no ordinary degree of activity and ad-
venture, he found means to indulge ; and which never deserted him,
however the calls of his country might demand his services in a dif-
ferent and more splendid career.

His appointment to the important office of governor of New South
Wales, however, put it in his power to execute to their fullest extent
and under the most favourable circumstances, plans of astronomical
investigation, which to a private individual would have been utterly
impracticable. The opportunity was embraced with eagerness. The
best instruments, — consisting of an excellent transit of 5 J feet focal
length, by Troughton ; a mural circle of two feet in diameter, the
workmanship also of Troughton, and said to have been the model on
which that of Greenwich was constructed, and which had long been
in his possession j and a fine 1 6-inch repeating circle of Reichenbach, —
were destined for this service : and two gentlemen engaged as assist-
ants at considerable salaries j the one a foreigner of high estimation
as a mathematician and calculator, the other Mr. Dunlop, of whom
I shall presently have occasion to say much more. It ought to be
mentioned, that this noble equipage was furnished entirely from Sir
Thomas's private fortune, and maintained wholly at his own expense.
Immediately on his arrival in the colony in 1821, and so soon as an
observatory could be erected, and the instruments established, the
work of observation commenced, and continued with little inter-
ruption under the immediate superintendence and direction of Sir
Thomas Brisbane himself, who, though the pressing and: important
duties of his high office would of necessity seldom admit of his de-
voting any material proportion of his time to actual observation, yet
frequently took a personal share in the labours of the observatory, as
a relaxation from higher duties, and in particular, a great portion of
the transits were observed by himself.

The first fruits of this enterprise, were the observations of the
December solstice of 1821, which were published in the Astrono-
mical Notices of Schumacher j in which work also appear those of both
the solstices of 1 822, and a number of detached and occasional ob-
servations, which reached Europe at different times by a variety of
channels, and found their way into that valuable collection. The

New Series. Vol. 3. No. 17. May 1828. 3 D solstices

386 Astronomical Society.

solstices of 1823, were communicated by Sir Thomas Brisbane to
this Society, in a letter to our late worthy president, together with a
considerably extensive series of observations of principal stars, chiefly
those visible in both hemispheres, and which have undergone a care-
ful reduction and close scrutiny in the hands of Dr. Brinkley, the
details of which, as well as the original observations, are printed in
the first part of the second volume of the Transactions of this Society,
and which justify, in the eyes of that experienced observer, as they
must in those of every practical astronomer, a decided opinion of the
great care and skill with which they have been made.

A great number of occasional observations, — such as eclipses, oc-
cultations, and observations of the planets Venus and Uranus, near
their conjunctions and oppositions, and of comets from the same
source, — are also printed in the same volume. One of the most re-
markable single results we owe to the establishment of Sir Thomas
Brisbane's observatory, consists in the re-discovery of the comet of
Encke in its predicted place, on the 2H June 1822. The history of
this extraordinary body is well known to all who hear me ; and as its
re-discovery at Paramatta by Mr. Rumker, has already been, on a
former occasion, distinctly noticed and rewarded by this Society,
there is no occasion that I should here enlarge on it ; and yet I can-
not help pausing a moment to figure the delight its celebrated dis-
coverer must have experienced, to find the calculations, on whose
exactness he had pledged himself, thus verified beyond the gaze of
European eyes ; and this strange visitant gliding, as if anxious to
elude pursuit, into its primitive obscurity, thus arrested on the very
eve of its escape, and held up to mankind, — a trophy at once of the
eertainty of our theories, and the progress of our civilization.

Observations of the length of the pendulum were not neglected
by Sir Thomas Brisbane ; and the determination of this important
element at Paramatta, forms the subject of a highly interesting and
valuable communication made by him to the Royal Society, and
printed by them in their Transactions for 1823, and discussed by
Captain Kater with his usual care and exactness.

The remainder, and indeed the great mass of the observations
made with the mural circle and the transit instrument, have at dif-
ferent periods been communicated to the Royal Society, and are for
the present deposited in its archives. Forming our judgement only
upon those of which an account has been publicly read at the meet-
ings of that illustrious body, but which are understood to constitute
only a comparatively small part of the whole, — they form one of the
most interesting and important series which has ever been made,
and must ever be regarded as marking a decided aera in the history
of Southern Astronomy.

It is for this long catalogue of observations — whether scattered
through the journals of Europe, printed in our own Transactions, or
deposited as a precious charge in the care of a body so capable of
appreciating their merits ; but still more for the noble and disinter-
ested example set by him in the establishment of an observatory on
such a scale, in so distant a station, and which would have equally

merited

Astronomical Society. 387

merited the present notice, had every observation perished in its
conveyance home — that your Council have thought Sir Thomas Mac-
dougal Brisbane deserving the distinction of a medal of this Society,
which, as he is unable personally to attend this meeting, I will now
deliver to his proxy, Mr. South.

Mr. South, — We request you to transmit to Sir Thomas Brisbane
this medal, accompanied with the strongest expressions of our admi-
ration of the patriotic and princely support he has given to Astro-
nomy, in regions so remote. It will be a source of honest pride to
him while he lives, to reflect that the first brilliant trait of Australian
history marks the aera of his government, and that his name will be
identified with the future glories of that colony in ages yet to come,
as the founder of her science. It is a distinction truly worthy of a
British governor. The colonial acquisitions of other countries have
been but too frequently wrested from unoffending inhabitants, and
the first pages of their history blackened by ferocious conquests and
tyrannical violence. The treasures of gold and silver they have
yielded — the fruits of rapine — have proved the bane of those who
gathered them j and in return, ignorance and bigotry have been the
boons bestowed on them by their parent nations. Here, however,
is a brighter prospect. Our first triumphs in those fair climes have
been the peaceful ones of science ; and the treasures they have trans-
mitted to us, are imperishable records of useful knowledge, speedily
to be returned with interest, to the improvement of their condition
and their elevation in the scale of nations.

{The President then resumed his address to the Members, as fol-
lows : — )

I have now to call your attention, Gentlemen, to the award of an-
other Medal, to Mr. Dunlop, who accompanied Sir Thomas Brisbane
in capacity of his assistant, and who, since the middle of the year
1823, when his companion Mr. Rumker left the observatory, re-
mained in the sole charge of the instruments ; and up to the period
of the departure of his principal from the colony, continued an unin-
terrupted series of observations with a care and diligence seldom
equalled, and never surpassed. In such cases it is not only the head
which plans, but the hand which faithfully and promptly executes,
that claims our applause. The most liberal provision of instrumental
means would have been comparatively unavailing, had the spirit of
him1 who supplied them, been seconded by any ordinary zeal on the
part of his assistants. The records of this Society already alluded
to, bear sufficient testimony to the merits of Mr. Rumker, and to
our sense of them. In Mr. Dunlop were combined qualities render-
ing him of all others, the very individual fitted for the duties imposed
on him — zealous, active, ready — but above all (and the combina-
tion is not an ordinary one), industrious and methodical. In the vast
mass of observations made and registered by him, all is equable and
smooth, as if the observations had all been made at a sitting :

" Servatur ad imum

Qualis ab incepto processerit" —

3 D 2 no

388 Astronomical Society.

no lacunae — no long intervals of inactivity — nothing hurried or
sketchy j but the same pains-taking, laborious filling in, pervading
the whole,— marking that the observer's whole heart and soul were in
his work, and that each individual observation possessed its own pe-
culiar, though momentary, interest. Nor is this wonderful. The
heavens visible to Europeans, have been so thoroughly examined,
and their contents so carefully registered, that there is not the slight-
est rational probability of any thing new or uncommon offering itself
to instruments of moderate power in the ordinary course of observa-
tion. Here, however, all was new ; — for the optical power of La-
caille's telescope was far too feeble to afford much insight into the
physical constitution of the objects determined with it : and thus all
the excitement of discovery was maintained during every step in the
progress of the work.

But to be susceptible of this excitement, so maintained, the ob-
server must be animated by the true spirit of the Astronomer ; and
few have possessed this spirit in a greater degree than Mr. Dunlop.
In a scientific point of view, therefore, he must be regarded as the
associate, rather than the assistant of his employer j and their diffe-
rence of situation becomes merged in their unity of sentiment and
object. — These considerations alone would have rendered it impos-
sible to your Council to disunite in any expression or mark of their
approbation, individuals who have thus, each in his sphere, gone
hand in hand together, towards the perfection of Southern Astro-
nomy, even had the labours of Mr. Dunlop been confined to the or-
dinary business of an observatory, or to observations with fixed in-
struments. But this is very far from having been the case. The
nebulous, as well as the sidereal heavens, have occupied his atten-
tion ; and in the prosecution of this most delicate and difficult branch
of Astronomy, he has availed himself entirely of his own resources,
in the most literal sense, — the instrument which he used being not
simply his own, but the work of his own hands ; and the observations
being performed by him after the departure of Sir Thomas Brisbane
from the colony, at a personal sacrifice of his private interests, and
in the face of difficulties which would have deterred any one not ani-
mated with a real and disinterested love of science from their prose-
cution. The results of these observations have been the description
and determination of the places of upwards of 600 nebulae and clus-
ters of stars. And when it is recollected that Lacaille was able to
observe not more than about 40 or 50 of these curious objects, we
may form some idea of the extent of this labour. In addition to these
interesting results, Mr. Dunlop has amassed a copious and valuable
collection of Southern double stars, which he is at present occupied
in reducing and arranging j and a variety of interesting and curious
particulars relative to the magnitudes, colours, and other peculia-
rities of all the more conspicuous single ones.

Shut out as we are by our geographical situation from the actual
contemplation of these wonders, the astronomers of Europe may
view, with something approaching to envy, the lot of these their more
fortunate brethren. The feeling, if an unworthy, is, however, but a

passing

Astronomical Society. 389

passing one, and merges in that of admiration of their zeal and en-
terprise, and of gratitude tor the information they have afforded us.
In testimony of that admiration and that gratitude, on the part of
this Society, towards Mr. Dunlop, I beg of you, Mr. South, to trans-
mit to him also, this our medal, and to accompany it with the assu-
rance that wheresoever his future fortunes may lead him — whether
in the land which has already witnessed his meritorious labours — to
complete and extend them, or in his native country, which is both able
and willing to appreciate his value, to put the finishing stroke to the
noble fabric he has been mainly instrumental in raising, by taking a
leading part in the less exciting, but not less useful or indispensable
work, of reducing the observations already made : — in either case he
will be attended by our best wishes for his prosperity and happiness,
and our confidence that science will continue to benefit by his exer-
tions.

( The President having quitted the chair, was succeeded by Mu. South,
one of the Vice Presidents, who addressed the Meeting as follows: — )

Gentlemen, — Our excellent President in his Address has informed
you of the appropriation of two of your Gold Medals, since our last
Anniversary : — a third, however, has been decreed by your Council j
and when it is known that Miss Caroline Herschel is the individual
to whom it stands adjudged, it is not difficult to determine why the
President has avoided the slightest allusion to it.

But that your Council has not selected one from the many of its
Members, infinitely more competent to do justice to the transcen-
dent merits of that illustrious lady, is most assuredly matter of.
regret. I must, therefore, throw myself upon your indulgence,
hoping that the goodness of the cause may in some measure com-
pensate for the inability of its advocate.

The labours of Miss Herschel are so intimately connected with,
and are generally so dependent upon, those of her illustrious brother;
that an investigation of the latter is absolutely necessary ere we can
form the most remote idea of the extent of the former : but when it
is considered that Sir W. Herschel's contributions to Astronomical
Science occupy sixty-seven Memoirs, communicated from time to
time to the Royal Society, and embrace a period of forty years, it
will not be expected that I should enter into their discussion. To
the Philosophical Transactions, 1 must refer you, and shall content
myself with the hasty mention of some of her more immediate claims
to the distinction now conferred. To deliver an eulogy (however de-
served) upon his memory is not the purpose for which 1 am placed here.

His first catalogue of new nebulae and clusters of stars, amounting
in number to one thousand, was made from observations with the
20-feet reflector, in the years 1783, -4, and -5. A second thousand
were furnished by means of the same instrument in 1785,-6,-7, and
-8 ; whilst the places of five hundred others were discovered between
1788 and 1802. But when we have thus enumerated the results ob-
tained in the course of sweeps with this instrument, and taken into
consideration the extent and variety of the other observations, which

were

390 Astronomical Society.

were at the same time in progress, a most important part yet re-
mains untold. Who participated in his toils ? Who braved with
him the inclemency of the weather ? Who shared his privations ? A
female. — Who was she ? His sister. — Miss Herschel it was, who by
night acted as his amanuensis. She it was whose pen conveyed to
paper his observations as they issued from his lips ; she it was who
noted the right ascensions and polar distances of the objects observed ;
she it was who having passed the night near the instruments, took
the rough manuscripts to her cottage at the dawn of day, and pro-
duced a fair copy of the night's work on the subsequent morning ;
she it was who planned the labour of each succeeding night ; she it
was who reduced every observation, and made every calculation ;
she it was who arranged every thing in systematic order j and she
it was who helped him to obtain an imperishable name.

But her claims to our gratitude end not here ; as an original
observer she demands, and I am sure she has, our most unfeigned
thanks. Occasionally her immediate attendance during the obser-
vations could be dispensed with. Did she pass the night in repose ?
No such thing ; wherever her illustrious brother was, there you were
sure to find her also. A sweeper planted on the lawn became her
object of amusement, but her amusements were of the higher order,
and to them we stand indebted for the discovery of the comet of 178(5 ;
of the comet of 1 788 ; of the comet of 1 79 1 ; of the comet of 1 793 ;
and of the comet of 1795, since rendered familiar to us by tjie re-
markable discovery of Encke. Many also of the nebulae contained in
Sir Wm. Herschel's catalogues were detected by her during these
hours of enjoyment. Indeed, in looking at the joint labours of these
extraordinary personages, we scarcely know, whether most to admire
the intellectual power of the brother, or the unconquerable industry
of the sister.

In the year 1797, she presented to the Royal Society a catalogue
of 560 stars taken from Flamsteed's observations, and not inserted in
the British catalogue ; together with a collection of errata that
should be noticed in the same volume.

Shortly after the death of her brother, Miss Herschel returned to
Hanover. Unwilling, however, to relinquish her astronomical la-
bours whilst any thing useful presented itself, she undertook, and
completed the laborious reduction of the places of 2500 nebulae, to
the 1st Jan. 1800, presenting in one view the results of all Sir Wm.
Herschel's observations on those bodies j thus bringing to a close
half a century spent in astronomical labour.

For this more immediately, and to mark their estimation of services
rendered during a whole life to Astronomy, your Council resolved to
confer on her the distinction of a medal of this Society. The pecu-
liarity of our President's situation, however, and the earnest manner
in which the feelings, naturally arising from it, were urged when the
subject was first brought forward, caused your Council to pause, — and
waive on that occasion the actual passing their proposed vote. The
discussion was however renewed on Monday last; and although there
was every disposition to meet the President's wishes, still under a

conviction

Obituary .—Sir J. E. Smith, 391

conviction tha£ the doing so would have been a dereliction of public
duty, it was

Resolved unanimously, "That a Gold Medal of this Society be given
to Miss Caroline Herschel, for her recent reduction, to January 1800,
of the Nebulae discovered by her illustrious brother, which may be
considered as the completion of a series of exertions probably unpa-
ralleled either in magnitude or importance, in the annals of astrono-
mical labour." A vote which I am Sure every one whom I have the
honour to address, will most heartily confirm.

Mr. Herschel. — In the name of the Astronomical Society of Lon-
don, I present this Medal to your illustrious Aunt. In transmitting it
to her, assure her that since the foundation of this Society no one
has been adjudged, which has been earned by services such as hers.
Convey to her our unfeigned regret that she is not resident amongst
us ; and join to it our wishes, nay, our prayers, that as her former
days have been glorious, so her future may be happy.

PROCEEDINGS AT THE FRIDAY-EVENING MEETINGS OF THE
ROYAL INSTITUTION OF GREAT BRITAIN.

March 21. — Mr. Millington entered into an experimental account
of the manufacture of paper, principally with a view of introducing
and explaining by working models the making of paper by machinery,
and especially some recent and important improvements. Numerous
specimens of paper, varying both in quality and size, were exhibited.

Some experiments on the deceptive appearances of coloured sha-
dows were shown in the Library by Mr. Marshall ; and a large meteoric
stone having a very peculiar polished metallic fracture was laid with
other things upon the table.

March 28. — Dr. Harwood gave an account of some parts of the
structure and (economy of the Greenland whale, during which he en-
tered into the illustration of certain views relative to the blubber and
the skin which he had been induced to entertain, from a close exami-
nation of these and other parts of the animal. The specimens ob-
tained for illustration from the museums of the Zoological Society,
by Mr. Brookes and Dr. Harwood, were very fine and numerous.

The library-tables were covered with objects of interest from the
East, from the museum of Lady Raffles and the collection of Mr.
Bennett.

April 18. — Mr. Ainger delivered an illustrated explanation of some
recent improvements in clock and watch escapements, especially of
the one invented by Mr. Hardy. The principles of the four great
divisions of escapements were exhibited and distinguished.

OBITUARY : — SIR J. E. SMITH.

On Monday the 17th of March, died at his residence in Norwich,
Sir James Edward Smith, President of the Linnaean Society. This
distinguished botanist was born at Norwich, December 2nd, 1759 ;
and to the locality of his birth we are probably to attribute his early
predilection for Natural History, for here he fell in with some of the

earliest

392 Obituary :—Sir J. E. Smith.

earliest and most devoted disciples of the great Linnaeus. Tins city
has for more than two hundred years been famous for its florists and
botanists. Here lived and flourished Sir Thomas Browne, the author
of M Vulgar Errors," and " The Garden of Cyrus, or the quincuncial,
lozenge, or network Plantations of the Ancients, artificially, natu-
rally, and mystically considered." A weaver of this commercial place
claims the honour of having been the first person who raised from
seed a Lycopodium ; as a Manchester weaver was the first to flower
one of our rarest Jungermannice. During the middle of the last cen-
tury Mr. Rose, the author of the Elements of Botany, Mr. Pitchford,
and Mr. Crowe, names familiar to every botanist, took the lead in
botanical science in their native city j and instilled into the youth-
ful mind of the future President an ardent attachment to their fa-
vourite pursuit, and a skill in discriminating species for which these
gentlemen were so eminent. Having remained the usual time at a
school in the city, he went in the year 1780 to the University of
Edinburgh, where he distinguished himself by obtaining the gold
medal given to the best proficient in botany.

Upon leaving Edinburgh he came up to London to finish his
studies, and soon became acquainted with the late Sir Joseph Banks.
This acquaintance, and the access it obtained fpr him to men of science,
only riveted more firmly his ardent attachment to botany j and ac-
cordingly, we find Sir Joseph recommending him as early as 1 783 to
become the purchaser of the Linnaean collection. As this circum-
stance laid the foundation of the President's future fame, and is one
of peculiar interest at the present moment, we shall detail the history
of the transaction.

The younger Linnaeus had died suddenly, November 1, 1783} and
his mother and sisters, desirous of making as large a profit as they
could by his Museum, within a few weeks after his death offered
through a mutual friend the whole collection of books, manuscripts, and
Natural History, including what belonged to the father as well as the
son, to Sir Joseph Banks, for the sum of one thousand guineas. Sir
Joseph declined the purchase, but strongly advised Sir James Smith
to make it, as a thing suitable to his taste, and which would do him
honour.

Sir James in consequence communicated his desire to become the
purchaser to Professor Acrel,the friend of the family of Linnaeus, and
who seems to have conducted the negotiation with scrupulous honour.
The owners now began to suspect they had been too precipitate ;
having received an unlimited offer from Russia, while also Dr. Sib-
thorpe was prepared to purchase it, to add to the treasures, already
famous, of Oxford. They wished to break off their treaty with Sir
James Smith ; but the worthy Swedish Professor would not consent
to it, and insisted on their waiting for his refusal.

In consequence of the subtraction of a small herbarium made by
the younger Linnaeus, and given to a Swedish baron to satisfy a debt
he claimed, a deduction of one hundred guineas was made in the
purchase-money j and in October 1784 the collection was received, in
twenty-six great boxes, perfectly safe. The whole cost, including the

freight

Obituary :—Sir J. E. Smith. 393

freight, was 1029/. The duty was remitted on application to the
Treasury. The ship which was conveying this precious treasure had
just sailed, when the King of Sweden (Gustavus III.), who had been
absent in France, returned, and hearing the story, sent a vessel in
pursuit, but happily it was too late.

The collection consists of every thing possessed by the great Lin-
naeus and his son relating to natural history and medicine. The
Library contains about 2500 volumes. The old herbarium of the
father comprehends all the plants described in the Species Plantarum,
except perhaps about 500 species (Fungi and Palmce excepted), and
it had then perhaps more than 500 undescribed.

The herbarium of young Linnaeus appears to have had more atten-
tion bestowed upon it, and is on better paper. It consists of most
of the plants of his Supplementum, except what are in his father's
herbarium, and has besides about 1500 very fine specimens from
Commerson's collection, from Dombey, La Marc, Pourrett, Gouan,
JSmeathman, Masson, &c, and a prodigious quantity from Sir Joseph
Banks, who gave him duplicates of almost every one of Aublett's spe-
cimens, as well as of his own West Indian plants, with a few of those
collected in his own voyages round the world.

The insects are not so numerous j but they consist of most of those
that are described by Linnaeus, and many new ones. The shells are
about thrice as many as are mentioned in the Systema Nature?, and
many of them very valuable. The fossils are also numerous, but
mostly bad specimens and in bad condition.

The number of the MSS. is very great. All his own works are in-
terleaved with abundance of notes, especially the Systema Natures,
Species Plantarum, Materia Medica, Philosophia Botanica, Clavis
Medicines, he. There are also the Iter Lapponicum (which was after-
wards published), Iter Dalecarlicum, and a Diary of the Life of Lin-
naeus for about thirty years of his life. The letters to Linnaeus, (from
which a selection was also published by the President,) are about
three thousand.

This splendid acquisition at once determined the bent of the pro-
prietor's studies. He considered himself, as he has declared, a trustee
only for the public, and for the purpose of making the collection
useful to the world and to natural history in general. How well he
has fulfilled this trust will appear from the sequel. He had no sooner
obtained quiet possession than he began to fulfill his engagement,
for we find him in the year 1785 making his first appearance as an
author, by translating the Preface to the Museum Regis Adolphi Fri-
derici of Linnaeus, being succinct and admirable reflections on the
study of nature.

In the year 1 786 he prepared himself for an extensive tour on the
Continent j in which his chief object was to examine into the state of
natural history in the different cities and towns he might pass through,
not neglecting the incidents, especially the fine arts, which usually
engage the attention of travellers. At Leyden he graduated in me-
dicine j but it does not appear that he tarried there a longer time
than was necessary for this purpose. On this occasion he published

New Series. Vol. 3. No. 17. 21% 1828. 3 E his

394. Obituary :—Sir J. E. Smith.

his Thesis De Generatione. The " Sketch of a Tour on the Con-
tinent," though long superseded as a companion to the tourist, is still
curious to the naturalist, as showing the state of science at that time.
It contains, too, a fund of good sense expressed with facility ; and to
those who enjoyed the acquaintance and friendship of the author, will
always remain valuable, as furnishing the truest image of his mind,
reviving his liberal opinions in their recollection, and his easy and
elegant manner of communicating them.

In the year 1788, when he had returned and was settled in London,
he with some other naturalists projected the establishment of the
Linnsean Society, which had for its object the cultivation of Natural
History in all its branches, and especially that of Great Britain. This
Society, which has grown now into considerable importance, was a
scion of the Royal Society, and had its origin in the jealousy which
some of the members of the parent Society entertained of the pre-
ference which they alleged was given to Natural History in their
Transactions ; while its then President was thought to favour the sub-
ject, to the exclusion of others of equal, if not of greater importance.
There are still some who recollect the argumentative and vehement
eloquence by which this side of the question was supported by a re-
verend Prelate.

It was during this stormy period that Sir James Smith, in conjunc-
tion with the late Bishop of Carlisle, Sir Joseph Banks, and others,
laid the foundation-stone of the Linnsean Society. Its first meeting-
was held April 8, 1788. The Society then consisted of fifty Fellows,
and about twice as many more Foreign Members, Dr. Smith being
the first President, Dr. Goodenough the first Treasurer, and Mr.
Marsham the first Secretary. Of these original Fellows, how few are
left ! and of those who are, their hoary locks, still seen oecasionally
at the meetings of the Society, remind us of the respect and gratitude
we owe to them as fathers. May their declining years derive con-
solation from the success of this their early project !

At the first Meeting, the President delivered a Discourse, judicious
and appropriate, On the Rise and Progress of Natural History. . We
find him also about this time producing a paper which was read before
the Royal Society, entitled Observations on the Irritability of Ve-
getables. It chiefly regards the mode of impregnation in the Bar-
berry ; and attracted considerable attention at the time, being trans-
lated into other languages, and appearing in different publications.

The next considerable work which we find him undertaking, is the
re-publication of the wooden blocks of Rudbeck, which had fallen into
his hands with the Linnsean collections. Linnaeus was possessed of
about 120 of these blocks, which had escaped the fire at Upsal, where
almost the whole impression of the second volume, and all but three
copies of the first, were burnt. As Rudbeck was the founder of a
school at Upsal destined afterwards to give laws to the rest of the
world, the re-publication of this fragment of his great work was a
tribute of gratitude to his profound and varied learning.

From 1789 to 1793, our author was engaged in various publica-
tions relating to his favourite science. Most of them terminated in

being

Obituary :—Sir J. E. Smith. 395

being only fragments, for want of patronage by the public. Such
were his Plantarum Icones hactenus inedita ; Icones pictce Plantarum
rariorum ,• Specilegium Botanicum ; and " Specimens of the Botany of
New Holland." One of these literary projects, " English Botany,"
however, did not suffer the shipwreck experienced by the others, but
has received the encouragement it deserved. This is not attributable
to its execution being superior to the other works which have failed,
but because it treats of the plants of our own country, in which all
are interested. It has the singular merit of being the only national
Flora" which has given a figure and description of every species native
to the country whose productions it professes lo investigate $ and
while other works of a similar kind have enjoyed the patronage of
foreign Crowns, and have even been supplied with funds to carry
them forward in their tardy progress, this work has been rendered
complete by the patronage of the public alone, and was brought to a
successful termination in 1814, by the united efforts of the President
of the Society, and of Mr. Sowerby, the draughtsman and engraver.

In the year 1793 appeared in the Memoirs of the Academy of
Turin, of which he was* a Member, his essay DeFilicum Generibus
dorsiferarum, and which was republished in English in his "Tracts on
Natural History."

Soon after our author's marriage in 1796 he removed to Norwich,
his native place, where he continued to reside, paying occasional visits
to London, for the remainder of his life.

The next considerable work upon which the reputation of our au-
thor is built, is the Flora Britannicu, which appeared in the years
1800 — 1804. It is remarkable, like all his other labours, for accu-
racy in observing, accuracy in recording, and unusual accuracy in
printing. It comprises descriptions of all the phsenogamous plants,
of the Filices, and the Musci ; and every species has been carefully
collated with those which Linnaeus described. Being written in the
Latin language, the information is condensed into a small compass j
while it has the rare advantage of having had every synonym com-
pared with the original author.

The Compendium Flora Britannicce has gone through four editions,
and is become the general text-book of English botanists. It is per-
haps the most complete example of a manual furnished on any subject.

While he was engaged in the Flora Britannica, the executors of
the late Professor Sibthorpe selected him as the fittest person to en-
gage in editing the splendid posthumous work of that liberal patron
of science ; a task for which the unrivalled attainments of the Presi-
dent, and his personal friendship with the Professor, peculiarly quali-
fied him. The drawings which were made by Ferdinand Bauer, and
the letter-press which was written by Sir James Smith from scanty ma-
terials furnished by Dr. Sibthorpe, are both worthy of so munificent an
undertaking. To complete the work, which is to consist of ten folio
volumes, and 100 coloured plates in each, Dr. Sibthorpe bequeathed
a freehold estate at South Leigh, in Oxfordshire ; which, after the
completion, is to be charged with the support of a Professor of Rural
Economy in the University of Oxford.

3 E 2 The

396 Obituary :—Sir J. E. Smith.

The Introduction to Physiological and Systematic Botany has also
been a most successful publication, having passed through five editions.
It is indebted for its popularity to a happy method which the author
has of communicating knowledge, to the good taste he every where
displays, and to that just mixture of the utile with the duke, which he
knew so well how to apportion.

In 1810 appeared his Tour to Hafod, the seat of his old and ac-
complished friend Thomas Johnes, Esq.

In 1814 he received the honour of knighthood from the hands of
his present Majesty, on the occasion of his Majesty consenting to
become the patron of the Linnaean Society, and granting them a
charter.

About 1818 the Professor of Botany at Cambridge encouraged the
President to offer himself for the Professorship of that University.
He obtained the countenance of many of the heads of houses, but
unfortunately it terminated in a controversy on his religious opinions,
which he could not, and never would, compromise. It produced two
small tracts from his pen, which at least show that he was not dis-
qualified by the absence of the most charitable spirit.

In 1812 his Grammar of Botany appeared -, and in the same
year, a " Selection of the Correspondence of Linnaeus and other Na-
turalists."

During a large portion of his literary life, he was in the habit of
writing articles for Dr. Rees's Cyclopcedia on different subjects in
botany and biography connected with it. Many of these biographical
memoirs are choice morsels of original information ; and we need
only refer to the words Curtis, Linnaeus, Hudson, and Sibthorpe, in
justification of our assertion. Most of his articles will be found marked
with the letter S, it being his undeviating rule never to publish any
thing on anonymous authority in science. Even some Reviews which
he had written early in life, he afterwards avowed by republishing them
in his " Tracts."

The second volume of the Supplement to the Encydopcedia Britan-
nica is indebted to our author's pen for a Review of the Modern State
of Botany, an article which supplies some deficiencies in his Introduc-
tion, though chiefly an abridgement of the Prcelectiones of Linnaeus,
as published by Giseke.

During the whole of his literary career he occasionally contributed
papers to the Linnaean Transactions. — But the last and best work of
the distinguished President is the " English Flora," consisting of four
volumes octavo, and describing the phaenogamous plants and Ferns of
Great Britain, though its title might imply a more limited range. Finis
coronat opus. There is no Flora of any nation so complete in flowering
species, and none of any country in which more accuracy and judge-
ment are displayed. If any person should in future contemplate a
work of this kind, — whatever the originality of his information, what-
ever the novelty of his subject,— let him imitate this illustrious author
in careful remark, in taking nothing upon trust, in tracing every syn-
onym to its source, and lastly in arranging his matter in such a
manrfer, by the aid of different types, as shall render it easy of refer-
ence,

Intelligence and Miscellaneous Articles. 397

ence, and point out at a glance the nature of it. However mechanical
some of this may appear, it is absolutely essential to be attended to
in Natural History, where the subjects are infinite in number, and
where aid must be derived from every mode of generalizing particulars.
In summing up the scientific character of the deceased, it may be
comprised in a few words. As a naturalist, he contributed greatly to
the advancement of science ; and stood pre-eminent for judgement,
accuracy, candour, and industry. He was disposed to pay due respect
to the great authorities that had preceded him, but without suffering
his deference for them to impede the exercise of his own judgement.
He was equally open to real improvement, and opposed to the affecta-
tion of needless innovation. He found the science of Botany when
he approached it, locked up in a dead language, — he set it free by
transfusing into it his own : he found it a severe study fitted only for
the recluse,— he left it of easy acquisition to all. In the hands of his
predecessors, with the exception of his immortal master, it was dry,
technical, and scholastic j in his, it was adorned with grace and ele-
gance, and might attract the poet as well as the philosopher.

LXI. Intelligence and Miscellaneous Articles.

NEW MINERALS.

PROF. BREITHAUPT (Schweigger's Journal der Chemie und
Physik, N. S. vol. xx. p. 314, &c.) gives a description of the fol-
lowing new mineral species :

I. Karphosiderite. Name derived from the straw-yellow colour.
Reniform masses, rarely from granular composition, uneven ; shining
and glimmering in the streak, with resinous lustre. Colour and
streak pale and high straw-yellow. Hardness =4*0... 4*5. Sp.
gr. z= 2'5. Feels greasy. Before the blowpipe upon the coal it
becomes black, and melts in a strong fire into a globule which is
attractible by the magnet. In glass of borax it is easily soluble,
and with salt of phosphorus it melts into a black scoria. It con-
tains oxide of iron, phosphoric acid, water, with small quantities of
oxide of manganese and zinc. It has a great similarity to oxalite,
yellow iron-ore, or iron-sinter. It occurs in Greenland.

II. Mesitine-spar. Name derived from psa-tys, that is, what
stands in the middle (of brachytypous lime-haloide, and brachy-
typous parachrose baryte). Rhombohedral, R — oo. R = 107° 14'
R -f ac. Cleavage distinct, parallel to R. Lustre vitreous. Colour
dark-grayish, and yellowish-white. . . yellowish-gray. Streak white.
Transparent . . .translucent. Hardness = 4. Sp.gr. = 3*34. . .3*37.
Before the blowpipe the mesitine-spar decrepitates. In muriatic
and nitric acid a feeble effervescence takes place, but it is entirely
soluble. It contains probably magnesia, lime, protoxide of iron,
and oxide of manganese. It is found in little crystals, in rhombo-
hedral quartz at Traversella in Pieroont.

III. Tauto-

398 Meteorological Observations for March 182S.

III. Tautolite.
pyramid.

a:b:c = 1:1-9451

Observed combinations :

Prismatic. Fundamental form, scalene four-sided
1-3648.

1, M

f

= ooa:£:c = 109°46'.

= 4 a : b : oo c = 51° 52'.
i = <x a : oo 6 : c fig. 9 of Mohs's treatise,

2, M;^;A;
i = oo a : | 6 : c = 86° 22'.
e=2<z:&ooc=88° 25'.

M ;"

Cleavage, only in traces and interrupted, parallel
toMand/j. Fracture conchoidal. . .uneven. Lustre
vitreous. Colour velvet-black. Streak gray. Opaque. Hardness
= 6-5. . .7*0. Sp. gr. = 3-865. Before the blowpipe, upon char-
coal, the tautolite melts to a blackish scoria, which is attracted by
the magnet ; with borax it melts to a clear green glass. These and
other reactions show that the mineral consists of silica, black prot-
oxide of iron, magnesia, and alumina. It is found in the volcanic
feldspath-rocks, in the neighbourhood of the Lake Laach Sea in
Rhein-Prussia. The tautolite seems to be related to the chrysolite,
as the Ceylanite to the Spinelle. — Brewster's Journal of Science.

METEOROLOGICAL OBSERVATIONS FOR MARCH 1828.

Gosport. — Numerical Results for the Month,
Barom. Max. 30-30 Mar. 16. Wind W.—Min. 29-02 Mar. 21. Wind S.W.
Range of the index 1*28.

Mean barometrical pressure for the month 29-879

Spaces described by the rising and falling of the mercury 5*640

Greatest variation in 24 hours 0-580. — Number of changes 1 7.
Therm. Max. 63° on several days.— Min. 30° March 6. Wind NW.
Range 33°.— Mean temp, of exter. air 47°-92. For 30 days with 0 in X 4972
Max. var. in 24 hours 23°-00— Mean temp, of spring water at 8 A.M. 50°-86

De Luc's Whalebone Hygrometer.
Greatest humidity of the air in the morning and evening of the 16th 100°
Greatest dryness of the air in the afternoons of the 19th & 24th... 44

Range of the index 56

Mean at 2 P.M. 58°-4 —Mean at 8 A.M. 73°'0— Mean at 8 P.M. 71-4

of three observations each day at 8, 2, and 8 o'clock 67*6

Evaporation for the month 1*90 inch.

Rain near ground 1-755 inch.— Rain 23 feet high 1-620 inch.

Summary of the Weather.
A clear sky, 4£ ; fine, with various modifications of clouds, 15; an over-
cast sky without rain, 7a ; foggy 1 ; rain, 3. — Total 31 days.
Clouds.
Cirrus. Cirrocumulus. Cirrostratus. Stratus. Cumulus. Cumulostr. Nimbus.
12 6 24 1 19 25 15

Scale of the prevailing Winds.
N. N.E. E. S.E. S. S.W. W. N.W. Days.
3* 2J 1 3 i 6 5i 9 31

General

Meteorological Observations for March 1828. 399

General Observations. — This month commenced with cold weather, which
kept up till the 7th ; and it was also cold and humid from the 23rd to the
end : the other part was mild for the season, the maximum temperature of
the external air in the day often being at 63°.

Rain, frequently accompanied with hail, fell on twelve different days,
but the quantity does not amount to two inches.

On the 14th, 15th, and 16th, thick fogs prevailed here.

In the afternoon of the 22nd there were two winds, the lower one from
N.W., and the upper one from the South, which, uniting the clouds, gra-
dually brought on several vivid flashes of lightning, and loud claps of thun-
der, which were immediately followed by a heavy shower of hailstones
coated with a snowy substance. Soon after 5 o'clock in the morning of
the 29th, a smart shower of snow fell, which covered the ground and the
surrounding hills for a short time only, as it was soon afterwards succeeded
by rain. In the evening of the 30th it again snowed a little, but it disap-
peared before the morning.

After the vernal equinox winter revisited us in keen northerly and easterly
winds in the days, and thick hoar frosts in the night ; so that winterly
weather was felt here some weeks after the beginning of spring.

The mean temperature of the air this month is about three degrees
higher than the mean of March for the last twelve years. The temperature
of spring water is nearly at a stand ; and the ground is now warmer than it
has been at the close of March since 1822. But this additional heat does
not appear to have modified the prevailing chill in the atmosphere, it being
either too small, or dissipated by evaporation, before it could arrive at a
sufficient altitude to have any effect.

The atmospheric and meteoric phcenomena that have come within our
observations this month, are one solar and one lunar halo, one meteor ;
lightning and thunder in the afternoon of the 22nd, and nine gales of wind,
or days on which they have prevailed ; namely, two from the North, two
from North-east, one from South-east, one from West, and three from
North-west.

REMARKS.

London. — March 1, 2. Cold and cloudy. 3 — 5. Fine. 6. Clear and cold.
7. Cloudy: showers at night. 8. Hazy: fine. 9, 10. Very fine. 11. Slight
fog: very fine. 12. Cloudy. 13 — 15. Very fine. 16, 17. Cloudy. ls.Fine:
stormy at night. 19. Very fine. 20,21. Cloudy: with showers of hail.

22. Cold with slight showers. 23 — 25. Clear and cold. 26. Cloudy: rain
at night. 27. Rain in morning : fine. 28. Drizzly : cloudy. 29. Cloudy
and cold. 30. Cloudy. 3 1 . Foggy : very fine.

Boston. — March 1. Cloudy: rain p.m. 2, 3. Cloudy. 4. Cloudy: stormy
night. 5. Fine. 6. Fine : snow a.m. 7. Cloudy : rain p.m. 8. Cloudy.
9—11. Fine. 12,13. Cloudy. 14,15.Fine. 16— 18.Cloudy. 19.Stormy.
20. Cloudy: rain at night. 21. Cloudy : rain p.m. 22. Fine : rain at night.

23. Fine. 24. Fine: rain p.m. 25, 26. Cloudy. 27. Stormy and rain: rain
a.m. 28. Cloudy. 29. Fine: rain a.m. 30. 31. Fine.

Penzance. — March l. Clear: fair. 2. Fair: clear. 3 — 6. Fair. 7.Fair:
showers. S.Clear. 9. Fair. 10. Fair : misty. 11. Misty: rain. 12 —
14. Fair. 15. Foggy. 16, 17. Fair. 18. Clear: rain. 1 9. Rain : fair.
20. Rain : showers. 21,22. Hail-showers. 23. Hail and snow. 24, 25. Clear :
hail-showers. 26. Cloudy : rain. 27. Cloudy: clear. 28. Cloudy: showers.
29, so. Clear : showers. 3 1 . Clear. — Rain-gauge ground level.

Meteoro-

i

I

1

J*

Si

jsog :

• S -2

dsOQ

o
:§

:§ :

o © o o o
: -> • to : tor* <n :
. © . — . -« — < o .

4 4 © o

:»oiO""

•zuaj :

1

© © © © © lO . lO © .

00 CO Ch CO — © • O O •

ci 9 cpci 9 ^ * 7? cp '

6666h6 66 666

pucj

: vo otco
.000

•dsoQ

:oo

[ I

m irt > » «• n! <*??•» «l

dsog

.J £

* 'a 15

u u

»• B S S .. . rf S . .. S E

ce c8 „

g l> 6

St *

25 55

•ACjt-^IS'ntttt'rt

2 2 " *_* * w * g §

£»££-£ i?££ st k* a >'■ k J* fel £ V £ '£. * si ir * « u u w"

™>d * £ * * £ X ££

I k' I i * * <* ***** i £ tt" i £ 5 £ i>£ i * : * 4< i *

ZZViZZ^^Sj

.pUO'J

X X A Z.

£ £ £ £ £ £ £ k £ £ £ £ £ £ £

•^ r« ** rrt m * * t/5 ■* <* r/i vi ►.»• "*

£ 1

•wtrf8j
nsog; I

to m 10 »o

10 lo to

^rf^^^oc^uo^iO^^rfiOiOiOu^Tt^^^^Tt.^^4^^^^^

^co^^ocorr^^^^^^^^^^^^rJ<Ti<cococococorj''

■•** CO co co co

1 co "3<ci 00 o>oo r^-o ©>o oco o%o coco ^vo -5?co "tfci

1 ic 10 -^ ^ io m ic o io<o «oo m*o<oio »o 10 »o 10 »o to

0100 ^a^eo-^toco^c^^ftfrf'^^fci coooooQo t^t^i

iLO^T^iOvoiOtOtOiOJOiOiOtOtOtOiOT^^^^ji^

-" CO^COC^OJ^^^CO^^^Tt<^^rf^cOrrcocoCOO<oTococNCOo1cTco

g\oiooio^<M w-"--- 01 go -^ co tj- «n ^ 00 10 co >o 00 00 t-» 01 1^ 10 o 10 c^ -rt< co

TtfT*iotO^CO^tOOVOOu^OOOOVOtOtOtOlOT*^T*Tr^<U^;o^^tO tO

CQ 00"

^C^OOOtO^OC^COLOtOGO<-'COCOOICCt^^-ilOrtiO--<i0010vovninC>

r^«o ip ^tcpipop r-r-»*o ^voipr^ap-^cioooo^oop gici tj< ip oi ci -<*(o oS
cVl6^6^6^6^cyl6^6^0^CT^C^cy^CT^CTlCylO^O^C^<XlGOCOcbGb 6iC>6>6\6i6vcViOn
ci cjqio»oioioioiojo<o<c*o<o<o»cioio<o<oio<c<oioi<noi Ol CI Ol Ol Ol

ooa>cp^^r.9c^cNr'0~c^c^T'r<Qpip>r<ocN rp«pt^<ococo^.cy>-r
6 6 6>6>icVv6xi6 6 o 6 o o o o o © © ^c^^6N<^<^6^6>ONa>6>iChcVi6
cococnc^cic*cocococococococococococ*oic*cnoic^c*^

99^^©7-c<cNO<CN9^c^CNcorHrY^Trrr5T^^^C^T^^^9^1 co

bOOONO^OOOOOOOOOCOOOOO^WCM^OO^GOiOOO

(0«30©CClO©OI©^GOCOCO©^1,00<©vO©Tt©

~c?>66o©6cio©o©o©c3>6icVic^cihcy\<^cy>cV>o^o\66

ClcOCOCOCOCOCICOCOrOCOCOCOClClCl01CI01C^C<01cVciC>>co

OOOodiOSoOOOOGOOOOOOOOi^O^
COCOCOCOOIOICOCOCOCOCOOICOCOCOCOCOCOC^OIOIOI

ooei ood^i 00000

Ol CO-^t^OO ■^'COiOCTiO CJ

© COO* Tf O G\CC

cr, © — — oj r* r*

— CNcp>pcNcpipqpop r^cp^-00 9 ci

066661600000
cocococoCNCOCOcocococoOlcocococococofNCNOlO^

C> O^ Cl

ol 01 ex

j

co-" O? — "^

1 co 00 "o co«o

O <^00 t^CT>

^"OO ^t<CN
VO — < (O rfiO

-< ^- Ol ^H OI

?^P ?? © © © © o^c^c^c^cyiOicicTK^^cyi© o

-■ 01 Ol CI OI lOCO

6 co~iooo co

i-^mooo

'■tf 1000 O^iCO

CO COCO
I>-lC en

Oh«

iflr)"i^O(»ON|>^0>-0
QOOIVOlOO^COClCOCOt^UDO

i c?> cti oi o> 6
1 ci oi o) d co

— <oo r^ — — <

C« Ol <0 CT>C»

-H O OGO —

_ ^ ^ co *<*

00 t--© r^co

01 Ol CO CI <N

>oo CMooMoot^o fhioo^ o""^o"6

^cicpcpcp^c<voyi<^cpLpcoa*!0;>
oo©ooooc?\6>6i6i6>6\cVicVi

COCOCOCOCOCOCO<NCICI<NO»C1CICJ

Ol CO «* CO GO

o r^-*ci co
up r^o^ci cp

c> cr* o> 6 6

CN CI CI CO CO

o ~

c
z

jr!

EJ

>S CO ** 10*0 t^OOOOH^O^iOCtNOOOlOr-iocoTf^lO
— — — — — -'-'-- -'-'CICICICJCJCICI

CJ CI CI CO CO

THE

PHILOSOPHICAL MAGAZINE

AND

ANNALS OF PHILOSOPHY.

[NEW SERIES.]

JUNE 1828.

LXII. On the Artificial Production of Cold. By Richard
Walker, Esq. of Oxford.

To the Editors of the Philosophical Magazine and Annals.
Gentlemen,

IT is now forty-one years since my discoveries on the " arti-
ficial production of cold " were first made public by their
appearance in the Philosophical Transactions for the year 1787,
and several succeeding volumes. Passing over what has al-
ready been published respecting them, I shall proceed to a
detail of a few other circumstances as a kind of appendix, which
I have for several seasons intended to offer for publication,
had not other matters, as professional avocations and profes-
sional communications, too much engaged my attention to al-
low of it.

Immediately on the announcement of the discoveries as above
stated, I received various proposals from respectable persons
respecting their practical utility in this country. I answered
these by a declaration that wherever natural ice could be ob-
tained and preserved, this must ever supersede the use of the
artificial means alluded-to. It is true that I had an eye to
their application in hot climates, as between the tropics ; and
so soon as my experiments became public, a treatise on the
diseases of tropical climates appeared from the pen of Dr.
Moseley, who fixed upon one, which he considered the most
appropriate, and strongly recommended its adoption as a very
valuable acquisition as well in a medicinal point of view, as a
luxury.

Relinquishing, from various causes, the design of applying
them myself to any such purpose, I took care however to point

New Series. Vol. 3. No. 18. June 1828. S F out,

402 Mr. Walker on the artificial Production of Cold.

out, in my original communications, the complete efficiency of
them for such intention to their utmost extent, and the best
mode, as it appeared to me, of applying them in hot climates.

Understanding, a few summers ago, that a manufactory had
been established for preparing ice-creams, as well without the
use of ice, as with it; and likewise for making for sale an ap-
paratus for the purpose, — I was induced to visit it. I examined
the apparatus, — a very appropriate one for the purpose, and
likewise the freezing powder, which I instantly recognized to
be the weakest in power of my various compositions for the
purpose, but possessing the advantage of being readily re-
covered repeatedly for the same purpose with undiminished
effect. This powder, by its taste and appearance, I found
to be a mixture of sal ammoniac and nitre, which I was in-
formed was repeatedly recoverable in a fit state for refrigera-
tion. I originally exerted every effort, in vain, to increase its
power by the addition of a third ingredient, possessing like-
wise the advantage merely by evaporation to dryness, of being
repeatedly recovered for the same use. This powder, as re-
lated in my original communications, consists of equal parts
by weight of sal ammoniac and nitre. By way of test, I reco-
vered it by evaporation twelve times, without any abatement
of its efficacy, as originally stated*.

It is unnecessary to enter into a description of the apparatus
just mentioned, or the principle and mode of its application,
especially as the whole is embraced in the following statement.

A circumstance occurred here (at Oxford) which occasioned
the method to be put to the test of useful application. A con-
fectioner, happening in a scarce season to be unprovided with
natural ice, applied to me for assistance. I assured him that
in the large way (as I have stated in my original communica-
tions) the best method was to freeze water first, and then to
use the ice in the usual way for freezing creams. Accordingly an
apparatus of large dimensions, of rather an oblong form, was
made of tin (fitter for the purpose if cased with wood) con-
sisting of channels so constructed that the water to be frozen
should be subjected to the freezing mixture on both sides. This,
properly prepared, was placed in a cool cellar during the night,
and early in the morning (the temperature in the open air in
the shade in the day-time being above 80°) the ice was col-
lected, which amounted to several pounds in weight. This ice,
which was as limpid as the finest flint-glass, was applied in the
usual way, and with the apparatus ordinarily used by confec-
tioners for the purpose of freezing creams, and the mixed

* The manufactory alluded-to is at * No. 41, New Bridge- street, Black-
friars, London (late Patterson's), now Armstrong's."

powder,

Mr. Walker on the artificial Production of Cold. 403

powder, of which lie had procured ah adequate quantity, re-
peatedly recovered by evaporation over his hot iron plates, for
fresh use.

I shall now present the immediate object of my present com-
munication ; viz. what I consider to be the best mode and fit-
test apparatus for cooling wine in summer, for freezing creams
in the small way for private use, and likewise for freezing a
small portion of water, merely as an experiment for public or
private exhibition.

The drawing annexed (Plate VII.) is designed to represent
on a small scale the construction and exact proportions of
each freezing apparatus, and likewise the construction and
form of the apparatus for cooling wine.

Fig. 1. is an apparatus for freezing water on the smallest
scale, as above mentioned, in the hottest weather. The vessel
for containing the freezing mixture is three inches and a half
in width, and its height equal in measure to its width; and
the tube for containing the water to be frozen five-eighths of
an inch in width, and reaching, as represented, very near to
the bottom of the vessel : there is likewise a rim or continua-
tion of the vessel, without a bottom, to insulate it from the
table or stand it rests upon. The apparatus itself consists of
two parts ; viz. the vessel for containing the freezing mixture,
and its cover, in one piece with the tube, fitting close over
it (represented together in the drawing). When the water is
frozen, upon taking off the cover and wiping the tube, the
solid ice will have become detached by the heat, and on in-
verting it drop out.

The process may be known to be completed by the going
off or melting of the hoar-frost which exhibits a curious ap-
pearance outside the apparatus.

Fig. 2. consists of an apparatus in one piece ; viz. the vessel
for containing the cooling mixture, and the cup or can (if I
may so call it) for receiving the decanter, its top rising some-
what above the height of the vessel for an obvious reason, with
a cover that will admit of easy removal (in the drawing repre-
sented together). This apparatus likewise has an appendage
or rim like the former, to insulate it from the table : — it may be
convenient to be possessed of a couple of these.

Fig. 3. The apparatus for freezing creams, in which the
freezing mixture is to act on both surfaces of the part contain-
ing it, as being more ceconomical and expeditious, is not so
simple. This however consists only of two parts; viz. the vessel
for containing the freezing mixture ; and a cover, to which is
attached, in the same piece (instead of a tube or cup as in
fig. 1.), a concentric annular cavity or chamber, in which the

3 F 2 prepared

4-04 Mr. Walker on the artificial Production of Cold.

prepared cream is to be frozen : this cavity, forming a circle
within the vessel itself, is open at the top, as represented, and of
course closed at the bottom, and reaching very nearly (as the
tube in fig. 1.) to the bottom of the vessel : this secondary part,
as likewise represented, fits close as in fig. 1. over the vessel
containing the freezing mixture. The proportions of the appa-
ratus when together are thus : The outer space in width, two
parts all round ; the middle space, or that which contains the
cream, one part all round ; and the inner space three parts in
width, — this serving as a general scale of proportions for an
apparatus of any size. The proportions for an efficient appa-
ratus, as my own, may be : for the first space ten-eighths of an
inch (one inch and one-fourth); for the second, five-eighths of
an inch ; and for the third space, fifteen-eighths, or rather two
inches, making the width of the apparatus itself somewhat above
five inches and a half; its height being equal to its width, a
projecting rim at the bottom likewise to insulate it from the
table. It will be perceived that in the figure there are seven
very small holes or apertures in the central part of this cover
(one in the centre and six round at due distances), just suffi-
cient for the escape of the air, to admit of the ascent of the
freezing mixture in the middle part of the vessel. This ap-
paratus is somewhat elevated at the top, or slightly convex,
and the part in which the apertures are placed guarded by a
shallow rim to prevent an accidental running-over of the mix-
ture into the part containing the cream. This apparatus should
be furnished (as expressed in the figure) with an outer cover
similar, but less elevated, to the one at fig. 2. Previously to
use it will be proper to ascertain the quantity of liquid the ap-
paratus will contain when together, and mark its height ; like-
wise the proportion of the ingredients for furnishing a given
quantity in measure should be known. Thus, if the three salts
are used (which I would recommend to a private individual,
always doing so myself, although these cannot be recovered
for future use, but being more efficacious than the two only)
for each pint, small or old measure, will be required of sal am-
moniac and nitre (each equal parts by weight reduced together
into fine powder) six ounces, and of Glauber's salt, in clear
crystals and dry, four ounces and a half, freely reduced to
fine powder, or kept from the access of air, and in a separate
parcel from the former ; and water ten ounces, or enough to
make up one pint in measure when added to the former in-
gredients :— of course, the whole must be well stirred together,
and expeditiously, before introducing that part of the apparatus
which contains the article to be frozen, and occasionally after-
wards, till the object is completed, avoiding as much as possi-
ble

Mr. Walker on the artificial Production of Cold. 405

ble any accidental accession of heat. A freezing mixture com-
posed of sal ammoniac and nitre with water, all at the tempe-
rature of 50°, to which temperature, or nearly so, they may
all be reduced by water from a pump by drawing off a suffi-
cient quantity first, will from 50° produce a cold of 22° below
the freezing point, and with the addition of Glauber's salt to
28°. The confectioners find a degree of cold at 12° or 15° be-
low the freezing point sufficient for their purpose ; but it must
be recollected that the cold produced by salts dissolved in water
is not so durable as with ice and salt ; the duration of the refri-
gerating power in the above mixtures will of course be in pro-
portion to the quantity and thickness of the apparatus. In the
way the confectioner managed, the mixture in the apparatus
retained its freezing property till the morning : my usual way
is, in extreme hot weather, to place the vessel containing the
powdered salts in the coldest water drawn from the pump pre-
viously ; but in the ordinary way it will suffice to add the cold
water without the above precaution : it may be advisable to be
provided with a second quantity of the ingredients to preserve
the cold by a renewal of the mixture. The drawings are taken
from an apparatus of each kind of my own, — they are made
of tin, for want here of a fitter material, and are painted out-
side of a grass-green colour. The confectioner abovemen-
tioned laid in a stock of a hundred weight of each of the arti-
cles ; viz. sal ammoniac and nitre ; the former at the rate of
one shilling per pound, and the nitre at fourpence — which of
course when mixed, was at the moderate price of only eight-
pence per pound. Glauber's salts may be procured in the large
way at the rate of about twopence per pound, and by the single
pound at fourpence. The apparatus abovementioned may be
only half or three parts filled for use ; care must be taken in
every instance that the surface of the subject to be acted upon
be rather below the surface of the freezing mixture.

For cooling wine, the coldest water drawn from a pump
will be quite sufficient ; however, if required, a small portion
of the cooling powder may be added to the water.

The addition of Glauber's salt, it may be observed, increases
the density of the mixture, which then becomes a better con-
ductor of the cold, if I may so express myself, and more-
over retains the same temperature longer: of course it will be
better of the two to overcharge than undercharge the propor-
tion of the salts to the water. It will be apparent, for obvious
reasons, that the part containing the subject to be cooled should
be as thin as may be, and the whole of the external part in
every apparatus thick.

This detail may probably appear prolix to any person in-
duced

406 On the Causes of Single and Erect Vision,

duced by curiosity only to look it over ; but to any one who
means to put it in practice, the whole will be found essential,
and with a little attention and experience become familiar and
easy, and in which I have endeavoured to combine every ad-
vantage the subject will admit of; and as coming from the
w fountain head," it may not prove uninteresting to some at least
of your numerous readers. I am, Gentlemen,

Your most obedient servant,
Oxford, April 28, 1828. RlCHARD Walker.

LXIII. On the Causes of Single and Erect Vision*. By

FN order to understand aright the reason of single and erect
*~ vision, it is necessary first of all to perceive the truth of
certain metaphysical positions in relation to vision, without
the establishment of which, confused ideas, hypothetical
assumptions, and inconclusive reasonings on optical experi-
ments and facts are presented to the mind, and tend to em-
barrass the simplicity of that truth which might otherwise be
immediately revealed.

First, — Vision is a consciousness in the mind, and its next
proximate cause must be a power equal to its production, and
which unites it to the material world.

Secondly,— Vision of one colour only can never yield the
vision of figure, because the proximate cause of the vision of
figure is a line of demarcation formed by the sensation of the
junction of two colours.

Thirdly, — The physical impulse producing such conscious-
ness of colouring, is an equal proportional variety upon the
retina of an eye ; one eye alone being first supposed, as it is
truly efficient to yield the idea of figure.

Fourthly, — An object cannot be in two places at the same time.

Fifthly, — An object cannot exist and put forth its action
wheie it is not.

These premises being supposed to be granted, let the ques-
tion be asked, Why with two eyes given, two objects are
not seen, although there be but one object given externally ?

The answer (when supported by the foregoing premises,
and conjoined with certain optical facts with which all
who are conversant with the subject, are acquainted) will
be, became there is not presented to the mind that variety
of colouring which is necessary and alone efficient as the next
proximate cause of vision; that is, there are not two lines of
separate demarcation between two objects, but one line qfdemar-

* Communicated by a friend of the Author.

f Author of " An Essay on the Relation of Cause and Effect " and of
" Essays on the Perception of an External Universe," &c.

cation

On the Causes of Single and Erect Vision. 407

cation only is presented, as in one eye supposed. Should it be
asked, whence is it that such a proportional variety is not
presented to the mind ? The answer which the premises and
optical experiments equally support, is, because the impulse
upon each eye {when the axes of both are directed to the same
point or object,) being precisely alike, there is no variety of
colouring painted upon either eye, equal to the production of
that variety of perception, necessary to yield the ideas of two
objects separated from each other, between their interior and
horizontal edges.

Let the letter A, for instance, be painted upon one eye, and
the perception of its figure arises in the mind, from the points
of distinction between the black letter and the white around
it : there is a sense of difference created. Place it on similar
points of two retinae, and each point of the figure painted on
each retina will yield to the mind but one point of conscious
black against one point of conscious white ; and not two points
of black against two points of white, because there is no inter-
vening white painted on either retina, which can yield a con-
sciousness of the separation of the two A's to a distance from
each other, thus, A- A.

The white space between the two A's is not painted on
either retina. How then can any idea of it arise in the mind ?

If, in order to render these ideas more intelligible, we ana-
lyse with still greater nicety the question, why we see dupli-
cates of similar figures with one eye only supposed, it will at
once appear obvious why we can perceive but duplicates of
such figures, instead of quadruplicates,v/hen two eyes are used.

Now if one eye should see but one colour only, it is sup-
posed to be granted that there could be no sense of any de-
fined figure whatever : one impulse therefore yields not figure.

If one and the same colour should be seen by two eyes, it
must still be acknowledged there would be no figure : two
similar impulses therefore cannot give the sense of figure to
the mind. Now upon one colour (say a purple ground) painted
upon one retina, mark a scarlet circle O ; a sense of one figure
will immediately arise from two varieties of colour being car-
ried to the mind, viz. a line of demarcation to the purple
ground by the scarlet circle : two impulsions, or two varieties
of colouring, are therefore necessary to the perception of one
figure. Again, if with one eye given, I wish to see two scarlet
circles upon the purple ground, what must I do? Will four
impulsions yield two similar figures ? I answer, No. There
must he five impulsions in order to convey to the mind the

2 5 4
sense of two figures : there must be ®~ip®; that is, the im-
pression

408 On the Causes of Single and Erect Vision.

pression of the purple ground must be repeated in two different
parts of the sentient retina ; two scarlet lines must be thence
impelled, and these made obvious by the intervening horizontal
impulse between the circles; for could the intervening space be
absorbed, and each point of scarlet coalesce with each point
of scarlet, and purple with purple, there would then be but

four impulsions of colouring, but four varieties, which would
be inefficient to the observation of two figures. A coalescence
of similar points of colour may perhaps produce a superposi-
tion or increment of colour, so as to create a superior bril-
liancy in the appearance of the object ; but a coalescence of
points cannot give a sense of the separation of points. There-
fore for the mind to have a sense of one figure, there must be two
consciousnesses of colour ; andto have a sense of two figures,
there must he five distinguishable consciousnesses of colour.
However often one colour only be repeated, there will be no
figure ; however often two similar colours be repeated, (no in-
tervening one being supposed,) hut one figure will arise; whilst
to entertain a sense of two figures, jfe impulsions are necessary.
I hold it therefore as an axiom in the laws of vision, that the
repetition of similar impulsions of colour will not yield a num-
ber of figures equal to the number of such impulsions ; but that
the number of figures perceived, arises from those proportional
intervals of the hnpidsions of colour, which must vary in a certain
ratio to the number of figures impelled.

However, therefore, the number of eyes may be multiplied,
the mind can have no consciousness of any additional number
of figures, whilst only similar impulsions of colour are yielded
to it.

Let us enter into some further detail. If one scarlet circle
on the purple ground be painted on the corresponding points
of two retinae, and thence impelled to the mind, there can still
only arise the sense of one scarlet circle ; for there have existed
but four physical varieties on the retinae, and but four varieties
have been impelled to the mind : and it has been proved that

five physical varieties are necessary to exist upon a retina, or
upon retinae however numerous, in order to impel correspond-
ing consciousnesses to the mind, and which would be necessary
for the mental apprehension of two figures. Let the figures
without an intervening horizontal colour be supposed to be

2 4
marked thus, d)-JL(|). The intervening horizontal colouring

necessary to separate the painting of two figures on the retinae,
is not painted on either retina ; it does not exist ; and therefore
no conscious separation of two figures can possibly arise to

the

On the Causes of Erect and Single Vision, 409

the mind. There exists indeed a certain space between the
two eyes outwardly on the face, but the colouring of this in-
tervening space is not painted on either retina, and therefore
cannot be noticed by the mind ; nor is there any intervening
horizontal purple presented to the mind: Each point of scarlet
does but coalesce with each point of scarlet, and each point of
purple on one retina, with each point of the similar purple on
the other retina ; there is no surplus intervening purple on
either retina, and it has been shown that " repetitions of similar
impressions of colour do not yield to the mind the sense of
an equal number of figures."

But should the scarlet circle be painted on joints of the
retinas which do not correspond, then there will necessarily
arise the sense of tivo figures ; because in that case dissimilar
impulsions of colour are carried forward to the mind, and
yield that proportional variety which determines the obser-
vation of conscious duplicates : for the pictures are then im-
mediately painted upon different parts of their respective
retinae, and the distance between two objects " will be pro-
portional to the arch of either retina, which lies between the
picture on that retina, and the point corresponding to that of
the picture on the other retina*." On this intervening arch a
surplus quantity of purple would be interiorly and horizontally
painted, and would thence separate the two scarlet figures :
Jive impulsions would carry five conscious colours to the mind,
and two separated figures would immediately be observed.

An illustration of these ideas, and especially of this last state-
ment of Dr. Reid's, might very easily be imagined, by con-
ceiving two small terrestrial globes to be painted with precisely
similar colours : Let them be rectified to the same degree of lati-
tude and longitude, and similar colours only will appear on the
visible surfaces of each ; turn them both so many degrees to
the east or west, still only similar colours will present them-
selves ; but let one of the globes remain at rest, and turn the
other any number of degrees of longitude to the west, a
new country will arise to the east on the globe so moved,
whose variety of colouring must necessarily prevent the notice
of a mere uniformity of colouring on the two globes, and which
variety will separate the appearance of. any given country on
them, ¥ proportionally to the number of degrees marked on the
arch of the horizon" through which the globe so moved had
passed. Inspire the colouring on their surfaces with a simul-
taneous single sensibility, and it will immediately be perceived,
that no consciousness of the existence of any two similar

* See Dr. Reid's Inquiry, ch. vi. sec. 13.
Nexv Series. Vol. 3. No. 18. June 1828. 3 G countries

410 On the Causes of Erect and Single Vision.

countries could arise, so long as the surfaces were regulated
to the same degree of latitude and longitude; but the moment
they were separated by an alteration of the longitude of either,
or both, the sense of that newly arisen continent, or sea, would
divide the sense of the remainder.

The following passage is extracted from the Encyclopedia
Britannica, and is a quotation from Dr. Wells's Essay on
Single Vision. " If the question be concerning an object at
the concourse of the optic axes, it is seen single ; because its
two similar appearances in regard to shape, size, and colour,
coincide with each other through the whole of their extent."

This opinion thus expressed, comes nearer to my meaning
than any other with which I am acquainted ; nevertheless Dr.
Wells's argument on the subject (and which is too long to
insert here,) is as fallacious as that of any of his predecessors;
inasmuch as it assumes an hypothetical law of vision, in order
to establish that coincidence of shape, size, and colour upon
which he perceived single vision did necessarily depend.

This laborious argument of his, is as entirely needless as
it is futile ; because it proceeds upon the supposition that
objects are seen by the mind, beyond the mind, at the angle formed
by the axes of the eyes, in their direction to the same point
of distance.

Now when, on the one hand, colour (conscious visible
colour) is admitted to be in the mind, and never to proceed
again out of it, in any line, or at any angle to form an ob-
ject ; and on the other hand, by those demonstrable laws of
optics established by Sir I. Newton and others, "that when
the axes of the eyes are directed to a given point or figure,
the said figure is painted on corresponding points of the re-
tinae,"— then the coincidence which Dr. Wells speaks of,
must of necessity take place ; and such coincidence can only
determine a consciousness of single vision to the mind ; or in
other words, can only determine those similar appearances of
colour, on which visible size and figure ultimately and alone
depend : for the centres coincide with the centres, and the
edges with the edges, of the figures ; without any variety, or
interval of colouring between the interior and horizontal edges,
— the conscious sense of which is absolutely necessary in order
to induce a sense of variety or plurality of figure. When the
figure is painted upon points of the retinae which do not cor-
respond, then there must necessarily arise a sense of 'two figures ;
because the centres not coinciding with the centres, nor the
edges with the edges, there exists a surplus colour in one eye
which divides the interior and horizontal edges of the two
figures. This surplus colouring is determined to the retina

by

On the Causes of Erect and Single Vision. 411

by some exterior object, which by the shifting of the axis finds
a place on which to paint its rays, " and is equal to the arch
between the picture of the given figure on that retina, and the
point corresponding to that of the picture on the other retina ;"
and which surplus colouring must determine a proportional
consciousness to the mind, observing thereby the same rule
which determines the " notice of two similar figures, when
one eye only is used;... when the apparent distance of two objects
seen with one eye is proportional to the arch of the retina which
lies between their pictures" and on which an interval of colour-
ing is necessarily painted, but which circumstance Dr. Reid did
not consider it material to notice *.

The optical facts to which I have alluded are very shortly and
very well expressed in Dr. Reid's " Inquiry f :" The passages in
the chapter from which I have partially quoted, and which it
may be as well to give entire, are the following ; and I repose
on them as stated facts, not containing either hypothesis,
opinion, or reasoning.

" First, — When the axes of both eyes are directed to one
point, an object is seen single ; and in this case the two pictures
which show the objects single, are in the centres of the retinae.
Now in this phenomenon it is evident that the two centres of
the retinae are on corresponding points.

" Secondly, — Pictures of objects seen double, do not fall
upon points of the retinae similarly situate with respect to the
centres of the retinae.

" Thirdly, — The apparent distance of two objects seen with
one eye, is proportioned to the arch of the retina which lies
between their pictures : in like manner the apparent distance
of two appearances seen with two eyes, is proportioned to the
arch of either retina, which lies between the picture on that
retina and the point corresponding to that of the picture on
the other retina."

These facts are valuable for many reasons ; but on no ac-
count more so, than because they serve to explain the manner
by which nature yields the knowledge of external tangible
figure, and the proportional motion which is in relation to it,
by means of corresponding varieties of colour.

Dr. Reid's arguments (although he was in possession of these
facts, which might have afforded premises for better reasoning)
are altogether inconclusive, not to say puerile; and that on
account of his steady adherence to the main object with which
he set out upon his " Inquiry," namely, to show upon the prin-
ciples of common sense whence comes the knowledge we have
of the existence of an external universe : Following up these

* See Dr. Reid's Inquiry, ch. vi. sec. 13. f Ibid.

3 G 2 principles,

4-12 On the Causes of Erect and Single Vision.

principles, he placed visible figure beyond the body, at a di-
stance from the perceiving mind, denying it to consist either
in a sensation, impression, or idea, — and as possible to be seen
without the intervention of colour *.

It appears to me strange, when contradiction is stamped
upon the very expressions which convey these ideas, that Dr.
Reid's notions should seem to be the data for the reasonings
of the author of the " Explanation of -Erect and Single Vision"
published in the " Library of Useful Knowledge."

I must however, in common honesty, here take notice of an
objection which I have known to be made to the views I en-
tertain on this subject : it is, " that we see objects in different
directions by either eye, when the other is alternately opened
or closed." This objection appears to me perfectly nugatory,
when it is considered, that both eyes being opened together,
they are allowed by the condition of the question to be directed
to one point; in which case neither of them can be directed to
any point beyond that point; it would be a contradiction in
terms to admit it. The axes cannot cross each other, and look
at points beyond the given point, and that with a separate con-
sciousness in the mind of so doing ; for then these would not
be merely one given point, but three given points; and the
figure, the cause of whose single vision is in question, would
be supposed to be placed, and at the same
time supposed not to be placed, at the junc-
tion of the axes. For instance, when two
eyes are directed to A, the left eye cannot
be turned to B, look by itself at 13, and the
right eye at the same time be made to look
by itself at C. Experience shows this to
be an impossibility ; but when either eye is
shut, the other may be moved in any direction we please.
However, were I in error in this statement, the argument of
my objector would by no means be conclusive against my
doctrine of single vision, provided only that A be placed at
the junction of the axes ; for the utmost which could happen
would be, that A plus B, plus C would appear to the mind ; but
not two A's (two B's and two C's), because there would still
be only a superposition, or increment of the colouring of A.

The central point of the colour of A would coincide on
each retina; the whole of the rest of the colouring in relation
to it would be painted on corresponding points, and coincide
on their respective retinae ; and there could in no wise arise
that proportional variety of colour, painted between the in-

* See Dr. Reid's " Inquiry," ch. vi. sect. 12. p. 135. 12mo.

terior

On the Causes of Erect and Single Vision. 413

terior horizontal edges of the two A's, which is necessary to
yield the ideas of their separate figures.

But to return " to the explanation of the Cause of Erect and
Single Vision, published by the Society for the Diffusion of
Useful Knowledge* ;" — it appears to me to be as much at va-
riance with abound, metaphysical, demonstrable conclusion
concerning the nature of the perception of visible figure by the
mind, as are the authors to whom I have alluded ; and as much
so with an acknowledged law, — with a proved physical fact, in
respect to the time required for the motion of light.

The author of the " Explanation of the Cause of Erect and
Single Vision," saysf: "As the lines of visible direction cross
each other at the centre of visible direction, an erect object is the
necessary result of an inverted image ;" but this is not the same
thing with the perception of an erect object. If it be said the
word perception is understood though not expressed, then the
mind is supposed to see the very erect object, out of itself, at a
distance from itself; that is, the mind feels colour, perceives
visible figure (its result), there, inhere it is not, which is im-
possible.

Again, it is a known fact, that the light emitted from the sun,
employs about eight minutes in its journey to the earth. Now
let an object be seen at that distance in an erect position, but
the moment after its light is effused, let it be obliterated: the
mind will still see it erect, eight minutes after its annihilation,
how then shall it signify the drawing of any rays back through
a centre, towards the place of an obliterated object, which once
stood there erect ? The author's explanation is little more than
the very circumstance in question, re-stated by an inversion
of words. M An erect object (at a distance) is the result of an
inverted image on the retina by the crossing of rays at a cen-
tre ;" is merely saying over again, that an inverted image on
the retina is the result of an erect object at a distance, when rays
cross at a centre.

The question still remains untouched and unexplained;
namely, why does the mind perceive an erect image, the re-
sult of an inverted image, which inverted image is the proxi-
mate cause of vision, and not the erect object which might be
obliterated without affecting the mental consciousness of it?
The only answer appears to me to be that, which I have for-
merly stated in my " Essay on Single and Erect Vision ;" viz.
" Inversion of figure is merely a relative quality: when all rays
from every object within the sphere of vision become inverted on
the retina, there truly can be no mental consciousness of any in-

* Optics, part ii. " Library of Useful Knowledge." f Ibid.

version

4H On the Causes of Erect and Si?igle Vision.

version whatever: for there is no relative variety by comparison
with any other set of similar images; and they will necessarily
bear a given relative proportion to the ideas of motion and tan-
gibility; and which ideas, taken collectively, include all the ele-
ments we have of the knowledge of the position, figure, and co-
lour of objects*"

No doubt the relations of these in indefinite modifications
are perceived by the judgement, as well as innumerable associa-
tions of them by the imagination ; and thence the large use of
vision in the world ; thence the warm affections which are ap-
proved of by the understanding, or delighted in by the fancy.

But instead of taking this simple and easy mode of viewing
the subject, philosophers, when they discuss the reason of
erect vision, really suppose (although they may not be willing
to allow it in so many words), that mental vision arises from,
and is occupied about, two sets of objects at the same time ;
viz. the external objects in nature, and the inverted images of
them on the retina: whereas the external object becomes vir-
tually null and void immediately upon the rays of light being
emitted from it.

The idea of inversion is the result of the comparison of the line
of demarcation of one object with that of another of a similar
kind placed in a contrary direction to it. But as in the picture
on the retina, the line of demarcation of each particular image
touches the line of demarcation of the rest, in the same man-
ner and after the same proportion as their corresponding ob-
jects do in external nature ; so no such comparison can take
place : for one set of images only is painted, and these in pre-
cisely the same relative positions to each other as are their
counterparts. The mind therefore necessarily perceives the
same positions with respect to each other; for no two objects
of a kind present themselves, by which a comparison can take
place.

Philosophers, therefore, when they compare the image on
the eye of an ox, for instance, with the object in external na-
ture of which such image is the reflection, forget that both to-
gether make but one picture on their own eyes: For any
given object forms on the human eye an inverted image, and
the mind sees it erect; but the image on the eye of the ox
(which is already inverted) makes on the eye of the person who
observes it, an image again inverted that is erect, and the
mind perceives it inverted.

In this latter case there is a comparison of the line ofdemar-

* See u Essays on the Perception of an External Universe," &c. by
Lady Mary Shepherd. 182/. Essay, xiv. p. 408.

cation

On the Causes of Erect and Sirigle Vision. 4? 15

cation of one object with that of another of a similar kind, placed
in a contrary direction to it. In the former case, two objects
do not present themselves, but only one of a kind, and that
surrounded by each and every line of demarcation, precisely
in the same relations to each other as are those of external
nature. The same observation holds good when drawings
are used with two images on them, placed contrariwise to each
other; as an arrow without the retina, and an arrow within
the retina. Did the arrow within the retina feel along with
the surrounding lines of colouring, there could be no sense of
an inverted arrow ; for there would exist no reference to an-
other arrow, which reference is only made by the observer,
who is looking on two arrows.

Observations analogous to these must be made on the at-
tempted explanation " of the cause of single vision," by the
same author, who says*, " Because the lines of visible direc-
tion from similar points of the image (on one retina) meet the
lines of visible direction from similar points of the other image
upon the other retina, each pair of similar points must be
seen as one point." How so, when the mind sees not out of it-
self at the junction of the points, and when if the object which
sent forth the rays were annihilated, there would still result a
single vision from separated points of colour painted on sepa-
rated RETiNiE at a distance from each other; such duplicate
separate, figures on the retinae being the proximate cause of
the single vision of the object, and not the junction of similar
points, when rays are drawn back again from the retinas to such
points of junction.

The question still recurs, and is still untouched and unex-
plained ; Why are pairs of points perceived by the mind as sin-
gle points ? No doubt the determination of rays upon the re-
tinae in such a manner that when drawn back again they will
meet at a central point, is a property closely connected with
the method of vision ; but it is rather a corollary or conse-
quence of the manner of the entry of the rays at the pupil oj the
eye by which equal arches are subtended upon the retina, than
the efficient cause of either single or erect vision. I again ask,
Why are two objects on the retinae perceived as only one ob-
ject by the mind? For it is not a junction of external points
which is perceived, but two sentient retinae determine two se-
parate images (equally perfect in their form, equally brilliant
in their colouring), as but one image to the mental capacity of
perception. Is not the answer, Because there are no points of

* Optics, part ii. " Library of Useful Knowledge."

colouring

416 Mr. Ewart on the Reaction oj 'effluent Water,

colouring 'painted, on either retina, by which the separation of
their forms can be distinguished ?

Press the axis of either eye sufficiently to the right or left,
a larger quantity of colouring will immediately be painted upon
one retina than upon the other, which will separate their in-
terior and horizontal edges, and two images will thence imme-
diately and necessarily arise upon the perception of the mind.

I feel convinced that the more these ideas are contemplated,
and the more clearly they are apprehended, the better will they
serve to elicit the reason of several other phaenomena concerning
vision, which it has hitherto been considered difficult to ex-
plain; and«what is of still greater importance, they may throw
some light upon those which belong to every analogous ope-
ration of the human senses and intellect.

LXIV. On the Reaction of effluent Water, and on the Maxi-
mum Effect of Machines. By Mr. P. Ewart*. With Notes
relating to the Theory of Barker's Mill. By J. Ivory, Esq.,
M.A.F.R.S.f

rT,HE following important proposition relating to this sub-
-*• ject, is laid down by Daniel Bernoulli in his " Hydrody-
namics," page 278. If a jet of water I (fig. 1.) issue from the
side of a vessel A, with the velocity which a body wrould ac-
quire in falling freely from the surface B to C, he says the re-
pulsion of the water in the opposite direction to the 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.

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 particularly engaged the
attention of Sir Isaac Newton, and from his having given a

* From a paper " On the measure of moving force," in the Memoirs of
the Lit. and Phil. Society of Manchester, second series, vol. ii. 1813.

We insert this extract because it treats, correctly we believe, of subjects
which have engaged the attention of many eminent mathematicians (in
former times as well as recently), whose reasonings and conclusions on the
points in question are at variance with each other. These discrepancies
are to be regretted, inasmuch as some of the essential points in the appli-
cation of the principles of mechanics to practical purposes are involved in
them. — Edit.

t Communicated by the Author.

We are glad to lay before those of our readers who have attended to the
various intricate theories that have been offered of the action of Barker's
Mill, Mr. Ivory's Notes on that subject — Edit.

solution

and on the Maximum Effect of Machines,

417

solution of the problem in the first edition of the "Principia"
which he materially altered in the succeeding editions. In the
first edition (book 2nd, prop. 37.) he infers, that the reaction is
equal to the weight of a column of water of 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 succeed-
ing edition, the subject 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 dif-
ferent manner demonstrated 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 sec-
tion of the contracted vein, at the point of its greatest contrac-
tion, in the ratio of \/ 2 : 1 nearly. He takes the reaction,
therefore, to be greater than what he understood it to -be when

he published the first edition, in the ratio of \/ 2 : 1 nearly.
He refers, however, more to experiment 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 reaction.

Sir Isaac Newton suggested (Principia, first edit. p. 332.) a
method by which the reaction may be easily measured. If
the vessel be suspended like a pendulum, he observes, it will

New Series, Vol. 3. No. 18. June 1828. 3 H recede

4-18 Mr. Ewart on the Reaction of. effluent Water,

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 accu-
rately as possible, I made use of a balance-beam furnished
with a perpendicular arm of the same length as the horizontal
arms, as represented at fig. 1. The scales were exactly ba-
lanced, and the end of the rod 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 ori-
fice was opened. The diameter of the vessel was 7 inches,
and the height BC exactly 3 feet. I tried orifices of various
diameters from #35 to *7 of an inch. Their exact diameters
were ascertained by a micrometer, and the time carefully ob-
served in which 30 lbs. of water were discharged through each
orifice.

When the orifice was made in a thin plate (^th of an inch in
thickness), I found the reaction to be greater than that stated in
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 in-
ference. 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.

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 con-
cluded 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 diame-
ter. 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 to 1.
The highest ratio was as '95 to 1, and the lowest '89 to 1.

From

and on the Maximum Effect of Machines. 419

1 "From these results it appears, that when the contracted vein
is not opaque, and when its velocity is nearly equal to that
which is due to the head, the reaction is nearly equal to what
it was concluded to be by Sir Isaac Newton and M. Dan. Ber-
noulli; and the great apparent difference between Sir Isaac
Newton's first and second conclusions arises from his having
been misled by some experiments to which he alludes. He
says — " Per experimenta vero constat, quod quantitas aquae,
quae, per foramen circulare in fundo vasis factum, dato tem-
pore effluit, ea sit, quae cum velocitate praedicta," [viz. the velo-
city 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 pre-
sume, however, that he refers to experiments 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 esta-
blished 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 requires that the ve-
locity at the contracted vein shall be equal to that which is
due to the head. Now that velocity cannot be determined by
measuring the imperfectly contracted vein in cases of water
spouting through a hole in a thin plate.

We may safely indeed infer, that, in such cases, the velo-
city is considerably less than what 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 is projected on a horizontal
plane, confirms that inference. The demonstration, therefore,
of the reaction, can be properly applied 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.

These results agree also with the explanations which have
been given of moving force f . 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 as it issues.

Let a represent the area of the smallest section of the ori-
fice. Then while the vessel has moved through a space as

2 BC, a quantity of water represented by a x 2BC has de-

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

t By moving force is meant the product of the pressure into the space
through which it acts, or of the quantity of water into the height through
which it falls. The same sense in which the term is used by Euler.

3 H 2 scended

w j]

420 Mr. Ewart on the Reaction of effluent Water ^

scended from B to C, and has been brought to rest. But the
reaction is = a x 2 BC, and this multiplied by 2 BC, the space

through which it has acted, gives a x 2BCi2 for the amount of
the moving force produced, which is exactly the quantity of
moving force necessary to raise the column a x 2 BC to the
height BC, and to project it with the velocity 2 BC. For, a
moving force = a x 2 BC x BC will raise that column from C
to B, and an equal moving force will generate the velocity
2BC in the same column, therefore 2a x2BC x BC=« x 2BCf
is the whole moving force necessary to restore that column to
the place and condition in which it was before it began to de-
scend; and as no moving force has been expended in pro-
ducing change 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, *l8' 2#

I apprehend, of the action of the hy-
draulic machine called Barker's Mill.
Let AB (fig. 2.) be the perpendicular
tube, and BC the horizontal arm ; let
v express, in feet per second, the ro-
tatory velocity of the arm at the ori-
fice C, and let the water be supposed
to issue with the velocity due to the
pressure*. Putg = 16^ feet.

If BC be a cylindrical tube, and
if q represent the quantity of water
it contains from B to C, the centrifugal pressure upon a

section of the arm at C, will be ^BC ; and whatever the

length BC may be, the diameter remaining the same, q being
as BC, the centrifugal pressure at C will always be as w2 ; and
it will be equal to the pressure of a perpendicular column of

water whose height in feet is wp Then if h express in feet

the height AB of the water in the vertical tube, h + -^- will be

the whole pressure at C ; and if a express in feet the area of

the most contracted section of the orifice, 2a (h -f —J will

* It is here understood that the areas of the sections of the perpendicular
tube and of the horizontal arm shall be indefinitely large when compared
with the area of the orifice.

express

and on the Maximum Effect of Machines. 421

express the reaction, which being multiplied by v, the space
through which it acts in a second, gives 2 av (h+ -j-) for

the total moving force of the arm in a second. But a part of
this moving force is expended in producing the rotatory mo-
tion 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 would stand at P, PR

being = — . 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 ex-
pended 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 h + .-— , (that is = AB + PR), the ve-

locity with which the water issues will be 4 / 4g (h + -~-)

or »J 4>gh + vK Let V express that velocity, then «V will
express the quantity of water which passes in a second ; and

2 a V — 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 2av(h + — \

— 2aY — for the effective moving force of the arm in a second.

That this is the effective moving force, may be shown also
in another manner, as follows :

The absolute velocity of the water after it has left the ma-
chine will be V— v, and ; ■ will be the head which would
produce that velocity; which being multiplied by «V, the
quantity of water delivered in a second, gives a V ^ for

the moving force which remains 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 a\ h — aV ~v* for the effective

moving force, which will be found to be equal to 2av(h + -^-)

The

2 a V-^, the effective moving force stated above.

422 Mr. Ewart on the Reaction of efflnmt IVater,

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 Me-
moirs of the Berlin Academy for 1750, p. 311 ; and for 1751,
p. 271. His demonstrations relating to this subject are very
complicated, and they do not appear to have been adopted by
succeeding authors*.

Mr. Waring, of America, has given quite a different theory,
which has been approved of by several good writers on hy-
draulics. He concludes that the greatest effect will be produced
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-
constructed undershot water-wheel f.

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, therefore, merely
as an attempt to solve an intricate 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 al-
though 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 in-
finite velocity. But when the water issues with a velocity which
is less than what is due to the pressure, as must always be the
case in practice, the velocity at which the maximum of effect is
produced, may be found as follows. It should first be ascer-
tained by experiment how near the issuing velocity can be
brought to that which is due to the pressure. From the ex-
periments which I have made, I have been led to conclude
that no greater issuing velocity can possibly be obtained 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 \ 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 orifice C ; and if the velocity of the ma-
chine be such that PC = 5 AB, the 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 in
producing change of figure.

For, the head due to V, the issuing velocity, will in this case

* M. Euler says, " In employing the same quantity of water, and the
same fall, this machine will produce an effect nearly four times greater than
the ordinary machines."

f American Philos. Trans, vol. Hi. |Cl91 and 192.

be

and on the Maximum Effect of Machines. 423

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 moving force necessary to raise the water from C to
P, CR = AB will represent that part of it which is expended
in producing change of figure. The greatest velocity, there-
fore, that the orifice, when the machine meets with no resist-
ance, can acquire, will be V 4gx4A.

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 *J #8 (4<gh + v*)— v. The
head or the moving force expended in producing that velocity

winbeMv^±gg>'.

The moving force expended in producing change of figure

will be as '2 (h + ^— )• Now when the sum of these two

\ 4g /

^2

quantities, or — — i-j- - — + '2( h + — j, is a minimum,

we shall find v = V c2gh{^~b' — l) = 6-3056 V~h for the
velocity of the orifice when the machine produces a maximum
of effect; and in that case the above sum becomes = '4472^.

We shall therefore have h — #4472^ = *5528h for the maxi-
mum of effect, supposing h to represent the whole moving
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 pro-
perly 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 ex-
plained by examining the sim-
ple case where a given weight
P, (fig. 3) connected with an-
other W, by a string passing
over the pulley F, descends
vertically and raises W, with-
out friction, from the hori-
zontal line AC along the in-
clined plane AB. If we
make AB : BC : : 2 W : P, W will be raised to B in the least

time ;

424 Mr. Ewart on the Reaction of effluent Water, fyc.

time*; and upon this principle, the maximum of effect in
machines is usually demonstrated in theory. In practice, how-
ever, 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 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 = JAB only. For, if we
make BD= JAB, and let W ascend along any concave sur-
face DEB, of which BD is the chord, 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. It 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 in the least time. To determine the curve by
which W will ascend from D to B in the least time, is an in-
tricate problem, and I do not know that it has ever been
solved f; 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 problem. 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 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 advantage.

By proceeding on the principle that when W is raised to B
in the least time, the maximum 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 J." 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.

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

f This difficult problem, we understand, has lately been solved by the
Rev. E. Sibson of Ashton, in Makerfield, Lancashire, and the solution will
appear in the next volume of the Memoirs of the Lit. and Phil. Society of
Manchester. — Edit.

X Gregory's Mechanics, vol. i. p. 447.

Notes

Mr. Ivory's Notes relating to the Theory of Barker's Mill, 425

Notes relating to the Theory of Barker's Mill, By
J. Ivory, Esq, M.A. F.Il.S.

I. On the Pressure caused by the Centrifugal Force.

The centrifugal pressure may be investigated in the manner
following. — The whole pressure at the orifice is the sum of
the variable pressures of all the molecules, or infinitely small
portions of the fluid, in the length of the arm. Let r be the
length of the arm between the orifice and the axis; g = 16^
feet ; v9 the absolute velocity of the orifice in feet : then if d x
(or x) be a small portion of the fluid in the arm at the di-
stance x from the axis, the centrifugal pressure of dx will be

sfiv* dx v^.xdx

X

** 2xg 2gr* '

and the pressure of the prism of the fluid, of which the length

V1 x^

is x, will be = - — j- ; and the whole pressure of all the fluid
in the length r9 will be = 4~ r = tt-

The same thing may be more shortly stated, thus: The
centrifugal force of every small portion of the fluid in the arm
being as the distance from the axis, we may assume that every
portion is acted upon by the force which takes place at the
middle of the arm, or at the distance J r from the axis. Now

this force is m >j+* ; which multiplied by r, the sum of the

portions of the fluid, gives -7— x r = ^-5 the same as be-
fore. ier W

And since we have,

v2 — / v V*

4g " 4g \ r / 9

-- being the angular velocity of the machine, or the angle

through which it turns in a second ; it follows that the angular
velocity being the same, the centrifugal pressure varies as the
square of the length of the arm.

Some authors, and in particular Bossut (Hydrod, torn. i.
§ 429), reckon the centrifugal pressure, not in the whole
length r, but in the distance between the upright tube and the
orifice in the horizontal arm. Let r1 be the radius of the up-

New Series, Vol. 3. No. 18. June 1828. 3 I right

4-26 Mr. Ivory's Notes relating to

right tube; then, according to the authors mentioned, the
centrifugal pressure at the orifice will be equal to

lg~ x ~^~'

being the difference between the pressures at the distances r
and ?J, from the axis.

II. Velocity with which the Fluid issues from the horizontal
Arm, supposing that v is the absolute Velocity of the Ori-
fice,
The velocity required is produced by the pressure of the
fluid in the upright tube increased by the centrifugal pressure.
Wherefore if h denote the length of the upright tube, sup-
posed to be kept constantly full, the sum of the two pressures

mentioned will be = h + jj- ; and, if V denote the velocity
of the effluent water, we shall have,

Tg
And, if we put & = 4 gf9 then

V2=* 4 £(/*+/)

V2=*g(h+-^) = 4gh + v>

III. Demonstration of Daniel Bernoulli's Proposition respect-
ing the Reaction of effluent Water (or, Cor, 2. prop. 36.
lib. 2. Principia).
Suppose that water issues from a small orifice in the side,
or bottom, of a vessel which is kept full ; let k be the height
of the surface above the level of the orifice: then, 2 V gk is
the velocity in a second with which the water issues ; and, if
a be the area of the orifice, the quantity of water discharged
in a second is equal to the prism a x 2 4/ g k ; and, as the
water issues with the velocity 2 \/ g k, the quantity of motion
in the water discharged in a second is equal to,

a x2 \/gkx2\/gk = 2akx2g;

and the same quantity of motion; viz. 2akx2g, is evidently
the reaction of the water projected in a second. But the prism
or weight, 2 a k9 by falling, produces a quantity of motion equal
to 2akx2g in a second : wherefore the reaction of the pro-
jected fluid is equal to the weight 2 a k ; that is, to the weight
of a prism of the fluid having its base equal to the orifice a,
and its altitude equal to 2 k.

This proposition supposes that the water has acquired its
complete velocity of projection, due to the head k. Before the

efflux

o' the Theory of Barker's Mill. 427

efflux commences, and while the fluid is at rest, the weight
a k is sufficient to counteract the tendency to begin motion.

IV. Computation of the Moving Force of Barker's Mill, or of
the impulse produced by the Reaction of the projected Wa-
ter; supposing that h is the length of the upright Tube
kept constantly fully and v the absolute Velocity of the
Orifices in the horizontal Arms.

This machine has generally two horizontal arms diametri-
cally opposite ; but it may have any number of such arms with
an orifice in each. Whatever be the number of the arms, I
shall suppose that all the orifices are at the same distance, r,
from the axis ; and I shall use the symbol a to denote the sum
of the areas of all the orifices.

The velocity V with which the water issues from the ori-
fices is known by the formula,

And, since the water is propelled from the orifices with the
velocity V, and has acquired from the machine the velocity v
in the opposite direction, the velocity with which it is pro-
jected from the arms, is equal to V— v: but cV is the quantity
of water so projected in a second ; wherefore the momentum
of the projected water is equal to aVx(V-i)); and the same
expression is equal to the impulse communicated to the ma-
chine by reaction. Wherefore, since the impulse is exerted
at the end of the lever r9 its effect to turn the machine, or the
motive force, is equal to

r XflVx(V-w). (1)

We may likewise measure the motive force by the momentary
impulse multiplied by the space through which it acts ; and
the force accelerating the machine will be,

v xaV x (V-v). (2)

These two formulae seem to be the most elementary expres-
sions of the motive force of this machine.

. -

Mr. Ewarfs Formula.

T I aVx(V-„) n

Let us put ^ = P ;

then, aV x(V-p)ssP x 2g; wherefore the reaction is
equal to the momentum which the weight P acquires in a se-
cond by falling; in other words, the momentary impulse of
reaction is equal to the pressure of the weight P. The mo-

3 I 2 tive

428 Mr. Ivory's Notes relating to

tive force of the machine, according to the formula (2), is
therefore equal to P x v. Now

F xv = 2avx -£ -2aV x >&.%
and, by substituting the value of V2,

?xv=2av(hx-£-)-2a\^-.

Eider's Formula,

In the formula (1), put 2 V g (h+f) and 2 s/ gf for V
and v; then the impulse to turn the machine will be,

2arx2g(h+f-s/ hf+f>),

which is Euler's formula.

N. B. It must be observed that Euler makes gravity the
unit of forces; that is, he denotes it by 1, and expresses the
velocities by the square roots of the heights : and, in order to
make the foregoing expression agree with Euler's assumption,
we must make 2g = 1 ; because 2g has been taken for the
measure of the force of gravity.

Bossufs Formula.

This author considers the machine in a form more compli-
cated than we have here contemplated ; but, when we make
allowance for the peculiar mechanism he supposes, the re-
sult of his investigation will be found to agree with the ex-
pression (1).

V. Effect of the Machine.

We have found that the moving power of the machine is
Vxv; and

P x v = v x = aV x — x ( 1).

Now a X V is the prism of water that issues from the orifices
in a second, which quantity we shall denote by Q ; then the
equation,

Q = a x V (A)

will express the relation between the water expended, the ve-
locity of expenditure, and the sum of the areas of the orifices.
Further, put

x- v - V7~

and

the Theory of Barker's Mill 429

and x will be a number less than 1 : then
/*— x2fl

£+m °f- 2sflh

wherefore, by substitution,

Pxc = ,Vxix(I-l)=Q4x^.

If we make Jt == 1, which supposes that jf and w are infinitely
great, then P xv = Qh; and the effect of the machine would
be equal to the whole mechanic power in the quantity of water
Q falling from the head h. This is an unattainable limit ; but
the nearer x is to 1, the greater will be the moving force of
the machine ; which seems to be the only general rule we can
have to guide us in the construction of this machine. Having
pitched upon the most convenient value of x ; then,

2Vgh

v =

a/-!-**

a ; = 5^5 x *JF**

effect of the machine, Px»=QAx TJ~' If j? = £, that is,

if V be double of v9 then the effect of the machine is § x Qh.
In what goes before we have taken the full velocity due to
the head, which is always greater than the real velocity in
practice. But although the real velocities are less than ac-
cording to theory, yet they still nearly follow the same pro-
portion ; that is, their squares are as the pressures, or as the
heights of the head. We may therefore assume

V2=4g.W (£+/),

m being a quantity less than 1, to be determined experimen-
tally. It is evident that this assumption does not affect the
equation (A). We shall now have,

j- » = Vf_

430 Mr. Ivory's Notes relating to the Theory of Barker's Mill.

= 2/ = 2h x - —
<j l — '

Q,g J 1 — m i*

t» tt k f2 / V _ \ ~ , 2m(x—x*)

P x v = aV x — x( 1 ) = Q# x -^ — -r*

Now it is obvious that the expression ' ~Z is susceptible of
a maximum ; and, by applying the usual rule, the value of x
answering to the maximum will be found ; viz. x = 1~v 1~^

m

This expression shows that, whatever fraction of unit m stands
for, x is contained between the limits \ and 1* ; so that, when
the machine works to the greatest advantage, v is greater than
^ V and less than V. With a given value of m, the rules for
constructing the machine so as to work to the greatest effect,

are contained in the following formulas, in which n = — , viz.

i?= 2 s/ g h x .-

° sy/n-x*

V=2 4/jA X

a/ n— x*

Q

«=77= * */ n-x\

effect of the machine, P x v = Q h x (l — V 1 — m) f. It now
appears that, m falling short of 1, the effect of the machine
decreases rapidly. If m = -8, then Pxd=Q^X 0*5528,
or P x t> = | x Qh9 nearly.

If m = |, that is, if half the pressure were lost in forcing
the water through the tubes, the effect of the machine would
be reduced to Qh x 0*293, or nearly T3n X Q h.

* i"

* ™ = 2 + 8 + 16 + 128 ^

when m = 0, * = \ ; when m = 1, x - 1.

+ 1- jyT^m
i -j _- 2L ,

m

mx% = 2 a* — 1,
1 — WJ79 = 2(1 — .r)

2«(i-i') 2m(i-^) . ,-

LXV. Ow

[ 481 ]

LXV. On the Figure of the Earth, as deduced from Measure-
ments of the Meridian. By J. Ivory, Esq. M.A. F.B.S.*

TN my last communication I have shown that the five por-
•*■ tions of the meridian which have been most exactly mea-
sured, belong to one and the same elliptical spheroid, although
they occupy very dissimilar situations on the earth's surface.
The almost perfect precision with which the elliptical elements
agree with the actual measurements, is indeed not a little re-
markable, and seems hitherto to have escaped notice. In re-
turning to this subject, which is of great importance in the
question about the figure of the earth, my intention is to dis-
cuss it more thoroughly, by examining it in every point of
view that may throw light upon it.

The equations deduced from the five measurements are as
follows (Phil; Mag. for May, pp. 345, 346):

188510= A (3*117500— 6*2261. s + 3*095. s2)
598630= A (9*895891 — 18*1985. e + 6*163. e«)
751567 = A (12*370302— 6*2811 . £-10*466. e2)f
172751 =A (2*840172— 0*3844. e— 2*166. e2)
98870 =A (1*622022+ 0*8378. e- 0*022. e2).

In solving these equations I before supposed that the ele-
ments sought were approximately knowrn; but I shall here
proceed by a more direct method, which is independent of any
previous knowledge of the elements. For this purpose, as-
sume, A=R(1 + As + Bc2),
R, A and B being quantities to be determined : substitute the
value of A in every one of the five equations, neglecting the
powers of e above the square ; and, having added all the re-
sulting expressions into one sum, equate the coefficients of e
and s2 to zero : then,

1810328 = 29*845887 X R ; R = 60655*9

29*8459 X A = 30*2523, A = 1*0136

29*846 B = 30*252 A + 0*396, B = 1*141
and, consequently,

A = R (1 + 1*0136 . s + 1*141 . g*).

It is obvious that R is the radius of the circle in which the
sum of the lengths of all the arcs answers to the sum of their
amplitudes. The element A now depends upon e, which is
the only unknown quantity. In order to find e, substitute the
value of A in every one of the five equations, bringing all the

* Communicated by the Author.

f In the Phil. Mag. for May, the coefficient off* is 6-266; but the inad-
vertence does not affect any of the results.

terms

432 Mr. Ivory on the Figure of the Earth, as deduced

terms to one side after having divided by R ; by which pro-
cedure we shall obtain these five equations,

afl)= -009642 — 3-0662.6 + 0-341 . e2
afv= -026612— 8-1680. 6-0992. e2
.r(3)= -020364-6-2574. e + 2-719. e2
,r<4>= -007875—2-4944 . e— 0*684 . s2
af5)= -007992—2-4819 . e-2'678 . e2
The symbols afx\ af2\ &c. stand for the errors, or rather, for
the quantities which the want of perfect exactness in the ex-
perimental numbers, makes it necessary to supply in order that
the same value of e may produce an equality in all the five ex-
pressions. The best mode of solution is to employ the me-
thod of the least squares, or to determine s so as to satisfy this
equation, viz.

di dt

Thus we have,

0 = (-009642-3-0662. e + 0-341 e2) ( — 3-0662 + 0-682 s)
+ (-026612-8-1680 e +0*992 e2) (-8-1680 + 1-984 e)
+ &c.
All the operations being performed, this final equation will be
obtained, viz.

0-413829= 127*666. 6 + 4-795. e2;
from which we get I = -00324. And if this value of g be
substituted in the foregoing expression of A, we shall find
A si 60655-9 x 1-003295 = 60855-7, or 60856. The direct
method of calculation here followed, has therefore brought us
to the same elements as before, which, as has already been
shown, represent all the five measurements with very small
errors*.

It is easy to verify the value that has been found for A ;
namely, by combining the original equations so as to eliminate
the terms containing e, or so as to render the same terms so
small that they may be neglected. Thus, if the expression of
the French measurement be multiplied by 2*9, we shall have,

2179544= A(35-8739-18-2152. 6-30-351. e2);

and, if the Indian expression be subtracted from this, the re-
mainder will be,

1580914 = A (25-9780-0-0167 . e-36'514 . 62),
from which we get A =60856 as before. We are therefore
sure that there is no uncertainty in the values that have been
assigned to the two elementary quantities.

The elements of the elliptical meridian being known, we

* Phil. Mng. for May, p. 34C.

may

from Measurements of the Meridian, 433

may thence deduce its curvature at certain fixed points ; and,
in order to judge more accurately of the near agreement of
the measurements with the theory, we may compare them se-
parately with the curvature of that portion of the meridian to
which they are nearest in situation. For this purpose I shall
use the notation D (a) to denote the length of a degree of
which the middle point is placed in the latitude A. The ex-
treme latitudes of the degree will therefore be A + ^ and A — \ ;
and, in the formula (A)*, we shall have n = 1°, p sin n = 1°,
cos n = I, m = 2 A; consequently,

D(A) =A{1-S(i + f cos 2 A) % ? (TV + U COS4A)}. (C)

In this expression put A successively equal to 0°, 45°, 90° ; and
we shall have, for the length of 1 °,

Fathoms.
At the equator, D(0°) = A(l - 2e + s9) = 60462-4

At latitude 45°, D (45°) = A(l -J i - £s2) = 60757
At the pole, D (90°) = A(l + « + e2) = 61054
Let us now compare the arcs measured in Peru and India,
with the curvature of the meridian at the equator. From the
expressions just set down, we get,

A=D(0°).(1 + 2s + 3e2);
and if we substitute this value in the two measurements men-
tioned, we shall get these three equations, the last being the
sum of the other two, viz.

188510 = D(0°) (3-11750 + 0*0089 . s -0*005. s2)
598630 = D (0°) (9-89589 + 1*5933 . s-0'546 . s2)
787140 = D(0°) (13*01339 + 1*6022 . s-0*551 . s8)
In the first of these expressions the terms containing g may be
neglected, and D (0°) will be found equal to 60468, or near
6 fathoms too long, which arises from the Peruvian arc
being about 20 fathoms too long. If we substitute the value
of s in the two remaining expressions, we shall get 60461*3
and 60462*9 for the value of D (0°), hardly different from the
length previously deduced from the two elements.

The French arc is nearly bisected by the parallel of 45°,
and it must be compared with the curvature at that latitude.

NoW' • A = D(45°).(1 +i + §s*);

and, this value being substituted in the expression of the mea-
surement in question, we shall obtain,

751567 = D (45°) . (12*3703-0*0960 . i + 0*310 «-).

* Phil. Mag. and Annals for May, p. 344.
New Series. Vol. 3. No. 18. June 182S. 3 K Here

434 Mr. Ivory on the Figure of the Earth, as deduced

Here the factor on the right-hand side is but slightly affected
by the terms containing s, which reduce it to 12*37; and
D (45°) is found equal to 60757, the same value derived from
the two elements, and very nearly the same that results from
the actual measurement without any assumption about the
figure of the earth*. It is therefore certain that the elements
which have been found represent with great exactness both
the whole arc between Dunkirk and Formentera, and also its
mean curvature. I have likewise found that the same elements
represent, with small errors, the partial arcs between Dunkirk
and Montjouy, and Montjouy and Formentera. But it is well
known that the four sections of the arc between Dunkirk and
Montjouy are very irregular ; and the causes of the irregu-
larity have not been very well explained. Whatever these
causes may be, they extend their influence to the measure-
ments that have been made in England. Unless I have been
misinformed, a re-measurement between Greenwich and Paris
has lately been executed, the results of which, when made
public, will probably help to clear up the perplexing anoma-
lies that occur in the comparison of the partial arcs.

We may now compare the Swedish, or most northerly, arc
with the curvature at the pole. We have,

A = D(90°) x (1-s);

and, by substitution, we get,

98870 = D (90°) . (1-622022-0-7842 . s-0'860 . s2).

From this equation, taking the foregoing value of e, D (90°)
will be found equal to 61051, or only three fathoms less than
the value deduced from the two elements; and even this dif-
ference will disappear, if we take into account the error of the
arc itself.

If in the expression (C) we make

Cos 2 A = - £, A = 54° 44',

we shall get cos 4 X = — ^, and

D(X) = A(1 -fi«) = A.

It appears, therefore, that a degree of the meridian in Britain,
very nearly midway between York and Edinburgh, is equal
to a degree of the earth's equator. Although the Trigono-
metrical Survey has been extended between the extreme north
and south points of the island, yet, as far I know, the calcula-
tions have not been completed except for a small part of the
meridian between Dunnose and Clifton. We cannot there-
fore verify what has just been shown by comparing it with any

* Phil. Mag. and Annals for May, pp. 346, 347.

actual

from Measuremefits of the Meridian. 435

actual measurement in the proper latitude ; but we may in
some measure be enabled to judge of its exactness by em-
ploying the portion of the meridian that has been calculated.
Let A' represent the mean latitude between Dunnose and Clif-
ton, then

A = 54° 44' 0"

A' = 52 2 20 ;
and, by means of formula (C), we shall readily obtain,

D(a')-D(a) = f A e (cos 2 A- cos 2 A'),

the term containing e2 being insensible. Now, by dividing
the length of the English arc by its amplitude, we get D (A)
= 60824:1 ; and hence,

D (A') = 60824-1 + 26*6 = 60850-7,
which is only five fathoms less than the exact value of A, and
this deficiency is caused by the small error of the arc, which
is too short

It follows, from the foregoing minute examination, that the
five arcs are represented with great precision by the elements
that have been found ; and further, that each arc, taken se-
parately, agrees accurately with the curvature of that portion
of the meridian in which it is situated. And there cannot be
a more satisfactory way of proving that the meridian of the
earth is an ellipsis, than by showing that it coincides with that
figure, at the equator, at the mean latitude of 45°, at the pa-
rallel of 54° 44' where the curvature is identical to the equa-
torial circle, and at the pole. We have briefly endeavoured
to accomplish this task as far as the measurements in our
possession put it in our power to do so; but the proof would
have been much more complete, if we could have confirmed
it by the length of the meridian through the whole extent of
Britain.

To the fixt points on the meridian that have already been
mentioned, we may add another intermediate 'between the
equator and the parallel of 45°. In the expression (C), put,

Cos 2A = + £, A = 35° 16';

then, D(x)=A (1-f - f e2) =A(1- 0-

At this latitude, which is the complement of 54° 44', the radius
of curvature of the meridian is equal to half the polar axis.
The length of the degree depends upon the elements of the
ellipsis ; and it may serve as a quantity of reference for judging
of the consistency of any measurement made near its parallel
of latitude. In the present state of this research there is no
measurement that can be compared with it. The nearest to

3 K 2 it

436 Royal Society.

it is the degree of La Caille at the Cape of Good Hope, in
latitude 33° 18'; but this is so disproportionately great, that no
use can be made of it.

May 12, 1828. J. Ivory.

LXVI. On the characteristic Equation of Curve-surfaces
capable of being evolved in a Plane. By M. Fayolle.

To the Editors of the Philosophical Magazine and Annals.
Messieurs,
/^E n'est pas sans surprise que j'ai lu, dans votre dernier
V^ N°; du Philosophical Magazine, le passage suivant, p. 334 :

d*x d*x / d* z \ 3 _

dx2 ' dy1 V dxdy J

" an equation which, indeed, has long been known, but in the
opinion of Mr. Gauss has never yet been rigorously demon-
strated."

Les geometres savent que Monge et Meusnier ont donne
des demonstrations rigoureuses de cette equation differentielle
partielle du second ordre, qui appartient aux surfaces develop-
pables. Pour s'en assurer, je renvoie vos lecteurs aux volumes
9 et 1 0 de la collection des Memoir es des Savans etrangers.

Ce 15 Mai, 1828. Fayolle,

Ancien chef d' etude a lecole Polytechnique.

LXVI I. Proceedings of Learned Societies.

ROYAL SOCIETY.

[Being enabled to resume our regular reports of the proceedings of
this Society, we commence at present with a list of the papers
read before the Society during the present session, which have
not hitherto been noticed in the Philosophical Magazine.]

Dec. 20, 1827.— OESE ARCHES to discover the faculties of
-i-V pulmonary absorption with respect to char-
coal. By G. Pearson, M.D. F.R.S. — A Catalogue of nebulae and
clusters of stars in the southern hemisphere, observed at Paramatta
in New South Wales. By James Dunlop, Esq. in a letter addressed
to Sir Thomas M. Brisbane, Bart. Communicated by Mr. Herschel.

Jan. 10, 1828. — On the life of plants and animals. By Sir G.
Gibbs, M.D. F.R.S. — Observations on the comparative magnetic
intensity shown by a horizontal needle at the bottom and on the
tops of mountains at Port Bowen and Spitzbergen. By Captain
Henry Foster, R.N. F.R.S.

17. — On Capt. Parry's and Lieut. Foster's experiments on the
velocity of sounds. By Dr. G. Moll, Professor of Natural Philoso-
phy in the University of Utrecht. Communicated by Capt. Henry
Kater, V.P.R.S. — An account of a series of experiments, made

with

Royal Society. 437

with a view to the construction of an achromatic telescope with a
fluid concave lens, instead of the usual lens of flint glass. In a let-
ter addressed to the President. By P. Barlow, Esq. F.R.S.

24. —On the structure and use of the capsulae renales. By Sir
Everard Home, Bart.V.P.R.S.— Abstract of a meteorological journal
kept at Benares in the years 1824, -25, and -26 ; with remarks. By
James Prinsep, Esq. Communicated by Dr. Roget. — Description
of a percussion rifle, igniting by a spring instead of a lock. By
Lieut.-Col. Miller, F.R.S.*

31. Feb. 7. — An account of trigonometrical operations in the
years 1821, -22, and -23, for determining the difference of longitude
between the royal observatories of Paris and Greenwich. By Capt.
Henry Kater, V.P.R.S.

14. — On the mode in which the nerves belonging to the organs-
of sense terminate. By Sir E. Home, Bart. V.P.R.S. — Experiments
on heated iron, in reference to the magnetic and electric fluids.
By William Ritchie, Esq. A.M. Rector of the Royal Academy of
Tain. Communicated by Captain Sabine.

April 24. — A paper was read, containing An account of experi-
ments on the elastic curve. By B. Bevan, Esq. Communicated by
the President.

In inquiries on the strength of materials, it is often desirable to
know the real nature of the curve assumed by a prismatic rod, when
acted upon by the weight of its own parts. This curve has generally
been stated to be the parabola ; but repeated observation has led
the author to doubt the accuracy of the theory from which this con-
clusion has been deduced; and with a view, therefore, to determine,
by direct trial, the real form of the curve, he instituted a series of
experiments on prismatic rods, of various substances, and of various
depths and lengths, some fixed at one end, and others supported at
both ends, in a horizontal position. In every instance he found the
actual curve to differ from a parabola, and the deviations in the se-
veral points examined were such as indicated a regular and deter-
minate species of curve. No modification of the exponent of the or-
der of the parabola was adequate to express the relation of the co-
ordinates with sufficient accuracy in all cases. He found, however,
after many trials, that the following formula, which is that of the
common hyperbola, gave a very near approximation in all practi-
cal cases, namely, Ax2 + Bar = y*

The accurate determination of the elastic curve is a subject -of
some importance in practical mechanics ; since the rules at present
used by mathematicians and engineers for determining the modulus
of elasticity of different materials, are founded upon the parabolic
theory, and must therefore be liable to error.

May 1. — A paper was read, intitled, " A description of a verti-
cal floating collimator, and an account of its application to astro-
nomical observations, with a circle, and with a zenith telescope.
By Capt. Henry Kater, V.P.R.S.

The construction of the instrument which forms the subject of

* See Phil. Mag. and Annals, vol. iii. p. $77 >

this

438 Royal Society,

this paper is a material improvement on that of the horizontal float-
ing collimator, of which an account was given by the author in the
Philosophical Transactions for 1825. Its superiority is derived from
its adaptation to the vertical, instead of the horizontal, position ;
by which the sources of error arising from the necessity of trans-
ferring the instrument to different sides of the observatory, and of
taking the float out of the mercury and replacing it at each obser-
vation, are wholly obviated. The vertical floating collimator has
the further advantage of being adapted for use, not only with a cir-
cle, but also with a telescope, either of the refracting or reflecting
kind. Such a telescope, furnished with a wire micrometer, and
directed to the zenith, becomes a zenith telescope, free from all the
objections to which the zenith sector, and the zenith telescope, with
a plumb-line, are liable-

The instrument itself is supported on a square mahogany stand,
which slides on two parallel beams, fixed at the upper part of the
observatory, in the direction of the meridian, and which has a cir-
cular aperture in the centre, having at its edge a projecting rim
of iron, to admit of the passage of the telescope. The telescope
having a focal length of eight inches, and an aperture of one inch
and a quarter, is supported in the vertical position by a bridge,
connecting it with a circular iron ring, ten inches and six-tenths
in diameter, which floats in mercury. The mercury is contained
in a circular iron trough, the central aperture of which is suffici-
ently large to allow of its turning freely* round the rim which
rises from the margin of the aperture of the stand. The object-
glass of the telescope is placed at its lowest end, and its focus is
occupied by a diaphragm, composed of two brass plates, each
cut so as to form an angle of 135 deg. and placed opposite to each
other, so that the angular points are brought to an accurate coin
cidence, thus leaving on each side intervening spaces, which form
vertical angles of 4-5 deg. each. The telescope below, whether be-
longing to a circle or a zenith telescope, is to be directed so that
the image of these angles shall be bisected by the micrometer wire;
for which purpose the diaphragm of the collimator is illuminated
by a bull's-eye lantern, placed at a convenient distance upon one of
the beams crossing the observatory ; the light being reflected down-
wards by a plane mirror placed in a screen, with a suitable aper-
ture immediately above the collimator. The collimator is then to
be turned half round in azimuth, the motion being facilitated by
rollers, and limited at its extent by two catches, which receive
a projecting wire fixed to the outer circle of the trough. When in
this situation, the observation of the diaphragm by the telescope,
and the bisection of its angles, are to be repeated, and the mean of
the two positions will indicate the exact point of the zenith. Minute
directions are given by the author for the construction of all the
parts of the collimator, and for their proper adjustments; together
with an account of the precautions to be taken in the employment
of the instrument. The time required for completing the determi-
nation of the zenith point by its means need not exceed two mi-
nutes ; and if to this be added the time necessary for a second set of

observation*

Royal Society. £39

observations of the same kind, for the purpose of verification, and
of a nearer approach to accuracy, the whole time required will not
be more than five minutes, during which it is not probable that any
sensible disturbance can have taken place in the position of the in-
strument from changes of temperature.

Tables are given containing registers of numerous series of ex-
periments made, both by the author and by several of his friends,
with a view to determine the stability of the instrument, and the
degree of reliance that can be placed in the results. In the first
series, out of sixty independent determinations of the zenith point,
there are twenty-five, the error of each of which does not exceed
one-tenth of a second ; thirty-seven under two-tenths ; forty-seven
under three-tenths ; fifty-five under four-tenths ; three between four
and five-tenths ; and two a little above half a second. But the* author
thinks it probable that the greater part of these errors, minute as
they are, must be attributed to want of power in the micrometer,
which power is directly as the focal length of the object-glass, or
mirror, of the telescope to which it is attached, and which neces-
sarily limits the precision of which it is capable.

The author next gives the results of some experiments with a
collimator made for Captain Foster, having a float of only five inches
in diameter, and with a telescope five inches long : the errors, gene-
rally, do not amount to more than two-tenths of a second.

He then enters into details as to the manner of using the vertical
floating collimator in astronomical observations, beginning with the
portable azimuth and altitude circle described by the Rev. F.Wol-
iaston in his Fasciculus Astronomicus, and applicable to other similar
instruments. The new collimator affords, also, the most perfect me-
thod of adjusting the line of collimation of a mural circle, or of
placing it at right angles to the axis.

The author next proceeds to describe the method of applying the
instrument to the zenith telescope. In comparing the observations
made by the zenith sector belonging to the Board of Ordnance, with
the zenith telescope used in conjunction with the vertical floating
collimator, the mean of errors in the former case was -f 0"*54? and
— 0"-75; in the latter, +0"44 and — 0"-66. From observations
made on y Draconis, the zenith distance of which at Greenwich is
0° 2' 6"-36, and atYork Gate 0° 0' 35"*67, the difference of latitude
between the two places was found to be 0° 2' 42"*03, that of
Greenwich being 51° 28' 38"-96, and of York Gate 51° 31' 20"*99.
The decimals of a second, by the azimuth and altitude circle and
horizontal floating collimator were '94; by the same instrument
and the vertical floating collimator -76, and by the zenith telescope,
and the vertical floating collimator *99 : the mean being -9".

From the greater degree of precision attainable by the employ-
ment of the vertical floating collimator, from the facility of its con-
struction and application, and the time saved by using it, the author
deems it not unreasonable to infer, that, ere long, the use of the
level and plumb-line in celestial observations will be wholly aban-
doned.

LIN-

44-0 Linruean Society.

LTNNiEAN SOCIETY.

May 4. — The reading of Mr. Morgan's paper On the mammary
organs of the kangaroo was continued, containing further particulars
of the dissection of these parts, as well as of the muscles attached
to the marsupial bones, in the adult and impregnated animal.
These bones, with their ligamentous and muscular connections, were
described, and several errors in Sir Everard Home's published ac-
count of these parts were pointed out. The author then stated his
own opinions respecting the use of these structures. He stated that
the marsupial bones are formed, 1st, for the purpose of giving that
firm support to the superincumbent abdominal viscera which the
narrow pelvis of the animal is incapable of affording while in the
erect posture ; and, 2ndly, for the purpose of constituting a fixed
point of resistance against which the mammae are squeezed by the
muscular girdle already described as inclosing those glands be-
tween their fibres. By this arrangement the female is enabled to
empty by compression the excretory ducts of its mammae, and thus
to force their secretions into the mouth of the imperfectly organized
young, which during the earlier periods of its existence appears in-
capable of extracting a nutritious fluid from that part by the usual
means.

It appears that the secretion of this fluid (or milk) takes place
only in the larger and lower gland, and that its ejection through
the inferior and longer teat is assisted by a muscular investment
which incloses the ducts throughout their whole course from the gland
to the extremity of the nipple. The existence of this structure
has been noticed by M. Geoffroy St. Hilaire, who has assigned to
it the same use. Under this compressing muscle of the lower (or
as Mr. Morgan has named it, the true marsupial) teat, a congeries
of vessels which principally consisted of veins was described as form-
ing a plexus around the central fasciculus of ducts. These veins,
together with those of the gland, were stated to occasion a con-
siderable distention of the mammary organ during the time of suck-
ling, in consequence of the congestion which must necessarily oc-
cur in the vessels at that period, from the pressure made upon their
main trunks by the action of the compressing muscle of the mamma ;
for it has been found that the size of the organ on such occasions
exceeds that which a loaded state of the ducts only could produce.
The mammae were found, as in the virgin animal, to consist in dou-
ble glands on each side, the upper and smaller presenting the same
anatomical characters as in the former instance ; its excretory ducts,
however, in their course towards the upper nipple were found to be
inclosed in an indistinct muscular sheath, and there was a faint in-
dication of the existence of a plexus of vessels similar to that which
was found in the lower or true marsupial teat. This smaller mam-
mary organ is considered by the author as analogous to the super-
numerary mammae and teats of other mammiferous animals, since
the lower or true marsupial mammary glands and their teats ap-
pear to perform exclusively the office of preparing a nutritious
fluid for the support of the young animal.

May

Geological Society. 441

May 24. — This day the Anniversary Meeting of the Society took
place, at which Edward, Lord Stanley, was elected President, in the
room of the late Sir J. E. Smith ; and Edward Forster, J . E. Bicheno,
and R. Taylor, Esqs. respectively re-elected to the offices of Trea-
surer, Secretary, and Under Secretary.

GEOLOGICAL SOCIETY.

March 21.— Benjamin Silliman, M.D. LL.D. of Yale College,
North America, was elected a Foreign Member of this Society.
Francis Finch, Esq. and Thomas Winter, Esq., both of West Brom-
wich, Staffordshire, were elected Fellows of this Society.

A paper was read, intitled " Topographical and Geological No-
tices, from information collected during the Expedition to the North-
west coast of America under the command of Captain Franklin j by
John Richardson, M.D. F.R.S., &c."

The expedition under Captain Franklin having arrived at their in-
tended winter-quarters on the shore of Great Bear Lake, examined
in J 825 the vicinity of that lake, and the course of the Mackenzie
River from thence to the sea. The author subsequently accompanied
Captain Franklin down the river, as far as Point Separation, in lat.
67° 38' ; from whence the latter proceeded westward to lat. 70° 26',
long. 148° 52' :— the extreme western point seen by the expedition
being in long. 149° 37' west. Dr. Richardson at the same time
went eastward to the mouth of the Copper Mine River, and thence
returned overland and across the Great Bear Lake, to the head-
quarters.

This paper contains an account of the specimens collected, and the
geological observations made by both divisions of the party ; and
gives in considerable detail a description of the vicinity of Great Bear
Lake, with a more general one of the banks of the Mackenzie and
of the coast to the East of it ; to which are subjoined some observa-
tions respecting the country previously passed over by the expedi-
tion, between Lake Superior and Fort Franklin. The distances
traversed being, in latitude, about 23 degrees N. of Lake Supe-
rior ; and in longitude, altogether about 80 degrees ; — 60 degrees
to the west of Lake Superior, and 20 degrees on the coast, east-
ward from the mouth of the Mackenzie. The total extent passed
over in America by the expedition, in going and returning, was about
14,000 miles ; and that surveyed and laid down for the first time on
the maps, is about 5000 miles.

The author however mentions, that a very limited portion of his
time could be devoted to geological researches ; the ground being for
eight months in the year covered with snow ; and the other objects
of the journey demanding his principal attention during the short
summer.

The country described consists, in general, of three or four forma-
tions, or series of beds, which occupy well marked divisions : —

1 . The most western division comprehends the Rocky Mountains,,
which appear to be composed of primitive rocks ; and the course of
the ranges is from about S.E. to N.W. ; the faces of the hills to

Neiv Series. Vol. 3. No. 18. June 1828. 3 L the

442 Geological Society.

the eastward being abrupt, but the slope towards the W. more gra-
dual. These mountains join the sea on the west of the Mackenzie ;
and at their termination are divided into four groups or chains, to
which Captain Franklin has given the names of Richardson s, Buck-
land's, the British, and Romanzoff chains. The land again becomes
lower to the west of the chain last mentioned, and continues to be so
from thence to the remotest point arrived at ; no prominent elevations
having been observed to the west of long. 146°.

2. Another very extensive tract of primitive rocks in the north of
America has nearly the same direction with the range of the Rocky
Mountains, but the two ranges converge towards the north j the
distance between them being, in lat. 50°, 700 miles ; — about 220 miles
where it was traversed by Captain Franklin, in going from Hudson's
Bay to Lake Winipeg ; — and in lat. 66° only 200 miles. This east-
ern primitive tract consists principally of granite and gneiss ; it ex-
hibits great uniformity of character, contains no very elevated ground,
and is in fact traversed by several rivers which arise in the Rocky
Mountains. It is flanked on both sides by extensive calcareous tracts.

3. The north-eastern extremity of the Rocky Mountain chain, near
the mouth of the Mackenzie, consists of grauwacke and other transi-
tion-rocks, interposed apparently between the primary and the cal-
careous districts. In some of the other places described, a rock
resembling the old-red-sandstone of England, occupies a similar si-
tuation.

4. The tract that intervenes between the Rocky Mountains and the
eastern primary band above mentioned, consists principally of cal-
careous strata, and is remarkable from its including, throughout, a
series of great lakes or lake-like rivers, with which a very large pro-
portion of the surface is occupied, and the bottoms of which appear
in several instances to be below the level of the sea. This interme-
diate calcareous band was traced in one place by the author, to the
width of about 280 miles from the eastern primary tract j and one of
its highest summits, about a mile from Bear Lake, was supposed to
be about 950 feet above the sea. The limestone of which this district
is composed, as well as that of the calcareous tract on the east of
the primary band above mentioned, presents considerable uniformity
of character : the ridges of hills are nearly parallel to those of the
Rocky Mountains j and a very large proportion of the rocks observed
by the author, was found to be magnesian limestone, — apparently
belonging either to the magnesian limestone formation of England,
or to our mountain-limestone, which it is well known includes in
Europe numerous beds of dolomite.

The fossils also of this calcareous formation, are of the same genera
with those of our mountain-limestone and of the magnesian beds in
the north of England ; including corallines, products, terebratulites,
and a cardium : and in several places the calcareous beds contain a
large proportion of chert and flinty slate. The correct determination
of the relations of this great calcareous tract, is one of the chief
points of interest remaining for future research, in the country de-
scribed by the author ; for while he agrees with other geologists in

assigning

Geological Society, 443

assigning a portion of it, (as in the vicinity of Lake Winipeg,) to the
mountain-limestone of Europe, he justly remarks that in other places
the quantity of gypsum, in connection with copious salt springs, and
great abundance of petroleum, together with the occurrence of soft
marly-sandstone, and beds of breccia interstratified with those of
dolomite, and above all, the fact that dolomitic limestone is by far
the most common and extensive rock in the deposit, would lead to its
identification with the zechstein of continental geologists, — the mag-
nesian limestone of the North of England.

5. Above the limestones, and in some cases, it would appear,
alternating with the dolomite, is a very extensive deposition of sand-
stone, bituminous-shale, and slaty- clay (which last exhibits in some
places the peculiar structure denominated cone-in -cone) containing
nodular ranges of clay-iron-stone and beds of lignite. The shales
include impressions of ferns, lepidodendrons, and other vegetable
remains $ and among the fossils of this formation was also found an
ammonite, supposed by Mr. Sowerby to belong to a part of the
oolitic series of England. It deserves inquiry therefore, whether
this may not be the equivalent of the carboniferous strata which form
a portion of the oolitic series in Yorkshire, and at Brora in Scotland.

The series of beds above described occurs extensively in the
course of the Mackenzie River, and on the shores of the Great Bear
Lake j and from its being found also on the northern coast, at a
distance of about 300 miles from thence, and in a direction precisely
corresponding, it not improbably occupies the intervening country.

About Cape Bathurst (lat. 70° 36', long. 127° 35') cliffs of alum
shale form the coast for more than 60 geographical miles, and are
described as resembling those of Whitby in Yorkshire.

6. On the promontory of Cape Lyon are extensive ridges of co-
lumnar trap associated with limestone and slate-clay j and green-
stone is of frequent occurrence there and in some other places.
Porphyry also, forms low conical hills in the high ground between
the Copper Mountains and Bear Lake.

7. Near the western boundary of the limestone, and not far from
the base of the Rocky Mountains, there occur at intervals, from lat.
50° to 69° N. extensive [tertiary?) deposits, consisting generally of
sandstone, gravel, clay more or less bituminous, and brown wood-
coal. In some spots the wood-coal was replaced by an excellent
pitch-coal, the fractured surface of which is marked with very peculiar
concentric semicircular depressions j and it is interesting to know
that this coal, which would be excellent fuel for a steam-vessel, occurs
on the coast of the Polar sea near the Mackenzie in considerable
quantity. This formation contains layers of a variety of pipe-clay which
is eaten by the natives, and is said to sustain life for a considerable
time. The deposit at the mouth of Bear Lake River includes some
beds of impure porcelain earth. The author found occasionally much
difficulty in distinguishing the sandstones and shales of this deposit,
from those of the formation mentioned above in Section 5.

8. Among the indications of other strata more recent than the
magnesian limestone, was a loose fragment of soft limestone found

3L2 at

444 Geological Society.

at the mouth of Babbage River, on the coast west of the Mackenzie,
containing the species of Cyclas (C. medius) which occurs extensively
in the weald-clay of England.

This memoir, which will be published in full in the Appendix to
Captain Franklin's Narrative of the expedition, is illustrated by maps
and drawings, and accompanied by a catalogue in detail, of the speci-
mens referred to, which have been presented to the Geological Society.
April \8. — William Hutton, Esq. of Newcastle-upon-Tyne, Beriah
Botfield, Esq. of Christchurch Oxford, and William Parker Hamond,
Esq. of St. John's College Cambridge, were elected Fellows of this
Society.

A Paper was read, " On the fossil remains of two new species of
Mastodon, and of other vertebrated animals, found on the left bank of
the Irawadi j by William Clift, Esq. F.G.S. F.R.S., conservator of the
Museum of the Royal College of Surgeons."

The author having been requested to describe the fossil remains
which the zeal and liberality of Mr. Crawfurd have transferred from
the deserts of the Irawadi to the Museum of the Geological Society,
confines himself strictly to zoological and anatomical details ; and fol-
lowing the system of Cuvier, commences with the

Pachydermata proboscidifera. — The only genus of this order indi-
cated by the remains is the Mastodon ; and of this there are two spe-
cies, Mastodon latidens and Mastodon elephantoides, not only com-
manding attention from their novelty, but from the beautiful gradation
which they exhibit between the mastodons already described and the
elephant. On comparing the teeth of Mastodon latidens with those
of the mastodon of the Ohio (M. giganteum) the denticules are found
to be more numerous, and less distant, and the interstices less deep
than in those of the latter. The teeth, in short, begin to assume the
appearance of those of the elephant. On advancing to Mastodon
elephantoides, these features of similarity are more strongly deve-
loped : the many-pointed denticules are still more numerous and
more compressed j and the structure, were it not for the absence of
crusta petrosa, becomes almost that of the tooth of the elephant.
In both, though the teeth are formed upon the principle by which
the tooth of the mastodon is distinguished from that of the elephant,
the crown of the tooth wears away more like that of the elephant t,han
that of the other mastodons.

The species are thus characterized :

Mastodon latidens. — Mastodon dentibus molaribus latissimis, den-
ticulis rotundatis, elevatis. Palato vald& angusto.

The dentition very much resembles that of the ' elephant. The
molar tooth is gradually pushed forward, and rises as the fangs are
added, according to the demand occasioned by the abrasion of the ex-
posed crown, and the consequent absorption of the anterior fang ; the
posterior part of the tooth not having yet cut the gum, while the an-
terior portion is completely worn away. Before it are seen the relics
of the preceding tooth, the place of which the tooth in use was pro-
gressively supplying.

The lower jaw in this species is less square and deeper than it is in
M. tngantcum.

The

Geological Society. 445

The tusks, judging from the alveoli, must have been of equal vo-
lume with those of the largest living elephant.

The following is the measurement of some of the remains of M.
latidens.

Extreme breadth of fragment of cranium (upper jaw

with the greatest part of both grinders) 1 Ft. 3 In.

Length of ditto I 8

Extreme length of right anterior grinder (6 denticuli

and the spur) 0 8^

Extreme breadth at third denticulus 0 4

Circumference of lower jaw, measured over the grind-
ing surface of the tooth 2 4

Extreme length of tooth 0 1 If

Extreme breadth 0 4±

Circumference of the lower extremity of right femur 2 2

Same, round the condyles 2 4

Mastodon elephantoides. — M. dentibus latis j denticulis numerosis,
compressis.

This species must have been smaller than the last. There is a fine
example of the lower jaw, showing the tooth in the highest degree
of perfection. The tooth is 11 inches long and 3j inches broad,
has no less than ten denticules, and each of these denticules is ma-
millated with small points 5 five being the smallest, and eight the
greatest number on any one denticule. In front of this tooth is
seen the remnant of the preceding one, worn down and disappear-
ing j and behind it is the cavity wherein the young tooth, intended
as a successor to that in existence, was in the course of formation.
The denticules are much more compressed than those in the species
last described j they are closer together, and the whole tooth ap-
proaches still more nearly to that of the elephant, while the jaw is in
unison with the appearance of the tooth.

Pachydermata ordinaria. — In this group we have the remains of
the genera Sus, Hippopotamus, and Rhinoceros. Of the first there
is only a single specimen, consisting of a small' portion of the lower
jaw, containing one molar tooth and the fragment of another. Of
the second there are but few fragments, nor are they sufficiently cha-
racteristic to warrant a definition of the species, which must have been
comparatively small. Of the third there is a portion of the upper
jaw, containing two molar teeth ; and portions of the lower jaw with
molares, which seem to approach nearer to those of the rhinoceros
of Java than to those of any other living species.

Ruminantia. — In this group we have fragments of the ox and of
the deer.

Reptilia.

Qiqlonia, Cuv. — (Testudinatq, Bell). — There are many fragments
of a large species of trionyx, and some of an emys. But the remains,
are not sufficiently defined for specific description.

Sauria. — Fam. CrocodilicUe. — Of this family we have the remains
of two genera ; viz. a Leptorhynchus allied to, if not identical with,

the

446 Geological Society.

the great gavial ; and a crocodile resembling Crocodilus vulgaris. Of
the former there are portions of the lower jaw and several vertebrae j
of the latter, there is the anterior termination of the lower jaw, which
must have belonged to a very large individual.

The specimens, in general, do not appear to have undergone any
mineral change, with the exception of being abundantly penetrated
with iron, and are very brittle. This last circumstance, arising from
the loss of their animal gluten, indicates great antiquity, and that they
have not been imbedded in any very compact soil ; unlike the teeth
of the mastodon of the Ohio, which lie in a strong blue clay, and have
almost as much animal matter as is to be found in a recent tooth.

The bones are almost in every instance broken ; and from the
firmness of texture of most of them, the direction and cleanness of the
fracture, and the sharpness of its edges, the injury, which must have
been the result of an immense power operating with sudden violence,
appears to have taken place at the period, or very soon after the
period, of the destruction of the animal.

A paper was next read " On a collection of vegetable and animal
remains, and rocks, from the Burmese Country, presented to the
Geological Societv by J. Crawfurd, Esq," by the Rev. W. Buckland,
D.D. V.P.G.S. F.R.S. &c.

Mr. Crawfurd collected these specimens during his voyage up the
Irawadi in a steam-boat, on an embassy to Ava, in the latter part of
the year 1 826. The author considers them to be of high importance,
as affording an answer to the curious, and till now undecided ques-
tion, whether there be, or be not, in the southern regions of Asia, any
remains of fossil quadrupeds analogous to those which are found so
widely dispersed in the diluvium of northern Asia, and of Europe and
America.

The evidence which Mr. Crawfurd has imported, consists of several
chests full of fossil wood and fossil bones, and of specimens of the
strata that are found along the course of the Irawadi, from Prome up
to Ava, being a distance of nearly 500 miles. The greater part of the
fossil wood is beautifully silicified ; other specimens of it are calca-
reous j they are mostly portions of large trees, both monocotyledo-
nous and dicotyledonous, and were found along the whole valley of
the Irawadi from Ava to Prome. The bones were all collected from
a small district near some wells of petroleum, about halfway between
these towns, and on the left bank of the river. From Mr. Cliffs exa-
mination, it appears, that although we have among them no remains
of fossil elephants, we have the same fossil pachydermata that are
found associated with elephants in Europe 5 namely, rhinoceros,
hippopotamus, mastodon, and hog. We have also two or three spe-
cies of ruminantia resembling the ox, antelope and deer, with the
addition of the gavial and alligator, and two freshwater tortoises,
namely, trionyx and emys.

The teeth of the mastodon belong to two unknown species of that
genus, both of them approaching in size to the largest elephant. Mr.
Clift has designated them by the names of Mastodon latidens and
M. elpphanloides. The teeth arc from animals of all ages 5 and there

are

Geological Society. 447

are many fragments of ivory, derived probably also from the mas-
todon.

The remains of the mastodon are by far the most abundant in this
collection, and amount to about 150 fragments.

Of the rhinoceros there are about 10 fragments.

Of a small species of hippopotamus, 2.

Of the hog, 1 j and of the ox, deer and antelope, about 20.

Of the gavial and alligator, about 50.

Of the emys, 20 j and trionyx, 10.

One fragment of emys is so large, that the animal of which it
formed a part, must have been several feet in width.

The state of preservation of these bones is very perfect, from their
being penetrated with hydrate of iron, and thereby rendered strong.
Not one of them is silicified, though they have been erroneously
stated to be so, in some of the periodical journals.

The district in which they were found is a little North of the town
of Wetmasut, and is composed of barren sand-hills and beds of gravel
intersected by ravines, and cemented occasionally into a breccia by
carbonate of lime, and sometimes by hydrate of iron. Over the sur-
face of these hills were scattered the fragments of bones and wood,
some quite naked and loose, others half buried in the sand and gravel.
Many fragments of wood lay also at the bottom of the ravines.
About one-third of the bones have been slightly rolled j and the rest
had all been broken before they were lodged in the places where Mr.
Crawfurd found them, and where they appear to have been dispersed
and buried, by the action of the same waters that produced the dilu-
vial sand and gravel, whence they have since been washed out, and
left bare by the action of rains and torrents.

Concretions of sand and gravel adhere to many of the bones, but
they contain no traces of shells, and differ mineralogically from all
the rock specimens in this collection, which we recognize as belong-
ing to tertiary and freshwater strata.

Indications of freshwater formation were found in one spot only,
not far from the fossil bones, and they consist of a marly blue clay,
abounding with shells of a large and thick species of Cyrena.

The tertiary rocks are : 1st, a dark slaty limestone, containing
many shells, that have been identified by Mr. Sowerby with those of
the London clay. 2nd, a yellow sandy limestone containing shells,
and resembling the calcaire grossier, and 3rd, a soft greenish sand-
stone resembling the sandy beds of our plaslic clay formation.

This London clay and calcaire grossier afford an additional locality
of these strata to those indicated by the specimens described by Mr.
Colebrooke, in vol. i. Part 1 , 2nd series of the Geological Transactions,
— which had already established the existence of this formation in
the N.E. border of Bengal.

Mr. Crawfurd states distinctly, that it is impossible to refer the si-
tuation of the bones, or the origin of the hills containing them, to any
operations of the existing river : these hills are sixty feet above the
level of its highest flood ; the effect of its actual operations, he ob-
serves also, is distinctly visible in the shifting islands of mud and sand

that

44# Geological Soviet!/.

that abound along the whole course of the river within this high
flood level, and in the great alluvial delta that extends from a little
below Prome to Rangoon and the gulf of Martaban.

The recent bones and recent wood which he observed to be stranded
on some of these islands, were not in a state of progress towards
becoming mineralized, but were falling rapidly to decay.

The existence Of so many animal remains analogous to those that
occur in the diluvium of Europe, in a matrix which so nearly re-
sembles that diluvium, and which so decidedly differs from the allu-
vium, and freshwater, and tertiary strata of the adjacent country,
seems to authorize us to refer this matrix to a similar diluvial de-
posit in the valley of the Irawadi* reposing irregularly upon the ter-
tiary and other stratified rocks, that form the basis of that district.

Besides the tertiary strata above enumerated, there are specimens
of grauwacke and transition-limestone from several distant points in
the valley of the Irawadi between Prome and Ava, which render it
probable that the fundamental rocks of this valley belong to the trans-
ition series.

On the north of Ava there are chains of primitive mountains
abounding with statuary marble, associated, as usual, with horn-
blende and mica slate.

We may therefore consider it as now established, on the authority
of Mr. Crawfurd's notes and specimens, that the Burmese country
not only contains the remains of fossil animals above enumerated,
but also affords examples of the following geological formations,
which can be identified with those of Europe j namely —

1, Alluvium.

2. Diluvium.

&. Freshwater Marl.

4* London Clay and Calcaire grossier.

5. Plastic Clay, with its sands and gravel.

6. Transition limestone and grauwacke.
7- Primitive marble and mica slate.

On the same evening, after the ordinary business of the Society
had been transacted, a special general meeting was held, when the
President having stated, that the Lords Commissioners of his Ma-
jesty's Treasury had been pleased to transfer to this Society some of
the apartments in Somerset House, formerly used as the Lottery
Office, and lately in tl>e possession of the Royal Society j and that a
sum not less than 1 000/. would be required for preparing the said
apartments for the reception of the Society, and the removal of their
Library and Collections : —

It was resolved unanimously,

I. On the motion of Davies Gilbert, Esq. M.P., Pres. R.S., se-
conded by Henry Warburton, Esq., M.P.,— That the thanks of this
Society be given to the Right Honourable the Lords Commissioners
of his Majesty's Treasury, for the grant which they have been pleased
to make to this Society, of apartments in Somerset House.

II. On the motion of the Rev. Dr. Buckland, Professor of Geology
at Oxford, seconded by the Rev. A. Sedgwick, Woodwardian Pro-
fessor

Geological Society. 449

fessor at Cambridge, — That the thanks of this Society be given to
Davies Gilbert, Esq. the President, and to the Council of the Royal
Society, for their aid and cooperation in obtaining from the Lords of
his Majesty's Treasury a grant of the apartments in Somerset House.

III. On the motion of Robert Ferguson, Esq., seconded by Leo-
nard Horner, Esq., — That a Subscription be immediately entered
upon, to defray the expense of the necessary repairs in the apartments
recently granted to the Society in Somerset House, and of the re-
moval thereto.

May 2. — At a special general meeting holden this day at one
o'clock, for the purpose of electing a Member of the Council in the
room of Ashhurst Majendie, Esq. ; and also for electing a Secretary
in the room of R. I. Murchison, Esq., and a Foreign Secretary in the
room of Henry Heuland, Esq., who had retired from their re-
spective offices ;

It was resolved unanimously,

I. That the thanks of this Society be given to Ashhurst Majendie,
Esq., retiring from the Council.

II. That the thanks of this Society be given to Henry Heuland,
Esq., for his long services in the office of Foreign Secretary, and for
the high regard which he has always manifested for the welfare of the
Society.

III. That the thanks of this Society be presented to R. I. Mur-
chison, Esq. on his retiring from the office of Secretary.

A ballot having been held for electing a Member of Council in the
room of Ashhurst Majendie, Esq., the scrutineers reported that Dr.
Henry Burton was duly elected.

A ballot having been held for electing a Secretary in the room of
R. I. Murchison, Esq., and a Foreign Secretary in the room of
Henry Heuland, Esq., the scrutineers reported that Dr. Burton was
elected Secretary ; and that R. I. Murchison, Esq., was elected Fo-
reign Secretary.

At the Ordinary Meeting holden on the same evening, John Clau-
dius Loudon, Esq., of Porchester Terrace, Bays water ; and Thomas
Copeland, Esq., of Golden Square, were elected Fellows of this So-
ciety.

An extract of a letter was read from Lieutenant William Glennie,
R.N., dated Mexico, May 6th, 1827, intitled "The Ascent of Popo-
catapetl."

Many contradictory reports having long existed respecting the
volcanic nature of this mountain, the author felt desirous of ascer-
taining its actual condition in person.

The ascent commenced during the month of April 1827, from the
village of Ameca, situated in the province of Puebla, and near the
N.W. foot of the volcano, at an elevation of 8216 feet above the
level of the sea, and distant 1 4 leagues from Mexico.

The author describes the sides of the mountain as thickly wooded
with forests of pines, extending to the height of near 12,693
feet, beyond which altitude vegetation ceased entirely. The ground
consisted of loose black sand of considerable depth, on which nume-

New Seizes. Vol. 3. No. 1 8. June 1 828. 3 M rous

450 Geological Society.

rous fragments of basalt and pumice-stone were dispersed. At a
greater elevation, several projecting ridges, composed of loose frag-
ments of basalt, arranged one above another, and overhanging preci-
pices 600 or 700 feet deep, presented formidable impediments to the
author's progress j and, in one direction only, a ravine was observed
to pass through these ridges, having its surface covered with loose
black sand, down which fragments of rocks ejected from the crater
continually descended.

After twelve hours of incessant fatigue the author gained the highest
point of the mountain on the western side of the crater, 1 7,884 feet
above the sea ; at which station the mercury in the barometer sub-
sided to 15*63 inches, and the temperature indicated by the attached
and detached thermometers, was respectively 39° and 33° Fahr. at
5 o'clock P.M., when exposed to the direct rays of the sun. The
plain of Mexico was enveloped in a thick haze, and the only distant
objects visible at that time, were the volcanoes of Orizaba and Iztac-
cihuatl. The crater of Popocatapetl appeared to extend one mile in
diameter, and its edges of unequal thickness descended towards the
east. The interior walls consisted of masses of rock arranged per-
pendicularly, and marked by numerous vertical channels, in many
places filled with black sand. Four horizontal circles of rock diffe-
rently coloured were also noticed within the crater- and from the
edges of the latter, as well as from its perpendicular walls, several
small columns of vapour arose smelling strongly of sulphur. The
noise was incessant, resembling that heard at a short distance from
the sea shore during a storm ; and at intervals of two or three mi-
nutes the sound increased, followed by an eruption of stones of va-
rious dimensions ; the smaller were projected into the ravine before
mentioned, the larger fell again within the crater.

The sensations experienced by the author were analogous to those
usually felt by travellers at considerable elevations -, viz. weariness,
difficult respiration, and headache, the latter inconvenience having
been first perceived at a height of 16,895 feet. Tobacco smoke and
spirituous liquors were also found to produce an unusually rapid eU
feet upon the sensorium.

At the same meeting a letter was read from J. B. Pentland, Esq.,
addressed to W. H. Fitton, M.D. P.G.S., respecting the fossil re-
mains of some animals from the N.E. border of Bengal.

The author has discovered among the mutilated fragments of bones*
obtained from the tertiary deposits on the Bramahpootra River in the
small state of Cooch-Behar, — presented to the Society some years ago,
by David Scott/ Esq., and referred to in a former volume of the
Transactions *, — the remains of four distinct species of mammalia,
making an interesting addition to the list already published by Mr.
Colebrooke, viz. —

1. A species of the genus Anthracotherium of Cuvier, which the
author proposes to distinguish by the name of A. Silistrense, — a spe-
cific denomination derived from one of the many names by which the-

* Geol. Trans. 2nd Series, vol. i. p. 135.

great

Astronomical Society.

451

great Bramahpootra river appears to have been designated by ancient
geographers.

2. A small species of the order Ruminantia allied to the genus
Moschus.

3. A small species of herbivorous animal referable to the Pachy-
dermata, but more diminutive than any of the fossil or living species
of that family at present known.

4. A carnivorous animal of the genus Viverra.

ASTRONOMICAL SOCIETY.

March 14. — The first paper read this evening was the following:
Ephemeris of the place of Encke's Comet, during the time of its
reappearance at the end of the present year. Drawn up at the re-
quest of the Council of the Society. By F. Baily, Esq.

1828.

JR.

Dec.

1828.

JR.

Dec. *

h m s

O '

h m s

O '

Aug. 23

1 47 24

+ 22 43

Nov. 15

21 58 4

+ 18 25

27

1 47 8

23 20

17

21 49 36

17 20

31

1 46 12

23 57

19

21 41 20

16 13

Sept. 4

1 44 40

24 34

21

21 33 16

15 5

8

1 42 16

25 11

23

21 25 20

13 57

12

1 39 0

25 48

25

21 17 36

12 48

16

1 35 44

26 24

27

21 9 56

11 38

20

1 29 20

26 58

29

21 2 20

10 27

24

I 22 36

27 30

Dec. 1

20 54 44

9 14

28

1 14 28

27 59

3

20 47 4

8 1

30

1 9 48

28 12

5

20 39 20

6 45

Oct. 2

I 4 48

28 23

7

20 31 20

5 27

4

0 59 16

28 32

9

20 23 12

4 7

6

0 53 24

28 40

11

20 14 40

2 42

8

0 47 4

28 45

13

20 5 48

+ 1 14

10

0 40 16

28 47

15

19 56 28

- 0 20

12*

0 33 4

28 47

17

19 46 40

1 58:

14

0 25 24

28 43

19

19 36 20

3 42

16

0 17 24

28 36

21

19 25 32

5 32

18

0 9 0

28 25

23

19 14 20

7 28

20

0 0 16

28 9

25

19 2 48

9 28

22

23 51 12

27 50

27

18 51 16

11 31

24

23 41 52

27 25

29

18 40 0

13 35

26

23 32 24

26 56

31

18 29 28

15 38

28

23 22 44

26 23

1829.

30

23 13 0

25 44

Jan. 10

18 4 24

24 14

Nov. 1

23 3 12

25 1

13

18 10 16

25 50

3

22 53 28

24 14

16

18 20 12

26 57

5

22 43 48

23 23

19

18 31 4

27 43

7

22 34 16

22 29

21

18 39 20

28 4

9

22 24 52

21 32

26

19 . 0 40

28 24 '

11

22 15 .44

.20 31

31

19 21 4

28 19

13

22 6 48

+ 19 29

Feb. 9

19 53 52

-27 34

3M2

The

VB2

Astronomical Society.

The first part of the above ephemeris (to the end of the year 1 828)
is taken from Mr. Encke's own computations for Paris time 0d.3, as in-
serted in Professor Schumacher's Astronomische Nachrichten, No. 123.
That part of it which belongs to the ensuing year 1829, is taken from
a letter addressed to the President of this Society by Dr. Olbers, and
is computed for the time of midnight at Paris. The positions are
computed for every third or fourth day only, at the beginning and end
of the ephemeris, and, for every second day towards the middle : this
being quite sufficient to enable the observer to find the place of the
comet in the heavens. The original computations are extended only
to minutes of space ; but the right ascensions are here converted into
the nearest second of time, for the convenience of the observer.

[It being desirable that as many observations should be made of this
comet as possible, particularly in the southern hemisphere, where it
will probably be seen after its return from the sun, an extra number of
copies of the above ephemeris have been struck off for distribution, not
only amongst the Members of the Society, but also for circulation in
various parts of the world where the comet is likely to be seen. And
Capt. Foster has kindly undertaken to distribute them as much as
possible in those parts of the southern hemisphere at which he may
touch during the scientific voyage in which he is about to embark.]

There was next read a paper, " On finding the rates of time-
keepers s'' by E. Riddle, Esq. In this communication the author ob-
serves, that there are many persons fond of astronomy who are not
possessed of a transit instrument, or who have not a convenient situ-
ation in which to place it : and many others, such as nautical men in
particular, who have not the means of using one, who are desirous on
many accounts, of knowing the rates of their chronometers, indepen-
dent of the absolute time which they indicate. The method of equal
altitudes on each side of the meridian is the course usually pursued on
such occasions : but Mr. Riddle proposes another mode, often much
more convenient in practice and equally correct in its results ; viz. by
taking equal altitudes of a fixed star on the same side of the meridian,
on successive nights. It is well known that a star will, at the same
sidereal hour, arrive at the same altitude, for several succeeding nights :
the only difference which occurs, arising from the small change in the
aberration, and also from the variation in the refraction. The former
is insensible, if the interval between the observations be not too long -}
and for the latter, appropriate tables are given. The best time for
the observation of such stars is when they are due east or due
west ; and any known star may be chosen for the purpose. All
we have to do therefore, is to note the difference of the two consecu-
tive times at which the star attains the same altitude (whatever it be)
on the same side of the meridian ; and if that difference be less than
3m 55%91, the chronometer (presuming that it is regulated to mean
solar time) will have gained ; and if more, it will have lost so much in a
sidereal day. And, if the observations are made at an interval of n
days, the nth part of the difference between the times of observation,
compared with 3m 55s,91, will in like manner give the mean rate for
that interval j and if this quantity be multiplied by 1,0027, it will give

the

Astronomical Society. 453

the rate for a mean solar day. The author concludes his paper with
several practical examples of the method j and also with a formula
for reducing a series of observations made on any one night, to the
same altitude as shown by a series made on any other night : whereby
the whole become strictly comparable.

Lastly, there was read the following communication from the Rev.
Thomas John Hussey, to Francis Baity, Esq.

" In forming a correct catalogue of the stars situated between 15° N.
and 15° S. declination, and extending from 13h 56m to 15h 4m R.A.
from the catalogues of Piazzi and Bradley, and the observations of
Lalande and Bessel, Mr. Dawson and myself have been much struck
with the difference between the places of particular stars, as laid down
by Piazzi and Bradley, and the places assigned by reducing the ob-
servations of M. Bessel. The results obtained from the Histoire
Celeste come as nearly to the standard catalogue as can be expected,
considering the nature of the instrument employed for determining
the zenith distances, and thence the declination in which principally
the differences exist : some few of these between observations of the
same star are rather unaccountable, others may be attributed to
errors of the press ; they are as follow. — Histoire Celeste,

Page 154

JR.

h m s
14 42 44-5

O / II

ZD. 57 2 12

read 34'

— 155

—

14 13 43

— 50 2 36

— 12'

— 155

—

"14 59 385

— 50 30 16

— 13h

— 155

—

14 32 52-4

— 59 5 42

— 49°

— 156

—

14 37 47

— 50 45 34

— 38 47 6

-r- 58°

- 167

15 2 36

— 27'

— 289

—

14 44 33-5

— 61 10 8

— 32*?

— 291

—

14 52 7'3

— 46 59 0

— 58'

— 340

—

14 45 56-5

— 54 20 49

- 50*

- 471

—

14 46 18

— 39 5 22

— 8'

Between the places shown by the observations of Lalande and those
of M. Bessel, even where there are more than one observation by
each of these astronomers, there are differences more or less consi-
derable in almost every instance ; occasionally, however, there is a sur-
prising coincidence. On this subject we may hereafter trouble you
with some remarks, my present object being to point out the differ-
ences between the standard catalogue of M. Piazzi and a catalogue
reduced to 1800 from the observations of M. Bessel, of the only stars
comprised within the above limits, which have been observed more
than once by M. Bessel, so as that the place of the star may be con-
sidered as pretty nearly ascertained by this indefatigable astronomer
alone. Their number amounts to 31, and the results are exhibited
in the following table. The differences are expressed in space.

454

Astronomical Society.

+ 0-9872 annual proper mo-
tion?

This star is double, and the
observations are of the one
which is of Mag. 6.

Bessel's obs. quite close.
Bessel's obs. quite close.

i E

CO CO Tf CO COCO CO "* ^ TF rp

O*Tt<O*'^O*O*^c0G*O*O*O*TfC003O*^O}O*Tt<O*O*O4COO*"^Tt<-t<C0-*',tf
O*0^G*GtO*Gl0*©*O*©*©*O*0*©*G*©<O*G*O*G<G*O*O}O*©>©*O*G*O<O*Gl

00000000000000000000000000*00X00000000000000 00 00000000000000

•sqo

G*G*0*COG}0*COG*G^O*COO*COO*COCOCOG*0*0>0*0*GtG^O*G*G}G*0*0*CO

»■:

jn cposi^oo©osgs^©ip^i^^©©>px^>oo*o*osost^.©cs©iaTt<ao

c^h cb^O}^d*^©d*^ao^^'^cb^^cboo^t>»6ooG^©cb^©^^o*

l + l + l l + l 1 1 I+ + +I | + l 1 ++ 1 ++ 1 ++++++

c
o
•a

1
c

%
Q

1

■

Tfii-<as^5iO©©«OQOCO<-Hl>.04>.05t^COi— iW<B©«QOXr-iN»CO:rHK5rHD:

so* •«^^i^i^oj©^i^-^^i^cpi^©»posco>p©0'i'^i-Ht>«^Oi'i!t<o^coco
cbdsw^,^G*G^os^©©cb^^G*^^©©©©c^6*6^^©»bd^cb^&

^, $* r_, hh^M^K) CO»OCOr^t iOia»-Or-iiOCO*OGlCO "f 0* CO

„r>» © ©* © »o >— •i>»i>»©c©©*''f©^ci©;DO<©co©©^kOQ}coiacoc©©*co

>«< CO ^h "* O* iO *Q »0 *0 Gl .-< ^ T}*iOC<IiOCOrirti^rii-i
o^h MrtrHFHiC«00>C(^rHi-iC00105050S'ONXCO't^U50)'^QON©'*o:

+7+7++ i + i7-+ n +++ i ++ i i i i i +7 i i i 77

•2
?2

©©©©©©©©©©©©©©©©©©©©©©©©»o©©©©©©

©o^w©^©©©c^©©©<^^^©i>.»p©t>.io»p©<©TjHoaoi>.c^>o

~4< ©6^obds^6b©i^©6sob6s©©os©^^©cb*^©dsG^cb^tbw©as

— i G* Gt i« i-i G< CO M >0 iQ (J) io CO m ifl *0 ^ O* "tf G* O* CO iO CO O* G*

.Jx.© G* OS *C hNNO ©G*CO©—.OS©W5©*—iCO©©Tf»OCOCO>OQ*«©©*eO
"*C0i-t>O^tl<M>OlO "S X50) <- 1 -tf< ■* iO CO »0 CO rn ■* t)< m fh

QF_« i-«r-H©i-HiOXX^O*.-HF-t©OS©CSOS^txaOCO'*'«t<iOO*-'t<aCt>»©-«tiCO

+7+7++ i + i ++ 1 i +++ 1 ++ 1 i i i i +T f i i 77

Diff.

©©©©OSr- i'«tH->»QOCO©O^OS©OSCO».Or-iTt<^HQOQOCO»OCO»0»OCO',*CO»0

=^co^^o*^-*^©©©cbd^©G*^d<^G<^^t^d<cb©6<<^Qo*>.cb

1 ++++ 1 ++++++++ 1 ++++ 1 +++ 1 + 1 +++++

J

s
I

1

<

J,

"So

3

"3
1

©OSXtx^kO^©rHCO*X.©»OlO©©OSOS*>.-<t«tOOSGtOS©r--l<<*Tt<CSO*0<

Q} Tt< CO 0* CO O O »>0 *0 Tt" CO >O*tf3r-iC0C0Tti©*COQ*r-iCO -h irj r)<

s© t^cs © .-i o* co •<*< >o ^-< o* co ■* -^ *>»g* co ao © j>.qo © w -* co © o* co oo

<= ifS »0 *0 ^^r-ti-(1-i^&10^0>C^O)C^COCO-^'<tiiOiOi0^5

^co •*

M

t>.^Ht>.©©'*©t^©©©t>.©©t>.'*©©t>.(N.©t>.TjHTt<©CO©©©Tt*|>.

aO^txO* r-i ©00 QO ^ F-H^iO «* 00 txtx© O^OS^tx 00 *x OS © OS >-0 00 — < CO 0* »0 tx ©

"■ >o~© cs"»o ©"^^""co tx©"co ©"* Vof © x -^^©wco"'* os^oo'' e>Gio$cc<z>G*

0*C0C0O*C0*O'O"3lft "^ CO Gl»O,-H©}G0'<tiO}GtG*'-<C0 .-i io "<*<

,. © tx. OS © ** ' Ot CO Tt< io — to^eo-*^t>»©^'co»o?oi>.QO©»>.— i CO © O* CO X
B i- >0 »0 *-< — ' — • ^h i-h r-* Gl 0) r>* O* G* O* CO CO Tf «* io in io vrj

-2: s

!

OSQO 00 X OS X X »0

xxxxx($Dtxxt^,tx.©©x©t>.i>.t^xxxxt^,c$r) OS t^OC.^,^, 00 OS 00

6

*-HO}CO"f*0©t>»XOS©~<0>CO'<f>«>©*>.XOS©~HO*eO''*'>0©WXOS©.-i
_ p* ^ _ _ -h m ^ p-i -. G* G* 0* 0* 0* G* Ot 01 0* 0* CO CO

Astronomical Society. ' 4>55

1

" In many of the above cases it is probable that the difference be-
tween Piazzi's catalogue for 1800, and one reduced to that epoch from
Bessel's observations, may arise from error of observation : in others
the almost identity of the observations seems to prove at once the skill
of the observer, and a proper motion in the star j while again there
is one (No. 2.) which possibly may be regarded as conclusive on the
latter point. I would also suggest two instances of what appear
errors of the press, or perhaps in reading off the instrument, in M.
Bessel's zones.

Z. 154. JR. 14h 33m 33-7." Dec. 12° 4P 22"-4 + Unless 26' be
read for 41' this star of the sixth magnitude, 32 Bootis, will
differ from Piazzi's catalogue +14' 56"-88.

Z. 162. JR. 14h37m 10s-3.Dec. 9"° 55' 36"'8 + Unless 8° be read
for 9° this star of the 7*8 magnitude will differ from Piazzi
1° 0' 0"-39."

April 11. — A paper was read " On the construction of large Achro-
matic Telescopes." By A. Rogers, Esq. — In this paper the author de-
scribes a new construction of an Achromatic Telescope, the object of
which is to render a small disc of flint glass available to perform the office
of compensation to a much larger one of crown, and thus to render
possible the construction of telescopes of much larger aperture than
are now common, without hindrance from the difficulty at present ex-
perienced in procuring large discs of flint glass. It is well known that
in the ordinary construction of an achromatic object-glass, in which
a single crown lens is compensated by a single one of flint, the two
lenses admit of being separated only by an interval too small to afford
any material advantage in diminishing the diameter of the flint lens,
by placing it in a narrower part of the cone of rays, the actual amount
of their difference in point of dispersive power being such as to
render the correction of the chromatic aberration impossible, when
their mutual distance exceeds a certain limit.

This inconvenience Mr. Rogers proposes to obviate, and obtain
the advantage in question, by employing as a correcting lens, not a
single lens of flint, but a compound one consisting of a convex crown,
and concave flint, whose foci are such as to cause their combination
to act as a plane glass on the mean refrangible rays. Then it is
evident that by reason of the greater dispersive power of flint than
of crown glass, this will act as a concave on the violet, and as a con-
vex on the red rays ; and that, the more powerfully, according as the
lenses separately have greater powers or curvatures. If then, such a
compound lens be interposed between the object-glass of a telescope,
supposed to be a single lens of plate or crown glass, and its focus, it
will cause no alteration in the focus for mean rays, while it will
lengthen the focus for violet, and shorten it for red rays. Now this
is precisely what is wanted to produce an achromatic union of all the
rays in the focus ; and, as nothing in this construction limits the
powers of the individuals composing the correcting lenses, they may
therefore be applied any where, that convenience may dictate j and
thus, theoretically speaking, a disc of flint glass, however small, may
be made to correct the colour of one of crown, however large.

But

456 'Royal Institution of Great Britain.

But this construction possesses other and very remarkable ad-
vantages. For, first, when the correcting lens is approximately con-
structed on a calculation founded on its intended aperture, and on
the refractive and dispersive indices of its materials, the final and
complete destruction of colour may be effected not by altering the
lenses by grinding them anew, but by sliding the combination nearer
to, or further from, the object-glass, as occasion may require, along
the tube of the telescope by a screw motion, till the condition of
achromaticity is satisfied in the best manner possible. And, secondlv,
the spherical aberration may in like manner be finally corrected by
slightly separating the lenses of the correcting glass, whose surfaces
should for this purpose be figured to curvatures previously determined
by calculation, to admit of this mode of correction — a condition which
the author finds to be always possible.

Mr. Rogers explains his construction by reference to a diagram,
and states the rule for the determination of the foci of the lenses of
the correcting glass in a formula which may be thus interpreted.
" The focal length of either lens of the correcting lens is to that of
the object-glass, in a ratio compounded of the ratio of the square of
the aperture of the correcting lens to that of the object-glass, and of
the ratio of the difference of the dispersive indices of crown and flint
glass, to the dispersive index of crown :" — for example, to correct
the colour of a lens of crown or plate glass of nine inches aperture,
and fourteen feet focal length (the dimensions of the celebrated tele-
scope of Fraunhofer at Dorpat) by a disc of flint glass three inches in
diameter, the focus of either lens of the correcting lens will require
to be about nine inches. To correct it by a four inch disc will require
a focus of about sixteen inches for each.

The author then remarks, that it is not indispensable to make the
correcting glass act as a plane lens. It is sufficient if it be so ad-
justed as to have a shorter focus for red rays than for violet. If, pre-
serving this condition, it be made to act as a concave lens, the ad-
vantage procured by Mr. Barlow's construction of reducing the
length of the telescope with the same focal power, is secured : and
he considers, moreover, that by a proper adaptation of the distances,
foci, &c. of the lenses, we might hope to combine with all these ad-
vantages, that of the destruction of the secondary spectrum, and thus
obtain a perfect telescope.

There was also read a portion of a paper " On the Occupation of
$ Piscium observed in Blackman-street, in the month of February
1821. References to recorded observations of occultations in which
peculiarities have been apparently seen, either at the moon's limb, or
upon her disc ; together with an enquiry how far certain hypotheses
seem adequate to account for the phenomena. By James South, Esq."

PROCEEDINGS AT THE FRIDAY-EVENING MEETINGS OF THE
ROYAL INSTITUTION OF GREAT BRITAIN.

April 25. — The lecture-room subject was practical sculpture, and
was delivered by Mr. Sievier. It consisted of an account of the
various processes adopted by the sculptor from the commencement

of

Royal Institution of Great Britain. 457

of modelling in clay, to the last touch required to complete his sub-
ject in marble ; and the various operations of modelling, casting,
chiseling, and the use and theory of the different instruments used,
were explained and illustrated by examples. For these purposes
clay-models, .plastQr-casts, and blocks of marble in different pro-
gressive states, were placed upon the table, upon which the work-
men carried on their several operations.

May 9. — Mr. Faraday gave a lecture on the production of musi-
cal sound, with an explication of the principles of action in some
new musical instruments. He stated his information to be derived
altogether from Mr.Wheatstone, to whom, of course, the new facts
brought forward belonged. The nature of the pitch of sounds was
first explained, and stated to be the quality by wnich musical sounds
are distinguished from mere noise. The credit of the first philoso-
phical account of this quality was attributed to Gallileo, who proved
that it depended altogether upon the number of impulses in a given
time. An experiment by that philosopher, apparently forgotten in
modern times, but described in his Dialogues, was repeated : — it con-
sisted in drawing the point of a blade over a metal plate so as to
produce sound, and counting or comparing the dots which are al-
ways produced upon the plates, and which are the records of the
number of vibrations necessary to the pitch of sound produced.

Hook's experiment, in which the teeth of a revolving wheel were
made to beat against a card, was repeated, and the pitch of sound
shown to correspond with the number of impulses in a given time. An
extension of this experiment by Mr.Wheatstone was also described,
in which the harmonics of a stretched string were produced by
holding it against the wheel ; the string producing sound whenever
the velocity of the wheel was such that the impulses of the teeth
corresponded in frequency with the vibrations of the string or of
any of its aliquot parts.

Robison's mode of producing musical sounds by air passing
through a stop-cock rapidly revolving, was then explained and il-
lustrated ; afterwards, Cagniard de la Tour's syren was set in ac-
tion j and from these were drawn the explanation of the principles
of two new musical instruments from Germany, the Munt-harmonica
and the Acol-harmonica.

May 2 and 16. — On these evenings Mr. Knowles, of the Navy
Board, gave an account of the rise, progress, and present state
of naval architecture. To make his historical observations more
clear, he first stated the elements concerned in the structure of
ships, as stability, floatation, masts and yard, &c.&c, and then traced
the state of the navy from the reign of Alfred to the present day ;
pointing out the times and progression of its increase ; the period
when any improvement had taken place ; and more minutely en-
tering into the important alterations introduced of late years by Sir
W. Rich, Sir Robert Seppings, and others. All the observations
relating to construction were fully illustrated by numerous models
from the magnificent collection belonging to the Navy Board.

New Series. Vol. 3. No. 1 8. June 1 828. 3 N LX VIII. In-

[ +58 ]
LX.VIII. Intelligence and Miscellaneous Articles.

ORIGIN OF TRAP ROCKS.

[The following is an abstract of a Paper on this subject by Mr. S.
Solly, read before the Royal Society on the 6th of March last.]

WHILE Mr. Solly was examining the hills of porphyry near
Christiania, he discovered a low, detached, quadrangular
rock of trap of the species called diorite* which exhibited in a
manner that had never before been noticed, except in the experi-
ments of Gregory Watt, the gradual development of crystallization
commencing with globules of green pyroxene and white felspar,
sometimes enveloping each other, and varying in size from that of
a small pea to extreme minuteness ; they were thickly strewed on a
perpendicular side of the rock near the ground, and at a distance
had the appearance of cryptogamia.

On a close examination he found some of the globules stretched
out, and in other parts close to the former; the felspar had shot into
parallel lines, which here and there had united to form rhombs. He
likewise found the pyroxene standing out upon the surface in re-
gular crystals, exhibiting a curious variety of modification 5 some of
them crossing each other like the double crystals of harmotome.

To his communication of this fact, Mr. Solly has prefixed some
remarks on the probable history of rocks of trap, derived from a
comparison of the different situations in which he has met with
them. From observing their partial resemblance to lava, and that
they are most frequently met with in coal-fields, Mr. Solly infers that
they owe their origin to internal combustion ; and as little doubt
seems to remain that our beds of coal were formerly bogs, which
have been compressed and protected by a covering of clay and sand,
he conjectured that other masses of bog and combustible strata lying
more exposed have been converted into trap. The position of the
Swedish rocks, (from whose quadrangular form this name is derived,)
strengthened this conjecture, which was confirmed by his meeting
with a stone perfectly similar in all its characters, recently formed
by the spontaneous combustion of substances which perfectly cor-
respond with some of the strata* found beneath the Swedish rocks.

Mr. Solly introduced the subject with observations on the assist-
ance geology ought to derive from the discoveries in experimental
science. Various observations on currents are interspersed through
this paper, to explain the difference of stratification in different si-
tuations. From the insulated character of the formations in coun-
tries intersected by granite, Mr. S. infers that the latter cannot be
a rock of posterior formation as the Scotch Plutonists imagine.

An explanation is given of some instances of high temperature
in the lower part of deep mines, from which erroneous conclusions
have been drawn. Mr. S. touches on the subject of electrical as

* They are sufficiently impregnated with bitumen and sulphur to be used
as fuel or roasted for alum. See Thomson's Travels.

well

Intelligence and Miscella?ieous Articles, 459

well as chemical action beneath the surface of the earth, and is of
opinion that the gaseous products of beds of coal have assisted in
converting their covering of loose sand and clay into coal sandstone
and clay ironstone.

As the subject of internal changes is of practical importance to
the miner, Mr. S. recommends its investigation. The garnets and
zeolites found in shale by Mr. Henslow, are decided instances of
internal changes, and coincide with some of the facts previously
noticed by Mr. S.

His distinction between lava and trap, which we more generally
call Basalt, and in Scotland is chiefly known by the name of Whin,
is confirmed by the authority of Sir James Hall : " Calcareous spar
frequently occurs in whinstone, either in veins, or in detached no-
dules, but is never found in lava, and could not exist in a volcanic
stream. It is generally supposed that some lavas of iEtna contain
calcareous spar and zeolites; but this I conceive to be a mistake.
It is true I have seen that many rocks of iEtna contain these sub-
stances in abundance, but in my opinion these rocks are not lavas,
but have flowed subterraneously like our whins, and are the same
with them in every respect. A particular district of iEtna, com-
prehending the Cyclopian Isles, and the country round La Trizza,
and the Castle of Jaci, is decidedly of this description; and vestiges
of this kind occur in other parts of the mountain. In one place
fossil coal has been found, and in another we saw marine shells. In
the neighbourhood of Bronte, we observed a high ridge formed of
strata of sandstone and limestone, partly overflowed and concealed
by recent lava, but so placed as to render it evident that its con-
struction formed no inconsiderable part of the mountain."

Mr. S. has heard disciples of Werner mention, that from its con-
tiguity to basalt, he supposed iEtna was erected on the site of a
coal mine: the additional coincidences in Sir James Hall's descrip-
tion seem to prove that coal is a part of the fuel of iEtna. Breis-
lack, who has spent many years in examining Vesuvius, is of opi-
nion that it is fed by the bituminous strata of the Appenines.

The principal objection to this opinion has been removed by Sir
Humphry Davy, whose genius has been scarcely more conspicuous
in anticipating the discoveries made by the galvanic battery, than
in drawing those inferences from them which have assisted his con-
temporaries in bringing other discoveries to light. Thus our know-
ledge of the properties of iodine is a natural consequence of his
observations on the nature of chlorine: these and every other
agent of combustion ought to be enumerated in discoursing on the
infinite variety of chemical and electro-chemical operations which
may take place in the vast laboratory of Vesuvius. Since with the
assistance of the electrical energies of iron we can make potash
yield up its oxygen, is it not possible that the earths may be reduced
to a metallic state by a similar process in the bowels of the moun-
tain? These considerations show there is no necessity for any
contrivance or reservoir to keep up the supply of elastic oxygen.
By placing at the command of the philosopher powers which are
always close at hand, and are capable of producing tremendous

3 N 2 results,

460

Intelligence and Miscellaneous Articles,

results, — by teaching him to conjure up inflammatory spirits from
the surface of the "vasty deep," and to turn water into fire, — Sir H.
Davy has shown it is not necessary that Pluto should ascend from
the lowest depths of his empire to produce the phenomena of vol-
canos, and much less so to bring about a chemical union between
silex, alumina, lime, and iron, the chief constituents of basalt or
trap. Nee Deus intersit dignus nisi vindice nodus.

ANALYSES OF TOURMALINES.

M. Gmelin has analysed a great many varieties of this mineral • the
method adopted is the following : — The mineral reduced to a fine
powder is mixed with carbonate of barytes, and strongly heated. The
mass is afterwards treated with a sufficient quantity of muriatic acid
to dissolve it entirely, and the solution is evaporated upon a sand
bath to dryness. M. Gmelin ascertained by direct experiment that at
this temperature the quantity of boracic acid volatilized is so minute
that it may be neglected without any sensible error. The silica is ob-
tained in the usual manner, by treating the residuum of evaporation
with water. Carbonate of ammonia is added to the solution, and
after filtration, and evaporation to dryness, the residuum is gradually
heated to low redness. In this manner, no boracic acid can be lost,
because it is combined with ammonia • and thus during calcination at
a red heat, no acid or aqueous vapour is evolved, as in the decompo-
sition of sulphate of ammonia. The residuum after being weighed, is
washed with alcohol mixed with a little muriatic acid j the alcohol
being separated is burnt • the operation is repeated until the alcohol
does not give a green flame. All the boracic which is combined with
the ammonia is thus obtained. The residuum again heated and dried,
and the loss of weight determines the quantity of boracic acid.

Tourmalines are divided by M. Gmelin into three classes : the first
of which contains lithia : — I. Red Tourmaline from Rdsna in Moravia ;
sp.gr. 2*96 to 3*02. II. Red Tourmaline from Perm in Siberia; sp.
gr.3'059. III. Celadon Green Tourmaline from Brazil ; sp. gr. 3*079.

I.

II.

III.

Boracic acid

574
42-13
36-43

6-32

4-18
39-37
44-00

5-02

459

39-16

40-00

5-96

214

Silica

Alumina

Oxidulous oxide of iron

manganese

Lime ...

1-20
2-41
2-04
1-31

97-58

1-29
252
1-58

3*59 with potash.
1-58

Potash

Lithia .

Volatile matter

97-96

97*02

Tourmalines

Intelligence and Miscellaneous Articles,

461

Tourmalines which contain potash or soda, or both together, without
lithia, and without a notable quantity of magnesia. The following
are the varieties : — I.' Black Tourmaline from Bovey in Devonshire,
found with quartz and phosphate of lime ; sp. gr. 3*246. II. Black
Tourmaline from Eibenstock in Saxony; sp. gr. 3' 123. III. Green
Tourmaline from Chesterfield, North America, sp. gr. 3' 102.

I.

II.

III.

Boracic acid

Silica

411
35-20
35-50
17*86

0*43 with magnesia
0*70 with manganese
0-55
209

1-89
33-05
38-23

2386

0-86

3-17*

0-45

3-88
38-80
39-61

7-43

2-88 f

4-95
0-78

98-33

Alumina

Oxidulous oxide of iron
Protoxide of iron

Magnesia

Lime

Soda

Loss in the fire

9644

101-51

Tourmalines which contain a considerable quantity of magnesia. —
Four specimens were analysed : — I. Black Tourmaline from Karing-
bricka, a province of Westmanland in Sweden ; sp. gr. 3044. II.
Black Tourmaline from Rabenstein in Bavaria; sp. gr. 3*113. III.
Black Tourmaline from Greenland ; sp. gr. 3*062. IV. Deep Brown
Tourmaline, from the mica slate of St.-Gothard.

I.

II.

III.

IV.

Boracic acid

Silica .

3-83
37*65
33*46
10*98

9-38

4*02
35-48
34*75

4*68
17*44

3*63

38-79

37*19

5*86

5-81

4*18
37*81
31*61

5-99

7'77

Alumina ••

Magnesia

Oxidulous oxide of iron

Oxide of manganese . .

Potash *)

Soda /

Lime

2*53

0-25
0-03

1*89

f0*48

11*75

trace.

trace.
0*22
313

1-86

1*20

0*98
0*24

Loss in the fire

98-11

100-49

96*48

90*89

M. Gmelin is at a loss to what cause to attribute the deficiency in
the last analysis. He thinks the tourmaline from St.-Gothard should
be again examined; especially as the loss in Bucholz's analysis is
still greater. — Ann. de Chimie etde Phys. Nov. 1827.

* With potash and a trace of magnesia.

f With a trace of magnesia.
A NEW

462 Intelligence and Miscellaneous Articles.

A NEW METHOD OF SEPARATING MANGANESE FROM LIME AND
MAGNESIA. BY PROFESSOR STROMEYER.

We are informed in a letter from Professor Stromeyer, that he has
found the following method successful in procuring the complete se-
paration of manganese from magnesia and lime. To an acid liquid
containing the peroxide of iron together with manganese, lime, and
magnesia, the carbonate of soda is added in the usual manner, so as
to precipitate the first, while the three latter oxides are held in solu-
tion by an excess of carbonic acid j and in order to prevent any man-
ganese from falling, the actual precipitation of the iron is effected by
the bicarbonate instead of the carbonate of soda. After acidulating
the filtered solution and concentrating it by evaporation, a current of
chlorine gas is transmitted through it. On neutralizing the free acid
by the gradual addition of bicarbonate of soda, the manganese sub-
sides in the form of the red oxide, being thus completely separated
from the magnesia and lime. — Brewster s Journal, April 1828.

SINGULAR ACTION OF PHOSPHORIC ACID ON ALBUMEN.

In his essays on the animal fluids Berzelius stated, that a solution
of albumen is not precipitated by phosphoric acid -, whereas Engel-
hart, in his interesting researches on the colouring matter of, the
blood, found that albumen is coagulated even in a dilute solution by
phosphoric acid. As Engelhart was at Stockholm last winter, he and
Berzelius inquired into the cause of difference in their statements,
and discovered that they were both right. A solution of phosphoric
acid, which had been kept some time in the laboratory, did not preci-
pitate a solution of albumen ; but phosphoric acid, recently prepared
either by the action of nitric acid on phosphorus or by direct combus-
tion, caused an abundant precipitate. On further examination, it
was found that phosphoric acid, recently ignited, always throws down
albumen j but that after being kept in solution for a few days, it
loses that property. The coagulating power is restored by heating
the acid to redness, but disappears again after the interval of a day.

The cause of these phenomena is by no means apparent. It does
not depend on a higher degree of oxidation, for the change ensues in
close vessels equally as by exposure to the air. Perhaps, says Ber-
zelius, there may be some peculiar compound of water and the acid,
which is not formed at the moment of solution, and which has not
the property of precipitating albumen. — Annates de Chimieetde Phy-
sique, xxxv. 110.

Remark on the preceding notice, by Dr. Turner. — On comparing
the facts observed by Berzelius and Dr. Engelhart, with the
formation of the pyrophosphate of soda, described by Mr. Clark in
the fourteenth Number of this Journal, it appeared probable that
phosphoric acid heated to redness may be converted into pyrophos-
phoric acid, or undergo that change which enables it to form a white
salt with silver. To put this supposition to the test of experiment,
some fragments of phosphorus were treated in a platinum crucible

by

Intelligence and Miscellaneous Articles. 463

by nitric acid, and the product heated to redness. The solution of
the resulting pure phosphoric acid precipitated a dilute solution of
albumen j but when carefully neutralized by carbonate of soda, and
then mixed with a solution of the nitrate of silver, the common yellow
phosphate subsided. Consequently, it was not in the state of pyro-
phosphoric acid. — Brewster's Journal, April 1 828.

LIST OF EARTHQUAKES WHICH OCCURRED IN 1827.

Jan. 2. — At Mortagne (Orne) and the environs. A violent shock
of short duration, accompanied with an intense noise. Chimneys
and household furniture were thrown down. The, commotion reach-
ed as far as Alengon. The day was cloudy, the, weather thick and
stormy, which is not usual at that time of the year.

Feb. 9. — At seven o'clock in the evening ; in the north-west part
of Wales and the Isle of Anglesea. The shocks continued from forty
seconds to a minute j they were sufficiently violent to overturn se-
veral pieces of furniture. A noise was heard like that of a heavy
laden cart going on the stones.

April 2. — At Bevers, at twenty minutes past one in the morning;
two strong consecutive shocks. The inhabitants of Basse-Engadine
assert that they counted twenty similar shocks during the winter.
May 29. — At Vajaca, in Mexico ; two slight shocks.
June 3. — At Martinique j a slight shock.

June 12. — At Tehenacan, in Mexico, at half-past one o'clock ; a
violent shock, with a frightful noise. Many buildings damaged.

June 16. — At Aquila, in the kingdom of Naples j a shock at five
o'clock in the morning.

June 21. — At Palermo, at eleven o'clock in the morning. Four
strong shocks in the space of seven seconds ; it was an oscillatory
motion from the west to the east.

Aug. 14. — At Palermo, at 2 p.m. Several shocks ; they continued
about eighteen minutes, with very short intervals 5 the motion was
always oscillatory.

Sept. 18.— At Lisbon. A slight shock.

Oct. 10.— At Zurich, and all the shores of the lake. At twelve
minutes before 3 p.m., a strong shock.

Oct. 15. — At Jassy, at eight in the evening. Two violent shocks,
directed from north to south, and accompanied by a subterraneous
noise ; two or three days after, the heat was very great.

Oct 30. — At Corsica, in the cantons of Taravo, Taliano, and Sar-
tene. Two shocks at twenty minutes past 5, a.m.

Nov. 30. — At Pointe-a-Petre, Guadaloupe, at three in the morn-
ing. Violent earthquake. At Mariegalante it was preceded by a
strong and sudden storm. — Ann. de Chimie et de Phys. Nov, 1827.

RED RAIN SUPPOSED TO ARISE FROM BUTTERFLIES.

The following narrative seems curious and important in connection
with the various accounts of red rain. It is extracted from Gassendi's Life
of Peiresc, p. 1 1 0- 1 1 3 . " Through the whole of this year ( 1 C08) no-
thing

464 Intelligence and Miscellaneous Articles.

thing gave M. Peiresc greater pleasure than his observations upon the
bloody rain, said to have fallen about the beginning of July. Large
drops were seen both in Paris itself upon the walls of the cemetery of
the greater church, which is near the walls of the city, upon the walls
of the city, and likewise upon the walls of villas, hamlets, and towns
for some miles round the city. In the first place, M. Peiresc went to
examine the drops themselves, with which the stones were reddened,
and spared no pains to obtain the means of conversing with some
husbandmen beyond Lambesc, who were reported to have been so
astonished at the shower, as to leave their labour and fly for safety
into the neighbouring houses. This story he ascertained to be with-
out foundation. To the explanation offered by the philosophers, who
said that the rain might have come from vapours, which had been
raised out oi red earth, he objected that evaporated fluids do not re-
tain their former hues, as is plainly exemplified in the colourless wa-
ter distilled from red roses. Nor was he better satisfied with the
opinion of the vulgar, countenanced by some of the theologians, who
maintained that the appearance was produced by demons, or witches,
shedding the blood of innocent babes. This he thought was a mere
conjecture, scarcely reconcileable with the goodness and providence
of God. In the meantime an accident happened, which discovered
to him, as he thought, the true cause of the phenomenon. He had
found some months before a chrysalis of a remarkable size and form,
which he enclosed in a box. He thought no more of it, until, hearing
a buzz within the box, he opened it, and perceived that the chrysalis
had been changed into a most beautiful butterfly, which immediately
flew away, leaving at the bottom of the box a red drop of the size of
a shilling. As this happened about the time when the shower was
supposed to have fallen, and when a vast multitude of those insects
was observed fluttering through the air in every direction, he con-
cluded that" the drops in question were some kind of excrementitious
matter emitted by them, when they alighted upon the walls. He
therefore examined the drops again, and remarked, that they were not
upon the upper surfaces of stones and buildings, as they would have
been, if a shower of blood had fallen from the sky, but rather in cavi-
ties and holes, where insects might nestle. Besides this, he took
notice that they were to be seen upon the walls of those houses only,
which were near the fields, and not upon the more elevated parts of
them, but only up to the same moderate height at which the butter-
flies were accustomed to flutter. In this way he explained the story,
told by Gregory of Tours, of a bloody shower seen at Paris in the
time of Childebert, at different places, and upon a house in the vici-
nity of Senlis ; and another said to have fallen in the time of King
Robert, about the end of June, the drops of which could not be washed
out by means of water, when they had fallen upon flesh, garments, or
stones, but might be washed out from wood ; for the lime here stated
was the season for the butterflies ; and he showed that no water could
wash out these red marks from stones. After discussing these and
similar arguments in the presence of much company at the house of
his friend Varius, they determined to inspect the appearance together,

and

Intelligence and Miscellaneous Articles. 4>65

and, as they wandered through the fields, they saw many drops upon
stones and rocks, but only in hollows or upon sloping surfaces, and
not upon those which were presented to the sky." The butterfly
observed by Peiresc was probably the Papilio C. album, or common
butterfly. It has been observed to deposit the same red fluid in En-
gland.

WEATHER IN PARIS.

The following was the state of the weather during the last year in

Paris. Rain 146 days.

Snow 21

Hail or hoar frost. ... 6

Frost 59

Thunder ' 21

Very cloudy 178

Ann. de Chimie et de Phys. Dec. 1827.

ANALYSIS OF ALCOHOL, iETHER, &C. BY MM. DUMAS AND
BOULLAY.

In the Philosophical Magazine and Journal for April, I gave some ac-
count of the paper by the above-named chemists, and proposed to offer
some remarks upon it in the present Number : the Royal Institution
Journal for April contains some observations so much to the point
which I had intended to notice, that I shall content myself with copying
them.— R. P.

*' MM. Dumas and Boullay then consider the formation and nature
of the sulphuric acid, stating the opinions of MM. Vogel and Gay
Lussac, that it is a compound of hyposulphuric acid with a vegetable
matter ; and also that of Mr. Hennel, that it is an acid in which half
the saturating power of the sulphuric acid present is neutralized by
the hydrocarbon in combination. With the latter opinion they also
class that entertained by Mr. Faraday relative to the nature of sul-
phonaphthalic acid. MM. Dumas and Boullay consider the question,
and decide in favour of the former opinion ; after which they say they
have observed facts which are better explained by the latter. We
think it a pity that these philosophers did not refer to Mr. Hennel's
paper in the Philosophical Transactions for 1826, p. 240, where they
would have gained the knowledge of a compound produced by the
action of sulphuric acid and alcohol, of which they seem at present al-
together ignorant, and which would have probably caused serious
alterations in their views, at least with regard to the sulphovinic acid.
We refer to what is known in London, and sold at Apothecaries' Hall,
by the name of oil of wine; not the hydrocarbon referred to by MM.
Dumas and Boullay, but a neutral compound of sulphuric acid with
hydrocarbon, containing, with the same proportion, of sulphuric acid,
twice as much hydrocarbon as the sulphovinic acid. It is of this com-
pound that Mr. Hennel speaks in the following passage, which we
cannot refrain from quoting : • Mr. Vogel, who has particularly de-
scribed some of these salts (sulphovinates), and I believe also M. Gay
Lussac, have supposed that this loss of saturating power arises from
the formation of hyposulphuric acid, and that the hyposulphates and

NewSeiies. Vol. 3. No. 18. June 1828. 3 O sul-

466 New Patents.

sulphovinates only differ in the latter containing some aethereal oil,
which in some way acts the part of water of crystallization. It is
evident that the properties of oil of wine cannot be thus explained ;
and it appears to me more probable that the power of combination
which hydrocarbon is shown to be possessed of in oil of wine is effective
in neutralizing half the acid of the salts formed from it (sulphovinates)
as before described.' "

TEST OF THE PRESENCE OF AMMONIA.

M. Plessin having occasion to ascertain whether the action of a
salifiable base upon a body containing azote was simply that of
evolving ammonia previously existing, or that of forming ammonia by
combination, endeavoured to find a base, which would effect the
former object but not the latter. Potash, lime, magnesia, and many
other bodies, do both 5 but the hydrated oxide of lead answered the
purpose very well. It gives no indication of ammonia when put into
contact with azotated substances, not containing that alkali 5 even
urea is not effected by it j but being put in contact with an ammoniacal
salt, ammonia was instantly evolved, and rendered evident by the
visible fumes which arose upon the approximation of a little acetic
acid. — Annates de Chimie, xxxvi. p. 377.

LIST OF NEW PATENTS.

To Jane B. Lowrey, wife of T. S. Lowrey, of Exeter, for her im-
provements in the manufacture of hats and bonnets. — Dated the 25th
of March 1828. — 6 months allowed to enrol specification.

To E. Cowper, of Clapham-road Place, Lambeth, for improvements
in cutting paper. — 26th of March. — 6 months.

To F. de Fourville, of Piccadilly, for improvements on filtering ap-
paratus.— 26th of March. — 6 months.

To T. Lawes, of the Strand, for an improved thread to be used in
the manufacture of bobbin net lace. — 29th of March. — 6 months.

To H. Marriott, of Fleet-street, and Augustus Siebe, of Princes-
street, Leicester-square, for certain improvements in hydraulic ma-
chines.— 29th of March. — 6 months.

To Peter Taylor, of ttollinwood, Lancaster, for certain improve-
ments in machinery for hackling, dressing or combing flax, hemp,
&c. — 29th of March. — 6 months.

To John Davis, of Leman-street, Goodman's-fields, for an improve-
ment (communicated from abroad) in boiling or evaporating solutions
of sugar and other liquids. — 29th of March. — 6 months.

To C. Harsleben, of New Ormond-street, Esq., for improvements
in machinery to be used in navigation and the propelling of ships. —
3rd of April. — 6 months.

To S. W. Wright, of Webber-street, Lambeth, engineer, for im-
provements in the construction of wheel carriages. — 15th of April. —
6 months.

To J. G. Ulrich,of Cornhill, for his improvements on chronometers.
19th of April.— 6 months.

SCIENTIFIC

Meteorological Observations for April 1828. 467

SCIENTIFIC BOOKS.

Just Published.

On the Methods of determining Terrestrial Longitudes by the
Moon's Right Ascension, as deduced from her Altitudes and Cul-
minations. By John Crisp, Captain in the Madras Army. In quarto,
Price 6s.

It is the intention of the Medico-Botanical Society of London, to
print their Transactions in the shape of an octavo Quarterly Journal,
in conjunction with those of the Academy of Minute Anatomy at
the London Ophthalmic Infirmary. The first Number of this Journal
will appear shortly illustrated with coloured Engravings in quarto.

The Astronomical Doctrine of a Plurality of Worlds irreconcilable
with the Popular Systems of Theology, but in perfect harmony with
the True Christian Religion. By the Rev. S. Noble.

A Series of Treatises on the principal Branches of Manufacturing
Chemistry, by Mr. Astley of Edinburgh, is about to be published.
The manufacture of Common Salt will form the subject of the first,
which will shortly be published separately, comprising full details
of its history, physical, chemical, commercial, and ceconomicalj
with suggestions for the material improvement of the manufacture,
and a full digest of the results of the experiments in the use of salt
by agriculturists, since the repeal of the duty.

METEOROLOGICAL OBSERVATIONS FOR APRIL 1828.

Gosport. — Numerical Results for the Month.

Barom. Max. 30-28 April 30. WindNE.— Min. 29-10 April 8. Wind S.E.
Range of the index 1-18.

Mean barometrical pressure for the month 29-736

Spaces described by the rising and falling of the mercury. 5-550

Greatest variation in 24 hours 0-380. — Number of changes 1 8.
Therm. Max. 69° April 29. Wind S.E.— Min. 35° April 3. Wind N.
1 Range 34°.— Mean temp.of exter. air 51°-33. For 30 days with 0 in V 48*22
Max. var. in 24 hours 20°-00— Mean temp, of spring water at 8 A.M. 50°-89

De Luc's Whalebone Hygrometer.

. Greatest humidity of the air in the evening of the 24th 88°

. Greatest dryness of the air in the afternoon of the 28th 42

. Range of the index 46

Mean at 2 P.M. 60°-0 —Mean at 8 A.M. 65°-0— Mean at 8 P.M. 74-4

, of three observations each day at 8, 2, and 8 o'clock 66-5

. Evaporation for the month 2-20 inches.
. Rain. near ground 2-725 inch.

Summary of the Weather.
A clear sky, 2; fine, with various modifications of clouds, W\$ an over-
cast sky without rain, 9£ ; rain, 7- — Total 30 days.
Clouds.
- Cirrus. Cirrocumulus. Cirrostratus. Stratus. Cumulus. Ciumilostr. Nimbus.
20 12 26 0 15 25

3 0 2 Scale

468 Meteorological Observations for April 18l2S.

Scale of the prevailing Winds.
N. N.E. E. S.E. S. S.W. W. N.W. Days.
1 5 0 5* li 10 3* 3£ 30

General Observations. — The first five days of this month were dry and
cold; afterwards it rained more or less every day till the 26th : but the last
four days were dry and warm, in which more progress appeared to have
been made in the blooming and growth of fruit and vegetation, than during
the preceding fortnight.

The North-east and North-west winds on several days were blighty, the
effects of which maykbe traced in the formation of the young wall-fruit, &c.
The 4th and 22nd were very cold days, whose maximum temperature in
the shade was only 46 and 47 degrees, which is three or four degrees
colder than some of the nights. The first swallow appeared here in the
morning of the 21st, and the nightingale was first heard on the 11th
instant.

At noon of the 27th three winds prevailed in different directions : the
first next the earth, as pointed out by a vane, was from South-east ; the next,
which was ascertained by keeping the eye in a line with a fixed object
whose bearing on the horizon was known, and observing the motion of the
passing cumulus clouds directly from the same point, was from South-west
by South ; and the upper one, ascertained in the same way by observing the
direction of plumose cirri, was from North North-west.

The planet Venus, which has now the appearance of a half-moon, was
conspicuous with the naked eye at the same time ; and its apparent distance
from the Sun's centre, as measured by a sextant, was 44° 8', which is only
a few minutes of a degree less than it will be at its greatest elongation on
the 19th of next May.

The mean temperature of the external air this month is 1^ degree higher
than the mean of April for the last twelve years.

The atmospheric and meteoric phenomena that have come within our
observations this month, are four solar and two lunar halos, one rainbow,
one meteor, and eight gales of wind, or days on which they have prevailed ;
namely, one from the South-east, two from the South, four from the South-
west, and one from the North-west.

REMARKS.

London.— April 1, 2. Fine. 3, 4. Clear and cold. 5. Cloudy, with rain
at night. 6. Cloudy. 7. Rain in morning: fine. 8. Fine. 9. Drizzly:
fine. 10. Drizzly: very fine. 11. Fine: rain at night. 12. Showery.
13. Stormy, but fair. 14. Very fine: rain at night. 15. Wet morning:
showery. 16. Cloudy: with showers. 17, 18. Wet. 19,20. Cloudy.

21. Cold and showery. 22. Showery. 23. Fine: stormy and wet at night.

24. Very fine. 25. Fine : stormy and wet at night. 26. Clear and fine.
27 — 30. Very fine.

Boston. — April 1, 2. Fine. 3 — 5. Cloudy. 6. Rain. 7, 8. Cloudy.
9- Fine. 10. Cloudy. 11. Fine. 12. Cloudy. 13, 14. Fine. 15. Rain.

16. Fine. 17—20. Cloudy. 21. Rain. 22, 23. Cloudy. 24. Fine.

25. Cloudy. 26—30. Fine.

Penzance. — April 1. Clear: fair: heavy rain at night. ,2, 3. Fair.
4. Clear: fair. 5. Clear: a shower. 6, 7. Clear : showers. 8. Rain.
9. Fair : showers. 10. Hail-showers : fair. 11. Rain. 12. Rain : showers.
13. Showers. 14. Fair: clear. 1 5. Rain : clear. 16. Clear: showers.

1 7. Showers. 18. Rain : clear. 19. Clear : showers. 20, 21. Fair: showers.

22. Fair. 23. Clear: rain. 24. Misty: rain. 25. Rain. 26. Clear: fair.
27—so. Fair : clear. — Rain-gauge ground level.

Metcoro-

lOiO «OOOOChO\ Tf ^J< t^ T -* 00

*Jsoa : : : : i7'® : : : »v fT1 v v T $■ T* :rr???? : : : :

3

*5

i

•dsoQ

-OQOiDkCOOiOOOOOOOOOOOOOO
.... ;iO(O(N'n^Tf0Clb(O OOCOOlCOtN«SxfMrfH ....

: : : : :<n 0 © 0 0 — <n 0 0 <n -h -<**<*© 0 0 0 01 0 ~ 0 : : : :
6

CI

•zuaj

.0 .. .0©iO*0©©»00 .OOOOOQO .OlOOO . . . .
. VO • .00*00^000110 • O^O l>. <© rf © CO • O -h O O ....
* C" ' * * 7* T5 V <~* T 91 9< "^ * <?• ■-- <N »p cd t^ ci *^©.-c50i • • • •

^4 66666666 6666666 6666

0
5
>o

•puoi

: : : r^t^io I't^ioai :-x*o cooo o\ • • t>»oo 0 :<n :. : : r :

. . . .0407/ .0900 . *-< ** •? <n ^ : :ot/(n :<n : : . 1 t

-r

I

>

•dsog

6

C4

i

c

•}sog

$(*H wi ri - 1* *i ^ ^i < ►II * it **A4$* * *

•dsor)

* 8 si Ni f i S • t ;f t\ fi i fe * y i' i f f H Si *■ H ■<

•zuaj

ss i i i ii Hi a ti i a & i i i i a g a i s *

i

I

o

H

.pucj

« * % £** * i i H H » « i* *i & * $£$$%*;** *

u
H

1

6>

g

0

i
0

a

oocitoooco-^rN TttxjoaooooocyiO^oooooor^ocoio^ot^iocv^c^r^

in

11

S3

S
a

U^u^iO'*U^KOiO»O»O'O»O«*jU^U0iOkOU0iO»O»OkO-^tiOiOiOlO(O^OVO<O

o>

§

s

0l

i

mc^OQOrfTli^QOO t^^OX lOOQOQO ixo in m IC f*3 V5 *o 00 ^O l> C\ C\ w

30

cc

s

(NOOO)HP!(X)OOC«5(Sf*5*0(ONiOT|'xtH(N^ooO'<JWiO»0 0>aiH«

u^u^io*Oko»o^ri<40to»oto>oiour)u^u^iotou^^Loioio»o»o»o>ovoio

0

5*3

B

e

o r^o ^vooo"^<^ oooi>c^-' cn m m m ci m tc o in io<©i>-o^h iooooo

^COCO<>J roocOrf^cOrf^^rt^TtTtrt^rt^rr^^-^cO'^Tt^.co

:^

Si

1 ■

B

c

k-5

i

xtot^ct^ninmt^-o^OMfNisMC r-co no- <n oo^cor^c" 1000

>nin-^'Tfxficin'ninioinoinciinininin>nkn'^inin©kntoor»^o

1.0

1 £

So

V

E
o

«

pa

b J
W 00

tNOh>oooiot<)'i,o>oio>n(MOQO(N'*«nooo«Jio(soMMon
op t^o^o coc<9 9919^7- 9>(Ncooo>o>'7'7tco(Nc^^co7J<r^i^ot^
6>6*6>6\6i6i6i6voo o><^^iob o^o^o^oo ob c^oic^o^o^o^cio^dio^c^di

CO

E

5
0

. I"^<<0 O^iO — ' 00 LOO O^O COCOO^^O «tf CO t-^ -«1« t-* £*» O ^foO Tft^-OJ TfOMO

q o^cf\<Kosi>»o«Oi— ct «* p*-«5 *w $- vp coo* <n <irvpfe<5 i>^r*>9>« 5* •*$<

1

rc 0 cno 6^^6><^6><^6>^^^^6><f^6>^<^<^(^i<^ic^6><yiO 0 0 6 0

6

«3

0"
1

1

BE

00<MO^OOOOOVO-rfOOx-«oOOOOOIO<MVCOOOOiOr^iO

oooo^ooi^xjonin^in^oinn^ini^^opoccccpopO'H-HW

O 616 ^O^O^O^^^O^O^CTs^O^O^O^O^^^O^OnO 0 0 0

O
O

1

s

«9

!!O'O'O0OOOiflOOOOOOCQ0OO(NCO«OO'<tOC)W3O«5

•a 0 0 0 0 6^6^o^c^o^o^©^©^©^c^o^©^o^c^o^<^6^o^o^6^o^6 6 0 0 0

MB

Cl

6

CC

1

1
E

1

B

0

i.

^Qo^cy\-oooci>cinnt^c>«t^t^in*oinr»i>ocot^oininn(NO>
-oo9i>^o(s^^i^ipip^9wn9^i>w^Ni>^9<N(N(Noi
606 6» 6> ^ o> <^ ^1 o> o^i 0 ooic^ci o> 0*1 0 o^i 0 ^> o^ o^ o\ o> o © o o
nonc<<Nc<^^w^c<^o<^c<cicic)<Nc<CJ<N(Noi(N<Nnnc<5o

0
I-
»

s

X

M

■

kooo tinTft^^o-ont^-arfON-oooot^eiinnoooi^io-oo

oS^oiC'i,®ocoeiO'Ninooo'*Tto>nNin'i,oC)0>Tt(oo>cocooo

co^^OOpo^cp*poi^i^vpcpi^o^^t^cp»^opopcpo^7<o^

6 6 6 6 6>6>a^6^6^6^6^<"^lC^<^O^6^O\0^6^6l6^6^6^6^0^© 0 0 0 0

COCOCOCOC^C*WCNC»CSOiC^C^C^C<C^CiCiC*C*C*C<C^

1

o

°Soo

5 § a

~ c* orf 100 r-ao oso -j cj ^^^^ t^ao oo - gj g^-gg gjgg^g
< « • « O

IB

>
<

INDEX to VOL. III.

ACID, preparation of iodous, 146
acetic or vinegar, analysis of, 107
oxalic and citric, analysis of, 109
malic, analysis of, 110; phosphoric,
its action on albumen, 462 ; saclactic,
analysis of, 110.

./Ether, analysis of, 309.

Air, currents of, Mr. Younge on Des-
orme's experiments on, 282.

Albumen, action of phosphoric acid on,
462.

Alcohol, analysis of, 309.

Alps, Mr. Bakewell on the thermal
waters of, 1 4.

Ammonia, test of its presence, 466.

Analysis of organized substances, 33 ;
of sugars, 99 ; of acetic acid, or vine-
gar, 1 07 ; of oxalic and citric acids,
109; of malicand saclactic acids, 1 10;
of a salivary concretion, 146 ; of some
vegetable products, 150 ; of alloys
of bismuth, 230 ; of alcohol, aether,
&c, 309, 465 ; of tourmaline, 460.

Astronomy, 26, 64, 136, 227, 377, 451.

Atmosphere and the gases, electricity
of, 148.

Aurora borealis of 26th Sept., Dr.
Forster on, 75.

Bakewell (R.) on the thermal waters
of the Alps, 14 ; review of his intro-
duction to geology, 289.

Barium, peroxide of, 152.

Barker's Mill, Mr. Ivory's notes rela-
ting to the theory of, 425.

Bevan's (B.) remarks on Mr. J. Tay-
lor's rain-gauge, 29; notice of an
error in Mr. Galbraith 's mathema-
tical tables, 153.

Bicheno (J. E.) on systems and me-
thods in Natural History, 213, 265.

Bismuth, analysis of some alloys of,
230.

Books, new, 40, 77, 126, 234, 289,
368, 467.

Botany, 183, 223.

Brandes (Dr. R.) on a gelatinous sub-
stance found in a damp meadow, 27 1 .

Bromide of selenium, 147.

Bromine, elementary nature of, 145;
quantity of in sea water, 145; sale

of, 146 ; bromine and water, power
of in conducting electricity, 151.

Burney's (Dr.) meteorological obser-
vations, 78, 157, 337, 317, 398 ; Me-
teorological Journal for 1827, 312.

Cadmium, iodine in, 234.

Capillary action, Mr. Ivory on, 1 .

Chama concamerata, Mr. Gray on the
nursing pouch of, 117.

Clark (B.) on the insect called Oistros
by the ancients, 283.

Combustion, heat given outduring, 233.

Continuity, Dr. Roget on a violation
of the law of, 118, 203.

Copper, examination of, 231.

Crystalline form of some salts, 27.

Currents of aeriform fluids, 74, 282.

Curve-surfaces, on the equation of, 436.

Davy (Sir H.)'on the phaenomena of
volcanoes, 373.

Desorme, (C.) new phaenomena of va-
pour observed by, 74 ; experiments
on currents of air, Mr. Younge on,
282.

Diopside, Dr. Wackenroder's exami-
nation of, 349.

Earth, figure of the, 165, 206, 241 ;
Mr. Galbraith on, 321 ; Mr. Ivory
on, 343.

Earthquakes, 463.

Efflorescence, on, 231.

Electricity, 148, 151.

Ellipticity of the earth, Mr. Ivory on,
165, 206, 241 ; Mr. Galbraith on,
321.

Encke's comet, 451.

Entomology, 283, 368, 370.

Equations, linear, differential, Mr.
Herapath on, 19, 210; reply to by
and B., 96, 262 ; reply to by F.R. S.
97.

Ewart (P.) on the reaction of effluent
water, and on the maximum effect jof
machines, 416.

Faraday (M.) on the fluidity of sul-
phur and phosphorus, 144.

Farey's (J.) treatise on the steam-en-
gine, review of, 40.

Fayolle, M., on the equation of curve-
surfaces, 436.

Figure of the earth, Mi*. Ivory on, 165,

INDEX.

471

$06, 241, 343, 431 ; Mr. Galbraith

on, 321.
Fire-ball, 74.
Fluids, Mr. Tredgold's new theory of

the resistance of, 249.
F.R.S.'s reply to F.R.S.L.'s remarks

on compound interest, 30.
Galbraith's mathematical tables, notice

of an error in, 153.
Gas, inflammable, from salt mines, em-
ployed for producing light, 233 ;

natural gas lights at Fredonea, 233.
Gases and the atmosphere, electricity

of, 148.
Gauss, (Prof.) account of his "Disqui-

sitiones generates circa Superficies

Curvas," 331.
Gay Lussac on efflorescence, 231.
Geology, 132, 188, 225, 243, 289, 291,

436, 441, 458, 463.
Geometrical problem, 234.
German Ocean, on the subsidence of,

188.
Giddy, (E. C.) meteorological results

of observations made at Penzance

for 21 years, 173.
Oilbert (D.) on the regular or platonic

solids, 161.
Giraffa, Sir E. Home on, 46.
Gmelin, M., his analyses of tourma-
lines, 460.
Gray (J. E.) on the nursing pouch of

the Chama concamerata, 117.
Haidingerite, a new mineral, 146.
Haworth (A. H.) on new succulent

plants, 183.
Haytor, iron mine at, Mr. Kingston's

account of, 359.
Heat, effects of, upon sulphur, 152;

heat given out during combustion,

233.
Herapath (J.) On linear differential

equations, 19, 210; replies to, 96,

97, 262.
Hordein, analysis of, 150.
Hunefeld (Prof.) on titaniferous iron-
slag, 121.
Hutton's log tables, errors in, 154.
Hydrosilicite, a new mineral, 71.
Instruments, ancient, chemical exami-
nation of, 154.
Iodine in cadmium, 234.
Iodous acid, preparation of, 146.
Iron ore, green, analysis of, 234.
Iron -slag, titaniferous, Prof. Hunefeld

on, 121.
Isopyre, a new mineral, 70.
Ivory (J.) on the theory of capillary
action, 1 ; on the figure of the earth,
165, 206, 241, 343, 431 ; notes re-
lating to the theory of Barker's Mill,
416.

Karphosiderite, a new mineral, 397.

Kendal, state of the barometer, &c. in
for 1827, 236.

Kingston's (J. T.) account of the iron
mine at Haytor, 359.

Lead, arseniate of, 234.

Mageough (W.) on a new method of
mounting thermometers, 365.

Main (J.) on the phenomena of wa-
ter-spouts, 114.

Manganese, new chloride of, 151.

separation of from lime and

magnesia, 462.

Marshall, (S.) meteorological summary
for 1827, 236.

Mastodontes, 444.

Membranes, motions of, Dr. Weber on
Lavart's experiments on, 336, 342.

Mesitine-spar, a new mineral, 397.

Meteorology, 78, 157, 173, 236, 312,
398, 467.

Miller (Lieut.-Col.) on a percussion
rifle, 277 ; on a percussion shell, 358.

Mineralogy, 70, 71, 146, 349, 397.

Natural History, Mr. Bicheno on sy-
stems and methods in, 213, 265.

Nixon (J.) on the heights of the prin-
cipal beds of Ingleborough Hill and
Moughton Fell, Yorkshire, 13;
heights of the principal hills in the
vicinity of Dent, Hawes, and Sed-
bergh, Yorkshire, 82, 189.

— — — on errors in Hutton's log
tables, 154.

Noutronite, a new mineral, 149.

Obituary of Sir J. E.Smith, 307,391.

Oistros, of the ancients, Mr. Bracy
Clark on, 283.

Osmelite, a new mineral, 71.

Patents, list of, 76, 155, 236,311, 466.

Penzance, meteorological results of
observations made at for 21 years,
173.

Peroxide of barium, 152.

Petrosilex, rose-coloured, 149.

Phillips (J.) on the geology of the
vale of Pickering, 243.

.Phillips, (R.) on ascertaining the pu-
rity of sulphate of quina, 111.

Phosphoric acid, its action on albumen,
462.

Phosphorus and sulphur, on the flu-
idity of, 144 ; crystallization of phos-
phorus, 154.

Platina-sand, Russian, 72 ; native pla-
tina, 232.

Popocatapetl, 449.

Potash, chromate of, and sulphate of
zinc, Dr. Thomson on the decompo-
sition of, 81.

Prout (Dr.) on simple alimentary sub-
stances, 31, 98.

472

INDEX.

Quina, Mr. R. Phillips on ascertaining
the purity of, 111.

Rain-gauge, Mr. Bevan's remarks on
Mr. J. Taylor's, 29.

Rain, red, 463.

Riddle (E.) on the occultation of /S
Scorpii, Sept. 25, 1827.

Rifle, a percussion, Lieut-Col. Miller
on, 277.

Robotham's (J.) geometrical problem,
234.

Roget (Dr.) on an apparent violation
of the law of continuity, 118, 203.

Salivary concretion, analysis of, 146.

Sea water, quantity of bromine in, 145.

Selenium, bromide of, 147.

Serullas (M.) on bromide of selenium,
147.

Sepiae, Mr. Slight on certain habitudes
of, 153.

Shell, a percussion, Lieut. -Col. Miller
on, 358.

Slight (H.) on certain habitudes of
sepiae, 153.

Smith, Sir J. E., 291, 307, 374, 391.

Societies learned: Royal Society, 46,
128, 370, 436; Linnaean Society, 130,
223, 290, 374, 440; Geological So-
ciety, 132, 225, 291, 441; Astrono-
mical Society, 64, 136, 227, 377,
451 ; Zoological Society, 68 ; Royal
Geological Society of Cornwall, 138 ;
Royal Academy of Sciences of Pa-
ris, 139, 305; Royal Institution of
Great Britain, 229, 304, 391, 456;
London Institution, 154.

Soda, new borate of, 146.

Solids, regular or platonic, Mr. Davies
Gilbert on, 161.

Solly, Mr. S. on trap-rocks, 458.

Sound, Dr. Weber on the interference
of, 342.

Starch, common and roasted, analysis
of, 150.

Steam, new phenomena of, 74.

Steam-engine, on, 40, 219.

Stromeyer, Prof., on the separation of
manganese from lime and magnesia,
462.

Subsidence of the German Ocean, 188.

Substances, simple alimentary, Dr.
Prout on, 31, 98.

Succulent plants, new, 183.

Sulphur and phosphorus, fluidity of,
144; effects of heat upon snlphur,
152.

Surfaces, curve, Prof. Gauss on, 331.

Tautolite, a new mineral, 398.

Teschemacher (E. F.) on the crystal-
line form of some salts, 27.

Thermal waters of the Alps, Mr.
Bakewell on, 14.

Thermometers, new method of mount-
ing, Mr. Mageough on, 365.

Thomson (Dr.) on the decomposition
of sulphate of zinc and chromate of
potash, 81.

Tourmalines, analyses of, 460.

Trap-rocks, 458.

Tredgold (T.) on the steam-engine,
219 ; new theory of the resistance of
fluids, 249.

Ultramarine, manufacture of, 232.

Vapour, new phaenomena of, 74.

Vegetable products, analysis of some,
150.

Vision, single and erect, on the causes
of, 406.

Wackenroder's (Dr. H.) examination
of diopside, 349.

Walker (R.) on the artificial produc-
tion of cold, 401.

Water and bromine, power of, in con-
ducting electricity, 151.

Water-spouts, Mr. Main on, U4«

Weber (Dr. W.) on Savart's experi-
ments on the motions of membranes,
336 ; on the interference of sound,
342.

Yorkshire, heights of the principal beds
of Ingleborough Hill and Moughton
Fell in, 13 ; heights of the hills in the
vicinity of Dent, Hawes, and Sed-
bergh in, 82, 189.

Younge (R-) on Desorme's experi-
ments on currents of air, 282.

Zinc, sulphate of, and chromate of
potash, Dr. Thomson on the decora-
position of, 81.

Zoology, 46, 68, 117.

END OF THE THIRD VOLUME.

LONDON:

TRINTKR BT RICHARD TAYLOR, RED WON COURT, FLEET STREET.

1828.

FhilMayScAivnals. Pl.L ToU D

S. Porter.

W5aJ.v

////.' MaQ&Annah.PLW . VotlSL

^tia.i

//jco.S.

J&4AJ.

fljni fri renin

S. Jbrttr.se.

Tfiti.JUaa. t^tnnais. MS. Vol. 3.17. 3.

+ 8EDBEBGB JSawJWo

ORysseH

QColrn

TVherrisideG

®Grayonlh

0

Aftr na

GiraJboar-Tell

© Shu/uiorJ eil

* .

Zovelv Seat
O

HAWES +

Q>2?ou0?iti>erfy7liU Si<><»s 2fead

TaiXnd

&WhawJ?eZL

© Snqys TeU © Jjod Tell

QBZeaMoor ©

Cam, Teil

©Gearstones Irai

0 IhffUborouah

\-y-oent
© '

ctfrt^nwri <&/&// Jta&ttm / cr&c+nes %^6lt& cp&ie /%*/** Cfu

//„/. J/,/,/.,; ,/W/. . :S.Vdl.3 .I'l.W.

S.Tertcr Sc

PhaMa^.kAmiaU.ES. Vel.5.FlV.

*'

-.
*

SJfijrUr. Si

i i ;

.. J i

t i

«s

-•«-- ■■•'

PR

55 ft

o>

I

m

_ —

TZ7"

. «9

CD "

I

•

0 ■ 0" "Ea

* *

L±

>

O

-. .

*

•<5

A /"

>

Ml

n

J /r\ s

N

V~Vi

--

-ffl

•«

*

^

/ /

//.

1 1

1 i

)c?

A{

■■ >

"

i t

•o (

N \\

&

1

i

•

Architectural Library, 59, High Holbom.
Just Published by J. Taylor,

THE STEAM ENGINE, by Thomas Tredgold ; comprising an
Account of its Invention and Progressive Improvements, with an
Investigation of its Principles, and the Proportion of its Parts for Effi-
ciency and Strength ; detailing also its Application to Navigation, Mining,
impelling Machines, &c. and the Results collected in numerous Tables for
Practical Use. Illustrated by 20 Plates and numerous Wood-cuts, in
4to. Price c2l. 2s. boards.

Where may be had, by the same Author,

1. An Essay on the Strength of Cast Iron and other Metals. With Plates,
Svo. Price 155. boards.

2. Principles of Warming and Ventilating Public Buildings, Dwelling-
houses, &c. With Plates, 8vo. Price 15s. boards.

3. Elementary Principles of Carpentry, &c. 22 Plates, 4to. Price
1/. 45. boards.

4. A Practical Treatise on Rail- Roads. With Plates, Svo. Price 105.6^.
boards.

THE PRINCIPLES of MECHANICS ; Explaining and Demon-
strating the General Laws of Motion, the Laws of Gravity, Motion of
Descending Bodies, Projectiles, Mechanic Powers, Pendulums, Centres
of Gravity, &c. ; Strength and Stress of Timber, Hydrostatics, and Con-
struction of Machines. By William Emerson. To which is now added
an Appendix, containing Explanatory Notes, Illustrations, and Obser-
vations, by G. A. Smeaton, Civil Engineer.

A New Edition, corrected ; illustrated by 83 Copper-plates, and other
Figures in Wood. 8vo. Price 155.

TRACTS on HYDRAULICS, Edited by Thomas Tredgold, Civil
Engineer; viz. 1. Smeaton's Experimental Papers on the Powers of
Water and Wind to turn Mills, &c. 2. Venturi's Experiments on the
Motion of Fluids. 3. Dr. Young's Summary of Practical Hydraulics ;
chiefly from the German of Eytelwein. With Notes by the Editor. Illus-
trated by Seven Plates. In 8vo. Price 125. boards.

A TREATISE on MILLS ; in Four Parts. Part First, On Circular
Motion ; Part Second, On the Maximum of Moving Bodies, Machines,
Engines, &c. ; Part Third, On the Velocity of Effluent Water; Part Fourth,
Experiments on Circular Motion, Water Wheels, &c. By John Banks,
Lecturer in Experimental Philosophy. Second Edition. Price 85. boards.

This day is published, by Baldwin and Cradock, Paternoster Row,

THE FIRST PART of VOL. III. of the MEMOIRS of the AS-
TRONOMICAL SOCIETY of LONDON. 4to. Price 125.
*** The Members of the Society may obtain their Copies, (price 6s.)
of Mr. Harrison, the Collector, 41 Bedford Street, Covent Garden.

NEW EXCISE REGULATION ACT.
Just Published, Price I5. 6d.

AN ABSTRACT OF THE EXCISE GENERAL REGULATION
ACT. 7 and 8 GEO. IV. Cap. 53. Intituled " An Act to Conso-
lidate and Amend the Laws relating to the Collection and Management
of the Revenue of Excise throughout Great Britain and Ireland." To
commence on the 5th of January 1828.

Printed from an Abstract used by the Officers of Excise. With a co-
pious Index.

London : Printed and sold by Richard Taylor, Red Lion Court, Fleet
Street; sold also by Simpkin and Marshall, Stationers' Court ; and by
R. B. Bate, Mathematical Instrument Maker to the Honourable Board
©f Excise, 17, Poultry.

CONTENTS of N° 13.— New Series.

I. On the Theory of Capillary Action, and the Depression of the
Mercury in the Tubes of Barometers. By J. Ivory, Esq. M.A.
F.R.S page 1

II. Heights of some of the principal Beds of Ingleborough Hill
and Moughton Fell, Yorkshire. By John Nixon, Esq 11

III. On the Thermal Waters of the Alps. By R. Bakewell, Esq. 14?

IV. On the Integration of Linear Differential Equations having
Constant Coefficients and last Term any Function of the Indetermi-
nate Quantity a;. By John Herapath, Esq 19

V. On the Occultation of |3 Scorpii, September 25, 1827. By

E. Riddle, Esq 26

VI. On the Crystalline Form of some Salts. By Mr. E.F.Tesche-
macher 27

VII. Remarks on Mr. J. Taylor's Rain-gauge. By B. Bevan, Esq. 29

VIII. Reply to F.R.S.L.'s Remarks on Compound Interest. ... 30

IX. On the ultimate Composition of simple alimentary Substances ;
with some preliminary Remarks on the Analysis of organized Bodies

in general. By William Prout, M.D. F.R.S. (To be continued) 31

X. Notices respecting New Books :— Mr. John Farey's Treatise

on the Steam-Engine 40

XI. Proceedings of Learned Societies: Royal Society — President's
Anniversary Address ; Astronomical Society ; Zoological Society 46 — 69

XII. Intelligence and Miscellaneous Articles : — Isopyre, a new
Mineral Species; Osmelite, a new Mineral Species ; Hydrosilicite,
a new Mineral Species $ Russian Platina-Sand ; New Phenomena of
Vapour observed by Clement Desormes ; Notice of a Fire-Bail, by
the Rev. S. E. Dwight ; On the Aurora Borealis of 26th Septem-
ber, by Dr.Forster; New Patents; Scientific Books, &c. ; Meteorolo-
gical Observations, Table,&c 70—80

%* It is requested that all Communications for this Work may be addressed,
post paid, to the Care of Mr. R. Taylor, Printer, Red-Lion-Court, Fleet-
Street, London.

CONTENTS or the PHILOSOPHICAL MAGAZINE and ANNALS.
Vol. I.— New Series. January — July 1827.

On the Elastic Force of Steam at different Temperatures. By J. Ivory, Esq.
M.A. F.R.S.— On the Identity of Epistilbite and Heulandite. By A. Levy, Esq.
M.A. F.G.S. — Reply to Mr. Galbraith's Remarks on the Experiments for ascertain-
ing the Velocity of Sound at Port Bowen. By Capt. W. E. Parry, R.N. F.R.S.,
and Lieut. H. Foster, R.N. F.R.S. — Experiments on the Cohesion of Cast-iron.
By B. Bevan, Esq.— Table and Formulae for reducing Registers of the Height of
the Barometer to the Standard Temperature and Level. By Mr. J. Nixon. —
Further List of Errors in Piazzi's Catalogue of Stars.— On the Inflammation of
Gunpowder and other Substances by Electricity. By Mr. W. Sturgeon — On some
newly-discovered Siberian Minerals. By A. Levy, Esq. M.A. F.G.S. — Observations
on the Solar Eclipse, November 29th, 1826. By the Rev. Baden Powell, M.A.
F.R.S. — The Bakerian Lecture. On the Relations of Electrical and Chemical
Changes. By Sir H. Davy, Bart. Pres. R.S. — Observations on a Mineral from near
Hay Tor, in Devonshire. By C. Tripe, Esq. — Remarks on the Crystalline Form of
the Haytorite. By W. Phillips, F.G.S. &c. — On the Origin of the Crystalline Forms
of the Haytorite. By A. Levy, Esq. M.A. F.G.S. — Astronomical Observations 1826.
By Lieut. Beaufoy, R.N.— A List of Moon-culminating Stars for 1827. By F. Baily,
Esq. F.R.S. — Observations on the late Solar Eclipse. By T. Squire, Esq. — On Fus-
tic, and its Application to Dyeing. By E. S. George, Esq. F.L.S. — On some new
auxiliary Tables for determining the apparent Places of Greenwich Stars. By
Francis Baily, Esq. F.R.S. — Investigation of the Heat extricated from Air when it un-
dergoes a given Condensation. By J. Ivory, Esq. M.A. F.R S. — A Mode of Heating
Water for a Bath. By E. Deas Thompson, Esq.— On the Finite Extent of the At-
mosphere. By T. Graham, M. A.— On the Triple Prussiate of Potash. By R. Phil-
lips, F.R.S. L. & E.— On Capillary Attraction. By the Rev. J. B. Emmett. — A new
Method of Bleaching and preparing Flax. By the Rev. J. B. Emmett.— Description
of New Succulent Plants. By A. H. Haworth, Esq. F.L.S. — On the Accidents inci-
dent to Steam Boilers. By J. Taylor, Esq. F.R.S.— On the Crystalline Forms of
Wagnerite. By A. Levy, Esq. M.A. F.G.S. — On Captain Parry's and Lieut. Fos-
ter's Experiments for ascertaining the Velocity of Sound at Port Bowen. By W.
Galbraith, Esq. M.A. — Biographical Notice of M. Piazzi. — Continuation of the
Subject relating to the Absorption and Extrication of Heat in a Mass of Air that
changes itsVolume. By J. Ivory, Esq. M.A.F. R.S. — Notice relating to the Seconds
Pendulum at Port Bowen. By J. Ivory, Esq. M.A. F.R.S.— An Accountof M. Long-
champ's Theory of Nitrification j with an Extension of it. By T. Graham, M.A. —
A Sketch of the Natural Affinities of the Lepidoptera Diurna of Latreille. By W.
Swainson, Esq. F.R.S. F.L.S.— On the Crystalline Form of the Hyalosiderite. By
W. Phillips, Esq. F.G.S. — Outlines of a Philosophical Inquiry into the Nature and
Properties of the Blood. By J. Spurgin, M.D. — On Contemporaneous Meteorolo-
gical Observations, as proposed by the Royal Society of Edinburgh. By T. Squire,
Esq. — On the expected Occupation of Venus in February. By T. Squire, Esq. —
Some Account of an Orang Outang of remarkable Height found on the Islaad of
Sumatra. By Clarke Abel, M.D. F.R.S. — Astronomical Observations 1827. By
Lieut. G. Beaufoy, R.N. — On a new Mineral Species. By A. Levy, Esq. M.A. F.G.S.
— Description of a Horizontal Pumping Engine erected on the Mine of Moran
in Mexico. By P. Taylor, Esq. — Analysis of a Sulphuretted Water from the
Northern Part of the Yorkshire Coal-field. By E. S. George, F.L.S.— Application
of the Variations of Temperature in Air that changes its Volume to account for
the Velocity of Sound. By J. Ivory, Esq. M.A. F.R.S. — Theory of the Spirit-Level.
By Mr. J. Nixon. — Observations on the Crystalline Form, &c. of the Gaylussite.
By W. Phillips, F.L.S. G.S.— New Phenomena caused by the Elfect of Electric
Influence ; and Suggestions for ascertaining the Extent of the Terrestrial Magnetic
Atmosphere. By J. H. Abraham, F.L.S.— On the Geology of East Norfolk ;
with Remarks upon the Hypothesis of Mr. Robberds, respecting the former Level
of the German Ocean. By R. C. Taylor, Esq. F.G.S. — Astronomical Observations
1827. By Lieut. G. Beaufoy, R.N. — On the Orange Phosphate of Lead. By the Rev.
Wm. V. Vernon, F.R.S.— Some Remarks on a Memoir by M. Poisson. By J. Ivory,
Esq. M.A. F.R.S.— On Capillary Attraction. By the Rev. J. B. Emmett.— On the
Velocity of Sound. By W. Galbraith, Esq. M.A— Result? of the Meteorological
Observations made at Wick,in Scotland. By W. Burney, LL.D. — Remarks on Mr.
Sturgeon's Paper "On the Inflammation of Gunpowder by Electricity." By Mr.
Thomas Hnwldv On Chromate of Silver. Bv Mr. E. F. Tescheraacher.

CONTENTS of N° 14.— New Series.

XIII. On the mutual Decomposition of Sulphate of Zinc and
Chromate of Potash. By T. Thomson, M.D. F.R.S. L. & E. Pro-
fessor of Chemistry in the University of Glagow page 81

XIV. On the Measurement by Trigonometry of the Heights of
the principal Hills in the Vicinity of Dent, Hawes, and Sedbergh, in
Yorkshire. By John Nixon, Esq. ( To be continued.) 82

XV. On Mr. Herapath's Method for the Integration of Linear
Equations with constant Coefficients 96

XVI. On the Error imputed by Mr. Herapath to Lagrange in hie
Method of integrating Linear Differential Equations. By A Cor-
respondent 97

XVII. On the ultimate Composition of simple alimentary Sub-
stances ; with some preliminary Remarks on the Analysis of or-
ganized Bodies in general. By William Prout, M.D. F.R.S 98

XVIII. On the Means of ascertaining the Purity of Sulphate of
Quina. By R. Phillips, F.R.S. L. & E. &c Ill

XIX. On the Phaenomena of Water-spouts. By Mr. James
Main 114

XX. On the Nursing Pouch or Chamber of the Chama concamerata

of Gmelin. By John Edw. Gray, Esq. F.G.S. &c 117

XXI. On an Apparent Violation of the Law of Continuity. By
P.M.Roget,M.D.F.R.S ^... 118

XXII. On the Titaniferous Iron-slag of Konigshiitte in Upper
Silesia, and on the Probability of its containing Tantalium. By
Prof. Hunefeld, of Greifswalde 121

XXIII. Notices respectingNew Books: — Philosophical Transactions
for 1827. Part II. : Transactions of the Linnean Society of London.
Vol. 15th. Part II. : Memoirs of the Astronomical Society. Vol. 3rd.
Part 1 126

XXIV. Proceedings of Learned Societies: Royal Society ; Linnaean
Society ; Geological Society ; Astronomical Society ; Royal Geo-
logical Society of Cornwall ; Royal Academy of Sciences of Paris.

128— 144

XXV. Intelligence and Miscellaneous Articles : — On the Fluidity
of Sulphur and Phosphorus at common Temperatures, by Mr. Fara-
day ; Elementary Nature of Bromine ; Quantity of* Bromine in Sea
Water; Sale of Bromine ; Preparation of Iodous Acid ; New Borate
of Soda ; Analysis of a Salivary Concretion ; Haidingerite, a new
Mineral Species ; Bromide of Selenium, by M. Serullas ; Electricity
of Gases and the Atmosphere ; Rose-coloured Petrosilex from Sahl-
bergh in Sweden ; Nontronite, a new Mineral ; Analysis of some
Vegetable Products; New Chloride of Manganese; On the Power
of Water and Bromine in conducting Electricity : Effects of Heat
upon Sulphur ; Peroxide of Barium ; on certain habitudes of Sepia ;
Notice of an Error in Galbraith's Mathematical Tables and Formulae;
Errors in Hutton's Log. Tables (Fifth Edition) ; Crystallization of
Phosphorus ; Chemical Examination of Ancient Instruments, &c. ;
London Institution ; New Patents ; Meteorological Observations,
Table, &c 144—160

\* It is requested that all Communications for this Work may be addressed,
post paid, to the Care of Mr. R. Taylor, Printer, Red- Lion-Court, Fleet-

THE REV. H. R. BOWLES,

QUEEN STREET,
YARMOUTH, NORFOLK,

RECEIVES as Boarders a small number of YOUNG GENTLEMEN,
who are carefully instructed in the Latin and Greek Languages ;
strict attention being paid to the niceties of Grammatical Construction and
Prosody. The Hebrew is taught if desired.

While a thorough knowledge of the Classics is afforded them, by a
judicious distribution of studies, the Pupils are made well acquainted with
the Mathematics ; and at the same time, due attention is paid to the For-
mation of a correct and elegant English style.

Pupils intended for the learned Professions are prepared for the English
or Scotch Universities. The Modern Languages are taught in the School.
Music and Drawing by approved Masters.

To encourage habitual affection and confidence between himself and his
Pupils has always been a principal object in Mr. Bowles's plan of Educa-
tion, from a belief that this is the only means of securing their moral and
intellectual improvement.

Terms may be known by applying at the School. Reference may be
had to Mr. R. Taylor, Red Lion Court, Fleet Street, London ; Mrs.
Reeve, Norwich ; S. Paget, Esq., H. V. Worship, Esq., Mr. G, Errington,
Mr. Lettis, &c, Yarmouth.

CONTENTS of N° 15.— New Series.

XXVI. On the Regular or Platonic Solids. By Davies Gilbert,
F.R.S. &c page 161

XXVII. On the Ellipticity of the Earth as deduced from Experi-
ments with the Pendulum. By J. Ivory, M.A. F.R.S 165

XXVIII. The Climate of Penzance, Cornwall.— Meteorological
Results of the Temperature, Wind and Weather deduced from diur-
nal Observations made at Penzance for 21 Years : (the Thermome-
trical Observations made at 8 a.m. and 2 p.m.) to which are added
the Maxima, Minima, and Media of the Register Thermometer for
7 Years, with the Inches of Rain fallen during that Period. By Ed-
ward Collins Giddy, Curator of the Cabinet of the Royal Geo-
logical Society of Cornwall 173

XXIX. Description of New Succulent Plants. By A. H. Ha-
worth, Esq. F.L.S 183

XXX. On the supposed Subsidence of the German Ocean. By

A Correspondent ] 8S

XXXI. On the Measurement by Trigonometry of the Heights of
the principal Hills in the Vicinity of Dent, Hawes, and Sedbergh, in
Yorkshire. By John Nixon, Esq 189.

XXXII. On an Apparent Violation of the Law of Continuity. By

P. M. Roget, M.D. F.R.S 203

XXXIII. Additional Discussion respecting the Ellipticity of the
Earth as determined by Experiments made with the Pendulum. By

J. Ivory, Esq. M.A. F.R.S 206

XXXIV. Failure of Lagrange's Method of integrating Linear with
Constant Coefficients. By John Herapath, Esq 210

XXXV. On Systems and Methods in Natural History. By J. E.
Bicheno, Esq., F.R.S., Sec. L.S., &c. ( To be continued.) 213

XXXVI. Notices respecting New Books : — Tredgold on the
Stescm-Engine. — Young's Elements of Geometry, with Notes 219-222

XXXVII. Proceedings of Learned Societies: — Linnaean Society;
Geological Society ; Astronomical Society ; Proceedings at the Fri-
day Evening Meetings of the Royal Institution of Great Britain 223 — 230

XXXVIII. Intelligence and Miscellaneous Articles : — Analysis of
some Alloys of Bismuth ; Examination of Copper ; On Efflorescence;
Native Platina ; Manufacture of Ultramarine ; Heat given out during
Combustion ; Inflammable Gas arising after Boring for Salt, Inflam-
mable Gas from Salt Mines employed for producing Light ; Natural
Gas Lights at Fredonea ; Iodine in Cadmium ; Analysis of the Green
Iron Ore and Arseniate of Lead ; Geometrical Problem, by Mr. J. Ro-
botham ; Scientific Books ; New Patents ; Meteorological Observa-
tions ; Table, &c 230—240

It is requested that all Communications for this Work may be addressed,
post paid, to the Care of Mr. R. Taylor, Printer, Red-Lion-Court, Fleet-
Street, London.

CONTENTS of the PHILOSOPHICAL MAGAZINE and ANNALS.
Vol. I.— New Series. January — July 1827.

On the Elastic Force of Steam at different Temperatures. By J. Ivory, Esq.

M.A. F.R.S On the Identity of Epistilbite and Heulandite. By A. Levy, Esq.

M.A. F.G.S. — Reply to Mr. Galbraith's Remarks on the Experiments for ascertain-
ing the Velocity of Sound at Port Bowen. By Capt. W. E. Parry, R.N. F.R.S.,
and Lieut. H. Foster, R.N. F.R.S. — Experiments on the Cohesion of Cast-Iron.
By B. Bevan, Esq.— Table and Formulae for reducing Registers of the Height of
the Barometer to the Standard Temperature and Level. By Mr. J. Nixon. —
Further List of Errors in Piazzi's Catalogue of Stars.— On the Inflammation of
Gunpowder and other Substances by Electricity. By Mr. W. Sturgeon — On some
newly- discovered Siberian Minerals. By A. Levy, Esq.1 M.A. F.G.S.— -Observations
on the Solar Eclipse, November 29th, 1826. By the Rev. Baden Powell, M.A.
F.R.S. — The Bakerian Lecture. On the Relations of Electrical and Chemical
Changes. By Sir H. Davy, Bart. Pres. R.S. — Observations on a Mineral from near
Hay Tor, in Devonshire. By C. Tripe, Esq. — Remarks on the Crystalline Form of
the Haytorite. By W. Phillips, F.G.S. &c— On the Origin of the Crystalline Forms
of the Haytorite. By A. Levy, Esq. M.A. F.G.S. — Astronomical Observations 1826.
By Lieut. Beaufoy, R.N. — A List of Moon-culminating Stars for 1827. By F. Baily,
Esq. F.R.S. — Observations on the late Solar Eclipse. By T. Squire, Esq. — On Fus-
tic, and its Application to Dyeing. By E. S. George, Esq. F.L.S. — On some new
auxiliary Tables for determining the apparent Places of Greenwich Stars. By
Francis Baily, Esq. F.R.S. — Investigation of the Heat extricated from Air when it un-
dergoes a given Condensation. By J. Ivory, Esq. M.A. F.R.S. — A Mode of Heating
Water for a Bath. By E. Deas Thompson, Esq.— On the Finite Extent of the At-
mosphere. By T. Graham, M. A.— On the Triple Prussiate of Potash. By R. Phil-
lips, F.R.S. L. & E. — On Capillary Attraction. By the Rev. J. B.Emmett. — Anew
Method of Bleaching and preparing Flax. By the Rev. J. B. Emmett.— Description
of New Succulent Plants. By A. H. Haworth, Esq. F.L.S. — On the Accidents inci-
dent to Steam Boilers. By J. Taylor, Esq. F.R.S. — On the Crystalline Forms of
Wagnerite. By A. Levy, Esq. M.A. F.G.S. — On Captain Parry's and Lieut. Fos-
ter's Experiments for ascertaining the Velocity of Sound at Port Bowen. By W.
Galbraith, Esq. M.A. — Biographical Notice of M. Piazzi. — Continuation of the
Subject relating to the Absorption and Extrication of Heat in a Mass of Air that
changes itsVolume. By J. Ivory, Esq. M.A.F. R.S. — Notice relating to the Seconds
Pendulum at Port Bowen. By J. Ivory, Esq. M.A.F.R.S.— An AccountofM. Long-
champ's Theory of Nitrification j with an Extension of it. By T. Graham, M.A. —
A Sketch of the Natural Affinities of the Lepidoptera Diurna of Latreille. By W.
Swainson, Esq. F.R.S. F.L.S. — On the Crystalline Form of the Hyalosiderite. By
W. Phillips, Esq. F-G.S. — Outlines of a Philosophical Inquiry into the Nature and
Properties of the Blood. By J. Spurgin, M.D. — On Contemporaneous Meteorolo-
gical Observations, as proposed by the Royal Society of Edinburgh. By T. Squire,
Esq.— On the expected Occupation of Venus in February. By T. Squire, Esq. —
Some Account of an Orang Outang of remarkable Height found on the Island of
Sumatra. By Clarke Abel, M.D. F.R.S.— Astronomical Observations 1827. By
Lieut. G. Beaufoy, R.N. — On a new Mineral Species. By A. Levy, Esq. M.A. F.G.S.
— Description of a Horizontal Pumping Engine erected on the Mine of Moran
in Mexico. By P. Taylor, Esq. — Analysis of a Sulphuretted Water from the
Northern Part of the Yorkshire Coal-field. By E. S. George, F.L.S. — Application
of the Variations of Temperature in Air that changes its Volume to account for
the Velocity of Sound. By J. Ivory, Esq. M.A. F.R.S. — Theory of the Spirit-Level.
By Mr. J. Nixon. — Observations on the Crystalline Form, &c. of the Gaylussite.
By W. Phillips, F.L.S. G.S.—New Phenomena caused by the Effect of Electric
Influence ; and Suggestions for ascertaining the Extent of the Terrestrial Magnetic
Atmosphere. By J. H. Abraham, F.L.S. — On the Geology of East Norfolk ;
with Remarks upon the Hypothesis of Mr. Robberds, respecting the former Level
of the German Ocean. By R. C. Taylor, Esq. F.G.S. — Astronomical Observations
1827. By Lieut. G. Beaufoy, R.N. — On the Orange Phosphate of Lead. By the Rev,
Wm. V. Vernon, F.R.S. — Some Remarks on a Memoir by M. Poisson. By J. Ivory,
E*q. M.A. F.R.S.— On Capillary Attraction. By the Rev. J. B. Emmett.— On the
Velocity of Sound. By W. Galbraith, Esq. M. A.— Results of the Meteorological
Observations made at Wick,in Scotland. By W. Burney, LL.D. — Remarks on Mr.
Sturgeon's Paper " On the Inflammation of Gunpowder by Electricity." By Mr.
Thomas Howldy.— On Chromate of Silver. By Mr. E. F. Teschemacher.

CONTENTS of N° 16.— New Series.

XXXIX. A Letter to the Editors relating to the Ellipticity of
the Earth as deduced from Experiments with the Pendulum. By
J. Ivory, M.A. F.R.S page 241

XL. Remarks on the Geology of the North Side of the Vale of
Pickering. By John Phillips, F.G.S., Keeper of the Museum of
the Yorkshire Philosophical Society. ( With a Plate.) „ 243

XLI. A new Theory of the Resistance of Fluids, compared with
the best Experiments. By Mr. Thomas Tredgold, Civil Engineer;
Hon. M. Inst. Civ. En., and of the Liter, and Phil. Society of New-.
castle-upon-Tyne. ( With a Plate.) 249

XLII. On Mr. Herapath's Second Attack on Lagrange's Method ;
by a /3 262

XLIII. On Systems and Methods in Natural History. By J. E.
Bicheno, Esq., F.R.S., Sec. L.S., &c 265

XLIV. Examination of a gelatinous Substance found in a damp
Meadow; — as a Contribution to the Knowledge of the Meteors called
Shooting-Stars. By Dr. R. Brandes 271

XLV. Description of a Percussion Rifle, igniting by a Spring in-
stead of aLock. By Lieut.-Col. Miller, F.R.S 277

XL VI. Account of an improved Form of Apparatus for exhi-
biting M. Clement Desormes's Experiments on Currents of Air, &c.
By Robert Younge, Esq 182

XLVII. Of the Insect called Oistros by the Ancients, and of the
true Species intended by them under this Appellation: in reply to
the Observations of W. S. MacLeay, Esq., and the French Natural-
ists. To which is added, A Description of a new Species of Cutere-
bra. By Bracy Clark, F.L.S., and Foreign Member of the Royal
Academy of Sciences of Paris 283

XL VI II. Notices respecting New Books: — Bakewell's Introduction
to Geology 289

XLIX. Proceedings of Learned Societies: — Linnaean Society;
Geological Society ; Proceedings at the Friday Evening Meetings of
the Royal Institution of Great Britain; Royal Academy of Sciences
of Paris 290—307

Obituary :— Sir J. E. Smith 307

L. Intelligence and Miscellaneous Articles: — Analysis of Alcohol,
xEther, &c. ; New Patents ; Meteorological Observations ; Tables,
ice 309—320

•#* It is requested that all Communications for this Work may be addressed,
post paid, to the Care of Mr. R. Taylor, Printer, Red- Lion-Court, Fleet-
Street, London.

This Day is published, in 12mo, with Plates, Price 8s. boards,

THE FIRST LINES OF PHILOSOPHICAL AND EXPERI-
MENTAL CHEMISTRY, including the recent Discoveries and
Improvements in that Science.

By J. S. FORSYTH,
Author of the Medical Pocket-Book, &c. &c.

In a few days by the same Author, THE FIRST LINES OF ANA-
LYTICAL AND EXPERIMENTAL MINERALOGY.

Sustenance and Stretch, Percy street, Bedford-square.

This Day is published, by W. Wood, 428, Strand, second edition, 8vo.
Price 21. 12s. 6d. plain; or with the Plates coloured, 51. 5s.

INDEX TESTACEOLOGICUS, or A Catalogue of Shells, Bri-
tish and Foreign, arranged according to the Linnaean System, with
the Latin and English Names, References to Authors, and Places where
found. Illustrated with 2300 figures.

By W. WOOD, F.R.S. F.L.S.,
Author of " Zoography," " General Conchology," &c. &c.

The figures contained in this volume are for the most part original,
and have been drawn from specimens with the greatest possible attention
to accuracy. All Shells, even the most minute, that have been noticed
as British by Montagu, Donovan, Walker, and others, as well as all the
Foreign Species described in the volumes of Martini and Chemnitz, &c,
have been introduced. The divisions of Lamarck have been added, and
his Genera referred to the figures in the Catalogue.

Also, A Supplement to the above, containing 480 figures of Shells,
chiefly nondescript, from the British Museum.

In 8vo, Price 10s. 6d. boards,
LEPIDOPTERA BRITANNICA, sistens Digestionem Novam In-
sectorum quae in Magna Britannia reperiuntur.

Auctore A. H. HA WORTH.

This Part concludes the work on British Lepidoptera, forming a Mono-
graph of the lesser Moths, and containing a complete Index of all the
Species.

This Day is published, Price Is. 6d.

THE ASTRONOMICAL DOCTRINE OF A PLURALITY OF
WORLDS irreconcilable with the popular Systems of Theology, but
in perfect Harmony with the true Christian Religion : being a Lecture
delivered April 13, 1828, at the New Jerusalem Church, Cross-Street,
Hatton Garden. With an APPENDIX, including additional Strictures
on Dr. Chalmers, and other of the principal Theological Writers on
the Subject.

By the Rev. S. NOBLE,

Author of" The Plenary Inspiration of the Scriptures asserted with a

view to the Refutation of all Infidel Objections;" and " An Appeal in

behalf of the Views and Doctrines of the New Jerusalem Church."

Printed for J. S. Hodson, 15, Cross-street, Hatton Garden: and sold

by W. Simpkin and R. Marshall, Stationers' Hall Court, Ludgate-street.

CONTENTS of N° 17.— New Series.

LI. On the Ellipticity of the Earth, as deduced from Experiments
with the Pendulum ; and on the Formulae employed for obtaining it.

By William Galbraith, Esq. A.M page 321

LII. Account of a Paper by Prof. Gauss, intitled" Disquisitiones
generates circa Supeijicies Curvas:" communicated to the Royal So-
ciety of Gottingen on the Sth of October 1827 331

LIN. On Savart's Experiments on the Motions of mediately agi-
tated Membranes. By Dr. Wm. Weber, Academical Teacher at

Halle. ( With a Plate.) 336

Supplement : — On the Employment of a resounding Membrane
for the Observation of the Interference of the Undulations of

Sound 342

L1V. On the Figure of the Earth, as deduced from Measurements
of different Portions of the Meridian. By J. Ivory, Esq. M.A. F.R.S. 343

LV. Mineralogical and Chemical Examination of the Diopside of
Fassa in the Tyrol. By Dr. H. Wackenroder, Professor of Che-
mistry at Gottingen 349

L VI. Description of a Shell, exploding by Percussion when trod
upon. By Lieut.-Col. Miller, F.R.S.. 358

LVII. Account of the Iron-Mine at Haytor, in Devonshire. By
J. T. Kingston, Esq 359

LVIII. Account of a new Method of mounting Thermometers.
By Mr. W. Mageough 365

LIX. Notices respecting New Books: — Horsfield's Descriptive
Catalogue of Lepidopterous Insects in the Museum of the East
India Company ; Haworth's Lepidoptera Britannica 368 — 370

LX. Proceedings of Learned Societies : — Royal Society ; Linnsean
Society ; Astronomical Society ; Proceedings at the Friday- Evening

Meetings of the Royal Institution of Great Britain 370 — 391

Obituary : — Sir J. E. Smith 39J

LXI. Intelligence and Miscellaneous Articles : — New Minerals;
Meteorological Observations ; Tables, &c 397—400

.%• It is requested that all Communications for this Work may be addressed,
post paid, to the Care of Mr. R. Taylor, Printer, Red- Lion-Court, Fleet-
Street, London.

CONTENTS or the PHILOSOPHICAL MAGAZINE and ANNALS.
Vol. I. — New Series. January — July 1827.

On the Elastic Force of Steam at different Temperatures. By J. Ivory, Esq.

M.A. F.R.S On the Identity of Epistilbite and Heulandite. By A. Levy, Esq.

M.A. F.G.S. — Reply to Mr. Galbraith's Remarks on the Experiments for ascertain-
ing the Velocity of Sound at Port Bowen. By Capt. VV. E. Parry, R.N. F.R.S.,
and Lieut. H. Foster, R.N. F.R.S. — Experiments on the Cohesion of Cast-iron.
By B. Bevan, Esq.— Table and Formulae for reducing Registers of the Height of
the Barometer to the Standard Temperature and Level. By Mr. J. Nixon. —
Further List of Errors in Piazzi's Catalogue of Stars.— On the Inflammation of
Gunpowder and other Substances by Electricity. By Mr. W. Sturgeon — On some
newly-discovered Siberian Minerals. By A. Levy, Esq. M.A. F.G.S. — Observations
on the Solar Eclipse, November 29th, 1826. By the Rev. Baden Powell, M.A.
F.R.S. — The Bakerian Lecture. On the Relations of Electrical and Chemical
Changes. By Sir H. Davy, Bart. Pres. R.S. — Observations on a Mineral from near
Hay Tor, in Devonshire. By C. Tripe, Esq. — Remarks on the Crystalline Form of
the Haytorite. By W. Phillips, F.G.S. &c— On the Origin of the Crystalline Forms
of the Haytorite. By A. Levy, Esq. M.A. F.G.S. — Astronomical Observations 1826.
By Lieut. Beaufoy, R.N. — A List of Moon-culminating Stars for 1827. By F. Baily,
Esq. F.R.S. — Observations on the late Solar Eclipse. By T. Squire, Esq. — On Fus-
tic, and its Application to Dyeing. By E. S. George, Esq. F.L.S. — On some new
auxiliary Tables for determining the apparent Places of Greenwich Stars. By
Francis Baily,Esq. F.R.S. — Investigation of the Heat extricated from Air when it unr
dergoes a given Condensation. By J. Ivory, Esq. M.A. F.R.S. — A Mode of Heating
Water for a Bath. By E. Deas Thompson, Esq.— On the Finite Extent of the At-
mosphere. By T. Graham, M. A. — On the Triple Prussiate of Potash. By R. Phil-
lips, F.R.S. L. & E.— On Capillary Attraction. By the Rev. J. B. Emmett.— A new
Method of Bleaching and preparing Flax. By the Rev. J. B. Emmett.— Description
of New Succulent Plants. By A. H. Haworth, Esq. F.L.S. — On the Accidents inci-
dent to Steam Boilers. By J. Taylor, Esq. F.R.S. — On the Crystalline Forms cf
Wagnerite. By A. Levy, Esq. M.A. F.G.S. — On Captain Party's and Lieut. Fos-
ter's Experiments for ascertaining the Velocity of Sound at Port Bowen. By W.
Galbraith, Esq. M.A. — Biographical Notice of M. Piazzi. — Continuation of the
Subject relating to the Absorption and Extrication of Heat in a Mass of Air that
changes itsVolume. By J. Ivory, Esq. M.A. F.R.S. — Notice relating to the Seconds
Pendulum at Port Bowen. By J. Ivory, Esq. M.A. F.R.S.— An Accountof M. Long-
ehamp's Theory of Nitrification j with an Extension of it. By T. Graham, M.A. —
A Sketch of the Natural Affinities of the Lepidojrtera Diuma of Latreille. By W.
Swainson, Esq. F.R.S. F.L.S. — On the Crystalline Form of the Hyalosiderite. By
W. Phillips, Esq. F.G.S. — Outlines of a Philosophical Inquiry into the Nature and
Properties of the Blood. By J. Spurgin, M.D. — On Contemporaneous Meteorolo-
gical Observations, as proposed by the Royal Society of Edinburgh. By T. Squire,
Esq. — On the expected Occultation of Venus in February. By T. Squire, Esq. —
Some Account of an Orang Outang of remarkable Height found on the Islawd of
Sumatra. By Clarke Abel, M.D. F.R.S.— Astronomical Observations 1827. By
Lieut. G. Beaufoy, R.N. — On a new Mineral Species. By A. Levy, Esq. M.A. F.G.S.
— Description of a Horizontal Pumping Engine erected on the Mine of Moran
in Mexico. By P. Taylor, Esq. — Analysis of a Sulphuretted Water from the
Northern Part of the Yorkshire Coal-field. By E. S. George, F.L.S. — Application
of the Variations of Temperature in Air that changes its Volume to account for
the Velocity of Sound. By J. Ivory, Esq. M.A. F.R.S. — Theory of the Spirit-Level.
By Mr. J. Nixon. — Observations on the Crystalline Form, &c. of the Gaylussite.
By W. Phillips, F.L.S. G.S.— New Phaenomena caused by the Eifect of Electric
Influence ; and Suggestions for ascertaining the Extent of the Terrestrial Magnetic
Atmosphere. By J. H. Abraham, F.L.S. — On the Geology of East Norfolk ;
with Remarks upon the Hypothesis of Mr. Robberds, respecting the former Level
of the German Ocean. By R. C. Taylor, Esq. F.G.S. — Astronomical Observations
1827. By Lieut. G. Beaufoy, R.N.— On the Orange Phosphate of Lead. By the Rev.
Win. V. Vernon, F.R.S. — Some Remarks on a Memoir by M. Poisson. By J. Ivory,
Esq. M.A. F.R.S.— On Capillary Attraction. By the Rev. J. B. Emmett.— On the
Velocity of Sound. By W. Galbraith, Esq. M.A. — Results of the Meteorological
Observations made at Wick, in Scotland. ByW. Burney, LL.D. — Remarks on Mr.
Sturgeon's Paper " On the Inflammation of Gunpowder by Electricity." By Mr.
Thomas Howldy. — On Chromate of Silver. By Mr. E. F. Teschemacher.

CONTENTS of N° 18.— New Series.

LXII. On the Artificial Production of Cold. By Richard

Walker, Esq., of Oxford. ( With a Plate.) .... page 401

LXIII. On the Causes of Single and Erect Vision. By L. M. S. 406

LXIV. On the Reaction of Effluent Water, and on the Maximum
Effect of Machines. By Mr. P. Ewart. With Notes relating to the
Theory of Barker's Mill. By J. Ivory, Esq. M.A. F.R.S 416

LXV. On the Figure of the Earth, as deduced from Measurements
of the Meridian. By J. Ivory, Esq. M.A. F.R.S 431

LXVI. On the characteristic Equation of Curve-surfaces capable
of being evolved in a Plane. By M. Fayolle 436

LXVII. Proceedings of Learned Societies :— Royal Society;
Linnsean Society ; Geological Society; Astronomical Society; Pro-
ceedings at the Friday-Evening Meetings of the Royal Institution
of Great Britain 436-456

LXVIII. Intelligence and Miscellaneous Articles :—- Origin of
Trap Rocks; Analyses of Tourmalines; Prof. Stromeyer's New
Method of separating Manganese from Lime and Magnesia ; Sin-
gular Action of Phosphoric Acid on Albumen; List of Earthquakes
which occurred in 1827; Red Rain supposed to arise from Butter-
flies ; Weather in Paris ; MM. Dumas and Boullay's Analysis of
Alcohol, iEther, &c. ; Test of the Presence of Ammonia ; List of New
Patents; Scientific Books; Meteorological Observations ; Table, &c.

458—469

Index : *70

• * It is requested that all Communications for this Work may be addressed,
post paid, to the Care of Mr. R. Taylor, Printer, Red- Lion-Court, Fleet-
Street, London.

>v^