HANDBOUND
AT THE

UNIVERSITY OF
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PHILOSOPHICAL
TRANSACTIONS,

OF THE

ROYAL SOCIETY

OF

LONDON.

FOR THE YEAR MDCCCII.

PART I. ::

LONDON,

PRINTED BY W. BULMER AND CO. CLEVELAND-ROW, ST. JAMES S ;
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AND PRINTERS TO THE ROYAL SOCIETY.
MDCCCII.

0

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895779

n "i 3

ADVERTISEMENT.

JL HE Committee appointed by the Rojral Society to direct the pub-
lication of the Philosophical Transactions, take this opportunity to
acquaint the Public, that it fully appears, as well from the council-
books and journals of the Society, as from repeated declarations which
have been made in several former Transactions, that the printing of
them was always, from time to time, the single act of the respective
Secretaries, till the Forty-seventh Volume : the Society, as a Body,
never interesting themselves any further in their publication, than by
occasionally recommending the revival of them to some of their Se-
cretaries, when, from the particular circumstances of their affairs, the
Transactions had happened for any length of time to be intermitted.
And this seems principally to have been done with a view to satisfy
the Public, that their usual meetings were then continued, for the im-
provement of knowledge, and benefit of mankind, the great ends of
their first institution by the Royal Charters, and which they have ever
since steadily pursued.

But the Society being of late years greatly enlarged, and their com-
munications more numerous, it was thought advisable, that a Com-
mittee of their members should be appointed, to reconsider the papers
read before them, and select out of them such as they should judge
most proper for publication in the future Transactions ; which was
accordingly done upon the 26th of Maixh, 1752. And the ground*

A 2

of their choice are, and will continue to be, the importance and sin-
gularity of the subjects, or the advantageous manner of treating them ;
without pretending to answer for the certainty of die facts, or pro-
priety of the leasonings, contained in the several papers so published,
which must still rest on the credit or judgment of their respective
authors.

It is likewise necessary on this occasion to remark, that it is an esta-
blished rule of the Society, to which they will always adhere, never to
give their opinion, as a Body, upon any subject, either of Nature or
Art, that comes before them. And therefore the thanks which are
frequently proposed from the Chair, to be given to the audiors of such
papers as are read at their accustomed meetings, or to the persons through
whose hands they receive them, are to be considered in no other light
than as a matter of civility, in return for the respect shewn to the So-
ciety by those communications. The like also is to be said with re-
gard to the several projects, inventions, and curiosities of various
kinds, which are often exhibited to the Society; the authors whereof,
or those who exhibit them, frequently take the liberty to report, and
even to certify in the public news-papers, that they have met with the
highest applause and approbation. And therefore it is hoped, that no
regard will hereafter be paid to such reports and public notices ; which
in some instances have been too lightly credited, to the dishonour of
the Society.

CONTENTS.

I. T^UE Croo7iian Lecture. On the Pozver of the Eye to adjust
itself to different Distances, when deprived oj the Crystalline
Lens. By Everard Home, Esq. F. R. S. page i

II. The Bakerian Lecture. On the Theory of Light and Colours.
By Thomas Young, M. D. F. R. S. Professor of Natural Phi-
losophy in the Royal Institution. p. 12

III. An Analysis of a mineral Substance from North America,
containing a Metal hitherto unknown. By Charles Hatchett,
Esq. F. R. S. p. 49

IV. A Description of the Anatomy of the Ornithorhynchus
paradoxus. By Everard Home, Esq. F. R. S. p. 67

V. On the Independence of the analytical and geometrical Methods
of Livestigaiion ; and on the Advantages to be derived from
their Separation. By Robert Woodhouse, A. M. Fellow of
Caius College, Cambridge. Communicated by Joseph Planta,
Esq. Sec. R. S. p. 85

VI. Observations and Experiments upon oxygenized and hyper-
oxygenized ?nuriatic Acid; and tipon some Combinations of the
muriatic Acid in its three States. By Richard Chenevix, Esq.
F.R.S. and M. R. LA. p. 126

VII. Experiments and Observations on certain stojiy ajid metalline
Substances, xvhich at different Titnes are said to have fallen on
the Earth ; also on various Kifids of native Iron. By Edward
Howard, Esq. F. R. S. p. 168

C vi3

APPENDIX.

Meteorological Journal kept at the Apartments of the Royal
Society, by Order of the President and Council.

THE President and Councii. of the Royal Society adjudged,
for die year 1801, die Medal on Sir Godfrey Copley's Donation,
to Mr. Astley Cooper, for his Papers On the Effects which take
place from die Destruction of the Membrana Tympani of the Ear ;
with an Account of an Operation for the removal of a particular
species of Deafness.

ERRATA.

Page 133, line 2 and 3, /or 38,3, read 383.

■ 134, — penult, for hyperoxygenized, rrad oxygenized-

PHILOSOPHICAL
TRANSACTIONS.

I, The Croonian Lecture. On the Power of the Eye to adjust
itself to different Distances, when deprived oj the Crystalline
Lens. By Everard Home, Esq. F.R. S.

Read November 5, 1801.

It is intended, on the present occasion, to state some facts and
observations, in support of an opinion advanced in a former
lecture, that the adjustment of the eye to see objects at different
distances, does not depend upon any internal changes in the
crystalline lens.

The first of the experiments which will be stated, was made
with the assistance of the late Mr. Ramsden; and, had not
the death of that valuable member of this Society deprived me of
his further aid, the following observations would undoubtedly
have been more deserving the attention of my learned audience.

It is impossible for me to mention Mr. Ramsden, from whom
I have received so much assistance in every pursuit connected
with optics and mathematics, in which I have been engaged,

MDcccn. B

2 Mr. Home's Lecture on the Power of the Eye,

without availing myself of this opportunity of paying that tribute
of gratitude to his memory, v/hich feelings of delicacy prevented
me from offering to liim v^hile alive. It is unnecessary here to
mention his genius, his merits, qr his exertions for the promo-
tion of science ; these are equally well known to every member
present, as to myself. It is only my individual obligations, in
the prosecution of inquiries connected with the objects of this
learned Society, that are meant to be taken notice of

To his friendly and zealous assistance I am indebted for the
information which was necessary to enable me to prosecute
investigations upon the subject of vision ; and, without such
assistance, I should have shrunk from the inquiry. It is also
to his early friendship, and his readiness to communicate to me
his knowledge, that I look back, as among the sources of my
early exertions, and love of philosophical pursuits.

In the year 1794,, I laid before this learned Society some
experiments, suggested and made by Mr. Ramsden, upon the
comparative powers of adjustment of the eye, when in a perfect
state, and when deprived of the crystalline lens. From the
result of these experiments it appeared, that the removal of the
lens did not deprive the eye of the power of seeing distinctly at
diHerent distances. As the person upon whom the experiments
were tried did not see very distinctly, without a substitute for
the lens, in making them, a double convex glass, of 2^ inches
focus, was placed before his eye ; and, to render the image dis-
tinct, by correcting the spherical aberrations, the aperture was
diminished to ~ths of an inch ; a less degree of diminution
not answering that purpose.

The subject of these experiments was Benjamin Clekk,
twenty-one years of age ; one of iiis eyes was in a very i)erfect

when deprived of the Crystalline Lens. 3

state, and the other without defect, except wiiat arose from the
removal of the lens : and the resuks appeared to be satisfactory
in deciding, that the eye, when deprived of the crystalline lens,
retains a power of adjustment.

Opportunities of instituting experiments of this kind very
rarely occur ; the patients who have had their lenses extracted,
either not seeing sufficiently well, or being too much advanced
in life to be fit subjects for that purpose; but, in the year 1798,
the following case came under my care, which enabled me to
make some further observations, in confirmation of the former
experiments.

Henry Miles, a carpenter, at Westborough Green in Sussex,
fifty years of age, applied, in the month of August, 1 798, at
St. George's Hospital, to be admitted as a patient, on account of
blindness, from having a cataract in each eye ; and was received
under my care. Both the cataracts were extracted ; and tlie
eyes recovered from the effects of the operation, without suffer-
ing from inflammation. The right eye had the power of seeing
objects with unusual distinctness ; but the left was less perfect,
the iris having been slightly torn, by the lens being too big to
pass through the aperture, without injuring the membrane.

As soon as this man's eyes had recovered, I requested Mr.
Ramsden to repeat some of the former experiments, on his right
eye; which he readily agreed to do. Before tlie experiments
were made, upon trying what was his power of vision with the
naked eye, we were agreeably surprised to find that he saw
so distinctly, as to admit of our ascertaining, without the aid of
glasses, what were the ranges of his eye's adjustment. [^

A piece of pasteboard, with a letter of a moderate size, as an
object upon it, was put into his hands ; as he could not read, the

Ba

4 Mr. Home's Lecture on the Poiver of the Eye,

page of a book might have confused him : he was directed to
vary the distance of the pasteboard from liis eye, till he had
ascertained the nearest and most distant situations, in which the
object appeared distinct; these distances, by measurement, were
7 inches, and 18 inches. In repeating this experiment several
different times, he brought tiie object very correctly to the same
situations.

This result convinced Mr. Ramsden, that the eye possessed
the power of varying its adjustment ; and he did not think any
more complex experiments would be nearly so satisfactory;
consequently, no others were made, and the man was allowed
to go into the country.

It was intended to make him a present of a pair of spectacles,
allowing him to choose those best adapted to his eye ; but his
sight was so very good, that we entirely forgot it, till some time
after he was gone.

These experiments confirmed the former ones so very strong-
ly, and from their simplicity were so much less liable to error,
that Mr. Ramsden and myself considered the object of our
inquiry completely attained ; the reason for not, at the time,
laying them before this' learned Society was, that they estab-
lished no new fact, and the former ones did hot appear to require
their support. "'" ^' ' : ■ ■

This inquiry, always regarded as highly important by phy-
siologists, has continued to engage their attention ; and, in the
Bakerian Lecture for last year. Dr. Young has advanced some
experiments to prove, that the adjustment of the eye to different
distances, depends upon the cry stallhie lens : he considers the
results of the experiments made by Mr. Ramsden, upon Ben-
jamin Clerk's eyes, as inconclusive ; and the phenomena met

when deprived of the Crystalline Lens. 5

with, as arising from the smaUness of the aperture, and not from
any power of adjustment in the eye. Dr. Young, therefore,
with a view to obviate all possibility of deception in future,
constructed an optometer, upon the principle of that of Dr.
PoRTERFiELD. In this instrument, when applied to presbyopic
eyes, the eye, by looking along a line through a small convex
lens, before which is placed a card with two narrow slits in it,
near enough to each other to be within the limits of the pupil,
will see the line as two lines, crossing each other at the point
of perfect vision ; and every eye that has the power of adjust-
ment, will make the lines cross in different places, when adjusted
to different distances.

With this instrument. Dr. Young made experiments upon
several eyes which had been deprived of the crystalline lens ;
and with all of them found, that the crossing of the lines was
seen only at one point ; he therefore concludes, that the power
of adjustment was lost.

These experiments of Dr. Young led me to reconsider the
subject; and it was matter of regret that Benjamin Clerk
was not in this country, as making a trial with the optometer
on his eye, would have determined, in the most satisfactory
manner, whether there had been a fallacy in the former expe-
riments.

This not being in my power, I made inquiry after Henry
Miles, upon whom the second experiments were tried ; and I
had the pleasure to hear, that he was in good health, and that
his eyes continued to have very distinct vision, so much so, that
he never had occasion to make use of any glasses, from the time
the operation had been performed.

With the view of making some experiments on this man's eyes,
with Dr. Young's optometer, I procured that instrument from

6 Mr. Home's Lecture on the Power of the Eye,

Mr. Gary, the optician, made exactly in the same manner aS
that which had been executed under Dr. Young's direction. I
first, however, tried the exjxjriments upon my own eye ; but liad
the mortification to find myself unable to make the lines cross
in two diflferent situations. This led me to try the eyes of
several of my friends ; who were equally unable to make the
lines cross any where, except at one point. Young people,
indeed all those under thirty years of age, wc;e capable of vary-
ing the place of intersection ; but none who were above forty,
could produce any change in it.

As 1 could not doubt of my own eye having the power of
varying its adjustment, I was led to believe that the instrument
required some address in the management, which I had not
acquired; and therefore despaired of making Henry Miles
sufficiently master of it, to do justice to my views.

To obviate these difficulties, I adapted the optometer, without
the lens, to presbyopic eyes, by making a line 4, feet long,
upon strong paper, divided into inches, and having the same
slits to look through as in the other. This instrument, and
Dr. Young's, I put into the hands of my friend Sir Henry
Englefield, with a request that he would examine them, and,
when he had become perfectly master of them, and of the best
mode of using them, that he would assist me in making expe-
riments with them ; for, as he was more in the habit of chang-
ing the focus of his eye, in using optical instruments, he would
more readily detect the circumstance which prevented me from
succeeding in the experiment.

After several trials with this optometer, and seeing its de-
fects, Sir Henry Englefield improved it, by having the
paper pasted upon a strong board, 4, feet long, which rendered
the surface free from the slightest inequalities ; and, instead of

zvben deprived of the Crystalline Lens. 7

a line marked with ink, a thread of black silk was stretched
along the middle of the board. With this instrument, he found
that his eye could make the lines cross at two different points,
at several inches distance from each other. The readiest mode
of making the experiment succeed, was first fixing his eye
upon some near object, held above and a little on one side of
the silk thread, and, when the focus of his eye was adapted
to that distance, then to look at the thread ; afterwards to look
at some distant object, and, when that had become very dis-
tinct, again to look at the thread. Upon trying the instru-
ment with my own eye, in this way, I found the crossing of
the lines changed its situation, with every change of adjust-
ment; and, after being accustomed to make this experiment, I
was enabled to produce a similar change in the optometer with
the lens, but by no means in so satisfactory a manner, nor did
it last more than an instant ; my eye probably not being so well
fitted as many others, for experiments of this kind.

The optometer without the lens was hence admitted to be
the most easily managed, by the eye of a person unaccustomed
to such experiments, and therefore it was determined to make
use of it in the trials upon Henry Miles's eye ; which we were
enabled to do, as his vision was sufficiently distinct without the
aid of glasses, and as, from never having used them, he saw
much better with his naked eye.

The following experiments were made with the optometer
v/ithout the lens, on the 27th of August, 1801.

The first trials were upon Sir Henry Englefield's eye;
which, being most familiar with the use of the instrument, be-
came a standard with which the others might be compared.

Sir Henry Einglefield's eye made the lines to intersect

8 Mr. Home's Lecture on the Power of the Eye,

each other at 12^ inches, as the near distance; and at 28|-
inches, as the furthest distance. The experiment was repeated
several different times, and the results were very nearly the
same.

My own eye made the lines intersect at i2|- inches, as the
near distance ; and at 29^ inches, as the furthest distance.

A man servant of Sir Henry Englefield's, twenty-five years
of age, made the lines intersect at 12 inches, and at 31^ inches.

Henry Miles, fifty years of age, whose eye had been de-
prived of the crystalline lens for three years, made the lines
intersect at 8^ inches, as the near distance; and at 13^, as
the furthest distance.

This experiment was repeated two different times in the fore-
noon, with the same result, and again in the afternoon, without
there being any considerable variation; but, upon trying it
again, after the eye had been fatigued, he was unable to make
the lines cross nearer than 1 1| inches, although he could make
them cross at iSto hiches; so that adjusting the eye to a
near distance, was more difficult after it had been much used,
than before.

Henry Miles was unable, in the optometer with the lens, to
produce any change in the crossing of the lines, nor did he see
them cross with sufficient distinctness to make us consider it a
fair experiment.

The following experiment was made upon Miles's eye, at
the suggestion of Sir Henry Englefield, with a view to ascer-
tain in another though less decisive way, whether any change
took place in it, \\ hen directed from a near object to a more
distant one.

A piece of pasteboard, in which a black circle, about ^ of an

when deprived of tJje Oystalline 'Lem. g

inch in diameter, with a dot in the centre, had been described
near to its edge, was placed perpendicularly to the horizon, at
5 inches distance from the eye ; another piece of pasteboard,
with a circle and dot in it, was placed at the distance of 18
inches ; the farthest circle was made a little larger than the
other, that it might appear equally distinct at the greater dis-
tance. When the eye was directed towards these two objects,
they appeared upon the same level ; and the circumference of
the circles, had they been projected on the same perpendicular
plane, would have been nearly in contact.

Miles was placed opposite these objects, with his head made
steady, and prevented from moving : he was then told to look
at one, till it became very distinct ; and, when he had done so,
this was removed, and he was directed to look at the other,
which did not immediately appear to him with the same dis-
tinctness. Tills was equally the case, whether he looked from
the near one to the distant one, or the reverse : the eye did
not see the object to which it was so suddenly directed, with
the same defined outline as that from which it had been with-
drawn.

This man sees best in a strong light ; and it was in that light
all the experiments were made : he can see very well in any
degree of daylight ; but his eyes are much fatigued by candle-
light. Upon examining the eye attentively, the pupil was rather
larger than in perfect eyes ; the iris was in a very perfect state ;
and the cicatrix of the wound, in the inferior part of the cornea,
was scarcely visible.

The sight being so good, without the aid of glasses, is not
common; and, had not the lenses been extracted in a public

MDCCCII. C

lo Mr. Home's Lecture on the Power of the Eye,

hospital, before a number of spectators, some doubts might be
entertained whether they had been i-emoved.

From the experiments which have been stated, it appeared to
Sir Henky Englefield, that Miles's eye was not deprived of
its power of adjustment ; and, by whatever circumstances my
own judgment might be deceived, or rendered partial, there was
nothing by which his could be biassed, as he could have no
object in view, but the promotion of science. His knowledge
of optics, and his habit of making experiments, are the best
pledges of these having been as accurately performed as the
nature of the subject admits of; for, certainly, the sources of
fallacy, in optical experiments, are numerous. Those that have
been related, to be made with perfect accuracy, should be tried
upon the eye of a person skilled in optics, and accustomed to
such experiments ; and whose eye had been deprived of the
crystalline lens, without having received the slightest degree of
injury in any of its other parts.

The experiments were instituted in the Isle of Wight, which
prevented me from requesting several of my friends to be pre-
sent at them, whose knowledge of the subject would have made
me desirous of their assistance.

Haller mentions the case of a nobleman, from whose eye
the crystalline lens had been extracted, who used glasses, and
could see with them objects at different distances. As this was
an observation made upon a particular friend of his own, and
as he refers to Pe.mberton, who mentions a case of depressed
crystalline lens, in which no such effect took place, it is natural
to suppose, that he had given considerable attention to the
subject; and that, although the experiments he instituted are

when deprived of th Crystalline Lens. ii

not mentioned, the opinion was not advanced, without what
appeared to liim sufficient authority.*

• Et lente ob cataractam extracta vel deposita, oculum tamen ad varias distantias
videre, ut coram in nobili viro video, absque uUo experimento, quo earn facultatcm
recuperaverit. Et si eiiim tunc, ob diminutas vires, qua: radios uniunt, aeger lente
vitrea opus habet, eadem lens in omnia distantia sufficit.

Haller. Elementa Pbysiologia. Tom. V. Lib. xvi. §. 25. p. 514,

C 2

n i« D

II. The Bakerian Lecture. On the Theory of Light and Colours.
By Thomas Young, M. D. F. R. S. Professor of Natural Phi-
losophy in the Royal Institution.

Read November 12, 1801.

Although the invention of plausible hypotheses, independent
of any connection with experimental observations, can be of
very little use in the promotion of natural knowledge ; yet the
discovery of simple and uniform principles, by which a great
number of apparently heterogeneous phenomena are reduced
to coherent and universal laws, must ever be allowed to be of
considerable importance towards the improvement of the human
intellect.

The object of the present dissertation is not so much to pro-
pose any opinions which are absolutely new, as to refer some
theories, which have been already advanced, to their original
inventors, to support them by additional evidence, and to apply
them to a great number of diversified facts, which have hitherto
been buried in obscurity. Nor is it absolutely necessary in this
instance to produce a single new experiment; for of experi-
ments there is already an ample store, which are so much the
more unexceptionable, as they must have been conducted with-
out the least partiality for the system by which they will be
explained ; yet some facts, hitherto unobserved, will be brought
forwards, in order to show the perfect agreement of that system
with the multifarious phenomena of nature.

Dr. Young's Lecture, &c, 13

The optical observations of Newton are yet unrivalled ; and,
excepting some casual inaccuracies, they only rise in our esti-
mation, as we compare them with later attempts to improve
on them. A further consideration of the colours of thin plates,
as they are described in the second book of Newton's optics,
has converted that prepossession which I before entertained for
the undulatory system of light, into a very strong conviction of
its truth and sufficiency; a conviction which has been since most
strikingly confirmed, by an analysis of the colours of striated
substances. The phenomena of thin plates are indeed so sin-
gular, that their general complexion is not without great diffi-
culty reconcileable to any theory, however complicated, that
has hitherto been apphed to them ; and some of the principal
circumstances have never been explained by the most gratuitous
assumptions; but it will appear, that the minutest particulars of
these phenomena, are not only perfectly consistent with the
theory which will now be detailed, but that they are all the
necessary consequences of that theory, without any auxiliary
suppositions; and this by inferences so simple, that they be-
come particular corollaries, which scarcely require a distinct
enumeration.

A more extensive examination of Newton's various writings
has shown me, that he was in reality the first that suggested
such a theory as I shall endeavour to maintain ; that his own
opinions varied less from this theory than is now ahnost uni-
versally supposed ; and that a variety of arguments have been
advanced, as if to confute him, which may be found nearly in
a similar form in his own works ; and this by no less a mathe-
matician than Leonard Euler, whose system of light, as far
as it is worthy of notice, either was, or might have been,

14 Dr. Young's Lecture on

wholly borrowed from Newton, Hooke, Huygens, and Male-

BRANCHE.

Those who are attached, as they may be with the greatest
justice, to every doctrine which is stamped with the Newtonian
approbation, will probably be disposed to bestow on these con-
siderations so much the more of their attention, as they appear
to coincide more nearly with Newton's own opinions. For
this reason, after having briefly stated each particular position
of my theory, I shall collect, from Newton's various writings,
such passages as seem to be the most favourable to its admis-
sion ; and, although I shall quote some papers which may be
thought to have been partly retracted at the publication of the
optics, yet I shall borrow nothing from them that can be sup-
posed to militate against his maturer judgment.

hypothesis I.

A luminiferous Ether pervades the Universe, rare a?id elastic in a

high degree.

Passages Jrom Newton.

" The hypothesis certainly has a much greater affinity with
" his own," that is. Dr. Hooke's, " hypothesis, than he seems
" to be aware of; the vibrations of the ether being as useful and
" necessary in this, as in his." (Phil. Trans. Vol. VII. p. 5087,
Abr. Vol. I. p. 14,5. Nov. 1672.)

" To proceed to the h3'pothesis : first, it is to be supposed
" therein, that there is an ethereal medium, much of the same
" constitution with air, but far rarer, subtler, and more strongly
" elastic. — It is not to be supposed, that this medium is one
" uniform matter, but compounded, partly of the main phleg-
" matic body of ether, partly of other various ethereal spirits.

the Theory of Light and Colours, 15

" much after the manner that air is compounded of the phleg-
" matic body of air, intermixed with various vapours and
" exhalations : for the electric and magnetic effluvia, and gravi-
" tating principle, seem to argue such variety." (Birch: Hist, of
R. S. Vol. III. p. 249. Dec. 167J.)

" Is not the heat (of the warm room) conveyed through the
" vacuum by the vibrations of a much subtiler medium than air?
" — And is not this medium the same with that medium by which
" light is refracted and reflected, and by whose vibrations light
" communicates heat to bodies, and is put into fits of easy re-
" flection, and easy transmission .'' And do not the vibrations of
" this medium in hot bodies, contribute to the intenseness and
" duration of their heat ^ And do not hot bodies commiUnicate
" their heat to contiguous cold ones, by the vibrations of this me-
" dium propagated from them into the cold ones ? And is not this
" medium exceedingly more rare and subtile than the air, and
" exceedingly more elastic and active .'' And doth it not readily
" pervade all bodies ^ And is it not, by its elastic force, expanded
" through all the heavens ^ — May not planets and comets, and
" all gross bodies, perform their motions in this ethereal me-
" dium } — And may not its resistance be so small, as to be
" inconsiderable.? For instance, if this ether (for so I will call
" it) should be supposed 700,000 times more elastic tlian our
" air, and above 700,000 times more rare, its resistance would
" be about 600,000000 times less than that of water. And
" so small a resistance would scarce make any sensible altera-
*' tion in the motions of the planets, in ten thousand years.
" If any one would ask how a medium can be so rare, let him
" tell me — how an electric body can by fnction emit an exha-
« lation so rare and subtile, and yet so potent ? — And how the

i6 Dr. Young's Lecture on

" effluvia of a magnet can pass through a plate of glass, with-
" out resistance, and yet turn a magnetic needle beyond the
" glass?" (Optics, Ou. 18, 22 )

HYPOTHESIS II.

Undulations are excited in this Ether whenever a Body becomes
luminous.
Scholium. I use the word undulation, in preference to vibra-
tion, because vibration is generally understood as implying a
motion which is continued alternately backwards and forwards,
by a combination of the momentum of the body with an acce-
lerating force, and which is naturally more or less permanent ;
but an undulation is supposed to consist in a vibratory motion,
transmitted successively through different parts of a medium,
without any tendency in each particle to continue its motion,
except in consequence of the transmission of succeeding undu-
lations, from a distinct vibrating body ; as, in the air, the vibra-
tions of a chord produce the undulations constituting sound.

Passages from Newton,

" Were I to assume an hypothesis, it should be this, if pro-
" pounded more generally, so as not to determine what light is,
" further than that it is something or other capable of exciting
** vibrations in the ether ; for thus it will become so general and
" comprehensive of other hypotheses, as to leave little room for
" new ones to be invented." (Birch. Vol. III. p. 249. Dec. 1675.)

" In the second place, it is to be supposed, that the ether is a
" vibrating medium like air, only the vibrations far more swift
" and minute; those of air, made by a man's ordinary voice,
" succeeding one another at more than half a foot, or a foot

the Theory of Light and Colours. 1 7

" distance ; but those of ether at a less distance than the hun-
" dred thousandth part of an inch. And, as in air the vibra-
" tions are some larger than others, but yet all equally swift,
" (for in a ring of bells the sound of every tone is heard at two
" or three miles distance, in the same order that the bells are
"struck,) so, I suppose, the ethereal vibrations differ in big-
" ness, but not in swiftness. Now, these vibrations, beside their
" use in reflection and refraction, may be supposed the chief
" means by which the parts of fermenting or putrifying sub-
" stances, fluid liquors, or melted, burning, or other hot bodies,
" continue in motion." (Birch Vol. Ill, p. 251. Dec. 1675.)

" When a ray of light falls upon the surface of any pellucid
" body, and is there refracted or reflected, may not waves of
" vibrations, or tremors, be thereby excited in the refracting or
" reflecting medium } — And are not these vibrations proj^agated
" from the point of incidence to great distances ? And do they
" not overtake the rays of light, and by overtaking them suc-
" cessively, do not they put them into the fits of easy reflection
" and easy transmission described above ':" (Optics. Qu. 17.)

'• Light is in fits of easy reflection and easy transmission,
" before its incidence on transparent bodies. And probably it is
" put into such fits at its first emission from luminous bodies,
" and continues in them during all its progress." (Optics.
Second Book. Part III. Prop. 13.)

MDCCCII. D

i8 Dr. Young's Lecture on

HYPOTHESIS HI.

The Sensation of different Colours depends on the different fre-
quency of Vibrations, excited by Light in the Retitia.

Passages from Newton.
" The objector's hypothesis, as to the fundamental part of it,
" is not against me. That fundamental supposition is, that the
" parts of bodies, when briskly agitated, do excite vibrations in
" the ether, which are propagated every way from those bodies
" in straight lines, and cause a sensation of light by beating
" and dashing against the bottom of the eye, something after
" the manner that vibrations in the air cause a sensation of
" sound by beating against the organs of hearing. Now, the
" most free and natural application of this hypothesis to the
" solution of phenomena, I take to be this : that the agitated
" parts of bodies, according to their several sizes, figures, and
" motions, do excite vibrations in the ether of various depths
" or bignesses, which, being promiscuously propagated through
" that medium to our eyes, effect in us a sensation of light of a
•* white colour ; but if by any means those of unequal bignesses
" be separated from one another, the largest beget a sensation
" of a red colour, the least or shortest of a deep violet, and
" the intermediate ones of intermediate colours ; much after
" the manner that bodies, according to their several sizes,
" shapes, and motions, excite vibrations in the air of various
" bignesses, which, according to those bignesses, make several
" tones in sound : that the largest vibrations are best able to
" overcome the resistance of a refracting superficies, and so
" break through it with least refraction ; whence the vibrations

the Theory of Light and Colours. 19

« of several bignesses, that is, the rays of several colours, which
" are blended together in light, must be parted from one an-
« other by refraction, and so cause the phenomena of prisms,
" and other refracting substances ; and that it depends on the
" thickness of a thin transparent plate or bubble, whether a
«' vibration shall be reflected at its further superficies, or trans-
" mitted ; so that, according to the number of vibrations, inter-
" ceding the two superficies, they may be reflected or transmitted
" for many successive thicknesses. And, since the vibrations
" which make blue and violet, are supposed shorter than those
" which make red and yellow, they must be reflected at a less
" thickness of the plate : which is sufficient to explicate all the
" ordinary phenomena of those plates or bubbles, and also of
" all natural bodies, whose parts are like so many fragments of
" such plates. These seem to be the most plain, genuine, and
" necessary conditions of this hypothesis. And they agree so
" justly with my theory, that if the animadversor think fit to
« apply them, he need not, on that account, apprehend a divorce
" from it. But yet, how he will defend it from other difficulties,
" I know not." (Phil. Trans. Vol. VII. p. 5088. Abr. Vol. I.
p. 145. Nov. 1672.)

" To explain colours, I suppose, that as bodies of various
" sizes, densities, or sensations, do by percussion or other
" action excite sounds of various tones, and consequently vi-
*« brations in the air of diflTerent bigness ; so the rays of light,
" by impinging on the stiff" refracting superficies, excite vibra-
« tions in the ether, — of various bigness ; the biggest, strongest,
" or most potent rays, the largest vibrations ; and others shorter,
" according to their bigness, strength, or power: and therefore
" tlie ends of the capillamenta of the optic nerve, which pave

D 2

20 Dr. Young's Lecture on

" or face the retina, being such refracting superficies, when the
" rays impinge upon them, they must there ej^cite these vibra-
" tions, which vibrations (hke those of sound in a trunk or
" trumpet) will run along the aqueous pores or crystalline pith
" of tile capillamenta, through the optic nerves, into the senso-
" rium ; — and there, I suppose, aft'ect the sense with various
" colours, according to their bigness and mixture ; the biggest
" with the strongest colours, reds and yellows ; the least with
" the weakest, blues and violets ; the middle with green ; and a
" confusion of all with white, much after the manner that, in
" the sense of hearing, nature makes use of aerial vibrations of
" several bignesses, to generate sou'nds of divers tones ; for the
" analogy of nature is to be observed." (Birch Vol, III. p. 262.
Dec. 1675.)

" Considering the lastingness of the motions excited in the
" bottom of the eye by light, are they not of a vibrating nature ?
" — Do not the most refrangible rays excite the shortest vibra-
" tions, — the least refrangible the largest ? May not the harmony
" and discord of colours arise from the proportions of the vibra-
" tions propagated through the fibres of the optic nerve into
" the brain, as the harmony and discord of sounds arise from
*' the proportions of the vibrations of the air ?" (Optics, Qu.
16, 13, 14.)

Scholium. Since, for the reason here assigned by Newton,
it is probable that the motion of the retina is rather of a vibra-
tory than of an undulatory nature, the frequency of the vibrations
must be dependent on the constitution of this substance. Now,
as it is almost impossible to conceive each sensitive point of the
retina to contain an infinite number of particles, each capable
of vibrating in perfect unison with every possible undulation, it

the Theory of Light and Colours. 2 1

becomes necessary to suppose the number limited, for instance,
to the three principal colours, red, yellow, and blue, of which
the undulations are related in magnitude nearly as the numbers
8, 7, and 6 ; and that each of the particles is capable of being
put In motion less or more forcibly, by undulations differing
less or more from a perfect unison ; for instance, the undula-
tions of green light being nearly in the ratio of 6^, will affect
equally the particles in unison with yellow and blue, and pro-
duce the same effect as a light composed of those two species :
and each sensitive filament of the nerve may consist of three
portions, one for each principal colour. Allowing this statement,
it appears that an}^ attempt to produce a musical effect from
colours, must be unsuccessful, or at least that nothing more
than a very simple melody could be imitated by them; for the
period, which in fact constitutes the harmony of any concord,
being a multiple of the periods of the single undulations, would
in this case be wholly without the limits of sympathy of the
retina, and would lose its effect; in the same manner as the
harmony of a third or a fourth is destroyed, by depressing it to
the lowest notes of the audible scale. In hearing, there seems
to be no permanent vibration of any part of the organ.

HYPOTHESIS IV.

All material Bodies have an Attraction for the ethereal Medium^
by means ofxvhich it is accumulated zvithin their Substance, and
for a small Distance around them, in a Sl^te of greater Density,
but not of greater Elasticity.

It has been shewn, that the three former hypotheses, which
may be called essential, are literally parts of the more compli-
cated Newtonian system. This fourth hypothesis differs perhaps

22 Dr. Young's Lecture on

in some degree from any that have been proposed by former
authors, and is diametrically opposite to that of Newton ; but,
both being in themselves equally probable, tne opposition is
merely accidental ; and it is only to be inquired which is the
best capable of explaining the phenomena. Other suppositions
might perhaps be substituted for this, and therefore I do not
consider it as fundamental, yet it appears to be the simplest and
best of any that have occurred to me.

PROPOSITION I.

All Impulses are propagated in a homogeneous elastic Medium
with an equable Velocity.
Every experiment relative to sound coincides with the obser-
vation already quoted from Newton, that all undulations are
propagated through the air witli equal velocity; and this is
further confirmed by calculations. (Lagrange. Misc. Taur.
Vol. I. p. 91. Also, much more concisely, in my Syllabus of a
course of Lectures on Natural and Experimental Philosophy,
about to be published. Article 289. ) If the impulse be so great
as materially to disturb the density of the medium, it will be no
longer homogeneous ; but, as far as concerns our senses, the
quantity of motion may be considered as infinitely small. It is
surprising that Euler, although aware of the matter of fact,
should still have maintained, that the more frequent undulations
are more rapidly propagated. (Theor. mus. and Conject. phys.)
• It is possible, that the actual velocity of the particles of the
luminiferous ether may bear a much less proportion to the velo-
city of the undulations than in sound ; for light may be excited
by the motion of a body moving at the rate of only one mile
in the time that light moves a hundred millions.

the Theory of Light and Colours. 23

Scholiutn 1. It has been demonstrated, that in different
mediums the velocity varies in the subduphcate ratio of the
force directly, an9 of the density inversely. (Misc. Taur. Vol. I.
p. 91. Young's Syllabus. Art. 294.)

Scholium 2. It is obvious, from the phenomena of elastic
bodies and of sounds, that the undulations may cross each other
without interruption. But there is no necessity that the various
colours of white light should intermix their undulations ; for,
supposing the vibrations of the retina to continue but a five hun-
dredth of a second after their excitement, a million undulations
of each of a million colours may arrive in distinct succession
within this interval of time, and produce the same sensible
effect, as if all the colours arrived precisely at the same instant,

PROPOSITION II.

An Undulation conceived to originate from the Vibration of a
single Particle, must expand through a homogeneous Medium
in a spherical Form, but xvith differetit quantities of Motion in
different Parts.

For, since every impulse, considered as positive or negative,
is propagated with a constant velocity, each part of the undu-
lation must in equal times have past through equal distances
from the vibrating point. And, supposing the vibrating particle,
in the course of its motion, to proceed forwards to a small dis-
tance in a given direction, the principal strength of the undula-
tion will naturally be straight before it ; behind it, the motion
will be equal, in a contrary direction ; and, at right angles to
the line of vibration, the undulation will be evanescent.

Now, in order that such an undulation may continue its pro-
gress to any considerable distance, there must be in each part
of it, a tendency to preserve its own motion in a right line from

24( Dr. Young's Lecture on

the centre ; for, if the excess of force at any part were commu-
nicated to the neighbouring particles, there can be no reason
why it should not very soon be equafised throughout, or, in
other words, become wholly extinct, since the motions in con-
trary directions would naturally destroy each other. The
origin of sound from the vibration of a chord is evidently of
this nature ; on the contrary, in a circular wave of water, every
part is at the same instant either elevated or depressed. It may
be difficult to show mathematically, the mode in which this
inequality of force is preserved ; but the inference from the
matter of fact, appears to be unavoidable ; and, while the science
of hydrodynamics is so imperfect that we cannot even solve the
simple problem of the time required to empty a vessel by a
given aperture, it cannot be expected that we should be able to
account perfectly for so complicated a series of phenomena, as
those of elastic fluids. The theory of Huygens indeed explains
the circumstance in a manner tolerably satisfactory : he sup-
poses every particle of the medium to propagate a distinct un-
dulation in all directions ; and that the general effect is only
perceptible where a portion of each undulation conspires in
direction at the same instant ; and it is easy to show that such a
general undulation would in all cases proceed rectirinearly, with
proportionate force; but, upon this supposition, it seems to
follow, that a greater quantity of force must be lost by the
divergence of the partial undulations, than appears to be con-
sistent with the propagation of the effect to any considerable
distance. Yet it is obvious, that some such limitation of the
motion must naturally be expected to take place ; for, if the
intensity of the motion of any particular part, instead of conti-
nuing to be propagated straight forwards, were supposed to
affect the intensity of a neighbouring part of the undulation, an

the Theory of Light and Colours. 25

impulse must then have travelled from an internal to an exter-
nal circle in an oblique direction, in the same time as in the
direction of the radius, and consequently with a greater velo-
city; against the first proposition. In the case of water, the
velocity is by no means so rigidly limited as in that of an
elastic medium. Yet it is not necessary to suppose, nor is it
indeed probable, that there is absolutely not the least lateral
communication of the force of the undulation, but that, in highly
elastic mediums, this communication is almost insensible. In
the air, if a chord be perfectly insulated, so as to propagate
exactly such vibrations as have been described, they will in
fact be much less forcible than if the chord be placed in
the neighbourhood of a sounding board, and probably in some
measure because of this lateral communication of motions of an
opposite tendency. And the different intensity of different parts
of the same circular undulation may be observed, by holding a
common tuning fork at arm's length, while sounding, and
turning it, from a plane directed to the ear, into a position per-
pendicular to that plane.

PROPOSITION III.

A Portion of a spherical Undulation, admitted through an Aper-
ture into a quiescent Medium, will proceed to be further propa-
gated rectilinearly in concentric Superficies, terminated laterally
by zveak and irregular Portions of newly diverging Undula-
tions.

At the instant of admission, the circumference of each of the
undulations may be supposed to generate a partial undulation,
filling up the nascent angle between the radii and the surface
terminating the medium ; but no sensible addition will be made

MDCCCII. E

o6 Dr. Young's Lecture on

to its strength by a divergence of motion from any other parts
of the undulation, for want of a coincidence in time, as has
already been explained with respect to the various force of a
spherical undulation. If indeed the aperture bear but a small
proportion to the breadth of an undulation, the newly generated
undulation may nearly absorb the whole force of the jwrtion
admitted; and this is the case considered by Newton in the
Principia. But no experiment can be made under these circum-
stances with light, on account of the minuteness of its undula-
tions, and the interference of inflection; and yet some faint
radiations do actually diverge beyond any probable limits of
inflection, rendering the margin of the aperture distinctly visible
in all directions ; these are attributed by Newton to some un-
known cause, distinct from inflection; (Optics, Third Book,
Obs. 5.) and they fully answer the description of this propo-
sition.

Let the concentric lines in Fig. 1. (Plate I.) represent the con-
temporaneous situation of similar parts of a number of suc-
cessive undulations diverging from the point A ; they will also
represent the successive situations of each individual undulation:
let the force of each undulation be represented by the breadth of
the line, and let the cone of light ABC be admitted through
the aperture BC ; then the jjrincipal undulations will proceed
in a rectilinear direction towards GH, and the faint radiations
on each side will diverge from B and C as centres, without
receiving any additional force from any intermediate point D
of the undulation, on account of the inequality of the lines DE
and DF. But, if we allow some little lateral divergence from
the extremities of the undulations, it must diminish their force,
without adding materially to that of the dissipated light; and their

the Theory of Light and Colours. 27

termination, instead of the right line BG, will assume the form
CH; since the loss of force must be more considerable near to C
than at grea*^ r distances. This line corresponds with the boun-
dary of the shadow m Newton's first observation, Fig. 1; and
it is much more probable that such a dissipation of light was
the cause of the increase of the shadow in that observation,
than that it was owing to the action of the inflecting atmo-
sphere, which must have extended a thirtieth of an inch each
way in order to produce it ; especially when it is considered
that the shadow was not diminished by surrounding the hair
with a denser medium than air, which must in all probability
have weakened and contracted its inflecting atmosphere. In
other circumstances, the lateral divergence might appear to in-
crease, instead of diminishing, the breadth of the beam.

As the subject of this proposition has always been esteemed
the most difficult part of the undulatory system, it will be
proper to examine here the objections which Newton has
grounded upon it.

" To me, the fundamental supposition itself seems impossible ;
" namely, that the waves or vibrations of any fluid can, like the
" rays of light, be propagated in straight lines, without a con-
" tinual and very extravagant spreading and bending every
" way into the quiescent medium, where they are terminated
" by it. I mistake, if there be not both experiment and demon-
" stration to the contrary." (Phil. Trans. VII. 5089, Abr. I.
14,6. Nov. 1672.)

" Motus omnis per fluidum propagatus divergit a recto tra-
" mite in spatia immota."

" Quoniam medium ibi," in the middle of an undulation

E 2

a8 Dr. Young's Lecture on

admitted, " densius est, quam in spatiis hinc inde, dilatabit sese
" tarn versus spatia utrinque sita, quam versus pulsuum rariora
" intervalla; eoque pacto — pulsus eadem. fere celeritate sese in
"medii partes quiescentes hinc inde relaxare debent; — ideoque
" spatium totum occupabunt. — Hoc experimur in sonis." ( Prin-
cip. Lib. II. Prop. 42.

" Are not all hypotheses erroneous, in which light is supposed
" to consist in pression or motion, propagated through a fluid
" medium ? — If it consisted in pression or motion, propagated
" either in an instant, or in time, it would bend into the shadow,
" For pression or motion cannot be propagated in a fluid in
" right lines beyond an obstacle which stops pai't of the motion,
" but will bend and spread every way into the quiescent medium
" which lies beyond the obstacle. — The waves on the surface of
" stagnating water, passing by the sides of a broad obstacle
" which stops part of them, bend afterwards, and dilate them-
" selves gradually into the quiet water behind the obstacle.
" The waves, pulses, or vibrations of the air, wherein sounds
" consist, bend manifestly, though not so much as the waves
" of water. For a bell or a cannon may be heard beyond a
" hill, which intercepts the sight of the sounding body; and
" sounds are propagated as readily through crooked pipes as
" straight ones. But light is never known to follow crooked
" passages, nor to bend into the shadow. For the fixed stars,
" by the interposition of any of the planets, cease to be seen.
" And so do the parts of the sun, by the interposition of the
" moon. Mercury, or Venus. The rays which pass very near
" to the edges of any body, are bent a little by the action of the
" body ; — but this bending is not towards but from the shadow,

the Theory of Light and Colours. 29

« and is performed only in the passage of the ray by the body,
« and at a very small distance from it. So soon as the ray is
" past the body, it goes right on." (Optics, Qu. 28.)

Now the proposition quoted from the Principia does not di-
rectly contradict this proposition; for it does not assert that
such a motion must diverge equally in all directions; neither
can it with truth be maintained, that the parts of an elastic me-
dium communicating any motion, must propagate that motion
equally in all directions. (Phil. Trans, for 1800. p. 109-112.
All that can be inferred by reasoning is, that the marginal
parts of the undulation must be somewhat weakened, and that
there must be a faint divergence in every direction; but whe-
ther either of these effects might be of sufficient magnitude to
be sensible, could not have been inferred from argument, if the
affirmative had not been rendered probable by experiment.

As to the analogy with other fluids, the most natural inference
from it is this : « The waves of the air, wherein sounds consist,
« bend manifestly, though not so much as the waves of water;"
water being an inelastic, and air a moderately elastic medium;
but ether being most highly elastic, its waves bend very far less
than those of the air, and therefore almost imperceptibly.
Sounds are propagated through crooked passages, because then-
sides are capable of reflecting sound, just as light would be pro-
pagated through a bent tube, if perfectly polished within.

The light of a star is by far too weak to produce, by its faint
divergence, any visible illumination of the margin of a planet
eclipsing it ; and the interception of the sun's light by the moon,
is as foreign to the question, as the statement of inflection is

inaccurate.

To the argument adduced by Huygens, in favour of the

so Dr. Young's Lecture on

rectilinear propagation of undulations, Newton 1ms made no
reply ; perhajis because of his own misconception of the nature of
the motions of elastic mediums, as dependent on a peculiar law
of vibration, which has been corrected by later mathematicians.
(Phil. Trans, for 1800, p. 116.) On the whole, it is presumed,
that this proposition may be safely admitted, as perfectly con-
sistent with analogy and with experiment.

PROPOSITION IV.

frhen an Undulation arrives at a Surface which is the Limit of
Mediums of different Densities, a partial Reflection takes place,
proportionate in Force to the Diffei'ence of the Densities.

This may be illustrated, if not demonstrated, by the analogy
of elastic bodies of different sizes. " If a smaller elastic body
" strikes against a larger one, it is well known that the smaller
" is reflected more or less powerfully, according to the diffe-
" rence of their magnitudes : thus, there is always a reflection
" when the rays of light pass from a rarer to a denser stratum
" of ether ; and frequently an echo when a sound strikes
" against a cloud. A greater body striking a smaller one, pro-
" pels it, without losing all its motion : thus, tiie particles of a
" denser stratum of ether, do not impart the whole of their
" motion to a rarer, but, in their effort to proceed, they are
" recalled by the attraction of the refracting substance with
" equal force ; and thus a reflection is always secondarily pro-
" duced, when the rays of light pass from a denser to a rarer
" stratum." (Phil. Trans, for 1800. p. 127.J But it is not ab-
solutely necessary to suppose an attraction in the latter case,
since the effort to proceed would be propagated backwards
without it, and the undulation would be reversed, a rarefaction

the Theory of Light and Colours. 31

returning in place of a condensation ; and this will perhaps be
found most consistent with the phenomena.

PROPOSITION V.

When an Undulation is transmitted through a Surface terminati?ig
different Mediums, it proceeds in such a Direction, that the Sines
of the Angles of Incidence and Refraction are in the consta?it
Ratio of the Velocity of Propagation in the tzvo Mediums.
(Barrow, Lect. Opt. II, p. 4. Huygens, de la Lum. cap. 3.
EuLER, Co7JJ. Ph'ys. Phil. Trans, for 1800, p. 128. Young's
Syllabus. Art. 382.)

Corollary 1 . The same demonstrations prove the equality of
the angles of reflection and incidence.

Corollary 2. It appears from experiments on the refraction of
condensed air, that the ratio of the difference of the sines varies
simply as the density. Hence it follows, by Schol. I. Prop. I.
that the excess of the density of the ethereal medium is in the
duplicate ratio of the density of the air ; each particle cooperating
with its neighbours in attracting a greater portion of it.

PROPOSITION VI.

When an Undulation falls on the Surface of a rarer Medium, so
obliquely that it cannot he regularly refracted, i't is totally re-
flected, at an Angle equal to that of its Incidence.
(Phil. Trans, for 1800, p. 128.)

Corollary. This phenomenon tends to prove the gradual in-
crease and diminution of density at the surface terminating two
mediums, as supposed in hypothesis iv ; although Huygens
has attempted to explain it somewhat differently.

32 Dr. Young's Lecture on

PROPOSITION VII.

If equidistant Undulations be supposed to pass through a Medium,
of which the Parts are susceptible of perma7ient Fibrations some-
what slower than the Undulations, their Velocity will be some-
zvhat lessened by this vibratory Tendency ; and, in the same
Medium., the more, as the Undulations are fnore frequent.

For, as often as the state of the undulation requires a change
in the actual motion of the particle which transmits it, that
change will be retarded by the propensity of the particle to
continue its motion somewhat longer : and this retardation will
be more frequent, and more considerable, as the difference be-
tween the periods of the undulation and of the natural vibration
is greater.

Corollary. It was long an established opinion, that heat con-
sists in vibrations of the particles of bodies, and is capable of
being transmitted by undulations through an apparent va-
cuum. (Newt. Opt. Ou. 18.) This opinion has been of late
very much abandoned. Count Rumford, Professor Pictet, and
Mr. Davy, are almost the only authors who have appeared to
favour it ; but it seems to have been rejected without any good
grounds, and will probably very soon recover its popularity.

Let us suppose that these vibrations are less frequent than
those of light; all bodies therefore are liable to permanent
vibrations slower than those of light; and indeed almost all are
liable to luminous vibrations, either when in a state of ignition,
or in the circumstances of solar phosphori ; but much less easily,
and in a much less degree, than to the vibrations of heat. It will
follow from these suppositions, that the more frequent luminous
undulations will be more retarded than the less frequent ; and

the Theory of Light and Colours. 03

consequently, tliat blue light will be more refrangible than red,
and radiant heat least of all ; a consequence which coincides
exactly with the highly interesting experiments of Dr. Her-
scHEL. (Phil. Trans, for 1800. p. 284.) It may also be easily
conceived, that the actual existence of a state of slower vibra-
tion may tend still more to retard the more frequent undulations,
and that the refractive power of solid bodies may be sensibly
increased by an increase of temj^erature, as it actually appears
to have been in Euler's experiments. (Acad, de Berlin. 1762.
p. 328.)

Scholium. If, notwithstanding, this proposition should appear
to be insufficiently demonstrated, it must be allowed to be at
least equally explanatory of the phenomena with any thing that
can be advanced on the other side, from the doctrine of projec-
tiles ; since a supposed accelerating force must act in some other
proportion than that of the bulk of the particles ; and, if we call
this an elective attraction, it is only veiling under a chemical
term, our incapacity of assigning a mechanical cause. Mr.
Short, when he found by observation the equality of the velo-
city of light of all colours, felt the objection so forcibly, that he
immediately drew an inference from it in favour of the undula-
tory system. It is assumed in the proposition, that when light
is dispersed by refraction, the corpuscles of the refracting sub-
stance are in a state of actual alternate motion, and contribute
to its transmission ; but it must be confessed, that we cannot at
present form a very decided and accurate conception of the
forces concerned in maintaining these corpuscular vibrations.

MDCCCII.

34 -Dr. Young's Lecture on

PROPOSITIOxV VIII.

Whe7i itvo Uiidulatiofis, from different Origins, coincide either
perfectly or very nearly in Direction, their joint effect is a Com-
bination of the Motions belonging to each.

Since every particle of the medium is affected by each undu-
lation, wherever the directions coincide, the undulations can
proceed no otherwise than by uniting their motions, so that
the joint motion may be the sum or difference of the separate
motions, accordingly as similar or dissimilar parts of the undu-
lations are coincident.

I have, on a former occasion, insisted at large on the appli-
cation of this principle to harmonics; (Phil. Trans, for 1800.
p. 130.) and it will appear to be of still more extensive utility in
explaining the phenomena of colours. The undulations which
are now to be compared are those of equal frequency. When
the two series coincide exactly in point of time, it is obvious
that the united velocity of the particular motions must be
greatest, and, in effect at least, double the separate velocities ;
and also, that it must be smallest, and if the undulations are of
equal strength, totall}^ destroyed, when the time of the greatest
direct motion belonging to one undulation coincides with that
of the greatest retrograde motion of the other. In intermediate
states, the joint undulation will be of intermediate strength ;
but by what laws this intermediate strength must vary, cannot
be determined without further data. It is well kno\\n that a
similar cause produces in sound, that effect which is called a
beat; two series of undulations of nearly equal magnitude co-
operating and destroying each other alternately, as they coincide

the Theory of Light and Colours, 35

more or less perfectly in the times of performing their respective
motions.

Corollary i. Of the Colours of striated Surfaces.

Boyle appears to have been the first that observed the colours
of scratches on polished surfaces. Newton has not noticed them.
Mazeas and Mr. Brougham have made some experiments on
the subject, yet without deriving any satisfactory conclusion. But
all the varieties of these colours are very easily deduced from
this proposition.

Let there be in a given plane two reflecting points very near
each other, and let the plane be so situated that the reflected
image of a luminous object seen in it may appear to coincide
with the points ; then it is obvious that the length of the inci-
dent and reflected ray, taken together, is equal with respect to
both points, considering them as capable of reflecting in all
directions. Let one of the points be now depressed below the
given plane; then the whole path of the light reflected from it,
will be lengthened by a line which is to the depression of the
point as twice the cosine of incidence to the radius. Fig. 2.

If, therefore, equal undulations of given dimensions be reflected
from two points, situated near enough to appear to the eye but
as one, wherever this line is equal to half the breadth of a whole
undulation, the reflection from the depressed point will so in-
terfere with the reflection from the fixed point, that the pro-
gressive motion of the one will coincide with the retrograde
motion of the other, and they will both be destroyed ; but, when
this line is equal to the whole breadth of an undulation, the
effect will be doubled ; and when to a breadth and a half, again
destroyed ; and thus for a considerable number of alternations ;
and, if the reflected undulations be of different kinds, they will

Fa

g6 Dr. Young's Lecture on

be variously affected, according to tiieir proportions to the vari-
ous length of the line which is the difference between the
lengths of their two paths, and which may be denominated the
interval of retardation.

In order that the effect may be the more perceptible, a num-
ber of pairs of points must be united into two parallel lines ;
and, if several such pairs of lines be placed near each other,
they will facilitate the observation. If one of the lines be made
to revolve round the other as an axis, the depression below the
given plane will be as the sine of the inclination ; and, while
the eye and luminous object remain fixed, the difference of the-
length of the paths will vary as this sine.

The best subjects for the experiment are Mr. Coventry's
exquisite micrometers ; such of them as consist of parallel lines
drawn on glass, at the distance of one five hundredth of an
inch, are the most convenient. Each of these lines appears
under a microscope to consist of two or more finer lines, exactly
parallel, and at the distance of somewhat more than a twentietli-
of that of the adjacent lines. I placed one of these so as to reflect
the sun's light at an angle of 45°, and fixed it in such a manner,
that while it revolved round one of the lines as an axis, I could
measure its angular motion ; and I found, that the brightest red
colour occurred at the inclinations 10^°, 2of°, 32°, and 45°; of
which the sines are as the numbers 1, 2, 3, and 4. At all other
angles also, when the sun's light was reflected from the sur-
face, the colour vanished with the inclination, and was equal at
equal inclinations on either side.

This experiment affords a very strong confirmation of the
theory. It is impossible to deduce any explanation of it from
any hypothesis hitherto advanced ; and I believe it would be

the Theory of Light and Colours. 37

difficult to invent any other that would account for it. There
is a striking analogy between this separation of colours, and the
production of a musical note by successive echoes from equi-
distant iron palisades ; which I have found to correspond pretty
accurately with the known velocity of sound, and the distances
of the surfaces.

It is not improbable that the coloui-s of the integuments of
some insects, and of some other natural bodies, exhibiting in
different lights the most beautiful versatility, may be found to
be of this description, and not to be derived from thin plates.
In some cases, a single scratch or furrow may produce similar
effects, by the reflection of its opposite edges.

Corollary ii. Of the Colours of thin Plates.

When a beam of light falls on two parallel refracting sur-
feces, the partial reflections coincide perfectly in direction ; and,
in this case, the interval of retardation, taken between the sur-
faces, is to their distance as twice the cosine of the angle of
refraction to the radius. For, in Fig. 3, drawing AB and CD
perpendicular to the rays, the times of passing through BC and
AD will be equal, and DE will be half the interval of retarda-
tion; but DE is to CE as the sine of DCE to the radius. Hence,
that DE may be constant, or that the same colour may be re-
flected, the thickness CE must vary as the secant of the angle
of refraction GED : which agrees exactly with Newton's expe-
riments ; for the correction is perfectly inconsiderable.

Let the medium between the surfaces be rarer than the sur-
rounding mediums ;_ then the impulse reflected at the second
surface, meeting a subsequent undulation at the first, will render
the particles of the rarer medium capable of wholly stopping.

38 Dr. Young's Lecture on

the motion of the denser, and destroying the reflection, (prop.
IV.) while they themselves will be more strongly propelled
than if they had been at rest ; and the transmitted light will be
increased. So that the colours by reflection will be destroyed,
and those by transmission rendered more vivid, when the double
thicknesses, or inten^als of retardation, are any multiples of the
whole breadths of the undulations ; and, at intermediate thick-
nesses the effects will be reversed; according to the Newtoni a.v
observations.

If the same proportions be found to hold good with respect
to thin plates of a denser medium, which is indeed not impro-
bable, it will be necessary to adopt the corrected demonstration
of PROP. IV. but, at any rate, if a thin plate be interposed be-
tween a rarer and a denser medium, the colours by reflection
and transmission may be expected to change places.

From Newton's measures of the thicknesses reflecting the
different colours, the breadth and duration of their respective
undulations may be very accurately determined ; although it is
not improbable, that when the glasses approacii very near, the
atmosphere of ether may produce some little irregularity. The
whole visible spectrum appears to be comprised within tlie ratio
of three to five, or a major sixth in music ; and the undulations
of red, yellow, and blue, to be related in magnitude as the
numbers 8, 7, and 6; so that the interval from red to blue
is a fourth. The absolute frequency expressed in numbers is
too great to be distinctly conceived, but it may be better ima-
gined by a comparison with sound. If a chord sounding the
tenor c, could be continually bisected 40 times, and should
then vibrate, it would aftbrd a yellow green light : this being

41 40 ■»!

denoted by c, the extreme red would be a, and the blue d.

the Theory of Light and Colours.

39

The absolute length and frequency of each vibration is ex-
pressed in the table ; supposing light to travel in 8| minutes
500,000,000000 feet.

Colours.

Length of an
Undulation
in parts of an
Inch, in Air.

Number of
Undulations
in an Inch.

Number of Undulations
in a Second.

Extreme

.0000266

37640

463 millions of millions

Red -

.0000256

39180

482

Intermediate

.0000246

40720

501

Orange

.0000240

41610

512

Intermediate

.0000235

42510

523

Yellow

.0000227

44000

54^ , , ^

Intermediate

.OOCO219

45600

561 (=2^' nearly)

Green -

.000021 1

47460

584

Intermediate

.0000203

49320

607

Blue -

.0000196

51110

629

Intermediate

.0000189

52910

652

Indigo

.0000185

54070

665

Intermediate

.0000181

55240

680

Violet -

.0000174

57490

707

Extreme -

.0000167

5975^

735

1

Scholium. It was not till I had satisfied myself respecting all
these phenomena, that I found in Hooke's Micrographia, a pas-
sage which might have led me earlier to a similar conckision.
"It is most evident that the reflection from the under or fur-
" ther side of the body, is the principal cause of the production
" of these colours. — Let the ray fall obliquely on the thin
" plate, part therefore is reflected back by the first superficies,
" — part refracted to the second surface, — whence it is reflected
" and refracted again. — So that, after two refractions and one

40 Dr. Young's Lecture on

"reflection, there is propagated a kind of fainter ray — ," and,
" by reason of tlie time spent in passing and repassing, — this
" fainter pulse comes behind the" former reflected " pulse ; so
" that hereby, (the surfaces being so near together that the eye
" cannot discriminate them from one,) this confused or duplicated
" pulse, whose strongest part precedes, and whose weakest fol-
" lows, does produce on the retina, the sensation of a yellow.
" If these surfaces are further removed asunder, the weaker
"pulse may become coincident with the" reflection of the
" second," or next following pulse, from the first surface, " and
" lagg behind that also, and be coincident with the third,
" fourth, fifth, sixth, seventh, or eighth — ; so that, if there be
" a thin transparent body, that from the greatest thinness requi-
" site to produce colours, does by degrees grow to the greatest
" thickness, — the colours shall be so often repeated, as the
" weaker pulse does lose paces with its primary or first pulse,
" and is coincident with a" subsequent " pulse. And this, as
" it is coincident, or follows from the first hypothesis I took of
" colours, so upon experiment have I found it in multitudes of
"instances that seem to prove it." (P. 6^ — 6y.) This was
printed about seven years before any of Newton's experiments
were made. We are informed by Newton, that Hooke was
afterwards disposed to adopt his " suggestion" of the nature of
colours ; and yet it does not appear that Hooke ever applied that
improvement to his explanation of these phenomena, or inquired
into the necessary consequence of a change of obliquity, upon
his original supposition, otherwise he could not but have dis-
covered a striking coincidence with the measures laid down by
Newton from experiment. All former attempts to explain the
colours of thin plates, have either proceeded on suppositions

the Theory of Light afid Colours. 41

which, like Newton's, would lead us to expect the greatest irre-
gularities in the direction of the refracted rays ; or, like Mr.
Michell's, would require such effects from the change of the
angle of incidence, as are contrary to the effects observed ; or
they are equally deficient with respect to both these circum-
stances, and are inconsistent with the most moderate attention
to the principal phenomena.

Corollary hi. Of the Colours of thick Plates.

"When a beam of light passes through a refracting surface,
especially if imperfectly polished, a portion of it is irregularly
scattered, and makes the surface visible in all directions, but
most conspicuously in directions not far distant from that of
the light itself: and, if a reflecting surface be placed parallel to
the refracting surface, this scattered light, as well as the prin-
cipal beam, will be reflected, and there will also be a new dis-
sipation of light, at the return of the beam through the refracting
surface. These two portions of scattered light will coincide in
direction ; and, if the surfaces be of such a form as to collect
the similar effects, will exhibit rings of colours. The interval
of retardation is here, the difference between the paths of the
principal beam and of the scattered light between the two sur-
faces ; of coui-se, wherever the inclination of the scattered light
is equal to that of the beam, although in different planes,, the
interval will vanish, and all the undulations will conspire. At
other inclinations, the interval will be the difference of the
secants from tlie secant of the inclination or angle of refraction
of the principal beatn. From these causes, all the colours of
concave mirrors observed by Newton and others are necessary
consequences : and it appears that their production, tiiough

MDCCCII. G

4« Dr. Young's Lecture on

somewhat similar, is by no means, as Newton imagined, iden-
tical with the production of those of thin plates.

Corollary iv. Of Blackness.

In the three preceding corollaries, we have considered the
refracting and reflecting substances as limited by a mathema-
tical surface ; but this is perhaps never physically true. The
ethereal atmospheres may extend on each side the surface as
far as the breadth of one or more undulations ; and, if they be
supposed to vary equally in density at every part, the partial
reflections from each of the infinite number of surfaces, where
the density changes, will very much interfere with each other,
and destroy a considerable portion of the reflected light, so that
the substance may become positively black; and this effect may
take place in a greater or less degree, as the density of the
ethereal atmosphere varies more or less equably; and, in some
cases, particular undulations being more affected than others,
a tinge of colour may be produced. Accordingly, M. Bouguer
has observed a considerable loss of light, and in some instances
a tinge of colour, in total reflections at the surface of a rarer
medium.

Corollary v. Of Colours by hifleclion.

Whatever ma}' be the cause of the inflection of light passing
through a small aperture, the light nearest its centre must be
the least diverted, and the nearest to its sides the most : ano-
ther portion of light falling very obliquely on the margin of the
aperture, will be copiously reflected in various directions ; some
of which will either perfectly or very nearly coincide in direc-
tion with the unreflected light, and, having taken a circuitous

the Theory of Light and Colours. 43

route, will so interfere with it, as to cause an appearance of
colours. The length of the two tracks will diftbr the less, as
the direction of the reflected light has been less changed by its
reflection, that is, in the light passing nearest to the margin ; so
that the blues will appear in the light nearest the shadow. The
effect will be increased and modified, when the reflected light
falls within the influence of the opposite edge, so as to interfere
with the light simply inflected by that also.

But, in order to examine the consequences more minutely, it
will be' convenient to suppose the inflection caused by an ethereal
atmosphere, of a density varying as a given power of the dis-
tance from a centre, as in the eighth proposition of the last
Bakerian Lecture. (Phil. Trans, for 1801, p. 83.) Puttmg
r = s^ and x =i, I have constructed .a diagram, (Fig. 4O which
shows, by the two pairs of curves, the relative position of the re-
flected and unreflected portions of any one undulation at two
successive times, and also, by shaded lines drawn across, the parts
where the intervals of retardation are in arithmetical progression,
and where similar colours will be exhibited at different distances
from the inflecting substance. The result fully agrees with the
observations of Newton's third book, and with those of later
writers. But I do not consider it as quite certain, until further
experiments have been made on the inflecting power of dif-
ferent substances, that Dr. Hooke's explanation of inflection,
by the tendency of light to diverge, may not have some preten-
sions to truth. I am sorry to be obliged to recall here the assent
which, at first sight, 1 was induced to give to a supposed im-
provement of a late author. (Phil. Trans, for iSco, p. 128.)

Scholium. In the construction of the diagram, it becomes ne-
cessary to find the time spent by each ray in its passage.

G 3

4,4 Dr. Young's Lecture on

1
Since the velocity was denoted by x~ T, on the sup^wsition of a

projectile, it will be as j: 7 on the contrary supposition, (Phil.

Trans, for i8oi, p. 27. Schol. 2. Prop. I.) and the fluxion of the

I

distance described being ;^— ^, that of the time will be ^7==='

or-^. , of which the fluent is — ^. — . v/i — vy.

1
Therefore, with the radius x'"'- , describe a circle concentric

w'ith the surfaces of the inflecting atmosphere, then the angle

described by the ray during its passage through the atmosphere,

will always be to the angle subtended by the line cut off by

this circle from the incident ray produced, in the ratio of r to

r — 1; and the time spent in this passage, will be in the same

ratio to the time that would have been spent in describing this

intercepted portion with the initial velocity. For^, being equal

to sxT~^, is the sine of tlie inclination of the incident ray to the
radius, where it meets this circle ; therefore, by the proposition
quoted, the angle described is in a given ratio to the angle at
the centre, which is the difference of the inclinations. Making
X'-Tor— radius, the sine, instead ofj, becomes s, and the co-
sine \/ T- — ■^^» o^ — v/i — yy, and, when y = ss, \/ 1 — ss;
therefore the line intercepted is to the difference of the fluents
as r to r — i. (See also Young's Syllabus, Art. 372.)

PROPOSITION IX.

Radiant Light consists in Undulations of the luminiferous Ether.

This proposition is the general conclusion from all the pre-
ceding ; and it is conceived that they conspire to prove it in as
satisfactory a manner as can possibly be expected from the

the Theory of Light and Colours. 45

nature of the subject. It is clearly granted by Newton that
there are undulations, yet he denies that they constitute hght;
but it is shown in the three first Corollaries of the last Proposi-
tion, that all cases of the increase or diminution of light are
referable to an increase or diminution of such undulations, and
that all the affections to which the undulations would be liable,
are distinctly visible in the phenomena of light; it may there-
fore be very logically inferred, that the undulations are hght.

A few detached remarks will serve to obviate some objections
which may be raised against this theory.

1 Newton has advanced the singular refraction of the Ice-
land crystal, as an argument that the particles of light must be
projected corpuscles; since he thinks it probable that the de-
ferent sides of these particles must be differently attracted by
the crystal, and since Huyoeks has confessed his inability to
account in a satisfactory manner for all the phenomena. But,
contrarily to what might have been expected from Newton s
usual accuracy and candour, he has laid down a new law for
the refraction, without giving a reason for rejecting that of
HuYGENs, which Mr. Hauy has found to be more accurate than
Newton's; and, without attempting to deduce from his ow^n
system any explanation of the more universal and striking effects
of doubhng spars, he has omitted to observe that Huvoenss
most elegant and ingenious theory perfectly accords with these
general effects, in all particulars, and of course derives from
them additional pretensions to truth: this he omits, m order to
point out a difficulty, for which only a verbal solution can be
found in his own theory, and which will probably long remain
unexplained by any other. _

2 Mr MicHELL has made some experiments, which appear
to show that the rays of light have an actual momentum, by

4,6 Dr. Young's Lecture on

means of which a motion is produced when they fall on a thin
plate of copper delicately suspended. (Priestley's Optics.)
But, taking for granted the exact perpendicularity of the plate,
and the absence of any ascending current of air, yet since, in
every such experiment, a greater quantity of heat must be com-
municated to the air at the surface on which the light falls than
at the opposite surface, the excess of expansion must necessarily
produce an excess of pressure on the first surface, and a very
perceptible recession of the plate in the direction of the light,
Mr. Bennet has repeated the experiment, with a much more
sensible apparatus, and also in the absence of air ; and very justly
infers from its total failure, an argument in favour of the undu-
latory system of light. (Phil. Trans, for 1792, p. 87.) For,
granting the utmost imaginable subtility of the corpuscles of
light, their effects might naturally be expected to bear some
proportion to the effects of the much less rapid motions of the
electrical fluid, which are so very easily perceptible, even in
their weakest states.

3. There are some phenomena of the light of solar phosphor),
which at first sight might seem to favour the corpuscular sys-
tem ; for instance, its remaining many months as if in a latent
state, and its subsequent re-emission by the action of heat.
But, on further consideration, there is no difficulty in supposing
the particles of the phosphori which have been made to vibrate
by the action of light, to have this action abruptly suspended
by the intervention of cold, whether as contracting the bulk of
the substance or otherwise; and again, after the restraint is
removed, to proceed in their motion, as a spring would do which
had been held fast for a time in an intermediate stage of its vibra-
tion ; nor is it impossible that heat itself may, in some circum-
stances, become in a similar manner latent. (Nicholson's

the Theory of Light and Colours. 47

/oumal. Vol. II. p. 399. ) But the affections of heat may perhaps
hereafter be rendered more inteUigible to us; at present, it .seems
highly probable that light differs from heat only in tiie frequency
of its undulations or vibrations ; those undulations which are
within certain limits, with respect to frequency, being caj^ableof
affecting the optic nerve, and constituting light; and those which
are slower, and probably stronger, constituting heat only ; that
light and heat occur to us, each in two predicaments, the vibratory
or permanent, and the undulatory or transient state; vibratory
light being the minute motion of ignited bodies, or of solar phos-
phori, and undulatory or radiant light the motion of the ethereal
medium excited by these vibrations; vibratory heat being a motion
to which all material substances are liable, and which is more or
less permanent ; and undulatory heat that motion of the same
ethereal medium, which has been shown by Mr. King, (Mor-
sels of Criticism. 1786. p. gg,) and M. Pictet, (Essais de Phy-
sique. 1790,) to be as capable of reflection as light, and by Dr.
Herschel to be capable of separate refraction. (Phil. Trans, for
1800. p. 284,.) How much more readily heat is communicated
by the free access of colder substances, than either by radiation
or by transmission through a quiescent medium, has been shown
by the valuable experiments of Count Rumford. It is easy to
conceive that some substances, permeable to light, may be unfit
for the transmission of heat, in the same manner as particular
substances may transmit some kinds of light, while they are
opaque with respect to others.

On the whole it appears, that the few optical phenomena
which admit of explanation by the corpuscular system, are
equally consistent with this theory ; that many others, which
have long been known, but never understood, become by these
means perfectly intelligible; and that several new facts are

48 Dr. Young's Lecture, Sec.

found to be thus only reducible to a perfect analogy with other
facts, and to the simple principles of the undulatory system. It is
presumed, that henceforth the second and third books of New-
ton's Optics will be considered as more fully understood than
the first has hitherto been; but, if it should appear to impartial
judges, that additional evidence is wanting for the establishment
of the theory, it will be easy to enter more minutely into the
details of various experiments, and to show the insuperable dif-
ficulties attending the Newtonian doctrines, which, without
necessity, it would be tedious and invidious to enumerate. The
merits of their author in natural philosophy, are great beyond all
contest or comparison ; his optical discovery of the composition
of white light, would alone have immortalised his name ; and the
very arguments which tend to overthrow his system, give the
strongest proofs of the admirable accuracy of his experiments.
Sufficient and decisive as these arguments appear, it cannot
be suj5erfluous to seek for further confirmation; which may with
considerable confidence be expected, from an experiment very in-
geniously suggested by Professor RoBisoN, on the refractionof the
light returning to us from the opposite margins of Saturn's ring ;
for, on the corpuscular theory, the ring must be considerably
distorted when viewed through an achromatic prism : a similar
distortion ought also to be observed in the disc of Jupiter; but,
if it be found that an equal deviation is produced in the whole
light reflected from these planets, there can scarcely be any re-
maining hope to explain the affections of light, by a comparison
with the motions of projectiles.

mim. Trans Ml ) I : < ' C ' 1 1 f-ltile i./> /i

C 49 3

III. An Analysis of a miiieral Substance from North America,
co7itaining a Metal hitherto unknown. By Charles Hatchett,
Esq. F.R.S.

Read November 26, 1801.

In the course of the last summer, when I was examining and
arranging some minerals in the British Museum, I observed a
small specimen of a dark-coloured heavy substance, which
attracted my attention, on account of some resemblance which
it had with the Siberian chromate of iron, on which at that
time I was making experiments.

Upon referring, to Sir Hans Sloane's catalogue, I found that
this specimen was only described as " a very heavy black stone,
" with golden streaks," which proved to be yellow mica ; and
it appeared, that it had been sent, with various specimens of iron
ores, to Sir Hans Sloane, by Mr. Winthrop, of Massachu-
sets. The name of the mine, or place where it was found, is also
noted in the catalogue ; the writing however is scarcely legible :
it appears to be an Indian name, (Nautneauge;) but I am in-
formed by several American gentlemen, that many of the Indian
names (by which certain small districts, hills, &c. were forty
or fifty years ago distinguished,) are now totally forgotten, and
European names have been adopted in the room of them. Tnis
may have been the case in the present instance; but, as the
other specimens sent by Mr. Winthrop were from the inmes
of Massachusets, there is every reason to believe that tlie

MDCccir. H

50 Mr. Hatchett's Analysis of

mineral substance in question came from one of them, although
it may not now be easy to identify the particular mine.

§ I. DESCRIPTION OF THE ORE.

The external colour is dark brownish gray.

The internal colour is the same, inclining to iron gray.

The longitudinal fracture is imperfectly lamellated ; and the
cross fracture shews a fine grain.

The lustre is vitreous, slightly inclining in some parts to
metallic lustre.

It is moderately hard, and is veiy brittle.

The colour of the streak or powder is dark chocolate brown.

The particles are not attracted by the magnet.

The specific gravity, at temp. 65°, is 5918.*

Experiment i.

Some of the ore, reduced to fine powder, was digested in
boiling muriatic acid for about one hour.

The acid appeared to have acted but slightl}^ upon the powder;
as tlie former remained colourless, and the latter did not seem
to be diminished. A portion, however, chiefly of iron, was found
to be dissolved ; for ammonia formed a yellow flocculent pre-
cipitate; prussiate of potash produced one which was blue;

• The following results of some experiments which I have purposely made, will
shew how much the specific gravity of this ore is different from that of Wolfram, and
Siberian chromate of iron.

Pure Wolfram, free from extraneous substances, at temp. 65" - - 6955.

Siberian chromate of iron, containing some of the green oxide - 3728.

Pure Siberian chromate of iron ... 4355-

The Siberian chromate of iron, lilce all other mineral substances which are not
crystallized, and which consequently are not always homogeneous, must evidently be
liable to considerable variations in specific gravity.

a mineral Substance from North America. 51

and tincture of galls, when the excess of acid had been pre-
viously saturated by an alkali, formed a precipitate of a rich
purplish brown colour.

Experiment 11.

Another portion of the powder was, in like manner, digested
with nitric acid; but, excepting some slight traces of iron, this
acid afforded nothing worthy of notice ; the action of it upon
the ore, was indeed scarcely perceptible.

Experiment iii.

Some of the pulverized ore was digested with concentrated
sulphuric acid, in a strongly-heated sand-bath, until nearly the
whole of the acid was evaporated ; the edges of the mass then
appeared bluish, and became white, when boiling distilled water
was added.

This acid certainly acted much more powerfully than those
which have been mentioned ; but still only a small part of the
ore was dissolved. It must however be observed, that a very
copious blue precipitate was obtained by prussiate of potash ; a
plentiful purplish brown precipitate was also produced by tinc-
ture of galls, after the excess of acid had been saturated by an
alkali; and, lastly, when the yellow ferruginous precipitate
formed by ammonia was dissolved in diluted nitric acid, some
white flocculi remained, which were completely insoluble in
the acid, even when it was added so as to be in considerable
excess.

From these experiments it was evident, that the ore could
not readily be decomposed by the direct application of the
mineral acids; and I therefore had recourse to the following

Ha

52 Mr. Hatchett's Analysis of

method, wliich has frequently been employed with success in
similar cases.

ANALYSIS,

A. •

A mixture of 200 grains of the powdered ore with five times
the weight of carbonate of potash, was exposed to a strong red
heat, in a silver crucible. As soon as the matter began to flow,
a very perceptible effervescence took place ; and, when this had
subsided, the whole was poured into a proper vessel.

The mass, when cold, was grayish-brown.

Boiling distilled water was poured upon it ; and the brown
residuum, which was considerable, was well edulcorated upon a
filter.

The filtrated liquor had a slight yellowish tinge, and, being
supersaturated with nitric acid, affbrded a copious white floccu-
lent precipitate, which speedily subsided ; but, although a very
considerable additional quantity of nitric acid was poured upon
the precipitate, it was not re-dissolved.

The residuum of the ore was dark brown, and was again
melted with potash, and treated as before; but scarcely any
effect was thus produced ; the alkali was therefore washed off)
and the powder was digested with muriatic acid, which soon
assumed the deep yellow colour usually communicated to it by
iron. After half an hour, the acid was decanted, and the resi-
duum was washed with distilled water.

This powder was now of a much paler colour; and, being
mixed with potash, it was melted and treated as before. A
considerable precipitate was again obtained by the addition of
nitric acid ; and the residuum, after being digested with mu-
riatic acid, was again fused with potash, by which means the

a mineral Substaiice from North America. 53

whole was completely decomposed, after about five repetitions
of each operation.

B.

The muriatic solution was dikited, and, being saturated with
ammonia, afforded a plentiful ochraccous precipitate; which
again was dissolved in cold dilute nitric acid, and afforded a
small quantity of a white insoluble substance, similar to that
which was obtained from the alkaline solution. From this
nitric solution, I tlien obtained, by means of ammonia, a pre-
cipitate of oxide of iron, which, being properly dried, weighed
40 grains.

C.

The different alkaline solutions which had been made subse-
quent to that which has been first mentioned, were mixed
together, and, being supersaturated with nitric acid, afforded
the same white insoluble precipitate; the total quantity of which,
obtained from 200 grains of the ore, amounted to about 155
grains.

The liquor from which this precipitate had been separated
by nitric acid, was jthen saturated with ammonia, and, being
boiled, afforded about 2 grains of oxide of iron.

I obtained, therefore, from 200 grains of tlie ore.

Grains.
Oxide of iron - - - 42 T Grains.

And of the white precipitated substance ^55 J ' *

But, as I could not repeat the analysis withovit destroying the
remaining part of the only specimen at present known of this
ore, I do not wish the above stated proportions to be regarded
as rigidly exact ; it will be sufficient, therefore, to say at present,
that the ore is composed of about three parts of the white matter,
and rather less than one of iron.

5i -W/-. Hatchett's Analysis of

§ II. PROPERTIES OF THE WHITE PRECIPITATE.

A.

It is of a pure white, and is not extremely heavy.

It has scarcely any perceptible flavour, nor does it appear to
be soluble in boiling water; when, however, some of tiie powder
is placed upon litmus paper moistened with distilled water, the
paper in a few minutes evidently becomes red.

B,

1 . When examined by the blow-pipe, it is not fusible per se
in a spoon of platina, nor upon charcoal, but only becomes of a
less brilliant white.

2. Borax does not api>ear to act upon it; for the white par-
ticles are only dispersed throughout the globule.

3. It produces an effervescence when fused witli carbonate of
soda, and forms a colourless salt ; but, if too much of it be
added, then the mass, when cold, appears like a white opaque
enamel,

4. When carbonate of potash is employed, the effects are
similar in every respect to those of soda ; and it may here be
remarked, that the saline combinations thus formed with soda,
or potash, are soluble in water ; and that these solutions have
the same properties as that which was formed when the ore
was decomposed by an alkali. The portion of the white preci-
pitate which may be in excess, subsides unaltered, when the
globules are dissolved in water.

5. Phosphate of ammonia produces a very marked effect;
for, when melted in a platina spoon, if some of the white sub-
stance be added, a considerable effervescence takes place, and
the two substances rapidly unite. The globule, when cold, is

a mineral Substance from North America. 55

deep blue, with a tinge of purple, but, when held between tlic
eye and the light, it appears of a greenish gray colour.

C.

It is perfectly insoluble, and remains unchanged in colour,
and in every other respect, when digested in boiling concen-
trated nitric acid.

D.

It is dissolved by boiling sulphuric acid, and forms a tran-
sparent colourless solution, wliich is however ohly permanent
while the acid remains in a concentrated state ; for, if a large
quantity of water be added to the solution, or if the latter be
poured into a vessel of distilled water, the whole in a few
minutes assumes a milky appearance, and a white precipitate is
gradually deposited, which cracks as it becomes dry upon the
filter, and, from white, changes to a lavender-blue colour, and
again, when completely dry, to a brownish gray. It is then
insoluble in water, has not any flavour, is semi-transparent, and
breaks with a glossy vitreous fracture.

This substance is much heavier than the original white pre-
cipitate ; and in a very slight degree may be dissolved by boiling
muriatic acid, or by boiling lixivium of potash.

Upon examining these solutions, I found that both contained
the original white substance, together with some sulphuric acid;
so that the precipitate obtained from the sulphuric solution by
the addition of water, is a sulphate of the white matter.*

The whole is not however precipitated by water ; for a part

* This sulphate is also precipitated when the sulphuric solution has been long ex-
posed in an open vessel to the air; and, according as this may be moist or dry, the
effect is produced sooner or later.

56 Mr. Hatchett's Analysis of

remains in solution, which may be separated from the sulphuric
acid by either of the fixed alkalis, or by ammonia.

The sulphuric solution is not rendered turbid by the addition
of water, until some minutes at least have elapsed ; when, there-
fore, some prussiate of potash was added immediately after the
water, the colour of the liquor became olive green, and a copious
precipitate, of a beautiful olive colour, was gradually deposited.

Tincture of galls, after a few minutes, caused the liquor to
become turbid, and a very high orange-coloured precipitate was
obtained.

A few drops of phosphoric acid were added to a part of the
concentrated sulphuric solution; and, after about 12 hours, the
whole became a white opaque stiff jelly, which was insoluble in
water.

Potash, soda, and ammonia, whether pure or in the state of
carbonates, separate the substance in question from the sul-
phuric solution, in the form of a white flocculent precipitate;
and, when these alkalis are added to a considerable excess, they
do not redissolve the precipitate, unless they are heated ; then,
indeed, the fixed alkalis act upon it, and form combinations
which have already been mentioned, but which we shall soon
h^ve occasion more particularly to notice.

1 . The white precipitate, when recently separated from pot-
ash, is soluble in boiling muriatic acid ; and this solution may
be considerably diluted with water, without any change being
produced.

2. A part was evaporated to dryness, and left a pale yellow
substance, which was not soluble in water, and was dissolved

a mineral Substance from North America. 57

with great difficulty, when it was again digested with muriatic
acid.

3 . Prussiate of potash changed tlie colour of the muriatic
solution to an olive-green ; the liquor then gradually became
turbid, and an olive-coloured precipitate was obtained, similar
to that which has been lately mentioned. But,

4. If some nitric acid was previously added to the muriatic
solution, then the prussiate changed the liquor to a grass-green,
but did not produce any precipitate.

5. Tincture of galls, in a few minutes, formed an orange-
coloured precipitate, like that which has been mentioned ; but,
if the acid w^as in too great an excess, it was necessary to add a
small quantity of lixivium of potash or soda, before the preci-
pitate could be obtained.

6. A small quantity of phosphoric acid, being added to tlie
muriatic solution, in a few hours formed a white flocculent
precipitate.

7. Potash, soda, and ammonia, also produced white floccu-
lent precipitates, which were not redissolved by an excess of
the alkalis, unless the liquors were heated ; and, in that case,
part was dissolved by the fixed alkalis, but not by ammonia.

8. The muriatic solution did not yield any precipitate, when
the muriates of lime, magnesia, and strontian, were added; but
muriate of barytes formed a slight cloud.

g. When a piece of zinc was immersed in the muriatic so-
lution, a white flocculent precipitate was obtained.*

* This appears to indicate the obstinacy with which this substance retains a certain
portion of oxygen ; for we here see that zinc does not precipitate it in the metallic
state, but only reduces it to an insoluble, oxide.

MDCCCII. I

^8 Mr. Hatchett's Atialysis of

F.

The acetous acid has not any apparent effect on the white
precipitate, when long digested with it.

G.

The fixed alkahs readily combine with this substance, both in

the dry and in the humid way.

We have already seen, that the former method was employed
with success in the analysis of the ore; and the experiments
made with the blow-pipe may be regarded as an additional con-
firmation. In each of these cases, the white precipitate com-
bined with the alkali, as soon as the heat was sufficient to cause
the latter to flow ; and, when a carbonate was employed, a
portion of carbonic acid was expelled.

The carbonic acid was in like manner disengaged, when the
white precipitate was boiled with lixivium of carbonate of pot-
ash, or of soda ; and the solutions thus prepared, resembled in
every respect those which were formed by dissolving in water
the salts which had been produced in the dry way.

It will be proper here to give a more particular account of
these combinations.

1, Some of the white precipitate was digested, during nearly
one hour, with boiling lixivium of pure or caustic potash : about
one-fourth of the powder was dissolved ; and the remainder,
which appeared little if at all altered, subsided to the bottom of
the vessel.

The clear solution, which contained a great excess of alkali,
was decanted ; and, by gentle evaporation, yielded a white glit-
tering salt, in scales, very much resembling the concrete boracic
acid.

a mineral Substance from North America. 59

The salt was placed upon a fiher, so that the Hxivium might
be separated. It was then washed with a small quantity of cold
distilled water; and, being dried, remained as above described,
although constantly exposed to the open air.

This salt had an acrid disagreeable flavour, and contained a
small excess of alkali. It did not dissolve very readily in cold
water ; but, when dissolved, the solution was perfect and per-
manent.

Some nitric acid was added to part of the solution, and im-
mediately rendered it white and turbid. In a short time, a white
precipitate was collected, similar to that which had been em-
ployed to neutralise the potash ; and the clear supernatant liquor,
being evaporated, only afforded nitre.

Prussiate of potash was added to another portion ; but did
not produce any effect, until some muriatic acid was dropped
into the liquor, which then immediately assumed a tinge of
olive green, and slowly deposited a precipitate of the same colour.

Tincture of galls did not affect the solution at first; but,
when a few drops of muriatic acid had been added, it gradually
lost its transparency, and yielded an orange-coloured precipitate.

2. As so large a part of the white precipitate had remained
undissolved in the foregoing experiment, it was digested agam
with another portion of the same lixivium, but without any
effect. I therefore washed off the alkali, and boiled some nitric
acid with the powder, until the acid was completely evaporated.
After this, the powder was exposed to a strong heat in a sand-
bath. It was then again digested with the lixivium, and a part
was dissolved as before ; but still the residuum required to be
treated with nitric acid, before the alkahne liquor could again
act upon it ; so that it was necessary to repeat these alternate

I 2

6o Mr. Hatchett's Analysis of

operations several times, before the whole of the powder could
be united with the alkali.

3, When the white precipitate was digested with solution of
carbonate of potash, or of soda, it was dissolved, much in the
same manner as above related ; and the properties of the solu-
tions, when examined by reagents, were also similar, excepting
that the orange- coloured precipitates produced by tincture of
galls were of a paler colour.

Tungstate of potash, molybdate of potash, and cobaltate of
ammonia, being severally added to the solution of the white
substance in potash, produced white flocculent precipitates.

Hydro-sulphuret of ammonia produced a reddish chocolate-
coloured precipitate.

4. As the ore was decomposed by being fused with potash,
the following experiment affords a curious instance (among the
many already known) of the change in the order of affinities
produced by a difference of temperature.

Some of the solution of the white precipitate in potash, was
poured into the alkaline solution of iron, which was formerly
known by the name of Stahl's Tinctura Alkalina Martis. Pot-
ash was in excess in both of these solutions ; but nevertheless a
cloud was immediately produced, and a brown ferruginous pre-
cipitate was deposited.

Part of this precipitate was dissolved in muriatic acid ; and
the solution, being examined in the usual way, yielded a blue
precipitate when prussiate of potash was added, and a purplish
brown precipitate with tincture of galls.

The other part of the precipitate was digested with dilute
nitric acid ; which dissolved the ferruginous part, but left un-
touched a white flocculent matter, perfectly resembling the

a mineral Substance from North America. 6'i

substance which has been so often mentioned. The precipitate
therefore produced by the mixture of the two alkahnc solutions,
was a combination of the white matter with oxide of iron, very
similar to the original ore.

H.

The white precipitate, when distilled with four parts of sul-
phur, remained pulverulent, and, from white, was only changed
to a pale ash colour.

Nitric acid was digested on the powder, and, being heated,
afforded some nitrous gas ; after this, the powder became white,
and in every respect recovered its original properties.

I.

Before I conclude this section, I must observe, that when the
olive-green precipitates, obtained by prussiate of potash, were
digested in an alkaline lixivium, they were decomposed; for
the alkali combined with the prussic acid, and with a small part
of the white matter ; but the greater part of the latter remained
undissolved, in the same white flocculent state which was noticed
when the alkaline combinations were mentioned.

The orange-coloured precipitates, formed by tincture of galls,
were also decomposed when digested in boiling nitric acid ; and
the white matter was recovered in its original state.

§ III. REMARKS.

The preceding experiments shew, that the ore which has
been analysed, consists of iron combined with an unknown sub-
stance, and that the latter constitutes more than three-fourths
of the whole. This substance is proved to be of a metallic nature,
by the coloured precipitates which it forms with prussiate of
potash, and with tincture of galls; by the effects which zinc

6i Mr. Hatchett's Analysis of

produces, when immersed in the acid solutions ; and by the
colour which it communicates to phosphate of ammonia, or
rather to concrete phosphoric acid, when melted with it.

Moreover, from the experiments made with the blovv-piiie, it
seeins to be one of those metallic substances which retain oxy-
gen with great obstinacy, and are therefore of difficult reduction.

It is an acidifiable metal ; for the oxide reddens litmus paper,
expels carbonic acid, and forms combinations with the fixed
alkalis. But it is very different from the acidifiable metals which
have of late been discovered ; for,

1. It remains white when digested with nitric acid.

2. It is soluble in the sulphuric and muriatic acids, and forms
colourless solutions, from which it may be precipitated, in tlie
state of a white flocculent oxide, by zinc, by the fixed alkalis,
and by ammonia. Water also precipitates it from the sulphuric
solution, in the state of a sulphate.

g. Prussiate of potash produces a copious and beautiful olive-
green precipitate.

4. Tincture of galls forms orange or deep yellow precipitates.

5. Unlike the other metallic acids, it refuses to unite with
ammonia.

6. "When mixed and distilled with sulphur, it does not com-
bine with it so as to form a metallic sulphuret.

7. It does not tinge any of the fluxes, except phosphoric acid,
with which, even in the humid way, it appears to have a very
great affinity.

8. "When combined with potash and dissolved in water, it
forms precipitates, upon being added to solutions of tungstate
of potash, molybdate of potash, cobaltate of ammonia, and
the alkaline solution of iron.

These properties completely distinguish it from the other

a mineral Substance from North America. 63

acidifiable metals, viz. arsenic, tungsten, melybdena, and cln"o-
mium; as to the other metals lately discovered, such as ura-
nium, titanium, and tellurium, they are still farther removed
from it.

The colours of the precipitates produced by prussiate of pot-
ash and tinciure of galls, approach the nearest to those afforded
by titanium. But the prussiate of the latter is much browner;
and the gallate is not of an orange colour, but of a brownish
red, inclining to the colour of blood. Besides, even if these pre-
cipitates were more like each other, still the obstinacy with
which titanium refuses to unite with the fixed alkalis, and the
insolubility of it in acids when heated, sufficiently denote the
different nature of these two substances.

The iron in the ore which has been examined, is apparently
in the same state as it is in wolfram, viz. brown oxide; and
this oxide is mineralised by the metallic acid which has been
described, in the same manner as the oxides of iron and man-
ganese are inineralised by the tungstic acid or rather oxide.
For, from several experiments made upon a large scale, I have
reason to believe that in wolfram, the tungsten has not attained
the maximum of oxidation. Several facts in the course of the
experiments lately described, seem to prove, that this new metal
differs from tungsten and the other acidifiable metals, by a more
limited extent of oxidation; for, unlike these, it seems to be
incapable of retaining oxygen sufficient to enable the total
quantity to combine with the fixed alkalis. In § II. G. 2, this
is very evident; for, from the experiment there described it
appears, that when the metallic acid or oxide was digested with
lixivium of potash, only a part was dissolved ; and that the re-
mainder was insoluble in the same lixivium, till it had received

64 Air. Hatch ett's Analysis of

an additional portion of oxygen, by being treated with nitric
acid; also that several of these alternate operations were required,
before any given quantity of the metallic oxide could be com-
pletely combined with the alkali. Now there is mucii reason to
believe, that in this case, when the metallic oxide or acid was
digested with potash, the portion which was dissolved, received
an accession of oxygen at the expense of the other part, which
of course was thus reduced to the state of an insoluble oxide,
and therefore required to be again oxidated by nitric acid,
before it could combine with the alkaline solution ; but still it
appeared, that an adequate proportion of oxygen could never
be superinduced, so as to render the oxide totally and imme-
diately soluble in the alkalis by one operation, or even by two.
"We may, therefore, regard this as an instance of the effects
resulting from disposing affinity, and as very similar to those
observed in respect to copper, which have been noticed by my
ingenious friend Mr. Chenevix, in his valuable analysis of the
arseniates of copper and of iron.*

My researches into the properties of this metal, have of course
been much limited by the smallness of the quantity which I had
to operate upon ; but I flatter myself that more of the ore may
soon be procured from the Massachuset mines, particularly as
a gentleman now in England, (Mr. Smith, Secretary to the
American Philosophical Society,) has obligingly offered his as-
sistance on this occasion. We shall then be able more fully to «
investigate the nature of this substance; and shall be more
capable of judging how far it may be a])plicable to useful pur-
poses. At present, all that can be said is, that the olive green
prussiate and the orange-coloured gallate are fine colours;

• Phil. Trans, for 1801, p. 233.

a mineral Substance from North America. 65

and, as they do not appear to fade when exposed to light and
air, they might probably be employed with advantage as
pigments.

I am much inclined to believe, that the time is perhaps not
very distant, when some of the newl)'-discovered metals, and
other substances, which are now considered as simple, primi-
tive, and distinct bodies, will be found to be compounds. Yet I
only entertain and state this opinion as a probability ; for, until
an advanced state of chemical knowledge shall enable us to
compose, or at least to decompose, these bodies, each must be
classed and denominated as a substance sui generis. Consi-
dering, therefore, that the metal which has been examined is so
very different from those hitherto discovered, it appeared proper
that it should be distinguished by a peculiar name ; and, having
consulted with several of the eminent and ingenious chemists
of this country, I have been induced to give it the name of
Columbium.

POSTSCRIPT.

It appears proper to mention some unsuccessful attempts,
which I have lately made to reduce the white oxide.

Fifty grains were put into a crucible coated with charcoal ;
and, being covered with the same, the crucible was closely luted,
and was exposed to a strong heat, in a small wind-furnace,
during about one hour and an half When the crucible was
broken, the oxide was found in a pulverulent state ; and, from
white, was become perfectly black.

In order to form a phosphuret, some phosphoric acid was
poured upon a portion of the white oxide ; and, being evaporated

MDCCCII. K

66 Mr. Hatchett's Analysis, &c.

to dryness, the whole was put into a crucible coated with char-
coal, as above described. The crucible was then placed in a
forge belonging to Mr. Chenevix ; and a strong heat was kept
up for half an hour.

The inclosed matter was spongy, and of a dark brown ; it in
some measure resembled phosphuret of titanium.

After this, we wished to try the eflfect of a still greater heat ;
but in this experiment tlie crucible was melted.

The above experiments shew, that the white oxide, like
several other metallic substances, may be deoxidated to a certain
degree, without much difficulty, but that the complete reduction
of it is still far from being easily effected.

C67D

IV. A Description of the Anatomy of the Omithorhynchus
paradoxus. By Everard Home, Esq. F. R. S.

Read December 17, 1801.

1 HE subjects from which the following description is taken,
were sent from New South Wales, to Sir Joseph Banks, who
very obligingly submitted them to my examination.

These were two specimens preserved in spirit ; one male, the
other female. The male was rather larger than the female, and
in every respect a much stronger animal ; they had both arrived
at their full growth, or nearly so, as the epiphyses were com-
pletely united to the bodies of the bones, which is not the case
in growing animals.

The natural history of this animal is at present very little
known. Governor Hunter, who has lately returned from New
South Wales, where he had opportunities of seeing them alive,
has favoured me with the following particulars respecting them.

The Omithorhynchus is only found in tlie fresh-water lakes,
of which there are many in the interior parts of the country,
some three quarters of a mile long, and several hundred yards
broad. This animal does not swim upon the surface of the
water, but comes up occasionally to breathe, which it does in
the same manner as tlie turtle. The natives sit upon the banks,
with small wooden spears, and watch them every time they
come to the surface, till they get a proper opportunity of striking

K 2

68 Mr. Home's Description of the A?iatomy

them. Tills tliey do with much dexterity ; and frequently suc-
ceed in catching them in this way.

Governor Hunter saw a native watch one for above an hour
before he attempted to spear it, which he did through the neck
and fore leg : when on shore, it used its claws w ith so much
force, that they were obliged to confine it between two pieces
of board, while they were cutting off the barbs of the spear, to
disengage it. When let loose, it ran upon the ground with as
much activity as a land tortoise ; which is faster tlian the struc-
ture of its fore feet would have led us to believe. It inhabits
the banks of the lakes, and is supposed to feed in the muddy
places which surround them ; but the particular kind of food on
which it subsists, is not known.

Description of the external Appearances.

The male is ly^ inches in length, from the point of the bill
to the extremity of the tail. The bill is s^ inches long ; and the
tail, measuring from the anus, 4^ inches.

The body of the animal is compressed, and nearly of the
same general thickness throughout, except at the shoulders,
where it is rather smaller. The circumference of the body is
11 inches. There is no fat deposited between the skin and the
muscles.

The female measures in length 16^ inches, and in circumfe-
rence 11 inches. The size of the body is rendered proportionally
larger than that of the male, by a quantity of fat lying every'
where under the skin.

The male is of a very dark brown colour, on the back, legs,
bill, and tail ; the under surface of the neck and belly is of a
silver gray. In the female, the colour of the belly is lighter.

of the Ornithorhynchus paradoxus, 6g

The hair is made up of two kinds ; a very fine thick fur, i- of
an incli long, and a very uncommon kind of hair, \ of an
inch long ; the portion next the root has the common appear-
ance of hair, but, for ^ of an inch towards the point, it be-
comes flat, giving it some faint resemblance to very fine
feathers : this portion has a gloss upon it ; and, when the hair
is dry, the different reflections from the edges and surfaces of
these longer hairs, give the whole a very uncommon appear-
ance. The fur and hair upon the belly, is longer than that upon
the back.

Externally there is no appearance of the organs of generation,
in either sex ; the orifice of the anus being a common opening
to the rectum and prepuce in the male, and to the rectum and
vagina in the female.

There is no appearance, that could be detected, of nipples ;
although the skin on the belly of the female was examined with
the utmost accuracy for that purpose.

The head is rather compressed. The bill, which projects be-
yond the mouth, in its appearance resembles that of the duck ;
but is in its structure more like that of the spoonbill, the middle
part being composed of bone, as in that bird ; it has a very
strono; cuticular covering:.

In the upper portion of the bill, the lip extends for half an
inch anteriorly, and laterally, beyond the bony part, and is thick
and fleshy. The upper surface of the bill is uniformly smooth,
and does not terminate where the hair begins, but is continued
on for \ of an inch, forming a cuticular flap, which lies loose
uix)n the hair. In the dried specimens that have been brought
to Europe, the flap has been contracted in drying, and stands

7® Mr. HOxMe's Description of the Anatomy

up perpendicularly ; this, however, is now ascertained not to be
its natural situation.

The under surface of the upper half of the bill is also smooth ;
but has two hard ridges of a horny nature, an inch long and
-'- of an inch broad, situated longitudinally, one on each side of
the middle line of the bill.

The lower portion of the bill is much smaller than the upper;
and, when opposed to it, the lip of the upper extends beyond it
for the whole of its breadth. The edges of the lip of this lower
portion have deep serree, in a transverse direction, like those in
the duck's bill, but they are entirely confined to the fleshy lip ;
and, immediately within these serrated edges are grooves, lined
with a horny substance, which receive, in the closed state of
the bill, the ridges of the upper portion above described. There
is also a cuticular flap extended upon the hair, as in the upper
portion of the bill.

The nostrils are two orifices, very close to each other, near
the end of the bill ; the upper lip projecting -^ of an inch beyond
them.

The eyes are very small ; they are situated more upon the
upper part of the head than is usual, and are directly behind
the loose edge of the cuticular flap belonging to tiie bill. The
eyelids are circular orifices, concealed in the hair; and in the
male are with difficulty discovered, but in the female there is a
tuft of lighter hair, which marks their situation.

The external ears are two oval slits, directly behind the eyes,
and much larger than the orifices of the eyelids.

The teeth, if th.ey can be so called, are all grinders; they
are four in number, situated in the posterior part of the mouth,

o/"//5^ Ornithorhyncus paradoxus. 71

one on each side of the upper and under jaw, and have broad
flattened crowns. In the smaller specimens before examined,
each of these large teeth appeared to be made up of two smaller
ones, distinct from each other. The animal, therefore, most
probably sheds its teeth as it increases in size. They differ from
common teeth very materially, having neither enamel nor bone,
but being composed of a horny substance only embedded in the
gum, to which they are connected by an irregular surface, in
the place of fangs. When cut through, which is readily done
by a knife, the internal structure is fibrous, like nail ; the di-
rection of the fibres is from the crown downwards.

This structure is similar to that of the horny crust which
lines the gizzard in birds.

Between the cheek and the jaw, on each side of the mouth,
there is a pouch, as in the monkey tribe, lined with a cuticle.
Wlien laid open, it is i^ inch long, and the same in breadth. _
In the female, it contained a concreted substance, the size of a
very small nut, one in each pouch: this, when examined in
the microscope, was made up of very small portions of broken
crystals.

Besides these grinding teeth, there are two small pointed
horny teeth upon the projecting part of the posterior portion of
the tongue, the points of which are directed forwards, seemingly
to prevent the food from being pushed into the fauces during
the process of mastication. ' This circumstance, of small teeth on
the tongue, is, I believe, peculiar to this animal, not being met
with in other quadrupeds. In the tongue of the flamingo there
is a row of short teeth on each side, but in no other bird that I
have seen. The teeth are represented in the annexed drawing.

The fore legs are short, and the feet webbed ; the length of

72 Mr. Home's Description of the Anatomy

the leg and foot, to the end of the web, is about three inches.
On each foot there are five toes, united together by the web,
^^'hich is very broad, and is continued beyond the points of
the toes, for nearly an inch. On each toe tliere is a rounded
straight nail, which lies loose upon the membrane forming
the web. The palms of the feet are covered with a strong
cuticle ; and there is a small prominence at the heel.

The hind legs are nearly of the same length as the fore legs,
but stronger. Each leg has five toes, with curved cla^\'s ; these
are webbed, but the web does not extend beyond the points of
the toes. The four outer toes are at equal distances from each
other ; but the inner one is at a much greater distance from the
one next it. The under surface of the foot is defended by a
strong cuticular covering.

In the male, just at the setting on of the heel, there is a strong
crooked spur, 4 an inch long, with a sharp point, which has a
joint between it and the foot, and is capable of motion in two
directions. When the point of it is brought close to the leg, the
spur is almost completely concealed among the hair ; when di-
rected outwards, it projects considerably, and is very conspicu-
ous. It is probably by means of these spurs or hooks, that the
female is kept from withdrawing herself in the act of copulation ;
since they are very conveniently placed for laying hold of her
body on that particular occasion. The female has no spur of
this kind.

The tail, in its general shape, is very similar to that of the
beaver. The hair upon its upper surface is long and strong ; it
has a coarse appearance. The under surface, if superficially
examined, appears to have no hair; but, when more closely
inspected, is found to be covered with short straggling hairs.

of the Ornithorhynchus paradoxus. 75

Description of the internal Parts.

The panniculus carnosus, which lies immediately under the
skin, and extends over the greatest part of the body, is exceed-
ingly strong.

The tongue is two inches long; it lies in the hollow between
the two jaws, but does not project any way into the bill, being
confined to its situation, except a very small portion at the tip.
It is smallest at the point, and becomes larger towards the root ;
the posterior portion becomes very large, and rises considerably
higher than the rest, forming a projection, on the anterior part
of which are the two small teeth already mentioned. The
tongue is covered with short cuticular papillae, the points of
which are directed backwards.

The velum pendulum of the palate is very broad. The glottis
is uncommonly narrow; and the epiglottis proportionally small.
The rings of the trachea are broad for their size ; they do not
meet behind, but nearly so. The tongue and epiglottis are re-
presented in Plate II. Fig. 2.

In the structure of the bones of the chest, there are some
peculiarities which deserve notice.

The ribs are sixteen in number : the six superior are united
to the sternum, which is narrow and very moveable ; the other
ten terminate anteriorly in broad, flattened, oval, bony plates,
which overlap each other in the contracted state of the chest, and
are united together by a very elastic ligamentous substance, which
admits of their being pulled to some distance ; so that the capa-
city of the chest can undergo a very unusual degree of change.

The ribs are not connected to the sternum by their cartilages,
as in other quadrupeds, but by bone ; the cartilaginous portion

MDCCCII. L

74 -^/*- Home's Description of the Anatomy

being only about an inch long, and situated at some distance
from the sternum, between two portions of rib, forming a kind
of joint at that part. There is no ensiform cartilage.

On the upper end of the sternum is a bone an inch long,
which at its upper part has two processes that answer the pur-
pose of clavicles, and unite with the upper part of the scapula^,
keeping them at a proper distance. The scapulas have a very
luiusual shape: the posterior part is more like the imperfect
scapula in the bird ; and the flat part is situated with one edge
under the bone, immediately above the sternum. The other edge
forms the glenoid cavity, for the articulation of the os humeri ;
so that the fore legs have their connection with the trunk more
forward than in other quadrupeds ; and the scapula itself is much
more firmly confined to its situation.

This bone above the sternum, with the anterior part of the
two scapulas, forms a bony covering of some strength, under
which pass the great blood-vessels of the neck, secured from
compression.

The appearance of the ribs, sternum, and other bones, is
represented in Plate III.

The heart is situated in the middle line of the chest, its apex
pointing to the sternum, and is inclosed in a strong pericardium :
it is made up of two auricles and two ventricles. The foramen
ovale between the auricles was closed, nor was there any com-
munication between the ventricles. The right auricle is very
large, and has two ascending venae cavse; that to the left
winding round the basis of the heart, and forming the subcla-
vian and jugular vein of that side, after giving off the vena
azygos. Tiiis is similar to the kangaroo, beaver, otter, and many
other animals. The aorta and other arteries are small.

(^the Omithorhynchus paradoxus. 75

The lungs are large in size, corresponding to the capacity of
the chest. On the right side there are two lobes ; there is a
small azygos lobe under the heart ; and in the left side only one.
Instead of a portion of the lungs being above the heart, as in
other animals, the heart may be said to be above the lungs ; for
they only embrace its sides, and do not surround its upper sur-
face, but extend downwards, into the more moveable part of the
cavity of the chest.

The diaphragm is very broad, and every where towards the
circumference is muscular, having only a small central portion,
which is tendinous, immediately under the heart.

The oesophagus is extremely small, more particularly at its
origin behind the larynx, where the fauces terminate in it.

The stomach is a membranous bag, of an oval form, into
which the oesophagus can hardly be said to enter, being rather
continued along one end of the oval, till it forms the duodenum ;
so that the stomach appears to be a lateral dilatation of a canal,
which is the oesophagus where the dilatation is formed, and
becomes the duodenum immediately afterwards, at which part
the coats are thickened, forming the valve of the pylorus.

The stomach is smaller than in most other animals ; in this
respect it is like the true stomach of birds. In the collapsed
state it is only i-|- inch long, and ^ of an inch broad. This
is exactly double the size of one of the pouches in the cheek.

The duodenum makes a turn in the right side of the
abdomen ; then crosses the spine, and becomes a loose intestine.
The small intestines are strung upon a loose, broad, transparent
mesentery. The origin of the colon is only to be distinguished
by a small lateral appendage, i^ inch long, and ^ of an inch in
diameter, going off from the side of the intestine, which is not

La

7<? Mr. Home's Description of the A7tatomy

altered in its size at this part. Tliis process corresponds to the
c^cum : it is unlike tlie caecum in quadrupeds, but resembles
that in birds, only is much smaller, and in general they have
two ; but the bittern and heron have only one. From this part,
tile colon passes up the left side, fixed to its situation by being
attached to the omentum ; then goes across the body, and be-
comes rectum, which gradually increases in size, and is very
capacious before it terminates at the anus.

The small intestines are four feet four inches long. The colon
and rectum are one foot four inches long.

The rectum opens externally at the root of the tail, i\ inch
below the pelvis. On each side of the anus is a large solid body,
about the size of the testicle, which proves to be a gland, whose
ducts open by several orifices into the rectum. In the female,
the same glands are met with, but of a much smaller size.

The mesentery is free from fat ; nor are there any fatty ap-
pendages, or longitudinal bands, on the colon. The mesenteric
glands are of the size of millet-seeds ; they are numerous, and
scattered over the mesentery. The lacteals are small.

The internal surface of the stomach is uniformly smooth.
The duodenum has valvulce conniventes, which are transverse :
these are not met with in the jejunum and ilium ; but in them
the internal membrane is studded over with glands. There is no.
appearance whatever of valve at the beginning of the colon ; but
there are ten dotted lines, which run in a longitudinal direction,
at equal distances from one another, and have their origin at
the orifice of the caecum : these dots, upon a close inspection,
prove to be the projecting orifices of ducts belonging to the
glands of the intestine. The cavity of the small cascum is very
cellular, as is shown in Plate II. Fig. 3.

of the Ornithorhynchus paradoxus. 77

The omentum is a tliin transparent membrane, without any-
fat in it, originating from the side of the stomach next the
duodenum, and also from that intestine anteriorly: on the left
side it hangs loose, and the spleen is connected to it ; but, on the
right, after it reaches the colon, it surrounds that gut, and re-
turns to the spine ; so that, although the colon is confined by
the omentum, there is no part of that membranous bag pro-
jecting beyond it.

The liver is composed of four lobes, besides the sm.all lobe
or lobulus Spigelii. The gall-bladder is in the usual situation,
and of the common size. The cystic and hepatic ducts unite
into one, and are joined by the pancreatic duct before their ter-
mination in the duodenum, which is about an inch from the
pylorus.

The pancreas is spread upon the great and little omentum, as
ill the sea-otter, and is made up of small parts, in a very similar
manner.

The spleen consists of two very long slender bodies, united
together at one end for the length of half an inch : one of these
portions is six inches, the other four inches long.

The kidnies are conglobate, and lie in the usual situation.
The capsulae renales are rather small. The ureters are pellucid.
and small.

The urinary bladder is not situated in the pelvis, but just
above it, in the cavity of the abdomen, and is attached to the
peritonjeum lining the abdominal muscles.

The skull is rather flattened upon the upper surface: its
cavity is capacious ;. and there is a bony process projecting from
the cranium, in the place of the falx of the dura mater. This,
I believe, is not the case in any other quadruped : it is met with

78 Mr. Home's Description of the Anatomy

in some birds in a less degree, as in the parrot and the spoon-
bill ; which last bird, in the structure of its beak, bears some
analogy to this animal. The tentorium is entirely membranous.

The brain was not in a state to admit of its structure being
accurately examined ; but it appears to be made up of the same
parts as those of quadrupeds in general.

The olfactory nerves are small, and so are the optic nerves ;
but the fifth pair, which supplies the muscles of the face, are
uncommonly large. We should be led, from this circumstance,
to believe that the sensibility of the different parts of the bill is
very great, and therefore that it answers the purpose of a hand,
and is capable of nice discrimination in its feeling.*

The eye is very small, and is nearly spherical : the globe is
about i of an inch in diameter; the cornea ~\ of an inch in
diameter. There is a membrana nictitans; and the eyelid is very
loose upon the eyeball ; it is probably capable of great dilata-
tion and contraction.

The organ of smell, in its construction resembles that of other
quadrupeds, and may be said to consist of two turbinated bones
in each nostril ; that next the bill is the largest, and has the
Ions: axis in the direction of the nostril ; its external surface is
very irregular. The posterior one is shorter, projects further
into the nostril, and is situated transversely, with respect to the
nostril. As the external openings of the nose are at the end of
the bill, there is a canal of an unusual length for the air to pass
through, before it is applied to the immediate organ, unless there
is an extension of the branches of the olfactory nerve upon the
linings of the cavity, so as to make it a part of it. The external

• The same observations were made by Professor Blumenbach, ofGottingen,
who first dissected these nerves.

of the Ornithorhyilchus paradoxus. >^q

opening of the ear is at a great distance from the organ ; and
there is a cartilaginous canal, the size of a crow-quill, winding
round the side of the head, upon the outside of the temporal
muscle, leading to the orifice in the temporal bone.

The membrana tym|jani is larger than in other quadrupeds of
die same size : it is of an oval form ; and the central part is drawn
in, making its external surface concave. It has only two bones ;
one passing directly from the membrane towards the foramen
ovale, upon which there is a second bone, imperfectly resem-
bling the stapes, having a flat surface of a circular form upon
the orifice, and a small neck, by which it is united to the other
bone.

This structure of the bones is less perfect or complex than in
other quadrupeds ; so that the organ altogether bears a greater
resemblance to that of the bird.

The organs of generation in this animal have several pecu-
liarities of a very extraordinary nature.

The male organs do not appear externally ; so that the dis-
tinguishing mark of the sex is the spur on the hind leg.

The testicles are situated in the cavity of the abdomen, imme-
diately below the kidneys : they are large for the size of the
animal. The epididymis is connected to the body of the testicle
by a broad membrane, which admits of its lying very loose..

The penis in this animal does not, as in other quadrupeds,
give passage to the urine. It is entirely appropriated to the pur-
pose of conveying the semen ; and a distinct canal conducts the
urine into the rectum, by an opening about an incii from the
external orifice of the intestine. The gut, at this part, is de-
fended from the acrimony of the urine, by the mucus secreted
by two glands already described, which probably for this reason

So Mr. Home's Descriptiott of the Anatomy

are very large in the male, but small in the female. The open-
ing of the meatus urinarius, and the orifices of the glands, are
represented in Plate IV.

The penis is short and small in its relaxed state; and its body
does not appear capable of being very much enlarged when
erected. The prepuce is a fold of the internal membrane of the
verge of the anus, as in the bird ; and the penis, when retracted,
is entirely concealed.

Tlie glans penis is double; one glans having its extremity
<iirected to the right, the other to the left ; and, as they supply
two distinct cavities with semen, they may be considered as two
penises. This is an approach to the bird, many of which have
two. Each glans has, at its extremity, pointed conical papillae,
surrounding a central depression. In one glans, the papillae are
five in number, in the other four. When the urethra is laid
open from the bladder into the rectum, about half an inch from
its termination it communicates with the proper urethra of the
penis, which afterwards divides into two, one going to each
glans, in the centre of which is a cavity communicating di-
rectly with the papillje, the points of which are pervious, forming
the orifices by whicli the semen is evacuated.

The vasa deferentia open into the membranous part of the
urethra, before it comes to the root of the penis.

Not being awcire of so extraordinary a structure, and the parts
not being in a perfect state of preservation, they were too much
injured by dissection before it was discovered, to admit of their
being prepared by injection. The appearance of these parts is
delineated in Plate IV.

There was no appearance of vesiculae seminales.

The female organs open into the rectum, as in the bird. Just

of the Ornithorhynchus paradoxus, 81

within the anus there is a valvular projection, between the rec-
tum and vagina, which appears to be tlie proper termination of
the rectum. This also is similar to the bird.

There was no appearance of clitoris, that could be observed.

The vagina is i|- inch long : its internal membrane is rugous ;
the ruga? being in a longitudinal direction. At the end of tlie
va^na, instead of an os tinca^, as in other quadrupeds, is the
meatus urinarius ; on each side of which is an opening leading
into a cavit}^ resembling the horn of the uterus in the quadru-
ped, only thinner in its coats. Each of these cavities terminates
in a fallopian tube, which opens into the capsule of an ovarium.

The ovaria are very small : they were not in a very perfect
state of preservation^ but bore a general resemblance to those
of other quadrupeds.

This structure of the female organs is unlike any thing
hitherto met with in quadrupeds; since, in all of them that I
have examined, there is the bod}^ of the uterus, from which the
horns go off, as appendages. The opossum differs from all
other animals in the structure of these parts, but has a perfectly
formed uterus ; nor can I suppose it wanting in any of the class
Mammalia.

This animal having no nipples, and no regularly formed
uterus, led me to examine the female organs in birds, to see if
there was any analogy between the oviducts in any of that class,
and the two membranous uteri of this animal ; but none could be
observed ; nor would it be easy to explain how an egg could He
in the vagina^-to receive its shell, as the urine from the bladder
must pass directly over it. Finding they had no resemblance to
the oviducts in birds, I was led to compare them with the uteri of
those lizards which form an egg, that is afterwards deposited in

MDCCCII. M

82 Mr. Home's Description of the Anatomy

a cavity corresponding to the uterus of other animals, where it
is liatched; which hzards may therefore be called ovi-viviparous;
and I find a very close resemblance between them. In these
lizards there are two uteri, that open into one common canal or
vagina, which is extremely short ; and the meatus urinarius
is situated between these openings. The coats of these uteri are
thinner than those of the uteri of quadrupeds of the same size.

In the ovi-viviparous dog-fish, the internal organs of the fe-
male have a very similar structure. There is therefore every
reason to believe, that this animal also is ovi-viviparous in its
mode of generation.

EXPLANATION OF THE DRAWINGS.

See Plates II. III. and IV.

Plate II.

Fig. 1. Represents th.e hind leg of the male, in order to shew
the situation and appearance of the spur.

Fig. 3. Represents the tongue, in its natural situation; and
shows its relative position to the grinding teeth, and the lov^'er
portion of the bill ; also the two pointed teeth upon the tongue
itself.

On the outside of the jaw, on each side, are the pouches for
tlie food.

The glottis, epiglottis, and oesophagus, are represented of the
natural size.

Fig. 3. The loculated ccecum, with a portion of the ilium
and colon.

Plate III.

Represents the bones of the chest and pelvis, in their relative

of the Ornithorhynclnis paradoxus. 83

situation, to show the uncommon shape of the scapulae, which
are not connected with the chest, but with a bone placed above
the sternum, the upper part of which answers the purpose of
clavicles ; the anterior part of each scapula passes under this
bone laterally, forming with it a bony case for this part of the
neck.

Another peculiarity is, the cartilages of the ribs not being
placed next the sternum, but between two portions of the rib.
The false ribs have their cartilages terminated by thin bony
scales, which slide on one another in the motions of the chest.

The pelvis is unusually small, and has the two moveable
bones, attached to the os pubis, which are met with in the
kangaroo.

a a a. The bone which corresponds to the clavicles in other
animals.

bhb. The left scapula.

ccc. The bony scales along the margin of the chest.

ddd. The cartilages of the true ribs.

ee. The moveable bones of the pelvis.

Plate IV.

Fig. 1. Represents the penis in a relaxed state, but drawn
out to its full extent, with its relative situation to the rectum
and testicles, which are contained in the cavity of the abdomen.

aa. The bodies of the testicles.

bh. The epididymis.

c. The urinary bladder.

dd. The rectum.

ee. Two glands, whose ducts enter the rectum by a number
of small orifices.

Ms

84 Mr. Home's Description of t/je Anatomy, &c.

f. The body of the jjenis, whose external covering is a con-
tinuation of tlie hning of the lower part of the rectum.

gg. The double glans : at the point of the right one are five
conical papillce, and at the point of the left only four, which
are open at their extremities ; through these orifices tlie semen
passes.

h. The opening of the urethra into the rectum.

Fig. 2. A view of the uteri and vagina.

aa. The vestibulum, common to the rectum and vagina.

bb. The cut edges of the rectum ; the gut being dissected off
to expose the vagina.

c. The vagina.

d. The meatus urinarius.

e. The bladder.

ff. The orifices leading to the uteri.

gg. The two uteri.

hh. The fallopian tubes.

ii. The ovaria, enclosed in the capsules.

/'/«ygj.ggw.Mr)cccTl./'/gfeIl./'. y//

lf///-/,'A'r ,/^/

/'////,•..■ /A«(.r Ml )(■(■(■ II. /y,//^ III ./'..v./.

IViilos /w//.f.MDC' (" ClI V'/rf/r Vk.fKSji

C % J

V. On the Independence of the analytical and geometrical Methods
of Investigation ; and on the Advantages to be derived from
their Separation. By Robert Woodhouse, A. M. Fellow of
Cains College, Cambridge. Communicated by Joseph Planta,
Esq. Sec. R. S.

Read January 14, 1802.

One of the objects of the paper which last year I had the
honour of presenting to the Royal Society, was to shew the in-
sufficiency in mathematical reasoning, of a principle of analogy,
by which the properties demonstrated for one figure were to be
transferred to another, to which the former was supposed to
bear a resemblance ; and the argument for the insufficiency of
the principle was this, that the analogy IxJtwcen the two figures
was neither antecedent to calculation, nor independent of it,
and consequently could not regulate it ; that analogy was the
object of investigation, not the guide ; the result of demonstra-
tion, not its directing principle.

Having shewn tliat analogy could not establish the truth of
certain mathematical conclusions, I next endeavoured to shew
why such conclusions had been rightly inferred ; not by pro-
posing any new excogitated principle, nor by pointing out an
hitherto unobserved intellectual process ; but I conceived they
might be obtained by operations conducted in a manner similar
to that by which all reasoning with general terms is conducted,

86 Mr. WooDHOusE on the Independence of the

and that the relations between the symbols or general terms
were to be established by giving the true meaning to the con-
necting signs, which indicate not so much the arithmetical
computation of quantities, as certain algebraical operations. It
was further observed, that, from certain established formulas,
abridged symbols or general terms might be formed, which
consequently must have their signification dependent on such
formulas ; and that, although the parts of certain abridged ex-
pressions could not separately be arithmetically computed, yet
the expressions themselves might be legitimately employed in
all algebraic operations.

The chief object of my paper was to shew, that operations
with imaginary quantities, as they are called, were strictly and
logically conducted, that is, conducted after the same manner
as operations with quantities that can be arithmetically com-
puted : the question, whether calculation with imaginary sym-
bols is commodious or not, was then slightly discussed. I have
since attentively considered it, and, what usually happens in
such cases, my inquiries have been extended beyond their origi-
nal object; for, actual research has convinced me of what there
were antecedent reasons for suspecting, that not only in the
theory of angular functions, demonstration is most easy and
direct by giving to quantities their true and natural* represen-
tation ; but, that the introduction of expressions and formulas "
not analytical, into analytical investigation, has caused much
ambiguity, confused notion, and paradox ; that it has made

S:c. I call the natural representations of the cosines, sines, &c. of an arc x; because,
admitting the algebraical notation, they, by strict inference, adequately, unambigu-
ously, and solely, represent the cosines, sines, &c.

analytical and geometrical Methods of ItivesUgation. 87

demonstration prolix, by rendering it less direct, and has made it
deficient in precision and exactness, by diverting the mind
from the true source and derivation of analytical expression.

The expressions and formulas alluded to are geometrical,
that is, taken from the language of geometry, and established
by its rules: they are to be found mixed with analytical* ex-
pressions and reasonings, in all works on abstract science ; and,
as they are certainly foreign and circumlocutory, if it can be
shewn that they are not essentially necessary, there will exist
an argument for their exclusion, especially if it appears that in
analytical investigation they are productive of tlie evils above
mentioned.

That, in algebraical calculation, geometrical expressions and
formulas are not essentially necessary, perhaps this short and
easy consideration may convince us ; since algebra is an uni-
versal language, it ought surely to be competent to express the
conditions belonging to any subject of inquiry ; and, if adequate
expressions be obtained, then there is no doubt that with such,
reasoning or deduction may be carried on.

All expressions and formulas, such as, siii. x, cos. x, hyp.
log. ,v, sin, 71 X = 2 cos. x. sin. (n — 1 ) .r — sin. (71 — 2) a-.

• The terms analysis, analytical, algebra, algebraical, have been so often distin-
guished, and so often confounded, that I shall not take the trouble again to distinguish
them. I use the words analytical, algebraical, indifferently, in contradistinction to
geometrical. The first relates to an arbitrary system of characters; the latter to a system
of signs, that are supposed to bear a resemblance to the things signified, and in which
system, lines and diagrams are used as the representatives of quantity : and I am prin-
cipally induced to use the words indifferently, because, if analytical were properly
defined, another word with a sufiicienl extent of meaning could not be found ; for,
by an improper limitation, the word algebraical has not an extensive signification,
being firequently used in contradistinction to transcendental, exponential. Sec.

88 Mr. WooDHOusE on the Independence of the

Jx- [i — x^)t = circular arc, /a- .v/ ' ^^ t =elliptical arc,&c.
are geometrical, or involve geometrical language : they suppose
the existence of a particular system of signs, and method of de-
duction; and relate to certain tlieorems, established conformably
to such system and method.

I. Sin. X, cos. X, tang, x, &c. These expressions are borrowed
from geometry ; but, analytically, denote certain functions of x.
Typographically considered, these expressions are more commo-
dious than (2S/^)~'|£"V^-'— 6-''^-^], (2)-' I £'V-«-[-

£-^V=rr \ Sic. but this is the sole advantage; for, all analytical
operations with these latter signs are much easier, and more
expeditious, than with the former; since they are carried on
after a manner analogous to that by which operations with
similar expressions are. But, if the geometrical expressions be
retained, then, in order to calculate with them, recourse must
be had to the geometrical method, proceeding by the similarity
of triangles, the doctrines of proportions, and of prime and ulti-
mate ratios; so that, in the same investigation, two methods of
deduction, betv.een which there is no similarity, must be em-
ployed.

II. The value offx- ( 1 + x)-', is said to be a portion of the
area of an hyperbola intercepted between two ordinates to its
assymptotes ; but this is a foreign and circumlocutory mode of
expression; since, to find the value of the area, x'. (1 -{-x)~'
must be expanded, and the integrals of the several terms taken;
and this same operation must have taken place, in order to ap-
proximate to the value of/x* ( 1 -\-x)~\ if no such curve as the
hyperbola had ever been invented.

III. fx' 1^1 — x'*[~i is said to equal the arc of the circle

analytical and geometrical Methods of Investigation. 89

rads. 1 , sin. x ; but notliing is gained by this ; since, in order to
find the arc of a circle, x- ( 1 — j;')-f is expanded, and the inte-
grals of the several parts taken and added together. To shew
(if it is necessary to add any thing more on so clear a point)
that/x" 1 1 — a:* j-f =:arc circle, is merely a mode of expres-
sion borrowed from geometry ; suppose the investigation of the
properties of motion to have been prior to the investigation of
the properties of extension, for, that the science of geometry was
first invented is properly an accidental circumstance, then, such
an expression as/x- | 1 — x*| — I might have occurred, and its
value must have been exhibited as it really is now, that is, by
expanding it, and integrating the several terms.

IV. It is an objection certainly against these modes of ex-
pression, tiiat they are foreign, and tend to produce confused
and erroneous notions ; for the student may be led by them to
believe, that the determination of the values of certain analytical
expressions, essentially require the existence of certain curves,
and the investigation of their properties. But there is a more
valid objection against them, which is, that they divert the mind
from the true derivation of such expressions as — , x- ( 1 — x")- i,
&c. and consequently tend to produce ambiguity and indirect
methods ; for although, in order to obtain approximately the
numerical value oiJ—,fx- (1 — x'')~\, &c. it is convenient to
expand the expressions, and to take the integrals of the result-
ing terms, yet, if the symbol / denotes a reverse operation,
f—,fx • ( 1 — x*)~i are not properly and by strict inference equal
to(x— 1) —I J^x — iy + ^{x-iy—, &c. and x-f^-f-
■^ -}-, &c. But, in order to explain clearly what I mean, it is

MDCCCII. N

9© Mr. WooDHOUSE on the Independence of the

necessary to state what I understand by the integral or fluent
of an expression.

V. Let <px denote a function of x ; if x be increased by o,
then ifx becomes (p[x-\-o), and $ (x -f o), developed according

O R

to the powers of o, becomes (px -\-Po-\- ■—o'' -\- jj- o\ &c.
where P is derived from <px, Q from P, R from Q, &c. by the
same law ; so that the manner of deriving P being known, O,
R, &c. are known. The entire difference or increment of (px
is <p [x-\- o) — (px ; the differential or fluxion of (px is only a
part of the difference or P.o. If, instead of o, dx, or x-, be
put, it is F.dx or Fx-; the integral or fluent of Px- is that
function from which Px- is derived; and, in order to re-
mount to it, we must observe the manner or the operation
by which it was deduced ; and, by reversing such operation, the
integral or fluent is obtained. Now, in taking the fluxion
of certain functions of x, it appears there are conditions to
which the indices of x without and under the vinculum are
subject : hence, whether or not a proposed fluxion can have its
fluent assigned, we must see if the fluxion has the necessary
conditions. Expressions such as — , — ^ — , -— — r, &c. have not
these conditions ; and consequently there is no function (px of x,
such that the second term of the developement of <p{x-{- x-) is
equal either to -^, or -4-, or :f -, or, &c. There are, how-
ever, integral equations from which such expressions may be de-
rived. Thus, let X = 6', then -^ ^=z-, let i + i' = a' . • . - ^'

Now, from these equations, the differential equations -~ = z;
-J— - = 2 • , --t:^==:, &c. may, by expunging the exponential

analytical and geometrical Methods of Investigation. g t

quantities, be derived; consequently, if the symbol /is to de-
signate a reverse operation, I can only know what that reverse
operation is, by attending to the manner by which the expres-
sions affected with the symbol/ were derived. Hence,
VI. f-^ = z when x = e\

f-^ = z when i4- x=r.

/^■^ —^ when X = (sv/— O-'f^zV" — ^-zV^" ).
In like manner,

/x • ( 1 -h x") -l=iz,x-\- \/i-|-x*=£' or X = '"~'~".*
Jx' (2JC-}-x*)-v = 2;, 1 -l-x+\/3a;-j-^=e^

/- 2X- ^ 1+X ^ i^ — I

•^ I X^ "* l—X £^+1*

Again, suppose
X=:[ 2 v/UTI |— I £V-» ^e-V-i I ...jc- = 2-'X- J £«t^— +eV-i I

but \/i— x*=2-', [riyZ-j.^r-z^-i. j; consequently x-=2;*v/i — x*,
or r • = ■ : hence, reversely,

/^;;=§=^ = r, X being = (2 ^:=ri )-. (,,^- _ ^.v/ -] .

In like manner,
/-j^=r = ^, X = 2— . { ^zt^-. + r-=^-. ).

• I take no notice, at present, of the arbitrary quantities which may be introduced
in the integration of these equations.

N2

gs Mr. WooDHoosE on the Independence of the

J r=z, x = -7=

-' I — z^ ' V 1

^/—,j^f^-^-^r-^-^y'''^v—,(^^ry-.^l)■

r z ■'

And a variety of forms may be obtained, by substituting for x
different functions of x, in the expression ^ Hence, if

V I — x^

the symbol/ is made to denote a reverse operation, the integral
equations of the preceding differential equations have been
rightly assigned. All other methods of assigning the integrals,
by the properties of logarithms, by circular arcs, by logarithmic
and hyperbolic curves,* are indirect, foreign, and ambiguous.

VII. An instance or two will shew the advantage of adhering
to the true and natural derivation of analytical expressions.
Let X and y be the co-ordinates of a circle; then,
i=x*+y,andjv = v/(i--x*),now (arc)- or 2;- = v^C-^ '+.)'■*)
=, in this instance, x- (1 — x')—\: but it has appeared, that
ifx={2v/=^}— {;zV^=T-.f-^- },%- = x-(i-j;*)-i;
consequently, in a circle, the co-ordinate x, or, in the language
of trigonometry, the sine x = developement of

(,v/— 1)-.. |,.v^-._^.VZT}=z--^ + 77777 -&c.

and J or cosine = 2-'.|fi^~ -\- ^■y~\=i YT'^TTTI — ^'''

1. This method of determining the series for the sine in
terms of the arc, is, I think, simple, direct, and exact; it requires
no assumption of a series with indeterminate coefficients, nor

• By the strange way of determining the meaning and value of analytical expres-
sions from geometrical considerations, it should seem, as if certain curves were believed
to have an existtnce indt-pendent of arbitrary appointment.

analytical and geo?netrical Methods of Investigation. 93

any preparatory process to shew that tlie value of the first co-
efficient must =1.*

VIII. EuLLR demonstrated this formula to be true, viz.
-^=sin. arc — i sin. sai-c + i- sin. 3 arc — ^ sin. 4, arc -f &c.
The following is its analytical deduction,

_ r s-y— ] r ^:-v/- 1

_ f ;:V-. _;:!/-. -f ^:V/_. _ &;c. 1

■~ ^' 1 + f-^^-' - S-^--y~^ + f-3zV/-_ &C. j

and^ = (2 v/-i)-'.j ^v- _;-,•-, } _ ± (2^37)-,
{ ^^=^=^ - ^^^^-' }• + i (2 v/llT)- { ,3.^^ _ ,3.y - j _ &c.

which is the analytical translation of Euler's formula.
IX. EuLER likewise shewed that

sin. X = 2". cos. ~. COS. J . COS. ~ cos. ~ • sin. ■— .

Which may be thus demonstrated,

sin. x=i (2v/— i)— '/^r;,v'::T_ C-..V— |.

but (2 v/^)-'| ...vr; _ _.•-. J = 2 . 2-'| .,V-I_{_ ^~,'v^=H 1

(2v/-i)-'. (^.:-v-'_^-:-v/z:7j

• See Lagrange, Fonctions AnaJytiques. p, 26. Lacroix, Traite' rfu Calciri dif.
ferentiel, &c. p. 56. Le S£ur, Sur le Cakul. diff. p. ,05. Eul£r, Anal. Inf
An. 133, 134.

P4 ^^^ WooDHOusE on the Independence of the

= 2 . 2-i(/,v/-i_^^-',v/i:i) .3.2-1 (/jv'— ^f-i^-i)

or, generally,

Which is the analytical translation of sin. a; = 2'. cos. -^ • cos.— &c.
EuLER, and after liim other authors, have demonstrated these
formulas by the aid of logarithms, and of theorems drawn from
geometry.

X. EuLER and Lagrange have treated certain differential
equations, which are said to admit for their complete integration
an algebraic form, although the integration of each particular
term depends on the quadrature of the circle and hyperbola. I
purpose to integrate these differential equations, by the method
adopted in Articles V. VI.

het fxyfy, denote functions of xand^.

Suppose the differential equation to be
— 4-^ = 0; thenfx -\-fy = a when x = e-^', y = t^>. Hence,
xy = ef^+fy = e" = A, a constant quantity.

2dly. Let -j.^ + -i==- = 0

.../a:+/y = ^, x being = {2n/-i }--(-/^^--,->^-).

and jy; = a v/^)-'. (/>^=^-/>^-> ) ; or s/{,\—x^) — 2-\
( ,/V-' 4- ^_/.v^-), and n/i —/=: 2—. (f/^V— -j- ^-/>i/:n).

Hence, x.v/(i—/) +3' v/(i— -2^*)

~ (2 v/^)-'. { £(/^+/>)v'-« — ^-f>+/vV-' }

=: (o^_i)-i, I ^fa^~'_-r-V->| = A, a constant quantity.

analytical and geometrical Methods of Investigation 95

Sdly." Let -=!== +

+

C C ^ C C I

Let a 4- • — ■ = V, y -j = v' and ;•* = — ^

■\/c v't/^-f r=- ycVv' -l-r* '

taking the integrals

.-q V + V'} = « . . = ^''-;-^\ .■=^" -'•/-"•

= A, and restoring the values of x and y,

ll5J±^[a^by-^cf]Jr ^ v/(^ + 6:c + .x') = A'.
. By the above operation it appears, that certain algebraical ex-
pressions, as xv^i — j'^+jv^i — •^^ v^^i+^J'+O'* &c. may

be deduced, which answer the equations/ -\-J — 1==- &c.

But, strictly spealcing, such algebraical expressions are not the
integrals : they are rather expressions deduced from the true
integral equations, from which other algebraical expressions,
besides those put down, might be deduced.*

• For the integration of this sort of differential equations, see Mem. de Turin. Vol.
IV. p. 98. " Sur I'Integration de quclques Equations differentielles, dont les indetermi-
«' nees sont separees, mais dont chaque Membre en particulier n'est point integrable."
In this Memoir are given three different methods of integrating x- {i—x^)~^ z=.
-,» (i_^^)~T ; by circular arcs and certain trigonometrical theorems, by impossible
logarithms, and by partial integrations. Strictly speaking, all these methods are indi-
rect; and the two first are only different but circuitous modes of expressing the method
given in Art. X. See likewise Euler, Calc. integral Vol. II. Novi Comm. Petrop.
Tom. VI. p. 37. Tom. VII. p. i. It is to be observed, that in the present state of
analytic science, there is no certain and direct method of integrating differential equa-

96 Mr. WooDHOUSE on the Independence of the

XI. In the irreducible case of cubic equations, the root, it is
said, may be exhibited by means of certain lines drawn in a
circle. There is, however, independently of all geometrical con-
siderations, a method of analytically expressing the root; and,
from the analytical expression, although it is not the formula
which from the time of Cardan mathematicians have been
seeking, the value of the root may in all cases be arithmetically
computed ; but, previously, it is necessary to shew what are the
different symbols that may be substituted for z in the equations,
jc = (2v/^=T)-'|f:^-. — r-^1/^}, and v/(i— x*) = 2-'
S^zV~ _j_ ^:t/~ I . Let x= i, and tt be the value of z that
answers the equations 1 == (2\/ — i)~'|£''V~» -sk f-^VIT, land
0 = 2'-'(£'rv^~ + £— '■V~), which value of IT may be numerically
computed from the expression . . w =: 2; = x + -— - + "Tg" +
-i;^ + &c.(x=i). _ _ _

Hence, f'^- = - f-'^''-' = v/-i .-. ^»''^-* = r*'"""' = - 1

.-.f^ =£ =l--jf — £ —1..

« •■ ^ fMTV-,1

and ^m.^/Zr^^-mW-^ ^ L,=- .-. ,^'-^=^ = l).

Again, since f+'^~ = 1 and /'^~ = 1, ^'^'^^ = 1; and

Mom such as jc- ^ a + bx-^ cx*+dx' -\^tj:*\'^^i +y- ) a+by + cy*+dy^ + ty*\~i = 0,
because no analytical expression or equation of a finite fornn has hitherto been in-
vented, from which, according to the processes of the differential Calculus, such diffe-
rential equations may be deduced. To find the algebraical expressions which answer to
these equations, recourse must be had to what are properly to be denominated artifices.
For such, see Mem. de Turin. Vol. IV. Comm. Petr. Tom. VI. VII. Lacramce,
FoHct. Analyt. p. 80. Lacroix, Calc. diff. p. 417, Sec.

analytical and geometiical Methods of Investigation. 97

generally ^4"'f^-« = --4"'i-v -i __ j^ ^j ^„y number of the pro-
gression o, 1, 2, 3, 4, &c.
And, since ^^-^~'=,-^-^~' = - i .-. r''~ x .^^""""^ =

— 27rV/~ ^ —AnW~l , , (2n+l) 27!-V — I __(2H+027rV^_l_ -

£ X f •• > '-'^ C k — — '

n any number of the progression o, 1, 2, 3, 4, 5, &c.
Hence it appears, that if x= ( 2 v^ — 1 ) - ' | ,^:^ ~ — r"-'^—' | , ^ x 1
= {2v/=:T}-'{ £^v/~_^-^v/=1J 5, W=^ = (since,^'^'"^^~ =

Again, since /^"+')^'^^~=.-^^" + ') *"'^~ = — 1

xx-i=(2v/=:t)-'{/v/^_,-^v/-j^^(2«+.).v/-^

= (2\/~)'~'(_ ^((2«+03'r_j)v'ZT_^^_((2«+i)27r_«)VrT^

consequently,

X= (2\/^^)~'( ^((2"+02'r-«)x'~_^-((2«+l)2^_2:)\^Zn j

or the equation x = (2v/ — O"'! c-*^— ' — c— :V~, | is true, when
instead of z is put (47r+2;) or (Srr-f Jr), or generally (4?Z7r+2;) ;
and is moreover true, when instead of 2; is put

(27r — 2;), [Gtt — z), or generally (2«-|-i) 27r — z.
In like manner, the equation v/i — x'' =2""'/^':^— i-j-^— :V~ 1
is true, when instead of r is put

4774-2:, STT-fz, or io.'!T-\-z, or generally ^inr-^-z;
and is moreover true, when instead of z is put

47r — 2;, jStt' — z, or i27r — », or generally ^utt — z.
Let now x'—qx=r, then, by Cardan's solution,

a-=V(T+^/(f-f^))+V(W(T-?^)^

puty=a,^-f^=_^%then.v=V('^+^v/^ + V'^(— 6v^~.

Let a -^ b v/ l=»Z^r:V/~ .-, ^ — l, \/~{ = ;;/r-:V'II7

MDCCCII. O

§8 Mr. WooDHousE on the Independence of the

rt +0 =;n , ^=i:w-^ ^ Zil , b=m\ i i f ,

or 2-'.{,:^-.+,-:V^-}=;^;^,and (^ v/- 1 )"' { .=^-. -

f— :^~1 = — ==; but, from what has been premised, these

equations are true, when instead of z is put 6-\-z, or 29-\-z, or
/\)d-\-z, or generally n§-\-z, (47r=S).
Hence, V(«+^v/=ri)4- V(rt- V— i)ismi|^ft/:n_|. ^-vr: |,

ij^ ^ -f^'- ^ J, or generally w I J ' +

f ' J : there are, hqwever, only 3 different values of .v,

for the index of s in the fourth value is , and s ^ =

c ~' X £ ' "■' == 1 X £ ' "' .•. the fourth value is the same as
the first. Again, the index of s m the fifth value is -^-i^ VZT;

v — i V_i — 7— v_.i — j—v — i

orm3[f

but, ' "-'=, -'x,^ "-'^ixf' '. The 5th
value is the same as 2d, and so on; and, consequently, the

indices of ^ in the 3 different values of .v are =tz — \/ — 1, =+=

3 3

If, instead of the index of e in the 3d value, db -^ \/ — 1 be
put, the value of the root remains the same ; for, since eW~i =

r 20 + X _28-f-

-W-i , ^. «^ — 5 — V_i -GV-1 , — 3 — V-i
r == 1 .-. .r X 1 = w* X [ f X f + :

1 r _8_^ , 6-z ,

vztI J — I— V-. , -7-v—

This mode of representing the roots is not, as has been

analytical and geometrical Methods of Investigation. 99

already stated, according to the conditions* of the formula de-
manded by mathematicians. It enables us, however, imme-
diately to ascertain that the roots are possible, and to calculate
their approximate value; for, when \/i — ./ or j)' = 2~'

when %■= 0 y ■=■ 2~'| e' -|- £~* | = 1

••• «=i+Tr + T«- + TTo-+ &c.l = ^.

Hence, we ma)' numerically approximate to the value of z from
the expression - = tt — | 3' -f -^—r + "fy + ^c. | when y is
given, and < 1. Now, in the case of tlie cubic equation,

v = — - = - — ^: and, smce — < -^ .-. - ■_ is < 1, conse-

quently the value of c: may be obtained; suppose it t, then the
roots are to be approximated to, by means of the series that result
from the developements of the forms by ^^'hich they are repre-
sented ; to wit.

V ,1 1.2.3'- '-2

^V 3 "i^ 1.2.3' ' 1-234 z i

2V^ 3 I 1.2.3- 1 1.2.3.4 3+ /

2 V 3 I 1.2.3^- ' 1.2.3.4 3* /

Now these series converge ; for, since t is finite, we must at
length arrive at a term '^^, in which [n — i)?z is > I — J ; and.

A \ -,. _ A ^ ILV ^ • . A

since (n-l-i)th term (^,^, ) is = ^ x (y) y<-^,J^T)■^' «+.

IS

* The conditions of the formula are, that it should be finite in regard to the num.
ber of terms, free from imaginary quantities, and containing only the coefficients
^ and r. See Mem. de I'Acad. 1738.

O 2

lOo Mr. WooDHOusE on the Independence of the

< „, a fortiori, „^, is < „^.,, and so on; the terms after the
n — ith term constantly diminishing.*

The above method is purely analytical : it has no tacit
reference to other methods ; it does not virtually suppose the
existence either of an hyperbola or circle. If practical commodi-
ousness, however, be aimed at, it is convenient to give a different
expression to the values of the roots, or to translate them into
geometrical language : and this, because tables have been calcu-
lated, exhibiting the numerical values of the cosines, &c. of
circular arcs. Now, since it has already appeared that the cosine
of an arc z = 2~' | ^?: V~i _j- ^-y~ \ the 3 roots of the equation
.v' — qx = /• may be said to equal

~q~ t / q h-\-l / a &—t

'^— . COS. — , 2 V/ —2— cos. — !— , 2\/ — ^— , cos. .

3 3 3 3 3 3

XII. In the fifth volume of his Opuscules, -f D'Alembert

• In the Phil. Trans, for i8oi. p. ii6, I mentioned M. Nicole as the first ma.
thematician who shewed the expression of the root in the irreducible case, when
expanded, to be real. But the subjoined passage, in Leibnitz's Letter to Wallis,
causes me to retract my assertion. " Diu est quod ipse quoque judicavi v^ij-j-iv^ — i
" ■i-'^^u-i-b^ t zz z esse quantitatem realem, etsi speciem habeat iraaginarice;
" cb virtualem nimirum iniaginarix destructionem, perlnde ac in destructione actiiali
" a-\-b "^ — \ -\-a~b ^ — \ z=.2a. Hinc, si ex \/^''±i^— ' extrahamus radiccm
" ope seriei infinitae, ad inveniendum valorem ipsius z serie tali expressum, efficcre
" possumus, ut reapse evanescat imaginaria quantitas. Atque ita etiam, in casu ima-
" ginario, regulis Cardanicis cum fructu utimur," &c. Vol. IIL p. 1 26. See also p. 54.

■J- " EUe etoit neanmoins d'autant plus essentielle, que I'expression de I'arc par le

" iinus, fondee surla serie connue, qui est I'intcgrale de — " ne pent etre regardee

\' I — x^
" comme exacte, c'est a dire, comme representant a la fois tous les arcs qui ont le
" meme sinus ; puisque cette serie ne represente evidemment qu'un seul des arcs qui
" repondent au sinus dont il s'agit, savoir, le plus petit de ces arcs, celui qui est infc-
" rieur, ou tout au plus egal, a 90 degres. Cependant, c'est d'un autre cote une sorte
" de paradoxe remarquable, que I'expression de I'arc par le sinus ne representant qu'un

analytical a?id geometrical Methods of Investigation. loi

mentions it as a remarkable paradox, that the series for the arc
in terms of tiie sine represents only one arc, viz. the arc less
than go degrees; whereas the series for the sine, produced by
reversion from the former series, exhibits all possible arcs that
have the same sine. I shall endeavour to solve this paradox,
which, I think, originated partly from the introduction of geo-
metrical considerations into an analytical investigation, by which
the true derivation of certain expressions was concealed.
It has appeared that the equation x=(2v/ — i )~' | f;V~ _ ^—.V—i \
is true, when instead of 2; is put, 6-\-z, or aS-f-s;, .... or nQ-\-z,

or z, or — z .... or — — -5 — z.

22 2

Now, if the fluxions of these equations are taken, and the equa-
tions cleared of exponential quantities, there results from each
the same equation, to wit, z- = —S==. Hence, if the symbol
/ denotes the operation by which we are to ascend to the ori-
ginal equations from which r-= —^=r is derived, the only

VI— .1- ' •'

strict consequence from/'^r- z=:J '^" —

y \ — x^

is that a: = (v/-^i)~'i/ ~'c— "' ~' ),or== (sn/— 1)-^

L ■. t j J

or generally = (2 v^ir7)-{/«H^~)v'-_ ^_(,vs^..)^/- j^ ^^.

= (2v/-ir|,

[ 2>;+i /-— - —{zn-yi-) ^ — -{

" seul arc de 90 degres au plus, I'expression du sinus par Tare, qu'oH peut dsduire (par
" la methode du retour de suites) de {'expression de Tare par le sinus, repres.nte
" exactement, etant poussee a I'infini, le sinus de tous les arcs possibles, plus petits
" ou plus grands que 90", et memo que la tirconference ou dtmi circoiiference, prise
" tant de lois qu'on voudra. Je laisse a d'autres geometres, Je soin d'eclaircir ce
'■> mystere, ainsi que plusieurs autres," &c. p. 183,

1 02 Mr. WooDHousE 071 the hidependence of the

Hence, to answer the equation x- = ■^-——._ >

x may = z- -^ + -

2.3.4.5

— &c.

or %' — — 1 &c.

1.23 ' 1Z3.45

"^^ ^ I 2.3 ' 123 + 5

|s', s", z'", &c. representing 6+r, 26+r, s^-f-, &c. j.
Suppose now it is necessary to deduce x, z', z", &c. in terms
of .V and its powers, by reversion of series. What does the
reversion of series mean? Merely this; a certain method or
operation, according to which, one quantity being expressed in
terms of another, the second may be expressed in terms of the
first. Hence, in all similar series, tlie operation must be the
same; consequently, the result, whicli is merely the exhibitioji
of a formula, must be the same ; so that, whatever is the series
in terms of .r, produced by reversion m

X = z ! &c. the same must be produced

•^ - 1.23 ^ 12-3-4-5 ^^ ^^ ^

by reversion in .v = z' j^ + yTJTT — ^^^

in .r = z" — -^ + &c.
&c.
The series produced by reversion in these cases is, x -| — \-

-HL _j_ &c. Hence it appears, that we know, a priori, that must

5.8

happen which D'Alembert considers as a paradox to have
happened. Why this paradox found reception in the mind of
this acute mathematician, I have stated, as my opinion, one
cause to have been, an inattention, from geometrical considera-
tions, to the real origin and derivation of certain expressions that
appeared in the course of the calculation. Another cause I ajv
prehend was, the want of precise notions on the force and

analytical and geometrical Methods of Investigation. 103

signification of the symbol =. It is true that its signification
entirely depends on definition ; but, if the definition given of it
in elementary treatises be adhered to, I believe it will be impos-
sible to shew the justness and legitimacy of most mathematical
processes. It scarcely ever denotes numerical equality. In its
general and extended meaning,* it denotes the result of certain
operations. Thus, when from

* 12-3 ' '2-3-4 5' ' »-2-3

X or z' is inferred = ;c -I- — h -^ &c. nothing is affirmed

I 3.2 I 5.8 "

concerning a numerical equality ; and all that is to be under-
stood is, that .V 4- -^ 1- -^r + Sec. is the result of a certain

^ 3.2 ' ,-.8 I

operation performed on x = z j— - -f- ^ ^ — &c.

XIII. It appears then, that according to the reversion of
series, z, z', z". Sec. must all be represented by the same series,
proceeding according to the powers of x ; but, if a form for z be
required, which shall in all cases afford us a means of numeri-
cally computing its value, such a form must involve certain
arbitrary quantities. These arbitrary quantities are to be deter-
mined by conditions which depend either on the original form
of tlie equation between .v and z, or on the nature of the object
to which the calculus is applied.
Let now f mean-f -v -I 1 — —, — I- &c.

* This is consistent with what I advanced in the PhiL Trans, for 1801. p. gp, con-
cerning the meaning of the symbols x +, &c. It is beside my present purpose, to
insist farther on the necessity of attaching precise notions to the symbols employed in

calculation ; and the subject deserves a separate and ample discussion.

.r"
f It is not so easy to prove as it may be imagined, th.at / . zz x -\-

V I _,r'

104 -^''- WooDHousE on the Independence of the

then, if z represent the arc of a circle, and x the sine, this equa-
lity* z=: X -\- -~ -\ — ^^8 — 1~ ^^' '^ subject to restrictions,
for X cannot exceed i ; consequently, the greatest value of z that-
can be determined from the equation, must be so determined
by putting x-:=i. Let tt = i -| — ^— -f -~y &c.
Now, from the definition of sine and the nature of the circle, the
arcs 27r — z, Gtt — z .... (27^ + 1 ) Stt — z .... ^tv-\-Z .... ^7r-\-Z ....
^n7r-\-z, have the same sine ; let these arcs be z, z', z", z'", &c.

and let a; 4- -^ + -^ 4- &c. = X,

' 3.2 ' s*^ '

then z' = 27r — X, z"= Gtt—X, &c. or generally
2;'/....m__ |2«4-i| 277— X, or = 4«7r-f-X,

n any number of the progression o, 1,2, 3, 4, Sec.
Or thus, from the conditions contained in the form of the equa-
tion between z and x,

since Vi—x"= 2-\| f^'^^^ -f- ^-'^^'-^ |= 1 f^ -\- &c.

there is no possible value of z that answers the equation when
.r is V 1,

Let/— 7^=== X -}-«•■• when z and x begin together,
a = 0 and s = X.
But the equation — ^^— =z- may be derived from.v=(2V' — 1 )-'

when instead of 2; is put ^t^ — z, Stt—z .... {^n-\-i) ^.tt^z,

* In the expression z =.r+ ■ \- + &c. considered abstractedly from its ori-

gin and application, there is nothing that limits the value of .r. Again, by applying

the oneration of reversion, x is represented by this form, z -I &c.

i 1-23 1.2.3.45

But there is no method, I believe, of proving (I purposely exclude that unproved pro-
position that every equation has as many roots as dimensions) that instead of z in

z^

x—zA S.C. = 0, other quantities, as «', ;^' , Sec. may be substituted.

1.2.3

analytical and geometrical Methods of Investigation. 105

or 47r+5:; .... 47Z7r-f -.

Hence, z' or stt — 2= —X+ a. Let 2 = 0 .-. X=o .-. 277-= a.
Again, 2;" or Stt — 5:= ~X+ a. Let 2=0 .-. X=o .-. 6,r= «.
Hence, the arbitrary quantity a. may generally be represented
by (2?z-j-i)27r, orby4«7r .-. ^"•■••"=(2«+i)27r— X,

or = 4n7r-}-X.
XIV. I shall now shew, by a purely analytical process, what
are the divisors of x"=pa". It seems a very strange and absurd
method, to refer to the pi'operties of geometrical figures, for tlie
knowledge of the composition of analytical expressions.

Let x=m " £ « ^ .-. a-'=m s ~' .-. w= ■ t , and m will

-:V— I

be always positive, if /' ' =j^. But (Art. XI. ) the values of v:
that answer the equation e'^^ ~' = i, are o9,-=±z9,=i=2d, ±35, or o-e-
nerally d=s9,s, any number of the progression o, 1, 2, q &c

Hence, x=a e " "'generally,

_e_ — 9 29 29

orvaluesof.rarea, c7£" '"~',fl.~^ ~\as~" ^'~\aB~^^^~' &c

.:x"-a"={x-a) {x-^a[e" ' -f , « ^ "' [+^-) /^>_^

f £i ^— - z:£i ^_ I

[e" '+ E « ~'j+a'), 8cc. ?z being odd;

when n is even, (and of the form 2/., p odd,) there must be a

number (.?) in the progression (o, 1, 2, 3, &c.) that = -I-

consequently, there must be a value of x, ae" '=ae~^~'

I 9

= — a, since (Art. XI.) ^^ ~' , or J^ ^'~' = — 1.

Hence, a quadratic divisor of x'— a" will be (x-a). (.r-fa), or

x'— a^ when n is even, and of the form ^p, p even or odd,

MDCCCII. p

io6 Mr. WooDHOusE on the Independence of the

there must be a number [s) in the progression (o, i, 2, 3 ....)

±^Q

= — ; consequently, tlicre must be a value o[ x, as " ^ ~' =

±6 ±9

a£ + ~ =rtx=±= V — i, since (Art. XI.) £~ ,or£ 4 ~'

Hence, one quadratic divisor of .r'— a' will be of the form x*-j-a*
= {x-\-aV — 1). [x — aV — 1); another, as it has been al-
ready shewn, will be of the form x^—a\

There are only 71 different divisors, for (?i odd) the (/i — i]th

±"^ fi^/—
and «th divisors are comprised under the form x=zas " ;

the succeeding divisors would be comprised under the form
x=a e ^" =:aB X £ ^"

= fl £ 2" , (since £ = 1 ) the same as preceding form.

If .r^-f a''=o, then m = • ~"— , to have fn always positive.

Let e" ~' = — i,then (Art.XI.)thevaluesofs;are=t27r,=ii:67r...&c.

Let27r = p, then generally s ""' = — 1 ; consequently,

x=ae " ,s any number of the progression o, i , 2, &c.

or the values of r are ^£ " ,ae " ~' dec.

{ L. /— ILL j:z~ 1 / ^ i/IT

+ £ « J+^') &C.

When n is odd, there must be a number ( 2s-{- 1 ) in the progres-
sion (1,3, 5, 7, &c.) = «; consequently, one value of x must

analytical and geometrical Methods of Investigatioii. lof

= ae ~' = — a, or .r + ^ must be a divisor cf x" -\- a'.
XV. Resolution of x-" — 2 1 a" x"-{-a-" into its quadratic factors

Ui.

Now, from the equation x'=a''-[ /=t= \//' — 1 j= A =t= B s/ — 1 .

Let.r=w"6 " ~\-.r,ii ~' = A4-B\/ — 1, ?«£ ""' =

A_B^— ,;«=v'(A^+B--),.->{s^^~ + r^^~} = -^=/,

but (Art. XI.) these equations are true, when instead of s; are put
^■\-x, 2S-f2^j 3^+" generally 55 -f-^-

±56 + ^

Hence, the general value of a; is ^£ " , and the values

±« , ±e+z ±26-f^ —

of .r are at " , as " , ae " ,

era.-" — 2/tz'JC'--l-a^"=' A-= — aye"^~^-\-B « ^ ~' j +aVx\ a'"'—

a[t » '""'+£ " '~ j+a-)j x&c.

XVI. Such are the analytical processes according to which
the resolutions of ^''z+za", A'-"=p2/a'' x"-\-a^" are effected; and

thence the fluents of — — , — ; ^ — — ^-, Sec. &c. may be ob-

tained, by resolving the fractions „_|_ „ &c. into a series of partial

fractions, of the form -^ —

Since the above resolution of .v'^i^a" into its quadratic factors
would, it appears to me, be strictly true, if such a curve as the
circle had never been invented, nor its properties investigated,
it is erroneous to suppose that the theorem of Cotes is essen-
tially necessary for the integration of certain differential forms.

P 2

io8 Mr. WooDHOusE on the Independence of the

That analytical science was advanced by the discovery of this
theorem, is indeed true ; but the circle and its lines were no farther
useful or necessary, than as they afforded a mode of expressing,
in geometrical language, an analytical truth. "What is analyti-
cally expressed, may be analytically combined and resolved;
and, if Cotes, by the properties of figures, has expi'essed his
discovery, it is because the mathematicians of the time in which
he lived, were more skilful and dexterous with the geometrical
method than with tlie analytical.

In order to demonstrate Cotes's property of the circle, consi-
dered as such, one of two different methods must be pursued.
Either let the demonstration be strictly geometrical, according
to the method of the ancients, or as completely analytical as pos-
sible ; that is, let the demonstration be effected by the analytical
method, from as few fundamental principles as possible. I know
not on what grounds of perspicuity and rigour, the propriety of
a demonstration half geometrical, half algebraical, can be estab-
lished ; for, besides the want of symmetry in such a demon-
stration, in strictness of reasoning, a separate discussion is
necessary, to shew the propriety and justness of the application
of analysis to certain properties of extension demonstrated
geometrically.

It is beside my present purpose, to inquire whether Cotes's
theorem can be demonstrated strictly ^after the method of the
ancients: hitherto it has not been so demonstrated. To demon-
strate it analytically, in the most simple and direct manner, we
must proceed from as few fundamental principles as possible ; *
and give to the quantities concerned, their true and natural

• For the analytical demonstration, all that is necessary to be known, is what is
proved in the 47th of the Elements.

analytical and geometrical Methods of Investigation. \ 09

representation. I think, therefore, the analytical demonstration
in which the symbol >/ — 1 is introduced, (for the cosine of an
arc cannot be adequately and abridgedly represented in terms
of the arc, except by means of the symbol \/ — 1,) to be the
most simple and direct that can be exhibited. I have endea-
voured, in a former paper, to shew that demonstration with
such symbols as V^ — 1 may be strict and rigorous.

XVII. One or two more instances of the advantage accruing
to calculation, from giving to quantities in analytical investiga-
tion their true analytical representation, I now offer, in the de-
monstrations of the series for the chord of the supplement of a
multiple arc, in terms of the chord of the supplement of the
simple arc, for the sine of the multiple arc, &c.

Chord o^—z = {V —i)-\i ^ ~E ^ . 7,

= 6^ +6 ,smce£ = V — 1, andg -_v_i.

nz , — >i~ I z ,

Again, chord ( 27r — n%]-=.z~ " -|" ^ ^ "'• Lets^ "~'=«,

£ - ~' = ,G .•. a/3 = i ; what we have to do dien, is to find
«''-f jQ' in terms of «-j-/S; and, for facility of computation, a
new mode of notation may be advantageously introduced, w'hich
requires a brief explanation only.*

' I had obtained the forms for chords nz, &c, given in the following pages, by
actually expressing in terms of « and h, the coefficient of jf, in the developement cf

the trinomial •{ i-^-bx+x'^ f , when the very admirable work of Arbog \st, Du
Calcul des Derivations, came to my hands. The great simplicity and conve;i:ence of
his notation have caused me to adopt it, although it does not harm onize well with the
fluxionary notation which I have employed in the pressnt Paper.

1 lo Mr. WooDHousE on the Independence of the

By Art. V. ?, (x + o) = <px + Po + ^ + -^ &c.
Let D be the note of the operation to be performed on (pz, in order
to deduce P, then P= Dtpx, 0 = dP=dd(PX = d'<i:x 8cc.

Hence, ?> (x + o) = (p x + d (p x o + ^' ^ ""^ °' + &c.

or, representing — — j by d" (p x,

<p {x -{- o) z= (p X -\- Ti (p X . 0 -\- d'' <p X . d^ -\- jy ip X . o'^ -\- &c.
To resume the demonstration :

I , 1 2 -f (g + /3) X 2 -\- bx

\ + a. X ' 1 -)- |3j- 1 + (a + /=) .f + a |3 .r- i + // ^ -}. c jr^'

now — ^ = 1 — a X 4- a'' '^''^ =t a" X" . . .

I + a .r '

and ' _ =1 — iG X + /^^ -^'^ =t= /3" x"

.-. term affected with x" in developement of ' ^ ^ -j- 7x77
is± {«"+/G"}.

Again, ^4^^^ = (^^ +-^'^-) (^ + ^^ + ^■^^)~"
now(i + 6xp=: r" + Di~'.6j: + D'i~'.6'x'-f D'i~'.6'.r'4-&c.
for -6 put b-\-c X, and for 6", ^b -{-cxl "', or 6'" -f d b'". ex -\- d' t^.c^x^Scc.
then
( 1 -f 6x •4''^^^^)" ' = i~' + D i~\ Z).r -|- D i~". 6j: . ex

4-D^-'. 6\r' + B^"~\D6\fx^+ D^-W&c.

-fP'r\6V4-i/i~".DRrx^&c.

+ 1/ i~'./)\v*&c.
Hence, terms affected witTi x" and x"— ' are

B"-^-.D'6"-\-'+&c.
and »""' i~' . 6""' + b""" i~' . d 6"~'f-f- &c. Now, the »ith term

analytical and geometrical Methods of Investigation, ii i

from the beginning in first series, is^ 'i'.^6 c';
which, n even and m = -^ = i? i .c

n odd and m =: ^^—— = ^ i .m A- i b.

2 C '

At these terms the series terminates ; all the succeeding terms
being equal o, since 0"+' b", d'°+- 6'"—', are respectively
= m . m — 1 7n — 2 ...3.2.1.0 = m — 1 m — 2 ...3.2.1.0 and ::= o.
Hence, the series written in a reverse order is [n even)

D^i-.c" -L d'"+'i-\d'"-'.6'"+'.c"-' -1- jf"^' i-'.d'"-^6'"+"-.c'"-\.. dT '.6"'

C i^ C C ' c c ••' C

{n odd)

orD^i .D6^.c-fD^l .D b .c +&c Di .6

Now, ^"i = — ' — ^•— 3 " _. J ^^^ even) or = — i (n odd)
and .-. the former series becomes

zi=b^=*=-D b"~\ c =p: D" />" -\ c"" =i= &c. and consequently, the term
affected with x" m (2 -{-bx) (1 -\-bx -\- ex'')—''

is f =t: 2 fc" =?^ 2D 6"— ' , C =!= 2D*6""~=. t"'' == &C.

c ^^

z b"- =t: Dl''~\bc=i:: D' b''-3 . bc'"=i:z 8cc.

or =i=b"=i^" D b''-\c' z±: '^— D^- 6"-^ e =^- D^ b"-3. €'=*= &C,

n—l n — 2 ^^ n — x

{

tor, smce 9 /) x 6 = y b

X 6 = -^^ Y b"

n — m I

, n — 2

Hence, a" + (3"= b" d6 -I ^ 6 — &c. r beino^

' ' ' n—i ' » — z <- »

= «^ = i.

The law of the series is truly and unambiguously represented,
by means of the symbol or note of derivation d : but, if it is
required to express tlie law numerically, in turns of n, since

113 Mr. WooDHousE on the Independence of the

D"* a"""* (" — '") " — "* — 0 (« — "I — 2) (h — : w) -I- i) • n— »ffl

c 1.2.3 7n

'' '1.2 1.2.3

the series for the chord of the supplement of a multiple arc, in
terras of the chord (6) of the supplement of the simple arc.

XVIII. Similar serias may be found for the sines and cosines
of multiple arcs ; thus,

COS.Z =2-' I e'^~'-\- £-~^-' |,COS. 7J2; = 2-'|£'''''^-'+ e-"^-' j-

Now, a, = £^^~* .-. a" = e"'^— \ Let COS. z = p,
.-. «-|-/3 = 2/) = 6,

.-. COS. nz = ^^^^ = i • ( ^y—n . 2"-= />"-=' + ^^^^ 0—4^'— 4_ 8:c,

__ ^r-^pr. _ ji ^,-3p.-2 _|. li-ii-J 2,'-sp'—i _ &c

or = i {(2*)" - ;z . (2^))'- + 1^^ (2/>)-4 _ &c.}

Suppose it were required to write the series in an inverse
order : let n be even, then the series b" — - — d b'-"" &c. termi-

' n — I

nates at a term - — d" b ", m = — ^, and .-. - — = 2, and

«" 4- iG''= =*= 2 =+= r— D b ^ =fc — D 6 =;z:&C.

or, in terms of n,

= =t: 2 =;=-:LL:Lfc^^L_i ^ i [ 6*=;= &C.

^^ 1.2.2 1.2.3.4 ^^

Consequently, cos. wz = — r — = =*= i=^ -^ tt —^ — — &c.

Where the upper or lower sign takes place, as n is of the form
4.S (5 an even or odd number), or 25, {s an odd number);
let n be odd, then the series terminates at a term — ^ i?" b ,
?n = , and .-. .^ b =nb,

2 ' n — m C '

and u''-j-fi'' = ^nb=j= b""' 6"-'"+' =±= &c.

analytical and geometrical Methods of Investigation. 1 13
or in terms of n .' ± :^ j^

nu-^ 2\i.2.3 2+.1.2.3. + .5 ^^

Consequently,

cos.;zjr = — ^— = 3|=i=w6-t--7-7:j^=i= ,.,.3.^.3 17 1

'/'-*- 1.2.3^ i.2.3.4.5r

Where the upper or lower sign is to be used, as n is of the form

(45 + ij, or45 + 3. __

XIX. Again, sine 2; = (av/— 1)-' (e^^-' - e—^-' },
sine«:.=(2v/ir-i]-' {s"V/-_,-n-v/-}^
.-. it is necessary to find u' — jS' in terms of a — 13.
Let n be odd,
then term affected with x" in developement of {^- + 77^}

■ J 1 , 1 2— (» — g) r 2 — bx

= a"— /3% ana-j^3^ + j_^g^ — ,_ (a,_3) jr_«i3x^ i_&x— cx^'
and the term affected with x" in the developement of (3 — 6 x)

or in terms of n (c = 1)

butsines = --^ = /».-.(6)''=(2y~^)'' = =i=3V=n^%

2 V — I

where the upper or lower sign is to be used, according as n is
of the form 45 -f 1, or 45 + 3. Hence,
sme«»=^^^===i=2 />=P2 .np =i=2 . j— j-;-^ p

&c.

If it is required to write the series in a reverse order, it is to

be observed, that the series 6» + ~j d b"-' &c. terminates at

MDCCCII. Q

114 ^f- WooDHOusE on the Independence of the

a term — 2_d- f-™ «i = 2lJ: ... _-l_ p- /,»-'» = -!±- ;
consequently,

or in terms of ?z,

__, _«i_ , n. («+i) (>;— 0 _6f__ , n. {n+i) (x— i) («+3)»— 3 .^ ^^

2 "I" 1.2.3 * 2'^ ' 1.2.3.4.5 * 2*

Hence, ^^^^^^ (sine «x) =/> - JLJUjzII _ y,^ + &c.

' 2v^_i >• J I 1.2.3 ■' '

XX. Let « be even, then term affected with x" in develope-
ment of {- ^ l = «"— /3".

Now -^ ^-—r- = , a> s-^. and the term affected

with x""' in the developement of (i — bx — cx*)—^
is b"-' -f- D 6-^-^ c-\-Jf b"-^ c'+ D' d'-a c' + &c.

.-. term affected with x" in 6' a'| i — 6.r— ex''}"', |a -f ]G = 6' |
isb'S If-' + D 6"^^ t+lD* 6"^3if-^ &c. J

or in terms of n (c=i )

is &'{/>-' +{n~-2}6'-3+ ("-3;^"-^ lf-5-^^c. ]

Hence, since sine z= •—■ — = — -==p .•. ^-7=- = =i= 2*—' />"— ' ,

' 2v'— I 2v^_, '^ V— I ■'^

and cosme r = = = p .-. sme nz =^ — ■==

Or=/*|^^(2/))'— ' =:p (« 2) (S/*)"- 3 =t=&C.|

X p"-^ rp: &c. the upper signs taking place, if n is of tlie form
25 (5 odd), the lower, if n is of the form 4.V, s even or odd.

If it is required to write the series in a reverse order, it is to
be observed, that the series 6«—' •\- d^"^" 4- ^^ terminates at a
termp" i,*-""-', when //i = — — 1 ; consequently, ?" 6""""""' =i 1^

and .-. «''_i2''=6'{^ + ?""' 6""™ + &c. }

analytical and geometrical Methods of Investigation. 1 15

L z ' 1.2.4 2 ■'

consequently, sine nz or -^JI ■

XXI. The sine nz (« even) may be expressed by series, in
terms of the cosine of z ;

thus, ^ 1^- = -i-=J ,

and, equating the terms affected with x" in each developement,
we shall have
sin. «^=/.{(2j!.')''-— ^ (2/.-J«-3 + Ii:illl|i:il(2/)-s— &c.|
when n is even, a series may be found for sin. ns; in terms of
p (sin. 5;) only; but this series will not terminate as all the
foregoing series do.

To find this series, expand -/(i — p^) =p' into a series,
IT— Dli/>'+ D" lip* —8cc.

then sin. nz= I i-Di*/»-+ D* li/.*— &c. j ^l „^_!Lfc£:i^' + &c. j
= np + A;.'+ a, />'+ A„f + &c.
in which series, the law of the coefficients, or a general expression

for A may be found. But it cannot now be done, without too

«•••» "^

long a digression from the present objects of inquiry.

From what has been done, the series* of the chord of the

• Demonstrations of these forms have been given by reversion of series, and by
induction ; which demonstrations are imperfect, since they do not exhibit the general
law of the coefficients. See De Moivre Miscell. analytica. Epistola de Cotesii
Inventis, Sec, Newtoni Opera omnia, p. 306. Euler in Analyt. inf. Cap. 14.
Warikg has deduced the chord of the supplement of a multiple arc, in terms of the
chord of the supplement of the simple arc, from his theorem for the powers of roots :

Q2

1 16 Mr. WooDHOusE on the Independence of the

multiple arc may be found in terms of the chord of the simple

arc ; for, chord nz = { v/ — i j £ * — e ^ j .

XXII. In the above demonstrations, no formulas are borrowed
from geometry ; and the general law of the coefficients is clearly
expressed ; it is, I think, most conveniently expressed by means
of the symbol or note of derivation d. The operation which
this symbol indicates is as certain as any other operation,
whether arithmetical or algebraical.

XXIII. The demonstrations and method of deduction given
in this paper shew, I think, with sufficient evidence, the intro-
duction of geometrical expressions and formulas into analytical
investigation to be perfectly unnecessary. It has appeared hke-
wise, that such introduction embarrasses investigation, and
causes ambiguity, by concealing the true derivation of expres-
sions; and, although I do not wish to give importance to my
own observations, by supposing a greater confusion of notion
to exist than really docs, yet, I think, in what has been v/ritten
and said, there may be detected a lurking opinion, that the
value of certain expressions essentially demand the existence of
geometrical curves and figures, and the investigation of their
properties.

XXIV. In the Appendix to the Arithmetica Universalis,
p. 200. 219. &c. Newton, with great clearness and force of
argument, has shewn the distinction to be made between the
order of classing curves, analytically considered, that is, defined

but the demonstration of the latter theorem is not, it appears to me, to be reckoned in
the number of strict demonstrations. The only objection against the demonstration of
the very learned and ingenious author of the Calcul des Derivations, is, that it is rather
indirect, and blended with geometrical expressions and formulas.

analytical and geometiical Methods of Investigation. 1 1 7

by equations, and the order of classing them, considered as
generated by description. Moreover, he animadverts on the
custom of confounding the two sciences of algebra and geo-
metry ;* and, if any authority is attached to his assertion, that
the two sciences ought not to be confounded togetlier, tlie
separation of geometry from algebra will thereby be equally
urged as the separation of algebra from geometry. And it can-
not be said with greater truth, that the simplicity of geometry
is vitiated with algebraic equations, than that the simpHcity of
analysis is vitiated with geometrical forms and expressions. In
fact, each science ought to be kept distinct ; and be made to
derive its riches from its proper sources.

XXV. It will not demand much meditation to be assured of
this truth, that, in any mathematical investigation, the geome-
trical method, properly so called, is not essentially or absolutely
necessar)'. The properties of extension and figure, to which this
method has been especially appropriated, may be analytically
treated ; and here it is proper to state a distinction neces-
sary to be made, between what may be called analytical geo-
metry, and the application of analysis to geometry. The first
does not suppose or require the existence of such a method as
the geometrical ; but, from a few fundamental principles, analy-
tically investigates the properties of extension ; whereas, in the
latter, analysis is applied to propositions already established by
the geometrical method: so that, strictly, to shew the justness
and propriety of the application, a separate investigation is

• " Multiplicationes, divisiones, et ejusmodi computa, in geometriam recens intro-
" ducta sunt: idque inconsulto, et contra primum institutum scieniia; hiijus, ic.

" Proinde hse duje scientiae confundi non debent, &c. Et recente?, utramque

" confundendo, amiserunt simplicitate.-n in qua geometriae elegantiaomnis consistit,"'

1 18 Mr. WooDHousE 071 the Independence of the

necessary. We find, however, in general, a vague analogy sub-
stituted, as a connecting principle between the two methods.

XXVI. Tiie application of algebra to geometry, gives to
Descartes the fairest title to fame for mathematical invention ;
yet the cause and nature of the benefit conferred on science by
that application, seems to be indistinctly apprehended.* For, the
Analytical Calculus, when applied to geometry, was not en-
riched with the truths of the latter science, because some con-
necting principle had been discovered, or some process invented
by which the property of the two methods became common,
and might, fi:om one to the other, without formality be trans-
ferred; but because the investigation of certain properties could
not proceed, without first improving the means by which they
were to be investigated. These means Descartes improved :
he found, when certain conditions in problems concerning ex-
tension were translated into the language of algebra, that the
process of deduction with the general terms was slow and in-
commodious, because, such was the low state of the algebraic
Calculus, the relation between the general terms had not been
established. The aim and merit of Descartes's speculations is
to have established this relation. If illustration were needed to
make my meaning clear, I should say that Descartes, New-
ton, and D'Alembert, benefited science precisely after the
same manner. The first applied the analytical Calculus to
extension ; the second to motion ; the third to the equilibrium,
resistance, &c. of fluids. As the object of investigation became

• Thus far was the Analytical Calculus benefited by the existence of the geome-
trical method : certain properties of figure and extension, discovered by the latter,
became to the former, objects of investigation.

analytical and geometrical Methods of Investigation. 119

more abstruse, it was found necessary to improve more and
more the means or instrument of investigation,

XXVII. As the question concerning the respective advan-
tages of the ancient geometry and modern analysis, is not foreign
to the subject of this Paper, I shall briefly state it, and endea-
vour to afford the means of amving therein at something like a
precise determination.

The superiority of one method above another, must consist
in being either more logically strict in its deductions, or more
luminous, or more commodious for investigation. The discus-
sion concerning the strictness and accuracy may, I conceive,
be immediately put aside, since no method of deduction is essen-
tially inaccurate ; and, if in geometry the inferences are more
strictly deduced than in the algebraic Calculus, the advantage
is to be reckoned an accidental one, and arising from the great
attention with which the former science has been cultivated.

One method may, however, be essentially more perspicuous
and more commodious for investigation than another ; or, in
other words, the perspicuity and commodiousness of a method
may depend on circumstances inherent in its nature and plan.
Now, a person not sensible of the superior perspicuity of the
geometrical method, would demand these circumstances, the
necessary causes of perspicuity, to be pointed out to him ; which
might be done, by stating that geometry, instead of a generic
term, employs, as a particular individual, the sign or represen*
tative of a genus ; and that, as in algebra, the signs are alto-
gether arbitrary, in geometry, they bear a resemblance to the
things signified, and are called ?iaiural signs, since the figure of
a triangle, or square, suggests to the mind the same tangible
figure in Europe, that it does in America : and this resemblance.

120 Mr. WooDHOUSE on the Indepeiidence of the

of the sign to the thing signified, is supposed to be the chief
cause of the superior clearness of geometrical demonstration.*
Another cause may perhaps be thought to exist in this circum-
stance, that whatever is demonstrated, of a triangle or other
diagram, considered as the representative of all triangles and
diagrams, is moreover demonstrated of that individual triangle
or diagram. A third, and more satisfactory cause than the last,
may be, that in investigation, for the purpose of preventing
ambiguity and mistake, it is frequently necessary to recur from
the sign to the thing signified ; which is more easily done, the
less general and arbitrary the modes of representation are ; and,
consequently, in geometry more easily than in algebra.

I do not pretend to have assigned, accurately, and all, the
causes of perspicuity of geometrical reasoning. It may depend
on certain intellectual acts and processes, which it is beyond
the power of philosophy to explain. The circumstance, how-
ever, of the signs employed in geometry being natural signs,
will prove its perspicuity only to a certain extent, and in certain
cases. It must fail to prove it, when the properties of solids are
treated geometrically ; because the representation of solids on a
plane by diagrams, is not a natural representation, that is, would
not suggest to all minds the same tangible portion of extension.

It must fail likewise to prove it, in questions concerning radii
of curvature, areas of curves, &c. or in all questions in which
the fluxionary or differential Calculus is usually employed. The

• Does there not, however, here arise a consideration that takes away from the
cause of the perspicuity of geometrical demonstration } For the reasoning with a
diagram cannot be generally true, except the diagram be considered abstractedly, and
independent of those peculiar and distinguishing properties that determine its indi-
viduality.

analytical and geometrical Methods of Investigation, lei

lines and mixtilinear triangles therein exhibited cannot be called
natural signs, since they are only imperfect and inadequate
representations of other imaginary lines and triangles, of which
the mind must form what notion it can. Not, however, to infer
want of perspicuity from inefficiency in the cause assigned, if
we employ the geometrical method, or view its employment in
investigation, concerning motion, curves, &c. it will not appear
a perspicuous method ; and, if instances of its obscurity were re-
quired of me, I could find them, even in the immortal work of
the Principia. Whether we consider the fact, or speculate about
the cause, I think the geometrical method can only be allowed
to have superior evidence in investigations of a simple nature.

That the analytical calculus is more commodious for the de-
duction of truth than the geometrical, will not perhaps be con-
tested; and, an examination into its nature, would shew why it
is so well adapted for easy combination and extensive gene-
ralization. No language like the language of analysis, one of
the greatest of modern matliematicians has observed, is capable
of such elegance as flows from the developement of a long
series of expressions connected one with the other, and all de-
pendent on the same fundamental idea.

If we view what has been respectively done by each method,
in the explanation of natural phenomena, the superiority of the
one above the other will appear immense : yet the cultivators
of geometry were men of consummate abilities, and possessed
this great advantage, that the method or instrument of tliought
and reasoning which they employed had, during preceding
times, received the greatest improvement. Tlie analytical cal-
culus, which has verified the principle of gravitation, was a
hundred 3'ears ago in its infancy.

MDCCCII. R

122 Mr. WooDHousE on the Independence of the

The question, then, concerning the respective advantages of
the ancient geometry and modern analysis, may be comprised
within a short compass. If mental discipline and recreation are
sought for, they may be found in both methods ; neither is
essentially inaccurate; and, although in simple inquiries the
geometrical has greater evidence, in abstruse and intricate inves-
tigation the analytical is most luminous : but, if the expeditious
deduction of truth is the object, then I conceive the analytical
calculus ought to be preferred. To arrive at a certain end, we
should surely use the simplest means ; and there is, I think,
little to praise or emulate, in the labours of those who resolutely
seek truth through the most difficult paths, who love what is
arduous because it is arduous, and in subjects naturally difficult
toil with instruments the most incommodious.

XXVIII. If in matters of abstract science deference is ever
due to authority, it must be paid to that by which the study and
use of the method of the ancients has been recommended.
Newton has, however, brought forward no precise arguments
in favour of synthesis ; and it is easy to conceive, that he would
be naturally attached to a method long known and familiar to
him,* and by means of which he was enabled to connect his
own theory of curvilinear motions, with the researches of the
ancients on conic sections, and with Huygens's discoveries
relative to central forces and the evolutes of curves.

The very ingenious and learned Matthew Stewart -f endea-

» The circumstance of mathematicians having acquired a considerable dexterity in
the management of the geometrical method, seems to be the reason why they endea-
voured to explain the doctrine of logarithms (a subject purely algebraical) by the
introduction of the properties of curves.

f Words are frequently i-rated in a delusive and imposing manner, not always

analytical and geometrical Methods of Investigation. 1 23

voured to shew, that the geometrical calculus was competent to
the explanation of natural phenomena ; and with astonishing
perseverance applied it to many investigations in physical astro-
nomy. The labours of such a man are not hastily to be judged :
yet every one must determine for himself; and to me it seems,
his reasonings, from their intricacy, call up so great a contention
of the mind, that they prove, in no small degree, the unfitness
of the geometrical method in all abstruse and intricate inves-
^tigations.

XXIX. It may, however, be asked, are not there some sub-
jects of inquiry to which the geometrical method is better adapted
than the analytical ? and is not the theory of angular functions
one of these subjects ?* I apprehend not: for, if the conditions

intentionally. Dr. Stewart, (Preface to Sun's Distance.) and after him his ingenious
biographer, for the purpose-of holding up the superior simplicity of the geometrical
calculus, has said, that in order to understand his solution, a knowledge of the ele-
ments and conic sections only is requisite. But, in fact, the solution is effected by
proposition heaped on proposition ; and with equal truth and justness it might be
said, that in order to understand the analytical solution, a knowledge only of common
algebra is requisite ; since the methods by which the solution is effected, are really and
properly branches of algebra.

• D'Alembert says, "there are cases in which analysis, instead of expediting,
cmbarasses demonstration. These cases happen in the computation of angles : for angles
can analytically be expressed only by their sines; and the expression of the sines of
angles is often very complicated," &c. He adds, " that it must depend on mathema-
ticians, whether the method of the ancients or the modern analysis is to be employed,
since it would be difiicult to give on this head exact and general rules." In the very
case adduced, I think demonstration expedited by the analytical calculus ; and.although
J-' f xi/— i_j_j_;tVTI| i3 i^oj so speedily put down as cos. x; yet all processes of
evolution, differentiation, integration, &c. are much more easily performed with the
former expression than with the latter. Other instances of subjects of inquiry, to which
the geometrical method is said to be peculiarly well adapted, have been adduced ; but^
I still find no convincing reason, why a mathematician must submit to the necessity of

Ra

124 ^^' WooDHousE on the Independence of the

can be adequately and unambiguously stated in the general
terms of algebra, then deduction with such terms may be
strictly made, and expeditiously ; since it is to be made accord-
ing to a known and established process. I have shewn at some
length, that reasoning may be conducted with terms which
separately cannot be arithmetically computed : for the mere
process of deduction, it is not necessary to have distinct and
complete notions of the things signified by the general terms.

The principal object of the present paper is to shew, that the
analytical calculus needs no aid from geometry, and ought to
reject it, relying entirely on its own proper resources. By this
means, it would gain perspicuity, precision, and conciseness;
advantages not to be lightly estimated, by any one who has a
regard to certainty and demonstration, or considers the bulk to
which scientific treatises have of late years swelled.

In order to prove and illustrate the opinion I wished to
establish, I directed my search to those cases which have been
always thought to require the aid of the geometrical method.
By a purely analytical process, I have traced the origin and
derivation of certain fluxionary expressions, usually referred to
logarithms and circular arcs. I have given demonstrations of
the series for the sine of an arc in terms of the arc ; of the ana-
lytical formula for the root of a cubic equation in the irreducible
case ; of the resolution of x^ =j= a, into quadratic factors ; of the
series for the chord, &c. of a multiple arc in terms of the
simple arc, &c, which demonstrations, with as much confi-

learnlng half a series of truths by one method, and half by another. These considera-
tions, however, depreciate the value of the geometrical method only in one point of
view ; for, after all, the finest exemplar of clear and accurate reasoning is contained in
the works of Euclid.

analytical and geometrical Methods of Investigation . 1 25

dence as I dare assume, knowing how fallaciously we judge of
our own performances, I affirm to be strict and direct ; estab-
lished without artiiices, and without foreign aid drawn from
geometrical theorems and the properties of curves. In some
parts of this paper, the subjects, for their importance, may be
thought to be too slightly discussed ; the fear of appearing
prolix, has perhaps driven me into brevity and obscurity. In
other parts, what I have advanced may be remote from com-
mon apprehension, or contrary to received opinion : but here
I make no apology ; for, what I have written, has been written
only after long meditation, and from no love of singularity.
" If I cannot add to truth," I do not desire distinction from " the
" heresies of paradox."

C 1263

VI, Observations and Experiments upon oxygenized* and Ijyper-
oxygenized muriatic Acid; and upon some Combinations of the
muriatic Acid in its three States. By Richard Chcnevix, Esq.
F. R. S. and M. R. I. A.

Read January 28, 1802.

When Mr. Berthollet made known the combination of
what was then called oxygenated muriatic acid with potash,
he gave as his opinion, that the proportion of oxygen, rela-
tively to the quantity of acid, was greater in the salt than in
uncombined oxygenized muriatic acid. This conjecture was
fairly founded upon the observation, that, in his mode of pre-
paring this salt, a large portion of common muriate was formed
in the liquor, along with the hyperoxygenized muriate. The
Memoir which he published in the year 1788, is the last with
which I am acquainted, upon this subject. It does not contain
any thing that, considering the accuracy which is now required
in experiments, amounts to a demonstration of the relative
proportions of oxygen, in oxygenized and hyperox^^genized
muriatic acids. Unfortunately, this chemist has not pursued his
researches any farther ; although, from his own words, we had
every reason to hope that they would have been continued.
In the Systeme des Coiinoissances chimiques of Mr. Fourcroy,

• I have preferred this word to oxygenated, because aie is the appropriate termi-
nation of certain salts formed by the acids in ic. Some further remarks upon this
subject will be made in a work now in the press, entitled Rcmarki upon Cbtmkal
Nomenclature.

Mr. Chenevix's Obsercations and Experiments, Sec. 127

we find a summary of the experiments that had preceded the
impression of his work, together with the following sentence.
" Tons les muriates suroxygends sont d^compos(§s par les acides,
" soin'ent avec une violente decrepitation, avec une degagement
" de vapeur jaune verdStre, et une odeur tres-forte. Cette vapeur
" est de veritable acide muriatique suroxygene. Elle est lourde,
" tombe en goutellettes d'un jaune vert, et foi'me des stries
" comme de I'huile, sur les corps auxquels elle adhere." This
assertion carries no confirmation along with it; and does not
amount so near to proof as the position of the former chemist :
so that, in fact, the existence of hyperoxygenized muriatic acid,
and of its combination with potash, rests, at present, upon the
conjecture of Mr. Berthollet ; a conjecture however which,
as well as his whole dissertation upon the subject, bears all the
marks of genius which so strongly characterise every produc-
tion of that sagacious philosopher. Some notice has been taken
of other saline combinations, formed by causing a current of
oxA'genized muriatic acid to pass through solutions of the alkalis,
or earths, or by otherwise combining them. Mess. D'Olfus,
Gadolin, Van-Mons, Lavoisier, and others, have slightly
mentioned some of these combinations. But, with the exception
of Mr. Berthollet, I know of no chemist who has approached
so near to the real state of the combination of muriatic acid
and oxygen with potash, as Mr. Hoyle, of Manchester. The
true nature of this salt, however, is one of those things which
many persons have credited without proof; and which many
others have been on the eve of discovering.

I shall now proceed to lay before the Society, an account of
the observations and experiments which have led me to con-
clude, that* muriatic acid does exist in the form of oxygenized

128 Mr. Chenevix's Observations and Experiments

and liyperoxygcnized muriatic acid, as announced in the title of
tlie present communication ; and that, in either state, it is
capable of entering into saline combinations.

With this view, I shall describe,

ist. The means by which I think I have succeeded^ in ascer-
taining the constituent parts, as well as the proportions, in
oxygenized and hyperoxygenized muriatic acid.

sdly. I shall mention some of the combinations of the muriatic
acid, in its three states.

In treating upon the first of these objects, I must in some
measure anticipate the second ; and must suppose some things
known, which are hereafter to be described. This inconve-
nience is inevitable ; as the natural order of tilings leads me to
treat of the acid, before I consider the bodies into the compo-
sition of which it enters.

I exposed to the heat of a lamp, loo grains of hyperoxyge-
nized muriate of potash. It decrepitated gently, and in a short
time melted. After remaining in fusion nearly an hour, I al-
lowed it to cool: it crystallized as formerly, and had lost 2,5
per cent.. I increased the heat to redness, in a furnace. The
salt boiled with a violent effervescence, and rapid disengage-
ment of gaseous fluid, together with a thin white vapour, and
tlien sunk suddenly into a white spongy mass. The loss of
weight usually varied from 42 to 48 or 50 per cent.

I put 100 grains into a coated glass retort, luted to a small
and perfectly dry receiver, having a tube communicating with a
glass bell in the pneumatic tub. The fire had not been lighted
very long, when a slight dew began to iine the inside of the
receiver ; and, as soon as the retort was nearly red hot, a dis-
engagement of gas, so sudden as almost to be explosive, took

upon oxygenized and hyper oxygenized muriatic Acid, &c. 1 29

place. A quantity of thin white vapour arose, which afterwards
was deposited, in the form of a white sublimate, in the receiver
and the tube. When the extrication of gas had ceased, the ap-
paratus was allowed to cool. The gas, with the usual correc-
tions of temperature and pressure, measured 1 1 2,5 cubic inches,
= 38,3 grains. The 2,5 mentioned above, as the loss of this
salt at a low heat, were water. ^<y„^ remained in the retort ;
and the white sublimate in the tube and receiver amounted to 5.
The products of this operation were therefore.

Water - - - -2,5

Oxygen - - . . 38,3

Salt in the tube and receiver - 5

Salt remaining in the retort - - 53,5

To find the proportions of oxygen and muriatic acid, in hy-
peroxygenized muriatic acid, it now only remains to determine
the sum of the quantities of muriatic acid, contained in the ^o,,^
of the retort and the 5 of the tube and receiver. The ^O)^^ gave,
by nitrate of silver, a precipitate corresponding to 18,21 ; and
the 5, a precipitate corresponding to 1,76; in all, 20 of muriatic
acid. Therefore, 38,3 of oxygen, and 20 of muriatic acid, com-
bine to form 58,3 of hyperoxygenized muriatic acid ; or, 100 of
hyperoxygenized muriatic acid contain, within a fraction.
Oxygen - _ . g^

Muriatic acid - - _ _ g^

100.
And the elements of hyperoxygenized muriate of potash, should
be thus stated :

Oxygen - 38,3 j hyperoxygenized 7 _ _ g

Muriatic acid 20 t muriatic acid 3 ~ ~ o ^^

Potash _ _ _ 3^,2

Water - - - 2,5

100,0.

MDCCCII. S

igo ^r. Chenevix's Observations and Experiments

It may be observed, that the 53,5 of the retort did not yieU
the same proportion of acid as the 5 of the tube and receiver.
The fact is, that all muriates lose a Httle of their acid at a red
heat, as I shall presently mention more particularly; and the
small loss was, in all probability, owing to a portion of acid
disengaged by the heat to which the salt was necessarily ex-
posed during the operation.

Having thus ascertained the proportion of oxygen in hyper-
oxygenized muriatic acid, by means of its combination with
potash, a ready method occun'ed to arrive at the knowledge of
that contained in oxygenized muriatic acid. For tliis purpose,
I disposed in the following manner, a Woulfe's apparatus, con-
sisting of three bottles, and connected with the pneumatic tub.
In the first bottle, I put a solution of potash,* in about six parts
of water. In the second, a solution of the same; but so dilute,
as that no part of the salt, which might be formed, should crys-
tallize during the operation. About twenty parts of water was
the proportion there employed. In the third bottle, I put common
carbonate of potash. Through this apparatus, I sent a current
of oxygenized muriatic acid, disengaged by suJphuric acid, from
a mixture of muriate of soda and black oxide of manganese, in
the well known manner. Crystals of hyperoxygenized muriate
of potash were formed in the liquor of the first bottle ; and, as
long as they remained, I was certain, from previous experiment,
that no sulphuric or muriatic acid could pass into the second
bottle. The current was continued, till the liquor of that bottle
contained an excess of acid. The carbonate of potash, in the
third bottle, absorbed the superabundant vapours; and the

• Whenever potash, soda, barytes, an acid, an alkali, water, or the names of other
substances are used without an epithet, they are meant to denote them in that state
which is commonly called pure.

upon oxygenized and hyperoxygenized muriatic Acid, "&c. 131

pneumatic apparatus was ready to collect any gases that might
be evolved. By these means, I obtained, in tlie second bottle, a
solution of whatever substance might result from the action of
potash upon hypcroxygenized muriatic acid.

I took a portion of this liquor, which I shall call entire
liquor* and distilled it to dryness in a glass retort, taking
care to screen it from light. A tube from the receiver commu-
nicated with the pneumatic tub. My object was to ascertain,
whether the change observed by Mr. Berthollet, in the distribu-
tion of the elements of ox}'genized muriatic acid, to form, with
potash, a simple and a hyperoxygenized muriate, really took
place among those elements themselves, independently of any
absorption of oxygen from the atmosphere, or extrication of it
from the salt. Nothing but some water, and a few inches of the
dilated air of the vessels, passed into the receiver and the
pneumatic apparatus ; and I found, in the retort, a saline
massj-j- perfectly dry and crystallized. Hence it is evident, that
the same quantity of oxygen as that formerly contained in the
oxygenized muriatic acid, w-hich had been united to the alkali,
to form the total mass of salt, was now condensed, in that part
which had become hyperoxygenized muriate.

To ascertain this quantity, I dissolved 100 grains of the entire
salt in water, and precipitated by nitrate of silver. 1 thus ob-
tained a quantity of muriate of silver, which, by proportions
previously determined, I knew to correspond to 84, of muriate

• I am well aware that, upon philosophical principles, this appellation is objection-
able ; but, for the sake of brevity, I have used it as a temporary name, for a substance
which has only a relative existence among chemical bodies.

t This salt, I shall call entirt salt.

S 2

132 Mr. Chenevix's Observatiotis and Experiments

of potash : tlicrefore, 16 were liypcroxygenized muriate of
potash.* But, according to the proportions estabhshed above
in hyperoxygenized muriate of potash, 16 of this salt contain 6
of oxygen, with 3,20 of acid, the remainder being alkah and
water; and, by preliminary experiments, I found that 84. of
muriate of potash contained 27,88 of muriatic acid. Therefore,
27,884-3,20 = 31,08 of muriatic acid, with 6 of oxygen, cr,
to reduce it to the quintal.

Muriatic acid - - - 84,

Oxygen - - - - 16

1 00, are the proportions
which combine to form oxygenized muriatic acid.

To corroborate this evidence, I distilled 100 grains of the
entire salt mentioned above; and obtained nearly 16,5 cubic
inches of ox3'gen gas ; which as accurately corresponds with the
trial by nitrate of silver, as can be expected in experiments of
this nature.

Mr. Berthollet, in his Memoir upon oxygenized muriatic
acid, gives, if I understand him rightly, the following state-
ment of the proportions, and of the means by which he ob-
tained his results. He exposed to the light of the sun, 50
.cubic inches of water, saturated with oxygenized muriatic
acid; and collected in the pneumatic tub, 15 cubic inches of
oxygen gas. I here neglect fractions ; because our results ap-
pear, at first sight, to differ so widely as not to require great
accuracy in giving their comparative statement. He then preci-

• I must observe here, that hyperoxygenised muriate of potash does not, like simple
muriate, decompose the salts of silver. This shall be further animadverted upotij and
prove*) in its proper place.

upon oxygenized and hyperoxygenized muriatic Acid, &c. 133

pitated, by nitrate of silver, the 50 cubic inclies of liquor, which
had become simple muriatic acid, and obtained 38,3 grains of
muriate of silver. But, by experiments, I found that 38,3 of mu-
riate of silver contain 65 of muriatic acid. Therefore, 65 of
muriatic acid combine with 15 cubic inches* ( = 8 grains) of
oxygen, to fortn 73 of oxygenized muriatic acid. But 73 -. 8 : :
100 : 11, or nearly. For this difference, however, it may be
easy to account. Perhaps Mr. Berthollet's 50 cubic inches
of oxygenized muriatic acid, contained originally a little simple
muriatic acid ; and he says besides, that he suspects all the
oxygen was not disengaged. This indeed is most probable ; and
I am happy that I can reconcile the proportions which I have
found, to the opinion of so skilful a chemist.

Mr. Cruikshank likewise, in his additional Observations
upon Hydrocarbonates, has stated that 2,3 parts of oxygenized
muriatic acid contain 1 of oxygen, or about 4,3,5 per cent. But
this able chemist, to whom we are indebted for the discovery of
the gaseous oxide of carbone, procured his oxygenized muriatic
acid by a peculiar method, which I shall notice, in speaking of
the action of acids upon hyperoxygenized muriate of potash.
The substance he obtained was, in fact, not oxygenized muriatic
acid gas, but a mixture of that gas with hyperoxygenized mu-
riatic acid. I have not ihe smallest doubt of the accuracy of his
statement ; but, being the proportion of a mixture, it in no way
contradicts either of those I have determined in this Paper.

Before I dismiss this part cf the subject, I wish to anticipate
an objection, founded upon an observation of Mr. Berthollet,
which may be made to the above experiments. He says, that
when the alkaline solution is very concentrate, an effervescence

• Mr. Berthollet's proportior.s are in the old French weights and measures.

i34f ^f' Chenevix's Observations and Experiments

takes place during the whole of the saturation, and for some
days after; and this effervescence, he attributes to the escape
of oxygen. But I have already said, that no oxygen gas was
disengaged in any part of my process ; and no effervescence
took place in any of the bottles, except the third ; so that, no
superabundance of oxygen could have passed from one into the
other, nor could any diminution of the total quantity have been
produced. By repeating the experiments, sometimes with a so-
lution of alkali, and sometimes with water alone, in the first
bottle, I obtained the liquor in the second bottle uniform in all
c-^ses. Indeed, as potash prepared in Mr. Berthollet's man-
ner, was not in such general use at the time lie performed his
experiments as at present, I suspect that a great part of this
effervescence was owing to a disengagement of carbonic acid
from the alkali.

Having thus proved the difference between the states of these
two acids, I shall now proceed to the combination of each with
salifiable bases.

OXYGENIZED MURIATES.

As many properties of the entire liquor, before it had been
evaporated to dryness, had led me to imagine that the acid was
■united with the alkali, and remained in combination with it, in
the state of oxygenized muriatic acid, till the moment of crys-
tallization, I think it necessary to state at length the appear-
ances which induced me to draw that conclusion, and the expe-
riments which afterwards convinced me that it was erroneous.

A few drops of sulphuric acid, poured into some of the entire
liquor, caused an effervescence, and a smell of hyperoxygenized
muriatic acid.

upon oxygenized and hyperoxygenized muriatic Acid, &c. 135

Very strong acetic acid produced the same effect.
By other experiments, I had ascertained that acetic acid could
not decompose any part of the entire salt ; and hence I con-
cluded, that in the entire liquor, before evaporation, some of the
salt remained in the state of oxygenized muriate, the acid of
which was expelled by the sulphuric or acetic acid ; and, that
it t\-as not till the moment of crystallization, that the elements
of the salt underwent a total resolution into muriate, and hyper-
oxygenized muriate, of potash. However, a small quantity of
any of the very soluble neutral salts, such as nitrate or muriate
of ammonia, or even a little alcohol, produced the same effects ;
and- 1 was then convinced, that the effervescence was owing to
some uncombined oxygenized muriatic acid gas, remaining in
the liquor; and which was disengaged, in proportion as the
water was taken from it, by the superior affinity of the salt, or
the alcohol, I had used.

By some previous experiments, I had ascertained, as I have
just mentioned, that acetic or acetous acids do not decompose hy-
peroxygenized muriate of potash. I sent a current of oxygenized
muriatic acid.through a solution of acetite of potash ; and, upon
evaporation, I found that the acetous acid had been disengaged,
and that muriate, with hyperoxygenized muriate, of potash had
been formed. But, from some trials, which I shall presently
relate, I was induced to believe, that oxygenized muriatic acid
attracts the salifiable bases with a much weaker affinity than
acetous acid. It is well known that the contact of oxygenized
muriatic acid with an alkali, is sufficient to produce a combina-
tion of that acid with the alkali; and, from the last-mentioned
experiments it appears, that it is not absolutely necessary that

13^ ^ti"- Chenevix's Observations and Experiments

the alkali should be in a free state. If it be combined with an
acid weaker than hypcroxygenized muriatic acid, the original
acid will be expelled ; and muriate and hyperoxygenized muriate
will be formed, as if the alkali had been free.

As a further proof, that the change in the distribution of
oxygenized muriate of potash takes place at the moment of
contact of the acid and the alkali, and consequently long before
the crystallization, I mention the following experiments.

I precipitated, by nitrate of silver, 400 grains of the entire
liquor, previously to its being evaporated ; and obtained 7 1 grains
of muriate of silver.

I evaporated to dryness, 400 grains of the same liquor, redis-
solved the residuum, and, by dropping in nitrate of silver, ob-
tained 70 grains of muriate. The difference of one grain, in
these experiments, docs not amount to 0,2 of a grain of mu-
riate of silver ; and ought not to be regarded.

From these experiments, it is past all doubt, that the original
entire liquor did not contain oxygenized muriate of potash.
For, if such a coinbination had existed in it, I should have ob-
tained a smaller portion of muriate of silver in tUe first than in
the second case, on account of the total separation into muriate
and hyperoxygenized muriate having not yet taken place.

We are not however to conclude, from these experiments,
that there are no such things as oxygenized muriates. Although
they cannot be exhibited in a palpable state, it is easy to
demonstrate that they do really exist. I shall prove, in the
proper place, that hyperoxygenized muriate of ammonia is not
an incompatible combination; and must, for the present, assume
the datum, in order that I may demonstrate the necessary

upon arygenized and hyperoxygenhed niuriiUic Acid, &c. 1 37

existence of oxygenized muriates. Therefore : If muriatic acid,
or if hyperoxygenized muriatic acid, be brought in contact with
ammonia, the result will be muriate, or hyperoxygenized mu-
riate, of ammonia. But, if the acid, disengaged by sulpliuric
acid, from a mixture of blaclc oxide of manganese and muriate
of soda, be sent through ammonia, both are decomposed.
Hence it is evident, that the acid combines with the alkalis, in
the state of oxygenized muriatic acid ; and that the separation
into muriate and hyperoxygenized muriate, is produced by a
subsequent action, among the eleraents of oxygenized muriate of
potash.

Upon the whole, it appears to me fair to conclude,
1st. That the salts of this genus do really exist, previous to
the formation of hyperoxygenized muriate of potash.

2d. That the affinity exercised by hyperoxygenized muriatic
^cid for ammonia, and (by very strong analogy) for the other
bases, is much greater than that of oxygenized muriatic acid.
For, hyperoxygenized muriatic acid, as shall presently be shewn,
having a much more powerful action upon all combustible
bodies, whether simple or compound, than oxygenized muriatic
acid, it would be natural to suppose that the former acid would
act more powerfully upon the inflammable element of ammonia.
But oxygenized muriatic acid combines with the hydrogen of
that alkali ; which, however, is not decomposed by hyperoxy-
genized muriatic acid; yet the affinity of hyperoxygenized
muriatic acid for ammonia, is the only cause that determines the
union of the acid and the alkali, without decomposition. But
these affinities shall be more fully treated of, in speaking of
hyperoxygenized muriate of ammonia.

MDCCCII.

138 Mr. Chenevix's Observations ajid Experiments

ALKALINE AND EARTHY HYPEROXYGENIZED MURIATES.

Generic Characters.

Hyperoxygenized muriates are formed by passing a current
of oxygenized muriatic acid through the basis, dissolved or
suspended in water, as in the formation of the last mentioned
genu*. Their first formation is owing to the separation of the ele-
ments of an oxygenized muriate, into hyperoxygenized muriate
and simple muriate ; from which latter, they may be separated
by crystallization, or by another process, which I shall mention,
in treating of the earthy hyperoxygenized muriates. By simple
trituration, they scintillate, with noise. They are decomposed by
a low red heat ; and give out a considerable quantity of oxygen,
as they become simple muriates. They cannot be brought down,
by any means that I have tried, to that diminished state of oxy-
genizement, which would constitute oxygenized muriates. They
inflame all combustible bodies with violence, as is well known.
They are soluble in water ; many of them, in alcohol ; and some
are deliquescent. The acid is expelled, with particular pheno-
mena, by sulphuric, nitric, and muriatic acids, without heat;
and, a little below a boiling heat, by phosphoric, oxalic, tar-
tareous, citric, and arsenic acids : but they are not acted upon
by benzoic, acetic, acetous, boracic, prussic, or carbonic acids.
Those vegetable acids which are powerful enough to decompose
them, give out, towards the end, a gas of a peculiar nature,
which has not so much smell as oxygenized muriatic acid gas,
but which affects the eyes in an extraordinary manner, and
promotes an uncommon and rather painful secretion of tears.
I have not yet examined this gas, as there was invariably an
inflammation of the mixture, with explosion and rupture of the

upon oxygenized and hyperoxygenized muriatic Acid, &c. 139

vessels, almost as soon as it began to be evolved. "When pure,
the hyperoxygenized muriates do not precipitate any of the
metallic salts, although I believe they decompose some. The
order in which the bases seem to be attracted by the acid, is,
potash, soda, barytes, strontia, lime, ammonia, magnesia, alu-
mina, silica. The other earths I have not tried, and but few of
the metallic oxides.

15/ Species. Hyperoxygenized Muriate of Potash.

This salt is the best known of all the saline combinations of
this acid. It has been erroneously considered as simply oxyge-
nized, for its acid is really hyperoxygenized. It is soluble in
about sixteen parts of cold water, but in much less of warm ;
and is easily separated, by crystallization, from muriate of pot-
ash. Alcohol can dissolve a small portion of it. It seems capable
of existing in more states than one ; for, in passing a current of
oxygenized muriatic acid, very slowly, and in the dark, through
a solution of potash, till saturated, I have obtained flexible and
shining needle-like crystals. This leads me to suspect, either a
hyperoxygenized muriate of potash with excess of acid, or that
acid with a superaddition of oxygen. It would be superfluous to
enter into a minute description of a substance so well known as
hyperoxygenized muriate of potash ; but, it being the substance
whence I have chiefly attempted to disengage the acid, I shall
enter into a particular detail of the action of the more powerful
acids upon this salt.

If concentrate sulphuric acid be poured upon hyperoxygenized
muriate of potash, a violent decrepitation, sometimes but rarely
accompanied by a flash, takes place. A thick heavy vapour, of a
greenish yellow colour, which rises wath difficulty to the top of
the vessel, if it be deep, is disengaged. The smell is not altogether

140 Mr. Chekevix's Observations and Experiments

unlike nitrous gas ; but is peculiarly fetid, and may be compared'
to that which is emitted by brick-kilns, mixed with that of
nitrous gas. It differs much from oxygenized muriatic acid gas ;
the latter being pungent and penetrating, the other heavy and
oppressive ; and it does not produce, at least in so great a degree,
the catarrhal symptoms caused by the other. At the bottom of
this vapour is a bright orange-coloured liquor,, which has the
same smell as the vapour. This is the acid contained in the
salt; and I have proved it to be hyperoxygenized muriatic
acid. But, although the salt from which the acid is disen-
gaged be pure, the acid itself is never so; because the very
act of disengaging it effects its decomposition, and some of it
is converted into oxygenized muriatic acid. The colour of litmus
paper, on this account, is generally destroyed by the liquor. I
say on this account, because I have some reason to believe, from
having observed this not to be uniformly the case, that hyper-
oxygenized muriatic acid reddens the vegetable blues. However,
it must be considered, that the sulphuric acid used to disengage
the hyperoxygenized muriatic acid is still present; and we can
draw no certain conclusion, until we have obtained this acid
free from all other substances. If to this mixture of hyperoxy-
genized muriate of potash and sulphuric acid, heat be applied,
an exceedingly violent explosion, with a white and vivid flash,
takes place, before the liquor has attained the temperature of
125 of Fahrenheit. lii order to obtain this acid, I attempted
to distil 500 grains, in a glass retort, in a water bath, with
every precaution against such accidents as I could not but
in some measure expect; when, almost as soon as I had.
kindled the fire, I saw, in tlie bottom of the retort, an ex-
tremely white, vivid, and rapid flash, which was immediately
followed by a loud report. The retort was reduced almost to

2ipon oxygenized and hyperoxygettized muriatic Acid, &c. 141
powder; so that scarcely any fragments of it could be found in
the laboratory. The windows, and several glass vessels, were
broken. I happened to be holding the neck of the retort, at the
moment of the explosion, yet received no injury, except a slight
contusion in the hand. But Dr. Vandier, a French gentlemaa
of considerable chemical and medical talents, to wliom I am
indebted for much able assistance in my laboratory, was
wounded in several places; particularly, the tunica conjunctiva
of the eye was so lacerated, that a piece of it hung down, and,
by getting under the inferior eyelid, caused the most painful
irritation, and eiidangered his sight. One of the frontal arteries
also was divided. I relate these circumstances thus fully, as the
most effectual means of putting upon their guard, those who
would repeat the experiment. If the sulphuric acid be dilute,
heat may be applied with- more safety ; and the phenomena-
^re different. The hyperoxygenized muriatic acid is disengaged
from the basis; but, as the heat requisite to distil the acid is
more than sufficient to decompose it, oxygenized muriatic acid
comes over with it; and oxysren gas is collected in the pneu-
matic tub. If the distillation be continued, the same danger
arises as in the former case, because the sulphuric acid becomes
concentrated ; and it would seem, that its action upon die salt is
slight and partial at a low temperature, but violent and instan-
taneous when heated and concentrate. I could not, therefore
hope, by these means, to obtain the acid disengaged and pure.

If the manner of bringing the sulphuric acid and the salt into
contact be reversed, and the salt be dropped into tlie acid, the
yellow vapours and the orange-coloured liquor are produced,
but generally without decrepitation. If tliey be allowed to re-
main some days, in contiict, the vapours contituie, and oxygen
gas is constantly disengaged, even in the common light.of the

143 ■^^^' Chenevix's Observations and Experiments

day, and at the temperature of the atmosphere. By cooling the
first receiver with ice, I thought that I had once obtained
this acid crystallized in the form of four-sided pyramids, of an
orange colour. But, though I really believe this to have been
the case, I do not positively affirm it.

Nitric acid produces nearly the same phenomena ; but tiie
smell and other properties are rather less distinct and marked,
than with sulphuric acid.

Muriatic acid decomposes this salt, and unites to its basis ;
but neither the yellow vapours, nor the orange-coloured liquor,
are produced. The circumstances which attend the contact of
the acid and the salt, are as follows. If no more muriatic
acid be present than is merely necessary to decompose the salt,
I do not doubt that hyperoxygenized muriatic acid will be
driven off, as little decomposed as with the other acids, supposing
the action to be instantaneous ; but, during the contact of these
two bodies, the acid expelled must meet muriatic acid not yet
combined, and, uniting with it, always forms a portion of oxy-
genized muriatic acid. The quantity of the last acid must vary,
according to the quantity of muriatic acid employed, and not
combined with the alkali. It was by this method that Mr.
Cruickshank obtained the muriatic acid gas, which he stated
to contain 43,5 per cent, of oxygen.

Phosphoric and arsenic acids do not act upon this salt, till
lieated with it ; and then much oxygen gas is evolved. These,
therefore, aiibrd no better method of disengaging hyperoxyge-
nized muriatic acid without decomposition.

Oxalic, tartareous, and citric acids, act as I before men-
tioned ; and the hyperoxygenized muriatic acid holds its place,
in the order of affinities for potash, immediately before the
benzoic.

upon oxygenized and byperoxygenized muriatic Add, &c. 145

I shall not stop to detail a number of amusing phenomena
that may be produced, by projecting into the stronger acids,
mixtures of combustible bodies, whether metallic or not, and
byperoxygenized muriate of potash. The cause of them is well
understood, and the theory points them out : they are, there-
fore, no longer objects of philosophical admiration. But I must
mention one experiment, which, had it succeeded, I sliould have
thought important. I projected various mixtures of very mi-
nutely pulverised diamond and this salt, into the different acids;
but found the diamond undiminished, by every attempt to com-
bine it with oxygen in the humid way.*

Another, but imponderable, part of this salt, as indeed of all
byperoxygenized muriates, seems to be an extraordinary quan-
tity of caloric. For, during their formation, scarcely any heat
is disengaged, as by other acids ; and, very little heat applied to
the salts, gives the gaseous form to their oxygen.

An opinion has prevailed among some ingenious chemists,
that, from a mixture of this salt with sulphuric acid, nitrous gas
is disengaged, and sulphate of lime formed in the retort. But
this is a mistake, arising, on the one hand, from the smell and
vapour"of the byperoxygenized muriatic acid, and, on the other,
from sulphate of lead, which the common sulphuric acid of this

• I roust confess, that the vivid flashes of light» emitted from the mixfUre of this
jalt and combustible bodies thrown into an Jicid, appear to me, in some measure, to
prove the mo-iification proposed byLEOuHARDj.RicHTER, Gren, &c. to that part
of the Lavoisierian theory which regards the emission of light during combustion.
Another testimony in favour of their modification, may be drawn from the vegetable
kingdom. All plants growing in places deprived of light, are merely mucilaginous.
But the mucilage of these plants burns without the emission of light. Light, there-
fore, appears not to be disengaged from oxygen ; else, why not by this mucilage, as
Well as by other combustible bodies i

T44 ^f- Chenevix's Observations and Experiments

country frequently contains in solution, and which is precipi-
tated from it by water. Before we assert a fact, we should be
well assured of the pureness of our chemical agents. Tiiis
supposed conversion of muriatic or hyperoxygenized muriatic
acid into nitrous gas, will not pass for a decomposition, or a
transmutation, of that refractory radical ; and the idea of tiie
<;hange of potash into lime, is as erroneous as some other late
assertions respecting the decomposition of the alkalis.
The proportions of this salt are, as I before stated,
Hyperoxygenized muriatic acid - - 58,3
Potash ------ 2^,2

Water - - :, - 2,5

100,0.

2d Species. Hyperoxygenized Muriate of Soda.
This salt is prepared in the same manner, and with the same
phenomena, as the former. It is extremely difficult to obtain it
pure, as it has nearly the same degree of solubility in water
as muriate of soda. It is soluble in three parts of cold, and
less of warm water ; and is slightly deliquescent. It is soluble
in alcohol ; but this property alone is not sufficient to enable us
to obtain it free from the muriate of soda, formed along with it
in the entire liquor ; as the latter salt, contrary to the assertions
of all authors, is soluble in alcohol, and seems to be much more
so, when accompanied by the hyperoxygenized muriate. It was
by taking a large quantity of the entire salt, formed by sending
a current of oxygenized muriatic acid gas through a solution of
carbonate of soda, and repeatedly crystallizing in alcohol, that,
with great difficulty, I obtained a little pure hyperoxygenized
muriate of soda. It crystallizes in cubes, or in rhomboids little

upon oxygenized and hyperoxygenized muriatic Acid, &c. 145

diflferent from cubes. It produces a sensation of cold in the

mouth ; and its taste is easily distinguished from muriate of soda.

It is decomposed by heat, by combustible bodies, and by acids,

in the same manner as the former species ; and the acid holds

its place for soda, as for potash, immediately before the benzoic.

The basis is separated by potash only. This salt is composed of,

Hyperoxygenized muriatic acid - - 66,2

Soda ... - oQ^6

Watei' - - - - 4>3

100,0.

^d Species. Hyperoxygenized Muriate of Barytes.
The earthy bases seem'fo follow, in the order of affinities for
this acid, at a grcat distance from the alkalis. They are all
superseded by the two just mentioned ; and it is much more dif-
ficult to accomplish their union with the acid, than is the case
with potash or soda. The most advantageous method is, to pour
warm water upon a large quantity of this earth, procured by
Mr. Vauquelin's method ; and to cause a current of oxygenized
muriatic acid to pass through the liquor, kept warm; so that
the barytes already dissolved being saturated, a fresh portion of
it may be taken up by tiie water, and presented in a state of
great division to the acid. This salt is soluble in about four
parts of cold, and less of warm water. It crystallizes like the
muriate of this earth ; and resembles it so much in solubility,
that I could not separate them effectually by crystallization
repeated several times. At first, indeed, I despaired of ever
obtaining any of the earthy hyperoxygenized muriates in a
state sufficiently pure for analysis. If we consider them as a
genus distinct from the alkaline hyperoxygenized muriates,

MDCCCII. U

146 Mr. Chenevix's Observations and Experiments

a leading character may be, their great resemblance to their
respective species of earthy muriates. I thought, however, that
I might, if not by direct, at least by double affinity, decompose
the one without the other ; and phosphate of silver occurred to
me as the most likely agent. If phosphate of silver be boiled
with muriate of lime, of barytes, &c. a double decomposition en-
sues; and muriate of silver, together with phosphate of the earth,
botli insoluble, are precipitated. To increase the action, the
phosphate of silver may be dissolved in a weak acid, such as
the acetous ; and, though the earthy phosphate be at first re-
tained in solution, it will be separated by expelling the acid.
The only condition absolutely necessary is, that the silver em-
ployed be free from copper. For, in preparing phosphate of
silver by phosphate of soda, and by nitrate of silver thus impure,
copper would be thrown down by the phosphoric acid ; and the
phosphate of copper would be afterwards decomposed by muriate
of lime. Muriate of copper would therefore remain with the
earthy hyperoxygenized muriates ; or, what is still worse, a
part of the muriatic acid being easily expelled from oxide of
copper, the hyperoxygenized muriatic acid would be driven off
from its basis, by the more powerful agency of the former.
This salt has all the properties enumerated as belonging to the
genus of hyperoxygenized muriates ; and, with heat, the acid is
expelled by all acids above the benzoic. I had hoped that, without
distillation, I could procure the acid from the salt by means of
sulphuric acid, which would have left an insoluble salt with
barytes ; but hyperoxygenized muriatic acid is so easily decom-
posed by light, that I have not yet obtained it, to my satisfaction,
disengaged and pure. A fact well worthy of attention is, that
the stronger acids disengage this acid with a flash of light.

upon oxygenized and hyperoxygenized muriatic Add, &c. 147

more frequently from the earthy than from the alkaline hyper-
oxygenized muriates ; a phenomenon which, I suppose, depends
upon the relative proportionate affinities, and consequently the
gi'eater rapidity of the disengagement. But, where all is hypo-
thesis, it is useless to draw any inference from a single fact.
The proportions of this salt are,

Hyperoxygenized muriatic acid - - 47
Barytes - - - - 42,2

Water - - - - 10,8

100,0.

/i^th Species. Hyperoxygenized Muriate of Strotitia.

The foregoing observations apply to the formation of this
salt, to the mode of obtaining it pure by phosphate of silver, to
its conduct with the acids, to the rank of its acid in the order
of affinities, and to its other properties. It is deliquescent; and
more soluble in alcohol than muriate of strontia. It melts in
the mouth immediately, and produces cold. Its crystals assume
the shape of needles.
It is composed of,

Hyperoxygenized muriatic acid - - 46
Strontia - - - - 26

Water - - - - 28

100.

5^^ Species. Hyperoxygenized Muriate of Lime.
Tliis salt is obtained pure, in the same manner as the other
earthy salts. It is extremely deliquescent; liquifies at a low
heat, by means of its water of crystallization; and is very

Us

14,8 Mr. Chenevix's Observations and Experiments

soluble in alcohol. It produces much cold, and a sharp bitter

taste in the mouth.
It is composed of,

Hyperoxygenized muriatic acid - - 55,2
Lime . _ _ « 28,3

Water - - ... 16,5

IQOjO.

6th Species. Hyperoxygejiized Muriate of Ammonia.

From the property which oxygenized muriatic acid possesses
of decomposing ammonia, this combination may be thought
paradoxical. For, how can an acid much m.ore active than
oxygenized muriatic acid exist with ammonia, which is de-
stroyed by the latter .'' But this argument may be opposed by
the sum of affinities that act in either case. If the affinity of
composition of oxygenized muriatic acid and of ammonia, toge-
ther with the affinity of oxygenized muriatic acid for ammonia,
to form oxygenized muriate of ammonia, be not more powerful
than the affinity of oxygen for hydrogen, of azote for caloric,
and of muriatic acid for ammonia, tlie divellent affinities will
prevail ; and this is what actually happens. But, although oxy-
gen may be held witli less force of attraction in oxygenized
than in hyperoxygenized murii-tic acid, yet the affinity of the
latter acid for ammonia may increase in a much greater ratio,
and favour the quiescent affinities. If carbonate of ammonia be
poured into any earthy salt of this genus, a double decomposition
takes place; and hyperoxygenized muriate of ammonia is formed.
This salt is very soluble in water, and in alcohol. It is de-
composed at a very low temperature, and gives out a quantity

tip07i oxygenized and hyperoxygenized muriatic Acid, &c. 149

of gas, together with a smell of hyperox3'genized muriatic acid.
Such a smell is doubtless owing to the great quantity of oxy-
gen contained in the acid; it being more than is necessary to
combine with the quantity of hydrogen contained in the alkali,
and therefore some of the acid is disengaged, without decom-
position. All the attempts I have made to ascertain the propor-
tions of its principles, have been fruitless. The formation and
existence of this salt, as I before said, are very strong proofs
of what I have advanced respecting the state in which hyper-
oxygenized muriates at first exist ; and very fully prove the dif-
ferent degree of affinity exercised by each acid toward the basis.

"jth Species. Hyperoxygenized Muriate of Magnesia.

Its chemical and physical properties are nearl}' the same with
those of the 5th species, only that, in addition to the other
bases, lime and ammonia cause a precipitate in this salt.
Its proportions are,

Hyperoxygenized muriatic acid - - 60
Magnesia - _ _ _ 25,7

Water - - - - 14,3

100,0.

^ih species. Hyperoxygenized Muriate of Alumina.

I put some alumina, precipitated from muriate of alumina, and
well washed, but still moist, into a Woulfe's apparatus, disposed
as for the other earths, and sent a current of oxygenized muriatic
acid gas through the liquor. The alumina shortly disappeared ;
and, upon pouring sulphuric acid into the liquor, a strong smell
of hyperoxygenized muriatic acid was perceivable. When I at-
tempted to obtain the salt pure, by phosphate of silver, in the

1^0 Mr. Chenevix's Observations and Experiments

usual way, I found nothing in solution but hyperoxygenized
muriate of silver ; * and all the hyperoxygenized muriate of alu-
mina had been decomposed. This salt, however, appears to be
very deliquescent, and is soluble in alcohol ; but I could not
ascertain the proportion of its principles, because I did not obtain
it sufficiently free from the simple muriate.

Qth Species. Hypei-ozygenized Muriate of Silica.

I am inclined to think this salt does not really exist. A cur-
rent of oxygenized muriatic acid, sent through some silica which
had been precipitated from an acid by ammonia, and collected
moist from the filter, did not seem to dissolve any portion
of it. In all barytes and strontia, prepared according to Mr.
Vauquelin's method, a portion of silica from the crucibles is
attacked, and taken up, by whatever acid those earths may
afterwards be dissolved in; and, in all potash of commerce,
there is some silica ; but I have never perceived that any portion
of this earth had been dissolved by this acid.

The very small portion of earth which, in attempts to form
the different species of this genus of salts, is taken up by acids,
and the still smaller portion of the salt so formed, which is
really in the state of hyperoxygenized muriate, render the
operation so tedious, that I have confined myself to form
what was necessary to determine their analysis, in such a
manner as I believe to be nearly accurate. It cannot, there-
fore, be expected that I make myself responsible, without a
right of appeal to further experiments, for the accuracy with
which the crystalline forms, and other physical properties,

* This salt shall be particularly mentioned and described in another part of this
Paper. For the present, it is sufficient to say, that it is very soluble in water ; and, in
that property, as in many others, is totally different from muriate of silver.

npoji oxygenized and hyperoxygeiiized muriatic Acid, Sec. 151

may have been stated. It is impossible to obtain satisfactory
crystals from a very small portion of salt; and I have at-
tached myself more particularly to chemical than to physical
characters, as being a much more important and certain mode
of determination. For the same reason, I have not exa-
mined the combination of the new and rarer earths with this
acid. But I do not doubt, that whatever chemist undertakes a
further investigation of these extraordinary bodies, will be amply
repaid for his labour.

I have mentioned, in a former part of this Paper, that all
muriates lost a portion ©f their acid at a red heat. I exposed one
hundred parts of muriate of potash, in a crucible, to a red heat,
for some minutes, and found that they lost five. I dissolved them
ia water, and they manifested alkaline properties. Treated by
nitrate of silver, they gave a precipitate, which shewed one per
cent, less of muriatic acid, than 100 parts of the same salt that
had not been exposed to fire. A violent heat may be necessary
to expel the last portion of water of crystallization from certain
salts, as we know particularly is the case with sulphate of lime.
But, if any of the acid can be expelled at the same temperature,
there is no longer any certainty. The quantity of water, as stated
by different chem.ists, varies much ; and, from some experiments
I have made, I do not believe it to have been accurately deter-
mined. The method I used to ascertain tiiis, was as follows :
I exposed a given quantity of the salt to a violent heat, and
noted its loss of weight. I then precipitated, by nitrate of
silver; and thus knew, how much the quantity of muriatic
acid which this salt contained, was less than that in a like
portion which had not been exposed to heat. I subtracted the
difference in this quantity, from the total loss of weight in the:

153 Mr. Chenevix's Ohsetrations and Experiments

salt exposed to heat ; and the remainder I considered as water.
It was upon results obtained in this manner, that I founded
many of the j)roportions I have given in this Paper.

It is stated in the tables of Bergman, corrected by Dr.
Pearson, that lime and strontia prefer acetous to arsenic acid.
But arsenic acid can expel hyperoxygenized muriatic acid from
its basis, although the acetous cannot act in the same manner ;
therefore, this order of affinities is erroneous. It was not till
lately, that we had potash and soda so pure as to be relied
upon in delicate experiments ; and it is not surprising that we
find mistakes with regard to their taking the acid from barytes,
strontia, and lime. But real potash and soda both precipitate
even barytes from hyperoxygenized muriatic acid. If ever it
becomes easy to obtain hyperoxygenized muriate of barytes, we
may prepare that earth from it in tlie humid way, and more
near to purity, than in the method proposed by Vauquelin.

METALLIC COMBINATIONS OF MURIATIC ACID, IN ITS
DIFFERENT STATES.

The action of hyperoxygenized muriatic acid upon metals,
is, as may well be expected, rapid, and without disengagement
of gas. It appears to dissolve every metal, not excepting gold and
platina. If the metal be presented to the acid at the moment
when it is disengaged from the salt, inflammation ensues ; and
the phenomena of light and heat vary according to the metal ;
but the salts thus produced are merely muriates. In order to
form real hyperoxygenized muriates, it is necessary to take the
metal in its fullest state of oxidizement, and combine it with the
acid, either by double decomposition, or by passing a current
of oxygenized muriatic acid gas through the oxide suspended

upon oxygenized and byperoxygenized muriatic Acid, &c. 153

in water. The acid is thus separated into muriatic and hyperoxy-
genized muriatic acid ; and, in these states, combines with the
metalhc oxide. The metallic hyperoxygenized muriates are differ-
ent, in every respect, from the metallic muriates. Red oxide of
iron is dissolved with difficulty. Oxide of copper more easily.
Red oxide of lead exhibits the same appearances, during its com-
bination with this acid, as with nitric acid. When nitric acid is
poured, even in excess, upon red oxide of lead, only a part of the
oxide is dissolved, unless heat be applied ; and what remains
becomes a blackish brown powder. But, if metallic lead be
added, in a just proportion, all the red oxide disappears, and none
of the brown powder is formed ; neither is there any disengage-
ment of nitrous gas, when the metallic lead is dissolved. The
precipitates caused in either case, by pouring an alkali into the
nitric solution, are yellow. Hence it appears, that red oxide of
lead contains too much oxygen to be dissolved by nitric acid.
One part of the oxide takes up the excess of oxygen, and
becomes brown; while the portion which loses oxygen, be-
comes yellow, and is soluble in nitric acid. The presence of
metallic lead promotes the total solution of the red oxide, by
taking up the superabundant oxygen. I found that a current of
oxygenized muriatic acid gas, like the nitric acid, dissolved a part
of the red oxide, and caused the brown powder to be formed,
upon which it could not act. Hyperoxygenized muriate of lead
is much more soluble than muriate of lead; and the acid is
very slightly attracted by the basis.

But, of all the metallic salts formed by the combination of
the muriatic acid, in any of its different states, none so much
deserve attention as those which have for their bases, the oxides
of mercury. The nature of the salts which result from the

MDCCCII. X

154. ■^''- Chenevix's Observations and Experiments

combination of common murjeitic acid with the different oxides
of thi3 metal, has been stated in the most contradictory manner,
by diffei-ent chemists. But, as the knowledge of hyperoxyge-
nized muriatic acid has thrown some light upon the true state
of calomel and corrosive sublimate,* I must beg leave to dwell
at some length upon this important part of my subject.

It would be useless to repeat the opinions of the old authors,
who have treated of corrosive sublimate, and of calomel. They
are to be found in the works of those respective chemists, and I
must refer to them for particulars.

In the Memoirs of the Academy of Sciences of Paris, for
1780, we find a Paper of Mr. Berthollet, upon the causticity
of metallic salts ; in which he appears t9 think, that the acid in
corrosive sublimate is in the state of what was then called
dephlogisticated marine acid. In 1785, when he had examined
the oxygenized muriatic acid with more care, Itc renounced his
former opinion ; and gave the reasons why he no longer ad-
hered to it. Some late experiments of Mr. Proust shew, that
this chemist thinks as Mr. Berthollet now does. And these
may be ranked among the first of modern authorities.

Notwithstanding those opinions, Mr. Fourcroy, in his Sys-
teme des Connoissances chimiques, still considers corrosive subli-
mate as a hyperoxygenized muriate of mercury ; and designs it

• I regret very much, that I am under the necessity of using these unmeaning terms.
But the French nomenclature has made no distinction between salts formed by me-
tallic oxides in different states of oxidizement, except by the colour, which is an
extremely defective and unmeaning method. At all events, this metal is so uncom-
plaisant as to retain the white colour, in its different oxides combined with muriatic
acid. I prefer, however, using the old name, to proposing any provisional substitute
that might be found defective. This will be farther explained in Remarks upon
cbemical li amend aim e.

tipon oxygenized and hyperoxygenized muriatic Acid, &c. 155

throughout by that name.* This chemist, one of the founders of
the methodical Nomenclature, is too well acquainted with its
principles, to apply the term hyperoxygenized muriate to any
thing but a combination of hyperoxygenized muriatic acid. It
is evident, therefore, that he considers the portion of oxygen,
which, in equal quantities of corrosive sublimate and calomel,
is greater in the former, to be combined with the acid, and not
with the oxide of mercuiy. As soon as I have stated some
experiments that prove Mr. Fourcroy's opinion to be errone-
ous, and endeavoured to establish the analysis of corrosive
subhmate and of calomel, I shall take notice of a salt hitherto
unknown, which really is hyperoxygenized muriate of mercury.

I took a portion of corrosive sublimate, and precipitated by
potash. The liquor was filtered ; and, upon being tried, nothing
but muriate of potash was found. No reagent could discover
the smallest trace of hyperoxygenized muriatic acid.

Sulphuric, nitric, phosphoric, and many other acids, poured
upon corrosive sublimate, did not disengage either muriatic, or
hyperoxygenized muriatic acid. Nitrate of silver, poured into
a solution of corrosive sublimate, gave an abundant white
precipitate.

From these experiments it is evident, that muriatic acid, not
hyperoxygenized muriatic acid, is combined with the oxide of
mercury in corrosive sublimate.

To determine the proportions of this salt, I took one hundred
parts, and precipitated by nitrate of silver. I then took another
hundred, and precipitated by potash. The result of these two

• I have said before, that this acid was talked of by many chemists, as if the existence
of It had really been proved.

X2

156 Mr. Chenevix's Observations and Experiments

experiments was such as to establish tlie proportions of coito-

sive sublimate as follows :

Oxide of mercury - - - 82

Muriatic acid - - - - 18

100.
But, the acid of this salt not being charged with a super-
abundance of oxygen, we must look for the excess in the
metallic oxide. I took 100 grains of mercury, and dissolved
them in nitric acid ; then poured in muriatic acid ; and, at a
very gentle heat, evaporated to dryness. I afterwards sublimed,
in a Florence flask, the salt that remained, and obtained 143,5
of corrosive sublimate. -But, 143,5 of corrosive sublimate, con-
tain 26 of acid; which will leave 117,5 for the mercurial
oxide; and, if 117,5 contain 100 of mercury, 100 of the oxide
will contain 85. Therefore, the oxide of mercury, in corrosive
sublimate, is oxidized at the rate of 15 per cent.

To determine the proportions in calomel, I dissolved 100
grains of it in nitric acid. The phenomena of the solution have
been so accurately described by Mr. Berthollet, that I shall
not repeat them. I precipitated by nitrate of silver ; and ob-
tained a quantity of muriate of silver, corresponding with 11,5
of muriatic acid. The oxide of mercury I obtained apart.
Therefore, calomel is composed of,

Oxide of mercury _ - - 88,5

Muriatic acid - - - - 11,5

100,0.
To ascertain the state of oxidizement of the oxide in calomel,
I took 100 grains, and boiled them with nitro-muriatic acid;

iipo7i oxygenized and hyperoxygenized muriatic Acid, &c. 157

then evaporated very slowly, and sublimed as above. The
calomel was totally converted into corrosive sublimate, and
weighed 113. But 113 of corrosive sublimate contain 20,3 of
muriatic acid, of which, 11,5 were originally in the calomel.
The total addition of weight was 1 3. But the quantity of acid
in these 13, amounts to 20,3 — 11,5 = 8,8. Therefore, 13 — 8,8
= 4,2, remain for that part of the additional weight which is
oxygen. On the other hand, 100 of calomel contain the same
quantity of mercury as 1 13 of corrosive sublimate, = 79. These
79, with 11,5 of acid, are equal to 90,5, and leave 9,5 for the
quantity of oxygen contained in calomel. It would appear, from
these experiments, that corrosive sublimate contains 6,5 per
cent, more acid, and but 2,8 per cent, more oxygen, than calomel;.
But this quantity of oxygen is combined witli a much greater
proportion of mercury ; and forms an oxide of a very different
degree of oxidizement. For, 88,5 : q,s : : 100 : 10,7. There-
fore, we may establish the following comparative table.

CALOMEL.

The oxide of mercury in calo-
mel is composed of.

Mercury - - 89,3

Oxygen - - 10,7

100,0.
And calomel is composed of,

Mercury 79 /oxide ofij^n
Oxygen 9,5 1 mercury J '"^

Muriatic acid - 11,5

100,0.

CORROSIVE SUBLIMATE.

The oxide of mercury in corro-
sive sublimate is composed of.

Mercury - - - 85

Oxygen. - - 15

100.
And corrosive sublimate is com-
posed of.

Mercury 69,7/- oxide ofi ^^
Oxygen 12,31 mercury i

Muriatic acid - i8"

100..

1^8 Mr. Chenevix's Observations and Experimaits

These proportions are different from those given by Lemery,
Geoffroy, Bergman, &c. But, without calling in question the
accuracy and skill of these chemists, it is fair to assert, tiiat
the pure materials used by modern chemists, are more likely to
lead to sure results, than the impure reagents of the ancients.

In these salts we find another instance, that, in proportion as
metallic oxides contain a greater quantity of oxygen, they require
a greater quantity of acid to enter into combination with them.

The method I have followed, to ascertain the proportions just
stated, may appear, at first view, not to be the shortest that I
might have adopted. But I have tried others, and have found
none so accurate. It is impossible, synthetically, to convert a
given quantity of mercury into calomel, in such a manner as to
be certain that none of it is in a different state from that re-
quired. And, if we would attack calomel analytically, the action
of the alkalis, without which we cannot proceed, is such as to
alter the nature of the oxides. I have also made many com-
parative experiments, by dissolving calomel in nitro-muriatic
acid, (which converted it into corrosive sublimate,) and then
precipitating by ammonia ; but I have not found these trials so
successful as those I have described. The nature of the preci-
pitate from corrosive sublimate by ammonia, certainly differs, ac-
cording to the excess of acid that may be present ; and mercury
seems to have the power of existing in many degrees of combi-
nation with oxygen. The only precaution absolutely necessary,
in this mode of operating, is, that while the mercurial salt is in
an open vessel, it should not be exposed to a degree of heat
capable of volatilizing any part of it.

The quantity of mercury ordered in the London Pliarma-
copoeia, to convert corrosive sublimate into calomel, is 9 pounds

upon oxygenized and hyper oxygenized muriatic Acid, &c, 1 59

of mercury for every 12 pounds of corrosive sublimate. But,
from the above experiments, it would appear, that a smaller
quantity of mercury might strictly answer. However, from
the resuUs of minute investigation, we should not conclude
too hastily upon preparations on the great scale ; and, I rather
think, that the excess of mercury ordered by the Pharmacopoeia
is a useful precaution.

In my experiments, I attempted to reduce, by means of
copper, iron, or zinc, the mercury contained in the mercurial
salts. Iron did not answer the purpose : zinc precipitated the
mercury a little better ; and copper produced a change which I
did not expect. If a bit of copper be put into a solution of cor-
rosive sublimate, a white powder shortly falls to the bottom;
and that powder is calomel. When washed, it does not contain
an atom of copper, nor of corrosive sublimate.

Before I conclude these considerations, I must say, that
whether calomel be prepared in the dry or in the humid way,*
it does not seem to differ chemically; nor does it contain any

» By the humid way, I do not mean precisely the method ofScHEELE. That che-
mist desires us to boil the acid with the mercur)', after they have ceased to act upon
each other at a low temperature. By this method, the nitric acid takes up an excess of
mercurial oxide ; and the nitrate of mercury thus formed, precipitates by water.
Therefore, when this nitrate of mercury is poured into the dilute solution of muriate
of soda, according to the formulaof So he ele, the action, on the part of the solution,

is twofold.

1st. The water acts upon one part, and precipitates an oxide, or rather an insoluble

subnitrate of mercury, v^nd,

2dly. A double decomposition takes place between the nitrate of mercury and the
muriate of soda. It is with reason, that the medical world have supposed the calomel
of ScHEELE to be different from that prepared in the humid way; for it is, in fact,
calomel, plus an insoluble subnitrate of mercury. In the first part of Schbels's

i6o Mr. Chenevix's Observations and Experiments

sensible portion of water of crystallization. The same may be
said of corrosive sublimate.

It now remains to speak of the real hyperoxygenized muriate
of mercury. I passed a current of oxygenized muriatic acid
gas through some water, in which there was red oxide of mer-
cury.* After a short time, the oxide became of a very dark
brown colour; and a solution appeared to have taken place. The
current was continued for some time; and, when I thought
that a sufficient quantity of the oxide had been dissolved, I
stopped the operation. The liquor was evaporated to dryness ;
and the salt was thus obtained. There evidently was in the
mass a great proportion of corrosive sublimate, as might be
expected, from what I had observed to take place in the forma-
tion of the other salts of this acid ; but, by carefully separating

process, there is disengagement of nitrous gas, together with oxidizement and solution
of some of the mercury. When he boils the acid upon the remaining mercury, there
is no further disengagement of gas ; yet more mercury is dissolved. The nitrate of
mercury, therefore, rather contains an oxide less oxidized after ebullition than before
it. The true difference is in the subnitrate of mercury, precipitated, as I before said, by
the water in which the muriate of soda was dissolved. And the orange coloured powder,
which remains after an attempt to sublime Scheele's calomel, is to be attributed to
the same cause. To prepare calomel in the humid way, uniform as to itself, and in all
respects similar to that prepared in the dry way, it is necessary, either to use the nitric
solution before it has boiled, or to pour some muriatic acid into the solution of muriate
of soda, previously to mixing it with the boiled solution of nitrate of mercury. In the
first case, no precaution is necessary ; and, in the latter, the oxide of mercury, which
the nitrate of mercury has, by boiling, taken up in excess, finds an acid which is ready
to saturate it. All the mercurial oxide being thus converted into calomel, none of that
subnitrate of mercury can be present.

The objections made by a medical gentleman against Scheele's calomel, when this
Paper was read before the Royal Society, led me to reconsider the subject, and to
undertake the investigation detailed in this note.

• I used either of the red oxides of mercury, indiscriminately.

vp07i oxygenized and hyperoxygenized muriatic Acid, &c. 161

the last formed crystals, I could pick out some hyperoxygenized
muriate of mercury. I then crystallized it over again ; and, in
this manner, I obtained it nearly pure. This salt is more soluble
than corrosive sublimate : about four parts of water retain it
in solution. The shape of its crystals, I cannot well determine.
When sulphuric, or even weaker acids, are poured upon it, it
gives out the usual smell of hyperoxygenized muriatic acid ;
and the liquor becomes of an orange colour. This is a sufficient
proof, that corrosive sublimate is not a hyperoxygenized muriate
of mercury.

I have just mentioned that, in the formation of this salt, the
oxide of mercury, which was not dissolved by the acid, became
of a very dark brown colour. I procured a portion of this
oxide, which seemed different from the red oxide. It however
retained the form, and the crystalline appearance, of the latter.
It was soluble in nitric acid, without disengagement of gas ; and
was precipitated from it, in a yellow oxide, by all tlie alkalis,
except ammonia. It formed corrosive sublimate with muriatic
acid ; and the precipitate by the alkalis, v/as the same as that
from corrosive sublimate, made with the red oxide. Yet I am
inclined to think, that the dark brown oxide differs in some
essential point from the red ; but I have not yet made sufficient
experiments to prove this opinion. At all events, the present
object being to examine the mercurial oxides only as combined
with muriatic acid, it would be foreign to the purpose, to enter
upon too minute an investigation of the other states of the
metal. This, and some other objects hinted at in this Paper,
must be reserved for future inquiry.

In treating the earthy hyperoxygenized muriates with phos-
pliate of silver, as I mentioned before, I observed that the liquor

MDCCCII, Y

i62 Mr. Chenevix's Observations and Experiments

sometimes contained in solution oxide of silver ; which, upon
examination, 1 found to be combined with hyperoxygenized
muriatic acid. As the salt which is thus formed is different, in
every respect, from simple muriate of silver, it may be of some
importance to consider it with attention. In the first place, it
will aRbrd the most convincing proof of the difference between
muriatic and hyperoxygenized muriatic acid ; and, in the next
place, it particularly deserves to be remarked, for possessing, in
the most eminent degree, one of the great characteristic features
of the genus to which it belongs. Hyperoxygenized muriate of
silver is soluble in about two parts of warm water ; but, by
cooling, it crystallizes in tb.e shape of small rhomboids, opaque
and dull, like nitrate cf lead or of barytes. It is somewhat
soluble in alcohol. Muriatic acid decomposes it; as does nitric,
and even acetous acid : but the result of this decomposition is
not, as might be expected, nitrate or acetite of silver. At the
moment that the acid is expelled from hyperoxygenized muriate
of silver, a reaction takes place among its elements : oxygen is
disenojajred; and the muriatic acid remains in combination
with the oxide of silver. If this fact be compared with the
manner in which nitric and acetous acids act upon hyperoxy-
genized muriate of potash, it will give a strong proof of the
proportionate affinities of all these acids for oxide of silver, in
comparison with that which they exercise towards the alkali.

Hyperoxygenized muriate of silver, when exposed to a very
moderate heat, begins by melting, and then gives out a consi-
derable quantity of oxygen gas, with effervescence ; and muriate
of silver remains behind. These phenomena however differ
much, according to the degree of heat applied. When hyper-
oxygenized muriate of silver is mixed with about half its weight

upon oxygenized and hyperoxygenizcd nutriatic Acid, &c. 163

of sulphur, it detonates in the most violent manner; and does not,
like hyperoxygenized muriate of potash, require the addition of
charcoal, to possess a very great force of explosion. The sHghtest
pressure is sufficient to cause this mixture to detonate; and
I think I shall be within bounds, when I state, that half a grain
of hyperoxygenizcd muriate of silver, with a quarter of a grain
of sulphur, explodes with a violence at least equal to five grains of
hyperoxygenizcd muriate of potash, with the due quantities
of sulphur and charcoal. Tlie flash is white and vivid, and is
accompanied by a sharp and quick noise, like the fulminating
silver so ably described by Mr. Howard ; and the silver is
reduced to the metallic state, and vaporized.

I think it right to add a few remarks, upon what I have
termed tlie proportionate affinities of acids and of bases, one for
the other. It is a law, not indeed universally, but frequently-
observed, and very well wortliy of consideration, that the acids
are attracted by metallic oxides, in a very different order from
that in which they are disposed to unite to alkaline and earthy
bases.

Nitric acid, which holds so high a place in the order of
affinities for alkahs, is expelled from metallic oxides by most
acids. Phosphoric, fluoric, all the vegetable acids, except two.
or three, and the animal acids, attract the latter bases more
strongly. Nay, we shall find, upon an attentive examination,
that acids commonly attract metallic oxides, in the inverse
ratio of their action upon metals, or, in other words, in pro-
portion to their own affinity of composition. Thus, the phos-
phoric and fluoric acids sometimes rank before the sulphuric; and
the nitric, as I before said, is generally very low. Hyperoxyge-
nized muriatic acid seems to follow the same rule ; and takes its

Y 2

1^4 Mr. Chenevix's Obsenations and Experiments

place, in the order of affinities for metallic oxides, after many of
those acids which it can expel from earths and alkalis.

Tlic other hyperoxygenized muriates, I have not yet suffi-
ciently examined. I shall, however, mention at present, that I
have ascertained the muriatic salts, formerly known by the
strange name of butters of the ?netuls, to be muriates, and not
hyperoxygenized muriates; and the extraordinary proportion
of oxygen, to be combined, not in the acid, but in the metallic
oxide.

In the course of different experiments, I have known hyper-
oxygenized muriatic acid to be formed in two cases, where I
could not have expected it.

In the analysis of some menachanite from Botany Bay, given
to me last year by the President of the Royal Society, I observed,
that while the oxide of titanium was precipitated from the
muriatic acid in which it was dissolved, the excess of oxygen in
the oxide passed over to the muriatic acid and the potash,
already in the liquor, and that hyperoxygenized muriate of
potash was formed. I have attempted the same experiment with
black oxide of manganese, but could not succeed.

There is, however, a still more extraordinary formation of this
acid, in the distillation of nitro-muriatic acid upon platina. Oxy-
gen is absorbed by the metal ; yet, not only oxygenized, but also
hyperoxygenized muriatic acid is formed. I have repeated the
experiment several times ; and am well convinced of the fact,
however contrary to theory it may appear. I have tried the
action of oxygenized muriatic acid upon nitric acid, in the hopes
of forming hyperoxygenized muriatic acid; but there was no
action to this effect among their elements.

The fact of the production of a peculiar gas, by the distilla-

upon oxygenized and hyperoxygenized muriatic Acid, &c. 165

tion of nitro-muriatic acid upon platina, has been observed by
Mr. Davy, in his Researches* But, as hyperoxygenized muriatic
acid was not known at that tim.^ he coulJ not say the real
nature of that gas. Had Mr. D \vy carried his ingenious expe-
riments a httle farther, we should have been much earher
acquainted with the last degree of oxygenizement of muriatic
acid.

Mr. Berthollet terminates his Paper upon hyperoxygenized
muriate of potash, by saying, that he will consider muriatic
acid as the radical ; oxygenized muriatic acid, as corresponding
with sulphureous and nitrous acid ; and the acid which he
conjectured to exi t in tiiis sah, as corresponding with sulphuric
and nitric acid. I shall now conclude, by stating the arguments
in favour of each denomination, and the analogies upon which
they are founded.

Muriatic acid is for us a simple body ; but it has acid pro-
perties of the strongest kind ; therefore, from analogy, we
suppose it to contain oxygen. But may not this be too hasty
a conclusion ? Are we not very doubtful concerning the ex-
istence of oxygen in prussic acid '^ And are we not, on the
contrary, certain that sulphurated hydrogen, which possesses
many of the characteristics of acids, does not contain any .'' Of
the oxygenizement of fluoric and boracic acids, we have no proof:
but then we cannot affirm that any one of these acids exists in
three states of combination with oxygen; and the muriatic is
the only radical of which we admit this fact. We must not,
however, pretend to limit the number or degrees of combi-
nations between combustible bodies and oxygen; but we can

* Dr. Priestley, also, mentions a peculiar gas, produced by distilling a solution of
gold in aqua regia.

t66 Mr. Chenevix's Observations and Experiments

speak, with certainty, only of those things which are proved.
Besides its acid properties, tl is substance l;as others, coinmon
to ox3^genizable bodies. "With 16 of oxygen, it forms an acid,
which, in many of its properties, is to its radical what the
sulphureous is to sulphur. Like the sulphureous, it is volatile;
has little attraction for salifiable bases; destroys vegetable blues;
and is capable of further oxygenizement. With 65 of oxygen,
it becomes more fixed, like sulphuric acid; has a stronger
aflRnity for salifiable bases ; and acquires more truly acid pro-
perties. Upon these considerations, I submit to the chemical
world, whether, in the present state of our knowledge, it be
not more philosophical to say,

r

Muriatic radical, or

some single word

ofthesameimport, Mnstead oU
Muriatous acid,
Muriatic acid, j

Muriatic acid ;

Oxygenized muriatic acid ;
Hyperoxygenised muriatic acid.

I am fully aware that, at first sight, this may appear extraor-
dinary; and the more so, as we have no positive facts that
prove muriatic acid to be a simple body. All we can, therefore,
consider fairly, is, in favour of which appellation does the sum
of analogies seem to preponderate. And, to give the cause a
candid investigation, we should begin by considering, whether
the presence of oxygen in all bodies that have acid properties,
has been rigidly demonstrated ; and not determine by this law
of the French chemistry, till we are well convinced it has not
been too generally assumed.

If a nomenclature be not subservient to the uses of science,
and does not keep pace with its progTess, the relation between

upoji oxygenized and hyperoxygenized muriatic Acid, &c. 167

substances and their names will become so relaxed, that confu-
sion will be brought about, by the very means we take to avoid
it; and if, while we continue to extend our acquaintance with
chemical bodies, nomenclature remains confined within its
former limits, the bonds that unite these two parts of the science
must inevitably be broken.

Ci68:i

VII. Experiments and Observations on certain stony and metalline
Substances, ivhicb at different Times are said to have fallen oji
the Earth ; also on various Kinds of Jiative Iron. By Edward
Howard, Esq. F. R. S.

Read February 25, 1802.

Th e concordance of a variety of facts seems to render it most
indisputable, that certain stony and metalline substances have,
at different periods, fallen on the earth. Whence their origin,
or whence they came, is yet, in my judgment, involved in
complete obscurity.

The accounts of these peculiar substances, in the early annals,
even of the Royal Society, have unfortunately been blended with
relations which we now consider as fabulous ; and the more
ancient histories of stones fallen from heaven, from Jupiter, or
from the clouds, have evidently confounded such substances
with what have been termed Ceraunia, Bd'tilia, Ombria, Brontia,
&c. names altogether unappropriate to substances fallen on our
globe. Indeed some mislead, and others are inexpressive.

The term Ceraunia, by a misnomer, deduced from its sup-
posed origin, seems, as well as Boetilia,* to have been anciently
used to denote many species of stones, which were polisiied
and shaped into various forms, though mostly wedge-like or
triangular, sometimes as instruments, sometimes as oracles,
and sometimes as deities. The import of the names, Ombria,
Brontia, &c. seems subject to the same uncertainty.

In very early ages, it was believed, that stones did in reality

* Mercati, Metallotheca Vaticana. page 241.

Mr. Howard's Experiments arid Observations, Sec. i6g

fall, as it was said, from heaven, or from the gods ; these,
either from ignorance, or perhaps from superstitious views,
were confounded with other stones, which, by their compact
aggregation, were better calculated to be shaped into different
instruments, and to which it was convenient to attach a species
of mysterious veneration. In modern days, because explosion
and report have generally accompanied the descent of such
substances, the name of thunderbolt, or thunderstone, has igno-
rantly attached itself to them ; and, because a variety of sub-
stances accidentally present, near buildings and trees struck
with lightning, have, with the same ignorance, been collected as
thunderbolts, the thunderbolt and the fallen metalline substance
have been ranked in the same class of absurdity. Certainly,
since the phenomena of lightning and electricity have been so
well identified, the idea of a thunderbolt is ridiculous. But the
existence of peculiar substances fallen on the earth, I cannot
hesitate to assert ; and, on the concordance of remote and
authenticated facts, I shall rest the assertion.

Mr. King, the learned author of Remarks concetymig Stones said
to have fallen frofft the Clouds, in these Days, and in ancient Ti?nes,
has adduced quotations of the greatest antiquity, descriptive of
the descent of fallen stones ; and, could it be thought necessary
to add antique testimonies to those instanced by so profound an
antiquarian, the quotations of Mons. Falconet, in his papers
upon Boetilia, inserted in the Histoire des hiscriptiojis et Belles-
Lettres;* the quotations in Zahn's Specula Physico-rnathematica
Historia?ta ;'\- the Fisica Sotterranea of Giacinto Gemma; the
works of Pliny, and others, might be referred to.

• Tom. VI. p. 519. etTotn. XXIII. P. 228.

f Fol. 1696. Vol, I. p. 385. where a long enumeration of stones fallen from the sky
is given.

MDCCCII. Z

170 Mr. Howard's Experiments and Observations

Dr. Chladni, in liis Observations on the Mass of Iron found
in Siberia, and on other Masses of the like Kind, as well as in
his Observations on Fire-balls and hard Bodies fallen from the
Atmosphere, has collected almost every modern instance of
phenomena of this nature.

Mr. SouTHEY relates an account, juridically authenticated, of
a stone weighing 10 lbs. which was heard to fall in Portugal,
Feb. 19, 1796', and was taken, still warm, from the ground.*

The first of these peculiar substances with which chemistry
has interfered, was the stone presented by the Abbe Bachelay
to the Royal French Academy. It was found on the 13th of
September, 1768, yet hot, by persons who saw it fall. It is
described as follows :

" La substance de cette pierre est d'un gris cendre pale;
" lorsqu'on en regarde le grain a la loupe, on appercoit que
" cette pierre est parsemee d'une infinite de petits points bril-
" lans metalliqucs, d'un jaune pale; sa surface exterieure, celle
" qui, suivant M. TAbbe Bachelay, n'^toit point engagee dans
" la terre, dtoit couverte d'une petite couche tres-mince d'une
" matiere noire, boursoufflee dans des endroits, et qui parois-
" soit avoir 6te fondue. Cette pierre, frapp(§e dans I'interieur
" avec Tacier, ne donnoit aucune etincelle ; si on frappoit, au
*' contraire, sur la petite couche exterieure, qui paroissoit avoir
" 6t6 attaqu^e par le feu, on parvenoit a en tirer quelques-unes."
The specific gravity of this stone was as 3535 to 1000.

The academicians analyzed the stone, and found it to contain,
Sulphur - - - 8-i-

Iron - - - 3^

Vitrifiable earth _ - - 55!-

100.

• Letters written during a short residence in Spain and Portugal. Page 239.

on certain stony and metalline Substances, &c. 171

Of their mode of analysis, I shall have occasion to speak
hereafter. Tiiey were induced to conclude, that the stone, pre-
sented to the Academy by the Abb6 Bachelay, did not owe
its origin to thunder ; that it did not fall from heaven ; that it
was not formed by mineral substances, fused by lightning ; and
that it was nothing but a species of pyrites, without peculiarity,
except as to the hepatic smell disengaged from it by marine
acid. " Que cette pierre, qui peut-etre ^toit couverte d'une
" petite couche de terre ou de gazon, aura ete frapp^e par la
" foudre, et qu'elle aura 6t^ ainsi mise en evidence : la chaleur
*' aura 6t6 assez grande pour fondre la superficie de la partie
" frapp^e, mais elle n'aura pas 6t€ assez long-tems continuee
" pour pouvoir penetrer dans I'interieur; c'est ce qui fait que
" la pierre n'a point ^te decomposee. La quantite de matieres
" m^talliques qu'elle contenoit, en opposant moins de resistance
" qu'un autre corps au courant de matiere electrique, aura peut-
" etre pu contribuer meme a determiner la direction de la
" foudre."

The Memoir is however concluded, by observing it to be
sufficiently singular, that M. Moraxd le Fils had presented a
frao-ment of a stone, from the environs of Coutances, also said
to have fallen from heaven, which only differed from that of
the Abbe Bachelay, because it did not exhale the hepatic
smell. with spirit of salt. Yet the academicians did not think
any conclusion could be drawn from this resemblance, unless
that the lightning had fallen by preference on pyritical matter.*

Mons. Barthold, Professeur a i'Ecole centrale du Haut-
Rhin, gave I believe the next, and last,f analytical account of

• See Journal de Physique. Tom. II. page 251.

+ A very interesting detail of a meteor, and of stones fallen in July, 1 790, was given
by Professeur Baudin, in the Magazinjiir das JTeueste aus der Pbyiik, by Professor

VOIGT.

Z 2

17* Mr. Howard's Experiments and Observations

what he also denominates Pierre de Tonnerre. He describes it
thus : " La masse de pierre connue sous le nom de Pierre de
" Tonnerre d'Ensisheim, pesant environ deux quintaux, a la
" forme ext^rieure arrondie, presque ovale, raboteuse, d'un
«' aspect terne et terreux.

" Le fond de la pierre est d'une couleur grise bleuatre, par-
" semee de cristaux de pyrites, isoles, d'une cristalisation
" confuse, en quelques endroits ^cailleuses, ramass^s, formant
" des noeuds et des petites veines, qui le parcourent en tout
*" sens : la couleur des pyrites est dor6e ; le poli leur donne un
" eclat d'acier, et, exposees a I'atmosphere, elles ternissent et
" brunissent. On distingue de plus, a I'oeil nud, de la mine
" de fer grise, ^cailleuse, non sulfureuse, attirable a I'aimant,
" dissoluble dans les acides, peu oxid^, ou s'approchant beau-
" coup de r^tat metallique.

" La cassure est irrdguliere, grenue, d'un grain un peu
" serr6 : dans I'interieur on voit de tres petites fezites. Elle ne
" fait pas feu au briquet ; sa contexture est si lache qu'elle se
" laisse entamer au couteau. En la pilant, elle se reduit assez
" facilement en une poudre grise bleuatre, d'une odeur terreuse.
" Quelquefois il se trouve des petits cristaux de mine de fer,
" qui r^sistent plus aux coups du pilon."

The specific gravity of the piece in Professor Barthold's
possession, was 3233, distilled water being taken at looo.

The analysis of Mons. Bakthold, of which I shall also have
occasion to speak hereafter, gave in the 100,

Sulphur _ _ _ 2

Iron - - - - 20

Magnesia - - - 14

Alumina - - - 17

Lime _ - _ s

Silica - - - - 42

on certain stony and metalline Substances, &c. 173

From the external characters, and from his analysis, the
Pruressor considers the stone of Ensisheim to be argillo-ferru-
ginous ; and is of opinion that ignorance and superstition have
attributed to it a miraculous existence, at variance with the first
notions of natural philosophy.*

The account next in succession is already printed in the
Transactions of the Royal Society ; but cannot be omitted, as it
immediately relates to one of the substances I have examined.
I allude to the letter received by Sir William HaiMilton, from
the Earl of Bristol, dated from Sienna, July 12th, 1794,. " In
" the midst of a most violent thunder-storm, about a dozen
" stones, of various weights and dimensions, fell at the feet of
" different persons, men, women, and children. The stones are
" of a quality not found in any part of the Siennese territory ;
" they fell about eighteen hours after the enormous eruption of
" Mount Vesuvius ; which circumstance leaves a choice of dif-
" ficulties in the solution of this extraordinary phenomenon.
" Either these stones have been generated in this igneous mass
*' of clouds, which produced such unusual thunder; or, which is
" equally incredible, they were thrown from Vesuvius, at a
" distance of at least 250 miles; judge then of its parabola.
" The philosophers here incline to the first solution. I wish
" much. Sir, to know your sentiments. My first objection was
" to the fact itself; but of this there are so many eye witnesses,
" it seems impossible to withstand their evidence." (Phil. Trans.
for 1795. p. 103.) Sir William Hamilton, it seems, also
received a. piece of one of the largest stones, which weighed
upwards of five pounds ; and had seen another, which weighed
about one. He likewise observed, that the outside of every stone
which had been found, and had been ascertained to have fallen.
* See Journal de Physique, Ventose, An 8. p, 169,

174 -^^' Howard's Experiments and Observations

from the clouds near Sienna, was evidently freshly vitrified, and
was black, having every sign of having passed through an
extreme heat ; the inside was of a liglit gray colour, mixed with
black spots and some shining particles, which the learned there
had decided to be pyrites.

In 1796, a stone weighing 56 lbs. was exhibited in London,
with several attestations of persons who, on the 13th of Decem-
ber, 1795, saw it fall, near Wold Cottage, in Yorkshire, at about
three o'clock in the afternoon . It had penetrated through 1 2 inches
of soil and 6 inches of solid chalk rock; and, in burying itself, had
thrown up an immense quantity of earth, to a great distance : as
it fell, a number of explosions were heard, about as loud as pistols.
In the adjacent villages, the sounds heard were taken for guns
at sea^ but, at two adjoining villages, were so distinct of some-
thing singular passing through the air, towards the habitation
of Mr. ToPHAM, that five or six people came up, to see if any
thing extraordinary had happened to his house or grounds.
When the stone was extracted, it was warm, smoked, and
smelt very strongly of sulphur. Its course, as far as could be
collected from different accounts, was from the south-west. The
day was mild and hazy, a sort of weather very frequent in the
W^old hills, when there are no winds or storms ; but there was
not any thunder or lightning the whole day. No such stone is
known in the country. There was no eruption in the earth ;
and, from its form, it could not come from any building; and,
as the day was not tempestuous, it did not seem probable that
it could have been forced from any rocks, the nearest of which
are those of Hamborough Head, at a distance of twelve miles.*
The neai-est volcano, I believe to be Hecla, in Iceland.

• Extra. t(d from the printed paper delivered at the place of exhibition.

on certain stony and metalluie Substances, &c. 175

The exhibition of this stone, as a sort of show, did not tend
to accredit the account of its descent, delivered in a hand-bill at
the place of exhibition ; much less could it contribute to remove
the objections made to the fall of the stones presented to the
Royal French Academy. But the Right Hon. President of the
Royal Society, ever alive to the interest and promotion of
science, observing the stone so exliibited to resemble a stone
sent to him as one of those fallen at Sienna, could not be misled
by prejudice : he obtained a piece of this extraordinary mass, and
collected many references to descriptions of similar phenomena.
At length, in 1799, an account of stones fallen in the East Indies
was sent to the President, by John Lloyd Williams, Esq.
which, by its unquestionable authenticity, and by the striking
resemblance it bears to other accounts of fallen stones, must
remove all prejudice, Mr. Williams has since drawn up the
following more detailed narrative of flicts.

Account of the Explosion of a Meteor, near Benares, in the East
Indies ; and of the falling of some Stones at the same Time,
about 14 Miles from that City. By John Lloyd Williams,
Esq. F. R. S.

A circumstance of so extraordinary a nature as the fall of
stones from the heavens, could not fail to excite the w^onder,
and attract the attention, of every inquisitive mind.

Among a superstitious people, any preternatural appearance
is viewed with silent awe and reverence ; attributing the causes
to the will of the Supreme Being, they do not presume to judge
the means by which they were produced, nor the purposes for
which they were ordered ; and we are naturally led to suspect
tlie influence of prejudice and superstition, in their descriptions

176 Mr. Howard's Experiments and Observations

of such phenomena; my inquiries were therefore chiefly directed
to the Europeans, who were but thinly dispersed about that part
of the country.

The information I obtained was, that on the 19th of Decem-
ber, 1 798, about eight o'clock in the evening, a very luminous
meteor was observed in the heavens, by the inhabitants of Benares
and the parts adjacent, in the form of a large ball of fire ; that it
was accompanied by a loud noise, resembling thunder ; and
that a number of stones were said to have fallen from it, near
Krakhut, a village on the north side of the river Goomty,
about 14 miles from the city of Benares.

The meteor appeared in the western part of the hemisphere,
and was but a short time visible: it was observed by several
Europeans, as well as natives, in different parts of the country.

In the neighbourhood of Juanpoor, about 1 2 miles from the
spot where the stones are said to have fallen, it was very dis-
tinctly observed by several European gentlemen and ladies ;
who described it as a large ball of fire, accompanied with a loud
rumbling noise, not unlike an ill discharged platoon of mus-
quetry. It was also seen, and the noise heard, by various
persons at Benares. Mr. Davis observed the light come into
the room where he was, through a glass window, so strongly
as to project shadows, from the bars between the panes, on a
dark coloured carpet, very distinctly ; and it appeared to him as
luminous as the brightest moonlight.

When an account of the fall of the stones reached Benares,
Mr. Davis, the judge and magistrate of the district, sent an
intelligent person to make inquiry on the spot. When the person
arrived at the village near which the stones were said to have
fallen, the natives, in answer to his inquiries, told him, that they

on certain stony and metalline Substances, &c. 177

liad either broken to pieces, or given away to the Tesseldar
(native collector) and others, all that they had picked ifp; but
that he might easily find some in the adjacent fields, where
they would be readily discovered, (the crops being then not
above two or three inches above the ground,) by observing
where the earth appeared recently turned up. Following these
directions, he found four, which he brougiit to Mr. Davis : most
of these, the force of the fall had buried, according to a measure
he produced, about six inches deep, in fields which seemed
to have been recently watered; and it appeared, from the man's
description, that they must have lain at the distance of about a
hundred yards from each other.

What he further learnt from the inhabitants of the village,
concerning the phenomenon, was, tliat about eight o'clock in
the evening, when retired to their habitations, they observed a
very bright light, proceeding as from tlie sky, accompanied with
a loud clap of tinuidLr, which was immediately followed by the
noise of heavy bodies falling in the vicinity. Uncertain whether
some of their deities might not liave been concerned in this
occurrence, they did not venture out to inquire into it until the
next morning: when the first circumstance which attracted
their attention was, the appearance of the earth being turned
up in different parts of their fields, as beibre mentioned,
where, on examining, they found the stones.

The assistant to the collector of the district, Mr. Erskine, a
very intelligent young gentleman, on seeing one of the stones,
brought to him by the native superintendant of the collections,
was also induced to send a person to that part of the country,
to make inquiry ; who returned with several of the stones, and
brought an account similar to that given by the person sent by
Mr. Davis, together with a confirmation of it from the Cauzy,

MDCccii. A a

178 Mr. Howard's Experiments and Observations

(who had been directed to make the inquiry,) under his hand
and seal.

Mr. Maclane, a gentleman who resided very near the village
of Krakhut, gave me part of a stone tluit had been brought
to him the morning after the appearance of the phenomenon,
by the watchman who was on duty at his house; this, he said,
had fallen through the top of his hut, which was close by, and
buried itself several inches in the floor, which was of consoli-
dated earth. The stone must, by his account, previous to its
having been broken, have weighed upwards of two pounds.

At the time the meteor appeared, the sky was perfectly
serene ; not the smallest vestige of a cloud had been seen since
the 1 itli of the month, nor were any observed for many days
after.

Of these stones, I have seen eight, nearly perfect, besides
parts of several others, which had been broken by the possessors,
to distribute among their friends. The form of the more perfect
ones, appeared to be that of an irregular cube, rounded off at the
edges ; but the angles were to be observed on most of them.
They were of various sizes, from about three to upwards of four
inches in their largest diameter; one of them, measuring four
inches and a quarter, weighed two pounds twelve ounces. In
appearance, they were exactly similar : externally, they were
covered with a hard black coat or incrustation, which in some
parts had the appearance of varnish, or bitumen; and, on most
of them were fractures, which, from their being covered with a
matter similar to that of the coat, seemed to have been made in
the fall, b}^ the stones striking against each other, and to have
passed through some medium, probably an intense heat, pre-
vious to their reaching the earth. Internally, they consisted of
a number of small spherical bodies, of a slate colour, embedded

on certain stony and metalline Substances, &c. 17c)

in a whitish gritty substance, interspersed with bright shining
spiculae, of a metalhc or pyritical nature. The spherical bodies
were much harder than the rest of the stone : the wliite gritt\'
part readily crumbled, on being rubbed with a hai-d body ; and,
on being broken, a quantity of it attached itself to tiic magnet,
but more particularly the outside coat or crust, which appeared
almost w-holly attractable by it.

As two of the more perfect stones whicii I had obtained, as
well as parts of some others, have been examined by several
gentlemen well versed in mineralogy and chemistry, I shall
not attempt any further description of their constituent parts ;
nor shall I offer any conjecture respecting the formation of such
singular productions, or even record those which I have heard
of others, but leave tlie world to draw their own inferences from
the facts above related. I sliall only observe, that it is well
known there are no volcanos on the continent of India; and,
as far as I can learn, no stones have been met with in the
earth, in that part of the v.orld, which bear the smallest resem-
blance to those above described.

It remains for me to speak of a substance mentioned in the
Litbopbylacium Bornianum, Parti, page 125, described tlius :
" Ferrum retractorium, granulis nitentibus, matrice virescenti
" immixtis, (Femim virens Linn.) cujus fragmenta, ab unius
" ad vigenti usque librarum pondus, cortice nigro scoriaceo
" circumdata, ad Plann, prope Tabor, circuli Bechinensis Bohe-
•' mias, passim reperiuntur."

The iron thus described, is moreover made remarkable by a
A a 2

i8o Mr. Howard's Experimenls and Observations

note,* which observes, that creckilous people assert it to have
(alien from heaven, during a thunder storm, on the 3d of July,

1753-
The collection of Baron Born, it is well known, has a place

in the cabinet of the Right Hon. Charles Greville, who,
from the effect produced by comparing the histories and struc-
ture of the Italian and Yorkshire stones with the description of
this iron, was induced to search the collection of Born, where
lie discovered the very substance asserted to have fallen on the
3d of July, 1753. How far these four substances have resem-
blance to each other, it will soon appear not to be my province
to anticipate.

The President having done me the honour to submit his
specimens of the Yorkshire and Italian stones to my examina-
tion, I became indebted to Mr. Greville and Mr. Williams
for a similar distinction : and, being thus possessed of four
substances, to all of which the same origin had been attributed,
the necessity of describing them mineralogically did not fail to
present itself. To execute this task, no one could be more eager,
and certainly no one better qualified, than the Count de
Bournon. He has very obligingly favoured me with the fol-
lowing descriptions.

Mineralogical Description of the various Stones said to have
fallen upo?i the Earth. By the Count de Bournon, F. R. S.

The stones I am about to describe, are not of any regular
shape; and those which were found in an entire state, that is,
those which had not been broken, either by their fall or other-

* Qua; (fragmenta) 3 Julii, aniii i753> inter tonitrua, e coelo pluisse crcduliores
quidam asseninf.

on certain stony and metalliyie Substances, &c. 181

wise, were entirely covered with a black crust, the thickness
of which was very inconsiderable.

The stones which fell at Benares, are those of which the
mineralogical characters are the most striking : I shall therefore
begin the following description with them ; and shall afterwards
make use of them, as objects of comparison, in describing the
others.

STONES FROM BENARES.

These stones, as well as the others described in this Paper,
whatever may be their size, are covered over the whole extent
of their surface, with a thin crust, of a deep black colour : they
have not the smallest gloss ; and their surface is sprinkled over
with small asperities, which cause it to feel, in some measure,
like shagreen, or fish skin.

When these stones are broken, so as to shew their internal
appearance, they are found to be of a grayish ash colour ; and
of a granulated texture, very similar to that of a coarse grit-
stone : they appear evidently to be composed of four different
substances, which may be easily distinguished, by making use
of a lens.

One of these substances, which is in great abundance, appears
in the form of small bodies, some of which are perfectly glo-
bular, others rather elongated or elliptical. They are of various
sizes, from that of a small pin's head to that of a pea, or nearly
so: some of them, however, but very few, are of a larger
size. The colour of these small globules is gray, sometimes
inclining very much to brown : and they are completely
opaque. They may, with great ease, be broken in all directions :
their fracture is conchoid, and shews a fine, smooth, compact

i82 Mr. Howard's Experiments and Observations

grain, having a small degree of lustre, resembling in some
measure that of enamel. Their hardness is such, that, being
rubbed upon glass, they act upon it in a slight degree; this
action is sufficient to take ofFits polish, but not to cut it: they
give faint sparks, when struck with steel.

Another of these substances, is a martial pyrites, of an inde-
terminate form : its colour is a reddish yellow, slightly inclining
to the colour of nickel, or to that of artificial pyrites. The
texture of this substance is granulated, and not very strongly
connected : when powdered, it is of a black colour. This pyrites
is not attractable by the magnet; and is irregularly distributed
through the substance of the stone.

The third of these substances consists in small particles of
iron, in a jjerfectly metallic state, so that they may easily be
flattened or extended, by means of a hammer. These particles
give to the whole mass of the stone, the property of being
attractable by the magnet ; they are, however, in less projjor-
tion than those of pyrites just mentioned. When a piece of the
stone was powdered, and the particles of iron separated from it,
as accurately as possible, by means of a magnet, they appeared
to compose about -^ of the whole weight of the stone.

The tliree substances just described, are united together
by means of a fourth, which is nearly of an earthy consistence.
For this reason, it is easy to separate, with the point of a knife,
or even with the nail, the little globular bodies above mentioned,
or any other of the constituent parts of the stone we may wish
to obtain. Indeed the stone itself may readily be broken, merely
by the action of the fingers. The colour of this fourth substance,
which serves as a kind of cement to unite the others, is a
whitish gray.

on certain stony and metalline Substances, &c. 183

The black crust with which the surface of the stone is coated,
although it is of no great thickness, emits bright sparks, when
struck with steel : it may be broken by a stroke with a hammer ;
and seems to possess the same properties as the very attractable
black oxide of iron. This crust is, however, like the substance
of the stone, here and there mixed with small particles of iron
in the metallic state : they may easily be made visible, by passing
a file over the crust, as they then become evident, on account
of their metallic lustre. This is more particularly the case witli
respect to the crust of those stones which remain to be men-
tioned, they being much more rich in iron than that I have just
described ; a circumstance I think it needless to repeat, in the
following descriptions of them. The stone now treated of, does
not, when breathed upon, emit an argillaceous smell : the same
remark may be applied to all the others.

The specific gravity of this stone is 3352.

STONE FROM YORKSHIRE.

This Stone, the constituent parts of which are exactly the
same as those of the stones from Benares, differs from them,
however,

First. In having a finer grain.

Secondly. That the substance described as being in the form
of small globular or elliptical bodies, is not so constantly in those
forms, but is also found in particles of an irregular shape ; a
circumstance that is not met with in the other stones : these
bodies are likewise, in general, of a smaller size.

Thirdly. The proportion of martial pyrites, which has pre-
cisely the same characters as that in the stones from Benares, is
less ; on the contrary, that of the iron in a metallic state, is
much greater. The quantity I was able to separate by means

184 Mj: Howard's Experiments and Observations

of the magnet, appeared to me to compose about eight or nine
parts, in one Iiundred, of the weight of the whole mass. I
observed many pieces of this iron, of a pretty considerable size;
one of them, taken from a portion of the stone I had powdered,
in order to separate the iron, weighed several grains.

The part of the stone which is in an earthy state, and which
serves to connect the other parts together, has rather more
consistence than that of the preceding stones ; and its appearance
does not differ much from that of decomposed felspar or kaolin.
The stone itself, therefore, although by no means hard, is rather
more difficult to break with the fingers.

The specific gravity of this stone is 3508.

STONE FROM ITALY.

This Stone was in a perfectly entire state; consequently, it.s
whole surface wa.s covered over with the black crust peculiar to
all stones of this kind. As the stone was of a verv s:i;all size,
it became necessary to sacrifice the whole of it to the investi-
gation of its nature. Its grain was coarse, similar to that of the
stones from Benares : in it might be perceived the same gray
globular bodies, the same kind of martial pyrites, and the same
particles of iron in the metallic state. The proportion of these
last was much less than in the stone from Yorksliire; but
rather greater than in the stones from Benares. The same
kind of gray earthy substance served to connect the different
parts together ; and nothing more could be perceived, except
a. few globules, which consisted wholly of black oxide of iron,
attractable by the magnet, and one single globule of another
substance, which appeared to differ from all those we have
already described. This last substance had a perfectly vitreous
li^istre, and was completely transparent : it was of a pale yellow

on certain stony and metalline Substances, &c. 185

colour, slightly inclining to green ; and its hardness was rather
inferior to that of calcareous spar. The quantity of it, however,
was too small to be submitted to such an investigation as might
have determined its nature. The black crust which covered
the stone, was rather thinner than that of the stones already
described ; and seemed to have undergone a kind of contraction,
which had produced in it a number of fissures or furrows,
tliereby tracing upon the surface the appearance of compart-
ments, similar in some measure to what is observed in the stones
called Septaria.

The specific gravity of this stone was 34,18.

STONE FROM BOHEMIA.

The internal structure of this stone is very similar to that of
the stone from Yorkshire. Its grain is finer than that of the
stones from Benares : in it may be observed the same gray sub-
stance, both in small globules and in particles of an irregular
shape; also the same particles of metallic iron. The same kind
of earthy substance likewise served to connect the other parts
together.

This stone, however, differs materially from the others.

First. The particles of pyrites cannot be seen without a lens.

Secondly. It contains a much larger quantity of iron in the
metallic state; insomuch, that the proportion of that metal,
separated from it by means of the magnet, amounted to about
.^^ of the weight of the whole.

This stone has also (owing perhaps to its having remained a
much longer time in the earth than the preceding ones, all of
which were taken up nearly at the very instant of their fall, )
another difference, viz. many of the particles of iron in a

MDCCCII. B b

i86 Mr. Howard's Experiments and Observations

metallic state, have undergone an oxidizement at their surface;
a circumstance that has produced a great number of spots, of
a yellowish brown colour, and very near to each other, over a
part of its internal substance. This oxidizement, by adding to the
bulk, and to the force of action, of the part we have described
as serving by way of cement to the other constituent parts of
the stone, has occasioned a greater degree of adhesion between
these parts, and has rendered the substance of the stone more
compact.

The great quantity of iron in a metallic state which tliis
stone contains, added to its greater compactness, makes it
capable of receiving a slight degree of polish ; whereas it is im-
possible to give any polish to the others. When polished, the
iron becomes very evident, in the polished part ; appearing in
the form of small specks, almost close to each other, which have
the colour and lustre peculiar to that metal : these specks are,
in general, nearly of an equal size.

The black crust of this stone is similar to that of the others.
The specific gravity of the stone is 4281 .
It is easy to perceive, from the foregoing description, that
these stones, although they have not the smallest analogy with
any of the mineral substances already known, either of a volcanic
or any other nature, have a very peculiar and striking analogy
with each other. This circumstance renders them truly worthy
to engage the attention of philosophers ; and naturally excites
a desire of knowing to what causes they owe their existence.

I proceed to consider the assistance to be derived from
chemistry, in distinguishing these stones from all other known

on certain sto7ty and metalline Substances, 8cc. 187

substances, arid in establishing the assertion, that they have
fallen on the earth.

The analysis made by the French Academicians, of the
stone presented to them by the Abb6 Bachelay, was, in part,
conducted by the ever to be deplored Lavoisier ; but it was
performed before that celebrated author had enriched chemistry
with his last discoveries, and before he had given birth to the
system under which it flourishes. The result of this analysis
might well induce the conclusion, that the subject of it was
common pyritical matter. It was unfortunately made of an
aggregate portion of the stone, and not of each distinct substance,
irregularly disseminated through it. The proportions obtained
were, consequently, as accidental as the arrangement of every
substance in the mass.

The analysis of M. Barthold, of the stone of Ensisheim, is
subject to the same objections : but, after having the advantage
of the foregoing descriptions, the researches which follow cannot
be supposed altogether liable to a similar fatality.

EXAMINATION OF THE STONE FROM BENARES.

This stone, as the Count de Bournon has already re-
marked, has the most distinguished characters. Indeed it is
the only one of the four, sufficiently perfect (if I be allowed
that expression) to be subjected to any thing approaching to
a regular analysis.

The crust, or external black covering, is the first substance
to which the attention is naturally directed. When a portion of
this crust had been detached with a knife, or a file, and finely
pulverized, I separated the particles attractable by a magnet;

Bb 2

i88 Mr. Howard's Experiments and Observations

and digested the unattractable portion with nitric acid, which
was presently decomposed ; but, owing to a strong adherence
of some of the interior and earthy parts of the stone, it did not
disentangle the coating or metalline part without some difficulty.
The acid being sufficiently neutralized, the solution was passed
tiirough a filtre, and saturated to excess with ammonia. An
abundant precipitate of oxide of iron was produced ; and, when
this oxide was separated, I observed the saline liquor to have a
greenish colour. I evaporated it to dryness ; and redissolved the
dry salt in distilled water. No precipitate was formed during
the evaporation, nor was the colour of the solution entirely
destroyed. It appeared to me like a triple salt, described by Mr.
Hermstadt* as an ammoniacal nitrate of nickel. By exami-
nation with prussiate of ammonia, it yielded a whitish precipitate,
inclining to a violet colour ; and, by various properties, I was
soon confirmed in the opinion, that nickel was present. Since
I shall have occasion more than once to treat of the triple
compound, and since it has been only mentioned by Mr.
Hermstadt, it is necessary now to detail some of its distinctive
characters. The same chemist informs us, that the three mineral
acids, with ammonia, enter into similar combinations with nickel ;
and I have observed, that oxide of nickel can be dissolved by
nitrate and muriate of ammonia. The muriate seems to take up
the largest quantity. The colour of this salt is by no means
uniform : it is sometimes grass green, violet, rose colour,
inclining to purple, and I have seen it almost colourless. It
seems to be purple, and to incline to rose colour and violet,
when all the oxide of nickel is not united to both acid and
alkali, but, from the deficiency of salt, is held in solution by an
• Annalci de Cbimit. Tom. XXII. p, io8.

on certain stony and metalline Substances, &c. 189

excess of ammonia. In this case, evaporation, of course, pre-
cipitates the nickel in the state of oxide, which is of a whitish
green colour.

The nickel cannot be precipitated from a perfectly formed
triple salt, by any reagent I have tried, except by a prussiate,
or a hydrogenized sulphuret of ammonia. Potash and lime,
as well as, I presume, other bodies, standing in the order of
affinities before ammonia, decompose the salt ; but the nickel is
then continued in solution by the disengaged ammonia.

As it may be imagined that I have occasionally met with
copper, when I describe a violet or purple ammoniacal solution,
it is right to observe, that to avoid this error, I have either
reduced the liquor to a neutral state, and endeavoured, without
success, to obtain from it a precipitate, with a solution of sul-
phureted hydrogen gas ; or, by adding an acid to slight excess,
and immersing a piece of iron, I have not been able to detect a
trace of copper. These, and many other trials, when they do
not appear to be made before the estimation of the quantities ol"
nickel, have been constantly made afterwards.

But, to return to the incrustation or coating of the stone, the
decomposition of the nitric acid shewed the presence of matter
at least nearly metallic, although not attractable; and the exa-
minations made of. the liquor, from which the iron was precipi-
tated, ascertained the presence of nickel beyond dispute. The
difficulty of obtaining the coating of the stone, either distinct
from matter not belonging to it, or in sufficient quantity, induced
me to relinquish the idea of attempting to give the proportions
of its constituent parts.

The stone being deprived of its covering, the shining particles
irregularly disseminated, next demand examination. I first

igo JV/r. Howard's Experiments and Observations

examined the pyrites. Tlieir very loose texture made it ex-
ceedingly difficult to collect the weight of 16 grains, which was
however effected by the dexterity of the Count de Bournon.

I digested these, at a low heat, with weak muriatic acid;
which acted gradually, and disengaged a trifling but sensible
quantity of sulphureted hydrogen gas. After several hours, 1
found the acid discontinued its action. The whole metalline part
appeared in solution ; but sulphur and earthy particles were
observable. The sulphur, from its small specific gravity, was
suspended through the solution ; whilst the earthy matter, which
could not be separated by mechanical means, was fortunately
left at the bottom of the digesting vessel. I decanted off' the
solution, holding suspended the sulphur; and, by repeated
washing, separated every thing belonging to the pyrites from
the insoluble earthy matter, the subtraction of which reduced the
weight of real pyrites to 14 grains. I next obtained the sulphur,
by filtration. When it was as dry as I could make it, without
fear of its being sublimed, its weight was two grains. To the
filtrated liquor I added nitrate of barytes, by way of detecting
any sulphuric acid which might have been present; but no
cloudiness ensued. I then separated, by sulphate of ammonia,
the barytes thus added, and precipitated tlie iron with ammonia.
The liquor, on the subsidence of oxide of iron, appeared of a
violet purple colour : it contained nickel, which I threw down
with sulphureted hydrogen gas, there being already a sufficient
excess of ammor.ia in the saline liquor to form an alkaline
hydrogenized sulphuret. The oxide of iron, after ignition,
weighed ij grains; and the sulphuret of nickel, reduced to an
oxide, weighed, after the same trei.tment, something more than
one grain. The proportions of the substances contained in the

on certain stony mid metallme Substances, &c. 191

pyrites of the stone from Benares, may therefore be considered

nearly thus : Grains.

Sulphur - - . - - 2

Iron - - - _ - iQi

Since 15 grains of the oxide represent about that quan-
tity of iron.

Nickel, nearly » . - - 1

Extraneous earthy matter _ - - 2

It is observable that, notwithstanding the loss appears to be
only half a grain, it was probably more, because the sulphur
could not be reduced to the same state of dryness in which it
existed when in combination with the iron ; not to say that it
was, in a small degree, volatilized with the hydrogen gas dis-
engaged during the solution.

The weight of nickel is a mere estimation. We are not yet
sufficiently acquainted with that metal to speak of it with
accuracy, except as to its presence. Upon the whole, however,
it may be concluded, that these pyrites are of a very particular
nature ; for, although Henkel has observed that sulphur may
be separated froin pyrites by muriatic acid, it is by no means
the usual habitude of pyrites to be of such easy decomposition.

The other shining particles immediately seen, when the
internal structure of the stone is exposed, are the malleable
iron. Before I state the examination of this iron, I must remark,
that preliminary experiments having shewn me it contained
nickel, I treated several kinds of the most pure irons I could
obtain, with nitric acid; and precipitated the oxide from the
metallic sa't by ammonia. The quantity of oxide I obtained
from 100 grains of iron, was from 144 to 1 46. I may consequently

1^2 Mr. Howard's Expenments mid Observations

infer, that loo grains of pure iron acquires, by such a process,
45 grains of oxygen ; and that, whenever a metallic substance,
supposed to be iron, does not, under the same circumstances,
acquire the same proportionate weight, something is either
volatilized, or left in solution. Hence, when a metallic alloy of
nickel and iron presents itself, a judgment ma}-, at least, be
formed of the quantity of nickel, by the deficiency of weight in
the precipitated oxide of iron.

This mode of treatment was not allowed me in the examina-
tion of tlie coating of the stone, because it was impossible to
know in what state of oxidizement the iron existed. But, as the
particles disseminated through the whole mass, are clearly
metallic, a very tolerable idea of the quantities of nickel con-
tained in them will be obtained, by noting the quantity of oxide
of iron separated, as above described. 25 grains of these metallic
particles were therefore heated with a quantity of nitric acid,
much more than sufficient to dissolve the whole. Some earthy
matter, which, as in a former case, was not separable by me-
chanical means, remained after a complete solution of the metal
had been effected. This earthy matter, after being ignited,weighed
two grains. The real matter of the present examination, was
therefore reduced to 23 grains, and was in complete solution. I
added ammonia to a very sensible excess. The oxide of iron
was thereby precipitated, and, being collected and ignited, it
weighed 24 grains; whereas, according to my experiments,
33i grains should have been produced from the solution, had it
contained nothing but iron. I examined the saline liquor, when
free from ferruginous particles, and discovered it to be the triple
salt of nickel. Hence, allowing for loss, the quantity of nickel
may be estimated, by calculating the quantity of iron contained

on certaifi stony and metalline Substances, &c. ig^

in 24 grains of oxide. Thus, if 145 grains of oxide contain 100
of iron, about i6\ are contained in 24, of oxide. This would
suppose the 23 grains of alloy to consist of 16^ iron and 6^^
nickel; which, if the usual loss be added to the i6^ grains of
iron, and deducted from the nickel, may not be very remote
from the truth.

I shall next examine the globular bodies, also irregularly dis-
persed throughout tlie stone. A number of them were reduced
to fine powder ; but nothing metallic could be separated by the
magnet. As a preliminary experiment, I sought for pyrites, by
digestion with muriatic acid ; but no hepatic smell was in the
least perceivable, nor was white carbonate of lead at all altered
by being held over the mixture. I therefore conclude these
globular bodies do not envelope either iron or pyrites. By
way of analysis, I treated 100 grains with potash, in a silver
crucible: and, after the usual application of a red heat, sepa-
rated as much silica as possible, by muriatic acid and evaporation.
The silica being collected on a Mitre, carbonate of potash was
added to the filtrated liquor ; by which, a precipitate, almost
wholly ferruginous, was produced. This precipitate was col-
lected in the common way ; then boiled with potash, to extract
alumina ; and, by supersaturating the alkaline liquor with
muriatic acid, and precipitating by carbonate of ammonia, an
earth was gathered, which I afterwards found to be partly, if
not entirely, siliceous. After redissolving, in muriatic acid, the
'portion of the ferruginous matter rejected by. the potash, I pre-
cipitated by ammonia, what I took to be entirely oxide of iron ;
but, after igniting it, and again attempting to redissolve the
whole in muriatic acid, more silica was left. The non-existence
of lime was proved, by the addition of carbonate of ammonia,

MDCCCII. C c

194« ^r. Howard's Experiments and Observations

immediately after the same alkali, pure, had thrown down what
I took wholly for oxide of iron. I had now obtained every thing
in the subject of my analysis, except magnesia and nickel. The
former, and a trace of the latter, were held by carbonic acid in
the liquor, from which the ferruginous precipitate was, in the
first instance, throw-n down by carbonate of potash; and the
latter was found in the last named muriate of ammonia. I dis-
engaged the magnesia, by the assistance of potash, and by
evaporating to dryness. The oxide of nickel was precipitated
by hydrogenized sulphuret of ammonia.

Under all circumstances, I am induced to state the proportions
of constituent parts thus :

Silica - - - - 50

Magnesia - - - 15

Oxide of iron - - - 34

Oxide of nickel - - - 2^

101^.
The excess of weight, instead of the usual loss, is owing to
the difference of oxidizement of the iron, in the stone and in
the result of the analysis ; which will be found to be the case
in all analyses of these substances ; indeed it is always necessary
to reduce the oxide to the red state, as being the only one to be
depended upon. To avoid future repetition, I shall also observe,
first, that by preliminary experiments, I could not detect any
other substance than those mentioned. Secondly, that the earth
obtained as alumina, appeared to me to be mostly, if not
entirely, siliceous ; because, after it had been ignited, and again
treated with potash and muriatic acid, I found it was very
nearly all precipitated by evaporation. Thirdly, I examined,
and judged of, the silica collected from the oxide of iron, in the

071 certain stony and metalline Substances, &c. 195

same way. Fourthly, the weight of the magnesia is given, not
immediately, as obtained by evaporation, but after a subsequent
solution in an acid, and precipitation by potash. And, fifthly,
the proportions are taken from the mean of two analyses.

Nothing remains to be examined, of the stone from Benares,
except the earthy matter, forming a cement or matrix for the
substances already examined. 100 grains of this matter were,
by mechanical means, separated as perfectly as possible, from
the pyrites, iron, and globular bodies, and analysed as above.
Tiie mean result of two analyses gave.

Silica - - - - 48

Magnesia - - - - 18

Oxide of iron - - - 34,

Oxide of nickel - - - s^-

102^.

EXAMINATION OF THE STONE FROM SIENNA.

The external coating of this stone appeared to have the same
characters as that of the stone from Benares.

The pyrites, although certainly present, were not crystallized
in such groups as in the preceding stone ; nor could they be
separated by mechanical means.

The attractable metal was easily separated by the magnet ;
but Sf grains only were collected. I treated them with nitric
acid and ammonia, as in a preceding case. Nearly one grain of
earthy matter was insoluble ; the weight was therefore reduced
to rather less than 8 grains. The oxide of iron, precipitated by
ammonia, \yeighed 8 grains ; and the saline liquor gave abun-
dant indications of nickel. As 8 grains of this oxide of iron
contain nearly 6 of metal, the quantity of nickel, in the bare 8

Cos

igS Mr. Howard's Experiments and Observations

grains, may be estimated between i and 2 grains. Some glo-
bular bodies were extracted, but too few to analyze.

Since the pyrites could not be separated, I collected 150
grains of the stone, freed from iron by the magnet, and as
exempt as possible from globular bodies. These 150 grains, I
first digested with muriatic acid, that the pyrites might be
decomposed, and every thing taken up which could be dissolved
by that menstruum. A very decided disengagement of sul-
phureted hydrogen gas was occasioned. When the acid could
produce no further action, I collected the undissolved matter on
a filtre, and boiled it with the most concentrate nitric acid, in
hopes of being able to convert the sulphur, previously liberated,
into sulphuric acid; but my endeavours were fruitless; for,
upon the addition of nitrate of barytes to the nitric solution,
rendered previously transparent, a very insignificant quantity
of sulphate of barytes was obtained. The surplus of barytic
nitrate was removed by sulphate of potash. I next completely
edulcorated the mass which remained insoluble, after the action
of the muriatic and nitric acids ; and, adding the water of edul-
coration to the muriatic and nitric liquors, evaporated the whole
for silica. I then submitted the mass, undissolved by the acids
and the water, to the treatment with potash, muriatic acid, and
evaporation, which was, in the first instance, applied to the
stone from Benares. The first precipitation was, as in that ana-
lysis, also effected with carbonate of potash; but, instead of
endeavouring immediately to extract alumina, I ignited the
precipitate, that the alumina or silica remaining might be ren-
dered insoluble. After the ignition, I separated the oxide of iron
with very concentrate muriatic acid; and the earths, which
were left perfectly w hite, I heated with potash, until they were

on certain stony and metalline Substances, &c. 197

again capable of being taken up by the same acid. The solution
so made, was slowly evaporated; and, as very nearly every
thing was deposited during the evaporation, I conclude all was
silica. The proportions resulting from this single analysis,
without the weight of sulphur contained in the pyrites irregu-
larly disseminated through the whole, were.

Silica - - - - 70

Magnesia - - - - 34

Oxide of iron - - - 53

Oxide of nickel - - - 3

-^59-

EXAMINATION OF THE STONE FROM YORKSHIRE.

The mechanical separation of the substances in this stone
being as difficult as in the preceding case, I was necessarily
satisfied with submitting it to the same treatment. I collected,
however, 34, grains of malleable particles ; which, by the process
already more than once mentioned, left 4 grains of earthy
matter; and, by yielding 37^ of oxide of iron, indicated about
4 grains of nickel.

150 grains of the earthy part of the stone were, by analysis,
resolved into,

Silica - - - 75

Magnesia - - - 37

Oxide of iron - - - 48

Oxide of nickel - - - 2

162.

EXAMINATION OF THE STONE FROM BOHEMIA.

The probability of never being able to obtain another spe-
cimen of tlie very remarkable fragment of this substance, did

198 Mr. Howard's Experiments and Observations

not allow me to trespass more on the liberality of Mr. Greville,
than to detach a small portion. I found it of similar composition
to that of the three preceding stones ; and the Count de Bournon
has already shewn tlie proportionate quantity of the attractable
metal to be very considerable. i6i grains, left 2y of extraneous
earthy matter ; and yielded, by the treatment with nitric acid
- and ammonia, 17^ grains of oxide of iron. This would seem
to induce an estimation of 1^ of nickel in 14, grains, or about
9 per cent.

55 grains of the earthy part of the stone, by the analytical
treatment of the two former, afforded,

Silica - _ _ « 25

Magnesia _ _ - qL

Oxide of iron _ _ _ o^l.

Oxide of nickel - - i^

59h
The unusual increase of weight in the result of the three last
analyses, notwithstanding the entire loss of the sulphur in the
pyrites, is obviously owing to the metallic state of the iron
combined with the sulphur, as was shewn in a former instance.
I have now concluded the chemical examination of these four
extraordinary substances. It unfortunately differs from the ana-
lysis made by the French Academicians, of the stone presented
to them by the Abbe Bachelay, as well as from that made by
Professor Barthold, of the stone of Ensisheim. It is at variance
with that of the Academicians, inasmuch as they found neither
magnesia nor nickel. It differs from that of Mr. Barthold, as
he did not find nickel, but discovered some lime, with 17 per
cent, of alumina. With regard to these differences, I have to
submit to the chemical world, whether magnesia might not

071 certain stony and metalline Substances, &c. 199

have eluded the action of an acid, when the aggregation of
the integrant parts of the stone was not destroyed by treat-
ment with potash. As to the existence of alumina, I do not
absolutely deny it ; yet I must observe, that the whole of the
earth which seemed to have any resemblance, however small,
to alumina, was at most 3 per cent, and there seems good
reason to consider it as silica. Respecting the existence of lime
in the stone of Ensisheim, I must appeal to Professor Bar-
THOLD, whether, supposing lime a constituent part, sulphate
of lime should not have been formed, as well as sulphate of
magnesia, when sulphuric acid was generated by igniting the
earths and pyrites. And, as to the proportion of alumina, in
the same stone, I would ask, at least, whether it would have
been so considerable, if the solutions formed by acids, after
the treatment with potash, had been evaporated to the requisite
dryness : not to observe, that no mention is made of any exami-
nation of the properties of the earth called alumina. In the
proportion of magnesia, I have the satisfaction to find my ana-
lysis correspond very nearly with that of Professor Barthold;
and, if what he considered alumina were supposed silica, the
stone presented to the French Academy, the stone of Ensisheim,
and the four I have examined, would agree very nearly in sili-
ceous proportions. With respect to the nickel, I am confident
it would have been found in all, had the metallio particles been
separately examined. But, whatever be these variations, the
mineratogical description of the Frencii Academicians, of Mr.
Barthold, and of the Count de Bournon, all exhibit a striking
conformity of character, common to each of these stones ; and
I doubt not but the similarity of component parts, especially of
the malleable alloy, together with the near approach of the

200 Mr. Howard's Experimints and Observalmis

constituent proportions of the earths contained in eacli of the
four stones, tlie immediate subject of this Paper, will establish
very strong evidence in favour of the assertion, that they iiave
fallen on our globe. They have been found at places very
remote from each other, and at periods also sufficiently distant.
The mineralogists who have examined them, agree that they
have no resemblance to mineral substances, properly so called ;
nor have they been described by mineralogical authors. I would
further urge the authenticity of accounts of fallen stones, and the
similarity of circuinstances attendant on such phenomena ; but,
to the impartial it would be superfluous, and, to tho.se who dis-
believe whatever they cannot explain, it would be fruitless. At-
tempts to reconcile occurrences of this nature with known prin-
ciples of philosophy, it is true, are already abundant ; but (as the
Earl of Bristol has well expressed ) they leave us a choice of dif-
ficulties equally perplexing. It is however remarkable, that
Dr. Chladni, who seems to have indulged in these specula-
tions with most success, should have connected the descent
of fallen stones with meteors ; and that, in tlie narrative of
Mr. Williams, the descent of the stones near Benares, should
have been immediately accompanied with a meteor.

No luminous appearance having been perceived during the
day on whicli the stone fell in Yorkshire, it must be admitted,
rather militates against the idea, that these stones are the sub-
stances which produce or convey the light of a meteor, or that a
meteor must necessarily accompany them.* Yet the stones from
Sienna feir amidst what was imagined ligiitning, but what
might in reality have been a meteor. Stones were also found,

• In the account of the stone which fell in Portugal, no mention is made, either of
a meteor or ligiitning.

on certain stony and metalline Substances, &c. 201

after the meteor seen in Gascony, in July, 1790. And Mr.
Falconet, in the memoir I have already quoted, relates, that
the stone which was adored as the mother of the gods, was a
Bcetilia; and that it fell at the feet of the poet Pindar, enveloped
in a ball of fire. He also obsen^es, that all the Bcetilia had the

same ongm.

I ought not perhaps to suppress, that in endeavouring to form
an artificial black coating on the interior surface of one of the
stones from Benares, by sending over it the electrical charge of
about 37 square feet of glass, it was observed to become lumi-
nous, in the dark, for nearly a quarter of an hour; and that the
tract of the electrical fluid was rendered black. I by no means
wish to lay any stress upon this circumstance ; for I am well
aware, that many substances become luminous by electricity.

But, should it ever be discovered that fallen stones are actually
the bodies of meteors, it would not appear so problematical, that
such masses as these stones are sometimes represented, do not
penetrate further into the earth : for meteors move more in a
horizontal than in a perpendicular direction ; and we are as
absolutely unacquainted with the force which impels the meteor,
as with the origin of the fallen stone.

Before I close this subject, I may be particularly expected to
notice the meteor which, a few months ago, traversed the
county of Suffolk. It was said, that part of it fell near Saint
Edmundsbury, and even that it set fire to a cottage in that
vicinity. It appeared, from inquiries made on the spot, that
something, seemingly from the meteor, was, with a degree of
reason, believed to have fallen in the adjacent meadows ; but the
time of the combustion of the house did not correspond with
the moment of the meteor's transition. A phenomenon much

MDCCCll,

D d

aoa Mr. Howard's Experiments and Observations

more worthy of attention, has shice been described in the Philo-
sophical Magazine. On the night of the 5th of April, 1800, a
body wholly luminous, was seen, in America, to move with
prodigious velocity. Its apparent size was that of a large house,
70 feet long ; and its elevation above the surface of the earth,
about 200 yards. The light produced effects little short of sun-
beams; and a considerable degree of heat was felt by those
who saw it, but no electric sensation. Immediately after it dis-
appeared in the north-west, a violent rushing noise was heard,
as if the phenomenon were bearing down the forest before it ;
and, in a few seconds after, there was a tremendous crash,
causing a very sensible earthquake. Search being afterwards
made in the place where the burning body fell, every vegetable
was found burnt, or greatly scorched, and a considerable portion
of the surface of the earth broken up. We have to lament, that
the authors of this account did not search deeper than the sur-
face of the ground. Such an immense body, though moving in
a horizontal direction, could not but be buried to a considerable
depth. Should it have been more than the semblance of a body
of a peculiar nature, the lapse of ages may perhaps effect what
has now been neglected ; and its magnitude and solitary situation
become the astonishment of future philosophers.

This leads me to speak of the solitary mass of what has been
called native iron, which was discovered in South America, and
has been described by Don Rubin de Celis. Its weight was
about 15 tons. The same author mentions another insulated
mass of the same nature. The whole account is exceedingly
interesting ; but, being already published in the Philosophical
Transactions for the year 1788, it needs not be here repeated.

Mr. Proust has shewn the mass particularly described, not to

on certain stony and metalline Substances, &c. 203

be wholly iron, but a mixture of nickel and iron. The Trustees
of the British Museum, who are in possession of some fragments
of this mass, sent to the Royal Society by Don Rubin de Celis,
have done me the honour to permit me to examine them; and
I have great satisfaction in agreeing with a chemist so justly
celebrated as Mr. Proust.

The connexion which naturally exists between one mass of
native iron and another, immediately turns our attention to
the native iron in Siberia, described by Pallas; and this,
we are told, the Tartars considered as a sacred relic, which
had dropped from heaven. The nickel found in the one mass,
and the traditional history of the other, not to compare the
globular bodies of the stone from Benares with the globular
concavities and the earthy matter of the Siberian iron, tend to
the formation of a chain between fallen stones and all kinds
of native iron. How far any real affinity exists between these
several substances, very obliging friends have afforded me an
opportunity to form some judgment. I am indebted to Mr.
Greville and Mr. Hatchett for portions of almost every
known native iron : and the Count de Bournon has done me
the favour particularly to describe them as follows.

Description of various Kinds of native Iron. By the Count de
Bournon.

The great number of particles of iron, in a perfectly metallic
state, contained in the stone from Bohemia, and the said par-
ticles being so near each other, naturally lead to some re-
flections respecting the existence of native iron, which, by
many mineralogists, is still considered as problematical. Let
us suppose for a moment, that these particles of iron were to

Dd 2

«04 Mr. Howard's Experiments and Observations

approach still more nearly to each other, so as absolutely to come
into contact, and in that manner to form a kind of chain, folded
upon itself in tlie interior part of the substance, and leaving a
great number of cavities between tlie links of the chain so
folded. Let us then suppose, that the earthy substance with
which these cavities are filled, being very porous, and having
but a small degree of consistence, should (as may happen by a
variety of causes) be destroyed. It is plain, that if such a
destruction were to take place, the iron alone would remain ;
and, being thus left bare, it would appear in the form of a mass,
more or less considerable, of a cellular texture, and as it were
ramified ; such a form, in short, as that in which most of the
native irons we are acquainted with have been found. May it
not be fair to attribute to such an origin, the native iron found
in Bohemia, a specimen of which was presented by the Academy
of Freyberg to Baron Born, and which came, with the rest of
his collection, into the hands of Mr. Greville } May not such
also, notwithstanding the enormity of its bulk, be the origin of
the mass of native iron found in Siberia, near Mount Kemirs,
by the celebrated Pallas r

We have already seen, in the results of the analyses made b}'
Mr. Howard, of the various stones above described, that he
constantly found a certain proportion of nickel mixed with the
iron they contained. This circumstance recalls to our notice
the observations that were made by Mr Proust, some time ago,
respecting the mixture of nickel in the native iron of South
America ; and tends to give some additional support to the opi-
nion hinted at in the foregoing paragraph.

The circumstances just mentioned, naturally gave to Mr.
Howard, as well as to me, a desire to knov.- whether the

on certain stony and metalline Substances, 8cc. 205

native iron from Siberia, and that from Bohemia, were also
mixed with nickel. Mr. Howard, consequently, lostiio time in
proceeding upon this important investigation. The native iron
of Siberia presents some very interesting peculiarities, and has
often been referred to, but has not yet been properly described ;
it is therefore with great pleasure that I add the following
description of it, and of some other kinds of native iron, to the
description I have already given of the various stones said to
have fallen on the earth.

I feel the greater satisfaction in doing this, as the noble col-
lection of Mr. Greville contains two specimens of this iron,
in perfect condition ; one of which weighs several pounds, and
was sent to Mr. Greville by Mr. Pallas himself: on this
account, therefore, I enjoy an advantage that many of the authors
who have spoken of this iron probably wanted.

One of these pieces has a cellular and ramified texture, ana-
logous to that of some very porous and light volcanic scoria :
this is the usual texture of the specimens of this kind of iron,
which are preserved in the various mineralogical collections in
Europe. When it is attentively examined, there may be per-
ceived in it, not only emptv cells, but also impressions or cavities,
of greater or less depth, and sometimes perfectly round, which
appear evidently to be the result of the compression of hard
bodies, which were situated there, and which, when they came
away, left the surface of these cavities quite smooth, and having
the lustre of polished metal. Here and there, in some of these
cavities, there remains a transparent substance, of a yellowish
green colour, of which I shall treat more particularly, when I
come to the description of the second of the specimens above
mentioned. It is very clear, that the cavities here spoken of

2o6 Mr. Howard's Experiments and Observations

owe their existence to this transparent substance ; and that the
polish of the cavities arises merely from the compression of the
said substance, and is the natural consequence of its surface
having been in perfect contact with that of the iron.

This iron is very malleable : it may be easily cut with a knife ;
and may be as easily flattened or extended by means of a
hammer. Its specific gravity is 6487; which, however, is very
much under that of iron which has been merely melted, and has
not been forged. The specific gravity of the native iron of
Bohemia, which is nearly as malleable and as easy to be cut, is
still less : I found it not to exceed 6146. This low degree of
gravity, appears to be owing partly to the oxidizement of the
surface of the iron, and partly to there being, in the interior
part of its substance, a number of small cavities, which
are often rendered visible by fracture, and which have their
surfaces also oxidized. The fracture of this iron, presents the
same shining and silvery white colour as the common cast iron,
known by the name of white cast iron ; but its grain is much
smoother and finer : it is also much more malleable when cold.
Bergman says that this iron is brittle, when heated to a red
heat. I have frequently tried it in that state, and have constantly
found it to be malleable. The same remark may be applied to
the native iron from South America; and also to that from
Senegal.

The second of the two specimens mentioned above, and
which weighs several pounds, presents an aspect that differs, in
some respects, from that of the preceding specimen. The most
considerable part of it forms a solid compact mass, in which
there is not to be perceived the smallest appearance of pores or
cavities; but there arises upon its surface, a kind of ramified

071 certain stony a?id 7netalline Substafices, Sec. 507

or cellular part, similar, m every respect, to the specimen
already described, and every where completely connected with
the substance of the mass itself.

If the compact part of this piece is examined with attention,
it will be perceived, that it is not entirely composed of iron in
the metallic state, but that it is mixed with nearly an equal
quantity of the transparent substance of a yellowish green
colour, (sometimes also of a greenish yellow,) already spoken
of in the description of the other specimen. This substance is
mixed with the iron, in such a manner, that if the whole of the
former could be removed, the remaining part would consist
merely of iron in the metallic state, and would present the same
cellular appearance as the preceding specimen, and the ramified
or cellular part of the specimen now described.

This stony part, separated from the iron, appears in the form
of small nodules, generally of an irregular shape, but sometimes
nearly globular: they have a perfectly smooth and shining
surface, so as very often to present the appearance of small
balls of glass ; a circumstance that has led many persons to
suppose them the result of a real vitrification. Some of these
nodules have several irregular facets, produced by the com-
pression of the iron in which they were inclosed ; but I have
never observed in fhem, any appearances that could lead me to
suspect they had the slightest tendency whatever to assume a
determined crystalline form.

This substance is always more or less transparent. It is suffi-
ciently hard to cut glass; but has no effect upon quartz. It is
very brittle : its fracture is usually conchoid ; but I could not
perceive that it broke in any particular direction, in such a way
that I could consider the fracture as a natural one. It becomes

2o8 Mr. Howard's Experimeiits and Observations

electric by friction. Its specific gravity is from 3263 to 3300. It
is very refractory : I kept it, for some time, exposed to a degree
of heat sufficiently strong to oxidize, to a considerable depth, the
iron crucible in which it was placed, \\ithout its having under-
gone any alteration, except that of having acquired a greater
degree of intensity in its colour. Its transparency was not at all
diminished. I think, therefore, there is not the smallest reason
to allow any probability to the opinion that it ought to be con-
sidered as a kind of glass.

Of all substances hitherto known, that with which it seems to
have the greatest analogy, is the peridot, (the chrysolite of Wer-
ner,) to which some mineralogists have referred it. The result
of Mr. Howard's analysis of it, is nearly the same as that of
the analysis of the peridot, made by Mr. Klaproth.

The hardness and infusibility of this substance are nearly
the same as those of the peridot ; but it seems to have a rather
less degree of specific gravity : that of two very perfect crystals
of peridot, I found to be from 3340 to 3375. The crystalline
forms of the substance here described, if ever we should be able
to determine them, would clear up our doubts respecting the
analogy between the two substances. If we consider the compact
part of the specimen now treated of, particularly the strong con-
nexion that appears to exist between the iron and the transparent
substance, and the great resistance we experience when we
attempt to separate them, we cannot help being surprised, that
almost all the specimens of this mass of metallic iron that
have been brought to Europe, are in the cellular state already
described, owing apparently to the total, or almost total, de-
struction of the transparent substance. But, besides the fra-
gility of this substance, the specimen in question helps very

on certain stony and meialline Substances, &c. 209

much to explain the above circumstance, inasmuch as nianj' of
the nodules of the transparent substance belonging to it, are in
a state of real decomposition. In that state, they are changed
into a white opaque substance, which, upon being lightly pressed
or squeezed between the fingers, crumbles into a gritty dry
powder. This decomposition may be observed to have taken
place in various degrees : in many of the nodules, the sub-
stance is merely become friable, without being much altered in
its appearance ; whereas, some of those which are in a state of
complete decomposition, are of an ochreous reddish yellow
colour ; it is, however, easy to distinguish that this colour does
not belong to them, but is owing only to the oxidizeraent of
the adjacent particles of iron.

From the above observations, it will not be difficult to conceive
the possibility of the total, or nearly total, destruction of the
transparent substance ; and also, the appearance the pieces of
iron must naturally present, when deprived of it. I cannot help
observing likewise, that there appears to exist a very interesting
analogy, between these transparent nodules and the globules I
described as making part of the stones said to have fallen on
the earth. This analogy, though not a very strong one, may
lead us to suppose that the two substances are similar in their
nature, but that the globules are less pure, and contain a
greater quantity of iron.

The native iron from Bohemia is a compact mass, similar
to the compact part of the large specimen of iron from Siberia,
which has just been described : like that, also, it contains a
number of globular bodies or nodules; but they are not in
such great proportion as in the Siberian iron. They are besides
perfectly opaque, and very much resemble the most compact of

MDcccii. E e

21 o Mr. Howard's Expcrments and Observations

the globules belonging to the stones said to have fallen on the
earth.

EXAMINATION OF THE IRON FROM SOUTH AMERICA.

I have already observed, that my experiments coincided with
those of Mr. Proust. He obtained 50 grains of sulphate of
nickel, from 100 of this mass. The process I have so frequently
mentioned, yielded me 80 grains of oxide of iron from 62 of
the metal; which indicates about 74- of nickel, or about lo per
cent.

EXAMINATION OF THE SIBERIAN IRON.

100 grains of this iron, gave 127 of oxide of iron : hence, it
should contain about 17 per cent, of nickel.

The yellow substance belonging to this iron, was analyzed
in the same way as the globular bodies, and the earthy parts,
of the stone from Benares.

The proportions, resulting from the analysis of 50 grains,
and from some previous experiments on other particles, were,
Silica _ _ _ _ 27

Magnesia - - - ~ ^Si

Oxide of iron _ _ , 8^

Oxide of nickel ' - ' i

EXAMINATION OF THE BOHEMIAN IRON.

26^ grains of this metal, left about i| grain of earthy matter,
insoluble in nitric acid ; and, by ammonia, afforded 30 grains
of oxide of iron, inducing an estimation of nearly 5 of nickel.

071 certain stony and ?netalline Substances, Sec. 211

EXAMINATION OF IRON FROM SENEGAL, BROUGHT BY GENERAL
o'haRA, AND GIVEN TO ME BY MR. HATCHETT.

In this experiment, 199 grains of oxide were produced from
1 4.5 grains of metal : hence, there may be an estimation of 8
grains in 145, or between 5 and 6 per cent, of nickel.

It will appear, from a collected view of tlie preceding pages
and authorities, that a number of stones asserted to have fallen
under similar circumstances, have precisely the same characters.
The stones from Benares, the stone from Yorkshire, that from
Sienna, and a fragment of one from Bohemia, have a relation to
each other not to be questioned.

]st. They have all pyrites of a peculiar character.

2dly. They have all a coating of black oxide of iron.

3dly. They all contain an alloy of iron and nickel. And,

4thly. The earths which serve to them as a sort of con-
necting medium, correspond in their nature, and nearly in their
proportions.

Moreover, in the stones from Benares, pyrites and globular
bodies are exceedingly distinct. In the others they are more or
less definite ; and that from Sienna had one of its globules trans-
parent. Meteors, or lightning, attended the descent of the stones
at Benares, and at Sienna. Such coincidence of circumstances,
and the unquestionable authorities I have adduced, must, I
imagine, remove all doubt as to the descent of these stony
substances ; for, to disbelieve on the mere ground of incompre-
hensibility, would be to dispute most of the works of nature.

Respecting the kinds of iron called native, they all contain
nickel. The mass in South America is hollow, has concavities,

212 Mr. Howard's Experiments and Observaliom, &c.

and appears to have been in a soft or welding state, because it
has received various impressions.

The Siberian iron has globular concavities, in part filled with
a transparent substance, which, the proportional quantity of
oxide of iron excepted, has nearly the composition of the glo-
bules in the stone from Benares.

The iron from Bohemia adheres to earthy matter studded
with globular bodies.

The Senegal iron had been completely mutilated before it
came under my examination.

From these facts, I shall draw no conclusion, but submit the
following queries.

ist. Have not all fallen stones, and what are called native
irons, the same origin ?

adly. Are all, or any, the produce or the bodies of meteors .?

And, lastly. Might not the stone from Yorkshire have formed
a meteor in regions too elevated to be discovered ?

Specimens of the Benares and Yorkshire stones have been
deposited, by the President, in the British Museum.

PHILOSOPHICAL
TRANSACTIONS,

OF THE

ROYAL SOCIETY

OF

LONDON.
.FOR THE YEAR MDCCCII.

^ PART II.

LONDON,

PRINTED BY W. BULMER AND CO. CLEVELAND-ROW, ST. JAMEs's ;

AND SOLD BY G. AND \V. NICOL, PALL-MALL, BOOKSELLERS TO HIS MAJESTY,

AND PRINTERS TO THE ROYAL SOCIETY.

MDCCCII.

895780

CONTENTS.

VIII. Observations on the two lately discovered celestial Bodies.
By William Herschel, LL. D. F. R. S. p. 213

IX. Description of the Corundum Stone, and its Varieties, com-
monly knozvn by the Names of Oriental Ruby, Sapphire, &c. ;
zvith Observations on some other mineral Substances, By the
Count de Bournon, F. R. S. P- 233

X. Analysis of Corundum, and of some of the Substances which
accompany it; zvith Observations on the Affinities zvhich the
Earths have been supposed to have for each other, in the humid
Way. By Richard Chenevix, Esq. F. R. S. and M. R. I. A.

P-327

XI. Description of the Anatomy of the Ornithorhynchus Hystrix.
By F^^^aia ' '-"'^-, Esq. F. R. S. P- U^

XII. A l^Mhpd-J^' xjmining refractive and dispersive Pozvers,
by prisTT-c^ic keflection. By William Hyde Wollaston, M. D.
F. R. S. '^ P- 365

XIII. On the oblique Refraction of Iceland Ciystal. By William
Hyde WoUaston, M. D. F. R. S. p. 381

XIV. An Account of some Cases of the Production of Colours, not
hitherto described. By Thomas Young, M. D. F. R. S.
F. L. S. Professor of Natural Philosophy in the Royal Insti-
tution. "P- ^^7

XV. On the Composition of Emery. By Smithson Teiinant,
Esq. F. R. S. P- 3^8

XVI. Qiielques Remarques sur la Chaleur,et sur I' Action des Corps
qui I'interceptetit. Par P. Pi-evost, Projesseur de Philosopbie
a Geneve, &c. Communicated by Thomas Young, M. D.
F. R. S. p. 403

XVII. Of the Reclijication of the Cotiic Sections. By the Rev.
John Hellins, B. D. F. R. S. and Vicar of Potter' s-Pury, in
Nortbamptojishire . p. 44,8

XVIII. Catalogue 0/500 new Nebulce, nebulous Stars, planetary
Nebula, and Clusters of Stars; with Remarks on the Con-
struction of the Heavens. By WiUiam Herschel, LL. D.
F.R.S p. 477

Presents received by the Royal Society, from November 1801 to

July 1802. p. 529

Index. V- 537

PHILOSOPHICAL
TRANSACTIONS.

VIII. Observations on the two lately discovered celestial Bodies.
By William Herschel, LL. D. K R. S,

Read May 6, i8os.

«

In my early account of the moving star discovered by Mr.
PiAzzi, I have already shewn that it is of a remarkably small
size, deviating much from that of all the primary planets.*

It was not my intention to rest satisfied with an estimation
of the diameter of this curious object, obtained by comparing it
with the GEa^'i^lrf M jplanet, and, having now been very successful
in the applic^ifjjn/»,of the lucid disk micrometer, I shall relate
the resultji^f my investigations.

•But the very interesting discovery of Dr. Olbers having
introduced another moving star to our knowledge, I have
extended my researches to the magnitude, and physical con-
struction, of that also. Its very particular nature, which, from
the observations I shall relate, appears to be rather cometary

* By comparing its apparent disk with that of the Georgian planet, it was
estimated, that the real diameter of this new star could not amount to Jths of that of
our moon.

MDCCCII. F f

214! Dr. Herschel's Observations on

than planetary, will possibly tlirow also considerable light upon
the circumstances belonging to the other celestial body ; and,
by that means, enable us to form some judgment of the nature
of both the two last-discovered phenomena.

As the measures I have taken will obfige me to give a result
which must appear extraordinary, it will be highly necessary
to be particular in the circumstances of these measures, and to
mention the condition and powers of the telescopes that were
used to obtain them.

Magnitude of the nerv Stars.

April 1, 1802. Having placed a lucid disk at a considerable
distance from the eye, but so that I might view it with perfect
distinctness, I threw the image of Mr. Piazzi's star, seen in a
7-feet reflector, very near it, in order to have the projected
picture of the star and the lucid disk side by side, that I might
ascertain their comparative magnitudes. I soon perceived that
the length of my garden would not allow me to remove the
disk-micrometer, which must be placed at. rigm angles to the
telescope, far enough to make it appear no l^;g^ *-har. the star;
and, not having disks of a less diameter prepared, ^ placed the
smallest I had, as far from me as the situation of the star would
allow. Then, bringing its image again by the side of the disk,
and viewing, at the same time, with one eye the magnified star,
while the other eye saw the lucid disk, I perceived that Ceres,
which is the name the discoverer has given to the star, was
hardly more than one third of the diameter of the disk, and
certainly less than one half of it.

This being repeated, and always appearing the same, we

the izco lately discovered celestial Bodies. 215

shall not under-rate the size of the star, by admitting its
diameter to have been 45 hundredths of the lucid disk.

The power of the telescope, very precisely ascertained, by
terrestrial geometrical measures properly reduced to the focus
of the mirror on the stars, was 370,4,3. The distance of the
lucid disk from the eye, was 2131 inches ; and its diameter 3,4,
Inches, Hence we compute, that the disk was SQen under an
angle of 5' 29",09 ; and Ceres, when magnified 370 times,
appearing, as we have shewn, 45 hundredths of that magnitude,
its real diameter could not exceed o",40. Had this diameter
amounted to as much as was formerly estimated, the power of
370 would have made it appear of 6' 10", which is more than
the whole lucid disk.

This extraordinary result, raised in me a suspicion, that the
power 370 of a 7-feet telescope, and i-ts aperture of 6,3 inches,
might not be sufficient to shew the planet's feeble light properly.
J therefore adapted my 10-feet instrument to observations with
lucid disks ; which require a different arrangement of the head
of the telescope an^. finder : I also made some small transpa-
rencies, to, represent the object I intended to measure.

April ii. l^ex light being pretty clear, though perhaps not
quite so j»'.':oper for delicate vision as I could have wished, I
directed my 10-feet reflector, with a magnifying power of
516,54, also ascertained by geometrical terrestrial measures
reduced to the focus of the instrument on celestial objects, to
Mr. PiAZZi's star, and compared it with a lucid disk, placed at
i486 inches from the eye, and of 1,4 inch in diameter. I varied
the distance of the lucid disk many times ; and fixed at last on
the above-mentioned one, as the best I could find. There was,
however, a haziness about the star, which resembled a faint

Ff 3

2i6 Dr. Herschel's Observations on

coma ; and this, it may be supposed, must render the measure
less satisfactory than it would otherwise have been.

From tliese data we compute, that the disk appeared to the
natural eye under an angle of 3' i4",33; while Ceres, when
magnified 516^ times, was seen by the other eye of an equal
magnitude ; and that consequently its real diameter, by mea-
surement, was only o",38.

April 22. 11'' 38', sidereal time. I used now a more perfect
small mirror ; the former one having been injured by long con-
tinued solar observations. This gave me the apparent diameters
of the stars uncommonly well defined ; to which, perhaps, the
very favourable and undisturbed clearness of the atmosphere
might contribute considerably.

With a magnifying power of 881,51, properly ascertained,
like those which have been mentioned before, I viewed Dr.
Olbers's star, and compared it with a* lucid disk of 1,4, inch in
diameter, placed at 1514 inches from the eye, measured, like
the rest of the distances, with long deal rods. The star appeared
to me so ill defined, that, ascribing it to the eye-p-lass, I thought
it not adviseable to compare the object, a? it then appeared,
with a well defined lucid disk. Exchanging the glass for that
which gives the telescope a magnifying power of 51 '^\, I found
Pallas, as the discoverer wishes to have it called, better defined ;
and saw, when brought together, that it was considerably less
in diameter than the lucid disk.

In order to produce an equality, I removed the disk to 194,2
inches ; and still found Pallas considerably less than the disk.

Before I changed the distance again, I wished to ascertain
whether Ceres or Pallas would appear under the largest angle,
especially as the air was now more pure than last night. On

the two lately discovered celestial Bodies. 217

comparing the diameter of Ceres with that of the lucid disk, I
found it certainly less than the disk. By proper attention, and
continued examination, for at least an hour, I judged it to be
nearly ^ of the lucid disk.

Then, if we calculate as before, it appears by this observa-
tion, in which there is great reason to place confidence, that
the angle under which this star appeared, was only o".22. For,
a lucid disk of 1,4 inch diameter, at the distance of 1943 inches,
would be seen under an angle of 2' 28",7; three quarters of
which are 1' 51 ",52. This quantity, divided by the power
516,54,, gives o",2i59, or, as we have given it abridged, o",22.

13'' 7'. I removed the micrometer to the greatest convenient
distance, namely, 2136 inches, and compared Dr. Olbers's
star, which, on account of its great altitude, I saw now in high
perfection, with the lucid disk. It was, even at this distance,
less than the diameter of the disk, in the proportion of 2 to 3.

When, by long continued attention, the appearance of Pallas
was reduced to its smallest size, I judged it to bear no greater
proportion to the diameter of the lucid disk of the micrometer,
than as 1 to 2.

In consequence of these measures, it appears that the diameter
of Pallas, according to the first of them, is ©",17; and, accord-
ing to the last, where the greatest possible distinctness was
obtained, only o",i3.

If it should appear almost incredible that these curious objects
could give so small an image, had they been so much magnified
as has been reported, I can say, that curiosity led me to throw
the picture of Jupiter, given by the same telescope and magni-
fying power, on a wall at the distance of 1318 inches, of which
it covered a space that measured 12 feet 11 inches, I do not

2i8 Dr. Herschel's Observations on

mention this as a measure of Jupiter, for the wall \vzs not per-
fectly at right angles to the telescope, on which account the
projected image would be a little larger than it should have
been, nor was I very attentive to other necessary minute cir-
cumstances, which would be required for an accurate measure ;
but we see at once, from the size of this picture, that the power
of the telescope exerted itself to the full of what has been stated.

As we generally can judge best of comparative magnitudes,
when the measures are, as it were, brought home to us ; it will
not be amiss to reduce them to miles. This, however, cannot
be done with great precision, till we are more perfectly ac-
quainted with the elements of tiie orbits of these stars. But, for
our present purpose, it will be sufficiently accurate, if we admit
their mean distances from the sun, as the most recent informa-
tion at present states them ; for Ceres 2,6024 ' ^"^ ^o"" Pallas
2,8. The geocentric longitudes and north latitudes, at the time
of observation, were, for Ceres, about »R 20° 4,', 13° 20'; and for
Pallas, nji 23° 40', 17° 30'. With these data, I have calculated
the distances of the stars from the earth at the time of obser-
vation, partly by the usual method, and, where the . elements
were wanting, by a graphical process, which is sufficiently
accurate for our purpose. My computed distance<J were 1,634
for Ceres, and 1,8333 for Pallas ; and, by them we find, that the
diameter of Ceres, at the mean distance of the earth from the
sun, w^ould subtend an angle of o",g5i27; and that, conse-
quently, its real diameter is 161,6 miles.

It also follows, that Pallas would be seen, at the same
distance from the sun, under an angle of o",3ig9; and that its
real diameter, if the largest measure be taken, is 147 miles;
butj if we take the most distinct observation, which gives the

the two lately discovered celestial Bodies. 219

smallest measure, the angle under which it would be seen from
the sun, will be only o",2 399; and its diameter, no more than
iiQi miles.

Of Satellites.

After Avhat has just now been shewn, with regard to the size
of these new stars, there can be no great reason to expect that
they should have any satellites. The little quantity of matter
they contain, would hardly be adequate to the retention of a
secondary body ; but, as I have made many observations with
a view to ascertain this point, it will not be amiss to relate them.

Feb. 25. 20-feet reflector. There is no small star near Ceres,
that could be supposed to be a satellite.

Feb. 28. There is no small star within 3 or 4 minutes of
Ceres, that might be taken for a satellite,

March 4. 9^ 45', sidereal time. A very small star, south-
preceding Ceres, may be a satellite. See Plate V. Fig. 1. where
C is Ceres, S the supposed satellite, abed ef, are delineation
stars, c and d are very small. S makes nearly a right angle with
them; e is larger than either c or d. There is an extremely faint
star/, between e and d.

14'' 16'. Ceres has left the supposed satellite behind.

March 5. There are two very small stars, which may be
satellites; see Fig. 2. where they are marked, 1st S, 2d S. The
rest, as before, are delineation stars.

March 6. The two supposed satellites of last night remain
in their situation, Ceres having left them far behind.

lo"* x6'. There is a very small star, like a satellite, about 75°
south-following Ceres. See Fig. 3. It is in a line from C to 6
of last night.

S20 Dr. Herschel's Obscrvatiofis on

ii"" 20'. Ceres has advanced in its orbit; but has left the
supposed satellite behind.

March 30. g^ 35'. A supposed 1st satellite is directly fol-
lowing Ceres : it is extremely faint. A 2d supposed satellite is
north-following. See Fig. 4. The supposed satellites are so
small, that, with a 20-feet telescope, they require a power of
300 to be seen ; and the planet should be hidden beiiind a thick
wire, placed a little out of the middle of the field of view, which
must be left open to look for the supposed satellites.

12'' 17'. Ceres has changed its place, and left both the sup-
posed satellites behind.

March 31. 9'' 20'. There is a very small star, on the north-
preceding side of Ceres, which may be a satellite.

n*" 50'. Ceres has moved forwards in its path; but the sup-
posed satellite remains in its former situation. The nearest star
is 20" of time from Ceres ; so that, within a circle of 40" of
time, there certainly is no satellite that can be seen with the
space-penetrating power of this instrument.

It is evident, that when the motion of a celestial body is so
considerable, we need never be long in doubt whether a small
star be a satellite belonging to it, since a few hours must
decide it.

May 1. le** 51'. I viewed Pallas with the 20-feet reflector,
power 300 ; there was no star within 3', that could be taken for
a satellite.

Of the Colour of the nnv Stars.
Feb. 13. The colour of Ceres is ruddy, but not very deep.
April 21. Ceres is much more ruddy than Pallas.
April 22. Pallas is of a dusky whitish colour.

the two lately discovered celestial Bodies. 221

Of the Appeanvices oj the nezv Stars, with regard to a Disk.

Feb. 7. Ceres, witli a magnifying power of 5164, shews an
ill defined planetary disk, hardly to be distinguished from the
surrounding haziness.

Feb. 13. Ceres has a visible disk.

April 22. In viewing Pallas, I cannot, with the utmost atten-
tion, and under the most favourable present circumstances,
perceive any sharp termination which might denote a disk ; it
is rather what I would call a nucleus.

April 28. In the finder, Pallas is less than Ceres. It is also
rather less than when I first saw it.

Of the Appearances of the new Stars, with regard to an
Atmosphere, or Coma.

April 21. I viewed Ceres for nearly an hour together. There
was a haziness about it, resembling a faint coma, which was,
however, easily to be distinguished from the body,

April 22. I see the disk of Ceres better defined, and smaller,
than I did last night. There does not seem to be any coma ;
and I am inclined to ascribe the appearance of last night to a
deception, as I now and then, with long attention, saw it
without; at which times, it was always best defined, and
smallest.

April 28. Ceres is surrounded with a strong haziness.
Power 550,

With 516^, which is a better glass, the breadth of the coma
beyond the disk may amount to the extent of a diameter of the
disk, which is not very sharply defined. Were the whole coma
and star taken together, they would be at least three times as

MDCCCII. G g

222 Dr. Herschel's Observations on

large as my measure of the star. The coma is very dense near
the nucleus ; but loses itself pretty abruptly on the outside,
though a gradual diminution is still very perceptible.

April 30. Ceres has a visible, but very small coma about it.
This cannot be seen with low powers ; as the whole of it together
is not large enough, unless much magnified, to make up a
visible quantity.

May 1. The diameter of the coma of Ceres, is about .5 times
as large as the disk, or extends nearly 2 diameters beyond it.

13'' 19'. 20-feet reflector; power 477. The disk of Ceres is
much better defined than that of Pallas. The coma about it is
considerable, but not quite so extended as that of Pallas.

May 2. 13'' 20'. Ceres is better defined than I have generally
seen it. Its disk is strongly marked ; and, when I see it best,
the haziness about it hardly exceeds that of the stars of an
equal size.

Memorandum, This may be owing to a particular disposition
of the atmosphere, which shews all the stars without twinkling,
but not quite so bright as they appear at other times. Jupiter
likewise has an extremely faint scattered light about it, which
extends to nearly 4 or 5 degrees in diameter.

April 22. Pallas, with a power of 88iy, appears to be very
ill defined. The glass is not in fault; for, in the day time, I
can read with it the smallest letters on a message card, fixed
up at a great distance.

13*" 17'. The appearance of Pallas is cometary; the disk, if
it has any, being ill defined. When I see it to the best advan-
tage, it appears like a much compressed, extremely small, but ill
defined, planetary nebula.

April 28. Pallas is very ill defined : no determined disk can

the two lately discovered celestial Bodies. 220

be seen. The coma about it, or rather the coma itself, for
no star appears within it, would certainly measure, at first
sight, 4 or 5 times as much as it will do after it has been
properly kept in view, in order to distinguish between the hazi-
ness which surrounds it, and that part which may be called the
body.

May 1. Pallas has a very ill defined appearance; but the
whole coma is compressed into a very small compass.

13'' 5'. 20-feet reflector; power 477. I see Pallas well, and
perceive a very small disk, with a coma of some extent about it,
the whole diameter of which may amount to 6 or 7 times that
of the disk alone.

Maya. 13*^0'. 10-feet reflector, A star of exactly the same
size, in the finder, with Pallas, viewed with 516^, has a different
appearance. In the centre of it is a round lucid point, which is
not visible in Pallas. The evening is uncommonly calm and
beautiful. I see Pallas better defined than I have seen it before.
The coma is contracted into a very narrow compass ; so that
perhaps it is little more than the common aberration of light of
every small star. See the memorandum to the observation of
Ceres, May 2,

On the Nature of the new Stars.
From the account which we have now before us, a very im-
portant question will arise, which is. What are these new stars,
are they planets, or are they comets t And, before we can enter
into a proper examination of the subject, it will be necessary to
lay down some definition of the meaning we have hitherto affixed
to the term planet. This cannot be difficult, since we have seven

Gg 2

224 -D/". Herschel's Observations on

patterns to adjust our definition by. I should, for instance, say
of planets,

1. They are celestial bodies, of a certain very considerable
size.

2. They move in not very excentric ellipses round the sun.

3. The planes of their orbits do not deviate many degrees
from the plane of the earth's orbit.

4. Their motion is direct.

5. They may have satellites, or rings.

6. They have an atmosphere of considerable extent, which
however bears hardly any sensible proportion to their diameters.

7. Their orbits are at certain considerable distances from
each other.

Now, if we may judge of these new stars by our first criterion,
which is their size, we certainly cannot class them in the list
of planets : for, to conclude from the measures I have taken.
Mercury, which is the smallest, if divided, would make up more
than 135 thousand such bodies as that of Pallas, in bulk.

In the second article, their motion, they agree perhaps suffi-
ciently well.

The third, which relates to the situation of their orbits, seems
again to point out a considerable difference. The geocentric lati-
tude of Pallas, at present, is not less than between 17 and 18 de-
grees; and that of Ceres between 15 and 16; whereas, that of the
planets does not amount to one half of that quantity. If bodies
of this kind were to be admitted into the order of planets, we
should be obliged to give up the zodiac ; for, by extending it to
them, should a few more of these stars be discovered, still
farther and farther deviating from the path of the earth, which

the two lately discovered celestial Bodies. 225

IS not unlikely, we might soon be obliged to convert the whole
firmament into zodiac ; that is to say, we should have none left.

In the fourth article, which points out the direction of the
motion, these stars agrte with the planets.

With regard to the fifth, concerning satellites, it may not be
easy to prove a negative; though even that, as far as it can
be done, has been shewn. But the retention of a satellite in its
orbit, it is well known, requires a proper mass of matter in the
central body, which it is evident these stars do not contain.

The sixth article seems to exclude these stars from the con-
dition of planets. The small comas which they shew, give them
so far the resemblance of comets, that in this respect we should
be rather inclined to rank them in that order, did other circum-
stances permit us to assent to this idea.

In the seventh article, they are again unlike planets ; for it
appears, that their orbits are too near each other to agree with
the general harmony that takes place among the rest ; perhaps
one of them might be brought in, to fill up a seeming vacancy
between Mars and Jupiter. There is a certain regularity in the
arrangement of planetary orbits, which has been pointed out by
a very intelligent astronomer, so long ago as the year 1 772 ;
but this, by the admission of the two new stars into the order
of planets, would be completely overturned ; whereas, if they
are of a different species, it may still remain established.

As we have now sufficiently shewn that our new stars can-
not be called planets, we proceed to compare them also with the
other proposed species of celestial bodies, namely, coinets. The
criteria by which we have hitherto distinguished these from
planets, may be enumerated as follows.

226 Dr. Herschel's Observations on

1. They are celestial bodies, generally of a very small size,
though liow far this may be limited, is yet unknown.

2. They move in very excentric ellipses, or apparently para-
bolic arches, round the sun.

3. The planes of their motion admit of the greatest variety
in their situation.

4. The direction of their motion also is totally undetermined.

5. They have atmospheres of very great extent, which shew
themselves in various forms of tails, coma, haziness, &c.

On casting our eye over these distinguishing marks, it appears,
that in the first point, relating to size, our new stars agree sufli-
ciently well ; for the magnitude of comets is not only small, but
very unlimited. Mr. Pigott's comet, for instance, of the year
1781, seemed to have some kind of nucleus; though its mag-
nitude was so ill defined, that I probably over- rated it much,
when, November 22, I guessed it might amount to 3 or 4" in
diameter. But, even this, considering its nearness to the earth,
proves it to have been very small.

That of the year 1783, also discovered by Mr. Pigott, I saw
to more advantage, in the meridian, with a 20-feet reflector. It
had a small nucleus, which, November 29, was coarsely esti-
mated to be of perhaps 3" diameter. In all my other pretty
numerous observations of comets, it is expressly remarked, that
they had none that could be seen. Besides, what I have called
a nucleus, would still be far from what I now should have mea-
sured as a disk ; to constitute which, a more determined outline
is required.

In the second article, their motions differ much from that of
comets; for, so far as we have at present an account of the

the two lately discovered celestial Bodies. 227

orbits of these new stars, they move in ellipses which are not
very excentric.

Nor are the situations of the planes of their orbits so much
unlike those of the planets, that we should think it necessary
to bring them under the third article of comets, which leaves
them quite unlimited.

In the fourth article, relating to the direction of their motion,
these stars agree with planets, rather than with comets.

The fifth article, which refers to the atmosphere of comets,
seems to point out these stars as belonging to that class; it
will, however, on a more particular examination, appear that
the difference is far too considerable to allow us to call them
comets.

The following account of the size of the comas of the smallest
comets I have observed, will shew that they are beyond com-
parison larger than those of our new stars.

Nov. 22, 1781. Mr. Pigott's comet had a coma of 5 or 6'
in diameter.

Nov. 29, 1783. Another of Mr. Pigott's comets had a coma
of 8' in diameter.

Dec. 22, J 788. My sister's comet had a coma of 5 or & in
diameter.

Jan. 9, 1790. Another of her comets was surrounded by
haziness of 5 or 6' in diameter.

Jan. 18, 1790. Mr. Mechain's comet had a coma of 5 or 6'
in diameter.

Nov. 7, 1795. My sister's comet had a coma of 5 or 6' in
diameter.

Sept. 8, 1799. Mr. Stephen Lee's comet had a coma of not
less than 10' in diameter, and also a small tail of 15' in length.

228 D?-. Herschel's Observations on

From these observations, which give us the dimensions of
the comas of the smallest comets that have been observed v/ith
good instruments, we conclude, that the comas of these new
stars, which at most amount only to a few times the diameter
of the bodies to which they belong, bear no resemblance to the
comas of comets, which, even when smallest, exceed theirs
above a hundred times. Not to mention the extensive atmo-
spheres, and astonishing length of the tails, of some comets that^
have been observed, to which these new stars have nothing in
the least similar.

Since, therefore, neither the appellation of planets, nor that
of comets, can with any propriety of language be given to these
two stars, we ought to distinguish them by a new name, denoting
a species of celestial bodies hitherto unknown to us, but which
the interesting discoveries of Mr. Piazzi and Dr. Olbers have
brought to light.

With this intention, therefore, I have endeavoured to find
out a leading feature in the character « f tliese new stars; and,
as planets are distinguished from the fixv.d stars by their visible
change of situation in the zodiac, and comets by their remark-
able comas, so the quality in which these objects differ consi-
derably from the two former species, is that they resemble small
stars so much as hardly to be distinguished from them, even
by very good telescopes. It is owing to this very circumstance,
that they have been so long concealed from our view. From
this, their asteroidical appearance, if I may use that expression,
therefore, I shall take my naine, and call them Asteroids;
reserving to myself, however, the liberty of changing that name,
if another, more expressive of their nature, should occur. These
bodies will hold a middle rank, between the two species that

the izc'O lately discovered celestial Bodies. 229

were known before; so tliat planets, asteroids, and comets, will
in future comprehend all the primary celestial bodies that either
remain with, or only occasionally visit, our solar system.

I shall now give a definition of our new astronomical term,
which ought to be considerably extensive, that it may not only
take in the asteroid Ceres, as well as the asteroid Pallas, but
that any other asteroid which may hereafter be discovered, let
its motion or situation be whatever it may, shall also be fully
delineated by it. This will stand as follows.

Asteroids are celestial bodies, which move in orbits either of little
or of considerable excentricity round the sun, the plane of which
may be inclined to the ecliptic in any angle whatsoever. Their
motion may be direct, or retrograde : and they may or may not
have considerable atmospheres, very small comas, disks, or
nuclei.

As I have given a definition which is sufficiently extensive to
take in future discoveries, it may be proper to state the reasons
we have for expecting that additional asteroids may probably
be soon found out. From the appearance of Ceres and Pallas
it is evident, that the discovery of asteroids requires a particular
method of examining the heavens, which hitherto astronomers
have not been in the habit of using. I have already made five
reviews of the zodiac, without detecting any of these concealed
objects. Had they been less resembling the small stars of the
heavens, I must have discovered them. But the method which
will now be put in practice, will completely obviate all difficulty
arising from the asteroidical appearance of these objects ; as their
motion, and not their appearance, will in future be the mark to
which the attention of observers will be directed.

A laudable zeal has induced a set of gentlemen on the

MDCCCII. H h

230 Dr. Hf.rschei/s Observations on

Continent, to form an association for the examination of the
zodiac. I hope they will extend their attention, by degrees, to
every part of the heavens; and that the honourable distinction
which is justly due to the successful investigators of nature,
will induce many to join in the meritorious pursuit. As the
new method of observing the zodiac has already produced such
interesting discoveries, we have reason to believe that a number
of asteroids may remain concealed ; for, how improbable it would
be, that if there were but two, they should have been so near
together as almost to force themselves to our notice. But a
more extended consideration adds to the probability that many
of them may soon be discovered. It is well known that the
comas and tails of comets gradually increase in their approach
to the sun, and contract again when they retire into the distant
regions of space. Hence we have reason to expect, that when
comets have been a considerable time in retirement, their comas
may subside, if not intirely, at least sufficiently to make them
assume the resemblance of stars ; that is, to become asteroids,
in which state we have a good chance to detect them. It is true
that comets soon grow so faint, in retiring from their perihelia,
that we lose sight of them ; but, if their comas, which are ge-
nerally of great extent, should be compressed into a space so
small as the diameters of our two asteroids, we can hardly
entertain a doubt but that they would again become visible
with good telescopes. Now, should we see a comet in its aphe-
lion, under the conditions here pointed out, and that there are
many which may be in such situations, we have the greatest
inducements to believe, it would be a favourable circumstance
to lead us to a more perfect knowledge of the nature of comets
and their orbits ; for instance, the comet of the year 1770, which

the two lately discovered celestial Bodies. 231

Mr. Lexell has shewn to have moved in an elliptical orbit,
such as would make the time ol" its periodical return only about
5^ years : if this should still remain in our sj'stem, which is
however doubtful, we ought to look for it under the form of an
asteroid.

If these considerations should be admitted, it might be ob-
jected, that asteroids were only comets in disguise ; but, if we
were to allow that comets, asteroids, and even planets, might
possibly be the same sort of celestial bodies under different cir-
cumstances, the necessary distinction arising from such diffe-
rence, would fully authorise us to call them by different names.

It is to be hoped that time will soon throw a greater light
upon this subject ; for which reason, it would be premature to
add any other remarks, though many extensive views relating
to the solar system might certainly be hinted at.

Additional Observations relating to the Appearances of the
Asteroids Ceres and Pallas.

May 4, 12*' 40'. 10-feet reflector; power 5i6|-. I compared
Ceres with two fixed stars, which, in the finder, appeared to be
of very nearly the same magnitude with the asteroid, and found
that its coma exceeds their aberration but in a very small
degree.

IS** 50'. 20-feet reflector; power ^\^y'J. I viewed Ceres, in
order to compare its appearance with regard to haziness, aber-
ration, atmosphere, or coma, whatever we may call it, to the
same phenomena of the fixed stars ; and found that the coma
of the asteroid did not much exceed that of the stars.

Hh 2

232 Dr. Herschel's Observations, &c.

I also found, tliat even the fixed stars diflfer considerably in
this respect among themselves. The smaller they are, the larger
in proportion will the attendant haziness shew itself. A star
that is scarcely perceptible, becomes a small nebulosity.

10-feet reflector. 13'' 10'. I compared the appearance of
Pallas with two equal fixed stars ; and found that the coma of
this asteroid but very little exceeds the aberration of the stars,

14** 5', 20-feet reflector. I viewed Pallas ; and, with a magni-
fying power of 477, its disk was visible. The coma of this
asteroid is a little stronger than that which fixed stars of the
same size generally have.

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i 233 3

IX, Description of the Corundum Stone, and its Varieties, com-
monly known by the Names of Oriental Ruby, Sapphire, &c. ;
with Observations oti some other mineral Substances. By the
Cou7it de Bournon, F. R. S.

Read March 25, 1802.

When, in the year 1798, I presented to the Royal Society,
in conjunction with Mr. Greville, a Paper on the Corundum
Stone,* I gave some hints of an opinion which I, as well
as Mr. Greville, had already formed, namely, that the said
stone was absolutely of the same nature with those stones
or gems which mineralogists, following the example of the
jewellers, had hitherto distinguished by the epithet oriental.
This opinion was founded upon circumstances which appeared
to me perfectly satisfactory ; but these circumstances had not yet
been sufficiently examined, nor were they sufficiently striking, to

• See PhiL Trans, for 1798. p. 428. My principal intention, in the Paper here
referred to, was, to bring together the various observations which had been then made
respecting the stone here treated of. The great number of specimens which have
since been successively sent from different parts of the East Indies, have enabled me
to form a more correct, and, in some respects, a different opinion of it. I therefore
thought it would be of more advantage to science, instead of presenting to the Royal
Society a supplement to my former Paper, to collect into one point of view, every
information I could obtain upon the subject. I have consequently endeavoured, in
the following Paper, to give, as far as I am able, a complete mineralogical history of
this stone ; my former account being, when compared with this, a very imperfect
one.

234 Count de Bournon's Description of

obviate every possible objection ; and, consequently, my opinion
was not yet in a state fit to be presented to the Royal Society,
as an established truth. Since that time, I have never lost sight
of this object, nor have I neglected any means in my power,
which could conduce to the end I had in view ; and I may say,
tliat my success has far surpassed my expectations. The spe-
cimens of corundum that have been lately sent from India,
joined to the very considerable collection of oriental gems, in
their perfect crystalline forms, which I have been able to pro-
cure, have afforded me the most satisfactory demonstration that
a mineralogist can wish for; and notliing was now wanting to
fix, in a complete and decisive manner, the general opinion
respecting this stone, except to give it that additional support
which is furnished by chemical investigation. Mr. Klaproth
indeed had already published an analysis of the corundum stone,
and of the sapphire; but he had not submitted to the same
scrutin}^ the perfect red corundum or oriental ruby ; it is
possible also, that the specimens of corundum he made use of
in his analysis, which had been taken from among the first spe-
cimens of this stone sent from India, were not so pure as
might have been wished, and that this impurity was tiie cause
of the difference, (which however was very trifling,) between
the result of their analysis and that of the sappliire. I there-
fore chose, from among the specimens of corundum which had
been sent from China, from the kingdom of Ava, from the
Carnatic, and from the coast of Malabar, such pieces as ap-
peared to me the most pure; and, after having added to them
a quantity of oriental rubies and sapphires, sufficient for many
repeated analyses, I requested Mr. Chenevix, whose chemical
labours are so useful to mineralogy, by his constant application

the Corundum Stone, and its Varieties, &c. 235

of them to that science, to have the kindness to join with me in
the investigation I had undertaken. The Royal Society will
perceive, in the detail given by Mr. Chenevix himself, of the
analyses which he has made, not only of the different varieties
of corundum, but also of the substances which accompany this
stone in its matrix, how very satisfactory to science are the
results of those analyses ; insomuch, that I can now offer to the
Society, as one of the best established truths, what, in the year
1798, I mentioned merely as a suspicion which had great pro-
bability in its favour; and can also, in consequence of the
particular study I have made of all the varieties of stones
that I have here joined together, under the general denomi-
nation of corundum, present to the Society a collection of facts,
for the most part unknown, which, altogether, may be considered
as forming a mineralogical history of this substance.

Although the epithet oriental has been for a long time used
by the lapidaries, to express, in gems or precious stones, a
degree of hardness superior to that of other stones, (the
diamond excepted,) which made them capable of taking a
more brilliant polish ; and although, following the example of
the lapidaries, naturalists had employed the same term by
way of distinguishing them, there still remained a great uncer-
tainty, respecting the nature of the analogy which really existed
between the various stones to which the above epithet was
applied.

The nomenclature here spoken of was not, at its origin, the
result of any mineralogical knowledge; in consequence of
which, a number of stones, of a totally different nature, were
united together, for no other reason but because, among those
of the same colour, some were found to be of a much superior

236 Count de Bournon's Description of

degree of hardness to others ; and, as those which were the hard-
est most commonly came from the East Indies, all hard gems were
called oriental, as a general mark of discrimination. The chief
distinguishing character of gems was then derived from their
colour, which had caused them to be denominated sappliire,
ruby, amethyst, topaz, emerald, chrysolite, &c. and it was
thought sufficient to add to these names the epithet oriental, to
distinguish those among them whose hardness was superior to
that of the others.

Rome' de Lisle was the first mineralogist who threw a
gleam of light, into the obscurity wliich existed in this confused
assemblage of stones. His classification of gems, although it had
not yet attained the degree of perfection to whicii the science of
crystallography (of which he had just laid the foundation)
may hereafter carry it, was undoubtedly one of the greatest
steps mineralogy had made, at the time when the second edition
of his work, upon this new character of stones, was published.
After having fixed, according to their different characters, and
particularly according to that which was derived from their
crystalline forms, the place which each of the species com-
posing this particular class of lithology ought to occupy, he
placed at the head of them, under the title of oriental ruby,
all those stones which, being possessed of a degree of hard-
ness superior to that of all others, (except the diamond,) ad-
miitted a more brilliant polish, and appeared under the form
of a hexaedral pyramid, or of two, joined base to base, the solid
angle of whose summit, taken upon two of the opposite faces,
varied, according to him, from 20° to 30°. He added also, that
this stone presented all sorts of colours, either separately, or
united together in the same stone. Nearly at the same time,

the Corundum Stone, and its Varieties, &c. 237

Mr. Werner, following the system his genius had just then
formed in mineralogy, was conducted to exactly the same
results.

The very small number of perfectly defined crystals of this
stone which existed in the cabinets of Europe, (they being
much more rich in cut and polished specimens,) did not permit
either of the above-mentioned mineralogists to obtain a clear
idea of the whole of its characters, so as to enable him to
give a proper description of it. Rome' de Lisle, indeed, may
be said to have made a step backwards, by excluding from the
number of its crystalline forms, the rhomboid, which, in the first
edition of his Crystallography, he had assigned to it, on account
of a crystal of that form, which was among the stones preserved
in the Garde Meuhle of the King of France. This stone,
which was of a blue colour inclining to purple, and of a very
considerable size, (since it weighed no less than 133 carats,) had
been polished ; a circumstance which had necessarily altered its
form in some measure, although there is reason to believe that
it had been polished only upon its natural surfaces. Rome' de
Lisle, however, who had, merely for the above reason, excluded
the rhomboid from the forms of the sapphire, being induced
afterwards to recur to his former opinion, made another mistake,
by assigning to this substance, the rhomboid of sulphate of iron
or martial vitriol, (the measures of which are very nearly from
82° to 98°,) as that which properly belonged to it.

Our mineralogical knowledge with respect to corundum, was
therefore very little advanced, when we became acquainted with
that which was sent from India. Mr, Greville, in the Paper to
which I have already referred, has given a very interesting and
instructive account, not only respecting the introduction of this

MDCCCII. I i

238 Count de Bournon's Description of

stone into Europe, but also respecting the information which,
in consequence of his repeated inquiries, he had been able to
obtain with regard to its local situation; and it is chiefly to him
that we are indebted, for nearly all the specimens of this stone
which exist in the various collections, as well as for the attention
which has been paid to it.

From the moment when this stone became known, the
opinions which were formed, respecting the place it ought
to occupy in mineralogy, were very various ; indeed, it was
natural they should be so, with regard to a stone which, as yet,
was only known by means of a few specimens, (by no means
sufficiently numerous to supply every collection,) and whose
local situation, as well as every thing else relating to it,
was totally unknown. It has suffered, in this respect, the fate
usually attendant on things so circumstanced; yet, whatever
erroneous notions have hitherto been entertained respecting it,
it has at last, I trust, found the place assigned to it by nature
and truth.

The progress of chemistry, with respect to this stone, has
not been more certain than that of mineralogy. It was first
placed among those substances which were considered as com-
posed of new earths; afterwards it was classed among those
which were found by analysis to be chiefly, and indeed almost
exclusively, composed of argill. Tiiis was already a great step
towards the knowledge of its real nature; since it was thereby
placed, if not by the side of, at least at a very inconsiderable
distance from, the oriental gems, then known chiefly by the
name of sapphire.

It is, in fact, among those gems or stones, now known by
the names of sapphire, oriental ruby, &c. that corundum ought

the Corundum Stone, and its Varieties, &c. 239

to be placed ; but the progress by which we have arrived at this
degree of knowledge was necessarily very slow, and was im-
peded by continual obstacles : for the scarcity and smallness of
the crystals of corundum, and the impression naturally made
upon our minds by the various appearances it exhibited to us,
were by no means likely to lead us to form a true judgment
respecting it. So that Mr .Werner, whose great and acknow-
ledged talents have justly caused his opinion to be considered,
nearly throughout all Germany, as of the highest importance
in all mineralogical decisions, has hitherto continued to place
corundum between pitchstone and felspar; consequently, he
has removed it to a considerable distance from the sapphire,
since there exists, according to his classification, nearly thirty
intermediate substances.

Crystallography also offers some difficulties with respect to
this stone ; and these difficulties are only to be guarded against
by a very particular study of it, and especially by an accurate
examination of all its varieties, as objects of comparison.
The Abb6 Hauy, to whose great knowledge of cr}rstallo-
graphy all Europe is eager to do justice, although he gave
some indications that he began to waver in his opinion, did
not think there were reasons sufficiently strong to adopt that
which I had, without satisfactory evidence, advanced in 1798;
and has continued to separate the corundum from the sap-
phire, giving to the latter the name of Telesie. In the new
System of Mineralogy, which the Abbe Hauy has just pub-
lished, he places corundum immediately after felspar, and before
ceylonite, the name of which he has changed into Pleonaste.
One cannot lielp being astonished that the very great hardness
of tliis stone, as well as its great gravity, did not lead him to

I i 3

240 Count de Bournon's Description of

place it nearer those stones with which, from their possessing
those two qualifies, it seemed to have some analogy. Perhaps
he was not in possession of specimens of sapphire, or of ori-
ental ruby, or of corundum, sufficiently characterised to serve
as objects of comparison ; and I cannot iielp expressing great
regret, that the crystals of corundum which were sent to him
by Mr. Greville, selected by myself from his superb col-
lection, and to which I had the pleasure of adding an almost
equal number from my own, were not sufficient to carry con-
viction to Mr. Hauy's mind; as it would have given me great
satisfaction to find that my observations, upon this interesting
substance, perfectly coincided with his. The opinion of a na-
turalist so justly celebrated as Mr. Hauy, will naturally have
great weight in the minds of those who pursue the study of
mineralogy ; for which reason, after giving a particular descrip-
tion of corundum, comprehending all the characters which are
peculiar to it, I shall endeavour to remove every objection which
this mineralogist still tiiinks it right to offer, against its union
with the sappiiire, oriental ruby. Sec.

The substance here treated of, has hitherto presented itself to
our notice under two appearances, which differ so much from
each c ther, in the greater number of those characters which
most forcibly affect ojr senses, particularly those which concern
the organ of sight, that we cannot be much surprised to find
that mineralogists feel some reluctance, at the idea of uniting
together substances which appear so very dissimilar.

Under one of these appearances, in which it is known by the
name of corundum, this substance presents itself cither in frag-
ments, or in crystals of a pretty large size; sometimes, indeed,
of a very considerable one. The surface of these crystals is

the Corundum Stone, atid its Varieties, &c. 241

generally dull and rough; their texture, which is veiy much
lamellated, is shown to be so by their fracture, which is ob-
tained without much difficulty, as the adherence of their crys-
talline lamince to each other is not very strong, and is easily
overcome ; and the crystal or fragment may always be brought
to the rhomboid, its primitive form. Their colour, which is most
commonly rather dull, is a whitish, greenish, and sometimes
yellowish gray. Specimens of a purplish red, or of a blue colour,
have always been extremely rare ; indeed, a short time since,
no such specimens were known, excepting a very few, preserved
in the collection of Mr. Greville, and some small fragments
he had given away; but the specimens which have been lately
sent from the district of EUor, have contributed to increase their
number.

Under the other appearance, (in which this substance is known
by the names of sapphire, ruby, &c.) it offers itself, on the con-
trary, in crystals which are generally of a very small size, and
have a smooth and brilliant surface. Their transparency is often
very great ; and it seldom happens that they are not semi-
transparent, in a greater or less degree. They are more diffi-
cult to break in the direction of their crystalline laminae ; and
this difficulty increases, in proportion to their purity and their
brilliancy. Their colours are much more beautiful, more varie-
gated, and more lively.

With respect to the name of this substance, as, in its most
common state, it is known in India, (its native country,) by the
name of corundum, and as that name has been generally adopted
in Europe, I have thought proper to continue it, and shall
distinguish, by the terms perfect and imperfect, the two different
states in which it presents itself to our observation. Notliing,

Count de Bournon's Description of

in my opinion, occasions greater obstacles to the progress of
a science, than making a change in its nomenclature, especially
^vhen that change is made without a general agreement. For,
by this means there exists no fixed basis; and, consequently,
every one thinks he has a right to exercise an arbitrary power
in this respect, and to reject the name given to a substance by
those who first observed and described it, for the purpose of
giving it one more suitable to his own ideas. And thus, at last,
it becomes necessary, (in order that the labours of our prede-
cessors may not be wholly useless,) to fill the new works on
the subject with a tedious list of synonyms, which too often
becomes in the end a mass of uncertainty, and a subject of
everlasting discussion.

COLOUR.

Although the colour of stones, strictly speaking, may be
considered as a very variable circumstance, and as one which
can by no means be included among those fixed characters
which determine the nature of the stone, it is nevertheless cer-
tain, that many stones seem disposed to assume some colours in
preference toothers; and, therefore, the colour of a stone, though
an uncertain character, may sometimes serve as a secondary
mark of distinction ; particularly, if we are cautious not to draw
any inferences from it, except in conjunction with other cha-
racters. As its chief use is, to fix the value of precious stones,
and as, in those here treated of, it has served as a basis for the
former classification of them, it becomes more necessary to
give a minute description of it in this substance than in any
other.

I have already said, that the colour of common corundum,

the Corundum Stone, and its Varieties, &c. 243

(wliicli I shall in future distinguish by the name of imperfect
corundum,) has, in general, very little brilliancy; but, in pro-
portion as the crystals announce, by their greater transparency,
a greater degree of purity and perfection, their colour becomes
more lively and more brilliant; this, however, seldom happens,
except in crystals of a small size. The colour of these crystals
is various, and seems to depend very much upon the place
where they are found. In the Carnatic, the prevailing colour
is a grayish white; which, however, very often approaches
to a pale green, and sometimes to a yellowish cast. They are
also found, but much more rarely, of a red, and of a blue co-
lour; and, when they are of those colours, the red always
inclines to the purple, and the blue is of that azure kind which
is generally known by the name of sapphire blue. In the corun-
dum of China, and in that of the kingdom of Ava, the colour
is generally a green, more or less deep, with a dull appear-
ance ; or it is brown. The corundum of the coast of Malabar,
appears of a reddish brown in those parts which are opaque;
but, whenever there is, in any part of it, the smallest degi-ee
of transparency, the forementioned colour always appears to be
accompanied by a tinge of purple.

In the perfect corundum, which is found in Pep-u and in
Ceylon, but which is now most commonly brought (when in
its natural or unpolished state) from the last mentioned place,
the colours are much more various, and more lively. The chief
of these colours are, red, blue, and yellow. The red colour con-
stitutes the stone known by the name of oriental ruby ; but it
seldom happens that this colour has not a small mixtureof blue,
which gives it a tinge slightly inclining to purple. The blue
colour is always that which is known by the name of azure

S44i Count de Bournon's Description of

blue ; and the stone wliich possesses this colour is distinguished
by the name of sapphire. The yellow colour is seldom pure,
being in general more or less mixed with a reddish tint. The
oriental gem of this colour is called the oriental topaz. From
a duly proportioned mixture of the blue and the red, is pro-
duced the purple colour, which constitutes the oriental amethyst.
Sometimes the red colour is predominant, at other times the
blue; and, in the latter case, the stone possesses that beautiful
purple colour which is so pleasing to the eye. Stones of this
colour are among the most rare of those belonging to this
substance. By the union of tlie blue colour with the yellow,
is formed the green, which produces the oriental emerald ; but
there is usually mixed with this colour a small proportion of
red, which gives to the green a brown and rather dull tinge.
Sometimes however the yellow colour is predominant, which of
course gives the green a yellowish cast, and then the stone
becomes the oriental chr3^solite. I have not yet seen any of the
green stones, or oriental emeralds, in which the green colour
w^as perfectly pure and brilliant, as it appears in the true emerald,
called the peruvian one. In the mixtures of which I have just
spoken, the colours are, in general, {perfectly blended together;
sometimes however they exist in a separate state, and so dis-
tinctly, in the same stone, that the mixed colour is only per-
ceptible at the point where the different colours meet. At other
times, these colours being only coarsely mixed, and not blended
together, the stone presents the one or the other of them more
distinctly, according to the position in which it is held.

TRANSPARENCY.

The crystals of corundum from the Carnatic, having their

the Corundum Stone, and its Varieties, &c, 24s

surface always rough, and being usually more or less impreg-
nated with fine particles of the various substances which compose
their matrix, very seldom possess any degree of transparency ;
but, when these crystals are broken, their fragments generally
have a degree of semi-transparency, but most commonly a very
slight one, unless the fragments happen to be very thin ; even
then, I have never found them perfectly transparent.

If such of these fragments as have the greatest degree of
semi-transparency, are held between the eye and the light, there
may be observed, within their substance, a great number of lines
or fissures, which cross each other, and prevent the free passage
of the light, the greater part of which is reflected. These fis-
sures, which arise from there not being a complete adherence
between all the parts of the crystalline laminae, are tlie principal
cause of the slight degree of transparency commonly met with
in the kind of corundum here spoken of; which kind may truly
be said not to have attained, in its crystallization, all the perfec-
tion it is capable of acquiring, and which may be observed in the
perfect corundum of Ceylon.

I think it also right to observe, that the corundum of the
Carnatic, when of a red or a blue colour, has always a greater
degree of transparency, and is more pure, than that which is of
any other colour ; and, in these respects, the corundum of a
blue colour is much superior to that which is red.

In the imperfect corundum of China and of Malabar, although
the surface of the crystals is also generally rough, yet, as they
are less impregnated with foreign substances, it is not uncom-
mon to observe in them a greater or less degree of transparency
at their edges. Some crystals have, indeed, been sent to us from
China, (very small ones, I confess, but very perfect,) which

MDCCCTI. K k

94.6 Count de Bournon's Description of

possessed a degree of transparency very little inferior to that of
the perfect corundum of Ceylon. The terminal faces of the
crystals from the two last mentioned places, are very frequently
what is called chatoyant ; a property of which I shall hereafter
speak more particularly.

The perfect corundum of Ceylon, whatever may be its colour,
always has a greater or less degree of semi-transparency ; and
very often is perfectly transparent. Sometimes, indeed, the
crossed fissures already spoken of, as existing in the imperfect
corundum, are also to be observed in the interior part of this ;
but, when that is the case, they are less strong, and less nu-
merous. The crystals of the perfect corundum have a smooth
and brilliant surface ; and they show all the transparency their
substance "possesses, without its being necessary, as in the im-
perfect corundum, to break them for that purpose. In general,
when they have an inferior degree of transparency, whatever
their colour may be, their terminal surfaces possess the appear-
ance called chatoyant, which, as I have already said, is very
frequently observed in the corundum of China, and in that of
the coast of Malabar.

In general, although the perfect corundum of a blue colour,
or sapphire, has exactly the same characters as that which
is of a different colour, it appears to me certain, if I may judge
from the great number of specimens I have seen, that it more
commonly possesses a perfect transparency, than that which
is of any other colour. I have already made a similar obser-
vation, in speaking of the imperfect corundum of the Camatic.
To this circumstance must be attributed, the superior value of
an oriental ruby, if without defect and of a certain size, when
compared with that of a sapphire of equal size and equally

tJje Corundum Stone, and its Varieties, &c. 24,7

perfect. To the same cause must also be ascribed, the scarcity of
fragments of sapphires, in comparison with those of rubies, in
the sand of Ceylon which has passed through the hands of the
lapidaries; the fragments of the former being usually more
transparent, they are selected from it, as more worthy to be cut
and polished.

HARDNESS.

Corundum is, next to the diamond, the hardest of all stones ;
but, with respect to this character, the degrees of intensity are
various ; and this variety depends principally upon the degree
of purity, and the colour, of the stone.

When the imperfect corundum of the Carnatic is neither of
a blue nor of a red colour, its hardness is less considerable, in
proportion as its transparency is less, and its internal substance
more full of those lines or fissures, which, as I have already
said, are commonly observed in it. Such corundum may be
scratched by that which is more transparent, though of the same
colour. The latter, (supposing the degree of purity to be nearly
equal, ) may in its turn be scratched by that which is of a purplish
red ; and this last, by the corundum of a blue colour ; which is
the hardest of all those varieties of this stone that I have dis-
tinguished by the name of imperfect corundum. The hardness
of the imperfect corundum of China, and of that from the coast
of Malabar, appear to be equal. This hardness, wliich is rather
inferior to that of the blue corundum of the Carnatic, is how-
ever somewhat greater than that of the other varieties.

The perfect corundum of Ceylon of a red colour, or oriental
ruby, the hardness of which seems to be nearly the same as
that of the imperfect blue corundum, is superior in hardness

Kk a

s^S- Count de Bournon's Description of

to all the other varieties of the latter kind. In the perfect corun-
dum of otlier colours, the hardness is nearly the same as in the
red ; that which is of a blue colour, or sapphire, and only that,
rather exceeds the others in hardness. We have just seen, that
in the imperfect corundum also, the blue colour was accompa-
nied by a degree of hardness greater than that of the other
colours.

This substance emits pretty briglit sparks, when struck with
a piece of steel ; but they are by no means proportioned to its
hardness. If a piece of flint be struck with the same force, the
sparks it produces are more numerous, as well as more bright ;
and it is possible to obtain sparks from flint, by a very slight
blow, such as would not be sufficient to produce them from
perfect corundum. It is also necessary, in order to obtain sparks
from corundum, that the stone should have pretty sharp edges :
if the part that is struck is obtuse, it is with some difticulty that
any sparks can be obtained. The imperfect corundum, however,
has, in this respect, some advantage over the perfect kind.

PHOSPHORESCENCE.

The substance here treated of becomes, like quartz, phos-
phorescent by collision ; it requires only, in order to exhibit tiiis
property, a somewhat stronger degree of friction. The light
which it emits has also less intensity ; and does not appear to be
accompanied by the smell which is peculiar to that obtained
from quartz. A very remarkable circumstance may likewise be
observed respecting this light. In all the varieties of this stone
which are of a red colour, whether of the imperfect or of the
perfect kind, or oriental ruby, the light here spoken of is of a
very deep fire colour, similar to that of red hot iron, when

the Corundum Sto?ie, and its Varieties, Sec. 249

heated to the degree known by the term cbcrry red. The sparks
which are obtained from this stone by means oi" a piece of steel,
have also some appearance of tiie above colour. These phe-
nomena may perhaps serve to assist us in acquiring further
knowledge respecting the cause of tlie phosphorescence of stones,
of which we have hitherto had no very satisfactory explanation.

GRAVITY.

The specific gravity of corundum, in its different varieties,
presents a stries of interesting facts, particularly when they are
compared with w!iat has been already observed with respect to
its different degrees of hardness. Tlie great interest I have felt
in the study of this substance, has caused me to take particular
care in the examination of such of its properties as might lead
to a perf.'Ct knowledge of it. I will now state the results of
the ob3er\..tions with which the character now treated of has
furnished ine.

Of _-33 specimens of the ditlerent varieties of imperfect corun-
dum, the mean specific gravity was 3531. The lightest was
3875; and the heaviest 3981. Six of the 33 were above 3900.
Eleven were between .^900 and 3931 ; and the remaining sixteen
were above 3931, which, as I have already stated, was the mean
proportion.

The mean specific gravity of the perfect red corundum, as
determined by 20 specimens of oriental ruby, was S977- The
lightest of these was 3933. Five of the specimens were above
4000. One alone was as high as 4087 ; it was of a deep red
colour, was perfectly transparent, and had been cut.

Sixteen different specimens of sapphire, gave a mean specific
gravity of 4016. The lightest was 3907; it had scarcely any

250 Count de Bournon's Description of

colour, and was nearly opaque. The heaviest was as high as
4161 ; this was of a beautiful deep blue colour, and was very
transparent. Three of the 16 were above 4100.

The inferences which I think myself warranted to draw from
the results of the above-mentioned trials, are,

1. That tlie specific gravity of the imperfect corundum is
always less considerable than that of the perfect kind.

2. That this gravity varies according to the degree of per-
fection of the crystallization ; and, consequently, according as
the stone is more or less transparent.

3. That, in general, the corundum of a blue colour, whether
of the perfect or the imperfect kind, is of a greater specific
gravity than that of any other colour.

What is here stated respecting the specific gravity of the
different kinds of corundum, is exactly analogous to what has
been already mentioned respecting their various degrees of
hardness.

CRYSTALLINE FORMS.

The primitive form of corundum, whatever may be its degree
of perfection, is a rhomboid slightly acute ; the obtuse angles of
the planes measuring 94°, and the acute ones 86°. (See Plate
VI. Fig. 1.) The description of the crystalline forms will be
more easily and more clearly understood, by considering (as I
shall constantly do in what follows) this rhomboid as being
formed by the union of two triedral pyramids, united at their
bases ; the solid angle of the summit will then be formed by
the meeting of three of the more acute angles : and its measure,
taken upon one of its edges, and in the middle of the opposite
face, will be very nearly 95° 30'.

the Corundum Stone, and its Varieties, &c.

54.^1

Whatever the form of the crystals of this substance are, they
may always, by dividing them, be ultimately brought to the
rhomboid here spoken of; and, when they are broken, such of
the fragments as are made in the direction of the lamince, very
often present the same rhomboid, in a very regular form. In-
deed, it is the only method of obtaining this crystal, in the
imperfect corundum; for, among all the crystals of that kind
of corundum which have been sent from the East Indies, not one
has yet presented its primitive form. With respect to the per-
fect corundum, I have been more fortunate ; as, besides several
fragments which exhibited this rhomboid very exactly, I have
found four of these primitive crystals perfectly defined. One of
them is a sapphire, and is in the collection of Sir John St.
AuBYN ; tlie three others are oriental rubies, and are in the col-
lection of Mr. Greville.

First Modification. The summit of the pyramid, (as very
frequently happens in calcareous spar, and in most of the
stones which have a rhomboid for their primitive form,) is often
replaced by a plane which is perpendicular to the axis. This
plane then makes, with those of the rhomboid, an angle which
differs very little from 122° 30'; and, as the extent of the plane
is more or less considerable, it often causes great difference
in the appearance of the crystals. Sometimes it does not descend
so low upon the faces of the rhomboid, as to reach their small
diagonal. (Fig. 2.) At other times, it exactly reaches to the
diagonal. (Fig. 3.) And, very often, it descends more or less
below it. ( Fig. 4). This last variety is frequently met with in the
perfect red corundum, or oriental ruby. I also know four in-
stances of this form in the sapphire. The variety shown in Fig. 3
is rather scarce; but that of Fig. 2 is the most rare of the

252 Comit de Bournon's Description of

whole. I have likewise observed the two last, among some small
crystals of imperfect corundum from China, which were pretty
transparent.

Second Modification. At other times, the edges of the base of
the primitive rhomboid are each of them replaced by a single
plane, which is parallel to the axis, and which, when its extent
is rather considerable, separates the two pyramids by a hexae-
dral prism with rhombic planes. I have never seen this modifi-
cation with complete pyramids, as it is represented in Fig. 5,
but I have often observed it combined with the preceding
modification. This combination is not unfrequently met with
in the oriental ruby, in which, the two varieties represented in
Figs. 3 and 4 are found with a small beginning of a prism, as
is shewn in Figs. 6 and 7. There are also in the collection of
Sir John St. Aubyn, two crystals of sapphire, belonging to the
same variety, one of which is tolerably regular in its form ; but
it is much more common to find these crystals with prisms
of rather greater length, as is represented in Figs. 8 and 9. In
Mr. Greville's collection also, there is contained a crystal of
a pretty large size, and very perfect, in which the plane that
has replaced the solid angle of the summit of the pyramid is
very small, as in Fig. 10. All these varieties, but particularly
those represented in Figs. 8 and 9, are likewise found among
the small transparent crystals of imperfect corundum brought
from China.

When the decrease produced by the plane which has replaced
the solid angle of the summit of the rhomboid, has begun to
take place nearly at the same time with, or even previous
to, that which gives rise to the planes which replace tlie edges
of the base, (as is indicated by the length of the sides of the

the Corundum Stone, audits Varieties, &c. 253

prism,) it often happens that there remains no trace of the
planes of the primitive rhomboid : the crystal is then a regu-
lar hexaedral prism. (Fig. 11.) This variety, which is very
common in the perfect corundum of a red or of a blue colour,
is also common in the imperfect kind ; it is indeed, in certain
districts, particularly in the Carnatic, almost the only form that
is met with. In all these crystals, the prism here spoken of
differs considerably in its length ; sometimes it is very much
elongated ; at other times it is very short, as is represented in
Fig. 12.

Third Modification. The primitive rhomboid is frequently
observed to have undergone, in its crystalline laminae, a de-
crease at those flat angles which rest upon the common base.
This decrease occasions, in each of the pyramids of the rhom-
boid, six new planes equally inclined, which thereby render the
pyramids enneaedral, (as is seen in Fig. 20,) and which, when
this modification is perfect, (that is to say, when the planes be-
longing to it have destroyed every trace of the primitive rhom-
boid,) change the crystal into a dodecaedron, formed by the
union, base to base, of two hexaedral pyramids with isosceles
triangular faces, as in Fig. 13. At present, I shall only take
notice of the pyramidal form of these crystals, without paying
any attention to the inclination of the faces of the pyramids ;
for we shall see, at the end of this modification, that the
decrease which occasions it is subject to considerable variation,
changing, at the same time, the inclination the faces of the
pyramids have to each other.

It very rarely happens that we find this dodecaedron perfectly
complete, that is to say, with each of its pyramids terminating in
a single point, by the exact meeting of all its faces. I know only

MDCCCII. L I

254< Count de Bournon's Description of

one instance of this form, which I met with in a small sapphire,
that I have placed in the collection of Mr. Greville. There
are indeed two specimens, nearly similar to the above, in the
collection of Sir John St. Aubyn ; but two of the opposite faces
of their pyramids have increased to a greater degree than the
others, which renders them cuneiform.

It is much more common to find the crystals of this modifi-
cation combined with the first, and consequently having the solid
angle of their summits replaced by a plane. Sometimes this
new plane is very small, as is shown in Fig. 14. At other
times, it is more considerable, as in Fig. 15. The above va-
rieties are less common in the red perfect corundum, or oriental
ruby, than in the blue perfect corundum, or sapphire, of which
it is the most usual crystalline form, and in which, the plane
that has replaced the summits of the pyramids is frequently very
small. These varieties are likewise often found among the
crystals of imperfect corundum of China ; but it is very rare, on
account of the irregularity of their surface, to meet with them
perfectly defined. They are met with in a much more perfect
state, among the crystals from the coast of Malabar ; some of
these indeed are so perfect, that, were it not for their reddish
colour, they would certainly be taken for very beautiful sapphires.
One of these crystals, which is in Mr. Greville's collection, is
more than an inch in length. Another, which is cuneiform, and
has one of its pyramids broken, is above two inches long. In
the crystals of imperfect corundum from the Carnatic, I have
never met with any thing more than very slight traces or ele-
ments of this pyramidal form.

There frequently remain upon the crystals belonging to these
varieties, particularly when the terminal faces are of a pretty

the Conmdum Stone, audits Varieties, &c. 255

considerabJe size, more or less evident traces of the planes of the
primitive rhomboid; as appears by small isosceles triangular
planes, of greater or less extent, situated upon three of the al-
ternate solid angles, formed by the meeting of the terminal faces
with those of the pyramid, (Fig. 16.)

It very often happens, in this modification, that the plane
which has replaced the solid angle of the summit, acquires a
more considerable increase in one of the pyramids than in the
other; and indeed, most commonly, this increase is such as to
cause the pyramid entirely to disappear. The crystal then be-
comes a simple hexaedral pyramid, which is either complete, as
in Fig. 17, Plate VII. (but this very rarely happens,) or has its
summit more or less replaced. (Fig. 18, A.) This variety, which
is very common in the crystals of perfect corundum, is also fre-
quently met with in those of the imperfect corundum from
China ; and it is very usual to see, upon the solid angles of its
terminal faces, small isosceles triangles, which are occasioned
by the preservation of some parts of the planes of the primitive
rhomboid; (Fig. 19.) but they are seldom so regular in their
form as they are represented in the figure.

I have often seen small crystals of oriental ruby that exhi-~
bited a very pretty variety, as they showed, at the same time, the
primitive rhomboid with its summit strongly replaced, and the
incipient change to the form of the hexaedral pyramid which
constitutes this third modification : this variety is represented in
Fig. 20. There are, in Mr. Greville's collection, two very
perfect crystals of this form.

The second modification, that in which the pyramids of the
primitive rhomboid are separated by an intermediate hexaedral
prism, is often combined with the abovementioned union of

LI 2

256 Count de Bournon's Description of

the first and third modifications. There exists, for example, in
Mr. Greville's collection, an oriental ruby, which exhibits the
variety shown in Fig. 20, with the rudiments of an interme-
diate prism, as is seen in Fig, 21. This variety is also sometimes
found among the small transparent crystals of imperfect corun-
dum from China.

In four other crystals, also in Mr. Greville's collection, the
prism is very much elongated ; and the plane which has replaced
the solid angle of the summit of the pyramid is much more
extended, as in Fig. 22. These crystals, which are oriental
rubies, are in perfect preservation at their two extremities.

There is besides, in the same collection, another crystal, also
an oriental ruby, which differs from the preceding, in having no
traces left of the planes of the primitive rhomboid. The crystal,
consequently, appears to be a regular hexaedral prism, with the
edges of its terminal faces bevelled. (Fig. 23.)

In five others, the pyramid has made more progress ; and, in
all of them are to be seen, on their terminal faces, some slight
traces of the primitive rhomboid. (Fig. 24.)

Lastly, in one other specimen, the pyramid is nearly complete,
as in Fig. 25. I also know two sapphires, which exhibit an inter-
mediate variety, between the two last-mentioned forms.

One of the most striking characters of corundum is, the great
variety exhibited by this pyramidal modification, in the incli-
nation of the faces of the pyramids to the axis of the crystal,
and, consequently, in the more or less rapid decrease that has
taken place in the crystalline laminae, at the plane angles
situated on the common base of the two pyramids which com-
pose tlie primitive rhomboid. Among the crystals of imperfect
corundum, from the different districts in which this substance

the Corundum Stone, and its Varieties, &c. 257

has been hitherto found, which form part of Mr. Gueville's
collection, and are sufficiently perfect to admit of being mea-
sured with accuracy, there is one, of which the solid angle at the
summit, taken in the middle of two of the opposite pyramidal
faces, is 50°; two of 40 ; two of 35°; nine of 24,°; and seven
of 12°. Among the pyramidal crystals of oriental ruby are, one
of 50°; one of 40°; four of 30°; one of 24°; and four of 12°.
In the sapphire there are, one of 50"; two of 40""; one of 35°;
nvo of 30°; one of 24°; and two of 12°. If to these measures we
add those of two sapphires, and of two oriental rubies, in the col-
lection of Sir John St. Aubyn, we shall also have 58° and 20';
and we may consequently state, from our present knowledge
respecting this substance, that it admits no less than eight dif-
ferent decrements of the laminae, at the same angle of the base ;
each of which produces a pyramidal modification. And the
measure of the solid angle of their summits, (considering the
pyramids as complete, and supposing at the same time that
the very great care I have taken has prevented me from com-
mitting any error,) are 5S^ jo", 40°, 35°, 30°, 24°, 20°, and
12°.*

This difference in the inclination of the faces of the pyramids,
in the corundum of a pyramidal form, often appears in a very
striking manner in the same crystal. I have frequently met
with oriental rubies, and also with sapphires, in which the faces
of the pyramids, after having for some time preserved a certain
degree of inclination, evidently appeared to have changed it, in

* In Figs. 18 A, 18B, and i8C, are represented this simple pyramidal modification,
having 58°, 35°, and 12°, for the measures of the solid angle of the summit of the
pyramid : from these figures, it will be easy to form an idea of the appearance of those
crystals which have the other measures above enumerated.

258 Coimt de Bournon's Description of

order to assume another ; this change caused the crystal to ter-
minate by a pyramid less sharp; and, in many instances, it
was evident that it had iiappened several times successively.
These variations do not always take place in a regular order
in the same crystal ; for it very often happens, that some of the
faces have undergone two, three, or even foui changes of in-
clination, while others have not undergone so many ; and some-
times, indeed, have not undergone any at all. I have seen some
of these crystals, of which the irregularity was such that, upon
some of the faces, the degree of inclination was changed from a
greater to a less ; a circumstance which necessarily formed a
depressed angle, and thereby produced a very irregular and
even deformed shape, in the crystal itself. Among the very
small number of crystals from the Carnatic wliich shew any
disposition to assume the p3Tamidal form, I particularly observed
one, in which this irregularity in the mode of decrease is very
remarkable. This crystal, on three of its adjacent sides, appears
to be a regular hexaedral prism ; but, from nearly the middle of
two others, also adjacent, it becomes pyramidal, and of that
modification in which the solid angle of the summit is of 50°;
and, from about one-third of the remaining side, it also assumes
a pyramidal inclination, but of that modification in which the
solid angle of the summit is of 40'. This crystal, which is
represented in Fig. 26, is preserved in Mr. Greville's collection.
These pyramidal modifications also very frequently demonstrate,
by the great number of transverse stri^ which are on their faces,
and which sometimes resemble the steps of a staircase, the irre-
gularity with which their decrements have taken place.

Fourth Modification. The primitive rhomboid sometimes un-
dergoes, in those acute angles which contribute to the formation

the Corutidum Stone, and its Varieties, &c. 259

of the solid angle of the summit, a decrease much more rapid
than that we have already mentioned, when speaking of the
first modification. This decrease replaces the solid angle by
three new planes ; which planes, if they were to become of
such extent as to cause the primitive faces of the rhomboid to
disappear, would occasion a secondary obtuse rhomboid, that
would have considerable analogy, in the measure of its angles,
with that rhomboid of calcareous spar which is called lejiti-
cidar ; that is to say, the solid angle of its summit would
measure about 139°; and the plane angles of its rhombs 114,°
and 66°. I have not yet met with this rhomboid perfectly
formed ; but it exists, or at least one of its halves, in a very
well defined state, at the summit of a simple pyramid, eight or
nine lines in height, the solid angle of which summit measures
12°; it is represented in Fig. 27. The great number of stri^,
parallel to the small diagonals of the primitive rhombic planes,
with which the faces of the secondary rhomboid are covered,
prevent me from being perfectly certain respecting the accuracy
of the measures I have just stated; but, if they are not strictly
exact, they must at least be very nearly so. The crystal I have
just described is from the coast of Malabar, and is in Mr.
Greville's collection. The planes of the secondary rhomboid
are slightly chatoyant.

Fifth Modification. Anotiier mode of decrease, of a similar
kind, but still more rapid, sometimes takes place at the same
solid angle of the summit of the primitive rhomboid. The
triedral pyramid which replaces this angle, is then much less
elevated than in the preceding modification. When it is com-
plete, that is to say, when there remains no trace of the planes
of the primitive rhomboid, the crystal becomes changed into a

2^0 Count de Bournon's Description of

new rhomboid, wliich is mucli more obtuse tlian the former one.
(Fig. 28.) The rhombic planes have 1 17", for the measure of
their obtuse angles ; and 63°, for the measure of their acute
ones. The solid angle of tlie summit of the pyramid is very
nearly 150° 30'; consequently, the angle formed by the meeting
of the bases is about 29° 30'.*

There are, in Mr. Greville's collection, two oriental rubies
which exhibit this rhomboid completely formed ; its planes
are deeply striated, in the direction of the decrease ; a circum-
stance which is very common in all planes that are the result
of a rnpid decrease, or in which the edges of the laminae last
deposited, deviate considerably from the edges of those which
were already formed.

There are also, in the same collection, two perfect hexaedral
prisms of corundum from the Carnatic, in which this modi-
fication shows itself by small isosceles triangular planes, si-
tuated upon three of the alternate solid angles of each extre-
mity. (Fig. 29.) These planes may easily be distinguished

» After having, in this substance, met with a secondary rhomboid that exactly agrees
with one of those belonging to calcareous spar, (although the planes which pro-
duce it are differently situated upon the primitive crystal,) it appeared to me very
extraordinary to meet with a second, which had exactly the same proportions as
another of the obtuse rhomboids of the abovementioned substance. In fact, there
exists in calcareous spar, a rhomboid much more obtuse than that which Rome'
DE Lisle named lenticular, (called equlaxe by the Abbe Hauy,) of which the
measures are exactly the same as those which have just been assigned to the rhomboid
of corundum ; but there is the following difference between them, viz. in calcareous
spar, this rhomboid is the result of a decrease along the edges of the pyramid
belonging to the primitive rhomboid; whereas, in corundum, it is the result of a
decrease at the angles which contribute to the formation of the solid angle of the
summit. This modification of calcareous spar has not yet been described ; but, indeed,
the same thing may be said of many other modifications of that substance.

the Corundum Stone, and its Varieties, 6cc. 261

from those belonging to the primitive rhomboid : first, by their
inclination, which is very different, as they make, at their meet-
ing with the edges of the prism, an angle of 110°, whereas the
others make an angle of 147° 30'. Secondly, they are usually
very deeply striated; a circumstance which rarely occurs in the
others. Of the two crystals I have just described, one is nine
lines in diameter, and six lines in height; it is also slightly
transparent at the edges. The other is much smaller, more
transparent, and of a purplish red colour, but rather pale. It is
one of the purest specimens of imperfect corundum, particularly
of that from the Carnatic, I have ever seen.

There are frequently observed, in the small prisms of imper-
fect corundum, some traces of the planes above described ; they
may in general be easily known by their striiB. I have also
seen crystals in which were united, at the same time, traces of
the two secondary rhomboids of the fourth and fifth modifica-
tions, in the manner represented in Fig. 30.

Sixth Modification. There also appears to exist, in this sub-
stance, a third rhomboid, which is much more obtuse than
either of the two preceding ones ; at least it is only to such a
modification that I can refer several crystals, both prismatic and
pyramidal, of imperfect corundum, which made part of a
parcel lately sent to Mr. Greville, from the district of EUore,
in the northern part of the government of Madras. Among
these crystals are many hexaedral prisms, of a perfectly regular
form, which have their terminal faces inclined in a contrary
direction, so as always to make, upon the edges of the prism on
which they incline, angles of 100° and 8o^ (Fig. 31. Plate VIII.)
These terminal faces appear to me to belong to a very obtuse
rhomboid, of which, the acute angles of the rhombic planes would

MDCccir. M m

aSa Comit de Bournon's Description of

be 60° 46'; the obtuse ones 1 19° 14' ; and the sohd angle of the
summit l65^ Tlie crystal I have just described, would then be
nothing more than the prismatic modification, combined v>ith
that which occasions this rhomboid ; at both extremities of which,
one of the faces of each of the obtuse triedral pyramids, be-
longing to the new rhomboid, would have acquired (in a con-
trary direction with respect to its extremities] such an increase
as would cause the other faces 'o disappear. These two faces,
having now become the terminal ones of the hexaedrttl prism,
would in fact make, with those edges of the prism on which
they would incline, angles of ico° and 80°. This very obtuse
rhomboid would be the result of a decrease analogous to
the two preceding ones, but still more rapid. IVLiny pyra-
midal crystals of this kind of corundum, present such inclined
terminal faces ; but with a difference, in the measure of their
angles, conformable to the inclination of the edges of the
pyramids.

Seventh Modification. The primitive rhomboid of this sub-
stance also undergoes sometimes, tliough very rarely, a decrease
at those acute angles which rest upon the base; and this de-
crease is such, that it replaces each of the solid angles of this
same base, by a plane which is parallel to the axis of the rhom-
boid. If tl'.is modifiaation were complete, it would give rise to
a regular hexaedral prism, which would differ from the prism of
the second modihcation, in having its sides corresponding with
the solid angles of the base of the rhomboid ; whereas the sides
of the other correspond with the edges of the said base. I know
this modification onlv by a single crystal, which is in the col-
lection of Mr. Greville; in it is combined the modification
here spoken of with the three first. This crystal, which is

the Corundum Stone, and its Varieties, ^c. oQn

of perfect red corundum, or oriental ruby, is almost exactly
similar to that represented in Fig. 22, and indeed only differs
from it by the prism being dodecaedral, as in Fig. 32.

Eighth Modification. I am also acquainted with this modifica-
tion only by a single crystal. This crystal, which is a sapphire
of a beautiful deep blue colour, is likewise in Mr. Greville's
collection. Its form is a simple hexaedral pyramid, which is
almost complete, and has 24° for the measure of the solid angle
of its summit. Eacii of its six edges are replaced by a very
narrow plane, which is equally inclined upon the two faces that
are adjacent to it. This renders the pyramid dodecaedral, with
broad and narrow faces alternately, as in Fig. ^q. Three of
these new planes appear to me to be occasioned by a decrease,
which has taken place at the obtuse plane angles that rest
upon the base of the rhomboid, but which differs from those
which occasion pyramidal modifications, and is of such a nature
that (the new planes to which it gives rise being in pairs, and
on the same level,) each of the solid angles of the base is re-
placed only by a single plane. The three others appear to
me to be caused by a decrease at the acute plane angles that
rest upon the base ; but this decrease differs from that of the
seventh modification, in being more rapid, and in having the
planes to which it gives rise inclined upon the axis of the crys-
tal. The three latter planes have the following peculiarity, viz.
their inclination is exactly equal to that of the thre^ others ; so
that, if the two modifications whicli are united together in this
crystal were complete and separate, they would produce two
acute rhomboids, perfectly similar to each other.

M m 2

2^4 Count de Bournon's Description of

FRACTURE AND TEXTURE.

I have already observed, that all the stones which compose
the various kinds of this substance, to which I have given the
general name of corundum, have a lamellated texture, in a
direction parallel to the faces of a rhomboid of c^6° and 84° ; and
also, that they break in a direction parallel to the said faces.

The blue variety of perfect corundum, or sapphire, follows
the above law, as well as all the other varieties. It is true,
however, as I have already had occasion to mention, that the
ease with which the crystals of this substance may be divided,
is very various ; but observation shows, at the same time, that
these variations are governed, in th.e first place, by the degree
of force existing in tiie attraction of the molecules which com-
pose the crystals, as well as by the perfect adhesion of the
crystalline lamina? (composed of these molecules) at all points
of their surface; two facts, the existence of which is shown
by the difference in the degrees of hardness and transparency of
this stone, and which appears to be very considerable. In the
second place, the variations here spoken of seem also to depend
very much upon the colour these stones possess ; for, as I have
already observed, they must be governed by the force of
attraction, which, in my opinion, varies witii the colour. This
force appears to exist nn the highest degree, in the perfect co-
rundum of a blue colour, or sapphire; it being with great diffi-
culty that this kind of corundum can be broken, in the direction
of its laminse, in such a manner that its fracture shall present
that even surface, and that kind of gloss, which fractures made
in the above direction generally exhibit. It may be broken with
equal ease in any other direction ; for instance, in a direction

the Corundum Stone, and its Varieties, &c. 265

perpendicular to the axis of the crystal ; but, in this last case,
the fractures by no means possess such characters as might
cause them to be taken for fractures made in the direction of
the lamince; they are always unequal, and partially conchoid.
I will even confess, that I have not yet succeeded in break-
ing a sapphire, according to the direction of its lamina, in a
satisfactory manner. But that which art is not able to perform,
is executed by nature : for, besides such sapphires as, upon theit
terminal faces, retain complete traces of the planes of the pri-
mitive rhomboid, I have frequently met with sapphires, both of
the prismatic modification and the pyramidal one, in which there
were, upon the said foces, one or more fractures, made exactly
in the direction of the lamim^ ; and it was necessary to examine
them with great attention, in order not to mistake them for
true planes, representing those of the primitive rhomboid.* This
kind of fracture is obtained with greater ease in the perfect red
corundum, or oriental ruby; and still more easily, in the im-
perfect corundum. The latter presents, in this respect, a less
degree of resistance, in proportion as it is less transparent, and
has less colour. This character, however, is subject to great va-
riation : there exist some specimens of this stone, in which such
fractures as are here described may be made almost as easily
as in calcareous spar; whereas, in others, they are obtained with
much more difficulty. I have even seen some pieces which

* I have placed several of these crystals in Mr. Greville's collection, and also in
that of Sir John St. Aubyn, and in that of Sir Abraham Hume. The owners of
these collections have confided to me the care and arrangement of them, with a degree
of liberality which gives me every advajitage that could be derived from the absolute
possession of them, and consequently diminishes my regret for the loss of my own. I
feel too sensibly these advantages, and many others resulting from their friendship and
society, not to embrace with pleasure this opportunity of testifying my gratitude.

266 Coujit de Bournon's Description of

might be broken, with almost as much ease, in a direction
contrary to that of the laminae, as in the direction of the laminae ;
but it most frequently happens, in this case, that the fracture,
although made in the natural direction, has not the evenness
such fractures usually have, but presents some irregularities, and
likewise some conchoidal parts : this remark, however, applies
only to such pieces as approach nearly to perfection, with respect
to transparency.

There may frequently be observed, in these stones, a cha-
racter which serves to confirm what I have said respecting
the imperfection sometimes observed in their crystallization,
which appears to me to arise principally from a want of abso-
lute contact between all the parts of their crystalline laminas.
When some of the faces of the crystals correspond to those
of the primitive rhomboid, whether these faces are natural ones
or are produced by fracture, the edges of the crystalline laminae
are shown upon them, and sometimes very plainl}^ by lines
which cross each other, in such a manner as to form rhombs of
q6° and 84,°. This character even becomes of great use in this
substance, as it serves to distinguish, in fragments, (which are
generally of hexaedral prisms, that being the most common
form,) those faces which are occasioned by fracture, from those
which correspond to the terminal faces of the prism. These last,
also, frequently exhibit lines, w'hich are likewise caused by the
edges of the crystalline laminae; but, as they extend to three
only of the alternate angles of the terminal hexagonal face, they
trace on it, by crossing each other, either equilateral triangles,
or rhombs of 60" and 120°. Figs. 34,, A, and 34,, B, represent
these two different appearances; the first upon the planes of the
rhomboid ; the second upon the terminal faces.

the Corundum Stone, and its Varieties, &c. 'zGj

As it is by no means uncommon, in corundum, (in the same
manner as is observed in the beryl,) to meet with elongated
prisms, formed merely by the connection or contact of several
prisms at their terminal faces, it frequently happens that these
prisms, after being separated from each other, exhibit, upon the
terminal faces which were in contact, a polisli or lustre that
might easily cause those faces to be taken for fractures, in a
direction perpendicular to the axis. But this appearance is an
illusion we must guard against : for, if we endeavour to make
any fractures at the extremities of these crystals, they will take
place, as usual, upon three of the alternate solid angles ; and we
shall find it impossible to succeed in making any fractures
perpendicular to the axis, except such as are extremely irre-
gular, and exhibit an appearance very different from that exhi-
bited by natural ones. It sometimes happens also, that, by means
of the above connection, as well as by some causes of com-
pression, which must necessarily have been frequent with respect
to crystals inclosed in their matrix, in the manner those of
felspar are inclosed in granite or porphyry, that the terminal
faces have varied from their natural position, and have as-
sumed another, which inclines more or less upon the sides of
the prism. We must, however, distinguish these accidental
varieties, from those crystals in which such an inclination really
belongs to the mode of crystallization, and which I have already
described, in speaking of the sixth modification. In this latter
case, the inclination of the terminal faces is constantly the same ;
whereas, in the accidental case here treated of, it varies consi-
derably.

There exists also, in this substance, and even among the
same crysta/s, (when hexaedral prisms,) not only of imperfect

268 Count de Bournon's Description of

corundum but likewise of the perfect kind, of all colours, ano-
ther accidental variety, which is particularly met with when their
irregularity and their opacity announce a want of perfection in
their cr3^stallizat!on. Sometimes the edges of the crystalline
kmins may be perceived upon their terminal faces ; and, there
beijig more or less distance betw^een them, they exhibit very
much the appearance of an irregularity, or a kind of disturbance,
in those laminee which seem to have been deposited upon these
faces, and in a direction parallel to them. But, with a little
attention, we may perceive that these laminae, the edges of which
are in the direction of three of the alternate solid angles of this
extremity of the crystal, can only belong to the laminse depo-
sited upon the faces of the primitive rhomboid ; and, we are very
often able, at the same time, to discover their degree of incli-
nation.

A third circumstance attending these crystals, and one which
it is more difficult to explain, consists in the appearance of con-
centric hexagons, parallel to the hexagon formed by the exterior
edges of the crystal. These hexagons may sometimes be ob-
served upon the terminal faces, as is shewn in Fig. 35. Their
edges have a degree of thickness very perceptible by the eye ;
and may besides be frequently distinguished from each other,
by a difference in their transparency, and sometimes also by
a greater or less intensity in their colour. There are preserved,
in Mr. Greville's collection, amongst a pretty large number
of crystals in which this circumstance has taken place, two
crystals of imperfect corundum from the coast of Malabar, that
exhibit it in a very striking manner. In the first of them, one
only of these hexagons, placed at nearly an equal distance
from the centre and the edges of the terminal face, is of a blue

the Corundum Slo?ie, and ils Varieties, &c. 269

colour, wliile all the rest of this face is gray, slightly tinged
with red, and chatoyant. (Fig. 36.) In the other, the last
concentric hexagon alone, or that wliich at the same time
forms the exterior part of the crystal, is (for the thickness of
about half a line) of a blackish-brown colour, dull and opaque;
while the rest of the terminal face (which likewise exhibits
concentric hexagons) is of a gray colour, but has a silvery
hue, because this part of the stone is chatoyant. (Fig. 37.)
The above circumstance seems to announce a deposition of
laminae upon the sides of the hexaedral prism ; nevertheless,
if we attempt to break these crystals according to that direc-
tion, we find that it is absolutely impossible to succeed, in such
a way as to obtain a fracture that has the appearance of being
made in the natural joints of the stone; whereas, on the con-
trary, fractures may be made with sufficient ease, in a direc-
tion corresponding to the faces of the primitive rhomboid.
Notwithstanding these concentric hexagons, there may be some-
times perceived, upon the same terminal faces of the prism, traces
of the edges of the laminaj already mentioned ; and the crystal
then exhibits the ajjpearance represented in Fig. 38. As the real
direction of the laminec (which is shown in these crystals by
their natural fractures) indicates that the rhomboid of q6° and
84,° is the primitive form of this substance, it seems necessarily
to exclude the other direction, of the existence of which (as we
have seen) tliere is some appearance, and which would give the
hexaedral prism, as the form of the primitive crystal.

The above appearance, however, is certainly owing to a parti-
cular cause; but it seems to me, that the laws hitherto established
in crystallography, are by no means capable of furnishing one
that can account for it in a satisfactory manner. The only

MDCccii. N n

270 Count de Bournon's Description of

explanation of the circumstance which occurs to me, does not
agree with the idea we have formed respecting those laws; but
the circumstance itself may be perfectly explained by it. It is
founded upon a supposition that the primitive rhomboid may
have passed, very nearly at the time the crystallization began,
to the form determined by the combination of the two modifi-
cations which produce the hexaedral prism, and that, in conse-
quence of a law not yet acknowledged, the sides of the prism
may have become, at the very moment of their formation, a
new centre of attraction, for the regular deposition of a part of
the cr3'staliine molecules. This supposition, however, would
require another, but which perhaps may be fairly considered as
nothing more than a consequence of the former, namely, that
the mutual attraction of the molecules situated upon these se-
condary faces, is more strong than that which exists in the
same way between those upon the primitive ones. This stronger
degree of attraction between the molecules on one of the faces
of a crystal than between those of the other, is already ad-
mitted ; so that it may rather be considered liere, as giving rise
to an additional observation, than as affording matter for discus-
sion. I am perfectly sensible of, and make no scruple to allow,
every objection that may be made against this explanation, to
arrive at which, I have been obliged to make a supposition not
yet admitted ; but the fact itself exists, and seems naturally to
lead to the explanation I have given. I offer it, however, merely
as a hypothesis, which still requires the support of observation ;
and I shall only add, that it is not the first time that the study
of crystals has led me to form such an idea.

With respect to the cause which, notwithstanding the above-
mentioned mode of crystallization, would still occasion the frac-

the Corundum Stone, and its Varieties, 5cc. 271

ture to have the same direction as if the increase of the crystal
had been produced by a deposition on the faces of tlie primitive
rhomboid, it may, I think, be explained by supposing that, in
this case, the elements of the crystallization might already be
real, though small, secondary crystals, for instance, small hex-
aedral prisms ; and that the fracture would then be nothing more
than the result of the sum of all the partial fractures of each of
them. *

PHENOMENA WITH RESPECT TO LIGHT.

The prismatic crystals of corundum, as well as tlie pyramidal
ones, when their extremities are terminated by faces which are
perpendicular to their axes, very frequently have those termi-
nal faces chatoyant. This property is the natural effect of the

• I had finislied writing this Paper, when Mr. Grevjlle had the curiosity to
cause one of the hexaedral prisms of imperfect corundum, from the coast of Malabar,
the terminal faces of which exhibited the concentric hexagons above spoken of, to
be cut transversely. This section shewed a very interesting fact, and one that adds
some probability to what I have said respecting the cause which produces this plieno-
tnenon. One of the parts of this crystal (which crystal is sawed into three, and po-
lished,) exhibits the appearance represented in Fig. 38, A. The whole substance of this
segtnent is of a pale purplish-red colour ; but there is, in its centre, a triangular spot,
similar to that represented in the above figure, which indicates very clearly that the
section was made below the summit of the primitive rhomboid, and perpendicularly to
its axis. This spot is also of a purplish-red colour, but much more deep than the rest
of the crystal, and therefore strikes the eye very forcibly. It is only to be perceived
upon one of the terminal faces; the other terminal face does not show the smallest
trace of it. There may, however, be perceived at its centre, a hexagonal plane, nearly
as large as that represented surrounding the spot in Fig'. 38, A ; it is of a different
colour from the other part of the substance of this segment, being of a dirty gray.
The spot is also seen, but of a smaller size, upon the terminal face corresponding to
the segment taken from the top of the preceding ; but there are not any traces of it
opon the other terminal face.

N n 2

272 Count de Bournon's Description of

reflection of lisht, in tlie small intervals which remain between
the small crystalline lamin«, in those parts where these laminae
are not in perfect contact ; it is necessary, therefore, that the
crystal, or fragment, which possesses this property, should be in
the state most favourable to its developement. On this account,
it must not be completely transparent; there being, in that
case, loo perfect a contact between the laminse; so that the
light, not meeting with any medium to reflect it, but being
entirely refracted, cannot occasion any appearance of the pro-
perty here spoken of. Neither must the crystal, or fragment,
be quite opaque ; it being necessary that the light, in order to
undergo the reflection which produces this pleasing phenome-
non, should at least be able to pass through the exterior lamina
of that part of the crystal against which it strikes. The above
circumstances are, in fact, those which appear to take place
with respect to corundum. The imperfect corundum of the
Carnatic, the cr3^stals of which are generally more or less
opaque, show no trace of this property upon their terminal
faces ; whereas, it is frequently observed upon the terminal faces
of the crystals of imperfect corundum from China, and also of
that from the coast of Malabar, because those crystals generally
possess a slight degree of semi-transparency. This character is
still more common in the perfect corundum, whether sapphire
or oriental ruby. There is not, however, the smallest appear-
ance of it, when these stones possess the beautiful transparency
belonging to them in their highest degree of perfection ; w here-
as, on the contrary, it is frequently seen to take place in a very
lively and brilliant manner, in such of the stones as have an
inferior degree of transparency. It rarely happens, that the crys-
tals of perfect corundum are prevented by opacity from exhibit-

the Conmdim Stone, arid its Varieties, &c. 273

ing the property here treated of; but, as I have already said, the
terminal faces which, by their position, replace the solid angles
of the summit of the primitive rhomboid, are absolutely the
only ones which can in any degree possess it : no appearance
of it can be seen in any other part. This is not surprising ;
for, as the effect here spoken of proceeds from the reflection
of light, in the spaces between the crystalline lamince, the
plane which may be considered as produced by a section which
would expose the edges of all these laminae, must necessarily
be tlie most proper to occasion it. This effect also takes place
when the crvstals are broken, by chance, in a direction more
or less approaching to that which is parallel to the abovemen-
tioned plane, notwithstanding the fracture then exhibits a very
rugged appearance. It even happens sometimes, that tliis frac-
ture is such that the edges of the lamina? protrude, in the manner
observed in the fibres of wood when it is broken across the
grain ; yet the property here treated of is not less evident ;
and, in this last case, it is often very distinctly seen proceeding
from between the lamince.

To the above property must also be referred, that beautiful
reflection of light, in the form of a star with six rays, which
is frequently given, by cutting, to oriental rubies, sapphires, &c.
and which causes those stones to be then called by the name
of star-stones. The manner of cutting which brings the per-
fect corundum into this state is, most commonly, on the part
of the lapidary, rather the result of chance, than the conse-
quence of any determined theory respecting the cause of the
effect he means to produce. Accordingly, in the greater number
of the stones which have this property, the point from whence
the starry reflection proceeds, instead of being in the middle

274 Count de Bournon's Description of

of the stone, is observed to be situated in a part more or less
near to its base; a circumstance which considerably diminishes
the beauty of the star-stone. The reflection which produces
this effect, arises from the same cause as that of which w^e
have already spoken, and proceeds from the same part of the
stone ; consequently, when an oriental ruby, or a sapphire,
which has the qualities necessary for the purpose, is intended
by the lapidary to be formed into a star-stone, he ought to make
his section pass below that part of the stone which he has found
to correspond with the summit of the primitive rhomboid. As
the kind of cutting most proper to produce this effect in the
stone, is that rounded form which is called en cabocbon, with
as high an ellipsis as is possible, the lapidary ought, at the
same time, to take great care that the summit of this ellipsis
be situated exactly under the point which corresponds with the
summit of the rhomboid ; in that case,, the light reflected in
the interval of the laminte upon the three edges of the primi-
tive rhomboid, and upon the middle of its three faces, will trace
upon the stone, a star, the six rays of which will include the
circumference of the rounded part, or ellipsis. The same effect
may also be made to take place on one of the solid angles of
the base, but in a much less perfect manner.

I have met with many fragments of sapphires, as well as of
oriental rubies, which naturally produced the effect here spoken
of, in consequence of tlieir having been broken, by chance, in
u manner proper to occasion it ; that is, they were broken, ac-
cidentally, in a direction contrary to that of the laminae, and
perpendicular to an axis passing through the two summits of
the pyramid of the primitive riiomboid ; after which, the frag-
ment had been a little rounded by friction.

the Corundwn Stone, audits Varieties, &c. 275

The imperfect corundum may likewise be cut in sucli a man-
ner as to produce tiie starry reflection : but it is more rare than in
the perfect kind, to meet with pieces which have all the qualities
requisite for this purpose. There is, in Mr. Greville's collec-
tion, a large piece of imperfect corundum, of a brown colour,
which has been cut en cabochon, with the above-mentioned in-
tention ; but, the cutting not having been made in the proper
direction, the starry reflection is exhibited in a very imperfect
manner, as it proceeds from a point near the plane of the base
of the stone. The effect produced, however, is sufficient to
remove all doubts respecting the existence of the property here
spoken of, in this kind of corundum.

CHARACTER AFFORDED BY ANALYSIS.

In order to complete the proofs I have already given, that all
the stones which form the subject of this Paper are of one and
the same nature, I shall borrow this last mentioned character
from the analyses made by Mr. Chenevix, which will hereafter
be described at length by that able chemist; and it may be
observed, that few instances can be met with where the chemist
and the mineralogist, after having jointly employed themselves
in their different provinces, upon the same substance, have
arrived at a more satisfactory and correspondent result.

According to Mr. Chenevix's analyses, the constituent parts
of the various substances here treated of, are as follows.

276

Coimt de Bournon's Description of

IMPERFECT CORUNDUM.

From the

From

From

From

Carnatic.

Malabar.

China.

Ava.

Silica -

5.0

- 7,0

-

5,25

-

6,5

Alumina -

- 91.0

- 86,5

-

86,50

-

87,0

Iron

- 1,5

4,0

-

6,50

-

4,5

Loss

2,5

- 2,5

100,00

2,0

100,0

100,0

100,0.

PERFECT CORUNDUM

.

Blue, or

Red

, or

sapphire.

orienta:

Iru

by.

Silica

-

5,25

-

- 7.

,0

Alumina

-

92,0

-

- 90=

,0

Iron

-

1,0

-

1,

,2

Loss

-

i>75

-

1,

,8

100,00

100,0.

From what has been said it appears, that the analogy
existing between the stones hitherto known by the names of
corundum, sapphire, oriental ruby, oriental hyacinth, &c. is
so strong and complete, as no longer to permit us to doubt
that they ought all to be considered merely as varieties of the
same substance, to which I have therefore given the general
name of corundum.

In the learned work on mineralogy which the Abb^ Hauy
has just published, this celebrated naturalist says, that near-
ly at the same time I communicated to the Royal Society
my first observations on this substance, he had himself ob-
served the existence of corundum, among the crystals of

the Corundum Stone, a?id its Varieties, &c. 277

different substances contained in the sand of Ceylon ; having,
as he says, seen therein some small hexaedral prisms, of a ruby
red colour, and transparent, which, from the analogy that ap-
peared to exist between their external characters and those
peculiar to corundum, might very naturally be ranged with that
substance. Some particular circumstances certainly prevented
him from making the same observations respecting the pyramidal
crystals, of the above colour, which are also found in that sand ;
and he consequently thought it right, (although he appears to
have had some doubts upon the subject,) to continue to separate
the sapphire from corundum, giving to the former the name of
telesie : indeed he has placed them at a considerable distance
from each other, the sapphire being the third species of his
second class of stones, and the corundum the fourteenth. What
he seems to consider as the strongest arguments in favour of
this separation, are, the laminated texture so evident in all crystals
of corundum, and the direction of the laminae being according
to the inclination of the faces of a rhomboid ; whereas, in the
sapphire, tiiis laminated texture seemed to him not to exist;
and he adds, that the fractures of sapphire appeared to him
to follow a direction perpendicular to the long axis of the
crystal.

With regard to this, I shall observe, that in the foregoing
descriptions of the characters peculiar to this substance, (which
have been given with all the circumstantial detail necessary in a
demonstration which is intended to leave no doubt upon the
subject,) the observations of the Abb6 Hauy appear to me to
have been completely answered. It has there been stated, that
one of the peculiar properties of this stone was, that it always
preserved a very distinct laminated texture, in all those varieties

MDCCCII. O o

278 Coimt de Bournon's Description of

wherein the crystallization appeared not to have attained its
highest degree of perfection, which varieties I have distinguished
by tlie name of imperfect corundum. But it has also been
stated, that in proportion as tlie crystallization possessed a
greater degree of perfection, the texture exhibited a less lami-
nated appearance ; and that, in this case, it was less easy to
obtain a fracture in the real direction of the laminae.

Another circumstance has likewise been taken notice of, which
appears to me to deserve some attention, namely, that in all the
different varieties of this substance, the blue colour was gene-
rally accompanied with a greater degree of transparency, of
gravity, and of hardness ; and that, under these circumstances,
in proportion as the adhesion of the lamina was more complete,
the laminated texture of the stone became less evident, and it
was much more difficult, and sometimes scarcely possible, to
obtain fractures in the direction of the laminae. Nevertheless,
among crystals and fragments of sapphire which had but a
small degree of transparency, I have frequently met with some,
in which the laminated texture was as evident as in the red
prismatic variety of perfect corundum, or oriental ruby.

With respect to what concerns the fracture of the sapphire,
if the Abbe Hauy was not deceived by an illusive appearance
by no means rare in this stone, both in its perfect and imperfect
state, (according to which the terminal faces seem to indicate a
laminated texture perpendicular to the axis, or a fracture in that
direction,) I cannot account for his thinking that he had obtained
such a fracture as he describes. I have often tried to obtain
fractures of that kind, but without success; never having been
able to procure any, except such as were more or less irregular,
and exhibited an appearance very different from that of fractures

the Corundum Stone, and its Varieties, Sec. 279

made in a natural direction. Moreover, I have examined a great
number of crystals of sapphire, many of which had one of
their extremities, many others both their extremities, broken
in a direction approaching more or less to that uhicli is per-
pendicular to their axes, but have never seen, among these
fractures, any one that had the appearance of being made in
the natural direction of the lamince ; although, at the same
time, I have, in many crystals, seen fractures which were per-
fectly even, and often of considerable extent, in the direction
of the planes of a rhomboid, exactly similar (^\ith respect to
the measure of its angles) to that belonging to the primitive
crystal of imperfect corunckun. I have already observed that
there sometimes remain, upon the terminal faces of the crystals
of sapphire, small facets belonging to the above planes.

I cannot help mentioning also, in this place, a very interesting
crystal of sapphire, that is in Mr. Grkville's collection. This
sapphire, which is of a pale blue colour, is a simple hexaedral
pyramid, the solid angle of whose summit measures 40°, and re-
tains upon one of the angles of the summit, which is incom-
plete, a large triangular facet, belonging to one of the planes of
the primitive rhomboid. This plane is striated transversely, in
a manner that shews some derangement in the crystallization,
perhaps from too great rapidity ; and, in the upper part, a still
more rapid decrease changes its degree of inclination, causing
it to take one which is greater, and which belongs to the se-
condary obtuse rhomboid already described, in speaking of the
fifth modification. These planes, together, completely terminate
the crystal at this extremity, in the manner represented in Fig.
gg. There may also be observed, two other planes, between
M'liich is comprehended the plane I have just described as ane

Oo 2

28o Count de Bournon's Description of

of those of the primitive rhomboid : they are produced by the
passing of the crystal to a less obtuse pyramidal modification.

Corundum is not the first mineral substance that has exhi-
bited, even in its crystallized state, very striking differences,
according to the circumstances tliat have governed its forma-
tion, and the greater or less degree of perfection that has taken
place in its crystallization. Felspar is a substance to which
the very same remarks may be applied. In the interior part of
most kinds of granite and porphyry, it appears in the form of
very rugged crystals, generally opaque ; whereas, in the fissures
of primitive rocks, it frequently has a beautiful transparency ;
and, when this happens, it rather exceeds the former kind in
hardness and in gravity. This difference, which for a long time
prevented the latter kind from being joined with the felspar
of granites, is so striking, that most naturalists have thought it
right still to continue to separate it, at least as a variety, al-
though they allow it a place in the same genus, under the name
of adularia.

There exists also in the same genus (felspar) a third variety,
which, though it had long been known by the name of zvbite
schorl of Dauphiny, was not, till lately, brought into its pro-
per place. This kind of felspar, which is still more perfect,
presents, in such of its crystals as have the greatest degree of
transparency, a brilliancy tliat is even superior to that of the
most perfect adularia; this transparency is less similar to that
of glass, and approaches nearer to tliat which is peculiar to the
stones that have been hitherto distinguished by the names of
gems or precious stones. Indeed, it always appeared to me to
possess, in general, the two characters of hardness and gravity,
in a somewhat greater degree than adularia. It rather scratches

tlje Corundum Stone, and its Varieties, &c. 281

adularia than is scratched by it. In the division which I usually
make of the different kinds of felspar, I distinguish this latter,
in consequence of the above-mentioned character, by the name
of brilliant jelspar.

We shall see hereafter, that there probably exists a fourth
variety of felspar, without reckoning that which is known by
its greasy aspect. The fracture of this greasy kind is dull, and
resembles that of wax. It exists, in great quantity, in certain
granite rocks, which usually abound with hornblende ; of which
rocks there is a great number in Scotland. In these, it is
frequently of a green colour, which gives it exactly the appear-
ance of jade. This kind of felspar may very probably be a
particular kind of substance, nearly allied to one of those (very
different from each other) to which French mineralogists give
at present the name of petrosilex.

COMPACT CORUNDUM.

We have hitherto seen corundum only in a form more or less
perfect or determined ; it is, however, sometimes met with in a
state in which there does not appear the smallest rudiments of
crystallization. In this state, (to express which, mineralogists
have agreed to make use of the term compact,) it resembles, in
many respects, a coarse jasper ; but its much greater degree of
hardness, and its much higher specific gravity, render its true
nature easily distinguishable.

In Mr. Greville's collection are many specimens of this
compact corundum ; they are all of a purplish red colour, not
very deep, and are perfectly opaque. By means of a lens, there

c82 Count de Bournon's Tkscription of

may be perceived, here and there, some small particles, in which
an incipient laminated texture is discernible. These particles
are rendered visible by the reflection iroin the laminie; they
are of a beautiful rose colour, and have a slight degree of trans-
parency. The lens also shows, at the same time, a great
number of small globules, of a deep black colour, and of a very
brilliant lustre : these globules do not consist of attractable oxide
of iron, although that oxide is very common in the substance
here treated of; but, on account of their small size, it has not
yet been possible to determine their nature.
- The compact corundum of a red colour gives pretty strong
sparks, when struck with steel ; it also gives, by collision, the
same phosphorescent fiery red light as the other red varieties of
corundum, both perfect and imperfect.

The mean specific gravity of compact corundum, taken from
three trials, which differed very little from each other, was
5902.

MATRIX OF IMPERFECT CORUNDUM FROM THE PENINSULA OF
INDIA, AND CHIEFLY FROM THE CARNATIC.

This matrix, which, as far as our present knowledge extends,
appears to be peculiar to the imperfect corundum of this part of
Asia, is a stone of a particular nature : it is sometimes in masses
of a loose and granulated texture, with very coarse grains, and
pretty much resembles a coarse sand stone ; at other times, it has
a closer texture, the grains being nearer each other, and less
distinct, so as either to give it an appearance similar to the kind
of marble known by the name of coarse-grained saline marble,
,or to that kind of prehnite which is composed of a mass of

the Corundum Stone, and its Varieties, Sec. 283

crystals confusedly aggregated. In this matrix, the crystals of
imperfect corundum are dispersed, in the same manner as
those of felspar are dispersed in porphyry, or rather in certain
granites which, besides the aggregated constituent parts be-
longing to that kind of rock, also contain crystals of felspar
which are of a more or less considerable size, and of a perfectly
determined form.

When this substance is of that texture in which the grains
are closely connected together, it is of a pearly gray colour,
sometimes slightly tinged with green, and has a degree of semi-
transparency, not unlike that of calcedony. If a piece of this
kind is moved about in a strong light, its surface shows a con-
siderable number of small brilliant particles. This appearance
arises from tlie reflection of the light, by the small laminae that
are exposed, in consequence of the fracture of the grains of
which the stone consists ; and this circumstance proves that it
has a laminated texture.

In the last mentioned state, (the most perfect one in which I
have observed this stone,) its hardness, although sufficient to
scratch glass very easily, is rather inferior to that of felspar.
It gives sparks when struck with steel ; and, by means of strong
collision, emits a phosphorescent light, of a bluish white colour.
Friction does not produce any signs of electricity. When put
into nitric acid, no effervescence was perceptible.

The specific gravity of this stone, as determined by four trials,
which scarcely differed from each other, was 2742 ; but it is
difficult to procure pieces of a tolerable size, which are not
mixed, either with hornblende, or with particles of corundum.

It is fusible by means of the blowpipe.

This substance is more usually met with in pieces of a coarser

284. Count de Bournon's Desm'ptio7i of

texture, in which the grains are often pretty large, so as to be
easily distinguishable by the naked eye. When these pieces are
in a perfect state, the grains have exactly the same colour, and
the same degree of semi-transparency, as those of the preceding
more compact kind. If examined with a lens, the laminated tex-
ture of these grains is very evident ; and there seems to be, at
the first view, a very distinct crystal in each of them. But, if
we endeavour to determine the form of any one of these crystals,
we find that it is absolutely impossible to do so ; as the greatest
part of the small facets we perceive, are nothing more than
facets formed by compression. I thought, indeed, that I could
distinguish some traces that indicated an obtuse rhomboid ; but
not in such a manner as to permit me to state the fact with
certainty. These grains have but a weak degree of adherence to
each other; in consequence of which, the stone may often be
broken by a very slight effort.

It is, however, still more common to meet with this substance
in a state wherein it has undergone, at the surface of each of
the grains of which it is composed, an incipient decomposition,
that gives them a whiter colour, thereby obscuring, and indeed
often destroying, that semi-transparency which I mentioned
as being a character of this substance, in its two preceding
states. When this is the case, if some pieces of the stone are
put into nitric acid, an effervescence soon takes place, the
strength of wliich is in proportion to the degree of decomposition
the stone has undergone ; but this effervescence, in a short
time, entirely ceases. It seems, from this circumstance, that the
lime contained in the stone, (which, as will be hereafter seen in
the account of its analysis, Mr. Chenevix found to amount to
15 parts in 100,) being exposed to the action of the air, by the

the Conindum Stone, and its Varieties, Sec. 2S5

alteration or decomposition of the stone, had afterwards com-
bined with a portion of carbonic acid.

To the above mentioned hme, (carried away by the rains
which wash the exposed parts of the rocks composed of this
substance, and deposited upon the fragments of corundum scat-
tered at the feet of those rocks,) ought no doubt to be attributed,
that calcareous incrustation which is frequently observed to
cover, either partially or entirely, many fragments of imperfect
corundum, found among the specimens of that substance sent
to us from India.

If we let a piece of this matrix remain for a certain time in
nitric acid, it is attacked by it, without being dissolved, and
without changing its form ; but if, after being taken out, it is
pressed between the fingers, it ma}'' be crumbled by a very
trifling effort, and may, by being rubbed, be reduced to a sort
of paste.

SUBSTANCES WHICH ACCOMPANY THE IMPERFECT CORUNDUM, IN
THE ABOVE MENTIONED MATRIX, FROM THE PENINSULA OF
INDIA.

Felspar. There are sometimes found, in the matrix here
treated of, pieces, more or less considerable in size, of a lami-
nated substance, which has the same greenish gray colour, the
same brilliancy, and, in short, the same appearance, in many
respects, as the corundum itself. It is indeed the more easy to
confound this substance with corundum, as it is frequently ac-
companied with crystals of the latter. I have myself been several
times led into this mistake, before I had paid such particular

MDCCCII. P p

286 Count de Bournon's Description of

attention as I have since clone, not only to corundum, but
also to every thing relating to the substances which accom-
pany it.

The most usual colour of this substance, as I have already
said, is gray, slightly inclining to green, which is sometimes
mixed with a small portion of brown. It possesses a pretty con-
siderable degree of semi-transparency, which may be compared
to that of calcedony, or more properly to that of the stone known
by the name of cat's eye. Its hardness is inferior to that of
quartz ; but appears to be exactly the same as that of felspar. It
gives sparks, when struck by steel ; and, by collision, emits a
yellowish phosphorescent light. Friction does not cause it to
give any signs of electricity.

This stone may be divided with great facility, in the direction
of two opposite and parallel faces ; and the fractures thereby
obtained have a brilliant lustre, exactly resembling that of the
fractures of corundum. Upon these fractures may be observed
very fine but very evident strice, which indicate that the laminae
have a direction difrerent from the above ; but I have not yet
been able to obtain an even fracture, in the direction of these
striae. All fractures made in any other direction than that first
mentioned, are irregular and unequal ; very often also they are
dull, and somewhat similar to that of wax.

The mean specific gravity of tliis substance, taken from four
trials, which differed very little from each other, is 2643.

This substance is fusible by the blowpipe, like common
felspar.

The result of the analysis of this substance, made by Mr.
Chenevix, is, in many respects, similar to that of the analysis

the Corundum Stone, audits Varieties, &c. 287

ofadularia, made by Mr. Vauquelin; yet it differs very essen-
tially from that, by the want of potash, and by the proportion
of lime being more considerable.* The presence of the last-
mentioned earth is sometimes rendered evident, in the parts
which are slightly decomposed, by the weak and momentary
effervescence that takes place in those parts, when the substance
is put into nitric acid.

On the other hand, many of its external cliaracters are such
as naturally lead to its being ranged with adularia. It differs
from it, however, in the facility with which the latter may be
broken in two different directions ; while, in the substance here
treated of, fractures can never be obtained, except in one of
those directions ; nor have I ever been able to observe on the
fractures of any other kind of felspar, those fine striae which,

• The analyses made by Mr. Vauciuelin, of the different kinds of felspar,
naturally lead me to make some further remarks upon that substance ; which, indeed,
may be equally applied to many other substances. The able chemist above mentioned,
found 14 parts of potash in loo of adularia, and 13 in 100 of the green felspar of
Siberia ; whereas, he did not find an atom of that substance in another kind of felspar,
which was in a laminated mass ; nor in that decomposed felspar which is known by
the name of kaolin. Potash may therefore be considered as not being one of the con-
stituent parts of felspar, but merely as a foreign substance, accidentally interposed
therein. Adularia, in that case, would be nothing but an impure kind of felspar; and
would present the astonishing phenomenon of a substance constantly impure, \n its
most perfect state of transparency and ciystallization. It is indeed difficult to con-
ceive that the potash is merely interposed, in such very considerable proportion, in
the kind of felspar called adularia; yet, if it really formed one of its constituent
parts, it would necessarily produce a substance totally different from those which do
not contain any of it ; whereas, all the mineralogical characters of felspar and adularia,
evidently demonstrate that these two substances are perfectly similar in their nature.
There still remain, in my opinion, many discoveries to be made, in that part of
chemistry which relates to the composition of mineral substances, before the chemist
and the mineralogist shall be enabled to proceed together, with a certainty of agree-
ment respecting the object of their inquiries.

Pp 2

288 Count de Bournon's Description of

as I have already said, are very evident on this stone. It differs
also from common felspar, in not being capable of acquiring
electric properties by friction; whereas common felspar may, by
long continued friction, be made to acquire such properties. The
semi-transparency of this stone likewise, and the nature of its
lustre, are such as give it a greater analogy to gems or precious
stones ; and, in these respects, it is very similar to the variety
which I have called shining felspar.

As this substance appeared to me to have a great analogy
with another, which sometimes, in small fragments, accompa-
nies the perfect corundum in the sand of Ceylon, (in which,
however, they are more rare than corundum itself,) I desired
Mr. Chenevix to be so good as to add to the analyses he was
about to make, that of these fragments. The result of his ana-
lysis of them differs so little from that afforded by the substance
above described, that it strongly confirms the analogy I had
supposed to exist between them.

Having been so fortunate as to find, among the few fragments
I could collect of the last mentic^ied substance, three crystals,
in which the crystalline form is perfectly determined, I am
enabled, by their means, to add the crystalline character of the
substance, to those I have given in the foregoing paragraph.
These crystals are rhomboi.ial tetraedral prisms, of about 100°
and 80°, the two terminal faces of which are inclined, in a con-
trary direction, upon the obtuse edges of 100", in such a manner
as to make with them, an angle of 105° on one side, and one
of 75° on the other; and as, (in the only three crystals it has
yet been in my power to examine,) the planes of the prisms are
very nearly equal to the terminal faces, their appearance is
exactly that of a rhomboid. The terminal faces of the crystals

the Corundum Stone, and its Varieties, Sic. izSgr

here spoken of are chatoyant ; and, in the fragments, the planes
which correspond to these faces have a similar property, when
held in a proper direction. In some, these faces then appear of
a pearly white colour; in others, the colour is rather yellowish :
some of them reflect a pale blue colour ; in many others, the
colour reflected is a beautiful deep sapphire blue, that entirely
occupies the whole extent of the face which possesses the pro-
perty here spoken of To this stone ought to be referred, that
which is known by the name of moon-stone of Ceylon, when it
is not of the kind called cimophane, (the chrysoheryl of Werner,)
which is often found also in the sand of this island, mixed with
rubies, sapphires, &c.

The opinion I am naturally led to adopt, in consequence
of the detail I have just given respecting this stone, is, that
it most probably is a kind of felspar, and ought to be ranged
with that substance, as forming an additional variety.

In some of the pieces of this stone, which are found in the
same matrix with the imperfect corundum of the Carnatic, a
talcy earth (which often also appears in a separate state) is in-
terspersed throughout their substance, and causes them to have
a less compact texture, and a very inferior degree of hardness.
The stone, at the same time, acquires a slight greasiness to the
touch, and loses the semi-transparency which is peculiar to it :
it may still, however, be easily divided, in the direction already
described as that in which it is naturally divisible,

FibroUte. The substance I have distinguished by tliis name,
which sometimes also accompanies the imperfect corundum from
the Carnatic, in its matrix, has always offered itself to my obser-
vation, either of a white colour, or of a dirty gray. Its hardness
appeared to me to be rather superior to that of quartz : as, after

'2gQ Count de Bournon's Description of

having rubbed them together, the latter seemed to be the most
worn of the two. It gives bright sparks, upon being struck with
steel. Collision causes it to emit a phosphorescent light, of a
deep reddish colour. It cannot, by friction, be made to give
signs of electricity.

Its mean specific gravity, taken from four trials, is 3214.
This substance was tried with a blowpipe, by Mr. Fleuriau
DE Bellevue, a mineralogist much accustomed to such opera-
tions, and found to be absolutely infusible, even when placed,
in very minute particles, upon cyanite.

The external texture of this substance is usually fibrous ; the
fibres being very fine, and closely connected together. When
it is broken according to the direction of the fibres, its internal
texture appears to be exactly the same ; but, if it is broken in a
direction transverse to the fibres, its texture appears to be com-
pact. The lustre of the last kind of fracture is rather vitre-
ous ; and there is nothing in its appearance that gives reason
to think it was made in the direction of the laminje. When we
wish to try the hardness of this stone, it should be done in a
direction which is transverse or perpendicular to the fibres ; not
in a direction parallel to them.

There exist many pieces of this substance that are merely
irregular aggregations, in which the fibres cross eac]i other, in
bundles, in different directions. I have only once seen it in a
form which could be considered as a determined one; viz. a
rhomboidal tetraedral prism, of about 80° and 100°, the ter-
minal faces of which are imperfect. But, as this prism, although
pretty regular in its form, is the only one I have yet been able
to discover, the above observation requires to be repeated,
before we can safely make any dependence upon it. I must

the Corundum Slone, and its Varieties, 8cc. 291

however add, that among the pieces of this substance, I have
met with several, which appeared to have more or less tendency
to the above-mentioned form.

The analysis of this substance, made by Mr. Ciienevix,
concurs with the whole of its external characters, in warranting
us to consider it as being different from any of the mineral
substances hitherto known ; in consequence of which, I have
thought it right to distinguish it by the name o^Jibrolite.

Thallite. The substance called thallite (the epidote of the
Abb6 Hauy) also sometimes accompanies the corundum from
the Carnatic, in its matrix. This substance is found in three
distinct states, hitherto unobserved, in all of whicli its appearance
is so different from its usual one, as to have prevented me, for
some time, from knowing it.

In one of the above states, this substance is inclosed in the
matrix, in small detached masses, from the size of a pea to that
of a hazle nut, and even larger. Its usual colour is either a
brownish green or a yellowish green ; and it has ojily a slight
degree of semi-transparency, even at the edges.

Its hardness is the same as that of the other known kinds of
thallite, which I have always found to be rather superior to that
of quartz ; and, as most of the other characters belonging to this
kind of thallite are similar to those of the kinds already known,
I shall, in the following description, mention only such of its
characters as, on account of their being different, migiit lead to
false ideas respecting it.

The major part of these small masses present no determined
form; in some of them, however, a perfectly regular crystalU-
zation may be observed. In this latter state, the greater number
of crystals appear in the form of rhomboidal tetraedral prisms,
of 128° 30' and 51° 30', in which the terminal faces are perpen-

292 Count de Bournon's Description of

dicular upon the sides, as in Fig. 40. (Plate IX.) This form,
which was before unknown in the thallite, and which might at
first view be taken for a primitive one, was very hkely to lead to
an erroneous idea ; it may however be explained by another form,
which is also met with in perfectly determined crystals. In these
last, the prism is hexaedral, with two edges of 1 14° 30', two others
of 128° 30', and the two last of 117°; its terminal faces are also
perpendicular upon the sides of the prism, as in Fig. 41. Now
this form is exactly the same as one of those already observed
in the prism of the common thallite, and is produced in the fol-
lowing manner, viz. the primitive rhomboid, the edges of which
are 1 14" 30' and 65" 30', has each of its acute edges replaced
by a plane, inclined, in a contrary direction, upon one of the sides
of the prism, so as to make with it an angle of 128° 30'. I
have often found this hexaedral prism terminated, in the same
way, by planes perpendicular to its sides, among the crystals of
thallite from the Alps of Dauphiny. The preceding rhomboidal
tetraedral prism, consequently, is produced by an increase of the
faces which have replaced the edges of 65° 30'; whicli increase
has been such as to cause the sides of the primitive rhomboidal
prism, on which each of them incline, to disappear: this is
represented by the dotted lines in Fig. 42. The direction of
the lamince, in these crystals, strongly supports the foregoing
explanation. Sometimes the rhomboidal prisms become of an
indeterminate form, by being flattened so as to render the edges
of 128° 30' much more obtuse; when that happens, they have
no longer any regular measure.

In this first state of the thallite which accompanies the imper-
fect corundum from the Carnatic, the pieces, whether they are
crystallized or of an indeterminate form, have their surface co-
vered with little asperities, thereby exhibiting an appearance

the Corundum Slone, and Us Varieties, &c. 293

which cannot be better described, than by comparing it to tliat
preparation of fish-skin which is called shagreen. This is the
natural effect of their peculiar texture ; for, if one of these
pieces is broken, we perceive very plainly, that it is not of a ho-
mogeneous texture, but is mixed with small particles of the
substance we have already described as the matrix of corundum ;
which mixture is often in such proportion, that the quantity of
the latter substance is equal, or nearly so, to that of the thallite
itself.*

The appearance the surface of these pieces exhibits, is owing
to the destruction, at the said surface, of the forementioned small
particles of the matrix, which, as is well known, is very easily
decomposed. There sometimes even remains, in the little cavi-
ties, which are very numerous, small particles of this matrix,
generally in a state of decomposition. In this case, if the
pieces are immersed in nitric acid, a slight and momentary
effervescence takes place ; and, if this immersion is continued
for some days, the acid then acts upon those particles of the
matrix which are inclosed in the interior part of the substance,
as has been already mentioned in the description of tiiis matrix ;

* The regularity of the form in which these crystals are found, will certainly
appear surprising, when we consider the immense quantity of heterogeneous particles
which are interposed within their substance, and, consequently, between their crys-
talline molecules, the attraction of which for each other, it would appear, must be
thereby considerably obstructed ; but the same circumstance takes place in other
substances, for instance, in the calcareous spar known by the name of rbomboidal
sand-stone of Fontainb/euu. The Abbe Hauy, in the article axinUe, (the ibunicr-
siein of Werner,) makes the same observation, and gives a very ingenious expla-
nation of the circumstance. This calls to our mind the remark of the celebrated
DoLOMJEU, viz. that it appears, in some cases, that a foreign substance, when inter-
posed in a crystal, instead of obstructing its cr)'stallization, tends rather to give it
n greater degree of regularity.

MDCCCII. Oq

254 Count de Bournon's Description of

in consequence of which, the pieces, when taken out of the acid,
may be easily crumbled by the slightest pressure of the fingers ;
and nothing remains in its former state, except the small par-
ticles of the thallite.

There exist some pieces, in which the particles of the matrix
are infinitely more numerous than those of the thallite itself;
the latter then only appears in the form of small greenish or
yellowish points, disseminated in greater or less proportion, and
in detached spots.

In the second of the states in which this substance is found
in tlie matrix of corundum, it appears in the form of pretty thick
prisms J these prisms have deep grooves or channels, which, as
is often observed in the crystals of tourmalin, render their shape
absolutely deformed. The substance, in this second state, is
more pure ; no particles of the matrix, which were said to be
mixed with it in its first described state, are to be seen. The
semi-transparency is more general, and in a greater degree.
Tlie green or yellowish coloiu: is also more deep ; and sometimes
a slight tinge of red is mixed with those colours. Some parts
of the pieces are less grooved than others ; and those parts in-
dicate the forementioned rhomboidal prismatic form of 128'' 30'
and 51° 30'; but it is very difficult to obtain an even fractm^e of
this stone.

In the third state, this substance is so very similar to the
purest imperfect corundum, that at first I supposed it to be of
the same nature ; and it was not until I had examined it more
particularly, that its specific gravity and its hardness, so dif-
ferent from those of corundum, led me to think it could not
possibly belong to that substance, and that it ought, from those
characters, to be ranged with the thallite. The analysis of

the Corundum Stone, and its Varieties, &c. 295

it, made by Mr. Chenevix, has proved the truth of my obser-
vations.

Its semi-transparency, in this state, is more considerable, and
approaches very nearly to complete transparency. Its colour is
generally a beautiful topaz yellow, which sometimes inclines
slightly to green. I have hitherto met with it only in pieces of
an indeterminate and irregular form, the size of which, though
more or less considerable, never exceeded that of a small nut.
Its fracture is generally irregular, and often partially con-
choid. In some pieces, however, may be perceived small particles
which seem to have a laminated texture, the direction of the
laminae being such as to announce the primitive crystal of the
thallite ; but I have never been able to bring this substance to
the shape of that crystal, by any artificial division or fracture
of it.

Hornblende. This substance is that which is most constantly,
and most abundantly, contained in tlie matrix now treated of.
There are indeed some pieces of the matrix, wherein the pro-
portion of hornblende is as great as in some granite rocks of
which it constitutes the principal component part; and those
pieces have an appearance very similar to that of such rocks.
It is generally of a deep black colour, and opaque; but I have
sometimes seen it in the form of small elongated crystals, of a
fine green colour, and transparent. Its texture is very evidently
laminated ; and it is seldom that any determinate form can be
perceived in it ; sometimes, however, the rhomboidal tetraedral
form of its prism may be distinguished.

Quartz. In this matrix is also found quartz, in small detached
fragments, of an indeterminate shape. This substance, however,
is by no means common; on the contrary, of the various

2q6 Count de Bournon's Description of

substances that are met with in this matrix, quartz is one of the
most rare. It is generally of a dull white colour, and has but a
small degree of transparency.

Mica and Talc. These two substances are not very common
in this matrix, yet they are more so than quartz. The mica has
a silvery hue, sometimes slightly inclining to green ; and, in the
pieces of the matrix in which it is found, it generally appears in
small detached spangles.

The talc is generally of a pale green colour ; and, in those
parts of the matrix where it is met with, it is in pieces nearer
each other than was the case with respect to the spangles of
•mica. Sometimes it forms small masses, little or not at all mixed
with any other substance. At other times, it is found in that
very divided or earthy state (seldom without some heterogeneous
mixture) which has been hitherto distinguished, after Mr.
Werner, by the name oi chlorite.

There are also, but more rarely, met with in this matrix,
pieces of real steatite, of a white or a greenish colour.

According to a letter written from Tritchinopoly, the i oth of
November, 1793, to Sir Charles Oakley, then governor of
Madras, and communicated by hizn to Mr. Greville, it ap-
pears that the imperfect corundum of the Carnatic, as well as
the matrix in which it is contained, forms, in the place from
whence it is procured, distinct strata ; and that these strata are
accompanied by a substance which is in considerable abun-
dance, and which cannot be better distinguished than by the
name of talcy mica. This substance is easily separated from the
matrix of corundum ; and it is usual to separate it, on the spot,
before the pieces containing the corundum are sent away for
the purposes of commerce. Some of it was sent to Mr. Greville

the Corundum Stone, and its Varieties, &c. 297

by Sir Charles Oakley himself. The colour of this is a
blackish brown ; and its exterior appearance is nearly similar
to that of mica ; but the lustre of its surface is somewhat less
bright. Its texture is very distinctly laminated ; the lamina?,
which are very thin, being chiefly evident at the edges ; they ad-
here, however, more strongly to each other than those of mica.
These lamincE may be bent, without breaking; but they do not
show the smallest signs of elasticity. This substance possesses
but a small degree of transparency, and that only when it is
brought into the state of very thin lamins&^ its colour then ap-
pears a brownish yellow, not much unlike that of resin. It is
much more greasy to the touch than, mica; it is also less
hard, so that it may be easily scratched with the nail; and,
if we scratch it with the point of a penknife, we are not sen-
sible of that kind of slight shivering whicii takes place when
mica is so treated. Mr. Greville, in the Paper upon corun-
dum which he presented to the Royal Society, in June, 1798,
was perfectly aware of the difference between this substance
jind that properly called mica. In the collection he received
of the former, are many crystals, several of which are nearly
an inch in length, and two or three lines in thickness. Some
of these are in the form of a rhomboidal prism, of 60° and 120°;
others have the form of a regular hexaedral prism. Upon the
whole, the characters of this substance may be considered as
partaking both of those belongmg to mica and those belonging
to talc.

Its mean specific gravity, taken from three trials, which dif-
fered very little from each other, is 2709.

Garnets. In the matrix here spoken of, and also in the corun-
dum itself, garnets are sometimes met with ; they are of a deep

298 Count de Bouunon's Description of

red colour, and of a roundish form. There was lately sent to
Mr. Grevillk, u parcel of ijnperfect corundum, found among
the sands of tlie river Kirtna, in tlie district of Ellore,* in the
northern part of the government of Madras. This corundum,
some of the crystals of which w^ere the best defined of any I
had yet seen, w-as mixed with pretty large angular fragments of
garnets, of a very deep blood-red colour, and of the most beau-
tiful transparency.

Zircon. The same parcel of imperfect corundum, of which I
have just spoken, from the district of Ellore, was also mixed
with crystals of zircon, the jargon of the lapidaries. These
crystals, which were in perfect condition, deserve to be men-
tioned, not only on account of their size, but also on account of
the great number of varieties and rare forms they exhibit. Such,
for instance, is the primitive very obtuse octaedron, which is
in large crystals, with sides of more than six lines in length.
I had observed this form, for the first time, fifteen years ago,
in some crystals found in the sands of a rivulet, called Riou
Pezzouliou, which nms between the volcanic rocks at Expailly,
near Puy in Velay ; but these crystals were very small, Tlie
celebrated Rome' de Lisle, who published my account of these
crystals, in his excellent work on the external characters of
minerals, mentions the opinion I then entertained, and had com-
municated to him, that the jargon and the hyacinth were only
two differently-coloured varieties of the same substance, and
were both derived from the same primitive form.

The most usual colour of these crystals of zircon, is a brown,
which sometimes inclines to yellow : they often, however, have
tiiat fine yellowish red colour, which causes this stone to be
• This district is contiguous to that in which tlie diamond mir.es are situated.

the Corundum Stone, and its Varieties, Sec. 299

distinguished by the name of hyacintli. Their size, and the
perfection of their crystallization, enabled me to ascertain, that
the angle formed by the meeting of the planes of the octaedron
at the base, measures 85°; and that formed by their meeting at
tlie summit, 95°; as is stated in the work I have just mentioned.
The Abb6 Hauy, in his excellent work on Mineralogy, fixes
the first of these measures at 83° 50', and the other at 97° lo'.
I imagine he must have been deceived, eitlier by the crystals
having been of too small a size, or by their not having been of
a perfectly regular form.

Amongst the pieces of the stone which serves as a matrix
for the imperfect corundum, are found some, in which may be
perceived a great number of very brilliant small points,, of a
yellowish red or orange colour. When viewed with a lens,
these points appear to be minute crystals, perfectly transparent ;
but it is impossible to ascertain their form. On some of them
may be perceived small facets; others have the appearance
of prisms : they are of very considerable hardness. I am unable
to form a decided opinion respecting the true nature of these
microscopic crystals: but, all things considered, I am inclined
to think it probable that they belong to the zircon.

Although these crystals, in the state I have just described, are
extremely small, that state is by no means tlie smallest in which
they are found in this substance ; they also exist in it, so very
minute in size, that our eyes, even when assisted with instru-
ments, are scarcely able to distinguish them. In this state,
they become a real colouring matter, for those parts of the
matrix in which they are contained ; which parts thereby acquire
a fine orange colour, more or less deep. By attentively examining
these pans with a lens of sufficient power, we may perceive

300 Count cle Bournon's Description of

tlie crystals approaching nearer to each other, and diminish-
ing in size, so as at last to become invisible: very often, they
shew themselves only in the form of small filaments, scarcely
perceptible.

The above is not the only substance which presents the phe-
nomena just described, even in the stones here treated of;
the thallite sometimes has the same appearances ; and, in that
case, it gives to the matrix a green colour, similar to its own.
When this happens, we may sometimes, by means of a lens,
perceive small microscopic crystals of thallite; very often, how-
ever, they are too small to be distinguished.

It appears therefore that coloured stony substances, by inter-
posing themselves, in particles too small to be seen, in stones,
may sometimes produce the same effects (and probably in the
same manner) as are produced by the various metallic oxides.

Fery attractable black Oxide of Irofi. This ore of iron (which
is the fer oxidule of tiie Abbe Hauy, and the inagnetic iron ore
of the Germans,) is also found sometimes in the matrix of im-
perfect corundum from the peninsula of India; but, as we shall
hereafter see, it is by no means so general, nor so abundant, in
that matrix, as it is in the matrix of imperfect corundum from
China. In the former, it appears in small grains of an indeter-
minate shape, which are sometimes interposed between the
particles of hornblende, in such a way as might easily lead us
to suppose, that the latter substance has the property of being
acted upon by the magnet. In those parts of the matrix which
contain tliis oxide of iron, are found hexaedral prisms of corun-
dum, the surface of which is entirely covered by a layer of the
oxide, about a quarter of an inch in thickness, and absolutely
moulded upon them.

the Conmdum Stone, and its Varieties, &c. 301

MATRIX OF IMPERFECT CORUNDUM FROM CHINA, AND SUE-
STANCES WITH WHICH IT IS ACCOMPANIED.

This matrix is totally different from that of the imperfect
corundum of the Carnatic, being a granite rock, composed of an
aggregated mixture of felspar, fibrolite, mica, and very attract-
able black oxide of iron. I have not yet seen in it any particles
of that particular substance, already described, which composes
the principal part of the matrix of imperfect corundum from
the Carnatic.

The four substances above-mentioned, are unequally distri-
buted throughout the mass ; some pieces being composed almost
entirely of one of them ; while, in other pieces, those substances
are mixed together in various proportions, and sometimes in
nearly equal ones. The crystals of corundum are disseminated
in the mass, in the same manner as those of the Carnatic are
in their matrix ; but, as the particles of the matrix now treated
of have a much stronger adherence to each other, and also to
the crystals of corundum, it is difficult to detach the said crystals
from the matrix, without breaking them.

The felspar has, in this matrix, the same appearance it usually
has in granites. Its colour is generally reddish; very often,
however, it is of a grayish white colour. I have never observed
it to have any determined crystalline form ; but, when it is in
masses of a certain size, their texture is evidently laminated.

The mica has a silvery appearance, sometimes inclining a
little to a yellowish colour, at other times to a greenish one. Its
lamina are frequently united together, so as to form prisms,
which are pretty thick, but most commonly of an irregular

MDcccii. R r

502 Count de Bournon's Description of

shape ; sometimes, however, the appearance of a regular form
may be observed in them.

The fibrolite is in much greater proportion in this matrix,
than in that of the imperfect corundum from the Carnatic; and
it is more generally dispersed throughout its substance; its
fibres, however, are shorter, and form small detached diverging
pencils, which unite together, crossing and penetrating each
other in all directions, so as to present masses of a more con-
siderable size. In this manner, it often entirely surrounds the
crystals of corundum, and it is then impossible to disengage
them from it. Its most usual colour is a whitish gray, but it is
also frequently of a dull white. It is sometimes mixed, nearly
in equal proportions, with felspar, and the attractable black
oxide of iron ; and thus produces a stone which, if polished,
would have a very beautiful appearance. The analysis which
Mr. Chenevix has made of this substance, concurs with all
its other characters to demonstrate, that it is decidedly of the
same nature as the fibrolite of which I have already spoken, as
being found in the matrix of imperfect corundum from the
Carnatic.

The very attractable black oxide of iron is, of the various
substances found in the matrix of imperfect corundum from
China, that which is most constantly, and most universally,
mixed with it. In the smallest piece of this matrix that can be
broken off, some particles of the oxide may generally be per-
ceived; even the crystals of the corundum itself are hardly
ever free from it, it being observable, not only upon their ex-
terior surface, but also within their substance. This oxide of
iron is usually disseminated, in this matrix, in small masses

the Corundum Stone, and its Varieties, &c. 303

of an indeterminate shape, which very often are nearly conti-
guous to each other. It is very rare to find among them any
crystals perfectly formed ; yet I have sometimes observed oc-
taedrons, dodecaedrons, and segments of the first of these two
forms, or octaedrons, which had in each pyramid, and exactly
opposite, one of the faces much larger than the three others.
This last form, appeared to me to be the most common one.

This oxide sometimes exists also in masses of a much larger
size; but they are almost always of an irregular shape. I
have often observed pieces as large as a hazel nut ; and some-
times, though much less frequently, of a still more considerable
size.

The mean specific gravity of this oxide of iron, taken from
four trials, was 5073. This is rather superior to what has been
considered as the specific gravity of this ore of iron, it having
been always estimated at less than 5000. I know nothing to
which I can attribute this difference, except to the peculiar
texture of the oxide here described ; which, as far as I have
been able to observe, has always appeared to me to be much
more compact than is usual in this species of iron ore. In other
respects, it has, when perfectly pure, all the other characters
belonging to this species.

There are some pieces of the matrix now treated of, in which
the small masses of the above oxide, by being mixed witli
fibrolite and mica, exhibit an appearance that might cause them
to be considered as pieces of a true granite ; in others, it is
mixed, in different proportions, with the substance of the co-
rundum itself, in such a manner, that it is impossible, by the
eye, to distinguish this mixture from the pure metallic oxide.
Mr. Chenevix analyzed one of these pieces; and found that

Rr 2

go4( Count de Bournon's Description of

it contained nearly equal quantities of coninduin and of oxide
of iron.

If, to what has been already said, I add, that there are some-
times found in this matrix, small pieces of green pulverulent
talc, (chlorite,) and small masses of thallite, in thin elongated
crystals, of a beautiful yellowish green colour, in the form of
diverging rays, I shall have mentioned all the substances I
have been able to observe, in the matrix of imperfect corundum
from China.

Of the matrix of imperfect corundum from the kingdom of
Ava, a small quantity only was sent; but that quantity was
sufficient to demonstrate, that its nature is exactly the same as
that of the matrix of imperfect corundum from China.

MATRIX OF PERFECT CORUNDUM FROM THE rSLAND OF CEYLON,
AND SUBSTANCES WITH WHICH IT IS ACCOMPANIED.

I cannot help regretting, that it is not in my power to give
much information respecting the matrix of perfect corundum
from Ceylon, The precious stones comprised under that deno-
mination, which are selected from the sands w^ashed down by
the rivers of the island, and sold under the name of sand oj Ceylon,
have never been brought to Europe in any kind of matrix, nor
has any account of their matrix ever been transmitted to us.
Perhaps, indeed, no more information on this head could be pro-
cured on the spot, than was obtained by those naturalists who
sought for the origin of the sapphires, &c. found in the sands of
the small rivulet at Expailly, already spoken of. I may also
observe, that tlie great care taken to free the sand of Ceylon
from every substance, except such as, on account of tiieir

the Corundum Sto7ie, and its Varieties, See. 305

hardness and their histre, are considered as of vakie in com-
merce, deprives us of all chance of obtaining tliat knowledge
respecting the matrix here treated of, which might otherwise be
acquired, from an attentive examination of the various substances
which it is natural to sup])0se are brought down, with the sand,
by the streams. We shall, however, presently see, that one of
those fortunate events by which nature sometimes rewards the
labours of those who devote themselves to the study of her
works, has presented us with some very interesting facts on this
subject.

In order to render as complete as possible, every information
which is connected with the investigation of corundum in ge-
neral, and particularly to make known every thing I have
been able to learn respecting this stone in its highest degree
of perfection, I think it riglit to make some remarks on the
various substances with which it is accompanied, in the sand
sent to us from Ceylon ; although I cannot undertake to assert
positively, that these substances really accompany it, when in
its matrix.

Spinelle. The first of these substances, and one which com-
poses more than nine parts in ten of the wiiole mass of the
sand, is the spinelle ruby, now generally known b}' the name of
spinelle. Notwithstanding the great number of crystals of this
substance which are found in the sand, it is ver}^ uncommon to
meet with one of a tolerable size, that is both transparent and
of a perfect form : indeed most of them ai-e merely fragments.
The selection that has already been made in India, where
these stones receive their first pohsh,.in order to be distributed
for sale, is no doubt the chief reason of the above circumstance :

3oS Coiait de Bournon's Description of

we cannot therefore hope to find in the sand, any crystals of
consequence, except such as have by accident escaped this first
search ; some of these, however, I have liad the good fortune to
meet with.

Among the beautiful series of crystals of this substance which
I have been so Iiappy as to procure, and to place in the several
collections with the care of which I am entrusted by the friend-
ship of their proprietors, there are four, in Mr. Greville's
collection, tiiat I think it right here to take notice of. The forms
of these crystals appear to me to be hitherto absolutely un-
known; for the Abb6 Hauy, who may be justly considered as
the most learned of those who devote themselves to the study
of crystallography, does not even mention them, in the treatise
on mineralogy he has just published.

One of these forms, is a complete tetraedron, as in Fig. 43.
It is produced by the enlargement of four of the faces of the
octaedron, at the expence of the other four, which it has entirely
caused to disappear. There are, in the same collection, many
otlier crystals which are passing into this form, and are more or
less advanced towards it. One of them, in which there still
remain some traces of the octaedron, which had entirely dis-
appeared in the preceding, deserves also to be mentioned. This
variety, which is more common than the preceding, is repre-
sented in Fig. 44,.

The second of the above forms, is a very acute rhomboid, the
rhombic planes of which have 120° for the measure of their
obtuse angles, and 60° for the measure of their acute ones.
^'S- 45- fliis crystal is produced by the enlargement of six of
the faces of the octaedron, at the expence of two opposite faces,

the Corundum Stone, and its Varieties, 8cc< 307

one in each pyramid ; which last faces have entirely disappeared.
There are also several crystals in a progressive state, and more
or less advanced, from the octaedron to this form. (Fig. 46.)

The third form, is a complete dodecaedron, with rhombic
planes. Fig. 47. It is produced by the enlargement of the planes
which have replaced the twelve edges of the octaedron ; a mo-
dification to which the Abb6 Hauy has given the name of
emarginee. This enlargement is such as to have caused the
entire disappearance of the eight primitive planes of the octae-
dron. There are also, in Mr. Greville's collection, crystals
more or less advanced towards this form, some of which no
longer show any traces of the planes of the octaedron, except
by extremely small equilateral triangular planes, as in Fig. 48.
In these crystals, it is very common to find the decrease of the
laminae evidently indicated by strise.

The fourth form, is a rectangular tetraedral prism, terminated
by two pyramids, also tetraedral, which are situated upon the
sides of the prism, and have equilateral triangular planes. This
crystal is produced merely by the edges of the base of the oc-
taedron being replaced ; which replacement separates the two
pyramids, by a prism more or less elongated. There are some
crystals in which this prism is pretty long, as in Fig. 49 ; others
in which it is, on the contrary, very short, as in Fig. 50.

Although the Abb6 H.\uy has described the cuneiform oc-
taedron, I think it right to add to his description, that, in this
variety, the separation of the two opposite faces in each of the
pyramids, becomes sometimes so considerable, that the crystal
thereby changes its appearance, and acquires that of a rhom-
boidal tetraedral prism, of 1 09° 30', and 70° 30'. This prism is
terminated by two diedral summits, with isosceles triangular

3o8 Count de Bournon's Description of

planes, the apices of which are situated upon those edges of the
prism which measure 70° 30', making with them an angle of
125° 15', and meeting, by their bases, at the top of the crystal,
in an angle of 109° 30', as in Fig. 51.*

I also think it right to add, to what the Abb6 Hauy has said
respecting the colours of this substance, that it is sometimes
perfectly colourless, sometimes of a yellow colour, and some-
times of a bluish one.

We w^ere as completely ignorant of the nature of the stone
which serves as a matrix to the spinelle, as we were respecting
that of the matrix of the perfect corundum of Ceylon, when a
number of specimens were sent from India to Sir John St.
AuBYN, by Mr. White, amongst which were two pieces of the
highest value, inasmuch as they served to show us, for the first
time, the substance now treated of, inclosed in its matrix, I
flatter myself a description of these two pieces will be thought
worthy the attention of the Royal Society, particularly as they
also contain a species of iron ore hitherto unknown.

One of these pieces is a calcareous spar, of a granulated
texture; the grains are very large, and are intermixed with
each other, so as to adhere very strongly together, but their

* The dodecaedron, and the octaedron passing very rapidly to the tetraedron, had
ah-eady been mentioned by Mr. Eslinger, (Journal de Physique, Vol. LII. p. 225,)
as making part of the collection of crystals of this substance in Mr. Werner's
possession : the other varieties had not yet been described. According to some of the
external characters by which Mr. Eslinger describes the spinelle, I am inclined to
think, that he includes some Ceylanites in that description, and also some oriental
rubies. Such, for instance, I suspect to be, that which he says has a starry reflection;
also the hexagonal prism with the alternate angles of the base replaced ; and the cube,
(without doubt, slightly rhomboidal,) which has a small plane upon two of its solid
angles diagonally opposite to each other: a form that is very rarely met with, even in
the oriental ruby.

the Corundum Stone, and its Farieties, &c. 309

fracture shows that they are very evidently laminated. In tlie
substance of this spar are contained a great number of small
prismatic crystals of mica, of a beautiful yellow colour, like
that of the topaz ; they have also the lustre, and the transpa-
rency, of that precious stone, for which they might the more
easily be mistaken, as several of them, which show the sides of
their prisms on the exterior part of the stone, appear to have
their surface slightly rounded.* Very thin lamince may without
difficulty be detached from the terminal faces of the crystals ;
these lamina are perfectly elastic.

There are also, in this calcareous spar, small pieces of a
metallic substance, which deserves to be particularly described.

The colour of this substance is gray, slightly inclining to red,
so as very much to resemble that of arsenical cobalt, or of nickel.
The substance is very brittle; the slightest blow breaks it; and
it may, by a moderate degree of pressure, be reduced into a
black powder. Its fracture is conchoid, with a very fine and
compact grain ; and it has a very brilliant lustre. The magnet

* All the authors who have treated of mica, say that it is transparent only when ia
very thin lamins. This is a mistake. When the crystals of this substance are in as
perfect a state as they possibly can be, that is to say, when their crystalline lamin» are
in complete contact with each other throughout the whole extent of their surface, (a
circumstance very uncommon, but which is known by the sides of their prisms being
perfectly smooth,) they are usually transparent. I have seen crystals of mica, of a pretty
considerable thickness, which were perfectly transparent, in whatever direction they
were viewed ; although sometimes such crystals, when their terminal faces have a very
shining silvery lustre, (which shows that they reflect all the light that falls upon
them.) have not the smallest transparency, when viewed in a direction perpendicular
to their axis ; many of them, however, appear transparent, when viewed through the
edges of the lamina;, that is to say, in a direction parallel to that of their axis. The
above is not the only mistake that has been made with respect to tliis substance ;
a correct description of which, I hope, some time hence, to be able to lay before the
Royal Society.

MDCCCII. S S

gio Count de Bournon's Description of

acts upon it, very nearly as strongly as it does upon iron in a
perfectly metallic state. When this substance is immersed in
nitric acid, no effervescence takes place. By means of a file, or
merely by the blade of a knife, a black powder may easily be
obtained from it, without in the least diminishing the lustre of
the part from which it is taken. If a magnet be brought near
this powder, it is instantly attracted by it. Those parts of this
substance which appear to have been exposed for any length of
time to the contact of the air, are become of a black colour.

I know no other metallic ore whose exterior characters are
analogous to those I have just described; and I very much
regret that the scarcity and the consequent value of this speci-
men, as well as of that about to be described, prevent their
being made use of for the purpose of an analysis, the result of
which it would be so desirable to be acquainted with. If,
without such analysis, I might be permitted to form an opinion
respecting this substance, I should be much inclined to consider
it as a martial pyrites, or sulphuret of iron ; but in which the
iron, in a metallic state, is combined with a much smaller quan-
tity of sulphur than in common pyrites ; some small traces
of the latter, however, may be perceived in this specimen, by
the side of the metallic substance above described."*

In this same calcareous spar may also be observed, small
crystals of a greenish colour, which have hexaedral prisms;
they are of very inconsiderable hardness. I believe they belong
to that particular species of phosphate of lime, which the Ger-
mans have distinguished by the name of spargelstein,

• Since the above was written, I gave a Few grains of this substance to Mr.
Chenevix ; who, from that small quantity, was able to determine that it contained
nothing but iron and sulphur.

the Corundum Stone, and its Varieties, &c. 311

But, what renders the specimen I am now describing, in the
highest degree interesting, is, that there are some perfectly well
formed octaedral crystals of spinelle, of a pale purplish red
colour, inclosed therein. Here then we have a fair and unques-
tionable instance of the spinelle within its matrix: we shall
however see presently, that the nature of this matrix is not
constantly the same.

The second of the two pieces I have mentioned above, as
being the matrix of the spinelle, is a mass of adularia, of a
grayish white colour, about six inches in length, and of a pro-
portionate thickness. This adularia is tolerably pure, in one half
of the piece ; but, in the other half, it is mixed with particles
(much more considerable in size, and in much greater propor-
tion than in the preceding piece,) of the very brittle and very
attractable metallic substance already described. There may
also be observed in it, some small pieces of a substance of a
brownish green colour, but which becomes grayish when
scraped ; this substance, which is by no means hard, appears to
me to be of the nature of steatite. If this specimen is moved
about in a very strong light, there may be perceived in it, here
and there, small particles, which have a silvery appearance, and
which are rendered very evident, by their laminae being in a
direction contrary to those of the adularia which is near them.
I consider these small pieces as belonging to the kind of felspar
I have already described, and mentioned as being found in the
sand of Ceylon which contained the perfect corundum and the
spinelle, and as frequently reflecting a beautiful deep sapphire
blue colour. This specimen contains fewer crystals of spinelle
than the preceding one ; sotne, however, may be perceived in it.
It seems also to contain particles of calcareous earth, which

S s 2

318 Count de Bournon's Description of

appear to be situated between the lamirice of felspar ; at least, if
a piece of it be broken oW, and put into nitric acid, a slight effer-
vescence is produced, which however is but momentary. These
particles are most numerous, at those parts where the felspar
and the metallic substance already described come into contact
with each other.

I have placed a specimen of each of these stones in Mr,
Greville's collection.

Notwithstanding there is a considerable difference in the na-
ture of the matter which may be considered as the basis of these
two pieces, yet the particular nature of the substances contained
in them, which are perfectly similar to each other, seems to
render it highly probable that the place of their origin was the
same. But it also appears jDrobable, from every circumstance
respecting these stones, that they must iiave come, not from a
mass of rock of the same nature as themselves, but Irom some
veins, to the destruction of which may also very likely be owing
the great quantity of spinelles contained in the sands of certain
rivers of Ceylon. Would it be hazarding too much, to suppose
that the crystals of perfect corundum which are found in this
sand have also the same origin; and that (being much more
rarely met with, and in much less quantity,) they have only
a partial existence, or one that is confined to certain parts of
the veins already spoken of. The small portions of felspar, and
also of calcareous spar, which are sometimes, although very
rarely, found in this sand, (perhaps because the sand has been
already freed from such substances,) tends to suppoit the sup-
position I have just made, namely, that these two substances
are a mong those which compose the real matrix of the stones
here treated of.

the Conindum Stone, and its Varieties, Sec. 313

Tourmalin. Tliis substance is also frequently found in the
sand of Ceylon : indeed it is in this sand that the most per-
fect crystals of tourmalin, the most transparent, and the most
various in colour, are generally found. It is certainly to be la-
mented, that these crystals are seldom of any considerable size ;
but that defect is compensated by the perfection and regularity
of their form. Among these, I have found two in particular, of
which, as they have not hitherto been noticed, I think it right
to give a description.

The first of these forms, is the very obtuse rhomboid which
is represented in Fig. 52, and is the primitive crystal of this
substance. The Abbe Hauy, who also thinks that this rhom-
boid is really the primitive form of this substance, appears not
yet to have met with it ; for he has not placed it at the head
of the description of tourmahn given in his mineralogy, as he
has done with respect to the other substances of which he has
observed the primitive form. It is indeed very scarce. I have,
however, met with it several times ; and have placed a very fine
specimen of it in Sir John St. Aubyn's collection. This crystal,
which is about four lines in diameter, and nearly two lines in
thickness, is of a brown colour with a tinge of orange; it is
also pretty transparent, even in the direction of its axis. Its
form is perfectly well defined ; and the two pyramids, of which
its rhomboid may be considered to be formed, are exactly similar
to each other; neither of them having any supernumerary
facets.

I th.ink it right here to observe, that there appears to me to
have been an error committed, with regard to the measures that
have been given as those belonging to the primitive crystal of
the tourmalin. The Abbe Hauy fixes the measure of the solid

314) Count de Bournon's Description of

angle of the summit of the pyramid at 136* 54' 4.1". RoMEf
DE Lisle's measure is nearly the same, namely, 137'. I have
measured this angle with more than usual care, (on account of
my not agreeing with these two celebrated naturalists,) having
taken the precaution of using several different goniometers, and
I have constantly found it to be 139°; which would make the
angles of the rhombic planes 114= 12', and 65" 48', instead of
1 13° 34' 41", and 66" 25' 19", as stated by the Abb6 Hauy.

The second of the forms abovementioned is a prism, either
hexaedra],enneaedral, or dodecaedral, of which the terminal faces
are perpendicular to the axis. This variety is produced in the
following manner, viz. the plane that has replaced the solid
angle of the summit of the pyramid, (which plane is represented
by the Abb6 Hauy in Figs, 119 and 120, Plate LII. of his
Mineralogy,) has acquired an increase of sufficient extent to
cause the planes of the pyramid entirely to disappear.

I think it right to add here, a variety of this substance, which
also comes from Ceylon, and has not yet been described, namely,
a prism which has become of a triedral form, with equilateral
bases, by the enlargement of the planes that have replaced the
three alternate edges ; the formation of which planes is known
to change tlie hexaedral prism into an enneaedral one ; and the
enlargement is such as to cause the six others entirely to disap-
pear. The tourmalins of Ceylon are not the only ones in which
I have observed this triedral prism: I have also met with it
among the tourmalins of Saxony, and among those of Bohemia.

Lastly, I shall add, as forms not yet described, (although
they do not belong to tourmalins of Ceylon,) two complete
triedral pyramids, which, if they were not separated by an inter-
mediate prism, would produce two secondary rlwmboids, the

the Corundum Stone, and its Varieties, &c. 315

one more acute, the other more obtuse, than the primitive
rhomboid.

The first of these pyramids, is the natural produce of the in-
crease of the planes which have replaced the acute angles of the
rhombic planes of the primitive crystal : these planes are repre-
sented at the letter 0, in Figs. 114, 115, 116, and 121, Plate LII.
of the Mineralogy lately published by the Abbe Hauy. This
learned mineralogist has indeed represented a considerable in-
crease, but not a complete one, of the above-mentioned planes,
in Fig. 121, which he says was communicated to him by Mr.
La Metherie. From the appearance of this form. I think it
probably belongs to the tourmalins of Regeiisberg, in the Upper
Palatinate; for many crystals of tourmalin from that place ex-
hibit, at one of their extremities, the pyramid represented at Fig.
121 of the work just mentioned, and the pyramid I have Iiere
described, at the other. This triedral pyramid measures 107°, at
the solid angle of its summit.

The second of tlie pyramids, is produced by the increase
of tiie planes which have replaced the edges of the pyramids
of the primitive rhomboid : these planes are represented by the
Abb6 Hauy at letter n, in Figs. 118, 119, and 120, also of
Plate LII. The triedral pyramid which these planes produce,
after having caused every trace of the planes of the primitive
rhomboid entirely to disappear, has, very nearly, 159° for
the measure of the solid angle of its summit. 1 have seen
this variety among the tourmalins from the Ural mountains, in
which, very often, the solid angle of their summit is replaced by
a plane, of greater or less extent, which is perpendicular to
their axis.

Among the various colours exhibited by the tourmalins which

3it» Count de Bournon's Description of

are found in the sand of Ceylon, there are three which deserve
notice, because they have not yet beeri mentioned by any author ;
these are, a hght yellow, like the colour of honey, a beautiful
clear emerald green, and a red slightly inclining to purple. The
green variety, which indeed might easily lead to a false idea of
the stone, is, most probably, what has caused some authors to
mention the true emerald as being indigenous to Ceylon, where,
hitherto, no trace of that stone appears to have been met with.
This error was the more likely to be committed, as it was not
then known that the regular hexaedral prism, with terminal
faces perpendicular to the axis, was one of the crystalline forms
belonging to the tourmalin ; and that tourmalins of a beautiful
emerald green colour, and perfectly transparent, were sometimes
met with of that form, I have placed some very pretty small
crystals of this kind in Mr. Greville's collection.

The tourmalin of a purplish red colour, found in the sand of
Ceylon, is exactly similar to that of Siberia, to which the names
of nibellite, of daourite, and of Siberite, have been successively
given, and which the Abb6 Hauy has ultimately distinguished
by the name of apyrous tourmalin. Its form is precisely the
same as that of the tourmalin, properly so called ; nor does the
measure of its angles exhibit any difference ; especially if that
measure is taken upon crystals which are of a perfectly deter-
mined form, and which have not, upon their pyramidal planes,
any aggregation that can cause a change in the form of those
planes. I have placed in Mr. Greville's collection, a small
group of this kind of tourmalin, from Ceylon, the colour of
which is a beautiful red ; among its crystals, which have triedral
pyramids with rhombic planes, may be observed one that has
a dodecaedral prism, with its terminal faces perpendicular to its

the Corundum Stone, and its Varieties, &c. 317

axis. In Sir John St. Aubyn's collection, I have placed a de-
tached crystal, which has also a dodecaedral prism; one of the
extremities of this crystal is of a green colour.*
- Lastly, I have, in this same sand, met with a crystal, per-
fectly colourless, the prism of which is completely triedral;

* The scarcity of the red tourmalin of Siberia, which hitherto has been known only
by very small specimens, for which the dealers demand an extraordinary price, seems
to be what has hitherto prevented naturalists from forming a decided opinion respecting
its proper place in the system of minerals. I am therefore happy in announcing, that
there is in Mr. Greville's collection, a specimen of this kind of tourmalin, (from
India,) the size and perfection of which are truly admirable. This specimen, which is
not accompanied with any kind of matrix, is nearly as large as a man's head ; and is
entirely composed of crystals placed by the side of each other, in a diverging form, or
rather penetrating each other at one of their extremities, and separating or diverging
a little at the other extremity. Every one of these crystals, most of which are as long
as the height of the specimen, is nearly as thick as the little finger. Their form is a
hexaedral prism, which is deeply striated, and terminated by a triedral pyramid with
rhombic planes, the angles of which, measure exactly the same as those of the corres-
ponding pyramid in the common tourmalin. All the crystals are pretty transparent ;
and terminate on the top of the specimen, by the forementioned pyramids, but at dif-
ferent heights; a circumstance that gives to the top also a triedral pyramidal form,
but much less obtuse than that belonging to each crystal of which it is composed.
The greatest part of this specimen is of a pale purplish red, or flesh colour; but, to-
wards the base, this colour grows much more deep, so that, at last, it becomes abso-
lutely black. I have observed the same division of colour, in specimens of this red
tourmalin from Siberia.

The superb specimen here described was brought from the kingdom of Ava: it was
given by the sovereign of that country, as a present of very great value, to Colonel
Symes, who was sent on an embassy to him, by the English government. Colonel
Symes placed it in Mr. Greville's collection; and he could not possibly make a
better use of it ; that collection being, in my opinion, one of tTie finest in Europe,
with respect to the beauty of the specimens and the instructive series of each sub-
stance which composes it, and certainly superior to all others, with respect to precious
stones in a state of perfect crystallization.

The Abbe Hauy, in his Mineralogy, expresses a wish, that the prismit'c enneae-
dral form, terminated by the triedral pyramid of the primitive rhomboid, (which he

MDCCCII. T t

3i8 Count de Bournon's Description of

and the pyramidal planes of which, in the only extremity of
the crystal that remains, are situated upon the edges of the
prism.

Ceylanite. The stone called Ceylanite, by Mr. La Metherie,
who is the first author that has considered it as a particular and
distinct species, (distinguished by the name of pleonaste, in the
Mineralogy of the Abbe Hauy,) is also sometimes found in the
sand of Ceylon ; it is, however, in general, by no means com-
mon. Of the crystals of this substance that I have collected
from this sand, many are perfectly transparent; a character
which appears to have been hitherto unobserved in it. Its
colours are very various. Besides black and green, which have
already been mentioned by authors, I have seen it of a reddish
or flesh colour, with a yellowish cast; of a fine bluish green,
like the aqua marine ; and of a fine sky blue, rather pale. When
the Ceylanite is of the last-mentioned colour, whether it be a frag-
ment or a flattened octaedron, it might very easily be mistaken
for a sapphire. Its most usual colour is a brownish green.

As this substance has, in all its external characters, a striking
resemblance to the spinelle, of which it is perhaps only a species,
I think I cannot be too particular in pointing out those cha-
racters which may in some measure serve to distinguish it ; I
shall therefore add, that its hardness is rather inferior to thatof the
spinelle, the Ceylanite being scratched by the spinelle, while the
latter cannot be scratched by the Ceylanite; also, that it usually
exhibits, by irregular stuse, parallel to the edges of the regular

calls isogone,) may be met with in this substance, in order to determine its nature.
He will no doubt feel satisfaction in hearing, that there exists, in the collection of Sir
John St. Aubyn, a small detached crystal of this substance, of a fine red colour,
which has exactly the above-mentioned form. This crystal I found in the sand of Ceylon.

the Corundum Stojie, and its Varieties, Sec. 319

octaedron, its primitive crystal, a tendency to the replacing of
all those edges ; an appearance which is very common in the
octaedron of the diamond, I shall remark also, that the surface
of its crystals has generally less lustre than is commonly ob-
served in the crystals of spinelle, ,

The desire of contributing every thing in my power, to render
as complete as possible our knowledge respecting this substance,
which has been but lately known to mineralogists, induces me
to add to the variety of forms that have been described by the
Abb6 Hauy, those I'epresented in Figs, gg and 54, although
the Ceylanite to which those figures belong comes from a dif-
ferent place. The first is nothing more than the modification
represented by the Abb^ Hauy in Fig. 104, Plate L, of his
work, but in which the four planes that have replaced each of
the solid angles of the octaedron, are situated upon these same
angles, in the primitive crystal itself, instead of being situated
upon the planes that have replac-ed the edges. I have fre-
quently seen these planes encroach upon each other, to such a
degree as to render it very probable that there exists, in the
Ceylanite, that form of crystal which consists of 24 trapezoidal
facets, and which, by its derivation from the cube, the regular
octaedron, and the regular dodecaedron, is already so very com-
mon in crystallography.

The second of the forms just spoken of, (Fig. 54.) is the
same variety, but with a very slight replacement of the edges
of the octaedron : it is the beginning of the change to the above-
mentioned Fig. 104, of the Abb^ Hauy. These two varieties
belong to the Ceylanite which is inclosed in pieces of stone
brought from Somma; and are indeed the most common

Tt 2

320 Count de Bournon's Description of

varieties found in them, except tliat in which the edges only
are replaced.

Zircon. This substance is, next to the spinelie, that which is
most frequently found in the sand of Ceylon. It is true, that it
is generally in crystals of a very small size ; but these crystals
often possess the most beautiful transparency, and they are of
many different colours. To the colours already mentioned as
belonging to them, I may add, that they are sometimes of a
reddish purple, and sometimes of a pale blue.

Lastly, if to the substances which have already been described,
I add, that there are also some small scattered fragments, but
in very inconsiderable quantity, of quartz, of felspar, of calca-
reous spar, of a brownish yellow mica, and of attractable oxide
of iron, I shall have enumerated all the substances that are
found in the sand of Ceylon, in the state in which it is sent
to us. I have always been astonished at not finding in it any
of the peridot, which, as is well known, also comes from
Ceylon : hitherto, however, I have not perceived the smallest
trace of it.

Of the various substances that have been here described, the
spinelie is that which more particularly constitutes the sand of
Ceylon, such as it comes into Europe; but it is natural to
suppose, as I have already had occasion to observe, that the sand
has been previously examined, and deprived of every substance,
except those which are found by experience to be fit for the
purposes of commerce. The other substances above mentioned,
are not so constantly found in it, nor are they found ahvays
in any regular proportion. I have seen, for instance, some
of this sand which did not contain an atom of perfect corun-

the Corundum Stone, a?id its Varieties, &c. 321

dum; other parcels which contained only a very small quan-
tity ; and others in which the proportion of that substance was
pretty considerable : the same remark may be applied to every
one of the other substances. It is therefore, I think, fair to
conclude, from the above circumstances, that these sands come
from different rivers or rivulets, or, if from one river only, from
one into which other rivers discharge themselves ; and that the
nature of the sand varies, according to the particular circum-
stances which may have caused one or more of those rivers to
bring down a greater, and others a less proportion, of the sub-
stances of which it consists. It may indeed also be asked, if what
is called the sand of Ceylon comes exclusively from that island ?
To this question, I can give no decisive answer. I shall only
observe, that the length of time it has gone under that deno-
mination, without any alteration, gives some reason for thinking
it has really some claim to it.

It is, at this time^ a doubtful point, whether corundum is found
in any part of the world, besides certain districts of the East
Indies ; although, as will presently be seen, I have strong
reasons for thinking that it also exists in one of the mountain-
ous provinces of France,

I have seen many specimens which were sent from Ger-
many, under the name of corundum ; some of them were nothing
more than felspar of a brownish red colour ; others were the
stone called schorlartiger beryl, by Werner, {^xhe pycnite of the
Abbe Hauy,) but in p.eces which were rather less striated than
is usually the case with respect to that stone.

It was thought, for some time, that a stone found at Tiree, on
the eastern coast of Scotland, was of the nature of corundum.

322 Count de Bournon's Description of

But, after examining a specimen of that stone, which is in the
British Museum, I found that its hardness, and its specific gravity,
were both very inferior to those of corundum. In its exterior
appearance, it very much resembles the felspar that accompanies
the imperfect corundum from the Carnatic, and which I have
already described, when speaking of the substances which ac-
company that kind of corundum in its matrix.

It is also said that corundum has been found in America, at
Chesnut Hill, near Philadelphia. But there are, in the Philo-
sophical Magazine, No. 45, for February last, some observations
made by Mr. Richard Philips, upon the external characters
of the American stone, intended to show that it cannot pos-
sibly be corundum. Mr. Philips has since told me, that the
specimen upon which his observations were founded, was sent
to him directly from Philadelphia, as a piece of the corundum
found near that city. He also recalled to my mind, (which
I had entirely forgot,) that he had shown me the specimen
some time before ; and that I then gave it as my opinion, that
the crystal it contained, supposed to be corundum, was nothing
more than an ill-deiined crystal of quartz. Nevertheless, Mr.
Smith, a well-informed mineralogist, from America, has since
assured me of the truth of the discovery of corundum, in the
neighbourhood of Philadelphia. In that case, there must have
been some mistake respecting the specimen that was sent to Mr.
Philips. Upon the whole, there still remains some uncertainty
with regard to the existence of corundum in the neighbourhood
of Philadelphia ; and it is necessary, in order to remove all doubt
on this head, either that some of the substiance should be sent
to us, or that some mineralogist in that country should give

the Corundwn Stone, and its Varieties, &c. 323

such an accurate description of its characters as may serve
to ascertain its real nature.

It remains for me to speak of the corundum I formerly
found, or at least thought I found, in Forez, in the mountainous
parts of that province which are near Montbrison. I find, by
the Mineralogy of the Abbe Hauy, (Vol. IV. p. 362.) that the
substance I had considered as corundum, is now looked upon
in France to be of a different nature. That learned mineralo-
gist, in the abovementioned work, seems inclined to consider
it as a species of felspar, and gives it the name of apyrous
felspar. He admits however, at the same time, that it scratches
quartz; that its specific gravity is 3165; and that it is infusible
by means of the blowpipe. All these characters seem to place
it at a considerable distance from felspar.

The total loss of a very considerable collection of minerals,
intended expressly for the purposes of study, (and which I
regret the more from its having been entirely formed, and most
of the specimens collected in their native places, by my own
hands,) leaving me no objects of comparison, I can only consult,
with regard to the above substance, the few notes I have been so
fortunate as to preserve, assisting them with such circumstances
as my memory has been able to retain.

I find in my notes.

First, That this substance was inclosed in a yellowish felspar,
which formed a small vein in a granite rock ; that, in some
parts of the felspar, it appeared in the form of small spots,
easily distinguishable by their colour, which was red with a
purplish tinge; and that, in other parts, it was in masses of
a rather larger size, from which I w^as able to extract some
fragments.

g24 Count de Bournon's Description of

Secondly, That the appearance of this substance was entirely
different from that of felspar ; and that, where it came in contact
with the felspar, it seemed to mix itself with it in such an in-
sensible manner, that, after having sawed and polished a piece
composed partly of felspar and partly of the substance here
spoken of, it was impossible, by the eye, to distinguish exactly
where the felspar began, or, which is the same thing, where the
other substance terminated.

Thirdly, I find also by my notes, that the pieces I had col-
lected, varied considerably in their degree of hardness, although
all of them were harder than felspar usually is ; for many
of these pieces would scarcely scratch felspar ; whereas others
could scarcely be scratched by the greatest number of gems
or precious stones. The characters of the last mentioned or
hardest pieces, appeared to me to be very similar to those of
the imperfect corundum from China, a crystal of which Rome'
DE Lisle had sent me a short time before. The above obser-
vations, joined to the remarkable manner in which this sub-
stance is mixed with felspar, made me adopt the erroneous
opinion mentioned by the Abb6 Hauy, in his observations upon
corundum, namely, that this substance might be nothing more
than a more dense variety of felspar. I soon, however, entirely
gave up this idea, after I had it in my power to examine more
particularly the nature of corundum.

Fourthly, and lastly, I find by my notes, (and I also remem-
ber it perfectly well,) that among the pieces I was able, by pa-
tiently and carefully using the tools employed for that purpose
by mineralogists, to extract from the vein above mentioned,
there were some to which adhered small irregularly shaped
pieces of a substance that was perfectly transparent, and had

the Corwidion S/oue, and its Varieties, &c. 325

a fine sapphire blue colour. Tlie hardness of this substance
was such as to be equalled onlv by that of the sapphire itself;
and, in some of the pieces, instead of adiierinj^ to the outside,
it was dispersed, in very small particles, within the interior
part.

As I cannot, even at this time, consider this blue substance
as any thing else than the blue perfect corundum known by the
name of sapphire, I still retain the opinion I formerly thought it
right to adopt, namely, that the substance to which it adhered,
and whicli I found in the province of Forez, was really a kind of
corundum. I still think also, that the variety I observed in the
degree of hardness, and in the specific gravity, of different pieces,
was owing to their being mixed, in various proportions, with
felspar. If it should happen that, among the remains of a col-
lection of which nothing is left to me but a painful remembrance,
(although, as I have before said, my present situation is such as
much alleviates m}' regret,) any of the specimens above spoken
of still exist, and should fall into the hands of well informed
naturalists, I hope they will let them serve as a basis for fresh
observations. The description of the Abbe Hauy is alone suf-
ficient to show, that the above substance cannot possibly be a
kind of felspar. I am sorry, however, that he did not join to his
description, the analysis of the substance; it certainly would
have been very interesting, particularly if, as would most pro-
bably have been the case, the hardest pieces had been selected
for that purpose.

The great difference sometimes observed in different speci-
mens of the same substance, is exhibited in a very striking
manner, in the emeralds which I found, at the same period, in
a large vein of the fore-mentioned rock, but which was situated

MDCCCII. U u

326" Count de Bournon's Description, &c.

in the part of tlie rock opposite to that wherein I discovered the
bhie substance ah-eady described. The Abbc^ Hauy, in his Mi-
neralogy, (Vol. IV. page 361,) mentions these emeralds, but
expresses some doubts respecting them. These doubts I think
would be removed, if I had it in my power to send him the
specimens I then collected. Among them were some crystals,
which possessed a degree of hardness fully equal to tliat which
is known to belong to the emerald : the hardness of many others
was, however, very inferior; owing no doubt to the interposition
of some heterogeneous substance, which I always suspected to
be of a magnesian nature.

The Khh€ Hauy, in order to fix his opinion respecting this
substance, appears to require nothing but to see some crystals
of it which possess the additional facets peculiar to the true
emerald. I cannot indeed shew him such crystals; but I can
supply the want of them, not only b}^ my notes, but also by
models cut in wood, which I was so fortunate as to bring away
with me, as well as the whole collection of models of which
they form a part. I find, among the models I made of these
emeralds from Forez, all the varieties the Abbe Hauy has re-
presented in Plate XLV. of his work, excepting only Fig. 50,
of that Plate.

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X. Analysis of Coninclum, mid of some of the Substances zvbicb
accompany it; zvith Observations on the Affinities xvhich the
Ea7'ths have been supposed to have for each other, in the humid
JFay. By Richard Chenevix, Esq. F. R. S. and M. R. I. A.

Read May 20, 1802.

§ I.

iSoME kinds of corundum, such as the adamantine spar of
China, and the sapphire, have already been analyzed by Mr.
Klaproth. This wou!d have rendered any further experiments
unnecessary, were it not, that I have had at my disposal many
kinds of corundum he did not possess, and also some substances
accompanying it, which were unknown before the preceding
communication of the Count de Bournon.

As, from the result of my analyses, it appears that all the
different kinds of corundum are nearly similar in their consti-
tuent parts, and differ only in their proportions, it would be
tedious to mention every experiment I made upon each kind.
I shall therefore confine myself to stating, once for all, such
modes of analysis as were employed with stones of a similar
nature; and then present a summary of the results: lastl}', I
shall conclude with an enquiry into a much contested point,
which lately threatened a revolution in docimastic chemistry.

A principal character of corundum in general, as may be
found in the Count de Bournon's mineralogical description, is

Uu 2

328 Mr. Chenevix's A^ialysis of Corundum, and of

extreme hardness ; and thence, the difficulty of reducing that
substance into fine powder will be easily conceived. We are told
by docimastic chemists, that the most advantageous method of
pulverizing hard stones, is to make them red hot ; and, in that
state, to plunge them into cold water. But I found that this
operation, when performed but once, was by no means sufficient
for corundum. I therefore repeated it, till the stone appeared to
be fissured in every direction. After this, the specimen to be
pulverized was put into a steel mortar, about three-fourths of
an inch in diameter, and tiu^ee inches in depth, into which a
steel pestle was very closely adjusted. A few blows upon the
pestle caused the stone to crumble; and the fragments were
then easily reduced into an impalpable powder, in an agate
mortar, with a pestle of the same material. The abrasion from
the mortar, usual in the pulverization of hard stones, was much
diminished by the above precaution ; rubies and sapphires being,
in a short time, ground to a powder nearly as minute as the finest
precipitate.

Mr. Klaproth, in his analysis before mentioned, had ob-
served with how much difficulty the stones were acted upon by
potash or soda. I found that tlie greatest heat a silver crucible
could support, without melting, was not sufficient to produce
a satisfactory fusion of one part of corundum, with six parts of
either of those alkalis ; nor did an exposure to that tempera-
ture during several hours, seem to render the treatment more
effectual. Not more than half the quantity of the corundum
was ever rendered soluble in any acid ; and what remained was
the powder of the stone, wholly unchanged. The repeated
filtrations and evaporations with which this treatment must
be attended, not only render it tedious, but also produce

some of the Substances which accompany it, &c. 329

uncertainty in the results. Even when very finely powdered
corundum was exposed, with six times its weight of potash, in
a platina crucible, to a heat of 140° of Wedgwood, for two hours
together, it was not acted upon in such a manner as to be fit
for analysis. From all these experiments I concluded, that some
more efficacious mode of rendering corundum soluble in acids
was to be sought,

I boiled a great quantity of sulphuric acid upon very finely
powdered corundum, in a platina crucible. But, although the
acid, after a great length of time, had dissolved a little of the
stone, I did not fi:nd this method more satisfactory than the others.
Nitric, muriatic, and nitro-muriatic acids, were less effectual than
the sulphuric. Phosphoric acid, held in fusion with corundum,
did not dissolve any notable portion of that stone, or render it
soluble in other acids.

I then had recourse to sub-borate of soda, (borax,) which I
found to answer beyond my expectation. Two parts of that salt,
calcined, and one of corundum, enter into fusion, at a tem-
perature which I judged to be about 80° of Wedgwood ;* and
a glass, more or less coloured, is formed. This glass is soluble
in muriatic acid ; and, by this method, it is easy to obtain a
complete solution of corundum. My general method of ope-
rating was as follows,

I took one hundred grains of corundum ; and, having several
times made it red hot, and plunged it into cold water, I put it
into the steel mortar, and treated it as already mentioned. I
then poured some very dilute muriatic acid upon it, to wash off^
whatever iron might have adhered, in consequence of its me-
chanical action upon the mortar. After it was dried and weigh.ed,
• I have no doubt that a lower temperature would be sufficient.

O'

330 Mr. Chenevix's Analysis of Corundum, and of

I put it into the agate mortar, and ground it as fine as I could.
The augmentation of weight was then noted ; and was always
taken into account in the general result. I then put the whole
into a platina crucible, with 200 grains of calcined sub-borate
of soda, and exposed the mixture for an hour or two to a
violent heat. When the crucible was cool, muriatic acid was
boiled upon it and its contents ; and, in about twelve hours, all
the glass disappeared. If I wished to obtain the silica directly, I
evaporated the whole to dryness ; but, if otherwise, I precipi-
tated by an alkaline carbonate, and washed the precipitate, in
order to get rid of all the salts contained in the liquor. This
latter mode I believe to be preferable. I then re-dissolved the
precipitate in muriatic acid, and evaporated for silica. But, as
corundum contains only a small portion of this earth, there was
little or no appearance of jelly. When the silica was thus pre-
cipitated by evaporation, I filtered the liquor, and boiled it with
an excess of potash. By this operation, the alumina was preci-
pitated, and then re-dissolved by the excess of potash, from
which it was finally obtained by muriate of ammonia ; the iron
which had remained undissolved by the potash, having of course
been previously separated from the alumina. This earth, and
the silica, after being washed and dried, were ignited, and thus
the w-eight of both was obtained.

I shall exemplify, in a single instance, this mode of treat-
ment; and then present the results obtained from the different
kinds of corundum. For this purpose, I shall select the blue
perfect corundum, or sapphire, as the stone which has been the
most ably analyzed by Mr. Klaproth. From a view of both
analyses, the efficacy of the fusion with borax will be evident;
and the results of the several experiments may be compared.

some of the Substances which accompany it, &c. 331

1. 100 grains of sapphire, pulverized in the agate mortar, as
above stated, had increased to 105. These 105 were mixed
with 250 of calcined sub-borate of soda, and put into a platina
crucible. They were then exposed to a violent heat fur two
hours, and afterwards allowed to cool. The mass was vitrified,
and had the appearance of a greenish blue glass, fissured in
many directions.

s. This glass being strongly attached to the platina crucible,
the whole was put into muriatic acid, and boiled for some hours.
By these means, a total and limpid solution was obtained.

3. The matter of the stone was next precipitated, by ammonia
not entirely saturated with carbonic acid ; the liquor was filtered ;
and the precipitate well washed and dried. Lt was then redis-
solved in muriatic acid, and evaporated.

4. By this evaporation a precipitate was formed, which, when
well washed and ignited, weighed 10,25 grains, and was silica.

5. The liquor, together with that which had washed the pre-
cipitate, was boiled in a silver vessel, with an excess of potash ;
this redissolved all the precipitate, except one grain.

Q. Muriate of ammonia was poured into the alkaline solution.
(No. 5.) The potash expelled the ammonia from the muriatic
acid, and, forming muriate of potash, could no longer retain
the earth in solution ; a very copious precipitate, therefore, was
formed. This precipitate had all the properties of alumina ; and,
when well washed and ignited, weighed 92 grains. Conse-
quentl}^, deducting 5 from the silica, for the abrasion of the
mortar, we shall have for result,

Silica _ _ > _ ^,25

Alumina - - - - 92

Iron - - - - 1

Loss _ _ _ _ '^■,75

100,00.

33S Mr. Chenevix's Analysis of Corundum, and of

The chief difference between these proportions and those
estabhshed by Mr. Klaproth, is in the silica. That chemist
did not find any notable portion of it in the specimens he exa-
mined. This naturally induced me to make a very strict research,
into every possible means by which any silica might have been
introduced into the results ; whether by the borax, the alkali,
or any of the other re-agents I had used. But, finding very
clearly, that none of these substances did contain any, I could
no longer hesitate to believe, that the proportion I have here
stated, was actually contained in the sapphire I analyzed. I ara
likewise convinced, that no more than the quantity I have
mentioned was worn from the agate mortar and pestle; for my
constant practice was, to weigh them, both before and after I
liad used them, in scales which, when charged with four pounds
on each end, turn easily with the tenth part of a grain.

The general results, from all the different kinds of corundum,
were as follows.

Blue perfect Corundum, or
Sapphire.
Silica - - 5,25

Alumina - - 92
Iron - - - 1
Loss - . - 1,75

100,00.

Imperfect Corundutn from the

Carnatic.
Silica - - 5

Alumina - - 91
Iron - - 1,5

Loss - - 2,5

100,0.

Red perfect Corundum, or
Ruby.
Silica - - 7

Alumina - - 90

Iron - - 1,2

Loss - - 1,8

100,0.

Imperfect Corundum from
Malabar.
Silica
Alumina
Iron
Loss

7

4>
2,5

100,0.

some of the Substances which accompany it. Sec. 333

Imperfect Corundum from China.
Silica - - 5,25

Alumina - - 86,50
Iron - - 6,50

Loss - - 1j75

100,00.

Imperfect Corundum fro7n Ava.
Silica - - Gs

Alumina - - 87,0

Iron - - 4,5

Loss - - 2,0

100,0.

As I could not discover chrome, or any other colouring sub-
stance, except iron, in these stones, I can attribute their difference
of colour only to the different state of oxidizement of the iron ;
but it is impossible to ascertain what that state may be, from
so small a quantity.

The matrices of tiiese stones, and the substances accompa-
nying them, are more easily fused than the six kinds of corun-
dum just mentioned. The usual and well known mode of
treatment by potash, was sufficient to render these substances
soluble in the acids. Since the many experiments of Klaproth,
Vauquelin, and others, the mode of analyzing mineral bodies
is become so familiar to chemists, that I shall mention particu-
lars with respect to one only of the following substances.

MATRIX OF CORUNDUM FROM THE PENINSULA OF INDIA.

1. A certain quantity of this matrix was reduced to powder,
in the manner already described. 100 grains of it were treated
with potash, in a silver crucible: they then afforded a limpid
solution in muriatic acid. The liquor was evaporated ; and, long
before the mass was entirely dry, it had assumed the appearance
of a jelly. When the saline matter in the evaporating-dish was
dissolved in a slight excess of acid, a white powder remained at

MDCCCII. X X

334 ^^- Chenevix's A7ialysis of Corundum, and of

bottom, which liad all the properties of silica, and, w hen washed
and ignited, weighed 42,5 grains.

2. Into the liquor which had served to wash tlie above
powder, I poured ammonia. A copious precipitate v.as thus
formed, which was separated by filtration, and well washed.

3. Carbonate of potash also caused a precipitate in the liquor
of No. 2. This precipitate was found to be carbonate of lime,
and weighed 23,5 grains, = 15 of lime.

4. The precipitate of No. 2. was redissolved in muriatic acid ;
then boiled with an excess of potash, and filtered. There re-
mained undissolved, 3 grains, which were iron.

5. The liquor of No. 4. was precipitated by muriate of am-
monia, and afforded alumina ; which, being washed and ignited,
weighed Qy,^ grains.

I could also perceive a trace of manganese.

The proportions therefore are,

Silica - - - - 42,5

Alumina - - - - S7>5

Lime _ _ - - 15,0

Iron _ _ - - - 3,0

Loss, with a trace of manganese - 2,0

100,0.

By a similar treatment, the following substances, contained
in this matrix, afforded the under-mentioned results.

Felspar.

■ Silica - - - - 64

Alumina - - - - 24 ,

Lime . _ . - 6,25

Iron _ _ - - - 2,00

Loss - - - - 3'75

100,00.

some of the Substances xvhicb accompany it, &c, 33^

Fibrolite.

Silica - - - - 38

Alumina _ » _ 58,25

A trace of iron, and loss - - 3,75

100,00.
This is the only stone I have ever met with, that yielded
nothing but silica and alumina ; for the quantity of iron was so
small as hardly to be taken into account. I have repeated this
analysis three times ; and have not found a difference of half a
grain.

Thallite in Crystals, zvith a rough Surface.

Silica - - - - 45

Alumina - - - - 28

Lime - _ _ - 15

Iron - - - - - n

Loss _ _ _ _ 1

100.

Thallite in Prisms like the Tourmalin .

Silica - - - - 40

Alumina - - - 25

Lime _ _ _ _ 31^^

Iron - - - - - 11,5

Loss _ - _ _ 2

100,0.

Xx 2

336 Mr. Chenevix's Analysis of Corundum, and of _

Tballite in Fragments, of a fine transparent Tellow Colour.

Silica - - - - 42

Alumina - - « - 25^

Lime - . _ - 16

Iron - - - - - 14,

Loss _ _ _ _ 2,5

100,0.

Fibrolite accompayiying the Matrix of Corundum from China.

Silica _ . _ - 38

Alumina - - - - 46

Iron - - - - 13

Loss - - - " " 3

100.
Felspar from the Sand of Ceylon.
Silica - . . - 68,5

Alumina _ - - 20,5

Lime _ - _ _ 7

Iron - - - - - 1,5

Loss _ _ _ _ 2,5

100,0.
As the greater part of the above substances were fusible
without difficulty in potash, I preferred using a silver crucible to
any other. It may be laid down as a general rule, with respect to
delicate experiments, that in the treatment of metallic substances,
we should not use metallic crucibles ; but, in tlie treatment of
earthy bodies, they alone are to be depended upon. The easily
oxidizable metals cannot be employed ; but silver and platina
present advantages which no other metals seem to possess.

some of the Substances which accompany it, &c. 337

Theory would certainly give a general preference to platina,
from its resistance both to heat and to acids ; and practice will
justify this preference, in all but a single instance. If a quantity
of potash be kept for some time in fusion, in a platina crucible,
it will be found that the crucible has lost several grains of its
weight. The platina so dissolved may be looked for in the pot-
ash ; and, if this be saturated with muriatic acid, and evaporated,
we shall find the well-known triple salt, formed by tlie combi-
nation of muriatic acid with potash and oxide of platina. This
action of potash upon platina, does not depend upon any me-
chanical cause, such as friction, the force that determines it being
purely chemical. If a salt formed by potash, or a salt formed
by ammonia, be mixed with a salt of platina, a precipitate en-
sues, which is a triple salt ; and it is by this method, that the
Spanish government detects the platina, in the ingots of gold
sent from their American possessions. It is therefore evident,
that an affinity does exist between potash and platina, in a cer-
tain state ; and I imagine it to be this affinity, which causes the
oxidizement of the platina, when potash is kept in fusion upon
that metal. I must however observe, that my crucible was
prepared by Janetty, in Paris, according to a method he
has published in the Annales de Chimie ; and that he always
employs arsenic, a little of which certainly remains united
to the platina. What influence arsenic may have, remains to be
determined. Soda does not form a triple salt with the oxide of
platina ; for I have frequently kept this alkali in fusion, in a
platina crucible, for a long time ; yet very httle action was pro-
duced upon the metal. This fact seems to corroborate my
assertion, that the affinity of potash for oxide of platina, deter-
mines the oxidizement of the metal.

338 Mr. CiiENEVix's Analysis of Corundum, and of

Whenever I suspected that platina had been dissolved, I could
easily detect the smallest portion of" it. A solution of platina, so
dilute as to be nearly colourless, manifests, in a very short time,
the colour of a much more concentrate solution, and becomes
reddish, by the addition of a solution of tin in muriatic acid.
This I have found to be, by many degrees, the most sensible
test for platina ; and it would answer the purposes of the Spanish
government, much better than that they usually employ.

The alkalis have no immediate action upon silver ; but I have
observed, that crucibles of this metal, after they have been a
long time in use, become somewhat more brittle than they were
before.

Potash and soda have long been termed fixed alkalis ; and
it is certain that, if we compare them with ammonia, they are
so. Bxxl fixed is an absolute term, and cannot admit of degrees.
If potash, such as we obtain from Mr. Berthollet's method
of preparing it, be kept in fusion at a very strong heat, it may
be totally volatilized. The vapour of the alkali may be perceived
in the room; and vegetable colours will undergo the change
which is usually produced by alkalis. Indeed, in preparing Mr.
Berthollet's potash, the vapour of the alkali may be easily
perceived. Soda is not quite so volatile ; though far from being
fixed. It appears also, that a little water increases the volatility
of both potash and soda, as happens with boracic acid. This
volatility of potash, has been advantageously applied of late to
the art of bleaching.

some of the Substances which accompany it, &c. 339

§ n.

On the Affinities the Earths have been supposed to have for each
other, in the humid zvay.

In the course of the foregoing analysis, I had occasion to
make some further observations concerning a subject upon
which I had been formerly engaged, namely, on the affinities
the earths have been supposed to have for each other, when
held in solution by acid or alkaline menstrua.

In the XXVIIIth volume of the Annales de Chimie, page 189,
I published a paper upon the analysis of some magnesian stones.
In this paper, I took notice of the following affinities of the
earths for each other, namely, the affinity of alumina for mag-
nesia, of alumina for lime, and of alumina for silica. In the
XXXIst volume, page 246, there is a memoir, by Guyton de
MoRVEAUjUpon a similar subject;* and he there reports some
experiments of his own, by which he was induced to think,
that the earths do really possess a chemical attraction for one
another. Since that time, the affinity of the earths has been
received among chemists as an undoubted fact ; and, at the end
of Mr. Kirwan's Essay on the Analysis of mineral Waters, we
find a list of earthy salts which produce a reaction upon one
another, supposed to be caused by an affinity that tends to
unite their bases, in the form of a precipitate, insoluble in the
acids. Some other detached observations are to be found, in the
Journal de Physique, and in the Annales de Chimie. The fact
is certainly one of the most important in the docimastic art,
and merits all the attention of the skilful in that branch.

In the XLth volume of the Annales de Chimie, page 5c,

• He has taken no notice of any of the experiments contained in my paper.

34.0 ^^''- Chenevix's Analysis of Cormidum, and of

Darracq has published a paper, intended as a refutation of tlie
conclusions drawn by Guyton. I had myself repeated the greater
part of the experiments of the latter; and the results I ob-
tained were exactly similar to those of Darracq. In fact, I
had intended to continue the researches ; but the very satisfac-
tory paper of Darracq, appeared to me to render a further
prosecution of them totally useless. However, a paragraph
inserted in the A?males de Chimie, (Tom. XLI. p. 206.) and
of which Guyton appears to be the author, shows that he
has not derived from the Memoir of Darracq, that conviction
which it certainly conveys. The paragraph in question is founded
upon a letter, written from Freyberg, by Dr. G. M. to Dr.
Babington, dated December 17, 1800, and inserted in thelVth
volume of Nicholson's Journal, page 511. This letter contains
an opinion which deserves to be canvassed, as it is not perfectly
just ; and the use Guyton has made of it, has determined me
to add my observations to those of Darracq.

I shall follow the order of Guyton's experiments, in the
enumeration of those I made.

Exp. 1. From a mixture of lime-water and barytes-water,
Guyton obtained a precipitate. I obtained none.

Exp. 2. A solution of alumina in potash, mixed with a solu-
tion of silica ill the same, gave a precipitate, after standing some
time. This had been observed by Darracq, and by Guyton,
and agrees perfectly with the affinity which, before Guyton
published his paper, I had asserted to exist between these two
earths.

Exp. 3, 4, 5. Lime-water, strontia-water, and barytes-water,
produce a somewhat similar effect upon a solution of silica in
potash.

some of the Substances which accompany it, &c. 341

Exp. 6. No precipitate took place from a mixture of barytes-
vvater and strontia- water ; nor from solutions of the carbonates
of those earths, in water impregnated with carbonic acid.

Exp. 7. GuYTON obtained a precipitate, by mixing solutions
of muriate of lime and muriate of alumina. I could not obtain
any.

Exp. 8. Solutions of muriate of lime and muriate of magnesia,
W'hen mixed, did not afford a precipitate.

Exp. g. Muriate of barytes did not, as Guyton has asserted,
form a precipitate with muriate of lime. He was right in saying,
that muriate of strontia gave no precipitate with muriate of lime.

Exp. 10. Muriate of magnesia and of alumina, afforded me
no precipitate. Guyton says, that the liquors became milky.

Exp. 11. Muriate of magnesia, whether mixed with muriate
of barytes or of strontia, afforded me no change; although
Guyton says he obtained an abundant precipitate, by mixing
muriate of magnesia with muriate of barytes.

Exp. 12, Muriate of alumina and of barytes, did not, when
mixed together, yield any precipitate. Guyton asserts, that
there is a precipitate in this case.

Exp. 13. Muriate of barytes and of strontia, did not form a
precipitate. Guyton has remarked the same.

Exp. 14. From muriate of strontia and of alumina, I obtained
no precipitate. With Guyton the liquor became milky.

From all these experiments it appears very clearly, that
Guyton has pronounced too hastily, upon the affinity which he
supposes barytes to entertain for lime, for magnesia, and for
alumina ; and that he is equally in the wrong, with regard to
the affinity of strontia and alumina. With regard to Exp. 3, 4,
and 5, although they appear to be true, yet it would require the

MDCCCii. Y y

342 Mr. Chenevix's Analysis of Corujidum, and of

respective precipitates to be further examined, before we admit a
decided affinity between the earths. The quantity of carbonic
acid also, which must of course combine with the potash, during
the treatment of the silica by that alkali, should be taken into
account, in considering the cause of the precipitate.

The solutions which I used, of ail the above salts, were in the
most concentrate state ; therefore, in the state most favourable
for showing precipitation, if any had taken place.

It is not very difficult to account for the appearances that
deceived Mr. Guyton in his experiments, and for the cause that
produced them. In one instance, he obtained a precipitate from
muriate of lime and of alumina, because, in all probability, the
alumina he dissolved in muriatic acid had been precipitated from
alum ; and alumina, thus prepared, retains a small portion of
sulphuric acid.* In the next place, it is very likely that his
solutions were sufficiently concentrate to give a precipitate of
sulphate of lime. The same was the case with regard to his
mixture of muriate of strontia with muriate of alumina. As to
the general conclusion, that barytes has an affinity for lime,
magnesia, and alumina, which strontia does not appear to pos-
sess, it is to be explained as follows. Lime often contains a little
sulphate of lime. Mr. Guyton's magnesia, as well as his alu-
mina, had probably been obtained from the sulphate ; and we
are indebted to Mr. Berthollet, for the true nature of many
similar precipitates.

• It is somewhat singular, that Guyton should have observed this fact elsewhere.
See his experiments on the diamond, in the Annales de Chimie. The preparation of
abarytic salt, by alumina prepared from the sulphate of this earth, had been observed
by ScHEELE, in his Essuy on the Affinities of Bodies. But that great chemist referred
the phenomenon to its right cause, viz, to some sulphuric acid remainirg in all
alumina thus prepared.

some of the Substances wbkb accompany it, &c. 343

Barytes is a much more delicate test than strontia, for sul-
phuric acid ; and, therefore, barytic solutions were afFected by
quantities of sulpiiuric acid, which strontia could not render
sensible. This I have ascertained to be the case : for I have
obtained copious precipitates, by barytes, in a liquor composed
for the purpose, wherein strontia did not produce the smallest
cloud, or show the presence of sulphuric acid.

A little care and attention are necessary, in preparing the
earths, which are to be dissolved in the muriatic acid, for these
experiments ; and, if Mr. Guyton had taken the requisite pre-
cautions, he would not have been led into error. The object to
be kept in view is, to free the earth from sulphuric acid ; and,
if this be obtained, there is not the smallest precipitate or cloud,
in any of the cases I have mentioned. If any further proof be
necessary, with regard to the cause of precipitates obtained in
the manner stated by Mr. Guyton, I may add, that I have re-
peated his experiments, and have always found the precipitates
to be sulphate of barytes.

The general conclusion to be drawn from the observations of
Mr. KiRWAN, already alluded to, is, that barytes has an affinity
for lime, magnesia, and alumina, upon which earths strontia
does not seem to have any influence. But these mistakes are to
be accounted for in the same manner as those of Mr. Guyton,
viz. by sulphate of barytes being much less soluble than sul-
phate of strontia, and therefore showing the presence of a smaller
portion of sulphuric acid, or, in other words, being a much more
delicate test for that substance.

With regard to the letter already mentioned as being inserted
in Nicholson's Journal, and which drew some reflections from

Yy s

54.4? ^^' Chenevix's Analysis of Corundum, and of

Mr. GuYTON, it is necessary to examine as much of it as may
be thought objectionable.

The author says, that he repeated the experiments of Mr.
GuYTON, with an alkaline solution of silica and alumina, and
that he obtained a precipitate ; which precipitate^ though con-
taining silica, was totally soluble in the acids. " Here," he says,
" the properties of the silex must be considerably altered. This
" must render all analysis with alkalis suspicious ; and shows on
" what fallacious grounds the proud dominion of chemistry rests,
" which she has exercised so long, in such an arbitrary and over-
«• bearing manner, in the mineral kingdom." This opinion is by
no means likely to overthrow the pretensions of chemistry ; for
the very circumstance of rendering silica soluble in the acids, is
one of the discoveries that has most contributed to render certain,
and to extend, our knowledge of analysis. No earthy substance
is now thought fit to be submitted to further experiment, till a
complete solution of it in an acid be first obtained; and, when
that solution cannot be effected directly by the acid, it is always
attempted by previous fusion with an alkali. This mode of
rendering silica soluble in acids, is no new discovery ; it has
been long known ; and the analysis of minerals has never been
brought so near to truth, as since it has become an indispensable
condition.

I have no doubt as to the fact of a precipitate being formed,
by mixing together an alkaline solution of silica and alumina.
Alumina indeed appears to exercise an attraction, as I before
stated, for silica, for magnesia, and for lime. All stones in which
there is but little alumina, and a great quantity of silica, leave,
after fusion with potash, a light and flocculent substance, which

seme of the Substances which accompany it, &c. 34,5

cannot be dissolved by the acids : this substance, however,
which is silica, has been in solution in the alkali. But, if a
greater proportion of alumina be present, none of this flocculent
precipitate appears; hence it is evident, that alumina musC
determine its solution. Its easy solubility, in the latter casci
cannot depend upon the division of the particles of the silica in
the stone ; for, in the first pkce, after being fused with potash,
the tenuity of the particles of every stone must be nearly the
same; and, in the next place, I have not observed, that any
earth, except alumina, can promote the chemical solution of the
silica, though they must all occasion its miechanical division.

As to the affinity of alumina for magnesia, it is by much
the most powerful of all those which any of the earths have
for each other. I attempted to precipitate magnesia from
muriatic acid, by ammonia, even in excess ; but found that the
whole muriate of magnesia had not been decomposed, and that
a triple salt, or an ammoniacal muriate of magnesia,* had been
formed. I then poured an excess of ammonia into a solution
of muriate of magnesia, mixed with a large proportion of a
solution of muriate of alumina. All the earth was precipitated ,-
and nothing remained in solution, except muriate of ammonia.
The liquor was then filtered, and the precipitate washed and
dried. I dissolved it in muriatic acid, and boiled it with a great
excess of potash. Some alumina was taken up, but by no means
all the quantity that had been used. The precipitate which had
resisted the action of potash, was again dissolved in muriatic
acid, and precipitated by carbonate of potash. The carbonate of
magnesia was held in solution by the excess of carbonic acid ;
and, by using potash and carbonic acid alternately, (the first to

• This salt is well known in chemistry.

34^ Mr. Chenevix's Analysis of Corundum, and of

dissolve alumina, the second to dissolve carbonate of magnesia,)
I effected a separation of the earths. These experiments show,
that there is an affinity between alumina and magnesia, and a
certain point of saturation, where the action of potash upon
alumina is wholly counteracted by the affinity of that earth for
magnesia.

When a solution of potash is boiled upon a mixture of lime
and alumina, the alumina is dissolved, together with a much
greater portion of lime than can be attributed to the dissolving
power of the water alone. But, if a solution of potash be boiled
upon lime, without alumina, no more lime is taken up than
would have been dissolved by an equal quantity of water not
containing potash in solution ; consequently, alumina seems
really to promote the solution of lime in potash. The affinity of
alumina for lime, I had mentioned in the paper to which I
allude; and it has since been noticed by Mr. Vauquelin.*

If the conclusions of Mr. Guyton had been well founded, it
would have been chemically impossible to arrive at truth in
analysis. There were already real difficulties enough to be over-
come; and Mr. Berthollet has lately discovered some, which
are not so easily answered as those I have just considered. The
position of this chemist, however, has been too generally ex-
tended by him. If the power of masses were as great as he
represents it to be, and if it increased ad itifinitum, in proportion
to the mass, it must follow, that, with any given substance, we
could decompose any compound, provided the mass of the
decompounding body were sufficiently great; but this is well
known not to be the case.

• ScHEELE was, in fact, the first who perceived this affinity. See bis Essay on SileT,
Clay, and Alumina,

some of the Substances which accompany it, &c. 34,7

From the experiments which I have related, it appears to be
proved.

1st. That there exists an affinity between sih'ca and ahimina.

sdly. That there exists a very powerful affinity between
ahimina and magnesia.

3dly. That alumina shews an affinity for lime; but that
the said affinity is not so strong as Mr. Guyton had supposed,
nor, if pure reagents be used, is it to be perceived under the
circumstances stated by him.

4thly. That Mr. Guyton was mistaken in every instance of
affinity between the earths, excepting in the case of silica with
alumina, which had been observed before his experiments ; and
that, in the other cases, he has attributed to a cause which does
not exist, phenomena that must have resulted from the impurity
of his reagents.

A;thly. That neither the experiments of Mr. Guyton, nor the
opinion maintained in the letter from Freyberg, are sufficient to
diminish, in any degree, the value of the assistance mineralogy
derives from chemical investigation.

c: 348 3

XI. Description of the Anatomy of the Omithorhynchus
Hystrix. By Everard Home, Esq. F. R. S.

Read June 3, 1802.

At the time I had the honour of laying before this learned
Society, an anatomical description of the Omithorhynchus para-
doxus, (see page 67,) I did not attempt to point out any quadru-
peds as being nearly alHed to it, there being none at that time
within my knowledge; but the discovery of another of the same
tribe, which is the subject of the present Paper, enables me to
trace one step further, in the gradation between that extraor-
dinary animal and the more perfect quadruped.

The subject from which the following description was taken,
was sent from New South Wales, preserved in spirit. It is a
male, and had arrived nearly at its full growth, as the epiphyses
were completely united to the bodies of the bones, which is not
the case in growing animals,

A description and figure of this animal is given by Dr. Shaw,
in his Zoology, under the name of Myrmecophaga aculeata.

Description of the external Appearances.

The animal is 37 inches long, from the point of the bill to
the extremity of the tail: the bill is 1^ inch long, and the tail
half an inch.

The body of the animal is nearly of the same general thick-

Mr. Home's Description of the Anatomy, &c. 34,9

ness, but rather larger just below the shoulders. The greatest
circumference of the body is 17 inches.

The back and sides are covered with short coarse hair, half
an incli long, and with quills like those of the porcupine, only
shorter and less pointed ; they appear to be ranged in rows, in
the direction of the animal's length ; those on the sides are 2^
inches long, the others between one and two inches. The quills
on each side of the body, between the setting on of the hind legs
and the tail, have a direction forwards, so as to be opposed to
the others.

The head and neck are covered with a coarser hair than the
rest of the body, and are almost entirely without quills.

On the breast, the hair is long and soft, and without quills:
on the skin of the belly, it is almost entirely wanting.

No appearance of false nipples could be detected, either on
the belly or breast.

Externally there is no appearance of organs of generation ;
the orifice of the anus being a common opening to the rectum
and the prepuce of the penis.

The bill, which projects from the head in a tubular form, is
i-| inch long. It is conical in its shape, convex upon the upper
surface, and flat upon the lower ; at its point, it is a of an inch
in diameter, and ^ at its base : it has the same smooth cuticular
covering as the bill of the Ornithorhynchus paradoxus, but has
not the lateral lips, the sides being closed to within half an inch
of their extremity. The upper part of the bill is formed by
an elongation of the nose and palate ; and the lower portion by
a continuation of the two bones of the under jaw, as in the
paradoxus.

MDCCCII. Z z

350 Mr. Home's Description of the Anatomy

The nostrils are two small orifices, close to each other, within
a quarter of an inch of the end of the bill.

The eyes are very small, and are situated laterally on the
head, close to the base of the bill.

The external ears are two oval slits, an inch long, situated
nearer to the upper part of the head than the eyes, and 2^
inches further back.

The teeth, if they can be so called, being, like those of the
paradoxus, composed of a horny substance, and not of ivory and
enamel, as in all other quadrupeds, are not situated on the mar-
gin of the palate and lower jaw, but are confined to the tongue
and surface of the palate. On the posterior part of the tongue,
which is thicker and broader than the rest, there is a space, one
inch in length and ^ broad, covered with a strong cuticle, and
having about 20 small teeth, blunt at their ends, projecting
about -1^ of an inch ; there are also several others, less promi-
nent. On that part of the palate immediately opposite, there are
seven transverse rows of very slender horny teeth, with their
points directed backwards : each row looks somewhat like a
small-toothed comb, laid flat upon the palate.*

The appearance of these horny teeth, and a general view of
the palate and tongue, are represented in Plate XI.

The fore legs are short and thick, and have five toes, with
strong blunt claws, intended probably for the purpose of dig-
ging; the middle claw is the longest, the others becoming
gradually shorter. The leg, to the end of the longest claw, is

• In the duck, both upon the tongue and palate, there are horny papillse, which
have a slight resemblance to the horny teeth just described ; those on the tongue are
lateral, six on each side.

of the Omithorhynchus Hystrix. 351

three inches long ; the palms of the feet are covered with a
strong cuticle.

The hind legs are longer than the fore legs, and have five
toes ; four of these have long strong claws, the innermost is the
longest. The fifth toe is short, and, being opposed to the others,
resembles a thumb. The length of the leg, to the point of the
longest claw, is six inches. Just at the setting on of the heel
there is a spur, similar to that of the paradoxus, only weaker
and smaller ; it is | of an inch long.

The tail is covered with hair, and is about half an inch in
diameter; it terminates in a blunt end.

Description of the internal Parts.

The internal structure so nearly resembles that of the Omi-
thorhynchus paradoxus, that a particular description of many of
the parts will be unnecessary.

The panniculus carnosus is similar to that of the paradoxus.
The tongue is cylindrical, very small towards the point, and
eight inches long. Near the root there is an oval portion, more
massy than the rest, on which are placed the horny teeth al-
ready described.

The velum pendulum palati, and glottis, resemble those of the
paradoxus ; but, at the termination of the fauces in the oeso-
phagus, there is a projecting fold or valve, peculiar to this
species ; and the epiglottis is bifid in a small degree.

In the structure of the bones of the chest, there are the same
general peculiarities as in the paradoxus ; but, in the Hystrix,
there is a xiphoid cartilage, having its origin from the under
surface of the sternum, and being about one inch in length.

Zz 2

352 Mr. Home's Description of the Anatomy

The heart and lungs, both in their structure and rc]ative
situation, resemble those of the paradoxus, with the exception of
the heart having only one vena cava superior, instead of two.

The diaphragm is similar to that of the paradoxus.

The oesophagus is small, but has several longitudinal folds,
which render it capable of dilatation ; it is lined with a strong
cuticle, which is continued down to the cavity of the stomach.

The stomach is a thin membranous bag, nearly of the shape
of the human stomach ; in its collapsed state, it measured 4.-J
inches in length, and 3 inches in breadth.

Its internal membrane is smooth, and without the appearance
of glands, except towards the pylorus : it is lined with a cuticle;
and the glandular part has horny papillae, -'- of an inch long,
which appear to be the excretory ducts through which the
gastric juice is conveyed into the cavity. This uncommon ap-
pearance is represented in Plate XI.

Similar cuticular papillae are to be observed in the paradoxus ;
but they are so extremely small as to require a particular exa-
mination to detect them : the stomach of that animal also
appears to be hned with a thin cuticle.

Along with the food, a quantity of sand is received into the
stomach, and passes down through the bowels ; it was met with
in different parts of the small intestines, and also in the colon ;
it was very fine, and of a white colour.

It is deserving of observation, that in this animal, the mode
of managing the food is different from that employed in the
paradoxus; which accounts for the difference in the appearance
both of the teeth and stomach.

In this species, the food is bruised between the teeth placed
upon the tongue and those of the palate ; and, immediately after-

of the Omithorhynchus Hystrix. 353

wards, the whole is conveyed into the stomach, and along with
it a quantity of sand.

The stomach therefore is sufficiently large to contain the food,
and the extraneous matter connected with it ; and is defended
from injury by its cuticular lining. In the paradoxus, the food
is received into the mouth, is retained in the lateral pouches,
and is prevented, by the two projecting teeth on the tongue,
from getting into the stomacli, till all the indigestible parts are
separated ; the nutritious matter alone being allowed to reach
the stomach, which is of a very small size.

The course of the intestines, and the form of the caecum, are
the same as in the paradoxus ; the cgecum is shorter, being only
half an inch long.

The small intestines are seven feet, the colon and rectum
two feet long.

The rectum is similar in every respect to that of the para-
doxus.

The mysentery, its glands, and the lacteals, are also similar
to those of the paradoxus.

The internal membrane of the duodenum has a corrugated
appearance, but no valvulse conniventes. The cavity of the small
caecum is not loculated ; and there are ten or twelve excretory
ducts of glands on the membrane of the colon, near the open-
ing of the caecum ; but these are placed irregularly ; and there
are many similar orifices, in different parts of its course.

The liver and gall-bladder, with their ducts, and also the
omentum, are similar to those of the paradoxus.

The pancreas is not so much separated into detached parts as
in the paradoxus ; but is less compact than in quadrupeds in
general.

354 ^^1'- Home's Description of the Anatomy

The spleen is shorter and thicker than in the paradoxus ; but
has the same general shape.

The kidneys and bladder are exactly similar to those of the
paradoxus.

The skull, in its general shape, is similar to that of the duck;
and has not the bony falciform process observed in the paradoxus.

The brain was not in a state to admit of particular exa-
mination.

The olfactory nerves are divided into numerous branches.

The optic nerves are small ; and the fifth pair of nerves is
much smaller than in the paradoxus ; the second branch, which
in that species is very large, and supplies the ujjper part of
the bill, is either extremely small, or altogether wanting. This
animal has therefore, probably, a less acute sense of feeling in
the bill than the paradoxus ; and, as the organ of smell is more
complex, the increase of that sense may make a nice discrimi-
nation by touch less necessary.

The eye-lid is very loose upon the eye-ball, has a circular
aperture, and appears to have great extent of contraction and
relaxation. The membrana nictitans is wanting.

The eve-ball is -?_ of an inch in diameter; the cornea -i-,

.' 20 20'

surrounded by a zone of a black pigment, -*- in breadth.

The organ of smell differs materially from that of the para-
doxus. Immediately below the cribriform plate of the ethmoid
bone there are bony processes, forming a cellular structure,
nearly half an inch thick, which constitutes the principal part
of the organ; from this there is a convex projecting turbi-
nated bone, of a very slender form, extending half way to the
external opening of the nostril, with a corresponding concave
one to receive it, in each nostril ; and there is a small slit or

of the Ornithorhynchus Hystrix, 355

opening between the two nostrils. The structure of the organ
is shown in Plate XI.

The external opening of the ear is large enough to admit the
end of the finger; the meatus takes the same sweep as in the
paradoxus; just before it reaches the membrana tympani, it
contracts to the size of a crow-quill, then again dilates, forming
a cavity round the membrana tympani : it is lined with hair,
till it forms this constriction.

The membrana tympani is externally concave, and is covered
by a cuticle. It is of an oval form ; the long axis of the oval is
^- of an inch, the short one -5-. Its centre is attached to a small
bone, connected with the bony rim by which the circumference
of the membrane is supported : this bone corresponds to the
malleus of the quadruped. On the inner side of this, and united
to it by a smooth surface, is a small bone, in the form of a
trumpet, which may be considered as the stapes, as it fills the
opening of the foramen ovale.

There is no perfect cochlea, as in quadrupeds in general; but
there is the imperfect cochlea met with in the bird, which has
been accurately described by Mr. Cuvier.* It consists of a
conical cavity, a little bent, in the middle of which there is a
double cartilaginous septum : the two laminee unite before they
reach the end of the cone; by this means, the surrounding cavity
becomes a spiral canal, one end of which opens into tlie vesti-
bulum, the other terminates at the foramen rotundum.

The male organs of generation bear a close resemblance to
those of the paradoxus. The testicles are in every respect similar :
the vasa deferentia open into the urethra, close to the neck of
the bladder, as is seen in Plate XII. and it is at the same part
they open in the paradoxus.

• Leqons d' Anutomie comparee. Vol, II. p. 464,

35^ Mr. Home's Description of the Anatomy

The urethra for the urine opens into the rectum, about an
inch from the anus ; and the passage for the semen goes into
the penis, in the same manner as in the paradoxus.

The penis is very elastic in its substance ; when drawn out, it
is about three inches long ; but, from having been so long kept
in spirit, is not sufficiently ductile to allow of an accurate judg-
ment respecting its real length. The glans is externally subdi-
vided into four equal processes; in the centre of each of these
is an orifice, surrounded by concentric circles of infinitely small
prominent papillae.

There is a gland on each side of the rectum, the size and
situation of which are dehneated in Plate XII.; each of these has
a small excretory duct, which passes to the root of the penis,
where they unite, and then open by one common orifice into
the urethra for the semen, -j^ of an inch after it has entered
the penis.

These glands must be considered as corresponding to Cowper's
glands in the human subject, and not as a substitute for the
prostate gland, or the vesiculse seminales, since something ana-
logous is met with in the female.

In my account of the Ornithorhynchus paradoxus, these
glands are described as belonging to the rectum. This mistake
arose from the parts being so much coagulated, by long con-
tinuance in strong spirit, as to make it impossible to distinguish
the excretory duct from the surrounding blood-vessels, or
other parts. In the specimen of the Hystrix from which this
description is taken, the parts were in the same state, and
would have led me into a similar error, had I not been fa-
voured by Sir Joseph Banks with a specimen of the paradoxus,
brought from New Souta Wales by Mr. Belmain, which had

of the Ornithorhynchus Hystrix, q^"^

been kept in weak spirit ; and, although many other parts had
become putrid, those connected with the organs of generation
had been preserved, and were in a flaccid state, moi-e favourable
for anatomical examination.

I was not only enabled to examine these glands and their ducts,
but also, by fixing a pipe into the urethra where it enters the
penis, to inject water along that canal, so as to make it fill a small
cavity in the centre of each glans, and from that pass through
all the papillce, which became erect as soon as the glans was
turgid, and scattered the water by so many small streams, about
the size of a horse-hair, in every direction.

Upon re-examining the female organs of the paradoxus, after
they had been steeped in water, I was enabled to trace the ducts
of the glands, which correspond with those of the male, to one
common orifice on the posterior surface of the vagina, -^ of an
inch within the orifice of that canal.

A clitoris was also detected, with two crura, arising from the
outer side of the common vestibulum to. the rectum and vagina.
The clitoris was very slender, half an inch long; its glans a
little bifid, and inclosed in a thin prepuce ; the end of the glans
only projected into the vestibulum.

The female organs of the Hystrix have not been examined;
but there can be no doubt of their bearing the same resemblance
to those of the male as in the paradoxus.

Another species of Ornithorhynchus, of the same size as the
Hystrix, was shot at Adventure Bay, Van Diemen's Land, by
Lieutenant Guthrie, in the year 1790, a drawing of which was
made by Captain Bligh, and sent to Sir Joseph Banks, who
has allowed me to annex a copy of it to this Paper. The quills

MDCCCII. 3 A

S5^ Mr. Home's Description of the Anatomy

of this species, as I am informed by Captain Bligii, are so
short, that the points only are seen projecting beyond the hair.

The Ornithorhynchus Hystrix is a nearer approach to the
more perfect quadruped than the paradoxus ; and, as its tongue
is similar in some respects to those of the Manis and Myrmeco-
pliaga, it was natural to look among the different species of
these genera, for other points of resemblance.

I have examined a figure of the Manis of Sumatra, drawn by
the late Mr. Bell, while resident there, ^^•hose abilities as an
anatomist and draughtsman, make his death a considerable loss
to science.* The form of the head, the opening of the mouth,
and the general appearance of the animal, led me to believe it a
still further remove from the Ornithorhynchus than the Myr-
raecophaga; and the following circumstances, in the internal
structure of these two genera, confirm this opinion. The Myr-
mecophaga has two cceca, which resemble that of the Ornitho-
rhynchus ; whereas the Manis has no appearance whatever of
cscum.

There are two specimens of Manis preserved in spirit, in the
Hunter IAN Museum, one male, the other female ; both of these
I have examined.

The tongue was small, cylindrical, and very long ; and the
muscle by which it is retracted lay between the abdominal
muscles and peritonaeum of the right side, forming a semicircle
between the lower end of the sternum and the navel : the theca
in which it was inclosed, had an attachment to the lower end of
the sternum. The tongue was smooth; and there was no ap-
pearance of teeth on it, or on the palate.

• This drawing is in the possession of Mr. Marsden, who proposes publishing it
in the next edition of. his History of Sumatra.

of the Ornithorhynchus Hystrix. 3^^

There was no Ccecum, "the intestine suddenly enlarging to
form the colon : on each side of the anus there was a bag, as in
the otter, and most other animals which have no csecum.

The organs of generation, in both sexes, were distinct from
the anus ; the penis was small. In the female there were two
nipples upon the breast. The uterus was broad at its fundus ;
and the two horns separated from each other, nearly at right
angles to the middle line of the uterus.

The didactyla is the only species of Myrmecopliaga which
has come under my observation. The Trustees of the British
Museum allowed me, in the most liberal manner, to examine
both the male and female. The tongue had a general resem-
blance to that of^he Ornithorhynchus Hystrix ; but there were
no cuticular teeth upon it, or on tlie palate. The csecum was of
the same kind, but double, and each of them was only i- of an
mch in length. In the otiier parts there was no similarity. The
male had four false nipples, two on the breast and two on the
belly, corresponding with the true nipples of the female.

The organs of generation were not connected with the
rectum. The uterus was nearly of the shape of the human
uterus ; its coats were very thin ; and the cavity larger in pro-
portion than in most quadrupeds. There were no horns ; and
the fallopian tubes went oft' from the posterior part. This is an
approach to the uterus of the Opossum.

M'lth a view to procure information respecting the other
species of Myrmecophaga, I wrote to Mr. Cuvier of Paris,
whose abilities and extensive researches in comparative anatomy,
have so deservedly distinguished him in that branch of science.'
By a letter from him, I find that the Myrmecophaga jubata,
Tamandua,and capensis, belong decidedly to the class Mammalia;

3A 2

3^0 Mr. Home's Description of the Anatomy

and tlierefore are not so nearly allied to the Ornithorhynchus
as I had at first been led to imagine. The Myrmecophaga jubata,
which is described by Mr. Zan to have the organs of genera-
tion, in both sexes, concealed witliin the verge of the anus,
appears to be a nearer approach to it than the other species.

The peculiar characters of the Ornithorhynchus, as a genus,
or more properly a tribe of animals, are.

The male having a spur on the two hind legs, close to the
heel.

The female having no nipples.

The beak being smooth, while the rest of the animal is co-
vered with hair.

The tongue having homy processes, answeri-ng the purposes of
teeth.

The penis of the male being appropriated to the passage of
the semen ; and its external orifice being subdivided into several
openings, so as to scatter the semen over an extent of surface,
while the urine passes by a separate canal into the rectum.

The female having no common uterus ; and the tubes which
correspond to the horns of the uterus in other quadrupeds, re-
ceiving the semen immediately from the penis of the male.

These characters distinguish the Ornithorhynchus, in a very
remarkable manner, from all other quadrupeds, giving this new
tribe a resemblance in some respects to birds, in others to the
Amphibia ; so that it may be considered as an intermediate link
between the classes Mammalia, Aves, and Amphibia; and, al-
though the great difference that exists between it and the Myr-
mecophaga, the nearest genus we are at present acquainted
with, shows that the nicer gradations towards the more perfect
quadrupeds are not at present known, the facts which have

of the Ornithorhynchus Hystrix. 361

been stated may induce others to prosecute the inquiry, and
render tliat part of the chain more complete.

Between it and the bird, no link of importance seems to be
wanting.

The great affinity between the male organs of tjie Ornitho-
rhynchus and those of birds, is best illustrated by comparing the
penis of the former with that of the drake, a figure of which is
annexed. (Plate XII. Fig. 2.) It is six inches long when drawn
out to its full extent; but, when left to itself, (so great is the
contractile power of the urethra,) it retracts, and confines the
whole penis within the verge of the rectum.

The urethra begins by a blunt end ; and the vasa deferentia
open into it close to its origin : its sole use, as in the Ornitho-
rhynchus, is to eject the semen.

When more of this extraordinary tribe of animals, which,
although quadrupeds, are not Mammalia, shall have been disco-
vered, and naturalists thereby enabled to divide them properly,
the two which I have described will doubtless be arranged
under different genera; till then, I have thought it best to con-
sider them as species of the same genus, rather than encumber
science with an additional name, or attempt to frame generic
characters from one species only.

362 Mr. Home's Description of the Anatomy

Plate X.

A figure of the Ornithorhynchus Hystrix, (on a scale of half
an inch to an inch,) to show its general appearance, but more
particularly its cuticular bill.

Plate XI.

Fig. 1. A view of the bill and throat, laid open, to show the
tongue and palate.

a. The tongue in its natural situation.

b. The cuticular teeth upon the tongue.

c. The cuticular teeth upon the palate.

d. The bifid epiglottis immediately above the glottis.

e. The valvular projection at the beginning of the oesophagus.

Fig. 2. A section of the nose and skull, to show the pecu-
liarities of the organ of smell, and the shape of the cavity of
the skull, in which the bony falx met with in the paradoxus is
wanting.

a. The cavity of the skull.

6. The peculiar structure of bone through which the branches
of the olfactory nerve pass, after leaving the cavity of the
skull.

c. The turbinated bone, or what corresponds to it.

d. The septum of the nose.

€. The slit through the septum.
/. The posterior nostrils.

Fig. 3. The appearance of cuticular papillae on the internal

of the Ornithorhynchus Hystrix. 363

membrane of the stomach, situated at the termination of the
pylorus in the duodenum.

Plate XII. ♦

Fig. 1. The penis and testicles in their relative situation, to
show the urethra for the passage of the urine, and that for the
semen,

aa. The glans penis divided into four projecting processes,
which in the relaxed state are concave; the orifice is in the
centre of each of the projections.

b. The body of the penis.

cc. The rectum laid open.

dd. The orifices of the glands of the rectum.

ee. The two glands which correspond to Cowper's glands,
their excretory ducts opening into the urethra of the penis.
/. The termination of the urinary urethra in the rectum. •

g. The urethra laid open through its whole course.

h. The opening leading to the urethra for the semen.

/. The orifice of the neck of the bladder.

k. The urinary bladder.

//. The openings of the vasa deferentia into the urethra.

mm. The bodies of the testicles.

nn. The epididymis of the testicles.

Fig. 2. The penis of the drake, in its extended state.
aa. The verge of the fundament surrounded by the feathers.
■bb. The urethra laid open through its whole extent.
cc. Tiie orifices of the vasa deferentia.
dd. The prepuce of the penis laid open, and, from its elasti-
city, thrown into serpentine folds.

q6^ Mr, Home's "Description, &c.

Plate XIII.
Another species of Ornithorhynchus, 17 inches long, with
small quills, about one inch long. The animal, when it walked,
had its body raised about two inches from the ground. It was
shot at Adventure Bay, Van Diemen's Land.

r/,i/c'.r.Jm,i.^M\iCVC\\ r/<rlf\ /> .v/./

n'.<-/i/i ,M.

/V>i/o.i rr,i„..- M I )(•(■(■ 1 1 V7./A- W./,. Jo./

y:M./

n-^rii/'r Jt/

y%/y>'j.//Vw.r.MDcccji/y,//^xn.//.v;,/

ir"ai/t jf/

/'////,•.. y;„„.,MDcc cnj-Ai/rXHi/' .

ifr//// ,M

c: 365:1

XII. A Method of examinmg refractive and dispersive Pozvers,
by prismatic Rejlection. By William Hyde Wollaston, M. D.
F. R. S.

Read June 24, 1802.

In examining the power with which various substances refract
and disperse light, I have for some time past employed a me-
thod unnoticed by writers on optical subjects ; and, as it is not
only convenient in common cases of refraction, but also capable
of affording results not attainable by other means, I have been
induced to draw up a short account of the method itself, and of
the most remarkable instances of its application.

This method was suggested by a consideration of Sir Isaac
Newton's prismatic eye-glass, the principle of which depends
on the reflection of light at the inner surface of a dense re-
fracting medium.

Since the range of inclination within which total reflection
takes place, depends not only on the density of the reflecting
prism, but also on the rarity of the medium adjacent to it, the
extent of that range varies with the difference of the densities
of the two media. When, therefore, the refractive power of one
medium is known, that of any rarer medium may be learned,
by examining at what angle a ray of light will be reflected
from it.

For instance, when any object is laid under a prism of f]int-
glass, with air alone interposed, the internal angle of incidence at
which the vi^ial ray begins to be totally reflected, and at which

MDCCCII. 3 B

3^6 Df\ Wollaston's Method of examining

the object ceases to be seen by refraction, is about 39° 10'; but,
\vhen the object has been dipped in water, and brought into
contact with the glass, it continues visible, by means of the
higher refractive power of the water, as far as 57^° of incidence.
When any kind of oil, or any resinous cement, is interposed,
this angle is still greater, according to the refractive power of
the medium employed; and, by cements that refract more
strongly than the glass, the object may be seen through the
prism, at whatever angle of incidence it is viewed.

In examining the refractive powers of fluids, or of fusible
substances, the requisite contact is easily obtained ; but, with
solids, which can in few instances be made to touch to any great
extent, this cannot be effected without the interposition of some
fluid, or cement, of higher refractive power than the medium
under examination. Since the surfaces of a stratum so interposed
are parallel, it will not effect the total deviation of a ray passing
through it, and may therefore be employed without risk of any
error in consequence.

Thus, resin, or oil of sassafras, interposed between plate glass
and any other prism, will not alter the result.

If, on the same prism, a piece of selenite and another of plate-
glass be cemented near each other, their powers may be com-
pared with the same accuracy as if they were both in absolute
contact with it.

For such a mere comparison of any two bodies, a common
triangular prism is best adapted ; but, for the purpose of actual
measurement of refractive powers, I have preferred the use of a
square prism, because, with a very simple apparatus, it shows
the sine of refractive power sought, without the need of any
calculation.

refractive and dispersive Powers. 067

Let A, Fig. 1, Plate XIV. be a square or rectangular prism,
to which any substance is apphed at b, and let any ray of light
parallel to cb be refracted through the prism, in the direction
bde.

Then, if ef and ed be taken proportional to tiie sines that
represent the refractive powers of the prism and of air, /^, which
is intercepted between / and the perpendicular eg, will be the
corresponding sine to represent the refractive power of the
medium b. For, since edg (opposite to ef ) is the angle of re-
fraction, efg (opposite to ed) must be equal to the angle of
incidence bdb; and ef -.fg : : bd : dh : : sine of cbi : sine of
hbd.

All therefore that is requisite for determining the refractive
power of b, is to find means of measuring the line fg. On this
principle, the instrument in the annexed sketch (Fig. 2.) is con-
structed. On a board a 6 is fixed a piece of flat deal cd, to which,
by a hinge at d, is jointed a second piece de, 10 inches long, car-
rying two plane sights at its extremities. At £■ is a second hinge,
connecting ef, 1^,83 inches long; and a third at the other extre-
mity of ef by which^ is connected with it. At i also is a hinge,
uniting the radius ig to the middle of ef; and then, since g
moves in a semicircle egf, a line joining e andg would be per-
pendicular tofg.

The piece cd has a cavity in the middle of it, so that, wiien
any substance is applied to the middle of the prism P, it may
continue to rest horizontally on its extremities. When ed has
been so elevated that the yellow rays in the fringe of colours
(observable where perfect reflection terminates) are seen through
the sights, the point g, by means of a vernier which it carries,
shows by inspection the length of the sine of refraction sought.

3B2

368 Dr. Wollaston's Method of examining

The advantages which this method possesses above the usual
mode of examining refractive powers, are greater than they may
at first sight api)ear. The usual practice has been, to form two
surfaces of the substance under examination, so inchned to each
other that the deviation occasioned by them iiiight be measured.
The inchnation of these surfaces to each other must also be
known; and thence the refractive power might be computed.
But, in the method here proposed, it is sufficient to have only one
surface, and the result is obtained at once, without computation.

The facility of determining refractive powers, is consequently
such as to render this property of bodies a very convenient test
in many philosophical inquiries. For discovering the purity of
essential oils, such an examination may be of considerable utility,
on account of the smallness of the quantity requisite for trial.
In oil of cloves, for instance, I have met with a wide difference.
The refractive power of genuine oil of cloves, is as high as
1,535; but I have also purchased oil by this name, which did
not exceed 1,498, and which had probably been adulterated by
some less refractive oil.

For such purposes, the refractive power of opaque substances
may often be deserving of inquiry, which could not be learned
by any means at present in use. For, in the usual mode, a
certain degree of transparency is absolutely necessar}^ ; but, for
trial by contact, the most perfect opacity does not occasion the
least impediment.

Among other instances in which I have taken advantage of
this circumstance, I may mention a substance that had been fouiKi
in one of the islands of the North Pacific Ocean, which, to all
outward appearance and by various trials, seemed to be perfect
bees-wax, although it is supix)sed that there are no bees in the

refractive and dispersive Pozvevs. 369

island from which it was brought. On placing it by the side of
a piece of bees -wax, in contact with a prism, the perfect equality
of their refractive powers aiforded a strong confirmation of the
opinion before formed of their identity.

For the examination also of media of which the refractive
density is not uniform, the general method of trial by deviation
wholly fails ; on the contrary, by placing a varied medium in
contact with a prism, all its gradations of density, from greatest
to least, become at once the object of mere inspection. An in-
stance of this may very readily be seen with a piece of gum,
the surface of which has been moistened for a few minutes ;
when, by close application to a prism, a refractive power may
be discerned, varying from that of the water on the surface,
1,336, to nearly 1,51, the refractive power of gum arable.

I should not so much insist on this advantage, were it not
for the opportunity hereby afforded of examining the crystalline
lens of the eye, which is now known to be generally more dense
in the centre than at its surface.

Mr. Hauksbee, who was not aware of this difference, has
estimated the refractive power of the crystalline lens, bv forming
it into a wedge by plates of glass, somewhat higher than I find
it to be ; but, with his accustomed accuracy, he remarked the
apparent enlargement of an object, occasioned by the variations
of its density, which he was unable to explain.

In the table that follows, I have set down, not only the limits
of refractive power in a crystalline lens of an ox, ascertained by
trial, but also an average, computed from the refractive density
of a dried crystalline of an ox, of which the weight had been
first taken in the recent state, and the quantity of water lost by
drying also measured.

57o D/'. Wo LL Alton's Method of examining

The table exhibits a series of substances, arranged according
to their refractive powers. That of the diamond is copied from
Sir Isaac Newton; of other bodies to which (on account of
their being more dense than glass) the machine for measurement
would not apply, the refractive powers have been found by
other means, for the sake of furnishing a more continued series
of subjects for comparative experiments. The rest have been
compared by this method ; and their power, when expressed in
numbers, actually measured.

Table I.

Diamond - - 2,44

Plumbago -

Native sulphur (double) 2,04
Glass, consisting of lead

6 and sand 1 - i)987

Glass of antimony - 1,98

Jargon - - 1,95

Spinelle ruby - 1,812

Arsenic - - 1,811
Muriate of antimony, variable

White sapphire - 1,768

Gum dragon - —

Iceland spar, strongest 1,657
Sulphate of barytes

(double) - 1,646

Balsam of Tola - 1,60

Guaiacum - - 1,596

Benzoin - —

Flint glass - - 1,586

Ditto - - 1,583

Horn

Phosphorus

Mica

Opium

Amber

Rock crystal (double)

Old plate glass

Colophony

Box-wood

Bees-wax

Oil of sassafras

Red sealing-wax

Spermaceti, cold

Sugar, after fusion

Arseniate of potash

Mastic

Elemi

White wax (cold)

Oil of cloves

Copal

'^,579

1.547
i'547
1.545
1.543

1.542
1.536

1.535

refractive and dispersive Powers,

371

Anime

1,535

Oil of turpentine, com-

Raddiffe crozcn glass -

1.533

mon

1,47s

Pitch

—

. rectified

1,470

Centre of crystalline of

Oil of almonds

—

fish, and dry crystal-

olives

1,469

line of an ox

1,530

peppermint

1,468

Canada balsam

1,528

lavender

1,467

Crozvn glass, co?nmon

1,525

Tallow, melted

1,460

Selenite

1,525

Alum - - -

i>457

Caoutchouc

1,524

Spermaceti, melted -

1,446

Gum lac

—

Crystalline lens of an ox

1,447

Dutch plate glass

1,517

to

1,380

Human cuticle

—

Computed average of

Gum arabic

1,514

ditto

1,430

Balsam of capivi

1,507

Sulphuric acid

1,435

Oil of amber

1,505

Fluor spar

1,433

English plate glass

1,504

Nitric acid (sp. gr. 1 ,48)

1,410

French plate glass

1,500

Alcohol

1,37

Oil of nutmeg

1,497

White of an egg

1,36

Sulphate of potash -

1,495

iEther

1,358

Tallow, cold

1,49

Vitreous humour of an

Iceland spar, weakest

1,488

eye

1,336

Camphor

1,487

Water

1,336

Linseed oil

1,485

Atmospheric air

Butter, cold

1,480

(Hauksbee) - 1

00035

Essence of lemon

1,476

37* l^i- Wollaston's Method of examming

ON THE DISPERSION OF LIGHT.

The method above described for investigating refractive
powers, may also be employed with similar advantage for
inquiries into the dispersion of light by different bodies, and the
consequences that result from their combined action.

When a glass prism is placed in contact with water, and
brought near the eye, in such a position that it reflects the light
from a window, the extent of perfect reflection is seen to be
bounded by a fringe of the prismatic colours, in the order of
their refrangibility.* The violet rays, being in this case tlie
most refrangible, appear strongest and lowest, on account of
the less obliquity that is requisite for their reflection.

But it may happen that two media, which refract unequally
at the same incidence, may disperse equally at that incidence.
Under these circumstances, a j^encil of rays passing from one
of such media into the other, will be refracted, without dispersion
of its colours. The boundary of prismatic reflection would then
be found a well defined line, free from colour, if the surface at
which the reflected light emerges from the prism were at right
angles to its course.

When the disparity of the dispersive powers of the media is
still greater, it may also happen, that the usual order of pris-
matic colours will be reversed ; and then the red will appear
strongest and lowest in the fringe, unless the colours so pro-
duced are counteracted by refraction at their emergence from
the prism.

An instance in which the colours are so reversed, may be
seen by application of oil of sassafras to a prism of flint glass.

• Newton's Optics. Book i. part z. Exp. 16.

refractive and dispersive Powers. 373

So high is the dispersive power of this oil, that, in refractions
from flint glass into it, the red rays are refracted more than tlie
violet.

It must be observed that, in this experiment, when the angle
of reflection within a triangular prism exceeds 60°, the angle of
emergence is such as would alone occasion the red rays to
appear lowermost; but, when the glass used is rectangular, the
refraction at emergence has an opposite effect ', any reversion
of colour will therefore be in some degree corrected, and may not
be seen, unless the dispersive power of the medium in contact
much exceeds that of the glass.

A case of refraction with an inverted order of colours, has
been observed by Dr. Blair,* in a compound object-glass,
where crown-glass was in contact with oil of turpentine. From
trials with lenses, he likewise inferred, that several other fluids
have the same effect, when applied to that glass.

With this glass, and also with plate-glass, I have tried oil of
turpentine, and many other fluids that afford a similar reversion
of colours, as linseed-oil, olive-oil, the essential oils of berga-
mot, lemon, lavender, pennyroyal, and peppermint, strong nitric
acid, and many artificial compounds that I shall presently have
occasion to mention.

The dispersive power of fluor spar is the least of any sub-
stance yet examined ; so that, although its refractive power is
also remarkably low, (considering its great specific gravity,) a
prism of fluor, in contact with water or alcohol, shows the
prismatic colours to be refracted in an inverted order.

With heavy spar, the instances of reversion are very nume-
rous, as its dispersive power is low, and is accompanied with

• Edinb. Trans. Vol. III.
MDCCCII. 3 C

^y^! ^^' Wollaston's Method of examining

great refractive density. In the refractions from this spar into
flint glass, and into all oils or resins, I believe, without excep-
tion, the colours are seen reversed.

Rock crystal likewise disperses so little, that it exhibits tlie
colours reversed, when it is in contact with many substances of
less refractive power than itself. I have tried it with Dutch
plate-glass, with Canada balsam and balsam of capivi, with
many oils essential and expressed, and have found the colours
in all these cases reversed.

By solutions of metallic salts, a great variety of such appear-
ances may be produced. Most of these compounds have a highly
dispersive power; and many of them may be rendered suffi-
ciently dense to occasion reversion, even when applied to flint-
glass. In a more dilute state, they may be used with crown-
glass, or plate-glass, to produce the same effect. And since,
when further diluted by a less dispersive medium, they will also
present an appearance of colourless refraction, we may, by
examining the degree of dilution necessary for that purpose,
compare the dispersive powers of any ingredients contained in
them, and may gradually extend our knowledge of this property
to the elements of any bodies, however compounded.

As a specimen of the method, I have in this way compared a
few solutions of metals, and of other substances, tiiat were each
diluted till the limit of reflection appeared void of colour, when
they were in contact with a rectangular piece of plate-glass;
and, in the table which follows, I have expressed their refractive
powers in that state of dilution, as nearly as the eye can discern
the disappearance of colour.

refractive and dispersive Powers.

275

Table II.

Nitro-muriate of gold

Nitro-muriate of platina

Nitrate of iron _ _ -

Sulphuret of potash

Red muriate of iron

Nitrate of magnesia

Nitric acid - - -

Nitrate of jargon

Balsam of Tola , - -

Acetite of litharge (extract of lead)

Nitrate of silver

Nitrate of copper

Oil of sassafras

Muriate of antimony

Nitrate of lime

Nitrate of zinc

Green muriate of iron

Muriate of magnesia

of lime - _ -

of zinc

Essence of lemon _ _ _
Balsam of capivi - - -

la Water.

1,3^4
i>37o
i'375
i>375
i>385

1.395

1,400

1,410

1,415
1,416

1.425
1,425

In Alcohol.
1.390

1,400

1*405-
1,410
1,422

1,440

1.430
1,440

It may here be seen, that several of the metals increase the
dispersive powers of nitric and muriatic acids, and consequently
exceed them in that respect. Of all these substances that I have
yet tried, gold and platina are the most dispersive. The least
dispersive of the metals is zinc,

3C 2

37^ -Dr. Wollaston's Method of examining

The earths also are found to possess tl.is property in very
different degrees : that of the jargon and magnesia differ but
little from nitric acid in dispersive power; but siliceous earth,
on the contrary, is inferior to water.

By comparing the salts formed with the nitric and muriatic
acids, it appeared probable that the former had the higher dis-
persive power; but a more direct comparison could not be made
by means of the rectangular piece of plate-glass, as muriatic
acid could not be rendered sufficiently dense for such a trial; I
therefore made use of a triangular prism of crown gLiss, wiiich
is in itself less dispersive than any plate-glass, and, from the
relative position of its surfaces, occasioned less correction of the
colours. With this prism, I found that strong muriatic acid
(having a refractive power 1,394) exhibited the colours reversed;
and that, when it was diluted till the limit of reflection appeared
void of colour, its refractive power was reduced to 1,382. But
the dispersive power of nitric acid, when tried by the same
prism, proved to be greater ; for this acid required to be diluted
till its refractive power did not exceed 1,375, before the colour
was wholly destroyed.

In the table it may be observed, that the red and g-ecn mu-
riates of iron, though consisting of the same metal and acid,
differ very much in dispersive power; and, consequently, that
some caution will be necessary, in attempting to compare the
different metals with each ( ther by means of the sa]ts contain-
ing them, as any difference observed may be owing in part to
a difference in the quantity of acid to whxh tlicy ure u.iited,
and in pa.t to their difftreni- proportion of oxygen.

A striking instance of th< latter is manifest, from a compa-
rison of sulphur with the sulphuric acid ; for, while the former

refractive and dispersive Powers.

377

appears to exceed the metallic oxides in dispersive power, the
latter is inferior even to water.

As I have likewise, at various times, made many experiments
on dispersion by means of wedges, in a manner nearly similar
to that employed by Mr. Dollond, Dr. Blair, and others, I
have endeavoured to reduce the several substances thus exa-
mined to one table ; but, as the limits of colour are in few in-
stances sufficiently well defined for accurate mensuration, I have
not attempted to add any numerical estimate of their powers,
but have merely ascertained the order in which they succeed
each other; and, in the following table, have arranged them
according to the excess of their effect on violet above red light,
at a given angle of deviation.

Table III.

Order of dispersive
Powers.

Sulphur

Glass of lead (i-sand

Balsam of Tclu

Oil of sassafras -

Muriate of antimony

Guaiacum

Oil of cloves

Flint-i'lass -

Colophony

Canada balsam

Oil of amber

Jargon

0;l of turpentine

Copal

Balsam of capivi

Anime

Iceland spar -

Refr. Power.

2,04,

i,6"o

1^535
1,586"

1.543
1,528

i 95

i>47

1-507
h535
^fi57

Order of dispersive
Powers.

Amber
Diamond
Alum

Plate-glass, Dutch
Ditto, English
Crown glass
Ruby (spinelle)
Water

Sulphuric acid
Alcohol -
Sulphate of barytes
Selcnite
Rock crystal
Sulphate of potash
White sapphire
Fluor spar

Refr. Power.

1.547

- 2,44,

- 1.457

- 1.517
1.504

- 1.533

- 1,812

- 1-33^'
1.435

- 137

- 1,046

1.525

- 1.547

- 1^495
1,768

- 1.433

378 Dr. Wollaston's Method of examining

By comparison of this table with the order of refractive
powers, as contained in tlie first tabic, it will be seen how little
correspondence there is between them ; and, accordingly, how
numerous are the combinations by means of which a pencil of
rays that passes through two media, may be made to deviate
without dispersion of its colours.

I cannot conclude these observations on dispersion, without
remarking that the colours into which a beam of white ligiit is
separable by refraction, appear to me to be neither 7, as they
usually are seen in the rainbow, nor reducible by any means
(that I can find) to 3, as some persons have conceived ; but
that, by employing a very narrow pencil of light, 4 primary
divisions of the prismatic spectrum may be seen, with a degree
of distinctness that, I believe, has not been described nor ob-
served before.

If a beam of day-light be admitted into a dark room by a crevice
-- of an inch broad, and received by the eye at the distance of
10 or 12 feet, through a prism of flint-glass, //y^ //■o;;^ veins,
held near the eye, the beam is seen to be separated into the four
following colours only, red, yellowish green, blue, and violet;
in the proportions represented in Fig. 3.

The line A that bounds the red side of the spectrum is
somewhat confused, which seems in part owing to want of
power in the eye to converge red light. The line B, between
red and green, in a certain position of the prism, is perfectly
distinct; so also are D and E, the two limits of violet. But
C, the limit of green and blue, is not so clearly marked as the
rest ; and there are also, on each side of this limit, other distinct
dark lines, / and g, cither of which, in an imperfect experi-
ment, might be mistaken for the boundary of these colours.

refractive and dispersive Powers. 379

The position of the prism in which the colours are most
clearly divided, is when the incident light makes about equal
angles with two of its sides. I then found that the spaces AB,
BC, CD, DE, occupied by them, were nearly as the numbers
16, 23, 36, 25.

Since the proportions of these colours to each other have been
supposed by Dr. Blair to vary according to the medium by
which they are produced, I have compared with this appearance,
the coloured imager caused by prismatic vessels containing sub-
stances supposed by him to differ most in this respect, such as
strong but colourless nitric acid, rectified oil of turpentine, very
pale oil of sassafras, and Canada balsam, also nearly colour-
less. With each of these, I have found the same arrangement of
these 4 colours, and, in similar positions of the prisms, as nearly
as I could judge, the same proportions of them.

But, when the inclination of any prism is altered so as to
increase the dispersion of the colours, the proportions of them
to each other are then also changed, so that the spaces AC and
CE, instead of being as before 39 and 61, may be found altered
as far as 42 and 58.*

• Although what I have above described comprises the whole of the prismatic
spectrum that can be rendered visible, there also pass on each side of it other rays,
whereof the eye is not sensible. From Dr. Herschel's experiments (Phil. Trans, for
1800) we learn, that on one side there are invisible rays occasioning heat, that are
less refrangible than red light ; and on the other I have myself observed, (and the
same remark has been made by Mr. Ritter,) that there are likewise invisible rays of
another kind, that are more refracted than the violet. It is by their chemical effects
alone that the existence of these can be discovered ; and, by far the most delicate test
of their presence is the white muriate of silver.

To ScHEELE, among many valuable discoveries, we are indebted for having first
duly distinguished between radiant heat and light; (Traite de VAir et du Feu. § 56,
57 ;) and to him also we owe the observation, that when muriate of silver is exposed

380 Dr. Wollaston's Method of examining, &c.

By candle-ligjht, a different set of appearances may be dis-
tinguished. When a very narrow line of the blue light at the
lower part of the flame is examined alone, in the same manner,
tlirough a prism, the spectrum, instead of appearing a series of
lights of different hues contiguous, may be seen divided into 5
images, at a distance from each other. The 1st is broad red,
terminated by a bright line of yellow; the 2d and 3d are both
green ; the 4th and 5th are blue, the last of which appears to
correspond with the division of blue and violet in the solar
spectrum, or the line D of Fig. 3.

When the object viewed is a blue line of electric light, I have
found the spectrum to be also separated into several images;
but the phenomena are somewhat different from the preceding.
It is, however, needless to describe minutely, appearances which
var}' according to the brilliancy of the light, and which I cannot
undertake to explain.

to the common prismatic spectrum, it is blackened more in the violet than in any other
kind of light. (§ 66.) In repeating this experiment, I found that the blackness ex-
tended not otJy through the space occupied by the violet, but to an equal degree, and
to about an equal distance, beyond the visible spectrum ; and that, by narrowing the
pencil of light received on the prism, the discoloration may be made to fall almost
entirely beyond the violet.

It would appear therefore, that this and other effects usually attributed to light, are
not in tact owing to any of the rays usually perceived, but to invis ble rays that
accompany them ; and that, if we include two kinds that are invisible, we may distin-
guish, upon the whole, six species of rays into which a sun-beam is divisible by
refraction.

>%/fej-gfc///-<-MDCCCn^///AXB^/'3A>

cssi :\

XIII. On the oblique Refraction of Iceland Crystal. By William
Hyde WoUaston, M. D. F. R. S.

Read June 24,, 1802.

In the preceding communication, I have inserted two different
measures of refractive powers, distinctly observable in the Ice-
land crystal, as well as an estimate of its dispersive power ; but
have reserved for a separate treatise, some remarks which the
same mode of investigation has enabled me to make on its
oblique refraction.

The optical properties of this body have been so amply de-
scribed by HuYGENS, in his Traite de la Lumiere, that it could
answer little purpose to attempt to make any addition to those
which he has enumerated. But, as the law to which he has
reduced the oblique refractions occasioned by it, could not be
verified by former methods of measurement, without considerable
difficulty, it may be worth while to offer a new and easy proof
of the justness of his conclusions. For, since the theory by
which he was guided in his inquiries, affords (as has lately been
shown by Dr. Young*) a simple explanation of several phe-
nomena not yet accounted for by any other hypotliesis, it must
be admitted that it is entitled to a higher degree of consideration
than it has in general received.

According to that hypothesis, light proceeding from any
luminous centre, is propagated by vibrations of a medium highly

• Bakerian Lecture. Phil. Trans, for 1801.

MDCCcir. 3D

383 Dr. W0LL.VSTON oji the oblique

elastic, that pervades all space. In ordinary cases, the incipient
undulations are of a spherical form; but, in the Iceland crystal,
light appeared to IIuygens to proceed as if the undulations
were portions of an oblate spheroid, of which the axis is parallel
to the short diagonal of an equilateral piece of the crystal, and
its centre the point of incidence of the ray.

From this spheroidical form of the undulations, he deduces
the obliquity of refraction ; and lays down a law, observable
in all refractions, at any surface of the spar, whether natural
or artificial, which bears the closest analogy to that which ob-
tains universally at other refracting surfaces ; for as, in other
cases, the ratio is given between the sine of incidence and sine
of refraction, (or ordinate of the spherical undulation propagated,)
so, in the Iceland crystal, the ratio between the sine of incidence
and ordinate of refraction (in anyone section of the spheroidical
undulation) is a given ratio.

If ABD (Fig. 1, Plate XV.) be any surface of the spar, let
FHOK be a section of the spheroid through its centre C, and
RC any ray of light falling on that surface ; draw FO a dia-
meter of the spheroid, in the plane of incidence RVO, and CT,
its semiconjugate diameter, in the plane of refraction FTO.
Then, if CI be the refracted ray, VR, the sine of incidence, shall
be to EI, the ordinate of refraction parallel to FC, in the con-
stant ratio of a given line N to the semidiameter FC.

In any other plane of incidence, the ratio of sine to ordi-
nate is also constant ; but it is a different ratio, according to the
magnitude of that diameter in which the plane of incidence
intersects the ellipse FHOK.

When the incidence of a ray passing from any medium of
greater density upon a surface of this spar, is such that the

Refraction o/" Iceland Crystal. 383

emergent ray becomes parallel to the surface, tlie ordinate of
refraction is then a semidiameter of the spheroid ; and, accord-
ingly, the refractive power of this spar, when examined by
means of a prism in different directions, should be found to vary
as that semidiameter which coincides with the plane of inci-
dence and refracting surface.

The observations that I have made on this substance, accord
throughout with this hypothesis of Huygens ; the measures
that I have taken, correspond more nearly than could well hap-
pen to a false theory, and are the more to be depended on, as
all my experiments, excepting the last, were made prior to my
acquaintance with the theory, and their agreement was deduced
by subsequent computation,

Exp. 1. The oblique refraction of this spar is rendered visible,
by cementing a surface of it to a prism of flint-glass, with a
little balsam of Tolu. ^Vhen the hne of sight bisects an acute
angle of a natural surface of the spar, the refractive power is
seen to be less than in any other direction, and may be expressed
by the sine 1,488, or its reciprocal 0,67304,.

Exp. 2. When the plane of incidence is parallel to one of
the sides, the power is 1,518, of which the reciprocal is 0,6587.
Exp. 3. In a direction at right angles with either side, it is
found still higher, being i,537> or its reciprocal 0,6506.

Exp. 4. And, in the plane bisecting an obtuse angle, the re-
fractive power of the natural surface appears greatest, and is
expressed by the sine 1,571, or its reciprocal 0,6365.

Exp. 5. When either of the two greatest sohd angles of the
spar contained under three obtuse angles, is cut oif by a po-
lished surface making equal angles with each of its sides, the
same refractive power 1,4.88 is found in all directions. By the

3D 2

384 Dr. WoLLASTON on the oblique

theory also, the section of the spheroid is in tliis case a circle,
and every scmidiameter (FC) the same, since the plane is at
right angles to the minor axis.

Exp. 6. If a plane surface be formed bisecting an obtuse
angle of the spar, and applied to a prism, the same minimum of
refraction 1,488, is found in a direction that coincides with the
preceding plane, and therefore with the major axis of the gene-
rating ellipse; but, as the direction is varied, it increases so
rapidly as soon to exceed the power of glass, and to be no longer
ascertainable by the angle of incipient reflection.

Exp. 7. The regular refraction of this spar is also too great
for examination by means of any prism, for want of a medium
of union of sufficient density ; but, by trial in the usual method,
it measured, on an average of several experiments, 1,657, or its
reciprocal 0,6035.

By assuming, as Huygens has done, the equality of this
power with the maximum of the oblique refraction, we have
sufficient data for construction of the spheroid by which the
refractions are regulated; for we have 0,67204 (Exp. 1.) as
major axis of the generating ellipse, and 0,6035 (Exp. 7.) will
be the minor axis, parallel in position to the short axis of the
spar.

The angle of inclination of this axis to the surfaces of the spar,
if supposed to be equilateral, may be computed by spherical
trigonometry, from any other angle that has been ascertained
by measurement.

The measures that I have taken are not exactly those of
Huygens; but I nevertheless hold them in equal estimation,
from the conformity which I find they bear to each other, by
assistance of his theory.

Refraction q/" Iceland Crystal. 385

Exp. 8. I measured with care, an angle at which two surfaces
of the spar are inclined to each other, and found it to be 105° 5'.
Hence, the greater angle of the surfaces themselves may be
computed to be 101° So'-' ai^d the angle which the short axis
makes with each plane surface is 45" 23' 25".

If GSMP (Fig. 2.) be a plane bisecting an obtuse angle of
the spar, the section of the spheroid in that plane passes through
the axis CS, and therefore is the generating ellipse. By calcu-
lating from the known dimensions of its major axis CP 0,67204,
its minor axis CS 0,6035, and the angle GCS = 45° 23' 25",
CG will be found* to be 0,6365, of which the reciprocal 15
1,5736, differing but little from 1,571, as it appeared by mea-
surement. (Exp. 4.)

Again, if ABDE (Fig. 4.) be one of the natural surfaces, and
VGp the ellipse formed by that section of the spheroid, PC
being as before 0,67204, and CG 0,6^^65, the reciprocal of 1,571
found by measurement, (Exp. 4.) then the semidiameter CT,
parallel to the side AE, which makes an angle TCP 39° 2^',
will be found to be 0,6573, instead of 0,6587, and its reciprocal
1,5215, instead of 1,518. (Exp. 2.)

The semidiameter also, in the direction of CL, perpendicular to
the side, at an angle LCP 50° 5-]^', is found by calculation 0,650,
and its reciprocal 1,539, instead of 0,6506 and 1,537. (^^P- 3-)

From the foregoing data, the course of a ray perpendicular to
the surface of the spar may likewise be computed ; for, since the
sine of incidence is then nothing, the ordinate of refraction
must be also nothing, and the ray will be refracted along the
semiconjugate diameter CM. (Fig. 2.)

• (Fig- 3-) CS : CP :: tang. PCG : tang. PC^.
sec. PC^ : sec. PCG :: CP : CG.

386 Dr. WoLLASTON on the oblique Refraction, Sec.

By calculation,* the angle which this conjugate makes with
the perpendicular is 6° y^'. But, by the following measurement,
it appears to be 6° 16'.

Exp.g. A piece of spar that measured 1,145 '"ch in thick-
ness, was laid upon a line, and showed two images that were
removed from each other -^^q of an inch. Then, as 1,14,5:
0,1 26 : : radius : tang, of 6° 16'.

The different results deduced from theory and from observa-
tion, will be seen at one view in the following statement.

In Exp. 2d, observed 1,518; calculated 1,5215.

3d, 1,53; 1,539.

4th, 1,571 1,573^-

9th, angle observed 6" 16' - - 6° 7^'.

The angle observed differs from that obtained by computa-
tion, in a greater degree than any of the former measures ; but,
when the difficulty of measuring this angle with accuracy is
considered, and also the greater effect of any incorrectness in the
data from which asemiconjugate is computed, I think the result
of this, as well of the preceding comparisons, must be admitted
to be highly favourable to the Huygenian theory; and, al-
though the existence of two refractions at the same time, in the
same substance, be not well accounted for, and still less their
interchange with each other, when a ray of light is made to pass
through a second piece of spar situated transversely to the first,
yet the oblique refraction, when considered alone, seems nearly
as well explained as any other optical phenomenon.

• (F'S- 5 ) CS : CP :; tang. PCG : tang. /.CO or co-tang. PCQj
then CP : CS :: tang. PCCi.: tang. PCM;
and LCP _ PCM = MCL.

P/n/osTra/is^^WC irCYL/'/a/fyS /' :iso

'if-''

^^~~---^^_jp»'

r/^.

l^/:<f/.:6.

C387 3

XIV. An Account of some Cases of the Production of Colours, not
hitherto described. By Thomas Young, M. D. F. R. S.
F. L. S. Professor of Natural Philosophy in the Royal Insti-
tution.

Read July i, 1802.

Whatever opinion may be entertained of the theor)^ of hght
and colours which I have lately had the honour of submitting
to the Royal Society, it must at any rate be allowed that it has
given birth to the discovery of a simple and general law, capable
of explaining a number of the phenomena of coloured light,
which, without this law, would remain insulated and unintelli-
gible. The law is, that " wherever two portions of the same
« lio-lit arrive at the eye by different routes, either exactly or
«' very nearly in the same direction, the light becomes most
"'intense when the difference of the routes is any multiple of a
«' certain length, and least intense in the intermediate state of
" the interfering portions ; and this length is different for light
" of different colours."

I have already shown in detail, the sufficiency of this law for
explaining all the phenomena described in the second and third
books of Newton's Optics, as well as some others not men-
tioned by Newton. But it is still more satisfactory to observe
its conformity to other facts, which constitute new and distinct
classes of phenomena, and which could scarcely have agreed so
well with any anterior law, if that law had been erroneous or
imaginary : these are, the colours of fibres, and the colours of
mixed plates.

388 Dr. Young's Account of some Cases

As I was observing the appearance of the fine parallel lines
of light which are seen upon the margin of an object held
near the eye, so as to intercept the greater part of the light of a
distant luminous object, and which are produced by the fringes
caused by the inflection of light already known, I observed that
they were sometimes accompanied by coloured fringes, much
broader and more distinct ; and I soon found, that these broader
fringes were occasioned by the accidental interposition of a hair.
In order to make them more distinct, I employed a horse-hair;
but they were then no longer visible. With a fibre of wool, on
the contrary, they became very large and conspicuous : and,
with a single silk-worm's thread, their magnitude was so mucli
increased, that two or three of them seemed to occupy the
whole field of view. They appeared to extend on each side of
the candle, in the same order as the colours of thin plates, seen
by transmitted light. It occurred to me, that their cause must
be sought in the interference of two portions of light, one re-
flected from the fibre, the other bending round its opposite side,
and at last coinciding nearly in direction with the former por-
tion ; that, accordingly as both portions deviated more from a
rectilinear direction, the difference of the length of their paths
would become gradually greater and greater, and would conse-
quently produce the appearances of colour usual in such cases;
that, supposing them to be inflected at right angles, the dif-
ference would amount nearly to the diameter of the fibre, and
that this difference must consequently be smaller as the fibre
became smaller; and, the number of fringes in a right angle
becoming smaller, that their angular distances would conse-
quently become greater, and the whole appearance would be
dilated. It was easy to calculate, that for the light least inflected,

of the Production of Colours. 389

the difference of the paths would be to the diameter of the fibre,
very nearly as the deviation of the ray, at any point, from the
rectilinear direction, to its distance from the fibre.

I therefore made a rectangular hole in a card, and bent its
ends so as to support a hair parallel to the sides of the hole :
then, upon applying the eye near the hole, the hair of course
appeared dilated by indistinct vision into a surface, of which the
breadth was determined by the distance of the hair and the
magnitude of the hole, independently of the temporary aperture
of the pupil. When the hair approached so near to the direction
of the margin of a candle that the inflected light was sufficiently
copious to produce a sensible effect, the fringes began to ap-
pear ; and it was easy to estimate the proportion of their breadth
to the apparent breadth of the hair, across the image of which
they extended. I found that six of the brightest red fringes,
nearly at equal distances, occupied the whole of that image.
The breadth of the aperture was y-^, and its distance from
the hair -j^^ of an inch : the diameter of the hair was less than
-ig of an inch; as nearly as I could ascertain, it was -^~,
Hence, we have ' ' for the deviation of the first red fringe at

' 1000 o

the distance ^; and, as ^ : -j^ ■■Tho- tj^^' o^ -^^^^ for
the difference of the routes of the red light where it was most
intense. The measure deduced from Newton's experiments is
3^1 oo- ^ thought this coincidence, with only an error of one-
ninth of so minute a quantity, sufficiently perfect to warrant
completely the explanation of the phenomenon, and even to
render a repetition of the experiment unnecessary; for there
are several circumstances which make it difficult to calculate
much more precisely what ought to be the result of the mea-
surement.

MDCCCII. 3 E

39© Dr. Young's Account of some Cases

When a number of fibres of the same kind, for instance, a
uniform lock of wool, are held near to the eye, we see an appear-
ance of hales surrounding a distant candle ; but their brilliancy,
and even their existence, depends on the uniformity of the
dimensions of the fibres ; and they are larger as the fibres are
smaller. It is obvious that they are the immediate consequences
of the coincidence of a number of fringes of the same size,
which, as the fibres are arranged in all imaginable directions,
must necessarily surround the luminous object at equal distances
on all sides, and constitute circular fringes.

There can be little doubt that the coloured atmospherical
halos are of the same kind : tlaeir appearance must depend on
the existence of a number of particles of water, of equal dimen-
sions, and in a proper position, with respect to the luminary and
to the eye. As there is no natural limit to the magnitude of the
spherules of water, we may expect these halos to vary without
limit in their diameters; and, accordingly, Mr. Jordan has
observed that their dimensions are exceedingly various, and
has remarked that they frequently change during the time of
observation.

I first noticed the colours of mixed plates, in looking at a
candle through two pieces of plate-glass, with a little moisture
between them. I observed an appearance of fringes resembling
the common colours of thin plates; and, upon looking for the
fringes by reflection, I found that these new fringes were always
in the same direction as the other fringes, but many times larger.
By examining the glasses with a magnifier, I perceived that
wherever these fringes were visible, the moisture was intermixed
with portions of air, producing an appearance similar to dew.
I then supposed that the origin of the colours was the same as

of the Production of Colours. 391

that of the colours of halos ; but, on a more minute examination,
I found that the magnitude of the portions of air and water was
by no means uniform, and that the explanation was therefore
inadmissible. It was, however, easy to find two portions of light
sufficient for the production of these fringes ; for, the light trans-
mitted through the water, moving in it with a velocity different
from that of the light passing through the interstices filled only
with air, the two portions would interfere with each other, and
produce effects of colour according to the general law. The
ratio of the velocities in water and in air, is that of 3 to 4 ; the
fringes ought therefore to appear where the thickness is 6 times
as o-reat as that which corresponds to the same colour in the
common case of thin plates ; and, upon making the experiment
with a plane glass and a lens slightly convex, I found the sixth
dark circle actually of the same diameter as the first in the new
fringes. The colours are also very easily produced, when butter
or tallow is substituted for water ; and the rings then become
smaller, on account of the greater refractive density of the oils :
but, when water is added, so as to fill up the interstices of the
oil, the rings are very much enlarged ; for here the difference
only of the velocities in water and in oil is to be considered,
and this is much smaller than the difference between air and
water. All these circumstances are sufficient to satisfy us with
respect to the truth of the explanation ; and it is still more con-
firmed by the effect of inclining the plates to the direction of
the light ; for then, instead of dilating, like the colours of thin
plates, these rings contract : and this is the obvious consequence
of an increase of the length of the paths of the light, which
now traverses both mediums obliquely ; and the effect is every
where the same as that of a thicker plate.

3E 2

3^a Dr. Young's Account of some Cases

It must however be observed, that tlie colours are not pro-
duced in the whole light tliat is transmitted through the me-
diums : a small portion only of each pencil, passing through the
water contiguous to the edges of the particle, is sufficiently
coincident with the light ti'ansmitted by the neighbouring por-
tions of air, to produce the necessary interference ; and it is
easy to show that, on account of the natural concavity of the
surface of each portion of the fluid adhering to the two pieces
of glass, a considerable portion of the light which is beginning
to pass through the water will be dissipated laterally by reflec-
tion at its entrance, and that much of the light passing through
the air will be scattered by refraction at the second surface.
For these reasons, the fringes are seen when the plates are not
directly interposed between the eye and the luminous object;
and, on account of the absence of foreign hght, even more dis-
tinctly than when they are in the same right line with that
object. And, if we remove the plates to a considerable distance
out of this line, the rings are still visible, and become larger
than before; for here the actual route of the light passing
through the air, is longer than that of the light passing more
obliquely through the water, and the difference in the times of
passage is lessened. It is hov^ever impossible to be quite confi-
dent with respect to the causes of these minute variations,
without some means of ascertaining accurately the forms of the
dissipating surfaces.

In applying the general law of interference to these colours,
as well as to those of thin plates already known, I must confess
that it is impossible to avoid another supposition, which is a
part of the undulatory theory, that is, that the velocity of light
is the greater, the rarer the medium ; and that there is also a

of the Production of Colours. qq»

condition annexed to the explanation of the colours of thin
plates, which involves another part of the same theory, that is,
that where one .of the portions of light has been reflected at the
surface of a rarer medium, it must be supposed to be retarded
one half of the appropriate interval, for instance, in the cen-
tral black spot of a soap-bubble, where the actual lengths of
the paths very nearly coincide, but the effect is the same as if
one of the portions had been so retarded as to destroy the other.
From considering the nature of this circumstance, I ventured to
predict, that if the two reflections were of the same kind, made
at the surfaces of a thin plate, of a density intermediate between
the densities of the mediums containing it, the effect would be
reversed, and the central spot, instead of black, would become
white ; and I have now the pleasure of stating, that I have fully
verified this prediction, by interposing a drop of oil of sassafras
between a prism of flint-glass and a lens of crown glass : the
central spot seen by reflected light was white, and surrounded
by a dark ring. It was however necessary to use some force, in
order to produce a contact sufficiently intimate; and the white
spot differed, even at last, in the same degree from perfect
whiteness, as the black spot usually does from perfect blackness.
The colours of mixed plates suggested to me an idea which
appears to lead to an explanation of the dispersion of colours by
refraction, more simple and satisfactory than that which I ad-
vanced in the last Bakerian lecture. We may suppose that
every refractive medium transmits the undulations constituting
light in two separate portions, one passing through its ultimate
particles, and the other through its pores ; and that these por-
tions re-unite continually, after each successive separation, the
one having preceded the other by a very minute but constant

394? ■^'■- Young's Account of some Cases

interval, depending on the regular arrangement of the particles
of a homogeneous medium. Now, if these two portions were
always equal, each point of the undulations resulting from their
re-union, would always be found half way between the places
of the corresponding point in the separate portions ; but, sup-
posing the preceding portion to be the smaller, the newly
combined undulation will be less advanced than if both had
been equal, and the difference of its place will depend, not only
on the difference of the length of the two routes, which will be
constant for all the undulations, but also on the law and mag-
nitude of those undulations ; so that the larger undulations will
be somewhat further advanced after each re-union than the
smaller ones, and, the same operation recurring at every par-
ticle of the medium, the whole progress of the larger undula-
tions will be more rapid than that of the smaller ; hence the
deviation, in consequence of the retardation of the motion of
light in a denser medium, will of course be greater for the
smaller than for the larger undulations. Assuming the law of
the harmonic curve for the motions of the particles, we might
without much difficulty reduce this conjecture to a comparison
with experiment ; but it would be necessary, in order to warrant
our conclusions, to be provided with very accurate measures of
the refractive and dispersive powers of various substances, for
rays of all descriptions.

Dr. Wollaston's very interesting observations would furnish
great assistance in this inquiry, when compared with the sepa-
ration of colours by thin plates. I have repeated his experiments
on the spectrum with perfect success, and have made some
attempts to procure comparative measures from thin plates ;
and I have found that, as Sir Isaac Newton has already

of the Production of Colours. 295

observed, the blue and violet light is more dispersed by re-
fraction, than in proportion to the difference of the appropriate
dimensions deduced from the phenomena of thin plates. Hence
it happens, that when a line of the light proceeding to form an
image of the rings of colours of thin plates, is intercepted by a
prism, and an actual picture is formed, resembling the scale de-
lineated by Newton from theory, for estimating the colours of
particles of given dimensions, the oblique spectrums, formed by
the diff^erent colours of each series, are not straight, but curved,
the lateral refraction of the prism separating the violet end
more widely than the red. The thickness corresponding to the
extreme red, the line of yellow, bright green, bright blue, and
extreme violet, I found to be inversely as the numbers 27, 30,
35, 40, and 45, respectively. In consequence of Dr.WoLLASTON's
correction of the description of the prismatic spectrum, com-
pared with these observations, it becomes necessary to modify
the supposition that I advanced in the last Bakerian lecture,
respecting the proportions of the sympathetic fibres of the
retina; substituting red, green, and violet, for red, yellow, and
blue, and the numbers 7, 6, and 5, for 8, 7, and 6.

The same prismatic analysis of the colours of thin plates,
appears to furnish a satisfactory explanation of the subdivision
of the light of the lower part of a candle : for, in fact, the light
transmitted through every part of a thin plate, is divided in a
similar manner into distinct portions, increasing in number with
the thickness of the plate, until they become too minute to be
visible. At the thickness corresponding to the ninth or tenth
portion of red light, the number of portions of different colours
is five; and their proportions, as exhibited by refraction, are
nearly the same as in the light of a candle, the violet being the

396 Dr. Young's Account of some Cases

broadest. We have only to suppose each particle of tallow to
be, at its first evaporation, of such dimensions as to produce the
same effect as the thin plate of air at tliis point, where it is
about — i-— of an inch in thickness, and to reflect, or perhaps

lOOOO ' ^ r r

rather to transmit, the mixed light produced by the incipient
combustion around it, and we shall have a light completely re-
sembling that wliich Dr. Wollaston has observed. There
appears to be also a fine line of strong yellow light, separate
from the general spectrum, principally derived from the most
superficial combustion at the margin of the flame, and increas-
ing in quantity as the flame ascends. Similar circumstances might
undoubtedly be found in other cases of the production or modi-
fication of light ; and experiments upon this subject might tend
greatly to establish the Newtonian opinion, that the colours of
all natural bodies are similar in their origin to those of thin plates ;
an opinion which appears to do the highest honour to the sa-
gacity of its author, and indeed to form a very considerable
Step in our advances towards an acquaintance with the intimate
constitution and arrangement of material substances.

I have lately had an opportunity of confirming my former
observations on the dispersive powers of the eye. I find that,
at the respective distances of 10 and 15 inches, the extreme red
and extreme violet rays are similarly refracted, the difference
being expressed by a focal Itngth of 30 inclies. Now the interval
between red and yellow is about one-fourth of the whole spec-
trum; consequently, a focal length of 120 inches expresses a
power equivalent to the dispersion of the red and yellow, and
this ditrers but little Irom 132, which was the result of the
observation already described. I do not know that these expe-
riments are more accurate than the former one; but I have

of the Pro(hictio7i of Colours. 397

repeated them several times under different circumstances, and
I have no doubt that the dispersion of coloured light in the
human eye is nearly such as I have stated it. How it happens
to be no greater, I cannot at present undertake to explain.

CORRECTION OF A FORMER PAPER.

In the Philosophical Transactions for 1800,
P. 146, line 12, for 83810, read 841975
line 15, for .0011562, read .0010116.

In F'g- S3. (Plate VII.) the Ed (Q^) is too near D ;
and the E6 (Y) should be above, instead of below it.

MDCCCII. 3 F

C398D

XV. On the Composition of Emery. By Smithson Tennant,
Esq. F.R.S,

Read July i, 1802.

1 HE substance called emery, which, from its great hardness,
has been long used in various manufactures, for grinding and
polishing other bodies, has not, it appears, been hitherto cor-
rectly analyzed. In books of mineralogy, it is considered as an
ore of iron ; an opinion probably derived from its great specific
gravity, as well as from the iron which it frequently contains.
But, where this metal is most abundant, it could not be extracted
from it with advantage, and ought rather to be regarded as an
impurity, as it does not contribute to produce the peculiar hard-
ness for which this substance is distinguished. In Mr. Kirwan's
mineralogy, he mentions an examination of emery made by
Mr. WiEGLEB, from which he inferred that 100 parts consisted
of 95,6 of silex, and 4,4 of iron. Mr. Kirwan, however, justly
suspects the con*ectness of this account, and observes that he
had no doubt but some other stone was imposed upon Mr.
WiEGLEB for emery.

When powder of emery is boiled in acids, it becomes of a
lighter colour, from the loss of part of the iron ; after which, it
does not seem to undergo any further alteration. As acids produce
so little effect on it, I exposed it to a pretty strong red heat,
with carbonate of soda, in a crucible of platina. On adding
water to the mass contained in the crucible, the greater part of

Mr. Ten N ANT on the Composition of Emery. 399

the emery was found in powder ; having only become of a light
colour, from the extraction of part of the iron. Though this
process was twice repeated with the remaining powder, and in
a stronger heat, a great proportion of it remained undissolved.

The alkaline solution, after a red calx of iron had subsided
from it, was saturated with acid ; and gave a precipitate of a
white earth, which I found to be almost purely argillaceous.

The result of these experiments, was so similar to those of
Mr. Klapkoth on diamond spar, as to render it very probable
that emery was in reality the same substance, though usually
mixed with a larger proportion of iron ; and the subsequent ex-
periments appear to confirm this opinion.

In order to obtain a quantity of emery as free from iron as I
could, I reduced to a coarse powder, a piece.which consisted of
different strata, some of which were of much lighter colour
than others ; and afterwards separated, by a magnet, the par-
ticles which were attracted by it. The part which was not
attracted by the magnet, I observed to have the usual degree of
hardness, (by the scratches which might be made with it on
flint.) I then reduced it to a finer powder, in an agate mortar;
and, as this was principally done by pressure, and not by
grinding, hardly any sensible addition was made to its weight.
In the same manner, I found that diamond spar might be
powdered to the same degree of fineness, without any material
increase of weight from the mortar.

Of the emery powder thus prepared, 20 grains were taken,
and heated in the manner before described, with 120 grains of
soda, which had been previously deprived of carbonic acid, and
boiled to dryness in a silver pan. By nearly the same process

3F s

4;00 Mr. Tennant on the Composition of Emery.

as that used by Mr. Klaproth, I obtained about 16,0 grains of
argillaceous earth, ,Gof siliceous earth, ,8 or ,9 of iron, and ,6 of
a grain remained undissolved. These numbers, reduced to parts
of a hundred, are therefore.

Argillaceous earth - - - 80

Silex - - - - - 3

Iron ----- 4,

Undissolved - - - "3

90-
Mr. Klaproth obtained from the Chinese corundum, after'

separating from it the particles which were attracted by the

magnet,

Argillaceous earth - - - 84

Silex - _ - - 6,5

Iron ----- _7^

98.
As this analysis was no doubt conducted with greater care
than mine, the loss of weight was less ; but the proportion of
the ingredients is sufficiently near to show that the substances
are essentially the same.

From 25 grains of emery which appeared the most impreg-
nated with iron, and yet retained its usual hardness, I obtained,
argillaceous earth 12,5, silex 2, iron 8, and one grain was not
dissolved ; or, per cent.

Argillaceous earth - - - 50

Silex - - - - - 8

Iron - - - - - 3«

Undissolved . _ - - 4

94-

Mr. Tennant on the Composition of Emery. 4,01

As such emery can easily be had of uniform quality in large
pieces, I procured the powder employed in this experiment, by
rubbing two pieces against each other.

From S5 grains of emery, similar in appearance to the pre-
ceding, but which had been digested with marine acid previous
to the action of the alkali, I had, ^^^ ^^^^^

Of argillaceous earth - - i^4 ^5.^

Siliceous earth - - - ,8 3'^

T - - 2. 8,

Iron - - -, .

Not dissolved - - " 4>5 ^^f_

23'7 9^'S-

The hardness of emery, as far as I could judge by its cutting
rock crystal and flint, appeared to be equal to that of diamond
spar. The latter could not be scratched by the former ; but, as
emery has not a surface sufficiently polished to render a mark
visible, the converse of this could not be tried.

All the emery which is used in England, is said to be brought
from the Islands of the Archipelago, and principally from
Naxos. In those places, it is probably very abundant; as the
price of it in London, which I was told was 8 or 10 shillings
the hundred weight, appears little more than sufficient for the
charges of carriage. Though I saw a very large quantity in one
place, (more than a thousand hundred weight,) I could not find
any pieces of a crystallized form ; possibly the great proportion
of iron usually mixed with it, may prevent its crystallization.
The whole consisted of angular blocks incrusted with iron ore,
sometimes of an octaedral form, with pyrites, and very often
with mica. The latter frequently penetrates the whole sub-
stance of the mass, giving it, when broken, a silvery appearance,

4oa Mr. Tennant o?i the Composition of Emery.

if seen in the direction in which the flat surfaces present
themselves to the eye. As these substances have no chemical
relation to the emery itself, it is remarkable that they should
also accompany the diamond spar from China; for Mr. Klap-
ROTH observes, " that its lateral facets are mostly coated with a
" firmly-adhering crust of micaceous scales, of a silvery lustre :"
he also mentions, besides felspar, pyrites, and grains of mag-
netic iron ore.

C 403 D

XVI. Qiietques Rernarques mr la Chaleur, et siirl' Action des Corps
qui I'interceptetit. Par P. Prevost, Professeur de PhilosopJjie
a Geneve, &c. Communicated by Thomas Young, M. D.
F. R. S.

Read July 1, 1802.

Partie I.

§ 1. J^E Dr. Herschel, voulant estimer la quantite de lumiere
transmise par divers corps, a employe un appareil dont il
donne la description d^taill^e.* Au moyen de cet appareil, il
apprecie I'effet d'une m^me source de chaleur, agissant d'un cote
sans obstacle, et de I'autre a travers une lame qui I'arrete en
partie. Qu'on se repr^sente un rayon solaire tombant sur deux
thermom^tres pareils, sur I'un directement, et sur I'autre a tra-
vers un verre; qu'on ecarte soigneusement toutes les causes
dtrangeres qui pourroient influer ici ; et Ton aura une id^e de
cet appareil, construit avec tout le soin et toute la sagacite qu'on
a droit d'attendre d'un excellent observateur.

Ce physicien a fait avec cet appareil un grand nombre d'ex-
p^riences, toutes de meme forme. Chacune d'elles offre six
observations, pour chacun des deux thermom^tres. La ire
observation indique le degre au commencement de I'experience,
et avant que la source de chaleur ait pu agir ; les autres indi-
quent successivement, de minute en minute, les degr^s de la
chaleur croissante, jusqu'a la 5me minute, ^poque ou finit
• Phil. Trans, for 1800. p. 446.

404 Professor Prevosi's Remarks on Heat,

rexp^riencc* Ces nombreuses experiences ne different entr'elles,
que par la nature du corps dont est formee la lame interccp-
tante, ou par la nature de la source de chaleur qui est employee.

A la fin de chaque experience, I'auteur en donne le r^sultat.
Pour cet efFet, il retranche le degre initial du d6gr6 final, et,
faisant s^parement cettc soustraction pour chacun des deux
thermom^tres, il se borne a comparer les restes, pour en con-
clure la transmission.

Voici le detail de la ire des experiences de ce genre, qui est
la 24me de I'ouvrage.

A travers un verrc
blanc bleuatre.

6f

%i

70

Soustrayant done le degre initial du final, on a au soleil
direct 6° de chaleur acquise ; tandis qu'a travers le verre on n'en
a que 4^. Le rapport de ce dernier nombre au premier, rdpre-
sente la transmission par le verre. C'est en milliemes 0,750;
dont le complement 0,250 exprime les rayons intercept's.

§ 2. Les experiences multipli^es dont je viens de donner
sommairement I'idee, ont 'te faites surement avcc toute I'ex-
fictitude qui peut leur donner du prix : elles ouvrent un nouveau
champ de speculation, et font esperer des r'sultats int^ressans.
Mais celui que I'auteur a eu en vue, je veux dire, I'appreciation

• Une partie de ces experiences n'a dure que trois minutes : je ne citerai pas cette
classe d'experiences, c'est pourquoi j'emploic ici une expression generale.

Au sokil

direct.

0'

6f

1

6'8i

s

7oi

3

7ii

4

72t

5

73

ajid on the Action of Bodies which ijitenept it. 405

de la faculty interceptante de la lame mise en experience, n'est
pas aussi simple qu'il le paroit au premier coup-d'oeil, et exige
une nouvelle recherche.

Et d'abord, si de Texp^rience que j'ai citee et transcrite ci-
dessus, on pouvoit inf(6rer d'une maniere g^n^rale, que le nombre
des rayons intercept's par le verre blanc bleuatre est exprimd
par la fraction 0,250, cela ne devroit pas etre particulier au
temps de la duree de Texperience. Si, par exemple, elle avoit
dur6 six ou sept minutes, on devroit trouver le meme re-
sultat ; le meme encore, si elle n'avoit dure que trois ou quatre
minutes. Nous ne pouvons parler experimentalement que de ce
dernier cas, qui est consigne dans le r'gistre de I'experience.
Or, il est facile de voir, que si I'auteur s'^toit arrets a la 4me
minute, il auroit trouv6 la transmission exprimee par le rapport
3|- : 5| = 0,720, et par consequent la faculty interceptante =
0,280. S'il se flit arret' a la 3me minute, I'interception eut
ete 0,314; a la 2de minute, 0,320 ; et a la ire minute, 0,357.
Ensorte qu'on devroit croire, en suivant la marche tenue ici,
qu'a la ire minute le verre interceptoit plus de rayons qu'a la
2de; plus a la 2de qu'a la 3me ; a la 3me qu'a la 4me: a la
4me qu'a la 5me.

Le meme r'sultat, a une seule irr'gularite pres,* peut se
deduire de I'exp'rience suivante, (oii I'auteur a substitue une
lame de flint glass a celle de verre blanc bleuatre de la prece-
dente, et dont il donne le d'tail,) que je transcrirai ci-dessous.
(§9.) L'auteur dit lui-meme, que ce r'sultat a 't' commun a
toutes les experiences analogues, a I'exception d'une seule, qui
lui a paru anomale a d'autres 'gards.-j- II emploie meme ce fait

* A la fin de la 3me minute, la transmission a ete excedente.

f P. 479- Exp. 122. Je rapporterai bientot cette experience en detail. (§ ii.)

MDCCCII. 3 G

4o6 Professor Prevost's Remarks on Heat,

comme un argument, pour prouvcr que les ra3^ons chauds et
lumineux sont diff^rens.* On peut done envisager cc r^sultat
comme g^ndral et constant. Ensorte que, si la mesure de la
transmission adoptee ici est juste, on doit croire que la faculte
interceptante des corps va toujours en croissant, de minute en
minute, au moins jusqu'a la 5me ; et, si jamais un raisonne-
ment analogique est admissible, on doit croire que cette pro-
gression croissante dureroit apres les cinq minutes ^coul^es ;
si bien qu'en prolongeant I'experience, on fait croitre la faculty
interceptante de la lame, et la chaleur transmise doit a la
longue diminuer beaucoup, ou meme enfin se r^duire a rien.

Cette consequence, qui est inevitable dans cette m^tliode
d'estimation, doit peut-etre inspirer du doute sur le principe
dont elle derive ; car on ne sauroit concevoir aucune raison
probable, pour laquelle la faculty de transmettre ou d'intercepter
la chaleur doive varier dans un corps, parcequ'il y a plus ou
moins long-temps qu'il la transmet ou I'intercepte.

Cette difficult^ nous ramene a la th^orie de la chaleur, et en
particulier de la communication de la chaleur, de son passage
d'un lieu dans un autre, ou d'un corps dans un autre corps. En
effet on voit ici, de part et d'autre, la boule d'un thermom^tre
plong^e dans une source de chaleur, telle qu'un rayon solaire,
par exemple ; on voit la chaleur passer de la source dans la
boule, et amener celle-ci, peu-a-peu, a une temperature plus
haute que celle dont elle jouissoit ; on voit qu'il s'^coule plusieurs

• p. 522. " L'Interception de la chaleur solaire," dit-il, " a constamment ete plus
" grandc pres du commencement des cinq minutes que vers la fin ; or, cela n'a pas
" lieu dans la transmission de la lumiere, qui est sensiblement instantanee. Cela
" indique que la loi de transmission n'est pas la meme pour la lumiere que pour la
" chaleur." Ce sont la ses expressions abregees, et reduites au seul objet que j'ai en

YUC.

and on the AdioJi of Bodies xvbich intercept it. 407

minutes avant que cet accroissement de temperature vienne
a cesser ; et il ne paroit pas qu'on ait atteint le terme de son
maximum. II y auroit done de I'importance a connoitre la loi de
cet accroissement ; car il est facile de comprendre que, selon la
nature de cette loi, I'accroissement partiel produit pendant un
temps limite (tel que 5') sera, ou ne sera pas, proportionnel a la
chaleur de la source. Or, c'est cette chaleur qu'il s'agit d'estimer,
d'une et d'autre part, pour pouvoir comparer la chaleur trans-
mise par le verre avec la chaleur entiere qui passe sans obstacle.
Tournons done notre attention vers un objet si evidemment
requis.

§ 3. La loi dont nous avons besoin, a ete reconnue et deter-
minee par des experiences directes. II r^sulte de celles de M M.
Kraft et Richmann,* que dans un ynilieu d'lme temperature
constante, un corps s'^chauffe ou se refroidit de sorte que les
differences de sa chaleur a celle du inilieu sent en progression geo-
metrique,tandis que les temps de I'^chauflfementou du r^froidisse-
ment 50^2^ eji progression arithtnetique. Cette loi, d^duite, je le
r^p^te, d'exp^riences directes et faites avec soin, est parfaite-
ment d'accord avec la th^orie g^ndrale de la chaleur, qui se
fonde sur d'autres faits, et dont je dirai un mot en finissant ce
m^moire. En ce moment, je laisse cette loi Isolde, et je I'admets
simplement comme une v^rite particuliere, que Texperience a
d^montr^e.

§ 4. II r^sulte de cette loi d'accroissement, que si deux corps
de meme temperature sont plong^s dans deux milieux de tem-
perature constante, mais in^gale, les accroissemens op^r^s en
temps ^gaux ne seront point, en general, proportionnels a la
temperature de ces milieux, puisqu'il n'y a que quelques c^

• Nov. Comm. Acad. Pttrop. Tom. I. p. 195.
3G 2

4o8 Professor Prevost's Remarks on Heat,

tres-particuliers et tres-rares on cette proportion puisse avoir
lieu, comme il est facile de s'en assurer; par consequent, les
deux thermometres des experiences prec(^dentes n'indiquent pas,
par le rapport de leurs mouvemens en cinq minutes, le rapport
de la chaleur totale a la partie de cette chaleur qui a ^te trans-
mise par la lame interposee. II faut s'y prendre d'une autre
maniere, pour faire cette estimation. La plus simple, peut-etre,
eiit ete de n'avoir aucun egard au temps, et de laisser chaque
thermometre atteindre la temperature de la source de chaleur
dans laquelle il est plonge ; mais la dur^e de I'exp^rience entre-
prise sur ce principe offre peut-etre des inconv^niens, et Ton
verra d'ailleurs, par ce qui va suivre, que cette m^thode meme
exigeroit encore une analyse ulterieure. Ouoiqu'il en soit, on
peut encore tirer des consequences legitimes, des experiences
qui ont ete faites dans un temps limits. Je vais m'appliquer a
tirer ces consequences, du moins les principales ; et I'auteur de
cette belle suite d'observations verra, j'espere, avec plaisir, que
les resultats qu'elles offrent sous cette nouvelle forme deviennent
plus reguliers et plus probables.

§ 5. Je commence par discuter I'experience 24me de Touvrage
de M. Herschel ; c'est celle dont j'ai transcrit le detail ci-
dessus. (§1.) Les temps croissant en proportion arithmetique,
o, 1, 2, 3, 4, 5, les differences de chaleur du thermometre et
du milieu doivcnt d^croitre en progression geometrique. Les
degres observes au thermometre expose a la chaleur libre du
soleil sont, au commencement des trois premieres minutes, Gy,
68^, 7o|, ou en huitiemes de degre, 536, 550, 561. Maintenant,
si Ton suppose que la temperature du jayon solaire ait ete (en
huitiemes de degre) = 601, on trouvera que les difTerences de
la chaleur du thermometre a celle du milieu, savoir, 65, ^j, 40,

and on the Action of Bodies which intercept it. 409

sont en progression g^ometrique; ce qu'on n'obtiendra par aucim
autre nombre. La loi prescrite nous force done d'admettre
ce nombre, pour I'expression de la chaleur du milieu ou etoit
place le thermom^tre. Cela etant, nous calculerons les termes
suivans de la progression, nous en conclurrons les d^gr^s du
thermometre pour les minutes suivantes, et nous les compa-
rerons aux d^gr^s observes. C'est I'objet de la petite table sui-
vante, ou tous les nombres expriment des huitiemes de degre.

Chaleur du milieu, conclue des ^premiers termes .... 601,

Degres
observes.

o' 53^

1 55°

Degres

calcLiles.

Differences
en progr. geon

536

65

550

51

561

40

570

3^

576

25

582

19

s 561

3 57^

4 579

5 584
On pent observer, que les trois derniers d^grds calculus sont

d'accord avec les degres observes, avec un 6cart de moins de
trois huitiemes de d^gr^.

§ 6. Maintenant nous allons faire la meme operation pour les
observations coDat^rales, faites avec le thermometre que garan-
tissoit un peu une lame de verre blanc bleuatre. Mais il y a
id une remarque a faire : la progression des differences du
premier thermometre et du milieu a pour quotient f f ; il paroit
que celle du second thermometre doit avoir le meme quotient,
car il part du meme point, son 6chelle d'^chauffement est com-
prise en entier dans celle du premier thermomt^tre, et ces deux
thermom^tres ont et^ choisis avec une attention scrupuleuse, de
maniere a avoir pr^cis^ment la meme sensibility ; ainsi, par un

41 o Professor Prevost's Remarks on Heat,

ineme accroissement de chaleur, chacun d'eux, en menie temps,
se mcut d'une meme quantity. Si, par exemple, la temperature
du milieu exc^de, de part et d'autre, celle du thermom^tre de 65
luiitiemes de d^gr^, on doit s'attendre que Tun et I'autre en une
minute en acquerra 14, et ne dift'erera plus de la source que de
51 huitiemes de d^gr^; mais, en chaque thermometre, cette pro-
portion etant constante dans les echauffemens subs^quens,
(d'apres la loi,) il est clair que le quotient est le meme pour les
deux thermom6tres, dans toute I'^tendue de la progression.

II n'en seroit pas ainsi, si les thermom^tres n'^toient pas
^galement sensibles ; par cons(^quent, en passant d'une expe-
rience a I'autre, il conviendra de remarquer si les thermometres
ont change; et, en ce cas, de chercher de nouveau le quotient de
la progression.

§ 7. Je viens a la partie de I'experience qui nous reste a
examiner ; il s'agit du thermometre garanti de Taction du soleil,
par une lame de verre blanc bleuatre. Prenant done les deux
premiers nombres donnes par Tobservation, savoir, ceux qui
repondent au commencement et a la fin de la ire minute de
I'experience, nous determinerons celui qui a du exprimer la
chaleur du milieu, pour que les differences des deux premiers
nombres a celui-ci soient entr'eux comme 65 est a 51 ; et,
forraant successivement les autres termes de cette progression,
nous en conclurons les degres pour les quatres minutes sui-
vantes, afin de les comparer aux degres observes. C'est I'objet
de la petite table suivante, en huitiemes de degre.

and on the Action of Bodies which intercept it. 41 1
Cbaleur dii milieu 578.

Degres
observes.

Degres
calcules.

Differences en
progr. geom.

0'

536

536

4a

1

54<5

545

33

3

553

55^

26

3

560

558

20

4

567

562

16

5

57^

565

13

Les nombres calculus et observes different ici de 1 jusqu'a 7
huitiemes de d6gr^. Je dirai plus bas a quoi j'attribue cet ^cart.
(§• 12.)

§. 8. Supposant maintenant que la chaleur de Tun et de
I'autre milieu (celle du rayon libre et celle du courant qui agit
sous le verre) ait ^t^ bien appr^ciee, il ne reste plus qu'a les
comparer; leur rapport est celui de 601 a 578 ; et par conse-
quent la quantite intercept^e = 0,038.

§. 9. Passons a Texp^rience suivante, qui est la 25me de
I'buvrage. Celle-ci a et6 faite avec les memes thermomdtres
que la prdcedente. Le corps mis en experience etoit une lame
dejlint glass ; et en voici le r^sultat, tel que le donne I'auteur,

Degres

ob:

serves.

Au soleil libre.

A travers lefiii:

( glass.

0'

%i

69h

1

7H

71

2

7H

'7H

3

74i

73i

4

74^

74

5

75i

74i . • .

"5i'5 = 0,905

413

Professor Prevost's Remarks on Heat,

En calculant cette experience comme la pr^cddentc, et en
prenant -^4^ pour le quotient de la progression des differences, on
aura, en huitiemes de degr6, Ics resultats compares qu'indique
la table suivante.

All soleil libre.
Chaleur du milieu 614.

Dcgres Degres Differ, en
observes, calcules. progr. geoni.

0'

558

558

56

1

570

570

44

3

581

579

35

3

593

587

27

4

599

593

21

5

602

597

17

A travers le flint glass.
Chaleur du 7nilieu 604.

Degres Degres Differ, en

observes. calcules. progr. geom.

558

558

46

568

568

36

577

576

28

591

582

22

592

587

17

598

59^

14

Rapport des deux chaleurs 604 : 614.
Interception - - 0,015.

§.10. En jettant les yeux sur cette table, on voit queles deux
thermom^tres ont montr^ un ^chaufFement plus rapide dans les
dernieres minutes que le calcul ne I'annongoit. Le thermo-
m6tre au soleil libre, pr^sente un exces de 1 jusqu'a 6 huitiemes
de d^gr^, qui diminue a la fin, et se reduit a 5 huitiemes. Le
thermom^tre garanti par le Jlint glass, presente un exces qui
varie irregulierement de 1 a 9 huitiemes. Get ecart, pour le
thermom^tre garanti, est dans le meme sens que celui de I'ex-
pdrience prec^dente, et sera expliqu6 de meme ci-dessous. (§.
12.) L'ecart du thermometre cxpos6 au soleil libre, ne peut
s'expliquer qu'en supposant quclque cause particuliere d'irre-
gularite.

and on the Action of Bodies which intercept it. 413

§,11. II y a une troisieme experience clont I'observateur donne
le detail, et qu'il nous reste a examiner; c'est la i2 2me de
I'ouvrage; elle a ^t6 faite avec une lame de talc, sous I'influ-
ence de la chaleur d'un feu de charbon bicn mc^nage. En voici
les rdsultats donnes par I'auteur.

Degrcs observes.
All feu libre, A travers le talc.

0'

%

65

1

72

67

2

77

68i

3

80J-

69i

4

83'

70

5

85

7of • • ■

, .. 20 : jl = 0,287.

Ici les thermom^tres ne sont plus les memes que ceux qui
ont ^t6 employes dans les deux experiences que nous avons
discutees ; ceux-ci ^toient d^sign^s No. 5, et No. 1 ; ceux-la
sont distingu^s par les lettres D, C ; il faut done chercher de
nouveau, pour ces deux thermom^tres, ^galement sensibles
entr'eux, (mais peut-etredifFerensen sensibilite des precedens,)
selon quelle progression s'est fait I'^chauffement au soleil libre,
pendant le cours des deux premieres minutes, (§ 6,) afin d'en
conclure les d^gres suivans. II r^sultera de ce calcul, et de
I'emploi de la progression ainsi d<§termin^e pour le thermometre
garanti, la table suivante, toujours en huitiemes de degr^.

MDcccir, 3 H

4H

Professor Prevost's Remarks on Heat,

All feu litre.

^ travers le talc.

Cbaleur

dufeu 'j\6

Cbaleur du milieu 576.

Dcgrfs

D^gres

Differ, en

Degr^s

Degrts Diftcr. en

observes

calcules. progr. geom.

observes.

calcules. progr. geom.

o'

520

.520

i()6

520

520 56

1

576

576

140

536

536 40

2

616

6\6

100

550

547 29

3

644

645

71

556

555 21

4

664

665

51

560

561 15

5

680

680

36

566

t^66 10

La progression des differences a icl pour quotient ^, au lieu
de ^4^ : ainsi les thermom^tres recevoient, en temps 6gal, de la
source calorifique, une aliquot de chaleur un peu moindre que
les pr^c(^"dens ; cependant, la difference n'est pas tres conside-
rable ; du reste, on peut bien dire, que dans cette experience le
calcul et I'observation sont parfaitement d'accord. Ce n'est
pas la peine de remarquer des differences aussi petites, et qui
seroient encore plus insensibles, si j'avois tcnu compte des frac-
tions de degre inferieures a une huitieme, ce que je n'ai pas cru
devoir faire. Cet accord est d'autant plus remarquable, que c'est
precisement ici I'experience qui a offert quelque chose de parti-
culier, qui auroit dii, a ce qu'il semble, introduire de I'irregula-
rite dans les resultats. Le talc s'est calcine par I'action du feu,
dans le cours de I'experience, et de transparent qu'il etoit, il est
devenu parfaitement opaque; neanmoins, il paroit que Taction
de la chaleur sous le talc, de minute en minute, a suivi un cours
parfaitement regulicr et uniforme. En voici le calcul.

Rapport des deux chaleurs 576 : 716.

Interception - - 0,196".

§ 12. Tels sont les resultats que nous offrent les trois expe-
riences dont I'auteur a consigne le detail dans son ouvrage. II

and on the Action of Bodies which intercept it. 415

est temps de dire un mot de la cause a laquelle j'attribuc, dans
les deux premieres experiences, I'exces d'echaufFement qui a
^te observe au thermometre garanti, dans les dernieres minutes
de leur duree. (§§ 7 et 10.) Je crois qu'il depend de la chaleur
accumulee dans le corps interceptant. A I'instant ou ce corps
s'c^chaufte, il contribue a faire monter le thermometre voisin.
Si la marche de cette accumulation de chaleur etoit tres regu-
liere, son eftet se confondroit avec celui des rayons transmis ;
(c'est, je pense, ce qui a eu lieu dans la 3me experience, ou la pro-
gression des differences n'est gueres moins exacte pour le ther-
mometre garanti que pour I'autre ; ) mais, si I'accumulation est
accel^ree, (c'est-a-dire, si le rapport des rayons accumul^s aux
transmis est plus grand en meme temps vers la fin de I'expe-
rience qu'au commencement,) son effet croissant se fera sentir
au thermometre, qui se mouvra comme il s'est mii dans les
deux premieres experiences. A quoi done peut tenir une pareille
acceleration, et quelle raison peut on imaginer pour qu'elle ait
lieu dans un cas, et non dans I'autre ? On ne sauroit, je crois,
I'imputer a aucune cause plus probable qu'a I'epaisseur de la
lame, ou a la foiblesse de la source de chaleur.

§ 13. Supposons qu'on presente un verre ^pais a un foyer
de chaleur ; il s'echauffera du cote du feu, et, conduisant mal la
chaleur, il restera quelque temps froid du cote oppose ; ainsi,
pendant la ire minute, peut-etre, un thermometre place de ce
dernier cote n'accuseroit aucun echauffement ; mais, peu-a-peu,
dans les suivantes, cet echauffement se feroit sentir. Je presume
que c'est ainsi que les choses se sont passdes dans les deux pre-
mieres experiences, et en particulier dans la seconde; (la 2,5me
de I'ouvrage;) dans celle-ci, la lame Aefiint glass avoit environ
trois lignes d'epaisseur. L'observateur donne cette mesure,

3H2

4i6 Professor Prevost's Remarks on Heat,

tandis qu'il ne dit rien de I'^paisseur des autres lames. II est
probable que cclles-ci etoicnt plus minces, en particulier celle
de talc ; et cela pourroit expliquer la regularity de I'une de ces
experiences, et Tirregularit^ de I'autre.

Joigncz a cela, que dans la troisieme des experiences que j'ai
analysees, (la i22mc de I'ouvrage), la source de chaleur (le feu
de charbon) avoit plus d'intensite, ou d'activit^, que celles (les
rayons solaires) qui agissoicnt dans les deux autres; puisque,
dans le meme espace de cinq minutes, elle a amend le thermo-
mdtre libre de 65° a 85 ; tandis que le thermom^tre libre dans les
deux autres experiences, n'a montd que de 50U 6 ddgrds, compris
entre ces extremes. Or, il est probable, que si deux lames sont
de meme nature et de meme epaisseur, mais que I'une soit
exposde a une chaleur forte et I'autre a une chaleur foible, la
premiere sera traversde plutot que la seconde, par la chaleur
accumulee ; ensorte que, touchant, a la fin de la ire minute, par
exemple, la face non exposde de chacune des deux lames, il se
pourra faire qu'on sente I'une froide et I'autre chaude.

Par deux raisons done, I'experience isame a du offrir des
rdsultats reguliers ; 1. parceque probablement la lame dloit
inince ; 2. parceque la source de chaleur ^toit grande; d'oii
il rdsultoit, que la chaleur accumulee I'avoit traversee des la fin
de la ire minute; ensorte que Taccumulation, et le rayonnement
qui en est la suite, croissoient, de minute en minute, selon la
meme loi d'echauffement selon laquelle s'^chauffoit d'ailleurs la
boule du thermometre, si quelque chaleur 6toit transmise sans
obstacle.

Et si la 2de experience (la 25me de I'ouvrage) offre plus
d'irregularitds que la premiere, (la 24me de I'ouvrage,) cela
pourroit bien tenir en partie a la plus grande Epaisseur dwjlint

ayid on the Action of Bodies zvhich intercept it. 4.17

glass. Cependant, d'uii c6t6 nous ne pouvons rien affirmer sur
I't^paisseLir du verre blanc bleuatre, qui n'est pas indiquee ; et
de I'autre, I'^chaufFement au soleil libre ofFre, dans cette meme
experience, (la 25me,) des hearts qui vont jusqu'a |mes de
d^gre. Pourroit on les attribuer a quelque legere variation dans
la source meme de la chaleur, pendant le cours de I'exp^rience ?

Je pense en avoir dit assez, pour rendre probable la cause a
laquellej'attribue cette espece d'irregularit^ apparente,qui con-
siste dans Tacc^l^ration de I'echaufFement du thermom^tre
garanti ; cette cause doit avoir ete, I'in^gale action de la chaleur
accumul^e sur le corps interceptant, au commencement et a la
fin de I'experience.

§ 14. II r^sulte de ces considerations, et de la distinction cntre
les deux chaleurs, transmise et accumulee, que I'interception
calcul^e ci-dessus, dans chacune des trois expt^riences que nous
avons rapportees, n'est, a proprement parler, qu'une limite en
dessous, et laisse ind^terminee la limite superieure. Car, comme
nous ne savons point le rapport des deux chaleurs, (transmise
et accumulee,) nous ne pouvons point affirmer I'influence de
ehacune d'elles sur le r^sultat. Si la chaleur librement transmise
agissoit seule, nous aurions une progression reguliere de diffe-
rences, (comme on I'a au soleil libre,.) et les degres calculus
s'accorderoient aussi bien avec ceux qu'a donnes I'observation.
Mais il y a exces dans les derniers termes ; et cet exces doit pro-
venir de la chaleur accumulee ; celle-ci a done agi, et manifeste
son influence. D'un autre cote, la transmission libre peut avoir
6te fort petite; on pourroit meme la supposer nulle, et attribuer
a la chaleur accumulee, tout I'efFet observe sur le thermometre
garanti. Ainsi Ton peut bien dire, que la transmission reelle n'a
pas 6te plus grande que la calculee, puisque le calcul suppose

4t8 Professor Prevost's Remarks on Heat,

tout reffet produit par cette chaleur; mais elle pcut trds
bien avoir etc nioindre, puisque cet efFet a certainement et6
produit, en partie au moins, et peut-etrc en totalite, par unc
autre cause. L'iiiterception peut done avoir etc totale, ou tres
grande, mais jamais moindre que celle que le calcul nous a
donnee. C'est en ce sens qu'il faut prendre tous nos r^sultats
obtenus jusqu'ici, et tous ceux que nous allons rechercher encore.

§ 15. II y auroit maintenant quelque interet a examiner,
d'apres les calculs prdcedens, combien auroit du durcr chaque
experience, pour que le thermom^tre atteignit le maximum
d'echaufFement, c'est-a-dire, la temperature de la source, ou du
milieu dans lequel il etoit plonge ; car c'est a cette ^poque
qu'on auroit pu comparer immediatement les d^gr^s des deux
thermom^tres, exposes, I'un a la chaleur libre, et I'autre a la
chaleur gen^e par I'interception. Cependant, une difficulte se
pr^sente. II est facile de continuer les termes de la progression
au soleil libre, et d'en conclure les d^gr^s qu'on auroit observes
dans les minutes suivantes ; mais, pour le thermom^tre garanti,
comment tenir compte de I'effet in^gal de la chaleur accumul^e
dans la lame interceptante ? Arrivee a. un certain }X)int, cette
chaleur accumul^e, n'en ddveloppera-t-eile point meme de nou-
velle, comma il senible que cela a lieu dans les boules d'argile
^chauff^es au feu d'un foyer ? Quoiqu'il en soit, comme ceci
n'interesse point I'^chauffement au soleil libre, nous pouvons du
moins examiner ce cas. J'y joindrai le calcul de I'^chauft'ement
sous le talc, a cause de sa r6gularit6, qui semble indiquer que,
dans les termes suivans, la progression auroit (^te constante.

Comme I'observateur tient compte des huitiemes de degr6, et
non d'aucune fraction moindre, I'echauffement paroitra fini
plutot qu'il ne Ic sera r^ellement. Ainsi, vers la fin, on ne re-

a?id on the Action of Bodies zvbich intercept it. 419

marquera plus de difference sensible pendant une minute; mais,
en attendant deux ou trois minutes, cet accroissement se fera re-
marquer. Je trouve que dans la ire experience, (la 24,me de
I'ouvrage,) au soleil libre, le thermometre auroit continue jusqu'a
la 12 me minute, d'accuser, de minute en minute, un accroisse-
ment de chaleur sensible : il auroit alors marque 598 huitiemes
de ddgre. II se seroit pass6 encore quelques minutes, avant que
le thermometre eut acquis sensiblement (c'est-a-dire, a un
huitieme pres) la chaleur totale de la source, qui, selon notre
calcul, (§ 5,) etoit de 601 huitiemes de degrt^.

Je laisse I'experience faite avec le flint glass, (la 25me de
Touvrage,) a cause de son irrdgularite.

Celle ou le talc a 6te employe (la i22me de I'ouvrage) nous
fait voir, qu'au soleil libre il auroit aussi fallu 12' pour amener le
thermometre assez pres de la temperature du milieu, pour que
I'echauffement en une minute fut devenu insensible ; (c'est-a-
dire, moindre qu'un huitieme de degre;) a cette ^poque, il
n'auroit differ^ que d'environ |-mes de la temperature du milieu,
qu'il auroit assez vite atteint.

Dans cette meme experience, le thermometre couvert de la
lame detalc n'auroit rcquis que 9', pour arriver au terme auquel
une m.inute de plus ne produit aucun effet sensible; a cette epoque,
la chaleur du thermometre auroit differe de celle du milieu d'un
peu moins de -|mes de degre; et 3 minutes apres, c'est-a-dire, a
la isme minute de I'expi^rience, ces deux chaleurs n'auroient
pas differ^ sensiblement ; je veux dire, qu'elles auroient differ^
d'une quantite moindre qu'un huitieme de degre, qui est la
fraction la plus petite dont I'observateur ait tenu compte.

§ 16. Jusqu'ici je n'ai dis'cut^ que trois experiences, entre toutes
celles du meme genre, parceque ce sont les seules dont I'auteur

420 Professor Prevost's Remarh on Heat,

donne le detail. Pour toutes les autres, il se contente de rapporter
]e degr^ initial ct le d^gr6 final de chaqiie thermom^tre, parce-
qu'en effet ce sont les seuls qu'il emploie, pour en conclure, par
sa methodc, la quantity des rayons transmis et intercept's. II
sera facile a I'auteur de verifier ces remarques, par I'examen de
ses r'gistres plus detailles. Pour supplier a cette recherche,
qui n'est pas en mon pouvoir, j'ai essay' d'employer, d'une ma-
niere conforme aux principes exposes ci-dessus, quelques-uns
des resultats abreg's, qui s'ofFrent a nous en grand nombre.

§ 17. On peut remarquer que le rapport de 13 a 10, est moyen
entre ceux qui ont 't' employ's comme quotients de la pro-
gression des differences, et que I'observation a determines. ( §§ 5
et 11.) Je me tiendrai done a ce rapport; et je d'terminerai la
chaleur constante dii milieu par la proportion suivante. Les dif-
ferences cntre cette chaleur et chacun des nombres donnes par
I'observation, (I'initial et le final,) sont entr'elles comme le ler
terme de la progression est au 6me, c'est-a-dire, comme les
nombres 13 et 10 el'ves a la cinquieme puissance.

§ 18, Ainsi, prenant la sGme experience de Touvrage, on I'y
trouvera ainsi abregee :

All soleil A travers du

libre. crown glass verdatre.

o' 66i 66i

5 7S 7H 6|- 5 = 0,741

J'en conclus, (en partant du rapport de 13 a 10 pour la pro-
gression des differences,) que la chaleur constante du soleil libre
'toit, en huitiemes de degr', 604 ; et a travers le verre 584.
Rapport de ces chaleurs 0,967
Interception 0,033.

and on the Action of Bodies xvhich intercept it. 421

Z'lme.

o'

Soleil.
68^

5 151

Chaleur au soleil libre 267
Sous le verre - - 611
Rapport 0,974,
Interception 0,026

Coach glass (verre de carrosse.)

682-

741

7:51 — 0,786

Soleil.

o' 67

5 7H

Chaleur au soleil libre
Sous le cristal d'Islande 583
Rapport 0,975
Interception 0,025.

zSme.

Cristal d'Islande.
67

717 5f : 4i = 0,156

59^

stgme.

Soleil.

o' 67I:

5 72

Chaleur au soleil libre 590
Sous le talc - - 584
Rapport 0,990
Interception 0,010.

Talc.

7H

41- : Si- = 0,861

2ome.

Soleil.

o' 50

5 54i

Chaleur au soleil libre 453
Sous le talc calcinable 443
Rapport 0,978
In rception 0,022.

MDCCCH.

Talc aiscment
calcinable.

50

53i 4^:31 = 0,816

3I

428 Professor Prevost's Remarks on Heat,

^ime.

Soleil.

Verre rouge
tres obscur.

o' 73

73

5 79i

74i . . .

. . 6| : 1:^ = 0,200

Chaleur au soleil libre

- 654,

Sous le verre rouge obscur 598

Rapport 0,914

Interception o,c86.

j^ome.

Soleil.

Verre indigo.

0' 61 1

6i|

5 m

64 . . .

..61:2^ = 0,367

Chaleur au soleil libre 562
Sous le verre indigo 519
Rapport 0,923
Interception 0,077.
§ 19. Je vais encore rapporter quelques experiences, et en
tirer les rdsultats, comme ci-dessus. Mais je dois remarquer, que
dans les suivantes, il arrive souvent que les thermom^tres ne
sont pas d'accord au point de depart. J'ignore d'ou cela peut
dependre,

44W^ Experience.

Soleil. Les deux fonds de verre d'un tube

fernie, long de 3 pouces.

o' 53 53

5 59 55i 6 : 2f = 0,458

Chaleur au soleil libre - - 490
Sous les deux fonds de verre 454
Rapport 0,927
Interception 0,073.

and on the Action of Bodies which intercept it. 423

4;5^e.

Soldi.

Eau, et les deux fonds de verre du
meiiic tube ferme qui lacontient.

0'

5H

52i

5

sH

55 '

....6i

: 2^ =

: 0,442

Chaleur au

soleil libre

- - -

490

Sous I'eau et les deux fonds de verre

449

Rapport

0,917

Intercept

ion 0,083.

47;n^.

Soleil.

Esprit de vin, et les deux fonds de verre
du meme tube qui le contient.

0'

5H

5i|

5

bH

54 •

....6i

• =^8

: 0,388

Chaleur au

soleil libre

_

-

494

Sous I'esprit de vin et les deux fonds de verre 439
Rapport 0,889
Interception 0,111.

Soleil.
0' 52

5 57\
Chaleur au soleil libre

48w<r.

Ciri, (liqueur spiritueuse,) et les deux fonds de verre.

53t 5i: 1^ = 0,261

- - - 480

Sous le gin et les deux fonds de verre 434

Rapport 0,904
Interception 0,096.

some.

Soleil. Crown glass use a I'eraeri du cote expos*.

0' 67 G'j

5 74 7of 7 '3i = 0,52,6

Chaleur au soleil libre 61 4

Sous le verre - -

578

Rapport 0,941
Interception 0,059.

3I a

424( Professor Prevost's Remarks on Heat,

Sime.

Soleil. Coac/i glass (glace de carrosse) use i I'dmeri

du cote oppose.

o' 66i 66\

5 73i 69^ 7-3 = 0^429

Chaleur au soleil libre 660
Sous le verre - 568
Rapport o,S6i
Interception 0,139.

i4,Sme.

Aux rayons invisibles A ces memes rayons a travers un verre

du soleil libre. blanc bleuatre.

o' 48 47

5 49i 48f H'H = 0'929

Chaleur aux rayons libres 404
Sous le verre - - 394
Rapport 0,975
Interception 0,025.

1 ^gme.

Rayons invisibles. flint glass.

o' 5oi 49f

5 52 5H 1^:1^=3,000

Chaleur aux rayons libres 420
Sous le verre - - 413
Rapport 0,983
Interception 0,017.

150;??^.

Rayons invisibles. Cnwn glass.

o' 5oi 49i

5 5H 5o| i|: 11 = 0,818

Chaleur aux rayons libres 419
Sous le verre - - - 410
Rapport 0,978
Interception 0,022.

and on the Action of Bodies which intercept it. 425

iSime.

Rayons invisibles. CoacA glass (verre de carrosse.)

5 55i 54f i •• i = 0,857

Chaleur aux rayons libres 44,6
Sous le verre - - - ^^9

Rapport 0,984

Interception 0,016.

•iSzme.

Rayons invisibles.

Talc calcinable.

p' 5i|

50i

5 52|-

5ii....

.1^:1-1- = 0,750

Chaleur aux rayons libres 428
Sous le talc calcinable 419

Rapport 0,979

Interception 0,021.

§ 20. Cette comparaison, entre mes r^sultats et ceux que
I'auteur a deduit des memes experiences, donne lieu a quelques
remarques.

Premiere Remarque. Nous pouvons nous faire quelque id^e
de Tinexactitude de mes rc^sultats, fondes sur les deux nombres
extremes, en calculant aipsi les trois experiences que nous avons
deja calcules sur des donn^es plus d^taillees. Quant a la i22me,
(§ 11,) comme la progression est tres r^guliere, nous sommes
assures que les deux raetliodes co-incident, et toute comparai-
son est inutile. Dans les deux autres, au contraire, nous sommes
assures d'avance, qu'elles ne co-incident pas: et c'est cet ecart
qui nous interesse.

426 Professor Prevost's Remarks on Heat,

Q^me Experience.

Soleil. Verre blanc bleuatre.

o' 67 6y

5 73 717 6:41 = 0,750

Chaleur au soleil libre 602
Sous le verre - - 588
Rapport 0,974
Interception 0,026.
Mon r^sultat pr^c^dent (§8) donnoit pr6cis6ment, ou a un
huitieme pres, la raeme chaleur au soleil libre. Sous le verre
elle donnoit seulement 578 ; ce qui est bien naturel, puisque
I'^chaufFement sous le verre a exc6d^ la progression dans les
derniers temps ; en consequence, les rayons intercept's 'toient
exprimds par 0,038.

Le rapport des interceptions, d'termin'es par ces deux me-
thodes, est celui de 13 a 19, qui est tres voisin de celui de 2 a 3.
Ici done, pour trouver I'interception resultant du calcul fond6
sur toutes les donndes de rexp'rience, 11 falloit augmenter I'in-
terception determin'e par les deux nombres extremes, dans le
rapport de 2 33.

Q5me Experience.

5i' 5 = 0*909

Soleil.

Flint glass.

0' 6gi

%i

5 75t

74l

Chaleur au soleil libre 619

Sous le verre - 613

Rapport 0,990

Interception 0,010.

and on the Action of Bodies zchicb intercept it. 427

Mon r^sLiltat precedent (§ 9) clonnoit 614, au lieu de 6iq,
pour la chaleur au soleil libre ; et 604,, au lieu de 613, sous le
verre; et Tinterception ^toit 0,015, au lieu de 0,010. Ici done
encore, il auroit convenu d'augmenter I'interception, determinee
par deux nombres seulenient, selon le rapport de 2 33, afin
d'avoir I'interception resultant dc toutes les donnees.

On doit pr^sumer, qu'il en est de meme de la plupart des
autres experiences dont nous n'avons pas le detail. En appli-
quant cette correction a toutes celles qui sont dans ce cas, dont
j'ai fait ci-dessus le calcul, (§§ 18 et 19,') il en r^sulteroit la
table suivante, dans laquelle mes rdsultats sont rapproches
de ceux de I'observateur, tant pour la chaleur que pour la lu-
miere ; et ou Ton remarquera, que I'interception de la chaleur,
calcul^e selon ma ra^tliode, (d'apres la loi du § 3,) est con-
stamment moindre que I'interception de la lumiere, dont elle
est une fraction qui varie entre un et sept dixiemes.

428 Professor Prevost's Remarks on Heat,

Interceptioji de la chaleur par differentes matieres.
Sur 1000 rayons.

Kumeros

desexie- All SoleU.

riences.

24,. Verre blanc bleuatre

25. Flint glass

26. Crown glass verdatre

27. Coach glass (glace de car-

rosse) -. -

28. Cristal d'Islande

29. Talc - _ -

30. Talc ais^ment calcinable

31. Verre rouge tres obscur -
40. Verre indigo

44. Les deux fonds de verre d'un

tubeferme, long de3pouces

45. Les deux fonds de verre, et

I'eau que le tube contient

47. Les deux fonds de verre, et

I'esprit de vin contenu

48. Les deux fonds, et le gin

contenu

50. Crown glass \xs6 a r^meri

du cote expos6

51. Coach glass (glace de car-

rosse) us6 a I'^meri du

c6t6 expos^ - - 208 571 885

Aux rayons invisibles.

148. Verre blanc bleuatre - 38 71 —

149. Flint glass _ - - 25 — —

150. Crown glass - - - 33 182 —

151. Coach glass (glace de car-

rosse) _ - _ 24 143 —

152. Talc calcinable - - 31 250 —

Aufeu de charbon.
123. Talc calcine pendant I'ex-

perience - - 196 713 288

Interception

Interception

selon I'obscr.

selon la

vateur.

loi (ill k 3.

Chaleur.

LumiSre.

38

' 250

86

15

91

34

49

259

203

39

214

168

38

244

150

15

139

90

33

184

288

129

800

999^9

115

633

999^7

109

542

204

124

558

211

166

612

224

144

739

626

88

464

854

and on the Action of Bodies which intercept it. 429

Mais, outre qu'il y a probablement des cas auxquels la cor-
rection aura ^te appliquee mal-a-propos, (cas qu'il m'cst impos-
sible de determiner,) je crois, qu'avant de prononcer d'unc
manierc generale sur la quality de chaque corps, il conviendroit
de les rdduire tous en lames d'une ^gale dpaisseur, et de les
exposer a des chaleurs 6gales, par les raisons que j'ai expose
ci-dessus. (§ 13.) Mais il est probable, que ces causes d'erreur
ne masquent pas entierement la v6rit6.

§ 21. ^de Retnarqiie. La faculte interceptante de cinq sub-
stances, relativement aux rayons invisibles, conclue des expe-
riences i4,8me et suivantes, par les deux observations extremes,
est, selon mon r^sultat, (fonde sur la loi du § 3,) fort rap-
prochee de celle de ces memes substances, relativement a tout
le rayon solaire. [Exp. 34, et suivantes.)

Selon le resultat de Tobservateur, la difference est plus consi-
derable; elle est meme infinie par rapport au/m^^/fl55, puisquG,
selon cette maniere d'apprecier la transmission, les rayons in-
visibles ont tous traverse le jiint glass, et n'ont point ete inter-
cept's. Ce rdsultat, qui paroit invrarsemblable, surtout lorsqu'on
a sous les yeux la suite de ces experiences, suffit seul pour
ebranler la confiance en la methode par laquelle il a ete deduit.
On eprouveroit encore plus de defiance, si cette methode
venoit a presenter quelques cas, on la quantite des rayons
transmis parut plus grande que celle des rayons libres. Or, ce
cas peut tres bien se presenter; puisqu'il suffit pour cela, qu au
ler instant, la difference de la temperature du thermometre
place sous le corps interceptant, a celle du milieu ou il est
plonge, soit moindre que la difference de la temperature du
thermometre expose aux rayons libres, a celle de ces memes
rayons. Si ce cas ne s'est pas presente ici, c'est, sans doute, par-
MDCccii. 3 K

430 Professor Prevost's Remarks o« Heat,

ceque I'observateur avoit a dessein pris soin de mettre ces deux
thermometres an meme d6gr6 initial, Cependant, cela n'a pas
toujours eu lieu ; et, en consequence, il est arriv^ une fois, que
les deux thermometres ont varie ^galement pendant la dur^e de
I'experience. S'il tentoit de nouvelles experiences, en ayant soin
de tenir, au premier instant, la temperature du thermometre ga-
ranti beaucoup plus basse que celle du thermometre expos6 aux
rayons libres, on peut prevoir qu'il arriveroit souvent, en suivant
sa methode de calcul, que la transmission paroitroit avoir accru
le nombre des rayons.

§ 22. ^me Remarque. En jettant les yeux sur mes r^sultats,
compares a ceux de M. Herschel, on verra que ceux-ci don-
nent tous des interceptions beaucoup plus fortes. Une experience
de M. PicTET* donne une interception encore plus forte, et qui
surpasse toutes celles qu'indiquent les tables de M. Herschel,
du moins pour les verres polis et sans couleur. Un thermo-
metre, expose a une source de chaleur, monta de lo*; garanti
par un carreau de verre, ce thermometre baissa de 6°. II paroit
done, que ce verre interceptoit les -|- de la chaleur, ou 6oo
milliemes.

Ici I'observateur n'a point voulu limiter le temps, et paroit
avoir eu dessein de laisser son thermometre atteindre la tempe-
rature de la source, soit libre, soit genee; ensorte qu'on ne
peut se refuser a cette consequence, que le verre a derobe au
thermometre plus de la moitie de la chaleur, a I'influence de
laquellc on I'avoit expose.

Ce resultat s'eioignera moins de ceux qu'on peut deduire des
observations de M. Herschel, si Ton a egard aux considera-
tions suivantes. i. Quelle que soit lafaculte interceptante d'une

• Ess;ii sur le Feu, § 52.

and on the Action of Bodies which intercept it. 431

lame, I'interception doit croitre, si I'on augmente son ^paisscur.
Si done le carreau de M. Pictet 6toit plus epais que les lames
employees par M. Herschel, la transmission devoit 6tre moindre.
Cette circonstance de I'experience est inconnue de part et d'autre;
je n'en fais mention que comme d'une simple possibility. La
suivante est moins indeterminee. 2. Dans ^experience de M.
PicTET, le verre interposd etoit probablement froid, par com-
paraison au thermom^tre; la presence de ce corps froid, (quoi-
qu'a la distance de 5 pieds 7 pouces,) doit avoir eu quelque
influence. 3. De plus, ce carreau interceptoit un courant d'air
favorable a I'echauffement du thermom^tre. 4. Enfin, la source
de chaleur, absorbee en partie par le verre, n'auroit pas manque
de I'^chaufter a la fin sensiblement, et cet ^chaufFement se seroit
fait sentir au thermomare. Mais I'experience finit probable-
ment a cette epoque; car I'observateur dut naturellement etre
satisfait, quand il eut obtenu le maximum de refroidissement,
qui ^toit I'objet unique de son attention. D'ailleurs, I'appareil de
M. PicTET est tel, que I'action directe du verre echaufF^ ne peut
se faire sentir, que lorsqu'elle est deja assez grande.

Au contraire, dans les experiences de M. Herschel, on voit
des thermom^tres places a environ 2 pouces de la lame inter-
ceptante, et participant au moindre ^chauffement de cette lame.
11 n'y a d'ailleurs aucune cause de refroidissement; et les lames
sont probablement tres-minces,

Telles sont les causes auxquelles j'attribue les differences ob-
servees dans les r^sultats d^duits des experiences de ces deux
habiles physiciens ; et ces considerations nousramenent a dire,
que ces rdsultats, de quelque facon qu'on les calcule, varieront
tant qu'on ne prendra pas des lames de meme epaisseur. lis
varieroient encore probablement, si I'on faisoit varier la distance

3K 2

433 Professor Prevost's Remarks on Heat,

de la lame au therinom^tre, puisqu'on feroit varier par cela
mfime, I'influence de la chaleur qui s'accumule dans la lame.

Du reste, la petitcsse de mes resultats (fond^s sur la loi da
§ 3) n'a rien qui puisse surprendre, puisque nous avons re-
connu des I'entr^e, que nos calculs ne pouvoient nous donner
qu'une limite de petitesse. (§ 14). II est done tres vraisem-
blable, que lors qu'on sera parvenu a mesurer a-part la chaleur
transmise, on trouvera qu'elle est bien moindre, et rinterception
bien plus grande, que nos resultats ne la presentent.

§ 23. j^me Remarque. Et par quel moyen pourra-t-on par-
venir a faire cette appreciation, a decomposer I'efFet en ses deux
Siemens ? II me semble que ce doit etre, en observant I'efFet in-
stantan^e de la chaleur a travers un obstacle, et non son efFet
au bout d'un temps fini. II faudra done recourir a des thermo-
m^tres tres sensibles, tels que ceux d'air, employes et decrits
par M. PicTET.* En voyant comment ils se comportent sous le
verre, a I'instant meme ou celui-ci re9oit I'impression calo-
rifique, on jugera d'abord de I'influence de la chaleur transmise,
car on salt bien qu'il faut un certain temps pour que I'accumuiee
ait son effet; mais ce temps n'est pas suffisamment determine,
et le phenomene varie probablement a differentes ^poques.

§ 24,. ^me Remarque. Tout ce que je viens de dire s'accorde
fort bien avec un phenomene que M. Pictet a observd, et
avec I'explication qu'il en donne. Un grand miroir concave de
verre etame, ne renvoyoit presque aucune chaleur a son foyer,
sous I'influence des memes rayons qui, dans la meme situa-
tion, eievoient le thermometre de plus de 10°, au foyer d'un
miroir metallique. " Dans les miroirs de verre," dit M. Pictet,-{-
♦' ce n'est point la surface anterieure qui reflechit la plus grande
• Essai sur le Feu, § 56. f Ibid. § 67.

and on the Action of Bodies zvhich intercept it. 433

c< partie des ravons, c'est surtout la surface m^tallique appliqu^e
« derriere le verre. La chalcur, pour arriver a cette surface, a
" toute I'epaisseur du verre a traverser ; elle ne peut se refl^chir
" sans la traverser de nouveau, et, 6tant ainsi doublement tamisee
« par une substance qui ne lui laisse qu'un passage bien difficile,

« il n'en ^chappe que peu pour agir sur le thermom^tre

- mais, que devient cette chaleur ainsi interceptde par le verre ?

"....'.. Elle reste dans le verre, et s'emploie a le r^-

«' chauft'er; elle se repand dans sa substance, a raison de la
" chaleur specifique du verre, et on s'appercevroit sans doute de
" son effet, si le mircir restoit longtemps exposd a Taction du
" foyer calcrifique." Remarquons seulement, que cette action,
n'^lant point concentric au foyer, seroit peu sensible.

§ 25. 6me Remarque. En consequence de toutes nos dis-
tinctions et explications pr^cedentes, je me demande, quels sont
les phenomenes successifs que doit oftrir un thermometre place
derriere une lame interceptante ? 1. Au premier instant, la
chaleur transmise doit agir; mais probablement elle n'est qu'une
foible aliquote de la source de chaleur qui atteint la lame. 2.
Bicntot la chaleur absorb^e par la lame s'y accumule assez pour
rayonner, et envoyer au thermometre des emanations calo-
rifiques. Cette influence suit le progres de I'echaulfement de
la lame. 3. Enfin la lame s'echauffe au maximum qu'elle peut
atteindre; alors le thermometre se trouve dans un courant de
chaleur constante, et se fixe.

§ 26. ^me Remarciue. De quelle quantity, la chaleur sous
cette lame difF6rera-t-elle finalement de la chalcur libre ?

Si la lame 6toit plongee toute entiere dans la source de cha-
leur, de scrte que celle-ci I'enveloppat de toutes parts, comme
un bain, on sak que la lame acquerroit enfin la temperature de

Professor Prevost's Remarks on Heat,

la source ; mais, n'6tant en contact avcc elle que par une de ses
faces, elle doit sY^chaufFer moins que si toutcs deux lui fournis-
soient du feu ; ensorte que, par cette raison, elle ne peut
atteindre le d6gr6 de chaleur de la source. II y a un moment
oil la lame a acquis son maximum de chaleur; c'est celui oil
elle perd autant par ses deux surfaces, qu'elle acquiert par une
seule ; et ce maximum est n^cessairement moindre que si elle
acqueroit par toutes deux, par consequent, moindre que la tem-
perature de la source.

De plus, la chaleur r^flechie n'^chaufFe pas le corps qui la
refl^chit ; il faut done d^duire de la source de chaleur, tous les
rayons r^flechis, lorsqu'il s'agit d'estimer I'echauffement de la
lame interceptante.

Le thermometre plac6 sous le verre re9oit done, i . les rayons
transmis instantan^ment ; 2. les Emanations de la chaleur accu-
mul^e dans le verre ; mais il ne refoit pas les rayons refl^chis ;
et la chaleur du verre a un maximum peu eievE.

§ 27. Sme Remarque. Ceci Etant suffisamment Eclairci, on
concevra en quels cas le calcul des expdriences de M. Herschel,
par les deux extremes, donnera, ou ne donnera pas, des resultats
qui s'ecartent de ceux qu'on auroit ddduit de toutes les obser-
vations successives. Dans presquc tous les cas de ce genre, il
doit y avoir, en vertu de la chaleur accumulde dans la lame, un
echauffement final plus grand que ne le comporte la loi. En
consequence, si Ton ne prend que les extremes de chaleur, (le
degrd initial et le degrd final,) et qu'on suppose I'accroissement
de chaleur regulier, (c'est-a-dire conforme a la loi,) on sera
conduit ndcessairement a trouver I'interception moindre que si
on I'eiit calculde par les degrds observes aux premieres minutes.
C'est ce que nous avons verifie sur les experiences s^me et

and on the Action of Bodies which intercept it. 435

25me. Nous avons reconnu que, daiis ces expi^riences, cette
difference alloit a-peu-pres a la moitie dc I'interception estim^e
par les deux extremes ; ensorte que ces deux r^sultats etoient
entr'eux comme Ics nombres 2 et 3. (§ 20.)

Comparons maintenant, sous ce point de vue, deux sources de
chaleur in(5gales. Nous supposerons deux experiences, ou cha-
cune de ces sources agit, d'un cdt6 librement, de I'autre a
travers la meme lame interceptante. Si I'accroissement de cha-
leur sous le verre etoit proportionnel a celui qui a lieu sous
I'influence de la source libre, il est facile de voir que le calcul
de I'interception la feroit paroitre plus grande a la source la
plus chaude. En voici un exemple, fictif, mais propre a rendre
la chose sensible.

No. I.

Soleil. Verre.

o' 600 600

5 64,0 620
Ciialeur au soleil libre (555
Sous le verre - - 628
Interception 0,04,3

No. II.

Soleil. Verre.

6"oo 600

680 64,0

Chaleur au soleil libre 710

Sous le verre - - 655

Interception 0,077

II est vrai que les deux accroissemens, que j'ai supposes pro-
portionnels, ne le sont pas; mais, comme iis augmentent et
diminuent ensemble, et par la meme cause, on pent bien affirmer,
que la meme lame fera paroitre, au calcul, I'interception plus
grande sous I'influence dune source plus chaude, et reci-
proquement.

C'est aussi ce qu'on peut remarquer dans les experiences de
M. Herschel, ou, a travers les memes lames, on voit una
chaleur de feu de charbon, d'environ 730, produire une intercep-
tion d'environ 200; taiidis que, dans les experiences au soleil,

436 Professor Prevost's Remarks o« Heat,

une chaleur d' environ 600, n'a produit qu'une interception
d'environ 30.

§ 28. gme Remarque. C'est par la meme cause, qu'a travcrs

4, verres, au feu de charbon, I'lnterception a paru moindre qu'a
travers un seul ; car, dans rexpt^rience des quatre verres, la
chaleur du feu n'etoit que 635, au lieu que dans celles ou il n'y
avoit qu'un verre, elle 6toit 757, 731, 782, 741. Dans celle oil
il y avoit deux verres, la chaleur etoit 700, moyenne entre celles
que je viens de comparer, et I'interception a aussi 6t6 moyenne.
C'est ce qui resulte du calcul suivant, ou j'expose les experiences
et leur rdsultats, en huitiemes de degr6, deduits selon la m€-
thode expliqu^e ci-dessus, (§ 17,) en supposant, de minute en
minute, la progression des differences dans le rapport de 7 a

5, parceque ce rapport est celui que nous a indique rexp^rience
122, dont nous avons les details, (§ 11,) et qui a et^ faite dans
les raemes circonstances.

Experiences faites aufeu de charhon.
iiyme.

Feu.
0' 528

5 688
Chaleur du feu libre 724

Vcrre blanc bleuatre.
528

568

Sous le verre 577

Interception 0,203.

iiSme.

Feu.

5 %S

Flint glass,

57^

and on the Action of Bodies which intercept it. 437

Chaleur clu feu libre 73s

Sous le verre - 585

Interception 0,201.

ligme.

Feu.

Creinn gtasi.

0' 53(^

536

5 694,

580

Chaleur du feu libre 729

Sous le verre - 590

Interception 0,191.

iS6me.

Feu.

Crownglass use a I'emeri du
cote expose seulement.

0' 54,1

541

5 718

590

Chaleur du feu libre 757

Sous le verre - 601

Interception 0,20^.

i^'jme.

Feu, Coac/t glass (glace de carrosse) use a

I'emeri du cote expose seulement.

o' 544 540

5 %7 577

Chaleur du feu libre 731

Sous le verre - 585
Interception 0,200

MDCccri. 3 L

438 Professor Prevost's Remarks on Heat,

i^Sme.

Feu. CroziHi glass use 4 I'^meri des deux cotes.

o' 548 544.

5 739 5H

Chaleur du feu libre 782

Sous le verre - 593
Interception 0,244,.

Feu. CcacA glass use a remeri des deux cotes,

5 704. 564

Chaleur du feu libre 741
Sous le verre - 570
Interception 0,231.

140^^.

Feu. Les deux verres de crown et coaci glass

uses a I'emeri d'un cote seulement.

o' 528 528

5 688 ^59

Chaleur du feu libre 724
Sous les deux verres 566
Interception 0,232.

141;?/^.

Feu. Les deux mSmcs verres, uses a

I'emeri des deux cotes.

o' 534 534

5 670 548

Chaleur du feu libre 700
Sous les deux verres 551
Interception 0,213.

and on the Aclion of Bodies xvbich intercept it. 439
i^^me.

Feu, Les quatre verrcs dcs deux

experiences precedentes.

o' 528 528

5 640 539

Chaleur du feu libre - 665

Sous les quatre verres - 541
Interception o,i86.

Je viens a I'exposition de cette partie de la theorie de la
chaleur, dont j'ai dit que dependoit la loi de I'^chaufFement, que
I'observation directe a fait reconnoitre. (§3.)

Partie II.

§ 29. Plusieurs raisons m'engagent a suivre, dans I'expos^ de
la theorie que j'ai en vue, un ordre relatif a I'histoire de sa dd-
couverte. II resultera de la, que je paroitrai d'abord m'ecarter
un peu de mon sujet; mais j'y rentrerai tres vite, ou plutot je
n'en sortirai point.

Bacon proposoit cette experience: "Les chaleurs brillantes
" et radieuses sont exaltees par les verres : les chaleurs obscures
" et opaques, (comme celles des pierres et des metaux, avant
" d'etre rougis par la force du feu,) sont elles sujettes a la meme
"impression?"*

Plusieurs physicians post^rieurs avoient observe qu'un char-
bon ardent, plac^ entre deux miroirs concaves, ailumoit un corps
combustible a plus de 20 pieds de distance. Lambert attribuoit
cet efFet a !a chaleur obscure, et non a la chaleur lumineuse. II
6toit conduit a penser ainsi, parce qu'un feu tres ardent ne lui pa-
roissoit donner aucune chaleur au foyer d'une lentille convexe.-f-

* Inslaurat. 1. 5. c. z.

f Pyromctrie, § 378 et suiv. cite par M. De Saussure. Voyage aux Alpes, § 926.

3 L 2

44.0 Professor Pkevost's Remarks on Heat,

M. De Saussure r^solut de verifier cette id^e de Lambert, en
substituant au charbon un boulet cliaud, sans ^tre rouge. II
s'adressa a M. Pictet, pour faire ccttc experience, qui reussit
parfaitemcnt. Le boulet, occupant le foyer d'un dcs miroirs,
fit monter de lo^ d^gres le thermometre plac6 a I'autre
foyer. Un matras d'eau bouillantc, substitue par M. Pictet
au boulet chaud, produisit le mcme efFet, quoiqu'avec moins
d 'intensity.*

Ces experiences prouvdrent Incontestablement, que la chaleur
etoit susceptible d'etre reflechie, sous la meme loi que la lumiere,
M. Pictet a prouve de plus, que la Vitesse de la chaleur est si
grande en ce cas, qu'elle parcourt 6q pieds, dans un instant
sensiblement indivisible.-f

§ 30. Ces faits, quelque curieux et importans qu'ils soient, ne
forcent peut-etre pas le physicien a se decider sur la nature de
I'agent qui produit la chaleur, et en particulier sur le moyen par
lequel s'^tablit et se maintient I'equilibre de temperature entre
deux corps, ou entre deux espaces voisins. On se contentoit
done d'exprimer par le mot de tension, ou par quelque autre
equivalent, I'espece d'effort par lequel il s'operoit. Ainsi, lorsque
deux espaces sont inegalement chauds, la tension superieure du
plus chaud, I'emportant sur celle de I'autre, amene enfin un etat
dans lequel les deux tensions sont egales, et se balancent. Et,
quoique ce langage n'ofFrit a I'esprit qu'une conception indeter-
minee, on se crut oblige de s'en contenter, et de la recevoir
comme une loi de la nature, Cette loi etoit d'ailleurs semblable
a celle qu'on observe dans les fluides eiastiques plus grossiers,
par une suite de la compression qu'ils eprouvent. On ne savoit
pas si Ic feu etoit precisement de meme nature; mais cette com-

• Voyage aux Alpes, § 926. f Essai sur le Feu, § 64.

and on the Action of Bodies which intercept it. ^^p

paraison servoit a satisfaire I'esprit, et paroissoit en quelque sorte
^clairer le ph^nom^ne.

§ 31, Une experience nouvelle vint tirerles physiciens deleur
s<§curit^, et dut leur faire sentir I'insuffisance du langage con-
venu, dont ils s'etoient fait une liabitude. Bacon I'avoit indiqu^e.
" La chaleur, par les verres," dit-il, " acquiert de I'intensite ; en
" est-il de memc du froid ?"* C'est de lui, probablement, que
quelques auteurs subsequens avoient empruntd la meme idee.-}'
Mais cette idee ^toit restee sans execution, jusqu'a I'epoque,
encore recente, oii M. Pictet I'a r^alis^. M. Bertrand, Pro-
fesseur de Mathematiques, lui en suggera I'id^e; et voici com-
ment M. PicTET rend compte de Texp^rience. " Je disposal I'ap-
" pared precisement comme pour la reflexion de la chaleur ;
" j'employai les deux miroirs d'<^tain, a la distance de 10^ pieds
" I'un de I'autre. Au foyer de I'un ^toit un thermometre d'air,
" qu'on observoit avec les precautions requises ; et au foyer de
" I'autre, un matras plein de neige. — A I'instant ou le matras
" fut en experience, le thermometre plac6 a I'autre foyer des-
" cendit de plusieurs d^gres ; il remonta des qu'on enleva le
" matras. — Apres avoir remis le matras au foyer, et fait ainsi
" descendre le thermometre jusqu'a un certain degre, ou il de-
" meura stationnaire, je versai de I'acide nitreux sur la neige ; et
" le froid ainsi produit, fit a I'instant descendre le thermometre
" de 5 a 6 degr^s plus bas,"*

§ 32. A la vue de ce resultat, M, Pictet eprouva d'abord

• Instaurat. 1. 5. c. 2.

f "Les miroirs ardens concentrent la chaleur; peuvent-ils concentrer le froid ?"
Log'ique de Felice, T. II. p. 62. J'ai oui dire (mais je n'en ai point la preuve) que
I'auteur de cette logique avoit fait usage dss cr.hiers ilii celebre Professeur Cramer.

• Essai sur le Feu, § 69.

4,4,3 Professor Prevost's Remarks on Heat,

quelque surprise ; mais il n'liesita point a prononcer, que cette
reflexion du froid n'^toit qu'apparente, et qu'elle ne pouvoit etre
que la reflexion de la chaleur, en sens inverse.

§ 33. Cependant, aucune explication fondle sur les id^es de
tension, de pression, d'equilibre sans mouvement, ne pouvoit
faire comprendre comment cette inarche inverse de la chaleur
^toit d^terminee. En effet, les miroirs, Tair, et tous les corps
voisins du matras froid, etant tous entr'eux a meme temperature,
doivent, selon ces systemes, lacher leur chaleur vers ce gouffre,
et non dans aucune autre direction. On n'y voit point de raison
pour qu'un rayon parte du thermom^tre, et se porte vers le
miroir dont il occupe le foyer.

§ 34. Accoutume des long-temps a envisager le feu sous un
autre aspect, j'exposai ces difficult^s, et je tachai d'attircr I'at-
tention des physiciens sur cet objet, dans un memoire sur I'Eqid-
libre du Feu,* et dans mes Recherches sur la Chaleur. '\- Ces Merits
sont, si je ne me trompe, les premiers oii Von ait propose de
substituer un ^quilibre mobile, a I'equilibre immobile que les
physiciens ont coutume d'admettre en cette matiere ; et la con-
sequence de cette substitution fut, que le phenomene de la re-
flexion du froid s'expliqua aussi ais^ment, et aussi pleinement, que
celui de la reflexion de la chaleur. C'est, je pense, un caractere
de veritd ; car on sent bien, que ces deux faits sont honiogenes, et
qu'une bonne th^orie doit les expliquer a la fois, et les com-
prendre, pour ainsi dire, sous une meme formule. Qu'il me soit
permis de rappeler ici cette th^orie, que j'ai eu la satisfaction de
voir adopter par M. Pictet,]] et par d'autres bons juges. Peu

• Journal de Physique, Avjil, 1791. f Publiccs a Geneve, en 1792.

J Bibl. Brit. Sc. et Arts, T. IV. p. 30, et ailleurs.

ajid on the Action if Bodies zvhich intercept it. 4,43

de mots suffisent pour en faire saisir Ic principe ; c'est le seul
but que je me propose ici.

§ 35. Le feu -est un fluide discret, agite : chaque molecule de
feu libre est mue avec une grande vitesse ; Tune se meut dans
un sens, I'autre dans I'autre, de sorte qu'en tout sens, un corps
chaud eniet des rayons caloriliques ; et ces molecules sont assez
ecart^es les unes des autres, p ;ur que deux ou plusicurs courans
puissent s'entrecroiser, comme la lumiere, sans se troubier mu-
tuellement dans leur cours. Cette constitution du feu 6tant bien
concue, si Ton feint deux espaces voisins ou il abonde, on verra,
qu'en tre ces espaces il y a de continuels ^changes. Si, dans les
deux espaces, le feu est ^galement abondant, les ^changes
seront ^gaux, il y aura equilibre. Si I'un des espaces contient
plus de feu qje I'autre, les ^changes seront inegaux; le moins
chaud recevra plus de molecules ignees qu'il n'en donnera ; et,
apres un temps sL.ffisant,:a repetition cuntuiuelle deces echanges
retablira I'^qiilibre.

§ 36. De ces principes decoulent toutes les lois de la chaleur
croissante et decroissante ; en particulicr celle qui a servi de base
a nos calculs comparatifs de la raarche de deux thermom^tres
exposd^ a une meme source de chaieur, !'un sous une lame in-
terceptante, et I'autre sans aucun obstacle. (§ 3 )

En ertet, supposons un corps place cians un milieu plus chaud
que !ui, ct que ce milieu jouisse toujours d'une temperature con-
stante; on doit considerer la chaleur du milieu comme com-
posee de deux parties, I'une egale a celle du corps, I'autre egale
a la difference des deux chaleurs. Quant a ia premiere, les
echanges sont egaux entre le corps et ie milieu, il y a dquilibre.
L'exces de chaleur du milieu peat done etre consid^re seul ; et,
relativement a cet exces, le corps est absolument froid. Suppo^ions,

444j Professor Prevost's Remarks on Heat,

qu'eii line seconde le corps rc^oive la Y^rme partie de ce feu ; a
la fin de de ccttc seconde, I'exces ne sera plus que de -j^. La
JLme de ce nouvel exces passera dans le corps pendant le cours
de la 2me seconde, et I'exces sera r^duit aux -'-mes des -^mes.

' I O I o

On voit, en suivant ce raisonnement,qu'a la fin de la 3ine seconde,
I'exces sera la 3me puissance de -^•, et ainsi de suite; de ma-
niere que, (conformement a la loi observ^e) les temps croissant
selon une progression arithm^tique o, 1,2, 3, &c. les differences
d^croissent selon une progression geometrique 1, ^, (— )*,

On deduit, avec la meme facility, la m^me loi de r^froidisse-
ment, pour le corps plonge dans un milieu plus froid que lui.*

C'est ainsi que la vraie th^orie de la chaleur, fondee sur des
faits totalement diff^rens de ceux par lesquels Richmann a
prouv^ cette loi, nous y ramene n^cessairement.

§ 37. Nous avons vu, dans la ire Partie, I'applicatipn de ce
principe. Sous ce point de vue, les experiences de M, Herschel
acquierent un grand interet, non seulement en confirmant la
loi, mais en determinant le quotient de la progression des diff"d-
rences dans I'^chauffement de ses thermom^tres ; ce qui ne peut
manquer d'exciter sur cet objet I'attention des observateurs, et
de donner des idt^es tres precises sur le d^grd de sensibility de
I'instrument qu'on emploie.

Cette reraarque m'engage a ajouter encore ici le calcul d'une
experience de meme genre, faite a la lumiere reflediie d'une chan-
delle. Cette experience est rapport^e dans un memoire precedent
du meme auteur, lie etroitement avec celui que j'ai discut^.-f-

• Recherches sur la Chaleur, § 19.

■f Trans. Phil, pour 1800, p. 297. Exp. 2.

and on the Action of Bodies zcbicb ijitercept it. 445

D^n-rcs Dcgres calcules par Ic

observes. rapport de 6j a ji.

o' 432 432

1 440 440

2 448 44^

3 456 451

4 458 455

5 458 458

La chaleur du rayon etoit ici de 469 huitiemes de d^gre.

Les autres experiences de ce m^moire ne peuvent pas etre
ais6ment souniises au calcul, parce que, dans plusieurs, les temps
ne sont pas en progression arithmetique; et que, dans d'autres,
la chaleur du lieu varioit pendant le cours de I'experience, inde-
pendamment de cellc qui etoit communiqu^e immediatement
par la source ; ce qui trouble tous les resultats.

§ 38. La theorie exposee ci-dessus, {% S5,) explique la re-
flexion du froid pr6cis<^ment comme la reflexion du chaud, sans
plus ni moins de difficulte. Concevez, dans I'appareil du double
miroir, deux thermometres, places, I'un a un foyer, I'autre a
I'autre; et d'abord, que ces deux thermometres soient au meme
degre. 11 y a equilibre; le feu 6mis par chacun, et renvoye a
I'autre, en vertu d'une double reflexion, se trouve exactement
compense par le feu que I'autre lui renvoie par la meme voie,
mais en sens contraire. Maintenant, concevons que I'un des
thermometres hausse ou baisse ; aussitot (les echanges etant
inegaux) I'autre haussera ou baissera conform^ment.

§ 39. Cette theorie presente, en tout ^chaufFement, trois

especes de chaleur. La ire est celle qui est immediatement recue,

dans un instant donn6, par le corps qui s'echaufFe. La sde est

la chaleur accumulee, et emmagazinee, dans ce meme corps, en

MDCCCir. 3 M

44.6 Professor Prevost's Remarks on Heat,

vertu de r^chauffement qui a eu lieu dans les instans pr^cddens.
La 3me est la chalcur rayonnantc, qui est I'efFet des deux pr^-
c^dentes, et qui sort incessammcnt du corps, a mesure que les
autres )'• entrent. La consideration de ces trois chaleurs dis-
tinctes, a de I'influence dans plusieurs phenomenes, surtout dans
la metcorologie. J'ai eu occasion de faire remarquer, que I'esti-
jnation de la temperature des saisons en depend.*

En un mot, le nombre des faits auxquels cette th6orie s'ap-
plique, est assez considerable pour inspirer quelque confiance ; et
je ne sais pas voir quelle difficulte r^elle elle presente. -J-

§ 40. A la verite, quelques physiciens semblent disposes a
substituer dans la nature, les fluides continus aux fluides discrets,
et le mouvement ondulatoire a celui de translation. Je pourrois
dire, comme il est assez commode de faii'e, que je ne determine
rien a cet egard, et qu'on n'a qu'a mettre partout, dans ce qui
precede, des ondes qui se croisent, au lieu de courants et de
particules distinctes. Mais je ne crois pas cette substitution
legitime; et, sans parler de plusieurs raisons qui la combattent,
il en est une g^n^rale, qui seule devroit, a ce qu'il me semble,
la faire rejetter : les agens continus obstrueroient I'univers, et
s'opposeroient aux mouvemefts libres et rapides qu'on y observe.

§ 41. Pour me resumer, je dis, 1. Que I'efFet d'une source
de chaleur constante sur le thermom^tre, en un temps limitd,
n'cst pas proportionnel a la chaleur de la source. 2. Qu'on a

• Reflexions sur la Chaleur solaire, &c. Journ. de Phys. Fevrier, 1793.

f Je n'ai point parle de la communication de la chaleur par les corps qui la con-
duisent ; et je ne me suis point occupe, dans ce mcmoire, du feu latent et combine ;
ce n'etoit pas mon sujet. II est du reste facile a voir, que ces efFets ne contrarient en
rien la theorie que j'ai expose; mais s'allient, au contraire, ties bien avec les pheno-
menes de la chaleur rayonnante et librc.

and 011 the Action of Bodies which intercept it. 447

n^anmoins un nioyen dc conclure la chaleur de la source, de
son effet sur le thermometre ; parcequ'on connoit la loi que
suit cet effet, dans ses accroisscmens successifs. 3. Que cette
m^thode est la seule qu on doive employer, lorsqu'il s'agit de
comparer deux sources de chaleur, d'apres leur effet en un temps
limite, moindre que celui qui est requis pour le maximum de
I'effet. 4 . Qae, lorsqu'il s'agit de chaleur transmise, il faut dis-
tinguer celle qui est transmise immediatement, de celle que le
corps transmettant y ajoute des qu'il s'echauffe. 5. Que, lors-
qu'on neglige cette distinction, I'interception de chaleur attribute
a la lame n'est qu'une limite de petitesse ; ensorte qu'il reste
indecis, si I'interception n'a pas ete beaucoup plus grande, ou
meme totale. 6. Qu'en appliquapt ces principes aux experiences
de M. Herschel, I'appreciation devient plus exacte, mais de-
pend n^anmoins de quelques circonstances accessoires, et jusqu'
ici indeterminees. 7°. Que, dans ces memes experiences, la dif-
ference apparente entre I'interception de la chaleur et celle de
la lumiere, par les memes matieres, n'^tablit aucune conclusion
legitime sur la difference ou I'identit^ de la lumiere et de la
chaleur. 8. Que la loi mentionnee ci-dessus (et que j'ai
enonce au § 3) n'est pas seulement prouvee par I'experience
directe, mais par son accord avec la vraie theorie de la chaleur.
p. Oue cette theorie est etablie sur des faits varies, tout-a-fait
differens de cette loi, en particulier sur la reflexion du froid ; et
qu'elle est la seule qui s'accorde avec les phenomenes gen^raux
de la nature.

3M 3

C448 3

XVII. Of the Rectification of the Conic Sections. By the Rev.
John Hellins, B. D. F. R. S. and Vicar of Potter s-Pury, in
Northa mptonshire .

Read July 8, 1802.

PART I.

Of the Rectification of the Hyperbola : containing several new
Series for that Purpose ; together with the Methods of cojnputing
the constajit Qiiaiitities by ivhich the ascending Series differ from
the descending ones.

INTRODUCTION.

The conic sections are a part of geometry so requisite in men-
suration, in optics, astronomy, and other branches of natural
philosophy, that the properties of these curves have been much
studied in the course of the last hundred and fifty 5'ears: and
there is hardly a writer on fluxions, of any note, who has not
treated of their rectification. It inay therefore seem, that little
is now left to the industry of the present and future generations,
in this part of the mathematics, but the proper application of
theorems already investigated. Yet, while we admire the skill,
and praise the industry, of those who have discovered new
truths, or thrown new light on old ones, within that period, we
shall do well to recollect, that it is now no more than one hun-
dred and thirty-seven years, since the two great discoveries of
fluxions and infnite series were mude by Sir Isaac Newton ;
and that the observation of the late Mr. Emerson, respecting

Mr. Hellixs oii the Rectification, &c. 449

the state of fluxions in his time, is in a great measure appli-
cable to it in ours; viz. " If arts and sciences of ni uiy hundred
" yeai's standing receive daily improvernents and additions, it can-
" not be supposed that this most sublime art of all, found out but
"yesterday, can be arrived at perfection all on a sudden. If this
" art be so exceedingly useful and valuable, it certainly deserves
" the pains and attention of the learned mathematicians ."''^ — And
indeed, whoever considers the great number of mathematical
and ph3'sico-maLhematical problems which are solved b}^ means
of fluxions and series only, the several different ways in which
series may be applied to the solution of the same problem, the
fewness of those who employ themselves at all about these
abstract sciences, and the still smaller number of those who
have skill, leisure, and resolution enough to attempt any im-
provement in them ; I say, whoever duly considers these tilings,
(even without making allowance for the want of patronage
which the liberal arts have of late years experienced, ) will see
reason to think, that many ages must yet elapse, before this
most sublime and extensively useful method of computation
will receive all the improvements of which it is capable. He
will perceive, that, of the large field opened by Sir Isaac New-
ton, a considerable part is still covered with briars and thorns.
He will have no doubt, that the mine is not yet exhausted, but
that, although the first workers of it have carried away the
largest and most brilliant diamonds, enough still remain to
reward the labour of those who shall have the resolution to dig
deeper, and the patience of those who shall 3'et carefull}^ sift
the rubbish which has been thrown up by former adventurers.
The subject of the following sheets was first offered to my

* Preface to his Fluxions.

450 Mr. Hellins on the Redif cation

consideration in tlie year 1770, when a problem requiring the
rectification of a large portion of an equilateral hyperbola was
proposed in a periodical work; which problem I then solved by
means of descending series ; but, for want of an easy method
of correcting the fluent so found, I laid it aside for the exercise
of maturer judgment. Afterwards, the subject was resumed at
different times, as leisure permitted, and put into nearly the
same form in which it now appears, in the year 1795; since
which time, till now, the duties of my station, and unexpected
occurrences, have left me no opportunity to revise my papers.

As the investigation of the following theorems is very obvious
and easy, I thought it probable that they might have been dis-
covered by some other person before me ; yet, upon perusal of
Dr. Button's mathematical and philosophical Dictionary, lately
published, I find but one of them. And since, in the compilation
of that work, as the learned and industrious author professes,
" Not only jnost of the encyclopedias already extant, and the
" various transacliojis of the learned societies thronghout Europe,
" have been carefully consulted, but also all the original works, of
" any reputation, which have hitherto appeared npo?i these sub-
" jects,"* I therefore conclude that all the rest are new.

The subject of this Paper is naturally divided into three sec-
tions: the first containing the investigations of the several
series; the second, the methods of computing the constant
quantities by which the ascending series differ from the de-
scending ones ; and the third, examples of their use, by way of
illustration. But, for more convenient reference, I have further
divided it into articles, or minor sections,

• See Dr. Huttok's Address to the public, on the publication of the first part of
the Diclionary above mentioned, in 1795 ; and preface to the Dicl'tonary.

oj the Conic Seclions. 4^1

Sect. I. The Investigations of the several Series.

1, That the following processes ma}' not be incumbered with
symbols, and that the rate of convergency of the series obtained
therefrom may be the more obvious, let the transverse axis of
any hyperbola be called qu, and the conjugate axis 2; (by
which notation, any ratio that these two lines can possibly have
to each other may be expressed;)* let the abscissa be called x,
the corresponding ordinate to the aiis, y, and the length of the
curve from the vertex to the ordinate, z. Then, by the well-
known property of the curve, we have 2ax -f- ^'^' = a^yy I from
which X is found z= a\/ (\ -f vy ) — a, and x = ,, "/ — r, and

equation, by writing ee for 1 + aa, will become s ==^-^--j^— ^-y^.

2. Now, the fluent of the expression on the right-hand side
of the last equation may be taken in different series, according
as the numerator or denominator of it is converted into series,
and according as 1, eeyy, ov yy, is made the leading term. By
converting the numerator, \/ (^1 -\- eeyy), into series, making 1
the leading term, w^e get z = —rr^, — r x : 1 + ^^ — — h

%e_y hliy^ &c. and then, by taking; the fluents of -rr^, — r,

2.4.6 2.4.6.8' 'J t> V(i-l->7)

,/y , , ./-f ,, &c, and denoting them by A, B, C, &c.

respectively, we shall have

• With respect to homogeneity, about which some have shown more scrupulosity
than discernment, I shall add a few words in a subsequent part.

452 Mr. Hellins o)i the Rectification

A = H. L. ofj + V(i+;;y),
jj__ yV{i + yy) —a

2 '

r yWii+yy) — 3B
^— -4 .

T->_yV(' + 3'.v) - 5C

■^ — 6 '

Tr_3'V(i + yj) -7D
r._ - ,

&c. &c.

And, lastly, by multiplying these quantities by their proper
coefficients, we obtain ( Theorem I, )

^ = A + -i^B fl-C + ^D-^i^E,&c. where

' 2 2.4 ' 2 4.6 2.4.0 8 '

it is manifest that, unless the quantities B, C, D, &c. decrease
in the ratio o^ ee to 1, the series will at last cease to converge;
or, in other words, if yy be greater than — ^, the terms of the
series, at a great distance from the first, will diverge. And, of
the nine theorems now produced, this is the only one that I
have found in any other book,

3. But, by converting ■v/(i -\-yy), the denominator of the
fraction in the fluxionary equation in Art. I. into series, making

1 the leading term, we have z=^y s/ {\ -{- c^yy) x : 1 ~

M Ml .3J21 _i. JLipl &c. and, by taking the fluents of

' 2.4 2.4.6 ' 2.4.6.8 ' » J o

>v/(i + ^^yy)^ nyVi^i- <^ny)^ j/v/(i + ^ny)> ^^- ^"^

calling them A, B, C, &c. we shall have

A=-f-v/(i + ^O.v; + -ij- y^H.L. ey + V {I + eeyy J,

B =

y {'+ eeyy)T: — A

i__ v'(i+ ecyy)i — 3B
bee

D =

j!(l+ ceyy)% — 5C

»ce
£ y (1+ eeyy)i — 7D

I oce
&C. &C.

of the conic Sections. 453

And then, by multiplying these quantities by their respective
coefficients, we obtain (Theorem II,)

Avhich series will converge till y becomes greater than 1 ; and
consequently is a better series than that above found, which
ceases to converge whenjy becomes ^eater than •^. But, when
y is much greater than 1, each of these series will diverge very
swiftly; and, notwithstanding tliey are of that form which
admits of a transformation to others which will converge, still,
even by that means, their values will not be obtained without
great labour. But here we shall have the pleasure of finding
scries which will quickly answer the purpose. For,

4. By converting the denominator, -/(:».>' + 1), into series,
making >;y the leading term, we get z = y ^ {eeyy -^ 1)

And here, again, by denoting the fluents of-^^^ — ~—^ — j

yv/(rgvy+0 yx'jeeyyJr^) ,^ ^^^ by p^^ g^ Q &£. respectively, WC

,,3 5 ^s

shaU have A = v/ {<^eyy + 1 ) + H. L. '' J^ ,

n - \eeyy + l)i . ee\

- [eeyy -\- i)l ee'S

Ay* 4

- {eeyy + -)i __ ^eeC
6y' 6

- {ee^y+ i)l _ 5^"^
»y^ 8

&C. &C.

C =
D=
E =

and then, (Theorem III,)

^_rA-iB+^C-^D + -^E,6cc.

MDCCCII. 3N

454) ^f- Hellins on the Rectification

which series will converge the swifter the greater jy is in com-
parison of 1, but will diverge when y is less than i. It also
wants a correction, (here denoted by the letter d,) which shall
be given in its due place. This series then, when y becomes
great in comparison of i, will converge very swiftly, and be-
comes useful in those cases where the ascending series above
investigated fail.

But, since the value of z may be expressed in another de-
scending series, it will be proper to consider that also.

5. The expression -^y;.-^;f is evidently = -^ v^ ( 1 +

J^,^ J, which, by converting v' (1 + -jf^j into series, making

1 the leading term, becomes ^ J^^^,^) x : 1 + -j^— 7:^

J 3^ >-|-s-T-, &c. Here, the fluent of ,./f . ,

the first term of the series, is e\/ {1 -\- yy) ; and, calling the

fluentsof^^^f^^^^, -j^r^, T7C.TW ^'- ^' ^' ^' ^'^
respectively, we have

g_ -Vto+O

zyy 2

-V(xv+i) 3K

C:

^— 6/ 6

&C. &C.

and thence, (Theorem IV,)

^=U-i-A-TirB + -■^:^C--^g3^D, &c.

L—d:
which series will converge the swifter, the greater y is in com-

of the conic Sectiom. 455

parison of 1, and has an evident advantage over the last, in that
it converges by the powers of ee, as well as by those of yy ; so
that its convergency will not cease, till the quantities B, C, D,
Sec. increase in the ratio of 1 to ee, that is, when y becomes
equal to, or less than, — ^. This series, therefore, will be very
useful for the greatest part of the hyperbola, when it is corrected
by the constant quantity here denoted by d, the value of which
is attainable several ways, as will appear in the next section,

6. These four theorems, or indeed two of them only, are
sufficient for the rectification of any portion whatever of any
conical hyperbola. Yet, as I liave discovered several other series
for that purpose, which are more convenient in particular cases,
and of which some are useful in computing the constant quan-
tity above denoted by d, (by which the ascending series differ
from the descending ones,) it may be proper now to give the
investigations of them also.

7. Put 1 -j- eeyy = uii ; then will yy be == -" ~ ', and 1 -{-yy
= "" + "^^ ~ ' = (by the notation in Art. 1, where ee was put

= aa-\- 1,) "" + '"' , and therefore v^ (i +yy) — VC^ + ^^i)
and thence </ fi-ifi2Z. ) =: '''- — — . Moreover, y will be =

— r-> aiid we shall have y </

(uu — I ) ' y V

u ml u u u u

I + eeyy

X

\\ j^\K -r ; v/(""— i)Xv^(i + —

uu]

-^ + -^ - -^ + -^'f^, &c. Now the fluent of

zuu ' 2.4H+ 2.4.0!^ ' 2.4.o.8«'' '

/'" — is ^{un — 1) ; and, if the fluents of —-7-'-^ — -, -rrr- — r,

'uWU'x-i) ' ^^' '^^"^ denoted by A, B, C, &c, respectively, we
shall have

3N 2

45^ ^f' Hellins on the Rectification

A = circ. arch, rad. being i, and sec. u.

V{uu-i) , A

2UU '^ 2

V(""— 0 , 3B

4"* ' 4 '

n V(""— 0 1 5C

^ — — bl? r-6-'

&c. &c.

And, lastly, by multiplying these quantities by their proper co-
efficients, and collecting the several terms in due order, we
shall have (Theorem V,)

5r = ^(zm - 1) - -^ A + -i^B - -fif C + iifL' D, &c.
^ ^ ^ 2 ' 2.4 2.46 < 2.4.68 '

Here it is remarkable, that the terms -^'^^i=^, ^Jllll^^ '^^^.

' 2UU ' 4I(+ ' tu''

&c. which enter into the values of B, C, D, &c. always decrease
while y increases from o ad injinitiim; and indeed decrease
more swiftly than the terms of either of the descending series
in the preceding articles ; and therefore this series may be used
for computing the length of any portion of the hyperbola. For
although the terms of it, taken at a great distance from the first,
will diverge by the powers of aa, when a is greater than 1, yet,
as the signs of these terms are alternately -\- and — , it admits
of an easy transformation into another series, which will always

converge by the powers of "^ . It also wants no correction ;
in consequence of which it has a peculiar use, which will appear
in the next section.

8. But the fluxionary expression '^,„u_iV"'^iuu+aay obtained

in the preceding Art. is = '^^ — = ^~:^ x :

V(««+«<Oxv'(i- — J

1 4. _L_ J 1_ J 11—. J ^:^^, Sec. Here the fluent

of the conic Sections. 457

<3f ,, "'! — r- is 1/ (uu + a^z ) ; and, if the fluents of — — r-.

■ , ,, " , — r, , ,, "-; — :-> &c. are denoted by A, B, C, &c. we
shall have

B =
C

'[iiu-^aa) A

Ziui i/» 2aa
~\/{iui + aa) 3B

— v/{!"< + '?") 5C

baa ii^ baa '

&C. &C.

And, by multiplying these quantities by their proper coefficients,
and collecting the products together, we shall have (Theorem
VI,)
^_r,/(m. + ^^) + iA+-^B + ^C + ^-iJI.D,&c.

Here also, the terms _^±ffL, _V(iiii±££L, -^+^, &c.

which are component parts of this series, always decrease while
y increases from o ad infinitum ; and therefore the length of any
portion whatever of the hyperbola may be computed by this
series also, when the value of the constant quantity d, to be
taken from it, is known. But the case to which this theorem
ought to be applied is, when y is equal to, or greater than 1.
And it has an advantage over some of the descending series, in

that the terms — ;-, -^ B, -|-C, Sec. are divided by aa, as will
appear in the use of it.

9. When a=.i, that is, when the hyperbola is equilateral, the
fluxionary equation in Article 7 becomes z = --: t^^, — t— r

45^ Mr. Hellins on the Rectification

v/(«+— I) ,, I i "T" 2M-* ' 2.4H» ~l Z.A.O" ~r 2.4.6. 8tt'*'

V(>-— J
&c.; the correct fluents of which arc (Theorem VII,)

ru I I hi 3-;.7 ^^^

^ I 2.3M^ 2.4.7!*' z.4,6,iim" 2.4,6.8.i5m'5 '

Whicli series is better adapted to tliis case than either of the
preceding ones, in that it is much simpler, and converges twice
as fast. And the correction of it is easily attainable by various
methods.

10. But the original fluxionary equation in Art. 1, admits of
a conversion mto series, two different ways from any of those
which have yet been taken. For, by the Binomial theorem,

V /ri _j_ ""yy \ ;q — V _L-±L yyy "* yy* 1 3'^°

JV ;,i-t- ^^yy] J^— jC-t- 2 • ^J^yy ^.^ ' (,+^^.)" "^ ^-^ ^

-it— U£^, y/ , &c. where, putting A, B, C, &c.

for the fluents of -j^, -^t^^ , {i+yyy ^^* respectively, we
have

A =:j' — circ. arch, rad. 1, and tang.^y,

B — yl u J^

c_ y" ljJL

dec. &c.

and thence (Theorem VIII,)

js = y_L_ff_A— ^B + -^VC ^D,&c.

y > 2 2.4 ' 2.4.6 2. 4.6 8 '

In which series, it is pretty evident, the quantities A, B, C, D,
&c. will have a convergency while y increases from o ad infi-
nitum, although the convergency will be but slow after y
becomes greater than 1. It is obvious too, that this series

of the conic Sections. 45c)

vanishes together with j, and therefore needs no correction. And
for this reason chiefly I have introduced it, as it affords us ano-
ther mean of obtaining the value of the constant quantity d, by
which the descending series are to be corrected.

11. But the fluxionary expression j/ v/ (— ^r^ > obtained in

Art. 1, is evidently =j)/ V{^^ + ,_ , ] =also toj ^/[ee -j ;

and this expression converted into series, by the Binomial
theorem, becomes ey

aay a* y 3" i

2e{\-\-yy) 2^e'{\-\-yyY 2.j^.6e' {^].-\-yyY

z-^^rt^, — TT-i &c. Here arain, denoting^ the fluents of

z.4.6.bt'' (i +_)'v)* ' o ' o

-f — , , / ,„ -7— r— r„ &c. by A, B, C, &c. we shall have
A^ circ. arch, rad. i, and tang, y,
p_ y I A

2(I+XV)

.•5B

y , sc

^~ b,i+yyV ' 6 '
&c. &c.

And, by proceeding as before directed, we get (Theorem IX,)
z = ey A T-^ V^-^ . „ ,-D, &c.

•^ ze 2.^e' 2.4.6«' 2.4.6.8e' '

And this series, it is obvious, will converge the swifter the
greater jy is, so that it will begin to converge swiftly when the
preceding series begins to converge slowly. It is evident too,
that this series vanishes together with y, and therefore wants no
correction. Moreover, it has an advantage over the preceding
series, in that the coefficients of it decrease by the powers of
-^, that is, by -~^. And it supplies us with a different ex-
pression of the value of cl, as will appear in the next section, to
which I now proceed.

4^o Mr. Hell INS on the Rectification

Sect. II. The Methods of computing the Values of the constant
Quantities by zvhich the ascending Series differ from the de-
scending ones.

12. Now the methods of obtaining these constant quantities
are such as are shewn in my Mathematical Essays, (pubHshed in
1788,) pages 100, 101, 102, &c. to 112; viz. either by com-
puting the value of both an ascending and a descending series,
taking forjy some small definite quantity, or by comparing the
values of those series together when y is taken immensely groat :
the former of which methods is more general, but the latter,
when it can be applied, commonly affords the easiest compu-
tation. In this section, I shall make use of both these methods,
as the one or the other is best suited to the case in hand. I
begin with the use of the latter method, in comparing together
all the diflferent expressions of the value of r, which are reduced
to few terms in the case when y becomes immensely great.

Now, when y is taken immensely great, the value of z in
Theorem III, Art. 4, becomes barely = ey — d. For, in this

case, the H. L. '^-^"^ becomes the logarithm of the

ratio of equality, which is = o. And then A is barely =
^{eeyy +i)+o = ^j + -rJj — -^-pjr, S^c. all which terms,
after the first, vanish in this case; and therefore eeA, which
occurs in the value of B, becomes barely e^y. Moreover, the

radical expression __iii£iZ->L+12l which enters into the value of
B, becomes barely = ~^ ^ ; and tiience we have B = ~'^ ■^'+^2

A 1 • 1 r^L • (eevv-i-i)i {e<rvv+l)x „

:= o. And, since each 01 the expressions ^ , '^^J , &c.
evidently becomes = o, in this case, and since B has been

of the conic Sections. 4,6' i

shown to be = o, it will thence follow, that all the terms denoted
by C, D, E, &c. will vanish, and there will be left z = ey — d.

13. And in like manner it will appear, that the value of z
in Theorem IV, Art. 5, when y becomes immensely great, is

also = ey — d. For, in this case, II. L. -^^ becomes

= 0; and each of the expressions -^^^'■^'tlL -LJZliL gcc. also

becomes = o ; and, consequent!}', ^=\ ^^ y^ ' ^ '' Bui , since
<? is a finite quantity, the expression ^ \/{yy -\- 1) = ey -\-

~ -7-, &c. when y is immensely great, becomes barely

= ey. Therefore, in this case, we have z = ey — a.

14. Corollary. And hence it appears, that the series in
these two theorems are equal to each other, and, consequentl}^
that the constant quantity to be subtracted from each of them,
by way of correctic^n, is the same.

15. The first term of the series which expresses the value
of ;r in Theorem V, Art. 7, is ^{\m — 1), which, by the nota-
tion there used, is always = ey. And, when y becomes im-

mensely frreat, the terms -^-^ -, -^ — ■. — -, -^-4-z — — , &c.

w hich enter into the values of B, C, D, &c. vanish ; but A be-
comes = the quadrantal arch of the circle, oj which the radius is

1 ; and thence we have B = -^, C = i B, = -^ A, D = -|-

2 ' + ' 2.4. ' 6

C == ~~r- A, &c. and these values beinjr written for B, C, D,

2.4.6 O 5 ) >

&c. in the series, we have, in this case, z = ey — -^ A -f-

-iSV^ ITTTr ^ + T^W^V&c- And, since this series

always gives the correct value of z, we hive now discovered the
value of d, the constant quantity to bo subtracted from tlic

MDCCCII. qO

463 Mr. Helliks on the Rectification

descending series given in Theorems III and IV. The series to

w Inch (i IS =, VIZ. A X : \- ^ />, a'>

2 2.2.4 2.2.4 4.0 2.2.4.4.6 6.3

dec. will indeed diverge when a is greater than 1 ; yet, as was
observed in Art. 7, it is of that form which admits of transfor-
mation into another which will always converge.

16. For the reasons above given in Articles 12 and 13, each
of the terms A, B, C, &c. in Theorem VI, Art. 8, vanishes
when y becomes immensely great, and z is then barely

= I ^S ' ^ And, since y^ [iiu -\- aa) is, by the notation

in Art. 1 and 7, = \/{eeyy -\- e^'j, which, in this case, becomes
barely = ey, we have z=^ey — d. Here we see that the series
in this Theorem, and in Theorems III and IV, are always =
to each other, and consequently differ from each of the ascending
series by the same constant quantity d, the value of which was
discovered in the preceding Article.

17. When y becomes immensely great, the value of z in
Theorem VII, Art. 9, becomes barely := « — d. And, since 11 is
universally = \/{_i'eyy + 1 ), it will, in this case, be = ey ; and
we shall have z = ey — d, which is the very expression given
by all the other descending series in the like case. But, when
the hyperbola is equilateral, as was supposed in Art. g, a is
= 1, and we have d = 1-57079632 x : i — -^ + TT^^fiT

3-3 5-5-7

&C.

2.2.4.4.6.t).S '

Moreover, when y is = o, s; is also = o, and « is = 1 ; and

therefore, by this theorem, w^e have o =

' r 1 1 1 ^ i^^, &c. or

J 23 2.4.7 2.46.11 2.4.68.15'

{-d
d — i ! I ^ ^^- , &c.

2-3 2-42 2.4.6-11 2.4.6.6.15

of the conic Sections. 463

And hence it follows, that this very slowly converging series is

= 1 -57079632 X : i - ^ + -rrfra - -rft^' ^'- ^y

which expression its value is easily attainable, and will be found
to be =: 0-599070 1 2.

I observe, in transitu, that tlie ratio of this slowly converging

series, 1 ' ^ ^— — ,^2'L- » ^^- ^° ^ ^^""'^^

' 2.3 2.4.7 2.4..6.11 2.4.0.5.15

of good convergency, is easily attainable ; by which mean we
may likewise compute its value to any degree of exactness.

18. A general expression of the value of d being found in
Art. 15, by which it may be computed, whatever be the ratio
of the two axes of the hyperbola, I might now proceed to show
the use of the theorems by a few examples ; but, as the same
series is attainable another way, and the same value of d is
attainable also by different series, it will be no less curious than
useful to show in what manner.

10. Tiie ?/th term of the series of quantities -7-— — r, -tttttt^'
-T~— T7-, &c. which enter into the values of B, C, D, &c. in
Theorem VIII, Art. 10, is evidently ~^ , ^^, , which, by the

_,. . 1 , • _v=' + " _2H —zn—z , n-\-i

Binomial theorem, is = — x : JV — ny -\- n . — ;;—

^ — 2« — 4 ?I-f-I «4 2 _2M — 6 n , V I ' n-\- I r,

y ' 2 ' 2 -^ ' ' ' 2'i iy 4)'^ '

which, when y becomes immensely great, is barely = — — . And
the value of A, in this case, is y — the quadrantal arch of a circle,
of which the radius is 1. Let this quadrantal arch be denoted
by «; then, by substituting For A, B, C, &c. their proper values
as they thus arise, we have

3O 2

464 ^^- Hellins on the Rectification
A= y —

2 "•" 2 2 -^ 2

3-5 „ 3-5

c = --^ + ^ — J4-«=>'-

4 ' 4 2-4 -^ 2-4

6 ' 6 2.4.6 -^ 2.46

&C. &C.

And, lastly, by writing these values of A, B, C, &c. in the
Theorem, we have, in this case,

y + -T^y - -r^y' &^-
2.2.4 2.2.4.4.0 ' 2.2.4.4.6.6.8 '

But the series y + -^y - -~y + -^y - -^^y, &c. is
evidently = j' \/(i + aa), which, by the notation in Art. 1, is
= ey. We therefore have, in this case,

^ — ey — ay. . — ^^^ -t- 2.2 ^.4.6 2 2.4.4.6.6 8 ' "'^•

And, since this theorem always gives the correct value of z, we
have now the satisfaction of seeing a confirmation of the truth
of our conclusion in Art. 15, by obtaining the very same ex-
pression by a very different process.

20. From what has been shewn in Articles 12, 13, &c it will
be very evident to any one who runs his eye over the coinpo-
nent parts of the series given in Theorem IX, Art. 1 a, that, when
y becomes immensely great, A becomes = the quadrantal arch
of a circle, of ivbich the radius is 1, which arch was denoted in
the preceding Art. by a; and that

B = o+-^= i u,

C = o -4- -^ = — ^— a
"1" 4 24 >

D = o + 4-=-^«,

' b 2.4.0

&c. &c.

of the conic Sections. 465

And, these values being written for A, B, C, &c. in the Theorem,
it gives, in this case,

Z=iey a. r a , , « ■ ' ^. ,«, &C.

•^ ze 2.2.41'^ 2 2.4.461' 2 2.4.4., 6 be'

And, since this Theorem also always gives the correct value of
z, we sliall, by comparing the expression now obtained with
those which were found for z, in the like case, in Articles 12,
^3> 15> "i^j ^nd 13, see that we have now got another general
expression of the value of d, viz. a. x : -^ -| — 7 — j -|

13"'

2.2.4C^ ' 2 2.4.4.06'

H ^'^ '^^I' , , &c. in which series f<? is = aa 4- 1 . and there-

' 2.2.4.4.6.6.)ie' ' "• I '

fore it must alwaj^s converge. Yet it should not be hastily
concluded, that this expression of the value of <i is always pre-
ferable to that which was obtained in Articles 15 and 19; for,
when rt is a large number, the powers of -^ = , by wiiich

the series converges, will decrease very slowly.

21 . However, when it happens that a is a large number, the
value of d may be obtained by means of two series, which, in
that case, will converge pretty swiftly ; or indeed by means of
three series, each of which will converge about twice as fast as
either of the two series. But, for the sake of brevity, I shall at
present describe tlie method of computing the value o{ d by two
series only, and so conclude this section.

The series proper to be used on this occasion, it is obvious,
are those which are given in Theorems II and IV, Articles 3
and 5; and the value of jf to be assumed, is — ^, with which va-
lue each of the series will have nearly the same rate of con-
vergency. As this will best appear by an example, I will give
one, taking a='j. Now, with this value of a, we have ee = aa
+ 1 = 50, and y= -L.=^ -J—. — o-i^i^sis^S ; and, by

466 Mr. Hellins 071 the Rectification

allies for e and y in Theorem

>/(i + 0 + -l7-H.L.(v/^4-V'(i+^))=o-6547,32o,

writing these values for e and y in Theorem II, Art. 3, we
have

A =
B =

e i(.+e)l -A

j^ee

c =

(1+C';I- 3B

bee

E =

Ue

F =

(14^)1 _9E

S^V {l+^)i — llF

G =

&c.

and thence

&C.

• = 0-0398,4,09,
= 00036,665,
= 0-0003,853.

= 0-0000,4,34,
= 0-0000,051,
= 0*0000,006,

+

A = 06547,320

-^7^ = 0-0013,750
Z.4

3-5-7
2.4.6.8

3-5-7 9"
2.4.6.8.10.12

E = 0-0000,119
G = 0-0000,001

+ 0-6561,190

— 0-0200,422

iB = 0-0199,205

^■^ D =: 00001, 204

2.4,6

3-5-7-9

—I'l F = 0-0000,0 1 Q

.4.6.8.10 ' J

2.4

— 0-0200,422

and z = 0-6360,768 ; which value of z needs no cor-
rection.

We must now, in order to find the value of ^, write the same
values of e and y in Theorem IV, Art. 5, where we shall then
have

of the C07UC Sections. ^^7

A = H.L. (v/(i +0 — V^O'

_cv/(-+i)-A

B

-f^v/l — + i)-3B

c= '

D

E =

4
6

-«H' — + 0 -9E
F = ^^r.

&c. &c.

But, since the terms A, B, C, &c. are to be divided by e, e\ e\
Sec. respective!}', it will be best to divide them by these quan-
tities, before we begin the arithmetical calculations ; otherwise
much unnecessary labour must be taken. The terms, then,
being so divided, and the proper value of e being written for it,
viz. \/ 50, we shall have as below :

4- = -^( v/( 1 +e)-^e = - 0-2410,905,

J- = Li —A = — 0.0082,728,

-V - + 0

4c 3 4^

6c+ 6

->'(4-+o

F -^It+'>

6-" loe°

&C. , &C.

^ - -= — o'ooo6,3i4,

— ^ = — 0-0000,607,

be'

— -^ = — 0-0000,065,

2_^^ = — 0-0000,007,

468 Mr. Hellins on the Reclijicalion

And thence

+

A

B

= o-ooio,34,i,
= 0-0000,024,

3;D

2.4.6.8e'

+ T 5555.1 6-^
— 0-1205,849

+
+

3C

3 5-7E

= 0-1205,452,

= 0-0000,395

H ^3 TT = 0-C000,002

— 0-1205,849

and z = 7-4349,912 — (I.

But, by the foregoing part of this article, z = 0-6360,768 ;
we therefore have ^== 74349,91 2 — 0-6360,768 = 6 7989, 144.

22. With the value of a above given, viz. 7, we see a swift
convergency, both in the ascending and in the descending series ;
but, if a were given = ^3, (which is as small a value of a as
need be used in these theorems, for this purpose, because if it
were less than, or even =z ^ ^, the value of d might be com-
puted by one series only, as was observed in Art. 15,) eacli
of the series would converge but slowly, — , in this case, being
= 1^; to remedy which, as the terms of each of the series have
the signs + and — alternately, it would be expedient to com-
pute a moderate number (from six to ten, as the case shall
require,) of the initial terms of each, and then to transform the
remainders into other series, which should converge by the
powers of — ^ — , instead of the powers of —. This increase of
convergency in the geometrical progression, assisted as it would
be by the decrease of the coefficients of the new series, would
enable us to get a result accurate enough for all common uses,
by computing ten (or fewer) terms of each of the new series.

of the conic Sections. j^Qq

But, as the transformation now mentioned requires but a mo-
derate skill in series, I shall, for the sake of brevity, omit
examples of it, and proceed to

Sect. III. Examples of the Use of the foregoing Theorems.

23. My intention in this section is, to illustrate the use of the
foregoing theorems by a few examples, selecting at the same
time such of the theorems as are best adapted to the case in
hand; by which, and attention to what was said in the first
section, of the limits of the convergency of the several series, I
hope the reader will be directed how to make a proper choice
of theorems on all other occasions.

Example i.

Let there be an hyperbola of which the semi-axes are 40 and
30 respectively, and the ordinate is 10 ; it is required to find the
length of the arch from the vertex of the ordinate.

Since the conjugate semi-axis of this hyperbola is 30, we
must, in order to fit the given numbers to our theorems, divide
them all by 30 ; and then we shall have the corresponding di-
mensions of a similar hyperbola as follows ; viz. the transverse
semi-axis = |-, the conjugate semi-axis = 1, and the ordinate
= J-. And the proper theorem to be used in this case is the
second.

Writing, then, ± for a, and | for y, in the lid Theorem, we
have ee = aa + 1 = ^, and

MDCCCII. 3 P

470 Mr. Hellins on the Rectification

B =
C =

D =

y^{\Jt-ecyy)i -jB

bee
3'5 ( \Jrecy\)k — cC

y''[i-irfeyy)\ — 7D

E = .
F =

G =

and thence

\oee
y^' \ -\-eeyy)T^ — 9E

I zee
v'"(i -\-ee yy)i — iiF

14^^

•=00134,3234,
= 0-0009,0892,
= 0-0000,7272,
= 0-0000,0632,
== 0-0000,0058,

•= 0-0000,0005;

A = 0-3497,6260,

-^ C = 0-0003,4084,
2.4

- ^'^/^ E = 0-0000,0173,

2.4.6 !J ' I yJ^

1-B = 0-0067,1617,

^'^ - D =: 0-0000,2273,

2 4.6
2.4.6.8.10

0-0000,0014,

3v79i'
2. 4. t). 8. 10. 12

G = 0-0000,0001,

and the sum = -|- o - 350 1 ,05 1 8,
— 0-0067,3904,

and the sum = — 00067,3904.

"^'^'sums'if *^"' } o'3433'^^M. = -, the length of the arch of an
hyperbola, from the vertex to the ordinate, of which the trans-
verse and conjugate semi-axes are ^ and 1, and the ordinate i.
And, since hke parts of similar hyperbolas are to each other as
their semi-axes, we shall have, by multiplying 0-3433,6614 by
30, the semi- conjugate of the hyperbola proposed, 103009,842
for the length required.

Having in this example shown how to adapt these theorems
to hyperbolas that have a conjugate semi-axis ditferent from 1,

of the cojiic Sections. 471

it need not be repeated again. I shall therefore, in the remain-
ing examples, show the convergency of these new series in
most of the different cases that can occur.

Example ii.

24. Given a = 1 , and j' = 1 , to find z.

This arch, it is obvious, may be computed by Theorem IVth,
Vlth, Vllth, and some others ; but the Vllth is the proper one
to be chosen on this occasion, as the series there given has the
swifter convergency.

Writing, then, 1 for a, and 1 for y, in Theorem VII, we
have (by Article 1,) ee = aa-{- 1=^, and, (by Art. 7,) uu
z=z 1 -f eeyy = 3 ; and then, (by Art. 9,)

+

-^2i ^=0-0320,7501,

= 0-0000,6750,

— ^1 W~'^=: 0-0000,0481,

2.4.6.8.15 ^

3-5v9 ,;~'9__ 0-0000,0038,
2i~'^= 0-0000,0003;

2.4.6.8. 10.19

3-5-79-1I
2.4.6.8.10.12.23

sum of the neg. terms — o 0332, 932 7;

sum of the series -\- i-6987,5754;
correction of the fluent — 0-5990,7012 z=z ~d, (by Art. 17;]

the difference of which is -f 1 •0995,8 742 = %.
3P 3

473 Mr. Hellins on the Rectification

Example hi.

25. Given a = 1, and y = y/( 1000000 — 1) = g9Q'99Q5
nearly, to find z.

This arch, it is very obvious, may be computed by Theorem
Tlld, IVth, Vlth, and Vllth, the series in each of them con-
verging, in this case, very swiftly. And it may be computed
also by the IXth ; but the proper Theorem to be used in this
case is the Vllth.

Now, since ee is = 2, and y = y/( 1000000 — 1), we have
(by Article 7,) u = ■v/(2j>'+i] = ■/ (2000000 — i)= ^2 x

^(i 000000 — -i-) = -|/2 X (1000 *- — ] very nearly, =

1000 v/2 ^^ =r 1414,' 2 132088, which may be taken for the

value of the whole series, since ^u~^, the second term of it,
does not give a 1 in the tenth place of decimals. If, therefore,
from u = 1414-2132088, we subtract d = 05990701, (by
Article 17,) we shall have c = 1413-6141387,* the length
required.

Example iv.

26. Let a be given = 7, and ^ = 10, to find z.

This Example may be computed by Theorem Illd, IVth,
Vlth, and some others; the Vlth is to be chosen rather than
the Hid, and the IVth rather than the Vlth.

• The computation of the value of z, in this example, is the problem alluded to in
the Introduction to this Paper, which first turned my thoughts to the subject of it, in
the year 1770. In the next year, two answers were given to it, by two persons of good
reputation for their skill in mathematics, one of thcni making z = 1414-2 132088, the
other, 2 =: 1413-8921. These two are the only solutions of this problem that I know
of; and, if my calculation be right, both are erroneous.

of the conic Sections. 473

Now, if 10 be written for j' in Theorem IVtli, we shall have

A = n.L.-^'I^ = - 00998,34^,

B = Lii-J—i = — 0'000Q,Q2q,

C = 1-H:-X_i 1^ = _ 0-0000,020 ;

of whicii terms, two only are wanted to obtain a result true to
seven places of figures. And then, ee being = aa -\- 1 =: 50,
we have

+ -

e^{yy + 1) = 71-0633.520, 4- -L A = 0-0070,593,

- li? B = o-oooo.ooi, 1 ^ =:6-7cjS9,i44,(Art.2i,)

sum of the posit, terms 7 1 "0633,52 1 ; the SUm — 6-8059,737 ;
neg. term, and correct. — 6-o059>737'

the difference is + 64,-2573,74,8 = z.

Example v.

27. Let a be given = ^, and j/ = lo, to find z.

This example may be computed by Theorem II Id, IVth,
Vth, Vlth, Vlllth, and IXth ; of which the IVth, Vth, and
IXth, are more eligible than the other three. I n^ake choice of
the fourth, on account of the facility of the computation by it,
with the present value of jy.

Now, by writing lo for jy in Theorem IV, we shall have (as
in the preceding example,)

A = H. L. V(xv+0-. ^ _ 0-0998,341,

= ;,/ — = - 0-0003,323,

C = ""^^-^:+'^ _ JL = _ 0-0000,020 ;
and then, ee being = aa + i = 4> we have

4,74 ^^f- Hellins oji the Rectificatioti

+ —

«s/{yy + 0 = 11-2361,025, _A- = o'0446,472,

24'^' ' ^" — ^C= 0-0000,001,

s.m of affirm, ternis + ll-236l,3oo; - d= O'l 803,793, (Art. I5,)

neg. terms and corr. 0'2250,266;

the sum is — 0-2250,266.

the difFerence is =11'0111 ,0^6,

which is = z.

28. Having now produced series, of good convergency, for
computing the length of tiie arch from the vertex to the ordi-
nate, (and consequently any portion of such an arch,) of any
conical hyperbola, I shall conclude tiiis Paper with a few
remarks : reserving some other theorems which I have disco-
vered for the purpose, till I shall have found an opportunity to
describe nearly an equal number of theorems, which I have long
had by me, for the Rectification of the Ellipsis.

The utility of hyperbolic and elliptic arches, in the solution
of various problems, and particularly in the business of com-
puting fluents, has been shown by those eminent mathema-
ticians, M'^Laurin, Simpson, and Landen ; the last of whom
hath written a very ingenious paper on hyperbolic and elliptic
arches, which was published in the 1st volume of his Malhema^
iical Memoirs, in the year 1780. I have indeed heard, that some
improvement in the rectification of the ellipsis and hyperbola
had been produced, and some of the same theorems discovered,
by a learned Italian, many years before Mr. Landen 's Mathe-
matical Memoirs were published; bur, as Mr. Landen has
declared that he had never seen nor heard any thing of that
work, and as various instances are to be found of different men

of the conic Sections. 475

discovering the same truth, without any knowledge of each
other's works, I see no reason for disbelieving him. But I have
seen no writings on this subject which contain any thing more
than what is very common, besides those of the three gentle-
men above mentioned, and Dr. Waking's Meditationes Ana-
lytics; and, while I have nc^ inclination to detract from their
merits, I may be allowed to say that I have borrowed nothing
from their works.

29. With respect to Dr. Waring, (who was well known to
be a profound mathematician, and I can testify that he was a
good-natured man,) he has given, in page 470 of his Medita-
tiones Analytics, {\>uh\\shed in 1776,) these two series, as ex-
pressions of the length of an arch of an equilateral hyperbola ;

VIZ.

Arcus hyperbolicus exprimi possit per seriem — -7 + —•2-''

I 7 , M .• IM r-' J lIJ-2 x"'

" 2^2X7 ^ "T" 2^2.3x11 2*.2.3-4Xi5 "^ 2\2.3.4SX«9

" &c. ubi X denotat abscissam ad asymptoton."

« Si vero requiratur descendens series, turn erit x — 77] •^'~
a I ' r~7 ^ x~^\ &c. qu«, quoad coefficientes

« attinet, prorsus eandem observat legem ac priecedens."

30. These series, as they now stand, are of little use. But, if
proper corrections were applied to them, (which may easily be
done from what has been shewn in this Paper, and in my Ma-
theinatical Essays,) and the first of them were transformed into
another series converging by the powers of -y^, they would
become very useful for computing any arch of an equilateral

• In the onginal, this term is erroneously printed, there being a i in the numerator,
instead of a 3.

47^ Mr. Hellins on the Rectification, &c.

hyperbola, when the abscissa is taken on the asymptote. This
I thought it might be proper to remark, that the less experienced
readers of this Paper might not be misled by so great an autho-
rity as that of Dr. Waring. Whether or not he ever corrected
these oversights in any of his subsequent publications, I cannot
ascertain, for want of books. •

C 477 3

XVIII. Catalogue of ^oo nezv Nebula, nebulous Stars, planetary
Nebula, and Clusters of Stars ; with Remarks on the Con-

■ struction of the Heavens. By William Herschel, LL. D.
F. R. S.

Read July i, 1802.

OiNCE the publication of my former two catalogues of nebulse,
I have, in the continuation of my telescopic sweeps, met with a
number of objects that will enrich our natural history, as it
may be called, of the heavens. A catalogue of them will be
found at the end of this paper, containing 500 new nebulae,
nebulous stars, planetary nebulce, and clusters of stars. These
objects have been arranged in eight classes, in conformity
with the former catalogues, of which the present one is there-
fore a regular continuation. This renders it unnecessary to give
any further explanation, either of the contents of its columns, or
the abbreviations which have been used in the description of
the objects.

It has hitherto been the chief employment of the physical
astronomer, to search for new celestial objects, whatsoever might
be their nature or condition ; but our stock of materials is now
so increased, that we should begin to arrange them more scien-
tifically. The classification adopted in my catalogues, is little
more than an arrangement of the objects for the convenience
of the observer, and may be compared to the disposition of llie
books in a library, where the different sizes of the volumes is

MDCCCII, 3 Q

478 Dr. Herschel's Catalogue

often more considered than their contents. But here, in dividing
the different parts of which the sidereal heavens are composed
into proper classes, I shall have to examine the nature of the
various celestial objects that have been hitherto discovered, in
order to arrange them in a manner most conformable to their
construction. This will bring on some extensive considerations,
which would be too long for the compass of a single paper; I
shall therefore now only give an enumeration of the species
that offer themselves already to our view, and leave a particular
examination of the separate divisions, for some early future
occasions.

In proceeding from the most simple to tlie more complex
arrangements, several methods, taken from the known laws of
gravitation, will be suggested, by which the various systems
under consideration may be maintained ; but here also we shall
confine ourselves to a general review of the subject, as obser-
vation must furnish us first with the necessary data, to establish
the application of any one of these methods on a proper
foundation .

ENUMERATION OF THE PARTS THAT ENTER INTO THE CONSTRUC-
TION OF THE HEAVENS.

I. Of insulated Stars.

In beginning our proposed enumeration, it might be expected
that the solar system would stand foremost in the list ; whereas,
by treating of insulated stars, we seem, as it were, to overlook one
of the great component parts of the universe. It will, however,
soon appear that this very system, magnificent as it is, can only
rank as a single individual belonging to the species which we
are going to consider.

of ^00 finv NebidcP, and Cluslers of Stars. 479

By calling a star insulated, I do not mean to denote its being
totally unconnected with all other stars or systems ; for no one,
by the laws of gravitation, can be intirely free from the in-
fluence of other celestial bodies. But, when stars are situated at
such immense distances from each other as our sun, Arcturus,
Capella, Lyra, Sirius, Canobus, Markab, Bellatrix, Menkar,
Shedir, Algorah, Propus, and numberless others probably are,
w^e may then look upon them as sufficiently out of the reach of
mutual attractions, to deserve the name of insulated stars.

In order not to take this assertion for granted, without some-
examination, let us admit, as is highly probable, that the whole
orbit of the earth's annual motion does not subtend more than
an angle of one second of a degree, when seen from Sirius. In
consequence of this, it appears by computation, that our sun and
Sirius, if we suppose their masses to be equal, would not fall
together in less than 33 millions of years, even though they
were not impeded by many contrary attractions of other neigh-
bouring insulated stars ; and that, consequently, with the
assistance of the opposite energies exerted by such surrounding
stars, these two bodies may remain for millions of ages, in a
state almost equal to undisturbed rest. A star thus situated may
certainly deserve to be called insulated, since it does not imme-
diately enter into connection with any neighbouring star ; and
it is therefore highly probable, that our sun is one of a great
number that are in similar circum.stances. To this may be
added, that the stars we consider as insulated are also sur-
rounded by a magiiificent collection of innumerable stars, called
the milky- wa}', which must occasion a very powerful balance
of opposite attractions, to hold the intermediate stars in a state
of rest. For, though our sun, and all the stars we see, may

3 O 2

480 Dr. Herschel's Catalogue

truly be said to be in the plane of the milky-^vay, yet I am now
convinced, by a long inspection and continued examination of
it, that the milky-way itself consists of stars very differently
scattered from those which are immediately about us. But of
this, more will be said on another occasion.

From the detached situation of insulated stars, it appears that
they are capable of being the centres of extensive planetary
systems. Of this we have a convincing proof in our sun, which,
according to our classification, is one of these stars. Now, as
we enjoy the advantage of being able to view the solar system
in all its parts, by means of our telescopes, and are therefore
sufficiently acquainted with it, there will be no occasion to enter
into a detail of its construction.

The question will now arise, whether every insulated star be
a sun like ours, attended with planets, satellites, and numerous
comets ? And here, as nothing appears against the supposition,
we may from analogy admit the probability of it. But, were we
to extend this argument to other sidereal constructions, or, still
farther, to every star of the heavens, as has been done fre-
quently, I should not only hesitate, but even think that, from
what w ill be said of stars which enter into complicated sidereal
systems, the contrary is far more likely to be the case ; and that,
probably, we can only look for solar systems among insulated
stars.

II. Of Binary sidereal Systetns, or double Stars.

The next part in the construction of the heavens, that offers
itself to our consideration, is the union of two stars, that are
formed together into one system, by the laws of attraction.

If a certain star. should be situated at any, perhaps immense.

of 500 7iexv Nebuhv, and Clusters of Stars. 481

distance behind another, and but very little deviating from the
line in which we see the first, we should then have the ap-
pearance of a double star. But these stars, being totally uncon-
nected, would not form a binary system. If, on the contrary,
two stars should really be situated very near each other, and at
the same time so far insulated as not to be materially affected
by the attractions of neighbouring stars, they will then compose
a separate system, and remain united by the bond of their own
mutual gravitation towards each other. This should be called a
real double star; and any two stars that are thus mutually
connected, form the binary sidereal system which we are now
to consider.

It is easy to prove, from the doctrine of gravitation, that two
stars may be so connected together as to perform circles, or
similar ellipses, round their common centre of gravity. In this
case, they will always move in directions opposite and parallel
to each other ; and their system, if not destroyed by some foreign
cause, will remain permanent.

Figure 1 (Plate XVI.) represents two equal stars a and b,
moving in one common circular orbit round the centre 0, but
in the opposite directions oi at and bt. In Fig. 2 we have a
similar connection of the two stars a b; but, as they are of dif-
ferent m.agnitudes, or contain unequal quantities of matter, they
will move in circular orbits of different dimensions round their
common centre of gravity 0. Fig. 3 represents equal, and Fig. 4
unequal stars, moving in similar elliptical orbits round a com-
mon centre ; and, in all these cases, the directions of the tangents
1 1, in the places a b, where the stars are, will be opposite and
parallel, as will be more fully explained hereafter.

These four orbits, simple as they are, open an extensive field

4,82 Dr. Hersciiel's Catalogue

for reflection, and, I may add, for calculation. They shew, even
before we come to more complicated combinations, \Nhere the
same will be confirmed, that there is an essential difference
between the construction of solar and sidereal systems. In
each solar system, we have a very ponderous attractive centre,
by which all the planets, satellites, and comets are governed,
and kept in their orbits. Sidereal systems take a greater scope :
the stars of which they are comjjosed move round an empty
centre, to which they are nevertheless as firmly bound as tiie
planets to their massy one. It is however not necessary here to
enlarge on distinctions which will hereafter be strongly sup-
ported by facts, when clusters of stars come to be considered.
I shall only add, that in the subordinate bodies of the solar
system itself, we have already instances, in miniature, as it may
be called, of the principle whereby the laws of attraction are
applicable to the solution of the most complicated phenomena
of the heavens, by means of revolutions round empty centres.
For, although both the earth and its moon are retained in their
orbits by the sun, yet their mutual subordinate system is such,
that they perform secondary monthly revolutions round a centre
without a body placed in it. The same indeed, though under
very narrow limits, may be said of the sun and each planet
itself.

That no insulated stars, of nearly an equal size and distance,
can appear double to us, may be proved thus. Let Arcturus and
Lyra be the stars : these, by the rule of insulation, which we
must now suppose can only take place when their distance from
each other is not less than that of Sirius from us, if very accu-
rately placed, would be seen imder an angle of 60 degrees from
each other. They really are at about 59°. Now, in order to

of soo flew Nebidcc, and Clusters of Stars. 483

make these stars appear to us near enough to come under the
denomination of a double star of the first class, we should re-
move the earth from them at least 41253 times farther than
Sirius is from us. But the space-penetrating power of a 7-feet
reflector, by which my observations on double stars have been
made, cannot intitle us to see stars at such an immense distance ;
for, even the 40-feet telescope, as has been shewn,* can only
reach stars of the i342d magnitude. It follows, therefore, that
these stars could not remain visible in a 7-feet reflector, if they
were so far removed as to make their angular distance less than
about 24^ minutes ; nor could even the 40-feet telescope, under the
same circumstances of removal, shew them, unless they were to
be seen at least 2y minutes asunder. Moreover, this calculation
is made on a supposition that the stars of which a double star is
composed, might be as small as any that can possibl}' be per-
ceived ; but if, on the contrary, they should still appear of a
considerable size, it will then be so much the more evident that
such stars cannot have any great real distance, and that, con-
sequently, insulated stars cannot appear double, if they are situ-
ated at equal distances from us. If, however, their arrangement
should be such as has been mentioned before, then, one of them
being far behind the other, an apparent double star may cer-
tainly be produced ; but here the appearance of proximity
would be deceptive ; and the object so circumstanced could not
be classed in the list of binary systems. However, as we must
grant, that in particular situations stars apparently double may
be composed of such as are insulated, it cannot be improper to
consult calculation, in order to see whether it be likely that the
700 double stars I have given in two catalogues, as well as

• See Phil. Trans, for 1800, Part I. page 83.

484, Dr. Herschel's Catalogue

many more I have since collected, should be of that kind. Such
an inquiry, though not very material to our present purpose,
will hereafter be of use to us, when we come to consider more
complicated systems. For, if it can be shown that the odds are
very much against the casual production of double stars, the
same argument will be still more forcible, when applied to treble,
quadruple, or multiple compositions.

Let us take ^ Aquarii, for an instance of computation. This
star is admitted, by Flamsteed, De la Caille, Bradley, and
Mayer, to be of the 4th magnitude. The two stars that com-
pose it being equal in brightness, each of them may be supposed
to shine with half the light of the whole lustre. This, according
to our way of reckoning magnitudes,* would make them 4,m
X v/2 = 5ym ; that is, of between the 6th and 5th magnitude
each. Now, the light we receive from a star being as the square
of its diameter directly, and as the square of its distance in-
versely, if one of the stars of ^ Aquarii be farther off' than the
stars of between the 6th and 5th magnitude are from us, it must
be so much larger in diameter, in order to give us an equal
quantity of light. Let it be at the distance of the stars of the
7th magnitude; then its diameter will be to the diameter of
the star which is nearest to us as 7 to 53-, and its bulk as 1,885
to 1 ; which is almost double that of the nearest star. Then,
putting the number of stars we call of between the 6th and
5th magnitude at 450, we shall have 686 of the 7th magnitude
to combine with them, so that they may make up a double star
of the first class, that is to say, that the two stars may not be
more than 5" asunder. The surface of the globe contains

• The expressions 21T1, 3m, 4m, &c. stand for stars at the distance of 2, 3, 4, &c.
times that of Sirius, supposed unity.

of joo new NebuLe, and Clusters of Stars. 485

34.036131547 circular spaces, each of 5" in diameter; so that
each of the 686 stars will have 49615357 of these circles in
which it might be placed ; but, of all that number, a single one
would only be the proper situation in ^^ hich it could make up a
double star with one of tiie 450 given stars. But these odds,
which are above yt^^ millions to one against the composition of
^ Aquarii, are extremely increased by our foregoing calculatioji
of the required size of the star, which must contain nearly
double the mass allotted to other stars of the 7th magnitude;
of which, therefore, none but this one can be proper for making
up the required double star. If the stars of the 8th and 9th
magnitudes, of which there will be 896 and 1134, should be
taken in, by way of increasing the chance in favour of the sup-
posed composition of our double star, the advantage intended to
be obtained by the addition of numbers, will be completely
counteracted by the requisite uncommon bulk of the star which
is to serve the purpose ; for, one of the 8th magnitude, ought
to be more than 2^ times bigger than the rest; and, if the
composition were made by a star of the 9th magnitude, no less
than four times the bulk of the other star which is to enter the
composition of the double star would answer the purpose of its
required brightness. Hence therefore it is evident, that casual
situations will not account for the multiplied phenomena of
double stars, and that consequently their existence must be
owing to the influence of some general law of nature ; now, as
the mutual gravitation of bodies towards each other is quite suf-
ficient to account for the union of two stars, we are authorised
to ascribe such combinations to that principle.

It will not be necessary to insist any further on arguments
drawn from calculation, as I shall soon communicate a series of

MDCCCII. 3 R

486 Dr. He^scuel's Catalogue

observations made on double stars, whereby it will be seen, that
tnany of them have aclually changed their situation with regard to
each other, in a progressive course, denoting a periodical revo-
lution round each other; and that the motion of some of them is
direct, while that of others is retrograde. Should these observa-
tions be found sufficiently conclusive, we may already have their
periodical times near enough to calculate, within a certain de-
gree of approximation, the parallax and mutual distance of the
stars which compose these systems, by measuring their orbits,
which subtend a visible angle.

Before we leave the subject of binary systems, I should
remark, that it evidently appears, that our sun does not enter
into a combination with any other star, so as to form one of
these systems with it. This could not take place without our
immediately perceiving it; and, though we may have good
reason to believe that our system is not perfectly at rest, yet the
causes of its proper motion are more probably to be ascribed to
some perturbations arising from the proper motion of neigii-
bouring stars or systems, than to be placed to the account of a
periodical revolution round some imaginary distant centre.

III. Of 7nore complicated sidereal Systems, or treble, quadruple,
quintuple, and multiple Stars.

Those who have admitted our arguments for the existence of
real double stars, will easily advance a step farther, and allow
that three stars may be connected in one mutual system of re-
ciprocal attraction. And, as we have from theory pointed out,
in figures 1, 2, 3, and 4, how two stars may be maintained
in a binary system, we shall here shew that tliree stars may

o/"joo nezv NebuLe, and Clusters of Stars. 487

likewise be preserved in a permanent connection, by revolving
in proper orbits about a common centre of motion.

In all cases where stars are supposed to move round an empty
centre, in equal periodical times, it may be proved that an ima-
ginary attractive force may be sup))osed to be lodged in that
centre, which increases in a direct ratio of the distances. For
since, in different circles, by the law of centripetal forces, the
squares of the periodical times are as the radii divided by the
central attractive forces, it follows, that when these periodical
times are equal, the forces will be as the radii. Hence we con-
clude, that in any system of bodies, where the attractive forces
of all the rest upon any one of them, when reduced to a direc-
tion as coming from the empty centre, can be shewn to be in a
direct ratio of the distance of that body from the centre, the
system may revolve together without perturbation, and remain
permanently connected without a central body.

Hence may be proved, as has been mentioned before, that
two stars will move round a hypothetical centre of attraction.
For, let it be supposed that the empty centre 0, in Fig. 1 and 3,
is possessed of an attractive force, increasing in the direct ratio
of the distances oa : ob. Then, since here ao and bo are equal,
the hypothetical attractions will be equal, and the bodies will
revolve in equal times. That this agrees with the general law
of attraction, is proved thus. The real attraction of b upon a is

— rr; and that of a upon b is -^; and, since b = a,.it will be

-^ : ■—■ :: ao: bo ; which was required.

In Figures 2 and 4, when the stars a and b are unequal, and
their distances from 0 also unequal, let oa = «, and ob = ?n ; '
and let the mass of matter in a = m, and in b = ;z. Then the

3 R 2

488 Dr. Herschel's Catalogue

attraction of b on a=. -77-, will be to the attraction of a on 6

= -;j2;r> ^s n:m ; which is again directly as ao : bo.

I proceed now to explain a combination of three bodies,
moving round a centre of hypothetical attraction. Fig. 5 con-
tains a single orbit, wherein three equal bodies a b c, placed at
equal distances, may revolve permanently. For, the real attrac-
tion of b on a will be expressed by — ^ ; but this, reduced to the

direction ao, will be only — '-—- ; for, the attraction in the direc-
tion ba is to that in the direction by, parallel to ao, as -^ to

■ ^J'- . The attraction also of c on a is equal to that of b on a ;
therefore the whole attraction on a, in a direction towards 0, will
be expressed by - '/■. In the same manner we prove, that the

attraction of a and c on b, in the direction bo, is ^^— ; and that

of a and b on c, in the direction co, is '^" '^. Hence, a b and

' ' ub> '

c being equal, the attractions in tlie directions ao bo and co will
also be equal ; and, consequently, in the direct ratio of these
distances. Or rather, the hypothetical attractions being equal, it
proves that, in order to revolve permanently, a b and c must be
equal to each other.

Instead of moving in one circular orbit, the three stars may
revolve in three equal ellipses, round their common centre of
gravity, as in Fig. 6. And here w'e sliould remark, that this
centre of gravity will be situated in the common focus 0, of the
three ellipses ; and that tlie absolute attraction towards that
focus, will vary in the inverse ratio of the squares of the distances
of any one of the stars from that centre, while the relative
attractions remain in the direct ratio of their several distances

oj 500 nezv Nebula', and Clusters 0/ Stars. 489

from tlic same centre. This will be more fully explained, when
we come to consider the motion of four stars.

A very singular straight-lined orbit, if so it may be called,
may also exist in the following manner. If a and b, Fig. 7, are
two large equal stars, which are connected together by their
mutual gravitation towards each other, and have such projectile
motions as would cause them to move in a circular orbit about
their common centre of gravity, then may a third small star c,
situated in a line drawn through 0, and at rectangles to the plane
described by the stars a b, fall freely from rest, with a gradually
acquired motion to 0 ; then, passing through the plane of the
orbit of the two stars, it will proceed, but with a gradually re-
tarded motion, to a second point of rest d; and, in this manner,
the star c may continue to oscillate between c and d, in a straight
line, passing from c, through the centre 0, to d, and back again
to c.

In order to see the possibility and permanency of this con-
nection the better, let 0 be the centre of gravity of the three
bodies, Vv'hen the oscillating body is at c ; then, supposing the
bodies a and b to be at that moment in the plane p I, and ad-
mitting m to represent a body equal in mass to the two bodies
a b, 0 will be the common centre of gravity of m and c. Then,
by the force of attraction, the body c and the fictitious body m
will meet in 0 ; that is to say, the plane p I, of the bodies a b,
will now be at p' I'. The fictitious body jn may then be con-
ceived to move on till it comes to ji, while the body c goes to
d ; or, which is the same, the plane of the bodies a b will now
be in the position p" I", as much beyond the centre of gravity 0,
as it was on the opposite side m. By this time, both the ficti-
tious body w, now at n, and the real body c, now at d, have lost

490 Dr. IIerschel's Catalogue

their motion in opposite directions, and begin to approach to
tlieir common centre of gravity o, in which they will meet a
second time. It is evident that the orbit of the two large stars
will suffer considerable perturbations, not only in its plane, but
also in its curvature, which will not remain strictly circular;
the construction of the system, however, is such as to contain a
sufficient compensation for every disturbing force, and will con-
sequently be in its nature permanent.

In order to add an oscillating star, it is not necessary that the
two large stars siiould be so situated as to move in a circular
orbit, without the oscillating star. In Fig. 8, the stars a and 6
may have such projectile forces gi\en them as would cause them
to describe equal ellipses, of any degree of excentricity. If now
the small star c be added, the perturbations will undoubtedly
affect not only the plane of the orbits of the stars, but also their
figures, which will become irregular moveable ovals. The extent
also of the oscillations of the star c will be affected ; and will
sometimes exceed the limits c d, and sometimes fall short of
them. All these varieties may easily be deduced from what has
been already said, when Fig. 7 was considered. It is however
very evident, that this system also must be permanent ; since
not only the centre of gravity 0 will always be at rest, but a 0,
whatever may be the perturbations arising from the situation of
c, will still remain equal to bo.

It should be remarked, that the vibratory motion of the star c
will differ much from a comctary orbit, even though the latter
should be compressed into an evanescent ellipsis. For, while the
former extends itself over the diameter of a globe in which it
may be supposed to be inscribed, the hypothetical attractive
force being supposed to be placed in its centre, the cometary

of 500 Jieiv Nebulce, and Clusters of Stars. 431

orbit will only describe a radius of the same globe, on account
of its requiring a solid attractive centre.

After what has been said, it will hardly be necessary to add,
that with the assistance of any proper one of the combinations
pointed out in the four last figures, the appearance of every
treble star may be completely explained; especially when the
different inclinations of the orbits of the stars, to the line of sight,
are taken into consideration.

If we admit of treble stars, we can have no reason to oppose
more complicated connections ; and, in order to form an idea
how the laws of gravitation may easily support such sj'stems, I
have joined some additional delineations. A very short expla-
nation of them will be sufficient.

Fig. 9 ( Plate XVII. ) represents four stars, ahc and cl, arranged
in a line; a being equal to b, and c equal to d. Then, if ao =
bo, and co = do, the centre of gravity will be in 0 ; and, with a
proper adjustment of projectile forces, the four stars will revolve in
two circular orbits round their common centre. By calculating
in the manner already pointed out, it will be found, that when,
for instance, ao = 1, co = 2, and c = d = 1, then the mass of
matter in a = b, will be required to be equal to 1,3492.

It is not necessary tliat the projectile force of the four stars
should be such as will occasion them to revolve in circles. The
system will be equally permanent when they describe similar
ellipses about the common centre of gravity, which will also be
the common focus of the four ellipses. In Fig. 10, the stars
abed, revolving in ellipses that are similar, will always
describe, at the same time, equal angles in each ellipsis about the
centre of hypothetical attraction ; and, when they are removed
from a b c d to a'b' c' d', they will still be situated in a straight

49S Dr. Herschel's Catalogue

line, and at the same proportionate distances from each other as
before. By tliis it appears, as we iiave already observed, that
the absolute hyi)othctical force in the situation a' b' c' d', com-
pared to wliat it was when the stars were oX. ab c d,\s inversely
as tlie squares of the distances ; but that its comparative exertion
on the stars, in their present situation, is still in a direct ratio of
their distances from the centre o, just as it was when they were
ixi a b c d; or, to express the same perhaps more clearly, the
force exerted on a', is to that which was exerted on a as
r=~- : -=iT-. But the force exerted on a is to that exerted

a o\ a o\

on c, in our present instance, as jo = i to co = 9i; and still
i^emains in the same ratio when the stars are at a' and c' ; for
the exertion will here be likewise as ^j'o = i to c'o = 3.

Fig. 1 1 represents four stars in one circular orbit ; and its
calculation is so simple, that, after what has been said of Fig. 5,
I need only remark that the stars may be of any size, provided
their masses of matter are equal to each other.

It is also evident, that the projectile motion of four equal stars
is not confined to that particular adjustment which will make
them revolve in a circle. It will be sufficient, in order to pro-
duce a permanent system, if the stars abed, in Fig. 12, nre
impressed with such projectile forces as will make them describe
equal ellipses round the common centre 0. And, as the saine
method of calculation which has been explained with Figs. 6
and 10 may here be used, it will not be necessary to enter into
particulars.

Fig. 13 represents four stars, placed so that, with properly
adjusted projectile forces, they may revolve in equal times, and
in two difterent circles, round their common centre of gravity 0.

of goo nezv Nehtilcr, and Clusters of Stars. 493

If <io = 60 = 4, CO = do = 5, and c = d = i, then will the
mass of matter in a = b, required for the purpose, be 1,5136.
This arrangement, remarkable as it may appear, cannot be
made in all situations ; for instance, if the distance ao=bo were
assumed equal to 1, that of co = do being 2, it would be im-
possible to find such quantities of matter in a and b as would
unite the four stars into one system.

As we have shewn how the arrangement in Y'lg. 10 may be
derived from that of Fig. 9, so it will equally appear, that four
stars may revolve in different but similar ellipses round their
common centre, as in Fig. 14. For here the four stars, wiien
placed at a b c d, are exactly in the situation represented in
Fig. 13; but, on account of different projectile forces, they re-
volve, not as before in concentric circles, but in similar elliptical
orbits.

Fig. 15 represents three stars, ab c, in the situation of Fig. 5,
to which a small oscillating star, d, is added. The addition of
such a star to Fig. 1, has been sufficiently explained in Fig. 7;
and, what has been remarked there, may easily be applied to
our present figure. As tiie fictitious body 7n, m Fig. 7, was made
to represent the stars a and b, it will now stand for the three
stars a b and c. If we suppose these stars to be of an equal
magnitude in both figures, the centre of gi-avity 0, of the three
stars, will not be so far from m and n as in Fig. 7; and the
perturbations will be proportionally lessened.

Fig. 16 gives the situation of three stars, a b c, moving in
equal elliptical orbits about their common focus 0, while the
star d performs oscillations between d and e. What has been
said in explaining Fig. 8, will be sufficient to shew, that the

MDCCCII. 3 S

454. ^^' Herschel's Catalogue

present arrangement is equally to be admitted among the con-
structions of sidereal systems that may be permanent.

We have before remarked, that any appearance of treble
stars might be explained, by admitting the combinations pointed
out in Figs. 5, 6, 7, and 8 ; and it must be equally obvious, that
quadruple systems, under what shape soever they may show
themselves, whether in straight lines, squares, trapezia, or any
other seemingly the most irregular configurations, will readily
find a solution from one or other of the arrangements of the
eight last figures.

More numerous combinations of stars may still take place,
by admitting simple and regular perturbations; for then all
sorts of erratic orbits of multiple flexures may have a permanent
existence. But, as it would lead me too far, to apply calculation
to them, I forbear entering upon the subject at present.

Before I proceed, it will be proper to remark, that it may
possibly occur to many, who are not much acquainted with the
arrangement of the numberless stars of the heavens, that what
has been said may all be mere useless surmise; and that, possibly,
there may not be the least occasion for any such speculations
upon the subject. To this, however, it may be answered, that
such combinations as I have mentioned, are not the inventions
of fancy : they have an actual existence ; and, were it necessary,
I could point them out by thousands. There is not a single
night when, in passing over the zones of the heavens by sweep-
ing, I do not meet with numerous collections of double, treble,
quadruple, quintuple, and multiple stars, apparently insulated
from other groups, and probably joined in some small sidereal
system of their own. I do not imagine that I have pointed out

of ^00 new Nebulcv, and Clusters of Stars. 4,95

the actual manner in which they are held together; but it will
always be a desirable step towards information, if the possibility
of such unions, in many different ways, can be laid before us;
and, very probably, those who have more leisure to consider the
different combinations of central forces, than a practical astro-
nomer can have, may easily enlarge on what has been laid down
in the foregoing paragraphs.

IV. Of clustering Stars, and the MiJky-ivay.

From quadruple, quintuple, and multiple stars, we are na-
turally led to a consideration of the vast collections of small
stars that are profusely scattered over the railky-vvay. On a
very slight examination, it will appear that this immense starry
aggregation is by no means uniform. The stars of which it is
composed are very unequally scattered, and show evident marks
of clustering together into many separate allotments. By referring
to some one of these clustering collections in the heavens, what
will be said of tliem will be much better understood, than if we
were to treat of them merely in a general way. Let us take the
space between /3 and y Cygni for an example, in which tiie
stars are clustering with a kind of division between them, so
that we may suppose them to be clustering towards two different
regions. By a computation, founded on observations which
ascertain the number of stars in different fields of view, it ap-
pears that our space between ,G and y, taking an average breadth
of about five degrees of it, contains more than 331 thousand
stars ; and, admitting them to be clustering two different ways,
we have 165 thousand for each clustering collection. Now, as
a more particular account of the milky-way will be the subject
of a separate paper, I shall only observe, that the above mentioned

3S 3

49^ Dr. Hersciiel's Catalogue

milky appearances deserve tlie name of clustering collections,
as they are certainly brighter about the middle, and fainter
near their undefined borders. For, in my sweeps of the heavens,
it has been fully ascertained, that the brightness of the milky-
way arises only from stars ; and that their compression in-
creases in jjroportion to the brigJitness of the milky-way.

We may indeed partly ascribe the increase, both of brightness
and of apparent compression, to a greater depth of the space
which contains these stars ; but this will equally tend to shew
their clustering condition : for, since the increase of brightness
is gradual, the space containing the clustering stars must tend
to a spherical form, if the gradual increase of brightness is to
be explained by the situation of the stars.

V. Of Groups of Stars.

From clustering stars there is but a short transition to groups
of stars; they are, however, sufficiently distinct to deserve a
separate notice. A group is a collection of closely, and almost
equally compressed stars, of any figure or outline ; it contains
no particular condensation that might point out the seat of an
hypothetical central force; and is sufficiently separated from
neighbouring stars to shew that it makes a peculiar system of its
own. It must be remembered, that its being a separate system
does not exclude it from the action or influence of other systems.
We are to understand tliis witli the same reserve that has been
pointed out, when we exjilained what we called insulated stars.

The construction of groups of stars is perhaps, of all the ob-
jects in the heavens, the most difficult to explain; much less
can we now enter into a detail of the numerous observations I

of goo new Nebula, and Clusters of Stars. 497

have already made upon this subject. I therefore proceed in my
enumeration.

VI. Of Clusters of Stars.

These are certainly the most magnificent objects that can
be seen in the heavens. They are totally different from mere
groups of stars, in their beautiful and artificial arrangement:
their form is generally round ; and the compression of the stars
shews a gradual, and pretty sudden accumulation towards the
centre, where, aided by the depth of the cluster, which we can
have no doubt is of a globular form, the condensation is such,
that the stars are sufficiently compressed to produce a mottled
lustre, nearly amounting to the semblance of a nucleus. A
centre of attraction is so strongly indicated, by all the circum-
stances of the appearance of the cluster, that we cannot doubt a
single moment of its existence, either in a state of real solidity,
or in that of an empty centre, possessed of an hypothetical force,
arising fi'om the joint exertion of the numerous stars that enter
into the composition of the cluster.

The number of observations I have to give relating to this
article, in which my telescopes, especially those of high space-
penetrating power, have been of the greatest service, of course
can find no room in this enumeration,

VII. OfNehulce.

These curious objects, which, oil account of their great dis-
tance, can only be seen by instruments of great space-pene-
trating power, are perhaps all to be resolved into the three
last mentioned species. Clustering collections of stars, for
instance, may easily be supposed sufficiently removed to present

^8 Dr. Herschel's Catalogue

us with the appearance of a nebula of any shape, which, like
the real object of which it is the miniature, w ill seem to be gra-
dually brighter in the middle. Groups of stars also may, by
distance, assume the semblance of nebulous patches ; and real
clusters of stars, for the same reason, when their composition
is beyond the reach of our most powerful instruments to resolve
them, will appear like round nebula that are gradually much
brighter in the middle. On this occasion I must remark, that
with instruments of high space-penetrating powers, such as my
40-feet telescope, nebulee are the objects that may be perceived
at the greatest distance. Clustering collections of stars, much
less than those we have mentioned before, may easily contain
50000 of them ; and, as that number has been chosen for an
instance of calculating the distance at which one of the most
remote objects might be stiil visible,* I shall take notice of an
evident consequence attending the result of the computation ;
which is, tiiat a telescope with a power of penetrating into space,
like my 40-feet one, has also, as it may be called, a power of
penetrating into time past. To explain this, we must consider
that, from the known velocity of ligiit, it may be proved, that
when we look at Sirius, the rays which enter the eye cannot
have been less than 6 years and 4|- months coming from that
star to the observer. Hence it follows, that when we see an
object of the calculated distance at which one of these very
remote nebulse may still be perceived, the rays of light which
convey its image to the eye, must have been more than nine-
teen hundred and ten thousand, that is, almost two millions of
years on their way ; and that, conscquentl}', so many years ago,

• See Phil. Trans, for 1800, page 83. N. B, In the same page, line 22, for jcoo
read 50090.

of 500 new Nebula, and Clusters of Stars. 499

this object must already have had an existence in the sidereal
heavens, in order to send out those rays by which we now
perceive it,

VIII. Of Stars with Burs, or Stellar Nebulce.

Situated as we are, at an immense distance from the remote
parts of tlie heavens, it is not in the power of telescopes to
resolve many phenomena we can but just perceive, which, could
we have a nearer view of them, might probably shew them-
selves as objects that have long been known to us. A stellar
nebula, perhaps, may be a real cluster of stars, the whole light of
which is gathered so nearly into one point, as to leave but just
enough of the light of the cluster visible to produce the appear-
ance of burs. This, however, admits of a doubt.

IX. Of milky Nebulosity.

The phenomenon of milky nebulosity is certainly of a most
interesting nature : it is probably of two different kinds ; one of
them being deceptive, namely, such as arises from widely ex-
tended regions of closely connected clustering stars, contiguous
to each other, like the collections that construct our milky-way.
The other, on the conti'ary, being real, and possibly at no very
great distance from us. The changes I have observed in the
great milky nebulosity of Orion, 23 years ago, and which have
also been noticed by other astronomers, cannot permit us to
look upon this phenomenon as arising from immensely distant
regions of fixed stars. Even Huygens, the discoverer of it,
was already of opinion that, in viewing it, we saw, as it were,
through an opening into a region of light.* Much more would

* See Si;stema Suturnhan, page 8 and 9.

500 Dr. Herschel's Catalogue

he be convinced now, when changes in its shape and lustre have
been seen, that its light is not, like that of the milky-way, com-
posed of stars. To attempt even a guess at what this light may
be, would be presumptuous. If it should be surmised, for in-
stance, that this nebulosity is of the nature of the zodiacal
light, we should then be obliged to admit the existence of an
effect without its cause. An idea of its phosphorical condition, is
not more philosophical, unless we could shew from what source
of phosphorical matter, such immeasurable tracts of luminous
phenomena could draw their existence, and permanency ; for,
though minute changes have been observed, yet a general re-
semblance, allowing for the difference of telescopes, is still to be
perceived in the great nebulosity of Orion, even since the time
of its first discovery.

X. Of nebulous Stars.
The nature of these remarkable objects is enveloped in much
obscurity. It will probably require ages of observations, before
we can be enabled to form a proper estimate of their condition.
That stars should have visible atmospheres, of such an extent
as those of which I have given the situation in this and my
former catalogues, is truly surprising, unless we attribute to
such atmospheres, the quality of self-luminous milky nebulosity.
"We can have no reason to doubt of the starry nature of the
central point; for, in no respect whatever does its appearance
differ from that of a star of an equal magnitude ; but, when the
great distance of such stars is taken into consideration, the real
extent of the surrounding nebulosity is truly wonderful. A very
curious one of this kind will be found in the 4th class. No. 6g,
of the annexed catalogue.

of 500 new Nebular, and Clusters of Stars. 501

XI. Planetary Nebulae.

This seems to be a species of bodies that demands a particu-
lar attention. To investigate the planetary nature of these
nebula, is not an easy undertaking. If we admit them to con-
tain a great mass of matter, such as that of which our sun is
composed, and that tliey are, hke the sun, surrounded by dense
luminous clouds, it appears evidently that the intrinsic bright-
ness of these clouds must be far inferior to those of the sun. A
part of the sun's disk, equal to a circle of 15" in diameter, would
far exceed the greatest lustre of the full moon ; whereas, tlie
light of a planetary nebula, of an equal size, is hardly equal to
that of a star of the 8th or gth magnitude. If, on the other
hand, we sliould suppose them to be groups, or clusters of stars,
at a distance sufficiently great to reduce them to so small an
apparent diameter, we shall be at a loss to account for their
uniform light, if clusters ; or for their circular forms, if mere
groups of stars.

Perhaps they may be rather allied to nebulous stars. For,
should the planetary nebulee with lucid centres, of which the
next article will give an account, be an intermediate step be-
tween planetary nebute and nebulous stars, the appearances of
these different species, when all the individuals of them are fully
examined, might throw a considerable light upon the subject.

XII. Of planetaiy Nebula with Centres.

In my second catalogue of nebula, a single instance of a
planetary nebula with a bright central point was mentioned;
and, in the annexed one, No. 73 of the 4th class, is another of
very nearly the same diameter, which has also a lucid, though

MDCCCII, 3 T

50« Dr. Hekscuel's Catalogue

not quite so regular a centre. From several particularities
observed in their construction, it would seem as if they were
related to nebulous stars. If we might suppose that a gradual
condensation of the nebulosity about a nebulous star could take
place, this would be one of them, in a very advanced state of
compression. A further discussion of this point, however, must
be reserved to a future opportunity.

CORRECTION OF A FORMER PAPER.

In my Paper on two lately discovered celestial Bodies,
Page 224, line 18, of this volume, instead of 135, read 31.

oj 500 nexv Nebula, and Clusters of Stars

503

Catalogue of 500 additional new Nebulae, and
Clusters of Stars.

First Class, Bright Nebulce.

I.

1788.

Stars.

M.

S.

D. M. ?

Description.

216

Dec. 322 Urs<e

P 13

52/

3 42

t;B.^L. iF. r. mbM. Towards

the Jf, within the nebulo-

sity, is a vS.ft.

217

2754 Persei

f 9

25

n

0 462

cB. cL. mbM. Stands nearly

in the center of a trape-

zium.

218

31^3 Auriga

1789 1 ^

fo6

43/

0 201

cB. R. vgmbM. about 3'^.

219

Mar. 23 55 Ursre

f 5

33 «

0 gG.i^vB. cL.iF.vgmbM.

220

Apr. 1264 {y) UrsK

/'|43

.59/

0 20 2cB. ;«E. 70° np JJ'. 3 or 4'/,
2' b.

221

__

___ -^

P

21

41/

0 37 2 ^B. R. zgmbM, 4 or g'd.

222

—

—

p 20

20/ 0 352ICB. zE. near mer. ^6M. 2'/.

223

—

f\6

4^/12 45;2|77B.;»E. np Jf. BN.5'/. i^'b.

224

—

1 Canum

P\ 9

19

/I3 io2lcB./)L. wE. SN.

225

— 1 — —

PlS

31

/ 0 46'2!^'B./'L. BrN. just/a eft.

226

14J64 {y) Urs^e

P 33

32

J 0 341 6B.R.SB/Nandi'Fchev.4'^.

227

— —

P^5

28

n 2 37 2 cB cL. zF. r. t'^^-^M. 3'/. 2'b.

228

—

— —

P 5

20

n 2 242!t'B. t'BzN. andF. bran. 1^7.
?z 1 47 1 The 2d of 2. t'B. R. t;g-6M.

229

f 3

46

See II. 791.

230

—

83 Urs«

/

20

24

« 0 272CB. S. E.y/) «/. cBN. and F

linn

231

—

— —

/

2-t

34

;z 0 io2cB./>S. z'R.

232

—

— —

/

27

7

no 16 I The 2dof 2 <rB.S.R.?7^7»6M.
See III 791.

233

1 7,44 Ursas

/

1

14

/ 0 162 tB. E. Q,Q°Jp nj. r. ?)ibM. 3'/.

li'b.

3T3

■504

Dr. Herschel's Catalogue

1789.

Stars.

234 Apr. 1774. Vrsx

1790
Feb. 17

Mar. 17

18

^35
236'

237
238

239

240

241

242

243
244
245
246
247
248
2491

250
251

252
253
254

255
256

257

2.j8|Dec. 28

12 (() Draconis

24% UrscC Hev.

M.

1

66
59

I
P
P
P\5^

i9(|]Hyd.Crat.'/>

19

15 (i) Ursffi
77 (e) Ursce
39 Ursae

66 Ursae

1 7 Ursaj

76 Urs«

Oct.

69 Ursce Hev.

12 Eridani
47 (x) Persei

15

/36
/39

28

4
50

41

41

1

19

21
16

3

31
52
56-
10

55
10

34

'4 43

40
47
44
27

19

13

5

M. D

Description.

28I2 cB. S. /E. Just/> <7 /»L/i?.
^^'^c'&.iYrgmbM. 7'/. 5' 6.
i33't;B. S. zK. B/rN. vgmbM*
52 i|B. / oval. vgmbM.
32 2 tB./)L. ;R VgmbM.
ly^cB.ph. E. 7h61vI.
172 6B.^L.E. SBN.

f° 57

2
o

'1

n J2
n 2

Oj 71 Ig

2l!l

251

402

583

202
02

522
432

47

n

3

171

4«7

2,

31

1^/

0

341

4<^",/

0

5»i

47

J

1

81

26

n

1

11

33' «

0

131

5817

1

58ji

41

n

1

01

rB. E. 70° npjf. vgbM 7'/,
4'6. vsithin a parallelo-
gram.

z^'B. LBaN. with vF chev.

cB. S. R. ^6M.

cB.R. VgmbM \\' d.

vB. cL. R. VgbM'

cB./>L. E.

t'B./>L. /E. near par. mbM.

cB./'L.zF.

cB E. near par. er. bM. 4' /,
2' 6. I suj)pose, with a
higlier power and longer
attention, the stars would
become visible.

vB. cL. IE. LBNM.

vB. perfectly R. BN and F
chev. t;^6M. 1^'^.

t;B. cL. R.

z;B. t'L. E.

eB. E. par. 5' /. all over
equally B. except just on
the edges.

z;B. BENM. 3'/.i'6.

vB.ph. i¥. suddenly mbM.

cB.iRvgvibM. i^'d.

vB.iF.r.bM.5'f.j^'b.ApL
star in it towards the f
side, but unconnected.

of joo nezv Nebula, and Clusters of Stars.

5^5

1791.

Stars.

M

ejyMar. 7

260 Apr. 2

I 1793

261 Feb. 4

262 Apr. 6
263

264,
265
266
267

268
269
270
271

17 Hy elite Crat. /

23 (/6) Ursce

38ofthe Co;2;/o/iM /

1 (x) Draconis
4 Draconis -

8:37 UrscC
QQ Ursce

1796
272 Mar. 4

273;Nov.22

274

275
276'

277

278

Dec. 1 o

12

Georgian planet

A double star

Dracon. Hev,

/

18 31

I 49

3 7

2 6

22 48
14 18
16' 16

13 35
11 21

12 46
18

S5 36

/

3-5 54 n

o 53

45

D. Mig

o 271

341

1 35 T-

I

41 1
231
361

5|i

iiji
10 1

393

243

10 i3|/

1 32 n [o 12

2 45|Wp 12
6 20 7i lO 20

Description.

cB.pL.lE.gbM. Thebright-
ness takes up a large space
of it.

vB. vS. iR. mbM.

vB. iR. z'gbM. 5'd. Seems
to have 1 or 2 stars in
the middle, or an /N ; the
chev. diminishes vg.

cB. f S. /F. N. with vY. chev.

6-6. /E. 6M.

cB. S. 6M.

cB. S. iR. vgmbM.

cB. pL. iF. gbM.

cB.pL. iR. ifd. The great-
est part of it almost e-
qually B.

7'B. vS. R. Stellar.

cB. R. 1'^. just wof a Sft.

vB. ch. E. par. SN. E par.

vB. cL. E. mbM.

2cB.S. iR. BN. mbM. This
nebula was seen at g^ 2 7',
sidereal time; the tele-
scope being out of the
meridian.
vB. 7'L. E. near par. The
determining star follows
5DraconisHevelii 13' 54"
in time, and is 0° 23' more
south.
cB. vS. iR. bM.

2>cB. S. R.

2'cB. cL. iF. IE. mbM.

2vB. t-L. IF. mbM.

11 5\f\oi5\i\cB.cL.iR.mbM,

50(5

Di: Herschel's Catalogue

I.

1796.

Stars.

1

M. S.

D. M -

i Description,

279

Dec. 12

__ ^_

P

10 28j ?z

1 38'-

cB. cL. /E. 6M.

280

17.98

i6(^)Urs6emin.

J

51 33

n

0 3;

5 1'B. cL. /E. //)M. The great-
est brightnes confined to

281

Dec. 9

T Apps. Sculps.

a small point.

L.C.95 -

P

1 47

n

0 27

t-B. E. np jj. NM. m. \^h.

1801

282'Apr. 2

2o8(N)Camelop.

of Bode's Cat.

P

153 15

1

2 43

f B. pL. iY.

28 s

—

— —

P

113 4^

J

3 4

tB. cL. ^r.

284

—

— — -

P

85 18

1

0 23

^B. rS. zF.

285

Nov. 8

24. (d) UrsEe

./

13 14

1

1 ^3

v^. T.'L. E. ;?/)^. 6'/. 2'&,

286

J

30 0

1
J

1 8

I z;B. cL. R. 7'gmbM. On the
north-followingside there
is a F ray interrupting the
roundness.

287'DeC. 7

1 (x) Draconis

P

4 SI

n

1 13

I cB. niE.npJf. 7nhM. 3'/, I'b.

j 1802

288 Sept. 26

184, Camelopar.

1

of Bode's Cat.

P

11 58

J

2 34

1 I'B. cL. /E. suddenly w^M.

Second Class. Faint Nebula.

769

770

771
772
773
774
775
776

777
778

779

780

Feb. 22
Mar.2o

2.q

26

Stars.

8i f^) Geminor,
62 Ursje
-^'(z) Virginis

g^f) Ursae

26' (%) Virginis

26 (;>/) Virginis
46 (7) HydrK

M. S.

37 58
13 44

7 o
3 9
3 5
6 27

3 31

8 19

17 '5

21 12

22 44
1 22

D. M

Description.

pB. pL. iR. er. bM.

pB. ph. R. IbM.

pB. tL. i¥. er.mbM. 4 or ^'d.

F. S. E.

F. S. E.' bM.

pB. S. /R. nibM.
ilpB.ch. lE.vg7nbM.
iJF. vL. er.
iF. S. R. 6M.
ijF. S.Jf. a double star.
1 F. S.
1 F. R. r. T'^/bM. 4W.

of 500 nezv Nehulce, and Clusters of Stars.

507

II. 1789.

Stars.

M. S.

D. M p Description.

78i^Apr. 12! 1 Canum -

P

10 55. J

0 53'2]A/)S.y/. involved in nebu-

losity of no great extent ;

the Jt. does not seem to

belong to it.

782

i4'64 (•)/) Ursse

i

P

31 7

n

0 7 ]

/)B. S. R. vgmbU. just /a

SJt.
/)B. ph. bM.

783

__

P

18 40

n

0 501

784

—

— —

P

17 4'

n

0 371

pB. cL. IE. 3'/.

785

—

— —

P

7 3! n

2 181

pB. S. IE.

786

—

— —

P

3 31 "

1 S9

F. E.

787
788

)-

— —

P

<^ 2

3 7

1 27^
1 24

r Two nebula: the ist/)B. S,
lThe2d/>B. S.

789
790

}-

— —

J

1 35 n

1 38]

f Two nebulre; the ist/>B.E.
1 The 2d F. S.

791

—

f

3 24 72 1 48J1

The 1st of 2. pB. S.E. See

792

_.

1 Canum -

P

3 12

7Z 2 47]

I. 229.
F. S. R. bM.

793

—

— — .

P

057

n 2 36 s

F. pL. iF. bM,

794

—

77 (s) Ursse

P

11 32

fp 492

. F. S.

795

—

— —

P

8 25 /'i i3^s

, pB. vS. jnbM.

796

—

— —

P

7 20/1 2,52

pB. cS. /E. BrN.

797

— 81 Ursa -

P

3 33/2 182

/.F. pS. R. T'^6M,

798

—

83 Urs£e -

I

0 49i n 1 i|i

/.B. E. li'/, i'6.

799

—

— —

f

21 27, n\i 72

/)B. rL. E.

800

—

— —

J

25 7j « 1 2 J

pB. S.

801

—

— —

J

27 27 w 0 232

F. rL.

8C2

1771 Ursce -

P

15 20 n 1 331

F. S. E.

803

—

— —

P

'3 57\no 59^

F. S. R.

804

—

— —

P

5 43 fo 3 1

pB. pL. iF.

805

~~

"■^ __

P

4 41 n 1 201

The 2d of 2. pB. pL. mbM.
See III. 798.

806

—

— —

P

2 i3| w 1 42 1

pB.

807

—

12 (() Draconis

P

55 48 n 0 42 1

pB. E. mer. i^7, ^b.

808

24;Neb. 11. 756

P

24 16 no 41 ]

pB. S. zF. «>?". mixed with

some/iL. stars, which may

perhaps belong to it.

809

—

— —

P

15 5

J

0 26 1

F. S. E.

.".oS

jDr. Herschel's Calalogue

ir.

1789.

St:irs.

M. S.

D. M

^ Description.

810

Apr. 24

21 (jt^) Draconis

P

4^ 31

w

3 231

/)F. /»S. /E.

811

—

— —

P

44 9

n

0 50 ]

/)B. ?R. TgT'/6M.

812

—

— —

J

10 4

«

2 55 1

F. S. K. vglbM.

813

26

^ Caniim

P

10 53 /

0 501^

/>B. S. /E.

814

—

7 Canuin

f

20 24! n

1 20]

F. S. vfmbM.

815

—

82 Ursee

P

31 48 /

0 52 ]

F. z^S. Stellar.

816

—

— —

P

26 52

/

1 36 i

F. S. /R. vgmbM.

817

—

— —

P

3 42

/

1 40 ]

I/)B. S. R. r^'-6M.

818

1790

1 2 Draconis

P

40 i()

;i

0 33'

I/F. 6-8. R. t^^^-6M.

819

Mar. 8

i3(x)Hycl.Crat.

P

1 1 58, n

0 31 1

IpF.pL. /F. 6M.

820

10I65 AurigiE

I

7 22 n

0 1 1

|/)B. S. Stellar.

821

—

7oGeminorum

P

1 43,^'

0 12 ]

\pB. cS. r. p a eft.

822

17

27 Lyncis -

P

25 42

»

0 4T ]

\pY. K.r. vgbM.

8^3

15 (I) Ursa?

P

12 10

/

0 18]

pB. S. R. mbM.

824

—

26 Ursce -

J

139 17

/

0 1 ]

pB. mY. 61, ^'b.

825

—

— —

J

139 40

/

1 441

pB. S. iY. 6M.

826

—

77 (0 Ursa?

f

28 0

n

1 421

F. S. E.

827

—

I

69 19

71

3 271

pB. S. iY. fnbU.

828

18

17 Ursee

P

6 25

J

2 c: '

pB. S. VgmbM.

829

—

6'6" Ursas

P

31 14

n

1 9-

Y.E.npjf.er.ii'l.

830

—

— —

P

15 23

J

0 201

I/.B. E.

831

—

— —

P

11 44

n

1 22 1

pB.vS.lY..

832

~

P

^ 53

n

2 522

pB.pL.R. The nebulosity
of this runs into that of
I. 248.

833

—

— —

P

1 1

n

1 46 1

F. S.

834

19

17 Ursse

P

11 34

n

3 101

pY.pS. iY. er.

835

—

29 (u) Urs£e

I

5 11

n

0 152

Y. S. E. near par.

836

—

76 Ursce

P

70 4'

J

0 531

Y. S. R. r. almost of equal
light throughout.

837

—

— —

P

66 54

J

1 O]

pB. IE.

838

—

— —

P

66 15

J

3 9 1

pB. S.

839

— —

P

63 0

J

2 281

pB. cS R, 77ihM.

840

—

— —

P

47 30

J

2 i6'i

F. S. bM.

841

—

6q UrsEeHev.

J

4 24

71 2 46,2

The istof 2./)B. S. iY.

842

—

— —

j\

4 35

«

2 50:2

The 2d of 2./)B./>L. ?F.

o/'5oo neri

' Nebulie, and Clust

ns of Stars. 5^9

II.

1790.

Stars.

M. S.

D. M. 5 Description.

843

Mar. 19

J

26" 40

11

0 42 ]

F. S.

S-W

—

— —

J

27 43

I

0 291

/)B. fL.

845

20

50 (a) UrSiE

J

22 41

n

1 44 3|/'B./'L.fK. 6M.

846

—

76" iJrsse -

P

23 9

71

3 13^

I pB.mY..Jpnj.mi. 5'l,^'l).

847

—

— —

P

19 1

n

3 81

I /)B. S. /E.

848

—

— —

P

14 21

n

2 8 ]

L F. z'F. bM. Stellar.

849

—

— —

P

9 7

n

1 15

t pB. x>?>. IE. SN.

850

— —

P

7 16

n

0 48

I pB. pL. /R. ?-. vghM.

851 pet. 9

72 Pegasi

f

18 3

I

0 6<

2 pF.pL. iR. IbM.Jp.aTSJl

852

—

0- Fornacis L. C.

285 - -

P

4 15

Jo 34I

iF.pL.iR.gbM.

853!Nov.2629 (tt) Androm.

P

25 38

/

0 24

1 F. S. E. near mer.

854Dec. 2544 Piscium -

f

3 49

n

0 5^

1 ^B. vS. R. vgmbM. pretty

well detined on the mar-

855

—

— —

f

4 44

n

0 10

gin.
2 pB. cL. iR. r. vgbM. fp. a

856

—

— —

f

13 52

n

1 8

1 F. S. z^^feM.

857

—

— —

I

13 52

n

0 53

1 F. S. VgbM.

858

—

— —

f

14 lO

« 0 58

1 /)B. S. VgbM.

859

—

98 (tt) Piscium

I

20 28

n 0 1

1 /)B. S. E. near par.fp. a S/i^.

860

sSMayer's Zod.

Cat. No. 18

P

5 48

w 0 39

1 pF. vS. VgbM.

861

—

57 Auriga -

J

17 30

« 1 54

1 /.B. ph. iF. gbM.

862

—

— —

f

23 5

n\ 29

''^•^^- ;t^ ;..

863 29

1 ^r\ 1

63 ( (J) Piscium

P

0 39

no 44

i---pL.lE.r.gbM.

1/91
864 Mar. 7

17 Hyd. Crat.

I

16 46

/o 1

1 pB S. R. VgmbM. almost
resembling a N.

8651
8661 f ~

r Two nebula, both F.S.R.

— —

f

34 2

/o 31

1 . bM. and nearly in the

[ same par.

867

April 2

73 Ursa3

P

14 8

/jl 12

1 pB. vS. Stellar.

868
869

10 38

11 8

r Two nebuItCj the 1st F. S.

} 3

14, (t) Ursce

I

n

0 47

1 iF.
[TheadF.^L.E.

MDCCCII.

3 U

.Tio

Dr. Herschel's Catalogue

870

791.

Stars.

April 335 Ursce -

871
870

873 May 6
24

874
875

13 (yjUrscemin
37 (£) Bootis
30J25 Herculis
1792 I
876!Apr.ijo22 (f) Bootis

877I - .

3 Cephei Hev

878|Sept.i6

-^793 ,
April 6'

«79

880

882
883
884
885

1 (a) Draconis

4 Draconis
837 Ursae
39 Ursae

9
May 12

887
888
88c,
890
891
892

893
894
895
896

897 Sept. 6

1794

898 Mar/'"

4,2 Ursae

19 Bootis Hev.

13

93 (t) Virginis
53 Aquarii
Georgian planet

M.

2 50

3 37
21 30

D. M. 0

37

53

34

48

3

10

15

58

13

27

29

15

9 49/

7 44"

45 43 "

10 4,0^

8 36, «
22 42/
37 4V^^
44 5./

2 41

7 21
26' 4,5
13 20

6 44

7 44

9 37
10 4b"

21 54
21 49
16 29

o 36'

o 52

0 11

1 17

1 12

2 12

0 26

1 21

o 25

5

6

Description.

0121

3 o

3

8

37

42

1
1
1
1

56I1

111
20 1

33I1
1
1
1
1
1
I
1

8
24
22

31

40

40
7

n o 33

F. S ill. Almost of equal

ligiit throughout.
F. vS. mbU.

F rL. a\.

F. R. bU. id.
pB.ph. /R. z^gwfcM.
pB. S. IE. vgmbM.

pB. vS.

pB. pL. iF.

pB. /F.6M. contains 2 stars.

pB. S. R. bM.

F. S. IE. fp nf. but near

mer. gbM..
F. mE. npjf. but near par.

/)B.>L. IE. bM.

F. S. R. ^>M.

F. S. R. bM.

F. S. IE. npff.

pB. iF.

F.pL. iF. bM.

F. S. R. bM.

pB.pL. R. just foil. aS/i,

pB.pL. iR.

pB. pL. IE. BM.

F. S. E. near mer;

pB. S. iF.

F. S.

F. S. iR.

F. S. iR.

pB. IE. r. if/, -i^'b.

F. 3' north of a pE. red ft.
This nebula was seen at
8'' 49', sidereal time, the

of ^00 ncxv Nebula, a?id Clusters of Stars.

511

II.

1797-

Stars.

M. S.

D. M.

0

Description.

telescope being out of the
meridian.

^99

900

Dec. 20

^79^
Dec. 10

4(6) Urseemin.
18 (e) Eridani

P

P

26 13
20 53

J
J

0 40

1 5

1

1

F. S. E. near mer. I'l.

F. E.fp nf. near par. 3'/, \'b.

901
902

1799
June29

1801

93 Herculis -

P
J

27 30

7 47

I
n

0 11

0 49

1

1

F. S. iV. er. ^'l.
F.pL. R. vgbM.s^'d.

9^S
904
Q06

April 2

N0V.28

l802

June 26

2o8(N)Camelop.
of Bode's Cat.

11 («)Draconis

P
P
P
J

139 19
5-8 9

36 53
86" 13

I
J

J

n

1 39

1 58

2 22
0 8

1
1

1
1

F.pL.r.

F. pL. ibU.

pB.pL.

F.S. IE. fpnfvglbM.

907

2 (^) Lyras

I

5 21

n

0 18

1

F. S. zF.

Third Class. Very faint Nehulce.

III.

1788.

Stars.

M.

s.

D. M.

!
1

Description,

74«

Dec. 3

43 Camelop.

A

?,5

5

7i

0 29

vF. vS. has a t^F. bran wf.

749

—

22 Urate

/>

12

45

/

0 24

1

c'F. vS.

75"^

31

5"3 Aurigas -

./

48

5«

n

0 43

1

vF. S. R. IbM.

751

1789

39 Lyncis -

./

?5

15

7

0 30

2

eF. S.

752 Feb. 22

16 (^) Cancri

P

4

19

w

0 8

1

^F. lE.fofavSft.

753

—

33 {71) Cancri

P

8

11

/

0 4

1

vF. S. R. t^/6M.

754

24

"iMar.
J 20

6" Corvi

P

17

33

y

I 43

1

^F. vS. R.

r Two nebulse, botht'F. vS.
E. witlun 1^' of each
I other.

/6b

756'

26 (%) Virginis

P

13

3

n

0 20

1

757

^ "

P

5

25

n

0 38

2

2 vS. stars involved in t'F.
nebulosity of no great ex-
tent.

3U 2

512

Dr. Herschel's Catalogue

HI.

1789.

Stars.

M. S.

D. M

0 Description.

758

759

T Mar.
i 23

J

20 55

n

1 53

1 Two nebulas, both vY. f S.

760

/

23 47

I

0 9

1 cY. z/S. R.

76'!

—

—

J

24 55\ n |o i8|

1 t;F. S.

762

—

102 (Li')Virginis

P

11 30

n 0 36'

1 vY. z;S.

763

—

i05((p) Virginis

P

1 1

/o 1

1 eY. S.

764

26

g {B) Corvi

P

4 55

n 0 15

1 cY. pS. R. Stellar.

765

—

45 (4') Hydr«

P

1 35

I ^ 53

ivY.pL.iY.

766

—

— —

J

0 39

Jo 16

ivY. vS.

767

Apr. 1 2

^4 (y) Ursce

P

78 24

Is 45

1 vY. pS. iY.

768

—

— —

P

30 48

/o 49

2 T'F. 7'S. Stellar.

769

—

— —

P

1 40

/

1 44

icY.S.

770

14

— —

P

39 32 n

2 2

ivY. vS. Stellar.

771

P

19 37

n

1 8

i^F. S. zE. On account of
the brightness of 1 79 Ur-
s£e maj. of Bode's Cat.
which was in the held of
view with it, 1 hud near-
ly overlooked it.

772

—

— —

P

19 2

?i

1 16

1 vY. Stellar.

773

—

— —

P

14 0

n

2 32'

1 cY. pS. IE. just/ a vSft.

774

—

— —

P

10 37

I

0 58

2vY. S.

775

—

— —

P

10 17

J

1 1

1 vY. vS.

776

—

— —

P

9 SS

n

2 12

1 eY. pL. IE.

777

—

1 Canum -

P

1 54

J

0 33

leY. S. Stellar.

778

—

77 (e) Ursse

P

9 10

I

1 4;

2 6F. S. lE.iY.

779

—

— —

I

11 2)^\n

0 20

2 vY. S.

780

—

— —

I

12 37

J

6 19

1 cY. S.

781
782

}-

— —

I

12 30
12 44

I

2 22
2 20

1 1 Two nebulce. Both z;F. S,

783

—

— —

I

12 33

f

2 28

1 vY. S. E.

784

—

81 Ursce -

P

7 6] 71

0 9

1 cF. S. iR.

785

—

83 Ursas -

I

4 34' '^

0 37

1 2 ^F. ff. with nebulosity.

786'

—

— —

f

14 3

I

0 22

ir'F. T'S. Stellar.

787

— •

— —

J

22 27

J

0 28

1 vY. vS.

788

—

— —

J

23 47

I

0 24

1 vY. vS.

78s

—

— —

J

23 54

J

0 22

1 z;F. rS.

of 500 nezu Nebulce, and Clusters of Stars.

513

III.

1789.

790 Apr. 1483 Ursse

791 —

792
79S

794
795

79^
797
79^

799
800
801

802

803

804
805
806

807

808
809
810
811
812

813
814

815
8i6"
817

818

44 Ursaa
48 (i3) Ursse

}-

Stars.

74 Ursse

69 Ursse Hev.

26

71 Ursag p

P
P
P
P

P
P
J

J
J
I
P
I

P
I
I
I
P
P
P
I
I

M. S.

i2(<) Draconis
2474 Ursse

6^ Ursce Hev.

Neb. II. 756
21 (/it) Dracoiiis

5 Canum
7 Canum

25 23
27 7

3 11
1 25

23 30

16 8

11 23

lO 56

5 4

1 12

1 9
4 54

D. M. ?

^ I
71 p

n |o
Jo

17
16

50
10

9 3Sf
I
I
34 20
26

4^' 59
48 9

4

52|l

ii;2

20|1

371
302

532
182

13
811

341

Description.

7 S5
27 7
30 44

o 32
55 20
36"
15
18 48

25 11J7Z

26' '43 n
33 41/

/■I

19
25

13
2

18
14
32
22

33

4511

711

v¥. pL.

The 1st of 2. r'F. S. 4' dist,
from I. 232.

T'F. S. E. 20°j^ nf. er.

vV. vS. Stellar. The bright-
ness of |G Ursae is so con-
siderable, that it requires
much attention to perceive
this nebula.

cY. S. ver 300.

z'F. S. i¥. r.

eY.

vY.S.

The 1st of 2. cY. IE. IF. II.
805.

vY. rS.

r Two nebulae, both eY. cS.

I R.

The 1st of 2. vY. S. IE. See
III. 807.

eY. vS.

eY. S. E. r.

eF. rS. R. Stellar.

rF. fS. IE.

The 2d of 3. eY. S. E. diffe-
rently from III. 802.
F. S. E.

vY. vS.

cY. vS. R.

vY. S. E.

vY. vS. IE.

vY. vS. iR.

z'F. S. er.

S. Stellar.

^F. S. IE.

cY. S. iY.

cV.S.R.vglbM.

514

Dr. Herschel's Catalogue

III.

1739.

Stars.

M. S.

D. M.

=r Description.

819

Apr. 26

S3 Ursse

P

32 15

./

3 12

1 ?7F.

820

P

29 17

,/

2 48

i2Z'S Stars at less than I'd.
with vF. nebulosity be-
tween them.

821

—

— —

P

12 59

/

0 7

1 cF. Stellar.

822

—

— —

P

6 23

./

1 2.0

icF.pS.iR.lbM.

823

1790

— —

P

5 5

/

1 18

icF.pL.R.vlbM.

824

Mar. 8

7(a;)Hyd.Crat.

f

7 26

/

1 9

1 vF. vS. iR. glbM.

82.5

10

S9 Lyncis

P

12 5S

/

1 31

iz'F.S.R.bM.foraSJt.

826'

—

— —

P

5 55

/

1 56-

1 T'F. S r.

827

—

— —

f

2 11

/

1 29

leF.vS.ffavSft.

828

•~~"

Hyd. L. C. 1039

P

2 1

/

1 11 '

jeF.pS.R.T'gbM. Stellar. just

p a vSft.

829

17

27 Lyncis

P

23 49 n

1 30

1 ^F. z;S. R. 6M.

830

—

— _

P

10 40 n

1 19

i(:F./.S.6M.

831

—

15 (f) Urs^e

P

12 8 ;z

0 23

iz'F. t'S.

832

—

— —

f

9 S9 n

0 57

ivF.S.lE.

833

—

26 Ursse

f

134 3/

1 43

t z^F. z'S.

834

—

74 Urste

f

2 4 A

1 56-

i^F. S.iF.

835

—

77 Ursie

f

82 37

n

1 52

I ^F. S. E. but nearly R.

836

18

17 Ursee -

P

79 17

I

0 33

I z'F. z'S. may be a patch of
stars.

837

—

— —

P

75 32/

0 40

eF. vS.

838

—

— —

P

75 10;/

0 15

i^F. Z'S.

839

—

— —

P

72 221/

3 401

^F. Z'S.

840

—

— —

P

% 56;/

1 28 ]

cF. cS.

841

—

— —

P

16- 9/

1 91

vF. S.

842

—

43 Ursze

P

5 81/

^ 39^

z^F. Z'S. R.

843

—

66 Ursie

P

19 23 «

1 52 ]

Z'F. Stellar, np a Sft.

844

—

— —

P

16' 1 «

2 2 ]

vF. S. wE.

845

—

69 ((J) Ursce

P

4 55 n

1 17 ]

Z'F. S. E. par.

846

19

20 Ursas

J

7 53 /

3 2'^

cF. S. wE. very narrow.

847

—

76' Ursse

P

67 53/

2 50 ]

eF. t'S. IF.

848

—

69 Urste Hev.

P

19 5 n

2 13 1

Z'F. Z'S.

849

—

— —

f

23 5S 1

0 8]

I Z'F. Z'S.

8jo

20

76' Ursce

P

26 56

n

3 17

ivF.pS.

of ,^oo new Nebula', and Clusters of Stars.

515

III.

851
850

854

856"

857
858

Mar.s>c

Apr. 1
Oct. (J

}-

10

Stars.

76 UrsK

30 {(p) Ursce
72 Pegasi

M.

<T Fornacis L.
C. 285
6 Pearasi

:}

8.59

86'oNov. 2 72 Pegasi

861

862
863
864

865
866

867

868
869

870
871

872
^7S

874
87

8

i LacertaeHev,

1326 Aurigje
2629(7r) Androm,

Dec. 6

Mayer's Zod. i
Cat. 20 - '

25'44 Piscium

28 Mayer's Zod

Cat. 18

57 Aurigas

'."■}

25 251 n
16 38' /2

8 55
15 8

27 1.

12 30
24 40

M. D

43
12

23

o 3::

7 5^, «

5 19 "

37 5o|/

3 i7i"

3 9 «

4 37 n
1 9' n

27 37/

49 19/

39 35/

Description.

54
43

17
7

17
19

48;
50

31

20

1 S9

o
3 35; « o

1 2 48} 72

8 i\n

5 52' w
5 3-1 '^

17 56
21 42

/

42
55

49

44

41
S9

50
7

^F. S. /F.

z'F. Stellar, w/a S triangle of

Bft.
vY.S. vglbM.
2f S dose ft. with nebulosity

between,
r Two nebulae, both ^F. Stel-
l lar. dist. 1' from 30°yj>
l to nf.

vF. S. ?F. IbM.

eF. ph. iR. vlbM. requires
great attention to be seen.

cF. z;S.7R. mbM. neara vS/t.

vF. S. IbM.

^F.S.

eF.ph.iR. r.
1 z;F. T^S. mbM.
1 \vF. S. wE. 75° n/.^. 6M.
i^.vF.vS.R.bM.
i!r.'F. TvS. The «/» corner of a
square.

^F.^S. /R./^M.

1 ^F. pS. iF.

1 t;F. vS. bM. p. and in the
field with II. 854. 7if. 2.

vF. S. zR. vgbM.

vF. S. R. VgbM.

vF. vS. bM.
1 ^F. cL,. In the field with, the

foregoing, and with II.

860,
1 z;F. vS. IF.
1 vF. vS.

5i6

Dr. Herschel's Catalogue

III.

1790.

S^ars.

M. S.

D. M.

? Desciiption.

876

Dec. 29 51 Piscium

J

5 44

«

1 43

1 vF. pL. iR.ffa SJt which is

partly involved in the ne-

bulosity.

1791

877

Feb. 23

26 Hydrse

P

73 5«

7J

0 22

1 vF. iR. r. Q'd. almost of equal
light throughout.

878

Apr. 2

14 (t) Ursee

J

9 14 «

0 38

2 vF. cL. R. ?nbM. near 5V/.

^79

—

73 Urs£e

P

2 39\J

1 12

1 cF. S. ?F.

880

—

— —

f

8 13. A

1 26

1 eF. S.

881

S'35 Urs^ -

I

21 51

ii

0 13

1 vF. S.

882

May 6

9 Ursce rain.

P

34 52

f

2 0

1 T'F. pL. R. 6M.

883

—

i3(y)Urssemin.

J

43 41

I

1 36

1 ^F. vS. ver. 300.

884

— :

— —

f

44 51

f

2 22

1 7:'F. vS. with 300 cL.

885 24

37 (?) Bootis

P

3 44

f

0 35

1 eF. vS. E. near par.

886^

rTwo nebulee, both ^-F vS.
1 the p is the most n. dist.

887

y 26

7 Serpentis

P

15 32

n

0 20

888

27

19 (^) Coronse

P

6 41

71

1 7

1 eF. ?7S. R. with 300 />L.

889

28

17 (0-) Coronae

P

2 1

1

0 52

1 z^F. S. R. 7>glbM.

890

—

20 (v) Coronas

f

8 9«

1 20

ivF.pL.lE./bM.

891

30

25 Herculis

P

3 41, «

0 37

1 eF. t;S. R. /6M.

892

—

— —

P

2 5!/

0 9

ieF.S.6M.

893

1792

44 (ij) Herculis

P

6 26 ;z

0 8

1 eF. vS. zF. ver. 300.

894

Apr. 20

22 (f) Bootis

f

12 29 «

1 15

1 vF. vS.

895

—

— —

f

13 55 «

0 47

I vF. z'S.

896

—

— —

I

16 45 /

0 25

1 eF. S. vibM.

-^793

897
8^8

f Two nebulae. The most n.
1 -' and p. eF. S. The other
I ^F. vS. dist. y.

}Feb.4

34 (Q) Gemin.

P

1 33 J

0 31

899

—

— —

f

15 18 «

1 17

1 7^F. S. nearly R. bM.

900
901

}-

— —

f

36 2 1 , rt

0 9

r Two nebulse just prece-
U ding III. 703. BotheF.

902

Mar. 8

18 Navis

f

10 36 «

0 32

1 vF. lE^r. bM.

903 Apr. 6

4 Draconis

P

30 43;/

0 10'

leF.S.iF.vlbM.

904

-

— —

P

23 25

n

0 24'

1 eF. z'S. E. mer.

of goo new Nebula, mid Clusters of Stars

517

III.

>793-

Stars.

M. S.

D. M.

r Description.

9^5

Apr. 7

4 Draconis

P

37 3

n

0 8]

^F. vS. ver. 300.

906

—

6' Draconis

f

12 31

n

I 8]

rF. E. Q'l, ^'b.

9^7

—

— —

f

16 26"

n

1 35^

v¥. E. 7ipff. li-V, i'6.

908

—

— —

f

23 36

n

0 101

I ^F. rS. zR. vlbM.

909

—

— —

f

39 10

11

0 35^

I t;F. vS. R.

910

837 Ursa2

P

15 47

n

0 19

I vF. pL. iF. r. some of the

stars visible.

911

—

— —

P

n 47

I

0 5

I vF . cL. iF .

912

— ^

— —

f

0 59

n

1 27]

I ^F. T'S. ver 300.

913

— '

39 UrsiE -

f

8 14

71

1 141

I T'F. rS.

9H

—

— —

f

10 29

f

0 2 :

vF. S. IF.

915

—

— —

f

25 35| «

0 3]

L vF. S.

916

9'42 Ursa3

P

48 48; n

0 39^

eF . T'S. Stellar near a S/f.

917

}-

P

15 19

I

0 44

f Two nebula.
^ lBothz;F./.S. R. /6M. ^

918

15 10

0 47

919

—

— —

P

0 1

11

2 2 :

I vF . rS. near a x^Jt.

920I —

— —

I

19 23

n

2 1 ]

eF . tS. E. near mer.

921

—

— —

f

24 11

n

1 22

eF.pl.. E.

922

—

— —

f

35 14

n

1 11 ]

L vF . T'S. 2i'S. Stars in it.

923

May 5

Hydr.L.C.1179

P

1 25

n

0 5]

r;F. rS. R. /6M.

9^4<

—

6 HydriE conti

J

11 2

I

1 271

I ^F. S. r. ver. 300.

9^5

1264 Virginis

f

1 18

n

1 10 ]

I cF. S.

926

—

— —

f

13 5

n

1 17]

L vF. S. fp, a cF>ft.

927

—

19 Bootis Hev.

P

0 20

71

0 44

vF. S.

928

13

93 {^) Virgin.

P

26 17

I

0 5]

t;F. S.

929

—

— —

P

9 25

71

0 35^

t'F. S. E. mer.

930

Sept. 6

53 Aquarii

P

27 19

71

0 18]

^F. ver. 300.

931

—

— —

P

12 23/

0 19]

eF. S. zR.

932

P

8 50

71

1 11 ]

^F. S. /E./of a S/. to which
it seems almost to be at-
tached, but is free from it.
The star is the 1st of 3,
making a S triangle.

933

1794

— —

P

6' 7 n

0 581

vF. S. R. 6M.

934

Apr. 1

Georgian planet

P

0 16/

0 2 ]

vF. This nebula was seen
at 9''45', sidereal time, the

M

DCCCII.

3^

K

5i8

Dr. Herschel's Catalogue

III.

1794.

Stars.

M.

s.

D. M.

0

0-

Description.

telescope being out of the

meridian.

935 Apr. 19

12 (^) Hydr«

crateris

/

15

11

n

0 40

I'eF.S.bM.

936 Oct. 15

5 («) Cephei

/

7

54

n

0 l6l vY. €7',

1797

937

Nov. 22

Neb. I. 274

/

25

3

n

0 53^

vF. S. iR. bU.

938

Dec. 10

A double st*

P

9

5

n

0 101

eF.pL.iF/'^ See I. 273.

939

—

— —

f

4

o\f

0 351

^F. S.

940

12

5 Dracon.Hev.

P

32

24 /

0 491

vF. S. R. 6M.

941

—

— —

P

8

21

n

0 571

t'F. pS. 2 S Tif stars make a
a triangle with it.

942

—

— —

f

4

16

n

0 59^

eF. E. near mer. ver. 300.

943 )

944 J

5 (a) Urs^e mi.

f

46

2

I

0 28

J Two nebulas.
[Botht'F.fS.r.dist. i^'par.

945

—

gQ Draconis

P

47

10

J

1 ly

7'F. S. E. 71 of a S/t.

946'

20

4f{b) Ursx mi.

P

29

31

n

1 57

vF. vS. R.

947

—

— —

P

14 39\^^

0 42

vF. cL. iF. vlhM.fofapB.

ft-

948

—

— — /

2

20 71

1 3

1 ^F. vS. E. near mer.

949

—

— —

f

14

44

n

2 29

1 ^F. S. /E. near par.

950

f

24

18

n

1 13

vF. S. r. It is preceded by a
S. patch oijt. which ap-
pears almost like this ne-
bula, but more resolved.

95^

—

4 Cephei of

Bode's Cat.

P

21

18

I

1 25

1

cF. S. better with 320.

1798

JDec.9

rTvvo nebulze within I'of
1 each other ; mer! Both
I vF. tS.

95^
953

2 (77') Orionis

P

10

20

J

1 34

1

954

ic

8 Ceti -

f

17

5

J

1 15

1

eF. S.

955

—

21 Ceti

P

3

46

n

0 4

1

cF. vS. iR.

95^^

1799

18 (e) Eridani

P

15

21

I

0 53

1

vF. vS. 2 or 3' 71 of^Sft.

957
958

1 Jtir.e
J 29

93 Herculis

A

4
3

3

59

71

1 S3

1 37

1

J Two nebulae.
1 Both rF, vS.

of goo nezv Nebula, a7id Clusters of Stars.

5^9

III.

I 7(j.j.

Stars.

M.

s.

D. M.

~ Description.

959

Dec. 19

16' Eridani -

J

6

37

n

0 26

1 Tiie 2d of 2 T.'F. rS. i^'/J I.
60.

960

—

19 Eridani

f

1

19

n

1 13

1 T'F. z^'S. ver. 300.

g6i

—

— —

J

2

43

n

0 4,6

1 vY. t'S.

962

1801

— —

J

20

51

n

1 15

I vF.vS. pp. QpBft.

963

Apr. 2

2o8(N)Camelop.

of Bode's Cat.

P

^57 3^^

J

1 16

I eF. S. IF.

964

—

— —

P

119

54

J

3 5

I tF. S. Stellar, ver. 300. just
p. a Sp.

9^5

—

— —

P

117

22

J

2 56

I ^'F. vS.

966

—

— —

P

iiS

0

n

0 29

1 T'F. T'S.

967
968

T

r Two nebulce. The 1st vF.

}-

— —

P

72

10

J

1 52

i\ S.
lThe2d;//. the ist^F. I'S.

9%

—

— —

P

37

31

J

2 39

I ^F. S.

970

—

— —

P

24,

19

n

0 28

1 vF.pL. r.

971

" —

— —

P

20

34

I

2 31

I eF. vS. R.

972

Nov. 28

50 (a) UrsEe

P

5

7

J

0 10

1 vF. vS. R. 6M.

973

Dec. 6

1802

16 (^) UrsK mi.

I

14

15

n

1 8

1 7;F. S. IE. mer. r.
TTwo nebulae ; the preced-

ing ^F. S. bU. the foil.

974

jjan. 1

22 (e) Ursce mi.

P

10

49

n

0 37

1 < vF. vS. it follows the 1st

975

a few seconds, and is 3'

I more north.

976

May 21

2 (ij) Coroiite

P

26

50

n

0 2

1 ^F. S. iF.

977

Sep. 26

186P. Camelop.

of Bode's Cat.

f

9

49

f

1 33

I eF. vS. 300 confir.

978

—

— —

f

33

19

f

0 58

1 eF.pL. r/6M. just ti o^aft.

3X3

520

Dr. Herschel's Catalogue

Fourth Class. Planetary Nebula.
Stars ivitb Btirs, with milky Chevelures, with short Rays, remarkable Shapes, 8:c.

IV. 1789.

59

60

Stars.

61

62

63

64,

Mar. 23 .55 Ursae

Apr. 12 36 UrscE

64 (y) Urs^

14

24,69 Ursse Hev.

1790
Mar. 4

6 Navis

528 Monocerotis

/

M.

/

/

/

4 51

/ 8 37

3 56 f

2 27

1 24;/

7 41

51 49

/

D. M

o 23 1

2 202

o 192

1 251

1 33

1 2

O 26

Description.

cB.S.R. BN. The N is con-
siderably well defined, and
the chevelure t:;F.

vB. R. Planetary, but very
ill defined. The indis-
tinctness on the edges is
sufficiently extensive to
make this a step between
planetary neb. and those
which are described
vfmbM.

cE. BrN with z;FE branches
about 30° 7ip JJ. 7 or 8V,
4 or 5'6.

cB. quite R. A large place in
the middle is nearly of an
equal brightness. To-
wards the margin it is less
bright.

cB. cL. /R. er. vgrnb^i. 4'
diam. I suppose, with a
higher power, I might
have seen the stars.

A beautiful planetary nebu-
la, of a considerable de-
gree of brightness; not
very well defined, about
12 or 15" diam.

A pretty considerable star,
9 or 10m. visibly affect-
ed with z'F. nebulosity,
of very little extent all

o/^co 7iew Nebula, and Clusters of Slurs.

521

IV.

1790.

Stars.

66':Mar.i8|i7 Ursa^

67

68

— 66 Ursre

^945 Lyncis

D. M.

16 29 /i3 6 1

o 39

4 1.^

69Nov.3o(2^ A"j;g'^,.. ^i ^8 24
"^ !lor 31 Hevelii yi 24 59

1 55 1

1 44

/

0 11")

1 26J

Description.

around. A power of 300
shewed the same, but gave
a little more extent to the
nebulosity. The sad Mon-
cerotis was quite free from
nebulosity.

A small star with apB. fan-
shaped nebula. The star
is on the p side of the di-
verging chevelure, and
seems to be connected
with it.

pB. ph. R. The greatest
part of it equally B, then
fading away p suddenly ;
between 2 and 3' diam.

vB. S. exactly R. BNM.and
vF. chev. vg. joining to
the N. In a lower situa-
tion the chev. might not
be visible, and this neb.
would then appear like an
ill defined planetary one.

A most singular phenome-
non; A/i^ 8m. with a faint
luminous atmosphere of a
circular form, about 3' in
diam. The star is perfect-
ly in the centre, and the
atmosphere is so diluted,
faint, and equal through-
out, that there can be no
surmise of its consisting of
stars, nor can there be a
doubt of the evident con-
nection between the at-
mosphere and the star.

522

Dr. Herschel's Catalogue

IV.

1790.

Mar. 6

71

May 24 37 [I) Bootis

1793
.73 Sep. 6

Stairs.

6 Draconis

1793
72Sep. i534Cygni -

16 {c') Cygni

/

M. S.

50 27

16

.T 10

2 51

/

/

D. M

37

o 44,

o 33

Description.

Another star, not much
less in brightness, and in
the same field with the
above, was perfectly free
from any such appear-
ance.

cB. R. ahnost equally B
throughout, resembling a
very ill defined planetary
neb. about i'diam.

A star 7.6)m. enveloped in
extensive milky nebulo-
sity. Another star 7m. is
perfectly free from such
appearance.

A double star of the 8th
magnitude, with a faint
south - preceding milky
ray joining to it, 8'/, and
1^' broad.

A bright point, a little ex-
tended, like two points
close to one another; as
bright as a star of the 8.9
magnitude, surrounded by
a very bright milky nebu-
losity suddenly termina-
ted, having the appearance
of a planetary nebula with
a lucid centre; the border
however is not very well
defined. It is perfectly
round,and I suppose about
half a minute in diam. It

of t;oo jieiv Nebula, and Clusters of Stars.

523

IV.

1793-

Stars.

1794 '■

74 Oct. 18 7 Cephei

75

7 Cephei -

1798
76Sept. 9! 3 (-^) Cephei

/

P

77 Dec. 19

i6Eridani

M.

\M. d:

24 57 n

14 40

1 22 1

10 31

4 5^

/o 46

Description.

/I 36

n o 14

is of a middle species, be-
tween the planetary ne-
bulas and nebulous stars,
and is a beautiful pheno-
menon.

A star 7m. very much af-
fected with nebulosity,
which more than fills the
field. It seems to extend
to at least a degree all
around ; smaller stars,
such as 9 or 1 cm . of which
there are many, are per-
fectly free from this ap-
pearance.

A star 7.8m. is perfectly
free from this appearance.

Three stars about 9m. in-
volved in nebulosity. The
whole takes up a space of
about i^'diam. other stars
of the same size are free
from nebulosity.

1 cF. vL. iF. a sort of BNM.
The nebulosity 6 or 7'.
The N seems to consist
of stars, the nebulosity is
of the milky kind. It is a
pretty object.
A star about 9 or 10m. with
a nebulous ray to the
south-precedingside. The
ray is about i^-' Ion"-. The
star may not be connected
with it.

.524.

Dr. Herschel's Catalogue

IV.

1801. Stars.

1

M. S.

D. M.l

?| Description.

78 Nov. 8 8Urs^min.of
1 Bode's Cat.

1
1

P

25 0

71

0 12

1 I'cB. R. about li' diam.

i< Somewhat approaching

1 to a planetary nebula,

1 L with a strong hazy border.

Fifth

Class. Very large Nebula.

V.

1789.

Stars.

M. S.

M. D. .

r Description.

45

Apr. 12

64 (■)/) Ursce -

f

0 9

/

1 232

cB. iY. E. mer. LBN. with
F. branches 7 or 8'/, 5 or
Q'h.

46

17
1790

48 (iS) Ursee

f

10 4

/

0 412

vVi. wE. r. io7, 2'6. There
is an unconnected pretty
bright star in the middle.

47
48

April 1
Oct. 9

30 ((p) Ursag
; Fornacis L. C.

J

10 9

n

1 391

t/B. wE. np Jj. vgmbM. 8'/,
2 '6.

182 - -

J

8 7

J

0 2 1

t;B. E.75'';z/'y7:8'Iong. A
very bright nucleus, con-
fined to a small part, or
about 1' diam.

49

Dec. 28
1793

41 Persei Hev.

f

22 0

n

0 151

6 or 7 small stars, with faint
nebulosity between them,
of considerable extent,
and of an irregular figure.

50

Mar. 4

s Pixidis Na. L.

C. 831 -

f

35 26

J

0 431

vY. rS. /E. \5^fpnf. IbU.
8'/, 5 or 6'b.

51

April 6

4 Draconis -

P

14 48

n

0 20 2

vY. niE. Jo" npjf. About
25'/, and losing itself im-
perceptibly, about 6 or 7'
broad.

of ^00 new Nebula', and Clusters of Stars.

52;

V. 1801.

Stars.

M. S.

D. M

0
1

Description.

52|Nov.28

50 (a) Urs2e

P

17 49

nil 30

cB. E. mer. vgbM. About

5'/. and 3' broad ; the ne-

bulosity seems to be of

the miiky kind ; it loses

itself imperceptibly all a-

round. The whole breadth

of the sweep seems to be

affected with very faint

nebulosity.

Sixth Class. Very compressed and rich Clusters of Stars.

Additional Tel. Cluster, com. compressed.
Abbreviations .] sc. scattered, co. coarsely.

VI.

36

i-go.

Star s

Mar. 4; 6 Navis

i75i
37 Feb. 23 26 Hydr:e -

38 Aug. 25
39

1793
Mar. 3

50 (7) Aquilce

'C, Pixidis Naut.
L.C.777 -

M. S.

8 4.5

/

79 30 «

i-i 50

/

MDCCCII.

20 39| /

3Y

D. M

1 55

1 o 1

1 18

o 19

Description.

A V. com. el. of S, and some
luft. E near mer. The
most compressed part is
about 87, and ^'b. with
many scattered to a con-
siderable distance.

A V. com. and very rich cl.
of stars. The stars are of
2 sizes, some considerably
L. and the rest next to
invisible. The coai. part
5 or 6' in diam.

<:V>. S. i¥. er. Some of the/^.
are visible.

A cl. of "Lft. considerably
rich /R. above 1 5' diam.

526

Dr. H'-.rschel's Catalogue

VI.

40

41

'793-

42

May 1 2

1797
Dec. 1 2

1798
Sep. 9

Stars.

M. S.

,53 [v) Serpentis

35 Draconis -

3 [v) Cephei

D. M

4,8 17 ?t

22 6

13 26

1 6

Description.

A very beautiful e com. cl.
of ft extremely rich, 5 or
6'in diam. gradually more
comj)ressed towards the
centre.

R. r. about 3' diam. f^tM.
I suppose it to be a clus-
ter of stars extremely
compressed. 300 confirms
thesupposition, and shews
a few of the stars ; it must
be immen.sely rich.

A beautiful compressed cl.
of Sft. extr. rich, of an
/F. The preceding part of
it is round, and branching
out on the following side,
both towards the n. and
towards the /. 8 or g in
diam.

Seventh (

Class. Pretty m

ich

compresse(

/ Clusters of large or sma'l Stars.

VII.

1-88.

Stars.

M. S.

K M. ?
3 6' 1

De'ciiption.

5f>

D^-c. 16' 1 1 (/G) Cassiop

P

9 ^7

;/

A />. co'H. cl. of Sft. of se-

veral .size.s, cons. rich. E.

near par. 5 or 67.

57

31

^790

i,o Aurigas -

J

8 2&

/2

1

A coiupressed cl. of t'S '^'^ars
zF. 6' diam. consid. rich.

5^

Mcir. 4

6 Navis

J

5 18

y

0 291

A p. com, and rich cl. of S
stars /R. 7 or 8' diam.

59

Sept. 11

18 (^) Cygni

f

18 3:

./

I 41
1

A y. rich cl. of L/. conside-
rably compressed, above

of 500 new Nebula, and Clusters of Stars.

527

VII

1790.

Stars.

60 Dec. 28 4.7 (x) Persei
6i — 4,1 Persei Hev.

1791
62 Aug;. 21

63
6.^

1793
Mar. 3

19 Aquilse -

^ Pixidis Naut.
L. C. 777 -

8 2 Navis

66 Oct. 18

67

1799
Jan. 30

7 Cephei -

15 (tt') Canis

M.

3 30
3 8

o 26
2 25

16 10
16 45

42 33

/

D. M.

/

/

0 561

1 ?4i

0 24,12

1 91

o 3S1

Description.

o 142

15' diam. by the size of
Xhe ft. it is situated in the
milk3'^-way, towards us.

A L. cl. of cL/i. p. com. and
very rich. /'R. 7' diam.

A beautiful cl. of hft. v rich,
and considerably com.
about 15' diam.

A S. p. com. cl. of stars not
very rich.

A L. cl. of scattered SJt. iY.
considerably rich.

A L. cl. of /if. of a middling
size, i E. considerably
rich. The stars are chiefly
in rows.

A S. cl. of vS ft. considera-
bly rich and compressed.

A cl. of cons. com. rS and
L. stars about 12' diam.
considerably rich.

A cl. of com. stars, consi-

derably rich.

SYs

.T28

Di; Herschel's CataIoo;ue, &c.

Eigblb Class.

Coarsely scattered Clusters of Stars.

VIII

17SS. Stars.

M. S.

D. M.

P Description.

79

Dec. 16,11 (/3) Cassiop

f

20 35

71

1 5

1 A coarsely sc. cl. of L/if.

mixed with smaller ones.

not very rich.

80

18
1780

1 Camelopar.

P

41 36

I

1 29

1 A cl. of S. stars, containing
one large one, 10; 9m. 3
or 3' diam. not rich.

81 July 18

5 Viilpeculos

P

2 46

n

2 4

1 A sc. cl. of cl. ft. /F. pretty

rich, above 15' in e.\tent.

1790

82 Sept. 1 1

57 Cygni -

f

1 0

n

0 52

1 A L. cl, of/'S. stars of se-

veral sizes.

83

30

51 Cygni -

P.

25 24

Jo 1

1 A cl. of sc. stars, above 15'

diam. pretty rich, joining

to the milky-wav, or a

projecting part of it.

84

Dec. 28

33 («) Persei

f

9 14

n

1 36

1 A cl. of SJt. not very rich.

85

—

4,1 Persei Hev.

f

2 42

Jo oj

1 A coarsely sc. cl. of L//,

pretty rich.

1792

86

Sept. 15

34 Cygni -

P

9 43!"

0 15

1 A coarsely sc. cl. of L stars.

of a right-angled triangu-

lar shape.

■^793

87

Mar. 8
1799

3 Navis

P

7 10

/

0 15

1 A small cl. of S. stars, not
very rich.

88

Dec. 28

46 (1) Persei

P

27 13

n

1 29^

2 A cl. of coarsely sc. hjt.
about 15' diam.

FMlos.TmnsMDCCV'a.riaif SXI.p. siS

^t^.S.

l'hilos:Jkui.< M I ) ( 'CCW ]'/„lf.\\7f./i. siB .

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]rhn Cojklcy Lettsom,
M. D. F.R. S.

Mr. William Nicholson.

Mr. Alexander Tilloch.

The National Institute

of France.
M. Lebkuc.

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Royal Institution.

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Manutactures, and
Com mt ice.

George Biggin, Esq.

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M. M.;ngin.

c; 532 ;]

PRESENTS.

it. Journals of the Royal Institution of Great Britain.
No. 6.

A Walk through Southampton, by Sir H. C. Engle-
field. Southampton, 1801. 8°

25. Kongl Vetenskaps Academiens Nya Handlingar,
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and 1 80 1.

Theatre de M. Cailhava. Paris, 1781. Tomes II.

8°

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hava. Paris, 1802. 8°

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h.iva. Paris, 1791. 8°

Athenes pacifiee, Comedie, par Cailhava. Paris, An
6. 8"

Essai sur la Tradition Theatrale, par Cailhava.
Pari<;, An 6. 8°

Notices pour servir a I'Histoire des Theatres, par
Cailhava. Paris, An 6. 8"

La Descente de Bonaparte en Egypte, par P. Bru-
neti, traduit de I'Espagnol par Cailhava. Paris,
An 8. 8°

Le Depit amoureux, retabli en cinq actes, par Cail-
hava. Paris, An 9. 8°

Hydrogeologie, par J. B. Lamarck. Paris, An 10.

8°

J. G. Schneider Historix Amphibiorimi naturalis et
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Mflr.4. A Journal of Natural Philosophy, by W. Nichol-
son. No. 3.

The Philosophical Magazine, by A. Tilloch. No.

45-

fi. An Account of a new Mode of Operation for the
Removal of the Cataract, by Sir J. Earle. Lon-
don, 1801. 8°
Disquisitiones arithmetics, Auctore C. F. Gauss.
Lipsia;, I 80 1. 8"

18. Bibliotheque Britannique, No. 141 — 144.

25. An entirely new Survey of the County of Kent, by
the Surveying Draftsmen of the Board of Ord-
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the Condition of the Poor. London, 1801. 8°

Journal de Chimie, par J. B. Van Mens. No. I —
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Royal Institution.

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Bart. F. R. S.

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Sciences of Stockholm.

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Esq.

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tut de France.
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Frankfort on the Oder.
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F. R. S.

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Ph. D.
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The Board of Ordnance.

The Committee of the
Society for bettering
the Condition of the
Poor.

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stitut de France.

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PRESENTS.

April I. Flora Batava. No. i — 3. Amsterdam.

Journals of the Royal Institution of Great Britain,
No. 7.

Supplement II. to the General Synopsis of Birds.
London, 1802.

A Journal of Natural Philosophy, by W. Nichol-
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4'5- ...

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of Manchester. Vol. V. Part 2. Manchester,

1802. 8°

Royal Humane Society Annual Report, 1802. Lon-
don, 1802. 8°

Literary Antiquities of Greece, by P. Allwood.
London, lygg. 4°

Annals of Medicine, for the year 1801, by A. Dun-
can, sen. and A. Duncan, jun. Vol. I. Lustrum 2.
Edinburgh, 1801. 8°

Bibliotheque Britannique. No. 14; — 150.

Captain Cook's Second Voyage, translated into Rus-
sian by L. Kutuzov. Petersburg, 1796 — 1799.
4 Vols. 4°

De' Benificamenti delle Terre Pontine, da N. Nico-
laj. Roma, 1800. fol.

Melanges mathenwtiques, par le Commandeur de
Nieuport. 1 Recueil. Bruxelles, 1 794. 2 Recueil
1799. 40

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Tome 3me des trois Classes. Paris, An 9. Tomes
III. 4°

Hints d;'signed to promote Beneficence, Tempe-
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A Journal of Natural Philosophy, by W. Nichol-
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The Philosophical Magazine, by A. Tilloch. No.

47-
The Works in Natural History of the late Rev.
Gilbert White. London, 1S02. 2 Vols. 8°

13. Transactions of the American Philosophical So-
ciety, held at Philadelphia. Vol. 111. Philadel-
phia, 1793. Vol. IV. 1799. 4°
Philosophical Papers, by B. Count of Rumford.
Vol. I. London, 1802. 8°
27. [ournals of the Royal Institution of Great Britain.
No. 8.
A Series of Engravings to illustrate the Morbid
Anatomy of the Human Body, by M. Baillic.
Fascic. IX. London, 1802. ' 4°

The Minister of Politi-
cal Economy of the
Batavian Republic.

The Managers of the
Royal Ir.stitution.

John Latham, M. D.
. F. R. S.

Mr. William Nicholson.

Mr. Alexander Tilloch,

The Literary and Philo-
sophical Society of
Manchester.

The Royal Humane So-
ciety.

The Rev. Philip All-
vvood, M. A.

Andrew Duncan, sen.
M. D. and Andrew
Duncan, jun. M. D.

Professor Pictet, F.R.S-

M. Kutuzov.

Abate Nicolo Nicolaj.

M. De Nieuport, de
I'Institut de France.

The National Institute
of France.

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

Mr. William Nicholson.

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Mr. John White.

The .■\merican Philoso-
phical Society.

Benjamin Count of
Rumford, F. R. S.

The Managers of the
Royal Institution.

Matthew Eaillie, M. D.
F. R. S.

MDCCCH.

3'/^

C 534 ]

PRESENTS.

R. Relhan Flora Cantabrigiciisis. Editio altera.

Cantabrigix, i8c2. 8°

'June 5. Transactions of the Linneau Society. Vol. VI.

London, 1802. 4°

Remarks upon chemical Nomenclature, according

to the Principles of the French Neologists, by R.

Chenevix. London, 180Z. 12°

Anacreontis Odaria, cura E. Forster. Londini,

1802. i"

A Discourse, introductory to a Course of Lectures

on Chemistry, delivered in the Theatre of the

Royal Institution, by H. Davy. London, i8oz.

8°
A Journal of Natural Philosophy, by W. Nicholson.

No. 6.
17. The philosophical Magazine, by A.Tilloch. No. 48.
Catalogue of the Manuscripts in the Cottonian

Library, deposited in the British Museum, 1802.

fol.
Calendarium Rotulorum Patentium in Turri Lon-

dinensis, 1802. ful.

Taxatio ecclesiastica Angliae et Walliae, auctoritate

P. Nicolai, IV. 1802. fol.

A Sermon preached in the Chapel of the Magdalen

Hospital, by C. P. Layard. London, 1802. 4°

Recrea9a6 filosofica, pelo T. d'Almeida, Tomos X.
Lisboa, 1781 — 1800. 8°

Cartas fisico-mathematicas, para servir de Compli-
mento a Recrea9a6 filoiofica. Tomos IlL Lis-
boa, 1784 — 17'>7. 8°

Thesouro de Pacicncla nas Chagas de Jesu Christo,
pelo T. de Almeida. Lisboa, 1784. 12°

T. He Almeida Physicarum Institutionum Libri x.
Tomi HI. Olisipon^, 1785— 1793. 8=>

O feliz Iiidependente do Mundo e da Fortiiiia, pelo
T. d'AlmL-ida. Tomos III. Lisboa, 1786. 8°

Methodo para a Geografia, par T. A. Lisboa, 1787.

Sermoes de T. de Almeida. Tomos III. Lisboa,
1787. . 8°

Entretenimentos do Coracao devoto. Luboa, 1790.

8°

Estimulos do Amor da V. Maria, pelo T. de Al-
meida. Lisboa, 1791. •2*'

Exercicios do Christao, segundo o Espirito da Igrej^.
Lisboa, 1791. '2°

Meditacoes dos Attributes divinos, pelo T. A. Tomos
JV. Lisboa, 1796. 8"^

Opuscules sobrc diversos Assumptos, par T. A.
Tome I. Lisboa, 1797. ^^

O Pastor evangelic©, per T. A. Tomos IV. Lisboa,
"797— » 799- ^°

DONORS.

The Rev. Richard Rel-
han, M. A. F. R. S.
The Linnean Society.

Richard Chenevix, Esq.
F. R.S.

The Rev. Edward Fors-
ter, M. A. F. R. S.
Mr. Humphry Davy.

Mr. William Nicholson.

Mr. Alexander Tilloch.

Tlie Commissioners for

the Public Records.

The Rev. Charles Peter
Layard, D. D. Dean
of Bristol, F. R. S.

Father Theodore d'Al-
meida, F. R. S.

C; 535 3

PRESENTS.

24. Journals of the Royal Institution of Great Britain.

No. 9.
BibliothequeBritannique, No. 151, 152.
Arithmetique universelle de Newton, traduite du

Latin, avec des Notes, par Noel Beaudeux. Pans,

1802. Tomes II. P

Histoire du Galvanisme, par P.Sue, aine. Pans,

1802. Tomes II. 8°

St-ance publique de rAcademie de Chirurgie du 1 1

April, 1793. Paris, 1793. 8°

Memoire sur la Vie et sur les Ouvrages de Jean

Goulin, par P. Sue. Paris, An 8. 8'

Memoire sur I'Etat de la Chirurgie a la Chine, par

P. Sue. Paris, An 9. .8'

Commentaires sur quelques Passages des Lettres de

Seneque, relatils a la Medecine, par P. Sue. 8°
July I. Illustrations of the Huttonian Theory of the Earth,

by J. Playfair. Edinburgh, 1802. 8°

The Philosophical Magazine, by A.Tilloch. No. 49.

8. Etudes sur Moliere, par Cailhava. Paris, 1802. 8°

Memoire sur un nouveau Genre d'Insecte trouve en
Afrique, par le C. Palisot Beauvois. 8°

Traite de I'lnoculation, par les Cits. F. Derotaux

et L. Valentin. Paris, I'an 8. 8="

15. Journal des Mines, public par le Conseil des Mines

de la Republique Fran5aise. No. i — 67. Paris,

an 3 — 10. 8°

DONORS.

The Managers of the

Royal Institution.
Professor Pictet, F. R. S.
M. Beaudeux.

M. P. Sue, aine.

Professor Playfair.

Mr. Alexander Tilloch.
M. Cailhava, de I'ln-

stitut de France.
M. Palisot Beauvois, dc

rinstitut de France.
L. Valentin, M. D.

Le Conseil des Mines de
la Republique Fran-
gaise.

INDEX

TO THE

PHILOSOPHICAL TRANSACTIONS

FOR THE YEAR 1802.

A page

Acid, muriatiCy on the metallic combinations of, - - 152

— oxygoiized and hyperoxygoiixed, observations on, 126

Adularia, remarks on, - - - - 280, 287
Alumina, hyperoxygenizcd muriate of, remarks on, - 149
Amethvst, oriental, remarks on, _ _ _ _ 244
Ammonia, hyperoxvgenized muriate of, remarks on, - - 148
Analytical and geometrical metbods of investigation, on their inde-
pendence, - - - - -85
Asteroids, name proposed to be given to certain celestial bodies, 228
definition of that name, _ _ _ 229

B

Bachelay, Abbe, account of a stone said to have fallen on the earth, 170
Bartbold, M. account of a stone called Pie' re de Tonnerre, - 171
Barytcs, byperoxygenized muriate of , remarks on, - - 145
Blackness, remarks on, - - - - 43
BouRNON, THE CouNT DE. Mincralogical description of the
various stones said to have fallen upon the earth, - - 180
Description of various kinds of

native iron _____

Description of the corundum stone,

and its varieties, commonly known by the names of oriental ruby,
sapphire, &:c. ; with observations on some other mineral sub-
stances _ _ _ _ _

203

233

Butters of the Metals, remarks on, - - - - 164

c

Calomel, remarV-s on, - - - - - i^j

on Scheele's method of preparing it, - - -159

Cf/t-j/Zai ijO(f/>5, on two lately discovered ones, - - 213

INDEX.

page

Ceres, observations on a star so called, - - - 214, 231

Ceylanite, remarks on, - - - - - 3 1 8

Chatoyaute, remarks on that property, - - - 271
Chen evix, Richard, Esq. Observations and Experiments upon
oxygenized and hyperoxygenized muriatic acid; and upon some

combinations of the muriatic acid in its three states - 126

• Analysis of corundum, and of some

of the substances which accompany it; with observations on the

affinities which the earths have been supposed to have for each

other, in the humid way, _ _ _ _ 327

Chromate of Iron, Siberian, remarks on, _ _ _ go

Chrysolite, oriental, remarks on, - - - - 244

Colours, on the theory of light and colours, - - - 12

■ on those of striated surfaces, _ - _ gg

on those of thin plates, - - - - 37

• on those of thick plates, - - - - 41

> on those by inflection, - - - - 42

account of some cases of their production, - - 387

on their dispersion by refraction, _ _ « ggg

Coliimbium, account of a metal so called, - - _ 6g

Comets, definition of them, _ _ _ _ 225

■ observations on them, - - - - 226
Conic Sections, on their rectification, - - 448
Corundum stone, description of, and its varieties, the oriental ruby,

sapphire, &c. _ _ _ _ 233

on its diflferent appearances, - - 240

distinguished into perfect and imperfect, - 241

on its colour, _ _ _ 242

■ on its transparency, - - 244

on its hardness, - - - 247

on its phosphorescence, - - 248

■ on its gravity, _ _ _ 249

on its crystalline forms, - - 250

on its fracture and texture, - - 264

■ phenomena with respect to light, - - 271

character afforded by analysis, - 275

on the kind called compact, - - 281

on the matiix of imperfect corundum from India, 282
on the sub.siances whicli accompany the imperfect

corundum from India, - - - - 285

on the matrix of imperfect corundum from China, 301

on the matrix of imperfect corundum from Ava, 304

on the matrix of perfect corundum from Ceylon, 304

INDEX.

page

Corundum stone, on that supposed to be found in America, - 322

. on that supposed to be found in France, - 323

analysis of, - - - - "3^7

—- analysis of its matrix, - - - 333

. analysis of some substances contained in its matrix, 334

Ci/c5, remarks on a theorem of his, - - - 107

Cryitnl, Iceland, on its oblique refraction, - - - 381

Crystalline lens, on the power of the eye, when deprived of it, - i

D

D'Alembert, remarks on a paradox mentioned by him, - lOO

Darracq, remarks on some experiments of his, - - 340

Dispersive powers, method of examining, - - 365, 372

^ ■ on those of the eye, - - 396

Z);-afe, remarks on its organs of generation, - - ' - 361

E

Earths, on the affinity they have been supposed to have for each

other, ----- 3-^7' 339

Emerald, oriental, remarks on, - - - 244

Emeralds, on some found in France, - - - 3^5

Emery, on its composition, - - - - 39^

Eslinger, Mr. remarks on his description of the spinelle, - 308

Ether, remarks on that of Sir Isaac Xewton, - - 14

JE)'^, on its power to adjust itself to different distances, - 1

on its dispersive powers, . . - - 396

F

Felspar, remarks on, - - - - 285, 301

analysis of, . _ - - 334, 336

Fibrolite, remarks on, - - - aby, 302
analysis of, - - - 335> 33^

G

Garnets, remarks on, _ _ - - 297

Guyton de Morveaa, remarks on some experiments of his, - 339

H

Hatckett, Charles, Esq. An analysis of a mineral substance
from North America, containing a metal hitherto unknown, - 49

Hauy, Abbe. Remarks on some opinions of his respecting the co-
rundum stone and the sapphire, - ... 239, 276^

Heat, remarks on, - - - - 3^

some remarks on, and on the action of bodies which intercept it, 403

INDEX.

page
Hellins, THii Rev. John. Of the rectification of the conic sections, 448
Herschel, William, LL. D. Observations on the two lately

discovered celestial bodies, - - - 213

• Catalogue of 500 new nebula;,

nebulous stars, planetary nebulae, and clusters of stars ; with re-
marks on the construction of the heavens, - - 477

remarkson some experimentsof his, 403

Home, Everard, Esq. The Croonian lecture. On the power of
the eye to adjust itself to different distances, when deprived of
the crystalline lens, _ _ _ _ 1

A description of the anatomy of the

Orniihorhynchus paradoxus, - - - Sj

Description of the anatomy of the Omi-

thorhyiichus Hvstrix, - . - . 348

Hornblende, remarks on, - _ _ _ 295

Howard, Edward, Esq. Experiments and observations on cer-
tain stony and metalline substances, which at different times are

said to have fallen on the earth; alsoon various kinds of native iron, 168

Huygens, remarks on his theory of light, - - 381

I

Investigation, on the independence of the analytical and geometri-
cal methods of, - - - -85
Iron, Siberian Chromate of, remarks on, - - _ 50
— — native, observations on, ... 168, 203
attractable oxide of, remarks on, - - 300, 302

K

Klaprotb, Mr. Remarks on his analysis of the corundum stone

and the sapphire, . _ _ _ 234

Kraft and Richmann, Mess. Their law of the increase of heat, 407

Lecture, Bakerian, - - - - 12

Croonian, . . _ « i

Light, on the theory of light and colours, - - 12

on its refraction, _ . _ 365

un its dispersion, _ - - 3655372

on the colours into which it is separable, - 378

on the effects of its invisible rays, - - 379

radiant, remarks on, - - - 44

Lime, byperoxygcnized muriate of, remarks on, - - 147

INDEX.

M page

Magnesia, hyperoxygenizid muriate of, remarks on, - 149

Manis, remarks on, - - - - 35°

lihrcury, on its combination with muriatic acid, - - '53

Meful, analysis of a substance containing one iiitherto unknown, 49

Meteor, account of the explosion of one near Benares, - 175

account of one seen in America, - - 202

Mica, remarks on, - - - - 296, 301

. mistake respecting it, - - - 3°9

Milky-vcay, remarks on, _ _ - - 495

Muriate of potash, hyperoxygeiiized, remarks on, - - i39

of soda, hyperoxvgeiiized, remarks on, - - i44

.. of harytes, hvperoxygenized, remarks on, - - 145

of strontia, hyperoxygenized, remarks on, - 147

of lime, hyperoxygenized, remaiks on, - - i47

of ammonia, hvperoxygcfiized, remarks on, - 148

of mugnesid, hyperoxygenized, remarks on, - 149

of alumina, loypcroxygenized, remarks on, - - i49

. of silica, hyperoxygenized, remarks on, - - iS'^

Muriates, oxygenized, remarks on, - - - 1 34
allmline and earthy hyperoxygenized, remarks on, - 138

melallir, remarks on, - - - ^5^

Myrmecophaga, remarks on various species of, - - 359

N

Nebula, Catalogue of 500 new ones, - - 477^ 5^3

remarks on, - - - - - 497

. on stellar ones, _ - - - 499

• on planetary ones, - - - ~ 5^1

Nebulosity, milky, remarks on, - - - 499

Newton, remarks on various passages in his works, - - 14

O

Olbers, Dr. Observations on a moving star discovered by him, 213

Optometer, remarks on that instrument, " ' ' ^

Oriental, remarks on that term, - - - * ^35

Ornithurhvnchus paradoxus, description of, - - ^7

correcuon of an error concerning it, 356

Hystrix, description of, - - * 34"

account of a new species, - - 357

Oxygenated, remarks on ihat word,
MDCCCII. 4 ^

26

INDEX.

P page

Pfl/to, observations on a star so called, - - 216,23a

Piazzi, Air. Observations on a moving star discovered by him, 2 13
Pictet, M. Remarks on some experiments of his, - 430,440

■ Account of a phenomenon observed by him, - 432

P/ffwe'/.s, definition of them, _ _ - - 224

P/a//«a, on the action of potash upon it, _ _ _ 2^7

-■ method used to detect it in gold, - - 337

most sensible test for, _ _ , _ 338

Potash, on its action upon platina, • _ _ 337

■ ■ on its volatility, - - - - 338

hyperoxygenized muriate of, rtmarks on, - - ^39

Presents iect\\ed by the Royal Society, from November 1801 to

July 1802, - - - - - 529
Prevost, p. Ouelques remarques sur la chaleur, et sur Taction

des corps qui 1 interceptent, . . _ 403

His theory of heat, - - - 442

Prismatic rejection^ method of examining refractive and dispersive

powers by, - - - - - 3^5

Quartz, remarks on, _ - - - 295

Sapphire, description of, - - - ~ 233

analysis of, - - - ~ 33^

• See Corundum.

Scheelc, on his method of preparing calomel, - - 159

Sidereal systems, of binary ones, - - 480

of complicated ones, - - - 4^^

Silica, hyperoxygenized muriate of, remarks on, - 150

Soia, on its volatility, - _ _ _ 338

hyperoxygenized muriate of, remarks on, - - 1 44

Spar^ calcareous, reinarks on, - - - 260

Spinelle, remarks on, . _ - - 305

on its matrix, . - - - 308

S/rfri, catalogue of clusters of, - - - 477' S^S

. of insulated ones, . - - - 478

— — of double ones, - - - - 480

of treble ones, &c. - - - 4^6

of clustering ones, - - - - 495

— — of groups of them, - - - 49^

INDEX.

page

Stiirs, of clusters of them, . . _ ^gj

of those with burs, - - - - 499

— — — of nebulous ones, - . - 500

Star-stones, remarks on, ... - 275

Stone, account of one which fell in Yorkshire, - 174

Sto?ies, account of some which fell in Italy, - - 173

account of some which fell near Benares, - 175

— mineralogical description of some, said to have fallen on

the earth,. - - - - 180
Stony and metalline substances, account of some, said to have fallen

on the earth, - - - - 168

Strontia,hyperoxygenizcd muriate of, remarks on, - 147

Sublimate, corrosive, remarks on, - • - 151

Talc, remarks on, . . , - 296

Tenn ANT, Smithson, Esq. On the composition of emery, 398

Thallite, remarks on, - - - - 291

analysis of, - - - "335

Tirce, remarks on a stone found there, - - 3.21
Tourmalin, remarks on, - - - - 3>3
red, remarkable specimen of, - - 317

V

Vauquelin, Mr. Remarks on his analyses of felspar, - 287

w

Waring, Dr. Remarks on two series given by him, - 475

Williams, John Lloyd, Esq. Account of the explosion of a
meteor, near Benares, in the East Indies; and of the falling of
some stones, at the same time, about 14 miles from that city, 175

IVoJfram, remarks on, - - - 50

WoLLASTON, William Hyde, M. D. A method of examining

refractive and dispersive powers, by prismatic reflection, 365
• On the oblique refrac-
tion of Iceland crystal, - - - 381
Wood HO USE, Robert, A. M. On the independence of the
analytical and geometrical methods of investigation ; and on the
advantages to be derived from their separation, - 85

4 A 3

INDEX.

Y page

Young, Thomas, M. D. The Bakerian Lecture. On the theory

of light and colours, - - - 12

An account of some cases of the pro-
duction of colours, not hitherto described, - 387

. Remarks on some experiments of his, 4

Zircon, remarks on, « • - - 298

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